id sid tid token lemma pos ajst-24979 1 1 academic academic ADJ ajst-24979 1 2 journal journal NOUN ajst-24979 1 3 of of ADP ajst-24979 1 4 science science NOUN ajst-24979 1 5 and and CCONJ ajst-24979 1 6 technology technology NOUN ajst-24979 1 7 issn issn NOUN ajst-24979 1 8 : : PUNCT ajst-24979 1 9 2771 2771 NUM ajst-24979 1 10 - - SYM ajst-24979 1 11 3032 3032 NUM ajst-24979 1 12 | | NOUN ajst-24979 1 13 vol vol NOUN ajst-24979 1 14 . . PROPN ajst-24979 2 1 12 12 NUM ajst-24979 2 2 , , PUNCT ajst-24979 2 3 no no INTJ ajst-24979 2 4 . . NOUN ajst-24979 2 5 1 1 NUM ajst-24979 2 6 , , PUNCT ajst-24979 2 7 2024 2024 NUM ajst-24979 2 8 172 172 NUM ajst-24979 2 9 homotopy homotopy NOUN ajst-24979 2 10 analysis analysis NOUN ajst-24979 2 11 method method NOUN ajst-24979 2 12 for for ADP ajst-24979 2 13 solving solve VERB ajst-24979 2 14 fuzzy fuzzy ADJ ajst-24979 2 15 fractional fractional ADJ ajst-24979 2 16 volterra‐fredholmintegro‐differential volterra‐fredholmintegro‐differential ADJ ajst-24979 2 17 equations equation NOUN ajst-24979 3 1 qin qin PROPN ajst-24979 3 2 chen chen PROPN ajst-24979 3 3 * * PUNCT ajst-24979 3 4 school school NOUN ajst-24979 3 5 of of ADP ajst-24979 3 6 mathematics mathematic NOUN ajst-24979 3 7 and and CCONJ ajst-24979 3 8 information information NOUN ajst-24979 3 9 , , PUNCT ajst-24979 3 10 china china PROPN ajst-24979 3 11 west west PROPN ajst-24979 3 12 normal normal PROPN ajst-24979 3 13 university university PROPN ajst-24979 3 14 , , PUNCT ajst-24979 3 15 nanchong nanchong NOUN ajst-24979 3 16 , , PUNCT ajst-24979 3 17 637009 637009 NUM ajst-24979 3 18 , , PUNCT ajst-24979 3 19 china china PROPN ajst-24979 3 20 * * PUNCT ajst-24979 3 21 corresponding correspond VERB ajst-24979 3 22 author author NOUN ajst-24979 3 23 email email NOUN ajst-24979 3 24 : : PUNCT ajst-24979 3 25 1751743987@qq.com 1751743987@qq.com NUM ajst-24979 3 26 abstract abstract NOUN ajst-24979 3 27 : : PUNCT ajst-24979 3 28 the the DET ajst-24979 3 29 fuzzy fuzzy ADJ ajst-24979 3 30 fractional fractional ADJ ajst-24979 3 31 volterra volterra NOUN ajst-24979 3 32 - - PUNCT ajst-24979 3 33 fredholm fredholm NOUN ajst-24979 3 34 integro integro ADJ ajst-24979 3 35 - - PUNCT ajst-24979 3 36 differential differential NOUN ajst-24979 3 37 equation equation NOUN ajst-24979 3 38 is be AUX ajst-24979 3 39 introduced introduce VERB ajst-24979 3 40 by by ADP ajst-24979 3 41 using use VERB ajst-24979 3 42 the the DET ajst-24979 3 43 fuzzy fuzzy ADJ ajst-24979 3 44 caputo caputo PROPN ajst-24979 3 45 derivative derivative NOUN ajst-24979 3 46 under under ADP ajst-24979 3 47 the the DET ajst-24979 3 48 generalized generalize VERB ajst-24979 3 49 hukuhara hukuhara ADJ ajst-24979 3 50 difference difference NOUN ajst-24979 3 51 , , PUNCT ajst-24979 3 52 and and CCONJ ajst-24979 3 53 the the DET ajst-24979 3 54 existence existence NOUN ajst-24979 3 55 and and CCONJ ajst-24979 3 56 uniqueness uniqueness NOUN ajst-24979 3 57 of of ADP ajst-24979 3 58 the the DET ajst-24979 3 59 solution solution NOUN ajst-24979 3 60 of of ADP ajst-24979 3 61 this this DET ajst-24979 3 62 equation equation NOUN ajst-24979 3 63 are be AUX ajst-24979 3 64 proved prove VERB ajst-24979 3 65 by by ADP ajst-24979 3 66 using use VERB ajst-24979 3 67 the the DET ajst-24979 3 68 fixed fix VERB ajst-24979 3 69 point point NOUN ajst-24979 3 70 theorem theorem VERB ajst-24979 3 71 . . PUNCT ajst-24979 4 1 the the DET ajst-24979 4 2 homotopy homotopy NOUN ajst-24979 4 3 analysis analysis NOUN ajst-24979 4 4 method method NOUN ajst-24979 4 5 is be AUX ajst-24979 4 6 used use VERB ajst-24979 4 7 to to PART ajst-24979 4 8 study study VERB ajst-24979 4 9 the the DET ajst-24979 4 10 numerical numerical ADJ ajst-24979 4 11 solutions solution NOUN ajst-24979 4 12 of of ADP ajst-24979 4 13 linear linear PROPN ajst-24979 4 14 and and CCONJ ajst-24979 4 15 nonlinear nonlinear ADJ ajst-24979 4 16 fuzzy fuzzy ADJ ajst-24979 4 17 fractional fractional ADJ ajst-24979 4 18 integro integro ADJ ajst-24979 4 19 - - PUNCT ajst-24979 4 20 differential differential NOUN ajst-24979 4 21 equations equation NOUN ajst-24979 4 22 . . PUNCT ajst-24979 5 1 several several ADJ ajst-24979 5 2 numerical numerical ADJ ajst-24979 5 3 examples example NOUN ajst-24979 5 4 are be AUX ajst-24979 5 5 given give VERB ajst-24979 5 6 to to PART ajst-24979 5 7 illustrate illustrate VERB ajst-24979 5 8 the the DET ajst-24979 5 9 effectiveness effectiveness NOUN ajst-24979 5 10 and and CCONJ ajst-24979 5 11 applica applica NOUN ajst-24979 5 12 - - PUNCT ajst-24979 5 13 bility bility NOUN ajst-24979 5 14 of of ADP ajst-24979 5 15 the the DET ajst-24979 5 16 method method NOUN ajst-24979 5 17 . . PUNCT ajst-24979 6 1 keywords keyword NOUN ajst-24979 6 2 : : PUNCT ajst-24979 6 3 volterra volterra NOUN ajst-24979 6 4 - - PUNCT ajst-24979 6 5 fredholm fredholm NOUN ajst-24979 6 6 integro integro ADJ ajst-24979 6 7 - - PUNCT ajst-24979 6 8 differential differential NOUN ajst-24979 6 9 equations equation NOUN ajst-24979 6 10 ; ; PUNCT ajst-24979 6 11 fixed fix VERB ajst-24979 6 12 point point NOUN ajst-24979 6 13 theorem theorem VERB ajst-24979 6 14 ; ; PUNCT ajst-24979 6 15 homotopy homotopy VERB ajst-24979 6 16 analysis analysis NOUN ajst-24979 6 17 method method NOUN ajst-24979 6 18 ; ; PUNCT ajst-24979 6 19 caputo caputo PROPN ajst-24979 6 20 fractional fractional PROPN ajst-24979 6 21 derivative derivative NOUN ajst-24979 6 22 . . PUNCT ajst-24979 7 1 1 1 X ajst-24979 7 2 . . X ajst-24979 7 3 introduction introduction NOUN ajst-24979 7 4 the the DET ajst-24979 7 5 motivation motivation NOUN ajst-24979 7 6 of of ADP ajst-24979 7 7 fractional fractional ADJ ajst-24979 7 8 calculus calculus NOUN ajst-24979 7 9 research research NOUN ajst-24979 7 10 is be AUX ajst-24979 7 11 its its PRON ajst-24979 7 12 application application NOUN ajst-24979 7 13 in in ADP ajst-24979 7 14 biology biology NOUN ajst-24979 7 15 , , PUNCT ajst-24979 7 16 electrochemistry electrochemistry NOUN ajst-24979 7 17 , , PUNCT ajst-24979 7 18 fractal fractal ADJ ajst-24979 7 19 theory theory NOUN ajst-24979 7 20 , , PUNCT ajst-24979 7 21 control control PROPN ajst-24979 7 22 theory theory NOUN ajst-24979 7 23 , , PUNCT ajst-24979 7 24 fluid fluid ADJ ajst-24979 7 25 flow flow NOUN ajst-24979 7 26 and and CCONJ ajst-24979 7 27 viscoelasticity viscoelasticity NOUN ajst-24979 8 1 [ [ X ajst-24979 8 2 1–3 1–3 NOUN ajst-24979 8 3 ] ] X ajst-24979 8 4 . . PUNCT ajst-24979 9 1 in in ADP ajst-24979 9 2 1823 1823 NUM ajst-24979 9 3 , , PUNCT ajst-24979 9 4 the the DET ajst-24979 9 5 application application NOUN ajst-24979 9 6 of of ADP ajst-24979 9 7 fractional fractional ADJ ajst-24979 9 8 derivatives derivative NOUN ajst-24979 9 9 was be AUX ajst-24979 9 10 introduced introduce VERB ajst-24979 9 11 by by ADP ajst-24979 9 12 abel abel PROPN ajst-24979 9 13 , , PUNCT ajst-24979 9 14 who who PRON ajst-24979 9 15 applied apply VERB ajst-24979 9 16 fractional fractional ADJ ajst-24979 9 17 calculus calculus NOUN ajst-24979 9 18 to to PART ajst-24979 9 19 solve solve VERB ajst-24979 9 20 the the DET ajst-24979 9 21 integral integral ADJ ajst-24979 9 22 equation equation NOUN ajst-24979 9 23 in in ADP ajst-24979 9 24 the the DET ajst-24979 9 25 tautochrone tautochrone NOUN ajst-24979 9 26 problem problem NOUN ajst-24979 9 27 [ [ X ajst-24979 9 28 4 4 NUM ajst-24979 9 29 ] ] PUNCT ajst-24979 9 30 . . PUNCT ajst-24979 10 1 the the DET ajst-24979 10 2 fixed fix VERB ajst-24979 10 3 point point NOUN ajst-24979 10 4 theorem theorem NOUN ajst-24979 10 5 is be AUX ajst-24979 10 6 often often ADV ajst-24979 10 7 used use VERB ajst-24979 10 8 to to PART ajst-24979 10 9 study study VERB ajst-24979 10 10 the the DET ajst-24979 10 11 existence existence NOUN ajst-24979 10 12 and and CCONJ ajst-24979 10 13 uniqueness uniqueness NOUN ajst-24979 10 14 of of ADP ajst-24979 10 15 solutions solution NOUN ajst-24979 10 16 of of ADP ajst-24979 10 17 fractional fractional ADJ ajst-24979 10 18 calculus calculus NOUN ajst-24979 10 19 equations equation NOUN ajst-24979 11 1 [ [ X ajst-24979 11 2 5–9 5–9 X ajst-24979 11 3 ] ] X ajst-24979 11 4 , , PUNCT ajst-24979 11 5 and and CCONJ ajst-24979 11 6 its its PRON ajst-24979 11 7 numerical numerical ADJ ajst-24979 11 8 methods method NOUN ajst-24979 11 9 are be AUX ajst-24979 11 10 also also ADV ajst-24979 11 11 widely widely ADV ajst-24979 11 12 studied study VERB ajst-24979 11 13 . . PUNCT ajst-24979 12 1 because because SCONJ ajst-24979 12 2 of of ADP ajst-24979 12 3 its its PRON ajst-24979 12 4 wide wide ADJ ajst-24979 12 5 application application NOUN ajst-24979 12 6 of of ADP ajst-24979 12 7 fractional fractional ADJ ajst-24979 12 8 calculus calculus NOUN ajst-24979 12 9 equations equation NOUN ajst-24979 12 10 , , PUNCT ajst-24979 12 11 in in ADP ajst-24979 12 12 many many ADJ ajst-24979 12 13 models model NOUN ajst-24979 12 14 , , PUNCT ajst-24979 12 15 such such ADJ ajst-24979 12 16 as as ADP ajst-24979 12 17 the the DET ajst-24979 12 18 novel novel ADJ ajst-24979 12 19 coronavirus coronavirus NOUN ajst-24979 12 20 infection infection NOUN ajst-24979 12 21 system system NOUN ajst-24979 12 22 model model NOUN ajst-24979 12 23 in in ADP ajst-24979 12 24 recent recent ADJ ajst-24979 12 25 years year NOUN ajst-24979 12 26 , , PUNCT ajst-24979 12 27 researchers researcher NOUN ajst-24979 12 28 often often ADV ajst-24979 12 29 face face VERB ajst-24979 12 30 parameter parameter NOUN ajst-24979 12 31 uncertainties uncertainty NOUN ajst-24979 12 32 . . PUNCT ajst-24979 13 1 in in ADP ajst-24979 13 2 order order NOUN ajst-24979 13 3 to to PART ajst-24979 13 4 solve solve VERB ajst-24979 13 5 this this DET ajst-24979 13 6 problem problem NOUN ajst-24979 13 7 , , PUNCT ajst-24979 13 8 fuzzy fuzzy ADJ ajst-24979 13 9 concepts concept NOUN ajst-24979 13 10 are be AUX ajst-24979 13 11 introduced introduce VERB ajst-24979 13 12 . . PUNCT ajst-24979 14 1 zadeh zadeh NOUN ajst-24979 15 1 [ [ X ajst-24979 15 2 10,11 10,11 NOUN ajst-24979 15 3 ] ] PUNCT ajst-24979 15 4 introduced introduce VERB ajst-24979 15 5 the the DET ajst-24979 15 6 concept concept NOUN ajst-24979 15 7 of of ADP ajst-24979 15 8 fuzzy fuzzy ADJ ajst-24979 15 9 numbers number NOUN ajst-24979 15 10 and and CCONJ ajst-24979 15 11 its its PRON ajst-24979 15 12 arithmetic arithmetic ADJ ajst-24979 15 13 operations operation NOUN ajst-24979 15 14 , , PUNCT ajst-24979 15 15 mizumoto mizumoto NOUN ajst-24979 15 16 and and CCONJ ajst-24979 15 17 tanaka tanaka PROPN ajst-24979 16 1 [ [ X ajst-24979 16 2 12 12 NUM ajst-24979 16 3 ] ] X ajst-24979 16 4 further far ADV ajst-24979 16 5 enriched enrich VERB ajst-24979 16 6 the the DET ajst-24979 16 7 related relate VERB ajst-24979 16 8 concepts concept NOUN ajst-24979 16 9 of of ADP ajst-24979 16 10 fuzzy fuzzy ADJ ajst-24979 16 11 numbers number NOUN ajst-24979 16 12 . . PUNCT ajst-24979 17 1 dubois dubois PROPN ajst-24979 17 2 and and CCONJ ajst-24979 17 3 prade prade NOUN ajst-24979 17 4 [ [ X ajst-24979 17 5 13 13 NUM ajst-24979 17 6 ] ] PUNCT ajst-24979 17 7 introduced introduce VERB ajst-24979 17 8 the the DET ajst-24979 17 9 concept concept NOUN ajst-24979 17 10 of of ADP ajst-24979 17 11 fuzzy fuzzy ADJ ajst-24979 17 12 function function NOUN ajst-24979 17 13 sets set NOUN ajst-24979 17 14 . . PUNCT ajst-24979 18 1 the the DET ajst-24979 18 2 hukuhara hukuhara ADJ ajst-24979 18 3 derivative derivative NOUN ajst-24979 18 4 of of ADP ajst-24979 18 5 fuzzy fuzzy ADJ ajst-24979 18 6 valued value VERB ajst-24979 18 7 functions function NOUN ajst-24979 18 8 and and CCONJ ajst-24979 18 9 fuzzy fuzzy ADJ ajst-24979 18 10 initial initial ADJ ajst-24979 18 11 value value NOUN ajst-24979 18 12 problems problem NOUN ajst-24979 18 13 was be AUX ajst-24979 18 14 proposed propose VERB ajst-24979 18 15 in in ADP ajst-24979 18 16 [ [ X ajst-24979 18 17 14 14 NUM ajst-24979 18 18 ] ] PUNCT ajst-24979 18 19 and and CCONJ ajst-24979 18 20 studied study VERB ajst-24979 18 21 in in ADP ajst-24979 18 22 [ [ X ajst-24979 18 23 15 15 NUM ajst-24979 18 24 ] ] PUNCT ajst-24979 18 25 . . PUNCT ajst-24979 19 1 in in ADP ajst-24979 19 2 1992 1992 NUM ajst-24979 19 3 , , PUNCT ajst-24979 19 4 liao liao PROPN ajst-24979 19 5 proposed propose VERB ajst-24979 19 6 a a DET ajst-24979 19 7 general general ADJ ajst-24979 19 8 analytical analytical ADJ ajst-24979 19 9 method method NOUN ajst-24979 19 10 for for ADP ajst-24979 19 11 solving solve VERB ajst-24979 19 12 linear linear NOUN ajst-24979 19 13 and and CCONJ ajst-24979 19 14 nonlinear nonlinear ADJ ajst-24979 19 15 problems problem NOUN ajst-24979 19 16 by by ADP ajst-24979 19 17 using use VERB ajst-24979 19 18 the the DET ajst-24979 19 19 basic basic ADJ ajst-24979 19 20 idea idea NOUN ajst-24979 19 21 of of ADP ajst-24979 19 22 homotopy homotopy NOUN ajst-24979 19 23 in in ADP ajst-24979 19 24 topology topology NOUN ajst-24979 19 25 and and CCONJ ajst-24979 19 26 differential differential ADJ ajst-24979 19 27 geometry geometry NOUN ajst-24979 20 1 [ [ X ajst-24979 20 2 16 16 NUM ajst-24979 20 3 ] ] X ajst-24979 20 4 , , PUNCT ajst-24979 20 5 which which PRON ajst-24979 20 6 is be AUX ajst-24979 20 7 called call VERB ajst-24979 20 8 homotopy homotopy NOUN ajst-24979 20 9 analysis analysis NOUN ajst-24979 20 10 method method NOUN ajst-24979 20 11 ( ( PUNCT ajst-24979 20 12 ham ham PROPN ajst-24979 20 13 ) ) PUNCT ajst-24979 20 14 . . PUNCT ajst-24979 21 1 hamoud hamoud NOUN ajst-24979 21 2 and and CCONJ ajst-24979 21 3 ghadle ghadle NOUN ajst-24979 21 4 applied apply VERB ajst-24979 21 5 ham ham NOUN ajst-24979 21 6 to to PART ajst-24979 21 7 solve solve VERB ajst-24979 21 8 fuzzy fuzzy ADJ ajst-24979 21 9 volterra volterra NOUN ajst-24979 21 10 - - PUNCT ajst-24979 21 11 fredholm fredholm NOUN ajst-24979 21 12 integro integro ADJ ajst-24979 21 13 - - PUNCT ajst-24979 21 14 differential differential NOUN ajst-24979 21 15 equations equation NOUN ajst-24979 21 16 [ [ X ajst-24979 21 17 17 17 NUM ajst-24979 21 18 ] ] PUNCT ajst-24979 21 19 . . PUNCT ajst-24979 22 1 hussain hussain PROPN ajst-24979 23 1 [ [ X ajst-24979 23 2 18 18 NUM ajst-24979 23 3 ] ] PUNCT ajst-24979 23 4 used use VERB ajst-24979 23 5 ham ham PROPN ajst-24979 23 6 to to PART ajst-24979 23 7 study study VERB ajst-24979 23 8 fuzzy fuzzy ADJ ajst-24979 23 9 integral integral ADJ ajst-24979 23 10 - - PUNCT ajst-24979 23 11 differential differential NOUN ajst-24979 23 12 equations equation NOUN ajst-24979 23 13 . . PUNCT ajst-24979 24 1 hanan hanan PROPN ajst-24979 25 1 [ [ X ajst-24979 25 2 19 19 NUM ajst-24979 25 3 ] ] PUNCT ajst-24979 25 4 uses use VERB ajst-24979 25 5 ham ham NOUN ajst-24979 25 6 to to PART ajst-24979 25 7 solve solve VERB ajst-24979 25 8 multifractional multifractional ADJ ajst-24979 25 9 order order NOUN ajst-24979 25 10 integro integro ADJ ajst-24979 25 11 - - PUNCT ajst-24979 25 12 differential differential NOUN ajst-24979 25 13 equations equation NOUN ajst-24979 25 14 . . PUNCT ajst-24979 26 1 adomian adomian NOUN ajst-24979 26 2 decomposition decomposition NOUN ajst-24979 26 3 method method NOUN ajst-24979 26 4 ( ( PUNCT ajst-24979 26 5 adm adm PROPN ajst-24979 26 6 ) ) PUNCT ajst-24979 27 1 [ [ X ajst-24979 27 2 20,21 20,21 NUM ajst-24979 27 3 ] ] PUNCT ajst-24979 27 4 , , PUNCT ajst-24979 27 5 laplace laplace NOUN ajst-24979 27 6 transform transform VERB ajst-24979 27 7 method method NOUN ajst-24979 27 8 [ [ X ajst-24979 27 9 22,23 22,23 NOUN ajst-24979 27 10 ] ] PUNCT ajst-24979 27 11 , , PUNCT ajst-24979 27 12 implicit implicit ADJ ajst-24979 27 13 finite finite ADJ ajst-24979 27 14 difference difference NOUN ajst-24979 27 15 method method NOUN ajst-24979 27 16 [ [ X ajst-24979 27 17 24 24 NUM ajst-24979 27 18 ] ] PUNCT ajst-24979 27 19 , , PUNCT ajst-24979 27 20 variational variational ADJ ajst-24979 27 21 iteration iteration NOUN ajst-24979 27 22 method method NOUN ajst-24979 27 23 [ [ X ajst-24979 27 24 25 25 NUM ajst-24979 27 25 ] ] PUNCT ajst-24979 27 26 and and CCONJ ajst-24979 27 27 other other ADJ ajst-24979 27 28 numerical numerical ADJ ajst-24979 27 29 methods method NOUN ajst-24979 27 30 are be AUX ajst-24979 27 31 also also ADV ajst-24979 27 32 applied apply VERB ajst-24979 27 33 to to PART ajst-24979 27 34 solve solve VERB ajst-24979 27 35 fuzzy fuzzy ADJ ajst-24979 27 36 integral integral ADJ ajst-24979 27 37 , , PUNCT ajst-24979 27 38 differential differential ADJ ajst-24979 27 39 and and CCONJ ajst-24979 27 40 integro integro ADJ ajst-24979 27 41 - - PUNCT ajst-24979 27 42 differential differential NOUN ajst-24979 27 43 equations equation NOUN ajst-24979 27 44 . . PUNCT ajst-24979 28 1 in in ADP ajst-24979 28 2 this this DET ajst-24979 28 3 paper paper NOUN ajst-24979 28 4 , , PUNCT ajst-24979 28 5 we we PRON ajst-24979 28 6 mainly mainly ADV ajst-24979 28 7 study study VERB ajst-24979 28 8 ham ham NOUN ajst-24979 28 9 processing processing NOUN ajst-24979 28 10 fuzzy fuzzy ADJ ajst-24979 28 11 fractional fractional ADJ ajst-24979 28 12 volterrafredholm volterrafredholm NOUN ajst-24979 28 13 integro integro ADJ ajst-24979 28 14 - - PUNCT ajst-24979 28 15 differential differential NOUN ajst-24979 28 16 equation equation NOUN ajst-24979 28 17 . . PUNCT ajst-24979 29 1 in in ADP ajst-24979 29 2 addition addition NOUN ajst-24979 29 3 , , PUNCT ajst-24979 29 4 the the DET ajst-24979 29 5 existence existence NOUN ajst-24979 29 6 of of ADP ajst-24979 29 7 solutions solution NOUN ajst-24979 29 8 of of ADP ajst-24979 29 9 fuzzy fuzzy ADJ ajst-24979 29 10 equations equation NOUN ajst-24979 29 11 is be AUX ajst-24979 29 12 also also ADV ajst-24979 29 13 the the DET ajst-24979 29 14 focus focus NOUN ajst-24979 29 15 of of ADP ajst-24979 29 16 researchers researcher NOUN ajst-24979 29 17 . . PUNCT ajst-24979 30 1 in in ADP ajst-24979 30 2 2015 2015 NUM ajst-24979 30 3 , , PUNCT ajst-24979 30 4 arshad arshad VERB ajst-24979 30 5 et et PROPN ajst-24979 30 6 al al PROPN ajst-24979 31 1 [ [ X ajst-24979 31 2 26 26 NUM ajst-24979 31 3 ] ] PUNCT ajst-24979 31 4 studied study VERB ajst-24979 31 5 the the DET ajst-24979 31 6 existence existence NOUN ajst-24979 31 7 and and CCONJ ajst-24979 31 8 uniqueness uniqueness NOUN ajst-24979 31 9 of of ADP ajst-24979 31 10 solutions solution NOUN ajst-24979 31 11 for for ADP ajst-24979 31 12 riemann riemann PROPN ajst-24979 31 13 - - PUNCT ajst-24979 31 14 liouville liouville VERB ajst-24979 31 15 fuzzy fuzzy ADJ ajst-24979 31 16 fractional fractional ADJ ajst-24979 31 17 differential differential ADJ ajst-24979 31 18 equations equation NOUN ajst-24979 31 19 . . PUNCT ajst-24979 32 1 in in ADP ajst-24979 32 2 [ [ X ajst-24979 32 3 27 27 NUM ajst-24979 32 4 ] ] PUNCT ajst-24979 32 5 , , PUNCT ajst-24979 32 6 the the DET ajst-24979 32 7 existence existence NOUN ajst-24979 32 8 and and CCONJ ajst-24979 32 9 uniqueness uniqueness NOUN ajst-24979 32 10 of of ADP ajst-24979 32 11 solutions solution NOUN ajst-24979 32 12 for for ADP ajst-24979 32 13 a a DET ajst-24979 32 14 class class NOUN ajst-24979 32 15 of of ADP ajst-24979 32 16 fractional fractional ADJ ajst-24979 32 17 differential differential ADJ ajst-24979 32 18 equations equation NOUN ajst-24979 32 19 with with ADP ajst-24979 32 20 fuzzy fuzzy ADJ ajst-24979 32 21 initial initial ADJ ajst-24979 32 22 values value NOUN ajst-24979 32 23 defined define VERB ajst-24979 32 24 in in ADP ajst-24979 32 25 the the DET ajst-24979 32 26 sense sense NOUN ajst-24979 32 27 of of ADP ajst-24979 32 28 fuzzy fuzzy ADJ ajst-24979 32 29 caputo caputo PROPN ajst-24979 32 30 were be AUX ajst-24979 32 31 discussed discuss VERB ajst-24979 32 32 . . PUNCT ajst-24979 33 1 ahmad ahmad PROPN ajst-24979 33 2 and and CCONJ ajst-24979 33 3 ullah ullah PROPN ajst-24979 34 1 [ [ X ajst-24979 34 2 28 28 NUM ajst-24979 34 3 ] ] PUNCT ajst-24979 34 4 also also ADV ajst-24979 34 5 studied study VERB ajst-24979 34 6 the the DET ajst-24979 34 7 existence existence NOUN ajst-24979 34 8 and and CCONJ ajst-24979 34 9 uniqueness uniqueness NOUN ajst-24979 34 10 of of ADP ajst-24979 34 11 solutions solution NOUN ajst-24979 34 12 of of ADP ajst-24979 34 13 fuzzy fuzzy ADJ ajst-24979 34 14 fractional fractional ADJ ajst-24979 34 15 volterra volterra NOUN ajst-24979 34 16 - - PUNCT ajst-24979 34 17 fredholm fredholm NOUN ajst-24979 34 18 integrodifferential integrodifferential ADJ ajst-24979 34 19 equation equation NOUN ajst-24979 34 20 in in ADP ajst-24979 34 21 the the DET ajst-24979 34 22 sense sense NOUN ajst-24979 34 23 of of ADP ajst-24979 34 24 caputo caputo PROPN ajst-24979 34 25 . . PUNCT ajst-24979 35 1 allahviranloo allahviranloo PROPN ajst-24979 35 2 et et PROPN ajst-24979 35 3 al al PROPN ajst-24979 35 4 . . PUNCT ajst-24979 36 1 [ [ X ajst-24979 36 2 29 29 NUM ajst-24979 36 3 ] ] PUNCT ajst-24979 36 4 studied study VERB ajst-24979 36 5 the the DET ajst-24979 36 6 fuzzy fuzzy ADJ ajst-24979 36 7 fractional fractional ADJ ajst-24979 36 8 volterra volterra NOUN ajst-24979 36 9 - - PUNCT ajst-24979 36 10 fredholm fredholm NOUN ajst-24979 36 11 integro integro ADJ ajst-24979 36 12 - - PUNCT ajst-24979 36 13 differential differential NOUN ajst-24979 36 14 equation equation NOUN ajst-24979 36 15 in in ADP ajst-24979 36 16 the the DET ajst-24979 36 17 sense sense NOUN ajst-24979 36 18 of of ADP ajst-24979 36 19 fuzzy fuzzy ADJ ajst-24979 36 20 caputo caputo PROPN ajst-24979 36 21 derivative derivative NOUN ajst-24979 36 22 under under ADP ajst-24979 36 23 the the DET ajst-24979 36 24 generalized generalize VERB ajst-24979 36 25 hukuhara hukuhara ADJ ajst-24979 36 26 difference(ghdifference difference(ghdifference PROPN ajst-24979 36 27 ) ) PUNCT ajst-24979 36 28 , , PUNCT ajst-24979 36 29 and and CCONJ ajst-24979 36 30 proved prove VERB ajst-24979 36 31 the the DET ajst-24979 36 32 existence existence NOUN ajst-24979 36 33 and and CCONJ ajst-24979 36 34 uniqueness uniqueness NOUN ajst-24979 36 35 of of ADP ajst-24979 36 36 the the DET ajst-24979 36 37 solution solution NOUN ajst-24979 36 38 of of ADP ajst-24979 36 39 the the DET ajst-24979 36 40 equation equation NOUN ajst-24979 36 41 . . PUNCT ajst-24979 37 1 armand armand PROPN ajst-24979 37 2 and and CCONJ ajst-24979 37 3 gouyandeh gouyandeh PROPN ajst-24979 38 1 [ [ X ajst-24979 38 2 30 30 NUM ajst-24979 38 3 ] ] PUNCT ajst-24979 38 4 introduced introduce VERB ajst-24979 38 5 the the DET ajst-24979 38 6 existence existence NOUN ajst-24979 38 7 and and CCONJ ajst-24979 38 8 uniqueness uniqueness NOUN ajst-24979 38 9 of of ADP ajst-24979 38 10 solutions solution NOUN ajst-24979 38 11 of of ADP ajst-24979 38 12 nonlinear nonlinear ADJ ajst-24979 38 13 fuzzy fuzzy ADJ ajst-24979 38 14 fractional fractional ADJ ajst-24979 38 15 fredholm fredholm NOUN ajst-24979 38 16 integral integral ADJ ajst-24979 38 17 - - PUNCT ajst-24979 38 18 differential differential NOUN ajst-24979 38 19 equations equation NOUN ajst-24979 38 20 under under ADP ajst-24979 38 21 generalized generalized ADJ ajst-24979 38 22 fuzzy fuzzy ADJ ajst-24979 38 23 caputo caputo PROPN ajst-24979 38 24 derivative derivative NOUN ajst-24979 38 25 . . PUNCT ajst-24979 39 1 in in ADP ajst-24979 39 2 this this DET ajst-24979 39 3 paper paper NOUN ajst-24979 39 4 , , PUNCT ajst-24979 39 5 we we PRON ajst-24979 39 6 will will AUX ajst-24979 39 7 discuss discuss VERB ajst-24979 39 8 the the DET ajst-24979 39 9 existence existence NOUN ajst-24979 39 10 and and CCONJ ajst-24979 39 11 uniqueness uniqueness NOUN ajst-24979 39 12 of of ADP ajst-24979 39 13 fuzzy fuzzy ADJ ajst-24979 39 14 fractional fractional ADJ ajst-24979 39 15 volterra volterra NOUN ajst-24979 39 16 - - PUNCT ajst-24979 39 17 fredholm fredholm NOUN ajst-24979 39 18 integro integro ADJ ajst-24979 39 19 - - PUNCT ajst-24979 39 20 differential differential NOUN ajst-24979 39 21 equation equation NOUN ajst-24979 39 22 solution solution NOUN ajst-24979 39 23 in in ADP ajst-24979 39 24 the the DET ajst-24979 39 25 sense sense NOUN ajst-24979 39 26 of of ADP ajst-24979 39 27 fuzzy fuzzy ADJ ajst-24979 39 28 caputo caputo PROPN ajst-24979 39 29 under under ADP ajst-24979 39 30 gh gh PROPN ajst-24979 39 31 - - PUNCT ajst-24979 39 32 difference difference NOUN ajst-24979 39 33 . . PUNCT ajst-24979 40 1 1 1 NUM ajst-24979 40 2 1 1 NUM ajst-24979 40 3 1 1 NUM ajst-24979 40 4 2 2 NUM ajst-24979 40 5 20 20 NUM ajst-24979 40 6 0 0 NUM ajst-24979 40 7 ( ( PUNCT ajst-24979 40 8 , , PUNCT ajst-24979 40 9 ) ) PUNCT ajst-24979 40 10 ( ( PUNCT ajst-24979 40 11 , , PUNCT ajst-24979 40 12 ) ) PUNCT ajst-24979 40 13 ( ( PUNCT ajst-24979 40 14 ) ) PUNCT ajst-24979 40 15 ( ( PUNCT ajst-24979 40 16 , , PUNCT ajst-24979 40 17 ) ) PUNCT ajst-24979 40 18 ( ( PUNCT ajst-24979 40 19 , , PUNCT ajst-24979 40 20 ) ) PUNCT ajst-24979 40 21 ( ( PUNCT ajst-24979 40 22 ( ( PUNCT ajst-24979 40 23 , , PUNCT ajst-24979 40 24 ) ) PUNCT ajst-24979 40 25 ) ) PUNCT ajst-24979 40 26 ( ( PUNCT ajst-24979 40 27 , , PUNCT ajst-24979 40 28 ) ) PUNCT ajst-24979 40 29 ( ( PUNCT ajst-24979 40 30 ( ( PUNCT ajst-24979 40 31 , , PUNCT ajst-24979 40 32 ) ) PUNCT ajst-24979 40 33 ) ) PUNCT ajst-24979 40 34 , , PUNCT ajst-24979 40 35 c c NOUN ajst-24979 40 36 x x PUNCT ajst-24979 41 1 d d X ajst-24979 41 2 w w NOUN ajst-24979 41 3 x x X ajst-24979 41 4 r r NOUN ajst-24979 41 5 g g NOUN ajst-24979 41 6 x x SYM ajst-24979 41 7 r r NOUN ajst-24979 41 8 a a NOUN ajst-24979 41 9 x x X ajst-24979 41 10 w w NOUN ajst-24979 41 11 x x SYM ajst-24979 42 1 r r NOUN ajst-24979 42 2 k k NOUN ajst-24979 42 3 x x SYM ajst-24979 43 1 t t NOUN ajst-24979 43 2 f f PROPN ajst-24979 43 3 w w PROPN ajst-24979 43 4 t t PROPN ajst-24979 43 5 r r NOUN ajst-24979 44 1 dt dt NOUN ajst-24979 44 2 k k NOUN ajst-24979 44 3 x x SYM ajst-24979 45 1 t t NOUN ajst-24979 45 2 f f PROPN ajst-24979 45 3 w w PROPN ajst-24979 45 4 t t PROPN ajst-24979 45 5 r r NOUN ajst-24979 45 6 dt dt X ajst-24979 45 7   NUM ajst-24979 45 8   PROPN ajst-24979 45 9   ADV ajst-24979 45 10   X ajst-24979 45 11   NUM ajst-24979 45 12   PUNCT ajst-24979 45 13 ( ( PUNCT ajst-24979 45 14 1 1 NUM ajst-24979 45 15 ) ) PUNCT ajst-24979 45 16 ( ( PUNCT ajst-24979 45 17 0 0 NUM ajst-24979 45 18 , , PUNCT ajst-24979 45 19 ) ) PUNCT ajst-24979 45 20 [ [ PUNCT ajst-24979 45 21 ( ( PUNCT ajst-24979 45 22 0 0 NUM ajst-24979 45 23 , , PUNCT ajst-24979 45 24 ) ) PUNCT ajst-24979 45 25 , , PUNCT ajst-24979 45 26 ( ( PUNCT ajst-24979 45 27 0 0 NUM ajst-24979 45 28 , , PUNCT ajst-24979 45 29 ) ) PUNCT ajst-24979 46 1 ] ] PUNCT ajst-24979 46 2 , , PUNCT ajst-24979 46 3 w w PROPN ajst-24979 46 4 r r NOUN ajst-24979 46 5 w w PROPN ajst-24979 46 6 r r NOUN ajst-24979 46 7 w w NOUN ajst-24979 46 8 r r X ajst-24979 46 9 ( ( PUNCT ajst-24979 46 10 2 2 NUM ajst-24979 46 11 ) ) PUNCT ajst-24979 46 12 cd cd PROPN ajst-24979 46 13 denotes denote VERB ajst-24979 46 14 the the DET ajst-24979 46 15 caputo caputo PROPN ajst-24979 46 16 fractional fractional PROPN ajst-24979 46 17 generalized generalize VERB ajst-24979 46 18 derivative derivative NOUN ajst-24979 46 19 of of ADP ajst-24979 46 20 order order NOUN ajst-24979 46 21   NUM ajst-24979 46 22 , , PUNCT ajst-24979 46 23 0 0 NUM ajst-24979 46 24 1 1 NUM ajst-24979 46 25   NOUN ajst-24979 46 