id sid tid token lemma pos iajs-2992 1 1 ihjpas ihjpas PROPN iajs-2992 1 2 . . PUNCT iajs-2992 2 1 36(2)2023 36(2)2023 NUM iajs-2992 2 2 331 331 NUM iajs-2992 2 3 this this DET iajs-2992 2 4 work work NOUN iajs-2992 2 5 is be AUX iajs-2992 2 6 licensed license VERB iajs-2992 2 7 under under ADP iajs-2992 2 8 a a DET iajs-2992 2 9 creative creative ADJ iajs-2992 2 10 commons common NOUN iajs-2992 2 11 attribution attribution NOUN iajs-2992 2 12 4.0 4.0 NUM iajs-2992 2 13 international international ADJ iajs-2992 2 14 license license NOUN iajs-2992 2 15 abstract abstract NOUN iajs-2992 2 16 this this DET iajs-2992 2 17 paper paper NOUN iajs-2992 2 18 is be AUX iajs-2992 2 19 concerned concern VERB iajs-2992 2 20 with with ADP iajs-2992 2 21 the the DET iajs-2992 2 22 quaternary quaternary ADJ iajs-2992 2 23 nonlinear nonlinear ADJ iajs-2992 2 24 hyperbolic hyperbolic ADJ iajs-2992 2 25 boundary boundary ADJ iajs-2992 2 26 value value NOUN iajs-2992 2 27 problem problem NOUN iajs-2992 2 28 ( ( PUNCT iajs-2992 2 29 qnlhbvp qnlhbvp NOUN iajs-2992 2 30 ) ) PUNCT iajs-2992 2 31 studding stud VERB iajs-2992 2 32 constraints constraint NOUN iajs-2992 2 33 quaternary quaternary ADJ iajs-2992 2 34 optimal optimal ADJ iajs-2992 2 35 classical classical ADJ iajs-2992 2 36 continuous continuous ADJ iajs-2992 2 37 control control NOUN iajs-2992 2 38 vector vector NOUN iajs-2992 2 39 ( ( PUNCT iajs-2992 2 40 cqocccv cqocccv PROPN iajs-2992 2 41 ) ) PUNCT iajs-2992 2 42 , , PUNCT iajs-2992 2 43 the the DET iajs-2992 2 44 cost cost NOUN iajs-2992 2 45 function function NOUN iajs-2992 2 46 ( ( PUNCT iajs-2992 2 47 cf cf NOUN iajs-2992 2 48 ) ) PUNCT iajs-2992 2 49 , , PUNCT iajs-2992 2 50 and and CCONJ iajs-2992 2 51 the the DET iajs-2992 2 52 equality equality NOUN iajs-2992 2 53 and and CCONJ iajs-2992 2 54 inequality inequality NOUN iajs-2992 2 55 quaternary quaternary ADJ iajs-2992 2 56 state state NOUN iajs-2992 2 57 and and CCONJ iajs-2992 2 58 control control NOUN iajs-2992 2 59 constraints constraint NOUN iajs-2992 2 60 vector vector NOUN iajs-2992 2 61 ( ( PUNCT iajs-2992 2 62 eiqsccv eiqsccv ADJ iajs-2992 2 63 ) ) PUNCT iajs-2992 2 64 . . PUNCT iajs-2992 3 1 the the DET iajs-2992 3 2 existence existence NOUN iajs-2992 3 3 of of ADP iajs-2992 3 4 a a DET iajs-2992 3 5 cqocccv cqocccv NOUN iajs-2992 3 6 dominating dominating NOUN iajs-2992 3 7 by by ADP iajs-2992 3 8 the the DET iajs-2992 3 9 qnlhbvp qnlhbvp NOUN iajs-2992 3 10 is be AUX iajs-2992 3 11 stated state VERB iajs-2992 3 12 and and CCONJ iajs-2992 3 13 demonstrated demonstrate VERB iajs-2992 3 14 using use VERB iajs-2992 3 15 the the DET iajs-2992 3 16 aubin aubin PROPN iajs-2992 3 17 compactness compactness NOUN iajs-2992 3 18 theorem theorem NOUN iajs-2992 3 19 ( ( PUNCT iajs-2992 3 20 acth acth NOUN iajs-2992 3 21 ) ) PUNCT iajs-2992 3 22 under under ADP iajs-2992 3 23 appropriate appropriate ADJ iajs-2992 3 24 hypotheses hypothesis NOUN iajs-2992 3 25 ( ( PUNCT iajs-2992 3 26 hyps hyps NOUN iajs-2992 3 27 ) ) PUNCT iajs-2992 3 28 . . PUNCT iajs-2992 4 1 furthermore furthermore ADV iajs-2992 4 2 , , PUNCT iajs-2992 4 3 mathematical mathematical ADJ iajs-2992 4 4 formulation formulation NOUN iajs-2992 4 5 of of ADP iajs-2992 4 6 the the DET iajs-2992 4 7 quaternary quaternary ADJ iajs-2992 4 8 adjoint adjoint NOUN iajs-2992 4 9 equations equation NOUN iajs-2992 4 10 ( ( PUNCT iajs-2992 4 11 qaes qaes PROPN iajs-2992 4 12 ) ) PUNCT iajs-2992 4 13 related relate VERB iajs-2992 4 14 to to ADP iajs-2992 4 15 the the DET iajs-2992 4 16 quaternary quaternary ADJ iajs-2992 4 17 state state NOUN iajs-2992 4 18 equations equation NOUN iajs-2992 4 19 ( ( PUNCT iajs-2992 4 20 qse qse PROPN iajs-2992 4 21 ) ) PUNCT iajs-2992 4 22 are be AUX iajs-2992 4 23 discovere discovere ADJ iajs-2992 4 24 so so SCONJ iajs-2992 4 25 as as ADP iajs-2992 4 26 its its PRON iajs-2992 4 27 weak weak ADJ iajs-2992 4 28 form form NOUN iajs-2992 4 29 ( ( PUNCT iajs-2992 4 30 wf wf PROPN iajs-2992 4 31 ) ) PUNCT iajs-2992 4 32 . . PUNCT iajs-2992 5 1 the the DET iajs-2992 5 2 directional directional ADJ iajs-2992 5 3 derivative derivative ADJ iajs-2992 5 4 ( ( PUNCT iajs-2992 5 5 dd dd NOUN iajs-2992 5 6 ) ) PUNCT iajs-2992 5 7 of of ADP iajs-2992 5 8 the the DET iajs-2992 5 9 hamiltonian hamiltonian NOUN iajs-2992 5 10 ( ( PUNCT iajs-2992 5 11 ham ham PROPN iajs-2992 5 12 ) ) PUNCT iajs-2992 5 13 is be AUX iajs-2992 5 14 calculated calculate VERB iajs-2992 5 15 . . PUNCT iajs-2992 6 1 the the DET iajs-2992 6 2 necessary necessary ADJ iajs-2992 6 3 and and CCONJ iajs-2992 6 4 sufficient sufficient ADJ iajs-2992 6 5 conditions condition NOUN iajs-2992 6 6 for for ADP iajs-2992 6 7 optimality optimality NOUN iajs-2992 6 8 ( ( PUNCT iajs-2992 6 9 ncso ncso NOUN iajs-2992 6 10 ) ) PUNCT iajs-2992 6 11 theorems theorem NOUN iajs-2992 6 12 for for ADP iajs-2992 6 13 the the DET iajs-2992 6 14 proposed propose VERB iajs-2992 6 15 problem problem NOUN iajs-2992 6 16 are be AUX iajs-2992 6 17 stated state VERB iajs-2992 6 18 and and CCONJ iajs-2992 6 19 proved prove VERB iajs-2992 6 20 . . PUNCT iajs-2992 7 1 keywords keyword NOUN iajs-2992 7 2 : : PUNCT iajs-2992 7 3 necessary necessary ADJ iajs-2992 7 4 and and CCONJ iajs-2992 7 5 sufficient sufficient ADJ iajs-2992 7 6 conditions condition NOUN iajs-2992 7 7 fro fro NOUN iajs-2992 7 8 optimality optimality NOUN iajs-2992 7 9 , , PUNCT iajs-2992 7 10 nonlinear nonlinear ADJ iajs-2992 7 11 hyperbolic hyperbolic ADJ iajs-2992 7 12 system system NOUN iajs-2992 7 13 , , PUNCT iajs-2992 7 14 quaternary quaternary ADJ iajs-2992 7 15 optimal optimal ADJ iajs-2992 7 16 classical classical ADJ iajs-2992 7 17 continuous continuous ADJ iajs-2992 7 18 control control NOUN iajs-2992 7 19 vector vector NOUN iajs-2992 7 20 . . PUNCT iajs-2992 8 1 1 1 NUM iajs-2992 8 2 . . X iajs-2992 8 3 introduction introduction NOUN iajs-2992 8 4 optimal optimal ADJ iajs-2992 8 5 control control NOUN iajs-2992 8 6 problems problem NOUN iajs-2992 8 7 ( ( PUNCT iajs-2992 8 8 ocps ocp NOUN iajs-2992 8 9 ) ) PUNCT iajs-2992 8 10 are be AUX iajs-2992 8 11 important important ADJ iajs-2992 8 12 in in ADP iajs-2992 8 13 a a DET iajs-2992 8 14 wide wide ADJ iajs-2992 8 15 range range NOUN iajs-2992 8 16 of of ADP iajs-2992 8 17 practical practical ADJ iajs-2992 8 18 applications application NOUN iajs-2992 8 19 , , PUNCT iajs-2992 8 20 including include VERB iajs-2992 8 21 robotics robotic NOUN iajs-2992 8 22 robotics[1 robotics[1 ADJ iajs-2992 8 23 ] ] PUNCT iajs-2992 8 24 , , PUNCT iajs-2992 8 25 economics[2 economics[2 PROPN iajs-2992 8 26 ] ] PUNCT iajs-2992 8 27 , , PUNCT iajs-2992 8 28 weather weather NOUN iajs-2992 8 29 conditions[3 conditions[3 PROPN iajs-2992 8 30 ] ] PUNCT iajs-2992 8 31 , , PUNCT iajs-2992 8 32 community community NOUN iajs-2992 8 33 health[4 health[4 NOUN iajs-2992 8 34 ] ] X iajs-2992 8 35 , , PUNCT iajs-2992 8 36 and and CCONJ iajs-2992 8 37 a a DET iajs-2992 8 38 variety variety NOUN iajs-2992 8 39 of of ADP iajs-2992 8 40 other other ADJ iajs-2992 8 41 scientific scientific ADJ iajs-2992 8 42 fields field NOUN iajs-2992 8 43 . . PUNCT iajs-2992 9 1 nonlinear nonlinear ADJ iajs-2992 9 2 odes ode NOUN iajs-2992 9 3 [ [ X iajs-2992 9 4 5]or 5]or NUM iajs-2992 9 5 nonlinear nonlinear ADJ iajs-2992 9 6 pdes pde NOUN iajs-2992 9 7 ( ( PUNCT iajs-2992 9 8 nlpdes nlpde NOUN iajs-2992 9 9 ) ) PUNCT iajs-2992 10 1 [ [ X iajs-2992 10 2 6 6 NUM iajs-2992 10 3 ] ] PUNCT iajs-2992 10 4 usually usually ADV iajs-2992 10 5 dominate dominate VERB iajs-2992 10 6 ocps ocp NOUN iajs-2992 10 7 . . PUNCT iajs-2992 11 1 this this DET iajs-2992 11 2 significance significance NOUN iajs-2992 11 3 pushed push VERB iajs-2992 11 4 many many ADJ iajs-2992 11 5 researchers researcher NOUN iajs-2992 11 6 to to PART iajs-2992 11 7 be be AUX iajs-2992 11 8 concerned concern VERB iajs-2992 11 9 about about ADP iajs-2992 11 10 ocps ocp NOUN iajs-2992 11 11 in in ADP iajs-2992 11 12 general general ADJ iajs-2992 11 13 and and CCONJ iajs-2992 11 14 optimal optimal ADJ iajs-2992 11 15 classical classical ADJ iajs-2992 11 16 continuous continuous ADJ iajs-2992 11 17 control control NOUN iajs-2992 11 18 problems problem NOUN iajs-2992 11 19 ( ( PUNCT iajs-2992 11 20 occcps occcp NOUN iajs-2992 11 21 ) ) PUNCT iajs-2992 11 22 in in ADP iajs-2992 11 23 particular particular ADJ iajs-2992 11 24 . . PUNCT iajs-2992 12 1 during during ADP iajs-2992 12 2 the the DET iajs-2992 12 3 last last ADJ iajs-2992 12 4 decade decade NOUN iajs-2992 12 5 much much ADJ iajs-2992 12 6 emphasis emphasis NOUN iajs-2992 12 7 has have AUX iajs-2992 12 8 been be AUX iajs-2992 12 9 place place NOUN iajs-2992 12 10 on on ADP iajs-2992 12 11 studying study VERB iajs-2992 12 12 the the DET iajs-2992 12 13 ocps ocp NOUN iajs-2992 12 14 for for ADP iajs-2992 12 15 system system NOUN iajs-2992 12 16 dominating dominate VERB iajs-2992 12 17 by by ADP iajs-2992 12 18 nonlinear nonlinear ADJ iajs-2992 12 19 pdes pde NOUN iajs-2992 12 20 ( ( PUNCT iajs-2992 12 21 nlpdes nlpde NOUN iajs-2992 12 22 ) ) PUNCT iajs-2992 12 23 of of ADP iajs-2992 12 24 the the DET iajs-2992 12 25 three three NUM iajs-2992 12 26 types type NOUN iajs-2992 12 27 in in ADP iajs-2992 12 28 general general ADJ iajs-2992 12 29 ; ; PUNCT iajs-2992 13 1 hyperbolic hyperbolic ADJ iajs-2992 13 2 , , PUNCT iajs-2992 13 3 elliptic elliptic ADJ iajs-2992 13 4 and and CCONJ iajs-2992 13 5 parabolic parabolic ADJ iajs-2992 13 6 [ [ X iajs-2992 13 7 7 7 NUM iajs-2992 13 8 - - SYM iajs-2992 13 9 9 9 NUM iajs-2992 13 10 ] ] PUNCT iajs-2992 13 11 . . PUNCT iajs-2992 14 1 later later ADV iajs-2992 14 2 the the DET iajs-2992 14 3 study study NOUN iajs-2992 14 4 of of ADP iajs-2992 14 5 this this DET iajs-2992 14 6 subject subject NOUN iajs-2992 14 7 , , PUNCT iajs-2992 14 8 in in ADP iajs-2992 14 9 particular particular ADJ iajs-2992 14 10 for for ADP iajs-2992 14 11 hyperbolic hyperbolic ADJ iajs-2992 14 12 type type NOUN iajs-2992 14 13 of of ADP iajs-2992 14 14 pdes pde NOUN iajs-2992 14 15 was be AUX iajs-2992 14 16 generalized generalize VERB iajs-2992 14 17 to to PART iajs-2992 14 18 deal deal VERB iajs-2992 14 19 with with ADP iajs-2992 14 20 ccocps ccocp NOUN iajs-2992 14 21 dominated dominate VERB iajs-2992 14 22 by by ADP iajs-2992 14 23 coupled couple VERB iajs-2992 14 24 nlpdes nlpde NOUN iajs-2992 14 25 of of ADP iajs-2992 14 26 it it PRON iajs-2992 15 1 [ [ X iajs-2992 15 2 10 10 NUM iajs-2992 15 3 ] ] PUNCT iajs-2992 15 4 , , PUNCT iajs-2992 15 5 and and CCONJ iajs-2992 15 6 then then ADV iajs-2992 15 7 to to PART iajs-2992 15 8 ccocps ccocps VERB iajs-2992 15 9 dominating dominating NOUN iajs-2992 15 10 by by ADP iajs-2992 15 11 triple triple ADJ iajs-2992 15 12 nlpdes nlpde NOUN iajs-2992 15 13 of of ADP iajs-2992 15 14 it it PRON iajs-2992 15 15 [ [ X iajs-2992 15 16 11 11 NUM iajs-2992 15 17 ] ] PUNCT iajs-2992 15 18 . . PUNCT iajs-2992 16 1 the the DET iajs-2992 16 2 problem problem NOUN iajs-2992 16 3 in in ADP iajs-2992 16 4 each each DET iajs-2992 16 5 type type NOUN iajs-2992 16 6 of of ADP iajs-2992 16 7 these these DET iajs-2992 16 8 occcps occcp NOUN iajs-2992 16 9 was be AUX iajs-2992 16 10 typically typically ADV iajs-2992 16 11 comprised comprise VERB iajs-2992 16 12 of of ADP iajs-2992 16 13 an an DET iajs-2992 16 14 initial initial ADJ iajs-2992 16 15 and and CCONJ iajs-2992 16 16 boundary boundary ADJ iajs-2992 16 17 value value NOUN iajs-2992 16 18 problem problem NOUN iajs-2992 16 19 , , PUNCT iajs-2992 16 20 the the DET iajs-2992 16 21 cf cf NOUN iajs-2992 16 22 and and CCONJ iajs-2992 16 23 the the DET iajs-2992 16 24 constraints constraint NOUN iajs-2992 16 25 on on ADP iajs-2992 16 26 the the DET iajs-2992 16 27 state state NOUN iajs-2992 16 28 and and CCONJ iajs-2992 16 29 the the DET iajs-2992 16 30 control control NOUN iajs-2992 16 31 vectors vector NOUN iajs-2992 16 32 ( ( PUNCT iajs-2992 16 33 cscv cscv NOUN iajs-2992 16 34 ) ) PUNCT iajs-2992 16 35 . . PUNCT iajs-2992 17 1 the the DET iajs-2992 17 2 study study NOUN iajs-2992 17 3 of of ADP iajs-2992 17 4 each each DET iajs-2992 17 5 one one NUM iajs-2992 17 6 of of ADP iajs-2992 17 7 these these DET iajs-2992 17 8 problems problem NOUN iajs-2992 17 9 had have AUX iajs-2992 17 10 been be AUX iajs-2992 17 11 included include VERB iajs-2992 17 12 of of ADP iajs-2992 17 13 ; ; PUNCT iajs-2992 17 14 the the DET iajs-2992 17 15 existence existence NOUN iajs-2992 17 16 theorem theorem NOUN iajs-2992 17 17 of of ADP iajs-2992 17 18 constraints constraint NOUN iajs-2992 17 19 occc occc VERB iajs-2992 17 20 vector vector NOUN iajs-2992 17 21 satisfying satisfy VERB iajs-2992 17 22 the the DET iajs-2992 17 23 sccv sccv NOUN iajs-2992 17 24 had have AUX iajs-2992 17 25 been be AUX iajs-2992 17 26 stated state VERB iajs-2992 17 27 and and CCONJ iajs-2992 17 28 demonstrated demonstrate VERB iajs-2992 17 29 under under ADP iajs-2992 17 30 appropriate appropriate ADJ iajs-2992 17 31 hyps hyp NOUN iajs-2992 17 32 , , PUNCT iajs-2992 17 33 the the DET iajs-2992 17 34 mathematical mathematical ADJ iajs-2992 17 35 formulation formulation NOUN iajs-2992 17 36 for for ADP iajs-2992 17 37 the the DET iajs-2992 17 38 qaes qaes NOUN iajs-2992 17 39 related relate VERB iajs-2992 17 40 to to ADP iajs-2992 17 41 the the DET iajs-2992 17 42 given give VERB iajs-2992 17 43 qses qse NOUN iajs-2992 17 44 had have AUX iajs-2992 17 45 been be AUX iajs-2992 17 46 obtained obtain VERB iajs-2992 17 47 , , PUNCT iajs-2992 17 48 doi.org/10.30526/36.2.2992 doi.org/10.30526/36.2.2992 PROPN iajs-2992 17 49 article article NOUN iajs-2992 17 50 history history NOUN iajs-2992 17 51 : : PUNCT iajs-2992 17 52 received receive VERB iajs-2992 17 53 5 5 NUM iajs-2992 17 54 september september PROPN iajs-2992 17 55 2022 2022 NUM iajs-2992 17 56 , , PUNCT iajs-2992 17 57 accepted accept VERB iajs-2992 17 58 9 9 NUM iajs-2992 17 59 october october NOUN iajs-2992 17 60 2022 2022 NUM iajs-2992 17 61 , , PUNCT iajs-2992 17 62 published publish VERB iajs-2992 17 63 in in ADP iajs-2992 17 64 april april PROPN iajs-2992 17 65 2023 2023 NUM iajs-2992 17 66 . . PUNCT iajs-2992 18 1 ibn ibn PROPN iajs-2992 18 2 al al PROPN iajs-2992 18 3 - - PUNCT iajs-2992 18 4 haitham haitham PROPN iajs-2992 18 5 journal journal PROPN iajs-2992 18 6 for for ADP iajs-2992 18 7 pure pure ADJ iajs-2992 18 8 and and CCONJ iajs-2992 18 9 applied applied ADJ iajs-2992 18 10 sciences sciences PROPN iajs-2992 18 11 journal journal PROPN iajs-2992 18 12 homepage homepage NOUN iajs-2992 18 13 : : PUNCT iajs-2992 18 14 jih.uobaghdad.edu.iq jih.uobaghdad.edu.iq NOUN iajs-2992 18 15 constraints constraint VERB iajs-2992 18 16 optimal optimal ADJ iajs-2992 18 17 classical classical ADJ iajs-2992 18 18 continuous continuous ADJ iajs-2992 18 19 control control NOUN iajs-2992 18 20 vector vector NOUN iajs-2992 18 21 problem problem NOUN iajs-2992 18 22 for for ADP iajs-2992 18 23 quaternary quaternary ADJ iajs-2992 18 24 nonlinear nonlinear ADJ iajs-2992 18 25 hyperbolic hyperbolic ADJ iajs-2992 18 26 system system NOUN iajs-2992 18 27 mayeada mayeada PROPN iajs-2992 18 28 abd abd PROPN iajs-2992 18 29 alsatar alsatar PROPN iajs-2992 18 30 hassan hassan PROPN iajs-2992 18 31 department department PROPN iajs-2992 18 32 of of ADP iajs-2992 18 33 mathematics mathematics PROPN iajs-2992 18 34 , , PUNCT iajs-2992 18 35 college college NOUN iajs-2992 18 36 of of ADP iajs-2992 18 37 science science NOUN iajs-2992 18 38 , , PUNCT iajs-2992 18 39 mustansiriyah mustansiriyah NOUN iajs-2992 18 40 university university NOUN iajs-2992 18 41 , , PUNCT iajs-2992 18 42 baghdad baghdad PROPN iajs-2992 18 43 , , PUNCT iajs-2992 18 44 iraq iraq PROPN iajs-2992 18 45 . . PUNCT iajs-2992 19 1 mayeadabd1989@uomustanriyah.edu.iq mayeadabd1989@uomustanriyah.edu.iq PROPN iajs-2992 19 2 jamil jamil PROPN iajs-2992 19 3 a. a. PROPN iajs-2992 19 4 ali ali PROPN iajs-2992 19 5 al al PROPN iajs-2992 19 6 - - PUNCT iajs-2992 19 7 hawasy hawasy PROPN iajs-2992 19 8 department department NOUN iajs-2992 19 9 of of ADP iajs-2992 19 10 mathematics mathematics PROPN iajs-2992 19 11 , , PUNCT iajs-2992 19 12 college college NOUN iajs-2992 19 13 of of ADP iajs-2992 19 14 science science NOUN iajs-2992 19 15 , , PUNCT iajs-2992 19 16 mustansiriyah mustansiriyah NOUN iajs-2992 19 17 university university NOUN iajs-2992 19 18 , , PUNCT iajs-2992 19 19 baghdad baghdad PROPN iajs-2992 19 20 , , PUNCT iajs-2992 19 21 iraq iraq PROPN iajs-2992 19 22 . . PUNCT iajs-2992 20 1 jhawassy17@uomustansiriyah.edu.iq jhawassy17@uomustansiriyah.edu.iq PROPN iajs-2992 20 2 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-2992 20 3 mailto:mayeadabd1989@uomustanriyah.edu.iq mailto:mayeadabd1989@uomustanriyah.edu.iq PROPN iajs-2992 20 4 mailto:jhawassy17@uomustansiriyah.edu.iq mailto:jhawassy17@uomustansiriyah.edu.iq PROPN iajs-2992 20 5 mailto:jhawassy17@uomustansiriyah.edu.iq mailto:jhawassy17@uomustansiriyah.edu.iq PROPN iajs-2992 20 6 ihjpas ihjpa NOUN iajs-2992 20 7 . . PUNCT iajs-2992 21 1 36(2)2023 36(2)2023 NUM iajs-2992 21 2 332 332 NUM iajs-2992 21 3 and and CCONJ iajs-2992 21 4 the the DET iajs-2992 21 5 dd dd NOUN iajs-2992 21 6 for for ADP iajs-2992 21 7 the the DET iajs-2992 21 8 ham ham NOUN iajs-2992 21 9 had have AUX iajs-2992 21 10 been be AUX iajs-2992 21 11 derived derive VERB iajs-2992 21 12 . . PUNCT iajs-2992 22 1 the the DET iajs-2992 22 2 theorems theorem NOUN iajs-2992 22 3 of of ADP iajs-2992 22 4 necessity necessity NOUN iajs-2992 22 5 and and CCONJ iajs-2992 22 6 sufficient sufficient ADJ iajs-2992 22 7 conditions condition NOUN iajs-2992 22 8 for for ADP iajs-2992 22 9 optimality optimality NOUN iajs-2992 22 10 had have AUX iajs-2992 22 11 been be AUX iajs-2992 22 12 stated state VERB iajs-2992 22 13 and and CCONJ iajs-2992 22 14 demonstrated demonstrate VERB iajs-2992 22 15 . . PUNCT iajs-2992 23 1 all all PRON iajs-2992 23 2 of of ADP iajs-2992 23 3 these these DET iajs-2992 23 4 concerns concern NOUN iajs-2992 23 5 motivated motivate VERB iajs-2992 23 6 us we PRON iajs-2992 23 7 to to PART iajs-2992 23 8 consider consider VERB iajs-2992 23 9 extending extend VERB iajs-2992 23 10 the the DET iajs-2992 23 11 study study NOUN iajs-2992 23 12 of of ADP iajs-2992 23 13 the the DET iajs-2992 23 14 ccocp ccocp NOUN iajs-2992 23 15 dominating dominate VERB iajs-2992 23 16 by by ADP iajs-2992 23 17 triple triple ADJ iajs-2992 23 18 nlpdes nlpde NOUN iajs-2992 23 19 of of ADP iajs-2992 23 20 hyperbolic hyperbolic ADJ iajs-2992 23 21 type type NOUN iajs-2992 23 22 to to ADP iajs-2992 23 23 a a DET iajs-2992 23 24 ccocp ccocp NOUN iajs-2992 23 25 dominating dominate VERB iajs-2992 23 26 by by ADP iajs-2992 23 27 qnlhbvp qnlhbvp NOUN iajs-2992 23 28 . . PUNCT iajs-2992 24 1 as as ADP iajs-2992 24 2 a a DET iajs-2992 24 3 result result NOUN iajs-2992 24 4 of of ADP iajs-2992 24 5 this this DET iajs-2992 24 6 expansion expansion NOUN iajs-2992 24 7 , , PUNCT iajs-2992 24 8 there there PRON iajs-2992 24 9 was be VERB iajs-2992 24 10 a a DET iajs-2992 24 11 need need NOUN iajs-2992 24 12 to to PART iajs-2992 24 13 generalize generalize VERB iajs-2992 24 14 the the DET iajs-2992 24 15 mathematical mathematical ADJ iajs-2992 24 16 model model NOUN iajs-2992 24 17 and and CCONJ iajs-2992 24 18 then then ADV iajs-2992 24 19 to to PART iajs-2992 24 20 generalize generalize VERB iajs-2992 24 21 all all DET iajs-2992 24 22 the the DET iajs-2992 24 23 proofs proof NOUN iajs-2992 24 24 related relate VERB iajs-2992 24 25 to to ADP iajs-2992 24 26 this this DET iajs-2992 24 27 generalization generalization NOUN iajs-2992 24 28 , , PUNCT iajs-2992 24 29 and and CCONJ iajs-2992 24 30 accordingly accordingly ADV iajs-2992 24 31 . . PUNCT iajs-2992 25 1 the the DET iajs-2992 25 2 authors author NOUN iajs-2992 25 3 created create VERB iajs-2992 25 4 new new ADJ iajs-2992 25 5 theorems theorem NOUN iajs-2992 25 6 , , PUNCT iajs-2992 25 7 lemma lemma PROPN iajs-2992 25 8 and and CCONJ iajs-2992 25 9 then then ADV iajs-2992 25 10 proved prove VERB iajs-2992 25 11 them they PRON iajs-2992 25 12 in in ADP iajs-2992 25 13 this this DET iajs-2992 25 14 paper paper NOUN iajs-2992 25 15 . . PUNCT iajs-2992 26 1 the the DET iajs-2992 26 2 existence existence NOUN iajs-2992 26 3 theorem theorem NOUN iajs-2992 26 4 ( ( PUNCT iajs-2992 26 5 eth eth NOUN iajs-2992 26 6 ) ) PUNCT iajs-2992 26 7 of of ADP iajs-2992 26 8 a a DET iajs-2992 26 9 cqocccv cqocccv NOUN iajs-2992 26 10 dominating dominating NOUN iajs-2992 26 11 by by ADP iajs-2992 26 12 the the DET iajs-2992 26 13 qnlhbvps qnlhbvps PROPN iajs-2992 26 14 with with ADP iajs-2992 26 15 eiqsccv eiqsccv PROPN iajs-2992 26 16 was be AUX iajs-2992 26 17 stated state VERB iajs-2992 26 18 and and CCONJ iajs-2992 26 19 demonstrated demonstrate VERB iajs-2992 26 20 in in ADP iajs-2992 26 21 this this DET iajs-2992 26 22 work work NOUN iajs-2992 26 23 using use VERB iajs-2992 26 24 the the DET iajs-2992 26 25 acth acth NOUN iajs-2992 26 26 under under ADP iajs-2992 26 27 appropriate appropriate ADJ iajs-2992 26 28 hyps hyp NOUN iajs-2992 26 29 . . PUNCT iajs-2992 27 1 moreover moreover ADV iajs-2992 27 2 mathematical mathematical ADJ iajs-2992 27 3 formulation formulation NOUN iajs-2992 27 4 of of ADP iajs-2992 27 5 the the DET iajs-2992 27 6 qaes qaes NOUN iajs-2992 27 7 related relate VERB iajs-2992 27 8 to to ADP iajs-2992 27 9 qses qse NOUN iajs-2992 27 10 was be AUX iajs-2992 27 11 discovered discover VERB iajs-2992 27 12 as as SCONJ iajs-2992 27 13 was be AUX iajs-2992 27 14 the the DET iajs-2992 27 15 wf wf PROPN iajs-2992 27 16 of of ADP iajs-2992 27 17 the the DET iajs-2992 27 18 qaes qaes NOUN iajs-2992 27 19 . . PUNCT iajs-2992 28 1 the the DET iajs-2992 28 2 derivative derivative NOUN iajs-2992 28 3 of of ADP iajs-2992 28 4 dd dd NOUN iajs-2992 28 5 was be AUX iajs-2992 28 6 obtained obtain VERB iajs-2992 28 7 . . PUNCT iajs-2992 29 1 lastly lastly ADV iajs-2992 29 2 , , PUNCT iajs-2992 29 3 both both CCONJ iajs-2992 29 4 the the DET iajs-2992 29 5 theorems theorem NOUN iajs-2992 29 6 for for ADP iajs-2992 29 7 the the DET iajs-2992 29 8 ncso ncso NOUN iajs-2992 29 9 of of ADP iajs-2992 29 10 the the DET iajs-2992 29 11 proposed propose VERB iajs-2992 29 12 problems problem NOUN iajs-2992 29 13 were be AUX iajs-2992 29 14 stated state VERB iajs-2992 29 15 and and CCONJ iajs-2992 29 16 demonstrated demonstrate VERB iajs-2992 29 17 . . PUNCT iajs-2992 30 1 2 2 X iajs-2992 30 2 . . X iajs-2992 30 3 problem problem NOUN iajs-2992 30 4 description description NOUN iajs-2992 30 5 : : PUNCT iajs-2992 30 6 let let VERB iajs-2992 30 7 𝐼 𝐼 PROPN iajs-2992 30 8 = = PUNCT iajs-2992 31 1 [ [ X iajs-2992 31 2 0 0 NUM iajs-2992 31 3 , , PUNCT iajs-2992 31 4 𝑇 𝑇 PROPN iajs-2992 31 5 ] ] PUNCT iajs-2992 31 6 , , PUNCT iajs-2992 31 7 t t X iajs-2992 31 8 < < X iajs-2992 31 9 ∞ ∞ PROPN iajs-2992 31 10 , , PUNCT iajs-2992 31 11 Ο‰ Ο‰ PROPN iajs-2992 31 12 βŠ‚ βŠ‚ PROPN iajs-2992 31 13 ℝ2 ℝ2 PROPN iajs-2992 31 14 , , PUNCT iajs-2992 31 15 be be AUX iajs-2992 31 16 an an DET iajs-2992 31 17 open open ADJ iajs-2992 31 18 bounded bounded ADJ iajs-2992 31 19 regular regular ADJ iajs-2992 31 20 region region NOUN iajs-2992 31 21 with with ADP iajs-2992 31 22 boundary boundary ADJ iajs-2992 31 23 Ξ³ Ξ³ X iajs-2992 31 24 = = SYM iajs-2992 31 25 πœ•Ο‰ πœ•Ο‰ PROPN iajs-2992 31 26 , , PUNCT iajs-2992 32 1 𝑄 𝑄 PROPN iajs-2992 32 2 = = SYM iajs-2992 32 3 Ο‰ Ο‰ NUM iajs-2992 32 4 Γ— Γ— PROPN iajs-2992 32 5 𝐼 𝐼 PROPN iajs-2992 32 6 , , PUNCT iajs-2992 32 7 Οƒ Οƒ NOUN iajs-2992 32 8 = = PUNCT iajs-2992 32 9 Ξ³ Ξ³ X iajs-2992 32 10 Γ— Γ— PROPN iajs-2992 32 11 𝐼. 𝐼. PROPN iajs-2992 32 12 the the DET iajs-2992 32 13 cqocccv cqocccv NOUN iajs-2992 32 14 including include VERB iajs-2992 32 15 of of ADP iajs-2992 32 16 the the DET iajs-2992 32 17 qses qse NOUN iajs-2992 32 18 are be AUX iajs-2992 32 19 given give VERB iajs-2992 32 20 by by ADP iajs-2992 32 21 the the DET iajs-2992 32 22 following follow VERB iajs-2992 32 23 qnlhbvp qnlhbvp NOUN iajs-2992 32 24 : : PUNCT iajs-2992 32 25 𝑦1𝑑𝑑 𝑦1𝑑𝑑 PUNCT iajs-2992 32 26 βˆ’ βˆ’ PROPN iajs-2992 33 1 βˆ†π‘¦1 βˆ†π‘¦1 ADV iajs-2992 33 2 + + CCONJ iajs-2992 33 3 𝑦1 𝑦1 PROPN iajs-2992 33 4 βˆ’ βˆ’ PROPN iajs-2992 33 5 𝑦2 𝑦2 PROPN iajs-2992 33 6 + + CCONJ iajs-2992 33 7 𝑦3 𝑦3 PROPN iajs-2992 33 8 + + CCONJ iajs-2992 33 9 𝑦4 𝑦4 PROPN iajs-2992 33 10 = = SYM iajs-2992 33 11 𝑓1(π‘₯ 𝑓1(π‘₯ NUM iajs-2992 33 12 , , PUNCT iajs-2992 33 13 𝑑 𝑑 NOUN iajs-2992 33 14 , , PUNCT iajs-2992 33 15 𝑦1 𝑦1 NOUN iajs-2992 33 16 , , PUNCT iajs-2992 33 17 𝑒1 𝑒1 NOUN iajs-2992 33 18 ) ) PUNCT iajs-2992 33 19 , , PUNCT iajs-2992 33 20 in in ADP iajs-2992 33 21 𝑄 𝑄 PROPN iajs-2992 33 22 , , PUNCT iajs-2992 33 23 ( ( PUNCT iajs-2992 33 24 1 1 NUM iajs-2992 33 25 ) ) PUNCT iajs-2992 33 26 𝑦2𝑑𝑑 𝑦2𝑑𝑑 PUNCT iajs-2992 33 27 βˆ’ βˆ’ PUNCT iajs-2992 34 1 βˆ†π‘¦2 βˆ†π‘¦2 NOUN iajs-2992 34 2 + + CCONJ iajs-2992 34 3 𝑦1 𝑦1 PROPN iajs-2992 34 4 + + CCONJ iajs-2992 34 5 𝑦2 𝑦2 PROPN iajs-2992 34 6 βˆ’ βˆ’ PROPN iajs-2992 34 7 𝑦3 𝑦3 PROPN iajs-2992 34 8 βˆ’ βˆ’ PROPN iajs-2992 34 9 𝑦4 𝑦4 PROPN iajs-2992 34 10 = = SYM iajs-2992 34 11 𝑓2(π‘₯ 𝑓2(π‘₯ PROPN iajs-2992 34 12 , , PUNCT iajs-2992 34 13 𝑑 𝑑 PROPN iajs-2992 34 14 , , PUNCT iajs-2992 34 15 𝑦2 𝑦2 NOUN iajs-2992 34 16 , , PUNCT iajs-2992 34 17 𝑒2 𝑒2 PROPN iajs-2992 34 18 ) ) PUNCT iajs-2992 34 19 , , PUNCT iajs-2992 34 20 in in ADP iajs-2992 34 21 𝑄 𝑄 PROPN iajs-2992 34 22 , , PUNCT iajs-2992 34 23 ( ( PUNCT iajs-2992 34 24 2 2 NUM iajs-2992 34 25 ) ) PUNCT iajs-2992 34 26 𝑦3𝑑𝑑 𝑦3𝑑𝑑 X iajs-2992 34 27 βˆ’ βˆ’ DET iajs-2992 34 28 βˆ†π‘¦3 βˆ†π‘¦3 NOUN iajs-2992 34 29 βˆ’ βˆ’ NOUN iajs-2992 34 30 𝑦1 𝑦1 PROPN iajs-2992 34 31 + + CCONJ iajs-2992 34 32 𝑦2 𝑦2 PROPN iajs-2992 34 33 + + CCONJ iajs-2992 34 34 𝑦3 𝑦3 PROPN iajs-2992 34 35 + + CCONJ iajs-2992 34 36 𝑦4 𝑦4 PROPN iajs-2992 34 37 = = SYM iajs-2992 34 38 𝑓3(π‘₯ 𝑓3(π‘₯ PROPN iajs-2992 34 39 , , PUNCT iajs-2992 34 40 𝑑 𝑑 PROPN iajs-2992 34 41 , , PUNCT iajs-2992 34 42 𝑦3 𝑦3 PROPN iajs-2992 34 43 , , PUNCT iajs-2992 34 44 𝑒3 𝑒3 PROPN iajs-2992 34 45 ) ) PUNCT iajs-2992 34 46 , , PUNCT iajs-2992 34 47 in in ADP iajs-2992 34 48 𝑄 𝑄 PROPN iajs-2992 34 49 , , PUNCT iajs-2992 34 50 ( ( PUNCT iajs-2992 34 51 3 3 NUM iajs-2992 34 52 ) ) PUNCT iajs-2992 34 53 𝑦4𝑑𝑑 𝑦4𝑑𝑑 NOUN iajs-2992 34 54 βˆ’ βˆ’ PROPN iajs-2992 34 55 βˆ†π‘¦4 βˆ†π‘¦4 PROPN iajs-2992 34 56 βˆ’ βˆ’ PROPN iajs-2992 34 57 𝑦1 𝑦1 PROPN iajs-2992 34 58 + + CCONJ iajs-2992 34 59 𝑦2 𝑦2 PROPN iajs-2992 34 60 βˆ’ βˆ’ PROPN iajs-2992 34 61 𝑦3 𝑦3 PROPN iajs-2992 34 62 + + CCONJ iajs-2992 34 63 𝑦4 𝑦4 PROPN iajs-2992 34 64 = = SYM iajs-2992 34 65 𝑓4(π‘₯ 𝑓4(π‘₯ PROPN iajs-2992 34 66 , , PUNCT iajs-2992 34 67 𝑑 𝑑 PROPN iajs-2992 34 68 , , PUNCT iajs-2992 34 69 𝑦4 𝑦4 NOUN iajs-2992 34 70 , , PUNCT iajs-2992 34 71 𝑒4 𝑒4 NOUN iajs-2992 34 72 ) ) PUNCT iajs-2992 34 73 , , PUNCT iajs-2992 34 74 in in ADP iajs-2992 34 75 𝑄 𝑄 PROPN iajs-2992 34 76 , , PUNCT iajs-2992 34 77 ( ( PUNCT iajs-2992 34 78 4 4 NUM iajs-2992 34 79 ) ) PUNCT iajs-2992 34 80 with with ADP iajs-2992 34 81 the the DET iajs-2992 34 82 following following ADJ iajs-2992 34 83 boundary boundary ADJ iajs-2992 34 84 conditions condition NOUN iajs-2992 34 85 ( ( PUNCT iajs-2992 34 86 bcs bcs NOUN iajs-2992 34 87 ) ) PUNCT iajs-2992 34 88 and and CCONJ iajs-2992 34 89 the the DET iajs-2992 34 90 initial initial ADJ iajs-2992 34 91 conditions condition NOUN iajs-2992 34 92 ( ( PUNCT iajs-2992 34 93 ics ics NOUN iajs-2992 34 94 ) ) PUNCT iajs-2992 34 95 𝑦𝑖(π‘₯ 𝑦𝑖(π‘₯ PROPN iajs-2992 34 96 , , PUNCT iajs-2992 34 97 𝑑 𝑑 X iajs-2992 34 98 ) ) PUNCT iajs-2992 34 99 = = SYM iajs-2992 34 100 0 0 NUM iajs-2992 34 101 , , PUNCT iajs-2992 34 102 on on ADP iajs-2992 34 103 Οƒ Οƒ PROPN iajs-2992 34 104 , , PUNCT iajs-2992 34 105 for for ADP iajs-2992 34 106 𝑖 𝑖 DET iajs-2992 34 107 = = SYM iajs-2992 34 108 1,2,3,4 1,2,3,4 NUM iajs-2992 34 109 . . PUNCT iajs-2992 35 1 ( ( PUNCT iajs-2992 35 2 5 5 X iajs-2992 35 3 ) ) PUNCT iajs-2992 35 4 𝑦1(π‘₯ 𝑦1(π‘₯ NUM iajs-2992 35 5 , , PUNCT iajs-2992 35 6 0 0 NUM iajs-2992 35 7 ) ) PUNCT iajs-2992 36 1 = = SYM iajs-2992 36 2 𝑦𝑖 𝑦𝑖 NUM iajs-2992 36 3 0(π‘₯),and 0(π‘₯),and NUM iajs-2992 36 4 𝑦𝑖𝑑(π‘₯ 𝑦𝑖𝑑(π‘₯ PROPN iajs-2992 36 5 , , PUNCT iajs-2992 36 6 0 0 NUM iajs-2992 36 7 ) ) PUNCT iajs-2992 36 8 = = SYM iajs-2992 36 9 𝑦𝑖 𝑦𝑖 ADP iajs-2992 36 10 1(π‘₯ 1(π‘₯ NUM iajs-2992 36 11 ) ) PUNCT iajs-2992 36 12 , , PUNCT iajs-2992 36 13 in in ADP iajs-2992 36 14 Ο‰ Ο‰ NUM iajs-2992 36 15 for for ADP iajs-2992 36 16 𝑖 𝑖 NOUN iajs-2992 36 17 = = NOUN iajs-2992 36 18 1,2,3,4 1,2,3,4 NUM iajs-2992 36 19 . . PUNCT iajs-2992 37 1 ( ( PUNCT iajs-2992 37 2 6 6 NUM iajs-2992 37 3 ) ) PUNCT iajs-2992 37 4 where where SCONJ iajs-2992 37 5 οΏ½ οΏ½ NOUN iajs-2992 37 6 βƒ— βƒ— X iajs-2992 37 7 οΏ½ οΏ½ NOUN iajs-2992 37 8 = = SYM iajs-2992 37 9 ( ( PUNCT iajs-2992 37 10 𝑦1 𝑦1 PROPN iajs-2992 37 11 , , PUNCT iajs-2992 37 12 𝑦2 𝑦2 PROPN iajs-2992 37 13 , , PUNCT iajs-2992 37 14 𝑦3 𝑦3 PROPN iajs-2992 37 15 , , PUNCT iajs-2992 37 16 𝑦4 𝑦4 PROPN iajs-2992 37 17 ) ) PUNCT iajs-2992 37 18 ∈ ∈ PROPN iajs-2992 37 19 π‘―πŸ(𝛀 π‘―πŸ(𝛀 PROPN iajs-2992 37 20 ) ) PUNCT iajs-2992 37 21 = = PUNCT iajs-2992 38 1 ( ( PUNCT iajs-2992 38 2 𝐻1(Ο‰))4is 𝐻1(Ο‰))4is X iajs-2992 38 3 the the DET iajs-2992 38 4 quaternary quaternary ADJ iajs-2992 38 5 solution solution NOUN iajs-2992 38 6 vectors vector NOUN iajs-2992 38 7 ( ( PUNCT iajs-2992 38 8 qsvs qsvs PROPN iajs-2992 38 9 ) ) PUNCT iajs-2992 38 10 , , PUNCT iajs-2992 38 11 corresponding correspond VERB iajs-2992 38 12 to to ADP iajs-2992 38 13 the the DET iajs-2992 38 14 quaternary quaternary ADJ iajs-2992 38 15 classical classical ADJ iajs-2992 38 16 continuous continuous ADJ iajs-2992 38 17 control control NOUN iajs-2992 38 18 vector vector NOUN iajs-2992 38 19 ( ( PUNCT iajs-2992 38 20 qcccv qcccv ADV iajs-2992 38 21 ) ) PUNCT iajs-2992 38 22 οΏ½ οΏ½ PROPN iajs-2992 38 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 38 24 οΏ½ οΏ½ PROPN iajs-2992 38 25 = = SYM iajs-2992 38 26 ( ( PUNCT iajs-2992 38 27 𝑒1 𝑒1 PROPN iajs-2992 38 28 , , PUNCT iajs-2992 38 29 𝑒2 𝑒2 PROPN iajs-2992 38 30 , , PUNCT iajs-2992 38 31 𝑒3 𝑒3 PROPN iajs-2992 38 32 , , PUNCT iajs-2992 38 33 𝑒4 𝑒4 NOUN iajs-2992 38 34 ) ) PUNCT iajs-2992 38 35 ∈ ∈ PROPN iajs-2992 38 36 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 38 37 ) ) PUNCT iajs-2992 38 38 = = PRON iajs-2992 38 39 ( ( PUNCT iajs-2992 38 40 𝐿2(𝑄))4 𝐿2(𝑄))4 PROPN iajs-2992 38 41 and and CCONJ iajs-2992 38 42 ( ( PUNCT iajs-2992 38 43 𝑓1 𝑓1 ADJ iajs-2992 38 44 , , PUNCT iajs-2992 38 45 𝑓2 𝑓2 ADJ iajs-2992 38 46 , , PUNCT iajs-2992 38 47 𝑓3 𝑓3 NOUN iajs-2992 38 48 , , PUNCT iajs-2992 38 49 𝑓4 𝑓4 PROPN iajs-2992 38 50 ) ) PUNCT iajs-2992 38 51 ∈ ∈ PROPN iajs-2992 38 52 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 38 53 ) ) PUNCT iajs-2992 38 54 is be AUX iajs-2992 38 55 a a DET iajs-2992 38 56 vector vector NOUN iajs-2992 38 57 of of ADP iajs-2992 38 58 a a DET iajs-2992 38 59 given give VERB iajs-2992 38 60 function function NOUN iajs-2992 38 61 on on ADP iajs-2992 38 62 ( ( PUNCT iajs-2992 38 63 𝑄 𝑄 NOUN iajs-2992 38 64 Γ— Γ— NOUN iajs-2992 38 65 ℝ ℝ PROPN iajs-2992 38 66 Γ— Γ— NOUN iajs-2992 38 67 π‘ˆ1 π‘ˆ1 NOUN iajs-2992 38 68 ) ) PUNCT iajs-2992 38 69 Γ— Γ— NOUN iajs-2992 38 70 ( ( PUNCT iajs-2992 38 71 𝑄 𝑄 PROPN iajs-2992 38 72 Γ— Γ— NOUN iajs-2992 38 73 ℝ ℝ PROPN iajs-2992 38 74 Γ— Γ— NOUN iajs-2992 38 75 π‘ˆ2 π‘ˆ2 PROPN iajs-2992 38 76 ) ) PUNCT iajs-2992 38 77 Γ— Γ— NOUN iajs-2992 38 78 ( ( PUNCT iajs-2992 38 79 𝑄 𝑄 PROPN iajs-2992 38 80 Γ— Γ— NOUN iajs-2992 38 81 ℝ ℝ PROPN iajs-2992 38 82 Γ— Γ— NOUN iajs-2992 38 83 π‘ˆ3 π‘ˆ3 NOUN iajs-2992 38 84 ) ) PUNCT iajs-2992 38 85 Γ— Γ— NOUN iajs-2992 38 86 ( ( PUNCT iajs-2992 38 87 𝑄 𝑄 PROPN iajs-2992 38 88 Γ— Γ— NOUN iajs-2992 38 89 ℝ ℝ PROPN iajs-2992 38 90 Γ— Γ— NOUN iajs-2992 38 91 π‘ˆ4 π‘ˆ4 NOUN iajs-2992 38 92 ) ) PUNCT iajs-2992 38 93 , , PUNCT iajs-2992 38 94 with with ADP iajs-2992 38 95 π‘ˆπ‘– π‘ˆπ‘– PROPN iajs-2992 38 96 βŠ‚ βŠ‚ PROPN iajs-2992 38 97 ℝ ℝ PROPN iajs-2992 38 98 , , PUNCT iajs-2992 38 99 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 38 100 = = NOUN iajs-2992 38 101 1,2,3,4 1,2,3,4 NUM iajs-2992 38 102 . . PUNCT iajs-2992 39 1 the the DET iajs-2992 39 2 qsccs qsccs NOUN iajs-2992 39 3 are be AUX iajs-2992 39 4 οΏ½ οΏ½ PROPN iajs-2992 39 5 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 39 6 οΏ½ οΏ½ PROPN iajs-2992 39 7 ∈ ∈ PROPN iajs-2992 39 8 π‘Š π‘Š PROPN iajs-2992 39 9 βƒ—βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ—βƒ— NOUN iajs-2992 39 10 , , PUNCT iajs-2992 39 11 π‘Š π‘Š PROPN iajs-2992 39 12 βƒ—βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ—βƒ— VERB iajs-2992 39 13 βŠ‚ βŠ‚ PROPN iajs-2992 40 1 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 40 2 ) ) PUNCT iajs-2992 40 3 where where SCONJ iajs-2992 40 4 οΏ½ οΏ½ PROPN iajs-2992 40 5 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— PROPN iajs-2992 40 6 οΏ½ οΏ½ PROPN iajs-2992 40 7 = = SYM iajs-2992 40 8 { { PUNCT iajs-2992 40 9 οΏ½ οΏ½ PROPN iajs-2992 40 10 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— NOUN iajs-2992 40 11 οΏ½ οΏ½ PROPN iajs-2992 40 12 ∈ ∈ PROPN iajs-2992 40 13 π‘ˆ π‘ˆ PROPN iajs-2992 40 14 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— VERB iajs-2992 41 1 βŠ‚ βŠ‚ X iajs-2992 41 2 ℝ4 ℝ4 PROPN iajs-2992 41 3 , , PUNCT iajs-2992 41 4 π‘Ž. π‘Ž. PROPN iajs-2992 41 5 𝑒 𝑒 PROPN iajs-2992 41 6 𝑖𝑛 𝑖𝑛 NOUN iajs-2992 41 7 𝑄 𝑄 PROPN iajs-2992 41 8 } } PUNCT iajs-2992 41 9 , , PUNCT iajs-2992 41 10 with with SCONJ iajs-2992 41 11 is be AUX iajs-2992 41 12 a a DET iajs-2992 41 13 convex convex NOUN iajs-2992 41 14 ( ( PUNCT iajs-2992 41 15 co co NOUN iajs-2992 41 16 ) ) PUNCT iajs-2992 41 17 . . PUNCT iajs-2992 42 1 the the DET iajs-2992 42 2 cf cf NOUN iajs-2992 42 3 is be AUX iajs-2992 42 4 given give VERB iajs-2992 42 5 and and CCONJ iajs-2992 42 6 the the DET iajs-2992 42 7 eineqscc eineqscc NOUN iajs-2992 42 8 on on ADP iajs-2992 42 9 the the DET iajs-2992 42 10 qsccs qsccs NOUN iajs-2992 42 11 are be AUX iajs-2992 42 12 resp resp NOUN iajs-2992 42 13 . . PUNCT iajs-2992 43 1 𝐺0( 𝐺0( VERB iajs-2992 43 2 οΏ½ οΏ½ PROPN iajs-2992 43 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 43 4 οΏ½ οΏ½ PROPN iajs-2992 43 5 ) ) PUNCT iajs-2992 44 1 = = PUNCT iajs-2992 44 2 Οƒ Οƒ NOUN iajs-2992 44 3 𝑖=1 𝑖=1 PROPN iajs-2992 44 4 4 4 NUM iajs-2992 44 5 ∫ ∫ NOUN iajs-2992 44 6 𝑄 𝑄 PROPN iajs-2992 44 7 𝑔0𝑖 𝑔0𝑖 NOUN iajs-2992 44 8 ( ( PUNCT iajs-2992 44 9 π‘₯ π‘₯ PROPN iajs-2992 44 10 , , PUNCT iajs-2992 44 11 𝑑 𝑑 PROPN iajs-2992 44 12 , , PUNCT iajs-2992 44 13 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 44 14 , , PUNCT iajs-2992 44 15 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 44 16 , , PUNCT iajs-2992 44 17 ( ( PUNCT iajs-2992 44 18 7 7 X iajs-2992 44 19 ) ) PUNCT iajs-2992 44 20 𝐺1( 𝐺1( PROPN iajs-2992 44 21 οΏ½ οΏ½ PROPN iajs-2992 44 22 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 44 23 οΏ½ οΏ½ PROPN iajs-2992 44 24 ) ) PUNCT iajs-2992 44 25 = = PUNCT iajs-2992 45 1 Οƒ Οƒ NOUN iajs-2992 45 2 𝑖=1 𝑖=1 PROPN iajs-2992 45 3 4 4 NUM iajs-2992 45 4 ∫ ∫ NOUN iajs-2992 45 5 𝑄 𝑄 PROPN iajs-2992 45 6 𝑔1𝑖 𝑔1𝑖 NOUN iajs-2992 45 7 ( ( PUNCT iajs-2992 45 8 π‘₯ π‘₯ NOUN iajs-2992 45 9 , , PUNCT iajs-2992 45 10 𝑑 𝑑 PROPN iajs-2992 45 11 , , PUNCT iajs-2992 45 12 𝑦𝑖 𝑦𝑖 NOUN iajs-2992 45 13 , , PUNCT iajs-2992 45 14 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 45 15 = = SYM iajs-2992 45 16 0 0 NUM iajs-2992 45 17 , , PUNCT iajs-2992 45 18 ( ( PUNCT iajs-2992 45 19 8) 8) NUM iajs-2992 45 20 𝐺2( 𝐺2( NUM iajs-2992 45 21 οΏ½ οΏ½ NOUN iajs-2992 45 22 βƒ—βƒ— βƒ—βƒ— NOUN iajs-2992 45 23 οΏ½ οΏ½ PROPN iajs-2992 45 24 ) ) PUNCT iajs-2992 45 25 = = PUNCT iajs-2992 46 1 Οƒ Οƒ NOUN iajs-2992 46 2 𝑖=1 𝑖=1 PROPN iajs-2992 46 3 4 4 NUM iajs-2992 46 4 ∫ ∫ NOUN iajs-2992 46 5 𝑄 𝑄 PROPN iajs-2992 46 6 𝑔2𝑖 𝑔2𝑖 NOUN iajs-2992 46 7 ( ( PUNCT iajs-2992 46 8 π‘₯ π‘₯ PROPN iajs-2992 46 9 , , PUNCT iajs-2992 46 10 𝑑 𝑑 PROPN iajs-2992 46 11 , , PUNCT iajs-2992 46 12 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 46 13 , , PUNCT iajs-2992 46 14 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 46 15 ≀ ≀ NUM iajs-2992 46 16 0 0 NUM iajs-2992 46 17 , , PUNCT iajs-2992 46 18 ( ( PUNCT iajs-2992 46 19 9 9 X iajs-2992 46 20 ) ) PUNCT iajs-2992 46 21 the the DET iajs-2992 46 22 set set NOUN iajs-2992 46 23 of of ADP iajs-2992 46 24 admissible admissible ADJ iajs-2992 46 25 quaternary quaternary ADJ iajs-2992 46 26 control control NOUN iajs-2992 46 27 ( ( PUNCT iajs-2992 46 28 aqc aqc PROPN iajs-2992 46 29 ) ) PUNCT iajs-2992 46 30 is be AUX iajs-2992 46 31 : : PUNCT iajs-2992 46 32 οΏ½ οΏ½ PROPN iajs-2992 46 33 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 46 34 οΏ½ οΏ½ PROPN iajs-2992 46 35 𝐴 𝐴 NOUN iajs-2992 46 36 = = SYM iajs-2992 46 37 { { PUNCT iajs-2992 46 38 οΏ½ οΏ½ PROPN iajs-2992 46 39 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 46 40 οΏ½ οΏ½ PROPN iajs-2992 46 41 ∈ ∈ PROPN iajs-2992 46 42 π‘Š π‘Š PROPN iajs-2992 46 43 βƒ—βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ—βƒ— NOUN iajs-2992 46 44 ∣ ∣ VERB iajs-2992 46 45 𝐺1( 𝐺1( NUM iajs-2992 46 46 οΏ½ οΏ½ PROPN iajs-2992 46 47 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 46 48 οΏ½ οΏ½ PROPN iajs-2992 46 49 ) ) PUNCT iajs-2992 46 50 = = SYM iajs-2992 46 51 0 0 NUM iajs-2992 46 52 , , PUNCT iajs-2992 46 53 𝐺2( 𝐺2( PROPN iajs-2992 46 54 οΏ½ οΏ½ PROPN iajs-2992 46 55 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 46 56 οΏ½ οΏ½ PROPN iajs-2992 46 57 ) ) PUNCT iajs-2992 46 58 ≀ ≀ NOUN iajs-2992 46 59 0 0 NUM iajs-2992 46 60 } } PUNCT iajs-2992 46 61 . . PUNCT iajs-2992 47 1 the the DET iajs-2992 47 2 cqocccv cqocccv NOUN iajs-2992 47 3 is be AUX iajs-2992 47 4 to to PART iajs-2992 47 5 find find VERB iajs-2992 47 6 οΏ½ οΏ½ PROPN iajs-2992 47 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 47 8 οΏ½ οΏ½ PROPN iajs-2992 47 9 ∈ ∈ PROPN iajs-2992 47 10 οΏ½ οΏ½ PROPN iajs-2992 47 11 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 47 12 οΏ½ οΏ½ PROPN iajs-2992 47 13 𝐴 𝐴 PROPN iajs-2992 47 14 , , PUNCT iajs-2992 47 15 s.t s.t PROPN iajs-2992 47 16 . . PROPN iajs-2992 47 17 𝐺0( 𝐺0( PROPN iajs-2992 47 18 οΏ½ οΏ½ PROPN iajs-2992 47 19 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 47 20 οΏ½ οΏ½ PROPN iajs-2992 47 21 ) ) PUNCT iajs-2992 47 22 = = SYM iajs-2992 47 23 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN iajs-2992 47 24 οΏ½ οΏ½ PROPN iajs-2992 47 25 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 47 26 οΏ½ οΏ½ PROPN iajs-2992 47 27 ∈ ∈ PROPN iajs-2992 47 28 οΏ½ οΏ½ PROPN iajs-2992 47 29 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 47 30 οΏ½ οΏ½ PROPN iajs-2992 47 31 𝐴 𝐴 PROPN iajs-2992 47 32 𝐺0 𝐺0 NOUN iajs-2992 47 33 ( ( PUNCT iajs-2992 47 34 οΏ½ οΏ½ NOUN iajs-2992 47 35 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— NOUN iajs-2992 47 36 οΏ½ οΏ½ PROPN iajs-2992 47 37 ) ) PUNCT iajs-2992 47 38 . . PUNCT iajs-2992 48 1 let let VERB iajs-2992 48 2 οΏ½ οΏ½ PROPN iajs-2992 48 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 48 4 οΏ½ οΏ½ PROPN iajs-2992 48 5 = = SYM iajs-2992 48 6 { { PUNCT iajs-2992 48 7 οΏ½ οΏ½ NOUN iajs-2992 48 8 βƒ— βƒ— NOUN iajs-2992 48 9 οΏ½ οΏ½ NOUN iajs-2992 48 10 = = SYM iajs-2992 48 11 ( ( PUNCT iajs-2992 48 12 𝑣1 𝑣1 PROPN iajs-2992 48 13 , , PUNCT iajs-2992 48 14 𝑣2 𝑣2 PROPN iajs-2992 48 15 , , PUNCT iajs-2992 48 16 𝑣3 𝑣3 ADJ iajs-2992 48 17 , , PUNCT iajs-2992 48 18 𝑣4 𝑣4 NOUN iajs-2992 48 19 ) ) PUNCT iajs-2992 48 20 ∈ ∈ PROPN iajs-2992 48 21 π‘―πŸ(𝛀 π‘―πŸ(𝛀 PROPN iajs-2992 48 22 ) ) PUNCT iajs-2992 48 23 , , PUNCT iajs-2992 48 24 𝑣1 𝑣1 NOUN iajs-2992 48 25 = = PROPN iajs-2992 48 26 𝑣2 𝑣2 PROPN iajs-2992 48 27 = = SYM iajs-2992 48 28 𝑣3 𝑣3 PROPN iajs-2992 48 29 = = SYM iajs-2992 48 30 𝑣4 𝑣4 NOUN iajs-2992 48 31 = = SYM iajs-2992 48 32 0 0 NUM iajs-2992 48 33 π‘œπ‘› π‘œπ‘› PROPN iajs-2992 48 34 πœ•Ο‰},vβƒ—βƒ—βƒ— πœ•Ο‰},vβƒ—βƒ—βƒ— PROPN iajs-2992 48 35 = = PUNCT iajs-2992 48 36 π‘―πŸŽ π‘―πŸŽ PROPN iajs-2992 48 37 𝟏(𝛀 𝟏(𝛀 NOUN iajs-2992 48 38 ) ) PUNCT iajs-2992 48 39 = = PUNCT iajs-2992 49 1 ( ( PUNCT iajs-2992 49 2 𝐻0 𝐻0 PROPN iajs-2992 49 3 1(Ο‰))4 1(Ο‰))4 NUM iajs-2992 49 4 , , PUNCT iajs-2992 49 5 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 49 6 , , PUNCT iajs-2992 49 7 𝑽 𝑽 PROPN iajs-2992 49 8 ) ) PUNCT iajs-2992 49 9 = = SYM iajs-2992 49 10 ( ( PUNCT iajs-2992 49 11 𝐿2(𝐼 𝐿2(𝐼 PROPN iajs-2992 49 12 , , PUNCT iajs-2992 49 13 𝑉))4 𝑉))4 PROPN iajs-2992 49 14 and and CCONJ iajs-2992 49 15 𝑉 𝑉 PROPN iajs-2992 49 16 = = PROPN iajs-2992 49 17 𝐻0 𝐻0 PROPN iajs-2992 49 18 1(Ο‰ 1(Ο‰ NUM iajs-2992 49 19 ) ) PUNCT iajs-2992 49 20 , , PUNCT iajs-2992 49 21 the the DET iajs-2992 49 22 inner inner ADJ iajs-2992 49 23 product product NOUN iajs-2992 49 24 ( ( PUNCT iajs-2992 49 25 ip ip NOUN iajs-2992 49 26 ) ) PUNCT iajs-2992 49 27 and and CCONJ iajs-2992 49 28 the the DET iajs-2992 49 29 norm(nr norm(nr PROPN iajs-2992 49 30 ) ) PUNCT iajs-2992 49 31 in in ADP iajs-2992 49 32 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 49 33 ) ) PUNCT iajs-2992 49 34 are be AUX iajs-2992 49 35 denoted denote VERB iajs-2992 49 36 by by ADP iajs-2992 49 37 ( ( PUNCT iajs-2992 49 38 οΏ½ οΏ½ PROPN iajs-2992 49 39 βƒ— βƒ— NOUN iajs-2992 49 40 οΏ½ οΏ½ PROPN iajs-2992 49 41 , , PUNCT iajs-2992 49 42 οΏ½ οΏ½ PROPN iajs-2992 49 43 βƒ— βƒ— NOUN iajs-2992 49 44 οΏ½ οΏ½ PROPN iajs-2992 49 45 ) ) PUNCT iajs-2992 49 46 and and CCONJ iajs-2992 49 47 βˆ₯ βˆ₯ NUM iajs-2992 49 48 οΏ½ οΏ½ NOUN iajs-2992 49 49 βƒ— βƒ— NOUN iajs-2992 49 50 οΏ½ οΏ½ NOUN iajs-2992 49 51 βˆ₯π‘³πŸ(𝐐)= βˆ₯π‘³πŸ(𝐐)= X iajs-2992 49 52 Οƒ Οƒ PROPN iajs-2992 49 53 𝑖=1 𝑖=1 PROPN iajs-2992 49 54 4 4 NUM iajs-2992 49 55 βˆ₯ βˆ₯ NOUN iajs-2992 49 56 𝑣1 𝑣1 NOUN iajs-2992 49 57 βˆ₯𝐿2(q βˆ₯𝐿2(q PROPN iajs-2992 49 58 ) ) PUNCT iajs-2992 49 59 2 2 NUM iajs-2992 49 60 resp resp NOUN iajs-2992 49 61 . . PUNCT iajs-2992 50 1 , , PUNCT iajs-2992 50 2 the the DET iajs-2992 50 3 nr nr PROPN iajs-2992 50 4 in in ADP iajs-2992 50 5 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 50 6 , , PUNCT iajs-2992 50 7 𝑽 𝑽 PROPN iajs-2992 50 8 ) ) PUNCT iajs-2992 50 9 by by ADP iajs-2992 50 10 βˆ₯ βˆ₯ PROPN iajs-2992 50 11 οΏ½ οΏ½ NOUN iajs-2992 50 12 βƒ— βƒ— NOUN iajs-2992 50 13 οΏ½ οΏ½ NOUN iajs-2992 50 14 βˆ₯π‘³πŸ(𝑰,𝑽)= βˆ₯π‘³πŸ(𝑰,𝑽)= PROPN iajs-2992 50 15 Οƒ Οƒ NOUN iajs-2992 50 16 𝑖=1 𝑖=1 PROPN iajs-2992 50 17 4 4 NUM iajs-2992 50 18 βˆ₯ βˆ₯ NOUN iajs-2992 50 19 𝑣1 𝑣1 NOUN iajs-2992 50 20 βˆ₯𝐿2(𝐼,𝑉 βˆ₯𝐿2(𝐼,𝑉 PROPN iajs-2992 50 21 ) ) PUNCT iajs-2992 50 22 2 2 NUM iajs-2992 50 23 , , PUNCT iajs-2992 50 24 and and CCONJ iajs-2992 50 25 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 50 26 , , PUNCT iajs-2992 50 27 π‘½βˆ— π‘½βˆ— VERB iajs-2992 50 28 ) ) PUNCT iajs-2992 50 29 is be AUX iajs-2992 50 30 the the DET iajs-2992 50 31 dual dual ADJ iajs-2992 50 32 of of ADP iajs-2992 50 33 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 50 34 , , PUNCT iajs-2992 50 35 𝑽 𝑽 PROPN iajs-2992 50 36 ) ) PUNCT iajs-2992 50 37 . . PUNCT iajs-2992 51 1 the the DET iajs-2992 51 2 wf wf PROPN iajs-2992 51 3 of of ADP iajs-2992 51 4 ( ( PUNCT iajs-2992 51 5 ( ( PUNCT iajs-2992 51 6 1)-(6 1)-(6 NUM iajs-2992 51 7 ) ) PUNCT iajs-2992 51 8 ) ) PUNCT iajs-2992 51 9 with with ADP iajs-2992 51 10 οΏ½ οΏ½ NOUN iajs-2992 51 11 βƒ— βƒ— NOUN iajs-2992 51 12 οΏ½ οΏ½ PROPN iajs-2992 51 13 ∈ ∈ PROPN iajs-2992 51 14 π‘―πŸŽ π‘―πŸŽ PROPN iajs-2992 51 15 𝟏(𝛀 𝟏(𝛀 NOUN iajs-2992 51 16 ) ) PUNCT iajs-2992 51 17 is be AUX iajs-2992 51 18 given give VERB iajs-2992 51 19 ( ( PUNCT iajs-2992 51 20 a.e a.e PROPN iajs-2992 51 21 . . PROPN iajs-2992 51 22 on on ADP iajs-2992 51 23 i i PROPN iajs-2992 51 24 and and CCONJ iajs-2992 51 25 βˆ€π‘£π‘– βˆ€π‘£π‘– PROPN iajs-2992 51 26 , , PUNCT iajs-2992 51 27 𝑦𝑖(0 𝑦𝑖(0 PROPN iajs-2992 51 28 , , PUNCT iajs-2992 51 29 𝑑 𝑑 NOUN iajs-2992 51 30 ) ) PUNCT iajs-2992 51 31 ∈ ∈ PROPN iajs-2992 51 32 𝑉,βˆ€π‘– 𝑉,βˆ€π‘– NOUN iajs-2992 51 33 = = SYM iajs-2992 51 34 1,2,3,4 1,2,3,4 NUM iajs-2992 51 35 ) ) PUNCT iajs-2992 51 36 by by ADP iajs-2992 51 37 : : PUNCT iajs-2992 51 38 ( ( PUNCT iajs-2992 51 39 𝑦1𝑑𝑑 𝑦1𝑑𝑑 X iajs-2992 51 40 , , PUNCT iajs-2992 51 41 𝑣1 𝑣1 NOUN iajs-2992 51 42 ) ) PUNCT iajs-2992 51 43 + + CCONJ iajs-2992 51 44 ( ( PUNCT iajs-2992 51 45 βˆ‡π‘¦1 βˆ‡π‘¦1 NOUN iajs-2992 51 46 , , PUNCT iajs-2992 51 47 βˆ‡π‘£1 βˆ‡π‘£1 NOUN iajs-2992 51 48 ) ) PUNCT iajs-2992 51 49 + + CCONJ iajs-2992 51 50 ( ( PUNCT iajs-2992 51 51 𝑦1 𝑦1 PROPN iajs-2992 51 52 , , PUNCT iajs-2992 51 53 𝑣1 𝑣1 NOUN iajs-2992 51 54 ) ) PUNCT iajs-2992 51 55 βˆ’ βˆ’ PROPN iajs-2992 51 56 ( ( PUNCT iajs-2992 51 57 𝑦2 𝑦2 PROPN iajs-2992 51 58 , , PUNCT iajs-2992 51 59 𝑣1 𝑣1 PROPN iajs-2992 51 60 ) ) PUNCT iajs-2992 51 61 + + CCONJ iajs-2992 51 62 ( ( PUNCT iajs-2992 51 63 𝑦3 𝑦3 PROPN iajs-2992 51 64 , , PUNCT iajs-2992 51 65 𝑣1 𝑣1 PROPN iajs-2992 51 66 ) ) PUNCT iajs-2992 51 67 + + CCONJ iajs-2992 51 68 ( ( PUNCT iajs-2992 51 69 𝑦4 𝑦4 NOUN iajs-2992 51 70 , , PUNCT iajs-2992 51 71 𝑣1 𝑣1 NOUN iajs-2992 51 72 ) ) PUNCT iajs-2992 51 73 = = PUNCT iajs-2992 51 74 ( ( PUNCT iajs-2992 51 75 𝑓1 𝑓1 PROPN iajs-2992 51 76 , , PUNCT iajs-2992 51 77 𝑣1 𝑣1 PROPN iajs-2992 51 78 ) ) PUNCT iajs-2992 51 79 , , PUNCT iajs-2992 51 80 ( ( PUNCT iajs-2992 51 81 10 10 X iajs-2992 51 82 ) ) PUNCT iajs-2992 51 83 ihjpas ihjpa NOUN iajs-2992 51 84 . . PUNCT iajs-2992 52 1 36(2)2023 36(2)2023 NUM iajs-2992 52 2 333 333 NUM iajs-2992 52 3 ( ( PUNCT iajs-2992 52 4 𝑦1 𝑦1 PROPN iajs-2992 52 5 0 0 NUM iajs-2992 52 6 , , PUNCT iajs-2992 52 7 𝑣1 𝑣1 NOUN iajs-2992 52 8 ) ) PUNCT iajs-2992 52 9 = = PUNCT iajs-2992 52 10 ( ( PUNCT iajs-2992 52 11 𝑦1(0 𝑦1(0 PROPN iajs-2992 52 12 ) ) PUNCT iajs-2992 52 13 , , PUNCT iajs-2992 52 14 𝑣1 𝑣1 NOUN iajs-2992 52 15 ) ) PUNCT iajs-2992 52 16 , , PUNCT iajs-2992 52 17 and and CCONJ iajs-2992 52 18 ( ( PUNCT iajs-2992 52 19 𝑦1𝑑 𝑦1𝑑 PROPN iajs-2992 52 20 1 1 NUM iajs-2992 52 21 , , PUNCT iajs-2992 52 22 𝑣1 𝑣1 NOUN iajs-2992 52 23 ) ) PUNCT iajs-2992 52 24 = = PUNCT iajs-2992 52 25 ( ( PUNCT iajs-2992 52 26 𝑦1𝑑(0 𝑦1𝑑(0 PROPN iajs-2992 52 27 ) ) PUNCT iajs-2992 52 28 , , PUNCT iajs-2992 52 29 𝑣1 𝑣1 PROPN iajs-2992 52 30 ) ) PUNCT iajs-2992 52 31 , , PUNCT iajs-2992 52 32 ( ( PUNCT iajs-2992 52 33 11 11 NUM iajs-2992 52 34 ) ) PUNCT iajs-2992 52 35 ( ( PUNCT iajs-2992 52 36 𝑦2𝑑𝑑 𝑦2𝑑𝑑 X iajs-2992 52 37 , , PUNCT iajs-2992 52 38 𝑣2 𝑣2 PROPN iajs-2992 52 39 ) ) PUNCT iajs-2992 52 40 + + CCONJ iajs-2992 52 41 ( ( PUNCT iajs-2992 52 42 βˆ†π‘¦2 βˆ†π‘¦2 PROPN iajs-2992 52 43 , , PUNCT iajs-2992 52 44 βˆ‡π‘£2 βˆ‡π‘£2 PROPN iajs-2992 52 45 ) ) PUNCT iajs-2992 52 46 + + CCONJ iajs-2992 52 47 ( ( PUNCT iajs-2992 52 48 𝑦1 𝑦1 PROPN iajs-2992 52 49 , , PUNCT iajs-2992 52 50 𝑣2 𝑣2 PROPN iajs-2992 52 51 ) ) PUNCT iajs-2992 52 52 + + CCONJ iajs-2992 52 53 ( ( PUNCT iajs-2992 52 54 𝑦2 𝑦2 PROPN iajs-2992 52 55 , , PUNCT iajs-2992 52 56 𝑣2 𝑣2 PROPN iajs-2992 52 57 ) ) PUNCT iajs-2992 52 58 βˆ’ βˆ’ PROPN iajs-2992 52 59 ( ( PUNCT iajs-2992 52 60 𝑦3 𝑦3 PROPN iajs-2992 52 61 , , PUNCT iajs-2992 52 62 𝑣2 𝑣2 PROPN iajs-2992 52 63 ) ) PUNCT iajs-2992 52 64 βˆ’ βˆ’ PROPN iajs-2992 52 65 ( ( PUNCT iajs-2992 52 66 𝑦4 𝑦4 PROPN iajs-2992 52 67 , , PUNCT iajs-2992 52 68 𝑣2 𝑣2 NOUN iajs-2992 52 69 ) ) PUNCT iajs-2992 52 70 = = SYM iajs-2992 52 71 ( ( PUNCT iajs-2992 52 72 𝑓2 𝑓2 PROPN iajs-2992 52 73 , , PUNCT iajs-2992 52 74 𝑣2 𝑣2 NOUN iajs-2992 52 75 ) ) PUNCT iajs-2992 52 76 , , PUNCT iajs-2992 52 77 ( ( PUNCT iajs-2992 52 78 12 12 NUM iajs-2992 52 79 ) ) PUNCT iajs-2992 52 80 ( ( PUNCT iajs-2992 52 81 𝑦2 𝑦2 PROPN iajs-2992 52 82 0 0 NUM iajs-2992 52 83 , , PUNCT iajs-2992 52 84 𝑣2 𝑣2 NUM iajs-2992 52 85 ) ) PUNCT iajs-2992 52 86 = = PUNCT iajs-2992 52 87 ( ( PUNCT iajs-2992 52 88 𝑦2(0 𝑦2(0 PROPN iajs-2992 52 89 ) ) PUNCT iajs-2992 52 90 , , PUNCT iajs-2992 52 91 𝑣2 𝑣2 PROPN iajs-2992 52 92 ) ) PUNCT iajs-2992 52 93 , , PUNCT iajs-2992 52 94 and and CCONJ iajs-2992 52 95 ( ( PUNCT iajs-2992 52 96 𝑦2𝑑 𝑦2𝑑 NOUN iajs-2992 52 97 1 1 NUM iajs-2992 52 98 , , PUNCT iajs-2992 52 99 𝑣2 𝑣2 PROPN iajs-2992 52 100 ) ) PUNCT iajs-2992 52 101 = = PUNCT iajs-2992 52 102 ( ( PUNCT iajs-2992 52 103 𝑦2𝑑(0 𝑦2𝑑(0 PROPN iajs-2992 52 104 ) ) PUNCT iajs-2992 52 105 , , PUNCT iajs-2992 52 106 𝑣2 𝑣2 PROPN iajs-2992 52 107 ) ) PUNCT iajs-2992 52 108 , , PUNCT iajs-2992 52 109 ( ( PUNCT iajs-2992 52 110 13 13 NUM iajs-2992 52 111 ) ) PUNCT iajs-2992 52 112 ( ( PUNCT iajs-2992 52 113 𝑦3𝑑𝑑 𝑦3𝑑𝑑 PROPN iajs-2992 52 114 , , PUNCT iajs-2992 52 115 𝑣3 𝑣3 ADJ iajs-2992 52 116 ) ) PUNCT iajs-2992 52 117 + + CCONJ iajs-2992 52 118 ( ( PUNCT iajs-2992 52 119 βˆ‡π‘¦3 βˆ‡π‘¦3 PROPN iajs-2992 52 120 , , PUNCT iajs-2992 52 121 βˆ‡π‘£3 βˆ‡π‘£3 NOUN iajs-2992 52 122 ) ) PUNCT iajs-2992 52 123 βˆ’ βˆ’ PROPN iajs-2992 52 124 ( ( PUNCT iajs-2992 52 125 𝑦1 𝑦1 NOUN iajs-2992 52 126 , , PUNCT iajs-2992 52 127 𝑣3 𝑣3 ADJ iajs-2992 52 128 ) ) PUNCT iajs-2992 52 129 + + CCONJ iajs-2992 52 130 ( ( PUNCT iajs-2992 52 131 𝑦2 𝑦2 NOUN iajs-2992 52 132 , , PUNCT iajs-2992 52 133 𝑣3 𝑣3 ADJ iajs-2992 52 134 ) ) PUNCT iajs-2992 52 135 + + CCONJ iajs-2992 52 136 ( ( PUNCT iajs-2992 52 137 𝑦3 𝑦3 PROPN iajs-2992 52 138 , , PUNCT iajs-2992 52 139 𝑣3 𝑣3 ADJ iajs-2992 52 140 ) ) PUNCT iajs-2992 52 141 + + CCONJ iajs-2992 52 142 ( ( PUNCT iajs-2992 52 143 𝑦4 𝑦4 NOUN iajs-2992 52 144 , , PUNCT iajs-2992 52 145 𝑣3 𝑣3 ADJ iajs-2992 52 146 ) ) PUNCT iajs-2992 52 147 = = SYM iajs-2992 52 148 ( ( PUNCT iajs-2992 52 149 𝑓3 𝑓3 NOUN iajs-2992 52 150 , , PUNCT iajs-2992 52 151 𝑣3 𝑣3 ADJ iajs-2992 52 152 ) ) PUNCT iajs-2992 52 153 , , PUNCT iajs-2992 52 154 ( ( PUNCT iajs-2992 52 155 14 14 NUM iajs-2992 52 156 ) ) PUNCT iajs-2992 52 157 ( ( PUNCT iajs-2992 52 158 𝑦3 𝑦3 PROPN iajs-2992 52 159 0 0 NUM iajs-2992 52 160 , , PUNCT iajs-2992 52 161 𝑣3 𝑣3 ADJ iajs-2992 52 162 ) ) PUNCT iajs-2992 52 163 = = SYM iajs-2992 52 164 ( ( PUNCT iajs-2992 52 165 𝑦3(0 𝑦3(0 PROPN iajs-2992 52 166 ) ) PUNCT iajs-2992 52 167 , , PUNCT iajs-2992 52 168 𝑣3 𝑣3 ADJ iajs-2992 52 169 ) ) PUNCT iajs-2992 52 170 , , PUNCT iajs-2992 52 171 and and CCONJ iajs-2992 52 172 ( ( PUNCT iajs-2992 52 173 𝑦3𝑑 𝑦3𝑑 PROPN iajs-2992 52 174 1 1 NUM iajs-2992 52 175 , , PUNCT iajs-2992 52 176 𝑣3 𝑣3 ADJ iajs-2992 52 177 ) ) PUNCT iajs-2992 52 178 = = SYM iajs-2992 52 179 ( ( PUNCT iajs-2992 52 180 𝑦3𝑑(0 𝑦3𝑑(0 PROPN iajs-2992 52 181 ) ) PUNCT iajs-2992 52 182 , , PUNCT iajs-2992 52 183 𝑣3 𝑣3 NOUN iajs-2992 52 184 ) ) PUNCT iajs-2992 52 185 , , PUNCT iajs-2992 52 186 ( ( PUNCT iajs-2992 52 187 15 15 NUM iajs-2992 52 188 ) ) PUNCT iajs-2992 52 189 ( ( PUNCT iajs-2992 52 190 𝑦4𝑑𝑑 𝑦4𝑑𝑑 NOUN iajs-2992 52 191 , , PUNCT iajs-2992 52 192 𝑣4 𝑣4 NOUN iajs-2992 52 193 ) ) PUNCT iajs-2992 52 194 + + CCONJ iajs-2992 52 195 ( ( PUNCT iajs-2992 52 196 βˆ‡π‘¦4 βˆ‡π‘¦4 ADJ iajs-2992 52 197 , , PUNCT iajs-2992 52 198 βˆ‡π‘£4 βˆ‡π‘£4 NUM iajs-2992 52 199 ) ) PUNCT iajs-2992 52 200 βˆ’ βˆ’ PROPN iajs-2992 52 201 ( ( PUNCT iajs-2992 52 202 𝑦1 𝑦1 NOUN iajs-2992 52 203 , , PUNCT iajs-2992 52 204 𝑣4 𝑣4 NOUN iajs-2992 52 205 ) ) PUNCT iajs-2992 52 206 + + CCONJ iajs-2992 52 207 ( ( PUNCT iajs-2992 52 208 𝑦2 𝑦2 NOUN iajs-2992 52 209 , , PUNCT iajs-2992 52 210 𝑣4 𝑣4 NOUN iajs-2992 52 211 ) ) PUNCT iajs-2992 52 212 βˆ’ βˆ’ PROPN iajs-2992 52 213 ( ( PUNCT iajs-2992 52 214 𝑦3 𝑦3 PROPN iajs-2992 52 215 , , PUNCT iajs-2992 52 216 𝑣4 𝑣4 NOUN iajs-2992 52 217 ) ) PUNCT iajs-2992 52 218 + + CCONJ iajs-2992 52 219 ( ( PUNCT iajs-2992 52 220 𝑦4 𝑦4 NOUN iajs-2992 52 221 , , PUNCT iajs-2992 52 222 𝑣4 𝑣4 NOUN iajs-2992 52 223 ) ) PUNCT iajs-2992 52 224 = = PUNCT iajs-2992 52 225 ( ( PUNCT iajs-2992 52 226 𝑓4 𝑓4 PROPN iajs-2992 52 227 , , PUNCT iajs-2992 52 228 𝑣4 𝑣4 NOUN iajs-2992 52 229 ) ) PUNCT iajs-2992 52 230 , , PUNCT iajs-2992 52 231 ( ( PUNCT iajs-2992 52 232 16 16 NUM iajs-2992 52 233 ) ) PUNCT iajs-2992 52 234 ( ( PUNCT iajs-2992 52 235 𝑦4 𝑦4 PROPN iajs-2992 52 236 0 0 NUM iajs-2992 52 237 , , PUNCT iajs-2992 52 238 𝑣4 𝑣4 NOUN iajs-2992 52 239 ) ) PUNCT iajs-2992 52 240 = = SYM iajs-2992 52 241 ( ( PUNCT iajs-2992 52 242 𝑦4(0 𝑦4(0 NOUN iajs-2992 52 243 ) ) PUNCT iajs-2992 52 244 , , PUNCT iajs-2992 52 245 𝑣4 𝑣4 NOUN iajs-2992 52 246 ) ) PUNCT iajs-2992 52 247 , , PUNCT iajs-2992 52 248 and and CCONJ iajs-2992 52 249 ( ( PUNCT iajs-2992 52 250 𝑦4𝑑 𝑦4𝑑 NOUN iajs-2992 52 251 1 1 NUM iajs-2992 52 252 , , PUNCT iajs-2992 52 253 𝑣4 𝑣4 NOUN iajs-2992 52 254 ) ) PUNCT iajs-2992 52 255 = = SYM iajs-2992 52 256 ( ( PUNCT iajs-2992 52 257 𝑦4𝑑(0 𝑦4𝑑(0 PROPN iajs-2992 52 258 ) ) PUNCT iajs-2992 52 259 , , PUNCT iajs-2992 52 260 𝑣4 𝑣4 NOUN iajs-2992 52 261 ) ) PUNCT iajs-2992 52 262 , , PUNCT iajs-2992 52 263 ( ( PUNCT iajs-2992 52 264 17 17 NUM iajs-2992 52 265 ) ) PUNCT iajs-2992 52 266 assums assum NOUN iajs-2992 52 267 ( ( PUNCT iajs-2992 52 268 a a X iajs-2992 52 269 ): ): PUNCT iajs-2992 52 270 suppose suppose VERB iajs-2992 52 271 that that SCONJ iajs-2992 52 272 𝑓𝑖 𝑓𝑖 PROPN iajs-2992 52 273 is be AUX iajs-2992 52 274 of of ADP iajs-2992 52 275 carathΓ©odory carathΓ©odory ADJ iajs-2992 52 276 type type NOUN iajs-2992 52 277 ( ( PUNCT iajs-2992 52 278 carat carat NOUN iajs-2992 52 279 ) ) PUNCT iajs-2992 52 280 on on ADP iajs-2992 52 281 𝑄 𝑄 PROPN iajs-2992 52 282 Γ— Γ— NOUN iajs-2992 52 283 ( ( PUNCT iajs-2992 52 284 ℝ ℝ PROPN iajs-2992 52 285 Γ— Γ— NOUN iajs-2992 52 286 π‘ˆπ‘– π‘ˆπ‘– NOUN iajs-2992 52 287 ) ) PUNCT iajs-2992 52 288 satisfies satisfie NOUN iajs-2992 52 289 ( ( PUNCT iajs-2992 52 290 w.r.t w.r.t NOUN iajs-2992 52 291 . . PUNCT iajs-2992 53 1 𝑦𝑖&𝑒𝑖 𝑦𝑖&𝑒𝑖 ADV iajs-2992 53 2 ) ) PUNCT iajs-2992 54 1 the the DET iajs-2992 54 2 following follow VERB iajs-2992 54 3 ( ( PUNCT iajs-2992 54 4 i)|𝑓𝑖(π‘₯ i)|𝑓𝑖(π‘₯ PROPN iajs-2992 54 5 , , PUNCT iajs-2992 54 6 𝑑 𝑑 PROPN iajs-2992 54 7 , , PUNCT iajs-2992 54 8 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 54 9 , , PUNCT iajs-2992 54 10 𝑒𝑖)| 𝑒𝑖)| VERB iajs-2992 54 11 ≀ ≀ ADJ iajs-2992 54 12 𝐹𝑖(π‘₯ 𝐹𝑖(π‘₯ NOUN iajs-2992 54 13 , , PUNCT iajs-2992 54 14 𝑑)+∣ 𝑑)+∣ ADJ iajs-2992 54 15 𝑒𝑖| 𝑒𝑖| PROPN iajs-2992 54 16 + + NUM iajs-2992 54 17 𝛽𝑖|𝑦𝑖| 𝛽𝑖|𝑦𝑖| NOUN iajs-2992 54 18 , , PUNCT iajs-2992 54 19 where where SCONJ iajs-2992 54 20 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 54 21 , , PUNCT iajs-2992 54 22 𝑒𝑖 𝑒𝑖 DET iajs-2992 54 23 ∈ ∈ PROPN iajs-2992 54 24 ℝ ℝ PROPN iajs-2992 54 25 , , PUNCT iajs-2992 54 26 𝛽𝑖 𝛽𝑖 VERB iajs-2992 54 27 > > X iajs-2992 54 28 0 0 PUNCT iajs-2992 54 29 and and CCONJ iajs-2992 54 30 𝐹𝑖 𝐹𝑖 PROPN iajs-2992 54 31 ∈ ∈ PROPN iajs-2992 54 32 𝐿2(q 𝐿2(q NUM iajs-2992 54 33 ) ) PUNCT iajs-2992 54 34 . . PUNCT iajs-2992 55 1 ( ( PUNCT iajs-2992 55 2 ii ii NOUN iajs-2992 55 3 ) ) PUNCT iajs-2992 55 4 𝑓𝑖 𝑓𝑖 PROPN iajs-2992 55 5 is be AUX iajs-2992 55 6 satisfied satisfied ADJ iajs-2992 55 7 lipschitz lipschitz NOUN iajs-2992 55 8 condition condition NOUN iajs-2992 55 9 ( ( PUNCT iajs-2992 55 10 lpc lpc NOUN iajs-2992 55 11 ) ) PUNCT iajs-2992 55 12 w.r.t w.r.t PROPN iajs-2992 55 13 . . PUNCT iajs-2992 56 1 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 56 2 , , PUNCT iajs-2992 56 3 i.e. i.e. X iajs-2992 56 4 |𝑓𝑖(π‘₯ |𝑓𝑖(π‘₯ X iajs-2992 56 5 , , PUNCT iajs-2992 56 6 𝑑 𝑑 PROPN iajs-2992 56 7 , , PUNCT iajs-2992 56 8 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 56 9 , , PUNCT iajs-2992 56 10 𝑒𝑖 𝑒𝑖 PROPN iajs-2992 56 11 ) ) PUNCT iajs-2992 56 12 βˆ’ βˆ’ PROPN iajs-2992 56 13 𝑓𝑖(π‘₯ 𝑓𝑖(π‘₯ NUM iajs-2992 56 14 , , PUNCT iajs-2992 56 15 𝑑 𝑑 PROPN iajs-2992 56 16 , , PUNCT iajs-2992 56 17 οΏ½ οΏ½ NOUN iajs-2992 56 18 Μ… Μ… NOUN iajs-2992 56 19 οΏ½ οΏ½ NOUN iajs-2992 56 20 𝑖 𝑖 NUM iajs-2992 56 21 , , PUNCT iajs-2992 56 22 𝑒𝑖)| 𝑒𝑖)| VERB iajs-2992 56 23 ≀ ≀ NUM iajs-2992 56 24 𝐿𝑖|𝑦𝑖 𝐿𝑖|𝑦𝑖 VERB iajs-2992 56 25 βˆ’ βˆ’ PROPN iajs-2992 56 26 οΏ½ οΏ½ PROPN iajs-2992 56 27 Μ… Μ… NOUN iajs-2992 56 28 οΏ½ οΏ½ NOUN iajs-2992 56 29 𝑖| 𝑖| PROPN iajs-2992 56 30 , , PUNCT iajs-2992 56 31 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 56 32 , , PUNCT iajs-2992 56 33 οΏ½ οΏ½ NOUN iajs-2992 56 34 Μ… Μ… NOUN iajs-2992 56 35 οΏ½ οΏ½ NOUN iajs-2992 56 36 𝑖 𝑖 NOUN iajs-2992 56 37 , , PUNCT iajs-2992 56 38 𝑒𝑖 𝑒𝑖 DET iajs-2992 56 39 ∈ ∈ PROPN iajs-2992 56 40 ℝ ℝ PROPN iajs-2992 56 41 , , PUNCT iajs-2992 56 42 𝐿𝑖 𝐿𝑖 PROPN iajs-2992 56 43 > > X iajs-2992 56 44 0 0 NUM iajs-2992 56 45 , , PUNCT iajs-2992 56 46 for for ADP iajs-2992 56 47 ( ( PUNCT iajs-2992 56 48 π‘₯ π‘₯ PROPN iajs-2992 56 49 , , PUNCT iajs-2992 56 50 𝑑 𝑑 NOUN iajs-2992 56 51 ) ) PUNCT iajs-2992 56 52 ∈ ∈ NOUN iajs-2992 56 53 𝑄. 𝑄. NOUN iajs-2992 56 54 proposition proposition NOUN iajs-2992 56 55 2.1[12 2.1[12 NOUN iajs-2992 56 56 ] ] PUNCT iajs-2992 56 57 : : PUNCT iajs-2992 56 58 let let VERB iajs-2992 56 59 𝐷 𝐷 PROPN iajs-2992 56 60 βŠ‚ βŠ‚ PROPN iajs-2992 56 61 ℝ2 ℝ2 VERB iajs-2992 56 62 be be AUX iajs-2992 56 63 measurable measurable ADJ iajs-2992 56 64 , , PUNCT iajs-2992 56 65 𝑓 𝑓 X iajs-2992 56 66 : : PUNCT iajs-2992 56 67 𝐷 𝐷 PROPN iajs-2992 56 68 Γ— Γ— NOUN iajs-2992 56 69 ℝ𝑛 ℝ𝑛 NOUN iajs-2992 56 70 ⟢ ⟢ NOUN iajs-2992 56 71 β„π‘š β„π‘š NOUN iajs-2992 56 72 is be AUX iajs-2992 56 73 of of ADP iajs-2992 56 74 carat carat NOUN iajs-2992 56 75 satisfies satisfie NOUN iajs-2992 56 76 : : PUNCT iajs-2992 56 77 ‖𝑓(𝑣 ‖𝑓(𝑣 NUM iajs-2992 56 78 , , PUNCT iajs-2992 56 79 π‘₯)β€– π‘₯)β€– ADJ iajs-2992 56 80 ≀ ≀ ADJ iajs-2992 56 81 휁(𝑣 휁(𝑣 NOUN iajs-2992 56 82 ) ) PUNCT iajs-2992 57 1 + + CCONJ iajs-2992 57 2 νœ‚(𝑣)β€–π‘₯‖𝛼 νœ‚(𝑣)β€–π‘₯‖𝛼 NOUN iajs-2992 57 3 , , PUNCT iajs-2992 57 4 where where SCONJ iajs-2992 57 5 π‘₯ π‘₯ DET iajs-2992 57 6 ∈ ∈ PROPN iajs-2992 57 7 𝐿𝑝(𝐷 𝐿𝑝(𝐷 NOUN iajs-2992 57 8 Γ— Γ— NOUN iajs-2992 57 9 ℝ𝑛),휁 ℝ𝑛),휁 PUNCT iajs-2992 57 10 ∈ ∈ PROPN iajs-2992 57 11 𝐿1(𝐷 𝐿1(𝐷 PROPN iajs-2992 57 12 Γ— Γ— NOUN iajs-2992 57 13 ℝ ℝ PROPN iajs-2992 57 14 ) ) PUNCT iajs-2992 57 15 , , PUNCT iajs-2992 57 16 νœ‚ νœ‚ ADP iajs-2992 57 17 ∈ ∈ PROPN iajs-2992 57 18 𝐿 𝐿 PROPN iajs-2992 57 19 𝑝 𝑝 PROPN iajs-2992 57 20 π‘βˆ’π›Ό(𝐷 π‘βˆ’π›Ό(𝐷 NUM iajs-2992 57 21 Γ— Γ— NOUN iajs-2992 57 22 ℝ ℝ PROPN iajs-2992 57 23 ) ) PUNCT iajs-2992 57 24 , , PUNCT iajs-2992 57 25 𝛼 𝛼 PROPN iajs-2992 57 26 ∈ ∈ PROPN iajs-2992 58 1 [ [ X iajs-2992 58 2 0 0 NUM iajs-2992 58 3 , , PUNCT iajs-2992 58 4 ∞ ∞ PROPN iajs-2992 58 5 ) ) PUNCT iajs-2992 58 6 . . PUNCT iajs-2992 59 1 then then ADV iajs-2992 59 2 the the DET iajs-2992 59 3 functional functional ADJ iajs-2992 59 4 ( ( PUNCT iajs-2992 59 5 funl funl NOUN iajs-2992 59 6 ) ) PUNCT iajs-2992 59 7 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-2992 59 8 ) ) PUNCT iajs-2992 60 1 = = SYM iajs-2992 60 2 ∫ ∫ PROPN iajs-2992 60 3 𝐷 𝐷 PROPN iajs-2992 60 4 𝑓(𝑣 𝑓(𝑣 PROPN iajs-2992 60 5 , , PUNCT iajs-2992 60 6 π‘₯(𝑣))𝑑𝑣 π‘₯(𝑣))𝑑𝑣 PROPN iajs-2992 60 7 is be AUX iajs-2992 60 8 continuous continuous ADJ iajs-2992 60 9 ( ( PUNCT iajs-2992 60 10 cont cont NOUN iajs-2992 60 11 . . PUNCT iajs-2992 60 12 ) ) PUNCT iajs-2992 60 13 . . PUNCT iajs-2992 61 1 theorem2.1 theorem2.1 NUM iajs-2992 61 2 ( ( PUNCT iajs-2992 61 3 eth eth NOUN iajs-2992 61 4 of of ADP iajs-2992 61 5 a a DET iajs-2992 61 6 unique unique ADJ iajs-2992 61 7 qsvs)[13 qsvs)[13 NOUN iajs-2992 61 8 ] ] PUNCT iajs-2992 61 9 : : PUNCT iajs-2992 61 10 if if SCONJ iajs-2992 61 11 assums assum NOUN iajs-2992 61 12 ( ( PUNCT iajs-2992 61 13 a a X iajs-2992 61 14 ) ) PUNCT iajs-2992 61 15 hold hold NOUN iajs-2992 61 16 , , PUNCT iajs-2992 61 17 then then ADV iajs-2992 61 18 for for ADP iajs-2992 61 19 each each DET iajs-2992 61 20 given give VERB iajs-2992 61 21 οΏ½ οΏ½ PROPN iajs-2992 61 22 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 61 23 οΏ½ οΏ½ PROPN iajs-2992 61 24 ∈ ∈ PROPN iajs-2992 61 25 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 61 26 ) ) PUNCT iajs-2992 61 27 , , PUNCT iajs-2992 61 28 the the DET iajs-2992 61 29 wf wf PROPN iajs-2992 61 30 ( ( PUNCT iajs-2992 61 31 1017 1017 NUM iajs-2992 61 32 ) ) PUNCT iajs-2992 61 33 has have VERB iajs-2992 61 34 a a DET iajs-2992 61 35 unique unique ADJ iajs-2992 61 36 qsvs qsvs ADJ iajs-2992 61 37 οΏ½ οΏ½ NOUN iajs-2992 61 38 βƒ— βƒ— NOUN iajs-2992 61 39 οΏ½ οΏ½ NOUN iajs-2992 61 40 = = SYM iajs-2992 61 41 ( ( PUNCT iajs-2992 61 42 𝑦1 𝑦1 PROPN iajs-2992 61 43 , , PUNCT iajs-2992 61 44 𝑦2 𝑦2 PROPN iajs-2992 61 45 , , PUNCT iajs-2992 61 46 𝑦3 𝑦3 PROPN iajs-2992 61 47 , , PUNCT iajs-2992 61 48 𝑦4 𝑦4 PROPN iajs-2992 61 49 ) ) PUNCT iajs-2992 61 50 ∈ ∈ PROPN iajs-2992 61 51 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 61 52 , , PUNCT iajs-2992 61 53 𝑽 𝑽 PROPN iajs-2992 61 54 ) ) PUNCT iajs-2992 61 55 with with ADP iajs-2992 61 56 οΏ½ οΏ½ PROPN iajs-2992 61 57 βƒ— βƒ— NOUN iajs-2992 61 58 οΏ½ οΏ½ NOUN iajs-2992 61 59 𝑑 𝑑 NOUN iajs-2992 61 60 = = SYM iajs-2992 61 61 ( ( PUNCT iajs-2992 61 62 𝑦1𝑑 𝑦1𝑑 PROPN iajs-2992 61 63 , , PUNCT iajs-2992 61 64 𝑦2𝑑 𝑦2𝑑 NOUN iajs-2992 61 65 , , PUNCT iajs-2992 61 66 𝑦3𝑑 𝑦3𝑑 NUM iajs-2992 61 67 , , PUNCT iajs-2992 61 68 𝑦4𝑑 𝑦4𝑑 NUM iajs-2992 61 69 ) ) PUNCT iajs-2992 61 70 ∈ ∈ PROPN iajs-2992 61 71 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 61 72 ) ) PUNCT iajs-2992 61 73 , , PUNCT iajs-2992 61 74 οΏ½ οΏ½ PROPN iajs-2992 61 75 βƒ— βƒ— NOUN iajs-2992 61 76 οΏ½ οΏ½ NOUN iajs-2992 61 77 𝑑𝑑 𝑑𝑑 ADJ iajs-2992 61 78 = = SYM iajs-2992 61 79 ( ( PUNCT iajs-2992 61 80 𝑦1𝑑𝑑 𝑦1𝑑𝑑 X iajs-2992 61 81 , , PUNCT iajs-2992 61 82 𝑦2𝑑𝑑 𝑦2𝑑𝑑 NUM iajs-2992 61 83 , , PUNCT iajs-2992 61 84 𝑦3𝑑𝑑 𝑦3𝑑𝑑 PROPN iajs-2992 61 85 , , PUNCT iajs-2992 61 86 𝑦4𝑑𝑑 𝑦4𝑑𝑑 NOUN iajs-2992 61 87 ) ) PUNCT iajs-2992 61 88 ∈ ∈ PROPN iajs-2992 61 89 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 61 90 , , PUNCT iajs-2992 61 91 π‘½βˆ— π‘½βˆ— NOUN iajs-2992 61 92 ) ) PUNCT iajs-2992 61 93 . . PUNCT iajs-2992 62 1 assums assums PROPN iajs-2992 62 2 ( ( PUNCT iajs-2992 62 3 b b NOUN iajs-2992 62 4 ): ): PUNCT iajs-2992 62 5 consider consider VERB iajs-2992 62 6 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 62 7 ( ( PUNCT iajs-2992 62 8 for for ADP iajs-2992 62 9 𝑖 𝑖 PRON iajs-2992 62 10 = = SYM iajs-2992 62 11 1,2,3,4 1,2,3,4 NUM iajs-2992 62 12 & & CCONJ iajs-2992 62 13 𝑙 𝑙 NOUN iajs-2992 62 14 = = SYM iajs-2992 62 15 0,1,2 0,1,2 NUM iajs-2992 62 16 ) ) PUNCT iajs-2992 62 17 is be AUX iajs-2992 62 18 of of ADP iajs-2992 62 19 the the DET iajs-2992 62 20 carat carat NOUN iajs-2992 62 21 on on ADP iajs-2992 62 22 𝑄 𝑄 PROPN iajs-2992 62 23 Γ— Γ— NOUN iajs-2992 62 24 ( ( PUNCT iajs-2992 62 25 ℝ ℝ PROPN iajs-2992 62 26 Γ— Γ— NOUN iajs-2992 62 27 π‘ˆπ‘– π‘ˆπ‘– PROPN iajs-2992 62 28 ) ) PUNCT iajs-2992 62 29 and and CCONJ iajs-2992 62 30 satisfies:|𝑔𝑙𝑖(π‘₯ satisfies:|𝑔𝑙𝑖(π‘₯ NOUN iajs-2992 62 31 , , PUNCT iajs-2992 62 32 𝑑 𝑑 PROPN iajs-2992 62 33 , , PUNCT iajs-2992 62 34 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 62 35 , , PUNCT iajs-2992 62 36 𝑒𝑖)| 𝑒𝑖)| VERB iajs-2992 62 37 ≀ ≀ PROPN iajs-2992 62 38 𝐺𝑙𝑖(π‘₯ 𝐺𝑙𝑖(π‘₯ PROPN iajs-2992 62 39 , , PUNCT iajs-2992 62 40 𝑑 𝑑 X iajs-2992 62 41 ) ) PUNCT iajs-2992 62 42 + + NUM iajs-2992 62 43 𝐢𝑙𝑖(𝑦𝑖 𝐢𝑙𝑖(𝑦𝑖 NOUN iajs-2992 62 44 ) ) PUNCT iajs-2992 62 45 2 2 NUM iajs-2992 63 1 + + NUM iajs-2992 63 2 𝐢𝑙𝑖(𝑒𝑖 𝐢𝑙𝑖(𝑒𝑖 NOUN iajs-2992 63 3 ) ) PUNCT iajs-2992 63 4 2 2 NUM iajs-2992 63 5 , , PUNCT iajs-2992 63 6 where where SCONJ iajs-2992 63 7 𝐺𝑙𝑖 𝐺𝑙𝑖 PROPN iajs-2992 63 8 ∈ ∈ PROPN iajs-2992 63 9 𝐿1(𝑄 𝐿1(𝑄 PROPN iajs-2992 63 10 ) ) PUNCT iajs-2992 63 11 , , PUNCT iajs-2992 63 12 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 63 13 ∈ ∈ PROPN iajs-2992 63 14 ℝ ℝ PROPN iajs-2992 63 15 & & CCONJ iajs-2992 63 16 𝑒𝑖 𝑒𝑖 DET iajs-2992 63 17 ∈ ∈ PROPN iajs-2992 63 18 π‘ˆπ‘–. π‘ˆπ‘–. PROPN iajs-2992 63 19 lemma lemma PROPN iajs-2992 63 20 2.1 2.1 NUM iajs-2992 63 21 : : PUNCT iajs-2992 63 22 with with ADP iajs-2992 63 23 assums assum NOUN iajs-2992 63 24 ( ( PUNCT iajs-2992 63 25 b b NOUN iajs-2992 63 26 ) ) PUNCT iajs-2992 63 27 , , PUNCT iajs-2992 63 28 the the DET iajs-2992 63 29 funl funl PROPN iajs-2992 63 30 οΏ½ οΏ½ PROPN iajs-2992 63 31 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 63 32 οΏ½ οΏ½ PROPN iajs-2992 63 33 β†’ β†’ SYM iajs-2992 63 34 𝐺𝑙( 𝐺𝑙( NOUN iajs-2992 63 35 οΏ½ οΏ½ PROPN iajs-2992 63 36 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 63 37 οΏ½ οΏ½ PROPN iajs-2992 63 38 ) ) PUNCT iajs-2992 63 39 , , PUNCT iajs-2992 63 40 βˆ€π‘™ βˆ€π‘™ NOUN iajs-2992 63 41 = = SYM iajs-2992 63 42 0,1,2 0,1,2 NOUN iajs-2992 63 43 is be AUX iajs-2992 63 44 cont cont ADJ iajs-2992 63 45 . . PUNCT iajs-2992 64 1 on on ADP iajs-2992 64 2 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 64 3 ) ) PUNCT iajs-2992 64 4 . . PUNCT iajs-2992 65 1 proof proof NOUN iajs-2992 65 2 : : PUNCT iajs-2992 65 3 the the DET iajs-2992 65 4 proof proof NOUN iajs-2992 65 5 is be AUX iajs-2992 65 6 obtained obtain VERB iajs-2992 65 7 from from ADP iajs-2992 65 8 the the DET iajs-2992 65 9 assums assums NOUN iajs-2992 65 10 ( ( PUNCT iajs-2992 65 11 b b NOUN iajs-2992 65 12 ) ) PUNCT iajs-2992 65 13 and and CCONJ iajs-2992 65 14 proposition proposition NOUN iajs-2992 65 15 1 1 NUM iajs-2992 65 16 . . PUNCT iajs-2992 66 1 lemma lemma PROPN iajs-2992 66 2 2.2[12 2.2[12 PROPN iajs-2992 66 3 ] ] X iajs-2992 66 4 : : PUNCT iajs-2992 66 5 let let VERB iajs-2992 66 6 𝑔 𝑔 NUM iajs-2992 66 7 : : PUNCT iajs-2992 66 8 𝑄 𝑄 PROPN iajs-2992 66 9 Γ— Γ— NOUN iajs-2992 66 10 ℝ ℝ PROPN iajs-2992 66 11 β†’ β†’ PUNCT iajs-2992 66 12 ℝ ℝ PROPN iajs-2992 66 13 is be AUX iajs-2992 66 14 of of ADP iajs-2992 66 15 carat carat NOUN iajs-2992 66 16 on on ADP iajs-2992 66 17 𝑄 𝑄 PROPN iajs-2992 66 18 Γ— Γ— NOUN iajs-2992 66 19 ( ( PUNCT iajs-2992 66 20 ℝ ℝ PROPN iajs-2992 66 21 Γ— Γ— NOUN iajs-2992 66 22 ℝ ℝ PROPN iajs-2992 66 23 ) ) PUNCT iajs-2992 66 24 and and CCONJ iajs-2992 66 25 satisfies satisfie NOUN iajs-2992 66 26 |𝑔 |𝑔 NOUN iajs-2992 66 27 ( ( PUNCT iajs-2992 66 28 π‘₯ π‘₯ PROPN iajs-2992 66 29 , , PUNCT iajs-2992 66 30 𝑑 𝑑 PROPN iajs-2992 66 31 , , PUNCT iajs-2992 66 32 𝑦 𝑦 NUM iajs-2992 66 33 , , PUNCT iajs-2992 66 34 𝑒)| 𝑒)| VERB iajs-2992 66 35 ≀ ≀ PROPN iajs-2992 66 36 𝐺 𝐺 PROPN iajs-2992 66 37 ( ( PUNCT iajs-2992 66 38 π‘₯ π‘₯ PROPN iajs-2992 66 39 , , PUNCT iajs-2992 66 40 𝑑 𝑑 NOUN iajs-2992 66 41 ) ) PUNCT iajs-2992 67 1 + + CCONJ iajs-2992 67 2 𝑐 𝑐 PROPN iajs-2992 67 3 𝑦 𝑦 SYM iajs-2992 67 4 2 2 NUM iajs-2992 67 5 + + NUM iajs-2992 67 6 οΏ½ οΏ½ PROPN iajs-2992 67 7 ́ ́ NOUN iajs-2992 67 8 οΏ½ οΏ½ NOUN iajs-2992 67 9 𝑒 𝑒 PRON iajs-2992 67 10 2 2 NUM iajs-2992 67 11 , , PUNCT iajs-2992 67 12 where where SCONJ iajs-2992 67 13 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-2992 67 14 , , PUNCT iajs-2992 67 15 𝑑 𝑑 NOUN iajs-2992 67 16 ) ) PUNCT iajs-2992 67 17 ∈ ∈ PROPN iajs-2992 67 18 𝐿1(q),𝑒 𝐿1(q),𝑒 NUM iajs-2992 67 19 ∈ ∈ PROPN iajs-2992 67 20 π‘ˆ π‘ˆ PROPN iajs-2992 67 21 , , PUNCT iajs-2992 67 22 𝑐 𝑐 PROPN iajs-2992 67 23 , , PUNCT iajs-2992 67 24 𝑐́ 𝑐́ VERB iajs-2992 67 25 β‰₯ β‰₯ NOUN iajs-2992 67 26 0 0 NUM iajs-2992 67 27 , , PUNCT iajs-2992 67 28 π‘ˆ π‘ˆ PROPN iajs-2992 67 29 βŠ‚ βŠ‚ PUNCT iajs-2992 67 30 ℝ ℝ PROPN iajs-2992 67 31 , , PUNCT iajs-2992 67 32 is be AUX iajs-2992 67 33 compact(com compact(com NOUN iajs-2992 67 34 ) ) PUNCT iajs-2992 67 35 . . PUNCT iajs-2992 68 1 then then ADV iajs-2992 68 2 ∫ ∫ PROPN iajs-2992 68 3 𝑄 𝑄 PROPN iajs-2992 68 4 𝑔 𝑔 PROPN iajs-2992 68 5 ( ( PUNCT iajs-2992 68 6 π‘₯ π‘₯ PROPN iajs-2992 68 7 , , PUNCT iajs-2992 68 8 𝑦 𝑦 NOUN iajs-2992 68 9 , , PUNCT iajs-2992 68 10 𝑒 𝑒 NOUN iajs-2992 68 11 ) ) PUNCT iajs-2992 68 12 𝑑π‘₯ 𝑑π‘₯ VERB iajs-2992 68 13 is be AUX iajs-2992 68 14 cont cont ADJ iajs-2992 68 15 . . PUNCT iajs-2992 69 1 on on ADP iajs-2992 69 2 𝐿2(𝑄 𝐿2(𝑄 PROPN iajs-2992 69 3 ) ) PUNCT iajs-2992 69 4 w.r.t w.r.t NOUN iajs-2992 69 5 . . PUNCT iajs-2992 70 1 𝑦. 