mathematical and software engineering, vol 5, no 2 (2019), 34–38. varεpsilon ltd, http://varepsilon.com patient information software designed for medical specialists mihaela todorova1, aleksandar kutsarov2, and krasimir kordov3 1konstantin preslavsky university of shumen, 9712 shumen, bulgaria, email: mihaela.todorova@shu.bg 2konstantin preslavsky university of shumen, 9712 shumen, bulgaria, email: al.kutsarov@gmail.com 3konstantin preslavsky university of shumen, 9712 shumen, bulgaria, email: krasimir.kordov@shu.bg abstract the paper presents software designed for medical specialists for managing their patients information. this type of software products are needed for facilitating the work of doctors. by using this type of software products, the medical specialists are able to easily record, edit and maintain their patients information, which supports diagnosis and treatment of the patients. keywords: software, medical specialists software, information system 1 introduction the rapid progress of information technology and the development of tools for acquiring, processing and storing information, leads to the need for the development and operation of specialized software products [5, 6] in various fields of work. one of the most important sectors of public life is healthcare, where the proper use of technology can improve the process of managing large information flows reducing the risk of errors [1]. during the last decades medical institutions implement various type of information systems in order to improve the medical doctors’ productivity. the medical information system is a complex of technologies and methods for the planned collection, processing, analysis, archiving and transferring medical data and information. the goals and objectives of information systems in medicine and health care are to automate the information process to minimize the risk of errors, accelerate the decision making process, facilitate staff in routine activities, standardized methods of information retrieval, personnel and financial management, control over information, etc [1, 2]. medical specialist are not always located in general medical facilities and often chose to use specific software best suited to their medical practice such as betagp [9], niset-simp [10], hipokrat gp [11] and global medics [12]. all these software products are developed according to bulgarian standard with option for regular archiving and exporting patient information to national health insurance fund. considering the small number software available for medical specialists we developed a new information system for patients data managing, consulting with medical specialist about the specific requirements for medical software. 34 2 modelling and database organization of a new information system the model of a new software for managing medical information from medical specialists is required to contain the following functionalities: • module for patients data gives the medical specialists opportunity to service all primary documents at a new ambulatory examination • module for reports provides an opportunity for a combined report for all the examinations performed and hospitalizations • module nomenclatures provides list of nomenclatures for avoiding errors • service module allows import and export of all medical information for backup and restoring the patients data the information is organized in database with the following tables: • patients contains patients data such as identification number, regional health insurance fund number, region number, code of the country, patient name, date of birth, patient address, gender etc. • medical doctors contains information about the medical staff such as unique identification number, registration number, medical specialty code, doctor’s name, contact information • medical institutions contains information about hospitals and medical healthcare institutions available • regional health insurance funds contains all available regional health insurance funds • medical specialties codes and types of every medical specialties • referrals information about referrals for patients consultations and other medical specialists, medical diagnostic centers and patients hospitalizations • clinical treatments contains codes and types of available clinical treatments • ambulatory examinations contains information about performed examinations from medical specialists such as time and date of examination, identification number of the patient, personal identification number of the medical specialist, patient condition, patient immunizations, performed medical procedures etc. 3 medical software amedical in this section we present some of the menus of the software for medical specialists. the software has working name amedical and is realized using microsoft visual studio 2013 and odbc (open data base connector) technology. figure 1 shows the home screen of amedical software. all the modules are available by the menu of the home-screen. figure 2 shows the dialog window for inserting a new patient. every time the medical specialist extend their practice, they need to create new files for the new patients. the software provides notifications if mandatory information is now inserted. similar dialog windows are being use for the rest of the modules allowing the medical specialists to easily manage their patients’ information. figure 3 shows the dialog window for creating new ambulatory list for a patient. there are various elements easing the process for medical specialists minimizing the possible errors. some of the elements are realized with drop-down menus making available only one option (like primary or secondary examination of the patient). other option groups can be marked several at a time such as reason for doctor visitation (consultation, medical check, hospitalization, etc.) immunizations are fixed and can be selected from a list one by one. all the modules described in the previous section are realized with similar dialog windows, but they are too many to be presented in a single paper. 35 figure 1: home screen of amedical software figure 2: amedical insert new patient window 36 figure 3: ambulatory examinations 4 future work concerning the global problems with information security the proposed system can be updated with cryptographic data transfer [3, 4, 7] of the sensitive information and steganographic data transfer [8] of system information. 5 conclusion the healthcare is one of the fastest growing and important sectors of public life and the lack of enough software products is noticeable. more software products are needed to meet the requirements of medical specialists, improving and easing their work. 37 in this paper we presented such software, containing the mandatory modules for medical specialists’ practices. amedical is realized with suitable interface and simple navigation to facilitate the work and to minimize the errors. acknowledgement this work is partially supported by the scientific research fund of konstantin preslavski university of shumen under the grant no. rd-08-71/29.01.2019. references [1] becchetti, c., neri, a. (2013). medical instrument design and development: from requirements to market placements. john wiley & sons. [2] hota, c., srimani, p. k. (eds.). (2013). distributed computing and internet technology: 9th international conference, icdcit 2013, bhubaneswar, india, february 5-8, 2013, proceedings (vol. 7753). springer. [3] kordov, k. m. (2014). modified chebyshev map based pseudo-random bit generator. in aip conference proceedings (vol. 1629, no. 1, pp. 432-436). aip. [4] kordov, k. (2015). signature attractor based pseudorandom generation algorithm. advanced studies in theoretical physics, 9(6), 287-293. [5] kordov, k., eminov, d. (2018). applied software for managing a small business. mathematical and software engineering, 4(1), 12-17. [6] stoyanov, b., kordov, k. (2014). open source software alternatives in higher education following computer science curricula 2013. research journal of applied sciences, engineering and technology, 8(9), 1160-1163. [7] stoyanov, b., szczypiorski, k., kordov, k. (2017). yet another pseudorandom number generator. international journal of electronics and telecommunications, 63(2), 195-199. [8] stoyanov, b. p., zhelezov, s. k., kordov, k. m. (2016). least significant bit image steganography algorithm based on chaotic rotation equations. comptes rendus de l’academie bulgare des sciences, 69(7), 845-850. [9] url: https://www.bgbit.com/ betagp medical software official page (visited 01.09.2019) [10] url: http://nisetbg.com/ niset-simp medical software official page (visited 01.09.2019) [11] url: http://hippocrates.kontrax.bg/hippocrates-gp hipokrat gp medical software official page (visited 01.09.2019) [12] url: https://www.globalmedics.com/ global medics medical software official page (visited 01.09.2019) copyright c© 2019 mihaela todorova, aleksandar kutsarov, krasimir kordov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 38 9 mathematical and software engineering, vol. 5, no. 1 (2019), 9-14. varεpsilon ltd, http://varepsilon.com web school diary krasimir harizanov and kristiyan konstantinov konstantin preslavsky university of shumen, shumen, bulgaria, emails: kr.harizanov@shu.bg, fiksit@abv.bg abstract the article presents the role of web school diaries in organizing and conducting training in the bulgarian school. some online technologies have been explored to enable the preparation and implementation of a web school diary, in keeping with modern requirements. it is proposed that the web-based electronic diary should be created in accordance with the requirements of contemporary bulgarian education. here are some of the web app's capabilities can be used to evaluate students, web plans and assignments, as well as a parent's announcement of changes made during the school day. here are some screenshots visualize the main features of the application. keywords: web school diary; education; learning; e-learning 1 introduction the good opportunities that information technology offers are the reason for their rapid development and application in all spheres of life. one of the areas in which communication technologies are most widely used and best-valued is education. since the age in which we live and develop is the age of technology, the methods by which students are valued and on which their assessments are made are constantly changing in order to improve. evaluating and visualizing ratings using information technology makes it easier for both teachers and parents to work. studies conducted in the field of education show that information technology and its implementation are of paramount importance as it informs and facilitates teachers, students and parents. the key feature of the web school diary is the facilitated opportunity to obtain information that is essential in working with students for both teachers and parents. it is the development of this kind of technology that assists and structures the work of teachers, and at the same time, in their hectic daily lives, parents have the opportunity to control their children by seeing their results at school. with the proposed software, we tried to separate the most commonly used features and postgraduate profiles related to school life. the interface is built with the latest versions of html and css, enabling it to adapt to any mobile technology. the processing of the information is realized with the php language and the database is stored in mysql. a feature of the web school diary is awareness. creating such a web application not only facilitates the work of teachers but also encourages children to make more effort. in this way, children become more responsible and consistent in learning, teachers do not burden themselves with additional work, but easily and quickly introduce ratings and absences, and parents have control over their children by getting a true assessment of what level the child's education is theirs. http://varepsilon.com/ 10 the web school diary is an integral part of the life of teachers, students and parents. it is a small part of the changes that have occurred in the education system. it is developing at a rapid pace, with the main goal of improving and more productive work. creating a new system for assessing and presenting knowledge or choosing a ready system requires decisions to be made by looking at relevant theoretical foundations. depending on their capabilities, there are currently several web school diaries integrated into the learning process [1] and [2] (see fig. 1 and fig. 2). these online applications provide access to assessments, messages, information about the school or teachers, and a description of the annual curriculum. because of their specificity, platforms also have their positive sides and limitations. more common problems include funding, logon loss, limited features, pending authorizations, unclear management, and more. this paper offers an online web diary designed to integrate into the school administration, allowing quick and easy servicing of key features of web school diary functions. the application has its own installation so it can be installed on web hosting at the request of the school management. figure 1: web school diary – shkolo.bg figure 2: web school diary admin plus 11 2 web school diary the html 5 and css 3 languages are used to visualize the interface, making application also available on mobile devices. the school information database is mysql type. one of the most widely used web-based applications. the functional part of the application is realized through the php language script, widely used and preferred for dynamic content applications. the proposed web school diary has three main levels: administrator, teacher, and parent, each of which has different levels of access to the application and the format of the information visualization. the administrative role in the web school diary is designed to provide the necessary data those teachers, parents or school administration should work with. this profile features the most features, such as class and class introductions, lecturers, news, as well as many associations between syllabi, out-of-class activities, teachers and students. one of the important functions of an administrator is to maintain an up-to-date list of teachers and their information so that parents have information, which teacher teaches in what discipline they teach. the administrator can add (figure 3) at any time of the school year or remove the teachers, depending on the changes in the school organization, also update their profiles. the "teachers" menu also includes the "associate" button. its function is that each teacher should be associated with the subjects and classes he / she will teach. during the school year, it is very often necessary for a teacher to replace a colleague within a certain period of time, which requires associating the new teacher with the classes in which he / she will teach. here, it is very easy to associate a teacher, discipline and class, which also affects the introduction of assessments and absences. another function of an administrator is the introduction of the disciplines. he has to introduce, for each school year, the classes in the school. the curricula for the upcoming academic year are drawn up for the entered classes and profiles. thus, each class has associated teaching subjects and lecturers, fig. 4. figure 3: add, edit, or delete a teacher 12 teacher account is related to the daily introduction of teacher's notes, assessments, messages and absences to student profiles. here are the main features that are needed for their implementation. any changes to the learner's student profile are updated by the active lecturer and an email message notifies the parent of the changes. from the "annual distribution" menu, each teacher draws up the topics, the type of lesson, the concepts and knowledge to be studied in each term unit. in practice, one teacher in a particular discipline can teach in several classes, requiring the use of the same thematic content to be repeated. here, the thematic distribution can be associated with the classes specified by the lecturer without having to re-enter it, fig. 5. one of the most important functions of a teacher is the introduction of assessments and absenteeism of students during the sessions. from the students-> estimates menu, the teacher chooses which of the subjects he / she is taught wishes to introduce an assessment or an inexistence absence, fig. 6 and fig. 7. figure 4: associating teaching subjects to a class curriculum figure 5: creating and associating a thematic plan with a school discipline 13 in the field "current assessments" you can see all the introduced assessments so far in the chosen discipline. thus the teacher sees the actual assessments up to the current date. the "final rating" area is provided for cases where the teacher would like to delete the last introduced grade. if an evaluation of a certain timeframe is introduced, then the "final assessment" and "new assessment" areas will remove and become inaccessible the possibility, after a timely assessment, of editing the current grades from the school term. the time rating can be edited if the old one is first deleted and a new rating is inserted in its place. figure 6: entering assessments and absences figure 7: student profile view 14 the database also provides a list of qualitative assessments for children with sen or those who are exempt from certain disciplines. the last role provided in the web school diary is that of the parent. his account is pre-created by the administrator of the diary with a password he or she has chosen or has been entered ex officio. after the initial login, the parent could change their data so that they are up to date and the system can send messages to it. the next step from the parent's initial actions in the web school diary is to identify and associate which pupil / student he / she is a guardian. for this purpose, he / she must choose from all classes and classes the student's class. when the specific class is indicated, a list of all students is displayed on the screen. from the "select" button, the selected student associates with the parent profile, and he will no longer appear for choice to other parents in the class. if the parent has made a mistake, the "unsubscribe" button can unsubscribe the student from your account. from the "diary" menu, the parent can see all associated students with it and their current status as regards assessments and absences. for each student selected from the journal, a list of the subjects in his / her curriculum, current grades, and the number of excuses and excuses for each subject are displayed. 3 conclusions and future work online web diary designed to integrate into the school administration, allowing quick and easy servicing of key features of web school diary functions, is presented. it is envisaged to develop new functionalities related to the export of student files, the introduction of dzi (state matriculation exam) and nvo (national exams) assessments, and the issuing of certificates for completed specialization. acknowledgements the research presented in this paper is partially funded by the project of shumen university: rd08-117/04.02.2019. references [1] http://shkolo.bg. [2] https://login.adminplus.bg/ copyright © 2019 krasimir harizanov and kristiyan konstantinov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mse-18002 7 mathematical and software engineering, vol. 4, no. 1 (2018), 7-11. varεpsilon ltd, http://varepsilon.com approach to find optimal graphic container using segmental steganographic algorithm hristo paraskevov and aleksandar stefanov department of computer systems and technologies, faculty of mathematics and informatics, konstantin preslavsky university of shumen, 9712 shumen, bulgaria abstract the article proposes an approach to selecting a suitable graphic container from multiple images for a specific message. searching for an optimal container requires an analysis that takes into account both the human perception of the image and the mathematical relationships that can be analyzed in detail about the contents of the container. experimental results have shown that if one image is split into separate zones, and in each one a steganographic embedding of information is applied, in one of them the changes are the least. keywords: steganography; image processing; steganalysis; information security 1 introduction most of the research is aimed at creating improved stereotypes in order to increase the processing speed of embedding and retrieving the secret message, increasing the capacity, increasing the stability of the hidden message after various attacks, using different types of containers, and messages, the use of complex mathematical dependencies, etc. when improving steganographic methods in image files, the right approach to container selection is also very important. in practice, this choice has to be transformed into a well-thought-out and conducted analysis, where the right indicators must be selected and used to make the best choice. incorrect container selection could compromise the hidden transmission of information, regardless of the well selected steganographic algorithm. 2 methods and algorithms vision is a heuristic process. the three-dimensional vision can be explained as a synthesis. this requires a clear view of vision as a phenomenon and a visual process as a function of the viewer. "we" do not reflect the world outside, and "our brain" transforms the impulses from the eye. the brain adjusts to see what it sees and does not receive it passively. the brain blends memory, expectation and sensation to generate visual integrity [1,2,3]. one looks upwards when he makes a decision. this is what the prefrontal cortex is responsible for. when it is concentrated from the bottom up the sensory crust. one can only see one thing at a time [4]. man performs sensory sorting, fills the holes in reality. the images are formed in the visual cortex, for positioning using the shadows of the 8 objects, trusting them to determine the place of the object in the space. this gave rise to the idea of the algorithm to find a suitable area for embedding the hidden message in order to reduce the changes in the container. to make the right choice, not only one but multiple images are used. the algorithm divides each of the files into zones (sectors) and embeds the hidden message into them. on the basis of certain criteria, all the results obtained are analyzed both in all areas of the file and in all files. the file on the base where the smallest modification was made in a particular area is selected as a container. from the point of view of obscurity, it is advisable that the size of the carrier file is not too large, because its larger size raises the suspicion that it may be the carrier of other, invisible information at first glance. there is no precompression block in the algorithm that would allow the volume of the inserted message to be increased. for this reason, the maximum amount of information to be deployed in the image is determined by the size of the sector minus the header information divided by eight. the size of the carrier file does not change when a message is embedded. 3 results and discussion experiment 1: in this experiment, all images from the 100 image database were used, and a 14 000 byte text message was generated by lorem ipsum. it aims to fill almost the capacity of the picture container and examine the new file for visual defects and changes in image color, fig. 1. (а) original (b) stego file fig. 1 visual analysis after the visual evaluation, the histograms of the original images and stefofiles were also analyzed, fig. 2. (а) original (b) stego file fig. 2 histogram analysis 9 experiment 2: embedding efficiency ee is the ratio of the size of the largest message that can be embedded in the container to the container size. c mes e v v е .= (1) where: vmes – size of hidden message in kb or mb vc – size of the container in kb or mb. all baseline images were used to examine the embedding efficiency of the container, with the built-in message of different sizes. the experimental data of randomly selected images is presented in the following table 1. table 1 coefficient values embedding efficiency image number message size in kb embedding efficiency 1 4 0.048911356 2 5 0.054345951 3 6 0.059840094 4 7 0.066666667 5 8 0.070649737 6 9 0.075851852 7 10 0.091657716 8 11 0.086636261 9 12 0.092388117 10 13 0.109338435 52 14 0.102616034 64 15 0.108691903 66 16 0.114126592 68 17 0.119561093 96 18 0.124347298 98 19 -- the results clearly show the gradual increase in the value of the built-in coefficient. image 98 shows that the size of the message is larger than the lsb allowable embedding and therefore can not be calculated correctly. this proves that the algorithm fully meets the requirements of the lsb method. experiment 3: in the psnr study, all images from the base were used, with the embedded message of varying sizes. the following table, table 2, presents the experiment data of randomly selected images using sector embedding. the results clearly show the difference of two units of psnr values in the same image, depending on the particular sector in which the image is inserted. this means that there is a container from the base that will be most suitable for creating a stegofile. experiment 4: in order to find an optimal container selection in one database of many images, it is necessary to select criteria to be selected. one of the important indicators is to minimize the changes of the zeros and units in the stego file relative to the container. 10 table 2 values of psnr for different sectors image number psnr sector 1 sector 2 sector 3 sector 4 1 102.8529925 103.3467767 102.9493283 104.8151443 2 101.5558889 102.0496730 101.6522247 103.5180407 3 100.2587853 100.7525694 100.3551211 102.2209371 4 98.96168170 99.45546582 99.05801750 100.9238335 5 97.66457809 98.15836221 97.76091388 99.62672990 6 96.36747448 96.86125860 96.46381028 98.32962630 7 95.07037087 95.56415499 95.16670666 97.03252268 8 93.77326726 94.26705138 93.86960306 95.73541908 9 92.47616365 92.96994777 92.57249944 94.43831546 10 91.17906004 91.67284416 91.27539584 93.14121186 52 89.88195643 90.37574055 89.97829222 91.84410824 64 88.58485282 89.07863694 88.68118862 90.54700464 66 87.28774921 87.78153333 87.38408500 89.24990102 68 85.99064560 86.48442972 86.08698140 87.95279742 96 84.69354199 85.18732611 84.78987778 86.65569380 98 83.39643838 83.89022250 83.49277418 85.35859020 the search for the appropriate container for the respective message can be done by looking at the minimum value between the difference in the number of zeros in the container and the stereo file to the difference between the zeros and the units in the container. (2) where: s0 count of zeros in the stego file c0 count of zeros in the container c1 count of units in the container following the experiment, the following data are obtained, table 3. table 3 targetcover coefficient values image number container stegofile targetcover count of zeros count of units count of zeros count of units 1 622729 583175 626681 579223 9.991404 2 643600 562304 647266 558638 4.509447 3 633218 571486 635749 568955 4.099981 4 624673 554975 628273 551375 5.165141 5 647594 558310 651318 554586 4.170960 6 530851 678749 537953 671647 4.801958 7 654026 418486 657266 415246 1.375563 8 625098 585222 630523 579797 13.60467 9 696528 509376 697594 508310 0.569590 10 526601 567415 530636 563380 9.886314 the resulting values are in quite a large range, but in the results of image # 9 it is noted that the changes made in the stego file are minimal. therefore, this file will be selected 11 as a container and will further seek to select the sector with the smallest changes. 4 conclusion searching for an optimal container requires an analysis that takes into account both the human perception of the image and the mathematical relationships that can be analyzed in detail about the contents of the container. from the point of view of human perception, it turned out that the eye of a person does not look at all the details of an image, and on the basis of his experience and sensation, the brain complements the areas "not seen" by the eyes. based on this analysis, the idea of searching for zones in the file, in which changes even if made, will be the least reported. the analysis of mathematical dependencies has proved the hypothesis that areas can be selected in the file where the changes are minimal. the experiments have shown a very close connection between the container and the secret message the same secret message inserted into different files brings different changes to the containers. acknowledgements this work is partially supported by the scientific fund rd-08-101/06.02.2017. references [1] palmer, s. (1999) science of vision:photons to phenomenology. cambridge: the mit press. [2] marr, d. (1982) vision. a computional investigation into the human representation and proccssing of visual information. new york: w. h. freeman and co., 1982. [3] gibson, j. (1986) ecological approach to visual perception. hillsdale, new jersey london & lawrence erlbaum associates. [4] helmholtz, h. von (1867) handbuch der physiologischen optik. copyright © 2018 hristo paraskevov and aleksandar stefanov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 7 mathematical and software engineering vol. 6, no. 1 (2020), 7-11. varεpsilon ltd, http://varepsilon.com/index.php/mse/ automated system for development of doctoral documentation stanimir zhelezov1 and denitsa ts. harizanova2 1 s.zhelezov@shu.bg konstantin preslavsky university of shumen, bulgaria 2 deni_tsvetkova@abv.bg konstantin preslavsky university of shumen, bulgaria abstract the article presents a web application through which doctoral study documentation can be prepared and developed. the main functions and characteristics of the various user roles involved in the development of the documentation are presented. an example of an adaptation related to the learning process is described. several screenshots of the application are presented. future plans for the development of the application are shared. keywords: education documents; web-based application; educational application; doctoral documentation 1 introduction the creation of documentation in electronic form is a trend that has long proven to be successful and applicable. the use of this type of resources at any time and place is a convenience that more and more institutions are focusing on, using good practice for their accessibility. a time when digitalization is everyday, requires the use of modern information and communication technologies to provide electronic services accessible to every user. the use of web-based applications provides users with fast, useful and up-to-date information that they can receive in real time. it provides an opportunity for joint activities and teamwork from any point [2]. modern technologies allow the created applications to be adaptable to any digital devices having access to the internet. this article proposes an author's application, which aims to support and automate the preparation and creation of doctoral study documentation. automated and unified to process entered information and to eliminate the possibility of human error. the approbation of the considered application is to be presented to the academic staff of fmi, at konstantin preslavsky university of shumen and to be realized experimentally. 2 main features of the application the application is an author's realization for the creation of doctoral study documentation providing the educational process of doctoral students enrolled in fmi, and in the future, it is planned to integrate it with other major structural units at konstantin preslavsky university of shumen. the choice to create such an application stems from the need for a tool to help both the doctoral students themselves and their supervisors and department heads. 8 the educational documentation, by its nature, contains a general and individual plan, in which various educational, scientific and creative activities are planned, for which the respective number of credits is awarded [9]. all these requirements the head of the department, plans and structures according to the approved rules of the university. the structure and content of the documentation will help the heads of doctoral students at the respective department to plan the activities related to the training of doctoral students faster and easier. the main roles of the application are presented in fig. 1, as in general they are: • administrator: registers and defines the role of each user in the application and prepares the hierarchical relationship between the areas, fields and doctoral programs in education; • head of department: prepares and implements the doctoral study documentation. introduces doctoral students and associates them with the relevant supervisor; • supervisor: introduces the main activities related to the individual doctoral plan, interim and annual reports, as well as the doctoral student's participation in various projects. it determines the disciplines that the doctoral student must study; • phd student: introduces the activities related to research / artistic activity, as well as monitors the implementation of his / her individual plan. the technical implementation of the application is in line with the latest standards for building web applications. the latest versions of html, css, php, mysql are used, and ajax technology is used for dynamic processes. various popular methods of data protection related to their security on the internet have been applied [1]. the application is quickly and easily managed by the latest web browsers for both desktop operating systems and mobile devices [6, 7, 8]. head of department administrator phd students supervisor fig. 1 visual model of user roles 9 adaptation of the application to the learning process of faculty mathematics and informatics the application is distinguished by its universality in the development of doctoral documentation. such applications make a major contribution to the development of online resources accessible to a wide range of users [4,5]. we will now look at some of the main functions set out in it to see its capabilities in developing doctoral documentation. each general curriculum created by the head of department consists of three main sections: "educational activity", "research / artistic activity" and "teaching-methodical and teaching activity". the structure of the section "educational activity" includes compulsory, elective and optional disciplines, which carry the appropriate number of credits. if there are more disciplines planned for the respective type of disciplines, then a value "from the application list" is determined. the supervisor chooses at a later stage any discipline in the individual plan. a user form is displayed on the screen, through which the new activities and sections are added to the curriculum. each activity that is planned must bring credits to the doctoral student, so that at the end of his / her studies, he / she has collected the necessary credits for deduction. fig. 2 show the structure of a specific curriculum. if a change in the structural elements of the plan is required in the process of work, then by "delete" each element can be removed and a new one can be planned in its place. thus, it is not necessary to delete an already entered curriculum fields that can be used. in order to add or edit the information on the elective, optional, compulsory disciplines and the doctoral minimum, the user must select the menu "disciplines" and proceed to the appropriate action. each discipline has different fields related to the number of hours and credits. the number of credits is formed automatically, and for every 30 hours 1 credit is provided (fig.3). fig. 2 generating a general curriculum 10 in the supervisor profile, the user can see each individual plan of the phd students associated with it. each curriculum is accompanied by the "report" tool, which determines the desired interval for generating a report on the implementation of the planned activities. the view of the report visualizes each performed activity to the respective section and the number of accumulated and remaining credits. the generated report can be downloaded in text format for ms word. another important part of the training phase of doctoral students is their participation in projects. in the section "participation in projects" (fig. 5) the head of the doctoral student enters all participations in projects of the doctoral student during his training. the projects that may include doctoral students are domestic, national or international for the respective calendar year. at a later stage in the development of the application, a reference could be made to the number of doctoral students participating in projects and the creation of reports or reports related to accreditation activities. each registered doctoral student can visualize his / her individual plan according to which he / she is studying and prepare his / her reports. in his / her profile, the doctoral student could change his / her personal data, as well as introduce activities related to his / her fig. 3 adding a new course fig. 1 preview and download a generated report fig. 2 participation in the project 11 scientific and artistic activity. in the menu "individual curriculum" the doctoral student can review his individual plan and monitor its implementation. in case of inaccuracies or missed activities, the doctoral student may promptly notify his / her supervisor. in the activity related to the scientific or artistic activity, for the doctoral students it is envisaged that each of them introduces his / her respective activities. in electronic form it is necessary to enter the main things related to this activity, as there is a place for authors and a list of scientific bases, in case the activity is published. throughout the training period, doctoral students can introduce various activities or update them without any restrictions. conclusion in the proposed software implementation of an automated system for developing doctoral documentation with a web-based interface, it can support the administration and the process of training doctoral students. the application can contribute to the purposes of accreditations, audits or the preparation of other documentation. all faculty members involved as supervisors or department heads can create the necessary curricula regardless of where they are located and what digital device they work with. the developed application can support the preparation and unification of the training documentation and improve the time for its implementation. future work the presented web application can be developed with the following functionalities: • sending messages between different user roles; • filtering the results; • creating a support system; • integration in other structural units of konstantin preslavsky university of shumen. the research presented in this paper is partially funded by the project of scientific foundation of shumen university rd-08-134/04.02.2020. references 1. kordov, k. (2014) heartbleed bug: threat for internet security and methods for protection, mattex 2014, conference proceedings 2016, 145—148. 2. pavlova, n, harizanov, k. (2016) adaptation of webplatform.info, mattex 2016, conference proceedings 2016, 316—321. 3. farkas, d. k., & farkas, j. b. (2001) principles of web design. longman publishing group. 4. kolisnichenko, d. (2014) php and mysql. development of web applications. -st. petersburg: bhv-petersburg. 5. karlins, d. (2013) html5 and css3 for dummies. john wiley & sons. 6. hong, p. (2018). practical web design: learn the fundamentals of web design with html5, css3, bootstrap, jquery, and vue. js. packt publishing ltd. 7. welling, l., & thomson, l. (2009) php et mysql. pearson education france. 8. russell, c. (1999) html in easy steps. computer step. 9. university of shumen phd programms (2020, february 20), retrieved from https://www.shu.bg/doktoranti/cod/. https://www.shu.bg/doktoranti/cod/ 24 mathematical and software engineering, vol. 4, no. 2 (2018), 24-27. varεpsilon ltd, http://varepsilon.com application of sorting algorithms for convex hull determination mihaela todorova 1 , stoyan kapralov 2 , and valentina dyankova 1 1 konstantin preslavsky university of shumen, shoumen, bulgaria, emails: mihaela.todorova@shu.bg, v.dyankova@shu.bg 2 technical university of gabrovo, gabrovo, bulgaria, email: s.kapralov@gmail.com abstract the proposed research explores the possibilities of applying some base algorithms for sorting to the process of finding a convex in order to optimize the time indicators of this process. a comparative analysis of the time characteristics has been performed using different time approaches in graham’s algorithm. the empirical results obtained have been used as a basis for building a pattern model of the process of finding a convex hull. it performs point sorting by a given criterion and finds a convex hull on a two-dimensional set of points. for this model, a visualization module has been developed that can be used as a learning environment in the courses of computing and complexity of algorithms. keywords: algorithms for sorting; convex hull; graham’s algorithm 1 introduction in modern computer systems, a number of basic and improved algorithms are used to organize and process large amounts of data. the process of rearranging objects in a particular order is known as sorting. in this sense sorting is a universal, basic activity, with wide application in different algorithms. one of the untraditional applications of sorting is in computational-geometric algorithms to find a convex hull of a set of points. the basis of these algorithms is the processing of a large number of multipoint points by a given criterion. the definition of the convex hull finds interesting practical applications such as finger pointing [4], wireless sensor node recovery [5], virtual body digitalization [6], modelling of human solutions in games [7], machine learning [8] etc. for this reason, sorting is essential in the algorithms for finding a convex envelope. it is possible to sort out a large number of elements to take significant computing resources, and in this sense the question arises as to how exactly the type of sorting affects the efficiency and performance of the algorithm when used and applied. in the context of the discussed issues, the objectives of the present study are: 1. suggest different approaches for integrating sorting algorithms into algorithms to find a convex envelope. 2. perform studies of the influence of the sorting algorithm type in the process of finding a convex envelope and analyze and summarize the resulting experimental time results. 3. using the optimal of the approaches studied, suggest an example algorithm on the basis of which a class for finding a convex envelope can be created. 25 2 exposition the essence of sorting as a process of rearranging a given set of objects in a particular order [3] determines the two underlying operations on which the complexity of each sorting algorithm depends. these are the operations of comparison and exchange of values. since interest in the study is a sorting application in graham's algorithm to find a convex shell, three of the main sorts will be examined. these are pyramidal sorting, bubble sorting and quick sorting. the quick sort algorithm requires a time proportionally averaged over nlogn to sort the n element. the main drawback of the algorithm is that it is not stable and in worst-case uses n2 operations. bubble method is one of the most popular sorting algorithms. the average and worst case of this algorithm is o (n2) and is not used to sort large unordered datasets [1]. heapsort is a kind of sorting algorithm by direct selection. with the complexity of o(n log n) it has the advantage of a more favorable worst case because he does not use many arrays or recursion. graham's algorithm for finding a convex envelope on multiple points consists of three basic steps. in its first step, using a sorting, there is a base point of the hull with minimum x and y coordinates. when searching for this point, all points in the set are sorted by the y coordinate, and if there are several points with a minimum y coordinate, they are sorted by the x coordinate. in the second step of the algorithm follows an angular range of points [2]. all points are sorted by the angle that forms the straight line passing through the base point and the point with the abscissa axis. this angular sort is replaced by checking the coordinates of the points. in its third step, the algorithm finds among the sorted points the ones that are from the shell and constructs it. figure 1: аngular sorting for an empirical comparison of the timing characteristics when applying sorting in the graham algorithm, the following approaches were considered: 1. apply bubble method for the angular sorting. when applying this algorithm, the base point of the set is detected and angularly sorted by the bubble method. the main modification in the algorithm is to compare the points of their location to their baseline and previous point. the array of points crawls in sequence and at each step compares the point a [i] and a [i +1]. if the point a [i +1] is located in the left half of the starting beam point and the point a [i], the algorithm continues with the check for points a [i +1] and a [i +2]. if the point a [i +1] is in the right half equal to this beam or lies on it, then the elements a [i] and a [i+1] change their positions. 2. apply a quick sort order for angular sorting. 26 in the quick sort order to sort the stack of points first, a point x is selected as the last point in the array with which the other points are compared. after comparing with an auxiliary function, the goal is to the left of the x point in the array to be points which, compared to the base, make smaller angles with the abscissa and to the right of x points that make larger angles. then, by recurs, the left and right parts of the array are sorted. 3. apply a heapsort to find a base point. when applying this sorting, there is a quick element with a minimum coordinate that stands at the top of the pyramid. table 1: time performance input data bubble sort (seconds) quick sort (seconds) bubble sort and heap sort (seconds) quick sort and heap sort (seconds) 500 0.0146 0.0013 0.0123 0.0013 6000 1.686 0.035 1.676 0.0136 45000 96.514 0.5246 94.528 0.118 250000 / 4.539 / 0.782 using a pyramid sorting in graham's algorithm to find a base point, it is matched with a quick sort or a sorting method by arranging the points of the set relative to the angle. in the table 1 are given time results from the application of the three approaches for sorting the same data from the set of points. it can be seen that graham's algorithm's time efficiency using a pyramidal point-to-point pairing in combination with a quick sorting of the remaining points gives the best time results from the approaches considered. in the context of these results, graham's sample algorithm, using a pyramidal and quick sort, and the basis on which to create a convex hull class can be proposed. the algorithm has the following form: int grahamscan(point a[], int n){ sort(a,a+n,compy); int k=1; while(k<n && a[k-1].y==a[k].y) k++; if(k>1){ sort(a,a+k,compx); swap(a[1],a[k-1]); if(k==n){ if(a[0].x==a[n-1].x) return 1; return 2; } sort(a+k,a+n,compt); } else{ sort(a+1,a+n,compt); k=2; while(k<n && dir(a[0],a[k-1],a[k])==0) k++; sort(a+1,a+k,compy); swap(a[1],a[k-1]); } int m=1; for(int i=k; i<n; i++){ while (dir(a[m-1],a[m],a[i]) <= 0) m--; m++; swap(a[m],a[i]); } return m+1; } 27 3 conclusions applying a sort of algorithm to find a convex envelope can be explored in two main directions: 1. approaches for adapting sorting algorithms when searching for convex envelope. 2. ability to improve the efficiency and speed of algorithms for finding a convex hull. the proposed algorithm successfully adapts the gram's algorithm to look for a convex envelope, improving its performance and efficiency. for the application of sorting in other algorithms to find a convex envelope and their improvement, this is a good guideline for developing an optimal class that can be used to construct a convex envelope at a set of points references [1] nakov, p., dobrikov, p. (2018) programming = ++ algorithms, www.programirane.org. [2] cormen, t.h., leiserson, ch.e., rivest, r.l., stein, c. (2009) introduction to algorithms, third edition, mit press. [3] wirth, n., (1980) algorithms + data structures = programs, prentice-hall. [4] nagai, к., sakabe, h., ohka, m. (2017) finger direction recognition toward human-and-robot cooperative tasks, international symposium on micro-nanomechatronics and human science (mhs), 3-6 dec. 2017, nagoya, japan, ieee. [5] lakshmi, m., r. (2017) modified convex hull algorithm for recovering smashed wireless sensor networks, international journal of scientific research in computer science, engineering and information technology, volume 2, issue 4, 495-502. [6] xu, y., hou, w. (2017) calculation of operational domain of virtual maintenance based on convex hull algorithm, second international conference on reliability systems engineering (icrse), 10-12 july 2017, beijing, china. [7] tim rach, alexandra kirsch. (2016) modelling human problem solving with data from an online game. cognitive processing, springer verlag, 2016, 17 (4), pp.415-428. [8] pihera, j., musliu, n. (2014) application of machine learning to algorithm selection for tsp, 2014 ieee 26th international conference on tools with artificial intelligence, 15 december 2014, limassol, cyprus. copyright © 2018 mihaela todorova and stoyan kapralov and valentina dyankova. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. https://www.amazon.com/algorithms-structures-prentice-hall-automatic-computation/dp/0130224189 https://scholar.google.bg/citations?user=q5uxnz4aaaaj&hl=bg&oi=sra https://ieeexplore.ieee.org/abstract/document/8305242/ https://ieeexplore.ieee.org/abstract/document/8305242/ https://ieeexplore.ieee.org/xpl/mostrecentissue.jsp?punumber=8301387 https://ieeexplore.ieee.org/xpl/mostrecentissue.jsp?punumber=8301387 https://ieeexplore.ieee.org/xpl/mostrecentissue.jsp?punumber=8024047 https://ieeexplore.ieee.org/xpl/mostrecentissue.jsp?punumber=8024047 https://scholar.google.bg/citations?user=35owm6eaaaaj&hl=bg&oi=sra https://ieeexplore.ieee.org/xpl/mostrecentissue.jsp?punumber=6979774 mse-vol2-no1-(2016)-30-34-etokebe 30 mathematical and software engineering, vol. 2, no. 1 (2016), 30-34 varεpsilon ltd, http://varepsilon.com determination of atmospheric effective earth radius factor (k-factor) under clear air in lagos, nigeria 1etokebe iniobong jackson, 2kufre m. udofia, 3ezenugu isaac a. 1,2department of electrical/electronic and computer engineering, university of uyo, akwa ibom, nigeria. 3department of electrical engineering, imo state university (imsu), owerri, nigeria. isaac.ezenugu@yahoo.com *corresponding author: isaac.ezenugu@yahoo.com abstract due to it cost effectiveness and ease of accessibility, as well as adaptability, radio wave communication at microwave frequencies has earned enormous attention over time. importantly, secondary radio variables remained very significant in carrying out calculations especially on effective earth radius factor. this study was carried out in lagos, south west of nigeria. three year atmospheric parameters data from nigerian meteorological agency (nimet) was used. international telecommunication union (itu) recommendation models were applied in determining point refractivity gradient and effective earth radius factor based on radiosonde data obtained from nimet for lagos state. the calculated values of effective earth radius factor showed a variation between 1.31 and 1.73 while the point refractivity gradient varied between -398.5034 and -56.42. also, the yearly average value of dn1 and k-factor for lagos are -210.111392 and 1.494358 respectively. keywords: earth radius factor, refractivity gradient. 1 introduction the concept of radio wave communication over time has been in application in greater magnitude as compared to other communication modes. the wireless communication links are utilized for various services; voice, data and video. the point to point radio line of sight link is also being used to fix terrestrial communications, as well as mobile communications [1]. the areas of application earlier stated can be seen in both civil and military operations across the globe. 