id sid tid token lemma pos iajs-2292 1 1 153 153 NUM iajs-2292 1 2 ibn ibn PROPN iajs-2292 1 3 al al PROPN iajs-2292 1 4 - - PUNCT iajs-2292 1 5 haitham haitham PROPN iajs-2292 1 6 jour jour X iajs-2292 1 7 . . PROPN iajs-2292 1 8 for for ADP iajs-2292 1 9 pure pure ADJ iajs-2292 1 10 & & CCONJ iajs-2292 1 11 appl appl PROPN iajs-2292 1 12 . . PUNCT iajs-2292 2 1 sci sci PROPN iajs-2292 2 2 . . PROPN iajs-2292 2 3 32 32 NUM iajs-2292 2 4 ( ( PUNCT iajs-2292 2 5 3 3 NUM iajs-2292 2 6 ) ) PUNCT iajs-2292 2 7 2019 2019 NUM iajs-2292 2 8 mahdi mahdi PROPN iajs-2292 2 9 a. a. PROPN iajs-2292 2 10 sabaa sabaa PROPN iajs-2292 2 11 sinan sinan PROPN iajs-2292 2 12 hatif hatif PROPN iajs-2292 2 13 abd abd PROPN iajs-2292 2 14 almjeed almjeed PROPN iajs-2292 2 15 abstract abstract NOUN iajs-2292 2 16 in in ADP iajs-2292 2 17 this this DET iajs-2292 2 18 paper paper NOUN iajs-2292 2 19 , , PUNCT iajs-2292 2 20 our our PRON iajs-2292 2 21 aim aim NOUN iajs-2292 2 22 is be AUX iajs-2292 2 23 to to PART iajs-2292 2 24 solve solve VERB iajs-2292 2 25 analytically analytically ADV iajs-2292 2 26 a a DET iajs-2292 2 27 nonlinear nonlinear ADJ iajs-2292 2 28 social social ADJ iajs-2292 2 29 epidemic epidemic NOUN iajs-2292 2 30 model model NOUN iajs-2292 2 31 as as ADP iajs-2292 2 32 an an DET iajs-2292 2 33 initial initial ADJ iajs-2292 2 34 value value NOUN iajs-2292 2 35 problem problem NOUN iajs-2292 2 36 ( ( PUNCT iajs-2292 2 37 ivp ivp NOUN iajs-2292 2 38 ) ) PUNCT iajs-2292 2 39 of of ADP iajs-2292 2 40 ordinary ordinary ADJ iajs-2292 2 41 differential differential ADJ iajs-2292 2 42 equations equation NOUN iajs-2292 2 43 . . PUNCT iajs-2292 3 1 the the DET iajs-2292 3 2 mathematical mathematical ADJ iajs-2292 3 3 social social ADJ iajs-2292 3 4 epidemic epidemic NOUN iajs-2292 3 5 model model NOUN iajs-2292 3 6 under under ADP iajs-2292 3 7 study study NOUN iajs-2292 3 8 is be AUX iajs-2292 3 9 applied apply VERB iajs-2292 3 10 to to ADP iajs-2292 3 11 alcohol alcohol NOUN iajs-2292 3 12 consumption consumption NOUN iajs-2292 3 13 model model NOUN iajs-2292 3 14 in in ADP iajs-2292 3 15 spain spain PROPN iajs-2292 3 16 . . PUNCT iajs-2292 4 1 the the DET iajs-2292 4 2 economic economic ADJ iajs-2292 4 3 cost cost NOUN iajs-2292 4 4 of of ADP iajs-2292 4 5 alcohol alcohol NOUN iajs-2292 4 6 consumption consumption NOUN iajs-2292 4 7 in in ADP iajs-2292 4 8 spain spain PROPN iajs-2292 4 9 is be AUX iajs-2292 4 10 affected affect VERB iajs-2292 4 11 by by ADP iajs-2292 4 12 the the DET iajs-2292 4 13 amount amount NOUN iajs-2292 4 14 of of ADP iajs-2292 4 15 alcohol alcohol NOUN iajs-2292 4 16 consumed consume VERB iajs-2292 4 17 . . PUNCT iajs-2292 5 1 this this DET iajs-2292 5 2 paper paper NOUN iajs-2292 5 3 refers refer VERB iajs-2292 5 4 to to ADP iajs-2292 5 5 the the DET iajs-2292 5 6 study study NOUN iajs-2292 5 7 of of ADP iajs-2292 5 8 alcohol alcohol NOUN iajs-2292 5 9 consumption consumption NOUN iajs-2292 5 10 using use VERB iajs-2292 5 11 some some DET iajs-2292 5 12 analytical analytical ADJ iajs-2292 5 13 methods method NOUN iajs-2292 5 14 . . PUNCT iajs-2292 6 1 adomian adomian NOUN iajs-2292 6 2 decomposition decomposition NOUN iajs-2292 6 3 and and CCONJ iajs-2292 6 4 variation variation NOUN iajs-2292 6 5 iteration iteration NOUN iajs-2292 6 6 methods method NOUN iajs-2292 6 7 for for ADP iajs-2292 6 8 solving solve VERB iajs-2292 6 9 alcohol alcohol NOUN iajs-2292 6 10 consumption consumption NOUN iajs-2292 6 11 model model NOUN iajs-2292 6 12 have have AUX iajs-2292 6 13 used use VERB iajs-2292 6 14 . . PUNCT iajs-2292 7 1 finally finally ADV iajs-2292 7 2 , , PUNCT iajs-2292 7 3 a a DET iajs-2292 7 4 compression compression NOUN iajs-2292 7 5 between between ADP iajs-2292 7 6 the the DET iajs-2292 7 7 analytic analytic ADJ iajs-2292 7 8 solutions solution NOUN iajs-2292 7 9 of of ADP iajs-2292 7 10 the the DET iajs-2292 7 11 two two NUM iajs-2292 7 12 used use VERB iajs-2292 7 13 methods method NOUN iajs-2292 7 14 and and CCONJ iajs-2292 7 15 the the DET iajs-2292 7 16 previous previous ADJ iajs-2292 7 17 actual actual ADJ iajs-2292 7 18 values value NOUN iajs-2292 7 19 from from ADP iajs-2292 7 20 1997 1997 NUM iajs-2292 7 21 to to ADP iajs-2292 7 22 2007 2007 NUM iajs-2292 7 23 years year NOUN iajs-2292 7 24 is be AUX iajs-2292 7 25 obtained obtain VERB iajs-2292 7 26 using use VERB iajs-2292 7 27 the the DET iajs-2292 7 28 absolute absolute ADJ iajs-2292 7 29 and and CCONJ iajs-2292 7 30 relative relative ADJ iajs-2292 7 31 errors error NOUN iajs-2292 7 32 . . PUNCT iajs-2292 8 1 the the DET iajs-2292 8 2 analysis analysis NOUN iajs-2292 8 3 results result NOUN iajs-2292 8 4 obtained obtain VERB iajs-2292 8 5 have have AUX iajs-2292 8 6 been be AUX iajs-2292 8 7 discussed discuss VERB iajs-2292 8 8 tabularly tabularly ADV iajs-2292 8 9 and and CCONJ iajs-2292 8 10 graphically graphically ADV iajs-2292 8 11 . . PUNCT iajs-2292 9 1 keywords keyword NOUN iajs-2292 9 2 : : PUNCT iajs-2292 9 3 ordinary ordinary ADJ iajs-2292 9 4 differential differential ADJ iajs-2292 9 5 equations equation NOUN iajs-2292 9 6 , , PUNCT iajs-2292 9 7 adomian adomian NOUN iajs-2292 9 8 decomposition decomposition NOUN iajs-2292 9 9 method method NOUN iajs-2292 9 10 , , PUNCT iajs-2292 9 11 variation variation NOUN iajs-2292 9 12 iteration iteration NOUN iajs-2292 9 13 method method NOUN iajs-2292 9 14 , , PUNCT iajs-2292 9 15 social social ADJ iajs-2292 9 16 epidemiology epidemiology NOUN iajs-2292 9 17 . . PUNCT iajs-2292 10 1 1 1 X iajs-2292 10 2 . . X iajs-2292 10 3 introduction introduction NOUN iajs-2292 10 4 the the DET iajs-2292 10 5 type type NOUN iajs-2292 10 6 of of ADP iajs-2292 10 7 epidemiological epidemiological ADJ iajs-2292 10 8 models model NOUN iajs-2292 10 9 had have AUX iajs-2292 10 10 been be AUX iajs-2292 10 11 used use VERB iajs-2292 10 12 in in ADP iajs-2292 10 13 the the DET iajs-2292 10 14 study study NOUN iajs-2292 10 15 of of ADP iajs-2292 10 16 many many ADJ iajs-2292 10 17 social social ADJ iajs-2292 10 18 diseases disease NOUN iajs-2292 10 19 . . PUNCT iajs-2292 11 1 in in ADP iajs-2292 11 2 recent recent ADJ iajs-2292 11 3 years year NOUN iajs-2292 11 4 , , PUNCT iajs-2292 11 5 several several ADJ iajs-2292 11 6 researchers researcher NOUN iajs-2292 11 7 were be AUX iajs-2292 11 8 interested interested ADJ iajs-2292 11 9 to to PART iajs-2292 11 10 study study VERB iajs-2292 11 11 and and CCONJ iajs-2292 11 12 analyze analyze VERB iajs-2292 11 13 the the DET iajs-2292 11 14 social social ADJ iajs-2292 11 15 epidemics epidemic NOUN iajs-2292 11 16 , , PUNCT iajs-2292 11 17 ecstasy ecstasy NOUN iajs-2292 11 18 or or CCONJ iajs-2292 11 19 heroin heroin NOUN iajs-2292 11 20 addiction addiction NOUN iajs-2292 11 21 [ [ X iajs-2292 11 22 1 1 NUM iajs-2292 11 23 , , PUNCT iajs-2292 11 24 2 2 NUM iajs-2292 11 25 ] ] PUNCT iajs-2292 11 26 . . PUNCT iajs-2292 12 1 smoking smoking NOUN iajs-2292 12 2 habit habit NOUN iajs-2292 12 3 evaluation evaluation NOUN iajs-2292 12 4 in in ADP iajs-2292 12 5 spain spain PROPN iajs-2292 13 1 [ [ X iajs-2292 13 2 3 3 NUM iajs-2292 13 3 - - SYM iajs-2292 13 4 5 5 NUM iajs-2292 13 5 ] ] PUNCT iajs-2292 13 6 . . PUNCT iajs-2292 14 1 a a DET iajs-2292 14 2 cocaine cocaine NOUN iajs-2292 14 3 abuse abuse NOUN iajs-2292 14 4 in in ADP iajs-2292 14 5 spain spain PROPN iajs-2292 15 1 [ [ X iajs-2292 15 2 6 6 NUM iajs-2292 15 3 , , PUNCT iajs-2292 15 4 7 7 NUM iajs-2292 15 5 ] ] PUNCT iajs-2292 15 6 . . PUNCT iajs-2292 16 1 campaigns campaign NOUN iajs-2292 16 2 on on ADP iajs-2292 16 3 reducing reduce VERB iajs-2292 16 4 excess excess ADJ iajs-2292 16 5 weight weight NOUN iajs-2292 16 6 in in ADP iajs-2292 16 7 valencia valencia PROPN iajs-2292 17 1 [ [ X iajs-2292 17 2 8 8 NUM iajs-2292 17 3 - - SYM iajs-2292 17 4 10 10 NUM iajs-2292 17 5 ] ] PUNCT iajs-2292 17 6 . . PUNCT iajs-2292 18 1 alcohol alcohol NOUN iajs-2292 18 2 consumption consumption NOUN iajs-2292 18 3 habit habit NOUN iajs-2292 18 4 is be AUX iajs-2292 18 5 considered consider VERB iajs-2292 18 6 a a DET iajs-2292 18 7 disease disease NOUN iajs-2292 18 8 that that PRON iajs-2292 18 9 spread spread VERB iajs-2292 18 10 out out ADP iajs-2292 18 11 rapidly rapidly ADV iajs-2292 18 12 by by ADP iajs-2292 18 13 social social ADJ iajs-2292 18 14 pressure pressure NOUN iajs-2292 18 15 or or CCONJ iajs-2292 18 16 social social ADJ iajs-2292 18 17 contact contact NOUN iajs-2292 18 18 which which PRON iajs-2292 18 19 influences influence VERB iajs-2292 18 20 the the DET iajs-2292 18 21 spread spread NOUN iajs-2292 18 22 of of ADP iajs-2292 18 23 social social ADJ iajs-2292 18 24 disease disease NOUN iajs-2292 18 25 . . PUNCT iajs-2292 19 1 recently recently ADV iajs-2292 19 2 , , PUNCT iajs-2292 19 3 the the DET iajs-2292 19 4 rate rate NOUN iajs-2292 19 5 of of ADP iajs-2292 19 6 alcohol alcohol NOUN iajs-2292 19 7 consumption consumption NOUN iajs-2292 19 8 has have AUX iajs-2292 19 9 increased increase VERB iajs-2292 19 10 more more ADV iajs-2292 19 11 with with ADP iajs-2292 19 12 the the DET iajs-2292 19 13 developing develop VERB iajs-2292 19 14 countries country NOUN iajs-2292 19 15 , , PUNCT iajs-2292 19 16 so so CCONJ iajs-2292 19 17 alcohol alcohol NOUN iajs-2292 19 18 consumption consumption NOUN iajs-2292 19 19 represents represent VERB iajs-2292 19 20 a a DET iajs-2292 19 21 big big ADJ iajs-2292 19 22 problem problem NOUN iajs-2292 19 23 that that PRON iajs-2292 19 24 efforts effort NOUN iajs-2292 19 25 not not PART iajs-2292 19 26 only only ADV iajs-2292 19 27 on on ADP iajs-2292 19 28 the the DET iajs-2292 19 29 human human ADJ iajs-2292 19 30 health health NOUN iajs-2292 19 31 , , PUNCT iajs-2292 19 32 but but CCONJ iajs-2292 19 33 also also ADV iajs-2292 19 34 on on ADP iajs-2292 19 35 the the DET iajs-2292 19 36 community community NOUN iajs-2292 19 37 economy economy NOUN iajs-2292 19 38 . . PUNCT iajs-2292 20 1 the the DET iajs-2292 20 2 public public ADJ iajs-2292 20 3 health health NOUN iajs-2292 20 4 care care NOUN iajs-2292 20 5 becomes become VERB iajs-2292 20 6 more more ADV iajs-2292 20 7 expensive expensive ADJ iajs-2292 20 8 when when SCONJ iajs-2292 20 9 the the DET iajs-2292 20 10 number number NOUN iajs-2292 20 11 of of ADP iajs-2292 20 12 people people NOUN iajs-2292 20 13 who who PRON iajs-2292 20 14 are be AUX iajs-2292 20 15 suffering suffer VERB iajs-2292 20 16 from from ADP iajs-2292 20 17 such such ADJ iajs-2292 20 18 diseases disease NOUN iajs-2292 20 19 increased increase VERB iajs-2292 20 20 , , PUNCT iajs-2292 20 21 so so CCONJ iajs-2292 20 22 the the DET iajs-2292 20 23 community community NOUN iajs-2292 20 24 economy economy NOUN iajs-2292 20 25 will will AUX iajs-2292 20 26 be be AUX iajs-2292 20 27 damaged damage VERB iajs-2292 20 28 . . PUNCT iajs-2292 21 1 with with ADP iajs-2292 21 2 regard regard NOUN iajs-2292 21 3 to to ADP iajs-2292 21 4 the the DET iajs-2292 21 5 health health NOUN iajs-2292 21 6 effects effect NOUN iajs-2292 21 7 of of ADP iajs-2292 21 8 chloride chloride NOUN iajs-2292 21 9 that that DET iajs-2292 21 10 impact impact NOUN iajs-2292 21 11 on on ADP iajs-2292 21 12 the the DET iajs-2292 21 13 healthy healthy ADJ iajs-2292 21 14 body body NOUN iajs-2292 21 15 , , PUNCT iajs-2292 21 16 the the DET iajs-2292 21 17 chloride chloride NOUN iajs-2292 21 18 can can AUX iajs-2292 21 19 damage damage VERB iajs-2292 21 20 some some DET iajs-2292 21 21 parts part NOUN iajs-2292 21 22 of of ADP iajs-2292 21 23 the the DET iajs-2292 21 24 body body NOUN iajs-2292 21 25 , , PUNCT iajs-2292 21 26 such such ADJ iajs-2292 21 27 as as ADP iajs-2292 21 28 heart heart NOUN iajs-2292 21 29 and and CCONJ iajs-2292 21 30 liver liver NOUN iajs-2292 21 31 , , PUNCT iajs-2292 21 32 influence influence NOUN iajs-2292 21 33 also also ADV iajs-2292 21 34 on on ADP iajs-2292 21 35 the the DET iajs-2292 21 36 other other ADJ iajs-2292 21 37 functions function NOUN iajs-2292 21 38 . . PUNCT iajs-2292 22 1 an an DET iajs-2292 22 2 addition addition NOUN iajs-2292 22 3 that that SCONJ iajs-2292 22 4 , , PUNCT iajs-2292 22 5 the the DET iajs-2292 22 6 cost cost NOUN iajs-2292 22 7 of of ADP iajs-2292 22 8 alcohol alcohol NOUN iajs-2292 22 9 affects affect VERB iajs-2292 22 10 the the DET iajs-2292 22 11 economy economy NOUN iajs-2292 22 12 [ [ X iajs-2292 22 13 11 11 NUM iajs-2292 22 14 , , PUNCT iajs-2292 22 15 12 12 NUM iajs-2292 22 16 ] ] PUNCT iajs-2292 22 17 . . PUNCT iajs-2292 23 1 adomian adomian NOUN iajs-2292 23 2 decomposition decomposition NOUN iajs-2292 23 3 method method NOUN iajs-2292 23 4 ( ( PUNCT iajs-2292 23 5 adm adm PROPN iajs-2292 23 6 ) ) PUNCT iajs-2292 23 7 is be AUX iajs-2292 23 8 a a DET iajs-2292 23 9 reliable reliable ADJ iajs-2292 23 10 method method NOUN iajs-2292 23 11 to to PART iajs-2292 23 12 solve solve VERB iajs-2292 23 13 many many ADJ iajs-2292 23 14 various various ADJ iajs-2292 23 15 kinds kind NOUN iajs-2292 23 16 of of ADP iajs-2292 23 17 problems problem NOUN iajs-2292 23 18 so so SCONJ iajs-2292 23 19 it it PRON iajs-2292 23 20 is be AUX iajs-2292 23 21 a a DET iajs-2292 23 22 trusty trusty ADJ iajs-2292 23 23 method method NOUN iajs-2292 23 24 which which PRON iajs-2292 23 25 emerging emerge VERB iajs-2292 23 26 in in ADP iajs-2292 23 27 applied apply VERB iajs-2292 23 28 science science NOUN iajs-2292 23 29 , , PUNCT iajs-2292 23 30 linear linear ADJ iajs-2292 23 31 and and CCONJ iajs-2292 23 32 nonlinear nonlinear PROPN iajs-2292 23 33 ibn ibn PROPN iajs-2292 23 34 al al PROPN iajs-2292 23 35 haitham haitham PROPN iajs-2292 23 36 journal journal PROPN iajs-2292 23 37 for for ADP iajs-2292 23 38 pure pure ADJ iajs-2292 23 39 and and CCONJ iajs-2292 23 40 applied apply VERB iajs-2292 23 41 science science NOUN iajs-2292 23 42 journal journal PROPN iajs-2292 23 43 homepage homepage NOUN iajs-2292 23 44 : : PUNCT iajs-2292 23 45 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index PROPN iajs-2292 23 46 doi:10.30526/32.3.2292 doi:10.30526/32.3.2292 PROPN iajs-2292 23 47 maha maha PROPN iajs-2292 23 48 a. a. 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PROPN iajs-2292 29 8 for for ADP iajs-2292 29 9 pure pure ADJ iajs-2292 29 10 & & CCONJ iajs-2292 29 11 appl appl PROPN iajs-2292 29 12 . . PUNCT iajs-2292 30 1 sci sci PROPN iajs-2292 30 2 . . PROPN iajs-2292 30 3 32 32 NUM iajs-2292 30 4 ( ( PUNCT iajs-2292 30 5 3 3 NUM iajs-2292 30 6 ) ) PUNCT iajs-2292 30 7 2019 2019 NUM iajs-2292 30 8 as as ADV iajs-2292 30 9 well well ADV iajs-2292 30 10 . . PUNCT iajs-2292 31 1 the the DET iajs-2292 31 2 adomian adomian NOUN iajs-2292 31 3 decomposition decomposition NOUN iajs-2292 31 4 method method NOUN iajs-2292 31 5 was be AUX iajs-2292 31 6 introduced introduce VERB iajs-2292 31 7 and and CCONJ iajs-2292 31 8 developed develop VERB iajs-2292 31 9 by by ADP iajs-2292 31 10 george george PROPN iajs-2292 31 11 adomian adomian NOUN iajs-2292 31 12 . . PUNCT iajs-2292 32 1 this this DET iajs-2292 32 2 method method NOUN iajs-2292 32 3 has have AUX iajs-2292 32 4 been be AUX iajs-2292 32 5 used use VERB iajs-2292 32 6 by by ADP iajs-2292 32 7 many many ADJ iajs-2292 32 8 researchers researcher NOUN iajs-2292 32 9 as as ADV iajs-2292 32 10 well well ADV iajs-2292 32 11 as as ADP iajs-2292 32 12 it it PRON iajs-2292 32 13 has have VERB iajs-2292 32 14 extensive extensive ADJ iajs-2292 32 15 applications application NOUN iajs-2292 32 16 of of ADP iajs-2292 32 17 linear linear ADJ iajs-2292 32 18 and and CCONJ iajs-2292 32 19 nonlinear nonlinear ADJ iajs-2292 32 20 ordinary ordinary ADJ iajs-2292 32 21 differential differential ADJ iajs-2292 32 22 equations equation NOUN iajs-2292 32 23 , , PUNCT iajs-2292 32 24 partial partial ADJ iajs-2292 32 25 differential differential ADJ iajs-2292 32 26 equations equation NOUN iajs-2292 32 27 and and CCONJ iajs-2292 32 28 integral integral ADJ iajs-2292 32 29 equations equation NOUN iajs-2292 32 30 [ [ X iajs-2292 32 31 13 13 NUM iajs-2292 32 32 , , PUNCT iajs-2292 32 33 14 14 NUM iajs-2292 32 34 ] ] PUNCT iajs-2292 32 35 . . PUNCT iajs-2292 33 1 the the DET iajs-2292 33 2 modified modify VERB iajs-2292 33 3 adm adm PROPN iajs-2292 33 4 and and CCONJ iajs-2292 33 5 its its PRON iajs-2292 33 6 applications application NOUN iajs-2292 33 7 on on ADP iajs-2292 33 8 some some DET iajs-2292 33 9 equations equation NOUN iajs-2292 33 10 have have AUX iajs-2292 33 11 also also ADV iajs-2292 33 12 been be AUX iajs-2292 33 13 given give VERB iajs-2292 33 14 ; ; PUNCT iajs-2292 33 15 see see VERB iajs-2292 33 16 examples example NOUN iajs-2292 33 17 in in ADP iajs-2292 33 18 [ [ PUNCT iajs-2292 33 19 15 15 NUM iajs-2292 33 20 - - SYM iajs-2292 33 21 18 18 NUM iajs-2292 33 22 ] ] PUNCT iajs-2292 33 23 . . PUNCT iajs-2292 34 1 adm adm PROPN iajs-2292 34 2 was be AUX iajs-2292 34 3 introduced introduce VERB iajs-2292 34 4 and and CCONJ iajs-2292 34 5 developed develop VERB iajs-2292 34 6 by by ADP iajs-2292 34 7 george george PROPN iajs-2292 34 8 adomian adomian NOUN iajs-2292 34 9 , , PUNCT iajs-2292 34 10 1976 1976 NUM iajs-2292 34 11 . . 