id sid tid token lemma pos cana-5017 1 1 communications communication NOUN cana-5017 1 2 on on ADP cana-5017 1 3 applied apply VERB cana-5017 1 4 nonlinear nonlinear ADJ cana-5017 1 5 analysis analysis NOUN cana-5017 1 6 issn issn NOUN cana-5017 1 7 : : PUNCT cana-5017 1 8 1074 1074 NUM cana-5017 1 9 - - PUNCT cana-5017 1 10 133x 133x NUM cana-5017 1 11 vol vol NOUN cana-5017 1 12 31 31 NUM cana-5017 1 13 no no NOUN cana-5017 1 14 . . PUNCT cana-5017 2 1 8s 8s PROPN cana-5017 2 2 ( ( PUNCT cana-5017 2 3 2024 2024 NUM cana-5017 2 4 ) ) PUNCT cana-5017 2 5 911 911 NUM cana-5017 2 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 2 7 lrs lrs PROPN cana-5017 2 8 bianchi bianchi PROPN cana-5017 2 9 type type PROPN cana-5017 2 10 - - PUNCT cana-5017 2 11 i i NOUN cana-5017 2 12 magnetized magnetize VERB cana-5017 2 13 dark dark ADJ cana-5017 2 14 energy energy NOUN cana-5017 2 15 cosmological cosmological ADJ cana-5017 2 16 model model NOUN cana-5017 2 17 in in ADP cana-5017 2 18 bimetric bimetric ADJ cana-5017 2 19 theory theory NOUN cana-5017 2 20 of of ADP cana-5017 2 21 relativity relativity NOUN cana-5017 2 22 with with ADP cana-5017 2 23 cosmological cosmological ADJ cana-5017 2 24 term term NOUN cana-5017 2 25 – – PUNCT cana-5017 2 26 𝜦 𝜦 NUM cana-5017 2 27 swapnil swapnil NOUN cana-5017 2 28 s. s. PROPN cana-5017 2 29 charjan1 charjan1 PROPN cana-5017 2 30 , , PUNCT cana-5017 2 31 n. n. PROPN cana-5017 2 32 p. p. PROPN cana-5017 2 33 gaikwad2 gaikwad2 PROPN cana-5017 2 34 , , PUNCT cana-5017 2 35 s. s. PROPN cana-5017 2 36 s. s. PROPN cana-5017 2 37 charjan3 charjan3 PROPN cana-5017 2 38 , , PUNCT cana-5017 2 39 p. p. NOUN cana-5017 2 40 v. v. CCONJ cana-5017 3 1 gaykwad4 gaykwad4 PROPN cana-5017 3 2 1 1 NUM cana-5017 3 3 research research NOUN cana-5017 3 4 scholar scholar NOUN cana-5017 3 5 , , PUNCT cana-5017 3 6 post post VERB cana-5017 3 7 graduate graduate PROPN cana-5017 3 8 teaching teaching NOUN cana-5017 3 9 department department NOUN cana-5017 3 10 of of ADP cana-5017 3 11 mathematics mathematic NOUN cana-5017 3 12 , , PUNCT cana-5017 3 13 rashtrasant rashtrasant ADJ cana-5017 3 14 tukadoji tukadoji PROPN cana-5017 3 15 maharaj maharaj PROPN cana-5017 3 16 nagpur nagpur PROPN cana-5017 3 17 university university PROPN cana-5017 3 18 , , PUNCT cana-5017 3 19 nagpur-440033 nagpur-440033 ADJ cana-5017 3 20 email email NOUN cana-5017 3 21 : : PUNCT cana-5017 3 22 charjan91@gmail.com charjan91@gmail.com X cana-5017 3 23 2associate 2associate NUM cana-5017 3 24 professor professor NOUN cana-5017 3 25 , , PUNCT cana-5017 3 26 department department NOUN cana-5017 3 27 of of ADP cana-5017 3 28 mathematics mathematic NOUN cana-5017 3 29 , , PUNCT cana-5017 3 30 dharampeth dharampeth PROPN cana-5017 3 31 m.p m.p PROPN cana-5017 3 32 . . PROPN cana-5017 3 33 deo deo PROPN cana-5017 3 34 memorial memorial PROPN cana-5017 3 35 science science NOUN cana-5017 3 36 college college NOUN cana-5017 3 37 , , PUNCT cana-5017 3 38 nagpur-440033 nagpur-440033 NOUN cana-5017 3 39 , , PUNCT cana-5017 3 40 maharashtra maharashtra PROPN cana-5017 3 41 , , PUNCT cana-5017 3 42 india india PROPN cana-5017 3 43 . . PUNCT cana-5017 3 44 email email NOUN cana-5017 3 45 : : PUNCT cana-5017 4 1 np_gaikwad@rediffmail.com np_gaikwad@rediffmail.com PROPN cana-5017 4 2 3assistant 3assistant NUM cana-5017 4 3 professor professor NOUN cana-5017 4 4 , , PUNCT cana-5017 4 5 department department NOUN cana-5017 4 6 of of ADP cana-5017 4 7 mathematics mathematic NOUN cana-5017 4 8 , , PUNCT cana-5017 4 9 late late ADJ cana-5017 4 10 k.z.s k.z.s PROPN cana-5017 4 11 . . PUNCT cana-5017 5 1 science science PROPN cana-5017 5 2 college college PROPN cana-5017 5 3 bramhani bramhani PROPN cana-5017 5 4 , , PUNCT cana-5017 5 5 kalmeshwar441502 kalmeshwar441502 PROPN cana-5017 5 6 , , PUNCT cana-5017 5 7 maharashtra maharashtra PROPN cana-5017 5 8 , , PUNCT cana-5017 5 9 india india PROPN cana-5017 5 10 . . PUNCT cana-5017 5 11 email email NOUN cana-5017 5 12 : : PUNCT cana-5017 5 13 sscharjan1967@gmail.com sscharjan1967@gmail.com X cana-5017 6 1 4assistant 4assistant NUM cana-5017 6 2 professor professor NOUN cana-5017 6 3 , , PUNCT cana-5017 6 4 department department NOUN cana-5017 6 5 of of ADP cana-5017 6 6 mathematics mathematics PROPN cana-5017 6 7 , , PUNCT cana-5017 6 8 a. a. PROPN cana-5017 6 9 d. d. PROPN cana-5017 6 10 college college PROPN cana-5017 6 11 , , PUNCT cana-5017 6 12 bharshingi-441305 bharshingi-441305 NOUN cana-5017 6 13 , , PUNCT cana-5017 6 14 maharashtra maharashtra PROPN cana-5017 6 15 , , PUNCT cana-5017 6 16 india india PROPN cana-5017 6 17 . . PUNCT cana-5017 6 18 email email NOUN cana-5017 6 19 : : PUNCT cana-5017 7 1 pvgayakwad07@gmail.com pvgayakwad07@gmail.com X cana-5017 7 2 article article NOUN cana-5017 7 3 history history NOUN cana-5017 7 4 : : PUNCT cana-5017 7 5 received receive VERB cana-5017 7 6 : : PUNCT cana-5017 7 7 1 1 NUM cana-5017 7 8 - - SYM cana-5017 7 9 11 11 NUM cana-5017 7 10 - - PUNCT cana-5017 7 11 2024 2024 NUM cana-5017 7 12 revised revise VERB cana-5017 7 13 : : PUNCT cana-5017 7 14 17 17 NUM cana-5017 7 15 - - SYM cana-5017 7 16 12 12 NUM cana-5017 7 17 - - PUNCT cana-5017 7 18 2024 2024 NUM cana-5017 7 19 accepted accept VERB cana-5017 7 20 : : PUNCT cana-5017 7 21 25 25 NUM cana-5017 7 22 - - SYM cana-5017 7 23 12 12 NUM cana-5017 7 24 - - PUNCT cana-5017 7 25 2024 2024 NUM cana-5017 7 26 abstract abstract NOUN cana-5017 7 27 : : PUNCT cana-5017 7 28 in in ADP cana-5017 7 29 this this DET cana-5017 7 30 paper paper NOUN cana-5017 7 31 , , PUNCT cana-5017 7 32 to to PART cana-5017 7 33 study study VERB cana-5017 7 34 locally locally ADV cana-5017 7 35 rotationally rotationally ADV cana-5017 7 36 symmetric symmetric ADJ cana-5017 7 37 ( ( PUNCT cana-5017 7 38 lrs lrs PROPN cana-5017 7 39 ) ) PUNCT cana-5017 7 40 bianchi bianchi NOUN cana-5017 7 41 type type NOUN cana-5017 7 42 - - PUNCT cana-5017 7 43 i i NOUN cana-5017 7 44 magnetized magnetize VERB cana-5017 7 45 dark dark ADJ cana-5017 7 46 energy energy NOUN cana-5017 7 47 cosmological cosmological ADJ cana-5017 7 48 models model NOUN cana-5017 7 49 with with ADP cana-5017 7 50 cosmological cosmological ADJ cana-5017 7 51 constant constant ADJ cana-5017 7 52 -𝛬 -𝛬 NOUN cana-5017 7 53 , , PUNCT cana-5017 7 54 we we PRON cana-5017 7 55 have have AUX cana-5017 7 56 calculated calculate VERB cana-5017 7 57 rosen rosen PROPN cana-5017 7 58 , , PUNCT cana-5017 7 59 s s PART cana-5017 7 60 field field NOUN cana-5017 7 61 equations equation NOUN cana-5017 7 62 for for ADP cana-5017 7 63 lrs lrs PROPN cana-5017 7 64 bianchi bianchi PROPN cana-5017 7 65 type type NOUN cana-5017 7 66 -i -i PUNCT cana-5017 7 67 spacetimes spacetime NOUN cana-5017 7 68 in in ADP cana-5017 7 69 the the DET cana-5017 7 70 presence presence NOUN cana-5017 7 71 of of ADP cana-5017 7 72 dark dark ADJ cana-5017 7 73 energy energy NOUN cana-5017 7 74 and and CCONJ cana-5017 7 75 discuss discuss VERB cana-5017 7 76 their their PRON cana-5017 7 77 geometrical geometrical ADJ cana-5017 7 78 as as ADV cana-5017 7 79 well well ADV cana-5017 7 80 as as ADP cana-5017 7 81 physical physical ADJ cana-5017 7 82 significances significance NOUN cana-5017 7 83 using use VERB cana-5017 7 84 two two NUM cana-5017 7 85 cases case NOUN cana-5017 7 86 ( ( PUNCT cana-5017 7 87 i i NOUN cana-5017 7 88 ) ) PUNCT cana-5017 7 89 𝜌 𝜌 ADP cana-5017 7 90 + + X cana-5017 7 91 πœ† πœ† X cana-5017 7 92 = = SYM cana-5017 7 93 0 0 NUM cana-5017 7 94 ( ( PUNCT cana-5017 7 95 ii ii NOUN cana-5017 7 96 ) ) PUNCT cana-5017 7 97 𝜌 𝜌 ADP cana-5017 7 98 βˆ’ βˆ’ PROPN cana-5017 7 99 πœ† πœ† SYM cana-5017 7 100 = = NOUN cana-5017 7 101 0 0 PROPN cana-5017 7 102 . . PUNCT cana-5017 7 103 to to PART cana-5017 7 104 obtain obtain VERB cana-5017 7 105 the the DET cana-5017 7 106 determinate determinate ADJ cana-5017 7 107 solution solution NOUN cana-5017 7 108 of of ADP cana-5017 7 109 the the DET cana-5017 7 110 model model NOUN cana-5017 7 111 , , PUNCT cana-5017 7 112 we we PRON cana-5017 7 113 considered consider VERB cana-5017 7 114 i i PRON cana-5017 7 115 ) ) PUNCT cana-5017 7 116 scalar scalar ADJ cana-5017 7 117 expansion expansion NOUN cana-5017 7 118 πœƒ πœƒ NOUN cana-5017 7 119 is be AUX cana-5017 7 120 directly directly ADV cana-5017 7 121 proportional proportional ADJ cana-5017 7 122 to to PART cana-5017 7 123 share share VERB cana-5017 7 124 𝜎 𝜎 PROPN cana-5017 7 125 ii ii X cana-5017 7 126 ) ) PUNCT cana-5017 7 127 𝛬 𝛬 NOUN cana-5017 7 128 = = NOUN cana-5017 8 1 𝛼 𝛼 X cana-5017 8 2 𝛒𝛣2 𝛒𝛣2 PROPN cana-5017 8 3 . . PUNCT cana-5017 9 1 in in ADP cana-5017 9 2 the the DET cana-5017 9 3 presence presence NOUN cana-5017 9 4 of of ADP cana-5017 9 5 a a DET cana-5017 9 6 magnetic magnetic ADJ cana-5017 9 7 field field NOUN cana-5017 9 8 for for ADP cana-5017 9 9 the the DET cana-5017 9 10 conditions condition NOUN cana-5017 9 11 𝜌 𝜌 X cana-5017 9 12 + + CCONJ cana-5017 9 13 πœ† πœ† NOUN cana-5017 9 14 = = SYM cana-5017 9 15 0 0 NUM cana-5017 9 16 , , PUNCT cana-5017 9 17 scalar scalar ADJ cana-5017 9 18 expansion expansion NOUN cana-5017 9 19 πœƒ πœƒ NOUN cana-5017 9 20 attains attain VERB cana-5017 9 21 its its PRON cana-5017 9 22 minimum minimum NOUN cana-5017 9 23 and and CCONJ cana-5017 9 24 increases increase NOUN cana-5017 9 25 with with ADP cana-5017 9 26 increase increase NOUN cana-5017 9 27 in in ADP cana-5017 9 28 𝑇 𝑇 PROPN cana-5017 9 29 indicating indicate VERB cana-5017 9 30 that that SCONJ cana-5017 9 31 the the DET cana-5017 9 32 universe universe NOUN cana-5017 9 33 is be AUX cana-5017 9 34 expanding expand VERB cana-5017 9 35 with with ADP cana-5017 9 36 increment increment NOUN cana-5017 9 37 in in ADP cana-5017 9 38 𝑇 𝑇 PROPN cana-5017 9 39 , , PUNCT cana-5017 9 40 for for ADP cana-5017 9 41 the the DET cana-5017 9 42 case case NOUN cana-5017 9 43 𝜌 𝜌 ADP cana-5017 9 44 βˆ’ βˆ’ PROPN cana-5017 9 45 πœ† πœ† SYM cana-5017 9 46 = = SYM cana-5017 9 47 0 0 NUM cana-5017 9 48 scalar scalar ADJ cana-5017 9 49 expansion expansion NOUN cana-5017 9 50 πœƒ πœƒ NOUN cana-5017 9 51 attains attain VERB cana-5017 9 52 its its PRON cana-5017 9 53 maximum maximum NOUN cana-5017 9 54 and and CCONJ cana-5017 9 55 decreases decrease VERB cana-5017 9 56 with with ADP cana-5017 9 57 increase increase NOUN cana-5017 9 58 in in ADP cana-5017 9 59 𝑇 𝑇 PROPN cana-5017 9 60 indicate indicate VERB cana-5017 9 61 that that PRON cana-5017 9 62 slows slow VERB cana-5017 9 63 down down ADP cana-5017 9 64 the the DET cana-5017 9 65 rate rate NOUN cana-5017 9 66 of of ADP cana-5017 9 67 expansion expansion NOUN cana-5017 9 68 . . PUNCT cana-5017 10 1 keywords keyword NOUN cana-5017 10 2 : : PUNCT cana-5017 10 3 lrs lrs PROPN cana-5017 10 4 bianchi bianchi PROPN cana-5017 10 5 type type NOUN cana-5017 10 6 i i PRON cana-5017 10 7 ; ; PUNCT cana-5017 10 8 bimetric bimetric ADJ cana-5017 10 9 ; ; PUNCT cana-5017 10 10 gravitation gravitation NOUN cana-5017 10 11 ; ; PUNCT cana-5017 10 12 dark dark ADJ cana-5017 10 13 energy energy NOUN cana-5017 10 14 ; ; PUNCT cana-5017 10 15 dark dark ADJ cana-5017 10 16 matter matter NOUN cana-5017 10 17 . . PUNCT cana-5017 11 1 1 1 X cana-5017 11 2 . . X cana-5017 11 3 introduction introduction NOUN cana-5017 11 4 it it PRON cana-5017 11 5 presently presently ADV cana-5017 11 6 appears appear VERB cana-5017 11 7 that that SCONJ cana-5017 11 8 the the DET cana-5017 11 9 cosmos cosmos PROPN cana-5017 11 10 is be AUX cana-5017 11 11 composed compose VERB cana-5017 11 12 of of ADP cana-5017 11 13 4.9 4.9 NUM cana-5017 11 14 % % NOUN cana-5017 11 15 baryonic baryonic NOUN cana-5017 11 16 ( ( PUNCT cana-5017 11 17 ordinary ordinary ADJ cana-5017 11 18 ) ) PUNCT cana-5017 11 19 matter matter NOUN cana-5017 11 20 , , PUNCT cana-5017 11 21 26.8 26.8 NUM cana-5017 11 22 % % NOUN cana-5017 11 23 dark dark ADJ cana-5017 11 24 matter matter NOUN cana-5017 11 25 , , PUNCT cana-5017 11 26 and and CCONJ cana-5017 11 27 68.3 68.3 NUM cana-5017 11 28 % % NOUN cana-5017 11 29 dark dark ADJ cana-5017 11 30 energy energy NOUN cana-5017 11 31 in in ADP cana-5017 11 32 the the DET cana-5017 11 33 form form NOUN cana-5017 11 34 of of ADP cana-5017 11 35 energy energy NOUN cana-5017 11 36 densities density NOUN cana-5017 11 37 . . PUNCT cana-5017 12 1 recently recently ADV cana-5017 12 2 , , PUNCT cana-5017 12 3 various various ADJ cana-5017 12 4 cosmological cosmological ADJ cana-5017 12 5 theories theory NOUN cana-5017 12 6 including include VERB cana-5017 12 7 dark dark ADJ cana-5017 12 8 matter matter NOUN cana-5017 12 9 as as ADV cana-5017 12 10 well well ADV cana-5017 12 11 as as ADP cana-5017 12 12 dark dark ADJ cana-5017 12 13 energy energy NOUN cana-5017 12 14 have have AUX cana-5017 12 15 been be AUX cana-5017 12 16 investigated investigate VERB cana-5017 12 17 . . PUNCT cana-5017 13 1 due due ADP cana-5017 13 2 to to ADP cana-5017 13 3 the the DET cana-5017 13 4 development development NOUN cana-5017 13 5 of of ADP cana-5017 13 6 the the DET cana-5017 13 7 dark dark ADJ cana-5017 13 8 energy energy NOUN cana-5017 13 9 problem problem NOUN cana-5017 13 10 , , PUNCT cana-5017 13 11 the the DET cana-5017 13 12 constraints constraint NOUN cana-5017 13 13 of of ADP cana-5017 13 14 general general ADJ cana-5017 13 15 relativity relativity NOUN cana-5017 13 16 have have AUX cana-5017 13 17 once once ADV cana-5017 13 18 more more ADJ cana-5017 13 19 become become VERB cana-5017 13 20 apparent apparent ADJ cana-5017 13 21 . . PUNCT cana-5017 14 1 it it PRON cana-5017 14 2 has have AUX cana-5017 14 3 been be AUX cana-5017 14 4 assumed assume VERB cana-5017 14 5 that that SCONJ cana-5017 14 6 dark dark ADJ cana-5017 14 7 energy energy NOUN cana-5017 14 8 will will AUX cana-5017 14 9 explain explain VERB cana-5017 14 10 how how SCONJ cana-5017 14 11 the the DET cana-5017 14 12 universe universe NOUN cana-5017 14 13 is be AUX cana-5017 14 14 clearly clearly ADV cana-5017 14 15 expanding expand VERB cana-5017 14 16 at at ADP cana-5017 14 17 an an DET cana-5017 14 18 acceleration acceleration NOUN cana-5017 14 19 rate rate NOUN cana-5017 14 20 . . PUNCT cana-5017 15 1 dark dark ADJ cana-5017 15 2 energy energy NOUN cana-5017 15 3 has have AUX cana-5017 15 4 been be AUX cana-5017 15 5 suggested suggest VERB cana-5017 15 6 to to PART cana-5017 15 7 be be AUX cana-5017 15 8 responsible responsible ADJ cana-5017 15 9 for for ADP cana-5017 15 10 of of ADP cana-5017 15 11 the the DET cana-5017 15 12 universe universe NOUN cana-5017 15 13 's 's PART cana-5017 15 14 observed observe VERB cana-5017 15 15 acceleration acceleration NOUN cana-5017 15 16 in in ADP cana-5017 15 17 expansion expansion NOUN cana-5017 15 18 . . PUNCT cana-5017 16 1 dark dark ADJ cana-5017 16 2 energy energy NOUN cana-5017 16 3 ( ( PUNCT cana-5017 16 4 de de ADJ cana-5017 16 5 ) ) PUNCT cana-5017 16 6 is be AUX cana-5017 16 7 a a DET cana-5017 16 8 speculative speculative ADJ cana-5017 16 9 type type NOUN cana-5017 16 10 of of ADP cana-5017 16 11 energy energy NOUN cana-5017 16 12 acting act VERB cana-5017 16 13 appallingly appallingly ADV cana-5017 16 14 which which PRON cana-5017 16 15 allows allow VERB cana-5017 16 16 all all PRON cana-5017 16 17 of of ADP cana-5017 16 18 space space NOUN cana-5017 16 19 and and CCONJ cana-5017 16 20 will will AUX cana-5017 16 21 in in ADP cana-5017 16 22 general general ADJ cana-5017 16 23 speed speed NOUN cana-5017 16 24 up up ADP cana-5017 16 25 the the DET cana-5017 16 26 extension extension NOUN cana-5017 16 27 of of ADP cana-5017 16 28 the the DET cana-5017 16 29 cosmos cosmos PROPN cana-5017 16 30 . . PUNCT cana-5017 17 1 this this DET cana-5017 17 2 sped speed VERB cana-5017 17 3 - - PUNCT cana-5017 17 4 up up ADP cana-5017 17 5 extension extension NOUN cana-5017 17 6 of of ADP cana-5017 17 7 the the DET cana-5017 17 8 cosmos cosmo NOUN cana-5017 17 9 was be AUX cana-5017 17 10 affirmed affirm VERB cana-5017 17 11 by by ADP cana-5017 17 12 the the DET cana-5017 17 13 perceptions perception NOUN cana-5017 17 14 like like ADP cana-5017 17 15 supernovae supernovae NOUN cana-5017 17 16 type type NOUN cana-5017 17 17 i i PROPN cana-5017 17 18 , , PUNCT cana-5017 17 19 lss lss PROPN cana-5017 17 20 , , PUNCT cana-5017 17 21 sds sds PROPN cana-5017 17 22 survey survey NOUN cana-5017 17 23 , , PUNCT cana-5017 17 24 wma wma NOUN cana-5017 17 25 probe probe PROPN cana-5017 17 26 , , PUNCT cana-5017 17 27 bao bao PROPN cana-5017 17 28 and and CCONJ cana-5017 17 29 cmbr cmbr NOUN cana-5017 17 30 some some DET cana-5017 17 31 authors author NOUN cana-5017 17 32 have have AUX cana-5017 17 33 discussed discuss VERB cana-5017 17 34 this this DET cana-5017 17 35 aspect aspect NOUN cana-5017 17 36 viz viz NOUN cana-5017 17 37 ; ; PUNCT cana-5017 17 38 borkar borkar PROPN cana-5017 17 39 et et NOUN cana-5017 17 40 al.(1 al.(1 ADV cana-5017 17 41 ) ) PUNCT cana-5017 17 42 , , PUNCT cana-5017 17 43 mamon mamon PROPN cana-5017 17 44 et et PROPN cana-5017 17 45 al.(2 al.(2 PROPN cana-5017 17 46 ) ) PUNCT cana-5017 17 47 , , PUNCT cana-5017 17 48 riess riess PROPN cana-5017 17 49 et et PROPN cana-5017 17 50 al.(3 al.(3 PROPN cana-5017 17 51 ) ) PUNCT cana-5017 17 52 , , PUNCT cana-5017 17 53 perlmutter perlmutter NOUN cana-5017 17 54 et et PROPN cana-5017 17 55 al.(4 al.(4 PROPN cana-5017 17 56 ) ) PUNCT cana-5017 17 57 , , PUNCT cana-5017 17 58 spergel spergel PROPN cana-5017 17 59 et et PROPN cana-5017 17 60 al.(5 al.(5 PROPN cana-5017 17 61 ) ) PUNCT cana-5017 17 62 , , PUNCT cana-5017 17 63 tegmark tegmark PROPN cana-5017 17 64 et et PROPN cana-5017 17 65 al.(6 al.(6 PROPN cana-5017 17 66 ) ) PUNCT cana-5017 17 67 , , PUNCT cana-5017 17 68 hinshaw hinshaw PROPN cana-5017 17 69 et et PROPN cana-5017 17 70 al.(7 al.(7 NOUN cana-5017 17 71 ) ) PUNCT cana-5017 17 72 , , PUNCT cana-5017 17 73 nolta nolta VERB cana-5017 17 74 et et NOUN cana-5017 17 75 al.(8 al.(8 ADJ cana-5017 17 76 ) ) PUNCT cana-5017 17 77 , , PUNCT cana-5017 17 78 hinshaw hinshaw PROPN cana-5017 17 79 et et PROPN cana-5017 17 80 al.(9 al.(9 NOUN cana-5017 17 81 ) ) PUNCT cana-5017 17 82 , , PUNCT cana-5017 17 83 mailto:charjan91@gmail.com mailto:charjan91@gmail.com PROPN cana-5017 17 84 mailto:np_gaikwad@rediffmail.com mailto:np_gaikwad@rediffmail.com PROPN cana-5017 17 85 mailto:sscharjan1967@gmail.com mailto:sscharjan1967@gmail.com PROPN cana-5017 17 86 communications communication NOUN cana-5017 17 87 on on ADP cana-5017 17 88 applied apply VERB cana-5017 17 89 nonlinear nonlinear ADJ cana-5017 17 90 analysis analysis NOUN cana-5017 17 91 issn issn NOUN cana-5017 17 92 : : PUNCT cana-5017 17 93 1074 1074 NUM cana-5017 17 94 - - PUNCT cana-5017 17 95 133x 133x NUM cana-5017 17 96 vol vol NOUN cana-5017 17 97 31 31 NUM cana-5017 17 98 no no NOUN cana-5017 17 99 . . PUNCT cana-5017 18 1 8s 8s PROPN cana-5017 18 2 ( ( PUNCT cana-5017 18 3 2024 2024 NUM cana-5017 18 4 ) ) PUNCT cana-5017 18 5 912 912 NUM cana-5017 18 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 18 7 anderson anderson PROPN cana-5017 18 8 et et PROPN cana-5017 18 9 al.(10 al.(10 PROPN cana-5017 18 10 ) ) PUNCT cana-5017 18 11 . . PUNCT cana-5017 19 1 cosmologists cosmologist NOUN cana-5017 19 2 such such ADJ cana-5017 19 3 as as ADP cana-5017 19 4 kamenshchik kamenshchik NOUN cana-5017 19 5 et et PROPN cana-5017 19 6 al.(11 al.(11 PROPN cana-5017 19 7 ) ) PUNCT cana-5017 19 8 , , PUNCT cana-5017 19 9 katore katore VERB cana-5017 19 10 et et PRON cana-5017 19 11 al.(12 al.(12 ADJ cana-5017 19 12 ) ) PUNCT cana-5017 19 13 , , PUNCT cana-5017 19 14 borkar borkar NOUN cana-5017 19 15 et et PROPN cana-5017 19 16 al.(13 al.(13 NOUN cana-5017 19 17 ) ) PUNCT cana-5017 19 18 presented present VERB cana-5017 19 19 several several ADJ cana-5017 19 20 contenders contender NOUN cana-5017 19 21 for for ADP cana-5017 19 22 dark dark ADJ cana-5017 19 23 energy energy NOUN cana-5017 19 24 based base VERB cana-5017 19 25 on on ADP cana-5017 19 26 these these DET cana-5017 19 27 senses sense NOUN cana-5017 19 28 and and CCONJ cana-5017 19 29 their their PRON cana-5017 19 30 theories theory NOUN cana-5017 19 31 about about ADP cana-5017 19 32 it it PRON cana-5017 19 33 . . PUNCT cana-5017 20 1 the the DET cana-5017 20 2 cosmological cosmological ADJ cana-5017 20 3 steady steady ADJ cana-5017 20 4 up up ADV cana-5017 20 5 - - PUNCT cana-5017 20 6 and and CCONJ cana-5017 20 7 - - PUNCT cana-5017 20 8 comer comer NOUN cana-5017 20 9 experiences experience NOUN cana-5017 20 10 two two NUM cana-5017 20 11 notable notable ADJ cana-5017 20 12 issues issue NOUN cana-5017 20 13 , , PUNCT cana-5017 20 14 specifically specifically ADV cana-5017 20 15 , , PUNCT cana-5017 20 16 the the DET cana-5017 20 17 tweaking tweaking NOUN cana-5017 20 18 and and CCONJ cana-5017 20 19 the the DET cana-5017 20 20 grandiose grandiose ADJ cana-5017 20 21 incidental incidental ADJ cana-5017 20 22 problems problem NOUN cana-5017 20 23 studied study VERB cana-5017 20 24 by by ADP cana-5017 20 25 copeland copeland PROPN cana-5017 20 26 et et PROPN cana-5017 20 27 al.