id sid tid token lemma pos american_scientific_journal-1665 1 1 52 52 NUM american_scientific_journal-1665 1 2 american american ADJ american_scientific_journal-1665 1 3 scientific scientific ADJ american_scientific_journal-1665 1 4 research research NOUN american_scientific_journal-1665 1 5 journal journal NOUN american_scientific_journal-1665 1 6 for for ADP american_scientific_journal-1665 1 7 engineering engineering NOUN american_scientific_journal-1665 1 8 , , PUNCT american_scientific_journal-1665 1 9 technology technology NOUN american_scientific_journal-1665 1 10 , , PUNCT american_scientific_journal-1665 1 11 and and CCONJ american_scientific_journal-1665 1 12 sciences science NOUN american_scientific_journal-1665 1 13 ( ( PUNCT american_scientific_journal-1665 1 14 asrjets asrjet NOUN american_scientific_journal-1665 1 15 ) ) PUNCT american_scientific_journal-1665 1 16 issn issn PROPN american_scientific_journal-1665 1 17 ( ( PUNCT american_scientific_journal-1665 1 18 print print NOUN american_scientific_journal-1665 1 19 ) ) PUNCT american_scientific_journal-1665 1 20 2313 2313 NUM american_scientific_journal-1665 1 21 - - SYM american_scientific_journal-1665 1 22 4410 4410 NUM american_scientific_journal-1665 1 23 , , PUNCT american_scientific_journal-1665 1 24 issn issn PROPN american_scientific_journal-1665 1 25 ( ( PUNCT american_scientific_journal-1665 1 26 online online ADJ american_scientific_journal-1665 1 27 ) ) PUNCT american_scientific_journal-1665 1 28 2313 2313 NUM american_scientific_journal-1665 1 29 - - SYM american_scientific_journal-1665 1 30 4402 4402 NUM american_scientific_journal-1665 1 31 Β© Β© PROPN american_scientific_journal-1665 1 32 global global ADJ american_scientific_journal-1665 1 33 society society NOUN american_scientific_journal-1665 1 34 of of ADP american_scientific_journal-1665 1 35 scientific scientific ADJ american_scientific_journal-1665 1 36 research research NOUN american_scientific_journal-1665 1 37 and and CCONJ american_scientific_journal-1665 1 38 researchers researcher NOUN american_scientific_journal-1665 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ VERB american_scientific_journal-1665 1 40 on on ADP american_scientific_journal-1665 1 41 study study NOUN american_scientific_journal-1665 1 42 kh kh PROPN american_scientific_journal-1665 1 43 generalized generalize VERB american_scientific_journal-1665 1 44 birecurrent birecurrent NOUN american_scientific_journal-1665 1 45 affinely affinely ADV american_scientific_journal-1665 1 46 connected connect VERB american_scientific_journal-1665 1 47 space space NOUN american_scientific_journal-1665 1 48 fahmi fahmi PROPN american_scientific_journal-1665 1 49 yaseen yaseen PROPN american_scientific_journal-1665 1 50 abdo abdo PROPN american_scientific_journal-1665 1 51 qasema qasema VERB american_scientific_journal-1665 1 52 * * PROPN american_scientific_journal-1665 1 53 , , PUNCT american_scientific_journal-1665 1 54 amani amani PROPN american_scientific_journal-1665 1 55 mohammed mohammed PROPN american_scientific_journal-1665 1 56 abdulla abdulla PROPN american_scientific_journal-1665 1 57 hanballab hanballab PROPN american_scientific_journal-1665 1 58 adepartment adepartment NOUN american_scientific_journal-1665 1 59 of of ADP american_scientific_journal-1665 1 60 mathematics mathematic NOUN american_scientific_journal-1665 1 61 , , PUNCT american_scientific_journal-1665 1 62 faculty faculty NOUN american_scientific_journal-1665 1 63 of of ADP american_scientific_journal-1665 1 64 education education NOUN american_scientific_journal-1665 1 65 - - PUNCT american_scientific_journal-1665 1 66 aden aden PROPN american_scientific_journal-1665 1 67 , , PUNCT american_scientific_journal-1665 1 68 university university PROPN american_scientific_journal-1665 1 69 of of ADP american_scientific_journal-1665 1 70 aden aden PROPN american_scientific_journal-1665 1 71 , , PUNCT american_scientific_journal-1665 1 72 khormaksar khormaksar PROPN american_scientific_journal-1665 1 73 , , PUNCT american_scientific_journal-1665 1 74 aden aden PROPN american_scientific_journal-1665 1 75 , , PUNCT american_scientific_journal-1665 1 76 yemen yemen PROPN american_scientific_journal-1665 1 77 bdepartment bdepartment NOUN american_scientific_journal-1665 1 78 of of ADP american_scientific_journal-1665 1 79 mathematics mathematics PROPN american_scientific_journal-1665 1 80 , , PUNCT american_scientific_journal-1665 1 81 community community NOUN american_scientific_journal-1665 1 82 college college NOUN american_scientific_journal-1665 1 83 , , PUNCT american_scientific_journal-1665 1 84 dar dar PROPN american_scientific_journal-1665 1 85 - - PUNCT american_scientific_journal-1665 1 86 saad saad PROPN american_scientific_journal-1665 1 87 , , PUNCT american_scientific_journal-1665 1 88 aden aden PROPN american_scientific_journal-1665 1 89 , , PUNCT american_scientific_journal-1665 1 90 yemen yemen PROPN american_scientific_journal-1665 1 91 a a DET american_scientific_journal-1665 1 92 , , PUNCT american_scientific_journal-1665 1 93 bemail bemail NOUN american_scientific_journal-1665 1 94 : : PUNCT american_scientific_journal-1665 1 95 fahmiyassen1@gmail.com fahmiyassen1@gmail.com X american_scientific_journal-1665 1 96 , , PUNCT american_scientific_journal-1665 1 97 ahanballa@yahoo.com ahanballa@yahoo.com PUNCT american_scientific_journal-1665 2 1 abstract abstract ADJ american_scientific_journal-1665 2 2 in in ADP american_scientific_journal-1665 2 3 the the DET american_scientific_journal-1665 2 4 present present ADJ american_scientific_journal-1665 2 5 paper paper NOUN american_scientific_journal-1665 2 6 we we PRON american_scientific_journal-1665 2 7 introduce introduce VERB american_scientific_journal-1665 2 8 a a DET american_scientific_journal-1665 2 9 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 2 10 – – PUNCT american_scientific_journal-1665 2 11 generalized generalize VERB american_scientific_journal-1665 2 12 birecurrent birecurrent ADJ american_scientific_journal-1665 2 13 space space NOUN american_scientific_journal-1665 2 14 which which PRON american_scientific_journal-1665 2 15 characterized characterize VERB american_scientific_journal-1665 2 16 by by ADP american_scientific_journal-1665 2 17 the the DET american_scientific_journal-1665 2 18 condition condition NOUN american_scientific_journal-1665 2 19 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 2 20 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 2 21 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 2 22 = = PUNCT american_scientific_journal-1665 2 23 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 2 24 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 2 25 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 3 1 + + CCONJ american_scientific_journal-1665 3 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 3 3 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 3 4 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 3 5 , , PUNCT american_scientific_journal-1665 3 6 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 3 7 β‰  β‰  PROPN american_scientific_journal-1665 3 8 0 0 NUM american_scientific_journal-1665 3 9 , , PUNCT american_scientific_journal-1665 3 10 where where SCONJ american_scientific_journal-1665 3 11 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 3 12 and and CCONJ american_scientific_journal-1665 3 13 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 3 14 are be AUX american_scientific_journal-1665 3 15 non non ADJ american_scientific_journal-1665 3 16 - - ADJ american_scientific_journal-1665 3 17 zero zero ADJ american_scientific_journal-1665 3 18 covariant covariant ADJ american_scientific_journal-1665 3 19 vector vector NOUN american_scientific_journal-1665 3 20 fields field NOUN american_scientific_journal-1665 3 21 and and CCONJ american_scientific_journal-1665 3 22 covariant covariant ADJ american_scientific_journal-1665 3 23 tensor tensor NOUN american_scientific_journal-1665 3 24 field field NOUN american_scientific_journal-1665 3 25 of of ADP american_scientific_journal-1665 3 26 second second ADJ american_scientific_journal-1665 3 27 order order NOUN american_scientific_journal-1665 3 28 , , PUNCT american_scientific_journal-1665 3 29 respectively respectively ADV american_scientific_journal-1665 3 30 . . PUNCT american_scientific_journal-1665 4 1 this this DET american_scientific_journal-1665 4 2 space space NOUN american_scientific_journal-1665 4 3 satisfies satisfy VERB american_scientific_journal-1665 4 4 the the DET american_scientific_journal-1665 4 5 condition condition NOUN american_scientific_journal-1665 4 6 of of ADP american_scientific_journal-1665 4 7 affinely affinely ADV american_scientific_journal-1665 4 8 connected connected ADJ american_scientific_journal-1665 4 9 space space NOUN american_scientific_journal-1665 4 10 called call VERB american_scientific_journal-1665 4 11 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 4 12 – – PUNCT american_scientific_journal-1665 4 13 generalized generalize VERB american_scientific_journal-1665 4 14 birecurrent birecurrent NOUN american_scientific_journal-1665 4 15 affinely affinely ADV american_scientific_journal-1665 4 16 connected connected ADJ american_scientific_journal-1665 4 17 space space NOUN american_scientific_journal-1665 4 18 . . PUNCT american_scientific_journal-1665 5 1 keywords keyword NOUN american_scientific_journal-1665 5 2 : : PUNCT american_scientific_journal-1665 5 3 finsler finsler NOUN american_scientific_journal-1665 5 4 space space NOUN american_scientific_journal-1665 5 5 ; ; PUNCT american_scientific_journal-1665 5 6 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 5 7 βˆ’ βˆ’ ADP american_scientific_journal-1665 5 8 generalized generalize VERB american_scientific_journal-1665 5 9 birecurrent birecurrent ADJ american_scientific_journal-1665 5 10 space space NOUN american_scientific_journal-1665 5 11 ; ; PUNCT american_scientific_journal-1665 5 12 ricci ricci PROPN american_scientific_journal-1665 5 13 tensor tensor NOUN american_scientific_journal-1665 5 14 . . PROPN american_scientific_journal-1665 6 1 1 1 X american_scientific_journal-1665 6 2 . . X american_scientific_journal-1665 6 3 introduction introduction NOUN american_scientific_journal-1665 6 4 h. h. PROPN american_scientific_journal-1665 6 5 d. d. PROPN american_scientific_journal-1665 6 6 pande pande PROPN american_scientific_journal-1665 6 7 and and CCONJ american_scientific_journal-1665 6 8 b. b. PROPN american_scientific_journal-1665 6 9 single single NOUN american_scientific_journal-1665 7 1 [ [ X american_scientific_journal-1665 7 2 4 4 X american_scientific_journal-1665 7 3 ] ] PUNCT american_scientific_journal-1665 7 4 discussed discuss VERB american_scientific_journal-1665 7 5 the the DET american_scientific_journal-1665 7 6 recurrence recurrence NOUN american_scientific_journal-1665 7 7 property property NOUN american_scientific_journal-1665 7 8 in in ADP american_scientific_journal-1665 7 9 an an DET american_scientific_journal-1665 7 10 affinely affinely ADV american_scientific_journal-1665 7 11 connected connected ADJ american_scientific_journal-1665 7 12 space space NOUN american_scientific_journal-1665 7 13 . . PUNCT american_scientific_journal-1665 8 1 p. p. NOUN american_scientific_journal-1665 8 2 k. k. PROPN american_scientific_journal-1665 9 1 dwivedi dwivedi PROPN american_scientific_journal-1665 10 1 [ [ X american_scientific_journal-1665 10 2 7 7 X american_scientific_journal-1665 10 3 ] ] PUNCT american_scientific_journal-1665 10 4 worked work VERB american_scientific_journal-1665 10 5 out out ADP american_scientific_journal-1665 10 6 the the DET american_scientific_journal-1665 10 7 role role NOUN american_scientific_journal-1665 10 8 of of ADP american_scientific_journal-1665 10 9 π‘ƒπ‘ƒβˆ— π‘ƒπ‘ƒβˆ— PROPN american_scientific_journal-1665 10 10 – – PUNCT american_scientific_journal-1665 10 11 reducible reducible ADJ american_scientific_journal-1665 10 12 space space NOUN american_scientific_journal-1665 10 13 in in ADP american_scientific_journal-1665 10 14 affinely affinely ADV american_scientific_journal-1665 10 15 connected connected ADJ american_scientific_journal-1665 10 16 space space NOUN american_scientific_journal-1665 10 17 . . PUNCT american_scientific_journal-1665 11 1 a. a. NOUN american_scientific_journal-1665 11 2 a. a. PROPN american_scientific_journal-1665 11 3 m. m. PROPN american_scientific_journal-1665 11 4 saleem saleem PROPN american_scientific_journal-1665 12 1 [ [ X american_scientific_journal-1665 12 2 2 2 NUM american_scientific_journal-1665 12 3 ] ] PUNCT american_scientific_journal-1665 12 4 obtained obtain VERB american_scientific_journal-1665 12 5 some some DET american_scientific_journal-1665 12 6 results result NOUN american_scientific_journal-1665 12 7 when when SCONJ american_scientific_journal-1665 12 8 the the DET american_scientific_journal-1665 12 9 πΆπΆβ„Ž πΆπΆβ„Ž NOUN american_scientific_journal-1665 12 10 – – PUNCT american_scientific_journal-1665 12 11 generalized generalize VERB american_scientific_journal-1665 12 12 birecurrent birecurrent NOUN american_scientific_journal-1665 12 13 and and CCONJ american_scientific_journal-1665 12 14 πΆπΆβ„Ž πΆπΆβ„Ž NOUN american_scientific_journal-1665 12 15 – – PUNCT american_scientific_journal-1665 12 16 special special ADJ american_scientific_journal-1665 12 17 generalized generalize VERB american_scientific_journal-1665 12 18 birecurrent birecurrent NOUN american_scientific_journal-1665 12 19 are be AUX american_scientific_journal-1665 12 20 affinely affinely ADV american_scientific_journal-1665 12 21 connected connected ADJ american_scientific_journal-1665 12 22 spaces space NOUN american_scientific_journal-1665 12 23 . . PUNCT american_scientific_journal-1665 13 1 a. a. NOUN american_scientific_journal-1665 13 2 a. a. PROPN american_scientific_journal-1665 13 3 a. a. NOUN american_scientific_journal-1665 13 4 muhib muhib NOUN american_scientific_journal-1665 14 1 [ [ X american_scientific_journal-1665 14 2 1 1 NUM american_scientific_journal-1665 14 3 ] ] PUNCT american_scientific_journal-1665 14 4 obtained obtain VERB american_scientific_journal-1665 14 5 some some DET american_scientific_journal-1665 14 6 results result NOUN american_scientific_journal-1665 14 7 when when SCONJ american_scientific_journal-1665 14 8 π‘…π‘…β„Ž π‘…π‘…β„Ž NOUN american_scientific_journal-1665 14 9 – – PUNCT american_scientific_journal-1665 14 10 generalized generalize VERB american_scientific_journal-1665 14 11 trirecurrent trirecurrent NOUN american_scientific_journal-1665 14 12 and and CCONJ american_scientific_journal-1665 14 13 π‘…π‘…β„Ž π‘…π‘…β„Ž NOUN american_scientific_journal-1665 14 14 – – PUNCT american_scientific_journal-1665 14 15 special special ADJ american_scientific_journal-1665 14 16 generalized generalize VERB american_scientific_journal-1665 14 17 trirecurrent trirecurrent NOUN american_scientific_journal-1665 14 18 are be AUX american_scientific_journal-1665 14 19 affinely affinely ADV american_scientific_journal-1665 14 20 connected connected ADJ american_scientific_journal-1665 14 21 spaces space NOUN american_scientific_journal-1665 14 22 . . PUNCT american_scientific_journal-1665 15 1 m. m. NOUN american_scientific_journal-1665 15 2 a. a. PROPN american_scientific_journal-1665 15 3 a. a. PROPN american_scientific_journal-1665 15 4 ali ali PROPN american_scientific_journal-1665 16 1 [ [ X american_scientific_journal-1665 16 2 5 5 NUM american_scientific_journal-1665 16 3 ] ] PUNCT american_scientific_journal-1665 16 4 obtained obtain VERB american_scientific_journal-1665 16 5 certain certain ADJ american_scientific_journal-1665 16 6 identities identity NOUN american_scientific_journal-1665 16 7 in in ADP american_scientific_journal-1665 16 8 a a DET american_scientific_journal-1665 16 9 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 16 10 – – PUNCT american_scientific_journal-1665 16 11 birecurrent birecurrent VERB american_scientific_journal-1665 16 12 affinely affinely ADV american_scientific_journal-1665 16 13 connected connected ADJ american_scientific_journal-1665 16 14 spaces space NOUN american_scientific_journal-1665 16 15 . . PUNCT american_scientific_journal-1665 17 1 n. n. PROPN american_scientific_journal-1665 17 2 s. s. PROPN american_scientific_journal-1665 17 3 h. h. PROPN american_scientific_journal-1665 17 4 hussien hussien PROPN american_scientific_journal-1665 18 1 [ [ X american_scientific_journal-1665 18 2 6 6 NUM american_scientific_journal-1665 18 3 ] ] PUNCT american_scientific_journal-1665 18 4 obtained obtain VERB american_scientific_journal-1665 18 5 certain certain ADJ american_scientific_journal-1665 18 6 identities identity NOUN american_scientific_journal-1665 18 7 in in ADP american_scientific_journal-1665 18 8 a a DET american_scientific_journal-1665 18 9 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 18 10 – – PUNCT american_scientific_journal-1665 18 11 recurrent recurrent VERB american_scientific_journal-1665 18 12 affinely affinely ADV american_scientific_journal-1665 18 13 connected connected ADJ american_scientific_journal-1665 18 14 spaces space NOUN american_scientific_journal-1665 18 15 . . PUNCT american_scientific_journal-1665 19 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-1665 20 1 * * PUNCT american_scientific_journal-1665 20 2 corresponding correspond VERB american_scientific_journal-1665 20 3 author author NOUN american_scientific_journal-1665 20 4 . . PUNCT american_scientific_journal-1665 21 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-1665 21 2 mailto:fahmiyassen1@gmail.com mailto:fahmiyassen1@gmail.com X american_scientific_journal-1665 21 3 mailto:ahanballa@yahoo.com mailto:ahanballa@yahoo.com X american_scientific_journal-1665 21 4 65- 65- X american_scientific_journal-1665 21 5 ) ) PUNCT american_scientific_journal-1665 21 6 volume volume NOUN american_scientific_journal-1665 21 7 20 20 NUM american_scientific_journal-1665 21 8 , , PUNCT american_scientific_journal-1665 21 9 no no DET american_scientific_journal-1665 21 10 1 1 NUM american_scientific_journal-1665 21 11 , , PUNCT american_scientific_journal-1665 21 12 pp pp ADP american_scientific_journal-1665 21 13 522016 522016 NUM american_scientific_journal-1665 21 14 ( ( PUNCT american_scientific_journal-1665 21 15 ) ) PUNCT american_scientific_journal-1665 21 16 research research NOUN american_scientific_journal-1665 21 17 journal journal NOUN american_scientific_journal-1665 21 18 for for ADP american_scientific_journal-1665 21 19 engineering engineering NOUN american_scientific_journal-1665 21 20 , , PUNCT american_scientific_journal-1665 21 21 technology technology NOUN american_scientific_journal-1665 21 22 , , PUNCT american_scientific_journal-1665 21 23 and and CCONJ american_scientific_journal-1665 21 24 sciences science NOUN american_scientific_journal-1665 21 25 ( ( PUNCT american_scientific_journal-1665 21 26 asrjets asrjet NOUN american_scientific_journal-1665 21 27 scientificamerican scientificamerican NOUN american_scientific_journal-1665 21 28 53 53 NUM american_scientific_journal-1665 21 29 let let VERB american_scientific_journal-1665 21 30 𝐹𝐹𝑛𝑛 𝐹𝐹𝑛𝑛 PROPN american_scientific_journal-1665 21 31 be be AUX american_scientific_journal-1665 21 32 an an DET american_scientific_journal-1665 21 33 𝑛𝑛-dimensional 𝑛𝑛-dimensional ADJ american_scientific_journal-1665 21 34 finsler finsler NOUN american_scientific_journal-1665 21 35 space space NOUN american_scientific_journal-1665 21 36 equipped equip VERB american_scientific_journal-1665 21 37 with with ADP american_scientific_journal-1665 21 38 the the DET american_scientific_journal-1665 21 39 metric metric ADJ american_scientific_journal-1665 21 40 function function NOUN american_scientific_journal-1665 21 41 a a DET american_scientific_journal-1665 21 42 𝐹𝐹(π‘₯π‘₯,𝑦𝑦 𝐹𝐹(π‘₯π‘₯,𝑦𝑦 NOUN american_scientific_journal-1665 21 43 ) ) PUNCT american_scientific_journal-1665 21 44 satisfying satisfy VERB american_scientific_journal-1665 21 45 the the DET american_scientific_journal-1665 21 46 request request NOUN american_scientific_journal-1665 21 47 conditions condition NOUN american_scientific_journal-1665 22 1 [ [ X american_scientific_journal-1665 22 2 3 3 NUM american_scientific_journal-1665 22 3 ] ] PUNCT american_scientific_journal-1665 22 4 . . PUNCT american_scientific_journal-1665 23 1 the the DET american_scientific_journal-1665 23 2 vectors vector NOUN american_scientific_journal-1665 23 3 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-1665 23 4 , , PUNCT american_scientific_journal-1665 23 5 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-1665 23 6 and and CCONJ american_scientific_journal-1665 23 7 the the DET american_scientific_journal-1665 23 8 metric metric ADJ american_scientific_journal-1665 23 9 tensor tensor NOUN american_scientific_journal-1665 23 10 g𝑖𝑖𝑗𝑗 g𝑖𝑖𝑗𝑗 PROPN american_scientific_journal-1665 23 11 satisfies satisfy VERB american_scientific_journal-1665 23 12 the the DET american_scientific_journal-1665 23 13 following follow VERB american_scientific_journal-1665 23 14 relations relation NOUN american_scientific_journal-1665 23 15 ( ( PUNCT american_scientific_journal-1665 23 16 1.1 1.1 NUM american_scientific_journal-1665 23 17 ) ) PUNCT american_scientific_journal-1665 23 18 a a X american_scientific_journal-1665 23 19 ) ) PUNCT american_scientific_journal-1665 23 20 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 23 21 |𝑗𝑗 |𝑗𝑗 X american_scientific_journal-1665 23 22 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 24 1 = = SYM american_scientific_journal-1665 24 2 0 0 NUM american_scientific_journal-1665 24 3 and and CCONJ american_scientific_journal-1665 24 4 b b NOUN american_scientific_journal-1665 24 5 ) ) PUNCT american_scientific_journal-1665 24 6 g g NOUN american_scientific_journal-1665 24 7 𝑖𝑖𝑗𝑗|𝑗𝑗 𝑖𝑖𝑗𝑗|𝑗𝑗 PROPN american_scientific_journal-1665 24 8 = = SYM american_scientific_journal-1665 24 9 0 0 NUM american_scientific_journal-1665 24 10 , , PUNCT american_scientific_journal-1665 24 11 the the DET american_scientific_journal-1665 24 12 β„Ž β„Ž PROPN american_scientific_journal-1665 24 13 βˆ’ βˆ’ PROPN american_scientific_journal-1665 24 14 covariant covariant ADJ american_scientific_journal-1665 24 15 differentiation differentiation NOUN american_scientific_journal-1665 24 16 with with ADP american_scientific_journal-1665 24 17 respect respect NOUN american_scientific_journal-1665 24 18 to to ADP american_scientific_journal-1665 24 19 π‘₯π‘₯ π‘₯π‘₯ ADP american_scientific_journal-1665 24 20 𝑗𝑗 𝑗𝑗 ADV american_scientific_journal-1665 24 21 , , PUNCT american_scientific_journal-1665 24 22 commute commute VERB american_scientific_journal-1665 24 23 with with ADP american_scientific_journal-1665 24 24 the the DET american_scientific_journal-1665 24 25 partial partial ADJ american_scientific_journal-1665 24 26 differentiation differentiation NOUN american_scientific_journal-1665 24 27 with with ADP american_scientific_journal-1665 24 28 respect respect NOUN american_scientific_journal-1665 24 29 to to ADP american_scientific_journal-1665 24 30 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 NOUN american_scientific_journal-1665 24 31 according accord VERB american_scientific_journal-1665 24 32 to to ADP american_scientific_journal-1665 24 33 ( ( PUNCT american_scientific_journal-1665 24 34 1.2 1.2 NUM american_scientific_journal-1665 24 35 ) ) PUNCT american_scientific_journal-1665 24 36 a a DET american_scientific_journal-1665 24 37 ) ) PUNCT american_scientific_journal-1665 24 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 39 Μ‡ Μ‡ VERB american_scientific_journal-1665 24 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 41 πœ•π‘—π‘— πœ•π‘—π‘— X american_scientific_journal-1665 24 42 οΏ½ οΏ½ NOUN american_scientific_journal-1665 24 43 𝑋𝑋 𝑋𝑋 PROPN american_scientific_journal-1665 24 44 |𝑗𝑗 |𝑗𝑗 PROPN american_scientific_journal-1665 24 45 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 24 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 47 βˆ’ βˆ’ PROPN american_scientific_journal-1665 24 48 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 49 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 50 Μ‡ Μ‡ NOUN american_scientific_journal-1665 24 51 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 52 πœ•π‘—π‘—π‘‹π‘‹ πœ•π‘—π‘—π‘‹π‘‹ NOUN american_scientific_journal-1665 24 53 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 24 54 οΏ½ οΏ½ X american_scientific_journal-1665 24 55 |𝑗𝑗 |𝑗𝑗 X american_scientific_journal-1665 24 56 = = SYM american_scientific_journal-1665 24 57 π‘‹π‘‹π‘Ÿπ‘Ÿ π‘‹π‘‹π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 24 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 59 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 60 Μ‡ Μ‡ PROPN american_scientific_journal-1665 24 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 62 πœ•π‘—π‘—Ξ³ πœ•π‘—π‘—Ξ³ PROPN american_scientific_journal-1665 24 63 π‘Ÿπ‘Ÿπ‘—π‘— π‘Ÿπ‘Ÿπ‘—π‘— ADJ american_scientific_journal-1665 24 64 βˆ— βˆ— NOUN american_scientific_journal-1665 24 65 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 24 66 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 67 βˆ’ βˆ’ PROPN american_scientific_journal-1665 24 68 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 69 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 70 Μ‡ Μ‡ PROPN american_scientific_journal-1665 24 71 οΏ½ οΏ½ PROPN american_scientific_journal-1665 24 72 πœ•π‘Ÿπ‘Ÿπ‘‹π‘‹ πœ•π‘Ÿπ‘Ÿπ‘‹π‘‹ SYM american_scientific_journal-1665 24 73 𝑖𝑖 𝑖𝑖 ADJ american_scientific_journal-1665 24 74 οΏ½ οΏ½ NOUN american_scientific_journal-1665 24 75 𝑃𝑃 𝑃𝑃 PROPN american_scientific_journal-1665 24 76 𝑗𝑗𝑗𝑗 𝑗𝑗𝑗𝑗 VERB american_scientific_journal-1665 24 77 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 24 78 , , PUNCT american_scientific_journal-1665 24 79 where where SCONJ american_scientific_journal-1665 24 80 ( ( PUNCT american_scientific_journal-1665 24 81 1.2 1.2 NUM american_scientific_journal-1665 24 82 ) ) PUNCT american_scientific_journal-1665 24 83 b b NOUN american_scientific_journal-1665 24 84 ) ) PUNCT american_scientific_journal-1665 25 1 𝑃𝑃𝑗𝑗𝑗𝑗 𝑃𝑃𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 25 2 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 25 3 ∢= ∢= NUM american_scientific_journal-1665 25 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 25 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 25 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 25 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 25 8 πœ•π‘—π‘—Ξ³ πœ•π‘—π‘—Ξ³ PROPN american_scientific_journal-1665 25 9 β„Žπ‘—π‘— β„Žπ‘—π‘— VERB american_scientific_journal-1665 25 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 25 11 οΏ½ οΏ½ NOUN american_scientific_journal-1665 25 12 π‘¦π‘¦β„Ž π‘¦π‘¦β„Ž NOUN american_scientific_journal-1665 25 13 = = PUNCT american_scientific_journal-1665 25 14 Ξ³ Ξ³ X american_scientific_journal-1665 25 15 π‘—π‘—β„Žπ‘—π‘— π‘—π‘—β„Žπ‘—π‘— PROPN american_scientific_journal-1665 25 16 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 25 17 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 25 18 β„Ž β„Ž ADP american_scientific_journal-1665 25 19 the the DET american_scientific_journal-1665 25 20 tensor tensor NOUN american_scientific_journal-1665 25 21 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 25 22 π‘Ÿπ‘Ÿπ‘—π‘—β„Ž π‘Ÿπ‘Ÿπ‘—π‘—β„Ž NOUN american_scientific_journal-1665 25 23 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 25 24 is be AUX american_scientific_journal-1665 25 25 called call VERB american_scientific_journal-1665 25 26 cartan cartan PROPN american_scientific_journal-1665 25 27 's 's PART american_scientific_journal-1665 25 28 fourth fourth ADJ american_scientific_journal-1665 25 29 curvature curvature NOUN american_scientific_journal-1665 25 30 tensor tensor NOUN american_scientific_journal-1665 25 31 which which PRON american_scientific_journal-1665 25 32 is be AUX american_scientific_journal-1665 25 33 skew skew ADJ american_scientific_journal-1665 25 34 - - PUNCT american_scientific_journal-1665 25 35 symmetric symmetric ADJ american_scientific_journal-1665 25 36 in in ADP american_scientific_journal-1665 25 37 its its PRON american_scientific_journal-1665 25 38 last last ADJ american_scientific_journal-1665 25 39 two two NUM american_scientific_journal-1665 25 40 lower low ADJ american_scientific_journal-1665 25 41 indices index NOUN american_scientific_journal-1665 25 42 π‘˜π‘˜ π‘˜π‘˜ PROPN american_scientific_journal-1665 25 43 and and CCONJ american_scientific_journal-1665 25 44 β„Ž β„Ž PROPN american_scientific_journal-1665 25 45 , , PUNCT american_scientific_journal-1665 25 46 i. i. PROPN american_scientific_journal-1665 25 47 e. e. PROPN american_scientific_journal-1665 25 48 ( ( PUNCT american_scientific_journal-1665 25 49 1.3 1.3 NUM american_scientific_journal-1665 25 50 ) ) PUNCT american_scientific_journal-1665 25 51 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 25 52 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 25 53 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 25 54 = = SYM american_scientific_journal-1665 26 1 βˆ’ βˆ’ PROPN american_scientific_journal-1665 26 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 26 3 π‘—π‘—β„Žπ‘—π‘— π‘—π‘—β„Žπ‘—π‘— NOUN american_scientific_journal-1665 26 4 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 26 5 . . PUNCT american_scientific_journal-1665 27 1 the the DET american_scientific_journal-1665 27 2 associate associate ADJ american_scientific_journal-1665 27 3 tensor tensor NOUN american_scientific_journal-1665 27 4 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 27 5 π‘–π‘–π‘—π‘—π‘—π‘—β„Ž π‘–π‘–π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 27 6 of of ADP american_scientific_journal-1665 27 7 the the DET american_scientific_journal-1665 27 8 curvature curvature NOUN american_scientific_journal-1665 27 9 tensor tensor NOUN american_scientific_journal-1665 27 10 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 27 11 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 27 12 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 27 13 is be AUX american_scientific_journal-1665 27 14 given give VERB american_scientific_journal-1665 27 15 by by ADP american_scientific_journal-1665 27 16 ( ( PUNCT american_scientific_journal-1665 27 17 1.4 1.4 NUM american_scientific_journal-1665 27 18 ) ) PUNCT american_scientific_journal-1665 27 19 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 27 20 π‘–π‘–π‘—π‘—π‘—π‘—β„Ž π‘–π‘–π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 27 21 ∢= ∢= NUM american_scientific_journal-1665 28 1 g g NOUN american_scientific_journal-1665 28 2 π‘Ÿπ‘Ÿπ‘—π‘— π‘Ÿπ‘Ÿπ‘—π‘— ADJ american_scientific_journal-1665 28 3 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 29 1 π‘–π‘–π‘—π‘—β„Ž π‘–π‘–π‘—π‘—β„Ž INTJ american_scientific_journal-1665 29 2 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ INTJ american_scientific_journal-1665 29 3 . . PUNCT american_scientific_journal-1665 30 1 the the DET american_scientific_journal-1665 30 2 ricci ricci PROPN american_scientific_journal-1665 30 3 tensor tensor NOUN american_scientific_journal-1665 30 4 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 30 5 𝑗𝑗𝑗𝑗 𝑗𝑗𝑗𝑗 NOUN american_scientific_journal-1665 30 6 of of ADP american_scientific_journal-1665 30 7 the the DET american_scientific_journal-1665 30 8 curvature curvature NOUN american_scientific_journal-1665 30 9 tensor tensor NOUN american_scientific_journal-1665 30 10 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 30 11 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 30 12 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 30 13 is be AUX american_scientific_journal-1665 30 14 given give VERB american_scientific_journal-1665 30 15 by by ADP american_scientific_journal-1665 30 16 ( ( PUNCT american_scientific_journal-1665 30 17 1.5 1.5 NUM american_scientific_journal-1665 30 18 ) ) PUNCT american_scientific_journal-1665 30 19 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 30 20 𝑗𝑗𝑗𝑗𝑖𝑖 𝑗𝑗𝑗𝑗𝑖𝑖 VERB american_scientific_journal-1665 30 21 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 31 1 = = PUNCT american_scientific_journal-1665 31 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 31 3 𝑗𝑗𝑗𝑗. 𝑗𝑗𝑗𝑗. NOUN american_scientific_journal-1665 31 4 the the DET american_scientific_journal-1665 31 5 curvature curvature NOUN american_scientific_journal-1665 31 6 tensor tensor NOUN american_scientific_journal-1665 31 7 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 31 8 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 31 9 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 31 10 satisfies satisfy VERB american_scientific_journal-1665 31 11 the the DET american_scientific_journal-1665 31 12 following follow VERB american_scientific_journal-1665 31 13 relations relation NOUN american_scientific_journal-1665 31 14 too too ADV american_scientific_journal-1665 31 15 ( ( PUNCT american_scientific_journal-1665 31 16 1.6 1.6 NUM american_scientific_journal-1665 31 17 ) ) PUNCT american_scientific_journal-1665 31 18 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 31 19 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 31 20 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 31 21 𝑦𝑦 𝑦𝑦 INTJ american_scientific_journal-1665 31 22 𝑗𝑗 𝑗𝑗 VERB american_scientific_journal-1665 31 23 = = PUNCT american_scientific_journal-1665 31 24 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 31 25 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 32 1 and and CCONJ american_scientific_journal-1665 32 2 ( ( PUNCT american_scientific_journal-1665 32 3 1.7 1.7 NUM american_scientific_journal-1665 32 4 ) ) PUNCT american_scientific_journal-1665 33 1 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 33 2 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 33 3 βˆ’ βˆ’ PROPN american_scientific_journal-1665 33 4 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 33 5 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 33 6 = = PUNCT american_scientific_journal-1665 33 7 𝑃𝑃𝑗𝑗𝑗𝑗|β„Ž 𝑃𝑃𝑗𝑗𝑗𝑗|β„Ž VERB american_scientific_journal-1665 33 8 𝑖𝑖 𝑖𝑖 PRON american_scientific_journal-1665 33 9 + + X american_scientific_journal-1665 33 10 𝑃𝑃𝑗𝑗𝑗𝑗 𝑃𝑃𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 33 11 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 33 12 𝑃𝑃 𝑃𝑃 PROPN american_scientific_journal-1665 33 13 π‘Ÿπ‘Ÿβ„Ž π‘Ÿπ‘Ÿβ„Ž PROPN american_scientific_journal-1665 33 14 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 33 15 βˆ’ βˆ’ PUNCT american_scientific_journal-1665 33 16 β„Ž β„Ž PROPN american_scientific_journal-1665 33 17 π‘˜π‘˜β„ π‘˜π‘˜β„ NOUN american_scientific_journal-1665 33 18 . . PUNCT american_scientific_journal-1665 34 1 berwald berwald NOUN american_scientific_journal-1665 34 2 curvature curvature NOUN american_scientific_journal-1665 34 3 tensor tensor NOUN american_scientific_journal-1665 34 4 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 34 5 satisfies satisfy VERB american_scientific_journal-1665 34 6 the the DET american_scientific_journal-1665 34 7 relation relation NOUN american_scientific_journal-1665 34 8 ( ( PUNCT american_scientific_journal-1665 34 9 1.8 1.8 NUM american_scientific_journal-1665 34 10 ) ) PUNCT american_scientific_journal-1665 34 11 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 34 12 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 34 13 𝑦𝑦 𝑦𝑦 INTJ american_scientific_journal-1665 34 14 𝑗𝑗 𝑗𝑗 VERB american_scientific_journal-1665 34 15 = = PUNCT american_scientific_journal-1665 34 16 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 34 17 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 34 18 and and CCONJ american_scientific_journal-1665 34 19 65- 65- NUM american_scientific_journal-1665 34 20 ) ) PUNCT american_scientific_journal-1665 34 21 volume volume NOUN american_scientific_journal-1665 34 22 20 20 NUM american_scientific_journal-1665 34 23 , , PUNCT american_scientific_journal-1665 34 24 no no DET american_scientific_journal-1665 34 25 1 1 NUM american_scientific_journal-1665 34 26 , , PUNCT american_scientific_journal-1665 34 27 pp pp ADP american_scientific_journal-1665 34 28 522016 522016 NUM american_scientific_journal-1665 34 29 ( ( PUNCT american_scientific_journal-1665 34 30 ) ) PUNCT american_scientific_journal-1665 34 31 research research NOUN american_scientific_journal-1665 34 32 journal journal NOUN american_scientific_journal-1665 34 33 for for ADP american_scientific_journal-1665 34 34 engineering engineering NOUN american_scientific_journal-1665 34 35 , , PUNCT american_scientific_journal-1665 34 36 technology technology NOUN american_scientific_journal-1665 34 37 , , PUNCT american_scientific_journal-1665 34 38 and and CCONJ american_scientific_journal-1665 34 39 sciences science NOUN american_scientific_journal-1665 34 40 ( ( PUNCT american_scientific_journal-1665 34 41 asrjets asrjet NOUN american_scientific_journal-1665 34 42 scientificamerican scientificamerican NOUN american_scientific_journal-1665 34 43 54 54 NUM american_scientific_journal-1665 34 44 ( ( PUNCT american_scientific_journal-1665 34 45 1.9 1.9 NUM american_scientific_journal-1665 34 46 ) ) PUNCT american_scientific_journal-1665 34 47 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 34 48 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 34 49 = = PUNCT american_scientific_journal-1665 34 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 34 51 Μ‡ Μ‡ PROPN american_scientific_journal-1665 34 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 34 53 πœ•π‘—π‘—π»π»π‘—π‘—β„Ž πœ•π‘—π‘—π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 34 54 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 34 55 , , PUNCT american_scientific_journal-1665 34 56 where where SCONJ american_scientific_journal-1665 34 57 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 34 58 π‘—π‘—β„Ž π‘—π‘—β„Ž X american_scientific_journal-1665 34 59 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 34 60 called call VERB american_scientific_journal-1665 34 61 β„Ž(𝑣𝑣 β„Ž(𝑣𝑣 NOUN american_scientific_journal-1665 34 62 ) ) PUNCT american_scientific_journal-1665 34 63 βˆ’ βˆ’ PROPN american_scientific_journal-1665 34 64 torsion torsion NOUN american_scientific_journal-1665 34 65 tensor tensor NOUN american_scientific_journal-1665 34 66 . . PUNCT american_scientific_journal-1665 35 1 also also ADV american_scientific_journal-1665 35 2 , , PUNCT american_scientific_journal-1665 35 3 satisfies satisfy VERB american_scientific_journal-1665 35 4 bianchi bianchi NOUN american_scientific_journal-1665 35 5 identity identity NOUN american_scientific_journal-1665 35 6 ( ( PUNCT american_scientific_journal-1665 35 7 1.10 1.10 NUM american_scientific_journal-1665 35 8 ) ) PUNCT american_scientific_journal-1665 35 9 a a X american_scientific_journal-1665 35 10 ) ) PUNCT american_scientific_journal-1665 36 1 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 36 2 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 37 1 + + CCONJ american_scientific_journal-1665 37 2 π»π»β„Žπ‘—π‘—π‘—π‘— π»π»β„Žπ‘—π‘—π‘—π‘— PROPN american_scientific_journal-1665 37 3 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 38 1 + + CCONJ american_scientific_journal-1665 39 1 π»π»π‘—π‘—β„Žπ‘—π‘— π»π»π‘—π‘—β„Žπ‘—π‘— PROPN american_scientific_journal-1665 39 2 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 39 3 = = SYM american_scientific_journal-1665 39 4 0 0 PUNCT american_scientific_journal-1665 40 1 and and CCONJ american_scientific_journal-1665 40 2 it it PRON american_scientific_journal-1665 40 3 is be AUX american_scientific_journal-1665 40 4 skewsymmetric skewsymmetric ADJ american_scientific_journal-1665 40 5 in in ADP american_scientific_journal-1665 40 6 its its PRON american_scientific_journal-1665 40 7 last last ADJ american_scientific_journal-1665 40 8 two two NUM american_scientific_journal-1665 40 9 lower low ADJ american_scientific_journal-1665 40 10 indices index NOUN american_scientific_journal-1665 40 11 , , PUNCT american_scientific_journal-1665 40 12 i.e. i.e. X american_scientific_journal-1665 40 13 ( ( PUNCT american_scientific_journal-1665 40 14 1.10 1.10 NUM american_scientific_journal-1665 40 15 ) ) PUNCT american_scientific_journal-1665 40 16 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-1665 40 17 ) ) PUNCT american_scientific_journal-1665 41 1 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 41 2 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 41 3 = = PUNCT american_scientific_journal-1665 41 4 βˆ’ βˆ’ PROPN american_scientific_journal-1665 41 5 π»π»π‘—π‘—β„Žπ‘—π‘— π»π»π‘—π‘—β„Žπ‘—π‘— PROPN american_scientific_journal-1665 41 6 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 41 7 . . PUNCT american_scientific_journal-1665 42 1 the the DET american_scientific_journal-1665 42 2 deviation deviation NOUN american_scientific_journal-1665 42 3 tensor tensor NOUN american_scientific_journal-1665 42 4 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 42 5 𝑗𝑗 𝑗𝑗 NOUN american_scientific_journal-1665 42 6 𝑖𝑖 𝑖𝑖 VERB american_scientific_journal-1665 42 7 is be AUX american_scientific_journal-1665 42 8 positively positively ADV american_scientific_journal-1665 42 9 homogeneous homogeneous ADJ american_scientific_journal-1665 42 10 of of ADP american_scientific_journal-1665 42 11 degree degree NOUN american_scientific_journal-1665 42 12 two two NUM american_scientific_journal-1665 42 13 in in