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PUNCT iajs-3598 3 1 this this PRON iajs-3598 3 2 is be AUX iajs-3598 3 3 an an DET iajs-3598 3 4 open open ADJ iajs-3598 3 5 - - PUNCT iajs-3598 3 6 access access NOUN iajs-3598 3 7 article article NOUN iajs-3598 3 8 distributed distribute VERB iajs-3598 3 9 under under ADP iajs-3598 3 10 the the DET iajs-3598 3 11 terms term NOUN iajs-3598 3 12 of of ADP iajs-3598 3 13 the the DET iajs-3598 3 14 creative creative ADJ iajs-3598 3 15 commons common NOUN iajs-3598 3 16 attribution attribution NOUN iajs-3598 3 17 4.0 4.0 NUM iajs-3598 3 18 international international ADJ iajs-3598 3 19 license license NOUN iajs-3598 3 20 the the DET iajs-3598 3 21 local local ADJ iajs-3598 3 22 bifurcation bifurcation NOUN iajs-3598 3 23 of of ADP iajs-3598 3 24 food food NOUN iajs-3598 3 25 web web NOUN iajs-3598 3 26 prey prey NOUN iajs-3598 3 27 - - PUNCT iajs-3598 3 28 predator predator NOUN iajs-3598 3 29 model model NOUN iajs-3598 3 30 involving involve VERB iajs-3598 3 31 fear fear NOUN iajs-3598 3 32 and and CCONJ iajs-3598 3 33 anti anti ADJ iajs-3598 3 34 - - ADJ iajs-3598 3 35 predator predator ADJ iajs-3598 3 36 behavior behavior NOUN iajs-3598 3 37 hanna hanna NOUN iajs-3598 3 38 rasool rasool PROPN iajs-3598 3 39 hadi1 hadi1 PROPN iajs-3598 3 40 * * PUNCT iajs-3598 3 41 and and CCONJ iajs-3598 3 42 azhar azhar PROPN iajs-3598 3 43 abbas abbas PROPN iajs-3598 3 44 majeed2 majeed2 PROPN iajs-3598 4 1 1,2department 1,2department NUM iajs-3598 4 2 of of ADP iajs-3598 4 3 mathematics mathematic NOUN iajs-3598 4 4 , , PUNCT iajs-3598 4 5 college college NOUN iajs-3598 4 6 of of ADP iajs-3598 4 7 science science NOUN iajs-3598 4 8 , , PUNCT iajs-3598 4 9 university university NOUN iajs-3598 4 10 of of ADP iajs-3598 4 11 baghdad baghdad PROPN iajs-3598 4 12 , , PUNCT iajs-3598 4 13 city city PROPN iajs-3598 4 14 baghdad baghdad PROPN iajs-3598 4 15 , , PUNCT iajs-3598 4 16 country country NOUN iajs-3598 4 17 iraq iraq PROPN iajs-3598 4 18 . . PUNCT iajs-3598 5 1 * * PUNCT iajs-3598 5 2 corresponding correspond VERB iajs-3598 5 3 author author NOUN iajs-3598 5 4 . . PUNCT iajs-3598 6 1 received:12 received:12 X iajs-3598 6 2 june june PROPN iajs-3598 6 3 2023 2023 NUM iajs-3598 6 4 accepted:27 accepted:27 ADP iajs-3598 6 5 august august PROPN iajs-3598 6 6 2023 2023 NUM iajs-3598 6 7 published:20 published:20 NOUN iajs-3598 6 8 january january PROPN iajs-3598 6 9 2025 2025 NUM iajs-3598 7 1 doi.org/10.30526/38.1.3598 doi.org/10.30526/38.1.3598 NOUN iajs-3598 7 2 abstract abstract NOUN iajs-3598 7 3 in in ADP iajs-3598 7 4 this this DET iajs-3598 7 5 paper paper NOUN iajs-3598 7 6 , , PUNCT iajs-3598 7 7 the the DET iajs-3598 7 8 conditions condition NOUN iajs-3598 7 9 under under ADP iajs-3598 7 10 which which PRON iajs-3598 7 11 the the DET iajs-3598 7 12 occurrence occurrence NOUN iajs-3598 7 13 of of ADP iajs-3598 7 14 the the DET iajs-3598 7 15 local local ADJ iajs-3598 7 16 bifurcation bifurcation NOUN iajs-3598 7 17 ( ( PUNCT iajs-3598 7 18 such such ADJ iajs-3598 7 19 as as ADP iajs-3598 7 20 saddlenode saddlenode NOUN iajs-3598 7 21 ( ( PUNCT iajs-3598 7 22 sn sn PROPN iajs-3598 7 23 ) ) PUNCT iajs-3598 7 24 , , PUNCT iajs-3598 7 25 transcritical transcritical ADJ iajs-3598 7 26 ( ( PUNCT iajs-3598 7 27 tc tc NOUN iajs-3598 7 28 ) ) PUNCT iajs-3598 7 29 , , PUNCT iajs-3598 7 30 and and CCONJ iajs-3598 7 31 pitchfork pitchfork NOUN iajs-3598 7 32 ( ( PUNCT iajs-3598 7 33 pt pt NOUN iajs-3598 7 34 ) ) PUNCT iajs-3598 7 35 ) ) PUNCT iajs-3598 7 36 of of ADP iajs-3598 7 37 all all DET iajs-3598 7 38 stable stable ADJ iajs-3598 7 39 points point NOUN iajs-3598 7 40 of of ADP iajs-3598 7 41 a a DET iajs-3598 7 42 food food NOUN iajs-3598 7 43 web web NOUN iajs-3598 7 44 model model NOUN iajs-3598 7 45 have have AUX iajs-3598 7 46 been be AUX iajs-3598 7 47 investigated investigate VERB iajs-3598 7 48 . . PUNCT iajs-3598 8 1 fear fear NOUN iajs-3598 8 2 and and CCONJ iajs-3598 8 3 anti anti ADJ iajs-3598 8 4 - - ADJ iajs-3598 8 5 predator predator ADJ iajs-3598 8 6 responses response NOUN iajs-3598 8 7 involving involve VERB iajs-3598 8 8 the the DET iajs-3598 8 9 holling holling NOUN iajs-3598 8 10 - - PUNCT iajs-3598 8 11 type type NOUN iajs-3598 8 12 iv iv NOUN iajs-3598 8 13 and and CCONJ iajs-3598 8 14 growly growly ADJ iajs-3598 8 15 - - PUNCT iajs-3598 8 16 martin martin NOUN iajs-3598 8 17 functional functional ADJ iajs-3598 8 18 responses response NOUN iajs-3598 8 19 have have AUX iajs-3598 8 20 been be AUX iajs-3598 8 21 found find VERB iajs-3598 8 22 . . 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PUNCT iajs-3598 10 1 in in ADP iajs-3598 10 2 addition addition NOUN iajs-3598 10 3 , , PUNCT iajs-3598 10 4 there there PRON iajs-3598 10 5 is be VERB iajs-3598 10 6 a a DET iajs-3598 10 7 saddle saddle NOUN iajs-3598 10 8 - - PUNCT iajs-3598 10 9 node node NOUN iajs-3598 10 10 bifurcation bifurcation NOUN iajs-3598 10 11 in in ADP iajs-3598 10 12 close close ADV iajs-3598 10 13 to to ADP iajs-3598 10 14 the the DET iajs-3598 10 15 positive positive ADJ iajs-3598 10 16 equilibrium equilibrium NOUN iajs-3598 10 17 point point NOUN iajs-3598 10 18 . . PUNCT iajs-3598 11 1 these these DET iajs-3598 11 2 divergences divergence NOUN iajs-3598 11 3 have have AUX iajs-3598 11 4 materialised materialise VERB iajs-3598 11 5 into into ADP iajs-3598 11 6 existence existence NOUN iajs-3598 11 7 . . PUNCT iajs-3598 12 1 in in ADP iajs-3598 12 2 conclusion conclusion NOUN iajs-3598 12 3 , , PUNCT iajs-3598 12 4 to to PART iajs-3598 12 5 prove prove VERB iajs-3598 12 6 that that SCONJ iajs-3598 12 7 the the DET iajs-3598 12 8 analytical analytical ADJ iajs-3598 12 9 results result NOUN iajs-3598 12 10 are be AUX iajs-3598 12 11 correct correct ADJ iajs-3598 12 12 , , PUNCT iajs-3598 12 13 a a DET iajs-3598 12 14 numerical numerical ADJ iajs-3598 12 15 simulation simulation NOUN iajs-3598 12 16 of of ADP iajs-3598 12 17 a a DET iajs-3598 12 18 set set NOUN iajs-3598 12 19 of of ADP iajs-3598 12 20 parameters parameter NOUN iajs-3598 12 21 and and CCONJ iajs-3598 12 22 starting start VERB iajs-3598 12 23 conditions condition NOUN iajs-3598 12 24 has have AUX iajs-3598 12 25 been be AUX iajs-3598 12 26 used use VERB iajs-3598 12 27 . . PUNCT iajs-3598 13 1 keywords keyword NOUN iajs-3598 13 2 : : PUNCT iajs-3598 13 3 preypredator preypredator NOUN iajs-3598 13 4 , , PUNCT iajs-3598 13 5 local local ADJ iajs-3598 13 6 bifurcation bifurcation NOUN iajs-3598 13 7 , , PUNCT iajs-3598 13 8 global global ADJ iajs-3598 13 9 bifurcation bifurcation NOUN iajs-3598 13 10 , , PUNCT iajs-3598 13 11 sotomayor sotomayor PROPN iajs-3598 13 12 ’s ’s PART iajs-3598 13 13 theorem theorem PROPN iajs-3598 13 14 . . PROPN iajs-3598 13 15 1 1 NUM iajs-3598 13 16 . . X iajs-3598 13 17 introduction introduction NOUN iajs-3598 13 18 in in ADP iajs-3598 13 19 the the DET iajs-3598 13 20 past past ADJ iajs-3598 13 21 few few ADJ iajs-3598 13 22 decades decade NOUN iajs-3598 13 23 , , PUNCT iajs-3598 13 24 a a DET iajs-3598 13 25 prominent prominent ADJ iajs-3598 13 26 topic topic NOUN iajs-3598 13 27 in in ADP iajs-3598 13 28 population population NOUN iajs-3598 13 29 dynamics dynamic NOUN iajs-3598 13 30 has have AUX iajs-3598 13 31 been be AUX iajs-3598 13 32 the the DET iajs-3598 13 33 study study NOUN iajs-3598 13 34 of of ADP iajs-3598 13 35 dynamical dynamical ADJ iajs-3598 13 36 behaviors behavior NOUN iajs-3598 13 37 for for ADP iajs-3598 13 38 massive massive ADJ iajs-3598 13 39 predator predator NOUN iajs-3598 13 40 - - PUNCT iajs-3598 13 41 prey prey NOUN iajs-3598 13 42 models model NOUN iajs-3598 13 43 . . PUNCT iajs-3598 14 1 numerous numerous ADJ iajs-3598 14 2 outcomes outcome NOUN iajs-3598 14 3 have have AUX iajs-3598 14 4 been be AUX iajs-3598 14 5 reported report VERB iajs-3598 14 6 . . PUNCT iajs-3598 15 1 any any DET iajs-3598 15 2 biological biological ADJ iajs-3598 15 3 or or CCONJ iajs-3598 15 4 environmental environmental ADJ iajs-3598 15 5 characteristics characteristic NOUN iajs-3598 15 6 are be AUX iajs-3598 15 7 liable liable ADJ iajs-3598 15 8 to to PART iajs-3598 15 9 change change VERB iajs-3598 15 10 over over ADP iajs-3598 15 11 time time NOUN iajs-3598 15 12 in in ADP iajs-3598 15 13 the the DET iajs-3598 15 14 actual actual ADJ iajs-3598 15 15 world world NOUN iajs-3598 15 16 . . PUNCT iajs-3598 16 1 since since SCONJ iajs-3598 16 2 the the DET iajs-3598 16 3 selection selection NOUN iajs-3598 16 4 pressures pressure NOUN iajs-3598 16 5 on on ADP iajs-3598 16 6 systems system NOUN iajs-3598 16 7 in in ADP iajs-3598 16 8 a a DET iajs-3598 16 9 fluctuating fluctuate VERB iajs-3598 16 10 environment environment NOUN iajs-3598 16 11 differ differ VERB iajs-3598 16 12 from from ADP iajs-3598 16 13 those those PRON iajs-3598 16 14 in in ADP iajs-3598 16 15 a a DET iajs-3598 16 16 stable stable ADJ iajs-3598 16 17 environment environment NOUN iajs-3598 16 18 , , PUNCT iajs-3598 16 19 the the DET iajs-3598 16 20 impacts impact NOUN iajs-3598 16 21 of of ADP iajs-3598 16 22 a a DET iajs-3598 16 23 periodically periodically ADV iajs-3598 16 24 altering alter VERB iajs-3598 16 25 environment environment NOUN iajs-3598 16 26 are be AUX iajs-3598 16 27 crucial crucial ADJ iajs-3598 16 28 for for ADP iajs-3598 16 29 evolutionary evolutionary ADJ iajs-3598 16 30 theory(1,2 theory(1,2 NOUN iajs-3598 16 31 ) ) PUNCT iajs-3598 16 32 . . 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PUNCT iajs-3598 25 1 ( ( PUNCT iajs-3598 25 2 saddle saddle NOUN iajs-3598 25 3 - - PUNCT iajs-3598 25 4 node node NOUN iajs-3598 25 5 , , PUNCT iajs-3598 25 6 transcritical transcritical ADJ iajs-3598 25 7 , , PUNCT iajs-3598 25 8 pitchfork pitchfork NOUN iajs-3598 25 9 , , PUNCT iajs-3598 25 10 period period NOUN iajs-3598 25 11 - - PUNCT iajs-3598 25 12 doubling double VERB iajs-3598 25 13 , , PUNCT iajs-3598 25 14 neimark neimark NOUN iajs-3598 25 15 - - PUNCT iajs-3598 25 16 sacker sacker NOUN iajs-3598 25 17 , , PUNCT iajs-3598 25 18 and and CCONJ iajs-3598 25 19 hopf hopf ADJ iajs-3598 25 20 bifurcations bifurcation NOUN iajs-3598 25 21 ) ) PUNCT iajs-3598 25 22 but but CCONJ iajs-3598 25 23 the the DET iajs-3598 25 24 most most ADV iajs-3598 25 25 significant significant ADJ iajs-3598 25 26 ones one NOUN iajs-3598 25 27 are be AUX iajs-3598 25 28 ( ( PUNCT iajs-3598 25 29 sn sn NOUN iajs-3598 25 30 ) ) PUNCT iajs-3598 25 31 , , PUNCT iajs-3598 25 32 ( ( PUNCT iajs-3598 25 33 tc tc NOUN iajs-3598 25 34 ) ) PUNCT iajs-3598 25 35 , , PUNCT iajs-3598 25 36 ( ( PUNCT iajs-3598 25 37 pt pt NOUN iajs-3598 25 38 ) ) PUNCT iajs-3598 25 39 , , PUNCT iajs-3598 25 40 and and CCONJ iajs-3598 25 41 hopf hopf ADJ iajs-3598 25 42 bifurcations bifurcation NOUN iajs-3598 25 43 . . PUNCT iajs-3598 26 1 if if SCONJ iajs-3598 26 2 the the DET iajs-3598 26 3 differential differential ADJ iajs-3598 26 4 equation equation NOUN iajs-3598 26 5 x x NOUN iajs-3598 26 6 = = NOUN iajs-3598 26 7 f(x,πœ‡ f(x,πœ‡ NUM iajs-3598 26 8 ) ) PUNCT iajs-3598 26 9 had have AUX iajs-3598 26 10 taken take VERB iajs-3598 26 11 into into ADP iajs-3598 26 12 account account NOUN iajs-3598 26 13 the the DET iajs-3598 26 14 point point NOUN iajs-3598 26 15 at at ADP iajs-3598 26 16 which which PRON iajs-3598 26 17 this this DET iajs-3598 26 18 dynamic dynamic ADJ iajs-3598 26 19 system system NOUN iajs-3598 26 20 's 's PART iajs-3598 26 21 behavior behavior NOUN iajs-3598 26 22 qualitatively qualitatively ADV iajs-3598 26 23 changed change VERB iajs-3598 26 24 , , PUNCT iajs-3598 26 25 or or CCONJ iajs-3598 26 26 what what PRON iajs-3598 26 27 is be AUX iajs-3598 26 28 described describe VERB iajs-3598 26 29 mathematically mathematically ADV iajs-3598 26 30 as as ADP iajs-3598 26 31 a a DET iajs-3598 26 32 bifurcation(14–16 bifurcation(14–16 NOUN iajs-3598 26 33 ) ) PUNCT iajs-3598 26 34 . . PUNCT iajs-3598 27 1 many many ADJ iajs-3598 27 2 researchers researcher NOUN iajs-3598 27 3 have have AUX iajs-3598 27 4 been be AUX iajs-3598 27 5 studying study VERB iajs-3598 27 6 bifurcation bifurcation NOUN iajs-3598 27 7 in in ADP iajs-3598 27 8 dynamical dynamical ADJ iajs-3598 27 9 systems system NOUN iajs-3598 27 10 accurately accurately ADV iajs-3598 27 11 in in ADP iajs-3598 27 12 the the DET iajs-3598 27 13 ordinary ordinary ADJ iajs-3598 27 14 differential differential ADJ iajs-3598 27 15 equations equation NOUN iajs-3598 27 16 in in ADP iajs-3598 27 17 both both CCONJ iajs-3598 27 18 linear linear ADJ iajs-3598 27 19 and and CCONJ iajs-3598 27 20 nonlinear nonlinear ADJ iajs-3598 27 21 , , PUNCT iajs-3598 27 22 autonomous autonomous ADJ iajs-3598 27 23 and and CCONJ iajs-3598 27 24 non non ADJ iajs-3598 27 25 - - PROPN iajs-3598 27 26 autonomous(17,18 autonomous(17,18 NOUN iajs-3598 27 27 ) ) PUNCT iajs-3598 27 28 . . PUNCT iajs-3598 28 1 orrell orrell ADJ iajs-3598 28 2 and and CCONJ iajs-3598 28 3 smith(19 smith(19 ADJ iajs-3598 28 4 ) ) PUNCT iajs-3598 28 5 , , PUNCT iajs-3598 28 6 studied study VERB iajs-3598 28 7 visualizing visualize VERB iajs-3598 28 8 bifurcation bifurcation NOUN iajs-3598 28 9 in in ADP iajs-3598 28 10 high high ADJ iajs-3598 28 11 dimensional dimensional ADJ iajs-3598 28 12 systems system NOUN iajs-3598 28 13 . . PUNCT iajs-3598 29 1 yuan yuan NOUN iajs-3598 29 2 and and CCONJ iajs-3598 29 3 zhao zhao X iajs-3598 29 4 ( ( PUNCT iajs-3598 29 5 20 20 NUM iajs-3598 29 6 ) ) PUNCT iajs-3598 29 7 studied study VERB iajs-3598 29 8 bifurcation bifurcation NOUN iajs-3598 29 9 for for ADP iajs-3598 29 10 a a DET iajs-3598 29 11 fractional fractional ADJ iajs-3598 29 12 order order NOUN iajs-3598 29 13 predator predator NOUN iajs-3598 29 14 – – PUNCT iajs-3598 29 15 prey prey NOUN iajs-3598 29 16 system system NOUN iajs-3598 29 17 involving involve VERB iajs-3598 29 18 two two NUM iajs-3598 29 19 nonidentical nonidentical ADJ iajs-3598 29 20 . . PUNCT iajs-3598 30 1 while while SCONJ iajs-3598 30 2 majeed majeed PROPN iajs-3598 30 3 and and CCONJ iajs-3598 30 4 ismaeeb ismaeeb PROPN iajs-3598 30 5 ( ( PUNCT iajs-3598 30 6 21 21 NUM iajs-3598 30 7 ) ) PUNCT iajs-3598 30 8 studied study VERB iajs-3598 30 9 the the DET iajs-3598 30 10 bifurcation bifurcation NOUN iajs-3598 30 11 analysis analysis NOUN iajs-3598 30 12 of of ADP iajs-3598 30 13 a a DET iajs-3598 30 14 prey prey NOUN iajs-3598 30 15 - - PUNCT iajs-3598 30 16 predator predator NOUN iajs-3598 30 17 model model NOUN iajs-3598 30 18 in in ADP iajs-3598 30 19 the the DET iajs-3598 30 20 presence presence NOUN iajs-3598 30 21 of of ADP iajs-3598 30 22 a a DET iajs-3598 30 23 stage stage NOUN iajs-3598 30 24 structured structure VERB iajs-3598 30 25 with with ADP iajs-3598 30 26 harvesting harvesting NOUN iajs-3598 30 27 and and CCONJ iajs-3598 30 28 toxicity toxicity NOUN iajs-3598 30 29 in in ADP iajs-3598 30 30 this this DET iajs-3598 30 31 paper paper NOUN iajs-3598 30 32 , , PUNCT iajs-3598 30 33 the the DET iajs-3598 30 34 conditions condition NOUN iajs-3598 30 35 of of ADP iajs-3598 30 36 the the DET iajs-3598 30 37 local local ADJ iajs-3598 30 38 bifurcation bifurcation NOUN iajs-3598 30 39 ( ( PUNCT iajs-3598 30 40 lb lb NOUN iajs-3598 30 41 ) ) PUNCT iajs-3598 30 42 of of ADP iajs-3598 30 43 the the DET iajs-3598 30 44 food food NOUN iajs-3598 30 45 web web NOUN iajs-3598 30 46 model model NOUN iajs-3598 30 47 with with ADP iajs-3598 30 48 fear fear NOUN iajs-3598 30 49 and and CCONJ iajs-3598 30 50 antipredator antipredator ADJ iajs-3598 30 51 model model NOUN iajs-3598 30 52 have have AUX iajs-3598 30 53 been be AUX iajs-3598 30 54 found find VERB iajs-3598 30 55 . . PUNCT iajs-3598 31 1 2 2 X iajs-3598 31 2 . . X iajs-3598 31 3 model model NOUN iajs-3598 31 4 formulation formulation NOUN iajs-3598 31 5 ( ( PUNCT iajs-3598 31 6 22 22 NUM iajs-3598 31 7 ): ): PUNCT iajs-3598 31 8 the the DET iajs-3598 31 9 following follow VERB iajs-3598 31 10 section section NOUN iajs-3598 31 11 includes include VERB iajs-3598 31 12 an an DET iajs-3598 31 13 ecological ecological ADJ iajs-3598 31 14 model model NOUN iajs-3598 31 15 with with ADP iajs-3598 31 16 three three NUM iajs-3598 31 17 species specie NOUN iajs-3598 31 18 that that PRON iajs-3598 31 19 had have AUX iajs-3598 31 20 been be AUX iajs-3598 31 21 proposed propose VERB iajs-3598 31 22 : : PUNCT iajs-3598 31 23 the the DET iajs-3598 31 24 first first ADJ iajs-3598 31 25 and and CCONJ iajs-3598 31 26 second second ADJ iajs-3598 31 27 preys prey NOUN iajs-3598 31 28 with with ADP iajs-3598 31 29 just just ADV iajs-3598 31 30 one one NUM iajs-3598 31 31 predator predator NOUN iajs-3598 31 32 , , PUNCT iajs-3598 31 33 which which PRON iajs-3598 31 34 are be AUX iajs-3598 31 35 indicated indicate VERB iajs-3598 31 36 by by ADP iajs-3598 31 37 the the DET iajs-3598 31 38 magnitude magnitude NOUN iajs-3598 31 39 of of ADP iajs-3598 31 40 their their PRON iajs-3598 31 41 populations population NOUN iajs-3598 31 42 at at ADP iajs-3598 31 43 the the DET iajs-3598 31 44 time time NOUN iajs-3598 31 45 . . PUNCT iajs-3598 32 1 𝐿1(t 𝐿1(t PROPN iajs-3598 32 2 ) ) PUNCT iajs-3598 32 3 , , PUNCT iajs-3598 32 4 l2(t)and l2(t)and PUNCT iajs-3598 32 5 l3(t l3(t CCONJ iajs-3598 32 6 ) ) PUNCT iajs-3598 32 7 respectively respectively ADV iajs-3598 32 8 . . PUNCT iajs-3598 33 1 𝑑𝐿1 𝑑𝐿1 PROPN iajs-3598 33 2 𝑑𝑑 𝑑𝑑 ADP iajs-3598 33 3 = = SYM iajs-3598 33 4 𝑆1𝐿1 𝑆1𝐿1 X iajs-3598 33 5 ( ( PUNCT iajs-3598 33 6 1 1 NUM iajs-3598 33 7 βˆ’ βˆ’ NOUN iajs-3598 33 8 𝐿1 𝐿1 PROPN iajs-3598 33 9 𝐾1 𝐾1 PROPN iajs-3598 33 10 ) ) PUNCT iajs-3598 33 11 βˆ’ βˆ’ PUNCT iajs-3598 33 12 𝐢1𝐿1𝐿3 𝐢1𝐿1𝐿3 PROPN iajs-3598 33 13 π‘Ž1 π‘Ž1 NOUN iajs-3598 33 14 + + CCONJ iajs-3598 33 15 𝐿1 𝐿1 PROPN iajs-3598 33 16 2 2 NUM iajs-3598 33 17 𝑑𝐿2 𝑑𝐿2 VERB iajs-3598 33 18 𝑑𝑑 𝑑𝑑 ADP iajs-3598 33 19 = = NOUN iajs-3598 33 20 𝑆2 𝑆2 VERB iajs-3598 33 21 𝐿2 𝐿2 PROPN iajs-3598 33 22 1 1 NUM iajs-3598 33 23 + + CCONJ iajs-3598 33 24 𝑓1 𝑓1 PROPN iajs-3598 33 25 𝐿3 𝐿3 NOUN iajs-3598 33 26 βˆ’ βˆ’ PROPN iajs-3598 33 27 𝐢𝐿2 𝐢𝐿2 ADJ iajs-3598 33 28 2 2 NUM iajs-3598 33 29 βˆ’ βˆ’ PROPN iajs-3598 33 30 𝐢2𝐿2𝐿3 𝐢2𝐿2𝐿3 NOUN iajs-3598 33 31 ( ( PUNCT iajs-3598 33 32 1 1 NUM iajs-3598 33 33 + + CCONJ iajs-3598 33 34 π‘Ž2𝐿2)(1 π‘Ž2𝐿2)(1 NOUN iajs-3598 33 35 + + CCONJ iajs-3598 33 36 π‘Ž3𝐿3 π‘Ž3𝐿3 NUM iajs-3598 33 37 ) ) PUNCT iajs-3598 33 38 ( ( PUNCT iajs-3598 33 39 1 1 X iajs-3598 33 40 ) ) PUNCT iajs-3598 33 41 𝑑𝐿3 𝑑𝐿3 NOUN iajs-3598 33 42 𝑑𝑑 𝑑𝑑 ADP iajs-3598 33 43 = = SYM iajs-3598 33 44 𝑔1𝐿1𝐿3 𝑔1𝐿1𝐿3 PUNCT iajs-3598 33 45 π‘Ž1 π‘Ž1 NOUN iajs-3598 33 46 + + CCONJ iajs-3598 33 47 𝐿1 𝐿1 PROPN iajs-3598 33 48 2 2 NUM iajs-3598 33 49 + + CCONJ iajs-3598 33 50 𝑔2𝐿2𝐿3 𝑔2𝐿2𝐿3 PROPN iajs-3598 33 51 ( ( PUNCT iajs-3598 33 52 1 1 NUM iajs-3598 33 53 + + CCONJ iajs-3598 33 54 π‘Ž2𝐿2)(1 π‘Ž2𝐿2)(1 NOUN iajs-3598 33 55 + + CCONJ iajs-3598 33 56 π‘Ž3𝐿3 π‘Ž3𝐿3 NUM iajs-3598 33 57 ) ) PUNCT iajs-3598 33 58 βˆ’ βˆ’ NOUN iajs-3598 33 59 πœ‡πΏ1𝐿3 πœ‡πΏ1𝐿3 NOUN iajs-3598 33 60 βˆ’ βˆ’ NOUN iajs-3598 33 61 𝑑𝐿3 𝑑𝐿3 VERB iajs-3598 33 62 the the DET iajs-3598 33 63 following follow VERB iajs-3598 33 64 table table NOUN iajs-3598 33 65 can can AUX iajs-3598 33 66 be be AUX iajs-3598 33 67 used use VERB iajs-3598 33 68 to to PART iajs-3598 33 69 describe describe VERB iajs-3598 33 70 the the DET iajs-3598 33 71 positive positive ADJ iajs-3598 33 72 system system NOUN iajs-3598 33 73 ( ( PUNCT iajs-3598 33 74 1 1 X iajs-3598 33 75 ) ) PUNCT iajs-3598 33 76 parameters parameter NOUN iajs-3598 33 77 . . PUNCT iajs-3598 34 1 table table NOUN iajs-3598 34 2 1 1 NUM iajs-3598 34 3 : : PUNCT iajs-3598 34 4 the the DET iajs-3598 34 5 system system NOUN iajs-3598 34 6 's 's PART iajs-3598 34 7 ( ( PUNCT iajs-3598 34 8 1 1 X iajs-3598 34 9 ) ) PUNCT iajs-3598 34 10 parameters parameter NOUN iajs-3598 34 11 are be AUX iajs-3598 34 12 as as SCONJ iajs-3598 34 13 follows follow VERB iajs-3598 34 14 : : PUNCT iajs-3598 34 15 parameters parameter NOUN iajs-3598 34 16 biological biological ADJ iajs-3598 34 17 meaning meaning NOUN iajs-3598 34 18 𝑆𝑖 𝑆𝑖 PROPN iajs-3598 34 19 . . PUNCT iajs-3598 35 1 𝑖 𝑖 X iajs-3598 35 2 = = NOUN iajs-3598 36 1 1.2 1.2 NUM iajs-3598 36 2 first first ADJ iajs-3598 36 3 and and CCONJ iajs-3598 36 4 second second ADJ iajs-3598 36 5 preys prey NOUN iajs-3598 36 6 growth growth NOUN iajs-3598 36 7 rates rate NOUN iajs-3598 36 8 , , PUNCT iajs-3598 36 9 respectively respectively ADV iajs-3598 36 10 𝐾1 𝐾1 X iajs-3598 36 11 > > X iajs-3598 36 12 0 0 NUM iajs-3598 36 13 carrying carry VERB iajs-3598 36 14 capacity capacity NOUN iajs-3598 36 15 of of ADP iajs-3598 36 16 first first ADJ iajs-3598 36 17 prey prey NOUN iajs-3598 36 18 𝐢𝑖 𝐢𝑖 PROPN iajs-3598 36 19 > > X iajs-3598 36 20 0 0 NUM iajs-3598 36 21 , , PUNCT iajs-3598 36 22 𝑖 𝑖 SYM iajs-3598 36 23 = = SYM iajs-3598 36 24 1,2 1,2 NUM iajs-3598 36 25 attack attack NOUN iajs-3598 36 26 rate rate NOUN iajs-3598 36 27 of of ADP iajs-3598 36 28 the the DET iajs-3598 36 29 first first ADJ iajs-3598 36 30 prey prey NOUN iajs-3598 36 31 and and CCONJ iajs-3598 36 32 second second ADJ iajs-3598 36 33 prey prey NOUN iajs-3598 36 34 by by ADP iajs-3598 36 35 predator predator NOUN iajs-3598 36 36 respecively respecively ADV iajs-3598 36 37 π‘Ž1 π‘Ž1 VERB iajs-3598 36 38 > > SYM iajs-3598 36 39 0 0 NUM iajs-3598 36 40 protection protection NOUN iajs-3598 36 41 rate rate NOUN iajs-3598 36 42 to to ADP iajs-3598 36 43 the the DET iajs-3598 36 44 prey prey NOUN iajs-3598 36 45 and and CCONJ iajs-3598 36 46 predator predator NOUN iajs-3598 36 47 by by ADP iajs-3598 36 48 the the DET iajs-3598 36 49 environment environment NOUN iajs-3598 36 50 c c VERB iajs-3598 36 51 the the DET iajs-3598 36 52 rate rate NOUN iajs-3598 36 53 of of ADP iajs-3598 36 54 internal internal ADJ iajs-3598 36 55 competition competition NOUN iajs-3598 36 56 for for ADP iajs-3598 36 57 the the DET iajs-3598 36 58 second second ADJ iajs-3598 36 59 prey prey NOUN iajs-3598 36 60 𝑓1 𝑓1 PROPN iajs-3598 36 61 the the DET iajs-3598 36 62 second second ADJ iajs-3598 36 63 prey prey NOUN iajs-3598 36 64 's 's PART iajs-3598 36 65 fear fear NOUN iajs-3598 36 66 rate rate NOUN iajs-3598 36 67 from from ADP iajs-3598 36 68 predator predator NOUN iajs-3598 36 69 𝑔𝑖 𝑔𝑖 NOUN iajs-3598 36 70 , , PUNCT iajs-3598 36 71 𝑖 𝑖 NOUN iajs-3598 36 72 = = SYM iajs-3598 36 73 1,2 1,2 NUM iajs-3598 36 74 conversion conversion NOUN iajs-3598 36 75 rate rate NOUN iajs-3598 36 76 of of ADP iajs-3598 36 77 food food NOUN iajs-3598 36 78 from from ADP iajs-3598 36 79 first first ADJ iajs-3598 36 80 prey prey NOUN iajs-3598 36 81 and and CCONJ iajs-3598 36 82 second second ADJ iajs-3598 36 83 prey prey NOUN iajs-3598 36 84 to to PART iajs-3598 36 85 predator predator VERB iajs-3598 36 86 respecively respecively ADV iajs-3598 36 87 π‘Ž2 π‘Ž2 NOUN iajs-3598 36 88 handling handling NOUN iajs-3598 36 89 time time NOUN iajs-3598 36 90 of of ADP iajs-3598 36 91 the the DET iajs-3598 36 92 second second ADJ iajs-3598 36 93 prey prey NOUN iajs-3598 36 94 π‘Ž3 π‘Ž3 PROPN iajs-3598 36 95 the the DET iajs-3598 36 96 magnitude magnitude NOUN iajs-3598 36 97 of of ADP iajs-3598 36 98 interference interference NOUN iajs-3598 36 99 among among ADP iajs-3598 36 100 predators predator NOUN iajs-3598 36 101 πœ‡ πœ‡ ADP iajs-3598 36 102 the the DET iajs-3598 36 103 rate rate NOUN iajs-3598 36 104 of of ADP iajs-3598 36 105 anti anti ADJ iajs-3598 36 106 - - ADJ iajs-3598 36 107 predator predator ADJ iajs-3598 36 108 behavior behavior NOUN iajs-3598 36 109 of of ADP iajs-3598 36 110 first first ADJ iajs-3598 36 111 prey prey NOUN iajs-3598 36 112 to to ADP iajs-3598 36 113 predator predator VERB iajs-3598 36 114 d d X iajs-3598 36 115 the the DET iajs-3598 36 116 natural natural ADJ iajs-3598 36 117 death death NOUN iajs-3598 36 118 rate rate NOUN iajs-3598 36 119 of of ADP iajs-3598 36 120 predator predator NOUN iajs-3598 36 121 ihjpas ihjpa NOUN iajs-3598 36 122 . . PUNCT iajs-3598 37 1 2025 2025 NUM iajs-3598 37 2 , , PUNCT iajs-3598 37 3 38 38 NUM iajs-3598 37 4 ( ( PUNCT iajs-3598 37 5 1 1 NUM iajs-3598 37 6 ) ) PUNCT iajs-3598 37 7 430 430 NUM iajs-3598 37 8 3 3 NUM iajs-3598 37 9 . . PUNCT iajs-3598 37 10 local local ADJ iajs-3598 37 11 bifurcation bifurcation NOUN iajs-3598 37 12 analysis analysis NOUN iajs-3598 37 13 : : PUNCT iajs-3598 37 14 the the DET iajs-3598 37 15 analysis analysis NOUN iajs-3598 37 16 of of ADP iajs-3598 37 17 the the DET iajs-3598 37 18 ( ( PUNCT iajs-3598 37 19 lb lb NOUN iajs-3598 37 20 ) ) PUNCT iajs-3598 37 21 of of ADP iajs-3598 37 22 model model NOUN iajs-3598 37 23 ( ( PUNCT iajs-3598 37 24 1 1 X iajs-3598 37 25 ) ) PUNCT iajs-3598 37 26 has have AUX iajs-3598 37 27 been be AUX iajs-3598 37 28 explored explore VERB iajs-3598 37 29 in in ADP iajs-3598 37 30 this this DET iajs-3598 37 31 section section NOUN iajs-3598 37 32 , , PUNCT iajs-3598 37 33 with with ADP iajs-3598 37 34 a a DET iajs-3598 37 35 particular particular ADJ iajs-3598 37 36 emphasis emphasis NOUN iajs-3598 37 37 on on ADP iajs-3598 37 38 the the DET iajs-3598 37 39 changes change NOUN iajs-3598 37 40 that that PRON iajs-3598 37 41 occur occur VERB iajs-3598 37 42 around around ADP iajs-3598 37 43 each each DET iajs-3598 37 44 equilibrium equilibrium NOUN iajs-3598 37 45 point point NOUN iajs-3598 37 46 when when SCONJ iajs-3598 37 47 the the DET iajs-3598 37 48 parameter parameter NOUN iajs-3598 37 49 values value VERB iajs-3598 37 50 in in ADP iajs-3598 37 51 the the DET iajs-3598 37 52 dynamic dynamic ADJ iajs-3598 37 53 behavior behavior NOUN iajs-3598 37 54 change change NOUN iajs-3598 37 55 . . PUNCT iajs-3598 38 1 with with ADP iajs-3598 38 2 the the DET iajs-3598 38 3 support support NOUN iajs-3598 38 4 of of ADP iajs-3598 38 5 sotomayor sotomayor PROPN iajs-3598 38 6 's 's PART iajs-3598 38 7 theorem theorem NOUN iajs-3598 38 8 , , PUNCT iajs-3598 38 9 our our PRON iajs-3598 38 10 goal goal NOUN iajs-3598 38 11 is be AUX iajs-3598 38 12 to to PART iajs-3598 38 13 give give VERB iajs-3598 38 14 higher high ADJ iajs-3598 38 15 order order NOUN iajs-3598 38 16 conditions condition NOUN iajs-3598 38 17 that that PRON iajs-3598 38 18 guarantee guarantee VERB iajs-3598 38 19 the the DET iajs-3598 38 20 appearance appearance NOUN iajs-3598 38 21 of of ADP iajs-3598 38 22 the the DET iajs-3598 38 23 most most ADV iajs-3598 38 24 frequent frequent ADJ iajs-3598 38 25 local local ADJ iajs-3598 38 26 bifurcations bifurcation NOUN iajs-3598 38 27 . . PUNCT iajs-3598 39 1 now now ADV iajs-3598 39 2 , , PUNCT iajs-3598 39 3 according accord VERB iajs-3598 39 4 to to ADP iajs-3598 39 5 jacobean jacobean PROPN iajs-3598 39 6 matrix matrix NOUN iajs-3598 39 7 𝐽(𝐿1 𝐽(𝐿1 NOUN iajs-3598 39 8 , , PUNCT iajs-3598 39 9 𝐿2 𝐿2 PROPN iajs-3598 39 10 , , PUNCT iajs-3598 39 11 𝐿3 𝐿3 NOUN iajs-3598 39 12 ) ) PUNCT iajs-3598 39 13 of of ADP iajs-3598 39 14 the the DET iajs-3598 39 15 system system NOUN iajs-3598 39 16 ( ( PUNCT iajs-3598 39 17 1 1 X iajs-3598 39 18 ) ) PUNCT iajs-3598 39 19 which which PRON iajs-3598 39 20 is be AUX iajs-3598 39 21 given give VERB iajs-3598 39 22 in in ADP iajs-3598 39 23 ( ( PUNCT iajs-3598 39 24 22 22 NUM iajs-3598 39 25 ) ) PUNCT iajs-3598 39 26 as as SCONJ iajs-3598 39 27 follows follow VERB iajs-3598 39 28 : : PUNCT iajs-3598 39 29 𝐽 𝐽 PROPN iajs-3598 39 30 = = PUNCT iajs-3598 40 1 [ [ X iajs-3598 40 2 π‘Žπ‘–π‘— π‘Žπ‘–π‘— X iajs-3598 40 3 ] ] X iajs-3598 40 4 3Γ—3 3Γ—3 NUM iajs-3598 40 5 ( ( PUNCT iajs-3598 40 6 2 2 NUM iajs-3598 40 7 ) ) PUNCT iajs-3598 40 8 where where SCONJ iajs-3598 40 9 : : PUNCT iajs-3598 40 10 π‘Ž11 π‘Ž11 VERB iajs-3598 40 11 = = NOUN iajs-3598 40 12 𝑆1 𝑆1 NOUN iajs-3598 40 13 βˆ’ βˆ’ PROPN iajs-3598 40 14 2𝑆1𝐿1 2𝑆1𝐿1 NUM iajs-3598 40 15 𝐾1 𝐾1 NOUN iajs-3598 40 16 βˆ’ βˆ’ PROPN iajs-3598 40 17 𝐢1𝐿3(π‘Ž1βˆ’πΏ1 𝐢1𝐿3(π‘Ž1βˆ’πΏ1 PROPN iajs-3598 40 18 2 2 NUM iajs-3598 40 19 ) ) PUNCT iajs-3598 40 20 ( ( PUNCT iajs-3598 40 21 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 40 22 2 2 NUM iajs-3598 40 23 ) ) SYM iajs-3598 40 24 2 2 NUM iajs-3598 40 25 , , PUNCT iajs-3598 40 26 π‘Ž12 π‘Ž12 NOUN iajs-3598 40 27 = = SYM iajs-3598 40 28 0 0 NUM iajs-3598 40 29 , , PUNCT iajs-3598 40 30 π‘Ž13 π‘Ž13 VERB iajs-3598 40 31 = = SYM iajs-3598 40 32 βˆ’ βˆ’ PROPN iajs-3598 40 33 𝐢1𝐿1 𝐢1𝐿1 ADJ iajs-3598 40 34 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 40 35 2 2 NUM iajs-3598 40 36 , , PUNCT iajs-3598 40 37 π‘Ž21 π‘Ž21 NOUN iajs-3598 40 38 = = SYM iajs-3598 40 39 0 0 NUM iajs-3598 40 40 , , PUNCT iajs-3598 40 41 π‘Ž22 π‘Ž22 NOUN iajs-3598 40 42 = = PUNCT iajs-3598 40 43 𝑆2 𝑆2 NOUN iajs-3598 40 44 1 1 NUM iajs-3598 40 45 + + NUM iajs-3598 40 46 𝑓1𝐿3 𝑓1𝐿3 NUM iajs-3598 41 1 βˆ’ βˆ’ ADP iajs-3598 41 2 2𝐢𝐿2 2𝐢𝐿2 ADJ iajs-3598 41 3 βˆ’ βˆ’ PROPN iajs-3598 41 4 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 41 5 ( ( PUNCT iajs-3598 41 6 1 1 NUM iajs-3598 41 7 + + CCONJ iajs-3598 41 8 π‘Ž2𝐿2)(1 π‘Ž2𝐿2)(1 NOUN iajs-3598 41 9 + + CCONJ iajs-3598 41 10 π‘Ž3𝐿3 π‘Ž3𝐿3 NUM iajs-3598 41 11 ) ) PUNCT iajs-3598 41 12 π‘Ž23 π‘Ž23 NOUN iajs-3598 41 13 = = NOUN iajs-3598 41 14 βˆ’ βˆ’ NOUN iajs-3598 41 15 𝑆2𝑓1𝐿2 𝑆2𝑓1𝐿2 NOUN iajs-3598 41 16 ( ( PUNCT iajs-3598 41 17 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 41 18 βˆ’ βˆ’ PROPN iajs-3598 41 19 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 41 20 ( ( PUNCT iajs-3598 41 21 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 41 22 π‘Ž31 π‘Ž31 NOUN iajs-3598 41 23 = = PUNCT iajs-3598 41 24 𝑔1𝐿3(π‘Ž1βˆ’πΏ1 𝑔1𝐿3(π‘Ž1βˆ’πΏ1 ADJ iajs-3598 41 25 2 2 NUM iajs-3598 41 26 ) ) PUNCT iajs-3598 41 27 ( ( PUNCT iajs-3598 41 28 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 41 29 2 2 NUM iajs-3598 41 30 ) ) PUNCT iajs-3598 41 31 2 2 NUM iajs-3598 41 32 βˆ’ βˆ’ PROPN iajs-3598 41 33 πœ‡πΏ3 πœ‡πΏ3 PROPN iajs-3598 41 34 . . PUNCT iajs-3598 41 35 π‘Ž32 π‘Ž32 PROPN iajs-3598 41 36 = = SYM iajs-3598 41 37 𝑔2𝐿3 𝑔2𝐿3 PROPN iajs-3598 41 38 ( ( PUNCT iajs-3598 41 39 1+π‘Ž2𝐿2)2 1+π‘Ž2𝐿2)2 NUM iajs-3598 41 40 ( ( PUNCT iajs-3598 41 41 1+π‘Ž3𝐿3 1+π‘Ž3𝐿3 NUM iajs-3598 41 42 ) ) PUNCT iajs-3598 41 43 . . PUNCT iajs-3598 42 1 π‘Ž33 π‘Ž33 NOUN iajs-3598 42 2 = = SYM iajs-3598 43 1 𝑔1𝐿1 𝑔1𝐿1 NOUN iajs-3598 43 2 π‘Ž1+𝐿1 π‘Ž1+𝐿1 VERB iajs-3598 43 3 2 2 NUM iajs-3598 43 4 + + CCONJ iajs-3598 43 5 𝑔2𝐿2 𝑔2𝐿2 NUM iajs-3598 43 6 ( ( PUNCT iajs-3598 43 7 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NUM iajs-3598 43 8 βˆ’ βˆ’ PROPN iajs-3598 43 9 πœ‡πΏ1 πœ‡πΏ1 NOUN iajs-3598 43 10 βˆ’ βˆ’ NOUN iajs-3598 43 11 𝑑. 