(14 al.(14 PROPN cana-5017 20 28 ) ) PUNCT cana-5017 20 29 . . PUNCT cana-5017 21 1 positive positive ADJ cana-5017 21 2 energy energy NOUN cana-5017 21 3 thickness thickness NOUN cana-5017 21 4 and and CCONJ cana-5017 21 5 negative negative ADJ cana-5017 21 6 tension tension NOUN cana-5017 21 7 are be AUX cana-5017 21 8 combined combine VERB cana-5017 21 9 in in ADP cana-5017 21 10 the the DET cana-5017 21 11 pith pith NOUN cana-5017 21 12 dynamical dynamical ADJ cana-5017 21 13 dark dark ADJ cana-5017 21 14 energy energy NOUN cana-5017 21 15 model model NOUN cana-5017 21 16 . . PUNCT cana-5017 22 1 the the DET cana-5017 22 2 basic basic ADJ cana-5017 22 3 scenario scenario NOUN cana-5017 22 4 is be AUX cana-5017 22 5 further far ADV cana-5017 22 6 inspired inspire VERB cana-5017 22 7 by by ADP cana-5017 22 8 the the DET cana-5017 22 9 tracker tracker NOUN cana-5017 22 10 field field NOUN cana-5017 22 11 this this DET cana-5017 22 12 study study NOUN cana-5017 22 13 was be AUX cana-5017 22 14 done do VERB cana-5017 22 15 by by ADP cana-5017 22 16 saha saha PROPN cana-5017 22 17 et et PROPN cana-5017 22 18 al.(15 al.(15 PROPN cana-5017 22 19 ) ) PUNCT cana-5017 22 20 and and CCONJ cana-5017 22 21 sing sing VERB cana-5017 22 22 et et PROPN cana-5017 22 23 al.(16 al.(16 PROPN cana-5017 22 24 ) ) PUNCT cana-5017 22 25 . . PUNCT cana-5017 23 1 the the DET cana-5017 23 2 chaplygin chaplygin ADJ cana-5017 23 3 gas gas NOUN cana-5017 23 4 model model NOUN cana-5017 23 5 , , PUNCT cana-5017 23 6 which which PRON cana-5017 23 7 is be AUX cana-5017 23 8 seen see VERB cana-5017 23 9 as as ADP cana-5017 23 10 the the DET cana-5017 23 11 combined combined ADJ cana-5017 23 12 effect effect NOUN cana-5017 23 13 of of ADP cana-5017 23 14 dark dark ADJ cana-5017 23 15 matter matter NOUN cana-5017 23 16 along along ADP cana-5017 23 17 with with ADP cana-5017 23 18 dark dark ADJ cana-5017 23 19 energy energy NOUN cana-5017 23 20 , , PUNCT cana-5017 23 21 is be AUX cana-5017 23 22 another another DET cana-5017 23 23 option option NOUN cana-5017 23 24 to to ADP cana-5017 23 25 the the DET cana-5017 23 26 dynamical dynamical ADJ cana-5017 23 27 dark dark ADJ cana-5017 23 28 energy energy NOUN cana-5017 23 29 model model NOUN cana-5017 23 30 studied study VERB cana-5017 23 31 by by ADP cana-5017 23 32 dev dev PROPN cana-5017 23 33 et et PROPN cana-5017 23 34 al.(17 al.(17 PROPN cana-5017 23 35 ) ) PUNCT cana-5017 23 36 , , PUNCT cana-5017 23 37 bento bento NOUN cana-5017 23 38 et et NOUN cana-5017 23 39 al.(18 al.(18 PROPN cana-5017 23 40 ) ) PUNCT cana-5017 23 41 , , PUNCT cana-5017 23 42 abdusattar abdusattar NOUN cana-5017 23 43 et et PROPN cana-5017 23 44 al.(19 al.(19 PROPN cana-5017 23 45 ) ) PUNCT cana-5017 23 46 . . PUNCT cana-5017 24 1 rosen(20),(21 rosen(20),(21 CCONJ cana-5017 24 2 ) ) PUNCT cana-5017 24 3 investigated investigate VERB cana-5017 24 4 the the DET cana-5017 24 5 importance importance NOUN cana-5017 24 6 of of ADP cana-5017 24 7 attractiveness attractiveness NOUN cana-5017 24 8 in in ADP cana-5017 24 9 the the DET cana-5017 24 10 cosmos cosmos NOUN cana-5017 24 11 is be AUX cana-5017 24 12 important important ADJ cana-5017 24 13 , , PUNCT cana-5017 24 14 given give VERB cana-5017 24 15 that that SCONJ cana-5017 24 16 the the DET cana-5017 24 17 attractive attractive ADJ cana-5017 24 18 field field NOUN cana-5017 24 19 exists exist VERB cana-5017 24 20 in in ADP cana-5017 24 21 the the DET cana-5017 24 22 space space NOUN cana-5017 24 23 between between ADP cana-5017 24 24 universes universe NOUN cana-5017 24 25 and and CCONJ cana-5017 24 26 plays play VERB cana-5017 24 27 a a DET cana-5017 24 28 very very ADV cana-5017 24 29 important important ADJ cana-5017 24 30 role role NOUN cana-5017 24 31 in in ADP cana-5017 24 32 cosmology cosmology NOUN cana-5017 24 33 . . PUNCT cana-5017 25 1 melvin melvin PROPN cana-5017 25 2 proposes propose VERB cana-5017 25 3 that that DET cana-5017 25 4 matter matter NOUN cana-5017 25 5 was be AUX cana-5017 25 6 severely severely ADV cana-5017 25 7 ionized ionize VERB cana-5017 25 8 during during ADP cana-5017 25 9 the the DET cana-5017 25 10 creation creation NOUN cana-5017 25 11 of of ADP cana-5017 25 12 the the DET cana-5017 25 13 cosmos cosmos PROPN cana-5017 25 14 also also ADV cana-5017 25 15 , , PUNCT cana-5017 25 16 because because SCONJ cana-5017 25 17 of of ADP cana-5017 25 18 the the DET cana-5017 25 19 expansion expansion NOUN cana-5017 25 20 of of ADP cana-5017 25 21 the the DET cana-5017 25 22 cosmos cosmos PROPN cana-5017 25 23 , , PUNCT cana-5017 25 24 this this DET cana-5017 25 25 matter matter NOUN cana-5017 25 26 is be AUX cana-5017 25 27 once once ADV cana-5017 25 28 more more ADV cana-5017 25 29 flawlessly flawlessly ADV cana-5017 25 30 united unite VERB cana-5017 25 31 with with ADP cana-5017 25 32 the the DET cana-5017 25 33 attractive attractive ADJ cana-5017 25 34 field field NOUN cana-5017 25 35 and and CCONJ cana-5017 25 36 builds build VERB cana-5017 25 37 unbiased unbiased ADJ cana-5017 25 38 matter matter NOUN cana-5017 25 39 . . PUNCT cana-5017 26 1 therefore therefore ADV cana-5017 26 2 , , PUNCT cana-5017 26 3 it it PRON cana-5017 26 4 makes make VERB cana-5017 26 5 sense sense NOUN cana-5017 26 6 that that SCONJ cana-5017 26 7 there there PRON cana-5017 26 8 would would AUX cana-5017 26 9 be be AUX cana-5017 26 10 an an DET cana-5017 26 11 attracting attract VERB cana-5017 26 12 field field NOUN cana-5017 26 13 throughout throughout ADP cana-5017 26 14 the the DET cana-5017 26 15 cosmos cosmos PROPN cana-5017 26 16 . . PUNCT cana-5017 27 1 the the DET cana-5017 27 2 incredible incredible ADJ cana-5017 27 3 result result NOUN cana-5017 27 4 of of ADP cana-5017 27 5 general general ADJ cana-5017 27 6 relativity relativity NOUN cana-5017 27 7 did do AUX cana-5017 27 8 not not PART cana-5017 27 9 stop stop VERB cana-5017 27 10 any any DET cana-5017 27 11 other other ADJ cana-5017 27 12 explanations explanation NOUN cana-5017 27 13 for for ADP cana-5017 27 14 the the DET cana-5017 27 15 universe universe NOUN cana-5017 27 16 's 's PART cana-5017 27 17 expanding expand VERB cana-5017 27 18 pace pace NOUN cana-5017 27 19 and and CCONJ cana-5017 27 20 the the DET cana-5017 27 21 existence existence NOUN cana-5017 27 22 of of ADP cana-5017 27 23 dark dark ADJ cana-5017 27 24 matter matter NOUN cana-5017 27 25 from from ADP cana-5017 27 26 being be AUX cana-5017 27 27 put put VERB cana-5017 27 28 forth forth ADV cana-5017 27 29 . . PUNCT cana-5017 28 1 in in ADP cana-5017 28 2 actuality actuality NOUN cana-5017 28 3 , , PUNCT cana-5017 28 4 a a DET cana-5017 28 5 short short ADJ cana-5017 28 6 while while NOUN cana-5017 28 7 after after SCONJ cana-5017 28 8 einstein einstein PROPN cana-5017 28 9 's 's PART cana-5017 28 10 theory theory NOUN cana-5017 28 11 was be AUX cana-5017 28 12 published publish VERB cana-5017 28 13 , , PUNCT cana-5017 28 14 numerous numerous ADJ cana-5017 28 15 elective elective ADJ cana-5017 28 16 speculations speculation NOUN cana-5017 28 17 have have AUX cana-5017 28 18 arisen arise VERB cana-5017 28 19 telling tell VERB cana-5017 28 20 the the DET cana-5017 28 21 best good ADJ cana-5017 28 22 way way NOUN cana-5017 28 23 to to PART cana-5017 28 24 expand expand VERB cana-5017 28 25 , , PUNCT cana-5017 28 26 how how SCONJ cana-5017 28 27 to to PART cana-5017 28 28 connect connect VERB cana-5017 28 29 with with ADP cana-5017 28 30 other other ADJ cana-5017 28 31 theories theory NOUN cana-5017 28 32 , , PUNCT cana-5017 28 33 and and CCONJ cana-5017 28 34 how how SCONJ cana-5017 28 35 to to PART cana-5017 28 36 consolidate consolidate VERB cana-5017 28 37 . . PUNCT cana-5017 29 1 the the DET cana-5017 29 2 bimetric bimetric ADJ cana-5017 29 3 theory theory NOUN cana-5017 29 4 of of ADP cana-5017 29 5 gravity gravity NOUN cana-5017 29 6 proposed propose VERB cana-5017 29 7 by by ADP cana-5017 29 8 rosen rosen PROPN cana-5017 29 9 is be AUX cana-5017 29 10 one one NUM cana-5017 29 11 of of ADP cana-5017 29 12 the the DET cana-5017 29 13 other other ADJ cana-5017 29 14 alternatives alternative NOUN cana-5017 29 15 , , PUNCT cana-5017 29 16 which which PRON cana-5017 29 17 is be AUX cana-5017 29 18 free free ADJ cana-5017 29 19 of of ADP cana-5017 29 20 singularities singularity NOUN cana-5017 29 21 as as ADV cana-5017 29 22 well well ADV cana-5017 29 23 as as ADP cana-5017 29 24 black black ADJ cana-5017 29 25 holes hole NOUN cana-5017 29 26 which which PRON cana-5017 29 27 where where SCONJ cana-5017 29 28 appear appear VERB cana-5017 29 29 in in ADP cana-5017 29 30 the the DET cana-5017 29 31 big big PROPN cana-5017 29 32 bang bang PROPN cana-5017 29 33 theory theory NOUN cana-5017 29 34 of of ADP cana-5017 29 35 the the DET cana-5017 29 36 cosmological cosmological ADJ cana-5017 29 37 model model NOUN cana-5017 29 38 . . PUNCT cana-5017 30 1 the the DET cana-5017 30 2 theory theory NOUN cana-5017 30 3 is be AUX cana-5017 30 4 consistent consistent ADJ cana-5017 30 5 with with ADP cana-5017 30 6 the the DET cana-5017 30 7 most most ADV cana-5017 30 8 recent recent ADJ cana-5017 30 9 observational observational ADJ cana-5017 30 10 evidence evidence NOUN cana-5017 30 11 on on ADP cana-5017 30 12 gr gr PROPN cana-5017 30 13 , , PUNCT cana-5017 30 14 and and CCONJ cana-5017 30 15 it it PRON cana-5017 30 16 substantially substantially ADV cana-5017 30 17 agrees agree VERB cana-5017 30 18 with with ADP cana-5017 30 19 the the DET cana-5017 30 20 covariance covariance NOUN cana-5017 30 21 and and CCONJ cana-5017 30 22 equivalence equivalence NOUN cana-5017 30 23 principles principle NOUN cana-5017 30 24 of of ADP cana-5017 30 25 gr gr PROPN cana-5017 30 26 . . PUNCT cana-5017 31 1 therefore therefore ADV cana-5017 31 2 , , PUNCT cana-5017 31 3 rosen rosen PROPN cana-5017 31 4 's 's PART cana-5017 31 5 btg btg PROPN cana-5017 31 6 is be AUX cana-5017 31 7 significant significant ADJ cana-5017 31 8 and and CCONJ cana-5017 31 9 is be AUX cana-5017 31 10 dependent dependent ADJ cana-5017 31 11 on on ADP cana-5017 31 12 two two NUM cana-5017 31 13 matrices matrix NOUN cana-5017 31 14 namely namely ADV cana-5017 31 15 fundamental fundamental ADJ cana-5017 31 16 metric metric ADJ cana-5017 31 17 and and CCONJ cana-5017 31 18 flat flat ADJ cana-5017 31 19 metric metric NOUN cana-5017 31 20 . . PUNCT cana-5017 32 1 the the DET cana-5017 32 2 metric metric ADJ cana-5017 32 3 tensor tensor NOUN cana-5017 32 4 𝑔𝑖𝑗 𝑔𝑖𝑗 NOUN cana-5017 32 5 is be AUX cana-5017 32 6 the the DET cana-5017 32 7 riemannian riemannian ADJ cana-5017 32 8 metric metric ADJ cana-5017 32 9 tensor tensor NOUN cana-5017 32 10 depicts depict VERB cana-5017 32 11 the the DET cana-5017 32 12 gravitational gravitational ADJ cana-5017 32 13 potential potential NOUN cana-5017 32 14 whereas whereas SCONJ cana-5017 32 15 the the DET cana-5017 32 16 metric metric ADJ cana-5017 32 17 tensor tensor NOUN cana-5017 32 18 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5017 32 19 is be AUX cana-5017 32 20 background background NOUN cana-5017 32 21 metric metric ADJ cana-5017 32 22 tensor tensor NOUN cana-5017 32 23 depicts depict VERB cana-5017 32 24 the the DET cana-5017 32 25 inertial inertial ADJ cana-5017 32 26 forces force NOUN cana-5017 32 27 related relate VERB cana-5017 32 28 to to ADP cana-5017 32 29 the the DET cana-5017 32 30 speed speed NOUN cana-5017 32 31 increase increase NOUN cana-5017 32 32 of of ADP cana-5017 32 33 the the DET cana-5017 32 34 reference reference NOUN cana-5017 32 35 frame frame NOUN cana-5017 32 36 and and CCONJ cana-5017 32 37 it it PRON cana-5017 32 38 has have VERB cana-5017 32 39 no no DET cana-5017 32 40 direct direct ADJ cana-5017 32 41 actual actual ADJ cana-5017 32 42 importance importance NOUN cana-5017 32 43 except except SCONJ cana-5017 32 44 for for ADP cana-5017 32 45 shows show NOUN cana-5017 32 46 up up ADP cana-5017 32 47 in in ADP cana-5017 32 48 the the DET cana-5017 32 49 field field NOUN cana-5017 32 50 equation equation NOUN cana-5017 32 51 . . PUNCT cana-5017 33 1 the the DET cana-5017 33 2 gravitational gravitational ADJ cana-5017 33 3 potential potential NOUN cana-5017 33 4 represented represent VERB cana-5017 33 5 by by ADP cana-5017 33 6 the the DET cana-5017 33 7 metric metric ADJ cana-5017 33 8 tensor tensor NOUN cana-5017 33 9 𝑔𝑖𝑗is 𝑔𝑖𝑗is NOUN cana-5017 33 10 not not PART cana-5017 33 11 fixed fix VERB cana-5017 33 12 by by ADP cana-5017 33 13 the the DET cana-5017 33 14 field field NOUN cana-5017 33 15 equation equation NOUN cana-5017 33 16 or or CCONJ cana-5017 33 17 by by ADP cana-5017 33 18 interactions interaction NOUN cana-5017 33 19 between between ADP cana-5017 33 20 matter matter NOUN cana-5017 33 21 and and CCONJ cana-5017 33 22 gravity gravity NOUN cana-5017 33 23 . . PUNCT cana-5017 34 1 in in ADP cana-5017 34 2 this this DET cana-5017 34 3 way way NOUN cana-5017 34 4 , , PUNCT cana-5017 34 5 the the DET cana-5017 34 6 flat flat ADJ cana-5017 34 7 spacetime spacetime NOUN cana-5017 34 8 metric metric ADJ cana-5017 34 9 collaborates collaborate NOUN cana-5017 34 10 with with ADP cana-5017 34 11 the the DET cana-5017 34 12 riemannian riemannian ADJ cana-5017 34 13 metric metric NOUN cana-5017 34 14 yet yet ADV cana-5017 34 15 not not PART cana-5017 34 16 straightforwardly straightforwardly ADV cana-5017 34 17 with with ADP cana-5017 34 18 matter matter NOUN cana-5017 34 19 . . PUNCT cana-5017 35 1 without without ADP cana-5017 35 2 a a DET cana-5017 35 3 trace trace NOUN cana-5017 35 4 of of ADP cana-5017 35 5 matter matter NOUN cana-5017 35 6 , , PUNCT cana-5017 35 7 one one PRON cana-5017 35 8 would would AUX cana-5017 35 9 have have VERB cana-5017 35 10 𝑔𝑖𝑗= 𝑔𝑖𝑗= PROPN cana-5017 35 11 𝛾𝑖𝑗 𝛾𝑖𝑗 ADV cana-5017 35 12 fulfilling fulfil VERB cana-5017 35 13 the the DET cana-5017 35 14 standards standard NOUN cana-5017 35 15 covariance covariance NOUN cana-5017 35 16 as as ADV cana-5017 35 17 well well ADV cana-5017 35 18 as as ADP cana-5017 35 19 the the DET cana-5017 35 20 equivalence equivalence NOUN cana-5017 35 21 of of ADP cana-5017 35 22 the the DET cana-5017 35 23 development development NOUN cana-5017 35 24 of of ADP cana-5017 35 25 gr gr PROPN cana-5017 35 26 . . PUNCT cana-5017 36 1 in in ADP cana-5017 36 2 this this DET cana-5017 36 3 manner manner NOUN cana-5017 36 4 at at ADP cana-5017 36 5 each each DET cana-5017 36 6 point point NOUN cana-5017 36 7 of of ADP cana-5017 36 8 space space NOUN cana-5017 36 9 - - PUNCT cana-5017 36 10 time time NOUN cana-5017 36 11 in in ADP cana-5017 36 12 bimetric bimetric ADJ cana-5017 36 13 relativity relativity NOUN cana-5017 36 14 , , PUNCT cana-5017 36 15 there there PRON cana-5017 36 16 are be VERB cana-5017 36 17 two two NUM cana-5017 36 18 matrices matrix NOUN cana-5017 36 19 as as SCONJ cana-5017 36 20 follows follow VERB cana-5017 36 21 . . PUNCT cana-5017 37 1 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 37 2 = = SYM cana-5017 37 3 𝑔𝑖𝑗𝑑π‘₯𝑖𝑑π‘₯𝑗 𝑔𝑖𝑗𝑑π‘₯𝑖𝑑π‘₯𝑗 VERB cana-5017 37 4 ( ( PUNCT cana-5017 37 5 1 1 X cana-5017 37 6 ) ) PUNCT cana-5017 37 7 𝑑𝑛2 𝑑𝑛2 NOUN cana-5017 37 8 = = SYM cana-5017 37 9 𝛾𝑖𝑗𝑑π‘₯𝑖𝑑π‘₯𝑗 𝛾𝑖𝑗𝑑π‘₯𝑖𝑑π‘₯𝑗 X cana-5017 37 10 ( ( PUNCT cana-5017 37 11 2 2 X cana-5017 37 12 ) ) PUNCT cana-5017 37 13 the the DET cana-5017 37 14 bimetric bimetric ADJ cana-5017 37 15 theory theory NOUN cana-5017 37 16 of of ADP cana-5017 37 17 gravitation gravitation NOUN cana-5017 37 18 via via ADP cana-5017 37 19 rosen rosen PROPN cana-5017 37 20 's 's PART cana-5017 37 21 field field NOUN cana-5017 37 22 equations equation NOUN cana-5017 37 23 is be AUX cana-5017 37 24 𝑁𝑖 𝑁𝑖 PROPN cana-5017 37 25 𝑗 𝑗 PRON cana-5017 37 26 βˆ’ βˆ’ NUM cana-5017 37 27 1 1 NUM cana-5017 37 28 2 2 NUM cana-5017 37 29 𝑁𝛿𝑖 𝑁𝛿𝑖 NOUN cana-5017 37 30 𝑗 𝑗 NOUN cana-5017 37 31 βˆ’ βˆ’ PROPN cana-5017 38 1 𝛬𝑔𝑖 𝛬𝑔𝑖 PROPN cana-5017 38 2 𝑗 𝑗 PROPN cana-5017 38 3 = = PUNCT cana-5017 38 4 βˆ’8πœ‹π‘˜π‘‡π‘– βˆ’8πœ‹π‘˜π‘‡π‘– PROPN cana-5017 38 5 𝑗 𝑗 X cana-5017 38 6 ( ( PUNCT cana-5017 38 7 3 3 NUM cana-5017 38 8 ) ) PUNCT cana-5017 38 9 ( ( PUNCT cana-5017 38 10 ) ) PUNCT cana-5017 38 11 rpsi rpsi VERB cana-5017 38 12 sjprj sjprj NOUN cana-5017 38 13 i i PRON cana-5017 38 14 ggn ggn VERB cana-5017 38 15   NUM cana-5017 38 16 2 2 NUM cana-5017 38 17 1 1 NUM cana-5017 38 18 = = NOUN cana-5017 38 19 , , PUNCT cana-5017 38 20 here here ADV cana-5017 38 21 ( ( PUNCT cana-5017 38 22 ) ) PUNCT cana-5017 39 1 | | ADV cana-5017 39 2 denotes denote VERB cana-5017 39 3   NUM cana-5017 39 4 – – PUNCT cana-5017 39 5 covariant covariant ADJ cana-5017 39 6 derivative derivative NOUN cana-5017 39 7 and and CCONJ cana-5017 39 8 j j NOUN cana-5017 39 9 it it PRON cana-5017 39 10 represents represent VERB cana-5017 39 11 energy energy NOUN cana-5017 39 12 – – PUNCT cana-5017 39 13 momentum momentum NOUN cana-5017 39 14 tensor tensor NOUN cana-5017 39 15 . . PUNCT cana-5017 40 1 i i PRON cana-5017 40 2 inn inn PROPN cana-5017 41 1 = = PUNCT cana-5017 41 2 , , PUNCT cana-5017 41 3 π‘˜ π‘˜ X cana-5017 41 4 = = X cana-5017 41 5 βˆšπ‘” βˆšπ‘” X cana-5017 41 6 𝛾⁄ 𝛾⁄ PROPN cana-5017 41 7 together together ADV cana-5017 41 8 with𝑔 with𝑔 NOUN cana-5017 41 9 = = SYM cana-5017 41 10 π‘‘π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘›π‘‘(𝑔𝑖𝑗 π‘‘π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘›π‘‘(𝑔𝑖𝑗 NOUN cana-5017 41 11 ) ) PUNCT cana-5017 41 12 and and CCONJ cana-5017 41 13 𝛾 𝛾 X cana-5017 41 14 = = PUNCT cana-5017 41 15 π‘‘π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘›π‘‘ π‘‘π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘›π‘‘ PROPN cana-5017 41 16 ( ( PUNCT cana-5017 41 17 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5017 41 18 ) ) PUNCT cana-5017 41 19 . . PUNCT cana-5017 42 1 communications communication NOUN cana-5017 42 2 on on ADP cana-5017 42 3 applied apply VERB cana-5017 42 4 nonlinear nonlinear ADJ cana-5017 42 5 analysis analysis NOUN cana-5017 42 6 issn issn NOUN cana-5017 42 7 : : PUNCT cana-5017 42 8 1074 1074 NUM cana-5017 42 9 - - PUNCT cana-5017 42 10 133x 133x NUM cana-5017 42 11 vol vol NOUN cana-5017 42 12 31 31 NUM cana-5017 42 13 no no NOUN cana-5017 42 14 . . PUNCT cana-5017 43 1 8s 8s PROPN cana-5017 43 2 ( ( PUNCT cana-5017 43 3 2024 2024 NUM cana-5017 43 4 ) ) PUNCT cana-5017 43 5 913 913 NUM cana-5017 43 6 https://internationalpubls.com https://internationalpubls.com NUM cana-5017 43 7 numerous numerous ADJ cana-5017 43 8 specialists specialist NOUN cana-5017 43 9 have have AUX cana-5017 43 10 fostered foster VERB cana-5017 43 11 the the DET cana-5017 43 12 hypothesis hypothesis NOUN cana-5017 43 13 and and CCONJ cana-5017 43 14 examined examine VERB cana-5017 43 15 numerous numerous ADJ cana-5017 43 16 models model NOUN cana-5017 43 17 of of ADP cana-5017 43 18 the the DET cana-5017 43 19 cosmos cosmos PROPN cana-5017 43 20 , , PUNCT cana-5017 43 21 in in ADP cana-5017 43 22 btg btg NOUN cana-5017 43 23 and and CCONJ cana-5017 43 24 concentrated concentrate VERB cana-5017 43 25 on on ADP cana-5017 43 26 their their PRON cana-5017 43 27 way way NOUN cana-5017 43 28 of of ADP cana-5017 43 29 behaving behave VERB cana-5017 43 30 geometrically geometrically ADV cana-5017 43 31 as as ADV cana-5017 43 32 well well ADV cana-5017 43 33 as as ADP cana-5017 43 34 physically physically ADV cana-5017 43 35 and and CCONJ cana-5017 43 36 this this PRON cana-5017 43 37 was be AUX cana-5017 43 38 studied study VERB cana-5017 43 39 by by ADP cana-5017 43 40 karade karade NOUN cana-5017 43 41 et et PROPN cana-5017 43 42 al.(22 al.(22 PROPN cana-5017 43 43 ) ) PUNCT cana-5017 43 44 , , PUNCT cana-5017 43 45 reddy reddy PROPN cana-5017 43 46 et et PROPN cana-5017 43 47 al.(23 al.(23 NOUN cana-5017 43 48 ) ) PUNCT cana-5017 43 49 , , PUNCT cana-5017 43 50 gaikwad gaikwad NOUN cana-5017 43 51 et et PROPN cana-5017 43 52 al.(24 al.