id sid tid token lemma pos american_scientific_journal-1305 1 1 american american PROPN american_scientific_journal-1305 1 2 scientific scientific ADJ american_scientific_journal-1305 1 3 research research NOUN american_scientific_journal-1305 1 4 journal journal NOUN american_scientific_journal-1305 1 5 for for ADP american_scientific_journal-1305 1 6 engineering engineering NOUN american_scientific_journal-1305 1 7 , , PUNCT american_scientific_journal-1305 1 8 technology technology NOUN american_scientific_journal-1305 1 9 , , PUNCT american_scientific_journal-1305 1 10 and and CCONJ american_scientific_journal-1305 1 11 sciences science NOUN american_scientific_journal-1305 1 12 ( ( PUNCT american_scientific_journal-1305 1 13 asrjets asrjet NOUN american_scientific_journal-1305 1 14 ) ) PUNCT american_scientific_journal-1305 1 15 issn issn PROPN american_scientific_journal-1305 1 16 ( ( PUNCT american_scientific_journal-1305 1 17 print print NOUN american_scientific_journal-1305 1 18 ) ) PUNCT american_scientific_journal-1305 1 19 2313 2313 NUM american_scientific_journal-1305 1 20 - - SYM american_scientific_journal-1305 1 21 4410 4410 NUM american_scientific_journal-1305 1 22 , , PUNCT american_scientific_journal-1305 1 23 issn issn PROPN american_scientific_journal-1305 1 24 ( ( PUNCT american_scientific_journal-1305 1 25 online online ADJ american_scientific_journal-1305 1 26 ) ) PUNCT american_scientific_journal-1305 1 27 2313 2313 NUM american_scientific_journal-1305 1 28 - - SYM american_scientific_journal-1305 1 29 4402 4402 NUM american_scientific_journal-1305 1 30 Β© Β© PROPN american_scientific_journal-1305 1 31 global global ADJ american_scientific_journal-1305 1 32 society society NOUN american_scientific_journal-1305 1 33 of of ADP american_scientific_journal-1305 1 34 scientific scientific ADJ american_scientific_journal-1305 1 35 research research NOUN american_scientific_journal-1305 1 36 and and CCONJ american_scientific_journal-1305 1 37 researchers researcher NOUN american_scientific_journal-1305 1 38 http://asrjetsjournal.org/ http://asrjetsjournal.org/ VERB american_scientific_journal-1305 1 39 an an DET american_scientific_journal-1305 1 40 aperiodic aperiodic ADJ american_scientific_journal-1305 1 41 stable stable ADJ american_scientific_journal-1305 1 42 chaos chaos NOUN american_scientific_journal-1305 1 43 with with ADP american_scientific_journal-1305 1 44 lyapunov lyapunov ADJ american_scientific_journal-1305 1 45 exponents exponent NOUN american_scientific_journal-1305 1 46 in in ADP american_scientific_journal-1305 1 47 time time NOUN american_scientific_journal-1305 1 48 series series PROPN american_scientific_journal-1305 1 49 saleem saleem PROPN american_scientific_journal-1305 1 50 iqbal iqbal PROPN american_scientific_journal-1305 2 1 a a PROPN american_scientific_journal-1305 2 2 * * PROPN american_scientific_journal-1305 2 3 , , PUNCT american_scientific_journal-1305 2 4 farhana farhana ADJ american_scientific_journal-1305 2 5 sarwar sarwar PROPN american_scientific_journal-1305 2 6 b b PROPN american_scientific_journal-1305 2 7 , , PUNCT american_scientific_journal-1305 2 8 syed syed ADJ american_scientific_journal-1305 2 9 mohsin mohsin PROPN american_scientific_journal-1305 2 10 raza raza PROPN american_scientific_journal-1305 2 11 c c PROPN american_scientific_journal-1305 2 12 , , PUNCT american_scientific_journal-1305 2 13 abdul abdul PROPN american_scientific_journal-1305 2 14 rehman rehman PROPN american_scientific_journal-1305 2 15 d d PROPN american_scientific_journal-1305 2 16 , , PUNCT american_scientific_journal-1305 2 17 yasmin yasmin PROPN american_scientific_journal-1305 2 18 zahra zahra PROPN american_scientific_journal-1305 2 19 jafri jafri PROPN american_scientific_journal-1305 2 20 e e PROPN american_scientific_journal-1305 2 21 a a X american_scientific_journal-1305 2 22 , , PUNCT american_scientific_journal-1305 2 23 ddepartment ddepartment NOUN american_scientific_journal-1305 2 24 of of ADP american_scientific_journal-1305 2 25 mathematics mathematic NOUN american_scientific_journal-1305 2 26 , , PUNCT american_scientific_journal-1305 2 27 university university NOUN american_scientific_journal-1305 2 28 of of ADP american_scientific_journal-1305 2 29 balochistan balochistan PROPN american_scientific_journal-1305 2 30 , , PUNCT american_scientific_journal-1305 2 31 quetta quetta PROPN american_scientific_journal-1305 2 32 87300 87300 NUM american_scientific_journal-1305 2 33 , , PUNCT american_scientific_journal-1305 2 34 pakistan pakistan PROPN american_scientific_journal-1305 2 35 bdepartment bdepartment NOUN american_scientific_journal-1305 2 36 of of ADP american_scientific_journal-1305 2 37 mathematics mathematics PROPN american_scientific_journal-1305 2 38 f.g.girls f.g.girl NOUN american_scientific_journal-1305 2 39 degree degree NOUN american_scientific_journal-1305 2 40 college college NOUN american_scientific_journal-1305 2 41 , , PUNCT american_scientific_journal-1305 2 42 madrissa madrissa NOUN american_scientific_journal-1305 2 43 road road NOUN american_scientific_journal-1305 2 44 , , PUNCT american_scientific_journal-1305 2 45 quetta quetta PROPN american_scientific_journal-1305 2 46 , , PUNCT american_scientific_journal-1305 2 47 cantt cantt PROPN american_scientific_journal-1305 2 48 , , PUNCT american_scientific_journal-1305 2 49 87300 87300 NUM american_scientific_journal-1305 2 50 , , PUNCT american_scientific_journal-1305 2 51 pakistan pakistan PROPN american_scientific_journal-1305 2 52 . . PUNCT american_scientific_journal-1305 3 1 cdepartmen cdepartman NOUN american_scientific_journal-1305 3 2 of of ADP american_scientific_journal-1305 3 3 physics physics PROPN american_scientific_journal-1305 3 4 , , PUNCT american_scientific_journal-1305 3 5 university university NOUN american_scientific_journal-1305 3 6 of of ADP american_scientific_journal-1305 3 7 balochistan balochistan PROPN american_scientific_journal-1305 3 8 , , PUNCT american_scientific_journal-1305 3 9 quetta quetta PROPN american_scientific_journal-1305 3 10 87300 87300 NUM american_scientific_journal-1305 3 11 , , PUNCT american_scientific_journal-1305 3 12 pakistan pakistan ADJ american_scientific_journal-1305 3 13 edepartmen edepartman NOUN american_scientific_journal-1305 3 14 of of ADP american_scientific_journal-1305 3 15 statistics statistic NOUN american_scientific_journal-1305 3 16 , , PUNCT american_scientific_journal-1305 3 17 university university NOUN american_scientific_journal-1305 3 18 of of ADP american_scientific_journal-1305 3 19 balochistan balochistan PROPN american_scientific_journal-1305 3 20 , , PUNCT american_scientific_journal-1305 3 21 quetta quetta PROPN american_scientific_journal-1305 3 22 87300 87300 NUM american_scientific_journal-1305 3 23 , , PUNCT american_scientific_journal-1305 3 24 pakistan pakistan PROPN american_scientific_journal-1305 3 25 aemail aemail NOUN american_scientific_journal-1305 3 26 : : PUNCT american_scientific_journal-1305 4 1 saleemiqbal81@yahoo.com saleemiqbal81@yahoo.com X american_scientific_journal-1305 4 2 bemail bemail NOUN american_scientific_journal-1305 4 3 : : PUNCT american_scientific_journal-1305 4 4 f_saleem10@yahoo.com f_saleem10@yahoo.com X american_scientific_journal-1305 4 5 cemail cemail NOUN american_scientific_journal-1305 4 6 : : PUNCT american_scientific_journal-1305 4 7 smraza7@yahoo.com smraza7@yahoo.com X american_scientific_journal-1305 4 8 demail demail NOUN american_scientific_journal-1305 4 9 : : PUNCT american_scientific_journal-1305 4 10 abdul_maths@yahoo.com abdul_maths@yahoo.com X american_scientific_journal-1305 4 11 eemail eemail NOUN american_scientific_journal-1305 4 12 : : PUNCT american_scientific_journal-1305 4 13 jafri_yasmin@yahoo.com jafri_yasmin@yahoo.com X american_scientific_journal-1305 4 14 abstract abstract VERB american_scientific_journal-1305 4 15 a a DET american_scientific_journal-1305 4 16 new new ADJ american_scientific_journal-1305 4 17 formula formula NOUN american_scientific_journal-1305 4 18 is be AUX american_scientific_journal-1305 4 19 developed develop VERB american_scientific_journal-1305 4 20 to to PART american_scientific_journal-1305 4 21 reproduce reproduce VERB american_scientific_journal-1305 4 22 the the DET american_scientific_journal-1305 4 23 shape shape NOUN american_scientific_journal-1305 4 24 of of ADP american_scientific_journal-1305 4 25 energy energy NOUN american_scientific_journal-1305 4 26 profiles profile NOUN american_scientific_journal-1305 4 27 for for ADP american_scientific_journal-1305 4 28 aperiodic aperiodic ADJ american_scientific_journal-1305 4 29 stable stable ADJ american_scientific_journal-1305 4 30 attractors attractor NOUN american_scientific_journal-1305 4 31 with with ADP american_scientific_journal-1305 4 32 lyapunov lyapunov ADJ american_scientific_journal-1305 4 33 exponents exponent NOUN american_scientific_journal-1305 4 34 , , PUNCT american_scientific_journal-1305 4 35 ±𝑛𝑓 ±𝑛𝑓 ADJ american_scientific_journal-1305 4 36 by by ADP american_scientific_journal-1305 4 37 using use VERB american_scientific_journal-1305 4 38 the the DET american_scientific_journal-1305 4 39 fractional fractional ADJ american_scientific_journal-1305 4 40 fourier fourier NOUN american_scientific_journal-1305 4 41 transform transform NOUN american_scientific_journal-1305 4 42 ( ( PUNCT american_scientific_journal-1305 4 43 frft frft ADJ american_scientific_journal-1305 4 44 ) ) PUNCT american_scientific_journal-1305 4 45 , , PUNCT american_scientific_journal-1305 4 46 .i.e .i.e X american_scientific_journal-1305 4 47 . . PUNCT american_scientific_journal-1305 5 1 πœ“Β±π‘›π‘“(Β±πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ πœ“Β±π‘›π‘“(Β±πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ VERB american_scientific_journal-1305 5 2 ) ) PUNCT american_scientific_journal-1305 5 3 = = PROPN american_scientific_journal-1305 5 4 οΏ½ οΏ½ PROPN american_scientific_journal-1305 5 5 πœ”0𝑑 πœ”0𝑑 SYM american_scientific_journal-1305 5 6 βˆšπœ‹ βˆšπœ‹ X american_scientific_journal-1305 5 7 οΏ½ οΏ½ PROPN american_scientific_journal-1305 5 8 1 1 NUM american_scientific_journal-1305 5 9 2 2 NUM american_scientific_journal-1305 5 10 2Β± 2Β± NUM american_scientific_journal-1305 5 11 𝑛𝑓 𝑛𝑓 NOUN american_scientific_journal-1305 5 12 2 2 NUM american_scientific_journal-1305 5 13 where where SCONJ american_scientific_journal-1305 5 14 πœ‹ πœ‹ NOUN american_scientific_journal-1305 5 15 2 2 NUM american_scientific_journal-1305 5 16 < < X american_scientific_journal-1305 5 17 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 5 18 ≀ ≀ NUM american_scientific_journal-1305 5 19 2πœ‹ 2πœ‹ NUM american_scientific_journal-1305 5 20 , , PUNCT american_scientific_journal-1305 5 21 0 0 NUM american_scientific_journal-1305 5 22 ≀ ≀ NUM american_scientific_journal-1305 5 23 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ VERB american_scientific_journal-1305 5 24 ≀ ≀ NUM american_scientific_journal-1305 5 25 πœ‹ πœ‹ DET american_scientific_journal-1305 5 26 2 2 NUM american_scientific_journal-1305 5 27 , , PUNCT american_scientific_journal-1305 5 28 πœ”πœŠ πœ”πœŠ NOUN american_scientific_journal-1305 5 29 is be AUX american_scientific_journal-1305 5 30 the the DET american_scientific_journal-1305 5 31 initial initial ADJ american_scientific_journal-1305 5 32 angular angular ADJ american_scientific_journal-1305 5 33 frequency frequency NOUN american_scientific_journal-1305 5 34 of of ADP american_scientific_journal-1305 5 35 the the PRON american_scientific_journal-1305 5 36 of of ADP american_scientific_journal-1305 5 37 the the DET american_scientific_journal-1305 5 38 attractor attractor NOUN american_scientific_journal-1305 5 39 and and CCONJ american_scientific_journal-1305 5 40 tatt tatt NOUN american_scientific_journal-1305 5 41 , , PUNCT american_scientific_journal-1305 5 42 the the DET american_scientific_journal-1305 