𝑑. NOUN iajs-3598 43 12 for for ADP iajs-3598 43 13 any any DET iajs-3598 43 14 nonzero nonzero PROPN iajs-3598 43 15 vector vector NOUN iajs-3598 43 16 v v PROPN iajs-3598 43 17 =( =( NOUN iajs-3598 43 18 𝑣1 𝑣1 PROPN iajs-3598 43 19 , , PUNCT iajs-3598 43 20 𝑣2 𝑣2 PROPN iajs-3598 43 21 , , PUNCT iajs-3598 43 22 𝑣3)𝑇 𝑣3)𝑇 PROPN iajs-3598 43 23 : : PUNCT iajs-3598 43 24 𝐷2πΉπœ‡(𝑋 𝐷2πΉπœ‡(𝑋 NOUN iajs-3598 43 25 , , PUNCT iajs-3598 43 26 πœ‡)(𝑉 πœ‡)(𝑉 NOUN iajs-3598 43 27 , , PUNCT iajs-3598 43 28 𝑉 𝑉 PROPN iajs-3598 43 29 ) ) PUNCT iajs-3598 43 30 = = PUNCT iajs-3598 44 1 [ [ X iajs-3598 44 2 𝐴𝑖1]3Γ—1 𝐴𝑖1]3Γ—1 ADJ iajs-3598 44 3 , , PUNCT iajs-3598 44 4 ( ( PUNCT iajs-3598 44 5 3 3 X iajs-3598 44 6 ) ) PUNCT iajs-3598 44 7 𝐴11 𝐴11 PROPN iajs-3598 44 8 = = PUNCT iajs-3598 44 9 βˆ’ βˆ’ PROPN iajs-3598 44 10 2𝑆1 2𝑆1 NUM iajs-3598 44 11 𝐾1 𝐾1 PROPN iajs-3598 44 12 + + X iajs-3598 44 13 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NUM iajs-3598 44 14 ( ( PUNCT iajs-3598 44 15 π‘Ž1 π‘Ž1 NOUN iajs-3598 44 16 + + CCONJ iajs-3598 44 17 𝐿1 𝐿1 PROPN iajs-3598 44 18 2)2 2)2 NUM iajs-3598 44 19 𝑣1 𝑣1 NOUN iajs-3598 44 20 2 2 NUM iajs-3598 44 21 βˆ’ βˆ’ NOUN iajs-3598 44 22 𝐢1 𝐢1 NOUN iajs-3598 44 23 ( ( PUNCT iajs-3598 44 24 π‘Ž1 π‘Ž1 NOUN iajs-3598 44 25 + + CCONJ iajs-3598 44 26 𝐿1 𝐿1 PROPN iajs-3598 44 27 2 2 NUM iajs-3598 44 28 ) ) PUNCT iajs-3598 44 29 ( ( PUNCT iajs-3598 44 30 ( ( PUNCT iajs-3598 44 31 π‘Ž1 π‘Ž1 X iajs-3598 44 32 + + CCONJ iajs-3598 44 33 𝐿1 𝐿1 PROPN iajs-3598 44 34 2 2 NUM iajs-3598 44 35 ) ) PUNCT iajs-3598 44 36 βˆ’ βˆ’ PROPN iajs-3598 44 37 2𝐿1 2𝐿1 NUM iajs-3598 44 38 2 2 NUM iajs-3598 44 39 + + CCONJ iajs-3598 44 40 ( ( PUNCT iajs-3598 44 41 π‘Ž1 π‘Ž1 X iajs-3598 44 42 + + CCONJ iajs-3598 44 43 2𝐿1))𝑣1𝑣3 2𝐿1))𝑣1𝑣3 NUM iajs-3598 44 44 , , PUNCT iajs-3598 44 45 𝐴21 𝐴21 PROPN iajs-3598 44 46 = = SYM iajs-3598 44 47 βˆ’2𝐢 βˆ’2𝐢 PROPN iajs-3598 44 48 + + CCONJ iajs-3598 44 49 𝐢2𝐿3 𝐢2𝐿3 PROPN iajs-3598 44 50 ( ( PUNCT iajs-3598 44 51 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 44 52 ) ) PUNCT iajs-3598 44 53 𝑣1 𝑣1 NOUN iajs-3598 44 54 2 2 NUM iajs-3598 44 55 βˆ’ βˆ’ PROPN iajs-3598 44 56 ( ( PUNCT iajs-3598 44 57 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 44 58 ( ( PUNCT iajs-3598 44 59 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 44 60 βˆ’ βˆ’ NOUN iajs-3598 44 61 𝐢2π‘Ž2𝐿3 𝐢2π‘Ž2𝐿3 NOUN iajs-3598 44 62 ( ( PUNCT iajs-3598 44 63 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 44 64 + + CCONJ iajs-3598 44 65 𝐢2 𝐢2 ADJ iajs-3598 44 66 ( ( PUNCT iajs-3598 44 67 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 44 68 ) ) PUNCT iajs-3598 44 69 𝑣2𝑣3 𝑣2𝑣3 PROPN iajs-3598 44 70 + + CCONJ iajs-3598 44 71 ( ( PUNCT iajs-3598 44 72 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 44 73 2𝐿3 2𝐿3 NUM iajs-3598 44 74 ( ( PUNCT iajs-3598 44 75 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 44 76 βˆ’ βˆ’ PROPN iajs-3598 44 77 𝐢2(1βˆ’π‘Ž3𝐿3 𝐢2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 44 78 ) ) PUNCT iajs-3598 44 79 ( ( PUNCT iajs-3598 44 80 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 X iajs-3598 44 81 ) ) PUNCT iajs-3598 44 82 𝑣3 𝑣3 ADJ iajs-3598 44 83 2 2 NUM iajs-3598 44 84 , , PUNCT iajs-3598 44 85 𝐴31 𝐴31 PROPN iajs-3598 44 86 = = SYM iajs-3598 44 87 2𝑔1𝐿1𝐿3 2𝑔1𝐿1𝐿3 NUM iajs-3598 44 88 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 44 89 2 2 NUM iajs-3598 44 90 𝑣1 𝑣1 NOUN iajs-3598 44 91 2 2 NUM iajs-3598 44 92 + + CCONJ iajs-3598 44 93 ( ( PUNCT iajs-3598 44 94 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 44 95 2 2 NUM iajs-3598 44 96 ) ) PUNCT iajs-3598 44 97 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 44 98 2 2 NUM iajs-3598 44 99 + + NUM iajs-3598 44 100 𝑔1 𝑔1 PROPN iajs-3598 44 101 βˆ’ βˆ’ PROPN iajs-3598 44 102 2πœ‡ 2πœ‡ NOUN iajs-3598 44 103 ) ) PUNCT iajs-3598 45 1 𝑣1𝑣3 𝑣1𝑣3 NUM iajs-3598 45 2 βˆ’ βˆ’ NUM iajs-3598 45 3 2π‘Ž2𝑔2𝐿3 2π‘Ž2𝑔2𝐿3 NUM iajs-3598 45 4 ( ( PUNCT iajs-3598 45 5 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 45 6 ) ) PUNCT iajs-3598 45 7 𝑣2 𝑣2 NOUN iajs-3598 45 8 2 2 NUM iajs-3598 45 9 βˆ’ βˆ’ NOUN iajs-3598 45 10 𝑔2 𝑔2 NOUN iajs-3598 45 11 ( ( PUNCT iajs-3598 45 12 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 NOUN iajs-3598 45 13 ( ( PUNCT iajs-3598 45 14 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 45 15 βˆ’ βˆ’ PROPN iajs-3598 45 16 1)𝑣2𝑣3 1)𝑣2𝑣3 NOUN iajs-3598 45 17 βˆ’ βˆ’ PROPN iajs-3598 45 18 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 45 19 ( ( PUNCT iajs-3598 45 20 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 45 21 𝑣3 𝑣3 ADJ iajs-3598 45 22 2 2 NUM iajs-3598 45 23 . . PUNCT iajs-3598 45 24 and and CCONJ iajs-3598 45 25 𝐷3πΉπœ‡(𝑋 𝐷3πΉπœ‡(𝑋 PROPN iajs-3598 45 26 , , PUNCT iajs-3598 45 27 πœ‡)(𝑉 πœ‡)(𝑉 PROPN iajs-3598 45 28 , , PUNCT iajs-3598 45 29 𝑉 𝑉 PROPN iajs-3598 45 30 , , PUNCT iajs-3598 45 31 𝑉 𝑉 PROPN iajs-3598 45 32 ) ) PUNCT iajs-3598 45 33 = = PUNCT iajs-3598 46 1 [ [ X iajs-3598 46 2 𝐡𝑖1]3Γ—1 𝐡𝑖1]3Γ—1 X iajs-3598 46 3 , , PUNCT iajs-3598 46 4 ( ( PUNCT iajs-3598 46 5 4 4 X iajs-3598 46 6 ) ) PUNCT iajs-3598 46 7 𝐡11 𝐡11 PROPN iajs-3598 47 1 = = PUNCT iajs-3598 47 2 4𝐢1π‘Ž1𝐿3(1βˆ’4𝐿1 4𝐢1π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 47 3 2 2 NUM iajs-3598 47 4 ) ) PUNCT iajs-3598 47 5 ( ( PUNCT iajs-3598 47 6 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 47 7 2 2 NUM iajs-3598 47 8 ) ) SYM iajs-3598 47 9 2 2 NUM iajs-3598 47 10 𝑣1 𝑣1 NOUN iajs-3598 47 11 3 3 NUM iajs-3598 47 12 βˆ’ βˆ’ NUM iajs-3598 47 13 1 1 NUM iajs-3598 47 14 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 47 15 2 2 NUM iajs-3598 47 16 ( ( PUNCT iajs-3598 47 17 2𝐿1(𝐢1 2𝐿1(𝐢1 NUM iajs-3598 47 18 βˆ’ βˆ’ PROPN iajs-3598 47 19 2 2 NUM iajs-3598 47 20 ) ) PUNCT iajs-3598 47 21 βˆ’ βˆ’ NOUN iajs-3598 48 1 2𝐢1𝐿1((π‘Ž1 2𝐢1𝐿1((π‘Ž1 NUM iajs-3598 48 2 + + NUM iajs-3598 48 3 𝐿1 𝐿1 PROPN iajs-3598 48 4 2 2 NUM iajs-3598 48 5 ) ) PUNCT iajs-3598 48 6 βˆ’ βˆ’ PROPN iajs-3598 48 7 2𝐿1 2𝐿1 NUM iajs-3598 48 8 2 2 NUM iajs-3598 48 9 ) ) PUNCT iajs-3598 48 10 + + CCONJ iajs-3598 48 11 2𝐢1(1 2𝐢1(1 NUM iajs-3598 48 12 βˆ’ βˆ’ NOUN iajs-3598 48 13 𝐿1(π‘Ž1 𝐿1(π‘Ž1 ADJ iajs-3598 48 14 + + CCONJ iajs-3598 48 15 2𝐿1 2𝐿1 NUM iajs-3598 48 16 ) ) PUNCT iajs-3598 48 17 ) ) PUNCT iajs-3598 49 1 + + CCONJ iajs-3598 49 2 4𝐢1π‘Ž1𝐿1 4𝐢1π‘Ž1𝐿1 NUM iajs-3598 49 3 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 49 4 2 2 NUM iajs-3598 49 5 ) ) PUNCT iajs-3598 49 6 𝑣1 𝑣1 PROPN iajs-3598 49 7 2𝑣3 2𝑣3 PROPN iajs-3598 49 8 , , PUNCT iajs-3598 49 9 ihjpas ihjpas PROPN iajs-3598 49 10 . . PUNCT iajs-3598 50 1 2025 2025 NUM iajs-3598 50 2 , , PUNCT iajs-3598 50 3 38 38 NUM iajs-3598 50 4 ( ( PUNCT iajs-3598 50 5 1 1 NUM iajs-3598 50 6 ) ) PUNCT iajs-3598 50 7 431 431 NUM iajs-3598 51 1 𝐡21 𝐡21 NOUN iajs-3598 51 2 = = PUNCT iajs-3598 52 1 βˆ’ βˆ’ PROPN iajs-3598 52 2 2𝐢2π‘Ž2𝐿3 2𝐢2π‘Ž2𝐿3 NUM iajs-3598 52 3 ( ( PUNCT iajs-3598 52 4 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 52 5 ) ) PUNCT iajs-3598 52 6 𝑣1 𝑣1 NOUN iajs-3598 52 7 2𝑣2 2𝑣2 NUM iajs-3598 52 8 + + CCONJ iajs-3598 52 9 ( ( PUNCT iajs-3598 52 10 2𝐢2π‘Ž2 2𝐢2π‘Ž2 NUM iajs-3598 52 11 2𝐿3 2𝐿3 NUM iajs-3598 52 12 ( ( PUNCT iajs-3598 52 13 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 52 14 + + SYM iajs-3598 52 15 𝐢2π‘Ž2 𝐢2π‘Ž2 PROPN iajs-3598 52 16 ( ( PUNCT iajs-3598 52 17 1+π‘Ž2𝐿2 1+π‘Ž2𝐿2 PROPN iajs-3598 52 18 ) ) PUNCT iajs-3598 52 19 ) ) PUNCT iajs-3598 53 1 𝑣2 𝑣2 X iajs-3598 53 2 2𝑣3 2𝑣3 NUM iajs-3598 53 3 + + CCONJ iajs-3598 53 4 𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 53 5 ) ) PUNCT iajs-3598 53 6 ( ( PUNCT iajs-3598 53 7 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 53 8 𝑣2𝑣3 𝑣2𝑣3 ADP iajs-3598 53 9 2 2 NUM iajs-3598 53 10 + + CCONJ iajs-3598 53 11 𝐢2 𝐢2 ADJ iajs-3598 53 12 ( ( PUNCT iajs-3598 53 13 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 53 14 𝑣1 𝑣1 NOUN iajs-3598 53 15 2𝑣3 2𝑣3 PROPN iajs-3598 53 16 + + CCONJ iajs-3598 53 17 ( ( PUNCT iajs-3598 53 18 4𝑆2𝑓1𝐿3 4𝑆2𝑓1𝐿3 NUM iajs-3598 53 19 ( ( PUNCT iajs-3598 53 20 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 53 21 βˆ’ βˆ’ NOUN iajs-3598 53 22 𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 NOUN iajs-3598 53 23 ) ) PUNCT iajs-3598 53 24 ( ( PUNCT iajs-3598 53 25 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 53 26 + + X iajs-3598 54 1 2𝐢2π‘Ž3 2𝐢2π‘Ž3 PROPN iajs-3598 54 2 ( ( PUNCT iajs-3598 54 3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 NUM iajs-3598 54 4 ) ) PUNCT iajs-3598 54 5 ) ) PUNCT iajs-3598 55 1 𝑣2𝑣3 𝑣2𝑣3 ADP iajs-3598 55 2 2 2 NUM iajs-3598 55 3 + + CCONJ iajs-3598 55 4 ( ( PUNCT iajs-3598 55 5 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 55 6 2(1βˆ’2𝑓1𝐿3 2(1βˆ’2𝑓1𝐿3 NUM iajs-3598 55 7 ) ) PUNCT iajs-3598 55 8 ( ( PUNCT iajs-3598 55 9 1+𝑓1𝐿3)6 1+𝑓1𝐿3)6 NUM iajs-3598 55 10 + + CCONJ iajs-3598 55 11 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 55 12 ( ( PUNCT iajs-3598 55 13 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 55 14 ) ) PUNCT iajs-3598 56 1 𝑣3 𝑣3 ADJ iajs-3598 56 2 3 3 NUM iajs-3598 56 3 , , PUNCT iajs-3598 56 4 𝐡31 𝐡31 PROPN iajs-3598 56 5 = = SYM iajs-3598 56 6 2𝑔1𝐿3(π‘Ž1βˆ’πΏ1 2𝑔1𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 56 7 2 2 NUM iajs-3598 56 8 ) ) PUNCT iajs-3598 57 1 ( ( PUNCT iajs-3598 57 2 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 57 3 2 2 NUM iajs-3598 57 4 ) ) SYM iajs-3598 57 5 2 2 NUM iajs-3598 57 6 𝑣1 𝑣1 NOUN iajs-3598 57 7 3 3 NUM iajs-3598 57 8 βˆ’ βˆ’ NOUN iajs-3598 57 9 2𝑔1𝐿1(2π‘Ž1 2𝑔1𝐿1(2π‘Ž1 NUM iajs-3598 57 10 + + NOUN iajs-3598 57 11 1 1 NUM iajs-3598 57 12 ) ) PUNCT iajs-3598 57 13 ( ( PUNCT iajs-3598 57 14 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 57 15 2 2 NUM iajs-3598 57 16 ) ) SYM iajs-3598 57 17 2 2 NUM iajs-3598 57 18 𝑣1 𝑣1 NOUN iajs-3598 57 19 2𝑣3 2𝑣3 NUM iajs-3598 57 20 + + CCONJ iajs-3598 57 21 6π‘Ž2 6π‘Ž2 NUM iajs-3598 57 22 2𝑔2𝐿3 2𝑔2𝐿3 NUM iajs-3598 57 23 ( ( PUNCT iajs-3598 57 24 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 57 25 ) ) PUNCT iajs-3598 57 26 𝑣2 𝑣2 NOUN iajs-3598 57 27 3 3 NUM iajs-3598 57 28 + + NUM iajs-3598 57 29 2π‘Ž2𝑔2 2π‘Ž2𝑔2 NUM iajs-3598 57 30 ( ( PUNCT iajs-3598 57 31 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 57 32 ( ( PUNCT iajs-3598 57 33 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 57 34 βˆ’ βˆ’ PROPN iajs-3598 57 35 2)𝑣2 2)𝑣2 NUM iajs-3598 57 36 2𝑣3 2𝑣3 NUM iajs-3598 58 1 + + CCONJ iajs-3598 58 2 2𝑔1𝐿1 2𝑔1𝐿1 NUM iajs-3598 58 3 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 58 4 2 2 NUM iajs-3598 58 5 𝑣1 𝑣1 NOUN iajs-3598 58 6 2𝑣3 2𝑣3 PROPN iajs-3598 58 7 + + CCONJ iajs-3598 58 8 π‘Ž3𝑔2 π‘Ž3𝑔2 X iajs-3598 58 9 ( ( PUNCT iajs-3598 58 10 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 58 11 ( ( PUNCT iajs-3598 58 12 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 58 13 + + NUM iajs-3598 58 14 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 58 15 βˆ’ βˆ’ PROPN iajs-3598 58 16 2)𝑣2𝑣3 2)𝑣2𝑣3 NOUN iajs-3598 58 17 2 2 NUM iajs-3598 58 18 βˆ’ βˆ’ PROPN iajs-3598 58 19 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 58 20 ) ) PUNCT iajs-3598 58 21 ( ( PUNCT iajs-3598 58 22 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 NUM iajs-3598 58 23 𝑣3 𝑣3 ADJ iajs-3598 58 24 3 3 NUM iajs-3598 58 25 . . PUNCT iajs-3598 58 26 where where SCONJ iajs-3598 58 27 𝑋 𝑋 PROPN iajs-3598 58 28 = = SYM iajs-3598 58 29 ( ( PUNCT iajs-3598 58 30 𝐿1 𝐿1 PROPN iajs-3598 58 31 , , PUNCT iajs-3598 58 32 𝐿2 𝐿2 PROPN iajs-3598 58 33 , , PUNCT iajs-3598 58 34 𝐿3 𝐿3 NOUN iajs-3598 58 35 ) ) PUNCT iajs-3598 58 36 and and CCONJ iajs-3598 58 37 πœ‡ πœ‡ SCONJ iajs-3598 58 38 be be VERB iajs-3598 58 39 any any DET iajs-3598 58 40 parameter parameter NOUN iajs-3598 58 41 . . PUNCT iajs-3598 59 1 theorem theorem NOUN iajs-3598 59 2 ( ( PUNCT iajs-3598 59 3 1):system 1):system NUM iajs-3598 59 4 ( ( PUNCT iajs-3598 59 5 1 1 NUM iajs-3598 59 6 ) ) PUNCT iajs-3598 59 7 , , PUNCT iajs-3598 59 8 with with ADP iajs-3598 59 9 the the DET iajs-3598 59 10 value value NOUN iajs-3598 59 11 of of ADP iajs-3598 59 12 the the DET iajs-3598 59 13 parameter parameter NOUN iajs-3598 59 14 οΏ½ οΏ½ PROPN iajs-3598 59 15 ́ ́ PROPN iajs-3598 59 16 οΏ½ οΏ½ NOUN iajs-3598 59 17 = = SYM iajs-3598 59 18 𝑑 𝑑 PROPN iajs-3598 59 19 = = X iajs-3598 59 20 πœ‡πΎ1 πœ‡πΎ1 PROPN iajs-3598 59 21 βˆ’ βˆ’ PROPN iajs-3598 60 1 𝑔1π‘˜1 𝑔1π‘˜1 PROPN iajs-3598 60 2 π‘Ž1+𝐾1 π‘Ž1+𝐾1 X iajs-3598 60 3 2 2 NUM iajs-3598 60 4 βˆ’ βˆ’ PROPN iajs-3598 60 5 𝑔2𝑆2 𝑔2𝑆2 NUM iajs-3598 60 6 𝐢+π‘Ž2𝑆2 𝐢+π‘Ž2𝑆2 PROPN iajs-3598 60 7 , , PUNCT iajs-3598 60 8 has have VERB iajs-3598 60 9 a a DET iajs-3598 60 10 transcritical transcritical ADJ iajs-3598 60 11 and and CCONJ iajs-3598 60 12 pitchfork pitchfork NOUN iajs-3598 60 13 bifurcation bifurcation NOUN iajs-3598 60 14 at at ADP iajs-3598 60 15 𝐻3 𝐻3 NOUN iajs-3598 60 16 = = SYM iajs-3598 60 17 ( ( PUNCT iajs-3598 60 18 𝐾1 𝐾1 PROPN iajs-3598 60 19 , , PUNCT iajs-3598 60 20 𝑆2 𝑆2 PROPN iajs-3598 60 21 𝐢 𝐢 PROPN iajs-3598 60 22 , , PUNCT iajs-3598 60 23 0 0 NUM iajs-3598 60 24 , , PUNCT iajs-3598 60 25 ) ) PUNCT iajs-3598 60 26 if if SCONJ iajs-3598 60 27 the the DET iajs-3598 60 28 following follow VERB iajs-3598 60 29 conditions condition NOUN iajs-3598 60 30 : : PUNCT iajs-3598 60 31 πœ‡πΎ1 πœ‡πΎ1 PROPN iajs-3598 60 32 > > PUNCT iajs-3598 61 1 𝑔1π‘˜1 𝑔1π‘˜1 X iajs-3598 61 2 π‘Ž1 π‘Ž1 X iajs-3598 61 3 + + CCONJ iajs-3598 61 4 𝐾1 𝐾1 PROPN iajs-3598 61 5 2 2 NUM iajs-3598 61 6 + + SYM iajs-3598 61 7 𝑔2𝑆2 𝑔2𝑆2 PROPN iajs-3598 61 8 𝐢 𝐢 PROPN iajs-3598 61 9 + + CCONJ iajs-3598 61 10 π‘Ž2𝑆2 π‘Ž2𝑆2 PROPN iajs-3598 61 11 , , PUNCT iajs-3598 61 12 ( ( PUNCT iajs-3598 61 13 5 5 X iajs-3598 61 14 ) ) PUNCT iajs-3598 61 15 1 1 NUM iajs-3598 61 16 2 2 NUM iajs-3598 61 17 > > PUNCT iajs-3598 61 18 𝐿1 𝐿1 PROPN iajs-3598 61 19 2 2 NUM iajs-3598 61 20 ( ( PUNCT iajs-3598 61 21 6 6 NUM iajs-3598 61 22 ) ) PUNCT iajs-3598 61 23 οΏ½ οΏ½ PROPN iajs-3598 61 24 ́ ́ NOUN iajs-3598 61 25 οΏ½ οΏ½ PROPN iajs-3598 61 26 1 1 NUM iajs-3598 61 27 β‰  β‰  PROPN iajs-3598 61 28 οΏ½ οΏ½ PROPN iajs-3598 61 29 ́ ́ NOUN iajs-3598 61 30 οΏ½ οΏ½ NOUN iajs-3598 61 31 2 2 NUM iajs-3598 61 32 , , PUNCT iajs-3598 61 33 ( ( PUNCT iajs-3598 61 34 7 7 X iajs-3598 61 35 ) ) PUNCT iajs-3598 61 36 οΏ½ οΏ½ NOUN iajs-3598 61 37 ́ ́ NOUN iajs-3598 61 38 οΏ½ οΏ½ PROPN iajs-3598 61 39 3 3 NUM iajs-3598 61 40 β‰  β‰  PROPN iajs-3598 61 41 οΏ½ οΏ½ PROPN iajs-3598 61 42 ́ ́ NOUN iajs-3598 61 43 οΏ½ οΏ½ NOUN iajs-3598 61 44 4 4 NUM iajs-3598 61 45 . . PUNCT iajs-3598 62 1 ( ( PUNCT iajs-3598 62 2 8) 8) NUM iajs-3598 62 3 where where SCONJ iajs-3598 62 4 : : PUNCT iajs-3598 62 5 οΏ½ οΏ½ PROPN iajs-3598 62 6 ́ ́ NOUN iajs-3598 62 7 οΏ½ οΏ½ NOUN iajs-3598 62 8 1 1 NUM iajs-3598 62 9 = = SYM iajs-3598 62 10 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 62 11 2𝐿1𝐿3 2𝐿1𝐿3 NUM iajs-3598 62 12 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 62 13 2 2 NUM iajs-3598 62 14 + + CCONJ iajs-3598 62 15 𝑔1𝑀1(1βˆ’2𝐿1 𝑔1𝑀1(1βˆ’2𝐿1 PROPN iajs-3598 62 16 2 2 NUM iajs-3598 62 17 ) ) PUNCT iajs-3598 62 18 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 62 19 2 2 NUM iajs-3598 62 20 + + CCONJ iajs-3598 62 21 𝑔1𝑀1 𝑔1𝑀1 PROPN iajs-3598 62 22 + + CCONJ iajs-3598 62 23 𝑔2𝑀2 𝑔2𝑀2 NUM iajs-3598 62 24 ( ( PUNCT iajs-3598 62 25 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 NOUN iajs-3598 62 26 , , PUNCT iajs-3598 62 27 οΏ½ οΏ½ PROPN iajs-3598 62 28 ́ ́ NOUN iajs-3598 62 29 οΏ½ οΏ½ ADJ iajs-3598 62 30 2 2 NUM iajs-3598 62 31 = = SYM iajs-3598 62 32 2π‘Ž2𝑔2𝑀2 2π‘Ž2𝑔2𝑀2 NUM iajs-3598 62 33 2𝐿3 2𝐿3 NUM iajs-3598 62 34 ( ( PUNCT iajs-3598 62 35 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 62 36 ) ) PUNCT iajs-3598 63 1 + + CCONJ iajs-3598 63 2 π‘Ž2𝐿2𝑔2𝑀2 π‘Ž2𝐿2𝑔2𝑀2 X iajs-3598 63 3 ( ( PUNCT iajs-3598 63 4 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 63 5 + + CCONJ iajs-3598 63 6 2πœ‡π‘€1 2πœ‡π‘€1 NUM iajs-3598 63 7 + + CCONJ iajs-3598 63 8 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 63 9 ( ( PUNCT iajs-3598 63 10 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 63 11 , , PUNCT iajs-3598 63 12 οΏ½ οΏ½ NOUN iajs-3598 63 13 ́ ́ NOUN iajs-3598 63 14 οΏ½ οΏ½ NOUN iajs-3598 63 15 3 3 NUM iajs-3598 63 16 = = SYM iajs-3598 63 17 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 63 18 3𝐿3(π‘Ž1βˆ’πΏ1 3𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 63 19 2 2 NUM iajs-3598 63 20 ) ) PUNCT iajs-3598 63 21 ( ( PUNCT iajs-3598 63 22 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 63 23 2 2 NUM iajs-3598 63 24 ) ) PUNCT iajs-3598 63 25 2 2 NUM iajs-3598 63 26 + + CCONJ iajs-3598 63 27 6π‘Ž2 6π‘Ž2 NUM iajs-3598 63 28 2𝑔2𝑀1 2𝑔2𝑀1 NUM iajs-3598 63 29 3𝐿3 3𝐿3 NUM iajs-3598 63 30 ( ( PUNCT iajs-3598 63 31 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 63 32 ) ) PUNCT iajs-3598 63 33 + + CCONJ iajs-3598 63 34 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 63 35 2𝐿1 2𝐿1 NUM iajs-3598 63 36 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 63 37 2 2 NUM iajs-3598 63 38 + + NUM iajs-3598 63 39 2π‘Ž2 2π‘Ž2 NUM iajs-3598 63 40 2𝑔2𝑀2 2𝑔2𝑀2 NUM iajs-3598 63 41 2𝐿2 2𝐿2 NUM iajs-3598 63 42 ( ( PUNCT iajs-3598 63 43 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 63 44 + + NOUN iajs-3598 63 45 π‘Ž3𝑔2𝑀2 π‘Ž3𝑔2𝑀2 ADP iajs-3598 63 46 ( ( PUNCT iajs-3598 63 47 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 63 48 ( ( PUNCT iajs-3598 63 49 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 63 50 + + NUM iajs-3598 63 51 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 63 52 ) ) PUNCT iajs-3598 63 53 , , PUNCT iajs-3598 63 54 οΏ½ οΏ½ PROPN iajs-3598 63 55 ́ ́ NOUN iajs-3598 63 56 οΏ½ οΏ½ NOUN iajs-3598 63 57 4 4 NUM iajs-3598 63 58 = = SYM iajs-3598 63 59 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 63 60 2𝐿1(2π‘Ž1 2𝐿1(2π‘Ž1 NUM iajs-3598 63 61 + + NOUN iajs-3598 63 62 1 1 NUM iajs-3598 63 63 ) ) PUNCT iajs-3598 63 64 ( ( PUNCT iajs-3598 63 65 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 63 66 2 2 NUM iajs-3598 63 67 ) ) PUNCT iajs-3598 63 68 2 2 NUM iajs-3598 63 69 + + CCONJ iajs-3598 63 70 4π‘Ž2𝑔2𝑀2 4π‘Ž2𝑔2𝑀2 ADV iajs-3598 63 71 2 2 NUM iajs-3598 63 72 ( ( PUNCT iajs-3598 63 73 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 63 74 + + NOUN iajs-3598 63 75 2π‘Ž3𝑔2𝑀2 2π‘Ž3𝑔2𝑀2 NUM iajs-3598 63 76 ( ( PUNCT iajs-3598 63 77 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NOUN iajs-3598 63 78 + + NOUN iajs-3598 63 79 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 63 80 ) ) PUNCT iajs-3598 63 81 ( ( PUNCT iajs-3598 63 82 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 X iajs-3598 63 83 . . PUNCT iajs-3598 64 1 proof proof NOUN iajs-3598 64 2 : : PUNCT iajs-3598 64 3 using use VERB iajs-3598 64 4 the the DET iajs-3598 64 5 jacobian jacobian ADJ iajs-3598 64 6 matrix matrix NOUN iajs-3598 64 7 in in ADP iajs-3598 64 8 eq eq PROPN iajs-3598 64 9 . . PUNCT iajs-3598 65 1 ( ( PUNCT iajs-3598 65 2 1.8 1.8 NUM iajs-3598 65 3 ) ) PUNCT iajs-3598 65 4 in in ADP iajs-3598 65 5 ( ( PUNCT iajs-3598 65 6 22 22 NUM iajs-3598 65 7 ) ) PUNCT iajs-3598 65 8 𝐽3 𝐽3 NOUN iajs-3598 66 1 = = SYM iajs-3598 66 2 𝐽3(𝐻3 𝐽3(𝐻3 PROPN iajs-3598 66 3 , , PUNCT iajs-3598 66 4 𝑑 𝑑 NOUN iajs-3598 66 5 ) ) PUNCT iajs-3598 66 6 = = PUNCT iajs-3598 67 1 [ [ PUNCT iajs-3598 67 2 οΏ½ οΏ½ PROPN iajs-3598 67 3 ́ ́ NOUN iajs-3598 67 4 οΏ½ οΏ½ NOUN iajs-3598 67 5 𝑖𝑗 𝑖𝑗 NOUN iajs-3598 67 6 ] ] X iajs-3598 67 7 3Γ—3 3Γ—3 NUM iajs-3598 67 8 , , PUNCT iajs-3598 67 9 where where SCONJ iajs-3598 67 10 οΏ½ οΏ½ PROPN iajs-3598 67 11 ́ ́ NOUN iajs-3598 67 12 οΏ½ οΏ½ NOUN iajs-3598 67 13 𝑖𝑗 𝑖𝑗 NOUN iajs-3598 67 14 = = PUNCT iajs-3598 67 15 π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— PROPN iajs-3598 67 16 , , PUNCT iajs-3598 67 17 except except SCONJ iajs-3598 67 18 οΏ½ οΏ½ PROPN iajs-3598 67 19 ́ ́ NOUN iajs-3598 67 20 οΏ½ οΏ½ NOUN iajs-3598 67 21 33 33 NUM iajs-3598 67 22 = = SYM iajs-3598 67 23 0 0 NUM iajs-3598 67 24 . . PUNCT iajs-3598 68 1 the the DET iajs-3598 68 2 characterizing characterizing NOUN iajs-3598 68 3 eq eq NOUN iajs-3598 68 4 . . PROPN iajs-3598 68 5 of of ADP iajs-3598 68 6 οΏ½ οΏ½ PROPN iajs-3598 68 7 ́ ́ NOUN iajs-3598 68 8 οΏ½ οΏ½ X iajs-3598 68 9 3 3 NUM iajs-3598 68 10 then then ADV iajs-3598 68 11 has have VERB iajs-3598 68 12 an an DET iajs-3598 68 13 eigenvalue eigenvalue NOUN iajs-3598 68 14 of of ADP iajs-3598 68 15 zero(say zero(say NOUN iajs-3598 68 16 Ξ»3l3 Ξ»3l3 VERB iajs-3598 68 17 ) ) PUNCT iajs-3598 68 18 . . PUNCT iajs-3598 69 1 now now ADV iajs-3598 69 2 , , PUNCT iajs-3598 69 3 let let VERB iajs-3598 69 4 𝑉1 𝑉1 NOUN iajs-3598 69 5 = = SYM iajs-3598 69 6 ( ( PUNCT iajs-3598 69 7 𝑣1 𝑣1 NOUN iajs-3598 69 8 [ [ X iajs-3598 69 9 1 1 NUM iajs-3598 69 10 ] ] PUNCT iajs-3598 69 11 , , PUNCT iajs-3598 69 12 𝑣2 𝑣2 X iajs-3598 69 13 [ [ X iajs-3598 69 14 1 1 NUM iajs-3598 69 15 ] ] PUNCT iajs-3598 69 16 , , PUNCT iajs-3598 69 17 𝑣3 𝑣3 ADJ iajs-3598 69 18 [ [ X iajs-3598 69 19 1 1 NUM iajs-3598 69 20 ] ] PUNCT iajs-3598 69 21 ) ) PUNCT iajs-3598 70 1 𝑇be 𝑇be NUM iajs-3598 70 2 the the DET iajs-3598 70 3 eigenvector eigenvector NOUN iajs-3598 70 4 corresponding correspond VERB iajs-3598 70 5 to to ADP iajs-3598 70 6 the the DET iajs-3598 70 7 eigenvalue eigenvalue ADJ iajs-3598 70 8 Ξ»3l3 Ξ»3l3 PROPN iajs-3598 70 9 = = NOUN iajs-3598 70 10 0 0 NUM iajs-3598 70 11 . . PUNCT iajs-3598 71 1 thus,(𝐽3 thus,(𝐽3 ADJ iajs-3598 71 2 βˆ’ βˆ’ PROPN iajs-3598 71 3 Ξ»3l3 Ξ»3l3 PROPN iajs-3598 71 4 𝐼)𝑉1 𝐼)𝑉1 NUM iajs-3598 71 5 = = SYM iajs-3598 71 6 0 0 NUM iajs-3598 71 7 , , PUNCT iajs-3598 71 8 this this PRON iajs-3598 71 9 gives give VERB iajs-3598 71 10 : : PUNCT iajs-3598 71 11 𝑣1 𝑣1 NOUN iajs-3598 71 12 [ [ X iajs-3598 71 13 1 1 NUM iajs-3598 71 14 ] ] X iajs-3598 71 15 = = SYM iajs-3598 72 1 𝑀1𝑣3 𝑀1𝑣3 ADJ iajs-3598 72 2 [ [ X iajs-3598 72 3 1 1 NUM iajs-3598 72 4 ] ] PUNCT iajs-3598 72 5 , , PUNCT iajs-3598 72 6 𝑣2 𝑣2 X iajs-3598 72 7 [ [ X iajs-3598 72 8 1 1 NUM iajs-3598 72 9 ] ] PUNCT iajs-3598 72 10 = = SYM iajs-3598 72 11 𝑀2 𝑀2 PROPN iajs-3598 72 12 𝑣3 𝑣3 PROPN iajs-3598 72 13 [ [ X iajs-3598 72 14 1 1 NUM iajs-3598 72 15 ] ] PUNCT iajs-3598 72 16 , , PUNCT iajs-3598 72 17 where where SCONJ iajs-3598 72 18 𝑀1 𝑀1 ADV iajs-3598 72 19 = = SYM iajs-3598 72 20 βˆ’ βˆ’ PROPN iajs-3598 72 21 𝐢1𝐾1 𝐢1𝐾1 PROPN iajs-3598 72 22 ( ( PUNCT iajs-3598 72 23 π‘Ž1+𝐾1 π‘Ž1+𝐾1 X iajs-3598 72 24 2)𝑆1 2)𝑆1 NUM iajs-3598 72 25 , , PUNCT iajs-3598 72 26 𝑀2 𝑀2 PROPN iajs-3598 72 27 = = SYM iajs-3598 72 28 βˆ’ βˆ’ PROPN iajs-3598 72 29 𝑆2𝑓1 𝑆2𝑓1 PROPN iajs-3598 72 30 2𝐢 2𝐢 PROPN iajs-3598 72 31 . . PUNCT iajs-3598 73 1 and and CCONJ iajs-3598 73 2 𝑣3 𝑣3 ADJ iajs-3598 73 3 [ [ X iajs-3598 73 4 1 1 NUM iajs-3598 73 5 ] ] PUNCT iajs-3598 73 6 any any DET iajs-3598 73 7 non non ADJ iajs-3598 73 8 - - ADJ iajs-3598 73 9 zero zero ADJ iajs-3598 73 10 real real ADJ iajs-3598 73 11 number number NOUN iajs-3598 73 12 . . PUNCT iajs-3598 74 1 ihjpas ihjpas PROPN iajs-3598 74 2 . . PUNCT iajs-3598 75 1 2025 2025 NUM iajs-3598 75 2 , , PUNCT iajs-3598 75 3 38 38 NUM iajs-3598 75 4 ( ( PUNCT iajs-3598 75 5 1 1 NUM iajs-3598 75 6 ) ) PUNCT iajs-3598 75 7 432 432 NUM iajs-3598 75 8 consider consider VERB iajs-3598 75 9 𝑍[1 𝑍[1 NOUN iajs-3598 75 10 ] ] X iajs-3598 75 11 = = SYM iajs-3598 75 12 ( ( PUNCT iajs-3598 75 13 𝑧1 𝑧1 NOUN iajs-3598 75 14 [ [ X iajs-3598 75 15 1 1 NUM iajs-3598 75 16 ] ] PUNCT iajs-3598 75 17 , , PUNCT iajs-3598 75 18 𝑧2 𝑧2 PROPN iajs-3598 76 1 [ [ X iajs-3598 76 2 1 1 NUM iajs-3598 76 3 ] ] PUNCT iajs-3598 76 4 , , PUNCT iajs-3598 76 5 𝑧3 𝑧3 PROPN iajs-3598 76 6 [ [ X iajs-3598 76 7 1 1 NUM iajs-3598 76 8 ] ] PUNCT iajs-3598 76 9 ) ) PUNCT iajs-3598 76 10 𝑇 𝑇 PROPN iajs-3598 76 11 be be VERB iajs-3598 76 12 the the DET iajs-3598 76 13 eigenvector eigenvector NOUN iajs-3598 76 14 connected connect VERB iajs-3598 76 15 with with ADP iajs-3598 76 16 an an DET iajs-3598 76 17 eigenvalue eigenvalue ADJ iajs-3598 76 18 Ξ»3l3 Ξ»3l3 NOUN iajs-3598 76 19 = = NOUN iajs-3598 76 20 0 0 NUM iajs-3598 76 21 of of ADP iajs-3598 76 22 the the DET iajs-3598 76 23 matrix matrix NOUN iajs-3598 76 24 𝐽3 𝐽3 ADP iajs-3598 76 25 𝑇.then 𝑇.then ADV iajs-3598 76 26 , , PUNCT iajs-3598 76 27 ( ( PUNCT iajs-3598 76 28 𝐽3 𝐽3 PROPN iajs-3598 76 29 𝑇 𝑇 PROPN iajs-3598 76 30 βˆ’ βˆ’ PROPN iajs-3598 76 31 Ξ»3l3 Ξ»3l3 PROPN iajs-3598 76 32 𝐼 𝐼 PROPN iajs-3598 76 33 ) ) PUNCT iajs-3598 76 34 𝑍[1 𝑍[1 PROPN iajs-3598 76 35 ] ] X iajs-3598 76 36 = = SYM iajs-3598 76 37 0 0 X iajs-3598 76 38 . . PUNCT iajs-3598 77 1 by by ADP iajs-3598 77 2 solving solve VERB iajs-3598 77 3 this this DET iajs-3598 77 4 equation equation NOUN iajs-3598 77 5 for for ADP iajs-3598 77 6 , , PUNCT iajs-3598 77 7 𝑍[1 𝑍[1 PROPN iajs-3598 77 8 ] ] X iajs-3598 77 9 = = SYM iajs-3598 77 10 ( ( PUNCT iajs-3598 77 11 0,0 0,0 NOUN iajs-3598 77 12 , , PUNCT iajs-3598 77 13 𝑧3 𝑧3 PROPN iajs-3598 77 14 [ [ X iajs-3598 77 15 1 1 NUM iajs-3598 77 16 ] ] PUNCT iajs-3598 77 17 ) ) PUNCT iajs-3598 77 18 𝑇 𝑇 PROPN iajs-3598 77 19 , , PUNCT iajs-3598 77 20 where where SCONJ iajs-3598 77 21 𝑍3 𝑍3 PROPN iajs-3598 77 22 [ [ X iajs-3598 77 23 1 1 X iajs-3598 77 24 ] ] PUNCT iajs-3598 77 25 any any DET iajs-3598 77 26 non non ADJ iajs-3598 77 27 - - ADJ iajs-3598 77 28 zero zero ADJ iajs-3598 77 29 real real ADJ iajs-3598 77 30 number number NOUN iajs-3598 77 31 . . PUNCT iajs-3598 78 1 now now ADV iajs-3598 78 2 , , PUNCT iajs-3598 78 3 consider consider VERB iajs-3598 78 4 that that PRON iajs-3598 78 5 : : PUNCT iajs-3598 78 6 πœ•π‘“ πœ•π‘“ ADJ iajs-3598 78 7 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 78 8 = = SYM iajs-3598 78 9 𝑓𝑑(𝑋 𝑓𝑑(𝑋 PROPN iajs-3598 78 10 , , PUNCT iajs-3598 78 11 𝑑 𝑑 NOUN iajs-3598 78 12 ) ) PUNCT iajs-3598 78 13 = = SYM iajs-3598 78 14 ( ( PUNCT iajs-3598 78 15 πœ•π‘“1 πœ•π‘“1 NOUN iajs-3598 78 16 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 78 17 , , PUNCT iajs-3598 78 18 πœ•π‘“2 πœ•π‘“2 PROPN iajs-3598 78 19 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 78 20 , , PUNCT iajs-3598 78 21 πœ•π‘“3 πœ•π‘“3 PROPN iajs-3598 78 22 πœ•π‘‘ πœ•π‘‘ PROPN iajs-3598 78 23 ) ) PUNCT iajs-3598 78 24 𝑇 𝑇 PROPN iajs-3598 78 25 = = SYM iajs-3598 78 26 ( ( PUNCT iajs-3598 78 27 0 0 NUM iajs-3598 78 28 , , PUNCT iajs-3598 78 29 0 0 NUM iajs-3598 78 30 , , PUNCT iajs-3598 78 31 βˆ’πΏ3)𝑇 βˆ’πΏ3)𝑇 PROPN iajs-3598 78 32 . . PUNCT iajs-3598 79 1 so so ADV iajs-3598 79 2 , , PUNCT iajs-3598 79 3 𝑓𝑑(𝐻3 𝑓𝑑(𝐻3 PROPN iajs-3598 79 4 , , PUNCT iajs-3598 79 5 οΏ½ οΏ½ PROPN iajs-3598 79 6 ́ ́ NOUN iajs-3598 79 7 οΏ½ οΏ½ NOUN iajs-3598 79 8 ) ) PUNCT iajs-3598 79 9 = = PUNCT iajs-3598 80 1 ( ( PUNCT iajs-3598 80 2 0,0,0)𝑇 0,0,0)𝑇 PRON iajs-3598 80 3 and and CCONJ iajs-3598 80 4 hence hence ADV iajs-3598 80 5 ( ( PUNCT iajs-3598 80 6 𝑍[1 𝑍[1 PROPN iajs-3598 80 7 ] ] PUNCT iajs-3598 80 8 ) ) PUNCT iajs-3598 80 9 𝑇 𝑇 PROPN iajs-3598 80 10 𝑓𝑑(𝐻3 𝑓𝑑(𝐻3 PROPN iajs-3598 80 11 , , PUNCT iajs-3598 80 12 οΏ½ οΏ½ PROPN iajs-3598 80 13 ́ ́ NOUN iajs-3598 80 14 οΏ½ οΏ½ NOUN iajs-3598 80 15 ) ) PUNCT iajs-3598 80 16 = = SYM iajs-3598 80 17 0 0 PUNCT iajs-3598 81 1 the the DET iajs-3598 81 2 ( ( PUNCT iajs-3598 81 3 sd sd NOUN iajs-3598 81 4 ) ) PUNCT iajs-3598 81 5 bifurcation bifurcation NOUN iajs-3598 81 6 requirement requirement NOUN iajs-3598 81 7 can can AUX iajs-3598 81 8 not not PART iajs-3598 81 9 be be AUX iajs-3598 81 10 satisfied satisfied ADJ iajs-3598 81 11 according accord VERB iajs-3598 81 12 to to ADP iajs-3598 81 13 sotomayor sotomayor PROPN iajs-3598 81 14 's 's PART iajs-3598 81 15 theorem theorem ADJ iajs-3598 81 16 . . PROPN iajs-3598 82 1 as as ADP iajs-3598 82 2 a a DET iajs-3598 82 3 result result NOUN iajs-3598 82 4 , , PUNCT iajs-3598 82 5 the the DET iajs-3598 82 6 first first ADJ iajs-3598 82 7 requirement requirement NOUN iajs-3598 82 8 for for ADP iajs-3598 82 9 ( ( PUNCT iajs-3598 82 10 tc tc NOUN iajs-3598 82 11 ) ) PUNCT iajs-3598 82 12 bifurcation bifurcation NOUN iajs-3598 82 13 is be AUX iajs-3598 82 14 realized realize VERB iajs-3598 82 15 . . PUNCT iajs-3598 83 1 now now ADV iajs-3598 83 2 𝐷𝑓𝑑(𝑋 𝐷𝑓𝑑(𝑋 ADV iajs-3598 83 3 , , PUNCT iajs-3598 83 4 𝑑 𝑑 NOUN iajs-3598 83 5 ) ) PUNCT iajs-3598 83 6 = = PUNCT iajs-3598 84 1 [ [ PUNCT iajs-3598 84 2 0 0 NUM iajs-3598 84 3 0 0 NUM iajs-3598 84 4 0 0 NUM iajs-3598 84 5 0 0 NUM iajs-3598 84 6 0 0 NUM iajs-3598 84 7 0 0 NUM iajs-3598 84 8 0 0 NUM iajs-3598 84 9 0 0 NUM iajs-3598 84 10 βˆ’1 βˆ’1 NOUN iajs-3598 84 11 ] ] PUNCT iajs-3598 84 12 where where SCONJ iajs-3598 84 13 , , PUNCT iajs-3598 84 14 𝐷𝑓𝑑(𝑋 𝐷𝑓𝑑(𝑋 ADV iajs-3598 84 15 , , PUNCT iajs-3598 84 16 𝑑 𝑑 NOUN iajs-3598 84 17 ) ) PUNCT iajs-3598 84 18 represents represent VERB iajs-3598 84 19 the the DET iajs-3598 84 20 derivative derivative NOUN iajs-3598 84 21 of of ADP iajs-3598 84 22 𝑓𝑑(𝑋 𝑓𝑑(𝑋 ADJ iajs-3598 84 23 , , PUNCT iajs-3598 84 24 𝑑 𝑑 NOUN iajs-3598 84 25 ) ) PUNCT iajs-3598 84 26 with with ADP iajs-3598 84 27 respect respect NOUN iajs-3598 84 28 to to ADP iajs-3598 84 29 𝑋 𝑋 PROPN iajs-3598 84 30 = = SYM iajs-3598 84 31 ( ( PUNCT iajs-3598 84 32 𝐿1 𝐿1 PROPN iajs-3598 84 33 , , PUNCT iajs-3598 84 34 𝐿2 𝐿2 PROPN iajs-3598 84 35 , , PUNCT iajs-3598 84 36 𝐿3)𝑇 𝐿3)𝑇 PUNCT iajs-3598 84 37 . . PUNCT iajs-3598 85 1 furthermore furthermore ADV iajs-3598 85 2 , , PUNCT iajs-3598 85 3 it it PRON iajs-3598 85 4 is be AUX iajs-3598 85 5 observed observe VERB iajs-3598 85 6 that that SCONJ iajs-3598 85 7 : : PUNCT iajs-3598 85 8 𝐷𝑓𝑑(𝐻3 𝐷𝑓𝑑(𝐻3 NOUN iajs-3598 85 9 , , PUNCT iajs-3598 85 10 𝑑)𝑉[1 𝑑)𝑉[1 PROPN iajs-3598 85 11 ] ] PUNCT iajs-3598 85 12 = = PUNCT iajs-3598 85 13 [ [ PUNCT iajs-3598 85 14 0 0 NUM iajs-3598 85 15 0 0 NUM iajs-3598 85 16 0 0 NUM iajs-3598 85 17 0 0 NUM iajs-3598 85 18 0 0 NUM iajs-3598 85 19 0 0 NUM iajs-3598 85 20 0 0 NUM iajs-3598 85 21 0 0 NUM iajs-3598 85 22 βˆ’1 βˆ’1 NOUN iajs-3598 85 23 ] ] PUNCT iajs-3598 86 1 [ [ PUNCT iajs-3598 86 2 𝑀1𝑣3 𝑀1𝑣3 ADV iajs-3598 86 3 [ [ X iajs-3598 86 4 1 1 NUM iajs-3598 86 5 ] ] PUNCT iajs-3598 86 6 𝑀2 𝑀2 PROPN iajs-3598 86 7 𝑣3 𝑣3 PROPN iajs-3598 86 8 [ [ X iajs-3598 86 9 1 1 NUM iajs-3598 86 10 ] ] PUNCT iajs-3598 86 11 𝑣3 𝑣3 ADJ iajs-3598 86 12 [ [ X iajs-3598 86 13 1 1 NUM iajs-3598 86 14 ] ] PUNCT iajs-3598 86 15 ] ] PUNCT iajs-3598 87 1 = = PUNCT iajs-3598 87 2 [ [ PUNCT iajs-3598 87 3 0 0 NUM iajs-3598 87 4 0 0 NUM iajs-3598 87 5 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 87 6 [ [ X iajs-3598 87 7 1 1 X iajs-3598 87 8 ] ] PUNCT iajs-3598 87 9 ] ] X iajs-3598 87 10 ( ( PUNCT iajs-3598 87 11 𝑍[1 𝑍[1 PROPN iajs-3598 87 12 ] ] PUNCT iajs-3598 87 13 ) ) PUNCT iajs-3598 87 14 𝑇 𝑇 PROPN iajs-3598 88 1 [ [ X iajs-3598 88 2 𝐷𝑓𝑑(𝐻3 𝐷𝑓𝑑(𝐻3 NOUN iajs-3598 88 3 , , PUNCT iajs-3598 88 4 𝑑)𝑉[1 𝑑)𝑉[1 PROPN iajs-3598 88 5 ] ] PUNCT iajs-3598 88 6 ] ] X iajs-3598 88 7 = = SYM iajs-3598 88 8 ( ( PUNCT iajs-3598 88 9 0,0 0,0 NOUN iajs-3598 88 10 , , PUNCT iajs-3598 88 11 𝑧3 𝑧3 PROPN iajs-3598 88 12 [ [ X iajs-3598 88 13 1 1 NUM iajs-3598 88 14 ] ] PUNCT iajs-3598 88 15 ) ) PUNCT iajs-3598 88 16 𝑇 𝑇 PROPN iajs-3598 88 17 ( ( PUNCT iajs-3598 88 18 0,0 0,0 NOUN iajs-3598 88 19 , , PUNCT iajs-3598 88 20 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 89 1 [ [ X iajs-3598 89 2 1 1 NUM iajs-3598 89 3 ] ] PUNCT iajs-3598 89 4 ) ) PUNCT iajs-3598 90 1 = = PUNCT iajs-3598 90 2 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 91 1 [ [ X iajs-3598 91 2 1 1 X iajs-3598 91 3 ] ] X iajs-3598 91 4 𝑧3 𝑧3 NOUN iajs-3598 92 1 [ [ X iajs-3598 92 2 1 1 NUM iajs-3598 92 3 ] ] PUNCT iajs-3598 92 4 β‰  β‰  PROPN iajs-3598 92 5 0 0 X iajs-3598 92 6 . . PUNCT iajs-3598 92 7 by by ADP iajs-3598 92 8 substituting substitute VERB iajs-3598 92 9 𝑉[1 𝑉[1 PROPN iajs-3598 92 10 ] ] PUNCT iajs-3598 92 11 in in ADP iajs-3598 92 12 ( ( PUNCT iajs-3598 92 13 3 3 X iajs-3598 92 14 ) ) PUNCT iajs-3598 92 15 we we PRON iajs-3598 92 16 get get VERB iajs-3598 92 17 : : PUNCT iajs-3598 92 18 𝐷2πΉπœ‡(𝐻3 𝐷2πΉπœ‡(𝐻3 PROPN iajs-3598 92 19 , , PUNCT iajs-3598 92 20 𝑑)(𝑉[1 𝑑)(𝑉[1 NOUN iajs-3598 92 21 ] ] PUNCT iajs-3598 92 22 , , PUNCT iajs-3598 92 23 𝑉[1 𝑉[1 PROPN iajs-3598 92 24 ] ] PUNCT iajs-3598 92 25 ) ) PUNCT iajs-3598 93 1 = = SYM iajs-3598 93 2 ( ( PUNCT iajs-3598 93 3 𝐴𝑖1 𝐴𝑖1 X iajs-3598 93 4 ́ ́ PROPN iajs-3598 93 5 ) ) PUNCT iajs-3598 93 6 3Γ—1 3Γ—1 NUM iajs-3598 93 7 , , PUNCT iajs-3598 93 8 οΏ½ οΏ½ PROPN iajs-3598 93 9 ́ ́ NOUN iajs-3598 93 10 οΏ½ οΏ½ NOUN iajs-3598 93 11 11 11 NUM iajs-3598 93 12 = = SYM iajs-3598 93 13 βˆ’ βˆ’ PROPN iajs-3598 93 14 2𝑆1 2𝑆1 NUM iajs-3598 93 15 𝐾1 𝐾1 NOUN iajs-3598 93 16 + + CCONJ iajs-3598 93 17 ( ( PUNCT iajs-3598 93 18 𝑣3 𝑣3 ADJ iajs-3598 93 19 [ [ X iajs-3598 93 20 1 1 NUM iajs-3598 93 21 ] ] PUNCT iajs-3598 93 22 ) ) PUNCT iajs-3598 93 23 2 2 NUM iajs-3598 93 24 [ [ PUNCT iajs-3598 93 25 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NUM iajs-3598 93 26 ( ( PUNCT iajs-3598 93 27 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 93 28 2 2 NUM iajs-3598 93 29 ) ) PUNCT iajs-3598 93 30 2 2 NUM iajs-3598 93 31 𝑀1 𝑀1 NOUN iajs-3598 93 32 2 2 NUM iajs-3598 93 33 βˆ’ βˆ’ NOUN iajs-3598 93 34 𝐢1 𝐢1 PROPN iajs-3598 93 35 ( ( PUNCT iajs-3598 93 36 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 93 37 2 2 NUM iajs-3598 93 38 ) ) PUNCT iajs-3598 93 39 ( ( PUNCT iajs-3598 93 40 ( ( PUNCT iajs-3598 93 41 π‘Ž1 π‘Ž1 X iajs-3598 93 42 + + CCONJ iajs-3598 93 43 𝐿1 𝐿1 PROPN iajs-3598 93 44 2 2 NUM iajs-3598 93 45 ) ) PUNCT iajs-3598 93 46 βˆ’ βˆ’ PROPN iajs-3598 93 47 2𝐿1 2𝐿1 NUM iajs-3598 93 48 2 2 NUM iajs-3598 93 49 + + CCONJ iajs-3598 93 50 ( ( PUNCT iajs-3598 93 51 π‘Ž1 π‘Ž1 X iajs-3598 93 52 + + CCONJ iajs-3598 93 53 2𝐿1))𝑀1 2𝐿1))𝑀1 NUM iajs-3598 93 54 ] ] X iajs-3598 93 55 , , PUNCT iajs-3598 93 56 οΏ½ οΏ½ PROPN iajs-3598 93 57 ́ ́ NOUN iajs-3598 93 58 οΏ½ οΏ½ NOUN iajs-3598 93 59 21 21 NUM iajs-3598 93 60 = = SYM iajs-3598 93 61 βˆ’2𝐢 βˆ’2𝐢 NOUN iajs-3598 93 62 + + CCONJ iajs-3598 93 63 ( ( PUNCT iajs-3598 93 64 𝑣3 𝑣3 ADJ iajs-3598 93 65 [ [ X iajs-3598 93 66 1 1 NUM iajs-3598 93 67 ] ] PUNCT iajs-3598 93 68 ) ) PUNCT iajs-3598 93 69 2 2 NUM iajs-3598 93 70 [ [ PUNCT iajs-3598 93 71 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 93 72 ( ( PUNCT iajs-3598 93 73 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 93 74 ) ) PUNCT iajs-3598 93 75 𝑀1 𝑀1 PROPN iajs-3598 93 76 2 2 NUM iajs-3598 93 77 βˆ’ βˆ’ NOUN iajs-3598 93 78 ( ( PUNCT iajs-3598 93 79 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 93 80 ( ( PUNCT iajs-3598 93 81 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 93 82 βˆ’ βˆ’ NOUN iajs-3598 93 83 𝐢2π‘Ž2𝐿3 𝐢2π‘Ž2𝐿3 NOUN iajs-3598 93 84 ( ( PUNCT iajs-3598 93 85 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 93 86 + + CCONJ iajs-3598 93 87 𝐢2 𝐢2 ADJ iajs-3598 93 88 ( ( PUNCT iajs-3598 93 89 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 93 90 ) ) PUNCT iajs-3598 93 91 𝑀2 𝑀2 PROPN iajs-3598 93 92 + + CCONJ iajs-3598 93 93 ( ( PUNCT iajs-3598 93 94 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 93 95 2𝐿3 2𝐿3 NUM iajs-3598 93 96 ( ( PUNCT iajs-3598 93 97 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 93 98 βˆ’ βˆ’ PROPN iajs-3598 93 99 𝐢2(1βˆ’π‘Ž3𝐿3 𝐢2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 93 100 ) ) PUNCT iajs-3598 93 101 ( ( PUNCT iajs-3598 93 102 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 93 103 ) ) PUNCT iajs-3598 93 104 ] ] PUNCT iajs-3598 93 105 , , PUNCT iajs-3598 93 106 οΏ½ οΏ½ PROPN iajs-3598 93 107 ́ ́ NOUN iajs-3598 93 108 οΏ½ οΏ½ PROPN iajs-3598 93 109 31 31 NUM iajs-3598 93 110 = = SYM iajs-3598 93 111 ( ( PUNCT iajs-3598 93 112 𝑣3 𝑣3 PROPN iajs-3598 93 113 [ [ X iajs-3598 93 114 1 1 NUM iajs-3598 93 115 ] ] PUNCT iajs-3598 93 116 ) ) PUNCT iajs-3598 93 117 2 2 NUM iajs-3598 93 118 [ [ PUNCT iajs-3598 93 119 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 93 120 2𝐿1𝐿3 2𝐿1𝐿3 NUM iajs-3598 93 121 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 93 122 2 2 NUM iajs-3598 93 123 + + CCONJ iajs-3598 93 124 ( ( PUNCT iajs-3598 93 125 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 93 126 2 2 NUM iajs-3598 93 127 ) ) PUNCT iajs-3598 93 128 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 93 129 2 2 NUM iajs-3598 93 130 + + NUM iajs-3598 93 131 𝑔1 𝑔1 PROPN iajs-3598 93 132 βˆ’ βˆ’ PROPN iajs-3598 93 133 2πœ‡ 2πœ‡ PROPN iajs-3598 93 134 ) ) PUNCT iajs-3598 93 135 𝑀1 𝑀1 PROPN iajs-3598 93 136 βˆ’ βˆ’ PROPN iajs-3598 93 137 2π‘Ž2𝑔2𝑀2 2π‘Ž2𝑔2𝑀2 ADJ iajs-3598 93 138 2𝐿3 2𝐿3 NUM iajs-3598 93 139 ( ( PUNCT iajs-3598 93 140 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 93 141 ) ) PUNCT iajs-3598 93 142 βˆ’ βˆ’ NOUN iajs-3598 93 143 π‘Ž2𝐿2𝑔2𝑀2 π‘Ž2𝐿2𝑔2𝑀2 NOUN iajs-3598 93 144 ( ( PUNCT iajs-3598 93 145 