(24 PROPN cana-5017 43 53 ) ) PUNCT cana-5017 43 54 . . PUNCT cana-5017 44 1 in in ADP cana-5017 44 2 this this DET cana-5017 44 3 examination examination NOUN cana-5017 44 4 note note NOUN cana-5017 44 5 , , PUNCT cana-5017 44 6 we we PRON cana-5017 44 7 will will AUX cana-5017 44 8 focus focus VERB cana-5017 44 9 on on ADP cana-5017 44 10 the the DET cana-5017 44 11 locally locally ADV cana-5017 44 12 rotationally rotationally ADV cana-5017 44 13 symmetric symmetric ADJ cana-5017 44 14 bianchi bianchi NOUN cana-5017 44 15 type type NOUN cana-5017 44 16 - - PUNCT cana-5017 44 17 i i NOUN cana-5017 44 18 magnetized magnetize VERB cana-5017 44 19 dark dark ADJ cana-5017 44 20 energy energy NOUN cana-5017 44 21 cosmological cosmological ADJ cana-5017 44 22 model model NOUN cana-5017 44 23 in in ADP cana-5017 44 24 the the DET cana-5017 44 25 bimetric bimetric ADJ cana-5017 44 26 theory theory NOUN cana-5017 44 27 of of ADP cana-5017 44 28 gravity gravity NOUN cana-5017 44 29 ( ( PUNCT cana-5017 44 30 btg btg PROPN cana-5017 44 31 ) ) PUNCT cana-5017 44 32 since since SCONJ cana-5017 44 33 it it PRON cana-5017 44 34 has have VERB cana-5017 44 35 a a DET cana-5017 44 36 great great ADJ cana-5017 44 37 deal deal NOUN cana-5017 44 38 more more ADJ cana-5017 44 39 fidelity fidelity NOUN cana-5017 44 40 to to ADP cana-5017 44 41 the the DET cana-5017 44 42 physics physics NOUN cana-5017 44 43 of of ADP cana-5017 44 44 spatial spatial ADJ cana-5017 44 45 homogeneous homogeneous ADJ cana-5017 44 46 cosmology cosmology NOUN cana-5017 44 47 . . PUNCT cana-5017 45 1 according accord VERB cana-5017 45 2 to to ADP cana-5017 45 3 theories theory NOUN cana-5017 45 4 of of ADP cana-5017 45 5 gravitation gravitation NOUN cana-5017 45 6 , , PUNCT cana-5017 45 7 the the DET cana-5017 45 8 main main ADJ cana-5017 45 9 issue issue NOUN cana-5017 45 10 with with ADP cana-5017 45 11 the the DET cana-5017 45 12 advancement advancement NOUN cana-5017 45 13 of of ADP cana-5017 45 14 the the DET cana-5017 45 15 cosmos cosmos PROPN cana-5017 45 16 is be AUX cana-5017 45 17 focusing focus VERB cana-5017 45 18 on on ADP cana-5017 45 19 the the DET cana-5017 45 20 singularity singularity NOUN cana-5017 45 21 's 's PART cana-5017 45 22 situation situation NOUN cana-5017 45 23 and and CCONJ cana-5017 45 24 knowing know VERB cana-5017 45 25 its its PRON cana-5017 45 26 nature nature NOUN cana-5017 45 27 . . PUNCT cana-5017 46 1 rosen(20),(21 rosen(20),(21 X cana-5017 46 2 ) ) PUNCT cana-5017 46 3 joined join VERB cana-5017 46 4 the the DET cana-5017 46 5 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5017 46 6 along along ADV cana-5017 46 7 with with ADP cana-5017 46 8 𝑔𝑖𝑗 𝑔𝑖𝑗 NOUN cana-5017 46 9 to to PART cana-5017 46 10 keep keep VERB cana-5017 46 11 away away ADV cana-5017 46 12 from from ADP cana-5017 46 13 the the DET cana-5017 46 14 singularities singularity NOUN cana-5017 46 15 in in ADP cana-5017 46 16 his his PRON cana-5017 46 17 btg btg NOUN cana-5017 46 18 . . PUNCT cana-5017 47 1 any any DET cana-5017 47 2 actual actual ADJ cana-5017 47 3 hypothesis hypothesis NOUN cana-5017 47 4 should should AUX cana-5017 47 5 be be AUX cana-5017 47 6 released release VERB cana-5017 47 7 from from ADP cana-5017 47 8 singularity singularity NOUN cana-5017 47 9 since since SCONJ cana-5017 47 10 its its PRON cana-5017 47 11 presence presence NOUN cana-5017 47 12 suggests suggest VERB cana-5017 47 13 the the DET cana-5017 47 14 breakdown breakdown NOUN cana-5017 47 15 of of ADP cana-5017 47 16 the the DET cana-5017 47 17 rules rule NOUN cana-5017 47 18 propounded propound VERB cana-5017 47 19 by by ADP cana-5017 47 20 the the DET cana-5017 47 21 theory theory NOUN cana-5017 47 22 . . PUNCT cana-5017 48 1 this this PRON cana-5017 48 2 has have AUX cana-5017 48 3 led lead VERB cana-5017 48 4 to to ADP cana-5017 48 5 the the DET cana-5017 48 6 development development NOUN cana-5017 48 7 of of ADP cana-5017 48 8 the the DET cana-5017 48 9 bimetric bimetric ADJ cana-5017 48 10 theory theory NOUN cana-5017 48 11 of of ADP cana-5017 48 12 gravity gravity NOUN cana-5017 48 13 , , PUNCT cana-5017 48 14 which which PRON cana-5017 48 15 is be AUX cana-5017 48 16 now now ADV cana-5017 48 17 free free ADJ cana-5017 48 18 of of ADP cana-5017 48 19 singularities singularity NOUN cana-5017 48 20 . . PUNCT cana-5017 49 1 numerous numerous ADJ cana-5017 49 2 experts expert NOUN cana-5017 49 3 , , PUNCT cana-5017 49 4 including include VERB cana-5017 49 5 borkar borkar NOUN cana-5017 49 6 et et PROPN cana-5017 49 7 al.(22 al.(22 PROPN cana-5017 49 8 ) ) PUNCT cana-5017 49 9 , , PUNCT cana-5017 49 10 karade karade VERB cana-5017 49 11 et et NOUN cana-5017 49 12 al.(23 al.(23 NOUN cana-5017 49 13 ) ) PUNCT cana-5017 49 14 ) ) PUNCT cana-5017 49 15 , , PUNCT cana-5017 49 16 kruskal kruskal NOUN cana-5017 49 17 et et PROPN cana-5017 49 18 al.(24 al.(24 PROPN cana-5017 49 19 ) ) PUNCT cana-5017 49 20 , , PUNCT cana-5017 49 21 and and CCONJ cana-5017 49 22 so so ADV cana-5017 49 23 forth forth ADV cana-5017 49 24 in in ADP cana-5017 49 25 gr gr NOUN cana-5017 49 26 are be AUX cana-5017 49 27 focused focus VERB cana-5017 49 28 on on ADP cana-5017 49 29 it it PRON cana-5017 49 30 . . PUNCT cana-5017 50 1 there there PRON cana-5017 50 2 are be VERB cana-5017 50 3 two two NUM cana-5017 50 4 types type NOUN cana-5017 50 5 of of ADP cana-5017 50 6 singularity singularity NOUN cana-5017 50 7 one one NUM cana-5017 50 8 is be AUX cana-5017 50 9 removable removable ADJ cana-5017 50 10 and and CCONJ cana-5017 50 11 the the DET cana-5017 50 12 other other ADJ cana-5017 50 13 is be AUX cana-5017 50 14 non non ADJ cana-5017 50 15 - - ADJ cana-5017 50 16 removable removable ADJ cana-5017 50 17 . . PUNCT cana-5017 51 1 the the DET cana-5017 51 2 nonremovable nonremovable ADJ cana-5017 51 3 singularity singularity NOUN cana-5017 51 4 problem problem NOUN cana-5017 51 5 has have AUX cana-5017 51 6 attracted attract VERB cana-5017 51 7 the the DET cana-5017 51 8 attention attention NOUN cana-5017 51 9 of of ADP cana-5017 51 10 experts expert NOUN cana-5017 51 11 in in ADP cana-5017 51 12 several several ADJ cana-5017 51 13 gravitational gravitational ADJ cana-5017 51 14 theories theory NOUN cana-5017 51 15 studied study VERB cana-5017 51 16 by by ADP cana-5017 51 17 penrose penrose PROPN cana-5017 51 18 et et NOUN cana-5017 51 19 al.(25 al.(25 PROPN cana-5017 51 20 ) ) PUNCT cana-5017 51 21 , , PUNCT cana-5017 51 22 karade karade VERB cana-5017 51 23 et et PROPN cana-5017 51 24 al.(26 al.(26 PROPN cana-5017 51 25 ) ) PUNCT cana-5017 51 26 , , PUNCT cana-5017 51 27 borkar borkar NOUN cana-5017 51 28 et et NOUN cana-5017 51 29 al.(27 al.(27 NOUN cana-5017 51 30 ) ) PUNCT cana-5017 51 31 , , PUNCT cana-5017 51 32 pradhan pradhan PROPN cana-5017 51 33 et et PROPN cana-5017 51 34 al.(28 al.(28 PROPN cana-5017 51 35 ) ) PUNCT cana-5017 51 36 . . PUNCT cana-5017 52 1 to to PART cana-5017 52 2 depict depict VERB cana-5017 52 3 the the DET cana-5017 52 4 gravitational gravitational ADJ cana-5017 52 5 field field NOUN cana-5017 52 6 around around ADP cana-5017 52 7 large large ADJ cana-5017 52 8 things thing NOUN cana-5017 52 9 with with ADP cana-5017 52 10 singularities singularity NOUN cana-5017 52 11 , , PUNCT cana-5017 52 12 schwarzschild schwarzschild PROPN cana-5017 52 13 deduced deduce VERB cana-5017 52 14 an an DET cana-5017 52 15 alternative alternative ADJ cana-5017 52 16 arrangement arrangement NOUN cana-5017 52 17 for for ADP cana-5017 52 18 einstein einstein NOUN cana-5017 52 19 's 's PART cana-5017 52 20 vacuum vacuum PROPN cana-5017 52 21 spacetime spacetime PROPN cana-5017 52 22 field field NOUN cana-5017 52 23 equation equation NOUN cana-5017 52 24 borkar borkar VERB cana-5017 52 25 et et NOUN cana-5017 52 26 al.(27 al.(27 NOUN cana-5017 52 27 ) ) PUNCT cana-5017 52 28 . . PUNCT cana-5017 53 1 there there PRON cana-5017 53 2 is be VERB cana-5017 53 3 exactly exactly ADV cana-5017 53 4 one one NUM cana-5017 53 5 singularity singularity NOUN cana-5017 53 6 at at ADP cana-5017 53 7 r r NOUN cana-5017 53 8 = = SYM cana-5017 53 9 0 0 NUM cana-5017 53 10 in in ADP cana-5017 53 11 btg btg PROPN cana-5017 53 12 for for ADP cana-5017 53 13 circularly circularly ADJ cana-5017 53 14 symmetric symmetric ADJ cana-5017 53 15 static static ADJ cana-5017 53 16 spacetime spacetime NOUN cana-5017 53 17 in in ADP cana-5017 53 18 the the DET cana-5017 53 19 case case NOUN cana-5017 53 20 of of ADP cana-5017 53 21 emptiness emptiness NOUN cana-5017 53 22 , , PUNCT cana-5017 53 23 and and CCONJ cana-5017 53 24 it it PRON cana-5017 53 25 would would AUX cana-5017 53 26 disappear disappear VERB cana-5017 53 27 in in ADP cana-5017 53 28 the the DET cana-5017 53 29 unlikely unlikely ADJ cana-5017 53 30 event event NOUN cana-5017 53 31 that that PRON cana-5017 53 32 the the DET cana-5017 53 33 molecule molecule NOUN cana-5017 53 34 represented represent VERB cana-5017 53 35 by by ADP cana-5017 53 36 a a DET cana-5017 53 37 matter matter NOUN cana-5017 53 38 tensor tensor NOUN cana-5017 53 39 differs differ VERB cana-5017 53 40 from from ADP cana-5017 53 41 zero zero NUM cana-5017 53 42 in in ADP cana-5017 53 43 a a DET cana-5017 53 44 specific specific ADJ cana-5017 53 45 area area NOUN cana-5017 53 46 given give VERB cana-5017 53 47 by by ADP cana-5017 53 48 rosen(20),(21 rosen(20),(21 NOUN cana-5017 53 49 ) ) PUNCT cana-5017 53 50 . . PUNCT cana-5017 54 1 in in ADP cana-5017 54 2 this this DET cana-5017 54 3 work work NOUN cana-5017 54 4 , , PUNCT cana-5017 54 5 we we PRON cana-5017 54 6 study study VERB cana-5017 54 7 the the DET cana-5017 54 8 lrs lrs PROPN cana-5017 54 9 bianchi bianchi PROPN cana-5017 54 10 type type PROPN cana-5017 54 11 - - PUNCT cana-5017 54 12 i i NOUN cana-5017 54 13 magnetized magnetize VERB cana-5017 54 14 dark dark ADJ cana-5017 54 15 energy energy NOUN cana-5017 54 16 cosmological cosmological ADJ cana-5017 54 17 model model NOUN cana-5017 54 18 in in ADP cana-5017 54 19 btg btg NOUN cana-5017 54 20 by by ADP cana-5017 54 21 solving solve VERB cana-5017 54 22 rosen rosen PROPN cana-5017 54 23 ’s ’s PART cana-5017 54 24 equations equation NOUN cana-5017 54 25 and and CCONJ cana-5017 54 26 also also ADV cana-5017 54 27 study study VERB cana-5017 54 28 physical physical ADJ cana-5017 54 29 as as ADV cana-5017 54 30 well well ADV cana-5017 54 31 as as ADP cana-5017 54 32 geometrical geometrical ADJ cana-5017 54 33 significance significance NOUN cana-5017 54 34 . . PUNCT cana-5017 55 1 2 2 X cana-5017 55 2 . . NOUN cana-5017 55 3 line line NOUN cana-5017 55 4 element element PROPN cana-5017 55 5 & & CCONJ cana-5017 55 6 field field PROPN cana-5017 55 7 equations equation NOUN cana-5017 55 8 lrs lrs PROPN cana-5017 55 9 bianchi bianchi PROPN cana-5017 55 10 type type NOUN cana-5017 55 11 i i PRON cana-5017 55 12 space space NOUN cana-5017 55 13 - - PUNCT cana-5017 55 14 time time NOUN cana-5017 55 15 can can AUX cana-5017 55 16 be be AUX cana-5017 55 17 considered consider VERB cana-5017 55 18 as as ADP cana-5017 55 19 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 55 20 = = PUNCT cana-5017 55 21 βˆ’π‘‘π‘‘2 βˆ’π‘‘π‘‘2 PROPN cana-5017 55 22 + + CCONJ cana-5017 55 23 𝐴2𝑑π‘₯2 𝐴2𝑑π‘₯2 NOUN cana-5017 55 24 + + CCONJ cana-5017 55 25 𝐡2(𝑑𝑦2 𝐡2(𝑑𝑦2 PROPN cana-5017 55 26 + + CCONJ cana-5017 55 27 𝑑𝑧2 𝑑𝑧2 NOUN cana-5017 55 28 ) ) PUNCT cana-5017 55 29 ( ( PUNCT cana-5017 55 30 4 4 X cana-5017 55 31 ) ) PUNCT cana-5017 55 32 where where SCONJ cana-5017 55 33 a a PRON cana-5017 55 34 and and CCONJ cana-5017 55 35 b b NOUN cana-5017 55 36 rely rely NOUN cana-5017 55 37 upon upon SCONJ cana-5017 55 38 enormous enormous ADJ cana-5017 55 39 time time NOUN cana-5017 55 40 t t PROPN cana-5017 55 41 as as SCONJ cana-5017 55 42 it it PRON cana-5017 55 43 were be AUX cana-5017 55 44 . . PUNCT cana-5017 56 1 the the DET cana-5017 56 2 flat flat ADJ cana-5017 56 3 metric metric NOUN cana-5017 56 4 relating relate VERB cana-5017 56 5 to to ADP cana-5017 56 6 metric metric ADJ cana-5017 56 7 ( ( PUNCT cana-5017 56 8 4 4 NUM cana-5017 56 9 ) ) PUNCT cana-5017 56 10 is be AUX cana-5017 56 11 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 56 12 = = SYM cana-5017 56 13 βˆ’π‘‘π‘‘2 βˆ’π‘‘π‘‘2 PROPN cana-5017 56 14 + + NUM cana-5017 56 15 𝑑π‘₯2 𝑑π‘₯2 NOUN cana-5017 56 16 + + CCONJ cana-5017 56 17 𝑑𝑦2 𝑑𝑦2 X cana-5017 56 18 + + CCONJ cana-5017 56 19 𝑑𝑧2 𝑑𝑧2 NOUN cana-5017 56 20 ( ( PUNCT cana-5017 56 21 5 5 NUM cana-5017 56 22 ) ) PUNCT cana-5017 56 23 where where SCONJ cana-5017 56 24 , , PUNCT cana-5017 56 25 𝑇𝑗 𝑇𝑗 PROPN cana-5017 56 26 𝑖 𝑖 PROPN cana-5017 56 27 is be AUX cana-5017 56 28 energy energy NOUN cana-5017 56 29 - - PUNCT cana-5017 56 30 momentum momentum NOUN cana-5017 56 31 tensor tensor NOUN cana-5017 56 32 for for ADP cana-5017 56 33 a a DET cana-5017 56 34 cloud cloud ADJ cana-5017 56 35 string string NOUN cana-5017 56 36 with with ADP cana-5017 56 37 a a DET cana-5017 56 38 magnetic magnetic ADJ cana-5017 56 39 field field NOUN cana-5017 56 40 in in ADP cana-5017 56 41 the the DET cana-5017 56 42 presence presence NOUN cana-5017 56 43 of of ADP cana-5017 56 44 perfect perfect ADJ cana-5017 56 45 fluid fluid NOUN cana-5017 56 46 is be AUX cana-5017 56 47 given give VERB cana-5017 56 48 by by ADP cana-5017 56 49 𝑇𝑖 𝑇𝑖 PROPN cana-5017 56 50 𝑗 𝑗 PROPN cana-5017 56 51 = = PUNCT cana-5017 56 52 ( ( PUNCT cana-5017 56 53 𝜌 𝜌 X cana-5017 56 54 + + X cana-5017 56 55 𝑝)πœπ‘–πœ 𝑝)πœπ‘–πœ NOUN cana-5017 56 56 𝑗 𝑗 X cana-5017 57 1 + + X cana-5017 57 2 𝑝𝑔𝑖 𝑝𝑔𝑖 NOUN cana-5017 57 3 𝑗 𝑗 INTJ cana-5017 57 4 βˆ’ βˆ’ NOUN cana-5017 57 5 πœ†π‘₯𝑖π‘₯𝑗 πœ†π‘₯𝑖π‘₯𝑗 NOUN cana-5017 58 1 + + CCONJ cana-5017 58 2 𝐸𝑖 𝐸𝑖 PROPN cana-5017 58 3 𝑗 𝑗 X cana-5017 58 4 ( ( PUNCT cana-5017 58 5 6 6 NUM cana-5017 58 6 ) ) PUNCT cana-5017 58 7 πœπ‘–πœπ‘– πœπ‘–πœπ‘– NOUN cana-5017 58 8 = = SYM cana-5017 58 9 βˆ’π‘₯𝑖π‘₯𝑖 βˆ’π‘₯𝑖π‘₯𝑖 ADP cana-5017 58 10 = = PUNCT cana-5017 58 11 βˆ’1 βˆ’1 NOUN cana-5017 58 12 and and CCONJ cana-5017 58 13 πœπ‘–π‘₯𝑖 πœπ‘–π‘₯𝑖 NOUN cana-5017 59 1 = = NOUN cana-5017 59 2 0 0 NUM cana-5017 59 3 here here ADV cana-5017 59 4 , , PUNCT cana-5017 59 5 ρ ρ PROPN cana-5017 59 6 , , PUNCT cana-5017 59 7 Ξ» Ξ» PROPN cana-5017 59 8 , , PUNCT cana-5017 59 9 π‘₯𝑖 π‘₯𝑖 PROPN cana-5017 59 10 , , PUNCT cana-5017 59 11 πœπ‘– πœπ‘– PROPN cana-5017 59 12 is be AUX cana-5017 59 13 proper proper ADJ cana-5017 59 14 energy energy NOUN cana-5017 59 15 density density NOUN cana-5017 59 16 , , PUNCT cana-5017 59 17 string string NOUN cana-5017 59 18 tension tension NOUN cana-5017 59 19 density density NOUN cana-5017 59 20 , , PUNCT cana-5017 59 21 unit unit NOUN cana-5017 59 22 space space NOUN cana-5017 59 23 - - PUNCT cana-5017 59 24 like like ADJ cana-5017 59 25 vector vector NOUN cana-5017 59 26 unit unit NOUN cana-5017 59 27 time time NOUN cana-5017 59 28 - - PUNCT cana-5017 59 29 like like ADJ cana-5017 59 30 vector vector NOUN cana-5017 59 31 respectively respectively ADV cana-5017 59 32 . . PUNCT cana-5017 60 1 we we PRON cana-5017 60 2 choose choose VERB cana-5017 60 3 a a DET cana-5017 60 4 comoving comoving NOUN cana-5017 60 5 coordinate coordinate NOUN cana-5017 60 6 system system NOUN cana-5017 60 7 as as ADP cana-5017 60 8 πœπ‘– πœπ‘– NOUN cana-5017 60 9 = = SYM cana-5017 60 10 ( ( PUNCT cana-5017 60 11 0,0,0,1 0,0,0,1 NUM cana-5017 60 12 ) ) PUNCT cana-5017 60 13 ; ; PUNCT cana-5017 60 14 π‘₯𝑖 π‘₯𝑖 PROPN cana-5017 60 15 = = PUNCT cana-5017 60 16 ( ( PUNCT cana-5017 60 17 1 1 NUM cana-5017 60 18 𝐴 𝐴 PROPN cana-5017 60 19 , , PUNCT cana-5017 60 20 0,0,0 0,0,0 NUM cana-5017 60 21 ) ) PUNCT cana-5017 60 22 communications communication NOUN cana-5017 60 23 on on ADP cana-5017 60 24 applied apply VERB cana-5017 60 25 nonlinear nonlinear ADJ cana-5017 60 26 analysis analysis NOUN cana-5017 60 27 issn issn NOUN cana-5017 60 28 : : PUNCT cana-5017 60 29 1074 1074 NUM cana-5017 60 30 - - PUNCT cana-5017 60 31 133x 133x NUM cana-5017 60 32 vol vol NOUN cana-5017 60 33 31 31 NUM cana-5017 60 34 no no NOUN cana-5017 60 35 . . PUNCT cana-5017 61 1 8s 8s PROPN cana-5017 61 2 ( ( PUNCT cana-5017 61 3 2024 2024 NUM cana-5017 61 4 ) ) PUNCT cana-5017 61 5 914 914 NUM cana-5017 61 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 61 7 we we PRON cana-5017 61 8 consider consider VERB cana-5017 61 9 particle particle NOUN cana-5017 61 10 density density NOUN cana-5017 61 11 πœŒπ‘ πœŒπ‘ NOUN cana-5017 61 12 of of ADP cana-5017 61 13 configuration configuration NOUN cana-5017 61 14 as as ADP cana-5017 61 15 𝜌 𝜌 ADP cana-5017 61 16 = = SYM cana-5017 61 17 πœŒπ‘ πœŒπ‘ PROPN cana-5017 61 18 + + NOUN cana-5017 61 19 πœ† πœ† DET cana-5017 61 20 𝐸𝑖 𝐸𝑖 PROPN cana-5017 61 21 𝑗 𝑗 PROPN cana-5017 61 22 is be AUX cana-5017 61 23 the the DET cana-5017 61 24 electromagnetic electromagnetic ADJ cana-5017 61 25 field field NOUN cana-5017 61 26 defined define VERB cana-5017 61 27 as as ADP cana-5017 61 28 𝐸𝑖 𝐸𝑖 PROPN cana-5017 61 29 𝑗 𝑗 NOUN cana-5017 61 30 = = PUNCT cana-5017 61 31 οΏ½ οΏ½ NOUN cana-5017 61 32 Μ… Μ… NOUN cana-5017 61 33 οΏ½ οΏ½ NOUN cana-5017 62 1 [ [ X cana-5017 62 2 |β„Ž|2 |β„Ž|2 PROPN cana-5017 62 3 ( ( PUNCT cana-5017 62 4 πœπ‘–πœ πœπ‘–πœ PROPN cana-5017 62 5 𝑗 𝑗 PROPN cana-5017 62 6 + + ADJ cana-5017 62 7 1 1 NUM cana-5017 62 8 2 2 NUM cana-5017 62 9 𝑔𝑖 𝑔𝑖 NOUN cana-5017 62 10 𝑗 𝑗 NOUN cana-5017 62 11 ) ) PUNCT cana-5017 62 12 βˆ’ βˆ’ PROPN cana-5017 62 13 β„Žπ‘–β„Žπ‘— β„Žπ‘–β„Žπ‘— NOUN cana-5017 62 14 ] ] X cana-5017 62 15 ( ( PUNCT cana-5017 62 16 7 7 X cana-5017 62 17 ) ) PUNCT cana-5017 62 18 where where SCONJ cana-5017 62 19 πœ‡ πœ‡ ADV cana-5017 62 20 is be AUX cana-5017 62 21 the the DET cana-5017 62 22 magnetic magnetic ADJ cana-5017 62 23 permeability permeability NOUN cana-5017 62 24 and and CCONJ cana-5017 62 25 β„Žπ‘– β„Žπ‘– NOUN cana-5017 62 26 is be AUX cana-5017 62 27 the the DET cana-5017 62 28 magnetic magnetic ADJ cana-5017 62 29 flux flux NOUN cana-5017 62 30 vector vector NOUN cana-5017 62 31 characterized characterize VERB cana-5017 62 32 as as ADP cana-5017 62 33 β„Žπ‘– β„Žπ‘– NOUN cana-5017 62 34 = = SYM cana-5017 62 35 βˆšβˆ’π‘” βˆšβˆ’π‘” PROPN cana-5017 62 36 2πœ‡ 2πœ‡ NUM cana-5017 62 37 βˆˆπ‘–π‘—π‘˜π‘™ βˆˆπ‘–π‘—π‘˜π‘™ PROPN cana-5017 63 1 πΉπ‘˜π‘™πœπ‘— πΉπ‘˜π‘™πœπ‘— PROPN cana-5017 63 2 here here ADV cana-5017 63 3 πΉπ‘˜π‘™ πΉπ‘˜π‘™ PROPN cana-5017 63 4 and and CCONJ cana-5017 63 5 βˆˆπ’Šπ’‹π’Œπ’ βˆˆπ’Šπ’‹π’Œπ’ PROPN cana-5017 63 6 are be AUX cana-5017 63 7 electromagnetic electromagnetic ADJ cana-5017 63 8 field field NOUN cana-5017 63 9 tensor tensor NOUN cana-5017 63 10 and and CCONJ cana-5017 63 11 levi levi PROPN cana-5017 63 12 - - PUNCT cana-5017 63 13 cevita cevita PROPN cana-5017 63 14 tensor tensor NOUN cana-5017 63 15 density density NOUN cana-5017 63 16 respectively respectively ADV cana-5017 63 17 . . PUNCT cana-5017 64 1 we we PRON cana-5017 64 2 can can AUX cana-5017 64 3 write write VERB cana-5017 64 4 a a DET cana-5017 64 5 set set NOUN cana-5017 64 6 of of ADP cana-5017 64 7 maxwell maxwell PROPN cana-5017 64 8 ’s ’s PART cana-5017 64 9 equations equation NOUN cana-5017 64 10 as as ADP cana-5017 64 11 𝐹[𝑖𝑗,π‘˜ 𝐹[𝑖𝑗,π‘˜ NOUN cana-5017 64 12 ] ] PUNCT cana-5017 64 13 = = SYM cana-5017 64 14 0 0 NUM cana-5017 64 15 yield yield NOUN cana-5017 64 16 f23 f23 NOUN cana-5017 64 17 = = SYM cana-5017 64 18 h h PROPN cana-5017 64 19 ( ( PUNCT cana-5017 64 20 say say INTJ cana-5017 64 21 ) ) PUNCT cana-5017 64 22 = = VERB cana-5017 64 23 constant constant ADJ cana-5017 64 24 because because SCONJ cana-5017 64 25 it it PRON cana-5017 64 26 's be AUX cana-5017 64 27 believed believe VERB cana-5017 64 28 that that SCONJ cana-5017 64 29 electrical electrical ADJ cana-5017 64 30 conductivity conductivity NOUN cana-5017 64 31 never never ADV cana-5017 64 32 ends end VERB cana-5017 64 33 , , PUNCT cana-5017 64 34 so so ADV cana-5017 64 35 we we PRON cana-5017 64 36 have have VERB cana-5017 64 37 𝐹14 𝐹14 PROPN cana-5017 64 38 = = NOUN cana-5017 64 39 𝐹24 𝐹24 NOUN cana-5017 64 40 = = PUNCT cana-5017 65 1 𝐹34 𝐹34 NOUN cana-5017 65 2 = = PUNCT cana-5017 65 3 0 0 PUNCT cana-5017 65 4 the the DET cana-5017 65 5 one one NUM cana-5017 65 6 element element NOUN cana-5017 65 7 that that PRON cana-5017 65 8 does do AUX cana-5017 65 9 not not PART cana-5017 65 10 vanish vanish VERB cana-5017 65 11 of of ADP cana-5017 65 12 𝐹𝑖𝑗 𝐹𝑖𝑗 PROPN cana-5017 65 13 is be AUX cana-5017 65 14 𝐹23 𝐹23 VERB cana-5017 65 15 . . PUNCT cana-5017 66 1 so so SCONJ cana-5017 66 2 that that SCONJ cana-5017 66 3 , , PUNCT cana-5017 66 4 β„Ž1 β„Ž1 PROPN cana-5017 66 5 = = SYM cana-5017 66 6 𝐴𝐻 𝐴𝐻 PROPN cana-5017 66 7 πœ‡π΅2 πœ‡π΅2 PROPN