26 , , PUNCT ajst-24979 46 27 ( ( PUNCT ajst-24979 46 28 , , PUNCT ajst-24979 46 29 ) ) PUNCT ajst-24979 47 1 [ [ PUNCT ajst-24979 47 2 ( ( PUNCT ajst-24979 47 3 , , PUNCT ajst-24979 47 4 ) ) PUNCT ajst-24979 47 5 , , PUNCT ajst-24979 47 6 ( ( PUNCT ajst-24979 47 7 , , PUNCT ajst-24979 47 8 ) ) PUNCT ajst-24979 47 9 ] ] X ajst-24979 47 10 w w X ajst-24979 47 11 x x PUNCT ajst-24979 47 12 r r NOUN ajst-24979 47 13 w w NOUN ajst-24979 47 14 x x X ajst-24979 47 15 r r NOUN ajst-24979 47 16 w w NOUN ajst-24979 47 17 x x NOUN ajst-24979 47 18 r r X ajst-24979 47 19 is be AUX ajst-24979 47 20 a a DET ajst-24979 47 21 fuzzy fuzzy ADJ ajst-24979 47 22 function function NOUN ajst-24979 47 23 . . PUNCT ajst-24979 48 1 1 1 NUM ajst-24979 48 2 ( ( PUNCT ajst-24979 48 3 , , PUNCT ajst-24979 48 4 ) ) PUNCT ajst-24979 48 5 , , PUNCT ajst-24979 48 6 { { PUNCT ajst-24979 48 7 ( ( PUNCT ajst-24979 48 8 , , PUNCT ajst-24979 48 9 ) ) PUNCT ajst-24979 48 10 : : PUNCT ajst-24979 49 1 k k X ajst-24979 49 2 e e PUNCT ajst-24979 49 3 x x X ajst-24979 49 4 t t PROPN ajst-24979 49 5   PUNCT ajst-24979 49 6   PUNCT ajst-24979 50 1   NOUN ajst-24979 50 2 0 0 NUM ajst-24979 51 1 t t NOUN ajst-24979 51 2 x x PROPN ajst-24979 51 3   NUM ajst-24979 51 4 1}, 1}, NUM ajst-24979 51 5 2 2 NUM ajst-24979 51 6 ( ( PUNCT ajst-24979 51 7 [ [ X ajst-24979 51 8 0,1 0,1 X ajst-24979 51 9 ] ] PUNCT ajst-24979 52 1 [ [ X ajst-24979 52 2 0,1 0,1 NUM ajst-24979 52 3 ] ] PUNCT ajst-24979 52 4 , , PUNCT ajst-24979 52 5 ) ) PUNCT ajst-24979 52 6 , , PUNCT ajst-24979 52 7 ( ( PUNCT ajst-24979 52 8 [ [ X ajst-24979 52 9 0,1 0,1 NUM ajst-24979 52 10 ] ] PUNCT ajst-24979 52 11 , , PUNCT ajst-24979 52 12 ) ) PUNCT ajst-24979 52 13 ( ( PUNCT ajst-24979 52 14 1 1 NUM ajst-24979 52 15 , , PUNCT ajst-24979 52 16 2)ik 2)ik PROPN ajst-24979 52 17 c c NOUN ajst-24979 52 18 e e NOUN ajst-24979 52 19 f f PROPN ajst-24979 52 20 c c NOUN ajst-24979 52 21 e e X ajst-24979 52 22 e e PROPN ajst-24979 52 23 i i PROPN ajst-24979 52 24   PROPN ajst-24979 52 25   PROPN ajst-24979 52 26   PROPN ajst-24979 53 1   PROPN ajst-24979 53 2 and and CCONJ ajst-24979 53 3 e e NOUN ajst-24979 53 4 denotes denote VERB ajst-24979 53 5 the the DET ajst-24979 53 6 fuzzy fuzzy ADJ ajst-24979 53 7 number number NOUN ajst-24979 53 8 space space NOUN ajst-24979 53 9 . . PUNCT ajst-24979 54 1 inspired inspire VERB ajst-24979 54 2 by by ADP ajst-24979 54 3 the the DET ajst-24979 54 4 above above ADJ ajst-24979 54 5 literature literature NOUN ajst-24979 54 6 , , PUNCT ajst-24979 54 7 the the DET ajst-24979 54 8 main main ADJ ajst-24979 54 9 contributions contribution NOUN ajst-24979 54 10 of of ADP ajst-24979 54 11 this this DET ajst-24979 54 12 paper paper NOUN ajst-24979 54 13 are be AUX ajst-24979 54 14 as as SCONJ ajst-24979 54 15 follows follow VERB ajst-24979 54 16 . . PUNCT ajst-24979 55 1 we we PRON ajst-24979 55 2 know know VERB ajst-24979 55 3 that that SCONJ ajst-24979 55 4 ham ham NOUN ajst-24979 55 5 is be AUX ajst-24979 55 6 often often ADV ajst-24979 55 7 used use VERB ajst-24979 55 8 to to PART ajst-24979 55 9 solve solve VERB ajst-24979 55 10 linear linear ADJ ajst-24979 55 11 and and CCONJ ajst-24979 55 12 nonlinear nonlinear ADJ ajst-24979 55 13 differentialintegral differentialintegral ADJ ajst-24979 55 14 problems problem NOUN ajst-24979 55 15 . . PUNCT ajst-24979 56 1 in in ADP ajst-24979 56 2 this this DET ajst-24979 56 3 paper paper NOUN ajst-24979 56 4 , , PUNCT ajst-24979 56 5 ham ham PROPN ajst-24979 56 6 is be AUX ajst-24979 56 7 used use VERB ajst-24979 56 8 to to PART ajst-24979 56 9 solve solve VERB ajst-24979 56 10 the the DET ajst-24979 56 11 approximate approximate ADJ ajst-24979 56 12 solutions solution NOUN ajst-24979 56 13 of of ADP ajst-24979 56 14 linear linear PROPN ajst-24979 56 15 and and CCONJ ajst-24979 56 16 nonlinear nonlinear ADJ ajst-24979 56 17 fuzzy fuzzy ADJ ajst-24979 56 18 fractional fractional ADJ ajst-24979 56 19 volterra volterra NOUN ajst-24979 56 20 - - PUNCT ajst-24979 56 21 fredholm fredholm NOUN ajst-24979 56 22 integro integro ADJ ajst-24979 56 23 - - PUNCT ajst-24979 56 24 differential differential NOUN ajst-24979 56 25 equation equation NOUN ajst-24979 56 26 , , PUNCT ajst-24979 56 27 and and CCONJ ajst-24979 56 28 the the DET ajst-24979 56 29 effectiveness effectiveness NOUN ajst-24979 56 30 and and CCONJ ajst-24979 56 31 applicability applicability NOUN ajst-24979 56 32 of of ADP ajst-24979 56 33 the the DET ajst-24979 56 34 method method NOUN ajst-24979 56 35 are be AUX ajst-24979 56 36 illustrated illustrate VERB ajst-24979 56 37 by by ADP ajst-24979 56 38 numerical numerical ADJ ajst-24979 56 39 examples example NOUN ajst-24979 56 40 . . PUNCT ajst-24979 57 1 another another DET ajst-24979 57 2 contribution contribution NOUN ajst-24979 57 3 is be AUX ajst-24979 57 4 to to PART ajst-24979 57 5 prove prove VERB ajst-24979 57 6 the the DET ajst-24979 57 7 existence existence NOUN ajst-24979 57 8 and and CCONJ ajst-24979 57 9 uniqueness uniqueness NOUN ajst-24979 57 10 of of ADP ajst-24979 57 11 solution solution NOUN ajst-24979 57 12 by by ADP ajst-24979 57 13 using use VERB ajst-24979 57 14 fixed fix VERB ajst-24979 57 15 point point NOUN ajst-24979 57 16 theorem theorem VERB ajst-24979 57 17 . . PROPN ajst-24979 58 1 based base VERB ajst-24979 58 2 on on ADP ajst-24979 58 3 the the DET ajst-24979 58 4 parametric parametric ADJ ajst-24979 58 5 representation representation NOUN ajst-24979 58 6 of of ADP ajst-24979 58 7 fuzzy fuzzy ADJ ajst-24979 58 8 numbers number NOUN ajst-24979 58 9 , , PUNCT ajst-24979 58 10 the the DET ajst-24979 58 11 set set NOUN ajst-24979 58 12 of of ADP ajst-24979 58 13 one one NUM ajst-24979 58 14 - - PUNCT ajst-24979 58 15 dimensional dimensional ADJ ajst-24979 58 16 fuzzy fuzzy ADJ ajst-24979 58 17 numbers number NOUN ajst-24979 58 18 can can AUX ajst-24979 58 19 be be AUX ajst-24979 58 20 regarded regard VERB ajst-24979 58 21 as as ADP ajst-24979 58 22 a a DET ajst-24979 58 23 closed closed ADJ ajst-24979 58 24 convex convex NOUN ajst-24979 58 25 set set VERB ajst-24979 58 26 in in ADP ajst-24979 58 27 banach banach NOUN ajst-24979 58 28 space space NOUN ajst-24979 58 29 . . PUNCT ajst-24979 59 1 the the DET ajst-24979 59 2 structure structure NOUN ajst-24979 59 3 of of ADP ajst-24979 59 4 this this DET ajst-24979 59 5 paper paper NOUN ajst-24979 59 6 is be AUX ajst-24979 59 7 as as SCONJ ajst-24979 59 8 follows follow VERB ajst-24979 59 9 : : PUNCT ajst-24979 59 10 section section NOUN ajst-24979 59 11 2 2 NUM ajst-24979 59 12 mainly mainly ADV ajst-24979 59 13 introduces introduce VERB ajst-24979 59 14 the the DET ajst-24979 59 15 fuzzy fuzzy ADJ ajst-24979 59 16 definition definition NOUN ajst-24979 59 17 and and CCONJ ajst-24979 59 18 fixed fix VERB ajst-24979 59 19 point point NOUN ajst-24979 59 20 theorem theorem VERB ajst-24979 59 21 . . PROPN ajst-24979 59 22 173 173 NUM ajst-24979 59 23 section section NOUN ajst-24979 59 24 3 3 NUM ajst-24979 59 25 introduces introduce VERB ajst-24979 59 26 the the DET ajst-24979 59 27 iterative iterative NOUN ajst-24979 59 28 scheme scheme NOUN ajst-24979 59 29 of of ADP ajst-24979 59 30 ham ham NOUN ajst-24979 59 31 and and CCONJ ajst-24979 59 32 its its PRON ajst-24979 59 33 application application NOUN ajst-24979 59 34 in in ADP ajst-24979 59 35 fuzzy fuzzy ADJ ajst-24979 59 36 fractional fractional ADJ ajst-24979 59 37 volterra volterra NOUN ajst-24979 59 38 - - PUNCT ajst-24979 59 39 fredholm fredholm NOUN ajst-24979 59 40 integrodifferential integrodifferential ADJ ajst-24979 59 41 equation equation NOUN ajst-24979 59 42 . . PUNCT ajst-24979 60 1 in in ADP ajst-24979 60 2 section section NOUN ajst-24979 60 3 4 4 NUM ajst-24979 60 4 , , PUNCT ajst-24979 60 5 the the DET ajst-24979 60 6 existence existence NOUN ajst-24979 60 7 and and CCONJ ajst-24979 60 8 uniqueness uniqueness NOUN ajst-24979 60 9 of of ADP ajst-24979 60 10 solutions solution NOUN ajst-24979 60 11 for for ADP ajst-24979 60 12 fuzzy fuzzy ADJ ajst-24979 60 13 fractional fractional ADJ ajst-24979 60 14 volterrafredholm volterrafredholm NOUN ajst-24979 60 15 integro integro ADJ ajst-24979 60 16 - - PUNCT ajst-24979 60 17 differential differential NOUN ajst-24979 60 18 equation equation NOUN ajst-24979 60 19 are be AUX ajst-24979 60 20 studied study VERB ajst-24979 60 21 . . PUNCT ajst-24979 61 1 we we PRON ajst-24979 61 2 provide provide VERB ajst-24979 61 3 several several ADJ ajst-24979 61 4 numerical numerical ADJ ajst-24979 61 5 examples example NOUN ajst-24979 61 6 and and CCONJ ajst-24979 61 7 analysis analysis NOUN ajst-24979 61 8 of of ADP ajst-24979 61 9 numerical numerical ADJ ajst-24979 61 10 results result NOUN ajst-24979 61 11 in in ADP ajst-24979 61 12 section section NOUN ajst-24979 61 13 5 5 NUM ajst-24979 61 14 . . PUNCT ajst-24979 62 1 finally finally ADV ajst-24979 62 2 , , PUNCT ajst-24979 62 3 section section NOUN ajst-24979 62 4 6 6 NUM ajst-24979 62 5 gives give VERB ajst-24979 62 6 a a DET ajst-24979 62 7 brief brief ADJ ajst-24979 62 8 conclusion conclusion NOUN ajst-24979 62 9 . . PUNCT ajst-24979 63 1 2 2 X ajst-24979 63 2 . . X ajst-24979 63 3 preliminaries preliminary NOUN ajst-24979 63 4 in in ADP ajst-24979 63 5 this this DET ajst-24979 63 6 section section NOUN ajst-24979 63 7 , , PUNCT ajst-24979 63 8 we we PRON ajst-24979 63 9 will will AUX ajst-24979 63 10 give give VERB ajst-24979 63 11 the the DET ajst-24979 63 12 related relate VERB ajst-24979 63 13 concepts concept NOUN ajst-24979 63 14 of of ADP ajst-24979 63 15 fuzzy fuzzy ADJ ajst-24979 63 16 numbers number NOUN ajst-24979 63 17 , , PUNCT ajst-24979 63 18 and and CCONJ ajst-24979 63 19 some some DET ajst-24979 63 20 important important ADJ ajst-24979 63 21 theorems theorem NOUN ajst-24979 63 22 and and CCONJ ajst-24979 63 23 symbols symbol NOUN ajst-24979 63 24 used use VERB ajst-24979 63 25 in in ADP ajst-24979 63 26 the the DET ajst-24979 63 27 article article NOUN ajst-24979 63 28 . . PUNCT ajst-24979 64 1 definition2.1 definition2.1 VERB ajst-24979 64 2 . . PUNCT ajst-24979 65 1 [ [ X ajst-24979 65 2 31,32 31,32 NUM ajst-24979 65 3 ] ] X ajst-24979 65 4 r r NOUN ajst-24979 65 5 denotes denote VERB ajst-24979 65 6 the the DET ajst-24979 65 7 set set NOUN ajst-24979 65 8 of of ADP ajst-24979 65 9 all all DET ajst-24979 65 10 fuzzy fuzzy ADJ ajst-24979 65 11 sets set NOUN ajst-24979 65 12 on on ADP ajst-24979 65 13 r. r. PROPN ajst-24979 65 14 let let VERB ajst-24979 65 15 h h PRON ajst-24979 65 16 ∈ ∈ PROPN ajst-24979 65 17 r r NOUN ajst-24979 65 18 , , PUNCT ajst-24979 65 19 if if SCONJ ajst-24979 65 20 h h NOUN ajst-24979 65 21 satisfies satisfie NOUN ajst-24979 65 22 ( ( PUNCT ajst-24979 65 23 i i NOUN ajst-24979 65 24 ) ) PUNCT ajst-24979 65 25 h h PROPN ajst-24979 65 26 is be AUX ajst-24979 65 27 a a DET ajst-24979 65 28 normal normal ADJ ajst-24979 65 29 fuzzy fuzzy ADJ ajst-24979 65 30 set set NOUN ajst-24979 65 31 , , PUNCT ajst-24979 65 32 i.e. i.e. X ajst-24979 65 33 , , PUNCT ajst-24979 65 34 there there PRON ajst-24979 65 35 exists exist VERB ajst-24979 65 36 s s PROPN ajst-24979 65 37 ∈ ∈ PROPN ajst-24979 65 38 r r NOUN ajst-24979 65 39 such such ADJ ajst-24979 65 40 that that SCONJ ajst-24979 65 41 h h NOUN ajst-24979 65 42 s s VERB ajst-24979 65 43 1 1 NUM ajst-24979 65 44 , , PUNCT ajst-24979 65 45 ( ( PUNCT ajst-24979 65 46 ii ii NOUN ajst-24979 65 47 ) ) PUNCT ajst-24979 65 48 h h NOUN ajst-24979 65 49 is be AUX ajst-24979 65 50 a a DET ajst-24979 65 51 convex convex ADJ ajst-24979 65 52 fuzzy fuzzy ADJ ajst-24979 65 53 set set NOUN ajst-24979 65 54 , , PUNCT ajst-24979 65 55 i.e. i.e. X ajst-24979 65 56 , , PUNCT ajst-24979 65 57 h h NOUN ajst-24979 65 58 δs δs VERB ajst-24979 65 59 1 1 NUM ajst-24979 65 60 δ δ PROPN ajst-24979 65 61 s s PART ajst-24979 65 62 min min NOUN ajst-24979 65 63 h h PROPN ajst-24979 65 64 s s PROPN ajst-24979 65 65 , , PUNCT ajst-24979 65 66 h h PROPN ajst-24979 65 67 s s PROPN ajst-24979 65 68 for for ADP ajst-24979 65 69 all all DET ajst-24979 65 70 s s NOUN ajst-24979 65 71 , , PUNCT ajst-24979 65 72 s s NOUN ajst-24979 65 73 ∈ ∈ PROPN ajst-24979 65 74 r r NOUN ajst-24979 65 75 and and CCONJ ajst-24979 65 76 δ δ PROPN ajst-24979 65 77 ∈ ∈ PROPN ajst-24979 65 78 0,1 0,1 NUM ajst-24979 65 79 , , PUNCT ajst-24979 65 80 ( ( PUNCT ajst-24979 65 81 iii iii X ajst-24979 65 82 ) ) PUNCT ajst-24979 65 83 h h NOUN ajst-24979 65 84 is be AUX ajst-24979 65 85 an an DET ajst-24979 65 86 upper upper ADJ ajst-24979 65 87 semi semi ADJ ajst-24979 65 88 - - ADJ ajst-24979 65 89 continuous continuous ADJ ajst-24979 65 90 function function NOUN ajst-24979 65 91 , , PUNCT ajst-24979 65 92 ( ( PUNCT ajst-24979 65 93 iv iv X ajst-24979 65 94 ) ) PUNCT ajst-24979 65 95 the the DET ajst-24979 65 96 closure closure NOUN ajst-24979 65 97 of of ADP ajst-24979 65 98 the the DET ajst-24979 65 99 support support NOUN ajst-24979 65 100 of of ADP ajst-24979 65 101 h h NOUN ajst-24979 65 102 is be AUX ajst-24979 65 103 compact compact ADJ ajst-24979 65 104 , , PUNCT ajst-24979 65 105 i.e. i.e. X ajst-24979 65 106 , , PUNCT ajst-24979 65 107 h h NOUN ajst-24979 65 108 is be AUX ajst-24979 65 109 compact compact ADJ ajst-24979 65 110 ; ; PUNCT ajst-24979 65 111 then then ADV ajst-24979 65 112 h h NOUN ajst-24979 65 113 is be AUX ajst-24979 65 114 called call VERB ajst-24979 65 115 as as ADP ajst-24979 65 116 a a DET ajst-24979 65 117 fuzzy fuzzy ADJ ajst-24979 65 118 number number NOUN ajst-24979 65 119 . . PUNCT ajst-24979 66 1 the the DET ajst-24979 66 2 set set NOUN ajst-24979 66 3 of of ADP ajst-24979 66 4 all all DET ajst-24979 66 5 fuzzy fuzzy ADJ ajst-24979 66 6 numbers number NOUN ajst-24979 66 7 is be AUX ajst-24979 66 8 known know VERB ajst-24979 66 9 as as ADP ajst-24979 66 10 the the DET ajst-24979 66 11 fuzzy fuzzy ADJ ajst-24979 66 12 number number NOUN ajst-24979 66 13 space space NOUN ajst-24979 66 14 , , PUNCT ajst-24979 66 15 denoted denote VERB ajst-24979 66 16 by by ADP ajst-24979 66 17 e. e. PROPN ajst-24979 66 18 definition2.2 definition2.2 PROPN ajst-24979 66 19 . . PUNCT ajst-24979 67 1 [ [ X ajst-24979 67 2 33 33 NUM ajst-24979 67 3 ] ] PUNCT ajst-24979 67 4 given give VERB ajst-24979 67 5 0 0 NUM ajst-24979 67 6 r r NOUN ajst-24979 67 7 1 1 NUM ajst-24979 67 8 , , PUNCT ajst-24979 67 9 a a DET ajst-24979 67 10 fuzzy fuzzy ADJ ajst-24979 67 11 number number NOUN ajst-24979 67 12 h h NOUN ajst-24979 67 13 in in ADP ajst-24979 67 14 parametric parametric ADJ ajst-24979 67 15 form form NOUN ajst-24979 67 16 is be AUX ajst-24979 67 17 represented represent VERB ajst-24979 67 18 by by ADP ajst-24979 67 19 an an DET ajst-24979 67 20 ordered order VERB ajst-24979 67 21 function function NOUN ajst-24979 67 22 pairs pair NOUN ajst-24979 67 23 h h NOUN ajst-24979 67 24 r r NOUN ajst-24979 67 25 , , PUNCT ajst-24979 67 26 h h NOUN ajst-24979 67 27 r r NOUN ajst-24979 67 28 satisfying satisfying NOUN ajst-24979 67 29 ( ( PUNCT ajst-24979 67 30 i i NOUN ajst-24979 67 31 ) ) PUNCT ajst-24979 68 1 h h NOUN ajst-24979 68 2 r r NOUN ajst-24979 68 3 is be AUX ajst-24979 68 4 a a DET ajst-24979 68 5 bounded bound VERB ajst-24979 68 6 left leave VERB ajst-24979 68 7 continuous continuous ADJ ajst-24979 68 8 non non ADJ ajst-24979 68 9 decreasing decrease VERB ajst-24979 68 10 function function NOUN ajst-24979 68 11 , , PUNCT ajst-24979 68 12 ( ( PUNCT ajst-24979 68 13 ii ii NOUN ajst-24979 68 14 ) ) PUNCT ajst-24979 68 15 h h NOUN ajst-24979 69 1 r r NOUN ajst-24979 69 2 is be AUX ajst-24979 69 3 a a DET ajst-24979 69 4 bounded bound VERB ajst-24979 69 5 left leave VERB ajst-24979 69 6 continuous continuous ADJ ajst-24979 69 7 non non ADJ ajst-24979 69 8 increasing increase VERB ajst-24979 69 9 function function NOUN ajst-24979 69 10 , , PUNCT ajst-24979 69 11 ( ( PUNCT ajst-24979 69 12 iii iii X ajst-24979 69 13 ) ) PUNCT ajst-24979 69 14 h h NOUN ajst-24979 70 1 r r NOUN ajst-24979 70 2 h h NOUN ajst-24979 70 3 r r NOUN ajst-24979 70 4 . . PUNCT ajst-24979 71 1 for for ADP ajst-24979 71 2 h h PROPN ajst-24979 71 3 h h PROPN ajst-24979 71 4 , , PUNCT ajst-24979 71 5 h h NOUN ajst-24979 71 6 , , PUNCT ajst-24979 71 7 v v NOUN ajst-24979 71 8 v v NOUN ajst-24979 71 9 , , PUNCT ajst-24979 71 10 v v NOUN ajst-24979 71 11 ∈ ∈ NOUN ajst-24979 71 12 e e NOUN ajst-24979 71 13 and and CCONJ ajst-24979 71 14 δ δ PROPN ajst-24979 71 15 ∈ ∈ PROPN ajst-24979 71 16 r r NOUN ajst-24979 71 17 , , PUNCT ajst-24979 71 18 the the DET ajst-24979 71 19 sum sum NOUN ajst-24979 71 20 of of ADP ajst-24979 71 21 v v NOUN ajst-24979 71 22 h h NOUN ajst-24979 71 23 and and CCONJ ajst-24979 71 24 the the DET ajst-24979 71 25 scalar scalar ADJ ajst-24979 71 26 multiplication multiplication NOUN ajst-24979 71 27 δh δh NOUN ajst-24979 71 28 can can AUX ajst-24979 71 29 be be AUX ajst-24979 71 30 defined define VERB ajst-24979 71 31 by by ADP ajst-24979 71 32 v v NUM ajst-24979 71 33 h h NOUN ajst-24979 71 34 r r NOUN ajst-24979 71 35 v v NOUN ajst-24979 71 36 r r NOUN ajst-24979 71 37 h h NOUN ajst-24979 71 38 r r NOUN ajst-24979 71 39 , , PUNCT ajst-24979 71 40     SPACE ajst-24979 71 41 v v NOUN ajst-24979 72 1 h h NOUN ajst-24979 72 2 r r NOUN ajst-24979 72 3 v v NOUN ajst-24979 72 4 r r NOUN ajst-24979 72 5 h h NOUN ajst-24979 72 6 r r NOUN ajst-24979 72 7 , , PUNCT ajst-24979 72 8     SPACE ajst-24979 72 9 ∀r ∀r SYM ajst-24979 72 10 ∈ ∈ NOUN ajst-24979 72 11 0,1 0,1 NUM ajst-24979 72 12 , , PUNCT ajst-24979 72 13 and and CCONJ ajst-24979 72 14 δh δh ADP ajst-24979 72 15 δh δh NOUN ajst-24979 72 16 , , PUNCT ajst-24979 72 17 δh δh INTJ ajst-24979 72 18 , , PUNCT ajst-24979 72 19 δ δ PROPN ajst-24979 72 20 0 0 NUM ajst-24979 72 21 , , PUNCT ajst-24979 72 22 δh δh NOUN ajst-24979 72 23 , , PUNCT ajst-24979 72 24 δh δh INTJ ajst-24979 72 25 , , PUNCT ajst-24979 72 26 δ δ PROPN ajst-24979 72 27 0 0 NUM ajst-24979 72 28 . . PUNCT ajst-24979 73 1 definition2.3 definition2.3 VERB ajst-24979 73 2 . . PUNCT ajst-24979 74 1 [ [ X ajst-24979 74 2 29 29 NUM ajst-24979 74 3 ] ] PUNCT ajst-24979 74 4 for for ADP ajst-24979 74 5 any any DET ajst-24979 74 6 two two NUM ajst-24979 74 7 fuzzy fuzzy ADJ ajst-24979 74 8 numbers number NOUN ajst-24979 74 9 w w ADJ ajst-24979 74 10 and and CCONJ ajst-24979 74 11 h h NOUN ajst-24979 74 12 , , PUNCT ajst-24979 74 13 defin defin NOUN ajst-24979 74 14 d d NOUN ajst-24979 74 15 : : PUNCT ajst-24979 74 16 e e X ajst-24979 74 17 e e X ajst-24979 74 18 → → SYM ajst-24979 74 19 r r NOUN ajst-24979 74 20 ∪ ∪ NOUN ajst-24979 74 21 0 0 NUM ajst-24979 74 22 by by ADP ajst-24979 74 23 d d PROPN ajst-24979 74 24 v v PROPN ajst-24979 74 25 , , PUNCT ajst-24979 74 26 h h NOUN ajst-24979 74 27 sup sup NOUN ajst-24979 74 28 ∈ ∈ PROPN ajst-24979 74 29 , , PUNCT ajst-24979 74 30 max max PROPN ajst-24979 74 31 ∣ ∣ PROPN ajst-24979 74 32 v v NOUN ajst-24979 74 33 r r NOUN ajst-24979 74 34 h h NOUN ajst-24979 74 35 r r NOUN ajst-24979 74 36 ∣ ∣ NOUN ajst-24979 74 37 , , PUNCT ajst-24979 74 38 ∣ ∣ ADJ ajst-24979 74 39 v v NOUN ajst-24979 74 40 r r NOUN ajst-24979 74 41 h h NOUN ajst-24979 74 42 r r NOUN ajst-24979 74 43 ∣ ∣ PROPN ajst-24979 74 44 . . PUNCT ajst-24979 75 1 where where SCONJ ajst-24979 75 2 v v ADP ajst-24979 75 3 v v NOUN ajst-24979 75 4 r r NOUN ajst-24979 75 5 , , PUNCT ajst-24979 75 6 v v NOUN ajst-24979 75 7 r r NOUN ajst-24979 75 8 , , PUNCT ajst-24979 75 9 h h NOUN ajst-24979 75 10 h h NOUN ajst-24979 76 1 r r NOUN ajst-24979 76 2 , , PUNCT ajst-24979 76 3 h h NOUN ajst-24979 76 4 r r NOUN ajst-24979 76 5 . . PUNCT ajst-24979 77 1 it it PRON ajst-24979 77 2 has have VERB ajst-24979 77 3 the the DET ajst-24979 77 4 following follow VERB ajst-24979 77 5 useful useful ADJ ajst-24979 77 6 propertie propertie NOUN ajst-24979 77 7 . . PUNCT ajst-24979 78 1 for for ADP ajst-24979 78 2 ∀w ∀w PROPN ajst-24979 78 3 , , PUNCT ajst-24979 78 4 h h NOUN ajst-24979 78 5 , , PUNCT ajst-24979 78 6 v v NOUN ajst-24979 78 7 , , PUNCT ajst-24979 78 8 α α NOUN ajst-24979 78 9 ∈ ∈ PROPN ajst-24979 78 10 e e NOUN ajst-24979 78 11 , , PUNCT ajst-24979 78 12 there there PRON ajst-24979 78 13 are be VERB ajst-24979 78 14 ( ( PUNCT ajst-24979 78 15 i i NOUN ajst-24979 78 16 ) ) PUNCT ajst-24979 78 17 e e X ajst-24979 78 18 , , PUNCT ajst-24979 78 19 d d PRON ajst-24979 78 20 is be AUX ajst-24979 78 21 a a DET ajst-24979 78 22 complete complete ADJ ajst-24979 78 23 metric metric ADJ ajst-24979 78 24 space space NOUN ajst-24979 78 25 , , PUNCT ajst-24979 78 26 ( ( PUNCT ajst-24979 78 27 ii ii NOUN ajst-24979 78 28 ) ) PUNCT ajst-24979 78 29 d d PROPN ajst-24979 78 30 w w PROPN ajst-24979 78 31 v v PROPN ajst-24979 78 32 , , PUNCT ajst-24979 78 33 h h NOUN ajst-24979 79 1 v v NOUN ajst-24979 79 2 d d PROPN ajst-24979 79 3 w w PROPN ajst-24979 79 4 , , PUNCT ajst-24979 79 5 h h NOUN ajst-24979 79 6 , , PUNCT ajst-24979 79 7 ( ( PUNCT ajst-24979 79 8 iii iii X ajst-24979 79 9 ) ) PUNCT ajst-24979 79 10 d d PROPN ajst-24979 79 11 w w PROPN ajst-24979 79 12 , , PUNCT ajst-24979 79 13 h h NOUN ajst-24979 80 1 d d X ajst-24979 80 2 w w PROPN ajst-24979 80 3 , , PUNCT ajst-24979 80 4 v v NOUN ajst-24979 80 5 d d PROPN ajst-24979 80 6 v v NOUN ajst-24979 80 7 , , PUNCT ajst-24979 80 8 h h NOUN ajst-24979 80 9 , , PUNCT ajst-24979 80 10 ( ( PUNCT ajst-24979 80 11 iv iv X ajst-24979 80 12 ) ) PUNCT ajst-24979 80 13 d d NOUN ajst-24979 80 14 αw αw ADP ajst-24979 80 15 , , PUNCT ajst-24979 80 16 αh αh ADP ajst-24979 80 17 ∥ ∥ NOUN ajst-24979 80 18 α α NOUN ajst-24979 80 19 ∥ ∥ PUNCT ajst-24979 80 20 d d NOUN ajst-24979 80 21 w w NOUN ajst-24979 80 22 , , PUNCT ajst-24979 80 23 h h NOUN ajst-24979 80 24 , , PUNCT ajst-24979 80 25 ( ( PUNCT ajst-24979 80 26 see see VERB ajst-24979 80 27 [ [ X ajst-24979 80 28 23 23 NUM ajst-24979 80 29 ] ] PUNCT ajst-24979 80 30 ) ) PUNCT ajst-24979 80 31 . . PUNCT ajst-24979 81 1 ( ( PUNCT ajst-24979 81 2 v v NOUN ajst-24979 81 3 ) ) PUNCT ajst-24979 81 4 ∥ ∥ PUNCT ajst-24979 81 5 w w NOUN ajst-24979 81 6 ∥ ∥ PUNCT ajst-24979 81 7 d d NOUN ajst-24979 81 8 w w NOUN ajst-24979 81 9 , , PUNCT ajst-24979 81 10 0 0 NUM ajst-24979 81 11 , , PUNCT ajst-24979 81 12 ( ( PUNCT ajst-24979 81 13 see see VERB ajst-24979 81 14 [ [ X ajst-24979 81 15 24 24 NUM ajst-24979 81 16 ] ] PUNCT ajst-24979 81 17 ) ) PUNCT ajst-24979 81 18 . . PUNCT ajst-24979 82 1 ( ( PUNCT ajst-24979 82 2 vi vi X ajst-24979 82 3 ) ) PUNCT ajst-24979 82 4 d d X ajst-24979 82 5 w w PROPN ajst-24979 82 6 s s X ajst-24979 82 7 ds ds PROPN ajst-24979 82 8 , , PUNCT ajst-24979 82 9 h h NOUN ajst-24979 82 10 s s NOUN ajst-24979 82 11 ds ds PROPN ajst-24979 82 12 d d X ajst-24979 82 13 w w PROPN ajst-24979 82 14 s s PROPN ajst-24979 82 15 , , PUNCT ajst-24979 83 1 h h PROPN ajst-24979 83 2 s s X ajst-24979 83 3 ds ds PROPN ajst-24979 83 4 , , PUNCT ajst-24979 83 5 ( ( PUNCT ajst-24979 83 6 vii vii PROPN ajst-24979 83 7 ) ) PUNCT ajst-24979 83 8 d d PROPN ajst-24979 83 9 w w PROPN ajst-24979 83 10 ∗ ∗ PROPN ajst-24979 83 11 h h NOUN ajst-24979 83 12 , , PUNCT ajst-24979 83 13 0 0 NUM ajst-24979 83 14 d d NOUN ajst-24979 83 15 w w PROPN ajst-24979 83 16 , , PUNCT ajst-24979 83 17 0 0 NUM ajst-24979 83 18 d d NOUN ajst-24979 83 19 h h NOUN ajst-24979 83 20 , , PUNCT ajst-24979 83 21 0 0 NUM ajst-24979 83 22 with with ADP ajst-24979 83 23 the the DET ajst-24979 83 24 fuzzy fuzzy ADJ ajst-24979 83 25 multiplication multiplication NOUN ajst-24979 83 26 ∗ ∗ NOUN ajst-24979 83 27 is be AUX ajst-24979 83 28 based base VERB ajst-24979 83 29 on on ADP ajst-24979 83 30 the the DET ajst-24979 83 31 extension extension NOUN ajst-24979 83 32 principle principle NOUN ajst-24979 83 33 that that PRON ajst-24979 83 34 can can AUX ajst-24979 83 35 be be AUX ajst-24979 83 36 proved prove VERB ajst-24979 83 37 by by ADP ajst-24979 83 38 α α PROPN ajst-24979 83 39 -cuts -cut NOUN ajst-24979 83 40 of of ADP ajst-24979 83 41 fuzzy fuzzy ADJ ajst-24979 83 42 numbers number NOUN ajst-24979 83 43 w w PROPN ajst-24979 83 44 , , PUNCT ajst-24979 83 45 h h PROPN ajst-24979 83 46 ∈ ∈ PROPN ajst-24979 83 47 e. e. PROPN ajst-24979 83 48 here here ADV ajst-24979 83 49 0 0 NUM ajst-24979 84 1 ∈ ∈ NOUN ajst-24979 84 2 e e NOUN ajst-24979 84 3 is be AUX ajst-24979 84 4 defined define VERB ajst-24979 84 5 by by ADP ajst-24979 84 6 ( ( PUNCT ajst-24979 84 7 see see VERB ajst-24979 84 8 [ [ X ajst-24979 84 9 25 25 NUM ajst-24979 84 10 ] ] SYM ajst-24979 84 11 ) ) PUNCT ajst-24979 84 12 1 1 NUM ajst-24979 84 13 , , PUNCT ajst-24979 84 14 0 0 NUM ajst-24979 84 15 , , PUNCT ajst-24979 84 16 0 0 NUM ajst-24979 84 17 ( ( PUNCT ajst-24979 84 18 ) ) PUNCT ajst-24979 84 19 0 0 NUM ajst-24979 84 20 , , PUNCT ajst-24979 84 21 . . PUNCT ajst-24979 85 1 s s AUX ajst-24979 85 2 t t PROPN ajst-24979 85 3 elsewhere elsewhere ADV ajst-24979 85 4   NOUN ajst-24979 85 5   PROPN ajst-24979 86 1   NUM ajst-24979 86 2   NUM ajst-24979 86 3   NOUN ajst-24979 87 1 3 3 NUM ajst-24979 87 2 . . X ajst-24979 87 3 homotopy homotopy VERB ajst-24979 87 4 analysis analysis NOUN ajst-24979 87 5 method method NOUN ajst-24979 87 6 to to PART ajst-24979 87 7 illustrate illustrate VERB ajst-24979 87 8 the the DET ajst-24979 87 9 basic basic ADJ ajst-24979 87 10 idea idea NOUN ajst-24979 87 11 of of ADP ajst-24979 87 12 ham ham NOUN ajst-24979 87 13 , , PUNCT ajst-24979 87 14 consider consider VERB ajst-24979 87 15 the the DET ajst-24979 87 16 following follow VERB ajst-24979 87 17 differential differential ADJ ajst-24979 87 18 equation equation NOUN ajst-24979 87 19 [ [ PUNCT ajst-24979 87 20 ( ( PUNCT ajst-24979 87 21 ) ) PUNCT ajst-24979 87 22 ] ] PUNCT ajst-24979 88 1 0,n 0,n ADJ ajst-24979 88 2 w w ADP ajst-24979 88 3 x x SYM ajst-24979 88 4   NOUN ajst-24979 88 5                                                                 SPACE ajst-24979 88 6 ( ( PUNCT ajst-24979 88 7 3 3 NUM ajst-24979 88 8 ) ) PUNCT ajst-24979 88 9     SPACE ajst-24979 88 10 where where SCONJ ajst-24979 88 11 n n PRON ajst-24979 88 12 is be AUX ajst-24979 88 13 a a DET ajst-24979 88 14 nonlinear nonlinear ADJ ajst-24979 88 15 operator operator NOUN ajst-24979 88 16 and and CCONJ ajst-24979 88 17 ( ( PUNCT ajst-24979 88 18 ) ) PUNCT ajst-24979 88 19 w w X ajst-24979 88 20 x x PUNCT ajst-24979 88 21 is be AUX ajst-24979 88 22 an an DET ajst-24979 88 23 unknown unknown ADJ ajst-24979 88 24 function function NOUN ajst-24979 88 25 . . PUNCT ajst-24979 89 1 the the DET ajst-24979 89 2 following follow VERB ajst-24979 89 3 homotopy homotopy NOUN ajst-24979 89 4 can can AUX ajst-24979 89 5 be be AUX ajst-24979 89 6 constructed construct VERB ajst-24979 89 7 when when SCONJ ajst-24979 89 8 [ [ PUNCT ajst-24979 89 9 ( ( PUNCT ajst-24979 89 10 ) ) PUNCT ajst-24979 89 11 ] ] PUNCT ajst-24979 89 12 0n 0n NOUN ajst-24979 89 13 w w NOUN ajst-24979 89 14 x x X ajst-24979 89 15   NOUN ajst-24979 89 16 . . PUNCT ajst-24979 90 1 0 0 NUM ajst-24979 90 2 1 1 NUM ajst-24979 90 3 0 0 NUM ajst-24979 90 4 1 1 NUM ajst-24979 90 5 ( ( PUNCT ajst-24979 90 6 1 1 NUM ajst-24979 90 7 ) ) PUNCT ajst-24979 90 8 [ [ PUNCT ajst-24979 90 9 ( ( PUNCT ajst-24979 90 10 ; ; PUNCT ajst-24979 90 11 ) ) PUNCT ajst-24979 90 12 ( ( PUNCT ajst-24979 90 13 ) ) PUNCT ajst-24979 90 14 ] ] PUNCT