5 43 time time NOUN american_scientific_journal-1305 5 44 of of ADP american_scientific_journal-1305 5 45 flight flight NOUN american_scientific_journal-1305 5 46 of of ADP american_scientific_journal-1305 5 47 the the DET american_scientific_journal-1305 5 48 attractor attractor NOUN american_scientific_journal-1305 5 49 . . PUNCT american_scientific_journal-1305 6 1 with with ADP american_scientific_journal-1305 6 2 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 6 3 = = PUNCT american_scientific_journal-1305 6 4 πœ‹ πœ‹ X american_scientific_journal-1305 6 5 2 2 NUM american_scientific_journal-1305 6 6 , , PUNCT american_scientific_journal-1305 6 7 the the DET american_scientific_journal-1305 6 8 energy energy NOUN american_scientific_journal-1305 6 9 profile profile NOUN american_scientific_journal-1305 6 10 for for ADP american_scientific_journal-1305 6 11 periodic periodic ADJ american_scientific_journal-1305 6 12 unstable unstable ADJ american_scientific_journal-1305 6 13 attractors attractor NOUN american_scientific_journal-1305 6 14 at at ADP american_scientific_journal-1305 6 15 different different ADJ american_scientific_journal-1305 6 16 values value NOUN american_scientific_journal-1305 6 17 of of ADP american_scientific_journal-1305 6 18 lyapunov lyapunov ADJ american_scientific_journal-1305 6 19 exponents exponent NOUN american_scientific_journal-1305 6 20 ±𝑛𝑓 ±𝑛𝑓 ADJ american_scientific_journal-1305 6 21 is be AUX american_scientific_journal-1305 6 22 obtained obtain VERB american_scientific_journal-1305 6 23 , , PUNCT american_scientific_journal-1305 6 24 for for ADP american_scientific_journal-1305 6 25 πœ‹ πœ‹ NOUN american_scientific_journal-1305 6 26 2 2 NUM american_scientific_journal-1305 6 27 < < X american_scientific_journal-1305 6 28 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ X american_scientific_journal-1305 6 29 ≀ ≀ ADV american_scientific_journal-1305 6 30 2 2 NUM american_scientific_journal-1305 6 31 πœ‹ πœ‹ ADP american_scientific_journal-1305 6 32 π‘Žnd π‘Žnd X american_scientific_journal-1305 6 33 0 0 NUM american_scientific_journal-1305 6 34 ≀ ≀ NUM american_scientific_journal-1305 6 35 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ VERB american_scientific_journal-1305 6 36 ≀ ≀ NUM american_scientific_journal-1305 6 37 πœ‹ πœ‹ SYM american_scientific_journal-1305 6 38 2 2 NUM american_scientific_journal-1305 6 39 aperiodic aperiodic ADJ american_scientific_journal-1305 6 40 stable stable ADJ american_scientific_journal-1305 6 41 attraction attraction NOUN american_scientific_journal-1305 6 42 at at ADP american_scientific_journal-1305 6 43 different different ADJ american_scientific_journal-1305 6 44 values value NOUN american_scientific_journal-1305 6 45 of of ADP american_scientific_journal-1305 6 46 lyapunov lyapunov ADJ american_scientific_journal-1305 6 47 exponents exponent NOUN american_scientific_journal-1305 6 48 ±𝑛𝑓 ±𝑛𝑓 ADJ american_scientific_journal-1305 6 49 are be AUX american_scientific_journal-1305 6 50 observed observe VERB american_scientific_journal-1305 6 51 . . PUNCT american_scientific_journal-1305 7 1 the the DET american_scientific_journal-1305 7 2 critical critical ADJ american_scientific_journal-1305 7 3 analysis analysis NOUN american_scientific_journal-1305 7 4 about about ADP american_scientific_journal-1305 7 5 chaos chaos NOUN american_scientific_journal-1305 7 6 is be AUX american_scientific_journal-1305 7 7 presented present VERB american_scientific_journal-1305 7 8 with with ADP american_scientific_journal-1305 7 9 emphasis emphasis NOUN american_scientific_journal-1305 7 10 to to ADP american_scientific_journal-1305 7 11 time time NOUN american_scientific_journal-1305 7 12 series series PROPN american_scientific_journal-1305 7 13 modeling modeling NOUN american_scientific_journal-1305 7 14 and and CCONJ american_scientific_journal-1305 7 15 simulation simulation NOUN american_scientific_journal-1305 7 16 . . PUNCT american_scientific_journal-1305 8 1 ----------------------------------------------------------------- ----------------------------------------------------------------- PUNCT american_scientific_journal-1305 9 1 * * PUNCT american_scientific_journal-1305 9 2 corresponding correspond VERB american_scientific_journal-1305 9 3 author author NOUN american_scientific_journal-1305 9 4 . . PUNCT american_scientific_journal-1305 10 1 282 282 NUM american_scientific_journal-1305 10 2 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-1305 10 3 american american ADJ american_scientific_journal-1305 10 4 scientific scientific ADJ american_scientific_journal-1305 10 5 research research NOUN american_scientific_journal-1305 10 6 journal journal NOUN american_scientific_journal-1305 10 7 for for ADP american_scientific_journal-1305 10 8 engineering engineering NOUN american_scientific_journal-1305 10 9 , , PUNCT american_scientific_journal-1305 10 10 technology technology NOUN american_scientific_journal-1305 10 11 , , PUNCT american_scientific_journal-1305 10 12 and and CCONJ american_scientific_journal-1305 10 13 sciences science NOUN american_scientific_journal-1305 10 14 ( ( PUNCT american_scientific_journal-1305 10 15 asrjets asrjet NOUN american_scientific_journal-1305 10 16 ) ) PUNCT american_scientific_journal-1305 10 17 ( ( PUNCT american_scientific_journal-1305 10 18 2016 2016 NUM american_scientific_journal-1305 10 19 ) ) PUNCT american_scientific_journal-1305 10 20 volume volume NOUN american_scientific_journal-1305 10 21 15 15 NUM american_scientific_journal-1305 10 22 , , PUNCT american_scientific_journal-1305 10 23 no no DET american_scientific_journal-1305 10 24 1 1 NUM american_scientific_journal-1305 10 25 , , PUNCT american_scientific_journal-1305 10 26 pp pp ADV american_scientific_journal-1305 10 27 282 282 NUM american_scientific_journal-1305 10 28 - - SYM american_scientific_journal-1305 10 29 289 289 NUM american_scientific_journal-1305 10 30 keywords keyword NOUN american_scientific_journal-1305 10 31 : : PUNCT american_scientific_journal-1305 10 32 fractional fractional ADJ american_scientific_journal-1305 10 33 fourier fourier NOUN american_scientific_journal-1305 10 34 transform transform NOUN american_scientific_journal-1305 10 35 ; ; PUNCT american_scientific_journal-1305 10 36 lyapunov lyapunov NOUN american_scientific_journal-1305 10 37 exponents exponent NOUN american_scientific_journal-1305 10 38 ; ; PUNCT american_scientific_journal-1305 10 39 aperiodic aperiodic ADJ american_scientific_journal-1305 10 40 stable stable ADJ american_scientific_journal-1305 10 41 chaos chaos NOUN american_scientific_journal-1305 10 42 ; ; PUNCT american_scientific_journal-1305 10 43 periodic periodic ADJ american_scientific_journal-1305 10 44 instable instable ADJ american_scientific_journal-1305 10 45 attractors attractor NOUN american_scientific_journal-1305 10 46 . . PUNCT american_scientific_journal-1305 11 1 1 1 X american_scientific_journal-1305 11 2 . . X american_scientific_journal-1305 11 3 introduction introduction NOUN american_scientific_journal-1305 11 4 deterministic deterministic ADJ american_scientific_journal-1305 11 5 nonlinear nonlinear ADJ american_scientific_journal-1305 11 6 model model NOUN american_scientific_journal-1305 11 7 techniques technique NOUN american_scientific_journal-1305 11 8 of of ADP american_scientific_journal-1305 11 9 complex complex ADJ american_scientific_journal-1305 11 10 data datum NOUN american_scientific_journal-1305 11 11 series series NOUN american_scientific_journal-1305 11 12 , , PUNCT american_scientific_journal-1305 11 13 .i.e .i.e PUNCT american_scientific_journal-1305 11 14 . . PROPN american_scientific_journal-1305 11 15 , , PUNCT american_scientific_journal-1305 11 16 uncorrelated uncorrelated ADJ american_scientific_journal-1305 11 17 series series NOUN american_scientific_journal-1305 11 18 with with ADP american_scientific_journal-1305 11 19 a a DET american_scientific_journal-1305 11 20 flat flat ADJ american_scientific_journal-1305 11 21 fourier fourier NOUN american_scientific_journal-1305 11 22 spectrum spectrum NOUN american_scientific_journal-1305 11 23 have have AUX american_scientific_journal-1305 11 24 received receive VERB american_scientific_journal-1305 11 25 a a DET american_scientific_journal-1305 11 26 great great ADJ american_scientific_journal-1305 11 27 deal deal NOUN american_scientific_journal-1305 11 28 of of ADP american_scientific_journal-1305 11 29 attention attention NOUN american_scientific_journal-1305 11 30 because because SCONJ american_scientific_journal-1305 11 31 it it PRON american_scientific_journal-1305 11 32 can can AUX american_scientific_journal-1305 11 33 be be AUX american_scientific_journal-1305 11 34 used use VERB american_scientific_journal-1305 11 35 to to PART american_scientific_journal-1305 11 36 forecast forecast VERB american_scientific_journal-1305 11 37 the the DET american_scientific_journal-1305 11 38 evaluation evaluation NOUN american_scientific_journal-1305 11 39 of of ADP american_scientific_journal-1305 11 40 a a DET american_scientific_journal-1305 11 41 chaotic chaotic ADJ american_scientific_journal-1305 11 42 system system NOUN american_scientific_journal-1305 12 1 [ [ X american_scientific_journal-1305 12 2 1 1 NUM american_scientific_journal-1305 12 3 ] ] PUNCT american_scientific_journal-1305 12 4 . . PUNCT american_scientific_journal-1305 13 1 the the DET american_scientific_journal-1305 13 2 dynamic dynamic ADJ american_scientific_journal-1305 13 3 variables variable NOUN american_scientific_journal-1305 13 4 are be AUX american_scientific_journal-1305 13 5 usually usually ADV american_scientific_journal-1305 13 6 unknown unknown ADJ american_scientific_journal-1305 13 7 in in ADP american_scientific_journal-1305 13 8 chaotic chaotic ADJ american_scientific_journal-1305 13 9 systems system NOUN american_scientific_journal-1305 13 10 . . PUNCT american_scientific_journal-1305 14 1 the the DET american_scientific_journal-1305 14 2 cross cross ADJ american_scientific_journal-1305 14 3 - - ADJ american_scientific_journal-1305 14 4 correlation correlation ADJ american_scientific_journal-1305 14 5 function function NOUN american_scientific_journal-1305 14 6 between between ADP american_scientific_journal-1305 14 7 observed observe VERB american_scientific_journal-1305 14 8 and and CCONJ american_scientific_journal-1305 14 9 predicted predict VERB american_scientific_journal-1305 14 10 values value NOUN american_scientific_journal-1305 14 11 from from ADP american_scientific_journal-1305 14 12 nonlinear nonlinear ADJ american_scientific_journal-1305 14 13 model model NOUN american_scientific_journal-1305 14 14 techniques technique NOUN american_scientific_journal-1305 14 15 such such ADJ american_scientific_journal-1305 14 16 as as ADP american_scientific_journal-1305 14 17 arima arima PROPN american_scientific_journal-1305 14 18 ( ( PUNCT american_scientific_journal-1305 14 19 auto auto NOUN american_scientific_journal-1305 14 20 regressive regressive ADJ american_scientific_journal-1305 14 21 integrated integrated ADJ american_scientific_journal-1305 14 22 moving move VERB american_scientific_journal-1305 14 23 average average ADJ american_scientific_journal-1305 14 24 ) ) PUNCT american_scientific_journal-1305 14 25 provides provide VERB american_scientific_journal-1305 14 26 estimated estimated ADJ american_scientific_journal-1305 14 27 values value NOUN american_scientific_journal-1305 14 28 of of ADP american_scientific_journal-1305 14 29 lyapunov lyapunov ADJ american_scientific_journal-1305 14 30 exponents exponent NOUN american_scientific_journal-1305 14 31 of of ADP american_scientific_journal-1305 14 32 dynamic dynamic ADJ american_scientific_journal-1305 14 33 variables variable NOUN american_scientific_journal-1305 14 34 even even ADV american_scientific_journal-1305 14 35 for for ADP american_scientific_journal-1305 14 36 sparse