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 93 146 + + CCONJ iajs-3598 93 147 𝑔2𝑀2 𝑔2𝑀2 NUM iajs-3598 93 148 ( ( PUNCT iajs-3598 93 149 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 VERB iajs-3598 93 150 βˆ’ βˆ’ NOUN iajs-3598 93 151 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 93 152 ( ( PUNCT iajs-3598 93 153 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 93 154 ] ] PUNCT iajs-3598 93 155 . . PUNCT iajs-3598 94 1 hence hence ADV iajs-3598 94 2 , , PUNCT iajs-3598 94 3 it it PRON iajs-3598 94 4 was be AUX iajs-3598 94 5 obtained obtain VERB iajs-3598 94 6 ( ( PUNCT iajs-3598 94 7 𝑍[1 𝑍[1 PROPN iajs-3598 94 8 ] ] PUNCT iajs-3598 94 9 ) ) PUNCT iajs-3598 94 10 𝑇 𝑇 PROPN iajs-3598 95 1 [ [ X iajs-3598 95 2 𝐷2πΉπœ‡(𝐻3 𝐷2πΉπœ‡(𝐻3 PROPN iajs-3598 95 3 , , PUNCT iajs-3598 95 4 𝑑)(𝑉[1 𝑑)(𝑉[1 PROPN iajs-3598 95 5 ] ] PUNCT iajs-3598 95 6 , , PUNCT iajs-3598 95 7 𝑉[1 𝑉[1 PROPN iajs-3598 95 8 ] ] PUNCT iajs-3598 95 9 ) ) PUNCT iajs-3598 95 10 ] ] PUNCT iajs-3598 96 1 = = PUNCT iajs-3598 96 2 𝑧3 𝑧3 NOUN iajs-3598 97 1 [ [ X iajs-3598 97 2 1 1 NUM iajs-3598 97 3 ] ] X iajs-3598 97 4 ( ( PUNCT iajs-3598 97 5 𝑣3 𝑣3 ADJ iajs-3598 97 6 [ [ X iajs-3598 97 7 1 1 NUM iajs-3598 97 8 ] ] PUNCT iajs-3598 97 9 ) ) PUNCT iajs-3598 97 10 2 2 NUM iajs-3598 97 11 ( ( PUNCT iajs-3598 97 12 οΏ½ οΏ½ NOUN iajs-3598 97 13 ́ ́ NOUN iajs-3598 97 14 οΏ½ οΏ½ NOUN iajs-3598 97 15 1 1 NUM iajs-3598 97 16 βˆ’ βˆ’ PROPN iajs-3598 97 17 οΏ½ οΏ½ PROPN iajs-3598 97 18 ́ ́ NOUN iajs-3598 97 19 οΏ½ οΏ½ NOUN iajs-3598 97 20 2 2 NUM iajs-3598 97 21 ) ) PUNCT iajs-3598 97 22 β‰  β‰  PROPN iajs-3598 97 23 0 0 NUM iajs-3598 97 24 . . PUNCT iajs-3598 98 1 so so ADV iajs-3598 98 2 , , PUNCT iajs-3598 98 3 by by ADP iajs-3598 98 4 condition condition NOUN iajs-3598 98 5 ( ( PUNCT iajs-3598 98 6 7 7 NUM iajs-3598 98 7 ) ) PUNCT iajs-3598 98 8 that that DET iajs-3598 98 9 system system NOUN iajs-3598 98 10 ( ( PUNCT iajs-3598 98 11 1 1 X iajs-3598 98 12 ) ) PUNCT iajs-3598 98 13 has have VERB iajs-3598 98 14 a a DET iajs-3598 98 15 ( ( PUNCT iajs-3598 98 16 tc tc NOUN iajs-3598 98 17 ) ) PUNCT iajs-3598 98 18 bifurcation bifurcation NOUN iajs-3598 98 19 at at ADP iajs-3598 98 20 𝐻3 𝐻3 NOUN iajs-3598 98 21 with with ADP iajs-3598 98 22 a a DET iajs-3598 98 23 parameter parameter NOUN iajs-3598 98 24 οΏ½ οΏ½ NOUN iajs-3598 98 25 ́ ́ PROPN iajs-3598 98 26 οΏ½ οΏ½ NOUN iajs-3598 98 27 = = SYM iajs-3598 98 28 𝑑 𝑑 PROPN iajs-3598 98 29 , , PUNCT iajs-3598 98 30 if if SCONJ iajs-3598 98 31 the the DET iajs-3598 98 32 requirement requirement NOUN iajs-3598 98 33 ( ( PUNCT iajs-3598 98 34 7 7 NUM iajs-3598 98 35 ) ) PUNCT iajs-3598 98 36 is be AUX iajs-3598 98 37 not not PART iajs-3598 98 38 met meet VERB iajs-3598 98 39 . . PUNCT iajs-3598 99 1 ihjpas ihjpas PROPN iajs-3598 99 2 . . PUNCT iajs-3598 100 1 2025 2025 NUM iajs-3598 100 2 , , PUNCT iajs-3598 100 3 38 38 NUM iajs-3598 100 4 ( ( PUNCT iajs-3598 100 5 1 1 NUM iajs-3598 100 6 ) ) PUNCT iajs-3598 100 7 433 433 NUM iajs-3598 100 8 by by ADP iajs-3598 100 9 substituting substitute VERB iajs-3598 100 10 𝑉[1 𝑉[1 PROPN iajs-3598 100 11 ] ] PUNCT iajs-3598 100 12 into into ADP iajs-3598 100 13 ( ( PUNCT iajs-3598 100 14 4 4 X iajs-3598 100 15 ) ) PUNCT iajs-3598 100 16 we we PRON iajs-3598 100 17 get get VERB iajs-3598 100 18 : : PUNCT iajs-3598 100 19 𝐷3πΉπœ‡(𝐻3 𝐷3πΉπœ‡(𝐻3 NOUN iajs-3598 100 20 , , PUNCT iajs-3598 100 21 𝑑)(𝑉[1 𝑑)(𝑉[1 PROPN iajs-3598 100 22 ] ] PUNCT iajs-3598 100 23 , , PUNCT iajs-3598 100 24 𝑉[1 𝑉[1 PROPN iajs-3598 100 25 ] ] PUNCT iajs-3598 100 26 , , PUNCT iajs-3598 100 27 𝑉[1 𝑉[1 PROPN iajs-3598 100 28 ] ] PUNCT iajs-3598 100 29 ) ) PUNCT iajs-3598 100 30 = = SYM iajs-3598 100 31 ( ( PUNCT iajs-3598 100 32 οΏ½ οΏ½ PROPN iajs-3598 100 33 ́ ́ NOUN iajs-3598 100 34 οΏ½ οΏ½ NOUN iajs-3598 100 35 𝑖1 𝑖1 NOUN iajs-3598 100 36 ) ) PUNCT iajs-3598 100 37 3Γ—1 3Γ—1 NUM iajs-3598 100 38 οΏ½ οΏ½ PROPN iajs-3598 100 39 ́ ́ NOUN iajs-3598 100 40 οΏ½ οΏ½ NOUN iajs-3598 100 41 11 11 NUM iajs-3598 100 42 = = SYM iajs-3598 100 43 ( ( PUNCT iajs-3598 100 44 𝑣3 𝑣3 PROPN iajs-3598 100 45 [ [ X iajs-3598 100 46 1 1 NUM iajs-3598 100 47 ] ] PUNCT iajs-3598 100 48 ) ) PUNCT iajs-3598 100 49 3 3 NUM iajs-3598 100 50 [ [ PUNCT iajs-3598 100 51 4𝐢1π‘Ž1𝐿3(1βˆ’4𝐿1 4𝐢1π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 100 52 2 2 NUM iajs-3598 100 53 ) ) PUNCT iajs-3598 100 54 ( ( PUNCT iajs-3598 100 55 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 100 56 2 2 NUM iajs-3598 100 57 ) ) PUNCT iajs-3598 100 58 2 2 NUM iajs-3598 100 59 𝑀1 𝑀1 NOUN iajs-3598 100 60 3 3 NUM iajs-3598 100 61 βˆ’ βˆ’ NOUN iajs-3598 100 62 𝑀1 𝑀1 PROPN iajs-3598 100 63 2 2 NUM iajs-3598 100 64 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 100 65 2 2 NUM iajs-3598 100 66 ( ( PUNCT iajs-3598 100 67 2𝐿1(𝐢1 2𝐿1(𝐢1 NUM iajs-3598 100 68 βˆ’ βˆ’ PROPN iajs-3598 100 69 2 2 NUM iajs-3598 100 70 ) ) PUNCT iajs-3598 100 71 βˆ’ βˆ’ NOUN iajs-3598 101 1 2𝐢1𝐿1((π‘Ž1 2𝐢1𝐿1((π‘Ž1 NUM iajs-3598 101 2 + + NUM iajs-3598 101 3 𝐿1 𝐿1 PROPN iajs-3598 101 4 2 2 NUM iajs-3598 101 5 ) ) PUNCT iajs-3598 101 6 βˆ’ βˆ’ PROPN iajs-3598 101 7 2𝐿1 2𝐿1 NUM iajs-3598 101 8 2 2 NUM iajs-3598 101 9 ) ) PUNCT iajs-3598 101 10 + + CCONJ iajs-3598 101 11 2𝐢1(1 2𝐢1(1 NUM iajs-3598 101 12 βˆ’ βˆ’ NOUN iajs-3598 101 13 𝐿1(π‘Ž1 𝐿1(π‘Ž1 ADJ iajs-3598 101 14 + + CCONJ iajs-3598 101 15 2𝐿1 2𝐿1 NUM iajs-3598 101 16 ) ) PUNCT iajs-3598 101 17 ) ) PUNCT iajs-3598 102 1 + + CCONJ iajs-3598 102 2 4𝐢1π‘Ž1𝐿1 4𝐢1π‘Ž1𝐿1 NUM iajs-3598 102 3 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 102 4 2 2 NUM iajs-3598 102 5 ) ) PUNCT iajs-3598 102 6 ] ] PUNCT iajs-3598 102 7 , , PUNCT iajs-3598 102 8 οΏ½ οΏ½ PROPN iajs-3598 102 9 ́ ́ NOUN iajs-3598 102 10 οΏ½ οΏ½ NOUN iajs-3598 102 11 21 21 NUM iajs-3598 102 12 = = SYM iajs-3598 102 13 ( ( PUNCT iajs-3598 102 14 𝑣3 𝑣3 PROPN iajs-3598 102 15 [ [ X iajs-3598 102 16 1 1 NUM iajs-3598 102 17 ] ] PUNCT iajs-3598 102 18 ) ) PUNCT iajs-3598 102 19 3 3 NUM iajs-3598 103 1 [ [ X iajs-3598 103 2 βˆ’ βˆ’ NOUN iajs-3598 103 3 2𝑀1 2𝑀1 NUM iajs-3598 103 4 2𝑀2𝐢2π‘Ž2𝐿3 2𝑀2𝐢2π‘Ž2𝐿3 NUM iajs-3598 103 5 ( ( PUNCT iajs-3598 103 6 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 103 7 ) ) PUNCT iajs-3598 103 8 + + CCONJ iajs-3598 103 9 2𝐢2𝑀2 2𝐢2𝑀2 NUM iajs-3598 103 10 2π‘Ž2 2π‘Ž2 NUM iajs-3598 103 11 2𝐿3 2𝐿3 NUM iajs-3598 103 12 ( ( PUNCT iajs-3598 103 13 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 103 14 + + CCONJ iajs-3598 103 15 𝑀2 𝑀2 PROPN iajs-3598 103 16 2𝐢2π‘Ž2 2𝐢2π‘Ž2 PROPN iajs-3598 103 17 ( ( PUNCT iajs-3598 103 18 1+π‘Ž2𝐿2 1+π‘Ž2𝐿2 PROPN iajs-3598 103 19 ) ) PUNCT iajs-3598 103 20 + + NUM iajs-3598 103 21 𝑀2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 𝑀2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 103 22 ) ) PUNCT iajs-3598 103 23 ( ( PUNCT iajs-3598 103 24 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 103 25 + + CCONJ iajs-3598 103 26 𝐢2𝑀1 𝐢2𝑀1 PROPN iajs-3598 103 27 2 2 NUM iajs-3598 103 28 ( ( PUNCT iajs-3598 103 29 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 103 30 + + CCONJ iajs-3598 103 31 ( ( PUNCT iajs-3598 103 32 4𝑆2𝑀2𝑓1𝐿3 4𝑆2𝑀2𝑓1𝐿3 NUM iajs-3598 103 33 ( ( PUNCT iajs-3598 103 34 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 103 35 βˆ’ βˆ’ PROPN iajs-3598 103 36 𝑀2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 𝑀2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 103 37 ) ) PUNCT iajs-3598 103 38 ( ( PUNCT iajs-3598 103 39 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 103 40 + + SYM iajs-3598 103 41 2𝑀2𝐢2π‘Ž3 2𝑀2𝐢2π‘Ž3 NUM iajs-3598 103 42 ( ( PUNCT iajs-3598 103 43 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 NUM iajs-3598 103 44 ) ) PUNCT iajs-3598 103 45 ) ) PUNCT iajs-3598 104 1 + + CCONJ iajs-3598 104 2 ( ( PUNCT iajs-3598 104 3 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 104 4 2(1βˆ’2𝑓1𝐿3 2(1βˆ’2𝑓1𝐿3 NUM iajs-3598 104 5 ) ) PUNCT iajs-3598 104 6 ( ( PUNCT iajs-3598 104 7 1+𝑓1𝐿3)6 1+𝑓1𝐿3)6 NUM iajs-3598 104 8 + + CCONJ iajs-3598 104 9 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 104 10 ( ( PUNCT iajs-3598 104 11 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 104 12 ) ) PUNCT iajs-3598 104 13 ] ] PUNCT iajs-3598 104 14 , , PUNCT iajs-3598 104 15 οΏ½ οΏ½ PROPN iajs-3598 104 16 ́ ́ NOUN iajs-3598 104 17 οΏ½ οΏ½ PROPN iajs-3598 104 18 31 31 NUM iajs-3598 104 19 = = SYM iajs-3598 104 20 ( ( PUNCT iajs-3598 104 21 𝑣3 𝑣3 PROPN iajs-3598 104 22 [ [ X iajs-3598 104 23 1 1 NUM iajs-3598 104 24 ] ] PUNCT iajs-3598 104 25 ) ) PUNCT iajs-3598 104 26 3 3 NUM iajs-3598 104 27 [ [ PUNCT iajs-3598 104 28 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 104 29 3𝐿3(π‘Ž1βˆ’πΏ1 3𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 104 30 2 2 NUM iajs-3598 104 31 ) ) PUNCT iajs-3598 104 32 ( ( PUNCT iajs-3598 104 33 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 104 34 2 2 NUM iajs-3598 104 35 ) ) PUNCT iajs-3598 104 36 2 2 NUM iajs-3598 105 1 βˆ’ βˆ’ NOUN iajs-3598 105 2 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 105 3 2𝐿1(2π‘Ž1 2𝐿1(2π‘Ž1 NUM iajs-3598 105 4 + + NOUN iajs-3598 105 5 1 1 NUM iajs-3598 105 6 ) ) PUNCT iajs-3598 105 7 ( ( PUNCT iajs-3598 105 8 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 105 9 2 2 NUM iajs-3598 105 10 ) ) PUNCT iajs-3598 105 11 2 2 NUM iajs-3598 105 12 + + CCONJ iajs-3598 105 13 6π‘Ž2 6π‘Ž2 NUM iajs-3598 105 14 2𝑔2𝑀1 2𝑔2𝑀1 NUM iajs-3598 105 15 3𝐿3 3𝐿3 NUM iajs-3598 105 16 ( ( PUNCT iajs-3598 105 17 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 105 18 ) ) PUNCT iajs-3598 106 1 + + CCONJ iajs-3598 106 2 2π‘Ž2 2π‘Ž2 NUM iajs-3598 106 3 2𝑔2𝑀2 2𝑔2𝑀2 NUM iajs-3598 106 4 2𝐿2 2𝐿2 NUM iajs-3598 106 5 ( ( PUNCT iajs-3598 106 6 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 106 7 βˆ’ βˆ’ NOUN iajs-3598 107 1 4π‘Ž2𝑔2𝑀2 4π‘Ž2𝑔2𝑀2 ADJ iajs-3598 107 2 2 2 NUM iajs-3598 107 3 ( ( PUNCT iajs-3598 107 4 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 107 5 + + CCONJ iajs-3598 107 6 2𝑔1𝑀1 2𝑔1𝑀1 NUM iajs-3598 107 7 2𝐿1 2𝐿1 NUM iajs-3598 107 8 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 107 9 2 2 NUM iajs-3598 107 10 + + CCONJ iajs-3598 107 11 π‘Ž3𝑔2𝑀2 π‘Ž3𝑔2𝑀2 ADP iajs-3598 107 12 ( ( PUNCT iajs-3598 107 13 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 107 14 ( ( PUNCT iajs-3598 107 15 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 107 16 + + NUM iajs-3598 107 17 π‘Ž2𝐿2 π‘Ž2𝐿2 NOUN iajs-3598 107 18 ) ) PUNCT iajs-3598 108 1 βˆ’ βˆ’ ADP iajs-3598 108 2 2π‘Ž3𝑔2𝑀2 2π‘Ž3𝑔2𝑀2 NUM iajs-3598 108 3 ( ( PUNCT iajs-3598 108 4 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 VERB iajs-3598 108 5 βˆ’ βˆ’ PROPN iajs-3598 108 6 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 108 7 ) ) PUNCT iajs-3598 108 8 ( ( PUNCT iajs-3598 108 9 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 X iajs-3598 108 10 . . PUNCT iajs-3598 109 1 ( ( PUNCT iajs-3598 109 2 𝑍[1 𝑍[1 PROPN iajs-3598 109 3 ] ] PUNCT iajs-3598 109 4 ) ) PUNCT iajs-3598 109 5 𝑇 𝑇 PROPN iajs-3598 110 1 [ [ X iajs-3598 110 2 𝐷3πΉπœ‡(𝐻3 𝐷3πΉπœ‡(𝐻3 NOUN iajs-3598 110 3 , , PUNCT iajs-3598 110 4 𝑑)(𝑉[1 𝑑)(𝑉[1 PROPN iajs-3598 110 5 ] ] PUNCT iajs-3598 110 6 , , PUNCT iajs-3598 110 7 𝑉[1 𝑉[1 PROPN iajs-3598 110 8 ] ] PUNCT iajs-3598 110 9 , , PUNCT iajs-3598 110 10 𝑉[1 𝑉[1 PROPN iajs-3598 110 11 ] ] PUNCT iajs-3598 110 12 ) ) PUNCT iajs-3598 110 13 ] ] PUNCT iajs-3598 111 1 = = PUNCT iajs-3598 111 2 𝑧3 𝑧3 NOUN iajs-3598 112 1 [ [ X iajs-3598 112 2 1 1 NUM iajs-3598 112 3 ] ] X iajs-3598 112 4 ( ( PUNCT iajs-3598 112 5 𝑣3 𝑣3 ADJ iajs-3598 112 6 [ [ X iajs-3598 112 7 1 1 NUM iajs-3598 112 8 ] ] PUNCT iajs-3598 112 9 ) ) PUNCT iajs-3598 112 10 3 3 NUM iajs-3598 112 11 ( ( PUNCT iajs-3598 112 12 οΏ½ οΏ½ NOUN iajs-3598 112 13 ́ ́ NOUN iajs-3598 112 14 οΏ½ οΏ½ NOUN iajs-3598 112 15 3 3 NUM iajs-3598 112 16 βˆ’ βˆ’ PROPN iajs-3598 112 17 οΏ½ οΏ½ PROPN iajs-3598 112 18 ́ ́ NOUN iajs-3598 112 19 οΏ½ οΏ½ NOUN iajs-3598 112 20 4 4 NUM iajs-3598 112 21 ) ) PUNCT iajs-3598 112 22 β‰  β‰  PROPN iajs-3598 112 23 0 0 PUNCT iajs-3598 113 1 so so ADV iajs-3598 113 2 , , PUNCT iajs-3598 113 3 there there PRON iajs-3598 113 4 is be VERB iajs-3598 113 5 pitchfork pitchfork NOUN iajs-3598 113 6 bifurcation bifurcation NOUN iajs-3598 113 7 at at ADP iajs-3598 113 8 𝐻3 𝐻3 PROPN iajs-3598 113 9 where where SCONJ iajs-3598 113 10 οΏ½ οΏ½ PROPN iajs-3598 113 11 ́ ́ PROPN iajs-3598 113 12 οΏ½ οΏ½ NOUN iajs-3598 113 13 = = SYM iajs-3598 113 14 𝑑. 𝑑. NOUN iajs-3598 113 15 theorem theorem NOUN iajs-3598 113 16 ( ( PUNCT iajs-3598 113 17 2 2 NUM iajs-3598 113 18 ): ): PUNCT iajs-3598 113 19 suppose suppose VERB iajs-3598 113 20 that that SCONJ iajs-3598 113 21 condition condition NOUN iajs-3598 113 22 ( ( PUNCT iajs-3598 113 23 1.9b 1.9b NUM iajs-3598 113 24 ) ) PUNCT iajs-3598 113 25 , , PUNCT iajs-3598 113 26 revers rever NOUN iajs-3598 113 27 conditions condition NOUN iajs-3598 113 28 ( ( PUNCT iajs-3598 113 29 1.9c 1.9c NUM iajs-3598 113 30 ) ) PUNCT iajs-3598 113 31 and and CCONJ iajs-3598 113 32 ( ( PUNCT iajs-3598 113 33 1.9d 1.9d NUM iajs-3598 113 34 ) ) PUNCT iajs-3598 113 35 in in ADP iajs-3598 113 36 ( ( PUNCT iajs-3598 113 37 22 22 NUM iajs-3598 113 38 ) ) PUNCT iajs-3598 113 39 with with ADP iajs-3598 113 40 the the DET iajs-3598 113 41 following follow VERB iajs-3598 113 42 conditions condition NOUN iajs-3598 113 43 are be AUX iajs-3598 113 44 satisfied satisfied ADJ iajs-3598 113 45 : : PUNCT iajs-3598 113 46 𝐿1 𝐿1 PROPN iajs-3598 113 47 2 2 NUM iajs-3598 113 48 < < SYM iajs-3598 113 49 1 1 NUM iajs-3598 113 50 4 4 NUM iajs-3598 113 51 , , PUNCT iajs-3598 113 52 ( ( PUNCT iajs-3598 113 53 8) 8) NUM iajs-3598 113 54 𝐿3 𝐿3 NOUN iajs-3598 113 55 < < X iajs-3598 113 56 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN iajs-3598 113 57 { { PUNCT iajs-3598 113 58 1 1 NUM iajs-3598 113 59 π‘Ž3 π‘Ž3 NOUN iajs-3598 113 60 , , PUNCT iajs-3598 113 61 1 1 NUM iajs-3598 113 62 2𝑓1 2𝑓1 NUM iajs-3598 113 63 } } PUNCT iajs-3598 113 64 , , PUNCT iajs-3598 113 65 ( ( PUNCT iajs-3598 113 66 9 9 X iajs-3598 113 67 ) ) PUNCT iajs-3598 113 68 οΏ½ οΏ½ PROPN iajs-3598 113 69 Μ‡ Μ‡ VERB iajs-3598 113 70 οΏ½ οΏ½ PROPN iajs-3598 113 71 31 31 NUM iajs-3598 113 72 οΏ½ οΏ½ PROPN iajs-3598 113 73 Μ‡ Μ‡ PROPN iajs-3598 113 74 οΏ½ οΏ½ PROPN iajs-3598 113 75 13 13 NUM iajs-3598 113 76 = = SYM iajs-3598 113 77 οΏ½ οΏ½ PROPN iajs-3598 113 78 Μ‡ Μ‡ PROPN iajs-3598 113 79 οΏ½ οΏ½ PROPN iajs-3598 113 80 32 32 NUM iajs-3598 113 81 οΏ½ οΏ½ PROPN iajs-3598 113 82 Μ‡ Μ‡ NOUN iajs-3598 113 83 οΏ½ οΏ½ PROPN iajs-3598 113 84 23 23 NUM iajs-3598 113 85 ( ( PUNCT iajs-3598 113 86 10 10 NUM iajs-3598 113 87 ) ) PUNCT iajs-3598 113 88 οΏ½ οΏ½ PROPN iajs-3598 113 89 Μ‡ Μ‡ VERB iajs-3598 113 90 οΏ½ οΏ½ PROPN iajs-3598 113 91 1 1 NUM iajs-3598 113 92 β‰  β‰  PROPN iajs-3598 113 93 οΏ½ οΏ½ PROPN iajs-3598 113 94 Μ‡ Μ‡ NOUN iajs-3598 113 95 οΏ½ οΏ½ PROPN iajs-3598 113 96 2 2 NUM iajs-3598 113 97 , , PUNCT iajs-3598 113 98 ( ( PUNCT iajs-3598 113 99 11 11 NUM iajs-3598 113 100 ) ) PUNCT iajs-3598 113 101 οΏ½ οΏ½ PROPN iajs-3598 113 102 Μ‡ Μ‡ VERB iajs-3598 113 103 οΏ½ οΏ½ PROPN iajs-3598 113 104 3 3 NUM iajs-3598 113 105 β‰  β‰  PROPN iajs-3598 113 106 οΏ½ οΏ½ PROPN iajs-3598 113 107 Μ‡ Μ‡ NOUN iajs-3598 113 108 οΏ½ οΏ½ PROPN iajs-3598 113 109 4 4 NUM iajs-3598 113 110 , , PUNCT iajs-3598 113 111 ( ( PUNCT iajs-3598 113 112 12 12 NUM iajs-3598 113 113 ) ) PUNCT iajs-3598 113 114 where where SCONJ iajs-3598 113 115 : : PUNCT iajs-3598 113 116 οΏ½ οΏ½ PROPN iajs-3598 113 117 Μ‡ Μ‡ PROPN iajs-3598 113 118 οΏ½ οΏ½ PROPN iajs-3598 113 119 1 1 NUM iajs-3598 113 120 = = SYM iajs-3598 113 121 ( ( PUNCT iajs-3598 113 122 𝑣3 𝑣3 PROPN iajs-3598 113 123 [ [ X iajs-3598 113 124 2 2 NUM iajs-3598 113 125 ] ] PUNCT iajs-3598 113 126 ) ) PUNCT iajs-3598 113 127 2 2 NUM iajs-3598 113 128 ( ( PUNCT iajs-3598 113 129 4π‘Ž1𝐢1 4π‘Ž1𝐢1 NUM iajs-3598 113 130 οΏ½ οΏ½ NOUN iajs-3598 113 131 Μ‡ Μ‡ NOUN iajs-3598 113 132 οΏ½ οΏ½ PROPN iajs-3598 113 133 3𝛼1Μ‡ 3𝛼1Μ‡ PROPN iajs-3598 113 134 2𝐿1𝐿3 2𝐿1𝐿3 NUM iajs-3598 113 135 ( ( PUNCT iajs-3598 113 136 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 113 137 2 2 NUM iajs-3598 113 138 ) ) PUNCT iajs-3598 113 139 2 2 NUM iajs-3598 113 140 + + SYM iajs-3598 113 141 2𝐢1𝛼1 2𝐢1𝛼1 PROPN iajs-3598 113 142 οΏ½ οΏ½ NOUN iajs-3598 113 143 Μ‡ Μ‡ NOUN iajs-3598 113 144 οΏ½ οΏ½ PROPN iajs-3598 113 145 3Μ‡ 3Μ‡ PROPN iajs-3598 113 146 𝐿1 𝐿1 X iajs-3598 113 147 2 2 NUM iajs-3598 113 148 ( ( PUNCT iajs-3598 113 149 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 113 150 2 2 NUM iajs-3598 113 151 ) ) PUNCT iajs-3598 113 152 + + CCONJ iajs-3598 113 153 οΏ½ οΏ½ PROPN iajs-3598 113 154 Μ‡ Μ‡ VERB iajs-3598 113 155 οΏ½ οΏ½ PROPN iajs-3598 113 156 1 1 NUM iajs-3598 113 157 2 2 NUM iajs-3598 113 158 οΏ½ οΏ½ PROPN iajs-3598 113 159 Μ‡ Μ‡ NOUN iajs-3598 113 160 οΏ½ οΏ½ PROPN iajs-3598 113 161 4𝐢2𝐿3 4𝐢2𝐿3 PROPN iajs-3598 113 162 ( ( PUNCT iajs-3598 113 163 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 113 164 ) ) PUNCT iajs-3598 113 165 + + CCONJ iajs-3598 113 166 οΏ½ οΏ½ PROPN iajs-3598 113 167 Μ‡ Μ‡ VERB iajs-3598 113 168 οΏ½ οΏ½ PROPN iajs-3598 113 169 2 2 NUM iajs-3598 113 170 οΏ½ οΏ½ PROPN iajs-3598 113 171 Μ‡ Μ‡ NOUN iajs-3598 113 172 οΏ½ οΏ½ PROPN iajs-3598 113 173 4𝐢2π‘Ž2𝐿3 4𝐢2π‘Ž2𝐿3 PRON iajs-3598 113 174 ( ( PUNCT iajs-3598 113 175 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 113 176 + + CCONJ iajs-3598 113 177 2 2 NUM iajs-3598 113 178 οΏ½ οΏ½ NOUN iajs-3598 113 179 Μ‡ Μ‡ VERB iajs-3598 113 180 οΏ½ οΏ½ NOUN iajs-3598 113 181 4𝑆2𝑓1 4𝑆2𝑓1 NUM iajs-3598 113 182 2𝐿3 2𝐿3 NUM iajs-3598 113 183 ( ( PUNCT iajs-3598 113 184 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 113 185 + + SYM iajs-3598 113 186 2𝑔1 2𝑔1 NUM iajs-3598 113 187 οΏ½ οΏ½ PROPN iajs-3598 113 188 Μ‡ Μ‡ NOUN iajs-3598 113 189 οΏ½ οΏ½ PROPN iajs-3598 113 190 1 1 NUM iajs-3598 113 191 2 2 NUM iajs-3598 113 192 οΏ½ οΏ½ PROPN iajs-3598 113 193 Μ‡ Μ‡ NOUN iajs-3598 113 194 οΏ½ οΏ½ PROPN iajs-3598 113 195 4𝐿1𝐿3 4𝐿1𝐿3 PRON iajs-3598 113 196 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 113 197 2 2 NUM iajs-3598 113 198 + + CCONJ iajs-3598 113 199 ( ( PUNCT iajs-3598 113 200 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 113 201 2 2 NUM iajs-3598 113 202 ) ) PUNCT iajs-3598 113 203 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 113 204 2 2 NUM iajs-3598 113 205 + + NUM iajs-3598 113 206 𝑔1 𝑔1 PROPN iajs-3598 113 207 ) ) PUNCT iajs-3598 114 1 οΏ½ οΏ½ PROPN iajs-3598 114 2 Μ‡ Μ‡ VERB iajs-3598 114 3 οΏ½ οΏ½ PROPN iajs-3598 114 4 1 1 NUM iajs-3598 114 5 + + NUM iajs-3598 114 6 𝑔2 𝑔2 NOUN iajs-3598 114 7 οΏ½ οΏ½ NOUN iajs-3598 114 8 Μ‡ Μ‡ NOUN iajs-3598 114 9 οΏ½ οΏ½ X iajs-3598 114 10 2 2 NUM iajs-3598 114 11 ( ( PUNCT iajs-3598 114 12 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 NOUN iajs-3598 114 13 ) ) PUNCT iajs-3598 114 14 , , PUNCT iajs-3598 114 15 οΏ½ οΏ½ PROPN iajs-3598 114 16 Μ‡ Μ‡ PROPN iajs-3598 114 17 οΏ½ οΏ½ PROPN iajs-3598 114 18 2 2 NUM iajs-3598 114 19 = = SYM iajs-3598 114 20 2𝑆1 2𝑆1 NUM iajs-3598 114 21 οΏ½ οΏ½ PROPN iajs-3598 114 22 Μ‡ Μ‡ NOUN iajs-3598 114 23 οΏ½ οΏ½ PROPN iajs-3598 114 24 3 3 NUM iajs-3598 114 25 𝐾1 𝐾1 PROPN iajs-3598 114 26 + + CCONJ iajs-3598 114 27 2𝐢 2𝐢 PROPN iajs-3598 114 28 οΏ½ οΏ½ PROPN iajs-3598 114 29 Μ‡ Μ‡ PROPN iajs-3598 114 30 οΏ½ οΏ½ PROPN iajs-3598 114 31 4 4 NUM iajs-3598 114 32 + + CCONJ iajs-3598 114 33 ( ( PUNCT iajs-3598 114 34 𝑣3 𝑣3 ADJ iajs-3598 114 35 [ [ X iajs-3598 114 36 2 2 NUM iajs-3598 114 37 ] ] PUNCT iajs-3598 114 38 ) ) PUNCT iajs-3598 114 39 2 2 NUM iajs-3598 114 40 ( ( PUNCT iajs-3598 114 41 𝐢1 𝐢1 PROPN iajs-3598 114 42 οΏ½ οΏ½ NOUN iajs-3598 114 43 Μ‡ Μ‡ NOUN iajs-3598 114 44 οΏ½ οΏ½ PROPN iajs-3598 114 45 1 1 NUM iajs-3598 114 46 ( ( PUNCT iajs-3598 114 47 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 114 48 2 2 NUM iajs-3598 114 49 ) ) PUNCT iajs-3598 114 50 ( ( PUNCT iajs-3598 114 51 ( ( PUNCT iajs-3598 114 52 π‘Ž1 π‘Ž1 X iajs-3598 114 53 + + CCONJ iajs-3598 114 54 𝐿1 𝐿1 PROPN iajs-3598 114 55 2 2 NUM iajs-3598 114 56 ) ) PUNCT iajs-3598 114 57 + + CCONJ iajs-3598 114 58 ( ( PUNCT iajs-3598 114 59 π‘Ž1 π‘Ž1 X iajs-3598 114 60 + + PRON iajs-3598 114 61 2𝐿1 2𝐿1 NUM iajs-3598 114 62 ) ) PUNCT iajs-3598 114 63 ) ) PUNCT iajs-3598 115 1 + + CCONJ iajs-3598 115 2 ( ( PUNCT iajs-3598 115 3 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 115 4 ( ( PUNCT iajs-3598 115 5 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 115 6 + + CCONJ iajs-3598 115 7 𝐢2 𝐢2 PROPN iajs-3598 115 8 ( ( PUNCT iajs-3598 115 9 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 PROPN iajs-3598 115 10 ) ) PUNCT iajs-3598 115 11 οΏ½ οΏ½ PROPN iajs-3598 115 12 Μ‡ Μ‡ VERB iajs-3598 115 13 οΏ½ οΏ½ PROPN iajs-3598 115 14 2 2 NUM iajs-3598 115 15 οΏ½ οΏ½ PROPN iajs-3598 115 16 Μ‡ Μ‡ VERB iajs-3598 115 17 οΏ½ οΏ½ NOUN iajs-3598 115 18 4 4 NUM iajs-3598 115 19 + + NUM iajs-3598 115 20 𝐢2(1βˆ’π‘Ž3𝐿3 𝐢2(1βˆ’π‘Ž3𝐿3 NOUN iajs-3598 115 21 ) ) PUNCT iajs-3598 115 22 ( ( PUNCT iajs-3598 115 23 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 115 24 + + NUM iajs-3598 115 25 2πœ‡ 2πœ‡ PROPN iajs-3598 115 26 οΏ½ οΏ½ PROPN iajs-3598 115 27 Μ‡ Μ‡ NOUN iajs-3598 115 28 οΏ½ οΏ½ PROPN iajs-3598 115 29 1 1 NUM iajs-3598 115 30 + + NUM iajs-3598 115 31 2π‘Ž2𝑔2 2π‘Ž2𝑔2 NUM iajs-3598 115 32 οΏ½ οΏ½ NOUN iajs-3598 115 33 Μ‡ Μ‡ NOUN iajs-3598 115 34 οΏ½ οΏ½ PROPN iajs-3598 115 35 2 2 NUM iajs-3598 115 36 2𝐿3 2𝐿3 NUM iajs-3598 115 37 ( ( PUNCT iajs-3598 115 38 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 115 39 ) ) PUNCT iajs-3598 116 1 + + CCONJ iajs-3598 116 2 π‘Ž2𝐿2𝑔2 π‘Ž2𝐿2𝑔2 PROPN iajs-3598 116 3 οΏ½ οΏ½ PROPN iajs-3598 116 4 Μ‡ Μ‡ NOUN iajs-3598 116 5 οΏ½ οΏ½ X iajs-3598 116 6 2 2 NUM iajs-3598 116 7 ( ( PUNCT iajs-3598 116 8 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 116 9 + + CCONJ iajs-3598 116 10 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 116 11 ( ( PUNCT iajs-3598 116 12 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 116 13 ) ) PUNCT iajs-3598 116 14 , , PUNCT iajs-3598 116 15 ihjpas ihjpas PROPN iajs-3598 116 16 . . PUNCT iajs-3598 117 1 2025 2025 NUM iajs-3598 117 2 , , PUNCT iajs-3598 117 3 38 38 NUM iajs-3598 117 4 ( ( PUNCT iajs-3598 117 5 1 1 NUM iajs-3598 117 6 ) ) PUNCT iajs-3598 117 7 434 434 NUM iajs-3598 117 8 οΏ½ οΏ½ NOUN iajs-3598 117 9 Μ‡ Μ‡ VERB iajs-3598 117 10 οΏ½ οΏ½ PROPN iajs-3598 117 11 3 3 NUM iajs-3598 117 12 = = SYM iajs-3598 117 13 2𝐢1 2𝐢1 NUM iajs-3598 117 14 οΏ½ οΏ½ PROPN iajs-3598 117 15 Μ‡ Μ‡ VERB iajs-3598 117 16 οΏ½ οΏ½ PROPN iajs-3598 117 17 1 1 NUM iajs-3598 117 18 3 3 NUM iajs-3598 117 19 οΏ½ οΏ½ PROPN iajs-3598 117 20 Μ‡ Μ‡ NOUN iajs-3598 117 21 οΏ½ οΏ½ PROPN iajs-3598 117 22 3π‘Ž1𝐿3(1βˆ’4𝐿1 3π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 117 23 2 2 NUM iajs-3598 117 24 ) ) PUNCT iajs-3598 117 25 ( ( PUNCT iajs-3598 117 26 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 117 27 2 2 NUM iajs-3598 117 28 ) ) SYM iajs-3598 117 29 2 2 NUM iajs-3598 117 30 + + NUM iajs-3598 117 31 οΏ½ οΏ½ PROPN iajs-3598 117 32 Μ‡ Μ‡ VERB iajs-3598 117 33 οΏ½ οΏ½ PROPN iajs-3598 117 34 1 1 NUM iajs-3598 117 35 2 2 NUM iajs-3598 117 36 οΏ½ οΏ½ PROPN iajs-3598 117 37 Μ‡ Μ‡ NOUN iajs-3598 117 38 οΏ½ οΏ½ PROPN iajs-3598 117 39 3𝐢1𝐿1 3𝐢1𝐿1 PROPN iajs-3598 117 40 + + SYM iajs-3598 117 41 οΏ½ οΏ½ PROPN iajs-3598 117 42 Μ‡ Μ‡ NOUN iajs-3598 117 43 οΏ½ οΏ½ PROPN iajs-3598 117 44 1 1 NUM iajs-3598 117 45 2 2 NUM iajs-3598 117 46 οΏ½ οΏ½ PROPN iajs-3598 117 47 Μ‡ Μ‡ NOUN iajs-3598 117 48 οΏ½ οΏ½ PROPN iajs-3598 117 49 3𝐿1 3𝐿1 NUM iajs-3598 117 50 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 117 51 2 2 NUM iajs-3598 117 52 + + NUM iajs-3598 117 53 οΏ½ οΏ½ PROPN iajs-3598 117 54 Μ‡ Μ‡ VERB iajs-3598 117 55 οΏ½ οΏ½ PROPN iajs-3598 117 56 1 1 NUM iajs-3598 117 57 2 2 NUM iajs-3598 117 58 οΏ½ οΏ½ PROPN iajs-3598 117 59 Μ‡ Μ‡ NOUN iajs-3598 117 60 οΏ½ οΏ½ PROPN iajs-3598 117 61 3𝐢1𝐿1(π‘Ž1 3𝐢1𝐿1(π‘Ž1 NUM iajs-3598 117 62 + + NOUN iajs-3598 117 63 2𝐿1 2𝐿1 NUM iajs-3598 117 64 ) ) PUNCT iajs-3598 117 65 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 117 66 2 2 NUM iajs-3598 117 67 + + SYM iajs-3598 117 68 4 4 NUM iajs-3598 117 69 οΏ½ οΏ½ NOUN iajs-3598 117 70 Μ‡ Μ‡ VERB iajs-3598 117 71 οΏ½ οΏ½ PROPN iajs-3598 117 72 1 1 NUM iajs-3598 117 73 2 2 NUM iajs-3598 117 74 οΏ½ οΏ½ PROPN iajs-3598 117 75 Μ‡ Μ‡ NOUN iajs-3598 117 76 οΏ½ οΏ½ PROPN iajs-3598 117 77 3𝐢1π‘Ž1𝐿1 3𝐢1π‘Ž1𝐿1 NUM iajs-3598 117 78 ( ( PUNCT iajs-3598 117 79 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 117 80 2 2 NUM iajs-3598 117 81 ) ) SYM iajs-3598 117 82 2 2 NUM iajs-3598 117 83 + + SYM iajs-3598 117 84 2𝐢2 2𝐢2 NUM iajs-3598 117 85 οΏ½ οΏ½ PROPN iajs-3598 117 86 Μ‡ Μ‡ NOUN iajs-3598 117 87 οΏ½ οΏ½ PROPN iajs-3598 117 88 2 2 NUM iajs-3598 117 89 2 2 NUM iajs-3598 117 90 οΏ½ οΏ½ PROPN iajs-3598 117 91 Μ‡ Μ‡ VERB iajs-3598 117 92 οΏ½ οΏ½ PROPN iajs-3598 117 93 4π‘Ž2 4π‘Ž2 NUM iajs-3598 117 94 2𝐿3 2𝐿3 NUM iajs-3598 117 95 ( ( PUNCT iajs-3598 117 96 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 117 97 + + SYM iajs-3598 117 98 οΏ½ οΏ½ PROPN iajs-3598 117 99 Μ‡ Μ‡ NOUN iajs-3598 117 100 οΏ½ οΏ½ PROPN iajs-3598 117 101 2 2 NUM iajs-3598 117 102 2 2 NUM iajs-3598 117 103 οΏ½ οΏ½ NOUN iajs-3598 117 104 Μ‡ Μ‡ NOUN iajs-3598 117 105 οΏ½ οΏ½ DET iajs-3598 117 106 4𝐢2π‘Ž2 4𝐢2π‘Ž2 PROPN iajs-3598 117 107 ( ( PUNCT iajs-3598 117 108 1+π‘Ž2𝐿2 1+π‘Ž2𝐿2 PROPN iajs-3598 117 109 ) ) PUNCT iajs-3598 117 110 + + CCONJ iajs-3598 117 111 οΏ½ οΏ½ PROPN iajs-3598 117 112 Μ‡ Μ‡ VERB iajs-3598 117 113 οΏ½ οΏ½ PROPN iajs-3598 117 114 2 2 NUM iajs-3598 117 115 οΏ½ οΏ½ PROPN iajs-3598 117 116 Μ‡ Μ‡ PROPN iajs-3598 117 117 οΏ½ οΏ½ PROPN iajs-3598 117 118 4𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 4𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 117 119 ) ) PUNCT iajs-3598 117 120 ( ( PUNCT iajs-3598 117 121 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 117 122 + + CCONJ iajs-3598 117 123 𝐢2 𝐢2 PROPN iajs-3598 117 124 οΏ½ οΏ½ PROPN iajs-3598 117 125 Μ‡ Μ‡ NOUN iajs-3598 117 126 οΏ½ οΏ½ PROPN iajs-3598 117 127 1 1 NUM iajs-3598 117 128 2 2 NUM iajs-3598 117 129 οΏ½ οΏ½ NOUN iajs-3598 117 130 Μ‡ Μ‡ NOUN iajs-3598 117 131 οΏ½ οΏ½ NOUN iajs-3598 117 132 4 4 NUM iajs-3598 117 133 ( ( PUNCT iajs-3598 117 134 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 117 135 + + CCONJ iajs-3598 117 136 4𝑆2 4𝑆2 NUM iajs-3598 117 137 οΏ½ οΏ½ PROPN iajs-3598 117 138 Μ‡ Μ‡ VERB iajs-3598 117 139 οΏ½ οΏ½ PROPN iajs-3598 117 140 2 2 NUM iajs-3598 117 141 οΏ½ οΏ½ PROPN iajs-3598 117 142 Μ‡ Μ‡ NOUN iajs-3598 117 143 οΏ½ οΏ½ NOUN iajs-3598 117 144 4𝑓1𝐿3 4𝑓1𝐿3 NUM iajs-3598 117 145 ( ( PUNCT iajs-3598 117 146 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 117 147 + + SYM iajs-3598 117 148 2 2 NUM iajs-3598 117 149 οΏ½ οΏ½ NOUN iajs-3598 117 150 Μ‡ Μ‡ VERB iajs-3598 117 151 οΏ½ οΏ½ PROPN iajs-3598 117 152 2 2 NUM iajs-3598 117 153 οΏ½ οΏ½ PROPN iajs-3598 117 154 Μ‡ Μ‡ NOUN iajs-3598 117 155 οΏ½ οΏ½ PROPN iajs-3598 117 156 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 117 157 ( ( PUNCT iajs-3598 117 158 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 NUM iajs-3598 117 159 ) ) PUNCT iajs-3598 117 160 + + CCONJ iajs-3598 118 1 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 118 2 2(1βˆ’2𝑓1𝐿3 2(1βˆ’2𝑓1𝐿3 NUM iajs-3598 118 3 ) ) PUNCT iajs-3598 118 4 ( ( PUNCT iajs-3598 118 5 1+𝑓1𝐿3)6 1+𝑓1𝐿3)6 NUM iajs-3598 118 6 + + CCONJ iajs-3598 118 7 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 118 8 ( ( PUNCT iajs-3598 118 9 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 118 10 + + SYM iajs-3598 118 11 2𝑔1 2𝑔1 NUM iajs-3598 118 12 οΏ½ οΏ½ NOUN iajs-3598 118 13 Μ‡ Μ‡ NOUN iajs-3598 118 14 οΏ½ οΏ½ PROPN iajs-3598 118 15 1 1 NUM iajs-3598 118 16 3𝐿3(π‘Ž1βˆ’πΏ1 3𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 118 17 2 2 NUM iajs-3598 118 18 ) ) PUNCT iajs-3598 118 19 ( ( PUNCT iajs-3598 118 20 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 21 2 2 NUM iajs-3598 118 22 ) ) PUNCT iajs-3598 118 23 2 2 NUM iajs-3598 118 24 + + NUM iajs-3598 118 25 6π‘Ž2 6π‘Ž2 NUM iajs-3598 118 26 2𝑔2 2𝑔2 NUM iajs-3598 118 27 οΏ½ οΏ½ NOUN iajs-3598 118 28 Μ‡ Μ‡ NOUN iajs-3598 118 29 οΏ½ οΏ½ PROPN iajs-3598 118 30 1 1 NUM iajs-3598 118 31 3𝐿3 3𝐿3 NUM iajs-3598 118 32 ( ( PUNCT iajs-3598 118 33 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 118 34 ) ) PUNCT iajs-3598 118 35 + + CCONJ iajs-3598 118 36 2π‘Ž2 2π‘Ž2 NUM iajs-3598 118 37 2𝑔2 2𝑔2 NUM iajs-3598 118 38 οΏ½ οΏ½ NOUN iajs-3598 118 39 Μ‡ Μ‡ VERB iajs-3598 118 40 οΏ½ οΏ½ PROPN iajs-3598 118 41 2 2 NUM iajs-3598 118 42 2𝐿2 2𝐿2 NUM iajs-3598 118 43 ( ( PUNCT iajs-3598 118 44 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 118 45 + + CCONJ iajs-3598 118 46 2𝑔1 2𝑔1 NUM iajs-3598 118 47 οΏ½ οΏ½ NOUN iajs-3598 118 48 Μ‡ Μ‡ NOUN iajs-3598 118 49 οΏ½ οΏ½ PROPN iajs-3598 118 50 1 1 NUM iajs-3598 118 51 2𝐿1 2𝐿1 NUM iajs-3598 118 52 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 53 2 2 NUM iajs-3598 118 54 + + CCONJ iajs-3598 118 55 π‘Ž3𝑔2 π‘Ž3𝑔2 NOUN iajs-3598 118 56 οΏ½ οΏ½ NOUN iajs-3598 118 57 Μ‡ Μ‡ NOUN iajs-3598 118 58 οΏ½ οΏ½ X iajs-3598 118 59 2 2 NUM iajs-3598 118 60 ( ( PUNCT iajs-3598 118 61 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 118 62 ( ( PUNCT iajs-3598 118 63 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 118 64 + + NUM iajs-3598 118 65 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 118 66 ) ) PUNCT iajs-3598 118 67 , , PUNCT iajs-3598 118 68 οΏ½ οΏ½ PROPN iajs-3598 118 69 Μ‡ Μ‡ PROPN iajs-3598 118 70 οΏ½ οΏ½ PROPN iajs-3598 118 71 4 4 NUM iajs-3598 118 72 = = SYM iajs-3598 118 73 οΏ½ οΏ½ PROPN iajs-3598 118 74 Μ‡ Μ‡ NOUN iajs-3598 118 75 οΏ½ οΏ½ PROPN iajs-3598 118 76 1 1 NUM iajs-3598 118 77 2 2 NUM iajs-3598 118 78 οΏ½ οΏ½ PROPN iajs-3598 118 79 Μ‡ Μ‡ NOUN iajs-3598 118 80 οΏ½ οΏ½ PROPN iajs-3598 118 81 3𝐢1𝐿1 3𝐢1𝐿1 NUM iajs-3598 118 82 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 83 2 2 NUM iajs-3598 118 84 + + SYM iajs-3598 118 85 2 2 NUM iajs-3598 118 86 οΏ½ οΏ½ NOUN iajs-3598 118 87 Μ‡ Μ‡ NOUN iajs-3598 118 88 οΏ½ οΏ½ PROPN iajs-3598 118 89 1 1 NUM iajs-3598 118 90 2 2 NUM iajs-3598 118 91 οΏ½ οΏ½ PROPN iajs-3598 118 92 Μ‡ Μ‡ NOUN iajs-3598 118 93 οΏ½ οΏ½ PROPN iajs-3598 118 94 3𝐢1𝐿1 3𝐢1𝐿1 NUM iajs-3598 118 95 3 3 NUM iajs-3598 118 96 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 97 2 2 NUM iajs-3598 118 98 + + NUM iajs-3598 118 99 οΏ½ οΏ½ PROPN iajs-3598 118 100 Μ‡ Μ‡ VERB iajs-3598 118 101 οΏ½ οΏ½ PROPN iajs-3598 118 102 1 1 NUM iajs-3598 118 103 2 2 NUM iajs-3598 118 104 οΏ½ οΏ½ PROPN iajs-3598 118 105 Μ‡ Μ‡ VERB iajs-3598 118 106 οΏ½ οΏ½ PROPN iajs-3598 118 107 3𝐢1 3𝐢1 NUM iajs-3598 118 108 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 109 2 2 NUM iajs-3598 118 110 + + SYM iajs-3598 118 111 2 2 NUM iajs-3598 118 112 οΏ½ οΏ½ NOUN iajs-3598 118 113 Μ‡ Μ‡ NOUN iajs-3598 118 114 οΏ½ οΏ½ PROPN iajs-3598 118 115 1 1 NUM iajs-3598 118 116 2 2 NUM iajs-3598 118 117 οΏ½ οΏ½ PROPN iajs-3598 118 118 Μ‡ Μ‡ VERB iajs-3598 118 119 οΏ½ οΏ½ PROPN iajs-3598 118 120 3 3 NUM iajs-3598 118 121 οΏ½ οΏ½ PROPN iajs-3598 118 122 Μ‡ Μ‡ NOUN iajs-3598 118 123 οΏ½ οΏ½ NOUN iajs-3598 118 124 2𝐢2π‘Ž2𝐿3 2𝐢2π‘Ž2𝐿3 NUM iajs-3598 118 125 ( ( PUNCT iajs-3598 118 126 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 118 127 ) ) PUNCT iajs-3598 118 128 + + CCONJ iajs-3598 118 129 οΏ½ οΏ½ PROPN iajs-3598 118 130 Μ‡ Μ‡ PROPN iajs-3598 118 131 οΏ½ οΏ½ PROPN iajs-3598 118 132 2𝐢2π‘Ž2 2𝐢2π‘Ž2 NUM iajs-3598 118 133 οΏ½ οΏ½ NOUN iajs-3598 118 134 Μ‡ Μ‡ NOUN iajs-3598 118 135 οΏ½ οΏ½ NOUN iajs-3598 118 136 4(1βˆ’π‘Ž3𝐿3 4(1βˆ’π‘Ž3𝐿3 NOUN iajs-3598 118 137 ) ) PUNCT iajs-3598 118 138 ( ( PUNCT iajs-3598 118 139 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 118 140 + + SYM iajs-3598 118 141 2𝑔1 2𝑔1 NUM iajs-3598 118 142 οΏ½ οΏ½ PROPN iajs-3598 118 143 Μ‡ Μ‡ NOUN iajs-3598 118 144 οΏ½ οΏ½ PROPN iajs-3598 118 145 1 1 NUM iajs-3598 118 146 2𝐿1(2π‘Ž1 2𝐿1(2π‘Ž1 NUM iajs-3598 118 147 + + NOUN iajs-3598 118 148 1 1 NUM iajs-3598 118 149 ) ) PUNCT iajs-3598 118 150 ( ( PUNCT iajs-3598 118 151 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 118 152 2 2 NUM iajs-3598 118 153 ) ) SYM iajs-3598 118 154 2 2 NUM iajs-3598 118 155 + + SYM iajs-3598 118 156 4π‘Ž2𝑔2 4π‘Ž2𝑔2 NUM iajs-3598 118 157 οΏ½ οΏ½ NOUN iajs-3598 118 158 Μ‡ Μ‡ NOUN iajs-3598 118 159 οΏ½ οΏ½ PROPN iajs-3598 118 160 2 2 NUM iajs-3598 118 161 2 2 NUM iajs-3598 118 162 ( ( PUNCT iajs-3598 118 163 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NOUN iajs-3598 118 164 + + CCONJ iajs-3598 118 165 2π‘Ž3𝑔2 2π‘Ž3𝑔2 NUM iajs-3598 118 166 οΏ½ οΏ½ NOUN iajs-3598 118 167 Μ‡ Μ‡ NOUN iajs-3598 118 168 οΏ½ οΏ½ X iajs-3598 118 169 2 2 NUM iajs-3598 118 170 ( ( PUNCT iajs-3598 118 171 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 118 172 + + NOUN iajs-3598 118 173 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 118 174 ) ) PUNCT iajs-3598 118 175 ( ( PUNCT iajs-3598 118 176 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 X iajs-3598 118 177 . . PUNCT iajs-3598 119 1 then then ADV iajs-3598 119 2 , , PUNCT iajs-3598 119 3 system system NOUN iajs-3598 119 4 ( ( PUNCT iajs-3598 119 5 1 1 NUM iajs-3598 119 6 ) ) PUNCT iajs-3598 119 7 with with ADP iajs-3598 119 8 parameter parameter NOUN iajs-3598 119 9 value value NOUN iajs-3598 119 10 : : PUNCT iajs-3598 119 11 οΏ½ οΏ½ PROPN iajs-3598 119 12 Μ‡ Μ‡ NOUN iajs-3598 119 13 οΏ½ οΏ½ PROPN iajs-3598 119 14 = = PUNCT iajs-3598 119 15 𝑑 𝑑 PROPN iajs-3598 119 16 = = SYM iajs-3598 119 17 βˆ’ βˆ’ PROPN iajs-3598 119 18 ( ( PUNCT iajs-3598 119 19 π‘Ž1+ π‘Ž1+ PROPN iajs-3598 119 