ajst-24979 90 15 ( ( PUNCT ajst-24979 90 16 ) ) PUNCT ajst-24979 90 17 [ [ PUNCT ajst-24979 90 18 ( ( PUNCT ajst-24979 90 19 ; ; PUNCT ajst-24979 90 20 ) ) PUNCT ajst-24979 90 21 ] ] PUNCT ajst-24979 91 1 [ [ PUNCT ajst-24979 91 2 ( ( PUNCT ajst-24979 91 3 ; ; PUNCT ajst-24979 91 4 ) ) PUNCT ajst-24979 91 5 , , PUNCT ajst-24979 91 6 ( ( PUNCT ajst-24979 91 7 ) ) PUNCT ajst-24979 91 8 , , PUNCT ajst-24979 91 9 ( ( PUNCT ajst-24979 91 10 ) ) PUNCT ajst-24979 91 11 , , PUNCT ajst-24979 91 12 , , PUNCT ajst-24979 91 13 ] ] PUNCT ajst-24979 91 14 , , PUNCT ajst-24979 91 15 q q PUNCT ajst-24979 91 16 l l NOUN ajst-24979 92 1 x x X ajst-24979 92 2 q q X ajst-24979 92 3 w w X ajst-24979 92 4 x x X ajst-24979 92 5 qhh qhh NOUN ajst-24979 92 6 x x SYM ajst-24979 92 7 n n NOUN ajst-24979 92 8 x x X ajst-24979 92 9 q q NOUN ajst-24979 92 10 h h NOUN ajst-24979 93 1 x x X ajst-24979 93 2 q q PUNCT ajst-24979 93 3 w w NOUN ajst-24979 93 4 x x SYM ajst-24979 93 5 h h NOUN ajst-24979 94 1 x x NOUN ajst-24979 94 2 h h NOUN ajst-24979 94 3 q q X ajst-24979 94 4   ADJ ajst-24979 94 5   ADJ ajst-24979 94 6   PROPN ajst-24979 94 7   PROPN ajst-24979 94 8   PROPN ajst-24979 94 9   NOUN ajst-24979 94 10   NUM ajst-24979 94 11 ( ( PUNCT ajst-24979 94 12 4 4 NUM ajst-24979 94 13 ) ) PUNCT ajst-24979 95 1 where where SCONJ ajst-24979 95 2 0 0 NUM ajst-24979 95 3 ( ( PUNCT ajst-24979 95 4 ) ) PUNCT ajst-24979 95 5 w w X ajst-24979 95 6 x x PUNCT ajst-24979 95 7 is be AUX ajst-24979 95 8 the the DET ajst-24979 95 9 initial initial ADJ ajst-24979 95 10 conjecture conjecture NOUN ajst-24979 95 11 of of ADP ajst-24979 95 12 the the DET ajst-24979 95 13 exact exact ADJ ajst-24979 95 14 solution solution NOUN ajst-24979 95 15 ( ( PUNCT ajst-24979 95 16 ) ) PUNCT ajst-24979 95 17 w w PROPN ajst-24979 95 18 x x PUNCT ajst-24979 95 19 , , PUNCT ajst-24979 95 20 1,h 1,h NUM ajst-24979 95 21 h h NOUN ajst-24979 95 22 are be AUX ajst-24979 95 23 auxiliary auxiliary ADJ ajst-24979 95 24 parameters parameter NOUN ajst-24979 95 25 and and CCONJ ajst-24979 95 26 auxiliary auxiliary ADJ ajst-24979 95 27 functions function NOUN ajst-24979 95 28 , , PUNCT ajst-24979 95 29 respectively respectively ADV ajst-24979 95 30 . . PUNCT ajst-24979 96 1 l l NOUN ajst-24979 96 2 is be AUX ajst-24979 96 3 an an DET ajst-24979 96 4 auxiliary auxiliary ADJ ajst-24979 96 5 linear linear NOUN ajst-24979 96 6 operator operator NOUN ajst-24979 96 7 . . PUNCT ajst-24979 97 1 when when SCONJ ajst-24979 97 2 ( ( PUNCT ajst-24979 97 3 ) ) PUNCT ajst-24979 97 4 0 0 NUM ajst-24979 97 5 , , PUNCT ajst-24979 97 6 [ [ PUNCT ajst-24979 97 7 ( ( PUNCT ajst-24979 97 8 ) ) PUNCT ajst-24979 97 9 ] ] PUNCT ajst-24979 98 1 0w 0w X ajst-24979 98 2 x x X ajst-24979 99 1 l l NOUN ajst-24979 99 2 w w NOUN ajst-24979 99 3 x x NOUN ajst-24979 100 1   NUM ajst-24979 100 2 , , PUNCT ajst-24979 101 1 [ [ X ajst-24979 101 2 0,1]q 0,1]q X ajst-24979 101 3 is be AUX ajst-24979 101 4 the the DET ajst-24979 101 5 embedding embed VERB ajst-24979 101 6 parameter parameter NOUN ajst-24979 101 7 . . PUNCT ajst-24979 102 1 let let VERB ajst-24979 102 2 homotopy homotopy VERB ajst-24979 102 3 eq eq ADP ajst-24979 102 4 . . PUNCT ajst-24979 103 1 ( ( PUNCT ajst-24979 103 2 4 4 X ajst-24979 103 3 ) ) PUNCT ajst-24979 103 4 be be AUX ajst-24979 103 5 zero zero NUM ajst-24979 103 6 , , PUNCT ajst-24979 103 7 that that PRON ajst-24979 103 8 is be AUX ajst-24979 103 9 0 0 NUM ajst-24979 103 10 1 1 NUM ajst-24979 103 11 [ [ PUNCT ajst-24979 103 12 ( ( PUNCT ajst-24979 103 13 ; ; PUNCT ajst-24979 103 14 ) ) PUNCT ajst-24979 103 15 , , PUNCT ajst-24979 103 16 ( ( PUNCT ajst-24979 103 17 ) ) PUNCT ajst-24979 103 18 , , PUNCT ajst-24979 103 19 ( ( PUNCT ajst-24979 103 20 ) ) PUNCT ajst-24979 103 21 , , PUNCT ajst-24979 103 22 , , PUNCT ajst-24979 103 23 ] ] PUNCT ajst-24979 104 1 0.h 0.h NUM ajst-24979 104 2 x x PUNCT ajst-24979 104 3 q q X ajst-24979 104 4 w w NOUN ajst-24979 104 5 x x SYM ajst-24979 104 6 h h NOUN ajst-24979 104 7 x x NOUN ajst-24979 104 8 h h NOUN ajst-24979 104 9 q q NUM ajst-24979 104 10   NUM ajst-24979 104 11                     SPACE ajst-24979 104 12 ( ( PUNCT ajst-24979 104 13 5 5 NUM ajst-24979 104 14 ) ) PUNCT ajst-24979 104 15 the the DET ajst-24979 104 16 zero zero NUM ajst-24979 104 17 - - PUNCT ajst-24979 104 18 order order NOUN ajst-24979 104 19 deformation deformation NOUN ajst-24979 104 20 equation equation NOUN ajst-24979 104 21 from from ADP ajst-24979 104 22 eq.(4)and eq.(4)and PROPN ajst-24979 104 23 eq eq X ajst-24979 104 24 . . PUNCT ajst-24979 105 1 ( ( PUNCT ajst-24979 105 2 5 5 NUM ajst-24979 105 3 ) ) PUNCT ajst-24979 105 4 0 0 NUM ajst-24979 105 5 1(1 1(1 NUM ajst-24979 105 6 ) ) PUNCT ajst-24979 106 1 [ [ PUNCT ajst-24979 106 2 ( ( PUNCT ajst-24979 106 3 ; ; PUNCT ajst-24979 106 4 ) ) PUNCT ajst-24979 106 5 ( ( PUNCT ajst-24979 106 6 ) ) PUNCT ajst-24979 106 7 ] ] PUNCT ajst-24979 106 8 ( ( PUNCT ajst-24979 106 9 ) ) PUNCT ajst-24979 106 10 [ [ PUNCT ajst-24979 106 11 ( ( PUNCT ajst-24979 106 12 ; ; PUNCT ajst-24979 106 13 ) ) PUNCT ajst-24979 106 14 ] ] PUNCT ajst-24979 106 15 , , PUNCT ajst-24979 106 16 q q X ajst-24979 106 17 l l NOUN ajst-24979 106 18 x x X ajst-24979 106 19 q q X ajst-24979 106 20 w w X ajst-24979 106 21 x x X ajst-24979 106 22 qhh qhh NOUN ajst-24979 106 23 x x SYM ajst-24979 106 24 n n CCONJ ajst-24979 106 25 x x NOUN ajst-24979 106 26 q q PRON ajst-24979 106 27   ADJ ajst-24979 106 28   NOUN ajst-24979 106 29   PROPN ajst-24979 106 30 ( ( PUNCT ajst-24979 106 31 6 6 NUM ajst-24979 106 32 ) ) PUNCT ajst-24979 106 33 when when SCONJ ajst-24979 106 34 0q 0q VERB ajst-24979 106 35   PROPN ajst-24979 106 36 , , PUNCT ajst-24979 106 37 from from ADP ajst-24979 106 38 eq.(6 eq.(6 ADJ ajst-24979 106 39 ) ) PUNCT ajst-24979 106 40 0 0 NUM ajst-24979 106 41 ( ( PUNCT ajst-24979 106 42 ; ; PUNCT ajst-24979 106 43 0 0 NUM ajst-24979 106 44 ) ) PUNCT ajst-24979 106 45 ( ( PUNCT ajst-24979 106 46 ) ) PUNCT ajst-24979 106 47 , , PUNCT ajst-24979 106 48 x x X ajst-24979 106 49 w w NOUN ajst-24979 106 50 x x X ajst-24979 106 51   PROPN ajst-24979 106 52 ( ( PUNCT ajst-24979 106 53 7 7 NUM ajst-24979 106 54 ) ) PUNCT ajst-24979 106 55 and and CCONJ ajst-24979 106 56 when when SCONJ ajst-24979 106 57 1q 1q NUM ajst-24979 106 58   NOUN ajst-24979 106 59 , , PUNCT ajst-24979 106 60 due due ADP ajst-24979 106 61 to to ADP ajst-24979 106 62 10 10 NUM ajst-24979 106 63 , , PUNCT ajst-24979 106 64 0h 0h NUM ajst-24979 106 65 h h PROPN ajst-24979 106 66   PROPN ajst-24979 106 67 , , PUNCT ajst-24979 106 68 the the DET ajst-24979 106 69 eq.(6 eq.(6 NOUN ajst-24979 106 70 ) ) PUNCT ajst-24979 106 71 is be AUX ajst-24979 106 72 equivalent equivalent ADJ ajst-24979 106 73 to to ADP ajst-24979 106 74 ( ( PUNCT ajst-24979 106 75 ; ; PUNCT ajst-24979 106 76 1 1 X ajst-24979 106 77 ) ) PUNCT ajst-24979 106 78 ( ( PUNCT ajst-24979 106 79 ) ) PUNCT ajst-24979 106 80 .x .x PROPN ajst-24979 107 1 w w PROPN ajst-24979 107 2 x x X ajst-24979 107 3   PROPN ajst-24979 107 4 ( ( PUNCT ajst-24979 107 5 8) 8) NUM ajst-24979 107 6 it it PRON ajst-24979 107 7 can can AUX ajst-24979 107 8 be be AUX ajst-24979 107 9 obtained obtain VERB ajst-24979 107 10 from from ADP ajst-24979 107 11 eq.(7 eq.(7 NOUN ajst-24979 107 12 ) ) PUNCT ajst-24979 107 13 and and CCONJ ajst-24979 107 14 eq.(8 eq.(8 X ajst-24979 107 15 ) ) PUNCT ajst-24979 108 1 that that SCONJ ajst-24979 108 2 as as ADP ajst-24979 108 3 the the DET ajst-24979 108 4 embedding embed VERB ajst-24979 108 5 parameter parameter NOUN ajst-24979 108 6 q q NOUN ajst-24979 108 7 increases increase NOUN ajst-24979 108 8 from from ADP ajst-24979 108 9 0 0 NUM ajst-24979 108 10 to to ADP ajst-24979 108 11 1 1 NUM ajst-24979 108 12 , , PUNCT ajst-24979 108 13 ( ( PUNCT ajst-24979 108 14 ; ; PUNCT ajst-24979 108 15 ) ) PUNCT ajst-24979 108 16 x x X ajst-24979 108 17 q q DET ajst-24979 108 18 changes change NOUN ajst-24979 108 19 continuously continuously ADV ajst-24979 108 20 from from ADP ajst-24979 108 21 the the DET ajst-24979 108 22 initial initial ADJ ajst-24979 108 23 conjecture conjecture NOUN ajst-24979 108 24 0 0 PUNCT ajst-24979 109 1 ( ( PUNCT ajst-24979 109 2 ) ) PUNCT ajst-24979 109 3 w w NOUN ajst-24979 109 4 x x X ajst-24979 109 5 to to ADP ajst-24979 109 6 the the DET ajst-24979 109 7 exact exact ADJ ajst-24979 109 8 solution solution NOUN ajst-24979 109 9 , , PUNCT ajst-24979 109 10 which which PRON ajst-24979 109 11 is be AUX ajst-24979 109 12 called call VERB ajst-24979 109 13 homotopy homotopy NOUN ajst-24979 109 14 deformation deformation NOUN ajst-24979 109 15 . . PUNCT ajst-24979 110 1 using use VERB ajst-24979 110 2 taylor taylor PROPN ajst-24979 110 3 ’s ’s PART ajst-24979 110 4 theorem theorem PROPN ajst-24979 110 5 , , PUNCT ajst-24979 110 6 ( ( PUNCT ajst-24979 110 7 ; ; PUNCT ajst-24979 110 8 ) ) PUNCT ajst-24979 110 9 x x X ajst-24979 110 10 q q NUM ajst-24979 110 11 is be AUX ajst-24979 110 12 expanded expand VERB ajst-24979 110 13 to to ADP ajst-24979 110 14 the the DET ajst-24979 110 15 following follow VERB ajst-24979 110 16 power power NOUN ajst-24979 110 17 series series NOUN ajst-24979 110 18 with with ADP ajst-24979 110 19 respect respect NOUN ajst-24979 110 20 to to ADP ajst-24979 110 21 q q PROPN ajst-24979 110 22 0 0 NUM ajst-24979 110 23 1 1 NUM ajst-24979 110 24 ( ( PUNCT ajst-24979 110 25 ; ; PUNCT ajst-24979 110 26 ) ) PUNCT ajst-24979 110 27 ( ( PUNCT ajst-24979 110 28 ) ) PUNCT ajst-24979 110 29 ( ( PUNCT ajst-24979 110 30 ) ) PUNCT ajst-24979 110 31 , , PUNCT ajst-24979 111 1 n n CCONJ ajst-24979 111 2 n n CCONJ ajst-24979 111 3 n n NOUN ajst-24979 111 4 x x NOUN ajst-24979 111 5 q q PUNCT ajst-24979 111 6 w w NOUN ajst-24979 111 7 x x SYM ajst-24979 112 1 w w PROPN ajst-24979 112 2 x x PUNCT ajst-24979 112 3 q q NUM ajst-24979 112 4   VERB ajst-24979 112 5   NUM ajst-24979 112 6   PROPN ajst-24979 112 7   NOUN ajst-24979 112 8 ( ( PUNCT ajst-24979 112 9 9 9 NUM ajst-24979 112 10 ) ) PUNCT ajst-24979 112 11 where where SCONJ ajst-24979 112 12 0 0 NUM ajst-24979 112 13 1 1 NUM ajst-24979 112 14 ( ( PUNCT ajst-24979 112 15 ; ; PUNCT ajst-24979 112 16 ) ) PUNCT ajst-24979 112 17 ( ( PUNCT ajst-24979 112 18 ) ) PUNCT ajst-24979 112 19 . . PUNCT ajst-24979 113 1 ! ! PUNCT ajst-24979 114 1 n n CCONJ ajst-24979 115 1 n n ADV ajst-24979 115 2 qn qn NOUN ajst-24979 115 3 x x X ajst-24979 115 4 q q PROPN ajst-24979 115 5 w w NOUN ajst-24979 115 6 x x NOUN ajst-24979 115 7 n n PRON ajst-24979 115 8 q q NOUN ajst-24979 116 1   PROPN ajst-24979 116 2   PROPN ajst-24979 116 3   ADJ ajst-24979 117 1   PROPN ajst-24979 117 2   ADJ ajst-24979 117 3 ( ( PUNCT ajst-24979 117 4 10 10 NUM ajst-24979 117 5 ) ) PUNCT ajst-24979 117 6 by by ADP ajst-24979 117 7 choosing choose VERB ajst-24979 117 8 appropriate appropriate ADJ ajst-24979 117 9 , , PUNCT ajst-24979 117 10 etc.to etc.to PRON ajst-24979 117 11 make make VERB ajst-24979 117 12 ( ( PUNCT ajst-24979 117 13 ; ; PUNCT ajst-24979 117 14 ) ) PUNCT ajst-24979 117 15 x x X ajst-24979 117 16 q q NUM ajst-24979 117 17 converge converge NOUN ajst-24979 117 18 at at ADP ajst-24979 117 19 1q 1q NUM ajst-24979 117 20   NOUN ajst-24979 117 21 , , PUNCT ajst-24979 117 22 then then ADV ajst-24979 117 23 under under ADP ajst-24979 117 24 these these DET ajst-24979 117 25 assumptions assumption NOUN ajst-24979 117 26 , , PUNCT ajst-24979 117 27 we we PRON ajst-24979 117 28 have have VERB ajst-24979 117 29 the the DET ajst-24979 117 30 following follow VERB ajst-24979 117 31 series series NOUN ajst-24979 117 32 solution solution NOUN ajst-24979 117 33 0 0 NUM ajst-24979 117 34 1 1 NUM ajst-24979 117 35 ( ( PUNCT ajst-24979 117 36 ) ) PUNCT ajst-24979 117 37 ( ( PUNCT ajst-24979 117 38 ; ; PUNCT ajst-24979 117 39 1 1 X ajst-24979 117 40 ) ) PUNCT ajst-24979 117 41 ( ( PUNCT ajst-24979 117 42 ) ) PUNCT ajst-24979 117 43 ( ( PUNCT ajst-24979 117 44 ) ) PUNCT ajst-24979 117 45 .n .n PROPN ajst-24979 118 1 n n PRON ajst-24979 118 2 w w NOUN ajst-24979 118 3 x x X ajst-24979 118 4 x x X ajst-24979 118 5 w w AUX ajst-24979 118 6 x x X ajst-24979 118 7 w w NOUN ajst-24979 118 8 x x X ajst-24979 118 9   VERB ajst-24979 118 10   NUM ajst-24979 118 11   NUM ajst-24979 118 12   PROPN ajst-24979 118 13   NOUN ajst-24979 118 14 ( ( PUNCT ajst-24979 118 15 11 11 NUM ajst-24979 118 16 ) ) PUNCT ajst-24979 118 17 substituting substitute VERB ajst-24979 118 18 eq.(9 eq.(9 NOUN ajst-24979 118 19 ) ) PUNCT ajst-24979 118 20 into into ADP ajst-24979 118 21 eq.(6 eq.(6 ADJ ajst-24979 118 22 ) ) PUNCT ajst-24979 118 23 yields yield NOUN ajst-24979 118 24 0 0 NUM ajst-24979 118 25 1 1 NUM ajst-24979 118 26 1 1 NUM ajst-24979 118 27 ( ( PUNCT ajst-24979 118 28 1 1 NUM ajst-24979 118 29 ) ) PUNCT ajst-24979 118 30 [ [ PUNCT ajst-24979 118 31 ( ( PUNCT ajst-24979 118 32 ; ; PUNCT ajst-24979 118 33 ) ) PUNCT ajst-24979 118 34 ( ( PUNCT ajst-24979 118 35 ) ) PUNCT ajst-24979 118 36 ] ] PUNCT ajst-24979 119 1 ( ( PUNCT ajst-24979 119 2 1 1 X ajst-24979 119 3 ) ) PUNCT ajst-24979 119 4 [ [ PUNCT ajst-24979 119 5 ( ( PUNCT ajst-24979 119 6 ) ) PUNCT ajst-24979 119 7 ] ] PUNCT ajst-24979 119 8 ( ( PUNCT ajst-24979 119 9 ) ) PUNCT ajst-24979 119 10 [ [ PUNCT ajst-24979 119 11 ( ( PUNCT ajst-24979 119 12 ; ; PUNCT ajst-24979 119 13 ) ) PUNCT ajst-24979 119 14 ] ] PUNCT ajst-24979 119 15 , , PUNCT ajst-24979 119 16 n n CCONJ ajst-24979 119 17 n n CCONJ ajst-24979 119 18 n n CCONJ ajst-24979 119 19 q q NOUN ajst-24979 119 20 l l NOUN ajst-24979 119 21 x x X ajst-24979 119 22 q q X ajst-24979 119 23 w w NOUN ajst-24979 119 24 x x X ajst-24979 119 25 q q X ajst-24979 119 26 l l NOUN ajst-24979 119 27 w w NOUN ajst-24979 119 28 x x X ajst-24979 119 29 q q X ajst-24979 119 30 qhh qhh NOUN ajst-24979 119 31 x x SYM ajst-24979 119 32 n n NOUN ajst-24979 119 33 x x X ajst-24979 119 34 q q X ajst-24979 119 35   ADJ ajst-24979 119 36   ADJ ajst-24979 119 37   NOUN ajst-24979 119 38   PROPN ajst-24979 119 39   PROPN ajst-24979 119 40   PROPN ajst-24979 119 41   PROPN ajst-24979 119 42   PROPN ajst-24979 119 43   NOUN ajst-24979 119 44   X ajst-24979 119 45 ( ( PUNCT ajst-24979 119 46 12 12 NUM ajst-24979 119 47 ) ) PUNCT ajst-24979 119 48 simplifying simplify VERB ajst-24979 119 49 eq.(12 eq.(12 NOUN ajst-24979 119 50 ) ) PUNCT ajst-24979 119 51 yields yield VERB ajst-24979 119 52 0 0 NUM ajst-24979 119 53 1 1 NUM ajst-24979 119 54 , , PUNCT ajst-24979 119 55 , , PUNCT ajst-24979 119 56 w w PROPN ajst-24979 119 57 h h NOUN ajst-24979 119 58 h h NOUN ajst-24979 119 59 174 174 NUM ajst-24979 119 60 1 1 NUM ajst-24979 119 61 1 1 NUM ajst-24979 119 62 1 1 NUM ajst-24979 119 63 [ [ PUNCT ajst-24979 119 64 ( ( PUNCT ajst-24979 119 65 ) ) PUNCT ajst-24979 119 66 ] ] PUNCT ajst-24979 120 1 [ [ PUNCT ajst-24979 120 2 ( ( PUNCT ajst-24979 120 3 ) ) PUNCT ajst-24979 120 4 ] ] PUNCT ajst-24979 120 5 ( ( PUNCT ajst-24979 120 6 ) ) PUNCT ajst-24979 120 7 [ [ PUNCT ajst-24979 120 8 ( ( PUNCT ajst-24979 120 9 ; ; PUNCT ajst-24979 120 10 ) ) PUNCT ajst-24979 120 11 ] ] PUNCT ajst-24979 120 12 , , PUNCT ajst-24979 120 13 n n CCONJ ajst-24979 120 14 n n CCONJ ajst-24979 120 15 n n CCONJ ajst-24979 120 16 n n CCONJ ajst-24979 120 17 n n CCONJ ajst-24979 120 18 n n NOUN ajst-24979 120 19 l l NOUN ajst-24979 120 20 w w NOUN ajst-24979 120 21 x x X ajst-24979 120 22 q q X ajst-24979 120 23 ql ql X ajst-24979 120 24 w w NOUN ajst-24979 120 25 x x X ajst-24979 120 26 q q X ajst-24979 120 27 qhh qhh NOUN ajst-24979 120 28 x x SYM ajst-24979 120 29 n n CCONJ ajst-24979 120 30 x x PUNCT ajst-24979 120 31 q q NUM ajst-24979 120 32   VERB ajst-24979 120 33   VERB ajst-24979 120 34   NUM ajst-24979 120 35   PROPN ajst-24979 120 36   PROPN ajst-24979 120 37   NOUN ajst-24979 120 38   X ajst-24979 120 39   X ajst-24979 120 40 ( ( PUNCT ajst-24979 120 41 13 13 NUM ajst-24979 120 42 ) ) PUNCT ajst-24979 120 43 the the DET ajst-24979 120 44 n n ADV ajst-24979 120 45 - - PUNCT ajst-24979 120 46 th th VERB ajst-24979 120 47 differential differential NOUN ajst-24979 120 48 of of ADP ajst-24979 120 49 eq(13 eq(13 NOUN ajst-24979 120 50 ) ) PUNCT ajst-24979 120 51 with with ADP ajst-24979 120 52 respect respect NOUN ajst-24979 120 53 to to ADP ajst-24979 120 54 q q NOUN ajst-24979 120 55 is be AUX ajst-24979 120 56 calculated calculate VERB ajst-24979 120 57 and and CCONJ ajst-24979 120 58 assigned assign VERB ajst-24979 120 59 at at ADP ajst-24979 120 60 0q 0q NOUN ajst-24979 120 61   NUM ajst-24979 120 62 . . PUNCT ajst-24979 121 1 1 1 NUM ajst-24979 121 2 1 1 NUM ajst-24979 121 3 1 1 NUM ajst-24979 121 4 1 1 NUM ajst-24979 121 5 1 1 NUM ajst-24979 121 6 1 1 NUM ajst-24979 121 7 01 01 NUM ajst-24979 121 8 [ [ PUNCT ajst-24979 121 9 ( ( PUNCT ajst-24979 121 10 ) ) PUNCT ajst-24979 121 11 ] ] PUNCT ajst-24979 122 1 [ [ PUNCT ajst-24979 122 2 ( ( PUNCT ajst-24979 122 3 ) ) PUNCT ajst-24979 122 4 ] ] PUNCT ajst-24979 122 5 ( ( PUNCT ajst-24979 122 6 ) ) PUNCT ajst-24979 122 7 [ [ PUNCT ajst-24979 122 8 ( ( PUNCT ajst-24979 122 9 ; ; PUNCT ajst-24979 122 10 ) ) PUNCT ajst-24979 122 11 ] ] PUNCT ajst-24979 122 12 ! ! PUNCT ajst-24979 123 1 [ [ PUNCT ajst-24979 123 2 ( ( PUNCT ajst-24979 123 3 ) ) PUNCT ajst-24979 123 4 ( ( PUNCT ajst-24979 123 5 ) ) PUNCT ajst-24979 123 6 ( ( PUNCT ajst-24979 123 7 ; ; PUNCT ajst-24979 123 8 ) ) PUNCT ajst-24979 123 9 ( ( PUNCT ajst-24979 123 10 ) ) PUNCT ajst-24979 123 11 . . PUNCT ajst-24979 124 1 n n CCONJ ajst-24979 124 2 n n CCONJ ajst-24979 124 3 n n CCONJ ajst-24979 124 4 n n CCONJ ajst-24979 124 5 n n CCONJ ajst-24979 124 6 n n CCONJ ajst-24979 124 7 n n CCONJ ajst-24979 124 8 n n CCONJ ajst-24979 124 9 n n CCONJ ajst-24979 124 10 n n CCONJ ajst-24979 124 11 n n ADV ajst-24979 124 12 qn qn NOUN ajst-24979 124 13 l l PROPN ajst-24979 124 14 w w NOUN ajst-24979 124 15 x x X ajst-24979 124 16 q q X ajst-24979 124 17 ql ql X ajst-24979 124 18 w w NOUN ajst-24979 124 19 x x X ajst-24979 124 20 q q X ajst-24979 124 21 qhh qhh NOUN ajst-24979 124 22 x x SYM ajst-24979 124 23 n n PROPN ajst-24979 124 24 x x X ajst-24979 124 25 q q NOUN ajst-24979 124 26 n n NUM ajst-24979 124 27 l l NOUN ajst-24979 124 28 w w NOUN ajst-24979 125 1 x x X ajst-24979 125 2 w w NOUN ajst-24979 125 3 x x X ajst-24979 125 4 x x X ajst-24979 125 5 q q X ajst-24979 125 6 hh hh PROPN ajst-24979 125 7 x x X ajst-24979 125 8 n n CCONJ ajst-24979 125 9 q q ADJ ajst-24979 126 1   ADJ ajst-24979 126 2   ADJ ajst-24979 126 3   NOUN ajst-24979 126 4   VERB ajst-24979 126 5   NUM ajst-24979 126 6   PROPN ajst-24979 126 7   PROPN ajst-24979 126 8   PROPN ajst-24979 126 9   NOUN ajst-24979 126 10   ADP ajst-24979 127 1   PROPN ajst-24979 127 2   NOUN ajst-24979 127 3   INTJ ajst-24979 128 1   PROPN ajst-24979 128 2   PROPN ajst-24979 129 1   NUM ajst-24979 129 2   PROPN ajst-24979 129 3   PROPN ajst-24979 129 4   PROPN ajst-24979 129 5   PROPN ajst-24979 129 6   ADJ ajst-24979 129 7   X ajst-24979 129 8   X ajst-24979 129 9 ( ( PUNCT ajst-24979 129 10 14 14 NUM ajst-24979 129 11 ) ) PUNCT ajst-24979 129 12 therefore therefore ADV ajst-24979 129 13 11 11 NUM ajst-24979 129 14 1 1 NUM ajst-24979 129 15 [ [ PUNCT ajst-24979 129 16 ( ( PUNCT ajst-24979 129 17 ) ) PUNCT ajst-24979 129 18 ( ( PUNCT ajst-24979 129 19 ) ) PUNCT ajst-24979 129 20 ] ] PUNCT ajst-24979 129 21 ( ( PUNCT ajst-24979 129 22 ) ) PUNCT ajst-24979 129 23 ( ( PUNCT ajst-24979 129 24 ( ( PUNCT ajst-24979 129 25 ) ) PUNCT ajst-24979 129 26 ) ) PUNCT ajst-24979 129 27 , , PUNCT ajst-24979 129 28 nn nn PROPN ajst-24979 129 29 n n CCONJ ajst-24979 129 30 n n CCONJ ajst-24979 129 31 nl nl PROPN ajst-24979 129 32 w w PROPN ajst-24979 129 33 x x PROPN ajst-24979 129 34 w w NOUN ajst-24979 129 35 x x X ajst-24979 129 36 hh hh PROPN ajst-24979 129 37 x x X ajst-24979 129 38 w w NOUN ajst-24979 129 39 x x NOUN ajst-24979 129 40   NOUN ajst-24979 129 41   NUM ajst-24979 129 42   NUM ajst-24979 129 43   PROPN ajst-24979 129 44 ( ( PUNCT ajst-24979 129 45 15 15 NUM ajst-24979 129 46 ) ) PUNCT ajst-24979 129 47 where where SCONJ ajst-24979 129 48 1 1 NUM ajst-24979 129 49 1 1 NUM ajst-24979 129 50 01 01 NUM ajst-24979 129 51 1 1 NUM ajst-24979 129 52 [ [ PUNCT ajst-24979 129 53 ( ( PUNCT ajst-24979 129 54 ; ; PUNCT ajst-24979 129 55 ) ) PUNCT ajst-24979 129 56 ] ] PUNCT ajst-24979 129 57 ( ( PUNCT ajst-24979 129 58 ( ( PUNCT ajst-24979 129 59 ) ) PUNCT ajst-24979 129 60 ) ) PUNCT ajst-24979 129 61 , , PUNCT ajst-24979 129 62 ( ( PUNCT ajst-24979 129 63 1 1 NUM ajst-24979 129 64 ) ) PUNCT ajst-24979 129 65 ! ! PUNCT ajst-24979 130 1 0 0 NUM ajst-24979 130 2 , , PUNCT ajst-24979 130 3 1 1 NUM ajst-24979 130 4 , , PUNCT ajst-24979 130 5 1 1 NUM ajst-24979 130 6 , , PUNCT ajst-24979 130 7 1 1 NUM ajst-24979 130 8 . . X ajst-24979 130 9 n n CCONJ ajst-24979 131 1 nn nn PROPN ajst-24979 131 2 qn qn PROPN ajst-24979 131 3 n n PROPN ajst-24979 131 4 n n ADV ajst-24979 131 5 x x NOUN ajst-24979 131 6 q q X ajst-24979 131 7 w w NOUN ajst-24979 131 8 x x PROPN ajst-24979 131 9 n n PROPN ajst-24979 131 10 q q NOUN ajst-24979 131 11 n n CCONJ ajst-24979 131 12 n n CCONJ ajst-24979 131 13   NOUN ajst-24979 131 14   AUX ajst-24979 131 15   VERB ajst-24979 131 16   PROPN ajst-24979 131 17   PROPN ajst-24979 131 18   PROPN ajst-24979 132 1   PROPN ajst-24979 132 2   PROPN ajst-24979 132 3   PROPN ajst-24979 132 4   NOUN ajst-24979 132 5   ADJ ajst-24979 132 6   PROPN ajst-24979 132 7   PROPN ajst-24979 132 8   PROPN ajst-24979 132 9 ( ( PUNCT ajst-24979 132 10 16 16 NUM ajst-24979 132 11 ) ) PUNCT ajst-24979 132 12 application application NOUN ajst-24979 132 13 of of ADP ajst-24979 132 14 ham ham NOUN ajst-24979 132 15 to to ADP ajst-24979 132 16 fuzzy fuzzy ADJ ajst-24979 132 17 fractional fractional PROPN ajst-24979 132 18 volterra volterra NOUN ajst-24979 132 19 - - PUNCT ajst-24979 132 20 fredholm fredholm NOUN ajst-24979 132 21 integro integro ADJ ajst-24979 132 22 - - PUNCT ajst-24979 132 23 differential differential NOUN ajst-24979 132 24 equations equation NOUN ajst-24979 132 25 . . PUNCT ajst-24979 133 1 1 1 NUM ajst-24979 133 2 1 1 NUM ajst-24979 133 3 1 1 NUM ajst-24979 133 4 2 2 NUM ajst-24979 133 5 20 20 NUM ajst-24979 133 6 0 0 NUM ajst-24979 133 7 [ [ PUNCT ajst-24979 133 8 ( ( PUNCT ajst-24979 133 9 , , PUNCT ajst-24979 133 10 ; ; PUNCT ajst-24979 133 11 ) ) PUNCT ajst-24979 133 12 ] ] PUNCT ajst-24979 133 13 ( ( PUNCT ajst-24979 133 14 , , PUNCT ajst-24979 133 15 ; ; PUNCT ajst-24979 133 16 ) ) PUNCT ajst-24979 133 17 ( ( PUNCT ajst-24979 133 18 , , PUNCT ajst-24979 133 19 ) ) PUNCT ajst-24979 133 20 ( ( PUNCT ajst-24979 133 21 ) ) PUNCT ajst-24979 133 22 ( ( PUNCT ajst-24979 133 23 , , PUNCT ajst-24979 133 24 ; ; PUNCT ajst-24979 133 25 ) ) PUNCT ajst-24979 133 26 ( ( PUNCT ajst-24979 133 27 , , PUNCT ajst-24979 133 28 ) ) PUNCT ajst-24979 133 29 ( ( PUNCT ajst-24979 133 30 ( ( PUNCT ajst-24979 133 31 , , PUNCT ajst-24979 133 32 ; ; PUNCT ajst-24979 133 33 ) ) PUNCT ajst-24979 133 34 ) ) PUNCT ajst-24979 133 35 ( ( PUNCT ajst-24979 133 36 , , PUNCT ajst-24979 133 37 ) ) PUNCT ajst-24979 133 38 ( ( PUNCT ajst-24979 133 39 ( ( PUNCT ajst-24979 133 40 , , PUNCT ajst-24979 133 41 ; ; PUNCT ajst-24979 133 42 ) ) PUNCT ajst-24979 133 43 ) ) PUNCT ajst-24979 133 44 , , PUNCT ajst-24979 133 45 c c NOUN ajst-24979 133 46 x x PUNCT ajst-24979 133 47 n n PROPN ajst-24979 133 48 x x NOUN ajst-24979 133 49 r r NOUN ajst-24979 133 50 q q NOUN ajst-24979 134 1 d d NOUN ajst-24979 134 2 x x SYM ajst-24979 134 3 r r NOUN ajst-24979 134 4 q q NOUN ajst-24979 134 5 g g NOUN ajst-24979 134 6 x x NOUN ajst-24979 134 7 r r NOUN ajst-24979 134 8 a a NOUN ajst-24979 134 9 x x NOUN ajst-24979 134 10 x x SYM ajst-24979 134 11 r r NOUN ajst-24979 134 12 q q NOUN ajst-24979 135 1 k k NOUN ajst-24979 135 2 x x SYM ajst-24979 136 1 t t NOUN ajst-24979 136 2 f f PROPN ajst-24979 136 3 t t PROPN ajst-24979 136 4 r r NOUN ajst-24979 136 5 q q X ajst-24979 136 6 dt dt X ajst-24979 137 1 k k NOUN ajst-24979 137 2 x x SYM ajst-24979 138 1 t t NOUN ajst-24979 138 2 f f PROPN ajst-24979 138 3 t t PROPN ajst-24979 138 4 r r NOUN ajst-24979 138 5 q q X ajst-24979 138 6 dt dt X ajst-24979 138 7   NUM ajst-24979 138 8   ADJ ajst-24979 138 9   ADJ ajst-24979 138 10   ADJ ajst-24979 138 11   ADJ ajst-24979 138 12   ADJ ajst-24979 138 13   PROPN ajst-24979 138 14   PROPN ajst-24979 138 15   PROPN ajst-24979 138 16   NOUN ajst-24979 138 17   NOUN ajst-24979 138 18   PUNCT ajst-24979 138 19 ( ( PUNCT ajst-24979 138 20 17 17 NUM ajst-24979 138 21 ) ) PUNCT ajst-24979 138 22 where where SCONJ ajst-24979 138 23 0 0 NUM ajst-24979 138 24 0 0 NUM ajst-24979 138 25 ( ( PUNCT ajst-24979 138 26 , , PUNCT ajst-24979 138 27 ; ; PUNCT ajst-24979 138 28 ) ) PUNCT ajst-24979 139 1 [ [ PUNCT ajst-24979 139 2 ( ( PUNCT ajst-24979 139 3 , , PUNCT ajst-24979 139 4 ; ; PUNCT ajst-24979 139 5 ) ) PUNCT ajst-24979 139 6 , , PUNCT ajst-24979 139 7 ( ( PUNCT ajst-24979 139 8 , , PUNCT ajst-24979 139 9 ; ; PUNCT ajst-24979 139 10 ) ) PUNCT ajst-24979 139 11 ] ] PUNCT ajst-24979 139 12 , , PUNCT ajst-24979 139 13 ( ( PUNCT ajst-24979 139 14 , , PUNCT ajst-24979 139 15 ) ) PUNCT ajst-24979 139 16 [ [ PUNCT ajst-24979 139 17 ( ( PUNCT ajst-24979 139 18 , , PUNCT ajst-24979 139 19 ) ) PUNCT ajst-24979 139 20 , , PUNCT ajst-24979 139 21 x x PUNCT ajst-24979 139 22 r r NOUN ajst-24979 139 23 q q NOUN ajst-24979 139 24 x x X ajst-24979 139 25 r r NOUN ajst-24979 139 26 q q NOUN ajst-24979 139 27 x x X ajst-24979 139 28 r r NOUN ajst-24979 139 29 q q NOUN ajst-24979 139 30 w w NOUN ajst-24979 139 31 x x NOUN ajst-24979 139 32 r r NOUN ajst-24979 139 33 w w PROPN ajst-24979 139 34 x x SYM ajst-24979 139 35 r r NUM ajst-24979 139 36   PROPN ajst-24979 139 37   NOUN ajst-24979 139 38   NOUN ajst-24979 139 39 0 0 PUNCT ajst-24979 140 1 ( ( PUNCT ajst-24979 140 2 , , PUNCT ajst-24979 140 3 ) ) PUNCT ajst-24979 140 4 ] ] X ajst-24979 140 5 w w X ajst-24979 140 6 x x SYM ajst-24979 140 7 r r NOUN ajst-24979 140 8 construct construct VERB ajst-24979 140 9 the the DET ajst-24979 140 10 following follow VERB ajst-24979 140 11 zero zero NUM ajst-24979 140 12 - - PUNCT ajst-24979 140 13 order order NOUN ajst-24979 140 14 deformation deformation NOUN ajst-24979 140 15 equation equation NOUN ajst-24979 140 16 0(1 0(1 NUM ajst-24979 140 17 ) ) PUNCT ajst-24979 141 1 [ [ PUNCT ajst-24979 141 2 ( ( PUNCT ajst-24979 141 3 , , PUNCT ajst-24979 141 4 ; ; PUNCT ajst-24979 141 5 ) ) PUNCT ajst-24979 141 6 ( ( PUNCT ajst-24979 141 7 , , PUNCT ajst-24979 141 8 ) ) PUNCT ajst-24979 141 9 ] ] PUNCT ajst-24979 142 1 [ [ PUNCT ajst-24979 142 2 ( ( PUNCT ajst-24979 142 3 , , PUNCT ajst-24979 142 4 ; ; PUNCT ajst-24979 142 5 ] ] PUNCT ajst-24979 142 6 , , PUNCT ajst-24979 142 7 cq cq PROPN ajst-24979 142 8 d d NOUN ajst-24979 142 9 x x PUNCT ajst-24979 142 10 r r NOUN ajst-24979 142 11 q q NOUN ajst-24979 142 12 w w NOUN ajst-24979 142 13 x x NOUN ajst-24979 142 14 r r NOUN ajst-24979 142 15 qhn qhn NOUN ajst-24979 142 16 x x PUNCT ajst-24979 142 17 r r NOUN ajst-24979 142 18 q q NOUN ajst-24979 142 19   PROPN ajst-24979 142 20   NOUN ajst-24979 142 21   PROPN ajst-24979 142 22   PROPN ajst-24979 142 23 ( ( PUNCT ajst-24979 142 24 18 18 NUM