cana-5017 66 8 and and CCONJ cana-5017 66 9 |β„Ž|2 |β„Ž|2 PROPN cana-5017 66 10 = = PUNCT cana-5017 66 11 𝐻2 𝐻2 NOUN cana-5017 66 12 πœ‡ πœ‡ ADP cana-5017 66 13 2 2 NUM cana-5017 66 14 𝐡4 𝐡4 NOUN cana-5017 66 15 the the DET cana-5017 66 16 electromagnetic electromagnetic ADJ cana-5017 66 17 field field NOUN cana-5017 66 18 's 's PART cana-5017 66 19 constituent constituent NOUN cana-5017 66 20 parts part NOUN cana-5017 66 21 𝐸𝑖 𝐸𝑖 PROPN cana-5017 66 22 𝑗 𝑗 NOUN cana-5017 66 23 are be AUX cana-5017 66 24 given give VERB cana-5017 66 25 by by ADP cana-5017 66 26 𝐸1 𝐸1 NOUN cana-5017 66 27 1 1 NUM cana-5017 66 28 = = SYM cana-5017 66 29 βˆ’πΈ2 βˆ’πΈ2 PROPN cana-5017 66 30 2 2 NUM cana-5017 66 31 = = SYM cana-5017 66 32 βˆ’πΈ3 βˆ’πΈ3 NOUN cana-5017 66 33 3 3 NUM cana-5017 66 34 = = NOUN cana-5017 66 35 𝐸4 𝐸4 NOUN cana-5017 66 36 4 4 NUM cana-5017 66 37 = = SYM cana-5017 66 38 βˆ’ βˆ’ NOUN cana-5017 66 39 𝐻2 𝐻2 ADV cana-5017 66 40 πœ‡ πœ‡ ADP cana-5017 66 41 2 2 NUM cana-5017 66 42 𝐡4 𝐡4 NOUN cana-5017 66 43 ( ( PUNCT cana-5017 66 44 8) 8) NUM cana-5017 66 45 equation equation NOUN cana-5017 66 46 ( ( PUNCT cana-5017 66 47 6 6 NUM cana-5017 66 48 ) ) PUNCT cana-5017 66 49 of of ADP cana-5017 66 50 energy energy NOUN cana-5017 66 51 - - PUNCT cana-5017 66 52 momentum momentum NOUN cana-5017 66 53 tensor tensor NOUN cana-5017 66 54 yield yield NOUN cana-5017 66 55 𝑇1 𝑇1 NOUN cana-5017 66 56 1 1 NUM cana-5017 66 57 = = SYM cana-5017 66 58 ( ( PUNCT cana-5017 66 59 𝑝 𝑝 PROPN cana-5017 66 60 βˆ’ βˆ’ NOUN cana-5017 66 61 πœ† πœ† PRON cana-5017 66 62 βˆ’ βˆ’ PROPN cana-5017 66 63 𝐻2 𝐻2 NOUN cana-5017 66 64 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 66 65 ) ) PUNCT cana-5017 66 66 , , PUNCT cana-5017 66 67 𝑇2 𝑇2 NOUN cana-5017 66 68 2 2 NUM cana-5017 66 69 = = SYM cana-5017 66 70 𝑇3 𝑇3 PROPN cana-5017 66 71 3 3 NUM cana-5017 66 72 = = SYM cana-5017 66 73 ( ( PUNCT cana-5017 66 74 𝑝 𝑝 NOUN cana-5017 66 75 + + CCONJ cana-5017 66 76 𝐻2 𝐻2 PROPN cana-5017 66 77 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 66 78 ) ) PUNCT cana-5017 66 79 , , PUNCT cana-5017 66 80 𝑇4 𝑇4 PROPN cana-5017 66 81 4 4 NUM cana-5017 66 82 = = SYM cana-5017 66 83 ( ( PUNCT cana-5017 66 84 βˆ’πœŒ βˆ’πœŒ PROPN cana-5017 66 85 βˆ’ βˆ’ PROPN cana-5017 66 86 𝐻2 𝐻2 PROPN cana-5017 66 87 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 66 88 ) ) PUNCT cana-5017 66 89 ( ( PUNCT cana-5017 66 90 9 9 NUM cana-5017 66 91 ) ) PUNCT cana-5017 66 92 for for ADP cana-5017 66 93 the the DET cana-5017 66 94 metric metric ADJ cana-5017 66 95 ( ( PUNCT cana-5017 66 96 4 4 NUM cana-5017 66 97 ) ) PUNCT cana-5017 66 98 and and CCONJ cana-5017 66 99 ( ( PUNCT cana-5017 66 100 5 5 X cana-5017 66 101 ) ) PUNCT cana-5017 66 102 using use VERB cana-5017 66 103 equation equation NOUN cana-5017 66 104 ( ( PUNCT cana-5017 66 105 9 9 NUM cana-5017 66 106 ) ) PUNCT cana-5017 66 107 rosen rosen PROPN cana-5017 66 108 ’s ’s PART cana-5017 66 109 field field NOUN cana-5017 66 110 equations equation NOUN cana-5017 66 111 ( ( PUNCT cana-5017 66 112 3 3 X cana-5017 66 113 ) ) PUNCT cana-5017 66 114 gives give VERB cana-5017 66 115 , , PUNCT cana-5017 66 116 βˆ’π΄44 βˆ’π΄44 PROPN cana-5017 66 117 𝐴 𝐴 PROPN cana-5017 66 118 + + CCONJ cana-5017 66 119 2𝐡44 2𝐡44 PROPN cana-5017 66 120 𝐡 𝐡 NOUN cana-5017 66 121 + + CCONJ cana-5017 66 122 𝐴4 𝐴4 PROPN cana-5017 66 123 2 2 NUM cana-5017 66 124 𝐴2 𝐴2 NOUN cana-5017 66 125 βˆ’ βˆ’ PROPN cana-5017 66 126 2𝐡4 2𝐡4 NUM cana-5017 66 127 2 2 NUM cana-5017 66 128 𝐡2 𝐡2 NOUN cana-5017 66 129 = = SYM cana-5017 66 130 16πœ‹π΄π΅2 16πœ‹π΄π΅2 NUM cana-5017 66 131 ( ( PUNCT cana-5017 66 132 βˆ’π‘ βˆ’π‘ VERB cana-5017 66 133 + + CCONJ cana-5017 66 134 πœ† πœ† NOUN cana-5017 66 135 + + CCONJ cana-5017 66 136 𝐻2 𝐻2 ADJ cana-5017 66 137 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 66 138 ) ) PUNCT cana-5017 67 1 βˆ’ βˆ’ PROPN cana-5017 67 2 2𝛬 2𝛬 NOUN cana-5017 67 3 ( ( PUNCT cana-5017 67 4 10 10 NUM cana-5017 67 5 ) ) PUNCT cana-5017 67 6 𝐴44 𝐴44 PROPN cana-5017 67 7 𝐴 𝐴 PROPN cana-5017 67 8 βˆ’ βˆ’ PROPN cana-5017 67 9 𝐴4 𝐴4 PROPN cana-5017 67 10 2 2 NUM cana-5017 67 11 𝐴2 𝐴2 NOUN cana-5017 67 12 = = SYM cana-5017 67 13 16πœ‹π΄π΅2 16πœ‹π΄π΅2 PROPN cana-5017 67 14 ( ( PUNCT cana-5017 67 15 βˆ’π‘ βˆ’π‘ VERB cana-5017 67 16 βˆ’ βˆ’ PROPN cana-5017 68 1 𝐻2 𝐻2 PROPN cana-5017 69 1 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 69 2 ) ) PUNCT cana-5017 70 1 βˆ’ βˆ’ PROPN cana-5017 70 2 2𝛬 2𝛬 NOUN cana-5017 70 3 ( ( PUNCT cana-5017 70 4 11 11 NUM cana-5017 70 5 ) ) PUNCT cana-5017 70 6 𝐴44 𝐴44 PROPN cana-5017 70 7 𝐴 𝐴 PROPN cana-5017 70 8 + + CCONJ cana-5017 70 9 2𝐡44 2𝐡44 PROPN cana-5017 70 10 𝐡 𝐡 NOUN cana-5017 70 11 βˆ’ βˆ’ NOUN cana-5017 70 12 𝐴4 𝐴4 PROPN cana-5017 70 13 2 2 NUM cana-5017 70 14 𝐴2 𝐴2 NOUN cana-5017 70 15 βˆ’ βˆ’ PROPN cana-5017 70 16 2𝐡4 2𝐡4 NUM cana-5017 70 17 2 2 NUM cana-5017 70 18 𝐡2 𝐡2 NOUN cana-5017 70 19 = = SYM cana-5017 70 20 16πœ‹π΄π΅2 16πœ‹π΄π΅2 NUM cana-5017 70 21 ( ( PUNCT cana-5017 70 22 𝜌 𝜌 X cana-5017 70 23 + + CCONJ cana-5017 70 24 𝐻2 𝐻2 PROPN cana-5017 70 25 2πœ‡π΅4 2πœ‡π΅4 NUM cana-5017 70 26 ) ) PUNCT cana-5017 70 27 βˆ’ βˆ’ PROPN cana-5017 70 28 2𝛬 2𝛬 NOUN cana-5017 70 29 ( ( PUNCT cana-5017 70 30 12 12 NUM cana-5017 70 31 ) ) PUNCT cana-5017 70 32 3 3 NUM cana-5017 70 33 . . PUNCT cana-5017 70 34 solution solution NOUN cana-5017 70 35 of of ADP cana-5017 70 36 field field NOUN cana-5017 70 37 equations equation NOUN cana-5017 70 38 with with ADP cana-5017 70 39 magnetic magnetic ADJ cana-5017 70 40 field field NOUN cana-5017 70 41 the the DET cana-5017 70 42 field field NOUN cana-5017 70 43 equation equation NOUN cana-5017 70 44 ( ( PUNCT cana-5017 70 45 10 10 NUM cana-5017 70 46 ) ) PUNCT cana-5017 70 47 ( ( PUNCT cana-5017 70 48 11 11 NUM cana-5017 70 49 ) ) PUNCT cana-5017 70 50 and and CCONJ cana-5017 70 51 ( ( PUNCT cana-5017 70 52 12 12 NUM cana-5017 70 53 ) ) PUNCT cana-5017 70 54 are be AUX cana-5017 70 55 the the DET cana-5017 70 56 three three NUM cana-5017 70 57 equations equation NOUN cana-5017 70 58 along along ADP cana-5017 70 59 with with ADP cana-5017 70 60 six six NUM cana-5017 70 61 unknowns unknown NOUN cana-5017 70 62 𝐴 𝐴 PROPN cana-5017 70 63 , , PUNCT cana-5017 70 64 b b PROPN cana-5017 70 65 , , PUNCT cana-5017 70 66 Ξ» Ξ» PROPN cana-5017 70 67 , , PUNCT cana-5017 70 68 πœ† πœ† NOUN cana-5017 70 69 , , PUNCT cana-5017 70 70 𝜌 𝜌 X cana-5017 70 71 and and CCONJ cana-5017 70 72 𝑝. 𝑝. VERB cana-5017 70 73 therefore therefore ADV cana-5017 70 74 , , PUNCT cana-5017 70 75 the the DET cana-5017 70 76 system system NOUN cana-5017 70 77 is be AUX cana-5017 70 78 initially initially ADV cana-5017 70 79 unknown unknown ADJ cana-5017 70 80 , , PUNCT cana-5017 70 81 and and CCONJ cana-5017 70 82 to to PART cana-5017 70 83 obtain obtain VERB cana-5017 70 84 the the DET cana-5017 70 85 system system NOUN cana-5017 70 86 's 's PART cana-5017 70 87 full full ADJ cana-5017 70 88 solution solution NOUN cana-5017 70 89 , , PUNCT cana-5017 70 90 we we PRON cana-5017 70 91 need need VERB cana-5017 70 92 three three NUM cana-5017 70 93 more more ADJ cana-5017 70 94 equations equation NOUN cana-5017 70 95 . . PUNCT cana-5017 71 1 therefore therefore ADV cana-5017 71 2 , , PUNCT cana-5017 71 3 we we PRON cana-5017 71 4 supposed suppose VERB cana-5017 71 5 that that DET cana-5017 71 6 scalar scalar ADJ cana-5017 71 7 expansion expansion NOUN cana-5017 71 8 πœƒ πœƒ NOUN cana-5017 71 9 is be AUX cana-5017 71 10 directly directly ADV cana-5017 71 11 proportional proportional ADJ cana-5017 71 12 to to PART cana-5017 71 13 share share VERB cana-5017 71 14 𝜎. 𝜎. ADJ cana-5017 71 15 communications communication NOUN cana-5017 71 16 on on ADP cana-5017 71 17 applied apply VERB cana-5017 71 18 nonlinear nonlinear ADJ cana-5017 71 19 analysis analysis NOUN cana-5017 71 20 issn issn NOUN cana-5017 71 21 : : PUNCT cana-5017 71 22 1074 1074 NUM cana-5017 71 23 - - PUNCT cana-5017 71 24 133x 133x NUM cana-5017 71 25 vol vol NOUN cana-5017 71 26 31 31 NUM cana-5017 71 27 no no NOUN cana-5017 71 28 . . PUNCT cana-5017 72 1 8s 8s PROPN cana-5017 72 2 ( ( PUNCT cana-5017 72 3 2024 2024 NUM cana-5017 72 4 ) ) PUNCT cana-5017 72 5 915 915 NUM cana-5017 72 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 72 7 𝛒 𝛒 NOUN cana-5017 72 8 = = SYM cana-5017 73 1 𝛣𝑛 𝛣𝑛 ADP cana-5017 73 2 and and CCONJ cana-5017 73 3 𝛬 𝛬 X cana-5017 73 4 = = NOUN cana-5017 73 5 𝛼 𝛼 VERB cana-5017 73 6 𝛒𝛣2 𝛒𝛣2 PROPN cana-5017 73 7 under under ADP cana-5017 73 8 the the DET cana-5017 73 9 two two NUM cana-5017 73 10 scenarios scenario NOUN cana-5017 73 11 listed list VERB cana-5017 73 12 above above ADV cana-5017 73 13 , , PUNCT cana-5017 73 14 we we PRON cana-5017 73 15 assume assume VERB cana-5017 73 16 the the DET cana-5017 73 17 following follow VERB cana-5017 73 18 cases case NOUN cana-5017 73 19 : : PUNCT cana-5017 73 20 ( ( PUNCT cana-5017 73 21 i i NOUN cana-5017 73 22 ) ) PUNCT cana-5017 73 23 𝜌 𝜌 ADP cana-5017 73 24 + + X cana-5017 73 25 πœ† πœ† X cana-5017 73 26 = = SYM cana-5017 73 27 0 0 NUM cana-5017 73 28 and and CCONJ cana-5017 73 29 ( ( PUNCT cana-5017 73 30 ii ii NOUN cana-5017 73 31 ) ) PUNCT cana-5017 73 32 𝜌 𝜌 ADP cana-5017 73 33 βˆ’ βˆ’ PROPN cana-5017 73 34 πœ† πœ† SYM cana-5017 73 35 = = SYM cana-5017 73 36 0 0 NUM cana-5017 73 37 ( ( PUNCT cana-5017 73 38 13 13 NUM cana-5017 73 39 ) ) PUNCT cana-5017 73 40 case case NOUN cana-5017 74 1 i i PRON cana-5017 74 2 : : PUNCT cana-5017 74 3 𝜌 𝜌 X cana-5017 74 4 + + CCONJ cana-5017 74 5 πœ† πœ† X cana-5017 74 6 = = SYM cana-5017 74 7 0 0 NUM cana-5017 74 8 after after ADP cana-5017 74 9 adding add VERB cana-5017 74 10 equations equation NOUN cana-5017 74 11 ( ( PUNCT cana-5017 74 12 10 10 NUM cana-5017 74 13 ) ) PUNCT cana-5017 74 14 and and CCONJ cana-5017 74 15 ( ( PUNCT cana-5017 74 16 12 12 NUM cana-5017 74 17 ) ) PUNCT cana-5017 74 18 we we PRON cana-5017 74 19 get get VERB cana-5017 74 20 4𝐡44 4𝐡44 NUM cana-5017 74 21 𝐡 𝐡 NOUN cana-5017 74 22 βˆ’ βˆ’ NOUN cana-5017 74 23 4𝐡4 4𝐡4 NUM cana-5017 74 24 2 2 NUM cana-5017 74 25 𝐡2 𝐡2 NOUN cana-5017 74 26 = = SYM cana-5017 74 27 16πœ‹π΄π΅2 16πœ‹π΄π΅2 NUM cana-5017 74 28 ( ( PUNCT cana-5017 74 29 βˆ’π‘ βˆ’π‘ VERB cana-5017 74 30 + + CCONJ cana-5017 74 31 𝐻2 𝐻2 ADJ cana-5017 74 32 πœ‡π΅4 πœ‡π΅4 NOUN cana-5017 74 33 ) ) PUNCT cana-5017 74 34 βˆ’ βˆ’ PROPN cana-5017 74 35 4𝛬 4𝛬 NOUN cana-5017 74 36 ( ( PUNCT cana-5017 74 37 14 14 NUM cana-5017 74 38 ) ) PUNCT cana-5017 74 39 using use VERB cana-5017 74 40 equations equation NOUN cana-5017 74 41 ( ( PUNCT cana-5017 74 42 13 13 NUM cana-5017 74 43 ) ) PUNCT cana-5017 74 44 and and CCONJ cana-5017 74 45 ( ( PUNCT cana-5017 74 46 11 11 NUM cana-5017 74 47 ) ) PUNCT cana-5017 74 48 in in ADP cana-5017 74 49 equation equation NOUN cana-5017 74 50 ( ( PUNCT cana-5017 74 51 14 14 NUM cana-5017 74 52 ) ) PUNCT cana-5017 74 53 we we PRON cana-5017 74 54 get get VERB cana-5017 74 55 𝐡44 𝐡44 PROPN cana-5017 74 56 𝐡 𝐡 PROPN cana-5017 74 57 βˆ’ βˆ’ NOUN cana-5017 74 58 𝐡4 𝐡4 NOUN cana-5017 74 59 2 2 NUM cana-5017 74 60 𝐡2 𝐡2 NOUN cana-5017 74 61 = = SYM cana-5017 75 1 48πœ‹π›«π›£π‘›βˆ’2 48πœ‹π›«π›£π‘›βˆ’2 NUM cana-5017 75 2 4βˆ’π‘› 4βˆ’π‘› NUM cana-5017 76 1 βˆ’ βˆ’ NUM cana-5017 76 2 2𝛼 2𝛼 PROPN cana-5017 76 3 ( ( PUNCT cana-5017 76 4 4βˆ’π‘›)𝛣𝑛+2 4βˆ’π‘›)𝛣𝑛+2 NUM cana-5017 76 5 ( ( PUNCT cana-5017 76 6 15 15 NUM cana-5017 76 7 ) ) PUNCT cana-5017 76 8 on on ADP cana-5017 76 9 putting put VERB cana-5017 76 10 𝐡4 𝐡4 NOUN cana-5017 76 11 = = SYM cana-5017 76 12 𝑓(𝐡 𝑓(𝐡 X cana-5017 76 13 ) ) PUNCT cana-5017 76 14 and and CCONJ cana-5017 76 15 𝐡44 𝐡44 PROPN cana-5017 76 16 = = SYM cana-5017 76 17 𝑓𝑓′ 𝑓𝑓′ NOUN cana-5017 76 18 in in ADP cana-5017 76 19 equation equation NOUN cana-5017 76 20 ( ( PUNCT cana-5017 76 21 15 15 NUM cana-5017 76 22 ) ) PUNCT cana-5017 76 23 we we PRON cana-5017 76 24 obtain obtain VERB cana-5017 76 25 𝑑𝑓2 𝑑𝑓2 NOUN cana-5017 76 26 𝑑𝐡 𝑑𝐡 NOUN cana-5017 77 1 βˆ’ βˆ’ PROPN cana-5017 77 2 2𝑓2 2𝑓2 NUM cana-5017 77 3 𝐡 𝐡 NOUN cana-5017 77 4 = = SYM cana-5017 77 5 96πœ‹π›«π΅π‘›βˆ’1 96πœ‹π›«π΅π‘›βˆ’1 NUM cana-5017 77 6 4βˆ’π‘› 4βˆ’π‘› NUM cana-5017 78 1 βˆ’ βˆ’ PROPN cana-5017 78 2 4𝛼 4𝛼 NOUN cana-5017 78 3 ( ( PUNCT cana-5017 78 4 4βˆ’π‘›)𝐡𝑛+1 4βˆ’π‘›)𝐡𝑛+1 NUM cana-5017 78 5 ( ( PUNCT cana-5017 78 6 16 16 NUM cana-5017 78 7 ) ) PUNCT cana-5017 78 8 on on ADP cana-5017 78 9 integration integration NOUN cana-5017 78 10 , , PUNCT cana-5017 78 11 equation equation NOUN cana-5017 78 12 ( ( PUNCT cana-5017 78 13 16 16 NUM cana-5017 78 14 ) ) PUNCT cana-5017 78 15 leads lead VERB cana-5017 78 16 to to ADP cana-5017 78 17 𝑓2 𝑓2 NOUN cana-5017 78 18 = = SYM cana-5017 78 19 96πœ‹π›«π΅π‘› 96πœ‹π›«π΅π‘› NOUN cana-5017 78 20 ( ( PUNCT cana-5017 78 21 4βˆ’π‘›)(π‘›βˆ’2 4βˆ’π‘›)(π‘›βˆ’2 NUM cana-5017 78 22 ) ) PUNCT cana-5017 78 23 + + NUM cana-5017 78 24 4𝛼 4𝛼 NOUN cana-5017 78 25 ( ( PUNCT cana-5017 78 26 4βˆ’π‘›)(𝑛+2)𝐡𝑛 4βˆ’π‘›)(𝑛+2)𝐡𝑛 NUM cana-5017 78 27 + + CCONJ cana-5017 78 28 𝑀𝐡2 𝑀𝐡2 PROPN cana-5017 78 29 ( ( PUNCT cana-5017 78 30 17 17 NUM cana-5017 78 31 ) ) PUNCT cana-5017 78 32 here here ADV cana-5017 78 33 𝑀 𝑀 PROPN cana-5017 78 34 is be AUX cana-5017 78 35 the the DET cana-5017 78 36 integration integration NOUN cana-5017 78 37 constant constant ADJ cana-5017 78 38 . . PUNCT cana-5017 79 1 from from ADP cana-5017 79 2 ( ( PUNCT cana-5017 79 3 17 17 NUM cana-5017 79 4 ) ) PUNCT cana-5017 79 5 , , PUNCT cana-5017 79 6 we we PRON cana-5017 79 7 get get VERB cana-5017 79 8 ∫ ∫ PROPN cana-5017 79 9 𝑑𝐡 𝑑𝐡 NOUN cana-5017 79 10 √ √ ADP cana-5017 79 11 96πœ‹π›«π΅π‘› 96πœ‹π›«π΅π‘› NUM cana-5017 79 12 ( ( PUNCT cana-5017 79 13 4βˆ’π‘›)(π‘›βˆ’2 4βˆ’π‘›)(π‘›βˆ’2 NUM cana-5017 79 14 ) ) PUNCT cana-5017 80 1 + + NUM cana-5017 80 2 4𝛼 4𝛼 NOUN cana-5017 80 3 ( ( PUNCT cana-5017 80 4 4βˆ’π‘›)(𝑛+2)𝐡𝑛+𝑀𝐡2 4βˆ’π‘›)(𝑛+2)𝐡𝑛+𝑀𝐡2 NUM cana-5017 80 5 = = SYM cana-5017 80 6 𝑑 𝑑 PROPN cana-5017 80 7 + + X cana-5017 80 8 𝑉 𝑉 PROPN cana-5017 80 9 ( ( PUNCT cana-5017 80 10 18 18 NUM cana-5017 80 11 ) ) PUNCT cana-5017 80 12 here here ADV cana-5017 80 13 𝑉 𝑉 PROPN cana-5017 80 14 is be AUX cana-5017 80 15 the the DET cana-5017 80 16 constant constant ADJ cana-5017 80 17 of of ADP cana-5017 80 18 integration integration NOUN cana-5017 80 19 . . PUNCT cana-5017 81 1 the the DET cana-5017 81 2 value value NOUN cana-5017 81 3 of of ADP cana-5017 81 4 b b NOUN cana-5017 81 5 can can AUX cana-5017 81 6 be be AUX cana-5017 81 7 calculated calculate VERB cana-5017 81 8 from from ADP cana-5017 81 9 ( ( PUNCT cana-5017 81 10 18 18 NUM cana-5017 81 11 ) ) PUNCT cana-5017 81 12 . . PUNCT cana-5017 82 1 through through ADP cana-5017 82 2 the the DET cana-5017 82 3 proper proper ADJ cana-5017 82 4 coordinate coordinate NOUN cana-5017 82 5 transformation transformation NOUN cana-5017 82 6 𝐡 𝐡 NOUN cana-5017 82 7 = = SYM cana-5017 82 8 𝑇 𝑇 PROPN cana-5017 82 9 , , PUNCT cana-5017 82 10 π‘₯ π‘₯ NOUN cana-5017 82 11 = = SYM cana-5017 82 12 𝑋 𝑋 PROPN cana-5017 82 13 , , PUNCT cana-5017 82 14 𝑦 𝑦 NOUN cana-5017 82 15 = = SYM cana-5017 82 16 π‘Œ π‘Œ PROPN cana-5017 82 17 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ cana-5017 82 18 𝑧 𝑧 NOUN cana-5017 82 19 = = PUNCT cana-5017 82 20 𝑍 𝑍 ADP cana-5017 82 21 metric metric NOUN cana-5017 82 22 ( ( PUNCT cana-5017 82 23 4 4 NUM cana-5017 82 24 ) ) PUNCT cana-5017 82 25 becomes become VERB cana-5017 82 26 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 82 27 = = SYM cana-5017 82 28 βˆ’ βˆ’ PROPN cana-5017 82 29 𝑑𝑇2 𝑑𝑇2 PROPN cana-5017 82 30 [ [ PUNCT cana-5017 82 31 96πœ‹π›«π‘‡π‘› 96πœ‹π›«π‘‡π‘› NOUN cana-5017 82 32 ( ( PUNCT cana-5017 82 33 4βˆ’π‘›)(π‘›βˆ’2 4βˆ’π‘›)(π‘›βˆ’2 NUM cana-5017 82 34 ) ) PUNCT cana-5017 83 1 + + NUM cana-5017 83 2 4𝛼 4𝛼 NOUN cana-5017 83 3 ( ( PUNCT cana-5017 83 4 4βˆ’π‘›)(𝑛+2)𝑇𝑛+𝑀𝑇2 4βˆ’π‘›)(𝑛+2)𝑇𝑛+𝑀𝑇2 NOUN cana-5017 83 5 ] ] X cana-5017 83 6 + + CCONJ cana-5017 83 7 𝑇2𝑛𝑑𝑋2 𝑇2𝑛𝑑𝑋2 NUM cana-5017 83 8 + + CCONJ cana-5017 83 9 𝑇2(π‘‘π‘Œ2 𝑇2(π‘‘π‘Œ2 NOUN cana-5017 83 10 + + CCONJ cana-5017 83 11 𝑑𝑍2 𝑑𝑍2 PROPN cana-5017 83 12 ) ) PUNCT cana-5017 83 13 ( ( PUNCT cana-5017 83 14 19 19 NUM cana-5017 83 15 ) ) PUNCT cana-5017 83 16 case case NOUN cana-5017 83 17 ii ii PROPN cana-5017 83 18 : : PUNCT cana-5017 83 19 𝜌 𝜌 X cana-5017 83 20 βˆ’ βˆ’ PROPN cana-5017 83 21 πœ† πœ† SYM cana-5017 83 22 = = NOUN cana-5017 83 23 0 0 NUM cana-5017 83 24 on on ADP cana-5017 83 25 subtracting subtract VERB cana-5017 83 26 equations equation NOUN cana-5017 83 27 ( ( PUNCT cana-5017 83 28 10 10 NUM cana-5017 83 29 ) ) PUNCT cana-5017 83 30 from from ADP cana-5017 83 31 ( ( PUNCT cana-5017 83 32 12 12 NUM cana-5017 83 33 ) ) PUNCT cana-5017 83 34 we we PRON cana-5017 83 35 get get VERB cana-5017 83 36 , , PUNCT cana-5017 83 37 2 2 NUM cana-5017 83 38 [ [ PUNCT cana-5017 83 39 𝛒44 𝛒44 VERB cana-5017 83 40 𝛒 𝛒 NOUN cana-5017 83 41 βˆ’ βˆ’ ADP cana-5017 83 42 𝛒4 𝛒4 PROPN cana-5017 83 43 2 2 NUM cana-5017 83 44 𝛒2 𝛒2 NOUN cana-5017 83 45 ] ] PUNCT cana-5017 83 46 = = SYM cana-5017 83 47 16πœ‹π›’π›£2𝛲 16πœ‹π›’π›£2𝛲 NUM cana-5017 83 48 ( ( PUNCT cana-5017 83 49 20 20 NUM cana-5017 83 50 ) ) PUNCT cana-5017 83 51 using use VERB cana-5017 83 52 equations equation NOUN cana-5017 83 53 ( ( PUNCT cana-5017 83 54 13 13 NUM cana-5017 83 55 ) ) PUNCT cana-5017 83 56 and and CCONJ cana-5017 83 57 ( ( PUNCT cana-5017 83 58 11 11 NUM cana-5017 83 59 ) ) PUNCT cana-5017 83 60 in in ADP cana-5017 83 61 equation equation NOUN cana-5017 83 62 ( ( PUNCT cana-5017 83 63 20 20 NUM cana-5017 83 64 ) ) PUNCT cana-5017 83 65 we we PRON cana-5017 83 66 get get VERB cana-5017 83 67 𝛣44 𝛣44 ADP cana-5017 83 68 βˆ’ βˆ’ NOUN cana-5017 83 69 𝛣4 𝛣4 NOUN cana-5017 83 70 2 2 NUM cana-5017 83 71 𝛣 𝛣 NOUN cana-5017 83 72 = = SYM cana-5017 83 73 βˆ’16πœ‹π›«π›£π‘›βˆ’1 βˆ’16πœ‹π›«π›£π‘›βˆ’1 PROPN cana-5017 83 74 3𝑛 3𝑛 NUM cana-5017 83 75 βˆ’ βˆ’ PROPN cana-5017 83 76 2𝛼 2𝛼 PROPN cana-5017 83 77 3𝑛𝛣𝑛+1 3𝑛𝛣𝑛+1 PROPN cana-5017 83 78 ( ( PUNCT cana-5017 83 79 21 21 NUM cana-5017 83 80 ) ) PUNCT cana-5017 83 81 on on ADP cana-5017 83 82 putting put VERB cana-5017 83 83 𝐡4 𝐡4 NOUN cana-5017 83 84 = = SYM cana-5017 83 85 𝑓(𝐡 𝑓(𝐡 X cana-5017 83 86 ) ) PUNCT cana-5017 83 87 and and CCONJ cana-5017 83 88 𝐡44 𝐡44 PROPN cana-5017 83 89 = = PUNCT cana-5017 83 90 𝑓𝑓′in 𝑓𝑓′in PART cana-5017 83 91 equation equation NOUN cana-5017 83 92 ( ( PUNCT cana-5017 83 93 21 21 NUM cana-5017 83 94 ) ) PUNCT cana-5017 83 95 we we PRON cana-5017 83 96 obtain obtain VERB cana-5017 83 97 𝑑𝑓2 𝑑𝑓2 NOUN cana-5017 83 98 𝑑𝐡 𝑑𝐡 NOUN cana-5017 83 99 βˆ’ βˆ’ PROPN cana-5017 83 100 2𝑓2 2𝑓2 NUM cana-5017 83 101 𝐡 𝐡 NOUN cana-5017 83 102 = = SYM cana-5017 83 103 βˆ’32πœ‹π›«π›£π‘›βˆ’1 βˆ’32πœ‹π›«π›£π‘›βˆ’1 NOUN cana-5017 83 104 3𝑛 3𝑛 NUM cana-5017 83 105 βˆ’ βˆ’ NOUN cana-5017 83 106 4𝛼 4𝛼 NOUN cana-5017 83 107 3𝑛𝛣𝑛+1 3𝑛𝛣𝑛+1 PROPN cana-5017 83 108 ( ( PUNCT cana-5017 83 109 22 22 NUM cana-5017 83 110 ) ) PUNCT cana-5017 83 111 communications communication NOUN cana-5017 83 112 on on ADP cana-5017 83 113 applied apply VERB cana-5017 83 114 nonlinear nonlinear ADJ cana-5017 83 115 analysis analysis NOUN cana-5017 83 116 issn issn NOUN cana-5017 83 117 : : PUNCT cana-5017 83 118 1074 1074 NUM cana-5017 83 119 - - PUNCT cana-5017 83 120 133x 133x NUM cana-5017 83 121 vol vol NOUN cana-5017 83 122 31 31 NUM cana-5017 83 123 no no NOUN cana-5017 83 124 . . PUNCT cana-5017 84 1 8s 8s PROPN cana-5017 84 2 ( ( PUNCT cana-5017 84 3 2024 2024 NUM cana-5017 84 4 ) ) PUNCT cana-5017 84 5 916 916 NUM cana-5017 84 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 84 7 on on ADP cana-5017 84 8 integrating integrate VERB cana-5017 84 9 equation equation NOUN cana-5017 84 10 ( ( PUNCT cana-5017 84 11 22 22 NUM cana-5017 84 12 ) ) PUNCT cana-5017 84 13 we we PRON cana-5017 84 14 get get VERB cana-5017 84 15 , , PUNCT cana-5017 84 16 𝑓2 𝑓2 PROPN cana-5017 84 17 = = SYM cana-5017 84 18 βˆ’32πœ‹π›«π΅π‘› βˆ’32πœ‹π›«π΅π‘› NOUN cana-5017 84 19 3𝑛(π‘›βˆ’2 3𝑛(π‘›βˆ’2 NUM cana-5017 84 20 ) ) PUNCT cana-5017 85 1 + + NUM cana-5017 85 2 4𝛼 4𝛼 NOUN cana-5017 85 3 3𝑛(𝑛+2)𝐡𝑛 3𝑛(𝑛+2)𝐡𝑛 NUM cana-5017 85 4 + + CCONJ cana-5017 85 5 𝑁𝐡2 𝑁𝐡2 PROPN cana-5017 85 6 ( ( PUNCT cana-5017 85 7 23 23 NUM cana-5017 85 8 ) ) PUNCT cana-5017 85 9 here here ADV cana-5017 85 10 𝑁 𝑁 PROPN cana-5017 85 11 is be AUX cana-5017 85 12 the the DET cana-5017 85 13 constant constant ADJ cana-5017 85 14 of of ADP cana-5017 85 15 integration integration NOUN cana-5017 85 16 . . PUNCT cana-5017 86 1 ∫ ∫ PROPN cana-5017 86 2 𝑑𝐡 𝑑𝐡 PROPN cana-5017 86 3 √ √ PROPN cana-5017 86 4 βˆ’32πœ‹π›«π΅π‘› βˆ’32πœ‹π›«π΅π‘› PROPN