𝑦. PROPN iajs-2992 70 2 theorem theorem VERB iajs-2992 70 3 2.2 2.2 NUM iajs-2992 70 4 ( ( PUNCT iajs-2992 70 5 lp lp ADJ iajs-2992 70 6 cont cont NOUN iajs-2992 70 7 . . PUNCT iajs-2992 71 1 theorem)[13 theorem)[13 NOUN iajs-2992 71 2 ] ] PUNCT iajs-2992 71 3 : : PUNCT iajs-2992 71 4 in in ADP iajs-2992 71 5 addition addition NOUN iajs-2992 71 6 to to ADP iajs-2992 71 7 assums assums NOUN iajs-2992 71 8 ( ( PUNCT iajs-2992 71 9 a a X iajs-2992 71 10 ) ) PUNCT iajs-2992 71 11 , , PUNCT iajs-2992 71 12 if if SCONJ iajs-2992 71 13 οΏ½ οΏ½ NOUN iajs-2992 71 14 βƒ— βƒ— PART iajs-2992 71 15 οΏ½ οΏ½ PROPN iajs-2992 71 16 and and CCONJ iajs-2992 71 17 οΏ½ οΏ½ PROPN iajs-2992 71 18 βƒ— βƒ— PROPN iajs-2992 71 19 οΏ½ οΏ½ PROPN iajs-2992 71 20 + + CCONJ iajs-2992 71 21 𝛿 𝛿 PROPN iajs-2992 71 22 οΏ½ οΏ½ PROPN iajs-2992 71 23 βƒ— βƒ— NOUN iajs-2992 71 24 οΏ½ οΏ½ NOUN iajs-2992 71 25 are be AUX iajs-2992 71 26 the the DET iajs-2992 71 27 qsvs qsvs NOUN iajs-2992 71 28 corresponding corresponding NOUN iajs-2992 71 29 to to ADP iajs-2992 71 30 the the DET iajs-2992 71 31 bounded bounded PROPN iajs-2992 71 32 qcccvs qcccvs PROPN iajs-2992 71 33 οΏ½ οΏ½ PROPN iajs-2992 71 34 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 71 35 οΏ½ οΏ½ PROPN iajs-2992 71 36 and and CCONJ iajs-2992 71 37 οΏ½ οΏ½ PROPN iajs-2992 71 38 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 71 39 οΏ½ οΏ½ PROPN iajs-2992 71 40 + + CCONJ iajs-2992 71 41 𝛿 𝛿 PROPN iajs-2992 71 42 οΏ½ οΏ½ PROPN iajs-2992 71 43 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 71 44 οΏ½ οΏ½ PROPN iajs-2992 71 45 resp resp NOUN iajs-2992 71 46 . . PUNCT iajs-2992 72 1 in in ADP iajs-2992 72 2 𝐿2(𝑄 𝐿2(𝑄 PROPN iajs-2992 72 3 ) ) PUNCT iajs-2992 72 4 , , PUNCT iajs-2992 72 5 then then ADV iajs-2992 72 6 for for ADP iajs-2992 72 7 𝛿 𝛿 PROPN iajs-2992 72 8 ∈ ∈ PROPN iajs-2992 72 9 ℝ+ ℝ+ PUNCT iajs-2992 72 10 βˆ₯ βˆ₯ NUM iajs-2992 72 11 𝛿 𝛿 PROPN iajs-2992 72 12 οΏ½ οΏ½ PROPN iajs-2992 72 13 βƒ— βƒ— NOUN iajs-2992 72 14 οΏ½ οΏ½ PROPN iajs-2992 72 15 βˆ₯𝐿∞(𝐼,π‘³πŸ(𝛀))≀ βˆ₯𝐿∞(𝐼,π‘³πŸ(𝛀))≀ ADP iajs-2992 73 1 𝛿 𝛿 PRON iajs-2992 73 2 βˆ₯ βˆ₯ PUNCT iajs-2992 73 3 𝛿 𝛿 PROPN iajs-2992 73 4 οΏ½ οΏ½ PROPN iajs-2992 73 5 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 73 6 οΏ½ οΏ½ PROPN iajs-2992 73 7 βˆ₯π‘³πŸ(𝑸),βˆ₯ βˆ₯π‘³πŸ(𝑸),βˆ₯ PROPN iajs-2992 74 1 𝛿 𝛿 PROPN iajs-2992 74 2 οΏ½ οΏ½ PROPN iajs-2992 74 3 βƒ— βƒ— NOUN iajs-2992 74 4 οΏ½ οΏ½ PROPN iajs-2992 74 5 ∈ ∈ ADJ iajs-2992 74 6 βˆ₯π‘³πŸ(𝑰,𝑽)≀ βˆ₯π‘³πŸ(𝑰,𝑽)≀ NOUN iajs-2992 74 7 𝛿 𝛿 ADJ iajs-2992 74 8 βˆ₯ βˆ₯ PUNCT iajs-2992 74 9 𝛿 𝛿 PROPN iajs-2992 74 10 οΏ½ οΏ½ PROPN iajs-2992 74 11 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 74 12 οΏ½ οΏ½ PROPN iajs-2992 74 13 βˆ₯π‘³πŸ(𝑸)andβˆ₯ βˆ₯π‘³πŸ(𝑸)andβˆ₯ PROPN iajs-2992 74 14 𝛿 𝛿 PROPN iajs-2992 74 15 οΏ½ οΏ½ PROPN iajs-2992 74 16 βƒ— βƒ— NOUN iajs-2992 74 17 οΏ½ οΏ½ PROPN iajs-2992 74 18 βˆ₯𝐿2𝑄)≀ βˆ₯𝐿2𝑄)≀ PROPN iajs-2992 74 19 𝛿 𝛿 PRON iajs-2992 74 20 βˆ₯ βˆ₯ PUNCT iajs-2992 74 21 𝛿 𝛿 PROPN iajs-2992 74 22 οΏ½ οΏ½ PROPN iajs-2992 74 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 74 24 οΏ½ οΏ½ PROPN iajs-2992 74 25 βˆ₯π‘³πŸ(𝑸 βˆ₯π‘³πŸ(𝑸 PROPN iajs-2992 74 26 ) ) PUNCT iajs-2992 74 27 . . PUNCT iajs-2992 75 1 assums assums PROPN iajs-2992 75 2 ( ( PUNCT iajs-2992 75 3 c c X iajs-2992 75 4 ): ): PUNCT iajs-2992 75 5 assume assume VERB iajs-2992 75 6 that that SCONJ iajs-2992 75 7 for for ADP iajs-2992 75 8 each each PRON iajs-2992 75 9 ( ( PUNCT iajs-2992 75 10 𝑙 𝑙 X iajs-2992 75 11 = = SYM iajs-2992 75 12 0,1,2 0,1,2 NUM iajs-2992 75 13 & & CCONJ iajs-2992 75 14 𝑖 𝑖 NOUN iajs-2992 75 15 = = NOUN iajs-2992 75 16 1,2,3,4 1,2,3,4 NUM iajs-2992 75 17 ) ) PUNCT iajs-2992 75 18 , , PUNCT iajs-2992 75 19 the the DET iajs-2992 75 20 functions function NOUN iajs-2992 75 21 𝑓𝑖 𝑓𝑖 PROPN iajs-2992 75 22 , , PUNCT iajs-2992 75 23 𝑓𝑖𝑦𝑖 𝑓𝑖𝑦𝑖 ADJ iajs-2992 75 24 , , PUNCT iajs-2992 75 25 𝑓𝑖𝑒𝑖 𝑓𝑖𝑒𝑖 NOUN iajs-2992 75 26 , , PUNCT iajs-2992 75 27 𝑔𝑙𝑖𝑦𝑖 𝑔𝑙𝑖𝑦𝑖 ADJ iajs-2992 75 28 , , PUNCT iajs-2992 75 29 𝑔𝑙𝑖𝑒𝑖 𝑔𝑙𝑖𝑒𝑖 ADV iajs-2992 75 30 are be AUX iajs-2992 75 31 of of ADP iajs-2992 75 32 carat carat NOUN iajs-2992 75 33 on on ADP iajs-2992 75 34 𝑄 𝑄 PROPN iajs-2992 75 35 Γ— Γ— NOUN iajs-2992 75 36 ( ( PUNCT iajs-2992 75 37 ℝ ℝ PROPN iajs-2992 75 38 Γ— Γ— NOUN iajs-2992 75 39 π‘ˆβ€² π‘ˆβ€² ADJ iajs-2992 75 40 ) ) PUNCT iajs-2992 75 41 , , PUNCT iajs-2992 75 42 where where SCONJ iajs-2992 75 43 ( ( PUNCT iajs-2992 75 44 π‘ˆβ€² π‘ˆβ€² ADJ iajs-2992 75 45 is be AUX iajs-2992 75 46 an an DET iajs-2992 75 47 open open ADJ iajs-2992 75 48 set set NOUN iajs-2992 75 49 containing contain VERB iajs-2992 75 50 π‘ˆ π‘ˆ PROPN iajs-2992 75 51 ) ) PUNCT iajs-2992 75 52 , , PUNCT iajs-2992 75 53 s.t s.t PROPN iajs-2992 75 54 . . PROPN iajs-2992 75 55 ( ( PUNCT iajs-2992 75 56 for(π‘₯ for(π‘₯ PROPN iajs-2992 75 57 , , PUNCT iajs-2992 75 58 𝑑 𝑑 NOUN iajs-2992 75 59 ) ) PUNCT iajs-2992 75 60 ∈ ∈ PROPN iajs-2992 75 61 𝑄 𝑄 PROPN iajs-2992 75 62 ) ) PUNCT iajs-2992 75 63 : : PUNCT iajs-2992 75 64 |𝑓𝑖𝑦𝑖 |𝑓𝑖𝑦𝑖 ADV iajs-2992 75 65 ( ( PUNCT iajs-2992 75 66 π‘₯ π‘₯ PROPN iajs-2992 75 67 , , PUNCT iajs-2992 75 68 𝑑 𝑑 PROPN iajs-2992 75 69 , , PUNCT iajs-2992 75 70 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 75 71 , , PUNCT iajs-2992 75 72 𝑒𝑖)| 𝑒𝑖)| VERB iajs-2992 75 73 ≀ ≀ ADJ iajs-2992 75 74 𝐿𝑖 𝐿𝑖 NOUN iajs-2992 75 75 , , PUNCT iajs-2992 75 76 |𝑓𝑖𝑦𝑖 |𝑓𝑖𝑦𝑖 PROPN iajs-2992 75 77 ( ( PUNCT iajs-2992 75 78 π‘₯ π‘₯ NOUN iajs-2992 75 79 , , PUNCT iajs-2992 75 80 𝑑 𝑑 PROPN iajs-2992 75 81 , , PUNCT iajs-2992 75 82 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 75 83 , , PUNCT iajs-2992 75 84 𝑒𝑖)| 𝑒𝑖)| ADJ iajs-2992 75 85 ≀ ≀ NUM iajs-2992 75 86 𝐿′𝑖 𝐿′𝑖 NOUN iajs-2992 75 87 , , PUNCT iajs-2992 75 88 |𝑔𝑖𝑦𝑖 |𝑔𝑖𝑦𝑖 PROPN iajs-2992 75 89 ( ( PUNCT iajs-2992 75 90 π‘₯ π‘₯ PROPN iajs-2992 75 91 , , PUNCT iajs-2992 75 92 𝑑 𝑑 PROPN iajs-2992 75 93 , , PUNCT iajs-2992 75 94 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 75 95 , , PUNCT iajs-2992 75 96 𝑒𝑖)| 𝑒𝑖)| ADP iajs-2992 75 97 ≀ ≀ NUM iajs-2992 75 98 𝐺𝑙𝑖5(π‘₯ 𝐺𝑙𝑖5(π‘₯ PROPN iajs-2992 75 99 , , PUNCT iajs-2992 75 100 𝑑 𝑑 NOUN iajs-2992 75 101 ) ) PUNCT iajs-2992 75 102 + + CCONJ iajs-2992 75 103 𝐺𝑙𝑖5(π‘₯ 𝐺𝑙𝑖5(π‘₯ ADP iajs-2992 75 104 , , PUNCT iajs-2992 75 105 𝑑 𝑑 NOUN iajs-2992 75 106 ) ) PUNCT iajs-2992 75 107 ∣ ∣ ADJ iajs-2992 75 108 π‘¦π‘–βˆ£ π‘¦π‘–βˆ£ NOUN iajs-2992 75 109 , , PUNCT iajs-2992 75 110 |𝑔𝑖𝑒𝑖 |𝑔𝑖𝑒𝑖 ADV iajs-2992 75 111 ( ( PUNCT iajs-2992 75 112 π‘₯ π‘₯ NOUN iajs-2992 75 113 , , PUNCT iajs-2992 75 114 𝑑 𝑑 PROPN iajs-2992 75 115 , , PUNCT iajs-2992 75 116 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 75 117 , , PUNCT iajs-2992 75 118 𝑒𝑖)| 𝑒𝑖)| PROPN iajs-2992 75 119 ≀ ≀ PROPN iajs-2992 75 120 𝐺𝑙𝑖6(π‘₯ 𝐺𝑙𝑖6(π‘₯ PROPN iajs-2992 75 121 , , PUNCT iajs-2992 75 122 𝑑 𝑑 PROPN iajs-2992 75 123 ) ) PUNCT iajs-2992 75 124 + + CCONJ iajs-2992 76 1 𝐺𝑙𝑖6(π‘₯ 𝐺𝑙𝑖6(π‘₯ PROPN iajs-2992 76 2 , , PUNCT iajs-2992 76 3 𝑑 𝑑 PROPN iajs-2992 76 4 ) ) PUNCT iajs-2992 76 5 ∣ ∣ PROPN iajs-2992 76 6 π‘¦π‘–βˆ£,where𝑦𝑖 π‘¦π‘–βˆ£,where𝑦𝑖 PROPN iajs-2992 76 7 , , PUNCT iajs-2992 76 8 𝑒𝑖 𝑒𝑖 PRON iajs-2992 76 9 ∈ ∈ PROPN iajs-2992 76 10 ℝ ℝ PROPN iajs-2992 76 11 , , PUNCT iajs-2992 76 12 𝐺𝑙𝑖5 𝐺𝑙𝑖5 NUM iajs-2992 76 13 , , PUNCT iajs-2992 76 14 𝐺𝑙𝑖6 𝐺𝑙𝑖6 PROPN iajs-2992 76 15 ∈ ∈ PROPN iajs-2992 76 16 𝐿2(𝑄),𝐺𝑙𝑖5 𝐿2(𝑄),𝐺𝑙𝑖5 NOUN iajs-2992 76 17 , , PUNCT iajs-2992 76 18 𝐺𝑙𝑖6 𝐺𝑙𝑖6 NUM iajs-2992 76 19 β‰₯ β‰₯ NOUN iajs-2992 76 20 0 0 NUM iajs-2992 76 21 . . PUNCT iajs-2992 76 22 main main ADJ iajs-2992 76 23 results result NOUN iajs-2992 76 24 3.existence 3.existence NUM iajs-2992 76 25 of of ADP iajs-2992 76 26 the the DET iajs-2992 76 27 cqocccv cqocccv NOUN iajs-2992 76 28 theorem theorem VERB iajs-2992 76 29 3.1 3.1 NUM iajs-2992 76 30 : : PUNCT iajs-2992 76 31 in in ADP iajs-2992 76 32 addition addition NOUN iajs-2992 76 33 to to ADP iajs-2992 76 34 assums assums NOUN iajs-2992 76 35 ( ( PUNCT iajs-2992 76 36 ( ( PUNCT iajs-2992 76 37 a a NOUN iajs-2992 76 38 ) ) PUNCT iajs-2992 76 39 & & CCONJ iajs-2992 76 40 ( ( PUNCT iajs-2992 76 41 b b NOUN iajs-2992 76 42 ) ) PUNCT iajs-2992 76 43 ) ) PUNCT iajs-2992 76 44 , , PUNCT iajs-2992 76 45 if if SCONJ iajs-2992 76 46 the the DET iajs-2992 76 47 set set NOUN iajs-2992 76 48 οΏ½ οΏ½ PROPN iajs-2992 76 49 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 76 50 οΏ½ οΏ½ PROPN iajs-2992 76 51 is be AUX iajs-2992 76 52 co co VERB iajs-2992 76 53 and and CCONJ iajs-2992 76 54 com com PROPN iajs-2992 76 55 . . PROPN iajs-2992 76 56 , , PUNCT iajs-2992 76 57 οΏ½ οΏ½ PROPN iajs-2992 76 58 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 76 59 οΏ½ οΏ½ PROPN iajs-2992 76 60 𝐴 𝐴 PROPN iajs-2992 76 61 β‰  β‰  PROPN iajs-2992 76 62 πœ™ πœ™ NOUN iajs-2992 76 63 , , PUNCT iajs-2992 76 64 the the DET iajs-2992 76 65 function function NOUN iajs-2992 76 66 𝑓𝑖 𝑓𝑖 NOUN iajs-2992 76 67 ( ( PUNCT iajs-2992 76 68 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 76 69 = = SYM iajs-2992 76 70 1,2,3,4 1,2,3,4 NUM iajs-2992 76 71 ) ) PUNCT iajs-2992 76 72 has have VERB iajs-2992 76 73 the the DET iajs-2992 76 74 form form NOUN iajs-2992 76 75 : : PUNCT iajs-2992 76 76 𝑓𝑖(π‘₯ 𝑓𝑖(π‘₯ NUM iajs-2992 76 77 , , PUNCT iajs-2992 76 78 𝑑 𝑑 PROPN iajs-2992 76 79 , , PUNCT iajs-2992 76 80 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 76 81 , , PUNCT iajs-2992 76 82 𝑒𝑖 𝑒𝑖 INTJ iajs-2992 76 83 ) ) PUNCT iajs-2992 76 84 = = SYM iajs-2992 76 85 𝑓𝑖1(π‘₯ 𝑓𝑖1(π‘₯ PROPN iajs-2992 76 86 , , PUNCT iajs-2992 76 87 𝑑 𝑑 PROPN iajs-2992 76 88 , , PUNCT iajs-2992 76 89 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 76 90 ) ) PUNCT iajs-2992 76 91 + + CCONJ iajs-2992 76 92 𝑓𝑖2(π‘₯ 𝑓𝑖2(π‘₯ PROPN iajs-2992 76 93 , , PUNCT iajs-2992 76 94 𝑑)𝑒𝑖 𝑑)𝑒𝑖 PROPN iajs-2992 76 95 , , PUNCT iajs-2992 76 96 with with ADP iajs-2992 76 97 |𝑓𝑖1(π‘₯ |𝑓𝑖1(π‘₯ PROPN iajs-2992 76 98 , , PUNCT iajs-2992 76 99 𝑑 𝑑 PROPN iajs-2992 76 100 , , PUNCT iajs-2992 76 101 𝑦𝑖)| 𝑦𝑖)| PROPN iajs-2992 76 102 ≀ ≀ X iajs-2992 76 103 νœ‚π‘–(π‘₯ νœ‚π‘–(π‘₯ NUM iajs-2992 76 104 , , PUNCT iajs-2992 76 105 𝑑 𝑑 X iajs-2992 76 106 ) ) PUNCT iajs-2992 77 1 + + CCONJ iajs-2992 77 2 𝑐𝑖 𝑐𝑖 PART iajs-2992 77 3 ∣ ∣ PROPN iajs-2992 77 4 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 77 5 ∣,|𝑓𝑖2(π‘₯ ∣,|𝑓𝑖2(π‘₯ PROPN iajs-2992 77 6 , , PUNCT iajs-2992 77 7 𝑑)| 𝑑)| PROPN iajs-2992 77 8 ≀ ≀ PUNCT iajs-2992 78 1 𝐾𝑖 𝐾𝑖 PROPN iajs-2992 78 2 , , PUNCT iajs-2992 78 3 νœ‚π‘– νœ‚π‘– PROPN iajs-2992 78 4 ∈ ∈ PROPN iajs-2992 78 5 𝐿2(q 𝐿2(q NUM iajs-2992 78 6 ) ) PUNCT iajs-2992 78 7 , , PUNCT iajs-2992 78 8 𝑐𝑖 𝑐𝑖 NOUN iajs-2992 78 9 β‰₯ β‰₯ NOUN iajs-2992 78 10 0 0 NUM iajs-2992 78 11 . . PUNCT iajs-2992 78 12 ihjpas ihjpas PROPN iajs-2992 78 13 . . PUNCT iajs-2992 79 1 36(2)2023 36(2)2023 NUM iajs-2992 79 2 334 334 NUM iajs-2992 79 3 𝑔1𝑖 𝑔1𝑖 ADJ iajs-2992 79 4 is be AUX iajs-2992 79 5 independent independent ADJ iajs-2992 79 6 of of ADP iajs-2992 79 7 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 79 8 , , PUNCT iajs-2992 79 9 𝑔0𝑖 𝑔0𝑖 NOUN iajs-2992 79 10 and and CCONJ iajs-2992 79 11 𝑔2𝑖are 𝑔2𝑖are PROPN iajs-2992 79 12 co co NOUN iajs-2992 79 13 w.r.t w.r.t PROPN iajs-2992 79 14 . . PUNCT iajs-2992 80 1 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 80 2 for for ADP iajs-2992 80 3 fixed fix VERB iajs-2992 80 4 ( ( PUNCT iajs-2992 80 5 π‘₯ π‘₯ NOUN iajs-2992 80 6 , , PUNCT iajs-2992 80 7 𝑑 𝑑 PROPN iajs-2992 80 8 , , PUNCT iajs-2992 80 9 𝑦𝑖 𝑦𝑖 NOUN iajs-2992 80 10 ) ) PUNCT iajs-2992 80 11 , , PUNCT iajs-2992 80 12 βˆ€ βˆ€ PUNCT iajs-2992 80 13 𝑖 𝑖 NOUN iajs-2992 81 1 = = NOUN iajs-2992 81 2 1,2,3,4 1,2,3,4 NUM iajs-2992 81 3 . . PUNCT iajs-2992 82 1 then then ADV iajs-2992 82 2 there there PRON iajs-2992 82 3 is be VERB iajs-2992 82 4 a a DET iajs-2992 82 5 cqocccv cqocccv NOUN iajs-2992 82 6 . . PUNCT iajs-2992 83 1 proof proof NOUN iajs-2992 83 2 : : PUNCT iajs-2992 83 3 from from ADP iajs-2992 83 4 the the DET iajs-2992 83 5 assum assum NOUN iajs-2992 83 6 on on ADP iajs-2992 83 7 οΏ½ οΏ½ PROPN iajs-2992 83 8 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 83 9 οΏ½ οΏ½ PROPN iajs-2992 83 10 βŠ‚ βŠ‚ PROPN iajs-2992 83 11 ℝ ℝ PROPN iajs-2992 83 12 , , PUNCT iajs-2992 83 13 οΏ½ οΏ½ PROPN iajs-2992 83 14 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 83 15 οΏ½ οΏ½ PROPN iajs-2992 83 16 is be AUX iajs-2992 83 17 weakly weakly ADV iajs-2992 83 18 compact compact ADJ iajs-2992 83 19 ( ( PUNCT iajs-2992 83 20 wcom wcom NOUN iajs-2992 83 21 ) ) PUNCT iajs-2992 83 22 , , PUNCT iajs-2992 83 23 since since SCONJ iajs-2992 83 24 οΏ½ οΏ½ PROPN iajs-2992 83 25 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 83 26 οΏ½ οΏ½ PROPN iajs-2992 83 27 𝐴 𝐴 PROPN iajs-2992 83 28 β‰  β‰  PROPN iajs-2992 83 29 πœ™ πœ™ NOUN iajs-2992 83 30 , , PUNCT iajs-2992 83 31 then then ADV iajs-2992 83 32 there there PRON iajs-2992 83 33 is be VERB iajs-2992 83 34 a a DET iajs-2992 83 35 minimum minimum ADJ iajs-2992 83 36 sequence(seq sequence(seq NOUN iajs-2992 83 37 . . PUNCT iajs-2992 83 38 ) ) PUNCT iajs-2992 84 1 { { PUNCT iajs-2992 84 2 οΏ½ οΏ½ PROPN iajs-2992 84 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 84 4 οΏ½ οΏ½ PROPN iajs-2992 84 5 π‘˜ π‘˜ NOUN iajs-2992 84 6 } } PUNCT iajs-2992 84 7 = = SYM iajs-2992 84 8 { { PUNCT iajs-2992 84 9 ( ( PUNCT iajs-2992 84 10 𝑒1π‘˜ 𝑒1π‘˜ PROPN iajs-2992 84 11 , , PUNCT iajs-2992 84 12 𝑒2π‘˜ 𝑒2π‘˜ PROPN iajs-2992 84 13 , , PUNCT iajs-2992 84 14 𝑒3π‘˜ 𝑒3π‘˜ PROPN iajs-2992 84 15 , , PUNCT iajs-2992 84 16 𝑒4π‘˜ 𝑒4π‘˜ NOUN iajs-2992 84 17 ) ) PUNCT iajs-2992 84 18 } } PUNCT iajs-2992 84 19 ∈ ∈ PROPN iajs-2992 84 20 οΏ½ οΏ½ PROPN iajs-2992 84 21 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 84 22 οΏ½ οΏ½ PROPN iajs-2992 84 23 𝐴 𝐴 PROPN iajs-2992 84 24 , , PUNCT iajs-2992 84 25 βˆ€π‘˜ βˆ€π‘˜ X iajs-2992 84 26 s.t s.t PROPN iajs-2992 84 27 . . PROPN iajs-2992 84 28 π‘™π‘–π‘š π‘™π‘–π‘š PROPN iajs-2992 84 29 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 84 30 𝐺0( 𝐺0( SYM iajs-2992 84 31 οΏ½ οΏ½ NOUN iajs-2992 84 32 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 84 33 οΏ½ οΏ½ PROPN iajs-2992 84 34 π‘˜ π‘˜ NOUN iajs-2992 84 35 ) ) PUNCT iajs-2992 84 36 = = PUNCT iajs-2992 84 37 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 84 38 οΏ½ οΏ½ PROPN iajs-2992 84 39 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 84 40 οΏ½ οΏ½ NOUN iajs-2992 84 41 π‘˜βˆˆ π‘˜βˆˆ PROPN iajs-2992 84 42 οΏ½ οΏ½ PROPN iajs-2992 84 43 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 84 44 οΏ½ οΏ½ PROPN iajs-2992 84 45 𝐴 𝐴 PROPN iajs-2992 84 46 𝐺0( 𝐺0( NUM iajs-2992 84 47 οΏ½ οΏ½ PROPN iajs-2992 84 48 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 84 49 οΏ½ οΏ½ PROPN iajs-2992 84 50 ) ) PUNCT iajs-2992 84 51 . . PUNCT iajs-2992 85 1 since since SCONJ iajs-2992 85 2 οΏ½ οΏ½ PROPN iajs-2992 85 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 85 4 οΏ½ οΏ½ PROPN iajs-2992 85 5 π‘˜ π‘˜ PROPN iajs-2992 85 6 ∈ ∈ PROPN iajs-2992 85 7 οΏ½ οΏ½ PROPN iajs-2992 85 8 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 85 9 οΏ½ οΏ½ PROPN iajs-2992 85 10 𝐴 𝐴 PROPN iajs-2992 85 11 , , PUNCT iajs-2992 85 12 βˆ€π‘˜ βˆ€π‘˜ NOUN iajs-2992 85 13 and and CCONJ iajs-2992 85 14 οΏ½ οΏ½ PROPN iajs-2992 85 15 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 85 16 οΏ½ οΏ½ PROPN iajs-2992 85 17 is be AUX iajs-2992 85 18 wcom wcom NOUN iajs-2992 85 19 , , PUNCT iajs-2992 85 20 there there PRON iajs-2992 85 21 exists exist VERB iajs-2992 85 22 a a DET iajs-2992 85 23 subsequence subsequence NOUN iajs-2992 85 24 of of ADP iajs-2992 85 25 { { PUNCT iajs-2992 85 26 οΏ½ οΏ½ PROPN iajs-2992 85 27 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 85 28 οΏ½ οΏ½ PROPN iajs-2992 85 29 π‘˜ π‘˜ PRON iajs-2992 85 30 } } PUNCT iajs-2992 85 31 say say VERB iajs-2992 85 32 again again ADV iajs-2992 85 33 { { PUNCT iajs-2992 85 34 οΏ½ οΏ½ PROPN iajs-2992 85 35 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 85 36 οΏ½ οΏ½ PROPN iajs-2992 85 37 π‘˜ π‘˜ PROPN iajs-2992 85 38 } } PUNCT iajs-2992 85 39 s.t s.t PROPN iajs-2992 85 40 . . PROPN iajs-2992 85 41 . . PUNCT iajs-2992 86 1 οΏ½ οΏ½ PROPN iajs-2992 86 2 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 86 3 οΏ½ οΏ½ PROPN iajs-2992 86 4 π‘˜ π‘˜ PROPN iajs-2992 86 5 β†’ β†’ SYM iajs-2992 86 6 οΏ½ οΏ½ PROPN iajs-2992 86 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 86 8 οΏ½ οΏ½ PROPN iajs-2992 86 9 weakly weakly ADJ iajs-2992 86 10 ( ( PUNCT iajs-2992 86 11 wk wk NOUN iajs-2992 86 12 ) ) PUNCT iajs-2992 86 13 in in ADP iajs-2992 86 14 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 86 15 ) ) PUNCT iajs-2992 86 16 and and CCONJ iajs-2992 86 17 βˆ₯ βˆ₯ PROPN iajs-2992 86 18 οΏ½ οΏ½ PROPN iajs-2992 86 19 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 86 20 οΏ½ οΏ½ PROPN iajs-2992 86 21 π‘˜ π‘˜ DET iajs-2992 86 22 βˆ₯π‘³πŸ(𝐐)≀ βˆ₯π‘³πŸ(𝐐)≀ NOUN iajs-2992 86 23 𝑑,βˆ€π‘˜. 𝑑,βˆ€π‘˜. PUNCT iajs-2992 86 24 from from ADP iajs-2992 86 25 theorem theorem ADJ iajs-2992 86 26 1 1 NUM iajs-2992 86 27 , , PUNCT iajs-2992 86 28 corresponding correspond VERB iajs-2992 86 29 to to ADP iajs-2992 86 30 the the DET iajs-2992 86 31 seq seq NOUN iajs-2992 86 32 . . PUNCT iajs-2992 87 1 qcv qcv PROPN iajs-2992 87 2 { { PUNCT iajs-2992 87 3 οΏ½ οΏ½ PROPN iajs-2992 87 4 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 87 5 οΏ½ οΏ½ PROPN iajs-2992 87 6 π‘˜ π‘˜ NOUN iajs-2992 87 7 } } PUNCT iajs-2992 87 8 the the DET iajs-2992 87 9 wf wf PROPN iajs-2992 87 10 of of ADP iajs-2992 87 11 the the DET iajs-2992 87 12 qses qse NOUN iajs-2992 87 13 has have VERB iajs-2992 87 14 β€œ " PUNCT iajs-2992 87 15 a a DET iajs-2992 87 16 unique unique ADJ iajs-2992 87 17 ” " PUNCT iajs-2992 87 18 solution solution NOUN iajs-2992 87 19 { { PUNCT iajs-2992 87 20 οΏ½ οΏ½ PROPN iajs-2992 87 21 βƒ— βƒ— NOUN iajs-2992 87 22 οΏ½ οΏ½ PROPN iajs-2992 87 23 π‘˜ π‘˜ PRON iajs-2992 87 24 = = SYM iajs-2992 87 25 οΏ½ οΏ½ PROPN iajs-2992 87 26 βƒ— βƒ— NOUN iajs-2992 87 27 οΏ½ οΏ½ NOUN iajs-2992 87 28 π‘’π‘˜ π‘’π‘˜ NOUN iajs-2992 87 29 } } PUNCT iajs-2992 87 30 and and CCONJ iajs-2992 87 31 βˆ₯ βˆ₯ PUNCT iajs-2992 87 32 οΏ½ οΏ½ NOUN iajs-2992 87 33 βƒ— βƒ— NOUN iajs-2992 87 34 οΏ½ οΏ½ PROPN iajs-2992 87 35 π‘˜ π‘˜ PRON iajs-2992 87 36 βˆ₯π‘³πŸ(𝑰,𝑽 βˆ₯π‘³πŸ(𝑰,𝑽 NUM iajs-2992 87 37 ) ) PUNCT iajs-2992 87 38 , , PUNCT iajs-2992 87 39 βˆ₯ βˆ₯ PROPN iajs-2992 87 40 οΏ½ οΏ½ NOUN iajs-2992 87 41 βƒ— βƒ— NOUN iajs-2992 87 42 οΏ½ οΏ½ PROPN iajs-2992 87 43 π‘˜π‘‘ π‘˜π‘‘ PROPN iajs-2992 87 44 βˆ₯π‘³πŸ(𝑸 βˆ₯π‘³πŸ(𝑸 PROPN iajs-2992 87 45 ) ) PUNCT iajs-2992 87 46 are be AUX iajs-2992 87 47 bounded bound VERB iajs-2992 87 48 , , PUNCT iajs-2992 87 49 then then ADV iajs-2992 87 50 by by ADP iajs-2992 87 51 alaoglu alaoglu PROPN iajs-2992 87 52 ’s ’s PART iajs-2992 87 53 theorem theorem NOUN iajs-2992 87 54 ( ( PUNCT iajs-2992 87 55 ath ath NOUN iajs-2992 87 56 ) ) PUNCT iajs-2992 87 57 , , PUNCT iajs-2992 87 58 there there PRON iajs-2992 87 59 exists exist VERB iajs-2992 87 60 a a DET iajs-2992 87 61 subsequence subsequence NOUN iajs-2992 87 62 of of ADP iajs-2992 87 63 { { PUNCT iajs-2992 87 64 οΏ½ οΏ½ PROPN iajs-2992 87 65 βƒ— βƒ— NOUN iajs-2992 87 66 οΏ½ οΏ½ NOUN iajs-2992 87 67 π‘˜ π‘˜ PRON iajs-2992 87 68 } } PUNCT iajs-2992 87 69 and and CCONJ iajs-2992 87 70 { { PUNCT iajs-2992 87 71 οΏ½ οΏ½ PROPN iajs-2992 87 72 βƒ— βƒ— NOUN iajs-2992 87 73 οΏ½ οΏ½ NOUN iajs-2992 87 74 π‘˜π‘‘ π‘˜π‘‘ NOUN iajs-2992 87 75 } } PUNCT iajs-2992 87 76 , , PUNCT iajs-2992 87 77 say say VERB iajs-2992 87 78 again again ADV iajs-2992 87 79 { { PUNCT iajs-2992 87 80 οΏ½ οΏ½ PROPN iajs-2992 87 81 βƒ— βƒ— NOUN iajs-2992 87 82 οΏ½ οΏ½ NOUN iajs-2992 87 83 π‘˜ π‘˜ PRON iajs-2992 87 84 } } PUNCT iajs-2992 87 85 and and CCONJ iajs-2992 87 86 { { PUNCT iajs-2992 87 87 οΏ½ οΏ½ PROPN iajs-2992 87 88 βƒ— βƒ— NOUN iajs-2992 87 89 οΏ½ οΏ½ NOUN iajs-2992 87 90 π‘˜π‘‘ π‘˜π‘‘ NOUN iajs-2992 87 91 } } PUNCT iajs-2992 87 92 , , PUNCT iajs-2992 87 93 s.t s.t PROPN iajs-2992 87 94 . . PROPN iajs-2992 87 95 οΏ½ οΏ½ PROPN iajs-2992 87 96 βƒ— βƒ— NOUN iajs-2992 87 97 οΏ½ οΏ½ PROPN iajs-2992 87 98 π‘˜ π‘˜ PRON iajs-2992 87 99 β†’ β†’ SYM iajs-2992 87 100 οΏ½ οΏ½ NOUN iajs-2992 87 101 βƒ— βƒ— NOUN iajs-2992 87 102 οΏ½ οΏ½ PROPN iajs-2992 87 103 wk wk NOUN iajs-2992 87 104 in in ADP iajs-2992 87 105 π‘³πŸ(𝑰 π‘³πŸ(𝑰 PROPN iajs-2992 87 106 , , PUNCT iajs-2992 87 107 𝑽 𝑽 PROPN iajs-2992 87 108 ) ) PUNCT iajs-2992 87 109 , , PUNCT iajs-2992 87 110 οΏ½ οΏ½ PROPN iajs-2992 87 111 βƒ— βƒ— NOUN iajs-2992 87 112 οΏ½ οΏ½ PROPN iajs-2992 87 113 π‘˜π‘‘ π‘˜π‘‘ PROPN iajs-2992 87 114 β†’ β†’ SYM iajs-2992 87 115 οΏ½ οΏ½ PROPN iajs-2992 87 116 βƒ— βƒ— NOUN iajs-2992 87 117 οΏ½ οΏ½ PROPN iajs-2992 87 118 𝑑 𝑑 X iajs-2992 87 119 wk wk INTJ iajs-2992 87 120 in in ADP iajs-2992 87 121 ( ( PUNCT iajs-2992 87 122 𝐿2(𝑄))4 𝐿2(𝑄))4 PROPN iajs-2992 87 123 . . PUNCT iajs-2992 88 1 now now ADV iajs-2992 88 2 for for ADP iajs-2992 88 3 each each DET iajs-2992 88 4 π‘˜. π‘˜. NOUN iajs-2992 88 5 and and CCONJ iajs-2992 88 6 by by ADP iajs-2992 88 7 applying apply VERB iajs-2992 88 8 the the DET iajs-2992 88 9 acth[14 acth[14 PROPN iajs-2992 88 10 ] ] PUNCT iajs-2992 88 11 , , PUNCT iajs-2992 88 12 there there PRON iajs-2992 88 13 is be VERB iajs-2992 88 14 a a DET iajs-2992 88 15 subsequence subsequence NOUN iajs-2992 88 16 of{ of{ NUM iajs-2992 88 17 οΏ½ οΏ½ NOUN iajs-2992 88 18 βƒ— βƒ— NOUN iajs-2992 88 19 οΏ½ οΏ½ PROPN iajs-2992 88 20 π‘˜ π‘˜ PRON iajs-2992 88 21 } } PUNCT iajs-2992 88 22 say say VERB iajs-2992 88 23 a a DET iajs-2992 88 24 gain gain NOUN iajs-2992 88 25 { { PUNCT iajs-2992 88 26 οΏ½ οΏ½ PROPN iajs-2992 88 27 βƒ— βƒ— NOUN iajs-2992 88 28 οΏ½ οΏ½ PROPN iajs-2992 88 29 π‘˜ π‘˜ PRON iajs-2992 88 30 } } PUNCT iajs-2992 88 31 s.t s.t PROPN iajs-2992 88 32 . . PROPN iajs-2992 88 33 οΏ½ οΏ½ PROPN iajs-2992 88 34 βƒ— βƒ— NOUN iajs-2992 88 35 οΏ½ οΏ½ PROPN iajs-2992 88 36 π‘˜ π‘˜ PRON iajs-2992 88 37 β†’ β†’ SYM iajs-2992 88 38 οΏ½ οΏ½ NOUN iajs-2992 88 39 βƒ— βƒ— NOUN iajs-2992 88 40 οΏ½ οΏ½ PROPN iajs-2992 88 41 strongly strongly ADV iajs-2992 88 42 ( ( PUNCT iajs-2992 88 43 st st PROPN iajs-2992 88 44 ) ) PUNCT iajs-2992 88 45 in in ADP iajs-2992 88 46 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 88 47 ) ) PUNCT iajs-2992 88 48 . . PUNCT iajs-2992 89 1 now now ADV iajs-2992 89 2 , , PUNCT iajs-2992 89 3 for for ADP iajs-2992 89 4 each each DET iajs-2992 89 5 π‘˜ π‘˜ NOUN iajs-2992 89 6 , , PUNCT iajs-2992 89 7 substituting substitute VERB iajs-2992 89 8 the the DET iajs-2992 89 9 qsvs qsvs PROPN iajs-2992 89 10 οΏ½ οΏ½ NOUN iajs-2992 89 11 βƒ— βƒ— NOUN iajs-2992 89 12 οΏ½ οΏ½ NOUN iajs-2992 89 13 π‘˜ π‘˜ NOUN iajs-2992 89 14 in in ADP iajs-2992 89 15 the the DET iajs-2992 89 16 wf wf PROPN iajs-2992 89 17 ( ( PUNCT iajs-2992 89 18 ( ( PUNCT iajs-2992 89 19 10 10 NUM iajs-2992 89 20 ) ) PUNCT iajs-2992 89 21 , , PUNCT iajs-2992 89 22 ( ( PUNCT iajs-2992 89 23 12 12 NUM iajs-2992 89 24 ) ) PUNCT iajs-2992 89 25 , , PUNCT iajs-2992 89 26 ( ( PUNCT iajs-2992 89 27 14 14 NUM iajs-2992 89 28 ) ) PUNCT iajs-2992 89 29 , , PUNCT iajs-2992 89 30 ( ( PUNCT iajs-2992 89 31 16 16 NUM iajs-2992 89 32 ) ) PUNCT iajs-2992 89 33 ) ) PUNCT iajs-2992 89 34 , , PUNCT iajs-2992 89 35 multiplying multiply VERB iajs-2992 89 36 both both DET iajs-2992 89 37 sides side NOUN iajs-2992 89 38 ( ( PUNCT iajs-2992 89 39 mbss mbss NOUN iajs-2992 89 40 ) ) PUNCT iajs-2992 89 41 of of ADP iajs-2992 89 42 each each DET iajs-2992 89 43 one one NUM iajs-2992 89 44 by by ADP iajs-2992 89 45 πœ™π‘–(𝑑 πœ™π‘–(𝑑 NUM iajs-2992 89 46 ) ) PUNCT iajs-2992 89 47 , , PUNCT iajs-2992 89 48 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 89 49 = = SYM iajs-2992 89 50 1,2,3,4 1,2,3,4 NUM iajs-2992 89 51 ( ( PUNCT iajs-2992 89 52 with with ADP iajs-2992 89 53 πœ™π‘– πœ™π‘– NOUN iajs-2992 89 54 ∈ ∈ PROPN iajs-2992 89 55 𝐢2[0 𝐢2[0 PROPN iajs-2992 89 56 , , PUNCT iajs-2992 89 57 𝑇 𝑇 PROPN iajs-2992 89 58 ] ] PUNCT iajs-2992 89 59 , , PUNCT iajs-2992 89 60 s.t s.t PROPN iajs-2992 89 61 . . PROPN iajs-2992 89 62 πœ™π‘–(𝑇 πœ™π‘–(𝑇 ADP iajs-2992 89 63 ) ) PUNCT iajs-2992 89 64 = = SYM iajs-2992 89 65 πœ™π‘– πœ™π‘– NOUN iajs-2992 89 66 β€²(𝑇 β€²(𝑇 NOUN iajs-2992 89 67 ) ) PUNCT iajs-2992 90 1 = = SYM iajs-2992 90 2 0 0 NUM iajs-2992 90 3 , , PUNCT iajs-2992 90 4 πœ™π‘–(0 πœ™π‘–(0 NOUN iajs-2992 90 5 ) ) PUNCT iajs-2992 90 6 β‰  β‰  PROPN iajs-2992 90 7 0 0 NUM iajs-2992 90 8 , , PUNCT iajs-2992 90 9 πœ™π‘– πœ™π‘– ADP iajs-2992 90 10 β€²(0 β€²(0 NOUN iajs-2992 90 11 ) ) PUNCT iajs-2992 90 12 β‰  β‰  PROPN iajs-2992 90 13 0 0 NUM iajs-2992 90 14 ) ) PUNCT iajs-2992 90 15 , , PUNCT iajs-2992 90 16 rewriting rewrite VERB iajs-2992 90 17 the the DET iajs-2992 90 18 1st 1st ADJ iajs-2992 90 19 terms term NOUN iajs-2992 90 20 in in ADP iajs-2992 90 21 the the DET iajs-2992 90 22 lhs lhs PROPN iajs-2992 90 23 of of ADP iajs-2992 90 24 each each DET iajs-2992 90 25 one one NOUN iajs-2992 90 26 , , PUNCT iajs-2992 90 27 then then ADV iajs-2992 90 28 integrating integrate VERB iajs-2992 90 29 both both DET iajs-2992 90 30 sides side NOUN iajs-2992 90 31 ( ( PUNCT iajs-2992 90 32 ibs ibs PROPN iajs-2992 90 33 ) ) PUNCT iajs-2992 90 34 on on ADP iajs-2992 90 35 [ [ X iajs-2992 90 36 0 0 NUM iajs-2992 90 37 , , PUNCT iajs-2992 90 38 𝑇 𝑇 PROPN iajs-2992 90 39 ] ] PUNCT iajs-2992 90 40 , , PUNCT iajs-2992 90 41 and and CCONJ iajs-2992 90 42 then then ADV iajs-2992 90 43 integrating integrate VERB iajs-2992 90 44 by by ADP iajs-2992 90 45 parts part NOUN iajs-2992 90 46 ( ( PUNCT iajs-2992 90 47 ibps ibps NOUN iajs-2992 90 48 ) ) PUNCT iajs-2992 90 49 for for ADP iajs-2992 90 50 the the DET iajs-2992 90 51 1st 1st ADJ iajs-2992 90 52 terms term NOUN iajs-2992 90 53 , , PUNCT iajs-2992 90 54 yield yield VERB iajs-2992 90 55 to to ADP iajs-2992 90 56 ∫ ∫ PROPN iajs-2992 90 57 0 0 PUNCT iajs-2992 90 58 𝑇 𝑇 PROPN iajs-2992 90 59 𝑑 𝑑 PRON iajs-2992 90 60 𝑑𝑑 𝑑𝑑 ADP iajs-2992 90 61 ( ( PUNCT iajs-2992 90 62 𝑦1π‘˜π‘‘ 𝑦1π‘˜π‘‘ PROPN iajs-2992 90 63 , , PUNCT iajs-2992 90 64 𝑣1)πœ™1 𝑣1)πœ™1 NOUN iajs-2992 90 65 𝑑𝑑 𝑑𝑑 ADP iajs-2992 90 66 + + CCONJ iajs-2992 90 67 ∫ ∫ PROPN iajs-2992 90 68 0 0 X iajs-2992 90 69 𝑇 𝑇 PROPN iajs-2992 90 70 [ [ X iajs-2992 90 71 ( ( PUNCT iajs-2992 90 72 βˆ‡π‘¦1π‘˜ βˆ‡π‘¦1π‘˜ NOUN iajs-2992 90 73 , , PUNCT iajs-2992 90 74 βˆ‡π‘£1 βˆ‡π‘£1 NOUN iajs-2992 90 75 ) ) PUNCT iajs-2992 90 76 + + CCONJ iajs-2992 90 77 ( ( PUNCT iajs-2992 90 78 𝑦1π‘˜ 𝑦1π‘˜ PROPN iajs-2992 90 79 , , PUNCT iajs-2992 90 80 𝑣1 𝑣1 PROPN iajs-2992 90 81 ) ) PUNCT iajs-2992 90 82 βˆ’ βˆ’ PROPN iajs-2992 91 1 ( ( PUNCT iajs-2992 92 1 𝑦2π‘˜ 𝑦2π‘˜ PROPN iajs-2992 92 2 , , PUNCT iajs-2992 92 3 𝑣1 𝑣1 NOUN iajs-2992 92 4 ) ) PUNCT iajs-2992 92 5 + + CCONJ iajs-2992 92 6 ( ( PUNCT iajs-2992 92 7 𝑦3π‘˜ 𝑦3π‘˜ NOUN iajs-2992 92 8 , , PUNCT iajs-2992 92 9 𝑣1 𝑣1 NOUN iajs-2992 92 10 ) ) PUNCT iajs-2992 92 11 + + CCONJ iajs-2992 92 12 ( ( PUNCT iajs-2992 92 13 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 92 14 , , PUNCT iajs-2992 92 15 𝑣1)]πœ™1 𝑣1)]πœ™1 VERB iajs-2992 92 16 𝑑𝑑 𝑑𝑑 ADP iajs-2992 92 17 = = NOUN iajs-2992 92 18 ∫ ∫ PROPN iajs-2992 92 19 0 0 NUM iajs-2992 92 20 𝑇 𝑇 PROPN iajs-2992 92 21 ( ( PUNCT iajs-2992 92 22 𝑓11(π‘₯ 𝑓11(π‘₯ NOUN iajs-2992 92 23 , , PUNCT iajs-2992 92 24 𝑑 𝑑 PROPN iajs-2992 92 25 , , PUNCT iajs-2992 92 26 𝑦1π‘˜ 𝑦1π‘˜ PROPN iajs-2992 92 27 ) ) PUNCT iajs-2992 92 28 , , PUNCT iajs-2992 92 29 𝑣1)πœ™1 𝑣1)πœ™1 NOUN iajs-2992 92 30 ( ( PUNCT iajs-2992 92 31 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 92 32 + + NUM iajs-2992 92 33 ∫ ∫ PROPN iajs-2992 92 34 0 0 X iajs-2992 92 35 𝑇 𝑇 PROPN iajs-2992 92 36 ( ( PUNCT iajs-2992 92 37 𝑓12(π‘₯ 𝑓12(π‘₯ NOUN iajs-2992 92 38 , , PUNCT iajs-2992 92 39 𝑑)𝑒1π‘˜ 𝑑)𝑒1π‘˜ NOUN iajs-2992 92 40 , , PUNCT iajs-2992 92 41 𝑣1)πœ™1 𝑣1)πœ™1 NOUN iajs-2992 92 42 ( ( PUNCT iajs-2992 92 43 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 92 44 , , PUNCT iajs-2992 92 45 ( ( PUNCT iajs-2992 92 46 18 18 NUM iajs-2992 92 47 ) ) PUNCT iajs-2992 92 48 ∫ ∫ NOUN iajs-2992 92 49 0 0 NUM iajs-2992 93 1 𝑇 𝑇 PROPN iajs-2992 93 2 𝑑 𝑑 PRON iajs-2992 93 3 𝑑𝑑 𝑑𝑑 ADP iajs-2992 93 4 ( ( PUNCT iajs-2992 93 5 𝑦2π‘˜π‘‘ 𝑦2π‘˜π‘‘ NOUN iajs-2992 93 6 , , PUNCT iajs-2992 93 7 𝑣2)πœ™2 𝑣2)πœ™2 ADP iajs-2992 93 8 𝑑𝑑 𝑑𝑑 ADP iajs-2992 93 9 + + CCONJ iajs-2992 93 10 ∫ ∫ PROPN iajs-2992 93 11 0 0 X iajs-2992 93 12 𝑇 𝑇 PROPN iajs-2992 94 1 [ [ X iajs-2992 94 2 ( ( PUNCT iajs-2992 94 3 βˆ‡π‘¦2π‘˜ βˆ‡π‘¦2π‘˜ PROPN iajs-2992 94 4 , , PUNCT iajs-2992 94 5 βˆ‡π‘£2 βˆ‡π‘£2 PRON iajs-2992 94 6 ) ) PUNCT iajs-2992 95 1 + + CCONJ iajs-2992 95 2 ( ( PUNCT iajs-2992 95 3 𝑦1π‘˜ 𝑦1π‘˜ PROPN iajs-2992 95 4 , , PUNCT iajs-2992 95 5 𝑣2 𝑣2 PROPN iajs-2992 95 6 ) ) PUNCT iajs-2992 95 7 + + CCONJ iajs-2992 95 8 ( ( PUNCT iajs-2992 95 9 𝑦2π‘˜ 𝑦2π‘˜ PROPN iajs-2992 95 10 , , PUNCT iajs-2992 95 11 𝑣2 𝑣2 NOUN iajs-2992 95 12 ) ) PUNCT iajs-2992 95 13 βˆ’ βˆ’ PROPN iajs-2992 95 14 ( ( PUNCT iajs-2992 95 15 𝑦3π‘˜ 𝑦3π‘˜ PROPN iajs-2992 95 16 , , PUNCT iajs-2992 95 17 𝑣2 𝑣2 PROPN iajs-2992 95 18 ) ) PUNCT iajs-2992 95 19 βˆ’ βˆ’ PROPN iajs-2992 95 20 ( ( PUNCT iajs-2992 95 21 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 95 22 , , PUNCT iajs-2992 95 23 𝑣2)]πœ™2 𝑣2)]πœ™2 PROPN iajs-2992 95 24 𝑑𝑑 𝑑𝑑 ADP iajs-2992 95 25 = = SYM iajs-2992 95 26 ∫ ∫ PROPN iajs-2992 95 27 0 0 NUM iajs-2992 95 28 𝑇 𝑇 PROPN iajs-2992 95 29 ( ( PUNCT iajs-2992 95 30 𝑓21(π‘₯ 𝑓21(π‘₯ NOUN iajs-2992 95 31 , , PUNCT iajs-2992 95 32 𝑑 𝑑 NOUN iajs-2992 95 33 , , PUNCT iajs-2992 95 34 𝑦2π‘˜ 𝑦2π‘˜ PROPN iajs-2992 95 35 ) ) PUNCT