ajst-24979 142 25 ) ) PUNCT ajst-24979 142 26 and and CCONJ ajst-24979 142 27 meet meet VERB ajst-24979 142 28 the the DET ajst-24979 142 29 following following ADJ ajst-24979 142 30 initial initial ADJ ajst-24979 142 31 conditions condition NOUN ajst-24979 142 32 0 0 PUNCT ajst-24979 143 1 ( ( PUNCT ajst-24979 143 2 , , PUNCT ajst-24979 143 3 ) ) PUNCT ajst-24979 143 4 ( ( PUNCT ajst-24979 143 5 0 0 NUM ajst-24979 143 6 , , PUNCT ajst-24979 143 7 ; ; PUNCT ajst-24979 143 8 ) ) PUNCT ajst-24979 143 9 ( ( PUNCT ajst-24979 143 10 0 0 NUM ajst-24979 143 11 , , PUNCT ajst-24979 143 12 ) ) PUNCT ajst-24979 143 13 w w NOUN ajst-24979 143 14 x x PUNCT ajst-24979 143 15 r r NOUN ajst-24979 143 16 r r NOUN ajst-24979 143 17 q q NOUN ajst-24979 143 18 w w NOUN ajst-24979 144 1 r r NOUN ajst-24979 144 2   NOUN ajst-24979 144 3 ( ( PUNCT ajst-24979 144 4 19 19 NUM ajst-24979 144 5 ) ) PUNCT ajst-24979 144 6 the the DET ajst-24979 144 7 next next ADJ ajst-24979 144 8 steps step NOUN ajst-24979 144 9 are be AUX ajst-24979 144 10 similar similar ADJ ajst-24979 144 11 to to ADP ajst-24979 144 12 ( ( PUNCT ajst-24979 144 13 3)-(19 3)-(19 NUM ajst-24979 144 14 ) ) PUNCT ajst-24979 144 15 , , PUNCT ajst-24979 144 16 and and CCONJ ajst-24979 144 17 now now ADV ajst-24979 144 18 by by ADP ajst-24979 144 19 selecting select VERB ajst-24979 144 20 the the DET ajst-24979 144 21 appropriate appropriate ADJ ajst-24979 144 22 parameters parameter NOUN ajst-24979 144 23 , , PUNCT ajst-24979 144 24 we we PRON ajst-24979 144 25 can can AUX ajst-24979 144 26 make make VERB ajst-24979 144 27 converge converge NOUN ajst-24979 144 28 ( ( PUNCT ajst-24979 144 29 , , PUNCT ajst-24979 144 30 ; ; PUNCT ajst-24979 144 31 ) ) PUNCT ajst-24979 144 32 x x X ajst-24979 145 1 r r NOUN ajst-24979 145 2 q q PUNCT ajst-24979 145 3 to to ADP ajst-24979 145 4 1q 1q NUM ajst-24979 145 5   NOUN ajst-24979 145 6 , , PUNCT ajst-24979 145 7 and and CCONJ ajst-24979 145 8 obtain obtain VERB ajst-24979 145 9 the the DET ajst-24979 145 10 following follow VERB ajst-24979 145 11 series series NOUN ajst-24979 145 12 solution solution NOUN ajst-24979 145 13 11 11 NUM ajst-24979 145 14 [ [ PUNCT ajst-24979 145 15 ( ( PUNCT ajst-24979 145 16 , , PUNCT ajst-24979 145 17 ) ) PUNCT ajst-24979 145 18 ( ( PUNCT ajst-24979 145 19 , , PUNCT ajst-24979 145 20 ) ) PUNCT ajst-24979 145 21 ] ] PUNCT ajst-24979 145 22 ( ( PUNCT ajst-24979 145 23 ( ( PUNCT ajst-24979 145 24 , , PUNCT ajst-24979 145 25 ) ) PUNCT ajst-24979 145 26 ) ) PUNCT ajst-24979 145 27 , , PUNCT ajst-24979 145 28 c c PROPN ajst-24979 145 29 nn nn PROPN ajst-24979 145 30 n n PROPN ajst-24979 145 31 n n PROPN ajst-24979 145 32 nd nd ADV ajst-24979 145 33 w w NOUN ajst-24979 145 34 x x PUNCT ajst-24979 145 35 r r NOUN ajst-24979 145 36 w w NOUN ajst-24979 145 37 x x SYM ajst-24979 145 38 r r NOUN ajst-24979 145 39 h h NOUN ajst-24979 145 40 w w NOUN ajst-24979 145 41 x x X ajst-24979 145 42 r r NOUN ajst-24979 145 43   NOUN ajst-24979 145 44   VERB ajst-24979 145 45   NOUN ajst-24979 145 46   NUM ajst-24979 145 47   PROPN ajst-24979 145 48 ( ( PUNCT ajst-24979 145 49 20 20 NUM ajst-24979 145 50 ) ) PUNCT ajst-24979 145 51 where where SCONJ ajst-24979 145 52 1 1 NUM ajst-24979 145 53 1 1 NUM ajst-24979 145 54 01 01 NUM ajst-24979 145 55 1 1 NUM ajst-24979 145 56 1 1 NUM ajst-24979 145 57 1 1 NUM ajst-24979 145 58 1 1 NUM ajst-24979 145 59 1 1 NUM ajst-24979 145 60 1 1 NUM ajst-24979 145 61 2 2 NUM ajst-24979 145 62 2 2 NUM ajst-24979 145 63 10 10 NUM ajst-24979 145 64 0 0 NUM ajst-24979 145 65 1 1 NUM ajst-24979 145 66 [ [ PUNCT ajst-24979 145 67 ( ( PUNCT ajst-24979 145 68 ; ; PUNCT ajst-24979 145 69 ) ) PUNCT ajst-24979 145 70 ] ] PUNCT ajst-24979 145 71 ( ( PUNCT ajst-24979 145 72 ( ( PUNCT ajst-24979 145 73 , , PUNCT ajst-24979 145 74 ) ) PUNCT ajst-24979 145 75 ) ) PUNCT ajst-24979 145 76 ( ( PUNCT ajst-24979 145 77 1 1 NUM ajst-24979 145 78 ) ) PUNCT ajst-24979 145 79 ! ! PUNCT ajst-24979 146 1 ( ( PUNCT ajst-24979 146 2 , , PUNCT ajst-24979 146 3 ) ) PUNCT ajst-24979 146 4 ( ( PUNCT ajst-24979 146 5 ) ) PUNCT ajst-24979 146 6 ( ( PUNCT ajst-24979 146 7 , , PUNCT ajst-24979 146 8 ) ) PUNCT ajst-24979 146 9 ( ( PUNCT ajst-24979 146 10 1 1 X ajst-24979 146 11 ) ) PUNCT ajst-24979 146 12 ( ( PUNCT ajst-24979 146 13 , , PUNCT ajst-24979 146 14 ) ) PUNCT ajst-24979 146 15 ( ( PUNCT ajst-24979 146 16 , , PUNCT ajst-24979 146 17 ) ) PUNCT ajst-24979 146 18 ( ( PUNCT ajst-24979 146 19 ( ( PUNCT ajst-24979 146 20 , , PUNCT ajst-24979 146 21 ) ) PUNCT ajst-24979 146 22 ) ) PUNCT ajst-24979 146 23 ( ( PUNCT ajst-24979 146 24 , , PUNCT ajst-24979 146 25 ) ) PUNCT ajst-24979 146 26 ( ( PUNCT ajst-24979 146 27 ( ( PUNCT ajst-24979 146 28 , , PUNCT ajst-24979 146 29 ) ) PUNCT ajst-24979 146 30 ) ) PUNCT ajst-24979 146 31 . . PUNCT ajst-24979 147 1 n n CCONJ ajst-24979 147 2 nn nn PROPN ajst-24979 147 3 qn qn PROPN ajst-24979 147 4 c c PROPN ajst-24979 147 5 n n CCONJ ajst-24979 147 6 n n CCONJ ajst-24979 147 7 n n NOUN ajst-24979 147 8 x x SYM ajst-24979 147 9 n n CCONJ ajst-24979 147 10 n n CCONJ ajst-24979 147 11 n n NOUN ajst-24979 147 12 x x NOUN ajst-24979 147 13 q q PUNCT ajst-24979 147 14 w w NOUN ajst-24979 147 15 x x SYM ajst-24979 147 16 r r NOUN ajst-24979 148 1 n n NOUN ajst-24979 148 2 q q NOUN ajst-24979 149 1 d d NOUN ajst-24979 149 2 w w NOUN ajst-24979 149 3 x x X ajst-24979 149 4 r r NOUN ajst-24979 149 5 a a NOUN ajst-24979 149 6 x x X ajst-24979 149 7 w w NOUN ajst-24979 149 8 x x SYM ajst-24979 150 1 r r NOUN ajst-24979 150 2 g g NOUN ajst-24979 150 3 x x SYM ajst-24979 150 4 r r NOUN ajst-24979 150 5 k k NOUN ajst-24979 150 6 x x SYM ajst-24979 151 1 t t NOUN ajst-24979 151 2 f f PROPN ajst-24979 151 3 w w PROPN ajst-24979 151 4 t t PROPN ajst-24979 152 1 r r NOUN ajst-24979 153 1 dt dt NOUN ajst-24979 154 1 k k NOUN ajst-24979 154 2 x x SYM ajst-24979 155 1 t t NOUN ajst-24979 155 2 f f PROPN ajst-24979 155 3 w w PROPN ajst-24979 155 4 t t PROPN ajst-24979 155 5 r r NOUN ajst-24979 155 6 dt dt X ajst-24979 155 7   NUM ajst-24979 155 8   NOUN ajst-24979 155 9   VERB ajst-24979 155 10   VERB ajst-24979 155 11   PROPN ajst-24979 155 12   PROPN ajst-24979 155 13   PROPN ajst-24979 155 14   PROPN ajst-24979 155 15   PROPN ajst-24979 155 16   PROPN ajst-24979 155 17   PROPN ajst-24979 155 18   PROPN ajst-24979 155 19   PROPN ajst-24979 155 20   PROPN ajst-24979 155 21   PROPN ajst-24979 155 22   PROPN ajst-24979 155 23   PROPN ajst-24979 155 24   PROPN ajst-24979 155 25   NOUN ajst-24979 155 26   NOUN ajst-24979 155 27   PUNCT ajst-24979 155 28   PROPN ajst-24979 155 29 ( ( PUNCT ajst-24979 155 30 21 21 NUM ajst-24979 155 31 ) ) PUNCT ajst-24979 155 32 acting act VERB ajst-24979 155 33 on on ADP ajst-24979 155 34 operator operator NOUN ajst-24979 155 35 j j PROPN ajst-24979 155 36   NUM ajst-24979 155 37 on on ADP ajst-24979 155 38 both both DET ajst-24979 155 39 sides side NOUN ajst-24979 155 40 of of ADP ajst-24979 155 41 eq eq PROPN ajst-24979 155 42 . . PUNCT ajst-24979 156 1 ( ( PUNCT ajst-24979 156 2 20 20 NUM ajst-24979 156 3 ) ) PUNCT ajst-24979 156 4 , , PUNCT ajst-24979 156 5 there there PRON ajst-24979 156 6 is be VERB ajst-24979 156 7 1 1 NUM ajst-24979 156 8 1 1 NUM ajst-24979 156 9 1 1 NUM ajst-24979 156 10 1 1 NUM ajst-24979 156 11 1 1 NUM ajst-24979 156 12 1 1 NUM ajst-24979 156 13 2 2 NUM ajst-24979 156 14 2 2 NUM ajst-24979 156 15 10 10 NUM ajst-24979 156 16 0 0 NUM ajst-24979 156 17 ( ( PUNCT ajst-24979 156 18 , , PUNCT ajst-24979 156 19 ) ) PUNCT ajst-24979 156 20 ( ( PUNCT ajst-24979 156 21 ) ) PUNCT ajst-24979 156 22 ( ( PUNCT ajst-24979 156 23 , , PUNCT ajst-24979 156 24 ) ) PUNCT ajst-24979 157 1 [ [ PUNCT ajst-24979 157 2 ( ( PUNCT ajst-24979 157 3 ) ) PUNCT ajst-24979 157 4 ( ( PUNCT ajst-24979 157 5 , , PUNCT ajst-24979 157 6 ) ) PUNCT ajst-24979 157 7 ( ( PUNCT ajst-24979 157 8 1 1 X ajst-24979 157 9 ) ) PUNCT ajst-24979 157 10 ( ( PUNCT ajst-24979 157 11 , , PUNCT ajst-24979 157 12 ) ) PUNCT ajst-24979 157 13 ( ( PUNCT ajst-24979 157 14 , , PUNCT ajst-24979 157 15 ) ) PUNCT ajst-24979 157 16 ( ( PUNCT ajst-24979 157 17 ( ( PUNCT ajst-24979 157 18 , , PUNCT ajst-24979 157 19 ) ) PUNCT ajst-24979 157 20 ) ) PUNCT ajst-24979 157 21 ( ( PUNCT ajst-24979 157 22 , , PUNCT ajst-24979 157 23 ) ) PUNCT ajst-24979 157 24 ( ( PUNCT ajst-24979 157 25 ( ( PUNCT ajst-24979 157 26 , , PUNCT ajst-24979 157 27 ) ) PUNCT ajst-24979 157 28 ) ) PUNCT ajst-24979 157 29 ] ] PUNCT ajst-24979 157 30 . . PUNCT ajst-24979 158 1 n n CCONJ ajst-24979 158 2 n n CCONJ ajst-24979 158 3 n n CCONJ ajst-24979 158 4 n n CCONJ ajst-24979 158 5 n n NOUN ajst-24979 158 6 x x SYM ajst-24979 158 7 n n CCONJ ajst-24979 158 8 n n NOUN ajst-24979 158 9 w w NOUN ajst-24979 158 10 x x SYM ajst-24979 159 1 r r NOUN ajst-24979 159 2 h h NOUN ajst-24979 159 3 w w NOUN ajst-24979 159 4 x x PUNCT ajst-24979 159 5 r r AUX ajst-24979 159 6 hj hj VERB ajst-24979 159 7 a a PRON ajst-24979 159 8 x x X ajst-24979 159 9 w w NOUN ajst-24979 159 10 x x SYM ajst-24979 160 1 r r NOUN ajst-24979 160 2 g g NOUN ajst-24979 160 3 x x SYM ajst-24979 160 4 r r NOUN ajst-24979 160 5 k k NOUN ajst-24979 160 6 x x SYM ajst-24979 161 1 t t NOUN ajst-24979 161 2 f f PROPN ajst-24979 161 3 w w PROPN ajst-24979 161 4 t t PROPN ajst-24979 162 1 r r NOUN ajst-24979 163 1 dt dt NOUN ajst-24979 164 1 k k NOUN ajst-24979 164 2 x x SYM ajst-24979 165 1 t t NOUN ajst-24979 165 2 f f PROPN ajst-24979 165 3 w w PROPN ajst-24979 165 4 t t PROPN ajst-24979 165 5 r r NOUN ajst-24979 165 6 dt dt PROPN ajst-24979 165 7   PROPN ajst-24979 165 8   PROPN ajst-24979 165 9   PROPN ajst-24979 165 10   PROPN ajst-24979 165 11   PROPN ajst-24979 165 12   NUM ajst-24979 165 13   ADV ajst-24979 165 14   PROPN ajst-24979 165 15   VERB ajst-24979 165 16   PROPN ajst-24979 165 17   VERB ajst-24979 165 18   NUM ajst-24979 165 19   SYM ajst-24979 165 20 4 4 NUM ajst-24979 165 21 . . NOUN ajst-24979 165 22 existence existence NOUN ajst-24979 165 23 and and CCONJ ajst-24979 165 24 uniqueness uniqueness NOUN ajst-24979 165 25 of of ADP ajst-24979 165 26 the the DET ajst-24979 165 27 solution solution NOUN ajst-24979 165 28 in in ADP ajst-24979 165 29 this this DET ajst-24979 165 30 section section NOUN ajst-24979 165 31 , , PUNCT ajst-24979 165 32 we we PRON ajst-24979 165 33 will will AUX ajst-24979 165 34 give give VERB ajst-24979 165 35 the the DET ajst-24979 165 36 existence existence NOUN ajst-24979 165 37 and and CCONJ ajst-24979 165 38 uniqueness uniqueness ADJ ajst-24979 165 39 results result NOUN ajst-24979 165 40 of of ADP ajst-24979 165 41 the the DET ajst-24979 165 42 solutions solution NOUN ajst-24979 165 43 of of ADP ajst-24979 165 44 eq eq PROPN ajst-24979 165 45 . . PUNCT ajst-24979 166 1 ( ( PUNCT ajst-24979 166 2 1 1 NUM ajst-24979 166 3 ) ) PUNCT ajst-24979 166 4 , , PUNCT ajst-24979 166 5 and and CCONJ ajst-24979 166 6 prove prove VERB ajst-24979 166 7 it it PRON ajst-24979 166 8 . . PUNCT ajst-24979 167 1 the the DET ajst-24979 167 2 following follow VERB ajst-24979 167 3 assumptions assumption NOUN ajst-24979 167 4 are be AUX ajst-24979 167 5 given give VERB ajst-24979 167 6 before before ADP ajst-24979 167 7 proof proof NOUN ajst-24979 167 8 . . PUNCT ajst-24979 168 1 h(1 h(1 VERB ajst-24979 168 2 ) ) PUNCT ajst-24979 168 3 ( ( PUNCT ajst-24979 168 4 , , PUNCT ajst-24979 168 5 ) ) PUNCT ajst-24979 168 6 , , PUNCT ajst-24979 168 7 ( ( PUNCT ajst-24979 168 8 ) ) PUNCT ajst-24979 168 9 : : PUNCT ajst-24979 169 1 [ [ X ajst-24979 169 2 0,1]g 0,1]g NOUN ajst-24979 169 3 x x X ajst-24979 169 4 r r NOUN ajst-24979 169 5 a a NOUN ajst-24979 169 6 x x X ajst-24979 169 7 e e PROPN ajst-24979 169 8 , , PUNCT ajst-24979 169 9 assume assume VERB ajst-24979 169 10 that that SCONJ ajst-24979 169 11 g(x g(x NOUN ajst-24979 169 12 ) ) PUNCT ajst-24979 169 13 , , PUNCT ajst-24979 169 14 f(x f(x PROPN ajst-24979 169 15 ) ) PUNCT ajst-24979 169 16 are be AUX ajst-24979 169 17 continuous continuous ADJ ajst-24979 169 18 functions function NOUN ajst-24979 169 19 , , PUNCT ajst-24979 169 20 and and CCONJ ajst-24979 169 21 write write VERB ajst-24979 169 22 [ [ X ajst-24979 169 23 0,1 0,1 NUM ajst-24979 169 24 ] ] SYM ajst-24979 169 25 sup sup NOUN ajst-24979 169 26 ( ( PUNCT ajst-24979 169 27 ) ) PUNCT ajst-24979 169 28 x x X ajst-24979 169 29 a a DET ajst-24979 169 30 x x X ajst-24979 169 31   NOUN ajst-24979 169 32   NUM ajst-24979 169 33 . . PUNCT ajst-24979 170 1 h(2 h(2 NOUN ajst-24979 170 2 ) ) PUNCT ajst-24979 170 3 there there PRON ajst-24979 170 4 exist exist VERB ajst-24979 170 5 1 1 NUM ajst-24979 170 6 20 20 NUM ajst-24979 170 7 , , PUNCT ajst-24979 170 8 0,l 0,l X ajst-24979 170 9 l l NOUN ajst-24979 170 10   PRON ajst-24979 170 11 such such ADJ ajst-24979 170 12 that that PRON ajst-24979 170 13 for for ADP ajst-24979 170 14 any any DET ajst-24979 170 15 1 1 NUM ajst-24979 170 16 2 2 NUM ajst-24979 170 17 ( ( PUNCT ajst-24979 170 18 , , PUNCT ajst-24979 170 19 ) ) PUNCT ajst-24979 170 20 , , PUNCT ajst-24979 170 21 ( ( PUNCT ajst-24979 170 22 , , PUNCT ajst-24979 170 23 ) ) PUNCT ajst-24979 171 1 [ [ X ajst-24979 171 2 0,1]fw 0,1]fw X ajst-24979 171 3 x x SYM ajst-24979 171 4 r r NOUN ajst-24979 171 5 w w NOUN ajst-24979 171 6 x x SYM ajst-24979 171 7 r r NOUN ajst-24979 171 8 c c NOUN ajst-24979 171 9 satisfying satisfying NOUN ajst-24979 171 10 . . PUNCT ajst-24979 172 1 1 1 NUM ajst-24979 172 2 1 1 NUM ajst-24979 172 3 1 1 NUM ajst-24979 172 4 2 2 NUM ajst-24979 172 5 1 1 NUM ajst-24979 172 6 1 1 NUM ajst-24979 172 7 2 2 NUM ajst-24979 172 8 2 2 NUM ajst-24979 172 9 1 1 NUM ajst-24979 172 10 2 2 NUM ajst-24979 172 11 2 2 NUM ajst-24979 172 12 2 2 NUM ajst-24979 172 13 1 1 NUM ajst-24979 172 14 2 2 NUM ajst-24979 172 15 ( ( PUNCT ajst-24979 172 16 ( ( PUNCT ajst-24979 172 17 ( ( PUNCT ajst-24979 172 18 , , PUNCT ajst-24979 172 19 ) ) PUNCT ajst-24979 172 20 ) ) PUNCT ajst-24979 172 21 , , PUNCT ajst-24979 172 22 ( ( PUNCT ajst-24979 172 23 ( ( PUNCT ajst-24979 172 24 , , PUNCT ajst-24979 172 25 ) ) PUNCT ajst-24979 172 26 ) ) PUNCT ajst-24979 172 27 ) ) PUNCT ajst-24979 173 1 ( ( PUNCT ajst-24979 173 2 ( ( PUNCT ajst-24979 173 3 , , PUNCT ajst-24979 173 4 ) ) PUNCT ajst-24979 173 5 , , PUNCT ajst-24979 173 6 ( ( PUNCT ajst-24979 173 7 , , PUNCT ajst-24979 173 8 ) ) PUNCT ajst-24979 173 9 ) ) PUNCT ajst-24979 173 10 , , PUNCT ajst-24979 173 11 ( ( PUNCT ajst-24979 173 12 ( ( PUNCT ajst-24979 173 13 ( ( PUNCT ajst-24979 173 14 , , PUNCT ajst-24979 173 15 ) ) PUNCT ajst-24979 173 16 ) ) PUNCT ajst-24979 173 17 , , PUNCT ajst-24979 173 18 ( ( PUNCT ajst-24979 173 19 ( ( PUNCT ajst-24979 173 20 , , PUNCT ajst-24979 173 21 ) ) PUNCT ajst-24979 173 22 ) ) PUNCT ajst-24979 173 23 ) ) PUNCT ajst-24979 174 1 ( ( PUNCT ajst-24979 174 2 ( ( PUNCT ajst-24979 174 3 , , PUNCT ajst-24979 174 4 ) ) PUNCT ajst-24979 174 5 , , PUNCT ajst-24979 174 6 ( ( PUNCT ajst-24979 174 7 , , PUNCT ajst-24979 174 8 ) ) PUNCT ajst-24979 174 9 ) ) PUNCT ajst-24979 174 10 . . PUNCT ajst-24979 175 1 d d X ajst-24979 175 2 f f X ajst-24979 176 1 w w NOUN ajst-24979 176 2 x x PUNCT ajst-24979 176 3 r r NOUN ajst-24979 176 4 f f PROPN ajst-24979 176 5 w w NOUN ajst-24979 176 6 x x PUNCT ajst-24979 176 7 r r NOUN ajst-24979 177 1 l l NOUN ajst-24979 177 2 d d X ajst-24979 177 3 w w NOUN ajst-24979 177 4 x x X ajst-24979 177 5 r r NOUN ajst-24979 177 6 w w NOUN ajst-24979 177 7 x x SYM ajst-24979 177 8 r r NOUN ajst-24979 177 9 d d NOUN ajst-24979 177 10 f f PROPN ajst-24979 177 11 w w PROPN ajst-24979 177 12 x x PUNCT ajst-24979 178 1 r r NOUN ajst-24979 178 2 f f PROPN ajst-24979 178 3 w w NOUN ajst-24979 178 4 x x PUNCT ajst-24979 178 5 r r NOUN ajst-24979 178 6 l l NOUN ajst-24979 179 1 d d X ajst-24979 179 2 w w NOUN ajst-24979 179 3 x x X ajst-24979 179 4 r r NOUN ajst-24979 179 5 w w NOUN ajst-24979 179 6 x x SYM ajst-24979 179 7 r r NOUN ajst-24979 179 8   NUM ajst-24979 179 9   NOUN ajst-24979 179 10 h(3 h(3 NOUN ajst-24979 179 11 ) ) PUNCT ajst-24979 179 12 there there PRON ajst-24979 179 13 exist exist VERB ajst-24979 179 14 two two NUM ajst-24979 179 15 continuous continuous ADJ ajst-24979 179 16 functions function NOUN ajst-24979 179 17 1 1 NUM ajst-24979 179 18 0,m 0,m NOUN ajst-24979 179 19   ADJ ajst-24979 179 20 2 2 NUM ajst-24979 179 21 0 0 NUM ajst-24979 179 22 m m VERB ajst-24979 179 23   ADJ ajst-24979 179 24 satisfying satisfy VERB ajst-24979 179 25 1 1 NUM ajst-24979 179 26 1 1 NUM ajst-24979 179 27 1 1 NUM ajst-24979 179 28 2 2 NUM ajst-24979 179 29 10 10 NUM ajst-24979 179 30 0[0,1 0[0,1 NOUN ajst-24979 179 31 ] ] PUNCT ajst-24979 180 1 [ [ X ajst-24979 180 2 0,1 0,1 NUM ajst-24979 180 3 ] ] SYM ajst-24979 180 4 sup sup NOUN ajst-24979 180 5 ( ( PUNCT ajst-24979 180 6 , , PUNCT ajst-24979 180 7 ) ) PUNCT ajst-24979 180 8 , , PUNCT ajst-24979 180 9 sup sup NOUN ajst-24979 180 10 ( ( PUNCT ajst-24979 180 11 , , PUNCT ajst-24979 180 12 ) ) PUNCT ajst-24979 180 13 . . PUNCT ajst-24979 181 1 x x PUNCT ajst-24979 182 1 x x PUNCT ajst-24979 182 2 x x PUNCT ajst-24979 182 3 m m VERB ajst-24979 182 4 k k NOUN ajst-24979 182 5 x x SYM ajst-24979 182 6 t t NOUN ajst-24979 182 7 dt dt NOUN ajst-24979 182 8 m m VERB ajst-24979 182 9 k k NOUN ajst-24979 182 10 x x SYM ajst-24979 182 11 t t PROPN ajst-24979 182 12 dt dt PROPN ajst-24979 183 1   PROPN ajst-24979 183 2   NOUN ajst-24979 183 3   PRON ajst-24979 183 4   PROPN ajst-24979 183 5   VERB ajst-24979 183 6   PRON ajst-24979 183 7   PROPN ajst-24979 183 8   PRON ajst-24979 184 1   PUNCT ajst-24979 184 2 next next ADV ajst-24979 184 3 , , PUNCT ajst-24979 184 4 the the DET ajst-24979 184 5 uniqueness uniqueness NOUN ajst-24979 184 6 of of ADP ajst-24979 184 7 the the DET ajst-24979 184 8 solution solution NOUN ajst-24979 184 9 of of ADP ajst-24979 184 10 the the DET ajst-24979 184 11 equation equation NOUN ajst-24979 184 12 will will AUX ajst-24979 184 13 be be AUX ajst-24979 184 14 proved prove VERB ajst-24979 184 15 using use VERB ajst-24979 184 16 balach balach NOUN ajst-24979 184 17 's 's PART ajst-24979 184 18 fixed fix VERB ajst-24979 184 19 point point NOUN ajst-24979 184 20 theorem theorem VERB ajst-24979 184 21 . . PUNCT ajst-24979 184 22 theorem theorem NOUN ajst-24979 184 23 4.1 4.1 NUM ajst-24979 184 24 . . PUNCT ajst-24979 185 1 suppose suppose VERB ajst-24979 185 2 that that SCONJ ajst-24979 185 3 the the DET ajst-24979 185 4 hypotheses hypothesis NOUN ajst-24979 185 5 h(1)-h(3 h(1)-h(3 NOUN ajst-24979 185 6 ) ) PUNCT ajst-24979 185 7 hold hold VERB ajst-24979 185 8 , , PUNCT ajst-24979 185 9 if if SCONJ ajst-24979 185 10 1 1 NUM ajst-24979 185 11 1 1 NUM ajst-24979 185 12 2 2 NUM ajst-24979 185 13 2 2 NUM ajst-24979 185 14 1 1 NUM ajst-24979 185 15 , , PUNCT ajst-24979 185 16 ( ( PUNCT ajst-24979 185 17 1 1 X ajst-24979 185 18 ) ) PUNCT ajst-24979 185 19 l l NOUN ajst-24979 185 20 m m VERB ajst-24979 185 21 l l NOUN ajst-24979 185 22 m m PROPN ajst-24979 185 23   PROPN ajst-24979 185 24   ADV ajst-24979 185 25   ADV ajst-24979 185 26   PROPN ajst-24979 185 27   PROPN ajst-24979 185 28   PROPN ajst-24979 185 29 then then ADV ajst-24979 185 30 eqs eqs PROPN ajst-24979 185 31 . . PUNCT ajst-24979 186 1 ( ( PUNCT ajst-24979 186 2 1)-(2 1)-(2 NUM ajst-24979 186 3 ) ) PUNCT ajst-24979 186 4 has have VERB ajst-24979 186 5 a a DET ajst-24979 186 6 unique unique ADJ ajst-24979 186 7 solution solution NOUN ajst-24979 186 8 ( ( PUNCT ajst-24979 186 9 , , PUNCT ajst-24979 186 10 ) ) PUNCT ajst-24979 186 11 w w NOUN ajst-24979 186 12 x x SYM ajst-24979 186 13 r r NOUN ajst-24979 186 14   NOUN ajst-24979 186 15 . . PUNCT ajst-24979 187 1 [ [ X ajst-24979 187 2 0,1]fc 0,1]fc X ajst-24979 187 3 . . PUNCT ajst-24979 188 1 proof proof NOUN ajst-24979 188 2 . . PUNCT ajst-24979 189 1 let let VERB ajst-24979 189 2 the the DET ajst-24979 189 3 definition definition NOUN ajst-24979 189 4 of of ADP ajst-24979 189 5 operator operator NOUN ajst-24979 189 6 : : PUNCT ajst-24979 190 1 [ [ X ajst-24979 190 2 0,1]ft 0,1]ft X ajst-24979 190 3 c c NOUN ajst-24979 190 4   PUNCT ajst-24979 191 1 [ [ X ajst-24979 191 2 0,1]fc 0,1]fc X ajst-24979 191 3 , , PUNCT ajst-24979 191 4 1 1 NUM ajst-24979 191 5 2 2 NUM ajst-24979 191 6 , , PUNCT ajst-24979 191 7 , , PUNCT ajst-24979 191 8 [ [ X ajst-24979 191 9 0,1]w 0,1]w NUM ajst-24979 191 10 w w PROPN ajst-24979 191 11 e e PROPN ajst-24979 191 12 x x PROPN ajst-24979 191 13   PROPN ajst-24979 191 14   VERB ajst-24979 191 15   NOUN ajst-24979 191 16 1 1 NUM ajst-24979 191 17 0 0 NUM ajst-24979 191 18 1 1 NUM ajst-24979 191 19 0 0 NUM ajst-24979 191 20 1 1 NUM ajst-24979 191 21 ( ( PUNCT ajst-24979 191 22 ) ) PUNCT ajst-24979 191 23 ( ( PUNCT ajst-24979 191 24 , , PUNCT ajst-24979 191 25 ) ) PUNCT ajst-24979 191 26 ( ( PUNCT ajst-24979 191 27 0 0 NUM ajst-24979 191 28 , , PUNCT ajst-24979 191 29 ) ) PUNCT ajst-24979 191 30 ( ( PUNCT ajst-24979 191 31 ) ) PUNCT ajst-24979 191 32 ( ( PUNCT ajst-24979 191 33 , , PUNCT ajst-24979 191 34 ) ) PUNCT ajst-24979 191 35 ( ( PUNCT ajst-24979 191 36 ) ) PUNCT ajst-24979 191 37 1 1 NUM ajst-24979 191 38 ( ( PUNCT ajst-24979 191 39 ) ) PUNCT ajst-24979 191 40 ( ( PUNCT ajst-24979 191 41 ) ) PUNCT ajst-24979 191 42 ( ( PUNCT ajst-24979 191 43 , , PUNCT ajst-24979 191 44 ) ) PUNCT ajst-24979 191 45 ( ( PUNCT ajst-24979 191 46 ) ) PUNCT ajst-24979 192 1 x x X ajst-24979 192 2 i i NOUN ajst-24979 192 3 x x VERB ajst-24979 193 1 i i PRON ajst-24979 193 2 tw tw VERB ajst-24979 193 3 x x SYM ajst-24979 193 4 r r NOUN ajst-24979 193 5 w w NOUN ajst-24979 193 6 r r NOUN ajst-24979 193 7 x x SYM ajst-24979 193 8 s s NOUN ajst-24979 193 9 g g NOUN ajst-24979 193 10 s s NOUN ajst-24979 193 11 r r NOUN ajst-24979 193 12 ds ds NOUN ajst-24979 193 13 x x SYM ajst-24979 193 14 s s VERB ajst-24979 193 15 a a DET ajst-24979 193 16 s s NOUN ajst-24979 193 17 w w NOUN ajst-24979 193 18 s s NOUN ajst-24979 193 19 r r NOUN ajst-24979 193 20 ds ds NOUN ajst-24979 193 21   NUM ajst-24979 193 22   NUM ajst-24979 193 23   NUM ajst-24979 193 24   NUM ajst-24979 193 25   PROPN ajst-24979 193 26   PROPN ajst-24979 193 27   NUM ajst-24979 193 28   ADV ajst-24979 193 29   PROPN ajst-24979 193 30   NUM ajst-24979 193 31   PUNCT ajst-24979 193 32   NOUN ajst-24979 193 33   VERB ajst-24979 193 34   ADP ajst-24979 193 35   NOUN ajst-24979 194 1 1 1 NUM ajst-24979 194 2 1 1 NUM ajst-24979 194 3 10 10 NUM ajst-24979 194 4 0 0 NUM ajst-24979 194 5 1 1 NUM ajst-24979 194 6 2 2 NUM ajst-24979 194 7 20 20 NUM ajst-24979 194 8 1 1 NUM ajst-24979 194 9 ( ( PUNCT ajst-24979 194 10 ) ) PUNCT ajst-24979 194 11 ( ( PUNCT ajst-24979 194 12 ( ( PUNCT ajst-24979 194 13 , , PUNCT ajst-24979 194 14 ) ) PUNCT ajst-24979 194 15 ( ( PUNCT ajst-24979 194 16 ( ( PUNCT ajst-24979 194 17 , , PUNCT ajst-24979 194 18 ) ) PUNCT ajst-24979 194 19 ) ) PUNCT ajst-24979 195 1 ( ( PUNCT ajst-24979 195 2 ) ) PUNCT ajst-24979 195 3 ( ( PUNCT ajst-24979 195 4 , , PUNCT ajst-24979 195 5 ) ) PUNCT ajst-24979 195 6 ( ( PUNCT ajst-24979 195 7 ( ( PUNCT ajst-24979 195 8 , , PUNCT ajst-24979 195 9 ) ) PUNCT ajst-24979 195 10 ) ) PUNCT ajst-24979 195 11 ) ) PUNCT ajst-24979 195 12 , , PUNCT ajst-24979 195 13 ( ( PUNCT ajst-24979 195 14 1 1 NUM ajst-24979 195 15 , , PUNCT ajst-24979 195 16 2 2 NUM ajst-24979 195 17 ) ) PUNCT ajst-24979 195 18 . . PUNCT ajst-24979 196 1 x x X ajst-24979 196 2 s s AUX ajst-24979 196 3 i i INTJ ajst-24979 196 4 i i INTJ ajst-24979 196 5 x x X ajst-24979 196 6 s s AUX ajst-24979 196 7 k k X ajst-24979 196 8 s s X ajst-24979 196 9 f f PROPN ajst-24979 196 10 w w PROPN ajst-24979 196 11 r r PROPN ajst-24979 197 1 d d PROPN ajst-24979 197 2 k k PROPN ajst-24979 197 3 s s X ajst-24979 198 1 f f PROPN ajst-24979 198 2 w w PROPN ajst-24979 198 3 r r NOUN ajst-24979 198 4 d d NOUN ajst-24979 198 5 ds ds INTJ ajst-24979 199 1 i i PRON ajst-24979 199 2   VERB ajst-24979 199 3   NOUN ajst-24979 199 4   NOUN ajst-24979 199 5   NOUN ajst-24979 199 6   PROPN ajst-24979 199 7   NOUN ajst-24979 199 8   NOUN ajst-24979 199 9   NOUN ajst-24979 199 10   PROPN ajst-24979 199 11   PROPN ajst-24979 199 12   NUM ajst-24979 199 13   ADV ajst-24979 199 14   NOUN ajst-24979 199 15   NOUN ajst-24979 199 16   X ajst-24979 199 17   PUNCT ajst-24979 200 1 cording cord VERB ajst-24979 200 2 to to ADP ajst-24979 200 3 the the DET ajst-24979 200 4 definition definition NOUN ajst-24979 200 5 2.3 2.3 NUM ajst-24979 200 6 and and CCONJ ajst-24979 200 7 assumptions assumption VERB ajst-24979 200 8 h(1)-h h(1)-h NUM ajst-24979 200 9 ( ( PUNCT ajst-24979 200 10 3 3 NUM ajst-24979 200 11 ) ) PUNCT ajst-24979 200 12 , , PUNCT ajst-24979 200 13 there there PRON ajst-24979 200 14 is be VERB ajst-24979 200 15 1 1 NUM ajst-24979 200 16 2 2 NUM ajst-24979 200 17 1 1 NUM ajst-24979 200 18 0 0 NUM ajst-24979 200 19 1 1 NUM ajst-24979 200 20 10 10 NUM ajst-24979 200 21 1 1 NUM ajst-24979 200 22 1 1 NUM ajst-24979 200 23 1 1 NUM ajst-24979 200 24 10 10 NUM ajst-24979 200 25 0 0 NUM ajst-24979 200 26 1 1 NUM ajst-24979 200 27 2 2 NUM ajst-24979 200 28 2 2 NUM ajst-24979 200 29 10 10 NUM ajst-24979 200 30 1 1 NUM ajst-24979 200 31 0 0 NUM ajst-24979 200 32 1 1 NUM ajst-24979 200 33 0 0 NUM ajst-24979 200 34 ( ( PUNCT ajst-24979 200 35 ( ( PUNCT ajst-24979 200 36 , , PUNCT ajst-24979 200 37 ) ) PUNCT ajst-24979 200 38 , , PUNCT ajst-24979 200 39 ( ( PUNCT ajst-24979 200 40 , , PUNCT ajst-24979 200 41 ) ) PUNCT ajst-24979 200 42 ) ) PUNCT ajst-24979 200 43 1 1 NUM ajst-24979 200 44 ( ( PUNCT ajst-24979 200 45 ( ( PUNCT ajst-24979 200 46 0 0 NUM ajst-24979 200 47 , , PUNCT ajst-24979 200 48 ) ) PUNCT ajst-24979 200 49 ( ( PUNCT ajst-24979 200 50 ) ) PUNCT ajst-24979 200 51 ( ( PUNCT ajst-24979 200 52 , , PUNCT ajst-24979 200 53 ) ) PUNCT ajst-24979 200 54 ( ( PUNCT ajst-24979 200 55 ) ) PUNCT ajst-24979 200 56 1 1 NUM ajst-24979 200 57 ( ( PUNCT ajst-24979 200 58 ) ) PUNCT ajst-24979 200 59 ( ( PUNCT ajst-24979 200 60 ) ) PUNCT ajst-24979 200 61 ( ( PUNCT ajst-24979 200 62 , , PUNCT ajst-24979 200 63 ) ) PUNCT ajst-24979 200 64 ( ( PUNCT ajst-24979 200 65 ) ) PUNCT ajst-24979 200 66 1 1 NUM ajst-24979 200 67 ( ( PUNCT ajst-24979 200 68 ) ) PUNCT ajst-24979 200 69 ( ( PUNCT ajst-24979 200 70 ( ( PUNCT ajst-24979 200 71 , , PUNCT ajst-24979 200 72 ) ) PUNCT ajst-24979 200 73 ( ( PUNCT ajst-24979 200 74 ( ( PUNCT ajst-24979 200 75 , , PUNCT ajst-24979 200 76 ) ) PUNCT ajst-24979 200 77 ) ) PUNCT ajst-24979 201 1 ( ( PUNCT ajst-24979 201 2 ) ) PUNCT ajst-24979 201 3 ( ( PUNCT ajst-24979 201 4 , , PUNCT ajst-24979 201 5 ) ) PUNCT ajst-24979 201 6 ( ( PUNCT ajst-24979 201 7 ( ( PUNCT ajst-24979 201 8 , , PUNCT ajst-24979 201 9 ) ) PUNCT ajst-24979 201 10 ) ) PUNCT ajst-24979 201 11 ) ) PUNCT ajst-24979 201 12 , , PUNCT ajst-24979 201 13 ( ( PUNCT ajst-24979 201 14 0 0 NUM ajst-24979 201 15 , , PUNCT ajst-24979 201 16 ) ) PUNCT ajst-24979 201 17 1 1 NUM ajst-24979 201 18 ( ( PUNCT ajst-24979 201 19 ) ) PUNCT ajst-24979 201 20 ( ( PUNCT ajst-24979 201 21 , , PUNCT ajst-24979 201 22 ) ) PUNCT ajst-24979 201 23 ( ( PUNCT ajst-24979 201 24 ) ) PUNCT ajst-24979 201 25 1 1 NUM ajst-24979 201 26 ( ( PUNCT ajst-24979 201 27 ) ) PUNCT ajst-24979 201 28 ( ( PUNCT ajst-24979 201 29 ) ) PUNCT ajst-24979 201 30 