ADP american_scientific_journal-1665 42 14 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 42 15 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 42 16 and and CCONJ american_scientific_journal-1665 42 17 satisfies satisfie NOUN american_scientific_journal-1665 42 18 ( ( PUNCT american_scientific_journal-1665 42 19 1.11 1.11 NUM american_scientific_journal-1665 42 20 ) ) PUNCT american_scientific_journal-1665 42 21 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 42 22 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 42 23 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 42 24 β„Ž β„Ž PROPN american_scientific_journal-1665 42 25 = = PROPN american_scientific_journal-1665 42 26 𝐻𝐻𝑗𝑗 𝐻𝐻𝑗𝑗 PROPN american_scientific_journal-1665 42 27 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 42 28 , , PUNCT american_scientific_journal-1665 42 29 ( ( PUNCT american_scientific_journal-1665 42 30 1.12 1.12 NUM american_scientific_journal-1665 42 31 ) ) PUNCT american_scientific_journal-1665 42 32 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 42 33 = = SYM american_scientific_journal-1665 42 34 𝐻𝐻𝑗𝑗𝑗𝑗𝑖𝑖 𝐻𝐻𝑗𝑗𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 42 35 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 42 36 , , PUNCT american_scientific_journal-1665 42 37 ( ( PUNCT american_scientific_journal-1665 42 38 1.13 1.13 NUM american_scientific_journal-1665 42 39 ) ) PUNCT american_scientific_journal-1665 42 40 𝐻𝐻𝑗𝑗 𝐻𝐻𝑗𝑗 PROPN american_scientific_journal-1665 43 1 = = PUNCT american_scientific_journal-1665 44 1 𝐻𝐻𝑗𝑗𝑖𝑖 𝐻𝐻𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 44 2 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 44 3 , , PUNCT american_scientific_journal-1665 44 4 and and CCONJ american_scientific_journal-1665 44 5 ( ( PUNCT american_scientific_journal-1665 44 6 1.14 1.14 NUM american_scientific_journal-1665 44 7 ) ) PUNCT american_scientific_journal-1665 44 8 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 44 9 = = SYM american_scientific_journal-1665 44 10 1 1 NUM american_scientific_journal-1665 44 11 π‘›π‘›βˆ’1 π‘›π‘›βˆ’1 PROPN american_scientific_journal-1665 44 12 𝐻𝐻𝑖𝑖𝑖𝑖 𝐻𝐻𝑖𝑖𝑖𝑖 PROPN american_scientific_journal-1665 44 13 , , PUNCT american_scientific_journal-1665 44 14 where where SCONJ american_scientific_journal-1665 44 15 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 44 16 and and CCONJ american_scientific_journal-1665 44 17 𝐻𝐻 𝐻𝐻 NOUN american_scientific_journal-1665 44 18 are be AUX american_scientific_journal-1665 44 19 called call VERB american_scientific_journal-1665 44 20 β„Ž-ricci β„Ž-ricci PROPN american_scientific_journal-1665 44 21 tensor tensor NOUN american_scientific_journal-1665 44 22 and and CCONJ american_scientific_journal-1665 44 23 curvature curvature NOUN american_scientific_journal-1665 44 24 scalar scalar ADJ american_scientific_journal-1665 44 25 , , PUNCT american_scientific_journal-1665 44 26 respectively respectively ADV american_scientific_journal-1665 44 27 . . PUNCT american_scientific_journal-1665 45 1 since since SCONJ american_scientific_journal-1665 45 2 contraction contraction NOUN american_scientific_journal-1665 45 3 of of ADP american_scientific_journal-1665 45 4 the the DET american_scientific_journal-1665 45 5 indices index NOUN american_scientific_journal-1665 45 6 does do AUX american_scientific_journal-1665 45 7 not not PART american_scientific_journal-1665 45 8 affect affect VERB american_scientific_journal-1665 45 9 the the DET american_scientific_journal-1665 45 10 homogeneity homogeneity NOUN american_scientific_journal-1665 45 11 in in ADP american_scientific_journal-1665 45 12 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-1665 45 13 , , PUNCT american_scientific_journal-1665 45 14 hence hence ADV american_scientific_journal-1665 45 15 the the DET american_scientific_journal-1665 45 16 tensors tensor NOUN american_scientific_journal-1665 45 17 π»π»π‘Ÿπ‘Ÿπ‘—π‘— π»π»π‘Ÿπ‘Ÿπ‘—π‘— PROPN american_scientific_journal-1665 45 18 , , PUNCT american_scientific_journal-1665 45 19 π»π»π‘Ÿπ‘Ÿ π»π»π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 45 20 and and CCONJ american_scientific_journal-1665 45 21 the the DET american_scientific_journal-1665 45 22 scalar scalar ADJ american_scientific_journal-1665 45 23 𝐻𝐻 𝐻𝐻 NOUN american_scientific_journal-1665 45 24 are be AUX american_scientific_journal-1665 45 25 also also ADV american_scientific_journal-1665 45 26 homogeneous homogeneous ADJ american_scientific_journal-1665 45 27 of of ADP american_scientific_journal-1665 45 28 degree degree NOUN american_scientific_journal-1665 45 29 zero zero NUM american_scientific_journal-1665 45 30 , , PUNCT american_scientific_journal-1665 45 31 one one NUM american_scientific_journal-1665 45 32 and and CCONJ american_scientific_journal-1665 45 33 two two NUM american_scientific_journal-1665 45 34 in in ADP american_scientific_journal-1665 45 35 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-1665 45 36 , , PUNCT american_scientific_journal-1665 45 37 respectively respectively ADV american_scientific_journal-1665 45 38 . . PUNCT american_scientific_journal-1665 46 1 the the DET american_scientific_journal-1665 46 2 associate associate ADJ american_scientific_journal-1665 46 3 tensor tensor NOUN american_scientific_journal-1665 46 4 π»π»π‘–π‘–π‘—π‘—π‘—π‘—β„Ž π»π»π‘–π‘–π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 46 5 of of ADP american_scientific_journal-1665 46 6 berwald berwald NOUN american_scientific_journal-1665 46 7 curvature curvature NOUN american_scientific_journal-1665 46 8 tensor tensor NOUN american_scientific_journal-1665 46 9 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 46 10 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 46 11 is be AUX american_scientific_journal-1665 46 12 given give VERB american_scientific_journal-1665 46 13 by by ADP american_scientific_journal-1665 46 14 ( ( PUNCT american_scientific_journal-1665 46 15 1.15 1.15 NUM american_scientific_journal-1665 46 16 ) ) PUNCT american_scientific_journal-1665 46 17 π»π»π‘–π‘–π‘—π‘—π‘—π‘—β„Ž π»π»π‘–π‘–π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 46 18 = = PUNCT american_scientific_journal-1665 46 19 gπ‘Ÿπ‘Ÿπ‘—π‘— gπ‘Ÿπ‘Ÿπ‘—π‘— VERB american_scientific_journal-1665 46 20 π»π»π‘–π‘–π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘–π‘–π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 46 21 . . PUNCT american_scientific_journal-1665 47 1 the the DET american_scientific_journal-1665 47 2 contraction contraction NOUN american_scientific_journal-1665 47 3 of of ADP american_scientific_journal-1665 47 4 the the DET american_scientific_journal-1665 47 5 indices index NOUN american_scientific_journal-1665 47 6 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 47 7 and and CCONJ american_scientific_journal-1665 47 8 𝑗𝑗 𝑗𝑗 ADP american_scientific_journal-1665 47 9 in in ADP american_scientific_journal-1665 47 10 ( ( PUNCT american_scientific_journal-1665 47 11 1.10a 1.10a NUM american_scientific_journal-1665 47 12 ) ) PUNCT american_scientific_journal-1665 47 13 and and CCONJ american_scientific_journal-1665 47 14 by by ADP american_scientific_journal-1665 47 15 using use VERB american_scientific_journal-1665 47 16 ( ( PUNCT american_scientific_journal-1665 47 17 1.12 1.12 NUM american_scientific_journal-1665 47 18 ) ) PUNCT american_scientific_journal-1665 47 19 and and CCONJ american_scientific_journal-1665 47 20 the the DET american_scientific_journal-1665 47 21 skew skew ADJ american_scientific_journal-1665 47 22 - - PUNCT american_scientific_journal-1665 47 23 symmetric symmetric ADJ american_scientific_journal-1665 47 24 property property NOUN american_scientific_journal-1665 47 25 of of ADP american_scientific_journal-1665 47 26 the the DET american_scientific_journal-1665 47 27 curvature curvature NOUN american_scientific_journal-1665 47 28 tensor tensor NOUN american_scientific_journal-1665 47 29 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 47 30 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 47 31 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 47 32 in in ADP american_scientific_journal-1665 47 33 the the DET american_scientific_journal-1665 47 34 last last ADJ american_scientific_journal-1665 47 35 two two NUM american_scientific_journal-1665 47 36 lower low ADJ american_scientific_journal-1665 47 37 indices index NOUN american_scientific_journal-1665 47 38 , , PUNCT american_scientific_journal-1665 47 39 shows show VERB american_scientific_journal-1665 47 40 that that SCONJ american_scientific_journal-1665 47 41 the the DET american_scientific_journal-1665 47 42 β„Ž β„Ž PROPN american_scientific_journal-1665 47 43 βˆ’ βˆ’ PROPN american_scientific_journal-1665 47 44 ricci ricci PROPN american_scientific_journal-1665 47 45 tensor tensor NOUN american_scientific_journal-1665 47 46 satisfies satisfie NOUN american_scientific_journal-1665 47 47 ( ( PUNCT american_scientific_journal-1665 47 48 1.16 1.16 NUM american_scientific_journal-1665 47 49 ) ) PUNCT american_scientific_journal-1665 48 1 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 48 2 = = SYM american_scientific_journal-1665 48 3 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 48 4 βˆ’ βˆ’ PROPN american_scientific_journal-1665 48 5 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 48 6 . . PUNCT american_scientific_journal-1665 49 1 the the DET american_scientific_journal-1665 49 2 tensor tensor NOUN american_scientific_journal-1665 49 3 π»π»π‘—π‘—β„Ž.𝑗𝑗 π»π»π‘—π‘—β„Ž.𝑗𝑗 PROPN american_scientific_journal-1665 49 4 defined define VERB american_scientific_journal-1665 49 5 by by ADP american_scientific_journal-1665 49 6 ( ( PUNCT american_scientific_journal-1665 49 7 1.17 1.17 NUM american_scientific_journal-1665 49 8 ) ) PUNCT american_scientific_journal-1665 49 9 π»π»π‘—π‘—β„Ž.𝑗𝑗 π»π»π‘—π‘—β„Ž.𝑗𝑗 PROPN american_scientific_journal-1665 49 10 ∢= ∢= PROPN american_scientific_journal-1665 49 11 gπ‘–π‘–β„Žπ»π»π‘—π‘—π‘—π‘— gπ‘–π‘–β„Žπ»π»π‘—π‘—π‘—π‘— VERB american_scientific_journal-1665 49 12 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 49 13 . . PUNCT american_scientific_journal-1665 50 1 cartan cartan PROPN american_scientific_journal-1665 50 2 's 's PART american_scientific_journal-1665 50 3 fourth fourth ADJ american_scientific_journal-1665 50 4 curvature curvature NOUN american_scientific_journal-1665 50 5 tensor tensor NOUN american_scientific_journal-1665 50 6 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 50 7 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 50 8 satisfies satisfy VERB american_scientific_journal-1665 50 9 the the DET american_scientific_journal-1665 50 10 following follow VERB american_scientific_journal-1665 50 11 identity identity NOUN american_scientific_journal-1665 50 12 known know VERB american_scientific_journal-1665 50 13 as as ADP american_scientific_journal-1665 50 14 bianchi bianchi NOUN american_scientific_journal-1665 50 15 identity identity NOUN american_scientific_journal-1665 50 16 65- 65- NOUN american_scientific_journal-1665 50 17 ) ) PUNCT american_scientific_journal-1665 50 18 volume volume NOUN american_scientific_journal-1665 50 19 20 20 NUM american_scientific_journal-1665 50 20 , , PUNCT american_scientific_journal-1665 50 21 no no DET american_scientific_journal-1665 50 22 1 1 NUM american_scientific_journal-1665 50 23 , , PUNCT american_scientific_journal-1665 50 24 pp pp ADP american_scientific_journal-1665 50 25 522016 522016 NUM american_scientific_journal-1665 50 26 ( ( PUNCT american_scientific_journal-1665 50 27 ) ) PUNCT american_scientific_journal-1665 50 28 research research NOUN american_scientific_journal-1665 50 29 journal journal NOUN american_scientific_journal-1665 50 30 for for ADP american_scientific_journal-1665 50 31 engineering engineering NOUN american_scientific_journal-1665 50 32 , , PUNCT american_scientific_journal-1665 50 33 technology technology NOUN american_scientific_journal-1665 50 34 , , PUNCT american_scientific_journal-1665 50 35 and and CCONJ american_scientific_journal-1665 50 36 sciences science NOUN american_scientific_journal-1665 50 37 ( ( PUNCT american_scientific_journal-1665 50 38 asrjets asrjet NOUN american_scientific_journal-1665 50 39 scientificamerican scientificamerican NOUN american_scientific_journal-1665 50 40 55 55 NUM american_scientific_journal-1665 50 41 ( ( PUNCT american_scientific_journal-1665 50 42 1.18 1.18 NUM american_scientific_journal-1665 50 43 ) ) PUNCT american_scientific_journal-1665 50 44 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ PRON american_scientific_journal-1665 50 45 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 51 1 + + CCONJ american_scientific_journal-1665 51 2 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž VERB american_scientific_journal-1665 51 3 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 52 1 + + CCONJ american_scientific_journal-1665 52 2 πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗 πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗 PRON american_scientific_journal-1665 52 3 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 53 1 + + CCONJ american_scientific_journal-1665 53 2 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 53 3 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 53 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 7 Μ‡ Μ‡ VERB american_scientific_journal-1665 53 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 9 πœ•π‘ π‘ π›€π›€ πœ•π‘ π‘ π›€π›€ PART american_scientific_journal-1665 53 10 𝑗𝑗𝑗𝑗 𝑗𝑗𝑗𝑗 VERB american_scientific_journal-1665 53 11 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 53 12 οΏ½ οΏ½ ADP american_scientific_journal-1665 53 13 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ PROPN american_scientific_journal-1665 53 14 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 53 15 + + PROPN american_scientific_journal-1665 53 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 18 Μ‡ Μ‡ NOUN american_scientific_journal-1665 53 19 οΏ½ οΏ½ NOUN american_scientific_journal-1665 53 20 πœ•π‘ π‘ π›€π›€ πœ•π‘ π‘ π›€π›€ ADV american_scientific_journal-1665 53 21 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 53 22 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 53 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 24 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘ π‘  πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 53 25 + + NUM american_scientific_journal-1665 53 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 53 28 Μ‡ Μ‡ NOUN american_scientific_journal-1665 53 29 οΏ½ οΏ½ NOUN american_scientific_journal-1665 53 30 πœ•π‘ π‘ π›€π›€ πœ•π‘ π‘ π›€π›€ NOUN american_scientific_journal-1665 53 31 π‘—π‘—β„Ž π‘—π‘—β„Ž NOUN american_scientific_journal-1665 54 1 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 54 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 54 3 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— PROPN american_scientific_journal-1665 54 4 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 54 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 54 6 = = SYM american_scientific_journal-1665 54 7 0 0 PROPN american_scientific_journal-1665 54 8 . . PUNCT american_scientific_journal-1665 55 1 a a DET american_scientific_journal-1665 55 2 finsler finsler NOUN american_scientific_journal-1665 55 3 space space NOUN american_scientific_journal-1665 55 4 whose whose DET american_scientific_journal-1665 55 5 berwald berwald NOUN american_scientific_journal-1665 55 6 's 's PART american_scientific_journal-1665 55 7 connection connection NOUN american_scientific_journal-1665 55 8 parameter parameter NOUN american_scientific_journal-1665 55 9 𝐺𝐺𝑗𝑗𝑗𝑗𝑖𝑖 𝐺𝐺𝑗𝑗𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 55 10 is be AUX american_scientific_journal-1665 55 11 independent independent ADJ american_scientific_journal-1665 55 12 of of ADP american_scientific_journal-1665 55 13 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-1665 55 14 is be AUX american_scientific_journal-1665 55 15 called call VERB american_scientific_journal-1665 55 16 an an DET american_scientific_journal-1665 55 17 affinely affinely ADV american_scientific_journal-1665 55 18 connected connect VERB american_scientific_journal-1665 55 19 space space NOUN american_scientific_journal-1665 55 20 ( ( PUNCT american_scientific_journal-1665 55 21 berwald berwald NOUN american_scientific_journal-1665 55 22 space space NOUN american_scientific_journal-1665 55 23 ) ) PUNCT american_scientific_journal-1665 55 24 . . PUNCT american_scientific_journal-1665 56 1 thus thus ADV american_scientific_journal-1665 56 2 , , PUNCT american_scientific_journal-1665 56 3 an an DET american_scientific_journal-1665 56 4 affinely affinely ADV american_scientific_journal-1665 56 5 connected connected ADJ american_scientific_journal-1665 56 6 space space NOUN american_scientific_journal-1665 56 7 has have VERB american_scientific_journal-1665 56 8 some some DET american_scientific_journal-1665 56 9 properties property NOUN american_scientific_journal-1665 56 10 as as SCONJ american_scientific_journal-1665 56 11 follows follow VERB american_scientific_journal-1665 56 12 : : PUNCT american_scientific_journal-1665 56 13 ( ( PUNCT american_scientific_journal-1665 56 14 1.19 1.19 NUM american_scientific_journal-1665 56 15 ) ) PUNCT american_scientific_journal-1665 57 1 πΊπΊπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΊπΊπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 57 2 = = SYM american_scientific_journal-1665 57 3 0 0 NUM american_scientific_journal-1665 57 4 and and CCONJ american_scientific_journal-1665 57 5 ( ( PUNCT american_scientific_journal-1665 57 6 1.20 1.20 NUM american_scientific_journal-1665 57 7 ) ) PUNCT american_scientific_journal-1665 57 8 𝐢𝐢𝑖𝑖𝑗𝑗𝑗𝑗|β„Ž= 𝐢𝐢𝑖𝑖𝑗𝑗𝑗𝑗|β„Ž= ADV american_scientific_journal-1665 57 9 0 0 NUM american_scientific_journal-1665 57 10 . . PUNCT american_scientific_journal-1665 58 1 the the DET american_scientific_journal-1665 58 2 connection connection NOUN american_scientific_journal-1665 58 3 parameters parameter VERB american_scientific_journal-1665 58 4 Ξ³ Ξ³ X american_scientific_journal-1665 58 5 𝑗𝑗𝑗𝑗 𝑗𝑗𝑗𝑗 NOUN american_scientific_journal-1665 58 6 βˆ—π‘–π‘– βˆ—π‘–π‘– VERB american_scientific_journal-1665 58 7 of of ADP american_scientific_journal-1665 58 8 cartan cartan PROPN american_scientific_journal-1665 58 9 and and CCONJ american_scientific_journal-1665 58 10 𝐺𝐺𝑗𝑗𝑗𝑗𝑖𝑖 𝐺𝐺𝑗𝑗𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 58 11 of of ADP american_scientific_journal-1665 58 12 berwald berwald NOUN american_scientific_journal-1665 58 13 coincide coincide NOUN american_scientific_journal-1665 58 14 in in ADP american_scientific_journal-1665 58 15 an an DET american_scientific_journal-1665 58 16 affinely affinely ADV american_scientific_journal-1665 58 17 connected connect VERB american_scientific_journal-1665 58 18 space space NOUN american_scientific_journal-1665 58 19 and and CCONJ american_scientific_journal-1665 58 20 they they PRON american_scientific_journal-1665 58 21 are be AUX american_scientific_journal-1665 58 22 independent independent ADJ american_scientific_journal-1665 58 23 of of ADP american_scientific_journal-1665 58 24 the the DET american_scientific_journal-1665 58 25 direction direction NOUN american_scientific_journal-1665 58 26 arguments argument NOUN american_scientific_journal-1665 58 27 [ [ X american_scientific_journal-1665 58 28 3 3 NUM american_scientific_journal-1665 58 29 ] ] PUNCT american_scientific_journal-1665 58 30 , , PUNCT american_scientific_journal-1665 58 31 i.e. i.e. X american_scientific_journal-1665 58 32 ( ( PUNCT american_scientific_journal-1665 58 33 1.21 1.21 NUM american_scientific_journal-1665 58 34 ) ) PUNCT american_scientific_journal-1665 59 1 πΊπΊπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΊπΊπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 59 2 = = SYM american_scientific_journal-1665 59 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 59 4 Μ‡ Μ‡ NOUN american_scientific_journal-1665 59 5 οΏ½ οΏ½ NOUN american_scientific_journal-1665 59 6 πœ•π‘—π‘—πΊπΊπ‘—π‘—β„Žπ‘–π‘– πœ•π‘—π‘—πΊπΊπ‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 59 7 = = SYM american_scientific_journal-1665 59 8 0 0 NUM american_scientific_journal-1665 59 9 and and CCONJ american_scientific_journal-1665 59 10 ( ( PUNCT american_scientific_journal-1665 59 11 1.22 1.22 NUM american_scientific_journal-1665 59 12 ) ) PUNCT american_scientific_journal-1665 59 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 59 14 Μ‡ Μ‡ PROPN american_scientific_journal-1665 59 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 59 16 πœ•π‘—π‘—Ξ³ πœ•π‘—π‘—Ξ³ PRON american_scientific_journal-1665 59 17 π‘—π‘—β„Ž π‘—π‘—β„Ž NOUN american_scientific_journal-1665 59 18 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 59 19 = = PUNCT american_scientific_journal-1665 59 20 0 0 X american_scientific_journal-1665 59 21 . . PUNCT american_scientific_journal-1665 59 22 n. n. PROPN american_scientific_journal-1665 59 23 s. s. PROPN american_scientific_journal-1665 59 24 h. h. PROPN american_scientific_journal-1665 59 25 hussein hussein PROPN american_scientific_journal-1665 60 1 [ [ X american_scientific_journal-1665 60 2 3 3 NUM american_scientific_journal-1665 60 3 ] ] PUNCT american_scientific_journal-1665 60 4 introduce introduce VERB american_scientific_journal-1665 60 5 the the DET american_scientific_journal-1665 60 6 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 60 7 β„Žβ€“recurrent β„Žβ€“recurrent NOUN american_scientific_journal-1665 60 8 space space NOUN american_scientific_journal-1665 60 9 which which PRON american_scientific_journal-1665 60 10 characterized characterize VERB american_scientific_journal-1665 60 11 by by ADP american_scientific_journal-1665 60 12 the the DET american_scientific_journal-1665 60 13 condition condition NOUN american_scientific_journal-1665 60 14 ( ( PUNCT american_scientific_journal-1665 60 15 1.23 1.23 NUM american_scientific_journal-1665 60 16 ) ) PUNCT american_scientific_journal-1665 60 17 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ PRON american_scientific_journal-1665 60 18 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 60 19 = = PUNCT american_scientific_journal-1665 60 20 πœ†πœ†β„“ πœ†πœ†β„“ X american_scientific_journal-1665 61 1 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 61 2 , , PUNCT american_scientific_journal-1665 61 3 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 61 4 β‰  β‰  PROPN american_scientific_journal-1665 61 5 0 0 NUM american_scientific_journal-1665 61 6 , , PUNCT american_scientific_journal-1665 61 7 where where SCONJ american_scientific_journal-1665 61 8 the the DET american_scientific_journal-1665 61 9 covariant covariant ADJ american_scientific_journal-1665 61 10 vector vector NOUN american_scientific_journal-1665 61 11 field field NOUN american_scientific_journal-1665 61 12 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 61 13 being be AUX american_scientific_journal-1665 61 14 the the DET american_scientific_journal-1665 61 15 recurrence recurrence NOUN american_scientific_journal-1665 61 16 vector vector NOUN american_scientific_journal-1665 61 17 field field NOUN american_scientific_journal-1665 61 18 . . PUNCT american_scientific_journal-1665 62 1 2 2 X american_scientific_journal-1665 62 2 . . X american_scientific_journal-1665 62 3 an an DET american_scientific_journal-1665 62 4 𝑲𝑲 𝑲𝑲 NOUN american_scientific_journal-1665 62 5 𝒉𝒉 𝒉𝒉 PART american_scientific_journal-1665 62 6 βˆ’ βˆ’ PROPN american_scientific_journal-1665 62 7 generalized generalized ADJ american_scientific_journal-1665 62 8 birecurrent birecurrent NOUN american_scientific_journal-1665 62 9 space space NOUN american_scientific_journal-1665 62 10 let let VERB american_scientific_journal-1665 62 11 us we PRON american_scientific_journal-1665 62 12 consider consider VERB american_scientific_journal-1665 62 13 a a DET american_scientific_journal-1665 62 14 finsler finsler NOUN american_scientific_journal-1665 62 15 space space NOUN american_scientific_journal-1665 62 16 𝐹𝐹𝑛𝑛 𝐹𝐹𝑛𝑛 PRON american_scientific_journal-1665 62 17 whose whose DET american_scientific_journal-1665 62 18 cartan cartan PROPN american_scientific_journal-1665 62 19 's 's PART american_scientific_journal-1665 62 20 fourth fourth ADJ american_scientific_journal-1665 62 21 curvature curvature NOUN american_scientific_journal-1665 62 22 tensor tensor NOUN american_scientific_journal-1665 62 23 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 62 24 satisfies satisfy VERB american_scientific_journal-1665 62 25 the the DET american_scientific_journal-1665 62 26 condition condition NOUN american_scientific_journal-1665 62 27 ( ( PUNCT american_scientific_journal-1665 62 28 2.1 2.1 NUM american_scientific_journal-1665 62 29 ) ) PUNCT american_scientific_journal-1665 62 30 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 62 31 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 63 1 = = SYM american_scientific_journal-1665 63 2 πœ†πœ†β„“πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š πœ†πœ†β„“πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š NUM american_scientific_journal-1665 63 3 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 64 1 + + CCONJ american_scientific_journal-1665 64 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 64 3 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 64 4 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 64 5 , , PUNCT american_scientific_journal-1665 64 6 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 64 7 β‰  β‰  PROPN american_scientific_journal-1665 64 8 0 0 NUM american_scientific_journal-1665 64 9 , , PUNCT american_scientific_journal-1665 64 10 where where SCONJ american_scientific_journal-1665 64 11 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 64 12 and and CCONJ american_scientific_journal-1665 64 13 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 64 14 are be AUX american_scientific_journal-1665 64 15 non non ADJ american_scientific_journal-1665 64 16 - - ADJ american_scientific_journal-1665 64 17 zero zero NUM american_scientific_journal-1665 64 18 covariant covariant ADJ american_scientific_journal-1665 64 19 vector vector NOUN american_scientific_journal-1665 64 20 field field NOUN american_scientific_journal-1665 64 21 and and CCONJ american_scientific_journal-1665 64 22 covariant covariant ADJ american_scientific_journal-1665 64 23 tensor tensor NOUN american_scientific_journal-1665 64 24 field field NOUN american_scientific_journal-1665 64 25 of of ADP american_scientific_journal-1665 64 26 second second ADJ american_scientific_journal-1665 64 27 order order NOUN american_scientific_journal-1665 64 28 , , PUNCT american_scientific_journal-1665 64 29 respectively respectively ADV american_scientific_journal-1665 64 30 . . PUNCT american_scientific_journal-1665 65 1 the the DET american_scientific_journal-1665 65 2 space space NOUN american_scientific_journal-1665 65 3 satisfying satisfy VERB american_scientific_journal-1665 65 4 the the DET american_scientific_journal-1665 65 5 condition condition NOUN american_scientific_journal-1665 65 6 ( ( PUNCT american_scientific_journal-1665 65 7 2.1 2.1 NUM american_scientific_journal-1665 65 8 ) ) PUNCT american_scientific_journal-1665 65 9 will will AUX american_scientific_journal-1665 65 10 be be AUX american_scientific_journal-1665 65 11 called call VERB american_scientific_journal-1665 65 12 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-1665 65 13 β„Žβ€“generalized β„Žβ€“generalize VERB american_scientific_journal-1665 65 14 birecurrent birecurrent ADJ american_scientific_journal-1665 65 15 space space NOUN american_scientific_journal-1665 65 16 . . PUNCT american_scientific_journal-1665 66 1 we we PRON american_scientific_journal-1665 66 2 shall shall AUX american_scientific_journal-1665 66 3 denote denote VERB american_scientific_journal-1665 66 4 it it PRON american_scientific_journal-1665 66 5 briefly briefly ADV american_scientific_journal-1665 66 6 by by ADP american_scientific_journal-1665 66 7 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 66 8 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 66 9 . . PUNCT american_scientific_journal-1665 67 1 transvecting transvecte VERB american_scientific_journal-1665 67 2 ( ( PUNCT american_scientific_journal-1665 67 3 2.1 2.1 NUM american_scientific_journal-1665 67 4 ) ) PUNCT american_scientific_journal-1665 67 5 by by ADP american_scientific_journal-1665 67 6 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 NOUN american_scientific_journal-1665 67 7 , , PUNCT american_scientific_journal-1665 67 8 using use VERB american_scientific_journal-1665 67 9 ( ( PUNCT american_scientific_journal-1665 67 10 1.1a 1.1a NOUN american_scientific_journal-1665 67 11 ) ) PUNCT american_scientific_journal-1665 67 12 and and CCONJ american_scientific_journal-1665 67 13 ( ( PUNCT american_scientific_journal-1665 67 14 1.6 1.6 NUM american_scientific_journal-1665 67 15 ) ) PUNCT american_scientific_journal-1665 67 16 , , PUNCT american_scientific_journal-1665 67 17 we we PRON american_scientific_journal-1665 67 18 get get VERB american_scientific_journal-1665 67 19 ( ( PUNCT american_scientific_journal-1665 67 20 2.2 2.2 NUM american_scientific_journal-1665 67 21 ) ) PUNCT american_scientific_journal-1665 67 22 π»π»π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—β„Ž|β„“|π‘šπ‘š PROPN american_scientific_journal-1665 67 23 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 67 24 = = X american_scientific_journal-1665 67 25 πœ†πœ†β„“π»π»π‘—π‘—β„Ž|π‘šπ‘š πœ†πœ†β„“π»π»π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 67 26 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 68 1 + + CCONJ american_scientific_journal-1665 68 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 68 3 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 68 4 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 68 5 . . PUNCT american_scientific_journal-1665 69 1 65- 65- X american_scientific_journal-1665 69 2 ) ) PUNCT american_scientific_journal-1665 69 3 volume volume NOUN american_scientific_journal-1665 69 4 20 20 NUM american_scientific_journal-1665 69 5 , , PUNCT american_scientific_journal-1665 69 6 no no DET american_scientific_journal-1665 69 7 1 1 NUM american_scientific_journal-1665 69 8 , , PUNCT american_scientific_journal-1665 69 9 pp pp ADP american_scientific_journal-1665 69 10 522016 522016 NUM american_scientific_journal-1665 69 11 ( ( PUNCT american_scientific_journal-1665 69 12 ) ) PUNCT american_scientific_journal-1665 69 13 research research NOUN american_scientific_journal-1665 69 14 journal journal NOUN american_scientific_journal-1665 69 15 for for ADP american_scientific_journal-1665 69 16 engineering engineering NOUN american_scientific_journal-1665 69 17 , , PUNCT american_scientific_journal-1665 69 18 technology technology NOUN american_scientific_journal-1665 69 19 , , PUNCT american_scientific_journal-1665 69 20 and and CCONJ american_scientific_journal-1665 69 21 sciences science NOUN american_scientific_journal-1665 69 22 ( ( PUNCT american_scientific_journal-1665 69 23 asrjets asrjet NOUN american_scientific_journal-1665 69 24 scientificamerican scientificamerican VERB american_scientific_journal-1665 69 25 56 56 NUM american_scientific_journal-1665 69 26 theorem theorem VERB american_scientific_journal-1665 69 27 2.1 2.1 NUM american_scientific_journal-1665 69 28 . . PUNCT american_scientific_journal-1665 70 1 in in ADP american_scientific_journal-1665 70 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 70 3 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 70 4 , , PUNCT american_scientific_journal-1665 70 5 the the DET american_scientific_journal-1665 70 6 β„Ž(𝑣𝑣 β„Ž(𝑣𝑣 NUM american_scientific_journal-1665 70 7 ) ) PUNCT american_scientific_journal-1665 70 8 – – PUNCT american_scientific_journal-1665 70 9 torsion torsion NOUN american_scientific_journal-1665 70 10 tensor tensor NOUN american_scientific_journal-1665 70 11 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 70 12 is be AUX american_scientific_journal-1665 70 13 generalized generalized ADJ american_scientific_journal-1665 70 14 birecurrent birecurrent NOUN american_scientific_journal-1665 70 15 . . PUNCT american_scientific_journal-1665 71 1 differentiating differentiate VERB american_scientific_journal-1665 71 2 ( ( PUNCT american_scientific_journal-1665 71 3 2.2 2.2 NUM american_scientific_journal-1665 71 4 ) ) PUNCT american_scientific_journal-1665 71 5 partially partially ADV american_scientific_journal-1665 71 6 with with ADP american_scientific_journal-1665 71 7 respect respect NOUN american_scientific_journal-1665 71 8 to to ADP american_scientific_journal-1665 71 9 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 PRON american_scientific_journal-1665 71 10 and and CCONJ american_scientific_journal-1665 71 11 using use VERB american_scientific_journal-1665 71 12 ( ( PUNCT american_scientific_journal-1665 71 13 1.9 1.9 NUM american_scientific_journal-1665 71 14 ) ) PUNCT american_scientific_journal-1665 71 15 , , PUNCT american_scientific_journal-1665 71 16 we we PRON american_scientific_journal-1665 71 17 get get VERB american_scientific_journal-1665 71 18 ( ( PUNCT american_scientific_journal-1665 71 19 2.3 2.3 NUM american_scientific_journal-1665 71 20 ) ) PUNCT american_scientific_journal-1665 71 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 71 22 Μ‡ Μ‡ NOUN american_scientific_journal-1665 71 23 οΏ½ οΏ½ NOUN american_scientific_journal-1665 71 24 πœ•π‘—π‘—π»π»π‘—π‘—β„Ž|β„“|π‘šπ‘š πœ•π‘—π‘—π»π»π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 71 25 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 71 26 = = SYM american_scientific_journal-1665 71 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 71 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 71 29 Μ‡ Μ‡ PROPN american_scientific_journal-1665 71 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 71 31 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 71 32 οΏ½ οΏ½ PROPN american_scientific_journal-1665 71 33 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 71 34 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 72 1 + + CCONJ american_scientific_journal-1665 72 2 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 72 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 4 Μ‡ Μ‡ PROPN american_scientific_journal-1665 72 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 6 πœ•π‘—π‘— πœ•π‘—π‘— X american_scientific_journal-1665 72 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 72 8 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 72 9 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 72 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 11 + + CCONJ american_scientific_journal-1665 72 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 14 Μ‡ Μ‡ PROPN american_scientific_journal-1665 72 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 72 16 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 72 17 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 72 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 72 19 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 72 20 + + CCONJ american_scientific_journal-1665 72 21 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 72 22 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 72 23 . . PUNCT american_scientific_journal-1665 73 1 using use VERB american_scientific_journal-1665 73 2 the the DET american_scientific_journal-1665 73 3 commutation commutation NOUN american_scientific_journal-1665 73 4 formula formula NOUN american_scientific_journal-1665 73 5 exhibited exhibit VERB american_scientific_journal-1665 73 6 by by ADP american_scientific_journal-1665 73 7 ( ( PUNCT american_scientific_journal-1665 73 8 1.2a 1.2a NUM american_scientific_journal-1665 73 9 ) ) PUNCT american_scientific_journal-1665 73 10 for for ADP american_scientific_journal-1665 73 11 ( ( PUNCT american_scientific_journal-1665 73 12 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 73 13 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 73 14 ) ) PUNCT american_scientific_journal-1665 73 15 and and CCONJ american_scientific_journal-1665 73 16 ( ( PUNCT american_scientific_journal-1665 73 17 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 73 18 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 73 19 ) ) PUNCT american_scientific_journal-1665 73 20 in in ADP american_scientific_journal-1665 73 21 ( ( PUNCT american_scientific_journal-1665 73 22 2.3 2.3 NUM american_scientific_journal-1665 73 23 ) ) PUNCT american_scientific_journal-1665 73 24 and and CCONJ american_scientific_journal-1665 73 25 using use VERB american_scientific_journal-1665 73 26 ( ( PUNCT american_scientific_journal-1665 73 27 1.9 1.9 NUM american_scientific_journal-1665 73 28 ) ) PUNCT american_scientific_journal-1665 73 29 , , PUNCT american_scientific_journal-1665 73 30 we we PRON american_scientific_journal-1665 73 31 get get VERB american_scientific_journal-1665 73 32 ( ( PUNCT american_scientific_journal-1665 73 33 2.4 2.4 NUM american_scientific_journal-1665 73 34 ) ) PUNCT american_scientific_journal-1665 73 35 { { PUNCT american_scientific_journal-1665 73 36 οΏ½ οΏ½ PROPN american_scientific_journal-1665 73 37 Μ‡ Μ‡ PROPN american_scientific_journal-1665 73 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 73 39 πœ•π‘—π‘—(π»π»π‘—π‘—β„Ž|β„“ πœ•π‘—π‘—(π»π»π‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 73 40 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 73 41 ) ) PUNCT american_scientific_journal-1665 73 42 } } PUNCT american_scientific_journal-1665 73 43 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 74 1 + + CCONJ american_scientific_journal-1665 74 2 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 74 3 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 74 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 74 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 74 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 74 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 74 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 74 9 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 74 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 74 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 74 12 βˆ’ βˆ’ PROPN american_scientific_journal-1665 74 13 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 74 14 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 74 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 74 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 74 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 74 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 74 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 74 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 74 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 74 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 1 βˆ’ βˆ’ NOUN american_scientific_journal-1665 75 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 75 3 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 75 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 6 Μ‡ Μ‡ NOUN american_scientific_journal-1665 75 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 75 9 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 75 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 75 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 75 13 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 75 14 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 75 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 75 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 75 20 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 75 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 75 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 23 βˆ’ βˆ’ PROPN american_scientific_journal-1665 75 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 25 Μ‡ Μ‡ PROPN american_scientific_journal-1665 75 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 27 πœ•π‘Ÿπ‘Ÿ πœ•π‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 75 28 οΏ½ οΏ½ NOUN american_scientific_journal-1665 75 29 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 75 30 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 75 31 οΏ½ οΏ½ NOUN american_scientific_journal-1665 75 32 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 75 33 = = SYM american_scientific_journal-1665 75 34 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 36 Μ‡ Μ‡ PROPN american_scientific_journal-1665 75 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 75 38 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 75 39 οΏ½ οΏ½ X american_scientific_journal-1665 75 40 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 75 41 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 76 1 + + CCONJ american_scientific_journal-1665 76 2 πœ†πœ†β„“ πœ†πœ†β„“ SYM american_scientific_journal-1665 76 3 π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 76 4 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 77 1 + + CCONJ american_scientific_journal-1665 77 2 πœ†πœ†β„“ πœ†πœ†β„“ X american_scientific_journal-1665 77 3 [ [ PUNCT american_scientific_journal-1665 77 4 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 77 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 77 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 77 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 77 8 οΏ½ οΏ½ NOUN american_scientific_journal-1665 