31 during microwave link design, some parameters such as the effective earth radius factor, (k-factor), and the point refractivity gradient, (dn1), must be set carefully to optimize the performance of the microwave link [2]. the effective earth radius factor, (also called k-factor) greatly influence the transmission of radio signals through the atmosphere. due to its significance, the understanding of the effective earth radius factor distribution in a given area is of great importance in the telecommunication industry. however, the k-factor is largely dependent on refractivity gradient. as a result of variations in atmospheric refractivity, radio waves usually bend while propagating through the different layers in the atmosphere [2]. most of the atmospheric effects are very much noticeable when transmitted signals take different route to its target receiver and the arrival time also being different. consequently, in this paper, itu models are applied in determining point refractivity gradient and effective earth radius factor based on radiosonde atmospheric parameters data obtained from nimet for lagos state. 2 effective earth radius the concept of effective earth radius explains a situation where the clearance of the radio beam over the earth’s surface is dependent on the relative distance between two curves. an analysis for clearance is made convenient if one of the curves is assumed to be straight and the other given an extra curvature for compensation. the radio ray is imagined to be straight line relative to an effective earth’s radius, which has been adjusted by the refractivity gradient. this radius is the real earth’s radius which has been multiplied by an earth radius factor (k) that is dependent on the refractivity gradient [3]. according to abu-almal and al-ansari [2], the earth radius factor (k) is the radius of a hypothetical spherical earth, without the atmosphere, for which propagation paths follows straight lines, the heights and ground distances being the same as for the actual earth in an atmosphere with a constant vertical gradient of refractivity [2, 4]. hence, the effective earth radius factor can be estimated as follows [2, 4, 5, 6, 7]: k= �1 + � �� � �� � �� (1) 3 methodology more so, the estimation of effective earth radius factor is dependent on primary radio climatic variables, namely; temperature, pressure and humidity. the three primary radio climatic variables help to obtain another radio climatic variable called radio refractivity, n. the atmospheric refractivity n (n-units) is usually computed as follows [8, 9, 10]: � = �� − 1�10� (2) however, since n has a standard value of 1.000312 and if substituted in equation 2, it gives the value of refractivity (n) to be 312n-units.the refractive index n of air is related to refractivity, n as follows [8, 9, 10, 11]: � = �� − 1�10� = 77.6 ��� + 3.732� 10�� � ��� (3) where t is absolute temperature (k), p is atmospheric pressure (hpa), and e is the atmospheric water vapour pressure (hpa). the water vapour pressure is calculated as follows [12]: 32 = ! "�.��#� �$%� &'.()�* *+�,).-' �.. / (4) where t is temperature in celsius (º c) and h is the relative humidity. to obtain the gradient of refractivity, we consider the equation thus defined by [10]: g = 0102 (5) where the refractivity is expressed as a function of height. hence, g is given as: g = 0102 = 1#�1�2#�2� (6) where n2 is the refractivity at 65m, n1 is the refractivity at the ground level, h2 is the 65m altitude, and h1 is the ground level. in essence, the refractivity gradient shows the relationship of how refractivity changes with height which is of greater interest to line of sight link design engineers. finally, the effective earth radius factor (k) can be calculated by substituting 3134 is equation 1. 4 results and discussion the refractivity gradient for lagos from the distribution table 1 shows the highest occurrence in december with -56.4268n units and february with the lowest dn1 having -398.5034n units. the yearly average value of dn1 and k-factor for lagos are -210.111392 and 1.494358 respectively. table 1 the effective earth radius factor (ke ) and refractivity gradient (dn) for various months in lagos months ke for lagos dn for lagos jan 1.3627 -275.8573 feb 1.3605 -398.5034 mar 1.3337 -313.51 apr 1.6113 -99.8233 may 1.6365 -89.6555 jun 1.748 -172.883 jul 1.4977 -158.4198 aug 1.3128 -344.8771 sep 1.4059 -229.8108 oct 1.5395 -134.0033 nov 1.3881 -247.5664 dec 1.7356 -56.4268 yearly average 1.494358 -210.111392 also, the effective earth radius distribution for the various months in each of this location shows monthly and seasonal variations, figure 1 and figure 2. 33 figure 1 the distribution of effective earth radius factor in lagos figure 2 shows refractivity gradient for different months in lagos 5 conclusion in this study, the estimation of effective earth radius factor and refractivity gradient are carried out under clear air condition using local radiosonde data gotten from nigerian meteorological basically for lagos within the period of three years from 2012 to 2014. the calculated values of effective earth radius factor shows variation in values between 1.31 and 1.73 while the point refractivity gradient values vary between -398.5034and -56.42. the result distribution shows high refractivity occurrence in the rainy period while in the dry season the reverse is the case. 34 acknowledgement the authors are grateful to nigerian meteorological agency for providing meteorological data used for this work. references [1] chaudhary, n.k, trivedi, d.k, and gupta, r., the impact of k-factor on wireless link in indian semi-desert terrain, international journal of advanced networking and applications, 2(4), 2011, 776-779. [2] abu-almal, a., al-ansari, k., calculation of effective earth radius and point refractivity gradient in uae, international journal of antenna and propagation, article id 245070 (2010), 1-4. [3] manning, t., microwave radio transmission design guide, artech house, 2009, united kingdom. [4] skolnik, m., introduction to radar systems, 3rd edition, mcgraw-hill, 2001, new york. [5] odedina, p.k., afullo, t.j., on the k-factor distribution and diffraction fading for southern africa, saiee africa research journal, 97(2), 2006, 172-181. [6] nyete, a.m., afullo, t.j.o, seasonal distribution modelling and mapping of the effective earth radius factor for microwave link design in south africa, progress in electromagnetics research b, 51, 2013, 1-32. [7] okoro, o.n., agbo, g.a., the effect of variation of meteorological parameters on the tropospheric radio refractivity for minna, global journal of science frontier research, 12(2-a), 2012, 37-41. [8] adeyemi, b., emmanuel, i., monitoring tropospheric radio refractivity over nigeria using cm-saf data derived from noaa-15, 16 and 18 satellites, indian journal of radio & space physics, 40(6), 2011, 301-310. [9] gao, j., brewster, k., xue, m., variation of radio refractivity with respect to moisture and temperature and influence on radar ray path, advances in atmospheric sciences, 25(6), 2008, 1098-1106. [10] seybold j.s., introduction to rf propagation.wiley interscience, john willey and sons, inc., 2007. [11] bean, b.r., dutton, e.j., radio meteorology, us department of commerce, national bureau of standard monograph. dover publication co. newyork, 1966. [12] adediji, a.t., ajewole, m.o., vertical profile of radio refractivity gradient in akure, south-west nigeria, progress in electromagnetic research c, 4, 2008, 157-168. copyright © 2016 etokebe iniobong jackson, kufre m. udofia, ezenugu isaac a.. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 12 mathematical and software engineering, vol. 1, no. 1 (2015), 12-17 varεpsilon ltd, http://varepsilon.com online math tasks generator julia dimitrova, eleonora pavlova, kosyo nikolov, and aleksander bonin high school of mathematics “d-r petar beron”, varna, bulgaria abstract this article presents “math for all” – a web application that generates various algebraic equations and inequalities. we discuss algorithms and methods that are implemented in building the library that generates all the expressions, and some problems that are solved in the process of our work. subject codes (acm): g.4, h.3.5. keywords: online generator, algebraic expressions, equations and inequalities, restrictions for answers and quotients. 1 introduction this article presents “math for all” – a web application that generates various algebraic equations and inequalities. the generator can be used by math teachers and everyone who wants to better their skills in this particular part of mathematics. one of the main advantages of “math for all” is the bulgarian interface. the application is very easy to use and provides various settings through which the user can change the type of the equations and inequalities. the user can set the difficulty of the problem, the type of visualization of the answer, the number and the names of the variables, the power of the polynomials or roots, the overall complexity, and also they can choose the type of the answer. the program can generate a number of similar tasks. it solves every generated task and visualizes the result. 13 the application can be used online and is freely available. the intuitive user interface allows our application to be used even by people who are not experienced computer users. the most complex and interesting part of this application is the so-called “core” – a library which generates algebraic expressions, equations and inequalities. the description of the “core” is the main feature of this article. 2 methods and algorithms the application program was created by two 10th grade students at high school of mathematics who have in-depth knowledge of programming. kn is an active participant in c/c ++ programming competitions and ab is a contestant in various it competitions. the description of used data structures the core of the application generates and calculates algebraic expressions. it is written in c ++. a hierarchy of classes is created for the implementation of the algorithms classes ranging from simple monomials (e.g. x 2 ) to complex expressions and for specific tasks (equation equation, inequation inequality). stl (standard template library) [5] -containers vector and map are used too. algorithms many of the algorithms used in calculations were created by the authors with the help of [1-4]. optimizations were made to improve the speed of calculation. for example, the operation “multiplication of polynomials” is optimized into quick sorting, which shortens the computation time. therefore, the maximum complexity is о(n 2 .logn). generating tasks is easier after a shaping algebraic basis. appropriate methods are provided for this in class polynomial. the "heavy lifting", so to say, is done by the class named polynomial. it provides essential functions, such as addition, subtraction, multiplication and exponentiation of algebraic expressions. computing (4x+3/2y)*(23y+x)-(x+3)^2 in a single line of code greatly decreases the difficulty of doing more advanced operations like the generation of math problems. polynomial uses a lot of smaller classes to avoid the clustering of code that is too complex to understand. the hierarchy looks like this: number -> simple -> monomial -> polynomial. the number class is exactly what it sounds like a number. it is the implementation of the coefficients we use in algebra. primitive number types cannot provide the functionality needed for the program, such as fractions. floating point types would give an estimate, but number keeps the fractions 14 intact, so 2/3 will not become 0.66667. in addition, number can be upgraded to provide even more features, such as irrational coefficients (roots, logarithms and so on). this is not hard to do, as every other class uses number by default (with some minor exceptions), so all the changes required would be within number itself. simple is a class that denotes a letter with a power attached to it, for example x^2. its most important feature is that it can be compared in a fashion similar to a letter. monomial is a class for manipulating monomials (such as 5/3x^2y^3). it contains a vector of simples and a number coefficient. monomials can also be compared. this is done by a method you would normally use in a string, i.e. going from left to right and comparing each letter in this case, every simple. this feature of monomial is crucial for the fast operation of polynomial. as you may have guessed, polynomial contains a vector of monomials. those monomials are always sorted. let's look into some of the operations we can perform: addition: we use a modified version of the algorithm for the merging of two sorted arrays. we start with 2 indexes, both at the first monomial of the two polynomials. then we advance 1 position at a time: if the monomials at the respective indexes are the same, we add up their coefficients. if one is greater, we only advance the other index. we repeat this until we have used all the monomials. this gives us an o(n) performance. if the program were to use nonsorted vectors, it would have been o(n 2 ). subtraction is done the same way. multiplication uses the long multiplication algorithm, which has a complexity of o(n 2 ) for numbers. there are algorithms with better performance; however, one should note that they only perform better in practice for a very large number of digits (in our case, monomials). no one would need a polynomial with 5000 monomials and this is why the simplest algorithm is used. determining the asymptotic complexity of this algorithm is hard, though it is fast enough to output 25 expressions long and can sometimes fill a normal screen in under a second. exponentiation uses the fast method employing powers of 2. the multiplications for a given power k is o(log k). description of the generation algorithm: 1. the user fills in a descriptor from the website (currently there are three types equation, inequation and experssion) 2. depending on the type of problem selected, a function is called in interface.hpp. every such function has the same format: an input of the corresponding descriptor and a number of problems to generate, and an output consisting of two strings, for the problem and the answers respectively. 15 furthermore, let's discuss the generation of an equation. first, we need some parameters. those are supplied by equationdescriptor and regulate various aspects of the result – coefficients, power of the equation, number of solutions, complexity and more. in the beginning, the program builds a "base" equation. for example, if we have power=3, the program will end up with something like this: (x+1)(x+2)(x-4)=0. then it would compute the expression, so the answers aren't obvious. it would then proceed to "obfuscate" the equation by adding additional components. for instance, if we have x^2-4 = 0 at some step, after adding such a component it will become 2x^2-6x+5=(x-3)^2. the number of times this step is repeated is controlled by the descriptor. in the end, the program balances the resulting expression in such a way, that an approximately equal amount of characters is on either side of the symbol for equality. for inequations, the only difference is that we use a different sign. here is a method of the inequation class: 16 here is the algorithm which generates equivalent expressions: 1. initially, create two empty expressions (expression), answer and solution respectively. 2. first we determine the number of components to add. this is controlled by the minterms and maxterms members of the descriptor. 3. then we decide how many brackets the component should have. 4. generate polynomials to fill in the brackets. 5. all of the polynomials generated are multiplied together in a separate polynomial. by doing this, we have two expressions that are equal to each other one of them is in the bracket format, the other one is computed. 6. in the end, the same component is added to both expressions. we added to one of the expressions it in bracket format, and to the other – in computed format. 3 results and discussion the application consists of several parts, the main ones being the core and the user interface. the relationship between the core and the site ("web ui") is carried out by luajit [6] and uwsgi [7], to be as fast as possible, and because there luajit ffi (foreign function interface), which allows it to connect the core with the web server. reactjs library [8] is used to create the user interface which made the creation of the design considerably easier. we implemented json, because it is a modern industry standard, and it is very easy to use. the connection with the site, figure 1, is accomplished in the following way: the library receives the task type and its describer from the site. figure 1 17 the library returns two strings – the first one is for the problem and second – for the answer. these strings are rendered beautifully by katex javascript library which is the fastest drawing of latex. our web application is available at http://math4all-scholars.rhcloud.com/. 4 conclusion in conclusion, we created an interactive web application which is used by math teachers and students. they think that this is functional and useful and teachers often generate worksheets for classes and exercises with “math for all”. our goal is to help both teachers and students by giving them a powerful tool to design expressions and equations with particular properties and features. in the future we intend to expand our work in order to add more functions to the generator so as to create some power inequalities. acknowledgements this work is partially supported by net create which provided free access to their web servers. references [1] s. nakov, p. dobrikov, programming = ++ algorithms, 2nd edition, topteam co., sofia 2003. [2] t.h. cormen, c.e. leiserson, r.l. rivest, c. stein, introduction to algorithms, 2 nd ed., 2001. [3] j.m.de koninck, a. mercier, 1001 problems in classical number theory, american mathematical society, 2007. [4] s. petkova, j. ninova, s. matakieva, mathematics for 7th grade, prosveta publishing, 2013. [5] https://www.sgi.com/tech/stl/index.html [6] http://luajit.org/ [7] http://uwsgi-docs.readthedocs.org/en/latest/lua.html [8] https://facebook.github.io/react/ copyright © 2015 julia dimitrova, eleonora pavlova, kosyo nikolov and aleksander bonin. this is an open access article distributed under the creative commons attribution license (http://creativecommons.org/licenses/by/4.0/). http://math4all-scholars.rhcloud.com/ mse-vol1-no1-_2015_-6-11-nedzhibov 6 mathematical and software engineering, vol. 1, no. 1 (2015), 6-11 varεpsilon ltd, http://varepsilon.com inverse iterative methods for solving nonlinear equations gyurhan nedzhibov faculty of mathematics and informatics, shumen university, bulgaria abstract in his work we present an approach for obtaining new iterative methods for solving nonlinear equations. this approach can be applicable to arbitrary iterative process which is linearly or quadratically convergent. analysis of convergence of the new methods demonstrates that the new method preserve the convergence conditions of primitive functions. numerical examples are given to illustrate the efficiency and performance of presented methods. subject codes (pacs): 02.60.cb keywords: nonlinear equations; iterative methods; order of convergence; newton method. 1 introduction the problem of solving nonlinear equations is one of the classical problems which arise in several branches of pure and applied mathematics. including the fact that solution formulas do not in general exist, the finding new and efficient numerical algorithms for solving nonlinear equations always has been an attractive problem. in recent years, several numerical methods have been developed and analyzed under certain conditions. these methods have been constructed using different techniques such as taylor series, quadrature formulas, acceleration techniques, decomposition method, and etc. (see, [1-9] and references therein). our goal in this work is to suggest and explore a new approach of construction of iterative methods for solving nonlinear equations. the paper is organized as 7 follows. in section 2 we consider some preliminary results and the new method. analysis of convergence is provided in section 3. several sample iterative methods and numerical examples are explored in section 4. 2 main results let us consider the nonlinear equation (1.1) ,0)( =xf where rruf →⊂: is a scalar function and u is an open interval. in this work, we consider iterative methods for finding a simple root α of f and assume that f is a 2c function in a neighborhood of α . an iterative scheme for solving the equation (1.1), generally takes the form (1.2) ),(1 kk xx ϕ=+ for 0≥k , where )( xϕ is a fixed function and ux ∈0 is a given initial value of α . when studying the iterative methods, one of the most important aspects to consider is the convergence, and the order of convergence, respectively. theorem 4 (traub [1, theorem 2.2]) let ϕ be an iterative function such that ϕ and its derivatives )(,,, pϕϕϕ …′′′ are continuous in the neighborhood of a root α of a given function f . then ϕ defines an iterative method of order p if and only if 0)(,0)()(',)( )()1( ≠==== − αϕαϕαϕααϕ pp… . without loss of generality we assume that function ϕ in (1.2) has the form (1.3) )()( xgxx −=ϕ , where ),,,()( …ffxgxg ′= . investigations in this work are inspired by our previous results in [6,7], where we suggest the inverse newton method (1.4) )( 2 1 kk k k xux x x + =+ , where ( ) )(' )( k k k xf xf xu = . which is a modification of the well known newton iterative function (1.5) ( )kkk xuxx −=+1 . 8 iterative function (1.4) is obtained as consequence of companion matrix method and similarity transformations between some companion matrices. the purpose of this paper is to generalize the approach presented in [7]. let us consider an arbitrary, linearly or quadratically convergent iterative function (1.6) ),(1 kkk xgxx −=+ for 0≥k , then we call inverse iterative function of (1.6) the following function (1.7) ,)( 2 1 kk k k xgx x x + =+ for 0≥k . further we will show that iterative process (1.7) preserves the conditions of process (1.6) for nonzero roots. the following local convergence theorem is valid. theorem 1.2 let 0, ≠∈ αα u be a simple root of a sufficiently differentiable function rruf →⊂: for an open interval u . then if for 0x sufficiently close to α the iterative function (1.6) generates convergent sequence with order of convergence not higher than two, the iterative function (1.7) also generates convergent sequence with the same order of convergence. proof: according to theorem 1.1 for the function (1-3)-(1.6) are fulfilled (1.8) ααϕ =)( , i.e. 0)( =αg and )(1)( ααϕ g ′−=′ . then (i) in the case of linear convergence of (1.6), the error equation is fulfilled (1.9) )()).(1()().( 22 1 nnnnn ogo εεαεεαϕε +′−=+′=+ , where αε −= nn x and 1)(1)(' <′−= ααϕ g ; (ii) in the case of quadratic convergence of (1.6), the following error equation is fulfilled (1.10) )(. 2 )( )(. 2 )( 3232 1 nnnnn o g o εεαεεαϕε + ′′ −=+ ′′ =+ . let denote the function )( )( 2 xgx x x + =φ from the expression (1.7). it is not difficult to verify that ααφ =)( and (1.11) 2 2 ))(( ))(1( )( 2 )( xgx xgx xgx x xn + ′+ − + =′φ . 9 then from (1.8) and (1.11) it follows that (1.12) )()(1)( αϕααφ ′=′−=′ g . equations (1.9), (1.10) and (1.12) implies that the iterative process defined by (1.7) will have the same order of convergence as the process (1.6). theorem is proved. 3 sample iterative methods and numerical results in this we will consider some examples of well known iterative methods and their inverse version according approach (1.6)-(1.7). 3.1 newton modification method (3.1) )( )( 0 1 xf xf xx kkk ′ −=+ , which is linearly convergent and the corresponding inverse method is (3.2) )()( )( 0 0 2 1 kk k k xfxfx xfx x +′ ′ =+ . 3.2 consider the following quadratically convergent iterative function (3.3) ))(()( )(2 1 kkk k kk xfxfxf xf xx −− −=+ , and the inverse method function (3.4) )()))(()(( )))(()(( 2 2 1 kkkkk kkkk k xfxfxfxfx xfxfxfx x +−− −− =+ . further we present some results of numerical experiments to illustrate the performance of the considered inverse iterative methods. we compare the newton method (1.5) with the inverse method (1.4), modified newton methods (3.1) and (3.2), and the method s(3.3) and (3.4). we use the following stopping criteria (i) ε<−+ nn xx 1 , (ii) ε<)( nxf . we have used the fixed stopping criterion 1510 −=ε .when the stopping criterion is satisfied, 1+nx is taken as the exact root α computed. we have denoted: 0x initial approx. it the number of iterations to approximate the zero, nx the approximate root, nn xx −+1 the distance of two consecutive 10 aproximations , )( nxf the absolute value of f at nx , and cocthe computational order of convergence computed using the formula )/()(ln )/()(ln 211 11 −−− −+ −− −− = nnnn nnnn xxxx xxxx coc . we consider the following nonlinear equations as test problems. these equations can be found in many other papers on the subject, see for example [3,8,9]. 1) 1)1()( 3 1 −−= xxf ; 2) 1)(sin)( 22 2 +−= xxxf ; 3) 23)( 2 3 +−−= xexxf x ; the experimental results are included in the following table 1: table 1. experimental results. acknowledgements this work is partially supported by shumen university under grant no. rd-08-265/10.03.2015. references [1] j. f.traub, iterative methods for the solution of equations, prentice hall,englewood cliffs, new jersey, (1964). 0);( xxfi im it nx nn xx −+1 )( nxf coc (1.5) nm 6 2.0000 1.15e-14 0 2.00 (1.4) 6 2.0000 8.87e-11 0 2.00 (3.1) 29 2.0000 8.88e-16 1.33e-15 0.99 (3.2) 30 2.0000 4.44e-16 0 1.00 (3.3) 7 2.0000 1.79e-10 0 2.00 5.2);( 01 =xxf (3.4) 7 2.0000 7.79e-15 0 1.99 (1.5) nm 5 1.4044 2.04e-12 4.44 e-16 2.00 (1.4) 6 1.4044 2.75e-14 3.33 e-16 1.99 (3.1) 21 1.4044 4.44e-16 3.33e-16 0.94 (3.2) 20 1.4044 1.55e-15 4.44 e-16 0.93 (3.3) 7 1.4044 7.46e-14 3.33 e-16 2.00 2.1);( 02 =xxf (3.4) 78 1.4044 6.97e-12 3.33 e-16 2.00 (1.5) nm 5 0.257 3.36e-14 0 2.00 (1.4) 8 0.257 3.29e-11 0 1.99 (3.1) 10 0.257 4.38e-15 0 0.99 (3.2) 13 0.257 8.93e-15 8.88e-16 0.99 (3.3) 12 0.257 1.00e-11 0 2.00 5.1);( 03 =xxf (3.4) 15 0.257 1.97e-14 0 1.99 11 [2] g.h.nedzhibov, v.i.hasanov, m.g.petkov, on some families of multi-point iterative methods for solving nonlinear equations, numer. algor., 42, (2006), 127-136. [3] s. weerakoon and t. g. i. fernando, “a variant of newton’s method with accelerated third-order convergence,” applied mathematics letters, vol. 13, no. 8, pp. 87–93, 2000. [4] g.h. nedzhibov, an acceleration of iterative methods for solving nonlinear equations, applied mathematics and computation, sep2005, vol. 168, issue 1, 320–332 (2004). [5] m.a.noor, k.i. noor, e. al-said and m. waseem, some new iterative methods for nonlinear equations, math. prob. eng. (2010), article id, 98943: 12. [6] g.h.nedzhibov, similarity transformations between some companion matrices, application of mathematics in engineering and economics (amee14), aip conf. proc., 1631, pp. 375-382, (2014). [7] g.h.nedzhibov, on two modifications of weierstrass-dochev iterative method for solving polynomial equations, mathtech 2014, proceedings of the international conference, volume 1, pp. 84-90, (2014). [8] c. chun, construction of newton-like iteration methods for solving nonlinear equations, numerical mathematics 104, (2006), 297-315. [9] m. aslam noor and k. inayat noor, “some iterative schemes for nonlinear equations,” applied mathematics and computation, vol. 183, no. 2, pp.774–779, 2006. copyright © 2015 gyurhan nedzhibov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mathematical and software engineering 31 mathematical and software engineering, vol. 1, no. 2 (2015), 31-36 varεpsilon ltd, http://varepsilon.com modified algorithm for steganalysis stanimir zhelezov department of computer systems and technologies faculty of mathematics and informatics konstantin preslavski university of shumen, 9712 shumen, bulgaria abstract this paper proposes a modified algorithm for steganalysis based on data compression. the experimental results verify that the proposed steganalysis can detect the altered images with high accuracy. subject codes: 68u10, 94a60. keywords: steganalysis, steganography, information security. 1 introduction during the last years the use of stenography methods for hiding and transmitting of secret messages got spread. these methods can be also used for unauthorized leak of confidential information to people outside the organization. to detect such activity it is necessary to use the other component of steganology – steganalysis. the purpose of the steganalysis is to gather enough data for the existence of a hidden message, thus destroying the purpose of the steganography – the secret communication. by efficiency of the steganalysis system we understand the degree of its adaptability in terms of finding the fact that there is a hidden message in a given container [5]: ess =f (p(s/d), pbr,tsa, qm), (1) where tsa is the time of execution of the steganalysis, p(s/d) is the probability of finding a hidden message in the container in a given time interval under certain conditions, pbr is the probability of reliable system operation, qm – expenses for input and operation of the hardware and software [5]. when checking the effectiveness of the steganalysis the first two parameters 32 tsa and p(s/d) can be considered main criteria. during the analysis of the steganalysis methods using classifiers that are typical for the method of steganalysis based on autocorrelation coefficients [7] and the blind steganalysis based on empirical matrices [3], one major drawback is noticed – the need for continuous training in advance. this leads, in turn, to significant difficulties in implementation of the algorithms that realize this type of methods in actual working steganalysis systems. the methods, using calculation of the statistical dependencies between different elements of the analyzed files have a significant time advantage over the above. with them the time of algorithm execution depends mostly on the calculations, which are used as basis for defining these dependencies. for example, the methods using transformations (dwt and cwt) will take a lot more time for analysis than the methods using direct calculations of statistical dependencies. for example, in the method for universal blind steganalysis based on color wavelet decomposition [1], the time for calculating the dependencies is considerably more than it is in the method for histogram analysis (chi-square) [6], as the calculations with the second method are with considerably less mathematical complexity. 2 modified algorithm for steganalysis the main indicator for the effectiveness of a stego system is the accuracy of determining the existence of hidden information. for most of the steganalysis methods, based on calculating the statistical dependencies between different elements of the analyzed files, accumulation of preliminary statistics for analyzing each tangible object leads to a false indication of hidden information existence. this in turn leads to inaccuracies when determining the existence of a hidden message if it does not exceed 5-6% of the stego capacity of the file. to overcome this disadvantage, from the analyzed methods in this work, the steganalysis method based on data compression [8] was selected for further study. the proposed in this work algorithm is a modification of the method of steganalysis of image files by using this method [8]. it is based on the fact that the output container and the information added in it are statistically independent, so when adding hidden data to the container its size during compression is greater than the size of an empty output container during compression. the developed algorithm for steganalysis of image data checks the statistical independence of the data. widely spread archiving programs are used for compression. let arh(z) be an algorithm for compression, realized with the archiving program applied to the input sequence z of a container and let steg(z) be the stego algorithm realized with the software, that hides the sequence of the message м in the container. let ke(z) be the compression coefficient of the input sequence, defined by the formula: 33   )(zarh z zk e  (2) let kf(s) be the compression coefficient of s, defined by the formula:   )(sarh s sk f  (3) let ε be the subtraction of these two coefficients (2) and (3), set with:    skzk fe  (4) to determine the fact of inserting information, a limit for δ is chosen and evaluation is made whether the resulting value exceeds the limit. in fig.1 is shown a block diagram of the modified algorithm for steganalysis of image files using data compression. the algorithm execution starts with entering input data. the files that will be analyzed are verified for correspondence with the input requirements. difference is a reason to stop processing. in the absence of such difference it is proceeded with compression of the analyzed input file z and defining the compression coefficient ke(z). in the input sequence z a control message м is embedded with the help of the stego algorithm arh(z), it is subjected to compression and compression coefficient kf(s) is defined of the obtained stego file. in the next step, ε is defined – the difference between the two compression coefficients (e<δ) and depending on the result a decision is made for the existence of a stego message or its absence. a decision to continue or not the analysis of image files is made based on the result of the performed check in last steps. for conducting an analysis and evaluation of the effectiveness of the developed algorithm for finding steganography information, an experiment was conducted, including data processing and analysis of over 2500 files with different file formats (bmp, jpeg, doc, txt). for comparative analysis, the algorithm, based on the method of histogram analysis (chi-square) was used. to determine the effectiveness of the proposed algorithm, a base of 1000 stego files was created with the help of different stego programs. this base was subjected to steganalysis using the method, based on data compression, and the results are the following: 1. during embedding of a control message in containers of the base there is a significant difference in compression coefficients (fig. 1) of the “empty” containers  zk e and those with embedded control stego message  sk f . 2. this is not typical for the compression coefficients (fig. 2) of the stego files  sk f and the same with an extra embedded message  sk ff . 3. a clear differentiation can be made between  of a container and f  of a 34 stego file, which is at the core of the proposed algorithm (fig. 3). 4. there is a wild enough range of values (fig. 3), that can be selected as limits values for . therefore, the proposed algorithm allows clear determination of the existence of hidden information in arbitrary files. fig. 1 difference in compression coefficients in empty file and stego file 0.000000 0.500000 1.000000 1.500000 2.000000 2.500000 3.000000 3.500000 n e w 1 n e w 2 7 n e w 3 0 n e w 3 7 n e w 4 0 n e w 4 4 n e w 5 5 n e w 5 9 n e w 6 3 n e w 6 7 n e w 7 1 n e w 8 0 n e w 8 8 n e w 9 8 файлове с т о й н о с т и kf rar kf f rar fig. 2 difference between stego file and the same with re-inserted message in it. -0.200000 0.000000 0.200000 0.400000 0.600000 0.800000 1.000000 ne w 1 ne w 27 ne w 30 ne w 37 ne w 40 ne w 44 ne w 55 ne w 59 ne w 63 ne w 67 ne w 71 ne w 80 ne w 88 ne w 98 файлове с т о й н о с т и ε εf fig. 3 differentiation between container and stego file. to determine the effectiveness of the algorithm of steganalysis of image files using the method 2  verification tests of 800 files are carried out. for the purposes of the experiment, the base with containers was used to create a base with stego files and for that purpose messages with different format and size were embedded. the resulting base with stego files was analyzed. and the result was (fig.4): 0.000000 0.500000 1.000000 1.500000 2.000000 2.500000 3.000000 3.500000 4.000000 4.500000 ne w 1 ne w 27 ne w 30 ne w 37 ne w 40 ne w 44 ne w 55 ne w 59 ne w 63 ne w 67 ne w 71 ne w 80 ne w 88 ne w 98 файлове с т о й н о с т и ke rar kf rar files values files files values values 35 fig. 4 analysis of the stego files for files with small amount of embedded information (embedding coefficient less than 5%), the proposed algorithm does not always find the stego embedding. this applies to all analogical algorithms that use initial statistical information gathering. 3 conclusion from the comparative analysis of the received results is clear that using the proposed algorithm for finding stenographic information significantly reduces the error rate (less than 1%). based on the experimental results, the following main advantages and disadvantages of the analyzed algorithms were realized: from the point of view of the criterion of effectiveness in finding hidden information, the algorithm with data compression gives significantly better results than the one based on chi-square. for files with small amount of embedded information (embedding coefficient less than 5%), the chi-square based algorithm does not always find the stego embedding. this applies to all analogical algorithms that use initial statistical information gathering. using this algorithm significantly reduces the error rate (less than 1%). from the point of view of the speed criterion, the algorithm based on chi-square significantly surpasses the second algorithm. in conducting the experiments described above, the execution time of the steganalysis of the stego files the base was also noted. for the first algorithm this time is in the range of 5 minutes (275 seconds). with the proposed algorithm this delay is slightly greater (345 seconds). therefore, the use of these algorithms for steganalysis in real time is not very appropriate, because it would lead to a significant delay in the data transfer. for this purpose it is necessary to use high-performance systems and parallel calculations for improving the reviewed algorithms and reducing the execution time of the steganalysis. implementation of a program realization of the proposed algorithm, as a sub-module of the network security systems will increase their efficiency and will raise their security level [2], [4]. results of the analysis of file bases 90% 4% 6% found not found false positive 36 references [1] agaian, s., cai, h., color wavelet based universal blind steganalysis, san antonio, texas, usa, 2005. [2] boyanov, p., using http filter to analyze and monitor the vulnerability and security states in determined computer network, journal science education innovation, vol. 2 (2014), 45-51. [3] chen, x., blind image steganalysis based on statistical analysis of empirical matrix, pattern recognition, 2006, icpr 2006, vol.3, 1107-1110. [4] kordov, k., modified chebyshev map based pseudo-random bit generator, aip cp 1629, 432-436. [5] stanev, s., galyaev, v., smyslovoe sopostavlenie nauchnyh terminov na russkom i anglijskom jazykah v oblasti komp’juternoj steganografii, sbornik materialov mezhdunarodnoj nauchno-prakticheskoj konferencii gaou vpo dagestanskij gosudarstvennyj institut narodnogo hozjajstva, mahachkala, dginh, 2013, 51-56. [6] stanley, c.a., pairs of values and the chi-squared attack, department of mathematics, iowa state university, may 1, 2005. [7] yadollahpour, a., naimi, h.m., attack on lsb steganography in color and grayscale images using autocorrelation coefficients, european journal of scientific research, vol. 31 (2009), 172-183. [8] zhilkin, m.ju., information-theoretical methods of steganoanalysis of graphic data, diss. ph.d., novosibirsk: siberian state university of telecommunications and information sciences, 2009, 153 p. (in russian). copyright © 2015 stanimir zhelezov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. design of dual band microstrip antenna using reactive loading technique 114 mathematical and software engineering, vol. 2, no. 2 (2016), 114-121. varεpsilon ltd, http://varepsilon.com design of dual band microstrip antenna using reactive loading technique 1jeffrey c. saturday, 2kufre m. udofia, 3afolayan j. jimoh 1,2,3department of electrical/electronic and computer engineering, university of uyo, uyo, akwa ibom state, nigeria correspondence author: 2kmudofiaa@yahoo.com abstract the need in most communication devices to have two separate operating frequencies for a variety of applications cannot be over emphasized. microstrip antennas, as part of its inherent characteristics, have the ability to resonate at multiple frequencies depending on the design requirement. in this paper, the design of a dual band microstrip antenna for bandwidth enhancement using reactive loading technique is presented. the designed antenna is of rectangular shape, planar and compact for application in mobile devices. the antenna has a miniature size of 44×41×1.6 mm�, which resonated at a return loss of -19.619 and voltage standing wave ratio (vswr) of 1.303 at 2.4 ghz, and -17.55 db and vswr of 1.301 at 5.2 ghz. the results show that the antenna has a corresponding bandwidth of 124.6 mhz and radiation efficiency of 86.1 % at 2.4 ghz and 119.8 mhz and radiation efficiency of 77.4 % at 5.2 ghz. the substrate used in the proposed antenna is the flame retardant/resistant four (fr-4) with a dielectric constant of 4.4 and a loss tangent of 0.023. keywords: antenna; slot patch; dual frequency; miniature; inset feed 1 introduction rapid developments of various wireless local area network (wlan) protocols have sparked the requirements for miniaturized multi-band antennas. today, the most wide spread wlan protocols are ieee 802.11b/g, which utilizes the 2.4 ghz ism band (2.4–2.485 ghz), and ieee 802.11a which employs the 5 ghz u-nii band and ism band (5.15–5.825 ghz) [1]. small size and light weight antennas are required for portable cellular phones. microstrip antennas (msas) are small in size, low-cost and easy to mount and these good features make them excellent candidates for portable cellular phones [2]. the efficiency realized when one antenna works in different frequencies is more than the efficiency realized when several antennas are used for each frequency band. there are numerous devices that require the dual-band wireless antenna. wi-fi is an example of internet service that utilizes the dual-band networks. for instance, computers with wireless cards are in most cases wi-fi compatible, where wireless card transmits to a wireless router, which is connected to a network, cable modem or dsl modem [3]. microstrip patch antennas have light weight and cost low fabrication as well as mechanical robustness when they are fixed on rigid surfaces. in addition, they are capable of operating simultaneously at multiple frequencies. consequently, in view of its numerous good features, patch antenna many researchers have investigated the performance of such antenna in numerous ways. however, narrow bandwidth came as the major disadvantage for this type of antenna. several techniques have been applied to overcome this problem such as increasing the substrate thickness which in turn introduces parasitic elements, that mean, co-planar or stack configuration. another technique if modification of the shape of the patch [4]. modifying patch’s shape includes designing a rectangular shaped slot on the radiating patch antennas. several papers have been published highlighting different method of using dual frequency operation to enhance bandwidth [1-8] but the method proposed in this paper gives a complete 115 flexibility of mounting the antenna both on planar and non-planar surfaces aside using for mobile devices. the use of multiple patches was suggested by [5] but the ripples as observed from the return loss plot when used in practical application can interfere with adjacent frequencies. slotted square patch with inset feed was proposed by [6], it was supposed to cover 2.4 ghz, 5.2 ghz and 5.8 ghz respectively but it fell short as it only managed to cover only 2.6 ghz and 5.2 ghz from the result obtained. another square slotted patch with quarter-wave edge feed was proposed by [8] which resonated at 2.5 ghz and 5 ghz as designed. 2 conventional techniques for achieving dual band frequency a) use of orthogonal mode: these antennas are characterized by two resonances with orthogonal polarizations. the drawback on this method is that the two dissimilar frequencies excite two orthogonal polarizations. these antennas are simultaneously match the input impedance at the two frequencies by using a single feed structure. b) use of multiple patches: the dual band operation can be achieved through multiple radiating elements, whereby each of the radiating elements supports strong currents in addition to radiation at the resonance. this category includes multi-layer stacked patches that can use patches of various shapes. at the two frequencies, the multi-layer stacked patch antennas operate with the same polarization. c) use of reactive loading: a very popular technique for obtaining a dual band behaviour is to introduce a reactive loading to a single patch. the easiest method is connecting a stub to one radiating edge, so as to introduce an additional resonant length that is facilitate the second operating frequency. this is the technique adopted in this paper. 3 design calculations for single rectangular patch antenna 1. the first step in designing rectangular patch antenna is to specify the resonant frequency (f�), substrate relative permittivity (ε�) and substrate thickness (h). when h satisfies the criterion in equation 1, then the surface waves loss can be neglected [10]: ℎ ≤ 0.3 � �����√��� (1) λ��� = ��� (2) where h is the height of substrate, �� is the dielectric constant, �� � wavelength in free space (air), c = speed of light = 3× 10# m/s, loss tangent, tan & = 0.023 flame retardant 4 (fr-4) substrate is chosen for this design with substrate relative permittivity ε� of 4.4 and height, h of 1.6mm. the chosen substrate height is a good approximation since the proposed antenna is a narrow band antenna. 2. the width (wp) of the patch is calculate as follows[11]; '( = ���� ) ���*+ (3) 3. calculate the effective dielectric constant ��,-thus ; ε�.�� = ��*+� + ��0+� 11 − 12 45670 89 (4) for 564 > 1 4. calculate the normalized extension length ∆< given as: 116 ∆=4 = 0.412 (��@aa*b.�)de6f *b.�ghi(��@aa0b.�j# )de6f *b.#i (5) 5. calculate the value of the length of the patch lp thus, l= ����√�� − 2∆lp (6) 6. calculate the notch width, g using the equation l = � �� × +bmn ×h.gj × +bmn o���@aa (7) 7. calculate the resonant input resistance rin thus; r�q(y = ys) = +�(t8* t89) cos� w�xy=6 z (8) the equation for the characteristic impedance zo is given as; zs \ ]^o_�@aa `q1 afea* eabf 7 eaf c+ 89^do_�@aadeaf *+.�e�* b.ggf `q�eaf *+.hhh�i eaf g+ (9) in this design, the ratio, 5a4 = �.e#+.g = 1.863 > 1, so the second expression in equation 9 applies. rin(edge) = +�(t8∓ t89) (10) in order to evaluate the input resistance, other parameters such as wave number k, input current i1, input conductance g1 and mutual conductance g12 have to be known. hence, k = �� ��� (11) i1 = -2 + cos(x) + xsi(x) + l�q (m)m (12) x = kwp (13) g1 = n8+�b�9 (14) g12 = ++�bo9 p ql�q (re69 �sls)�sls t � js(klvsinθ)sin�θdθob (15) for the design in this paper, inset feed technique is used with a chosen input impedance of 50 ω. 8. calculate the inset feed recessed distance y0 and the width of the transmission line wf thus; z0 = rin(edge) {|}�( o~� �b) (16) �b = ~�o {|}0+ q) �^���(����) t (17) according to [12], the width ('-) of the transmission line is calculated thus: b = gbo9��√�� '= ���o � × �� − 1 − ln�2 × � − 1� + � ��0+��� � …… × �ln�� − 1� + 0.39 − b.g+�� � � for 5a4 > 2; (18) 9. calculate the ground plane dimensions as follows; the length of the ground plane (lg) is: lg = 6h + lp (19) the width of the ground plane is: wg = 6h + wp (20) 117 4 results and discussion the antenna is simulated using cst microwave. the design parameters used in the simulation are shown in table 1 while geometry of dual band microstrip antenna is given in fig. 1 and fig. 2. table 1: the design parameters for the dual band antenna variables wg lg wp lp wf lf g yo c value(mm) 44 41 24 21 2.96 10 2 5.2 10 variables b a l1 w1 l2 w2 n m value(mm) 13 2.3 20 4.5 22 12.3 12 26 figure 1: geometry of dual band microstrip antenna figure 2: designed antenna in cst mws (top view) the return loss of the antenna is given in figure 3. figure 3 shows that at -19.619 db, the resonance frequency is 2.4189 ghz and at -17.55 db the resonance frequency is 5.2034 ghz. this shows a bandwidth of 115 mhz at 2.4 ghz and 110 mhz at 5.2 ghz. 118 figure 3: return loss of the designed dual band antenna the bandwidth of the antenna is given as [13]: bandwidth at 2.4 ghz = �.h#0�.�j�.h × 100% = 5.4% bandwidth at 5.2 ghz = j.�f0j.+jj.� × 100% = 2.3% figures 4 (a) and 4 (b) show the vswr plot of the dual band antenna at 2.4 ghz and 5.2 ghz. the results show that the antenna resonated within the allowable limit of between 1 and 2; as seen from figure 4, a vswr of 1.303 and 1.301 at 2.4 ghz and 5.2 ghz respectively were obtained. (a) (b) figure 4: vswr of the designed antenna (a) at 2.4 ghz (b) at 5.2 ghz 119 figures 5 (a) and 5 (b) show that the dual band antenna has a directive gain of 6.1 dbi at 2.4 ghz and 6.3 dbi at 5.2 ghz. (a) (b) figure 5: directive gain of the designed antenna (a) at 2.4 ghz (b) at 5.2 ghz 5 effects of varying slot dimensions of the designed antenna for proper optimization of the design the antenna slot dimensions were altered within allowed limit as shown in figure 6. the value of l1 = 20 mm (green colour) produced the best fit for the antenna that met the required specification for the antenna to resonate at both 2.4 ghz and 5.2 ghz on the same patch. 120 figure 6: variation of slot dimensions for design optimization in cst mws. also, from figure 7, a radiation efficiency of 86.1 % at 2.4 ghz and 77.4 % at 5.2 ghz are achieved. figure 7: radiation efficiency of the designed dual band antenna 6 conclusion the results shown in the various figures show an appreciable level of compliance with the design specifications. with a bandwidth of 115 mhz which represents 5.4 % at 2.4 ghz and 110 mhz representing a bw of 2.3 % at 5.2 ghz, a vswr of 1.24 at 2.4 ghz and 1.3 at 5.2 ghz and a return loss below -10 db at both frequency bands on the return loss plot, the designed antenna has met the objectives outlined for the paper. references [1] ren, w. (2008). compact dual-band slot antenna for 2.4/5 ghz applications. progress in electromagnetics research, 8, 319-327. [2] alkanhal, m. a. (2009). composite compact triple-band microstrip antennas. progress in electromagnetics research, 93, 221-236. 121 [3] tze-meng, o., tan, k. g., and reza, a. w. (2010). a dual-band omni-directional microstrip antenna. progress in electromagnetics research, 106, 363-376. [4] jain, k., and sharma, s. (2013). dual band rectangular microstrip antenna for wireless communication systems. international journal of innovations in engineering and technology (ijiet), 2(4), 235-246. [5] asrokin, a., rahim, m. k. a., and aziz, m. a. (2005). dual band microstrip antenna for wireless lan application. in 2005 asia-pacific conference on applied electromagnetics, ieee, 26-29. [6] nag, v.r. and singh, g. (2012). design and analysis of dual band microstrip patch antenna with microstrip feed line and slot for multiband application in wireless communication. international journal of computer science and information technology and security (ijcsits). 2(6), 1266-1270. [7] subramanian, g. h., & prabhu, s. s. (2015). design, analysis and fabrication of 2× 1 rectangular patch antenna for wireless applications. international journal of advanced research in electronics and communication engineering (ijarece), 4, 599-603. [8] mansour, y. e. (2014). single slot dual band microstrip antenna for wimax application. atilim university, june. [9] vilaltella, r., hesselbarth, j., & barba, h. (2014). high-efficiency dual-polarized patch antenna array with common waveguide feed. in microwave conference (gemic), 2014 german, vde, 1-3. [10] kumar, g. and ray, k. p. (2003). broadband microstrip antennas. artech house. [11] balanis, c. a. (2016). antenna theory: analysis and design. john wiley & sons. [12] pozar, d. (2012). microwave engineering. wiley. [13] stutzman, w. l., & thiele, g. a. (2012). antenna theory and design. john wiley & sons. copyright © 2016 jeffrey c. saturday, kufre m. udofia, and afolayan j. jimoh. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mse-style.dvi mathematical and software engineering, vol 3, no 2 (2017), 183–189 varεpsilon ltd, varepsilon.com using circle map for audio encryption algorithm krasimir kordov and lachezar bonchev department of computer informatics, faculty of mathematics and informatics, konstantin preslavski university of shumen, 9712 shumen, bulgaria abstract in this paper we propose audio encryption algorithm based on standard circle map. the proposed scheme contains bit level sample permutation using pseudorandom generator. provided cryptanalysis includes number of tests demonstrating the security of proposed encryption algorithm. subject codes: 68p25, 94a60 keywords: encryption, audio encryption, wav encryption, encryption algorithm 1 introduction digital data encryption is a process for securing stored and transmitted data. according to the specific type of data, encryption algorithm are designed to work in specific way. in recent years multimedia files are often preferred as data carries in social networks, communications and internet as general. such files are audio files, video files and digital images. therefore our focus is on multimedia files and more concrete on audio files. securing audio files for safe storing and transmission requires designing of new encryption algorithms. most common approach for modeling encryption algorithms is bit level symmetric encryption using preudorandom generators(prg) [8, 9, 11]. pseudorandom bit generators are based on complex discrete mathematics or chaos based [5, 13, 14] but simple for programming realization. their goal is to produce unlimited sequence of random bits therefor they can be used as building units for cryptographic [12] and steganographic [15, 16] algorithms. audio encryption algorithms require strong level of security therefor they are subject of detailed cryptanalysis. various experiments can be performed for determining resistance of proposed algorithm to attacks, defining their level of security [3, 7]. 183 2 pseudorandom bit generator based on two circle maps and xor function 2.1 circle map description the circle map [2] maps points on the circle back onto a circle. the circle map is a nonlinear iterated map calculated by θn+1 = (θn + ω − k 2π sin(2πθn)) mod 1, (1) where ω is a constant that is the fixed angular progression of the sinusoidal oscillator, and k is the coupling strength. 2.2 bit generation scheme in our previous work we proposed a pseudorandom bit generator based on two circle maps and xor function [4]. the proposed scheme is based on the following two circle map equations: θ1,m+1 = (θ1,m + ω1 − k1 2π sin(2πθ1,m)) mod 1 θ2,n+1 = (θ2,n + ω2 − k2 2π sin(2πθ2,n)) mod 1, (2) where θ1,m, ω1, k1, θ2,n, ω2 and k2 are the initial conditions. the new generator consists of the following steps: step 1: the initial values θ1,m, ω1, k1, θ2,n, ω2 and k2 of the two circle maps from eq. (2) are determined. step 2: the two chaotic maps from eq. (2) are iterated for l1 and l2 times, respectively. step 3: the iteration of the eq. (2) continues, and as a result, two real fractions θ1,i and θ2,j, are generated and post-processed as follows: s1,i = mod(integer(θ1,i × 10 9)), 2) s2,j = mod(integer(θ2,j × 10 9)), 2), where integer(x) returns the integer part of x, truncating the value at the decimal point, and mod(x, y) returns the reminder after division. step 4: perform xor operation between s1,i and s2,j to get a single output bit. step 5: return to step 3 until the bit stream limit is reached. used initial values are: θ1,m = 0.5, θ2,n = −0.25, ω1 = ω2 = 0.7128281828459045, k1 = k2 = 0.5, l1 = l2 = 200. statistical tests were made for determining the necessary cryptographic security of the proposed generator in [4] and similar scheme can be found in [6, 10]. key space includes all the initial values indicating the key space is more than 2179 [4] providing sufficient security against brute-force key search attacks [1]. 184 3 audio encryption scheme in this section we present audio encryption algorithm using the pseudorandom generator described in 2.2. produced random bits are extracted for sample permutation of audio files. sample permutation is realized by using simple xor function. 3.1 encryption and decryption algorithm audio encryption algorithm consists of the following steps: step 1: header bits from plain audio file a are transfered into file a′ without cryptographic modifications. step 2: the bits in the sample are encrypted using xor operation with the same amount of bits prodused by the pseudorandom generator from 2.2. step 3: encrypted sample from step 2 is transfered into file a′ step 4: repeat steps 2-3 until end of plain file a is reached. step 5: the produced output file a′ is the final encrypted audio file. the proposed audio encryption method is implemented in programing language c++. keeping the header bits in both plain and encrypted audio files allows us to perform further cryptanalysis tests by comparing the samples values of both files. decryption algorithm is the same as encryption scheme because the proposed cryptographic algorithm is symmetric using the same steps and the same key for audio decryption. 4 cryptographic analysis the cryptanalysis determines the reliability of encryption algorithms. in this section we provide the results of empirical tests performed using proposed audio encryption algorithm in 3.1. 4.1 waveform plotting waveform plotting represents the amplitude of audio signal distributed in time. figure 1 shows wave amplitude of plain audio file 1(a) and wave amplitude of the same file, after encryption 1(b). simple visual analysis can determine that the two waves shown in 1 are completely different, indicating the good properties of the proposed audio encryption algorithm. 4.2 correlation analysis measuring correlation between samples values of plain and encrypted files is standard method for evaluating cryptographic algorithms. calculating correlation coefficient determines the level of correlation between two files. correlation coefficient can be calculated as follows: rxy = cov(x, y) √ d(x) √ d(y) , (3) 185 (a) plain audio file (b) encrypted audio file figure 1: waveform of plain audio file 1(a) and corresponding encrypted audio file 1(b) where d(x) = 1 n n ∑ i=1 (xi − x) 2, d(y) = 1 n n ∑ i=1 (yi − y) 2, cov(x, y) = n ∑ i=1 (xi − x)(yi − y), n is the number of samples processed from audio file (plain or encrypted), xi and yi are values of corresponding samples of both files, x and y are mean values of samples for each file, and finally cov(x, y) is covariance between both files. table 1 shows some of the obtained result values from our tests. experiments were made with different file size. plain encrypted file bytes in correlation audio file audio file size sample coefficient sample1.wav encsample1.wav 100kb 2 -0.020451 sample2.wav encsample2.wav 150kb 2 0.049001 sample3.wav encsample3.wav 500kb 2 -0.013219 sample4.wav encsample4.wav 1mb 2 -0.018381 sample5.wav encsample5.wav 5mb 2 0.006555 table 1: correlation between plain and encrypted audio files results in table 1 indicates that all values are close to zero which means there is no dependence between the two files. this demonstrates the good cryptographic properties of the proposed audio encryption algorithm. 186 4.3 key sensitivity analysis the secure encryption algorithms require strong resistance to secret key attacks. the following key sensitivity analysis provides encryption and decryption experiment using very similar secret keys. k1 is the secret key used for encryption and it contains all the initial values of the parameters and variables for prg in 2.2. very similar secret key k2 is used for decryption of the encrypted file. k2 is obtained by slightly changing a single variable from k1 and keeping all the other variables unchanged. θ2,n for k1 is -0.25 and for k2 is -0.26. (a) plain audio file (b) encrypted audio file with k1 (c) decrypted audio file with k2 figure 2: waveform of plain audio file 2(a), encrypted file using k1 2(b) and decrypted file using k2 2(c) figure 2 demonstrates unsuccessful attempt for decryption using very similar secret key. this indicates highly key sensitivity of the proposed audio encryption algorithm, proving resistibility against secret key attacks. 4.4 speed test performance the encryption time of cryptographic algorithms is important aspect for their evaluation. we have tested the encryption time for variety of files with different size to determine the algorithm encryption time. testing computer configuration was 2.40 ghz intel r© coretm i73630qm dell inspiron laptop. part of the results are shown in the following table 2 the results from table 2 determine encryption speed ≈ 0.45 mb/sec which indicates fast time performance of the proposed audio encryption algorithm. 187 file file bytes in encryption name size sample time sample1.wav 100kb 2 0.202s sample2.wav 150kb 2 0.320s sample3.wav 500kb 2 1.246s sample4.wav 1mb 2 2.230s sample5.wav 5mb 2 12.728s table 2: speed test performance 5 conclusion new model of audio encryption is presented in this paper. the audio encryption algorithm is modeled by using preudorandom bit generator based on two circle maps. the proposed method permutates data in samples with bit level operation xor using actual data in sample and binary sequence produced by pseudorandom generator. security analysis is provided by waveform plotting of plain and encrypted files, correlation coefficient is calculated for plain and encryption files, key sensitivity is tested, and speed test performance is measured. the obtained results demonstrate good cryptographic properties of the proposed audio encryption algorithm. considering the results, we can conclude that the proposed algorithm is resistant to cryptographic attacks and can be used for audio encryption. acknowledgement this work is partially supported by the scientific research fund of konstantin preslavski university of shumen under the grant no. rd-08-124/06.02.2017. references [1] alvarez, g., li, s., some basic cryptographic requirements for chaos-based cryptosystems, international journal of bifurcation and chaos, 16 (2006), 2129–2151. [2] essl, g., circle maps as a simple oscillators for complex behavior: i. basics, in icmc, 2006, pp. 356359. [3] hato, e., shihab, d., lorenz and rossler chaotic system for speech signal encryption, international journal of computer applications, vol 128, 2015, no. 11, 09758887. [4] kordov, k., modified pseudo-random bit generation scheme based on two circle maps and xor function, applied mathematical sciences, vol. 9, 2015, no. 3, 129-135, http: //dx.doi.org/10.12988/ams.2015.411887. [5] kordov, k., signature attractor based pseudorandom generation algorithm, advanced studies in theoretical physics vol. 9, 2015, no. 6, pp. 287-293, http://dx.doi.org/10. 12988/astp.2015.517 [6] malchev, d., ibryam, i., construction of pseudorandom binary sequences using chaotic maps, applied mathematical sciences, vol. 9, 2015, no. 78, 3847-3853, http://dx.doi. org/10.12988/ams.2015.52149. [7] sheu, l. j.,a speech encryption using fractional chaotic systems, nonlinear dynamics, vol. 65 2011, no.1, 103-108. 188 [8] stoyanov, b.p., chaotic cryptographic scheme and its randomness evaluation, in 4th amitans’12, aip conference proceedings, 1487, 397–404, 2012, http://dx.doi.org/ 10.1063/1.4758983. [9] stoyanov, b.p., pseudo-random bit generator based on chebyshev map, in 5th amitans’13, aip conference proceedings, 1561 (2013), 369–372, http://dx.doi.org/10. 1063/1.4827248. [10] stoyanov, b.p., using circle map in pseudorandom bit generation, in 6th amitans14, aip cp 1629 (2014), 460 463, http://dx.doi.org/10.1063/1.4902309. [11] stoyanov, b., pseudo-random bit generation algorithm based on chebyshev polynomial and tinkerbell map, applied mathematical sciences, vol. 8, 2014, no. 125, 6205– 6210, http://dx.doi.org/10.12988/ams.2014.48676. [12] stoyanov, b., kordov, k. image encryption using chebyshev map and rotation equation, entropy vol. 17 (2015), no.4, 2117-2139. 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[14] stoyanov, b., kordov, k., pseudorandom bit generator with parallel implementation, in large-scale scientific computing 2014, lecture notes in computer science, vol. 8353, pp. 557-564, issn: 0302-9743 [15] zhelezov s., modified algorithm for steganalysis, mathematical and software engineering, vol. 1, no. 2 (2015), 31-36. issn 2367-7449 [16] zhelezov, s., paraskevov, h., possibilities for steganographic parallel processing with a cluster system, contemporary engineering sciences, volume 8, issue 20, 2015, issn:1313-6569 copyright c© 2017 krasimir kordov and lachezar bonchev. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 189 microsoft word i.doc 1 mathematical and software engineering, vol. 1, no. 1 (2015), 1-5 varεpsilon ltd, http://varepsilon.com predictive models for post-operative life expectancy after thoracic surgery a. nachev and t. reapy business information systems, cairnes business school, national university of ireland, galway, ireland abstract this paper studies data mining techniques used in medical diagnosis, particularly for predicting chance of survival of a patient after undergoing thoracic surgery. we discuss models built using decision trees, naive bayes and support vector machines and explore suitability of each of the algorithms to perform on such data. subject codes (acm): i.5.2 keywords: data mining applications, support vector machines, decision trees, naive bayes, thoracic surgery. 1 introduction a major clinical decision problem in thoracic surgery is selecting patients for surgery, taking into account possible risks and benefits for the patient. among the factors considered are long-term, related to life expectancy and mortality prognosis in a time horizon one to five years, and short-term, related to post-operative complications. traditional methods for decision support include standard statistical modelling, based on kaplan–meier survival curves, hierarchical statistical models, multivariable logistic regression, or cox proportional hazards regression [1, 2, 3]. other methods used to predict post-optative survival are risk-scoring systems [5], web-based applications [4] or statistical software packages. zeiba et al. [1] also proposed boosted support vector machines for clinical diagnosis by using imbalanced datasets. taking into account limitations of the predictive methods for post-operative life expectancy and the data used for that, we explore the usage and performance of several machine learning and data mining techniques by empirical analysis 2 based on a real-life dataset. the paper is organised as follows: in section 2 we review the classification techniques and methods applied to predict life expectancy. in section 3 we discuss the experimental results. section 4 provides conclusions. 2 methods and algorithms support vector machines (svm) are common machine learning techniques, used for classification or regression. training data is a set of points of the form n ii p iii cxcxd 1}}1,1{,|),{( =−∈ℜ∈= , (1) where the ci is either 1 or -1, indicating the class to which the point xi belongs. during training, svm constructs a p-1-dimensional hyperplane that separates the points into two classes (figure 1). any hyperplane can be represented by 0=−⋅ bxw , where w is a normal vector. among all possible hyperplanes that might classify the data, svm selects one with maximal distance (margin) to the nearest data points (support vectors). building a linear svm classier is formally a constrained optimization problem (2). ∑ =+ n i ibw cw k 1 2 ,, 2 1 min ξξ (2) ibxwts ξ−≥+⋅ 1.. in dual form, (2) can be represented by: ∑∑ ∑ = = = −⋅ n i n j n i ijijiji xxyyi 1 1 1 2 1 min αααα (3) ∑ = =≤≤ n i iii ccts 1 0,0.. αα the resulting decision function bxwxf +⋅=)( has a weight vector ∑ == n k kkk xyaw 1 . data points xi for which α i > 0 are called support vectors, as they uniquely define the maximum-margin hyperplane. the svm’s major advantage lies with their ability to map variables onto an extremely high feature space. bayesian classifiers operate by using the bayes theorem, saying that: let x be the data record (case) whose class label is unknown. let h be some hypothesis, such as "data record x belongs to a specified class c." for classification, we want to determine p(h|x) the probability that the hypothesis h holds, given the observed data record x. p(h|x) is the posterior probability of h conditioned on x. similarly, p(x|h) is posterior probability of x conditioned on h. p(x) is the prior probability figure 1. hyperplane for a svm trained with two classes. samples on the margin are support vectors. 3 of x. bayes theorem is useful in that it provides a way of calculating the posterior probability, p(h|x), from p(h), p(x), and p(x|h). the bayes theorem is p(h | x ) = p(x | h )p(h ) p(x ) (4) a difficulty arises when we have more than a few variables and classes we would require an enormous number of records to estimate these probabilities. naive bayes (nb) classification gets around this problem by not requiring that we have lots of observations for each possible combination of the variables. in other words, nb classifiers assume that the effect of a variable value on a given class is independent of the values of other variable. studies comparing classification algorithms have found the nb to be comparable in performance with classification trees and with neural network classifiers. they have also exhibited high accuracy and speed when applied to large databases. a decision tree (dt) is a formalism for expressing mappings between attributes and their classes. it is made up of nodes that are linked to two or more sub-trees, and leaves or end-nodes that are the ultimate decision. dt are praised for their transparency in decision making. a path from the root to a leaf node is essentially a decision rule, or classification rule. there are two stages to building a decision tree growing and pruning. in the growing stage, the dataset is partitioned recursively until either every record that is associated with each leaf node has the same class, or else the record's cardinality is below a specific threshold value. pruning the tree involves using a validation sample to essentially cut off the branches lower down in the tree. there are a number of recognised algorithms for building dt, among which id3, and its upgrade, c4.5. both have a statistical grounding. id3 uses information gain to ensure that the best splitting is achieved. the information gain of an attribute can be formally defined as: ∑ ∈ −= )( )()(),( avalues sent s s sentasgain ν ν ν (5) where sν is a subset of s; a has the value v, and s is the size of s. whichever attribute a gives the greatest gain is the attribute that should be used. the information gain can therefore be used as a ranking mechanism, where the attribute with the greatest gain not yet considered in the path through the decision tree is at each node. decision trees, while extremely simple to understand, even to the untrained eye, remain very popular in data mining and classification for that very reason. 3 results and discussion for the purposes of data pre-processing, model building, and analysis, we used tools such as r, keel, and weka. the primary source for model estimation is the confusion matrix (a.k.a. contingency table), illustrated in figure 2. results from experiments were summarized in four categories: true positives (tp), true negatives (tn), false positives (fp), and false negatives (fn). the 4 numbers along the primary diagonal in the matrix represent correct predictions, as long as those outside the diagonal represent the errors. table 1 summarises experiment results and reveals that the three algorithms perform differently predicting the cases. using these summations, a number of measures can be derived, namely precision, recall, specificity, and accuracy. summary of the results are presented in table 2. the precision is the percentage of positive predictions that are correct, i.e. tp/(tp+fp). the precision of the dt classifier is 58.333%, svm provides 78.3% precision, but nb precision is 0% the it performs very poorly having no true positives. recall (a.k.a. sensitivity) is tp/(tp+fn), and shows how good the classifier is at picking out instances of a particular class. once again, the svm has the best recall rate of 62%, whilst the nb performs poorly once again. the dt has a moderare recall rate of 36.22%. however, as the number of negative samples heavily outweighs the number of positive samples to begin with, the next measure, specificity, may actually give a better indication of how well each classifier is performing. specificity, which is tn/(tn+fp) is in fact the inverse of the recall. in this measure, the nb outperforms both of the other classifiers. accuracy is probably the most intuitive of all of the performance measures, it uses all of the values in the confusion matrix: (tp+tn)/(tp+tn+fp+fn). in this case, the nb has once again finished bottom of the three, with an accuracy of 62.1%. the dt, whilst slightly better than the nb, still has a relatively poor accuracy rate. while 67% may seem decent to some, if one considers a concerned patient presenting with symptoms and about to undergo thoracic surgery, 67% certainty is not confident enough. on the other hand, the svm has good accuracy of 79.4%. in conclusion, it is evident that the svm classifier was the most consistent throughout, scoring very well on three of the metrics and acceptable on the fourth. dt was the next best, as even though it has poor recall and fairly poor precision, it at least had figures for these two metrics, unlike nb. table 1. confusion matrix values summary. classifier precision recall specificity accuracy dt 58.33% 36.22% 84.67% 66.67% nb n.a. n.a. 97.99% 62.10% svm 78.30% 62.00% 89.78% 79.40% classifier tp fn fp tn dt 21 37 15 83 nb 0 57 2 97 svm 36 22 10 88 table 2. performance metrics summary. true class positive negative p o s it iv e true positive count (tp) false positive count (fp) p re d ic te d c la ss n e g a ti v e false negative count (fn) true negative count (tn) figure 2. confusion matrix. 5 4 conclusion the goal of this research was to analyse several data mining techniques in search of discovering their strengths and weaknesses, dealing with an imbalanced dataset of thoracic surgery patient details. we aimed to identify a method that would perform with a high degree of accuracy in order to provide basis for future work on improving the model performance and tweak it to be transferable to similar datasets. three very different classifiers were explored in detail: naive bayes, decision trees, and support vector machines. each of them manifested specific benefits and drawbacks. the svm was deemed to be most suited, but its nature implies that changing any one of the input criteria can cause a big change. the imbalance in the classes does no allow it to obtain good margins in the hyper-plane; however, further pre-processing or expansion of the algorithm would improve the overall classification performance. while neither naive bayes nor decision trees proved up to the task of classifying this particular dataset with a high accuracy, it is also probable that with further algorithmic expansion, their accuracy could be improved. references [1] m. zieba, j. tomczak, m. lubicz, & j. swiatek, boosted svm for extracting rules from imbalanced data in application to prediction of the post-operative life expectancy in the lung cancer patients. applied soft computing, vol. 14 (2013), 99-108. [2] m. shapiro, s.j. swanson, c.d. wright, c. chin, s. sheng, j. wisnivesky, t.s. weiser, predictors of major morbidity and mortality after pneumonectomy utilizing the society for thoracic surgeons general thoracic surgery database, annals of thoracic surgery, vol. 90 (2010) 927–935. [3] p. icard, m. heyndrickx, l. guetti, f. galateau-salle, p. rosat, j.p. le rochais, j.l. hanouz, morbidity, mortality and survival after 110 consecutive bilobectomies over 12 years, interactive cardiovascular and thoracic surgery vol. 16 (2013) 179–185. [4] p.e. falcoz, m. conti, l. brouchet, s. chocron, m. puyraveau, m. mercier, j.p. etievent, m. dahan, the thoracic surgery scoring system (thoracoscore): risk model for in-hospital death in patients requiring thoracic surgery, the journal of thoracic and cardiovascular surgery vol. 133 (2007) 325–332. [5] a. barua, s.d. handagala, l. socci, b. barua, m. malik, n. johnstone, accuracy of two scoring systems for risk stratification in thoracic surgery, interactive cardiovascular and thoracic surgery vol. 14 (2012) 556–559. copyright © 2015 a. nachev and t. reapy. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mathematical and software engineering 12 mathematical and software engineering, vol. 6, no. 2 (2020), 12-18. varεpsilon ltd, http://varepsilon.com/index.php/mse/ bfs algorithm and sadt in knowledge management in e-learning on data structures valentina dyankova1 and milko yankov2 1department of mathematics and computer science, konstantin preslavsky university of shumen, bulgaria, v.spasova@shu.bg. 2reward gateway (uk) ltd branch, plovdiv, bulgaria, milkoyankov@gmail.com abstract the successful acquisition of knowledge and skills about the conceptual apparatus in a given subject area requires the concepts to be studied in mutual connection and conditionality. this requires a very precise refinement of the logical relationship between them. the present study presents an approach to building a formal model of the semantic relationship between the concepts in the course on data structures. emphasis is placed on the adaptation of the breadth-first search (bfs) algorithm to the established formal model in order to plan and optimize training time. the created training plan contains the minimum volume of necessary basic learning units, which allow the learner to move to the acquisition of a concept by data structures. keywords: bfs algorithm; sadt methodology; e-learning; data structures. 1 introduction the recently increasing use of information and communication technologies in education is characterized by widely available web-based educational resources, increased demand for lifelong learning opportunities, increased attention to the quality of education and the time to acquire knowledge and skills in the relevant subject area. these characteristics determine the need for both the provision of systematized learning materials for learners and the optimal administration of the learning process. these two activities must be planned according to the goals set by the learner. these are activities that require significant time resources, which can be reduced with the introduction of technological solutions based on effective knowledge management. the purpose of this article is to provide an approach to knowledge management in online training on data structures. two of the most important conditions for a competitive learning process are the design of logically connected 13 information flows, guaranteeing quality knowledge acquisition and the possibility for optimal distribution of learning time. the development of the methodology used for formalization of the learning process by data structures in the form of an oriented graph is presented and the possibility of using the breadth-first search (bfs) algorithm for planning and optimizing the training time is emphasized. the ideas presented in the development are based on the experience of the authors in the development of an online training system on data structures dslearning (www.dslearning.eu) and the training of computer science competitors (students and pupils), students who study individually, students who start working as interns in software companies; people who retrain as programmers, novice programmers. 2 using the sadt methodology to build a model of e-learning by data structures for each of the above groups of people are characterized by the following features: clear goal – striving to acquire specific knowledge of data structures. different background – the presence of different systems of already acquired knowledge, skills and habits in data structures. striving to optimize training time – the goal is to achieve the desired results in minimum time. the preparation of a training plan, consistent with the individual indicators of the learner for the listed characteristics, requires a structured system that integrates the concepts in the respective subject area and the logical connections between them. the logical connections between the concepts must reflect their conditionality – for the assimilation of some concepts the knowledge of others is used. therefore, for the formalization of this system it is necessary to choose a methodology that perceives the system through the perspective of the information that flows through it. one such approach is top-down analysis, which underlies the structured analysis and design technique (sadt) [1]. sadt is a software engineering methodology for describing systems as a hierarchy of functions and is successfully used to solve a wide range of tasks such as long-term strategic planning, automated production and others. sadt is used even in areas such as security in internet communication [2], providing effective solutions in company management [3], modeling and design of space probes [4]. sadt is used in the present development in order to create a formal model (graph) that implements a specific functional view, describing the concepts of data structures and their relationships. the underlying sadt analysis "top-down" allows for the study of concepts, starting with their most general 14 overview, subsequent detailing of the functionality of each concept and hierarchical organization of levels in the resulting system of concepts. in the created formal model for each concept are defined levels of knowledge, corresponding to the specifics of the acquired knowledge and intellectual initiative of the learners. in their most general form, these levels are: level a – formation of a logical idea of the concept, work with the definition and objects. level b – acquisition of knowledge and skills about the properties of the concept, as well as discovery of new ones. level c – formalization of the concept in the respective software system. level d – acquisition of knowledge and skills for free use of the software model. level e – acquisition of knowledge and skills for modeling real practical processes and expanding the functionality of the concept in terms of a specific software system. each of these levels has a hierarchical structure and includes other levels. since the process of building the overall hierarchical system is not the subject of this article, they will not be considered. the system of concepts, organized in this way, contributes to the successful acquisition of knowledge about the concepts of data structures in the ideology of integrity and interdependence between them. the vertices in the oriented graph, which is a formal model of this system, represent the concepts studied. two vertices p1 and p2 are connected by an oriented edge from p1 to p2, if the knowledge of the concept p1 is necessary for the acquisition of the knowledge of the concept p2. figure 1 shows an example of a simplified part of the graph connecting knowledge of several concepts. the graph shown in figure 1 do not reflect the considered levels of knowledge acquisition, as the purpose of the present study is to present its use, and not to detail the process of its acquisition. however, the information about the levels of knowledge will be specified in the context of its functionality to the problem under consideration and will be reflected in the software implementation in the pointer one-dimensiona l array priority queue list queue dequeue hash table figure 1: connection between concepts 15 next section. 3 bfs algorithm as an algorithmic strategy for learning process management after the already created formal model of functional dependence between the concepts in data structures, the question arises for assessing the way of acquiring knowledge about a given concept from the respective level. in order to optimize the training time, this time should not contain unnecessary waypoints. this draws attention to finding the minimum path in a graph by the number of vertices involved. the problem of finding the minimum path in a graph by the number of vertices naturally leads to the use of the bfs algorithm [5].the bfs algorithm is the basis of many developments with high practical value such as optimizing difficult to execute queries in a large database [6], creating an algorithm for searching for bird food [7], mapping the best route to achieve fast and adequate home movements for the elderly [8], efficient use of cluster resources in cpu-gpu based cluster calculations [9] and many others. the use of the bfs algorithm to optimize the time to obtain a certain knowledge of a given level requires appropriate formalization of the necessary information. this information will be presented in the form of java classes. each java class will be described only with the data/methods needed to understand the overall concept of using bfs to solve the problem in question. each concept is represented as an object of class concept: public class concept { // term/name of the concept private string term; // description of the acquired competencies after mastering the concept private string description; public concept(string term, string description) { this.term = term; this.description = description; } ... } each level of the hierarchical structure of knowledge for a given concept is represented as an object of class levelofknowledge, which inherits from class concept: public class levelofknowledge extends concept{ // level of knowledge private string level; // list of tasks that must be covered to acquire knowledge private arraylist<string> tasks; // list of required levels of knowledge required for this level of knowledge private hashset<levelofknowledge> requiredknowledge; 16 public levelofknowledge(string term, string description, int level, arraylist<levelofknowledge> list) { super(term,description); this.level = level; tasks = new arraylist<string>(); requiredknowledge = new hashset<levelofknowledge>(list); } ... } the adjacency list for a concept (vertex in the graph) is presented as an object of class adjacencylist. all neighbors of a vertex present the concepts directly related to it (knowledge of the respective level). the edges have weights equal to the time to acquire knowledge of these concepts. the quantitative assessment, which is assigned to each edge from vertex p1 to vertex p2, is the value of time in minutes for acquiring knowledge and skills from the respective level for the concept p2 with already acquired knowledge and skills from the required level for the concept p1. to estimate this time, the authors use information from the dslearning data structures online training system created by them. at each acquisition of new knowledge by each trainee registered in the system, information about the time spent by the trainee for acquiring the new knowledge is kept in the administrator panel of the system. the quantitative assessment of each of the edges in the graph is assumed to be equal to the arithmetic mean of the times of all registered users so far. the concepts from the adjacency list and the times for their assimilation are associated in pairs <level of knowledge about the concept, time>, which are integrated in hashmap. the time component is not a criterion for minimizing the path, but it is then used to calculate an estimate of the training time in the shortest path found by the number of vertices. public class adjacencylist{ private hashmap<levelofknowledge,integer> list; public adjacencylist() { list = new hashmap<levelofknowledge,integer>(); } ... } the graph itself is represented as a hashmap of associated pairs <knowledge at a given level for a concept, adjacency list>. the bfspath method of the graph class adapts the bfs algorithm to the presented formal knowledge model. the method returns a hashmap from associated pairs. the first component contains the vertex of the graph through which it passes. the second component in each pair contains the precursor in the path found at the vertex of the first component. in this way, the found path can be restored. public class graph{ private hashmap<levelofknowledge, adjacencylist > graph; public adjacencylist() { list = new hashmap<levelofknowledge,integer>(); } 17 public hashmap<levelofknowledge,levelofknowledge> bfspath(levelofknowledge start, levelofknowledge goal) throws interruptedexception { linkedblockingqueue<levelofknowledge> queue = new linkedblockingqueue<levelofknowledge>(); hashmap<levelofknowledge,levelofknowledge> used = new hashmap<levelofknowledge,levelofknowledge>(); queue.put(start); used.put(start,null); while(!queue.isempty() && !used.containskey(goal)) { int sizequeue = queue.size(); for(int currentnum = 0; currentnum < sizequeue; currentnum++) { levelofknowledge currentconcept = queue.poll(); adjacencylist list = graph.get(currentconcept); if(list != null) { iterator<entry<levelofknowledge, integer>> it = list.getlist().entryset().iterator(); while(it.hasnext()) { entry<levelofknowledge, integer> item = it.next(); if(!used.containskey(item.getkey())) { queue.put(item.getkey()); used.put(item.getkey(),currentconcept); } } } } } return used; } ... } the bfspath method returns a hashmap from associated pairs. the first component contains the vertex of the graph through which it passes. the second component in each pair contains the precursor in the path found at the vertex of the first component. in this way, starting from the final vertex in the path and following the predecessors, all the vertices of the path can be obtained. the following program fragment does this. hashmap<levelofknowledge,levelofknowledge> map = g.bfspath(start,goal); levelofknowledge current = goal; while(current != start) { action with the vertex current current = map.get(current); } 4 conclusion the received training plan is in accordance with the profile of the trainee. this profile contains information about all already acquired levels of knowledge, which allows to prepare an individual training plan. this approach cannot completely replace the role of the instructor in this process, as in many cases quite subjective characteristics for the learner have to be considered. however, it frees the instructor from the routine and laborious task of determining the sequence of 18 basic topics based on the complex and voluminous connections in the knowledge column. one possible further improvement may be to consider the time weights of the edges in the knowledge graph. the bfs algorithm can be integrated with the idea of partially minimizing actual training time. references [1] marca, d., a., mcgowan, c., l. (1987) sadt: structured analysis and design techniques, mcgraw-hill. [2] quan, l., guo, q., chen, h., xie, x., li, x., liu, y., hu, j., sadt: syntax-aware differential testing of certificate validation in ssl/tls implementations, 35th ieee/acm international conference on automated software engineering (ase), 21-25 sept. 2020, melbourne, vic, australia. [3] lakhoua, m., n., karoui, m., f., monitoring of a production system based on functional and dysfunctional analysis, journal of computer science and control systems, 2019, volume 12, issue 1. [4] lobanov, a., strogankova, n., bolbakov r., meta-modeling of space probe on-board computing complexes, international conference on high-performance computing systems and technologies in scientific research, automation of control and production, 15-16 may 2020, barnaul, russia. [5] nakov, p., dobrikov, p. (2018) programming = ++ algorithms. [6] mondal, s., mukherjee, n., a bfs-based pruning algorithm for disease-symptom knowledge graph database, information and communication technology for intelligent systems, smart innovation, systems and technologies, vol 107. springer, singapore. online isbn 978-981-13-1747-7. [7] zhang, z., huang, c., dong, k., huang, h., birds foraging search: a novel population-based algorithm for global optimization, memetic computing, 11, 221–250 (2019). [8] pinheiro, pr, pinheiro, pgcd, filho, rh, barrozo, jpa, rodrigues, jjpc, pinheiro, licc, pereira, mld, integration of the mobile robot and internet of things to monitor older people, ieee access, volume 8, 2020, issn: 2169-3536. [9] chandrashekhar, bn, sanjay, ha, srinivas, t., performance analysis of parallel programming paradigms on cpu-gpu clusters, international conference on artificial intelligence and smart systems (icais), 25-27 march 2021, coimbatore, india. copyright © 2020 valentina dyankova and milko yankov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. https://www.amazon.com/s/ref=dp_byline_sr_book_1?ie=utf8&field-author=david+a.+marca&text=david+a.+marca&sort=relevancerank&search-alias=books https://www.amazon.com/s/ref=dp_byline_sr_book_2?ie=utf8&field-author=clement+l.+mcgowan&text=clement+l.+mcgowan&sort=relevancerank&search-alias=books https://ieeexplore.ieee.org/author/37088701621 https://ieeexplore.ieee.org/author/37087233505 https://ieeexplore.ieee.org/author/37087231735 https://ieeexplore.ieee.org/author/37086128415 https://ieeexplore.ieee.org/author/37088700758 https://ieeexplore.ieee.org/author/37088700508 https://ieeexplore.ieee.org/author/38087548500 https://search.proquest.com/openview/2235dd15cf393c8bfc18911bf578102d/1?pq-origsite=gscholar&cbl=60389 https://search.proquest.com/openview/2235dd15cf393c8bfc18911bf578102d/1?pq-origsite=gscholar&cbl=60389 https://scholar.google.com/citations?user=z_gor0uaaaaj&hl=bg&oi=sra https://scholar.google.com/citations?user=ngdsbbwaaaaj&hl=bg&oi=sra https://ieeexplore.ieee.org/author/37088458228 https://ieeexplore.ieee.org/xpl/recentissue.jsp?punumber=6287639 https://ieeexplore.ieee.org/author/37085499413 https://ieeexplore.ieee.org/author/37680233100 https://ieeexplore.ieee.org/author/37088838832 mathematical and software engineering, vol. 4, no. 2, 18–23, 2018. varεpsilon ltd, http://varepsilon.com/index.php/mse a note on reducing the computation time for minimum distance and equivalence check of binary linear codes nikolay yankov1 and krassimir enev2 1faculty of mathematics and informatics konstantin preslavski university of shumen, 9712 shumen, bulgaria, e-mail: jankov_niki@yahoo.com, orcid 0000-0003-3703-5867 2college dobrich, konstantin preslavski university of shumen, 9712 shumen, bulgaria, e-mail: kr.enev@shu.bg abstract in this paper we show the usability of the gray code with constant weight words for computing linear combinations of codewords. this can lead to a big improvement of the computation time for finding the minimum distance of a code. we have also considered the usefulness of combinatorial 2-(t, k, 1) designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence. keywords: classification, combinatorial design, linear code 1 introduction binary linear codes and self-dual codes in particular are extensively studied for the plethora of connections to communication, cryptography, combinatorial designs, among many. when computing self-dual codes one should be aware that with the increase of the code length the number of codes also rises exponentially. the classification of binary self-dual codes begun in 1972 with [11] wherein all codes of lengths n ≤ 20 are classified. later pless, conway and sloane classify all codes for n ≤ 30 [7]. next lengths: 32 is due to bilous and van rees [2], 34 by bilous [1], 36 by harada and munemasa in [9]. latest development in this area are for length 38 in [5] and for n = 40 due to bouyukliev, dzumalieva-stoeva and monev in [4]. 18 http://varepsilon.com/index.php/mse jankov_niki@yahoo.com https://orcid.org/0000-0003-3703-5867 kr.enev@shu.bg as length of the code gets bigger the number of codewords rises exponentially and one need efficient algorithms for computing the minimum distance of a linear code, and also efficient ways to check codes for equivalence when there are memory limitations. this paper is organized as follows: in section 2 we outline an introduction to linear codes, self-dual codes, combinatorial designs and gray codes. next, in section 3, we discuss how a reduction in computation time for minimum distance of linear code with constant-weight gray code can be achieved. in section 4 we explain a method for reducing the computation time for code equivalence by the use of combinatorial 2-designs. we conclude in section 5 with a few final notes. 2 definitions and preliminaries let fq be the finite field of q elements, for a prime power q. a linear [n,k]q code c is a k-dimensional subspace of fnq . the elements of c are called codewords, and the (hamming) weight of a codeword v ∈ c is the number of the non-zero coordinates of v. we use wt(v) to denote the weight of a codeword. the minimum weight d of c is the minimum nonzero weight of any codeword in c and the code is called an [n,k,d]q code. a matrix whose rows form a basis of c is called a generator matrix of this code. let (u,v) ∈ fq for u,v ∈ fnq be an inner product in fnq . the dual code of an [n,k]q code c is c⊥ = {u ∈ fnq | (u,v) = 0 for all v ∈ c} and c⊥ is a linear [n,n − k]q code. in the binary case the inner product is the standard one, namely, (u,v) = ∑n i=1 uivi. if c ⊆ c⊥, c is termed self-orthogonal, and if c = c⊥, c is self-dual. we say that two binary linear codes c and c′ are equivalent if there is a permutation of coordinates which sends c to c′. in the above definition the code equivalence is an equivalence relation is a binary relation that is reflexive, symmetric and transitive. denote by eq(a,b) some function that checks for equivalence all pairs of elements in both sets of linear codes a and b. for more information on codes we encourage the reader to [10]. when working with linear codes it is often needed for certain algorithm to pass trough all (or part) of binary vectors of given length. one way to make the generation efficient is to ensure that successive elements are generated such that they differ in a small, pre-specified way. one of the earliest examples of such a process is the gray code generation. introduced in a pulse code communication system in 1953 [8], gray codes now have applications in diverse areas: analogue-to-digital conversion, coding theory, switching networks, and more. for the past 70 years gray codes have been extensively studied and currently there are many different types of gray code. a binary gray code of order n is a list of all 2n vectors of length n such that exactly one bit changes from one string to the next. a t-(v,k,λ) design d is a set x of v points together with a collection of k-subsets of x (named blocks) such that every t-subset of x is contained exactly in λ blocks. the block intersection numbers of d are the cardinalities of the intersections of any two distinct blocks. 19 3 reducing computation time for minimum distance of linear code with constant-weight gray code assume we have a linear binary [n,k] code c and we need to find its minimum distance d. denote by g the generator matrix of the code c with rows r1, . . . ,rk. the obvious and direct approach is to compute all codewords of c and find their weight. this means that all 2k linear combinations of t (1 ≤ t ≤ k) of the rows of g must be computed using algorithm 1. algorithm 1: the direct approach for (i1 = 1; i1 <= k-t+1; i1++) { for (i2 = i1+1; i2 <= k-t+2; i2++) { for (i3 = i2+1; i3 <= k-t+3; i3++) { ... for (it = itm1+1; it <= k; it++) {body}... }} then for each of the ( k t ) combination we need to compute t cycles and essentially t operations. furthermore, in the body of this algorithm we need to find the codeword c ∈c which is a linear combination of those rows of the generator matrix g that are chosen for the current combination, i.e. c = t∑ s=1 ris, which will be represented by t “exclusive or” (xor) operations c = ri1 ⊕ ri2 ⊕ . . .⊕ rit . our approach is to use gray code for generating combinations in such a way that each successive combination is generated by the previous one with only two xor operations. two xor operations are the absolute minimum since, if we have to switch from one combination of t elements to another, one xor will add or remove a position making a t + 1 or a t − 1 combination. in [12] it was proved that the set of ( k t ) -vectors of weight t, when chained according to the ordering on the gray code gk, has a hamming distance of exactly two between every pair of adjacent code vectors. also in [12] an algorithm for generating the constant-weight code vectors on a gray code was given. later in [3] a more efficient recursive algorithm was introduced (algorithm 2). what we want to do is to find in gray code gk those k-tuples that have the same weight t, for example when k = 4 for t = 1 we have: 0000→0001→0011→0010→0110→0111 →0101→0100→1100→1101→1111→1110→1010→1011→1001→1000 and similarly, for t = 2 we have: 0000→0001→0011→0010→0110→0111→0101→0100→1100→1101→ 1111→1110→1010 →1011→ 1001→1000. note that algorithm 2 starts with the word 1t0k−t and finishes with 0k−t1t. example 1: if we need to find all triples in g6 we have a total of 20 triples. we start with 000111 and from gray code we have the following sequence of positions to change [2, 4], [1, 2], [1, 3], [2, 5], [1, 2], [2, 3], [1, 4], [1, 2], [1, 3], [2, 6], [1, 2], [2, 3], [3, 4], [1, 5], [1, 2], [2, 3], [1, 4], [1, 2], [1, 3]. so the sequence of triples is as follows {1, 2, 3},{1, 3, 4},{2, 3, 4},{1, 2, 4},{1, 4, 5},{2, 4, 5},{3, 4, 5},{1, 3, 5},{2, 3, 5},{1, 2, 5}, {1, 5, 6},{2, 5, 6},{3, 5, 6},{4, 5, 6},{1, 4, 6},{2, 4, 6},{3, 4, 6},{1, 3, 6},{2, 3, 6},{1, 2, 6}. 20 algorithm 2: constant t-weight (0 < t ≤ k) gray code gt [3] for j = 1 to t do { gj = 1 τj = j + 1 for j = t + 1 to k + 1 do { gj = 0 τj = j + 1 s = k τ1 = k + 1 i = 0 while i<k+1 do   output (gk,gk−1 . . . ,g1) i = τ1 τ1 = τi τi = i + 1 if gi = 1 then   if s 6= 0 then gs = gs else gi−1 = gi−1 s = s + 1 else   if s 6= 1 then gs−1 = gs−1 else gi−1 = gi−1 s = s− 1 gi = gi if s = i− 1 or s = 0 then s = s + 1 else   s = s−gi−1 τi−1 = τi if s = 0 then τ1 = i− 1 else τ1 = i + 1 usually, when we need to compute the minimum weight of a binary code c, we start with the initializing r1⊕···⊕rt, then we need the pair of position that should be changed to obtain the next t-tiple and so on. since for given i(1 < i < 2t) it is easy to find the i-th t-weight vector and begin with the linear combination generated by it, the algorithm can be parallelized to accommodate its use on multiple cpu cores. 4 reducing computation time for code equivalence with combinatorial 2-designs what can be done when there are more linear codes that the equivalence algorithm can accommodate in the allowed memory. we consider the case when all codes have the same weight enumerator and also the same order of their automorphism group. this means that all other options for reducing the number of codes we are considering are exhausted. the question then is: how can we efficiently ensure that the algorithm will check every pair of codes. if we have s ∈ n times more codes that that algorithm can check, we can split this into 2s halves of sets of codes and then check all ( 2s 2 ) = s(2s− 1) pairs for equivalence. this is not very efficient since this has the quadratic o(s2) efficiency. the more efficient way is to use 2-(v,k, 1) combinatorial design, which ensures that every 21 pair of points (sets of codes in our case) appear exactly in one block and is checked for equivalence only once. such designs exists, for example, when λ = 1 and v = k2, we have a projective plane: x is the point set of the plane and the blocks are the lines [13]. for example, consider the case of 7 sets i1, . . . , i7 of binary self-dual codes. if we use the standard approach we should do the tests eq(ij, is), 1 ≤ ik < ij ≤ 7 for all ( 7 2 ) = 21 pairs of sets. now, consider using the combinatorial design approach, viz. the fano plane (see [6]) illustrated in fig. 1. it is well known that the fano plane is a combinatorial 2-(7, 3, 1)-design [6]. this means that every pair of sets (ij, is), 1 ≤ ij < is ≤ 7 appear in exactly one of the 7 blocks (the blocks of fano plane are the 6 lines and the circle), so if a code is present in different sets it is reduced to only one copy. figure 1: fano plane using the ordering of the sets ij ≺ is iff j < s, we can use the following sequence for automorphism testing: eq(i1,i2,i3), eq(i ′ 1,i4,i5), eq(i ′ 1, i6, i7), eq(i ′ 2, i ′ 4, i ′ 6), eq(i ′ 2, i ′ 5, i ′ 7), eq(i ′ 3, i ′′ 4, i ′′ 7), eq(i ′ 3, i ′′ 5, i ′′ 6), where i′j means that the interval ij is purged of the codes that are equivalent to codes from preceding sets, i′′j means that the interval i ′ j is purged of the codes that are equivalent to codes from preceding sets, and so on. as a result the reduced inequivalent set of codes will be the union i′1 ∪ i′2 ∪ i′3 ∪ i′′′4 ∪ i′′′5 ∪ i′′′6 ∪ i′′′7 . 5 conclusions in the present research we have considered the usability of the gray code with constant weight words for computing linear combinations of codewords. we have shown that, in this way, a big improvement of the computation time for finding the minimum distance of a code can be achieved. we have also considered the usefulness of combinatorial 2-(t,k, 1) designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence. in our example we have shown that using the fano plane one can achieve complete classification with as much as half of the computation time needed otherwise. it remains to find efficient designs for different number of sets to be checked for equivalence. 