x x PUNCT ajst-24979 202 1 x x PUNCT ajst-24979 202 2 x x X ajst-24979 202 3 s s NOUN ajst-24979 202 4 x x X ajst-24979 202 5 x x PUNCT ajst-24979 202 6 d d NOUN ajst-24979 202 7 t t PROPN ajst-24979 202 8 w w NOUN ajst-24979 203 1 x x SYM ajst-24979 203 2 r r NOUN ajst-24979 203 3 t t PROPN ajst-24979 203 4 w w NOUN ajst-24979 203 5 x x PUNCT ajst-24979 203 6 r r NOUN ajst-24979 203 7 d d NOUN ajst-24979 203 8 w w NOUN ajst-24979 203 9 r r NOUN ajst-24979 203 10 x x SYM ajst-24979 203 11 s s NOUN ajst-24979 203 12 g g NOUN ajst-24979 203 13 s s NOUN ajst-24979 203 14 r r NOUN ajst-24979 203 15 d d X ajst-24979 203 16 s s NOUN ajst-24979 203 17 x x X ajst-24979 203 18 s s VERB ajst-24979 203 19 a a DET ajst-24979 203 20 s s NOUN ajst-24979 203 21 w w NOUN ajst-24979 203 22 s s NOUN ajst-24979 203 23 r r NOUN ajst-24979 203 24 d d X ajst-24979 203 25 s s PROPN ajst-24979 203 26 x x X ajst-24979 203 27 s s X ajst-24979 203 28 k k PROPN ajst-24979 203 29 s s X ajst-24979 204 1 f f PROPN ajst-24979 204 2 w w PROPN ajst-24979 204 3 r r PROPN ajst-24979 204 4 d d PROPN ajst-24979 204 5 k k PROPN ajst-24979 204 6 s s X ajst-24979 205 1 f f PROPN ajst-24979 205 2 w w PROPN ajst-24979 205 3 r r NOUN ajst-24979 205 4 d d PROPN ajst-24979 205 5 d d X ajst-24979 205 6 s s PROPN ajst-24979 205 7 w w NOUN ajst-24979 205 8 r r NOUN ajst-24979 205 9 x x SYM ajst-24979 205 10 s s NOUN ajst-24979 206 1 g g NOUN ajst-24979 206 2 s s NOUN ajst-24979 206 3 r r NOUN ajst-24979 206 4 d d X ajst-24979 206 5 s s PROPN ajst-24979 206 6 x x X ajst-24979 206 7 s s PROPN ajst-24979 206 8   NUM ajst-24979 206 9   NUM ajst-24979 206 10   NUM ajst-24979 206 11   NUM ajst-24979 206 12   NUM ajst-24979 206 13   NUM ajst-24979 206 14   NUM ajst-24979 206 15   NOUN ajst-24979 206 16   NOUN ajst-24979 206 17   NOUN ajst-24979 206 18   PROPN ajst-24979 206 19   NOUN ajst-24979 206 20   NOUN ajst-24979 206 21   NOUN ajst-24979 206 22   NUM ajst-24979 206 23   NUM ajst-24979 206 24   PROPN ajst-24979 206 25   PROPN ajst-24979 206 26   PROPN ajst-24979 206 27   PROPN ajst-24979 206 28   PROPN ajst-24979 206 29   NUM ajst-24979 206 30   ADV ajst-24979 206 31   PROPN ajst-24979 206 32   NUM ajst-24979 206 33   PUNCT ajst-24979 206 34   NOUN ajst-24979 206 35   NUM ajst-24979 206 36   PUNCT ajst-24979 206 37   PROPN ajst-24979 206 38   NUM ajst-24979 206 39   ADV ajst-24979 206 40   PUNCT ajst-24979 206 41   PROPN ajst-24979 206 42   NUM ajst-24979 206 43   PUNCT ajst-24979 206 44   NOUN ajst-24979 206 45   VERB ajst-24979 206 46   ADP ajst-24979 206 47   X ajst-24979 206 48   X ajst-24979 206 49   NOUN ajst-24979 206 50   NOUN ajst-24979 206 51   SYM ajst-24979 207 1 2 2 NUM ajst-24979 207 2 1 1 NUM ajst-24979 207 3 1 1 NUM ajst-24979 207 4 1 1 NUM ajst-24979 207 5 20 20 NUM ajst-24979 207 6 0 0 NUM ajst-24979 207 7 1 1 NUM ajst-24979 207 8 2 2 NUM ajst-24979 207 9 2 2 NUM ajst-24979 207 10 20 20 NUM ajst-24979 207 11 1 1 NUM ajst-24979 207 12 10 10 NUM ajst-24979 207 13 1 1 NUM ajst-24979 207 14 20 20 NUM ajst-24979 207 15 1 1 NUM ajst-24979 207 16 1 1 NUM ajst-24979 207 17 1 1 NUM ajst-24979 207 18 10 10 NUM ajst-24979 207 19 0 0 NUM ajst-24979 207 20 1 1 NUM ajst-24979 207 21 20 20 NUM ajst-24979 207 22 ( ( PUNCT ajst-24979 207 23 ) ) PUNCT ajst-24979 207 24 ( ( PUNCT ajst-24979 207 25 , , PUNCT ajst-24979 207 26 ) ) PUNCT ajst-24979 207 27 1 1 NUM ajst-24979 207 28 ( ( PUNCT ajst-24979 207 29 ) ) PUNCT ajst-24979 207 30 ( ( PUNCT ajst-24979 207 31 ( ( PUNCT ajst-24979 207 32 , , PUNCT ajst-24979 207 33 ) ) PUNCT ajst-24979 207 34 ( ( PUNCT ajst-24979 207 35 ( ( PUNCT ajst-24979 207 36 , , PUNCT ajst-24979 207 37 ) ) PUNCT ajst-24979 207 38 ) ) PUNCT ajst-24979 208 1 ( ( PUNCT ajst-24979 208 2 ) ) PUNCT ajst-24979 208 3 ( ( PUNCT ajst-24979 208 4 , , PUNCT ajst-24979 208 5 ) ) PUNCT ajst-24979 208 6 ( ( PUNCT ajst-24979 208 7 ( ( PUNCT ajst-24979 208 8 , , PUNCT ajst-24979 208 9 ) ) PUNCT ajst-24979 208 10 ) ) PUNCT ajst-24979 208 11 ) ) PUNCT ajst-24979 208 12 ) ) PUNCT ajst-24979 209 1 1 1 NUM ajst-24979 209 2 ( ( PUNCT ajst-24979 209 3 ( ( PUNCT ajst-24979 209 4 ) ) PUNCT ajst-24979 209 5 ( ( PUNCT ajst-24979 209 6 ) ) PUNCT ajst-24979 209 7 ( ( PUNCT ajst-24979 209 8 , , PUNCT ajst-24979 209 9 ) ) PUNCT ajst-24979 209 10 , , PUNCT ajst-24979 209 11 ( ( PUNCT ajst-24979 209 12 ) ) PUNCT ajst-24979 209 13 1 1 NUM ajst-24979 209 14 ( ( PUNCT ajst-24979 209 15 ) ) PUNCT ajst-24979 209 16 ( ( PUNCT ajst-24979 209 17 ) ) PUNCT ajst-24979 209 18 ( ( PUNCT ajst-24979 209 19 , , PUNCT ajst-24979 209 20 ) ) PUNCT ajst-24979 209 21 ) ) PUNCT ajst-24979 210 1 ( ( PUNCT ajst-24979 210 2 ) ) PUNCT ajst-24979 210 3 1 1 NUM ajst-24979 210 4 ( ( PUNCT ajst-24979 210 5 ( ( PUNCT ajst-24979 210 6 ) ) PUNCT ajst-24979 210 7 ( ( PUNCT ajst-24979 210 8 ( ( PUNCT ajst-24979 210 9 , , PUNCT ajst-24979 210 10 ) ) PUNCT ajst-24979 210 11 ( ( PUNCT ajst-24979 210 12 ( ( PUNCT ajst-24979 210 13 , , PUNCT ajst-24979 210 14 ) ) PUNCT ajst-24979 210 15 ) ) PUNCT ajst-24979 211 1 ( ( PUNCT ajst-24979 211 2 ) ) PUNCT ajst-24979 211 3 ( ( PUNCT ajst-24979 211 4 , , PUNCT ajst-24979 211 5 ) ) PUNCT ajst-24979 211 6 x x SYM ajst-24979 211 7 s s X ajst-24979 211 8 x x X ajst-24979 211 9 x x SYM ajst-24979 211 10 x x SYM ajst-24979 211 11 s s VERB ajst-24979 211 12 a a DET ajst-24979 211 13 s s NOUN ajst-24979 211 14 w w NOUN ajst-24979 211 15 s s NOUN ajst-24979 211 16 r r NOUN ajst-24979 211 17 d d X ajst-24979 211 18 s s PROPN ajst-24979 211 19 x x X ajst-24979 211 20 s s X ajst-24979 211 21 k k PROPN ajst-24979 211 22 s s X ajst-24979 212 1 f f PROPN ajst-24979 212 2 w w PROPN ajst-24979 212 3 r r PROPN ajst-24979 212 4 d d PROPN ajst-24979 212 5 k k PROPN ajst-24979 212 6 s s X ajst-24979 213 1 f f PROPN ajst-24979 213 2 w w PROPN ajst-24979 213 3 r r NOUN ajst-24979 213 4 d d PROPN ajst-24979 213 5 d d X ajst-24979 213 6 s s PROPN ajst-24979 213 7 d d X ajst-24979 213 8 x x X ajst-24979 213 9 s s AUX ajst-24979 213 10 a a DET ajst-24979 213 11 s s NOUN ajst-24979 213 12 w w NOUN ajst-24979 213 13 s s NOUN ajst-24979 213 14 r r NOUN ajst-24979 213 15 d d NOUN ajst-24979 213 16 s s NOUN ajst-24979 213 17 x x X ajst-24979 213 18 s s VERB ajst-24979 213 19 a a DET ajst-24979 213 20 s s NOUN ajst-24979 213 21 w w NOUN ajst-24979 213 22 s s NOUN ajst-24979 213 23 r r NOUN ajst-24979 213 24 d d PROPN ajst-24979 213 25 s s PROPN ajst-24979 213 26 d d X ajst-24979 213 27 x x X ajst-24979 213 28 s s PROPN ajst-24979 213 29 k k PROPN ajst-24979 213 30 s s X ajst-24979 214 1 f f PROPN ajst-24979 214 2 w w PROPN ajst-24979 214 3 r r PROPN ajst-24979 214 4 d d PROPN ajst-24979 214 5 k k PROPN ajst-24979 214 6 s s PROPN ajst-24979 214 7   NUM ajst-24979 214 8   NUM ajst-24979 214 9   NUM ajst-24979 214 10   NUM ajst-24979 214 11   NOUN ajst-24979 214 12   NOUN ajst-24979 214 13   NOUN ajst-24979 214 14   PROPN ajst-24979 214 15   NOUN ajst-24979 214 16   NOUN ajst-24979 214 17   NOUN ajst-24979 214 18   NUM ajst-24979 214 19   NUM ajst-24979 214 20   NOUN ajst-24979 214 21   NOUN ajst-24979 214 22   NOUN ajst-24979 214 23   PROPN ajst-24979 214 24   PROPN ajst-24979 214 25   PROPN ajst-24979 214 26   PROPN ajst-24979 214 27   PROPN ajst-24979 214 28   PROPN ajst-24979 214 29   CCONJ ajst-24979 214 30   PROPN ajst-24979 214 31   NUM ajst-24979 214 32   ADV ajst-24979 214 33   NUM ajst-24979 214 34   NOUN ajst-24979 214 35   VERB ajst-24979 214 36   NOUN ajst-24979 214 37   NUM ajst-24979 214 38   ADV ajst-24979 214 39   NOUN ajst-24979 214 40   NUM ajst-24979 214 41   VERB ajst-24979 214 42   X ajst-24979 214 43   X ajst-24979 214 44   X ajst-24979 214 45   X ajst-24979 214 46   X ajst-24979 214 47   X ajst-24979 214 48   NOUN ajst-24979 214 49   NOUN ajst-24979 215 1   SYM ajst-24979 215 2 2 2 NUM ajst-24979 216 1 1 1 NUM ajst-24979 216 2 1 1 NUM ajst-24979 216 3 1 1 NUM ajst-24979 216 4 1 1 NUM ajst-24979 216 5 20 20 NUM ajst-24979 216 6 0 0 NUM ajst-24979 216 7 1 1 NUM ajst-24979 216 8 2 2 NUM ajst-24979 216 9 2 2 NUM ajst-24979 216 10 20 20 NUM ajst-24979 216 11 1 1 NUM ajst-24979 216 12 1 1 NUM ajst-24979 216 13 20 20 NUM ajst-24979 216 14 [ [ PUNCT ajst-24979 216 15 0 0 NUM ajst-24979 216 16 , , PUNCT ajst-24979 216 17 1 1 NUM ajst-24979 216 18 ] ] SYM ajst-24979 216 19 1 1 NUM ajst-24979 216 20 1 1 NUM ajst-24979 216 21 1 1 NUM ajst-24979 216 22 10 10 NUM ajst-24979 216 23 0 0 NUM ajst-24979 216 24 1 1 NUM ajst-24979 216 25 1 1 NUM ajst-24979 216 26 20 20 NUM ajst-24979 216 27 ( ( PUNCT ajst-24979 216 28 ( ( PUNCT ajst-24979 216 29 , , PUNCT ajst-24979 216 30 ) ) PUNCT ajst-24979 216 31 ) ) PUNCT ajst-24979 216 32 ) ) PUNCT ajst-24979 217 1 , , PUNCT ajst-24979 217 2 1 1 X ajst-24979 217 3 ( ( PUNCT ajst-24979 217 4 ) ) PUNCT ajst-24979 217 5 ( ( PUNCT ajst-24979 217 6 ( ( PUNCT ajst-24979 217 7 , , PUNCT ajst-24979 217 8 ) ) PUNCT ajst-24979 217 9 ( ( PUNCT ajst-24979 217 10 ( ( PUNCT ajst-24979 217 11 , , PUNCT ajst-24979 217 12 ) ) PUNCT ajst-24979 217 13 ) ) PUNCT ajst-24979 217 14 ( ( PUNCT ajst-24979 217 15 ) ) PUNCT ajst-24979 217 16 ( ( PUNCT ajst-24979 217 17 , , PUNCT ajst-24979 217 18 ) ) PUNCT ajst-24979 217 19 ( ( PUNCT ajst-24979 217 20 ( ( PUNCT ajst-24979 217 21 , , PUNCT ajst-24979 217 22 ) ) PUNCT ajst-24979 217 23 ) ) PUNCT ajst-24979 217 24 ) ) PUNCT ajst-24979 217 25 ) ) PUNCT ajst-24979 217 26 1 1 NUM ajst-24979 217 27 ( ( PUNCT ajst-24979 217 28 ) ) PUNCT ajst-24979 217 29 s s VERB ajst-24979 217 30 u u NOUN ajst-24979 217 31 p p X ajst-24979 217 32 ( ( PUNCT ajst-24979 217 33 ) ) PUNCT ajst-24979 217 34 ( ( PUNCT ajst-24979 217 35 ( ( PUNCT ajst-24979 217 36 , , PUNCT ajst-24979 217 37 ) ) PUNCT ajst-24979 217 38 , , PUNCT ajst-24979 217 39 ( ( PUNCT ajst-24979 217 40 , , PUNCT ajst-24979 217 41 ) ) PUNCT ajst-24979 217 42 ) ) PUNCT ajst-24979 218 1 ( ( PUNCT ajst-24979 218 2 ) ) PUNCT ajst-24979 218 3 1 1 NUM ajst-24979 218 4 ( ( PUNCT ajst-24979 218 5 ) ) PUNCT ajst-24979 218 6 ( ( PUNCT ajst-24979 218 7 ( ( PUNCT ajst-24979 218 8 , , PUNCT ajst-24979 218 9 ) ) PUNCT ajst-24979 218 10 ( ( PUNCT ajst-24979 218 11 ( ( PUNCT ajst-24979 218 12 , , PUNCT ajst-24979 218 13 ) ) PUNCT ajst-24979 218 14 ) ) PUNCT ajst-24979 218 15 , , PUNCT ajst-24979 218 16 ( ( PUNCT ajst-24979 218 17 ) ) PUNCT ajst-24979 218 18 ( ( PUNCT ajst-24979 218 19 , , PUNCT ajst-24979 218 20 ) ) PUNCT ajst-24979 218 21 ( ( PUNCT ajst-24979 218 22 ( ( PUNCT ajst-24979 218 23 , , PUNCT ajst-24979 218 24 ) ) PUNCT ajst-24979 218 25 ) ) PUNCT ajst-24979 219 1 x x PUNCT ajst-24979 219 2 s s X ajst-24979 219 3 x x X ajst-24979 219 4 s s X ajst-24979 219 5 x x X ajst-24979 219 6 s s X ajst-24979 219 7 s s X ajst-24979 219 8 f f NOUN ajst-24979 219 9 w w PROPN ajst-24979 219 10 r r NOUN ajst-24979 219 11 d d PROPN ajst-24979 219 12 d d X ajst-24979 219 13 s s X ajst-24979 219 14 x x X ajst-24979 219 15 s s X ajst-24979 219 16 k k PROPN ajst-24979 219 17 s s X ajst-24979 219 18 f f PROPN ajst-24979 219 19 w w PROPN ajst-24979 219 20 r r PROPN ajst-24979 220 1 d d PROPN ajst-24979 220 2 k k PROPN ajst-24979 220 3 s s X ajst-24979 221 1 f f PROPN ajst-24979 221 2 w w PROPN ajst-24979 221 3 r r NOUN ajst-24979 221 4 d d PROPN ajst-24979 221 5 d d X ajst-24979 221 6 s s X ajst-24979 221 7 x x X ajst-24979 221 8 s s VERB ajst-24979 221 9 a a PRON ajst-24979 221 10 s s X ajst-24979 221 11 d d X ajst-24979 221 12 w w PROPN ajst-24979 221 13 s s PROPN ajst-24979 221 14 r r NOUN ajst-24979 221 15 w w PROPN ajst-24979 221 16 s s NOUN ajst-24979 221 17 r r NOUN ajst-24979 221 18 d d NOUN ajst-24979 221 19 s s PROPN ajst-24979 221 20 x x X ajst-24979 221 21 s s PROPN ajst-24979 221 22 d d X ajst-24979 221 23 k k PROPN ajst-24979 221 24 s s PROPN ajst-24979 222 1 f f PROPN ajst-24979 222 2 w w PROPN ajst-24979 222 3 r r PROPN ajst-24979 222 4 d d PROPN ajst-24979 222 5 k k PROPN ajst-24979 222 6 s s PROPN ajst-24979 222 7 f f PROPN ajst-24979 222 8 w w PROPN ajst-24979 222 9 r r NOUN ajst-24979 222 10   NUM ajst-24979 222 11   NUM ajst-24979 222 12   NUM ajst-24979 222 13   NOUN ajst-24979 222 14   NOUN ajst-24979 222 15   NOUN ajst-24979 222 16   NOUN ajst-24979 222 17   NOUN ajst-24979 222 18   PROPN ajst-24979 222 19   NOUN ajst-24979 222 20   NOUN ajst-24979 222 21   NOUN ajst-24979 222 22   PROPN ajst-24979 222 23   NOUN ajst-24979 222 24   NOUN ajst-24979 222 25   NOUN ajst-24979 222 26   PROPN ajst-24979 222 27   PROPN ajst-24979 222 28   PROPN ajst-24979 222 29   PROPN ajst-24979 222 30   PROPN ajst-24979 222 31   PROPN ajst-24979 222 32   PROPN ajst-24979 222 33   PROPN ajst-24979 222 34   NUM ajst-24979 222 35   ADV ajst-24979 222 36   NUM ajst-24979 222 37   NOUN ajst-24979 222 38   NUM ajst-24979 222 39   ADV ajst-24979 222 40   NOUN ajst-24979 222 41   VERB ajst-24979 222 42   ADP ajst-24979 222 43   X ajst-24979 222 44   X ajst-24979 223 1   X ajst-24979 223 2   NOUN ajst-24979 224 1   NOUN ajst-24979 225 1   SYM ajst-24979 225 2 11 11 NUM ajst-24979 225 3 2 2 NUM ajst-24979 225 4 2 2 NUM ajst-24979 225 5 10 10 NUM ajst-24979 225 6 0 0 NUM ajst-24979 225 7 1 1 NUM ajst-24979 225 8 2 2 NUM ajst-24979 225 9 2 2 NUM ajst-24979 225 10 20 20 NUM ajst-24979 225 11 ) ) PUNCT ajst-24979 225 12 1 1 NUM ajst-24979 225 13 ( ( PUNCT ajst-24979 225 14 ) ) PUNCT ajst-24979 225 15 ( ( PUNCT ajst-24979 225 16 ( ( PUNCT ajst-24979 225 17 , , PUNCT ajst-24979 225 18 ) ) PUNCT ajst-24979 225 19 ( ( PUNCT ajst-24979 225 20 ( ( PUNCT ajst-24979 225 21 , , PUNCT ajst-24979 225 22 ) ) PUNCT ajst-24979 225 23 ) ) PUNCT ajst-24979 225 24 , , PUNCT ajst-24979 225 25 ( ( PUNCT ajst-24979 225 26 ) ) PUNCT ajst-24979 225 27 ( ( PUNCT ajst-24979 225 28 , , PUNCT ajst-24979 225 29 ) ) PUNCT ajst-24979 225 30 ( ( PUNCT ajst-24979 225 31 ( ( PUNCT ajst-24979 225 32 , , PUNCT ajst-24979 225 33 ) ) PUNCT ajst-24979 225 34 ) ) PUNCT ajst-24979 225 35 ) ) PUNCT ajst-24979 226 1 x x PUNCT ajst-24979 227 1 d d PUNCT ajst-24979 227 2 d d X ajst-24979 227 3 s s X ajst-24979 227 4 x x X ajst-24979 227 5 s s PROPN ajst-24979 227 6 d d X ajst-24979 227 7 k k PROPN ajst-24979 227 8 s s PROPN ajst-24979 227 9 f f PROPN ajst-24979 227 10 w w PROPN ajst-24979 227 11 r r PROPN ajst-24979 228 1 d d PROPN ajst-24979 228 2 k k PROPN ajst-24979 228 3 s s X ajst-24979 229 1 f f PROPN ajst-24979 229 2 w w PROPN ajst-24979 229 3 r r NOUN ajst-24979 229 4 d d PROPN ajst-24979 229 5 d d PROPN ajst-24979 229 6 s s PROPN ajst-24979 229 7   NUM ajst-24979 229 8   NOUN ajst-24979 229 9   NOUN ajst-24979 229 10   NOUN ajst-24979 229 11   NOUN ajst-24979 229 12   PROPN ajst-24979 229 13   NOUN ajst-24979 229 14   NOUN ajst-24979 229 15   NOUN ajst-24979 229 16   PUNCT ajst-24979 229 17   VERB ajst-24979 229 18   NOUN ajst-24979 229 19   NOUN ajst-24979 229 20   PUNCT ajst-24979 230 1 175 175 NUM ajst-24979 230 2 1 1 NUM ajst-24979 230 3 1 1 NUM ajst-24979 230 4 20 20 NUM ajst-24979 230 5 1 1 NUM ajst-24979 230 6 1 1 NUM ajst-24979 230 7 1 1 NUM ajst-24979 230 8 10 10 NUM ajst-24979 230 9 0 0 NUM ajst-24979 230 10 1 1 NUM ajst-24979 230 11 1 1 NUM ajst-24979 230 12 20 20 NUM ajst-24979 230 13 11 11 NUM ajst-24979 230 14 2 2 NUM ajst-24979 230 15 2 2 NUM ajst-24979 230 16 10 10 NUM ajst-24979 230 17 0 0 NUM ajst-24979 230 18 1 1 NUM ajst-24979 230 19 2 2 NUM ajst-24979 230 20 2 2 NUM ajst-24979 230 21 20 20 NUM ajst-24979 230 22 1 1 NUM ajst-24979 230 23 2 2 NUM ajst-24979 230 24 3 3 NUM ajst-24979 230 25 ( ( PUNCT ajst-24979 230 26 ) ) PUNCT ajst-24979 230 27 ( ( PUNCT ajst-24979 230 28 ( ( PUNCT ajst-24979 230 29 , , PUNCT ajst-24979 230 30 ) ) PUNCT ajst-24979 230 31 , , PUNCT ajst-24979 230 32 ( ( PUNCT ajst-24979 230 33 , , PUNCT ajst-24979 230 34 ) ) PUNCT ajst-24979 230 35 ) ) PUNCT ajst-24979 231 1 ( ( PUNCT ajst-24979 231 2 ) ) PUNCT ajst-24979 231 3 1 1 NUM ajst-24979 231 4 ( ( PUNCT ajst-24979 231 5 ) ) PUNCT ajst-24979 231 6 ( ( PUNCT ajst-24979 231 7 ( ( PUNCT ajst-24979 231 8 , , PUNCT ajst-24979 231 9 ) ) PUNCT ajst-24979 231 10 ( ( PUNCT ajst-24979 231 11 ( ( PUNCT ajst-24979 231 12 , , PUNCT ajst-24979 231 13 ) ) PUNCT ajst-24979 231 14 ) ) PUNCT ajst-24979 231 15 ) ) PUNCT ajst-24979 231 16 , , PUNCT ajst-24979 231 17 ( ( PUNCT ajst-24979 231 18 ) ) PUNCT ajst-24979 231 19 ( ( PUNCT ajst-24979 231 20 , , PUNCT ajst-24979 231 21 ) ) PUNCT ajst-24979 231 22 ( ( PUNCT ajst-24979 231 23 ( ( PUNCT ajst-24979 231 24 , , PUNCT ajst-24979 231 25 ) ) PUNCT ajst-24979 231 26 ) ) PUNCT ajst-24979 231 27 ) ) PUNCT ajst-24979 231 28 1 1 NUM ajst-24979 231 29 ( ( PUNCT ajst-24979 231 30 ) ) PUNCT ajst-24979 231 31 ( ( PUNCT ajst-24979 231 32 ( ( PUNCT ajst-24979 231 33 , , PUNCT ajst-24979 231 34 ) ) PUNCT ajst-24979 231 35 ( ( PUNCT ajst-24979 231 36 ( ( PUNCT ajst-24979 231 37 , , PUNCT ajst-24979 231 38 ) ) PUNCT ajst-24979 231 39 ) ) PUNCT ajst-24979 231 40 , , PUNCT ajst-24979 231 41 ( ( PUNCT ajst-24979 231 42 ) ) PUNCT ajst-24979 231 43 ( ( PUNCT ajst-24979 231 44 , , PUNCT ajst-24979 231 45 ) ) PUNCT ajst-24979 231 46 ( ( PUNCT ajst-24979 231 47 ( ( PUNCT ajst-24979 231 48 , , PUNCT ajst-24979 231 49 ) ) PUNCT ajst-24979 231 50 ) ) PUNCT ajst-24979 231 51 ) ) PUNCT ajst-24979 231 52 : : PUNCT ajst-24979 231 53 . . PUNCT ajst-24979 232 1 x x PUNCT ajst-24979 233 1 x x X ajst-24979 233 2 s s X ajst-24979 233 3 s s X ajst-24979 233 4 x x X ajst-24979 233 5 x x X ajst-24979 233 6 s s PROPN ajst-24979 233 7 d d X ajst-24979 233 8 w w PROPN ajst-24979 233 9 s s PROPN ajst-24979 233 10 r r NOUN ajst-24979 233 11 w w NOUN ajst-24979 233 12 r r NOUN ajst-24979 233 13 ds ds ADJ ajst-24979 233 14 x x SYM ajst-24979 233 15 s s PROPN ajst-24979 233 16 d d X ajst-24979 233 17 k k PROPN ajst-24979 233 18 s s PROPN ajst-24979 234 1 f f PROPN ajst-24979 234 2 w w PROPN ajst-24979 234 3 r r NOUN ajst-24979 234 4 d d PROPN ajst-24979 234 5 ds ds PROPN ajst-24979 234 6 k k PROPN ajst-24979 234 7 s s PROPN ajst-24979 234 8 f f PROPN ajst-24979 235 1 w w PROPN ajst-24979 235 2 r r NOUN ajst-24979 235 3 d d NOUN ajst-24979 235 4 ds ds NOUN ajst-24979 235 5 x x SYM ajst-24979 235 6 s s PROPN ajst-24979 235 7 d d X ajst-24979 235 8 k k PROPN ajst-24979 235 9 s s PROPN ajst-24979 236 1 f f PROPN ajst-24979 236 2 w w PROPN ajst-24979 236 3 r r PROPN ajst-24979 236 4 d d PROPN ajst-24979 236 5 k k PROPN ajst-24979 236 6 s s X ajst-24979 237 1 f f PROPN ajst-24979 237 2 w w PROPN ajst-24979 237 3 r r NOUN ajst-24979 237 4 d d NOUN ajst-24979 237 5 ds ds PROPN ajst-24979 237 6   NUM ajst-24979 237 7   NUM ajst-24979 237 8   NUM ajst-24979 237 9   NOUN ajst-24979 238 1   PROPN ajst-24979 238 2   PROPN ajst-24979 238 3   PROPN ajst-24979 238 4   NOUN ajst-24979 238 5   NOUN ajst-24979 238 6   PROPN ajst-24979 238 7   NOUN ajst-24979 238 8   NOUN ajst-24979 238 9   NOUN ajst-24979 238 10   NOUN ajst-24979 238 11   NOUN ajst-24979 238 12   NOUN ajst-24979 238 13   PROPN ajst-24979 238 14   NOUN ajst-24979 238 15   NOUN ajst-24979 238 16   NOUN ajst-24979 238 17   NOUN ajst-24979 238 18   NOUN ajst-24979 238 19   NOUN ajst-24979 238 20   PROPN ajst-24979 238 21   PROPN ajst-24979 238 22   NOUN ajst-24979 238 23   NOUN ajst-24979 238 24   NOUN ajst-24979 238 25   NUM ajst-24979 238 26   ADV ajst-24979 238 27   NOUN ajst-24979 238 28   NUM ajst-24979 238 29   PUNCT ajst-24979 238 30   NOUN ajst-24979 238 31   VERB ajst-24979 238 32   PROPN ajst-24979 238 33   ADJ ajst-24979 238 34   PUNCT ajst-24979 238 35   PUNCT ajst-24979 238 36   X ajst-24979 238 37   X ajst-24979 238 38   X ajst-24979 238 39   X ajst-24979 238 40   PUNCT ajst-24979 238 41   X ajst-24979 239 1 where where SCONJ ajst-24979 239 2 1 1 NUM ajst-24979 239 3 1 1 NUM ajst-24979 239 4 1 1 NUM ajst-24979 239 5 2 2 NUM ajst-24979 239 6 1 1 NUM ajst-24979 239 7 20 20 NUM ajst-24979 239 8 ( ( PUNCT ajst-24979 239 9 ) ) PUNCT ajst-24979 239 10 ( ( PUNCT ajst-24979 239 11 ( ( PUNCT ajst-24979 239 12 , , PUNCT ajst-24979 239 13 ) ) PUNCT ajst-24979 239 14 , , PUNCT ajst-24979 239 15 ( ( PUNCT ajst-24979 239 16 , , PUNCT ajst-24979 239 17 ) ) PUNCT ajst-24979 239 18 ) ) PUNCT ajst-24979 240 1 ( ( PUNCT ajst-24979 240 2 ( ( PUNCT ajst-24979 240 3 , , PUNCT ajst-24979 240 4 ) ) PUNCT ajst-24979 240 5 , , PUNCT ajst-24979 240 6 ( ( PUNCT ajst-24979 240 7 , , PUNCT ajst-24979 240 8 ) ) PUNCT ajst-24979 240 9 . . PUNCT ajst-24979 241 1 ( ( PUNCT ajst-24979 241 2 ) ) PUNCT ajst-24979 241 3 ( ( PUNCT ajst-24979 241 4 1 1 X ajst-24979 241 5 ) ) PUNCT ajst-24979 241 6 x x X ajst-24979 242 1 x x SYM ajst-24979 242 2 s s PROPN ajst-24979 242 3 d d X ajst-24979 242 4 w w PROPN ajst-24979 242 5 s s PROPN ajst-24979 242 6 r r NOUN ajst-24979 242 7 w w NOUN ajst-24979 242 8 r r NOUN ajst-24979 242 9 ds ds NOUN ajst-24979 242 10 d d X ajst-24979 242 11 w w PROPN ajst-24979 242 12 s s PROPN ajst-24979 242 13 r r NOUN ajst-24979 242 14 w w PROPN ajst-24979 242 15 r r NOUN ajst-24979 242 16   PUNCT ajst-24979 242 17   NOUN ajst-24979 242 18   NOUN ajst-24979 242 19   NUM ajst-24979 242 20   NUM ajst-24979 242 21   PROPN ajst-24979 242 22   PROPN ajst-24979 242 23   NOUN ajst-24979 242 24   VERB ajst-24979 242 25   VERB ajst-24979 242 26   NUM ajst-24979 242 27 1 1 NUM ajst-24979 242 28 2 2 NUM ajst-24979 242 29 1 1 NUM ajst-24979 242 30 1 1 NUM ajst-24979 242 31 1 1 NUM ajst-24979 242 32 1 1 NUM ajst-24979 242 33 20 20 NUM ajst-24979 242 34 0 0 NUM ajst-24979 242 35 1 1 NUM ajst-24979 242 36 1 1 NUM ajst-24979 242 37 1 1 NUM ajst-24979 242 38 2 2 NUM ajst-24979 242 39 11 11 NUM ajst-24979 242 40 3 3 NUM ajst-24979 242 41 2 2 NUM ajst-24979 242 42 2 2 NUM ajst-24979 242 43 1 1 NUM ajst-24979 242 44 2 2 NUM ajst-24979 242 45 20 20 NUM ajst-24979 242 46 0 0 NUM ajst-24979 242 47 2 2 NUM ajst-24979 242 48 2 2 NUM ajst-24979 242 49 1 1 NUM ajst-24979 242 50 2 2 NUM ajst-24979 242 51 1 1 NUM ajst-24979 242 52 ( ( PUNCT ajst-24979 242 53 ) ) PUNCT ajst-24979 242 54 ( ( PUNCT ajst-24979 242 55 , , PUNCT ajst-24979 242 56 ) ) PUNCT ajst-24979 242 57 ( ( PUNCT ajst-24979 242 58 ( ( PUNCT ajst-24979 242 59 ( ( PUNCT ajst-24979 242 60 , , PUNCT ajst-24979 242 61 ) ) PUNCT ajst-24979 242 62 ) ) PUNCT ajst-24979 242 63 , , PUNCT ajst-24979 242 64 ( ( PUNCT ajst-24979 242 65 ( ( PUNCT ajst-24979 242 66 , , PUNCT ajst-24979 242 67 ) ) PUNCT ajst-24979 242 68 ) ) PUNCT ajst-24979 242 69 ) ) PUNCT ajst-24979 243 1 ( ( PUNCT ajst-24979 243 2 ) ) PUNCT ajst-24979 243 3 ( ( PUNCT ajst-24979 243 4 ( ( PUNCT ajst-24979 243 5 , , PUNCT ajst-24979 243 6 ) ) PUNCT ajst-24979 243 7 , , PUNCT ajst-24979 243 8 ( ( PUNCT ajst-24979 243 9 , , PUNCT ajst-24979 243 10 ) ) PUNCT ajst-24979 243 11 . . PUNCT ajst-24979 244 1 ( ( PUNCT ajst-24979 244 2 1 1 X ajst-24979 244 3 ) ) PUNCT ajst-24979 244 4 1 1 NUM ajst-24979 244 5 ( ( PUNCT ajst-24979 244 6 ) ) PUNCT ajst-24979 244 7 ( ( PUNCT ajst-24979 244 8 , , PUNCT ajst-24979 244 9 ) ) PUNCT ajst-24979 244 10 ( ( PUNCT ajst-24979 244 11 ( ( PUNCT ajst-24979 244 12 ( ( PUNCT ajst-24979 244 13 , , PUNCT ajst-24979 244 14 ) ) PUNCT ajst-24979 244 15 ) ) PUNCT ajst-24979 244 16 , , PUNCT ajst-24979 244 17 ( ( PUNCT ajst-24979 244 18 ( ( PUNCT ajst-24979 244 19 , , PUNCT ajst-24979 244 20 ) ) PUNCT ajst-24979 244 21 ) ) PUNCT ajst-24979 244 22 ) ) PUNCT ajst-24979 245 1 ( ( PUNCT ajst-24979 245 2 ) ) PUNCT ajst-24979 245 3 ( ( PUNCT ajst-24979 245 4 ( ( PUNCT ajst-24979 245 5 , , PUNCT ajst-24979 245 6 ) ) PUNCT ajst-24979 245 7 , , PUNCT ajst-24979 245 8 ( ( PUNCT ajst-24979 245 9 , , PUNCT ajst-24979 245 10 ) ) PUNCT ajst-24979 245 11 . . PUNCT ajst-24979 246 1 ( ( PUNCT ajst-24979 246 2 1 1 X ajst-24979 246 3 ) ) PUNCT ajst-24979 246 4 x x SYM ajst-24979 246 5 s s NOUN ajst-24979 246 6 x x PUNCT ajst-24979 246 7 x x X ajst-24979 246 8 s s PROPN ajst-24979 246 9 k k X ajst-24979 246 10 s s PROPN ajst-24979 246 11 d d X ajst-24979 246 12 d d X ajst-24979 246 13 f f PROPN ajst-24979 246 14 w w PROPN ajst-24979 246 15 r r NOUN ajst-24979 246 16 f f PROPN ajst-24979 246 17 w w NOUN ajst-24979 246 18 r r NOUN ajst-24979 246 19 ds ds PROPN ajst-24979 246 20 pq pq NOUN ajst-24979 246 21 d d PROPN ajst-24979 246 22 w w PROPN ajst-24979 246 23 s s NOUN ajst-24979 246 24 r r NOUN ajst-24979 246 25 w w NOUN ajst-24979 246 26 r r NOUN ajst-24979 246 27 x x SYM ajst-24979 246 28 s s X ajst-24979 246 29 k k PROPN ajst-24979 246 30 s s PROPN ajst-24979 246 31 d d X ajst-24979 246 32 d d X ajst-24979 246 33 f f PROPN ajst-24979 246 34 w w PROPN ajst-24979 246 35 r r NOUN ajst-24979 246 36 f f PROPN ajst-24979 246 37 w w NOUN ajst-24979 246 38 r r NOUN ajst-24979 246 39 ds ds NOUN ajst-24979 246 40 p p NOUN ajst-24979 246 41 q q PROPN ajst-24979 246 42 d d X ajst-24979 246 43 w w PROPN ajst-24979 246 44 s s NOUN ajst-24979 246 45 r r NOUN ajst-24979 246 46 w w NOUN ajst-24979 246 47 r r NOUN ajst-24979 246 48   NUM ajst-24979 246 49   NUM ajst-24979 246 50   NOUN ajst-24979 246 51   NOUN ajst-24979 246 52   NOUN ajst-24979 246 53   NOUN ajst-24979 246 54   NOUN ajst-24979 246 55   PROPN ajst-24979 246 56   PROPN ajst-24979 246 57   NUM ajst-24979 246 58   NOUN ajst-24979 246 59   NOUN ajst-24979 246 60   NOUN ajst-24979 246 61   NOUN ajst-24979 246 62   NOUN ajst-24979 246 63   PROPN ajst-24979 246 64   PROPN ajst-24979 246 65   NUM ajst-24979 246 66   PROPN ajst-24979 246 67   PROPN ajst-24979 246 68   NOUN ajst-24979 246 69   NOUN ajst-24979 246 70   VERB ajst-24979 246 71   NOUN ajst-24979 246 72   NUM ajst-24979 246 73   ADJ ajst-24979 246 74   NUM ajst-24979 246 75   NOUN ajst-24979 246 76   VERB ajst-24979 246 77   NOUN ajst-24979 246 78   VERB ajst-24979 246 79   VERB ajst-24979 246 80   PUNCT ajst-24979 246 81   X ajst-24979 246 82   PUNCT ajst-24979 246 83   PUNCT ajst-24979 246 84 substitute substitute NOUN ajst-24979 246 85 1 1 NUM ajst-24979 246 86 , , PUNCT ajst-24979 246 87 2 2 NUM ajst-24979 246 88 and and CCONJ ajst-24979 246 89 3 3 NUM ajst-24979 246 90 for for ADP ajst-24979 246 91 it it PRON ajst-24979 246 92 1 1 NUM ajst-24979 246 93 2 2 NUM ajst-24979 246 94 1 1 NUM ajst-24979 246 95 1 1 NUM ajst-24979 246 96 2 2 NUM ajst-24979 246 97 2 2 NUM ajst-24979 246 98 1 1 NUM ajst-24979 246 99 2 2 NUM ajst-24979 246 100 ( ( PUNCT ajst-24979 246 101 ( ( PUNCT ajst-24979 246 102 , , PUNCT ajst-24979 246 103 ) ) PUNCT ajst-24979 246 104 , , PUNCT ajst-24979 246 105 ( ( PUNCT ajst-24979 246 106 , , PUNCT ajst-24979 246 107 ) ) PUNCT ajst-24979 246 108 ) ) PUNCT ajst-24979 247 1 ( ( PUNCT ajst-24979 247 2 ( ( PUNCT ajst-24979 247 3 , , PUNCT ajst-24979 247 4 ) ) PUNCT ajst-24979 247 5 , , PUNCT ajst-24979 247 6 ( ( PUNCT ajst-24979 247 7 , , PUNCT ajst-24979 247 8 ) ) PUNCT ajst-24979 247 9 , , PUNCT ajst-24979 247 10 ( ( PUNCT ajst-24979 247 11 1 1 X ajst-24979 247 12 ) ) PUNCT ajst-24979 247 13 d d NOUN ajst-24979 247 14 tw tw NOUN ajst-24979 247 15 x x SYM ajst-24979 247 16 r r NOUN ajst-24979 247 17 tw tw X ajst-24979 247 18 x x SYM ajst-24979 247 19 r r NOUN ajst-24979 247 20 l l NOUN ajst-24979 247 21 m m VERB ajst-24979 247 22 l l NOUN ajst-24979 247 23 m m VERB ajst-24979 247 24 d d X ajst-24979 247 25 w w PROPN ajst-24979 247 26 s s PROPN ajst-24979 247 27 r r NOUN ajst-24979 247 28 w w NOUN ajst-24979 247 29 r r NOUN ajst-24979 247 30   NOUN ajst-24979 247 31   PROPN ajst-24979 247 32   PROPN ajst-24979 247 33   ADV ajst-24979 247 34   PUNCT ajst-24979 