77 9 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 77 10 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 77 11 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 77 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 77 13 βˆ’ βˆ’ ADP american_scientific_journal-1665 77 14 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 77 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 77 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 77 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 77 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 77 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 77 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 77 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 77 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 1 βˆ’ βˆ’ ADP american_scientific_journal-1665 78 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 78 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 5 Μ‡ Μ‡ NOUN american_scientific_journal-1665 78 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 7 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 78 8 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 78 9 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 78 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 11 βˆ’ βˆ’ ADP american_scientific_journal-1665 78 12 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 78 13 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 78 14 ] ] PUNCT american_scientific_journal-1665 78 15 + + NUM american_scientific_journal-1665 78 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 18 Μ‡ Μ‡ PROPN american_scientific_journal-1665 78 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 78 20 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 78 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 79 1 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 79 2 + + CCONJ american_scientific_journal-1665 79 3 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 79 4 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 79 5 . . PUNCT american_scientific_journal-1665 80 1 again again ADV american_scientific_journal-1665 80 2 applying apply VERB american_scientific_journal-1665 80 3 the the DET american_scientific_journal-1665 80 4 commutation commutation NOUN american_scientific_journal-1665 80 5 formula formula NOUN american_scientific_journal-1665 80 6 exhibited exhibit VERB american_scientific_journal-1665 80 7 by by ADP american_scientific_journal-1665 80 8 ( ( PUNCT american_scientific_journal-1665 80 9 1.2a 1.2a NUM american_scientific_journal-1665 80 10 ) ) PUNCT american_scientific_journal-1665 80 11 for for ADP american_scientific_journal-1665 80 12 ( ( PUNCT american_scientific_journal-1665 80 13 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 80 14 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 80 15 ) ) PUNCT american_scientific_journal-1665 80 16 in in ADP american_scientific_journal-1665 80 17 ( ( PUNCT american_scientific_journal-1665 80 18 2.4 2.4 NUM american_scientific_journal-1665 80 19 ) ) PUNCT american_scientific_journal-1665 80 20 and and CCONJ american_scientific_journal-1665 80 21 using use VERB american_scientific_journal-1665 80 22 ( ( PUNCT american_scientific_journal-1665 80 23 1.9 1.9 NUM american_scientific_journal-1665 80 24 ) ) PUNCT american_scientific_journal-1665 80 25 , , PUNCT american_scientific_journal-1665 80 26 we we PRON american_scientific_journal-1665 80 27 get get VERB american_scientific_journal-1665 80 28 { { PUNCT american_scientific_journal-1665 80 29 π»π»π‘—π‘—π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 80 30 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 81 1 + + CCONJ american_scientific_journal-1665 81 2 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 81 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 81 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 7 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 81 8 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 81 9 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 81 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 11 βˆ’ βˆ’ ADP american_scientific_journal-1665 81 12 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 81 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 15 Μ‡ Μ‡ NOUN american_scientific_journal-1665 81 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 17 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 81 18 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 81 19 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 81 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 21 βˆ’ βˆ’ ADP american_scientific_journal-1665 81 22 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 81 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 25 Μ‡ Μ‡ NOUN american_scientific_journal-1665 81 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 27 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 81 28 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 81 29 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 81 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 31 βˆ’ βˆ’ ADP american_scientific_journal-1665 81 32 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 81 33 π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 81 34 } } PUNCT american_scientific_journal-1665 81 35 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 81 36 + + CCONJ american_scientific_journal-1665 81 37 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 81 38 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 81 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 41 Μ‡ Μ‡ PROPN american_scientific_journal-1665 81 42 οΏ½ οΏ½ NOUN american_scientific_journal-1665 81 43 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 81 44 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 81 45 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 81 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 47 βˆ’ βˆ’ PROPN american_scientific_journal-1665 81 48 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 81 49 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 81 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 51 οΏ½ οΏ½ PROPN american_scientific_journal-1665 81 52 Μ‡ Μ‡ PROPN american_scientific_journal-1665 81 53 οΏ½ οΏ½ NOUN american_scientific_journal-1665 81 54 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 81 55 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 81 56 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 81 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 1 βˆ’ βˆ’ NOUN american_scientific_journal-1665 82 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 82 3 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 82 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 6 Μ‡ Μ‡ NOUN american_scientific_journal-1665 82 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 82 9 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 82 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 82 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 82 13 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 82 14 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 82 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 82 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 82 20 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 82 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 82 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 82 23 βˆ’ βˆ’ PROPN american_scientific_journal-1665 82 24 { { PUNCT american_scientific_journal-1665 82 25 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 82 26 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 83 1 + + CCONJ american_scientific_journal-1665 83 2 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 83 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 83 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 7 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 83 8 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 83 9 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 83 10 οΏ½ οΏ½ NOUN american_scientific_journal-1665 83 11 βˆ’ βˆ’ ADP american_scientific_journal-1665 83 12 π»π»π‘ π‘ β„Žπ‘–π‘– π»π»π‘ π‘ β„Žπ‘–π‘– PROPN american_scientific_journal-1665 83 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 15 Μ‡ Μ‡ PROPN american_scientific_journal-1665 83 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 17 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 83 18 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 83 19 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 83 20 οΏ½ οΏ½ NOUN american_scientific_journal-1665 83 21 βˆ’ βˆ’ ADP american_scientific_journal-1665 83 22 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 PROPN american_scientific_journal-1665 83 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 25 Μ‡ Μ‡ PROPN american_scientific_journal-1665 83 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 27 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 83 28 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 83 29 βˆ—π‘ π‘  βˆ—π‘ π‘  PUNCT american_scientific_journal-1665 83 30 οΏ½ οΏ½ NOUN american_scientific_journal-1665 83 31 βˆ’ βˆ’ ADP american_scientific_journal-1665 83 32 π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 83 33 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 83 34 } } PUNCT american_scientific_journal-1665 83 35 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 83 36 = = SYM american_scientific_journal-1665 83 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 39 Μ‡ Μ‡ PROPN american_scientific_journal-1665 83 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 83 41 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 83 42 οΏ½ οΏ½ X american_scientific_journal-1665 83 43 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 83 44 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 84 1 + + CCONJ american_scientific_journal-1665 84 2 πœ†πœ†β„“ πœ†πœ†β„“ SYM american_scientific_journal-1665 84 3 π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 84 4 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 85 1 + + CCONJ american_scientific_journal-1665 85 2 πœ†πœ†β„“ πœ†πœ†β„“ X american_scientific_journal-1665 85 3 [ [ PUNCT american_scientific_journal-1665 85 4 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 85 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 8 οΏ½ οΏ½ NOUN american_scientific_journal-1665 85 9 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 10 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 85 11 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 85 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 13 βˆ’ βˆ’ ADP american_scientific_journal-1665 85 14 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 85 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 85 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 85 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 85 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 23 βˆ’π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– βˆ’π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– SYM american_scientific_journal-1665 85 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 26 Μ‡ Μ‡ NOUN american_scientific_journal-1665 85 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 28 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 29 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 85 30 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 85 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 32 βˆ’ βˆ’ ADP american_scientific_journal-1665 85 33 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 34 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 85 35 ] ] PUNCT american_scientific_journal-1665 85 36 + + NUM american_scientific_journal-1665 85 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 39 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 41 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 85 42 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 85 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 44 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 45 + + CCONJ american_scientific_journal-1665 85 46 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 85 47 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 48 which which PRON american_scientific_journal-1665 85 49 can can AUX american_scientific_journal-1665 85 50 be be AUX american_scientific_journal-1665 85 51 written write VERB american_scientific_journal-1665 85 52 as as ADP american_scientific_journal-1665 85 53 ( ( PUNCT american_scientific_journal-1665 85 54 2.5 2.5 NUM american_scientific_journal-1665 85 55 ) ) PUNCT american_scientific_journal-1665 85 56 π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š ADJ american_scientific_journal-1665 85 57 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 85 58 + + X american_scientific_journal-1665 85 59 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 60 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 85 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 62 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 63 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 65 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 66 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 85 67 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 85 68 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 69 βˆ’ βˆ’ ADP american_scientific_journal-1665 85 70 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 71 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 72 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 73 Μ‡ Μ‡ NOUN american_scientific_journal-1665 85 74 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 75 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 76 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 85 77 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 85 78 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 79 βˆ’ βˆ’ ADP american_scientific_journal-1665 85 80 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 85 81 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 82 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 83 Μ‡ Μ‡ NOUN american_scientific_journal-1665 85 84 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 85 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 86 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 85 87 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 85 88 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 89 βˆ’ βˆ’ ADP american_scientific_journal-1665 85 90 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 85 91 π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 85 92 οΏ½ οΏ½ X american_scientific_journal-1665 85 93 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 85 94 + + CCONJ american_scientific_journal-1665 85 95 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 85 96 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 85 97 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 98 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 99 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 100 οΏ½ οΏ½ NOUN american_scientific_journal-1665 85 101 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 85 102 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 85 103 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 85 104 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 105 βˆ’ βˆ’ PROPN american_scientific_journal-1665 85 106 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 85 107 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 85 108 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 109 οΏ½ οΏ½ PROPN american_scientific_journal-1665 85 110 Μ‡ Μ‡ PROPN american_scientific_journal-1665 85 111 οΏ½ οΏ½ NOUN american_scientific_journal-1665 85 112 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 85 113 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 85 114 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 85 115 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 1 βˆ’ βˆ’ NOUN american_scientific_journal-1665 86 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 86 3 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 86 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 6 Μ‡ Μ‡ NOUN american_scientific_journal-1665 86 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 86 9 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 86 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 86 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 86 13 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 86 14 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 86 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 86 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 86 20 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 86 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 86 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 86 23 βˆ’ βˆ’ PROPN american_scientific_journal-1665 86 24 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 86 25 𝑖𝑖 𝑖𝑖 PART american_scientific_journal-1665 87 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 87 2 βˆ’π»π»π‘—π‘—β„Žπ‘ π‘  βˆ’π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 87 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 87 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 7 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 87 8 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 87 9 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 87 10 οΏ½ οΏ½ NOUN american_scientific_journal-1665 87 11 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 87 12 + + CCONJ american_scientific_journal-1665 87 13 π»π»π‘ π‘ β„Žπ‘–π‘– π»π»π‘ π‘ β„Žπ‘–π‘– PROPN american_scientific_journal-1665 87 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 16 Μ‡ Μ‡ PROPN american_scientific_journal-1665 87 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 18 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 87 19 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 87 20 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 87 21 οΏ½ οΏ½ NOUN american_scientific_journal-1665 87 22 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 87 23 + + CCONJ american_scientific_journal-1665 87 24 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 PROPN american_scientific_journal-1665 87 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 27 Μ‡ Μ‡ PROPN american_scientific_journal-1665 87 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 87 29 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 87 30 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 87 31 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 87 32 οΏ½ οΏ½ NOUN american_scientific_journal-1665 87 33 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 87 34 + + PUNCT american_scientific_journal-1665 87 35 π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 87 36 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 87 37 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 87 38 = = SYM american_scientific_journal-1665 87 39 πœ†πœ†β„“ πœ†πœ†β„“ PRON american_scientific_journal-1665 87 40 π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 87 41 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 88 1 + + CCONJ american_scientific_journal-1665 88 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 88 3 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 88 4 + + NUM american_scientific_journal-1665 88 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 88 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 88 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 88 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 88 9 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 88 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 88 11 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 88 12 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 89 1 + + CCONJ american_scientific_journal-1665 89 2 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 89 3 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 89 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 89 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 89 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 89 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 89 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 89 9 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 89 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 89 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 89 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 89 13 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 89 14 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 89 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 89 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 89 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 89 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 89 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 89 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 89 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 90 1 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 2 βˆ’ βˆ’ NOUN american_scientific_journal-1665 90 3 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 90 4 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 90 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 7 Μ‡ Μ‡ NOUN american_scientific_journal-1665 90 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 9 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 90 10 β„Žπ‘šπ‘š β„Žπ‘šπ‘š DET american_scientific_journal-1665 90 11 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 90 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 13 βˆ’ βˆ’ NOUN american_scientific_journal-1665 90 14 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 90 15 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 90 16 + + SYM american_scientific_journal-1665 90 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 19 Μ‡ Μ‡ PROPN american_scientific_journal-1665 90 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 90 21 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 90 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 91 1 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 91 2 . . PUNCT american_scientific_journal-1665 92 1 this this PRON american_scientific_journal-1665 92 2 shows show VERB american_scientific_journal-1665 92 3 that that SCONJ american_scientific_journal-1665 92 4 65- 65- X american_scientific_journal-1665 92 5 ) ) PUNCT american_scientific_journal-1665 92 6 volume volume NOUN american_scientific_journal-1665 92 7 20 20 NUM american_scientific_journal-1665 92 8 , , PUNCT american_scientific_journal-1665 92 9 no no DET american_scientific_journal-1665 92 10 1 1 NUM american_scientific_journal-1665 92 11 , , PUNCT american_scientific_journal-1665 92 12 pp pp ADP american_scientific_journal-1665 92 13 522016 522016 NUM american_scientific_journal-1665 92 14 ( ( PUNCT american_scientific_journal-1665 92 15 ) ) PUNCT american_scientific_journal-1665 92 16 research research NOUN american_scientific_journal-1665 92 17 journal journal NOUN american_scientific_journal-1665 92 18 for for ADP american_scientific_journal-1665 92 19 engineering engineering NOUN american_scientific_journal-1665 92 20 , , PUNCT american_scientific_journal-1665 92 21 technology technology NOUN american_scientific_journal-1665 92 22 , , PUNCT american_scientific_journal-1665 92 23 and and CCONJ american_scientific_journal-1665 92 24 sciences science NOUN american_scientific_journal-1665 92 25 ( ( PUNCT american_scientific_journal-1665 92 26 asrjets asrjet NOUN american_scientific_journal-1665 92 27 scientificamerican scientificamerican VERB american_scientific_journal-1665 92 28 57 57 NUM american_scientific_journal-1665 92 29 π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 92 30 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 92 31 = = NOUN american_scientific_journal-1665 92 32 πœ†πœ†β„“ πœ†πœ†β„“ PRON american_scientific_journal-1665 92 33 π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 92 34 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 93 1 + + CCONJ american_scientific_journal-1665 93 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 93 3 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 93 4 if if SCONJ american_scientific_journal-1665 93 5 and and CCONJ american_scientific_journal-1665 93 6 only only ADV american_scientific_journal-1665 93 7 if if SCONJ american_scientific_journal-1665 93 8 ( ( PUNCT american_scientific_journal-1665 93 9 2.6 2.6 NUM american_scientific_journal-1665 93 10 ) ) PUNCT american_scientific_journal-1665 93 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 12 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 93 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 15 Μ‡ Μ‡ PROPN american_scientific_journal-1665 93 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 17 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 18 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 93 19 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 93 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 21 βˆ’ βˆ’ ADP american_scientific_journal-1665 93 22 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 93 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 25 Μ‡ Μ‡ NOUN american_scientific_journal-1665 93 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 27 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 28 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 93 29 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 93 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 31 βˆ’ βˆ’ ADP american_scientific_journal-1665 93 32 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 93 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 34 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 35 Μ‡ Μ‡ NOUN american_scientific_journal-1665 93 36 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 37 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 38 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 93 39 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 93 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 41 βˆ’ βˆ’ ADP american_scientific_journal-1665 93 42 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 93 43 π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 93 44 οΏ½ οΏ½ X american_scientific_journal-1665 93 45 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 93 46 + + CCONJ american_scientific_journal-1665 93 47 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 93 48 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 93 49 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 51 Μ‡ Μ‡ PROPN american_scientific_journal-1665 93 52 οΏ½ οΏ½ NOUN american_scientific_journal-1665 93 53 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 54 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 93 55 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 93 56 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 57 βˆ’ βˆ’ PROPN american_scientific_journal-1665 93 58 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 93 59 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 93 60 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 62 Μ‡ Μ‡ PROPN american_scientific_journal-1665 93 63 οΏ½ οΏ½ NOUN american_scientific_journal-1665 93 64 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 93 65 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 93 66 βˆ—π‘–π‘– βˆ—π‘–π‘– SYM american_scientific_journal-1665 93 67 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 68 βˆ’ βˆ’ PROPN american_scientific_journal-1665 93 69 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 93 70 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 93 71 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 72 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 73 Μ‡ Μ‡ NOUN american_scientific_journal-1665 93 74 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 75 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 76 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 93 77 βˆ—π‘–π‘– βˆ—π‘–π‘– ADJ american_scientific_journal-1665 93 78 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 79 βˆ’ βˆ’ PROPN american_scientific_journal-1665 93 80 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 93 81 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 93 82 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 83 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 84 Μ‡ Μ‡ PROPN american_scientific_journal-1665 93 85 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 86 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 93 87 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 93 88 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 93 89 οΏ½ οΏ½ PROPN american_scientific_journal-1665 93 90 βˆ’ βˆ’ PROPN american_scientific_journal-1665 93 91 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 93 92 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 94 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 94 2 βˆ’ βˆ’ PROPN american_scientific_journal-1665 94 3 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 94 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 8 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 94 9 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 94 10 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 94 11 οΏ½ οΏ½ NOUN american_scientific_journal-1665 94 12 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 94 13 + + CCONJ american_scientific_journal-1665 94 14 π»π»π‘ π‘ β„Žπ‘–π‘– π»π»π‘ π‘ β„Žπ‘–π‘– PROPN american_scientific_journal-1665 94 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 19 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 94 20 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 94 21 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 94 22 οΏ½ οΏ½ NOUN american_scientific_journal-1665 94 23 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 94 24 + + CCONJ american_scientific_journal-1665 94 25 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 PROPN american_scientific_journal-1665 94 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 28 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 30 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 94 31 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 94 32 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 94 33 οΏ½ οΏ½ NOUN american_scientific_journal-1665 94 34 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 94 35 + + PUNCT american_scientific_journal-1665 94 36 π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 94 37 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 94 38 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 94 39 = = SYM american_scientific_journal-1665 94 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 42 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 44 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 94 45 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 46 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 94 47 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 94 48 + + CCONJ american_scientific_journal-1665 94 49 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 94 50 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 94 51 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 53 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 54 οΏ½ οΏ½ NOUN american_scientific_journal-1665 94 55 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 94 56 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 94 57 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 94 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 59 βˆ’ βˆ’ NOUN american_scientific_journal-1665 94 60 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 94 61 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 94 62 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 63 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 64 Μ‡ Μ‡ PROPN american_scientific_journal-1665 94 65 οΏ½ οΏ½ NOUN american_scientific_journal-1665 94 66 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 94 67 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 94 68 βˆ—π‘–π‘– βˆ—π‘–π‘– SYM american_scientific_journal-1665 94 69 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 70 βˆ’ βˆ’ PROPN american_scientific_journal-1665 94 71 πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– ADJ american_scientific_journal-1665 94 72 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 73 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 74 Μ‡ Μ‡ NOUN american_scientific_journal-1665 94 75 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 76 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 94 77 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 94 78 βˆ—π‘–π‘– βˆ—π‘–π‘– ADP american_scientific_journal-1665 94 79 οΏ½ οΏ½ PROPN american_scientific_journal-1665 94 80 βˆ’πœ†πœ†β„“ βˆ’πœ†πœ†β„“ AUX american_scientific_journal-1665 95 1 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 95 2 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘–π‘– π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘–π‘– PROPN american_scientific_journal-1665 95 3 + + NUM american_scientific_journal-1665 95 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 95 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 95 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 95 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 95 8 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 95 9 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 95 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 95 11 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 95 12 . . PUNCT american_scientific_journal-1665 96 1 thus thus ADV american_scientific_journal-1665 96 2 , , PUNCT american_scientific_journal-1665 96 3 we we PRON american_scientific_journal-1665 96 4 conclude conclude AUX american_scientific_journal-1665 96 5 theorem theorem VERB american_scientific_journal-1665 96 6 2.2 2.2 NUM american_scientific_journal-1665 96 7 . . PUNCT american_scientific_journal-1665 97 1 in in ADP american_scientific_journal-1665 97 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 97 3 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 97 4 , , PUNCT american_scientific_journal-1665 97 5 berwald berwald NOUN american_scientific_journal-1665 97 6 curvature curvature NOUN american_scientific_journal-1665 97 7 tensor tensor NOUN american_scientific_journal-1665 97 8 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 97 9 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 97 10 is be AUX american_scientific_journal-1665 97 11 generalized generalize VERB american_scientific_journal-1665 97 12 birecurrent birecurrent ADJ american_scientific_journal-1665 97 13 if if SCONJ american_scientific_journal-1665 97 14 and and CCONJ american_scientific_journal-1665 97 15 only only ADV american_scientific_journal-1665 97 16 if if SCONJ american_scientific_journal-1665 97 17 ( ( PUNCT american_scientific_journal-1665 97 18 2.6 2.6 NUM american_scientific_journal-1665 97 19 ) ) PUNCT american_scientific_journal-1665 97 20 holds hold VERB american_scientific_journal-1665 97 21 good good ADJ american_scientific_journal-1665 97 22 . . PUNCT american_scientific_journal-1665 98 1 transvecting transvecte VERB american_scientific_journal-1665 98 2 ( ( PUNCT american_scientific_journal-1665 98 3 2.5 2.5 NUM american_scientific_journal-1665 98 4 ) ) PUNCT american_scientific_journal-1665 98 5 by by ADP american_scientific_journal-1665 98 6 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 98 7 , , PUNCT american_scientific_journal-1665 98 8 using use VERB american_scientific_journal-1665 98 9 ( ( PUNCT american_scientific_journal-1665 98 10 1.1b 1.1b NUM american_scientific_journal-1665 98 11 ) ) PUNCT american_scientific_journal-1665 98 12 and and CCONJ american_scientific_journal-1665 98 13 ( ( PUNCT american_scientific_journal-1665 98 14 1.15 1.15 NUM american_scientific_journal-1665 98 15 ) ) PUNCT american_scientific_journal-1665 98 16 , , PUNCT american_scientific_journal-1665 98 17 we we PRON american_scientific_journal-1665 98 18 get get VERB american_scientific_journal-1665 98 19 ( ( PUNCT american_scientific_journal-1665 98 20 2.7 2.7 NUM american_scientific_journal-1665 98 21 ) ) PUNCT american_scientific_journal-1665 98 22 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 98 23 + + CCONJ american_scientific_journal-1665 98 24 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 98 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 27 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 98 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 30 Μ‡ Μ‡ PROPN american_scientific_journal-1665 98 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 32 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 98 33 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 98 34 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 98 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 98 36 βˆ’ βˆ’ ADP american_scientific_journal-1665 99 1 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 99 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 4 Μ‡ Μ‡ NOUN american_scientific_journal-1665 99 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 6 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 99 7 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 99 8 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 99 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 10 βˆ’ βˆ’ ADP american_scientific_journal-1665 99 11 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 99 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 14 Μ‡ Μ‡ NOUN american_scientific_journal-1665 99 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 16 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 99 17 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 99 18 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 99 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 20 βˆ’ βˆ’ ADP american_scientific_journal-1665 99 21 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 99 22 π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 99 23 οΏ½ οΏ½ X american_scientific_journal-1665 99 24 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 99 25 + + PROPN american_scientific_journal-1665 99 26 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 99 27 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 99 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 30 Μ‡ Μ‡ PROPN american_scientific_journal-1665 99 31 οΏ½ οΏ½ NOUN american_scientific_journal-1665 99 32 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 99 33 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 99 34 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 99 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 36 βˆ’ βˆ’ PROPN american_scientific_journal-1665 99 37 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 99 38 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 99 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 99 41 Μ‡ Μ‡ PROPN american_scientific_journal-1665 99 42 οΏ½ οΏ½ NOUN american_scientific_journal-1665 99 43 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 99 44 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 99 45 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 99 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 1 βˆ’ βˆ’ NOUN american_scientific_journal-1665 100 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 100 3 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 100 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 6 Μ‡ Μ‡ NOUN american_scientific_journal-1665 100 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 100 9 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 100 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 100 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 100 13 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 100 14 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 100 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 100 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 100 20 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 100 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 100 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 100 23 βˆ’ βˆ’ PROPN american_scientific_journal-1665 100 24 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ NOUN american_scientific_journal-1665 100 25 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 101 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 101 2 βˆ’ βˆ’ PROPN american_scientific_journal-1665 101 3 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 101 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 101 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 8 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 101 9 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 101 10 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 101 11 οΏ½ οΏ½ NOUN american_scientific_journal-1665 101 12 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 101 13 + + CCONJ american_scientific_journal-1665 101 14 π»π»π‘ π‘ β„Žπ‘–π‘– π»π»π‘ π‘ β„Žπ‘–π‘– PROPN american_scientific_journal-1665 101 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 