sparse ADJ american_scientific_journal-1305 14 37 time time NOUN american_scientific_journal-1305 14 38 series series NOUN american_scientific_journal-1305 14 39 ( ( PUNCT american_scientific_journal-1305 14 40 containing contain VERB american_scientific_journal-1305 14 41 of of ADP american_scientific_journal-1305 14 42 the the DET american_scientific_journal-1305 14 43 order order NOUN american_scientific_journal-1305 14 44 of of ADP american_scientific_journal-1305 14 45 103 103 NUM american_scientific_journal-1305 14 46 data datum NOUN american_scientific_journal-1305 14 47 points point NOUN american_scientific_journal-1305 14 48 ) ) PUNCT american_scientific_journal-1305 14 49 . . PUNCT american_scientific_journal-1305 15 1 when when SCONJ american_scientific_journal-1305 15 2 the the DET american_scientific_journal-1305 15 3 fit fit NOUN american_scientific_journal-1305 15 4 is be AUX american_scientific_journal-1305 15 5 achieved achieve VERB american_scientific_journal-1305 15 6 by by ADP american_scientific_journal-1305 15 7 using use VERB american_scientific_journal-1305 15 8 nonlinear nonlinear ADJ american_scientific_journal-1305 15 9 modeling modeling NOUN american_scientific_journal-1305 15 10 , , PUNCT american_scientific_journal-1305 15 11 we we PRON american_scientific_journal-1305 15 12 can can AUX american_scientific_journal-1305 15 13 say say VERB american_scientific_journal-1305 15 14 it it PRON american_scientific_journal-1305 15 15 is be AUX american_scientific_journal-1305 15 16 better well ADJ american_scientific_journal-1305 15 17 than than ADP american_scientific_journal-1305 15 18 probalistic probalistic ADJ american_scientific_journal-1305 15 19 models model NOUN american_scientific_journal-1305 15 20 provided provide VERB american_scientific_journal-1305 15 21 a a DET american_scientific_journal-1305 15 22 deterministic deterministic ADJ american_scientific_journal-1305 15 23 mechanism mechanism NOUN american_scientific_journal-1305 15 24 governs govern VERB american_scientific_journal-1305 15 25 the the DET american_scientific_journal-1305 15 26 process process NOUN american_scientific_journal-1305 15 27 under under ADP american_scientific_journal-1305 15 28 study study NOUN american_scientific_journal-1305 15 29 [ [ X american_scientific_journal-1305 15 30 2,3 2,3 NUM american_scientific_journal-1305 15 31 ] ] PUNCT american_scientific_journal-1305 15 32 . . PUNCT american_scientific_journal-1305 16 1 most most ADJ american_scientific_journal-1305 16 2 of of ADP american_scientific_journal-1305 16 3 the the DET american_scientific_journal-1305 16 4 non non ADJ american_scientific_journal-1305 16 5 - - ADJ american_scientific_journal-1305 16 6 linear linear ADJ american_scientific_journal-1305 16 7 modeling modeling NOUN american_scientific_journal-1305 16 8 techniques technique NOUN american_scientific_journal-1305 16 9 follow follow VERB american_scientific_journal-1305 16 10 non non ADJ american_scientific_journal-1305 16 11 - - ADJ american_scientific_journal-1305 16 12 bayesian bayesian ADJ american_scientific_journal-1305 16 13 statistics statistic NOUN american_scientific_journal-1305 16 14 and and CCONJ american_scientific_journal-1305 16 15 are be AUX american_scientific_journal-1305 16 16 grouped group VERB american_scientific_journal-1305 16 17 in in ADP american_scientific_journal-1305 16 18 to to ADP american_scientific_journal-1305 16 19 major major ADJ american_scientific_journal-1305 16 20 classes class NOUN american_scientific_journal-1305 16 21 : : PUNCT american_scientific_journal-1305 16 22 global global ADJ american_scientific_journal-1305 16 23 and and CCONJ american_scientific_journal-1305 16 24 local local ADJ american_scientific_journal-1305 16 25 . . PUNCT american_scientific_journal-1305 17 1 the the DET american_scientific_journal-1305 17 2 local local ADJ american_scientific_journal-1305 17 3 non non ADJ american_scientific_journal-1305 17 4 - - ADJ american_scientific_journal-1305 17 5 bayesian bayesian ADJ american_scientific_journal-1305 17 6 statistics statistic NOUN american_scientific_journal-1305 17 7 has have VERB american_scientific_journal-1305 17 8 more more ADJ american_scientific_journal-1305 17 9 advantages advantage NOUN american_scientific_journal-1305 17 10 as as ADP american_scientific_journal-1305 17 11 compared compare VERB american_scientific_journal-1305 17 12 to to ADP american_scientific_journal-1305 17 13 global global ADJ american_scientific_journal-1305 17 14 non non ADJ american_scientific_journal-1305 17 15 - - ADJ american_scientific_journal-1305 17 16 bayesian bayesian ADJ american_scientific_journal-1305 17 17 statistics statistic NOUN american_scientific_journal-1305 17 18 . . PUNCT american_scientific_journal-1305 18 1 in in ADP american_scientific_journal-1305 18 2 the the DET american_scientific_journal-1305 18 3 bayesian bayesian NOUN american_scientific_journal-1305 18 4 approach approach NOUN american_scientific_journal-1305 18 5 [ [ X american_scientific_journal-1305 18 6 4 4 X american_scientific_journal-1305 18 7 ] ] PUNCT american_scientific_journal-1305 18 8 one one NUM american_scientific_journal-1305 18 9 assumes assume VERB american_scientific_journal-1305 18 10 that that SCONJ american_scientific_journal-1305 18 11 the the DET american_scientific_journal-1305 18 12 prior prior ADJ american_scientific_journal-1305 18 13 uncertainty uncertainty NOUN american_scientific_journal-1305 18 14 about about ADP american_scientific_journal-1305 18 15 unknown unknown ADJ american_scientific_journal-1305 18 16 parameters parameter NOUN american_scientific_journal-1305 18 17 which which PRON american_scientific_journal-1305 18 18 have have VERB american_scientific_journal-1305 18 19 to to PART american_scientific_journal-1305 18 20 be be AUX american_scientific_journal-1305 18 21 inferred infer VERB american_scientific_journal-1305 18 22 from from ADP american_scientific_journal-1305 18 23 random random ADJ american_scientific_journal-1305 18 24 data datum NOUN american_scientific_journal-1305 18 25 or or CCONJ american_scientific_journal-1305 18 26 from from ADP american_scientific_journal-1305 18 27 a a DET american_scientific_journal-1305 18 28 stochastic stochastic ADJ american_scientific_journal-1305 18 29 process process NOUN american_scientific_journal-1305 18 30 , , PUNCT american_scientific_journal-1305 18 31 can can AUX american_scientific_journal-1305 18 32 also also ADV american_scientific_journal-1305 18 33 be be AUX american_scientific_journal-1305 18 34 encoded encode VERB american_scientific_journal-1305 18 35 in in ADP american_scientific_journal-1305 18 36 a a DET american_scientific_journal-1305 18 37 probability probability NOUN american_scientific_journal-1305 18 38 distribution distribution NOUN american_scientific_journal-1305 18 39 , , PUNCT american_scientific_journal-1305 18 40 the the DET american_scientific_journal-1305 18 41 so so ADV american_scientific_journal-1305 18 42 called call VERB american_scientific_journal-1305 18 43 prior prior ADV american_scientific_journal-1305 18 44 . . PUNCT american_scientific_journal-1305 19 1 the the DET american_scientific_journal-1305 19 2 problem problem NOUN american_scientific_journal-1305 19 3 of of ADP american_scientific_journal-1305 19 4 distinguishing distinguish VERB american_scientific_journal-1305 19 5 chaos chaos NOUN american_scientific_journal-1305 19 6 from from ADP american_scientific_journal-1305 19 7 correlated correlate VERB american_scientific_journal-1305 19 8 noise noise NOUN american_scientific_journal-1305 19 9 or or CCONJ american_scientific_journal-1305 19 10 combinations combination NOUN american_scientific_journal-1305 19 11 of of ADP american_scientific_journal-1305 19 12 deterministic deterministic NOUN american_scientific_journal-1305 19 13 and and CCONJ american_scientific_journal-1305 19 14 randomness randomness NOUN american_scientific_journal-1305 19 15 is be AUX american_scientific_journal-1305 19 16 a a DET american_scientific_journal-1305 19 17 more more ADV american_scientific_journal-1305 19 18 difficult difficult ADJ american_scientific_journal-1305 19 19 task task NOUN american_scientific_journal-1305 19 20 [ [ X american_scientific_journal-1305 19 21 5 5 NUM american_scientific_journal-1305 19 22 ] ] PUNCT american_scientific_journal-1305 19 23 . . PUNCT american_scientific_journal-1305 20 1 jafri jafri PROPN american_scientific_journal-1305 21 1 [ [ X american_scientific_journal-1305 21 2 6 6 NUM american_scientific_journal-1305 21 3 ] ] PUNCT american_scientific_journal-1305 21 4 exploited exploit VERB american_scientific_journal-1305 21 5 concepts concept NOUN american_scientific_journal-1305 21 6 of of ADP american_scientific_journal-1305 21 7 bayesian bayesian NOUN american_scientific_journal-1305 21 8 and and CCONJ american_scientific_journal-1305 21 9 non non ADJ american_scientific_journal-1305 21 10 - - ADJ american_scientific_journal-1305 21 11 bayesian bayesian ADJ american_scientific_journal-1305 21 12 statistics statistic NOUN american_scientific_journal-1305 21 13 to to PART american_scientific_journal-1305 21 14 prove prove VERB american_scientific_journal-1305 21 15 mathematically mathematically ADV american_scientific_journal-1305 21 16 that that SCONJ american_scientific_journal-1305 21 17 the the DET american_scientific_journal-1305 21 18 chaotic chaotic ADJ american_scientific_journal-1305 21 19 time time NOUN american_scientific_journal-1305 21 20 series series NOUN american_scientific_journal-1305 21 21 is be AUX american_scientific_journal-1305 21 22 deterministic deterministic ADJ american_scientific_journal-1305 21 23 . . PUNCT american_scientific_journal-1305 22 1 she she PRON american_scientific_journal-1305 22 2 assumed assume VERB american_scientific_journal-1305 22 3 that that SCONJ american_scientific_journal-1305 22 4 the the DET american_scientific_journal-1305 22 5 optimum optimum ADJ american_scientific_journal-1305 22 6 metric metric NOUN american_scientific_journal-1305 22 7 ( ( PUNCT american_scientific_journal-1305 22 8 used use VERB american_scientific_journal-1305 22 9 as as ADP american_scientific_journal-1305 22 10 tool tool NOUN american_scientific_journal-1305 22 11 to to PART american_scientific_journal-1305 22 12 distinguish distinguish VERB american_scientific_journal-1305 22 13 chaos chaos NOUN american_scientific_journal-1305 22 14 from from ADP american_scientific_journal-1305 22 15 correlated correlate VERB american_scientific_journal-1305 22 16 noise noise NOUN american_scientific_journal-1305 22 17 ) ) PUNCT american_scientific_journal-1305 22 18 arises arise VERB american_scientific_journal-1305 22 19 from from ADP american_scientific_journal-1305 22 20 a a DET american_scientific_journal-1305 22 21 metric metric ADJ american_scientific_journal-1305 22 22 tensor tensor NOUN american_scientific_journal-1305 22 23 whose whose DET american_scientific_journal-1305 22 24 components component NOUN american_scientific_journal-1305 22 25 are be AUX american_scientific_journal-1305 22 26 𝛿𝑖𝑗 𝛿𝑖𝑗 X american_scientific_journal-1305 22 27 = = SYM american_scientific_journal-1305 22 28 πœ•π‘–π‘—π‘’2𝑖𝑐 πœ•π‘–π‘—π‘’2𝑖𝑐 PROPN american_scientific_journal-1305 22 29 ( ( PUNCT american_scientific_journal-1305 22 30 1 1 NUM american_scientific_journal-1305 22 31 ) ) PUNCT american_scientific_journal-1305 22 32 where where SCONJ american_scientific_journal-1305 22 33 𝛿𝑖𝑗 𝛿𝑖𝑗 PRON american_scientific_journal-1305 22 34 is be AUX american_scientific_journal-1305 22 35 the the DET american_scientific_journal-1305 22 36 kronecker kronecker NOUN american_scientific_journal-1305 22 37 delta delta NOUN american_scientific_journal-1305 22 38 function function NOUN american_scientific_journal-1305 22 39 and and CCONJ american_scientific_journal-1305 22 40 i i PRON american_scientific_journal-1305 22 41 and and CCONJ american_scientific_journal-1305 22 42 j j