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PUNCT iajs-2292 43 1 the the DET iajs-2292 43 2 variational variational ADJ iajs-2292 43 3 iteration iteration NOUN iajs-2292 43 4 method method NOUN iajs-2292 43 5 ( ( PUNCT iajs-2292 43 6 vim vim NOUN iajs-2292 43 7 ) ) PUNCT iajs-2292 43 8 was be AUX iajs-2292 43 9 established establish VERB iajs-2292 43 10 by by ADP iajs-2292 43 11 ji ji PROPN iajs-2292 43 12 - - PROPN iajs-2292 43 13 huan huan PROPN iajs-2292 43 14 in in ADP iajs-2292 43 15 1997 1997 NUM iajs-2292 43 16 where where SCONJ iajs-2292 43 17 it it PRON iajs-2292 43 18 is be AUX iajs-2292 43 19 considered consider VERB iajs-2292 43 20 as as ADP iajs-2292 43 21 one one NUM iajs-2292 43 22 of of ADP iajs-2292 43 23 the the DET iajs-2292 43 24 reliable reliable ADJ iajs-2292 43 25 iterative iterative NOUN iajs-2292 43 26 methods method NOUN iajs-2292 43 27 that that PRON iajs-2292 43 28 give give VERB iajs-2292 43 29 approximate approximate ADJ iajs-2292 43 30 solutions solution NOUN iajs-2292 43 31 for for ADP iajs-2292 43 32 the the PRON iajs-2292 43 33 of of ADP iajs-2292 43 34 differential differential ADJ iajs-2292 43 35 equations equation NOUN iajs-2292 43 36 [ [ X iajs-2292 43 37 27 27 NUM iajs-2292 43 38 , , PUNCT iajs-2292 43 39 28 28 NUM iajs-2292 43 40 ] ] PUNCT iajs-2292 43 41 . . 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PUNCT iajs-2292 45 1 vim vim PROPN iajs-2292 45 2 is be AUX iajs-2292 45 3 used use VERB iajs-2292 45 4 for for ADP iajs-2292 45 5 the the DET iajs-2292 45 6 analytical analytical ADJ iajs-2292 45 7 purpose purpose NOUN iajs-2292 45 8 because because SCONJ iajs-2292 45 9 it it PRON iajs-2292 45 10 is be AUX iajs-2292 45 11 an an DET iajs-2292 45 12 effective effective ADJ iajs-2292 45 13 and and CCONJ iajs-2292 45 14 reliable reliable ADJ iajs-2292 45 15 way way NOUN iajs-2292 45 16 in in ADP iajs-2292 45 17 the the DET iajs-2292 45 18 approaching approach VERB iajs-2292 45 19 quickly quickly ADV iajs-2292 45 20 to to ADP iajs-2292 45 21 the the DET iajs-2292 45 22 exact exact ADJ iajs-2292 45 23 solution solution NOUN iajs-2292 45 24 . . PUNCT iajs-2292 46 1 the the DET iajs-2292 46 2 vim vim PROPN iajs-2292 46 3 method method NOUN iajs-2292 46 4 differs differ VERB iajs-2292 46 5 from from ADP iajs-2292 46 6 the the DET iajs-2292 46 7 adm adm PROPN iajs-2292 46 8 , , PUNCT iajs-2292 46 9 where where SCONJ iajs-2292 46 10 vim vim NOUN iajs-2292 46 11 does do AUX iajs-2292 46 12 not not PART iajs-2292 46 13 require require VERB iajs-2292 46 14 specific specific ADJ iajs-2292 46 15 treatments treatment NOUN iajs-2292 46 16 for for ADP iajs-2292 46 17 nonlinear nonlinear ADJ iajs-2292 46 18 problems problem NOUN iajs-2292 46 19 [ [ X iajs-2292 46 20 14 14 NUM iajs-2292 46 21 ] ] PUNCT iajs-2292 46 22 . . PUNCT iajs-2292 47 1 many many ADJ iajs-2292 47 2 works work VERB iajs-2292 47 3 to to PART iajs-2292 47 4 solve solve VERB iajs-2292 47 5 nonlinear nonlinear ADJ iajs-2292 47 6 problems problem NOUN iajs-2292 47 7 using use VERB iajs-2292 47 8 vim vim NOUN iajs-2292 47 9 [ [ X iajs-2292 47 10 27 27 NUM iajs-2292 47 11 ] ] PUNCT iajs-2292 47 12 . . PUNCT iajs-2292 48 1 with with ADP iajs-2292 48 2 autonomous autonomous ADJ iajs-2292 48 3 ordinary ordinary ADJ iajs-2292 48 4 differential differential NOUN iajs-2292 48 5 systems system NOUN iajs-2292 48 6 [ [ X iajs-2292 48 7 29 29 NUM iajs-2292 48 8 ] ] PUNCT iajs-2292 48 9 . . PUNCT iajs-2292 49 1 and and CCONJ iajs-2292 49 2 to to PART iajs-2292 49 3 solve solve VERB iajs-2292 49 4 differential differential ADJ iajs-2292 49 5 equations equation NOUN iajs-2292 49 6 that that PRON iajs-2292 49 7 have have VERB iajs-2292 49 8 fractional fractional ADJ iajs-2292 49 9 order order NOUN iajs-2292 49 10 [ [ X iajs-2292 49 11 30 30 NUM iajs-2292 49 12 ] ] PUNCT iajs-2292 49 13 . . PUNCT iajs-2292 50 1 the the DET iajs-2292 50 2 application application NOUN iajs-2292 50 3 of of ADP iajs-2292 50 4 real real ADJ iajs-2292 50 5 social social ADJ iajs-2292 50 6 epidemic epidemic NOUN iajs-2292 50 7 alcohol alcohol NOUN iajs-2292 50 8 consumption consumption NOUN iajs-2292 50 9 model model NOUN iajs-2292 50 10 is be AUX iajs-2292 50 11 considered consider VERB iajs-2292 50 12 in in ADP iajs-2292 50 13 this this DET iajs-2292 50 14 paper paper NOUN iajs-2292 50 15 , , PUNCT iajs-2292 50 16 in in ADP iajs-2292 50 17 order order NOUN iajs-2292 50 18 to to PART iajs-2292 50 19 study study VERB iajs-2292 50 20 the the DET iajs-2292 50 21 behavior behavior NOUN iajs-2292 50 22 of of ADP iajs-2292 50 23 this this DET iajs-2292 50 24 social social ADJ iajs-2292 50 25 epidemic epidemic NOUN iajs-2292 50 26 during during ADP iajs-2292 50 27 sometimes sometimes ADV iajs-2292 50 28 under under ADP iajs-2292 50 29 study study NOUN iajs-2292 50 30 . . PUNCT iajs-2292 51 1 the the DET iajs-2292 51 2 feature feature NOUN iajs-2292 51 3 of of ADP iajs-2292 51 4 such such ADJ iajs-2292 51 5 model model NOUN iajs-2292 51 6 under under ADP iajs-2292 51 7 study study NOUN iajs-2292 51 8 that that SCONJ iajs-2292 51 9 the the DET iajs-2292 51 10 model model NOUN iajs-2292 51 11 has have AUX iajs-2292 51 12 multiple multiple ADJ iajs-2292 51 13 parameters parameter NOUN iajs-2292 51 14 and and CCONJ iajs-2292 51 15 multivariate multivariate NOUN iajs-2292 51 16 . . PUNCT iajs-2292 52 1 as as ADV iajs-2292 52 2 well well ADV iajs-2292 52 3 as as ADP iajs-2292 52 4 , , PUNCT iajs-2292 52 5 it it PRON iajs-2292 52 6 is be AUX iajs-2292 52 7 a a DET iajs-2292 52 8 nonlinear nonlinear ADJ iajs-2292 52 9 system system NOUN iajs-2292 52 10 of of ADP iajs-2292 52 11 first first ADJ iajs-2292 52 12 - - PUNCT iajs-2292 52 13 order order NOUN iajs-2292 52 14 ordinary ordinary ADJ iajs-2292 52 15 differential differential ADJ iajs-2292 52 16 equations equation NOUN iajs-2292 52 17 for for ADP iajs-2292 52 18 autonomous autonomous ADJ iajs-2292 52 19 initial initial ADJ iajs-2292 52 20 value value NOUN iajs-2292 52 21 problem problem NOUN iajs-2292 52 22 that that PRON iajs-2292 52 23 do do AUX iajs-2292 52 24 n't not PART iajs-2292 52 25 have have VERB iajs-2292 52 26 mostly mostly ADV iajs-2292 52 27 exact exact ADJ iajs-2292 52 28 solution solution NOUN iajs-2292 52 29 . . PUNCT iajs-2292 53 1 our our PRON iajs-2292 53 2 interested interested ADJ iajs-2292 53 3 is be AUX iajs-2292 53 4 to to PART iajs-2292 53 5 solve solve VERB iajs-2292 53 6 analytically analytically ADV iajs-2292 53 7 such such DET iajs-2292 53 8 these these DET iajs-2292 53 9 models model NOUN iajs-2292 53 10 . . PUNCT iajs-2292 54 1 this this DET iajs-2292 54 2 study study NOUN iajs-2292 54 3 is be AUX iajs-2292 54 4 organized organize VERB iajs-2292 54 5 as as SCONJ iajs-2292 54 6 follows follow VERB iajs-2292 54 7 : : PUNCT iajs-2292 54 8 in in ADP iajs-2292 54 9 section section NOUN iajs-2292 54 10 2 2 NUM iajs-2292 54 11 , , PUNCT iajs-2292 54 12 the the DET iajs-2292 54 13 mathematical mathematical ADJ iajs-2292 54 14 model model NOUN iajs-2292 54 15 of of ADP iajs-2292 54 16 alcohol alcohol NOUN iajs-2292 54 17 consumption consumption NOUN iajs-2292 54 18 is be AUX iajs-2292 54 19 described describe VERB iajs-2292 54 20 ; ; PUNCT iajs-2292 54 21 section section NOUN iajs-2292 54 22 3 3 NUM iajs-2292 54 23 derived derive VERB iajs-2292 54 24 the the DET iajs-2292 54 25 analytic analytic ADJ iajs-2292 54 26 methods method NOUN iajs-2292 54 27 adm adm PROPN iajs-2292 54 28 and and CCONJ iajs-2292 54 29 vim vim NOUN iajs-2292 54 30 to to PART iajs-2292 54 31 solve solve VERB iajs-2292 54 32 the the DET iajs-2292 54 33 nonlinear nonlinear ADJ iajs-2292 54 34 system system NOUN iajs-2292 54 35 of of ADP iajs-2292 54 36 alcohol alcohol NOUN iajs-2292 54 37 consumption consumption NOUN iajs-2292 54 38 model model NOUN iajs-2292 54 39 in in ADP iajs-2292 54 40 spain spain PROPN iajs-2292 54 41 . . PUNCT iajs-2292 55 1 following follow VERB iajs-2292 55 2 , , PUNCT iajs-2292 55 3 in in ADP iajs-2292 55 4 section section NOUN iajs-2292 55 5 4 4 NUM iajs-2292 55 6 , , PUNCT iajs-2292 55 7 the the DET iajs-2292 55 8 results result NOUN iajs-2292 55 9 of of ADP iajs-2292 55 10 the the DET iajs-2292 55 11 presented present VERB iajs-2292 55 12 methods method NOUN iajs-2292 55 13 is be AUX iajs-2292 55 14 discussed discuss VERB iajs-2292 55 15 . . PUNCT iajs-2292 56 1 finely finely ADV iajs-2292 56 2 , , PUNCT iajs-2292 56 3 section section NOUN iajs-2292 56 4 5 5 NUM iajs-2292 56 5 is be AUX iajs-2292 56 6 devoted devote VERB iajs-2292 56 7 to to ADP iajs-2292 56 8 the the DET iajs-2292 56 9 conclusion conclusion NOUN iajs-2292 56 10 of of ADP iajs-2292 56 11 the the DET iajs-2292 56 12 study study NOUN iajs-2292 56 13 . . PUNCT iajs-2292 57 1 2 2 X iajs-2292 57 2 . . X iajs-2292 57 3 mathematical mathematical ADJ iajs-2292 57 4 model model PROPN iajs-2292 57 5 alcohol alcohol PROPN iajs-2292 57 6 ireland ireland PROPN iajs-2292 57 7 and and CCONJ iajs-2292 57 8 the the DET iajs-2292 57 9 united united ADJ iajs-2292 57 10 kingdom kingdom PROPN iajs-2292 57 11 , , PUNCT iajs-2292 57 12 this this DET iajs-2292 57 13 problem problem NOUN iajs-2292 57 14 was be AUX iajs-2292 57 15 discussed discuss VERB iajs-2292 57 16 and and CCONJ iajs-2292 57 17 the the DET iajs-2292 57 18 data datum NOUN iajs-2292 57 19 were be AUX iajs-2292 57 20 reported report VERB iajs-2292 57 21 from from ADP iajs-2292 57 22 the the DET iajs-2292 57 23 first first ADJ iajs-2292 57 24 year year NOUN iajs-2292 57 25 of of ADP iajs-2292 57 26 2002 2002 NUM iajs-2292 57 27 until until ADP iajs-2292 57 28 the the DET iajs-2292 57 29 end end NOUN iajs-2292 57 30 of of ADP iajs-2292 57 31 2014 2014 NUM iajs-2292 58 1 [ [ X iajs-2292 58 2 31 31 NUM iajs-2292 58 3 ] ] PUNCT iajs-2292 58 4 . . PUNCT iajs-2292 59 1 in in ADP iajs-2292 59 2 spain spain PROPN iajs-2292 59 3 , , PUNCT iajs-2292 59 4 the the DET iajs-2292 59 5 effects effect NOUN iajs-2292 59 6 of of ADP iajs-2292 59 7 the the DET iajs-2292 59 8 different different ADJ iajs-2292 59 9 usage usage NOUN iajs-2292 59 10 of of ADP iajs-2292 59 11 alcohol alcohol NOUN iajs-2292 59 12 between between ADP iajs-2292 59 13 the the DET iajs-2292 59 14 female female ADJ iajs-2292 59 15 and and CCONJ iajs-2292 59 16 male male ADJ iajs-2292 59 17 in in ADP iajs-2292 59 18 spanish spanish ADJ iajs-2292 59 19 university university NOUN iajs-2292 59 20 alumni alumnus NOUN iajs-2292 59 21 was be AUX iajs-2292 59 22 studied study VERB iajs-2292 59 23 [ [ PUNCT iajs-2292 59 24 32].the 32].the NUM iajs-2292 59 25 mathematical mathematical ADJ iajs-2292 59 26 model model NOUN iajs-2292 59 27 of of ADP iajs-2292 59 28 alcohol alcohol NOUN iajs-2292 59 29 consumption consumption NOUN iajs-2292 59 30 was be AUX iajs-2292 59 31 explained explain VERB iajs-2292 59 32 and and CCONJ iajs-2292 59 33 described describe VERB iajs-2292 59 34 in in ADP iajs-2292 59 35 the the DET iajs-2292 59 36 current current ADJ iajs-2292 59 37 study study NOUN iajs-2292 59 38 by by ADP iajs-2292 59 39 santonja santonja PROPN iajs-2292 59 40 et et PROPN iajs-2292 59 41 al al PROPN iajs-2292 59 42 . . PROPN iajs-2292 59 43 , , PUNCT iajs-2292 59 44 ( ( PUNCT iajs-2292 59 45 2010 2010 NUM iajs-2292 59 46 ) ) PUNCT iajs-2292 59 47 . . PUNCT iajs-2292 60 1 this this DET iajs-2292 60 2 model model NOUN iajs-2292 60 3 consists consist VERB iajs-2292 60 4 of of ADP iajs-2292 60 5 three three NUM iajs-2292 60 6 subpopulations subpopulation NOUN iajs-2292 60 7 of of ADP iajs-2292 60 8 spanish spanish ADJ iajs-2292 60 9 population population NOUN iajs-2292 60 10 of of ADP iajs-2292 60 11 the the DET iajs-2292 60 12 age age NOUN iajs-2292 60 13 of of ADP iajs-2292 60 14 15 15 NUM iajs-2292 60 15 - - SYM iajs-2292 60 16 64 64 NUM iajs-2292 60 17 years year NOUN iajs-2292 60 18 old old ADJ iajs-2292 60 19 from from ADP iajs-2292 60 20 1997 1997 NUM iajs-2292 60 21 to to ADP iajs-2292 60 22 2007 2007 NUM iajs-2292 60 23 years year NOUN iajs-2292 60 24 that that PRON iajs-2292 60 25 represented represent VERB iajs-2292 60 26 as as ADP iajs-2292 60 27 the the DET iajs-2292 60 28 nonlinear nonlinear ADJ iajs-2292 60 29 system system NOUN iajs-2292 60 30 of of ADP iajs-2292 60 31 three three NUM iajs-2292 60 32 ordinary ordinary ADJ iajs-2292 60 33 differential differential ADJ iajs-2292 60 34 equations equation NOUN iajs-2292 60 35 of of ADP iajs-2292 60 36 the the DET iajs-2292 60 37 first first ADJ iajs-2292 60 38 order order NOUN iajs-2292 60 39 . . PUNCT iajs-2292 61 1 this this DET iajs-2292 61 2 system system NOUN iajs-2292 61 3 is be AUX iajs-2292 61 4 referred refer VERB iajs-2292 61 5 to to PART iajs-2292 61 6 analyze analyze VERB iajs-2292 61 7 the the DET iajs-2292 61 8 changing change VERB iajs-2292 61 9 in in ADP iajs-2292 61 10 the the DET iajs-2292 61 11 social social ADJ iajs-2292 61 12 epidemic epidemic NOUN iajs-2292 61 13 stages stage NOUN iajs-2292 61 14 ( ( PUNCT iajs-2292 61 15 non non ADJ iajs-2292 61 16 - - ADJ iajs-2292 61 17 drink drink ADJ iajs-2292 61 18 alcohol alcohol NOUN iajs-2292 61 19 people people NOUN iajs-2292 61 20 , , PUNCT iajs-2292 61 21 nonrisk nonrisk ADJ iajs-2292 61 22 - - PUNCT iajs-2292 61 23 drink drink NOUN iajs-2292 61 24 alcohol alcohol NOUN iajs-2292 61 25 people people NOUN iajs-2292 61 26 and and CCONJ iajs-2292 61 27 risk risk NOUN iajs-2292 61 28 - - PUNCT iajs-2292 61 29 drink drink NOUN iajs-2292 61 30 alcohol alcohol NOUN iajs-2292 61 31 people people NOUN iajs-2292 61 32 ) ) PUNCT iajs-2292 61 33 , , PUNCT iajs-2292 61 34 see see VERB iajs-2292 61 35 table table NOUN iajs-2292 61 36 1 1 NUM iajs-2292 61 37 . . PUNCT iajs-2292 62 1 the the DET iajs-2292 62 2 parameters parameter NOUN iajs-2292 62 3 of of ADP iajs-2292 62 4 the the DET iajs-2292 62 5 model model NOUN iajs-2292 62 6 are be AUX iajs-2292 62 7 described describe VERB iajs-2292 62 8 in in ADP iajs-2292 62 9 table table NOUN iajs-2292 62 10 2 2 NUM iajs-2292 62 11 . . PUNCT iajs-2292 62 12 alcohol alcohol NOUN iajs-2292 62 13 consumption consumption NOUN iajs-2292 62 14 model model NOUN iajs-2292 62 15 for for ADP iajs-2292 62 16 the the DET iajs-2292 62 17 spanish spanish ADJ iajs-2292 62 18 public public NOUN iajs-2292 62 19 appears appear VERB iajs-2292 62 20 155 155 NUM iajs-2292 62 21 ibn ibn PROPN iajs-2292 62 22 al al PROPN iajs-2292 62 23 - - PUNCT iajs-2292 62 24 haitham haitham PROPN iajs-2292 62 25 jour jour X iajs-2292 62 26 . . PROPN iajs-2292 63 1 for for ADP iajs-2292 63 2 pure pure ADJ iajs-2292 63 3 & & CCONJ iajs-2292 63 4 appl appl PROPN iajs-2292 63 5 . . PUNCT iajs-2292 64 1 sci sci PROPN iajs-2292 64 2 . . PROPN iajs-2292 64 3 32 32 NUM iajs-2292 64 4 ( ( PUNCT iajs-2292 64 5 3 3 NUM iajs-2292 64 6 ) ) PUNCT iajs-2292 64 7 2019 2019 NUM iajs-2292 64 8 as as ADP iajs-2292 64 9 the the DET iajs-2292 64 10 following follow VERB iajs-2292 64 11 nonlinear nonlinear ADJ iajs-2292 64 12 system system NOUN iajs-2292 64 13 of of ADP iajs-2292 64 14 ordinary ordinary ADJ iajs-2292 64 15 differential differential ADJ iajs-2292 64 16 equations equation NOUN iajs-2292 64 17 , , PUNCT iajs-2292 64 18 [ [ X iajs-2292 64 19 12 12 NUM iajs-2292 64 20 ] ] PUNCT iajs-2292 64 21 . . PUNCT iajs-2292 65 1 consumption consumption NOUN iajs-2292 65 2 is be AUX iajs-2292 65 3 a a DET