101 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 19 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 101 20 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 101 21 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 101 22 οΏ½ οΏ½ NOUN american_scientific_journal-1665 101 23 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 101 24 + + CCONJ american_scientific_journal-1665 101 25 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 PROPN american_scientific_journal-1665 101 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 28 Μ‡ Μ‡ PROPN american_scientific_journal-1665 101 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 30 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 101 31 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 101 32 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 101 33 οΏ½ οΏ½ NOUN american_scientific_journal-1665 101 34 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 101 35 + + PUNCT american_scientific_journal-1665 101 36 π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 101 37 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 101 38 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 101 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 40 = = SYM american_scientific_journal-1665 101 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 101 42 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 101 43 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 102 1 + + CCONJ american_scientific_journal-1665 102 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 102 3 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 102 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 102 5 + + CCONJ american_scientific_journal-1665 102 6 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 102 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 102 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 102 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 102 10 Μ‡ Μ‡ PROPN american_scientific_journal-1665 102 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 102 12 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 102 13 οΏ½ οΏ½ X american_scientific_journal-1665 102 14 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 102 15 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 103 1 + + CCONJ american_scientific_journal-1665 103 2 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 103 3 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 103 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 103 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 103 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 103 9 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 103 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 103 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 12 βˆ’ βˆ’ NOUN american_scientific_journal-1665 103 13 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 103 14 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 103 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 103 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 103 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 103 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 103 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 103 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 23 βˆ’ βˆ’ PROPN american_scientific_journal-1665 103 24 πœ†πœ†π‘™π‘™ πœ†πœ†π‘™π‘™ ADP american_scientific_journal-1665 103 25 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 103 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 28 Μ‡ Μ‡ NOUN american_scientific_journal-1665 103 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 30 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 103 31 β„Žπ‘šπ‘š β„Žπ‘šπ‘š DET american_scientific_journal-1665 103 32 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 103 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 103 34 βˆ’ βˆ’ NOUN american_scientific_journal-1665 104 1 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 104 2 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 104 3 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 104 4 + + SYM american_scientific_journal-1665 104 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 104 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 104 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 104 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 104 9 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 104 10 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 104 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 104 12 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 104 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 104 14 . . PUNCT american_scientific_journal-1665 105 1 this this PRON american_scientific_journal-1665 105 2 shows show VERB american_scientific_journal-1665 105 3 that that SCONJ american_scientific_journal-1665 105 4 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š=πœ†πœ†β„“ π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š=πœ†πœ†β„“ VERB american_scientific_journal-1665 105 5 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 105 6 + + CCONJ american_scientific_journal-1665 105 7 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 105 8 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 105 9 if if SCONJ american_scientific_journal-1665 105 10 and and CCONJ american_scientific_journal-1665 105 11 only only ADV american_scientific_journal-1665 105 12 if if SCONJ american_scientific_journal-1665 105 13 ( ( PUNCT american_scientific_journal-1665 105 14 2.8 2.8 NUM american_scientific_journal-1665 105 15 ) ) PUNCT american_scientific_journal-1665 105 16 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 105 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 19 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 105 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 22 Μ‡ Μ‡ PROPN american_scientific_journal-1665 105 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 24 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 25 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 105 26 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 105 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 28 βˆ’ βˆ’ ADP american_scientific_journal-1665 105 29 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 105 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 32 Μ‡ Μ‡ NOUN american_scientific_journal-1665 105 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 34 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 35 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 105 36 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 105 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 38 βˆ’ βˆ’ ADP american_scientific_journal-1665 105 39 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 105 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 42 Μ‡ Μ‡ NOUN american_scientific_journal-1665 105 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 44 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 45 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 105 46 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 105 47 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 48 βˆ’ βˆ’ ADP american_scientific_journal-1665 105 49 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 105 50 π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 105 51 οΏ½ οΏ½ X american_scientific_journal-1665 105 52 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 105 53 + + PROPN american_scientific_journal-1665 105 54 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 105 55 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 105 56 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 58 Μ‡ Μ‡ PROPN american_scientific_journal-1665 105 59 οΏ½ οΏ½ NOUN american_scientific_journal-1665 105 60 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 61 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 105 62 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 105 63 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 64 βˆ’ βˆ’ PROPN american_scientific_journal-1665 105 65 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 105 66 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 105 67 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 68 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 69 Μ‡ Μ‡ PROPN american_scientific_journal-1665 105 70 οΏ½ οΏ½ NOUN american_scientific_journal-1665 105 71 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 105 72 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 105 73 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 105 74 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 75 βˆ’ βˆ’ NOUN american_scientific_journal-1665 105 76 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 105 77 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 105 78 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 79 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 80 Μ‡ Μ‡ NOUN american_scientific_journal-1665 105 81 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 82 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 83 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 105 84 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 105 85 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 86 βˆ’ βˆ’ NOUN american_scientific_journal-1665 105 87 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 105 88 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 105 89 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 90 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 91 Μ‡ Μ‡ PROPN american_scientific_journal-1665 105 92 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 93 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 105 94 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 105 95 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 105 96 οΏ½ οΏ½ PROPN american_scientific_journal-1665 105 97 βˆ’ βˆ’ ADP american_scientific_journal-1665 105 98 65- 65- NOUN american_scientific_journal-1665 105 99 ) ) PUNCT american_scientific_journal-1665 105 100 volume volume NOUN american_scientific_journal-1665 105 101 20 20 NUM american_scientific_journal-1665 105 102 , , PUNCT american_scientific_journal-1665 105 103 no no DET american_scientific_journal-1665 105 104 1 1 NUM american_scientific_journal-1665 105 105 , , PUNCT american_scientific_journal-1665 105 106 pp pp ADP american_scientific_journal-1665 105 107 522016 522016 NUM american_scientific_journal-1665 105 108 ( ( PUNCT american_scientific_journal-1665 105 109 ) ) PUNCT american_scientific_journal-1665 105 110 research research NOUN american_scientific_journal-1665 105 111 journal journal NOUN american_scientific_journal-1665 105 112 for for ADP american_scientific_journal-1665 105 113 engineering engineering NOUN american_scientific_journal-1665 105 114 , , PUNCT american_scientific_journal-1665 105 115 technology technology NOUN american_scientific_journal-1665 105 116 , , PUNCT american_scientific_journal-1665 105 117 and and CCONJ american_scientific_journal-1665 105 118 sciences science NOUN american_scientific_journal-1665 105 119 ( ( PUNCT american_scientific_journal-1665 105 120 asrjets asrjet NOUN american_scientific_journal-1665 105 121 scientificamerican scientificamerican VERB american_scientific_journal-1665 105 122 58 58 NUM american_scientific_journal-1665 105 123 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 105 124 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 106 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 106 2 βˆ’ βˆ’ PROPN american_scientific_journal-1665 106 3 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 106 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 106 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 8 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 106 9 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 106 10 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 106 11 οΏ½ οΏ½ NOUN american_scientific_journal-1665 106 12 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 106 13 + + CCONJ american_scientific_journal-1665 106 14 π»π»π‘ π‘ β„Žπ‘–π‘– π»π»π‘ π‘ β„Žπ‘–π‘– PROPN american_scientific_journal-1665 106 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 106 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 19 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 106 20 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 106 21 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 106 22 οΏ½ οΏ½ NOUN american_scientific_journal-1665 106 23 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 106 24 + + CCONJ american_scientific_journal-1665 106 25 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 𝐻𝐻𝑗𝑗𝑠𝑠𝑖𝑖 PROPN american_scientific_journal-1665 106 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 28 Μ‡ Μ‡ PROPN american_scientific_journal-1665 106 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 30 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 106 31 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 106 32 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 106 33 οΏ½ οΏ½ NOUN american_scientific_journal-1665 106 34 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 106 35 + + PUNCT american_scientific_journal-1665 106 36 π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– π»π»π‘ π‘ π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 106 37 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 106 38 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 106 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 40 = = PUNCT american_scientific_journal-1665 106 41 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 106 42 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 44 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 45 Μ‡ Μ‡ PROPN american_scientific_journal-1665 106 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 47 πœ•π‘—π‘—πœ†πœ†π‘™π‘™ πœ•π‘—π‘—πœ†πœ†π‘™π‘™ NOUN american_scientific_journal-1665 106 48 οΏ½ οΏ½ PROPN american_scientific_journal-1665 106 49 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 106 50 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 107 1 + + CCONJ american_scientific_journal-1665 107 2 πœ†πœ†π‘™π‘™ πœ†πœ†π‘™π‘™ VERB american_scientific_journal-1665 107 3 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 107 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 107 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 107 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 107 9 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 107 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 107 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 12 βˆ’ βˆ’ PROPN american_scientific_journal-1665 107 13 πœ†πœ†π‘™π‘™ πœ†πœ†π‘™π‘™ ADP american_scientific_journal-1665 107 14 π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿβ„Žπ‘–π‘– PROPN american_scientific_journal-1665 107 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 107 18 οΏ½ οΏ½ NOUN american_scientific_journal-1665 107 19 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 107 20 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 107 21 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 107 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 23 βˆ’πœ†πœ†π‘™π‘™ βˆ’πœ†πœ†π‘™π‘™ AUX american_scientific_journal-1665 107 24 π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– π»π»π‘—π‘—π‘Ÿπ‘Ÿπ‘–π‘– PROPN american_scientific_journal-1665 107 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 27 Μ‡ Μ‡ NOUN american_scientific_journal-1665 107 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 29 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 107 30 β„Žπ‘šπ‘š β„Žπ‘šπ‘š PRON american_scientific_journal-1665 107 31 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 107 32 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 33 βˆ’ βˆ’ NOUN american_scientific_journal-1665 107 34 πœ†πœ†π‘™π‘™ πœ†πœ†π‘™π‘™ ADP american_scientific_journal-1665 107 35 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 107 36 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 107 37 + + SYM american_scientific_journal-1665 107 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 40 Μ‡ Μ‡ PROPN american_scientific_journal-1665 107 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 42 πœ•π‘—π‘—π‘π‘π‘™π‘™π‘šπ‘š πœ•π‘—π‘—π‘π‘π‘™π‘™π‘šπ‘š PROPN american_scientific_journal-1665 107 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 44 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 107 45 οΏ½ οΏ½ PROPN american_scientific_journal-1665 107 46 . . PUNCT american_scientific_journal-1665 108 1 thus thus ADV american_scientific_journal-1665 108 2 , , PUNCT american_scientific_journal-1665 108 3 we we PRON american_scientific_journal-1665 108 4 conclude conclude AUX american_scientific_journal-1665 108 5 theorem theorem VERB american_scientific_journal-1665 108 6 2.3 2.3 NUM american_scientific_journal-1665 108 7 . . PUNCT american_scientific_journal-1665 109 1 in in ADP american_scientific_journal-1665 109 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 109 3 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 109 4 , , PUNCT american_scientific_journal-1665 109 5 the the DET american_scientific_journal-1665 109 6 associate associate ADJ american_scientific_journal-1665 109 7 tensor tensor NOUN american_scientific_journal-1665 109 8 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 109 9 of of ADP american_scientific_journal-1665 109 10 berwald berwald NOUN american_scientific_journal-1665 109 11 curvature curvature NOUN american_scientific_journal-1665 109 12 tensor tensor NOUN american_scientific_journal-1665 109 13 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 109 14 is be AUX american_scientific_journal-1665 109 15 generalized generalize VERB american_scientific_journal-1665 109 16 birecurrent birecurrent ADJ american_scientific_journal-1665 109 17 if if SCONJ american_scientific_journal-1665 109 18 and and CCONJ american_scientific_journal-1665 109 19 only only ADV american_scientific_journal-1665 109 20 if if SCONJ american_scientific_journal-1665 109 21 ( ( PUNCT american_scientific_journal-1665 109 22 2.8 2.8 NUM american_scientific_journal-1665 109 23 ) ) PUNCT american_scientific_journal-1665 109 24 holds hold VERB american_scientific_journal-1665 109 25 good good ADJ american_scientific_journal-1665 109 26 . . PUNCT american_scientific_journal-1665 110 1 contracting contract VERB american_scientific_journal-1665 110 2 the the DET american_scientific_journal-1665 110 3 indices index NOUN american_scientific_journal-1665 110 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 110 5 and and CCONJ american_scientific_journal-1665 110 6 β„Ž β„Ž PROPN american_scientific_journal-1665 110 7 in in ADP american_scientific_journal-1665 110 8 ( ( PUNCT american_scientific_journal-1665 110 9 2.5 2.5 NUM american_scientific_journal-1665 110 10 ) ) PUNCT american_scientific_journal-1665 110 11 , , PUNCT american_scientific_journal-1665 110 12 using use VERB american_scientific_journal-1665 110 13 ( ( PUNCT american_scientific_journal-1665 110 14 1.12 1.12 NUM american_scientific_journal-1665 110 15 ) ) PUNCT american_scientific_journal-1665 110 16 and and CCONJ american_scientific_journal-1665 110 17 ( ( PUNCT american_scientific_journal-1665 110 18 1.13 1.13 NUM american_scientific_journal-1665 110 19 ) ) PUNCT american_scientific_journal-1665 110 20 , , PUNCT american_scientific_journal-1665 110 21 we we PRON american_scientific_journal-1665 110 22 get get VERB american_scientific_journal-1665 110 23 ( ( PUNCT american_scientific_journal-1665 110 24 2.9 2.9 NUM american_scientific_journal-1665 110 25 ) ) PUNCT american_scientific_journal-1665 110 26 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 110 27 + + CCONJ american_scientific_journal-1665 110 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 29 π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 110 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 32 Μ‡ Μ‡ NOUN american_scientific_journal-1665 110 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 34 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 110 35 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 110 36 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 110 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 38 βˆ’ βˆ’ PROPN american_scientific_journal-1665 110 39 π»π»π‘Ÿπ‘Ÿ π»π»π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 110 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 42 Μ‡ Μ‡ NOUN american_scientific_journal-1665 110 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 44 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 110 45 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 110 46 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 110 47 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 48 βˆ’ βˆ’ ADP american_scientific_journal-1665 110 49 π»π»π‘—π‘—π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 110 50 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 110 51 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 53 Μ‡ Μ‡ PROPN american_scientific_journal-1665 110 54 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 55 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 110 56 𝑖𝑖ℓ 𝑖𝑖ℓ NOUN american_scientific_journal-1665 110 57 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 110 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 59 βˆ’ βˆ’ ADP american_scientific_journal-1665 110 60 π»π»π‘Ÿπ‘Ÿπ‘—π‘— π»π»π‘Ÿπ‘Ÿπ‘—π‘— PROPN american_scientific_journal-1665 110 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 62 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 63 Μ‡ Μ‡ NOUN american_scientific_journal-1665 110 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 65 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 110 66 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 110 67 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 110 68 οΏ½ οΏ½ NOUN american_scientific_journal-1665 110 69 οΏ½ οΏ½ NOUN american_scientific_journal-1665 110 70 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 110 71 + + PRON american_scientific_journal-1665 110 72 𝐻𝐻𝑗𝑗𝑖𝑖|β„“ 𝐻𝐻𝑗𝑗𝑖𝑖|β„“ PROPN american_scientific_journal-1665 110 73 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 110 74 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 75 οΏ½ οΏ½ PROPN american_scientific_journal-1665 110 76 Μ‡ Μ‡ PROPN american_scientific_journal-1665 110 77 οΏ½ οΏ½ NOUN american_scientific_journal-1665 110 78 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 110 79 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 110 80 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 110 81 οΏ½ οΏ½ PROPN american_scientific_journal-1665 111 1 βˆ’ βˆ’ PROPN american_scientific_journal-1665 111 2 π»π»π‘Ÿπ‘Ÿ|β„“ π»π»π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 111 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 111 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 111 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 111 6 οΏ½ οΏ½ NOUN american_scientific_journal-1665 111 7 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 111 8 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 111 9 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 111 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 1 βˆ’ βˆ’ NOUN american_scientific_journal-1665 112 2 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 112 3 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 112 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 112 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 8 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 112 9 π‘–π‘–π‘šπ‘š π‘–π‘–π‘šπ‘š NOUN american_scientific_journal-1665 112 10 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 112 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 12 βˆ’ βˆ’ ADP american_scientific_journal-1665 112 13 𝐻𝐻𝑗𝑗|π‘Ÿπ‘Ÿ 𝐻𝐻𝑗𝑗|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 112 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 16 Μ‡ Μ‡ NOUN american_scientific_journal-1665 112 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 18 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 112 19 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 112 20 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 112 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 22 βˆ’ βˆ’ ADP american_scientific_journal-1665 112 23 π»π»π‘Ÿπ‘Ÿπ‘—π‘—|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—|β„“ PROPN american_scientific_journal-1665 112 24 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 112 25 βˆ’ βˆ’ PROPN american_scientific_journal-1665 112 26 𝐻𝐻𝑗𝑗𝑖𝑖𝑠𝑠 𝐻𝐻𝑗𝑗𝑖𝑖𝑠𝑠 PROPN american_scientific_journal-1665 112 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 29 Μ‡ Μ‡ PROPN american_scientific_journal-1665 112 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 31 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 112 32 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 112 33 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 112 34 οΏ½ οΏ½ NOUN american_scientific_journal-1665 112 35 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 112 36 + + CCONJ american_scientific_journal-1665 112 37 𝐻𝐻𝑠𝑠 𝐻𝐻𝑠𝑠 PROPN american_scientific_journal-1665 112 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 40 Μ‡ Μ‡ PROPN american_scientific_journal-1665 112 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 42 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 112 43 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 112 44 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 112 45 οΏ½ οΏ½ NOUN american_scientific_journal-1665 112 46 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 112 47 + + X american_scientific_journal-1665 112 48 𝐻𝐻𝑗𝑗𝑠𝑠 𝐻𝐻𝑗𝑗𝑠𝑠 PROPN american_scientific_journal-1665 112 49 𝑖𝑖 𝑖𝑖 DET american_scientific_journal-1665 112 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 51 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 52 Μ‡ Μ‡ PROPN american_scientific_journal-1665 112 53 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 54 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ PROPN american_scientific_journal-1665 112 55 𝑖𝑖ℓ 𝑖𝑖ℓ NOUN american_scientific_journal-1665 112 56 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 112 57 οΏ½ οΏ½ NOUN american_scientific_journal-1665 112 58 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 112 59 + + NOUN american_scientific_journal-1665 112 60 𝐻𝐻𝑠𝑠𝑗𝑗 𝐻𝐻𝑠𝑠𝑗𝑗 PROPN american_scientific_journal-1665 112 61 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 112 62 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 112 63 = = SYM american_scientific_journal-1665 112 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 112 65 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 112 66 𝐻𝐻𝑗𝑗𝑗𝑗|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑗𝑗|π‘šπ‘š ADV american_scientific_journal-1665 112 67 + + CCONJ american_scientific_journal-1665 113 1 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 113 2 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 113 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 4 + + CCONJ american_scientific_journal-1665 113 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 113 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 9 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 113 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 11 𝐻𝐻𝑗𝑗|π‘šπ‘š 𝐻𝐻𝑗𝑗|π‘šπ‘š PROPN american_scientific_journal-1665 113 12 + + NUM american_scientific_journal-1665 113 13 πœ†πœ†β„“π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 113 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 16 Μ‡ Μ‡ PROPN american_scientific_journal-1665 113 17 οΏ½ οΏ½ NOUN american_scientific_journal-1665 113 18 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 113 19 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 113 20 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 113 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 22 βˆ’πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿ βˆ’πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 113 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 25 Μ‡ Μ‡ NOUN american_scientific_journal-1665 113 26 οΏ½ οΏ½ NOUN american_scientific_journal-1665 113 27 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 113 28 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 113 29 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 113 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 31 βˆ’ βˆ’ PROPN american_scientific_journal-1665 113 32 πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 113 33 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 113 34 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 36 Μ‡ Μ‡ PROPN american_scientific_journal-1665 113 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 38 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 113 39 π‘–π‘–π‘šπ‘š π‘–π‘–π‘šπ‘š NOUN american_scientific_journal-1665 113 40 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 113 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 113 42 βˆ’ βˆ’ NOUN american_scientific_journal-1665 113 43 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘— πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘— NOUN american_scientific_journal-1665 114 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 2 + + SYM american_scientific_journal-1665 114 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 7 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 114 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 9 𝐻𝐻𝑗𝑗. 𝐻𝐻𝑗𝑗. PROPN american_scientific_journal-1665 114 10 this this PRON american_scientific_journal-1665 114 11 shows show VERB american_scientific_journal-1665 114 12 that that SCONJ american_scientific_journal-1665 114 13 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š=πœ†πœ†β„“π»π»π‘—π‘—π‘—π‘—|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š=πœ†πœ†β„“π»π»π‘—π‘—π‘—π‘—|π‘šπ‘š ADV american_scientific_journal-1665 114 14 + + CCONJ american_scientific_journal-1665 114 15 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 114 16 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 114 17 if if SCONJ american_scientific_journal-1665 114 18 and and CCONJ american_scientific_journal-1665 114 19 only only ADV american_scientific_journal-1665 114 20 if if SCONJ american_scientific_journal-1665 114 21 ( ( PUNCT american_scientific_journal-1665 114 22 2.10 2.10 NUM american_scientific_journal-1665 114 23 ) ) PUNCT american_scientific_journal-1665 114 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 25 π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 28 Μ‡ Μ‡ NOUN american_scientific_journal-1665 114 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 30 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 31 π‘Ÿπ‘Ÿβ„“ π‘Ÿπ‘Ÿβ„“ NOUN american_scientific_journal-1665 114 32 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 114 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 34 βˆ’ βˆ’ PROPN american_scientific_journal-1665 114 35 π»π»π‘Ÿπ‘Ÿ π»π»π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 36 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 38 Μ‡ Μ‡ NOUN american_scientific_journal-1665 114 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 40 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 41 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 114 42 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 114 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 44 βˆ’ βˆ’ ADP american_scientific_journal-1665 114 45 π»π»π‘—π‘—π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 46 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 114 47 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 48 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 49 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 51 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 52 𝑖𝑖ℓ 𝑖𝑖ℓ NOUN american_scientific_journal-1665 114 53 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 114 54 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 55 βˆ’ βˆ’ ADP american_scientific_journal-1665 114 56 π»π»π‘Ÿπ‘Ÿπ‘—π‘— π»π»π‘Ÿπ‘Ÿπ‘—π‘— PROPN american_scientific_journal-1665 114 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 59 Μ‡ Μ‡ NOUN american_scientific_journal-1665 114 60 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 61 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 62 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 114 63 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 114 64 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 65 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 66 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 114 67 + + PRON american_scientific_journal-1665 114 68 𝐻𝐻𝑗𝑗𝑖𝑖|β„“ 𝐻𝐻𝑗𝑗𝑖𝑖|β„“ PROPN american_scientific_journal-1665 114 69 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 114 70 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 71 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 72 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 73 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 74 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 75 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 114 76 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 114 77 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 78 βˆ’ βˆ’ PROPN american_scientific_journal-1665 114 79 π»π»π‘Ÿπ‘Ÿ|β„“ π»π»π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 114 80 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 81 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 82 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 83 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 84 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 114 85 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 114 86 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 114 87 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 88 βˆ’ βˆ’ NOUN american_scientific_journal-1665 114 89 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 114 90 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 114 91 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 92 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 93 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 94 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 95 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 96 π‘–π‘–π‘šπ‘š π‘–π‘–π‘šπ‘š NOUN american_scientific_journal-1665 114 97 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 114 98 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 99 βˆ’ βˆ’ ADP american_scientific_journal-1665 114 100 𝐻𝐻𝑗𝑗|π‘Ÿπ‘Ÿ 𝐻𝐻𝑗𝑗|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 101 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 102 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 103 Μ‡ Μ‡ NOUN american_scientific_journal-1665 114 104 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 105 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 114 106 β„“π‘šπ‘š β„“π‘šπ‘š ADJ american_scientific_journal-1665 114 107 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 114 108 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 109 βˆ’ βˆ’ ADP american_scientific_journal-1665 114 110 π»π»π‘Ÿπ‘Ÿπ‘—π‘—|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—|β„“ PROPN american_scientific_journal-1665 114 111 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 112 βˆ’ βˆ’ PROPN american_scientific_journal-1665 114 113 𝐻𝐻𝑗𝑗𝑖𝑖𝑠𝑠 𝐻𝐻𝑗𝑗𝑖𝑖𝑠𝑠 PROPN american_scientific_journal-1665 114 114 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 115 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 116 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 117 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 118 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 114 119 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 114 120 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 114 121 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 122 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 114 123 + + CCONJ american_scientific_journal-1665 114 124 𝐻𝐻𝑠𝑠 𝐻𝐻𝑠𝑠 PROPN american_scientific_journal-1665 114 125 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 126 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 127 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 128 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 129 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 114 130 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 114 131 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 114 132 οΏ½ οΏ½ NOUN american_scientific_journal-1665 114 133 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 114 134 + + X american_scientific_journal-1665 114 135 𝐻𝐻𝑗𝑗𝑠𝑠 𝐻𝐻𝑗𝑗𝑠𝑠 PROPN american_scientific_journal-1665 114 136 𝑖𝑖 𝑖𝑖 DET american_scientific_journal-1665 114 137 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 138 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 139 Μ‡ Μ‡ PROPN american_scientific_journal-1665 114 140 οΏ½ οΏ½ PROPN american_scientific_journal-1665 114 141 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ PROPN american_scientific_journal-1665 114 142 𝑖𝑖ℓ 𝑖𝑖ℓ NOUN american_scientific_journal-1665 114 143 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 115 1 οΏ½ οΏ½ NOUN american_scientific_journal-1665 115 2 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 115 3 + + NOUN american_scientific_journal-1665 115 4 𝐻𝐻𝑠𝑠𝑗𝑗 𝐻𝐻𝑠𝑠𝑗𝑗 PROPN american_scientific_journal-1665 115 5 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 115 6 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 115 7 = = SYM american_scientific_journal-1665 115 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 10 Μ‡ Μ‡ PROPN american_scientific_journal-1665 115 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 12 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 115 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 14 𝐻𝐻𝑗𝑗|π‘šπ‘š 𝐻𝐻𝑗𝑗|π‘šπ‘š PROPN american_scientific_journal-1665 115 15 + + NUM american_scientific_journal-1665 115 16 πœ†πœ†β„“π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘—π‘—π‘–π‘–π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 115 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 19 Μ‡ Μ‡ PROPN american_scientific_journal-1665 115 20 οΏ½ οΏ½ NOUN american_scientific_journal-1665 115 21 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 115 22 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 115 23 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 115 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 25 βˆ’ βˆ’ PROPN american_scientific_journal-1665 115 26 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 115 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 29 Μ‡ Μ‡ PROPN american_scientific_journal-1665 115 30 οΏ½ οΏ½ NOUN american_scientific_journal-1665 115 31 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ NOUN american_scientific_journal-1665 115 32 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 115 33 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 115 34 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 35 πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 115 36 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 115 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 38 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 39 Μ‡ Μ‡ PROPN american_scientific_journal-1665 115 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 41 πœ•π‘—π‘—π›€π›€ πœ•π‘—π‘—π›€π›€ PART american_scientific_journal-1665 115 42 π‘–π‘–π‘šπ‘š π‘–π‘–π‘šπ‘š NOUN american_scientific_journal-1665 115 43 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 115 44 οΏ½ οΏ½ PROPN american_scientific_journal-1665 115 45 βˆ’ βˆ’ NOUN american_scientific_journal-1665 115 46 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘— πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘— NOUN american_scientific_journal-1665 116 1 π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘—π‘—π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 116 2 + + SYM american_scientific_journal-1665 116 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 116 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 116 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 116 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 116 7 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 116 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 116 9 𝐻𝐻𝑗𝑗 𝐻𝐻𝑗𝑗 PROPN american_scientific_journal-1665 116 10 . . PUNCT american_scientific_journal-1665 117 1 theorem theorem VERB american_scientific_journal-1665 117 2 2.4 2.4 NUM american_scientific_journal-1665 117 3 . . PUNCT american_scientific_journal-1665 118 1 in in ADP american_scientific_journal-1665 118 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 118 3 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 118 4 , , PUNCT american_scientific_journal-1665 118 5 𝐾𝐾–ricci 𝐾𝐾–ricci NOUN american_scientific_journal-1665 118 6 tensor tensor NOUN american_scientific_journal-1665 118 7 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 118 8 in in ADP american_scientific_journal-1665 118 9 sense sense NOUN american_scientific_journal-1665 118 10 of of ADP american_scientific_journal-1665 118 11 cartan cartan PROPN american_scientific_journal-1665 118 12 is be AUX american_scientific_journal-1665 