PROPN american_scientific_journal-1305 22 43 run run VERB american_scientific_journal-1305 22 44 from from ADP american_scientific_journal-1305 22 45 i i PRON american_scientific_journal-1305 22 46 to to ADP american_scientific_journal-1305 22 47 𝑑 𝑑 PRON american_scientific_journal-1305 22 48 ( ( PUNCT american_scientific_journal-1305 22 49 embedding embed VERB american_scientific_journal-1305 22 50 dimension dimension NOUN american_scientific_journal-1305 22 51 on on ADP american_scientific_journal-1305 22 52 the the DET american_scientific_journal-1305 22 53 prediction prediction NOUN american_scientific_journal-1305 22 54 interval interval NOUN american_scientific_journal-1305 22 55 ) ) PUNCT american_scientific_journal-1305 22 56 for for ADP american_scientific_journal-1305 22 57 input input NOUN american_scientific_journal-1305 22 58 - - PUNCT american_scientific_journal-1305 22 59 output output NOUN american_scientific_journal-1305 22 60 data datum NOUN american_scientific_journal-1305 22 61 pairs pair NOUN american_scientific_journal-1305 22 62 . . PUNCT american_scientific_journal-1305 23 1 if if SCONJ american_scientific_journal-1305 23 2 the the DET american_scientific_journal-1305 23 3 parameter parameter NOUN american_scientific_journal-1305 23 4 𝑐 𝑐 PROPN american_scientific_journal-1305 23 5 in in ADP american_scientific_journal-1305 23 6 equation equation NOUN american_scientific_journal-1305 23 7 ( ( PUNCT american_scientific_journal-1305 23 8 1 1 X american_scientific_journal-1305 23 9 ) ) PUNCT american_scientific_journal-1305 23 10 is be AUX american_scientific_journal-1305 23 11 varied varied ADJ american_scientific_journal-1305 23 12 to to PART american_scientific_journal-1305 23 13 minimize minimize VERB american_scientific_journal-1305 23 14 the the DET american_scientific_journal-1305 23 15 root root NOUN american_scientific_journal-1305 23 16 mean mean VERB american_scientific_journal-1305 23 17 square square ADJ american_scientific_journal-1305 23 18 error error NOUN american_scientific_journal-1305 23 19 of of ADP american_scientific_journal-1305 23 20 the the DET american_scientific_journal-1305 23 21 forecast forecast NOUN american_scientific_journal-1305 23 22 , , PUNCT american_scientific_journal-1305 23 23 then then ADV american_scientific_journal-1305 23 24 there there PRON american_scientific_journal-1305 23 25 is be VERB american_scientific_journal-1305 23 26 a a DET american_scientific_journal-1305 23 27 single single ADJ american_scientific_journal-1305 23 28 global global ADJ american_scientific_journal-1305 23 29 minimum minimum NOUN american_scientific_journal-1305 23 30 corresponding corresponding NOUN american_scientific_journal-1305 23 31 to to ADP american_scientific_journal-1305 23 32 a a DET american_scientific_journal-1305 23 33 value value NOUN american_scientific_journal-1305 23 34 of of ADP american_scientific_journal-1305 23 35 c c PROPN american_scientific_journal-1305 23 36 closed close VERB american_scientific_journal-1305 23 37 to to ADP american_scientific_journal-1305 23 38 the the DET american_scientific_journal-1305 23 39 most most ADV american_scientific_journal-1305 23 40 negative negative ADJ american_scientific_journal-1305 23 41 lyapunov lyapunov ADJ american_scientific_journal-1305 23 42 exponent exponent NOUN american_scientific_journal-1305 23 43 of of ADP american_scientific_journal-1305 23 44 the the DET american_scientific_journal-1305 23 45 dynamics dynamic NOUN american_scientific_journal-1305 23 46 . . PUNCT american_scientific_journal-1305 24 1 chaos chaos NOUN american_scientific_journal-1305 24 2 is be AUX american_scientific_journal-1305 24 3 having have VERB american_scientific_journal-1305 24 4 an an DET american_scientific_journal-1305 24 5 impact impact NOUN american_scientific_journal-1305 24 6 on on ADP american_scientific_journal-1305 24 7 diverse diverse ADJ american_scientific_journal-1305 24 8 discipline discipline NOUN american_scientific_journal-1305 24 9 of of ADP american_scientific_journal-1305 24 10 knowledge knowledge NOUN american_scientific_journal-1305 24 11 including include VERB american_scientific_journal-1305 24 12 physics physics NOUN american_scientific_journal-1305 24 13 , , PUNCT american_scientific_journal-1305 24 14 biology biology NOUN american_scientific_journal-1305 24 15 , , PUNCT american_scientific_journal-1305 24 16 chemistry chemistry NOUN american_scientific_journal-1305 24 17 , , PUNCT american_scientific_journal-1305 24 18 economics economic NOUN american_scientific_journal-1305 24 19 and and CCONJ american_scientific_journal-1305 24 20 medicine medicine NOUN american_scientific_journal-1305 24 21 [ [ X american_scientific_journal-1305 24 22 7,12 7,12 NUM american_scientific_journal-1305 24 23 ] ] PUNCT american_scientific_journal-1305 24 24 . . PUNCT american_scientific_journal-1305 25 1 the the DET american_scientific_journal-1305 25 2 chaos chaos NOUN american_scientific_journal-1305 25 3 may may AUX american_scientific_journal-1305 25 4 behave behave VERB american_scientific_journal-1305 25 5 almost almost ADV american_scientific_journal-1305 25 6 linearly linearly ADV american_scientific_journal-1305 25 7 in in ADP american_scientific_journal-1305 25 8 some some DET american_scientific_journal-1305 25 9 part part NOUN american_scientific_journal-1305 25 10 of of ADP american_scientific_journal-1305 25 11 phase phase NOUN american_scientific_journal-1305 25 12 space space NOUN american_scientific_journal-1305 25 13 and and CCONJ american_scientific_journal-1305 25 14 highly highly ADV american_scientific_journal-1305 25 15 non non ADJ american_scientific_journal-1305 25 16 - - ADJ american_scientific_journal-1305 25 17 linearly linearly ADV american_scientific_journal-1305 25 18 in in ADP american_scientific_journal-1305 25 19 other other ADJ american_scientific_journal-1305 25 20 parts part NOUN american_scientific_journal-1305 25 21 . . PUNCT american_scientific_journal-1305 26 1 lorenz lorenz PROPN american_scientific_journal-1305 26 2 and and CCONJ american_scientific_journal-1305 26 3 rossele rossele PROPN american_scientific_journal-1305 27 1 [ [ X american_scientific_journal-1305 27 2 13,14 13,14 NUM american_scientific_journal-1305 27 3 ] ] PUNCT american_scientific_journal-1305 27 4 , , PUNCT american_scientific_journal-1305 27 5 identified identify VERB american_scientific_journal-1305 27 6 non non ADJ american_scientific_journal-1305 27 7 - - ADJ american_scientific_journal-1305 27 8 stable stable ADJ american_scientific_journal-1305 27 9 chaos chaos NOUN american_scientific_journal-1305 27 10 approximately approximately ADV american_scientific_journal-1305 27 11 in in ADP american_scientific_journal-1305 27 12 to to ADP american_scientific_journal-1305 27 13 different different ADJ american_scientific_journal-1305 27 14 ( ( PUNCT american_scientific_journal-1305 27 15 chaotic chaotic ADJ american_scientific_journal-1305 27 16 and and CCONJ american_scientific_journal-1305 27 17 non non ADJ american_scientific_journal-1305 27 18 - - ADJ american_scientific_journal-1305 27 19 chaotic chaotic ADJ american_scientific_journal-1305 27 20 ) ) PUNCT american_scientific_journal-1305 27 21 nonlinear nonlinear ADJ american_scientific_journal-1305 27 22 dynamical dynamical ADJ american_scientific_journal-1305 27 23 system system NOUN american_scientific_journal-1305 27 24 with with ADP american_scientific_journal-1305 27 25 their their PRON american_scientific_journal-1305 27 26 attractors attractor NOUN american_scientific_journal-1305 27 27 . . PUNCT american_scientific_journal-1305 28 1 but but CCONJ american_scientific_journal-1305 28 2 , , PUNCT american_scientific_journal-1305 28 3 the the DET american_scientific_journal-1305 28 4 recognition recognition NOUN american_scientific_journal-1305 28 5 of of ADP american_scientific_journal-1305 28 6 attractors attractor NOUN american_scientific_journal-1305 28 7 in in ADP american_scientific_journal-1305 28 8 a a DET american_scientific_journal-1305 28 9 chaotic chaotic ADJ american_scientific_journal-1305 28 10 system system NOUN american_scientific_journal-1305 28 11 is be AUX american_scientific_journal-1305 28 12 indeed indeed ADV american_scientific_journal-1305 28 13 difficult difficult ADJ american_scientific_journal-1305 28 14 . . PUNCT american_scientific_journal-1305 29 1 jafri jafri PROPN american_scientific_journal-1305 30 1 [ [ X american_scientific_journal-1305 30 2 15,16,21 15,16,21 NUM american_scientific_journal-1305 30 3 ] ] PUNCT american_scientific_journal-1305 30 4 , , PUNCT american_scientific_journal-1305 30 5 identified identify VERB american_scientific_journal-1305 30 6 an an DET american_scientific_journal-1305 30 7 aperiodic aperiodic ADJ american_scientific_journal-1305 30 8 stable stable ADJ american_scientific_journal-1305 30 9 chaos chaos NOUN american_scientific_journal-1305 30 10 with with ADP american_scientific_journal-1305 30 11 an an DET american_scientific_journal-1305 30 12 attractor attractor NOUN american_scientific_journal-1305 30 13 in in ADP american_scientific_journal-1305 30 14 mackeyglass mackeyglass NOUN american_scientific_journal-1305 30 15 simulation simulation NOUN american_scientific_journal-1305 30 16 on on ADP american_scientific_journal-1305 30 17 hourly hourly ADJ american_scientific_journal-1305 30 18 wind wind NOUN american_scientific_journal-1305 30 19 data datum NOUN american_scientific_journal-1305 30 20 and and CCONJ american_scientific_journal-1305 30 21 indeed indeed ADV american_scientific_journal-1305 30 22 followed follow VERB american_scientific_journal-1305 30 23 a a DET american_scientific_journal-1305 30 24 free free ADJ american_scientific_journal-1305 30 25 fuzzy fuzzy ADJ american_scientific_journal-1305 30 26 logic logic NOUN american_scientific_journal-1305 30 27 ( ( PUNCT american_scientific_journal-1305 30 28 ffl ffl PROPN american_scientific_journal-1305 30 29 ) ) PUNCT american_scientific_journal-1305 30 30 design design NOUN american_scientific_journal-1305 30 31 for for ADP american_scientific_journal-1305 30 32 prediction prediction NOUN american_scientific_journal-1305 30 33 . . PUNCT american_scientific_journal-1305 31 1 the the DET american_scientific_journal-1305 31 2 stable stable ADJ american_scientific_journal-1305 31 3 chaotic chaotic ADJ american_scientific_journal-1305 31 4 attractors attractor NOUN american_scientific_journal-1305 31 5 do do AUX american_scientific_journal-1305 31 6 not not PART american_scientific_journal-1305 31 7 influence influence VERB american_scientific_journal-1305 31 8 the the DET american_scientific_journal-1305 31 9 time time NOUN american_scientific_journal-1305 31 10 series series PROPN american_scientific_journal-1305 31 11 prediction prediction PROPN american_scientific_journal-1305 31 12 . . PUNCT american_scientific_journal-1305 32 1 jafri jafri PROPN american_scientific_journal-1305 33 1 [ [ X american_scientific_journal-1305 33 2 16 16 NUM american_scientific_journal-1305 33 3 , , PUNCT american_scientific_journal-1305 33 4 21 21 NUM american_scientific_journal-1305 33 5 ] ] PUNCT american_scientific_journal-1305 33 6 , , PUNCT american_scientific_journal-1305 33 7 also also ADV american_scientific_journal-1305 33 8 studied study VERB american_scientific_journal-1305 33 9 the the DET american_scientific_journal-1305 33 10 rule rule NOUN american_scientific_journal-1305 33 11 based base VERB american_scientific_journal-1305 33 12 on on ADP american_scientific_journal-1305 33 13 fuzzy fuzzy ADJ american_scientific_journal-1305 33 14 logic logic NOUN american_scientific_journal-1305 33 15 time time NOUN american_scientific_journal-1305 33 16 series series PROPN american_scientific_journal-1305 33 17 prediction prediction NOUN american_scientific_journal-1305 33 18 , , PUNCT american_scientific_journal-1305 33 19 feed feed VERB american_scientific_journal-1305 33 20 forward forward ADV