iajs-2992 95 36 , , PUNCT iajs-2992 95 37 𝑣2)πœ™2 𝑣2)πœ™2 ADP iajs-2992 95 38 ( ( PUNCT iajs-2992 95 39 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 95 40 + + NUM iajs-2992 95 41 ∫ ∫ PROPN iajs-2992 95 42 0 0 X iajs-2992 95 43 𝑇 𝑇 PROPN iajs-2992 95 44 ( ( PUNCT iajs-2992 95 45 𝑓22(π‘₯ 𝑓22(π‘₯ X iajs-2992 95 46 , , PUNCT iajs-2992 95 47 𝑑)𝑒2π‘˜ 𝑑)𝑒2π‘˜ ADJ iajs-2992 95 48 , , PUNCT iajs-2992 95 49 𝑣2)πœ™2 𝑣2)πœ™2 ADP iajs-2992 95 50 ( ( PUNCT iajs-2992 95 51 𝑑)𝑑𝑑 𝑑)𝑑𝑑 NOUN iajs-2992 95 52 , , PUNCT iajs-2992 95 53 ( ( PUNCT iajs-2992 95 54 19 19 NUM iajs-2992 95 55 ) ) PUNCT iajs-2992 95 56 ∫ ∫ NOUN iajs-2992 95 57 0 0 NUM iajs-2992 95 58 𝑇 𝑇 PROPN iajs-2992 95 59 𝑑 𝑑 PRON iajs-2992 95 60 𝑑𝑑 𝑑𝑑 ADP iajs-2992 95 61 ( ( PUNCT iajs-2992 95 62 𝑦3π‘˜ 𝑦3π‘˜ PROPN iajs-2992 95 63 , , PUNCT iajs-2992 95 64 𝑣3)πœ™3 𝑣3)πœ™3 X iajs-2992 95 65 𝑑𝑑 𝑑𝑑 ADP iajs-2992 95 66 + + PROPN iajs-2992 95 67 ∫ ∫ PROPN iajs-2992 95 68 0 0 X iajs-2992 95 69 𝑇 𝑇 PROPN iajs-2992 96 1 [ [ X iajs-2992 96 2 ( ( PUNCT iajs-2992 96 3 βˆ‡π‘¦3π‘˜ βˆ‡π‘¦3π‘˜ PROPN iajs-2992 96 4 , , PUNCT iajs-2992 96 5 βˆ‡π‘£3 βˆ‡π‘£3 NOUN iajs-2992 96 6 ) ) PUNCT iajs-2992 96 7 βˆ’ βˆ’ PROPN iajs-2992 96 8 ( ( PUNCT iajs-2992 96 9 𝑦1π‘˜ 𝑦1π‘˜ PROPN iajs-2992 96 10 , , PUNCT iajs-2992 96 11 𝑣3 𝑣3 ADJ iajs-2992 96 12 ) ) PUNCT iajs-2992 97 1 + + CCONJ iajs-2992 97 2 ( ( PUNCT iajs-2992 97 3 𝑦2π‘˜ 𝑦2π‘˜ ADJ iajs-2992 97 4 , , PUNCT iajs-2992 97 5 𝑣3 𝑣3 ADJ iajs-2992 97 6 ) ) PUNCT iajs-2992 98 1 + + CCONJ iajs-2992 98 2 ( ( PUNCT iajs-2992 98 3 𝑦3π‘˜ 𝑦3π‘˜ NOUN iajs-2992 98 4 , , PUNCT iajs-2992 98 5 𝑣3 𝑣3 ADJ iajs-2992 98 6 ) ) PUNCT iajs-2992 98 7 + + CCONJ iajs-2992 98 8 ( ( PUNCT iajs-2992 98 9 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 98 10 , , PUNCT iajs-2992 98 11 𝑣3)]πœ™3 𝑣3)]πœ™3 PROPN iajs-2992 98 12 𝑑𝑑 𝑑𝑑 ADP iajs-2992 98 13 = = SYM iajs-2992 98 14 ∫ ∫ PROPN iajs-2992 98 15 0 0 NUM iajs-2992 98 16 𝑇 𝑇 PROPN iajs-2992 98 17 ( ( PUNCT iajs-2992 98 18 𝑓31(π‘₯ 𝑓31(π‘₯ PROPN iajs-2992 98 19 , , PUNCT iajs-2992 98 20 𝑑 𝑑 NOUN iajs-2992 98 21 , , PUNCT iajs-2992 98 22 𝑦3π‘˜ 𝑦3π‘˜ NOUN iajs-2992 98 23 ) ) PUNCT iajs-2992 98 24 , , PUNCT iajs-2992 98 25 𝑣3)πœ™3 𝑣3)πœ™3 X iajs-2992 98 26 ( ( PUNCT iajs-2992 98 27 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 98 28 + + NUM iajs-2992 98 29 ∫ ∫ PROPN iajs-2992 98 30 0 0 X iajs-2992 98 31 𝑇 𝑇 PROPN iajs-2992 98 32 ( ( PUNCT iajs-2992 98 33 𝑓32(π‘₯ 𝑓32(π‘₯ NOUN iajs-2992 98 34 , , PUNCT iajs-2992 98 35 𝑑)𝑒3π‘˜ 𝑑)𝑒3π‘˜ PROPN iajs-2992 98 36 , , PUNCT iajs-2992 98 37 𝑣3)πœ™3 𝑣3)πœ™3 X iajs-2992 98 38 ( ( PUNCT iajs-2992 98 39 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 98 40 , , PUNCT iajs-2992 98 41 ( ( PUNCT iajs-2992 98 42 20 20 NUM iajs-2992 98 43 ) ) PUNCT iajs-2992 98 44 ∫ ∫ NOUN iajs-2992 98 45 0 0 NUM iajs-2992 99 1 𝑇 𝑇 PROPN iajs-2992 99 2 𝑑 𝑑 PRON iajs-2992 99 3 𝑑𝑑 𝑑𝑑 ADP iajs-2992 99 4 ( ( PUNCT iajs-2992 99 5 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 99 6 , , PUNCT iajs-2992 99 7 𝑣4)πœ™4 𝑣4)πœ™4 ADJ iajs-2992 99 8 𝑑𝑑 𝑑𝑑 ADP iajs-2992 99 9 + + CCONJ iajs-2992 99 10 ∫ ∫ PROPN iajs-2992 99 11 0 0 X iajs-2992 100 1 𝑇 𝑇 PROPN iajs-2992 100 2 [ [ X iajs-2992 100 3 ( ( PUNCT iajs-2992 100 4 βˆ‡π‘¦4π‘˜ βˆ‡π‘¦4π‘˜ NOUN iajs-2992 100 5 , , PUNCT iajs-2992 100 6 βˆ‡π‘£4 βˆ‡π‘£4 NUM iajs-2992 100 7 ) ) PUNCT iajs-2992 100 8 βˆ’ βˆ’ PROPN iajs-2992 101 1 ( ( PUNCT iajs-2992 101 2 𝑦1π‘˜ 𝑦1π‘˜ PROPN iajs-2992 101 3 , , PUNCT iajs-2992 101 4 𝑣4 𝑣4 NOUN iajs-2992 101 5 ) ) PUNCT iajs-2992 101 6 + + CCONJ iajs-2992 101 7 ( ( PUNCT iajs-2992 101 8 𝑦2π‘˜ 𝑦2π‘˜ PROPN iajs-2992 101 9 , , PUNCT iajs-2992 101 10 𝑣4 𝑣4 NOUN iajs-2992 101 11 ) ) PUNCT iajs-2992 101 12 βˆ’ βˆ’ PROPN iajs-2992 101 13 ( ( PUNCT iajs-2992 101 14 𝑦3π‘˜ 𝑦3π‘˜ NOUN iajs-2992 101 15 , , PUNCT iajs-2992 101 16 𝑣4 𝑣4 NOUN iajs-2992 101 17 ) ) PUNCT iajs-2992 101 18 + + CCONJ iajs-2992 101 19 ( ( PUNCT iajs-2992 101 20 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 101 21 , , PUNCT iajs-2992 101 22 𝑣4)]πœ™4 𝑣4)]πœ™4 NOUN iajs-2992 101 23 𝑑𝑑 𝑑𝑑 ADP iajs-2992 101 24 = = SYM iajs-2992 101 25 ∫ ∫ PROPN iajs-2992 101 26 0 0 X iajs-2992 101 27 𝑇 𝑇 PROPN iajs-2992 101 28 ( ( PUNCT iajs-2992 101 29 𝑓41(π‘₯ 𝑓41(π‘₯ NOUN iajs-2992 101 30 , , PUNCT iajs-2992 101 31 𝑑 𝑑 NOUN iajs-2992 101 32 , , PUNCT iajs-2992 101 33 𝑦4π‘˜ 𝑦4π‘˜ NOUN iajs-2992 101 34 ) ) PUNCT iajs-2992 101 35 , , PUNCT iajs-2992 101 36 𝑣4)πœ™4 𝑣4)πœ™4 VERB iajs-2992 101 37 ( ( PUNCT iajs-2992 101 38 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 101 39 + + NUM iajs-2992 101 40 ∫ ∫ PROPN iajs-2992 101 41 0 0 X iajs-2992 101 42 𝑇 𝑇 PROPN iajs-2992 101 43 ( ( PUNCT iajs-2992 101 44 𝑓42(π‘₯ 𝑓42(π‘₯ NOUN iajs-2992 101 45 , , PUNCT iajs-2992 101 46 𝑑)𝑒4π‘˜ 𝑑)𝑒4π‘˜ NOUN iajs-2992 101 47 , , PUNCT iajs-2992 101 48 𝑣4)πœ™4 𝑣4)πœ™4 ADJ iajs-2992 101 49 ( ( PUNCT iajs-2992 101 50 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN iajs-2992 101 51 , , PUNCT iajs-2992 101 52 ( ( PUNCT iajs-2992 101 53 21 21 NUM iajs-2992 101 54 ) ) PUNCT iajs-2992 101 55 at at ADP iajs-2992 101 56 this this DET iajs-2992 101 57 point point NOUN iajs-2992 101 58 , , PUNCT iajs-2992 101 59 the the DET iajs-2992 101 60 same same ADJ iajs-2992 101 61 steps step NOUN iajs-2992 101 62 which which PRON iajs-2992 101 63 were be AUX iajs-2992 101 64 utilized utilize VERB iajs-2992 101 65 in in ADP iajs-2992 101 66 the the DET iajs-2992 101 67 proof proof NOUN iajs-2992 101 68 of of ADP iajs-2992 101 69 theorem theorem ADJ iajs-2992 101 70 2.1 2.1 NUM iajs-2992 101 71 , , PUNCT iajs-2992 101 72 can can AUX iajs-2992 101 73 be be AUX iajs-2992 101 74 utilized utilize VERB iajs-2992 101 75 here here ADV iajs-2992 101 76 to to PART iajs-2992 101 77 passage passage VERB iajs-2992 101 78 the the DET iajs-2992 101 79 limit limit NOUN iajs-2992 101 80 in in ADP iajs-2992 101 81 the the DET iajs-2992 101 82 wf wf PROPN iajs-2992 101 83 of of ADP iajs-2992 101 84 ( ( PUNCT iajs-2992 101 85 ( ( PUNCT iajs-2992 101 86 18 18 NUM iajs-2992 101 87 ) ) PUNCT iajs-2992 101 88 – – PUNCT iajs-2992 101 89 ( ( PUNCT iajs-2992 101 90 21 21 NUM iajs-2992 101 91 ) ) PUNCT iajs-2992 101 92 ) ) PUNCT iajs-2992 101 93 , , PUNCT iajs-2992 101 94 to to PART iajs-2992 101 95 acquire acquire VERB iajs-2992 101 96 ( ( PUNCT iajs-2992 101 97 𝑦1𝑑 𝑦1𝑑 NOUN iajs-2992 101 98 , , PUNCT iajs-2992 101 99 𝑣1 𝑣1 PROPN iajs-2992 101 100 ) ) PUNCT iajs-2992 101 101 + + CCONJ iajs-2992 101 102 ( ( PUNCT iajs-2992 101 103 βˆ‡π‘¦1 βˆ‡π‘¦1 NOUN iajs-2992 101 104 , , PUNCT iajs-2992 101 105 βˆ‡π‘£1 βˆ‡π‘£1 NOUN iajs-2992 101 106 ) ) PUNCT iajs-2992 102 1 + + CCONJ iajs-2992 102 2 ( ( PUNCT iajs-2992 102 3 𝑦1 𝑦1 PROPN iajs-2992 102 4 , , PUNCT iajs-2992 102 5 𝑣1 𝑣1 NOUN iajs-2992 102 6 ) ) PUNCT iajs-2992 102 7 βˆ’ βˆ’ PROPN iajs-2992 102 8 ( ( PUNCT iajs-2992 102 9 𝑦2 𝑦2 PROPN iajs-2992 102 10 , , PUNCT iajs-2992 102 11 𝑣1 𝑣1 PROPN iajs-2992 102 12 ) ) PUNCT iajs-2992 102 13 + + CCONJ iajs-2992 102 14 ( ( PUNCT iajs-2992 102 15 𝑦3 𝑦3 PROPN iajs-2992 102 16 , , PUNCT iajs-2992 102 17 𝑣1 𝑣1 PROPN iajs-2992 102 18 ) ) PUNCT iajs-2992 102 19 + + CCONJ iajs-2992 102 20 ( ( PUNCT iajs-2992 102 21 𝑦4 𝑦4 NOUN iajs-2992 102 22 , , PUNCT iajs-2992 102 23 𝑣1 𝑣1 NOUN iajs-2992 102 24 ) ) PUNCT iajs-2992 102 25 = = PUNCT iajs-2992 102 26 ( ( PUNCT iajs-2992 102 27 𝑓11(π‘₯ 𝑓11(π‘₯ NOUN iajs-2992 102 28 , , PUNCT iajs-2992 102 29 𝑑 𝑑 NOUN iajs-2992 102 30 , , PUNCT iajs-2992 102 31 𝑦1 𝑦1 NOUN iajs-2992 102 32 ) ) PUNCT iajs-2992 102 33 + + NUM iajs-2992 102 34 𝑓12(π‘₯ 𝑓12(π‘₯ NOUN iajs-2992 102 35 , , PUNCT iajs-2992 102 36 𝑑)𝑒1 𝑑)𝑒1 PROPN iajs-2992 102 37 , , PUNCT iajs-2992 102 38 𝑣1 𝑣1 PROPN iajs-2992 102 39 ) ) PUNCT iajs-2992 102 40 , , PUNCT iajs-2992 102 41 βˆ€π‘£1 βˆ€π‘£1 PROPN iajs-2992 102 42 ∈ ∈ PROPN iajs-2992 102 43 𝑉 𝑉 PROPN iajs-2992 102 44 a.e a.e PROPN iajs-2992 102 45 . . PROPN iajs-2992 103 1 on on ADP iajs-2992 103 2 i i PRON iajs-2992 103 3 , , PUNCT iajs-2992 103 4 ( ( PUNCT iajs-2992 103 5 22 22 NUM iajs-2992 103 6 ) ) PUNCT iajs-2992 103 7 ( ( PUNCT iajs-2992 103 8 𝑦2𝑑 𝑦2𝑑 NOUN iajs-2992 103 9 , , PUNCT iajs-2992 103 10 𝑣2 𝑣2 NOUN iajs-2992 103 11 ) ) PUNCT iajs-2992 103 12 + + CCONJ iajs-2992 103 13 ( ( PUNCT iajs-2992 103 14 βˆ†π‘¦2 βˆ†π‘¦2 PROPN iajs-2992 103 15 , , PUNCT iajs-2992 103 16 βˆ‡π‘£2 βˆ‡π‘£2 PROPN iajs-2992 103 17 ) ) PUNCT iajs-2992 104 1 + + CCONJ iajs-2992 104 2 ( ( PUNCT iajs-2992 104 3 𝑦1 𝑦1 PROPN iajs-2992 104 4 , , PUNCT iajs-2992 104 5 𝑣2 𝑣2 PROPN iajs-2992 104 6 ) ) PUNCT iajs-2992 104 7 + + CCONJ iajs-2992 104 8 ( ( PUNCT iajs-2992 104 9 𝑦2 𝑦2 PROPN iajs-2992 104 10 , , PUNCT iajs-2992 104 11 𝑣2 𝑣2 PROPN iajs-2992 104 12 ) ) PUNCT iajs-2992 104 13 βˆ’ βˆ’ PROPN iajs-2992 104 14 ( ( PUNCT iajs-2992 104 15 𝑦3 𝑦3 PROPN iajs-2992 104 16 , , PUNCT iajs-2992 104 17 𝑣2 𝑣2 PROPN iajs-2992 104 18 ) ) PUNCT iajs-2992 104 19 βˆ’ βˆ’ PROPN iajs-2992 104 20 ( ( PUNCT iajs-2992 104 21 𝑦4 𝑦4 PROPN iajs-2992 104 22 , , PUNCT iajs-2992 104 23 𝑣2 𝑣2 NOUN iajs-2992 104 24 ) ) PUNCT iajs-2992 104 25 = = PUNCT iajs-2992 104 26 ( ( PUNCT iajs-2992 104 27 𝑓21(π‘₯ 𝑓21(π‘₯ NOUN iajs-2992 104 28 , , PUNCT iajs-2992 104 29 𝑑 𝑑 PROPN iajs-2992 104 30 , , PUNCT iajs-2992 104 31 𝑦2 𝑦2 NOUN iajs-2992 104 32 ) ) PUNCT iajs-2992 105 1 + + SYM iajs-2992 105 2 𝑓22(π‘₯ 𝑓22(π‘₯ NOUN iajs-2992 105 3 , , PUNCT iajs-2992 105 4 𝑑)𝑒2 𝑑)𝑒2 PROPN iajs-2992 105 5 , , PUNCT iajs-2992 105 6 𝑣2 𝑣2 PROPN iajs-2992 105 7 ) ) PUNCT iajs-2992 105 8 , , PUNCT iajs-2992 105 9 βˆ€π‘£2 βˆ€π‘£2 PROPN iajs-2992 105 10 ∈ ∈ PROPN iajs-2992 105 11 𝑉 𝑉 PROPN iajs-2992 105 12 a.e a.e PROPN iajs-2992 105 13 . . PROPN iajs-2992 106 1 on on ADP iajs-2992 106 2 i i PRON iajs-2992 106 3 , , PUNCT iajs-2992 106 4 ( ( PUNCT iajs-2992 106 5 23 23 NUM iajs-2992 106 6 ) ) PUNCT iajs-2992 106 7 ( ( PUNCT iajs-2992 106 8 𝑦3𝑑 𝑦3𝑑 NOUN iajs-2992 106 9 , , PUNCT iajs-2992 106 10 𝑣3 𝑣3 ADJ iajs-2992 106 11 ) ) PUNCT iajs-2992 106 12 + + CCONJ iajs-2992 106 13 ( ( PUNCT iajs-2992 106 14 βˆ‡π‘¦3 βˆ‡π‘¦3 PROPN iajs-2992 106 15 , , PUNCT iajs-2992 106 16 βˆ‡π‘£3 βˆ‡π‘£3 NOUN iajs-2992 106 17 ) ) PUNCT iajs-2992 106 18 βˆ’ βˆ’ PROPN iajs-2992 107 1 ( ( PUNCT iajs-2992 107 2 𝑦1 𝑦1 NOUN iajs-2992 107 3 , , PUNCT iajs-2992 107 4 𝑣3 𝑣3 ADJ iajs-2992 107 5 ) ) PUNCT iajs-2992 107 6 + + CCONJ iajs-2992 107 7 ( ( PUNCT iajs-2992 107 8 𝑦2 𝑦2 NOUN iajs-2992 107 9 , , PUNCT iajs-2992 107 10 𝑣3 𝑣3 ADJ iajs-2992 107 11 ) ) PUNCT iajs-2992 107 12 + + CCONJ iajs-2992 107 13 ( ( PUNCT iajs-2992 107 14 𝑦3 𝑦3 PROPN iajs-2992 107 15 , , PUNCT iajs-2992 107 16 𝑣3 𝑣3 ADJ iajs-2992 107 17 ) ) PUNCT iajs-2992 107 18 + + CCONJ iajs-2992 107 19 ( ( PUNCT iajs-2992 107 20 𝑦4 𝑦4 NOUN iajs-2992 107 21 , , PUNCT iajs-2992 107 22 𝑣3 𝑣3 ADJ iajs-2992 107 23 ) ) PUNCT iajs-2992 107 24 = = SYM iajs-2992 107 25 ( ( PUNCT iajs-2992 107 26 𝑓31(π‘₯ 𝑓31(π‘₯ NUM iajs-2992 107 27 , , PUNCT iajs-2992 107 28 𝑑 𝑑 PROPN iajs-2992 107 29 , , PUNCT iajs-2992 107 30 𝑦3 𝑦3 PROPN iajs-2992 107 31 ) ) PUNCT iajs-2992 107 32 + + NUM iajs-2992 107 33 𝑓32(π‘₯ 𝑓32(π‘₯ NOUN iajs-2992 107 34 , , PUNCT iajs-2992 107 35 𝑑)𝑒3 𝑑)𝑒3 PROPN iajs-2992 107 36 , , PUNCT iajs-2992 107 37 𝑣3 𝑣3 ADJ iajs-2992 107 38 ) ) PUNCT iajs-2992 107 39 , , PUNCT iajs-2992 107 40 βˆ€π‘£3 βˆ€π‘£3 PROPN iajs-2992 107 41 ∈ ∈ PROPN iajs-2992 107 42 𝑉 𝑉 PROPN iajs-2992 107 43 a.e a.e PROPN iajs-2992 107 44 . . PROPN iajs-2992 108 1 on on ADP iajs-2992 108 2 i i PRON iajs-2992 108 3 , , PUNCT iajs-2992 108 4 ( ( PUNCT iajs-2992 108 5 24 24 NUM iajs-2992 108 6 ) ) PUNCT iajs-2992 108 7 ( ( PUNCT iajs-2992 108 8 𝑦4𝑑 𝑦4𝑑 PROPN iajs-2992 108 9 , , PUNCT iajs-2992 108 10 𝑣4 𝑣4 NOUN iajs-2992 108 11 ) ) PUNCT iajs-2992 108 12 + + CCONJ iajs-2992 108 13 ( ( PUNCT iajs-2992 108 14 βˆ‡π‘¦4 βˆ‡π‘¦4 ADJ iajs-2992 108 15 , , PUNCT iajs-2992 108 16 βˆ‡π‘£4 βˆ‡π‘£4 NUM iajs-2992 108 17 ) ) PUNCT iajs-2992 108 18 βˆ’ βˆ’ PROPN iajs-2992 109 1 ( ( PUNCT iajs-2992 109 2 𝑦1 𝑦1 NOUN iajs-2992 109 3 , , PUNCT iajs-2992 109 4 𝑣4 𝑣4 NOUN iajs-2992 109 5 ) ) PUNCT iajs-2992 109 6 + + CCONJ iajs-2992 109 7 ( ( PUNCT iajs-2992 109 8 𝑦2 𝑦2 NOUN iajs-2992 109 9 , , PUNCT iajs-2992 109 10 𝑣4 𝑣4 NOUN iajs-2992 109 11 ) ) PUNCT iajs-2992 109 12 βˆ’ βˆ’ PROPN iajs-2992 109 13 ( ( PUNCT iajs-2992 109 14 𝑦3 𝑦3 PROPN iajs-2992 109 15 , , PUNCT iajs-2992 109 16 𝑣4 𝑣4 NOUN iajs-2992 109 17 ) ) PUNCT iajs-2992 109 18 + + CCONJ iajs-2992 109 19 ( ( PUNCT iajs-2992 109 20 𝑦4 𝑦4 NOUN iajs-2992 109 21 , , PUNCT iajs-2992 109 22 𝑣4 𝑣4 NOUN iajs-2992 109 23 ) ) PUNCT iajs-2992 109 24 = = PUNCT iajs-2992 109 25 ( ( PUNCT iajs-2992 109 26 𝑓41(π‘₯ 𝑓41(π‘₯ NOUN iajs-2992 109 27 , , PUNCT iajs-2992 109 28 𝑑 𝑑 NOUN iajs-2992 109 29 , , PUNCT iajs-2992 109 30 𝑦4 𝑦4 NOUN iajs-2992 109 31 ) ) PUNCT iajs-2992 110 1 + + CCONJ iajs-2992 110 2 𝑓42(π‘₯ 𝑓42(π‘₯ NOUN iajs-2992 110 3 , , PUNCT iajs-2992 110 4 𝑑)𝑒4 𝑑)𝑒4 PROPN iajs-2992 110 5 , , PUNCT iajs-2992 110 6 𝑣4 𝑣4 NOUN iajs-2992 110 7 ) ) PUNCT iajs-2992 110 8 , , PUNCT iajs-2992 110 9 βˆ€π‘£4 βˆ€π‘£4 NOUN iajs-2992 110 10 ∈ ∈ PROPN iajs-2992 110 11 𝑉 𝑉 PROPN iajs-2992 110 12 a.e a.e PROPN iajs-2992 110 13 . . PROPN iajs-2992 111 1 on on ADP iajs-2992 111 2 i i PRON iajs-2992 111 3 , , PUNCT iajs-2992 111 4 ( ( PUNCT iajs-2992 111 5 25 25 NUM iajs-2992 111 6 ) ) PUNCT iajs-2992 111 7 same same ADJ iajs-2992 111 8 manner manner NOUN iajs-2992 111 9 also also ADV iajs-2992 111 10 can can AUX iajs-2992 111 11 be be AUX iajs-2992 111 12 utilized utilize VERB iajs-2992 111 13 to to ADP iajs-2992 111 14 that that PRON iajs-2992 111 15 the the DET iajs-2992 111 16 ics ic NOUN iajs-2992 111 17 are be AUX iajs-2992 111 18 held hold VERB iajs-2992 111 19 . . PUNCT iajs-2992 112 1 thus thus ADV iajs-2992 112 2 οΏ½ οΏ½ NOUN iajs-2992 112 3 βƒ— βƒ— NOUN iajs-2992 112 4 οΏ½ οΏ½ PROPN iajs-2992 112 5 is be AUX iajs-2992 112 6 qsvs qsvs ADJ iajs-2992 112 7 ihjpas ihjpa NOUN iajs-2992 112 8 . . PUNCT iajs-2992 113 1 36(2)2023 36(2)2023 NUM iajs-2992 113 2 335 335 NUM iajs-2992 113 3 from from ADP iajs-2992 113 4 the the DET iajs-2992 113 5 other other ADJ iajs-2992 113 6 side side NOUN iajs-2992 113 7 , , PUNCT iajs-2992 113 8 since since SCONJ iajs-2992 113 9 𝐺1( 𝐺1( NUM iajs-2992 113 10 οΏ½ οΏ½ PROPN iajs-2992 113 11 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 113 12 οΏ½ οΏ½ PROPN iajs-2992 113 13 ) ) PUNCT iajs-2992 114 1 = = PUNCT iajs-2992 114 2 Οƒ Οƒ NOUN iajs-2992 114 3 𝑖=1 𝑖=1 PROPN iajs-2992 114 4 4 4 NUM iajs-2992 114 5 ∫ ∫ NOUN iajs-2992 114 6 𝑄 𝑄 PROPN iajs-2992 114 7 𝑔1𝑖 𝑔1𝑖 NOUN iajs-2992 114 8 ( ( PUNCT iajs-2992 114 9 π‘₯ π‘₯ NOUN iajs-2992 114 10 , , PUNCT iajs-2992 114 11 𝑑 𝑑 PROPN iajs-2992 114 12 , , PUNCT iajs-2992 114 13 π‘¦π‘–π‘˜)𝑑π‘₯𝑑𝑑 π‘¦π‘–π‘˜)𝑑π‘₯𝑑𝑑 PROPN iajs-2992 114 14 , , PUNCT iajs-2992 114 15 with with ADP iajs-2992 114 16 𝑔1𝑖 𝑔1𝑖 PROPN iajs-2992 114 17 ( ( PUNCT iajs-2992 114 18 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 114 19 = = NOUN iajs-2992 114 20 1,2,3,4 1,2,3,4 NUM iajs-2992 114 21 ) ) PUNCT iajs-2992 114 22 is be AUX iajs-2992 114 23 cont cont ADJ iajs-2992 114 24 . . PUNCT iajs-2992 115 1 w.r.t w.r.t PROPN iajs-2992 115 2 . . PUNCT iajs-2992 116 1 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 116 2 , , PUNCT iajs-2992 116 3 then then ADV iajs-2992 116 4 by by ADP iajs-2992 116 5 lemma lemma PROPN iajs-2992 116 6 2.1 2.1 NUM iajs-2992 116 7 , , PUNCT iajs-2992 116 8 ∫ ∫ PROPN iajs-2992 116 9 𝑄 𝑄 PROPN iajs-2992 116 10 𝑔1𝑖 𝑔1𝑖 ADJ iajs-2992 116 11 ( ( PUNCT iajs-2992 116 12 π‘₯ π‘₯ NOUN iajs-2992 116 13 , , PUNCT iajs-2992 116 14 𝑑 𝑑 PROPN iajs-2992 116 15 , , PUNCT iajs-2992 116 16 π‘¦π‘–π‘˜)𝑑π‘₯𝑑𝑑 π‘¦π‘–π‘˜)𝑑π‘₯𝑑𝑑 PROPN iajs-2992 116 17 is be AUX iajs-2992 116 18 cont cont NOUN iajs-2992 116 19 . . PUNCT iajs-2992 117 1 w.r.t w.r.t PROPN iajs-2992 117 2 . . PUNCT iajs-2992 118 1 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 118 2 but but CCONJ iajs-2992 118 3 οΏ½ οΏ½ PROPN iajs-2992 118 4 βƒ— βƒ— NOUN iajs-2992 118 5 οΏ½ οΏ½ ADP iajs-2992 118 6 π‘˜ π‘˜ PRON iajs-2992 118 7 β†’ β†’ SYM iajs-2992 118 8 οΏ½ οΏ½ NOUN iajs-2992 118 9 βƒ— βƒ— PROPN iajs-2992 118 10 οΏ½ οΏ½ PROPN iajs-2992 118 11 st st PROPN iajs-2992 118 12 in in ADP iajs-2992 118 13 π‘³πŸ(𝑸 π‘³πŸ(𝑸 PROPN iajs-2992 118 14 ) ) PUNCT iajs-2992 118 15 , , PUNCT iajs-2992 118 16 therefore therefore ADV iajs-2992 118 17 ∫ ∫ PROPN iajs-2992 118 18 𝑄 𝑄 PROPN iajs-2992 118 19 𝑔1𝑖(π‘₯ 𝑔1𝑖(π‘₯ PROPN iajs-2992 118 20 , , PUNCT iajs-2992 118 21 𝑑 𝑑 PROPN iajs-2992 118 22 , , PUNCT iajs-2992 118 23 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 118 24 ) ) PUNCT iajs-2992 118 25 𝑑π‘₯𝑑𝑑 𝑑π‘₯𝑑𝑑 NOUN iajs-2992 118 26 β†’ β†’ SYM iajs-2992 118 27 ∫ ∫ NOUN iajs-2992 118 28 𝑄 𝑄 PROPN iajs-2992 118 29 𝑔1𝑖 𝑔1𝑖 PUNCT iajs-2992 118 30 ( ( PUNCT iajs-2992 118 31 π‘₯ π‘₯ NOUN iajs-2992 118 32 , , PUNCT iajs-2992 118 33 𝑑 𝑑 PROPN iajs-2992 118 34 , , PUNCT iajs-2992 118 35 𝑦𝑖)𝑑π‘₯𝑑𝑑. 𝑦𝑖)𝑑π‘₯𝑑𝑑. PROPN iajs-2992 118 36 thus thus ADV iajs-2992 118 37 𝐺1( 𝐺1( NUM iajs-2992 118 38 οΏ½ οΏ½ PROPN iajs-2992 118 39 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 118 40 οΏ½ οΏ½ PROPN iajs-2992 118 41 ) ) PUNCT iajs-2992 118 42 = = PRON iajs-2992 118 43 π‘™π‘–π‘š π‘™π‘–π‘š VERB iajs-2992 118 44 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 118 45 𝐺1( 𝐺1( NUM iajs-2992 118 46 οΏ½ οΏ½ PROPN iajs-2992 118 47 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 118 48 οΏ½ οΏ½ PROPN iajs-2992 118 49 π‘˜ π‘˜ NOUN iajs-2992 118 50 ) ) PUNCT iajs-2992 118 51 = = SYM iajs-2992 118 52 0 0 X iajs-2992 118 53 . . PUNCT iajs-2992 119 1 as as ADV iajs-2992 119 2 well well ADV iajs-2992 119 3 , , PUNCT iajs-2992 119 4 since since SCONJ iajs-2992 119 5 for for ADP iajs-2992 119 6 𝑙 𝑙 PRON iajs-2992 119 7 = = SYM iajs-2992 119 8 0,2 0,2 NUM iajs-2992 119 9 & & CCONJ iajs-2992 119 10 𝑖 𝑖 NOUN iajs-2992 119 11 = = NOUN iajs-2992 119 12 1,2,3,4 1,2,3,4 NUM iajs-2992 119 13 , , PUNCT iajs-2992 119 14 𝑔𝑙𝑖(π‘₯ 𝑔𝑙𝑖(π‘₯ PROPN iajs-2992 119 15 , , PUNCT iajs-2992 119 16 𝑑 𝑑 PROPN iajs-2992 119 17 , , PUNCT iajs-2992 119 18 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 119 19 , , PUNCT iajs-2992 119 20 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 119 21 ) ) PUNCT iajs-2992 119 22 is be AUX iajs-2992 119 23 cont cont ADJ iajs-2992 119 24 . . PUNCT iajs-2992 120 1 w.r.t w.r.t PROPN iajs-2992 120 2 . . PUNCT iajs-2992 121 1 ( ( PUNCT iajs-2992 121 2 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 121 3 , , PUNCT iajs-2992 121 4 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 121 5 ) ) PUNCT iajs-2992 122 1 and and CCONJ iajs-2992 122 2 π‘ˆπ‘– π‘ˆπ‘– PROPN iajs-2992 122 3 is be AUX iajs-2992 122 4 com com NOUN iajs-2992 122 5 with with ADP iajs-2992 122 6 𝑒𝑖 𝑒𝑖 DET iajs-2992 122 7 ∈ ∈ PROPN iajs-2992 122 8 π‘ˆπ‘– π‘ˆπ‘– PROPN iajs-2992 122 9 a.e a.e PROPN iajs-2992 122 10 . . PROPN iajs-2992 122 11 in in ADP iajs-2992 122 12 𝑄 𝑄 PROPN iajs-2992 122 13 , , PUNCT iajs-2992 122 14 then then ADV iajs-2992 122 15 using use VERB iajs-2992 122 16 lemma lemma PROPN iajs-2992 122 17 2.2 2.2 NUM iajs-2992 122 18 to to PART iajs-2992 122 19 get get VERB iajs-2992 122 20 ∫ ∫ PROPN iajs-2992 122 21 𝑄 𝑄 PROPN iajs-2992 122 22 𝑔𝑙𝑖(π‘₯ 𝑔𝑙𝑖(π‘₯ PROPN iajs-2992 122 23 , , PUNCT iajs-2992 122 24 𝑑 𝑑 PROPN iajs-2992 122 25 , , PUNCT iajs-2992 122 26 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 122 27 , , PUNCT iajs-2992 122 28 π‘’π‘–π‘˜ π‘’π‘–π‘˜ NOUN iajs-2992 122 29 ) ) PUNCT iajs-2992 122 30 𝑑π‘₯𝑑𝑑 𝑑π‘₯𝑑𝑑 ADV iajs-2992 122 31 β†’ β†’ SYM iajs-2992 122 32 ∫ ∫ NOUN iajs-2992 122 33 𝑄 𝑄 PROPN iajs-2992 122 34 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 122 35 ( ( PUNCT iajs-2992 122 36 π‘₯ π‘₯ NOUN iajs-2992 122 37 , , PUNCT iajs-2992 122 38 𝑑 𝑑 PROPN iajs-2992 122 39 , , PUNCT iajs-2992 122 40 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 122 41 , , PUNCT iajs-2992 122 42 π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑 π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑 PROPN iajs-2992 122 43 , , PUNCT iajs-2992 122 44 ( ( PUNCT iajs-2992 122 45 26 26 NUM iajs-2992 122 46 ) ) PUNCT iajs-2992 122 47 but but CCONJ iajs-2992 122 48 𝑔𝑙𝑖(π‘₯ 𝑔𝑙𝑖(π‘₯ PROPN iajs-2992 122 49 , , PUNCT iajs-2992 122 50 𝑑 𝑑 PROPN iajs-2992 122 51 , , PUNCT iajs-2992 122 52 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 122 53 , , PUNCT iajs-2992 122 54 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 122 55 ) ) PUNCT iajs-2992 122 56 is be AUX iajs-2992 122 57 co co ADJ iajs-2992 122 58 and and CCONJ iajs-2992 122 59 cont cont NOUN iajs-2992 122 60 . . PUNCT iajs-2992 123 1 w.r.t w.r.t PROPN iajs-2992 123 2 . . PUNCT iajs-2992 124 1 𝑒𝑖 𝑒𝑖 INTJ iajs-2992 124 2 , , PUNCT iajs-2992 124 3 then then ADV iajs-2992 124 4 ∫ ∫ INTJ iajs-2992 124 5 𝑄 𝑄 PRON iajs-2992 124 6 𝑔𝑙𝑖 𝑔𝑙𝑖 X iajs-2992 124 7 ( ( PUNCT iajs-2992 124 8 π‘₯ π‘₯ NOUN iajs-2992 124 9 , , PUNCT iajs-2992 124 10 𝑑 𝑑 PROPN iajs-2992 124 11 , , PUNCT iajs-2992 124 12 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 124 13 , , PUNCT iajs-2992 124 14 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 124 15 is be AUX iajs-2992 124 16 weakly weakly ADJ iajs-2992 124 17 lowe lowe NOUN iajs-2992 124 18 semi semi ADJ iajs-2992 124 19 cont cont PROPN iajs-2992 124 20 . . PUNCT iajs-2992 125 1 ( ( PUNCT iajs-2992 125 2 wlsc wlsc NOUN iajs-2992 125 3 ) ) PUNCT iajs-2992 125 4 w.r.t w.r.t NOUN iajs-2992 125 5 . . PUNCT iajs-2992 126 1 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 126 2 , , PUNCT iajs-2992 126 3 βˆ€ βˆ€ NOUN iajs-2992 126 4 𝑙 𝑙 NOUN iajs-2992 126 5 = = SYM iajs-2992 126 6 0,2 0,2 NUM iajs-2992 126 7 & & CCONJ iajs-2992 126 8 𝑖 𝑖 NOUN iajs-2992 126 9 = = NOUN iajs-2992 126 10 1,2,3,4 1,2,3,4 NUM iajs-2992 126 11 , , PUNCT iajs-2992 126 12 i.e. i.e. X iajs-2992 126 13 ∫ ∫ X iajs-2992 126 14 𝑄 𝑄 NOUN iajs-2992 126 15 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 126 16 ( ( PUNCT iajs-2992 126 17 π‘₯ π‘₯ NOUN iajs-2992 126 18 , , PUNCT iajs-2992 126 19 𝑑 𝑑 PROPN iajs-2992 126 20 , , PUNCT iajs-2992 126 21 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 126 22 , , PUNCT iajs-2992 126 23 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 126 24 ≀ ≀ NUM iajs-2992 126 25 π‘™π‘–π‘š π‘™π‘–π‘š VERB iajs-2992 127 1 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 127 2 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 128 1 ∫ ∫ INTJ iajs-2992 129 1 𝑄 𝑄 PRON iajs-2992 130 1 [ [ PUNCT iajs-2992 130 2 𝑔𝑙𝑖 𝑔𝑙𝑖 X iajs-2992 130 3 ( ( PUNCT iajs-2992 130 4 π‘₯ π‘₯ NOUN iajs-2992 130 5 , , PUNCT iajs-2992 130 6 𝑑 𝑑 PROPN iajs-2992 130 7 , , PUNCT iajs-2992 130 8 𝑦𝑖 𝑦𝑖 NOUN iajs-2992 130 9 , , PUNCT iajs-2992 130 10 π‘’π‘–π‘˜ π‘’π‘–π‘˜ NOUN iajs-2992 130 11 ) ) PUNCT iajs-2992 130 12 βˆ’ βˆ’ NOUN iajs-2992 130 13 𝑔𝑙𝑖 𝑔𝑙𝑖 X iajs-2992 130 14 ( ( PUNCT iajs-2992 130 15 π‘₯ π‘₯ NOUN iajs-2992 130 16 , , PUNCT iajs-2992 130 17 𝑑 𝑑 PROPN iajs-2992 130 18 , , PUNCT iajs-2992 130 19 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 130 20 , , PUNCT iajs-2992 130 21 π‘’π‘–π‘˜)]𝑑π‘₯𝑑𝑑 π‘’π‘–π‘˜)]𝑑π‘₯𝑑𝑑 X iajs-2992 130 22 + + CCONJ iajs-2992 130 23 π‘™π‘–π‘š π‘™π‘–π‘š NUM iajs-2992 130 24 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 130 25 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 130 26 ∫ ∫ INTJ iajs-2992 131 1 𝑄 𝑄 NOUN iajs-2992 131 2 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 131 3 ( ( PUNCT iajs-2992 131 4 π‘₯ π‘₯ NOUN iajs-2992 131 5 , , PUNCT iajs-2992 131 6 𝑑 𝑑 PROPN iajs-2992 131 7 , , PUNCT iajs-2992 131 8 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 131 9 , , PUNCT iajs-2992 131 10 π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑 π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑 PROPN iajs-2992 131 11 ≀ ≀ NUM iajs-2992 131 12 π‘™π‘–π‘š π‘™π‘–π‘š VERB iajs-2992 132 1 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 132 2 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 132 3 ∫ ∫ INTJ iajs-2992 133 1 𝑄 𝑄 NOUN iajs-2992 133 2 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 133 3 ( ( PUNCT iajs-2992 133 4 π‘₯ π‘₯ NOUN iajs-2992 133 5 , , PUNCT iajs-2992 133 6 𝑑 𝑑 PROPN iajs-2992 133 7 , , PUNCT iajs-2992 133 8 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 133 9 , , PUNCT iajs-2992 133 10 π‘’π‘–π‘˜)𝑑π‘₯𝑑 π‘’π‘–π‘˜)𝑑π‘₯𝑑 PROPN iajs-2992 133 11 ⟹ ⟹ PUNCT iajs-2992 133 12 Οƒ Οƒ X iajs-2992 133 13 𝑖=1 𝑖=1 PROPN iajs-2992 133 14 4 4 NUM iajs-2992 133 15 ∫ ∫ NOUN iajs-2992 133 16 𝑄 𝑄 PROPN iajs-2992 133 17 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 133 18 ( ( PUNCT iajs-2992 133 19 π‘₯ π‘₯ NOUN iajs-2992 133 20 , , PUNCT iajs-2992 133 21 𝑑 𝑑 PROPN iajs-2992 133 22 , , PUNCT iajs-2992 133 23 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 133 24 , , PUNCT iajs-2992 133 25 𝑒𝑖)𝑑π‘₯𝑑𝑑 𝑒𝑖)𝑑π‘₯𝑑𝑑 NOUN iajs-2992 133 26 ≀ ≀ PUNCT iajs-2992 133 27 Οƒ Οƒ X iajs-2992 133 28 𝑖=1 𝑖=1 PROPN iajs-2992 133 29 4 4 NUM iajs-2992 133 30 ∫ ∫ NOUN iajs-2992 133 31 𝑄 𝑄 PROPN iajs-2992 133 32 𝑔𝑙𝑖 𝑔𝑙𝑖 NOUN iajs-2992 133 33 ( ( PUNCT iajs-2992 133 34 π‘₯ π‘₯ NOUN iajs-2992 133 35 , , PUNCT iajs-2992 133 36 𝑑 𝑑 PROPN iajs-2992 133 37 , , PUNCT iajs-2992 133 38 π‘¦π‘–π‘˜ π‘¦π‘–π‘˜ NOUN iajs-2992 133 39 , , PUNCT iajs-2992 133 40 π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑. π‘’π‘–π‘˜)𝑑π‘₯𝑑𝑑. ADV iajs-2992 133 41 thus thus ADV iajs-2992 133 42 𝐺𝑙( 𝐺𝑙( ADP iajs-2992 133 43 οΏ½ οΏ½ PROPN iajs-2992 133 44 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 45 οΏ½ οΏ½ PROPN iajs-2992 133 46 ) ) PUNCT iajs-2992 133 47 ≀ ≀ NUM iajs-2992 133 48 π‘™π‘–π‘š π‘™π‘–π‘š VERB iajs-2992 133 49 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 133 50 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 133 51 οΏ½ οΏ½ PROPN iajs-2992 133 52 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 133 53 οΏ½ οΏ½ NOUN iajs-2992 133 54 π‘˜βˆˆ π‘˜βˆˆ PROPN iajs-2992 133 55 οΏ½ οΏ½ PROPN iajs-2992 133 56 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 133 57 οΏ½ οΏ½ PROPN iajs-2992 133 58 𝐴 𝐴 PROPN iajs-2992 133 59 𝐺𝑙( 𝐺𝑙( NOUN iajs-2992 133 60 οΏ½ οΏ½ PROPN iajs-2992 133 61 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 62 οΏ½ οΏ½ PROPN iajs-2992 133 63 π‘˜ π‘˜ NOUN iajs-2992 133 64 ) ) PUNCT iajs-2992 133 65 , , PUNCT iajs-2992 133 66 then then ADV iajs-2992 133 67 𝐺2( 𝐺2( NOUN iajs-2992 133 68 οΏ½ οΏ½ PROPN iajs-2992 133 69 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 70 οΏ½ οΏ½ PROPN iajs-2992 133 71 ) ) PUNCT iajs-2992 133 72 ≀ ≀ NOUN iajs-2992 133 73 0 0 NUM iajs-2992 133 74 , , PUNCT iajs-2992 133 75 since since SCONJ iajs-2992 133 76 οΏ½ οΏ½ PROPN iajs-2992 133 77 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 78 οΏ½ οΏ½ PROPN iajs-2992 133 79 π‘˜ π‘˜ PROPN iajs-2992 133 80 ∈ ∈ PROPN iajs-2992 133 81 οΏ½ οΏ½ PROPN iajs-2992 133 82 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 133 83 οΏ½ οΏ½ PROPN iajs-2992 133 84 𝐴 𝐴 PROPN iajs-2992 133 85 , , PUNCT iajs-2992 133 86 βˆ€π‘˜ βˆ€π‘˜ NOUN iajs-2992 133 87 , , PUNCT iajs-2992 133 88 and and CCONJ iajs-2992 133 89 𝐺0( 𝐺0( PUNCT iajs-2992 133 90 οΏ½ οΏ½ PROPN iajs-2992 133 91 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 92 οΏ½ οΏ½ PROPN iajs-2992 133 93 ) ) PUNCT iajs-2992 133 94 ≀ ≀ NUM iajs-2992 133 95 π‘™π‘–π‘š π‘™π‘–π‘š VERB iajs-2992 133 96 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 133 97 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 133 98 οΏ½ οΏ½ PROPN iajs-2992 133 99 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 133 100 οΏ½ οΏ½ NOUN iajs-2992 133 101 π‘˜βˆˆ π‘˜βˆˆ PROPN iajs-2992 133 102 οΏ½ οΏ½ PROPN iajs-2992 133 103 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 133 104 οΏ½ οΏ½ PROPN iajs-2992 133 105 𝐴 𝐴 PROPN iajs-2992 133 106 𝐺0( 𝐺0( NUM iajs-2992 133 107 οΏ½ οΏ½ PROPN iajs-2992 133 108 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 133 109 οΏ½ οΏ½ PROPN iajs-2992 133 110 π‘˜ π‘˜ NOUN iajs-2992 133 111 ) ) PUNCT iajs-2992 133 112 = = SYM iajs-2992 134 1 π‘™π‘–π‘š π‘™π‘–π‘š PROPN iajs-2992 134 2 π‘˜β†’βˆž π‘˜β†’βˆž NUM iajs-2992 134 3 𝐺0( 𝐺0( NOUN iajs-2992 134 4 οΏ½ οΏ½ NOUN iajs-2992 134 5 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 134 6 οΏ½ οΏ½ PROPN iajs-2992 134 7 π‘˜ π‘˜ NOUN iajs-2992 134 8 ) ) PUNCT iajs-2992 134 9 = = PUNCT iajs-2992 134 10 𝑖𝑛𝑓 𝑖𝑛𝑓 NOUN iajs-2992 134 11 οΏ½ οΏ½ PROPN iajs-2992 134 12 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 134 13 οΏ½ οΏ½ NOUN iajs-2992 134 14 π‘˜βˆˆ π‘˜βˆˆ PROPN iajs-2992 134 15 οΏ½ οΏ½ PROPN iajs-2992 134 16 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 134 17 οΏ½ οΏ½ PROPN iajs-2992 134 18 𝐴 𝐴 PROPN iajs-2992 134 19 𝐺0( 𝐺0( NUM iajs-2992 134 20 οΏ½ οΏ½ PROPN iajs-2992 134 21 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 134 22 οΏ½ οΏ½ PROPN iajs-2992 134 23 ) ) PUNCT iajs-2992 134 24 ⟹ ⟹ NUM iajs-2992 134 25 𝐺0( 𝐺0( SYM iajs-2992 134 26 οΏ½ οΏ½ PROPN iajs-2992 134 27 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 134 28 οΏ½ οΏ½ PROPN iajs-2992 134 29 ) ) PUNCT iajs-2992 135 1 = = SYM iajs-2992 135 2 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN iajs-2992 135 3 οΏ½ οΏ½ PROPN iajs-2992 135 4 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 135 5 οΏ½ οΏ½ NOUN iajs-2992 135 6 π‘˜βˆˆ π‘˜βˆˆ PROPN iajs-2992 135 7 οΏ½ οΏ½ PROPN iajs-2992 135 8 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 135 9 οΏ½ οΏ½ PROPN iajs-2992 135 10 𝐴 𝐴 PROPN iajs-2992 135 11 𝐺0( 𝐺0( NUM iajs-2992 135 12 οΏ½ οΏ½ PROPN iajs-2992 135 13 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 135 14 οΏ½ οΏ½ PROPN iajs-2992 135 15 ) ) PUNCT iajs-2992 135 16 , , PUNCT iajs-2992 135 17 then then ADV iajs-2992 135 18 οΏ½ οΏ½ PROPN iajs-2992 135 19 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 135 20 οΏ½ οΏ½ PROPN iajs-2992 135 21 is be AUX iajs-2992 135 22 a a DET iajs-2992 135 23 qocccv qocccv PROPN iajs-2992 135 24 . . PUNCT iajs-2992 136 1 theorem theorem ADJ iajs-2992 136 2 3.2 3.2 NUM iajs-2992 136 3 : : PUNCT iajs-2992 136 4 neglecting neglect VERB iajs-2992 136 5 the the DET iajs-2992 136 6 index index NOUN iajs-2992 136 7 𝑙 𝑙 NOUN iajs-2992 136 8 from from ADP iajs-2992 136 9 𝐺𝑙 𝐺𝑙 PROPN iajs-2992 136 10 and and CCONJ iajs-2992 136 11 𝑔𝑙𝑖. 