118 13 generalized generalize VERB american_scientific_journal-1665 118 14 birecurrent birecurrent ADJ american_scientific_journal-1665 118 15 if if SCONJ american_scientific_journal-1665 118 16 and and CCONJ american_scientific_journal-1665 118 17 only only ADV american_scientific_journal-1665 118 18 if if SCONJ american_scientific_journal-1665 118 19 ( ( PUNCT american_scientific_journal-1665 118 20 2.10 2.10 NUM american_scientific_journal-1665 118 21 ) ) PUNCT american_scientific_journal-1665 118 22 holds hold VERB american_scientific_journal-1665 118 23 good good ADJ american_scientific_journal-1665 118 24 . . PUNCT american_scientific_journal-1665 119 1 65- 65- X american_scientific_journal-1665 119 2 ) ) PUNCT american_scientific_journal-1665 119 3 volume volume NOUN american_scientific_journal-1665 119 4 20 20 NUM american_scientific_journal-1665 119 5 , , PUNCT american_scientific_journal-1665 119 6 no no DET american_scientific_journal-1665 119 7 1 1 NUM american_scientific_journal-1665 119 8 , , PUNCT american_scientific_journal-1665 119 9 pp pp ADP american_scientific_journal-1665 119 10 522016 522016 NUM american_scientific_journal-1665 119 11 ( ( PUNCT american_scientific_journal-1665 119 12 ) ) PUNCT american_scientific_journal-1665 119 13 research research NOUN american_scientific_journal-1665 119 14 journal journal NOUN american_scientific_journal-1665 119 15 for for ADP american_scientific_journal-1665 119 16 engineering engineering NOUN american_scientific_journal-1665 119 17 , , PUNCT american_scientific_journal-1665 119 18 technology technology NOUN american_scientific_journal-1665 119 19 , , PUNCT american_scientific_journal-1665 119 20 and and CCONJ american_scientific_journal-1665 119 21 sciences science NOUN american_scientific_journal-1665 119 22 ( ( PUNCT american_scientific_journal-1665 119 23 asrjets asrjet NOUN american_scientific_journal-1665 119 24 scientificamerican scientificamerican VERB american_scientific_journal-1665 119 25 59 59 NUM american_scientific_journal-1665 119 26 contracting contract VERB american_scientific_journal-1665 119 27 the the DET american_scientific_journal-1665 119 28 indices index NOUN american_scientific_journal-1665 119 29 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 119 30 and and CCONJ american_scientific_journal-1665 119 31 𝑗𝑗 𝑗𝑗 ADP american_scientific_journal-1665 119 32 in in ADP american_scientific_journal-1665 119 33 ( ( PUNCT american_scientific_journal-1665 119 34 2.5 2.5 NUM american_scientific_journal-1665 119 35 ) ) PUNCT american_scientific_journal-1665 119 36 and and CCONJ american_scientific_journal-1665 119 37 using use VERB american_scientific_journal-1665 119 38 ( ( PUNCT american_scientific_journal-1665 119 39 1.16 1.16 NUM american_scientific_journal-1665 119 40 ) ) PUNCT american_scientific_journal-1665 119 41 , , PUNCT american_scientific_journal-1665 119 42 we we PRON american_scientific_journal-1665 119 43 get get VERB american_scientific_journal-1665 119 44 ( ( PUNCT american_scientific_journal-1665 119 45 2.11 2.11 NUM american_scientific_journal-1665 119 46 ) ) PUNCT american_scientific_journal-1665 119 47 ( ( PUNCT american_scientific_journal-1665 119 48 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 119 49 βˆ’ βˆ’ PROPN american_scientific_journal-1665 119 50 π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š PROPN american_scientific_journal-1665 119 51 + + SYM american_scientific_journal-1665 119 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 119 53 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 119 54 οΏ½ οΏ½ PROPN american_scientific_journal-1665 119 55 οΏ½ οΏ½ PROPN american_scientific_journal-1665 119 56 Μ‡ Μ‡ VERB american_scientific_journal-1665 119 57 οΏ½ οΏ½ NOUN american_scientific_journal-1665 119 58 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ ADP american_scientific_journal-1665 120 1 π‘Ÿπ‘Ÿπ‘™π‘™ π‘Ÿπ‘Ÿπ‘™π‘™ NOUN american_scientific_journal-1665 120 2 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 120 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 4 βˆ’ βˆ’ PROPN american_scientific_journal-1665 120 5 π»π»π‘Ÿπ‘Ÿβ„Ž π»π»π‘Ÿπ‘Ÿβ„Ž PROPN american_scientific_journal-1665 120 6 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 120 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 9 Μ‡ Μ‡ NOUN american_scientific_journal-1665 120 10 οΏ½ οΏ½ NOUN american_scientific_journal-1665 120 11 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 120 12 𝑗𝑗𝑙𝑙 𝑗𝑗𝑙𝑙 NOUN american_scientific_journal-1665 120 13 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 120 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 15 βˆ’ βˆ’ ADP american_scientific_journal-1665 120 16 π»π»π‘—π‘—π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 120 17 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 120 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 20 Μ‡ Μ‡ NOUN american_scientific_journal-1665 120 21 οΏ½ οΏ½ NOUN american_scientific_journal-1665 120 22 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ ADP american_scientific_journal-1665 120 23 β„Žπ‘™π‘™ β„Žπ‘™π‘™ PRON american_scientific_journal-1665 120 24 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 120 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 26 βˆ’ βˆ’ ADP american_scientific_journal-1665 120 27 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 120 28 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 120 29 π‘ƒπ‘ƒπ‘–π‘–β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 120 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 31 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 120 32 + + CCONJ american_scientific_journal-1665 120 33 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 120 34 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ ADP american_scientific_journal-1665 120 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 36 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 37 Μ‡ Μ‡ NOUN american_scientific_journal-1665 120 38 οΏ½ οΏ½ NOUN american_scientific_journal-1665 120 39 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 120 40 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 120 41 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 120 42 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 43 βˆ’ βˆ’ PROPN american_scientific_journal-1665 120 44 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 120 45 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 120 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 47 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 48 Μ‡ Μ‡ NOUN american_scientific_journal-1665 120 49 οΏ½ οΏ½ NOUN american_scientific_journal-1665 120 50 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ PROPN american_scientific_journal-1665 120 51 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 120 52 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 120 53 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 54 βˆ’ βˆ’ NOUN american_scientific_journal-1665 120 55 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 120 56 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 120 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 120 59 Μ‡ Μ‡ NOUN american_scientific_journal-1665 120 60 οΏ½ οΏ½ NOUN american_scientific_journal-1665 120 61 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 120 62 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 120 63 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ NUM american_scientific_journal-1665 120 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 1 βˆ’π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ βˆ’π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 121 2 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 121 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 5 Μ‡ Μ‡ NOUN american_scientific_journal-1665 121 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 7 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 121 8 β„“π‘šπ‘š β„“π‘šπ‘š VERB american_scientific_journal-1665 121 9 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 121 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 11 βˆ’ βˆ’ NOUN american_scientific_journal-1665 121 12 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 121 13 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 121 14 π‘ƒπ‘ƒπ‘ƒπ‘ƒπ‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘ƒπ‘ƒπ‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 121 15 βˆ’ βˆ’ PROPN american_scientific_journal-1665 121 16 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 121 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 19 Μ‡ Μ‡ PROPN american_scientific_journal-1665 121 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 21 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 121 22 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 121 23 βˆ—π‘–π‘– βˆ—π‘–π‘– SYM american_scientific_journal-1665 121 24 οΏ½ οΏ½ NOUN american_scientific_journal-1665 121 25 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 121 26 + + CCONJ american_scientific_journal-1665 121 27 π»π»π‘ π‘ β„Ž π»π»π‘ π‘ β„Ž PROPN american_scientific_journal-1665 121 28 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 121 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 31 Μ‡ Μ‡ PROPN american_scientific_journal-1665 121 32 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 33 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 121 34 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 121 35 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 121 36 οΏ½ οΏ½ NOUN american_scientific_journal-1665 121 37 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 121 38 + + CCONJ american_scientific_journal-1665 121 39 𝐻𝐻𝑗𝑗𝑠𝑠 𝐻𝐻𝑗𝑗𝑠𝑠 PROPN american_scientific_journal-1665 121 40 𝑖𝑖 𝑖𝑖 DET american_scientific_journal-1665 121 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 42 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 43 Μ‡ Μ‡ PROPN american_scientific_journal-1665 121 44 οΏ½ οΏ½ PROPN american_scientific_journal-1665 121 45 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 121 46 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 121 47 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 121 48 οΏ½ οΏ½ NOUN american_scientific_journal-1665 121 49 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 121 50 + + CCONJ american_scientific_journal-1665 121 51 π»π»π‘ π‘ π‘—π‘—β„Ž π»π»π‘ π‘ π‘—π‘—β„Ž PROPN american_scientific_journal-1665 121 52 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 122 1 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 122 2 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 122 3 = = SYM american_scientific_journal-1665 122 4 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 122 5 ( ( PUNCT american_scientific_journal-1665 122 6 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 122 7 βˆ’ βˆ’ PROPN american_scientific_journal-1665 122 8 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 122 9 ) ) PUNCT american_scientific_journal-1665 122 10 |π‘šπ‘š |π‘šπ‘š PROPN american_scientific_journal-1665 123 1 + + CCONJ american_scientific_journal-1665 123 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 123 3 ( ( PUNCT american_scientific_journal-1665 123 4 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 123 5 βˆ’ βˆ’ PROPN american_scientific_journal-1665 123 6 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 123 7 ) ) PUNCT american_scientific_journal-1665 123 8 + + CCONJ american_scientific_journal-1665 123 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 123 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 123 11 Μ‡ Μ‡ PROPN american_scientific_journal-1665 123 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 123 13 πœ•π‘–π‘–πœ†πœ†β„“ πœ•π‘–π‘–πœ†πœ†β„“ PROPN american_scientific_journal-1665 123 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 123 15 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 123 16 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 124 1 + + CCONJ american_scientific_journal-1665 124 2 πœ†πœ†β„“π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ πœ†πœ†β„“π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 124 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 5 Μ‡ Μ‡ NOUN american_scientific_journal-1665 124 6 οΏ½ οΏ½ NOUN american_scientific_journal-1665 124 7 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 124 8 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 124 9 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 124 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 11 βˆ’ βˆ’ PROPN american_scientific_journal-1665 124 12 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿβ„Ž πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿβ„Ž NOUN american_scientific_journal-1665 124 13 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 124 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 16 Μ‡ Μ‡ NOUN american_scientific_journal-1665 124 17 οΏ½ οΏ½ NOUN american_scientific_journal-1665 124 18 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ PROPN american_scientific_journal-1665 124 19 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 124 20 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 124 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 22 βˆ’πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ βˆ’πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 124 23 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 124 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 26 Μ‡ Μ‡ NOUN american_scientific_journal-1665 124 27 οΏ½ οΏ½ NOUN american_scientific_journal-1665 124 28 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 124 29 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 124 30 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 124 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 124 32 βˆ’ βˆ’ NOUN american_scientific_journal-1665 124 33 πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž πœ†πœ†β„“π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž NOUN american_scientific_journal-1665 124 34 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 125 1 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 125 2 + + NUM american_scientific_journal-1665 125 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 125 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 125 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 125 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 125 7 πœ•π‘–π‘–π‘π‘β„“π‘šπ‘š πœ•π‘–π‘–π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 125 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 125 9 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 125 10 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 125 11 . . PUNCT american_scientific_journal-1665 126 1 this this PRON american_scientific_journal-1665 126 2 shows show VERB american_scientific_journal-1665 126 3 that that SCONJ american_scientific_journal-1665 126 4 ( ( PUNCT american_scientific_journal-1665 126 5 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 126 6 βˆ’ βˆ’ PROPN american_scientific_journal-1665 126 7 π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š PROPN american_scientific_journal-1665 127 1 = = PUNCT american_scientific_journal-1665 127 2 πœ†πœ†β„“(π»π»β„Žπ‘—π‘— πœ†πœ†β„“(π»π»β„Žπ‘—π‘— ADJ american_scientific_journal-1665 127 3 βˆ’ βˆ’ NOUN american_scientific_journal-1665 128 1 π»π»π‘—π‘—β„Ž)|π‘šπ‘š π»π»π‘—π‘—β„Ž)|π‘šπ‘š NOUN american_scientific_journal-1665 128 2 + + CCONJ american_scientific_journal-1665 128 3 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 128 4 ( ( PUNCT american_scientific_journal-1665 128 5 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 128 6 βˆ’ βˆ’ PROPN american_scientific_journal-1665 128 7 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 128 8 ) ) PUNCT american_scientific_journal-1665 128 9 if if SCONJ american_scientific_journal-1665 128 10 and and CCONJ american_scientific_journal-1665 128 11 only only ADV american_scientific_journal-1665 128 12 if if SCONJ american_scientific_journal-1665 128 13 ( ( PUNCT american_scientific_journal-1665 128 14 2.12 2.12 NUM american_scientific_journal-1665 128 15 ) ) PUNCT american_scientific_journal-1665 128 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 17 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 20 Μ‡ Μ‡ VERB american_scientific_journal-1665 128 21 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 22 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ ADP american_scientific_journal-1665 128 23 π‘Ÿπ‘Ÿπ‘™π‘™ π‘Ÿπ‘Ÿπ‘™π‘™ NOUN american_scientific_journal-1665 128 24 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 128 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 26 βˆ’ βˆ’ PROPN american_scientific_journal-1665 128 27 π»π»π‘Ÿπ‘Ÿβ„Ž π»π»π‘Ÿπ‘Ÿβ„Ž PROPN american_scientific_journal-1665 128 28 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 31 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 32 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 33 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 128 34 𝑗𝑗𝑙𝑙 𝑗𝑗𝑙𝑙 NOUN american_scientific_journal-1665 128 35 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ SYM american_scientific_journal-1665 128 36 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 37 βˆ’ βˆ’ ADP american_scientific_journal-1665 128 38 π»π»π‘—π‘—π‘Ÿπ‘Ÿ π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 39 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 42 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 43 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 44 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ ADP american_scientific_journal-1665 128 45 β„Žπ‘™π‘™ β„Žπ‘™π‘™ PRON american_scientific_journal-1665 128 46 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ X american_scientific_journal-1665 128 47 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 48 βˆ’ βˆ’ VERB american_scientific_journal-1665 128 49 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 128 50 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 128 51 π‘ƒπ‘ƒπ‘–π‘–β„“π‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–β„“π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 53 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 128 54 + + PROPN american_scientific_journal-1665 128 55 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 128 56 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 58 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 59 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 60 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 61 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 128 62 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 128 63 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 128 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 65 βˆ’ βˆ’ PROPN american_scientific_journal-1665 128 66 π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ π»π»π‘Ÿπ‘Ÿβ„Ž|β„“ PROPN american_scientific_journal-1665 128 67 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 68 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 69 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 70 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 71 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 72 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ PROPN american_scientific_journal-1665 128 73 π‘—π‘—π‘šπ‘š π‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 128 74 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 128 75 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 76 βˆ’ βˆ’ NOUN american_scientific_journal-1665 128 77 π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ π»π»π‘—π‘—π‘Ÿπ‘Ÿ|β„“ PROPN american_scientific_journal-1665 128 78 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 79 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 80 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 81 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 82 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 83 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 128 84 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 128 85 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 128 86 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 87 βˆ’ βˆ’ NOUN american_scientific_journal-1665 128 88 π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Ž|π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 89 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 90 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 91 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 92 Μ‡ Μ‡ NOUN american_scientific_journal-1665 128 93 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 94 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 128 95 β„“π‘šπ‘š β„“π‘šπ‘š VERB american_scientific_journal-1665 128 96 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 97 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 98 βˆ’π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ βˆ’π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 128 99 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 128 100 π‘ƒπ‘ƒπ‘ƒπ‘ƒπ‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘ƒπ‘ƒπ‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 101 βˆ’ βˆ’ PROPN american_scientific_journal-1665 128 102 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 128 103 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 104 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 105 Μ‡ Μ‡ PROPN american_scientific_journal-1665 128 106 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 107 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 128 108 𝑠𝑠ℓ 𝑠𝑠ℓ VERB american_scientific_journal-1665 128 109 βˆ—π‘–π‘– βˆ—π‘–π‘– SYM american_scientific_journal-1665 128 110 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 111 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 112 + + CCONJ american_scientific_journal-1665 128 113 π»π»π‘ π‘ β„Ž π»π»π‘ π‘ β„Ž PROPN american_scientific_journal-1665 128 114 𝑖𝑖 𝑖𝑖 SYM american_scientific_journal-1665 128 115 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 116 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 117 Μ‡ Μ‡ PROPN american_scientific_journal-1665 128 118 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 119 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 128 120 𝑗𝑗ℓ 𝑗𝑗ℓ NOUN american_scientific_journal-1665 128 121 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 128 122 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 123 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 128 124 + + CCONJ american_scientific_journal-1665 128 125 𝐻𝐻𝑗𝑗𝑠𝑠 𝐻𝐻𝑗𝑗𝑠𝑠 PROPN american_scientific_journal-1665 128 126 𝑖𝑖 𝑖𝑖 DET american_scientific_journal-1665 128 127 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 128 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 129 Μ‡ Μ‡ PROPN american_scientific_journal-1665 128 130 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 131 πœ•π‘Ÿπ‘Ÿπ›€π›€ πœ•π‘Ÿπ‘Ÿπ›€π›€ NOUN american_scientific_journal-1665 128 132 β„Žβ„“ β„Žβ„“ NOUN american_scientific_journal-1665 128 133 βˆ—π‘ π‘  βˆ—π‘ π‘  NOUN american_scientific_journal-1665 128 134 οΏ½ οΏ½ NOUN american_scientific_journal-1665 128 135 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 128 136 + + CCONJ american_scientific_journal-1665 128 137 π»π»π‘ π‘ π‘—π‘—β„Ž π»π»π‘ π‘ π‘—π‘—β„Ž PROPN american_scientific_journal-1665 128 138 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 128 139 π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  π‘ƒπ‘ƒπ‘Ÿπ‘Ÿβ„“π‘ π‘  PROPN american_scientific_journal-1665 128 140 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 128 141 οΏ½ οΏ½ PROPN american_scientific_journal-1665 128 142 = = PRON american_scientific_journal-1665 128 143 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 128 144 ( ( PUNCT american_scientific_journal-1665 128 145 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 128 146 βˆ’ βˆ’ PROPN american_scientific_journal-1665 128 147 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 128 148 ) ) PUNCT american_scientific_journal-1665 129 1 + + CCONJ american_scientific_journal-1665 129 2 { { PUNCT american_scientific_journal-1665 129 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 129 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 129 5 Μ‡ Μ‡ PROPN american_scientific_journal-1665 129 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 129 7 πœ•π‘–π‘–πœ†πœ†β„“ πœ•π‘–π‘–πœ†πœ†β„“ PROPN american_scientific_journal-1665 129 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 129 9 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 129 10 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 130 1 + + CCONJ american_scientific_journal-1665 130 2 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 130 3 π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ π»π»π‘—π‘—β„Žπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 130 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 6 Μ‡ Μ‡ NOUN american_scientific_journal-1665 130 7 οΏ½ οΏ½ NOUN american_scientific_journal-1665 130 8 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 130 9 π‘Ÿπ‘Ÿπ‘šπ‘š π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 130 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 130 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 12 βˆ’πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ βˆ’πœ†πœ†β„“π»π»π‘—π‘—π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 130 13 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 130 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 16 Μ‡ Μ‡ NOUN american_scientific_journal-1665 130 17 οΏ½ οΏ½ NOUN american_scientific_journal-1665 130 18 πœ•π‘–π‘–π›€π›€ πœ•π‘–π‘–π›€π›€ NOUN american_scientific_journal-1665 130 19 β„Žπ‘šπ‘š β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 130 20 βˆ—π‘Ÿπ‘Ÿ βˆ—π‘Ÿπ‘Ÿ PUNCT american_scientific_journal-1665 130 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 130 22 βˆ’ βˆ’ NOUN american_scientific_journal-1665 130 23 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 131 1 π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž π»π»π‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 131 2 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 131 3 π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ π‘ƒπ‘ƒπ‘–π‘–π‘šπ‘šπ‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 131 4 + + NUM american_scientific_journal-1665 131 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 131 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 131 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 131 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 131 9 πœ•π‘–π‘–π‘π‘β„“π‘šπ‘š πœ•π‘–π‘–π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 131 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 131 11 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 131 12 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 131 13 . . PUNCT american_scientific_journal-1665 132 1 thus thus ADV american_scientific_journal-1665 132 2 , , PUNCT american_scientific_journal-1665 132 3 we we PRON american_scientific_journal-1665 132 4 conclude conclude AUX american_scientific_journal-1665 132 5 theorem theorem VERB american_scientific_journal-1665 132 6 2.5 2.5 NUM american_scientific_journal-1665 132 7 . . PUNCT american_scientific_journal-1665 133 1 in in ADP american_scientific_journal-1665 133 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 133 3 β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› β„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“πΉπΉπ‘›π‘› NOUN american_scientific_journal-1665 133 4 , , PUNCT american_scientific_journal-1665 133 5 the the DET american_scientific_journal-1665 133 6 tensor tensor NOUN american_scientific_journal-1665 133 7 ( ( PUNCT american_scientific_journal-1665 133 8 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 133 9 βˆ’ βˆ’ PROPN american_scientific_journal-1665 133 10 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 133 11 ) ) PUNCT american_scientific_journal-1665 133 12 is be AUX american_scientific_journal-1665 133 13 generalized generalize VERB american_scientific_journal-1665 133 14 birecurrent birecurrent ADJ american_scientific_journal-1665 133 15 if if SCONJ american_scientific_journal-1665 133 16 and and CCONJ american_scientific_journal-1665 133 17 only only ADV american_scientific_journal-1665 133 18 if if SCONJ american_scientific_journal-1665 133 19 ( ( PUNCT american_scientific_journal-1665 133 20 2.12 2.12 NUM american_scientific_journal-1665 133 21 ) ) PUNCT american_scientific_journal-1665 133 22 holds hold VERB american_scientific_journal-1665 133 23 good good ADJ american_scientific_journal-1665 133 24 . . PUNCT american_scientific_journal-1665 134 1 differentiating differentiate VERB american_scientific_journal-1665 134 2 ( ( PUNCT american_scientific_journal-1665 134 3 1.18 1.18 NUM american_scientific_journal-1665 134 4 ) ) PUNCT american_scientific_journal-1665 134 5 covariantly covariantly ADV american_scientific_journal-1665 134 6 with with ADP american_scientific_journal-1665 134 7 respect respect NOUN american_scientific_journal-1665 134 8 to to ADP american_scientific_journal-1665 134 9 π‘₯π‘₯π‘šπ‘š π‘₯π‘₯π‘šπ‘š NOUN american_scientific_journal-1665 134 10 in in ADP american_scientific_journal-1665 134 11 the the DET american_scientific_journal-1665 134 12 sense sense NOUN american_scientific_journal-1665 134 13 of of ADP american_scientific_journal-1665 134 14 cartan cartan PROPN american_scientific_journal-1665 134 15 and and CCONJ american_scientific_journal-1665 134 16 using use VERB american_scientific_journal-1665 134 17 ( ( PUNCT american_scientific_journal-1665 134 18 1.1a 1.1a NOUN american_scientific_journal-1665 134 19 ) ) PUNCT american_scientific_journal-1665 134 20 , , PUNCT american_scientific_journal-1665 134 21 we we PRON american_scientific_journal-1665 134 22 get get VERB american_scientific_journal-1665 134 23 ( ( PUNCT american_scientific_journal-1665 134 24 2.13 2.13 NUM american_scientific_journal-1665 134 25 ) ) PUNCT american_scientific_journal-1665 134 26 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 134 27 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 135 1 + + CCONJ american_scientific_journal-1665 135 2 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž|π‘šπ‘š 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž|π‘šπ‘š ADV american_scientific_journal-1665 135 3 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 136 1 + + CCONJ american_scientific_journal-1665 136 2 πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗|π‘šπ‘š πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗|π‘šπ‘š NUM american_scientific_journal-1665 136 3 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 137 1 + + ADJ american_scientific_journal-1665 137 2 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 137 3 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 137 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 137 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 9 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 137 10 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 137 11 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 137 12 οΏ½ οΏ½ NOUN american_scientific_journal-1665 137 13 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“|π‘šπ‘š PROPN american_scientific_journal-1665 137 14 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 137 15 + + PROPN american_scientific_journal-1665 137 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 18 Μ‡ Μ‡ PROPN american_scientific_journal-1665 137 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 20 πœ•π‘ π‘ π›€π›€π‘—π‘—β„“ πœ•π‘ π‘ π›€π›€π‘—π‘—β„“ PROPN american_scientific_journal-1665 137 21 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 137 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 23 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 137 24 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 137 25 + + ADJ american_scientific_journal-1665 137 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 28 Μ‡ Μ‡ PROPN american_scientific_journal-1665 137 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 30 πœ•π‘ π‘ π›€π›€π‘—π‘—β„Ž πœ•π‘ π‘ π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 137 31 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 137 32 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 33 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—|π‘šπ‘š NUM american_scientific_journal-1665 137 34 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 137 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 36 + + PROPN american_scientific_journal-1665 137 37 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 137 38 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 137 39 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 42 Μ‡ Μ‡ PROPN american_scientific_journal-1665 137 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 44 πœ•π‘ π‘ π›€π›€π‘—π‘—π‘—π‘— πœ•π‘ π‘ π›€π›€π‘—π‘—π‘—π‘— PROPN american_scientific_journal-1665 137 45 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 137 46 οΏ½ οΏ½ PROPN american_scientific_journal-1665 137 47 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 137 48 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ PROPN american_scientific_journal-1665 137 49 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 137 50 65- 65- NOUN american_scientific_journal-1665 137 51 ) ) PUNCT american_scientific_journal-1665 137 52 volume volume NOUN american_scientific_journal-1665 137 53 20 20 NUM american_scientific_journal-1665 137 54 , , PUNCT american_scientific_journal-1665 137 55 no no DET american_scientific_journal-1665 137 56 1 1 NUM american_scientific_journal-1665 137 57 , , PUNCT american_scientific_journal-1665 137 58 pp pp ADP american_scientific_journal-1665 137 59 522016 522016 NUM american_scientific_journal-1665 137 60 ( ( PUNCT american_scientific_journal-1665 137 61 ) ) PUNCT american_scientific_journal-1665 137 62 research research NOUN american_scientific_journal-1665 137 63 journal journal NOUN american_scientific_journal-1665 137 64 for for ADP american_scientific_journal-1665 137 65 engineering engineering NOUN american_scientific_journal-1665 137 66 , , PUNCT american_scientific_journal-1665 137 67 technology technology NOUN american_scientific_journal-1665 137 68 , , PUNCT american_scientific_journal-1665 137 69 and and CCONJ american_scientific_journal-1665 137 70 sciences science NOUN american_scientific_journal-1665 137 71 ( ( PUNCT american_scientific_journal-1665 137 72 asrjets asrjet NOUN american_scientific_journal-1665 137 73 scientificamerican scientificamerican VERB american_scientific_journal-1665 137 74 60 60 NUM american_scientific_journal-1665 138 1 + + NOUN american_scientific_journal-1665 138 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 3 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 4 Μ‡ Μ‡ PROPN american_scientific_journal-1665 138 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 6 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 138 7 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 138 8 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 138 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 10 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 138 11 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 138 12 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 138 13 + + PROPN american_scientific_journal-1665 138 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 16 Μ‡ Μ‡ PROPN american_scientific_journal-1665 138 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 18 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 138 19 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 138 20 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 138 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 22 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 138 23 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—π‘ π‘  πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—π‘ π‘  PROPN american_scientific_journal-1665 138 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 138 25 = = SYM american_scientific_journal-1665 138 26 0 0 X american_scientific_journal-1665 138 27 . . PUNCT american_scientific_journal-1665 139 1 using use VERB american_scientific_journal-1665 139 2 ( ( PUNCT american_scientific_journal-1665 139 3 2.1 2.1 NUM american_scientific_journal-1665 139 4 ) ) PUNCT american_scientific_journal-1665 139 5 in in ADP american_scientific_journal-1665 139 6 ( ( PUNCT american_scientific_journal-1665 139 7 2.13 2.13 NUM american_scientific_journal-1665 139 8 ) ) PUNCT american_scientific_journal-1665 139 9 , , PUNCT american_scientific_journal-1665 139 10 we we PRON american_scientific_journal-1665 139 11 get get VERB american_scientific_journal-1665 139 12 ( ( PUNCT american_scientific_journal-1665 139 13 2.14 2.14 NUM american_scientific_journal-1665 139 14 ) ) PUNCT american_scientific_journal-1665 139 15 πœ†πœ†β„“πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š πœ†πœ†β„“πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 139 16 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 140 1 + + CCONJ american_scientific_journal-1665 140 2 πœ†πœ†β„ŽπΎπΎπ‘—π‘—β„“π‘—π‘—|π‘šπ‘š πœ†πœ†β„ŽπΎπΎπ‘—π‘—β„“π‘—π‘—|π‘šπ‘š NUM american_scientific_journal-1665 140 3 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 141 1 + + CCONJ american_scientific_journal-1665 141 2 πœ†πœ†π‘—π‘— πœ†πœ†π‘—π‘— X american_scientific_journal-1665 141 3 πΎπΎπ‘—π‘—β„Žβ„“|π‘šπ‘š πΎπΎπ‘—π‘—β„Žβ„“|π‘šπ‘š ADV american_scientific_journal-1665 141 4 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 142 1 + + CCONJ american_scientific_journal-1665 142 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 142 3 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 142 4 + + CCONJ american_scientific_journal-1665 142 5 π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– ADJ american_scientific_journal-1665 142 6 + + CCONJ american_scientific_journal-1665 142 7 π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– X american_scientific_journal-1665 142 8 + + NOUN american_scientific_journal-1665 142 9 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 142 10 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 142 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 14 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 16 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 17 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 142 18 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 142 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 20 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“|π‘šπ‘š PROPN american_scientific_journal-1665 142 21 𝑠𝑠 𝑠𝑠 PROPN american_scientific_journal-1665 142 22 + + NUM american_scientific_journal-1665 142 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 24 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 25 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 27 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 28 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 142 29 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 142 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 31 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 142 32 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 142 33 + + NUM american_scientific_journal-1665 142 34 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 36 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 38 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 39 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 142 40 βˆ—π‘–π‘– βˆ—π‘–π‘– SYM american_scientific_journal-1665 142 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 42 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—|π‘šπ‘š πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘—|π‘šπ‘š NUM american_scientific_journal-1665 142 43 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 142 44 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 45 + + PROPN american_scientific_journal-1665 142 46 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 142 47 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 142 48 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 49 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 50 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 51 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 53 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 54 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 142 55 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 142 56 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 57 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 142 58 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ PROPN american_scientific_journal-1665 142 59 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 142 60 + + PROPN american_scientific_journal-1665 142 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 62 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 63 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 64 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 65 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 66 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 142 67 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 142 68 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 69 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 142 70 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘ π‘  πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 142 71 + + NUM american_scientific_journal-1665 142 72 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 73 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 74 Μ‡ Μ‡ PROPN american_scientific_journal-1665 142 75 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 76 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 142 77 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 142 78 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 142 79 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 80 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 142 81 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— PROPN american_scientific_journal-1665 142 82 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 142 83 οΏ½ οΏ½ PROPN american_scientific_journal-1665 142 84 = = SYM american_scientific_journal-1665 142 85 0 0 PROPN american_scientific_journal-1665 142 86 . . PUNCT american_scientific_journal-1665 143 1 if if SCONJ american_scientific_journal-1665 143 2 cartan cartan PROPN american_scientific_journal-1665 143 3 's 's PART american_scientific_journal-1665 143 4 fourth fourth ADJ american_scientific_journal-1665 143 5 curvature curvature NOUN american_scientific_journal-1665 143 6 tensor tensor NOUN american_scientific_journal-1665 143 7 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 143 8 is be AUX american_scientific_journal-1665 143 9 recurrent recurrent ADJ american_scientific_journal-1665 143 10 which which PRON american_scientific_journal-1665 143 11 is be AUX american_scientific_journal-1665 143 12 given give VERB american_scientific_journal-1665 143 13 by by ADP american_scientific_journal-1665 143 14 ( ( PUNCT american_scientific_journal-1665 143 15 1.23 1.23 NUM american_scientific_journal-1665 143 16 ) ) PUNCT american_scientific_journal-1665 143 17 , , PUNCT american_scientific_journal-1665 143 18 ( ( PUNCT american_scientific_journal-1665 143 19 2.14 2.14 NUM american_scientific_journal-1665 143 20 ) ) PUNCT american_scientific_journal-1665 143 21 becomes become VERB american_scientific_journal-1665 143 22 ( ( PUNCT american_scientific_journal-1665 143 23 2.15 2.15 NUM american_scientific_journal-1665 143 24 ) ) PUNCT american_scientific_journal-1665 143 25 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 143 26 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 143 27 + + CCONJ american_scientific_journal-1665 143 28 πœ†πœ†β„Ž πœ†πœ†β„Ž PROPN american_scientific_journal-1665 143 29 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– X american_scientific_journal-1665 143 30 + + PROPN american_scientific_journal-1665 143 31 πœ†πœ†π‘—π‘— πœ†πœ†π‘—π‘— INTJ american_scientific_journal-1665 143 32 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– X american_scientific_journal-1665 144 1 + + CCONJ american_scientific_journal-1665 144 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 144 3 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 144 4 + + CCONJ american_scientific_journal-1665 144 5 π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– ADJ american_scientific_journal-1665 144 6 + + CCONJ american_scientific_journal-1665 144 7 π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– X american_scientific_journal-1665 144 8 + + CCONJ american_scientific_journal-1665 144 9 πœ†πœ†π‘šπ‘š πœ†πœ†π‘šπ‘š PROPN american_scientific_journal-1665 144 10 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 144 11 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 144 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 144 13 οΏ½ οΏ½ PROPN american_scientific_journal-1665 144 14 οΏ½ οΏ½ PROPN american_scientific_journal-1665 144 15 Μ‡ Μ‡ PROPN american_scientific_journal-1665 144 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 144 17 πœ•π‘ π‘  πœ•π‘ π‘  PART american_scientific_journal-1665 144 18 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 144 19 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 144 20 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 1 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ PROPN american_scientific_journal-1665 145 2 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 3 + + PROPN american_scientific_journal-1665 145 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 6 Μ‡ Μ‡ PROPN american_scientific_journal-1665 145 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 8 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 145 9 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 145 10 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 145 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 12 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 145 13 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 14 + + PROPN american_scientific_journal-1665 145 15 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 17 Μ‡ Μ‡ PROPN american_scientific_journal-1665 145 18 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 19 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 145 20 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 145 21 βˆ—π‘–π‘– βˆ—π‘–π‘– PUNCT american_scientific_journal-1665 145 22 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 23 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— PROPN american_scientific_journal-1665 145 24 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 25 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 26 + + CCONJ american_scientific_journal-1665 145 27 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 145 28 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 145 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 30 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 32 Μ‡ Μ‡ PROPN american_scientific_journal-1665 145 33 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 34 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 145 35 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 145 36 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 145 37 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 38 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 145 39 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“ PROPN american_scientific_journal-1665 145 40 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 41 + + PROPN american_scientific_journal-1665 145 42 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 44 Μ‡ Μ‡ PROPN american_scientific_journal-1665 145 45 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 46 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 145 47 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 145 48 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 145 49 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 50 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 145 51 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 145 52 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 53 + + PROPN american_scientific_journal-1665 145 54 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 55 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 56 Μ‡ Μ‡ PROPN american_scientific_journal-1665 145 57 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 58 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 145 59 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 145 60 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 145 61 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 62 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 145 63 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— PROPN american_scientific_journal-1665 145 64 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 145 65 οΏ½ οΏ½ PROPN american_scientific_journal-1665 145 66 = = SYM american_scientific_journal-1665 145 67 0 0 PUNCT american_scientific_journal-1665 145 68 putting put VERB american_scientific_journal-1665 145 69 ( ( PUNCT american_scientific_journal-1665 145 70 1.18 1.18 NUM american_scientific_journal-1665 145 71 ) ) PUNCT american_scientific_journal-1665 145 72 in in ADP american_scientific_journal-1665 145 73 ( ( PUNCT american_scientific_journal-1665 145 74 2.15 2.15 NUM american_scientific_journal-1665 145 75 ) ) PUNCT american_scientific_journal-1665 145 76 , , PUNCT american_scientific_journal-1665 145 77 we we PRON american_scientific_journal-1665 145 78 get get VERB american_scientific_journal-1665 145 79 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 145 80 πœ†πœ†β„“ πœ†πœ†β„“ ADJ american_scientific_journal-1665 145 81 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 145 82 + + CCONJ american_scientific_journal-1665 145 83 πœ†πœ†β„Ž πœ†πœ†β„Ž PROPN american_scientific_journal-1665 145 84 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– X american_scientific_journal-1665 145 85 + + PROPN american_scientific_journal-1665 145 86 πœ†πœ†π‘—π‘— πœ†πœ†π‘—π‘— INTJ american_scientific_journal-1665 145 87 πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– πœ†πœ†π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– X american_scientific_journal-1665 146 1 + + CCONJ american_scientific_journal-1665 146 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 146 3 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 146 4 + + CCONJ american_scientific_journal-1665 146 5 π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– ADJ american_scientific_journal-1665 146 6 + + CCONJ american_scientific_journal-1665 146 7 π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– ADJ american_scientific_journal-1665 146 8 βˆ’ βˆ’ PROPN american_scientific_journal-1665 146 9 πœ†πœ†π‘šπ‘š πœ†πœ†π‘šπ‘š PROPN american_scientific_journal-1665 146 10 ( ( PUNCT american_scientific_journal-1665 146 11 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ πΎπΎπ‘—π‘—π‘—π‘—β„Ž|β„“ PROPN american_scientific_journal-1665 146 12 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 146 13 + + CCONJ american_scientific_journal-1665 146 14 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž 𝐾𝐾𝑗𝑗ℓ𝑗𝑗|β„Ž VERB american_scientific_journal-1665 146 15 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 147 1 + + CCONJ american_scientific_journal-1665 147 2 πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗 πΎπΎπ‘—π‘—β„Žβ„“|𝑗𝑗 PROPN american_scientific_journal-1665 147 3 𝑖𝑖 𝑖𝑖 PRON american_scientific_journal-1665 147 4 ) ) PUNCT american_scientific_journal-1665 148 1 + + CCONJ american_scientific_journal-1665 148 2 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 148 3 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 148 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 5 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 6 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 7 Μ‡ Μ‡ PROPN american_scientific_journal-1665 148 8 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 9 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 148 10 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 148 11 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 148 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 13 |π‘šπ‘š |π‘šπ‘š ADJ american_scientific_journal-1665 148 14 πΎπΎπ‘Ÿπ‘Ÿβ„Žπ‘™π‘™π‘ π‘  πΎπΎπ‘Ÿπ‘Ÿβ„Žπ‘™π‘™π‘ π‘  PROPN american_scientific_journal-1665 148 15 + + CCONJ american_scientific_journal-1665 148 16 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 17 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 18 Μ‡ Μ‡ PROPN american_scientific_journal-1665 148 19 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 20 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 148 21 𝛀𝛀𝑗𝑗𝑙𝑙 𝛀𝛀𝑗𝑗𝑙𝑙 PROPN american_scientific_journal-1665 148 22 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 148 23 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 24 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 148 25 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 148 26 𝑠𝑠 𝑠𝑠 PROPN american_scientific_journal-1665 148 27 + + PROPN american_scientific_journal-1665 148 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 30 Μ‡ Μ‡ PROPN american_scientific_journal-1665 148 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 148 32 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 149 1 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 149 2 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 149 3 οΏ½ οΏ½ ADP american_scientific_journal-1665 149 4 |π‘šπ‘š |π‘šπ‘š ADP american_scientific_journal-1665 149 5 πΎπΎπ‘Ÿπ‘Ÿπ‘™π‘™π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿπ‘™π‘™π‘—π‘— PROPN american_scientific_journal-1665 149 6 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 149 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 8 = = SYM american_scientific_journal-1665 149 9 0 0 NUM american_scientific_journal-1665 149 10 which which PRON american_scientific_journal-1665 149 11 can can AUX american_scientific_journal-1665 149 12 be be AUX american_scientific_journal-1665 149 13 written write VERB american_scientific_journal-1665 149 14 as as ADP american_scientific_journal-1665 149 15 ( ( PUNCT american_scientific_journal-1665 149 16 2.16 2.16 NUM american_scientific_journal-1665 149 17 ) ) PUNCT american_scientific_journal-1665 149 18 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 149 19 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 149 20 + + CCONJ american_scientific_journal-1665 149 21 π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– π‘π‘β„Žπ‘šπ‘šπΎπΎπ‘—π‘—β„“π‘—π‘—π‘–π‘– ADJ american_scientific_journal-1665 149 22 + + CCONJ american_scientific_journal-1665 149 23 π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– π‘π‘π‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– X american_scientific_journal-1665 149 24 + + CCONJ american_scientific_journal-1665 149 25 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 149 26 π‘Ÿπ‘Ÿ π‘Ÿπ‘Ÿ PROPN american_scientific_journal-1665 149 27 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 28 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 29 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 30 Μ‡ Μ‡ PROPN american_scientific_journal-1665 149 31 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 32 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 149 33 𝛀𝛀𝑗𝑗𝑗𝑗 𝛀𝛀𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 149 34 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 149 35 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 36 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 149 37 πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“π‘ π‘  πΎπΎπ‘Ÿπ‘Ÿβ„Žβ„“π‘ π‘  PROPN american_scientific_journal-1665 149 38 + + PROPN american_scientific_journal-1665 149 39 + + PROPN american_scientific_journal-1665 149 40 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 41 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 42 Μ‡ Μ‡ PROPN american_scientific_journal-1665 149 43 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 44 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 149 45 𝛀𝛀𝑗𝑗ℓ 𝛀𝛀𝑗𝑗ℓ PROPN american_scientific_journal-1665 149 46 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 149 47 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 48 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 149 49 πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž πΎπΎπ‘Ÿπ‘Ÿπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 149 50 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 149 51 + + PROPN american_scientific_journal-1665 149 52 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 53 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 54 Μ‡ Μ‡ PROPN american_scientific_journal-1665 149 55 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 56 πœ•π‘ π‘  πœ•π‘ π‘  PUNCT american_scientific_journal-1665 149 57 π›€π›€π‘—π‘—β„Ž π›€π›€π‘—π‘—β„Ž PROPN american_scientific_journal-1665 149 58 βˆ—π‘–π‘– βˆ—π‘–π‘– NOUN american_scientific_journal-1665 149 59 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 60 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 149 61 πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— πΎπΎπ‘Ÿπ‘Ÿβ„“π‘—π‘— PROPN american_scientific_journal-1665 149 62 𝑠𝑠 𝑠𝑠 ADP american_scientific_journal-1665 149 63 οΏ½ οΏ½ PROPN american_scientific_journal-1665 149 64 = = SYM american_scientific_journal-1665 149 65 0 0 PROPN american_scientific_journal-1665 149 66 . . PUNCT american_scientific_journal-1665 149 67 transvecting transvecte VERB american_scientific_journal-1665 149 68 ( ( PUNCT american_scientific_journal-1665 149 69 2.16 2.16 NUM american_scientific_journal-1665 149 70 ) ) PUNCT american_scientific_journal-1665 149 71 by by ADP american_scientific_journal-1665 149 72 𝑦𝑦 𝑦𝑦 PROPN american_scientific_journal-1665 149 73 𝑗𝑗 𝑗𝑗 PROPN american_scientific_journal-1665 149 74 , , PUNCT american_scientific_journal-1665 149 75 using use VERB american_scientific_journal-1665 149 76 ( ( PUNCT american_scientific_journal-1665 149 77 1.1a 1.1a NOUN american_scientific_journal-1665 149 78 ) ) PUNCT american_scientific_journal-1665 149 79 , , PUNCT american_scientific_journal-1665 149 80 ( ( PUNCT american_scientific_journal-1665 149 81 1.6 1.6 NUM american_scientific_journal-1665 149 82 ) ) PUNCT american_scientific_journal-1665 149 83 and and CCONJ american_scientific_journal-1665 149 84 ( ( PUNCT american_scientific_journal-1665 149 85 1.2b 1.2b NOUN american_scientific_journal-1665 149 86 ) ) PUNCT american_scientific_journal-1665 149 87 , , PUNCT american_scientific_journal-1665 149 88 we we PRON american_scientific_journal-1665 149 89 get get VERB american_scientific_journal-1665 149 90 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 149 91 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 149 92 + + CCONJ american_scientific_journal-1665 149 93 π‘π‘β„Žπ‘šπ‘š π‘π‘β„Žπ‘šπ‘š PROPN american_scientific_journal-1665 149 94 𝐻𝐻ℓ𝑗𝑗𝑖𝑖 𝐻𝐻ℓ𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 149 95 + + PUNCT american_scientific_journal-1665 149 96 π‘π‘π‘—π‘—π‘šπ‘š π‘π‘π‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 149 97 π»π»β„Žβ„“π‘–π‘– π»π»β„Žβ„“π‘–π‘– PROPN american_scientific_journal-1665 149 98 + + CCONJ american_scientific_journal-1665 149 99 𝑃𝑃𝑠𝑠𝑗𝑗|π‘šπ‘š 𝑃𝑃𝑠𝑠𝑗𝑗|π‘šπ‘š NOUN american_scientific_journal-1665 149 100 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 150 1 π»π»β„Žβ„“π‘ π‘  π»π»β„Žβ„“π‘ π‘  NOUN american_scientific_journal-1665 150 2 + + ADP american_scientific_journal-1665 150 3 𝑃𝑃𝑠𝑠ℓ|π‘šπ‘š 𝑃𝑃𝑠𝑠ℓ|π‘šπ‘š ADV american_scientific_journal-1665 150 4 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 150 5 π»π»π‘—π‘—β„Žπ‘ π‘  π»π»π‘—π‘—β„Žπ‘ π‘  PROPN american_scientific_journal-1665 150 6 + + PROPN american_scientific_journal-1665 150 7 π‘ƒπ‘ƒπ‘ π‘ β„Ž|π‘šπ‘š π‘ƒπ‘ƒπ‘ π‘ β„Ž|π‘šπ‘š ADV american_scientific_journal-1665 150 8 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 151 1 𝐻𝐻ℓ𝑗𝑗𝑠𝑠 𝐻𝐻ℓ𝑗𝑗𝑠𝑠 PROPN american_scientific_journal-1665 151 2 = = NOUN american_scientific_journal-1665 151 3 0 0 NUM american_scientific_journal-1665 151 4 . . PUNCT american_scientific_journal-1665 152 1 3 3 X american_scientific_journal-1665 152 2 . . X american_scientific_journal-1665 153 1 𝑲𝑲𝒉𝒉 𝑲𝑲𝒉𝒉 PRON american_scientific_journal-1665 153 2 – – PUNCT american_scientific_journal-1665 153 3 generalized generalize VERB american_scientific_journal-1665 153 4 birecurrent birecurrent NOUN american_scientific_journal-1665 153 5 affinely affinely ADV american_scientific_journal-1665 153 6 connected connect VERB american_scientific_journal-1665 153 7 space space NOUN american_scientific_journal-1665 153 8 let let VERB american_scientific_journal-1665 153 9 us we PRON american_scientific_journal-1665 153 10 consider consider VERB american_scientific_journal-1665 153 11 an an DET american_scientific_journal-1665 153 12 affinely affinely ADV american_scientific_journal-1665 153 13 connected connected ADJ american_scientific_journal-1665 153 14 or or CCONJ american_scientific_journal-1665 153 15 berwald berwald NOUN american_scientific_journal-1665 153 16 's 's PART american_scientific_journal-1665 153 17 space space NOUN american_scientific_journal-1665 153 18 which which PRON american_scientific_journal-1665 153 19 is be AUX american_scientific_journal-1665 153 20 characterized characterize VERB american_scientific_journal-1665 153 21 by by ADP american_scientific_journal-1665 153 22 any any DET american_scientific_journal-1665 153 23 one one NUM american_scientific_journal-1665 153 24 of of ADP american_scientific_journal-1665 153 25 the the DET american_scientific_journal-1665 153 26 equivalent equivalent ADJ american_scientific_journal-1665 153 27 conditions condition NOUN american_scientific_journal-1665 153 28 ( ( PUNCT american_scientific_journal-1665 153 29 1.19 1.19 NUM american_scientific_journal-1665 153 30 ) ) PUNCT american_scientific_journal-1665 153 31 , , PUNCT american_scientific_journal-1665 153 32 ( ( PUNCT american_scientific_journal-1665 153 33 1.20 1.20 NUM american_scientific_journal-1665 153 34 ) ) PUNCT american_scientific_journal-1665 153 35 , , PUNCT american_scientific_journal-1665 153 36 ( ( PUNCT american_scientific_journal-1665 153 37 1.21 1.21 NUM american_scientific_journal-1665 153 38 ) ) PUNCT american_scientific_journal-1665 153 39 and and CCONJ american_scientific_journal-1665 153 40 ( ( PUNCT american_scientific_journal-1665 153 41 1.22 1.22 NUM american_scientific_journal-1665 153 42 ) ) PUNCT american_scientific_journal-1665 153 43 . . PUNCT american_scientific_journal-1665 154 1 65- 65- X american_scientific_journal-1665 154 2 ) ) PUNCT american_scientific_journal-1665 154 3 volume volume NOUN american_scientific_journal-1665 154 4 20 20 NUM american_scientific_journal-1665 154 5 , , PUNCT american_scientific_journal-1665 154 6 no no DET american_scientific_journal-1665 154 7 1 1 NUM american_scientific_journal-1665 154 8 , , PUNCT american_scientific_journal-1665 154 9 pp pp ADP american_scientific_journal-1665 154 10 522016 522016 NUM american_scientific_journal-1665 154 11 ( ( PUNCT american_scientific_journal-1665 154 12 ) ) PUNCT american_scientific_journal-1665 154 13 research research NOUN american_scientific_journal-1665 154 14 journal journal NOUN american_scientific_journal-1665 154 15 for for ADP american_scientific_journal-1665 154 16 engineering engineering NOUN american_scientific_journal-1665 154 17 , , PUNCT american_scientific_journal-1665 154 18 technology technology NOUN american_scientific_journal-1665 154 19 , , PUNCT american_scientific_journal-1665 154 20 and and CCONJ american_scientific_journal-1665 154 21 sciences science NOUN american_scientific_journal-1665 154 22 ( ( PUNCT american_scientific_journal-1665 154 23 asrjets asrjet NOUN american_scientific_journal-1665 154 24 scientificamerican scientificamerican VERB american_scientific_journal-1665 154 25 61 61 NUM american_scientific_journal-1665 154 26 definition definition NOUN american_scientific_journal-1665 154 27 3.1 3.1 NUM american_scientific_journal-1665 154 28 . . PUNCT american_scientific_journal-1665 155 1 the the DET american_scientific_journal-1665 155 2 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 155 3 – – PUNCT american_scientific_journal-1665 155 4 generalized generalize VERB american_scientific_journal-1665 155 5 birecurrent birecurrent ADJ american_scientific_journal-1665 155 6 space space NOUN american_scientific_journal-1665 155 7 is be AUX american_scientific_journal-1665 155 8 called call VERB american_scientific_journal-1665 155 9 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 155 10 – – PUNCT american_scientific_journal-1665 155 11 generalized generalize VERB american_scientific_journal-1665 155 12 birecurrent birecurrent NOUN american_scientific_journal-1665 155 13 affinely affinely ADV american_scientific_journal-1665 155 14 connected connect VERB american_scientific_journal-1665 155 15 if if SCONJ american_scientific_journal-1665 155 16 it it PRON american_scientific_journal-1665 155 17 satisfies satisfy VERB american_scientific_journal-1665 155 18 any any DET american_scientific_journal-1665 155 19 one one NUM american_scientific_journal-1665 155 20 of of ADP american_scientific_journal-1665 155 21 the the DET american_scientific_journal-1665 155 22 conditions condition NOUN american_scientific_journal-1665 155 23 ( ( PUNCT american_scientific_journal-1665 155 24 1.19 1.19 NUM american_scientific_journal-1665 155 25 ) ) PUNCT american_scientific_journal-1665 155 26 , , PUNCT american_scientific_journal-1665 155 27 ( ( PUNCT american_scientific_journal-1665 155 28 1.20 1.20 NUM american_scientific_journal-1665 155 29 ) ) PUNCT american_scientific_journal-1665 155 30 , , PUNCT american_scientific_journal-1665 155 31 ( ( PUNCT american_scientific_journal-1665 155 32 1.21 1.21 NUM american_scientific_journal-1665 155 33 ) ) PUNCT american_scientific_journal-1665 155 34 and and CCONJ american_scientific_journal-1665 155 35 ( ( PUNCT american_scientific_journal-1665 155 36 1.22 1.22 NUM american_scientific_journal-1665 155 37 ) ) PUNCT american_scientific_journal-1665 155 38 and and CCONJ american_scientific_journal-1665 155 39 denoted denote VERB american_scientific_journal-1665 155 40 briefly briefly ADV american_scientific_journal-1665 155 41 by by ADP american_scientific_journal-1665 155 42 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 155 43 connected connected ADJ american_scientific_journal-1665 155 44 space space NOUN american_scientific_journal-1665 155 45 . . PUNCT american_scientific_journal-1665 156 1 let let VERB american_scientific_journal-1665 156 2 us we PRON american_scientific_journal-1665 156 3 consider consider VERB american_scientific_journal-1665 156 4 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 156 5 βˆ’ βˆ’ ADP american_scientific_journal-1665 156 6 𝐺𝐺𝐺𝐺𝑅𝑅 𝐺𝐺𝐺𝐺𝑅𝑅 VERB american_scientific_journal-1665 156 7 βˆ’ βˆ’ ADP american_scientific_journal-1665 156 8 affinely affinely ADV american_scientific_journal-1665 156 9 connected connected ADJ american_scientific_journal-1665 156 10 space space NOUN american_scientific_journal-1665 156 11 . . PUNCT american_scientific_journal-1665 157 1 if if SCONJ american_scientific_journal-1665 157 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 157 3 Μ‡ Μ‡ PROPN american_scientific_journal-1665 157 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 157 5 πœ•π‘—π‘— πœ•π‘—π‘— NOUN american_scientific_journal-1665 157 6 πœ†πœ†β„“ πœ†πœ†β„“ ADJ american_scientific_journal-1665 157 7 = = SYM american_scientific_journal-1665 157 8 0 0 NUM american_scientific_journal-1665 157 9 , , PUNCT american_scientific_journal-1665 157 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 157 11 Μ‡ Μ‡ PROPN american_scientific_journal-1665 157 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 157 13 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 157 14 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 157 15 = = NOUN american_scientific_journal-1665 157 16 0 0 NUM american_scientific_journal-1665 157 17 and and CCONJ american_scientific_journal-1665 157 18 in in ADP american_scientific_journal-1665 157 19 view view NOUN american_scientific_journal-1665 157 20 of of ADP american_scientific_journal-1665 157 21 the the DET american_scientific_journal-1665 157 22 conditions condition NOUN american_scientific_journal-1665 157 23 ( ( PUNCT american_scientific_journal-1665 157 24 1.2b 1.2b NOUN american_scientific_journal-1665 157 25 ) ) PUNCT american_scientific_journal-1665 157 26 and and CCONJ american_scientific_journal-1665 157 27 ( ( PUNCT american_scientific_journal-1665 157 28 1.22 1.22 NUM american_scientific_journal-1665 157 29 ) ) PUNCT american_scientific_journal-1665 157 30 , , PUNCT american_scientific_journal-1665 157 31 the the DET american_scientific_journal-1665 157 32 equation equation NOUN american_scientific_journal-1665 157 33 ( ( PUNCT american_scientific_journal-1665 157 34 2.5 2.5 NUM american_scientific_journal-1665 157 35 ) ) PUNCT american_scientific_journal-1665 157 36 reduces reduce VERB american_scientific_journal-1665 157 37 to to PART american_scientific_journal-1665 157 38 ( ( PUNCT american_scientific_journal-1665 157 39 1.3 1.3 NUM american_scientific_journal-1665 157 40 ) ) PUNCT american_scientific_journal-1665 157 41 π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 157 42 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 158 1 = = NOUN american_scientific_journal-1665 158 2 πœ†πœ†β„“ πœ†πœ†β„“ PRON american_scientific_journal-1665 158 3 π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 158 4 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 159 1 + + CCONJ american_scientific_journal-1665 159 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 159 3 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 159 4 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 159 5 . . PUNCT american_scientific_journal-1665 160 1 thus thus ADV american_scientific_journal-1665 160 2 , , PUNCT american_scientific_journal-1665 160 3 we we PRON american_scientific_journal-1665 160 4 conclude conclude AUX american_scientific_journal-1665 160 5 theorem theorem VERB american_scientific_journal-1665 160 6 3.1 3.1 NUM american_scientific_journal-1665 160 7 . . PUNCT american_scientific_journal-1665 161 1 in in ADP american_scientific_journal-1665 161 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 161 3 connected connected ADJ american_scientific_journal-1665 161 4 space space NOUN american_scientific_journal-1665 161 5 , , PUNCT american_scientific_journal-1665 161 6 if if SCONJ american_scientific_journal-1665 161 7 the the DET american_scientific_journal-1665 161 8 directional directional ADJ american_scientific_journal-1665 161 9 derivative derivative NOUN american_scientific_journal-1665 161 10 of of ADP american_scientific_journal-1665 161 11 covariant covariant ADJ american_scientific_journal-1665 161 12 vector vector NOUN american_scientific_journal-1665 161 13 field field NOUN american_scientific_journal-1665 161 14 and and CCONJ american_scientific_journal-1665 161 15 covariant covariant ADJ american_scientific_journal-1665 161 16 tensor tensor NOUN american_scientific_journal-1665 161 17 of of ADP american_scientific_journal-1665 161 18 second second ADJ american_scientific_journal-1665 161 19 order order NOUN american_scientific_journal-1665 161 20 are be AUX american_scientific_journal-1665 161 21 vanish vanish VERB american_scientific_journal-1665 161 22 , , PUNCT american_scientific_journal-1665 161 23 then then ADV american_scientific_journal-1665 161 24 berwald berwald NOUN american_scientific_journal-1665 161 25 curvature curvature NOUN american_scientific_journal-1665 161 26 tensor tensor NOUN american_scientific_journal-1665 161 27 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 161 28 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 161 29 is be AUX american_scientific_journal-1665 161 30 generalized generalize VERB american_scientific_journal-1665 161 31 bireurrent bireurrent NOUN american_scientific_journal-1665 161 32 . . PUNCT american_scientific_journal-1665 162 1 if if SCONJ american_scientific_journal-1665 162 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 162 3 Μ‡ Μ‡ VERB american_scientific_journal-1665 162 4 οΏ½ οΏ½ NOUN american_scientific_journal-1665 162 5 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 162 6 = = SYM american_scientific_journal-1665 162 7 0 0 NUM american_scientific_journal-1665 162 8 , , PUNCT american_scientific_journal-1665 162 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 162 10 Μ‡ Μ‡ PROPN american_scientific_journal-1665 162 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 162 12 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 162 13 = = SYM american_scientific_journal-1665 162 14 0 0 NUM american_scientific_journal-1665 162 15 and and CCONJ american_scientific_journal-1665 162 16 in in ADP american_scientific_journal-1665 162 17 view view NOUN american_scientific_journal-1665 162 18 of of ADP american_scientific_journal-1665 162 19 the the DET american_scientific_journal-1665 162 20 conditions condition NOUN american_scientific_journal-1665 162 21 ( ( PUNCT american_scientific_journal-1665 162 22 1.2b 1.2b NOUN american_scientific_journal-1665 162 23 ) ) PUNCT american_scientific_journal-1665 162 24 and and CCONJ american_scientific_journal-1665 162 25 ( ( PUNCT american_scientific_journal-1665 162 26 1.22 1.22 NUM american_scientific_journal-1665 162 27 ) ) PUNCT american_scientific_journal-1665 162 28 , , PUNCT american_scientific_journal-1665 162 29 the the DET american_scientific_journal-1665 162 30 equation equation NOUN american_scientific_journal-1665 162 31 ( ( PUNCT american_scientific_journal-1665 162 32 2.7 2.7 NUM american_scientific_journal-1665 162 33 ) ) PUNCT american_scientific_journal-1665 162 34 reduces reduce VERB american_scientific_journal-1665 162 35 to to ADP american_scientific_journal-1665 162 36 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 162 37 = = SYM american_scientific_journal-1665 162 38 πœ†πœ†β„“ πœ†πœ†β„“ CCONJ american_scientific_journal-1665 162 39 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 163 1 + + CCONJ american_scientific_journal-1665 163 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 163 3 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž. π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž. ADP american_scientific_journal-1665 163 4 thus thus ADV american_scientific_journal-1665 163 5 , , PUNCT american_scientific_journal-1665 163 6 we we PRON american_scientific_journal-1665 163 7 conclude conclude VERB american_scientific_journal-1665 163 8 theorem theorem VERB american_scientific_journal-1665 163 9 3.2 3.2 NUM american_scientific_journal-1665 163 10 . . PUNCT american_scientific_journal-1665 164 1 in in ADP american_scientific_journal-1665 164 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 164 3 connected connected ADJ american_scientific_journal-1665 164 4 space space NOUN american_scientific_journal-1665 164 5 , , PUNCT american_scientific_journal-1665 164 6 if if SCONJ american_scientific_journal-1665 164 7 the the DET american_scientific_journal-1665 164 8 directional directional ADJ american_scientific_journal-1665 164 9 derivative derivative NOUN american_scientific_journal-1665 164 10 of of ADP american_scientific_journal-1665 164 11 covariant covariant ADJ american_scientific_journal-1665 164 12 vector vector NOUN american_scientific_journal-1665 164 13 field field NOUN american_scientific_journal-1665 164 14 and and CCONJ american_scientific_journal-1665 164 15 covariant covariant ADJ american_scientific_journal-1665 164 16 tensor tensor NOUN american_scientific_journal-1665 164 17 of of ADP american_scientific_journal-1665 164 18 second second ADJ american_scientific_journal-1665 164 19 order order NOUN american_scientific_journal-1665 164 20 are be AUX american_scientific_journal-1665 164 21 vanish vanish VERB american_scientific_journal-1665 164 22 , , PUNCT american_scientific_journal-1665 164 23 then then ADV american_scientific_journal-1665 164 24 the the DET american_scientific_journal-1665 164 25 associate associate ADJ american_scientific_journal-1665 164 26 tensor tensor NOUN american_scientific_journal-1665 164 27 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 164 28 of of ADP american_scientific_journal-1665 164 29 berwald berwald NOUN american_scientific_journal-1665 164 30 curvature curvature NOUN american_scientific_journal-1665 164 31 tensor tensor NOUN american_scientific_journal-1665 164 32 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 164 33 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 164 34 is be AUX american_scientific_journal-1665 164 35 generalized generalize VERB american_scientific_journal-1665 164 36 bireurrent bireurrent NOUN american_scientific_journal-1665 164 37 . . PUNCT american_scientific_journal-1665 165 1 if if SCONJ american_scientific_journal-1665 165 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 165 3 Μ‡ Μ‡ VERB american_scientific_journal-1665 165 4 οΏ½ οΏ½ NOUN american_scientific_journal-1665 165 5 πœ•π‘—π‘—πœ†πœ†β„“ πœ•π‘—π‘—πœ†πœ†β„“ PROPN american_scientific_journal-1665 165 6 = = SYM american_scientific_journal-1665 165 7 0 0 NUM american_scientific_journal-1665 165 8 , , PUNCT american_scientific_journal-1665 165 9 οΏ½ οΏ½ PROPN american_scientific_journal-1665 165 10 Μ‡ Μ‡ PROPN american_scientific_journal-1665 165 11 οΏ½ οΏ½ PROPN american_scientific_journal-1665 165 12 πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š πœ•π‘—π‘—π‘π‘β„“π‘šπ‘š PROPN american_scientific_journal-1665 165 13 = = SYM american_scientific_journal-1665 165 14 0 0 NUM american_scientific_journal-1665 165 15 and and CCONJ american_scientific_journal-1665 165 16 in in ADP american_scientific_journal-1665 165 17 view view NOUN american_scientific_journal-1665 165 18 of of ADP american_scientific_journal-1665 165 19 the the DET american_scientific_journal-1665 165 20 conditions condition NOUN american_scientific_journal-1665 165 21 ( ( PUNCT american_scientific_journal-1665 165 22 1.2b 1.2b NOUN american_scientific_journal-1665 165 23 ) ) PUNCT american_scientific_journal-1665 165 24 and and CCONJ american_scientific_journal-1665 165 25 ( ( PUNCT american_scientific_journal-1665 165 26 1.22 1.22 NUM american_scientific_journal-1665 165 27 ) ) PUNCT american_scientific_journal-1665 165 28 , , PUNCT american_scientific_journal-1665 165 29 the the DET american_scientific_journal-1665 165 30 equation equation NOUN american_scientific_journal-1665 165 31 ( ( PUNCT american_scientific_journal-1665 165 32 2.9 2.9 NUM american_scientific_journal-1665 165 33 ) ) PUNCT american_scientific_journal-1665 165 34 reduces reduce VERB american_scientific_journal-1665 165 35 to to PART american_scientific_journal-1665 165 36 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑗𝑗|β„“|π‘šπ‘š VERB american_scientific_journal-1665 165 37 = = PUNCT american_scientific_journal-1665 165 38 πœ†πœ†β„“ πœ†πœ†β„“ X american_scientific_journal-1665 166 1 𝐻𝐻𝑗𝑗𝑗𝑗|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑗𝑗|π‘šπ‘š ADV american_scientific_journal-1665 166 2 + + CCONJ american_scientific_journal-1665 166 3 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 166 4 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 166 5 . . PUNCT american_scientific_journal-1665 167 1 thus thus ADV american_scientific_journal-1665 167 2 , , PUNCT american_scientific_journal-1665 167 3 we we PRON american_scientific_journal-1665 167 4 conclude conclude AUX american_scientific_journal-1665 167 5 theorem theorem VERB american_scientific_journal-1665 167 6 3.3 3.3 NUM american_scientific_journal-1665 167 7 . . PUNCT american_scientific_journal-1665 168 1 in in ADP american_scientific_journal-1665 168 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 168 3 connected connected ADJ american_scientific_journal-1665 168 4 space space NOUN american_scientific_journal-1665 168 5 , , PUNCT american_scientific_journal-1665 168 6 if if SCONJ american_scientific_journal-1665 168 7 the the DET american_scientific_journal-1665 168 8 directional directional ADJ american_scientific_journal-1665 168 9 derivative derivative NOUN american_scientific_journal-1665 168 10 of of ADP american_scientific_journal-1665 168 11 covariant covariant ADJ american_scientific_journal-1665 168 12 vector vector NOUN american_scientific_journal-1665 168 13 field field NOUN american_scientific_journal-1665 168 14 and and CCONJ american_scientific_journal-1665 168 15 covariant covariant ADJ american_scientific_journal-1665 168 16 tensor tensor NOUN american_scientific_journal-1665 168 17 of of ADP american_scientific_journal-1665 168 18 second second ADJ american_scientific_journal-1665 168 19 order order NOUN american_scientific_journal-1665 168 20 are be AUX american_scientific_journal-1665 168 21 vanish vanish VERB american_scientific_journal-1665 168 22 , , PUNCT american_scientific_journal-1665 168 23 then then ADV american_scientific_journal-1665 168 24 the the DET american_scientific_journal-1665 168 25 ricci ricci PROPN american_scientific_journal-1665 168 26 tensor tensor NOUN american_scientific_journal-1665 168 27 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 168 28 in in ADP american_scientific_journal-1665 168 29 sense sense NOUN american_scientific_journal-1665 168 30 of of ADP american_scientific_journal-1665 168 31 berwald berwald NOUN american_scientific_journal-1665 168 32 is be AUX american_scientific_journal-1665 168 33 generalized generalize VERB american_scientific_journal-1665 168 34 bireurrent bireurrent NOUN american_scientific_journal-1665 168 35 . . PUNCT american_scientific_journal-1665 169 1 if if SCONJ american_scientific_journal-1665 169 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 169 3 Μ‡ Μ‡ PROPN american_scientific_journal-1665 169 4 οΏ½ οΏ½ PROPN american_scientific_journal-1665 169 5 πœ•π‘—π‘— πœ•π‘—π‘— NOUN american_scientific_journal-1665 169 6 πœ†πœ†β„“ πœ†πœ†β„“ ADJ american_scientific_journal-1665 169 7 = = SYM american_scientific_journal-1665 169 8 0 0 NUM american_scientific_journal-1665 169 9 , , PUNCT american_scientific_journal-1665 169 10 οΏ½ οΏ½ PROPN american_scientific_journal-1665 169 11 Μ‡ Μ‡ PROPN american_scientific_journal-1665 169 12 οΏ½ οΏ½ PROPN american_scientific_journal-1665 169 13 πœ•π‘—π‘— πœ•π‘—π‘— PART american_scientific_journal-1665 169 14 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 169 15 = = NOUN american_scientific_journal-1665 169 16 0 0 NUM american_scientific_journal-1665 169 17 and and CCONJ american_scientific_journal-1665 169 18 in in ADP american_scientific_journal-1665 169 19 view view NOUN american_scientific_journal-1665 169 20 of of ADP