247 35   PROPN ajst-24979 247 36   VERB ajst-24979 247 37   VERB ajst-24979 247 38 the the DET ajst-24979 247 39 above above ADJ ajst-24979 247 40 equation equation NOUN ajst-24979 247 41 shows show VERB ajst-24979 247 42 that that SCONJ ajst-24979 247 43 t t PROPN ajst-24979 247 44 is be AUX ajst-24979 247 45 a a DET ajst-24979 247 46 compressive compressive ADJ ajst-24979 247 47 map map NOUN ajst-24979 247 48 , , PUNCT ajst-24979 247 49 and and CCONJ ajst-24979 247 50 the the DET ajst-24979 247 51 equation equation NOUN ajst-24979 247 52 has have VERB ajst-24979 247 53 a a DET ajst-24979 247 54 unique unique ADJ ajst-24979 247 55 solution solution NOUN ajst-24979 247 56 by by ADP ajst-24979 247 57 banach banach NOUN ajst-24979 247 58 's 's PART ajst-24979 247 59 fixed fix VERB ajst-24979 247 60 point point NOUN ajst-24979 247 61 theorem theorem VERB ajst-24979 247 62 . . PROPN ajst-24979 248 1 5 5 NUM ajst-24979 248 2 . . NOUN ajst-24979 248 3 numerical numerical ADJ ajst-24979 248 4 results result NOUN ajst-24979 248 5 example1 example1 AUX ajst-24979 248 6 consider consider VERB ajst-24979 248 7 the the DET ajst-24979 248 8 application application NOUN ajst-24979 248 9 of of ADP ajst-24979 248 10 ham ham NOUN ajst-24979 248 11 to to PART ajst-24979 248 12 solve solve VERB ajst-24979 248 13 the the DET ajst-24979 248 14 following following ADJ ajst-24979 248 15 linear linear ADJ ajst-24979 248 16 fuzzy fuzzy ADJ ajst-24979 248 17 fractional fractional ADJ ajst-24979 248 18 volterra volterra NOUN ajst-24979 248 19 - - PUNCT ajst-24979 248 20 fredholm fredholm NOUN ajst-24979 248 21 integrodifferential integrodifferential ADJ ajst-24979 248 22 equations equation NOUN ajst-24979 248 23 1/2 1/2 NUM ajst-24979 248 24 3 3 NUM ajst-24979 248 25 4 4 NUM ajst-24979 248 26 1/2 1/2 NUM ajst-24979 248 27 12 12 NUM ajst-24979 248 28 3 3 NUM ajst-24979 248 29 0 0 NUM ajst-24979 248 30 0 0 NUM ajst-24979 248 31 1/2 1/2 NUM ajst-24979 248 32 3 3 NUM ajst-24979 248 33 4 4 NUM ajst-24979 248 34 1/2 1/2 NUM ajst-24979 248 35 2 2 NUM ajst-24979 248 36 3 3 NUM ajst-24979 248 37 0 0 NUM ajst-24979 249 1 [ [ PUNCT ajst-24979 249 2 ( ( PUNCT ajst-24979 249 3 , , PUNCT ajst-24979 249 4 ) ) PUNCT ajst-24979 249 5 ] ] PUNCT ajst-24979 249 6 ( ( PUNCT ajst-24979 249 7 , , PUNCT ajst-24979 249 8 ) ) PUNCT ajst-24979 249 9 6 6 NUM ajst-24979 249 10 ( ( PUNCT ajst-24979 249 11 1/ 1/ NUM ajst-24979 249 12 2 2 NUM ajst-24979 249 13 ) ) PUNCT ajst-24979 249 14 72 72 NUM ajst-24979 249 15 3 3 NUM ajst-24979 249 16 ( ( PUNCT ajst-24979 249 17 , , PUNCT ajst-24979 249 18 ) ) PUNCT ajst-24979 249 19 ( ( PUNCT ajst-24979 249 20 1 1 X ajst-24979 249 21 ) ) PUNCT ajst-24979 249 22 ( ( PUNCT ajst-24979 249 23 , , PUNCT ajst-24979 249 24 ) ) PUNCT ajst-24979 249 25 , , PUNCT ajst-24979 249 26 ( ( PUNCT ajst-24979 249 27 0 0 NUM ajst-24979 249 28 , , PUNCT ajst-24979 249 29 ) ) PUNCT ajst-24979 249 30 0 0 NUM ajst-24979 249 31 , , PUNCT ajst-24979 249 32 ( ( PUNCT ajst-24979 249 33 2 2 X ajst-24979 249 34 ) ) PUNCT ajst-24979 249 35 ( ( PUNCT ajst-24979 249 36 2 2 X ajst-24979 249 37 ) ) PUNCT ajst-24979 249 38 [ [ PUNCT ajst-24979 249 39 ( ( PUNCT ajst-24979 249 40 , , PUNCT ajst-24979 249 41 ) ) PUNCT ajst-24979 249 42 ] ] PUNCT ajst-24979 249 43 ( ( PUNCT ajst-24979 249 44 , , PUNCT ajst-24979 249 45 ) ) PUNCT ajst-24979 249 46 6 6 NUM ajst-24979 249 47 ( ( PUNCT ajst-24979 249 48 1/ 1/ NUM ajst-24979 249 49 2 2 NUM ajst-24979 249 50 ) ) PUNCT ajst-24979 249 51 72 72 NUM ajst-24979 249 52 3 3 NUM ajst-24979 249 53 ( ( PUNCT ajst-24979 249 54 , , PUNCT ajst-24979 249 55 ) ) PUNCT ajst-24979 249 56 ( ( PUNCT ajst-24979 249 57 1 1 X ajst-24979 249 58 ) ) PUNCT ajst-24979 249 59 ( ( PUNCT ajst-24979 249 60 , , PUNCT ajst-24979 249 61 ) ) PUNCT ajst-24979 249 62 , , PUNCT ajst-24979 250 1 c c NOUN ajst-24979 250 2 x x PUNCT ajst-24979 251 1 c c NOUN ajst-24979 251 2 rx rx AUX ajst-24979 251 3 rx rx VERB ajst-24979 251 4 x x X ajst-24979 251 5 d d X ajst-24979 251 6 w w NOUN ajst-24979 251 7 x x X ajst-24979 251 8 r r NOUN ajst-24979 251 9 w w NOUN ajst-24979 251 10 x x SYM ajst-24979 251 11 r r NOUN ajst-24979 251 12 x x PUNCT ajst-24979 251 13 tw tw NOUN ajst-24979 251 14 t t NOUN ajst-24979 251 15 r r NOUN ajst-24979 251 16 dt dt X ajst-24979 251 17 x x SYM ajst-24979 252 1 t t PROPN ajst-24979 252 2 w w PROPN ajst-24979 252 3 t t PROPN ajst-24979 252 4 r r NOUN ajst-24979 252 5 dt dt NOUN ajst-24979 252 6 w w NOUN ajst-24979 252 7 r r NOUN ajst-24979 252 8 r r NOUN ajst-24979 252 9 x x PUNCT ajst-24979 252 10 r r NOUN ajst-24979 252 11 x x PUNCT ajst-24979 252 12 x x PUNCT ajst-24979 253 1 d d X ajst-24979 253 2 w w NOUN ajst-24979 253 3 x x X ajst-24979 253 4 r r NOUN ajst-24979 253 5 w w NOUN ajst-24979 253 6 x x SYM ajst-24979 253 7 r r NOUN ajst-24979 253 8 x x PUNCT ajst-24979 253 9 tw tw NOUN ajst-24979 253 10 t t NOUN ajst-24979 253 11 r r NOUN ajst-24979 253 12 dt dt X ajst-24979 253 13 x x SYM ajst-24979 253 14 t t PROPN ajst-24979 253 15 w w PROPN ajst-24979 253 16 t t PROPN ajst-24979 253 17 r r NOUN ajst-24979 253 18 dt dt X ajst-24979 253 19   ADP ajst-24979 254 1   PROPN ajst-24979 254 2   NOUN ajst-24979 254 3   VERB ajst-24979 254 4   PROPN ajst-24979 254 5   NUM ajst-24979 254 6   X ajst-24979 254 7   PUNCT ajst-24979 254 8   PUNCT ajst-24979 254 9   NUM ajst-24979 254 10   NOUN ajst-24979 254 11   NUM ajst-24979 254 12   PROPN ajst-24979 254 13   PROPN ajst-24979 254 14   PROPN ajst-24979 254 15   PROPN ajst-24979 254 16   PROPN ajst-24979 254 17   PROPN ajst-24979 254 18   NUM ajst-24979 254 19   ADV ajst-24979 254 20   PUNCT ajst-24979 254 21   PROPN ajst-24979 254 22   NOUN ajst-24979 254 23   PROPN ajst-24979 254 24 1 1 NUM ajst-24979 254 25 0 0 NUM ajst-24979 254 26 ( ( PUNCT ajst-24979 254 27 0 0 NUM ajst-24979 254 28 , , PUNCT ajst-24979 254 29 ) ) PUNCT ajst-24979 254 30 0 0 PUNCT ajst-24979 254 31 . . PUNCT ajst-24979 255 1 x x PUNCT ajst-24979 256 1 w w NOUN ajst-24979 256 2 r r NOUN ajst-24979 256 3   ADP ajst-24979 256 4   NUM ajst-24979 256 5   NUM ajst-24979 256 6   NUM ajst-24979 256 7   NUM ajst-24979 256 8   NUM ajst-24979 256 9   NUM ajst-24979 256 10   NOUN ajst-24979 256 11   NOUN ajst-24979 256 12   PRON ajst-24979 256 13   INTJ ajst-24979 256 14   NOUN ajst-24979 256 15   NOUN ajst-24979 256 16   NOUN ajst-24979 256 17   X ajst-24979 256 18   ADP ajst-24979 256 19 the the DET ajst-24979 256 20 exact exact ADJ ajst-24979 256 21 solution solution NOUN ajst-24979 256 22 is be AUX ajst-24979 256 23 2 2 NUM ajst-24979 256 24 ( ( PUNCT ajst-24979 256 25 , , PUNCT ajst-24979 256 26 ) ) PUNCT ajst-24979 257 1 [ [ PUNCT ajst-24979 257 2 ( ( PUNCT ajst-24979 257 3 , , PUNCT ajst-24979 257 4 ) ) PUNCT ajst-24979 257 5 , , PUNCT ajst-24979 257 6 ( ( PUNCT ajst-24979 257 7 , , PUNCT ajst-24979 257 8 ) ) PUNCT ajst-24979 257 9 ] ] PUNCT ajst-24979 258 1 [ [ PUNCT ajst-24979 258 2 , , PUNCT ajst-24979 258 3 ] ] X ajst-24979 258 4 , , PUNCT ajst-24979 258 5 [ [ X ajst-24979 258 6 0,1 0,1 NUM ajst-24979 258 7 ] ] SYM ajst-24979 258 8 12 12 NUM ajst-24979 258 9 12 12 NUM ajst-24979 258 10 r r NOUN ajst-24979 258 11 r r NOUN ajst-24979 258 12 w w NOUN ajst-24979 258 13 x x X ajst-24979 258 14 r r NOUN ajst-24979 258 15 w w NOUN ajst-24979 258 16 x x X ajst-24979 258 17 r r NOUN ajst-24979 258 18 w w NOUN ajst-24979 258 19 x x SYM ajst-24979 258 20 r r NOUN ajst-24979 258 21 x x SYM ajst-24979 258 22 x x SYM ajst-24979 258 23 r r NOUN ajst-24979 258 24   NOUN ajst-24979 258 25   NOUN ajst-24979 258 26   PROPN ajst-24979 258 27   NOUN ajst-24979 258 28 it it PRON ajst-24979 258 29 can can AUX ajst-24979 258 30 be be AUX ajst-24979 258 31 written write VERB ajst-24979 258 32 from from ADP ajst-24979 258 33 the the DET ajst-24979 258 34 recursive recursive ADJ ajst-24979 258 35 4 4 NUM ajst-24979 258 36 1 1 NUM ajst-24979 258 37 1 1 NUM ajst-24979 258 38 1/2 1/2 NUM ajst-24979 258 39 3 3 NUM ajst-24979 258 40 12 12 NUM ajst-24979 258 41 3 3 NUM ajst-24979 258 42 1 1 NUM ajst-24979 258 43 10 10 NUM ajst-24979 258 44 0 0 NUM ajst-24979 258 45 4 4 NUM ajst-24979 258 46 1 1 NUM ajst-24979 258 47 1 1 NUM ajst-24979 258 48 1/2 1/2 NUM ajst-24979 258 49 3 3 NUM ajst-24979 258 50 2 2 NUM ajst-24979 258 51 1 1 NUM ajst-24979 258 52 ( ( PUNCT ajst-24979 258 53 , , PUNCT ajst-24979 258 54 ) ) PUNCT ajst-24979 258 55 ( ( PUNCT ajst-24979 258 56 ) ) PUNCT ajst-24979 258 57 ( ( PUNCT ajst-24979 258 58 , , PUNCT ajst-24979 258 59 ) ) PUNCT ajst-24979 258 60 [ [ PUNCT ajst-24979 258 61 ( ( PUNCT ajst-24979 258 62 , , PUNCT ajst-24979 258 63 ) ) PUNCT ajst-24979 258 64 3 3 NUM ajst-24979 258 65 ( ( PUNCT ajst-24979 258 66 1 1 NUM ajst-24979 258 67 ) ) PUNCT ajst-24979 258 68 ( ( PUNCT ajst-24979 258 69 ) ) PUNCT ajst-24979 258 70 6 6 NUM ajst-24979 258 71 ( ( PUNCT ajst-24979 258 72 1/ 1/ NUM ajst-24979 258 73 2 2 NUM ajst-24979 258 74 ) ) PUNCT ajst-24979 258 75 72 72 NUM ajst-24979 258 76 ( ( PUNCT ajst-24979 258 77 , , PUNCT ajst-24979 258 78 ) ) PUNCT ajst-24979 258 79 ( ( PUNCT ajst-24979 258 80 1 1 X ajst-24979 258 81 ) ) PUNCT ajst-24979 258 82 ( ( PUNCT ajst-24979 258 83 , , PUNCT ajst-24979 258 84 ) ) PUNCT ajst-24979 258 85 ] ] PUNCT ajst-24979 258 86 , , PUNCT ajst-24979 258 87 ( ( PUNCT ajst-24979 258 88 , , PUNCT ajst-24979 258 89 ) ) PUNCT ajst-24979 258 90 ( ( PUNCT ajst-24979 258 91 ) ) PUNCT ajst-24979 258 92 ( ( PUNCT ajst-24979 258 93 , , PUNCT ajst-24979 258 94 ) ) PUNCT ajst-24979 258 95 [ [ PUNCT ajst-24979 258 96 ( ( PUNCT ajst-24979 258 97 , , PUNCT ajst-24979 258 98 ) ) PUNCT ajst-24979 258 99 3 3 NUM ajst-24979 258 100 ( ( PUNCT ajst-24979 258 101 2 2 NUM ajst-24979 258 102 ) ) PUNCT ajst-24979 258 103 ( ( PUNCT ajst-24979 258 104 2 2 X ajst-24979 258 105 ) ) PUNCT ajst-24979 258 106 ( ( PUNCT ajst-24979 258 107 1 1 NUM ajst-24979 258 108 ) ) PUNCT ajst-24979 258 109 ( ( PUNCT ajst-24979 258 110 ) ) PUNCT ajst-24979 258 111 6 6 NUM ajst-24979 258 112 ( ( PUNCT ajst-24979 258 113 1/ 1/ NUM ajst-24979 258 114 2 2 NUM ajst-24979 258 115 ) ) PUNCT ajst-24979 258 116 72 72 NUM ajst-24979 258 117 ( ( PUNCT ajst-24979 258 118 , , PUNCT ajst-24979 258 119 ) ) PUNCT ajst-24979 258 120 n n CCONJ ajst-24979 258 121 n n CCONJ ajst-24979 258 122 nn nn NUM ajst-24979 258 123 n n ADV ajst-24979 258 124 x x SYM ajst-24979 258 125 n n CCONJ ajst-24979 258 126 n n CCONJ ajst-24979 258 127 n n CCONJ ajst-24979 258 128 n n CCONJ ajst-24979 258 129 nn nn PROPN ajst-24979 258 130 n n CCONJ ajst-24979 258 131 n n NOUN ajst-24979 258 132 x x SYM ajst-24979 258 133 w w NOUN ajst-24979 258 134 x x SYM ajst-24979 259 1 r r NOUN ajst-24979 259 2 h h NOUN ajst-24979 259 3 w w NOUN ajst-24979 259 4 x x PUNCT ajst-24979 259 5 r r NOUN ajst-24979 259 6 hj hj PROPN ajst-24979 259 7 w w NOUN ajst-24979 259 8 x x NOUN ajst-24979 260 1 r r NOUN ajst-24979 260 2 rx rx VERB ajst-24979 260 3 rx rx NOUN ajst-24979 260 4 x x X ajst-24979 260 5 tw tw ADP ajst-24979 260 6 t t NOUN ajst-24979 260 7 r r NOUN ajst-24979 260 8 dt dt X ajst-24979 261 1 x x SYM ajst-24979 262 1 t t PROPN ajst-24979 262 2 w w PROPN ajst-24979 262 3 t t PROPN ajst-24979 262 4 r r NOUN ajst-24979 262 5 dt dt NOUN ajst-24979 262 6 x x SYM ajst-24979 262 7 w w NOUN ajst-24979 262 8 x x SYM ajst-24979 263 1 r r NOUN ajst-24979 263 2 h h NOUN ajst-24979 263 3 w w NOUN ajst-24979 263 4 x x PUNCT ajst-24979 263 5 r r NOUN ajst-24979 263 6 hj hj PROPN ajst-24979 263 7 w w NOUN ajst-24979 263 8 x x SYM ajst-24979 264 1 r r NOUN ajst-24979 264 2 r r NOUN ajst-24979 264 3 x x PUNCT ajst-24979 264 4 r r NOUN ajst-24979 264 5 x x PUNCT ajst-24979 264 6 x x NOUN ajst-24979 264 7 tw tw ADP ajst-24979 264 8 t t NOUN ajst-24979 264 9 r r NOUN ajst-24979 264 10   NUM ajst-24979 264 11   NUM ajst-24979 264 12   NOUN ajst-24979 264 13   VERB ajst-24979 264 14   NOUN ajst-24979 264 15   VERB ajst-24979 264 16   VERB ajst-24979 264 17   PROPN ajst-24979 264 18   PROPN ajst-24979 264 19   PROPN ajst-24979 264 20   PROPN ajst-24979 264 21   PROPN ajst-24979 264 22   PROPN ajst-24979 264 23   NUM ajst-24979 264 24   PUNCT ajst-24979 264 25   PROPN ajst-24979 264 26   PROPN ajst-24979 264 27   PUNCT ajst-24979 264 28   PROPN ajst-24979 264 29   PROPN ajst-24979 264 30   NUM ajst-24979 264 31   ADV ajst-24979 264 32   VERB ajst-24979 264 33   PROPN ajst-24979 264 34   PROPN ajst-24979 264 35   PUNCT ajst-24979 264 36   PROPN ajst-24979 264 37   PROPN ajst-24979 264 38   PROPN ajst-24979 264 39   PROPN ajst-24979 264 40   PUNCT ajst-24979 264 41   PROPN ajst-24979 264 42   PROPN ajst-24979 264 43   NUM ajst-24979 264 44   VERB ajst-24979 264 45   PUNCT ajst-24979 264 46   PROPN ajst-24979 264 47 1 1 NUM ajst-24979 264 48 3 3 NUM ajst-24979 264 49 1 1 NUM ajst-24979 264 50 0 0 NUM ajst-24979 264 51 0 0 NUM ajst-24979 264 52 ( ( PUNCT ajst-24979 264 53 1 1 NUM ajst-24979 264 54 ) ) PUNCT ajst-24979 264 55 ( ( PUNCT ajst-24979 264 56 , , PUNCT ajst-24979 264 57 ) ) PUNCT ajst-24979 264 58 ] ] PUNCT ajst-24979 264 59 . . PUNCT ajst-24979 265 1 x x PUNCT ajst-24979 265 2 ndt ndt INTJ ajst-24979 265 3 x x X ajst-24979 265 4 t t PROPN ajst-24979 265 5 w w PROPN ajst-24979 265 6 t t PROPN ajst-24979 265 7 r r NOUN ajst-24979 265 8 dt dt NOUN ajst-24979 265 9   NOUN ajst-24979 265 10   PUNCT ajst-24979 265 11 select select ADJ ajst-24979 265 12 1 1 NUM ajst-24979 265 13 , , PUNCT ajst-24979 265 14 0.4 0.4 NUM ajst-24979 265 15 , , PUNCT ajst-24979 265 16 3h 3h NUM ajst-24979 265 17 r r NOUN ajst-24979 265 18 n n NOUN ajst-24979 265 19   NOUN ajst-24979 265 20   NOUN ajst-24979 265 21   ADJ ajst-24979 265 22 . . PUNCT ajst-24979 266 1 the the DET ajst-24979 266 2 left left ADJ ajst-24979 266 3 and and CCONJ ajst-24979 266 4 right right ADJ ajst-24979 266 5 boundary boundary ADJ ajst-24979 266 6 errors error NOUN ajst-24979 266 7 between between ADP ajst-24979 266 8 the the DET ajst-24979 266 9 approximate approximate ADJ ajst-24979 266 10 solution solution NOUN ajst-24979 266 11 and and CCONJ ajst-24979 266 12 the the DET ajst-24979 266 13 exact exact ADJ ajst-24979 266 14 solution solution NOUN ajst-24979 266 15 are be AUX ajst-24979 266 16 obtained obtain VERB ajst-24979 266 17 in in ADP ajst-24979 266 18 table table NOUN ajst-24979 266 19 1 1 NUM ajst-24979 266 20 and and CCONJ ajst-24979 266 21 table table NOUN ajst-24979 266 22 2 2 NUM ajst-24979 266 23 . . PUNCT ajst-24979 266 24 table table NOUN ajst-24979 266 25 1 1 NUM ajst-24979 266 26 . . PUNCT ajst-24979 266 27 left leave VERB ajst-24979 266 28 bound bind VERB ajst-24979 266 29 of of ADP ajst-24979 266 30 error error NOUN ajst-24979 266 31 x x X ajst-24979 266 32 exact exact ADJ ajst-24979 266 33 ham ham NOUN ajst-24979 266 34 error error NOUN ajst-24979 266 35 0 0 NUM ajst-24979 266 36 0 0 NUM ajst-24979 266 37 0 0 NUM ajst-24979 266 38 0 0 NUM ajst-24979 266 39 0.2 0.2 NUM ajst-24979 266 40 6.6667e-03 6.6667e-03 NUM ajst-24979 267 1 6.6665e-03 6.6665e-03 NUM ajst-24979 267 2 2.1330e-07 2.1330e-07 NUM ajst-24979 267 3 0.4 0.4 NUM ajst-24979 267 4 1.3333e-02 1.3333e-02 NUM ajst-24979 267 5 1.3331e-02 1.3331e-02 NUM ajst-24979 267 6 2.3185e-06 2.3185e-06 NUM ajst-24979 267 7 0.6 0.6 NUM ajst-24979 267 8 2.0000e-02 2.0000e-02 NUM ajst-24979 267 9 1.9993e-02 1.9993e-02 NUM ajst-24979 267 10 7.4545e-06 7.4545e-06 NUM ajst-24979 267 11 0.8 0.8 NUM ajst-24979 267 12 2.6667e-02 2.6667e-02 NUM ajst-24979 267 13 2.6665e-02 2.6665e-02 NUM ajst-24979 267 14 1.9953e-06 1.9953e-06 NUM ajst-24979 267 15 1.0 1.0 NUM ajst-24979 267 16 3.3333e-02 3.3333e-02 NUM ajst-24979 267 17 3.3425e-02 3.3425e-02 NUM ajst-24979 267 18 9.1408e-05 9.1408e-05 NUM ajst-24979 267 19 table table NOUN ajst-24979 267 20 2 2 NUM ajst-24979 267 21 . . PUNCT ajst-24979 268 1 right right PROPN ajst-24979 268 2 left leave VERB ajst-24979 268 3 bound bind VERB ajst-24979 268 4 of of ADP ajst-24979 268 5 error error NOUN ajst-24979 268 6 x x X ajst-24979 268 7 exact exact ADJ ajst-24979 268 8 ham ham NOUN ajst-24979 268 9 error error NOUN ajst-24979 268 10 0 0 NUM ajst-24979 268 11 0 0 NUM ajst-24979 268 12 0 0 NUM ajst-24979 268 13 0 0 NUM ajst-24979 269 1 0.2 0.2 NUM ajst-24979 269 2 2.6667e-02 2.6667e-02 NUM ajst-24979 269 3 2.6666e-02 2.6666e-02 NUM ajst-24979 269 4 8.5319e-07 8.5319e-07 NUM ajst-24979 269 5 0.4 0.4 NUM ajst-24979 269 6 5.3333e-02 5.3333e-02 NUM ajst-24979 269 7 5.3324e-02 5.3324e-02 NUM ajst-24979 269 8 9.2740e-06 9.2740e-06 NUM ajst-24979 269 9 0.6 0.6 NUM ajst-24979 269 10 8.0000e-02 8.0000e-02 NUM ajst-24979 269 11 7.9970e-02 7.9970e-02 NUM ajst-24979 269 12 2.9818e-05 2.9818e-05 NUM ajst-24979 269 13 0.8 0.8 NUM ajst-24979 269 14 1.0667e-01 1.0667e-01 NUM ajst-24979 269 15 1.0666e-01 1.0666e-01 NUM ajst-24979 269 16 7.9813e-06 7.9813e-06 NUM ajst-24979 269 17 1.0 1.0 NUM ajst-24979 269 18 1.3333e-01 1.3333e-01 NUM ajst-24979 269 19 1.3370e-01 1.3370e-01 NUM ajst-24979 269 20 3.6563e-04 3.6563e-04 NUM ajst-24979 269 21 example example NOUN ajst-24979 269 22 2 2 NUM ajst-24979 269 23 consider consider VERB ajst-24979 269 24 the the DET ajst-24979 269 25 following follow VERB ajst-24979 269 26 nonlinear nonlinear ADJ ajst-24979 269 27 fuzzy fuzzy ADJ ajst-24979 269 28 fractions fraction NOUN ajst-24979 269 29 : : PUNCT ajst-24979 269 30 waltra waltra ADJ ajst-24979 269 31 - - ADJ ajst-24979 269 32 fredholm fredholm ADJ ajst-24979 269 33 integral integral ADJ ajst-24979 269 34 differential differential ADJ ajst-24979 269 35 equations equation NOUN ajst-24979 269 36 1/4 1/4 NUM ajst-24979 269 37 2 2 NUM ajst-24979 269 38 2 2 NUM ajst-24979 269 39 3 3 NUM ajst-24979 269 40 3/4 3/4 NUM ajst-24979 269 41 12 12 NUM ajst-24979 269 42 22 22 NUM ajst-24979 269 43 0 0 NUM ajst-24979 269 44 0 0 NUM ajst-24979 269 45 1/4 1/4 NUM ajst-24979 269 46 2 2 NUM ajst-24979 269 47 2 2 NUM ajst-24979 269 48 3/4 3/4 NUM ajst-24979 269 49 3 3 NUM ajst-24979 269 50 12 12 NUM ajst-24979 269 51 22 22 NUM ajst-24979 269 52 0 0 NUM ajst-24979 269 53 0 0 NUM ajst-24979 269 54 4 4 NUM ajst-24979 269 55 [ [ PUNCT ajst-24979 269 56 ( ( PUNCT ajst-24979 269 57 , , PUNCT ajst-24979 269 58 ) ) PUNCT ajst-24979 269 59 ] ] PUNCT ajst-24979 269 60 ( ( PUNCT ajst-24979 269 61 , , PUNCT ajst-24979 269 62 ) ) PUNCT ajst-24979 269 63 5 5 NUM ajst-24979 269 64 ( ( PUNCT ajst-24979 269 65 1/ 1/ NUM ajst-24979 269 66 4 4 NUM ajst-24979 269 67 ) ) PUNCT ajst-24979 269 68 100 100 NUM ajst-24979 269 69 15 15 NUM ajst-24979 269 70 ( ( PUNCT ajst-24979 269 71 , , PUNCT ajst-24979 269 72 ) ) PUNCT ajst-24979 269 73 ( ( PUNCT ajst-24979 269 74 , , PUNCT ajst-24979 269 75 ) ) PUNCT ajst-24979 269 76 , , PUNCT ajst-24979 269 77 ( ( PUNCT ajst-24979 269 78 0 0 NUM ajst-24979 269 79 , , PUNCT ajst-24979 269 80 ) ) PUNCT ajst-24979 269 81 0 0 NUM ajst-24979 269 82 , , PUNCT ajst-24979 269 83 4(2 4(2 NUM ajst-24979 269 84 ) ) PUNCT ajst-24979 269 85 ( ( PUNCT ajst-24979 269 86 2 2 X ajst-24979 269 87 ) ) PUNCT ajst-24979 269 88 [ [ PUNCT ajst-24979 269 89 ( ( PUNCT ajst-24979 269 90 , , PUNCT ajst-24979 269 91 ) ) PUNCT ajst-24979 269 92 ] ] PUNCT ajst-24979 269 93 5 5 NUM ajst-24979 269 94 ( ( PUNCT ajst-24979 269 95 1/ 1/ NUM ajst-24979 269 96 4 4 NUM ajst-24979 269 97 ) ) PUNCT ajst-24979 269 98 100 100 NUM ajst-24979 269 99 ( ( PUNCT ajst-24979 269 100 2 2 NUM ajst-24979 269 101 ) ) PUNCT ajst-24979 269 102 ( ( PUNCT ajst-24979 269 103 , , PUNCT ajst-24979 269 104 ) ) PUNCT ajst-24979 269 105 ( ( PUNCT ajst-24979 269 106 , , PUNCT ajst-24979 269 107 ) ) PUNCT ajst-24979 269 108 ( ( PUNCT ajst-24979 269 109 , , PUNCT ajst-24979 269 110 ) ) PUNCT ajst-24979 269 111 , , PUNCT ajst-24979 269 112 15 15 NUM ajst-24979 269 113 ( ( PUNCT ajst-24979 269 114 0 0 NUM ajst-24979 269 115 , , PUNCT ajst-24979 269 116 c c NOUN ajst-24979 269 117 x x X ajst-24979 269 118 c c NOUN ajst-24979 269 119 x x PART ajst-24979 269 120 rx rx VERB ajst-24979 269 121 r r NOUN ajst-24979 269 122 x x PUNCT ajst-24979 269 123 rx rx NOUN ajst-24979 269 124 d d PROPN ajst-24979 269 125 w w NOUN ajst-24979 269 126 x x X ajst-24979 270 1 r r NOUN ajst-24979 270 2 w w NOUN ajst-24979 270 3 x x SYM ajst-24979 270 4 r r NOUN ajst-24979 270 5 xw xw PROPN ajst-24979 270 6 t t PROPN ajst-24979 270 7 r r NOUN ajst-24979 270 8 dt dt X ajst-24979 270 9 x x PUNCT ajst-24979 270 10 tw tw INTJ ajst-24979 270 11 t t NOUN ajst-24979 270 12 r r NOUN ajst-24979 270 13 dt dt NOUN ajst-24979 270 14 w w NOUN ajst-24979 270 15 r r NOUN ajst-24979 270 16 r r NOUN ajst-24979 270 17 x x PUNCT ajst-24979 270 18 r r NOUN ajst-24979 270 19 x x PROPN ajst-24979 270 20 d d NOUN ajst-24979 270 21 w w NOUN ajst-24979 270 22 x x SYM ajst-24979 270 23 r r NOUN ajst-24979 270 24 r r NOUN ajst-24979 270 25 x x SYM ajst-24979 270 26 w w NOUN ajst-24979 270 27 x x SYM ajst-24979 270 28 r r NOUN ajst-24979 270 29 xw xw PROPN ajst-24979 270 30 t t PROPN ajst-24979 270 31 r r NOUN ajst-24979 270 32 dt dt X ajst-24979 270 33 x x PUNCT ajst-24979 270 34 tw tw INTJ ajst-24979 270 35 t t NOUN ajst-24979 270 36 r r NOUN ajst-24979 270 37 dt dt NOUN ajst-24979 270 38 w w NOUN ajst-24979 270 39   NOUN ajst-24979 270 40   PROPN ajst-24979 270 41   NOUN ajst-24979 270 42   VERB ajst-24979 270 43   PROPN ajst-24979 270 44   NUM ajst-24979 270 45   X ajst-24979 270 46   X ajst-24979 270 47   DET ajst-24979 270 48   NOUN ajst-24979 270 49   NUM ajst-24979 270 50   PROPN ajst-24979 270 51   PROPN ajst-24979 270 52   PROPN ajst-24979 270 53   PROPN ajst-24979 270 54   NOUN ajst-24979 270 55   VERB ajst-24979 270 56   PROPN ajst-24979 270 57   PROPN ajst-24979 270 58   PUNCT ajst-24979 270 59   ADV ajst-24979 270 60   PUNCT ajst-24979 270 61   X ajst-24979 270 62   NOUN ajst-24979 270 63   PUNCT ajst-24979 270 64 ) ) PUNCT ajst-24979 271 1 0.r 0.r NUM ajst-24979 271 2   ADP ajst-24979 271 3   NUM ajst-24979 271 4   NUM ajst-24979 271 5   NUM ajst-24979 271 6   NUM ajst-24979 271 7   NUM ajst-24979 271 8   NUM ajst-24979 271 9   NUM ajst-24979 271 10   NUM ajst-24979 271 11   PROPN ajst-24979 271 12   NOUN ajst-24979 271 13 the the DET ajst-24979 271 14 exact exact ADJ ajst-24979 271 15 solution solution NOUN ajst-24979 271 16 is be AUX ajst-24979 271 17 2 2 NUM ajst-24979 271 18 ( ( PUNCT ajst-24979 271 19 , , PUNCT ajst-24979 271 20 ) ) PUNCT ajst-24979 271 21 [ [ PUNCT ajst-24979 271 22 ( ( PUNCT ajst-24979 271 23 , , PUNCT ajst-24979 271 24 ) ) PUNCT ajst-24979 271 25 , , PUNCT ajst-24979 271 26 ( ( PUNCT ajst-24979 271 27 , , PUNCT ajst-24979 271 28 ) ) PUNCT ajst-24979 271 29 ] ] PUNCT ajst-24979 272 1 [ [ PUNCT ajst-24979 272 2 , , PUNCT ajst-24979 272 3 ] ] X ajst-24979 272 4 , , PUNCT ajst-24979 272 5 [ [ X ajst-24979 272 6 0,1 0,1 NUM ajst-24979 272 7 ] ] SYM ajst-24979 272 8 5 5 NUM ajst-24979 272 9 5 5 NUM ajst-24979 272 10 r r NOUN ajst-24979 272 11 r r NOUN ajst-24979 272 12 w w NOUN ajst-24979 272 13 x x X ajst-24979 272 14 r r NOUN ajst-24979 272 15 w w NOUN ajst-24979 272 16 x x X ajst-24979 272 17 r r NOUN ajst-24979 272 18 w w NOUN ajst-24979 272 19 x x SYM ajst-24979 272 20 r r NOUN ajst-24979 272 21 x x SYM ajst-24979 272 22 x x SYM ajst-24979 272 23 r r NOUN ajst-24979 272 24   NOUN ajst-24979 272 25   PROPN ajst-24979 272 26   PROPN ajst-24979 272 27   NOUN ajst-24979 272 28 \ \ PROPN ajst-24979 273 1 it it PRON ajst-24979 273 2 can can AUX ajst-24979 273 3 be be AUX ajst-24979 273 4 written write VERB ajst-24979 273 5 from from ADP ajst-24979 273 6 the the DET ajst-24979 273 7 recursive recursive ADJ ajst-24979 273 8 176 176 NUM ajst-24979 273 9 3 3 NUM ajst-24979 273 10 1 1 NUM ajst-24979 273 11 1 1 NUM ajst-24979 273 12 1/4 1/4 NUM ajst-24979 273 13 2 2 NUM ajst-24979 273 14 2 2 NUM ajst-24979 273 15 12 12 NUM ajst-24979 273 16 22 22 NUM ajst-24979 273 17 1 1 NUM ajst-24979 273 18 10 10 NUM ajst-24979 273 19 0 0 NUM ajst-24979 273 20 3 3 NUM ajst-24979 273 21 1 1 NUM ajst-24979 273 22 1 1 NUM ajst-24979 273 23 1/4 1/4 NUM ajst-24979 273 24 2 2 NUM ajst-24979 273 25 2 2 NUM ajst-24979 273 26 2 2 NUM ajst-24979 273 27 ( ( PUNCT ajst-24979 273 28 , , PUNCT ajst-24979 273 29 ) ) PUNCT ajst-24979 273 30 ( ( PUNCT ajst-24979 273 31 ) ) PUNCT ajst-24979 273 32 ( ( PUNCT ajst-24979 273 33 , , PUNCT ajst-24979 273 34 ) ) PUNCT ajst-24979 274 1 [ [ PUNCT ajst-24979 274 2 ( ( PUNCT ajst-24979 274 3 , , PUNCT ajst-24979 274 4 ) ) PUNCT ajst-24979 274 5 15 15 NUM ajst-24979 274 6 4 4 NUM ajst-24979 274 7 ( ( PUNCT ajst-24979 274 8 1 1 NUM ajst-24979 274 9 ) ) PUNCT ajst-24979 274 10 ( ( PUNCT ajst-24979 274 11 ) ) PUNCT ajst-24979 274 12 5 5 NUM ajst-24979 274 13 ( ( PUNCT ajst-24979 274 14 1/ 1/ NUM ajst-24979 274 15 4 4 NUM ajst-24979 274 16 ) ) PUNCT ajst-24979 274 17 100 100 NUM ajst-24979 274 18 ( ( PUNCT ajst-24979 274 19 , , PUNCT ajst-24979 274 20 ) ) PUNCT ajst-24979 274 21 ( ( PUNCT ajst-24979 274 22 , , PUNCT ajst-24979 274 23 ) ) PUNCT ajst-24979 274 24 ] ] PUNCT ajst-24979 274 25 , , PUNCT ajst-24979 274 26 ( ( PUNCT ajst-24979 274 27 2 2 X ajst-24979 274 28 ) ) PUNCT ajst-24979 274 29 ( ( PUNCT ajst-24979 274 30 , , PUNCT ajst-24979 274 31 ) ) PUNCT ajst-24979 274 32 ( ( PUNCT ajst-24979 274 33 ) ) PUNCT ajst-24979 274 34 ( ( PUNCT ajst-24979 274 35 , , PUNCT ajst-24979 274 36 ) ) PUNCT ajst-24979 274 37 [ [ PUNCT ajst-24979 274 38 ( ( PUNCT ajst-24979 274 39 , , PUNCT ajst-24979 274 40 ) ) PUNCT ajst-24979 274 41 15 15 NUM ajst-24979 274 42 4(2 4(2 NUM ajst-24979 274 43 ) ) PUNCT ajst-24979 274 44 ( ( PUNCT ajst-24979 274 45 2 2 X ajst-24979 274 46 ) ) PUNCT ajst-24979 274 47 ( ( PUNCT ajst-24979 274 48 1 1 NUM ajst-24979 274 49 ) ) PUNCT ajst-24979 274 50 ( ( PUNCT ajst-24979 274 51 ) ) PUNCT ajst-24979 274 52 5 5 NUM ajst-24979 274 53 ( ( PUNCT ajst-24979 274 54 1/ 1/ NUM ajst-24979 274 55 4 4 NUM ajst-24979 274 56 ) ) PUNCT ajst-24979 274 57 100 100 NUM ajst-24979 274 58 n n CCONJ ajst-24979 274 59 n n CCONJ ajst-24979 274 60 nn nn PROPN ajst-24979 274 61 n n ADV ajst-24979 274 62 x x SYM ajst-24979 274 63 n n CCONJ ajst-24979 274 64 n n CCONJ ajst-24979 274 65 n n CCONJ ajst-24979 274 66 n n CCONJ ajst-24979 274 67 nn nn PROPN ajst-24979 274 68 n n CCONJ ajst-24979 274 69 rx rx VERB ajst-24979 274 70 w w NOUN ajst-24979 274 71 x x SYM ajst-24979 274 72 r r NOUN ajst-24979 274 73 h h NOUN ajst-24979 274 74 w w NOUN ajst-24979 274 75 x x PUNCT ajst-24979 274 76 r r NOUN ajst-24979 274 77 hj hj PROPN ajst-24979 274 78 w w NOUN ajst-24979 274 79 x x PUNCT ajst-24979 274 80 r r NOUN ajst-24979 274 81 rx rx NOUN ajst-24979 274 82 r r NOUN ajst-24979 274 83 x x SYM ajst-24979 274 84 xw xw PROPN ajst-24979 274 85 t t PROPN ajst-24979 274 86 r r NOUN ajst-24979 274 87 dt dt X ajst-24979 274 88 x x PUNCT ajst-24979 274 89 tw tw INTJ ajst-24979 274 90 t t NOUN ajst-24979 274 91 r r NOUN ajst-24979 274 92 dt dt NOUN ajst-24979 274 93 r r NOUN ajst-24979 274 94 x x SYM ajst-24979 274 95 w w NOUN ajst-24979 274 96 x x SYM ajst-24979 274 97 r r NOUN ajst-24979 274 98 h h NOUN ajst-24979 274 99 w w NOUN ajst-24979 274 100 x x PUNCT ajst-24979 274 101 r r NOUN ajst-24979 274 102 hj hj PROPN ajst-24979 274 103 w w NOUN ajst-24979 274 104 x x SYM ajst-24979 274 105 r r NOUN ajst-24979 274 106 r r NOUN ajst-24979 274 107 x x SYM ajst-24979 274 108 r r NOUN ajst-24979 274 109 x x SYM ajst-24979 274 110 xw xw PROPN ajst-24979 