20 οΏ½ οΏ½ SYM iajs-3598 119 21 Μ‡ Μ‡ NOUN iajs-3598 119 22 οΏ½ οΏ½ PROPN iajs-3598 119 23 1 1 NUM iajs-3598 119 24 2)(𝑒11𝑒23𝑒32+𝑒13𝑒31𝑒22)+𝑔1 2)(𝑒11𝑒23𝑒32+𝑒13𝑒31𝑒22)+𝑔1 NUM iajs-3598 119 25 οΏ½ οΏ½ PROPN iajs-3598 119 26 Μ‡ Μ‡ VERB iajs-3598 119 27 οΏ½ οΏ½ PROPN iajs-3598 119 28 1𝑒11𝑒22βˆ’πœ‡ 1𝑒11𝑒22βˆ’πœ‡ NUM iajs-3598 119 29 οΏ½ οΏ½ PROPN iajs-3598 119 30 Μ‡ Μ‡ PROPN iajs-3598 119 31 οΏ½ οΏ½ PROPN iajs-3598 119 32 1𝑒11𝑒22(π‘Ž1+ 1𝑒11𝑒22(π‘Ž1+ NUM iajs-3598 119 33 οΏ½ οΏ½ NOUN iajs-3598 119 34 Μ‡ Μ‡ NOUN iajs-3598 119 35 οΏ½ οΏ½ PROPN iajs-3598 119 36 1 1 NUM iajs-3598 119 37 2 2 NUM iajs-3598 119 38 ) ) PUNCT iajs-3598 119 39 𝑒11𝑒22(π‘Ž1+ 𝑒11𝑒22(π‘Ž1+ X iajs-3598 119 40 οΏ½ οΏ½ NOUN iajs-3598 119 41 Μ‡ Μ‡ NOUN iajs-3598 119 42 οΏ½ οΏ½ PROPN iajs-3598 119 43 1 1 NUM iajs-3598 119 44 2 2 NUM iajs-3598 119 45 ) ) PUNCT iajs-3598 119 46 , , PUNCT iajs-3598 119 47 has have VERB iajs-3598 119 48 a a DET iajs-3598 119 49 transcritical transcritical ADJ iajs-3598 119 50 and and CCONJ iajs-3598 119 51 pitch pitch NOUN iajs-3598 119 52 fork fork NOUN iajs-3598 119 53 bifurcation bifurcation NOUN iajs-3598 119 54 at at ADP iajs-3598 119 55 𝐻4 𝐻4 PROPN iajs-3598 119 56 , , PUNCT iajs-3598 119 57 similary similary ADJ iajs-3598 119 58 for for ADP iajs-3598 119 59 𝐻5 𝐻5 NOUN iajs-3598 119 60 proof proof NOUN iajs-3598 119 61 : : PUNCT iajs-3598 119 62 using use VERB iajs-3598 119 63 the the DET iajs-3598 119 64 jacobian jacobian ADJ iajs-3598 119 65 matrix matrix NOUN iajs-3598 119 66 in in ADP iajs-3598 119 67 eq eq PROPN iajs-3598 119 68 . . PUNCT iajs-3598 120 1 ( ( PUNCT iajs-3598 120 2 1.9 1.9 NUM iajs-3598 120 3 ) ) PUNCT iajs-3598 120 4 in in ADP iajs-3598 120 5 ( ( PUNCT iajs-3598 120 6 22 22 NUM iajs-3598 120 7 ) ) PUNCT iajs-3598 120 8 𝐽4Μ‡ 𝐽4Μ‡ NOUN iajs-3598 120 9 = = SYM iajs-3598 120 10 𝐽4(𝐻4 𝐽4(𝐻4 PROPN iajs-3598 120 11 , , PUNCT iajs-3598 120 12 οΏ½ οΏ½ PROPN iajs-3598 120 13 Μ‡ Μ‡ PROPN iajs-3598 120 14 οΏ½ οΏ½ PROPN iajs-3598 120 15 ) ) PUNCT iajs-3598 120 16 = = PUNCT iajs-3598 121 1 [ [ PUNCT iajs-3598 121 2 οΏ½ οΏ½ PROPN iajs-3598 121 3 Μ‡ Μ‡ PROPN iajs-3598 121 4 οΏ½ οΏ½ PROPN iajs-3598 121 5 𝑖𝑗 𝑖𝑗 NOUN iajs-3598 121 6 ] ] X iajs-3598 121 7 3Γ—3 3Γ—3 NUM iajs-3598 121 8 , , PUNCT iajs-3598 121 9 where where SCONJ iajs-3598 121 10 οΏ½ οΏ½ PROPN iajs-3598 121 11 Μ‡ Μ‡ PROPN iajs-3598 121 12 οΏ½ οΏ½ PROPN iajs-3598 121 13 𝑖𝑗 𝑖𝑗 NOUN iajs-3598 121 14 = = SYM iajs-3598 121 15 𝑒𝑖𝑗 𝑒𝑖𝑗 NOUN iajs-3598 121 16 , , PUNCT iajs-3598 121 17 except except SCONJ iajs-3598 121 18 οΏ½ οΏ½ PROPN iajs-3598 121 19 Μ‡ Μ‡ PROPN iajs-3598 121 20 οΏ½ οΏ½ PROPN iajs-3598 121 21 33 33 NUM iajs-3598 121 22 = = PROPN iajs-3598 121 23 𝑔1 𝑔1 PROPN iajs-3598 121 24 οΏ½ οΏ½ PROPN iajs-3598 121 25 Μ‡ Μ‡ PROPN iajs-3598 121 26 οΏ½ οΏ½ PROPN iajs-3598 121 27 1 1 NUM iajs-3598 121 28 ( ( PUNCT iajs-3598 121 29 π‘Ž1+ π‘Ž1+ PROPN iajs-3598 121 30 οΏ½ οΏ½ SYM iajs-3598 121 31 Μ‡ Μ‡ VERB iajs-3598 121 32 οΏ½ οΏ½ PROPN iajs-3598 121 33 1 1 NUM iajs-3598 121 34 2 2 NUM iajs-3598 121 35 ) ) PUNCT iajs-3598 121 36 βˆ’ βˆ’ PROPN iajs-3598 121 37 πœ‡ πœ‡ ADP iajs-3598 121 38 οΏ½ οΏ½ PROPN iajs-3598 121 39 Μ‡ Μ‡ VERB iajs-3598 121 40 οΏ½ οΏ½ PROPN iajs-3598 121 41 1 1 NUM iajs-3598 121 42 βˆ’ βˆ’ PROPN iajs-3598 121 43 οΏ½ οΏ½ PROPN iajs-3598 121 44 Μ‡ Μ‡ PROPN iajs-3598 121 45 οΏ½ οΏ½ PROPN iajs-3598 121 46 . . PUNCT iajs-3598 122 1 the the DET iajs-3598 122 2 characterizing characterizing NOUN iajs-3598 122 3 eq eq NOUN iajs-3598 122 4 . . PROPN iajs-3598 122 5 of of ADP iajs-3598 122 6 𝐽4Μ‡ 𝐽4Μ‡ NOUN iajs-3598 122 7 then then ADV iajs-3598 122 8 has have VERB iajs-3598 122 9 an an DET iajs-3598 122 10 eigenvalue eigenvalue NOUN iajs-3598 122 11 of of ADP iajs-3598 122 12 zero zero NUM iajs-3598 122 13 ( ( PUNCT iajs-3598 122 14 say say INTJ iajs-3598 122 15 Ξ»4l3 Ξ»4l3 X iajs-3598 122 16 ) ) PUNCT iajs-3598 122 17 . . PUNCT iajs-3598 123 1 now now ADV iajs-3598 123 2 , , PUNCT iajs-3598 123 3 let let VERB iajs-3598 123 4 𝑉[2 𝑉[2 PRON iajs-3598 123 5 ] ] X iajs-3598 123 6 = = SYM iajs-3598 123 7 ( ( PUNCT iajs-3598 123 8 𝑣1 𝑣1 NOUN iajs-3598 123 9 [ [ X iajs-3598 123 10 2 2 NUM iajs-3598 123 11 ] ] PUNCT iajs-3598 123 12 , , PUNCT iajs-3598 123 13 𝑣2 𝑣2 X iajs-3598 123 14 [ [ X iajs-3598 123 15 2 2 NUM iajs-3598 123 16 ] ] PUNCT iajs-3598 123 17 , , PUNCT iajs-3598 123 18 𝑣3 𝑣3 ADJ iajs-3598 123 19 [ [ X iajs-3598 123 20 2 2 NUM iajs-3598 123 21 ] ] PUNCT iajs-3598 123 22 ) ) PUNCT iajs-3598 124 1 𝑇be 𝑇be NUM iajs-3598 124 2 the the DET iajs-3598 124 3 eigenvector eigenvector NOUN iajs-3598 124 4 corresponding correspond VERB iajs-3598 124 5 to to ADP iajs-3598 124 6 the the DET iajs-3598 124 7 eigenvalue eigenvalue ADJ iajs-3598 124 8 Ξ»4l3 Ξ»4l3 X iajs-3598 124 9 = = NOUN iajs-3598 124 10 0 0 NUM iajs-3598 124 11 . . PUNCT iajs-3598 124 12 thus,(𝐽4Μ‡ thus,(𝐽4Μ‡ X iajs-3598 125 1 βˆ’ βˆ’ NOUN iajs-3598 125 2 Ξ»4l3 Ξ»4l3 X iajs-3598 125 3 𝐼)𝑉[2 𝐼)𝑉[2 X iajs-3598 125 4 ] ] X iajs-3598 125 5 = = SYM iajs-3598 125 6 0 0 NUM iajs-3598 125 7 , , PUNCT iajs-3598 125 8 this this PRON iajs-3598 125 9 gives give VERB iajs-3598 125 10 : : PUNCT iajs-3598 125 11 𝑣1 𝑣1 NOUN iajs-3598 125 12 [ [ X iajs-3598 125 13 2 2 NUM iajs-3598 125 14 ] ] X iajs-3598 125 15 = = PUNCT iajs-3598 125 16 οΏ½ οΏ½ PROPN iajs-3598 125 17 Μ‡ Μ‡ PROPN iajs-3598 125 18 οΏ½ οΏ½ NOUN iajs-3598 125 19 1𝑣3 1𝑣3 NUM iajs-3598 125 20 [ [ X iajs-3598 125 21 2 2 NUM iajs-3598 125 22 ] ] PUNCT iajs-3598 125 23 , , PUNCT iajs-3598 125 24 𝑣2 𝑣2 X iajs-3598 126 1 [ [ X iajs-3598 126 2 2 2 NUM iajs-3598 126 3 ] ] X iajs-3598 126 4 = = PUNCT iajs-3598 126 5 οΏ½ οΏ½ PROPN iajs-3598 126 6 Μ‡ Μ‡ PROPN iajs-3598 126 7 οΏ½ οΏ½ PROPN iajs-3598 126 8 2𝑣3 2𝑣3 PROPN iajs-3598 126 9 [ [ X iajs-3598 126 10 2 2 NUM iajs-3598 126 11 ] ] PUNCT iajs-3598 126 12 . . PUNCT iajs-3598 127 1 where where SCONJ iajs-3598 127 2 : : PUNCT iajs-3598 127 3 οΏ½ οΏ½ PROPN iajs-3598 127 4 Μ‡ Μ‡ PROPN iajs-3598 127 5 οΏ½ οΏ½ PROPN iajs-3598 127 6 1 1 NUM iajs-3598 127 7 = = SYM iajs-3598 127 8 βˆ’ βˆ’ PROPN iajs-3598 127 9 οΏ½ οΏ½ PROPN iajs-3598 127 10 Μ‡ Μ‡ PROPN iajs-3598 127 11 οΏ½ οΏ½ PROPN iajs-3598 127 12 13 13 NUM iajs-3598 127 13 οΏ½ οΏ½ PROPN iajs-3598 127 14 Μ‡ Μ‡ PROPN iajs-3598 127 15 οΏ½ οΏ½ PROPN iajs-3598 127 16 11 11 NUM iajs-3598 127 17 , , PUNCT iajs-3598 127 18 οΏ½ οΏ½ PROPN iajs-3598 127 19 Μ‡ Μ‡ NOUN iajs-3598 127 20 οΏ½ οΏ½ PROPN iajs-3598 127 21 2 2 NUM iajs-3598 127 22 = = SYM iajs-3598 127 23 βˆ’ βˆ’ PROPN iajs-3598 127 24 οΏ½ οΏ½ PROPN iajs-3598 127 25 Μ‡ Μ‡ PROPN iajs-3598 127 26 οΏ½ οΏ½ PROPN iajs-3598 127 27 23 23 NUM iajs-3598 127 28 οΏ½ οΏ½ PROPN iajs-3598 127 29 Μ‡ Μ‡ PROPN iajs-3598 127 30 οΏ½ οΏ½ PROPN iajs-3598 127 31 22 22 NUM iajs-3598 127 32 , , PUNCT iajs-3598 127 33 and and CCONJ iajs-3598 127 34 𝑣3 𝑣3 ADJ iajs-3598 128 1 [ [ X iajs-3598 128 2 2 2 NUM iajs-3598 128 3 ] ] PUNCT iajs-3598 128 4 any any DET iajs-3598 128 5 non non ADJ iajs-3598 128 6 - - ADJ iajs-3598 128 7 zero zero ADJ iajs-3598 128 8 real real ADJ iajs-3598 128 9 number number NOUN iajs-3598 128 10 . . PUNCT iajs-3598 129 1 consider consider VERB iajs-3598 129 2 𝑍[2 𝑍[2 PROPN iajs-3598 129 3 ] ] X iajs-3598 130 1 = = SYM iajs-3598 130 2 ( ( PUNCT iajs-3598 130 3 𝑧1 𝑧1 NOUN iajs-3598 130 4 [ [ X iajs-3598 130 5 2 2 NUM iajs-3598 130 6 ] ] PUNCT iajs-3598 130 7 , , PUNCT iajs-3598 130 8 𝑧2 𝑧2 PROPN iajs-3598 130 9 [ [ X iajs-3598 130 10 2 2 NUM iajs-3598 130 11 ] ] PUNCT iajs-3598 130 12 , , PUNCT iajs-3598 130 13 𝑧3 𝑧3 PROPN iajs-3598 130 14 [ [ X iajs-3598 130 15 2 2 NUM iajs-3598 130 16 ] ] PUNCT iajs-3598 130 17 ) ) PUNCT iajs-3598 130 18 𝑇 𝑇 PROPN iajs-3598 130 19 be be VERB iajs-3598 130 20 the the DET iajs-3598 130 21 eigenvector eigenvector NOUN iajs-3598 130 22 connected connect VERB iajs-3598 130 23 with with ADP iajs-3598 130 24 an an DET iajs-3598 130 25 eigenvalue eigenvalue ADJ iajs-3598 130 26 Ξ»4l3 Ξ»4l3 X iajs-3598 130 27 = = NOUN iajs-3598 130 28 0 0 NUM iajs-3598 130 29 of of ADP iajs-3598 130 30 the the DET iajs-3598 130 31 matrix matrix NOUN iajs-3598 130 32 𝐽4Μ‡ 𝐽4Μ‡ NOUN iajs-3598 130 33 𝑇.then 𝑇.then ADV iajs-3598 130 34 , , PUNCT iajs-3598 130 35 ( ( PUNCT iajs-3598 130 36 𝐽4Μ‡ 𝐽4Μ‡ NOUN iajs-3598 130 37 𝑇 𝑇 PROPN iajs-3598 130 38 βˆ’ βˆ’ PROPN iajs-3598 130 39 Ξ»4l3 Ξ»4l3 X iajs-3598 130 40 𝐼 𝐼 PROPN iajs-3598 130 41 ) ) PUNCT iajs-3598 130 42 𝑍[2 𝑍[2 PROPN iajs-3598 130 43 ] ] X iajs-3598 130 44 = = SYM iajs-3598 130 45 0 0 X iajs-3598 130 46 . . PUNCT iajs-3598 131 1 by by ADP iajs-3598 131 2 solving solve VERB iajs-3598 131 3 this this DET iajs-3598 131 4 equation equation NOUN iajs-3598 131 5 for for ADP iajs-3598 131 6 , , PUNCT iajs-3598 131 7 𝑍[2 𝑍[2 PROPN iajs-3598 131 8 ] ] X iajs-3598 131 9 = = SYM iajs-3598 131 10 ( ( PUNCT iajs-3598 131 11 οΏ½ οΏ½ PROPN iajs-3598 131 12 Μ‡ Μ‡ PROPN iajs-3598 131 13 οΏ½ οΏ½ PROPN iajs-3598 131 14 3𝑧3 3𝑧3 NUM iajs-3598 131 15 [ [ X iajs-3598 131 16 2 2 NUM iajs-3598 131 17 ] ] PUNCT iajs-3598 131 18 , , PUNCT iajs-3598 131 19 οΏ½ οΏ½ PROPN iajs-3598 131 20 Μ‡ Μ‡ PROPN iajs-3598 131 21 οΏ½ οΏ½ PROPN iajs-3598 131 22 4𝑧3 4𝑧3 PROPN iajs-3598 131 23 [ [ X iajs-3598 131 24 2 2 NUM iajs-3598 131 25 ] ] PUNCT iajs-3598 131 26 , , PUNCT iajs-3598 131 27 𝑧3 𝑧3 PROPN iajs-3598 131 28 [ [ X iajs-3598 131 29 2 2 NUM iajs-3598 131 30 ] ] PUNCT iajs-3598 131 31 ) ) PUNCT iajs-3598 131 32 𝑇 𝑇 PROPN iajs-3598 131 33 , , PUNCT iajs-3598 131 34 where where SCONJ iajs-3598 131 35 : : PUNCT iajs-3598 131 36 οΏ½ οΏ½ PROPN iajs-3598 131 37 Μ‡ Μ‡ PROPN iajs-3598 131 38 οΏ½ οΏ½ PROPN iajs-3598 131 39 3 3 NUM iajs-3598 131 40 = = SYM iajs-3598 131 41 βˆ’ βˆ’ PROPN iajs-3598 131 42 οΏ½ οΏ½ PROPN iajs-3598 131 43 Μ‡ Μ‡ PROPN iajs-3598 131 44 οΏ½ οΏ½ PROPN iajs-3598 131 45 31 31 NUM iajs-3598 131 46 οΏ½ οΏ½ PROPN iajs-3598 131 47 Μ‡ Μ‡ PROPN iajs-3598 131 48 οΏ½ οΏ½ PROPN iajs-3598 131 49 11 11 NUM iajs-3598 131 50 , , PUNCT iajs-3598 131 51 οΏ½ οΏ½ PROPN iajs-3598 131 52 Μ‡ Μ‡ NOUN iajs-3598 131 53 οΏ½ οΏ½ PROPN iajs-3598 131 54 4 4 NUM iajs-3598 131 55 = = SYM iajs-3598 131 56 βˆ’ βˆ’ PROPN iajs-3598 131 57 𝑒32Μ‡ 𝑒32Μ‡ PROPN iajs-3598 131 58 𝑒22Μ‡ 𝑒22Μ‡ PROPN iajs-3598 131 59 , , PUNCT iajs-3598 131 60 and and CCONJ iajs-3598 131 61 𝑧3 𝑧3 PROPN iajs-3598 131 62 [ [ X iajs-3598 131 63 2 2 X iajs-3598 131 64 ] ] PUNCT iajs-3598 131 65 any any DET iajs-3598 131 66 non non ADJ iajs-3598 131 67 - - ADJ iajs-3598 131 68 zero zero ADJ iajs-3598 131 69 real real ADJ iajs-3598 131 70 number number NOUN iajs-3598 131 71 . . PUNCT iajs-3598 132 1 now now ADV iajs-3598 132 2 , , PUNCT iajs-3598 132 3 consider consider VERB iajs-3598 132 4 that that PRON iajs-3598 132 5 : : PUNCT iajs-3598 132 6 πœ•π‘“ πœ•π‘“ ADJ iajs-3598 132 7 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 132 8 = = SYM iajs-3598 132 9 𝑓𝑑(𝑋 𝑓𝑑(𝑋 PROPN iajs-3598 132 10 , , PUNCT iajs-3598 132 11 𝑑 𝑑 NOUN iajs-3598 132 12 ) ) PUNCT iajs-3598 132 13 = = SYM iajs-3598 132 14 ( ( PUNCT iajs-3598 132 15 πœ•π‘“1 πœ•π‘“1 NOUN iajs-3598 132 16 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 132 17 , , PUNCT iajs-3598 132 18 πœ•π‘“2 πœ•π‘“2 PROPN iajs-3598 132 19 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 132 20 , , PUNCT iajs-3598 132 21 πœ•π‘“3 πœ•π‘“3 PROPN iajs-3598 132 22 πœ•π‘‘ πœ•π‘‘ PROPN iajs-3598 132 23 ) ) PUNCT iajs-3598 132 24 𝑇 𝑇 PROPN iajs-3598 132 25 = = SYM iajs-3598 132 26 ( ( PUNCT iajs-3598 132 27 0,0 0,0 NOUN iajs-3598 132 28 , , PUNCT iajs-3598 132 29 βˆ’πΏ3)𝑇 βˆ’πΏ3)𝑇 PROPN iajs-3598 132 30 . . PUNCT iajs-3598 133 1 so so ADV iajs-3598 133 2 , , PUNCT iajs-3598 133 3 𝑓𝑑(𝐻4 𝑓𝑑(𝐻4 NOUN iajs-3598 133 4 , , PUNCT iajs-3598 133 5 𝑑 𝑑 NOUN iajs-3598 133 6 ) ) PUNCT iajs-3598 133 7 = = SYM iajs-3598 133 8 ( ( PUNCT iajs-3598 133 9 0,0,0)𝑇 0,0,0)𝑇 PRON iajs-3598 133 10 and and CCONJ iajs-3598 133 11 hence hence ADV iajs-3598 133 12 ( ( PUNCT iajs-3598 133 13 𝑍[2 𝑍[2 PROPN iajs-3598 133 14 ] ] X iajs-3598 133 15 ) ) PUNCT iajs-3598 133 16 𝑇 𝑇 PROPN iajs-3598 133 17 𝑓𝑑(𝐻4 𝑓𝑑(𝐻4 NOUN iajs-3598 133 18 , , PUNCT iajs-3598 133 19 𝑑 𝑑 NOUN iajs-3598 133 20 ) ) PUNCT iajs-3598 133 21 = = SYM iajs-3598 133 22 0 0 X iajs-3598 133 23 . . PUNCT iajs-3598 134 1 the the DET iajs-3598 134 2 ( ( PUNCT iajs-3598 134 3 sd sd NOUN iajs-3598 134 4 ) ) PUNCT iajs-3598 134 5 bifurcation bifurcation NOUN iajs-3598 134 6 requirement requirement NOUN iajs-3598 134 7 can can AUX iajs-3598 134 8 not not PART iajs-3598 134 9 be be AUX iajs-3598 134 10 satisfied satisfied ADJ iajs-3598 134 11 according accord VERB iajs-3598 134 12 to to ADP iajs-3598 134 13 sotomayor sotomayor PROPN iajs-3598 134 14 's 's PART iajs-3598 134 15 theorem theorem ADJ iajs-3598 134 16 . . PROPN iajs-3598 135 1 as as ADP iajs-3598 135 2 a a DET iajs-3598 135 3 result result NOUN iajs-3598 135 4 , , PUNCT iajs-3598 135 5 the the DET iajs-3598 135 6 first first ADJ iajs-3598 135 7 requirement requirement NOUN iajs-3598 135 8 for for ADP iajs-3598 135 9 ( ( PUNCT iajs-3598 135 10 tc tc NOUN iajs-3598 135 11 ) ) PUNCT iajs-3598 135 12 bifurcation bifurcation NOUN iajs-3598 135 13 is be AUX iajs-3598 135 14 realized realize VERB iajs-3598 135 15 . . PUNCT iajs-3598 136 1 now now ADV iajs-3598 136 2 ihjpas ihjpa VERB iajs-3598 136 3 . . PUNCT iajs-3598 137 1 2025 2025 NUM iajs-3598 137 2 , , PUNCT iajs-3598 137 3 38 38 NUM iajs-3598 137 4 ( ( PUNCT iajs-3598 137 5 1 1 NUM iajs-3598 137 6 ) ) PUNCT iajs-3598 137 7 435 435 NUM iajs-3598 138 1 𝐷𝑓𝑑(𝑋 𝐷𝑓𝑑(𝑋 NOUN iajs-3598 138 2 , , PUNCT iajs-3598 138 3 𝑑 𝑑 NOUN iajs-3598 138 4 ) ) PUNCT iajs-3598 138 5 = = PUNCT iajs-3598 139 1 [ [ PUNCT iajs-3598 139 2 0 0 NUM iajs-3598 139 3 0 0 NUM iajs-3598 139 4 0 0 NUM iajs-3598 139 5 0 0 NUM iajs-3598 139 6 0 0 NUM iajs-3598 139 7 0 0 NUM iajs-3598 139 8 0 0 NUM iajs-3598 139 9 0 0 NUM iajs-3598 139 10 βˆ’1 βˆ’1 NOUN iajs-3598 139 11 ] ] X iajs-3598 139 12 , , PUNCT iajs-3598 139 13 where where SCONJ iajs-3598 139 14 , , PUNCT iajs-3598 139 15 𝐷𝑓𝑑(𝑋 𝐷𝑓𝑑(𝑋 ADV iajs-3598 139 16 , , PUNCT iajs-3598 139 17 𝑑 𝑑 NOUN iajs-3598 139 18 ) ) PUNCT iajs-3598 139 19 represents represent VERB iajs-3598 139 20 the the DET iajs-3598 139 21 derivative derivative NOUN iajs-3598 139 22 of of ADP iajs-3598 139 23 𝑓𝑑(𝑋 𝑓𝑑(𝑋 ADJ iajs-3598 139 24 , , PUNCT iajs-3598 139 25 𝑑 𝑑 NOUN iajs-3598 139 26 ) ) PUNCT iajs-3598 139 27 with with ADP iajs-3598 139 28 respect respect NOUN iajs-3598 139 29 to to ADP iajs-3598 139 30 𝑋 𝑋 PROPN iajs-3598 139 31 = = SYM iajs-3598 139 32 ( ( PUNCT iajs-3598 139 33 𝐿1 𝐿1 PROPN iajs-3598 139 34 , , PUNCT iajs-3598 139 35 𝐿2 𝐿2 PROPN iajs-3598 139 36 , , PUNCT iajs-3598 139 37 𝐿3)𝑇 𝐿3)𝑇 PUNCT iajs-3598 139 38 . . PUNCT iajs-3598 140 1 furthermore furthermore ADV iajs-3598 140 2 , , PUNCT iajs-3598 140 3 it it PRON iajs-3598 140 4 is be AUX iajs-3598 140 5 observed observe VERB iajs-3598 140 6 that that SCONJ iajs-3598 140 7 : : PUNCT iajs-3598 140 8 𝐷𝑓𝑑(𝐻4 𝐷𝑓𝑑(𝐻4 NOUN iajs-3598 140 9 , , PUNCT iajs-3598 140 10 𝑑)𝑉[2 𝑑)𝑉[2 PROPN iajs-3598 140 11 ] ] PUNCT iajs-3598 140 12 = = PUNCT iajs-3598 140 13 [ [ PUNCT iajs-3598 140 14 0 0 NUM iajs-3598 140 15 0 0 NUM iajs-3598 140 16 0 0 NUM iajs-3598 140 17 0 0 NUM iajs-3598 140 18 0 0 NUM iajs-3598 140 19 0 0 NUM iajs-3598 140 20 0 0 NUM iajs-3598 140 21 0 0 NUM iajs-3598 140 22 βˆ’1 βˆ’1 NOUN iajs-3598 140 23 ] ] PUNCT iajs-3598 140 24 [ [ PUNCT iajs-3598 140 25 οΏ½ οΏ½ NOUN iajs-3598 140 26 Μ‡ Μ‡ PROPN iajs-3598 140 27 οΏ½ οΏ½ NOUN iajs-3598 140 28 1𝑣3 1𝑣3 NUM iajs-3598 140 29 [ [ X iajs-3598 140 30 2 2 NUM iajs-3598 140 31 ] ] PUNCT iajs-3598 140 32 οΏ½ οΏ½ PROPN iajs-3598 140 33 Μ‡ Μ‡ PROPN iajs-3598 140 34 οΏ½ οΏ½ PROPN iajs-3598 140 35 2𝑣3 2𝑣3 PROPN iajs-3598 140 36 [ [ X iajs-3598 140 37 2 2 NUM iajs-3598 140 38 ] ] PUNCT iajs-3598 140 39 𝑣3 𝑣3 ADJ iajs-3598 140 40 [ [ X iajs-3598 140 41 2 2 NUM iajs-3598 140 42 ] ] PUNCT iajs-3598 140 43 ] ] PUNCT iajs-3598 141 1 = = PUNCT iajs-3598 141 2 [ [ PUNCT iajs-3598 141 3 0 0 NUM iajs-3598 141 4 0 0 NUM iajs-3598 141 5 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 141 6 [ [ X iajs-3598 141 7 2 2 X iajs-3598 141 8 ] ] PUNCT iajs-3598 141 9 ] ] X iajs-3598 141 10 ( ( PUNCT iajs-3598 141 11 𝑍[2 𝑍[2 PROPN iajs-3598 141 12 ] ] PUNCT iajs-3598 141 13 ) ) PUNCT iajs-3598 141 14 𝑇 𝑇 PROPN iajs-3598 142 1 [ [ X iajs-3598 142 2 𝐷𝑓𝑑(𝐻4 𝐷𝑓𝑑(𝐻4 PROPN iajs-3598 142 3 , , PUNCT iajs-3598 142 4 𝑑)𝑉[2 𝑑)𝑉[2 PROPN iajs-3598 142 5 ] ] X iajs-3598 142 6 ] ] X iajs-3598 142 7 = = SYM iajs-3598 142 8 ( ( PUNCT iajs-3598 142 9 οΏ½ οΏ½ PROPN iajs-3598 142 10 Μ‡ Μ‡ PROPN iajs-3598 142 11 οΏ½ οΏ½ PROPN iajs-3598 142 12 3𝑧3 3𝑧3 NUM iajs-3598 142 13 [ [ X iajs-3598 142 14 2 2 NUM iajs-3598 142 15 ] ] PUNCT iajs-3598 142 16 , , PUNCT iajs-3598 142 17 οΏ½ οΏ½ PROPN iajs-3598 142 18 Μ‡ Μ‡ PROPN iajs-3598 142 19 οΏ½ οΏ½ PROPN iajs-3598 142 20 4𝑧3 4𝑧3 PROPN iajs-3598 142 21 [ [ X iajs-3598 142 22 2 2 NUM iajs-3598 142 23 ] ] PUNCT iajs-3598 142 24 , , PUNCT iajs-3598 142 25 𝑧3 𝑧3 PROPN iajs-3598 142 26 [ [ X iajs-3598 142 27 2 2 NUM iajs-3598 142 28 ] ] PUNCT iajs-3598 142 29 ) ) PUNCT iajs-3598 142 30 𝑇 𝑇 PROPN iajs-3598 142 31 ( ( PUNCT iajs-3598 142 32 0,0 0,0 NOUN iajs-3598 142 33 , , PUNCT iajs-3598 142 34 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 143 1 [ [ X iajs-3598 143 2 2 2 NUM iajs-3598 143 3 ] ] PUNCT iajs-3598 143 4 ) ) PUNCT iajs-3598 144 1 = = PUNCT iajs-3598 144 2 βˆ’π‘£3 βˆ’π‘£3 PROPN iajs-3598 145 1 [ [ X iajs-3598 145 2 2 2 X iajs-3598 145 3 ] ] X iajs-3598 145 4 𝑧3 𝑧3 NOUN iajs-3598 145 5 [ [ X iajs-3598 145 6 2 2 NUM iajs-3598 145 7 ] ] PUNCT iajs-3598 145 8 β‰  β‰  PROPN iajs-3598 145 9 0 0 NUM iajs-3598 145 10 𝐷2πΉπœ‡(𝐻4 𝐷2πΉπœ‡(𝐻4 PROPN iajs-3598 145 11 , , PUNCT iajs-3598 145 12 𝑑)(𝑉[2 𝑑)(𝑉[2 PROPN iajs-3598 145 13 ] ] X iajs-3598 145 14 , , PUNCT iajs-3598 145 15 𝑉[2 𝑉[2 PROPN iajs-3598 145 16 ] ] PUNCT iajs-3598 145 17 ) ) PUNCT iajs-3598 145 18 = = PUNCT iajs-3598 146 1 [ [ X iajs-3598 146 2 𝐴𝑖1 𝐴𝑖1 ADV iajs-3598 146 3 Μ‡ Μ‡ VERB iajs-3598 146 4 ] ] PUNCT iajs-3598 146 5 3Γ—1 3Γ—1 NUM iajs-3598 146 6 οΏ½ οΏ½ PROPN iajs-3598 146 7 Μ‡ Μ‡ PROPN iajs-3598 146 8 οΏ½ οΏ½ PROPN iajs-3598 146 9 11 11 NUM iajs-3598 146 10 = = SYM iajs-3598 146 11 βˆ’ βˆ’ PROPN iajs-3598 146 12 2𝑆1 2𝑆1 NUM iajs-3598 146 13 𝐾1 𝐾1 NOUN iajs-3598 147 1 + + CCONJ iajs-3598 147 2 ( ( PUNCT iajs-3598 147 3 𝑣3 𝑣3 ADJ iajs-3598 147 4 [ [ X iajs-3598 147 5 2 2 NUM iajs-3598 147 6 ] ] PUNCT iajs-3598 147 7 ) ) PUNCT iajs-3598 147 8 2 2 NUM iajs-3598 147 9 [ [ PUNCT iajs-3598 147 10 4π‘Ž1𝐢1𝛼1Μ‡ 4π‘Ž1𝐢1𝛼1Μ‡ NUM iajs-3598 147 11 2𝐿1𝐿3 2𝐿1𝐿3 NUM iajs-3598 147 12 ( ( PUNCT iajs-3598 147 13 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 147 14 2 2 NUM iajs-3598 147 15 ) ) PUNCT iajs-3598 147 16 2 2 NUM iajs-3598 147 17 βˆ’ βˆ’ PROPN iajs-3598 147 18 𝐢1 𝐢1 NUM iajs-3598 147 19 οΏ½ οΏ½ NOUN iajs-3598 147 20 Μ‡ Μ‡ NOUN iajs-3598 147 21 οΏ½ οΏ½ PROPN iajs-3598 147 22 1 1 NUM iajs-3598 147 23 ( ( PUNCT iajs-3598 147 24 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 147 25 2 2 NUM iajs-3598 147 26 ) ) PUNCT iajs-3598 147 27 ( ( PUNCT iajs-3598 147 28 ( ( PUNCT iajs-3598 147 29 π‘Ž1 π‘Ž1 X iajs-3598 147 30 + + CCONJ iajs-3598 147 31 𝐿1 𝐿1 PROPN iajs-3598 147 32 2 2 NUM iajs-3598 147 33 ) ) PUNCT iajs-3598 147 34 + + CCONJ iajs-3598 147 35 ( ( PUNCT iajs-3598 147 36 π‘Ž1 π‘Ž1 X iajs-3598 147 37 + + PRON iajs-3598 147 38 2𝐿1 2𝐿1 NUM iajs-3598 147 39 ) ) PUNCT iajs-3598 147 40 ) ) PUNCT iajs-3598 148 1 + + CCONJ iajs-3598 149 1 2𝐢1𝛼1̇𝐿1 2𝐢1𝛼1̇𝐿1 NUM iajs-3598 149 2 2 2 NUM iajs-3598 149 3 ( ( PUNCT iajs-3598 149 4 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 149 5 2 2 NUM iajs-3598 149 6 ) ) PUNCT iajs-3598 149 7 ] ] PUNCT iajs-3598 149 8 , , PUNCT iajs-3598 149 9 οΏ½ οΏ½ PROPN iajs-3598 149 10 Μ‡ Μ‡ PROPN iajs-3598 149 11 οΏ½ οΏ½ PROPN iajs-3598 149 12 21 21 NUM iajs-3598 149 13 = = SYM iajs-3598 149 14 βˆ’2𝐢 βˆ’2𝐢 NOUN iajs-3598 149 15 + + CCONJ iajs-3598 149 16 ( ( PUNCT iajs-3598 149 17 𝑣3 𝑣3 ADJ iajs-3598 149 18 [ [ X iajs-3598 149 19 2 2 NUM iajs-3598 149 20 ] ] PUNCT iajs-3598 149 21 ) ) PUNCT iajs-3598 149 22 2 2 NUM iajs-3598 149 23 [ [ PUNCT iajs-3598 149 24 οΏ½ οΏ½ NOUN iajs-3598 149 25 Μ‡ Μ‡ NOUN iajs-3598 149 26 οΏ½ οΏ½ PROPN iajs-3598 149 27 1 1 NUM iajs-3598 149 28 2𝐢2𝐿3 2𝐢2𝐿3 NUM iajs-3598 149 29 ( ( PUNCT iajs-3598 149 30 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 149 31 ) ) PUNCT iajs-3598 149 32 βˆ’ βˆ’ PROPN iajs-3598 149 33 ( ( PUNCT iajs-3598 149 34 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 149 35 ( ( PUNCT iajs-3598 149 36 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 149 37 + + CCONJ iajs-3598 149 38 𝐢2 𝐢2 PROPN iajs-3598 149 39 ( ( PUNCT iajs-3598 149 40 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 149 41 ) ) PUNCT iajs-3598 149 42 οΏ½ οΏ½ PROPN iajs-3598 149 43 Μ‡ Μ‡ VERB iajs-3598 149 44 οΏ½ οΏ½ PROPN iajs-3598 149 45 2 2 NUM iajs-3598 149 46 + + NUM iajs-3598 149 47 οΏ½ οΏ½ PROPN iajs-3598 149 48 Μ‡ Μ‡ PROPN iajs-3598 149 49 οΏ½ οΏ½ PROPN iajs-3598 149 50 2𝐢2π‘Ž2𝐿3 2𝐢2π‘Ž2𝐿3 NUM iajs-3598 149 51 ( ( PUNCT iajs-3598 149 52 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 149 53 + + CCONJ iajs-3598 149 54 ( ( PUNCT iajs-3598 149 55 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 149 56 2𝐿3 2𝐿3 NUM iajs-3598 149 57 ( ( PUNCT iajs-3598 149 58 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 149 59 βˆ’ βˆ’ PROPN iajs-3598 149 60 𝐢2(1βˆ’π‘Ž3𝐿3 𝐢2(1βˆ’π‘Ž3𝐿3 PROPN iajs-3598 149 61 ) ) PUNCT iajs-3598 149 62 ( ( PUNCT iajs-3598 149 63 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 149 64 ) ) PUNCT iajs-3598 149 65 ] ] PUNCT iajs-3598 149 66 , , PUNCT iajs-3598 149 67 οΏ½ οΏ½ PROPN iajs-3598 149 68 Μ‡ Μ‡ PROPN iajs-3598 149 69 οΏ½ οΏ½ PROPN iajs-3598 149 70 31 31 NUM iajs-3598 149 71 = = SYM iajs-3598 149 72 ( ( PUNCT iajs-3598 149 73 𝑣3 𝑣3 PROPN iajs-3598 149 74 [ [ X iajs-3598 149 75 2 2 NUM iajs-3598 149 76 ] ] PUNCT iajs-3598 149 77 ) ) PUNCT iajs-3598 149 78 2 2 NUM iajs-3598 149 79 [ [ PUNCT iajs-3598 149 80 2𝑔1 2𝑔1 NUM iajs-3598 149 81 οΏ½ οΏ½ PROPN iajs-3598 149 82 Μ‡ Μ‡ NOUN iajs-3598 149 83 οΏ½ οΏ½ PROPN iajs-3598 149 84 1 1 NUM iajs-3598 149 85 2𝐿1𝐿3 2𝐿1𝐿3 NUM iajs-3598 149 86 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 149 87 2 2 NUM iajs-3598 149 88 + + CCONJ iajs-3598 149 89 ( ( PUNCT iajs-3598 149 90 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 149 91 2 2 NUM iajs-3598 149 92 ) ) PUNCT iajs-3598 149 93 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 149 94 2 2 NUM iajs-3598 149 95 + + NUM iajs-3598 149 96 𝑔1 𝑔1 PROPN iajs-3598 149 97 ) ) PUNCT iajs-3598 149 98 οΏ½ οΏ½ PROPN iajs-3598 149 99 Μ‡ Μ‡ VERB iajs-3598 149 100 οΏ½ οΏ½ PROPN iajs-3598 149 101 1 1 NUM iajs-3598 149 102 βˆ’ βˆ’ PROPN iajs-3598 149 103 2πœ‡ 2πœ‡ PROPN iajs-3598 149 104 οΏ½ οΏ½ PROPN iajs-3598 149 105 Μ‡ Μ‡ PROPN iajs-3598 149 106 οΏ½ οΏ½ PROPN iajs-3598 149 107 1 1 NUM iajs-3598 149 108 βˆ’ βˆ’ PROPN iajs-3598 149 109 2π‘Ž2𝑔2 2π‘Ž2𝑔2 NUM iajs-3598 149 110 οΏ½ οΏ½ NOUN iajs-3598 149 111 Μ‡ Μ‡ NOUN iajs-3598 149 112 οΏ½ οΏ½ PROPN iajs-3598 149 113 2 2 NUM iajs-3598 149 114 2𝐿3 2𝐿3 NUM iajs-3598 149 115 ( ( PUNCT iajs-3598 149 116 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 149 117 ) ) PUNCT iajs-3598 149 118 βˆ’ βˆ’ PROPN iajs-3598 150 1 π‘Ž2𝐿2𝑔2 π‘Ž2𝐿2𝑔2 PROPN iajs-3598 150 2 οΏ½ οΏ½ PROPN iajs-3598 150 3 Μ‡ Μ‡ NOUN iajs-3598 150 4 οΏ½ οΏ½ X iajs-3598 150 5 2 2 NUM iajs-3598 150 6 ( ( PUNCT iajs-3598 150 7 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 150 8 + + CCONJ iajs-3598 150 9 𝑔2 𝑔2 NOUN iajs-3598 150 10 οΏ½ οΏ½ NOUN iajs-3598 150 11 Μ‡ Μ‡ NOUN iajs-3598 150 12 οΏ½ οΏ½ X iajs-3598 150 13 2 2 NUM iajs-3598 150 14 ( ( PUNCT iajs-3598 150 15 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 VERB iajs-3598 150 16 βˆ’ βˆ’ NOUN iajs-3598 150 17 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 150 18 ( ( PUNCT iajs-3598 150 19 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 150 20 ] ] PUNCT iajs-3598 150 21 . . PUNCT iajs-3598 151 1 hence hence ADV iajs-3598 151 2 , , PUNCT iajs-3598 151 3 it it PRON iajs-3598 151 4 was be AUX iajs-3598 151 5 obtained obtain VERB iajs-3598 151 6 . . PUNCT iajs-3598 152 1 ( ( PUNCT iajs-3598 152 2 𝑍[2 𝑍[2 PROPN iajs-3598 152 3 ] ] PUNCT iajs-3598 152 4 ) ) PUNCT iajs-3598 152 5 𝑇 𝑇 PROPN iajs-3598 153 1 [ [ X iajs-3598 153 2 𝐷2πΉπœ‡(𝐻4 𝐷2πΉπœ‡(𝐻4 PROPN iajs-3598 153 3 , , PUNCT iajs-3598 153 4 𝑑)(𝑉[2 𝑑)(𝑉[2 PROPN iajs-3598 153 5 ] ] X iajs-3598 153 6 , , PUNCT iajs-3598 153 7 𝑉[2 𝑉[2 PROPN iajs-3598 153 8 ] ] PUNCT iajs-3598 153 9 ) ) PUNCT iajs-3598 153 10 ] ] PUNCT iajs-3598 154 1 = = PUNCT iajs-3598 154 2 𝑧3 𝑧3 PROPN iajs-3598 154 3 [ [ X iajs-3598 154 4 2 2 NUM iajs-3598 154 5 ] ] PUNCT iajs-3598 154 6 ( ( PUNCT iajs-3598 154 7 οΏ½ οΏ½ PROPN iajs-3598 154 8 Μ‡ Μ‡ NOUN iajs-3598 154 9 οΏ½ οΏ½ PROPN iajs-3598 154 10 1 1 NUM iajs-3598 154 11 βˆ’ βˆ’ PROPN iajs-3598 154 12 οΏ½ οΏ½ PROPN iajs-3598 154 13 Μ‡ Μ‡ NOUN iajs-3598 154 14 οΏ½ οΏ½ PROPN iajs-3598 154 15 2 2 NUM iajs-3598 154 16 ) ) PUNCT iajs-3598 154 17 β‰  β‰  PROPN iajs-3598 154 18 0 0 NUM iajs-3598 154 19 , , PUNCT iajs-3598 154 20 this this PRON iajs-3598 154 21 implies imply VERB iajs-3598 154 22 that that DET iajs-3598 154 23 system system NOUN iajs-3598 154 24 ( ( PUNCT iajs-3598 154 25 1 1 X iajs-3598 154 26 ) ) PUNCT iajs-3598 154 27 has have VERB iajs-3598 154 28 a a DET iajs-3598 154 29 ( ( PUNCT iajs-3598 154 30 tc tc NOUN iajs-3598 154 31 ) ) PUNCT iajs-3598 154 32 bifurcation bifurcation NOUN iajs-3598 154 33 at at ADP iajs-3598 154 34 𝐻4 𝐻4 NOUN iajs-3598 154 35 with with ADP iajs-3598 154 36 a a DET iajs-3598 154 37 parameter parameter NOUN iajs-3598 154 38 οΏ½ οΏ½ NOUN iajs-3598 154 39 Μ‡ Μ‡ PROPN iajs-3598 154 40 οΏ½ οΏ½ PROPN iajs-3598 154 41 = = SYM iajs-3598 154 42 𝑑 𝑑 PROPN iajs-3598 154 43 , , PUNCT iajs-3598 154 44 if if SCONJ iajs-3598 154 45 the the DET iajs-3598 154 46 requirement requirement NOUN iajs-3598 154 47 ( ( PUNCT iajs-3598 154 48 11 11 NUM iajs-3598 154 49 ) ) PUNCT iajs-3598 154 50 unsatisfied unsatisfied ADJ iajs-3598 154 51 then then ADV iajs-3598 154 52 . . PUNCT iajs-3598 155 1 by by ADP iajs-3598 155 2 substituting substitute VERB iajs-3598 155 3 𝑉[2 𝑉[2 PROPN iajs-3598 155 4 ] ] PUNCT iajs-3598 155 5 in in ADP iajs-3598 155 6 ( ( PUNCT iajs-3598 155 7 4 4 X iajs-3598 155 8 ) ) PUNCT iajs-3598 155 9 we we PRON iajs-3598 155 10 get get VERB iajs-3598 155 11 : : PUNCT iajs-3598 155 12 𝐷3πΉπœ‡(𝐻4 𝐷3πΉπœ‡(𝐻4 NUM iajs-3598 155 13 , , PUNCT iajs-3598 155 14 𝑑)(𝑉[2 𝑑)(𝑉[2 PROPN iajs-3598 155 15 ] ] X iajs-3598 155 16 , , PUNCT iajs-3598 155 17 𝑉[2 𝑉[2 PROPN iajs-3598 155 18 ] ] PUNCT iajs-3598 155 19 , , PUNCT iajs-3598 155 20 𝑉[2 𝑉[2 PROPN iajs-3598 155 21 ] ] PUNCT iajs-3598 155 22 ) ) PUNCT iajs-3598 155 23 = = SYM iajs-3598 155 24 ( ( PUNCT iajs-3598 155 25 𝐡𝑖1 𝐡𝑖1 NOUN iajs-3598 155 26 Μ‡ Μ‡ PROPN iajs-3598 155 27 ) ) PUNCT iajs-3598 155 28 3Γ—1 3Γ—1 NUM iajs-3598 155 29 οΏ½ οΏ½ PROPN iajs-3598 155 30 Μ‡ Μ‡ VERB iajs-3598 155 31 οΏ½ οΏ½ PROPN iajs-3598 155 32 11 11 NUM iajs-3598 155 33 = = SYM iajs-3598 155 34 2 2 NUM iajs-3598 155 35 ( ( PUNCT iajs-3598 155 36 𝑣3 𝑣3 ADJ iajs-3598 155 37 [ [ X iajs-3598 155 38 1 1 NUM iajs-3598 155 39 ] ] PUNCT iajs-3598 155 40 ) ) PUNCT iajs-3598 155 41 3 3 NUM iajs-3598 155 42 [ [ PUNCT iajs-3598 155 43 2𝐢1 2𝐢1 NUM iajs-3598 155 44 οΏ½ οΏ½ PROPN iajs-3598 155 45 Μ‡ Μ‡ VERB iajs-3598 155 46 οΏ½ οΏ½ PROPN iajs-3598 155 47 1 1 NUM iajs-3598 155 48 3π‘Ž1𝐿3(1βˆ’4𝐿1 3π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 155 49 2 2 NUM iajs-3598 155 50 ) ) PUNCT iajs-3598 155 51 ( ( PUNCT iajs-3598 155 52 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 53 2 2 NUM iajs-3598 155 54 ) ) SYM iajs-3598 155 55 2 2 NUM iajs-3598 155 56 βˆ’ βˆ’ PROPN iajs-3598 155 57 οΏ½ οΏ½ PROPN iajs-3598 155 58 Μ‡ Μ‡ NOUN iajs-3598 155 59 οΏ½ οΏ½ PROPN iajs-3598 155 60 1 1 NUM iajs-3598 155 61 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 155 62 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 63 2 2 NUM iajs-3598 155 64 + + NUM iajs-3598 155 65 οΏ½ οΏ½ PROPN iajs-3598 155 66 Μ‡ Μ‡ VERB iajs-3598 155 67 οΏ½ οΏ½ PROPN iajs-3598 155 68 1 1 NUM iajs-3598 155 69 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 155 70 + + PROPN iajs-3598 155 71 οΏ½ οΏ½ PROPN iajs-3598 155 72 Μ‡ Μ‡ VERB iajs-3598 155 73 οΏ½ οΏ½ PROPN iajs-3598 155 74 1 1 NUM iajs-3598 155 75 2𝐿1 2𝐿1 NUM iajs-3598 155 76 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 77 2 2 NUM iajs-3598 155 78 βˆ’ βˆ’ PROPN iajs-3598 155 79 2 2 NUM iajs-3598 155 80 οΏ½ οΏ½ NOUN iajs-3598 155 81 Μ‡ Μ‡ NOUN iajs-3598 155 82 οΏ½ οΏ½ PROPN iajs-3598 155 83 1 1 NUM iajs-3598 155 84 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 155 85 3 3 NUM iajs-3598 155 86 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 87 2 2 NUM iajs-3598 155 88 βˆ’ βˆ’ PROPN iajs-3598 155 89 οΏ½ οΏ½ PROPN iajs-3598 155 90 Μ‡ Μ‡ NOUN iajs-3598 155 91 οΏ½ οΏ½ PROPN iajs-3598 155 92 1 1 NUM iajs-3598 155 93 2𝐢1 2𝐢1 NUM iajs-3598 155 94 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 95 2 2 NUM iajs-3598 155 96 + + NUM iajs-3598 155 97 οΏ½ οΏ½ PROPN iajs-3598 155 98 Μ‡ Μ‡ NOUN iajs-3598 155 99 οΏ½ οΏ½ NOUN iajs-3598 155 100 1 1 NUM iajs-3598 155 101 2𝐢1𝐿1(π‘Ž1 2𝐢1𝐿1(π‘Ž1 NUM iajs-3598 155 102 + + NOUN iajs-3598 155 103 2𝐿1 2𝐿1 NUM iajs-3598 155 104 ) ) PUNCT iajs-3598 155 105 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 106 2 2 NUM iajs-3598 155 107 + + SYM iajs-3598 155 108 4 4 NUM iajs-3598 155 109 οΏ½ οΏ½ NOUN iajs-3598 155 110 Μ‡ Μ‡ VERB iajs-3598 155 111 οΏ½ οΏ½ PROPN iajs-3598 155 112 1 1 NUM iajs-3598 155 113 2𝐢1π‘Ž1𝐿1 2𝐢1π‘Ž1𝐿1 NUM iajs-3598 155 114 ( ( PUNCT iajs-3598 155 115 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 155 116 2 2 NUM iajs-3598 155 117 ) ) PUNCT iajs-3598 155 118 2 2 NUM iajs-3598 155 119 ] ] PUNCT iajs-3598 155 120 , , PUNCT iajs-3598 155 121 οΏ½ οΏ½ PROPN iajs-3598 155 122 Μ‡ Μ‡ PROPN iajs-3598 155 123 οΏ½ οΏ½ PROPN iajs-3598 155 124 21 21 NUM iajs-3598 155 125 = = SYM iajs-3598 155 126 ( ( PUNCT iajs-3598 155 127 𝑣3 𝑣3 PROPN iajs-3598 155 128 [ [ X iajs-3598 155 129 1 1 NUM iajs-3598 155 130 ] ] PUNCT iajs-3598 155 131 ) ) PUNCT iajs-3598 155 132 3 3 NUM iajs-3598 156 1 [ [ X iajs-3598 156 2 βˆ’ βˆ’ PROPN iajs-3598 156 3 2 2 NUM iajs-3598 156 4 οΏ½ οΏ½ PROPN iajs-3598 156 5 Μ‡ Μ‡ VERB iajs-3598 156 6 οΏ½ οΏ½ PROPN iajs-3598 156 7 1 1 NUM iajs-3598 156 8 2 2 NUM iajs-3598 156 9 οΏ½ οΏ½ PROPN iajs-3598 156 10 Μ‡ Μ‡ NOUN iajs-3598 156 11 οΏ½ οΏ½ NOUN iajs-3598 156 12 2𝐢2π‘Ž2𝐿3 2𝐢2π‘Ž2𝐿3 NUM iajs-3598 156 13 ( ( PUNCT iajs-3598 156 14 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 156 15 ) ) PUNCT iajs-3598 157 1 + + CCONJ iajs-3598 157 2 2𝐢2 2𝐢2 NUM iajs-3598 157 3 οΏ½ οΏ½ PROPN iajs-3598 157 4 Μ‡ Μ‡ NOUN iajs-3598 157 5 οΏ½ οΏ½ ADP iajs-3598 157 6 2 2 NUM iajs-3598 157 7 2π‘Ž2 2π‘Ž2 NUM iajs-3598 157 8 2𝐿3 2𝐿3 NUM iajs-3598 157 9 ( ( PUNCT iajs-3598 157 10 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 157 11 + + SYM iajs-3598 157 12 οΏ½ οΏ½ PROPN iajs-3598 157 13 Μ‡ Μ‡ VERB iajs-3598 157 14 οΏ½ οΏ½ PROPN iajs-3598 157 15 2 2 NUM iajs-3598 157 16 2𝐢2π‘Ž2 2𝐢2π‘Ž2 NUM iajs-3598 157 17 ( ( PUNCT iajs-3598 157 18 1+π‘Ž2𝐿2 1+π‘Ž2𝐿2 PROPN iajs-3598 157 19 ) ) PUNCT iajs-3598 157 20 + + CCONJ iajs-3598 157 21 οΏ½ οΏ½ PROPN iajs-3598 157 22 Μ‡ Μ‡ PROPN iajs-3598 157 23 οΏ½ οΏ½ NOUN iajs-3598 157 24 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 NUM iajs-3598 157 25 ) ) PUNCT iajs-3598 158 1 ( ( PUNCT iajs-3598 158 2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 158 3 + + CCONJ iajs-3598 158 4 𝐢2 𝐢2 PROPN iajs-3598 158 5 οΏ½ οΏ½ PROPN iajs-3598 158 6 Μ‡ Μ‡ NOUN iajs-3598 158 7 οΏ½ οΏ½ PROPN iajs-3598 158 8 1 1 NUM iajs-3598 158 9 2 2 NUM iajs-3598 158 10 ( ( PUNCT iajs-3598 158 11 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 158 12 + + CCONJ iajs-3598 158 13 ( ( PUNCT iajs-3598 158 14 4𝑆2 4𝑆2 NUM iajs-3598 158 15 οΏ½ οΏ½ NOUN iajs-3598 158 16 Μ‡ Μ‡ VERB iajs-3598 158 17 οΏ½ οΏ½ NOUN iajs-3598 158 18 2𝑓1𝐿3 2𝑓1𝐿3 NUM iajs-3598 158 19 ( ( PUNCT iajs-3598 158 20 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 158 21 βˆ’ βˆ’ PROPN iajs-3598 158 22 οΏ½ οΏ½ PROPN iajs-3598 158 23 Μ‡ Μ‡ PROPN iajs-3598 158 24 οΏ½ οΏ½ NOUN iajs-3598 158 25 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 NUM iajs-3598 158 26 ) ) PUNCT iajs-3598 158 27 ( ( PUNCT iajs-3598 158 28 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 158 29 + + ADJ iajs-3598 158 30 2 2 NUM iajs-3598 158 31 οΏ½ οΏ½ NOUN iajs-3598 158 32 Μ‡ Μ‡ NOUN iajs-3598 158 33 οΏ½ οΏ½ SYM iajs-3598 158 34 2𝐢2π‘Ž3 2𝐢2π‘Ž3 PROPN iajs-3598 158 35 ( ( PUNCT iajs-3598 158 36 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 NUM iajs-3598 158 37 ) ) PUNCT iajs-3598 158 38 ) ) PUNCT iajs-3598 159 1 + + CCONJ iajs-3598 159 2 ( ( PUNCT iajs-3598 159 3 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 159 4 2(1βˆ’2𝑓1𝐿3 2(1βˆ’2𝑓1𝐿3 NUM iajs-3598 159 5 ) ) PUNCT iajs-3598 159 6 ( ( PUNCT iajs-3598 159 7 1+𝑓1𝐿3)6 1+𝑓1𝐿3)6 NUM iajs-3598 159 8 + + CCONJ iajs-3598 159 9 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 159 10 ( ( PUNCT iajs-3598 159 11 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 159 12 ) ) PUNCT iajs-3598 159 13 ] ] PUNCT iajs-3598 159 14 , , PUNCT iajs-3598 159 15 ihjpas ihjpas PROPN iajs-3598 159 16 . . PUNCT iajs-3598 160 1 2025 2025 NUM iajs-3598 160 2 , , PUNCT iajs-3598 160 3 38 38 NUM iajs-3598 160 4 ( ( PUNCT iajs-3598 160 5 1 1 NUM iajs-3598 160 6 ) ) PUNCT iajs-3598 160 7 436 436 NUM iajs-3598 160 8 οΏ½ οΏ½ PROPN iajs-3598 160 9 Μ‡ Μ‡ PROPN iajs-3598 160 10 οΏ½ οΏ½ PROPN iajs-3598 160 11 31 31 NUM iajs-3598 160 12 = = SYM iajs-3598 160 13 ( ( PUNCT iajs-3598 160 14 𝑣3 𝑣3 PROPN iajs-3598 160 15 [ [ X iajs-3598 160 16 1 1 NUM iajs-3598 160 17 ] ] PUNCT iajs-3598 160 18 ) ) PUNCT iajs-3598 160 19 3 3 NUM iajs-3598 160 20 [ [ PUNCT iajs-3598 160 21 2𝑔1 2𝑔1 NUM iajs-3598 160 22 οΏ½ οΏ½ PROPN iajs-3598 160 23 Μ‡ Μ‡ NOUN iajs-3598 160 24 οΏ½ οΏ½ PROPN iajs-3598 160 25 1 1 NUM iajs-3598 160 26 3𝐿3(π‘Ž1βˆ’πΏ1 3𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 160 27 2 2 NUM iajs-3598 160 28 ) ) PUNCT iajs-3598 160 29 ( ( PUNCT iajs-3598 160 30 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 160 31 2 2 NUM iajs-3598 160 32 ) ) PUNCT iajs-3598 160 33 2 2 NUM iajs-3598 160 34 βˆ’ βˆ’ PROPN iajs-3598 160 35 2𝑔1 2𝑔1 NUM iajs-3598 160 36 οΏ½ οΏ½ PROPN iajs-3598 160 37 Μ‡ Μ‡ NOUN iajs-3598 160 38 οΏ½ οΏ½ PROPN iajs-3598 160 39 1 1 NUM iajs-3598 160 40 2𝐿1(2π‘Ž1 2𝐿1(2π‘Ž1 NUM iajs-3598 160 41 + + NOUN iajs-3598 160 42 1 1 NUM iajs-3598 160 43 ) ) PUNCT iajs-3598 160 44 ( ( PUNCT iajs-3598 160 45 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 160 46 2 2 NUM iajs-3598 160 47 ) ) PUNCT iajs-3598 160 48 2 2 NUM iajs-3598 160 49 + + NUM iajs-3598 160 50 6π‘Ž2 6π‘Ž2 NUM iajs-3598 160 51 2𝑔2 2𝑔2 NUM iajs-3598 160 52 οΏ½ οΏ½ NOUN iajs-3598 160 53 Μ‡ Μ‡ NOUN iajs-3598 160 54 οΏ½ οΏ½ PROPN iajs-3598 160 55 1 1 NUM iajs-3598 160 56 3𝐿3 3𝐿3 NUM iajs-3598 160 57 ( ( PUNCT iajs-3598 160 58 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 160 59 ) ) PUNCT iajs-3598 161 1 + + CCONJ iajs-3598 161 2 2π‘Ž2 2π‘Ž2 NUM iajs-3598 161 3 2𝑔2 2𝑔2 NUM iajs-3598 161 4 οΏ½ οΏ½ NOUN iajs-3598 161 5 Μ‡ Μ‡ VERB iajs-3598 161 6 οΏ½ οΏ½ PROPN iajs-3598 161 7 2 2 NUM iajs-3598 161 8 2𝐿2 2𝐿2 NUM iajs-3598 161 9 ( ( PUNCT iajs-3598 161 10 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 161 11 βˆ’ βˆ’ PROPN iajs-3598 161 12 4π‘Ž2𝑔2 4π‘Ž2𝑔2 NUM iajs-3598 161 13 οΏ½ οΏ½ NOUN iajs-3598 161 14 Μ‡ Μ‡ NOUN iajs-3598 161 15 οΏ½ οΏ½ PROPN iajs-3598 161 16 2 2 NUM iajs-3598 161 17 2 2 NUM iajs-3598 161 18 ( ( PUNCT iajs-3598 161 19 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 161 20 + + CCONJ iajs-3598 161 21 2𝑔1 2𝑔1 NUM iajs-3598 161 22 οΏ½ οΏ½ NOUN iajs-3598 161 23 Μ‡ Μ‡ NOUN iajs-3598 161 24 οΏ½ οΏ½ PROPN iajs-3598 161 25 1 1 NUM iajs-3598 161 26 2𝐿1 2𝐿1 NUM iajs-3598 161 27 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 161 28 2 2 NUM iajs-3598 161 29 + + CCONJ iajs-3598 161 30 π‘Ž3𝑔2 π‘Ž3𝑔2 NOUN iajs-3598 161 31 οΏ½ οΏ½ NOUN iajs-3598 161 32 Μ‡ Μ‡ NOUN iajs-3598 161 33 οΏ½ οΏ½ X iajs-3598 161 34 2 2 NUM iajs-3598 161 35 ( ( PUNCT iajs-3598 161 36 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 161 37 ( ( PUNCT iajs-3598 161 38 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 161 39 + + NUM iajs-3598 161 40 π‘Ž2𝐿2 π‘Ž2𝐿2 NUM iajs-3598 161 41 ) ) PUNCT iajs-3598 161 42 βˆ’ βˆ’ ADP iajs-3598 161 43 2π‘Ž3𝑔2 2π‘Ž3𝑔2 NUM iajs-3598 161 44 οΏ½ οΏ½ NOUN iajs-3598 161 45 Μ‡ Μ‡ NOUN iajs-3598 161 46 οΏ½ οΏ½ X iajs-3598 161 47 2 2 NUM iajs-3598 161 48 ( ( PUNCT iajs-3598 161 49 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 VERB iajs-3598 161 50 βˆ’ βˆ’ PROPN iajs-3598 161 51 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 161 52 ) ) PUNCT iajs-3598 161 53 ( ( PUNCT iajs-3598 161 54 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 X iajs-3598 161 55 . . PUNCT iajs-3598 161 56 ( ( PUNCT iajs-3598 161 57 𝑍[2 𝑍[2 PROPN iajs-3598 161 58 ] ] PUNCT iajs-3598 161 59 ) ) PUNCT iajs-3598 161 60 𝑇 𝑇 PROPN iajs-3598 162 1 [ [ SYM iajs-3598 162 2 𝐷3πΉπœ‡(𝐻4 𝐷3πΉπœ‡(𝐻4 PROPN iajs-3598 162 3 , , PUNCT iajs-3598 162 4 𝑑)(𝑉[2 𝑑)(𝑉[2 PROPN iajs-3598 162 5 ] ] X iajs-3598 162 6 , , PUNCT iajs-3598 162 7 𝑉[2 𝑉[2 PROPN iajs-3598 162 8 ] ] PUNCT iajs-3598 162 9 , , PUNCT iajs-3598 162 10 𝑉[2 𝑉[2 PROPN iajs-3598 162 11 ] ] PUNCT iajs-3598 162 12 ) ) PUNCT iajs-3598 162 13 ] ] PUNCT iajs-3598 163 1 = = SYM iajs-3598 163 2 ( ( PUNCT iajs-3598 163 3 𝑣3 𝑣3 PROPN iajs-3598 163 4 [ [ X iajs-3598 163 5 2 2 NUM iajs-3598 163 6 ] ] PUNCT iajs-3598 163 7 ) ) PUNCT iajs-3598 163 8 3 3 NUM iajs-3598 163 9 𝑧3 𝑧3 NOUN iajs-3598 163 10 [ [ X iajs-3598 163 11 4 4 NUM iajs-3598 163 12 ] ] PUNCT iajs-3598 163 13 ( ( PUNCT iajs-3598 163 14 οΏ½ οΏ½ PROPN iajs-3598 163 15 Μ‡ Μ‡ PROPN iajs-3598 163 16 οΏ½ οΏ½ PROPN iajs-3598 163 17 3 3 NUM iajs-3598 163 18 βˆ’ βˆ’ PROPN iajs-3598 163 19 οΏ½ οΏ½ PROPN iajs-3598 163 20 Μ‡ Μ‡ PROPN iajs-3598 163 21 οΏ½ οΏ½ NOUN iajs-3598 163 22 4 4 NUM iajs-3598 163 23 ) ) PUNCT iajs-3598 163 24 β‰  β‰  PROPN iajs-3598 163 25 0 0 NUM iajs-3598 164 1 so so ADV iajs-3598 164 2 , , PUNCT iajs-3598 164 3 pitch pitch NOUN iajs-3598 164 4 fork fork NOUN iajs-3598 164 5 bifurcation bifurcation NOUN iajs-3598 164 6 can can AUX iajs-3598 164 7 be be AUX iajs-3598 164 8 found find VERB iajs-3598 164 9 at at ADP iajs-3598 164 10 𝐻4 𝐻4 PROPN iajs-3598 164 11 where where SCONJ iajs-3598 164 12 οΏ½ οΏ½ PROPN iajs-3598 164 13 Μ‡ Μ‡ PROPN iajs-3598 164 14 οΏ½ οΏ½ PROPN iajs-3598 164 15 = = SYM iajs-3598 164 16 𝑑. 