22 acknowledgement the authors express their gratitude to prof. borislav stoyanov for the invitation to publish in this journal. this work was supported by european regional development fund and the operational program “science and education for smart growth” under contract unite no bg05m2op001-1.001-0004-c01(2018-2023). references [1] r.t. bilous (2006) enumeration of the binary self-dual codes of length 34, journal of combinatorial mathematics and combinatorial computing, 59, 173–211. [2] r.t. bilous, g.h.j van rees (2002) an enumeration of binary self-dual codes of length 32, designs, codes and cryptography, 26, 61–86. [3] j.r. bitner, g. ehrlich, e.m. reingold (1975) efficient generation of the binary reflected gray code and its applications, commun. acm, 19(9), 517–521. [4] i. bouyukliev, m. dzhumalieva-stoeva, v. monev (2015) classification of binary self-dual codes of length 40, ieee transactions on information theory, 61(8), 4253–4258. [5] s. bouyuklieva, i. bouyukliev (2012) an algorithm for classification of binary self-dual codes, ieee transactions on information theory, 58(6), 3933–3940. [6] c.j. colbourn, j.h. dinitz, handbook of combinatorial designs, 2nd ed., crc press, 2010, isbn 978-1-5848-8-5061. [7] j.h conway, v. pless, n.j.a. sloane (1992) the binary self-dual codes of length up to 32: a revised enumeration, journal of combinatorial theory, series a, 60(2), 183–195. [8] f. gray (1953) pulse code communication, u.s. patent 2,632,058, march 17, 1953 [9] m. harada, a. munemasa (2010) classification of self-dual codes of length 36, advances in mathematics of communications, 2, 229–235. [10] w.c. huffman, v.s. pless (2003) fundamentals of error-correcting codes, cambridge university press, isbn 978-0-5211-3-1704. [11] v. pless (1972) a classification of self-orthogonal codes over gf(2), discrete mathematics, 3(1-3), 209–246. [12] d.t. tang, c.n. liu (1973) distance-2 cyclic chaining of constant-weight codes, ieee transactions on computers, 2, 176–180. [13] v. tonchev (2017) on resolvable steiner 2-designs and maximal arcs in projective planes, designs, codes and cryptography, 84(1-2), pp 165–172. copyright c© 2018 nikolay yankov and krassimir enev. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 23 introduction definitions and preliminaries reducing computation time for minimum distance of linear code with constant-weight gray code reducing computation time for code equivalence with combinatorial 2-designs conclusions flowchart for call management scheme through users mobility control 43 mathematical and software engineering, vol. 3, no. 1 (2017), 43-49. varεpsilon ltd, varepsilon.com flowchart for call management scheme through users mobility control isaac a. ezenugu1*, james eke2, g. n. onoh3 *corresponding author: isaac.ezenugu@yahoo.com 1department of electrical/electronic engineering, imo state university, owerri, nigeria. 2,3department of electrical/electronic engineering, enugu state university of science and technology enugu, nigeria. abstract the tremendous popularity of wireless technologies during the last decade has created a considerable expansion of wireless networks both in size and use. these facts, together with a great variety of mobile devices and numerous different services that are becoming increasingly resource-demanding, have attracted the attention of many researchers into the area of radio resource planning and optimization. in wireless cellular networks, it is important to develop model or schemes to facilitate effective and efficient utilization of the limited radio resources. in this paper, flowchart for call management scheme through users mobility control is presented. the flowchart along with the analytical expressions pertaining to the scheme are presented and discussed. particularly, the scheme improves channel allocation to handoff calls for mobile users by considering the direction of their movement. the direction of mobile users with respect to a base station is captured in terms of mobility factor. the mobility factor increases as the user moves closer to a base station. in this case, even if the signal strength of ongoing call of a mobile user is sufficient, it channel allocation can still be retained if its mobility factor is relatively high. in this case, the mobile user will be handed off to the base station it has higher mobility factor value. keywords: signal quality; prioritized handoff; call duration; call arrival rates; the mobility factor; radio resource management 1. introduction with the increased demand for wireless communication systems, a promised quality of service (qos) is required in a satisfactory manner, to manage the incoming new calls and handoff calls more efficiently .quality of service (qos) provisioning in wireless networks is a challenging problem due to the scarcity of wireless resources, i.e. radio channels, and the mobility of users. call admission control (cac) is a fundamental mechanism used for qos provisioning in a network. it restricts the access to the network based on resource availability in order to prevent network congestion and service degradation for already supported users. a new call request is accepted if there are enough idle resources to meet the qos requirements of the new call without violating the qos for already accepted calls. admitting too many users results in a situation where the mutual interference between the connections degrades the qos for the new user as well for the ongoing connections. 44 therefore, admission control play a very important role in providing the user with the requested qos as well as making an efficient use of the available capacity and preventing the system from an outage situation due to overloading [1]. with gsm communications, a user that initiates or receives a call may move around the area covered by the network. if the mobile user moves from one cell to another, and the call from/to the user has not finished, the network has to handoff the call from one cell to another at the cell boundary crossing without user’s awareness of handoff and without much degradation of the service quality. as the demand for wireless communication systems by the users keep increasing, a good quality of service (qos) is required to manage the incoming new calls and handoff calls more efficiently. radio resource management (rrm) plays a vital role in cellular networks to efficiently utilize the limited radio resources while guaranteeing the required qos for mobile users. call admission control (cac) is a fundamental mechanism used for qos provisioning in a network. it is the rule to admit requested calls maintaining the qos for the system [2]. cac is a key element in the provision of guaranteed qos in wireless networks. admission control decision is made using a traffic descriptor that specifies traffic characteristics and qos requirements. a new call request is accepted if there is free channel in the network resource, and also if the call meets the qos requirements of new calls without disrupting the qos for the already supported calls. too many calls lead to a situation where the mutual interference between the connections degrades the qos for the new call as well as for the ongoing connections. therefore, admission control plays a very important role in providing the user with the requested qos as well as making an efficient use of the available capacity and preventing the system from an outage situation due to overloading [1]. an accepted call that has not completed in the current cell may have to be handed off to another bts. call admission control (cac) is such a provisioning strategy to limit the number of call connections into the networks in order to reduce the network congestion and call dropping. in wireless networks, another dimension is added: call connection (or simply call) dropping is possible due to the users’ mobility. a good cac scheme has to balance the call blocking and call dropping in order to provide the desired qos requirements due to users’ mobility; cac becomes much more complicated in wireless networks. an accepted call that has not completed in the current cell may have to be handed off to another cell. during the process, the call may not be able to gain a channel in the new cell to continue its service due to the limited resource in wireless networks, which will lead to the call dropping. thus, the new calls and handoff calls have to be treated differently in terms of resource allocation. since users tend to be much more sensitive to call dropping than to call blocking, handoff calls are normally assigned higher priority over the new calls [3]. the continuation of an active call is one of the most important quality measurements in cellular systems. this process is known as handoff. it is the process of changing the channel (frequency, time slot, spreading code, or combination of them) associated with the current connection while a call is in progress. usually, this is initiated either by crossing a cell boundary or signal quality degradation in the current channel. therefore mobile station (ms) can move from one base station (bs) to another, without dropping the call or experiencing difficulties. there are basically two types of handoff principles – the soft handoff and the handoff. if a new bs has some unoccupied channels, then it assigns one of them to the handed off call. nevertheless, if at the time of the hand off, all the channels are in use, two things could happen; the call could be dropped or it is delayed for a while [4]. handoff process enables a cellular system to provide such a facility by transferring an active call from one cell to another. different approaches are proposed and applied in order to achieve better handoff service. the principal parameters used to 45 evaluate handoff techniques are usually forced termination probability and call blocking probability. mechanisms such as guard channels and queuing handoff calls decrease the forced termination probability while increasing the call blocking probability [5]. 2. review of related literature 2.1. call connection and performance metrics for wireless system in a wireless mobile network, a mobile user is at liberty to migrate from one cell to another and engages call connection in the process. handoff probability, handoff rate, call dropping probability, call blocking probability, channel utilization, outage probability and call completion rate are often used as metrics to assess the network systems performance [6]. according to [7], many optimization procedures applied to several service aspects are aimed at minimizing the call dropping/ blocking probabilities while trying to increase the utilization of the resources. these procedures include; the maximization of service coverage area and of network usage, the minimization of interference and congestion, the optimum traffic balancing among the different frequency layers. it has been shown by studies that the performance of wireless systems is affected by a number of propagation factors [8, 9, 10]. these include: background noise, fast fading, shadow fading, random slow shadowing, time dispersion, path-loss variation versus distance, interference, and rayleigh effect. diffraction we know is the phenomenon due to the effect of a radio wave striking a surface which causes its direction of propagation to change [11]. the loss due to diffraction loss is a function of the obstruction type including high rising buildings or towers. signal reception is greatly retarded by these factors and this leads to poor services quality. the rayleigh effect which is also referred to as rician is the effect which is as the result of fast variation of the level of signals in amplitude and phase. this often is between the transmitting and receiving antennas when there is no line of sight. there are two classes of rayleigh fading. these are: multipath fading and frequency-selective fading (fsf) [11,12]. shadowing on the other hand is the effect of diffraction. weak signal strength can also be caused by destruction interference of the signals from local towers in urban areas or by the construction materials used in some buildings. this often causes rapid alteration of signal strength. large buildings such as warehouses, hospitals and factories often have no usable signal further than a few meters from the outside walls. this is particularly true for network operating at higher frequency. 2.2. call blocking probability when a mobile terminal (mobile user) requests service, it may either be granted or denied service. this denial of service is known as call blocking, and its probability as call blocking probability. the overall blocking probability is the weighted sum of the blocking probability of each region. new calls in the soft region are blocked only if both calls are found in the blocking condition [6]. from [13], the overall blocking probability is given as pb = pbh + (1-p) pbs 2 (1) where: pb is the overall probability, pbh is the probability in the hard region, pbs is the probability in the soft region. 2.3. handoff probability handoff probability is the probability that a call connection needs at least one more handoff during its remaining lifetime is known. these probabilities are often referred to as handoff probability for a new call or the handoff probability for a handoff call, depending 46 on whether a call connection is a new call or a handoff call. according to [6], a new call needs at least one handoff if and only if the call holding time tc is greater than the residual cell residence time rc, tc > rc. 3. description of system model the m/m/c/c queuing approach from [14] is adopted in this model. the system is considered to be made of many cells. these cells are assumed to be homogenous. this system cell is made of a total of c channels. priority is given to the handoff calls. this is because mobile users are more sensitive to handoff failure (call drop) than new call blocking. the given priority will be implemented using the guard channel method. out of the c channels of the call, r channels are reserved exclusively for handoff calls while the remaining m = c-r channels are shared by handoff calls and new calls. the following assumptions are adopted in this system model. (i) both the new call and handoff arrival rates in the cell form a poisson process with mean values of λn and λh respectively. therefore total arrival rate is λ = λn + λh (ii) new call and handoff completion time are exponentially distributed with mean rates of µn and µh respectively. therefore the effective service rate is µ = µn + µh (iii) the change in arrival rates is moderate in that the network reaches steady state between any two changes in the arrival rate. therefore the incoming traffic rate (call arrival rate) is λ = λn + λh. the system model is as shown in figure 1. figure 1: system model for the new scheme λh =γh λh (2) λn = γn λn (3) it is assumed that γn and γh are the same and denoted as γ. therefore λh = γ λh (4) λn = γ λn (5) the effective service time for states zero to m is given as µ = µn + µh (6) the effective service time for states m+1 to c is given as µh. a concept known as mobility factor is employed in this work to maximize the priority given to handoff calls. this factor denoted as α is the ratio between the handoff c . . . . m . 2 1 2 1 (αλh) γ r = c m γ λn µ 47 and new call arrivals. one of the assumptions in this system is that new call arrivals are always greater than or equal to handoff, therefore the mobility factor lies between zero (0) and one (1). that is, 0 < α < 1. the relational activities of this scheme are shown in the schematic flowchart of figure 2. figure 2: schematic flowchart of the new scheme the proposed scheme is based on the idea that if the mobile terminal is approaching the base station, the poor signal handoff request can be accepted with probability α that yes call arrival signal strength factor γ>0.7? yes no free channel in the cell? assign channel no yes no end call yes assign channel ongoing call signal factor still γ>0.7? yes no release channel call completed ms approaching bts? no no handoff call? handoff call? end call no call approaching bts? i.e α =1 no reallocate call empty channel in shared cell? yes yes yes yes no end call 48 increases as the mobile terminal approaches the base station. the assumption is that the signal quality will improve as it nears the base station. in essence, this scheme ensures that α is always tending to one (1). this scheme is a prioritized handoff scheme which puts into consideration signal strength, number of channels, call duration, call arrival rates and the mobility factor. 4. conclusion this paper presents an approach for improving the qos for handoff calls by handling the poor signal quality request effectively. the mechanism uses a mobility factor to determine if an ongoing call with poor signal strength can still be accommodated. particularly, the mechanism ensures that mobile users with ongoing call and poor signal strength can still be sustained in the network and eventually handed off to a base station that the mobile user has a high mobility factor. references [1] el-dolil, s. a., al-nahari, a. y., desouky, m. i. & abd el-samie, f. e. ( 2008). uplink power based admission control in multi-cell wcdma networks with heterogeneous traffic: progress in electromagnetics research b, 1, 115–134. [2] shristop l., marco l., & axel t., (2004). “adaptive call admission control for qos/ revenue optimization in cdma cellular networks”, kluwer academic publishers, wireless networks 10, 457-472. [3] fang, y. & zhang, y. (2002). call admission control schemes and performance analysis in wireless mobile networks: ieee transactions on vehicular technology, 51(2). [4] felipe a., genaro h. & andrés r. (2011). call-level performance sensitivity in cellular networks, cellular networks positioning, performance analysis, reliability, dr. agassi melikov (ed.), isbn: 978-953-307-246-3, intech. [5] ekiz, n., salih, t., küçüköner, s. & fidanboylu, k. (2005). an overview of handoff techniques in cellular networks: international journal of information technology, 2 (2), 132-136. [6] fang, y. (2005). performance evaluation of wireless cellular networks under more realistic assumptions: wireless communications and mobile computing wirel. commun. mob. comput.; 5:867–885 published online in wiley interscience (www.interscience.wiley.com). doi: 10.1002/wcm.352. [7] boggia, g., camarda, p., d’alconzo, a., de biasi, a. & siviero, m. (2005). drop call probability in established cellular networks: from data analysis to modeling: dee – politecnico di bari, via e.orabona, 4 – 70125 bari (italy), proc. ieee vtc spring 2005,5, 27752779. [8] hagglund, f. (2005). improved power control for gsm/edge: masters thesis. lulea university of technology, luluea. [9] dajab, d.d. & parfait n. (2010). consideration of propagation loss models for gsm during harmattan in n’djamena (chad). international journal of computing and ict research, 4, (1), 43-48. 49 [10] zreikat, a., & al-begain, k. (2003). simulation of 3g networks in realistic propagation environments. mobile computing and networking research group, i.j. of simulation, 4 (3&4): 21-30. [11] mishra, a. r. (2004). fundamentals of cellular network planning & optimization, england: john wiley & sons, ltd. isbn: 0-470-86267-x. [12] nawrocki, m.j., dohler, m. & aghvami a. h., (2006). modern approaches to radio network modeling and planning –understanding umts radio network, modeling, planning and automated optimisation: england: john wiley & sons ltd. [13] zhang, m. & lea, c. t. (2006). impact of mobility on cdma call admission control. ieee transactions on vehicular technology, 55(6): 1908-1920. [14] giambene, g. (2005). queuing theory and telecommunications networks and applications: rome: springer science+business media, inc., pp. 238-400. copyright © 2017 isaac a. ezenugu, james eke, and g. n. onoh. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 19 mathematical and software engineering, vol. 8, no. 1-2 (2022), 19-23. varεpsilon ltd, http://varepsilon.com doi 10.5281/zenodo.7294898 using web scraping for real estate price analysis aleksandаr tsonev1, valentina dyankova2, yusuf yusufov3 1dreamix ltd, sofia, bulgaria, email: aleksandar.tsonev@dreamix.eu 2konstantin preslavsky university of shumen, shumen, bulgaria, email: v.dyankova@shu.bg 3konstantin preslavsky university of shumen, shumen, bulgaria, email: yusuf.yusufov969@gmail.com abstract in the present paper, a survey is being made of the areas, in which the use of web scraping is necessary for adaptation to dynamic changes, demanding processing and generalizing of large volume of data from different web sources. an exemplary implementation for web scraping is presented for price analysis of the real estate market. the technology that gives possibility of integration of the intended activities in development of the application has been reviewed. the overall procedure in the researching, development and realization of the proposed application can be used as a good practice in adaptation of the knowledge and skills of the graduating students for the requirements, dynamics and organization of the work in a software company as well as for the professional co-operation between the academic lecturers and representatives of the software business. keywords: web scraping; data extraction; databases; selenium; java; springboot; hibernate 1. introduction even with the abilities of new technology to present even more adapting complex solutions in all areas of contemporary life, more and more organizations acknowledge that the strategic use of data and the creation of a culture managed by data have a conclusive meaning for the competitive support of their activity. the increasing pace of digitalization in all areas of the social life makes a large volume of data. that makes the processes of their gathering and use more critical than ever. these characteristics determine the present significance of web scraping, which extracts big amounts of data usually from websites. the goal of this article is to introduce the usefulness of web scraping by reviewing areas where it is used and to suggest one type of its application for price analysis for the real estate market. the suggested article synthesizes activities and solutions from the diploma project of one of the authors. the technologies used are described from the point of view of the adaptive integration of knowledge and skills of a bachelor’s degree graduating student towards the work organization in a software company. the other two authors are representatives of the software industry and academic society and in this sense the overall activity on the research, designing and realization of the suggested application can be used as a good practice both for adaptation of knowledge and skills of the graduating students towards the 20 requirements and dynamics of a software company as well as professional collaboration between the academic lecturers and representatives of the software business in context of the central theme of acm computing curricula 2020 for competency. competency is reviewed as an integrated collectivity of knowledge studied in disciplines of the curriculum with their skillful implementation through specific technologies of the industrial area, motivated by a goal for execution of a task practically important for the present dynamics. the goal chosen for the graduation project is the web scraping entering all areas of social life. 2. web scraping web scraping is a process of retrieving valuable and interesting text information from web sites [1]. the goal of this process is the transformation of retrieved raw information into structured data, which are significant and plausible for assistance of a specific activity [2]. the present digitalization in all areas of social life is the basis for the use of web scraping in all regions of the human activities. some of them are: social life the web application such as facebook, twitter and instagram provide easy functions for sharing information. sometimes the information is not presented appropriately for the user or maybe he is troubled by its redundancy. in [3], the web scraping method is used that can search information, combine it and provide it in a way consistent with the user requirements. through web scraping analyzing of the social media posts from march 2020 till january 2021 research is done on the subjective use of loneliness in times of covid-19 [4]. the language markers of emotions such as depression, anxiety, anger, hate, helplessness and sadness have been researched. tourism because more and more users research and buy hotel and tourism services online, at hand is the present interest towards systematization of the information available in the web space. focusing on gathering of online data in multiple platforms, online tourism agents, web sites for reviews, and web sites for hotel brands in [5] are presented guidelines and realization of the gathering and systematization of publicly available online data for hotels with the goal of extracting ratings of satisfaction, performing of statistical analysis, assessment of correlation between price and rating on the webpage of the online tourism agent. machine learning machine learning presumes that data is given to machines for them to learn and improve themselves. the web is the ideal source for such data and web scraping serves for their retrieval and providing for machine learning. the platform described in [6] that provides user interface for visualization of data, analysis, prognostication and investing recommendations is based on algorithms for machine learning for prognostication using data retrieved with web scraping for purchase/sale on the spanish market. e-commerce the e-commerce market has made a big jump in the last decade and it continues to develop, because the digital devices are being integrated in people’s lives and they change their behavior during purchase. in the e-commerce, the companies have to own flexible competitive solutions for determining the prices, presenting the products, multiplying of the potential clients, improvement of the quality, protection of the brand. web scraping is exceptionally useful for price optimization. it gives the opportunity to follow the dynamic changes in the market prices and promotional events. web scraping can automate the process of granting images and descriptions of products faster than people by using information from different suppliers for the same product. potential clients can be found by analyzing the requirements of the audience of social networks. analyzing reviews and reviews of the users can help the business to 21 understand what is missing in their products and services and to identify how the competitors are distinguished. the online content can be identified fast by using web scraping (e.g. fake products), which can damage the respective trademark. web scrapers can help determine if the intellectual property protected with copyrights is used illegally. other areas there are many more areas of use of web scraping. for example, a surview is made in [7] of uses of web scraping in atrificial intelligence, data science, big data, cloud computing and cyber security. the variety of areas of use of the web scraping made it difficult to choose a problem that would integrate modern dynamics, the interest of the graduate and his opportunities for contact with real business representative in the relevant field. the choice of price analysis of the real estate market as an area for implementation of the web scraping is dictated by the rising in the last few years of interest towards investing in real estate, the interests of the student and the opportunities to discuss business logic with real estate companies. at the moment considerable interest towards the market of real estate is being observed. the variety of data and websites as well as the dependence of this market on many factors, make it incredibly hard for the end user to decide on the right moment for purchase/sale of a real estate. that’s why the system presented in [8] for prognostication of the price by extracting data from the network using web scraping is a valuable helper. the users are often only in need of generalization of the price data to choose the optimal offer for them. the search and offering of real estate are distinguished with great dynamics and frequently with great diversion in the financial parameters, which makes generalizing of the price data particularly important. the manual analysis is slow and labour-intensive. thus, is determined the interest of the authors towards development of an application that is using web scraping to retrieve data for the prices of real estate, systematizes them and performs a summary. 3. web scraping in real estate price analysis the overall activity of researching, designing and realization of the application that uses web scraping for price analysis of real estate market, is organized in the context of adaptation of academic knowledge of the student towards the visions and trends for technology in industry and is in line with the technologic time for developing of a graduation project. the assignment for the graduation project included the following tasks; researching of the functional capabilities of the existing methodologies for web scraping; familiarizing with the business logic in marketing with real estate; choice of technology used in the software industry for integrated solution of the previous two tasks; gaining knowledge and skills for work with the chosen technology; creation of an application for price analysis on real estate market. the task management platform trello was chosen to manage the collaboration of the team members on assigned tasks. trello is a tool that enables team management of the project development workflow. the use of boards, lists and maps makes it possible to both differentiate the assigned tasks and to track the progress on each of them. the version control system of choice was git, with an emphasis on both the collaboration capabilities between different people and teams and the flexible branching model, allowing independent local branches to be created in the code. the latter makes it possible both to experiment with new ideas as well as to correct existing ones. the use of these two systems provides an opportunity to develop skills such as time management, organization, collaboration, attention to detail, responsibility, self-motivation, work ethic. the conducted review of used web scraping methodologies against the set goals and their compatibility with using java as a programming language limited the study to a comparative analysis between the capabilities of jsoup [9,10] and selenium [11,12,13]. the fact that jsoup cannot handle dynamic content generated by javascript defined selenium as the software tool to implement the application. the main advantage of selenium used for its intended purpose is the use of cross-browser web drivers that build the dom tree of each page and provide access to individual parts of the page through selectors. selectors 22 are the way to identify an html element on a web page. the fragment below is an example application of using a selector in a text retrieval function: public static string gettextbyxpath(webdriver driver,string xpath){ try { return driver.findelement(by.xpath(xpath)).gettext(); } catch (nosuchelementexception e) { log.info(string.format("element with xpath [%s] don't exists", xpath)); return “"; } catch (nullpointerexception e) { return ""; } } the database technology used was hibernate due to the fact that it ensures consistency of data structures and their types and facilitates the basic crud (create, read, update, delete) operations. hibernate is an orm (object-relational mapping) library that works with classes (entities) containing meta information about the connections and structure of the database and the tables in it. in order to reduce the amount of code, the lombok library was used to generate the base methods of the classes (mainly getters and setters). checkstyle was used to ensure code quality and following accepted formatting rules. the springboot framework was chosen as the basis of the entire application due to its wide distribution in the industry and its ability to provide various features such as: scheduled jobs used to retrieve information at specified time intervals web interface used to visualize the processed data spring ioc container used for creating separate extraction units/beans the maven system was used to manage the dependencies and build the entire application. the developed application enables to track the maximum, minimum and average price of real estates by type, location and agency that offer the real estate for sale. this data would be useful both for proposing a sale price for a real estate and controlling the price at purchase. 4. conclusion the described process of researching and creating a web scraping application can be used to differentiate advantages that make this method popular among different industries. some of them are: achieving significant results with acceptable parameters of the invested efforts; easy implementation and maintenance; accurate data extraction, preventing opportunities for manual processing errors. as the internet continues to grow and businesses become increasingly dependent on data, the industry in these days is forced to access the latest data in every field. the development of such projects, on the other hand, enables the creation of useful links between industry and academic society. in many cases, the implementation of theoretically defined processes may require the use of specific technological solutions. such projects can help the future realization of students, who in many cases do not have the knowledge and skills to advertise outside of academic settings. references [1] erdinç uzun, a novel web scraping approach using the additional information obtained from web pages, ieee access, volume 8, 2020, issn: 2169-3536. [2] jay m. patel, getting structured data from the internet: running web crawlers/scrapers on a big data production scale, apress, 2020, isbn 978-1484265758. [3] lusiana citra dewi, meiliana, alvin chandra, social media web scraping using social media developers api and regex, procedia computer science, volume 157, 2019, elsevier. 23 [4] junk, yoonwon; lee, yoon kyung; hahn, sowon, web-scraping the expression of loneliness during covid-19, proceedings of the annual meeting of the cognitive science society, volume 43, 2021, e-issn 1069-7977. [5] saram han, christopher k. anderson, web scraping for hospitality research: overview, opportunities, and implications, cornell hospitality quarterly, volume 62, issue 1, 2020. [6] elena hernández-nieves, álvaro bartolomé del canto, pablo chamoso-santos, fernando de la prieta-pindato, juan m. corchado-rodríguez, a machine learning platform for stock investment recommendation systems, distributed computing and artificial intelligence, 17th international conference, italy, 17th–19th june, 2020. [7] moaiad ahmad khder, web scraping or web crawling: state of art, techniques, approaches and application, international journal of advances in soft computing and its applications, vol. 13, no. 3, november 2021. [8] tomasz jach, web scraping methods used in predicting real estate prices, advances in computational collective intelligence, 13th international conference, iccci 2021, kallithea, rhodes, greece, september 29 – october 1, 2021. [9] pete houston, instant jsoup how-to, packt publishing, 2013, isbn 978-1782167990. [10] ryan mitchell, instant web scraping with java, packt publishing, 2013, isbn 978-1849696883. [11] boni garcia, hands-on selenium webdriver with java: a deep dive into the development of end-to-end tests, o'reilly media, 2022, isbn 978-1098110000. [12] pallavi sharma, selenium with java – a beginner’s guide: web browser automation for testing using selenium with java, bpb publications, 2022. [13] kevin sahin, java web scraping handbook, leanpub, 2018-07-26. copyright © 2022 aleksandаr tsonev, valentina dyankova, and yusuf yusufov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. empirical models for estimation of rain rate in the fifteen itu rain zones 85 mathematical and software engineering, vol. 2, no. 2 (2016), 85-92 varεpsilon ltd, http://varepsilon.com empirical models for estimation of rain rate in the fifteen itu rain zones orogun avuvwakoghene jonathan1, kufre m. udofia2, constance kalu3 1,2,3department of electrical/electronic and computer engineering, university of uyo, akwaibom, nigeria. *corresponding author: 2kmudofiaa@yahoo.com abstract rain rate data are essential for the computation of rain attenuation that can be experienced by wireless signal passing through a given area. the international telecommunication union (itu) divided the world into fifteen rain zones and for each rain zone itu published rain rate data for just seven different link percentage availability, namely: 99%, 99.7%, 99.9%, 99.97%, 99.99%, 99.997% and 99.999%. in this paper, two empirical models are developed for estimating the rain rate for any given link percentage availability in all the fifteen itu rain zones. the goodness of fit of the models are indicated in terms of coefficient of determination (otherwise called 2r ), root mean square error and prediction accuracy. in all, 90.3777% is the lowest prediction accuracy recorded for model 1 for rain zone c and 91.6306% is the lowest prediction accuracy recorded for model 2 for rain zone b. the best prediction accuracy recorded for model 1 is 98.2456% for rain zone q and best prediction accuracy recorded for model 2 is 95.3553% for rain zone h. the models are useful for the estimation of rain rate and hence rain attenuation for any given link percentage availability in all the fifteen itu rain zones. keywords: rain rate, rain attenuation, percentage availability, rain zone, empirical models. 1 introduction when propagating through rain, radio waves suffer from power loss (attenuation) due to rain [1,2,3]. according to research findings, rain attenuation is the dominant propagation impairment at frequencies above about 10 ghz [4,5,6,7,8,9]. furthermore, rain attenuation depends on the rainfall rate and the raindrop size distribution. consequently, rain attenuation is computed with knowledge of rain rate for a given region [1,10,5,11,12]. however, the amount of rainfall an area receives depends on the geographic location and the climate of the area [13,14,15]. as such, in the international telecommunication union (itu) recommendations, itu-r p. 837-1 and itu-r p838, the climatic map for the whole world is divided into 15 climatic zones on rain rate distribution or rain intensities at 1% to 0.001% probabilities [16,17,18,19,20,21]. however, for each of the fifteen rain zones, itu published rain 86 rate data for just seven different link percentage availability, namely: 99%, 99.7%, 99.9%, 99.97%, 99.99%, 99.997% and 99.999%. in this paper, empirical models are developed and validated for the estimation of the rain rate for each of the fifteen rain zones and for any given percentage of time the rain rate is exceeded. such models will make it possible for researchers and wireless network designers to effectively study the variation of rain rate and rain attenuation with percentage of time exceeded in any of the rain zones. the models will also enable researchers and wireless network designers to effectively study the relationship between rain rate, percentage of time exceeded and wireless communication link outages or link availability. the two empirical models are developed based on the actual rain rate data published by itu for the fifteen rain zones. 2. methodology in this paper, the available itu rain rate data for the 15 itu rain zones are analysed in order to select the appropriate empirical model for estimating the rain rate for any given percentage of time exceeded. specifically, three different preliminary trend line curves are fitted on the plot of rain rate versus the percentage of time exceeded (fig. 1) for rain zone f. the error analysis on the trend line equations shows that power trend line model has the highest coefficients of determination ( 2r ) of above 0.98 followed by logarithmic trend line model with 0.92 < 2r < 0.98 and lastly the exponential trend line model with 0.73< 2r < 0.92. table 1. itu rain rate and percentage of time exceeded for rain zone e (source: [17, 18] ) percentage of time exceeded (%) rain rate (mm/h) 1 0.6 0.3 2.4 0.1 6 0.03 12 0.01 22 0.003 41 0.001 70 y = 0.872449x-0.703755 r² = 0.971276 power trend line model y = -6.598618ln(x) 5.166157 r² = 0.866371 logarithmic trend line model y = 15.967293e-3.587894x r² = 0.814051 exponential trend line model -10 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 1.2 r a in r a te ( m m / h ) percentage of time exceeded (%) figure 1. the graph of itu rain rate and percentage of time exceeded for rain zone e. 87 consequently, in order to predict rain rate for the itu rain zones, two empirical models are used, namely: model 1: y = cxeax 2 (1) model 2: y = cax b + 1 (2) model 1 is a product of power and exponential components, whereas model 2 is the inverse of the sum of power and constant components. in the two models y is the predicted rain rate in a particular rain zone, x is the percentage of time the rain rate is exceeded (otherwise called percentage of time exceeded), a, b and c are empirical constants determined for each model in each rain zone. (note, x = 100% – link percentage availability. so, link percentage availability of 99% amounts to x = 1%). statistical error analysis parameters such as coefficients of determination ( 2r ), root mean square error (rmse) and prediction accuracy (pa) for each of the models for each rain zone are determined to quantify the goodness of fit of the model for predicting the rain rate in the given rain zone. after selecting the two empirical models, matlab program is used to find the values of the empirical constants a, b and c for each of the model. afterwards, the nonlinear optimisation option in microsoft excel solver is used to determine a constant (kopt) that will be added to the model in order to minimise the prediction error. essentially, the effective models used for estimating the rain rate for each of the rain zones are: model 1: y = cxeax 2 + kopt (3) model 2: y = cax b + 1 + kopt (4) 3. goodness of fit measures the coefficients of determination ( 2r ): if n is the number of data items x and y, the correlation coefficient (r) is given as: ( ) ( )( )( ) ( ) ( )[ ] ( ) ( )[ ]      −− − = ∑∑∑∑ ∑∑∑ 2222 yynxxn yxxyn r (5) also, the coefficients of determination ( 2r ) is given as: ( ) ( )( )( ) ( ) ( )[ ] ( ) ( )[ ] 2 2222         −− − = ∑∑∑∑ ∑∑∑ yynxxn yxxyn r (6) prediction accuracy: the prediction accuracy (pa in %) is calculated as follows: %100* 1 1 1 ))(( ))(())((                     − −= ∑ = = ni i iactaul ipredictediactaul y yy n pa (7) root mean square error (rmse): the root mean square error (rmse) is calculated as follows: ( )2 1 2 ))(())(( 1       −= ∑ = = ni i ipredictediactaul yy n rmse (8) 88 where ))(( iactauly is the actual rain rate given by itu and ))(( ipredictedy is model predicted rain rate. 4. results and discussions table 2a and table 2b show the values for the empirical constants a, b, and c, the model optimization constant (kopt), and the goodness of fit parameters, coefficients of determination ( 2r ), root mean square error (rmse) and prediction accuracy (pa) of the two models for each rain zone. for rain zone a,c,d,e,g,j,p and q model 1 has better prediction accuracy and hence it is used for predicting the rain rate for the rain zone a,c,d,e,g,j,p and q (shown in table 2a). on the other hand, model 2 has better prediction accuracy for rain zones b,f,h,k,l,m and n and hence, model 2 is used for predicting the rain rate for the rain zones b,f,h,k,l,m and n (shown in table 2b). table 2a. model 1: values for the empirical constants a, b, and c, the model optimization constant (kopt), and the goodness of fit parameters, namely: coefficients of determination ( 2r ), root mean square error (rmse) and prediction accuracy (pa) of the two models for each itu rain zone a b c kopt rmse r2 prediction accuracy (%) a 1.261 -0.4148 -3.887 0.093228 0.1673 0.9996 93.0066 c 2.387 -0.4148 -3.887 0.749839 0.7819 0.9983 90.3777 d 3.976 -0.3416 -0.7553 0.161511 0.2257 0.9999 97.3823 e 2.309 -0.4945 -1.877 0.234747 0.3251 1.0000 96.8494 g 6.264 -0.3392 -0.8824 0.318893 0.4509 0.9998 97.0029 j 13.71 -0.2027 -0.6551 0.762792 1.0774 0.9977 95.9201 p 49.09 -0.2379 -2.091 3.741203 4.9247 0.9980 92.2942 q 53.91 -0.1668 -0.8625 1.118311 1.5616 0.9995 98.2456 table 2b. model 2: values for the empirical constants a, b, and c, the model optimization constant (kopt) the goodness of fit parameters, namely: coefficients of determination ( 2r ), root mean square error (rmse), and prediction accuracy (pa) of the two models for each itu rain zone a b c kopt rmse r2 prediction accuracy (%) b 1.392 0.6512 0.01577 -0.25442 0.3640 0.9995 91.6306 f 0.6567 0.6953 0.007375 0.169725 0.8671 0.9990 93.9921 h 0.4108 0.601 0.005593 -0.48374 0.6301 0.9997 95.3553 k 0.397 0.6739 0.006244 -0.76367 0.9533 0.9996 93.0746 l 0.3157 0.7038 0.004226 -0.52586 0.6459 0.9999 93.7753 m 0.1787 0.6364 0.006129 -0.74685 0.9745 0.9997 95.1533 n 0.1083 0.6198 0.004093 -2.72616 3.4914 0.9982 92.4932 from eq.3 and table 2a, the empirical model for the rain rates in rain zones a,c , d, e, g, j, p and q can be expressed as: 89 0.093228 e 1.261x -3.887x-0.4148a +=y (9) 0.749839 e x387.2 -3.887x-0.4148c +=y (10) 0.161511 e x976.3 -0.7553x-0.3416d +=y (11) 0.234747 e x309.2 -1.877x-0.4945e +=y (12) 0.318893 e x264.6 -0.8824x-0.3392g +=y (13) 0.762792 e x71.13 -0.6551x-0.2027j +=y (14) 3.741203 e x09.49 -2.091x-0.2379p +=y (15) 1.118311 e x91.53 -0.8625x-0.1668q +=y (16) similarly, from eq4 and table 2b, the empirical model for the rain rates in rain zones b, f, h, k, l,m and n can be expressed as: 25442.0 01577.0392.1 1 6512.0 − + = x yb (17) 169725.0 007375.06567.0 1 6953.0 + + = x yf (18) 48374.0 005593.04108.0 1 601.0 − + = x yh (19) 76367.0 006244.0397.0 1 6739.0 − + = x yk (20) 52586.0 004226.03157.0 1 7038.0 − + = x yl (21) 74685.0 006129.01787.0 1 6364.0 − + = x ym (22) 72616.2 004093.01083.0 1 6198.0 − + = x yn (23) fig. 2 and table 3 show the graph of the actual and model 1 predicted rain rate versus percentage of time exceeded for rain zone e in which model 1 has prediction accuracy of 96.8494% (as shown in table 2a). similarly, fig. 3 and table 4 show the graph of the actual and model 2 predicted rain rate versus percentage of time exceeded for rain zone f in which model 2 has prediction accuracy of 93.9921% (as shown in table 2b). table 3. actual and model 1 predicted rain rate for rain zone e. percentage of time exceeded (%) actual rain rate (mm/h) for rain zone e model 1 predicted rain rate (mm/h) for rain zone e 1 0.6 0.588136 0.3 2.4 2.619461 0.1 8 6.210696 0.03 12 12.59514 0.01 22 22.32864 0.003 41 40.83624 0.001 70 70.39785 90 figure 2. the actual and model 2 predicted rain rate for rain zone e table 4. the actual and model 2 predicted rain rate for rain zone f. fig. 3 the actual and model 2 predicted rain rate for rain zone f 5 conclusion in this paper, two different empirical models referred to as model 1 and model 2 are developed and evaluated for their suitability for predicting the rain rate for the 0 5 10 15 20 25 30 35 40 45 0 0.2 0.4 0.6 0.8 1 r a in r a te ( m m / h ) percentage of time exceeded (%) actual rain rate (mm/h) for rain zone e model 1 predicted rain rate (mm/h) for rain zone e 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 r a n i r a te ( m m / h ) percentage of time exceeded (%) actual rain rate (mm/h) for rain zone f model 2 predicted rain rate (mm/h) for rain zone f percentage of time exceeded (%) actual rain rate (mm/h) for rain zone f model 1 predicted rain rate (mm/h) for rain zone f 1 1.7 1.505854 0.3 4.5 3.428223 0.1 8 7.151562 0.03 15 15.45074 0.01 28 29.33349 0.003 54 52.79358 0.001 78 78.34848 91 fifteen itu rain zones across the world. the goodness of fit of the models are indicated in terms of coefficient of determination (otherwise called ��), root mean square error and prediction accuracy. for rain zone a,c,d,e,g,j,p and q model 1 has better prediction accuracy and hence it is used for predicting the rain rate for the rain zone a,c,d,e,g,j,p and q. on the other hand, model 2 has better prediction accuracy for rain zones b,f,h,k,l,m and n and hence, model 2 is used for predicting the rain rate for the rain zones b,f,h,k,l,m and n. the models are useful for the estimation of rain rate and hence rain attenuation for any given link percentage availability in all the fifteen itu rain zones. references [1] panagopoulos, a.d., arapoglou, p.d., & cottis, p.g. 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(2009, may). simulation of rain fading and scintillation on ka-band earth-leo satellite links. in electrical and computer engineering, 2009. ccece'09. canadian conference on (pp. 635-640). ieee. copyright © 2016 orogun avuvwakoghene jonathan, kufre m. udofia, constance kalu. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mathematical and software engineering 10 mathematical and software engineering, vol. 8, no. 1-2 (2022), 10-18. varεpsilon ltd, http://varepsilon.com doi 10.5281/zenodo.7093793 implementation of house of quality method for software tools evaluation veselina spasova1 and oleksii raiu1 1department of computer science, varna free university chernorizets hrabar, bulgaria abstract house of quality is well known method for products evaluation in manufacturing. in this study, we will demonstrate usage of the isixsigma “house of quality” method for quality evaluation in software engineering. we will analyze functionality and performance of two template engines twig and laravel. keywords: house of quality, software quality, software evaluation, customer needs 1 introduction the quality function deployment method is a well-known product evaluation method that allows bringing together the technical characteristics and the customer requirements the measurable and the empirical analytics [1]. the main tool for qfd is the house of quality [2], based on matrix, where the numerical and empirical technical characteristics and customer requirements are integrated in an evaluation scheme, allowing to achieve higher rates of customer acceptance, since not only objective measurable parameters get accounted for, but also the customer requirements, which may not be equally measurable. the qfd methodology works well with the six sigma practices and is compliant with iso 9001 (quality management systems standard). this model is very similar to the well-known classification model in bulgaria, popularized by the book "software engineering" by avram eskenazi and neli maneva [3], although it was published for the first time back in 1989 [4]. however, the method has a wider spread and application in production, and its use in software evaluation is a challenge. qfd is used as a tool to identify the explicit and implicit expectations of customers, and to turn those expectations into product requirements. besides the strength of considering the user requirements, there is important 11 strength that qfd has that it can work with diverse and versatile products, and maintain its relevance across many different use cases. thus, qfd is a very useful tool for evaluating template engines, since it can measure both technical parameters and the customer requirements. using the hoq methodology, we can evaluate how the twig and blade template engines answer the customer’s needs and requirements, and this will inform our results and observations. 2 methods house of quality (hoq) tool is a diagram used in the qfd process to convert the customer requirements into actual product specifications [2]. hoq diagram has the form of a house, hence its name. it is recommended that direct customer input is used to fill in the requirements. hoq can also serve a roadmap describing the journey from customer requirements and constraints to the final product or service specifications. the matrix has six main parts: 1. customer needs (cn); 2. customer critical requirements (ccr); 3. interrelationship matrix: evaluate the relationship between customer needs and ccrs. to simply put, how strong is the relation between a given requirement and a given need in this matrix. relationships can be “strong” (9 points), “medium” (3 points) and “weak” (1 point). 4. customer rating of competitors: twig and blade will be used as competitors of each other. 5. correlation matrix: compare ccrs to determine if they are in conflict with each other, leveraging each other, or have no effect on each other. 6. performance targets: determine the necessary performance targets (specs) for each ccr. these should preferably be some verifiable numbers measures of time, quality, or quantity. for the purposes of this study, the specific needs of users, in this case php programmers will be defined and evaluated. on this basis, a house of quality will be built and the two template engines compared. 3 results and discussion the most important step in making qfd work is to establish relevant and tangible customer needs. the first part of this study is mostly dedicated to establishing those needs as relevant to template engines. as for the common software characteristics, they are well described in the iso 9126 standard [5], and include: • functionality: are the requested functions present in the software? • reliability: how reliable is the software? • usability: is the software easy to use? • efficiency: how efficient is the software? 