274 111   NUM ajst-24979 274 112   PROPN ajst-24979 274 113   NOUN ajst-24979 274 114   AUX ajst-24979 274 115   NOUN ajst-24979 274 116   VERB ajst-24979 274 117   VERB ajst-24979 274 118   PROPN ajst-24979 274 119   PROPN ajst-24979 274 120   PROPN ajst-24979 274 121   PROPN ajst-24979 274 122   PROPN ajst-24979 274 123   NUM ajst-24979 274 124   PUNCT ajst-24979 274 125   PROPN ajst-24979 274 126   PROPN ajst-24979 274 127   PUNCT ajst-24979 274 128   PROPN ajst-24979 274 129   PROPN ajst-24979 274 130   NUM ajst-24979 274 131   ADV ajst-24979 274 132   VERB ajst-24979 274 133   PROPN ajst-24979 274 134   PROPN ajst-24979 274 135   PUNCT ajst-24979 274 136   PROPN ajst-24979 274 137   PROPN ajst-24979 274 138   PROPN ajst-24979 274 139   PROPN ajst-24979 274 140   PUNCT ajst-24979 274 141   PROPN ajst-24979 274 142   PROPN ajst-24979 274 143   NUM ajst-24979 274 144   VERB ajst-24979 274 145   PUNCT ajst-24979 274 146   PROPN ajst-24979 274 147 1 1 NUM ajst-24979 274 148 22 22 NUM ajst-24979 274 149 1 1 NUM ajst-24979 274 150 1 1 NUM ajst-24979 274 151 0 0 NUM ajst-24979 274 152 0 0 NUM ajst-24979 274 153 ( ( PUNCT ajst-24979 274 154 , , PUNCT ajst-24979 274 155 ) ) PUNCT ajst-24979 274 156 ( ( PUNCT ajst-24979 274 157 , , PUNCT ajst-24979 274 158 ) ) PUNCT ajst-24979 274 159 ] ] PUNCT ajst-24979 274 160 . . PUNCT ajst-24979 275 1 x x PUNCT ajst-24979 275 2 n n CCONJ ajst-24979 275 3 nt not PART ajst-24979 275 4 r r NOUN ajst-24979 275 5 dt dt NOUN ajst-24979 275 6 x x INTJ ajst-24979 275 7 tw tw INTJ ajst-24979 275 8 t t NOUN ajst-24979 275 9 r r NOUN ajst-24979 275 10 dt dt NUM ajst-24979 275 11   ADP ajst-24979 275 12   X ajst-24979 275 13 select select ADJ ajst-24979 275 14 1 1 NUM ajst-24979 275 15 , , PUNCT ajst-24979 275 16 0.5 0.5 NUM ajst-24979 275 17 , , PUNCT ajst-24979 275 18 3h 3h NUM ajst-24979 275 19 r r NOUN ajst-24979 275 20 n n NOUN ajst-24979 275 21   NOUN ajst-24979 275 22   NOUN ajst-24979 275 23   ADJ ajst-24979 275 24 . . PUNCT ajst-24979 276 1 the the DET ajst-24979 276 2 left left ADJ ajst-24979 276 3 and and CCONJ ajst-24979 276 4 right right ADJ ajst-24979 276 5 boundary boundary ADJ ajst-24979 276 6 errors error NOUN ajst-24979 276 7 between between ADP ajst-24979 276 8 the the DET ajst-24979 276 9 approximate approximate ADJ ajst-24979 276 10 solution solution NOUN ajst-24979 276 11 and and CCONJ ajst-24979 276 12 the the DET ajst-24979 276 13 exact exact ADJ ajst-24979 276 14 solution solution NOUN ajst-24979 276 15 are be AUX ajst-24979 276 16 obtained obtain VERB ajst-24979 276 17 in in ADP ajst-24979 276 18 table table NOUN ajst-24979 276 19 31 31 NUM ajst-24979 276 20 and and CCONJ ajst-24979 276 21 table table NOUN ajst-24979 276 22 4 4 NUM ajst-24979 276 23 . . PUNCT ajst-24979 276 24 table table NOUN ajst-24979 276 25 3 3 NUM ajst-24979 276 26 . . PUNCT ajst-24979 276 27 left leave VERB ajst-24979 276 28 bound bind VERB ajst-24979 276 29 of of ADP ajst-24979 276 30 error error NOUN ajst-24979 276 31 x x X ajst-24979 276 32 exact exact ADJ ajst-24979 276 33 ham ham NOUN ajst-24979 276 34 error error NOUN ajst-24979 276 35 0 0 NUM ajst-24979 276 36 0 0 NUM ajst-24979 276 37 0 0 NUM ajst-24979 276 38 0 0 NUM ajst-24979 276 39 0.2 0.2 NUM ajst-24979 276 40 2.0000e-02 2.0000e-02 NUM ajst-24979 276 41 2.0000e-02 2.0000e-02 NUM ajst-24979 276 42 2.1184e-07 2.1184e-07 NUM ajst-24979 276 43 0.4 0.4 NUM ajst-24979 276 44 4.0000e-02 4.0000e-02 NUM ajst-24979 276 45 3.9999e-02 3.9999e-02 NUM ajst-24979 276 46 1.4309e-06 1.4309e-06 NUM ajst-24979 276 47 0.6 0.6 NUM ajst-24979 276 48 6.0000e-02 6.0000e-02 NUM ajst-24979 277 1 5.9996e-02 5.9996e-02 NUM ajst-24979 277 2 4.4309e-06 4.4309e-06 NUM ajst-24979 277 3 0.8 0.8 NUM ajst-24979 277 4 8.0000e-02 8.0000e-02 NUM ajst-24979 277 5 7.9990e-02 7.9990e-02 NUM ajst-24979 277 6 1.0140e-05 1.0140e-05 NUM ajst-24979 277 7 1.0 1.0 NUM ajst-24979 277 8 1.0000e-01 1.0000e-01 NUM ajst-24979 277 9 9.9980e-02 9.9980e-02 NUM ajst-24979 277 10 2.0064e-05 2.0064e-05 NUM ajst-24979 277 11 table table NOUN ajst-24979 277 12 4 4 NUM ajst-24979 277 13 . . PUNCT ajst-24979 278 1 right right ADV ajst-24979 278 2 left leave VERB ajst-24979 278 3 bound bind VERB ajst-24979 278 4 of of ADP ajst-24979 278 5 error error NOUN ajst-24979 278 6 x x X ajst-24979 278 7 exact exact ADJ ajst-24979 278 8 ham ham NOUN ajst-24979 278 9 error error NOUN ajst-24979 278 10 0 0 NUM ajst-24979 278 11 0 0 NUM ajst-24979 278 12 0 0 NUM ajst-24979 278 13 0 0 NUM ajst-24979 278 14 0.2 0.2 NUM ajst-24979 278 15 6.0000e-02 6.0000e-02 NUM ajst-24979 278 16 5.9994e-02 5.9994e-02 NUM ajst-24979 279 1 5.6700e-06 5.6700e-06 NUM ajst-24979 279 2 0.4 0.4 NUM ajst-24979 279 3 1.2000e-01 1.2000e-01 NUM ajst-24979 279 4 1.1996e-01 1.1996e-01 NUM ajst-24979 279 5 3.8297e-05 3.8297e-05 NUM ajst-24979 279 6 0.6 0.6 NUM ajst-24979 279 7 1.8000e-01 1.8000e-01 NUM ajst-24979 279 8 1.7988e-01 1.7988e-01 NUM ajst-24979 279 9 1.1858e-04 1.1858e-04 NUM ajst-24979 279 10 0.8 0.8 NUM ajst-24979 279 11 2.4000e-01 2.4000e-01 NUM ajst-24979 279 12 2.3973e-01 2.3973e-01 NUM ajst-24979 279 13 2.7120e-04 2.7120e-04 NUM ajst-24979 279 14 1.0 1.0 NUM ajst-24979 279 15 3.0000e-01 3.0000e-01 NUM ajst-24979 279 16 2.9946e-01 2.9946e-01 NUM ajst-24979 279 17 5.3540e-04 5.3540e-04 NUM ajst-24979 279 18 from from ADP ajst-24979 279 19 the the DET ajst-24979 279 20 error error NOUN ajst-24979 279 21 results result NOUN ajst-24979 279 22 of of ADP ajst-24979 279 23 table table NOUN ajst-24979 279 24 1 1 NUM ajst-24979 279 25 - - PUNCT ajst-24979 279 26 table table NOUN ajst-24979 279 27 4 4 NUM ajst-24979 279 28 , , PUNCT ajst-24979 279 29 the the DET ajst-24979 279 30 error error NOUN ajst-24979 279 31 between between ADP ajst-24979 279 32 the the DET ajst-24979 279 33 exact exact ADJ ajst-24979 279 34 solution solution NOUN ajst-24979 279 35 and and CCONJ ajst-24979 279 36 the the DET ajst-24979 279 37 approximate approximate ADJ ajst-24979 279 38 solution solution NOUN ajst-24979 279 39 is be AUX ajst-24979 279 40 small small ADJ ajst-24979 279 41 , , PUNCT ajst-24979 279 42 so so CCONJ ajst-24979 279 43 ham ham PROPN ajst-24979 279 44 is be AUX ajst-24979 279 45 effective effective ADJ ajst-24979 279 46 and and CCONJ ajst-24979 279 47 practical practical ADJ ajst-24979 279 48 for for ADP ajst-24979 279 49 dealing deal VERB ajst-24979 279 50 with with ADP ajst-24979 279 51 linear linear ADJ ajst-24979 279 52 and and CCONJ ajst-24979 279 53 nonlinear nonlinear ADJ ajst-24979 279 54 fuzzy fuzzy ADJ ajst-24979 279 55 fractional fractional ADJ ajst-24979 279 56 integral integral ADJ ajst-24979 279 57 and and CCONJ ajst-24979 279 58 differential differential ADJ ajst-24979 279 59 problems problem NOUN ajst-24979 279 60 . . PUNCT ajst-24979 280 1 6 6 X ajst-24979 280 2 . . X ajst-24979 280 3 conclusion conclusion NOUN ajst-24979 280 4 in in ADP ajst-24979 280 5 this this DET ajst-24979 280 6 paper paper NOUN ajst-24979 280 7 , , PUNCT ajst-24979 280 8 a a DET ajst-24979 280 9 class class NOUN ajst-24979 280 10 of of ADP ajst-24979 280 11 fuzzy fuzzy ADJ ajst-24979 280 12 fractional fractional ADJ ajst-24979 280 13 order order NOUN ajst-24979 280 14 mixed mix VERB ajst-24979 280 15 integro integro ADJ ajst-24979 280 16 - - PUNCT ajst-24979 280 17 differential differential NOUN ajst-24979 280 18 equations equation NOUN ajst-24979 280 19 is be AUX ajst-24979 280 20 studied study VERB ajst-24979 280 21 . . PUNCT ajst-24979 281 1 the the DET ajst-24979 281 2 fixed fix VERB ajst-24979 281 3 point point NOUN ajst-24979 281 4 theorem theorem NOUN ajst-24979 281 5 is be AUX ajst-24979 281 6 used use VERB ajst-24979 281 7 to to PART ajst-24979 281 8 prove prove VERB ajst-24979 281 9 the the DET ajst-24979 281 10 existence existence NOUN ajst-24979 281 11 and and CCONJ ajst-24979 281 12 uniqueness uniqueness NOUN ajst-24979 281 13 of of ADP ajst-24979 281 14 the the DET ajst-24979 281 15 solution solution NOUN ajst-24979 281 16 . . PUNCT ajst-24979 282 1 the the DET ajst-24979 282 2 appropriate appropriate ADJ ajst-24979 282 3 auxiliary auxiliary ADJ ajst-24979 282 4 parameters parameter NOUN ajst-24979 282 5 and and CCONJ ajst-24979 282 6 initial initial ADJ ajst-24979 282 7 conditions condition NOUN ajst-24979 282 8 are be AUX ajst-24979 282 9 selected select VERB ajst-24979 282 10 to to PART ajst-24979 282 11 solve solve VERB ajst-24979 282 12 the the DET ajst-24979 282 13 fuzzy fuzzy ADJ ajst-24979 282 14 fractional fractional ADJ ajst-24979 282 15 volterrafredholm volterrafredholm NOUN ajst-24979 282 16 integro integro ADJ ajst-24979 282 17 - - PUNCT ajst-24979 282 18 differential differential NOUN ajst-24979 282 19 equation equation NOUN ajst-24979 282 20 by by ADP ajst-24979 282 21 using use VERB ajst-24979 282 22 the the DET ajst-24979 282 23 method method NOUN ajst-24979 282 24 of of ADP ajst-24979 282 25 homotopy homotopy NOUN ajst-24979 282 26 analysis analysis NOUN ajst-24979 282 27 . . PUNCT ajst-24979 283 1 the the DET ajst-24979 283 2 validity validity NOUN ajst-24979 283 3 and and CCONJ ajst-24979 283 4 applicability applicability NOUN ajst-24979 283 5 of of ADP ajst-24979 283 6 the the DET ajst-24979 283 7 method method NOUN ajst-24979 283 8 can can AUX ajst-24979 283 9 be be AUX ajst-24979 283 10 obtained obtain VERB ajst-24979 283 11 by by ADP ajst-24979 283 12 several several ADJ ajst-24979 283 13 numerical numerical ADJ ajst-24979 283 14 examples example NOUN ajst-24979 283 15 and and CCONJ ajst-24979 283 16 their their PRON ajst-24979 283 17 results result NOUN ajst-24979 283 18 . . PUNCT ajst-24979 284 1 in in ADP ajst-24979 284 2 the the DET ajst-24979 284 3 future future NOUN ajst-24979 284 4 , , PUNCT ajst-24979 284 5 the the DET ajst-24979 284 6 fuzzy fuzzy ADJ ajst-24979 284 7 nonlinear nonlinear PROPN ajst-24979 284 8 fractional fractional PROPN ajst-24979 284 9 volterra volterra NOUN ajst-24979 284 10 - - PUNCT ajst-24979 284 11 fredholm fredholm NOUN ajst-24979 284 12 integral integral ADJ ajst-24979 284 13 - - PUNCT ajst-24979 284 14 differential differential NOUN ajst-24979 284 15 will will AUX ajst-24979 284 16 be be AUX ajst-24979 284 17 studied study VERB ajst-24979 284 18 . . PUNCT ajst-24979 285 1 based base VERB ajst-24979 285 2 on on ADP ajst-24979 285 3 the the DET ajst-24979 285 4 ham ham NOUN ajst-24979 285 5 , , PUNCT ajst-24979 285 6 the the DET ajst-24979 285 7 nonlinear nonlinear ADJ ajst-24979 285 8 term term NOUN ajst-24979 285 9 will will AUX ajst-24979 285 10 be be AUX ajst-24979 285 11 approximated approximate VERB ajst-24979 285 12 and and CCONJ ajst-24979 285 13 its its PRON ajst-24979 285 14 stability stability NOUN ajst-24979 285 15 will will AUX ajst-24979 285 16 be be AUX ajst-24979 285 17 studied study VERB ajst-24979 285 18 . . PUNCT ajst-24979 286 1 references reference NOUN ajst-24979 286 2 [ [ X ajst-24979 286 3 1 1 NUM ajst-24979 286 4 ] ] PUNCT ajst-24979 286 5 a. a. NOUN ajst-24979 286 6 carpinteri carpinteri PROPN ajst-24979 286 7 , , PUNCT ajst-24979 286 8 f. f. PROPN ajst-24979 286 9 mainardi mainardi PROPN ajst-24979 286 10 . . PUNCT ajst-24979 287 1 fractals fractal NOUN ajst-24979 287 2 and and CCONJ ajst-24979 287 3 fractional fractional ADJ ajst-24979 287 4 calculus calculus NOUN ajst-24979 287 5 in in ADP ajst-24979 287 6 continuum continuum ADJ ajst-24979 287 7 mechanics mechanic NOUN ajst-24979 287 8 , , PUNCT ajst-24979 287 9 springer springer NOUN ajst-24979 287 10 , , PUNCT ajst-24979 287 11 vienna vienna PROPN ajst-24979 287 12 , , PUNCT ajst-24979 287 13 378(1997 378(1997 NUM ajst-24979 287 14 ) ) PUNCT ajst-24979 287 15 , , PUNCT ajst-24979 287 16 277 277 NUM ajst-24979 287 17 - - SYM ajst-24979 287 18 290 290 NUM ajst-24979 287 19 . . PUNCT ajst-24979 288 1 [ [ X ajst-24979 288 2 2 2 NUM ajst-24979 288 3 ] ] X ajst-24979 288 4 d. d. PROPN ajst-24979 288 5 baleanu baleanu PROPN ajst-24979 288 6 , , PUNCT ajst-24979 288 7 k. k. PROPN ajst-24979 288 8 diethelm diethelm PROPN ajst-24979 288 9 , , PUNCT ajst-24979 288 10 e. e. PROPN ajst-24979 288 11 scalas scalas PROPN ajst-24979 288 12 , , PUNCT ajst-24979 288 13 j. j. PROPN ajst-24979 288 14 trujillo trujillo PROPN ajst-24979 288 15 . . PUNCT ajst-24979 288 16 fractional fractional ADJ ajst-24979 288 17 calculus calculus NOUN ajst-24979 288 18 : : PUNCT ajst-24979 288 19 models model NOUN ajst-24979 288 20 and and CCONJ ajst-24979 288 21 numerical numerical ADJ ajst-24979 288 22 methods method NOUN ajst-24979 288 23 , , PUNCT ajst-24979 288 24 series series NOUN ajst-24979 288 25 on on ADP ajst-24979 288 26 complexity complexity NOUN ajst-24979 288 27 , , PUNCT ajst-24979 288 28 nonlinearity nonlinearity NOUN ajst-24979 288 29 and and CCONJ ajst-24979 288 30 chaos chaos NOUN ajst-24979 288 31 , , PUNCT ajst-24979 288 32 3(2012 3(2012 NUM ajst-24979 288 33 ) ) PUNCT ajst-24979 288 34 , , PUNCT ajst-24979 288 35 39133 39133 NUM ajst-24979 288 36 . . PUNCT ajst-24979 289 1 [ [ X ajst-24979 289 2 3 3 NUM ajst-24979 289 3 ] ] PUNCT ajst-24979 289 4 a. a. NOUN ajst-24979 289 5 a. a. NOUN ajst-24979 289 6 kilbas kilbas PROPN ajst-24979 289 7 , , PUNCT ajst-24979 289 8 h. h. PROPN ajst-24979 289 9 m. m. PROPN ajst-24979 289 10 srivastava srivastava PROPN ajst-24979 289 11 , , PUNCT ajst-24979 289 12 j. j. PROPN ajst-24979 289 13 j. j. PROPN ajst-24979 289 14 trujillo trujillo PROPN ajst-24979 289 15 . . PUNCT ajst-24979 289 16 theory theory NOUN ajst-24979 289 17 and and CCONJ ajst-24979 289 18 applications application NOUN ajst-24979 289 19 of of ADP ajst-24979 289 20 fractional fractional ADJ ajst-24979 289 21 differential differential ADJ ajst-24979 289 22 equations equation NOUN ajst-24979 289 23 . . PUNCT ajst-24979 290 1 elsevier elsevier PROPN ajst-24979 290 2 , , PUNCT ajst-24979 290 3 amsterdam amsterdam PROPN ajst-24979 290 4 , , PUNCT ajst-24979 290 5 204(2006 204(2006 NUM ajst-24979 290 6 ) ) PUNCT ajst-24979 290 7 , , PUNCT ajst-24979 290 8 1 1 NUM ajst-24979 290 9 - - SYM ajst-24979 290 10 523 523 NUM ajst-24979 290 11 . . PUNCT ajst-24979 291 1 [ [ X ajst-24979 291 2 4 4 X ajst-24979 291 3 ] ] X ajst-24979 291 4 n. n. PROPN ajst-24979 291 5 h. h. PROPN ajst-24979 291 6 abel abel PROPN ajst-24979 291 7 . . PUNCT ajst-24979 292 1 solution solution NOUN ajst-24979 292 2 de de X ajst-24979 292 3 quelques quelques X ajst-24979 292 4 problemes probleme NOUN ajst-24979 292 5 a a DET ajst-24979 292 6 l´aide l´aide NOUN ajst-24979 292 7 d´ıntegrales d´ıntegrale NOUN ajst-24979 292 8 definites definite NOUN ajst-24979 292 9 , , PUNCT ajst-24979 292 10 christiania christiania PROPN ajst-24979 292 11 grondahl grondahl PROPN ajst-24979 292 12 , , PUNCT ajst-24979 292 13 norway norway PROPN ajst-24979 292 14 , , PUNCT ajst-24979 292 15 1(1881 1(1881 NUM ajst-24979 292 16 ) ) PUNCT ajst-24979 292 17 , , PUNCT ajst-24979 292 18 16 16 NUM ajst-24979 292 19 - - SYM ajst-24979 292 20 18 18 NUM ajst-24979 292 21 . . PUNCT ajst-24979 293 1 [ [ X ajst-24979 293 2 5 5 NUM ajst-24979 293 3 ] ] PUNCT ajst-24979 293 4 a. a. NOUN ajst-24979 293 5 a. a. NOUN ajst-24979 293 6 hamoud hamoud PROPN ajst-24979 293 7 , , PUNCT ajst-24979 293 8 i. i. PROPN ajst-24979 293 9 y. y. PROPN ajst-24979 293 10 a. a. PROPN ajst-24979 293 11 alasadi alasadi PROPN ajst-24979 293 12 . . PUNCT ajst-24979 294 1 existence existence NOUN ajst-24979 294 2 and and CCONJ ajst-24979 294 3 stability stability NOUN ajst-24979 294 4 results result NOUN ajst-24979 294 5 for for ADP ajst-24979 294 6 fractional fractional ADJ ajst-24979 294 7 volterra volterra NOUN ajst-24979 294 8 - - PUNCT ajst-24979 294 9 fredholm fredholm NOUN ajst-24979 294 10 integro integro ADJ ajst-24979 294 11 - - PUNCT ajst-24979 294 12 dierential dierential ADJ ajst-24979 294 13 equation equation NOUN ajst-24979 294 14 with with ADP ajst-24979 294 15 mixed mixed ADJ ajst-24979 294 16 conditions condition NOUN ajst-24979 294 17 , , PUNCT ajst-24979 294 18 advances advance NOUN ajst-24979 294 19 in in ADP ajst-24979 294 20 dynamical dynamical ADJ ajst-24979 294 21 systems system NOUN ajst-24979 294 22 and and CCONJ ajst-24979 294 23 applications application NOUN ajst-24979 294 24 , , PUNCT ajst-24979 294 25 16(2021 16(2021 NUM ajst-24979 294 26 ) ) PUNCT ajst-24979 294 27 , , PUNCT ajst-24979 294 28 217 217 NUM ajst-24979 294 29 - - SYM ajst-24979 294 30 236 236 NUM ajst-24979 294 31 . . PUNCT ajst-24979 295 1 [ [ X ajst-24979 295 2 6 6 NUM ajst-24979 295 3 ] ] PUNCT ajst-24979 295 4 s. s. PROPN ajst-24979 295 5 andr´as andr´as PROPN ajst-24979 295 6 . . PUNCT ajst-24979 296 1 weakly weakly ADJ ajst-24979 296 2 singular singular PROPN ajst-24979 296 3 volterra volterra PROPN ajst-24979 296 4 and and CCONJ ajst-24979 296 5 fredholm fredholm NOUN ajst-24979 296 6 - - PUNCT ajst-24979 296 7 volterra volterra NOUN ajst-24979 296 8 integral integral ADJ ajst-24979 296 9 equations equation NOUN ajst-24979 296 10 , , PUNCT ajst-24979 296 11 studia studia PROPN ajst-24979 296 12 universitatis universitatis PROPN ajst-24979 296 13 babes babes PROPN ajst-24979 296 14 - - PUNCT ajst-24979 296 15 bolyai bolyai NOUN ajst-24979 296 16 . . PUNCT ajst-24979 297 1 mathematica mathematica PROPN ajst-24979 297 2 , , PUNCT ajst-24979 297 3 48(2003 48(2003 NUM ajst-24979 297 4 ) ) PUNCT ajst-24979 297 5 , , PUNCT ajst-24979 297 6 147 147 NUM ajst-24979 297 7 - - SYM ajst-24979 297 8 155 155 NUM ajst-24979 297 9 . . PUNCT ajst-24979 298 1 [ [ X ajst-24979 298 2 7 7 X ajst-24979 298 3 ] ] X ajst-24979 298 4 s. s. PROPN ajst-24979 298 5 abbas abbas PROPN ajst-24979 298 6 , , PUNCT ajst-24979 298 7 m. m. NOUN ajst-24979 298 8 benchohra benchohra NOUN ajst-24979 298 9 . . PUNCT ajst-24979 299 1 fractional fractional ADJ ajst-24979 299 2 order order NOUN ajst-24979 299 3 riemann riemann NOUN ajst-24979 299 4 - - PUNCT ajst-24979 299 5 liouville liouville VERB ajst-24979 299 6 integral integral ADJ ajst-24979 299 7 equations equation NOUN ajst-24979 299 8 with with ADP ajst-24979 299 9 multiple multiple ADJ ajst-24979 299 10 time time NOUN ajst-24979 299 11 delays delay NOUN ajst-24979 299 12 , , PUNCT ajst-24979 299 13 applied apply VERB ajst-24979 299 14 mathematics mathematic NOUN ajst-24979 299 15 e e NOUN ajst-24979 299 16 - - NOUN ajst-24979 299 17 notes note NOUN ajst-24979 299 18 [ [ X ajst-24979 299 19 electronic electronic ADJ ajst-24979 299 20 only only ADV ajst-24979 299 21 ] ] PUNCT ajst-24979 299 22 , , PUNCT ajst-24979 299 23 12(2012 12(2012 NUM ajst-24979 299 24 ) ) PUNCT ajst-24979 299 25 , , PUNCT ajst-24979 299 26 79 79 NUM ajst-24979 299 27 - - SYM ajst-24979 299 28 87 87 NUM ajst-24979 299 29 . . PUNCT ajst-24979 300 1 [ [ X ajst-24979 300 2 8 8 NUM ajst-24979 300 3 ] ] PUNCT ajst-24979 300 4 a. a. NOUN ajst-24979 300 5 atangana atangana PROPN ajst-24979 300 6 , , PUNCT ajst-24979 300 7 n. n. PROPN ajst-24979 300 8 bildik bildik VERB ajst-24979 300 9 . . PUNCT ajst-24979 301 1 existence existence NOUN ajst-24979 301 2 and and CCONJ ajst-24979 301 3 numerical numerical ADJ ajst-24979 301 4 solution solution NOUN ajst-24979 301 5 of of ADP ajst-24979 301 6 the the DET ajst-24979 301 7 volterra volterra NOUN ajst-24979 301 8 fractional fractional ADJ ajst-24979 301 9 integral integral ADJ ajst-24979 301 10 equations equation NOUN ajst-24979 301 11 of of ADP ajst-24979 301 12 the the DET ajst-24979 301 13 second second ADJ ajst-24979 301 14 kind kind NOUN ajst-24979 301 15 , , PUNCT ajst-24979 301 16 mathematical mathematical ADJ ajst-24979 301 17 problems problem NOUN ajst-24979 301 18 in in ADP ajst-24979 301 19 engineering engineering NOUN ajst-24979 301 20 , , PUNCT ajst-24979 301 21 2013(2013 2013(2013 NUM ajst-24979 301 22 ) ) PUNCT ajst-24979 301 23 , , PUNCT ajst-24979 301 24 1 1 NUM ajst-24979 301 25 - - SYM ajst-24979 301 26 11 11 NUM ajst-24979 301 27 . . PUNCT ajst-24979 302 1 [ [ X ajst-24979 302 2 9 9 NUM ajst-24979 302 3 ] ] PUNCT ajst-24979 302 4 v. v. ADP ajst-24979 302 5 laksmikantam laksmikantam NOUN ajst-24979 302 6 . . PUNCT ajst-24979 303 1 theory theory NOUN ajst-24979 303 2 of of ADP ajst-24979 303 3 fractional fractional ADJ ajst-24979 303 4 functional functional ADJ ajst-24979 303 5 differential differential NOUN ajst-24979 303 6 equations equation NOUN ajst-24979 303 7 , , PUNCT ajst-24979 303 8 nonlinear nonlinear ADJ ajst-24979 303 9 analysis analysis NOUN ajst-24979 303 10 : : PUNCT ajst-24979 303 11 theory theory NOUN ajst-24979 303 12 , , PUNCT ajst-24979 303 13 methods method NOUN ajst-24979 303 14 and and CCONJ ajst-24979 303 15 applications application NOUN ajst-24979 303 16 , , PUNCT ajst-24979 303 17 69(2008 69(2008 NOUN ajst-24979 303 18 ) ) PUNCT ajst-24979 303 19 , , PUNCT ajst-24979 303 20 3337 3337 NUM ajst-24979 303 21 - - SYM ajst-24979 303 22 3343 3343 NUM ajst-24979 303 23 . . PUNCT ajst-24979 304 1 [ [ X ajst-24979 304 2 10 10 NUM ajst-24979 304 3 ] ] PUNCT ajst-24979 304 4 s. s. PROPN ajst-24979 304 5 s. s. PROPN ajst-24979 304 6 l. l. PROPN ajst-24979 304 7 chang chang PROPN ajst-24979 304 8 , , PUNCT ajst-24979 304 9 l. l. PROPN ajst-24979 304 10 a. a. PROPN ajst-24979 304 11 zadeh zadeh PROPN ajst-24979 304 12 . . PUNCT ajst-24979 305 1 on on ADP ajst-24979 305 2 fuzzy fuzzy ADJ ajst-24979 305 3 mapping mapping NOUN ajst-24979 305 4 and and CCONJ ajst-24979 305 5 control control NOUN ajst-24979 305 6 , , PUNCT ajst-24979 305 7 ieee ieee NOUN ajst-24979 305 8 transactions transaction NOUN ajst-24979 305 9 on on ADP ajst-24979 305 10 systems system NOUN ajst-24979 305 11 , , PUNCT ajst-24979 305 12 man man NOUN ajst-24979 305 13 , , PUNCT ajst-24979 305 14 and and CCONJ ajst-24979 305 15 cybernetics cybernetic NOUN ajst-24979 305 16 , , PUNCT ajst-24979 305 17 2(1972 2(1972 NUM ajst-24979 305 18 ) ) PUNCT ajst-24979 305 19 , , PUNCT ajst-24979 305 20 30 30 NUM ajst-24979 305 21 - - SYM ajst-24979 305 22 34 34 NUM ajst-24979 305 23 . . PUNCT ajst-24979 306 1 [ [ X ajst-24979 306 2 11 11 NUM ajst-24979 306 3 ] ] PUNCT ajst-24979 306 4 l. l. PROPN ajst-24979 306 5 a. a. PROPN ajst-24979 306 6 zadeh zadeh PROPN ajst-24979 306 7 . . PUNCT ajst-24979 307 1 the the DET ajst-24979 307 2 concept concept NOUN ajst-24979 307 3 of of ADP ajst-24979 307 4 linguistic linguistic ADJ ajst-24979 307 5 variable variable NOUN ajst-24979 307 6 and and CCONJ ajst-24979 307 7 its its PRON ajst-24979 307 8 application application NOUN ajst-24979 307 9 to to PART ajst-24979 307 10 approximate approximate ADJ ajst-24979 307 11 reasoning reasoning NOUN ajst-24979 307 12 . . PUNCT ajst-24979 308 1 information information NOUN ajst-24979 308 2 sciences sciences PROPN ajst-24979 308 3 , , PUNCT ajst-24979 308 4 8 8 NUM ajst-24979 308 5 ( ( PUNCT ajst-24979 308 6 1975 1975 NUM ajst-24979 308 7 ) ) PUNCT ajst-24979 308 8 , , PUNCT ajst-24979 308 9 199 199 NUM ajst-24979 308 10 - - SYM ajst-24979 308 11 249 249 NUM ajst-24979 308 12 . . PUNCT ajst-24979 309 1 [ [ X ajst-24979 309 2 12 12 NUM ajst-24979 309 3 ] ] PUNCT ajst-24979 309 4 [ [ X ajst-24979 309 5 m. m. NOUN ajst-24979 309 6 mizumoto mizumoto NOUN ajst-24979 309 7 , , PUNCT ajst-24979 309 8 k. k. PROPN ajst-24979 309 9 tanaka tanaka PROPN ajst-24979 309 10 , , PUNCT ajst-24979 309 11 the the DET ajst-24979 309 12 four four NUM ajst-24979 309 13 operations operation NOUN ajst-24979 309 14 of of ADP ajst-24979 309 15 arithmetic arithmetic ADJ ajst-24979 309 16 on on ADP ajst-24979 309 17 fuzzy fuzzy ADJ ajst-24979 309 18 numbers number NOUN ajst-24979 309 19 , , PUNCT ajst-24979 309 20 systems system NOUN ajst-24979 309 21 comput comput NOUN ajst-24979 309 22 controls control NOUN ajst-24979 309 23 , , PUNCT ajst-24979 309 24 7(1976 7(1976 NUM ajst-24979 309 25 ) ) PUNCT ajst-24979 309 26 , , PUNCT ajst-24979 309 27 73 73 NUM ajst-24979 309 28 - - SYM ajst-24979 309 29 81 81 NUM ajst-24979 309 30 . . PUNCT ajst-24979 310 1 [ [ X ajst-24979 310 2 13 13 NUM ajst-24979 310 3 ] ] X ajst-24979 310 4 d. d. PROPN ajst-24979 310 5 dubois dubois PROPN ajst-24979 310 6 , , PUNCT ajst-24979 310 7 h. h. PROPN ajst-24979 310 8 prade prade PROPN ajst-24979 310 9 . . PUNCT ajst-24979 311 1 towards towards ADP ajst-24979 311 2 fuzzy fuzzy ADJ ajst-24979 311 3 differential differential ADJ ajst-24979 311 4 calculus calculus NOUN ajst-24979 311 5 , , PUNCT ajst-24979 311 6 part part NOUN ajst-24979 311 7 i i NOUN ajst-24979 311 8 : : PUNCT ajst-24979 311 9 integration integration NOUN ajst-24979 311 10 of of ADP ajst-24979 311 11 fuzzy fuzzy ADJ ajst-24979 311 12 mappings mapping NOUN ajst-24979 311 13 , , PUNCT ajst-24979 311 14 class class NOUN ajst-24979 311 15 of of ADP ajst-24979 311 16 second second ADJ ajst-24979 311 17 - - PUNCT ajst-24979 311 18 order order NOUN ajst-24979 311 19 . . PUNCT ajst-24979 312 1 fuzzy fuzzy ADJ ajst-24979 312 2 sets set NOUN ajst-24979 312 3 and and CCONJ ajst-24979 312 4 systems system NOUN ajst-24979 312 5 , , PUNCT ajst-24979 312 6 8(1982 8(1982 NUM ajst-24979 312 7 ) ) PUNCT ajst-24979 312 8 , , PUNCT ajst-24979 312 9 1 1 NUM ajst-24979 312 10 - - SYM ajst-24979 312 11 17 17 NUM ajst-24979 312 12 . . PUNCT ajst-24979 313 1 [ [ X ajst-24979 313 2 14 14 NUM ajst-24979 313 3 ] ] X ajst-24979 313 4 m. m. NOUN ajst-24979 313 5 puri puri PROPN ajst-24979 313 6 , , PUNCT ajst-24979 313 7 d. d. PROPN ajst-24979 313 8 ralescu ralescu PROPN ajst-24979 313 9 . . PUNCT ajst-24979 314 1 differentials differential NOUN ajst-24979 314 2 of of ADP ajst-24979 314 3 fuzzy fuzzy ADJ ajst-24979 314 4 functions function NOUN ajst-24979 314 5 . . PUNCT ajst-24979 315 1 journal journal NOUN ajst-24979 315 2 of of ADP ajst-24979 315 3 mathematical mathematical ADJ ajst-24979 315 4 analysis analysis NOUN ajst-24979 315 5 and and CCONJ ajst-24979 315 6 applications application NOUN ajst-24979 315 7 , , PUNCT ajst-24979 315 8 91 91 NUM ajst-24979 315 9 ( ( PUNCT ajst-24979 315 10 1983 1983 NUM ajst-24979 315 11 ) ) PUNCT ajst-24979 315 12 , , PUNCT ajst-24979 315 13 552558 552558 NUM ajst-24979 315 14 . . PUNCT ajst-24979 316 1 [ [ X ajst-24979 316 2 15 15 NUM ajst-24979 316 3 ] ] X ajst-24979 316 4 b. b. PROPN ajst-24979 316 5 bede bede PROPN ajst-24979 316 6 , , PUNCT ajst-24979 316 7 s. s. PROPN ajst-24979 316 8 g. g. PROPN ajst-24979 316 9 gal gal PROPN ajst-24979 316 10 . . PUNCT ajst-24979 317 1 generalizations generalization NOUN ajst-24979 317 2 of of ADP ajst-24979 317 3 the the DET ajst-24979 317 4 differentiability differentiability NOUN ajst-24979 317 5 of of ADP ajst-24979 317 6 fuzzy fuzzy ADJ ajst-24979 317 7 number number NOUN ajst-24979 317 8 valued value VERB ajst-24979 317 9 functions function NOUN ajst-24979 317 10 with with ADP ajst-24979 317 11 applications application NOUN ajst-24979 317 12 to to ADP ajst-24979 317 13 fuzzy fuzzy ADJ ajst-24979 317 14 differential differential ADJ ajst-24979 317 15 equations equation NOUN ajst-24979 317 16 . . PUNCT ajst-24979 318 1 fuzzy fuzzy ADJ ajst-24979 318 2 sets set NOUN ajst-24979 318 3 and and CCONJ ajst-24979 318 4 systems system NOUN ajst-24979 318 5 , , PUNCT ajst-24979 318 6 151(2005 151(2005 NUM ajst-24979 318 7 ) ) PUNCT ajst-24979 318 8 , , PUNCT ajst-24979 318 9 581 581 NUM ajst-24979 318 10 - - SYM ajst-24979 318 11 599 599 NUM ajst-24979 318 12 . . PUNCT