𝑔𝑙𝑖. NOUN iajs-2992 136 12 the the DET iajs-2992 136 13 qaes qaes PROPN iajs-2992 136 14 οΏ½ οΏ½ PROPN iajs-2992 136 15 βƒ— βƒ— NOUN iajs-2992 136 16 οΏ½ οΏ½ NOUN iajs-2992 136 17 = = SYM iajs-2992 136 18 ( ( PUNCT iajs-2992 136 19 𝑍1 𝑍1 PROPN iajs-2992 136 20 , , PUNCT iajs-2992 136 21 𝑍2 𝑍2 PROPN iajs-2992 136 22 , , PUNCT iajs-2992 136 23 𝑍3 𝑍3 NOUN iajs-2992 136 24 , , PUNCT iajs-2992 136 25 𝑍4 𝑍4 PROPN iajs-2992 136 26 ) ) PUNCT iajs-2992 136 27 of of ADP iajs-2992 136 28 the the DET iajs-2992 136 29 qses qse NOUN iajs-2992 136 30 in in ADP iajs-2992 136 31 ( ( PUNCT iajs-2992 136 32 ( ( PUNCT iajs-2992 136 33 1)-(6 1)-(6 NUM iajs-2992 136 34 ) ) PUNCT iajs-2992 136 35 ) ) PUNCT iajs-2992 136 36 can can AUX iajs-2992 136 37 be be AUX iajs-2992 136 38 formulated formulate VERB iajs-2992 136 39 as as ADP iajs-2992 136 40 𝑍1𝑑𝑑 𝑍1𝑑𝑑 NUM iajs-2992 136 41 βˆ’ βˆ’ NOUN iajs-2992 136 42 βˆ†π‘1 βˆ†π‘1 PROPN iajs-2992 136 43 + + NOUN iajs-2992 136 44 𝑍1 𝑍1 NOUN iajs-2992 137 1 + + CCONJ iajs-2992 137 2 𝑍2 𝑍2 VERB iajs-2992 137 3 βˆ’ βˆ’ PROPN iajs-2992 137 4 𝑍3 𝑍3 NOUN iajs-2992 137 5 βˆ’ βˆ’ NOUN iajs-2992 137 6 𝑍4 𝑍4 NOUN iajs-2992 137 7 = = SYM iajs-2992 137 8 𝑍1𝑓1𝑦1 𝑍1𝑓1𝑦1 NOUN iajs-2992 137 9 ( ( PUNCT iajs-2992 137 10 π‘₯ π‘₯ NOUN iajs-2992 137 11 , , PUNCT iajs-2992 137 12 𝑑 𝑑 PROPN iajs-2992 137 13 , , PUNCT iajs-2992 137 14 𝑦1 𝑦1 NOUN iajs-2992 137 15 , , PUNCT iajs-2992 137 16 𝑒1 𝑒1 NOUN iajs-2992 137 17 ) ) PUNCT iajs-2992 138 1 + + NUM iajs-2992 138 2 𝑔1𝑦1 𝑔1𝑦1 SYM iajs-2992 138 3 ( ( PUNCT iajs-2992 138 4 π‘₯ π‘₯ NOUN iajs-2992 138 5 , , PUNCT iajs-2992 138 6 𝑑 𝑑 PROPN iajs-2992 138 7 , , PUNCT iajs-2992 138 8 𝑦1 𝑦1 NOUN iajs-2992 138 9 , , PUNCT iajs-2992 138 10 𝑒1 𝑒1 NOUN iajs-2992 138 11 ) ) PUNCT iajs-2992 138 12 , , PUNCT iajs-2992 138 13 in in ADP iajs-2992 138 14 𝑄 𝑄 PROPN iajs-2992 138 15 , , PUNCT iajs-2992 138 16 ( ( PUNCT iajs-2992 138 17 27 27 NUM iajs-2992 138 18 ) ) PUNCT iajs-2992 138 19 𝑍1 𝑍1 X iajs-2992 139 1 = = PUNCT iajs-2992 139 2 0 0 NUM iajs-2992 140 1 on on ADP iajs-2992 140 2 Οƒ Οƒ PROPN iajs-2992 140 3 , , PUNCT iajs-2992 140 4 𝑍1(π‘₯ 𝑍1(π‘₯ PROPN iajs-2992 140 5 , , PUNCT iajs-2992 140 6 𝑇 𝑇 PROPN iajs-2992 140 7 ) ) PUNCT iajs-2992 140 8 = = SYM iajs-2992 140 9 𝑍1𝑑(π‘₯ 𝑍1𝑑(π‘₯ NOUN iajs-2992 140 10 , , PUNCT iajs-2992 140 11 𝑇 𝑇 PROPN iajs-2992 140 12 ) ) PUNCT iajs-2992 140 13 = = SYM iajs-2992 140 14 0 0 NUM iajs-2992 140 15 on on ADP iajs-2992 140 16 Ο‰ Ο‰ PROPN iajs-2992 140 17 , , PUNCT iajs-2992 140 18 ( ( PUNCT iajs-2992 140 19 28 28 NUM iajs-2992 140 20 ) ) PUNCT iajs-2992 140 21 𝑍2𝑑𝑑 𝑍2𝑑𝑑 NOUN iajs-2992 140 22 βˆ’ βˆ’ NOUN iajs-2992 141 1 βˆ†π‘2 βˆ†π‘2 NOUN iajs-2992 141 2 βˆ’ βˆ’ PROPN iajs-2992 141 3 𝑍1 𝑍1 PROPN iajs-2992 141 4 + + CCONJ iajs-2992 141 5 𝑍2 𝑍2 VERB iajs-2992 141 6 + + CCONJ iajs-2992 141 7 𝑍3 𝑍3 NOUN iajs-2992 141 8 + + CCONJ iajs-2992 141 9 𝑍4 𝑍4 NOUN iajs-2992 141 10 = = SYM iajs-2992 141 11 𝑍2𝑓2𝑦2 𝑍2𝑓2𝑦2 NOUN iajs-2992 141 12 ( ( PUNCT iajs-2992 141 13 π‘₯ π‘₯ PROPN iajs-2992 141 14 , , PUNCT iajs-2992 141 15 𝑑 𝑑 PROPN iajs-2992 141 16 , , PUNCT iajs-2992 141 17 𝑦2 𝑦2 NOUN iajs-2992 141 18 , , PUNCT iajs-2992 141 19 𝑒2 𝑒2 PROPN iajs-2992 141 20 ) ) PUNCT iajs-2992 142 1 + + CCONJ iajs-2992 142 2 𝑔2𝑦2 𝑔2𝑦2 X iajs-2992 142 3 ( ( PUNCT iajs-2992 142 4 π‘₯ π‘₯ PROPN iajs-2992 142 5 , , PUNCT iajs-2992 142 6 𝑑 𝑑 PROPN iajs-2992 142 7 , , PUNCT iajs-2992 142 8 𝑦2 𝑦2 NOUN iajs-2992 142 9 , , PUNCT iajs-2992 142 10 𝑒2 𝑒2 PROPN iajs-2992 142 11 ) ) PUNCT iajs-2992 142 12 , , PUNCT iajs-2992 142 13 in in ADP iajs-2992 142 14 𝑄 𝑄 PRON iajs-2992 142 15 , , PUNCT iajs-2992 142 16 ( ( PUNCT iajs-2992 142 17 29 29 NUM iajs-2992 142 18 ) ) PUNCT iajs-2992 142 19 𝑍2 𝑍2 VERB iajs-2992 142 20 = = SYM iajs-2992 142 21 0 0 NUM iajs-2992 142 22 on on ADP iajs-2992 142 23 Οƒ Οƒ PROPN iajs-2992 142 24 , , PUNCT iajs-2992 142 25 𝑍2(π‘₯ 𝑍2(π‘₯ PROPN iajs-2992 142 26 , , PUNCT iajs-2992 142 27 𝑇 𝑇 PROPN iajs-2992 142 28 ) ) PUNCT iajs-2992 142 29 = = SYM iajs-2992 143 1 𝑍2𝑑(π‘₯ 𝑍2𝑑(π‘₯ PROPN iajs-2992 143 2 , , PUNCT iajs-2992 143 3 𝑇 𝑇 PROPN iajs-2992 143 4 ) ) PUNCT iajs-2992 143 5 = = SYM iajs-2992 143 6 0 0 NUM iajs-2992 144 1 on on ADP iajs-2992 144 2 Ο‰ Ο‰ NUM iajs-2992 144 3 , , PUNCT iajs-2992 144 4 ( ( PUNCT iajs-2992 144 5 30 30 NUM iajs-2992 144 6 ) ) PUNCT iajs-2992 144 7 𝑍3𝑑𝑑 𝑍3𝑑𝑑 NOUN iajs-2992 144 8 βˆ’ βˆ’ X iajs-2992 144 9 βˆ†π‘3 βˆ†π‘3 PROPN iajs-2992 144 10 + + NUM iajs-2992 144 11 𝑍1 𝑍1 AUX iajs-2992 144 12 βˆ’ βˆ’ PROPN iajs-2992 144 13 𝑍2 𝑍2 VERB iajs-2992 144 14 + + CCONJ iajs-2992 144 15 𝑍3 𝑍3 NOUN iajs-2992 144 16 βˆ’ βˆ’ NOUN iajs-2992 144 17 𝑍4 𝑍4 PROPN iajs-2992 144 18 = = SYM iajs-2992 144 19 𝑍3𝑓3𝑦3 𝑍3𝑓3𝑦3 X iajs-2992 144 20 ( ( PUNCT iajs-2992 144 21 π‘₯ π‘₯ NOUN iajs-2992 144 22 , , PUNCT iajs-2992 144 23 𝑑 𝑑 PROPN iajs-2992 144 24 , , PUNCT iajs-2992 144 25 𝑦3 𝑦3 PROPN iajs-2992 144 26 , , PUNCT iajs-2992 144 27 𝑒3 𝑒3 PROPN iajs-2992 144 28 ) ) PUNCT iajs-2992 144 29 + + NUM iajs-2992 144 30 𝑔3𝑦3 𝑔3𝑦3 PROPN iajs-2992 144 31 ( ( PUNCT iajs-2992 144 32 π‘₯ π‘₯ PROPN iajs-2992 144 33 , , PUNCT iajs-2992 144 34 𝑑 𝑑 PROPN iajs-2992 144 35 , , PUNCT iajs-2992 144 36 𝑦3 𝑦3 PROPN iajs-2992 144 37 , , PUNCT iajs-2992 144 38 𝑒3 𝑒3 PROPN iajs-2992 144 39 ) ) PUNCT iajs-2992 144 40 , , PUNCT iajs-2992 144 41 in in ADP iajs-2992 144 42 𝑄 𝑄 PROPN iajs-2992 144 43 , , PUNCT iajs-2992 144 44 ( ( PUNCT iajs-2992 144 45 31 31 NUM iajs-2992 144 46 ) ) PUNCT iajs-2992 144 47 𝑍3 𝑍3 NOUN iajs-2992 145 1 = = SYM iajs-2992 145 2 0 0 NUM iajs-2992 146 1 on on ADP iajs-2992 146 2 Οƒ Οƒ PROPN iajs-2992 146 3 , , PUNCT iajs-2992 146 4 𝑍3(π‘₯ 𝑍3(π‘₯ PROPN iajs-2992 146 5 , , PUNCT iajs-2992 146 6 𝑇 𝑇 PROPN iajs-2992 146 7 ) ) PUNCT iajs-2992 146 8 = = SYM iajs-2992 146 9 𝑍3𝑑(π‘₯ 𝑍3𝑑(π‘₯ PROPN iajs-2992 146 10 , , PUNCT iajs-2992 146 11 𝑇 𝑇 PROPN iajs-2992 146 12 ) ) PUNCT iajs-2992 146 13 = = SYM iajs-2992 146 14 0 0 NUM iajs-2992 147 1 on on ADP iajs-2992 147 2 Ο‰ Ο‰ PROPN iajs-2992 147 3 , , PUNCT iajs-2992 147 4 ( ( PUNCT iajs-2992 147 5 32 32 NUM iajs-2992 147 6 ) ) PUNCT iajs-2992 147 7 𝑍4𝑑𝑑 𝑍4𝑑𝑑 NOUN iajs-2992 147 8 βˆ’ βˆ’ NOUN iajs-2992 148 1 βˆ†π‘4 βˆ†π‘4 ADV iajs-2992 148 2 + + NUM iajs-2992 148 3 𝑍1 𝑍1 PROPN iajs-2992 148 4 βˆ’ βˆ’ PROPN iajs-2992 148 5 𝑍2 𝑍2 VERB iajs-2992 148 6 + + CCONJ iajs-2992 148 7 𝑍3 𝑍3 NOUN iajs-2992 148 8 + + CCONJ iajs-2992 148 9 𝑍4 𝑍4 NOUN iajs-2992 148 10 = = SYM iajs-2992 148 11 𝑍4𝑓4𝑦4 𝑍4𝑓4𝑦4 X iajs-2992 148 12 ( ( PUNCT iajs-2992 148 13 π‘₯ π‘₯ NOUN iajs-2992 148 14 , , PUNCT iajs-2992 148 15 𝑑 𝑑 PROPN iajs-2992 148 16 , , PUNCT iajs-2992 148 17 𝑦4 𝑦4 NOUN iajs-2992 148 18 , , PUNCT iajs-2992 148 19 𝑒4 𝑒4 NOUN iajs-2992 148 20 ) ) PUNCT iajs-2992 148 21 + + NUM iajs-2992 148 22 𝑔4𝑦4 𝑔4𝑦4 PROPN iajs-2992 148 23 ( ( PUNCT iajs-2992 148 24 π‘₯ π‘₯ PROPN iajs-2992 148 25 , , PUNCT iajs-2992 148 26 𝑑 𝑑 PROPN iajs-2992 148 27 , , PUNCT iajs-2992 148 28 𝑦4 𝑦4 NOUN iajs-2992 148 29 , , PUNCT iajs-2992 148 30 𝑒4 𝑒4 PROPN iajs-2992 148 31 ) ) PUNCT iajs-2992 148 32 , , PUNCT iajs-2992 148 33 in in ADP iajs-2992 148 34 𝑄 𝑄 PROPN iajs-2992 148 35 , , PUNCT iajs-2992 148 36 ( ( PUNCT iajs-2992 148 37 33 33 NUM iajs-2992 148 38 ) ) PUNCT iajs-2992 148 39 𝑍4 𝑍4 NOUN iajs-2992 148 40 = = SYM iajs-2992 148 41 0 0 NUM iajs-2992 148 42 on on ADP iajs-2992 148 43 Οƒ Οƒ PROPN iajs-2992 148 44 , , PUNCT iajs-2992 148 45 𝑍4(π‘₯ 𝑍4(π‘₯ PROPN iajs-2992 148 46 , , PUNCT iajs-2992 148 47 𝑇 𝑇 PROPN iajs-2992 148 48 ) ) PUNCT iajs-2992 148 49 = = PUNCT iajs-2992 149 1 𝑍4𝑑(π‘₯ 𝑍4𝑑(π‘₯ PROPN iajs-2992 149 2 , , PUNCT iajs-2992 149 3 𝑇 𝑇 PROPN iajs-2992 149 4 ) ) PUNCT iajs-2992 149 5 = = SYM iajs-2992 149 6 0 0 NUM iajs-2992 150 1 on on ADP iajs-2992 150 2 Ο‰ Ο‰ NUM iajs-2992 150 3 , , PUNCT iajs-2992 150 4 ( ( PUNCT iajs-2992 150 5 34 34 NUM iajs-2992 150 6 ) ) PUNCT iajs-2992 150 7 and and CCONJ iajs-2992 150 8 the the DET iajs-2992 150 9 ham ham NOUN iajs-2992 150 10 is be AUX iajs-2992 150 11 defined define VERB iajs-2992 150 12 as as ADP iajs-2992 150 13 : : PUNCT iajs-2992 150 14 𝐻(π‘₯ 𝐻(π‘₯ NUM iajs-2992 150 15 , , PUNCT iajs-2992 150 16 𝑑 𝑑 PROPN iajs-2992 150 17 , , PUNCT iajs-2992 150 18 οΏ½ οΏ½ PROPN iajs-2992 150 19 βƒ— βƒ— PROPN iajs-2992 150 20 οΏ½ οΏ½ PROPN iajs-2992 150 21 , , PUNCT iajs-2992 150 22 οΏ½ οΏ½ PROPN iajs-2992 150 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 150 24 οΏ½ οΏ½ PROPN iajs-2992 150 25 , , PUNCT iajs-2992 150 26 οΏ½ οΏ½ PROPN iajs-2992 150 27 βƒ— βƒ— NOUN iajs-2992 150 28 οΏ½ οΏ½ PROPN iajs-2992 150 29 ) ) PUNCT iajs-2992 150 30 = = PUNCT iajs-2992 151 1 βˆ‘ βˆ‘ PUNCT iajs-2992 151 2 𝑖=1 𝑖=1 PROPN iajs-2992 151 3 4 4 NUM iajs-2992 151 4 ( ( PUNCT iajs-2992 151 5 𝑍𝑖𝑓𝑖(π‘₯ 𝑍𝑖𝑓𝑖(π‘₯ PROPN iajs-2992 151 6 , , PUNCT iajs-2992 151 7 𝑑 𝑑 PROPN iajs-2992 151 8 , , PUNCT iajs-2992 151 9 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 151 10 , , PUNCT iajs-2992 151 11 𝑒𝑖 𝑒𝑖 PROPN iajs-2992 151 12 ) ) PUNCT iajs-2992 151 13 + + CCONJ iajs-2992 151 14 𝑔𝑖(π‘₯ 𝑔𝑖(π‘₯ NUM iajs-2992 151 15 , , PUNCT iajs-2992 151 16 𝑑 𝑑 PROPN iajs-2992 151 17 , , PUNCT iajs-2992 151 18 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 151 19 , , PUNCT iajs-2992 151 20 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 151 21 ) ) PUNCT iajs-2992 151 22 ) ) PUNCT iajs-2992 151 23 , , PUNCT iajs-2992 151 24 where where SCONJ iajs-2992 151 25 𝐺 𝐺 PROPN iajs-2992 151 26 ( ( PUNCT iajs-2992 151 27 οΏ½ οΏ½ PROPN iajs-2992 151 28 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 151 29 οΏ½ οΏ½ PROPN iajs-2992 151 30 ) ) PUNCT iajs-2992 151 31 = = PUNCT iajs-2992 151 32 Οƒ Οƒ NOUN iajs-2992 151 33 𝑖=1 𝑖=1 PROPN iajs-2992 151 34 4 4 NUM iajs-2992 151 35 ∫ ∫ NOUN iajs-2992 151 36 𝑄 𝑄 PROPN iajs-2992 151 37 𝑔 𝑔 PROPN iajs-2992 151 38 𝑖 𝑖 SYM iajs-2992 151 39 ( ( PUNCT iajs-2992 151 40 π‘₯ π‘₯ PROPN iajs-2992 151 41 , , PUNCT iajs-2992 151 42 𝑑 𝑑 PROPN iajs-2992 151 43 , , PUNCT iajs-2992 151 44 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 151 45 , , PUNCT iajs-2992 151 46 𝑒𝑖)𝑑π‘₯𝑑𝑑. 𝑒𝑖)𝑑π‘₯𝑑𝑑. VERB iajs-2992 151 47 then then ADV iajs-2992 151 48 the the DET iajs-2992 151 49 dd dd NOUN iajs-2992 151 50 of of ADP iajs-2992 151 51 g g PROPN iajs-2992 151 52 is be AUX iajs-2992 151 53 𝐷𝐺( 𝐷𝐺( PROPN iajs-2992 151 54 οΏ½ οΏ½ PROPN iajs-2992 151 55 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 151 56 οΏ½ οΏ½ PROPN iajs-2992 151 57 , , PUNCT iajs-2992 151 58 οΏ½ οΏ½ PROPN iajs-2992 151 59 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 151 60 οΏ½ οΏ½ PROPN iajs-2992 151 61 βˆ’ βˆ’ PROPN iajs-2992 151 62 οΏ½ οΏ½ PROPN iajs-2992 151 63 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 151 64 οΏ½ οΏ½ PROPN iajs-2992 151 65 ) ) PUNCT iajs-2992 151 66 = = PROPN iajs-2992 151 67 lim lim PROPN iajs-2992 151 68 β†’0 β†’0 NOUN iajs-2992 151 69 𝐺( 𝐺( PROPN iajs-2992 151 70 οΏ½ οΏ½ PROPN iajs-2992 151 71 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 151 72 οΏ½ οΏ½ PROPN iajs-2992 151 73 + + CCONJ iajs-2992 151 74 𝛿 𝛿 PROPN iajs-2992 151 75 οΏ½ οΏ½ PROPN iajs-2992 151 76 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— NOUN iajs-2992 151 77 οΏ½ οΏ½ NOUN iajs-2992 151 78 )βˆ’πΊ( )βˆ’πΊ( NOUN iajs-2992 151 79 οΏ½ οΏ½ PROPN iajs-2992 151 80 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— NOUN iajs-2992 151 81 οΏ½ οΏ½ PROPN iajs-2992 151 82 ) ) PUNCT iajs-2992 151 83 = = SYM iajs-2992 152 1 ∫ ∫ PROPN iajs-2992 152 2 𝑄 𝑄 PROPN iajs-2992 152 3 𝐻 𝐻 PROPN iajs-2992 152 4 οΏ½ οΏ½ PROPN iajs-2992 152 5 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 152 6 οΏ½ οΏ½ PROPN iajs-2992 152 7 (π‘₯ (π‘₯ PROPN iajs-2992 152 8 , , PUNCT iajs-2992 152 9 𝑑 𝑑 PROPN iajs-2992 152 10 , , PUNCT iajs-2992 152 11 οΏ½ οΏ½ PROPN iajs-2992 152 12 βƒ— βƒ— PROPN iajs-2992 152 13 οΏ½ οΏ½ PROPN iajs-2992 152 14 , , PUNCT iajs-2992 152 15 οΏ½ οΏ½ PROPN iajs-2992 152 16 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 152 17 οΏ½ οΏ½ PROPN iajs-2992 152 18 , , PUNCT iajs-2992 152 19 οΏ½ οΏ½ PROPN iajs-2992 152 20 βƒ— βƒ— PROPN iajs-2992 152 21 οΏ½ οΏ½ PROPN iajs-2992 152 22 )( )( SYM iajs-2992 152 23 οΏ½ οΏ½ PROPN iajs-2992 152 24 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 152 25 οΏ½ οΏ½ PROPN iajs-2992 152 26 βˆ’ βˆ’ PROPN iajs-2992 152 27 οΏ½ οΏ½ PROPN iajs-2992 152 28 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 152 29 οΏ½ οΏ½ PROPN iajs-2992 152 30 )𝑑π‘₯𝑑𝑑 )𝑑π‘₯𝑑𝑑 PUNCT iajs-2992 152 31 . . PUNCT iajs-2992 153 1 proof proof NOUN iajs-2992 153 2 : : PUNCT iajs-2992 153 3 the the DET iajs-2992 153 4 wf wf PROPN iajs-2992 153 5 of of ADP iajs-2992 153 6 the the DET iajs-2992 153 7 qaes qaes PROPN iajs-2992 153 8 βˆ€π‘£π‘– βˆ€π‘£π‘– PROPN iajs-2992 153 9 ∈ ∈ PROPN iajs-2992 153 10 𝑉 𝑉 PROPN iajs-2992 153 11 and and CCONJ iajs-2992 153 12 𝑖 𝑖 SYM iajs-2992 153 13 = = NOUN iajs-2992 153 14 1,2,3,4 1,2,3,4 NUM iajs-2992 153 15 is be AUX iajs-2992 153 16 ( ( PUNCT iajs-2992 153 17 𝑍1𝑑𝑑 𝑍1𝑑𝑑 X iajs-2992 153 18 , , PUNCT iajs-2992 153 19 𝑣1 𝑣1 NOUN iajs-2992 153 20 ) ) PUNCT iajs-2992 153 21 + + CCONJ iajs-2992 153 22 ( ( PUNCT iajs-2992 153 23 βˆ‡π‘1 βˆ‡π‘1 ADJ iajs-2992 153 24 , , PUNCT iajs-2992 153 25 βˆ‡π‘£1 βˆ‡π‘£1 NOUN iajs-2992 153 26 ) ) PUNCT iajs-2992 154 1 + + CCONJ iajs-2992 154 2 ( ( PUNCT iajs-2992 154 3 𝑍1 𝑍1 PROPN iajs-2992 154 4 , , PUNCT iajs-2992 154 5 𝑣1 𝑣1 PROPN iajs-2992 154 6 ) ) PUNCT iajs-2992 154 7 + + CCONJ iajs-2992 154 8 ( ( PUNCT iajs-2992 154 9 𝑍2 𝑍2 ADJ iajs-2992 154 10 , , PUNCT iajs-2992 154 11 𝑣1 𝑣1 PROPN iajs-2992 154 12 ) ) PUNCT iajs-2992 154 13 βˆ’ βˆ’ PROPN iajs-2992 154 14 ( ( PUNCT iajs-2992 154 15 𝑍3 𝑍3 PROPN iajs-2992 154 16 , , PUNCT iajs-2992 154 17 𝑣1 𝑣1 PROPN iajs-2992 154 18 ) ) PUNCT iajs-2992 154 19 βˆ’ βˆ’ PROPN iajs-2992 154 20 ( ( PUNCT iajs-2992 154 21 𝑍4 𝑍4 PROPN iajs-2992 154 22 , , PUNCT iajs-2992 154 23 𝑣1 𝑣1 NOUN iajs-2992 154 24 ) ) PUNCT iajs-2992 154 25 = = PUNCT iajs-2992 154 26 ( ( PUNCT iajs-2992 154 27 𝑍1𝑓1𝑦1 𝑍1𝑓1𝑦1 NOUN iajs-2992 154 28 , , PUNCT iajs-2992 154 29 𝑣1 𝑣1 PROPN iajs-2992 154 30 ) ) PUNCT iajs-2992 154 31 + + CCONJ iajs-2992 154 32 ( ( PUNCT iajs-2992 154 33 𝑔1𝑦1 𝑔1𝑦1 NUM iajs-2992 154 34 , , PUNCT iajs-2992 154 35 𝑣1 𝑣1 PROPN iajs-2992 154 36 ) ) PUNCT iajs-2992 154 37 , , PUNCT iajs-2992 154 38 βˆ€π‘£1 βˆ€π‘£1 PROPN iajs-2992 154 39 ∈ ∈ PROPN iajs-2992 154 40 𝑉 𝑉 PROPN iajs-2992 154 41 a.e a.e PROPN iajs-2992 154 42 . . PROPN iajs-2992 155 1 on on ADP iajs-2992 155 2 𝐼 𝐼 PROPN iajs-2992 155 3 , , PUNCT iajs-2992 155 4 ( ( PUNCT iajs-2992 155 5 35 35 NUM iajs-2992 155 6 ) ) PUNCT iajs-2992 155 7 ( ( PUNCT iajs-2992 155 8 𝑍1(𝑇 𝑍1(𝑇 PROPN iajs-2992 155 9 ) ) PUNCT iajs-2992 155 10 , , PUNCT iajs-2992 155 11 𝑣1 𝑣1 NOUN iajs-2992 155 12 ) ) PUNCT iajs-2992 155 13 = = PUNCT iajs-2992 155 14 ( ( PUNCT iajs-2992 155 15 𝑍1𝑑(𝑇 𝑍1𝑑(𝑇 ADJ iajs-2992 155 16 ) ) PUNCT iajs-2992 155 17 , , PUNCT iajs-2992 155 18 𝑣1 𝑣1 NOUN iajs-2992 155 19 ) ) PUNCT iajs-2992 155 20 = = SYM iajs-2992 155 21 0 0 NUM iajs-2992 155 22 , , PUNCT iajs-2992 155 23 ( ( PUNCT iajs-2992 155 24 36 36 NUM iajs-2992 155 25 ) ) PUNCT iajs-2992 155 26 ( ( PUNCT iajs-2992 155 27 𝑍2𝑑𝑑 𝑍2𝑑𝑑 X iajs-2992 155 28 , , PUNCT iajs-2992 155 29 𝑣2 𝑣2 PROPN iajs-2992 155 30 ) ) PUNCT iajs-2992 155 31 + + CCONJ iajs-2992 155 32 ( ( PUNCT iajs-2992 155 33 βˆ‡π‘2 βˆ‡π‘2 ADJ iajs-2992 155 34 , , PUNCT iajs-2992 155 35 βˆ‡π‘£2 βˆ‡π‘£2 PROPN iajs-2992 155 36 ) ) PUNCT iajs-2992 156 1 βˆ’ βˆ’ PROPN iajs-2992 156 2 ( ( PUNCT iajs-2992 156 3 𝑍1 𝑍1 PROPN iajs-2992 156 4 , , PUNCT iajs-2992 156 5 𝑣2 𝑣2 PROPN iajs-2992 156 6 ) ) PUNCT iajs-2992 156 7 + + CCONJ iajs-2992 156 8 ( ( PUNCT iajs-2992 156 9 𝑍2 𝑍2 PROPN iajs-2992 156 10 , , PUNCT iajs-2992 156 11 𝑣2 𝑣2 PROPN iajs-2992 156 12 ) ) PUNCT iajs-2992 156 13 + + CCONJ iajs-2992 156 14 ( ( PUNCT iajs-2992 156 15 𝑍3 𝑍3 PROPN iajs-2992 156 16 , , PUNCT iajs-2992 156 17 𝑣2 𝑣2 PROPN iajs-2992 156 18 ) ) PUNCT iajs-2992 156 19 + + CCONJ iajs-2992 156 20 ( ( PUNCT iajs-2992 156 21 𝑍4 𝑍4 PROPN iajs-2992 156 22 , , PUNCT iajs-2992 156 23 𝑣2 𝑣2 PROPN iajs-2992 156 24 ) ) PUNCT iajs-2992 156 25 = = PUNCT iajs-2992 156 26 ( ( PUNCT iajs-2992 156 27 𝑍2𝑓2𝑦2 𝑍2𝑓2𝑦2 NOUN iajs-2992 156 28 , , PUNCT iajs-2992 156 29 𝑣2 𝑣2 PROPN iajs-2992 156 30 ) ) PUNCT iajs-2992 156 31 + + CCONJ iajs-2992 156 32 ( ( PUNCT iajs-2992 156 33 𝑔2𝑦2 𝑔2𝑦2 PROPN iajs-2992 156 34 , , PUNCT iajs-2992 156 35 𝑣2 𝑣2 PROPN iajs-2992 156 36 ) ) PUNCT iajs-2992 156 37 , , PUNCT iajs-2992 156 38 βˆ€π‘£2 βˆ€π‘£2 PROPN iajs-2992 156 39 ∈ ∈ PROPN iajs-2992 156 40 𝑉 𝑉 PROPN iajs-2992 156 41 a.e a.e PROPN iajs-2992 156 42 . . PROPN iajs-2992 157 1 on on ADP iajs-2992 157 2 , , PUNCT iajs-2992 157 3 ( ( PUNCT iajs-2992 157 4 37 37 NUM iajs-2992 157 5 ) ) PUNCT iajs-2992 157 6 ihjpas ihjpa NOUN iajs-2992 157 7 . . PUNCT iajs-2992 158 1 36(2)2023 36(2)2023 NUM iajs-2992 158 2 336 336 NUM iajs-2992 158 3 ( ( PUNCT iajs-2992 158 4 𝑍2(𝑇 𝑍2(𝑇 PROPN iajs-2992 158 5 ) ) PUNCT iajs-2992 158 6 , , PUNCT iajs-2992 158 7 𝑣2 𝑣2 PROPN iajs-2992 158 8 ) ) PUNCT iajs-2992 158 9 = = PUNCT iajs-2992 158 10 ( ( PUNCT iajs-2992 158 11 𝑍2𝑑(𝑇 𝑍2𝑑(𝑇 PROPN iajs-2992 158 12 ) ) PUNCT iajs-2992 158 13 , , PUNCT iajs-2992 158 14 𝑣2 𝑣2 PROPN iajs-2992 158 15 ) ) PUNCT iajs-2992 158 16 = = SYM iajs-2992 158 17 0 0 NUM iajs-2992 158 18 , , PUNCT iajs-2992 158 19 ( ( PUNCT iajs-2992 158 20 38 38 NUM iajs-2992 158 21 ) ) PUNCT iajs-2992 158 22 ( ( PUNCT iajs-2992 158 23 𝑍3𝑑𝑑 𝑍3𝑑𝑑 NOUN iajs-2992 158 24 , , PUNCT iajs-2992 158 25 𝑣3 𝑣3 ADJ iajs-2992 158 26 ) ) PUNCT iajs-2992 158 27 + + CCONJ iajs-2992 158 28 ( ( PUNCT iajs-2992 158 29 βˆ‡π‘3 βˆ‡π‘3 NOUN iajs-2992 158 30 , , PUNCT iajs-2992 158 31 βˆ‡π‘£3 βˆ‡π‘£3 NOUN iajs-2992 158 32 ) ) PUNCT iajs-2992 159 1 + + CCONJ iajs-2992 159 2 ( ( PUNCT iajs-2992 159 3 𝑍1 𝑍1 INTJ iajs-2992 159 4 , , PUNCT iajs-2992 159 5 𝑣3 𝑣3 ADJ iajs-2992 159 6 ) ) PUNCT iajs-2992 159 7 βˆ’ βˆ’ PROPN iajs-2992 159 8 ( ( PUNCT iajs-2992 159 9 𝑍2 𝑍2 INTJ iajs-2992 159 10 , , PUNCT iajs-2992 159 11 𝑣3 𝑣3 ADJ iajs-2992 159 12 ) ) PUNCT iajs-2992 160 1 + + CCONJ iajs-2992 160 2 ( ( PUNCT iajs-2992 160 3 𝑍3 𝑍3 NOUN iajs-2992 160 4 , , PUNCT iajs-2992 160 5 𝑣3 𝑣3 ADJ iajs-2992 160 6 ) ) PUNCT iajs-2992 160 7 βˆ’ βˆ’ PROPN iajs-2992 160 8 ( ( PUNCT iajs-2992 160 9 𝑍4 𝑍4 INTJ iajs-2992 160 10 , , PUNCT iajs-2992 160 11 𝑣3 𝑣3 ADJ iajs-2992 160 12 ) ) PUNCT iajs-2992 160 13 = = SYM iajs-2992 160 14 ( ( PUNCT iajs-2992 160 15 𝑍3𝑓3𝑦3 𝑍3𝑓3𝑦3 NUM iajs-2992 160 16 , , PUNCT iajs-2992 160 17 𝑣3 𝑣3 ADJ iajs-2992 160 18 ) ) PUNCT iajs-2992 160 19 + + CCONJ iajs-2992 160 20 ( ( PUNCT iajs-2992 160 21 𝑔3𝑦3 𝑔3𝑦3 INTJ iajs-2992 160 22 , , PUNCT iajs-2992 160 23 𝑣3 𝑣3 ADJ iajs-2992 160 24 ) ) PUNCT iajs-2992 160 25 , , PUNCT iajs-2992 160 26 βˆ€π‘£3 βˆ€π‘£3 PROPN iajs-2992 160 27 ∈ ∈ PROPN iajs-2992 160 28 𝑉 𝑉 PROPN iajs-2992 160 29 a.e a.e PROPN iajs-2992 160 30 . . PROPN iajs-2992 161 1 on on ADP iajs-2992 161 2 𝐼 𝐼 PROPN iajs-2992 161 3 , , PUNCT iajs-2992 161 4 ( ( PUNCT iajs-2992 161 5 39 39 NUM iajs-2992 161 6 ) ) PUNCT iajs-2992 161 7 ( ( PUNCT iajs-2992 161 8 𝑍3(𝑇 𝑍3(𝑇 PROPN iajs-2992 161 9 ) ) PUNCT iajs-2992 161 10 , , PUNCT iajs-2992 161 11 𝑣3 𝑣3 ADJ iajs-2992 161 12 ) ) PUNCT iajs-2992 161 13 = = SYM iajs-2992 161 14 ( ( PUNCT iajs-2992 162 1 𝑍3𝑑(𝑇 𝑍3𝑑(𝑇 NOUN iajs-2992 162 2 ) ) PUNCT iajs-2992 162 3 , , PUNCT iajs-2992 162 4 𝑣3 𝑣3 ADJ iajs-2992 162 5 ) ) PUNCT iajs-2992 162 6 = = SYM iajs-2992 162 7 0 0 NUM iajs-2992 162 8 , , PUNCT iajs-2992 162 9 ( ( PUNCT iajs-2992 162 10 40 40 NUM iajs-2992 162 11 ) ) PUNCT iajs-2992 162 12 ( ( PUNCT iajs-2992 162 13 𝑍4𝑑𝑑 𝑍4𝑑𝑑 NOUN iajs-2992 162 14 , , PUNCT iajs-2992 162 15 𝑣4 𝑣4 NOUN iajs-2992 162 16 ) ) PUNCT iajs-2992 162 17 + + CCONJ iajs-2992 162 18 ( ( PUNCT iajs-2992 162 19 βˆ‡π‘4 βˆ‡π‘4 NUM iajs-2992 162 20 , , PUNCT iajs-2992 162 21 βˆ‡π‘£4 βˆ‡π‘£4 NUM iajs-2992 162 22 ) ) PUNCT iajs-2992 163 1 + + CCONJ iajs-2992 163 2 ( ( PUNCT iajs-2992 163 3 𝑍1 𝑍1 INTJ iajs-2992 163 4 , , PUNCT iajs-2992 163 5 𝑣4 𝑣4 PROPN iajs-2992 163 6 ) ) PUNCT iajs-2992 163 7 βˆ’ βˆ’ PROPN iajs-2992 163 8 ( ( PUNCT iajs-2992 163 9 𝑍2 𝑍2 PROPN iajs-2992 163 10 , , PUNCT iajs-2992 163 11 𝑣4 𝑣4 NOUN iajs-2992 163 12 ) ) PUNCT iajs-2992 163 13 + + CCONJ iajs-2992 163 14 ( ( PUNCT iajs-2992 163 15 𝑍3 𝑍3 NOUN iajs-2992 163 16 , , PUNCT iajs-2992 163 17 𝑣4 𝑣4 PROPN iajs-2992 163 18 ) ) PUNCT iajs-2992 163 19 + + CCONJ iajs-2992 163 20 ( ( PUNCT iajs-2992 163 21 𝑍4 𝑍4 NOUN iajs-2992 163 22 , , PUNCT iajs-2992 163 23 𝑣4 𝑣4 NOUN iajs-2992 163 24 ) ) PUNCT iajs-2992 163 25 = = SYM iajs-2992 163 26 ( ( PUNCT iajs-2992 163 27 𝑍4𝑓4𝑦4 𝑍4𝑓4𝑦4 NUM iajs-2992 163 28 , , PUNCT iajs-2992 163 29 𝑣4 𝑣4 NOUN iajs-2992 163 30 ) ) PUNCT iajs-2992 163 31 + + CCONJ iajs-2992 163 32 ( ( PUNCT iajs-2992 163 33 𝑔4𝑦4 𝑔4𝑦4 PROPN iajs-2992 163 34 , , PUNCT iajs-2992 163 35 𝑣4 𝑣4 NOUN iajs-2992 163 36 ) ) PUNCT iajs-2992 163 37 , , PUNCT iajs-2992 163 38 βˆ€π‘£4 βˆ€π‘£4 NOUN iajs-2992 163 39 ∈ ∈ PROPN iajs-2992 163 40 𝑉 𝑉 PROPN iajs-2992 163 41 a.e a.e PROPN iajs-2992 163 42 . . PROPN iajs-2992 164 1 on on ADP iajs-2992 164 2 , , PUNCT iajs-2992 164 3 ( ( PUNCT iajs-2992 164 4 41 41 NUM iajs-2992 164 5 ) ) PUNCT iajs-2992 164 6 ( ( PUNCT iajs-2992 164 7 𝑍4(π‘₯ 𝑍4(π‘₯ PROPN iajs-2992 164 8 , , PUNCT iajs-2992 164 9 𝑇 𝑇 PROPN iajs-2992 164 10 ) ) PUNCT iajs-2992 164 11 , , PUNCT iajs-2992 164 12 𝑣4 𝑣4 NOUN iajs-2992 164 13 ) ) PUNCT iajs-2992 164 14 = = SYM iajs-2992 164 15 ( ( PUNCT iajs-2992 164 16 𝑍4𝑑(𝑇 𝑍4𝑑(𝑇 ADJ iajs-2992 164 17 ) ) PUNCT iajs-2992 164 18 , , PUNCT iajs-2992 164 19 𝑣4 𝑣4 NOUN iajs-2992 164 20 ) ) PUNCT iajs-2992 164 21 = = SYM iajs-2992 164 22 0 0 NUM iajs-2992 164 23 , , PUNCT iajs-2992 164 24 ( ( PUNCT iajs-2992 164 25 42 42 NUM iajs-2992 164 26 ) ) PUNCT iajs-2992 164 27 the the DET iajs-2992 164 28 wf wf PROPN iajs-2992 164 29 ( ( PUNCT iajs-2992 164 30 ( ( PUNCT iajs-2992 164 31 35-(42 35-(42 NUM iajs-2992 164 32 ) ) PUNCT iajs-2992 164 33 ) ) PUNCT iajs-2992 164 34 has have VERB iajs-2992 164 35 a a DET iajs-2992 164 36 unique unique ADJ iajs-2992 164 37 solution solution NOUN iajs-2992 164 38 οΏ½ οΏ½ NOUN iajs-2992 164 39 βƒ— βƒ— NOUN iajs-2992 164 40 οΏ½ οΏ½ NOUN iajs-2992 164 41 = = SYM iajs-2992 164 42 ( ( PUNCT iajs-2992 164 43 𝑍1 𝑍1 PROPN iajs-2992 164 44 , , PUNCT iajs-2992 164 45 𝑍2 𝑍2 PROPN iajs-2992 164 46 , , PUNCT iajs-2992 164 47 𝑍3 𝑍3 NOUN iajs-2992 164 48 , , PUNCT iajs-2992 164 49 𝑍4 𝑍4 NOUN iajs-2992 164 50 ) ) PUNCT iajs-2992 164 51 ∈ ∈ PROPN iajs-2992 164 52 ( ( PUNCT iajs-2992 164 53 𝐿2(𝑄))4 𝐿2(𝑄))4 PROPN iajs-2992 164 54 ( ( PUNCT iajs-2992 164 55 this this PRON iajs-2992 164 56 it it PRON iajs-2992 164 57 can can AUX iajs-2992 164 58 proved prove VERB iajs-2992 164 59 so so ADV iajs-2992 164 60 as as SCONJ iajs-2992 164 61 the the DET iajs-2992 164 62 proof proof NOUN iajs-2992 164 63 of of ADP iajs-2992 164 64 existence existence NOUN iajs-2992 164 65 a a DET iajs-2992 164 66 unique unique ADJ iajs-2992 164 67 qsvs qsvs NOUN iajs-2992 164 68 for for ADP iajs-2992 164 69 the the DET iajs-2992 164 70 wf wf PROPN iajs-2992 164 71 ( ( PUNCT iajs-2992 164 72 ( ( PUNCT iajs-2992 164 73 11)-(15 11)-(15 NUM iajs-2992 164 74 ) ) PUNCT iajs-2992 164 75 ) ) PUNCT iajs-2992 164 76 . . PUNCT iajs-2992 165 1 now now ADV iajs-2992 165 2 , , PUNCT iajs-2992 165 3 replacing replace VERB iajs-2992 165 4 𝑣𝑖 𝑣𝑖 ADP iajs-2992 165 5 = = SYM iajs-2992 165 6 𝛿𝑦𝑖 𝛿𝑦𝑖 NOUN iajs-2992 165 7 in in ADP iajs-2992 165 8 ( ( PUNCT iajs-2992 165 9 35 35 NUM iajs-2992 165 10 ) ) PUNCT iajs-2992 165 11 , , PUNCT iajs-2992 165 12 ( ( PUNCT iajs-2992 165 13 37 37 NUM iajs-2992 165 14 ) ) PUNCT iajs-2992 165 15 , , PUNCT iajs-2992 165 16 ( ( PUNCT iajs-2992 165 17 39 39 NUM iajs-2992 165 18 ) ) PUNCT iajs-2992 165 19 and and CCONJ iajs-2992 165 20 ( ( PUNCT iajs-2992 165 21 41 41 NUM iajs-2992 165 22 ) ) PUNCT iajs-2992 165 23 , , PUNCT iajs-2992 165 24 for for ADP iajs-2992 165 25 𝑖 𝑖 PRON iajs-2992 165 26 = = SYM iajs-2992 165 27 1,2,3,4 1,2,3,4 NUM iajs-2992 165 28 resp resp NOUN iajs-2992 165 29 . . PUNCT iajs-2992 166 1 ∫ ∫ PROPN iajs-2992 166 2 0 0 NUM iajs-2992 167 1 𝑇 𝑇 PROPN iajs-2992 167 2 ( ( PUNCT iajs-2992 167 3 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 167 4 , , PUNCT iajs-2992 167 5 𝑍1𝑑𝑑)𝑑𝑑 𝑍1𝑑𝑑)𝑑𝑑 PUNCT iajs-2992 167 6 + + CCONJ iajs-2992 167 7 ∫ ∫ PROPN iajs-2992 167 8 0 0 X iajs-2992 167 9 𝑇 𝑇 PROPN iajs-2992 168 1 [ [ X iajs-2992 168 2 ( ( PUNCT iajs-2992 168 3 βˆ‡π‘1 βˆ‡π‘1 NOUN iajs-2992 168 4 , , PUNCT iajs-2992 168 5 βˆ‡π›Ώπ‘¦1 βˆ‡π›Ώπ‘¦1 NOUN iajs-2992 168 6 ) ) PUNCT iajs-2992 168 7 + + CCONJ iajs-2992 168 8 ( ( PUNCT iajs-2992 168 9 𝑍1 𝑍1 ADJ iajs-2992 168 10 , , PUNCT iajs-2992 168 11 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 168 12 ) ) PUNCT iajs-2992 168 13 + + CCONJ iajs-2992 168 14 ( ( PUNCT iajs-2992 168 15 𝑍2 𝑍2 ADJ iajs-2992 168 16 , , PUNCT iajs-2992 168 17 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 168 18 ) ) PUNCT iajs-2992 168 19 βˆ’ βˆ’ PROPN iajs-2992 169 1 ( ( PUNCT iajs-2992 169 2 𝑍3 𝑍3 PROPN iajs-2992 169 3 , , PUNCT iajs-2992 169 4 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 169 5 ) ) PUNCT iajs-2992 169 6 βˆ’ βˆ’ PROPN iajs-2992 169 7 ( ( PUNCT iajs-2992 169 8 𝑍4 𝑍4 NOUN iajs-2992 169 9 , , PUNCT iajs-2992 169 10 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 169 11 ) ) PUNCT iajs-2992 169 12 ] ] PUNCT iajs-2992 169 13 𝑑𝑑 𝑑𝑑 ADP iajs-2992 169 14 = = SYM iajs-2992 169 15 ∫ ∫ PROPN iajs-2992 169 16 0 0 X iajs-2992 169 17 𝑇 𝑇 PROPN iajs-2992 169 18 ( ( PUNCT iajs-2992 169 19 𝑍1𝑓1𝑦1 𝑍1𝑓1𝑦1 NOUN iajs-2992 169 20 , , PUNCT iajs-2992 169 21 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 169 22 ) ) PUNCT iajs-2992 170 1 + + CCONJ iajs-2992 170 2 ( ( PUNCT iajs-2992 170 3 𝑔1𝑦1 𝑔1𝑦1 NOUN iajs-2992 170 4 , , PUNCT iajs-2992 170 5 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 170 6 ) ) PUNCT iajs-2992 170 7 𝑑𝑑 𝑑𝑑 ADP iajs-2992 170 8 , , PUNCT iajs-2992 170 9 ( ( PUNCT iajs-2992 170 10 43 43 NUM iajs-2992 170 11 ) ) PUNCT iajs-2992 171 1 ∫ ∫ PROPN iajs-2992 171 2 0 0 X iajs-2992 171 3 𝑇 𝑇 PROPN iajs-2992 171 4 ( ( PUNCT iajs-2992 171 5 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 171 6 , , PUNCT iajs-2992 171 7 𝑍2𝑑𝑑)𝑑𝑑 𝑍2𝑑𝑑)𝑑𝑑 X iajs-2992 171 8 + + CCONJ iajs-2992 171 9 ∫ ∫ PROPN iajs-2992 171 10 0 0 X iajs-2992 171 11 𝑇 𝑇 PROPN iajs-2992 172 1 [ [ X iajs-2992 172 2 ( ( PUNCT iajs-2992 172 3 βˆ‡π‘2 βˆ‡π‘2 ADJ iajs-2992 172 4 , , PUNCT iajs-2992 172 5 βˆ‡π›Ώπ‘¦2 βˆ‡π›Ώπ‘¦2 PROPN iajs-2992 172 6 ) ) PUNCT iajs-2992 172 7 βˆ’ βˆ’ PROPN iajs-2992 172 8 ( ( PUNCT iajs-2992 172 9 𝑍1 𝑍1 PROPN iajs-2992 172 10 , , PUNCT iajs-2992 172 11 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 172 12 ) ) PUNCT iajs-2992 172 13 + + CCONJ iajs-2992 172 14 ( ( PUNCT iajs-2992 172 15 𝑍2 𝑍2 PROPN iajs-2992 172 16 , , PUNCT iajs-2992 172 17 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 172 18 ) ) PUNCT iajs-2992 173 1 + + CCONJ iajs-2992 173 2 ( ( PUNCT iajs-2992 173 3 𝑍3 𝑍3 NOUN iajs-2992 173 4 , , PUNCT iajs-2992 173 5 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 173 6 ) ) PUNCT iajs-2992 173 7 + + CCONJ iajs-2992 173 8 ( ( PUNCT iajs-2992 173 9 𝑍4 𝑍4 PROPN iajs-2992 173 10 , , PUNCT iajs-2992 173 11 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 173 12 ) ) PUNCT iajs-2992 173 13 ] ] PUNCT iajs-2992 173 14 𝑑𝑑 𝑑𝑑 ADP iajs-2992 173 15 = = SYM iajs-2992 173 16 ∫ ∫ PROPN iajs-2992 173 17 0 0 NUM iajs-2992 173 18 𝑇 𝑇 PROPN iajs-2992 173 19 ( ( PUNCT iajs-2992 173 20 𝑍2𝑓2𝑦2 𝑍2𝑓2𝑦2 NOUN iajs-2992 173 21 , , PUNCT iajs-2992 173 22 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 173 23 ) ) PUNCT iajs-2992 174 1 + + CCONJ iajs-2992 174 2 ( ( PUNCT iajs-2992 174 3 𝑔2𝑦2 𝑔2𝑦2 X iajs-2992 174 4 , , PUNCT iajs-2992 174 5 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 174 6 ) ) PUNCT iajs-2992 174 7 𝑑𝑑 𝑑𝑑 ADP iajs-2992 174 8 , , PUNCT iajs-2992 174 9 ( ( PUNCT iajs-2992 174 10 44 44 NUM iajs-2992 174 11 ) ) PUNCT iajs-2992 174 12 ∫ ∫ PROPN iajs-2992 174 13 0 0 X iajs-2992 174 14 𝑇 𝑇 PROPN iajs-2992 174 15 ( ( PUNCT iajs-2992 174 16 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 174 17 , , PUNCT iajs-2992 174 18 𝑍3𝑑𝑑)𝑑𝑑 𝑍3𝑑𝑑)𝑑𝑑 PROPN iajs-2992 175 1 + + CCONJ iajs-2992 176 1 ∫ ∫ PROPN iajs-2992 176 2 0 0 X iajs-2992 176 3 𝑇 𝑇 PROPN iajs-2992 177 1 [ [ X iajs-2992 177 2 ( ( PUNCT iajs-2992 177 3 βˆ‡π‘3 βˆ‡π‘3 NOUN iajs-2992 177 4 , , PUNCT iajs-2992 177 5 βˆ‡π›Ώπ‘¦3 βˆ‡π›Ώπ‘¦3 NOUN iajs-2992 177 6 ) ) PUNCT iajs-2992 177 7 + + CCONJ iajs-2992 177 8 ( ( PUNCT iajs-2992 177 9 𝑍1 𝑍1 NOUN iajs-2992 177 10 , , PUNCT iajs-2992 177 11 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 177 12 ) ) PUNCT iajs-2992 177 13 βˆ’ βˆ’ PROPN iajs-2992 177 14 ( ( PUNCT iajs-2992 177 15 𝑍2 𝑍2 PROPN iajs-2992 177 16 , , PUNCT iajs-2992 177 17 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 177 18 ) ) PUNCT iajs-2992 178 1 + + CCONJ iajs-2992 178 2 ( ( PUNCT iajs-2992 178 3 𝑍3 𝑍3 NOUN iajs-2992 178 4 , , PUNCT iajs-2992 178 5 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 178 6 ) ) PUNCT iajs-2992 178 7 βˆ’ βˆ’ PROPN iajs-2992 178 8 ( ( PUNCT iajs-2992 178 9 𝑍4 𝑍4 NOUN iajs-2992 178 10 , , PUNCT iajs-2992 178 11 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 178 12 ) ) PUNCT iajs-2992 178 13 ] ] PUNCT iajs-2992 178 14 𝑑𝑑 𝑑𝑑 ADP iajs-2992 178 15 = = SYM iajs-2992 178 16 ∫ ∫ PROPN iajs-2992 178 17 0 0 NUM iajs-2992 178 18 𝑇 𝑇 PROPN iajs-2992 178 19 ( ( PUNCT iajs-2992 178 20 𝑍3𝑓3𝑦3 𝑍3𝑓3𝑦3 NUM iajs-2992 178 21 , , PUNCT iajs-2992 178 22 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 178 23 ) ) PUNCT iajs-2992 178 24 + + CCONJ iajs-2992 178 25 ( ( PUNCT iajs-2992 178 26 𝑔3𝑦3 𝑔3𝑦3 INTJ iajs-2992 178 27 , , PUNCT iajs-2992 178 28 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 178 29 ) ) PUNCT iajs-2992 178 30 𝑑𝑑 𝑑𝑑 ADP iajs-2992 178 31 , , PUNCT iajs-2992 178 32 ( ( PUNCT iajs-2992 179 1 45 45 NUM iajs-2992 179 2 ) ) PUNCT iajs-2992 179 3 ∫ ∫ PROPN iajs-2992 179 4 0 0 X iajs-2992 179 5 𝑇 𝑇 PROPN iajs-2992 179 6 ( ( PUNCT iajs-2992 179 7 𝛿𝑦4 𝛿𝑦4 NOUN iajs-2992 179 8 , , PUNCT iajs-2992 179 9 𝑍4𝑑𝑑)𝑑𝑑 𝑍4𝑑𝑑)𝑑𝑑 PUNCT iajs-2992 179 10 + + CCONJ iajs-2992 179 11 ∫ ∫ PROPN iajs-2992 179 12 0 0 X iajs-2992 179 13 𝑇 𝑇 PROPN iajs-2992 180 1 [ [ X iajs-2992 180 2 ( ( PUNCT iajs-2992 180 3 βˆ‡π‘4 βˆ‡π‘4 NOUN iajs-2992 180 4 , , PUNCT iajs-2992 180 5 βˆ‡π›Ώπ‘¦4 βˆ‡π›Ώπ‘¦4 PROPN iajs-2992 180 6 ) ) PUNCT iajs-2992 181 1 + + CCONJ iajs-2992 181 2 ( ( PUNCT iajs-2992 181 3 𝑍1 𝑍1 PROPN iajs-2992 181 4 , , PUNCT iajs-2992 181 5 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 181 6 ) ) PUNCT iajs-2992 182 1 βˆ’ βˆ’ PROPN iajs-2992 182 2 ( ( PUNCT iajs-2992 182 3 𝑍2 𝑍2 PROPN iajs-2992 182 4 , , PUNCT iajs-2992 182 5 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 182 6 ) ) PUNCT iajs-2992 183 1 + + CCONJ iajs-2992 183 2 ( ( PUNCT iajs-2992 183 3 𝑍3 𝑍3 PROPN iajs-2992 183 4 , , PUNCT iajs-2992 183 5 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 183 6 ) ) PUNCT iajs-2992 184 1 + + CCONJ iajs-2992 184 2 ( ( PUNCT iajs-2992 184 3 𝑍4 𝑍4 PROPN iajs-2992 184 4 , , PUNCT iajs-2992 184 5 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 184 6 ) ) PUNCT iajs-2992 184 7 ] ] PUNCT iajs-2992 184 8 𝑑𝑑 𝑑𝑑 ADP iajs-2992 184 9 = = SYM iajs-2992 184 10 ∫ ∫ PROPN iajs-2992 184 11 0 0 X iajs-2992 184 12 𝑇 𝑇 PROPN iajs-2992 184 13 ( ( PUNCT iajs-2992 184 14 𝑍4𝑓4𝑦4 𝑍4𝑓4𝑦4 NUM iajs-2992 184 15 , , PUNCT iajs-2992 184 16 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 184 17 ) ) PUNCT iajs-2992 185 1 + + CCONJ iajs-2992 185 2 ( ( PUNCT iajs-2992 185 3 𝑔4𝑦4 𝑔4𝑦4 PROPN iajs-2992 185 4 , , PUNCT iajs-2992 185 5 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 185 6 ) ) PUNCT iajs-2992 185 7 𝑑𝑑 𝑑𝑑 ADP iajs-2992 185 8 , , PUNCT iajs-2992 185 9 ( ( PUNCT iajs-2992 185 10 46 46 NUM iajs-2992 185 11 ) ) PUNCT iajs-2992 185 12 now now ADV iajs-2992 185 13 , , PUNCT iajs-2992 185 14 take take VERB iajs-2992 185 15 οΏ½ οΏ½ PROPN iajs-2992 185 16 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 185 17 οΏ½ οΏ½ PROPN iajs-2992 185 18 , , PUNCT iajs-2992 185 19 οΏ½ οΏ½ PROPN iajs-2992 185 20 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 185 21 οΏ½ οΏ½ PROPN iajs-2992 185 22 ∈ ∈ PROPN iajs-2992 185 23 π‘³πŸ(𝐐),set π‘³πŸ(𝐐),set PROPN iajs-2992 185 24 𝛿𝑒⃗⃗⃗⃗⃗ 𝛿𝑒⃗⃗⃗⃗⃗ PROPN iajs-2992 185 25 = = SYM iajs-2992 185 26 οΏ½ οΏ½ PROPN iajs-2992 185 27 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 185 28 οΏ½ οΏ½ PROPN iajs-2992 185 29 βˆ’ βˆ’ PROPN iajs-2992 185 30 οΏ½ οΏ½ PROPN iajs-2992 185 31 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 185 32 οΏ½ οΏ½ PROPN iajs-2992 185 33 , , PUNCT iajs-2992 186 1 οΏ½ οΏ½ PROPN iajs-2992 186 2 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 186 3 οΏ½ οΏ½ PROPN iajs-2992 186 4 = = SYM iajs-2992 186 5 οΏ½ οΏ½ PROPN iajs-2992 186 6 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 186 7 οΏ½ οΏ½ PROPN iajs-2992 187 1 + + CCONJ iajs-2992 187 2 νœ€π›Ώπ‘’βƒ—βƒ—βƒ—βƒ—βƒ— νœ€π›Ώπ‘’βƒ—βƒ—βƒ—βƒ—βƒ— PROPN iajs-2992 187 3 ∈ ∈ PROPN iajs-2992 187 4 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 187 5 ) ) PUNCT iajs-2992 187 6 for for ADP iajs-2992 187 7 νœ€ νœ€ NOUN iajs-2992 187 8 > > X iajs-2992 187 9 0 0 NUM iajs-2992 187 10 , , PUNCT iajs-2992 187 11 then then ADV iajs-2992 187 12 by by ADP iajs-2992 187 13 theorem theorem NOUN iajs-2992 187 14 1 1 NUM iajs-2992 187 15 , , PUNCT iajs-2992 187 16 οΏ½ οΏ½ NOUN iajs-2992 187 17 βƒ— βƒ— NOUN iajs-2992 187 18 οΏ½ οΏ½ PROPN iajs-2992 187 19 = = SYM iajs-2992 187 20 οΏ½ οΏ½ PROPN iajs-2992 187 21 βƒ— βƒ— PROPN iajs-2992 187 22 οΏ½ οΏ½ PROPN iajs-2992 187 23 οΏ½ οΏ½ PROPN iajs-2992 187 24 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 187 25 οΏ½ οΏ½ PROPN iajs-2992 187 26 & & CCONJ iajs-2992 187 27 οΏ½ οΏ½ PROPN iajs-2992 187 28 βƒ— βƒ— PROPN iajs-2992 187 29 οΏ½ οΏ½ PROPN iajs-2992 187 30 = = SYM iajs-2992 187 31 οΏ½ οΏ½ PROPN iajs-2992 187 32 βƒ— βƒ— PROPN iajs-2992 187 33 οΏ½ οΏ½ PROPN iajs-2992 187 34 οΏ½ οΏ½ PROPN iajs-2992 187 35 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 187 36 οΏ½ οΏ½ NOUN iajs-2992 187 37 πœ€ πœ€ NOUN iajs-2992 187 38 are be AUX iajs-2992 187 39 their their PRON iajs-2992 187 40 corresponding correspond VERB iajs-2992 187 41 qsvs qsvs NOUN iajs-2992 187 42 . . PUNCT iajs-2992 188 1 setting set VERB iajs-2992 188 2 𝛿𝑦⃗⃗⃗⃗⃗ 𝛿𝑦⃗⃗⃗⃗⃗ PROPN iajs-2992 188 3 = = PRON iajs-2992 188 4 ( ( PUNCT iajs-2992 188 5 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 188 6 , , PUNCT iajs-2992 188 7 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 188 8 , , PUNCT iajs-2992 188 9 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 188 10 , , PUNCT iajs-2992 188 11 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 188 12 ) ) PUNCT iajs-2992 189 1 = = SYM iajs-2992 189 2 οΏ½ οΏ½ PROPN iajs-2992 189 3 βƒ— βƒ— PROPN iajs-2992 