american_scientific_journal-1305 33 21 back back ADV american_scientific_journal-1305 33 22 propagation propagation NOUN american_scientific_journal-1305 33 23 neural neural ADJ american_scientific_journal-1305 33 24 networks network NOUN american_scientific_journal-1305 33 25 ( ( PUNCT american_scientific_journal-1305 33 26 ffbpnn ffbpnn NOUN american_scientific_journal-1305 33 27 ) ) PUNCT american_scientific_journal-1305 33 28 and and CCONJ american_scientific_journal-1305 33 29 artificial artificial ADJ american_scientific_journal-1305 33 30 neuro neuro NOUN american_scientific_journal-1305 33 31 fuzzy fuzzy ADJ american_scientific_journal-1305 33 32 information information NOUN american_scientific_journal-1305 33 33 system system NOUN american_scientific_journal-1305 33 34 ( ( PUNCT american_scientific_journal-1305 33 35 anfis anfis PROPN american_scientific_journal-1305 33 36 ) ) PUNCT american_scientific_journal-1305 33 37 . . PUNCT american_scientific_journal-1305 34 1 her her PRON american_scientific_journal-1305 34 2 arima arima NOUN american_scientific_journal-1305 34 3 and and CCONJ american_scientific_journal-1305 34 4 sarima sarima NOUN american_scientific_journal-1305 34 5 ( ( PUNCT american_scientific_journal-1305 34 6 seasonal seasonal ADJ american_scientific_journal-1305 34 7 auto auto NOUN american_scientific_journal-1305 34 8 regressive regressive ADJ american_scientific_journal-1305 34 9 integrated integrated ADJ american_scientific_journal-1305 34 10 moving move VERB american_scientific_journal-1305 34 11 average average ADJ american_scientific_journal-1305 34 12 ) ) PUNCT american_scientific_journal-1305 34 13 modeling model VERB american_scientific_journal-1305 34 14 techniques technique NOUN american_scientific_journal-1305 34 15 and and CCONJ american_scientific_journal-1305 34 16 statistical statistical ADJ american_scientific_journal-1305 34 17 tests test NOUN american_scientific_journal-1305 34 18 [ [ X american_scientific_journal-1305 34 19 16 16 NUM american_scientific_journal-1305 34 20 , , PUNCT american_scientific_journal-1305 34 21 21 21 NUM american_scientific_journal-1305 34 22 ] ] PUNCT american_scientific_journal-1305 34 23 , , PUNCT american_scientific_journal-1305 34 24 unraveled unravel VERB american_scientific_journal-1305 34 25 many many ADJ american_scientific_journal-1305 34 26 hidden hidden ADJ american_scientific_journal-1305 34 27 information information NOUN american_scientific_journal-1305 34 28 with with ADP american_scientific_journal-1305 34 29 particular particular ADJ american_scientific_journal-1305 34 30 emphasis emphasis NOUN american_scientific_journal-1305 34 31 to to ADP american_scientific_journal-1305 34 32 aperiodic aperiodic ADJ american_scientific_journal-1305 34 33 stable stable ADJ american_scientific_journal-1305 34 34 chaotic chaotic ADJ american_scientific_journal-1305 34 35 attractors attractor NOUN american_scientific_journal-1305 34 36 . . PUNCT american_scientific_journal-1305 35 1 lalarukh lalarukh PROPN american_scientific_journal-1305 35 2 and and CCONJ american_scientific_journal-1305 35 3 jafri jafri PROPN american_scientific_journal-1305 36 1 [ [ X american_scientific_journal-1305 36 2 17 17 NUM american_scientific_journal-1305 36 3 ] ] PUNCT american_scientific_journal-1305 36 4 an an DET american_scientific_journal-1305 36 5 arma arma NOUN american_scientific_journal-1305 36 6 process process NOUN american_scientific_journal-1305 36 7 on on ADP american_scientific_journal-1305 36 8 hourly hourly ADJ american_scientific_journal-1305 36 9 global global ADJ american_scientific_journal-1305 36 10 radiation radiation NOUN american_scientific_journal-1305 36 11 data datum NOUN american_scientific_journal-1305 36 12 , , PUNCT american_scientific_journal-1305 36 13 performed perform VERB american_scientific_journal-1305 36 14 stochastic stochastic NOUN american_scientific_journal-1305 36 15 modeling modeling NOUN american_scientific_journal-1305 36 16 through through ADP american_scientific_journal-1305 36 17 mtm mtm PROPN american_scientific_journal-1305 36 18 ( ( PUNCT american_scientific_journal-1305 36 19 markov markov NOUN american_scientific_journal-1305 36 20 transition transition NOUN american_scientific_journal-1305 36 21 matrix matrix NOUN american_scientific_journal-1305 36 22 ) ) PUNCT american_scientific_journal-1305 36 23 and and CCONJ american_scientific_journal-1305 36 24 generated generate VERB american_scientific_journal-1305 36 25 synthetic synthetic ADJ american_scientific_journal-1305 36 26 sequences sequence NOUN american_scientific_journal-1305 36 27 of of ADP american_scientific_journal-1305 36 28 hourly hourly ADJ american_scientific_journal-1305 36 29 global global ADJ american_scientific_journal-1305 36 30 solar solar ADJ american_scientific_journal-1305 36 31 radiation radiation NOUN american_scientific_journal-1305 36 32 . . PUNCT american_scientific_journal-1305 37 1 they they PRON american_scientific_journal-1305 37 2 found find VERB american_scientific_journal-1305 37 3 mtm mtm PROPN american_scientific_journal-1305 37 4 approached approach VERB american_scientific_journal-1305 37 5 relatively relatively ADV american_scientific_journal-1305 37 6 better well ADV american_scientific_journal-1305 37 7 as as ADP american_scientific_journal-1305 37 8 a a DET american_scientific_journal-1305 37 9 simulator simulator NOUN american_scientific_journal-1305 37 10 compared compare VERB american_scientific_journal-1305 37 11 to to ADP american_scientific_journal-1305 37 12 arma arma PROPN american_scientific_journal-1305 37 13 ( ( PUNCT american_scientific_journal-1305 37 14 auto auto NOUN american_scientific_journal-1305 37 15 regressive regressive ADJ american_scientific_journal-1305 37 16 moving move VERB american_scientific_journal-1305 37 17 average average ADJ american_scientific_journal-1305 37 18 ) ) PUNCT american_scientific_journal-1305 37 19 . . PUNCT american_scientific_journal-1305 38 1 but but CCONJ american_scientific_journal-1305 38 2 , , PUNCT american_scientific_journal-1305 38 3 their their PRON american_scientific_journal-1305 38 4 283 283 NUM american_scientific_journal-1305 38 5 american american ADJ american_scientific_journal-1305 38 6 scientific scientific ADJ american_scientific_journal-1305 38 7 research research NOUN american_scientific_journal-1305 38 8 journal journal NOUN american_scientific_journal-1305 38 9 for for ADP american_scientific_journal-1305 38 10 engineering engineering NOUN american_scientific_journal-1305 38 11 , , PUNCT american_scientific_journal-1305 38 12 technology technology NOUN american_scientific_journal-1305 38 13 , , PUNCT american_scientific_journal-1305 38 14 and and CCONJ american_scientific_journal-1305 38 15 sciences science NOUN american_scientific_journal-1305 38 16 ( ( PUNCT american_scientific_journal-1305 38 17 asrjets asrjet NOUN american_scientific_journal-1305 38 18 ) ) PUNCT american_scientific_journal-1305 38 19 ( ( PUNCT american_scientific_journal-1305 38 20 2016 2016 NUM american_scientific_journal-1305 38 21 ) ) PUNCT american_scientific_journal-1305 38 22 volume volume NOUN american_scientific_journal-1305 38 23 15 15 NUM american_scientific_journal-1305 38 24 , , PUNCT american_scientific_journal-1305 38 25 no no DET american_scientific_journal-1305 38 26 1 1 NUM american_scientific_journal-1305 38 27 , , PUNCT american_scientific_journal-1305 38 28 pp pp ADV american_scientific_journal-1305 38 29 282 282 NUM american_scientific_journal-1305 38 30 - - SYM american_scientific_journal-1305 38 31 289 289 NUM american_scientific_journal-1305 38 32 analysis analysis NOUN american_scientific_journal-1305 38 33 for for ADP american_scientific_journal-1305 38 34 arma arma NOUN american_scientific_journal-1305 38 35 process process NOUN american_scientific_journal-1305 38 36 to to PART american_scientific_journal-1305 38 37 simulate simulate VERB american_scientific_journal-1305 38 38 and and CCONJ american_scientific_journal-1305 38 39 forecast forecast VERB american_scientific_journal-1305 38 40 hourly hourly ADV american_scientific_journal-1305 38 41 averaged average VERB american_scientific_journal-1305 38 42 wind wind NOUN american_scientific_journal-1305 38 43 speed speed NOUN american_scientific_journal-1305 38 44 yielded yield VERB american_scientific_journal-1305 38 45 good good ADJ american_scientific_journal-1305 38 46 results result NOUN american_scientific_journal-1305 38 47 [ [ X american_scientific_journal-1305 38 48 18 18 NUM american_scientific_journal-1305 38 49 ] ] PUNCT american_scientific_journal-1305 38 50 . . PUNCT american_scientific_journal-1305 39 1 we we PRON american_scientific_journal-1305 39 2 observed observe VERB american_scientific_journal-1305 39 3 with with ADP american_scientific_journal-1305 39 4 critical critical ADJ american_scientific_journal-1305 39 5 analysis analysis NOUN american_scientific_journal-1305 39 6 [ [ X american_scientific_journal-1305 39 7 1,4,6,14 1,4,6,14 X american_scientific_journal-1305 39 8 ] ] PUNCT american_scientific_journal-1305 39 9 , , PUNCT american_scientific_journal-1305 39 10 [ [ X american_scientific_journal-1305 39 11 18 18 NUM american_scientific_journal-1305 39 12 - - SYM american_scientific_journal-1305 39 13 20 20 NUM american_scientific_journal-1305 39 14 ] ] PUNCT american_scientific_journal-1305 39 15 and and CCONJ american_scientific_journal-1305 39 16 with with ADP american_scientific_journal-1305 39 17 experimental experimental ADJ american_scientific_journal-1305 39 18 data datum NOUN american_scientific_journal-1305 39 19 modeling modeling NOUN american_scientific_journal-1305 39 20 and and CCONJ american_scientific_journal-1305 39 21 simulation simulation NOUN american_scientific_journal-1305 40 1 [ [ X american_scientific_journal-1305 40 2 15,18 15,18 NUM american_scientific_journal-1305 40 3 , , PUNCT american_scientific_journal-1305 40 4 21 21 NUM american_scientific_journal-1305 40 5 ] ] PUNCT american_scientific_journal-1305 40 6 that that SCONJ american_scientific_journal-1305 40 7 the the DET american_scientific_journal-1305 40 8 aperiodic aperiodic ADJ american_scientific_journal-1305 40 9 attractors attractor NOUN american_scientific_journal-1305 40 10 ( ( PUNCT american_scientific_journal-1305 40 11 usually usually ADV american_scientific_journal-1305 40 12 with with ADP american_scientific_journal-1305 40 13 sparse sparse ADJ american_scientific_journal-1305 40 14 time time NOUN american_scientific_journal-1305 40 15 delays delay NOUN american_scientific_journal-1305 40 16 ) ) PUNCT american_scientific_journal-1305 40 17 produced produce VERB american_scientific_journal-1305 40 18 stable stable ADJ american_scientific_journal-1305 40 19 chaos chaos NOUN american_scientific_journal-1305 40 20 whereas whereas SCONJ american_scientific_journal-1305 40 21 the the DET american_scientific_journal-1305 40 22 periodic periodic ADJ american_scientific_journal-1305 40 23 attractors attractor NOUN american_scientific_journal-1305 40 24 the the DET american_scientific_journal-1305 40 25 unstable unstable ADJ american_scientific_journal-1305 40 26 chaos chaos NOUN american_scientific_journal-1305 40 27 in in ADP american_scientific_journal-1305 40 28 any any DET american_scientific_journal-1305 40 29 nonlinear nonlinear ADJ american_scientific_journal-1305 40 30 dynamical dynamical ADJ american_scientific_journal-1305 40 31 systems system NOUN american_scientific_journal-1305 40 32 . . PUNCT american_scientific_journal-1305 41 1 jafri jafri PROPN american_scientific_journal-1305 42 1 [ [ X american_scientific_journal-1305 42 2 22 22 NUM american_scientific_journal-1305 42 3 ] ] PUNCT american_scientific_journal-1305 42 4 suggested suggest VERB american_scientific_journal-1305 42 5 methods method NOUN american_scientific_journal-1305 42 6 for for ADP american_scientific_journal-1305 42 7 kolmogorovsinai kolmogorovsinai ADJ american_scientific_journal-1305 