iajs-2292 65 4 dangerous dangerous ADJ iajs-2292 65 5 social social ADJ iajs-2292 65 6 habit habit NOUN iajs-2292 65 7 that that PRON iajs-2292 65 8 spread spread VERB iajs-2292 65 9 in in ADP iajs-2292 65 10 many many ADJ iajs-2292 65 11 countries country NOUN iajs-2292 65 12 such such ADJ iajs-2292 65 13 as as ADP iajs-2292 65 14 π‘ŽΛŠ(𝑑 π‘ŽΛŠ(𝑑 NOUN iajs-2292 65 15 ) ) PUNCT iajs-2292 66 1 = = SYM iajs-2292 66 2 𝛼 𝛼 X iajs-2292 66 3 + + X iajs-2292 66 4 𝛽 𝛽 NOUN iajs-2292 66 5 βˆ— βˆ— NOUN iajs-2292 66 6 π‘Ÿ π‘Ÿ X iajs-2292 66 7 βˆ’ βˆ’ NOUN iajs-2292 66 8 πœ‡ πœ‡ ADP iajs-2292 66 9 βˆ— βˆ— NOUN iajs-2292 66 10 π‘Ž π‘Ž PRON iajs-2292 66 11 βˆ’ βˆ’ NOUN iajs-2292 66 12 πœ‰ πœ‰ NOUN iajs-2292 66 13 βˆ— βˆ— NOUN iajs-2292 66 14 π‘Ž π‘Ž NOUN iajs-2292 66 15 βˆ— βˆ— NOUN iajs-2292 66 16 ( ( PUNCT iajs-2292 66 17 π‘š π‘š PROPN iajs-2292 66 18 + + NUM iajs-2292 66 19 π‘Ÿ π‘Ÿ NOUN iajs-2292 66 20 ) ) PUNCT iajs-2292 66 21 βˆ’ βˆ’ ADP iajs-2292 67 1 π‘Ž π‘Ž NOUN iajs-2292 67 2 βˆ— βˆ— NOUN iajs-2292 67 3 ( ( PUNCT iajs-2292 67 4 𝛼 𝛼 NOUN iajs-2292 67 5 βˆ’ βˆ’ NOUN iajs-2292 67 6 πœ‡ πœ‡ ADP iajs-2292 67 7 βˆ— βˆ— NOUN iajs-2292 67 8 π‘Ž π‘Ž PRON iajs-2292 67 9 βˆ’ βˆ’ NOUN iajs-2292 67 10 𝜎 𝜎 PROPN iajs-2292 67 11 βˆ— βˆ— NOUN iajs-2292 67 12 π‘š π‘š ADP iajs-2292 67 13 βˆ’ βˆ’ PROPN iajs-2292 67 14 𝜎 𝜎 PROPN iajs-2292 67 15 βˆ— βˆ— NOUN iajs-2292 67 16 π‘Ÿ π‘Ÿ NOUN iajs-2292 67 17 ) ) PUNCT iajs-2292 67 18 ( ( PUNCT iajs-2292 67 19 1 1 NUM iajs-2292 67 20 ) ) PUNCT iajs-2292 67 21 π‘šΛŠ(𝑑 π‘šΛŠ(𝑑 PUNCT iajs-2292 67 22 ) ) PUNCT iajs-2292 67 23 = = SYM iajs-2292 67 24 πœ‰ πœ‰ ADP iajs-2292 67 25 βˆ— βˆ— NOUN iajs-2292 67 26 π‘Ž π‘Ž NOUN iajs-2292 67 27 βˆ— βˆ— NOUN iajs-2292 67 28 ( ( PUNCT iajs-2292 67 29 π‘š π‘š PROPN iajs-2292 67 30 + + NUM iajs-2292 67 31 π‘Ÿ π‘Ÿ NOUN iajs-2292 67 32 ) ) PUNCT iajs-2292 67 33 βˆ’ βˆ’ NOUN iajs-2292 67 34 πœ‚ πœ‚ NOUN iajs-2292 67 35 βˆ— βˆ— NOUN iajs-2292 67 36 π‘š π‘š X iajs-2292 67 37 + + X iajs-2292 67 38 πœ‡ πœ‡ ADP iajs-2292 67 39 βˆ— βˆ— NOUN iajs-2292 67 40 π‘Ž π‘Ž NOUN iajs-2292 67 41 βˆ— βˆ— NOUN iajs-2292 67 42 π‘š π‘š ADP iajs-2292 67 43 βˆ’ βˆ’ PROPN iajs-2292 67 44 𝜎 𝜎 PROPN iajs-2292 67 45 βˆ— βˆ— NOUN iajs-2292 67 46 π‘Ž π‘Ž NOUN iajs-2292 67 47 βˆ— βˆ— NOUN iajs-2292 67 48 π‘š π‘š ADP iajs-2292 67 49 βˆ’ βˆ’ NOUN iajs-2292 67 50 𝛼 𝛼 X iajs-2292 67 51 βˆ— βˆ— NOUN iajs-2292 67 52 π‘š π‘š X iajs-2292 67 53 ( ( PUNCT iajs-2292 67 54 2 2 NUM iajs-2292 67 55 ) ) PUNCT iajs-2292 67 56 π‘ŸΛŠ(𝑑 π‘ŸΛŠ(𝑑 NUM iajs-2292 67 57 ) ) PUNCT iajs-2292 67 58 = = SYM iajs-2292 67 59 πœ‚ πœ‚ NOUN iajs-2292 67 60 βˆ— βˆ— NOUN iajs-2292 67 61 π‘š π‘š ADP iajs-2292 67 62 βˆ’ βˆ’ PROPN iajs-2292 67 63 𝛽 𝛽 NOUN iajs-2292 67 64 βˆ— βˆ— NOUN iajs-2292 67 65 π‘Ÿ π‘Ÿ NOUN iajs-2292 67 66 + + X iajs-2292 67 67 πœ‡ πœ‡ ADP iajs-2292 67 68 βˆ— βˆ— NOUN iajs-2292 67 69 π‘Ž π‘Ž NOUN iajs-2292 67 70 βˆ— βˆ— NOUN iajs-2292 67 71 π‘Ÿ π‘Ÿ X iajs-2292 67 72 βˆ’ βˆ’ PROPN iajs-2292 67 73 𝜎 𝜎 PROPN iajs-2292 67 74 βˆ— βˆ— NOUN iajs-2292 67 75 π‘Ž π‘Ž NOUN iajs-2292 67 76 βˆ— βˆ— NOUN iajs-2292 67 77 π‘Ÿ π‘Ÿ X iajs-2292 67 78 βˆ’ βˆ’ NOUN iajs-2292 67 79 𝛼 𝛼 X iajs-2292 67 80 βˆ— βˆ— NOUN iajs-2292 67 81 π‘Ÿ π‘Ÿ NOUN iajs-2292 67 82 ( ( PUNCT iajs-2292 67 83 3 3 X iajs-2292 67 84 ) ) PUNCT iajs-2292 67 85 the the DET iajs-2292 67 86 initial initial ADJ iajs-2292 67 87 conditions condition NOUN iajs-2292 67 88 of of ADP iajs-2292 67 89 equations equation NOUN iajs-2292 67 90 ( ( PUNCT iajs-2292 67 91 1 1 NUM iajs-2292 67 92 - - SYM iajs-2292 67 93 3 3 NUM iajs-2292 67 94 ) ) PUNCT iajs-2292 67 95 in in ADP iajs-2292 67 96 1997 1997 NUM iajs-2292 67 97 are be AUX iajs-2292 67 98 π‘Ž(𝑑 π‘Ž(𝑑 PROPN iajs-2292 67 99 = = SYM iajs-2292 67 100 0 0 NUM iajs-2292 67 101 ) ) PUNCT iajs-2292 67 102 = = SYM iajs-2292 67 103 0.362 0.362 NUM iajs-2292 67 104 , , PUNCT iajs-2292 67 105 π‘š(𝑑 π‘š(𝑑 X iajs-2292 67 106 = = SYM iajs-2292 67 107 0 0 NUM iajs-2292 67 108 ) ) PUNCT iajs-2292 67 109 = = SYM iajs-2292 67 110 0.581 0.581 NUM iajs-2292 67 111 , , PUNCT iajs-2292 67 112 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 67 113 = = SYM iajs-2292 67 114 0 0 NUM iajs-2292 67 115 ) ) PUNCT iajs-2292 67 116 = = NOUN iajs-2292 67 117 0.057 0.057 NUM iajs-2292 67 118 , , PUNCT iajs-2292 67 119 with with ADP iajs-2292 67 120 the the DET iajs-2292 67 121 predicted predict VERB iajs-2292 67 122 parameters parameter NOUN iajs-2292 67 123 are be AUX iajs-2292 67 124 given give VERB iajs-2292 67 125 as as ADP iajs-2292 67 126 : : PUNCT iajs-2292 67 127 𝛼 𝛼 X iajs-2292 67 128 = = NOUN iajs-2292 67 129 0.01 0.01 NUM iajs-2292 67 130 , , PUNCT iajs-2292 67 131 𝛽 𝛽 NOUN iajs-2292 67 132 = = SYM iajs-2292 67 133 0.0014 0.0014 NUM iajs-2292 67 134 , , PUNCT iajs-2292 67 135 πœ‡ πœ‡ X iajs-2292 67 136 = = PROPN iajs-2292 67 137 0.008 0.008 NUM iajs-2292 67 138 , , PUNCT iajs-2292 67 139 πœ‰ πœ‰ NOUN iajs-2292 67 140 = = SYM iajs-2292 67 141 0.0284534 0.0284534 NUM iajs-2292 67 142 , , PUNCT iajs-2292 67 143 𝜎 𝜎 NOUN iajs-2292 67 144 = = NOUN iajs-2292 67 145 0.009 0.009 NUM iajs-2292 67 146 , , PUNCT iajs-2292 67 147 and and CCONJ iajs-2292 67 148 πœ‚ πœ‚ X iajs-2292 67 149 = = SYM iajs-2292 67 150 0.000110247,[12 0.000110247,[12 PROPN iajs-2292 67 151 ] ] PUNCT iajs-2292 67 152 . . PUNCT iajs-2292 68 1 table table NOUN iajs-2292 68 2 1 1 NUM iajs-2292 68 3 . . PUNCT iajs-2292 69 1 variables variable NOUN iajs-2292 69 2 of of ADP iajs-2292 69 3 alcohol alcohol NOUN iajs-2292 69 4 consumption consumption NOUN iajs-2292 69 5 model model NOUN iajs-2292 69 6 , , PUNCT iajs-2292 69 7 [ [ X iajs-2292 69 8 12 12 NUM iajs-2292 69 9 ] ] PUNCT iajs-2292 69 10 . . PUNCT iajs-2292 70 1 𝒂(𝒕 𝒂(𝒕 NOUN iajs-2292 70 2 ) ) PUNCT iajs-2292 70 3 non non ADJ iajs-2292 70 4 - - ADJ iajs-2292 70 5 drink drink ADJ iajs-2292 70 6 alcohol alcohol NOUN iajs-2292 70 7 people people NOUN iajs-2292 70 8 are be AUX iajs-2292 70 9 subpopulations subpopulation NOUN iajs-2292 70 10 who who PRON iajs-2292 70 11 never never ADV iajs-2292 70 12 drink drink VERB iajs-2292 70 13 alcohol alcohol NOUN iajs-2292 70 14 in in ADP iajs-2292 70 15 their their PRON iajs-2292 70 16 life life NOUN iajs-2292 70 17 . . PUNCT iajs-2292 71 1 π’Ž(𝒕 π’Ž(𝒕 NOUN iajs-2292 71 2 ) ) PUNCT iajs-2292 71 3 non non ADJ iajs-2292 71 4 - - ADJ iajs-2292 71 5 risk risk NOUN iajs-2292 71 6 - - PUNCT iajs-2292 71 7 drink drink NOUN iajs-2292 71 8 alcohol alcohol NOUN iajs-2292 71 9 people people NOUN iajs-2292 71 10 are be AUX iajs-2292 71 11 subpopulations subpopulation NOUN iajs-2292 71 12 who who PRON iajs-2292 71 13 drink drink VERB iajs-2292 71 14 a a DET iajs-2292 71 15 little little ADJ iajs-2292 71 16 liquid liquid NOUN iajs-2292 71 17 of of ADP iajs-2292 71 18 alcohol alcohol NOUN iajs-2292 71 19 alcohol alcohol NOUN iajs-2292 71 20 that that PRON iajs-2292 71 21 means mean VERB iajs-2292 71 22 the the DET iajs-2292 71 23 men man NOUN iajs-2292 71 24 who who PRON iajs-2292 71 25 drink drink VERB iajs-2292 71 26 less less ADJ iajs-2292 71 27 than than ADP iajs-2292 71 28 50 50 NUM iajs-2292 71 29 cc cc NOUN iajs-2292 71 30 and and CCONJ iajs-2292 71 31 women woman NOUN iajs-2292 71 32 who who PRON iajs-2292 71 33 drink drink VERB iajs-2292 71 34 less less ADJ iajs-2292 71 35 than than ADP iajs-2292 71 36 30 30 NUM iajs-2292 71 37 cc cc NOUN iajs-2292 71 38 of of ADP iajs-2292 71 39 alcohol alcohol NOUN iajs-2292 71 40 every every DET iajs-2292 71 41 day day NOUN iajs-2292 71 42 . . PUNCT iajs-2292 72 1 𝒓(𝒕 𝒓(𝒕 NOUN iajs-2292 72 2 ) ) PUNCT iajs-2292 72 3 risk risk NOUN iajs-2292 72 4 - - PUNCT iajs-2292 72 5 drink drink NOUN iajs-2292 72 6 alcohol alcohol NOUN iajs-2292 72 7 people people NOUN iajs-2292 72 8 are be AUX iajs-2292 72 9 subpopulations subpopulation NOUN iajs-2292 72 10 who who PRON iajs-2292 72 11 drink drink VERB iajs-2292 72 12 a a DET iajs-2292 72 13 lot lot NOUN iajs-2292 72 14 of of ADP iajs-2292 72 15 alcohol alcohol NOUN iajs-2292 72 16 that that PRON iajs-2292 72 17 means mean VERB iajs-2292 72 18 the the DET iajs-2292 72 19 men man NOUN iajs-2292 72 20 who who PRON iajs-2292 72 21 drink drink VERB iajs-2292 72 22 more more ADJ iajs-2292 72 23 than than ADP iajs-2292 72 24 50 50 NUM iajs-2292 72 25 cc cc NOUN iajs-2292 72 26 and and CCONJ iajs-2292 72 27 the the DET iajs-2292 72 28 women woman NOUN iajs-2292 72 29 who who PRON iajs-2292 72 30 drink drink VERB iajs-2292 72 31 more more ADJ iajs-2292 72 32 than than ADP iajs-2292 72 33 30 30 NUM iajs-2292 72 34 cc cc NOUN iajs-2292 72 35 of of ADP iajs-2292 72 36 alcohol alcohol NOUN iajs-2292 72 37 every every DET iajs-2292 72 38 day day NOUN iajs-2292 72 39 . . PUNCT iajs-2292 73 1 table table NOUN iajs-2292 73 2 2 2 NUM iajs-2292 73 3 . . PUNCT iajs-2292 74 1 parameters parameter NOUN iajs-2292 74 2 of of ADP iajs-2292 74 3 alcohol alcohol NOUN iajs-2292 74 4 consumption consumption NOUN iajs-2292 74 5 model model NOUN iajs-2292 74 6 , , PUNCT iajs-2292 74 7 [ [ X iajs-2292 74 8 12 12 NUM iajs-2292 74 9 ] ] PUNCT iajs-2292 74 10 . . PUNCT iajs-2292 75 1 birth birth NOUN iajs-2292 75 2 rate rate NOUN iajs-2292 75 3 in in ADP iajs-2292 75 4 spain spain PROPN iajs-2292 75 5 𝜢 𝜢 ADP iajs-2292 75 6 the the DET iajs-2292 75 7 rate rate NOUN iajs-2292 75 8 at at ADP iajs-2292 75 9 which which PRON iajs-2292 75 10 a a DET iajs-2292 75 11 risk risk NOUN iajs-2292 75 12 - - PUNCT iajs-2292 75 13 drink drink NOUN iajs-2292 75 14 alcohol alcohol NOUN iajs-2292 75 15 people people NOUN iajs-2292 75 16 becomes become VERB iajs-2292 75 17 a a DET iajs-2292 75 18 non non ADJ iajs-2292 75 19 - - ADJ iajs-2292 75 20 drink drink ADJ iajs-2292 75 21 alcohol alcohol NOUN iajs-2292 75 22 people people NOUN iajs-2292 75 23 𝜷 𝜷 ADP iajs-2292 75 24 death death NOUN iajs-2292 75 25 rate rate NOUN iajs-2292 75 26 in in ADP iajs-2292 75 27 spain spain PROPN iajs-2292 75 28 𝝁 𝝁 PROPN iajs-2292 75 29 transmission transmission NOUN iajs-2292 75 30 rate rate NOUN iajs-2292 75 31 because because SCONJ iajs-2292 75 32 social social ADJ iajs-2292 75 33 pressure pressure NOUN iajs-2292 75 34 that that PRON iajs-2292 75 35 leads lead VERB iajs-2292 75 36 to to ADP iajs-2292 75 37 increasing increase VERB iajs-2292 75 38 the the DET iajs-2292 75 39 alcohol alcohol NOUN iajs-2292 75 40 drinking drinking NOUN iajs-2292 75 41 𝝃 𝝃 NOUN iajs-2292 75 42 growing grow VERB iajs-2292 75 43 death death NOUN iajs-2292 75 44 rate rate NOUN iajs-2292 75 45 due due ADP iajs-2292 75 46 to to ADP iajs-2292 75 47 alcohol alcohol NOUN iajs-2292 75 48 drinking drinking NOUN iajs-2292 75 49 𝝈 𝝈 DET iajs-2292 75 50 a a DET iajs-2292 75 51 rate rate NOUN iajs-2292 75 52 that that PRON iajs-2292 75 53 transmits transmit VERB iajs-2292 75 54 a a DET iajs-2292 75 55 non non ADJ iajs-2292 75 56 - - ADJ iajs-2292 75 57 risk risk ADJ iajs-2292 75 58 - - PUNCT iajs-2292 75 59 drink drink NOUN iajs-2292 75 60 alcohol alcohol NOUN iajs-2292 75 61 people people NOUN iajs-2292 75 62 moves move VERB iajs-2292 75 63 to to ADP iajs-2292 75 64 the the DET iajs-2292 75 65 risk risk NOUN iajs-2292 75 66 - - PUNCT iajs-2292 75 67 drink drink NOUN iajs-2292 75 68 alcohol alcohol NOUN iajs-2292 75 69 people people NOUN iajs-2292 75 70 𝜼 𝜼 VERB iajs-2292 75 71 3 3 NUM iajs-2292 75 72 . . PUNCT iajs-2292 75 73 analytic analytic ADJ iajs-2292 75 74 methods method NOUN iajs-2292 75 75 in in ADP iajs-2292 75 76 this this DET iajs-2292 75 77 section section NOUN iajs-2292 75 78 some some DET iajs-2292 75 79 analytic analytic ADJ iajs-2292 75 80 methods method NOUN iajs-2292 75 81 are be AUX iajs-2292 75 82 introduced introduce VERB iajs-2292 75 83 such such ADJ iajs-2292 75 84 3.1 3.1 NUM iajs-2292 75 85 adomian adomian NOUN iajs-2292 75 86 decomposition decomposition NOUN iajs-2292 75 87 method method NOUN iajs-2292 75 88 we we PRON iajs-2292 75 89 can can AUX iajs-2292 75 90 solve solve VERB iajs-2292 75 91 the the DET iajs-2292 75 92 nonlinear nonlinear ADJ iajs-2292 75 93 system system NOUN iajs-2292 75 94 of of ADP iajs-2292 75 95 equations equation NOUN iajs-2292 75 96 ( ( PUNCT iajs-2292 75 97 1 1 NUM iajs-2292 75 98 - - SYM iajs-2292 75 99 3 3 NUM iajs-2292 75 100 ) ) PUNCT iajs-2292 75 101 by by ADP iajs-2292 75 102 using use VERB iajs-2292 75 103 the the DET iajs-2292 75 104 adomian adomian NOUN iajs-2292 75 105 decomposition decomposition NOUN iajs-2292 75 106 method method NOUN iajs-2292 75 107 with with ADP iajs-2292 75 108 the the DET iajs-2292 75 109 above above ADJ iajs-2292 75 110 initial initial ADJ iajs-2292 75 111 condition condition NOUN iajs-2292 75 112 and and CCONJ iajs-2292 75 113 the the DET iajs-2292 75 114 given give VERB iajs-2292 75 115 parameters parameter NOUN iajs-2292 75 116 . . PUNCT iajs-2292 76 1 let let VERB iajs-2292 76 2 𝑙 𝑙 PART iajs-2292 76 3 be be AUX iajs-2292 76 4 an an DET iajs-2292 76 5 operator operator NOUN iajs-2292 76 6 that that PRON iajs-2292 76 7 is be AUX iajs-2292 76 8 given give VERB iajs-2292 76 9 by by ADP iajs-2292 76 10 = = PROPN iajs-2292 76 11 𝑑 𝑑 PROPN iajs-2292 76 12 𝑑𝑑 𝑑𝑑 ADP iajs-2292 76 13 , , PUNCT iajs-2292 76 14 the the DET iajs-2292 76 15 inverse inverse NOUN iajs-2292 76 16 of of ADP iajs-2292 76 17 this this DET iajs-2292 76 18 operation operation NOUN iajs-2292 76 19 is be AUX iajs-2292 76 20 π‘™βˆ’1 π‘™βˆ’1 PROPN iajs-2292 76 21 = = SYM iajs-2292 76 22 ∫ ∫ PROPN iajs-2292 76 23 ( ( PUNCT iajs-2292 76 24 . . PUNCT iajs-2292 76 25 ) ) PUNCT iajs-2292 76 26 𝑑𝑑 𝑑𝑑 ADP iajs-2292 76 27 𝑑 𝑑 PROPN iajs-2292 76 28 0 0 NUM iajs-2292 76 29 , , PUNCT iajs-2292 76 30 then then ADV iajs-2292 76 31 by by ADP iajs-2292 76 32 applying apply VERB iajs-2292 76 33 π‘™βˆ’1 π‘™βˆ’1 PROPN iajs-2292 76 34 for for ADP iajs-2292 76 35 both both DET iajs-2292 76 36 sides side NOUN iajs-2292 76 37 of of ADP iajs-2292 76 38 equations equation NOUN iajs-2292 76 39 ( ( PUNCT iajs-2292 76 40 1 1 NUM iajs-2292 76 41 - - SYM iajs-2292 76 42 3 3 NUM iajs-2292 76 43 ) ) PUNCT iajs-2292 76 44 , , PUNCT iajs-2292 76 45 we we PRON iajs-2292 76 46 obtain obtain VERB iajs-2292 76 47 : : PUNCT iajs-2292 76 48 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 76 49 ) ) PUNCT iajs-2292 76 50 βˆ’ βˆ’ PROPN iajs-2292 77 1 π‘Ž(0 π‘Ž(0 PROPN iajs-2292 77 2 ) ) PUNCT iajs-2292 77 3 = = SYM iajs-2292 77 4 π‘™βˆ’1 π‘™βˆ’1 PROPN iajs-2292 77 5 ( ( PUNCT iajs-2292 77 6 𝛼 𝛼 PROPN iajs-2292 77 7 + + NOUN iajs-2292 77 8 𝛽 𝛽 NOUN iajs-2292 77 9 βˆ— βˆ— NOUN iajs-2292 77 10 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 77 11 ) ) PUNCT iajs-2292 77 12 βˆ’ βˆ’ NOUN iajs-2292 77 13 πœ‡ πœ‡ ADP iajs-2292 77 14 βˆ— βˆ— X iajs-2292 77 15 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 77 16 ) ) PUNCT iajs-2292 77 17 βˆ’ βˆ’ ADP iajs-2292 77 18 πœ‰ πœ‰ ADP iajs-2292 77 19 βˆ— βˆ— NOUN iajs-2292 77 20 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 77 21 ) ) PUNCT iajs-2292 77 22 βˆ— βˆ— NOUN iajs-2292 77 23 ( ( PUNCT iajs-2292 77 24 π‘š(𝑑 π‘š(𝑑 NUM iajs-2292 77 25 ) ) PUNCT iajs-2292 77 26 + + CCONJ iajs-2292 77 27 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 77 28 ) ) PUNCT iajs-2292 77 29 ) ) PUNCT iajs-2292 78 1 βˆ’ βˆ’ PROPN iajs-2292 78 2 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 78 3 ) ) PUNCT iajs-2292 78 4 βˆ— βˆ— NOUN iajs-2292 78 5 ( ( PUNCT iajs-2292 78 6 𝛼 𝛼 NOUN iajs-2292 78 7 βˆ’ βˆ’ NOUN iajs-2292 78 8 πœ‡ πœ‡ ADP iajs-2292 78 9 βˆ— βˆ— X iajs-2292 78 10 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 78 11 ) ) PUNCT iajs-2292 78 12 βˆ’ βˆ’ PROPN iajs-2292 78 13 𝜎 𝜎 PROPN iajs-2292 78 14 βˆ— βˆ— NOUN iajs-2292 78 15 π‘š(𝑑 π‘š(𝑑 VERB iajs-2292 78 16 ) ) PUNCT iajs-2292 78 17 βˆ’ βˆ’ PROPN iajs-2292 78 18 𝜎 𝜎 PROPN iajs-2292 78 19 βˆ— βˆ— NOUN iajs-2292 78 20 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 78 21 ) ) PUNCT iajs-2292 78 22 ) ) PUNCT iajs-2292 78 23 ) ) PUNCT iajs-2292 78 24 , , PUNCT iajs-2292 78 25 where where SCONJ iajs-2292 78 26 π‘Ž0(𝑑 π‘Ž0(𝑑 NOUN iajs-2292 78 27 ) ) PUNCT iajs-2292 78 28 = = PUNCT iajs-2292 79 1 0.362 0.362 NUM iajs-2292 79 2 . . PUNCT iajs-2292 80 1 156 156 NUM iajs-2292 80 2 ibn ibn PROPN iajs-2292 80 3 al al PROPN iajs-2292 80 4 - - PUNCT iajs-2292 80 5 haitham haitham PROPN iajs-2292 80 6 jour jour X iajs-2292 80 7 . . PROPN iajs-2292 