cana-5017 86 5 3𝑛(π‘›βˆ’2 3𝑛(π‘›βˆ’2 NUM cana-5017 86 6 ) ) PUNCT cana-5017 87 1 + + NUM cana-5017 87 2 4𝛼 4𝛼 NOUN cana-5017 87 3 3𝑛(𝑛+2)𝐡𝑛+𝑁𝐡2 3𝑛(𝑛+2)𝐡𝑛+𝑁𝐡2 NUM cana-5017 87 4 = = SYM cana-5017 87 5 𝑑 𝑑 PROPN cana-5017 87 6 + + X cana-5017 87 7 π‘ˆ π‘ˆ PROPN cana-5017 87 8 ( ( PUNCT cana-5017 87 9 24 24 NUM cana-5017 87 10 ) ) PUNCT cana-5017 87 11 where where SCONJ cana-5017 87 12 π‘ˆ π‘ˆ PROPN cana-5017 87 13 is be AUX cana-5017 87 14 the the DET cana-5017 87 15 integration integration NOUN cana-5017 87 16 constant constant ADJ cana-5017 87 17 . . PUNCT cana-5017 88 1 the the DET cana-5017 88 2 value value NOUN cana-5017 88 3 of of ADP cana-5017 88 4 b b NOUN cana-5017 88 5 can can AUX cana-5017 88 6 be be AUX cana-5017 88 7 calculated calculate VERB cana-5017 88 8 from from ADP cana-5017 88 9 ( ( PUNCT cana-5017 88 10 24 24 NUM cana-5017 88 11 ) ) PUNCT cana-5017 88 12 through through ADP cana-5017 88 13 the the DET cana-5017 88 14 proper proper ADJ cana-5017 88 15 coordinate coordinate NOUN cana-5017 88 16 transformation transformation NOUN cana-5017 88 17 𝐡 𝐡 PROPN cana-5017 88 18 = = SYM cana-5017 88 19 𝑇 𝑇 PROPN cana-5017 88 20 , , PUNCT cana-5017 88 21 π‘₯ π‘₯ NOUN cana-5017 88 22 = = SYM cana-5017 88 23 𝑋 𝑋 PROPN cana-5017 88 24 , , PUNCT cana-5017 88 25 𝑦 𝑦 NOUN cana-5017 88 26 = = SYM cana-5017 88 27 π‘Œ π‘Œ PROPN cana-5017 88 28 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ cana-5017 88 29 𝑧 𝑧 NOUN cana-5017 88 30 = = PUNCT cana-5017 88 31 𝑍 𝑍 ADP cana-5017 88 32 metric metric ADJ cana-5017 88 33 ( ( PUNCT cana-5017 88 34 1 1 NUM cana-5017 88 35 ) ) PUNCT cana-5017 88 36 becomes become VERB cana-5017 88 37 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 88 38 = = SYM cana-5017 88 39 βˆ’ βˆ’ PROPN cana-5017 88 40 𝑑𝑇2 𝑑𝑇2 PROPN cana-5017 88 41 [ [ PUNCT cana-5017 88 42 βˆ’32πœ‹π›«π‘‡π‘› βˆ’32πœ‹π›«π‘‡π‘› NOUN cana-5017 88 43 3𝑛(π‘›βˆ’2 3𝑛(π‘›βˆ’2 NUM cana-5017 88 44 ) ) PUNCT cana-5017 89 1 + + NUM cana-5017 89 2 4𝛼 4𝛼 NOUN cana-5017 89 3 3𝑛(𝑛+2)𝑇𝑛+𝑁𝑇2 3𝑛(𝑛+2)𝑇𝑛+𝑁𝑇2 NUM cana-5017 89 4 ] ] X cana-5017 89 5 + + CCONJ cana-5017 89 6 𝑇2𝑛𝑑𝑋2 𝑇2𝑛𝑑𝑋2 NUM cana-5017 89 7 + + NUM cana-5017 89 8 𝑇2(π‘‘π‘Œ2 𝑇2(π‘‘π‘Œ2 NOUN cana-5017 89 9 + + CCONJ cana-5017 89 10 𝑑𝑍2 𝑑𝑍2 PROPN cana-5017 89 11 ) ) PUNCT cana-5017 89 12 ( ( PUNCT cana-5017 89 13 25 25 NUM cana-5017 89 14 ) ) PUNCT cana-5017 89 15 3.1 3.1 NUM cana-5017 89 16 geometrical geometrical ADJ cana-5017 89 17 and and CCONJ cana-5017 89 18 physical physical ADJ cana-5017 89 19 characteristics characteristic NOUN cana-5017 89 20 with with ADP cana-5017 89 21 magnetic magnetic ADJ cana-5017 89 22 field field NOUN cana-5017 89 23 for for ADP cana-5017 89 24 the the DET cana-5017 89 25 model model NOUN cana-5017 89 26 ( ( PUNCT cana-5017 89 27 19 19 NUM cana-5017 89 28 ) ) PUNCT cana-5017 89 29 all all DET cana-5017 89 30 the the DET cana-5017 89 31 physical physical ADJ cana-5017 89 32 quantities quantity NOUN cana-5017 89 33 are be AUX cana-5017 89 34 given give VERB cana-5017 89 35 by by ADP cana-5017 89 36 𝜌 𝜌 X cana-5017 89 37 = = PUNCT cana-5017 89 38 βˆ’πœ† βˆ’πœ† PROPN cana-5017 89 39 = = SYM cana-5017 89 40 𝛫(4𝑛+2 𝛫(4𝑛+2 PROPN cana-5017 89 41 ) ) PUNCT cana-5017 89 42 ( ( PUNCT cana-5017 89 43 4βˆ’π‘›)𝑇4 4βˆ’π‘›)𝑇4 NOUN cana-5017 89 44 βˆ’ βˆ’ NOUN cana-5017 89 45 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 NOUN cana-5017 89 46 ) ) PUNCT cana-5017 89 47 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NOUN cana-5017 89 48 ) ) PUNCT cana-5017 89 49 ( ( PUNCT cana-5017 89 50 26 26 NUM cana-5017 89 51 ) ) PUNCT cana-5017 89 52 πœŒπ‘ πœŒπ‘ NOUN cana-5017 89 53 = = ADJ cana-5017 89 54 2𝛫(4𝑛+2 2𝛫(4𝑛+2 NUM cana-5017 89 55 ) ) PUNCT cana-5017 89 56 ( ( PUNCT cana-5017 89 57 4βˆ’π‘›)𝑇4 4βˆ’π‘›)𝑇4 NOUN cana-5017 89 58 βˆ’ βˆ’ NOUN cana-5017 89 59 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 NOUN cana-5017 89 60 ) ) PUNCT cana-5017 89 61 2πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 2πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NUM cana-5017 89 62 ) ) PUNCT cana-5017 89 63 ( ( PUNCT cana-5017 89 64 27 27 NUM cana-5017 89 65 ) ) PUNCT cana-5017 89 66 𝛲 𝛲 NOUN cana-5017 89 67 = = SYM cana-5017 89 68 βˆ’(2𝑛+4)𝛫 βˆ’(2𝑛+4)𝛫 NOUN cana-5017 89 69 ( ( PUNCT cana-5017 89 70 4βˆ’π‘›)𝑇4 4βˆ’π‘›)𝑇4 NOUN cana-5017 89 71 + + CCONJ cana-5017 89 72 𝛼(π‘›βˆ’2 𝛼(π‘›βˆ’2 NOUN cana-5017 89 73 ) ) PUNCT cana-5017 89 74 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NUM cana-5017 89 75 ) ) PUNCT cana-5017 89 76 ( ( PUNCT cana-5017 89 77 28 28 NUM cana-5017 89 78 ) ) PUNCT cana-5017 89 79 πœƒ πœƒ NOUN cana-5017 89 80 = = PUNCT cana-5017 89 81 ( ( PUNCT cana-5017 89 82 𝑛 𝑛 PROPN cana-5017 89 83 + + NOUN cana-5017 89 84 2 2 NUM cana-5017 89 85 ) ) PUNCT cana-5017 89 86 [ [ PUNCT cana-5017 89 87 96πœ‹π›«π›΅π‘›βˆ’2 96πœ‹π›«π›΅π‘›βˆ’2 NOUN cana-5017 89 88 ( ( PUNCT cana-5017 89 89 4βˆ’π‘›)(π‘›βˆ’2 4βˆ’π‘›)(π‘›βˆ’2 NUM cana-5017 89 90 ) ) PUNCT cana-5017 90 1 + + NUM cana-5017 90 2 4𝛼 4𝛼 NOUN cana-5017 90 3 ( ( PUNCT cana-5017 90 4 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 NUM cana-5017 90 5 + + CCONJ cana-5017 90 6 𝑀 𝑀 PROPN cana-5017 90 7 ] ] PUNCT cana-5017 90 8 1 1 NUM cana-5017 90 9 2 2 NUM cana-5017 90 10 ( ( PUNCT cana-5017 90 11 29 29 NUM cana-5017 90 12 ) ) PUNCT cana-5017 90 13 𝜎 𝜎 NOUN cana-5017 90 14 = = SYM cana-5017 90 15 ( ( PUNCT cana-5017 90 16 π‘›βˆ’1 π‘›βˆ’1 NUM cana-5017 90 17 ) ) PUNCT cana-5017 90 18 √3 √3 PROPN cana-5017 90 19 [ [ PUNCT cana-5017 90 20 96πœ‹π›«π›΅π‘›βˆ’2 96πœ‹π›«π›΅π‘›βˆ’2 NOUN cana-5017 90 21 ( ( PUNCT cana-5017 90 22 4βˆ’π‘›)(π‘›βˆ’2 4βˆ’π‘›)(π‘›βˆ’2 NUM cana-5017 90 23 ) ) PUNCT cana-5017 91 1 + + NUM cana-5017 91 2 4𝛼 4𝛼 NOUN cana-5017 91 3 ( ( PUNCT cana-5017 91 4 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 NUM cana-5017 92 1 + + CCONJ cana-5017 92 2 𝑀 𝑀 PROPN cana-5017 92 3 ] ] PUNCT cana-5017 92 4 1 1 NUM cana-5017 92 5 2 2 NUM cana-5017 92 6 ( ( PUNCT cana-5017 92 7 30 30 NUM cana-5017 92 8 ) ) PUNCT cana-5017 92 9 communications communication NOUN cana-5017 92 10 on on ADP cana-5017 92 11 applied apply VERB cana-5017 92 12 nonlinear nonlinear ADJ cana-5017 92 13 analysis analysis NOUN cana-5017 92 14 issn issn NOUN cana-5017 92 15 : : PUNCT cana-5017 92 16 1074 1074 NUM cana-5017 92 17 - - PUNCT cana-5017 92 18 133x 133x NUM cana-5017 92 19 vol vol NOUN cana-5017 92 20 31 31 NUM cana-5017 92 21 no no NOUN cana-5017 92 22 . . PUNCT cana-5017 93 1 8s 8s PROPN cana-5017 93 2 ( ( PUNCT cana-5017 93 3 2024 2024 NUM cana-5017 93 4 ) ) PUNCT cana-5017 93 5 917 917 NUM cana-5017 93 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 93 7 from from ADP cana-5017 93 8 above above ADP cana-5017 93 9 it it PRON cana-5017 93 10 is be AUX cana-5017 93 11 clear clear ADJ cana-5017 93 12 that that SCONJ cana-5017 93 13 with with ADP cana-5017 93 14 magnetic magnetic ADJ cana-5017 93 15 field field NOUN cana-5017 93 16 for for ADP cana-5017 93 17 the the DET cana-5017 93 18 conditions condition NOUN cana-5017 93 19 𝜌 𝜌 X cana-5017 93 20 + + CCONJ cana-5017 93 21 πœ† πœ† X cana-5017 93 22 = = SYM cana-5017 93 23 0 0 NUM cana-5017 93 24 the the DET cana-5017 93 25 physical physical ADJ cana-5017 93 26 quantities quantity NOUN cana-5017 93 27 𝛲 𝛲 PROPN cana-5017 93 28 , , PUNCT cana-5017 93 29 𝜌 𝜌 PROPN cana-5017 93 30 , , PUNCT cana-5017 93 31 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN cana-5017 93 32 πœŒπ‘ πœŒπ‘ NOUN cana-5017 93 33 follows follow VERB cana-5017 93 34 straight straight ADJ cana-5017 93 35 line line NOUN cana-5017 93 36 path path NOUN cana-5017 93 37 with with ADP cana-5017 93 38 slight slight ADJ cana-5017 93 39 deviation deviation NOUN cana-5017 93 40 near near ADP cana-5017 93 41 𝑇 𝑇 PROPN cana-5017 93 42 = = SYM cana-5017 93 43 0 0 NUM cana-5017 93 44 , , PUNCT cana-5017 93 45 also also ADV cana-5017 93 46 scalar scalar ADJ cana-5017 93 47 expansion expansion NOUN cana-5017 93 48 πœƒ πœƒ PRON cana-5017 93 49 attains attain VERB cana-5017 93 50 its its PRON cana-5017 93 51 minimum minimum NOUN cana-5017 93 52 and and CCONJ cana-5017 93 53 increases increase NOUN cana-5017 93 54 with with ADP cana-5017 93 55 an an DET cana-5017 93 56 increase increase NOUN cana-5017 93 57 in in ADP cana-5017 93 58 𝑇 𝑇 NOUN cana-5017 93 59 and and CCONJ cana-5017 93 60 tends tend VERB cana-5017 93 61 to to ADP cana-5017 93 62 ∞ ∞ PROPN cana-5017 93 63 as as ADP cana-5017 93 64 𝑇 𝑇 PROPN cana-5017 93 65 β†’ β†’ SYM cana-5017 93 66 ∞. ∞. PROPN cana-5017 93 67 for for ADP cana-5017 93 68 the the DET cana-5017 93 69 model model NOUN cana-5017 93 70 ( ( PUNCT cana-5017 93 71 25 25 NUM cana-5017 93 72 ) ) PUNCT cana-5017 93 73 all all DET cana-5017 93 74 physical physical ADJ cana-5017 93 75 quantities quantity NOUN cana-5017 93 76 are be AUX cana-5017 93 77 given give VERB cana-5017 93 78 by by ADP cana-5017 93 79 𝜌 𝜌 ADP cana-5017 93 80 = = SYM cana-5017 93 81 πœ† πœ† PROPN cana-5017 93 82 = = SYM cana-5017 93 83 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 PROPN cana-5017 93 84 ) ) PUNCT cana-5017 93 85 12πœ‹π‘›π›΅2(𝑛+2 12πœ‹π‘›π›΅2(𝑛+2 PROPN cana-5017 93 86 ) ) PUNCT cana-5017 93 87 βˆ’ βˆ’ PROPN cana-5017 93 88 2𝐾(2𝑛+1 2𝐾(2𝑛+1 NUM cana-5017 93 89 ) ) PUNCT cana-5017 93 90 3𝑛𝑇4 3𝑛𝑇4 PROPN cana-5017 93 91 ( ( PUNCT cana-5017 93 92 31 31 NUM cana-5017 93 93 ) ) PUNCT cana-5017 93 94 πœŒπ‘ πœŒπ‘ NOUN cana-5017 93 95 = = SYM cana-5017 93 96 0 0 NUM cana-5017 93 97 ( ( PUNCT cana-5017 93 98 32 32 NUM cana-5017 93 99 ) ) PUNCT cana-5017 93 100 𝑃 𝑃 NOUN cana-5017 93 101 = = SYM cana-5017 93 102 βˆ’ βˆ’ PROPN cana-5017 93 103 𝛼 𝛼 NOUN cana-5017 93 104 12πœ‹π›΅2(𝑛+2 12πœ‹π›΅2(𝑛+2 ADV cana-5017 93 105 ) ) PUNCT cana-5017 93 106 βˆ’ βˆ’ PROPN cana-5017 93 107 2𝐾 2𝐾 NOUN cana-5017 93 108 3𝑇4 3𝑇4 NUM cana-5017 93 109 ( ( PUNCT cana-5017 93 110 33 33 NUM cana-5017 93 111 ) ) PUNCT cana-5017 93 112 πœƒ πœƒ NOUN cana-5017 93 113 = = PUNCT cana-5017 93 114 ( ( PUNCT cana-5017 93 115 𝑛 𝑛 PROPN cana-5017 93 116 + + NOUN cana-5017 93 117 2 2 NUM cana-5017 93 118 ) ) PUNCT cana-5017 93 119 [ [ PUNCT cana-5017 93 120 4𝛼 4𝛼 NOUN cana-5017 93 121 3𝑛(𝑛+2)𝑇𝑛+2 3𝑛(𝑛+2)𝑇𝑛+2 PROPN cana-5017 93 122 βˆ’ βˆ’ PROPN cana-5017 93 123 32πœ‹π›«π‘‡π‘›βˆ’2 32πœ‹π›«π‘‡π‘›βˆ’2 NUM cana-5017 93 124 3𝑛(π‘›βˆ’2 3𝑛(π‘›βˆ’2 NUM cana-5017 93 125 ) ) PUNCT cana-5017 94 1 + + CCONJ cana-5017 94 2 𝑁 𝑁 NOUN cana-5017 94 3 ] ] SYM cana-5017 94 4 1 1 NUM cana-5017 94 5 2 2 NUM cana-5017 94 6 ( ( PUNCT cana-5017 94 7 34 34 NUM cana-5017 94 8 ) ) PUNCT cana-5017 94 9 𝜎 𝜎 NOUN cana-5017 94 10 = = SYM cana-5017 94 11 ( ( PUNCT cana-5017 94 12 π‘›βˆ’1 π‘›βˆ’1 NUM cana-5017 94 13 ) ) PUNCT cana-5017 94 14 √3 √3 PROPN cana-5017 94 15 [ [ PUNCT cana-5017 94 16 4𝛼 4𝛼 PROPN cana-5017 94 17 3𝑛(𝑛+2)𝑇𝑛+2 3𝑛(𝑛+2)𝑇𝑛+2 PROPN cana-5017 94 18 βˆ’ βˆ’ PROPN cana-5017 94 19 32πœ‹π›«π‘‡π‘›βˆ’2 32πœ‹π›«π‘‡π‘›βˆ’2 NUM cana-5017 94 20 3𝑛(π‘›βˆ’2 3𝑛(π‘›βˆ’2 NUM cana-5017 94 21 ) ) PUNCT cana-5017 95 1 + + CCONJ cana-5017 95 2 𝑁 𝑁 NOUN cana-5017 95 3 ] ] SYM cana-5017 95 4 1 1 NUM cana-5017 95 5 2 2 NUM cana-5017 95 6 ( ( PUNCT cana-5017 95 7 35 35 NUM cana-5017 95 8 ) ) PUNCT cana-5017 95 9 from from ADP cana-5017 95 10 above above ADP cana-5017 95 11 it it PRON cana-5017 95 12 is be AUX cana-5017 95 13 clear clear ADJ cana-5017 95 14 that that SCONJ cana-5017 95 15 with with ADP cana-5017 95 16 magnetic magnetic ADJ cana-5017 95 17 field field NOUN cana-5017 95 18 for for ADP cana-5017 95 19 the the DET cana-5017 95 20 conditions condition NOUN cana-5017 95 21 𝜌 𝜌 ADP cana-5017 95 22 βˆ’ βˆ’ NOUN cana-5017 95 23 πœ† πœ† SYM cana-5017 95 24 = = SYM cana-5017 95 25 0 0 PROPN cana-5017 95 26 the the DET cana-5017 95 27 physical physical ADJ cana-5017 95 28 quantities quantity NOUN cana-5017 95 29 𝛲 𝛲 PROPN cana-5017 95 30 , , PUNCT cana-5017 95 31 𝜌 𝜌 PROPN cana-5017 95 32 , , PUNCT cana-5017 95 33 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN cana-5017 95 34 πœŒπ‘ πœŒπ‘ NOUN cana-5017 95 35 follows follow VERB cana-5017 95 36 a a DET cana-5017 95 37 straight straight ADJ cana-5017 95 38 line line NOUN cana-5017 95 39 path path NOUN cana-5017 95 40 with with ADP cana-5017 95 41 slight slight ADJ cana-5017 95 42 deviation deviation NOUN cana-5017 95 43 near near ADP cana-5017 95 44 𝑇 𝑇 PROPN cana-5017 95 45 = = SYM cana-5017 95 46 0 0 NUM cana-5017 95 47 , , PUNCT cana-5017 95 48 also also ADV cana-5017 95 49 the the DET cana-5017 95 50 scalar scalar ADJ cana-5017 95 51 expansion expansion NOUN cana-5017 95 52 πœƒ πœƒ PRON cana-5017 95 53 goes go VERB cana-5017 95 54 on on ADP cana-5017 95 55 decreasing decrease VERB cana-5017 95 56 with with ADP cana-5017 95 57 an an DET cana-5017 95 58 increase increase NOUN cana-5017 95 59 in in ADP cana-5017 95 60 the the DET cana-5017 95 61 value value NOUN cana-5017 95 62 of of ADP cana-5017 95 63 𝑇. 𝑇. PROPN cana-5017 95 64 4 4 NUM cana-5017 95 65 . . PUNCT cana-5017 95 66 solution solution NOUN cana-5017 95 67 of of ADP cana-5017 95 68 field field NOUN cana-5017 95 69 equations equation NOUN cana-5017 95 70 without without ADP cana-5017 95 71 magnetic magnetic ADJ cana-5017 95 72 field field NOUN cana-5017 95 73 case case NOUN cana-5017 96 1 i i PRON cana-5017 96 2 : : PUNCT cana-5017 96 3 𝜌 𝜌 X cana-5017 96 4 + + CCONJ cana-5017 96 5 πœ† πœ† X cana-5017 96 6 = = SYM cana-5017 96 7 0 0 NUM cana-5017 96 8 when when SCONJ cana-5017 96 9 the the DET cana-5017 96 10 magnetic magnetic ADJ cana-5017 96 11 field field NOUN cana-5017 96 12 is be AUX cana-5017 96 13 not not PART cana-5017 96 14 present present ADJ cana-5017 96 15 equation equation NOUN cana-5017 96 16 ( ( PUNCT cana-5017 96 17 19 19 NUM cana-5017 96 18 ) ) PUNCT cana-5017 96 19 becomes become VERB cana-5017 96 20 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 96 21 = = SYM cana-5017 96 22 βˆ’ βˆ’ PROPN cana-5017 96 23 𝑑𝑇2 𝑑𝑇2 PROPN cana-5017 96 24 [ [ PUNCT cana-5017 96 25 4𝛼 4𝛼 NOUN cana-5017 96 26 ( ( PUNCT cana-5017 96 27 4βˆ’π‘›)(𝑛+2)𝑇𝑛+𝑀𝑇2 4βˆ’π‘›)(𝑛+2)𝑇𝑛+𝑀𝑇2 NOUN cana-5017 96 28 ] ] X cana-5017 97 1 + + CCONJ cana-5017 97 2 𝑇2𝑛𝑑𝑋2 𝑇2𝑛𝑑𝑋2 NUM cana-5017 97 3 + + CCONJ cana-5017 97 4 𝑇2(π‘‘π‘Œ2 𝑇2(π‘‘π‘Œ2 NOUN cana-5017 97 5 + + CCONJ cana-5017 97 6 𝑑𝑍2 𝑑𝑍2 PROPN cana-5017 97 7 ) ) PUNCT cana-5017 97 8 ( ( PUNCT cana-5017 97 9 36 36 NUM cana-5017 97 10 ) ) PUNCT cana-5017 97 11 case case NOUN cana-5017 97 12 ii ii PROPN cana-5017 97 13 : : PUNCT cana-5017 97 14 𝜌 𝜌 X cana-5017 97 15 βˆ’ βˆ’ PROPN cana-5017 97 16 πœ† πœ† SYM cana-5017 97 17 = = NOUN cana-5017 97 18 0 0 NUM cana-5017 97 19 when when SCONJ cana-5017 97 20 the the DET cana-5017 97 21 magnetic magnetic ADJ cana-5017 97 22 field field NOUN cana-5017 97 23 is be AUX cana-5017 97 24 not not PART cana-5017 97 25 present present ADJ cana-5017 97 26 equation equation NOUN cana-5017 97 27 ( ( PUNCT cana-5017 97 28 25 25 NUM cana-5017 97 29 ) ) PUNCT cana-5017 97 30 becomes become VERB cana-5017 97 31 communications communication NOUN cana-5017 97 32 on on ADP cana-5017 97 33 applied apply VERB cana-5017 97 34 nonlinear nonlinear ADJ cana-5017 97 35 analysis analysis NOUN cana-5017 97 36 issn issn NOUN cana-5017 97 37 : : PUNCT cana-5017 97 38 1074 1074 NUM cana-5017 97 39 - - PUNCT cana-5017 97 40 133x 133x NUM cana-5017 97 41 vol vol NOUN cana-5017 97 42 31 31 NUM cana-5017 97 43 no no NOUN cana-5017 97 44 . . PUNCT cana-5017 98 1 8s 8s PROPN cana-5017 98 2 ( ( PUNCT cana-5017 98 3 2024 2024 NUM cana-5017 98 4 ) ) PUNCT cana-5017 98 5 918 918 NUM cana-5017 98 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 98 7 𝑑𝑠2 𝑑𝑠2 NOUN cana-5017 98 8 = = SYM cana-5017 98 9 βˆ’ βˆ’ PROPN cana-5017 98 10 𝑑𝑇2 𝑑𝑇2 PROPN cana-5017 98 11 [ [ PUNCT cana-5017 98 12 4𝛼 4𝛼 NOUN cana-5017 98 13 3𝑛(𝑛+2)𝑇𝑛+𝑁𝑇2 3𝑛(𝑛+2)𝑇𝑛+𝑁𝑇2 NUM cana-5017 98 14 ] ] X cana-5017 98 15 + + CCONJ cana-5017 98 16 𝑇2𝑛𝑑𝑋2 𝑇2𝑛𝑑𝑋2 NUM cana-5017 98 17 + + NUM cana-5017 98 18 𝑇2(π‘‘π‘Œ2 𝑇2(π‘‘π‘Œ2 NOUN cana-5017 98 19 + + CCONJ cana-5017 98 20 𝑑𝑍2 𝑑𝑍2 PROPN cana-5017 98 21 ) ) PUNCT cana-5017 98 22 ( ( PUNCT cana-5017 98 23 37 37 NUM cana-5017 98 24 ) ) PUNCT cana-5017 98 25 4.1 4.1 NUM cana-5017 98 26 geometrical geometrical ADJ cana-5017 98 27 and and CCONJ cana-5017 98 28 physical physical ADJ cana-5017 98 29 characteristics characteristic NOUN cana-5017 98 30 without without ADP cana-5017 98 31 magnetic magnetic ADJ cana-5017 98 32 field field NOUN cana-5017 98 33 for for ADP cana-5017 98 34 the the DET cana-5017 98 35 model model NOUN cana-5017 98 36 ( ( PUNCT cana-5017 98 37 36 36 NUM cana-5017 98 38 ) ) PUNCT cana-5017 98 39 all all DET cana-5017 98 40 physical physical ADJ cana-5017 98 41 quantities quantity NOUN cana-5017 98 42 are be AUX cana-5017 98 43 given give VERB cana-5017 98 44 by by ADP cana-5017 98 45 𝜌 𝜌 X cana-5017 98 46 = = PUNCT cana-5017 98 47 βˆ’πœ† βˆ’πœ† PROPN cana-5017 98 48 = = PUNCT cana-5017 98 49 βˆ’ βˆ’ PROPN cana-5017 98 50 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 PROPN cana-5017 98 51 ) ) PUNCT cana-5017 98 52 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NOUN cana-5017 98 53 ) ) PUNCT cana-5017 98 54 ( ( PUNCT cana-5017 98 55 38 38 NUM cana-5017 98 56 ) ) PUNCT cana-5017 98 57 πœŒπ‘ πœŒπ‘ NOUN cana-5017 98 58 = = SYM cana-5017 98 59 βˆ’ βˆ’ PROPN cana-5017 98 60 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 PROPN cana-5017 98 61 ) ) PUNCT cana-5017 98 62 2πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 2πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NUM cana-5017 98 63 ) ) PUNCT cana-5017 98 64 ( ( PUNCT cana-5017 98 65 39 39 NUM cana-5017 98 66 ) ) PUNCT cana-5017 98 67 𝛲 𝛲 NOUN cana-5017 98 68 = = PUNCT cana-5017 98 69 𝛼(π‘›βˆ’2 𝛼(π‘›βˆ’2 PROPN cana-5017 98 70 ) ) PUNCT cana-5017 98 71 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 4πœ‹(4βˆ’π‘›)𝑇2(𝑛+2 NUM cana-5017 98 72 ) ) PUNCT cana-5017 98 73 ( ( PUNCT cana-5017 98 74 40 40 NUM cana-5017 98 75 ) ) PUNCT cana-5017 98 76 πœƒ πœƒ NOUN cana-5017 98 77 = = PUNCT cana-5017 98 78 ( ( PUNCT cana-5017 98 79 𝑛 𝑛 PROPN cana-5017 98 80 + + NOUN cana-5017 98 81 2 2 NUM cana-5017 98 82 ) ) PUNCT cana-5017 98 83 [ [ PUNCT cana-5017 98 84 4𝛼 4𝛼 NOUN cana-5017 98 85 ( ( PUNCT cana-5017 98 86 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 NUM cana-5017 98 87 + + CCONJ cana-5017 98 88 𝑀 𝑀 PROPN cana-5017 98 89 ] ] PUNCT cana-5017 98 90 1 1 NUM cana-5017 98 91 2 2 NUM cana-5017 98 92 ( ( PUNCT cana-5017 98 93 41 41 NUM cana-5017 98 94 ) ) PUNCT cana-5017 98 95 𝜎 𝜎 NOUN cana-5017 98 96 = = SYM cana-5017 98 97 ( ( PUNCT cana-5017 98 98 π‘›βˆ’1 π‘›βˆ’1 NUM cana-5017 98 99 ) ) PUNCT cana-5017 98 100 √3 √3 PROPN cana-5017 98 101 [ [ PUNCT cana-5017 98 102 4𝛼 4𝛼 NOUN cana-5017 98 103 ( ( PUNCT cana-5017 98 104 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 4βˆ’π‘›)(𝑛+2)𝛡𝑛+2 NUM cana-5017 98 105 + + CCONJ cana-5017 98 106 𝑀 𝑀 PROPN cana-5017 98 107 ] ] PUNCT cana-5017 98 108 1 1 NUM cana-5017 98 109 2 2 NUM cana-5017 98 110 ( ( PUNCT cana-5017 98 111 42 42 NUM cana-5017 98 112 ) ) PUNCT cana-5017 98 113 for for ADP cana-5017 98 114 the the DET cana-5017 98 115 model model NOUN cana-5017 98 116 ( ( PUNCT cana-5017 98 117 37 37 NUM cana-5017 98 118 ) ) PUNCT cana-5017 98 119 all all DET cana-5017 98 120 physical physical ADJ cana-5017 98 121 quantities quantity NOUN cana-5017 98 122 are be AUX cana-5017 98 123 given give VERB cana-5017 98 124 by by ADP cana-5017 98 125 𝜌 𝜌 ADP cana-5017 98 126 = = SYM cana-5017 98 127 πœ† πœ† PROPN cana-5017 98 128 = = SYM cana-5017 98 129 𝛼(π‘›βˆ’1 𝛼(π‘›βˆ’1 PROPN cana-5017 98 130 ) ) PUNCT cana-5017 98 131 12πœ‹π‘›π›΅2(𝑛+2 12πœ‹π‘›π›΅2(𝑛+2 NUM cana-5017 98 132 ) ) PUNCT cana-5017 98 133 ( ( PUNCT cana-5017 98 134 43 43 NUM cana-5017 98 135 ) ) PUNCT cana-5017 98 136 𝛲 𝛲 PROPN cana-5017 98 137 = = PUNCT cana-5017 98 138 βˆ’ βˆ’ PROPN cana-5017 98 139 𝛼 𝛼 NOUN cana-5017 98 140 12πœ‹π‘‡2(𝑛+2 12πœ‹π‘‡2(𝑛+2 NUM cana-5017 98 141 ) ) PUNCT cana-5017 98 142 ( ( PUNCT cana-5017 98 143 44 44 NUM cana-5017 98 144 ) ) PUNCT cana-5017 98 145 πœŒπ‘ πœŒπ‘ NOUN cana-5017 98 146 = = SYM cana-5017 98 147 0 0 NUM cana-5017 98 148 ( ( PUNCT cana-5017 98 149 45 45 NUM cana-5017 98 150 ) ) PUNCT cana-5017 98 151 πœƒ πœƒ NOUN cana-5017 98 152 = = PUNCT cana-5017 98 153 ( ( PUNCT cana-5017 98 154 𝑛 𝑛 PROPN cana-5017 98 155 + + NOUN cana-5017 98 156 2 2 NUM cana-5017 98 157 ) ) PUNCT cana-5017 98 158 [ [ PUNCT cana-5017 98 159 4𝛼 4𝛼 NOUN cana-5017 98 160 3𝑛(𝑛+2)𝑇𝑛+2 3𝑛(𝑛+2)𝑇𝑛+2 PROPN cana-5017 98 161 + + CCONJ cana-5017 98 162 𝑁 𝑁 PROPN cana-5017 98 163 ] ] SYM cana-5017 98 164 1 1 NUM cana-5017 98 165 2 2 NUM cana-5017 98 166 ( ( PUNCT cana-5017 98 167 46 46 NUM cana-5017 98 168 ) ) PUNCT cana-5017 98 169 𝜎 𝜎 NOUN cana-5017 98 170 = = SYM cana-5017 98 171 ( ( PUNCT cana-5017 98 172 π‘›βˆ’1 π‘›βˆ’1 NUM cana-5017 98 173 ) ) PUNCT cana-5017 98 174 √3 √3 PROPN cana-5017 98 175 [ [ PUNCT cana-5017 98 176 4𝛼 4𝛼 PROPN cana-5017 98 177 3𝑛(𝑛+2)𝑇𝑛+2 3𝑛(𝑛+2)𝑇𝑛+2 PROPN cana-5017 99 1 + + CCONJ cana-5017 99 2 𝑁 𝑁 PROPN cana-5017 99 3 ] ] SYM cana-5017 99 4 1 1 NUM cana-5017 99 5 2 2 NUM cana-5017 99 6 ( ( PUNCT cana-5017 99 7 47 47 NUM cana-5017 99 8 ) ) PUNCT cana-5017 99 9 when when SCONJ cana-5017 99 10 the the DET cana-5017 99 11 magnetic magnetic ADJ cana-5017 99 12 field field NOUN cana-5017 99 13 is be AUX cana-5017 99 14 not not PART cana-5017 99 15 present present ADJ cana-5017 99 16 for for SCONJ cana-5017 99 17 both both CCONJ cana-5017 99 18 the the DET cana-5017 99 19 cases case NOUN cana-5017 99 20 𝜌 𝜌 X cana-5017 99 21 + + NOUN cana-5017 99 22 πœ† πœ† X cana-5017 99 23 = = SYM cana-5017 99 24 0 0 NUM cana-5017 99 25 and and CCONJ cana-5017 99 26 𝜌 𝜌 ADP cana-5017 99 27 βˆ’ βˆ’ PROPN cana-5017 99 28 πœ† πœ† SYM cana-5017 100 1 = = SYM cana-5017 100 2 0 0 NUM cana-5017 100 3 all all DET cana-5017 100 4 the the DET cana-5017 100 5 quantities quantity NOUN cana-5017 100 6 show show VERB cana-5017 100 7 slight slight ADJ cana-5017 100 8 deviation deviation NOUN cana-5017 100 9 from from ADP cana-5017 100 10 the the DET cana-5017 100 11 straight straight ADJ cana-5017 100 12 line line NOUN cana-5017 100 13 at at ADP cana-5017 100 14 𝑇 𝑇 PROPN cana-5017 100 15 = = SYM cana-5017 100 16 0 0 PROPN cana-5017 100 17 . . PUNCT cana-5017 101 1 for for ADP cana-5017 101 2 with with ADP cana-5017 101 3 and and CCONJ cana-5017 101 4 without without ADP cana-5017 101 5 magnetic magnetic ADJ cana-5017 101 6 field field NOUN cana-5017 101 7 for for ADP cana-5017 101 8 both both CCONJ cana-5017 101 9 the the DET cana-5017 101 10 cases case NOUN cana-5017 101 11 , , PUNCT cana-5017 101 12 also also ADV cana-5017 101 13 𝜎/πœƒ 𝜎/πœƒ VERB cana-5017 101 14 = = PUNCT cana-5017 101 15 π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ NOUN cana-5017 101 16 shows show VERB cana-5017 101 17 that that SCONJ cana-5017 101 18 the the DET cana-5017 101 19 model model NOUN cana-5017 101 20 does do AUX cana-5017 101 21 not not PART cana-5017 101 22 approach approach VERB cana-5017 101 23 isotropy isotropy VERB cana-5017 101 24 in in ADP cana-5017 101 25 general general ADJ cana-5017 101 26 studied study VERB cana-5017 101 27 by by ADP cana-5017 101 28 pradhan pradhan PROPN cana-5017 101 29 et et PROPN cana-5017 101 30 al.