42 8 disorder disorder NOUN american_scientific_journal-1305 42 9 in in ADP american_scientific_journal-1305 42 10 terms term NOUN american_scientific_journal-1305 42 11 of of ADP american_scientific_journal-1305 42 12 β€œ " PUNCT american_scientific_journal-1305 42 13 point point NOUN american_scientific_journal-1305 42 14 stochastic stochastic ADJ american_scientific_journal-1305 42 15 process process NOUN american_scientific_journal-1305 42 16 ” " PUNCT american_scientific_journal-1305 43 1 and and CCONJ american_scientific_journal-1305 43 2 found find VERB american_scientific_journal-1305 43 3 that that SCONJ american_scientific_journal-1305 43 4 this this DET american_scientific_journal-1305 43 5 stochastic stochastic ADJ american_scientific_journal-1305 43 6 process process NOUN american_scientific_journal-1305 43 7 can can AUX american_scientific_journal-1305 43 8 be be AUX american_scientific_journal-1305 43 9 measured measure VERB american_scientific_journal-1305 43 10 with with ADP american_scientific_journal-1305 43 11 a a DET american_scientific_journal-1305 43 12 positive positive ADJ american_scientific_journal-1305 43 13 lyapunov lyapunov NOUN american_scientific_journal-1305 43 14 exponent exponent NOUN american_scientific_journal-1305 43 15 . . PUNCT american_scientific_journal-1305 44 1 the the DET american_scientific_journal-1305 44 2 point point NOUN american_scientific_journal-1305 44 3 stochastic stochastic ADJ american_scientific_journal-1305 44 4 process process NOUN american_scientific_journal-1305 44 5 deals deal VERB american_scientific_journal-1305 44 6 with with ADP american_scientific_journal-1305 44 7 discrete discrete ADJ american_scientific_journal-1305 44 8 , , PUNCT american_scientific_journal-1305 44 9 independent independent ADJ american_scientific_journal-1305 44 10 and and CCONJ american_scientific_journal-1305 44 11 identically identically ADV american_scientific_journal-1305 44 12 distributed distribute VERB american_scientific_journal-1305 44 13 random random ADJ american_scientific_journal-1305 44 14 data datum NOUN american_scientific_journal-1305 44 15 . . PUNCT american_scientific_journal-1305 45 1 the the DET american_scientific_journal-1305 45 2 non non ADJ american_scientific_journal-1305 45 3 - - ADJ american_scientific_journal-1305 45 4 stationary stationary ADJ american_scientific_journal-1305 45 5 stochastic stochastic ADJ american_scientific_journal-1305 45 6 process process NOUN american_scientific_journal-1305 45 7 other other ADJ american_scientific_journal-1305 45 8 than than ADP american_scientific_journal-1305 45 9 point point NOUN american_scientific_journal-1305 45 10 stochastic stochastic ADJ american_scientific_journal-1305 45 11 process process NOUN american_scientific_journal-1305 45 12 in in ADP american_scientific_journal-1305 45 13 dynamical dynamical ADJ american_scientific_journal-1305 45 14 systems system NOUN american_scientific_journal-1305 45 15 depend depend VERB american_scientific_journal-1305 45 16 on on ADP american_scientific_journal-1305 45 17 negative negative ADJ american_scientific_journal-1305 45 18 lyapunov lyapunov ADJ american_scientific_journal-1305 45 19 exponents exponent NOUN american_scientific_journal-1305 45 20 . . PUNCT american_scientific_journal-1305 46 1 the the DET american_scientific_journal-1305 46 2 positive positive ADJ american_scientific_journal-1305 46 3 lyapunov lyapunov ADJ american_scientific_journal-1305 46 4 exponents exponent NOUN american_scientific_journal-1305 46 5 are be AUX american_scientific_journal-1305 46 6 preferably preferably ADV american_scientific_journal-1305 46 7 found find VERB american_scientific_journal-1305 46 8 in in ADP american_scientific_journal-1305 46 9 point point NOUN american_scientific_journal-1305 46 10 stochastic stochastic NOUN american_scientific_journal-1305 46 11 processes process NOUN american_scientific_journal-1305 46 12 [ [ X american_scientific_journal-1305 46 13 2,3,23,24 2,3,23,24 X american_scientific_journal-1305 46 14 ] ] X american_scientific_journal-1305 46 15 where where SCONJ american_scientific_journal-1305 46 16 disorder disorder NOUN american_scientific_journal-1305 46 17 introduces introduce VERB american_scientific_journal-1305 46 18 chaos chaos NOUN american_scientific_journal-1305 46 19 in in ADP american_scientific_journal-1305 46 20 dynamical dynamical ADJ american_scientific_journal-1305 46 21 systems system NOUN american_scientific_journal-1305 46 22 . . PUNCT american_scientific_journal-1305 47 1 such such ADJ american_scientific_journal-1305 47 2 chaotic chaotic ADJ american_scientific_journal-1305 47 3 dynamical dynamical ADJ american_scientific_journal-1305 47 4 system system NOUN american_scientific_journal-1305 47 5 have have AUX american_scientific_journal-1305 47 6 been be AUX american_scientific_journal-1305 47 7 studied study VERB american_scientific_journal-1305 47 8 by by ADP american_scientific_journal-1305 47 9 real real ADJ american_scientific_journal-1305 47 10 valued value VERB american_scientific_journal-1305 47 11 tine tine NOUN american_scientific_journal-1305 47 12 series series NOUN american_scientific_journal-1305 47 13 for for ADP american_scientific_journal-1305 47 14 random random ADJ american_scientific_journal-1305 47 15 process process NOUN american_scientific_journal-1305 48 1 [ [ X american_scientific_journal-1305 48 2 6,15,18 6,15,18 NUM american_scientific_journal-1305 48 3 , , PUNCT american_scientific_journal-1305 48 4 21,22,17,18 21,22,17,18 NUM american_scientific_journal-1305 48 5 ] ] PUNCT american_scientific_journal-1305 48 6 , , PUNCT american_scientific_journal-1305 48 7 jafri jafri X american_scientific_journal-1305 49 1 [ [ X american_scientific_journal-1305 49 2 24 24 NUM american_scientific_journal-1305 49 3 ] ] PUNCT american_scientific_journal-1305 49 4 also also ADV american_scientific_journal-1305 49 5 studied study VERB american_scientific_journal-1305 49 6 disorder disorder NOUN american_scientific_journal-1305 49 7 in in ADP american_scientific_journal-1305 49 8 a a DET american_scientific_journal-1305 49 9 stochastic stochastic ADJ american_scientific_journal-1305 49 10 system system NOUN american_scientific_journal-1305 49 11 in in ADP american_scientific_journal-1305 49 12 the the DET american_scientific_journal-1305 49 13 form form NOUN american_scientific_journal-1305 49 14 of of ADP american_scientific_journal-1305 49 15 fisher fisher PROPN american_scientific_journal-1305 49 16 information information NOUN american_scientific_journal-1305 49 17 matrix matrix NOUN american_scientific_journal-1305 49 18 in in ADP american_scientific_journal-1305 49 19 probability probability NOUN american_scientific_journal-1305 49 20 function function NOUN american_scientific_journal-1305 49 21 , , PUNCT american_scientific_journal-1305 49 22 using use VERB american_scientific_journal-1305 49 23 the the DET american_scientific_journal-1305 49 24 partition partition NOUN american_scientific_journal-1305 49 25 in in ADP american_scientific_journal-1305 49 26 the the DET american_scientific_journal-1305 49 27 family family NOUN american_scientific_journal-1305 49 28 of of ADP american_scientific_journal-1305 49 29 random random ADJ american_scientific_journal-1305 49 30 variables variable NOUN american_scientific_journal-1305 49 31 for for ADP american_scientific_journal-1305 49 32 their their PRON american_scientific_journal-1305 49 33 corresponding correspond VERB american_scientific_journal-1305 49 34 degree degree NOUN american_scientific_journal-1305 49 35 of of ADP american_scientific_journal-1305 49 36 randomness randomness NOUN american_scientific_journal-1305 49 37 for for ADP american_scientific_journal-1305 49 38 one one NUM american_scientific_journal-1305 49 39 - - PUNCT american_scientific_journal-1305 49 40 step step NOUN american_scientific_journal-1305 49 41 prediction prediction NOUN american_scientific_journal-1305 49 42 in in ADP american_scientific_journal-1305 49 43 time time NOUN american_scientific_journal-1305 49 44 series series NOUN american_scientific_journal-1305 49 45 , , PUNCT american_scientific_journal-1305 49 46 as as ADP american_scientific_journal-1305 49 47 a a DET american_scientific_journal-1305 49 48 consequence consequence NOUN american_scientific_journal-1305 49 49 of of ADP american_scientific_journal-1305 49 50 which which PRON american_scientific_journal-1305 49 51 , , PUNCT american_scientific_journal-1305 49 52 we we PRON american_scientific_journal-1305 49 53 obtained obtain VERB american_scientific_journal-1305 49 54 the the DET american_scientific_journal-1305 49 55 disjoint disjoint NOUN american_scientific_journal-1305 49 56 sets set NOUN american_scientific_journal-1305 49 57 of of ADP american_scientific_journal-1305 49 58 random random ADJ american_scientific_journal-1305 49 59 variables variable NOUN american_scientific_journal-1305 49 60 . . PUNCT american_scientific_journal-1305 50 1 there there PRON american_scientific_journal-1305 50 2 is be VERB american_scientific_journal-1305 50 3 a a DET american_scientific_journal-1305 50 4 literal literal ADJ american_scientific_journal-1305 50 5 difference difference NOUN american_scientific_journal-1305 50 6 between between ADP american_scientific_journal-1305 50 7 fractional fractional ADJ american_scientific_journal-1305 50 8 exponents exponent NOUN american_scientific_journal-1305 50 9 of of ADP american_scientific_journal-1305 50 10 heaviside heaviside ADJ american_scientific_journal-1305 50 11 step step NOUN american_scientific_journal-1305 50 12 function function NOUN american_scientific_journal-1305 50 13 and and CCONJ american_scientific_journal-1305 50 14 the the DET american_scientific_journal-1305 50 15 lyapunove lyapunove NOUN american_scientific_journal-1305 50 16 exponents exponent NOUN american_scientific_journal-1305 50 17 . . PUNCT american_scientific_journal-1305 51 1 the the DET american_scientific_journal-1305 51 2 lyapunov lyapunov ADJ american_scientific_journal-1305 51 3 exponents exponent NOUN american_scientific_journal-1305 51 4 define define VERB american_scientific_journal-1305 51 5 attractors attractor NOUN american_scientific_journal-1305 51 6 both both CCONJ american_scientific_journal-1305 51 7 in in ADP american_scientific_journal-1305 51 8 arbitrary arbitrary ADJ american_scientific_journal-1305 51 9 positive positive ADJ american_scientific_journal-1305 51 10 and and CCONJ american_scientific_journal-1305 51 11 negative negative ADJ american_scientific_journal-1305 51 12 directions direction NOUN american_scientific_journal-1305 51 13 ( ( PUNCT american_scientific_journal-1305 51 14 hence hence ADV american_scientific_journal-1305 51 15 positive positive ADJ american_scientific_journal-1305 51 16 and and CCONJ american_scientific_journal-1305 51 17 negative negative ADJ american_scientific_journal-1305 51 18 lyapunov lyapunov ADJ american_scientific_journal-1305 51 19 exponents exponent NOUN american_scientific_journal-1305 51 20 ) ) PUNCT american_scientific_journal-1305 51 21 while while SCONJ american_scientific_journal-1305 51 22 the the DET american_scientific_journal-1305 51 23 fractional fractional ADJ american_scientific_journal-1305 51 24 exponents exponent NOUN american_scientific_journal-1305 51 25 of of ADP american_scientific_journal-1305 51 26 exponential exponential ADJ american_scientific_journal-1305 51 27 function function NOUN american_scientific_journal-1305 51 28 in in ADP american_scientific_journal-1305 51 29 the the DET american_scientific_journal-1305 51 30 denominator denominator NOUN american_scientific_journal-1305 51 31 for for ADP american_scientific_journal-1305 51 32 the the DET american_scientific_journal-1305 51 33 heaviside heaviside ADJ american_scientific_journal-1305 51 34 step step NOUN american_scientific_journal-1305 51 35 function function NOUN american_scientific_journal-1305 51 36 show