80 8 for for ADP iajs-2292 80 9 pure pure ADJ iajs-2292 80 10 & & CCONJ iajs-2292 80 11 appl appl PROPN iajs-2292 80 12 . . PUNCT iajs-2292 81 1 sci sci PROPN iajs-2292 81 2 . . PROPN iajs-2292 81 3 32 32 NUM iajs-2292 81 4 ( ( PUNCT iajs-2292 81 5 3 3 NUM iajs-2292 81 6 ) ) SYM iajs-2292 81 7 2019 2019 NUM iajs-2292 81 8 similarity similarity NOUN iajs-2292 81 9 , , PUNCT iajs-2292 81 10 π‘š(𝑑 π‘š(𝑑 NUM iajs-2292 81 11 ) ) PUNCT iajs-2292 81 12 βˆ’ βˆ’ PROPN iajs-2292 82 1 π‘š(0 π‘š(0 NOUN iajs-2292 82 2 ) ) PUNCT iajs-2292 83 1 = = SYM iajs-2292 83 2 π‘™βˆ’1 π‘™βˆ’1 PROPN iajs-2292 83 3 ( ( PUNCT iajs-2292 83 4 πœ‰ πœ‰ NOUN iajs-2292 83 5 βˆ— βˆ— NOUN iajs-2292 83 6 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 83 7 ) ) PUNCT iajs-2292 83 8 βˆ— βˆ— NOUN iajs-2292 83 9 ( ( PUNCT iajs-2292 83 10 π‘š(𝑑 π‘š(𝑑 NUM iajs-2292 83 11 ) ) PUNCT iajs-2292 83 12 + + CCONJ iajs-2292 83 13 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 83 14 ) ) PUNCT iajs-2292 83 15 ) ) PUNCT iajs-2292 84 1 βˆ’ βˆ’ ADP iajs-2292 84 2 πœ‚ πœ‚ NOUN iajs-2292 84 3 βˆ— βˆ— NOUN iajs-2292 84 4 π‘š(𝑑 π‘š(𝑑 NUM iajs-2292 84 5 ) ) PUNCT iajs-2292 85 1 + + CCONJ iajs-2292 85 2 πœ‡ πœ‡ ADP iajs-2292 85 3 βˆ— βˆ— NOUN iajs-2292 85 4 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 85 5 ) ) PUNCT iajs-2292 85 6 βˆ— βˆ— NOUN iajs-2292 85 7 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 85 8 ) ) PUNCT iajs-2292 85 9 βˆ’ βˆ’ PROPN iajs-2292 85 10 𝜎 𝜎 PROPN iajs-2292 85 11 βˆ— βˆ— NOUN iajs-2292 85 12 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 85 13 ) ) PUNCT iajs-2292 85 14 βˆ— βˆ— NOUN iajs-2292 85 15 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 85 16 ) ) PUNCT iajs-2292 86 1 βˆ’ βˆ’ ADP iajs-2292 86 2 𝛼 𝛼 NOUN iajs-2292 86 3 βˆ— βˆ— NOUN iajs-2292 86 4 π‘š(𝑑 π‘š(𝑑 VERB iajs-2292 86 5 ) ) PUNCT iajs-2292 86 6 ) ) PUNCT iajs-2292 86 7 , , PUNCT iajs-2292 86 8 where where SCONJ iajs-2292 86 9 π‘š0(𝑑 π‘š0(𝑑 VERB iajs-2292 86 10 ) ) PUNCT iajs-2292 86 11 = = PUNCT iajs-2292 86 12 0.581 0.581 NUM iajs-2292 86 13 , , PUNCT iajs-2292 86 14 and and CCONJ iajs-2292 86 15 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 86 16 ) ) PUNCT iajs-2292 87 1 βˆ’ βˆ’ PROPN iajs-2292 87 2 π‘Ÿ(0 π‘Ÿ(0 PROPN iajs-2292 87 3 ) ) PUNCT iajs-2292 88 1 = = SYM iajs-2292 88 2 π‘™βˆ’1 π‘™βˆ’1 PROPN iajs-2292 88 3 ( ( PUNCT iajs-2292 88 4 πœ‚ πœ‚ NOUN iajs-2292 88 5 βˆ— βˆ— X iajs-2292 88 6 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 88 7 ) ) PUNCT iajs-2292 88 8 βˆ’ βˆ’ PROPN iajs-2292 88 9 𝛽 𝛽 NOUN iajs-2292 88 10 βˆ— βˆ— X iajs-2292 88 11 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 88 12 ) ) PUNCT iajs-2292 89 1 + + CCONJ iajs-2292 89 2 πœ‡ πœ‡ ADP iajs-2292 89 3 βˆ— βˆ— NOUN iajs-2292 89 4 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 89 5 ) ) PUNCT iajs-2292 89 6 βˆ— βˆ— NOUN iajs-2292 89 7 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 89 8 ) ) PUNCT iajs-2292 89 9 βˆ’ βˆ’ PROPN iajs-2292 89 10 𝜎 𝜎 PROPN iajs-2292 89 11 βˆ— βˆ— NOUN iajs-2292 89 12 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 89 13 ) ) PUNCT iajs-2292 89 14 βˆ— βˆ— NOUN iajs-2292 89 15 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 89 16 ) ) PUNCT iajs-2292 90 1 βˆ’ βˆ’ PROPN iajs-2292 90 2 𝛼 𝛼 X iajs-2292 90 3 βˆ— βˆ— NOUN iajs-2292 90 4 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 90 5 ) ) PUNCT iajs-2292 90 6 ) ) PUNCT iajs-2292 90 7 , , PUNCT iajs-2292 90 8 where where SCONJ iajs-2292 90 9 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 VERB iajs-2292 90 10 ) ) PUNCT iajs-2292 90 11 = = NOUN iajs-2292 90 12 0.057 0.057 NUM iajs-2292 90 13 . . PUNCT iajs-2292 91 1 the the DET iajs-2292 91 2 above above ADJ iajs-2292 91 3 equations equation NOUN iajs-2292 91 4 equivalent equivalent VERB iajs-2292 91 5 the the DET iajs-2292 91 6 following follow VERB iajs-2292 91 7 equations equation NOUN iajs-2292 91 8 ( ( PUNCT iajs-2292 91 9 4 4 NUM iajs-2292 91 10 - - SYM iajs-2292 91 11 6 6 NUM iajs-2292 91 12 ): ): PUNCT iajs-2292 91 13 π‘Žπ‘˜+1(𝑑 π‘Žπ‘˜+1(𝑑 NOUN iajs-2292 91 14 ) ) PUNCT iajs-2292 91 15 = = SYM iajs-2292 91 16 π‘™βˆ’1(𝛼 π‘™βˆ’1(𝛼 NOUN iajs-2292 91 17 + + CCONJ iajs-2292 91 18 𝛽 𝛽 NOUN iajs-2292 91 19 βˆ— βˆ— NOUN iajs-2292 91 20 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 91 21 ) ) PUNCT iajs-2292 91 22 βˆ’ βˆ’ NOUN iajs-2292 91 23 πœ‡ πœ‡ ADP iajs-2292 91 24 βˆ— βˆ— NOUN iajs-2292 91 25 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 91 26 ) ) PUNCT iajs-2292 91 27 βˆ’ βˆ’ ADP iajs-2292 91 28 πœ‰ πœ‰ ADP iajs-2292 91 29 βˆ— βˆ— X iajs-2292 91 30 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 91 31 ) ) PUNCT iajs-2292 91 32 βˆ’ βˆ’ ADP iajs-2292 91 33 πœ‰ πœ‰ ADP iajs-2292 91 34 βˆ— βˆ— NOUN iajs-2292 91 35 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 91 36 ) ) PUNCT iajs-2292 91 37 βˆ’ βˆ’ PROPN iajs-2292 91 38 𝛼 𝛼 SYM iajs-2292 91 39 βˆ— βˆ— NOUN iajs-2292 91 40 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 91 41 ) ) PUNCT iajs-2292 92 1 + + CCONJ iajs-2292 92 2 πœ‡ πœ‡ ADP iajs-2292 92 3 βˆ— βˆ— NOUN iajs-2292 92 4 πΆπ‘˜(𝑑 πΆπ‘˜(𝑑 ADP iajs-2292 92 5 ) ) PUNCT iajs-2292 92 6 + + CCONJ iajs-2292 92 7 𝜎 𝜎 PROPN iajs-2292 92 8 βˆ— βˆ— NOUN iajs-2292 92 9 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 92 10 ) ) PUNCT iajs-2292 93 1 + + PUNCT iajs-2292 93 2 𝜎 𝜎 PROPN iajs-2292 93 3 βˆ— βˆ— NOUN iajs-2292 93 4 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 93 5 ) ) PUNCT iajs-2292 93 6 ) ) PUNCT iajs-2292 93 7 , , PUNCT iajs-2292 93 8 forallπ‘˜ forallπ‘˜ VERB iajs-2292 93 9 β‰₯ β‰₯ NOUN iajs-2292 93 10 0 0 NUM iajs-2292 93 11 . . PUNCT iajs-2292 94 1 ( ( PUNCT iajs-2292 94 2 4 4 X iajs-2292 94 3 ) ) PUNCT iajs-2292 94 4 π‘šπ‘˜+1(𝑑 π‘šπ‘˜+1(𝑑 NOUN iajs-2292 94 5 ) ) PUNCT iajs-2292 95 1 = = SYM iajs-2292 95 2 π‘™βˆ’1(πœ‰ π‘™βˆ’1(πœ‰ PROPN iajs-2292 95 3 βˆ— βˆ— NOUN iajs-2292 95 4 ( ( PUNCT iajs-2292 95 5 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 95 6 ) ) PUNCT iajs-2292 95 7 + + CCONJ iajs-2292 95 8 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 95 9 ) ) PUNCT iajs-2292 95 10 ) ) PUNCT iajs-2292 95 11 βˆ’ βˆ’ ADP iajs-2292 95 12 πœ‚ πœ‚ NOUN iajs-2292 95 13 βˆ— βˆ— NOUN iajs-2292 95 14 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 95 15 ) ) PUNCT iajs-2292 96 1 + + CCONJ iajs-2292 96 2 πœ‡ πœ‡ SCONJ iajs-2292 96 3 βˆ— βˆ— NOUN iajs-2292 96 4 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 96 5 ) ) PUNCT iajs-2292 97 1 βˆ’ βˆ’ PROPN iajs-2292 97 2 𝜎 𝜎 PROPN iajs-2292 97 3 βˆ— βˆ— NOUN iajs-2292 97 4 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 97 5 ) ) PUNCT iajs-2292 97 6 βˆ’ βˆ’ ADP iajs-2292 97 7 𝛼 𝛼 NOUN iajs-2292 97 8 βˆ— βˆ— NOUN iajs-2292 97 9 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 97 10 ) ) PUNCT iajs-2292 97 11 ) ) PUNCT iajs-2292 97 12 , , PUNCT iajs-2292 97 13 for for ADP iajs-2292 97 14 all all DET iajs-2292 97 15 π‘˜ π‘˜ DET iajs-2292 97 16 β‰₯ β‰₯ NOUN iajs-2292 97 17 0 0 NUM iajs-2292 97 18 . . PUNCT iajs-2292 98 1 ( ( PUNCT iajs-2292 98 2 5 5 X iajs-2292 98 3 ) ) PUNCT iajs-2292 98 4 π‘Ÿπ‘˜+1(𝑑 π‘Ÿπ‘˜+1(𝑑 PROPN iajs-2292 98 5 ) ) PUNCT iajs-2292 99 1 = = SYM iajs-2292 99 2 π‘™βˆ’1(πœ‚ π‘™βˆ’1(πœ‚ PROPN iajs-2292 99 3 βˆ— βˆ— NOUN iajs-2292 99 4 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 PUNCT iajs-2292 99 5 ) ) PUNCT iajs-2292 99 6 βˆ’ βˆ’ ADP iajs-2292 99 7 𝛽 𝛽 NOUN iajs-2292 99 8 βˆ— βˆ— NOUN iajs-2292 99 9 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 99 10 ) ) PUNCT iajs-2292 100 1 + + CCONJ iajs-2292 100 2 πœ‡ πœ‡ ADP iajs-2292 100 3 βˆ— βˆ— NOUN iajs-2292 100 4 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 100 5 ) ) PUNCT iajs-2292 100 6 βˆ’ βˆ’ PROPN iajs-2292 100 7 𝜎 𝜎 PROPN iajs-2292 100 8 βˆ— βˆ— NOUN iajs-2292 100 9 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 100 10 ) ) PUNCT iajs-2292 101 1 βˆ’ βˆ’ PROPN iajs-2292 101 2 𝛼 𝛼 NOUN iajs-2292 101 3 βˆ— βˆ— NOUN iajs-2292 101 4 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 101 5 ) ) PUNCT iajs-2292 101 6 ) ) PUNCT iajs-2292 101 7 , , PUNCT iajs-2292 101 8 for for ADP iajs-2292 101 9 all all DET iajs-2292 101 10 π‘˜ π‘˜ DET iajs-2292 101 11 β‰₯ β‰₯ NOUN iajs-2292 101 12 0 0 NUM iajs-2292 101 13 . . PUNCT iajs-2292 102 1 ( ( PUNCT iajs-2292 102 2 6 6 NUM iajs-2292 102 3 ) ) PUNCT iajs-2292 102 4 the the DET iajs-2292 102 5 general general ADJ iajs-2292 102 6 form form NOUN iajs-2292 102 7 of of ADP iajs-2292 102 8 the the DET iajs-2292 102 9 non non ADJ iajs-2292 102 10 - - ADJ iajs-2292 102 11 linear linear ADJ iajs-2292 102 12 borders border NOUN iajs-2292 102 13 π΄π‘˜(𝑑 π΄π‘˜(𝑑 VERB iajs-2292 102 14 ) ) PUNCT iajs-2292 102 15 , , PUNCT iajs-2292 102 16 π΅π‘˜(𝑑 π΅π‘˜(𝑑 PROPN iajs-2292 102 17 ) ) PUNCT iajs-2292 102 18 and and CCONJ iajs-2292 102 19 πΆπ‘˜(𝑑 πΆπ‘˜(𝑑 NOUN iajs-2292 102 20 ) ) PUNCT iajs-2292 102 21 have have VERB iajs-2292 102 22 to to PART iajs-2292 102 23 be be AUX iajs-2292 102 24 : : PUNCT iajs-2292 102 25 π΄π‘˜(𝑑 π΄π‘˜(𝑑 NOUN iajs-2292 102 26 ) ) PUNCT iajs-2292 102 27 = = SYM iajs-2292 102 28 ( ( PUNCT iajs-2292 102 29 βˆ‘ βˆ‘ PROPN iajs-2292 102 30 π‘Žπ‘›(𝑑)2 π‘Žπ‘›(𝑑)2 PROPN iajs-2292 102 31 𝑛=0 𝑛=0 PROPN iajs-2292 102 32 ) ) PUNCT iajs-2292 102 33 βˆ— βˆ— NOUN iajs-2292 102 34 ( ( PUNCT iajs-2292 102 35 βˆ‘ βˆ‘ PROPN iajs-2292 102 36 π‘šπ‘›(𝑑)2 π‘šπ‘›(𝑑)2 PROPN iajs-2292 102 37 𝑛=0 𝑛=0 PROPN iajs-2292 102 38 ) ) PUNCT iajs-2292 102 39 , , PUNCT iajs-2292 102 40 for for ADP iajs-2292 102 41 all all PRON iajs-2292 102 42 π‘˜ π‘˜ PRON iajs-2292 102 43 = = SYM iajs-2292 102 44 0,1,2 0,1,2 NUM iajs-2292 102 45 ( ( PUNCT iajs-2292 102 46 7 7 NUM iajs-2292 102 47 ) ) PUNCT iajs-2292 102 48 π΅π‘˜(𝑑 π΅π‘˜(𝑑 NOUN iajs-2292 102 49 ) ) PUNCT iajs-2292 102 50 = = SYM iajs-2292 102 51 ( ( PUNCT iajs-2292 102 52 βˆ‘ βˆ‘ PROPN iajs-2292 102 53 π‘Žπ‘›(𝑑)2 π‘Žπ‘›(𝑑)2 PROPN iajs-2292 102 54 𝑛=0 𝑛=0 PROPN iajs-2292 102 55 ) ) PUNCT iajs-2292 102 56 βˆ— βˆ— NOUN iajs-2292 102 57 ( ( PUNCT iajs-2292 102 58 βˆ‘ βˆ‘ PROPN iajs-2292 102 59 π‘Ÿπ‘›(𝑑)2 π‘Ÿπ‘›(𝑑)2 PROPN iajs-2292 102 60 𝑛=0 𝑛=0 PROPN iajs-2292 102 61 ) ) PUNCT iajs-2292 102 62 , , PUNCT iajs-2292 102 63 for for ADP iajs-2292 102 64 all all PRON iajs-2292 102 65 π‘˜ π‘˜ PRON iajs-2292 102 66 = = SYM iajs-2292 102 67 0,1,2 0,1,2 NUM iajs-2292 102 68 ( ( PUNCT iajs-2292 102 69 8) 8) NUM iajs-2292 102 70 πΆπ‘˜(𝑑 πΆπ‘˜(𝑑 NOUN iajs-2292 102 71 ) ) PUNCT iajs-2292 102 72 = = SYM iajs-2292 103 1 ( ( PUNCT iajs-2292 103 2 βˆ‘ βˆ‘ INTJ iajs-2292 103 3 π‘Žπ‘› π‘Žπ‘› PROPN iajs-2292 103 4 2 2 NUM iajs-2292 103 5 𝑛=0 𝑛=0 NOUN iajs-2292 103 6 ( ( PUNCT iajs-2292 103 7 𝑑)),2 𝑑)),2 PROPN iajs-2292 103 8 for for ADP iajs-2292 103 9 all all PRON iajs-2292 103 10 π‘˜ π‘˜ PRON iajs-2292 103 11 = = SYM iajs-2292 103 12 0,1,2 0,1,2 NUM iajs-2292 103 13 ( ( PUNCT iajs-2292 103 14 9 9 NUM iajs-2292 103 15 ) ) PUNCT iajs-2292 103 16 the the DET iajs-2292 103 17 non non ADJ iajs-2292 103 18 - - ADJ iajs-2292 103 19 linear linear ADJ iajs-2292 103 20 borders border NOUN iajs-2292 103 21 of of ADP iajs-2292 103 22 𝐴0(𝑑 𝐴0(𝑑 PROPN iajs-2292 103 23 ) ) PUNCT iajs-2292 103 24 , , PUNCT iajs-2292 103 25 𝐡0(𝑑 𝐡0(𝑑 NUM iajs-2292 103 26 ) ) PUNCT iajs-2292 103 27 and and CCONJ iajs-2292 103 28 𝐢0(𝑑 𝐢0(𝑑 PROPN iajs-2292 103 29 ) ) PUNCT iajs-2292 103 30 as as ADP iajs-2292 103 31 the the DET iajs-2292 103 32 following following NOUN iajs-2292 103 33 : : PUNCT iajs-2292 103 34 𝐴0(𝑑 𝐴0(𝑑 NUM iajs-2292 103 35 ) ) PUNCT iajs-2292 103 36 = = SYM iajs-2292 104 1 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 104 2 ) ) PUNCT iajs-2292 104 3 βˆ— βˆ— NOUN iajs-2292 104 4 π‘š0(𝑑 π‘š0(𝑑 NUM iajs-2292 104 5 ) ) PUNCT iajs-2292 104 6 , , PUNCT iajs-2292 104 7 𝐡0(𝑑 𝐡0(𝑑 NUM iajs-2292 104 8 ) ) PUNCT iajs-2292 104 9 = = SYM iajs-2292 104 10 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 104 11 ) ) PUNCT iajs-2292 104 12 βˆ— βˆ— NOUN iajs-2292 104 13 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 PROPN iajs-2292 104 14 ) ) PUNCT iajs-2292 104 15 , , PUNCT iajs-2292 104 16 𝐢0(𝑑 𝐢0(𝑑 PROPN iajs-2292 104 17 ) ) PUNCT iajs-2292 104 18 = = SYM iajs-2292 105 1 ( ( PUNCT iajs-2292 105 2 π‘Ž0(𝑑)).2 π‘Ž0(𝑑)).2 NUM iajs-2292 105 3 substituting substitute VERB iajs-2292 105 4 for for ADP iajs-2292 105 5 all all DET iajs-2292 105 6 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 105 7 ) ) PUNCT iajs-2292 105 8 , , PUNCT iajs-2292 105 9 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 PROPN iajs-2292 105 10 ) ) PUNCT iajs-2292 105 11 , , PUNCT iajs-2292 105 12 𝐴0(𝑑 𝐴0(𝑑 PROPN iajs-2292 105 13 ) ) PUNCT iajs-2292 105 14 , , PUNCT iajs-2292 105 15 𝐡0(𝑑 𝐡0(𝑑 NUM iajs-2292 105 16 ) ) PUNCT iajs-2292 105 17 and and CCONJ iajs-2292 105 18 𝐢0(𝑑 𝐢0(𝑑 PROPN iajs-2292 105 19 ) ) PUNCT iajs-2292 105 20 by by ADP iajs-2292 105 21 eq.(4 eq.(4 ADJ iajs-2292 105 22 ) ) PUNCT iajs-2292 105 23 , , PUNCT iajs-2292 105 24 to to PART iajs-2292 105 25 obtain obtain VERB iajs-2292 105 26 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 105 27 ) ) PUNCT iajs-2292 105 28 = = SYM iajs-2292 105 29 βˆ’0.00009881𝑑 βˆ’0.00009881𝑑 NOUN iajs-2292 105 30 , , PUNCT iajs-2292 105 31 substituting substitute VERB iajs-2292 105 32 for for ADP iajs-2292 105 33 all all DET iajs-2292 105 34 π‘š0(𝑑 π‘š0(𝑑 PROPN iajs-2292 105 35 ) ) PUNCT iajs-2292 105 36 , , PUNCT iajs-2292 105 37 𝐴0(𝑑 𝐴0(𝑑 NUM iajs-2292 105 38 ) ) PUNCT iajs-2292 105 39 and and CCONJ iajs-2292 105 40 𝐡0(𝑑 𝐡0(𝑑 NUM iajs-2292 105 41 ) ) PUNCT iajs-2292 105 42 by by ADP iajs-2292 105 43 eq.(5 eq.(5 NOUN iajs-2292 105 44 ) ) PUNCT iajs-2292 105 45 , , PUNCT iajs-2292 105 46 to to PART iajs-2292 105 47 find find VERB iajs-2292 105 48 π‘š1(𝑑 π‘š1(𝑑 PRON iajs-2292 105 49 ) ) PUNCT iajs-2292 105 50 = = SYM iajs-2292 105 51 0.00048711𝑑 0.00048711𝑑 NOUN iajs-2292 105 52 , , PUNCT iajs-2292 105 53 substituting substitute VERB iajs-2292 105 54 for for ADP iajs-2292 105 55 all all DET iajs-2292 105 56 π‘š0(𝑑 π‘š0(𝑑 PROPN iajs-2292 105 57 ) ) PUNCT iajs-2292 105 58 , , PUNCT iajs-2292 105 59 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 PROPN iajs-2292 105 60 ) ) PUNCT iajs-2292 105 61 and and CCONJ iajs-2292 105 62 𝐡0(𝑑 𝐡0(𝑑 NUM iajs-2292 105 63 ) ) PUNCT iajs-2292 105 64 by by ADP iajs-2292 105 65 eq.(6 eq.