ajst-24979 319 1 [ [ X ajst-24979 319 2 16 16 NUM ajst-24979 319 3 ] ] PUNCT ajst-24979 319 4 s. s. PROPN ajst-24979 319 5 j. j. PROPN ajst-24979 319 6 liao liao PROPN ajst-24979 319 7 . . PROPN ajst-24979 320 1 on on ADP ajst-24979 320 2 the the DET ajst-24979 320 3 homotopy homotopy NOUN ajst-24979 320 4 analysis analysis NOUN ajst-24979 320 5 method method NOUN ajst-24979 320 6 for for ADP ajst-24979 320 7 nonlinear nonlinear ADJ ajst-24979 320 8 problem problem NOUN ajst-24979 320 9 , , PUNCT ajst-24979 320 10 applied apply VERB ajst-24979 320 11 mathematics mathematic NOUN ajst-24979 320 12 and and CCONJ ajst-24979 320 13 computation computation NOUN ajst-24979 320 14 , , PUNCT ajst-24979 320 15 147(2004 147(2004 NUM ajst-24979 320 16 ) ) PUNCT ajst-24979 320 17 , , PUNCT ajst-24979 320 18 499 499 NUM ajst-24979 320 19 - - SYM ajst-24979 320 20 513 513 NUM ajst-24979 320 21 . . PUNCT ajst-24979 321 1 [ [ X ajst-24979 321 2 17 17 NUM ajst-24979 321 3 ] ] PUNCT ajst-24979 321 4 a. a. NOUN ajst-24979 321 5 a. a. NOUN ajst-24979 321 6 hamoud hamoud PROPN ajst-24979 321 7 , , PUNCT ajst-24979 321 8 k. k. PROPN ajst-24979 321 9 p. p. PROPN ajst-24979 321 10 ghadle ghadle PROPN ajst-24979 321 11 . . PUNCT ajst-24979 322 1 homotopy homotopy VERB ajst-24979 322 2 analysis analysis NOUN ajst-24979 322 3 method method NOUN ajst-24979 322 4 for for ADP ajst-24979 322 5 the the DET ajst-24979 322 6 first first ADJ ajst-24979 322 7 order order NOUN ajst-24979 322 8 fuzzy fuzzy ADJ ajst-24979 322 9 volterra volterra NOUN ajst-24979 322 10 - - PUNCT ajst-24979 322 11 fredholm fredholm NOUN ajst-24979 322 12 integro integro ADJ ajst-24979 322 13 - - PUNCT ajst-24979 322 14 differential differential NOUN ajst-24979 322 15 equations equation NOUN ajst-24979 322 16 . . PUNCT ajst-24979 323 1 indonesian indonesian ADJ ajst-24979 323 2 journal journal PROPN ajst-24979 323 3 of of ADP ajst-24979 323 4 electrical electrical ADJ ajst-24979 323 5 engineering engineering NOUN ajst-24979 323 6 and and CCONJ ajst-24979 323 7 computer computer NOUN ajst-24979 323 8 science science NOUN ajst-24979 323 9 , , PUNCT ajst-24979 323 10 11(2018 11(2018 NUM ajst-24979 323 11 ) ) PUNCT ajst-24979 323 12 . . PUNCT ajst-24979 324 1 857 857 NUM ajst-24979 324 2 - - SYM ajst-24979 324 3 867 867 NUM ajst-24979 324 4 . . PUNCT ajst-24979 325 1 [ [ X ajst-24979 325 2 18 18 NUM ajst-24979 325 3 ] ] X ajst-24979 325 4 e. e. PROPN ajst-24979 325 5 hussain hussain PROPN ajst-24979 325 6 , , PUNCT ajst-24979 325 7 a. a. PROPN ajst-24979 325 8 ali ali PROPN ajst-24979 325 9 . . PUNCT ajst-24979 325 10 homotopy homotopy VERB ajst-24979 325 11 analysis analysis NOUN ajst-24979 325 12 method method NOUN ajst-24979 325 13 for for ADP ajst-24979 325 14 solving solve VERB ajst-24979 325 15 fuzzy fuzzy ADJ ajst-24979 325 16 integrodifferential integrodifferential ADJ ajst-24979 325 17 equations equation NOUN ajst-24979 325 18 , , PUNCT ajst-24979 325 19 modern modern ADJ ajst-24979 325 20 applied apply VERB ajst-24979 325 21 science science NOUN ajst-24979 325 22 , , PUNCT ajst-24979 325 23 7 7 NUM ajst-24979 325 24 ( ( PUNCT ajst-24979 325 25 2013 2013 NUM ajst-24979 325 26 ) ) PUNCT ajst-24979 325 27 , , PUNCT ajst-24979 325 28 15 15 NUM ajst-24979 325 29 - - SYM ajst-24979 325 30 25 25 NUM ajst-24979 325 31 . . PUNCT ajst-24979 326 1 [ [ X ajst-24979 326 2 19 19 NUM ajst-24979 326 3 ] ] X ajst-24979 326 4 i. i. PROPN ajst-24979 326 5 k. k. PROPN ajst-24979 326 6 hanan hanan PROPN ajst-24979 326 7 . . PUNCT ajst-24979 327 1 the the DET ajst-24979 327 2 homotopy homotopy NOUN ajst-24979 327 3 analysis analysis NOUN ajst-24979 327 4 method method NOUN ajst-24979 327 5 for for ADP ajst-24979 327 6 solving solve VERB ajst-24979 327 7 multifractional multifractional ADJ ajst-24979 327 8 orderintegro orderintegro ADJ ajst-24979 327 9 - - PUNCT ajst-24979 327 10 differential differential NOUN ajst-24979 327 11 equations equation NOUN ajst-24979 327 12 , , PUNCT ajst-24979 327 13 journal journal NOUN ajst-24979 327 14 of of ADP ajst-24979 327 15 alnahrain alnahrain PROPN ajst-24979 327 16 university university NOUN ajst-24979 327 17 science science NOUN ajst-24979 327 18 , , PUNCT ajst-24979 327 19 14(2011 14(2011 NUM ajst-24979 327 20 ) ) PUNCT ajst-24979 327 21 , , PUNCT ajst-24979 327 22 139 139 NUM ajst-24979 327 23 - - SYM ajst-24979 327 24 143 143 NUM ajst-24979 327 25 . . PUNCT ajst-24979 328 1 [ [ X ajst-24979 328 2 20 20 NUM ajst-24979 328 3 ] ] PUNCT ajst-24979 328 4 a. a. NOUN ajst-24979 328 5 a. a. NOUN ajst-24979 328 6 hamoud hamoud PROPN ajst-24979 328 7 , , PUNCT ajst-24979 328 8 k. k. PROPN ajst-24979 329 1 p. p. PROPN ajst-24979 329 2 ghadle ghadle PROPN ajst-24979 329 3 , , PUNCT ajst-24979 329 4 s. s. PROPN ajst-24979 329 5 m. m. PROPN ajst-24979 329 6 atshan atshan PROPN ajst-24979 329 7 . . PUNCT ajst-24979 330 1 the the DET ajst-24979 330 2 approximate approximate ADJ ajst-24979 330 3 solutions solution NOUN ajst-24979 330 4 offractional offractional ADJ ajst-24979 330 5 integro integro ADJ ajst-24979 330 6 - - PUNCT ajst-24979 330 7 differential differential NOUN ajst-24979 330 8 equations equation NOUN ajst-24979 330 9 by by ADP ajst-24979 330 10 using use VERB ajst-24979 330 11 modified modify VERB ajst-24979 330 12 adomian adomian NOUN ajst-24979 330 13 decomposition decomposition NOUN ajst-24979 330 14 method method NOUN ajst-24979 330 15 . . PUNCT ajst-24979 331 1 khayyam khayyam PROPN ajst-24979 331 2 journal journal PROPN ajst-24979 331 3 of of ADP ajst-24979 331 4 mathematics mathematic NOUN ajst-24979 331 5 , , PUNCT ajst-24979 331 6 5(2019 5(2019 NUM ajst-24979 331 7 ) ) PUNCT ajst-24979 331 8 , , PUNCT ajst-24979 331 9 21 21 NUM ajst-24979 331 10 - - SYM ajst-24979 331 11 39 39 NUM ajst-24979 331 12 . . PUNCT ajst-24979 332 1 [ [ X ajst-24979 332 2 21 21 NUM ajst-24979 332 3 ] ] X ajst-24979 332 4 m. m. NOUN ajst-24979 332 5 sh sh PROPN ajst-24979 332 6 . . PROPN ajst-24979 332 7 bani bani PROPN ajst-24979 332 8 issa issa PROPN ajst-24979 332 9 , , PUNCT ajst-24979 332 10 a. a. NOUN ajst-24979 332 11 a. a. NOUN ajst-24979 332 12 hamoud hamoud PROPN ajst-24979 332 13 , , PUNCT ajst-24979 332 14 k. k. PROPN ajst-24979 332 15 p. p. PROPN ajst-24979 332 16 ghadle ghadle PROPN ajst-24979 332 17 . . PUNCT ajst-24979 333 1 numerical numerical ADJ ajst-24979 333 2 solutions solution NOUN ajst-24979 333 3 of of ADP ajst-24979 333 4 fuzzy fuzzy ADJ ajst-24979 333 5 integro integro ADJ ajst-24979 333 6 - - PUNCT ajst-24979 333 7 differential differential NOUN ajst-24979 333 8 equations equation NOUN ajst-24979 333 9 of of ADP ajst-24979 333 10 the the DET ajst-24979 333 11 second second ADJ ajst-24979 333 12 kind kind NOUN ajst-24979 333 13 . . PUNCT ajst-24979 334 1 journal journal NOUN ajst-24979 334 2 of of ADP ajst-24979 334 3 mathematics mathematic NOUN ajst-24979 334 4 and and CCONJ ajst-24979 334 5 computer computer NOUN ajst-24979 334 6 science science NOUN ajst-24979 334 7 , , PUNCT ajst-24979 334 8 23(2021 23(2021 NUM ajst-24979 334 9 ) ) PUNCT ajst-24979 334 10 , , PUNCT ajst-24979 334 11 67 67 NUM ajst-24979 334 12 - - SYM ajst-24979 334 13 74 74 NUM ajst-24979 334 14 . . PUNCT ajst-24979 334 15 177 177 NUM ajst-24979 335 1 [ [ SYM ajst-24979 335 2 22 22 NUM ajst-24979 335 3 ] ] PUNCT ajst-24979 335 4 s. s. PROPN ajst-24979 335 5 salahshour salahshour PROPN ajst-24979 335 6 , , PUNCT ajst-24979 335 7 a. a. PROPN ajst-24979 335 8 ahmadian ahmadian PROPN ajst-24979 335 9 , , PUNCT ajst-24979 335 10 c. c. PROPN ajst-24979 335 11 s. s. PROPN ajst-24979 335 12 chan chan PROPN ajst-24979 335 13 . . PUNCT ajst-24979 336 1 a a DET ajst-24979 336 2 novel novel ADJ ajst-24979 336 3 technique technique NOUN ajst-24979 336 4 for for ADP ajst-24979 336 5 solving solve VERB ajst-24979 336 6 fuzzy fuzzy ADJ ajst-24979 336 7 differential differential ADJ ajst-24979 336 8 equations equation NOUN ajst-24979 336 9 of of ADP ajst-24979 336 10 fractional fractional ADJ ajst-24979 336 11 order order NOUN ajst-24979 336 12 using use VERB ajst-24979 336 13 laplace laplace NOUN ajst-24979 336 14 and and CCONJ ajst-24979 336 15 integral integral ADJ ajst-24979 336 16 transforms transform NOUN ajst-24979 336 17 , , PUNCT ajst-24979 336 18 2016 2016 NUM ajst-24979 336 19 ieee ieee NOUN ajst-24979 336 20 international international ADJ ajst-24979 336 21 conference conference NOUN ajst-24979 336 22 on on ADP ajst-24979 336 23 fuzzy fuzzy ADJ ajst-24979 336 24 systems system NOUN ajst-24979 336 25 ( ( PUNCT ajst-24979 336 26 fuzz fuzz NOUN ajst-24979 336 27 - - PUNCT ajst-24979 336 28 ieee ieee NOUN ajst-24979 336 29 ) ) PUNCT ajst-24979 336 30 , , PUNCT ajst-24979 336 31 2016 2016 NUM ajst-24979 336 32 , , PUNCT ajst-24979 336 33 1473 1473 NUM ajst-24979 336 34 - - SYM ajst-24979 336 35 1477 1477 NUM ajst-24979 336 36 . . PUNCT ajst-24979 337 1 [ [ X ajst-24979 337 2 23 23 NUM ajst-24979 337 3 ] ] PUNCT ajst-24979 337 4 s. s. PROPN ajst-24979 337 5 salahshour salahshour PROPN ajst-24979 337 6 , , PUNCT ajst-24979 337 7 t. t. PROPN ajst-24979 337 8 allahviranloo allahviranloo PROPN ajst-24979 337 9 , , PUNCT ajst-24979 337 10 s. s. PROPN ajst-24979 337 11 abbasbandy abbasbandy PROPN ajst-24979 337 12 . . PUNCT ajst-24979 338 1 solving solve VERB ajst-24979 338 2 fuzzy fuzzy ADJ ajst-24979 338 3 fractional fractional ADJ ajst-24979 338 4 differential differential ADJ ajst-24979 338 5 equations equation NOUN ajst-24979 338 6 by by ADP ajst-24979 338 7 fuzzy fuzzy ADJ ajst-24979 338 8 laplace laplace NOUN ajst-24979 338 9 transforms transform VERB ajst-24979 338 10 , , PUNCT ajst-24979 338 11 commun commun PROPN ajst-24979 338 12 nonlinear nonlinear PROPN ajst-24979 338 13 sci sci PROPN ajst-24979 338 14 numer numer PROPN ajst-24979 338 15 simulat simulat PROPN ajst-24979 338 16 , , PUNCT ajst-24979 338 17 17(2012 17(2012 NOUN ajst-24979 338 18 ) ) PUNCT ajst-24979 338 19 , , PUNCT ajst-24979 338 20 1372 1372 NUM ajst-24979 338 21 - - SYM ajst-24979 338 22 1381 1381 NUM ajst-24979 338 23 . . PUNCT ajst-24979 339 1 [ [ X ajst-24979 339 2 24 24 NUM ajst-24979 339 3 ] ] X ajst-24979 339 4 h. h. PROPN ajst-24979 339 5 zureigat zureigat PROPN ajst-24979 339 6 , , PUNCT ajst-24979 339 7 a. a. PROPN ajst-24979 339 8 i. i. PROPN ajst-24979 339 9 ismail ismail PROPN ajst-24979 339 10 , , PUNCT ajst-24979 339 11 s. s. PROPN ajst-24979 339 12 sathasivam sathasivam VERB ajst-24979 339 13 . . PUNCT ajst-24979 340 1 numerical numerical ADJ ajst-24979 340 2 solutions solution NOUN ajst-24979 340 3 of of ADP ajst-24979 340 4 fuzzy fuzzy ADJ ajst-24979 340 5 fractional fractional ADJ ajst-24979 340 6 diffusion diffusion NOUN ajst-24979 340 7 equations equation NOUN ajst-24979 340 8 by by ADP ajst-24979 340 9 an an DET ajst-24979 340 10 implicit implicit ADJ ajst-24979 340 11 finite finite ADJ ajst-24979 340 12 difference difference NOUN ajst-24979 340 13 scheme scheme NOUN ajst-24979 340 14 , , PUNCT ajst-24979 340 15 neural neural ADJ ajst-24979 340 16 computing computing NOUN ajst-24979 340 17 and and CCONJ ajst-24979 340 18 applications application NOUN ajst-24979 340 19 , , PUNCT ajst-24979 340 20 31 31 NUM ajst-24979 340 21 ( ( PUNCT ajst-24979 340 22 2018 2018 NUM ajst-24979 340 23 ) ) PUNCT ajst-24979 340 24 , , PUNCT ajst-24979 340 25 4085 4085 NUM ajst-24979 340 26 - - SYM ajst-24979 340 27 4094 4094 NUM ajst-24979 340 28 . . PUNCT ajst-24979 341 1 [ [ X ajst-24979 341 2 25 25 NUM ajst-24979 341 3 ] ] PUNCT ajst-24979 341 4 a. a. NOUN ajst-24979 341 5 a. a. NOUN ajst-24979 341 6 hamoud hamoud PROPN ajst-24979 341 7 , , PUNCT ajst-24979 341 8 a. a. PROPN ajst-24979 341 9 d. d. PROPN ajst-24979 341 10 azeez azeez PROPN ajst-24979 341 11 , , PUNCT ajst-24979 341 12 k. k. PROPN ajst-24979 342 1 p. p. PROPN ajst-24979 342 2 ghadle ghadle PROPN ajst-24979 342 3 . . PUNCT ajst-24979 343 1 a a DET ajst-24979 343 2 study study NOUN ajst-24979 343 3 of of ADP ajst-24979 343 4 some some DET ajst-24979 343 5 iterative iterative NOUN ajst-24979 343 6 methods method NOUN ajst-24979 343 7 for for ADP ajst-24979 343 8 solving solve VERB ajst-24979 343 9 fuzzy fuzzy ADJ ajst-24979 343 10 volterra volterra NOUN ajst-24979 343 11 - - PUNCT ajst-24979 343 12 fredholm fredholm NOUN ajst-24979 343 13 integral integral ADJ ajst-24979 343 14 equations equation NOUN ajst-24979 343 15 . . PUNCT ajst-24979 344 1 indonesian indonesian ADJ ajst-24979 344 2 journal journal PROPN ajst-24979 344 3 of of ADP ajst-24979 344 4 electrical electrical ADJ ajst-24979 344 5 engineering engineering NOUN ajst-24979 344 6 and and CCONJ ajst-24979 344 7 computer computer NOUN ajst-24979 344 8 science science NOUN ajst-24979 344 9 , , PUNCT ajst-24979 344 10 11(2018 11(2018 NUM ajst-24979 344 11 ) ) PUNCT ajst-24979 344 12 , , PUNCT ajst-24979 344 13 1228 1228 NUM ajst-24979 344 14 - - SYM ajst-24979 344 15 1235 1235 NUM ajst-24979 344 16 . . PUNCT ajst-24979 345 1 [ [ X ajst-24979 345 2 26 26 NUM ajst-24979 345 3 ] ] X ajst-24979 345 4 s. s. PROPN ajst-24979 345 5 arshad arshad PROPN ajst-24979 345 6 , , PUNCT ajst-24979 345 7 v. v. ADP ajst-24979 345 8 lupulescu lupulescu NOUN ajst-24979 345 9 . . PUNCT ajst-24979 346 1 on on ADP ajst-24979 346 2 the the DET ajst-24979 346 3 fractional fractional ADJ ajst-24979 346 4 differential differential ADJ ajst-24979 346 5 equations equation NOUN ajst-24979 346 6 with with ADP ajst-24979 346 7 uncertainty uncertainty NOUN ajst-24979 346 8 , , PUNCT ajst-24979 346 9 nonlinear nonlinear ADJ ajst-24979 346 10 analysis analysis NOUN ajst-24979 346 11 : : PUNCT ajst-24979 346 12 theory theory NOUN ajst-24979 346 13 , , PUNCT ajst-24979 346 14 methods method NOUN ajst-24979 346 15 and and CCONJ ajst-24979 346 16 applications application NOUN ajst-24979 346 17 , , PUNCT ajst-24979 346 18 74(2011 74(2011 PROPN ajst-24979 346 19 ) ) PUNCT ajst-24979 346 20 , , PUNCT ajst-24979 346 21 85 85 NUM ajst-24979 346 22 - - SYM ajst-24979 346 23 93 93 NUM ajst-24979 346 24 . . PUNCT ajst-24979 347 1 [ [ X ajst-24979 347 2 27 27 NUM ajst-24979 347 3 ] ] X ajst-24979 347 4 s. s. PROPN ajst-24979 347 5 arshad arshad PROPN ajst-24979 347 6 , , PUNCT ajst-24979 347 7 v. v. PROPN ajst-24979 347 8 luplescu luplescu PROPN ajst-24979 347 9 . . PUNCT ajst-24979 348 1 fractional fractional ADJ ajst-24979 348 2 differential differential ADJ ajst-24979 348 3 equation equation NOUN ajst-24979 348 4 with with ADP ajst-24979 348 5 fuzzy fuzzy ADJ ajst-24979 348 6 initial initial ADJ ajst-24979 348 7 conditon conditon NOUN ajst-24979 348 8 , , PUNCT ajst-24979 348 9 electronic electronic ADJ ajst-24979 348 10 journal journal NOUN ajst-24979 348 11 of of ADP ajst-24979 348 12 differential differential ADJ ajst-24979 348 13 equations equation NOUN ajst-24979 348 14 , , PUNCT ajst-24979 348 15 34(2011 34(2011 NUM ajst-24979 348 16 ) ) PUNCT ajst-24979 348 17 , , PUNCT ajst-24979 348 18 1 1 NUM ajst-24979 348 19 - - SYM ajst-24979 348 20 8 8 NUM ajst-24979 348 21 . . PUNCT ajst-24979 349 1 [ [ X ajst-24979 349 2 28 28 NUM ajst-24979 349 3 ] ] X ajst-24979 349 4 n. n. PROPN ajst-24979 349 5 ahmad ahmad PROPN ajst-24979 349 6 , , PUNCT ajst-24979 349 7 a. a. PROPN ajst-24979 349 8 ullah ullah PROPN ajst-24979 349 9 , , PUNCT ajst-24979 349 10 a. a. PROPN ajst-24979 349 11 ullah ullah PROPN ajst-24979 349 12 , , PUNCT ajst-24979 349 13 s. s. PROPN ajst-24979 349 14 ahmad ahmad PROPN ajst-24979 349 15 , , PUNCT ajst-24979 349 16 k. k. PROPN ajst-24979 349 17 shah shah PROPN ajst-24979 349 18 , , PUNCT ajst-24979 349 19 i. i. PROPN ajst-24979 349 20 ahmad ahmad PROPN ajst-24979 349 21 . . PUNCT ajst-24979 350 1 on on ADP ajst-24979 350 2 analysis analysis NOUN ajst-24979 350 3 of of ADP ajst-24979 350 4 the the DET ajst-24979 350 5 fuzzy fuzzy ADJ ajst-24979 350 6 fractional fractional ADJ ajst-24979 350 7 order order NOUN ajst-24979 350 8 volterra volterra NOUN ajst-24979 350 9 - - PUNCT ajst-24979 350 10 fredholm fredholm NOUN ajst-24979 350 11 integro integro ADJ ajst-24979 350 12 - - PUNCT ajst-24979 350 13 differential differential NOUN ajst-24979 350 14 equation equation NOUN ajst-24979 350 15 . . PUNCT ajst-24979 351 1 alexandria alexandria PROPN ajst-24979 351 2 engineering engineering PROPN ajst-24979 351 3 journal journal PROPN ajst-24979 351 4 , , PUNCT ajst-24979 351 5 60(2020 60(2020 NUM ajst-24979 351 6 ) ) PUNCT ajst-24979 351 7 , , PUNCT ajst-24979 351 8 1827 1827 NUM ajst-24979 351 9 - - SYM ajst-24979 351 10 1838 1838 NUM ajst-24979 351 11 . . PUNCT ajst-24979 352 1 [ [ X ajst-24979 352 2 29 29 NUM ajst-24979 352 3 ] ] X ajst-24979 352 4 t. t. NOUN ajst-24979 352 5 allahviranloo allahviranloo PROPN ajst-24979 352 6 , , PUNCT ajst-24979 352 7 a. a. PROPN ajst-24979 352 8 armand armand PROPN ajst-24979 352 9 , , PUNCT ajst-24979 352 10 z. z. PROPN ajst-24979 352 11 gouyandeh gouyandeh PROPN ajst-24979 352 12 , , PUNCT ajst-24979 352 13 h. h. PROPN ajst-24979 352 14 ghadiri ghadiri PROPN ajst-24979 352 15 . . PUNCT ajst-24979 353 1 existence existence NOUN ajst-24979 353 2 and and CCONJ ajst-24979 353 3 uniqueness uniqueness NOUN ajst-24979 353 4 of of ADP ajst-24979 353 5 solutions solution NOUN ajst-24979 353 6 for for ADP ajst-24979 353 7 fuzzy fuzzy ADJ ajst-24979 353 8 fractional fractional ADJ ajst-24979 353 9 volterra volterra NOUN ajst-24979 353 10 - - PUNCT ajst-24979 353 11 fredholm fredholm NOUN ajst-24979 353 12 integro integro ADJ ajst-24979 353 13 - - PUNCT ajst-24979 353 14 differential differential NOUN ajst-24979 353 15 equations equation NOUN ajst-24979 353 16 . . PUNCT ajst-24979 354 1 journal journal NOUN ajst-24979 354 2 of of ADP ajst-24979 354 3 fuzzy fuzzy ADJ ajst-24979 354 4 set set VERB ajst-24979 354 5 valued value VERB ajst-24979 354 6 analysis analysis NOUN ajst-24979 354 7 , , PUNCT ajst-24979 354 8 2013(2013 2013(2013 NUM ajst-24979 354 9 ) ) PUNCT ajst-24979 354 10 , , PUNCT ajst-24979 354 11 1 1 NUM ajst-24979 354 12 - - SYM ajst-24979 354 13 9 9 NUM ajst-24979 354 14 . . PUNCT ajst-24979 355 1 [ [ X ajst-24979 355 2 30 30 NUM ajst-24979 355 3 ] ] X ajst-24979 355 4 a. a. PROPN ajst-24979 355 5 armand armand PROPN ajst-24979 355 6 , , PUNCT ajst-24979 355 7 z. z. PROPN ajst-24979 355 8 gouyandeh gouyandeh PROPN ajst-24979 355 9 . . PUNCT ajst-24979 356 1 fuzzy fuzzy ADJ ajst-24979 356 2 fractional fractional ADJ ajst-24979 356 3 integrodifferential integrodifferential ADJ ajst-24979 356 4 equations equation NOUN ajst-24979 356 5 under under ADP ajst-24979 356 6 generalized generalized ADJ ajst-24979 356 7 capotu capotu NOUN ajst-24979 356 8 differentiability differentiability NOUN ajst-24979 356 9 , , PUNCT ajst-24979 356 10 annals annal NOUN ajst-24979 356 11 of of ADP ajst-24979 356 12 fuzzy fuzzy ADJ ajst-24979 356 13 mathematics mathematic NOUN ajst-24979 356 14 and and CCONJ ajst-24979 356 15 infor infor PROPN ajst-24979 356 16 matics matic NOUN ajst-24979 356 17 , , PUNCT ajst-24979 356 18 10(2015 10(2015 NUM ajst-24979 356 19 ) ) PUNCT ajst-24979 356 20 , , PUNCT ajst-24979 356 21 789 789 NUM ajst-24979 356 22 - - SYM ajst-24979 356 23 798 798 NUM ajst-24979 356 24 . . PUNCT ajst-24979 357 1 [ [ X ajst-24979 357 2 31 31 NUM ajst-24979 357 3 ] ] PUNCT ajst-24979 357 4 s. s. PROPN ajst-24979 357 5 salahshour salahshour PROPN ajst-24979 357 6 , , PUNCT ajst-24979 357 7 a. a. PROPN ajst-24979 357 8 ahmadian ahmadian PROPN ajst-24979 357 9 , , PUNCT ajst-24979 357 10 n. n. PROPN ajst-24979 357 11 senu senu PROPN ajst-24979 357 12 , , PUNCT ajst-24979 357 13 d. d. PROPN ajst-24979 357 14 baleanu baleanu PROPN ajst-24979 357 15 , , PUNCT ajst-24979 357 16 p. p. PROPN ajst-24979 357 17 agarwal agarwal PROPN ajst-24979 357 18 . . PUNCT ajst-24979 358 1 on on ADP ajst-24979 358 2 analytical analytical ADJ ajst-24979 358 3 solutions solution NOUN ajst-24979 358 4 of of ADP ajst-24979 358 5 the the DET ajst-24979 358 6 fractional fractional ADJ ajst-24979 358 7 differential differential ADJ ajst-24979 358 8 equation equation NOUN ajst-24979 358 9 with with ADP ajst-24979 358 10 uncertinity uncertinity NOUN ajst-24979 358 11 : : PUNCT ajst-24979 358 12 application application NOUN ajst-24979 358 13 to to ADP ajst-24979 358 14 the the DET ajst-24979 358 15 basset basset NOUN ajst-24979 358 16 problem problem NOUN ajst-24979 358 17 , , PUNCT ajst-24979 358 18 entropy entropy PROPN ajst-24979 358 19 , , PUNCT ajst-24979 358 20 17(2015 17(2015 NUM ajst-24979 358 21 ) ) PUNCT ajst-24979 358 22 , , PUNCT ajst-24979 358 23 855 855 NUM ajst-24979 358 24 - - SYM ajst-24979 358 25 902 902 NUM ajst-24979 358 26 . . PUNCT ajst-24979 359 1 [ [ X ajst-24979 359 2 32 32 NUM ajst-24979 359 3 ] ] X ajst-24979 359 4 d. d. PROPN ajst-24979 359 5 dubois dubois PROPN ajst-24979 359 6 , , PUNCT ajst-24979 359 7 h. h. PROPN ajst-24979 359 8 prade prade PROPN ajst-24979 359 9 . . PUNCT ajst-24979 360 1 operations operation NOUN ajst-24979 360 2 on on ADP ajst-24979 360 3 fuzzy fuzzy ADJ ajst-24979 360 4 numbers number NOUN ajst-24979 360 5 . . PUNCT ajst-24979 361 1 international international ADJ ajst-24979 361 2 journal journal PROPN ajst-24979 361 3 of of ADP ajst-24979 361 4 systems system NOUN ajst-24979 361 5 science science NOUN ajst-24979 361 6 , , PUNCT ajst-24979 361 7 9(1978 9(1978 NUM ajst-24979 361 8 ) ) PUNCT ajst-24979 361 9 , , PUNCT ajst-24979 361 10 613 613 NUM ajst-24979 361 11 - - SYM ajst-24979 361 12 626 626 NUM ajst-24979 361 13 . . PUNCT ajst-24979 362 1 [ [ X ajst-24979 362 2 33 33 NUM ajst-24979 362 3 ] ] PUNCT ajst-24979 362 4 s. s. PROPN ajst-24979 362 5 hajighasemi hajighasemi PROPN ajst-24979 362 6 . . PUNCT ajst-24979 363 1 fuzzy fuzzy ADJ ajst-24979 363 2 fredholm fredholm NOUN ajst-24979 363 3 - - PUNCT ajst-24979 363 4 volterra volterra NOUN ajst-24979 363 5 integral integral ADJ ajst-24979 363 6 equations equation NOUN ajst-24979 363 7 and and CCONJ ajst-24979 363 8 existance existance NOUN ajst-24979 363 9 and and CCONJ ajst-24979 363 10 uniqueness uniqueness NOUN ajst-24979 363 11 of of ADP ajst-24979 363 12 solution solution NOUN ajst-24979 363 13 of of ADP ajst-24979 363 14 them they PRON ajst-24979 363 15 , , PUNCT ajst-24979 363 16 australian australian ADJ ajst-24979 363 17 journal journal NOUN ajst-24979 363 18 of of ADP ajst-24979 363 19 basice basice PROPN ajst-24979 363 20 and and CCONJ ajst-24979 363 21 applied apply VERB ajst-24979 363 22 science science NOUN ajst-24979 363 23 , , PUNCT ajst-24979 363 24 5(2011 5(2011 NUM ajst-24979 363 25 ) ) PUNCT ajst-24979 363 26 , , PUNCT ajst-24979 363 27 1 1 NUM ajst-24979 363 28 - - SYM ajst-24979 363 29 8 8 NUM ajst-24979 363 30 . . PUNCT ajst-24979 364 1 [ [ X ajst-24979 364 2 34 34 NUM ajst-24979 364 3 ] ] X ajst-24979 364 4 b. b. PROPN ajst-24979 364 5 bede bede PROPN ajst-24979 364 6 , , PUNCT ajst-24979 364 7 l. l. PROPN ajst-24979 364 8 stefanini stefanini PROPN ajst-24979 364 9 . . PUNCT ajst-24979 365 1 generalized generalize VERB ajst-24979 365 2 differentiability differentiability NOUN ajst-24979 365 3 of of ADP ajst-24979 365 4 fuzzyvalued fuzzyvalue VERB ajst-24979 365 5 functions function NOUN ajst-24979 365 6 , , PUNCT ajst-24979 365 7 fuzzy fuzzy ADJ ajst-24979 365 8 sets set NOUN ajst-24979 365 9 and and CCONJ ajst-24979 365 10 systems system NOUN ajst-24979 365 11 , , PUNCT ajst-24979 365 12 in in ADP ajst-24979 365 13 press press NOUN ajst-24979 365 14 , , PUNCT ajst-24979 365 15 230(2013 230(2013 NUM ajst-24979 365 16 ) ) PUNCT ajst-24979 365 17 , , PUNCT ajst-24979 365 18 119 119 NUM ajst-24979 365 19 - - SYM ajst-24979 365 20 141 141 NUM ajst-24979 365 21 . . PUNCT ajst-24979 366 1 [ [ X ajst-24979 366 2 35 35 NUM ajst-24979 366 3 ] ] X ajst-24979 366 4 t. t. NOUN ajst-24979 366 5 allahviranloo allahviranloo PROPN ajst-24979 366 6 , , PUNCT ajst-24979 366 7 s. s. PROPN ajst-24979 366 8 salahshour salahshour PROPN ajst-24979 366 9 , , PUNCT ajst-24979 366 10 s. s. PROPN ajst-24979 366 11 abbasbandy abbasbandy PROPN ajst-24979 366 12 . . PUNCT ajst-24979 367 1 explicit explicit ADJ ajst-24979 367 2 solutions solution NOUN ajst-24979 367 3 of of ADP ajst-24979 367 4 fractional fractional ADJ ajst-24979 367 5 differential differential ADJ ajst-24979 367 6 equations equation NOUN ajst-24979 367 7 with with ADP ajst-24979 367 8 uncertainty uncertainty NOUN ajst-24979 367 9 . . PUNCT ajst-24979 368 1 soft soft ADJ ajst-24979 368 2 comput comput NOUN ajst-24979 368 3 , , PUNCT ajst-24979 368 4 16(2012 16(2012 NUM ajst-24979 368 5 ) ) PUNCT ajst-24979 368 6 , , PUNCT ajst-24979 368 7 297 297 NUM ajst-24979 368 8 - - SYM ajst-24979 368 9 302 302 NUM ajst-24979 368 10 . . PUNCT ajst-24979 369 1 [ [ X ajst-24979 369 2 36 36 NUM ajst-24979 369 3 ] ] X ajst-24979 369 4 r. r. PROPN ajst-24979 369 5 l. l. PROPN ajst-24979 369 6 pouso pouso PROPN ajst-24979 369 7 . . PUNCT ajst-24979 369 8 schauder schauder PROPN ajst-24979 369 9 ’s ’s PART ajst-24979 369 10 fixed fix VERB ajst-24979 369 11 - - PUNCT ajst-24979 369 12 point point NOUN ajst-24979 369 13 theorem theorem ADJ ajst-24979 369 14 : : PUNCT ajst-24979 369 15 new new ADJ ajst-24979 369 16 applications application NOUN ajst-24979 369 17 and and CCONJ ajst-24979 369 18 a a DET ajst-24979 369 19 new new ADJ ajst-24979 369 20 version version NOUN ajst-24979 369 21 for for ADP ajst-24979 369 22 discontinuous discontinuous ADJ ajst-24979 369 23 operators operator NOUN ajst-24979 369 24 . . PUNCT ajst-24979 370 1 boundary boundary ADJ ajst-24979 370 2 value value NOUN ajst-24979 370 3 problems problem NOUN ajst-24979 370 4 . . PUNCT ajst-24979 371 1 2012(2012 2012(2012 NUM ajst-24979 371 2 ) ) PUNCT ajst-24979 371 3 , , PUNCT ajst-24979 371 4 1 1 NUM ajst-24979 371 5 - - SYM ajst-24979 371 6 14 14 NUM ajst-24979 371 7 . . PUNCT ajst-24979 372 1 [ [ X ajst-24979 372 2 37 37 NUM ajst-24979 372 3 ] ] PUNCT ajst-24979 372 4 m. m. PROPN ajst-24979 372 5 r. r. PROPN ajst-24979 372 6 m. m. PROPN ajst-24979 372 7 shabestari shabestari PROPN ajst-24979 372 8 , , PUNCT ajst-24979 372 9 r. r. PROPN ajst-24979 372 10 ezzati ezzati PROPN ajst-24979 372 11 , , PUNCT ajst-24979 372 12 t.allahviranloo t.allahviranloo ADJ ajst-24979 372 13 . . PUNCT ajst-24979 373 1 numerical numerical ADJ ajst-24979 373 2 solution solution NOUN ajst-24979 373 3 of of ADP ajst-24979 373 4 fuzzy fuzzy ADJ ajst-24979 373 5 fractionalintegro fractionalintegro NOUN ajst-24979 373 6 - - PUNCT ajst-24979 373 7 differential differential NOUN ajst-24979 373 8 equation equation NOUN ajst-24979 373 9 via via ADP ajst-24979 373 10 two two NUM ajst-24979 373 11 - - PUNCT ajst-24979 373 12 dimensional dimensional ADJ ajst-24979 373 13 legendre legendre PROPN ajst-24979 373 14 wavelet wavelet NOUN ajst-24979 373 15 method method NOUN ajst-24979 373 16 , , PUNCT ajst-24979 373 17 journal journal NOUN ajst-24979 373 18 of of ADP ajst-24979 373 19 intelligent intelligent ADJ ajst-24979 373 20 and and CCONJ ajst-24979 373 21 fuzzy fuzzy ADJ ajst-24979 373 22 systems system NOUN ajst-24979 373 23 , , PUNCT ajst-24979 373 24 34(2018 34(2018 NUM ajst-24979 373 25 ) ) PUNCT ajst-24979 373 26 , , PUNCT ajst-24979 373 27 2453 2453 NUM ajst-24979 373 28 - - SYM ajst-24979 373 29 2465 2465 NUM ajst-24979 373 30 . . PUNCT