189 4 οΏ½ οΏ½ PROPN iajs-2992 189 5 βˆ’ βˆ’ PROPN iajs-2992 189 6 οΏ½ οΏ½ PROPN iajs-2992 189 7 βƒ— βƒ— NOUN iajs-2992 189 8 οΏ½ οΏ½ PROPN iajs-2992 189 9 , , PUNCT iajs-2992 189 10 substituting substitute VERB iajs-2992 189 11 𝑣𝑖 𝑣𝑖 ADP iajs-2992 190 1 = = SYM iajs-2992 190 2 𝑍𝑖 𝑍𝑖 PROPN iajs-2992 190 3 for for ADP iajs-2992 190 4 𝑖 𝑖 NOUN iajs-2992 190 5 = = NOUN iajs-2992 190 6 1,2,3,4 1,2,3,4 NUM iajs-2992 190 7 in in ADP iajs-2992 190 8 ( ( PUNCT iajs-2992 190 9 ( ( PUNCT iajs-2992 190 10 10)(17 10)(17 NUM iajs-2992 190 11 ) ) PUNCT iajs-2992 190 12 ) ) PUNCT iajs-2992 190 13 , , PUNCT iajs-2992 190 14 ibss ibss VERB iajs-2992 190 15 on on ADP iajs-2992 190 16 [ [ X iajs-2992 190 17 0 0 NUM iajs-2992 190 18 , , PUNCT iajs-2992 190 19 𝑇 𝑇 PROPN iajs-2992 190 20 ] ] PUNCT iajs-2992 190 21 , , PUNCT iajs-2992 190 22 then then ADV iajs-2992 190 23 integrating integrate VERB iajs-2992 190 24 by by ADP iajs-2992 190 25 parts part NOUN iajs-2992 190 26 twice twice ADV iajs-2992 190 27 ( ( PUNCT iajs-2992 190 28 ibps2 ibps2 NOUN iajs-2992 190 29 ) ) PUNCT iajs-2992 190 30 the the DET iajs-2992 190 31 1st 1st NOUN iajs-2992 190 32 in in ADP iajs-2992 190 33 the the DET iajs-2992 190 34 lhs lhs PROPN iajs-2992 190 35 of of ADP iajs-2992 190 36 each each DET iajs-2992 190 37 obtained obtain VERB iajs-2992 190 38 equation equation NOUN iajs-2992 190 39 , , PUNCT iajs-2992 190 40 finding find VERB iajs-2992 190 41 the the DET iajs-2992 190 42 frd frd NOUN iajs-2992 190 43 of of ADP iajs-2992 190 44 𝑓𝑖 𝑓𝑖 PROPN iajs-2992 190 45 ( ( PUNCT iajs-2992 190 46 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 190 47 = = NOUN iajs-2992 190 48 1,2,3,4 1,2,3,4 NUM iajs-2992 190 49 ) ) PUNCT iajs-2992 190 50 in in ADP iajs-2992 190 51 the the DET iajs-2992 190 52 rhs rhs PROPN iajs-2992 190 53 of of ADP iajs-2992 190 54 each each DET iajs-2992 190 55 one one NUM iajs-2992 190 56 equation equation NOUN iajs-2992 190 57 ( ( PUNCT iajs-2992 190 58 which which PRON iajs-2992 190 59 is be AUX iajs-2992 190 60 exists exist VERB iajs-2992 190 61 from from ADP iajs-2992 190 62 the the DET iajs-2992 190 63 assums assum NOUN iajs-2992 190 64 c c PROPN iajs-2992 190 65 ) ) PUNCT iajs-2992 190 66 , , PUNCT iajs-2992 190 67 then then ADV iajs-2992 190 68 from from ADP iajs-2992 190 69 the the DET iajs-2992 190 70 result result NOUN iajs-2992 190 71 of of ADP iajs-2992 190 72 theorem theorem ADJ iajs-2992 190 73 2.2 2.2 NUM iajs-2992 190 74 and and CCONJ iajs-2992 190 75 the the DET iajs-2992 190 76 minkowiski minkowiski ADJ iajs-2992 190 77 inequality inequality NOUN iajs-2992 190 78 ( ( PUNCT iajs-2992 190 79 min min NOUN iajs-2992 190 80 ) ) PUNCT iajs-2992 190 81 , , PUNCT iajs-2992 190 82 once once ADV iajs-2992 190 83 get get VERB iajs-2992 190 84 ∫ ∫ PROPN iajs-2992 190 85 0 0 PUNCT iajs-2992 190 86 𝑇 𝑇 PROPN iajs-2992 190 87 ( ( PUNCT iajs-2992 190 88 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 190 89 , , PUNCT iajs-2992 190 90 𝑍1𝑑𝑑)𝑑𝑑 𝑍1𝑑𝑑)𝑑𝑑 PUNCT iajs-2992 191 1 + + CCONJ iajs-2992 191 2 ∫ ∫ PROPN iajs-2992 191 3 0 0 X iajs-2992 191 4 𝑇 𝑇 PROPN iajs-2992 192 1 [ [ X iajs-2992 192 2 ( ( PUNCT iajs-2992 192 3 βˆ‡π›Ώπ‘¦1 βˆ‡π›Ώπ‘¦1 NOUN iajs-2992 192 4 , , PUNCT iajs-2992 192 5 βˆ‡π‘1 βˆ‡π‘1 ADJ iajs-2992 192 6 ) ) PUNCT iajs-2992 192 7 + + CCONJ iajs-2992 192 8 ( ( PUNCT iajs-2992 192 9 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 192 10 , , PUNCT iajs-2992 192 11 𝑍1 𝑍1 PROPN iajs-2992 192 12 ) ) PUNCT iajs-2992 193 1 + + CCONJ iajs-2992 193 2 ( ( PUNCT iajs-2992 193 3 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 193 4 , , PUNCT iajs-2992 193 5 𝑍1 𝑍1 PROPN iajs-2992 193 6 ) ) PUNCT iajs-2992 194 1 + + CCONJ iajs-2992 194 2 ( ( PUNCT iajs-2992 194 3 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 194 4 , , PUNCT iajs-2992 194 5 𝑍1 𝑍1 PROPN iajs-2992 194 6 ) ) PUNCT iajs-2992 195 1 + + CCONJ iajs-2992 195 2 ( ( PUNCT iajs-2992 195 3 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 195 4 , , PUNCT iajs-2992 195 5 𝑍1)]𝑑𝑑 𝑍1)]𝑑𝑑 PROPN iajs-2992 195 6 = = SYM iajs-2992 195 7 ∫ ∫ PROPN iajs-2992 195 8 0 0 X iajs-2992 195 9 𝑇 𝑇 PROPN iajs-2992 195 10 ( ( PUNCT iajs-2992 195 11 𝑓1𝑦1 𝑓1𝑦1 NOUN iajs-2992 195 12 𝛿𝑦1 𝛿𝑦1 NOUN iajs-2992 195 13 + + CCONJ iajs-2992 195 14 𝑓1𝑒1 𝑓1𝑒1 PUNCT iajs-2992 195 15 νœ€π›Ώπ‘’1 νœ€π›Ώπ‘’1 ADJ iajs-2992 195 16 , , PUNCT iajs-2992 195 17 𝑍1)𝑑𝑑 𝑍1)𝑑𝑑 NOUN iajs-2992 195 18 + + CCONJ iajs-2992 195 19 𝑂11(νœ€ 𝑂11(νœ€ NOUN iajs-2992 195 20 ) ) PUNCT iajs-2992 195 21 , , PUNCT iajs-2992 195 22 ( ( PUNCT iajs-2992 195 23 47 47 NUM iajs-2992 195 24 ) ) PUNCT iajs-2992 195 25 ∫ ∫ PROPN iajs-2992 195 26 0 0 X iajs-2992 195 27 𝑇 𝑇 PROPN iajs-2992 195 28 ( ( PUNCT iajs-2992 195 29 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 195 30 , , PUNCT iajs-2992 195 31 𝑍2𝑑𝑑)𝑑𝑑 𝑍2𝑑𝑑)𝑑𝑑 X iajs-2992 195 32 + + CCONJ iajs-2992 195 33 ∫ ∫ PROPN iajs-2992 195 34 0 0 X iajs-2992 195 35 𝑇 𝑇 PROPN iajs-2992 196 1 [ [ X iajs-2992 196 2 ( ( PUNCT iajs-2992 196 3 βˆ‡π›Ώπ‘¦2 βˆ‡π›Ώπ‘¦2 NOUN iajs-2992 196 4 , , PUNCT iajs-2992 196 5 βˆ‡π‘2 βˆ‡π‘2 VERB iajs-2992 196 6 ) ) PUNCT iajs-2992 197 1 + + CCONJ iajs-2992 197 2 ( ( PUNCT iajs-2992 197 3 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 197 4 , , PUNCT iajs-2992 197 5 𝑍2 𝑍2 PROPN iajs-2992 197 6 ) ) PUNCT iajs-2992 198 1 + + CCONJ iajs-2992 198 2 ( ( PUNCT iajs-2992 198 3 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 198 4 , , PUNCT iajs-2992 198 5 𝑍2 𝑍2 PROPN iajs-2992 198 6 ) ) PUNCT iajs-2992 199 1 + + CCONJ iajs-2992 199 2 ( ( PUNCT iajs-2992 199 3 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 199 4 , , PUNCT iajs-2992 199 5 𝑍2 𝑍2 ADJ iajs-2992 199 6 ) ) PUNCT iajs-2992 200 1 + + CCONJ iajs-2992 200 2 ( ( PUNCT iajs-2992 200 3 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 200 4 , , PUNCT iajs-2992 200 5 𝑍2)]𝑑𝑑 𝑍2)]𝑑𝑑 PROPN iajs-2992 200 6 = = SYM iajs-2992 200 7 ∫ ∫ PROPN iajs-2992 200 8 0 0 X iajs-2992 200 9 𝑇 𝑇 PROPN iajs-2992 200 10 ( ( PUNCT iajs-2992 200 11 𝑓2𝑦2 𝑓2𝑦2 PUNCT iajs-2992 200 12 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 200 13 + + PROPN iajs-2992 200 14 𝑓2𝑒2 𝑓2𝑒2 PROPN iajs-2992 200 15 νœ€π›Ώπ‘’2 νœ€π›Ώπ‘’2 PROPN iajs-2992 200 16 , , PUNCT iajs-2992 200 17 𝑍2)𝑑𝑑 𝑍2)𝑑𝑑 NOUN iajs-2992 200 18 + + NUM iajs-2992 200 19 𝑂12(νœ€ 𝑂12(νœ€ NOUN iajs-2992 200 20 ) ) PUNCT iajs-2992 200 21 , , PUNCT iajs-2992 200 22 ( ( PUNCT iajs-2992 200 23 48 48 NUM iajs-2992 200 24 ) ) PUNCT iajs-2992 200 25 ∫ ∫ PROPN iajs-2992 200 26 0 0 X iajs-2992 200 27 𝑇 𝑇 PROPN iajs-2992 200 28 ( ( PUNCT iajs-2992 200 29 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 200 30 , , PUNCT iajs-2992 200 31 𝑍3𝑑𝑑)𝑑𝑑 𝑍3𝑑𝑑)𝑑𝑑 PROPN iajs-2992 200 32 + + CCONJ iajs-2992 200 33 ∫ ∫ PROPN iajs-2992 200 34 0 0 X iajs-2992 200 35 𝑇 𝑇 PROPN iajs-2992 201 1 [ [ X iajs-2992 201 2 ( ( PUNCT iajs-2992 201 3 βˆ‡π›Ώπ‘¦3 βˆ‡π›Ώπ‘¦3 NOUN iajs-2992 201 4 , , PUNCT iajs-2992 201 5 βˆ‡π‘3 βˆ‡π‘3 NUM iajs-2992 201 6 ) ) PUNCT iajs-2992 201 7 + + CCONJ iajs-2992 201 8 ( ( PUNCT iajs-2992 201 9 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 201 10 , , PUNCT iajs-2992 201 11 𝑍3 𝑍3 PROPN iajs-2992 201 12 ) ) PUNCT iajs-2992 202 1 βˆ’ βˆ’ PROPN iajs-2992 203 1 ( ( PUNCT iajs-2992 203 2 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 203 3 , , PUNCT iajs-2992 203 4 𝑍3 𝑍3 PROPN iajs-2992 203 5 ) ) PUNCT iajs-2992 204 1 + + CCONJ iajs-2992 204 2 ( ( PUNCT iajs-2992 204 3 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 204 4 , , PUNCT iajs-2992 204 5 𝑍3 𝑍3 PROPN iajs-2992 204 6 ) ) PUNCT iajs-2992 205 1 + + CCONJ iajs-2992 205 2 ( ( PUNCT iajs-2992 205 3 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 205 4 , , PUNCT iajs-2992 205 5 𝑍3)]𝑑𝑑 𝑍3)]𝑑𝑑 PROPN iajs-2992 205 6 = = SYM iajs-2992 205 7 ∫ ∫ PROPN iajs-2992 205 8 0 0 X iajs-2992 205 9 𝑇 𝑇 PROPN iajs-2992 205 10 ( ( PUNCT iajs-2992 205 11 𝑓3𝑦3 𝑓3𝑦3 PUNCT iajs-2992 205 12 𝛿𝑦3 𝛿𝑦3 VERB iajs-2992 205 13 + + CCONJ iajs-2992 205 14 𝑓3𝑒3 𝑓3𝑒3 X iajs-2992 205 15 νœ€π›Ώπ‘’3 νœ€π›Ώπ‘’3 NOUN iajs-2992 205 16 , , PUNCT iajs-2992 205 17 𝑍3)𝑑𝑑 𝑍3)𝑑𝑑 NOUN iajs-2992 205 18 + + CCONJ iajs-2992 205 19 𝑂13(νœ€ 𝑂13(νœ€ NOUN iajs-2992 205 20 ) ) PUNCT iajs-2992 205 21 , , PUNCT iajs-2992 205 22 ( ( PUNCT iajs-2992 205 23 49 49 NUM iajs-2992 205 24 ) ) PUNCT iajs-2992 205 25 ∫ ∫ PROPN iajs-2992 205 26 0 0 X iajs-2992 205 27 𝑇 𝑇 PROPN iajs-2992 205 28 ( ( PUNCT iajs-2992 205 29 𝛿𝑦4 𝛿𝑦4 NOUN iajs-2992 205 30 , , PUNCT iajs-2992 205 31 𝑍4𝑑𝑑)𝑑𝑑 𝑍4𝑑𝑑)𝑑𝑑 PUNCT iajs-2992 205 32 + + CCONJ iajs-2992 205 33 ∫ ∫ PROPN iajs-2992 205 34 0 0 X iajs-2992 205 35 𝑇 𝑇 PROPN iajs-2992 206 1 [ [ X iajs-2992 206 2 ( ( PUNCT iajs-2992 206 3 βˆ‡π›Ώπ‘¦4 βˆ‡π›Ώπ‘¦4 PROPN iajs-2992 206 4 , , PUNCT iajs-2992 206 5 βˆ‡π‘4 βˆ‡π‘4 NUM iajs-2992 206 6 ) ) PUNCT iajs-2992 206 7 βˆ’ βˆ’ PROPN iajs-2992 206 8 ( ( PUNCT iajs-2992 206 9 𝛿𝑦1 𝛿𝑦1 ADJ iajs-2992 206 10 , , PUNCT iajs-2992 206 11 𝑍4 𝑍4 NOUN iajs-2992 206 12 ) ) PUNCT iajs-2992 207 1 βˆ’ βˆ’ PROPN iajs-2992 207 2 ( ( PUNCT iajs-2992 207 3 𝛿𝑦2 𝛿𝑦2 NOUN iajs-2992 207 4 , , PUNCT iajs-2992 207 5 𝑍4 𝑍4 NOUN iajs-2992 207 6 ) ) PUNCT iajs-2992 208 1 + + CCONJ iajs-2992 208 2 ( ( PUNCT iajs-2992 208 3 𝛿𝑦3 𝛿𝑦3 NOUN iajs-2992 208 4 , , PUNCT iajs-2992 208 5 𝑍4 𝑍4 NOUN iajs-2992 208 6 ) ) PUNCT iajs-2992 209 1 + + CCONJ iajs-2992 209 2 ( ( PUNCT iajs-2992 209 3 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 209 4 , , PUNCT iajs-2992 209 5 𝑍4)]𝑑𝑑 𝑍4)]𝑑𝑑 PROPN iajs-2992 209 6 ihjpas ihjpas PROPN iajs-2992 209 7 . . PUNCT iajs-2992 210 1 36(2)2023 36(2)2023 NUM iajs-2992 210 2 337 337 NUM iajs-2992 210 3 = = SYM iajs-2992 210 4 ∫ ∫ PROPN iajs-2992 210 5 0 0 X iajs-2992 210 6 𝑇 𝑇 PROPN iajs-2992 210 7 ( ( PUNCT iajs-2992 210 8 𝑓4𝑦4 𝑓4𝑦4 ADP iajs-2992 210 9 𝛿𝑦4 𝛿𝑦4 PROPN iajs-2992 210 10 + + CCONJ iajs-2992 210 11 𝑓4𝑒4 𝑓4𝑒4 PROPN iajs-2992 210 12 νœ€π›Ώπ‘’4 νœ€π›Ώπ‘’4 PROPN iajs-2992 210 13 , , PUNCT iajs-2992 210 14 𝑍4)𝑑𝑑 𝑍4)𝑑𝑑 PROPN iajs-2992 210 15 + + CCONJ iajs-2992 210 16 𝑂14(νœ€ 𝑂14(νœ€ PROPN iajs-2992 210 17 ) ) PUNCT iajs-2992 210 18 , , PUNCT iajs-2992 210 19 ( ( PUNCT iajs-2992 210 20 50 50 NUM iajs-2992 210 21 ) ) PUNCT iajs-2992 210 22 where where SCONJ iajs-2992 210 23 𝑂1𝑖(νœ€ 𝑂1𝑖(νœ€ NOUN iajs-2992 210 24 ) ) PUNCT iajs-2992 210 25 = = NUM iajs-2992 210 26 βˆ₯ βˆ₯ NUM iajs-2992 210 27 𝛿𝑦𝑖 𝛿𝑦𝑖 NOUN iajs-2992 210 28 βˆ₯𝑄 βˆ₯𝑄 ADP iajs-2992 210 29 2 2 NUM iajs-2992 210 30 + + CCONJ iajs-2992 210 31 νœ€ νœ€ NOUN iajs-2992 210 32 βˆ₯ βˆ₯ NOUN iajs-2992 210 33 𝛿𝑒𝑖 𝛿𝑒𝑖 VERB iajs-2992 210 34 βˆ₯𝑄 βˆ₯𝑄 NOUN iajs-2992 210 35 2 2 NUM iajs-2992 210 36 β†’ β†’ SYM iajs-2992 210 37 0 0 NUM iajs-2992 210 38 , , PUNCT iajs-2992 210 39 as as ADP iajs-2992 210 40 νœ€ νœ€ PRON iajs-2992 210 41 β†’ β†’ SYM iajs-2992 210 42 0 0 NUM iajs-2992 210 43 , , PUNCT iajs-2992 210 44 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 210 45 = = NOUN iajs-2992 210 46 1,2,3,4 1,2,3,4 NUM iajs-2992 210 47 . . X iajs-2992 211 1 subtracting subtract VERB iajs-2992 211 2 ( ( PUNCT iajs-2992 211 3 ( ( PUNCT iajs-2992 211 4 47 47 NUM iajs-2992 211 5 ) ) PUNCT iajs-2992 211 6 – – PUNCT iajs-2992 211 7 ( ( PUNCT iajs-2992 211 8 50 50 NUM iajs-2992 211 9 ) ) PUNCT iajs-2992 211 10 ) ) PUNCT iajs-2992 211 11 from from ADP iajs-2992 211 12 ( ( PUNCT iajs-2992 211 13 ( ( PUNCT iajs-2992 211 14 43)(46 43)(46 NOUN iajs-2992 211 15 ) ) PUNCT iajs-2992 211 16 ) ) PUNCT iajs-2992 211 17 resp resp NOUN iajs-2992 211 18 . . PUNCT iajs-2992 211 19 , , PUNCT iajs-2992 211 20 collecting collect VERB iajs-2992 211 21 the the DET iajs-2992 211 22 obtain obtain NOUN iajs-2992 211 23 equations equation NOUN iajs-2992 211 24 , , PUNCT iajs-2992 211 25 to to PART iajs-2992 211 26 acquire acquire VERB iajs-2992 211 27 νœ€ νœ€ DET iajs-2992 211 28 ∫ ∫ PROPN iajs-2992 211 29 0 0 PUNCT iajs-2992 211 30 𝑇 𝑇 PROPN iajs-2992 211 31 βˆ‘ βˆ‘ PROPN iajs-2992 211 32 𝑖=1 𝑖=1 PROPN iajs-2992 211 33 4 4 NUM iajs-2992 211 34 ( ( PUNCT iajs-2992 211 35 𝑓𝑖𝑒𝑖 𝑓𝑖𝑒𝑖 PROPN iajs-2992 211 36 𝛿𝑒𝑖 𝛿𝑒𝑖 VERB iajs-2992 211 37 , , PUNCT iajs-2992 211 38 𝑍𝑖)𝑑𝑑 𝑍𝑖)𝑑𝑑 X iajs-2992 211 39 + + CCONJ iajs-2992 211 40 𝑂1(νœ€ 𝑂1(νœ€ PROPN iajs-2992 211 41 ) ) PUNCT iajs-2992 211 42 = = PUNCT iajs-2992 212 1 νœ€ νœ€ PRON iajs-2992 212 2 ∫ ∫ PROPN iajs-2992 212 3 0 0 X iajs-2992 212 4 𝑇 𝑇 PROPN iajs-2992 212 5 βˆ‘ βˆ‘ PROPN iajs-2992 212 6 𝑖=1 𝑖=1 PROPN iajs-2992 212 7 4 4 NUM iajs-2992 212 8 ( ( PUNCT iajs-2992 212 9 𝑔𝑖𝑦𝑖 𝑔𝑖𝑦𝑖 ADJ iajs-2992 212 10 , , PUNCT iajs-2992 212 11 𝛿𝑦𝑖)𝑑𝑑 𝛿𝑦𝑖)𝑑𝑑 ADJ iajs-2992 212 12 , , PUNCT iajs-2992 212 13 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 212 14 = = SYM iajs-2992 212 15 1,2,3,4 1,2,3,4 NUM iajs-2992 212 16 , , PUNCT iajs-2992 212 17 ( ( PUNCT iajs-2992 212 18 51 51 NUM iajs-2992 212 19 ) ) PUNCT iajs-2992 212 20 where where SCONJ iajs-2992 212 21 𝑂1(νœ€ 𝑂1(νœ€ NOUN iajs-2992 212 22 ) ) PUNCT iajs-2992 212 23 = = PUNCT iajs-2992 213 1 βˆ‘ βˆ‘ PUNCT iajs-2992 213 2 𝑖=1 𝑖=1 PROPN iajs-2992 213 3 4 4 NUM iajs-2992 213 4 𝑂1𝑖(νœ€ 𝑂1𝑖(νœ€ ADJ iajs-2992 213 5 ) ) PUNCT iajs-2992 213 6 β†’ β†’ SYM iajs-2992 213 7 0 0 NUM iajs-2992 213 8 as as ADP iajs-2992 213 9 νœ€ νœ€ PRON iajs-2992 213 10 β†’ β†’ SYM iajs-2992 213 11 0 0 NUM iajs-2992 213 12 . . PUNCT iajs-2992 213 13 from from ADP iajs-2992 213 14 the the DET iajs-2992 213 15 other other ADJ iajs-2992 213 16 side side NOUN iajs-2992 213 17 , , PUNCT iajs-2992 213 18 by by ADP iajs-2992 213 19 employing employ VERB iajs-2992 213 20 the the DET iajs-2992 213 21 assums assum NOUN iajs-2992 213 22 ( ( PUNCT iajs-2992 213 23 c c NOUN iajs-2992 213 24 ) ) PUNCT iajs-2992 213 25 , , PUNCT iajs-2992 213 26 the the DET iajs-2992 213 27 definition definition NOUN iajs-2992 213 28 of of ADP iajs-2992 213 29 the the DET iajs-2992 213 30 frd frd NOUN iajs-2992 213 31 the the DET iajs-2992 213 32 result result NOUN iajs-2992 213 33 of of ADP iajs-2992 213 34 theorem theorem ADJ iajs-2992 213 35 2.2 2.2 NUM iajs-2992 213 36 , , PUNCT iajs-2992 213 37 and and CCONJ iajs-2992 213 38 using use VERB iajs-2992 213 39 the the DET iajs-2992 213 40 min min NOUN iajs-2992 213 41 , , PUNCT iajs-2992 213 42 one one PRON iajs-2992 213 43 has have VERB iajs-2992 213 44 𝐺( 𝐺( NOUN iajs-2992 213 45 οΏ½ οΏ½ PROPN iajs-2992 213 46 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 213 47 οΏ½ οΏ½ PROPN iajs-2992 213 48 ) ) PUNCT iajs-2992 213 49 βˆ’ βˆ’ PROPN iajs-2992 213 50 𝐺( 𝐺( PROPN iajs-2992 213 51 οΏ½ οΏ½ PROPN iajs-2992 213 52 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 213 53 οΏ½ οΏ½ PROPN iajs-2992 213 54 ) ) PUNCT iajs-2992 213 55 = = PUNCT iajs-2992 213 56 βˆ‘ βˆ‘ PUNCT iajs-2992 213 57 𝑖=1 𝑖=1 PROPN iajs-2992 213 58 4 4 NUM iajs-2992 213 59 ∫ ∫ NOUN iajs-2992 213 60 𝑄 𝑄 PROPN iajs-2992 213 61 ( ( PUNCT iajs-2992 213 62 𝑔𝑖𝑦𝑖 𝑔𝑖𝑦𝑖 NOUN iajs-2992 213 63 𝛿𝑦𝑖 𝛿𝑦𝑖 NOUN iajs-2992 213 64 + + CCONJ iajs-2992 213 65 𝑔𝑖𝑒𝑖 𝑔𝑖𝑒𝑖 VERB iajs-2992 213 66 νœ€π›Ώπ‘’π‘–)𝑑π‘₯𝑑𝑑 νœ€π›Ώπ‘’π‘–)𝑑π‘₯𝑑𝑑 X iajs-2992 213 67 + + PUNCT iajs-2992 213 68 𝑂2(νœ€ 𝑂2(νœ€ PROPN iajs-2992 213 69 ) ) PUNCT iajs-2992 213 70 , , PUNCT iajs-2992 213 71 ( ( PUNCT iajs-2992 213 72 52 52 NUM iajs-2992 213 73 ) ) PUNCT iajs-2992 213 74 where where SCONJ iajs-2992 213 75 𝑂2(νœ€ 𝑂2(νœ€ ADV iajs-2992 213 76 ) ) PUNCT iajs-2992 214 1 = = SYM iajs-2992 214 2 βˆ₯ βˆ₯ SYM iajs-2992 214 3 𝛿𝑦⃗⃗⃗⃗ 𝛿𝑦⃗⃗⃗⃗ PUNCT iajs-2992 214 4 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 214 5 βƒ— βƒ— PROPN iajs-2992 214 6 βˆ₯ βˆ₯ X iajs-2992 214 7 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 214 8 ) ) PUNCT iajs-2992 214 9 2 2 NUM iajs-2992 215 1 + + CCONJ iajs-2992 215 2 νœ€ νœ€ NOUN iajs-2992 215 3 βˆ₯ βˆ₯ X iajs-2992 215 4 𝛿𝑒 𝛿𝑒 NOUN iajs-2992 215 5 βƒ—βƒ—βƒ—βƒ—βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ—βƒ—βƒ—βƒ—βƒ— NOUN iajs-2992 215 6 βˆ₯ βˆ₯ X iajs-2992 216 1 π‘³πŸ(𝐐 π‘³πŸ(𝐐 PROPN iajs-2992 216 2 ) ) PUNCT iajs-2992 216 3 2 2 NUM iajs-2992 216 4 β†’ β†’ SYM iajs-2992 216 5 0 0 NUM iajs-2992 216 6 as as ADP iajs-2992 216 7 νœ€ νœ€ PRON iajs-2992 216 8 β†’ β†’ SYM iajs-2992 216 9 0 0 NUM iajs-2992 216 10 , , PUNCT iajs-2992 216 11 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 216 12 = = NOUN iajs-2992 216 13 1,2,3,4 1,2,3,4 NUM iajs-2992 216 14 . . PUNCT iajs-2992 217 1 now now ADV iajs-2992 217 2 , , PUNCT iajs-2992 217 3 by by ADP iajs-2992 217 4 using use VERB iajs-2992 217 5 ( ( PUNCT iajs-2992 217 6 51 51 NUM iajs-2992 217 7 ) ) PUNCT iajs-2992 217 8 in in ADP iajs-2992 217 9 ( ( PUNCT iajs-2992 217 10 52 52 NUM iajs-2992 217 11 ) ) PUNCT iajs-2992 217 12 , , PUNCT iajs-2992 217 13 to to PART iajs-2992 217 14 obtain obtain VERB iajs-2992 217 15 𝐺( 𝐺( NOUN iajs-2992 217 16 οΏ½ οΏ½ PROPN iajs-2992 217 17 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 217 18 οΏ½ οΏ½ PROPN iajs-2992 217 19 ) ) PUNCT iajs-2992 217 20 βˆ’ βˆ’ PROPN iajs-2992 217 21 𝐺( 𝐺( PROPN iajs-2992 217 22 οΏ½ οΏ½ PROPN iajs-2992 217 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 217 24 οΏ½ οΏ½ PROPN iajs-2992 217 25 ) ) PUNCT iajs-2992 217 26 = = PUNCT iajs-2992 217 27 νœ€ νœ€ PRON iajs-2992 217 28 ∫ ∫ PROPN iajs-2992 217 29 0 0 X iajs-2992 217 30 𝑇 𝑇 PROPN iajs-2992 217 31 βˆ‘ βˆ‘ PROPN iajs-2992 217 32 𝑖=1 𝑖=1 PROPN iajs-2992 217 33 4 4 NUM iajs-2992 217 34 ( ( PUNCT iajs-2992 217 35 𝑍𝑖𝑓𝑖𝑒𝑖 𝑍𝑖𝑓𝑖𝑒𝑖 PROPN iajs-2992 217 36 + + CCONJ iajs-2992 217 37 𝑔𝑖𝑒𝑖 𝑔𝑖𝑒𝑖 NOUN iajs-2992 217 38 ) ) PUNCT iajs-2992 217 39 𝛿𝑒𝑖𝑑π‘₯𝑑𝑑 𝛿𝑒𝑖𝑑π‘₯𝑑𝑑 PROPN iajs-2992 217 40 + + CCONJ iajs-2992 217 41 𝑂3(νœ€ 𝑂3(νœ€ NOUN iajs-2992 217 42 ) ) PUNCT iajs-2992 217 43 , , PUNCT iajs-2992 217 44 where where SCONJ iajs-2992 217 45 𝑂3(νœ€ 𝑂3(νœ€ NOUN iajs-2992 217 46 ) ) PUNCT iajs-2992 217 47 = = SYM iajs-2992 217 48 𝑂1(νœ€ 𝑂1(νœ€ PROPN iajs-2992 217 49 ) ) PUNCT iajs-2992 217 50 + + PUNCT iajs-2992 217 51 𝑂2(νœ€ 𝑂2(νœ€ PROPN iajs-2992 217 52 ) ) PUNCT iajs-2992 217 53 . . PUNCT iajs-2992 218 1 lastly lastly ADV iajs-2992 218 2 , , PUNCT iajs-2992 218 3 dividing divide VERB iajs-2992 218 4 both both DET iajs-2992 218 5 sides side NOUN iajs-2992 218 6 by by ADP iajs-2992 218 7 νœ€ νœ€ NOUN iajs-2992 218 8 , , PUNCT iajs-2992 218 9 then then ADV iajs-2992 218 10 taking take VERB iajs-2992 218 11 the the DET iajs-2992 218 12 limit limit NOUN iajs-2992 218 13 νœ€ νœ€ X iajs-2992 218 14 β†’ β†’ SYM iajs-2992 218 15 0 0 NUM iajs-2992 218 16 , , PUNCT iajs-2992 218 17 yields yield NOUN iajs-2992 218 18 to to ADP iajs-2992 218 19 𝐷𝐺( 𝐷𝐺( PROPN iajs-2992 218 20 οΏ½ οΏ½ PROPN iajs-2992 218 21 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 218 22 οΏ½ οΏ½ PROPN iajs-2992 218 23 , , PUNCT iajs-2992 218 24 οΏ½ οΏ½ PROPN iajs-2992 218 25 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 218 26 οΏ½ οΏ½ PROPN iajs-2992 218 27 βˆ’ βˆ’ PROPN iajs-2992 218 28 οΏ½ οΏ½ PROPN iajs-2992 218 29 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 218 30 οΏ½ οΏ½ PROPN iajs-2992 218 31 ) ) PUNCT iajs-2992 219 1 = = SYM iajs-2992 220 1 ∫ ∫ PROPN iajs-2992 220 2 𝑄 𝑄 PROPN iajs-2992 220 3 𝐻 𝐻 PROPN iajs-2992 220 4 οΏ½ οΏ½ PROPN iajs-2992 220 5 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 220 6 οΏ½ οΏ½ PROPN iajs-2992 220 7 (π‘₯ (π‘₯ PROPN iajs-2992 220 8 , , PUNCT iajs-2992 220 9 𝑑 𝑑 PROPN iajs-2992 220 10 , , PUNCT iajs-2992 220 11 οΏ½ οΏ½ PROPN iajs-2992 220 12 βƒ— βƒ— PROPN iajs-2992 220 13 οΏ½ οΏ½ PROPN iajs-2992 220 14 , , PUNCT iajs-2992 220 15 οΏ½ οΏ½ PROPN iajs-2992 220 16 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 220 17 οΏ½ οΏ½ PROPN iajs-2992 220 18 , , PUNCT iajs-2992 220 19 οΏ½ οΏ½ PROPN iajs-2992 220 20 βƒ— βƒ— PROPN iajs-2992 220 21 οΏ½ οΏ½ PROPN iajs-2992 220 22 )( )( SYM iajs-2992 220 23 οΏ½ οΏ½ PROPN iajs-2992 220 24 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 220 25 οΏ½ οΏ½ PROPN iajs-2992 220 26 βˆ’ βˆ’ PROPN iajs-2992 220 27 οΏ½ οΏ½ PROPN iajs-2992 220 28 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 220 29 οΏ½ οΏ½ PROPN iajs-2992 220 30 )𝑑π‘₯𝑑𝑑 )𝑑π‘₯𝑑𝑑 PUNCT iajs-2992 220 31 . . PUNCT iajs-2992 221 1 4.the 4.the DET iajs-2992 221 2 ncso ncso NOUN iajs-2992 221 3 and and CCONJ iajs-2992 221 4 scso scso VERB iajs-2992 221 5 4.1theorem 4.1theorem NUM iajs-2992 221 6 : : PUNCT iajs-2992 221 7 ( ( PUNCT iajs-2992 221 8 a a X iajs-2992 221 9 ) ) PUNCT iajs-2992 221 10 with with ADP iajs-2992 221 11 assums assum NOUN iajs-2992 221 12 ( ( PUNCT iajs-2992 221 13 a a NOUN iajs-2992 221 14 ) ) PUNCT iajs-2992 221 15 , , PUNCT iajs-2992 221 16 ( ( PUNCT iajs-2992 221 17 b b X iajs-2992 221 18 ) ) PUNCT iajs-2992 221 19 & & CCONJ iajs-2992 221 20 ( ( PUNCT iajs-2992 221 21 c c NOUN iajs-2992 221 22 ) ) PUNCT iajs-2992 221 23 , , PUNCT iajs-2992 221 24 if if SCONJ iajs-2992 221 25 οΏ½ οΏ½ PROPN iajs-2992 221 26 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— PROPN iajs-2992 221 27 οΏ½ οΏ½ PROPN iajs-2992 221 28 is be AUX iajs-2992 221 29 co. co. PROPN iajs-2992 221 30 , , PUNCT iajs-2992 221 31 the the DET iajs-2992 221 32 οΏ½ οΏ½ PROPN iajs-2992 221 33 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 221 34 οΏ½ οΏ½ PROPN iajs-2992 221 35 ∈ ∈ PROPN iajs-2992 221 36 π‘Šπ΄ π‘Šπ΄ PROPN iajs-2992 221 37 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 221 38 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 221 39 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 221 40 is be AUX iajs-2992 221 41 cqocccv cqocccv NOUN iajs-2992 221 42 , , PUNCT iajs-2992 221 43 then then ADV iajs-2992 221 44 there there PRON iajs-2992 221 45 exist exist VERB iajs-2992 221 46 πœ†π‘™ πœ†π‘™ PRON iajs-2992 221 47 ∈ ∈ PROPN iajs-2992 221 48 ℝ ℝ PROPN iajs-2992 221 49 , , PUNCT iajs-2992 221 50 𝑙 𝑙 X iajs-2992 221 51 = = SYM iajs-2992 221 52 0,1,2 0,1,2 NOUN iajs-2992 221 53 with with ADP iajs-2992 221 54 πœ†0 πœ†0 PROPN iajs-2992 221 55 β‰₯ β‰₯ NUM iajs-2992 221 56 0 0 NUM iajs-2992 221 57 , , PUNCT iajs-2992 221 58 πœ†2 πœ†2 NOUN iajs-2992 221 59 β‰₯ β‰₯ NOUN iajs-2992 221 60 0 0 NUM iajs-2992 221 61 , , PUNCT iajs-2992 221 62 βˆ‘ βˆ‘ PUNCT iajs-2992 221 63 𝑙=0 𝑙=0 PROPN iajs-2992 221 64 2 2 NUM iajs-2992 221 65 ∣ ∣ PROPN iajs-2992 221 66 πœ†π‘™ πœ†π‘™ PROPN iajs-2992 221 67 ∣= ∣= PROPN iajs-2992 221 68 1 1 NUM iajs-2992 221 69 , , PUNCT iajs-2992 221 70 s.t s.t PROPN iajs-2992 221 71 . . PUNCT iajs-2992 222 1 the the DET iajs-2992 222 2 following follow VERB iajs-2992 222 3 kuhn kuhn PROPN iajs-2992 222 4 - - PUNCT iajs-2992 222 5 tucher tucher PROPN iajs-2992 222 6 lagrange lagrange PROPN iajs-2992 222 7 ( ( PUNCT iajs-2992 222 8 ktl ktl PROPN iajs-2992 222 9 ) ) PUNCT iajs-2992 222 10 conditions condition NOUN iajs-2992 222 11 are be AUX iajs-2992 222 12 held hold VERB iajs-2992 222 13 : : PUNCT iajs-2992 222 14 βˆ‘ βˆ‘ PUNCT iajs-2992 222 15 𝑙=0 𝑙=0 PROPN iajs-2992 222 16 2 2 NUM iajs-2992 222 17 πœ†π‘™ πœ†π‘™ ADP iajs-2992 222 18 𝐷𝐺𝑙( 𝐷𝐺𝑙( PROPN iajs-2992 222 19 οΏ½ οΏ½ PROPN iajs-2992 222 20 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 222 21 οΏ½ οΏ½ PROPN iajs-2992 222 22 , , PUNCT iajs-2992 222 23 οΏ½ οΏ½ PROPN iajs-2992 222 24 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 222 25 οΏ½ οΏ½ PROPN iajs-2992 222 26 βˆ’ βˆ’ PROPN iajs-2992 222 27 οΏ½ οΏ½ PROPN iajs-2992 222 28 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 222 29 οΏ½ οΏ½ PROPN iajs-2992 222 30 ) ) PUNCT iajs-2992 222 31 β‰₯ β‰₯ NOUN iajs-2992 222 32 0 0 NUM iajs-2992 222 33 , , PUNCT iajs-2992 222 34 βˆ€ βˆ€ X iajs-2992 222 35 οΏ½ οΏ½ PROPN iajs-2992 222 36 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 222 37 οΏ½ οΏ½ PROPN iajs-2992 222 38 ∈ ∈ PROPN iajs-2992 222 39 οΏ½ οΏ½ PROPN iajs-2992 222 40 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 222 41 οΏ½ οΏ½ PROPN iajs-2992 222 42 , , PUNCT iajs-2992 222 43 ( ( PUNCT iajs-2992 222 44 53 53 NUM iajs-2992 222 45 ) ) PUNCT iajs-2992 222 46 πœ†2𝐺2( πœ†2𝐺2( PUNCT iajs-2992 222 47 οΏ½ οΏ½ PROPN iajs-2992 222 48 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 222 49 οΏ½ οΏ½ PROPN iajs-2992 222 50 ) ) PUNCT iajs-2992 222 51 = = SYM iajs-2992 222 52 0 0 NUM iajs-2992 222 53 , , PUNCT iajs-2992 222 54 ( ( PUNCT iajs-2992 222 55 54 54 NUM iajs-2992 222 56 ) ) PUNCT iajs-2992 222 57 ( ( PUNCT iajs-2992 222 58 b b X iajs-2992 222 59 ) ) PUNCT iajs-2992 222 60 inequality inequality NOUN iajs-2992 222 61 ( ( PUNCT iajs-2992 222 62 53 53 NUM iajs-2992 222 63 ) ) PUNCT iajs-2992 222 64 is be AUX iajs-2992 222 65 equivalent equivalent ADJ iajs-2992 222 66 to to PART iajs-2992 222 67 : : PUNCT iajs-2992 222 68 𝐻 𝐻 PROPN iajs-2992 222 69 οΏ½ οΏ½ PROPN iajs-2992 222 70 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 222 71 οΏ½ οΏ½ PROPN iajs-2992 222 72 (π‘₯ (π‘₯ PROPN iajs-2992 222 73 , , PUNCT iajs-2992 222 74 𝑑 𝑑 PROPN iajs-2992 222 75 , , PUNCT iajs-2992 222 76 οΏ½ οΏ½ PROPN iajs-2992 222 77 βƒ— βƒ— PROPN iajs-2992 222 78 οΏ½ οΏ½ PROPN iajs-2992 222 79 , , PUNCT iajs-2992 222 80 οΏ½ οΏ½ PROPN iajs-2992 222 81 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 222 82 οΏ½ οΏ½ PROPN iajs-2992 222 83 , , PUNCT iajs-2992 222 84 οΏ½ οΏ½ PROPN iajs-2992 222 85 βƒ— βƒ— PROPN iajs-2992 222 86 οΏ½ οΏ½ PROPN iajs-2992 222 87 ) ) PUNCT iajs-2992 222 88 οΏ½ οΏ½ PROPN iajs-2992 222 89 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 222 90 οΏ½ οΏ½ PROPN iajs-2992 222 91 (𝑑 (𝑑 PROPN iajs-2992 222 92 ) ) PUNCT iajs-2992 223 1 = = SYM iajs-2992 223 2 min min PROPN iajs-2992 223 3 οΏ½ οΏ½ PROPN iajs-2992 223 4 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 223 5 οΏ½ οΏ½ PROPN iajs-2992 223 6 ∈ ∈ PROPN iajs-2992 223 7 οΏ½ οΏ½ PROPN iajs-2992 223 8 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 223 9 οΏ½ οΏ½ PROPN iajs-2992 223 10 𝐻 𝐻 PROPN iajs-2992 223 11 οΏ½ οΏ½ PROPN iajs-2992 223 12 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 223 13 οΏ½ οΏ½ PROPN iajs-2992 223 14 (π‘₯ (π‘₯ PROPN iajs-2992 223 15 , , PUNCT iajs-2992 223 16 𝑑 𝑑 PROPN iajs-2992 223 17 , , PUNCT iajs-2992 223 18 οΏ½ οΏ½ PROPN iajs-2992 223 19 βƒ— βƒ— PROPN iajs-2992 223 20 οΏ½ οΏ½ PROPN iajs-2992 223 21 , , PUNCT iajs-2992 223 22 οΏ½ οΏ½ PROPN iajs-2992 223 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 223 24 οΏ½ οΏ½ PROPN iajs-2992 223 25 , , PUNCT iajs-2992 223 26 οΏ½ οΏ½ PROPN iajs-2992 223 27 βƒ— βƒ— PROPN iajs-2992 223 28 οΏ½ οΏ½ PROPN iajs-2992 223 29 ) ) PUNCT iajs-2992 223 30 οΏ½ οΏ½ PROPN iajs-2992 223 31 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 223 32 οΏ½ οΏ½ NOUN iajs-2992 223 33 (𝑑 (𝑑 NOUN iajs-2992 223 34 ) ) PUNCT iajs-2992 223 35 , , PUNCT iajs-2992 223 36 π‘Ž. π‘Ž. PROPN iajs-2992 223 37 𝑒. 𝑒. PROPN iajs-2992 223 38 π‘œπ‘› π‘œπ‘› PROPN iajs-2992 224 1 𝑄 𝑄 PROPN iajs-2992 224 2 , , PUNCT iajs-2992 224 3 ( ( PUNCT iajs-2992 224 4 55 55 NUM iajs-2992 224 5 ) ) PUNCT iajs-2992 224 6 where where SCONJ iajs-2992 224 7 𝐻 𝐻 PROPN iajs-2992 224 8 οΏ½ οΏ½ PROPN iajs-2992 224 9 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 224 10 οΏ½ οΏ½ PROPN iajs-2992 224 11 (π‘₯ (π‘₯ PROPN iajs-2992 224 12 , , PUNCT iajs-2992 224 13 𝑑 𝑑 PROPN iajs-2992 224 14 , , PUNCT iajs-2992 224 15 οΏ½ οΏ½ PROPN iajs-2992 224 16 βƒ— βƒ— PROPN iajs-2992 224 17 οΏ½ οΏ½ PROPN iajs-2992 224 18 , , PUNCT iajs-2992 224 19 οΏ½ οΏ½ PROPN iajs-2992 224 20 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 224 21 οΏ½ οΏ½ PROPN iajs-2992 224 22 , , PUNCT iajs-2992 224 23 οΏ½ οΏ½ PROPN iajs-2992 224 24 βƒ— βƒ— NOUN iajs-2992 224 25 οΏ½ οΏ½ PROPN iajs-2992 224 26 ) ) PUNCT iajs-2992 224 27 = = PUNCT iajs-2992 224 28 βˆ‘ βˆ‘ PUNCT iajs-2992 224 29 𝑖=1 𝑖=1 PROPN iajs-2992 224 30 4 4 X iajs-2992 224 31 ( ( PUNCT iajs-2992 224 32 𝑍𝑖𝑓𝑖𝑒𝑖 𝑍𝑖𝑓𝑖𝑒𝑖 PROPN iajs-2992 224 33 ( ( PUNCT iajs-2992 224 34 π‘₯ π‘₯ PROPN iajs-2992 224 35 , , PUNCT iajs-2992 224 36 𝑑 𝑑 PROPN iajs-2992 224 37 , , PUNCT iajs-2992 224 38 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 224 39 , , PUNCT iajs-2992 224 40 𝑒𝑖 𝑒𝑖 PRON iajs-2992 224 41 ) ) PUNCT iajs-2992 224 42 + + CCONJ iajs-2992 224 43 𝑔𝑖𝑒𝑖 𝑔𝑖𝑒𝑖 NOUN iajs-2992 224 44 ( ( PUNCT iajs-2992 224 45 π‘₯ π‘₯ PROPN iajs-2992 224 46 , , PUNCT iajs-2992 224 47 𝑑 𝑑 PROPN iajs-2992 224 48 , , PUNCT iajs-2992 224 49 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 224 50 , , PUNCT iajs-2992 224 51 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 224 52 ) ) PUNCT iajs-2992 224 53 ) ) PUNCT iajs-2992 224 54 . . PUNCT iajs-2992 225 1 proof proof NOUN iajs-2992 225 2 : : PUNCT iajs-2992 225 3 from from ADP iajs-2992 225 4 lemma lemma PROPN iajs-2992 225 5 2.1 2.1 NUM iajs-2992 225 6 , , PUNCT iajs-2992 225 7 the the DET iajs-2992 225 8 funl funl NOUN iajs-2992 225 9 . . PUNCT iajs-2992 226 1 𝐺𝑙( 𝐺𝑙( PROPN iajs-2992 226 2 οΏ½ οΏ½ PROPN iajs-2992 226 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 226 4 οΏ½ οΏ½ PROPN iajs-2992 226 5 ) ) PUNCT iajs-2992 226 6 ( ( PUNCT iajs-2992 226 7 for for ADP iajs-2992 226 8 𝑙 𝑙 NOUN iajs-2992 226 9 = = SYM iajs-2992 226 10 0,1,2 0,1,2 NUM iajs-2992 226 11 ) ) PUNCT iajs-2992 226 12 is be AUX iajs-2992 226 13 cont cont NOUN iajs-2992 226 14 . . PUNCT iajs-2992 227 1 w.r.t w.r.t PROPN iajs-2992 227 2 . . PUNCT iajs-2992 228 1 οΏ½ οΏ½ PROPN iajs-2992 228 2 βƒ—βƒ—Μ… βƒ—βƒ—Μ… PROPN iajs-2992 228 3 οΏ½ οΏ½ PROPN iajs-2992 228 4 βˆ’ βˆ’ PROPN iajs-2992 228 5 οΏ½ οΏ½ PROPN iajs-2992 228 6 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 228 7 οΏ½ οΏ½ PROPN iajs-2992 228 8 and and CCONJ iajs-2992 228 9 linear linear PROPN iajs-2992 228 10 in in ADP iajs-2992 228 11 οΏ½ οΏ½ PROPN iajs-2992 228 12 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 228 13 οΏ½ οΏ½ PROPN iajs-2992 228 14 βˆ’ βˆ’ PROPN iajs-2992 228 15 οΏ½ οΏ½ PROPN iajs-2992 228 16 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 228 17 οΏ½ οΏ½ PROPN iajs-2992 228 18 , , PUNCT iajs-2992 228 19 the the DET iajs-2992 228 20 𝐷𝐺𝑙( 𝐷𝐺𝑙( PROPN iajs-2992 228 21 οΏ½ οΏ½ PROPN iajs-2992 228 22 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 228 23 οΏ½ οΏ½ PROPN iajs-2992 228 24 ) ) PUNCT iajs-2992 228 25 is be AUX iajs-2992 228 26 m m NOUN iajs-2992 228 27 - - NOUN iajs-2992 228 28 differential differential NOUN iajs-2992 228 29 for for ADP iajs-2992 228 30 any any DET iajs-2992 228 31 m m NOUN iajs-2992 228 32 , , PUNCT iajs-2992 228 33 then then ADV iajs-2992 228 34 applying apply VERB iajs-2992 228 35 the the DET iajs-2992 228 36 ktl ktl PROPN iajs-2992 228 37 theorem[15 theorem[15 PRON iajs-2992 228 38 ] ] PUNCT iajs-2992 228 39 , , PUNCT iajs-2992 228 40 there there PRON iajs-2992 228 41 exist exist VERB iajs-2992 228 42 πœ†π‘™ πœ†π‘™ DET iajs-2992 228 43 ∈ ∈ PROPN iajs-2992 228 44 ℝ ℝ PROPN iajs-2992 228 45 , , PUNCT iajs-2992 228 46 𝑙 𝑙 X iajs-2992 228 47 = = SYM iajs-2992 228 48 0,1,2 0,1,2 NOUN iajs-2992 228 49 with with ADP iajs-2992 228 50 πœ†0 πœ†0 PROPN iajs-2992 228 51 , , PUNCT iajs-2992 228 52 πœ†2 πœ†2 PROPN iajs-2992 228 53 β‰₯ β‰₯ NOUN iajs-2992 228 54 0 0 NUM iajs-2992 228 55 , , PUNCT iajs-2992 228 56 βˆ‘ βˆ‘ PUNCT iajs-2992 228 57 𝑙=0 𝑙=0 PROPN iajs-2992 228 58 2 2 NUM iajs-2992 228 59 ∣ ∣ PROPN iajs-2992 228 60 πœ†π‘™ πœ†π‘™ PROPN iajs-2992 228 61 ∣= ∣= PROPN iajs-2992 228 62 1 1 NUM iajs-2992 228 63 s.t s.t PROPN iajs-2992 228 64 . . PROPN iajs-2992 229 1 ( ( PUNCT iajs-2992 229 2 ( ( PUNCT iajs-2992 229 3 53)-(54 53)-(54 NOUN iajs-2992 229 4 ) ) PUNCT iajs-2992 229 5 ) ) PUNCT iajs-2992 229 6 are be AUX iajs-2992 229 7 satisfied satisfied ADJ iajs-2992 229 8 , , PUNCT iajs-2992 229 9 then then ADV iajs-2992 229 10 by by ADP iajs-2992 229 11 utilizing utilize VERB iajs-2992 229 12 theorem theorem NOUN iajs-2992 229 13 3.2 3.2 NUM iajs-2992 229 14 , , PUNCT iajs-2992 229 15 ( ( PUNCT iajs-2992 229 16 53 53 NUM iajs-2992 229 17 ) ) PUNCT iajs-2992 229 18 becomes become VERB iajs-2992 229 19 ∫ ∫ PROPN iajs-2992 229 20 𝑄 𝑄 PROPN iajs-2992 229 21 ( ( PUNCT iajs-2992 229 22 𝑍1𝑓1𝑒1 𝑍1𝑓1𝑒1 NOUN iajs-2992 229 23 , , PUNCT iajs-2992 229 24 𝑍2𝑓2𝑒2 𝑍2𝑓2𝑒2 NUM iajs-2992 229 25 , , PUNCT iajs-2992 229 26 𝑍3𝑓3𝑒3 𝑍3𝑓3𝑒3 NOUN iajs-2992 229 27 , , PUNCT iajs-2992 229 28 𝑍4𝑓4𝑒4 𝑍4𝑓4𝑒4 NOUN iajs-2992 229 29 ) ) PUNCT iajs-2992 229 30 . . PUNCT iajs-2992 230 1 ( ( PUNCT iajs-2992 230 2 οΏ½ οΏ½ PROPN iajs-2992 230 3 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 230 4 οΏ½ οΏ½ PROPN iajs-2992 230 5 βˆ’ βˆ’ PROPN iajs-2992 230 6 οΏ½ οΏ½ PROPN iajs-2992 230 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 230 8 οΏ½ οΏ½ PROPN iajs-2992 230 9 )𝑑π‘₯𝑑𝑑 )𝑑π‘₯𝑑𝑑 PROPN iajs-2992 230 10 β‰₯ β‰₯ NOUN iajs-2992 230 11 0 0 NUM iajs-2992 230 12 , , PUNCT iajs-2992 230 13 βˆ€ βˆ€ X iajs-2992 230 14 οΏ½ οΏ½ PROPN iajs-2992 230 15 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 230 16 οΏ½ οΏ½ PROPN iajs-2992 230 17 ∈ ∈ PROPN iajs-2992 230 18 οΏ½ οΏ½ PROPN iajs-2992 230 19 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 230 20 οΏ½ οΏ½ PROPN iajs-2992 230 21 , , PUNCT iajs-2992 230 22 ( ( PUNCT iajs-2992 230 23 56 56 NUM iajs-2992 230 24 ) ) PUNCT iajs-2992 230 25 where where SCONJ iajs-2992 230 26 𝑔𝑖 𝑔𝑖 NOUN iajs-2992 230 27 = = PUNCT iajs-2992 230 28 βˆ‘ βˆ‘ PUNCT iajs-2992 230 29 𝑙=0 𝑙=0 NOUN iajs-2992 230 30 2 2 NUM iajs-2992 230 31 πœ†π‘™π‘”π‘™π‘– πœ†π‘™π‘”π‘™π‘– NOUN iajs-2992 230 32 and and CCONJ iajs-2992 230 33 𝑍𝑖 𝑍𝑖 PROPN iajs-2992 230 34 = = SYM iajs-2992 230 35 βˆ‘ βˆ‘ PUNCT iajs-2992 230 36 𝑙=0 𝑙=0 PROPN iajs-2992 230 37 2 2 NUM iajs-2992 230 38 πœ†π‘™π‘π‘™π‘– πœ†π‘™π‘π‘™π‘– NOUN iajs-2992 230 39 , , PUNCT iajs-2992 230 40 ( ( PUNCT iajs-2992 230 41 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 230 42 = = NOUN iajs-2992 230 43 1,2,3,4 1,2,3,4 NUM iajs-2992 230 44 ) ) PUNCT iajs-2992 230 45 . . PUNCT iajs-2992 231 1 ( ( PUNCT iajs-2992 231 2 b b X iajs-2992 231 3 ) ) PUNCT iajs-2992 231 4 let let VERB iajs-2992 231 5 { { PUNCT iajs-2992 231 6 οΏ½ οΏ½ NOUN iajs-2992 231 7 Μ… Μ… NOUN iajs-2992 231 8 οΏ½ οΏ½ NOUN iajs-2992 231 9 π‘˜βƒ—βƒ—βƒ—βƒ—βƒ— π‘˜βƒ—βƒ—βƒ—βƒ—βƒ— NOUN iajs-2992 231 10 } } PUNCT iajs-2992 231 11 be be AUX iajs-2992 231 12 dense dense ADJ iajs-2992 231 13 seq seq NOUN iajs-2992 231 14 ( ( PUNCT iajs-2992 231 15 dseq dseq NOUN iajs-2992 231 16 ) ) PUNCT iajs-2992 231 17 in in ADP iajs-2992 231 18 οΏ½ οΏ½ PROPN iajs-2992 231 19 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 231 20 οΏ½ οΏ½ PROPN iajs-2992 231 21 , , PUNCT iajs-2992 231 22 πœ‡ πœ‡ ADP iajs-2992 231 23 is be AUX iajs-2992 231 24 lebesgue lebesgue ADJ iajs-2992 231 25 measure measure NOUN iajs-2992 231 26 ( ( PUNCT iajs-2992 231 27 lm lm INTJ iajs-2992 231 28 ) ) PUNCT iajs-2992 231 29 on on ADP iajs-2992 231 30 𝑄 𝑄 PRON iajs-2992 231 31 and and CCONJ iajs-2992 231 32 let let VERB iajs-2992 231 33 𝑆 𝑆 PROPN iajs-2992 231 34 βŠ‚ βŠ‚ PRON iajs-2992 231 35 𝑄 𝑄 PRON iajs-2992 231 36 be be VERB iajs-2992 231 37 a a DET iajs-2992 231 38 measurable measurable ADJ iajs-2992 231 39 set set NOUN iajs-2992 231 40 ( ( PUNCT iajs-2992 231 41 ms ms PROPN iajs-2992 231 42 ) ) PUNCT iajs-2992 231 43 s.t s.t PROPN iajs-2992 231 44 . . PROPN iajs-2992 231 45 ihjpas ihjpas PROPN iajs-2992 231 46 . . PUNCT iajs-2992 232 1 36(2)2023 36(2)2023 NUM iajs-2992 232 2 338 338 NUM iajs-2992 232 3 οΏ½ οΏ½ PROPN iajs-2992 232 4 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 232 5 οΏ½ οΏ½ PROPN iajs-2992 232 6 (π‘₯ (π‘₯ PROPN iajs-2992 232 7 , , PUNCT iajs-2992 232 8 𝑑 𝑑 X iajs-2992 232 9 ) ) PUNCT iajs-2992 232 10 = = PRON iajs-2992 232 11 { { PUNCT iajs-2992 232 12 οΏ½ οΏ½ NOUN iajs-2992 232 13 Μ… Μ… NOUN iajs-2992 232 14 οΏ½ οΏ½ X iajs-2992 232 15 π‘˜βƒ—βƒ—βƒ—βƒ—βƒ—(π‘₯ π‘˜βƒ—βƒ—βƒ—βƒ—βƒ—(π‘₯ NOUN iajs-2992 232 16 , , PUNCT iajs-2992 232 17 𝑑 𝑑 PROPN iajs-2992 232 18 ) ) PUNCT iajs-2992 232 19 , , PUNCT iajs-2992 232 20 𝑖𝑓 𝑖𝑓 CCONJ iajs-2992 232 21 ( ( PUNCT iajs-2992 232 22 π‘₯ π‘₯ NOUN iajs-2992 232 23 , , PUNCT iajs-2992 232 24 𝑑 𝑑 NOUN iajs-2992 232 25 ) ) PUNCT iajs-2992 232 26 ∈ ∈ PROPN iajs-2992 232 27 𝑆 𝑆 PROPN iajs-2992 232 28 οΏ½ οΏ½ PROPN iajs-2992 232 29 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 232 30 οΏ½ οΏ½ PROPN iajs-2992 232 31 (π‘₯ (π‘₯ PROPN iajs-2992 232 32 , , PUNCT iajs-2992 232 33 𝑑 𝑑 PROPN iajs-2992 232 34 ) ) PUNCT iajs-2992 232 35 , , PUNCT iajs-2992 232 36 𝑖𝑓 𝑖𝑓 CCONJ iajs-2992 232 37 ( ( PUNCT iajs-2992 232 38 π‘₯ π‘₯ NOUN iajs-2992 232 39 , , PUNCT iajs-2992 232 40 𝑑 𝑑 PROPN iajs-2992 232 41 ) ) PUNCT iajs-2992 232 42 βˆ‰ βˆ‰ PROPN iajs-2992 232 43 𝑆 𝑆 PROPN iajs-2992 232 44 . . PUNCT iajs-2992 233 1 which which PRON iajs-2992 233 2 makes make VERB iajs-2992 233 3 ( ( PUNCT iajs-2992 233 4 56 56 NUM iajs-2992 233 5 ) ) PUNCT iajs-2992 233 6 , , PUNCT iajs-2992 233 7 gives give VERB iajs-2992 233 8 ∫ ∫ PROPN iajs-2992 233 9 𝑆 𝑆 PROPN iajs-2992 233 10 ( ( PUNCT iajs-2992 233 11 𝑍1𝑓1𝑒1 𝑍1𝑓1𝑒1 X iajs-2992 233 12 + + CCONJ iajs-2992 233 13 𝑔1𝑒1 𝑔1𝑒1 NOUN iajs-2992 233 14 , , PUNCT iajs-2992 233 15 𝑍2𝑓2𝑒2 𝑍2𝑓2𝑒2 NUM iajs-2992 233 16 + + CCONJ iajs-2992 233 17 𝑔2𝑒2 𝑔2𝑒2 PROPN iajs-2992 233 18 , , PUNCT iajs-2992 233 19 𝑍3𝑓3𝑒3 𝑍3𝑓3𝑒3 X iajs-2992 233 20 + + CCONJ iajs-2992 233 21 𝑔3𝑒3 𝑔3𝑒3 X iajs-2992 233 22 , , PUNCT iajs-2992 233 23 𝑍4𝑓4𝑒4 𝑍4𝑓4𝑒4 NOUN iajs-2992 233 24 + + CCONJ iajs-2992 233 25 𝑔4𝑒4 𝑔4𝑒4 PROPN iajs-2992 233 26 ) ) PUNCT iajs-2992 233 27 . . PUNCT iajs-2992 234 1 ( ( PUNCT iajs-2992 234 2 οΏ½ οΏ½ PROPN iajs-2992 234 3 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 234 4 οΏ½ οΏ½ PROPN iajs-2992 234 5 π‘˜ π‘˜ DET iajs-2992 234 6 βˆ’ βˆ’ PROPN iajs-2992 234 7 οΏ½ οΏ½ PROPN iajs-2992 234 8 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 234 9 οΏ½ οΏ½ PROPN iajs-2992 234 10 )𝑑π‘₯𝑑𝑑 )𝑑π‘₯𝑑𝑑 PROPN iajs-2992 234 11 β‰₯ β‰₯ NOUN iajs-2992 234 12 0 0 NUM iajs-2992 234 13 , , PUNCT iajs-2992 234 14 or or CCONJ iajs-2992 234 15 ( ( PUNCT iajs-2992 234 16 𝑍1𝑓1𝑒1 𝑍1𝑓1𝑒1 X iajs-2992 234 17 + + CCONJ iajs-2992 234 18 𝑔1𝑒1 𝑔1𝑒1 NOUN iajs-2992 234 19 , , PUNCT iajs-2992 234 20 𝑍2𝑓2𝑒2 𝑍2𝑓2𝑒2 NUM iajs-2992 234 21 + + CCONJ iajs-2992 234 22 𝑔2𝑒2 𝑔2𝑒2 PROPN iajs-2992 234 23 , , PUNCT iajs-2992 234 24 𝑍3𝑓3𝑒3 𝑍3𝑓3𝑒3 X iajs-2992 234 25 + + CCONJ iajs-2992 234 26 𝑔3𝑒3 𝑔3𝑒3 X iajs-2992 234 27 , , PUNCT iajs-2992 234 28 𝑍4𝑓4𝑒4 𝑍4𝑓4𝑒4 NOUN iajs-2992 234 29 + + CCONJ iajs-2992 234 30 𝑔4𝑒4 𝑔4𝑒4 PROPN iajs-2992 234 31 ) ) PUNCT iajs-2992 234 32 . . PUNCT iajs-2992 235 1 ( ( PUNCT iajs-2992 235 2 οΏ½ οΏ½ PROPN iajs-2992 235 3 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 235 4 οΏ½ οΏ½ PROPN iajs-2992 235 5 π‘˜ π‘˜ DET iajs-2992 235 6 βˆ’ βˆ’ PROPN iajs-2992 235 7 οΏ½ οΏ½ PROPN iajs-2992 235 8 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 235 9 οΏ½ οΏ½ PROPN iajs-2992 235 10 ) ) PUNCT iajs-2992 235 11 β‰₯ β‰₯ NOUN iajs-2992 235 12 0 0 NUM iajs-2992 235 13 , , PUNCT iajs-2992 235 14 π‘Ž. π‘Ž. PROPN iajs-2992 235 15 𝑒. 𝑒. PROPN iajs-2992 235 16 π‘œπ‘› π‘œπ‘› PROPN iajs-2992 236 1 𝑄 𝑄 PROPN iajs-2992 236 2 , , PUNCT iajs-2992 236 3 i.e. i.e. X iajs-2992 236 4 this this DET iajs-2992 236 5 inequality inequality NOUN iajs-2992 236 6 holds hold VERB iajs-2992 236 7 on on ADP iajs-2992 236 8 𝑄\π‘„π‘˜ 𝑄\π‘„π‘˜ ADJ iajs-2992 236 9 with with ADP iajs-2992 236 10 πœ‡(π‘„π‘˜ πœ‡(π‘„π‘˜ NOUN iajs-2992 236 11 ) ) PUNCT iajs-2992 236 12 = = SYM iajs-2992 236 13 0 0 NUM iajs-2992 236 14 , , PUNCT iajs-2992 236 15 βˆ€π‘˜ βˆ€π‘˜ X iajs-2992 236 16 , , PUNCT iajs-2992 236 17 where where SCONJ iajs-2992 236 18 πœ‡ πœ‡ ADV iajs-2992 236 19 is be AUX iajs-2992 236 20 a a DET iajs-2992 236 21 lm lm ADJ iajs-2992 236 22 , , PUNCT iajs-2992 236 23 i.e. i.e. X iajs-2992 236 24 it it PRON iajs-2992 236 25 is be AUX iajs-2992 236 26 satisfies satisfie NOUN iajs-2992 236 27 on on ADP iajs-2992 236 28 𝑄\βˆͺπ‘˜ 𝑄\βˆͺπ‘˜ PROPN iajs-2992 236 29 π‘„π‘˜ π‘„π‘˜ PROPN iajs-2992 236 30 , , PUNCT iajs-2992 236 31 with with ADP iajs-2992 236 32 πœ‡(βˆͺπ‘˜ πœ‡(βˆͺπ‘˜ NOUN iajs-2992 236 33 π‘„π‘˜ π‘„π‘˜ PROPN iajs-2992 236 34 ) ) PUNCT iajs-2992 236 35 = = SYM iajs-2992 236 36 0 0 NUM iajs-2992 236 37 , , PUNCT iajs-2992 236 38 but but CCONJ iajs-2992 236 39 { { PUNCT iajs-2992 236 40 οΏ½ οΏ½ NOUN iajs-2992 236 41 Μ… Μ… NOUN iajs-2992 236 42 οΏ½ οΏ½ NOUN iajs-2992 236 43 π‘˜βƒ—βƒ—βƒ—βƒ—βƒ— π‘˜βƒ—βƒ—βƒ—βƒ—βƒ— NOUN iajs-2992 236 44 } } PUNCT iajs-2992 236 45 is be AUX iajs-2992 236 46 a a DET iajs-2992 236 47 dseq dseq NOUN iajs-2992 236 48 in in ADP iajs-2992 236 49 οΏ½ οΏ½ PROPN iajs-2992 236 50 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 236 51 οΏ½ οΏ½ PROPN iajs-2992 236 52 , , PUNCT iajs-2992 236 53 then then ADV iajs-2992 236 54 there there PRON iajs-2992 236 55 is be VERB iajs-2992 236 56 οΏ½ οΏ½ PROPN iajs-2992 236 57 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 236 58 οΏ½ οΏ½ PROPN iajs-2992 236 59 ∈ ∈ PROPN iajs-2992 236 60 οΏ½ οΏ½ PROPN iajs-2992 236 61 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 236 62 οΏ½ οΏ½ PROPN iajs-2992 236 63 , , PUNCT iajs-2992 236 64 s.t s.t PROPN iajs-2992 236 65 . . PROPN iajs-2992 237 1 ( ( PUNCT iajs-2992 237 2 𝑍1𝑓1𝑒1 𝑍1𝑓1𝑒1 X iajs-2992 237 3 + + CCONJ iajs-2992 237 4 𝑔1𝑒1 𝑔1𝑒1 NOUN iajs-2992 237 5 , , PUNCT iajs-2992 237 6 𝑍2𝑓2𝑒2 𝑍2𝑓2𝑒2 NUM iajs-2992 237 7 + + CCONJ iajs-2992 237 8 𝑔2𝑒2 𝑔2𝑒2 PROPN iajs-2992 237 9 , , PUNCT iajs-2992 237 10 𝑍3𝑓3𝑒3 𝑍3𝑓3𝑒3 X iajs-2992 237 11 + + CCONJ iajs-2992 237 12 𝑔3𝑒3 𝑔3𝑒3 X iajs-2992 237 13 , , PUNCT iajs-2992 237 14 𝑍4𝑓4𝑒4 𝑍4𝑓4𝑒4 NOUN iajs-2992 237 15 + + CCONJ iajs-2992 237 16 𝑔4𝑒4 𝑔4𝑒4 PROPN iajs-2992 237 17 ) ) PUNCT iajs-2992 237 18 . . PUNCT iajs-2992 238 1 ( ( PUNCT iajs-2992 238 2 οΏ½ οΏ½ PROPN iajs-2992 238 3 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 238 4 οΏ½ οΏ½ PROPN iajs-2992 238 5 βˆ’ βˆ’ PROPN iajs-2992 238 6 οΏ½ οΏ½ PROPN iajs-2992 238 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 238 8 οΏ½ οΏ½ PROPN iajs-2992 238 9 ) ) PUNCT iajs-2992 238 10 β‰₯ β‰₯ NOUN iajs-2992 238 11 0 0 NUM iajs-2992 238 12 , , PUNCT iajs-2992 238 13 π‘Ž. π‘Ž. PROPN iajs-2992 238 14 𝑒. 𝑒. PROPN iajs-2992 238 15 π‘œπ‘› π‘œπ‘› PROPN iajs-2992 239 1 𝑄 𝑄 PROPN iajs-2992 239 2 , , PUNCT iajs-2992 239 3 βˆ€ βˆ€ NUM iajs-2992 239 4 οΏ½ οΏ½ NOUN iajs-2992 239 5 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 239 6 οΏ½ οΏ½ PROPN iajs-2992 239 7 ∈ ∈ PROPN iajs-2992 239 8 οΏ½ οΏ½ PROPN iajs-2992 239 9 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— PROPN iajs-2992 239 10 οΏ½ οΏ½ PROPN iajs-2992 239 11 . . PUNCT iajs-2992 240 1 i.e. i.e. X iajs-2992 240 2 ( ( PUNCT iajs-2992 240 3 53 53 NUM iajs-2992 240 4 ) ) PUNCT iajs-2992 240 5 gives give VERB iajs-2992 240 6 ( ( PUNCT iajs-2992 240 7 56 56 NUM iajs-2992 240 8 ) ) PUNCT iajs-2992 240 9 . . PUNCT iajs-2992 241 1 the the DET iajs-2992 241 2 converse converse NOUN iajs-2992 241 3 is be AUX iajs-2992 241 4 clear clear ADJ iajs-2992 241 5 . . PUNCT iajs-2992 242 1 4.2theorem 4.2theorem NUM iajs-2992 242 2 : : PUNCT iajs-2992 242 3 ( ( PUNCT iajs-2992 242 4 the the DET iajs-2992 242 5 scso scso NOUN iajs-2992 242 6 ) ) PUNCT iajs-2992 242 7 in in ADP iajs-2992 242 8 addition addition NOUN iajs-2992 242 9 to to ADP iajs-2992 242 10 the the DET iajs-2992 242 11 assums assum NOUN iajs-2992 242 12 ( ( PUNCT iajs-2992 242 13 a a X iajs-2992 242 14 ) ) PUNCT iajs-2992 242 15 , , PUNCT iajs-2992 242 16 ( ( PUNCT iajs-2992 242 17 b b X iajs-2992 242 18 ) ) PUNCT iajs-2992 242 19 & & CCONJ iajs-2992 242 20 ( ( PUNCT iajs-2992 242 21 c c NOUN iajs-2992 242 22 ) ) PUNCT iajs-2992 242 23 . . PUNCT iajs-2992 243 1 suppose suppose VERB iajs-2992 243 2 οΏ½ οΏ½ PROPN iajs-2992 243 3 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 243 4 οΏ½ οΏ½ PROPN iajs-2992 243 5 is be AUX iajs-2992 243 6 co. co. PROPN iajs-2992 243 7 , , PUNCT iajs-2992 243 8 𝑓𝑖 𝑓𝑖 PROPN iajs-2992 243 9 , , PUNCT iajs-2992 243 10 𝑔𝑖 𝑔𝑖 NOUN iajs-2992 243 11 are be AUX iajs-2992 243 12 affine affine NOUN iajs-2992 243 13 w.r.t w.r.t NOUN iajs-2992 243 14 . . PUNCT iajs-2992 244 1 ( ( PUNCT iajs-2992 244 2 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 244 3 , , PUNCT iajs-2992 244 4 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 244 5 ) ) PUNCT iajs-2992 244 6 for for ADP iajs-2992 244 7 each each DET iajs-2992 244 8 ( ( PUNCT iajs-2992 244 9 π‘₯ π‘₯ PROPN iajs-2992 244 10 , , PUNCT iajs-2992 244 11 𝑑 𝑑 NOUN iajs-2992 244 12 ) ) PUNCT iajs-2992 244 13 , , PUNCT iajs-2992 244 14 𝑔0𝑖 𝑔0𝑖 NOUN iajs-2992 244 15 , , PUNCT iajs-2992 244 16 𝑔2𝑖 𝑔2𝑖 NOUN iajs-2992 244 17 are be AUX iajs-2992 244 18 co. co. PROPN iajs-2992 244 19 w.r.t w.r.t NOUN iajs-2992 244 20 . . PUNCT iajs-2992 245 1 ( ( PUNCT iajs-2992 245 2 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 245 3 , , PUNCT iajs-2992 245 4 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 245 5 ) ) PUNCT iajs-2992 245 6 , , PUNCT iajs-2992 245 7 βˆ€(π‘₯ βˆ€(π‘₯ PROPN iajs-2992 245 8 , , PUNCT iajs-2992 245 9 𝑑 𝑑 NOUN iajs-2992 245 10 ) ) PUNCT iajs-2992 245 11 , , PUNCT iajs-2992 245 12 𝑖 𝑖 NOUN iajs-2992 245 13 = = NOUN iajs-2992 245 14 1,2,3,4 1,2,3,4 NUM iajs-2992 245 15 . . PUNCT iajs-2992 246 1 then then ADV iajs-2992 246 2 the the DET iajs-2992 246 3 ncso ncso NOUN iajs-2992 246 4 of of ADP iajs-2992 246 5 theorem theorem NOUN iajs-2992 246 6 4.1 4.1 NUM iajs-2992 246 7 , , PUNCT iajs-2992 246 8 with with ADP iajs-2992 246 9 πœ†0 πœ†0 NOUN iajs-2992 246 10 > > X iajs-2992 246 11 0 0 NUM iajs-2992 246 12 are be AUX iajs-2992 246 13 also also ADV iajs-2992 246 14 sufficient sufficient ADJ iajs-2992 246 15 . . PUNCT iajs-2992 247 1 proof proof NOUN iajs-2992 247 2 : : PUNCT iajs-2992 247 3 assume assume VERB iajs-2992 247 4 οΏ½ οΏ½ PROPN iajs-2992 247 5 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 247 6 οΏ½ οΏ½ PROPN iajs-2992 247 7 ∈ ∈ PROPN iajs-2992 247 8 οΏ½ οΏ½ PROPN iajs-2992 247 9 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 247 10 οΏ½ οΏ½ PROPN iajs-2992 247 11 𝐴 𝐴 PROPN iajs-2992 247 12 , , PUNCT iajs-2992 247 13 is be AUX iajs-2992 247 14 satisfied satisfied ADJ iajs-2992 247 15 the the DET iajs-2992 247 16 ktl ktl ADJ iajs-2992 247 17 condition condition NOUN iajs-2992 247 18 ( ( PUNCT iajs-2992 247 19 ( ( PUNCT iajs-2992 247 20 53)(54 53)(54 NOUN iajs-2992 247 21 ) ) PUNCT iajs-2992 247 22 ) ) PUNCT iajs-2992 247 23 . . PUNCT iajs-2992 248 1 let let VERB iajs-2992 248 2 𝐺( 𝐺( PROPN iajs-2992 248 3 οΏ½ οΏ½ PROPN iajs-2992 248 4 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 248 5 οΏ½ οΏ½ PROPN iajs-2992 248 6 ) ) PUNCT iajs-2992 249 1 = = PUNCT iajs-2992 249 2 βˆ‘ βˆ‘ PUNCT iajs-2992 249 3 𝑙=0 𝑙=0 PROPN iajs-2992 249 4 2 2 NUM iajs-2992 249 5 πœ†π‘™πΊπ‘™( πœ†π‘™πΊπ‘™( NOUN iajs-2992 249 6 οΏ½ οΏ½ PROPN iajs-2992 249 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 249 8 οΏ½ οΏ½ PROPN iajs-2992 249 9 ) ) PUNCT iajs-2992 249 10 , , PUNCT iajs-2992 249 11 then then ADV iajs-2992 249 12 using use VERB iajs-2992 249 13 theorem theorem NOUN iajs-2992 249 14 3.2 3.2 NUM iajs-2992 249 15 , , PUNCT iajs-2992 249 16 to to PART iajs-2992 249 17 get get VERB iajs-2992 249 18 𝐷𝐺( 𝐷𝐺( PROPN iajs-2992 249 19 οΏ½ οΏ½ PROPN iajs-2992 249 20 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 249 21 οΏ½ οΏ½ PROPN iajs-2992 249 22 , , PUNCT iajs-2992 249 23 οΏ½ οΏ½ PROPN iajs-2992 249 24 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 249 25 οΏ½ οΏ½ PROPN iajs-2992 249 26 βˆ’ βˆ’ PROPN iajs-2992 249 27 οΏ½ οΏ½ PROPN iajs-2992 249 28 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 249 29 οΏ½ οΏ½ PROPN iajs-2992 249 30 ) ) PUNCT iajs-2992 249 31 = = PUNCT iajs-2992 250 1 βˆ‘ βˆ‘ PUNCT iajs-2992 250 2 𝑙=0 𝑙=0 PROPN iajs-2992 250 3 2 2 NUM iajs-2992 250 4 πœ†π‘™ πœ†π‘™ NOUN iajs-2992 250 5 ∫ ∫ PROPN iajs-2992 250 6 𝑄 𝑄 PROPN iajs-2992 250 7 βˆ‘ βˆ‘ PUNCT iajs-2992 250 8 𝑖=1 𝑖=1 PROPN iajs-2992 250 9 4 4 NUM iajs-2992 250 10 𝑍𝑙𝑖𝑓𝑙𝑖𝑒𝑖 𝑍𝑙𝑖𝑓𝑙𝑖𝑒𝑖 PROPN iajs-2992 250 11 + + CCONJ iajs-2992 250 12 𝑔𝑙𝑖𝑒𝑖 𝑔𝑙𝑖𝑒𝑖 PROPN iajs-2992 250 13 𝛿𝑒𝑖𝑑π‘₯𝑑𝑑 𝛿𝑒𝑖𝑑π‘₯𝑑𝑑 PROPN iajs-2992 250 14 β‰₯ β‰₯ NOUN iajs-2992 250 15 0 0 NUM iajs-2992 250 16 , , PUNCT iajs-2992 250 17 since since SCONJ iajs-2992 250 18 𝑓𝑖(π‘₯ 𝑓𝑖(π‘₯ NUM iajs-2992 250 19 , , PUNCT iajs-2992 250 20 𝑑 𝑑 PROPN iajs-2992 250 21 , , PUNCT iajs-2992 250 22 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 250 23 , , PUNCT iajs-2992 250 24 𝑒𝑖 𝑒𝑖 INTJ iajs-2992 250 25 ) ) PUNCT iajs-2992 250 26 = = SYM iajs-2992 250 27 𝑓𝑖1(π‘₯ 𝑓𝑖1(π‘₯ NOUN iajs-2992 250 28 , , PUNCT iajs-2992 250 29 𝑑)𝑦𝑖 𝑑)𝑦𝑖 PROPN iajs-2992 250 30 + + SYM iajs-2992 250 31 𝑓𝑖2(π‘₯ 𝑓𝑖2(π‘₯ PROPN iajs-2992 250 32 , , PUNCT iajs-2992 250 33 𝑑)𝑒𝑖 𝑑)𝑒𝑖 PROPN iajs-2992 250 34 + + CCONJ iajs-2992 250 35 𝑓𝑖3(π‘₯ 𝑓𝑖3(π‘₯ PROPN iajs-2992 250 36 , , PUNCT iajs-2992 250 37 𝑑 𝑑 NOUN iajs-2992 250 38 ) ) PUNCT iajs-2992 250 39 . . PUNCT iajs-2992 251 1 let let VERB iajs-2992 251 2 οΏ½ οΏ½ PROPN iajs-2992 251 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 251 4 οΏ½ οΏ½ PROPN iajs-2992 251 5 & & CCONJ iajs-2992 251 6 οΏ½ οΏ½ PROPN iajs-2992 251 7 βƒ—βƒ—Μ… βƒ—βƒ—Μ… PROPN iajs-2992 251 8 οΏ½ οΏ½ PROPN iajs-2992 251 9 are be AUX iajs-2992 251 10 given give VERB iajs-2992 251 11 qcvs qcvs PROPN iajs-2992 251 12 , , PUNCT iajs-2992 251 13 then then ADV iajs-2992 251 14 οΏ½ οΏ½ PROPN iajs-2992 251 15 βƒ— βƒ— PROPN iajs-2992 251 16 οΏ½ οΏ½ PROPN iajs-2992 251 17 & & CCONJ iajs-2992 251 18 οΏ½ οΏ½ PROPN iajs-2992 251 19 βƒ—Μ… βƒ—Μ… PROPN iajs-2992 251 20 οΏ½ οΏ½ PROPN iajs-2992 251 21 are be AUX iajs-2992 251 22 their their PRON iajs-2992 251 23 corresponding correspond VERB iajs-2992 251 24 qsvs qsvs NOUN iajs-2992 251 25 . . PUNCT iajs-2992 252 1 substituting substitute VERB iajs-2992 252 2 the the DET iajs-2992 252 3 pair pair NOUN iajs-2992 252 4 ( ( PUNCT iajs-2992 252 5 οΏ½ οΏ½ NOUN iajs-2992 252 6 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 252 7 οΏ½ οΏ½ PROPN iajs-2992 252 8 , , PUNCT iajs-2992 252 9 οΏ½ οΏ½ PROPN iajs-2992 252 10 βƒ— βƒ— NOUN iajs-2992 252 11 οΏ½ οΏ½ PROPN iajs-2992 252 12 )in )in NOUN iajs-2992 252 13 ( ( PUNCT iajs-2992 252 14 ( ( PUNCT iajs-2992 252 15 1)-(6 1)-(6 NUM iajs-2992 252 16 ) ) PUNCT iajs-2992 252 17 ) ) PUNCT iajs-2992 252 18 and and CCONJ iajs-2992 252 19 mbs mb NOUN iajs-2992 252 20 by by ADP iajs-2992 252 21 𝛼 𝛼 PART iajs-2992 252 22 ∈ ∈ PROPN iajs-2992 252 23 [ [ X iajs-2992 252 24 0,1 0,1 NUM iajs-2992 252 25 ] ] PUNCT iajs-2992 252 26 once once ADV iajs-2992 252 27 , , PUNCT iajs-2992 252 28 and and CCONJ iajs-2992 252 29 then then ADV iajs-2992 252 30 substituting substitute VERB iajs-2992 252 31 the the DET iajs-2992 252 32 pair pair NOUN iajs-2992 252 33 ( ( PUNCT iajs-2992 252 34 οΏ½ οΏ½ PROPN iajs-2992 252 35 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 252 36 οΏ½ οΏ½ PROPN iajs-2992 252 37 , , PUNCT iajs-2992 252 38 οΏ½ οΏ½ PROPN iajs-2992 252 39 βƒ—Μ… βƒ—Μ… PROPN iajs-2992 252 40 οΏ½ οΏ½ PROPN iajs-2992 252 41 ) ) PUNCT iajs-2992 252 42 in in ADP iajs-2992 252 43 ( ( PUNCT iajs-2992 252 44 ( ( PUNCT iajs-2992 252 45 1)-(6 1)-(6 NUM iajs-2992 252 46 ) ) PUNCT iajs-2992 252 47 ) ) PUNCT iajs-2992 252 48 and and CCONJ iajs-2992 252 49 mbs mbs AUX iajs-2992 252 50 by by ADP iajs-2992 252 51 ( ( PUNCT iajs-2992 252 52 1 1 NUM iajs-2992 252 53 βˆ’ βˆ’ NOUN iajs-2992 252 54 𝛼 𝛼 NOUN iajs-2992 252 55 ) ) PUNCT iajs-2992 252 56 once once ADV iajs-2992 252 57 again again ADV iajs-2992 252 58 , , PUNCT iajs-2992 252 59 finally finally ADV iajs-2992 252 60 collecting collect VERB iajs-2992 252 61 each each DET iajs-2992 252 62 pair pair NOUN iajs-2992 252 63 from from ADP iajs-2992 252 64 the the DET iajs-2992 252 65 corresponding corresponding ADJ iajs-2992 252 66 equations equation NOUN iajs-2992 252 67 together together ADV iajs-2992 252 68 one one NUM iajs-2992 252 69 gets get VERB iajs-2992 252 70 ( ( PUNCT iajs-2992 252 71 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 252 72 + + CCONJ iajs-2992 252 73 ( ( PUNCT iajs-2992 252 74 1 1 NUM iajs-2992 252 75 βˆ’ βˆ’ PROPN iajs-2992 252 76 𝛼) 𝛼) PROPN iajs-2992 252 77 οΏ½ οΏ½ SYM iajs-2992 252 78 Μ… Μ… NOUN iajs-2992 252 79 οΏ½ οΏ½ NOUN iajs-2992 252 80 1)𝑑𝑑 1)𝑑𝑑 NUM iajs-2992 252 81 βˆ’ βˆ’ NOUN iajs-2992 253 1 βˆ†(𝛼𝑦1 βˆ†(𝛼𝑦1 X iajs-2992 253 2 + + X iajs-2992 253 3 ( ( PUNCT iajs-2992 253 4 1 1 NUM iajs-2992 253 5 βˆ’ βˆ’ PROPN iajs-2992 253 6 𝛼) 𝛼) PROPN iajs-2992 253 7 οΏ½ οΏ½ SYM iajs-2992 253 8 Μ… Μ… NOUN iajs-2992 253 9 οΏ½ οΏ½ NOUN iajs-2992 253 10 1 1 NUM iajs-2992 253 11 ) ) PUNCT iajs-2992 253 12 + + CCONJ iajs-2992 253 13 ( ( PUNCT iajs-2992 253 14 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 253 15 + + CCONJ iajs-2992 253 16 ( ( PUNCT iajs-2992 253 17 1 1 NUM iajs-2992 253 18 βˆ’ βˆ’ PROPN iajs-2992 253 19 𝛼) 𝛼) PROPN iajs-2992 253 20 οΏ½ οΏ½ SYM iajs-2992 253 21 Μ… Μ… NOUN iajs-2992 253 22 οΏ½ οΏ½ NOUN iajs-2992 253 23 1 1 NUM iajs-2992 253 24 ) ) PUNCT iajs-2992 253 25 βˆ’ βˆ’ PROPN iajs-2992 254 1 ( ( PUNCT iajs-2992 254 2 𝛼𝑦2 𝛼𝑦2 PROPN iajs-2992 254 3 + + CCONJ iajs-2992 255 1 ( ( PUNCT iajs-2992 255 2 1 1 NUM iajs-2992 255 3 βˆ’ βˆ’ PROPN iajs-2992 255 4 𝛼) 𝛼) PROPN iajs-2992 255 5 οΏ½ οΏ½ SYM iajs-2992 255 6 Μ… Μ… NOUN iajs-2992 255 7 οΏ½ οΏ½ NOUN iajs-2992 255 8 2 2 NUM iajs-2992 255 9 ) ) PUNCT iajs-2992 255 10 + + PROPN iajs-2992 255 11 ( ( PUNCT iajs-2992 255 12 𝛼𝑦3 𝛼𝑦3 NOUN iajs-2992 255 13 + + X iajs-2992 255 14 ( ( PUNCT iajs-2992 255 15 1 1 NUM iajs-2992 255 16 βˆ’ βˆ’ PROPN iajs-2992 255 17 𝛼) 𝛼) PROPN iajs-2992 255 18 οΏ½ οΏ½ SYM iajs-2992 255 19 Μ… Μ… NOUN iajs-2992 255 20 οΏ½ οΏ½ NOUN iajs-2992 255 21 3 3 NUM iajs-2992 255 22 ) ) PUNCT iajs-2992 256 1 + + CCONJ iajs-2992 256 2 ( ( PUNCT iajs-2992 256 3 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 256 4 + + CCONJ iajs-2992 256 5 ( ( PUNCT iajs-2992 256 6 1 1 NUM iajs-2992 256 7 βˆ’ βˆ’ PROPN iajs-2992 256 8 𝛼) 𝛼) PROPN iajs-2992 256 9 οΏ½ οΏ½ SYM iajs-2992 256 10 Μ… Μ… NOUN iajs-2992 256 11 οΏ½ οΏ½ NOUN iajs-2992 256 12 1 1 NUM iajs-2992 256 13 ) ) PUNCT iajs-2992 256 14 = = NOUN iajs-2992 256 15 𝑓11(π‘₯ 𝑓11(π‘₯ NOUN iajs-2992 256 16 , , PUNCT iajs-2992 256 17 𝑑)(𝛼𝑦1 𝑑)(𝛼𝑦1 X iajs-2992 256 18 + + CCONJ iajs-2992 256 19 ( ( PUNCT iajs-2992 256 20 1 1 NUM iajs-2992 256 21 βˆ’ βˆ’ PROPN iajs-2992 256 22 𝛼) 𝛼) PROPN iajs-2992 256 23 οΏ½ οΏ½ SYM iajs-2992 256 24 Μ… Μ… NOUN iajs-2992 256 25 οΏ½ οΏ½ NOUN iajs-2992 256 26 1 1 NUM iajs-2992 256 27 ) ) PUNCT iajs-2992 256 28 + + CCONJ iajs-2992 256 29 𝑓12(π‘₯ 𝑓12(π‘₯ NOUN iajs-2992 256 30 , , PUNCT iajs-2992 256 31 𝑑)(𝛼𝑒1 𝑑)(𝛼𝑒1 PROPN iajs-2992 256 32 + + CCONJ iajs-2992 256 33 ( ( PUNCT iajs-2992 256 34 1 1 NUM iajs-2992 256 35 βˆ’ βˆ’ PROPN iajs-2992 256 36 𝛼) 𝛼) PROPN iajs-2992 256 37 οΏ½ οΏ½ SYM iajs-2992 256 38 Μ… Μ… NOUN iajs-2992 256 39 οΏ½ οΏ½ NOUN iajs-2992 256 40 1 1 NUM iajs-2992 256 41 ) ) PUNCT iajs-2992 256 42 + + CCONJ iajs-2992 256 43 𝑓13(π‘₯ 𝑓13(π‘₯ NOUN iajs-2992 256 44 , , PUNCT iajs-2992 256 45 𝑑 𝑑 NOUN iajs-2992 256 46 ) ) PUNCT iajs-2992 256 47 , , PUNCT iajs-2992 256 48 ( ( PUNCT iajs-2992 256 49 57 57 NUM iajs-2992 256 50 ) ) PUNCT iajs-2992 256 51 𝛼𝑦1(π‘₯ 𝛼𝑦1(π‘₯ NUM iajs-2992 256 52 , , PUNCT iajs-2992 256 53 𝑑 𝑑 NOUN iajs-2992 256 54 ) ) PUNCT iajs-2992 256 55 + + CCONJ iajs-2992 256 56 ( ( PUNCT iajs-2992 256 57 1 1 NUM iajs-2992 256 58 βˆ’ βˆ’ PROPN iajs-2992 256 59 𝛼) 𝛼) PROPN iajs-2992 256 60 οΏ½ οΏ½ SYM iajs-2992 256 61 Μ… Μ… NOUN iajs-2992 256 62 οΏ½ οΏ½ NOUN iajs-2992 256 63 1(π‘₯ 1(π‘₯ NUM iajs-2992 256 64 , , PUNCT iajs-2992 256 65 0 0 NUM iajs-2992 256 66 ) ) PUNCT iajs-2992 256 67 = = SYM iajs-2992 256 68 0 0 NUM iajs-2992 256 69 , , PUNCT iajs-2992 256 70 ( ( PUNCT iajs-2992 256 71 58 58 NUM iajs-2992 256 72 ) ) PUNCT iajs-2992 256 73 𝛼𝑦1(π‘₯ 𝛼𝑦1(π‘₯ NUM iajs-2992 256 74 , , PUNCT iajs-2992 256 75 0 0 NUM iajs-2992 256 76 ) ) PUNCT iajs-2992 256 77 + + CCONJ iajs-2992 256 78 ( ( PUNCT iajs-2992 256 79 1 1 NUM iajs-2992 256 80 βˆ’ βˆ’ PROPN iajs-2992 256 81 𝛼) 𝛼) PROPN iajs-2992 256 82 οΏ½ οΏ½ SYM iajs-2992 256 83 Μ… Μ… NOUN iajs-2992 256 84 οΏ½ οΏ½ NOUN iajs-2992 256 85 1(π‘₯ 1(π‘₯ NUM iajs-2992 256 86 , , PUNCT iajs-2992 256 87 0 0 NUM iajs-2992 256 88 ) ) PUNCT iajs-2992 256 89 = = SYM iajs-2992 256 90 𝑦1 𝑦1 PROPN iajs-2992 256 91 0(π‘₯ 0(π‘₯ NUM iajs-2992 256 92 ) ) PUNCT iajs-2992 256 93 , , PUNCT iajs-2992 256 94 𝛼𝑦1𝑑(π‘₯ 𝛼𝑦1𝑑(π‘₯ NUM iajs-2992 256 95 , , PUNCT iajs-2992 256 96 0 0 NUM iajs-2992 256 97 ) ) PUNCT iajs-2992 257 1 + + CCONJ iajs-2992 257 2 ( ( PUNCT iajs-2992 257 3 1 1 NUM iajs-2992 257 4 βˆ’ βˆ’ PROPN iajs-2992 257 5 𝛼) 𝛼) PROPN iajs-2992 257 6 οΏ½ οΏ½ NOUN iajs-2992 257 7 Μ… Μ… NOUN iajs-2992 257 8 οΏ½ οΏ½ NOUN iajs-2992 257 9 1𝑑(π‘₯ 1𝑑(π‘₯ NUM iajs-2992 257 10 , , PUNCT iajs-2992 257 11 0 0 NUM iajs-2992 257 12 ) ) PUNCT iajs-2992 257 13 = = SYM iajs-2992 257 14 𝑦1 𝑦1 PROPN iajs-2992 257 15 1(π‘₯ 1(π‘₯ NUM iajs-2992 257 16 ) ) PUNCT iajs-2992 257 17 , , PUNCT iajs-2992 257 18 ( ( PUNCT iajs-2992 257 19 59 59 NUM iajs-2992 257 20 ) ) PUNCT iajs-2992 257 21 ( ( PUNCT iajs-2992 257 22 𝛼𝑦2 𝛼𝑦2 PROPN iajs-2992 257 23 + + CCONJ iajs-2992 257 24 ( ( PUNCT iajs-2992 257 25 1 1 NUM iajs-2992 257 26 βˆ’ βˆ’ PROPN iajs-2992 257 27 𝛼) 𝛼) PROPN iajs-2992 257 28 οΏ½ οΏ½ SYM iajs-2992 257 29 Μ… Μ… NOUN iajs-2992 257 30 οΏ½ οΏ½ NOUN iajs-2992 257 31 2)𝑑𝑑 2)𝑑𝑑 NUM iajs-2992 257 32 βˆ’ βˆ’ NOUN iajs-2992 257 33 βˆ†(𝛼𝑦2 βˆ†(𝛼𝑦2 X iajs-2992 258 1 + + CCONJ iajs-2992 258 2 ( ( PUNCT iajs-2992 258 3 1 1 NUM iajs-2992 258 4 βˆ’ βˆ’ PROPN iajs-2992 258 5 𝛼) 𝛼) PROPN iajs-2992 258 6 οΏ½ οΏ½ SYM iajs-2992 258 7 Μ… Μ… NOUN iajs-2992 258 8 οΏ½ οΏ½ NOUN iajs-2992 258 9 2 2 NUM iajs-2992 258 10 ) ) PUNCT iajs-2992 258 11 + + CCONJ iajs-2992 258 12 ( ( PUNCT iajs-2992 258 13 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 258 14 + + CCONJ iajs-2992 258 15 ( ( PUNCT iajs-2992 258 16 1 1 NUM iajs-2992 258 17 βˆ’ βˆ’ PROPN iajs-2992 258 18 𝛼) 𝛼) PROPN iajs-2992 258 19 οΏ½ οΏ½ SYM iajs-2992 258 20 Μ… Μ… NOUN iajs-2992 258 21 οΏ½ οΏ½ NOUN iajs-2992 258 22 1 1 NUM iajs-2992 258 23 ) ) PUNCT iajs-2992 258 24 + + CCONJ iajs-2992 258 25 ( ( PUNCT iajs-2992 258 26 𝛼𝑦2 𝛼𝑦2 PROPN iajs-2992 258 27 + + CCONJ iajs-2992 258 28 ( ( PUNCT iajs-2992 258 29 1 1 NUM iajs-2992 258 30 βˆ’ βˆ’ PROPN iajs-2992 258 31 𝛼) 𝛼) PROPN iajs-2992 258 32 οΏ½ οΏ½ SYM iajs-2992 258 33 Μ… Μ… NOUN iajs-2992 258 34 οΏ½ οΏ½ NOUN iajs-2992 258 35 2 2 NUM iajs-2992 258 36 ) ) PUNCT iajs-2992 258 37 βˆ’(𝛼𝑦3 βˆ’(𝛼𝑦3 NOUN iajs-2992 258 38 + + CCONJ iajs-2992 258 39 ( ( PUNCT iajs-2992 258 40 1 1 NUM iajs-2992 258 41 βˆ’ βˆ’ PROPN iajs-2992 258 42 𝛼) 𝛼) PROPN iajs-2992 258 43 οΏ½ οΏ½ SYM iajs-2992 258 44 Μ… Μ… NOUN iajs-2992 258 45 οΏ½ οΏ½ NOUN iajs-2992 258 46 3 3 NUM iajs-2992 258 47 ) ) PUNCT iajs-2992 258 48 βˆ’ βˆ’ PROPN iajs-2992 258 49 ( ( PUNCT iajs-2992 258 50 𝛼𝑦4 𝛼𝑦4 PROPN iajs-2992 258 51 + + CCONJ iajs-2992 258 52 ( ( PUNCT iajs-2992 258 53 1 1 NUM iajs-2992 258 54 βˆ’ βˆ’ PROPN iajs-2992 258 55 𝛼) 𝛼) PROPN iajs-2992 258 56 οΏ½ οΏ½ SYM iajs-2992 258 57 Μ… Μ… NOUN iajs-2992 258 58 οΏ½ οΏ½ NOUN iajs-2992 258 59 4 4 NUM iajs-2992 258 60 ) ) PUNCT iajs-2992 258 61 = = PUNCT iajs-2992 258 62 𝑓21(π‘₯ 𝑓21(π‘₯ NOUN iajs-2992 258 63 , , PUNCT iajs-2992 258 64 𝑑)(𝛼𝑦2 𝑑)(𝛼𝑦2 PROPN iajs-2992 259 1 + + CCONJ iajs-2992 259 2 ( ( PUNCT iajs-2992 259 3 1 1 NUM iajs-2992 259 4 βˆ’ βˆ’ PROPN iajs-2992 259 5 𝛼) 𝛼) PROPN iajs-2992 259 6 οΏ½ οΏ½ SYM iajs-2992 259 7 Μ… Μ… NOUN iajs-2992 259 8 οΏ½ οΏ½ NOUN iajs-2992 259 9 2 2 NUM iajs-2992 259 10 ) ) PUNCT iajs-2992 259 11 + + NUM iajs-2992 259 12 𝑓22(π‘₯ 𝑓22(π‘₯ NOUN iajs-2992 259 13 , , PUNCT iajs-2992 259 14 𝑑)(𝛼𝑒2 𝑑)(𝛼𝑒2 NUM iajs-2992 259 15 + + SYM iajs-2992 259 16 ( ( PUNCT iajs-2992 259 17 1 1 NUM iajs-2992 259 18 βˆ’ βˆ’ PROPN iajs-2992 259 19 𝛼) 𝛼) PROPN iajs-2992 259 20 οΏ½ οΏ½ SYM iajs-2992 259 21 Μ… Μ… NOUN iajs-2992 259 22 οΏ½ οΏ½ NOUN iajs-2992 259 23 2 2 NUM iajs-2992 259 24 ) ) PUNCT iajs-2992 259 25 + + CCONJ iajs-2992 259 26 𝑓23(π‘₯ 𝑓23(π‘₯ NOUN iajs-2992 259 27 , , PUNCT iajs-2992 259 28 𝑑 𝑑 NOUN iajs-2992 259 29 ) ) PUNCT iajs-2992 259 30 , , PUNCT iajs-2992 259 31 ( ( PUNCT iajs-2992 259 32 60 60 X iajs-2992 259 33 ) ) PUNCT iajs-2992 259 34 𝛼𝑦2(π‘₯ 𝛼𝑦2(π‘₯ PROPN iajs-2992 259 35 , , PUNCT iajs-2992 259 36 𝑑 𝑑 X iajs-2992 259 37 ) ) PUNCT iajs-2992 259 38 + + CCONJ iajs-2992 259 39 ( ( PUNCT iajs-2992 259 40 1 1 NUM iajs-2992 259 41 βˆ’ βˆ’ PROPN iajs-2992 259 42 𝛼) 𝛼) PROPN iajs-2992 259 43 οΏ½ οΏ½ SYM iajs-2992 259 44 Μ… Μ… NOUN iajs-2992 259 45 οΏ½ οΏ½ NOUN iajs-2992 259 46 2(π‘₯ 2(π‘₯ NUM iajs-2992 259 47 , , PUNCT iajs-2992 259 48 0 0 NUM iajs-2992 259 49 ) ) PUNCT iajs-2992 259 50 = = SYM iajs-2992 259 51 0 0 NUM iajs-2992 259 52 , , PUNCT iajs-2992 259 53 ( ( PUNCT iajs-2992 259 54 61 61 NUM iajs-2992 259 55 ) ) PUNCT iajs-2992 259 56 𝛼𝑦2(π‘₯ 𝛼𝑦2(π‘₯ PROPN iajs-2992 259 57 , , PUNCT iajs-2992 259 58 0 0 NUM iajs-2992 259 59 ) ) PUNCT iajs-2992 259 60 + + CCONJ iajs-2992 259 61 ( ( PUNCT iajs-2992 259 62 1 1 NUM iajs-2992 259 63 βˆ’ βˆ’ PROPN iajs-2992 259 64 𝛼) 𝛼) PROPN iajs-2992 259 65 οΏ½ οΏ½ SYM iajs-2992 259 66 Μ… Μ… NOUN iajs-2992 259 67 οΏ½ οΏ½ NOUN iajs-2992 259 68 2(π‘₯ 2(π‘₯ NUM iajs-2992 259 69 , , PUNCT iajs-2992 259 70 0 0 NUM iajs-2992 259 71 ) ) PUNCT iajs-2992 259 72 = = SYM iajs-2992 259 73 𝑦2 𝑦2 NOUN iajs-2992 259 74 0(π‘₯ 0(π‘₯ NUM iajs-2992 259 75 ) ) PUNCT iajs-2992 259 76 , , PUNCT iajs-2992 259 77 𝑦2𝑑(π‘₯ 𝑦2𝑑(π‘₯ PROPN iajs-2992 259 78 , , PUNCT iajs-2992 259 79 0 0 NUM iajs-2992 259 80 ) ) PUNCT iajs-2992 260 1 + + CCONJ iajs-2992 260 2 ( ( PUNCT iajs-2992 260 3 1 1 NUM iajs-2992 260 4 βˆ’ βˆ’ PROPN iajs-2992 260 5 𝛼) 𝛼) PROPN iajs-2992 260 6 οΏ½ οΏ½ SYM iajs-2992 260 7 Μ… Μ… NOUN iajs-2992 260 8 οΏ½ οΏ½ NOUN iajs-2992 260 9 2𝑑(π‘₯ 2𝑑(π‘₯ PROPN iajs-2992 260 10 , , PUNCT iajs-2992 260 11 0 0 NUM iajs-2992 260 12 ) ) PUNCT iajs-2992 260 13 = = SYM iajs-2992 260 14 𝑦2 𝑦2 NOUN iajs-2992 260 15 1(π‘₯ 1(π‘₯ NUM iajs-2992 260 16 ) ) PUNCT iajs-2992 260 17 , , PUNCT iajs-2992 260 18 ( ( PUNCT iajs-2992 260 19 62 62 NUM iajs-2992 260 20 ) ) PUNCT iajs-2992 260 21 ( ( PUNCT iajs-2992 260 22 𝛼𝑦3 𝛼𝑦3 NOUN iajs-2992 260 23 + + X iajs-2992 260 24 ( ( PUNCT iajs-2992 260 25 1 1 NUM iajs-2992 260 26 βˆ’ βˆ’ PROPN iajs-2992 260 27 𝛼) 𝛼) PROPN iajs-2992 260 28 οΏ½ οΏ½ SYM iajs-2992 260 29 Μ… Μ… NOUN iajs-2992 260 30 οΏ½ οΏ½ NOUN iajs-2992 260 31 3)𝑑𝑑 3)𝑑𝑑 NUM iajs-2992 260 32 βˆ’ βˆ’ NOUN iajs-2992 260 33 βˆ†(𝛼𝑦3 βˆ†(𝛼𝑦3 PUNCT iajs-2992 261 1 + + CCONJ iajs-2992 261 2 ( ( PUNCT iajs-2992 261 3 1 1 NUM iajs-2992 261 4 βˆ’ βˆ’ PROPN iajs-2992 261 5 𝛼) 𝛼) PROPN iajs-2992 261 6 οΏ½ οΏ½ SYM iajs-2992 261 7 Μ… Μ… NOUN iajs-2992 261 8 οΏ½ οΏ½ NOUN iajs-2992 261 9 3 3 NUM iajs-2992 261 10 ) ) PUNCT iajs-2992 261 11 βˆ’ βˆ’ PROPN iajs-2992 261 12 ( ( PUNCT iajs-2992 261 13 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 261 14 + + CCONJ iajs-2992 261 15 ( ( PUNCT iajs-2992 261 16 1 1 NUM iajs-2992 261 17 βˆ’ βˆ’ PROPN iajs-2992 261 18 𝛼) 𝛼) PROPN iajs-2992 261 19 οΏ½ οΏ½ SYM iajs-2992 261 20 Μ… Μ… NOUN iajs-2992 261 21 οΏ½ οΏ½ NOUN iajs-2992 261 22 1 1 NUM iajs-2992 261 23 ) ) PUNCT iajs-2992 261 24 + + CCONJ iajs-2992 261 25 ( ( PUNCT iajs-2992 261 26 𝛼𝑦2 𝛼𝑦2 PROPN iajs-2992 261 27 + + CCONJ iajs-2992 261 28 ( ( PUNCT iajs-2992 261 29 1 1 NUM iajs-2992 261 30 βˆ’ βˆ’ PROPN iajs-2992 261 31 𝛼) 𝛼) PROPN iajs-2992 261 32 οΏ½ οΏ½ SYM iajs-2992 261 33 Μ… Μ… NOUN iajs-2992 261 34 οΏ½ οΏ½ NOUN iajs-2992 261 35 2 2 NUM iajs-2992 261 36 ) ) PUNCT iajs-2992 261 37 + + PROPN iajs-2992 261 38 ( ( PUNCT iajs-2992 261 39 𝛼𝑦3 𝛼𝑦3 NOUN iajs-2992 261 40 + + X iajs-2992 261 41 ( ( PUNCT iajs-2992 261 42 1 1 NUM iajs-2992 261 43 βˆ’ βˆ’ PROPN iajs-2992 261 44 𝛼) 𝛼) PROPN iajs-2992 261 45 οΏ½ οΏ½ SYM iajs-2992 261 46 Μ… Μ… NOUN iajs-2992 261 47 οΏ½ οΏ½ NOUN iajs-2992 261 48 3 3 NUM iajs-2992 261 49 ) ) PUNCT iajs-2992 261 50 + + CCONJ iajs-2992 261 51 ( ( PUNCT iajs-2992 261 52 𝛼𝑦4 𝛼𝑦4 NOUN iajs-2992 261 53 + + CCONJ iajs-2992 261 54 ( ( PUNCT iajs-2992 261 55 1 1 NUM iajs-2992 261 56 βˆ’ βˆ’ PROPN iajs-2992 261 57 𝛼) 𝛼) PROPN iajs-2992 261 58 οΏ½ οΏ½ SYM iajs-2992 261 59 Μ… Μ… NOUN iajs-2992 261 60 οΏ½ οΏ½ NOUN iajs-2992 261 61 4 4 NUM iajs-2992 261 62 ) ) PUNCT iajs-2992 261 63 = = SYM iajs-2992 261 64 𝑓31(π‘₯ 𝑓31(π‘₯ NUM iajs-2992 261 65 , , PUNCT iajs-2992 261 66 𝑑)(𝛼𝑦3 𝑑)(𝛼𝑦3 VERB iajs-2992 261 67 + + X iajs-2992 261 68 ( ( PUNCT iajs-2992 261 69 1 1 NUM iajs-2992 261 70 βˆ’ βˆ’ PROPN iajs-2992 261 71 𝛼) 𝛼) PROPN iajs-2992 261 72 οΏ½ οΏ½ SYM iajs-2992 261 73 Μ… Μ… NOUN iajs-2992 261 74 οΏ½ οΏ½ NOUN iajs-2992 261 75 3 3 NUM iajs-2992 261 76 ) ) PUNCT iajs-2992 261 77 + + NUM iajs-2992 262 1 𝑓32(π‘₯ 𝑓32(π‘₯ NOUN iajs-2992 262 2 , , PUNCT iajs-2992 262 3 𝑑)(𝛼𝑒3 𝑑)(𝛼𝑒3 PROPN iajs-2992 262 4 + + CCONJ iajs-2992 262 5 ( ( PUNCT iajs-2992 262 6 1 1 NUM iajs-2992 262 7 βˆ’ βˆ’ PROPN iajs-2992 262 8 𝛼) 𝛼) PROPN iajs-2992 262 9 οΏ½ οΏ½ SYM iajs-2992 262 10 Μ… Μ… NOUN iajs-2992 262 11 οΏ½ οΏ½ NOUN iajs-2992 262 12 3 3 NUM iajs-2992 262 13 ) ) PUNCT iajs-2992 263 1 + + CCONJ iajs-2992 263 2 𝑓33(π‘₯ 𝑓33(π‘₯ ADJ iajs-2992 263 3 , , PUNCT iajs-2992 263 4 𝑑 𝑑 PROPN iajs-2992 263 5 ) ) PUNCT iajs-2992 263 6 , , PUNCT iajs-2992 263 7 ( ( PUNCT iajs-2992 263 8 63 63 NUM iajs-2992 263 9 ) ) PUNCT iajs-2992 263 10 𝛼𝑦3(π‘₯ 𝛼𝑦3(π‘₯ PROPN iajs-2992 263 11 , , PUNCT iajs-2992 263 12 𝑑 𝑑 X iajs-2992 263 13 ) ) PUNCT iajs-2992 264 1 + + CCONJ iajs-2992 264 2 ( ( PUNCT iajs-2992 264 3 1 1 NUM iajs-2992 264 4 βˆ’ βˆ’ PROPN iajs-2992 264 5 𝛼) 𝛼) PROPN iajs-2992 264 6 οΏ½ οΏ½ SYM iajs-2992 264 7 