12 • maintainability: how easy is it to maintain and modify the software? • portability: how easy is it to move the software to another environment? for lower-level design, sub-characteristic of the above-mentioned points can be provided. most of the customer needs directly derive from the common and expected functionality that the template engines must have. concisely put, here are those needs – “as a customer, i want …”. the methodological and technical aspects of the evaluation of the two engines from developer’s point of view (customer needs) are detailed and commented on in the article “comparison of template engines of php frameworks” [6]. we are using the data that have received from the measurements, to fill in the house of quality table. because this is not a usual competition with multiple competitors, we chose to slightly modify the competition matrix to be binary. the 0 indicates a “loss” and 1 indicates a “win”. when both competitors have 1, it’s a tie. the competition advantage was evaluated based on the amount of points that the template engines received in each category. figure 1. house of quality for blade and twig 13 figure 2. legend for used symbols 3.1. the interrelationships matrix while there are strong obvious relationships in the intersection points, there are other weak and strong relationships that can be seen in the interrelationship matrix. we can see that the more low-level and widely used functionality have more influence, while the more specific functionality and requirements have less relationship to the rest of them. the way that the template engine handles and prints simple and complex variables are strongly related to the level of flexibility of control structures and rendering logic. it also positively influences the level of stability and simplicity of code. to a lesser extent it also influences almost every other aspect of the template engine, because of how low-level and important this functionality is. the way variables are accessed and printed does not influence security much, or the way inheritance works. though it could be objected that forcing the developer to use the raw php in case with blade does in fact influence security quite a lot, it should still be noted that is this not because of how blade handles variables, but how it fails to handle them within its syntax, though we do agree that whether it could be considered “security-related”. as already noted, we consider the fact that blade exposes raw php to user a security threat, and don’t want to confuse it with how variables are or are not handled. the requirement to apply logic to the parts of templates strongly influences both the flexible rendering logic and the flexible control structures functionality. to a lesser degree, this requirement also influences the variables handling and the inheritance. since inheritance can be conditional, it is understandable how logic in templates comes into play here. to a large degree, blade has shown itself to be more flexible and versatile than twig, which is surprising, given how twig generally has a richer feature set. in the requirement of iterations and loops, functionality of flexible control structures is mostly involved. additionally, variable handling and flexible rendering logic also play a role. both twig and blade appear to be versatile enough as far as 14 iterations and loops are concerned, and they both score are tied in competition here. ability to have template inclusion and inheritance mostly maps to the vertical and horizontal inheritance functionality, but also to flexible rendering logic and control structures, and access to context. quality of both template engines is quite satisfactory here, satisfying the requirements for both horizontal and vertical inheritance and are able to pass relevant data to children templates. there is again, a competitive tie. in the security requirement, twig clearly is a winner. this requirement influences security functionality, and it also strongly influences stability, since having an insecure template in some cases also means having unstable templates. though this security hole is a design choice, aimed at giving more power to the developer (ultimate power, as far as access to raw php is concerned), this is still a strong disadvantage for many use cases where twig would be a more secure choice. stability of templates is influenced by simplicity and performance. having a simpler template eliminates human errors, and better performance minimizes the possibility of a server timeout or dos (denial of service) under a heavy load. as we have established, twig templates are much more stable, having better protection against undeclared or empty variables, array keys, and object attributes. both twig and blade provide access to relevant context data. blade has access to the app() class, which makes it more flexible. however, that class comes from the laravel context, and being a native part of laravel, it has this class out of the box, while twig, being an addon solution, does not have that much information about the framework, which is expected. both engines are tied here. both twig and blade can be extended, additional functionality can be written in the forms of plugins for functions, filters, or directives. again, both engines are tied competitively in this section. as far as performance is concerned, blade is a winner. if we look at its code output, we can see that it compiles to raw php very closely, while twig compiles to classes. thus, it is expected that blade will be faster. even though, as discussed, caching and saving compiled templates will level down some of this curve (blade is five times faster than twig as far as the full rendering cycle is concerned). blade is the winner in the performance section. the requirement is having a clear syntax. much functionality is related variables, rendering logic, loops and iterators, inheritance. having a clear and simple syntax makes every function of the template engine easier to use and makes it more proficient and less prone to human errors. both engines tie here, even though blade did seem more elegant to me in many points as far as the simplicity of code is concerned, its syntax being somewhat more succinct, still the difference is not so drastic as to clearly appoint a winner. having established the interrelationship between the requirements and functionality, and their competitive impact of the two template engines, we can't help but notice that there are aspects where blade holds advantage, and then there are those where twig does. blade holds advantage in the area of flexibility of logic and control structures, 15 and render times, and exposes raw php, while twig has an advantage in handling variables, security, and stability. 3.2. the correlation matrix the role of the correlation matrix is to show how two functionality items can be self-supporting or self-exclusive. self-supporting functionalities will provide additive effects to each other security will make templates more stable. at the same time, most “smart” functions will negatively affect performance and simplicity, because the more you add to the code, the slower and more complicated it will necessarily become. in our case we can say that making twig more secure and stable has likely affected its performance. another aspect is wrapping every template as a class. oop is generally slower than procedural programming, due to additional code required to handle all the oop. this alone would make twig slower. we are not going to argue for or against oop and procedural programming here, but it would suffice to say that there are objective reasons why oop is slower. 3.3. the importance rating the importance rating is derived from how each requirement is interrelated with other requirements horizontally, and how each function is interrelated with the other functionalities vertically in the matrix. this brings a new interesting dimension to the understanding of what ends up important to us and what not so important. it is customary to assign the levels of importance to every requirement. in our case, it’s the “customer importance” column. however, it is interesting how the “relative weight” row and column reflect the importance of the functionality and requirements according to the number and strength of relationships. from the number of relationships, variables handling, logic and control structures, and stability appear to be paramount, while performance appears to be so neglected as to have 0% importance. this is interesting, because more functionality and “smarter” template engines will provide an increase in development time and cost, and thus, the performance will not come into attention until much later, when the project will come under heavy load from the increasing number of visitors. on the other hand, if there is an increase of visitors, it will be more willing to buy a better server, because of winning, while faster development cycles will allow to develop cheaper and fail faster if product proves a pad idea (in the case of start-ups). roughly the same thing happens with functionality flexibility and control structures, template engine syntax appears to be paramount, while performance and security appears less important. 16 3.4. suggestions having tested blade and twig, and measured their performance, and having analyzed them using the house of quality method, we can now use the resulting empirical and objective information to produce suggestions for developers to be better informed which tools to use in each case. both template engines have some very important commonalities, and also some strong differences, that create appeal for different groups of users and scenarios. then, there will be some common and special cases, where we need to pay special attention to some aspects of those template engines 3.4.1. important commonalities of twig and blade both twig and blade are feature rich and powerful template engines. they allow reaching every goal the developer may have albeit by sometimes different means. they are both relatively fast, both can save and store their rendered files as php files to minimize rendering times, and both work well with caching. as far as syntax is concerned, they have good logic handling, iterators, loops, inheritance both vertical and horizontal, and access to the relevant context data. both template engines can be extended to provide additional functionality with plugins. both template engines have clear and succinct syntax that makes the templates readable and does not stand in the way. both twig and blade have matured enough support for inheritance to allow their use in atomic design patterns. those agencies that prefer working with atomic design will be able to work with both of these template engines. what this means is that regardless of which template engine of the two has been chosen, you will be able to reach your goal with it, although, depending on the goal, it may be better to prefer one to another. 3.4.2. important differences between blade and twig just as there are some similarities, there are also some important differences. these differences seem to be shaping into a philosophical approach: twig aims to be smart and abstracted, focusing on security and stability in the first place, sacrificing performance and some of its flexibility for the sake of stability and performance if needed. twig, on the other hand, aims to be flexible and performant, and giving users raw access to php, even if it means making it less secure. the first big difference is that blade gives a developer access to php and twig does not. this is probably the single most important difference between the two engines. with blade developer can access php, and that means that have more freedom in coding. with twig, developer is limited to its syntax, and while it's more secure and stable this way. another very important difference is that blade will compile to php directly, which makes it very easy to debug. html markup will remain html markup, and 17 only the template syntax will be replaced with php insertions. developer can in many cases only imagine how compiled php file will work, by looking at the template. twig will compile its template into a php class; html markup will be replaced by the “echo” statements. this reveals the key difference of approach: blade fundamentally treats templates as html markup with injections of php code, and twig fundamentally treats templates as code with html markup printed on the page. this is another thing that can make blade templates faster. finally, it should be noted that blade is a part of laravel. while twig can be used both in laravel and symfony; blade can be used only in laravel. this means, that if project will be built in laravel, we have a choice between the two engines, but if it’s built on symfony or a non-laravel symfony cms or cmf (such as drupal), blade can’t be used. 4 conclusion as a result, it is possible to summarize those use cases even further. blade seems to be more suitable for smaller teams, working on lower-level products (apis, web services), which are built of artisans, full-stack developers, who can operate both on front and back ends. on the other hand, twig appears to be more suited for the larger teams with front and back end separation, who have larger budgets, and who build websites, rather than web services. alternatively, the use of symfony or drupal cms will necessitate twig regardless of the other considerations. the hoq tool can be very beneficial for the evaluation process. here are some strengths and benefits that it carries: • hoq helps to organize the product planning around the customer and their needs and requirements. the whole core of the matrix is built around what the customer needs and which requirements will satisfy each need. • hoq brings customer needs and requirements into specification and development focus. this will greatly influence the acceptance rates. • hoq helps the developers to understand what the customer needs and prevents the bugs that come from misunderstanding the customer's implicit and explicit needs. references [1] zrymiak, daniel. “software quality function deployment.” isixsigma, https://www.isixsigma.com/tools-templates/qfd-house-of-quality/softwarequality-function-deployment/. accessed 13 april 2022. [2] “house of quality definition.” isixsigma, https://www.isixsigma.com/dictionary/house-of-quality, accessed april 2022. [3] eskenazi a., maneva, n., software engineering, klmn publishing, sofia, bulgaria (2006). [4] eskenazi a., evaluation of software quality by means of classification 18 methods, j. of systems and software, vol.10, no 3, october 1989, pp. 213216. [5] spasova, v., standards for quality management in the software business, university publishing house of vfu “chernorizets hrabar”, varna, bulgaria (2019) [6] spasova, v., raiu, o, comparison of template engines of php frameworks, mathematical and software engineering, vol. 8, no. 1-2 (2022), pp. 1-9, doi: 10.5281/zenodo.7091882, http://dx.doi.org/10.5281/zenodo.7091882. copyright © 2022 veselina spasova and oleksii raiu. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. http://dx.doi.org/10.5281/zenodo.7091882 software for fresnel-kirchoff single knife-edge diffraction loss model 76 mathematical and software engineering, vol. 2, no. 2 (2016), 76-84 varεpsilon ltd, http://varepsilon.com software for fresnel-kirchoff single knife-edge diffraction loss model okoye o. jude1, afolayan j. jimoh2, akinloye bolanle eunice3 1,2,3department of electrical/electronic and computer engineering, university of uyo, uyo, akwa ibom state, nigeria. abstract in this paper, development of software for computing single knife-edge diffraction loss based on fresnel-kirchoff model and lee’s analytical approximation model is presented. the mathematical expressions and algorithm for the single knife edge diffraction loss software are presented. the input required by the software includes frequency, height of the transmitter and receiver antennas, height of obstruction, distance of the obstruction from the transmitter or receiver. the output includes diffraction loss, fresnel diffraction parameter, path length and phase difference between the direct and diffracted paths, the number and radius of all fresnel zones block by the obstruction. moreover, the software is used to study the variation of diffraction parameter, diffraction loss and other link parameters with obstruction height. results are presented in tables, graphs and also as a list of parameters and their values. sample diffraction loss computation is conducted for a 9ghz microwave link with 25 m knife edge obstruction. at diffraction parameter of 5.4772255575 the corresponding diffraction loss is -27.72756218 db. more importantly, at diffraction parameter of 0 (zero) the corresponding diffraction loss is -6.02 db which is in agreement with the published works on single knife edge diffraction loss at diffraction parameter of 0 (zero). keywords: diffraction loss, diffraction parameter, diffraction, single knife diffraction, fresnel zone, microwave link, line-of-sight link 1 introduction over the years, wireless communication has grown to be the dominant communication systems across the globe [1]. accordingly, researchers and manufacturers are continuously inventing and improving on tools that can be used to advance the wireless communication technologies and their applications [2,3]. one of such tool is considered in this paper, namely, the software for computing diffraction loss of wireless communication links with single knife edge obstruction in the signal path. diffraction is the bending of radio waves around obstacles in the path of the waves, or as the radio waves pass through narrow openings [4,5]. diffraction allows radio signals to propagate around the curved surface of the earth, beyond the horizon, and to propagate behind obstructions [4,6,7]. diffraction results in a change of direction of path of the radio wave energy from the normal line-of-sight path. diffraction enables radio signal to be receive around the edges of an obstacle. the 77 ratio of the received signal power with and without the obstacle is referred to as the diffraction loss [8,9]. diffraction loss is a function of frequency of operation and the path geometry. if the direct line-of-sight of a radio wave or wireless signal is obstructed by a single object, such as a mountain or building, the attenuation resulting from diffraction over such obstacle can be determined by considering the obstacle as a single knife-edge [10,11]. single knife-edge diffraction model is used to predict diffraction losses caused by a single object such as a hill or mountain which lies in the path of the wireless signal [10,11]. such, diffraction losses over isolated obstacles can be estimated using the fresnel-kirchoff knife-edge model [12,13]. determination of diffraction loss is usually part of a larger network planning and design process that requires selection and fine-tuning of parameter values to suit a particular design specification. in other to facilitate the diffraction loss parameter selection and fine-tuning process, software tool is essential. in this paper, software that can be used to determine single knife edge diffraction loss and also perform parametric analysis on diffraction loss parameters is presented. sample diffraction loss computation for a 9ghz microwave link is used to demonstrate the applicability of the software. 2 the mathematics of the fresnel-kirchoff model for single knife edge diffraction loss the fresnel-kirchoff model for single knife edge diffraction loss computation is explained using schematic diagram of a wireless communication link in fig. 1. a simplified version of the link schematic diagram in fig. 2 is obtained by subtracting the smaller of the two antenna heights in fig. 1, from all other heights considered in the link. the communication link in fig. 1 and fig. 2 is for a wireless signal transmitted from the transmitter to the receiver with signal wavelength (λ) given as: λ = �� = ��� (1) ∴ c = λ�� = � (2) where: c is the speed of a radio wave (c = 3x10��/�; λ is wavelength of a radio wave in m; f is frequency of a radio wave in hz, and t is period of a radio wave in seconds. figure 1. schematic diagram for single knife edge diffraction loss computation. ℎ� �� ℎ�� transmitter ℎ� receiver α γ β �� ��� ℎ 78 figure 2. the simplified link schematic diagram for diffraction loss computation in fig. 1 and fig. 2, various link parameters are identified and defined as follows: ℎ� is the height of the transmitter antenna ℎ is the height of the receiver antenna ℎ! is the minimum antenna height between the transmitter and the receiver antennas, where ℎ! = min imum�ℎ , ℎ�) (3) ℎ& is the maximum antenna height between the transmitter and the receiver antennas, where ℎ& = maximum �ℎ , ℎ�) (4) ℎ��( is the height of the impenetrable knife-edge obstruction from the ground. ℎ�� is the height of the impenetrable knife-edge obstruction with respect to the straight line-of-sight path between the transmitter and the receiver. if ℎ�� is positive, it shows the obstruction height is above the line of sight. however, if ℎ�� is negative, it shows the obstruction height is below the line of sight. ℎ�� = ℎ��( − ℎ! (5) ��� is the distance of the obstruction from the transmitter �� is the distance of the obstruction from the receiver if α and β are very small in fig. 1 and fig. 2 and also, if (ℎ�� )≈ ℎ� �� then, the excess path length (∆ is the difference between the direct path and the diffracted path. then, ∆ is given as; ∆ ≈ ,�-./ 01 2 ,�3.453.6 �3.4 �3.6 2 (6) α = β + γ (7) α ≈ ℎ�� ,�3.453.6 �3.4 �3.6 2 (8) also, the fresnel-kirchoff diffraction parameter (v) is given as v = ℎ�� 9:1�3.453.6 ʎ�3.4 �3.6 < (9) v = α 9:1�3.4 �3.6 ʎ�3.453.6 < (10) where α is in radians. the phase difference (ϕ) between the direct path and the diffracted path is given as: φ = ,1a 2 ∆ = ,1a 2 b,�-./ 01 2 ,�3.453.6 �3.4 �3.6 2c = ,a1 2 v1 (11) hence, the phase difference (ϕ) depends on the height and position of the obstacle, as well as the transmitter and receiver locations. fresnel zones: fresnel zones represent successive regions where secondary ℎ��( − ℎ! transmitter ℎ& − ℎ! receiver α γ β �� ��� 79 waves have a path length from the transmitter to the receiver which are d� 1 greater than the total path length of a line-of-sight path. the radius of the nth fresnel zone (ef�g ) is given as [14]: ef�g = :dh �3.4 �3.6 i�3.453.6 , for n =1,2,3,… and ��� >> ef�g kl� �� >>ef�g (12) graphical solution can be used to compute diffraction loss mn�no as a function of the diffraction parameter, v using the knife-edge diffraction loss graph of fig. 3 [15,16]. numerical solutions can also be used to compute diffraction loss g3��q as a function of the diffraction parameter, v. lee’s approximation model for computing g3��q with respect to v is given as follows [15,16]. rs t su g3��q = 0 for v < −1g3��q = 20log �0.5 − 0.62v for − 1 ≤ v ≤ 0g3��q = 20log �0.5exp�−0.95v for 0 ≤ v ≤ 1g3��q = 20log h0.4 − e0.1184 − �0.38 − 0.1v 1i for 1 ≤ v ≤ 2.4 g3��q = 20log ,g.11hi 2 for v > 2.4 js k sl (13) figure 3: knife-edge diffraction loss graphed as a function of the fresnel-kirchoff diffraction parameter [15,16]. 3 algorithm for computing single knife-edge diffraction loss. the entire algorithm is given below. step 1 input the following (i) f frequency of the radio wave in hz. (ii) hn is the height of the transmitter antenna (in meters) from the ground or sea level. (iii) ℎ is the height of the receiver antenna (in meters) from the ground or sea level. (iv) ℎ��( is the height of the impenetrable knife-edge obstruction (in meters) from the ground or sea level. (v) ��� distance of the obstruction from the transmitter (in meters). (vi) �� distance of the obstruction from the receiver (in meters). step 2 compute ʎ, the wavelength of a radio wave (in meters) as follows: λ = ��. step 3 compute ℎ!, the minimum antenna height between the transmitter and the 80 receiver antennas (in meters), where ℎ! = min imum�ℎ , ℎ�). step 4 compute ℎ&, the maximum antenna height between the transmitter and the receiver antennas (in meters), where ℎ& = maximum �ℎ , ℎ�). step 5 compute ℎ��, the height of the knife-edge obstruction with respect to the straight line-of-sight path between the transmitter and the receiver, where ℎ�� = ℎ��( − ℎ!. step 6 compute the fresnel diffraction parameter, v as follows: v = ℎ�� op2���� + �� ʎ���� ��� q step 7 compute mn�no the diffraction loss as a function of the diffraction parameter v. using lee’s numerical (approximation) solution method as follows: rss t ssu mn�no = 0 for v < −1mn�no = 20log �0.5 − 0.62v for − 1 ≤ v ≤ 0mn�no = 20log �0.5exp�−0.95v for 0 ≤ v ≤ 1mn�no = 20log ,0.4 − e0.1184 − �0.38 − 0.1v 12 for 1 ≤ v ≤ 2.4 mn�no = 20log 90.225r < for v > 2.4 jss k ssl step 8 compute ∆, the path length difference between the direct and diffracted paths as follows: ∆ ≈ ,�-./ 01 2 ,�3.453.6 �3.4 �3.6 2 = ,ʎt 2 v1 step 9 find n, the fresnel zone in which the tip of the obstruction lies . the excess path length (∆ is also given in respect of n as ∆ = ,u 1 2, hence n = 1�∆ . step 10 find l��, the fresnel zones blocked by the obstruction. l�� = vnw, where v w means number truncated to the nearest lower integer. hence, l�� = x 1�∆ y. therefore, the obstruction blocks the first l�� fresnel zones. step 11 compute ϕ , the phase difference between the direct path and the diffracted path as follows; φ = ,1aʎ 2 ∆ = ,a1 2 v1 . step 12 compute ef�g , the radius (in meters) of the first l fresnel zones the obstruction blocks fully or partially as follows; ef�g = :dhʎ�3.4 �3.6 i�3.453.6 where n=1,2,3,… l ; ��� >> ef�g kl� �� >>ef�g . the software is written in visual basic language and a sample single knife-edge diffraction loss is used to demonstrate the application of the software. the sample diffraction loss computation is for 9ghz microwave link with transmitter antenna height of 100 m, receiver antenna height of 90 m, obstruction with height of 25 m from the line of sight and with obstruction distance of 2500 m from both the transmitter and the receiver. 4 results and discussion the results obtained from the sample run of the software is presented and discussed in this section. from fig. 4, the fresnel diffraction parameter (v) for the link is 81 5.4772255575 which correspond to diffraction loss of -27.72756218 db. in addition, from fig. 6, the path length difference is 0.25 and up to the 15th (that is, l�� = 15,as shown in fig.6 fresnel zones are completely blocked by the obstruction which is 115 metres high (|ℎk| }� ℎ�� = 115, as shown in fig.5 a where the radius of the 15th fresnel zone is 25 m (that is, ~��d = 47.13°, as shown in fig. 6 . also, in fig. 6, the phase difference is 47.13° (that is, � = 47.13°, as shown in fig.6 . figure 4. the input parameters for the sample diffraction loss computation figure 5. the first output screen for the sample diffraction loss computation the results are also presented in table 1 which shows how the diffraction parameter and diffraction loss vary with the obstruction height. in the link, for obstruction height less equal to -5m, the diffraction parameter (v) is less or equal to -1.1 and the corresponding diffraction loss for such range of values of v by lee’s model is 0 db. the various values diffraction loss and diffraction parameter are presented in table 1 and graph of fig. 7 for obstruction height from -50 m to 50 m where the obstruction height is measured with respect to the line of sight between the transmitter and the receiver antennas. 82 figure 6. the second output screen for the sample diffraction loss computation table 1. variation of diffraction parameter, diffraction loss and other link parameters with obstruction height height of obstruction (m) fresnel diffraction parameter diffractio n loss (db) number of fresnel zones affected radius of the highest fresnel zone blocked (m) path length difference (m) phase difference (°) s/n hob v g(db) n rf(nob) (m) δ φ (°) 1 -50 -10.95 0 60 50 1 188.52 2 -40 -8.76 0 38.4 39.79 0.64 120.65 3 -20 -4.38 0 9.6 19.36 0.16 30.16 4 -10 -2.19 0 2.4 9.13 0.04 7.54 5 -5 -1.1 0 0.6 0 0.01 1.89 6 0 0 -6.02 0 0 0 0 7 10 2.19 -20.37 2.4 9.13 0.04 7.54 8 20 4.38 -25.79 9.6 19.36 0.16 30.16 9 30 6.57 -29.31 21.6 29.58 0.36 67.87 10 50 10.95 -33.75 60 50 1 188.52 83 figure 7. diffraction loss, g(db) and fresnel diffraction parameter versus obstruction height, hob(m) 5 conclusion in this paper, mathematical expressions and algorithm for single knife edge diffraction loss software are presented. sample application of the software in diffraction loss computation is presented; also, the software is used to study the variation of diffraction parameter, diffraction loss and other link parameters with obstruction height. references [1] v. shankar, m. kleijnen, s. ramanathan, r. rizley, s. holland, and s. morrissey. mobile shopper marketing: key issues, current insights, and future research avenues. journal of interactive marketing 34 (2016): 37-48. 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[14] b. malila, o. falowo, n. ventura. millimeter wave small cell backhaul: an analysis of diffraction loss in nlos links in urban canyons. in africon, 2015, pp. 1-5. ieee, 2015. [15] baldassaro, paige marie. rf and gis: field strength prediction for frequencies between 900 mhz and 28 ghz. phd diss., virginia polytechnic institute and state university, 2001. [16] rappaport, t. (1996) wireless communications, principles and practices. prentice hall ptr, upper saddle river, new jersey. copyright © 2016 okoye o. jude, afolayan j. jimoh, akinloye bolanle eunice. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. development of optimal site selection method for large scale solar photovoltaic power plant 66 mathematical and software engineering, vol. 2, no. 2 (2016), 66-75 varεpsilon ltd, http://varepsilon.com development of optimal site selection method for large scale solar photovoltaic power plant jacob iniobong joseph1, umoren mfonobong anthony2*, and idorenyin markson3 1,3department of electrical/electronic engineering, akwa ibom state university mkpat enin, akwa ibom state, nigeria. 2department of electrical/electronic and computer engineering, university of uyo, akwa ibom, nigeria. 3 department of mechanical engineering, university of uyo, akwa ibom, nigeria *corresponding author: umoren_m.anthony@yahoo.com abstract in this paper, method selecting optimal location for large scale photovoltaic (pv) power plant in imo state is carried out. ten local government areas (lgas) in imo were selected out of the 27 lgas in the state. also, five parameters were used for ranking the selected lgas for their suitability for large scale pv power plant. the five parameters are; (i) global irradiation on horizontal plane (kwh/m²) (ii) available energy (kwh) (iii) yearly unit cost of energy (iv) population (v) land mass (km2). pvsyst software was used for the simulation of the pv energy generator output and unit cost at each of the selected lga. the meteorological data used for the simulation was obtained from nasa website. also, population density and land mass of each of the lgas were obtained from nigerian population commission publication. in all, umuapu has the highest pv site suitability factor (pvssf) of 142 while oguta has the least with 39. consequently, the optimal site for large scaled pv power plant among the selected lgas in imo state is umuapu. accordingly, umuapu has the pv site suitability rank (pvssr) of one (1) while oguta has the poorest pvssr value of 10. keywords: optimal site, photovoltaic, electric power, renewable energy, pvsyst, global radiation on horizontal plane, unit cost of energy, site suitability factor , suitability ranking. 1 introduction in recent years, there is increasing global pursuit for both environmental and energy security. in this wise, it has become established fact that the dependence on conventional energy resources has to be reduced and renewable energy resources are 67 one of the promising options available to meet the energy target. of all the several renewable energy resources solar energy is the most promising option because of its inherent advantages [1]. furthermore, as the cost of pv devices and systems drop, there is steady increase in the adoption of pv especially at large scale photovoltaic power (lspvp) plant. one important aspect for achieving such highly ambitious plan is to identify the promising geographical areas for establishing such spv plants since with the existing low conversion efficiencies, installation of solar pv power plant requires enormous amount of investment in terms of land, money and man power [2]. moreover, site selection for large scale pv power plant has a heavy impact, among other factors, on attracting both public and private investments and the overall sustainability of the system [1]. in response to these factors, there is need for a careful and thorough evaluation of potential sites for implementation in order to deliver both social and economic benefits to potential power consumers, as well as boost investment from the public and private sectors [1]. selection of a suitable site is based on a set of criteria mainly depending on the local conditions of its surrounding environment, availability of solar irradiation within years and even days, as well as some socio-economic criteria such as landmass, the proximity of the selected site to power transmission lines or converting stations and the proximity to main roads or populated areas. there are published works on optimal site selection for pv plants. some of the notable works that suggested methodologies for selection of optimal site for different kinds of renewable energy systems includes [3, 4, 5]. the potential for wind farm in india was reported in [6] whereas; in [7] the economic potential of different renewable technologies in karnataka was reported. also, solar photovoltaic potential and capacity of plant in patiala was reported in [8]. detailed work on site selection methodology for large scale pv power plant was reported in [9]. particularly, khan and rathiin [9] presented a decision and methodology to locate potential sites for large-scale solar pv (spv) plants focusing on various factors which they classified as “analysis criteria” and “exclusion criteria”. the criteria such as availability of empty land, availability of adequate solar radiation, distance from major roads and distance from existing transmission lines etc. are considered as analysis criteria [3]. variations of local climate, module soiling, topography of site etc. are exclusion criteria [9]. another study in kenya presented a methodology for optimal site selection for pv plant [1]. the study in [1] adopted yet a different approach for classifying and using its criteria for the selection of optimal site for large scaled pv power plant. in all, most of the published methods for determining the optimal pv plant site are quite complex and the data used are in most cases not readily available, especial in developing countries like nigeria [10]. in this paper, the focus is to develop and employ a simple optimal pv plant site selection method that is based on readily available data and which is easy to apply to any location. furthermore, the application of the model is demonstrated by employing it to identify optimum sites for lspvp plants in imo state. to achieve this objective, the solar energy potential and eventually, the unit energy cost for a hypothetical pv power plant in the various local government areas in imo state is used. the suitability of the various lgas is presented in a sorted list of increasing unit cost of pv generated energy. the optimal site is selected as the site with the lowest unit cost of pv generated energy. pvsyst software is used to conduct the economic analysis and unit cost calculation. 68 2 methodology normally, in site selection for large scale pv power plant, the first step is review of the site selection parameters and to determine if they are applicable to the sites under assessment [1]. knowledge on applicability of parameters can be gained through interviews of key area informants, observation, and literature reviews. in this paper, the following three key site selection parameters are obtained from the nasa website [11] and the pvsyst simulation software [12]; 1. the monthly and daily average global solar irradiation on horizontal plane (kwh/m²) 2. the available energy (kwh/year ) output from the pv modules per year 3. the unit cost of energy computed from the annual energy output. the two additional parameters considered for the site selection are: 1. population 2. land mass (km2) population density is computed from the data on population and landmass for each of the site considered. the data on the two additional parameters for large scale pv power plant site selection are obtained from the publication by the nation population commission (npc) of nigeria [13, 14]. the data on the first three parameters are obtained as follows: � 22-years average yearly, monthly, or daily solar radiation data, specifically, average hourly global irradiation on horizontal plane (kwh/m²) and air temperature are downloaded from nasa website for each of the 10 selected lgas in imo state studied. particularly, the data are obtained from the nasa langley research centre atmospheric science data centre surface meteorological and solar energy (sse) web portal supported by the nasa larc power project [11]. � with the nasa solar radiation data and a common or uniform available pv area (apv) of 100m2, the pvsyst [12] is used to simulate and hence determine the solar energy potential of each of the 10 selected lgas in imo state along with the corresponding unit cost of the energy. the yearly solar electric power generation potential of any given area can be estimated as follows [4, 9]: gp = sr ×ca × af × η (1) where, gp = electric power generation potential per year (kwh/day) sr = annual solar radiation received per unit horizontal area (kwh/m2/day) ca = calculated total area of suitable land (m2) af = the area factor, indicates what fraction of the calculated areas can be covered by solar panels η = pv system efficiency alternatively, the effective available area for pv installation can be represented as apv, where apv = ca x af (2) hence gp = sr ×apv × η (3) 69 after identifying the site selection parameters, weighting factors are assigned to each parameter based on how much influence the parameter has on the suitability of a site for large scale pv power plant [1]. let iw be the weight of parameter i where i=1, 2, 3, 4, 5. table 1: the weighting factor for each of the five pv site selection parameters unit cost of energy available energy (kwh) global irradiation on horizontal plane (kwh/m²) population density population weighing factor 5 4 3 2 1 also, each of the 10 locations is assigned rank for each of the 5 site selection parameters. let ijl , be the ranking of location j for parameter i where i=1, 2, 3, 4, 5 and j=1, 2, 3,…, 10. then, the pv site suitability factor (pvssf) for location j is given as; ( )( )( )∑ = = = 5 1 , i i iijj wlpvssf (4) the optimal location for the large scale pv power plant is therefore given as optimall where optimall =maximum ( jpvssf ) for j = 1, 2, 3,…, 10. (5) 3 results and discussion the values for each of the site selection parameter for the 10 selected local government areas (lgas) in imo state are shown in table 2. column 2 of table 2 shows the global irradiation on horizontal plane (kwh/m²) obtained from nasa website [11]. column 3 and column 4 of table 2 contain the unit cost of energy (naira/kwh) and available energy (kwh) respectively. the unit cost of energy (naira/kwh) and available energy (kwh) are obtained from pvsyst simulation of the pv potential and economic analysis of pv system for each of the selected 10 lgas in imo state. column 5 and column 6 contain data on population density and population respectively. the data on population density and population are obtained from the published bulletin of nation population commission (npc) of nigeria [13, 14]. table 3 shows the ranking of each lga for each of the five parameters listed in table 2 as well as the computed site suitability ranking factor (ssrf) and site suitability rank (ssr) for each of the 10 lgas. 70 table 2: the values for each of the site selection parameters for the 10 lgas in imo state global irradiation on horizontal plane (kwh/m²) unit cost of energy (naira /kwh) available energy (kwh) population density population dikenafai 1717.2 106 12256 812.4668 156,161 ideato north 1650.2 108 11692 812.4668 156,161 ihiagwa 1558.4 110 11066 342.4596 101,754 isinweke 1717.2 105 12328 1137.508 119,419 nekede 1558.4 111 10906 881.6876 176,334 oguta 1535.3 114 10591 291.6546 142,340 okigwe 1717.2 104 12422 409.9797 132,701 owerri 1535.3 112 10692 2143.356 125,337 umuaka 1535.3 113 10653 1692.679 143,485 umuakpu 1717.2 105 12418 203.6657 182,891 site suitability is directly proportional to global irradiation on horizontal plane (kwh/m²). with respect to global irradiation on horizontal plane (kwh/m²), fig. 1 shows that umuakpu has the highest value and hence is the most preferred site if only global irradiation on horizontal plane (kwh/m²) is considered. on the other hand, oguta is the worst location with respect to global irradiation on horizontal plane (kwh/m²). table 3: the site suitability factor and suitability ranking computation for the 10 lgas in imo state global irradiation on horizontal plane (kwh/m²) ( iw = 3) unit cost of energy ( iw =5) available energy (kwh) ( iw = 4) populati on density ( iw = 2) population ( iw =1) pv site suitability factor (pvssf) pv site suitability rank (pvssr) dikenafai 7 7 7 6 8 105 3 ideato north 6 6 6 5 7 90 5 ihiagwa 4 5 5 8 1 75 6 isinweke 8 8 8 3 2 105 4 nekede 5 4 4 4 9 69 7 oguta 1 1 1 9 5 36 10 okigwe 9 10 10 7 4 136 2 owerri 2 3 3 1 3 39 8 umuaka 3 2 2 2 6 38 9 umuakpu 10 9 9 10 10 142 1 71 figure 1: site ranking based on global irradiation on horizontal plane (kwh/m2) with respect to population density, fig. 2 shows that umuakpu has the lowest value and hence is the most preferred site if only population density is considered. on the other hand, owerri with the highest population density is the worst location with respect to population density. figure 2: site ranking based on population density actually, site suitability is inversely proportional to population density, consequently, in table 2, owerri has the highest population density, and so, owerri is the most unsuitable because it will require evacuation of more people and payment of more compensation if the large scale pv power plant is to be sited in owerri. umuakpu, on the other hand, has the lowest population density. figure 3: site ranking based on population density 72 site suitability is directly proportional to population, the higher the population, the higher the number of potential customers for the pv power plant. with respect to population, table 2 shows that umuakpu has the highest value and hence in fig. 3 umuakpu is the most preferred site if only population density is considered. on the other hand, ihiagwa is the worst location with respect to population. actually, in table 2, umuakpu has the highest population density. as such it is the most suitable because it will have more customers who will pay for the investment if the large scale pv power plant is to be sited in umuakpu. with respect to potential available yearly energy output from the pv plant, fig. 4 shows that okigwe has the highest value and so it is the most preferred site if only available yearly energy output from the pv plant is considered. on the other hand, oguta is the worst location with respect to available yearly energy output from the pv plant. essentially, site suitability is directly proportional to potential available yearly energy output. figure 4: site ranking based on available energy (kwh) figure 5: site ranking based on uint cost of energy obviously, site suitability is inversely proportional to unit cost of energy, the smaller the unit cost of energy the more suitable the site is for large scaled pv power plant. with respect to unit cost of energy (naira/kwh) from the pv plant, table 2 and fig. 5 show that okigwe has the lowest value and so it is the most preferred site if only unit cost of energy (naira/kwh) from the pv plant is considered. on the other hand, oguta is the worst location with respect to unit cost of energy (naira/kwh) 73 from the pv plant. when the five optimal site selection parameters are simultaneously considered using eq. (4) and eq. (5), a single value is obtained for ranking the different sites. table 3 and fig. 6 show the collective pv site suitability factor (pvssf) which is computed from the five site selection parameters. with respect to pvssf, table 3 and fig. 6 show that umuakpu has the highest value and so it is the most preferred site if all the five site selection parameters are simultaneously considered. on the other hand, oguta is the worst location if all the five site selection parameters are simultaneously considered. figure 7 shows the actual ranking of the 10 lgas based on the pvssf. again, umuakpu is ranked number 1 based on the pvssf in fig. 6 whereas oguta is ranked number 10. in all, umuakpu is the most suitable site for large scaled pv power plant in imo state. figure 6: pv site suitability factor (pvssf) figure 7: pv site suitability ranking (pvssr) 4 conclusion and recommendations 4.1 conclusion in this paper, comparative assessment of the various parameters that are essential for the selection of optimal location for siting large scale photovoltaic electric power generation plant in imo state is carried out. in order to determine the optimal location for siting large scale pv power plant in imo state, 10 local government areas (lgas) in imo are selected out of the 27 lgas in imo state. also, five key parameters are used for the ranking of the selected lgas for their suitability for large 74 scale pv power plant. the five parameters are: 1. global irradiation on horizontal plane (kwh/m²) 2. available energy (kwh) 3. yearly unit cost of energy 4. population 5. land mass (in ���) in all, umuapu has the highest pv site suitability factor (pvssf) of 142 while oguta has the least with 39. consequently, the optimal site for large scaled pv power plant among the selected lgas in imo state is umuapu. accordingly, umuapu has the pv site suitability rank (pvssr) of one (1) while oguta has the poorest pvssr value of 10. 4.2 recommendations the study so far covered only 10 lgas in imo state. further works are required to conduct the study for the whole lgas in imo state. also, the data used for the study are obtained from nasa sse website. it is always recommended that locally measured data should be used. references [1] murunga j. (2014) where shall we put it? solar mini-grid site selection handbook, published by deutsche gesellschaft für internationale zusammenarbeit (giz) gmbh, 2014. [2] khan, g., & rathi, s. (2014) optimal site selection for solar pv power plant in an indian state using geographical information system (gis). international journal of emerging engineering research and technology volume 2, issue 7, october 2014, 260-266. [3] adel gastli, yassine charabi (2011) pv site suitability analysis using gis-based spatial fuzzy multi-criteria evaluation, renewable energy, volume 36, issue 9, september 2011, 2554–2561. [4] gastli, a., charabi, y. (2010) solar electricity prospects in oman using gis based solar radiation maps, renewable and sustainable energy reviews, vol. 14, 790–797, 2010. [5] m. a. herrera-seara, f. aznar dols, m. zamorano, and e. alameda-hernández (2010) optimal location of a biomass power plant in the province of granada analyzed by multi-criteria evaluation using appropriate geographic information system according to the analytic hierarchy process, 2010, international conference on renewable energies and power quality (icrepq‟10). [6] hossain, jami, vinay sinha, and v. v. n. kishore (2011) a gis based assessment of potential for windfarms in india. renewable energy 36.12 (2011): 3257-3267. [7] mahmmud f., watson s., woods j., halliday j & hossain j. (1996) the economic potential for renewable energy sources in karnataka, in: proceedings of eurosun, 96 conference, freiburg, germany, september 1996, 1370. 75 [8] souvik ganguli, jasvir singh (2010) estimating the solar photovoltaic generation potential and possible plant capacity in patiala, 2010, international journal of applied engineering research, dindigul. volume 1, no 2, 2010. [9] khan, g., & rathi, s. (2014) optimal site selection for solar pv power plant in an indian state using geographical information system (gis). international journal of emerging engineering research and technology volume 2, issue 7, october 2014, pp 260-266. [10] miller, a., lumby, b. (2012) utility scale solar power plants: a guide for developers and investors. guidilines book written for ifc. world bank group, new delhi, india. [11] nasa surface meteorology and solar energy-location. atmospheric science data center. twenty two years average data of nasa sse model (1983–2005). http://www.eosweb.laec.nasa.gov. [12] mermoud, a. (2012) pvsyst: software for the study and simulation of photovoltaic systems. ise, university of geneva, www. pvsyst. com. [13] national population commission. (1991) population census of the federal republic of nigeria, analytic report at the national level. 1991. [14] national population commission. (2007) results of the 2006 population census. national population commission, abuja, nigeria. 2007. copyright © 2016 jacob iniobong joseph, umoren mfonobong anthony, and idorenyin markson. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 17021-chibuzo_ _ bulge--method i__determination of the minimum antenna mast heights with nonzero path inclination (1) 209 mathematical and software engineering, vol. 3, no. 2 (2017), 209-216. varεpsilon ltd, varepsilon.com determination of the minimum antenna mast height for microwave links with nonzero path inclination: method i swinton c. nwokonko1, vital k. onwuzuruike1, and chibuzo promise nkwocha2* *corresponding author chibuzo promise nkwocha: chibuzorpromise525@yahoo.com 1department of electrical/electronic engineering, imo state university, owerri, nigeria. 2department of chemical engineering, federal university of technology, owerri (futo), owerri, nigeria abstract in this paper, a method that can be used to determine the minimum antenna mast height when the path inclination is not equal to zero is presented. in this method, none of the antenna height is known. in this case, the two antenna mast heights are determined from the knowledge of the location and height of the maximum obstruction in the communication link path. the mathematical models and the algorithm pertaining to the method are presented in this paper along with sample numerical example using path profile data for a line of sight 4 ghz microwave communication link with path length of 38887.6 m. from the results, the receiver antenna height is 176.07 m and transmitter antenna height is 127.09 m. with respective to the elevation height, this gives the transmitter antenna mast height of 37.25m and the receiver antenna mast height of 127.2 m. in effect, the transmitter antenna is lower than the receiver antenna. the transmitter is also below the maximum height of the tip of the obstruction which is 144.21 m high. the path inclination is 1.26. the ideas presented in this study are useful for installation of entirely new line of sight microwave communication link. keywords: microwave communication link; line of sight, earth bulge; elevation profile; path inclination; antenna mast height; elevation height 1. introduction line of sight (los) communication links are very useful for terrestrial and satellite communications [1-6]. particularly, during the planning stage of terrestrial point to point los communication link, it is important to determine the minimum antenna heights that will ensure clear line of sight between the transmitter antenna and the receiver antenna [7-11]. from the antenna heights, the required antenna mast heights can be established. the method to be used in determining the minimum antenna heights depends on the available data. superficially, when the installation is an extension of existing los link, in that case, the height of one of the antennas is known, the method to be employed will take into consideration the know height of one of the antennas. this constraint helps the designer to narrow the possible values that can be obtained for the minimum height of the second antenna. 