show VERB american_scientific_journal-1305 51 37 fragmented fragmented ADJ american_scientific_journal-1305 51 38 wavelet wavelet NOUN american_scientific_journal-1305 51 39 or or CCONJ american_scientific_journal-1305 51 40 wave wave NOUN american_scientific_journal-1305 51 41 fronts front NOUN american_scientific_journal-1305 51 42 ( ( PUNCT american_scientific_journal-1305 51 43 piecewise piecewise NOUN american_scientific_journal-1305 51 44 step step NOUN american_scientific_journal-1305 51 45 function function NOUN american_scientific_journal-1305 51 46 ) ) PUNCT american_scientific_journal-1305 51 47 and and CCONJ american_scientific_journal-1305 51 48 do do AUX american_scientific_journal-1305 51 49 not not PART american_scientific_journal-1305 51 50 represent represent VERB american_scientific_journal-1305 51 51 attractors attractor NOUN american_scientific_journal-1305 51 52 . . PUNCT american_scientific_journal-1305 52 1 with with ADP american_scientific_journal-1305 52 2 this this DET american_scientific_journal-1305 52 3 limitation limitation NOUN american_scientific_journal-1305 52 4 , , PUNCT american_scientific_journal-1305 52 5 the the DET american_scientific_journal-1305 52 6 fourier fourier NOUN american_scientific_journal-1305 52 7 transform transform NOUN american_scientific_journal-1305 52 8 is be AUX american_scientific_journal-1305 52 9 changed change VERB american_scientific_journal-1305 52 10 in in ADP american_scientific_journal-1305 52 11 to to ADP american_scientific_journal-1305 52 12 laplace laplace NOUN american_scientific_journal-1305 52 13 transform transform NOUN american_scientific_journal-1305 52 14 . . PUNCT american_scientific_journal-1305 53 1 using use VERB american_scientific_journal-1305 53 2 the the DET american_scientific_journal-1305 53 3 generalized generalized ADJ american_scientific_journal-1305 53 4 definitions definition NOUN american_scientific_journal-1305 53 5 of of ADP american_scientific_journal-1305 53 6 heaviside heaviside ADJ american_scientific_journal-1305 53 7 step step NOUN american_scientific_journal-1305 53 8 function function NOUN american_scientific_journal-1305 53 9 . . PUNCT american_scientific_journal-1305 54 1 by by ADP american_scientific_journal-1305 54 2 bracewell bracewell NOUN american_scientific_journal-1305 55 1 [ [ X american_scientific_journal-1305 55 2 25 25 NUM american_scientific_journal-1305 55 3 ] ] PUNCT american_scientific_journal-1305 55 4 , , PUNCT american_scientific_journal-1305 55 5 we we PRON american_scientific_journal-1305 55 6 observe observe VERB american_scientific_journal-1305 55 7 that that SCONJ american_scientific_journal-1305 55 8 𝐻(π‘₯ 𝐻(π‘₯ NOUN american_scientific_journal-1305 55 9 ) ) PUNCT american_scientific_journal-1305 55 10 changes change NOUN american_scientific_journal-1305 55 11 between between ADP american_scientific_journal-1305 55 12 1 1 NUM american_scientific_journal-1305 55 13 and and CCONJ american_scientific_journal-1305 55 14 1 1 NUM american_scientific_journal-1305 55 15 2⁄ 2⁄ NUM american_scientific_journal-1305 55 16 for for ADP american_scientific_journal-1305 55 17 π‘₯ π‘₯ PROPN american_scientific_journal-1305 55 18 β‰₯ β‰₯ NUM american_scientific_journal-1305 55 19 0 0 NUM american_scientific_journal-1305 55 20 and and CCONJ american_scientific_journal-1305 55 21 changes change NOUN american_scientific_journal-1305 55 22 between between ADP american_scientific_journal-1305 55 23 0 0 NUM american_scientific_journal-1305 55 24 and and CCONJ american_scientific_journal-1305 55 25 1 1 NUM american_scientific_journal-1305 55 26 2⁄ 2⁄ NUM american_scientific_journal-1305 55 27 for for ADP american_scientific_journal-1305 55 28 π‘₯ π‘₯ NOUN american_scientific_journal-1305 55 29 ≀ ≀ NUM american_scientific_journal-1305 55 30 0 0 NUM american_scientific_journal-1305 55 31 . . PUNCT american_scientific_journal-1305 56 1 few few ADJ american_scientific_journal-1305 56 2 of of ADP american_scientific_journal-1305 56 3 the the DET american_scientific_journal-1305 56 4 expressions expression NOUN american_scientific_journal-1305 56 5 of of ADP american_scientific_journal-1305 56 6 the the DET american_scientific_journal-1305 56 7 heaviside heaviside ADJ american_scientific_journal-1305 56 8 step step NOUN american_scientific_journal-1305 56 9 function function NOUN american_scientific_journal-1305 56 10 [ [ X american_scientific_journal-1305 56 11 25 25 NUM american_scientific_journal-1305 56 12 ] ] PUNCT american_scientific_journal-1305 56 13 are be AUX american_scientific_journal-1305 56 14 written write VERB american_scientific_journal-1305 56 15 to to PART american_scientific_journal-1305 56 16 reflect reflect VERB american_scientific_journal-1305 56 17 our our PRON american_scientific_journal-1305 56 18 conjectures conjecture NOUN american_scientific_journal-1305 56 19 true true ADJ american_scientific_journal-1305 56 20 in in ADP american_scientific_journal-1305 56 21 the the DET american_scientific_journal-1305 56 22 above above ADJ american_scientific_journal-1305 56 23 paragraph paragraph NOUN american_scientific_journal-1305 56 24 . . PUNCT american_scientific_journal-1305 57 1 𝐻𝑛(π‘₯ 𝐻𝑛(π‘₯ NOUN american_scientific_journal-1305 57 2 ) ) PUNCT american_scientific_journal-1305 58 1 = = SYM american_scientific_journal-1305 58 2 lim lim PROPN american_scientific_journal-1305 58 3 𝑑→0 𝑑→0 PROPN american_scientific_journal-1305 58 4 οΏ½ οΏ½ PROPN american_scientific_journal-1305 58 5 1 1 NUM american_scientific_journal-1305 58 6 2 2 NUM american_scientific_journal-1305 58 7 𝑒π‘₯ 𝑒π‘₯ NOUN american_scientific_journal-1305 58 8 𝑑⁄ 𝑑⁄ NUM american_scientific_journal-1305 58 9 , , PUNCT american_scientific_journal-1305 58 10 if if SCONJ american_scientific_journal-1305 58 11 π‘₯ π‘₯ ADP american_scientific_journal-1305 58 12 ≀ ≀ NUM american_scientific_journal-1305 58 13 0 0 NUM american_scientific_journal-1305 58 14 1 1 NUM american_scientific_journal-1305 58 15 βˆ’ βˆ’ NUM american_scientific_journal-1305 58 16 1 1 NUM american_scientific_journal-1305 58 17 2 2 NUM american_scientific_journal-1305 58 18 π‘’βˆ’π‘₯ π‘’βˆ’π‘₯ NOUN american_scientific_journal-1305 58 19 𝑑⁄ 𝑑⁄ NUM american_scientific_journal-1305 58 20 , , PUNCT american_scientific_journal-1305 58 21 if if SCONJ american_scientific_journal-1305 58 22 π‘₯ π‘₯ PROPN american_scientific_journal-1305 58 23 β‰₯ β‰₯ X american_scientific_journal-1305 58 24 0 0 NUM american_scientific_journal-1305 58 25 ( ( PUNCT american_scientific_journal-1305 58 26 2 2 NUM american_scientific_journal-1305 58 27 ) ) PUNCT american_scientific_journal-1305 58 28 where where SCONJ american_scientific_journal-1305 58 29 π‘₯ π‘₯ PROPN american_scientific_journal-1305 58 30 𝑑⁄ 𝑑⁄ PROPN american_scientific_journal-1305 58 31 is be AUX american_scientific_journal-1305 58 32 a a DET american_scientific_journal-1305 58 33 fractional fractional ADJ american_scientific_journal-1305 58 34 exponent exponent NOUN american_scientific_journal-1305 58 35 . . PUNCT american_scientific_journal-1305 59 1 the the DET american_scientific_journal-1305 59 2 aperiodic aperiodic ADJ american_scientific_journal-1305 59 3 stable stable ADJ american_scientific_journal-1305 59 4 chaos chaos NOUN american_scientific_journal-1305 59 5 differs differ VERB american_scientific_journal-1305 59 6 from from ADP american_scientific_journal-1305 59 7 periodic periodic ADJ american_scientific_journal-1305 59 8 unstable unstable ADJ american_scientific_journal-1305 59 9 chaos chaos NOUN american_scientific_journal-1305 59 10 [ [ X american_scientific_journal-1305 59 11 20].the 20].the DET american_scientific_journal-1305 59 12 unstable unstable ADJ american_scientific_journal-1305 59 13 periodic periodic ADJ american_scientific_journal-1305 59 14 chaos chaos NOUN american_scientific_journal-1305 59 15 [ [ X american_scientific_journal-1305 59 16 13 13 NUM american_scientific_journal-1305 59 17 ] ] PUNCT american_scientific_journal-1305 59 18 , , PUNCT american_scientific_journal-1305 59 19 [ [ X american_scientific_journal-1305 59 20 14 14 NUM american_scientific_journal-1305 59 21 ] ] PUNCT american_scientific_journal-1305 59 22 , , PUNCT american_scientific_journal-1305 59 23 [ [ X american_scientific_journal-1305 59 24 20 20 NUM american_scientific_journal-1305 59 25 ] ] PUNCT american_scientific_journal-1305 59 26 is be AUX american_scientific_journal-1305 59 27 associated associate VERB american_scientific_journal-1305 59 28 with with ADP american_scientific_journal-1305 59 29 multiple multiple ADJ american_scientific_journal-1305 59 30 iterations iteration NOUN american_scientific_journal-1305 59 31 and and CCONJ american_scientific_journal-1305 59 32 for for ADP american_scientific_journal-1305 59 33 each each DET american_scientific_journal-1305 59 34 iterations iteration NOUN american_scientific_journal-1305 59 35 , , PUNCT american_scientific_journal-1305 59 36 periodicity periodicity NOUN american_scientific_journal-1305 59 37 is be AUX american_scientific_journal-1305 59 38 maintained maintain VERB american_scientific_journal-1305 59 39 whereas whereas SCONJ american_scientific_journal-1305 59 40 the the DET american_scientific_journal-1305 59 41 stable stable ADJ american_scientific_journal-1305 59 42 aperiodic aperiodic ADJ american_scientific_journal-1305 59 43 chaos chaos NOUN american_scientific_journal-1305 59 44 [ [ X american_scientific_journal-1305 59 45 15 15 NUM american_scientific_journal-1305 59 46 ] ] PUNCT american_scientific_journal-1305 59 47 follow follow VERB american_scientific_journal-1305 59 48 a a DET american_scientific_journal-1305 59 49 singlet singlet ADJ american_scientific_journal-1305 59 50 iteration iteration NOUN american_scientific_journal-1305 59 51 ( ( PUNCT american_scientific_journal-1305 59 52 closed closed ADJ american_scientific_journal-1305 59 53 loop loop NOUN american_scientific_journal-1305 59 54 ) ) PUNCT american_scientific_journal-1305 59 55 . . PUNCT american_scientific_journal-1305 60 1 we we PRON american_scientific_journal-1305 60 2 shall shall AUX american_scientific_journal-1305 60 3 consider consider VERB american_scientific_journal-1305 60 4 the the DET american_scientific_journal-1305 60 5 time time NOUN american_scientific_journal-1305 60 6 -frequency -frequency PROPN american_scientific_journal-1305 60 7 representation representation NOUN american_scientific_journal-1305 60 8 of of ADP american_scientific_journal-1305 60 9 fractional fractional ADJ american_scientific_journal-1305 60 10 fourier fourier NOUN american_scientific_journal-1305 60 11 transform transform NOUN american_scientific_journal-1305 60 12 ( ( PUNCT american_scientific_journal-1305 60 13 frft frft ADJ american_scientific_journal-1305 60 14 ) ) PUNCT american_scientific_journal-1305 60 15 , , PUNCT american_scientific_journal-1305 61 1 [ [ X american_scientific_journal-1305 61 2 26 26 NUM american_scientific_journal-1305 61 3 ] ] PUNCT american_scientific_journal-1305 61 4 . . PUNCT american_scientific_journal-1305 62 1 such such ADJ american_scientific_journal-1305 62 2 as as ADP american_scientific_journal-1305 62 3 the the DET american_scientific_journal-1305 62 4 wigner wigner ADJ american_scientific_journal-1305 62 5 distribution distribution NOUN american_scientific_journal-1305 62 6 ( ( PUNCT american_scientific_journal-1305 62 7 wd wd PROPN american_scientific_journal-1305 62 8 ) ) PUNCT american_scientific_journal-1305 62 9 , , PUNCT american_scientific_journal-1305 62 10 wiener wiener NOUN american_scientific_journal-1305 62 11 space space NOUN american_scientific_journal-1305 62 12 ( ( PUNCT american_scientific_journal-1305 62 13 ws ws NOUN american_scientific_journal-1305 62 14 ) ) PUNCT american_scientific_journal-1305 62 15 , , PUNCT american_scientific_journal-1305 62 16 the the DET american_scientific_journal-1305 62 17 ambiguity ambiguity NOUN american_scientific_journal-1305 62 18 function function NOUN