Μ… Μ… NOUN iajs-2992 264 8 οΏ½ οΏ½ NOUN iajs-2992 264 9 3(π‘₯ 3(π‘₯ NUM iajs-2992 264 10 , , PUNCT iajs-2992 264 11 0 0 NUM iajs-2992 264 12 ) ) PUNCT iajs-2992 264 13 = = SYM iajs-2992 264 14 0 0 NUM iajs-2992 264 15 , , PUNCT iajs-2992 264 16 ( ( PUNCT iajs-2992 264 17 64 64 NUM iajs-2992 264 18 ) ) PUNCT iajs-2992 264 19 𝛼𝑦3(π‘₯ 𝛼𝑦3(π‘₯ PROPN iajs-2992 264 20 , , PUNCT iajs-2992 264 21 0 0 NUM iajs-2992 264 22 ) ) PUNCT iajs-2992 265 1 + + CCONJ iajs-2992 265 2 ( ( PUNCT iajs-2992 265 3 1 1 NUM iajs-2992 265 4 βˆ’ βˆ’ PROPN iajs-2992 265 5 𝛼) 𝛼) PROPN iajs-2992 265 6 οΏ½ οΏ½ SYM iajs-2992 265 7 Μ… Μ… NOUN iajs-2992 265 8 οΏ½ οΏ½ NOUN iajs-2992 265 9 3(π‘₯ 3(π‘₯ NUM iajs-2992 265 10 , , PUNCT iajs-2992 265 11 0 0 NUM iajs-2992 265 12 ) ) PUNCT iajs-2992 265 13 = = SYM iajs-2992 265 14 𝑦3 𝑦3 PROPN iajs-2992 265 15 0(π‘₯ 0(π‘₯ NUM iajs-2992 265 16 ) ) PUNCT iajs-2992 265 17 , , PUNCT iajs-2992 265 18 𝛼𝑦3𝑑(π‘₯ 𝛼𝑦3𝑑(π‘₯ PROPN iajs-2992 265 19 , , PUNCT iajs-2992 265 20 0 0 NUM iajs-2992 265 21 ) ) PUNCT iajs-2992 265 22 + + CCONJ iajs-2992 265 23 ( ( PUNCT iajs-2992 265 24 1 1 NUM iajs-2992 265 25 βˆ’ βˆ’ PROPN iajs-2992 265 26 𝛼) 𝛼) PROPN iajs-2992 265 27 οΏ½ οΏ½ NOUN iajs-2992 265 28 Μ… Μ… NOUN iajs-2992 265 29 οΏ½ οΏ½ NOUN iajs-2992 265 30 3𝑑(π‘₯ 3𝑑(π‘₯ NOUN iajs-2992 265 31 , , PUNCT iajs-2992 265 32 0 0 NUM iajs-2992 265 33 ) ) PUNCT iajs-2992 265 34 = = SYM iajs-2992 265 35 𝑦3 𝑦3 PROPN iajs-2992 265 36 1(π‘₯ 1(π‘₯ NUM iajs-2992 265 37 ) ) PUNCT iajs-2992 265 38 , , PUNCT iajs-2992 265 39 ( ( PUNCT iajs-2992 265 40 65 65 NUM iajs-2992 265 41 ) ) PUNCT iajs-2992 265 42 ( ( PUNCT iajs-2992 265 43 𝛼𝑦4 𝛼𝑦4 NOUN iajs-2992 265 44 + + CCONJ iajs-2992 265 45 ( ( PUNCT iajs-2992 265 46 1 1 NUM iajs-2992 265 47 βˆ’ βˆ’ PROPN iajs-2992 265 48 𝛼) 𝛼) PROPN iajs-2992 265 49 οΏ½ οΏ½ SYM iajs-2992 265 50 Μ… Μ… NOUN iajs-2992 265 51 οΏ½ οΏ½ NOUN iajs-2992 265 52 4)𝑑𝑑 4)𝑑𝑑 NUM iajs-2992 265 53 βˆ’ βˆ’ NOUN iajs-2992 265 54 βˆ†(𝛼𝑦4 βˆ†(𝛼𝑦4 X iajs-2992 266 1 + + CCONJ iajs-2992 266 2 ( ( PUNCT iajs-2992 266 3 1 1 NUM iajs-2992 266 4 βˆ’ βˆ’ PROPN iajs-2992 266 5 𝛼) 𝛼) PROPN iajs-2992 266 6 οΏ½ οΏ½ SYM iajs-2992 266 7 Μ… Μ… NOUN iajs-2992 266 8 οΏ½ οΏ½ NOUN iajs-2992 266 9 4 4 NUM iajs-2992 266 10 ) ) PUNCT iajs-2992 266 11 βˆ’ βˆ’ PROPN iajs-2992 266 12 ( ( PUNCT iajs-2992 266 13 𝛼𝑦1 𝛼𝑦1 PROPN iajs-2992 266 14 + + CCONJ iajs-2992 266 15 ( ( PUNCT iajs-2992 266 16 1 1 NUM iajs-2992 266 17 βˆ’ βˆ’ PROPN iajs-2992 266 18 𝛼) 𝛼) PROPN iajs-2992 266 19 οΏ½ οΏ½ SYM iajs-2992 266 20 Μ… Μ… NOUN iajs-2992 266 21 οΏ½ οΏ½ NOUN iajs-2992 266 22 1 1 NUM iajs-2992 266 23 ) ) PUNCT iajs-2992 266 24 + + CCONJ iajs-2992 266 25 ( ( PUNCT iajs-2992 266 26 𝛼𝑦2 𝛼𝑦2 PROPN iajs-2992 266 27 + + CCONJ iajs-2992 266 28 ( ( PUNCT iajs-2992 266 29 1 1 NUM iajs-2992 266 30 βˆ’ βˆ’ PROPN iajs-2992 266 31 𝛼) 𝛼) PROPN iajs-2992 266 32 οΏ½ οΏ½ SYM iajs-2992 266 33 Μ… Μ… NOUN iajs-2992 266 34 οΏ½ οΏ½ NOUN iajs-2992 266 35 2 2 NUM iajs-2992 266 36 ) ) PUNCT iajs-2992 266 37 βˆ’(𝛼𝑦3 βˆ’(𝛼𝑦3 NOUN iajs-2992 266 38 + + CCONJ iajs-2992 266 39 ( ( PUNCT iajs-2992 266 40 1 1 NUM iajs-2992 266 41 βˆ’ βˆ’ PROPN iajs-2992 266 42 𝛼) 𝛼) PROPN iajs-2992 266 43 οΏ½ οΏ½ SYM iajs-2992 266 44 Μ… Μ… NOUN iajs-2992 266 45 οΏ½ οΏ½ NOUN iajs-2992 266 46 3 3 NUM iajs-2992 266 47 ) ) PUNCT iajs-2992 266 48 + + CCONJ iajs-2992 266 49 ( ( PUNCT iajs-2992 266 50 𝛼𝑦4 𝛼𝑦4 NOUN iajs-2992 266 51 + + CCONJ iajs-2992 266 52 ( ( PUNCT iajs-2992 266 53 1 1 NUM iajs-2992 266 54 βˆ’ βˆ’ PROPN iajs-2992 266 55 𝛼) 𝛼) PROPN iajs-2992 266 56 οΏ½ οΏ½ SYM iajs-2992 266 57 Μ… Μ… NOUN iajs-2992 266 58 οΏ½ οΏ½ NOUN iajs-2992 266 59 4 4 NUM iajs-2992 266 60 ) ) PUNCT iajs-2992 266 61 ihjpas ihjpa NOUN iajs-2992 266 62 . . PUNCT iajs-2992 267 1 36(2)2023 36(2)2023 NUM iajs-2992 267 2 339 339 NUM iajs-2992 267 3 = = PUNCT iajs-2992 267 4 𝑓41(π‘₯ 𝑓41(π‘₯ NOUN iajs-2992 267 5 , , PUNCT iajs-2992 267 6 𝑑)(𝛼𝑦4 𝑑)(𝛼𝑦4 PROPN iajs-2992 267 7 + + CCONJ iajs-2992 267 8 ( ( PUNCT iajs-2992 267 9 1 1 NUM iajs-2992 267 10 βˆ’ βˆ’ PROPN iajs-2992 267 11 𝛼) 𝛼) PROPN iajs-2992 267 12 οΏ½ οΏ½ SYM iajs-2992 267 13 Μ… Μ… NOUN iajs-2992 267 14 οΏ½ οΏ½ NOUN iajs-2992 267 15 4 4 NUM iajs-2992 267 16 ) ) PUNCT iajs-2992 267 17 + + CCONJ iajs-2992 267 18 𝑓42(π‘₯ 𝑓42(π‘₯ NOUN iajs-2992 267 19 , , PUNCT iajs-2992 267 20 𝑑)(𝛼𝑒4 𝑑)(𝛼𝑒4 AUX iajs-2992 267 21 + + CCONJ iajs-2992 267 22 ( ( PUNCT iajs-2992 267 23 1 1 NUM iajs-2992 267 24 βˆ’ βˆ’ PROPN iajs-2992 267 25 𝛼) 𝛼) PROPN iajs-2992 267 26 οΏ½ οΏ½ SYM iajs-2992 267 27 Μ… Μ… NOUN iajs-2992 267 28 οΏ½ οΏ½ NOUN iajs-2992 267 29 4 4 NUM iajs-2992 267 30 ) ) PUNCT iajs-2992 267 31 + + CCONJ iajs-2992 267 32 𝑓43(π‘₯ 𝑓43(π‘₯ ADJ iajs-2992 267 33 , , PUNCT iajs-2992 267 34 𝑑 𝑑 NOUN iajs-2992 267 35 ) ) PUNCT iajs-2992 267 36 , , PUNCT iajs-2992 267 37 ( ( PUNCT iajs-2992 267 38 66 66 NUM iajs-2992 267 39 ) ) PUNCT iajs-2992 267 40 𝛼𝑦4(π‘₯ 𝛼𝑦4(π‘₯ PROPN iajs-2992 267 41 , , PUNCT iajs-2992 267 42 𝑑 𝑑 X iajs-2992 267 43 ) ) PUNCT iajs-2992 267 44 + + CCONJ iajs-2992 267 45 ( ( PUNCT iajs-2992 267 46 1 1 NUM iajs-2992 267 47 βˆ’ βˆ’ PROPN iajs-2992 267 48 𝛼) 𝛼) PROPN iajs-2992 267 49 οΏ½ οΏ½ SYM iajs-2992 267 50 Μ… Μ… NOUN iajs-2992 267 51 οΏ½ οΏ½ NOUN iajs-2992 267 52 4(π‘₯ 4(π‘₯ NUM iajs-2992 267 53 , , PUNCT iajs-2992 267 54 0 0 NUM iajs-2992 267 55 ) ) PUNCT iajs-2992 267 56 = = SYM iajs-2992 267 57 0 0 NUM iajs-2992 267 58 , , PUNCT iajs-2992 267 59 ( ( PUNCT iajs-2992 267 60 67 67 NUM iajs-2992 267 61 ) ) PUNCT iajs-2992 267 62 𝛼𝑦4(π‘₯ 𝛼𝑦4(π‘₯ PROPN iajs-2992 267 63 , , PUNCT iajs-2992 267 64 0 0 NUM iajs-2992 267 65 ) ) PUNCT iajs-2992 268 1 + + CCONJ iajs-2992 268 2 ( ( PUNCT iajs-2992 268 3 1 1 NUM iajs-2992 268 4 βˆ’ βˆ’ PROPN iajs-2992 268 5 𝛼) 𝛼) PROPN iajs-2992 268 6 οΏ½ οΏ½ SYM iajs-2992 268 7 Μ… Μ… NOUN iajs-2992 268 8 οΏ½ οΏ½ NOUN iajs-2992 268 9 4(π‘₯ 4(π‘₯ NUM iajs-2992 268 10 , , PUNCT iajs-2992 268 11 0 0 NUM iajs-2992 268 12 ) ) PUNCT iajs-2992 268 13 = = SYM iajs-2992 268 14 𝑦4 𝑦4 NOUN iajs-2992 268 15 0(π‘₯ 0(π‘₯ NUM iajs-2992 268 16 ) ) PUNCT iajs-2992 268 17 , , PUNCT iajs-2992 268 18 𝛼𝑦4𝑑(π‘₯ 𝛼𝑦4𝑑(π‘₯ NUM iajs-2992 268 19 , , PUNCT iajs-2992 268 20 0 0 NUM iajs-2992 268 21 ) ) PUNCT iajs-2992 268 22 + + CCONJ iajs-2992 268 23 ( ( PUNCT iajs-2992 268 24 1 1 NUM iajs-2992 268 25 βˆ’ βˆ’ PROPN iajs-2992 268 26 𝛼) 𝛼) PROPN iajs-2992 268 27 οΏ½ οΏ½ NOUN iajs-2992 268 28 Μ… Μ… NOUN iajs-2992 268 29 οΏ½ οΏ½ NOUN iajs-2992 268 30 4𝑑(π‘₯ 4𝑑(π‘₯ VERB iajs-2992 268 31 , , PUNCT iajs-2992 268 32 0 0 NUM iajs-2992 268 33 ) ) PUNCT iajs-2992 268 34 = = NOUN iajs-2992 268 35 𝑦4 𝑦4 NOUN iajs-2992 268 36 1(π‘₯ 1(π‘₯ NUM iajs-2992 268 37 ) ) PUNCT iajs-2992 268 38 , , PUNCT iajs-2992 268 39 ( ( PUNCT iajs-2992 268 40 68 68 NUM iajs-2992 268 41 ) ) PUNCT iajs-2992 268 42 equalities equality NOUN iajs-2992 268 43 ( ( PUNCT iajs-2992 268 44 ( ( PUNCT iajs-2992 268 45 57)(68 57)(68 NUM iajs-2992 268 46 ) ) PUNCT iajs-2992 268 47 ) ) PUNCT iajs-2992 268 48 , , PUNCT iajs-2992 268 49 show show VERB iajs-2992 268 50 that that SCONJ iajs-2992 268 51 if if SCONJ iajs-2992 268 52 the the DET iajs-2992 268 53 qcv qcv NOUN iajs-2992 268 54 is be AUX iajs-2992 268 55 οΏ½ οΏ½ PROPN iajs-2992 268 56 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 268 57 οΏ½ οΏ½ PROPN iajs-2992 268 58 ( ( PUNCT iajs-2992 268 59 with with ADP iajs-2992 268 60 ( ( PUNCT iajs-2992 268 61 οΏ½ οΏ½ PROPN iajs-2992 268 62 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 268 63 οΏ½ οΏ½ PROPN iajs-2992 268 64 = = SYM iajs-2992 268 65 𝛼 𝛼 PROPN iajs-2992 268 66 οΏ½ οΏ½ PROPN iajs-2992 268 67 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 268 68 οΏ½ οΏ½ PROPN iajs-2992 268 69 + + CCONJ iajs-2992 268 70 ( ( PUNCT iajs-2992 268 71 1 1 NUM iajs-2992 268 72 βˆ’ βˆ’ PROPN iajs-2992 268 73 𝛼) 𝛼) PROPN iajs-2992 268 74 οΏ½ οΏ½ PROPN iajs-2992 268 75 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 268 76 οΏ½ οΏ½ PROPN iajs-2992 268 77 ) ) PUNCT iajs-2992 268 78 ) ) PUNCT iajs-2992 268 79 has have AUX iajs-2992 268 80 corresponding correspond VERB iajs-2992 268 81 qsvs qsvs ADJ iajs-2992 268 82 οΏ½ οΏ½ PROPN iajs-2992 268 83 βƒ—Μ… βƒ—Μ… NOUN iajs-2992 268 84 οΏ½ οΏ½ PROPN iajs-2992 268 85 with with ADP iajs-2992 268 86 ( ( PUNCT iajs-2992 268 87 οΏ½ οΏ½ NOUN iajs-2992 268 88 Μ… Μ… NOUN iajs-2992 268 89 οΏ½ οΏ½ NOUN iajs-2992 268 90 𝑖 𝑖 SYM iajs-2992 268 91 = = NOUN iajs-2992 268 92 𝑦𝑖𝑒𝑖 𝑦𝑖𝑒𝑖 NOUN iajs-2992 268 93 = = SYM iajs-2992 268 94 𝑦𝑖(𝛼𝑒𝑖+(1βˆ’ 𝑦𝑖(𝛼𝑒𝑖+(1βˆ’ PROPN iajs-2992 268 95 𝛼)𝑒𝑖 𝛼)𝑒𝑖 PROPN iajs-2992 268 96 ) ) PUNCT iajs-2992 268 97 ) ) PUNCT iajs-2992 268 98 . . PUNCT iajs-2992 269 1 this this PRON iajs-2992 269 2 means mean VERB iajs-2992 269 3 the the DET iajs-2992 269 4 operator operator NOUN iajs-2992 269 5 οΏ½ οΏ½ PROPN iajs-2992 269 6 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 269 7 οΏ½ οΏ½ PROPN iajs-2992 269 8 β†’ β†’ SYM iajs-2992 269 9 οΏ½ οΏ½ PROPN iajs-2992 269 10 βƒ— βƒ— PROPN iajs-2992 269 11 οΏ½ οΏ½ PROPN iajs-2992 269 12 οΏ½ οΏ½ PROPN iajs-2992 269 13 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 269 14 οΏ½ οΏ½ PROPN iajs-2992 269 15 is be AUX iajs-2992 269 16 co co ADJ iajs-2992 269 17 - - NOUN iajs-2992 269 18 linear linear ADJ iajs-2992 269 19 ( ( PUNCT iajs-2992 269 20 col col NOUN iajs-2992 269 21 ) ) PUNCT iajs-2992 269 22 w.r.t w.r.t NOUN iajs-2992 269 23 . . PUNCT iajs-2992 270 1 ( ( PUNCT iajs-2992 270 2 οΏ½ οΏ½ PROPN iajs-2992 270 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 270 4 οΏ½ οΏ½ PROPN iajs-2992 270 5 , , PUNCT iajs-2992 270 6 οΏ½ οΏ½ PROPN iajs-2992 270 7 βƒ— βƒ— NOUN iajs-2992 270 8 οΏ½ οΏ½ PROPN iajs-2992 270 9 ) ) PUNCT iajs-2992 270 10 in in ADP iajs-2992 270 11 𝑄. 𝑄. PROPN iajs-2992 270 12 now now ADV iajs-2992 270 13 , , PUNCT iajs-2992 270 14 since since SCONJ iajs-2992 270 15 𝑔1𝑖(π‘₯ 𝑔1𝑖(π‘₯ PROPN iajs-2992 270 16 , , PUNCT iajs-2992 270 17 𝑑 𝑑 PROPN iajs-2992 270 18 , , PUNCT iajs-2992 270 19 𝑦𝑖 𝑦𝑖 PROPN iajs-2992 270 20 , , PUNCT iajs-2992 270 21 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 270 22 ) ) PUNCT iajs-2992 270 23 is be AUX iajs-2992 270 24 affine affine NOUN iajs-2992 270 25 w.r.t w.r.t PROPN iajs-2992 270 26 . . PUNCT iajs-2992 271 1 ( ( PUNCT iajs-2992 271 2 𝑦𝑖 𝑦𝑖 INTJ iajs-2992 271 3 , , PUNCT iajs-2992 271 4 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 271 5 ) ) PUNCT iajs-2992 271 6 , , PUNCT iajs-2992 271 7 in in ADP iajs-2992 271 8 𝑄 𝑄 PROPN iajs-2992 271 9 , , PUNCT iajs-2992 271 10 then then ADV iajs-2992 271 11 𝐺1( 𝐺1( NUM iajs-2992 271 12 οΏ½ οΏ½ PROPN iajs-2992 271 13 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 271 14 οΏ½ οΏ½ PROPN iajs-2992 271 15 ) ) PUNCT iajs-2992 271 16 is be AUX iajs-2992 271 17 col col PROPN iajs-2992 271 18 w.r.t w.r.t NOUN iajs-2992 271 19 . . PUNCT iajs-2992 272 1 ( ( PUNCT iajs-2992 272 2 οΏ½ οΏ½ PROPN iajs-2992 272 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 272 4 οΏ½ οΏ½ PROPN iajs-2992 272 5 , , PUNCT iajs-2992 272 6 οΏ½ οΏ½ PROPN iajs-2992 272 7 βƒ— βƒ— NOUN iajs-2992 272 8 οΏ½ οΏ½ PROPN iajs-2992 272 9 ) ) PUNCT iajs-2992 272 10 , , PUNCT iajs-2992 272 11 also also ADV iajs-2992 272 12 , , PUNCT iajs-2992 272 13 since since SCONJ iajs-2992 272 14 𝑔0𝑖 𝑔0𝑖 PROPN iajs-2992 272 15 & & CCONJ iajs-2992 272 16 𝑔2𝑖 𝑔2𝑖 NOUN iajs-2992 272 17 are be AUX iajs-2992 272 18 co co ADP iajs-2992 272 19 w.r.t.(𝑦𝑖 w.r.t.(𝑦𝑖 ADV iajs-2992 272 20 , , PUNCT iajs-2992 272 21 𝑒𝑖 𝑒𝑖 NOUN iajs-2992 272 22 ) ) PUNCT iajs-2992 272 23 , , PUNCT iajs-2992 272 24 in in ADP iajs-2992 272 25 𝑄 𝑄 PROPN iajs-2992 272 26 , , PUNCT iajs-2992 272 27 βˆ€π‘– βˆ€π‘– PROPN iajs-2992 272 28 = = SYM iajs-2992 272 29 1,2,3,4 1,2,3,4 NUM iajs-2992 272 30 , , PUNCT iajs-2992 272 31 then then ADV iajs-2992 272 32 the the DET iajs-2992 272 33 funl funl NOUN iajs-2992 272 34 . . PUNCT iajs-2992 273 1 𝐺0( 𝐺0( VERB iajs-2992 273 2 οΏ½ οΏ½ PROPN iajs-2992 273 3 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 273 4 οΏ½ οΏ½ PROPN iajs-2992 273 5 ) ) PUNCT iajs-2992 273 6 , , PUNCT iajs-2992 273 7 𝐺2( 𝐺2( PROPN iajs-2992 273 8 οΏ½ οΏ½ PROPN iajs-2992 273 9 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 273 10 οΏ½ οΏ½ PROPN iajs-2992 273 11 ) ) PUNCT iajs-2992 273 12 are be AUX iajs-2992 273 13 co. co. PROPN iajs-2992 273 14 w.r.t w.r.t NOUN iajs-2992 273 15 . . PUNCT iajs-2992 274 1 ( ( PUNCT iajs-2992 274 2 οΏ½ οΏ½ PROPN iajs-2992 274 3 βƒ— βƒ— NOUN iajs-2992 274 4 οΏ½ οΏ½ PROPN iajs-2992 274 5 , , PUNCT iajs-2992 274 6 οΏ½ οΏ½ PROPN iajs-2992 274 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 274 8 οΏ½ οΏ½ PROPN iajs-2992 274 9 ) ) PUNCT iajs-2992 274 10 in in ADP iajs-2992 274 11 𝑄 𝑄 PROPN iajs-2992 274 12 ( ( PUNCT iajs-2992 274 13 from from ADP iajs-2992 274 14 the the DET iajs-2992 274 15 assum assum NOUN iajs-2992 274 16 . . PUNCT iajs-2992 275 1 on on ADP iajs-2992 275 2 the the DET iajs-2992 275 3 funl funl NOUN iajs-2992 275 4 𝑔𝑙𝑖 𝑔𝑙𝑖 X iajs-2992 275 5 ( ( PUNCT iajs-2992 275 6 βˆ€π‘™ βˆ€π‘™ NOUN iajs-2992 275 7 = = SYM iajs-2992 275 8 0,1,2 0,1,2 NUM iajs-2992 275 9 , , PUNCT iajs-2992 275 10 & & CCONJ iajs-2992 275 11 𝑖 𝑖 SYM iajs-2992 275 12 = = NOUN iajs-2992 275 13 1,2,3,4 1,2,3,4 NUM iajs-2992 275 14 ) ) PUNCT iajs-2992 275 15 and and CCONJ iajs-2992 275 16 from from ADP iajs-2992 275 17 the the DET iajs-2992 275 18 sum sum NOUN iajs-2992 275 19 of of ADP iajs-2992 275 20 two two NUM iajs-2992 275 21 integral integral ADJ iajs-2992 275 22 of of ADP iajs-2992 275 23 co co X iajs-2992 275 24 function function NOUN iajs-2992 275 25 is be AUX iajs-2992 275 26 also also ADV iajs-2992 275 27 co co NOUN iajs-2992 275 28 ) ) PUNCT iajs-2992 275 29 , , PUNCT iajs-2992 275 30 i.e. i.e. X iajs-2992 275 31 𝐺( 𝐺( X iajs-2992 275 32 οΏ½ οΏ½ PROPN iajs-2992 275 33 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 275 34 οΏ½ οΏ½ PROPN iajs-2992 275 35 ) ) PUNCT iajs-2992 276 1 is be AUX iajs-2992 276 2 co co X iajs-2992 276 3 w.r.t w.r.t PROPN iajs-2992 276 4 . . PUNCT iajs-2992 277 1 ( ( PUNCT iajs-2992 277 2 οΏ½ οΏ½ PROPN iajs-2992 277 3 βƒ— βƒ— NOUN iajs-2992 277 4 οΏ½ οΏ½ PROPN iajs-2992 277 5 , , PUNCT iajs-2992 277 6 οΏ½ οΏ½ PROPN iajs-2992 277 7 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 277 8 οΏ½ οΏ½ PROPN iajs-2992 277 9 ) ) PUNCT iajs-2992 277 10 , , PUNCT iajs-2992 277 11 in in ADP iajs-2992 277 12 𝑄 𝑄 PRON iajs-2992 277 13 in in ADP iajs-2992 277 14 the the DET iajs-2992 277 15 co co X iajs-2992 277 16 set set PROPN iajs-2992 277 17 οΏ½ οΏ½ PROPN iajs-2992 277 18 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 277 19 οΏ½ οΏ½ PROPN iajs-2992 277 20 , , PUNCT iajs-2992 277 21 and and CCONJ iajs-2992 277 22 has have VERB iajs-2992 277 23 a a DET iajs-2992 277 24 cont cont NOUN iajs-2992 277 25 . . PUNCT iajs-2992 278 1 dd dd NOUN iajs-2992 278 2 satisfies satisfie NOUN iajs-2992 278 3 𝐷𝐺( 𝐷𝐺( PROPN iajs-2992 278 4 οΏ½ οΏ½ PROPN iajs-2992 278 5 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 6 οΏ½ οΏ½ PROPN iajs-2992 278 7 , , PUNCT iajs-2992 278 8 οΏ½ οΏ½ PROPN iajs-2992 278 9 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 278 10 οΏ½ οΏ½ PROPN iajs-2992 278 11 βˆ’ βˆ’ PROPN iajs-2992 278 12 οΏ½ οΏ½ PROPN iajs-2992 278 13 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 14 οΏ½ οΏ½ PROPN iajs-2992 278 15 ) ) PUNCT iajs-2992 278 16 β‰₯ β‰₯ NOUN iajs-2992 278 17 0 0 NUM iajs-2992 278 18 , , PUNCT iajs-2992 278 19 which which PRON iajs-2992 278 20 means mean VERB iajs-2992 278 21 𝐺( 𝐺( PROPN iajs-2992 278 22 οΏ½ οΏ½ PROPN iajs-2992 278 23 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 24 οΏ½ οΏ½ PROPN iajs-2992 278 25 ) ) PUNCT iajs-2992 278 26 has have VERB iajs-2992 278 27 a a DET iajs-2992 278 28 minimum minimum NOUN iajs-2992 278 29 at at ADP iajs-2992 278 30 οΏ½ οΏ½ PROPN iajs-2992 278 31 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 32 οΏ½ οΏ½ PROPN iajs-2992 278 33 , , PUNCT iajs-2992 278 34 i.e. i.e. X iajs-2992 278 35 𝐺( 𝐺( X iajs-2992 278 36 οΏ½ οΏ½ PROPN iajs-2992 278 37 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 38 οΏ½ οΏ½ PROPN iajs-2992 278 39 ) ) PUNCT iajs-2992 278 40 ≀ ≀ NUM iajs-2992 278 41 𝐺( 𝐺( NOUN iajs-2992 278 42 οΏ½ οΏ½ PROPN iajs-2992 278 43 βƒ—βƒ—Μ… βƒ—βƒ—Μ… PROPN iajs-2992 278 44 οΏ½ οΏ½ PROPN iajs-2992 278 45 ),βˆ€ ),βˆ€ PROPN iajs-2992 278 46 οΏ½ οΏ½ PROPN iajs-2992 278 47 Μ… Μ… NOUN iajs-2992 278 48 οΏ½ οΏ½ PROPN iajs-2992 278 49 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 50 βƒ— βƒ— PROPN iajs-2992 278 51 ∈ ∈ PROPN iajs-2992 278 52 οΏ½ οΏ½ PROPN iajs-2992 278 53 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 278 54 οΏ½ οΏ½ PROPN iajs-2992 278 55 , , PUNCT iajs-2992 278 56 i.e. i.e. X iajs-2992 278 57 πœ†0𝐺0( πœ†0𝐺0( PUNCT iajs-2992 278 58 οΏ½ οΏ½ PROPN iajs-2992 278 59 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 60 οΏ½ οΏ½ PROPN iajs-2992 278 61 ) ) PUNCT iajs-2992 278 62 + + CCONJ iajs-2992 278 63 πœ†1𝐺0( πœ†1𝐺0( PUNCT iajs-2992 278 64 οΏ½ οΏ½ PROPN iajs-2992 278 65 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 66 οΏ½ οΏ½ PROPN iajs-2992 278 67 ) ) PUNCT iajs-2992 278 68 + + CCONJ iajs-2992 278 69 πœ†2𝐺2( πœ†2𝐺2( PUNCT iajs-2992 278 70 οΏ½ οΏ½ PROPN iajs-2992 278 71 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 72 οΏ½ οΏ½ PROPN iajs-2992 278 73 ) ) PUNCT iajs-2992 278 74 ≀ ≀ NOUN iajs-2992 278 75 πœ†0𝐺0( πœ†0𝐺0( PUNCT iajs-2992 278 76 οΏ½ οΏ½ PROPN iajs-2992 278 77 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 278 78 οΏ½ οΏ½ PROPN iajs-2992 278 79 ) ) PUNCT iajs-2992 278 80 + + CCONJ iajs-2992 278 81 πœ†1𝐺1( πœ†1𝐺1( PROPN iajs-2992 278 82 οΏ½ οΏ½ PROPN iajs-2992 278 83 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 278 84 οΏ½ οΏ½ PROPN iajs-2992 278 85 ) ) PUNCT iajs-2992 278 86 + + CCONJ iajs-2992 278 87 πœ†2𝐺2( πœ†2𝐺2( PUNCT iajs-2992 278 88 οΏ½ οΏ½ PROPN iajs-2992 278 89 βƒ—βƒ—Μ… βƒ—βƒ—Μ… NOUN iajs-2992 278 90 οΏ½ οΏ½ PROPN iajs-2992 278 91 ) ) PUNCT iajs-2992 278 92 , , PUNCT iajs-2992 278 93 βˆ€ βˆ€ X iajs-2992 278 94 οΏ½ οΏ½ NOUN iajs-2992 278 95 Μ… Μ… NOUN iajs-2992 278 96 οΏ½ οΏ½ PROPN iajs-2992 278 97 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 98 βƒ— βƒ— PROPN iajs-2992 278 99 ∈ ∈ PROPN iajs-2992 278 100 οΏ½ οΏ½ PROPN iajs-2992 278 101 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 278 102 οΏ½ οΏ½ PROPN iajs-2992 278 103 let let VERB iajs-2992 278 104 οΏ½ οΏ½ PRON iajs-2992 278 105 Μ… Μ… VERB iajs-2992 278 106 οΏ½ οΏ½ PROPN iajs-2992 278 107 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 108 βƒ— βƒ— PROPN iajs-2992 278 109 ∈ ∈ PROPN iajs-2992 278 110 οΏ½ οΏ½ PROPN iajs-2992 278 111 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— SYM iajs-2992 278 112 οΏ½ οΏ½ PROPN iajs-2992 278 113 𝐴 𝐴 PROPN iajs-2992 278 114 , , PUNCT iajs-2992 278 115 πœ†2 πœ†2 PROPN iajs-2992 278 116 β‰₯ β‰₯ NOUN iajs-2992 278 117 0 0 NUM iajs-2992 278 118 and and CCONJ iajs-2992 278 119 from from ADP iajs-2992 278 120 ( ( PUNCT iajs-2992 278 121 54 54 NUM iajs-2992 278 122 ) ) PUNCT iajs-2992 278 123 , , PUNCT iajs-2992 278 124 the the DET iajs-2992 278 125 above above ADJ iajs-2992 278 126 inequality inequality NOUN iajs-2992 278 127 becomes become VERB iajs-2992 278 128 πœ†0𝐺0( πœ†0𝐺0( PUNCT iajs-2992 278 129 οΏ½ οΏ½ NOUN iajs-2992 278 130 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 131 οΏ½ οΏ½ PROPN iajs-2992 278 132 ) ) PUNCT iajs-2992 278 133 ≀ ≀ NUM iajs-2992 278 134 πœ†0𝐺0( πœ†0𝐺0( PUNCT iajs-2992 278 135 οΏ½ οΏ½ NOUN iajs-2992 278 136 Μ… Μ… NOUN iajs-2992 278 137 οΏ½ οΏ½ PROPN iajs-2992 278 138 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 139 βƒ— βƒ— NOUN iajs-2992 278 140 ) ) PUNCT iajs-2992 278 141 , , PUNCT iajs-2992 278 142 βˆ€ βˆ€ X iajs-2992 278 143 οΏ½ οΏ½ NOUN iajs-2992 278 144 Μ… Μ… NOUN iajs-2992 278 145 οΏ½ οΏ½ PROPN iajs-2992 278 146 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 147 βƒ— βƒ— PROPN iajs-2992 278 148 ∈ ∈ PROPN iajs-2992 278 149 οΏ½ οΏ½ PROPN iajs-2992 278 150 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 278 151 οΏ½ οΏ½ PROPN iajs-2992 278 152 , , PUNCT iajs-2992 278 153 or or CCONJ iajs-2992 278 154 𝐺0( 𝐺0( PUNCT iajs-2992 278 155 οΏ½ οΏ½ NOUN iajs-2992 278 156 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 157 οΏ½ οΏ½ PROPN iajs-2992 278 158 ) ) PUNCT iajs-2992 278 159 ≀ ≀ NUM iajs-2992 278 160 𝐺0( 𝐺0( SYM iajs-2992 278 161 οΏ½ οΏ½ NOUN iajs-2992 278 162 Μ… Μ… NOUN iajs-2992 278 163 οΏ½ οΏ½ PROPN iajs-2992 278 164 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 165 βƒ— βƒ— NOUN iajs-2992 278 166 ) ) PUNCT iajs-2992 278 167 , , PUNCT iajs-2992 278 168 βˆ€ βˆ€ X iajs-2992 278 169 οΏ½ οΏ½ NOUN iajs-2992 278 170 Μ… Μ… NOUN iajs-2992 278 171 οΏ½ οΏ½ PROPN iajs-2992 278 172 βƒ—βƒ—βƒ— βƒ—βƒ—βƒ— PROPN iajs-2992 278 173 βƒ— βƒ— PROPN iajs-2992 278 174 ∈ ∈ PROPN iajs-2992 278 175 οΏ½ οΏ½ PROPN iajs-2992 278 176 βƒ—βƒ—βƒ—βƒ— βƒ—βƒ—βƒ—βƒ— NUM iajs-2992 278 177 οΏ½ οΏ½ PROPN iajs-2992 278 178 , , PUNCT iajs-2992 278 179 thus thus ADV iajs-2992 278 180 οΏ½ οΏ½ PROPN iajs-2992 278 181 βƒ—βƒ— βƒ—βƒ— PROPN iajs-2992 278 182 οΏ½ οΏ½ PROPN iajs-2992 278 183 ia ia PROPN iajs-2992 278 184 a a DET iajs-2992 278 185 cqocccv cqocccv NOUN iajs-2992 278 186 . . PUNCT iajs-2992 279 1 5.conclusions 5.conclusions NUM iajs-2992 279 2 and and CCONJ iajs-2992 279 3 discussions discussion NOUN iajs-2992 279 4 : : PUNCT iajs-2992 279 5 in in ADP iajs-2992 279 6 this this DET iajs-2992 279 7 work work NOUN iajs-2992 279 8 , , PUNCT iajs-2992 279 9 the the DET iajs-2992 279 10 cqocccvp cqocccvp NOUN iajs-2992 279 11 dominating dominate VERB iajs-2992 279 12 by by ADP iajs-2992 279 13 a a DET iajs-2992 279 14 qnlhbvp qnlhbvp NOUN iajs-2992 279 15 is be AUX iajs-2992 279 16 studied study VERB iajs-2992 279 17 . . PUNCT iajs-2992 280 1 the the DET iajs-2992 280 2 existence existence NOUN iajs-2992 280 3 of of ADP iajs-2992 280 4 a a DET iajs-2992 280 5 cqocccv cqocccv NOUN iajs-2992 280 6 dominating dominating NOUN iajs-2992 280 7 by by ADP iajs-2992 280 8 a a DET iajs-2992 280 9 qnlhbvp qnlhbvp NOUN iajs-2992 280 10 with with ADP iajs-2992 280 11 einqscc einqscc PROPN iajs-2992 280 12 is be AUX iajs-2992 280 13 stated state VERB iajs-2992 280 14 and and CCONJ iajs-2992 280 15 demonstrated demonstrate VERB iajs-2992 280 16 under under ADP iajs-2992 280 17 appropriate appropriate ADJ iajs-2992 280 18 hyp hyp PROPN iajs-2992 280 19 with with ADP iajs-2992 280 20 using use VERB iajs-2992 280 21 the the DET iajs-2992 280 22 acth acth NOUN iajs-2992 280 23 . . PUNCT iajs-2992 281 1 moreover moreover ADJ iajs-2992 281 2 mathematical mathematical ADJ iajs-2992 281 3 formulation formulation NOUN iajs-2992 281 4 of of ADP iajs-2992 281 5 the the DET iajs-2992 281 6 qaes qaes NOUN iajs-2992 281 7 related relate VERB iajs-2992 281 8 to to ADP iajs-2992 281 9 qses qse NOUN iajs-2992 281 10 is be AUX iajs-2992 281 11 found find VERB iajs-2992 281 12 so so SCONJ iajs-2992 281 13 as as ADP iajs-2992 281 14 its its PRON iajs-2992 281 15 wf wf PROPN iajs-2992 281 16 . . PUNCT iajs-2992 282 1 the the DET iajs-2992 282 2 derivation derivation NOUN iajs-2992 282 3 of of ADP iajs-2992 282 4 the the DET iajs-2992 282 5 dd dd NOUN iajs-2992 282 6 for for ADP iajs-2992 282 7 the the DET iajs-2992 282 8 ham ham NOUN iajs-2992 282 9 is be AUX iajs-2992 282 10 attained attain VERB iajs-2992 282 11 . . PUNCT iajs-2992 283 1 lastly lastly ADV iajs-2992 283 2 , , PUNCT iajs-2992 283 3 both both CCONJ iajs-2992 283 4 the the DET iajs-2992 283 5 ncso ncso NOUN iajs-2992 283 6 and and CCONJ iajs-2992 283 7 the the DET iajs-2992 283 8 scso scso NOUN iajs-2992 283 9 β€œ " PUNCT iajs-2992 283 10 theorems theorem NOUN iajs-2992 283 11 ” " PUNCT iajs-2992 283 12 optimality optimality NOUN iajs-2992 283 13 of of ADP iajs-2992 283 14 the the DET iajs-2992 283 15 proposed propose VERB iajs-2992 283 16 problem problem NOUN iajs-2992 283 17 are be AUX iajs-2992 283 18 stated state VERB iajs-2992 283 19 and and CCONJ iajs-2992 283 20 demonstrated demonstrate VERB iajs-2992 283 21 . . PUNCT iajs-2992 284 1 the the DET iajs-2992 284 2 study study NOUN iajs-2992 284 3 of of ADP iajs-2992 284 4 the the DET iajs-2992 284 5 proposed propose VERB iajs-2992 284 6 problem problem NOUN iajs-2992 284 7 is be AUX iajs-2992 284 8 considered consider VERB iajs-2992 284 9 very very ADV iajs-2992 284 10 interesting interesting ADJ iajs-2992 284 11 in in ADP iajs-2992 284 12 the the DET iajs-2992 284 13 field field NOUN iajs-2992 284 14 of of ADP iajs-2992 284 15 applied apply VERB iajs-2992 284 16 mathematics mathematic NOUN iajs-2992 284 17 since since SCONJ iajs-2992 284 18 the the DET iajs-2992 284 19 proposed propose VERB iajs-2992 284 20 model model NOUN iajs-2992 284 21 represents represent VERB iajs-2992 284 22 a a DET iajs-2992 284 23 generalization generalization NOUN iajs-2992 284 24 for for ADP iajs-2992 284 25 a a DET iajs-2992 284 26 wave wave NOUN iajs-2992 284 27 equation equation NOUN iajs-2992 284 28 ; ; PUNCT iajs-2992 284 29 from from ADP iajs-2992 284 30 a a DET iajs-2992 284 31 side side NOUN iajs-2992 284 32 , , PUNCT iajs-2992 284 33 and and CCONJ iajs-2992 284 34 from from ADP iajs-2992 284 35 the the DET iajs-2992 284 36 other other ADJ iajs-2992 284 37 , , PUNCT iajs-2992 284 38 these these DET iajs-2992 284 39 results result NOUN iajs-2992 284 40 are be AUX iajs-2992 284 41 very very ADV iajs-2992 284 42 important important ADJ iajs-2992 284 43 because because SCONJ iajs-2992 284 44 they they PRON iajs-2992 284 45 give give VERB iajs-2992 284 46 the the DET iajs-2992 284 47 green green ADJ iajs-2992 284 48 light light NOUN iajs-2992 284 49 about about ADP iajs-2992 284 50 the the DET iajs-2992 284 51 ability ability NOUN iajs-2992 284 52 for for ADP iajs-2992 284 53 solving solve VERB iajs-2992 284 54 such such ADJ iajs-2992 284 55 problems problem NOUN iajs-2992 284 56 numerically numerically ADV iajs-2992 284 57 . . PUNCT iajs-2992 285 1 references reference NOUN iajs-2992 285 2 1 1 NUM iajs-2992 285 3 . . PUNCT iajs-2992 286 1 rigatos rigato NOUN iajs-2992 286 2 , , PUNCT iajs-2992 286 3 g. g. PROPN iajs-2992 286 4 ; ; PUNCT iajs-2992 286 5 abbaszadeh abbaszadeh PROPN iajs-2992 286 6 , , PUNCT iajs-2992 286 7 m. m. NOUN iajs-2992 286 8 nonlinear nonlinear PROPN iajs-2992 286 9 optimal optimal ADJ iajs-2992 286 10 control control NOUN iajs-2992 286 11 for for ADP iajs-2992 286 12 multi multi ADJ iajs-2992 286 13 - - ADJ iajs-2992 286 14 dof dof ADJ iajs-2992 286 15 robotic robotic ADJ iajs-2992 286 16 manipulators manipulator NOUN iajs-2992 286 17 with with ADP iajs-2992 286 18 flexible flexible ADJ iajs-2992 286 19 joints joint NOUN iajs-2992 286 20 . . PUNCT iajs-2992 287 1 optim optim ADJ iajs-2992 287 2 . . PUNCT iajs-2992 288 1 control control PROPN iajs-2992 288 2 appl appl PROPN iajs-2992 288 3 . . PUNCT iajs-2992 289 1 methods method NOUN iajs-2992 289 2 2002,42(6),1708 2002,42(6),1708 NUM iajs-2992 289 3 - - SYM iajs-2992 289 4 1733 1733 NUM iajs-2992 289 5 . . PUNCT iajs-2992 290 1 2 2 X iajs-2992 290 2 . . X iajs-2992 290 3 syahrini syahrini PROPN iajs-2992 290 4 , , PUNCT iajs-2992 290 5 i. i. NOUN iajs-2992 290 6 ; ; PUNCT iajs-2992 290 7 masabar masabar PROPN iajs-2992 290 8 , , PUNCT iajs-2992 290 9 r. r. PROPN iajs-2992 290 10 ; ; PUNCT iajs-2992 290 11 aliasuddin aliasuddin PROPN iajs-2992 290 12 , , PUNCT iajs-2992 290 13 a. a. NOUN iajs-2992 290 14 ; ; PUNCT iajs-2992 290 15 munzir munzir NOUN iajs-2992 290 16 , , PUNCT iajs-2992 290 17 s. s. PROPN iajs-2992 290 18 ; ; PUNCT iajs-2992 290 19 hazim hazim NOUN iajs-2992 290 20 , , PUNCT iajs-2992 290 21 y. y. VERB iajs-2992 290 22 the the DET iajs-2992 290 23 application application NOUN iajs-2992 290 24 of of ADP iajs-2992 290 25 optimal optimal ADJ iajs-2992 290 26 control control NOUN iajs-2992 290 27 through through ADP iajs-2992 290 28 fiscal fiscal ADJ iajs-2992 290 29 policy policy NOUN iajs-2992 290 30 on on ADP iajs-2992 290 31 indonesian indonesian ADJ iajs-2992 290 32 economy economy NOUN iajs-2992 290 33 . . PUNCT iajs-2992 291 1 j. j. PROPN iajs-2992 291 2 asian asian PROPN iajs-2992 291 3 finance finance PROPN iajs-2992 291 4 econ econ PROPN iajs-2992 291 5 . . PUNCT iajs-2992 292 1 bus bus NOUN iajs-2992 292 2 . . PUNCT iajs-2992 293 1 2021,8(3),0741 2021,8(3),0741 NUM iajs-2992 293 2 - - SYM iajs-2992 293 3 0750 0750 NUM iajs-2992 293 4 . . PUNCT iajs-2992 294 1 3 3 X iajs-2992 294 2 . . X iajs-2992 294 3 derome derome PROPN iajs-2992 294 4 , , PUNCT iajs-2992 294 5 d. d. PROPN iajs-2992 294 6 ; ; PUNCT iajs-2992 294 7 razali razali VERB iajs-2992 294 8 , , PUNCT iajs-2992 294 9 h.;fazlizan h.;fazlizan PROPN iajs-2992 294 10 , , PUNCT iajs-2992 294 11 a. a. NOUN iajs-2992 294 12 ; ; PUNCT iajs-2992 294 13 jedi jedi PROPN iajs-2992 294 14 , , PUNCT iajs-2992 294 15 a. a. NOUN iajs-2992 294 16 ; ; PUNCT iajs-2992 295 1 purvis purvis PROPN iajs-2992 295 2 – – PUNCT iajs-2992 295 3 roberts roberts PROPN iajs-2992 295 4 , , PUNCT iajs-2992 295 5 k. k. NOUN iajs-2992 295 6 determination determination NOUN iajs-2992 295 7 of of ADP iajs-2992 295 8 optimal optimal ADJ iajs-2992 295 9 time time NOUN iajs-2992 295 10 -average -average NOUN iajs-2992 295 11 wind wind NOUN iajs-2992 295 12 speed speed NOUN iajs-2992 295 13 data datum NOUN iajs-2992 295 14 in in ADP iajs-2992 295 15 the the DET iajs-2992 295 16 southern southern ADJ iajs-2992 295 17 part part NOUN iajs-2992 295 18 of of ADP iajs-2992 295 19 malaysia malaysia PROPN iajs-2992 295 20 . . PUNCT iajs-2992 296 1 baghdad baghdad PROPN iajs-2992 296 2 sci sci PROPN iajs-2992 296 3 . . PUNCT iajs-2992 297 1 j. j. PROPN iajs-2992 297 2 2022 2022 PROPN iajs-2992 297 3 , , PUNCT iajs-2992 297 4 19(5)1111 19(5)1111 NUM iajs-2992 297 5 - - SYM iajs-2992 297 6 1122 1122 NUM iajs-2992 297 7 . . PUNCT iajs-2992 298 1 4 4 NUM iajs-2992 298 2 . . X iajs-2992 298 3 khalaf khalaf PROPN iajs-2992 298 4 , , PUNCT iajs-2992 298 5 w.s w.s PROPN iajs-2992 298 6 ; ; PUNCT iajs-2992 298 7 a a DET iajs-2992 298 8 fuzzy fuzzy ADJ iajs-2992 298 9 dynamic dynamic ADJ iajs-2992 298 10 programming programming NOUN iajs-2992 298 11 for for ADP iajs-2992 298 12 the the DET iajs-2992 298 13 optimal optimal ADJ iajs-2992 298 14 allocation allocation NOUN iajs-2992 298 15 of of ADP iajs-2992 298 16 health health NOUN iajs-2992 298 17 centers center NOUN iajs-2992 298 18 in in ADP iajs-2992 298 19 some some DET iajs-2992 298 20 villages village NOUN iajs-2992 298 21 around around ADP iajs-2992 298 22 baghdad baghdad PROPN iajs-2992 298 23 . . PUNCT iajs-2992 299 1 baghdad baghdad PROPN iajs-2992 299 2 sci sci PROPN iajs-2992 299 3 . . PUNCT iajs-2992 300 1 j. j. PROPN iajs-2992 300 2 2022 2022 PROPN iajs-2992 300 3 , , PUNCT iajs-2992 300 4 3 3 NUM iajs-2992 300 5 , , PUNCT iajs-2992 300 6 593 593 NUM iajs-2992 300 7 - - SYM iajs-2992 300 8 604 604 NUM iajs-2992 300 9 . . PUNCT iajs-2992 301 1 5 5 NUM iajs-2992 301 2 . . X iajs-2992 301 3 lin lin PROPN iajs-2992 301 4 p p PROPN iajs-2992 301 5 ; ; PUNCT iajs-2992 301 6 wang wang PROPN iajs-2992 301 7 w. w. PROPN iajs-2992 301 8 optimal optimal PROPN iajs-2992 301 9 control control NOUN iajs-2992 301 10 problems problem NOUN iajs-2992 301 11 for for ADP iajs-2992 301 12 some some DET iajs-2992 301 13 ordinary ordinary ADJ iajs-2992 301 14 differential differential ADJ iajs-2992 301 15 equations equation NOUN iajs-2992 301 16 with with ADP iajs-2992 301 17 behavior behavior NOUN iajs-2992 301 18 of of ADP iajs-2992 301 19 blowup blowup ADJ iajs-2992 301 20 or or CCONJ iajs-2992 301 21 quenching quenching NOUN iajs-2992 301 22 . . PUNCT iajs-2992 302 1 math math NOUN iajs-2992 302 2 . . PUNCT iajs-2992 303 1 control control PROPN iajs-2992 303 2 relat relat PROPN iajs-2992 303 3 . . PUNCT iajs-2992 304 1 fields field NOUN iajs-2992 304 2 . . PUNCT iajs-2992 305 1 2018 2018 NUM iajs-2992 305 2 , , PUNCT iajs-2992 305 3 8(4 8(4 NUM iajs-2992 305 4 ) ) PUNCT iajs-2992 305 5 , , PUNCT iajs-2992 305 6 809 809 NUM iajs-2992 305 7 - - SYM iajs-2992 305 8 828 828 NUM iajs-2992 305 9 . . PUNCT iajs-2992 306 1 6 6 NUM iajs-2992 306 2 . . X iajs-2992 306 3 manzoni manzoni PROPN iajs-2992 306 4 , , PUNCT iajs-2992 306 5 a. a. NOUN iajs-2992 306 6 ; ; PUNCT iajs-2992 306 7 quarteroni quarteroni NOUN iajs-2992 306 8 , , PUNCT iajs-2992 306 9 a. a. NOUN iajs-2992 306 10 ; ; PUNCT iajs-2992 306 11 salsa salsa PROPN iajs-2992 306 12 , , PUNCT iajs-2992 306 13 s. s. 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