210 however, when the installation is a fresh los link, no antenna height is specified, the method to be employed must be able to use the limited information on the obstruction heights and their locations to determine the possible minimum antenna heights for the link. in this paper, this second case is addressed, a situation where both antenna heights are to be determined based on the elevation profile , earth bulge and obstruction dataset for the link. particularly, the method utilizes the location and height of the maximum obstruction in the signal path to determine the minimum antenna mast heights. sample microwave link is used to demonstrate the applicability of the method. 2. theoretical background 2.1 fresnel geometry parameters for line of sight (los) link elevation profile : let n� be the number of elevation points taken from the transmitter location to the receiver location . also, let �� (�) be the elevation at point x, where x = 1,2,3,…, ��; let ��(�) be the distance of location x from the transmitter ; let ��(�) be the distance of location x from the receiver, where x = 1,2,3,…, �� and let � be the distance (in meters) between the transmitter and the receiver. then, � = ��(�) + ��(�) (1) ��(�) = � − ��(�) (2) h��� is the elevation at the transmitter location where x = 0, hence, h��� = h��(�) h��� is the elevation at the receiver location where x = n�, hence, h��� = h��(��) earth bulge :earth bulge is the height an obstruction is raised higher in elevation (into the path) owing to earth curvature. earth bulge is given as [13]; ���(�) = ���( )!��"( )!#$.%&∗( (5) where ���(�) is the height (in meters) of the earth bulge at location x between the transmitter and the receiver; ���� is the height (in meters) of the earth bulge at the transmitter mast location; ���� is the height (in meters) of the earth bulge at the receiver mast location; ��(�) and ��(�) are as defined earlier. radius of the nth fresnel : the radius of the nth fresnel zone ()(*,,)) at location x is given as [14 – 18]; )(*,,) = -./ʎ���( ) !��"( ) !1���( ) 2 �"( ) ! ; for n =1,2,3,… and ��(�) >> )(*,,) 4�� ��(�) >>)(*,,) (8) λ in metres is given as; ʎ = 56 (9) obstruction height: let h89(:) be the height of the obstruction at point x, where h89(:) is measured from the ground level (where the ground level is at the top of the elevation point at point x) and it does not include the elevation and earth bulge at point x. the elevation point is measured from the sea level. let h89(:) be the overall height of the obstruction at point x, where h89(:) is measured from the reference line. h89(:) includes the elevation at point x and also include the earth budge at point x, then ; h89(:) = h89(:) + h�9(:) + h��(:) (10) 211 percentage clearance: let p<(�) be the percentage clearance allowed for the fresnel zone n, given in % where p<(�) positive if the obstacle tip is below the line of sight and p<(�)is negative if the obstacle tip is above the line of sight. it must be noted that p<(�) = 0 % when the tip of the obstruction is on the los. let x@ab be the distance from the transmitter to the point at which the tip of the obstruction attains its maximum height, h@ab and let h@ab be the maximum height attained by the tip of the obstruction at location x@ab and at distance, d@ab from the transmitter. then, h@ab = maximum jh�9(:) + h��(:) + h89(:) + k/lm(n) #�� 1-�/ʎ�op(q) !�or(q) !1�op(q) 2 or(q) ! st (11) 2.2 development of the mathematical models for determining the transmitter and receiver antenna mast heights this paper resents a method of determining the transmitter and receiver antenna mast when the transmitter and receiver antenna heights are not. in this case, the path inclination is not equal to zero. particularly, for the method titled method i, analysis is based on the knowledge of the location (x@ab ) and height (h@ab) of the maximum obstruction in the signal path. in this analysis, a communication link (figure 1) with the transmitter (t) and the receiver (r) at distance d apart is considered. it is assumed that the higher antenna is the receiver antenna (h� ≤ h� ) but the actual heights of both the transmitter and receiver are not. if however, h� > h�, then the notation r for transmitter and t for receiver will have to be swapped, whereby the transmitter becomes the receiver and vice versa. figure 1 model for determining the antenna mast height when the path inclination is not equal to zero v w �xyz � �[�\(�$) ���$ ℎ^_`(�#) ℎ�a(�#) bc − bdef ��xyz �� �� ℎ5 \(�#) �[�(�#) ���# g h i j ���$ ���# k l ℎ�a(�#) m �[�(�$) n 212 the path length is d . the locations between the transmitter and receiver are represented as x where x = 0,1,2,3,…,ne. distance ��� are measure from the transmitter and distance ��� measured from the receiver. at the transmitter, x = 0 , ��(�) = 0 and x = ne , ��(.�) = d . ��� = d ��� (12) let ��a� bee defined as ��a� = ��xyz ��� let �[�\(�) be defined as the actual obstruction height at location x, where �[�\(�) = �� − �ℎ[�(�) + ���(�) + �� (�)! (13) let �[�(�) be defined as the expected line of sight obstruction height at location x. simply, �[�(�) is the maximum obstruction height that can be accommodated at location x without violating the los percentage clearance specified for the link. if �[�\(�) > �[�(�) , then the los percentage clearance specified for the link will be violated. the equation for determining �[�(�) is derived by considering two locations x1 and x2 at point a and b respectively in figure 1. by applying similar triangle relationships on triangle awg and triangle adr then, (orpoqrs)p�oqrspotu(qv)!op opqv = oqrspotu(qv)opqrspopqv (14) orpotu(qv) �" v = oqrspotu(qv)�"w v (15) h� = h89(:#) + x/ �" v�"w v1 �h@ab − h89(:#)!y (16) also, by applying similar triangle relationships on triangle acr and triangle adr then, orpotu(qz) �" z = orpotu(qv) �" v (17) h89(:$) = h� − x/�" z �" v1�h� − h89(:#)!y (18) �[�(�$) is the maximum obstruction height that can be accommodated at location x2 without violating the los percentage clearance specified for the link. if �[�\(�$) > �[�(�$) , then the los percentage clearance specified for the link will be violated at location x2. in order to satisfy the line of sight clearance requirement at point x the following condition must be met: �[�(�$) ≤ �[�\(�$) for all x = 0,1,2,3…��. (19) initially, {1 = { = 0 , and �[�(�#) = �[�(�) = �[�\(�) . also, at x1 = x = 0 , �� = 0 and ��� = � − 0 = �. in essence, with �[�(�#) = �[�(�) = �[�\(�) , the line of sight clearance requirement is satisfied at x1 = x = 0. then, �[�(�$) is computed for x2 = x1+1 , x1+2, x1+3,…, ��. at each point of x2, the line of sight clearance requirement conduction �[�(�$) ≤ �[�\(�$) is evaluated. if the condition is not satisfied, then , the current x2 becomes the x1 (that is, x1 = x2) and the current �[�(�#) becomes �[�\(�$) (that is, �[�(�#) = �[�\(�$) ). next, �[�(�$) is computed for x2 = x1+1 , x1+2, x1+3,…, ��. when all the points from x= 0 to x = �� are considered, the transmitter height is adjusted based on the last value of �[�(�#) which is at a distance of ���# from the receiver. the adjustment is done as follows; �[�(�) = / �"|�" v1�[�(�#) (20) �� = �� − �[�(�) (21) the height (in meters) of the transmitter antenna mast measured from the ground is given as h�(}~��) where; 213 h�(}~��)= �� �� � = �� − �[�(�) − �� � (22) where �� � is the elevation at the transmitter. the height (in meters) of the receiver antenna mast measured from the ground is denoted as h�(}~��) ; h�(}~��)= �� �� � (23) 2.3 the procedure for determining the minimum transmitter and receiver antenna mast height when the path inclination is nonzero the following algorithm states the procedure for determining the minimum transmitter and receiver antenna mast height when the path inclination is nonzero. step 1: ����� �� �,�� �,ℎ[�(�),�,�� step : �� = �� �; � =�� �; ���(�) = 0 step 2: �[�(�) =�[�\(�)=ℎ[�(�) + ℎ� (�) step 3: ���= � step 4: x1 = 0 step : input ���#, �xyz, �xyz step : ���# = � − ��# step : �a�# = �xyz − ��# step : h� = /�" v �w v1��xyz − h89(:#)! step 5: for x2 = x1 to �� increment 1 step : input ���$, ℎ[�(�$) , ���(�$) ,�� (�$) step : ���$ = � − ��$ step 6: h89(:$) = /�" z �" v1h89(:#) step 7: h89~(:$) = �� − �[�(�$ ) = �� − �ℎ[�(�$) + ���(�$) + �� (�$)! step 8: if (h89(:$) < h89~(:$) ) then step 9: h89(:#) = h89~(:$) step 10: x1 = x2 step : �a�# = �xyz − ��# step : ���# = � − ��# step : h� = /�" v �w v1��xyz − h89(:#)! step 11: endif step 12: next x2 step 13: h89(�) = / �"|�" v1�[�(�#) step 14: �� = h89(�) step 15: h�(}~��)= �� �� � = h89(�) − �� � step 16: h�(}~��)= �� �� � step 17:end 3. results and discussions the parameters of the microwave link used in the study are; path length = 38887.6 m, frequency = 4 ghz, k-factor = 1.33333 and obstruction height (hob) = 10 m. the specified minimum los percentage clearance with respect to fresnel zone 1 is 60%. the result show that the maximum height of the tip of the obstruction (hmax) is 144.21 m and it occurred at a distance of 14306.98 m from the transmitter. the receiver antenna 214 height is obtained as 176.07 m while the transmitter is 127.09 m high. in table 1, the minimum percentage clearance of 60% with respect to fresnel zone 1 occurred at a distance of 11415.14 m from the transmitter. the radius of the first fresnel zone at that point is 24.59317 m and the los clearance height at that point is -14.76 m which gives the percentage clearance of 60% at that point. the 60% percentage clearance tallies with the 60% clearance specified at the link design stage. table 1 the antenna mast computation result x, elevation point dx, distance (m) hel(x) elevation (m) heb(x) earth bulge (m) hx, los height (m) hlsc(x), los clearance height (m) r1, radius of the first fresnel zone (m) p(x,1 ) , percentage clearance of the first fresnel zone % 1 0 89.8 0 127.1 -27.25 0 #div/0! 24 1750.32 78 3.82 129.3 -37.48 11.19667 334.7813 48 3576.74 96 7.43 131.6 -18.14 15.60713 116.2299 72 5403.17 92.3 10.64 133.9 -20.93 18.67974 112.058 96 7229.59 97 13.46 136.2 -15.73 21.00989 74.87233 120 9056.01 94.4 15.89 138.5 -18.24 22.8261 79.92583 144 10882.44 94.2 17.93 140.8 -18.67 24.24416 77.02571 151 11415.14 98.3 18.45 141.5 -14.76 24.59317 60 168 12708.86 90.5 19.57 143.1 -23.03 25.33102 90.92611 192 14535.28 94 20.82 145.4 -20.58 26.12804 78.76856 216 16361.71 93 21.68 147.7 -22.98 26.66124 86.18608 240 18188.13 92.3 22.15 150 -25.54 26.94627 94.76332 256 19405.74 92.2 22.24 151.5 -27.05 27.00258 100.1825 264 20014.55 89.4 22.22 152.3 -30.68 26.991 113.6627 288 21840.97 30.8 21.9 154.6 -91.87 26.79663 342.8401 312 23667.4 23 21.19 156.9 -102.74 26.35788 389.7966 336 25493.82 29.8 20.09 159.2 -99.3 25.66221 386.9364 360 27320.24 26.8 18.59 161.5 -106.1 24.68791 429.7789 384 29146.67 49.9 16.7 163.8 -87.15 23.4002 372.4393 408 30973.09 20 14.42 166.1 -121.68 21.74348 559.6235 432 32799.51 22.4 11.75 168.4 -124.27 19.62451 633.2387 456 34625.93 18.3 8.68 170.7 -133.71 16.86999 792.6158 480 36452.36 36.7 5.22 173 -121.13 13.08453 925.7446 504 38278.78 29 1.37 175.3 -134.97 6.704158 2013.261 512 38887.59 48.9 0 176.1 -117.16 0 #div/0! also, the transmitter antenna mast height is 37.25m while the receiver antenna mast height is 127.2 m. this gives receiver antenna height of 176.07 m and transmitter antenna height of 127.09 m. in effect, the transmitter antenna is lower than the receiver antenna. the transmitter is also below the maximum height of the tip of the obstruction which is 144.21 m high. the path inclination is | orpop|o = | #%�.�% p#$%.��|��.��%&� = 1.26, where d is in km and h� and h� are in m. 4. conclusion in this paper, a first method that can be used to determine the minimum antenna mast height when the path inclination is not equal to zero is presented. in the second 215 method,(not presented here), one of the antenna height is known. in this first method, none of the antenna height is known. in this case, the two antenna mast heights are determined from the knowledge of the location and height of the maximum obstruction in the communication link path. the mathematical models and the algorithm pertaining to the method are presented in this paper along with sample numerical example using path profile data for a line of sight microwave communication link. references [1] kerczewski, r. j., wilson, j. d., & bishop, w. d. (2016, march). uas cnpc satellite link performance—sharing spectrum with terrestrial systems. in aerospace conference, 2016 ieee (pp. 1-9). [2] kerczewski, r. j., wilson, j. d., & bishop, w. d. (2015, april). parameter impact on sharing studies between uas cnpc satellite transmitters and terrestrial systems. in 2015 integrated communication, navigation and surveillance conference (icns) (pp. x2-1). ieee. [3] thompson, p., & evans, b. (2015, june). analysis of interference between terrestrial and satellite systems in the band 17.7 to 19.7 ghz. in 2015 ieee international conference on communication workshop (iccw) (pp. 1669-1674). [4] al mahmud, m. r. (2009). analysis and planning microwave link to established efficient wireless communications (doctoral dissertation, blekinge institute of technology). [5] wang, g., lee, b. s., & ahn, j. y. 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(2016). derive a methodology for the design of a broadband (over 1 gbps) microwave backhaul link in e-band. http://hdl.handle.net/10902/8446. [11] osman, m. a. a. (2015). a compartive study of microwave versus wimax link (doctoral dissertation, sudan university of science and technology). [12] dalbakk, l. e. (2014). antenna system for tracking of unmanned aerial vehicle. http://hdl.handle.net/11250/2371136. [13] ma, y., & wang, y. (2012, november). study of characteristic prediction of radio wave propagation loss on complex irregular terrain of wide-range distance. in environmental electromagnetics (ceem), 2012 6th asia-pacific conference on (pp. 67-71). [14] guo, y. j., & barton, s. k. (2013). fresnel zone antennas. springer science & business media. [15] kapusuz, k. y., & kara, a. (2014). determination of scattering center of multipath signals using geometric optics and fresnel zone concepts.engineering 216 science and technology, an international journal, 17(2), 50-57. [16] freeman, r. l. (2006). radio system design for telecommunication (vol. 98). john wiley & sons. [17] ratnayake, n. l., ziri-castro, k., suzuki, h., & jayalath, d. (2011, january). deterministic diffraction loss modelling for novel broadband communication in rural environments. in communications theory workshop (ausctw), 2011 australian (pp. 49-54). [18] mazar, h. (1991, march). los radio links, clearance above tall buildings. inelectrical and electronics engineers in israel, 1991. proceedings., 17th convention of (pp. 145-148). copyright © 2017 swinton c. nwokonko, vital k. onwuzuruike, chibuzo promise nkwocha. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. microsoft word 17013-modelling and forecasting of residential electricity consumption.docx 139 mathematical and software engineering, vol. 3, no. 1 (2017), 139-148. varεpsilon ltd, varepsilon.com modelling of nigerian residential electricity consumption using multiple regression model with one period lagged dependent variable runcie amlabu 1 , nseobong. i. okpura 2 , anthony mfonobong umoren 3 corresponding author: umoren_m.anthony@yahoo.com 1,2,3 department of electrical/electronic and computer engineering, university of uyo, akwa ibom, nigeria abstract this paper presents the modelling and forecasting of residential electricity consumption in nigeria based on nine years (2006 and 2014) data and multiple regression model with one period lagged dependent variable. a socio economic parameter (population), and climatic parameter (annual average temperature) are used as explanatory variables in modelling the and forecasting of residential electricity consumption in nigeria. the results of the multiple regression analysis applied to the data arrived at the model with the least sum of square error as ��� = −36.2458 + 9.7202�� − 12.0265�� + 0.1540���� , where t is the year; ��� is the predicted residential electricity demand in mw/h; �� is the annual population in millions; �� is the average annual temperature in °c and ���� is the residential electricity demand in the year before year t. the error analysis gave coefficient of determinant of 0.913, adjusted coefficient of determination of 0.86 and root mean square error of 61.86. the forecast results gave 5.11% annual average increase in the electric power demand of the residential sector with respect to the 2014 electricity consumption data. such results presented in this paper are useful for effective planning of power supply to the residential sector in nigeria. keywords: multiple regression; regression analysis; error analysis; least square method; sum of square error; forecast; residential electricity demand 1. introduction across the globe, electricity is one of the most dominant forms of energy. some of the most common advantages of electricity as a future carrier of energy include its cleanliness, versatility, accessibility and simplicity in distribution. the flexibility of electricity as an energy carrier has contributed to technological innovation and increased industrial productivity in many countries [1]. these advantages have contributed to the increased share of electricity in the total energy consumption in many countries. accordingly, in advanced economies, the ideal choice for the carrier of energy is electricity. furthermore, electricity power supply has been identified as the most important commodity for the development of a nation [2,3,4,5,6]. people become easily empowered to work and develop themselves when there is electricity power supply. this 140 development takes place from domestic level to industrial level and can also be transferred from small to medium and to large scale level. among other things, electricity consumption demand depends on the population and level of industrialization of a country [2,7,8,9,10,11,12]. the increased use of electricity from residential homes to industry has contributed to the increasing demand in electricity consumption worldwide. the growth in demand is even higher in developing countries as the robust economic growth boosts demand for new electrical appliances. although the rate of growth in electricity consumption may be slower in the industrialized countries, their dependence on electricity may even be higher than the developing countries [12,13,14]. the high demand due to the heavy dependence on electricity requires planning of resources of electricity well in advance to ensure a continuous supply of electricity in the future. in the power industry, proper planning of electric power system requires among other things, modelling of the electric power demand [15,16,17,18]. in this paper, the focus is on modelling of the residential electric power demand in nigeria. this has become necessary in view of the perennial shortfall in power supply across nigeria and the sweeping policy changes the government is making to address the challenges in the power sector [3,19,20]. particularly, multiple regression model with one period lagged dependent variable is considered in the paper for modelling the residential electricity consumption in nigeria [21,22]. the study is based on nine years (2006 and 2014) data on residential electric power demand in nigeria. a socio-economic variable is used as parameters along with climatic variable for the modelling of the residential electricity consumption in nigeria. the socio economic variable is population while the climatic variable is average annual temperature. finally, performance evaluation of the selected model is conducted using statistical measures such as the root mean square error(rmse), coefficient of determination ( �� ) and adjusted coefficient of determination (�����). 2. methodology 2.1. sources of data nine (9) years (2006-2014) data on yearly average residential electricity consumption expressed in megawatt hour (mw/h) are obtained from central bank of nigeria statistical bulletin [23] while data on yearly average temperature (in 0c) and population are obtained from the bulletin of the national bureau of statistics [24]. 2.2. description of the models for the predictor and the response variables multiple regressions with one period lagged of the dependent variable is used to express �� (the yearly average residential electricity consumption) in nigeria as a linear function of population (�� ), temperature (�� ) and ���� (which is the electricity consumption with one period lagged of the dependent variable). in the model, �� is defined as follows; �� = �(��,��,����) (1) �� = ! + ��� + ��� + "���� + #� (2) where �� is the yearly average residential electricity consumption (in mw/h) estimated at 141 time, t; �� is population at time t; �� is temperature at time t; t is time in years; �, � and " are regression coefficients. a regression coefficient in multiple regressions is the slope of the linear relationship between the dependent variable and the part of a dependent variable that is independent of all other independent variables. specifically, �, � and " are the contributions of population (p), temperature (t) and ���� respectively and ! is the intercept; #� is a random error or residuals term. measurement error for the dependent and independent variables, the random nature of human responses and effect of omitted variables are the main sources of the random disturbance [5]. in this study, data for the independent variable, namely, p � and �� are available for the years 2006 to 2014. mathematical expression for each of the independent variables �� and �� are themselves obtained from models applied to the data sets of these variables over time (t). particularly, the population for the years beyond 2014 are projected using the mathematical expression; p � = p ���(1 + �)% (3) where n is the number of years, p ��� is previous year population, p � is the population of the year to be estimated and r is the population growth rate of nigeria which is given as 3.2% according to 2006 population census [4,5]. also, temperature is predicted using simple linear regression model as follows; �� = &! + &�(') (4) where β! and β� are the simple linear regression coefficients and t is time in years. the model parameters β! and β� are estimated using matlab and the following values are obtained; β! = 34.602 and β� = 0.0613 . therefore, �� = 34.602 − 0.0613t (5) where t = time, t= 10,11,…,20. 3. regression analysis for the multiple regression model with one period lagged dependent variable the multiple regression model with one period lagged dependent variable (in eq. 2) can be written in matrix form as; e = x + ε (6) where • n is the number of sampled points • k is the number of predictor variables. in the given model, the predictors are p*,t* and e*��, hence, k = 3 • e = [e�, . . . , e0] is the n × 1 column vector (or n × 1 matrix) of the response variable which is the electricity consumption • x is an n × (k+ 1) design matrix determined by the regression model predictors whereby the values in the first column of the matrix are all 1. • = [ !, . . . , 1] is k × 1 column vector of parameters (or k × 1 matrix of predictor coefficient) • ε = [ε�, . . . , ε%] is an n × 1 column matrix called the error vector or vector of error terms let 3 = [ 3�, . . . , 31] be the vector of least squares estimator or predictor coefficient which give the predicted dependent variable e4 that has the least possible value to sum of the squares error. the regression coefficients or least squares 142 estimator, 3 that minimize the sum of the squared errors for the multiple regression are determined by solving the least squares normal equation given as ; x6x( 3) = x6e (7) then, the least squares estimator β� is given as; 3 = (x6x) �� (78e) (8) let 9� = x6x and 9��� = (x6x) �� and :� = (78e) , the vector of least squares estimators 3 = (x6x) �� (x8e) = ;9���<u� (9) from eq. 2, the error term #� can be expressed as follows #� = �� − ! − ��� − ��� − "���� (10) ε = e x (11) when 3 ( the vector of least squares estimator ) is considered, then ε = e 3 x (12) let e4 be the predicted electricity consumption with least square sum of errors, then; e4 = 3 x (13) ε = e e4 (14) 4. numerical computations, result, and discussion data on the residential electricity consumption, national population and yearly average temperature are given in table 1. table 1. nine (9) years (2006-2014) data on yearly average residential electricity consumption expressed in megawatt hour (mw/h), national population and yearly average temperature (in 0c) n year (t) (p* ) population in millions (t* ) temperature in °c (e* ) residential electricity consumption in mw/h 1 2006 140.43 34.64 894.11 2 2007 145.07 34.55 1151.94 3 2008 149.65 34.69 1165.5 4 2009 154.52 34.19 1104 5 2010 159.62 34.38 1365.5 6 2011 164.73 33.33 1401.01 7 2012 170.16 34.43 1437.43 8 2013 175.78 33.89 1474.81 9 2014 181.05 34.56 1513.15 (source: central bank of nigeria statistical bulletin and the bulletin of the national bureau of statistics) from the given data in table 1, n = 9 and from the model (eq. 2), the predictor variables are ��,�� and ���� , hence, k = 3. then, the 9 x4 design x matrix 143 determined by the regression model predictors is given as; x = a bb bb bc 1 140.43 34.64 34.641 145.07 34.55 1151.941 149.65 34.69 1165.501 154.52 34.19 11041 159.62 34.38 1365.51 164.73 33.33 1401.011 170.16 34.43 1437.431 175.78 33.89 1474.811 181.05 34.56 1513.15d ee ee ef (15) also, e (the column vector of the response variable) is given from table 1 as; e = a bb bb bc 894.111151.941165.511041365.51401.011437.431474.811513.15d ee ee ef (16) let 9� = x6x and 9��� = (x6x) �� , then 9� = g 9 1441.01 308.66 9994.301441.01308.669994.30 232284.01 49402.13 1641430.37 49402.13 10587.21 342089.101641430.37 342089.10 12772293.52h (17) 9��� = g1004.506 −0.3238 −27.69 −0.0038−0.3238−27.69−0.0038 0.0018 0.0023 −0.000044 0.0023 0.788 0.00026−0.000044 0.00026 0.0000018h (18) :� = (x6e) = i ��j!k.lj �mnl��o.ll"ol"jn.lon�"llj�lm.oop (19) 3 = ;9���<u� = i�"n.�ljm o.k�!����.!�nj!.�jl! p (20) from the numerical computations, the regression coefficients that gave the least sum of square error are : αr! = −36.2458 αr� = 9.7202 αr� = −12.0265 αr" = 0.1540 s (21) hence, the residential electricity consumption in nigeria can be effective modelled and hence predicted by the multiple regression model with one period lagged dependent variable given as; 144 �� = −36.2458 + 9.7202�� − 12.0265�� + 0.1540���� + #� (22) along with the regression analysis, the error analysis is also conducted to determine the goodness of fit for each of the two models. the regression goodness of fit are evaluated in terms of coefficient of determination (��) , adjusted coefficient of determination (�����) and root mean square error (rmse). the actual and predicted yearly average residential electricity consumption in nigeria from 2006 to 2014 are as shown in table 2 and figure 1. the results for the error analysis are also presented in table 2. table 2: the actual and model predicted residential electricity consumption (mwh) in nigeria from 2006 to 2014 along with the goodness of fit measures s/n year (et) actual residential electricity consumption (mwh) (êt) model predicted residential electricity consumption (mwh) 1 2006 894.11 912.1684 2 2007 1151.94 1096.002 3 2008 1165.5 1178.536 4 2009 1104 1233.979 5 2010 1365.5 1271.808 6 2011 1401.01 1374.363 7 2012 1437.43 1419.397 8 2013 1474.81 1486.131 9 2014 1513.15 1535.065 goodness of fit measures rmse 58.63386 r� 0.911244 r�uvw 0.857991 from the results in table 1 the coefficient of determination (��) of 0.911244 shows that 91.12% of the variation in residential electricity consumption was accounted for by the multiple regression model with one period lagged of the dependent variable. the root mean square error (rmse) of 58.63386 is achieved by the model with adjusted coefficient of determination(�����) of 0.857991. both �� and ����� are very high which shows good prediction results and that the model is not over fitted. also, from the model in eq. 22 the contribution of population ( αr� = 9.7202) is positive meaning that as population increases, residential electricity consumption also increases. on the other hand, based on the model, as the temperature increases, the residential electricity consumption decreases. 145 figure 1. the actual and predicted yearly average residential electricity consumption in nigeria from 2006 to 2014 furthermore, the result of the nigerian residential electricity consumption forecasted by the multiple regression model with one period lagged of the dependent variable is given in table 3 and figure 2. table 3. forecasted population, temperature and nigerian residential electricity consumption year populatio n (million) temperat ure ( 0 c) forecasted residential electricity consumption (mw/h) percentage increase over the previous year (%) percentage increase over 2014 (the year last with available d ata (%) 2014 181.05 34.56 1513.15 2015 186.84 33.99 1604.108642 6.011211182 6.011211182 2016 192.82 33.93 1676.968372 4.542069539 10.82631411 2017 198.99 33.87 1748.889014 4.288729782 15.57935525 2018 205.36 33.81 1822.609437 4.215271662 20.45133906 2019 211.93 33.74 1898.671472 4.173249269 25.47807369 2020 218.71 33.68 1977.015351 4.126247229 30.65560923 mean 1788.043715 4.55946311 5.109268204 800 900 1000 1100 1200 1300 1400 1500 1600 2006 2007 2008 2009 2010 2011 2012 2013 2014 a ct u al a n d p re d ic te d r es id en ti al e le ct ri ci ty c o n su m p ti o n i n m w /h (m w /h ) year (et) actual (êt) predicted 146 figure 2. forecasted residential electricity consumption (mw/h) the forecasted residential electricity consumption in nigeria shows that there is an annual average of 1788.04 mw/h of electricity consumption by the residential sector in nigeria. the consumption pattern shows 4.31% annual average increase in electricity consumption over the previous year which is equivalent to 4.56% annual average increase in electricity consumption over the year 2014 electricity consumption data. in essence, the authorities responsible for electricity supply to the residential sector can plan for 5.11% annual average increase in the electric power demand of the residential sector with respect to the 2014 electricity consumption data. over the six years period (2014 to 2020) there is a total of 30.66% increase in residential electricity consumption over the year 2014 electricity consumption data. 5. conclusion the paper presented the residential demand for electricity in nigeria, employing annual data over the period 2006 –2014. multiple regression model with one period lagged dependent variable is applied to estimate residential electricity consumption and to forecast medium-term residential demand for electricity. the results of the multiple regression analysis applied to the data arrived at the model with the least sum of square error as ��� = −36.2458 + 9.7202�� − 12.0265�� + 0.1540���� , where t is the year ; ��� is the predicted residential electricity demand in mw/h; �� is the annual population in millions; �� is the average annual temperature in °c and ���� is the residential electricity demand in the year before year t. the error analysis gave high coefficient of determinant, high adjusted coefficient of determinant and reasonably low and acceptable value of root mean square error. in addition, six years ahead forecast showed gave the average annual percentage increment in residential electricity consumption in nigeria. such results presented in this paper are useful for effective planning of power supply to the residential sector in nigeria. references [1] mohamed, e. 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(2000). world energy assessment: energy and the challenge of sustainability. energy and social issues, chapter 2, 39-60. [12] ahuja, d., tatsutani, m. (2009) sustainable energy for developing countries. sapi en. s. surveys and perspectives integrating environment and society, (2.1). [13] dahlman, c. (2007). technology, globalization, and international competitiveness: challenges for developing countries. industrial development for the 21st century, 29-83. [14] krymm, r., lane, j. a., and zheludev, i.s. (1977). future trends in nuclear power. iaea bulletin, twentieth anniversary issue, 19(4), 47-54. [15] beasley, b., & morris, d.f. (2012). modeling the electricity sector: a summary of recent analyses of new epa regulations. resources for the future discussion paper, rff dp 12-52. [16] drouineau, m., mazauric, v., maïzi, n., and assoumou, e. 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(2015). introductory econometrics: a modern approach. nelson education. [23] annual reports-central bank of nigeria, available at: https://www.cbn.gov.ng/documents/annualreports.asp. accessed on 10th july 2015. [24] national bureau of statistics. available at: http://www.nigerianstat.gov.ng/. accessed on 10th july 2015. copyright © 2017 runcie amlabu, nseobong. i. okpura, and anthony mfonobong umoren. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. microsoft word 17017__stev_bulg__--modelling and forecasting of residential electricity consumption using mlr and qrmwi 2 173 mathematical and software engineering, vol. 3, no. 2 (2017), 173-182. varεpsilon ltd, varepsilon.com modelling and forecasting of residential electricity consumption in nigeria using multiple linear regression model and quadratic regression model with interactions isaac a. ezenugu 1 , swinton c. nwokonko 1 , and idorenyin markson 2 1 department of electrical/electronic engineering, imo state university, owerri, nigeria 2 department of mechanical engineering, university of uyo, uyo, nigeria abstract in this paper statistical analysis of residential electricity demand in nigeria is presented. multiple linear regression model and quadratic regression model with interactions are applied to estimate residential electricity consumption and to forecast long-term residential electricity demand in nigeria. population and temperature are used as explanatory variables. the results show the quadratic regression with interaction has rmse of 52.77 and r-square value of 0.9389 which indicates that 93.89% of the variation in residential electricity consumption is explained by the model. on the other hand , the multiple linear regression model has rmse of 69.97 and r-square value of 0.873 which indicates that 87.3% of the variation in residential electricity consumption is explained by the model. essentially, the quadratic regression model with interaction with lower rmse and higher r-square value is selected and then used to forecast the residential electricity demand in nigeria from 2015 to 2029. from the results, the residential electricity consumption in nigeria will reach 6521.09 mw/h in the year 2029. furthermore, the results show that population has a positive sign and it is significant in the short run and in the long run forecasting. on the other hand, the result also revealed insignificant moderately weak relationship between residential electricity consumption and temperature. keywords: electricity; multiple linear regression model; quadratic regression model; regression model with interactions; statistical analysis; forecasting of residential electricity demand 1 introduction over the years , especially since the 1990s, nigerian electricity industry has been bedevilled by so much inefficiency [1-7]. equally, the demand for electricity in nigeria has continued to outstrip its capacity, the end result has been the delivery of poor and shoddy services, evidenced by frequent power failures [8-12]. available studies show 174 that electricity consumption in nigeria has been growing at a very rapid rate over the decades. between 1970-2004, consumption of electricity in the country increased from 752 million kwh to 8576.3 million kwh [1], [13]. given the current trends in population growth, industrialization, urbanization, modernization and income growth, electricity consumption is expected to increase substantially in the coming decades as well. all these require matching supply of infrastructure and public service to ensure sustainability. adequate supply and distribution of electricity constitute a central development issue which cannot be over-emphasized. the continuous electricity supply problems in nigeria has been extensively linked to the inability of energy and urban planners to accurately forecast the effect of the various socio-economic and climatic factors that influence the electricity consumption rate across the various geopolitical regions of the country [1], [14]. this study therefore is aimed at statically analysing the residential electricity consumption pattern in nigerian as well as determines the influence of the socio-economic and climatic parameters on residential electricity consumption. data for the study was collected through national bureau of statistics and cbn annual bulletin. two socio-economic and one climatic. 2 methodology in this paper, modelling of the yearly average residential electricity consumptions in nigeria is done using multiple linear regression model and quadratic regression with interaction model. performance evaluation of the model is also performed using prediction accuracy evaluation measures, particularly, the root mean square error (rmse) and coefficient of determination (r 2 ). data on residential electricity consumption (mw/h), between 2006 -2014 were obtained from central bank of nigeria statistical bulletin [15] while data on temperature ( 0 c) and population were obtained from the bulletin of the national bureau of statistics[16]. 2.1 the multiple linear regression model multiple linear regression model expresses electricity consumption (et) as a linear function of population (p) and temperature (tt) as follows: ( ) ttt tpfec ,= (1) tttt tpe εααα +++= 210 (2) where et is the yearly average residential electricity consumption (in mw/h) estimated at time, t; pt is population at time, t and tt is temperature at time, t. 0 α is the intercept 1 α and 2α are the regression coefficients that are used to quantify the contributions of population (pt) and temperature (tt) respectively. econometric views (eviews) statistical package is used to perform the regression from which the values of the intercept 0 α and the regression coefficients 1 α and 2 α are obtained for the multiple regression model. 175 2.2 the quadratic regression model with interaction terms. the quadratic regression model with interaction terms expresses electricity consumption (et) as a quadratic function of population (pt) and temperature (tt) as follows: tttttttt tptptpe εαααααα ++++++= 5 2 4 2 3210 (4) where et is the yearly average residential electricity consumption (in mw/h) estimated at time, t; pt is population at time, t and tt is temperature at time, t. 0 α is the intercept 1 α , 2α 3α , 4 α and 5α are the regression coefficients. again, econometric views (eviews) statistical package is used to perform the regression from which the values of the intercept 0 α and the regression coefficients 1 α , 2α 3α , 4 α and 5α are obtained for the quadratic regression model with interaction. 2.3 models for the explanatory variables in this study, data for the explanatory variables, namely, pt and tt are available for the years 2006 to 2014. mathematical expression for each of the independent variables pt and tt are themselves obtained from models applied to the data sets of each of the variables over time (t). particularly, the population for the years beyond 2014 are projected using the mathematical expression; n tt rpp )1( 1 += − (5) where n is the number of years, 1−t p is previous year population, t p is the population of the year to be estimated and r is the population growth rate of nigeria which is given as 3.2% according to 2006 population census [17]. also, temperature is predicted using simple linear regression model as follows; taatt 10 += . (6) where β0 and β1 are the simple linear regression coefficients and t is time. the model parameters β0 and β1 are estimated using microsoft excel and the following values are obtained; β0 = 34.602 and β1 = 0.0613 . therefore, tt 0613.0602.34 += . (7) where t = time, t= 10,11,…,20. 2.4 validation and diagnostic criteria 2.4.1 ftest to check the goodness of fit of the model, f test use where : mse msr f = (8) where 1− = p ssr msr (9) p is the number of parameters 176 pn sse mse − = (10) n = number of observation sst (sum of square total) = tttt jee n ee 11 1       − (11) sum of square regression, ssr, can be calculated for each model as follows: ssr (model 1) = ttaa jee n u 11 1       −α (12) ssr (model 2) = ttbb jee n u 11 1       −α (13) ssr (model 3) = ttcc jee n u 11 1       −α (14) 2.4.2 coefficient of determination. the coefficient of determination shows the percentage of the variation in the dependent variable explained by the independent variables. it is given as sst ssr r = 2 (15) 2.4.3 root mean square error (rmse). the square of the sum of square of differences between the predicted and observed value divided by the number of observation: it can be expressed mathematically as: ( )∑ = −= n i tt ee n rme 1 2 ˆ1 (16) 2.4.4 absolute mean error (mae) this is the mean of the absolute deviation of the predicted values from the observed value. n ee ame tt n t ˆ 1 − = ∑ = (17) where, t e and t ê are the observed and predicted residential electricity consumption. also, the error analysis is also conducted to determine the goodness of fit for each of the two models. the results of the analysis with econometric views (eviews) statistical package are then presented. 3 results and discussion from the result in table 1 the multiple linear regression model is given as: ttt tpe 32.3452.1335.290 −+= (18) 177 table 1 the model parameters and goodness of fit measures for the two models regression coefficients values for the model parameters goodness of fit measures multiple linear regression model quadratic regression model with interaction terms multiple linear regression model quadratic regression model with interaction terms α0 290.35 152014.9 α1 13.52 386.57 r 2 (%) 0.873 0.9389 α2 34.32 -10855.92 rmse 69.97 52.77 α3 -0.4 α4 177.38 α5 -7.05 result in table 1 shows that for the multiple linear regression model, population (pt) and temperature accounted for 87.3% of the total variation in residential electricity consumption while the remaining 12.7% was accounted for by other variables not in the model. the contribution of population (�� = 13.52) was found to be positive. this means that as the population increases, residential consumption of electricity also increases. the implication of this result is that as population increases, there is a corresponding increase in the quantity of residential electricity consumption. the actual and predicted electricity consumption for the multiple linear regression model is presented in the table 2. table 2: values of actual and predicted residential electricity consumption based on model 1. again , from the result in table 1, the quadratic regression with interaction is given as: ttttttt tptptpe 05.738.17740.092.1085557.38690.152014 22 −++−+= (19) year actual(mw/h) predicted(mw/h) 2006 894.11 1000.67 2007 1151.94 1066.51 2008 1165.72 1123.65 2009 1104.54 1206.68 2010 1365.50 1269.13 2011 1401.01 1374.28 2012 1437.43 1409.97 2013 1474.81 1504.51 2014 1513.15 1552.79 178 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14 800 1000 1200 1400 1600 1800 actual predicted year r e s id e n ti a l e le c tr ic it y c o n s u m p ti o n (m w /h ) figure1: graph of the actual and predicted residential electricity consumption for the multiple linear regression model. result in table 1 shows that for the quadratic regression with interaction has r-square value of 0.9389 which indicates that 93.89% of the variation in residential electricity consumption was explained by the model (r 2 = 93.89%). the model also reveals that the linear term of population (��=386.57) and the quadratic term for temperature (��= 177.38) have positive contribution to residential electricity consumption. this result indicates that as these variables increases in value, residential electricity consumption also increases. summary results of the actual and predicted residential electricity for the quadratic regression with interaction are as shown in table 3. table 3: values of actual and predicted electricity consumption using for the quadratic regression with interaction year actual(mw/h) predicted(mw/h) 2006 894.11 948.39 2007 1151.94 1045.49 2008 1165.72 1214.45 2009 1104.54 1179.20 2010 1365.50 1317.55 2011 1401.01 1400.75 2012 1437.43 1459.71 2013 1474.81 1480.52 2014 1513.15 1515.73 179 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14 800 1000 1200 1400 1600 actual predicted year r e s id e n ti a l e le c tr ic it y c o n s u m p ti o n (m w /h ) figure 2: graph of the actual and predicted residential electricity consumption for the quadratic regression with interaction. bolded values is the rsquare and least root mean square error table 4 shows performance evaluation of the two competing models. model 2 (the quadratic regression with interaction) gave the highest value of coefficient of determination (r 2) compared with model 1 (the multiple linear regression model). also, model 2 gave the least value of the root mean square error. hence, the quadratic regression with interaction is recommended for forecasting residential electricity consumption. the population for 2015 and 2029 were projected using eq 5, n tt rpp )1( 1 += − , where n= number of years, 1−t p = previous year population, t p = the population of the year to be estimated and r is the population growth rate of nigeria which is given to 3.2% according to 2006 population census. table 4: comparison of the performance of the two models also, the temperature was predicted using eq 6, taat 10 += . the temperature model parameters 0 a and 1 a were estimated using microsoft excel programme which gave 602.34 0 =a , 0613.0 1 =a . hence : t tt ε++= 0613.0602.34 , where t = time, 24,,10 �=t (20) table 5 and figure 3 show the forecasted residential electricity consumption in nigeria models r 2 (%) rmse model 1: for the multiple linear regression model 87.30 69.97 model 2: the quadratic regression with interaction. 93.87 52.77 180 from 2015-2029 using the quadratic regression with interaction. from the results in table 5, the residential electricity consumption in nigeria will reach 6521.09 mw/h in the year 2029. table 5: the forecast values for residential electricity consumption (2015-2029) using the quadratic regression with interaction s/ n year population (million) temp.( 0 c) forecasted residential electricity consumption (mw/h) using the quadratic regression with interaction 1 2015 186.84 33.99 2937.90 2 2016 192.82 33.93 3116.81 3 2017 198.99 33.87 3305.97 4 2018 205.36 33.81 3504.57 5 2019 211.93 33.74 3714.71 6 2020 218.71 33.68 3934.14 7 2021 225.71 33.62 4166.97 8 2022 232.94 33.56 4410.53 9 2023 240.39 33.5 4667.68 10 2024 248.08 33.44 4937.62 11 2025 256.02 33.38 5222.63 12 2026 264.21 33.31 5522.81 13 2027 272.67 33.25 5838.59 14 2028 281.39 33.19 6171.24 15 2029 290.4 33.13 6521.09 20 15 20 16 20 17 20 18 20 19 20 20 20 21 20 22 20 23 20 24 20 25 20 26 20 27 20 28 20 29 0 200 400 600 e population temp year m w /h figure 3: graph of forecasted residential electricity consumption (2015-2029) using the quadratic regression with interaction 181 result in table 6 shows highly positive significant relationship between residential electricity consumption and population (r = 0.932, p< 0.01). the result also reveal insignificant moderately weak relationship between residential electricity consumption and temperature (r = -0.406, p> 0.02). based on this result, the only independent variable found to significantly correlated with residential electricity consumption is population. this result implies that as the population increases, residential consumption of electricity also increases significantly. table 6: correlation matrix between the variables e p t e 1 p 0.932** 1 t -0.406 -0.369 1 e = electricity consumption, p = population, t = temperature 4 conclusion the paper presented statistical analysis of residential demand for electricity in nigeria, employing annual data over the period 2006–2014. multiple linear model and quadratic regression with interactions were applied to estimate residential electricity consumption and to forecast long-term residential demand for electricity. also , population and temperature were used as explanatory variables. the results shows that the quadratic regression model with interaction was more accurate due to the fact that it has the highest coefficient of determinant and the least value of root mean square error as compared to the linear regression model. also, population of demand has a positive sign and it is significant in the short run and in the long run forecasting. the result also revealed insignificant moderately weak relationship between residential electricity consumption and temperature. 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(2013). analysis of the electricity consumption in the south-east geopolitical region of nigeria. journal of energy technologies and policy, 3(1), 20-31. [2] mojeed, m. (2014). the epileptic nature of electricity supply and its consequences on industrial and economic performance in nigeria (error correction modelapproach). global journal of research in engineering, 14(4). [3] awosope, c. a. (2014). nigeria electricity industry: issues, challenges and solutions, covenant university public lecture series. vol. 3, no. 2. [4] alila, p. o., & atieno, r. (2006). agricultural policy in kenya: issues and processes. nairobi: institute of development studies. [5] adenikinju, a. (2008). efficiency of the energy sector and its impact on the competitiveness of the nigerian economy. international association for energy economics, 27-31. [6] agbo, c.o. (2011). a critical evaluation of motor vehicle manufacturing in nigeria. nigerian journal of technology, 30(1), 8-16. 182 [7] orji, j. i. (2005). an assessment of impacts of poverty reduction programmes in nigeria as a development strategy, 1970-2005. unpublished ph. d dissertation, st. clements university, turks and caicos island. [8] sambo, a. s. (2008). matching electricity supply with demand in nigeria. international association of energy economics, 4, 32-36. [9] essien, a. u., & igweonu, e. i. (2014). coal based generation: a solution to nigeria electricity problem. int archive appl sci technol, 5(1), 74-80 [10] ogunleye, e. k. (2016). political economy of nigerian power sector reform (no. unu-wider research paper wp2016-009). world institute for development economic research (unu-wider). [11] oyedepo, s. o. (2012). on energy for sustainable development in nigeria. renewable and sustainable energy reviews, 16(5), 2583-2598. [12] ubani, o. j., umeh, l., & ugwu, l. n. (2013). analysis of the electricity consumption in the south-east geopolitical region of nigeria. journal of energy technologies and policy, 3(1), 20-31. [13] central bank of nigeria statistical bulletin (2006), vol. 20, december 2006. [14] edenhofer, o. (2011). the ipcc special report on renewable energy sources and climate change mitigation. [15] annual reports central bank of nigeria, 2015. [16] national bureau of statistics, 2015. [17] agboola, b.m., & adeyemi, j.k. (2013). projecting enrollment for effective academic staff planning in nigerian universities. educational planning, 21(1). copyright © 2017 isaac a. ezenugu, swinton c. nwokonko, and idorenyin markson. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 17022-chibuzo_ _bulg__ prom_parametric analysis of isolated doubled edged hill diffraction (1) 217 mathematical and software engineering, vol. 3, no. 2 (2017), 217-225. varεpsilon ltd, varepsilon.com parametric analysis of isolated doubled edged hill diffraction loss based on rounded edge diffraction loss method and different radius of curvature methods mfonobong charles uko1, uduak etim udoka1, and chibuzo promise nkwocha2* *corresponding author: chibuzorpromise525@yahoo.com 1department of electrical/electronic and computer engineering, university of uyo, uyo, nigeria 2department of chemical engineering federal university of technology, owerri (futo), owerri, nigeria abstract in this paper, parametric analysis of isolated doubled edged hill diffraction loss based on rounded edge diffraction loss method is presented. particularly, the variation of the diffraction loss due to changes in frequency and radius of curvature of the rounded edge of isolated doubled edged hill obstruction are studied. also, the itu-r p.526-13 rounded edge diffraction method is used to compute the diffraction loss. however, the radius of curvature is computed using two approaches, namely, the itu-r p.526-13 method and the occultation distance based method. the results show that the rounded edge diffraction computed based on the itu-r p.526-13 radius of curvature method is much higher than the one computed with the occultation distance based radius of curvature approach. at frequency of 1 ghz, the percentage difference in diffraction loss is about 29 % and the difference increases with frequency to as high as 74.5 % at 36 ghz. similarly, the itu-r p.526-13 radius of curvature is extremely higher than the occultation distance based radius of curvature. at frequency of 1 ghz, the percentage difference in radius of curvature is about 218 % and the difference increases with frequency to as high as 395 % at 36 ghz. in view of the results, the itu-r p.526-13 radius of curvature method should be reviewed to ascertain the specific conditions it can be employed. keywords: radius of curvature; rounded edge obstruction; itu 526-13 method; occultation distance; double edged hilltop; single edged hilltop; fresnel zone; radius of fresnel zone. 1. introduction diffraction loss caused by obstruction is one of the components of path losses considered in the design of wireless network [1-9]. particularly, in line-of-sight communication links it is required that at least 60% clearance be maintained with respect to the first fresnel zone [10-14]. as such, experts have developed different methods for the determination of the diffraction caused by different kinds of obstruction. in most cases, isolated obstructions are modeled as knife edge obstruction [15-19]. however in reality , obstructions are much more complex than the knife edge obstruction model. besides, the knife edge model tends to under estimate the diffraction 218 loss some cases. consequently, the rounded edge diffraction model was introduced by expert to account for extra diffraction loss that real obstructions present beyond the values obtained through the knife edge model [20-21]. in order to determine the diffraction loss due to rounded edge, the radius of curvature or the rounded edge is first determined. accordingly, the international telecommunication union (itu) has developed the itu-r p.526-13 method for computing the radius of curvature for rounded edge diffraction loss computation [22]. in the itu-r p.526-13 method the radius of the first fresnel zone is used to determine the portion of the obstruction profile that will be used in the determination of the radius of curvature [22-25]. consequently, for a given obstruction, with the itu-r p.526-13 method the radius of curvature varies with frequency since the radius of the fresnel zone is a function of frequency. however, with another method that is based on the occultation distance [26-27], the radius of curvature does not vary with frequency. generally, the radius of curvature affects the value of rounded edge diffraction loss. in this paper, the effect of radius of curvature on diffraction loss over isolated doubled edged hill is studied. the itu-r p.526-13 method gives large values of radius of curvature as the occupation distance of the obstruction increases. double edged hill tend to have larger occultation distance. as such, this paper seeks to examine the impact of the radius of curvature on the diffraction loss over isolated doubled edged hill with relatively large occultation distance. sample elevation profile of double edge hill is used in this paper and the analysis is performed for different frequencies in the various microwave frequency band. the diffraction loss results are compared for the two methods of computing the radius of curvature, namely, one based on the itu-r p.526-13 method and the other on the occultation distance. 2. theoretical background 2.1 the path profile and double edged hill obstruction geometry path profile for a line of sight (los) link with double edged hill obstruction is shown in figure 1 in figure 2 , a rounded edge of radius, r is fitted in the vicinity of the double edged hilltop. tangent line referred to as tangent 1 is drawn from the transmitter to the path profile at point t1 . another tangent line referred to as tangent 2 is drawn from the receiver to the path profile at point t2 and extended to intersect the tangent t1 above the hill vertex. the los clearance , h is the height from the los to the point of intersection of tangent 1 and tangent 2, as shown in figure 2 . the occultation distance , d of the obstruction is the distance between t1 and t2. the angle tangent 1 makes with the los is denoted as α� while the angle tangent 2 makes with the los is denoted as α�. the angle the los makes with the horizontal is denoted β. figure 1: the path profile plot of the double edged hill 219 figure 2: the path profile and double edged hill obstruction geometry as shown in figure 2 , �� is distance from the transmitter to the point where the los clearance is measured and �� is distance from the receiver to the point where the los clearance is measured. let d be the distance between the transmitter and the receiver, then: d = d� + d� (1) from figure 2 , β which is the angle the los makes with the horizontal is given as: β = �� � ��� ��� � (2) where h� is the height of the transmitter and h� is the height of the receiver and d is the distance between the transmitter and the receiver. the values of d, h� and h� are obtained from the path profile data. in figure 2, α� is the angle (in radian) between the los and tangent 1 and α� is the angle (in radian) between the los and tangent 2. then, α is the external angle (in radian) between tangent 1 and tangent 2 at their point of intersection above the hill vertex, where α = α� + α� (3) the angles α� and α� are obtain by cosine rule as follows: cos�α�� = ���� ������� ����� ��������� (4) α� = cos � ����� ������� ����� ��������� � (5) similarly, α� = cos � ����� ������� ����� ��������� � (6) where s� is the length of the tangent 1 measured from the transmitter to the point of intersection of tangent 1 and tangent 2, as shown in figure 2. s� is the length of the tangent 2 measured from the receiver to the point of intersection of tangent 1 and tangent 2, as shown in figure 2. 220 s is the length of the los measured from the transmitter to receiver s�, s� and s are in meter and they are measured out from the path profile plot and the tangent line drawn on the path profile. the line of sight(los) clearance, h is given as; h = ��"�#$�%��&�#$�'( )� (7) the diffraction parameter, ν is given as: v = ℎ,��-��-��.�-���-�� (8) where ʎ is the signal wavelength which is given as: ʎ = 01 (9) f is the frequency in hz and c is the speed of light which is 3x104 m/s. 2.2 the rounded edge diffraction loss by itu-r p.526-13 method the diffraction loss for single rounded obstacle according to recommendation itu-r p.526-13 may be calculated as [22]: a-6 = 7�ν� + t�m,n� (10) where: j(ν) is the fresnel-kirchhoff loss due to an equivalent knife-edge placed with its peak at the vertex point. the diffraction parameter ν may be evaluated as given earlier in eq 3.15. where h and λ are in meters, and d1 and d2 are in kilometres. the knife edge diffraction loss , j(ν) may be obtained according to itu –r 526 where it is as given earlier in eq 3.17. t(m,n) is the additional attenuation due to the curvature of the obstacle and it is given as [22]: =>? @� ≤ 4 t�m,n�db = 7.2�@��/� − �2 − 12.5��@ + 3.6�@� /� − 0.8�@�� (11) =>? @� > 4 t�m,n� db = −6 − 20n>o�@�� + 7.2�@��/� − �2 − 17��@ + 3.6�@� /� − 0.8�@�� (12) m = p� �q�rq�� �q���q��� st�u�v w �/� (13) � = xs t�u� v w y �/ (14) 2.3 the radius of curvature for the rounded edge diffraction computation 2.3.1 the occultation distance based radius of curvature for the rounded edge diffraction computation the occultation distance-based method for computing the radius of curvature for the rounded edge obstruction is given as follows [26-27]: z = ��[��-���-���%�"�-�����-���& (15) where d is the occultation distance and it is obtained from the graph plot of the path profile and geometry of the obstruction, as shown in figure 2 . particularly, a line 221 (referred here as tangent 1) is drawn from the transmitter to be tangential to the path profile at the vicinity of the hill apex. let the tangent point of tangent 1 with the path profile be denoted as t1. again, another line (referred here as tangent 2) is drawn from the receiver to be tangential to the path profile at the vicinity of the hill apex . let the tangent point of tangent 1 with the path profile be denoted as t2. then, d is the distance between t1 and t2. the point at which the tangent 1 and tangent 2 intersect above the hill vertex, as shown in figure 2 . 2.3.2 the itu radius of curvature method for the rounded edge diffraction computation according to itu-r 526-13 method for computing the radius of curvature for the rounded edge obstruction is given as follows [22]; ?\ = ]^ � ��_^ � (16) where ?\ is the radius of curvature corresponding to the sample i of the vertical profile of the ridge in figure 3. figure 3: the geometry of the vertical profile of the obstruction used for the determination of the radius of the rounded edge fitted to the vicinity of the obstruction vertex according to itu method [22]. when fitting the parabola, the maximum vertical distance from the apex to be used in this procedure should be of the order of the first fresnel zone radius where the obstacle is located. as such, in figure 3, the maximum `\ is less or equal to the radius of first fresnel zone at the point of maximum elevation. in the case of n samples, the median radius of curvature of the obstacle is denoted as r where [22]: z = ∑ �?\�\bc\b� = ∑ � ]^ � ��_^ �� \bc\b� (17) according to the itu-r 526-13 recommendation, from the obstruction apex (in figure 2) the maximum value of `\ should be within the radius of the first fresnel zone denoted as �d�. essentially; @�ef@g@�`\� ≤ �d� (18) the radius of the first fresnel zone (r�) at distance �� from the transmitter and �� from the receiver is given as: r� = , iʎ��� ���� �j��� � �� � (19) 222 where ʎ is the signal wavelength. which is given as ʎ = 01 (20) f is the frequency in hz and c is the speed of light. 3. results and discussions sample numerical example is conducted based on path profile of microwave link with isolated double edged hilltop shown in table 1. microwave frequencies from 1. ghz in the l-band to 36ghz in the ka-band are considered. table 1: the path profiles data for the of microwave links with isolated double edged hilltop distance (m) elevation (m) distance (m) elevation (m) distance (m) elevation (m) distance (m) elevation (m) distance (m) elevation (m) 0.0 405.6 1595.3 394.4 3190.5 416.3 4785.8 426.5 6381.0 381.6 53.2 405.6 1648.4 392.6 3243.7 411.9 4838.9 427.3 6434.2 382.1 106.4 405.6 1701.6 391.9 3296.9 416.5 4892.1 427.1 6487.4 382.6 159.5 405.4 1754.8 391.0 3350.0 418.5 4945.3 426.4 6540.5 382.7 212.7 405.4 1808.0 389.7 3403.2 416.5 4998.5 426.7 6593.7 382.7 265.9 405.5 1861.1 388.6 3456.4 416.9 5051.6 426.4 6646.9 382.7 319.1 405.5 1914.3 388.1 3509.6 423.5 5104.8 422.1 6700.1 382.7 372.2 405.1 1967.5 387.6 3562.7 423.5 5158.0 395.4 6753.2 383.1 425.4 404.3 2020.7 387.6 3615.9 426.5 5211.2 394.9 6806.4 383.7 478.6 403.0 2073.8 387.3 3669.1 425.5 5264.3 393.9 6859.6 384.0 531.8 402.2 2127.0 396.7 3722.3 426.3 5317.5 392.5 6912.8 384.0 584.9 401.5 2180.2 396.2 3775.4 427.1 5370.7 391.5 6965.9 383.5 638.1 401.3 2233.4 395.8 3828.6 426.6 5423.9 390.7 7019.1 382.9 691.3 401.3 2286.5 395.1 3881.8 427.1 5477.0 389.5 7072.3 382.6 744.5 401.0 2339.7 393.7 3935.0 427.1 5530.2 388.1 7125.5 382.6 797.6 400.7 2392.9 393.7 3988.1 427.4 5583.4 387.0 7178.6 383.3 850.8 400.3 2446.1 395.9 4041.3 426.3 5636.6 386.1 7231.8 382.2 904.0 399.9 2499.2 398.7 4094.5 425.2 5689.7 385.8 7285.0 381.5 957.2 399.7 2552.4 402.1 4147.7 425.6 5742.9 385.7 7338.2 381.0 1010.3 400.0 2605.6 398.5 4200.8 423.9 5796.1 385.3 7391.3 381.0 1063.5 400.2 2658.8 401.8 4254.0 423.1 5849.3 384.8 7444.5 381.0 1116.7 400.3 2711.9 400.2 4307.2 423.6 5902.4 384.0 7497.7 380.9 1169.9 399.3 2765.1 402.2 4360.4 423.3 5955.6 383.0 7550.9 381.8 1223.0 398.0 2818.3 404.0 4413.5 423.4 6008.8 382.3 7604.0 380.6 1276.2 395.6 2871.5 405.7 4466.7 423.5 6062.0 381.4 7657.2 381.5 1329.4 392.5 2924.6 407.5 4519.9 425.6 6115.1 380.6 7710.4 382.4 1382.6 391.6 2977.8 410.7 4573.1 424.9 6168.3 380.2 7763.6 383.2 1435.7 390.7 3031.0 411.5 4626.2 426.8 6221.5 380.5 7816.7 385.5 1488.9 389.7 3084.2 413.0 4679.4 426.6 6274.7 380.9 7869.9 385.5 1542.1 388.7 3137.3 414.9 4732.6 426.6 6327.8 381.1 7923.1 385.5 223 table 2 shows the diffraction loss, radius of curvature and radius of fresnel zone for different frequencies and radius of curvature methods. according to the results in table 2, the rounded edge diffraction computed based on the itu-r p.526-13 radius of curvature is much higher than the one computed with the occultation distance based radius of curvature. at frequency of 1 ghz , the percentage difference in diffraction loss (%) is about 29% and the difference increases with frequency to as high as 74.5% at 36 ghz. similarly, the itu-r p.526-13 radius of curvature is extremely higher than the occultation distance based radius of curvature. at frequency of 1 ghz , the percentage difference in radius of curvature (%) is about 218% and the difference increases with frequency to as high as 395% at 36 ghz. in all the frequencies considered, the occultation distance remained constant at 1435.7 m. table 2: the diffraction loss, radius of curvature and radius of fresnel zone for different frequencies and radius of curvature methods f (ghz) r (m) by itu method r(m) by occultation method percentage difference in r (%) diffraction loss (db) based on itu r diffraction loss (db) based on itu occultation distance r percentage difference in diffraction loss (%) radius of first fresnel zone (m) occultation distance (m) 1 208913.4 65607.6 218.4 47.5 34.1 39.5 29.2 1435.7 3 244334.8 65607.6 272.4 64.6 43.9 47.4 16.9 1435.7 6 275391.7 65607.6 319.8 83.9 52.5 59.8 11.9 1435.7 12 317868.0 65607.6 384.5 111.1 64.0 73.5 8.4 1435.7 24 317868.0 65607.6 384.5 140.8 81.2 73.4 6.0 1435.7 36 324776.4 65607.6 395.0 163.2 93.6 74.5 4.9 1435.7 4. conclusions the effect of radius of curvature on the rounded edge diffraction loss computed by the itu-r p.526-13 rounded edge diffraction loss method is presented. the radius of curvature is computed using two methods , namely, the itu-r p.526-13 method and the occultation distance-based method. the path profile considered in the study is a double edged hilltop obstruction.the results show that the rounded edge diffraction loss computed by the itu 526 -13 method is significantly affected by the radius of curvature. also, for high occultation distance obstructions, the difference in the radius of curvature of the rounded edge and hence on the diffraction loss obtained can be very high. the result therefore shows that the itu 526 radius of curvature method should be reviewed to ascertain the specific conditions it can be employed. references [1] pradhan, c., & murthy, g. r. 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(2016). software for fresnel-kirchoff single knife-edge diffraction loss model. mathematical and software engineering, 2(2), 76-84. [17] ghasemi, a., abedi, a., & ghasemi, f. (2012). propagation engineering in wireless communications. berlin: springer. [18] baldassaro, p. m. (2001). rf and gis: field strength prediction for frequencies between 900 mhz and 28 ghz (doctoral dissertation, virginia tech). [19] östlin, e. (2009). on radio wave propagation measurements and modelling for cellular mobile radio networks (doctoral dissertation, blekinge institute of 225 technology). [20] gálvez, a. m. (2009) calculation of the coverage area of mobile broadband communications. focus on land. master’s thesis norwegian university of science and technology department of electronics and telecommunications. [21] pollock, p. (2001). a model to predict diffraction attentuation resulting from signal propagation over terrain in low earth orbit satellite systems (no. afit/gso/eng/01m-01). air force inst of tech wright-patterson afb oh school of engineering and management. [22] international telecommunication union, “recommendation itu-r p.526-13: “propagation by diffraction”, geneva, 2013. [23] joo, j., han, d. s., & jeong, h. j. (2015, october). first fresnel zone analysis in vehicle-to-vehicle communications. in connected vehicles and expo (iccve), 2015 international conference on , 196-197. [24] bassey, d. e., akpan, a. o., & udoeno, e. (2016). uhf wave propagation losses beyond 40 percent fresnel zone radius in south-south, nigeria. international journal of science and research (ijsr), 5(2), 470-475. [25] rad, p. b., gajewski, d., & vanelle, c. (2016). diffraction separation based on the projected first fresnel zone. 78th eage conference and exhibition 2016. [26] seybold, j. s. (2005). introduction to rf propagation. john wiley & sons. [27] barué, g. (2008). microwave engineering: land & space radiocommunications (vol. 9). john wiley & sons. copyright © 2017 mfonobong charles uko, uduak etim udoka, chibuzo promise nkwocha. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. mse-vol2-no1-(2016)-19-29-kalu 19 mathematical and software engineering, vol. 2, no. 1 (2016), 19-29 varεpsilon ltd, http://varepsilon.com comparative study of performance of three different photovoltaic technologies constance kalu 1, ezenugu isaac a.2, umoren mfonobong anthony3 1,3department of electrical/electronic and computer engineering, university of uyo, akwaibom, nigeria 2department of electrical engineering, imo state university (imsu), owerri, nigeria. 1constance.kalu@yahoo.com, 2isaac.ezenugu@yahoo.com, 3umoren_m.anthony@yahoo.com *corresponding author: constance.kalu@yahoo.com abstract in this project, simulation approach is used for the comparative analysis of different photovoltaic (pv) technologies, namely; poly crystalline, mono crystalline and thin film pv. the pvsyst industrial pv system planning software solution was selected to model and simulate the entire pv system. the meteorological data used in the study are compiled from national aeronautics and space administration (nasa) worldwide meteorological database. the meteorological data include 22-year monthly and annual averaged insolation incident on a horizontal surface (kwh/m2/day) and 22-year monthly averaged air temperature. a hypothetical electric load demand data is used for the simulation. according to the results, the thin film pv gave highest performance ratio (pr = 61.8%) and highest energy yield per year of 5516.8 kwh/year. however, in comparing pv generation technologies, conversion efficiency is the most important parameter to be determined. the results showed that the array efficiency of the poly crystalline and mono crystalline are comparable, whereas that of thin film is much lower, 4.10% as against the array efficiency of poly crystalline (7.76%) and the array efficiency of mono crystalline (7.62%). also, among the three technologies tested, the poly crystalline required minimum area of 33m2. so, the poly crystalline technology is preferred among the three pv technologies considered in this study. keywords: photovoltaic, poly crystalline silicon, mono crystalline silicon and a-sih thin film, pvsyst, stand alone pv system, unit cost of energy, loss of load probability, array efficiency. 1. introduction the quest for clean and sustainable sources of energy has given rise to diverse kinds of renewable energy generation technologies such as bioenergy, direct solar energy, geothermal energy, hydropower, ocean energy and wind energy [1, 2, 3, 4, 5, 6, 7, 8]. among these technologies, photovoltaic technologies have in recent 20 years attracted more attention [9, 10, 11, 12, 13]. today, different pv technologies have been installed for diverse applications such as power supply for consumer products, for power supply for residential buildings, water pumping and street lighting [14, 15, 16, 17]. also, large-scale pv power generation plant installations are increasingly being deployed across the globe [18, 19, 20, 21, 2]. as the demand for photovoltaic (pv) energy supply is growing, the pv industry grows with increasing number of different pv technologies. over the years, commercially, three different pv technologies have dominated the pv market and they include; monocrystalline, polycrystalline (or multicrystalline) and amorphous pv technologies [18, 23, 24]. the monocrystalline is the traditional solar panel which has been commercially developed since the 1960's [18]. monocrystalline panels are made by a single silicon crystal and they have the best space efficiency more than the other pv technologies [25,26]. also, they are highly efficient, with module’s efficiency of up to 15% [18]. the policrystalline (also known as multicrystalline) panels emerged in commercial quantity in the late 1970’s and have become more popular over time [18]. polycrystalline modules are made from cells containing lots of small silicon crystals. this makes them cheaper to produce but also slightly less efficient than monocrystalline modules [18, 27, 28, 29]. thin-film or amorphous panels emerged commercially since the 1980's [18]. in low light, thin film panels perform better than others pv technologies [23, 18, 10, 30]. as such, thin film panels have been used in calculators and watches. however, thin film panels take up much more space than the panels of the other pv technologies [18]. finally, although the efficiency of thinfilm panels is only about 10%, they use less material and are cheaper than crystalline modules [18, 24, 31, 30]. in this paper, simulation approach is used for the comparative analysis of different pv technologies. version 5.21 of pvsyst industrial pv system planning software solution is used to model and simulate the standalone pv (sapv) system [32, 33, 34, 35, 36]. the pvsyst 5.21 simulation requires the meteorological data at the sapv installation site, load demand profile and the specifications for the sapv performance requirements, as well as the pv module specifications and specification of the other sapv system components. particularly, the meteorological data used in the study are compiled from national aeronautics and space administration (nasa) worldwide meteorological database. the meteorological dataset includes 22-year monthly and annual averaged insolation incident on a horizontal surface (kwh/m2/day) and 22-year monthly averaged air temperature. also, the pvsyst is used to conduct the economic analysis of the sapv system with particular focus on the unit cost of energy generated from the sapv for each of the pv technologies. as regards the economic analysis, pvsyst uses life cycle cost analysis approach to determine the investment cost and unit cost of the energy generated from sapv system. in order to compare the technical and economic performance of the three different pv technologies. the pvsyst software is used to separately simulate the sapv based on each of the three pv technologies, namely, poly crystalline, mono crystalline and thin film pv. the simulations are run for the same site and the same sapv system specifications except the pv module specifications that correspond to the given pv technology being simulated. the simulation results 21 are eventually exported to microsoft excel software where all–in-one comparative tables and graphs are generated for the three pv technologies. 2. methodology 2.1 mathematical expression for determining the pv electric daily and yearly energy output of pv module generally, when pvsyst is supplied with daily or monthly average global radiation and ambient temperature data, it generates the hourly solar radiation and ambient temperature data. with these hourly data, the pvsyst simulates the daily and yearly energy output of the pv system. the mathematical relationship for estimating the daily energy production (��������) based on the hourly solar irradiance g�) at time t can be calculated as follows: �������� = ∑ ��������� ���) � ��) �) ���� ��1 + � %� ! ��� �"#� �) − 25'()"* +���)'"* ,,)'"* ��-�.)'"* �/0)'1� �234 �2� (1) where � ��� = daily energy production of pv modules with total array power rating of ������ ���) � �������� ���) = total array power rating (kwp) at standard test condition (stc) � 5� 678)= peak solar radiation at standard test condition (stc) =1000 w/m2 � # �) = pv module (cell) temperature at sampling time t � #� 678) = pv module (cell) temperature at standard test condition (stc) = 25°c � * +���) = dirt de-rate factor (per unit). typically 0.97 for new installation. � * ,,) = module mismatch factor (per unit) � * ��-�.) = cable loss factor (per unit). typically in the range of 0.95 to 0.99. � * �/0) = maximum efficiency of inverter (per unit) � %9 :,:) = power temperature coefficient, (%/˚c) let per unit power rating of the pv array at stc be �:.�;/���� ���). that is, per unit power is the power rating of each unit of the pv module. let the total number of pv module in the array be <��;/�� let the per unit area in =3 of each pv module in the array be >��;/�� let the total area in =3 of all the pv modules in the array be >������� <��;/�� = �?@abbac d�e) "� fbghi�?@ d�e)' (2) >������� = <��;/��) >��;/��) (3) the mathematical relationship for estimating the yearly energy production (ekl mnopqm)) based on the daily energy production (ekl rosqm)) can be calculated as follows: �������� = ∑ "�������� �)'�2tuv�2� (4) 22 2.2 the simulation data and procedure a hypothetical load demand profile is used for the comparative analysis. the load demand data is as follows; • total watts/day : 1250watts • number of hours/day: 10 hours • total wattshour/day : 12500wh/day the site used in the study is at the faculty of engineering of imo state university (with latitude = 5.508331, longitude = 7.043366). the meteorological data used are (table 1), namely, the monthly average global solar radiation on the horizontal plane and the monthly average ambient temperature. table 1 the meteorological data: the monthly average global solar radiation on the horizontal plane and the monthly average ambient temperature monthly average global solar radiation (kwh/m².mth) monthly average ambient temperature (°c) jan 171.4 25.4 feb 156.5 25.8 mar 164.9 25.7 apr 152.7 25.8 may 146.3 25.6 jun 129.3 24.8 jul 119.4 24.1 aug 116.9 23.9 sep 118.2 24.1 oct 132.4 24.4 nov 145.2 24.7 dec 164 24.7 year 1717.2 24.91 the pvsyst is used to simulate in three different instance for the technical and economic performance parameters of a standalone pv system using one of the three pv technologies at each of the instance. during the simulation, the meteorological data from nasa website are downloaded directly into the pvsyst using the pvsyst tools menu. optimal tilt angle of 8° is used based on the optimal tilt angle computed from the expression 3.7 + 0.69 (latitude of the site) which gives a value of 7.5° ≈8° for the site. furthermore, the load demand profile is also loaded using the pvsyst’s user’s need component of the system menu. pvsyst has a library containing numerous pv modules from different pv technologies and manufacturers. the pv module library is accessible through the system menu in the pvsyst. accordingly, through the system menu in the pvsyst, the particular pv module for each of the pv technologies is selected for the simulation. the simulation is then executed when all the necessary simulation parameters are selected. the simulation results are examined and the relevant components of the result for the study are extracted. 23 3. results and discussions 3.1 daily load demand profile figure 1 is the cut section of the pvsyst result screenshot showing the daily load demand used in the study. the daily electric load demand is 1250watts that runs for an average of 10 hours per day resulting in daily energy demand of 12500wh/day. figure 1 the user’s daily load demand 3.2 coordinates (latitude and longitude) of the project site the site used in the study is at the faculty of engineering of imo state university (with latitude = 5.508331, longitude = 7.043366), as shown in the google map screenshot of figure 2. figure 2 the google map coordinates for pv installation site at the faculty of engineering of imo state university according to the results in table 2, row number 1 and row number 3 show that for each of the three pv technologies, 40 pv modules, each with 100wp power rating at stc (standard test condition) are used to supply energy to the electric load. among the three pv technologies, the thin film technology, specified here as 100wp32v a-si-h single nh-100at, has the lowest array loss % at stc of 24 11.2% (row number 5 of table 2 ) and the lowest loss of load probability(lolp (%)) of 5.9% (row number 11 of table 2 ). the thin film technology also has the lowest unit cost of energy of energy of 132 naira/kwh (row number 12 of table 2 and figure 6) and the highest performance ratio of 61.8% (row number 8 of table 2 and figure 5). however, the thin film technology suffers from very low array efficiency of 4.1% (row number 10 of table 2 and figure 4) which resulted in excessive pv module area of 63 =3 (row number 2 of table 2 and figure 3). table 2 simulation results for the three pv technologies row number summary si-poly 100 wp29v titan 12-100 si-mono ase-100 – dg-ur/mono 100wp32v a-si-h single nh-100at 1 no of modules 40 40 40 2 module area (=3) 33 33.7 63 3 unit nominal power (wp) 100 100 100 4 nominal pv power (kwp) at stc 4.0 4.0 4.0 5 array loss % at stc 17.39 17.69 11.2 6 number of module in series 1 1 1 7 number of module in parallel 40 40 40 8 performance ratio % 61.4 61.5 61.8 9 energy produced per year (kwh/year) 5408 5434 5516.8 10 array efficiency 7.76 7.62 4.10 11 lolp (%) 6.44 6.39 5.9 12 unit cost of energy (naira/kwh) 133 133 132 on the other hand, the poly crystalline pv technology specified in this study as si-poly 100 wp29v titan 12-100 has the highest array efficiency of 7.76% (row number 10 of table 2 ) which resulted in the lowest pv module area of 33 =3. the high array efficiency with its attendant small pv area of the poly crystalline pv technology is preferred over the very low array efficiency with its attendant large pv area of the thin film pv technology. consequently, the poly crystalline pv technology is preferred. based on the same reason, the mono crystalline pv technology is also preferred over the thin film pv technology. in all, for the pv technologies considered in this paper and for the location of the pv installation, the poly crystalline pv technology is the best choice among the three pv technologies. 25 33 33.7 63 0 10 20 30 40 50 60 70 si-poly 100 wp29v titan 12100 si-mono ase-100 –dgur/mono 100wp32v a-si-h single nh100at m o d u le a re a i n s q u a re m e te rs figure 3 module area in square meters for the three pv technologies 7.76 7.62 4.1 0 1 2 3 4 5 6 7 8 9 si-poly 100 wp29v titan 12100 si-mono ase-100 –dgur/mono 100wp32v a-si-h single nh100at a rr a y e ff ic ie n c y ( % ) figure 4 array efficiency (%) for the three pv technologies 61.2 61.3 61.4 61.5 61.6 61.7 61.8 si-poly 100 wp29v titan 12100 si-mono ase-100 –dgur/mono 100wp32v a-si-h single nh100at p er fo rm an ce r at io ( % ) figure 5 performance ratio (%) for the three pv technologies 26 4 conclusion in this paper, simulation approach is used for comparative analysis of different pv technologies, namely, poly crystalline pv technology, mono crystalline pv technology and thin film pv technology. precisely, the pv modules used in the study are si-poly 100 wp29v titan 12-100 for the poly crystalline pv technology, si-mono ase-100 –dg-ur/mono for the mono crystalline pv technology and 100wp32v a-si-h single nh-100at for the thin film pv technology. among the three pv technologies studied, the thin film pv technology has the lowest array loss % at stc, the lowest loss of load probability (lolp (%)), lowest unit cost of energy of energy and the highest performance ratio. however, the downside of the thin film pv technology is that is has very low array efficiency and corresponding very large area (space) requirement for the pv module installation. on the other hand, the poly crystalline pv technology has very high array efficiency and corresponding very low area (space) requirement for the pv module installation. in all, the poly crystalline pv technology is the preferred pv technology for the pv installation site considered. references [1] coyle, e. d., & simmons, r. a. 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(2010). modeling systems losses in pvsyst. institute of the environmental sciences group of energy–pvsyst, universitè de genève. copyright © 2016 constance kalu, ezenugu isaac a., umoren mfonobong anthony. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. comparative analysis of mechanisms for categorization and moderation of user generated text contents on a social e-governance forum 78 mathematical and software engineering, vol. 3, no. 1 (2017), 78-86. varεpsilon ltd, http://varepsilon.com comparative analysis of mechanisms for categorization and moderation of user generated text contents on a social e-governance forum imeobong frank inyang, simeon ozuomba*, and chinedu pascal ezenkwu *corresponding author: simeonoz@yahoo.com electrical/electronic and computer engineering dept., university of uyo, uyo, nigeria abstract this paper presents a comparative analysis of two mechanisms for an automated categorization and moderation of user generated text contents (ugtcs) on a social e-governance forum. posts on the forum are categorized into “relevant”, “irrelevant but interesting” and “must be removed”. relevant posts are those posts that are capable of supporting government decisions; irrelevant but interesting category consists of posts that are not relevant but can entertain or enlighten other users; must be removed posts consists of abusive or obscene posts. two classifiers, support vector machine (svm) with one-vs-the-rest technique and multinomial naive bayes were trained, evaluated and compared using scikit-learn. the results show that svm with an accuracy score of 96% on test set performs better than naive bayes with 88.6% accuracy score on the same test set. keywords: moderation; ranking; ugc; ugtc; web 2.0; sentiment analysis; social e-governance. 1. introduction growing computerization and increasing internet connectivity have encouraged the use of information and communication technology (ict) in the coordination and facilitation of several businesses. moreover, the application of social network technologies for the purpose of improving governance has generated interest recently due to the emergence of web 2.0. in this paper, this has been referred to as social e-governance. the essence of social e-governance forums is that they encourage candid opinions from the citizens thereby promoting people-oriented decisions by the government. in view of this, there is a need for mechanisms that can be used to categorize and moderate users’ posts to ensure that only relevant or interesting posts are allowed on the platform. moderation is the process of reviewing a ugc and taking decision on whether to delete it or allow it to be accessed by other users. moderation can be an automated moderation, using computer applications and algorithms; community moderation, which leverages the online community to self-moderate contents and human moderation, in which there is a dedicated staff acting as a moderator. three moderation approaches include – pre-moderation, reactive moderation 79 and post-moderation. unlike in post-moderation where posts are allowed to appear online before moderation, in pre-moderation, all posts are moderated before they appear online. this moderation approach requires more prompt response; as such the best method for pre-moderation is the automated moderation. human moderation cannot provide 24 hours 7 weeks moderation because posts submitted overnight or in the weekend may not be moderated until the next working days. moreover, community moderation warrants other users to access posts and react accordingly. this, in other words, is a reactive moderation. reactive moderation is a variant of post-moderation whereby the online community, instead of a dedicated individual, carryout the function of moderation. the danger with post-moderation is that the post might already have a negative impact on the online community before it is deleted; as such, post-moderation is not encouraged where the risk associated with publishing inappropriate contents is high. furthermore, community moderation is prone to sybil or one-man-crowd attack, whereby a user creates multiple accounts or sockpuppets in order to influence votes on posts in an online community. in view of this, automated moderation is indispensable, since it does not give room to sybil attack, being human independent. there are several sentiment analytic techniques employed to automate the process of ugc moderation on online communities. some popular machine learning classifiers used in sentiment analysis include naive bayes classifier, svm, decision tree, random forest and so on. in this paper, mechanism for automated moderation of an e-governance forum is presented. the paper considered the performances of two classifiers, which are svm and naive bayes classifiers. the classifiers are trained and evaluated using text corpus generated by a group of three hundred (300) students on a locally hosted e-governance forum. each student was encouraged to generate at least eight different texts. the texts are to belong to “relevant”, “irrelevant but interesting” and “must be removed” categories. summarily, the text corpus used for the training and evaluation of the classifiers contains a total of two thousand and twenty (2020) texts. 730 of the texts belong in the relevant category; 653 belong in the irrelevant but interesting category while 637 belong in the must be removed category. using this text corpus, support vector machine (svm) with one-vs-the-rest technique and multinomial naive bayes were trained using scikit-learn. svm proved better than naive bayes for the e-governance system. subsequent sections of the paper include literature review, methodology, results and conclusion. 2. review of relevant literatures 2.1. e-governance according to keohane and nye [1], “governance implies the processes and institutions, both formal and informal, that guide and restrain the collective activities of a group. government is the subset that acts with authority and creates formal obligations. governance need not necessarily be conducted exclusively by governments. private firms, associations of firms, nongovernmental organizations (ngos), and associations of ngos all engage in it, often in association with governmental bodies, to create governance; sometimes without governmental authority.” in kettl [2] view, "governance is a way of describing the links between government and its broader environment political, social, and administrative." with the revolutionary changes that icts are bringing to our global society, governments worldwide continue to develop more sophisticated ways to digitize its routines and practices so that they can offer the public access to government services in more effective and efficient ways. the delivery 80 of government services and information to the public using ict is referred to as e-governance [3]. the unesco define e-governance as “the public sector’s use of information and communication technologies with the aim of improving information and service delivery, encouraging citizen participation in the decision-making process and making government more accountable, transparent and effective. e-governance involves new styles of leadership, new ways of debating and deciding policy and investment, new ways of accessing education, new ways of listening to citizens and new ways of organizing and delivering information and services. e-governance is generally considered as a wider concept than e-government, since it can bring about a change in the way citizens relate to governments and to each other. e-governance can bring forth new concepts of citizenship, both in terms of citizen needs and responsibilities. its objective is to engage, enable and empower the citizen” [4]. social networks provide the technological platform for individuals to connect, produce and share content online [5]. web 2.0 has changed the one-way notion of traditional e-governance, whereby information only flows from government to the citizens. nowadays, there is a need for government to access firsthand information from the citizens, so as to encourage grassroots development and targeted governance. the use of social networks as a tool to facilitate e-governance has been referred to this paper as social e-governance. 2.2. moderation in social networks according to ochoa and duval [6] “ugc is becoming the most popular and valuable information available on the www”. the explosive growth of ugc has stimulated interests in moderation on social networks. khadilkar, pai, and ghadiali [7] observed that “4.1 million minutes of video are uploaded to youtube everyday … six billion images per month are uploaded to facebook … 40% of images and 80% of videos [created]are inappropriate for business. ugc comes in different forms, including short-text content family such as tweets and forum comments; long-text posts on blogs and profiles; and multimedia material such as images, audio, video and applications”. moderation is the review of user generated content and the decision to publish, edit or delete the content or at times to engage with the online community [8]. interactive advertising bureau australia [9] opined that all stakeholders have a role in managing user comments on the web, as follows – “ users should think about the appropriateness of their content before they post it and take responsibility for their comments; platforms should remove comments reported to them which are illegal or violate their terms and conditions and empower organizations using their platforms with tools to assist them in moderating their properties; the community should report comments that violate applicable rules; and organizations should engage in responsible moderation of user comments posted to their social media channels”. maintaining a content is a foundation of a healthy and flourishing community platform. in order to maintain this quality, the community platform needs governance. governance of a web community can be understood as steering and coordinating the activities of community members. moderation is extremely important in social networking systems, sorting good from bad content and helping readers to find useful information. khadilkar et al [7] stated that moderation can be automated moderation; community moderation and human moderation. automated content moderation has grown into a discipline that requires expertise in pattern detection and labelling, the less downstream volume and analysis [7]. these automated moderation techniques are embodied under the subject of sentiment analysis. according to liu [10] “sentiment analysis, also called opinion mining, is the field of study that analyzes people’s opinions, sentiments, evaluations, 81 appraisals, attitudes, and emotions towards entities such as products, services, organizations, individuals, issues, events, topics, and their attributes”. most machine learning algorithms are often used for sentiment analysis. the following section reviews naive bayes algorithms and svm. 2.3. naive bayes algorithm naive bayes is a family of probabilistic classifiers that leverages the bayes’ theorem with strong independence assumptions among the features. naive bayes has been well-applied in text categorization. an important advantage of naive bayes is that a small number of training data is sufficient to estimate the parameters necessary for out-of-sample classifications [11]. given a class variable � and a dependent feature vector � through��, bayes’ theorem states the following relationship: ���|��,……. . ,��� = �� �����,……..,��| �����,……..,��� (1) introducing the naive bayes independence assumption that ����|�,��, …,����,����, . . , ��� = ����|�� for all i, the equation (1) is simplified to equation (2); ���|��,……. . ,��� = �� �∏ ����| � ���� ����,……..,��� (2) ����,……. . , ���is a normaliser and it is constant given the input. naive bayes uses maximum a posterior (map) decision rule in choosing the hypothesis that is most probable. naive bayes classifier uses the classification rule; �� � ������ ����∏ ����|������ (3) based on the distributions of features, naive bayes classifier can be gaussian, bernoulli or multinomial. gaussian naive bayes is used when dealing with continuous data with the assumption that the features are distributed according to gaussian distribution. ����|�� � �� !"#$ exp �( )���*#+ $ "#$ � (4) the parameters , and are estimated using maximum likelihood. bernoulli naive bayes is for data that is distributed according to bernoulli distributions. in the case of text classification using multivariate event model, word occurrence vectors, rather than word count vectors, are often used to train and use the classifier. multinomial naive bayes is used for multinomially distributed data. it is uses word count vectors instead of word training vectors in training and using the classifier. the distribution is parameterized by vectors . � �. �, …,. �� for each class �, where / is the number of features (in text classification, the size of the vocabulary) and . � is the probability ����|�� of feature 0 appearing in a sample belonging to class �. the parameter . is estimated by a smoothed version of maximum likelihood, i.e. relative frequency counting: .1 � 2#�� 32#� 3� (5) where, 4 �=∑ ���∈7 is the number of times feature appears in a sample of class � in the training set 8, and 4 = ∑ 4 �|7|��� is the total count of all features for class �. the smoothing priors ∝ : 0 accounts for features not present in the learning samples and prevents zero probabilities in further computations. setting < � 1 is called laplace smoothing, while < > 1 is called lidstone smoothing. 82 2.4. support vector machine (svm) svm constructs a hyper-plane or a set of hyper-planes in a high dimensional space for the purpose of classification, regression or outline detection. it chooses the hyper-plane that has the largest distance to the nearest data points of any class so as to lower the generalization error of the classifier. given training vectors ��?ℝa, 0 = 1,…,/,in two classes and a vector �?{1,−1}�, svm solves the following primal problem: ming,h,i � j7j + l ∑ m� � ��� subject to ���j 7n���� + o� ≥ 1-m m ≥ 0,0,……/ (6) its dual is min∝ � ∝7 p ∝ − q7 ∝ subject to �7 ∝ = 0 0 ≤∝≤ l,0 = 1,…,/ (7) where q is a vector of all ones, c>0 is the upper bound, p is an /o�/ positive semi-definite matrix. p�s = ���st)��,�s+; where, t)��, �s+ = n���� 7n)�s+is the kernel. the function n implicitly maps the training vectors to higher dimensional space. the decision function is given as (∑ �� ∝� t)��,�s+ � ��� + o). 3. methodology figure 1 presents the research process flow. the text corpus comprises 2020 texts generated by 300 university students on a locally hosted e-governance forum. summarily, the text corpus used for the training and evaluation of the classifiers contains a total of two thousand and twenty (2020) texts. 730 of the texts belong in the relevant category; 653 belong in the irrelevant but interesting category while 637 belong in the must be removed category. the texts were labeled accordingly for supervised learning. feature extraction: this is the process of converting the texts in the corpus into numerical features compatible with machine learning techniques. the processes of feature extraction include lower casing; removal of stop words from each text in the text corpus; removal of non-word and word stemming; lower casing – the entire texts in the corpus are converted to lower case so as to ignore capitalization. removal of stop wordsin python, nltk library can be used to import stop words in different languages. using this library, stop words in english language were imported and removed from each text in the text corpus. removal of words that occur too rarely in the corpus – to avoid over-fitting of the training set, words which occur less than 100 times in the corpus are removed. removal of non-words all non-words including punctuations are removed. white spaces such due to tabs, spaces, newlines, etc. are trimmed to single space character. word stemming – words are reduced to their stem forms. for examples, words like discounted and discounting are replaced with discount. words like include, includes, included and including are reduced to includ. this is achieved in python using a stemmer function present in nltk library. 83 figure 1: flow diagram for the research process bag-of-words representation a bag-of-word representation is the representation of a corpus of text documents in a matrix with one row per document and one column per token occurring in the corpus. the texts in the corpus are represented as numerical feature vectors with a fixed size rather than the raw text documents with variable lengths. scikit-learn has functionalities for building the bag of words. the strings are 1. obtain input text corpus 2. feature extraction 4. data segmentation 5a. training set 5b. test set 6. text learning ℋ[ . ] 7. classifier 8. performance score 9. good ? tune parameters of the learning algorithm no yes 10. deploy classifier in development of the application 3. pre-processing 84 tokenized using white spaces as separators. integer indexes are given to each possible token. the occurrences of tokens in each text document are counted. each individual token occurrence frequency is treated as a feature. the vector of all the token frequencies for a given document is considered a multivariate sample. in scikit-learn, the countvectorizer function is designed for this purpose. pre-processing: the features were scaled to lie between 0 and 1. this was achieved in scikit-learn using minmaxscaler function present in the preprocessing library of scikit-learn. data segmentation: the data is randomly split such that 80% were used for training while 20% were used for training. the essence of this is to ensure that each classifier is validated with out-of-sample inputs, as such, this is a better proof of the system’s generalization performance. 4. system implementation 4.1. training of classifiers the two classifiers, naive bayes and svm, considered in this paper, were trained on the text corpus. the classifiers were implemented using scikit-learn. scikit-learn involves 4-step modelling pattern. in step one the relevant classes are imported. step two involves the instantiation of the estimator, in which the hyper-parameters can as well be specified or left as defaults. in step three the model is fitted with data and step four is to apply the fitted model on the test set. for example, the 4-step modelling pattern of scikit –learn for the multinomial naive bayes is shown in the appendix. the svm classifier was also implemented using the same 4-step modelling pattern in scikit-learn. the svc class was used due to its ability to implement multiclass classification on a dataset. the default hyper-parameters were used without tuning. 4.2. performance scores of classifiers each of the classifiers were evaluated using the accuracy_score function in the accuracy library in scikit-learn. the result shows that svm classifier had a 96% out-of-sample performance while naive bayes had an 88.6% out-of-sample performance. figure 2 and 3 show the implementations of the naïve bayes and svm classifiers in scikit-learn. figure 2: multinomial naïve bayes implementation in scikit-learn 85 figure 3: one-vs-all svm implementation in scikit-learn 4.3. development of the application the social e-governance application was developed following an evolutionary software development process model. the process involves the system analysis, design, implementation, testing and deployment. the system was implemented with python as the scripting language and deployed locally on google app engine for demonstration and testing. svm classifier was used for the users’ posts moderation and categorization. figure 4 shows the screenshot of the system. figure 4: screenshot of the system 5. conclusion in this paper, two classifiers, naive bayes and svm were compared for ugtcs moderation and categorization using scikit-learn. the result shows that svm classifier had a 96% out-of-sample performance while naive bayes had an 88.6% out-of-sample performance. the social e-governance application was developed using python as scripting language. the svm classifier was employed for the users’ posts moderation 86 and categorization. furthermore, the application was deployed locally on google app engine for demonstration and testing. references [1] keohane, r.o., & nye, j.s.jr. (2002). governance in a globalization world. power and governance in a partially globalized world, 193-218. [2] kettl, d.f. (2015). the transformation of governance: public administration for the twenty-first century. jhu press. [3] ojo, j. s. (2014). e-governance: an imperative for sustainable grass root development in nigeria. journal of public administration and policy research, 6(4), 77-89. [4] palvia, s.c.j., & sharma, s.s. (2007). e-government and e-governance: definitions/domain framework and status around the world. in international conference on e-governance., 5 international conference on egovernance, foundations of e-government, 1-12. [5] cvijikj, i.p. and michahelles, f. (2012) understanding the user generated content and interactions on a facebook brand page, int. j. social and humanistic computing, vol. 2, no. 1-2, 118–140. [6] ochoa, x., duval, e. (2008). quantitative analysis of user-generated content on the web. proceedings of webevolve2008: web science workshop at www2008, 1-8. [7] khadilkar, a., pai, t., ghadiali, s. (2012). how to de-risk the creation and moderation of user-generated content, available at : http://www.cognizant.ch/insightswhitepapers/ how-to-de-risk-the-creation-and-moderation-of-user-generated-content.pdf. accessed on: 10th october 2016. [8] abc managing director (2011). moderating user generated content, 9, available at: http://about.abc.net.au/wp-content/uploads/2012/06/gnmoderationins.pdf. accessed on: 10th october 2016. [9] interactive advertising bureau australia (2013) best practice for user commentmoderation: including commentary for organisations using social media platforms. available at: https://www.iabaustralia.com.au/uploads/uploads/2013-09/ 1380477600_b054b0ef30db4de990bd1527ed6758e4.pdf, accessed on: 10th october 2016. [10] liu, b. (2012). sentiment analysis and opinion mining. synthesis lectures on human language technologies, 5(1), 1-167. [11] kumar, s. a., &vijayalakshmi, m. n. (2012). inference of naïve baye’s technique on student assessment data. in global trends in information systems and software applications, volume 270 of the series communications in computer and information science, 186-191. copyright © 2017 imeobong frank inyang, simeon ozuomba, and chinedu pascal ezenkwu. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 23 mathematical and software engineering, vol. 5, no. 2 (2019), 23-33. varεpsilon ltd, http://varepsilon.com new functionalities of a virtual computer model design and construction stoyan stoyanov 1 and stanimir zhelezov 2 1 konstantin preslavsky university of shumen, shumen, bulgaria, email: 404i90@gmail.com 2 konstantin preslavsky university of shumen, shumen, bulgaria, email: s.zhelezov@shu.bg abstract the purpose of this paper is to construct a virtual model of a computer system for student training, based on analysis of different platforms, creating virtual reality and its related 3d graphics. a classification of three-dimensional models was made. software platforms for threedimensional modelling and creation of virtual scenes have been analysed and selected. a virtual model has been developed. keywords: virtual reality; 3d–modelling; virtual scenes 1 introduction the purpose of the current paper is based on analysis of different platforms, for creating virtual reality and its related 3d graphics, and creating a virtual model for student training in the subjects computer assembling and computer architecture. for that objective the following tasks should be solved:  considering the principles of computer architecture, the basic components of a computer system and the assembly of a computer system, and common assembly errors;  analysing the principles of 3d computer graphics and virtual modelling;  choosing the right toolkit based on the analysis of the most popular 3d modelling and virtual reality tools;  developing an application for training needs. 2 assembling a computer system computer architecture is a specification that describes how a set of software and hardware technology standards interact to form a computer system or platform. in short, computer architecture refers to how a computer system is designed and what technologies it is compatible with. computer architecture was proposed by the mathematician john von neumann in 1945. he describes the design of an electronic computer with its processor, which includes arithmetic logic device, control unit, registers, data and instruction memory, input-output interface and external memory [1, 15]. in order to assemble a computer system, the components of such a system must be determined and whether the components given are consistent. the main computer hardware components that are found in every modern computer are: motherboard, central processing unit (cpu), random access memory (ram), power supply, video card, hard disk drive (hdd), optical device (for example bd / dvd / cd device), monitor, keyboard, and mouse. http://varepsilon.com/ 24 when assembling a computer system, the appropriate components should be carefully selected in terms of their compatibility. improper selection of components leads to risks of damage and “burns”, and as is well known the cost of all the above components is quite high. therefore, it can cause serious financial losses. the training of students [2, 3] in the subject computer assembling, which is one of the major ones in computer science direction, is related to the use of a serious financial resource to purchase the necessary set of components. in addition, during training, incorrect assembly of computer systems may result in additional costs. even with proper assembly, the so-called von neumann bottleneck can appear, which slows down the pc performance and is difficult to locate since the components are compatible with the motherboard but there is a difference between the specifications of the two components. this is the reason why the topic of this paper is focused on virtualization of the whole process of hardware assembly of the cs. for this purpose, it is necessary to properly select tools and software for both 3d modelling and virtualization of 3d models. additional functionalities, such as compatibility of hardware components, checking for the presence of a positioned object, etc., should also be implemented, which also depends on the choice of the programming environment. this selection is discussed in the next paragraph. 3 modelling 3d objects and selecting virtualization software each 3d image created by a computer requires three main components: 1. description of a three-dimensional scene; 2. one or more light sources; 3. camera description or scene view. scene description usually consists of one or more models or three-dimensional structures. usually, one thinks of a model as a standalone piece, such as a pencil or a tree, and the scene as an assembly of these parts in a complete three-dimensional environment. this attitude influences the most common procedure for building a three-dimensional scene: many models are built and then assembled. each model has two descriptions [4]: mathematical representation of the structure of the form and view of the shape when illuminated. the structural description is basically geometry. it tells us where the object is in space and where it is not. most computer programs use the built-in computing system in today’s computers. this hardware has very high but limited precision. some modelling methods are very close to this approach; they create points in the space or cut it very finely and label it blank or full. other methods try to allow the model to be described more abstractly, such as that a glass is a cylinder with a bottom. the other part of each model is the description of the surface. this is to describe the physics of the interaction of the surface of the model with the light. it turns out that this physics is guided by several descriptive terms that are intuitively relevant to humans, such as colour, brilliance and transparency [4]. since models often simulate real-world shapes, it must be determined how detailed the model should be [5, 6]. three-dimensional modelling is the process of creating a three-dimensional representation of any surface or object by manipulating polygons, edges, and vertices in a simulated three-dimensional space [7]. nowadays, modelling results can be seen everywhere. movies, animations, and video games that are filled with fantastic and imaginative creatures and structures. three-dimensional modelling can be accomplished manually with specialized three-dimensional production software that 25 allows the artist to create and manipulate polygonal surfaces or by scanning real objects into a set of data points that can be used to digitally represent a model that is capable of being fully animated, making it an essential process for animation and special effects [8]. the essence of the model is the grid that is best described as a collection of points in space. these points are mapped into a three-dimensional mesh and joined together as polygonal shapes, usually triangles or squares. each point or vertex has its own position in the mesh, and by combining these points in shapes, the surface of an object is created [4, 7]. models are often exported to other software for use in games or movies. however, some 3d modelling programs allow the creation of 2d images using a process called 3d rendering [5,9]. this technique is fantastic for creating hyper-realistic scenes using sophisticated lighting algorithms [9]. the model can also be physically created using the so-called 3d printers. in addition to the surfaces of the model, texture mapping can be added to make the object more realistic. when constructing three-dimensional models, one of the following techniques is being used: box/subdivision modelling, edge/contour modelling, nurbs/spline modelling, digital sculpting, image-based modelling, 3d scanning, and procedural modelling. box/subdivision modelling box modelling is a polygonal modelling technique in which the artist starts with a geometric primitive (cube, sphere, cylinder, etc.) and then refines its shape until the desired look is achieved. artists using this modelling technique often work in stages, starting with a low-grade grid, refining the shape and then subdividing the grid to smooth the hard edges and add detail [7,9]. the subdivision and refinement process is repeated until the grid begins to contain enough polygonal details to convey the intended concept properly. box modelling is probably the most common form of polygonal modelling and is often used in conjunction with edge modelling techniques [12]. edge/contour modelling edge modelling is another polygonal technique, although fundamentally different from box modelling. in edge modelling, instead of starting with primitive shape and refinement, the model is essentially constructed piece by piece, placing polygonal faces along contours and then filling all the gaps between them [10]. this may sound unnecessarily complicated, but some grids are difficult to be completed just by modelling boxes, such as the human face. proper face modelling requires very strict edge control of the mesh, which shapes it, and the precision provided by contour modelling can be invaluable [11]. instead of trying to shape a well-shaped cavity from a polygonal cube (which can be confusing and counter-intuitive), it is much easier to build the outline of the eye and then model the rest. after modelling the main parts of the human face (eyes, lips, forehead, nose, jaw), the other parts tend to fall into place almost automatically [10,12]. nurbs/spline modelling nurbs is a modelling technique mostly used in automotive and industrial modelling. unlike polygonal geometry, the nurbs grid has no faces, edges, or vertices. instead, nurbs models consist of smoothly interpreted surfaces created by a lofting grid between two or more bezier curves (also known as splines) [9]. nurbs curves are created with a tool that works very much like a pen tool in ms paint or adobe illustrator. the curve is drawn in 3d space and edited by moving a series of handles called cvs (control vertices). to model the surface of nurbs, the artist places curves on visible contours and the software automatically interpolates the space between them. alternatively, a nurbs surface can be created by rotating a profile curve around 26 the central axis [13]. this is a common (and very fast) technique for modelling objects that are radial in nature wine glasses, vases, plates and more. digital sculpting the tech industry likes to talk about some of the breakthroughs they call disruptive technologies. technological innovations that change the way we think about achieving a particular task. the automobile has changed the way we drive. the internet has changed the way information and communication are accessed. digital sculpting is a technology that allows you to create intuitively three-dimensional models in a way very similar to sculpting a “digital clay” sculpture. in digital sculptures, grids are organically created using a (wacom) tablet device to shape the model almost exactly like a sculptor who would use brushes on a real piece of clay [7]. digital sculpting has taken the modelling of characters and creatures to a new level, making the process faster, more efficient, and allowing artists to work with high-resolution grids containing millions of polygons. sculpture grids are known for previously unimaginable levels of surface detail and natural (even spontaneous) aesthetics. image-based modelling the image-based modelling is the process by which the transformable three-dimensional objects are algorithmically extracted from a set of static two-dimensional images [12]. image-based modelling is often used in situations where time or budget constraints do not allow the creation of a fully realized 3d asset manually. perhaps the most famous example of image modelling is in the matrix, where the team has neither the time nor the resources to model full 3d kits. they shot action scenes with 360-degree cameras and then used an interpretive algorithm to allow "virtual" motion of 3d cameras through traditional real-life scenes. 3d scanning 3d scanning is a method of digitizing real-world objects when incredibly high levels of photorealism are required. a real-world object (or even an actor) is scanned, analysed, and data (usually an x, y, z point cloud) is used to generate an accurate polygonal or nurbs grid [13]. scanning is often used when requiring a digital representation of a real actor, as in the curious case of benjamin button, where the main character (brad pitt) ages in the opposite direction. procedural modelling the word procedural in computer graphics refers to everything generated algorithmically, rather than created manually by the artist. in procedural modelling, scenes or objects are created based on user-defined rules or parameters [12]. in the popular vue, bryce and terragen environmental modelling packages, entire landscapes can be generated by setting and changing environmental parameters such as leaf density and altitude range, or by selecting landscapes such as the desert, the alps, coasts, etc. procedural modelling is often used for organic structures such as trees and greenery, where there are almost endless variations and complexities that would take a lot of time (or impossible) for the artist to capture by hand [14]. the speedtree application uses a recursive / fractal-based algorithm to generate unique trees and shrubs that can be modified by adjusting trunk height, branch density, angle, curl, and dozens, if not hundreds of other options. cityengine uses similar techniques to generate procedural urban landscapes. when selecting the software to build the 3d model needed for virtualization of the computer configuration, the most common 3d modelling software systems were analysed maya, cinema 4d, lightwave, modo, houdini, blender and 3ds max [10]. each of the systems under consideration has a number of advantages such as a powerful animation package, support for wide format import and export, a rich list of modelling tools, and more. of course, they also have many drawbacks poor particle system, insufficient intuition, 27 and delay in high-detailed models, poorly organized interface and more. some of these systems have a large set of tools and prefabricated objects, but they have disadvantages such as high cost, huge hardware requirements, steep learning curve, and more. on the other hand, free software is poor from built-in tools and objects, they are quite unstable, slow down their work on more detailed models, etc. from the analyses performed of the 3d modelling software systems, cinema 4d stands out the most suitable [11]. some of the main advantages over the others are:  clear interface: customizable floating and configurable dashboards allow space to be dedicated to the work, not the interface.  cinema 4d is known for its accessibility. easy to use by artists and designers, as well as by users without their prior knowledge of the field.  mograph is an incredible toolkit in cinema 4d that speeds up the process of creating animations and graphics for motion.  newly developed irradiance cache.  updated bevel tool.  intel embree in a physical renderer.  extremely stable.  cinema 4d is fully loaded with a rich library of predefined objects cinema 4d is intuitive and handy for both professional designers and beginners. it comes with an extremely large range of features and tools that make object modelling time significantly shorter. it renders comprehensive documentation that gives a full description provided by a number of examples, as well as video and text lessons and live training sessions. it also provides a friendly interface that makes it easy to build 3d models. last but not least, the program provides an opportunity for easy remodelling of objects in order to facilitate the construction of alternative three-dimensional objects, which is one of the goals of this paper in terms of future development [12]. for the implementation of the 3d model of the computer system (fig. 1), models of the basic elements of the system are built motherboard, power supply, hard disk and box (fig. 2). figure 1 three-dimensional model of a pc for the creation of the main objects additional sub-objects (their heirs) are being used, which are constituent parts of the object, and texture of the object. the motherboard is a collection of different types of slots (fig. 2) and the components located on these slots video card, processor, ram, coolers, etc. (fig. 3). and also various small details capacitors, etc. (fig. 2) 28 figure 2 main elements of the motherboard model each of these components can also be considered as a separate object. this allows the computer system configuration to be modified when modelling an additional set of components. this can increase the number of configurations available to the trainees. figure 3 components of the computer system in order to improve the application, by creating a number of component compatibility and slotchecking systems and others to create a sense of even greater realism than before, additional computer components were created, from several types of processors, ram, video cards and more that will be included in the compatibility and employment systems of the motherboard. to improve the player's experience and facilitate their work, a workshop was set up (fig. 4) to house the additional components and the computer system. figure 4 workshop in finished form and ready for export 29 4 virtualization application implementation after the successful modelling of the object, comes its import into the virtual environment. as with the choice of modelling environment, a comparative analysis of different virtualization software platforms has been made. the advantages and disadvantages of the most common products unity and unreal engine have been compared. to realize the virtual scene, the unity software platform was selected [13]. its advantages as an excellent balance of ease of use and power, built-in physically based rendering and high quality graphical effects, active development, regularly fixed bugs and regularly released new features, etc., determine its choice for the virtual scene. the ultimate goal of the application is to assemble and disassemble a computer configuration in a virtual environment. for this purpose, the model is exported from cinema4d to unity and is imported into the program using the unity's built-in tools while maintaining the detail of the three-dimensional model. after successful export/ import, the individual components of the model are “created” as moving objects so that the player can lift and leave them in different positions. one major component named mesh collider (fig. 5) is added to all major model objects (cover, motherboard, hard disk drive, power supply, processor, processor cooler, ram). mesh collision is used on complex objects with inaccurate shape, and it automatically takes the shape of the object. figure 5 mesh collider on the components of the computer, that is, they can now interact with the virtual environment the model and its sub-objects need a mesh collision in order to be lifted, left, etc., otherwise the collision would be static without the collision. a c# script is created to allow individual model objects to be raised, left, or rotated. by adding a function to the already created script, information is added to each object that has been selected (fig. 6). figure 6 motherboard and processor after removing and adding information after the components that were added to the computer system were created, they were exported to the virtual scene. the ultimate goal of the application is to add compliance/ compatibility and 30 employment options to the already ready for assembly/ disassembly, browsing and site information, as well as to improve the current ones. first step: the exported object, which will be a workshop (fig. 7), is sized to fit the size of the player and the computer components and placed on an already constructed plane in the virtual scene. the same is done for the new components, after which they are placed on the tables of the workshop. the box collider component is added to the walls and tables of the workshop to enable them to be interacting objects. otherwise the components would fall through the table and the player would go through the walls. box collider can be seen in (fig. 7) with the thin green lines along the edges of the table. second step: adding highlight object and hover text functions (fig. 8). until now, the application lacked these features and the player only had a sight in the center of the screen and could hardly tell when they were pointing to one component, which in turn made the “picking up” of components difficult. the addition of these features aims to improve the player’s conditions and experience in the simulation. figure 7 workshop located in the plane with stacked components figure 8 the highlight object features colour the object in green, indicating that the object is specified, and hover text provides information about the specified object the next step was to improve the placement of components on the motherboard or the computer case. because only the global coordinates were stored for the component so far, this meant that if 31 the parent object was moved anywhere randomly on the stage, then the object with the predefined coordinates would go where the parent object was located before moving it. to prevent this from happening, the local coordinates are already being saved. the component placement button was also removed. the distance between the given component and the slot it meets is checked instead and the component adheres to the given slot when the condition is met. along with the adherence of the objects, the function for checking the compatibility of the components was added (figs. 9 10). as noted in (fig. 11), there is a check for consistency between two objects using an additional checkcomp script that uses a public string variable predefined by the unity inspector panel for each object to which slot they are compatible. figure 9 when the object approaches the slot corresponding to the object, if it is incompatible, the object turns red and announces its incompatibility figure 10 ddr3-type ram incompatible with the motherboard that requires ddr2 and intel i7 processor incompatible with the am2 processor slot the addition of the following functionality employment of the slot (figs. 3.2.7 3.2.9) was implemented similarly to the incompatibility function by checking whether another object (component) is no longer present in the slot for which the given object, “carried” by the player, is intended. figure 11 when the object approaches the slot corresponding to the object, if the object is already inserted, the object carried by the player turns yellow and announces the presence of a component in the slot 32 5 conclusion the study of hardware-oriented courses, such as computer architecture and assembly, requires a large amount of technical resources. their presentation to students as hardware components leads to purely practical difficulties in terms of creating premises and repositories of this type of visual material. to avoid these inconveniences, the capabilities of virtual reality systems can be used. the developed virtual scene and the associated three-dimensional model can serve as a good basis for the subsequent construction of complete virtual systems for assembling and disassembling computers. with the help of these systems, students could, regardless of their location, acquire the necessary knowledge and skills for the hardware of various types of computer systems and their parameters, characteristics and compatibility. the proposed threedimensional model can be easily modified in order to expand the base of visualization components and thus to represent the development of computer technology over the years with visual means. acknowledgements the research presented in this paper is partially funded by the project of shumen university: rd 08-96/01.02.2019. references [1] stanev, s. 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(2008) virtual model of main frame computer es 1020b from computer museum of mathematics and informatics faculty in shumen university. in proceedings of the 9th international conference on computer systems and technologies and workshop for phd students in computing (compsystech '08), boris rachev and anger smrikarov (eds.). acm, new york, ny, usa, article 85 . doi=http://dx.doi.org/10.1145/1500879.1500973. copyright © 2019 stoyan stoyanov and stanimir zhelezov. this is an open access article distributed under the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. microsoft word 17011.docx 124 mathematical and software engineering, vol. 3, no. 1 (2017), 124-138. varεpsilon ltd, varepsilon.com comparative analysis of the solar potential of offshore and onshore photovoltaic power system anyanime tim umoette 1 , simeon ozuomba2*, nseobong i. okpura3 1department of electrical/electronic engineering, akwa ibom state university mkpat enin, akwa ibom state, nigeria. 2,3department of electrical/electronic and computer engineering, university of uyo, akwaibom, nigeria. * corresponding author: simeonoz@yahoo.com abstract in this paper, comparative analyses of performance parameters of onshore and offshore pv system are conducted and the result showed that the offshore pv system has better performance in terms of higher energy yield and performance ratio as well as improved temperature de-rating factor due to it lower cell temperature. the study is conducted for pv array site around bar beach in lagos, nigeria. meteorological data from nasa website and pv array with total area of 268�� are used for the study. according to the results, the offshore ambient temperature is about 5.57% less than that of onshore, the offshore wind speed is 74.86% more than that of the onshore, whereas, the offshore effective pv cell temperature is 9.96% less than that of the onshore . the cumulative effect of the differences in atmospheric parameters on the pv cell temperature also resulted to 1.99% higher and better offshore de-rating factor over that of the onshore as well as 1.99% improvement in energy output, the specific energy yield and performance ratio. evidently, the offshore pv with lower effective cell temperature performed better than the onshore pv system. keywords: photovoltaic; standalone pv system; cell temperature; temperature de-rating factor; onshore pv system; offshore pv system. 1. introduction over the years, solar energy has become very important source of energy all over the world, more especially in developing countries such as nigeria [1]. furthermore, in nigeria, due to the perennial severe shortfall in energy supply from the national grid, most residential and commercial consumers are resorting to alternative form of energy to meet their energy demands [2]. in this wise, photovoltaic (pv) energy system has become the best choice for alternative energy source for nigerian energy consumers given the abundant solar radiations that are readily available all over the country, all year round. in addition, in recent years, the added advantages of lower cell temperature of water cooled or floating pv systems have gained much attention of researchers [3,4]. however, nigerians are yet to key into such advancement in pv power technology. particularly, most tourist centers by seashores are still powered by diesel generators despite the higher solar energy potential that the sea climate with lower ambient 125 temperature can afford for pv power installation [5,6,7] in view of this oversight, this paper seeks to examine the performance of pv installation on seashore of bar beach in lagos state of nigeria and then compare the performance with that of offshore pv installation. according studies, pv power plants’ performance depends on numerous parameters that amount to many loss mechanisms [8,9,10]. notably, the specific losses associated with a given pv plant can be categorized into two groups, namely, system losses and capture losses. capture losses are caused by factors such as attenuation of the incoming light, soiling of pv module surface, ambient temperature, electrical mismatching , among others [9, 11]. for instance, module output power reduces as module temperature increases. dirt and dust that do accumulate on the pv module surface block some of the sunlight reaching the module and thereby reduce the module output power. on the other hand, system losses are caused by factors such as wiring losses, inverter inefficiency losses and transformer conversion losses [9,11]. for example, the inverters used in most pv systems have peak efficiencies that are less than 100%. consequently, some of the dc power generated by the pv modules is lost in the dc to ac conversion process. the cumulative effect of all the losses are captured as de-rating factor used to reduce the stc rated power of the pv module to the actual value that is dependent on the particular system components and environmental factors for the given pv installation. as such, in order to compare different pv installation some performance parameters that capture some or all of the system and environmental factors are required [10,12]. among others, the three most commonly used parameters are the yearly energy output of the pv installation, the specific energy yield and the performance ratio plant [13,14,15,16,17,18,19]. one common basis for comparing pv modules is through the use of standard test condition (stc) in specifying pv parameters; where the stc is given as 1000 �/�� irradiance, 25°c cell temperature, and am1.5 spectrum [20,21,22,23]. in particular, manufacturers often specify the peak power (wp) output of a pv panel. the peak power value specifies the output power achieved by a pv module under standard test conditions with peak solar radiation of 1,000 ��. in practice, the maximum power a pv installation can produce will usually be significantly lower than the peak power rating. one reason for this is that peak solar radiation of 1,000 �� is a high level of solar radiation achieved only in very sunny conditions. the actual solar radiation received in most cases will often be less than the peak solar radiation figure and will also be dependent on other system losses and capture losses associated with the pv installation. essentially, in most pv installations, the actual energy output of the pv is less than the rated peak energy output of the pv. the ratio of the actual power output to the peak power output is known as the performance ratio. the performance ratio (pr) is usually expressed in percentage. pr refers to the ratio of the actual energy output and the theoretical energy output of the pv [24]. hence, pr shows the percentage of the energy that is actually delivered to the load after subtracting the energy loss due to various system and capture losses associated with the pv installation. another key pv performance parameter considered in this paper is the specific energy yield. the specific energy yield is the net energy output divided by the nameplate dc power at the standard test condition (stc) of an installed pv array [25,26,27]. it represents the number of hours the pv array would need to operate at its rated power or peak rating to provide the same energy. the units are hours or kwh/kwp. the three key performance parameters, namely, yearly energy output of the pv installation, the specific energy yield and the performance ratio are used in this paper to compare the 126 performance of offshore and onshore pv installations sited around bar beach in lagos state, nigeria. the aim is to demonstrate the benefit of siting pv installation around the beach with it lower ambient temperature and higher wind speed when compared to the onshore environment. 2. description of the case study, lagos bar beach lagos is nigeria’s commercial capital, as well as the second most populous and second fastest-growing city in africa and the seventh fastest-growing city in the world [28,29]. lagos bar beach is the main (inner city) beach, the most accessible and most visited beach in lagos. at latitude of 6.422290° and longitude of 3.411700, bar beach is located in victoria island which is an affluent business and residential area in lagos island of lagos state. the beach runs from the west by the institute of oceanography all the way to eko hotel toward the east. bar beach is named after the sand bars that characterized the lagos atlantic ocean coastline which stretch up to 100 kilometres [30]. due to large influx of tourist, the beach is lined with numerous shops and recreational facilities. also, there are several hotels sited all around the beach. 3. methodology and algorithms 3.1. methodology in this study, among other things, the output energy, the specific energy yield and the performance ratio of offshore and onshore pv array located at around lagos bar beach are determined. the study is based on meteorological data obtained from nasa website and pv array that consists of schott ase-260-dg-ft/250w pv modules with total array area of 268m�. 3.2 meteorological data for lagos bar beach 3.2.1. onshore meteorological data for bar beach lagos lagos bar beach is located at latitude of 6.422290° and longitude of 3.411700°. hence, from nasa website, onshore meteorological data for the given latitude and longitude are used for the study. the meteorological data, in table 1, include the monthly averaged daily insolation incident on a horizontal surface, the monthly averaged daily insolation incident on an equator-pointed optimally tilted surface, the daily mean air temperature, and the monthly averaged wind speed at 10 m above the sea level. generally, solar irradiation is provided as kwh/m�. however, it can be stated as daily peak sun hours (psh) [31]. this is the equivalent number of hours of solar irradiance of 1 kwh/m�. hence, in table 1, solar irradiations (h� and h�) of say 5 kwh/m �/ day is equivalent to 5h in psh. 3.2.2. offshore meteorological data for bar beach lagos (i) offshore ambient temperature in °c (��): the offshore (or sea) ambient temperature (t�) is related to the onshore (or land) ambient temperature (t�) as follows [31,32]: �� = 5.0+0.75"�# ) (1) from table 1, the annual average onshore ambient temperature (t�) is 25.74°c, then the annual average offshore ambient temperature (t$) is given as; %& = '.( + (.)'∗ +'.), = +,.-('°/ (ii) offshore wind speed in m/s (011): the offshore (or sea) wind speed (2��) is related to the onshore (or land) wind speed (2�#) as follows [34,35,36]: 127 233 = 1.62+1.17"2�#) (2) from table 1, the annual average onshore wind speed (v$�) is 2.8 "�/6), then the annual average offshore wind speed (v$$) is given as; 0&& = 8.9++8.8)"+.: ) = ,.:;9"</=) table 1: the 22-year average onshore meteorological data for bar beach lagos located at latitude of 6.422290° and longitude of 3.411700°. month monthly averaged daily insolation incident on a horizontal surface ">1?/<+/@ab) monthly averaged daily insolation incident on an equator-pointed tilted surface, at tilt angle of 15.5° ">1?/<+/@ab) the daily mean air temperature "°c) monthly averaged wind speed at 10 m above the sea level "�/6) �� �� �d efd jan 5.28 5.87 26.1 3.28 feb 5.49 5.71 26.6 3.4 mar 5.46 5.43 26.5 3.17 apr 5.21 5.14 26.6 2.76 may 4.76 4.75 26.5 2.37 jun 4.04 4.04 25.7 2.46 jul 3.95 3.94 24.8 2.92 aug 3.98 3.93 24.5 3.06 sep 4.09 4.04 24.8 2.77 oct 4.55 4.61 25.2 2.24 nov 4.95 5.35 25.7 2.41 dec 5.17 5.88 26 2.88 annual 4.74 4.89 25.74 2.8 (source: nasa website at: https://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgi and https://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgi?&num=184097&lat=6.422&submit=submit&hgt=100&veg=17&s itelev=&email=&p=grid_id&p=ret_tlt0&p=t10m&p=wspd10arpt&step=2&lon=3.412) 3.3. pv cell temperatures for lagos bar beach onshore cell temperature: the onshore pv cell temperature (�g#) is given as follows [37]: �g# = 0.943 ∗ �# + 0.095 ∗ k −1.528∗ 23# + 0.3529 (3) where; k is the daily or monthly or yearly average insulation. in this paper, g is the daily insolation incident on a tilted surface (h�) which the annual average has been determined in table 1 as 4.89kwh/m�/day or 4.89h in terms of psh. also, from table 1, the annual average onshore (or land) ambient temperature (t�) is 25.74°c and the onshore (or land) wind speed temperature (2�#) is 2.8m/s, hence, %oa = (.;,-∗ +'.),+ (.(;'∗,.:;−8.'+:∗+.:∗ (.-'+; %oa = 20.8061°c offshore cell temperature: the offshore floating pv cell temperature (�g3) is given 128 as follows [37]: �g3 = 0.943 ∗ �3 + 0.095 ∗k −1.528 ∗233 + 0.3529 (4) where; k is the daily or monthly or yearly average insulation. again, k in this paper is 4.89kwh/m�/day or 4.89h in terms of psh. also, from table 1, the annual average offshore (or sea ambient temperature (t$) is 24.305°c and the offshore (or sea) wind speed temperature (2�$) is 4.896m/s. �pf = (.;,-∗ +,.-('+ (.(;'∗,.:;−8.'+:∗,.:;9∗ (.-'+; �pf = 16.24525°c 3.4. pv cell de-rating factors for lagos bar beach 3.4.1. onshore pv cell temperature de-rating factor the general expression relating the pv cell temperature and the pv cell temperature de-rating factor is given as follows [38]: stuvw = 1 −"x"�guyy,uzz −�[\])) (5) where x is the power temperature coefficients; 0.40%°c for the selected pv module t̂ _``,_aa is the effective avearage daily cell temperature, where; t̂ _``,_aa = �g n#o + �[\] = �g# + �[\] (6) generally, tq�r = 25°c . hence, for the onshore, t̂ _``,_aa is represented as t̂ _``,_aa"�) and the pv cell temperature de-rating factor represented as stuvw"#) is given as; t̂ _``,_aa"�) = �g n#o + �[\] = �g# + �[\] (7) %otuu,tvv"a) = +(.:(98+ +' = 45.8061°/ stuvw"#) = 1−"x"t̂ _``,_aa"�) −�[\])) = 1 −"x" �g# + �[\] −�[\])) (8) stuvw"#) = 1−x"�g#) (9) where, x must be divided by 100 if is given in %. vwt<x"a) = 8− (.,( 8(( "+(.:(98) = 0.9167756 3.4.2. offshore pv cell temperature de-rating factor similarly, for the offshore, t̂ _``,_aa is represented as t̂ _``,_aa"$) and the pv cell temperature de-rating factor represented as stuvw"3), where �guyy,uzz"3) = �g n#o + �[\] = �g3 + �[\] (10) %otuu,tvv"&) = 89.+,'+'+ +' = 41.24525°/ for the offshore, the pv cell temperature de-rating factor represented as stuvw"3) is given as follows; stuvw"3) = 1−"x"�guyy,uzz"3) −�[\])) = 1−"x" �g3 + �[\] −�[\])) (11) stuvw"3) = 1−x"�g3) (12) where, x must be divided by 100 if is given in %. 129 yz{|}"f) = 8− (.,( 8(( "89.+,'+') = 0.935019 3.4.3. the dc to ac de-rate factor (v@o/ao) apart from cell temperature, there are other factors that reduces the conversion efficiency of the pv panels. the factors lead to greater reduction in the ac power delivered at the inverter output of the pv power supply system. specifically, the cumulative effect of the all the factors that affects the overall dc to ac conversion efficiency of the pv power supply system are captured as dc to ac de-rate factor . the array dc power rating is multiplied by an overall dc to ac de-rate factor to determine the ac power rating. the overall dc to ac de-rate factor accounts for losses from the dc nameplate power rating and is the mathematical product of the de-rate factors for the components of the pv system. a list of the standard de-rate factors and their typical values are presented in table 3. table 2: de-rate factors for ac power rating at stc (source: [39]). component de-rate factors pvwatts default range pv module nameplate dc rating 0.95 0.80 1.05 inverter and transformer 0.92 0.88 0.98 mismatch 0.98 0.97 0.995 diodes and connections 0.995 0.99 0.997 dc wiring 0.98 0.97 0.99 ac wiring 0.99 0.98 0.993 soiling 0.95 0.30 0.995 system availability 0.98 0.00 0.995 shading 1.00 0.00 1.00 sun -tracking 1.00 0.95 1.00 age 1.00 0.70 1.00 overall dc-to-ac de-rate factor 0.77 based on table 2, the various de-rate factors are: sw~t�y = de-rating factor due to pv module nameplate tolerance dc rating. the de-rate factor for the pv module nameplate dc rating accounts for the accuracy of the manufacturer's nameplate rating. s��~ = de-rating factor due to inverter and transformer sv��v = de-rating factor due to mismatch sn��nu = de-rating factor due to diodes and connections sng3����� = de-rating factor due to dc wiring sw#g3����� = de-rating factor due to ac wiring s���y��� = de-rating factor due to soiling s�o�#~#�y = de-rating factor due to system availability 130 s��#n��� = de-rating factor due to shading s���t�#g� = de-rating factor due to sun -tracking s#���� = de-rating factor due to age sng/#g = dc to ac de-rating factor the overall dc to ac de-rate factor is calculated by multiplying the component de-rate factors. sng/#g = sw~t�y * sv��v* sn��nu* sng3�����* sw#g3�����* s���y���*s�o�#~#�y *s��#n��� * s���t�#g�* s#���� (13) hence, for the default values in column 2 of table 2 gives: v@o/ao = 0.95 x 0.92 x 0.98 x 0.995 x 0.98 x 0.99 x 0.95 x 0.98 x 1 x1x 1= 0.77 the value of 0.77 means that the ac power rating at stc is 77% of the nameplate dc power rating. in most cases, the overall default value of 0.77 will provide a reasonable estimate for modelling the energy production. in all, f�^/�^ includes de-rating due to manufacturer’s tolerances and de-rating due to dirt along with other relevant de-rating factors except the temperature de-rating factor. 3.5. selection of pv module in this paper, the pv module selected is the schott, ase-260-dgft/250w polycrystalline silicon pv module manufactured by schott solar with nominal power of 250wp at stc, nominal voltage of 48v, manufacturers tolerance of ± 5%, efficiency of 11.72%, temperature coefficient of -0.47%/°c and cell area of 2.144 m� as shown in figure 1. figure 1: the manufacturer specifications for the selected pv module in the study (source: [40,41,42]). 131 3.6. determination of the daily energy output of the pv array in this paper, the total energy is determined based on a specified available space (area) for the pv array. particularly, the specified available total area for all the pv modules is 268��. let ��� be the number of pv modules in the array; ��� ��� be the area of one pv module and let ���\�\�� be the total area of all the pv modules. then; number of pv modules, "���) = ����` ��_� �a �`` ��_ �� ����`_� ��_� �a ��_ �� ����`_ = � ¡¢£¢¤¥ � ¡ (14) ���\�\�� = 268� � and for the selected pv module , ��� = 2.144� �. therefore, ¦§0 = +9: +.8, = 8+' 3.6.1. the de-rated output power of the onshore pv modules the de-rated output power of the onshore pv modules can be determine as follows [43]: let ���_©ª"#) be the de-rated output power of the onshore pv modules and let ��� be the module power at stc = 250��. then, ���_©ª"#) = "���)«sng/#g¬ «stuvw"#)¬ (15) also, sng/#g is the dc to ac de-rating factor which is given as 0.77 and stuvw"#) is the onshore temperature de-rating factor which has a value of 0.9167756. then, �­e_®¯"d) = "+'() "(.))) "(.;89))'9) = 176.479303 3.6.2. the daily energy output from the onshore pv modules let °��_©_\�\��"#) be the daily energy output from the onshore pv modules, then; °��_©_\�\��"#) = «���_©ª"#) ¬ "���)"±\) (16) where; ���_©ª"#) is the de-rated output power of the onshore pv modules =176.479303 ��� is the number of modules = 125 ±\ is the irradiation for the tilt and azimuth angle of the array = 4.89 >1?/< +/ @ab = 4.89h in terms of psh. hence, ²­e_®_�³�´µ"d) = "8)9.,);-() "8+')",.:;) = 107872.97 wh ²­e_®_�³�´µ"d) = 107. 87297 kwh 3.6.3. the de-rated output power of the offshore pv modules similarly, the de-rated output power of the offshore pv modules can be determine as follows [43]: ���_©ª"3) = "���)«sng/#g¬ «stuvw"3)¬ (17) where ���_©ª"3) is the de-rated output power of the offshore pv modules 132 ��� is the module power at stc = 250�� sng/#g is the dc to ac de-rating factor = 0.77 stuvw"3) is the offshore temperature de-rating factor = 0.935019 �­e_®¯"f) = "+'() "(.))) "(.;-'(8;) = 179.9911575 3.6.4. the daily energy output from the offshore pv modules °��_©_\�\��"3) = «���_©ª"3) ¬ "���)"±\) (18) where °��_©_\�\��"3) is the daily energy output from the offshore pv modules ���_©ª"3)is the de-rated output power of the offshore pv modules =179.9911575 ��� is the number of modules = 125 ±\ is the irradiation for the tilt and azimuth angle of the array = 4.89 >1?/< +/ @ab ±\ = 4.89h in terms of psh. hence, ²­e_®_�³�´µ"f) = "8);.;;88')' ) "8+')",.:;) ²­e_®_�³�´µ"f) = 110019.60wh = 110.01960kwh 3.7. determination of the specific energy yield of the pv array the total rated power of the array at stc is w¶���·_q�r where [43]; w¶���·_q�r = "���)x"���) (19) ��� is the module power at stc = 250�� ��� is the number of modules = 125 therefore, �´¹¹dº_»�¼ = "+'()½"8+') = -8+'( wp= -8.+'( kwp 3.7.1. the specific energy yield for the onshore pv array the actual yearly energy output from the onshore pv modules is given as; °�o�"#) = «°��_©_\�\��"#)¬ "365) (20) where °�o�"#) is the actual yearly energy output from the onshore pv modules °��_©_\�\��"#) is the daily energy output from the onshore pv modules ²¾º¾"d) = "8():)+.;)�¿/àdº) "-9' àdº/º{d¹) ²¾º¾"d) = 39373634.05wh/year = 39373.63405 kwh/year the specific energy yield for the onshore pv ( áâã"#)) is expressed in kwh per kwp and it can be calculated as follows [43]: áâã"#)) = äåæå"ç) �èééêë_ìíî (21) »­ï"d)) = -;-)-.9-,(' ð�¿/º{d¹ -8.+'( ð�} = 8+';.;'9+:;9 kwh per kwp 3.7.2. the specific energy yield for the offshore pv array 133 the actual yearly energy output from the offshore pv modules is given as; °�o�"3) = «°��_©_\�\��"3)¬ "365) (22) where °�o�"3) is the actual yearly energy output from the offshore pv modules °��_©_\�\��"3) is the daily energy output from the offshore pv modules ²¾º¾"f) = "88((8;.9(�¿ /àdº) "-9' àdº/º{d¹) ²¾º¾"f) = 40157154wh/year = 40157.154kwh/year the specific energy yield for the offshore pv ( áâã"3)) is expressed in kwh per kwp and it can be calculated as follows [43]: áâã"3)) = äåæå"ñ) �èééêë_ìíî (23) »­ï"f)) = ,(8').8', ð�¿/º{d¹ -8.+'( ð�} = 8+:'.(+:;+: kwh per kwp 3.8. the performance ratio for the onshore pv array the performance ratio (pr) ratio is a reflection of the system losses and it is used to assess the installation quality. the performance ratio for the onshore pv array can be computed as follows [43]: âò"#) = äåæå"ç) äóôõçö (24) where âò"#) is the performance ratio for the onshore pv array °�o�"#) is the actual yearly energy yield from the onshore pv system °�nu#y is the ideal energy output of the array. now, ×ø@tau = «�´¹¹dº_»�¼¬x"��ï) (25) where �´¹¹dº_»�¼ is the total rated power of the array at stc = 31.250 kwp ù%ú is the yearly average daily irradiation, "inû�ℎ/� �ýþ ℎ ) incident on a tilted surface ù%ú = -9'"ù% ) (26) �� is the daily averaged irradiation, "inû�ℎ/� �ýþ ℎ ) incident on a tilted surface = = 4.89 >1?/<+/@ab or 4.89h therefore , ×ø@tau = "-9')x"ù% )x«�´¹¹dº_»�¼¬ (27) ×ø@tau = "-9')½",.:; )½"-8.+'() = 55776.5625 kwh now, °�o�"#) = 39373.63405 kwh/year. then; ­¯"d) = ²¾º¾"d) ²ßà{dà = -;-)-.9-,(' ''))9.'9+' = (.)('; 3.9. the performance ratio for the offshore pv array 134 the performance ratio (pr) ratio is a reflection of the system losses and it is used to assess the installation quality. the performance ratio for the offshore pv array can be computed as follows [43]: âò"3) = äåæå"ñ) äóôõçö (28) where âò"#) is the performance ratio for the offshore pv array °�o�"3) is the actual yearly energy yield from the offshore pv system °�nu#y is the ideal energy output of the array. again, ×ø@tau = "-9')x"4.89 )x"31.250) = 55776.5625 kwh now, °�o�"3) = 40157.154 kwh/year. then; ­¯"d) = ²¾º¾"f) ²ßà{dà = ,(8').8', ''))9.'9+' = (.)+( 4. results and discussion the summary of the results obtained from the foregoing computations are presented in table 3 along with the percentage increase or decrease between each pair of parameters obtained for the offshore and onshore pv array. according to the results, the offshore ambient temperature is about 5.57% less than that of onshore whereas, the offshore wind speed is 74.86% more than that of the onshore. furthermore, the offshore effective pv cell temperature is 9.96% less than that of the onshore . the cumulative effect of the differences in atmospheric parameters on the pv cell temperature also resulted to 1.99% higher and better offshore de-rating factor over that of the onshore. similar to the temperature de-rate factor, in all the other performance parameters considered in table 3, the offshore pv has 1.99% improvement over that of the onshore. in all, it can be stated that in the onshore and offshore pv systems that are considered, where all the system configurations are the same except the atmospheric (ambient temperature and wind speed) parameters, the effective cell temperature and hence the temperature de-rating factor becomes the differentiating factor. particularly, all the performance parameters considered and compared are proportionally the same as the temperature de-rating factor. in any case, the study has been based on annual average values of solar radiation and atmospheric parameters. the results for daily and monthly values may well differ from the annual values. however, such daily and monthly analyses are not considered here due to space constraint. however, from the annual results, the offshore system performs better than the onshore pv system with about 1.99% higher daily and yearly energy output. 135 table 3: summary of the onshore and offshore performance parameters. s/ n parameter onshore offshore percentage (%) increase or decrease of offshore parameter over the onshore parameters 1 the annual average ambient temperature (in °c) 25.74 24.305 -5.57 2 the annual average wind speed ( in m/s) 2.8 4.896 74.86 3 the effective average daily pv cell temperature (in °c) 45.8061 41.24525 -9.96 4 pv cell temperature de-rating factor 0.9167756 0.935019 1.99 5 de-rated output power of pv modules (watts) 176.479 179.991 1.99 6 the daily energy output of the pv array (wh/day) 107.873 110.0196 1.99 7 the actual yearly energy output (kwh/year) 39373.634 40157.154 1.99 8 the specific energy yield of pv array (in kwh per kwp ) 1259.956 1285.029 1.99 9 performance ratio 0.706 0.72 1.98 5. conclusion and recommendation 5.1. conclusion comparative analyses of the energy yield and other performance parameters of onshore and offshore pv system are conducted and the result showed that the offshore pv system has better performance in terms of higher energy output, better temperature de-rating factor due to lower cell temperature. it has also been found that for the onshore and offshore system analysed with the same system configuration except for the differences in atmospheric parameters, namely , ambient air temperature and wind speed, the main performance differentiating factor is the effective cell temperature and its resultant temperature de-rating factor. the lower the effective call temperature, the higher and better the temperature de-rating factor and hence the better the system performance parameters such as yearly energy, specific energy yield and performance ratio. consequently, the offshore pv with lower effective cell temperature performed better than the onshore pv system. 5.2. recommendation for further studies the study so far has considered the annual average values of the solar radiation and atmospheric parameters, the daily and monthly variations are also essential and require. the sizing and economic analysis of the offshore pv system are also needed. all these require further studies so as to provide more detailed techno-economic advantages of the offshore pv over the onshore pv system. 136 references [1] foroudastan, saeed d., and olivia dees. solar power and sustainability in developing countries. proceedings of the international conference on renewable energy for developing countries. 2006, 1-13. 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