(28 al.(28 PROPN cana-5017 101 31 ) ) PUNCT cana-5017 101 32 . . PUNCT cana-5017 102 1 5 5 X cana-5017 102 2 . . X cana-5017 102 3 quintessence quintessence NOUN cana-5017 102 4 model model NOUN cana-5017 102 5 of of ADP cana-5017 102 6 dark dark ADJ cana-5017 102 7 energy energy NOUN cana-5017 102 8 without without ADP cana-5017 102 9 magnetic magnetic ADJ cana-5017 102 10 field field NOUN cana-5017 102 11 one one NUM cana-5017 102 12 of of ADP cana-5017 102 13 the the DET cana-5017 102 14 models model NOUN cana-5017 102 15 of of ADP cana-5017 102 16 dark dark ADJ cana-5017 102 17 energy energy NOUN cana-5017 102 18 is be AUX cana-5017 102 19 the the DET cana-5017 102 20 quintessence quintessence NOUN cana-5017 102 21 model model NOUN cana-5017 102 22 which which PRON cana-5017 102 23 obeys obey VERB cana-5017 102 24 the the DET cana-5017 102 25 equation equation NOUN cana-5017 102 26 of of ADP cana-5017 102 27 state state NOUN cana-5017 102 28 . . PUNCT cana-5017 103 1 π‘ƒπ‘ž π‘ƒπ‘ž PROPN cana-5017 103 2 = = SYM cana-5017 103 3 πœ”π‘žπœŒπ‘ž πœ”π‘žπœŒπ‘ž NOUN cana-5017 103 4 , , PUNCT cana-5017 103 5 βˆ’1 βˆ’1 NOUN cana-5017 103 6 ≀ ≀ NOUN cana-5017 103 7 πœ”π‘ž πœ”π‘ž ADP cana-5017 103 8 ≀ ≀ ADJ cana-5017 103 9 0 0 NUM cana-5017 104 1 ( ( PUNCT cana-5017 104 2 48 48 NUM cana-5017 104 3 ) ) PUNCT cana-5017 104 4 in in ADP cana-5017 104 5 which which PRON cana-5017 104 6 πœ”π‘ž πœ”π‘ž ADP cana-5017 104 7 is be AUX cana-5017 104 8 the the DET cana-5017 104 9 equation equation NOUN cana-5017 104 10 of of ADP cana-5017 104 11 state state NOUN cana-5017 104 12 parameter parameter NOUN cana-5017 104 13 correlated correlate VERB cana-5017 104 14 with with ADP cana-5017 104 15 the the DET cana-5017 104 16 quintessence quintessence NOUN cana-5017 104 17 model model NOUN cana-5017 104 18 . . PUNCT cana-5017 105 1 for for ADP cana-5017 105 2 case case NOUN cana-5017 105 3 ( ( PUNCT cana-5017 105 4 i i NOUN cana-5017 105 5 ) ) PUNCT cana-5017 105 6 πœ”π‘ž πœ”π‘ž AUX cana-5017 105 7 is be AUX cana-5017 105 8 given give VERB cana-5017 105 9 by by ADP cana-5017 105 10 πœ”π‘ž πœ”π‘ž ADP cana-5017 105 11 = = SYM cana-5017 105 12 βˆ’ βˆ’ PROPN cana-5017 105 13 ( ( PUNCT cana-5017 105 14 π‘›βˆ’2 π‘›βˆ’2 PROPN cana-5017 105 15 ) ) PUNCT cana-5017 105 16 ( ( PUNCT cana-5017 105 17 π‘›βˆ’1 π‘›βˆ’1 NUM cana-5017 105 18 ) ) PUNCT cana-5017 105 19 ( ( PUNCT cana-5017 105 20 49 49 NUM cana-5017 105 21 ) ) PUNCT cana-5017 105 22 for for ADP cana-5017 105 23 case case NOUN cana-5017 105 24 ( ( PUNCT cana-5017 105 25 ii ii NOUN cana-5017 105 26 ) ) PUNCT cana-5017 105 27 πœ”π‘ž πœ”π‘ž ADP cana-5017 105 28 is be AUX cana-5017 105 29 given give VERB cana-5017 105 30 by by ADP cana-5017 105 31 πœ”π‘ž πœ”π‘ž ADP cana-5017 105 32 = = SYM cana-5017 105 33 βˆ’ βˆ’ PROPN cana-5017 105 34 𝑛 𝑛 PROPN cana-5017 105 35 ( ( PUNCT cana-5017 105 36 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-5017 105 37 ) ) PUNCT cana-5017 105 38 ( ( PUNCT cana-5017 105 39 50 50 NUM cana-5017 105 40 ) ) PUNCT cana-5017 105 41 communications communication NOUN cana-5017 105 42 on on ADP cana-5017 105 43 applied apply VERB cana-5017 105 44 nonlinear nonlinear ADJ cana-5017 105 45 analysis analysis NOUN cana-5017 105 46 issn issn NOUN cana-5017 105 47 : : PUNCT cana-5017 105 48 1074 1074 NUM cana-5017 105 49 - - PUNCT cana-5017 105 50 133x 133x NUM cana-5017 105 51 vol vol NOUN cana-5017 105 52 31 31 NUM cana-5017 105 53 no no NOUN cana-5017 105 54 . . PUNCT cana-5017 106 1 8s 8s PROPN cana-5017 106 2 ( ( PUNCT cana-5017 106 3 2024 2024 NUM cana-5017 106 4 ) ) PUNCT cana-5017 106 5 919 919 NUM cana-5017 106 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 107 1 we we PRON cana-5017 107 2 are be AUX cana-5017 107 3 interested interested ADJ cana-5017 107 4 in in ADP cana-5017 107 5 three three NUM cana-5017 107 6 values value NOUN cana-5017 107 7 of of ADP cana-5017 107 8 πœ”π‘ž πœ”π‘ž ADP cana-5017 107 9 which which PRON cana-5017 107 10 are be AUX cana-5017 107 11 βˆ’1,0 βˆ’1,0 NOUN cana-5017 107 12 , , PUNCT cana-5017 107 13 1 1 NUM cana-5017 107 14 3 3 NUM cana-5017 107 15 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ cana-5017 107 16 1 1 NUM cana-5017 107 17 . . PUNCT cana-5017 108 1 πœ”π‘ž πœ”π‘ž ADP cana-5017 108 2 = = PUNCT cana-5017 108 3 βˆ’1 βˆ’1 NOUN cana-5017 108 4 corresponds correspond VERB cana-5017 108 5 to to ADP cana-5017 108 6 the the DET cana-5017 108 7 vacuum vacuum NOUN cana-5017 108 8 fluid fluid NOUN cana-5017 108 9 , , PUNCT cana-5017 108 10 πœ”π‘ž πœ”π‘ž ADP cana-5017 108 11 = = SYM cana-5017 108 12 0 0 NUM cana-5017 108 13 corresponds correspond VERB cana-5017 108 14 to to ADP cana-5017 108 15 the the DET cana-5017 108 16 dust dust NOUN cana-5017 108 17 fluid fluid NOUN cana-5017 108 18 , , PUNCT cana-5017 108 19 πœ”π‘ž πœ”π‘ž ADP cana-5017 108 20 = = SYM cana-5017 108 21 1 1 NUM cana-5017 108 22 3 3 NUM cana-5017 108 23 corresponds correspond NOUN cana-5017 108 24 to to ADP cana-5017 108 25 the the DET cana-5017 108 26 radiating radiate VERB cana-5017 108 27 fluid fluid NOUN cana-5017 108 28 , , PUNCT cana-5017 108 29 πœ”π‘ž πœ”π‘ž ADP cana-5017 108 30 = = SYM cana-5017 108 31 1 1 NUM cana-5017 108 32 stiff stiff ADJ cana-5017 108 33 dominated dominate VERB cana-5017 108 34 universe universe NOUN cana-5017 108 35 . . PUNCT cana-5017 109 1 6 6 X cana-5017 109 2 . . X cana-5017 109 3 conclusion conclusion NOUN cana-5017 109 4 in in ADP cana-5017 109 5 this this DET cana-5017 109 6 work work NOUN cana-5017 109 7 , , PUNCT cana-5017 109 8 we we PRON cana-5017 109 9 examine examine VERB cana-5017 109 10 the the DET cana-5017 109 11 locally locally ADV cana-5017 109 12 rotationally rotationally ADV cana-5017 109 13 symmetric symmetric ADJ cana-5017 109 14 bianchi bianchi NOUN cana-5017 109 15 type type NOUN cana-5017 109 16 - - PUNCT cana-5017 109 17 i i NOUN cana-5017 109 18 magnetized magnetize VERB cana-5017 109 19 dark dark ADJ cana-5017 109 20 energy energy NOUN cana-5017 109 21 cosmological cosmological ADJ cana-5017 109 22 model model NOUN cana-5017 109 23 in in ADP cana-5017 109 24 btg btg NOUN cana-5017 109 25 by by ADP cana-5017 109 26 solving solve VERB cana-5017 109 27 rosen rosen PROPN cana-5017 109 28 ’s ’s PART cana-5017 109 29 field field NOUN cana-5017 109 30 equations equation NOUN cana-5017 109 31 . . PUNCT cana-5017 110 1 the the DET cana-5017 110 2 study study NOUN cana-5017 110 3 investigates investigate VERB cana-5017 110 4 the the DET cana-5017 110 5 model model NOUN cana-5017 110 6 's 's PART cana-5017 110 7 geometrical geometrical ADJ cana-5017 110 8 and and CCONJ cana-5017 110 9 physical physical ADJ cana-5017 110 10 characteristics characteristic NOUN cana-5017 110 11 with with ADP cana-5017 110 12 and and CCONJ cana-5017 110 13 without without ADP cana-5017 110 14 a a DET cana-5017 110 15 magnetic magnetic ADJ cana-5017 110 16 field field NOUN cana-5017 110 17 in in ADP cana-5017 110 18 two two NUM cana-5017 110 19 cases case NOUN cana-5017 110 20 ( ( PUNCT cana-5017 110 21 i i NOUN cana-5017 110 22 ) ) PUNCT cana-5017 110 23 𝜌 𝜌 ADP cana-5017 110 24 + + X cana-5017 110 25 πœ† πœ† X cana-5017 110 26 = = SYM cana-5017 110 27 0 0 NUM cana-5017 110 28 ( ( PUNCT cana-5017 110 29 ii ii NOUN cana-5017 110 30 ) ) PUNCT cana-5017 110 31 𝜌 𝜌 ADP cana-5017 110 32 βˆ’ βˆ’ PROPN cana-5017 110 33 πœ† πœ† SYM cana-5017 110 34 = = SYM cana-5017 110 35 0 0 NUM cana-5017 110 36 . . NOUN cana-5017 111 1 1 1 NUM cana-5017 111 2 . . X cana-5017 112 1 in in ADP cana-5017 112 2 the the DET cana-5017 112 3 presence presence NOUN cana-5017 112 4 of of ADP cana-5017 112 5 a a DET cana-5017 112 6 magnetic magnetic ADJ cana-5017 112 7 field field NOUN cana-5017 112 8 for for ADP cana-5017 112 9 the the DET cana-5017 112 10 case case NOUN cana-5017 112 11 𝜌 𝜌 ADP cana-5017 112 12 + + CCONJ cana-5017 112 13 πœ† πœ† X cana-5017 112 14 = = SYM cana-5017 112 15 0 0 NUM cana-5017 112 16 the the DET cana-5017 112 17 increasing increase VERB cana-5017 112 18 scalar scalar ADJ cana-5017 112 19 expansion expansion NOUN cana-5017 112 20 πœƒ πœƒ NOUN cana-5017 112 21 and and CCONJ cana-5017 112 22 shear shear NOUN cana-5017 112 23 𝜎 𝜎 NOUN cana-5017 112 24 over over ADP cana-5017 112 25 time time NOUN cana-5017 112 26 indicate indicate VERB cana-5017 112 27 ( ( PUNCT cana-5017 112 28 fig fig NOUN cana-5017 112 29 1 1 NUM cana-5017 112 30 ) ) PUNCT cana-5017 112 31 that that SCONJ cana-5017 112 32 the the DET cana-5017 112 33 expansion expansion NOUN cana-5017 112 34 of of ADP cana-5017 112 35 the the DET cana-5017 112 36 universe universe NOUN cana-5017 112 37 . . PUNCT cana-5017 113 1 this this DET cana-5017 113 2 concept concept NOUN cana-5017 113 3 is be AUX cana-5017 113 4 similar similar ADJ cana-5017 113 5 to to ADP cana-5017 113 6 the the DET cana-5017 113 7 big big PROPN cana-5017 113 8 bang bang PROPN cana-5017 113 9 theory theory NOUN cana-5017 113 10 , , PUNCT cana-5017 113 11 which which PRON cana-5017 113 12 suggests suggest VERB cana-5017 113 13 that that SCONJ cana-5017 113 14 the the DET cana-5017 113 15 origin origin NOUN cana-5017 113 16 of of ADP cana-5017 113 17 the the DET cana-5017 113 18 universe universe NOUN cana-5017 113 19 from from ADP cana-5017 113 20 an an DET cana-5017 113 21 extremely extremely ADV cana-5017 113 22 hot hot ADJ cana-5017 113 23 and and CCONJ cana-5017 113 24 dense dense ADJ cana-5017 113 25 point point NOUN cana-5017 113 26 and and CCONJ cana-5017 113 27 has have AUX cana-5017 113 28 been be AUX cana-5017 113 29 expanding expand VERB cana-5017 113 30 ever ever ADV cana-5017 113 31 since since ADV cana-5017 113 32 . . PUNCT cana-5017 114 1 the the DET cana-5017 114 2 observations observation NOUN cana-5017 114 3 of of ADP cana-5017 114 4 increasing increase VERB cana-5017 114 5 shear shear NOUN cana-5017 114 6 and and CCONJ cana-5017 114 7 scalar scalar ADJ cana-5017 114 8 expansion expansion NOUN cana-5017 114 9 obey obey VERB cana-5017 114 10 the the DET cana-5017 114 11 idea idea NOUN cana-5017 114 12 of of ADP cana-5017 114 13 an an DET cana-5017 114 14 expanding expand VERB cana-5017 114 15 universe universe NOUN cana-5017 114 16 . . PUNCT cana-5017 115 1 2 2 X cana-5017 115 2 . . X cana-5017 115 3 in in ADP cana-5017 115 4 presence presence NOUN cana-5017 115 5 of of ADP cana-5017 115 6 a a DET cana-5017 115 7 magnetic magnetic ADJ cana-5017 115 8 field field NOUN cana-5017 115 9 for for ADP cana-5017 115 10 the the DET cana-5017 115 11 case case NOUN cana-5017 115 12 𝜌 𝜌 ADP cana-5017 115 13 βˆ’ βˆ’ PROPN cana-5017 115 14 πœ† πœ† SYM cana-5017 115 15 = = SYM cana-5017 115 16 0 0 NUM cana-5017 115 17 scenario scenario NOUN cana-5017 115 18 suggested suggest VERB cana-5017 115 19 that that SCONJ cana-5017 115 20 the the DET cana-5017 115 21 universe universe NOUN cana-5017 115 22 in in ADP cana-5017 115 23 the the DET cana-5017 115 24 presence presence NOUN cana-5017 115 25 of of ADP cana-5017 115 26 a a DET cana-5017 115 27 magnetic magnetic ADJ cana-5017 115 28 field field NOUN cana-5017 115 29 influences influence VERB cana-5017 115 30 gravitational gravitational ADJ cana-5017 115 31 dynamics dynamic NOUN cana-5017 115 32 , , PUNCT cana-5017 115 33 leading lead VERB cana-5017 115 34 to to ADP cana-5017 115 35 a a DET cana-5017 115 36 contraction contraction NOUN cana-5017 115 37 despite despite SCONJ cana-5017 115 38 the the DET cana-5017 115 39 presence presence NOUN cana-5017 115 40 of of ADP cana-5017 115 41 constant constant ADJ cana-5017 115 42 pressure pressure NOUN cana-5017 115 43 and and CCONJ cana-5017 115 44 density density NOUN cana-5017 115 45 ( ( PUNCT cana-5017 115 46 fig fig NOUN cana-5017 115 47 2 2 NUM cana-5017 115 48 ) ) PUNCT cana-5017 115 49 . . PUNCT cana-5017 116 1 the the DET cana-5017 116 2 balance balance NOUN cana-5017 116 3 between between ADP cana-5017 116 4 matter matter NOUN cana-5017 116 5 energy energy NOUN cana-5017 116 6 density density NOUN cana-5017 116 7 and and CCONJ cana-5017 116 8 the the DET cana-5017 116 9 cosmological cosmological ADJ cana-5017 116 10 constant constant ADJ cana-5017 116 11 further further ADJ cana-5017 116 12 shapes shape NOUN cana-5017 116 13 the the DET cana-5017 116 14 overall overall ADJ cana-5017 116 15 evolution evolution NOUN cana-5017 116 16 of of ADP cana-5017 116 17 the the DET cana-5017 116 18 universe universe NOUN cana-5017 116 19 . . PUNCT cana-5017 117 1 3 3 X cana-5017 117 2 . . X cana-5017 117 3 when when SCONJ cana-5017 117 4 the the DET cana-5017 117 5 magnetic magnetic ADJ cana-5017 117 6 field field NOUN cana-5017 117 7 is be AUX cana-5017 117 8 not not PART cana-5017 117 9 present present ADJ cana-5017 117 10 for for ADP cana-5017 117 11 both both DET cana-5017 117 12 cases case NOUN cana-5017 117 13 ( ( PUNCT cana-5017 117 14 figures figure NOUN cana-5017 117 15 3 3 NUM cana-5017 117 16 & & CCONJ cana-5017 117 17 4 4 NUM cana-5017 117 18 ) ) PUNCT cana-5017 117 19 all all DET cana-5017 117 20 the the DET cana-5017 117 21 physical physical ADJ cana-5017 117 22 quantities quantity NOUN cana-5017 117 23 follow follow VERB cana-5017 117 24 a a DET cana-5017 117 25 straight straight ADJ cana-5017 117 26 - - PUNCT cana-5017 117 27 line line NOUN cana-5017 117 28 path path NOUN cana-5017 117 29 except except SCONJ cana-5017 117 30 at at ADP cana-5017 117 31 𝑇 𝑇 PROPN cana-5017 117 32 = = SYM cana-5017 117 33 0 0 PROPN cana-5017 117 34 . . PUNCT cana-5017 118 1 the the DET cana-5017 118 2 universe universe NOUN cana-5017 118 3 evolves evolves AUX cana-5017 118 4 predictably predictably ADV cana-5017 118 5 according accord VERB cana-5017 118 6 to to ADP cana-5017 118 7 a a DET cana-5017 118 8 straightline straightline NOUN cana-5017 118 9 path path NOUN cana-5017 118 10 for for ADP cana-5017 118 11 physical physical ADJ cana-5017 118 12 quantities quantity NOUN cana-5017 118 13 , , PUNCT cana-5017 118 14 with with ADP cana-5017 118 15 a a DET cana-5017 118 16 notable notable ADJ cana-5017 118 17 deviation deviation NOUN cana-5017 118 18 at at ADP cana-5017 118 19 the the DET cana-5017 118 20 beginning beginning NOUN cana-5017 118 21 of of ADP cana-5017 118 22 time time NOUN cana-5017 118 23 . . PUNCT cana-5017 119 1 this this PRON cana-5017 119 2 suggests suggest VERB cana-5017 119 3 that that SCONJ cana-5017 119 4 while while SCONJ cana-5017 119 5 the the DET cana-5017 119 6 absence absence NOUN cana-5017 119 7 of of ADP cana-5017 119 8 a a DET cana-5017 119 9 magnetic magnetic ADJ cana-5017 119 10 field field NOUN cana-5017 119 11 may may AUX cana-5017 119 12 not not PART cana-5017 119 13 directly directly ADV cana-5017 119 14 influence influence VERB cana-5017 119 15 the the DET cana-5017 119 16 overall overall ADJ cana-5017 119 17 evolution evolution NOUN cana-5017 119 18 of of ADP cana-5017 119 19 the the DET cana-5017 119 20 cosmos cosmo NOUN cana-5017 119 21 , , PUNCT cana-5017 119 22 there there PRON cana-5017 119 23 are be VERB cana-5017 119 24 still still ADV cana-5017 119 25 some some DET cana-5017 119 26 initial initial ADJ cana-5017 119 27 conditions condition NOUN cana-5017 119 28 that that PRON cana-5017 119 29 shape shape VERB cana-5017 119 30 its its PRON cana-5017 119 31 development development NOUN cana-5017 119 32 . . PUNCT cana-5017 120 1 4 4 X cana-5017 120 2 . . X cana-5017 120 3 in in ADP cana-5017 120 4 the the DET cana-5017 120 5 absence absence NOUN cana-5017 120 6 magnetic magnetic ADJ cana-5017 120 7 field field NOUN cana-5017 120 8 , , PUNCT cana-5017 120 9 the the DET cana-5017 120 10 equation equation NOUN cana-5017 120 11 of of ADP cana-5017 120 12 state state NOUN cana-5017 120 13 parameter parameter NOUN cana-5017 120 14 πœ”π‘ž πœ”π‘ž ADP cana-5017 120 15 for for ADP cana-5017 120 16 𝑛 𝑛 PROPN cana-5017 120 17 > > SYM cana-5017 120 18 2 2 NUM cana-5017 120 19 for for ADP cana-5017 120 20 both both PRON cana-5017 120 21 the the DET cana-5017 120 22 cases case NOUN cana-5017 120 23 comes come VERB cana-5017 120 24 out out ADP cana-5017 120 25 to to PART cana-5017 120 26 be be AUX cana-5017 120 27 negative negative ADJ cana-5017 120 28 and and CCONJ cana-5017 120 29 it it PRON cana-5017 120 30 is be AUX cana-5017 120 31 independent independent ADJ cana-5017 120 32 of of ADP cana-5017 120 33 𝑇. 