(6 ADJ iajs-2292 105 66 ) ) PUNCT iajs-2292 105 67 , , PUNCT iajs-2292 105 68 to to PART iajs-2292 105 69 get get VERB iajs-2292 105 70 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NOUN iajs-2292 105 71 ) ) PUNCT iajs-2292 105 72 = = PUNCT iajs-2292 105 73 βˆ’0.00060638𝑑 βˆ’0.00060638𝑑 X iajs-2292 105 74 , , PUNCT iajs-2292 105 75 now now ADV iajs-2292 105 76 we we PRON iajs-2292 105 77 will will AUX iajs-2292 105 78 find find VERB iajs-2292 105 79 π‘Ž2(𝑑 π‘Ž2(𝑑 NOUN iajs-2292 105 80 ) ) PUNCT iajs-2292 105 81 , , PUNCT iajs-2292 105 82 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 105 83 ) ) PUNCT iajs-2292 105 84 and and CCONJ iajs-2292 105 85 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 105 86 ) ) PUNCT iajs-2292 105 87 . . PUNCT iajs-2292 106 1 the the DET iajs-2292 106 2 non non ADJ iajs-2292 106 3 - - ADJ iajs-2292 106 4 linear linear ADJ iajs-2292 106 5 borders border NOUN iajs-2292 106 6 of of ADP iajs-2292 106 7 𝐴1(𝑑 𝐴1(𝑑 PROPN iajs-2292 106 8 ) ) PUNCT iajs-2292 106 9 , , PUNCT iajs-2292 106 10 𝐡1(𝑑 𝐡1(𝑑 NOUN iajs-2292 106 11 ) ) PUNCT iajs-2292 106 12 and and CCONJ iajs-2292 106 13 𝐢1(𝑑 𝐢1(𝑑 NOUN iajs-2292 106 14 ) ) PUNCT iajs-2292 106 15 are be AUX iajs-2292 106 16 given give VERB iajs-2292 106 17 in in ADP iajs-2292 106 18 the the DET iajs-2292 106 19 following follow VERB iajs-2292 106 20 formula formula NOUN iajs-2292 106 21 : : PUNCT iajs-2292 106 22 𝐴1(𝑑 𝐴1(𝑑 X iajs-2292 106 23 ) ) PUNCT iajs-2292 106 24 = = PUNCT iajs-2292 106 25 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 106 26 ) ) PUNCT iajs-2292 106 27 βˆ— βˆ— NOUN iajs-2292 106 28 π‘š1(𝑑 π‘š1(𝑑 NUM iajs-2292 106 29 ) ) PUNCT iajs-2292 106 30 + + NUM iajs-2292 107 1 π‘š0(𝑑 π‘š0(𝑑 NUM iajs-2292 107 2 ) ) PUNCT iajs-2292 107 3 + + NUM iajs-2292 107 4 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 107 5 ) ) PUNCT iajs-2292 107 6 , , PUNCT iajs-2292 107 7 𝐡1(𝑑 𝐡1(𝑑 NUM iajs-2292 107 8 ) ) PUNCT iajs-2292 107 9 = = PUNCT iajs-2292 107 10 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 107 11 ) ) PUNCT iajs-2292 107 12 βˆ— βˆ— NOUN iajs-2292 107 13 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NUM iajs-2292 107 14 ) ) PUNCT iajs-2292 107 15 + + NUM iajs-2292 108 1 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 X iajs-2292 108 2 ) ) PUNCT iajs-2292 108 3 βˆ— βˆ— NOUN iajs-2292 108 4 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 108 5 ) ) PUNCT iajs-2292 108 6 , , PUNCT iajs-2292 108 7 157 157 NUM iajs-2292 108 8 ibn ibn PROPN iajs-2292 108 9 al al PROPN iajs-2292 108 10 - - PUNCT iajs-2292 108 11 haitham haitham PROPN iajs-2292 108 12 jour jour X iajs-2292 108 13 . . PROPN iajs-2292 108 14 for for ADP iajs-2292 108 15 pure pure ADJ iajs-2292 108 16 & & CCONJ iajs-2292 108 17 appl appl PROPN iajs-2292 108 18 . . PUNCT iajs-2292 109 1 sci sci PROPN iajs-2292 109 2 . . PROPN iajs-2292 109 3 32 32 NUM iajs-2292 109 4 ( ( PUNCT iajs-2292 109 5 3 3 NUM iajs-2292 109 6 ) ) PUNCT iajs-2292 109 7 2019 2019 NUM iajs-2292 109 8 𝐢1(𝑑 𝐢1(𝑑 NOUN iajs-2292 109 9 ) ) PUNCT iajs-2292 109 10 = = SYM iajs-2292 109 11 2 2 NUM iajs-2292 109 12 βˆ— βˆ— NOUN iajs-2292 109 13 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 109 14 ) ) PUNCT iajs-2292 109 15 βˆ— βˆ— NOUN iajs-2292 109 16 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 109 17 ) ) PUNCT iajs-2292 109 18 , , PUNCT iajs-2292 109 19 substituting substitute VERB iajs-2292 109 20 for for ADP iajs-2292 109 21 all all DET iajs-2292 109 22 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 109 23 ) ) PUNCT iajs-2292 109 24 , , PUNCT iajs-2292 109 25 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NOUN iajs-2292 109 26 ) ) PUNCT iajs-2292 109 27 . . PUNCT iajs-2292 110 1 𝐴1(𝑑 𝐴1(𝑑 PROPN iajs-2292 110 2 ) ) PUNCT iajs-2292 110 3 , , PUNCT iajs-2292 110 4 𝐡1(𝑑 𝐡1(𝑑 NOUN iajs-2292 110 5 ) ) PUNCT iajs-2292 110 6 and and CCONJ iajs-2292 110 7 𝐢1(𝑑 𝐢1(𝑑 NOUN iajs-2292 110 8 ) ) PUNCT iajs-2292 110 9 by by ADP iajs-2292 110 10 eq.(4 eq.(4 ADJ iajs-2292 110 11 ) ) PUNCT iajs-2292 110 12 , , PUNCT iajs-2292 110 13 to to PART iajs-2292 110 14 obtain obtain VERB iajs-2292 110 15 π‘Ž2(𝑑 π‘Ž2(𝑑 NOUN iajs-2292 110 16 ) ) PUNCT iajs-2292 110 17 = = SYM iajs-2292 111 1 1.2117815 1.2117815 NUM iajs-2292 111 2 βˆ— βˆ— NOUN iajs-2292 111 3 10βˆ’8𝑑2 10βˆ’8𝑑2 NUM iajs-2292 111 4 substituting substitute VERB iajs-2292 111 5 also also ADV iajs-2292 111 6 for for ADP iajs-2292 111 7 all all DET iajs-2292 111 8 π‘š1(𝑑 π‘š1(𝑑 NOUN iajs-2292 111 9 ) ) PUNCT iajs-2292 111 10 , , PUNCT iajs-2292 111 11 𝐴1(𝑑 𝐴1(𝑑 PROPN iajs-2292 111 12 ) ) PUNCT iajs-2292 111 13 and and CCONJ iajs-2292 111 14 𝐡1(𝑑 𝐡1(𝑑 NOUN iajs-2292 111 15 ) ) PUNCT iajs-2292 111 16 by by ADP iajs-2292 111 17 eq.(5 eq.(5 NOUN iajs-2292 111 18 ) ) PUNCT iajs-2292 111 19 , , PUNCT iajs-2292 111 20 to to PART iajs-2292 111 21 get get VERB iajs-2292 111 22 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 111 23 ) ) PUNCT iajs-2292 111 24 = = SYM iajs-2292 111 25 βˆ’0.00000403𝑑2 βˆ’0.00000403𝑑2 PROPN iajs-2292 111 26 , , PUNCT iajs-2292 111 27 substituting substitute VERB iajs-2292 111 28 for for ADP iajs-2292 111 29 all all DET iajs-2292 111 30 π‘š1(𝑑 π‘š1(𝑑 NOUN iajs-2292 111 31 ) ) PUNCT iajs-2292 111 32 , , PUNCT iajs-2292 111 33 π‘Ÿ1(𝑑)π‘Žπ‘›π‘‘ π‘Ÿ1(𝑑)π‘Žπ‘›π‘‘ NUM iajs-2292 111 34 𝐡1(𝑑 𝐡1(𝑑 NOUN iajs-2292 111 35 ) ) PUNCT iajs-2292 111 36 by by ADP iajs-2292 111 37 eq.(6 eq.(6 NOUN iajs-2292 111 38 ) ) PUNCT iajs-2292 111 39 , , PUNCT iajs-2292 111 40 to to PART iajs-2292 111 41 have have VERB iajs-2292 111 42 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 111 43 ) ) PUNCT iajs-2292 111 44 = = SYM iajs-2292 112 1 0.00000359𝑑2 0.00000359𝑑2 NUM iajs-2292 112 2 , , PUNCT iajs-2292 112 3 at at ADP iajs-2292 112 4 the the DET iajs-2292 112 5 same same ADJ iajs-2292 112 6 previous previous ADJ iajs-2292 112 7 steps step NOUN iajs-2292 112 8 , , PUNCT iajs-2292 112 9 the the DET iajs-2292 112 10 non non ADJ iajs-2292 112 11 - - ADJ iajs-2292 112 12 linear linear ADJ iajs-2292 112 13 borders border NOUN iajs-2292 112 14 of of ADP iajs-2292 112 15 𝐴2(𝑑 𝐴2(𝑑 PROPN iajs-2292 112 16 ) ) PUNCT iajs-2292 112 17 , , PUNCT iajs-2292 112 18 𝐡2(𝑑 𝐡2(𝑑 NUM iajs-2292 112 19 ) ) PUNCT iajs-2292 112 20 and and CCONJ iajs-2292 112 21 𝐢2(𝑑 𝐢2(𝑑 PROPN iajs-2292 112 22 ) ) PUNCT iajs-2292 112 23 are be AUX iajs-2292 112 24 given give VERB iajs-2292 112 25 as as ADP iajs-2292 112 26 : : PUNCT iajs-2292 112 27 𝐴2(𝑑 𝐴2(𝑑 NOUN iajs-2292 112 28 ) ) PUNCT iajs-2292 112 29 = = PUNCT iajs-2292 112 30 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 112 31 ) ) PUNCT iajs-2292 112 32 βˆ— βˆ— NOUN iajs-2292 112 33 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 112 34 ) ) PUNCT iajs-2292 112 35 + + NUM iajs-2292 112 36 π‘Ž1(𝑑 π‘Ž1(𝑑 X iajs-2292 112 37 ) ) PUNCT iajs-2292 112 38 βˆ— βˆ— NOUN iajs-2292 112 39 π‘š1(𝑑 π‘š1(𝑑 NUM iajs-2292 112 40 ) ) PUNCT iajs-2292 112 41 + + NUM iajs-2292 113 1 π‘š0(𝑑 π‘š0(𝑑 X iajs-2292 113 2 ) ) PUNCT iajs-2292 113 3 βˆ— βˆ— NOUN iajs-2292 113 4 π‘Ž2(𝑑 π‘Ž2(𝑑 PROPN iajs-2292 113 5 ) ) PUNCT iajs-2292 113 6 , , PUNCT iajs-2292 113 7 𝐡2(𝑑 𝐡2(𝑑 NUM iajs-2292 113 8 ) ) PUNCT iajs-2292 113 9 = = SYM iajs-2292 113 10 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 113 11 ) ) PUNCT iajs-2292 113 12 βˆ— βˆ— NOUN iajs-2292 113 13 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 113 14 ) ) PUNCT iajs-2292 113 15 + + NUM iajs-2292 113 16 π‘Ž1(𝑑 π‘Ž1(𝑑 X iajs-2292 113 17 ) ) PUNCT iajs-2292 113 18 βˆ— βˆ— NOUN iajs-2292 113 19 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NUM iajs-2292 113 20 ) ) PUNCT iajs-2292 113 21 + + NUM iajs-2292 113 22 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 X iajs-2292 113 23 ) ) PUNCT iajs-2292 113 24 βˆ— βˆ— NOUN iajs-2292 113 25 π‘Ž2(𝑑 π‘Ž2(𝑑 PROPN iajs-2292 113 26 ) ) PUNCT iajs-2292 113 27 , , PUNCT iajs-2292 113 28 𝐢2(𝑑 𝐢2(𝑑 PROPN iajs-2292 113 29 ) ) PUNCT iajs-2292 113 30 = = SYM iajs-2292 113 31 2 2 NUM iajs-2292 113 32 βˆ— βˆ— NOUN iajs-2292 113 33 π‘Ž0(𝑑 π‘Ž0(𝑑 PROPN iajs-2292 113 34 ) ) PUNCT iajs-2292 113 35 βˆ— βˆ— NOUN iajs-2292 113 36 π‘Ž2(𝑑 π‘Ž2(𝑑 PROPN iajs-2292 113 37 ) ) PUNCT iajs-2292 113 38 + + CCONJ iajs-2292 113 39 ( ( PUNCT iajs-2292 113 40 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 113 41 ) ) PUNCT iajs-2292 113 42 ) ) PUNCT iajs-2292 113 43 2 2 NUM iajs-2292 113 44 , , PUNCT iajs-2292 113 45 substituting substitute VERB iajs-2292 113 46 for for ADP iajs-2292 113 47 all all DET iajs-2292 113 48 π‘Ž2(𝑑 π‘Ž2(𝑑 NOUN iajs-2292 113 49 ) ) PUNCT iajs-2292 113 50 , , PUNCT iajs-2292 113 51 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 113 52 ) ) PUNCT iajs-2292 113 53 . . PUNCT iajs-2292 114 1 𝐴2(𝑑 𝐴2(𝑑 PROPN iajs-2292 114 2 ) ) PUNCT iajs-2292 114 3 , , PUNCT iajs-2292 114 4 𝐡2(𝑑 𝐡2(𝑑 NUM iajs-2292 114 5 ) ) PUNCT iajs-2292 114 6 and and CCONJ iajs-2292 114 7 𝐢2(𝑑 𝐢2(𝑑 PROPN iajs-2292 114 8 ) ) PUNCT iajs-2292 114 9 by by ADP iajs-2292 114 10 eq.(4 eq.(4 ADJ iajs-2292 114 11 ) ) PUNCT iajs-2292 114 12 , , PUNCT iajs-2292 114 13 to to PART iajs-2292 114 14 be be AUX iajs-2292 114 15 π‘Ž3(𝑑 π‘Ž3(𝑑 PROPN iajs-2292 114 16 ) ) PUNCT iajs-2292 114 17 = = PUNCT iajs-2292 115 1 2.55439073 2.55439073 NUM iajs-2292 115 2 βˆ— βˆ— NOUN iajs-2292 115 3 10βˆ’11𝑑3 10βˆ’11𝑑3 NUM iajs-2292 115 4 , , PUNCT iajs-2292 115 5 substituting substitute VERB iajs-2292 115 6 for for ADP iajs-2292 115 7 all all DET iajs-2292 115 8 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 115 9 ) ) PUNCT iajs-2292 115 10 , , PUNCT iajs-2292 115 11 𝐴2(𝑑 𝐴2(𝑑 PROPN iajs-2292 115 12 ) ) PUNCT iajs-2292 115 13 and and CCONJ iajs-2292 115 14 𝐡2(𝑑 𝐡2(𝑑 NUM iajs-2292 115 15 ) ) PUNCT iajs-2292 115 16 by by ADP iajs-2292 115 17 eq.(5 eq.(5 NOUN iajs-2292 115 18 ) ) PUNCT iajs-2292 115 19 , , PUNCT iajs-2292 116 1 to to PART iajs-2292 116 2 find find VERB iajs-2292 116 3 π‘š3(𝑑 π‘š3(𝑑 PRON iajs-2292 116 4 ) ) PUNCT iajs-2292 116 5 = = PUNCT iajs-2292 116 6 1.27758808 1.27758808 NUM iajs-2292 116 7 βˆ— βˆ— NOUN iajs-2292 116 8 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 116 9 , , PUNCT iajs-2292 116 10 substituting substitute VERB iajs-2292 116 11 for for ADP iajs-2292 116 12 all all DET iajs-2292 116 13 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 116 14 ) ) PUNCT iajs-2292 116 15 , , PUNCT iajs-2292 116 16 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 116 17 ) ) PUNCT iajs-2292 116 18 and and CCONJ iajs-2292 116 19 𝐡2(𝑑 𝐡2(𝑑 NUM iajs-2292 116 20 ) ) PUNCT iajs-2292 116 21 by by ADP iajs-2292 116 22 eq.(6 eq.(6 NOUN iajs-2292 116 23 ) ) PUNCT iajs-2292 116 24 , , PUNCT iajs-2292 116 25 to to PART iajs-2292 116 26 get get VERB iajs-2292 116 27 π‘Ÿ3(𝑑 π‘Ÿ3(𝑑 PROPN iajs-2292 116 28 ) ) PUNCT iajs-2292 116 29 = = SYM iajs-2292 116 30 βˆ’1.42663059 βˆ’1.42663059 PROPN iajs-2292 116 31 βˆ— βˆ— NOUN iajs-2292 116 32 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 116 33 . . PUNCT iajs-2292 117 1 the the DET iajs-2292 117 2 adomian adomian NOUN iajs-2292 117 3 decomposition decomposition NOUN iajs-2292 117 4 method method NOUN iajs-2292 117 5 assumes assume VERB iajs-2292 117 6 that that SCONJ iajs-2292 117 7 the the DET iajs-2292 117 8 unknown unknown ADJ iajs-2292 117 9 functions function NOUN iajs-2292 117 10 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 117 11 ) ) PUNCT iajs-2292 117 12 , , PUNCT iajs-2292 117 13 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 117 14 ) ) PUNCT iajs-2292 117 15 and and CCONJ iajs-2292 117 16 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 117 17 ) ) PUNCT iajs-2292 117 18 that that PRON iajs-2292 117 19 can can AUX iajs-2292 117 20 be be AUX iajs-2292 117 21 written write VERB iajs-2292 117 22 by by ADP iajs-2292 117 23 series series NOUN iajs-2292 117 24 as as SCONJ iajs-2292 117 25 follows follow VERB iajs-2292 117 26 : : PUNCT iajs-2292 117 27 π‘Ž(𝑑 π‘Ž(𝑑 PROPN iajs-2292 117 28 ) ) PUNCT iajs-2292 117 29 = = PUNCT iajs-2292 118 1 βˆ‘ βˆ‘ PUNCT iajs-2292 118 2 π‘Žπ‘˜(𝑑),∞ π‘Žπ‘˜(𝑑),∞ NOUN iajs-2292 118 3 π‘˜=0 π‘˜=0 ADP iajs-2292 118 4 π‘š(𝑑 π‘š(𝑑 VERB iajs-2292 118 5 ) ) PUNCT iajs-2292 118 6 = = PUNCT iajs-2292 119 1 βˆ‘ βˆ‘ PUNCT iajs-2292 119 2 π‘šπ‘˜(𝑑)∞ π‘šπ‘˜(𝑑)∞ ADV iajs-2292 119 3 π‘˜=0 π‘˜=0 ADV iajs-2292 119 4 , , PUNCT iajs-2292 119 5 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 119 6 ) ) PUNCT iajs-2292 119 7 = = PUNCT iajs-2292 119 8 βˆ‘ βˆ‘ PUNCT iajs-2292 119 9 π‘Ÿπ‘˜(𝑑),∞ π‘Ÿπ‘˜(𝑑),∞ PROPN iajs-2292 119 10 π‘˜=0 π‘˜=0 X iajs-2292 119 11 βˆ‘ βˆ‘ ADV iajs-2292 119 12 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 PROPN iajs-2292 119 13 ) ) PUNCT iajs-2292 119 14 ∞ ∞ NUM iajs-2292 119 15 π‘˜=0 π‘˜=0 PROPN iajs-2292 119 16 = = SYM iajs-2292 119 17 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 119 18 ) ) PUNCT iajs-2292 119 19 + + PUNCT iajs-2292 119 20 π‘Ž2(𝑑 π‘Ž2(𝑑 X iajs-2292 119 21 ) ) PUNCT iajs-2292 119 22 + + NOUN iajs-2292 119 23 π‘Ž3(𝑑 π‘Ž3(𝑑 X iajs-2292 119 24 ) ) PUNCT iajs-2292 120 1 + + CCONJ iajs-2292 120 2 β‹― β‹― PROPN iajs-2292 120 3 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 120 4 ) ) PUNCT iajs-2292 120 5 = = PUNCT iajs-2292 121 1 0.362 0.362 NUM iajs-2292 121 2 β€Š β€Š SPACE iajs-2292 121 3 βˆ’ βˆ’ PROPN iajs-2292 121 4 0.00009881𝑑 0.00009881𝑑 PROPN iajs-2292 121 5 + + CCONJ iajs-2292 121 6 1.21178155 1.21178155 NUM iajs-2292 121 7 βˆ— βˆ— NOUN iajs-2292 121 8 10βˆ’8𝑑2 10βˆ’8𝑑2 NUM iajs-2292 121 9 + + SYM iajs-2292 121 10 2.55439073 2.55439073 NUM iajs-2292 121 11 βˆ— βˆ— NOUN iajs-2292 121 12 10βˆ’11𝑑3 10βˆ’11𝑑3 NUM iajs-2292 121 13 + + CCONJ iajs-2292 121 14 ( ( PUNCT iajs-2292 121 15 10 10 NUM iajs-2292 121 16 ) ) PUNCT iajs-2292 121 17 βˆ‘ βˆ‘ PUNCT iajs-2292 121 18 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 X iajs-2292 121 19 ) ) PUNCT iajs-2292 121 20 ∞ ∞ NUM iajs-2292 121 21 π‘˜=1 π‘˜=1 PUNCT iajs-2292 121 22 = = SYM iajs-2292 121 23 π‘š1(𝑑 π‘š1(𝑑 X iajs-2292 121 24 ) ) PUNCT iajs-2292 121 25 + + X iajs-2292 121 26 π‘š2(𝑑 π‘š2(𝑑 X iajs-2292 121 27 ) ) PUNCT iajs-2292 121 28 + + NUM iajs-2292 121 29 π‘š3(𝑑 π‘š3(𝑑 X iajs-2292 121 30 ) ) PUNCT iajs-2292 122 1 + + CCONJ iajs-2292 122 2 β‹― β‹― VERB iajs-2292 122 3 π‘š(𝑑 π‘š(𝑑 X iajs-2292 122 4 ) ) PUNCT iajs-2292 122 5 = = PUNCT iajs-2292 123 1 0.581 0.581 NUM iajs-2292 123 2 β€Š β€Š SPACE iajs-2292 123 3 + + SYM iajs-2292 123 4 0.00048711𝑑 0.00048711𝑑 PUNCT iajs-2292 124 1 βˆ’ βˆ’ NOUN iajs-2292 125 1 0.00000403𝑑2 0.00000403𝑑2 NUM iajs-2292 125 2 + + NUM iajs-2292 125 3 1.27758808 1.27758808 NUM iajs-2292 125 4 βˆ— βˆ— NOUN iajs-2292 125 5 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 125 6 + + CCONJ iajs-2292 125 7 ( ( PUNCT iajs-2292 125 8 11 11 NUM iajs-2292 125 9 ) ) PUNCT iajs-2292 125 10 158 158 NUM iajs-2292 125 11 ibn ibn PROPN iajs-2292 125 12 al al PROPN iajs-2292 125 13 - - PUNCT iajs-2292 125 14 haitham haitham PROPN iajs-2292 125 15 jour jour X iajs-2292 125 16 . . PROPN iajs-2292 125 17 for for ADP iajs-2292 125 18 pure pure ADJ iajs-2292 125 19 & & CCONJ iajs-2292 125 20 appl appl PROPN iajs-2292 125 21 . . PUNCT iajs-2292 126 1 sci sci PROPN iajs-2292 126 2 . . PROPN iajs-2292 126 3 32 32 NUM iajs-2292 126 4 ( ( PUNCT iajs-2292 126 5 3 3 NUM iajs-2292 126 6 ) ) PUNCT iajs-2292 126 7 2019 2019 NUM iajs-2292 126 8 βˆ‘ βˆ‘ PUNCT iajs-2292 126 9 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NUM iajs-2292 126 10 ) ) PUNCT iajs-2292 126 11 ∞ ∞ NUM iajs-2292 126 12 π‘˜=1 π‘˜=1 PUNCT iajs-2292 126 13 = = SYM iajs-2292 126 14 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 X iajs-2292 126 15 ) ) PUNCT iajs-2292 126 16 + + NUM iajs-2292 126 17 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 126 18 ) ) PUNCT iajs-2292 126 19 + + SYM iajs-2292 126 20 π‘Ÿ3(𝑑 π‘Ÿ3(𝑑 PROPN iajs-2292 126 21 ) ) PUNCT iajs-2292 126 22 + + NUM iajs-2292 126 23 β‹― β‹― NOUN iajs-2292 126 24 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 126 25 ) ) PUNCT iajs-2292 126 26 = = PUNCT iajs-2292 126 27 0.057 0.057 NUM iajs-2292 126 28 β€Š β€Š SPACE iajs-2292 126 29 βˆ’ βˆ’ PROPN iajs-2292 126 30 0.00060638𝑑 0.00060638𝑑 NOUN iajs-2292 127 1 + + CCONJ iajs-2292 128 1 0.00000359𝑑2 0.00000359𝑑2 NUM iajs-2292 128 2 βˆ’ βˆ’ NUM iajs-2292 128 3 1.42663059 1.42663059 NUM iajs-2292 128 4 βˆ— βˆ— NOUN iajs-2292 128 5 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 128 6 + + CCONJ iajs-2292 128 7 ( ( PUNCT iajs-2292 128 8 12 12 NUM iajs-2292 128 9 ) ) PUNCT iajs-2292 128 10 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 128 11 ) ) PUNCT iajs-2292 128 12 , , PUNCT iajs-2292 128 13 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 128 14 ) ) PUNCT iajs-2292 128 15 and and CCONJ iajs-2292 128 16 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 128 17 ) ) PUNCT iajs-2292 128 18 of of ADP iajs-2292 128 19 adm adm PROPN iajs-2292 128 20 results result NOUN iajs-2292 128 21 are be AUX iajs-2292 128 22 unsettled unsettled ADJ iajs-2292 128 23 terms term NOUN iajs-2292 128 24 . . PUNCT iajs-2292 129 1 3.2 3.2 NUM iajs-2292 129 2 variation variation NOUN iajs-2292 129 3 iteration iteration NOUN iajs-2292 129 4 method method NOUN iajs-2292 129 5 the the DET iajs-2292 129 6 vim vim NOUN iajs-2292 129 7 gives give VERB iajs-2292 129 8 a a DET iajs-2292 129 9 better well ADJ iajs-2292 129 10 approximate approximate ADJ iajs-2292 129 11 solution solution NOUN iajs-2292 129 12 by by ADP iajs-2292 129 13 constructing construct VERB iajs-2292 129 14 a a DET iajs-2292 129 15 correctional correctional ADJ iajs-2292 129 16 functional functional NOUN iajs-2292 129 17 that that PRON iajs-2292 129 18 uses use VERB iajs-2292 129 19 an an DET iajs-2292 129 20 initial initial ADJ iajs-2292 129 21 function function NOUN iajs-2292 129 22 . . PUNCT iajs-2292 130 1 where where SCONJ iajs-2292 130 2 lagrange lagrange PROPN iajs-2292 130 3 multiplier multiplier ADV iajs-2292 130 4 considers consider VERB iajs-2292 130 5 the the DET iajs-2292 130 6 key key NOUN iajs-2292 130 7 of of ADP iajs-2292 130 8 the the DET iajs-2292 130 9 correction correction NOUN iajs-2292 130 10 functional functional ADJ iajs-2292 130 11 which which PRON iajs-2292 130 12 can can AUX iajs-2292 130 13 be be AUX iajs-2292 130 14 specified