𝑑. NOUN iajs-3598 164 17 theorem theorem NOUN iajs-3598 164 18 ( ( PUNCT iajs-3598 164 19 3 3 NUM iajs-3598 164 20 ): ): PUNCT iajs-3598 164 21 system system NOUN iajs-3598 164 22 ( ( PUNCT iajs-3598 164 23 1 1 NUM iajs-3598 164 24 ) ) PUNCT iajs-3598 164 25 with with ADP iajs-3598 164 26 parameter parameter NOUN iajs-3598 164 27 value value NOUN iajs-3598 164 28 : : PUNCT iajs-3598 164 29 𝑆1Μ… 𝑆1Μ… X iajs-3598 164 30 = = PUNCT iajs-3598 164 31 𝑆1 𝑆1 NOUN iajs-3598 164 32 = = SYM iajs-3598 164 33 𝐢1 𝐢1 NUM iajs-3598 164 34 οΏ½ οΏ½ NOUN iajs-3598 164 35 Μ… Μ… NOUN iajs-3598 164 36 οΏ½ οΏ½ NOUN iajs-3598 164 37 3 3 NUM iajs-3598 164 38 π‘Ž1 π‘Ž1 NOUN iajs-3598 164 39 , , PUNCT iajs-3598 164 40 has have VERB iajs-3598 164 41 a a DET iajs-3598 164 42 transcritical transcritical ADJ iajs-3598 164 43 and and CCONJ iajs-3598 164 44 pitchfork pitchfork NOUN iajs-3598 164 45 bifurcation bifurcation NOUN iajs-3598 164 46 at at ADP iajs-3598 164 47 𝐻6.if 𝐻6.if PRON iajs-3598 164 48 the the DET iajs-3598 164 49 next next ADJ iajs-3598 164 50 conditions condition NOUN iajs-3598 164 51 hold hold VERB iajs-3598 164 52 : : PUNCT iajs-3598 164 53 οΏ½ οΏ½ NOUN iajs-3598 164 54 Μ… Μ… NOUN iajs-3598 164 55 οΏ½ οΏ½ NOUN iajs-3598 164 56 1 1 NUM iajs-3598 164 57 β‰  β‰  PROPN iajs-3598 164 58 οΏ½ οΏ½ NOUN iajs-3598 164 59 Μ… Μ… NOUN iajs-3598 164 60 οΏ½ οΏ½ NOUN iajs-3598 164 61 2 2 NUM iajs-3598 164 62 ( ( PUNCT iajs-3598 164 63 13 13 NUM iajs-3598 164 64 ) ) PUNCT iajs-3598 164 65 οΏ½ οΏ½ NOUN iajs-3598 164 66 Μ… Μ… NOUN iajs-3598 164 67 οΏ½ οΏ½ NOUN iajs-3598 164 68 3 3 NUM iajs-3598 164 69 β‰  β‰  PROPN iajs-3598 164 70 οΏ½ οΏ½ PROPN iajs-3598 164 71 Μ… Μ… NOUN iajs-3598 164 72 οΏ½ οΏ½ NOUN iajs-3598 164 73 4 4 NUM iajs-3598 164 74 ( ( PUNCT iajs-3598 164 75 14 14 NUM iajs-3598 164 76 ) ) PUNCT iajs-3598 165 1 where where SCONJ iajs-3598 165 2 : : PUNCT iajs-3598 165 3 οΏ½ οΏ½ PROPN iajs-3598 165 4 Μ… Μ… NOUN iajs-3598 165 5 οΏ½ οΏ½ NOUN iajs-3598 165 6 1 1 NUM iajs-3598 165 7 = = SYM iajs-3598 165 8 ( ( PUNCT iajs-3598 165 9 𝑣1 𝑣1 NOUN iajs-3598 165 10 [ [ X iajs-3598 165 11 3 3 NUM iajs-3598 165 12 ] ] PUNCT iajs-3598 165 13 ) ) PUNCT iajs-3598 165 14 2 2 NUM iajs-3598 165 15 [ [ PUNCT iajs-3598 165 16 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NUM iajs-3598 165 17 ( ( PUNCT iajs-3598 165 18 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 165 19 2 2 NUM iajs-3598 165 20 ) ) PUNCT iajs-3598 165 21 2 2 NUM iajs-3598 165 22 + + CCONJ iajs-3598 165 23 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 165 24 2 2 NUM iajs-3598 165 25 ( ( PUNCT iajs-3598 165 26 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 165 27 2 2 NUM iajs-3598 165 28 ) ) PUNCT iajs-3598 165 29 ] ] PUNCT iajs-3598 165 30 , , PUNCT iajs-3598 165 31 οΏ½ οΏ½ NOUN iajs-3598 165 32 Μ… Μ… NOUN iajs-3598 165 33 οΏ½ οΏ½ NOUN iajs-3598 165 34 1 1 NUM iajs-3598 165 35 = = SYM iajs-3598 165 36 2𝑆1 2𝑆1 NUM iajs-3598 165 37 𝐾1 𝐾1 NOUN iajs-3598 166 1 + + CCONJ iajs-3598 166 2 ( ( PUNCT iajs-3598 166 3 𝑣1 𝑣1 NOUN iajs-3598 166 4 [ [ X iajs-3598 166 5 3 3 NUM iajs-3598 166 6 ] ] PUNCT iajs-3598 166 7 ) ) PUNCT iajs-3598 166 8 2 2 NUM iajs-3598 166 9 𝐢1 𝐢1 NOUN iajs-3598 166 10 ( ( PUNCT iajs-3598 166 11 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 166 12 2 2 NUM iajs-3598 166 13 ) ) PUNCT iajs-3598 166 14 ( ( PUNCT iajs-3598 166 15 ( ( PUNCT iajs-3598 166 16 π‘Ž1 π‘Ž1 X iajs-3598 166 17 + + CCONJ iajs-3598 166 18 𝐿1 𝐿1 PROPN iajs-3598 166 19 2 2 NUM iajs-3598 166 20 ) ) PUNCT iajs-3598 166 21 + + CCONJ iajs-3598 166 22 ( ( PUNCT iajs-3598 166 23 π‘Ž1 π‘Ž1 X iajs-3598 166 24 + + PRON iajs-3598 166 25 2𝐿1 2𝐿1 NUM iajs-3598 166 26 ) ) PUNCT iajs-3598 166 27 ) ) PUNCT iajs-3598 166 28 , , PUNCT iajs-3598 166 29 οΏ½ οΏ½ PROPN iajs-3598 166 30 Μ… Μ… NOUN iajs-3598 166 31 οΏ½ οΏ½ NOUN iajs-3598 166 32 3 3 NUM iajs-3598 166 33 = = SYM iajs-3598 167 1 2𝐢1𝜎1 2𝐢1𝜎1 NUM iajs-3598 168 1 3π‘Ž1𝐿3(1βˆ’4𝐿1 3π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 168 2 2 2 NUM iajs-3598 168 3 ) ) PUNCT iajs-3598 168 4 ( ( PUNCT iajs-3598 168 5 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 168 6 2 2 NUM iajs-3598 168 7 ) ) SYM iajs-3598 168 8 2 2 NUM iajs-3598 168 9 + + NUM iajs-3598 168 10 οΏ½ οΏ½ PROPN iajs-3598 168 11 Μ‡ Μ‡ VERB iajs-3598 168 12 οΏ½ οΏ½ PROPN iajs-3598 168 13 1 1 NUM iajs-3598 168 14 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 169 1 + + CCONJ iajs-3598 169 2 𝜎1 𝜎1 ADJ iajs-3598 169 3 2𝐿1 2𝐿1 NUM iajs-3598 169 4 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 5 2 2 NUM iajs-3598 169 6 + + NOUN iajs-3598 169 7 𝜎1 𝜎1 ADJ iajs-3598 169 8 2𝐢1𝐿1(π‘Ž1 2𝐢1𝐿1(π‘Ž1 NUM iajs-3598 169 9 + + NOUN iajs-3598 169 10 2𝐿1 2𝐿1 NUM iajs-3598 169 11 ) ) PUNCT iajs-3598 169 12 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 13 2 2 NUM iajs-3598 169 14 + + CCONJ iajs-3598 169 15 4𝜎1 4𝜎1 NUM iajs-3598 169 16 2𝐢1π‘Ž1𝐿1 2𝐢1π‘Ž1𝐿1 NUM iajs-3598 169 17 ( ( PUNCT iajs-3598 169 18 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 19 2 2 NUM iajs-3598 169 20 ) ) SYM iajs-3598 169 21 2 2 NUM iajs-3598 169 22 , , PUNCT iajs-3598 169 23 οΏ½ οΏ½ NOUN iajs-3598 169 24 Μ… Μ… NOUN iajs-3598 169 25 οΏ½ οΏ½ NOUN iajs-3598 169 26 4= 4= NUM iajs-3598 169 27 𝜎1 𝜎1 ADJ iajs-3598 169 28 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 169 29 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 30 2 2 NUM iajs-3598 169 31 + + NUM iajs-3598 169 32 2𝜎1 2𝜎1 NUM iajs-3598 169 33 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 169 34 3 3 NUM iajs-3598 169 35 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 36 2 2 NUM iajs-3598 169 37 βˆ’ βˆ’ NOUN iajs-3598 169 38 𝜎1 𝜎1 ADJ iajs-3598 169 39 2𝐢1 2𝐢1 NUM iajs-3598 169 40 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 169 41 2 2 NUM iajs-3598 169 42 . . PUNCT iajs-3598 170 1 proof proof NOUN iajs-3598 170 2 : : PUNCT iajs-3598 170 3 using use VERB iajs-3598 170 4 the the DET iajs-3598 170 5 jacobian jacobian ADJ iajs-3598 170 6 matrix matrix NOUN iajs-3598 170 7 is be AUX iajs-3598 170 8 presented present VERB iajs-3598 170 9 in in ADP iajs-3598 170 10 equation equation NOUN iajs-3598 170 11 ( ( PUNCT iajs-3598 170 12 1.10 1.10 NUM iajs-3598 170 13 ) ) PUNCT iajs-3598 170 14 in in ADP iajs-3598 170 15 ( ( PUNCT iajs-3598 170 16 22 22 NUM iajs-3598 170 17 ) ) PUNCT iajs-3598 170 18 , , PUNCT iajs-3598 170 19 𝐽6Μ… 𝐽6Μ… NOUN iajs-3598 170 20 = = SYM iajs-3598 170 21 𝐽6(𝐻6 𝐽6(𝐻6 NOUN iajs-3598 170 22 , , PUNCT iajs-3598 170 23 𝑆1Μ… 𝑆1Μ… X iajs-3598 170 24 ) ) PUNCT iajs-3598 170 25 = = PUNCT iajs-3598 171 1 [ [ X iajs-3598 171 2 𝑑 𝑑 X iajs-3598 171 3 οΏ½ οΏ½ NOUN iajs-3598 171 4 Μ… Μ… NOUN iajs-3598 171 5 οΏ½ οΏ½ NOUN iajs-3598 171 6 𝑗 𝑗 NOUN iajs-3598 171 7 ] ] X iajs-3598 171 8 3Γ—3 3Γ—3 NUM iajs-3598 171 9 , , PUNCT iajs-3598 171 10 where where SCONJ iajs-3598 171 11 𝑑 𝑑 PRON iajs-3598 171 12 οΏ½ οΏ½ NOUN iajs-3598 171 13 Μ… Μ… NOUN iajs-3598 171 14 οΏ½ οΏ½ NOUN iajs-3598 171 15 𝑗 𝑗 NOUN iajs-3598 171 16 = = ADJ iajs-3598 171 17 𝑑𝑖𝑗 𝑑𝑖𝑗 NOUN iajs-3598 171 18 , , PUNCT iajs-3598 171 19 except except SCONJ iajs-3598 171 20 𝑑1Μ…1 𝑑1Μ…1 ADJ iajs-3598 171 21 = = SYM iajs-3598 171 22 0 0 NUM iajs-3598 171 23 . . PUNCT iajs-3598 172 1 then then ADV iajs-3598 172 2 the the DET iajs-3598 172 3 characterizing characterize VERB iajs-3598 172 4 equation equation NOUN iajs-3598 172 5 of of ADP iajs-3598 172 6 𝐽6Μ… 𝐽6Μ… NOUN iajs-3598 172 7 had have VERB iajs-3598 172 8 a a DET iajs-3598 172 9 zero zero NUM iajs-3598 172 10 eigenvalue eigenvalue NOUN iajs-3598 172 11 ( ( PUNCT iajs-3598 172 12 say say VERB iajs-3598 172 13 Ξ»6l1 Ξ»6l1 INTJ iajs-3598 172 14 ) ) PUNCT iajs-3598 172 15 . . PUNCT iajs-3598 173 1 now now ADV iajs-3598 173 2 , , PUNCT iajs-3598 173 3 let let VERB iajs-3598 173 4 𝑉[3 𝑉[3 PROPN iajs-3598 173 5 ] ] X iajs-3598 173 6 = = PUNCT iajs-3598 173 7 ( ( PUNCT iajs-3598 173 8 𝑣1 𝑣1 NOUN iajs-3598 173 9 [ [ X iajs-3598 173 10 3 3 NUM iajs-3598 173 11 ] ] PUNCT iajs-3598 173 12 , , PUNCT iajs-3598 173 13 𝑣2 𝑣2 X iajs-3598 173 14 [ [ X iajs-3598 173 15 3 3 NUM iajs-3598 173 16 ] ] PUNCT iajs-3598 173 17 , , PUNCT iajs-3598 173 18 𝑣3 𝑣3 ADJ iajs-3598 173 19 [ [ X iajs-3598 173 20 3 3 NUM iajs-3598 173 21 ] ] PUNCT iajs-3598 173 22 ) ) PUNCT iajs-3598 174 1 𝑇be 𝑇be NUM iajs-3598 174 2 the the DET iajs-3598 174 3 eigenvector eigenvector NOUN iajs-3598 174 4 corresponding correspond VERB iajs-3598 174 5 to to ADP iajs-3598 174 6 the the DET iajs-3598 174 7 eigenvalue eigenvalue PROPN iajs-3598 174 8 Ξ»6l1 Ξ»6l1 PROPN iajs-3598 174 9 = = NOUN iajs-3598 174 10 0 0 PROPN iajs-3598 174 11 . . PUNCT iajs-3598 174 12 thus,(𝐽6Μ… thus,(𝐽6Μ… NOUN iajs-3598 174 13 βˆ’ βˆ’ PROPN iajs-3598 175 1 Ξ»6l1 Ξ»6l1 CCONJ iajs-3598 175 2 𝐼)𝑉[3 𝐼)𝑉[3 X iajs-3598 175 3 ] ] X iajs-3598 175 4 = = SYM iajs-3598 175 5 0 0 NUM iajs-3598 175 6 , , PUNCT iajs-3598 175 7 this this PRON iajs-3598 175 8 gives give VERB iajs-3598 175 9 : : PUNCT iajs-3598 175 10 𝑣2 𝑣2 NUM iajs-3598 176 1 [ [ X iajs-3598 176 2 3 3 NUM iajs-3598 176 3 ] ] X iajs-3598 176 4 = = PUNCT iajs-3598 176 5 𝜎1𝑣1 𝜎1𝑣1 PROPN iajs-3598 176 6 [ [ X iajs-3598 176 7 3 3 NUM iajs-3598 176 8 ] ] PUNCT iajs-3598 176 9 , , PUNCT iajs-3598 176 10 𝑣3 𝑣3 ADJ iajs-3598 176 11 [ [ X iajs-3598 176 12 3 3 NUM iajs-3598 176 13 ] ] PUNCT iajs-3598 176 14 = = PUNCT iajs-3598 177 1 𝜎2𝑣1 𝜎2𝑣1 X iajs-3598 177 2 [ [ X iajs-3598 177 3 3 3 NUM iajs-3598 177 4 ] ] PUNCT iajs-3598 177 5 , , PUNCT iajs-3598 177 6 where where SCONJ iajs-3598 177 7 : : PUNCT iajs-3598 177 8 𝜎1 𝜎1 ADJ iajs-3598 177 9 = = PUNCT iajs-3598 177 10 βˆ’ βˆ’ PROPN iajs-3598 177 11 𝑑31𝑑23 𝑑31𝑑23 PROPN iajs-3598 177 12 𝑑32𝑑23+𝑑22𝑑33 𝑑32𝑑23+𝑑22𝑑33 PROPN iajs-3598 177 13 , , PUNCT iajs-3598 177 14 𝜎2 𝜎2 NOUN iajs-3598 177 15 = = SYM iajs-3598 177 16 𝑑31𝑑22 𝑑31𝑑22 PROPN iajs-3598 177 17 𝑑32𝑑23+𝑑22𝑑33 𝑑32𝑑23+𝑑22𝑑33 PROPN iajs-3598 177 18 and and CCONJ iajs-3598 177 19 𝑣1 𝑣1 NOUN iajs-3598 178 1 [ [ X iajs-3598 178 2 6 6 NUM iajs-3598 178 3 ] ] PUNCT iajs-3598 178 4 any any DET iajs-3598 178 5 non non ADJ iajs-3598 178 6 - - ADJ iajs-3598 178 7 zero zero ADJ iajs-3598 178 8 real real ADJ iajs-3598 178 9 number number NOUN iajs-3598 178 10 . . PUNCT iajs-3598 179 1 let let VERB iajs-3598 179 2 𝑍[3 𝑍[3 PRON iajs-3598 179 3 ] ] X iajs-3598 179 4 = = SYM iajs-3598 179 5 ( ( PUNCT iajs-3598 179 6 𝑧1 𝑧1 NOUN iajs-3598 179 7 [ [ X iajs-3598 179 8 3 3 NUM iajs-3598 179 9 ] ] PUNCT iajs-3598 179 10 , , PUNCT iajs-3598 179 11 𝑧2 𝑧2 PROPN iajs-3598 179 12 [ [ X iajs-3598 179 13 3 3 NUM iajs-3598 179 14 ] ] PUNCT iajs-3598 179 15 , , PUNCT iajs-3598 179 16 𝑧3 𝑧3 PROPN iajs-3598 179 17 [ [ X iajs-3598 179 18 3 3 NUM iajs-3598 179 19 ] ] PUNCT iajs-3598 179 20 ) ) PUNCT iajs-3598 179 21 𝑇 𝑇 PROPN iajs-3598 179 22 be be VERB iajs-3598 179 23 the the DET iajs-3598 179 24 eigenvector eigenvector NOUN iajs-3598 179 25 connected connect VERB iajs-3598 179 26 with with ADP iajs-3598 179 27 an an DET iajs-3598 179 28 eigenvalue eigenvalue NOUN iajs-3598 179 29 Ξ»6l1 Ξ»6l1 NOUN iajs-3598 179 30 = = PROPN iajs-3598 179 31 0 0 NUM iajs-3598 179 32 of of ADP iajs-3598 179 33 the the DET iajs-3598 179 34 matrix matrix NOUN iajs-3598 179 35 𝐽6Μ… 𝐽6Μ… NOUN iajs-3598 179 36 𝑇.then 𝑇.then ADV iajs-3598 179 37 , , PUNCT iajs-3598 179 38 ( ( PUNCT iajs-3598 179 39 𝐽6Μ… 𝐽6Μ… NOUN iajs-3598 179 40 𝑇 𝑇 PROPN iajs-3598 179 41 βˆ’ βˆ’ PROPN iajs-3598 179 42 Ξ»6l1 Ξ»6l1 PROPN iajs-3598 179 43 𝐼 𝐼 PROPN iajs-3598 179 44 ) ) PUNCT iajs-3598 179 45 𝑍[3 𝑍[3 PROPN iajs-3598 179 46 ] ] X iajs-3598 179 47 = = SYM iajs-3598 180 1 0 0 X iajs-3598 180 2 . . PUNCT iajs-3598 180 3 by by ADP iajs-3598 180 4 solving solve VERB iajs-3598 180 5 this this DET iajs-3598 180 6 equation equation NOUN iajs-3598 180 7 for for ADP iajs-3598 180 8 , , PUNCT iajs-3598 180 9 𝑍[3 𝑍[3 PROPN iajs-3598 180 10 ] ] X iajs-3598 180 11 = = SYM iajs-3598 180 12 ( ( PUNCT iajs-3598 180 13 𝑧1 𝑧1 NOUN iajs-3598 180 14 [ [ X iajs-3598 180 15 3 3 NUM iajs-3598 180 16 ] ] PUNCT iajs-3598 180 17 , , PUNCT iajs-3598 180 18 0,0 0,0 NUM iajs-3598 180 19 ) ) PUNCT iajs-3598 180 20 𝑇 𝑇 PROPN iajs-3598 180 21 , , PUNCT iajs-3598 180 22 where where SCONJ iajs-3598 180 23 𝑧1 𝑧1 NOUN iajs-3598 180 24 [ [ X iajs-3598 180 25 3 3 X iajs-3598 180 26 ] ] X iajs-3598 180 27 any any DET iajs-3598 180 28 non non ADJ iajs-3598 180 29 - - ADJ iajs-3598 180 30 zero zero ADJ iajs-3598 180 31 real real ADJ iajs-3598 180 32 number number NOUN iajs-3598 180 33 . . PUNCT iajs-3598 181 1 ihjpas ihjpas PROPN iajs-3598 181 2 . . PUNCT iajs-3598 182 1 2025 2025 NUM iajs-3598 182 2 , , PUNCT iajs-3598 182 3 38 38 NUM iajs-3598 182 4 ( ( PUNCT iajs-3598 182 5 1 1 NUM iajs-3598 182 6 ) ) PUNCT iajs-3598 182 7 437 437 NUM iajs-3598 182 8 now now ADV iajs-3598 182 9 , , PUNCT iajs-3598 182 10 consider consider VERB iajs-3598 182 11 that that PRON iajs-3598 182 12 : : PUNCT iajs-3598 182 13 πœ•π‘“ πœ•π‘“ ADJ iajs-3598 182 14 πœ•π‘†1 πœ•π‘†1 PROPN iajs-3598 182 15 = = SYM iajs-3598 182 16 𝑓𝑆1 𝑓𝑆1 PROPN iajs-3598 182 17 ( ( PUNCT iajs-3598 182 18 𝑋 𝑋 NOUN iajs-3598 182 19 , , PUNCT iajs-3598 182 20 𝑆1 𝑆1 NOUN iajs-3598 182 21 ) ) PUNCT iajs-3598 182 22 = = SYM iajs-3598 182 23 ( ( PUNCT iajs-3598 182 24 πœ•π‘“1 πœ•π‘“1 NOUN iajs-3598 182 25 πœ•π‘†1 πœ•π‘†1 NOUN iajs-3598 182 26 , , PUNCT iajs-3598 182 27 πœ•π‘“2 πœ•π‘“2 PROPN iajs-3598 182 28 πœ•π‘†1 πœ•π‘†1 PROPN iajs-3598 182 29 , , PUNCT iajs-3598 182 30 πœ•π‘“3 πœ•π‘“3 PROPN iajs-3598 182 31 πœ•π‘†1 πœ•π‘†1 PROPN iajs-3598 182 32 ) ) PUNCT iajs-3598 182 33 𝑇 𝑇 PROPN iajs-3598 182 34 = = SYM iajs-3598 182 35 ( ( PUNCT iajs-3598 182 36 𝐿1(1 𝐿1(1 ADJ iajs-3598 182 37 βˆ’ βˆ’ PROPN iajs-3598 182 38 1 1 NUM iajs-3598 182 39 𝐾1 𝐾1 NOUN iajs-3598 182 40 ) ) PUNCT iajs-3598 182 41 , , PUNCT iajs-3598 182 42 0,0 0,0 NUM iajs-3598 182 43 ) ) PUNCT iajs-3598 182 44 𝑇 𝑇 NOUN iajs-3598 182 45 . . PUNCT iajs-3598 183 1 so so ADV iajs-3598 183 2 , , PUNCT iajs-3598 183 3 𝑓𝑆1 𝑓𝑆1 PROPN iajs-3598 183 4 ( ( PUNCT iajs-3598 183 5 𝐻6 𝐻6 NOUN iajs-3598 183 6 , , PUNCT iajs-3598 183 7 𝑆1Μ… 𝑆1Μ… X iajs-3598 183 8 ) ) PUNCT iajs-3598 183 9 = = SYM iajs-3598 183 10 ( ( PUNCT iajs-3598 183 11 0,0,0)𝑇 0,0,0)𝑇 X iajs-3598 183 12 , , PUNCT iajs-3598 183 13 and and CCONJ iajs-3598 183 14 hence hence ADV iajs-3598 183 15 ( ( PUNCT iajs-3598 183 16 𝑍[3 𝑍[3 PROPN iajs-3598 183 17 ] ] X iajs-3598 183 18 ) ) PUNCT iajs-3598 183 19 𝑇 𝑇 PROPN iajs-3598 183 20 𝑓𝑆1 𝑓𝑆1 PROPN iajs-3598 183 21 ( ( PUNCT iajs-3598 183 22 𝐻6 𝐻6 NOUN iajs-3598 183 23 , , PUNCT iajs-3598 183 24 𝑆1Μ… 𝑆1Μ… X iajs-3598 183 25 ) ) PUNCT iajs-3598 183 26 = = SYM iajs-3598 184 1 0 0 X iajs-3598 184 2 . . PUNCT iajs-3598 185 1 the the DET iajs-3598 185 2 ( ( PUNCT iajs-3598 185 3 sd sd NOUN iajs-3598 185 4 ) ) PUNCT iajs-3598 185 5 bifurcation bifurcation NOUN iajs-3598 185 6 requirement requirement NOUN iajs-3598 185 7 can can AUX iajs-3598 185 8 not not PART iajs-3598 185 9 be be AUX iajs-3598 185 10 satisfied satisfied ADJ iajs-3598 185 11 according accord VERB iajs-3598 185 12 to to ADP iajs-3598 185 13 sotomayor sotomayor PROPN iajs-3598 185 14 's 's PART iajs-3598 185 15 theorem theorem ADJ iajs-3598 185 16 . . PROPN iajs-3598 186 1 as as ADP iajs-3598 186 2 a a DET iajs-3598 186 3 result result NOUN iajs-3598 186 4 , , PUNCT iajs-3598 186 5 the the DET iajs-3598 186 6 first first ADJ iajs-3598 186 7 requirement requirement NOUN iajs-3598 186 8 for for ADP iajs-3598 186 9 ( ( PUNCT iajs-3598 186 10 tc tc NOUN iajs-3598 186 11 ) ) PUNCT iajs-3598 186 12 bifurcation bifurcation NOUN iajs-3598 186 13 is be AUX iajs-3598 186 14 realized realize VERB iajs-3598 186 15 . . PUNCT iajs-3598 187 1 now now ADV iajs-3598 187 2 𝐷𝑓 𝐷𝑓 NOUN iajs-3598 187 3 οΏ½ οΏ½ PROPN iajs-3598 187 4 Μ… Μ… NOUN iajs-3598 187 5 οΏ½ οΏ½ NOUN iajs-3598 187 6 1 1 NUM iajs-3598 187 7 ( ( PUNCT iajs-3598 187 8 𝑋 𝑋 NOUN iajs-3598 187 9 , , PUNCT iajs-3598 187 10 𝑆1Μ… 𝑆1Μ… X iajs-3598 187 11 ) ) PUNCT iajs-3598 187 12 = = PUNCT iajs-3598 188 1 [ [ PUNCT iajs-3598 188 2 1 1 NUM iajs-3598 188 3 βˆ’ βˆ’ NUM iajs-3598 188 4 1 1 NUM iajs-3598 188 5 𝐾1 𝐾1 PROPN iajs-3598 188 6 0 0 NUM iajs-3598 188 7 0 0 NUM iajs-3598 188 8 0 0 NUM iajs-3598 188 9 0 0 NUM iajs-3598 188 10 0 0 NUM iajs-3598 188 11 0 0 NUM iajs-3598 188 12 0 0 NUM iajs-3598 188 13 0 0 NUM iajs-3598 188 14 ] ] PUNCT iajs-3598 188 15 , , PUNCT iajs-3598 188 16 where where SCONJ iajs-3598 188 17 , , PUNCT iajs-3598 188 18 𝐷𝑓 𝐷𝑓 PROPN iajs-3598 188 19 οΏ½ οΏ½ NOUN iajs-3598 188 20 Μ… Μ… NOUN iajs-3598 188 21 οΏ½ οΏ½ NOUN iajs-3598 188 22 1 1 NUM iajs-3598 188 23 ( ( PUNCT iajs-3598 188 24 𝑋 𝑋 NOUN iajs-3598 188 25 , , PUNCT iajs-3598 188 26 𝑆1Μ… 𝑆1Μ… NOUN iajs-3598 188 27 ) ) PUNCT iajs-3598 188 28 represents represent VERB iajs-3598 188 29 the the DET iajs-3598 188 30 derivative derivative NOUN iajs-3598 188 31 of of ADP iajs-3598 188 32 𝑓 𝑓 PRON iajs-3598 188 33 οΏ½ οΏ½ PROPN iajs-3598 188 34 Μ… Μ… NOUN iajs-3598 188 35 οΏ½ οΏ½ NOUN iajs-3598 188 36 1 1 NUM iajs-3598 188 37 ( ( PUNCT iajs-3598 188 38 𝑋 𝑋 NOUN iajs-3598 188 39 , , PUNCT iajs-3598 188 40 𝑆1Μ… 𝑆1Μ… NOUN iajs-3598 188 41 ) ) PUNCT iajs-3598 188 42 with with ADP iajs-3598 188 43 respect respect NOUN iajs-3598 188 44 to to ADP iajs-3598 188 45 𝑋 𝑋 PROPN iajs-3598 188 46 = = SYM iajs-3598 188 47 ( ( PUNCT iajs-3598 188 48 𝐿1 𝐿1 PROPN iajs-3598 188 49 , , PUNCT iajs-3598 188 50 𝐿2 𝐿2 PROPN iajs-3598 188 51 , , PUNCT iajs-3598 188 52 𝐿3)𝑇 𝐿3)𝑇 PUNCT iajs-3598 188 53 . . PUNCT iajs-3598 189 1 furthermore furthermore ADV iajs-3598 189 2 , , PUNCT iajs-3598 189 3 it it PRON iajs-3598 189 4 is be AUX iajs-3598 189 5 observed observe VERB iajs-3598 189 6 that that SCONJ iajs-3598 189 7 : : PUNCT iajs-3598 189 8 𝐷𝑓 𝐷𝑓 PROPN iajs-3598 189 9 οΏ½ οΏ½ NOUN iajs-3598 189 10 Μ… Μ… NOUN iajs-3598 189 11 οΏ½ οΏ½ NOUN iajs-3598 189 12 1 1 NUM iajs-3598 189 13 ( ( PUNCT iajs-3598 189 14 𝐻6 𝐻6 NOUN iajs-3598 189 15 , , PUNCT iajs-3598 189 16 𝑆1Μ…)𝑉[3 𝑆1Μ…)𝑉[3 PUNCT iajs-3598 189 17 ] ] PUNCT iajs-3598 189 18 = = PUNCT iajs-3598 189 19 [ [ PUNCT iajs-3598 189 20 1 1 NUM iajs-3598 189 21 βˆ’ βˆ’ NUM iajs-3598 189 22 1 1 NUM iajs-3598 189 23 𝐾1 𝐾1 PROPN iajs-3598 189 24 0 0 NUM iajs-3598 189 25 0 0 NUM iajs-3598 189 26 0 0 NUM iajs-3598 189 27 0 0 NUM iajs-3598 189 28 0 0 NUM iajs-3598 189 29 0 0 NUM iajs-3598 189 30 0 0 NUM iajs-3598 189 31 0 0 NUM iajs-3598 189 32 ] ] PUNCT iajs-3598 189 33 [ [ PUNCT iajs-3598 189 34 𝑣1 𝑣1 NOUN iajs-3598 189 35 [ [ X iajs-3598 189 36 3 3 NUM iajs-3598 189 37 ] ] PUNCT iajs-3598 189 38 𝜎1𝑣1 𝜎1𝑣1 PROPN iajs-3598 190 1 [ [ X iajs-3598 190 2 3 3 NUM iajs-3598 190 3 ] ] PUNCT iajs-3598 190 4 𝜎2𝑣1 𝜎2𝑣1 NOUN iajs-3598 190 5 [ [ X iajs-3598 190 6 3 3 X iajs-3598 190 7 ] ] PUNCT iajs-3598 190 8 ] ] PUNCT iajs-3598 191 1 = = PUNCT iajs-3598 191 2 [ [ PUNCT iajs-3598 191 3 ( ( PUNCT iajs-3598 191 4 1 1 NUM iajs-3598 191 5 βˆ’ βˆ’ NUM iajs-3598 191 6 1 1 NUM iajs-3598 191 7 𝐾1 𝐾1 PROPN iajs-3598 191 8 ) ) PUNCT iajs-3598 191 9 𝑣1 𝑣1 NOUN iajs-3598 191 10 [ [ X iajs-3598 191 11 3 3 NUM iajs-3598 191 12 ] ] SYM iajs-3598 191 13 0 0 NUM iajs-3598 191 14 0 0 NUM iajs-3598 191 15 ] ] PUNCT iajs-3598 191 16 ( ( PUNCT iajs-3598 191 17 𝑍[3 𝑍[3 PROPN iajs-3598 191 18 ] ] X iajs-3598 191 19 ) ) PUNCT iajs-3598 191 20 𝑇 𝑇 PROPN iajs-3598 192 1 [ [ X iajs-3598 192 2 𝐷𝑓 𝐷𝑓 PROPN iajs-3598 192 3 οΏ½ οΏ½ PROPN iajs-3598 192 4 Μ… Μ… NOUN iajs-3598 192 5 οΏ½ οΏ½ NOUN iajs-3598 192 6 1 1 NUM iajs-3598 192 7 ( ( PUNCT iajs-3598 192 8 𝐻6 𝐻6 NOUN iajs-3598 192 9 , , PUNCT iajs-3598 192 10 𝑆1Μ…)𝑉[3 𝑆1Μ…)𝑉[3 ADV iajs-3598 192 11 ] ] X iajs-3598 192 12 ] ] X iajs-3598 193 1 = = SYM iajs-3598 193 2 ( ( PUNCT iajs-3598 193 3 𝑧1 𝑧1 NOUN iajs-3598 193 4 [ [ X iajs-3598 193 5 3 3 NUM iajs-3598 193 6 ] ] PUNCT iajs-3598 193 7 , , PUNCT iajs-3598 193 8 0,0 0,0 NUM iajs-3598 193 9 ) ) PUNCT iajs-3598 193 10 𝑇 𝑇 PROPN iajs-3598 193 11 ( ( PUNCT iajs-3598 193 12 ( ( PUNCT iajs-3598 193 13 1 1 NUM iajs-3598 193 14 βˆ’ βˆ’ NUM iajs-3598 193 15 1 1 NUM iajs-3598 193 16 𝐾1 𝐾1 PROPN iajs-3598 193 17 ) ) PUNCT iajs-3598 193 18 𝑣1 𝑣1 NOUN iajs-3598 193 19 [ [ X iajs-3598 193 20 3 3 NUM iajs-3598 193 21 ] ] PUNCT iajs-3598 193 22 , , PUNCT iajs-3598 193 23 0,0 0,0 NOUN iajs-3598 193 24 ) ) PUNCT iajs-3598 193 25 = = SYM iajs-3598 193 26 ( ( PUNCT iajs-3598 193 27 1 1 NUM iajs-3598 193 28 βˆ’ βˆ’ NUM iajs-3598 193 29 1 1 NUM iajs-3598 193 30 𝐾1 𝐾1 PROPN iajs-3598 193 31 ) ) PUNCT iajs-3598 193 32 𝑣1 𝑣1 NOUN iajs-3598 193 33 [ [ X iajs-3598 193 34 3 3 NUM iajs-3598 193 35 ] ] X iajs-3598 193 36 𝑧1 𝑧1 NOUN iajs-3598 193 37 [ [ X iajs-3598 193 38 3 3 X iajs-3598 193 39 ] ] PUNCT iajs-3598 193 40 β‰  β‰  X iajs-3598 193 41 0 0 NUM iajs-3598 193 42 by by ADP iajs-3598 193 43 substituting substitute VERB iajs-3598 193 44 𝑉[6 𝑉[6 PRON iajs-3598 193 45 ] ] PUNCT iajs-3598 193 46 in in ADP iajs-3598 193 47 ( ( PUNCT iajs-3598 193 48 3 3 X iajs-3598 193 49 ) ) PUNCT iajs-3598 193 50 we we PRON iajs-3598 193 51 get get VERB iajs-3598 193 52 : : PUNCT iajs-3598 193 53 𝐷2πΉπœ‡(𝐻6 𝐷2πΉπœ‡(𝐻6 NOUN iajs-3598 193 54 , , PUNCT iajs-3598 193 55 𝑆1)(𝑉[3 𝑆1)(𝑉[3 PROPN iajs-3598 193 56 ] ] PUNCT iajs-3598 193 57 , , PUNCT iajs-3598 193 58 𝑉[3 𝑉[3 PROPN iajs-3598 193 59 ] ] X iajs-3598 193 60 ) ) PUNCT iajs-3598 193 61 = = PUNCT iajs-3598 194 1 [ [ PUNCT iajs-3598 194 2 οΏ½ οΏ½ NOUN iajs-3598 194 3 Μ… Μ… NOUN iajs-3598 194 4 οΏ½ οΏ½ NOUN iajs-3598 194 5 𝑖1]3Γ—1 𝑖1]3Γ—1 PROPN iajs-3598 194 6 , , PUNCT iajs-3598 194 7 οΏ½ οΏ½ PROPN iajs-3598 194 8 Μ… Μ… NOUN iajs-3598 194 9 οΏ½ οΏ½ NOUN iajs-3598 194 10 11 11 NUM iajs-3598 194 11 = = SYM iajs-3598 194 12 βˆ’ βˆ’ PROPN iajs-3598 194 13 2𝑆1 2𝑆1 NUM iajs-3598 194 14 𝐾1 𝐾1 NOUN iajs-3598 194 15 + + CCONJ iajs-3598 194 16 ( ( PUNCT iajs-3598 194 17 𝑣1 𝑣1 NOUN iajs-3598 194 18 [ [ X iajs-3598 194 19 3 3 NUM iajs-3598 194 20 ] ] PUNCT iajs-3598 194 21 ) ) PUNCT iajs-3598 194 22 2 2 NUM iajs-3598 194 23 [ [ PUNCT iajs-3598 194 24 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NUM iajs-3598 194 25 ( ( PUNCT iajs-3598 194 26 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 194 27 2 2 NUM iajs-3598 194 28 ) ) PUNCT iajs-3598 194 29 2 2 NUM iajs-3598 194 30 βˆ’ βˆ’ NOUN iajs-3598 194 31 𝐢1 𝐢1 PROPN iajs-3598 194 32 ( ( PUNCT iajs-3598 194 33 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 194 34 2 2 NUM iajs-3598 194 35 ) ) PUNCT iajs-3598 194 36 ( ( PUNCT iajs-3598 194 37 ( ( PUNCT iajs-3598 194 38 π‘Ž1 π‘Ž1 X iajs-3598 194 39 + + CCONJ iajs-3598 194 40 𝐿1 𝐿1 PROPN iajs-3598 194 41 2 2 NUM iajs-3598 194 42 ) ) PUNCT iajs-3598 194 43 + + CCONJ iajs-3598 194 44 ( ( PUNCT iajs-3598 194 45 π‘Ž1 π‘Ž1 X iajs-3598 194 46 + + PRON iajs-3598 194 47 2𝐿1 2𝐿1 NUM iajs-3598 194 48 ) ) PUNCT iajs-3598 194 49 ) ) PUNCT iajs-3598 195 1 + + CCONJ iajs-3598 196 1 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 196 2 2 2 NUM iajs-3598 196 3 ( ( PUNCT iajs-3598 196 4 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 196 5 2 2 NUM iajs-3598 196 6 ) ) PUNCT iajs-3598 196 7 ] ] PUNCT iajs-3598 196 8 , , PUNCT iajs-3598 196 9 οΏ½ οΏ½ PROPN iajs-3598 196 10 Μ… Μ… NOUN iajs-3598 196 11 οΏ½ οΏ½ NOUN iajs-3598 196 12 21 21 NUM iajs-3598 196 13 = = SYM iajs-3598 196 14 βˆ’2𝐢 βˆ’2𝐢 NOUN iajs-3598 196 15 + + CCONJ iajs-3598 196 16 ( ( PUNCT iajs-3598 196 17 𝑣3 𝑣3 ADJ iajs-3598 196 18 [ [ X iajs-3598 196 19 1 1 NUM iajs-3598 196 20 ] ] PUNCT iajs-3598 196 21 ) ) PUNCT iajs-3598 196 22 2 2 NUM iajs-3598 196 23 [ [ PUNCT iajs-3598 196 24 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 196 25 ( ( PUNCT iajs-3598 196 26 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 196 27 ) ) PUNCT iajs-3598 196 28 βˆ’ βˆ’ PROPN iajs-3598 196 29 ( ( PUNCT iajs-3598 196 30 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 196 31 ( ( PUNCT iajs-3598 196 32 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 196 33 + + CCONJ iajs-3598 196 34 𝐢2 𝐢2 PROPN iajs-3598 196 35 ( ( PUNCT iajs-3598 196 36 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 196 37 ) ) PUNCT iajs-3598 196 38 𝜎1 𝜎1 ADJ iajs-3598 196 39 + + CCONJ iajs-3598 196 40 𝜎1𝐢2π‘Ž2𝐿3 𝜎1𝐢2π‘Ž2𝐿3 NOUN iajs-3598 196 41 ( ( PUNCT iajs-3598 196 42 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 196 43 + + CCONJ iajs-3598 196 44 ( ( PUNCT iajs-3598 196 45 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 196 46 2𝜎2 2𝜎2 NUM iajs-3598 196 47 2𝐿3 2𝐿3 NUM iajs-3598 196 48 ( ( PUNCT iajs-3598 196 49 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 196 50 βˆ’ βˆ’ PROPN iajs-3598 196 51 𝜎2 𝜎2 NOUN iajs-3598 196 52 2𝐢2(1βˆ’π‘Ž3𝐿3 2𝐢2(1βˆ’π‘Ž3𝐿3 NUM iajs-3598 196 53 ) ) PUNCT iajs-3598 196 54 ( ( PUNCT iajs-3598 196 55 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 196 56 ) ) PUNCT iajs-3598 196 57 ] ] PUNCT iajs-3598 196 58 , , PUNCT iajs-3598 196 59 οΏ½ οΏ½ PROPN iajs-3598 196 60 Μ… Μ… NOUN iajs-3598 196 61 οΏ½ οΏ½ NOUN iajs-3598 196 62 31 31 NUM iajs-3598 196 63 = = SYM iajs-3598 196 64 ( ( PUNCT iajs-3598 196 65 𝑣1 𝑣1 NOUN iajs-3598 196 66 [ [ X iajs-3598 196 67 3 3 NUM iajs-3598 196 68 ] ] PUNCT iajs-3598 196 69 ) ) PUNCT iajs-3598 196 70 2 2 NUM iajs-3598 196 71 [ [ PUNCT iajs-3598 196 72 2𝑔1𝐿1𝐿3 2𝑔1𝐿1𝐿3 NUM iajs-3598 196 73 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 196 74 2 2 NUM iajs-3598 196 75 + + CCONJ iajs-3598 196 76 ( ( PUNCT iajs-3598 196 77 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 196 78 2 2 NUM iajs-3598 196 79 ) ) PUNCT iajs-3598 196 80 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 196 81 2 2 NUM iajs-3598 196 82 + + NUM iajs-3598 196 83 𝑔1 𝑔1 PROPN iajs-3598 196 84 ) ) PUNCT iajs-3598 196 85 𝜎2 𝜎2 PROPN iajs-3598 196 86 βˆ’ βˆ’ PROPN iajs-3598 196 87 2πœ‡πœŽ1 2πœ‡πœŽ1 NUM iajs-3598 196 88 βˆ’ βˆ’ PROPN iajs-3598 196 89 2π‘Ž2𝑔2𝜎1𝐿3 2π‘Ž2𝑔2𝜎1𝐿3 NUM iajs-3598 196 90 ( ( PUNCT iajs-3598 196 91 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 196 92 ) ) PUNCT iajs-3598 196 93 βˆ’ βˆ’ PROPN iajs-3598 196 94 π‘Ž2𝐿2𝑔2𝜎1𝜎2 π‘Ž2𝐿2𝑔2𝜎1𝜎2 PROPN iajs-3598 196 95 ( ( PUNCT iajs-3598 196 96 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 196 97 + + CCONJ iajs-3598 196 98 𝑔2𝜎1𝜎2 𝑔2𝜎1𝜎2 PROPN iajs-3598 196 99 ( ( PUNCT iajs-3598 196 100 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 196 101 βˆ’ βˆ’ PROPN iajs-3598 196 102 2𝑔2π‘Ž3𝜎1𝐿3 2𝑔2π‘Ž3𝜎1𝐿3 NUM iajs-3598 196 103 ( ( PUNCT iajs-3598 196 104 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 196 105 ] ] PUNCT iajs-3598 196 106 . . PUNCT iajs-3598 197 1 hence hence ADV iajs-3598 197 2 , , PUNCT iajs-3598 197 3 it it PRON iajs-3598 197 4 was be AUX iajs-3598 197 5 obtained obtain VERB iajs-3598 197 6 ( ( PUNCT iajs-3598 197 7 𝑍[3 𝑍[3 PROPN iajs-3598 197 8 ] ] X iajs-3598 197 9 ) ) PUNCT iajs-3598 197 10 𝑇 𝑇 PROPN iajs-3598 198 1 [ [ X iajs-3598 198 2 𝐷2πΉπœ‡(𝐻6 𝐷2πΉπœ‡(𝐻6 PROPN iajs-3598 198 3 , , PUNCT iajs-3598 198 4 𝑆1)(𝑉[3 𝑆1)(𝑉[3 PROPN iajs-3598 198 5 ] ] PUNCT iajs-3598 198 6 , , PUNCT iajs-3598 198 7 𝑉[3 𝑉[3 PROPN iajs-3598 198 8 ] ] X iajs-3598 198 9 ) ) PUNCT iajs-3598 198 10 ] ] PUNCT iajs-3598 199 1 = = PUNCT iajs-3598 199 2 𝑧1 𝑧1 NOUN iajs-3598 200 1 [ [ X iajs-3598 200 2 3]( 3]( NUM iajs-3598 200 3 οΏ½ οΏ½ NOUN iajs-3598 200 4 Μ… Μ… NOUN iajs-3598 200 5 οΏ½ οΏ½ NOUN iajs-3598 200 6 1 1 NUM iajs-3598 200 7 βˆ’ βˆ’ NOUN iajs-3598 200 8 οΏ½ οΏ½ NOUN iajs-3598 200 9 Μ… Μ… NOUN iajs-3598 200 10 οΏ½ οΏ½ NOUN iajs-3598 200 11 2 2 NUM iajs-3598 200 12 ) ) PUNCT iajs-3598 200 13 β‰  β‰  PROPN iajs-3598 200 14 0 0 NUM iajs-3598 200 15 , , PUNCT iajs-3598 200 16 so so ADV iajs-3598 200 17 , , PUNCT iajs-3598 200 18 system system NOUN iajs-3598 200 19 ( ( PUNCT iajs-3598 200 20 1 1 X iajs-3598 200 21 ) ) PUNCT iajs-3598 200 22 has have VERB iajs-3598 200 23 ( ( PUNCT iajs-3598 200 24 tc tc NOUN iajs-3598 200 25 ) ) PUNCT iajs-3598 200 26 bifurcation bifurcation NOUN iajs-3598 200 27 at at ADP iajs-3598 200 28 𝐻6 𝐻6 NOUN iajs-3598 200 29 with with ADP iajs-3598 200 30 a a DET iajs-3598 200 31 parameter parameter NOUN iajs-3598 200 32 𝑆1Μ… 𝑆1Μ… NOUN iajs-3598 200 33 = = SYM iajs-3598 200 34 𝑆1 𝑆1 NOUN iajs-3598 200 35 . . PUNCT iajs-3598 201 1 if if SCONJ iajs-3598 201 2 the the DET iajs-3598 201 3 requirement requirement NOUN iajs-3598 201 4 ( ( PUNCT iajs-3598 201 5 13 13 NUM iajs-3598 201 6 ) ) PUNCT iajs-3598 201 7 not not PART iajs-3598 201 8 satisfied satisfied ADJ iajs-3598 201 9 then then ADV iajs-3598 201 10 . . PUNCT iajs-3598 202 1 ihjpas ihjpas PROPN iajs-3598 202 2 . . PUNCT iajs-3598 203 1 2025 2025 NUM iajs-3598 203 2 , , PUNCT iajs-3598 203 3 38 38 NUM iajs-3598 203 4 ( ( PUNCT iajs-3598 203 5 1 1 NUM iajs-3598 203 6 ) ) PUNCT iajs-3598 203 7 438 438 NUM iajs-3598 203 8 by by ADP iajs-3598 203 9 substituting substitute VERB iajs-3598 203 10 𝑉[3 𝑉[3 PROPN iajs-3598 203 11 ] ] PUNCT iajs-3598 203 12 in in ADP iajs-3598 203 13 ( ( PUNCT iajs-3598 203 14 4 4 X iajs-3598 203 15 ) ) PUNCT iajs-3598 203 16 we we PRON iajs-3598 203 17 get get VERB iajs-3598 203 18 : : PUNCT iajs-3598 203 19 𝐷3πΉπœ‡(𝐻6 𝐷3πΉπœ‡(𝐻6 NOUN iajs-3598 203 20 , , PUNCT iajs-3598 203 21 𝑆1)(𝑉[3 𝑆1)(𝑉[3 PROPN iajs-3598 203 22 ] ] PUNCT iajs-3598 203 23 , , PUNCT iajs-3598 203 24 𝑉[3 𝑉[3 PROPN iajs-3598 203 25 ] ] PUNCT iajs-3598 203 26 , , PUNCT iajs-3598 203 27 𝑉[3 𝑉[3 PROPN iajs-3598 203 28 ] ] X iajs-3598 203 29 ) ) PUNCT iajs-3598 203 30 = = SYM iajs-3598 203 31 ( ( PUNCT iajs-3598 203 32 οΏ½ οΏ½ NOUN iajs-3598 203 33 Μ… Μ… NOUN iajs-3598 203 34 οΏ½ οΏ½ PROPN iajs-3598 203 35 𝑖1)3Γ—1 𝑖1)3Γ—1 SYM iajs-3598 203 36 οΏ½ οΏ½ NOUN iajs-3598 203 37 Μ… Μ… NOUN iajs-3598 203 38 οΏ½ οΏ½ NOUN iajs-3598 203 39 11 11 NUM iajs-3598 203 40 = = SYM iajs-3598 203 41 2 2 NUM iajs-3598 203 42 ( ( PUNCT iajs-3598 203 43 𝑣1 𝑣1 NOUN iajs-3598 203 44 [ [ X iajs-3598 203 45 3 3 NUM iajs-3598 203 46 ] ] PUNCT iajs-3598 203 47 ) ) PUNCT iajs-3598 203 48 3 3 NUM iajs-3598 204 1 [ [ PUNCT iajs-3598 204 2 2𝐢1𝜎1 2𝐢1𝜎1 NUM iajs-3598 204 3 3π‘Ž1𝐿3(1βˆ’4𝐿1 3π‘Ž1𝐿3(1βˆ’4𝐿1 NUM iajs-3598 204 4 2 2 NUM iajs-3598 204 5 ) ) PUNCT iajs-3598 204 6 ( ( PUNCT iajs-3598 204 7 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 204 8 2 2 NUM iajs-3598 204 9 ) ) PUNCT iajs-3598 204 10 2 2 NUM iajs-3598 204 11 βˆ’ βˆ’ NOUN iajs-3598 204 12 𝜎1 𝜎1 ADJ iajs-3598 204 13 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 204 14 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 204 15 2 2 NUM iajs-3598 204 16 + + NUM iajs-3598 204 17 οΏ½ οΏ½ PROPN iajs-3598 204 18 Μ‡ Μ‡ VERB iajs-3598 204 19 οΏ½ οΏ½ PROPN iajs-3598 204 20 1 1 NUM iajs-3598 204 21 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 205 1 + + CCONJ iajs-3598 205 2 𝜎1 𝜎1 ADJ iajs-3598 205 3 2𝐿1 2𝐿1 NUM iajs-3598 205 4 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 205 5 2 2 NUM iajs-3598 205 6 βˆ’ βˆ’ PROPN iajs-3598 205 7 2𝜎1 2𝜎1 NUM iajs-3598 205 8 2𝐢1𝐿1 2𝐢1𝐿1 NUM iajs-3598 205 9 3 3 NUM iajs-3598 205 10 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 205 11 2 2 NUM iajs-3598 205 12 βˆ’ βˆ’ NOUN iajs-3598 205 13 𝜎1 𝜎1 ADJ iajs-3598 205 14 2𝐢1 2𝐢1 NUM iajs-3598 205 15 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 205 16 2 2 NUM iajs-3598 205 17 + + NUM iajs-3598 205 18 𝜎1 𝜎1 ADJ iajs-3598 205 19 2𝐢1𝐿1(π‘Ž1 2𝐢1𝐿1(π‘Ž1 NUM iajs-3598 205 20 + + NOUN iajs-3598 205 21 2𝐿1 2𝐿1 NUM iajs-3598 205 22 ) ) PUNCT iajs-3598 205 23 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 205 24 2 2 NUM iajs-3598 205 25 + + CCONJ iajs-3598 205 26 4𝜎1 4𝜎1 NUM iajs-3598 205 27 2𝐢1π‘Ž1𝐿1 2𝐢1π‘Ž1𝐿1 NUM iajs-3598 205 28 ( ( PUNCT iajs-3598 205 29 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 205 30 2 2 NUM iajs-3598 205 31 ) ) PUNCT iajs-3598 205 32 2 2 NUM iajs-3598 205 33 ] ] PUNCT iajs-3598 205 34 , , PUNCT iajs-3598 205 35 οΏ½ οΏ½ NOUN iajs-3598 205 36 Μ… Μ… NOUN iajs-3598 205 37 οΏ½ οΏ½ NOUN iajs-3598 205 38 21 21 NUM iajs-3598 205 39 = = SYM iajs-3598 205 40 ( ( PUNCT iajs-3598 205 41 𝑣1 𝑣1 NOUN iajs-3598 205 42 [ [ X iajs-3598 205 43 3 3 NUM iajs-3598 205 44 ] ] PUNCT iajs-3598 205 45 ) ) PUNCT iajs-3598 205 46 3 3 NUM iajs-3598 206 1 [ [ X iajs-3598 206 2 βˆ’ βˆ’ PROPN iajs-3598 206 3 2 2 NUM iajs-3598 206 4 οΏ½ οΏ½ PROPN iajs-3598 206 5 Μ‡ Μ‡ VERB iajs-3598 206 6 οΏ½ οΏ½ PROPN iajs-3598 206 7 1 1 NUM iajs-3598 206 8 2 2 NUM iajs-3598 206 9 οΏ½ οΏ½ PROPN iajs-3598 206 10 Μ‡ Μ‡ NOUN iajs-3598 206 11 οΏ½ οΏ½ NOUN iajs-3598 206 12 2𝐢2π‘Ž2𝐿3 2𝐢2π‘Ž2𝐿3 NUM iajs-3598 206 13 ( ( PUNCT iajs-3598 206 14 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 206 15 ) ) PUNCT iajs-3598 207 1 + + CCONJ iajs-3598 207 2 2𝐢2 2𝐢2 NUM iajs-3598 207 3 οΏ½ οΏ½ PROPN iajs-3598 207 4 Μ‡ Μ‡ NOUN iajs-3598 207 5 οΏ½ οΏ½ ADP iajs-3598 207 6 2 2 NUM iajs-3598 207 7 2π‘Ž2 2π‘Ž2 NUM iajs-3598 207 8 2𝐿3 2𝐿3 NUM iajs-3598 207 9 ( ( PUNCT iajs-3598 207 10 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 207 11 + + SYM iajs-3598 207 12 οΏ½ οΏ½ PROPN iajs-3598 207 13 Μ‡ Μ‡ VERB iajs-3598 207 14 οΏ½ οΏ½ PROPN iajs-3598 207 15 2 2 NUM iajs-3598 207 16 2𝐢2π‘Ž2 2𝐢2π‘Ž2 NUM iajs-3598 207 17 ( ( PUNCT iajs-3598 207 18 1+π‘Ž2𝐿2 1+π‘Ž2𝐿2 PROPN iajs-3598 207 19 ) ) PUNCT iajs-3598 207 20 + + CCONJ iajs-3598 207 21 οΏ½ οΏ½ PROPN iajs-3598 207 22 Μ‡ Μ‡ PROPN iajs-3598 207 23 οΏ½ οΏ½ NOUN iajs-3598 207 24 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 NUM iajs-3598 207 25 ) ) PUNCT iajs-3598 208 1 ( ( PUNCT iajs-3598 208 2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 208 3 + + CCONJ iajs-3598 208 4 𝐢2 𝐢2 PROPN iajs-3598 208 5 οΏ½ οΏ½ PROPN iajs-3598 208 6 Μ‡ Μ‡ NOUN iajs-3598 208 7 οΏ½ οΏ½ PROPN iajs-3598 208 8 1 1 NUM iajs-3598 208 9 2 2 NUM iajs-3598 208 10 ( ( PUNCT iajs-3598 208 11 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 208 12 + + CCONJ iajs-3598 208 13 ( ( PUNCT iajs-3598 208 14 4𝑆2 4𝑆2 NUM iajs-3598 208 15 οΏ½ οΏ½ NOUN iajs-3598 208 16 Μ‡ Μ‡ VERB iajs-3598 208 17 οΏ½ οΏ½ NOUN iajs-3598 208 18 2𝑓1𝐿3 2𝑓1𝐿3 NUM iajs-3598 208 19 ( ( PUNCT iajs-3598 208 20 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 208 21 βˆ’ βˆ’ PROPN iajs-3598 208 22 οΏ½ οΏ½ PROPN iajs-3598 208 23 Μ‡ Μ‡ PROPN iajs-3598 208 24 οΏ½ οΏ½ NOUN iajs-3598 208 25 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 2𝐢2π‘Ž2(1βˆ’π‘Ž3𝐿3 NUM iajs-3598 208 26 ) ) PUNCT iajs-3598 208 27 ( ( PUNCT iajs-3598 208 28 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 208 29 + + ADJ iajs-3598 208 30 2 2 NUM iajs-3598 208 31 οΏ½ οΏ½ NOUN iajs-3598 208 32 Μ‡ Μ‡ NOUN iajs-3598 208 33 οΏ½ οΏ½ SYM iajs-3598 208 34 2𝐢2π‘Ž3 2𝐢2π‘Ž3 PROPN iajs-3598 208 35 ( ( PUNCT iajs-3598 208 36 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3 NUM iajs-3598 208 37 ) ) PUNCT iajs-3598 208 38 ) ) PUNCT iajs-3598 209 1 + + CCONJ iajs-3598 209 2 ( ( PUNCT iajs-3598 209 3 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 209 4 2(1βˆ’2𝑓1𝐿3 2(1βˆ’2𝑓1𝐿3 NUM iajs-3598 209 5 ) ) PUNCT iajs-3598 209 6 ( ( PUNCT iajs-3598 209 7 1+𝑓1𝐿3)6 1+𝑓1𝐿3)6 NUM iajs-3598 209 8 + + CCONJ iajs-3598 209 9 4𝐢2π‘Ž3 4𝐢2π‘Ž3 PROPN iajs-3598 209 10 ( ( PUNCT iajs-3598 209 11 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 209 12 ) ) PUNCT iajs-3598 209 13 ] ] PUNCT iajs-3598 209 14 , , PUNCT iajs-3598 209 15 οΏ½ οΏ½ PROPN iajs-3598 209 16 Μ… Μ… NOUN iajs-3598 209 17 οΏ½ οΏ½ NOUN iajs-3598 209 18 31 31 NUM iajs-3598 209 19 = = SYM iajs-3598 209 20 ( ( PUNCT iajs-3598 209 21 𝑣1 𝑣1 NOUN iajs-3598 209 22 [ [ X iajs-3598 209 23 3 3 NUM iajs-3598 209 24 ] ] PUNCT iajs-3598 209 25 ) ) PUNCT iajs-3598 209 26 3 3 NUM iajs-3598 209 27 [ [ PUNCT iajs-3598 209 28 2𝑔1 2𝑔1 NUM iajs-3598 209 29 οΏ½ οΏ½ PROPN iajs-3598 209 30 Μ‡ Μ‡ NOUN iajs-3598 209 31 οΏ½ οΏ½ PROPN iajs-3598 209 32 1 1 NUM iajs-3598 209 33 3𝐿3(π‘Ž1βˆ’πΏ1 3𝐿3(π‘Ž1βˆ’πΏ1 NUM iajs-3598 209 34 2 2 NUM iajs-3598 209 35 ) ) PUNCT iajs-3598 209 36 ( ( PUNCT iajs-3598 209 37 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 209 38 2 2 NUM iajs-3598 209 39 ) ) PUNCT iajs-3598 209 40 2 2 NUM iajs-3598 209 41 βˆ’ βˆ’ PROPN iajs-3598 209 42 2𝑔1 2𝑔1 NUM iajs-3598 209 43 οΏ½ οΏ½ PROPN iajs-3598 209 44 Μ‡ Μ‡ NOUN iajs-3598 209 45 οΏ½ οΏ½ PROPN iajs-3598 209 46 1 1 NUM iajs-3598 209 47 2𝐿1(2π‘Ž1 2𝐿1(2π‘Ž1 NUM iajs-3598 209 48 + + NOUN iajs-3598 209 49 1 1 NUM iajs-3598 209 50 ) ) PUNCT iajs-3598 209 51 ( ( PUNCT iajs-3598 209 52 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 209 53 2 2 NUM iajs-3598 209 54 ) ) PUNCT iajs-3598 209 55 2 2 NUM iajs-3598 210 1 + + NUM iajs-3598 211 1 6π‘Ž2 6π‘Ž2 NUM iajs-3598 211 2 2𝑔2 2𝑔2 NUM iajs-3598 211 3 οΏ½ οΏ½ NOUN iajs-3598 211 4 Μ‡ Μ‡ NOUN iajs-3598 211 5 οΏ½ οΏ½ PROPN iajs-3598 211 6 1 1 NUM iajs-3598 211 7 3𝐿3 3𝐿3 NUM iajs-3598 211 8 ( ( PUNCT iajs-3598 211 9 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)4(1+π‘Ž3𝐿3 NUM iajs-3598 211 10 ) ) PUNCT iajs-3598 211 11 + + CCONJ iajs-3598 211 12 2π‘Ž2 2π‘Ž2 NUM iajs-3598 211 13 2𝑔2 2𝑔2 NUM iajs-3598 211 14 οΏ½ οΏ½ NOUN iajs-3598 211 15 Μ‡ Μ‡ VERB iajs-3598 211 16 οΏ½ οΏ½ PROPN iajs-3598 211 17 2 2 NUM iajs-3598 211 18 2𝐿2 2𝐿2 NUM iajs-3598 211 19 ( ( PUNCT iajs-3598 211 20 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 211 21 βˆ’ βˆ’ PROPN iajs-3598 211 22 4π‘Ž2𝑔2 4π‘Ž2𝑔2 NUM iajs-3598 211 23 οΏ½ οΏ½ NOUN iajs-3598 211 24 Μ‡ Μ‡ NOUN iajs-3598 211 25 οΏ½ οΏ½ PROPN iajs-3598 211 26 2 2 NUM iajs-3598 211 27 2 2 NUM iajs-3598 211 28 ( ( PUNCT iajs-3598 211 29 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3)2 NUM iajs-3598 211 30 + + CCONJ iajs-3598 211 31 2𝑔1 2𝑔1 NUM iajs-3598 211 32 οΏ½ οΏ½ NOUN iajs-3598 211 33 Μ‡ Μ‡ NOUN iajs-3598 211 34 οΏ½ οΏ½ PROPN iajs-3598 211 35 1 1 NUM iajs-3598 211 36 2𝐿1 2𝐿1 NUM iajs-3598 211 37 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 211 38 2 2 NUM iajs-3598 211 39 + + CCONJ iajs-3598 211 40 π‘Ž3𝑔2 π‘Ž3𝑔2 NOUN iajs-3598 211 41 οΏ½ οΏ½ NOUN iajs-3598 211 42 Μ‡ Μ‡ NOUN iajs-3598 211 43 οΏ½ οΏ½ X iajs-3598 211 44 2 2 NUM iajs-3598 211 45 ( ( PUNCT iajs-3598 211 46 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 NUM iajs-3598 211 47 ( ( PUNCT iajs-3598 211 48 2π‘Ž2𝐿3 2π‘Ž2𝐿3 NUM iajs-3598 211 49 + + NUM iajs-3598 211 50 π‘Ž2𝐿2 π‘Ž2𝐿2 NUM iajs-3598 211 51 ) ) PUNCT iajs-3598 212 1 βˆ’ βˆ’ ADP iajs-3598 212 2 2π‘Ž3𝑔2 2π‘Ž3𝑔2 NUM iajs-3598 212 3 οΏ½ οΏ½ NOUN iajs-3598 212 4 Μ‡ Μ‡ NOUN iajs-3598 212 5 οΏ½ οΏ½ X iajs-3598 212 6 2 2 NUM iajs-3598 212 7 ( ( PUNCT iajs-3598 212 8 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)3 VERB iajs-3598 212 9 βˆ’ βˆ’ PROPN iajs-3598 212 10 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 2𝑔2π‘Ž3(1βˆ’2π‘Ž3𝐿3 NUM iajs-3598 212 11 ) ) PUNCT iajs-3598 212 12 ( ( PUNCT iajs-3598 212 13 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)4 X iajs-3598 212 14 . . PUNCT iajs-3598 213 1 ( ( PUNCT iajs-3598 213 2 𝑍[3 𝑍[3 PROPN iajs-3598 213 3 ] ] X iajs-3598 213 4 ) ) PUNCT iajs-3598 213 5 𝑇 𝑇 PROPN iajs-3598 214 1 [ [ X iajs-3598 214 2 𝐷3πΉπœ‡(𝐻6 𝐷3πΉπœ‡(𝐻6 PROPN iajs-3598 214 3 , , PUNCT iajs-3598 214 4 𝑆1)(𝑉[3 𝑆1)(𝑉[3 PROPN iajs-3598 214 5 ] ] PUNCT iajs-3598 214 6 , , PUNCT iajs-3598 214 7 𝑉[3 𝑉[3 PROPN iajs-3598 214 8 ] ] PUNCT iajs-3598 214 9 , , PUNCT iajs-3598 214 10 𝑉[3 𝑉[3 PROPN iajs-3598 214 11 ] ] X iajs-3598 214 12 ) ) PUNCT iajs-3598 214 13 ] ] PUNCT iajs-3598 215 1 = = SYM iajs-3598 215 2 2 2 NUM iajs-3598 215 3 ( ( PUNCT iajs-3598 215 4 𝑣1 𝑣1 NOUN iajs-3598 215 5 [ [ X iajs-3598 215 6 3 3 NUM iajs-3598 215 7 ] ] PUNCT iajs-3598 215 8 ) ) PUNCT iajs-3598 215 9 3 3 NUM iajs-3598 215 10 𝑧1 𝑧1 NOUN iajs-3598 215 11 [ [ X iajs-3598 215 12 3 3 NUM iajs-3598 215 13 ] ] X iajs-3598 215 14 ( ( PUNCT iajs-3598 215 15 οΏ½ οΏ½ NOUN iajs-3598 215 16 Μ… Μ… NOUN iajs-3598 215 17 οΏ½ οΏ½ NOUN iajs-3598 215 18 3 3 NUM iajs-3598 215 19 βˆ’ βˆ’ PROPN iajs-3598 215 20 οΏ½ οΏ½ PROPN iajs-3598 215 21 Μ… Μ… NOUN iajs-3598 215 22 οΏ½ οΏ½ NOUN iajs-3598 215 23 4 4 NUM iajs-3598 215 24 ) ) PUNCT iajs-3598 215 25 β‰  β‰  PROPN iajs-3598 215 26 0 0 NUM iajs-3598 216 1 so so ADV iajs-3598 216 2 , , PUNCT iajs-3598 216 3 pitchfork pitchfork NOUN iajs-3598 216 4 bifurcation bifurcation NOUN iajs-3598 216 5 can can AUX iajs-3598 216 6 be be AUX iajs-3598 216 7 found find VERB iajs-3598 216 8 at at ADP iajs-3598 216 9 𝐻6 𝐻6 NOUN iajs-3598 216 10 where where SCONJ iajs-3598 216 11 𝑆1Μ… 𝑆1Μ… VERB iajs-3598 216 12 = = SYM iajs-3598 216 13 𝑆1 𝑆1 NOUN iajs-3598 216 14 . . PUNCT iajs-3598 217 1 theorem theorem NOUN iajs-3598 217 2 ( ( PUNCT iajs-3598 217 3 4 4 NUM iajs-3598 217 4 ): ): PUNCT iajs-3598 217 5 if if SCONJ iajs-3598 217 6 conditions condition NOUN iajs-3598 217 7 ( ( PUNCT iajs-3598 217 8 1.11c 1.11c NUM iajs-3598 217 9 ) ) PUNCT iajs-3598 217 10 and and CCONJ iajs-3598 217 11 ( ( PUNCT iajs-3598 217 12 1.11d 1.11d NUM iajs-3598 217 13 ) ) PUNCT iajs-3598 217 14 in in ADP iajs-3598 217 15 ( ( PUNCT iajs-3598 217 16 22 22 NUM iajs-3598 217 17 ) ) PUNCT iajs-3598 217 18 are be AUX iajs-3598 217 19 reversing reverse VERB iajs-3598 217 20 if if SCONJ iajs-3598 217 21 the the DET iajs-3598 217 22 following follow VERB iajs-3598 217 23 requirements requirement NOUN iajs-3598 217 24 are be AUX iajs-3598 217 25 fulfilled fulfil VERB iajs-3598 217 26 : : PUNCT iajs-3598 217 27 β„ŽΜƒ31β„ŽΜƒ31 β„ŽΜƒ31β„ŽΜƒ31 PROPN iajs-3598 217 28 = = PUNCT iajs-3598 217 29 β„ŽΜƒ32β„ŽΜƒ23 β„ŽΜƒ32β„ŽΜƒ23 PROPN iajs-3598 217 30 . . PUNCT iajs-3598 218 1 ( ( PUNCT iajs-3598 218 2 15 15 NUM iajs-3598 218 3 ) ) PUNCT iajs-3598 218 4 β„ŽΜƒ13 β„ŽΜƒ13 PUNCT iajs-3598 219 1 = = SYM iajs-3598 219 2 β„ŽΜƒ22 β„ŽΜƒ22 PROPN iajs-3598 220 1 ( ( PUNCT iajs-3598 220 2 16 16 NUM iajs-3598 220 3 ) ) PUNCT iajs-3598 220 4 οΏ½ οΏ½ PROPN iajs-3598 220 5 Μƒ Μƒ PROPN iajs-3598 220 6 οΏ½ οΏ½ NOUN iajs-3598 220 7 1 1 NUM iajs-3598 220 8 > > SYM iajs-3598 220 9 οΏ½ οΏ½ PROPN iajs-3598 220 10 Μƒ Μƒ PROPN iajs-3598 220 11 οΏ½ οΏ½ NOUN iajs-3598 220 12 2 2 NUM iajs-3598 220 13 ( ( PUNCT iajs-3598 220 14 17 17 NUM iajs-3598 220 15 ) ) PUNCT iajs-3598 220 16 οΏ½ οΏ½ PROPN iajs-3598 220 17 Μƒ Μƒ PROPN iajs-3598 220 18 οΏ½ οΏ½ PROPN iajs-3598 220 19 1 1 NUM iajs-3598 220 20 β‰  β‰  PROPN iajs-3598 220 21 οΏ½ οΏ½ PROPN iajs-3598 220 22 Μƒ Μƒ PROPN iajs-3598 220 23 οΏ½ οΏ½ NOUN iajs-3598 220 24 2 2 NUM iajs-3598 220 25 , , PUNCT iajs-3598 220 26 ( ( PUNCT iajs-3598 220 27 18 18 NUM iajs-3598 220 28 ) ) PUNCT iajs-3598 220 29 where where SCONJ iajs-3598 220 30 : : PUNCT iajs-3598 220 31 οΏ½ οΏ½ PROPN iajs-3598 220 32 Μƒ Μƒ NOUN iajs-3598 220 33 οΏ½ οΏ½ NOUN iajs-3598 220 34 1 1 NUM iajs-3598 220 35 = = SYM iajs-3598 220 36 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NOUN iajs-3598 220 37 ( ( PUNCT iajs-3598 220 38 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 220 39 2 2 NUM iajs-3598 220 40 ) ) SYM iajs-3598 220 41 2 2 NUM iajs-3598 220 42 οΏ½ οΏ½ PROPN iajs-3598 220 43 Μƒ Μƒ NOUN iajs-3598 220 44 οΏ½ οΏ½ NOUN iajs-3598 220 45 1 1 NUM iajs-3598 220 46 + + NUM iajs-3598 220 47 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 220 48 ( ( PUNCT iajs-3598 220 49 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 220 50 ) ) PUNCT iajs-3598 220 51 οΏ½ οΏ½ PROPN iajs-3598 220 52 Μƒ Μƒ PROPN iajs-3598 220 53 οΏ½ οΏ½ NOUN iajs-3598 220 54 1 1 NUM iajs-3598 220 55 2 2 NUM iajs-3598 220 56 + + NUM iajs-3598 220 57 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 220 58 2𝐿3 2𝐿3 NUM iajs-3598 220 59 ( ( PUNCT iajs-3598 220 60 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 220 61 + + SYM iajs-3598 220 62 2𝑔1𝐿1𝐿3 2𝑔1𝐿1𝐿3 NUM iajs-3598 220 63 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 220 64 2 2 NUM iajs-3598 220 65 οΏ½ οΏ½ PROPN iajs-3598 220 66 Μƒ Μƒ NOUN iajs-3598 220 67 οΏ½ οΏ½ NOUN iajs-3598 220 68 1 1 NUM iajs-3598 220 69 2 2 NUM iajs-3598 220 70 + + CCONJ iajs-3598 220 71 ( ( PUNCT iajs-3598 220 72 𝑔1(1βˆ’2𝐿1 𝑔1(1βˆ’2𝐿1 PROPN iajs-3598 220 73 2 2 NUM iajs-3598 220 74 ) ) PUNCT iajs-3598 220 75 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 220 76 2 2 NUM iajs-3598 220 77 + + NUM iajs-3598 220 78 𝑔1 𝑔1 PROPN iajs-3598 220 79 βˆ’ βˆ’ PROPN iajs-3598 220 80 2πœ‡ 2πœ‡ PROPN iajs-3598 220 81 ) ) PUNCT iajs-3598 220 82 οΏ½ οΏ½ PROPN iajs-3598 220 83 Μƒ Μƒ PROPN iajs-3598 220 84 οΏ½ οΏ½ NOUN iajs-3598 220 85 1 1 NUM iajs-3598 220 86 , , PUNCT iajs-3598 220 87 οΏ½ οΏ½ PROPN iajs-3598 220 88 Μƒ Μƒ NOUN iajs-3598 220 89 οΏ½ οΏ½ NOUN iajs-3598 220 90 2 2 NUM iajs-3598 220 91 = = SYM iajs-3598 220 92 𝐢1 𝐢1 X iajs-3598 220 93 ( ( PUNCT iajs-3598 220 94 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 220 95 2 2 NUM iajs-3598 220 96 ) ) PUNCT iajs-3598 220 97 ( ( PUNCT iajs-3598 220 98 ( ( PUNCT iajs-3598 220 99 π‘Ž1 π‘Ž1 X iajs-3598 220 100 + + CCONJ iajs-3598 220 101 𝐿1 𝐿1 PROPN iajs-3598 220 102 2 2 NUM iajs-3598 220 103 ) ) PUNCT iajs-3598 220 104 βˆ’ βˆ’ PROPN iajs-3598 220 105 2𝐿1 2𝐿1 NUM iajs-3598 220 106 2 2 NUM iajs-3598 220 107 + + CCONJ iajs-3598 220 108 ( ( PUNCT iajs-3598 220 109 π‘Ž1 π‘Ž1 X iajs-3598 220 110 + + CCONJ iajs-3598 220 111 2𝐿1)) 2𝐿1)) NUM iajs-3598 220 112 οΏ½ οΏ½ PROPN iajs-3598 220 113 Μƒ Μƒ NOUN iajs-3598 220 114 οΏ½ οΏ½ NOUN iajs-3598 220 115 1 1 NUM iajs-3598 220 116 + + CCONJ iajs-3598 220 117 ( ( PUNCT iajs-3598 220 118 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 220 119 ( ( PUNCT iajs-3598 220 120 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 220 121 + + NUM iajs-3598 220 122 𝐢2π‘Ž2𝐿3 𝐢2π‘Ž2𝐿3 PROPN iajs-3598 220 123 ( ( PUNCT iajs-3598 220 124 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 220 125 + + CCONJ iajs-3598 220 126 𝐢2 𝐢2 ADJ iajs-3598 220 127 ( ( PUNCT iajs-3598 220 128 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 220 129 ) ) PUNCT iajs-3598 220 130 οΏ½ οΏ½ PROPN iajs-3598 220 131 Μƒ Μƒ PROPN iajs-3598 220 132 οΏ½ οΏ½ NOUN iajs-3598 220 133 1 1 NUM iajs-3598 220 134 + + NUM iajs-3598 220 135 2π‘Ž2𝑔2𝐿3 2π‘Ž2𝑔2𝐿3 NUM iajs-3598 220 136 ( ( PUNCT iajs-3598 220 137 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)3(1+π‘Ž3𝐿3 NUM iajs-3598 220 138 ) ) PUNCT iajs-3598 220 139 οΏ½ οΏ½ PROPN iajs-3598 220 140 Μƒ Μƒ PROPN iajs-3598 220 141 οΏ½ οΏ½ NOUN iajs-3598 220 142 2 2 NUM iajs-3598 220 143 2 2 NUM iajs-3598 220 144 + + CCONJ iajs-3598 220 145 𝑔2 𝑔2 NOUN iajs-3598 220 146 ( ( PUNCT iajs-3598 220 147 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 NOUN iajs-3598 220 148 ( ( PUNCT iajs-3598 220 149 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 220 150 βˆ’ βˆ’ PROPN iajs-3598 220 151 1) 1) NUM iajs-3598 220 152 οΏ½ οΏ½ PROPN iajs-3598 220 153 Μƒ Μƒ NOUN iajs-3598 220 154 οΏ½ οΏ½ NOUN iajs-3598 220 155 2 2 NUM iajs-3598 220 156 + + NUM iajs-3598 220 157 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 220 158 ( ( PUNCT iajs-3598 220 159 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)3 NUM iajs-3598 220 160 . . PUNCT iajs-3598 221 1 then then ADV iajs-3598 221 2 , , PUNCT iajs-3598 221 3 system system NOUN iajs-3598 221 4 ( ( PUNCT iajs-3598 221 5 1 1 NUM iajs-3598 221 6 ) ) PUNCT iajs-3598 221 7 with with ADP iajs-3598 221 8 parameter parameter NOUN iajs-3598 221 9 value value NOUN iajs-3598 221 10 : : PUNCT iajs-3598 221 11 οΏ½ οΏ½ PROPN iajs-3598 221 12 Μƒ Μƒ NOUN iajs-3598 221 13 οΏ½ οΏ½ NOUN iajs-3598 221 14 = = SYM iajs-3598 221 15 𝑑 𝑑 PROPN iajs-3598 221 16 = = SYM iajs-3598 221 17 οΏ½ οΏ½ PROPN iajs-3598 221 18 Μƒ Μƒ PROPN iajs-3598 221 19 οΏ½ οΏ½ PROPN iajs-3598 221 20 1βˆ’ 1βˆ’ NUM iajs-3598 221 21 οΏ½ οΏ½ PROPN iajs-3598 221 22 Μƒ Μƒ NOUN iajs-3598 221 23 οΏ½ οΏ½ NOUN iajs-3598 221 24 2 2 NUM iajs-3598 221 25 ( ( PUNCT iajs-3598 221 26 β„Ž11β„Ž22)(π‘Ž1+ β„Ž11β„Ž22)(π‘Ž1+ NOUN iajs-3598 221 27 οΏ½ οΏ½ PROPN iajs-3598 221 28 Μƒ Μƒ PROPN iajs-3598 221 29 οΏ½ οΏ½ NOUN iajs-3598 221 30 1 1 NUM iajs-3598 221 31 2)(1+π‘Ž2 2)(1+π‘Ž2 NUM iajs-3598 221 32 οΏ½ οΏ½ PROPN iajs-3598 221 33 Μƒ Μƒ PROPN iajs-3598 221 34 οΏ½ οΏ½ PROPN iajs-3598 221 35 2)(1+π‘Ž3 2)(1+π‘Ž3 NOUN iajs-3598 221 36 οΏ½ οΏ½ PROPN iajs-3598 221 37 Μƒ Μƒ PROPN iajs-3598 221 38 οΏ½ οΏ½ PROPN iajs-3598 221 39 3)2 3)2 NUM iajs-3598 221 40 , , PUNCT iajs-3598 221 41 where where SCONJ iajs-3598 221 42 : : PUNCT iajs-3598 221 43 οΏ½ οΏ½ PROPN iajs-3598 221 44 Μƒ Μƒ PROPN iajs-3598 221 45 οΏ½ οΏ½ NOUN iajs-3598 221 46 1 1 NUM iajs-3598 221 47 = = SYM iajs-3598 221 48 βˆ’(π‘Ž1 βˆ’(π‘Ž1 X iajs-3598 221 49 + + PROPN iajs-3598 221 50 οΏ½ οΏ½ PROPN iajs-3598 221 51 Μƒ Μƒ NOUN iajs-3598 221 52 οΏ½ οΏ½ NOUN iajs-3598 221 53 1 1 NUM iajs-3598 221 54 2)(1 2)(1 NUM iajs-3598 221 55 + + CCONJ iajs-3598 221 56 π‘Ž2 π‘Ž2 PROPN iajs-3598 221 57 οΏ½ οΏ½ PROPN iajs-3598 221 58 Μƒ Μƒ PROPN iajs-3598 221 59 οΏ½ οΏ½ NOUN iajs-3598 221 60 2)(1 2)(1 NUM iajs-3598 221 61 + + CCONJ iajs-3598 221 62 π‘Ž3 π‘Ž3 PROPN iajs-3598 221 63 οΏ½ οΏ½ PROPN iajs-3598 221 64 Μƒ Μƒ PROPN iajs-3598 221 65 οΏ½ οΏ½ NOUN iajs-3598 221 66 3 3 NUM iajs-3598 221 67 ) ) PUNCT iajs-3598 221 68 2 2 NUM iajs-3598 221 69 ( ( PUNCT iajs-3598 221 70 β„Ž11β„Ž23β„Ž32 β„Ž11β„Ž23β„Ž32 PROPN iajs-3598 221 71 + + NOUN iajs-3598 221 72 β„Ž13β„Ž31β„Ž22 β„Ž13β„Ž31β„Ž22 PROPN iajs-3598 221 73 ) ) PUNCT iajs-3598 221 74 + + CCONJ iajs-3598 221 75 ( ( PUNCT iajs-3598 221 76 β„Ž11β„Ž22)(1 β„Ž11β„Ž22)(1 ADP iajs-3598 221 77 + + CCONJ iajs-3598 221 78 π‘Ž2 π‘Ž2 PROPN iajs-3598 221 79 οΏ½ οΏ½ PROPN iajs-3598 221 80 Μƒ Μƒ PROPN iajs-3598 221 81 οΏ½ οΏ½ NOUN iajs-3598 221 82 2)(1 2)(1 NUM iajs-3598 221 83 + + CCONJ iajs-3598 221 84 π‘Ž3 π‘Ž3 PROPN iajs-3598 221 85 οΏ½ οΏ½ PROPN iajs-3598 221 86 Μƒ Μƒ PROPN iajs-3598 221 87 οΏ½ οΏ½ NOUN iajs-3598 221 88 3 3 NUM iajs-3598 221 89 ) ) SYM iajs-3598 221 90 2 2 NUM iajs-3598 221 91 𝑔1 𝑔1 PROPN iajs-3598 221 92 οΏ½ οΏ½ PROPN iajs-3598 221 93 Μƒ Μƒ PROPN iajs-3598 221 94 οΏ½ οΏ½ NOUN iajs-3598 221 95 1 1 NUM iajs-3598 221 96 + + CCONJ iajs-3598 221 97 ( ( PUNCT iajs-3598 221 98 β„Ž11β„Ž22)(π‘Ž1 β„Ž11β„Ž22)(π‘Ž1 PROPN iajs-3598 221 99 + + SYM iajs-3598 221 100 οΏ½ οΏ½ PROPN iajs-3598 221 101 Μƒ Μƒ NOUN iajs-3598 221 102 οΏ½ οΏ½ NOUN iajs-3598 221 103 1 1 NUM iajs-3598 221 104 2)𝑔2 2)𝑔2 NUM iajs-3598 221 105 οΏ½ οΏ½ SYM iajs-3598 221 106 Μƒ Μƒ NOUN iajs-3598 221 107 οΏ½ οΏ½ NOUN iajs-3598 221 108 2 2 NUM iajs-3598 221 109 , , PUNCT iajs-3598 221 110 οΏ½ οΏ½ PROPN iajs-3598 221 111 Μƒ Μƒ NOUN iajs-3598 221 112 οΏ½ οΏ½ NOUN iajs-3598 221 113 2 2 NUM iajs-3598 221 114 = = SYM iajs-3598 221 115 βˆ’(β„Ž11β„Ž22)(π‘Ž1 βˆ’(β„Ž11β„Ž22)(π‘Ž1 ADJ iajs-3598 221 116 + + NUM iajs-3598 221 117 οΏ½ οΏ½ PROPN iajs-3598 221 118 Μƒ Μƒ NOUN iajs-3598 221 119 οΏ½ οΏ½ NOUN iajs-3598 221 120 1 1 NUM iajs-3598 221 121 2)(1 2)(1 NUM iajs-3598 221 122 + + CCONJ iajs-3598 221 123 π‘Ž2 π‘Ž2 PROPN iajs-3598 221 124 οΏ½ οΏ½ PROPN iajs-3598 221 125 Μƒ Μƒ PROPN iajs-3598 221 126 οΏ½ οΏ½ NOUN iajs-3598 221 127 2)(1 2)(1 NUM iajs-3598 221 128 + + CCONJ iajs-3598 221 129 π‘Ž3 π‘Ž3 PROPN iajs-3598 221 130 οΏ½ οΏ½ PROPN iajs-3598 221 131 Μƒ Μƒ PROPN iajs-3598 221 132 οΏ½ οΏ½ NOUN iajs-3598 221 133 3)2πœ‡ 3)2πœ‡ PROPN iajs-3598 221 134 οΏ½ οΏ½ NOUN iajs-3598 221 135 Μƒ Μƒ NOUN iajs-3598 221 136 οΏ½ οΏ½ NOUN iajs-3598 221 137 1 1 NUM iajs-3598 221 138 . . PUNCT iajs-3598 221 139 ihjpas ihjpas PROPN iajs-3598 221 140 . . PUNCT iajs-3598 222 1 2025 2025 NUM iajs-3598 222 2 , , PUNCT iajs-3598 222 3 38 38 NUM iajs-3598 222 4 ( ( PUNCT iajs-3598 222 5 1 1 NUM iajs-3598 222 6 ) ) PUNCT iajs-3598 222 7 439 439 PROPN iajs-3598 222 8 has have VERB iajs-3598 222 9 a a DET iajs-3598 222 10 saddle saddle NOUN iajs-3598 222 11 - - PUNCT iajs-3598 222 12 node node NOUN iajs-3598 222 13 bifurcation bifurcation NOUN iajs-3598 222 14 at at ADP iajs-3598 222 15 𝐻7 𝐻7 NOUN iajs-3598 222 16 = = SYM iajs-3598 222 17 ( ( PUNCT iajs-3598 222 18 οΏ½ οΏ½ PROPN iajs-3598 222 19 Μƒ Μƒ NOUN iajs-3598 222 20 οΏ½ οΏ½ NOUN iajs-3598 222 21 1 1 NUM iajs-3598 222 22 , , PUNCT iajs-3598 222 23 οΏ½ οΏ½ PROPN iajs-3598 222 24 Μƒ Μƒ NOUN iajs-3598 222 25 οΏ½ οΏ½ NOUN iajs-3598 222 26 2 2 NUM iajs-3598 222 27 , , PUNCT iajs-3598 222 28 οΏ½ οΏ½ PROPN iajs-3598 222 29 Μƒ Μƒ NOUN iajs-3598 222 30 οΏ½ οΏ½ NOUN iajs-3598 222 31 3 3 NUM iajs-3598 222 32 ) ) PUNCT iajs-3598 222 33 . . PUNCT iajs-3598 223 1 proof proof NOUN iajs-3598 223 2 : : PUNCT iajs-3598 223 3 using use VERB iajs-3598 223 4 the the DET iajs-3598 223 5 jacobian jacobian ADJ iajs-3598 223 6 matrix matrix NOUN iajs-3598 223 7 given give VERB iajs-3598 223 8 by by ADP iajs-3598 223 9 eq eq PROPN iajs-3598 223 10 . . PUNCT iajs-3598 224 1 ( ( PUNCT iajs-3598 224 2 1.11 1.11 NUM iajs-3598 224 3 ) ) PUNCT iajs-3598 224 4 in in ADP iajs-3598 224 5 ( ( PUNCT iajs-3598 224 6 22 22 NUM iajs-3598 224 7 ) ) PUNCT iajs-3598 224 8 𝐽7 𝐽7 NOUN iajs-3598 224 9 = = SYM iajs-3598 224 10 𝐽7(𝐻7 𝐽7(𝐻7 PROPN iajs-3598 224 11 , , PUNCT iajs-3598 224 12 οΏ½ οΏ½ PROPN iajs-3598 224 13 Μƒ Μƒ PROPN iajs-3598 224 14 οΏ½ οΏ½ PROPN iajs-3598 224 15 ) ) PUNCT iajs-3598 224 16 = = PUNCT iajs-3598 225 1 [ [ X iajs-3598 225 2 β„ŽΜƒπ‘–π‘— β„ŽΜƒπ‘–π‘— X iajs-3598 225 3 ] ] X iajs-3598 225 4 3Γ—3 3Γ—3 NUM iajs-3598 225 5 , , PUNCT iajs-3598 225 6 where where SCONJ iajs-3598 225 7 β„ŽΜƒπ‘–π‘— β„ŽΜƒπ‘–π‘— NOUN iajs-3598 225 8 = = PUNCT iajs-3598 225 9 β„Žπ‘–π‘— β„Žπ‘–π‘— NOUN iajs-3598 225 10 , , PUNCT iajs-3598 225 11 except except SCONJ iajs-3598 225 12 β„ŽΜƒ33 β„ŽΜƒ33 NOUN iajs-3598 225 13 = = PROPN iajs-3598 225 14 𝑔1 𝑔1 PROPN iajs-3598 225 15 οΏ½ οΏ½ PROPN iajs-3598 225 16 Μƒ Μƒ PROPN iajs-3598 225 17 οΏ½ οΏ½ NOUN iajs-3598 225 18 1 1 NUM iajs-3598 225 19 π‘Ž1 π‘Ž1 PROPN iajs-3598 225 20 + + CCONJ iajs-3598 225 21 οΏ½ οΏ½ PROPN iajs-3598 225 22 Μƒ Μƒ PROPN iajs-3598 225 23 οΏ½ οΏ½ NOUN iajs-3598 225 24 1 1 NUM iajs-3598 225 25 2 2 NUM iajs-3598 225 26 + + NUM iajs-3598 225 27 𝑔2 𝑔2 PROPN iajs-3598 225 28 οΏ½ οΏ½ NOUN iajs-3598 225 29 Μƒ Μƒ NOUN iajs-3598 225 30 οΏ½ οΏ½ NOUN iajs-3598 225 31 2 2 NUM iajs-3598 225 32 ( ( PUNCT iajs-3598 225 33 1 1 NUM iajs-3598 225 34 + + NUM iajs-3598 225 35 π‘Ž2 π‘Ž2 PROPN iajs-3598 225 36 οΏ½ οΏ½ PROPN iajs-3598 225 37 Μƒ Μƒ PROPN iajs-3598 225 38 οΏ½ οΏ½ NOUN iajs-3598 225 39 2)(1 2)(1 NUM iajs-3598 225 40 + + CCONJ iajs-3598 225 41 π‘Ž3 π‘Ž3 PROPN iajs-3598 225 42 οΏ½ οΏ½ PROPN iajs-3598 225 43 Μƒ Μƒ PROPN iajs-3598 225 44 οΏ½ οΏ½ PROPN iajs-3598 225 45 3)2 3)2 NUM iajs-3598 225 46 βˆ’ βˆ’ NOUN iajs-3598 225 47 πœ‡ πœ‡ ADP iajs-3598 225 48 οΏ½ οΏ½ PROPN iajs-3598 225 49 Μƒ Μƒ NOUN iajs-3598 225 50 οΏ½ οΏ½ NOUN iajs-3598 225 51 1 1 NUM iajs-3598 225 52 βˆ’ βˆ’ PROPN iajs-3598 225 53 𝑑 𝑑 NOUN iajs-3598 225 54 the the DET iajs-3598 225 55 characterizing characterizing NOUN iajs-3598 225 56 eq eq NOUN iajs-3598 225 57 . . PROPN iajs-3598 225 58 𝐽7 𝐽7 PROPN iajs-3598 225 59 had have VERB iajs-3598 225 60 a a DET iajs-3598 225 61 zero zero NUM iajs-3598 225 62 eigenvalue eigenvalue NOUN iajs-3598 225 63 ( ( PUNCT iajs-3598 225 64 say say VERB iajs-3598 225 65 Ξ»7l3 Ξ»7l3 X iajs-3598 225 66 = = NOUN iajs-3598 225 67 0 0 NUM iajs-3598 225 68 ) ) PUNCT iajs-3598 226 1 if if SCONJ iajs-3598 226 2 and and CCONJ iajs-3598 226 3 only only ADV iajs-3598 226 4 if if SCONJ iajs-3598 226 5 οΏ½ οΏ½ PROPN iajs-3598 226 6 ΜΏ ΜΏ NOUN iajs-3598 226 7 οΏ½ οΏ½ NOUN iajs-3598 226 8 3 3 NUM iajs-3598 226 9 = = SYM iajs-3598 226 10 0 0 NUM iajs-3598 226 11 . . PUNCT iajs-3598 227 1 now now ADV iajs-3598 227 2 , , PUNCT iajs-3598 227 3 let let VERB iajs-3598 227 4 𝑉[7 𝑉[7 VERB iajs-3598 227 5 ] ] X iajs-3598 227 6 = = SYM iajs-3598 227 7 ( ( PUNCT iajs-3598 227 8 𝑣1 𝑣1 NOUN iajs-3598 227 9 [ [ X iajs-3598 227 10 7 7 NUM iajs-3598 227 11 ] ] PUNCT iajs-3598 227 12 , , PUNCT iajs-3598 227 13 𝑣2 𝑣2 X iajs-3598 227 14 [ [ X iajs-3598 227 15 7 7 NUM iajs-3598 227 16 ] ] PUNCT iajs-3598 227 17 , , PUNCT iajs-3598 227 18 𝑣3 𝑣3 ADJ iajs-3598 227 19 [ [ X iajs-3598 227 20 7 7 NUM iajs-3598 227 21 ] ] PUNCT iajs-3598 227 22 ) ) PUNCT iajs-3598 228 1 𝑇be 𝑇be NUM iajs-3598 228 2 the the DET iajs-3598 228 3 eigenvector eigenvector NOUN iajs-3598 228 4 corresponding correspond VERB iajs-3598 228 5 to to ADP iajs-3598 228 6 the the DET iajs-3598 228 7 eigenvalue eigenvalue ADJ iajs-3598 228 8 Ξ»7l3 Ξ»7l3 X iajs-3598 228 9 = = NOUN iajs-3598 228 10 0 0 PROPN iajs-3598 228 11 . . PUNCT iajs-3598 229 1 thus,(𝐽7 thus,(𝐽7 NOUN iajs-3598 230 1 βˆ’ βˆ’ PROPN iajs-3598 230 2 Ξ»7l3 Ξ»7l3 X iajs-3598 230 3 𝐼)𝑉[7 𝐼)𝑉[7 NOUN iajs-3598 230 4 ] ] X iajs-3598 230 5 = = SYM iajs-3598 230 6 0 0 NUM iajs-3598 230 7 , , PUNCT iajs-3598 230 8 this this PRON iajs-3598 230 9 gives give VERB iajs-3598 230 10 : : PUNCT iajs-3598 230 11 𝑣1 𝑣1 NOUN iajs-3598 230 12 [ [ X iajs-3598 230 13 7 7 NUM iajs-3598 230 14 ] ] X iajs-3598 230 15 = = PUNCT iajs-3598 230 16 οΏ½ οΏ½ PROPN iajs-3598 230 17 Μƒ Μƒ PROPN iajs-3598 230 18 οΏ½ οΏ½ NOUN iajs-3598 230 19 1𝑣3 1𝑣3 NUM iajs-3598 230 20 [ [ X iajs-3598 230 21 7 7 NUM iajs-3598 230 22 ] ] PUNCT iajs-3598 230 23 , , PUNCT iajs-3598 230 24 𝑣2 𝑣2 X iajs-3598 231 1 [ [ X iajs-3598 231 2 7 7 NUM iajs-3598 231 3 ] ] X iajs-3598 231 4 = = PUNCT iajs-3598 231 5 οΏ½ οΏ½ PROPN iajs-3598 231 6 Μƒ Μƒ PROPN iajs-3598 231 7 οΏ½ οΏ½ NOUN iajs-3598 231 8 2𝑣3 2𝑣3 PROPN iajs-3598 232 1 [ [ X iajs-3598 232 2 7 7 NUM iajs-3598 232 3 ] ] PUNCT iajs-3598 232 4 , , PUNCT iajs-3598 232 5 𝑣3 𝑣3 ADJ iajs-3598 232 6 [ [ X iajs-3598 232 7 7 7 NUM iajs-3598 232 8 ] ] PUNCT iajs-3598 232 9 and and CCONJ iajs-3598 232 10 𝑣3 𝑣3 ADJ iajs-3598 232 11 [ [ X iajs-3598 232 12 7 7 NUM iajs-3598 232 13 ] ] X iajs-3598 232 14 any any DET iajs-3598 232 15 non non ADJ iajs-3598 232 16 - - ADJ iajs-3598 232 17 zero zero ADJ iajs-3598 232 18 real real ADJ iajs-3598 232 19 number number NOUN iajs-3598 232 20 where where SCONJ iajs-3598 232 21 : : PUNCT iajs-3598 232 22 οΏ½ οΏ½ PROPN iajs-3598 232 23 Μƒ Μƒ PROPN iajs-3598 232 24 οΏ½ οΏ½ NOUN iajs-3598 232 25 1= 1= X iajs-3598 232 26 βˆ’ βˆ’ NOUN iajs-3598 232 27 β„Ž13 β„Ž13 INTJ iajs-3598 232 28 β„Ž11 β„Ž11 INTJ iajs-3598 232 29 , , PUNCT iajs-3598 232 30 οΏ½ οΏ½ PROPN iajs-3598 232 31 Μƒ Μƒ NOUN iajs-3598 232 32 οΏ½ οΏ½ NOUN iajs-3598 232 33 2 2 NUM iajs-3598 232 34 = = SYM iajs-3598 232 35 βˆ’ βˆ’ PROPN iajs-3598 232 36 β„Ž23 β„Ž23 NOUN iajs-3598 232 37 β„Ž22 β„Ž22 ADV iajs-3598 232 38 . . PUNCT iajs-3598 233 1 let let VERB iajs-3598 233 2 𝑍[7 𝑍[7 VERB iajs-3598 233 3 ] ] X iajs-3598 233 4 = = SYM iajs-3598 233 5 ( ( PUNCT iajs-3598 233 6 𝑧1 𝑧1 NOUN iajs-3598 233 7 [ [ X iajs-3598 233 8 7 7 NUM iajs-3598 233 9 ] ] PUNCT iajs-3598 233 10 , , PUNCT iajs-3598 233 11 𝑧2 𝑧2 PROPN iajs-3598 234 1 [ [ X iajs-3598 234 2 7 7 NUM iajs-3598 234 3 ] ] PUNCT iajs-3598 234 4 , , PUNCT iajs-3598 234 5 𝑧3 𝑧3 PROPN iajs-3598 234 6 [ [ X iajs-3598 234 7 7 7 NUM iajs-3598 234 8 ] ] PUNCT iajs-3598 234 9 ) ) PUNCT iajs-3598 234 10 𝑇 𝑇 PROPN iajs-3598 234 11 be be VERB iajs-3598 234 12 the the DET iajs-3598 234 13 eigenvector eigenvector NOUN iajs-3598 234 14 connected connect VERB iajs-3598 234 15 with with ADP iajs-3598 234 16 to to ADP iajs-3598 234 17 the the DET iajs-3598 234 18 eigenvalue eigenvalue ADJ iajs-3598 234 19 Ξ»7l3 Ξ»7l3 X iajs-3598 234 20 = = NOUN iajs-3598 234 21 0 0 NUM iajs-3598 234 22 of of ADP iajs-3598 234 23 the the DET iajs-3598 234 24 matrix matrix NOUN iajs-3598 234 25 𝐽7 𝐽7 NOUN iajs-3598 234 26 𝑇.then 𝑇.then ADV iajs-3598 234 27 , , PUNCT iajs-3598 234 28 ( ( PUNCT iajs-3598 234 29 𝐽7 𝐽7 PROPN iajs-3598 234 30 𝑇 𝑇 PROPN iajs-3598 234 31 βˆ’ βˆ’ PROPN iajs-3598 234 32 Ξ»7l3 Ξ»7l3 INTJ iajs-3598 234 33 𝐼 𝐼 PROPN iajs-3598 234 34 ) ) PUNCT iajs-3598 234 35 𝑍[7 𝑍[7 PROPN iajs-3598 234 36 ] ] X iajs-3598 234 37 = = SYM iajs-3598 234 38 0 0 X iajs-3598 234 39 . . PUNCT iajs-3598 235 1 by by ADP iajs-3598 235 2 solving solve VERB iajs-3598 235 3 this this DET iajs-3598 235 4 equation equation NOUN iajs-3598 235 5 for for ADP iajs-3598 235 6 , , PUNCT iajs-3598 235 7 𝑍[7 𝑍[7 PROPN iajs-3598 235 8 ] ] X iajs-3598 235 9 = = SYM iajs-3598 235 10 ( ( PUNCT iajs-3598 235 11 οΏ½ οΏ½ PROPN iajs-3598 235 12 Μƒ Μƒ NOUN iajs-3598 235 13 οΏ½ οΏ½ NOUN iajs-3598 235 14 3𝑧3 3𝑧3 NUM iajs-3598 235 15 [ [ X iajs-3598 235 16 7 7 NUM iajs-3598 235 17 ] ] PUNCT iajs-3598 235 18 , , PUNCT iajs-3598 235 19 οΏ½ οΏ½ PROPN iajs-3598 235 20 Μƒ Μƒ PROPN iajs-3598 235 21 οΏ½ οΏ½ PROPN iajs-3598 235 22 4𝑧3 4𝑧3 NOUN iajs-3598 235 23 [ [ X iajs-3598 235 24 7 7 NUM iajs-3598 235 25 ] ] PUNCT iajs-3598 235 26 , , PUNCT iajs-3598 235 27 𝑧3 𝑧3 PROPN iajs-3598 235 28 [ [ X iajs-3598 235 29 7 7 NUM iajs-3598 235 30 ] ] PUNCT iajs-3598 235 31 ) ) PUNCT iajs-3598 235 32 𝑇 𝑇 PROPN iajs-3598 235 33 , , PUNCT iajs-3598 235 34 and and CCONJ iajs-3598 235 35 𝑧3 𝑧3 VERB iajs-3598 236 1 [ [ X iajs-3598 236 2 7 7 X iajs-3598 236 3 ] ] X iajs-3598 236 4 any any DET iajs-3598 236 5 non non ADJ iajs-3598 236 6 - - ADJ iajs-3598 236 7 zero zero ADJ iajs-3598 236 8 real real ADJ iajs-3598 236 9 number number NOUN iajs-3598 236 10 . . PUNCT iajs-3598 237 1 where where SCONJ iajs-3598 237 2 : : PUNCT iajs-3598 237 3 οΏ½ οΏ½ PROPN iajs-3598 237 4 Μƒ Μƒ PROPN iajs-3598 237 5 οΏ½ οΏ½ AUX iajs-3598 237 6 3 3 NUM iajs-3598 237 7 = = SYM iajs-3598 237 8 βˆ’ βˆ’ PROPN iajs-3598 237 9 β„Ž31Μƒ β„Ž31Μƒ NOUN iajs-3598 237 10 β„Ž11Μƒ β„Ž11Μƒ ADJ iajs-3598 237 11 , , PUNCT iajs-3598 237 12 οΏ½ οΏ½ PROPN iajs-3598 237 13 Μƒ Μƒ NOUN iajs-3598 237 14 οΏ½ οΏ½ NOUN iajs-3598 237 15 4 4 NUM iajs-3598 237 16 = = SYM iajs-3598 237 17 βˆ’ βˆ’ PROPN iajs-3598 237 18 β„ŽΜƒ32 β„ŽΜƒ32 PROPN iajs-3598 237 19 β„Ž22Μƒ β„Ž22Μƒ NUM iajs-3598 237 20 . . PUNCT iajs-3598 238 1 now now ADV iajs-3598 238 2 , , PUNCT iajs-3598 238 3 consider consider VERB iajs-3598 238 4 that that PRON iajs-3598 238 5 : : PUNCT iajs-3598 238 6 πœ•π‘“ πœ•π‘“ ADJ iajs-3598 238 7 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 238 8 = = SYM iajs-3598 238 9 𝑓𝑑(𝑋 𝑓𝑑(𝑋 PROPN iajs-3598 238 10 , , PUNCT iajs-3598 238 11 𝑑 𝑑 NOUN iajs-3598 238 12 ) ) PUNCT iajs-3598 238 13 = = SYM iajs-3598 238 14 ( ( PUNCT iajs-3598 238 15 πœ•π‘“1 πœ•π‘“1 NOUN iajs-3598 238 16 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 238 17 , , PUNCT iajs-3598 238 18 πœ•π‘“2 πœ•π‘“2 PROPN iajs-3598 238 19 πœ•π‘‘ πœ•π‘‘ NOUN iajs-3598 238 20 , , PUNCT iajs-3598 238 21 πœ•π‘“3 πœ•π‘“3 PROPN iajs-3598 238 22 πœ•π‘‘ πœ•π‘‘ PROPN iajs-3598 238 23 ) ) PUNCT iajs-3598 238 24 𝑇 𝑇 PROPN iajs-3598 238 25 = = SYM iajs-3598 238 26 ( ( PUNCT iajs-3598 238 27 0,0 0,0 NOUN iajs-3598 238 28 , , PUNCT iajs-3598 238 29 βˆ’πΏ3)𝑇 βˆ’πΏ3)𝑇 PROPN iajs-3598 238 30 . . PUNCT iajs-3598 239 1 so so ADV iajs-3598 239 2 , , PUNCT iajs-3598 239 3 𝑓𝑑(𝐻7 𝑓𝑑(𝐻7 PROPN iajs-3598 239 4 , , PUNCT iajs-3598 239 5 𝑑 𝑑 NOUN iajs-3598 239 6 ) ) PUNCT iajs-3598 239 7 = = SYM iajs-3598 239 8 ( ( PUNCT iajs-3598 239 9 0,0 0,0 NOUN iajs-3598 239 10 , , PUNCT iajs-3598 239 11 βˆ’ βˆ’ PROPN iajs-3598 239 12 οΏ½ οΏ½ PROPN iajs-3598 239 13 Μƒ Μƒ NOUN iajs-3598 