𝑇. PROPN cana-5017 120 34 this this PRON cana-5017 120 35 indicates indicate VERB cana-5017 120 36 that that SCONJ cana-5017 120 37 there there PRON cana-5017 120 38 is be VERB cana-5017 120 39 other other ADJ cana-5017 120 40 than than ADP cana-5017 120 41 baryonic baryonic NOUN cana-5017 120 42 matter matter NOUN cana-5017 120 43 and and CCONJ cana-5017 120 44 the the DET cana-5017 120 45 universe universe NOUN cana-5017 120 46 is be AUX cana-5017 120 47 completely completely ADV cana-5017 120 48 occupied occupy VERB cana-5017 120 49 by by ADP cana-5017 120 50 dark dark ADJ cana-5017 120 51 energy energy NOUN cana-5017 120 52 and and CCONJ cana-5017 120 53 dark dark ADJ cana-5017 120 54 matter matter NOUN cana-5017 120 55 when when SCONJ cana-5017 120 56 the the DET cana-5017 120 57 magnetic magnetic ADJ cana-5017 120 58 field field NOUN cana-5017 120 59 is be AUX cana-5017 120 60 not not PART cana-5017 120 61 present present ADJ cana-5017 120 62 . . PUNCT cana-5017 121 1 the the DET cana-5017 121 2 equation equation NOUN cana-5017 121 3 of of ADP cana-5017 121 4 state state NOUN cana-5017 121 5 parameter parameter NOUN cana-5017 121 6 πœ”π‘ž πœ”π‘ž ADP cana-5017 121 7 is be AUX cana-5017 121 8 negative negative ADJ cana-5017 121 9 and and CCONJ cana-5017 121 10 remains remain VERB cana-5017 121 11 constant constant ADJ cana-5017 121 12 over over ADP cana-5017 121 13 time time NOUN cana-5017 121 14 . . PUNCT cana-5017 122 1 this this PRON cana-5017 122 2 indicates indicate VERB cana-5017 122 3 the the DET cana-5017 122 4 presence presence NOUN cana-5017 122 5 of of ADP cana-5017 122 6 a a DET cana-5017 122 7 dominant dominant ADJ cana-5017 122 8 energy energy NOUN cana-5017 122 9 component component NOUN cana-5017 122 10 with with ADP cana-5017 122 11 repulsive repulsive ADJ cana-5017 122 12 gravitational gravitational ADJ cana-5017 122 13 effects effect NOUN cana-5017 122 14 , , PUNCT cana-5017 122 15 similar similar ADJ cana-5017 122 16 to to ADP cana-5017 122 17 dark dark ADJ cana-5017 122 18 energy energy NOUN cana-5017 122 19 , , PUNCT cana-5017 122 20 which which PRON cana-5017 122 21 influences influence VERB cana-5017 122 22 the the DET cana-5017 122 23 overall overall ADJ cana-5017 122 24 evolution evolution NOUN cana-5017 122 25 of of ADP cana-5017 122 26 the the DET cana-5017 122 27 universe universe NOUN cana-5017 122 28 . . PUNCT cana-5017 123 1 7 7 X cana-5017 123 2 . . NUM cana-5017 123 3 references reference NOUN cana-5017 123 4 1 1 NUM cana-5017 123 5 ) ) PUNCT cana-5017 123 6 borkar borkar PROPN cana-5017 123 7 ms ms PROPN cana-5017 123 8 , , PUNCT cana-5017 123 9 gayakwad gayakwad NOUN cana-5017 123 10 pv pv PROPN cana-5017 123 11 , , PUNCT cana-5017 123 12 lrs lrs PROPN cana-5017 123 13 bianchi bianchi PROPN cana-5017 123 14 type type NOUN cana-5017 123 15 i i PRON cana-5017 123 16 magnetized magnetize VERB cana-5017 123 17 cosmological cosmological ADJ cana-5017 123 18 model model NOUN cana-5017 123 19 with with ADP cana-5017 123 20 perfect perfect ADJ cana-5017 123 21 fluid fluid NOUN cana-5017 123 22 and and CCONJ cana-5017 123 23 with with ADP cana-5017 123 24 quintessence quintessence NOUN cana-5017 123 25 , , PUNCT cana-5017 123 26 chaplygin chaplygin VERB cana-5017 123 27 gas gas NOUN cana-5017 123 28 dark dark ADJ cana-5017 123 29 energy energy NOUN cana-5017 123 30 in in ADP cana-5017 123 31 bimetric bimetric ADJ cana-5017 123 32 theory theory NOUN cana-5017 123 33 of of ADP cana-5017 123 34 gravitation gravitation NOUN cana-5017 123 35 . . PUNCT cana-5017 124 1 international international ADJ cana-5017 124 2 journal journal NOUN cana-5017 124 3 of of ADP cana-5017 124 4 modern modern ADJ cana-5017 124 5 physics physics PROPN cana-5017 124 6 d. d. PROPN cana-5017 124 7 2017;26(07 2017;26(07 NUM cana-5017 124 8 ) ) PUNCT cana-5017 124 9 . . PUNCT cana-5017 125 1 available available ADJ cana-5017 125 2 from from ADP cana-5017 125 3 : : PUNCT cana-5017 125 4 https://doi.org/10.1142/s0218271817500614 https://doi.org/10.1142/s0218271817500614 NUM cana-5017 125 5 . . NOUN cana-5017 125 6 2 2 X cana-5017 125 7 ) ) PUNCT cana-5017 125 8 mamon mamon NOUN cana-5017 125 9 aa aa PROPN cana-5017 125 10 , , PUNCT cana-5017 125 11 constraints constraint NOUN cana-5017 125 12 on on ADP cana-5017 125 13 a a DET cana-5017 125 14 generalized generalized ADJ cana-5017 125 15 deceleration deceleration NOUN cana-5017 125 16 parameter parameter NOUN cana-5017 125 17 from from ADP cana-5017 125 18 cosmic cosmic ADJ cana-5017 125 19 chronometers chronometer NOUN cana-5017 125 20 . . PUNCT cana-5017 126 1 modern modern ADJ cana-5017 126 2 physics physics NOUN cana-5017 126 3 letters letter NOUN cana-5017 126 4 a. a. PROPN cana-5017 126 5 2018 2018 NUM cana-5017 126 6 ; ; PUNCT cana-5017 126 7 33(10n11 33(10n11 NUM cana-5017 126 8 ) ) PUNCT cana-5017 126 9 . . PUNCT cana-5017 127 1 available available ADJ cana-5017 127 2 from from ADP cana-5017 127 3 : : PUNCT cana-5017 127 4 https://doi.org/10.1142/s0217732318500566 https://doi.org/10.1142/s0217732318500566 NUM cana-5017 127 5 . . NOUN cana-5017 127 6 3 3 X cana-5017 127 7 ) ) PUNCT cana-5017 127 8 riess riess PROPN cana-5017 127 9 ag ag PROPN cana-5017 127 10 , , PUNCT cana-5017 127 11 filippenko filippenko PROPN cana-5017 127 12 av av NOUN cana-5017 127 13 , , PUNCT cana-5017 127 14 challis challi NOUN cana-5017 127 15 p p NOUN cana-5017 127 16 , , PUNCT cana-5017 127 17 clocchiatti clocchiatti NOUN cana-5017 127 18 a a PRON cana-5017 127 19 , , PUNCT cana-5017 127 20 diercks diercks PROPN cana-5017 127 21 a a PRON cana-5017 127 22 , , PUNCT cana-5017 127 23 garnavich garnavich ADJ cana-5017 127 24 pm pm NOUN cana-5017 127 25 , , PUNCT cana-5017 127 26 gilliland gilliland PROPN cana-5017 127 27 rl rl PROPN cana-5017 127 28 , , PUNCT cana-5017 127 29 hogan hogan PROPN cana-5017 127 30 cj cj PROPN cana-5017 127 31 , , PUNCT cana-5017 127 32 jha jha PROPN cana-5017 127 33 s s PROPN cana-5017 127 34 , , PUNCT cana-5017 127 35 kirshner kirshner PROPN cana-5017 127 36 rp rp PROPN cana-5017 127 37 , , PUNCT cana-5017 127 38 et et PROPN cana-5017 127 39 al al PROPN cana-5017 127 40 . . PROPN cana-5017 127 41 , , PUNCT cana-5017 127 42 observational observational ADJ cana-5017 127 43 evidence evidence NOUN cana-5017 127 44 from from ADP cana-5017 127 45 supernovae supernovae NOUN cana-5017 127 46 for for ADP cana-5017 127 47 an an DET cana-5017 127 48 https://doi.org/10.1142/s0218271817500614 https://doi.org/10.1142/s0218271817500614 NUM cana-5017 127 49 https://doi.org/10.1142/s0217732318500566 https://doi.org/10.1142/s0217732318500566 NUM cana-5017 127 50 communications communication NOUN cana-5017 127 51 on on ADP cana-5017 127 52 applied apply VERB cana-5017 127 53 nonlinear nonlinear ADJ cana-5017 127 54 analysis analysis NOUN cana-5017 127 55 issn issn NOUN cana-5017 127 56 : : PUNCT cana-5017 127 57 1074 1074 NUM cana-5017 127 58 - - PUNCT cana-5017 127 59 133x 133x NUM cana-5017 127 60 vol vol NOUN cana-5017 127 61 31 31 NUM cana-5017 127 62 no no NOUN cana-5017 127 63 . . PUNCT cana-5017 128 1 8s 8s PROPN cana-5017 128 2 ( ( PUNCT cana-5017 128 3 2024 2024 NUM cana-5017 128 4 ) ) PUNCT cana-5017 128 5 920 920 NUM cana-5017 128 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 128 7 accelerating accelerate VERB cana-5017 128 8 universe universe NOUN cana-5017 128 9 and and CCONJ cana-5017 128 10 a a DET cana-5017 128 11 cosmological cosmological ADJ cana-5017 128 12 constant constant ADJ cana-5017 128 13 . . PUNCT cana-5017 129 1 astron astron PROPN cana-5017 129 2 . . PUNCT cana-5017 130 1 j. j. PROPN cana-5017 130 2 1998 1998 NUM cana-5017 130 3 ; ; PUNCT cana-5017 130 4 vol vol NOUN cana-5017 130 5 116 116 NUM cana-5017 130 6 . . PUNCT cana-5017 131 1 available available ADJ cana-5017 131 2 from from ADP cana-5017 131 3 : : PUNCT cana-5017 131 4 doi10.1086/300499 doi10.1086/300499 PROPN cana-5017 131 5 . . NOUN cana-5017 131 6 4 4 NUM cana-5017 131 7 ) ) PUNCT cana-5017 131 8 perlmutter perlmutter NOUN cana-5017 131 9 s s PART cana-5017 131 10 , , PUNCT cana-5017 131 11 aldering aldere VERB cana-5017 131 12 g g PRON cana-5017 131 13 , , PUNCT cana-5017 131 14 goldhaber goldhaber ADV cana-5017 131 15 g g PROPN cana-5017 131 16 , , PUNCT cana-5017 131 17 knop knop PROPN cana-5017 131 18 ra ra PROPN cana-5017 131 19 , , PUNCT cana-5017 131 20 nugent nugent PROPN cana-5017 131 21 p p PROPN cana-5017 131 22 , , PUNCT cana-5017 131 23 castro castro PROPN cana-5017 131 24 pg pg PROPN cana-5017 131 25 , , PUNCT cana-5017 131 26 deustua deustua VERB cana-5017 131 27 s s PROPN cana-5017 131 28 , , PUNCT cana-5017 131 29 fabbro fabbro PROPN cana-5017 131 30 s s PROPN cana-5017 131 31 , , PUNCT cana-5017 131 32 goobar goobar NOUN cana-5017 131 33 , , PUNCT cana-5017 131 34 groom groom X cana-5017 131 35 de de X cana-5017 131 36 , , PUNCT cana-5017 131 37 hook hook NOUN cana-5017 131 38 i i PRON cana-5017 131 39 m m PROPN cana-5017 131 40 , , PUNCT cana-5017 131 41 et et PROPN cana-5017 131 42 al al PROPN cana-5017 131 43 . . PROPN cana-5017 131 44 , , PUNCT cana-5017 131 45 measurements measurement NOUN cana-5017 131 46 of of ADP cana-5017 131 47 Ο‰ Ο‰ NUM cana-5017 131 48 and and CCONJ cana-5017 131 49 κ“₯ κ“₯ X cana-5017 131 50 from from ADP cana-5017 131 51 42 42 NUM cana-5017 131 52 high high ADJ cana-5017 131 53 - - PUNCT cana-5017 131 54 redshift redshift NOUN cana-5017 131 55 supernovae supernovae NOUN cana-5017 131 56 , , PUNCT cana-5017 131 57 astrophysical astrophysical NOUN cana-5017 131 58 . . PUNCT cana-5017 132 1 j. j. PROPN cana-5017 132 2 1999 1999 NUM cana-5017 132 3 ; ; PUNCT cana-5017 132 4 517 517 NUM cana-5017 132 5 . . PUNCT cana-5017 132 6 available available ADJ cana-5017 132 7 from from ADP cana-5017 132 8 : : PUNCT cana-5017 132 9 doi doi NOUN cana-5017 132 10 10.1086/307221 10.1086/307221 NUM cana-5017 132 11 . . NOUN cana-5017 132 12 5 5 NUM cana-5017 132 13 ) ) PUNCT cana-5017 132 14 spergel spergel NOUN cana-5017 132 15 dn dn PROPN cana-5017 132 16 , , PUNCT cana-5017 132 17 verde verde NOUN cana-5017 132 18 , , PUNCT cana-5017 132 19 peiris peiris PROPN cana-5017 132 20 hv hv PROPN cana-5017 132 21 , , PUNCT cana-5017 132 22 komatsu komatsu PROPN cana-5017 132 23 e e PROPN cana-5017 132 24 , , PUNCT cana-5017 132 25 nolta nolta PROPN cana-5017 132 26 mr mr PROPN cana-5017 132 27 , , PUNCT cana-5017 132 28 bennett bennett PROPN cana-5017 132 29 cl cl PROPN cana-5017 132 30 , , PUNCT cana-5017 132 31 halpern halpern PROPN cana-5017 132 32 m m PROPN cana-5017 132 33 , , PUNCT cana-5017 132 34 hinshaw hinshaw PROPN cana-5017 132 35 g g PROPN cana-5017 132 36 , , PUNCT cana-5017 132 37 jarosik jarosik NOUN cana-5017 132 38 n n CCONJ cana-5017 132 39 , , PUNCT cana-5017 132 40 kogut kogut VERB cana-5017 132 41 a a DET cana-5017 132 42 , , PUNCT cana-5017 132 43 first first ADJ cana-5017 132 44 - - PUNCT cana-5017 132 45 year year NOUN cana-5017 132 46 wilkinson wilkinson PROPN cana-5017 132 47 microwave microwave PROPN cana-5017 132 48 anisotropy anisotropy NOUN cana-5017 132 49 probe probe NOUN cana-5017 132 50 ( ( PUNCT cana-5017 132 51 wmap wmap ADJ cana-5017 132 52 ) ) PUNCT cana-5017 132 53 1 1 NUM cana-5017 132 54 observations observation NOUN cana-5017 132 55 : : PUNCT cana-5017 132 56 determination determination NOUN cana-5017 132 57 of of ADP cana-5017 132 58 cosmological cosmological ADJ cana-5017 132 59 parameters parameter NOUN cana-5017 132 60 . . PUNCT cana-5017 133 1 astrophys astrophy NOUN cana-5017 133 2 . . PUNCT cana-5017 134 1 j. j. PROPN cana-5017 134 2 suppl.2003;148 suppl.2003;148 PROPN cana-5017 134 3 : : PUNCT cana-5017 134 4 175 175 NUM cana-5017 134 5 - - SYM cana-5017 134 6 194 194 NUM cana-5017 134 7 . . PUNCT cana-5017 135 1 available available ADJ cana-5017 135 2 from from ADP cana-5017 135 3 : : PUNCT cana-5017 135 4 doi doi PROPN cana-5017 135 5 10.1086/377226 10.1086/377226 PROPN cana-5017 135 6 . . PROPN cana-5017 135 7 6 6 NUM cana-5017 135 8 ) ) PUNCT cana-5017 135 9 tegmark tegmark NOUN cana-5017 135 10 m m PROPN cana-5017 135 11 and and CCONJ cana-5017 135 12 costa costa PROPN cana-5017 135 13 a a X cana-5017 135 14 , , PUNCT cana-5017 135 15 cmb cmb PROPN cana-5017 135 16 multipole multipole NOUN cana-5017 135 17 measurements measurement NOUN cana-5017 135 18 in in ADP cana-5017 135 19 the the DET cana-5017 135 20 presence presence NOUN cana-5017 135 21 of of ADP cana-5017 135 22 foregrounds foreground VERB cana-5017 135 23 . . PUNCT cana-5017 136 1 physical physical ADJ cana-5017 136 2 review review PROPN cana-5017 136 3 d. d. PROPN cana-5017 136 4 2006 2006 NUM cana-5017 136 5 ; ; PUNCT cana-5017 136 6 4(2 4(2 NUM cana-5017 136 7 ) ) PUNCT cana-5017 136 8 . . PUNCT cana-5017 137 1 available available ADJ cana-5017 137 2 from from ADP cana-5017 137 3 : : PUNCT cana-5017 137 4 https://doi.org/10.1103 https://doi.org/10.1103 NOUN cana-5017 137 5 / / SYM cana-5017 137 6 physrevd.74.023005 physrevd.74.023005 NOUN cana-5017 137 7 . . PUNCT cana-5017 138 1 7 7 X cana-5017 138 2 ) ) PUNCT cana-5017 138 3 hinshaw hinshaw PROPN cana-5017 138 4 g g PROPN cana-5017 138 5 , , PUNCT cana-5017 138 6 weiland weiland PROPN cana-5017 138 7 jl jl PROPN cana-5017 138 8 , , PUNCT cana-5017 138 9 hill hill NOUN cana-5017 138 10 rs rs NOUN cana-5017 138 11 , , PUNCT cana-5017 138 12 odegard odegard NOUN cana-5017 138 13 n n CCONJ cana-5017 138 14 , , PUNCT cana-5017 138 15 larson larson PROPN cana-5017 138 16 d d PROPN cana-5017 138 17 , , PUNCT cana-5017 138 18 bennett bennett PROPN cana-5017 138 19 cl cl PROPN cana-5017 138 20 , , PUNCT cana-5017 138 21 dunkley dunkley NOUN cana-5017 138 22 , , PUNCT cana-5017 138 23 gold gold NOUN cana-5017 138 24 b b PROPN cana-5017 138 25 , , PUNCT cana-5017 138 26 greason greason PROPN cana-5017 138 27 mr mr PROPN cana-5017 138 28 , , PUNCT cana-5017 138 29 jarosik jarosik NOUN cana-5017 138 30 m m PROPN cana-5017 138 31 , , PUNCT cana-5017 138 32 five five NUM cana-5017 138 33 - - PUNCT cana-5017 138 34 year year NOUN cana-5017 138 35 wilkinson wilkinson PROPN cana-5017 138 36 microwave microwave PROPN cana-5017 138 37 anisotropy anisotropy VERB cana-5017 138 38 probe probe NOUN cana-5017 138 39 observations observation NOUN cana-5017 138 40 : : PUNCT cana-5017 138 41 data datum NOUN cana-5017 138 42 processing processing NOUN cana-5017 138 43 , , PUNCT cana-5017 138 44 sky sky NOUN cana-5017 138 45 maps map NOUN cana-5017 138 46 , , PUNCT cana-5017 138 47 and and CCONJ cana-5017 138 48 basic basic ADJ cana-5017 138 49 results result NOUN cana-5017 138 50 . . PUNCT cana-5017 139 1 the the DET cana-5017 139 2 astrophysical astrophysical ADJ cana-5017 139 3 journal journal PROPN cana-5017 139 4 supplement supplement NOUN cana-5017 139 5 series series PROPN cana-5017 139 6 . . PUNCT cana-5017 140 1 2009;180(2 2009;180(2 NUM cana-5017 140 2 ) ) PUNCT cana-5017 140 3 . . PUNCT cana-5017 141 1 available available ADJ cana-5017 141 2 from from ADP cana-5017 141 3 : : PUNCT cana-5017 141 4 doi doi PROPN cana-5017 141 5 10.1088/0067 10.1088/0067 PROPN cana-5017 141 6 - - PUNCT cana-5017 141 7 0049/180/2/225 0049/180/2/225 NOUN cana-5017 141 8 . . NOUN cana-5017 141 9 8 8 NUM cana-5017 141 10 nolta nolta PROPN cana-5017 141 11 mr mr PROPN cana-5017 141 12 , , PUNCT cana-5017 141 13 dunkley dunkley PROPN cana-5017 141 14 j j PROPN cana-5017 141 15 , , PUNCT cana-5017 141 16 hill hill NOUN cana-5017 141 17 rs rs PROPN cana-5017 141 18 , , PUNCT cana-5017 141 19 hinshaw hinshaw PROPN cana-5017 141 20 g g PROPN cana-5017 141 21 , , PUNCT cana-5017 141 22 komatsu komatsu PROPN cana-5017 141 23 e e PROPN cana-5017 141 24 , , PUNCT cana-5017 141 25 larson larson PROPN cana-5017 141 26 d d PROPN cana-5017 141 27 , , PUNCT cana-5017 141 28 page page NOUN cana-5017 141 29 l l NOUN cana-5017 141 30 , , PUNCT cana-5017 141 31 spergel spergel NOUN cana-5017 141 32 dn dn PROPN cana-5017 141 33 , , PUNCT cana-5017 141 34 bennett bennett PROPN cana-5017 141 35 cl cl PROPN cana-5017 141 36 , , PUNCT cana-5017 141 37 gold gold NOUN cana-5017 141 38 b b PROPN cana-5017 141 39 , , PUNCT cana-5017 141 40 et et PROPN cana-5017 141 41 al al PROPN cana-5017 141 42 . . PROPN cana-5017 141 43 , , PUNCT cana-5017 141 44 five five NUM cana-5017 141 45 - - PUNCT cana-5017 141 46 year year NOUN cana-5017 141 47 wilkinson wilkinson PROPN cana-5017 141 48 microwave microwave PROPN cana-5017 141 49 anisotropy anisotropy VERB cana-5017 141 50 probe probe NOUN cana-5017 141 51 * * PUNCT cana-5017 141 52 observations observation NOUN cana-5017 141 53 : : PUNCT cana-5017 141 54 angular angular ADJ cana-5017 141 55 power power NOUN cana-5017 141 56 spectra spectra PROPN cana-5017 141 57 . . PUNCT cana-5017 142 1 the the DET cana-5017 142 2 astrophysical astrophysical ADJ cana-5017 142 3 journal journal PROPN cana-5017 142 4 supplement supplement NOUN cana-5017 142 5 series series PROPN cana-5017 142 6 . . PUNCT cana-5017 142 7 2009 2009 NUM cana-5017 142 8 ; ; PUNCT cana-5017 142 9 180(2 180(2 NUM cana-5017 142 10 ) ) PUNCT cana-5017 142 11 . . PUNCT cana-5017 143 1 available available ADJ cana-5017 143 2 from from ADP cana-5017 143 3 : : PUNCT cana-5017 143 4 doi doi PROPN cana-5017 143 5 10.1088/0067 10.1088/0067 PROPN cana-5017 143 6 - - PUNCT cana-5017 143 7 0049/180/2/296 0049/180/2/296 NUM cana-5017 143 8 . . NOUN cana-5017 143 9 9 9 NUM cana-5017 143 10 ) ) PUNCT cana-5017 143 11 hinshaw hinshaw NOUN cana-5017 143 12 g g PROPN cana-5017 143 13 , , PUNCT cana-5017 143 14 larson larson PROPN cana-5017 143 15 d d PROPN cana-5017 143 16 , , PUNCT cana-5017 143 17 komatsu komatsu PROPN cana-5017 143 18 e e NOUN cana-5017 143 19 , , PUNCT cana-5017 143 20 spergel spergel NOUN cana-5017 143 21 dn dn PROPN cana-5017 143 22 , , PUNCT cana-5017 143 23 bennett bennett PROPN cana-5017 143 24 cl cl PROPN cana-5017 143 25 , , PUNCT cana-5017 143 26 dunkley dunkley PROPN cana-5017 143 27 jn jn PROPN cana-5017 143 28 , , PUNCT cana-5017 143 29 nolta nolta VERB cana-5017 143 30 mr mr PROPN cana-5017 143 31 , , PUNCT cana-5017 143 32 halpern halpern PROPN cana-5017 143 33 m m PROPN cana-5017 143 34 , , PUNCT cana-5017 143 35 hill hill NOUN cana-5017 143 36 rs rs NOUN cana-5017 143 37 , , PUNCT cana-5017 143 38 odegard odegard NOUN cana-5017 143 39 n n CCONJ cana-5017 143 40 , , PUNCT cana-5017 143 41 et et PROPN cana-5017 143 42 al al PROPN cana-5017 143 43 . . PROPN cana-5017 143 44 , , PUNCT cana-5017 143 45 nine nine NUM cana-5017 143 46 - - PUNCT cana-5017 143 47 year year NOUN cana-5017 143 48 wilkinson wilkinson PROPN cana-5017 143 49 microwave microwave PROPN cana-5017 143 50 anisotropy anisotropy NOUN cana-5017 143 51 probe probe NOUN cana-5017 143 52 ( ( PUNCT cana-5017 143 53 wmap wmap ADJ cana-5017 143 54 ) ) PUNCT cana-5017 143 55 observations observation NOUN cana-5017 143 56 : : PUNCT cana-5017 143 57 cosmological cosmological ADJ cana-5017 143 58 parameter parameter NOUN cana-5017 143 59 results result VERB cana-5017 143 60 . . PUNCT cana-5017 144 1 the the DET cana-5017 144 2 astrophysical astrophysical ADJ cana-5017 144 3 journal journal PROPN cana-5017 144 4 supplement supplement PROPN cana-5017 144 5 series.2013;208(2 series.2013;208(2 NOUN cana-5017 144 6 ) ) PUNCT cana-5017 144 7 . . PUNCT cana-5017 145 1 available available ADJ cana-5017 145 2 from from ADP cana-5017 145 3 : : PUNCT cana-5017 145 4 doi doi PROPN cana-5017 145 5 10.1088/0067 10.1088/0067 PROPN cana-5017 145 6 - - PUNCT cana-5017 145 7 0049/208/2/19 0049/208/2/19 NUM cana-5017 145 8 . . PUNCT cana-5017 145 9 10 10 NUM cana-5017 145 10 ) ) PUNCT cana-5017 145 11 anderson anderson PROPN cana-5017 145 12 rl rl PROPN cana-5017 145 13 , , PUNCT cana-5017 145 14 campagnola campagnola PROPN cana-5017 145 15 s s PROPN cana-5017 145 16 , , PUNCT cana-5017 145 17 lantoine lantoine PROPN cana-5017 145 18 g. g. PROPN cana-5017 145 19 , , PUNCT cana-5017 145 20 broad broad ADJ cana-5017 145 21 search search NOUN cana-5017 145 22 for for ADP cana-5017 145 23 unstable unstable ADJ cana-5017 145 24 resonant resonant NOUN cana-5017 145 25 orbits orbit NOUN cana-5017 145 26 in in ADP cana-5017 145 27 the the DET cana-5017 145 28 planar planar ADJ cana-5017 145 29 circular circular NOUN cana-5017 145 30 restricted restrict VERB cana-5017 145 31 three three NUM cana-5017 145 32 - - PUNCT cana-5017 145 33 body body NOUN cana-5017 145 34 problem problem NOUN cana-5017 145 35 . . PUNCT cana-5017 146 1 celestial celestial ADJ cana-5017 146 2 mechanics mechanic NOUN cana-5017 146 3 and and CCONJ cana-5017 146 4 dynamical dynamical ADJ cana-5017 146 5 astronomy astronomy NOUN cana-5017 146 6 . . PUNCT cana-5017 146 7 2016 2016 NUM cana-5017 146 8 ; ; PUNCT cana-5017 146 9 124:177 124:177 NUM cana-5017 146 10 - - SYM cana-5017 146 11 99 99 NUM cana-5017 146 12 . . PUNCT cana-5017 146 13 available available ADJ cana-5017 146 14 from from ADP cana-5017 146 15 : : PUNCT cana-5017 146 16 https://doi.org/10.1007/s10569-015-9659-7 https://doi.org/10.1007/s10569-015-9659-7 NUM cana-5017 146 17 . . PUNCT cana-5017 147 1 11 11 NUM cana-5017 147 2 ) ) PUNCT cana-5017 147 3 kamenshchik kamenshchik VERB cana-5017 147 4 a a PRON cana-5017 147 5 , , PUNCT cana-5017 147 6 moschella moschella NOUN cana-5017 147 7 u u NOUN cana-5017 147 8 , , PUNCT cana-5017 147 9 pasquier pasquier NOUN cana-5017 147 10 v v PROPN cana-5017 147 11 , , PUNCT cana-5017 147 12 an an DET cana-5017 147 13 alternative alternative NOUN cana-5017 147 14 to to ADP cana-5017 147 15 quintessence quintessence NOUN cana-5017 147 16 . . PUNCT cana-5017 148 1 physics physics NOUN cana-5017 148 2 letters letters PROPN cana-5017 148 3 b. b. PROPN cana-5017 148 4 2001 2001 NUM cana-5017 148 5 ; ; PUNCT cana-5017 148 6 511(2 511(2 NUM cana-5017 148 7 - - SYM cana-5017 148 8 4):265 4):265 NUM cana-5017 148 9 - - PUNCT cana-5017 148 10 8 8 NUM cana-5017 148 11 . . PUNCT cana-5017 148 12 available available ADJ cana-5017 148 13 from from ADP cana-5017 148 14 : : PUNCT cana-5017 148 15 https://doi.org/10.1016/s0370-2693(01)00571-8 https://doi.org/10.1016/s0370-2693(01)00571-8 PROPN cana-5017 148 16 . . PROPN cana-5017 148 17 12 12 NUM cana-5017 148 18 ) ) PUNCT cana-5017 148 19 katore