specify VERB iajs-2292 130 15 via via ADP iajs-2292 130 16 variation variation NOUN iajs-2292 130 17 theory theory NOUN iajs-2292 130 18 [ [ X iajs-2292 130 19 14 14 NUM iajs-2292 130 20 ] ] PUNCT iajs-2292 130 21 . . PUNCT iajs-2292 131 1 the the DET iajs-2292 131 2 nonlinear nonlinear ADJ iajs-2292 131 3 system system NOUN iajs-2292 131 4 of of ADP iajs-2292 131 5 alcohol alcohol NOUN iajs-2292 131 6 model model NOUN iajs-2292 131 7 under under ADP iajs-2292 131 8 study study NOUN iajs-2292 131 9 , , PUNCT iajs-2292 131 10 [ [ X iajs-2292 131 11 12 12 NUM iajs-2292 131 12 ] ] PUNCT iajs-2292 131 13 . . PUNCT iajs-2292 132 1 can can AUX iajs-2292 132 2 be be AUX iajs-2292 132 3 solved solve VERB iajs-2292 132 4 by by ADP iajs-2292 132 5 using use VERB iajs-2292 132 6 the the DET iajs-2292 132 7 vim vim NOUN iajs-2292 132 8 with with ADP iajs-2292 132 9 given give VERB iajs-2292 132 10 initial initial ADJ iajs-2292 132 11 condition condition NOUN iajs-2292 132 12 and and CCONJ iajs-2292 132 13 parameters parameter NOUN iajs-2292 132 14 . . PUNCT iajs-2292 133 1 the the DET iajs-2292 133 2 correction correction NOUN iajs-2292 133 3 functional functional ADJ iajs-2292 133 4 of of ADP iajs-2292 133 5 the the DET iajs-2292 133 6 system system NOUN iajs-2292 133 7 ( ( PUNCT iajs-2292 133 8 1 1 NUM iajs-2292 133 9 - - SYM iajs-2292 133 10 3 3 NUM iajs-2292 133 11 ) ) PUNCT iajs-2292 133 12 becomes become VERB iajs-2292 133 13 : : PUNCT iajs-2292 133 14 π‘Žπ‘˜+1(𝑑 π‘Žπ‘˜+1(𝑑 X iajs-2292 133 15 ) ) PUNCT iajs-2292 133 16 = = PUNCT iajs-2292 133 17 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 X iajs-2292 133 18 ) ) PUNCT iajs-2292 134 1 + + CCONJ iajs-2292 134 2 ∫ ∫ PROPN iajs-2292 134 3 πœ† πœ† X iajs-2292 134 4 ( ( PUNCT iajs-2292 134 5 π‘ŽΛŠπ‘˜(𝑑 π‘ŽΛŠπ‘˜(𝑑 PROPN iajs-2292 134 6 ) ) PUNCT iajs-2292 134 7 βˆ’ βˆ’ PROPN iajs-2292 134 8 ( ( PUNCT iajs-2292 134 9 𝛼 𝛼 X iajs-2292 134 10 + + X iajs-2292 134 11 𝛽 𝛽 NOUN iajs-2292 134 12 βˆ— βˆ— NOUN iajs-2292 134 13 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 SYM iajs-2292 134 14 ) ) PUNCT iajs-2292 134 15 βˆ’ βˆ’ NOUN iajs-2292 134 16 πœ‡ πœ‡ ADP iajs-2292 134 17 βˆ— βˆ— NOUN iajs-2292 134 18 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 134 19 ) ) PUNCT iajs-2292 135 1 βˆ’ βˆ’ ADP iajs-2292 135 2 πœ‰ πœ‰ ADP iajs-2292 135 3 βˆ— βˆ— NOUN iajs-2292 135 4 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 135 5 ) ) PUNCT iajs-2292 135 6 βˆ— βˆ— NOUN iajs-2292 135 7 ( ( PUNCT iajs-2292 135 8 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 135 9 ) ) PUNCT iajs-2292 135 10 + + CCONJ iajs-2292 135 11 𝑑 𝑑 X iajs-2292 135 12 0 0 NUM iajs-2292 135 13 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 135 14 ) ) PUNCT iajs-2292 135 15 ) ) PUNCT iajs-2292 136 1 βˆ’ βˆ’ PROPN iajs-2292 136 2 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 136 3 ) ) PUNCT iajs-2292 136 4 βˆ— βˆ— NOUN iajs-2292 136 5 ( ( PUNCT iajs-2292 136 6 𝛼 𝛼 NOUN iajs-2292 136 7 βˆ’ βˆ’ NOUN iajs-2292 136 8 πœ‡ πœ‡ ADP iajs-2292 136 9 βˆ— βˆ— NOUN iajs-2292 136 10 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 136 11 ) ) PUNCT iajs-2292 136 12 βˆ’ βˆ’ PROPN iajs-2292 136 13 𝜎 𝜎 PROPN iajs-2292 136 14 βˆ— βˆ— NOUN iajs-2292 136 15 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 PUNCT iajs-2292 136 16 ) ) PUNCT iajs-2292 136 17 βˆ’ βˆ’ PROPN iajs-2292 136 18 𝜎 𝜎 PROPN iajs-2292 136 19 βˆ— βˆ— NOUN iajs-2292 136 20 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 136 21 ) ) PUNCT iajs-2292 136 22 ) ) PUNCT iajs-2292 136 23 ) ) PUNCT iajs-2292 136 24 ) ) PUNCT iajs-2292 137 1 𝑑𝑑 𝑑𝑑 ADP iajs-2292 137 2 , , PUNCT iajs-2292 137 3 π‘“π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ ADV iajs-2292 137 4 π‘Žπ‘™π‘™ π‘Žπ‘™π‘™ VERB iajs-2292 137 5 π‘˜ π‘˜ DET iajs-2292 137 6 β‰₯ β‰₯ NOUN iajs-2292 137 7 0 0 NUM iajs-2292 137 8 . . PUNCT iajs-2292 138 1 ( ( PUNCT iajs-2292 138 2 13 13 NUM iajs-2292 138 3 ) ) PUNCT iajs-2292 138 4 π‘šπ‘˜+1(𝑑 π‘šπ‘˜+1(𝑑 NOUN iajs-2292 138 5 ) ) PUNCT iajs-2292 139 1 = = PUNCT iajs-2292 139 2 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 X iajs-2292 139 3 ) ) PUNCT iajs-2292 140 1 + + CCONJ iajs-2292 140 2 ∫ ∫ PROPN iajs-2292 140 3 πœ† πœ† X iajs-2292 140 4 ( ( PUNCT iajs-2292 140 5 π‘šΛŠπ‘˜(𝑑 π‘šΛŠπ‘˜(𝑑 PROPN iajs-2292 140 6 ) ) PUNCT iajs-2292 140 7 βˆ’ βˆ’ PROPN iajs-2292 141 1 ( ( PUNCT iajs-2292 141 2 πœ‰ πœ‰ NOUN iajs-2292 141 3 βˆ— βˆ— NOUN iajs-2292 141 4 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 141 5 ) ) PUNCT iajs-2292 141 6 βˆ— βˆ— NOUN iajs-2292 141 7 ( ( PUNCT iajs-2292 141 8 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 141 9 ) ) PUNCT iajs-2292 141 10 + + NUM iajs-2292 141 11 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 141 12 ) ) PUNCT iajs-2292 141 13 ) ) PUNCT iajs-2292 142 1 βˆ’ βˆ’ ADP iajs-2292 142 2 πœ‚ πœ‚ NOUN iajs-2292 142 3 βˆ— βˆ— NOUN iajs-2292 142 4 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 142 5 ) ) PUNCT iajs-2292 143 1 + + CCONJ iajs-2292 143 2 πœ‡ πœ‡ ADP iajs-2292 143 3 βˆ— βˆ— NOUN iajs-2292 143 4 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 143 5 ) ) PUNCT iajs-2292 143 6 βˆ— βˆ— NOUN iajs-2292 143 7 𝑑 𝑑 X iajs-2292 143 8 0 0 NUM iajs-2292 143 9 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 143 10 ) ) PUNCT iajs-2292 143 11 βˆ’ βˆ’ PROPN iajs-2292 143 12 𝜎 𝜎 PROPN iajs-2292 143 13 βˆ— βˆ— NOUN iajs-2292 143 14 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 143 15 ) ) PUNCT iajs-2292 143 16 βˆ— βˆ— NOUN iajs-2292 143 17 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 143 18 ) ) PUNCT iajs-2292 143 19 βˆ’ βˆ’ ADP iajs-2292 143 20 𝛼 𝛼 NOUN iajs-2292 143 21 βˆ— βˆ— NOUN iajs-2292 143 22 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 143 23 ) ) PUNCT iajs-2292 143 24 ) ) PUNCT iajs-2292 143 25 ) ) PUNCT iajs-2292 143 26 𝑑𝑑 𝑑𝑑 ADP iajs-2292 143 27 , , PUNCT iajs-2292 143 28 π‘“π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ ADV iajs-2292 143 29 π‘Žπ‘™π‘™ π‘Žπ‘™π‘™ VERB iajs-2292 143 30 π‘˜ π‘˜ DET iajs-2292 143 31 β‰₯ β‰₯ NOUN iajs-2292 143 32 0 0 NUM iajs-2292 143 33 . . PUNCT iajs-2292 144 1 ( ( PUNCT iajs-2292 144 2 14 14 NUM iajs-2292 144 3 ) ) PUNCT iajs-2292 144 4 π‘Ÿπ‘˜+1(𝑑 π‘Ÿπ‘˜+1(𝑑 PROPN iajs-2292 144 5 ) ) PUNCT iajs-2292 145 1 = = PUNCT iajs-2292 145 2 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 145 3 ) ) PUNCT iajs-2292 146 1 + + CCONJ iajs-2292 146 2 ∫ ∫ PROPN iajs-2292 146 3 πœ† πœ† X iajs-2292 146 4 ( ( PUNCT iajs-2292 146 5 π‘ŸΛŠπ‘˜(𝑑 π‘ŸΛŠπ‘˜(𝑑 PROPN iajs-2292 146 6 ) ) PUNCT iajs-2292 146 7 βˆ’ βˆ’ PROPN iajs-2292 147 1 ( ( PUNCT iajs-2292 147 2 πœ‚ πœ‚ NOUN iajs-2292 147 3 βˆ— βˆ— NOUN iajs-2292 147 4 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 147 5 ) ) PUNCT iajs-2292 147 6 βˆ’ βˆ’ ADP iajs-2292 147 7 𝛽 𝛽 NOUN iajs-2292 147 8 βˆ— βˆ— NOUN iajs-2292 147 9 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 147 10 ) ) PUNCT iajs-2292 148 1 + + CCONJ iajs-2292 148 2 πœ‡ πœ‡ ADP iajs-2292 148 3 βˆ— βˆ— NOUN iajs-2292 148 4 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 148 5 ) ) PUNCT iajs-2292 148 6 βˆ— βˆ— NOUN iajs-2292 148 7 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 148 8 ) ) PUNCT iajs-2292 149 1 βˆ’ βˆ’ PROPN iajs-2292 149 2 𝜎 𝜎 PROPN iajs-2292 149 3 βˆ— βˆ— NOUN iajs-2292 149 4 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 149 5 ) ) PUNCT iajs-2292 149 6 βˆ— βˆ— NOUN iajs-2292 149 7 𝑑 𝑑 X iajs-2292 149 8 0 0 NUM iajs-2292 149 9 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 SYM iajs-2292 149 10 ) ) PUNCT iajs-2292 149 11 βˆ’ βˆ’ ADP iajs-2292 149 12 𝛼 𝛼 SYM iajs-2292 149 13 βˆ— βˆ— NOUN iajs-2292 149 14 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 149 15 ) ) PUNCT iajs-2292 149 16 ) ) PUNCT iajs-2292 149 17 ) ) PUNCT iajs-2292 150 1 𝑑𝑑 𝑑𝑑 ADP iajs-2292 150 2 , , PUNCT iajs-2292 150 3 π‘“π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ ADV iajs-2292 150 4 π‘Žπ‘™π‘™ π‘Žπ‘™π‘™ VERB iajs-2292 150 5 π‘˜ π‘˜ DET iajs-2292 150 6 β‰₯ β‰₯ NOUN iajs-2292 150 7 0 0 NUM iajs-2292 150 8 ( ( PUNCT iajs-2292 150 9 15 15 NUM iajs-2292 150 10 ) ) PUNCT iajs-2292 150 11 the the DET iajs-2292 150 12 lagrange lagrange NOUN iajs-2292 150 13 multiplier multiplier ADV iajs-2292 150 14 is be AUX iajs-2292 150 15 πœ† πœ† PRON iajs-2292 150 16 = = PUNCT iajs-2292 150 17 βˆ’1 βˆ’1 NOUN iajs-2292 150 18 in in ADP iajs-2292 150 19 equations equation NOUN iajs-2292 150 20 ( ( PUNCT iajs-2292 150 21 10 10 NUM iajs-2292 150 22 - - SYM iajs-2292 150 23 12 12 NUM iajs-2292 150 24 ) ) PUNCT iajs-2292 150 25 . . PUNCT iajs-2292 151 1 by by ADP iajs-2292 151 2 substituting substitute VERB iajs-2292 151 3 this this DET iajs-2292 151 4 value value NOUN iajs-2292 151 5 in in ADP iajs-2292 151 6 equations equation NOUN iajs-2292 151 7 ( ( PUNCT iajs-2292 151 8 10 10 NUM iajs-2292 151 9 ) ) PUNCT iajs-2292 151 10 , , PUNCT iajs-2292 151 11 ( ( PUNCT iajs-2292 151 12 11 11 NUM iajs-2292 151 13 ) ) PUNCT iajs-2292 151 14 and and CCONJ iajs-2292 151 15 ( ( PUNCT iajs-2292 151 16 12 12 NUM iajs-2292 151 17 ) ) PUNCT iajs-2292 151 18 . . PUNCT iajs-2292 152 1 the the DET iajs-2292 152 2 zero zero NUM iajs-2292 152 3 borders border NOUN iajs-2292 152 4 will will AUX iajs-2292 152 5 be be AUX iajs-2292 152 6 : : PUNCT iajs-2292 152 7 π‘Ž0(𝑑 π‘Ž0(𝑑 ADJ iajs-2292 152 8 ) ) PUNCT iajs-2292 152 9 = = SYM iajs-2292 152 10 0.362 0.362 NUM iajs-2292 152 11 , , PUNCT iajs-2292 152 12 π‘š0(𝑑 π‘š0(𝑑 NUM iajs-2292 152 13 ) ) PUNCT iajs-2292 152 14 = = PUNCT iajs-2292 152 15 0.581 0.581 NUM iajs-2292 152 16 , , PUNCT iajs-2292 152 17 π‘Ÿ0(𝑑 π‘Ÿ0(𝑑 PROPN iajs-2292 152 18 ) ) PUNCT iajs-2292 152 19 = = NOUN iajs-2292 152 20 0.057 0.057 NUM iajs-2292 152 21 . . PUNCT iajs-2292 153 1 in in ADP iajs-2292 153 2 equations equation NOUN iajs-2292 153 3 ( ( PUNCT iajs-2292 153 4 13 13 NUM iajs-2292 153 5 - - SYM iajs-2292 153 6 15 15 NUM iajs-2292 153 7 ) ) PUNCT iajs-2292 153 8 , , PUNCT iajs-2292 153 9 if if SCONJ iajs-2292 153 10 we we PRON iajs-2292 153 11 substitute substitute VERB iajs-2292 153 12 ( ( PUNCT iajs-2292 153 13 k=0 k=0 PROPN iajs-2292 153 14 ) ) PUNCT iajs-2292 153 15 , , PUNCT iajs-2292 153 16 we we PRON iajs-2292 153 17 obtain obtain VERB iajs-2292 153 18 the the DET iajs-2292 153 19 following following ADJ iajs-2292 153 20 π‘Ž1(𝑑 π‘Ž1(𝑑 NOUN iajs-2292 153 21 ) ) PUNCT iajs-2292 153 22 , , PUNCT iajs-2292 153 23 π‘š1(𝑑 π‘š1(𝑑 NUM iajs-2292 153 24 ) ) PUNCT iajs-2292 153 25 and and CCONJ iajs-2292 153 26 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NUM iajs-2292 153 27 ) ) PUNCT iajs-2292 153 28 . . PUNCT iajs-2292 154 1 π‘Ž1(𝑑 π‘Ž1(𝑑 X iajs-2292 154 2 ) ) PUNCT iajs-2292 154 3 = = PUNCT iajs-2292 154 4 0.362 0.362 NUM iajs-2292 154 5 β€Š β€Š SPACE iajs-2292 154 6 + + NUM iajs-2292 154 7 0.00011927𝑑. 0.00011927𝑑. NOUN iajs-2292 154 8 π‘š1(𝑑 π‘š1(𝑑 NUM iajs-2292 154 9 ) ) PUNCT iajs-2292 154 10 = = PUNCT iajs-2292 154 11 0.581 0.581 NUM iajs-2292 154 12 β€Š β€Š SPACE iajs-2292 154 13 + + NUM iajs-2292 154 14 0.00048711𝑑. 0.00048711𝑑. NOUN iajs-2292 154 15 π‘Ÿ1(𝑑 π‘Ÿ1(𝑑 NOUN iajs-2292 154 16 ) ) PUNCT iajs-2292 154 17 = = NOUN iajs-2292 154 18 0.057 0.057 NUM iajs-2292 154 19 β€Š β€Š SPACE iajs-2292 154 20 βˆ’ βˆ’ NOUN iajs-2292 154 21 0.00060638𝑑. 0.00060638𝑑. PROPN iajs-2292 154 22 by by ADP iajs-2292 154 23 the the DET iajs-2292 154 24 same same ADJ iajs-2292 154 25 way way NOUN iajs-2292 154 26 , , PUNCT iajs-2292 154 27 if if SCONJ iajs-2292 154 28 we we PRON iajs-2292 154 29 have have VERB iajs-2292 154 30 ( ( PUNCT iajs-2292 154 31 k=1 k=1 NOUN iajs-2292 154 32 ) ) PUNCT iajs-2292 154 33 , , PUNCT iajs-2292 154 34 in in ADP iajs-2292 154 35 equations equation NOUN iajs-2292 154 36 ( ( PUNCT iajs-2292 154 37 13 13 NUM iajs-2292 154 38 - - SYM iajs-2292 154 39 15 15 NUM iajs-2292 154 40 ) ) PUNCT iajs-2292 154 41 we we PRON iajs-2292 154 42 get get VERB iajs-2292 154 43 the the DET iajs-2292 154 44 following follow VERB iajs-2292 154 45 π‘Ž2(𝑑 π‘Ž2(𝑑 NOUN iajs-2292 154 46 ) ) PUNCT iajs-2292 154 47 , , PUNCT iajs-2292 154 48 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 154 49 ) ) PUNCT iajs-2292 154 50 and and CCONJ iajs-2292 154 51 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 154 52 ) ) PUNCT iajs-2292 154 53 . . PUNCT iajs-2292 155 1 π‘Ž2(𝑑 π‘Ž2(𝑑 X iajs-2292 155 2 ) ) PUNCT iajs-2292 155 3 = = PUNCT iajs-2292 156 1 0.362 0.362 NUM iajs-2292 156 2 β€Š β€Š SPACE iajs-2292 156 3 + + CCONJ iajs-2292 156 4 0.00011927𝑑 0.00011927𝑑 ADP iajs-2292 156 5 βˆ’ βˆ’ VERB iajs-2292 156 6 0.00000147𝑑2 0.00000147𝑑2 PRON iajs-2292 156 7 + + PUNCT iajs-2292 156 8 1.30183484 1.30183484 NUM iajs-2292 156 9 βˆ— βˆ— NOUN iajs-2292 156 10 10βˆ’10𝑑3 10βˆ’10𝑑3 NUM iajs-2292 156 11 , , PUNCT iajs-2292 156 12 π‘š2(𝑑 π‘š2(𝑑 NOUN iajs-2292 156 13 ) ) PUNCT iajs-2292 156 14 = = PUNCT iajs-2292 156 15 0.581 0.581 NUM iajs-2292 156 16 β€Š β€Š SPACE iajs-2292 156 17 + + NUM iajs-2292 156 18 0.00048711𝑑 0.00048711𝑑 PUNCT iajs-2292 157 1 βˆ’ βˆ’ NOUN iajs-2292 157 2 0.00000212𝑑2 0.00000212𝑑2 NUM iajs-2292 158 1 βˆ’ βˆ’ PROPN iajs-2292 158 2 1.54291666 1.54291666 NUM iajs-2292 158 3 βˆ— βˆ— NOUN iajs-2292 158 4 10βˆ’10𝑑3 10βˆ’10𝑑3 NUM iajs-2292 158 5 , , PUNCT iajs-2292 158 6 π‘Ÿ2(𝑑 π‘Ÿ2(𝑑 NOUN iajs-2292 158 7 ) ) PUNCT iajs-2292 158 8 = = NOUN iajs-2292 158 9 0.057 0.057 NUM iajs-2292 158 10 β€Š β€Š SPACE iajs-2292 158 11 βˆ’ βˆ’ PROPN iajs-2292 158 12 0.00060638𝑑 0.00060638𝑑 NOUN iajs-2292 159 1 + + CCONJ iajs-2292 159 2 0.00000359𝑑2 0.00000359𝑑2 NUM iajs-2292 159 3 + + CCONJ iajs-2292 159 4 2.41081825 2.41081825 NUM iajs-2292 159 5 βˆ— βˆ— NOUN iajs-2292 159 6 10βˆ’11𝑑3 10βˆ’11𝑑3 NUM iajs-2292 159 7 , , PUNCT iajs-2292 159 8 continuing continue VERB iajs-2292 159 9 in in ADP iajs-2292 159 10 the the DET iajs-2292 159 11 same same ADJ iajs-2292 159 12 manner manner NOUN iajs-2292 159 13 when when SCONJ iajs-2292 159 14 ( ( PUNCT iajs-2292 159 15 k=2 k=2 PROPN iajs-2292 159 16 ) ) PUNCT iajs-2292 159 17 , , PUNCT iajs-2292 159 18 we we PRON iajs-2292 159 19 can can AUX iajs-2292 159 20 a a DET iajs-2292 159 21 achieved achieve VERB iajs-2292 159 22 the the DET iajs-2292 159 23 following follow VERB iajs-2292 159 24 π‘Ž3(𝑑 π‘Ž3(𝑑 PROPN iajs-2292 159 25 ) ) PUNCT iajs-2292 159 26 , , PUNCT iajs-2292 159 27 π‘š3(𝑑 π‘š3(𝑑 PROPN iajs-2292 159 28 ) ) PUNCT iajs-2292 159 29 and and CCONJ iajs-2292 159 30 π‘Ÿ3(𝑑 π‘Ÿ3(𝑑 PROPN iajs-2292 159 31 ) ) PUNCT iajs-2292 159 32 . . PUNCT iajs-2292 160 1 π‘Ž3(𝑑 π‘Ž3(𝑑 X iajs-2292 160 2 ) ) PUNCT iajs-2292 160 3 = = PUNCT iajs-2292 161 1 0.362 0.362 NUM iajs-2292 161 2 β€Š β€Š SPACE iajs-2292 161 3 + + CCONJ iajs-2292 161 4 0.00011928𝑑 0.00011928𝑑 NOUN iajs-2292 161 5 βˆ’ βˆ’ ADP iajs-2292 161 6 0.00000147𝑑2 0.00000147𝑑2 PRON iajs-2292 161 7 + + CCONJ iajs-2292 161 8 1.04339442 1.04339442 NUM iajs-2292 161 9 βˆ— βˆ— NOUN iajs-2292 161 10 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 161 11 βˆ’ βˆ’ PROPN iajs-2292 161 12 2.97475940 2.97475940 NUM iajs-2292 161 13 βˆ— βˆ— NOUN iajs-2292 161 14 10βˆ’12𝑑4 10βˆ’12𝑑4 NUM iajs-2292 161 15 + + CCONJ iajs-2292 161 16 1.20789692 1.20789692 NUM iajs-2292 161 17 βˆ— βˆ— NOUN iajs-2292 161 18 10βˆ’14𝑑5 10βˆ’14𝑑5 NOUN iajs-2292 161 19 βˆ’ βˆ’ PROPN iajs-2292 161 20 1.75446808 1.75446808 NUM iajs-2292 161 21 βˆ— βˆ— NOUN iajs-2292 161 22 10βˆ’18𝑑6 10βˆ’18𝑑6 NOUN iajs-2292 161 23 + + CCONJ iajs-2292 161 24 6.64675814 6.64675814 NUM iajs-2292 161 25 βˆ— βˆ— NOUN iajs-2292 161 26 10βˆ’23𝑑7 10βˆ’23𝑑7 NUM iajs-2292 161 27 ( ( PUNCT iajs-2292 161 28 16 16 NUM iajs-2292 161 29 ) ) PUNCT iajs-2292 161 30 π‘š3(𝑑 π‘š3(𝑑 PROPN iajs-2292 161 31 ) ) PUNCT iajs-2292 161 32 = = PUNCT iajs-2292 161 33 0.581 0.581 NUM iajs-2292 161 34 β€Š β€Š SPACE iajs-2292 161 35 + + CCONJ iajs-2292 161 36 0.00048710𝑑 0.00048710𝑑 ADJ iajs-2292 161 37 βˆ’ βˆ’ PROPN iajs-2292 161 38 0.00000212𝑑2 0.00000212𝑑2 NUM iajs-2292 161 39 + + CCONJ iajs-2292 161 40 3.66528836 3.66528836 NUM iajs-2292 161 41 βˆ— βˆ— NOUN iajs-2292 161 42 10βˆ’9𝑑3 10βˆ’9𝑑3 NUM iajs-2292 161 43 + + CCONJ iajs-2292 161 44 3.38204598 3.38204598 NUM iajs-2292 161 45 βˆ— βˆ— NOUN iajs-2292 161 46 10βˆ’12𝑑4 10βˆ’12𝑑4 NUM iajs-2292 161 47 βˆ’ βˆ’ PROPN iajs-2292 161 48 1.31514568 1.31514568 NUM iajs-2292 161 49 