american_scientific_journal-1665 169 21 the the DET american_scientific_journal-1665 169 22 conditions condition NOUN american_scientific_journal-1665 169 23 ( ( PUNCT american_scientific_journal-1665 169 24 1.2b 1.2b NOUN american_scientific_journal-1665 169 25 ) ) PUNCT american_scientific_journal-1665 169 26 and and CCONJ american_scientific_journal-1665 169 27 ( ( PUNCT american_scientific_journal-1665 169 28 1.22 1.22 NUM american_scientific_journal-1665 169 29 ) ) PUNCT american_scientific_journal-1665 169 30 , , PUNCT american_scientific_journal-1665 169 31 the the DET american_scientific_journal-1665 169 32 equation equation NOUN american_scientific_journal-1665 169 33 ( ( PUNCT american_scientific_journal-1665 169 34 2.11 2.11 NUM american_scientific_journal-1665 169 35 ) ) PUNCT american_scientific_journal-1665 169 36 reduces reduce VERB american_scientific_journal-1665 169 37 to to PART american_scientific_journal-1665 169 38 ( ( PUNCT american_scientific_journal-1665 169 39 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 169 40 βˆ’ βˆ’ PROPN american_scientific_journal-1665 169 41 π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š π»π»π‘—π‘—β„Ž)|β„“|π‘šπ‘š PROPN american_scientific_journal-1665 169 42 = = SYM american_scientific_journal-1665 169 43 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 169 44 ( ( PUNCT american_scientific_journal-1665 169 45 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 169 46 βˆ’ βˆ’ PROPN american_scientific_journal-1665 169 47 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 169 48 ) ) PUNCT american_scientific_journal-1665 169 49 |π‘šπ‘š |π‘šπ‘š PROPN american_scientific_journal-1665 170 1 + + CCONJ american_scientific_journal-1665 170 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 170 3 ( ( PUNCT american_scientific_journal-1665 170 4 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 170 5 βˆ’ βˆ’ PROPN american_scientific_journal-1665 170 6 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 170 7 ) ) PUNCT american_scientific_journal-1665 170 8 . . PUNCT american_scientific_journal-1665 171 1 thus thus ADV american_scientific_journal-1665 171 2 , , PUNCT american_scientific_journal-1665 171 3 we we PRON american_scientific_journal-1665 171 4 conclude conclude VERB american_scientific_journal-1665 171 5 65- 65- NUM american_scientific_journal-1665 171 6 ) ) PUNCT american_scientific_journal-1665 171 7 volume volume NOUN american_scientific_journal-1665 171 8 20 20 NUM american_scientific_journal-1665 171 9 , , PUNCT american_scientific_journal-1665 171 10 no no DET american_scientific_journal-1665 171 11 1 1 NUM american_scientific_journal-1665 171 12 , , PUNCT american_scientific_journal-1665 171 13 pp pp ADP american_scientific_journal-1665 171 14 522016 522016 NUM american_scientific_journal-1665 171 15 ( ( PUNCT american_scientific_journal-1665 171 16 ) ) PUNCT american_scientific_journal-1665 171 17 research research NOUN american_scientific_journal-1665 171 18 journal journal NOUN american_scientific_journal-1665 171 19 for for ADP american_scientific_journal-1665 171 20 engineering engineering NOUN american_scientific_journal-1665 171 21 , , PUNCT american_scientific_journal-1665 171 22 technology technology NOUN american_scientific_journal-1665 171 23 , , PUNCT american_scientific_journal-1665 171 24 and and CCONJ american_scientific_journal-1665 171 25 sciences science NOUN american_scientific_journal-1665 171 26 ( ( PUNCT american_scientific_journal-1665 171 27 asrjets asrjet NOUN american_scientific_journal-1665 171 28 scientificamerican scientificamerican VERB american_scientific_journal-1665 171 29 62 62 NUM american_scientific_journal-1665 171 30 theorem theorem VERB american_scientific_journal-1665 171 31 3.4 3.4 NUM american_scientific_journal-1665 171 32 . . PUNCT american_scientific_journal-1665 172 1 in in ADP american_scientific_journal-1665 172 2 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 172 3 βˆ’ βˆ’ ADP american_scientific_journal-1665 172 4 𝐺𝐺𝐺𝐺𝑅𝑅 𝐺𝐺𝐺𝐺𝑅𝑅 PROPN american_scientific_journal-1665 172 5 βˆ’affinely βˆ’affinely ADV american_scientific_journal-1665 172 6 connected connected ADJ american_scientific_journal-1665 172 7 space space NOUN american_scientific_journal-1665 172 8 , , PUNCT american_scientific_journal-1665 172 9 if if SCONJ american_scientific_journal-1665 172 10 the the DET american_scientific_journal-1665 172 11 directional directional ADJ american_scientific_journal-1665 172 12 derivative derivative NOUN american_scientific_journal-1665 172 13 of of ADP american_scientific_journal-1665 172 14 covariant covariant ADJ american_scientific_journal-1665 172 15 vector vector NOUN american_scientific_journal-1665 172 16 field field NOUN american_scientific_journal-1665 172 17 and and CCONJ american_scientific_journal-1665 172 18 covariant covariant ADJ american_scientific_journal-1665 172 19 tensor tensor NOUN american_scientific_journal-1665 172 20 of of ADP american_scientific_journal-1665 172 21 second second ADJ american_scientific_journal-1665 172 22 order order NOUN american_scientific_journal-1665 172 23 are be AUX american_scientific_journal-1665 172 24 vanish vanish VERB american_scientific_journal-1665 172 25 , , PUNCT american_scientific_journal-1665 172 26 then then ADV american_scientific_journal-1665 172 27 the the DET american_scientific_journal-1665 172 28 tensor tensor NOUN american_scientific_journal-1665 172 29 ( ( PUNCT american_scientific_journal-1665 172 30 π»π»β„Žπ‘—π‘— π»π»β„Žπ‘—π‘— PROPN american_scientific_journal-1665 172 31 βˆ’ βˆ’ PROPN american_scientific_journal-1665 172 32 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 172 33 ) ) PUNCT american_scientific_journal-1665 172 34 is be AUX american_scientific_journal-1665 172 35 generalized generalize VERB american_scientific_journal-1665 172 36 bireurrent bireurrent NOUN american_scientific_journal-1665 172 37 . . PUNCT american_scientific_journal-1665 173 1 now now ADV american_scientific_journal-1665 173 2 , , PUNCT american_scientific_journal-1665 173 3 transvecting transvecte VERB american_scientific_journal-1665 173 4 ( ( PUNCT american_scientific_journal-1665 173 5 3.1 3.1 NUM american_scientific_journal-1665 173 6 ) ) PUNCT american_scientific_journal-1665 173 7 by by ADP american_scientific_journal-1665 173 8 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 NOUN american_scientific_journal-1665 173 9 , , PUNCT american_scientific_journal-1665 173 10 using use VERB american_scientific_journal-1665 173 11 ( ( PUNCT american_scientific_journal-1665 173 12 1.1a 1.1a NOUN american_scientific_journal-1665 173 13 ) ) PUNCT american_scientific_journal-1665 173 14 and and CCONJ american_scientific_journal-1665 173 15 ( ( PUNCT american_scientific_journal-1665 173 16 1.8 1.8 NUM american_scientific_journal-1665 173 17 ) ) PUNCT american_scientific_journal-1665 173 18 , , PUNCT american_scientific_journal-1665 173 19 we we PRON american_scientific_journal-1665 173 20 get get VERB american_scientific_journal-1665 173 21 ( ( PUNCT american_scientific_journal-1665 173 22 3.2 3.2 NUM american_scientific_journal-1665 173 23 ) ) PUNCT american_scientific_journal-1665 173 24 π»π»π‘—π‘—β„Ž|β„“ π»π»π‘—π‘—β„Ž|β„“ X american_scientific_journal-1665 173 25 |π‘šπ‘š |π‘šπ‘š X american_scientific_journal-1665 173 26 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 173 27 = = PUNCT american_scientific_journal-1665 173 28 πœ†πœ†β„“ πœ†πœ†β„“ X american_scientific_journal-1665 174 1 π»π»π‘—π‘—β„Ž|π‘šπ‘š π»π»π‘—π‘—β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 174 2 𝑖𝑖 𝑖𝑖 PROPN american_scientific_journal-1665 175 1 + + CCONJ american_scientific_journal-1665 175 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 175 3 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 175 4 𝑖𝑖 𝑖𝑖 VERB american_scientific_journal-1665 175 5 . . PUNCT american_scientific_journal-1665 176 1 transvecting transvecte VERB american_scientific_journal-1665 176 2 ( ( PUNCT american_scientific_journal-1665 176 3 3.2 3.2 NUM american_scientific_journal-1665 176 4 ) ) PUNCT american_scientific_journal-1665 176 5 by by ADP american_scientific_journal-1665 176 6 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 PRON american_scientific_journal-1665 176 7 , , PUNCT american_scientific_journal-1665 176 8 using use VERB american_scientific_journal-1665 176 9 ( ( PUNCT american_scientific_journal-1665 176 10 1.1a 1.1a NOUN american_scientific_journal-1665 176 11 ) ) PUNCT american_scientific_journal-1665 176 12 and and CCONJ american_scientific_journal-1665 176 13 ( ( PUNCT american_scientific_journal-1665 176 14 1.11 1.11 NUM american_scientific_journal-1665 176 15 ) ) PUNCT american_scientific_journal-1665 176 16 , , PUNCT american_scientific_journal-1665 176 17 we we PRON american_scientific_journal-1665 176 18 get get VERB american_scientific_journal-1665 176 19 ( ( PUNCT american_scientific_journal-1665 176 20 3.3 3.3 NUM american_scientific_journal-1665 176 21 ) ) PUNCT american_scientific_journal-1665 176 22 π»π»β„Ž|β„“ π»π»β„Ž|β„“ NOUN american_scientific_journal-1665 176 23 |π‘šπ‘š |π‘šπ‘š PRON american_scientific_journal-1665 176 24 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 176 25 = = PUNCT american_scientific_journal-1665 176 26 πœ†πœ†β„“ πœ†πœ†β„“ ADJ american_scientific_journal-1665 176 27 π»π»β„Ž|π‘šπ‘š π»π»β„Ž|π‘šπ‘š NOUN american_scientific_journal-1665 176 28 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 177 1 + + CCONJ american_scientific_journal-1665 177 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 177 3 π»π»β„Ž π»π»β„Ž PROPN american_scientific_journal-1665 177 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 177 5 . . PUNCT american_scientific_journal-1665 178 1 contracting contract VERB american_scientific_journal-1665 178 2 the the DET american_scientific_journal-1665 178 3 indices index NOUN american_scientific_journal-1665 178 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 178 5 and and CCONJ american_scientific_journal-1665 178 6 β„Ž β„Ž PROPN american_scientific_journal-1665 178 7 in in ADP american_scientific_journal-1665 178 8 ( ( PUNCT american_scientific_journal-1665 178 9 3.2 3.2 NUM american_scientific_journal-1665 178 10 ) ) PUNCT american_scientific_journal-1665 178 11 and and CCONJ american_scientific_journal-1665 178 12 using use VERB american_scientific_journal-1665 178 13 ( ( PUNCT american_scientific_journal-1665 178 14 1.13 1.13 NUM american_scientific_journal-1665 178 15 ) ) PUNCT american_scientific_journal-1665 178 16 , , PUNCT american_scientific_journal-1665 178 17 we we PRON american_scientific_journal-1665 178 18 get get VERB american_scientific_journal-1665 178 19 𝐻𝐻𝑗𝑗|β„“|π‘šπ‘š 𝐻𝐻𝑗𝑗|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 178 20 = = SYM american_scientific_journal-1665 178 21 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 179 1 𝐻𝐻𝑗𝑗|π‘šπ‘š 𝐻𝐻𝑗𝑗|π‘šπ‘š PROPN american_scientific_journal-1665 179 2 + + NUM american_scientific_journal-1665 179 3 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 179 4 𝐻𝐻𝑗𝑗 𝐻𝐻𝑗𝑗 PROPN american_scientific_journal-1665 179 5 contracting contract VERB american_scientific_journal-1665 179 6 the the DET american_scientific_journal-1665 179 7 indices index NOUN american_scientific_journal-1665 179 8 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 179 9 and and CCONJ american_scientific_journal-1665 179 10 β„Ž β„Ž PROPN american_scientific_journal-1665 179 11 in in ADP american_scientific_journal-1665 179 12 ( ( PUNCT american_scientific_journal-1665 179 13 3.3 3.3 NUM american_scientific_journal-1665 179 14 ) ) PUNCT american_scientific_journal-1665 179 15 and and CCONJ american_scientific_journal-1665 179 16 using use VERB american_scientific_journal-1665 179 17 ( ( PUNCT american_scientific_journal-1665 179 18 1.14 1.14 NUM american_scientific_journal-1665 179 19 ) ) PUNCT american_scientific_journal-1665 179 20 , , PUNCT american_scientific_journal-1665 179 21 we we PRON american_scientific_journal-1665 179 22 get get VERB american_scientific_journal-1665 179 23 𝐻𝐻|β„“|π‘šπ‘š 𝐻𝐻|β„“|π‘šπ‘š NOUN american_scientific_journal-1665 179 24 = = SYM american_scientific_journal-1665 179 25 πœ†πœ†β„“ πœ†πœ†β„“ PRON american_scientific_journal-1665 180 1 𝐻𝐻|π‘šπ‘š 𝐻𝐻|π‘šπ‘š PROPN american_scientific_journal-1665 180 2 + + CCONJ american_scientific_journal-1665 180 3 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 180 4 𝐻𝐻. 𝐻𝐻. DET american_scientific_journal-1665 180 5 transvecting transvecte VERB american_scientific_journal-1665 180 6 ( ( PUNCT american_scientific_journal-1665 180 7 3.2 3.2 NUM american_scientific_journal-1665 180 8 ) ) PUNCT american_scientific_journal-1665 180 9 by by ADP american_scientific_journal-1665 180 10 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 180 11 , , PUNCT american_scientific_journal-1665 180 12 using use VERB american_scientific_journal-1665 180 13 ( ( PUNCT american_scientific_journal-1665 180 14 1.1b 1.1b NUM american_scientific_journal-1665 180 15 ) ) PUNCT american_scientific_journal-1665 180 16 and and CCONJ american_scientific_journal-1665 180 17 ( ( PUNCT american_scientific_journal-1665 180 18 1.17 1.17 NUM american_scientific_journal-1665 180 19 ) ) PUNCT american_scientific_journal-1665 180 20 , , PUNCT american_scientific_journal-1665 180 21 we we PRON american_scientific_journal-1665 180 22 get get VERB american_scientific_journal-1665 180 23 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž|β„“|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž|β„“|π‘šπ‘š PROPN american_scientific_journal-1665 180 24 = = PUNCT american_scientific_journal-1665 180 25 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 181 1 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž|π‘šπ‘š 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž|π‘šπ‘š PROPN american_scientific_journal-1665 182 1 + + CCONJ american_scientific_journal-1665 182 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 182 3 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž. 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž. INTJ american_scientific_journal-1665 182 4 thus thus ADV american_scientific_journal-1665 182 5 , , PUNCT american_scientific_journal-1665 182 6 we we PRON american_scientific_journal-1665 182 7 conclude conclude AUX american_scientific_journal-1665 182 8 theorem theorem VERB american_scientific_journal-1665 182 9 3.5 3.5 NUM american_scientific_journal-1665 182 10 . . PUNCT american_scientific_journal-1665 183 1 in in ADP american_scientific_journal-1665 183 2 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 183 3 βˆ’ βˆ’ ADP american_scientific_journal-1665 183 4 𝐺𝐺𝐺𝐺𝑅𝑅 𝐺𝐺𝐺𝐺𝑅𝑅 PROPN american_scientific_journal-1665 183 5 βˆ’affinely βˆ’affinely ADV american_scientific_journal-1665 183 6 connected connected ADJ american_scientific_journal-1665 183 7 space space NOUN american_scientific_journal-1665 183 8 , , PUNCT american_scientific_journal-1665 183 9 if if SCONJ american_scientific_journal-1665 183 10 the the DET american_scientific_journal-1665 183 11 directional directional ADJ american_scientific_journal-1665 183 12 derivative derivative NOUN american_scientific_journal-1665 183 13 of of ADP american_scientific_journal-1665 183 14 covariant covariant ADJ american_scientific_journal-1665 183 15 vector vector NOUN american_scientific_journal-1665 183 16 field field NOUN american_scientific_journal-1665 183 17 and and CCONJ american_scientific_journal-1665 183 18 covariant covariant ADJ american_scientific_journal-1665 183 19 tensor tensor NOUN american_scientific_journal-1665 183 20 of of ADP american_scientific_journal-1665 183 21 second second ADJ american_scientific_journal-1665 183 22 order order NOUN american_scientific_journal-1665 183 23 are be AUX american_scientific_journal-1665 183 24 vanish vanish VERB american_scientific_journal-1665 183 25 , , PUNCT american_scientific_journal-1665 183 26 then then ADV american_scientific_journal-1665 183 27 the the DET american_scientific_journal-1665 183 28 β„Ž(𝑣𝑣 β„Ž(𝑣𝑣 NUM american_scientific_journal-1665 183 29 ) ) PUNCT american_scientific_journal-1665 183 30 – – PUNCT american_scientific_journal-1665 183 31 torsion torsion NOUN american_scientific_journal-1665 183 32 tensor tensor NOUN american_scientific_journal-1665 183 33 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 183 34 𝑖𝑖 𝑖𝑖 VERB american_scientific_journal-1665 183 35 , , PUNCT american_scientific_journal-1665 183 36 the the DET american_scientific_journal-1665 183 37 deviation deviation NOUN american_scientific_journal-1665 183 38 tensor tensor NOUN american_scientific_journal-1665 183 39 π»π»β„Ž π»π»β„Ž PROPN american_scientific_journal-1665 183 40 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 183 41 , , PUNCT american_scientific_journal-1665 183 42 the the DET american_scientific_journal-1665 183 43 curvature curvature NOUN american_scientific_journal-1665 183 44 vector vector NOUN american_scientific_journal-1665 183 45 𝐻𝐻𝑗𝑗 𝐻𝐻𝑗𝑗 PROPN american_scientific_journal-1665 183 46 , , PUNCT american_scientific_journal-1665 183 47 the the DET american_scientific_journal-1665 183 48 curvature curvature NOUN american_scientific_journal-1665 183 49 scalar scalar ADJ american_scientific_journal-1665 183 50 𝐻𝐻 𝐻𝐻 NOUN american_scientific_journal-1665 183 51 and and CCONJ american_scientific_journal-1665 183 52 the the DET american_scientific_journal-1665 183 53 tensor tensor NOUN american_scientific_journal-1665 183 54 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž 𝐻𝐻𝑗𝑗𝑖𝑖.β„Ž NOUN american_scientific_journal-1665 183 55 are be AUX american_scientific_journal-1665 183 56 all all PRON american_scientific_journal-1665 183 57 generalized generalized ADJ american_scientific_journal-1665 183 58 birecurrent birecurrent NOUN american_scientific_journal-1665 183 59 . . PUNCT american_scientific_journal-1665 184 1 in in ADP american_scientific_journal-1665 184 2 view view NOUN american_scientific_journal-1665 184 3 of of ADP american_scientific_journal-1665 184 4 ( ( PUNCT american_scientific_journal-1665 184 5 1.22 1.22 NUM american_scientific_journal-1665 184 6 ) ) PUNCT american_scientific_journal-1665 184 7 , , PUNCT american_scientific_journal-1665 184 8 the the DET american_scientific_journal-1665 184 9 equation equation NOUN american_scientific_journal-1665 184 10 ( ( PUNCT american_scientific_journal-1665 184 11 2.14 2.14 NUM american_scientific_journal-1665 184 12 ) ) PUNCT american_scientific_journal-1665 184 13 can can AUX american_scientific_journal-1665 184 14 be be AUX american_scientific_journal-1665 184 15 written write VERB american_scientific_journal-1665 184 16 as as ADP american_scientific_journal-1665 184 17 ( ( PUNCT american_scientific_journal-1665 184 18 3.4 3.4 NUM american_scientific_journal-1665 184 19 ) ) PUNCT american_scientific_journal-1665 184 20 πœ†πœ†β„“ πœ†πœ†β„“ NOUN american_scientific_journal-1665 184 21 πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š πΎπΎπ‘—π‘—π‘—π‘—β„Ž|π‘šπ‘š ADJ american_scientific_journal-1665 184 22 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 185 1 + + CCONJ american_scientific_journal-1665 185 2 πœ†πœ†β„ŽπΎπΎπ‘—π‘—β„“π‘—π‘—|π‘šπ‘š πœ†πœ†β„ŽπΎπΎπ‘—π‘—β„“π‘—π‘—|π‘šπ‘š NUM american_scientific_journal-1665 185 3 𝑖𝑖 𝑖𝑖 PUNCT american_scientific_journal-1665 186 1 + + CCONJ american_scientific_journal-1665 186 2 πœ†πœ†π‘—π‘—πΎπΎπ‘—π‘—β„Žβ„“|π‘šπ‘š πœ†πœ†π‘—π‘—πΎπΎπ‘—π‘—β„Žβ„“|π‘šπ‘š ADJ american_scientific_journal-1665 186 3 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 187 1 + + CCONJ american_scientific_journal-1665 187 2 π‘π‘β„“π‘šπ‘š π‘π‘β„“π‘šπ‘š ADJ american_scientific_journal-1665 187 3 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– PROPN american_scientific_journal-1665 187 4 + + CCONJ american_scientific_journal-1665 187 5 π‘π‘β„Žπ‘šπ‘š π‘π‘β„Žπ‘šπ‘š PROPN american_scientific_journal-1665 187 6 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 187 7 + + CCONJ american_scientific_journal-1665 187 8 π‘π‘π‘—π‘—π‘šπ‘š π‘π‘π‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 187 9 πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– NOUN american_scientific_journal-1665 187 10 = = SYM american_scientific_journal-1665 187 11 0 0 X american_scientific_journal-1665 187 12 . . PUNCT american_scientific_journal-1665 188 1 in in ADP american_scientific_journal-1665 188 2 view view NOUN american_scientific_journal-1665 188 3 of of ADP american_scientific_journal-1665 188 4 ( ( PUNCT american_scientific_journal-1665 188 5 1.23 1.23 NUM american_scientific_journal-1665 188 6 ) ) PUNCT american_scientific_journal-1665 188 7 , , PUNCT american_scientific_journal-1665 188 8 ( ( PUNCT american_scientific_journal-1665 188 9 3.4 3.4 NUM american_scientific_journal-1665 188 10 ) ) PUNCT american_scientific_journal-1665 188 11 reduces reduce VERB american_scientific_journal-1665 188 12 to to PART american_scientific_journal-1665 188 13 ( ( PUNCT american_scientific_journal-1665 188 14 πœ†πœ†β„“ πœ†πœ†β„“ PROPN american_scientific_journal-1665 188 15 πœ†πœ†π‘šπ‘š πœ†πœ†π‘šπ‘š PROPN american_scientific_journal-1665 188 16 + + CCONJ american_scientific_journal-1665 188 17 π‘π‘π‘™π‘™π‘šπ‘š π‘π‘π‘™π‘™π‘šπ‘š PROPN american_scientific_journal-1665 188 18 ) ) PUNCT american_scientific_journal-1665 189 1 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 189 2 + + CCONJ american_scientific_journal-1665 189 3 ( ( PUNCT american_scientific_journal-1665 189 4 πœ†πœ†β„Ž πœ†πœ†β„Ž NOUN american_scientific_journal-1665 189 5 πœ†πœ†π‘šπ‘š+ πœ†πœ†π‘šπ‘š+ X american_scientific_journal-1665 189 6 π‘π‘β„Žπ‘šπ‘š π‘π‘β„Žπ‘šπ‘š NOUN american_scientific_journal-1665 189 7 ) ) PUNCT american_scientific_journal-1665 190 1 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 190 2 + + CCONJ american_scientific_journal-1665 190 3 ( ( PUNCT american_scientific_journal-1665 190 4 πœ†πœ†π‘—π‘— πœ†πœ†π‘—π‘— INTJ american_scientific_journal-1665 190 5 πœ†πœ†π‘šπ‘š+ πœ†πœ†π‘šπ‘š+ X american_scientific_journal-1665 190 6 π‘π‘π‘—π‘—π‘šπ‘š π‘π‘π‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 190 7 ) ) PUNCT american_scientific_journal-1665 191 1 πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– NOUN american_scientific_journal-1665 191 2 = = SYM american_scientific_journal-1665 191 3 0 0 NUM american_scientific_journal-1665 191 4 which which PRON american_scientific_journal-1665 191 5 can can AUX american_scientific_journal-1665 191 6 be be AUX american_scientific_journal-1665 191 7 written write VERB american_scientific_journal-1665 191 8 as as ADP american_scientific_journal-1665 191 9 ( ( PUNCT american_scientific_journal-1665 191 10 3.5 3.5 NUM american_scientific_journal-1665 191 11 ) ) PUNCT american_scientific_journal-1665 191 12 π‘Žπ‘Žβ„“π‘šπ‘š π‘Žπ‘Žβ„“π‘šπ‘š NOUN american_scientific_journal-1665 191 13 πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– πΎπΎπ‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 191 14 + + NUM american_scientific_journal-1665 191 15 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 191 16 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 𝐾𝐾𝑗𝑗ℓ𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 191 17 + + NUM american_scientific_journal-1665 191 18 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 191 19 πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– πΎπΎπ‘—π‘—β„Žβ„“π‘–π‘– NOUN american_scientific_journal-1665 191 20 = = SYM american_scientific_journal-1665 191 21 0 0 NUM american_scientific_journal-1665 191 22 , , PUNCT american_scientific_journal-1665 191 23 where where SCONJ american_scientific_journal-1665 191 24 π‘Žπ‘Žπ‘Ÿπ‘Ÿπ‘šπ‘š π‘Žπ‘Žπ‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 191 25 = = SYM american_scientific_journal-1665 192 1 πœ†πœ†π‘Ÿπ‘Ÿ πœ†πœ†π‘Ÿπ‘Ÿ NOUN american_scientific_journal-1665 192 2 πœ†πœ†π‘šπ‘š+ πœ†πœ†π‘šπ‘š+ X american_scientific_journal-1665 193 1 π‘π‘π‘Ÿπ‘Ÿπ‘šπ‘š π‘π‘π‘Ÿπ‘Ÿπ‘šπ‘š NOUN american_scientific_journal-1665 193 2 is be AUX american_scientific_journal-1665 193 3 covariant covariant ADJ american_scientific_journal-1665 193 4 tensor tensor NOUN american_scientific_journal-1665 193 5 field field NOUN american_scientific_journal-1665 193 6 of of ADP american_scientific_journal-1665 193 7 second second ADJ american_scientific_journal-1665 193 8 order order NOUN american_scientific_journal-1665 193 9 . . PUNCT american_scientific_journal-1665 194 1 65- 65- X american_scientific_journal-1665 194 2 ) ) PUNCT american_scientific_journal-1665 194 3 volume volume NOUN american_scientific_journal-1665 194 4 20 20 NUM american_scientific_journal-1665 194 5 , , PUNCT american_scientific_journal-1665 194 6 no no DET american_scientific_journal-1665 194 7 1 1 NUM american_scientific_journal-1665 194 8 , , PUNCT american_scientific_journal-1665 194 9 pp pp ADP american_scientific_journal-1665 194 10 522016 522016 NUM american_scientific_journal-1665 194 11 ( ( PUNCT american_scientific_journal-1665 194 12 ) ) PUNCT american_scientific_journal-1665 194 13 research research NOUN american_scientific_journal-1665 194 14 journal journal NOUN american_scientific_journal-1665 194 15 for for ADP american_scientific_journal-1665 194 16 engineering engineering NOUN american_scientific_journal-1665 194 17 , , PUNCT american_scientific_journal-1665 194 18 technology technology NOUN american_scientific_journal-1665 194 19 , , PUNCT american_scientific_journal-1665 194 20 and and CCONJ american_scientific_journal-1665 194 21 sciences science NOUN american_scientific_journal-1665 194 22 ( ( PUNCT american_scientific_journal-1665 194 23 asrjets asrjet NOUN american_scientific_journal-1665 194 24 scientificamerican scientificamerican VERB american_scientific_journal-1665 194 25 63 63 NUM american_scientific_journal-1665 194 26 transvecting transvecte VERB american_scientific_journal-1665 194 27 ( ( PUNCT american_scientific_journal-1665 194 28 3.5 3.5 NUM american_scientific_journal-1665 194 29 ) ) PUNCT american_scientific_journal-1665 194 30 by by ADP american_scientific_journal-1665 194 31 𝑦𝑦𝑗𝑗 𝑦𝑦𝑗𝑗 NOUN american_scientific_journal-1665 194 32 , , PUNCT american_scientific_journal-1665 194 33 using use VERB american_scientific_journal-1665 194 34 ( ( PUNCT american_scientific_journal-1665 194 35 1.1a 1.1a NOUN american_scientific_journal-1665 194 36 ) ) PUNCT american_scientific_journal-1665 194 37 and and CCONJ american_scientific_journal-1665 194 38 ( ( PUNCT american_scientific_journal-1665 194 39 1.6 1.6 NUM american_scientific_journal-1665 194 40 ) ) PUNCT american_scientific_journal-1665 194 41 , , PUNCT american_scientific_journal-1665 194 42 we we PRON american_scientific_journal-1665 194 43 get get VERB american_scientific_journal-1665 194 44 ( ( PUNCT american_scientific_journal-1665 194 45 3.6 3.6 NUM american_scientific_journal-1665 194 46 ) ) PUNCT american_scientific_journal-1665 194 47 π‘Žπ‘Žβ„“π‘šπ‘š π‘Žπ‘Žβ„“π‘šπ‘š NOUN american_scientific_journal-1665 195 1 π»π»π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 195 2 + + NUM american_scientific_journal-1665 195 3 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 195 4 𝐻𝐻ℓ𝑗𝑗𝑖𝑖 𝐻𝐻ℓ𝑗𝑗𝑖𝑖 PROPN american_scientific_journal-1665 195 5 + + NUM american_scientific_journal-1665 195 6 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š ADJ american_scientific_journal-1665 195 7 π»π»β„Žβ„“π‘–π‘– π»π»β„Žβ„“π‘–π‘– PROPN american_scientific_journal-1665 195 8 = = SYM american_scientific_journal-1665 195 9 0 0 NUM american_scientific_journal-1665 195 10 . . PUNCT american_scientific_journal-1665 196 1 thus thus ADV american_scientific_journal-1665 196 2 , , PUNCT american_scientific_journal-1665 196 3 we we PRON american_scientific_journal-1665 196 4 conclude conclude AUX american_scientific_journal-1665 196 5 theorem theorem VERB american_scientific_journal-1665 196 6 3.6 3.6 NUM american_scientific_journal-1665 196 7 . . PUNCT american_scientific_journal-1665 197 1 in in ADP american_scientific_journal-1665 197 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘… πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘… ADV american_scientific_journal-1665 197 3 – – PUNCT american_scientific_journal-1665 197 4 affinely affinely ADV american_scientific_journal-1665 197 5 connected connected ADJ american_scientific_journal-1665 197 6 space space NOUN american_scientific_journal-1665 197 7 , , PUNCT american_scientific_journal-1665 197 8 the the DET american_scientific_journal-1665 197 9 identities identity NOUN american_scientific_journal-1665 197 10 ( ( PUNCT american_scientific_journal-1665 197 11 3.5 3.5 NUM american_scientific_journal-1665 197 12 ) ) PUNCT american_scientific_journal-1665 197 13 and and CCONJ american_scientific_journal-1665 197 14 ( ( PUNCT american_scientific_journal-1665 197 15 3.6 3.6 NUM american_scientific_journal-1665 197 16 ) ) PUNCT american_scientific_journal-1665 197 17 are be AUX american_scientific_journal-1665 197 18 hold hold VERB american_scientific_journal-1665 197 19 good good ADJ american_scientific_journal-1665 197 20 . . PUNCT american_scientific_journal-1665 198 1 contracting contract VERB american_scientific_journal-1665 198 2 the the DET american_scientific_journal-1665 198 3 indices index NOUN american_scientific_journal-1665 198 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 198 5 and and CCONJ american_scientific_journal-1665 198 6 β„“ β„“ PROPN american_scientific_journal-1665 198 7 in in ADP american_scientific_journal-1665 198 8 ( ( PUNCT american_scientific_journal-1665 198 9 3.5 3.5 NUM american_scientific_journal-1665 198 10 ) ) PUNCT american_scientific_journal-1665 198 11 , , PUNCT american_scientific_journal-1665 198 12 using use VERB american_scientific_journal-1665 198 13 ( ( PUNCT american_scientific_journal-1665 198 14 1.3 1.3 NUM american_scientific_journal-1665 198 15 ) ) PUNCT american_scientific_journal-1665 198 16 and and CCONJ american_scientific_journal-1665 198 17 ( ( PUNCT american_scientific_journal-1665 198 18 1.5 1.5 NUM american_scientific_journal-1665 198 19 ) ) PUNCT american_scientific_journal-1665 198 20 , , PUNCT american_scientific_journal-1665 198 21 we we PRON american_scientific_journal-1665 198 22 get get VERB american_scientific_journal-1665 198 23 ( ( PUNCT american_scientific_journal-1665 198 24 3.7 3.7 NUM american_scientific_journal-1665 198 25 ) ) PUNCT american_scientific_journal-1665 198 26 π‘Žπ‘Žπ‘–π‘–π‘šπ‘š π‘Žπ‘Žπ‘–π‘–π‘šπ‘š NOUN american_scientific_journal-1665 199 1 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 199 2 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 199 3 βˆ’ βˆ’ PROPN american_scientific_journal-1665 199 4 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 199 5 𝐾𝐾𝑗𝑗𝑗𝑗 𝐾𝐾𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 199 6 + + NUM american_scientific_journal-1665 199 7 π‘Žπ‘Žπ‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Ž π‘Žπ‘Žπ‘—π‘—π‘šπ‘šπΎπΎπ‘—π‘—β„Ž X american_scientific_journal-1665 199 8 = = SYM american_scientific_journal-1665 199 9 0 0 NUM american_scientific_journal-1665 199 10 which which PRON american_scientific_journal-1665 199 11 can can AUX american_scientific_journal-1665 199 12 be be AUX american_scientific_journal-1665 199 13 written write VERB american_scientific_journal-1665 199 14 as as ADP american_scientific_journal-1665 199 15 ( ( PUNCT american_scientific_journal-1665 199 16 3.8 3.8 NUM american_scientific_journal-1665 199 17 ) ) PUNCT american_scientific_journal-1665 199 18 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 199 19 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 199 20 = = PUNCT american_scientific_journal-1665 199 21 οΏ½ οΏ½ PROPN american_scientific_journal-1665 199 22 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 199 23 πΎπΎπ‘—π‘—π‘—π‘—βˆ’ πΎπΎπ‘—π‘—π‘—π‘—βˆ’ PROPN american_scientific_journal-1665 199 24 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š PROPN american_scientific_journal-1665 199 25 πΎπΎπ‘—π‘—β„Ž πΎπΎπ‘—π‘—β„Ž PROPN american_scientific_journal-1665 199 26 οΏ½ οΏ½ PROPN american_scientific_journal-1665 199 27 π‘Žπ‘Žπ‘π‘π‘šπ‘š π‘Žπ‘Žπ‘π‘π‘šπ‘š PROPN american_scientific_journal-1665 199 28 . . PUNCT american_scientific_journal-1665 200 1 thus thus ADV american_scientific_journal-1665 200 2 , , PUNCT american_scientific_journal-1665 200 3 we we PRON american_scientific_journal-1665 200 4 conclude conclude AUX american_scientific_journal-1665 200 5 theorem theorem VERB american_scientific_journal-1665 200 6 3.7 3.7 NUM american_scientific_journal-1665 200 7 . . PUNCT american_scientific_journal-1665 201 1 in in ADP american_scientific_journal-1665 201 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 201 3 connected connected ADJ american_scientific_journal-1665 201 4 space space NOUN american_scientific_journal-1665 201 5 , , PUNCT american_scientific_journal-1665 201 6 cartan cartan PROPN american_scientific_journal-1665 201 7 's 's PART american_scientific_journal-1665 201 8 fourth fourth ADJ american_scientific_journal-1665 201 9 curvature curvature NOUN american_scientific_journal-1665 201 10 tensor tensor NOUN american_scientific_journal-1665 201 11 πΎπΎπ‘—π‘—π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 201 12 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 201 13 is be AUX american_scientific_journal-1665 201 14 defined define VERB american_scientific_journal-1665 201 15 by by ADP american_scientific_journal-1665 201 16 ( ( PUNCT american_scientific_journal-1665 201 17 3.8 3.8 NUM american_scientific_journal-1665 201 18 ) ) PUNCT american_scientific_journal-1665 201 19 . . PUNCT american_scientific_journal-1665 202 1 in in ADP american_scientific_journal-1665 202 2 view view NOUN american_scientific_journal-1665 202 3 of of ADP american_scientific_journal-1665 202 4 ( ( PUNCT american_scientific_journal-1665 202 5 1.2b 1.2b NOUN american_scientific_journal-1665 202 6 ) ) PUNCT american_scientific_journal-1665 202 7 and and CCONJ american_scientific_journal-1665 202 8 ( ( PUNCT american_scientific_journal-1665 202 9 1.22 1.22 NUM american_scientific_journal-1665 202 10 ) ) PUNCT american_scientific_journal-1665 202 11 , , PUNCT american_scientific_journal-1665 202 12 ( ( PUNCT american_scientific_journal-1665 202 13 1.7 1.7 NUM american_scientific_journal-1665 202 14 ) ) PUNCT american_scientific_journal-1665 202 15 reduces reduce VERB american_scientific_journal-1665 202 16 to to ADP american_scientific_journal-1665 202 17 ( ( PUNCT american_scientific_journal-1665 202 18 3.9 3.9 NUM american_scientific_journal-1665 202 19 ) ) PUNCT american_scientific_journal-1665 202 20 𝐻𝐻 𝐻𝐻 NOUN american_scientific_journal-1665 202 21 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 202 22 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 203 1 = = PUNCT american_scientific_journal-1665 203 2 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 203 3 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 203 4 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 203 5 . . PUNCT american_scientific_journal-1665 204 1 putting put VERB american_scientific_journal-1665 204 2 ( ( PUNCT american_scientific_journal-1665 204 3 3.9 3.9 NUM american_scientific_journal-1665 204 4 ) ) PUNCT american_scientific_journal-1665 204 5 in in ADP american_scientific_journal-1665 204 6 ( ( PUNCT american_scientific_journal-1665 204 7 3.5 3.5 NUM american_scientific_journal-1665 204 8 ) ) PUNCT american_scientific_journal-1665 204 9 , , PUNCT american_scientific_journal-1665 204 10 we we PRON american_scientific_journal-1665 204 11 get get VERB american_scientific_journal-1665 204 12 ( ( PUNCT american_scientific_journal-1665 204 13 3.10 3.10 NUM american_scientific_journal-1665 204 14 ) ) PUNCT american_scientific_journal-1665 204 15 π‘Žπ‘Žβ„“π‘šπ‘š π‘Žπ‘Žβ„“π‘šπ‘š NOUN american_scientific_journal-1665 205 1 π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– π»π»π‘—π‘—π‘—π‘—β„Žπ‘–π‘– NOUN american_scientific_journal-1665 205 2 + + NUM american_scientific_journal-1665 205 3 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 205 4 𝐻𝐻𝑗𝑗ℓ𝑗𝑗𝑖𝑖 𝐻𝐻𝑗𝑗ℓ𝑗𝑗𝑖𝑖 ADJ american_scientific_journal-1665 205 5 + + NUM american_scientific_journal-1665 205 6 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š NOUN american_scientific_journal-1665 205 7 π»π»π‘—π‘—β„Žβ„“π‘–π‘– π»π»π‘—π‘—β„Žβ„“π‘–π‘– PROPN american_scientific_journal-1665 205 8 = = SYM american_scientific_journal-1665 205 9 0 0 NUM american_scientific_journal-1665 205 10 . . PUNCT american_scientific_journal-1665 206 1 thus thus ADV american_scientific_journal-1665 206 2 , , PUNCT american_scientific_journal-1665 206 3 we we PRON american_scientific_journal-1665 206 4 conclude conclude AUX american_scientific_journal-1665 206 5 theorem theorem VERB american_scientific_journal-1665 206 6 3.8 3.8 NUM american_scientific_journal-1665 206 7 . . PUNCT american_scientific_journal-1665 207 1 in in ADP american_scientific_journal-1665 207 2 πΎπΎβ„Ž πΎπΎβ„Ž NOUN american_scientific_journal-1665 207 3 βˆ’ βˆ’ ADP american_scientific_journal-1665 207 4 𝐺𝐺𝐺𝐺𝑅𝑅 𝐺𝐺𝐺𝐺𝑅𝑅 VERB american_scientific_journal-1665 207 5 βˆ’ βˆ’ ADP american_scientific_journal-1665 207 6 affinely affinely ADV american_scientific_journal-1665 207 7 connected connected ADJ american_scientific_journal-1665 207 8 space space NOUN american_scientific_journal-1665 207 9 , , PUNCT american_scientific_journal-1665 207 10 berwald berwald NOUN american_scientific_journal-1665 207 11 curvature curvature NOUN american_scientific_journal-1665 207 12 tensor tensor NOUN american_scientific_journal-1665 207 13 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 207 14 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 207 15 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 207 16 coincide coincide NOUN american_scientific_journal-1665 207 17 with with ADP american_scientific_journal-1665 207 18 cartan cartan PROPN american_scientific_journal-1665 207 19 's 's PART american_scientific_journal-1665 207 20 fourth fourth ADJ american_scientific_journal-1665 207 21 curvature curvature NOUN american_scientific_journal-1665 207 22 tensor tensor NOUN american_scientific_journal-1665 207 23 𝐾𝐾 𝐾𝐾 PROPN american_scientific_journal-1665 207 24 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 207 25 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 207 26 and and CCONJ american_scientific_journal-1665 207 27 the the DET american_scientific_journal-1665 207 28 identity identity NOUN american_scientific_journal-1665 207 29 ( ( PUNCT american_scientific_journal-1665 207 30 3.10 3.10 NUM american_scientific_journal-1665 207 31 ) ) PUNCT american_scientific_journal-1665 207 32 holds hold VERB american_scientific_journal-1665 207 33 good good ADJ american_scientific_journal-1665 207 34 . . PUNCT american_scientific_journal-1665 208 1 contracting contract VERB american_scientific_journal-1665 208 2 the the DET american_scientific_journal-1665 208 3 indices index NOUN american_scientific_journal-1665 208 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 208 5 and and CCONJ american_scientific_journal-1665 208 6 β„“ β„“ PROPN american_scientific_journal-1665 208 7 in in ADP american_scientific_journal-1665 208 8 ( ( PUNCT american_scientific_journal-1665 208 9 3.10 3.10 NUM american_scientific_journal-1665 208 10 ) ) PUNCT american_scientific_journal-1665 208 11 , , PUNCT american_scientific_journal-1665 208 12 using use VERB american_scientific_journal-1665 208 13 ( ( PUNCT american_scientific_journal-1665 208 14 1.12 1.12 NUM american_scientific_journal-1665 208 15 ) ) PUNCT american_scientific_journal-1665 208 16 , , PUNCT american_scientific_journal-1665 208 17 ( ( PUNCT american_scientific_journal-1665 208 18 1.10b 1.10b NUM american_scientific_journal-1665 208 19 ) ) PUNCT american_scientific_journal-1665 208 20 and and CCONJ american_scientific_journal-1665 208 21 the the DET american_scientific_journal-1665 208 22 skew skew ADJ american_scientific_journal-1665 208 23 - - PUNCT american_scientific_journal-1665 208 24 symmetric symmetric ADJ american_scientific_journal-1665 208 25 property property NOUN american_scientific_journal-1665 208 26 of of ADP american_scientific_journal-1665 208 27 berwald berwald NOUN american_scientific_journal-1665 208 28 curvature curvature NOUN american_scientific_journal-1665 208 29 tensor tensor NOUN american_scientific_journal-1665 208 30 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-1665 208 31 π‘—π‘—π‘—π‘—β„Ž π‘—π‘—π‘—π‘—β„Ž NOUN american_scientific_journal-1665 208 32 𝑖𝑖 𝑖𝑖 INTJ american_scientific_journal-1665 208 33 in in ADP american_scientific_journal-1665 208 34 it it PRON american_scientific_journal-1665 208 35 's be AUX american_scientific_journal-1665 208 36 last last ADJ american_scientific_journal-1665 208 37 two two NUM american_scientific_journal-1665 208 38 lower low ADJ american_scientific_journal-1665 208 39 indices index NOUN american_scientific_journal-1665 208 40 , , PUNCT american_scientific_journal-1665 208 41 we we PRON american_scientific_journal-1665 208 42 get get VERB american_scientific_journal-1665 208 43 π‘Žπ‘Žπ‘–π‘–π‘šπ‘š π‘Žπ‘Žπ‘–π‘–π‘šπ‘š ADP american_scientific_journal-1665 208 44 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 208 45 𝑖𝑖 𝑖𝑖 ADP american_scientific_journal-1665 209 1 βˆ’ βˆ’ PROPN american_scientific_journal-1665 209 2 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 209 3 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 209 4 + + PUNCT american_scientific_journal-1665 209 5 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 209 6 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 209 7 = = PUNCT american_scientific_journal-1665 209 8 0 0 PROPN american_scientific_journal-1665 209 9 . . NOUN