katore NOUN cana-5017 148 20 sd sd NOUN cana-5017 148 21 , , PUNCT cana-5017 148 22 kapse kapse PROPN cana-5017 148 23 dv dv PROPN cana-5017 148 24 , , PUNCT cana-5017 148 25 tayade tayade NOUN cana-5017 148 26 gb gb ADP cana-5017 148 27 , , PUNCT cana-5017 148 28 bianchi bianchi NOUN cana-5017 148 29 type type NOUN cana-5017 148 30 vi vi PROPN cana-5017 148 31 0 0 NUM cana-5017 148 32 cosmological cosmological ADJ cana-5017 148 33 models model NOUN cana-5017 148 34 with with ADP cana-5017 148 35 perfect perfect ADJ cana-5017 148 36 fluid fluid ADJ cana-5017 148 37 and and CCONJ cana-5017 148 38 dark dark ADJ cana-5017 148 39 energy energy NOUN cana-5017 148 40 . . PUNCT cana-5017 149 1 international international ADJ cana-5017 149 2 journal journal PROPN cana-5017 149 3 of of ADP cana-5017 149 4 theoretical theoretical ADJ cana-5017 149 5 physics physics NOUN cana-5017 149 6 . . PUNCT cana-5017 150 1 2011;50:3299 2011;50:3299 NUM cana-5017 150 2 - - SYM cana-5017 150 3 312.available 312.available NUM cana-5017 150 4 from from ADP cana-5017 150 5 : : PUNCT cana-5017 150 6 https://doi.org/10.1007/s10773-011-0832-9 https://doi.org/10.1007/s10773-011-0832-9 NUM cana-5017 150 7 . . PUNCT cana-5017 150 8 13 13 NUM cana-5017 150 9 ) ) PUNCT cana-5017 150 10 borkar borkar PROPN cana-5017 150 11 ms ms PROPN cana-5017 150 12 , , PUNCT cana-5017 150 13 charjan charjan NOUN cana-5017 150 14 ss ss PROPN cana-5017 150 15 , , PUNCT cana-5017 150 16 lepse lepse NOUN cana-5017 150 17 vv vv NOUN cana-5017 150 18 , , PUNCT cana-5017 150 19 evaluation evaluation NOUN cana-5017 150 20 of of ADP cana-5017 150 21 bianchi bianchi NOUN cana-5017 150 22 type type NOUN cana-5017 150 23 vi0 vi0 PROPN cana-5017 150 24 cosmological cosmological ADJ cana-5017 150 25 models model NOUN cana-5017 150 26 with with ADP cana-5017 150 27 a a DET cana-5017 150 28 binary binary ADJ cana-5017 150 29 mixture mixture NOUN cana-5017 150 30 of of ADP cana-5017 150 31 perfect perfect ADJ cana-5017 150 32 fluid fluid ADJ cana-5017 150 33 and and CCONJ cana-5017 150 34 dark dark ADJ cana-5017 150 35 energy energy NOUN cana-5017 150 36 in in ADP cana-5017 150 37 bimetric bimetric ADJ cana-5017 150 38 theory theory NOUN cana-5017 150 39 of of ADP cana-5017 150 40 gravitation gravitation NOUN cana-5017 150 41 . . PUNCT cana-5017 151 1 international international ADJ cana-5017 151 2 journal journal NOUN cana-5017 151 3 of of ADP cana-5017 151 4 applied apply VERB cana-5017 151 5 mathematics mathematic NOUN cana-5017 151 6 . . PUNCT cana-5017 152 1 2013;28(2):2051 2013;28(2):2051 NUM cana-5017 152 2 . . X cana-5017 153 1 14 14 NUM cana-5017 153 2 ) ) PUNCT cana-5017 153 3 copeland copeland PROPN cana-5017 153 4 ej ej PROPN cana-5017 153 5 , , PUNCT cana-5017 153 6 sami sami PROPN cana-5017 153 7 m m PROPN cana-5017 153 8 , , PUNCT cana-5017 153 9 tsujikawa tsujikawa PROPN cana-5017 153 10 s. s. PROPN cana-5017 153 11 dynamics dynamics PROPN cana-5017 153 12 of of ADP cana-5017 153 13 dark dark ADJ cana-5017 153 14 energy energy NOUN cana-5017 153 15 . . PUNCT cana-5017 154 1 international international ADJ cana-5017 154 2 journal journal NOUN cana-5017 154 3 of of ADP cana-5017 154 4 modern modern ADJ cana-5017 154 5 physics physics PROPN cana-5017 154 6 d. d. PROPN cana-5017 154 7 2006;15(11):1753 2006;15(11):1753 PROPN cana-5017 154 8 - - PROPN cana-5017 154 9 935 935 NUM cana-5017 154 10 . . PUNCT cana-5017 154 11 available available ADJ cana-5017 154 12 from from ADP cana-5017 154 13 : : PUNCT cana-5017 154 14 https://doi.org/10.1142/s021827180600942x https://doi.org/10.1142/s021827180600942x NOUN cana-5017 154 15 . . NOUN cana-5017 154 16 15 15 NUM cana-5017 154 17 ) ) PUNCT cana-5017 154 18 saha saha PROPN cana-5017 154 19 b b PROPN cana-5017 154 20 , , PUNCT cana-5017 154 21 anisotropic anisotropic NOUN cana-5017 154 22 cosmological cosmological ADJ cana-5017 154 23 models model NOUN cana-5017 154 24 with with ADP cana-5017 154 25 perfect perfect ADJ cana-5017 154 26 fluid fluid ADJ cana-5017 154 27 and and CCONJ cana-5017 154 28 dark dark ADJ cana-5017 154 29 energy energy NOUN cana-5017 154 30 . . PUNCT cana-5017 155 1 arxiv arxiv PROPN cana-5017 155 2 preprint preprint NOUN cana-5017 155 3 grqc/0412078 grqc/0412078 NOUN cana-5017 155 4 . . PUNCT cana-5017 156 1 2004 2004 NUM cana-5017 156 2 . . PUNCT cana-5017 157 1 available available ADJ cana-5017 157 2 from from ADP cana-5017 157 3 : : PUNCT cana-5017 157 4 https://doi.org/10.48550/arxiv.gr-qc/0412078 https://doi.org/10.48550/arxiv.gr-qc/0412078 NOUN cana-5017 157 5 . . NOUN cana-5017 157 6 16 16 NUM cana-5017 157 7 ) ) PUNCT cana-5017 157 8 singh singh PROPN cana-5017 157 9 t t PROPN cana-5017 157 10 , , PUNCT cana-5017 157 11 chaubey chaubey NOUN cana-5017 157 12 r r NOUN cana-5017 157 13 , , PUNCT cana-5017 157 14 bianchi bianchi NOUN cana-5017 157 15 type type NOUN cana-5017 157 16 - - PUNCT cana-5017 157 17 v v NOUN cana-5017 157 18 cosmological cosmological ADJ cana-5017 157 19 models model NOUN cana-5017 157 20 with with ADP cana-5017 157 21 perfect perfect ADJ cana-5017 157 22 fluid fluid ADJ cana-5017 157 23 and and CCONJ cana-5017 157 24 dark dark ADJ cana-5017 157 25 energy energy NOUN cana-5017 157 26 . . PUNCT cana-5017 158 1 astrophysics astrophysic NOUN cana-5017 158 2 and and CCONJ cana-5017 158 3 space space NOUN cana-5017 158 4 science science NOUN cana-5017 158 5 . . PUNCT cana-5017 159 1 2009;319:149 2009;319:149 ADV cana-5017 159 2 - - SYM cana-5017 159 3 54 54 NUM cana-5017 159 4 . . PUNCT cana-5017 160 1 available available ADJ cana-5017 160 2 from from ADP cana-5017 160 3 : : PUNCT cana-5017 160 4 https://doi.org/10.1007/s10509008-9959-4 https://doi.org/10.1007/s10509008-9959-4 PROPN cana-5017 160 5 . . PUNCT cana-5017 161 1 https://doi.org/10.1016/s0370-2693(01)00571-8 https://doi.org/10.1016/s0370-2693(01)00571-8 NOUN cana-5017 161 2 https://doi.org/10.1142/s021827180600942x https://doi.org/10.1142/s021827180600942x NOUN cana-5017 161 3 https://doi.org/10.48550/arxiv.gr-qc/0412078 https://doi.org/10.48550/arxiv.gr-qc/0412078 PROPN cana-5017 161 4 communications communication NOUN cana-5017 161 5 on on ADP cana-5017 161 6 applied apply VERB cana-5017 161 7 nonlinear nonlinear ADJ cana-5017 161 8 analysis analysis NOUN cana-5017 161 9 issn issn NOUN cana-5017 161 10 : : PUNCT cana-5017 161 11 1074 1074 NUM cana-5017 161 12 - - PUNCT cana-5017 161 13 133x 133x NUM cana-5017 161 14 vol vol NOUN cana-5017 161 15 31 31 NUM cana-5017 161 16 no no NOUN cana-5017 161 17 . . PUNCT cana-5017 162 1 8s 8s PROPN cana-5017 162 2 ( ( PUNCT cana-5017 162 3 2024 2024 NUM cana-5017 162 4 ) ) PUNCT cana-5017 162 5 921 921 NUM cana-5017 162 6 https://internationalpubls.com https://internationalpubls.com X cana-5017 162 7 17 17 NUM cana-5017 162 8 ) ) PUNCT cana-5017 162 9 dev dev NOUN cana-5017 162 10 a a X cana-5017 162 11 , , PUNCT cana-5017 162 12 alcaniz alcaniz PROPN cana-5017 162 13 js js PROPN cana-5017 162 14 , , PUNCT cana-5017 162 15 jain jain PROPN cana-5017 162 16 d d PROPN cana-5017 162 17 , , PUNCT cana-5017 162 18 cosmological cosmological ADJ cana-5017 162 19 consequences consequence NOUN cana-5017 162 20 of of ADP cana-5017 162 21 a a DET cana-5017 162 22 chaplygin chaplygin ADJ cana-5017 162 23 gas gas NOUN cana-5017 162 24 dark dark NOUN cana-5017 162 25 energy energy NOUN cana-5017 162 26 . . PUNCT cana-5017 163 1 physical physical PROPN cana-5017 163 2 review review PROPN cana-5017 163 3 d. d. PROPN cana-5017 163 4 2003;67(2 2003;67(2 NUM cana-5017 163 5 ) ) PUNCT cana-5017 163 6 . . PUNCT cana-5017 164 1 available available ADJ cana-5017 164 2 from from ADP cana-5017 164 3 : : PUNCT cana-5017 164 4 https://doi.org/10.1103/physrevd.67.023515 https://doi.org/10.1103/physrevd.67.023515 NOUN cana-5017 164 5 . . PUNCT cana-5017 165 1 18 18 NUM cana-5017 165 2 ) ) PUNCT cana-5017 165 3 bento bento NOUN cana-5017 165 4 mc mc PROPN cana-5017 165 5 , , PUNCT cana-5017 165 6 bertolami bertolami PROPN cana-5017 165 7 o o NOUN cana-5017 165 8 , , PUNCT cana-5017 165 9 sen sen PROPN cana-5017 165 10 aa aa PROPN cana-5017 165 11 , , PUNCT cana-5017 165 12 generalized generalize VERB cana-5017 165 13 chaplygin chaplygin NOUN cana-5017 165 14 gas gas NOUN cana-5017 165 15 , , PUNCT cana-5017 165 16 accelerated accelerate VERB cana-5017 165 17 expansion expansion NOUN cana-5017 165 18 , , PUNCT cana-5017 165 19 and and CCONJ cana-5017 165 20 darkenergy darkenergy NOUN cana-5017 165 21 - - PUNCT cana-5017 165 22 matter matter NOUN cana-5017 165 23 unification unification NOUN cana-5017 165 24 . . PUNCT cana-5017 166 1 physical physical PROPN cana-5017 166 2 review review PROPN cana-5017 166 3 d. d. PROPN cana-5017 166 4 2002;66(4 2002;66(4 NUM cana-5017 166 5 ) ) PUNCT cana-5017 166 6 . . PUNCT cana-5017 167 1 available available ADJ cana-5017 167 2 from from ADP cana-5017 167 3 : : PUNCT cana-5017 167 4 https://doi.org/10.1103/physrevd.66.043507 https://doi.org/10.1103/physrevd.66.043507 NOUN cana-5017 167 5 . . PUNCT cana-5017 168 1 19 19 NUM cana-5017 168 2 ) ) PUNCT cana-5017 168 3 prajapati prajapati PROPN cana-5017 168 4 s s PART cana-5017 168 5 , , PUNCT cana-5017 168 6 lrs lrs PROPN cana-5017 168 7 bianchi bianchi PROPN cana-5017 168 8 type type PROPN cana-5017 168 9 - - PUNCT cana-5017 168 10 i i PRON cana-5017 168 11 perfect perfect ADJ cana-5017 168 12 fluid fluid ADJ cana-5017 168 13 cosmological cosmological ADJ cana-5017 168 14 model model NOUN cana-5017 168 15 with with ADP cana-5017 168 16 modified modify VERB cana-5017 168 17 generalized generalize VERB cana-5017 168 18 chaplygin chaplygin NOUN cana-5017 168 19 gas gas NOUN cana-5017 168 20 equation equation NOUN cana-5017 168 21 of of ADP cana-5017 168 22 state state NOUN cana-5017 168 23 . . PUNCT cana-5017 169 1 astrophysics astrophysic NOUN cana-5017 169 2 & & CCONJ cana-5017 169 3 space space NOUN cana-5017 169 4 science science NOUN cana-5017 169 5 . . PUNCT cana-5017 170 1 2011;332(2 2011;332(2 NUM cana-5017 170 2 ) ) PUNCT cana-5017 170 3 . . PUNCT cana-5017 171 1 available available ADJ cana-5017 171 2 from from ADP cana-5017 171 3 : : PUNCT cana-5017 171 4 10.1007 10.1007 NUM cana-5017 171 5 / / SYM cana-5017 171 6 s10509 s10509 NOUN cana-5017 171 7 - - PUNCT cana-5017 171 8 010 010 NUM cana-5017 171 9 - - PUNCT cana-5017 171 10 0508 0508 NUM cana-5017 171 11 - - PUNCT cana-5017 171 12 6 6 NUM cana-5017 171 13 . . NOUN cana-5017 171 14 20 20 NUM cana-5017 171 15 ) ) PUNCT cana-5017 171 16 rosen rosen PROPN cana-5017 171 17 n n CCONJ cana-5017 171 18 , , PUNCT cana-5017 171 19 a a DET cana-5017 171 20 bi bi ADJ cana-5017 171 21 - - ADJ cana-5017 171 22 metric metric ADJ cana-5017 171 23 theory theory NOUN cana-5017 171 24 of of ADP cana-5017 171 25 gravitation gravitation NOUN cana-5017 171 26 . . PUNCT cana-5017 172 1 general general ADJ cana-5017 172 2 relativity relativity NOUN cana-5017 172 3 and and CCONJ cana-5017 172 4 gravitation gravitation NOUN cana-5017 172 5 . . PUNCT cana-5017 173 1 1973;4:435 1973;4:435 NUM cana-5017 173 2 - - SYM cana-5017 173 3 47 47 NUM cana-5017 173 4 . . PUNCT cana-5017 174 1 available available ADJ cana-5017 174 2 from from ADP cana-5017 174 3 : : PUNCT cana-5017 174 4 https://doi.org/10.1007/bf01215403 https://doi.org/10.1007/bf01215403 NOUN cana-5017 174 5 . . NOUN cana-5017 174 6 21 21 NUM cana-5017 174 7 ) ) PUNCT cana-5017 174 8 rosen rosen PROPN cana-5017 174 9 n n CCONJ cana-5017 174 10 , , PUNCT cana-5017 174 11 a a DET cana-5017 174 12 bi bi ADJ cana-5017 174 13 - - ADJ cana-5017 174 14 metric metric ADJ cana-5017 174 15 theory theory NOUN cana-5017 174 16 of of ADP cana-5017 174 17 gravitation gravitation NOUN cana-5017 174 18 . . PUNCT cana-5017 175 1 ii ii PROPN cana-5017 175 2 . . PUNCT cana-5017 175 3 general general ADJ cana-5017 175 4 relativity relativity NOUN cana-5017 175 5 and and CCONJ cana-5017 175 6 gravitation gravitation NOUN cana-5017 175 7 . . PUNCT cana-5017 176 1 1975:259 1975:259 NUM cana-5017 176 2 - - SYM cana-5017 176 3 68 68 NUM cana-5017 176 4 . . PUNCT cana-5017 176 5 available available ADJ cana-5017 176 6 from from ADP cana-5017 176 7 : : PUNCT cana-5017 176 8 https://doi.org/10.1007/bf00751570 https://doi.org/10.1007/bf00751570 NOUN cana-5017 176 9 . . NOUN cana-5017 176 10 22 22 NUM cana-5017 176 11 ) ) PUNCT cana-5017 176 12 karade karade NOUN cana-5017 176 13 tm tm PROPN cana-5017 176 14 , , PUNCT cana-5017 176 15 spherically spherically NOUN cana-5017 176 16 symmetric symmetric ADJ cana-5017 176 17 space space NOUN cana-5017 176 18 - - PUNCT cana-5017 176 19 times time NOUN cana-5017 176 20 in in ADP cana-5017 176 21 bimetric bimetric ADJ cana-5017 176 22 relativity relativity NOUN cana-5017 176 23 theory theory NOUN cana-5017 176 24 i. i. PROPN cana-5017 176 25 indian indian PROPN cana-5017 176 26 j. j. PROPN cana-5017 176 27 pure pure PROPN cana-5017 176 28 - - PUNCT cana-5017 176 29 appl appl NOUN cana-5017 176 30 . . PUNCT cana-5017 176 31 math math PROPN cana-5017 176 32 .. .. PUNCT cana-5017 177 1 1980;11:1202 1980;11:1202 NUM cana-5017 177 2 - - SYM cana-5017 177 3 9 9 NUM cana-5017 177 4 . . NOUN cana-5017 177 5 23 23 NUM cana-5017 177 6 ) ) PUNCT cana-5017 177 7 reddy reddy PROPN cana-5017 177 8 dr dr PROPN cana-5017 177 9 , , PUNCT cana-5017 177 10 venkateswara venkateswara PROPN cana-5017 177 11 rao rao PROPN cana-5017 177 12 n n CCONJ cana-5017 177 13 , , PUNCT cana-5017 177 14 on on ADP cana-5017 177 15 some some DET cana-5017 177 16 bianchi bianchi NOUN cana-5017 177 17 type type NOUN cana-5017 177 18 cosmological cosmological ADJ cana-5017 177 19 models model NOUN cana-5017 177 20 in in ADP cana-5017 177 21 a a DET cana-5017 177 22 bimetric bimetric ADJ cana-5017 177 23 theory theory NOUN cana-5017 177 24 of of ADP cana-5017 177 25 gravitation gravitation NOUN cana-5017 177 26 . . PUNCT cana-5017 178 1 astrophysics astrophysic NOUN cana-5017 178 2 and and CCONJ cana-5017 178 3 space space NOUN cana-5017 178 4 science science NOUN cana-5017 178 5 . . PUNCT cana-5017 179 1 1997;257:293 1997;257:293 NUM cana-5017 179 2 - - SYM cana-5017 179 3 8 8 NUM cana-5017 179 4 . . PUNCT cana-5017 179 5 available available ADJ cana-5017 179 6 from from ADP cana-5017 179 7 : : PUNCT cana-5017 179 8 https://doi.org/10.1023/a:1001166619709 https://doi.org/10.1023/a:1001166619709 NOUN cana-5017 179 9 . . PUNCT cana-5017 180 1 24 24 NUM cana-5017 180 2 ) ) PUNCT cana-5017 180 3 gaikwad gaikwad NOUN cana-5017 180 4 np np PROPN cana-5017 180 5 , , PUNCT cana-5017 180 6 borkar borkar PROPN cana-5017 180 7 ms ms PROPN cana-5017 180 8 , , PUNCT cana-5017 180 9 charjan charjan NOUN cana-5017 180 10 ss ss PROPN cana-5017 180 11 , , PUNCT cana-5017 180 12 bianchi bianchi NOUN cana-5017 180 13 type type NOUN cana-5017 180 14 - - PUNCT cana-5017 180 15 i i PRON cana-5017 180 16 massive massive ADJ cana-5017 180 17 string string NOUN cana-5017 180 18 magnetized magnetize VERB cana-5017 180 19 barotropic barotropic ADJ cana-5017 180 20 perfect perfect ADJ cana-5017 180 21 fluid fluid ADJ cana-5017 180 22 cosmological cosmological ADJ cana-5017 180 23 model model NOUN cana-5017 180 24 in in ADP cana-5017 180 25 the the DET cana-5017 180 26 bimetric bimetric ADJ cana-5017 180 27 theory theory NOUN cana-5017 180 28 of of ADP cana-5017 180 29 gravitation gravitation NOUN cana-5017 180 30 . . PUNCT cana-5017 181 1 chinese chinese ADJ cana-5017 181 2 physics physics NOUN cana-5017 181 3 letters letter NOUN cana-5017 181 4 . . PUNCT cana-5017 182 1 2011;28(8 2011;28(8 NUM cana-5017 182 2 ) ) PUNCT cana-5017 182 3 . . PUNCT cana-5017 183 1 available available ADJ cana-5017 183 2 from from ADP cana-5017 183 3 : : PUNCT cana-5017 183 4 doi doi NOUN cana-5017 183 5 10.1088/0256 10.1088/0256 PROPN cana-5017 183 6 - - SYM cana-5017 183 7 307x/28/8/089803 307x/28/8/089803 NUM cana-5017 183 8 . . NOUN cana-5017 184 1 25 25 NUM cana-5017 184 2 ) ) PUNCT cana-5017 184 3 penrose penrose NOUN cana-5017 184 4 r r NOUN cana-5017 184 5 , , PUNCT cana-5017 184 6 gravitational gravitational ADJ cana-5017 184 7 collapse collapse NOUN cana-5017 184 8 and and CCONJ cana-5017 184 9 space space NOUN cana-5017 184 10 - - PUNCT cana-5017 184 11 time time NOUN cana-5017 184 12 singularities singularity NOUN cana-5017 184 13 . . PUNCT cana-5017 185 1 physical physical ADJ cana-5017 185 2 review review NOUN cana-5017 185 3 letters letter NOUN cana-5017 185 4 . . PUNCT cana-5017 186 1 1965;14(3):57 1965;14(3):57 X cana-5017 186 2 . . PUNCT cana-5017 186 3 available available ADJ cana-5017 186 4 from from ADP cana-5017 186 5 : : PUNCT cana-5017 186 6 https://doi.org/10.1103/physrevlett.14.57 https://doi.org/10.1103/physrevlett.14.57 PROPN cana-5017 186 7 . . PUNCT cana-5017 187 1 26 26 NUM cana-5017 187 2 ) ) PUNCT cana-5017 187 3 karade karade NOUN cana-5017 187 4 tm tm PROPN cana-5017 187 5 , , PUNCT cana-5017 187 6 the the DET cana-5017 187 7 nature nature NOUN cana-5017 187 8 of of ADP cana-5017 187 9 the the DET cana-5017 187 10 singularity singularity NOUN cana-5017 187 11 in in ADP cana-5017 187 12 the the DET cana-5017 187 13 gravitational gravitational ADJ cana-5017 187 14 field field NOUN cana-5017 187 15 of of ADP cana-5017 187 16 a a DET cana-5017 187 17 charged charge VERB cana-5017 187 18 particle particle NOUN cana-5017 187 19 . . PUNCT cana-5017 188 1 acta acta PROPN cana-5017 188 2 physica physica PROPN cana-5017 188 3 academiae academiae PROPN cana-5017 188 4 scientiarum scientiarum PROPN cana-5017 188 5 hungaricae hungaricae PROPN cana-5017 188 6 . . PUNCT cana-5017 189 1 1975:227 1975:227 NUM cana-5017 189 2 - - SYM cana-5017 189 3 31 31 NUM cana-5017 189 4 . . PUNCT cana-5017 190 1 available available ADJ cana-5017 190 2 from from ADP cana-5017 190 3 : : PUNCT cana-5017 190 4 https://doi.org/10.1007/bf03157140 https://doi.org/10.1007/bf03157140 PROPN cana-5017 190 5 . . NOUN cana-5017 190 6 27 27 NUM cana-5017 190 7 ) ) PUNCT cana-5017 191 1 borkar borkar PROPN cana-5017 191 2 ms ms PROPN cana-5017 191 3 , , PUNCT cana-5017 191 4 karade karade NOUN cana-5017 191 5 tm tm PROPN cana-5017 191 6 , , PUNCT cana-5017 191 7 on on ADP cana-5017 191 8 singularity singularity NOUN cana-5017 191 9 of of ADP cana-5017 191 10 spherically spherically NOUN cana-5017 191 11 symmetric symmetric ADJ cana-5017 191 12 space space PROPN cana-5017 191 13 times times PROPN cana-5017 191 14 . . PUNCT cana-5017 192 1 indian indian PROPN cana-5017 192 2 journal journal PROPN cana-5017 192 3 of of ADP cana-5017 192 4 pure pure ADJ cana-5017 192 5 and and CCONJ cana-5017 192 6 applied applied ADJ cana-5017 192 7 mathematics mathematic NOUN cana-5017 192 8 . . PUNCT cana-5017 193 1 2003;34(8):1219 2003;34(8):1219 NUM cana-5017 193 2 - - PUNCT cana-5017 193 3 24 24 NUM cana-5017 193 4 . . NOUN cana-5017 193 5 28 28 NUM cana-5017 193 6 ) ) PUNCT cana-5017 193 7 pradhan pradhan PROPN cana-5017 193 8 a a PROPN cana-5017 193 9 , , PUNCT cana-5017 193 10 amirhashchi amirhashchi PROPN cana-5017 193 11 h h PROPN cana-5017 193 12 , , PUNCT cana-5017 193 13 yadav yadav PROPN cana-5017 193 14 mk mk PROPN cana-5017 193 15 , , PUNCT cana-5017 193 16 lrs lrs PROPN cana-5017 193 17 bianchi bianchi PROPN cana-5017 193 18 type type PROPN cana-5017 193 19 ii ii PROPN cana-5017 193 20 string string NOUN cana-5017 193 21 cosmological cosmological ADJ cana-5017 193 22 models model NOUN cana-5017 193 23 for for ADP cana-5017 193 24 perfect perfect ADJ cana-5017 193 25 fluid fluid ADJ cana-5017 193 26 distribution distribution NOUN cana-5017 193 27 in in ADP cana-5017 193 28 general general ADJ cana-5017 193 29 relativity relativity NOUN cana-5017 193 30 . . PUNCT cana-5017 194 1 fizika fizika PROPN cana-5017 194 2 b b PROPN cana-5017 194 3 : : PUNCT cana-5017 194 4 a a DET cana-5017 194 5 journal journal NOUN cana-5017 194 6 of of ADP cana-5017 194 7 experimental experimental ADJ cana-5017 194 8 and and CCONJ cana-5017 194 9 theoretical theoretical ADJ cana-5017 194 10 physics physics NOUN cana-5017 194 11 . . PUNCT cana-5017 195 1 2009;18(1):35 2009;18(1):35 NUM cana-5017 195 2 - - SYM cana-5017 195 3 42 42 NUM cana-5017 195 4 . . PUNCT cana-5017 196 1 available available ADJ cana-5017 196 2 from from ADP cana-5017 196 3 : : PUNCT cana-5017 196 4 https://hrcak.srce.hr/304572 https://hrcak.srce.hr/304572 X cana-5017 196 5 . . PROPN cana-5017 196 6 https://doi.org/10.1103/physrevd.66.043507 https://doi.org/10.1103/physrevd.66.043507 PROPN cana-5017 196 7 https://hrcak.srce.hr/304572 https://hrcak.srce.hr/304572 PUNCT