Γ— Γ— NOUN iajs-2292 161 50 10βˆ’14𝑑5 10βˆ’14𝑑5 NUM iajs-2292 161 51 + + CCONJ iajs-2292 161 52 1.82643463 1.82643463 NUM iajs-2292 161 53 βˆ— βˆ— NOUN iajs-2292 161 54 10βˆ’18𝑑6 10βˆ’18𝑑6 NOUN iajs-2292 161 55 βˆ’ βˆ’ PROPN iajs-2292 161 56 6.60192260 6.60192260 NUM iajs-2292 161 57 βˆ— βˆ— NOUN iajs-2292 161 58 10βˆ’23𝑑7 10βˆ’23𝑑7 NUM iajs-2292 161 59 ( ( PUNCT iajs-2292 161 60 17 17 NUM iajs-2292 161 61 ) ) PUNCT iajs-2292 161 62 159 159 NUM iajs-2292 161 63 ibn ibn PROPN iajs-2292 161 64 al al PROPN iajs-2292 161 65 - - PUNCT iajs-2292 161 66 haitham haitham PROPN iajs-2292 161 67 jour jour X iajs-2292 161 68 . . PROPN iajs-2292 162 1 for for ADP iajs-2292 162 2 pure pure ADJ iajs-2292 162 3 & & CCONJ iajs-2292 162 4 appl appl PROPN iajs-2292 162 5 . . PUNCT iajs-2292 163 1 sci sci PROPN iajs-2292 163 2 . . PROPN iajs-2292 163 3 32 32 NUM iajs-2292 163 4 ( ( PUNCT iajs-2292 163 5 3 3 NUM iajs-2292 163 6 ) ) PUNCT iajs-2292 163 7 2019 2019 NUM iajs-2292 163 8 π‘Ÿ3(𝑑 π‘Ÿ3(𝑑 PROPN iajs-2292 163 9 ) ) PUNCT iajs-2292 163 10 = = NOUN iajs-2292 163 11 0.057 0.057 NUM iajs-2292 163 12 β€Š β€Š SPACE iajs-2292 163 13 βˆ’ βˆ’ PROPN iajs-2292 163 14 0.0006064𝑑 0.0006064𝑑 PROPN iajs-2292 164 1 + + CCONJ iajs-2292 165 1 0.00000359𝑑2 0.00000359𝑑2 NUM iajs-2292 165 2 βˆ’ βˆ’ NUM iajs-2292 165 3 1.40992325 1.40992325 NUM iajs-2292 165 4 βˆ— βˆ— NOUN iajs-2292 165 5 10βˆ’8𝑑3 10βˆ’8𝑑3 NUM iajs-2292 165 6 βˆ’ βˆ’ PROPN iajs-2292 165 7 4.07286579 4.07286579 NUM iajs-2292 165 8 βˆ— βˆ— NOUN iajs-2292 165 9 10βˆ’13𝑑4 10βˆ’13𝑑4 NOUN iajs-2292 166 1 + + CCONJ iajs-2292 166 2 1.07248763 1.07248763 NUM iajs-2292 166 3 βˆ— βˆ— NOUN iajs-2292 166 4 10βˆ’15𝑑5 10βˆ’15𝑑5 NOUN iajs-2292 167 1 βˆ’ βˆ’ PROPN iajs-2292 167 2 7.19665484 7.19665484 NUM iajs-2292 167 3 βˆ— βˆ— NOUN iajs-2292 167 4 10βˆ’20𝑑6 10βˆ’20𝑑6 NUM iajs-2292 167 5 βˆ’ βˆ’ PROPN iajs-2292 167 6 4.48355311 4.48355311 NUM iajs-2292 167 7 βˆ— βˆ— NOUN iajs-2292 167 8 10βˆ’25𝑑7 10βˆ’25𝑑7 NUM iajs-2292 167 9 ( ( PUNCT iajs-2292 167 10 18 18 NUM iajs-2292 167 11 ) ) PUNCT iajs-2292 167 12 and and CCONJ iajs-2292 167 13 so so ADV iajs-2292 167 14 on on ADV iajs-2292 167 15 , , PUNCT iajs-2292 167 16 continue continue VERB iajs-2292 167 17 in in ADP iajs-2292 167 18 order order NOUN iajs-2292 167 19 to to PART iajs-2292 167 20 get get VERB iajs-2292 167 21 better well ADJ iajs-2292 167 22 approximations approximation NOUN iajs-2292 167 23 : : PUNCT iajs-2292 167 24 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 167 25 ) ) PUNCT iajs-2292 167 26 = = SYM iajs-2292 167 27 limπ‘˜β†’βˆž limπ‘˜β†’βˆž NOUN iajs-2292 167 28 π‘Žπ‘˜(𝑑 π‘Žπ‘˜(𝑑 NOUN iajs-2292 167 29 ) ) PUNCT iajs-2292 167 30 , , PUNCT iajs-2292 167 31 π‘š(𝑑 π‘š(𝑑 X iajs-2292 167 32 ) ) PUNCT iajs-2292 167 33 = = SYM iajs-2292 167 34 limπ‘˜β†’βˆž limπ‘˜β†’βˆž NOUN iajs-2292 167 35 π‘šπ‘˜(𝑑 π‘šπ‘˜(𝑑 NOUN iajs-2292 167 36 ) ) PUNCT iajs-2292 167 37 and and CCONJ iajs-2292 167 38 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN iajs-2292 167 39 ) ) PUNCT iajs-2292 168 1 = = SYM iajs-2292 168 2 limπ‘˜β†’βˆž limπ‘˜β†’βˆž NOUN iajs-2292 168 3 π‘Ÿπ‘˜(𝑑 π‘Ÿπ‘˜(𝑑 NOUN iajs-2292 168 4 ) ) PUNCT iajs-2292 168 5 . . PUNCT iajs-2292 169 1 4 4 X iajs-2292 169 2 . . NOUN iajs-2292 169 3 results result NOUN iajs-2292 169 4 and and CCONJ iajs-2292 169 5 discussion discussion NOUN iajs-2292 169 6 the the DET iajs-2292 169 7 analytical analytical ADJ iajs-2292 169 8 solutions solution NOUN iajs-2292 169 9 for for ADP iajs-2292 169 10 nonlinear nonlinear ADJ iajs-2292 169 11 alcohol alcohol NOUN iajs-2292 169 12 consumption consumption NOUN iajs-2292 169 13 model model NOUN iajs-2292 169 14 in in ADP iajs-2292 169 15 spain spain PROPN iajs-2292 169 16 are be AUX iajs-2292 169 17 analyzed analyze VERB iajs-2292 169 18 and and CCONJ iajs-2292 169 19 discussed discuss VERB iajs-2292 169 20 in in ADP iajs-2292 169 21 this this DET iajs-2292 169 22 section section NOUN iajs-2292 169 23 then then ADV iajs-2292 169 24 listed list VERB iajs-2292 169 25 in in ADP iajs-2292 169 26 table table NOUN iajs-2292 169 27 3 3 NUM iajs-2292 169 28 . . PUNCT iajs-2292 170 1 the the DET iajs-2292 170 2 predicted predict VERB iajs-2292 170 3 values value NOUN iajs-2292 170 4 of of ADP iajs-2292 170 5 variables variable NOUN iajs-2292 170 6 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 170 7 ) ) PUNCT iajs-2292 170 8 , , PUNCT iajs-2292 170 9 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 170 10 ) ) PUNCT iajs-2292 170 11 and and CCONJ iajs-2292 170 12 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 170 13 ) ) PUNCT iajs-2292 170 14 for for ADP iajs-2292 170 15 alcohol alcohol NOUN iajs-2292 170 16 consumption consumption NOUN iajs-2292 170 17 model model NOUN iajs-2292 170 18 , , PUNCT iajs-2292 170 19 [ [ X iajs-2292 170 20 12 12 NUM iajs-2292 170 21 ] ] PUNCT iajs-2292 170 22 . . PUNCT iajs-2292 170 23 had have AUX iajs-2292 170 24 been be AUX iajs-2292 170 25 given give VERB iajs-2292 170 26 . . PUNCT iajs-2292 171 1 since since SCONJ iajs-2292 171 2 the the DET iajs-2292 171 3 exact exact ADJ iajs-2292 171 4 solution solution NOUN iajs-2292 171 5 is be AUX iajs-2292 171 6 not not PART iajs-2292 171 7 available available ADJ iajs-2292 171 8 for for ADP iajs-2292 171 9 the the DET iajs-2292 171 10 current current ADJ iajs-2292 171 11 model model NOUN iajs-2292 171 12 , , PUNCT iajs-2292 171 13 the the DET iajs-2292 171 14 predicted predict VERB iajs-2292 171 15 values value NOUN iajs-2292 171 16 are be AUX iajs-2292 171 17 used use VERB iajs-2292 171 18 to to PART iajs-2292 171 19 compare compare VERB iajs-2292 171 20 between between ADP iajs-2292 171 21 the the DET iajs-2292 171 22 current current ADJ iajs-2292 171 23 analytic analytic ADJ iajs-2292 171 24 solutions solution NOUN iajs-2292 171 25 of of ADP iajs-2292 171 26 adm adm PROPN iajs-2292 171 27 and and CCONJ iajs-2292 171 28 vim vim NOUN iajs-2292 171 29 with with ADP iajs-2292 171 30 the the DET iajs-2292 171 31 predicted predict VERB iajs-2292 171 32 values value NOUN iajs-2292 171 33 [ [ X iajs-2292 171 34 12 12 NUM iajs-2292 171 35 ] ] PUNCT iajs-2292 171 36 . . PUNCT iajs-2292 172 1 in in ADP iajs-2292 172 2 the the DET iajs-2292 172 3 interval interval NOUN iajs-2292 172 4 ( ( PUNCT iajs-2292 172 5 0,10 0,10 NUM iajs-2292 172 6 ) ) PUNCT iajs-2292 172 7 from from ADP iajs-2292 172 8 1997 1997 NUM iajs-2292 172 9 to to ADP iajs-2292 172 10 2007 2007 NUM iajs-2292 172 11 . . PUNCT iajs-2292 173 1 for for ADP iajs-2292 173 2 comparison comparison NOUN iajs-2292 173 3 purpose purpose NOUN iajs-2292 173 4 , , PUNCT iajs-2292 173 5 the the DET iajs-2292 173 6 corresponding corresponding ADJ iajs-2292 173 7 absolute absolute ADJ iajs-2292 173 8 error error NOUN iajs-2292 173 9 of of ADP iajs-2292 173 10 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 173 11 ) ) PUNCT iajs-2292 173 12 , , PUNCT iajs-2292 173 13 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 173 14 ) ) PUNCT iajs-2292 173 15 and and CCONJ iajs-2292 173 16 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 173 17 ) ) PUNCT iajs-2292 173 18 for for ADP iajs-2292 173 19 adm adm PROPN iajs-2292 173 20 and and CCONJ iajs-2292 173 21 vim vim PROPN iajs-2292 173 22 methods method NOUN iajs-2292 173 23 are be AUX iajs-2292 173 24 shown show VERB iajs-2292 173 25 numerically numerically ADV iajs-2292 173 26 in in ADP iajs-2292 173 27 table table NOUN iajs-2292 173 28 4 4 NUM iajs-2292 173 29 . . PUNCT iajs-2292 173 30 where where SCONJ iajs-2292 173 31 the the DET iajs-2292 173 32 absolute absolute ADJ iajs-2292 173 33 error error NOUN iajs-2292 173 34 in in ADP iajs-2292 173 35 this this DET iajs-2292 173 36 study study NOUN iajs-2292 173 37 is be AUX iajs-2292 173 38 the the DET iajs-2292 173 39 absolute absolute ADJ iajs-2292 173 40 value value NOUN iajs-2292 173 41 of of ADP iajs-2292 173 42 the the DET iajs-2292 173 43 difference difference NOUN iajs-2292 173 44 between between ADP iajs-2292 173 45 the the DET iajs-2292 173 46 analytic analytic ADJ iajs-2292 173 47 solutions solution NOUN iajs-2292 173 48 and and CCONJ iajs-2292 173 49 the the DET iajs-2292 173 50 predicted predict VERB iajs-2292 173 51 values value NOUN iajs-2292 173 52 . . PUNCT iajs-2292 174 1 moreover moreover ADV iajs-2292 174 2 , , PUNCT iajs-2292 174 3 the the DET iajs-2292 174 4 relative relative ADJ iajs-2292 174 5 error error NOUN iajs-2292 174 6 of of ADP iajs-2292 174 7 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 174 8 ) ) PUNCT iajs-2292 174 9 , , PUNCT iajs-2292 174 10 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 174 11 ) ) PUNCT iajs-2292 174 12 and and CCONJ iajs-2292 174 13 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 174 14 ) ) PUNCT iajs-2292 174 15 for for ADP iajs-2292 174 16 adm adm PROPN iajs-2292 174 17 and and CCONJ iajs-2292 174 18 vim vim PROPN iajs-2292 174 19 methods method NOUN iajs-2292 174 20 is be AUX iajs-2292 174 21 also also ADV iajs-2292 174 22 listed list VERB iajs-2292 174 23 in in ADP iajs-2292 174 24 table table NOUN iajs-2292 174 25 5 5 NUM iajs-2292 174 26 . . PUNCT iajs-2292 175 1 which which PRON iajs-2292 175 2 is be AUX iajs-2292 175 3 defined define VERB iajs-2292 175 4 as as ADP iajs-2292 175 5 the the DET iajs-2292 175 6 absolute absolute ADJ iajs-2292 175 7 value value NOUN iajs-2292 175 8 of of ADP iajs-2292 175 9 dividing divide VERB iajs-2292 175 10 the the DET iajs-2292 175 11 absolute absolute ADJ iajs-2292 175 12 error error NOUN iajs-2292 175 13 on on ADP iajs-2292 175 14 the the DET iajs-2292 175 15 predicted predict VERB iajs-2292 175 16 values value NOUN iajs-2292 175 17 in in ADP iajs-2292 175 18 this this DET iajs-2292 175 19 study study NOUN iajs-2292 175 20 . . PUNCT iajs-2292 176 1 in in ADP iajs-2292 176 2 table table NOUN iajs-2292 176 3 4,5 4,5 NUM iajs-2292 176 4 . . PUNCT iajs-2292 177 1 the the DET iajs-2292 177 2 absolute absolute ADJ iajs-2292 177 3 and and CCONJ iajs-2292 177 4 relative relative ADJ iajs-2292 177 5 errors error NOUN iajs-2292 177 6 of of ADP iajs-2292 177 7 adm adm PROPN iajs-2292 177 8 for for ADP iajs-2292 177 9 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 177 10 ) ) PUNCT iajs-2292 177 11 have have VERB iajs-2292 177 12 smaller small ADJ iajs-2292 177 13 values value NOUN iajs-2292 177 14 from from ADP iajs-2292 177 15 2003 2003 NUM iajs-2292 177 16 to to ADP iajs-2292 177 17 2005 2005 NUM iajs-2292 177 18 and and CCONJ iajs-2292 177 19 2007 2007 NUM iajs-2292 177 20 than than ADP iajs-2292 177 21 the the DET iajs-2292 177 22 vim vim NOUN iajs-2292 177 23 , , PUNCT iajs-2292 177 24 while while SCONJ iajs-2292 177 25 the the DET iajs-2292 177 26 absolute absolute ADJ iajs-2292 177 27 and and CCONJ iajs-2292 177 28 relative relative ADJ iajs-2292 177 29 errors error NOUN iajs-2292 177 30 of of ADP iajs-2292 177 31 adm adm PROPN iajs-2292 177 32 for for ADP iajs-2292 177 33 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 177 34 ) ) PUNCT iajs-2292 177 35 are be AUX iajs-2292 177 36 smaller small ADJ iajs-2292 177 37 than than ADP iajs-2292 177 38 vim vim NOUN iajs-2292 177 39 from from ADP iajs-2292 177 40 1999 1999 NUM iajs-2292 177 41 till till SCONJ iajs-2292 177 42 2001 2001 NUM iajs-2292 177 43 and and CCONJ iajs-2292 177 44 2007 2007 NUM iajs-2292 177 45 . . PUNCT iajs-2292 178 1 for for ADP iajs-2292 178 2 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 178 3 ) ) PUNCT iajs-2292 178 4 , , PUNCT iajs-2292 178 5 the the DET iajs-2292 178 6 absolute absolute ADJ iajs-2292 178 7 and and CCONJ iajs-2292 178 8 relative relative ADJ iajs-2292 178 9 errors error NOUN iajs-2292 178 10 of of ADP iajs-2292 178 11 adm adm PROPN iajs-2292 178 12 in in ADP iajs-2292 178 13 the the DET iajs-2292 178 14 interval interval NOUN iajs-2292 178 15 ( ( PUNCT iajs-2292 178 16 0,10 0,10 NUM iajs-2292 178 17 ) ) PUNCT iajs-2292 178 18 from from ADP iajs-2292 178 19 1997 1997 NUM iajs-2292 178 20 to to ADP iajs-2292 178 21 2007 2007 NUM iajs-2292 178 22 are be AUX iajs-2292 178 23 oscillatory oscillatory ADJ iajs-2292 178 24 with with ADP iajs-2292 178 25 vim vim NOUN iajs-2292 178 26 errors error NOUN iajs-2292 178 27 . . PUNCT iajs-2292 179 1 the the DET iajs-2292 179 2 figures figure NOUN iajs-2292 179 3 describe describe VERB iajs-2292 179 4 the the DET iajs-2292 179 5 behavior behavior NOUN iajs-2292 179 6 of of ADP iajs-2292 179 7 alcohol alcohol NOUN iajs-2292 179 8 drinking drinking NOUN iajs-2292 179 9 habit habit NOUN iajs-2292 179 10 from from ADP iajs-2292 179 11 1997 1997 NUM iajs-2292 179 12 to to ADP iajs-2292 179 13 2007 2007 NUM iajs-2292 179 14 . . PUNCT iajs-2292 180 1 figure figure NOUN iajs-2292 180 2 1a 1a NOUN iajs-2292 180 3 . . PUNCT iajs-2292 181 1 of of ADP iajs-2292 181 2 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 181 3 ) ) PUNCT iajs-2292 181 4 shows show VERB iajs-2292 181 5 the the DET iajs-2292 181 6 adm adm PROPN iajs-2292 181 7 and and CCONJ iajs-2292 181 8 vim vim PROPN iajs-2292 181 9 obtained obtain VERB iajs-2292 181 10 results result NOUN iajs-2292 181 11 near near ADP iajs-2292 181 12 to to ADP iajs-2292 181 13 some some DET iajs-2292 181 14 predicted predict VERB iajs-2292 181 15 values value NOUN iajs-2292 181 16 in in ADP iajs-2292 181 17 2001 2001 NUM iajs-2292 181 18 until until ADP iajs-2292 181 19 2005.while 2005.while NUM iajs-2292 181 20 figure figure NOUN iajs-2292 181 21 1b 1b NUM iajs-2292 181 22 . . PUNCT iajs-2292 182 1 of of ADP iajs-2292 182 2 π‘š(𝑑 π‘š(𝑑 NOUN iajs-2292 182 3 ) ) PUNCT iajs-2292 182 4 shows show VERB iajs-2292 182 5 the the DET iajs-2292 182 6 predicted predict VERB iajs-2292 182 7 values value NOUN iajs-2292 182 8 around around ADP iajs-2292 182 9 both both DET iajs-2292 182 10 adm adm PROPN iajs-2292 182 11 and and CCONJ iajs-2292 182 12 vim vim PROPN iajs-2292 182 13 obtained obtain VERB iajs-2292 182 14 results result NOUN iajs-2292 182 15 . . PUNCT iajs-2292 183 1 regarding regard VERB iajs-2292 183 2 to to PART iajs-2292 183 3 figure figure VERB iajs-2292 183 4 c. c. NOUN iajs-2292 183 5 of of ADP iajs-2292 183 6 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 183 7 ) ) PUNCT iajs-2292 183 8 , , PUNCT iajs-2292 183 9 both both CCONJ iajs-2292 183 10 adm adm PROPN iajs-2292 183 11 and and CCONJ iajs-2292 183 12 vim vim PROPN iajs-2292 183 13 curves curve NOUN iajs-2292 183 14 obtained obtain VERB iajs-2292 183 15 results result NOUN iajs-2292 183 16 converge converge VERB iajs-2292 183 17 to to ADP iajs-2292 183 18 the the DET iajs-2292 183 19 predicted predict VERB iajs-2292 183 20 values value NOUN iajs-2292 183 21 in in ADP iajs-2292 183 22 1999 1999 NUM iajs-2292 183 23 until until ADP iajs-2292 183 24 2005 2005 NUM iajs-2292 183 25 . . PUNCT iajs-2292 184 1 for for ADP iajs-2292 184 2 figure figure NOUN iajs-2292 184 3 1a 1a NOUN iajs-2292 184 4 . . PUNCT iajs-2292 185 1 that that PRON iajs-2292 185 2 related relate VERB iajs-2292 185 3 to to ADP iajs-2292 185 4 non non ADJ iajs-2292 185 5 - - ADJ iajs-2292 185 6 drink drink ADJ iajs-2292 185 7 alcohol alcohol NOUN iajs-2292 185 8 people people NOUN iajs-2292 185 9 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 185 10 ) ) PUNCT iajs-2292 185 11 , , PUNCT iajs-2292 185 12 the the DET iajs-2292 185 13 adm adm PROPN iajs-2292 185 14 curve curve NOUN iajs-2292 185 15 keeps keep VERB iajs-2292 185 16 on on ADP iajs-2292 185 17 its its PRON iajs-2292 185 18 level level NOUN iajs-2292 185 19 from from ADP iajs-2292 185 20 1997 1997 NUM iajs-2292 185 21 to to ADP iajs-2292 185 22 2007 2007 NUM iajs-2292 185 23 . . PUNCT iajs-2292 186 1 more more ADV iajs-2292 186 2 other other ADJ iajs-2292 186 3 , , PUNCT iajs-2292 186 4 there there PRON iajs-2292 186 5 exists exist VERB iajs-2292 186 6 a a DET iajs-2292 186 7 variation variation NOUN iajs-2292 186 8 between between ADP iajs-2292 186 9 them they PRON iajs-2292 186 10 such such ADJ iajs-2292 186 11 that that SCONJ iajs-2292 186 12 the the DET iajs-2292 186 13 vim vim PROPN iajs-2292 186 14 curve curve NOUN iajs-2292 186 15 is be AUX iajs-2292 186 16 higher high ADJ iajs-2292 186 17 level level NOUN iajs-2292 186 18 than than ADP iajs-2292 186 19 adm adm PROPN