american_scientific_journal-1665 209 10 which which PRON american_scientific_journal-1665 209 11 can can AUX american_scientific_journal-1665 209 12 be be AUX american_scientific_journal-1665 209 13 written write VERB american_scientific_journal-1665 209 14 as as ADP american_scientific_journal-1665 209 15 ( ( PUNCT american_scientific_journal-1665 209 16 3.11 3.11 NUM american_scientific_journal-1665 209 17 ) ) PUNCT american_scientific_journal-1665 209 18 π»π»π‘—π‘—π‘—π‘—β„Ž π»π»π‘—π‘—π‘—π‘—β„Ž PROPN american_scientific_journal-1665 209 19 𝑖𝑖 𝑖𝑖 NOUN american_scientific_journal-1665 210 1 = = PUNCT american_scientific_journal-1665 210 2 οΏ½ οΏ½ PROPN american_scientific_journal-1665 210 3 π‘Žπ‘Žβ„Žπ‘šπ‘š π‘Žπ‘Žβ„Žπ‘šπ‘š NOUN american_scientific_journal-1665 210 4 π»π»π‘—π‘—π‘—π‘—βˆ’ π»π»π‘—π‘—π‘—π‘—βˆ’ PROPN american_scientific_journal-1665 210 5 π‘Žπ‘Žπ‘—π‘—π‘šπ‘š π‘Žπ‘Žπ‘—π‘—π‘šπ‘š VERB american_scientific_journal-1665 210 6 π»π»π‘—π‘—β„Ž π»π»π‘—π‘—β„Ž PROPN american_scientific_journal-1665 210 7 οΏ½ οΏ½ PROPN american_scientific_journal-1665 210 8 π‘Žπ‘Žπ‘π‘π‘šπ‘š π‘Žπ‘Žπ‘π‘π‘šπ‘š NOUN american_scientific_journal-1665 210 9 . . PUNCT american_scientific_journal-1665 211 1 65- 65- X american_scientific_journal-1665 211 2 ) ) PUNCT american_scientific_journal-1665 211 3 volume volume NOUN american_scientific_journal-1665 211 4 20 20 NUM american_scientific_journal-1665 211 5 , , PUNCT american_scientific_journal-1665 211 6 no no DET american_scientific_journal-1665 211 7 1 1 NUM american_scientific_journal-1665 211 8 , , PUNCT american_scientific_journal-1665 211 9 pp pp ADP american_scientific_journal-1665 211 10 522016 522016 NUM american_scientific_journal-1665 211 11 ( ( PUNCT american_scientific_journal-1665 211 12 ) ) PUNCT american_scientific_journal-1665 211 13 research research NOUN american_scientific_journal-1665 211 14 journal journal NOUN american_scientific_journal-1665 211 15 for for ADP american_scientific_journal-1665 211 16 engineering engineering NOUN american_scientific_journal-1665 211 17 , , PUNCT american_scientific_journal-1665 211 18 technology technology NOUN american_scientific_journal-1665 211 19 , , PUNCT american_scientific_journal-1665 211 20 and and CCONJ american_scientific_journal-1665 211 21 sciences science NOUN american_scientific_journal-1665 211 22 ( ( PUNCT american_scientific_journal-1665 211 23 asrjets asrjet NOUN american_scientific_journal-1665 211 24 scientificamerican scientificamerican VERB american_scientific_journal-1665 211 25 64 64 NUM american_scientific_journal-1665 211 26 thus thus ADV american_scientific_journal-1665 211 27 , , PUNCT american_scientific_journal-1665 211 28 we we PRON american_scientific_journal-1665 211 29 conclude conclude AUX american_scientific_journal-1665 211 30 theorem theorem VERB american_scientific_journal-1665 211 31 3.9 3.9 NUM american_scientific_journal-1665 211 32 . . PUNCT american_scientific_journal-1665 212 1 in in ADP american_scientific_journal-1665 212 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 212 3 connected connected ADJ american_scientific_journal-1665 212 4 space space NOUN american_scientific_journal-1665 212 5 , , PUNCT american_scientific_journal-1665 212 6 berwald berwald NOUN american_scientific_journal-1665 212 7 curvature curvature NOUN american_scientific_journal-1665 212 8 tensor tensor NOUN american_scientific_journal-1665 212 9 is be AUX american_scientific_journal-1665 212 10 defined define VERB american_scientific_journal-1665 212 11 by by ADP american_scientific_journal-1665 212 12 ( ( PUNCT american_scientific_journal-1665 212 13 3.11 3.11 NUM american_scientific_journal-1665 212 14 ) ) PUNCT american_scientific_journal-1665 212 15 . . PUNCT american_scientific_journal-1665 213 1 contracting contract VERB american_scientific_journal-1665 213 2 the the DET american_scientific_journal-1665 213 3 indices index NOUN american_scientific_journal-1665 213 4 𝑖𝑖 𝑖𝑖 X american_scientific_journal-1665 213 5 and and CCONJ american_scientific_journal-1665 213 6 β„Ž β„Ž PROPN american_scientific_journal-1665 213 7 in in ADP american_scientific_journal-1665 213 8 ( ( PUNCT american_scientific_journal-1665 213 9 3.9 3.9 NUM american_scientific_journal-1665 213 10 ) ) PUNCT american_scientific_journal-1665 213 11 , , PUNCT american_scientific_journal-1665 213 12 using use VERB american_scientific_journal-1665 213 13 ( ( PUNCT american_scientific_journal-1665 213 14 1.12 1.12 NUM american_scientific_journal-1665 213 15 ) ) PUNCT american_scientific_journal-1665 213 16 and and CCONJ american_scientific_journal-1665 213 17 ( ( PUNCT american_scientific_journal-1665 213 18 1.5 1.5 NUM american_scientific_journal-1665 213 19 ) ) PUNCT american_scientific_journal-1665 213 20 , , PUNCT american_scientific_journal-1665 213 21 we we PRON american_scientific_journal-1665 213 22 get get VERB american_scientific_journal-1665 213 23 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 213 24 = = SYM american_scientific_journal-1665 213 25 𝐾𝐾𝑗𝑗𝑗𝑗 𝐾𝐾𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 213 26 . . PUNCT american_scientific_journal-1665 214 1 thus thus ADV american_scientific_journal-1665 214 2 , , PUNCT american_scientific_journal-1665 214 3 we we PRON american_scientific_journal-1665 214 4 conclude conclude AUX american_scientific_journal-1665 214 5 theorem theorem VERB american_scientific_journal-1665 214 6 3.10 3.10 NUM american_scientific_journal-1665 214 7 . . PUNCT american_scientific_journal-1665 215 1 in in ADP american_scientific_journal-1665 215 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 215 3 connected connected ADJ american_scientific_journal-1665 215 4 space space NOUN american_scientific_journal-1665 215 5 , , PUNCT american_scientific_journal-1665 215 6 ricci ricci PROPN american_scientific_journal-1665 215 7 tensor tensor NOUN american_scientific_journal-1665 215 8 𝐻𝐻𝑗𝑗𝑗𝑗 𝐻𝐻𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 215 9 in in ADP american_scientific_journal-1665 215 10 sense sense NOUN american_scientific_journal-1665 215 11 of of ADP american_scientific_journal-1665 215 12 berwald berwald NOUN american_scientific_journal-1665 215 13 coincide coincide NOUN american_scientific_journal-1665 215 14 with with ADP american_scientific_journal-1665 215 15 ricci ricci PROPN american_scientific_journal-1665 215 16 tensor tensor NOUN american_scientific_journal-1665 215 17 𝐾𝐾𝑗𝑗𝑗𝑗 𝐾𝐾𝑗𝑗𝑗𝑗 PROPN american_scientific_journal-1665 215 18 of of ADP american_scientific_journal-1665 215 19 cartan cartan PROPN american_scientific_journal-1665 215 20 's 's PART american_scientific_journal-1665 215 21 fourth fourth ADJ american_scientific_journal-1665 215 22 curvature curvature NOUN american_scientific_journal-1665 215 23 . . PUNCT american_scientific_journal-1665 216 1 transvecting transvecte VERB american_scientific_journal-1665 216 2 ( ( PUNCT american_scientific_journal-1665 216 3 3.9 3.9 NUM american_scientific_journal-1665 216 4 ) ) PUNCT american_scientific_journal-1665 216 5 by by ADP american_scientific_journal-1665 216 6 g𝑖𝑖𝑖𝑖 g𝑖𝑖𝑖𝑖 ADJ american_scientific_journal-1665 216 7 , , PUNCT american_scientific_journal-1665 216 8 using use VERB american_scientific_journal-1665 216 9 ( ( PUNCT american_scientific_journal-1665 216 10 1.1b 1.1b NUM american_scientific_journal-1665 216 11 ) ) PUNCT american_scientific_journal-1665 216 12 , , PUNCT american_scientific_journal-1665 216 13 ( ( PUNCT american_scientific_journal-1665 216 14 1.15 1.15 NUM american_scientific_journal-1665 216 15 ) ) PUNCT american_scientific_journal-1665 216 16 and and CCONJ american_scientific_journal-1665 216 17 ( ( PUNCT american_scientific_journal-1665 216 18 1.4 1.4 NUM american_scientific_journal-1665 216 19 ) ) PUNCT american_scientific_journal-1665 216 20 , , PUNCT american_scientific_journal-1665 216 21 we we PRON american_scientific_journal-1665 216 22 get get VERB american_scientific_journal-1665 216 23 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 216 24 = = SYM american_scientific_journal-1665 216 25 πΎπΎπ‘—π‘—π‘–π‘–π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 216 26 . . PUNCT american_scientific_journal-1665 217 1 thus thus ADV american_scientific_journal-1665 217 2 , , PUNCT american_scientific_journal-1665 217 3 we we PRON american_scientific_journal-1665 217 4 conclude conclude AUX american_scientific_journal-1665 217 5 theorem theorem VERB american_scientific_journal-1665 217 6 3.11 3.11 NUM american_scientific_journal-1665 217 7 . . PUNCT american_scientific_journal-1665 218 1 in in ADP american_scientific_journal-1665 218 2 πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely πΎπΎβ„Žβ€“πΊπΊπΊπΊπ‘…π‘…β€“affinely ADV american_scientific_journal-1665 218 3 connected connected ADJ american_scientific_journal-1665 218 4 space space NOUN american_scientific_journal-1665 218 5 , , PUNCT american_scientific_journal-1665 218 6 the the DET american_scientific_journal-1665 218 7 associate associate ADJ american_scientific_journal-1665 218 8 curvature curvature NOUN american_scientific_journal-1665 218 9 tensor tensor NOUN american_scientific_journal-1665 218 10 π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž π»π»π‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 218 11 of of ADP american_scientific_journal-1665 218 12 berwald berwald NOUN american_scientific_journal-1665 218 13 curvature curvature NOUN american_scientific_journal-1665 218 14 tensor tensor NOUN american_scientific_journal-1665 218 15 coincide coincide NOUN american_scientific_journal-1665 218 16 with with ADP american_scientific_journal-1665 218 17 the the DET american_scientific_journal-1665 218 18 associate associate ADJ american_scientific_journal-1665 218 19 curvature curvature NOUN american_scientific_journal-1665 218 20 tensor tensor NOUN american_scientific_journal-1665 218 21 πΎπΎπ‘—π‘—π‘–π‘–π‘—π‘—β„Ž πΎπΎπ‘—π‘—π‘–π‘–π‘—π‘—β„Ž PROPN american_scientific_journal-1665 218 22 of of ADP american_scientific_journal-1665 218 23 cartan cartan PROPN american_scientific_journal-1665 218 24 's 's PART american_scientific_journal-1665 218 25 fourth fourth ADJ american_scientific_journal-1665 218 26 curvature curvature NOUN american_scientific_journal-1665 218 27 tensor tensor NOUN american_scientific_journal-1665 218 28 . . PUNCT american_scientific_journal-1665 219 1 4 4 X american_scientific_journal-1665 219 2 . . X american_scientific_journal-1665 219 3 conclusion conclusion NOUN american_scientific_journal-1665 219 4 ( ( PUNCT american_scientific_journal-1665 219 5 3.1 3.1 NUM american_scientific_journal-1665 219 6 ) ) PUNCT american_scientific_journal-1665 219 7 the the DET american_scientific_journal-1665 219 8 kh kh PROPN american_scientific_journal-1665 219 9 – – PUNCT american_scientific_journal-1665 219 10 generalized generalize VERB american_scientific_journal-1665 219 11 birecurrent birecurrent ADJ american_scientific_journal-1665 219 12 space space NOUN american_scientific_journal-1665 219 13 is be AUX american_scientific_journal-1665 219 14 called call VERB american_scientific_journal-1665 219 15 kh kh PROPN american_scientific_journal-1665 219 16 – – PUNCT american_scientific_journal-1665 219 17 generalized generalized ADJ american_scientific_journal-1665 219 18 birecurrent birecurrent NOUN american_scientific_journal-1665 219 19 affinely affinely ADV american_scientific_journal-1665 219 20 connected connect VERB american_scientific_journal-1665 219 21 if if SCONJ american_scientific_journal-1665 219 22 it it PRON american_scientific_journal-1665 219 23 satisfies satisfy VERB american_scientific_journal-1665 219 24 any any DET american_scientific_journal-1665 219 25 one one NUM american_scientific_journal-1665 219 26 of of ADP american_scientific_journal-1665 219 27 the the DET american_scientific_journal-1665 219 28 conditions condition NOUN american_scientific_journal-1665 219 29 ( ( PUNCT american_scientific_journal-1665 219 30 1.19 1.19 NUM american_scientific_journal-1665 219 31 ) ) PUNCT american_scientific_journal-1665 219 32 , , PUNCT american_scientific_journal-1665 219 33 ( ( PUNCT american_scientific_journal-1665 219 34 1.20 1.20 NUM american_scientific_journal-1665 219 35 ) ) PUNCT american_scientific_journal-1665 219 36 , , PUNCT american_scientific_journal-1665 219 37 ( ( PUNCT american_scientific_journal-1665 219 38 1.21 1.21 NUM american_scientific_journal-1665 219 39 ) ) PUNCT american_scientific_journal-1665 219 40 and and CCONJ american_scientific_journal-1665 219 41 ( ( PUNCT american_scientific_journal-1665 219 42 1.22 1.22 NUM american_scientific_journal-1665 219 43 ) ) PUNCT american_scientific_journal-1665 219 44 . . PUNCT american_scientific_journal-1665 220 1 ( ( PUNCT american_scientific_journal-1665 220 2 3.2 3.2 NUM american_scientific_journal-1665 220 3 ) ) PUNCT american_scientific_journal-1665 220 4 in in ADP american_scientific_journal-1665 220 5 kh kh PROPN american_scientific_journal-1665 220 6 – – PUNCT american_scientific_journal-1665 220 7 gbr gbr PROPN american_scientific_journal-1665 220 8 – – PUNCT american_scientific_journal-1665 220 9 affinely affinely ADV american_scientific_journal-1665 220 10 connected connected ADJ american_scientific_journal-1665 220 11 space space NOUN american_scientific_journal-1665 220 12 , , PUNCT american_scientific_journal-1665 220 13 if if SCONJ american_scientific_journal-1665 220 14 the the DET american_scientific_journal-1665 220 15 directional directional ADJ american_scientific_journal-1665 220 16 derivative derivative NOUN american_scientific_journal-1665 220 17 of of ADP american_scientific_journal-1665 220 18 covariant covariant ADJ american_scientific_journal-1665 220 19 vector vector NOUN american_scientific_journal-1665 220 20 field field NOUN american_scientific_journal-1665 220 21 and and CCONJ american_scientific_journal-1665 220 22 covariant covariant ADJ american_scientific_journal-1665 220 23 tensor tensor NOUN american_scientific_journal-1665 220 24 of of ADP american_scientific_journal-1665 220 25 second second ADJ american_scientific_journal-1665 220 26 order order NOUN american_scientific_journal-1665 220 27 are be AUX american_scientific_journal-1665 220 28 vanish vanish VERB american_scientific_journal-1665 220 29 , , PUNCT american_scientific_journal-1665 220 30 then then ADV american_scientific_journal-1665 220 31 berwald berwald NOUN american_scientific_journal-1665 220 32 curvature curvature NOUN american_scientific_journal-1665 220 33 tensor tensor NOUN american_scientific_journal-1665 220 34 hjkh hjkh NOUN american_scientific_journal-1665 220 35 i i PRON american_scientific_journal-1665 220 36 is be AUX american_scientific_journal-1665 220 37 generalized generalize VERB american_scientific_journal-1665 220 38 bireurrent bireurrent NOUN american_scientific_journal-1665 220 39 . . PUNCT american_scientific_journal-1665 221 1 ( ( PUNCT american_scientific_journal-1665 221 2 3.3 3.3 NUM american_scientific_journal-1665 221 3 ) ) PUNCT american_scientific_journal-1665 221 4 in in ADP american_scientific_journal-1665 221 5 kh kh PROPN american_scientific_journal-1665 221 6 βˆ’ βˆ’ PROPN american_scientific_journal-1665 221 7 gbr gbr PROPN american_scientific_journal-1665 221 8 βˆ’affinely βˆ’affinely ADV american_scientific_journal-1665 221 9 connected connect VERB american_scientific_journal-1665 221 10 space space NOUN american_scientific_journal-1665 221 11 , , PUNCT american_scientific_journal-1665 221 12 if if SCONJ american_scientific_journal-1665 221 13 the the DET american_scientific_journal-1665 221 14 directional directional ADJ american_scientific_journal-1665 221 15 derivative derivative NOUN american_scientific_journal-1665 221 16 of of ADP american_scientific_journal-1665 221 17 covariant covariant ADJ american_scientific_journal-1665 221 18 vector vector NOUN american_scientific_journal-1665 221 19 field field NOUN american_scientific_journal-1665 221 20 a a PRON american_scientific_journal-1665 221 21 and and CCONJ american_scientific_journal-1665 221 22 covariant covariant ADJ american_scientific_journal-1665 221 23 tensor tensor NOUN american_scientific_journal-1665 221 24 of of ADP american_scientific_journal-1665 221 25 second second ADJ american_scientific_journal-1665 221 26 order order NOUN american_scientific_journal-1665 221 27 are be AUX american_scientific_journal-1665 221 28 vanish vanish VERB american_scientific_journal-1665 221 29 , , PUNCT american_scientific_journal-1665 221 30 then then ADV american_scientific_journal-1665 221 31 the the DET american_scientific_journal-1665 221 32 h(v h(v PROPN american_scientific_journal-1665 221 33 ) ) PUNCT american_scientific_journal-1665 221 34 – – PUNCT american_scientific_journal-1665 221 35 torsion torsion NOUN american_scientific_journal-1665 221 36 tensor tensor NOUN american_scientific_journal-1665 221 37 hkh hkh NOUN american_scientific_journal-1665 222 1 i i PRON american_scientific_journal-1665 222 2 , , PUNCT american_scientific_journal-1665 222 3 the the DET american_scientific_journal-1665 222 4 deviation deviation NOUN american_scientific_journal-1665 222 5 tensor tensor NOUN american_scientific_journal-1665 222 6 hh hh PROPN american_scientific_journal-1665 222 7 i i PRON american_scientific_journal-1665 222 8 , , PUNCT american_scientific_journal-1665 222 9 the the DET american_scientific_journal-1665 222 10 curvature curvature NOUN american_scientific_journal-1665 222 11 vector vector PROPN american_scientific_journal-1665 222 12 hk hk PROPN american_scientific_journal-1665 222 13 , , PUNCT american_scientific_journal-1665 222 14 the the DET american_scientific_journal-1665 222 15 curvature curvature NOUN american_scientific_journal-1665 222 16 scalar scalar ADJ american_scientific_journal-1665 222 17 h h NOUN american_scientific_journal-1665 222 18 and and CCONJ american_scientific_journal-1665 222 19 the the DET american_scientific_journal-1665 222 20 tensor tensor NOUN american_scientific_journal-1665 222 21 hkp.h hkp.h PROPN american_scientific_journal-1665 222 22 are be AUX american_scientific_journal-1665 222 23 all all PRON american_scientific_journal-1665 222 24 generalized generalized ADJ american_scientific_journal-1665 222 25 birecurrent birecurrent NOUN american_scientific_journal-1665 222 26 . . PUNCT american_scientific_journal-1665 223 1 ( ( PUNCT american_scientific_journal-1665 223 2 3.4 3.4 NUM american_scientific_journal-1665 223 3 ) ) PUNCT american_scientific_journal-1665 223 4 in in ADP american_scientific_journal-1665 223 5 kh kh PROPN american_scientific_journal-1665 223 6 – – PUNCT american_scientific_journal-1665 223 7 gbr gbr PROPN american_scientific_journal-1665 223 8 – – PUNCT american_scientific_journal-1665 223 9 affinely affinely ADV american_scientific_journal-1665 223 10 connected connected ADJ american_scientific_journal-1665 223 11 space space NOUN american_scientific_journal-1665 223 12 , , PUNCT american_scientific_journal-1665 223 13 cartan cartan PROPN american_scientific_journal-1665 223 14 's 's PART american_scientific_journal-1665 223 15 fourth fourth ADJ american_scientific_journal-1665 223 16 curvature curvature NOUN american_scientific_journal-1665 223 17 tensor tensor NOUN american_scientific_journal-1665 223 18 kjkh kjkh NOUN american_scientific_journal-1665 223 19 p p NOUN american_scientific_journal-1665 223 20 is be AUX american_scientific_journal-1665 223 21 defined define VERB american_scientific_journal-1665 223 22 by by ADP american_scientific_journal-1665 223 23 ( ( PUNCT american_scientific_journal-1665 223 24 3.8 3.8 NUM american_scientific_journal-1665 223 25 ) ) PUNCT american_scientific_journal-1665 223 26 . . PUNCT american_scientific_journal-1665 224 1 ( ( PUNCT american_scientific_journal-1665 224 2 3.5 3.5 NUM american_scientific_journal-1665 224 3 ) ) PUNCT american_scientific_journal-1665 224 4 in in ADP american_scientific_journal-1665 224 5 kh kh PROPN american_scientific_journal-1665 224 6 – – PUNCT american_scientific_journal-1665 224 7 gbr gbr PROPN american_scientific_journal-1665 224 8 – – PUNCT american_scientific_journal-1665 224 9 affinely affinely ADV american_scientific_journal-1665 224 10 connected connected ADJ american_scientific_journal-1665 224 11 space space NOUN american_scientific_journal-1665 224 12 , , PUNCT american_scientific_journal-1665 224 13 berwald berwald NOUN american_scientific_journal-1665 224 14 curvature curvature NOUN american_scientific_journal-1665 224 15 tensor tensor NOUN american_scientific_journal-1665 224 16 h h NOUN american_scientific_journal-1665 224 17 jkh jkh NOUN american_scientific_journal-1665 224 18 i i PRON american_scientific_journal-1665 224 19 coincide coincide VERB american_scientific_journal-1665 224 20 with with ADP american_scientific_journal-1665 224 21 cartan cartan PROPN american_scientific_journal-1665 224 22 's 's PART american_scientific_journal-1665 224 23 fourth fourth ADJ american_scientific_journal-1665 224 24 curvature curvature NOUN american_scientific_journal-1665 224 25 tensor tensor NOUN american_scientific_journal-1665 224 26 k k PROPN american_scientific_journal-1665 224 27 jkh jkh PROPN american_scientific_journal-1665 224 28 i i PRON american_scientific_journal-1665 224 29 and and CCONJ american_scientific_journal-1665 224 30 the the DET american_scientific_journal-1665 224 31 identity identity NOUN american_scientific_journal-1665 224 32 ( ( PUNCT american_scientific_journal-1665 224 33 3.10 3.10 NUM american_scientific_journal-1665 224 34 ) ) PUNCT american_scientific_journal-1665 224 35 holds hold VERB american_scientific_journal-1665 224 36 good good ADJ american_scientific_journal-1665 224 37 . . PUNCT american_scientific_journal-1665 225 1 ( ( PUNCT american_scientific_journal-1665 225 2 3.6 3.6 NUM american_scientific_journal-1665 225 3 ) ) PUNCT american_scientific_journal-1665 225 4 in in ADP american_scientific_journal-1665 225 5 kh kh PROPN american_scientific_journal-1665 225 6 – – PUNCT american_scientific_journal-1665 225 7 gbr gbr PROPN american_scientific_journal-1665 225 8 – – PUNCT american_scientific_journal-1665 225 9 affinely affinely ADV american_scientific_journal-1665 225 10 connected connected ADJ american_scientific_journal-1665 225 11 space space NOUN american_scientific_journal-1665 225 12 , , PUNCT american_scientific_journal-1665 225 13 ricci ricci PROPN american_scientific_journal-1665 225 14 tensor tensor NOUN american_scientific_journal-1665 225 15 hjk hjk PROPN american_scientific_journal-1665 225 16 in in ADP american_scientific_journal-1665 225 17 sense sense NOUN american_scientific_journal-1665 225 18 of of ADP american_scientific_journal-1665 225 19 berwald berwald NOUN american_scientific_journal-1665 225 20 coincide coincide NOUN american_scientific_journal-1665 225 21 with with ADP american_scientific_journal-1665 225 22 ricci ricci PROPN american_scientific_journal-1665 225 23 65- 65- PROPN american_scientific_journal-1665 225 24 ) ) PUNCT american_scientific_journal-1665 225 25 volume volume NOUN american_scientific_journal-1665 225 26 20 20 NUM american_scientific_journal-1665 225 27 , , PUNCT american_scientific_journal-1665 225 28 no no DET american_scientific_journal-1665 225 29 1 1 NUM american_scientific_journal-1665 225 30 , , PUNCT american_scientific_journal-1665 225 31 pp pp ADP american_scientific_journal-1665 225 32 522016 522016 NUM american_scientific_journal-1665 225 33 ( ( PUNCT american_scientific_journal-1665 225 34 ) ) PUNCT american_scientific_journal-1665 225 35 research research NOUN american_scientific_journal-1665 225 36 journal journal NOUN american_scientific_journal-1665 225 37 for for ADP american_scientific_journal-1665 225 38 engineering engineering NOUN american_scientific_journal-1665 225 39 , , PUNCT american_scientific_journal-1665 225 40 technology technology NOUN american_scientific_journal-1665 225 41 , , PUNCT american_scientific_journal-1665 225 42 and and CCONJ american_scientific_journal-1665 225 43 sciences science NOUN american_scientific_journal-1665 225 44 ( ( PUNCT american_scientific_journal-1665 225 45 asrjets asrjet NOUN american_scientific_journal-1665 225 46 scientificamerican scientificamerican VERB american_scientific_journal-1665 225 47 65 65 NUM american_scientific_journal-1665 225 48 tensor tensor NOUN american_scientific_journal-1665 225 49 kjk kjk PROPN american_scientific_journal-1665 225 50 of of ADP american_scientific_journal-1665 225 51 cartan cartan PROPN american_scientific_journal-1665 225 52 's 's PART american_scientific_journal-1665 225 53 fourth fourth ADJ american_scientific_journal-1665 225 54 curvature curvature NOUN american_scientific_journal-1665 225 55 . . PUNCT american_scientific_journal-1665 226 1 ( ( PUNCT american_scientific_journal-1665 226 2 3.7 3.7 NUM american_scientific_journal-1665 226 3 ) ) PUNCT american_scientific_journal-1665 226 4 in in ADP american_scientific_journal-1665 226 5 kh kh PROPN american_scientific_journal-1665 226 6 – – PUNCT american_scientific_journal-1665 226 7 gbr gbr PROPN american_scientific_journal-1665 226 8 – – PUNCT american_scientific_journal-1665 226 9 affinely affinely ADV american_scientific_journal-1665 226 10 connected connected ADJ american_scientific_journal-1665 226 11 space space NOUN american_scientific_journal-1665 226 12 , , PUNCT american_scientific_journal-1665 226 13 the the DET american_scientific_journal-1665 226 14 associate associate ADJ american_scientific_journal-1665 226 15 curvature curvature NOUN american_scientific_journal-1665 226 16 tensor tensor NOUN american_scientific_journal-1665 226 17 hjpkh hjpkh NOUN american_scientific_journal-1665 226 18 of of ADP american_scientific_journal-1665 226 19 berwald berwald PROPN american_scientific_journal-1665 226 20 curvature curvature NOUN american_scientific_journal-1665 226 21 tensor tensor NOUN american_scientific_journal-1665 226 22 coincide coincide NOUN american_scientific_journal-1665 226 23 with with ADP american_scientific_journal-1665 226 24 the the DET american_scientific_journal-1665 226 25 associate associate ADJ american_scientific_journal-1665 226 26 curvature curvature NOUN american_scientific_journal-1665 226 27 tensor tensor NOUN american_scientific_journal-1665 226 28 kjpkh kjpkh NOUN american_scientific_journal-1665 226 29 of of ADP american_scientific_journal-1665 226 30 cartan cartan PROPN american_scientific_journal-1665 226 31 's 's PART american_scientific_journal-1665 226 32 fourth fourth ADJ american_scientific_journal-1665 226 33 curvature curvature NOUN american_scientific_journal-1665 226 34 tensor tensor NOUN american_scientific_journal-1665 226 35 . . PUNCT american_scientific_journal-1665 227 1 5 5 X american_scientific_journal-1665 227 2 . . PUNCT american_scientific_journal-1665 227 3 recommendations recommendation NOUN american_scientific_journal-1665 227 4 authors author NOUN american_scientific_journal-1665 227 5 recommend recommend VERB american_scientific_journal-1665 227 6 the the DET american_scientific_journal-1665 227 7 need need NOUN american_scientific_journal-1665 227 8 for for ADP american_scientific_journal-1665 227 9 the the DET american_scientific_journal-1665 227 10 continuing continue VERB american_scientific_journal-1665 227 11 research research NOUN american_scientific_journal-1665 227 12 and and CCONJ american_scientific_journal-1665 227 13 development development NOUN american_scientific_journal-1665 227 14 in in ADP american_scientific_journal-1665 227 15 affinely affinely ADV american_scientific_journal-1665 227 16 connected connect VERB american_scientific_journal-1665 227 17 space space NOUN american_scientific_journal-1665 227 18 and and CCONJ american_scientific_journal-1665 227 19 its its PRON american_scientific_journal-1665 227 20 relation relation NOUN american_scientific_journal-1665 227 21 with with ADP american_scientific_journal-1665 227 22 other other ADJ american_scientific_journal-1665 227 23 spaces space NOUN american_scientific_journal-1665 227 24 . . PUNCT american_scientific_journal-1665 228 1 references reference NOUN american_scientific_journal-1665 228 2 [ [ X american_scientific_journal-1665 228 3 1 1 NUM american_scientific_journal-1665 228 4 ] ] PUNCT american_scientific_journal-1665 228 5 a. a. NOUN american_scientific_journal-1665 228 6 a. a. NOUN american_scientific_journal-1665 228 7 a. a. NOUN american_scientific_journal-1665 228 8 muhib muhib NOUN american_scientific_journal-1665 228 9 . . PUNCT american_scientific_journal-1665 229 1 " " PUNCT american_scientific_journal-1665 229 2 on on ADP american_scientific_journal-1665 229 3 independent independent ADJ american_scientific_journal-1665 229 4 components component NOUN american_scientific_journal-1665 229 5 of of ADP american_scientific_journal-1665 229 6 tensor tensor NOUN american_scientific_journal-1665 229 7 , , PUNCT american_scientific_journal-1665 229 8 irelative irelative ADJ american_scientific_journal-1665 229 9 tensor tensor NOUN american_scientific_journal-1665 229 10 and and CCONJ american_scientific_journal-1665 229 11 r r NOUN american_scientific_journal-1665 229 12 h h PROPN american_scientific_journal-1665 229 13 – – PUNCT american_scientific_journal-1665 229 14 generalized generalize VERB american_scientific_journal-1665 229 15 trirecurrent trirecurrent ADJ american_scientific_journal-1665 229 16 finsler finsler NOUN american_scientific_journal-1665 229 17 space space NOUN american_scientific_journal-1665 229 18 " " PUNCT american_scientific_journal-1665 229 19 , , PUNCT american_scientific_journal-1665 229 20 m. m. PROPN american_scientific_journal-1665 229 21 sc sc PROPN american_scientific_journal-1665 229 22 . . PUNCT american_scientific_journal-1665 230 1 thesis thesis PROPN american_scientific_journal-1665 230 2 , , PUNCT american_scientific_journal-1665 230 3 university university PROPN american_scientific_journal-1665 230 4 of of ADP american_scientific_journal-1665 230 5 aden aden PROPN american_scientific_journal-1665 230 6 , , PUNCT american_scientific_journal-1665 230 7 aden aden PROPN american_scientific_journal-1665 230 8 , , PUNCT american_scientific_journal-1665 230 9 yemen yemen PROPN american_scientific_journal-1665 230 10 , , PUNCT american_scientific_journal-1665 230 11 2009 2009 NUM american_scientific_journal-1665 230 12 . . PUNCT american_scientific_journal-1665 231 1 [ [ X american_scientific_journal-1665 231 2 2 2 NUM american_scientific_journal-1665 231 3 ] ] PUNCT american_scientific_journal-1665 231 4 a. a. NOUN american_scientific_journal-1665 231 5 a. a. NOUN american_scientific_journal-1665 231 6 m. m. PROPN american_scientific_journal-1665 231 7 saleem saleem PROPN american_scientific_journal-1665 231 8 . . PUNCT american_scientific_journal-1665 232 1 " " PUNCT american_scientific_journal-1665 232 2 on on ADP american_scientific_journal-1665 232 3 generalized generalized ADJ american_scientific_journal-1665 232 4 birecurrent birecurrent NOUN american_scientific_journal-1665 232 5 and and CCONJ american_scientific_journal-1665 232 6 trirecurrent trirecurrent ADJ american_scientific_journal-1665 232 7 finsler finsler NOUN american_scientific_journal-1665 232 8 spaces space NOUN american_scientific_journal-1665 232 9 " " PUNCT american_scientific_journal-1665 232 10 , , PUNCT american_scientific_journal-1665 232 11 m. m. PROPN american_scientific_journal-1665 232 12 sc sc PROPN american_scientific_journal-1665 232 13 . . PUNCT american_scientific_journal-1665 232 14 thesis thesis PROPN american_scientific_journal-1665 232 15 , , PUNCT american_scientific_journal-1665 232 16 university university PROPN american_scientific_journal-1665 232 17 of of ADP american_scientific_journal-1665 232 18 aden aden PROPN american_scientific_journal-1665 232 19 , , PUNCT american_scientific_journal-1665 232 20 aden aden PROPN american_scientific_journal-1665 232 21 , , PUNCT american_scientific_journal-1665 232 22 yemen yemen PROPN american_scientific_journal-1665 232 23 , , PUNCT american_scientific_journal-1665 232 24 2011 2011 NUM american_scientific_journal-1665 232 25 . . PUNCT american_scientific_journal-1665 233 1 [ [ X american_scientific_journal-1665 233 2 3 3 X american_scientific_journal-1665 233 3 ] ] X american_scientific_journal-1665 233 4 h. h. PROPN american_scientific_journal-1665 233 5 rund rund PROPN american_scientific_journal-1665 233 6 : : PUNCT american_scientific_journal-1665 233 7 the the DET american_scientific_journal-1665 233 8 differential differential ADJ american_scientific_journal-1665 233 9 geometry geometry NOUN american_scientific_journal-1665 233 10 of of ADP american_scientific_journal-1665 233 11 finsler finsler NOUN american_scientific_journal-1665 233 12 space space NOUN american_scientific_journal-1665 233 13 , , PUNCT american_scientific_journal-1665 233 14 springer springer NOUN american_scientific_journal-1665 233 15 verlag verlag PROPN american_scientific_journal-1665 233 16 , , PUNCT american_scientific_journal-1665 233 17 berlin berlin PROPN american_scientific_journal-1665 233 18 gottingen gottingen PROPN american_scientific_journal-1665 233 19 – – PUNCT american_scientific_journal-1665 233 20 heidelberg heidelberg NOUN american_scientific_journal-1665 233 21 , , PUNCT american_scientific_journal-1665 233 22 1959 1959 NUM american_scientific_journal-1665 233 23 ; ; PUNCT american_scientific_journal-1665 233 24 2nd 2nd ADJ american_scientific_journal-1665 233 25 edit edit NOUN american_scientific_journal-1665 233 26 . . PUNCT american_scientific_journal-1665 234 1 ( ( PUNCT american_scientific_journal-1665 234 2 in in ADP american_scientific_journal-1665 234 3 russian russian PROPN american_scientific_journal-1665 234 4 ) ) PUNCT american_scientific_journal-1665 234 5 , , PUNCT american_scientific_journal-1665 234 6 nauka nauka PROPN american_scientific_journal-1665 234 7 , , PUNCT american_scientific_journal-1665 234 8 ( ( PUNCT american_scientific_journal-1665 234 9 moscow moscow PROPN american_scientific_journal-1665 234 10 ) ) PUNCT american_scientific_journal-1665 234 11 , , PUNCT american_scientific_journal-1665 234 12 1981 1981 NUM american_scientific_journal-1665 234 13 . . PUNCT american_scientific_journal-1665 235 1 [ [ X american_scientific_journal-1665 235 2 4 4 X american_scientific_journal-1665 235 3 ] ] X american_scientific_journal-1665 235 4 h.d h.d PROPN american_scientific_journal-1665 235 5 . . PROPN american_scientific_journal-1665 235 6 pande pande PROPN american_scientific_journal-1665 235 7 and and CCONJ american_scientific_journal-1665 235 8 b. b. PROPN american_scientific_journal-1665 235 9 single single PROPN american_scientific_journal-1665 235 10 . . PUNCT american_scientific_journal-1665 236 1 '' '' PUNCT american_scientific_journal-1665 236 2 on on ADP american_scientific_journal-1665 236 3 existence existence NOUN american_scientific_journal-1665 236 4 of of ADP american_scientific_journal-1665 236 5 the the DET american_scientific_journal-1665 236 6 affinely affinely ADV american_scientific_journal-1665 236 7 connected connect VERB american_scientific_journal-1665 236 8 finsler finsler NOUN american_scientific_journal-1665 236 9 spaces space NOUN american_scientific_journal-1665 236 10 with with ADP american_scientific_journal-1665 236 11 recurrent recurrent ADJ american_scientific_journal-1665 236 12 tensor tensor NOUN american_scientific_journal-1665 236 13 field field NOUN american_scientific_journal-1665 236 14 , , PUNCT american_scientific_journal-1665 236 15 reprinted reprint VERB american_scientific_journal-1665 236 16 from from ADP american_scientific_journal-1665 236 17 india india PROPN american_scientific_journal-1665 236 18 journal journal PROPN american_scientific_journal-1665 236 19 pure pure ADJ american_scientific_journal-1665 236 20 and and CCONJ american_scientific_journal-1665 236 21 applied apply VERB american_scientific_journal-1665 236 22 of of ADP american_scientific_journal-1665 236 23 mathematics mathematic NOUN american_scientific_journal-1665 236 24 , , PUNCT american_scientific_journal-1665 236 25 vol vol NOUN american_scientific_journal-1665 236 26 . . PROPN american_scientific_journal-1665 236 27 8 8 NUM american_scientific_journal-1665 236 28 , , PUNCT american_scientific_journal-1665 236 29 no no INTJ american_scientific_journal-1665 236 30 . . PUNCT american_scientific_journal-1665 237 1 3,(march 3,(march NOUN american_scientific_journal-1665 237 2 1977 1977 NUM american_scientific_journal-1665 237 3 ) ) PUNCT american_scientific_journal-1665 237 4 , , PUNCT american_scientific_journal-1665 237 5 pp pp ADP american_scientific_journal-1665 237 6 . . PUNCT american_scientific_journal-1665 238 1 295 295 NUM american_scientific_journal-1665 238 2 - - SYM american_scientific_journal-1665 238 3 301 301 NUM american_scientific_journal-1665 238 4 . . PUNCT american_scientific_journal-1665 239 1 [ [ X american_scientific_journal-1665 239 2 5 5 X american_scientific_journal-1665 239 3 ] ] PUNCT american_scientific_journal-1665 239 4 m. m. NOUN american_scientific_journal-1665 239 5 a. a. PROPN american_scientific_journal-1665 239 6 a. a. PROPN american_scientific_journal-1665 239 7 ali ali PROPN american_scientific_journal-1665 239 8 '' '' PUNCT american_scientific_journal-1665 239 9 on on ADP american_scientific_journal-1665 239 10 kh kh PROPN american_scientific_journal-1665 239 11 birecurrent birecurrent ADJ american_scientific_journal-1665 239 12 finsler finsler NOUN american_scientific_journal-1665 239 13 space space NOUN american_scientific_journal-1665 239 14 . . PUNCT american_scientific_journal-1665 239 15 '' '' PUNCT american_scientific_journal-1665 240 1 m.sc m.sc PROPN american_scientific_journal-1665 240 2 . . PUNCT american_scientific_journal-1665 241 1 thesis thesis NOUN american_scientific_journal-1665 241 2 , , PUNCT american_scientific_journal-1665 241 3 university university PROPN american_scientific_journal-1665 241 4 of of ADP american_scientific_journal-1665 241 5 aden aden PROPN american_scientific_journal-1665 241 6 , , PUNCT american_scientific_journal-1665 241 7 aden aden PROPN american_scientific_journal-1665 241 8 , , PUNCT american_scientific_journal-1665 241 9 yemen yemen PROPN american_scientific_journal-1665 241 10 , , PUNCT american_scientific_journal-1665 241 11 2014 2014 NUM american_scientific_journal-1665 241 12 . . PUNCT american_scientific_journal-1665 242 1 [ [ X american_scientific_journal-1665 242 2 6 6 NUM american_scientific_journal-1665 242 3 ] ] X american_scientific_journal-1665 242 4 n.s.h n.s.h PROPN american_scientific_journal-1665 242 5 . . PUNCT american_scientific_journal-1665 242 6 hussien hussien PROPN american_scientific_journal-1665 242 7 '' '' PUNCT american_scientific_journal-1665 242 8 on on ADP american_scientific_journal-1665 242 9 khrecurrent khrecurrent NOUN american_scientific_journal-1665 242 10 finsler finsler NOUN american_scientific_journal-1665 242 11 space space NOUN american_scientific_journal-1665 242 12 . . PUNCT american_scientific_journal-1665 242 13 '' '' PUNCT american_scientific_journal-1665 243 1 m.sc m.sc PROPN american_scientific_journal-1665 243 2 . . PUNCT american_scientific_journal-1665 244 1 thesis thesis NOUN american_scientific_journal-1665 244 2 , , PUNCT american_scientific_journal-1665 244 3 university university PROPN american_scientific_journal-1665 244 4 of of ADP american_scientific_journal-1665 244 5 aden aden PROPN american_scientific_journal-1665 244 6 , , PUNCT american_scientific_journal-1665 244 7 aden aden PROPN american_scientific_journal-1665 244 8 , , PUNCT american_scientific_journal-1665 244 9 yemen,2014 yemen,2014 PROPN american_scientific_journal-1665 244 10 . . PUNCT american_scientific_journal-1665 245 1 [ [ X american_scientific_journal-1665 245 2 7 7 X american_scientific_journal-1665 245 3 ] ] PUNCT american_scientific_journal-1665 245 4 p. p. NOUN american_scientific_journal-1665 245 5 k. k. PROPN american_scientific_journal-1665 246 1 dwivedi dwivedi PROPN american_scientific_journal-1665 246 2 : : PUNCT american_scientific_journal-1665 246 3 pβˆ— pβˆ— ADJ american_scientific_journal-1665 246 4 reducible reducible ADJ american_scientific_journal-1665 246 5 finsler finsler NOUN american_scientific_journal-1665 246 6 spaces space NOUN american_scientific_journal-1665 246 7 and and CCONJ american_scientific_journal-1665 246 8 application application NOUN american_scientific_journal-1665 246 9 , , PUNCT american_scientific_journal-1665 246 10 int int NOUN american_scientific_journal-1665 246 11 . . PUNCT american_scientific_journal-1665 247 1 journal journal PROPN american_scientific_journal-1665 247 2 of of ADP american_scientific_journal-1665 247 3 math math NOUN american_scientific_journal-1665 247 4 . . PUNCT american_scientific_journal-1665 248 1 analysis analysis NOUN american_scientific_journal-1665 248 2 , , PUNCT american_scientific_journal-1665 248 3 vol vol NOUN american_scientific_journal-1665 248 4 . . PROPN american_scientific_journal-1665 248 5 5 5 NUM american_scientific_journal-1665 248 6 , , PUNCT american_scientific_journal-1665 248 7 no no INTJ american_scientific_journal-1665 248 8 . . NOUN american_scientific_journal-1665 248 9 5 5 NUM american_scientific_journal-1665 248 10 , , PUNCT american_scientific_journal-1665 248 11 2011 2011 NUM american_scientific_journal-1665 248 12 , , PUNCT american_scientific_journal-1665 248 13 pp pp ADJ american_scientific_journal-1665 248 14 . . PUNCT american_scientific_journal-1665 249 1 223 223 NUM american_scientific_journal-1665 249 2 - - SYM american_scientific_journal-1665 249 3 229 229 NUM american_scientific_journal-1665 249 4 . . PUNCT