239 14 οΏ½ οΏ½ NOUN iajs-3598 239 15 3 3 NUM iajs-3598 239 16 ) ) PUNCT iajs-3598 239 17 𝑇 𝑇 NOUN iajs-3598 239 18 and and CCONJ iajs-3598 239 19 hence hence ADV iajs-3598 239 20 ( ( PUNCT iajs-3598 239 21 𝑍[7 𝑍[7 ADJ iajs-3598 239 22 ] ] X iajs-3598 239 23 ) ) PUNCT iajs-3598 239 24 𝑇 𝑇 PROPN iajs-3598 239 25 𝑓𝑑(𝐻7 𝑓𝑑(𝐻7 PROPN iajs-3598 239 26 , , PUNCT iajs-3598 239 27 𝑑 𝑑 NOUN iajs-3598 239 28 ) ) PUNCT iajs-3598 239 29 = = SYM iajs-3598 239 30 βˆ’ βˆ’ NUM iajs-3598 239 31 οΏ½ οΏ½ PROPN iajs-3598 239 32 Μƒ Μƒ NOUN iajs-3598 239 33 οΏ½ οΏ½ NOUN iajs-3598 239 34 3𝑧3 3𝑧3 NUM iajs-3598 239 35 [ [ X iajs-3598 239 36 7 7 NUM iajs-3598 239 37 ] ] PUNCT iajs-3598 239 38 β‰  β‰  PROPN iajs-3598 239 39 0 0 X iajs-3598 239 40 . . PUNCT iajs-3598 240 1 by by ADP iajs-3598 240 2 substituting substitute VERB iajs-3598 240 3 𝑉[7 𝑉[7 NOUN iajs-3598 240 4 ] ] PUNCT iajs-3598 240 5 in in ADP iajs-3598 240 6 ( ( PUNCT iajs-3598 240 7 3 3 X iajs-3598 240 8 ) ) PUNCT iajs-3598 240 9 we we PRON iajs-3598 240 10 get get VERB iajs-3598 240 11 : : PUNCT iajs-3598 240 12 𝐷2πΉπœ‡(𝐻7 𝐷2πΉπœ‡(𝐻7 PROPN iajs-3598 240 13 , , PUNCT iajs-3598 240 14 𝑑)(𝑉[7 𝑑)(𝑉[7 NOUN iajs-3598 240 15 ] ] PUNCT iajs-3598 240 16 , , PUNCT iajs-3598 240 17 𝑉[7 𝑉[7 PROPN iajs-3598 240 18 ] ] PUNCT iajs-3598 240 19 ) ) PUNCT iajs-3598 240 20 = = SYM iajs-3598 240 21 ( ( PUNCT iajs-3598 240 22 𝐴𝑖𝑗 𝐴𝑖𝑗 PROPN iajs-3598 240 23 ) ) PUNCT iajs-3598 240 24 𝐴11 𝐴11 PROPN iajs-3598 240 25 = = PUNCT iajs-3598 240 26 βˆ’ βˆ’ PROPN iajs-3598 240 27 2𝑆1 2𝑆1 NUM iajs-3598 240 28 𝐾1 𝐾1 NOUN iajs-3598 241 1 + + CCONJ iajs-3598 241 2 ( ( PUNCT iajs-3598 241 3 𝑣3 𝑣3 ADJ iajs-3598 241 4 [ [ X iajs-3598 241 5 7 7 NUM iajs-3598 241 6 ] ] PUNCT iajs-3598 241 7 ) ) PUNCT iajs-3598 241 8 2 2 NUM iajs-3598 241 9 [ [ PUNCT iajs-3598 241 10 4π‘Ž1𝐢1𝐿1𝐿3 4π‘Ž1𝐢1𝐿1𝐿3 NUM iajs-3598 241 11 ( ( PUNCT iajs-3598 241 12 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 241 13 2 2 NUM iajs-3598 241 14 ) ) SYM iajs-3598 241 15 2 2 NUM iajs-3598 241 16 οΏ½ οΏ½ PROPN iajs-3598 241 17 Μƒ Μƒ NOUN iajs-3598 241 18 οΏ½ οΏ½ NOUN iajs-3598 241 19 1 1 NUM iajs-3598 241 20 βˆ’ βˆ’ NOUN iajs-3598 241 21 𝐢1 𝐢1 PROPN iajs-3598 241 22 ( ( PUNCT iajs-3598 241 23 π‘Ž1+𝐿1 π‘Ž1+𝐿1 NOUN iajs-3598 241 24 2 2 NUM iajs-3598 241 25 ) ) PUNCT iajs-3598 241 26 ( ( PUNCT iajs-3598 241 27 ( ( PUNCT iajs-3598 241 28 π‘Ž1 π‘Ž1 X iajs-3598 241 29 + + CCONJ iajs-3598 241 30 𝐿1 𝐿1 PROPN iajs-3598 241 31 2 2 NUM iajs-3598 241 32 ) ) PUNCT iajs-3598 241 33 βˆ’ βˆ’ PROPN iajs-3598 241 34 2𝐿1 2𝐿1 NUM iajs-3598 241 35 2 2 NUM iajs-3598 241 36 + + CCONJ iajs-3598 241 37 ( ( PUNCT iajs-3598 241 38 π‘Ž1 π‘Ž1 X iajs-3598 241 39 + + CCONJ iajs-3598 241 40 2𝐿1)) 2𝐿1)) NUM iajs-3598 241 41 οΏ½ οΏ½ PROPN iajs-3598 241 42 Μƒ Μƒ NOUN iajs-3598 241 43 οΏ½ οΏ½ NOUN iajs-3598 241 44 1 1 NUM iajs-3598 241 45 ] ] PUNCT iajs-3598 241 46 , , PUNCT iajs-3598 241 47 𝐴21 𝐴21 PROPN iajs-3598 241 48 = = PUNCT iajs-3598 241 49 βˆ’2𝐢 βˆ’2𝐢 PROPN iajs-3598 241 50 + + CCONJ iajs-3598 241 51 ( ( PUNCT iajs-3598 241 52 𝑣3 𝑣3 ADJ iajs-3598 241 53 [ [ X iajs-3598 241 54 7 7 NUM iajs-3598 241 55 ] ] SYM iajs-3598 241 56 ) ) PUNCT iajs-3598 241 57 2 2 NUM iajs-3598 241 58 [ [ PUNCT iajs-3598 241 59 𝐢2𝐿3 𝐢2𝐿3 NOUN iajs-3598 241 60 ( ( PUNCT iajs-3598 241 61 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3 NUM iajs-3598 241 62 ) ) PUNCT iajs-3598 241 63 οΏ½ οΏ½ PROPN iajs-3598 241 64 Μƒ Μƒ PROPN iajs-3598 241 65 οΏ½ οΏ½ NOUN iajs-3598 241 66 1 1 NUM iajs-3598 241 67 2 2 NUM iajs-3598 241 68 βˆ’ βˆ’ NOUN iajs-3598 241 69 ( ( PUNCT iajs-3598 241 70 2𝑆2𝑓1 2𝑆2𝑓1 PROPN iajs-3598 241 71 ( ( PUNCT iajs-3598 241 72 1+𝑓1𝐿3)2 1+𝑓1𝐿3)2 NUM iajs-3598 241 73 + + NUM iajs-3598 241 74 𝐢2π‘Ž2𝐿3 𝐢2π‘Ž2𝐿3 PROPN iajs-3598 241 75 ( ( PUNCT iajs-3598 241 76 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)2(1+π‘Ž3𝐿3)2 ADJ iajs-3598 241 77 + + CCONJ iajs-3598 241 78 𝐢2 𝐢2 ADJ iajs-3598 241 79 ( ( PUNCT iajs-3598 241 80 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 1+π‘Ž2𝐿2)(1+π‘Ž3𝐿3)2 NOUN iajs-3598 241 81 ) ) PUNCT iajs-3598 241 82 οΏ½ οΏ½ PROPN iajs-3598 241 83 Μƒ Μƒ PROPN iajs-3598 241 84 οΏ½ οΏ½ NOUN iajs-3598 241 85 1 1 NUM iajs-3598 241 86 + + SYM iajs-3598 241 87 2𝑆2𝑓1 2𝑆2𝑓1 NUM iajs-3598 241 88 2𝐿3 2𝐿3 NUM iajs-3598 241 89 ( ( PUNCT iajs-3598 241 90 1+𝑓1𝐿3)3 1+𝑓1𝐿3)3 NUM iajs-3598 241 91 ] ] PUNCT iajs-3598 241 92 , , PUNCT iajs-3598 241 93 ihjpas ihjpas PROPN iajs-3598 241 94 . . PUNCT iajs-3598 242 1 2025 2025 NUM iajs-3598 242 2 , , PUNCT iajs-3598 242 3 38 38 NUM iajs-3598 242 4 ( ( PUNCT iajs-3598 242 5 1 1 NUM iajs-3598 242 6 ) ) PUNCT iajs-3598 242 7 440 440 NUM iajs-3598 242 8 𝐴31 𝐴31 PROPN iajs-3598 242 9 = = SYM iajs-3598 242 10 ( ( PUNCT iajs-3598 242 11 𝑣3 𝑣3 PROPN iajs-3598 242 12 [ [ X iajs-3598 242 13 7 7 NUM iajs-3598 242 14 ] ] SYM iajs-3598 242 15 ) ) PUNCT iajs-3598 242 16 2 2 NUM iajs-3598 242 17 [ [ PUNCT iajs-3598 242 18 2𝑔1𝐿1𝐿3 2𝑔1𝐿1𝐿3 NUM iajs-3598 242 19 π‘Ž1 π‘Ž1 NOUN iajs-3598 242 20 + + CCONJ iajs-3598 242 21 𝐿1 𝐿1 PROPN iajs-3598 242 22 2 2 NUM iajs-3598 242 23 οΏ½ οΏ½ PROPN iajs-3598 242 24 Μƒ Μƒ PROPN iajs-3598 242 25 οΏ½ οΏ½ NOUN iajs-3598 242 26 1 1 NUM iajs-3598 242 27 2 2 NUM iajs-3598 242 28 + + CCONJ iajs-3598 242 29 ( ( PUNCT iajs-3598 242 30 𝑔1(1 𝑔1(1 ADJ iajs-3598 242 31 βˆ’ βˆ’ PROPN iajs-3598 242 32 2𝐿1 2𝐿1 NUM iajs-3598 242 33 2 2 NUM iajs-3598 242 34 ) ) PUNCT iajs-3598 242 35 π‘Ž1 π‘Ž1 NOUN iajs-3598 242 36 + + CCONJ iajs-3598 242 37 𝐿1 𝐿1 PROPN iajs-3598 242 38 2 2 NUM iajs-3598 242 39 + + PROPN iajs-3598 242 40 𝑔1 𝑔1 PROPN iajs-3598 242 41 βˆ’ βˆ’ PROPN iajs-3598 242 42 2πœ‡ 2πœ‡ PROPN iajs-3598 242 43 ) ) PUNCT iajs-3598 242 44 οΏ½ οΏ½ PROPN iajs-3598 242 45 Μƒ Μƒ PROPN iajs-3598 242 46 οΏ½ οΏ½ NOUN iajs-3598 242 47 1 1 NUM iajs-3598 242 48 βˆ’ βˆ’ NUM iajs-3598 242 49 2π‘Ž2𝑔2𝐿3 2π‘Ž2𝑔2𝐿3 NUM iajs-3598 242 50 ( ( PUNCT iajs-3598 242 51 1 1 NUM iajs-3598 242 52 + + CCONJ iajs-3598 242 53 π‘Ž2𝐿2)3(1 π‘Ž2𝐿2)3(1 ADJ iajs-3598 242 54 + + NOUN iajs-3598 242 55 π‘Ž3𝐿3 π‘Ž3𝐿3 NUM iajs-3598 242 56 ) ) PUNCT iajs-3598 242 57 οΏ½ οΏ½ PROPN iajs-3598 242 58 Μƒ Μƒ PROPN iajs-3598 242 59 οΏ½ οΏ½ NOUN iajs-3598 242 60 2 2 NUM iajs-3598 242 61 2 2 NUM iajs-3598 242 62 βˆ’ βˆ’ NOUN iajs-3598 242 63 𝑔2 𝑔2 NOUN iajs-3598 242 64 ( ( PUNCT iajs-3598 242 65 1 1 NUM iajs-3598 242 66 + + NUM iajs-3598 242 67 π‘Ž2𝐿2)2(1 π‘Ž2𝐿2)2(1 NOUN iajs-3598 242 68 + + CCONJ iajs-3598 242 69 π‘Ž3𝐿3)2 π‘Ž3𝐿3)2 PROPN iajs-3598 242 70 ( ( PUNCT iajs-3598 242 71 π‘Ž2𝐿2 π‘Ž2𝐿2 PROPN iajs-3598 242 72 βˆ’ βˆ’ PROPN iajs-3598 242 73 1) 1) NUM iajs-3598 242 74 οΏ½ οΏ½ PROPN iajs-3598 242 75 Μƒ Μƒ NOUN iajs-3598 242 76 οΏ½ οΏ½ NOUN iajs-3598 242 77 2 2 NUM iajs-3598 242 78 βˆ’ βˆ’ NOUN iajs-3598 242 79 2𝑔2π‘Ž3𝐿3 2𝑔2π‘Ž3𝐿3 NUM iajs-3598 242 80 ( ( PUNCT iajs-3598 242 81 1 1 NUM iajs-3598 242 82 + + CCONJ iajs-3598 242 83 π‘Ž2𝐿2)(1 π‘Ž2𝐿2)(1 X iajs-3598 242 84 + + X iajs-3598 242 85 π‘Ž3𝐿3)3 π‘Ž3𝐿3)3 PROPN iajs-3598 242 86 ] ] PUNCT iajs-3598 242 87 hence hence ADV iajs-3598 242 88 , , PUNCT iajs-3598 242 89 it it PRON iajs-3598 242 90 was be AUX iajs-3598 242 91 obtained obtain VERB iajs-3598 242 92 by by ADP iajs-3598 242 93 conditions condition NOUN iajs-3598 242 94 ( ( PUNCT iajs-3598 242 95 𝑍[7 𝑍[7 ADJ iajs-3598 242 96 ] ] X iajs-3598 242 97 ) ) PUNCT iajs-3598 242 98 𝑇 𝑇 PROPN iajs-3598 243 1 [ [ X iajs-3598 243 2 𝐷2πΉπœ‡(𝐻7 𝐷2πΉπœ‡(𝐻7 PROPN iajs-3598 243 3 , , PUNCT iajs-3598 243 4 𝑑)(𝑉[7 𝑑)(𝑉[7 NOUN iajs-3598 243 5 ] ] PUNCT iajs-3598 243 6 , , PUNCT iajs-3598 243 7 𝑉[7 𝑉[7 PROPN iajs-3598 243 8 ] ] PUNCT iajs-3598 243 9 ) ) PUNCT iajs-3598 243 10 ] ] PUNCT iajs-3598 244 1 = = SYM iajs-3598 244 2 ( ( PUNCT iajs-3598 244 3 𝑣3 𝑣3 PROPN iajs-3598 244 4 [ [ X iajs-3598 244 5 7 7 NUM iajs-3598 244 6 ] ] PUNCT iajs-3598 244 7 ) ) PUNCT iajs-3598 244 8 2 2 NUM iajs-3598 244 9 𝑧3 𝑧3 NOUN iajs-3598 244 10 [ [ X iajs-3598 244 11 7 7 NUM iajs-3598 244 12 ] ] X iajs-3598 244 13 ( ( PUNCT iajs-3598 244 14 οΏ½ οΏ½ PROPN iajs-3598 244 15 Μƒ Μƒ NOUN iajs-3598 244 16 οΏ½ οΏ½ PROPN iajs-3598 244 17 1 1 NUM iajs-3598 244 18 βˆ’ βˆ’ PROPN iajs-3598 244 19 οΏ½ οΏ½ PROPN iajs-3598 244 20 Μƒ Μƒ NOUN iajs-3598 244 21 οΏ½ οΏ½ NOUN iajs-3598 244 22 2 2 NUM iajs-3598 244 23 ) ) PUNCT iajs-3598 244 24 β‰  β‰  PROPN iajs-3598 244 25 0 0 X iajs-3598 244 26 . . PUNCT iajs-3598 245 1 this this PRON iajs-3598 245 2 implies imply VERB iajs-3598 245 3 that that DET iajs-3598 245 4 system system NOUN iajs-3598 245 5 ( ( PUNCT iajs-3598 245 6 1 1 X iajs-3598 245 7 ) ) PUNCT iajs-3598 245 8 has have VERB iajs-3598 245 9 no no DET iajs-3598 245 10 ( ( PUNCT iajs-3598 245 11 pt pt NOUN iajs-3598 245 12 ) ) PUNCT iajs-3598 245 13 bifurcation bifurcation NOUN iajs-3598 245 14 at at ADP iajs-3598 245 15 𝐻7 𝐻7 NOUN iajs-3598 245 16 where where SCONJ iajs-3598 245 17 οΏ½ οΏ½ PROPN iajs-3598 245 18 Μƒ Μƒ PROPN iajs-3598 245 19 οΏ½ οΏ½ NOUN iajs-3598 245 20 = = SYM iajs-3598 245 21 𝑑 𝑑 PROPN iajs-3598 245 22 , , PUNCT iajs-3598 245 23 and and CCONJ iajs-3598 245 24 has have VERB iajs-3598 245 25 a a DET iajs-3598 245 26 ( ( PUNCT iajs-3598 245 27 sn sn NOUN iajs-3598 245 28 ) ) PUNCT iajs-3598 245 29 bifurcation bifurcation NOUN iajs-3598 245 30 at at ADP iajs-3598 245 31 𝐻7 𝐻7 NOUN iajs-3598 245 32 with with ADP iajs-3598 245 33 a a DET iajs-3598 245 34 parameter parameter NOUN iajs-3598 245 35 οΏ½ οΏ½ PROPN iajs-3598 245 36 Μƒ Μƒ PROPN iajs-3598 245 37 οΏ½ οΏ½ NOUN iajs-3598 245 38 = = SYM iajs-3598 245 39 𝑑. 𝑑. NOUN iajs-3598 245 40 4 4 NUM iajs-3598 245 41 . . PUNCT iajs-3598 245 42 numerical numerical PROPN iajs-3598 245 43 simulation simulation PROPN iajs-3598 245 44 : : PUNCT iajs-3598 245 45 in in ADP iajs-3598 245 46 the the DET iajs-3598 245 47 following following ADJ iajs-3598 245 48 section section NOUN iajs-3598 245 49 the the DET iajs-3598 245 50 system system NOUN iajs-3598 245 51 's 's PART iajs-3598 245 52 ( ( PUNCT iajs-3598 245 53 1 1 NUM iajs-3598 245 54 ) ) PUNCT iajs-3598 245 55 dynamic dynamic ADJ iajs-3598 245 56 behaviour behaviour NOUN iajs-3598 245 57 has have AUX iajs-3598 245 58 been be AUX iajs-3598 245 59 investigated investigate VERB iajs-3598 245 60 . . PUNCT iajs-3598 246 1 to to PART iajs-3598 246 2 validate validate VERB iajs-3598 246 3 the the DET iajs-3598 246 4 findings finding NOUN iajs-3598 246 5 of of ADP iajs-3598 246 6 the the DET iajs-3598 246 7 study study NOUN iajs-3598 246 8 and and CCONJ iajs-3598 246 9 the the DET iajs-3598 246 10 influence influence NOUN iajs-3598 246 11 of of ADP iajs-3598 246 12 the the DET iajs-3598 246 13 parameters parameter NOUN iajs-3598 246 14 on on ADP iajs-3598 246 15 the the DET iajs-3598 246 16 dynamic dynamic ADJ iajs-3598 246 17 model model NOUN iajs-3598 246 18 , , PUNCT iajs-3598 246 19 calculations calculation NOUN iajs-3598 246 20 can can AUX iajs-3598 246 21 be be AUX iajs-3598 246 22 performed perform VERB iajs-3598 246 23 for for ADP iajs-3598 246 24 a a DET iajs-3598 246 25 number number NOUN iajs-3598 246 26 of of ADP iajs-3598 246 27 sets set NOUN iajs-3598 246 28 of of ADP iajs-3598 246 29 parameters parameter NOUN iajs-3598 246 30 with with ADP iajs-3598 246 31 various various ADJ iajs-3598 246 32 initial initial ADJ iajs-3598 246 33 points point NOUN iajs-3598 246 34 . . PUNCT iajs-3598 247 1 figure(1)(a figure(1)(a PROPN iajs-3598 247 2 - - PUNCT iajs-3598 247 3 b b NOUN iajs-3598 247 4 ) ) PUNCT iajs-3598 247 5 it it PRON iajs-3598 247 6 appears appear VERB iajs-3598 247 7 that that SCONJ iajs-3598 247 8 the the DET iajs-3598 247 9 system system NOUN iajs-3598 247 10 ( ( PUNCT iajs-3598 247 11 1 1 X iajs-3598 247 12 ) ) PUNCT iajs-3598 247 13 has have VERB iajs-3598 247 14 a a DET iajs-3598 247 15 positive positive ADJ iajs-3598 247 16 global global ADJ iajs-3598 247 17 equilibrium equilibrium NOUN iajs-3598 247 18 point point NOUN iajs-3598 247 19 at at ADP iajs-3598 247 20 the the DET iajs-3598 247 21 fictitious fictitious ADJ iajs-3598 247 22 set set NOUN iajs-3598 247 23 of of ADP iajs-3598 247 24 parameters parameter NOUN iajs-3598 247 25 ( ( PUNCT iajs-3598 247 26 19 19 NUM iajs-3598 247 27 ) ) PUNCT iajs-3598 247 28 . . PUNCT iajs-3598 248 1 𝑆1 𝑆1 NOUN iajs-3598 248 2 = = SYM iajs-3598 248 3 1 1 NUM iajs-3598 248 4 , , PUNCT iajs-3598 248 5 𝐾1 𝐾1 NOUN iajs-3598 248 6 = = SYM iajs-3598 248 7 0 0 NUM iajs-3598 249 1 βˆ™ βˆ™ NOUN iajs-3598 249 2 5 5 NUM iajs-3598 249 3 , , PUNCT iajs-3598 249 4 𝐢1 𝐢1 X iajs-3598 249 5 = = SYM iajs-3598 249 6 0 0 NUM iajs-3598 249 7 βˆ™ βˆ™ NOUN iajs-3598 249 8 0001 0001 NUM iajs-3598 249 9 , , PUNCT iajs-3598 249 10 π‘Ž1 π‘Ž1 NOUN iajs-3598 249 11 = = SYM iajs-3598 249 12 1.5 1.5 NUM iajs-3598 249 13 , , PUNCT iajs-3598 249 14 𝑆2 𝑆2 NOUN iajs-3598 249 15 = = SYM iajs-3598 249 16 0.5 0.5 NUM iajs-3598 249 17 , , PUNCT iajs-3598 249 18 𝑓1 𝑓1 PROPN iajs-3598 249 19 = = SYM iajs-3598 249 20 0 0 NUM iajs-3598 249 21 βˆ™ βˆ™ NOUN iajs-3598 249 22 001 001 NUM iajs-3598 249 23 , , PUNCT iajs-3598 249 24 𝐢 𝐢 PROPN iajs-3598 249 25 = = PROPN iajs-3598 249 26 0.5 0.5 NUM iajs-3598 249 27 , , PUNCT iajs-3598 249 28 𝐢2 𝐢2 X iajs-3598 249 29 = = SYM iajs-3598 249 30 0 0 NUM iajs-3598 250 1 βˆ™ βˆ™ PROPN iajs-3598 250 2 0001 0001 NUM iajs-3598 250 3 , , PUNCT iajs-3598 250 4 π‘Ž2 π‘Ž2 NOUN iajs-3598 250 5 = = SYM iajs-3598 250 6 1.5 1.5 NUM iajs-3598 250 7 , , PUNCT iajs-3598 250 8 π‘Ž3 π‘Ž3 NOUN iajs-3598 250 9 = = SYM iajs-3598 250 10 1.5 1.5 NUM iajs-3598 250 11 , , PUNCT iajs-3598 250 12 𝑔1 𝑔1 PROPN iajs-3598 250 13 = = SYM iajs-3598 250 14 0 0 NUM iajs-3598 250 15 βˆ™ βˆ™ PROPN iajs-3598 250 16 00001 00001 NUM iajs-3598 250 17 , , PUNCT iajs-3598 250 18 𝑔2 𝑔2 NOUN iajs-3598 250 19 = = SYM iajs-3598 250 20 0 0 NUM iajs-3598 250 21 βˆ™ βˆ™ PROPN iajs-3598 250 22 00001 00001 NUM iajs-3598 250 23 , , PUNCT iajs-3598 250 24 πœ‡ πœ‡ ADP iajs-3598 250 25 = = NOUN iajs-3598 250 26 0 0 NUM iajs-3598 250 27 βˆ™ βˆ™ PROPN iajs-3598 250 28 002 002 NUM iajs-3598 250 29 , , PUNCT iajs-3598 250 30 𝑑 𝑑 PROPN iajs-3598 250 31 = = SYM iajs-3598 250 32 0 0 NUM iajs-3598 250 33 βˆ™ βˆ™ NOUN iajs-3598 250 34 001 001 NUM iajs-3598 250 35 ( ( PUNCT iajs-3598 250 36 19 19 NUM iajs-3598 250 37 ) ) PUNCT iajs-3598 250 38 figure figure NOUN iajs-3598 250 39 1(a 1(a NUM iajs-3598 251 1 βˆ’ βˆ’ PROPN iajs-3598 252 1 b).time b).time PROPN iajs-3598 252 2 series series NOUN iajs-3598 252 3 of of ADP iajs-3598 252 4 the the DET iajs-3598 252 5 system system NOUN iajs-3598 252 6 's 's PART iajs-3598 252 7 solution solution NOUN iajs-3598 252 8 ( ( PUNCT iajs-3598 252 9 1 1 X iajs-3598 252 10 ) ) PUNCT iajs-3598 252 11 start start VERB iajs-3598 252 12 with with ADP iajs-3598 252 13 initial initial ADJ iajs-3598 252 14 point point NOUN iajs-3598 252 15 ( ( PUNCT iajs-3598 252 16 1 1 NUM iajs-3598 252 17 , , PUNCT iajs-3598 252 18 2 2 NUM iajs-3598 252 19 , , PUNCT iajs-3598 252 20 0.9 0.9 NUM iajs-3598 252 21 ) ) PUNCT iajs-3598 252 22 . . PUNCT iajs-3598 253 1 ( ( PUNCT iajs-3598 253 2 a a X iajs-3598 253 3 ) ) PUNCT iajs-3598 253 4 time time NOUN iajs-3598 253 5 series series NOUN iajs-3598 253 6 of of ADP iajs-3598 253 7 the the DET iajs-3598 253 8 solution solution NOUN iajs-3598 253 9 approaches approach NOUN iajs-3598 253 10 to to ADP iajs-3598 253 11 h7 h7 PROPN iajs-3598 253 12 =( =( NOUN iajs-3598 253 13 0.499,0.999,0.737 0.499,0.999,0.737 PROPN iajs-3598 253 14 ) ) PUNCT iajs-3598 253 15 , , PUNCT iajs-3598 253 16 ( ( PUNCT iajs-3598 253 17 b b X iajs-3598 253 18 ) ) PUNCT iajs-3598 253 19 solution solution NOUN iajs-3598 253 20 of of ADP iajs-3598 253 21 system system NOUN iajs-3598 253 22 ( ( PUNCT iajs-3598 253 23 1 1 NUM iajs-3598 253 24 ) ) PUNCT iajs-3598 253 25 . . PUNCT iajs-3598 254 1 in in ADP iajs-3598 254 2 order order NOUN iajs-3598 254 3 to to PART iajs-3598 254 4 investigate investigate VERB iajs-3598 254 5 the the DET iajs-3598 254 6 effects effect NOUN iajs-3598 254 7 of of ADP iajs-3598 254 8 parameters parameter NOUN iajs-3598 254 9 , , PUNCT iajs-3598 254 10 on on ADP iajs-3598 254 11 the the DET iajs-3598 254 12 dynamical dynamical ADJ iajs-3598 254 13 behavior behavior NOUN iajs-3598 254 14 of of ADP iajs-3598 254 15 the the DET iajs-3598 254 16 system system NOUN iajs-3598 254 17 ( ( PUNCT iajs-3598 254 18 1 1 NUM iajs-3598 254 19 ) ) PUNCT iajs-3598 254 20 , , PUNCT iajs-3598 254 21 the the DET iajs-3598 254 22 system system NOUN iajs-3598 254 23 ( ( PUNCT iajs-3598 254 24 1 1 X iajs-3598 254 25 ) ) PUNCT iajs-3598 254 26 has have AUX iajs-3598 254 27 been be AUX iajs-3598 254 28 numerically numerically ADV iajs-3598 254 29 solved solve VERB iajs-3598 254 30 using use VERB iajs-3598 254 31 the the DET iajs-3598 254 32 data datum NOUN iajs-3598 254 33 provided provide VERB iajs-3598 254 34 in in ADP iajs-3598 254 35 ( ( PUNCT iajs-3598 254 36 19 19 NUM iajs-3598 254 37 ) ) PUNCT iajs-3598 254 38 results result NOUN iajs-3598 254 39 can can AUX iajs-3598 254 40 be be AUX iajs-3598 254 41 achieved achieve VERB iajs-3598 254 42 by by ADP iajs-3598 254 43 changing change VERB iajs-3598 254 44 one one NUM iajs-3598 254 45 parameter parameter NOUN iajs-3598 254 46 at at ADP iajs-3598 254 47 a a DET iajs-3598 254 48 time time NOUN iajs-3598 254 49 . . PUNCT iajs-3598 255 1 summarizes summarize NOUN iajs-3598 255 2 how how SCONJ iajs-3598 255 3 additional additional ADJ iajs-3598 255 4 parameters parameter NOUN iajs-3598 255 5 affect affect VERB iajs-3598 255 6 dynamics dynamic NOUN iajs-3598 255 7 . . PUNCT iajs-3598 256 1 table table NOUN iajs-3598 256 2 2 2 NUM iajs-3598 256 3 . . PUNCT iajs-3598 257 1 the the DET iajs-3598 257 2 system system NOUN iajs-3598 257 3 's 's PART iajs-3598 257 4 ( ( PUNCT iajs-3598 257 5 1 1 NUM iajs-3598 257 6 ) ) PUNCT iajs-3598 257 7 point point NOUN iajs-3598 257 8 of of ADP iajs-3598 257 9 bifurcation bifurcation NOUN iajs-3598 257 10 . . PUNCT iajs-3598 258 1 range range NOUN iajs-3598 258 2 of of ADP iajs-3598 258 3 parameter parameter NOUN iajs-3598 258 4 the the DET iajs-3598 258 5 stable stable ADJ iajs-3598 258 6 point point NOUN iajs-3598 258 7 the the DET iajs-3598 258 8 bifurcation bifurcation NOUN iajs-3598 258 9 point point NOUN iajs-3598 258 10 0.1 0.1 NUM iajs-3598 258 11 ≀ ≀ NOUN iajs-3598 258 12 𝑆1 𝑆1 NOUN iajs-3598 258 13 < < X iajs-3598 258 14 1 1 NUM iajs-3598 258 15 𝐻7 𝐻7 NOUN iajs-3598 258 16 0.3 0.3 NUM iajs-3598 258 17 < < X iajs-3598 258 18 𝐾1 𝐾1 PROPN iajs-3598 258 19 < < X iajs-3598 258 20 1.99 1.99 NUM iajs-3598 258 21 𝐻7 𝐻7 NOUN iajs-3598 258 22 0.0001 0.0001 NUM iajs-3598 258 23 ≀ ≀ NUM iajs-3598 258 24 𝐢1 𝐢1 PROPN iajs-3598 258 25 < < X iajs-3598 258 26 1.79 1.79 NUM iajs-3598 258 27 1.79 1.79 NUM iajs-3598 258 28 ≀ ≀ NUM iajs-3598 258 29 𝐢1 𝐢1 NUM iajs-3598 258 30 ≀ ≀ NUM iajs-3598 258 31 2 2 NUM iajs-3598 258 32 𝐻7 𝐻7 NOUN iajs-3598 258 33 𝐻6 𝐻6 NOUN iajs-3598 258 34 𝐢1 𝐢1 NOUN iajs-3598 258 35 = = NUM iajs-3598 258 36 1.79 1.79 NUM iajs-3598 258 37 1.5 1.5 NUM iajs-3598 258 38 ≀ ≀ NUM iajs-3598 258 39 π‘Žπ‘– π‘Žπ‘– ADP iajs-3598 258 40 < < X iajs-3598 258 41 3 3 NUM iajs-3598 258 42 i=1,2,3 i=1,2,3 PART iajs-3598 258 43 𝐻7 𝐻7 NOUN iajs-3598 258 44 0.4 0.4 NUM iajs-3598 258 45 0.5 0.5 NUM iajs-3598 258 46 0.6 0.6 NUM iajs-3598 258 47 0.7 0.7 NUM iajs-3598 258 48 0.8 0.8 NUM iajs-3598 258 49 0.9 0.9 NUM iajs-3598 258 50 1 1 NUM iajs-3598 258 51 0.8 0.8 NUM iajs-3598 258 52 1 1 NUM iajs-3598 258 53 1.2 1.2 NUM iajs-3598 258 54 1.4 1.4 NUM iajs-3598 258 55 1.6 1.6 NUM iajs-3598 258 56 1.8 1.8 NUM iajs-3598 258 57 2 2 NUM iajs-3598 258 58 0.7 0.7 NUM iajs-3598 258 59 0.75 0.75 NUM iajs-3598 258 60 0.8 0.8 NUM iajs-3598 258 61 0.85 0.85 NUM iajs-3598 258 62 0.9 0.9 NUM iajs-3598 258 63 0.95 0.95 NUM iajs-3598 258 64 first first ADJ iajs-3598 258 65 prey prey NOUN iajs-3598 258 66 ( ( PUNCT iajs-3598 258 67 b b NOUN iajs-3598 258 68 ) ) PUNCT iajs-3598 258 69 seconed secone VERB iajs-3598 258 70 prey prey NOUN iajs-3598 258 71 p p NOUN iajs-3598 258 72 r r NOUN iajs-3598 258 73 e e PROPN iajs-3598 258 74 d d X iajs-3598 258 75 a a DET iajs-3598 258 76 t t NOUN iajs-3598 258 77 o o NOUN iajs-3598 258 78 r r NOUN iajs-3598 258 79 stable stable ADJ iajs-3598 258 80 point point NOUN iajs-3598 258 81 ( ( PUNCT iajs-3598 258 82 0.499 0.499 NUM iajs-3598 258 83 , , PUNCT iajs-3598 258 84 0.999,0.737 0.999,0.737 NUM iajs-3598 258 85 initial initial ADJ iajs-3598 258 86 point point NOUN iajs-3598 258 87 ( ( PUNCT iajs-3598 258 88 1,2,0.9 1,2,0.9 NOUN iajs-3598 258 89 ) ) PUNCT iajs-3598 258 90 0 0 NUM iajs-3598 259 1 1000 1000 NUM iajs-3598 259 2 2000 2000 NUM iajs-3598 259 3 3000 3000 NUM iajs-3598 259 4 4000 4000 NUM iajs-3598 259 5 5000 5000 NUM iajs-3598 259 6 6000 6000 NUM iajs-3598 259 7 7000 7000 NUM iajs-3598 259 8 8000 8000 NUM iajs-3598 259 9 9000 9000 NUM iajs-3598 259 10 10000 10000 NUM iajs-3598 259 11 0 0 NUM iajs-3598 259 12 0.5 0.5 NUM iajs-3598 259 13 1 1 NUM iajs-3598 259 14 1.5 1.5 NUM iajs-3598 259 15 2 2 NUM iajs-3598 259 16 2.5 2.5 NUM iajs-3598 259 17 time time NOUN iajs-3598 259 18 p p X iajs-3598 259 19 o o X iajs-3598 259 20 p p X iajs-3598 259 21 u u X iajs-3598 259 22 la la X iajs-3598 259 23 ti ti NOUN iajs-3598 259 24 o o NOUN iajs-3598 259 25 n n PROPN iajs-3598 259 26 ( ( PUNCT iajs-3598 259 27 a a X iajs-3598 259 28 ) ) PUNCT iajs-3598 259 29 l1 l1 PROPN iajs-3598 259 30 l2 l2 PROPN iajs-3598 259 31 l3 l3 PROPN iajs-3598 259 32 ihjpas ihjpas PROPN iajs-3598 259 33 . . PUNCT iajs-3598 260 1 2025 2025 NUM iajs-3598 260 2 , , PUNCT iajs-3598 260 3 38 38 NUM iajs-3598 260 4 ( ( PUNCT iajs-3598 260 5 1 1 NUM iajs-3598 260 6 ) ) PUNCT iajs-3598 260 7 441 441 NUM iajs-3598 260 8 0.5 0.5 NUM iajs-3598 260 9 ≀ ≀ NUM iajs-3598 260 10 𝑆2 𝑆2 NOUN iajs-3598 260 11 < < X iajs-3598 260 12 2 2 NUM iajs-3598 260 13 𝐻7 𝐻7 NOUN iajs-3598 260 14 0.001 0.001 NUM iajs-3598 260 15 ≀ ≀ NOUN iajs-3598 260 16 𝑑 𝑑 X iajs-3598 260 17 < < X iajs-3598 260 18 0.095 0.095 NUM iajs-3598 260 19 0.095 0.095 NUM iajs-3598 260 20 ≀ ≀ NUM iajs-3598 260 21 𝑑 𝑑 VERB iajs-3598 260 22 ≀ ≀ NUM iajs-3598 260 23 0.9 0.9 NUM iajs-3598 260 24 𝐻7 𝐻7 NOUN iajs-3598 260 25 𝐻3 𝐻3 PROPN iajs-3598 260 26 d=0.095 d=0.095 PROPN iajs-3598 260 27 0.002 0.002 NUM iajs-3598 260 28 ≀ ≀ NOUN iajs-3598 260 29 πœ‡ πœ‡ ADP iajs-3598 260 30 < < X iajs-3598 260 31 0.179 0.179 NUM iajs-3598 260 32 0.0179 0.0179 NUM iajs-3598 260 33 ≀ ≀ NUM iajs-3598 260 34 πœ‡ πœ‡ ADP iajs-3598 260 35 < < X iajs-3598 260 36 1 1 NUM iajs-3598 260 37 𝐻7 𝐻7 NOUN iajs-3598 260 38 𝐻3 𝐻3 NOUN iajs-3598 260 39 πœ‡ πœ‡ ADP iajs-3598 260 40 = = PROPN iajs-3598 260 41 0.077 0.077 NUM iajs-3598 260 42 0.0001 0.0001 NUM iajs-3598 260 43 ≀ ≀ NUM iajs-3598 260 44 𝐢2 𝐢2 PROPN iajs-3598 260 45 < < X iajs-3598 260 46 0.34 0.34 NUM iajs-3598 260 47 0.34 0.34 NUM iajs-3598 260 48 ≀ ≀ NUM iajs-3598 260 49 𝐢2 𝐢2 ADV iajs-3598 260 50 < < X iajs-3598 260 51 1 1 NUM iajs-3598 260 52 𝐻7 𝐻7 PROPN iajs-3598 260 53 𝐻4 𝐻4 PROPN iajs-3598 260 54 𝐢2 𝐢2 PROPN iajs-3598 260 55 < < X iajs-3598 260 56 0.34 0.34 NUM iajs-3598 260 57 0.001 0.001 NUM iajs-3598 260 58 ≀ ≀ NOUN iajs-3598 260 59 𝑓1 𝑓1 PROPN iajs-3598 260 60 < < X iajs-3598 260 61 0.99 0.99 NUM iajs-3598 260 62 𝐻7 𝐻7 NOUN iajs-3598 260 63 0.5 0.5 NUM iajs-3598 260 64 ≀ ≀ NUM iajs-3598 260 65 𝐢 𝐢 PROPN iajs-3598 260 66 < < X iajs-3598 260 67 1 1 NUM iajs-3598 260 68 𝐻7 𝐻7 NOUN iajs-3598 260 69 0.0001 0.0001 NUM iajs-3598 260 70 ≀ ≀ PROPN iajs-3598 260 71 𝑔1 𝑔1 PROPN iajs-3598 260 72 < < X iajs-3598 260 73 0.00001 0.00001 NUM iajs-3598 260 74 𝐻7 𝐻7 NOUN iajs-3598 260 75 the the DET iajs-3598 260 76 effect effect NOUN iajs-3598 260 77 of of ADP iajs-3598 260 78 changing change VERB iajs-3598 260 79 the the DET iajs-3598 260 80 parameter parameter NOUN iajs-3598 260 81 𝐢1 𝐢1 NOUN iajs-3598 260 82 in in ADP iajs-3598 260 83 the the DET iajs-3598 260 84 vicinity vicinity NOUN iajs-3598 260 85 0.0001 0.0001 NUM iajs-3598 260 86 ≀ ≀ NUM iajs-3598 260 87 𝐢1 𝐢1 PROPN iajs-3598 260 88 < < X iajs-3598 260 89 1.79 1.79 NUM iajs-3598 260 90 the the DET iajs-3598 260 91 solution solution NOUN iajs-3598 260 92 gets get VERB iajs-3598 260 93 closer close ADJ iajs-3598 260 94 to to ADP iajs-3598 260 95 h7 h7 PROPN iajs-3598 260 96 , , PUNCT iajs-3598 260 97 showing show VERB iajs-3598 260 98 in in ADP iajs-3598 260 99 figure figure NOUN iajs-3598 260 100 2a 2a NUM iajs-3598 260 101 , , PUNCT iajs-3598 260 102 increasing increase VERB iajs-3598 260 103 the the DET iajs-3598 260 104 range range NOUN iajs-3598 260 105 further far ADV iajs-3598 260 106 1.79 1.79 NUM iajs-3598 260 107 ≀ ≀ NUM iajs-3598 260 108 𝐢1 𝐢1 PROPN iajs-3598 260 109 < < X iajs-3598 260 110 2 2 NUM iajs-3598 260 111 the the DET iajs-3598 260 112 solution solution NOUN iajs-3598 260 113 gets get VERB iajs-3598 260 114 closer close ADJ iajs-3598 260 115 to to ADP iajs-3598 260 116 h6 h6 PROPN iajs-3598 260 117 , , PUNCT iajs-3598 260 118 showing show VERB iajs-3598 260 119 in in ADP iajs-3598 260 120 figure figure NOUN iajs-3598 260 121 2b 2b NUM iajs-3598 260 122 . . PUNCT iajs-3598 261 1 figure figure NOUN iajs-3598 261 2 2 2 NUM iajs-3598 261 3 ( ( PUNCT iajs-3598 261 4 a a DET iajs-3598 261 5 - - PUNCT iajs-3598 261 6 b b NOUN iajs-3598 261 7 ) ) PUNCT iajs-3598 261 8 . . PUNCT iajs-3598 262 1 ( ( PUNCT iajs-3598 262 2 a a X iajs-3598 262 3 ) ) PUNCT iajs-3598 262 4 time time NOUN iajs-3598 262 5 series series NOUN iajs-3598 262 6 of of ADP iajs-3598 262 7 the the DET iajs-3598 262 8 system system NOUN iajs-3598 262 9 's 's PART iajs-3598 262 10 solution solution NOUN iajs-3598 262 11 ( ( PUNCT iajs-3598 262 12 1 1 NUM iajs-3598 262 13 ) ) PUNCT iajs-3598 262 14 with with ADP iajs-3598 262 15 c1 c1 PROPN iajs-3598 262 16 = = PROPN iajs-3598 262 17 0.0001 0.0001 NUM iajs-3598 262 18 , , PUNCT iajs-3598 262 19 which which PRON iajs-3598 262 20 approaches approach VERB iajs-3598 262 21 to to ADP iajs-3598 262 22 h7 h7 PROPN iajs-3598 262 23 = = SYM iajs-3598 262 24 ( ( PUNCT iajs-3598 262 25 0.499,0.999,0.737 0.499,0.999,0.737 ADJ iajs-3598 262 26 ) ) PUNCT iajs-3598 262 27 , , PUNCT iajs-3598 262 28 and and CCONJ iajs-3598 262 29 ( ( PUNCT iajs-3598 262 30 b b NOUN iajs-3598 262 31 ) ) PUNCT iajs-3598 262 32 time time NOUN iajs-3598 262 33 series series NOUN iajs-3598 262 34 of of ADP iajs-3598 262 35 the the DET iajs-3598 262 36 solution solution NOUN iajs-3598 262 37 of of ADP iajs-3598 262 38 system system NOUN iajs-3598 262 39 ( ( PUNCT iajs-3598 262 40 1 1 NUM iajs-3598 262 41 ) ) PUNCT iajs-3598 262 42 with with ADP iajs-3598 262 43 c1 c1 PROPN iajs-3598 262 44 = = PUNCT iajs-3598 262 45 1.79 1.79 NUM iajs-3598 262 46 , , PUNCT iajs-3598 262 47 which which PRON iajs-3598 262 48 approaches approach VERB iajs-3598 262 49 to to ADP iajs-3598 262 50 h6 h6 PROPN iajs-3598 262 51 = = PUNCT iajs-3598 262 52 ( ( PUNCT iajs-3598 262 53 0 0 NUM iajs-3598 262 54 , , PUNCT iajs-3598 262 55 0.999,0.812 0.999,0.812 NUM iajs-3598 262 56 ) ) PUNCT iajs-3598 262 57 . . PUNCT iajs-3598 263 1 for for ADP iajs-3598 263 2 the the DET iajs-3598 263 3 parameter parameter NOUN iajs-3598 263 4 𝑑 𝑑 PROPN iajs-3598 263 5 in in ADP iajs-3598 263 6 the the DET iajs-3598 263 7 vicinity vicinity NOUN iajs-3598 263 8 0.001 0.001 NUM iajs-3598 263 9 ≀ ≀ NUM iajs-3598 263 10 𝑑 𝑑 X iajs-3598 263 11 < < X iajs-3598 263 12 0.095 0.095 NUM iajs-3598 263 13 the the DET iajs-3598 263 14 solution solution NOUN iajs-3598 263 15 gets get VERB iajs-3598 263 16 closer close ADJ iajs-3598 263 17 to to ADP iajs-3598 263 18 h7 h7 PROPN iajs-3598 263 19 , , PUNCT iajs-3598 263 20 showing show VERB iajs-3598 263 21 in in ADP iajs-3598 263 22 figure3a figure3a NOUN iajs-3598 263 23 , , PUNCT iajs-3598 263 24 increasing increase VERB iajs-3598 263 25 the the DET iajs-3598 263 26 range range NOUN iajs-3598 263 27 further far ADV iajs-3598 263 28 0.095 0.095 NUM iajs-3598 263 29 ≀ ≀ NUM iajs-3598 263 30 𝑑 𝑑 X iajs-3598 263 31 < < X iajs-3598 263 32 0.9 0.9 NUM iajs-3598 263 33 the the DET iajs-3598 263 34 solution solution NOUN iajs-3598 263 35 gets get VERB iajs-3598 263 36 closer close ADJ iajs-3598 263 37 to to ADP iajs-3598 263 38 h3 h3 NOUN iajs-3598 263 39 , , PUNCT iajs-3598 263 40 showing show VERB iajs-3598 263 41 in in ADP iajs-3598 263 42 figure figure NOUN iajs-3598 263 43 3b 3b NUM iajs-3598 263 44 . . PUNCT iajs-3598 264 1 0 0 NUM iajs-3598 265 1 1000 1000 NUM iajs-3598 265 2 2000 2000 NUM iajs-3598 265 3 3000 3000 NUM iajs-3598 265 4 4000 4000 NUM iajs-3598 265 5 5000 5000 NUM iajs-3598 265 6 6000 6000 NUM iajs-3598 265 7 7000 7000 NUM iajs-3598 265 8 8000 8000 NUM iajs-3598 265 9 9000 9000 NUM iajs-3598 265 10 10000 10000 NUM iajs-3598 265 11 0 0 NUM iajs-3598 265 12 0.2 0.2 NUM iajs-3598 265 13 0.4 0.4 NUM iajs-3598 265 14 0.6 0.6 NUM iajs-3598 265 15 0.8 0.8 NUM iajs-3598 265 16 1 1 NUM iajs-3598 265 17 1.2 1.2 NUM iajs-3598 265 18 1.4 1.4 NUM iajs-3598 265 19 1.6 1.6 NUM iajs-3598 265 20 1.8 1.8 NUM iajs-3598 265 21 2 2 NUM iajs-3598 265 22 time time NOUN iajs-3598 265 23 p p X iajs-3598 265 24 o o X iajs-3598 265 25 p p X iajs-3598 265 26 u u X iajs-3598 265 27 la la X iajs-3598 265 28 ti ti NOUN iajs-3598 265 29 o o NOUN iajs-3598 265 30 n n PROPN iajs-3598 265 31 ( ( PUNCT iajs-3598 265 32 b b NOUN iajs-3598 265 33 ) ) PUNCT iajs-3598 265 34 l1 l1 PROPN iajs-3598 265 35 l2 l2 PROPN iajs-3598 265 36 l3 l3 PROPN iajs-3598 265 37 0 0 NUM iajs-3598 265 38 1000 1000 NUM iajs-3598 265 39 2000 2000 NUM iajs-3598 265 40 3000 3000 NUM iajs-3598 265 41 4000 4000 NUM iajs-3598 265 42 5000 5000 NUM iajs-3598 265 43 6000 6000 NUM iajs-3598 265 44 7000 7000 NUM iajs-3598 265 45 8000 8000 NUM iajs-3598 265 46 9000 9000 NUM iajs-3598 265 47 10000 10000 NUM iajs-3598 265 48 0 0 NUM iajs-3598 265 49 0.5 0.5 NUM iajs-3598 265 50 1 1 NUM iajs-3598 265 51 1.5 1.5 NUM iajs-3598 265 52 2 2 NUM iajs-3598 265 53 2.5 2.5 NUM iajs-3598 265 54 time time NOUN iajs-3598 265 55 p p X iajs-3598 265 56 o o X iajs-3598 265 57 p p X iajs-3598 265 58 u u X iajs-3598 265 59 la la X iajs-3598 265 60 ti ti NOUN iajs-3598 265 61 o o NOUN iajs-3598 265 62 n n PROPN iajs-3598 265 63 ( ( PUNCT iajs-3598 265 64 a a X iajs-3598 265 65 ) ) PUNCT iajs-3598 265 66 l1 l1 PROPN iajs-3598 265 67 l2 l2 PROPN iajs-3598 265 68 l3 l3 PROPN iajs-3598 265 69 0 0 NUM iajs-3598 265 70 1000 1000 NUM iajs-3598 265 71 2000 2000 NUM iajs-3598 265 72 3000 3000 NUM iajs-3598 265 73 4000 4000 NUM iajs-3598 265 74 5000 5000 NUM iajs-3598 265 75 6000 6000 NUM iajs-3598 265 76 7000 7000 NUM iajs-3598 265 77 8000 8000 NUM iajs-3598 265 78 9000 9000 NUM iajs-3598 265 79 10000 10000 NUM iajs-3598 265 80 0 0 NUM iajs-3598 265 81 0.2 0.2 NUM iajs-3598 265 82 0.4 0.4 NUM iajs-3598 265 83 0.6 0.6 NUM iajs-3598 265 84 0.8 0.8 NUM iajs-3598 265 85 1 1 NUM iajs-3598 265 86 1.2 1.2 NUM iajs-3598 265 87 1.4 1.4 NUM iajs-3598 265 88 1.6 1.6 NUM iajs-3598 265 89 1.8 1.8 NUM iajs-3598 265 90 2 2 NUM iajs-3598 265 91 time time NOUN iajs-3598 265 92 p p X iajs-3598 265 93 o o X iajs-3598 265 94 p p X iajs-3598 265 95 u u X iajs-3598 265 96 la la X iajs-3598 265 97 ti ti NOUN iajs-3598 265 98 o o NOUN iajs-3598 265 99 n n PROPN iajs-3598 265 100 ( ( PUNCT iajs-3598 265 101 b b NOUN iajs-3598 265 102 ) ) PUNCT iajs-3598 265 103 l1 l1 PROPN iajs-3598 265 104 l2 l2 PROPN iajs-3598 265 105 l3 l3 PROPN iajs-3598 265 106 0 0 NUM iajs-3598 265 107 1000 1000 NUM iajs-3598 265 108 2000 2000 NUM iajs-3598 265 109 3000 3000 NUM iajs-3598 265 110 4000 4000 NUM iajs-3598 265 111 5000 5000 NUM iajs-3598 265 112 6000 6000 NUM iajs-3598 265 113 7000 7000 NUM iajs-3598 265 114 8000 8000 NUM iajs-3598 265 115 9000 9000 NUM iajs-3598 265 116 10000 10000 NUM iajs-3598 265 117 0 0 NUM iajs-3598 265 118 0.5 0.5 NUM iajs-3598 265 119 1 1 NUM iajs-3598 265 120 1.5 1.5 NUM iajs-3598 265 121 2 2 NUM iajs-3598 265 122 2.5 2.5 NUM iajs-3598 265 123 time time NOUN iajs-3598 265 124 p p X iajs-3598 265 125 o o X iajs-3598 265 126 p p X iajs-3598 265 127 u u X iajs-3598 265 128 la la X iajs-3598 265 129 ti ti NOUN iajs-3598 265 130 o o NOUN iajs-3598 265 131 n n PROPN iajs-3598 265 132 ( ( PUNCT iajs-3598 265 133 a a X iajs-3598 265 134 ) ) PUNCT iajs-3598 265 135 l1 l1 PROPN iajs-3598 265 136 l2 l2 PROPN iajs-3598 265 137 l3 l3 PROPN iajs-3598 265 138 ihjpas ihjpas PROPN iajs-3598 265 139 . . PUNCT iajs-3598 266 1 2025 2025 NUM iajs-3598 266 2 , , PUNCT iajs-3598 266 3 38 38 NUM iajs-3598 266 4 ( ( PUNCT iajs-3598 266 5 1 1 NUM iajs-3598 266 6 ) ) PUNCT iajs-3598 266 7 442 442 NUM iajs-3598 266 8 figure3 figure3 NOUN iajs-3598 266 9 . . PUNCT iajs-3598 267 1 ( ( PUNCT iajs-3598 267 2 a a DET iajs-3598 267 3 - - PUNCT iajs-3598 267 4 b b NOUN iajs-3598 267 5 ) ) PUNCT iajs-3598 267 6 . . PUNCT iajs-3598 268 1 ( ( PUNCT iajs-3598 268 2 a a X iajs-3598 268 3 ) ) PUNCT iajs-3598 268 4 time time NOUN iajs-3598 268 5 series series NOUN iajs-3598 268 6 of of ADP iajs-3598 268 7 the the DET iajs-3598 268 8 system system NOUN iajs-3598 268 9 's 's PART iajs-3598 268 10 solution solution NOUN iajs-3598 268 11 ( ( PUNCT iajs-3598 268 12 1.1 1.1 NUM iajs-3598 268 13 ) ) PUNCT iajs-3598 268 14 with with ADP iajs-3598 268 15 d d PROPN iajs-3598 268 16 = = SYM iajs-3598 268 17 0.001 0.001 NUM iajs-3598 268 18 , , PUNCT iajs-3598 268 19 which which PRON iajs-3598 268 20 approaches approach VERB iajs-3598 268 21 to to ADP iajs-3598 268 22 h7 h7 PROPN iajs-3598 268 23 = = SYM iajs-3598 268 24 ( ( PUNCT iajs-3598 268 25 0.499,0.999,0.737 0.499,0.999,0.737 ADJ iajs-3598 268 26 ) ) PUNCT iajs-3598 268 27 , , PUNCT iajs-3598 268 28 and and CCONJ iajs-3598 268 29 ( ( PUNCT iajs-3598 268 30 b b NOUN iajs-3598 268 31 ) ) PUNCT iajs-3598 268 32 time time NOUN iajs-3598 268 33 series series NOUN