iajs-2292 186 20 curve curve NOUN iajs-2292 186 21 . . PUNCT iajs-2292 187 1 on on ADP iajs-2292 187 2 the the DET iajs-2292 187 3 other other ADJ iajs-2292 187 4 hand hand NOUN iajs-2292 187 5 , , PUNCT iajs-2292 187 6 both both PRON iajs-2292 187 7 adm adm PROPN iajs-2292 187 8 and and CCONJ iajs-2292 187 9 vim vim PROPN iajs-2292 187 10 curves curve NOUN iajs-2292 187 11 of of ADP iajs-2292 187 12 non non ADJ iajs-2292 187 13 - - ADJ iajs-2292 187 14 risk risk ADJ iajs-2292 187 15 - - PUNCT iajs-2292 187 16 drink drink NOUN iajs-2292 187 17 alcohol alcohol NOUN iajs-2292 187 18 people people NOUN iajs-2292 187 19 π‘š(𝑑 π‘š(𝑑 VERB iajs-2292 187 20 ) ) PUNCT iajs-2292 187 21 have have AUX iajs-2292 187 22 higher high ADJ iajs-2292 187 23 that that PRON iajs-2292 187 24 appears appear VERB iajs-2292 187 25 during during ADP iajs-2292 187 26 the the DET iajs-2292 187 27 ten ten NUM iajs-2292 187 28 years year NOUN iajs-2292 187 29 from from ADP iajs-2292 187 30 1997 1997 NUM iajs-2292 187 31 till till SCONJ iajs-2292 187 32 2007 2007 NUM iajs-2292 187 33 in in ADP iajs-2292 187 34 figure figure NOUN iajs-2292 187 35 1b 1b NUM iajs-2292 187 36 . . PUNCT iajs-2292 188 1 figure figure NOUN iajs-2292 188 2 1c 1c NOUN iajs-2292 188 3 . . PUNCT iajs-2292 188 4 illustrates illustrate VERB iajs-2292 188 5 the the DET iajs-2292 188 6 decrease decrease NOUN iajs-2292 188 7 in in ADP iajs-2292 188 8 the the DET iajs-2292 188 9 risk risk NOUN iajs-2292 188 10 - - PUNCT iajs-2292 188 11 drink drink NOUN iajs-2292 188 12 alcohol alcohol NOUN iajs-2292 188 13 people people NOUN iajs-2292 188 14 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 188 15 ) ) PUNCT iajs-2292 188 16 through through ADP iajs-2292 188 17 the the DET iajs-2292 188 18 ten ten NUM iajs-2292 188 19 years year NOUN iajs-2292 188 20 under under ADP iajs-2292 188 21 study study NOUN iajs-2292 188 22 for for ADP iajs-2292 188 23 both both DET iajs-2292 188 24 adm adm PROPN iajs-2292 188 25 and and CCONJ iajs-2292 188 26 vim vim NOUN iajs-2292 188 27 curves curve NOUN iajs-2292 188 28 . . PUNCT iajs-2292 189 1 the the DET iajs-2292 189 2 results result NOUN iajs-2292 189 3 are be AUX iajs-2292 189 4 calculated calculate VERB iajs-2292 189 5 by by ADP iajs-2292 189 6 mathematica mathematica PROPN iajs-2292 189 7 software software PROPN iajs-2292 189 8 , , PUNCT iajs-2292 189 9 the the DET iajs-2292 189 10 figures figure NOUN iajs-2292 189 11 are be AUX iajs-2292 189 12 drawn draw VERB iajs-2292 189 13 by by ADP iajs-2292 189 14 the the DET iajs-2292 189 15 magic magic ADJ iajs-2292 189 16 plot plot NOUN iajs-2292 189 17 program program NOUN iajs-2292 189 18 . . PUNCT iajs-2292 190 1 finally finally ADV iajs-2292 190 2 , , PUNCT iajs-2292 190 3 the the DET iajs-2292 190 4 percentage percentage NOUN iajs-2292 190 5 of of ADP iajs-2292 190 6 non non ADJ iajs-2292 190 7 - - ADJ iajs-2292 190 8 drink drink ADJ iajs-2292 190 9 alcohol alcohol NOUN iajs-2292 190 10 people people NOUN iajs-2292 190 11 π‘Ž(𝑑 π‘Ž(𝑑 NOUN iajs-2292 190 12 ) ) PUNCT iajs-2292 190 13 and and CCONJ iajs-2292 190 14 the the DET iajs-2292 190 15 risk risk NOUN iajs-2292 190 16 - - PUNCT iajs-2292 190 17 drink drink NOUN iajs-2292 190 18 alcohol alcohol NOUN iajs-2292 190 19 people people NOUN iajs-2292 190 20 π‘Ÿ(𝑑 π‘Ÿ(𝑑 PROPN iajs-2292 190 21 ) ) PUNCT iajs-2292 190 22 are be AUX iajs-2292 190 23 almost almost ADV iajs-2292 190 24 decrease decrease NOUN iajs-2292 190 25 , , PUNCT iajs-2292 190 26 but but CCONJ iajs-2292 190 27 increase increase VERB iajs-2292 190 28 with with ADP iajs-2292 190 29 the the DET iajs-2292 190 30 non non ADJ iajs-2292 190 31 - - ADJ iajs-2292 190 32 risk risk ADJ iajs-2292 190 33 - - PUNCT iajs-2292 190 34 drink drink NOUN iajs-2292 190 35 alcohol alcohol NOUN iajs-2292 190 36 people people NOUN iajs-2292 190 37 π‘š(𝑑 π‘š(𝑑 VERB iajs-2292 190 38 ) ) PUNCT iajs-2292 190 39 . . PUNCT iajs-2292 191 1 table table NOUN iajs-2292 191 2 3 3 NUM iajs-2292 191 3 . . PUNCT iajs-2292 192 1 analytic analytic ADJ iajs-2292 192 2 solutions solution NOUN iajs-2292 192 3 and and CCONJ iajs-2292 192 4 predicted predict VERB iajs-2292 192 5 values value NOUN iajs-2292 192 6 [ [ X iajs-2292 192 7 12 12 NUM iajs-2292 192 8 ] ] PUNCT iajs-2292 192 9 .of .of PUNCT iajs-2292 193 1 alcohol alcohol NOUN iajs-2292 193 2 consumption consumption NOUN iajs-2292 193 3 model model NOUN iajs-2292 193 4 ( ( PUNCT iajs-2292 193 5 * * PUNCT iajs-2292 193 6 means mean VERB iajs-2292 193 7 present present ADJ iajs-2292 193 8 result result NOUN iajs-2292 193 9 ) ) PUNCT iajs-2292 193 10 . . PUNCT iajs-2292 194 1 2007 2007 NUM iajs-2292 194 2 2005 2005 NUM iajs-2292 194 3 2003 2003 NUM iajs-2292 194 4 2001 2001 NUM iajs-2292 194 5 1999 1999 NUM iajs-2292 194 6 1997 1997 NUM iajs-2292 194 7 method method NOUN iajs-2292 194 8 subpop subpop NOUN iajs-2292 194 9 . . PUNCT iajs-2292 195 1 0.400 0.400 NUM iajs-2292 195 2 0.354 0.354 NUM iajs-2292 195 3 0.359 0.359 NUM iajs-2292 195 4 0.363 0.363 NUM iajs-2292 195 5 0.383 0.383 NUM iajs-2292 195 6 0.362 0.362 NUM iajs-2292 195 7 santonj santonj NOUN iajs-2292 195 8 a a DET iajs-2292 195 9 at at ADP iajs-2292 195 10 . . PUNCT iajs-2292 196 1 el el PROPN iajs-2292 196 2 . . PUNCT iajs-2292 197 1 𝒂(𝒕 𝒂(𝒕 PROPN iajs-2292 197 2 ) ) PUNCT iajs-2292 197 3 160 160 NUM iajs-2292 197 4 ibn ibn PROPN iajs-2292 197 5 al al PROPN iajs-2292 197 6 - - PUNCT iajs-2292 197 7 haitham haitham PROPN iajs-2292 197 8 jour jour X iajs-2292 197 9 . . PROPN iajs-2292 198 1 for for ADP iajs-2292 198 2 pure pure ADJ iajs-2292 198 3 & & CCONJ iajs-2292 198 4 appl appl PROPN iajs-2292 198 5 . . PUNCT iajs-2292 199 1 sci sci PROPN iajs-2292 199 2 . . PROPN iajs-2292 199 3 32 32 NUM iajs-2292 199 4 ( ( PUNCT iajs-2292 199 5 3 3 NUM iajs-2292 199 6 ) ) SYM iajs-2292 199 7 2019 2019 NUM iajs-2292 199 8 table table NOUN iajs-2292 199 9 4 4 NUM iajs-2292 199 10 . . PUNCT iajs-2292 199 11 absolute absolute ADJ iajs-2292 199 12 error error NOUN iajs-2292 199 13 for for ADP iajs-2292 199 14 adm adm PROPN iajs-2292 199 15 and and CCONJ iajs-2292 199 16 vim vim PROPN iajs-2292 199 17 solutions solution NOUN iajs-2292 199 18 as as ADP iajs-2292 199 19 relative relative ADJ iajs-2292 199 20 the the DET iajs-2292 199 21 predicted predict VERB iajs-2292 199 22 values value NOUN iajs-2292 199 23 [ [ X iajs-2292 199 24 12 12 NUM iajs-2292 199 25 ] ] PUNCT iajs-2292 199 26 . . PUNCT iajs-2292 200 1 table table NOUN iajs-2292 200 2 5 5 NUM iajs-2292 200 3 . . PUNCT iajs-2292 200 4 relative relative ADJ iajs-2292 200 5 error error NOUN iajs-2292 200 6 for for ADP iajs-2292 200 7 adm adm PROPN iajs-2292 200 8 and and CCONJ iajs-2292 200 9 vim vim PROPN iajs-2292 200 10 solutions solution NOUN iajs-2292 200 11 as as ADP iajs-2292 200 12 relative relative ADJ iajs-2292 200 13 the the DET iajs-2292 200 14 predicted predict VERB iajs-2292 200 15 values value NOUN iajs-2292 200 16 [ [ X iajs-2292 200 17 12 12 NUM iajs-2292 200 18 ] ] PUNCT iajs-2292 200 19 . . PUNCT iajs-2292 201 1 in in ADP iajs-2292 201 2 2010 2010 NUM iajs-2292 201 3 0.36101316 0.36101316 NUM iajs-2292 201 4 0.36121033 0.36121033 NUM iajs-2292 201 5 0.36140759 0.36140759 NUM iajs-2292 201 6 0.36160497 0.36160497 NUM iajs-2292 201 7 0.36180243 0.36180243 NUM iajs-2292 201 8 0.362 0.362 NUM iajs-2292 201 9 adm adm PROPN iajs-2292 201 10 * * NOUN iajs-2292 201 11 0.36305586 0.36305586 NUM iajs-2292 202 1 0.36286526 0.36286526 NUM iajs-2292 202 2 0.36266487 0.36266487 NUM iajs-2292 202 3 0.36245419 0.36245419 NUM iajs-2292 202 4 0.36223274 0.36223274 NUM iajs-2292 202 5 0.362 0.362 NUM iajs-2292 202 6 vim vim PROPN iajs-2292 202 7 * * PROPN iajs-2292 202 8 0.566 0.566 NUM iajs-2292 202 9 0.591 0.591 NUM iajs-2292 202 10 0.588 0.588 NUM iajs-2292 202 11 0.581 0.581 NUM iajs-2292 202 12 0.578 0.578 NUM iajs-2292 202 13 0.581 0.581 NUM iajs-2292 202 14 santonj santonj NOUN iajs-2292 202 15 a a PRON iajs-2292 202 16 at at ADP iajs-2292 202 17 al.in al.in PROPN iajs-2292 202 18 2010 2010 NUM iajs-2292 202 19 π’Ž(𝒕 π’Ž(𝒕 NOUN iajs-2292 202 20 ) ) PUNCT iajs-2292 202 21 0.58548056 0.58548056 NUM iajs-2292 202 22 0.58464529 0.58464529 NUM iajs-2292 202 23 0.58378022 0.58378022 NUM iajs-2292 202 24 0.58288472 0.58288472 NUM iajs-2292 202 25 0.58195819 0.58195819 NUM iajs-2292 202 26 0.581 0.581 NUM iajs-2292 202 27 adm adm PROPN iajs-2292 202 28 * * PROPN iajs-2292 202 29 0.58566309 0.58566309 NUM iajs-2292 202 30 0.58476327 0.58476327 NUM iajs-2292 202 31 0.58384724 0.58384724 NUM iajs-2292 202 32 0.58291479 0.58291479 NUM iajs-2292 202 33 0.58196578 0.58196578 NUM iajs-2292 202 34 0.581 0.581 NUM iajs-2292 202 35 vim vim X iajs-2292 202 36 * * PROPN iajs-2292 202 37 0.034 0.034 NUM iajs-2292 202 38 0.055 0.055 NUM iajs-2292 202 39 0.053 0.053 NUM iajs-2292 202 40 0.056 0.056 NUM iajs-2292 202 41 0.039 0.039 NUM iajs-2292 202 42 0.057 0.057 NUM iajs-2292 202 43 santonj santonj NOUN iajs-2292 202 44 a a PRON iajs-2292 202 45 at at ADP iajs-2292 202 46 el el PROPN iajs-2292 202 47 . . PUNCT iajs-2292 203 1 in in ADP iajs-2292 203 2 2010 2010 NUM iajs-2292 203 3 𝒓(𝒕 𝒓(𝒕 NOUN iajs-2292 203 4 ) ) PUNCT iajs-2292 203 5 0.051281517 0.051281517 NUM iajs-2292 204 1 0.05237178 0.05237178 NUM iajs-2292 204 2 0.05348808 0.05348808 NUM iajs-2292 204 3 0.05463109 0.05463109 NUM iajs-2292 204 4 0.05580150 0.05580150 NUM iajs-2292 204 5 0.057 0.057 NUM iajs-2292 204 6 adm adm PROPN iajs-2292 204 7 * * NOUN iajs-2292 204 8 0.05128105 0.05128105 NUM iajs-2292 204 9 0.05237147 0.05237147 NUM iajs-2292 204 10 0.05348789 0.05348789 NUM iajs-2292 204 11 0.05463101 0.05463101 NUM iajs-2292 204 12 0.05580148 0.05580148 NUM iajs-2292 204 13 0.057 0.057 NUM iajs-2292 204 14 vim vim NOUN iajs-2292 204 15 * * PROPN iajs-2292 204 16 2007 2007 NUM iajs-2292 204 17 2005 2005 NUM iajs-2292 204 18 2003 2003 NUM iajs-2292 204 19 2001 2001 NUM iajs-2292 204 20 1999 1999 NUM iajs-2292 204 21 absolut absolut PROPN iajs-2292 204 22 error error NOUN iajs-2292 204 23 subpop subpop NOUN iajs-2292 204 24 . . PUNCT iajs-2292 205 1 0.03898684 0.03898684 NUM iajs-2292 206 1 0.00721033 0.00721033 NUM iajs-2292 206 2 0.00240759 0.00240759 NUM iajs-2292 206 3 0.00139503 0.00139503 NUM iajs-2292 206 4 0.02119757 0.02119757 NUM iajs-2292 206 5 adm adm PROPN iajs-2292 206 6 𝒂(𝒕 𝒂(𝒕 PROPN iajs-2292 206 7 ) ) PUNCT iajs-2292 206 8 0.03694414 0.03694414 NUM iajs-2292 206 9 0.00886526 0.00886526 NUM iajs-2292 206 10 0.00366487 0.00366487 NUM iajs-2292 206 11 0.00054581 0.00054581 NUM iajs-2292 206 12 0.02076726 0.02076726 NUM iajs-2292 206 13 vim vim NOUN iajs-2292 206 14 0.01948056 0.01948056 NUM iajs-2292 206 15 0.00635471 0.00635471 NUM iajs-2292 206 16 0.00421978 0.00421978 NUM iajs-2292 206 17 0.00188472 0.00188472 NUM iajs-2292 206 18 0.00395819 0.00395819 NUM iajs-2292 206 19 adm adm PROPN iajs-2292 206 20 π’Ž(𝒕 π’Ž(𝒕 NOUN iajs-2292 206 21 ) ) PUNCT iajs-2292 206 22 0.01966309 0.01966309 NUM iajs-2292 207 1 0.00623673 0.00623673 NUM iajs-2292 207 2 0.00415276 0.00415276 NUM iajs-2292 207 3 0.00191479 0.00191479 NUM iajs-2292 207 4 0.00396578 0.00396578 NUM iajs-2292 207 5 vim vim NOUN iajs-2292 207 6 0.017281517 0.017281517 NUM iajs-2292 207 7 0.00262822 0.00262822 NUM iajs-2292 207 8 0.00048808 0.00048808 NUM iajs-2292 207 9 0.00136891 0.00136891 NUM iajs-2292 207 10 0.01680150 0.01680150 NUM iajs-2292 207 11 adm adm PROPN iajs-2292 207 12 𝒓(𝒕 𝒓(𝒕 PROPN iajs-2292 207 13 ) ) PUNCT iajs-2292 207 14 0.01728105 0.01728105 NUM iajs-2292 207 15 0.00262853 0.00262853 NUM iajs-2292 207 16 0.00048789 0.00048789 NUM iajs-2292 207 17 0.00136899 0.00136899 NUM iajs-2292 207 18 0.01680148 0.01680148 NUM iajs-2292 207 19 vim vim NOUN iajs-2292 207 20 2007 2007 NUM iajs-2292 207 21 2005 2005 NUM iajs-2292 207 22 2003 2003 NUM iajs-2292 207 23 2001 2001 NUM iajs-2292 207 24 1999 1999 NUM iajs-2292 207 25 relative relative ADJ iajs-2292 207 26 error error NOUN iajs-2292 207 27 subpop subpop NOUN iajs-2292 207 28 . . PUNCT iajs-2292 208 1 0.0974671 0.0974671 NUM iajs-2292 208 2 0.02036816 0.02036816 NUM iajs-2292 208 3 0.00670638 0.00670638 NUM iajs-2292 208 4 0.00384306 0.00384306 NOUN iajs-2292 208 5 0.05534613 0.05534613 NUM iajs-2292 208 6 adm adm PROPN iajs-2292 208 7 𝒂(𝒕 𝒂(𝒕 PROPN iajs-2292 208 8 ) ) PUNCT iajs-2292 208 9 0.09236035 0.09236035 NUM iajs-2292 209 1 0.02504311 0.02504311 NUM iajs-2292 209 2 0.01020855 0.01020855 NUM iajs-2292 209 3 0.00150361 0.00150361 NUM iajs-2292 209 4 0.05422261 0.05422261 NUM iajs-2292 209 5 vim vim NOUN iajs-2292 209 6 0.03441795 0.03441795 NUM iajs-2292 209 7 0.01075247 0.01075247 NUM iajs-2292 209 8 0.00717649 0.00717649 NUM iajs-2292 209 9 0.00324392 0.00324392 NUM iajs-2292 209 10 0.00684808 0.00684808 NUM iajs-2292 209 11 adm adm PROPN iajs-2292 209 12 π’Ž(𝒕 π’Ž(𝒕 NOUN iajs-2292 209 13 ) ) PUNCT iajs-2292 209 14 0.03474044 0.03474044 NUM iajs-2292 210 1 0.01055284 0.01055284 NUM iajs-2292 210 2 0.00706252 0.00706252 NUM iajs-2292 210 3 0.00329567 0.00329567 NUM iajs-2292 210 4 0.00686121 0.00686121 NUM iajs-2292 210 5 vim vim PRON iajs-2292 210 6 0.50827991 0.50827991 NUM iajs-2292 210 7 0.04778582 0.04778582 NUM iajs-2292 210 8 0.00920906 0.00920906 NUM iajs-2292 210 9 0.02444482 0.02444482 NUM iajs-2292 210 10 0.43080769 0.43080769 NUM iajs-2292 210 11 adm adm PROPN iajs-2292 210 12 𝒓(𝒕 𝒓(𝒕 PROPN iajs-2292 210 13 ) ) PUNCT iajs-2292 210 14 0.50826617 0.50826617 NUM iajs-2292 211 1 0.04779145 0.04779145 NUM iajs-2292 211 2 0.00920547 0.00920547 NUM iajs-2292 211 3 0.02444625 0.02444625 NUM iajs-2292 211 4 0.43080718 0.43080718 NUM iajs-2292 211 5 vim vim NOUN iajs-2292 211 6 161 161 NUM iajs-2292 211 7 ibn ibn PROPN iajs-2292 211 8 al al PROPN iajs-2292 211 9 - - PUNCT iajs-2292 211 10 haitham haitham PROPN iajs-2292 211 11 jour jour X iajs-2292 211 12 . . PROPN iajs-2292 212 1 for for ADP iajs-2292 212 2 pure pure ADJ iajs-2292 212 3 & & CCONJ iajs-2292 212 4 appl appl PROPN iajs-2292 212 5 . . PUNCT iajs-2292 213 1 sci sci PROPN iajs-2292 213 2 . . PROPN iajs-2292 213 3 32 32 NUM iajs-2292 213 4 ( ( PUNCT iajs-2292 213 5 3 3 NUM iajs-2292 213 6 ) ) PUNCT iajs-2292 213 7 2019 2019 NUM iajs-2292 213 8 figure figure NOUN iajs-2292 213 9 1 1 NUM iajs-2292 213 10 . . 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PUNCT iajs-2292 215 1 5 5 X iajs-2292 215 2 . . X iajs-2292 215 3 conclusion conclusion NOUN iajs-2292 215 4 the the DET iajs-2292 215 5 current current ADJ iajs-2292 215 6 study study NOUN iajs-2292 215 7 , , PUNCT iajs-2292 215 8 the the DET iajs-2292 215 9 convergence convergence NOUN iajs-2292 215 10 of of ADP iajs-2292 215 11 the the DET iajs-2292 215 12 results result NOUN iajs-2292 215 13 for for ADP iajs-2292 215 14 the the DET iajs-2292 215 15 analytic analytic ADJ iajs-2292 215 16 methods method NOUN iajs-2292 215 17 which which PRON iajs-2292 215 18 are be AUX iajs-2292 215 19 adomian adomian ADJ iajs-2292 215 20 decomposition decomposition NOUN iajs-2292 215 21 and and CCONJ iajs-2292 215 22 variation variation NOUN iajs-2292 215 23 iteration iteration NOUN iajs-2292 215 24 methods method NOUN iajs-2292 215 25 are be AUX iajs-2292 215 26 examined examine VERB iajs-2292 215 27 in in ADP iajs-2292 215 28 the the DET iajs-2292 215 29 nonlinear nonlinear ADJ iajs-2292 215 30 case case NOUN iajs-2292 215 31 . . PUNCT iajs-2292 216 1 these these DET iajs-2292 216 2 methods method NOUN iajs-2292 216 3 have have AUX iajs-2292 216 4 been be AUX iajs-2292 216 5 known know VERB iajs-2292 216 6 as as ADP iajs-2292 216 7 a a DET iajs-2292 216 8 powerful powerful ADJ iajs-2292 216 9 device device NOUN iajs-2292 216 10 for for ADP iajs-2292 216 11 solving solve VERB iajs-2292 216 12 a a DET iajs-2292 216 13 system system NOUN iajs-2292 216 14 of of ADP iajs-2292 216 15 ordinary ordinary ADJ iajs-2292 216 16 , , PUNCT iajs-2292 216 17 partial partial ADJ iajs-2292 216 18 differential differential ADJ iajs-2292 216 19 equations equation NOUN iajs-2292 216 20 or or CCONJ iajs-2292 216 21 integral integral ADJ iajs-2292 216 22 equations equation NOUN iajs-2292 216 23 and and CCONJ iajs-2292 216 24 so so ADV iajs-2292 216 25 on on ADV iajs-2292 216 26 . . 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