iajs-3598 268 34 of of ADP iajs-3598 268 35 the the DET iajs-3598 268 36 solution solution NOUN iajs-3598 268 37 of of ADP iajs-3598 268 38 system system NOUN iajs-3598 268 39 ( ( PUNCT iajs-3598 268 40 1.1 1.1 NUM iajs-3598 268 41 ) ) PUNCT iajs-3598 268 42 with with ADP iajs-3598 268 43 d d PROPN iajs-3598 268 44 = = SYM iajs-3598 268 45 0.095 0.095 NUM iajs-3598 268 46 , , PUNCT iajs-3598 268 47 which which PRON iajs-3598 268 48 approaches approach VERB iajs-3598 268 49 to to ADP iajs-3598 268 50 h3 h3 NOUN iajs-3598 268 51 = = SYM iajs-3598 268 52 ( ( PUNCT iajs-3598 268 53 0.5,1,0 0.5,1,0 NUM iajs-3598 268 54 ) ) PUNCT iajs-3598 268 55 . . PUNCT iajs-3598 269 1 for for SCONJ iajs-3598 269 2 the the DET iajs-3598 269 3 parameter parameter NOUN iajs-3598 269 4 πœ‡ πœ‡ ADP iajs-3598 269 5 in in ADP iajs-3598 269 6 the the DET iajs-3598 269 7 vicinity vicinity NOUN iajs-3598 269 8 0.002 0.002 NUM iajs-3598 269 9 ≀ ≀ NOUN iajs-3598 269 10 πœ‡ πœ‡ ADP iajs-3598 269 11 < < X iajs-3598 269 12 0.179 0.179 NUM iajs-3598 269 13 the the DET iajs-3598 269 14 solution solution NOUN iajs-3598 269 15 gets get VERB iajs-3598 269 16 closer close ADJ iajs-3598 269 17 to to ADP iajs-3598 269 18 h7 h7 PROPN iajs-3598 269 19 , , PUNCT iajs-3598 269 20 showing show VERB iajs-3598 269 21 in in ADP iajs-3598 269 22 figure figure NOUN iajs-3598 269 23 4a 4a NOUN iajs-3598 269 24 , , PUNCT iajs-3598 269 25 increasing increase VERB iajs-3598 269 26 the the DET iajs-3598 269 27 range range NOUN iajs-3598 269 28 further far ADV iajs-3598 269 29 0.179 0.179 NUM iajs-3598 269 30 ≀ ≀ NOUN iajs-3598 269 31 πœ‡ πœ‡ ADP iajs-3598 269 32 < < X iajs-3598 269 33 1 1 NUM iajs-3598 269 34 the the DET iajs-3598 269 35 solution solution NOUN iajs-3598 269 36 gets get VERB iajs-3598 269 37 closer close ADJ iajs-3598 269 38 to to ADP iajs-3598 269 39 h3 h3 NOUN iajs-3598 269 40 , , PUNCT iajs-3598 269 41 showing show VERB iajs-3598 269 42 in in ADP iajs-3598 269 43 figure figure NOUN iajs-3598 269 44 4b 4b PROPN iajs-3598 269 45 . . PUNCT iajs-3598 270 1 figure figure NOUN iajs-3598 270 2 4 4 NUM iajs-3598 270 3 . . PUNCT iajs-3598 271 1 ( ( PUNCT iajs-3598 271 2 a a DET iajs-3598 271 3 - - PUNCT iajs-3598 271 4 b b NOUN iajs-3598 271 5 ) ) PUNCT iajs-3598 271 6 . . PUNCT iajs-3598 272 1 ( ( PUNCT iajs-3598 272 2 a a X iajs-3598 272 3 ) ) PUNCT iajs-3598 272 4 time time NOUN iajs-3598 272 5 series series NOUN iajs-3598 272 6 of of ADP iajs-3598 272 7 the the DET iajs-3598 272 8 system system NOUN iajs-3598 272 9 's 's PART iajs-3598 272 10 solution solution NOUN iajs-3598 272 11 ( ( PUNCT iajs-3598 272 12 1.1 1.1 NUM iajs-3598 272 13 ) ) PUNCT iajs-3598 272 14 with with ADP iajs-3598 272 15 ΞΌ ΞΌ PROPN iajs-3598 272 16 = = SYM iajs-3598 272 17 0.002 0.002 NUM iajs-3598 272 18 , , PUNCT iajs-3598 272 19 which which PRON iajs-3598 272 20 approaches approach VERB iajs-3598 272 21 to to ADP iajs-3598 272 22 h7 h7 PROPN iajs-3598 272 23 = = SYM iajs-3598 272 24 ( ( PUNCT iajs-3598 272 25 0.499,0.999,0.737 0.499,0.999,0.737 ADJ iajs-3598 272 26 ) ) PUNCT iajs-3598 272 27 , , PUNCT iajs-3598 272 28 and and CCONJ iajs-3598 272 29 ( ( PUNCT iajs-3598 272 30 b b NOUN iajs-3598 272 31 ) ) PUNCT iajs-3598 272 32 time time NOUN iajs-3598 272 33 series series NOUN iajs-3598 272 34 of of ADP iajs-3598 272 35 the the DET iajs-3598 272 36 solution solution NOUN iajs-3598 272 37 of of ADP iajs-3598 272 38 system system NOUN iajs-3598 272 39 ( ( PUNCT iajs-3598 272 40 1.1 1.1 NUM iajs-3598 272 41 ) ) PUNCT iajs-3598 272 42 with with ADP iajs-3598 272 43 ΞΌ ΞΌ PROPN iajs-3598 272 44 = = NOUN iajs-3598 272 45 0.179 0.179 NUM iajs-3598 272 46 , , PUNCT iajs-3598 272 47 which which PRON iajs-3598 272 48 approaches approach VERB iajs-3598 272 49 to to ADP iajs-3598 272 50 h3 h3 NOUN iajs-3598 272 51 = = SYM iajs-3598 272 52 ( ( PUNCT iajs-3598 272 53 0.5,1,0 0.5,1,0 NUM iajs-3598 272 54 ) ) PUNCT iajs-3598 272 55 . . PUNCT iajs-3598 273 1 for for ADP iajs-3598 273 2 the the DET iajs-3598 273 3 parameter parameter NOUN iajs-3598 273 4 𝐢2 𝐢2 INTJ iajs-3598 273 5 in in ADP iajs-3598 273 6 the the DET iajs-3598 273 7 vicinity vicinity NOUN iajs-3598 273 8 0.0001 0.0001 NUM iajs-3598 273 9 ≀ ≀ NUM iajs-3598 273 10 𝐢2 𝐢2 PROPN iajs-3598 273 11 < < X iajs-3598 273 12 0.34 0.34 NUM iajs-3598 273 13 the the DET iajs-3598 273 14 solution solution NOUN iajs-3598 273 15 gets get VERB iajs-3598 273 16 closer close ADJ iajs-3598 273 17 to to ADP iajs-3598 273 18 h7 h7 PROPN iajs-3598 273 19 , , PUNCT iajs-3598 273 20 showing show VERB iajs-3598 273 21 in in ADP iajs-3598 273 22 figure figure NOUN iajs-3598 273 23 5a 5a NUM iajs-3598 273 24 , , PUNCT iajs-3598 273 25 increasing increase VERB iajs-3598 273 26 the the DET iajs-3598 273 27 range range NOUN iajs-3598 273 28 further far ADV iajs-3598 273 29 0.34 0.34 NUM iajs-3598 273 30 ≀ ≀ NUM iajs-3598 273 31 𝐢2 𝐢2 ADV iajs-3598 273 32 < < X iajs-3598 273 33 1 1 NUM iajs-3598 273 34 the the DET iajs-3598 273 35 solution solution NOUN iajs-3598 273 36 gets get VERB iajs-3598 273 37 closer close ADJ iajs-3598 273 38 to to ADP iajs-3598 273 39 h4 h4 NOUN iajs-3598 273 40 , , PUNCT iajs-3598 273 41 showing show VERB iajs-3598 273 42 in in ADP iajs-3598 273 43 figurer figurer NOUN iajs-3598 273 44 5b 5b NUM iajs-3598 273 45 . . PUNCT iajs-3598 274 1 0 0 NUM iajs-3598 275 1 1000 1000 NUM iajs-3598 275 2 2000 2000 NUM iajs-3598 275 3 3000 3000 NUM iajs-3598 275 4 4000 4000 NUM iajs-3598 275 5 5000 5000 NUM iajs-3598 275 6 6000 6000 NUM iajs-3598 275 7 7000 7000 NUM iajs-3598 275 8 8000 8000 NUM iajs-3598 275 9 9000 9000 NUM iajs-3598 275 10 10000 10000 NUM iajs-3598 275 11 0 0 NUM iajs-3598 275 12 0.2 0.2 NUM iajs-3598 275 13 0.4 0.4 NUM iajs-3598 275 14 0.6 0.6 NUM iajs-3598 275 15 0.8 0.8 NUM iajs-3598 275 16 1 1 NUM iajs-3598 275 17 1.2 1.2 NUM iajs-3598 275 18 1.4 1.4 NUM iajs-3598 275 19 1.6 1.6 NUM iajs-3598 275 20 1.8 1.8 NUM iajs-3598 275 21 2 2 NUM iajs-3598 275 22 time time NOUN iajs-3598 275 23 p p X iajs-3598 275 24 o o X iajs-3598 275 25 p p X iajs-3598 275 26 u u X iajs-3598 275 27 la la X iajs-3598 275 28 ti ti NOUN iajs-3598 275 29 o o NOUN iajs-3598 275 30 n n PROPN iajs-3598 275 31 ( ( PUNCT iajs-3598 275 32 b b NOUN iajs-3598 275 33 ) ) PUNCT iajs-3598 275 34 l1 l1 PROPN iajs-3598 275 35 l2 l2 PROPN iajs-3598 275 36 l3 l3 PROPN iajs-3598 275 37 0 0 NUM iajs-3598 275 38 1000 1000 NUM iajs-3598 275 39 2000 2000 NUM iajs-3598 275 40 3000 3000 NUM iajs-3598 275 41 4000 4000 NUM iajs-3598 275 42 5000 5000 NUM iajs-3598 275 43 6000 6000 NUM iajs-3598 275 44 7000 7000 NUM iajs-3598 275 45 8000 8000 NUM iajs-3598 275 46 9000 9000 NUM iajs-3598 275 47 10000 10000 NUM iajs-3598 275 48 0 0 NUM iajs-3598 275 49 0.5 0.5 NUM iajs-3598 275 50 1 1 NUM iajs-3598 275 51 1.5 1.5 NUM iajs-3598 275 52 2 2 NUM iajs-3598 275 53 2.5 2.5 NUM iajs-3598 275 54 time time NOUN iajs-3598 275 55 p p X iajs-3598 275 56 o o X iajs-3598 275 57 p p X iajs-3598 275 58 u u X iajs-3598 275 59 la la X iajs-3598 275 60 ti ti NOUN iajs-3598 275 61 o o NOUN iajs-3598 275 62 n n PROPN iajs-3598 275 63 ( ( PUNCT iajs-3598 275 64 a a X iajs-3598 275 65 ) ) PUNCT iajs-3598 275 66 l1 l1 PROPN iajs-3598 275 67 l2 l2 PROPN iajs-3598 275 68 l3 l3 PROPN iajs-3598 275 69 0 0 NUM iajs-3598 275 70 1000 1000 NUM iajs-3598 275 71 2000 2000 NUM iajs-3598 275 72 3000 3000 NUM iajs-3598 275 73 4000 4000 NUM iajs-3598 275 74 5000 5000 NUM iajs-3598 275 75 6000 6000 NUM iajs-3598 275 76 7000 7000 NUM iajs-3598 275 77 8000 8000 NUM iajs-3598 275 78 9000 9000 NUM iajs-3598 275 79 10000 10000 NUM iajs-3598 275 80 0 0 NUM iajs-3598 275 81 0.2 0.2 NUM iajs-3598 275 82 0.4 0.4 NUM iajs-3598 275 83 0.6 0.6 NUM iajs-3598 275 84 0.8 0.8 NUM iajs-3598 275 85 1 1 NUM iajs-3598 275 86 1.2 1.2 NUM iajs-3598 275 87 1.4 1.4 NUM iajs-3598 275 88 1.6 1.6 NUM iajs-3598 275 89 1.8 1.8 NUM iajs-3598 275 90 2 2 NUM iajs-3598 275 91 time time NOUN iajs-3598 275 92 p p X iajs-3598 275 93 o o X iajs-3598 275 94 p p X iajs-3598 275 95 u u X iajs-3598 275 96 la la X iajs-3598 275 97 ti ti NOUN iajs-3598 275 98 o o NOUN iajs-3598 275 99 n n PROPN iajs-3598 275 100 ( ( PUNCT iajs-3598 275 101 b b NOUN iajs-3598 275 102 ) ) PUNCT iajs-3598 275 103 l1 l1 PROPN iajs-3598 275 104 l2 l2 PROPN iajs-3598 275 105 l3 l3 PROPN iajs-3598 275 106 ihjpas ihjpas PROPN iajs-3598 275 107 . . PUNCT iajs-3598 276 1 2025 2025 NUM iajs-3598 276 2 , , PUNCT iajs-3598 276 3 38 38 NUM iajs-3598 276 4 ( ( PUNCT iajs-3598 276 5 1 1 NUM iajs-3598 276 6 ) ) PUNCT iajs-3598 276 7 443 443 NUM iajs-3598 276 8 figure figure NOUN iajs-3598 276 9 5 5 NUM iajs-3598 276 10 . . PUNCT iajs-3598 277 1 ( ( PUNCT iajs-3598 277 2 a a DET iajs-3598 277 3 - - PUNCT iajs-3598 277 4 b b NOUN iajs-3598 277 5 ) ) PUNCT iajs-3598 277 6 . . 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PUNCT iajs-3598 279 1 5 5 X iajs-3598 279 2 . . X iajs-3598 279 3 conclusion conclusion NOUN iajs-3598 279 4 in in ADP iajs-3598 279 5 this this DET iajs-3598 279 6 article article NOUN iajs-3598 279 7 , , PUNCT iajs-3598 279 8 we we PRON iajs-3598 279 9 present present VERB iajs-3598 279 10 the the DET iajs-3598 279 11 mathematical mathematical ADJ iajs-3598 279 12 model model NOUN iajs-3598 279 13 of of ADP iajs-3598 279 14 three three NUM iajs-3598 279 15 differential differential ADJ iajs-3598 279 16 equations equation NOUN iajs-3598 279 17 for for ADP iajs-3598 279 18 organisms organism NOUN iajs-3598 279 19 that that PRON iajs-3598 279 20 characterize characterize VERB iajs-3598 279 21 the the DET iajs-3598 279 22 effect effect NOUN iajs-3598 279 23 of of ADP iajs-3598 279 24 anti anti ADJ iajs-3598 279 25 - - ADJ iajs-3598 279 26 predation predation ADJ iajs-3598 279 27 behavior behavior NOUN iajs-3598 279 28 in in ADP iajs-3598 279 29 the the DET iajs-3598 279 30 mathematical mathematical ADJ iajs-3598 279 31 model model NOUN iajs-3598 279 32 containing contain VERB iajs-3598 279 33 fear fear NOUN iajs-3598 279 34 have have AUX iajs-3598 279 35 been be AUX iajs-3598 279 36 analyzed analyze VERB iajs-3598 279 37 , , PUNCT iajs-3598 279 38 which which PRON iajs-3598 279 39 are be AUX iajs-3598 279 40 proposed propose VERB iajs-3598 279 41 .(lb .(lb PROPN iajs-3598 279 42 ) ) PUNCT iajs-3598 279 43 have have AUX iajs-3598 279 44 been be AUX iajs-3598 279 45 examined examine VERB iajs-3598 279 46 by by ADP iajs-3598 279 47 changing change VERB iajs-3598 279 48 a a DET iajs-3598 279 49 model model NOUN iajs-3598 279 50 's 's PART iajs-3598 279 51 parameter parameter NOUN iajs-3598 279 52 in in ADP iajs-3598 279 53 order order NOUN iajs-3598 279 54 to to PART iajs-3598 279 55 examine examine VERB iajs-3598 279 56 bifurcation bifurcation NOUN iajs-3598 279 57 curves curve NOUN iajs-3598 279 58 ' ' PART iajs-3598 279 59 ability ability NOUN iajs-3598 279 60 to to PART iajs-3598 279 61 predict predict VERB iajs-3598 279 62 dynamic dynamic ADJ iajs-3598 279 63 behavior behavior NOUN iajs-3598 279 64 as as ADV iajs-3598 279 65 well well ADV iajs-3598 279 66 as as ADP iajs-3598 279 67 its its PRON iajs-3598 279 68 occurrence occurrence NOUN iajs-3598 279 69 states state NOUN iajs-3598 279 70 of of ADP iajs-3598 279 71 ( ( PUNCT iajs-3598 279 72 sn sn NOUN iajs-3598 279 73 ) ) PUNCT iajs-3598 279 74 bifurcation bifurcation NOUN iajs-3598 279 75 occurring occur VERB iajs-3598 279 76 at at ADP iajs-3598 279 77 point point NOUN iajs-3598 279 78 𝐻7 𝐻7 NOUN iajs-3598 279 79 and and CCONJ iajs-3598 279 80 ( ( PUNCT iajs-3598 279 81 tc tc NOUN iajs-3598 279 82 ) ) PUNCT iajs-3598 279 83 and and CCONJ iajs-3598 279 84 ( ( PUNCT iajs-3598 279 85 pf pf NOUN iajs-3598 279 86 ) ) PUNCT iajs-3598 279 87 bifurcation bifurcation NOUN iajs-3598 279 88 occurring occur VERB iajs-3598 279 89 at at ADP iajs-3598 279 90 points point NOUN iajs-3598 279 91 𝐻3 𝐻3 PROPN iajs-3598 279 92 , , PUNCT iajs-3598 279 93 𝐻4 𝐻4 NOUN iajs-3598 279 94 , , PUNCT iajs-3598 279 95 𝐻6the 𝐻6the DET iajs-3598 279 96 bifurcation bifurcation NOUN iajs-3598 279 97 that that PRON iajs-3598 279 98 occurs occur VERB iajs-3598 279 99 at at ADP iajs-3598 279 100 point point NOUN iajs-3598 279 101 is be AUX iajs-3598 279 102 determined determine VERB iajs-3598 279 103 . . PUNCT iajs-3598 280 1 numerical numerical PROPN iajs-3598 280 2 simulation simulation PROPN iajs-3598 280 3 is be AUX iajs-3598 280 4 used use VERB iajs-3598 280 5 . . PUNCT iajs-3598 281 1 with with ADP iajs-3598 281 2 data datum NOUN iajs-3598 281 3 given give VERB iajs-3598 281 4 in in ADP iajs-3598 281 5 equation equation NOUN iajs-3598 281 6 ( ( PUNCT iajs-3598 281 7 19 19 NUM iajs-3598 281 8 ) ) PUNCT iajs-3598 281 9 . . PUNCT iajs-3598 282 1 which which PRON iajs-3598 282 2 are be AUX iajs-3598 282 3 summarized summarize VERB iajs-3598 282 4 as as ADP iajs-3598 282 5 follow follow NOUN iajs-3598 282 6 : : PUNCT iajs-3598 282 7 1 1 X iajs-3598 282 8 ) ) PUNCT iajs-3598 282 9 a a DET iajs-3598 282 10 periodic periodic ADJ iajs-3598 282 11 dynamics dynamic NOUN iajs-3598 282 12 for for ADP iajs-3598 282 13 the the DET iajs-3598 282 14 system system NOUN iajs-3598 282 15 ( ( PUNCT iajs-3598 282 16 1 1 X iajs-3598 282 17 ) ) PUNCT iajs-3598 282 18 does do AUX iajs-3598 282 19 not not PART iajs-3598 282 20 exist exist VERB iajs-3598 282 21 . . PUNCT iajs-3598 283 1 2 2 X iajs-3598 283 2 ) ) PUNCT iajs-3598 283 3 the the DET iajs-3598 283 4 parameters parameter NOUN iajs-3598 283 5 𝐢1 𝐢1 VERB iajs-3598 283 6 , , PUNCT iajs-3598 283 7 𝑑 𝑑 NOUN iajs-3598 283 8 , , PUNCT iajs-3598 283 9 𝐢2 𝐢2 PROPN iajs-3598 283 10 , , PUNCT iajs-3598 283 11 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-3598 283 12 πœ‡ πœ‡ ADV iajs-3598 283 13 , , PUNCT iajs-3598 283 14 have have VERB iajs-3598 283 15 an an DET iajs-3598 283 16 important important ADJ iajs-3598 283 17 effect effect NOUN iajs-3598 283 18 in in ADP iajs-3598 283 19 the the DET iajs-3598 283 20 dynamics dynamic NOUN iajs-3598 283 21 of of ADP iajs-3598 283 22 the the DET iajs-3598 283 23 system system NOUN iajs-3598 283 24 ( ( PUNCT iajs-3598 283 25 1 1 NUM iajs-3598 283 26 ) ) PUNCT iajs-3598 283 27 . . PUNCT iajs-3598 284 1 while while SCONJ iajs-3598 284 2 the the DET iajs-3598 284 3 others other NOUN iajs-3598 284 4 parameters parameter NOUN iajs-3598 284 5 not not PART iajs-3598 284 6 effect effect VERB iajs-3598 284 7 on on ADP iajs-3598 284 8 the the DET iajs-3598 284 9 bifurcation bifurcation NOUN iajs-3598 284 10 of of ADP iajs-3598 284 11 system system NOUN iajs-3598 284 12 1 1 NUM iajs-3598 284 13 . . 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PUNCT iajs-3598 286 1 conflict conflict NOUN iajs-3598 286 2 of of ADP iajs-3598 286 3 interest interest NOUN iajs-3598 286 4 the the DET iajs-3598 286 5 authors author NOUN iajs-3598 286 6 declare declare VERB iajs-3598 286 7 that that SCONJ iajs-3598 286 8 there there PRON iajs-3598 286 9 are be VERB iajs-3598 286 10 no no DET iajs-3598 286 11 competing compete VERB iajs-3598 286 12 interests interest NOUN iajs-3598 286 13 regarding regard VERB iajs-3598 286 14 the the DET iajs-3598 286 15 publication publication NOUN iajs-3598 286 16 of of ADP iajs-3598 286 17 this this DET iajs-3598 286 18 paper paper NOUN iajs-3598 286 19 . . PUNCT iajs-3598 287 1 funding fund VERB iajs-3598 287 2 this this DET iajs-3598 287 3 work work NOUN iajs-3598 287 4 is be AUX iajs-3598 287 5 not not PART iajs-3598 287 6 supported support VERB iajs-3598 287 7 by by ADP iajs-3598 287 8 any any DET iajs-3598 287 9 the the DET iajs-3598 287 10 foundation foundation NOUN iajs-3598 287 11 . . 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PUNCT iajs-3598 291 1 the the DET iajs-3598 291 2 bifurcation bifurcation NOUN iajs-3598 291 3 of of ADP iajs-3598 291 4 stage stage NOUN iajs-3598 291 5 - - PUNCT iajs-3598 291 6 structured structure VERB iajs-3598 291 7 prey prey NOUN iajs-3598 291 8 - - PUNCT iajs-3598 291 9 predator predator NOUN iajs-3598 291 10 food food NOUN iajs-3598 291 11 chain chain NOUN iajs-3598 291 12 model model NOUN iajs-3598 291 13 with with ADP iajs-3598 291 14 refuge refuge NOUN iajs-3598 291 15 . . PUNCT iajs-3598 292 1 int int NOUN iajs-3598 293 1 j j PROPN iajs-3598 293 2 mod mod PROPN iajs-3598 293 3 res res PROPN iajs-3598 293 4 eng eng PROPN iajs-3598 293 5 technol technol NOUN iajs-3598 293 6 . . PROPN iajs-3598 293 7 2016 2016 NUM iajs-3598 293 8 . . PUNCT iajs-3598 294 1 2 2 X iajs-3598 294 2 . . X iajs-3598 294 3 madhi madhi PROPN iajs-3598 294 4 zs zs PROPN iajs-3598 294 5 , , PUNCT iajs-3598 294 6 hussain hussain PROPN iajs-3598 294 7 maa maa PROPN iajs-3598 294 8 . . PROPN iajs-3598 294 9 bifurcation bifurcation NOUN iajs-3598 294 10 diagram diagram NOUN iajs-3598 294 11 of of ADP iajs-3598 294 12 w(u_j w(u_j PROPN iajs-3598 294 13 ; ; PUNCT iajs-3598 294 14 Ο„)-function Ο„)-function PUNCT iajs-3598 294 15 with with ADP iajs-3598 294 16 ( ( PUNCT iajs-3598 294 17 p p X iajs-3598 294 18 , , PUNCT iajs-3598 294 19 q)-parameters q)-parameter NOUN iajs-3598 294 20 . . PUNCT iajs-3598 295 1 iraqi iraqi PROPN iajs-3598 295 2 j j PROPN iajs-3598 295 3 sci sci PROPN iajs-3598 295 4 . . PROPN iajs-3598 295 5 2022;667 2022;667 NUM iajs-3598 295 6 - - PUNCT iajs-3598 295 7 674 674 NUM iajs-3598 295 8 . . 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PUNCT iajs-3598 302 1 ieee ieee PROPN iajs-3598 302 2 trans trans PROPN iajs-3598 302 3 smart smart PROPN iajs-3598 302 4 grid grid NOUN iajs-3598 302 5 . . PUNCT iajs-3598 303 1 2019;10:6580 2019;10:6580 NUM iajs-3598 303 2 - - SYM iajs-3598 303 3 6591 6591 NUM iajs-3598 303 4 . . PUNCT iajs-3598 304 1 https://doi.org/10.1109/tsg.2019.2907600 https://doi.org/10.1109/tsg.2019.2907600 NOUN iajs-3598 304 2 5 5 NUM iajs-3598 304 3 . . PUNCT iajs-3598 304 4 othman othman PROPN iajs-3598 304 5 kb kb PROPN iajs-3598 304 6 , , PUNCT iajs-3598 304 7 amen aman NOUN iajs-3598 304 8 ai ai VERB iajs-3598 304 9 . . PUNCT iajs-3598 305 1 periodic periodic ADJ iajs-3598 305 2 solutions solution NOUN iajs-3598 305 3 of of ADP iajs-3598 305 4 the the DET iajs-3598 305 5 forest forest NOUN iajs-3598 305 6 pest pest NOUN iajs-3598 305 7 system system NOUN iajs-3598 305 8 via via ADP iajs-3598 305 9 hopf hopf ADJ iajs-3598 305 10 bifurcation bifurcation NOUN iajs-3598 305 11 and and CCONJ iajs-3598 305 12 averaging averaging NOUN iajs-3598 305 13 theory theory NOUN iajs-3598 305 14 . . PUNCT iajs-3598 306 1 iraqi iraqi PROPN iajs-3598 306 2 j j PROPN iajs-3598 306 3 sci sci PROPN iajs-3598 306 4 . . PROPN iajs-3598 306 5 2022;5496 2022;5496 NUM iajs-3598 306 6 - - SYM iajs-3598 306 7 5509 5509 NUM iajs-3598 306 8 . . PUNCT iajs-3598 307 1 https://doi.org/10.24996/ijs.2022.63.12.35 https://doi.org/10.24996/ijs.2022.63.12.35 NOUN iajs-3598 307 2 6 6 NUM iajs-3598 307 3 . . PUNCT iajs-3598 308 1 jalal jalal PROPN iajs-3598 308 2 aa aa PROPN iajs-3598 308 3 , , PUNCT iajs-3598 308 4 amen amen INTJ iajs-3598 308 5 ai ai VERB iajs-3598 308 6 , , PUNCT iajs-3598 308 7 sulaiman sulaiman PROPN iajs-3598 308 8 na na PROPN iajs-3598 308 9 . . PROPN iajs-3598 308 10 darboux darboux VERB iajs-3598 308 11 integrability integrability NOUN iajs-3598 308 12 of of ADP iajs-3598 308 13 a a DET iajs-3598 308 14 generalized generalized ADJ iajs-3598 308 15 3d 3d NUM iajs-3598 308 16 chaotic chaotic ADJ iajs-3598 308 17 sprott sprott PROPN iajs-3598 308 18 et9 et9 PROPN iajs-3598 308 19 system system NOUN iajs-3598 308 20 . . PUNCT iajs-3598 309 1 baghdad baghdad PROPN iajs-3598 309 2 sci sci PROPN iajs-3598 309 3 j. j. PROPN iajs-3598 310 1 2022;19:542 2022;19:542 PROPN iajs-3598 310 2 . . PUNCT iajs-3598 311 1 http://dx.doi.org/10.21123/bsj.2022.19.3.0542 http://dx.doi.org/10.21123/bsj.2022.19.3.0542 PROPN iajs-3598 311 2 7 7 NUM iajs-3598 311 3 . . PUNCT iajs-3598 311 4 xu xu PROPN iajs-3598 312 1 c c X iajs-3598 312 2 , , PUNCT iajs-3598 312 3 liao liao PROPN iajs-3598 312 4 m. m. PROPN iajs-3598 312 5 bifurcation bifurcation NOUN iajs-3598 312 6 behaviours behaviour NOUN iajs-3598 312 7 in in ADP iajs-3598 312 8 a a DET iajs-3598 312 9 delayed delay VERB iajs-3598 312 10 three three NUM iajs-3598 312 11 - - PUNCT iajs-3598 312 12 species species NOUN iajs-3598 312 13 food food NOUN iajs-3598 312 14 - - PUNCT iajs-3598 312 15 chain chain NOUN iajs-3598 312 16 model model NOUN iajs-3598 312 17 with with ADP iajs-3598 312 18 holling holle VERB iajs-3598 312 19 type type NOUN iajs-3598 312 20 - - PUNCT iajs-3598 312 21 ii ii NOUN iajs-3598 312 22 functional functional ADJ iajs-3598 312 23 response response NOUN iajs-3598 312 24 . . PUNCT iajs-3598 313 1 appl appl PROPN iajs-3598 313 2 anal anal PROPN iajs-3598 313 3 . . PUNCT iajs-3598 314 1 2013;92:2468 2013;92:2468 NUM iajs-3598 314 2 - - SYM iajs-3598 314 3 2486 2486 NUM iajs-3598 314 4 . . PUNCT iajs-3598 315 1 https://doi.org/10.1080/00036811.2012.742187 https://doi.org/10.1080/00036811.2012.742187 NOUN iajs-3598 315 2 8 8 NUM iajs-3598 315 3 . . PUNCT iajs-3598 316 1 majeed majeed PROPN iajs-3598 316 2 ns ns PROPN iajs-3598 316 3 . . PUNCT iajs-3598 317 1 local local ADJ iajs-3598 317 2 bifurcation bifurcation NOUN iajs-3598 317 3 analysis analysis NOUN iajs-3598 317 4 for for ADP iajs-3598 317 5 a a DET iajs-3598 317 6 special special ADJ iajs-3598 317 7 type type NOUN iajs-3598 317 8 of of ADP iajs-3598 317 9 sir sir NOUN iajs-3598 317 10 epidemic epidemic NOUN iajs-3598 317 11 model model NOUN iajs-3598 317 12 . . PUNCT iajs-3598 318 1 int int PROPN iajs-3598 319 1 j j PROPN iajs-3598 319 2 sci sci PROPN iajs-3598 319 3 res re NOUN iajs-3598 319 4 ijsr ijsr VERB iajs-3598 319 5 . . PUNCT iajs-3598 320 1 2017;6:1143 2017;6:1143 NOUN iajs-3598 320 2 - - PUNCT iajs-3598 320 3 1146 1146 NUM iajs-3598 320 4 . . PUNCT iajs-3598 321 1 https://doi.org/10.21275/art2017872 https://doi.org/10.21275/art2017872 NOUN iajs-3598 321 2 9 9 NUM iajs-3598 321 3 . . PUNCT iajs-3598 322 1 majeed majeed PROPN iajs-3598 322 2 sn sn PROPN iajs-3598 322 3 . . PUNCT iajs-3598 323 1 dynamical dynamical ADJ iajs-3598 323 2 study study NOUN iajs-3598 323 3 of of ADP iajs-3598 323 4 an an DET iajs-3598 323 5 sir sir NOUN iajs-3598 323 6 epidemic epidemic NOUN iajs-3598 323 7 model model NOUN iajs-3598 323 8 with with ADP iajs-3598 323 9 nonlinear nonlinear ADJ iajs-3598 323 10 incidence incidence NOUN iajs-3598 323 11 rate rate NOUN iajs-3598 323 12 and and CCONJ iajs-3598 323 13 regress regress NOUN iajs-3598 323 14 of of ADP iajs-3598 323 15 treatment treatment NOUN iajs-3598 323 16 . . PUNCT iajs-3598 324 1 ibn ibn PROPN iajs-3598 324 2 al al PROPN iajs-3598 324 3 - - PUNCT iajs-3598 324 4 haitham haitham PROPN iajs-3598 324 5 j j PROPN iajs-3598 324 6 pure pure PROPN iajs-3598 324 7 appl appl PROPN iajs-3598 324 8 sci sci PROPN iajs-3598 324 9 . . PROPN iajs-3598 324 10 2018;510 2018;510 PROPN iajs-3598 324 11 - - PUNCT iajs-3598 324 12 522 522 NUM iajs-3598 324 13 . . PUNCT iajs-3598 325 1 https://doi.org/10.30526/2017.ihsciconf.1810 https://doi.org/10.30526/2017.ihsciconf.1810 NUM iajs-3598 325 2 10 10 NUM iajs-3598 325 3 . . PUNCT iajs-3598 326 1 xia xia PROPN iajs-3598 326 2 y y PROPN iajs-3598 326 3 , , PUNCT iajs-3598 326 4 huang huang PROPN iajs-3598 326 5 x x PROPN iajs-3598 326 6 , , PUNCT iajs-3598 326 7 chen chen PROPN iajs-3598 326 8 f f PROPN iajs-3598 326 9 , , PUNCT iajs-3598 326 10 chen chen PROPN iajs-3598 326 11 l. l. PROPN iajs-3598 326 12 stability stability PROPN iajs-3598 326 13 and and CCONJ iajs-3598 326 14 bifurcation bifurcation NOUN iajs-3598 326 15 of of ADP iajs-3598 326 16 a a DET iajs-3598 326 17 predator predator NOUN iajs-3598 326 18 - - PUNCT iajs-3598 326 19 prey prey NOUN iajs-3598 326 20 system system NOUN iajs-3598 326 21 with with ADP iajs-3598 326 22 multiple multiple ADJ iajs-3598 326 23 antipredator antipredator ADJ iajs-3598 326 24 behaviors behavior NOUN iajs-3598 326 25 . . PUNCT iajs-3598 327 1 j j PROPN iajs-3598 327 2 biol biol PROPN iajs-3598 327 3 syst syst PROPN iajs-3598 327 4 . . PUNCT iajs-3598 328 1 2024;32(2):889 2024;32(2):889 NUM iajs-3598 328 2 - - PUNCT iajs-3598 328 3 919 919 NUM iajs-3598 328 4 . . PUNCT iajs-3598 329 1 https://doi.org/10.1142/s021833902450030x https://doi.org/10.1142/s021833902450030x PROPN iajs-3598 329 2 11 11 NUM iajs-3598 329 3 . . PUNCT iajs-3598 330 1 prasad prasad PROPN iajs-3598 330 2 kd kd PROPN iajs-3598 330 3 , , PUNCT iajs-3598 330 4 sasmal sasmal NOUN iajs-3598 330 5 sk sk VERB iajs-3598 330 6 . . PROPN iajs-3598 330 7 dynamics dynamic NOUN iajs-3598 330 8 of of ADP iajs-3598 330 9 anti anti ADJ iajs-3598 330 10 - - ADJ iajs-3598 330 11 predator predator ADJ iajs-3598 330 12 behavior behavior NOUN iajs-3598 330 13 and and CCONJ iajs-3598 330 14 effect effect NOUN iajs-3598 330 15 of of ADP iajs-3598 330 16 fear fear NOUN iajs-3598 330 17 on on ADP iajs-3598 330 18 prey prey NOUN iajs-3598 330 19 - - PUNCT iajs-3598 330 20 predator predator NOUN iajs-3598 330 21 model model NOUN iajs-3598 330 22 . . PUNCT iajs-3598 331 1 j j PROPN iajs-3598 331 2 biol biol PROPN iajs-3598 331 3 syst syst PROPN iajs-3598 331 4 . . PUNCT iajs-3598 332 1 2022;30(4):887 2022;30(4):887 NUM iajs-3598 332 2 - - SYM iajs-3598 332 3 912 912 NUM iajs-3598 332 4 . . PUNCT iajs-3598 333 1 https://doi.org/10.1142/s0218339022500322 https://doi.org/10.1142/s0218339022500322 PRON iajs-3598 333 2 12 12 NUM iajs-3598 333 3 . . PUNCT iajs-3598 334 1 harianto harianto PROPN iajs-3598 334 2 j j PROPN iajs-3598 334 3 , , PUNCT iajs-3598 334 4 suparwati suparwati PROPN iajs-3598 334 5 t t PROPN iajs-3598 334 6 , , PUNCT iajs-3598 334 7 dewi dewi PROPN iajs-3598 334 8 alp alp PROPN iajs-3598 334 9 . . PUNCT iajs-3598 335 1 local local ADJ iajs-3598 335 2 stability stability NOUN iajs-3598 335 3 dynamics dynamic NOUN iajs-3598 335 4 of of ADP iajs-3598 335 5 equilibrium equilibrium NOUN iajs-3598 335 6 points point NOUN iajs-3598 335 7 in in ADP iajs-3598 335 8 predator predator NOUN iajs-3598 335 9 - - PUNCT iajs-3598 335 10 prey prey NOUN iajs-3598 335 11 models model NOUN iajs-3598 335 12 with with ADP iajs-3598 335 13 anti anti ADJ iajs-3598 335 14 - - ADJ iajs-3598 335 15 predator predator ADJ iajs-3598 335 16 behavior behavior NOUN iajs-3598 335 17 . . PUNCT iajs-3598 336 1 j j PROPN iajs-3598 336 2 ilmu ilmu PROPN iajs-3598 336 3 dasar dasar VERB iajs-3598 336 4 . . PUNCT iajs-3598 337 1 2021;22(2):153 2021;22(2):153 NUM iajs-3598 337 2 - - SYM iajs-3598 337 3 160 160 NUM iajs-3598 337 4 . . PUNCT iajs-3598 338 1 https://doi.org/10.19184/jid.v22i2.23991 https://doi.org/10.19184/jid.v22i2.23991 PROPN iajs-3598 338 2 13 13 NUM iajs-3598 338 3 . . PUNCT iajs-3598 339 1 naji naji PROPN iajs-3598 339 2 rk rk PROPN iajs-3598 339 3 , , PUNCT iajs-3598 339 4 majeed majeed PROPN iajs-3598 339 5 sj sj PROPN iajs-3598 339 6 . . PUNCT iajs-3598 340 1 the the DET iajs-3598 340 2 dynamical dynamical ADJ iajs-3598 340 3 analysis analysis NOUN iajs-3598 340 4 of of ADP iajs-3598 340 5 a a DET iajs-3598 340 6 prey prey NOUN iajs-3598 340 7 - - PUNCT iajs-3598 340 8 predator predator NOUN iajs-3598 340 9 model model NOUN iajs-3598 340 10 with with ADP iajs-3598 340 11 a a DET iajs-3598 340 12 refuge refuge ADJ iajs-3598 340 13 - - PUNCT iajs-3598 340 14 stage stage NOUN iajs-3598 340 15 structure structure NOUN iajs-3598 340 16 prey prey PROPN iajs-3598 340 17 population population NOUN iajs-3598 340 18 . . PUNCT iajs-3598 341 1 int int PROPN iajs-3598 341 2 j j PROPN iajs-3598 341 3 differ differ VERB iajs-3598 341 4 equ equ PROPN iajs-3598 341 5 . . PROPN iajs-3598 341 6 2016;2010464 2016;2010464 NUM iajs-3598 341 7 . . PUNCT iajs-3598 342 1 https://doi.org/10.1155/2016/2010464 https://doi.org/10.1155/2016/2010464 PROPN iajs-3598 342 2 14 14 NUM iajs-3598 342 3 . . PUNCT iajs-3598 343 1 naik naik PROPN iajs-3598 343 2 pa pa PROPN iajs-3598 343 3 , , PUNCT iajs-3598 343 4 eskandari eskandari PROPN iajs-3598 343 5 z z NOUN iajs-3598 343 6 , , PUNCT iajs-3598 343 7 shahkari shahkari ADJ iajs-3598 343 8 he he PRON iajs-3598 343 9 , , PUNCT iajs-3598 343 10 owolabi owolabi NOUN iajs-3598 343 11 km km PROPN iajs-3598 343 12 . . PUNCT iajs-3598 344 1 bifurcation bifurcation NOUN iajs-3598 344 2 analysis analysis NOUN iajs-3598 344 3 of of ADP iajs-3598 344 4 a a DET iajs-3598 344 5 discrete discrete ADJ iajs-3598 344 6 - - PUNCT iajs-3598 344 7 time time NOUN iajs-3598 344 8 prey prey NOUN iajs-3598 344 9 - - PUNCT iajs-3598 344 10 predator predator NOUN iajs-3598 344 11 model model NOUN iajs-3598 344 12 . . PUNCT iajs-3598 345 1 bull bull NOUN iajs-3598 345 2 biomathematics biomathematic NOUN iajs-3598 345 3 . . PUNCT iajs-3598 346 1 2023;1(2):111 2023;1(2):111 NUM iajs-3598 346 2 - - SYM iajs-3598 346 3 123 123 NUM iajs-3598 346 4 . . PUNCT iajs-3598 347 1 https://doi.org/10.59292/bulletinbiomath.2023006 https://doi.org/10.59292/bulletinbiomath.2023006 NOUN iajs-3598 347 2 15 15 NUM iajs-3598 347 3 . . PUNCT iajs-3598 348 1 akhtar akhtar PROPN iajs-3598 348 2 s s PROPN iajs-3598 348 3 , , PUNCT iajs-3598 348 4 ahmed ahmed PROPN iajs-3598 348 5 r r PROPN iajs-3598 348 6 , , PUNCT iajs-3598 348 7 batool batool NOUN iajs-3598 348 8 m m PROPN iajs-3598 348 9 , , PUNCT iajs-3598 348 10 shah shah PROPN iajs-3598 348 11 na na PROPN iajs-3598 348 12 , , PUNCT iajs-3598 348 13 chung chung PROPN iajs-3598 348 14 jd jd PROPN iajs-3598 348 15 . . PROPN iajs-3598 348 16 stability stability NOUN iajs-3598 348 17 , , PUNCT iajs-3598 348 18 bifurcation bifurcation NOUN iajs-3598 348 19 and and CCONJ iajs-3598 348 20 chaos chaos NOUN iajs-3598 348 21 control control NOUN iajs-3598 348 22 of of ADP iajs-3598 348 23 a a DET iajs-3598 348 24 discretized discretized ADJ iajs-3598 348 25 leslie leslie PROPN iajs-3598 348 26 prey prey NOUN iajs-3598 348 27 - - PUNCT iajs-3598 348 28 predator predator NOUN iajs-3598 348 29 model model NOUN iajs-3598 348 30 . . PUNCT iajs-3598 349 1 chaos chaos NOUN iajs-3598 349 2 solitons soliton NOUN iajs-3598 349 3 fractals fractal NOUN iajs-3598 349 4 . . PUNCT iajs-3598 350 1 2023;152:111345 2023;152:111345 NUM iajs-3598 350 2 . . PUNCT iajs-3598 351 1 https://doi.org/10.1016/j.chaos.2021.111345 https://doi.org/10.1016/j.chaos.2021.111345 PROPN iajs-3598 351 2 16 16 NUM iajs-3598 351 3 . . PUNCT iajs-3598 352 1 mezouaghi mezouaghi PROPN iajs-3598 352 2 a a PROPN iajs-3598 352 3 , , PUNCT iajs-3598 352 4 djilali djilali PROPN iajs-3598 352 5 s s PROPN iajs-3598 352 6 , , PUNCT iajs-3598 352 7 bentout bentout PROPN iajs-3598 352 8 s s PROPN iajs-3598 352 9 , , PUNCT iajs-3598 352 10 biroud biroud PROPN iajs-3598 352 11 k. k. PROPN iajs-3598 352 12 bifurcation bifurcation NOUN iajs-3598 352 13 analysis analysis NOUN iajs-3598 352 14 of of ADP iajs-3598 352 15 a a DET iajs-3598 352 16 diffusive diffusive ADJ iajs-3598 352 17 predator predator NOUN iajs-3598 352 18 - - PUNCT iajs-3598 352 19 prey prey NOUN iajs-3598 352 20 model model NOUN iajs-3598 352 21 with with ADP iajs-3598 352 22 prey prey PROPN iajs-3598 352 23 social social ADJ iajs-3598 352 24 behavior behavior NOUN iajs-3598 352 25 and and CCONJ iajs-3598 352 26 predator predator NOUN iajs-3598 352 27 harvesting harvesting NOUN iajs-3598 352 28 . . PUNCT iajs-3598 353 1 math math NOUN iajs-3598 353 2 methods method NOUN iajs-3598 353 3 appl appl PROPN iajs-3598 353 4 sci sci PROPN iajs-3598 353 5 . . PUNCT iajs-3598 354 1 2022;45(2):718 2022;45(2):718 NUM iajs-3598 354 2 - - PUNCT iajs-3598 354 3 731 731 NUM iajs-3598 354 4 . . PUNCT iajs-3598 355 1 https://doi.org/10.1002/mma.7807 https://doi.org/10.1002/mma.7807 PROPN iajs-3598 355 2 17 17 NUM iajs-3598 355 3 . . PUNCT iajs-3598 356 1 din din VERB iajs-3598 356 2 q. q. PROPN iajs-3598 356 3 stability stability PROPN iajs-3598 356 4 , , PUNCT iajs-3598 356 5 bifurcation bifurcation NOUN iajs-3598 356 6 analysis analysis NOUN iajs-3598 356 7 and and CCONJ iajs-3598 356 8 chaos chaos NOUN iajs-3598 356 9 control control NOUN iajs-3598 356 10 for for ADP iajs-3598 356 11 a a DET iajs-3598 356 12 predator predator NOUN iajs-3598 356 13 - - PUNCT iajs-3598 356 14 prey prey NOUN iajs-3598 356 15 system system NOUN iajs-3598 356 16 . . PUNCT iajs-3598 357 1 j j PROPN iajs-3598 357 2 vib vib PROPN iajs-3598 357 3 control control PROPN iajs-3598 357 4 . . PUNCT iajs-3598 358 1 2019;25(3):612 2019;25(3):612 NUM iajs-3598 358 2 - - PUNCT iajs-3598 358 3 626 626 NUM iajs-3598 358 4 . . PUNCT iajs-3598 359 1 https://doi.org/10.1177/1077546318790871 https://doi.org/10.1177/1077546318790871 PROPN iajs-3598 359 2 18 18 NUM iajs-3598 359 3 . . PUNCT iajs-3598 359 4 tang tang PROPN iajs-3598 360 1 b b PROPN iajs-3598 360 2 , , PUNCT iajs-3598 360 3 xiao xiao PROPN iajs-3598 360 4 y. y. PROPN iajs-3598 360 5 bifurcation bifurcation NOUN iajs-3598 360 6 analysis analysis NOUN iajs-3598 360 7 of of ADP iajs-3598 360 8 a a DET iajs-3598 360 9 predator predator NOUN iajs-3598 360 10 - - PUNCT iajs-3598 360 11 prey prey NOUN iajs-3598 360 12 model model NOUN iajs-3598 360 13 with with ADP iajs-3598 360 14 anti anti ADJ iajs-3598 360 15 - - ADJ iajs-3598 360 16 predator predator ADJ iajs-3598 360 17 behaviour behaviour NOUN iajs-3598 360 18 . . PUNCT iajs-3598 361 1 chaos chaos NOUN iajs-3598 361 2 solitons soliton NOUN iajs-3598 361 3 fractals fractal NOUN iajs-3598 361 4 . . PUNCT iajs-3598 362 1 2015;70:58 2015;70:58 NUM iajs-3598 362 2 - - SYM iajs-3598 362 3 68 68 NUM iajs-3598 362 4 . . PUNCT iajs-3598 362 5 https://doi.org/10.1016/j.chaos.2014.11.008 https://doi.org/10.1016/j.chaos.2014.11.008 NOUN iajs-3598 362 6 19 19 NUM iajs-3598 362 7 . . 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