american_scientific_journal-1305 62 19 , , PUNCT american_scientific_journal-1305 62 20 the the DET american_scientific_journal-1305 62 21 short short ADJ american_scientific_journal-1305 62 22 time time NOUN american_scientific_journal-1305 62 23 fourier fourier NOUN american_scientific_journal-1305 62 24 transform transform NOUN american_scientific_journal-1305 62 25 ( ( PUNCT american_scientific_journal-1305 62 26 stft stft PROPN american_scientific_journal-1305 62 27 ) ) PUNCT american_scientific_journal-1305 62 28 and and CCONJ american_scientific_journal-1305 62 29 the the DET american_scientific_journal-1305 62 30 spectrograms spectrogram NOUN american_scientific_journal-1305 62 31 used use VERB american_scientific_journal-1305 62 32 in in ADP american_scientific_journal-1305 62 33 speech speech NOUN american_scientific_journal-1305 62 34 processing processing NOUN american_scientific_journal-1305 62 35 , , PUNCT american_scientific_journal-1305 62 36 radar radar NOUN american_scientific_journal-1305 62 37 , , PUNCT american_scientific_journal-1305 62 38 image image NOUN american_scientific_journal-1305 62 39 rotations rotation NOUN american_scientific_journal-1305 62 40 , , PUNCT american_scientific_journal-1305 62 41 confocal confocal ADJ american_scientific_journal-1305 62 42 microscopy microscopy NOUN american_scientific_journal-1305 62 43 , , PUNCT american_scientific_journal-1305 62 44 etc etc X american_scientific_journal-1305 62 45 . . X american_scientific_journal-1305 62 46 with with ADP american_scientific_journal-1305 62 47 rotation rotation NOUN american_scientific_journal-1305 62 48 vector vector NOUN american_scientific_journal-1305 62 49 Ξ± Ξ± PRON american_scientific_journal-1305 62 50 to to PART american_scientific_journal-1305 62 51 define define VERB american_scientific_journal-1305 62 52 the the DET american_scientific_journal-1305 62 53 aperiodic aperiodic ADJ american_scientific_journal-1305 62 54 stable stable ADJ american_scientific_journal-1305 62 55 chaos chaos NOUN american_scientific_journal-1305 62 56 with with ADP american_scientific_journal-1305 62 57 lyapunov lyapunov ADJ american_scientific_journal-1305 62 58 exponents exponent NOUN american_scientific_journal-1305 62 59 in in ADP american_scientific_journal-1305 62 60 time time NOUN american_scientific_journal-1305 62 61 series series NOUN american_scientific_journal-1305 62 62 . . PUNCT american_scientific_journal-1305 63 1 2 2 X american_scientific_journal-1305 63 2 . . NUM american_scientific_journal-1305 63 3 results result NOUN american_scientific_journal-1305 63 4 and and CCONJ american_scientific_journal-1305 63 5 discussions discussion NOUN american_scientific_journal-1305 63 6 almeida almeida PROPN american_scientific_journal-1305 64 1 [ [ X american_scientific_journal-1305 64 2 26 26 NUM american_scientific_journal-1305 64 3 ] ] PUNCT american_scientific_journal-1305 64 4 define define VERB american_scientific_journal-1305 64 5 the the DET american_scientific_journal-1305 64 6 kernel kernel NOUN american_scientific_journal-1305 64 7 of of ADP american_scientific_journal-1305 64 8 frft frft ADJ american_scientific_journal-1305 64 9 in in ADP american_scientific_journal-1305 64 10 time time NOUN american_scientific_journal-1305 64 11 frequency frequency NOUN american_scientific_journal-1305 64 12 plane plane NOUN american_scientific_journal-1305 64 13 , , PUNCT american_scientific_journal-1305 64 14 .i.e .i.e PUNCT american_scientific_journal-1305 64 15 . . PUNCT american_scientific_journal-1305 64 16 , , PUNCT american_scientific_journal-1305 64 17 284 284 NUM american_scientific_journal-1305 64 18 american american ADJ american_scientific_journal-1305 64 19 scientific scientific ADJ american_scientific_journal-1305 64 20 research research NOUN american_scientific_journal-1305 64 21 journal journal NOUN american_scientific_journal-1305 64 22 for for ADP american_scientific_journal-1305 64 23 engineering engineering NOUN american_scientific_journal-1305 64 24 , , PUNCT american_scientific_journal-1305 64 25 technology technology NOUN american_scientific_journal-1305 64 26 , , PUNCT american_scientific_journal-1305 64 27 and and CCONJ american_scientific_journal-1305 64 28 sciences science NOUN american_scientific_journal-1305 64 29 ( ( PUNCT american_scientific_journal-1305 64 30 asrjets asrjet NOUN american_scientific_journal-1305 64 31 ) ) PUNCT american_scientific_journal-1305 64 32 ( ( PUNCT american_scientific_journal-1305 64 33 2016 2016 NUM american_scientific_journal-1305 64 34 ) ) PUNCT american_scientific_journal-1305 64 35 volume volume NOUN american_scientific_journal-1305 64 36 15 15 NUM american_scientific_journal-1305 64 37 , , PUNCT american_scientific_journal-1305 64 38 no no DET american_scientific_journal-1305 64 39 1 1 NUM american_scientific_journal-1305 64 40 , , PUNCT american_scientific_journal-1305 64 41 pp pp ADV american_scientific_journal-1305 64 42 282 282 NUM american_scientific_journal-1305 64 43 - - SYM american_scientific_journal-1305 64 44 289 289 NUM american_scientific_journal-1305 64 45 𝐾𝛼(𝑑,𝑒 𝐾𝛼(𝑑,𝑒 NOUN american_scientific_journal-1305 64 46 ) ) PUNCT american_scientific_journal-1305 64 47 = = SYM american_scientific_journal-1305 64 48 ⎩ ⎩ NUM american_scientific_journal-1305 64 49 βŽͺ βŽͺ NOUN american_scientific_journal-1305 64 50 ⎨ ⎨ ADJ american_scientific_journal-1305 64 51 βŽͺ βŽͺ NOUN american_scientific_journal-1305 64 52 ⎧ ⎧ PROPN american_scientific_journal-1305 64 53 οΏ½ οΏ½ PROPN american_scientific_journal-1305 64 54 1βˆ’π‘— 1βˆ’π‘— NUM american_scientific_journal-1305 64 55 cot cot NOUN american_scientific_journal-1305 64 56 𝛼 𝛼 NOUN american_scientific_journal-1305 64 57 2πœ‹ 2πœ‹ NOUN american_scientific_journal-1305 64 58 𝑒𝑗 𝑒𝑗 PUNCT american_scientific_journal-1305 64 59 𝑑2+𝑒2 𝑑2+𝑒2 SYM american_scientific_journal-1305 64 60 2 2 NUM american_scientific_journal-1305 64 61 cot cot NOUN american_scientific_journal-1305 64 62 π›Όβˆ’π‘—π‘’π‘‘ π›Όβˆ’π‘—π‘’π‘‘ NOUN american_scientific_journal-1305 64 63 csc csc PROPN american_scientific_journal-1305 64 64 𝛼 𝛼 PROPN american_scientific_journal-1305 64 65 if if SCONJ american_scientific_journal-1305 64 66 𝛼 𝛼 PRON american_scientific_journal-1305 64 67 β‰  β‰  PROPN american_scientific_journal-1305 64 68 πœ‹ πœ‹ PRON american_scientific_journal-1305 64 69 𝛿(𝑑 𝛿(𝑑 PROPN american_scientific_journal-1305 64 70 βˆ’ βˆ’ PROPN american_scientific_journal-1305 64 71 𝑒 𝑒 X american_scientific_journal-1305 64 72 ) ) PUNCT american_scientific_journal-1305 64 73 if if SCONJ american_scientific_journal-1305 64 74 𝛼 𝛼 NOUN american_scientific_journal-1305 64 75 = = NOUN american_scientific_journal-1305 64 76 2π‘›πœ‹ 2π‘›πœ‹ NOUN american_scientific_journal-1305 65 1 𝛿(𝑑 𝛿(𝑑 PROPN american_scientific_journal-1305 65 2 + + CCONJ american_scientific_journal-1305 65 3 𝑒 𝑒 X american_scientific_journal-1305 65 4 ) ) PUNCT american_scientific_journal-1305 65 5 if if SCONJ american_scientific_journal-1305 65 6 𝛼 𝛼 X american_scientific_journal-1305 65 7 = = SYM american_scientific_journal-1305 65 8 ( ( PUNCT american_scientific_journal-1305 65 9 2𝑛 2𝑛 PROPN american_scientific_journal-1305 65 10 βˆ’ βˆ’ PROPN american_scientific_journal-1305 65 11 1)πœ‹ 1)πœ‹ PROPN american_scientific_journal-1305 65 12 ( ( PUNCT american_scientific_journal-1305 65 13 3 3 NUM american_scientific_journal-1305 65 14 ) ) PUNCT american_scientific_journal-1305 65 15 where where SCONJ american_scientific_journal-1305 65 16 𝑛 𝑛 PROPN american_scientific_journal-1305 65 17 is be AUX american_scientific_journal-1305 65 18 an an DET american_scientific_journal-1305 65 19 integer integer NOUN american_scientific_journal-1305 65 20 . . PUNCT american_scientific_journal-1305 66 1 with with ADP american_scientific_journal-1305 66 2 𝛼 𝛼 NOUN american_scientific_journal-1305 66 3 = = X american_scientific_journal-1305 66 4 πœ‹ πœ‹ X american_scientific_journal-1305 66 5 2 2 NUM american_scientific_journal-1305 66 6 , , PUNCT american_scientific_journal-1305 66 7 the the DET american_scientific_journal-1305 66 8 kernel kernel NOUN american_scientific_journal-1305 66 9 in in ADP american_scientific_journal-1305 66 10 eq eq NOUN american_scientific_journal-1305 66 11 ( ( PUNCT american_scientific_journal-1305 66 12 3 3 NUM american_scientific_journal-1305 66 13 ) ) PUNCT american_scientific_journal-1305 66 14 coincides coincide VERB american_scientific_journal-1305 66 15 with with ADP american_scientific_journal-1305 66 16 the the DET american_scientific_journal-1305 66 17 kernel kernel NOUN american_scientific_journal-1305 66 18 of of ADP american_scientific_journal-1305 66 19 the the DET american_scientific_journal-1305 66 20 fourier fourier NOUN american_scientific_journal-1305 66 21 transform transform NOUN american_scientific_journal-1305 66 22 ( ( PUNCT american_scientific_journal-1305 66 23 ft ft NOUN american_scientific_journal-1305 66 24 ) ) PUNCT american_scientific_journal-1305 66 25 . . PUNCT american_scientific_journal-1305 67 1 almeida almeida PROPN american_scientific_journal-1305 68 1 [ [ X american_scientific_journal-1305 68 2 26 26 NUM american_scientific_journal-1305 68 3 ] ] PUNCT american_scientific_journal-1305 68 4 redefined redefine VERB american_scientific_journal-1305 68 5 the the DET american_scientific_journal-1305 68 6 frft frft NOUN american_scientific_journal-1305 68 7 of of ADP american_scientific_journal-1305 68 8 a a DET american_scientific_journal-1305 68 9 functionπ‘₯(𝑑 functionπ‘₯(𝑑 PROPN american_scientific_journal-1305 68 10 ) ) PUNCT american_scientific_journal-1305 68 11 , , PUNCT american_scientific_journal-1305 68 12 with with ADP american_scientific_journal-1305 68 13 an an DET american_scientific_journal-1305 68 14 angle angle NOUN american_scientific_journal-1305 68 15 𝛼 𝛼 NOUN american_scientific_journal-1305 68 16 , , PUNCT american_scientific_journal-1305 68 17 which which PRON american_scientific_journal-1305 68 18 is be AUX american_scientific_journal-1305 68 19 define define NOUN american_scientific_journal-1305 68 20 in in ADP american_scientific_journal-1305 68 21 eq eq NOUN american_scientific_journal-1305 68 22 ( ( PUNCT american_scientific_journal-1305 68 23 4 4 NUM american_scientific_journal-1305 68 24 ) ) PUNCT american_scientific_journal-1305 68 25 ℱ𝛼[π‘₯(𝑑 ℱ𝛼[π‘₯(𝑑 NUM american_scientific_journal-1305 68 26 ) ) PUNCT american_scientific_journal-1305 68 27 ] ] PUNCT american_scientific_journal-1305 69 1 = = SYM american_scientific_journal-1305 69 2 𝑋𝛼(𝑒 𝑋𝛼(𝑒 NOUN american_scientific_journal-1305 69 3 ) ) PUNCT american_scientific_journal-1305 69 4 = = SYM american_scientific_journal-1305 69 5 οΏ½ οΏ½ PROPN american_scientific_journal-1305 69 6 π‘₯(𝑑 π‘₯(𝑑 PROPN american_scientific_journal-1305 69 7 ) ) PUNCT american_scientific_journal-1305 69 8 ∞ ∞ NUM american_scientific_journal-1305 69 9 βˆ’βˆž βˆ’βˆž ADP american_scientific_journal-1305 69 10 𝐾𝛼(𝑑,𝑒)𝑑𝑑 𝐾𝛼(𝑑,𝑒)𝑑𝑑 NOUN american_scientific_journal-1305 69 11 = = SYM american_scientific_journal-1305 69 12 ⎩ ⎩ NUM american_scientific_journal-1305 69 13 ⎨ ⎨ PROPN american_scientific_journal-1305 69 14 ⎧ ⎧ PROPN american_scientific_journal-1305 69 15 οΏ½ οΏ½ PROPN american_scientific_journal-1305 69 16 1βˆ’π‘— 1βˆ’π‘— NUM american_scientific_journal-1305 69 17 cot cot NOUN american_scientific_journal-1305 69 18 𝛼 𝛼 PROPN american_scientific_journal-1305 69 19 2πœ‹ 2πœ‹ NUM american_scientific_journal-1305 69 20 𝑒𝑗 𝑒𝑗 PROPN american_scientific_journal-1305 69 21 𝑒2 𝑒2 PROPN american_scientific_journal-1305 69 22 2 2 NUM american_scientific_journal-1305 69 23 cot cot NOUN american_scientific_journal-1305 69 24 𝛼 𝛼 NOUN american_scientific_journal-1305 69 25 ∫ ∫ PROPN american_scientific_journal-1305 69 26 π‘₯(𝑑)𝑒𝑗 π‘₯(𝑑)𝑒𝑗 NUM american_scientific_journal-1305 69 27 𝑑2 𝑑2 PROPN american_scientific_journal-1305 69 28 2 2 NUM american_scientific_journal-1305 69 29 cot cot NOUN american_scientific_journal-1305 69 30 π›Όβˆ’π‘—π‘’π‘‘ π›Όβˆ’π‘—π‘’π‘‘ NOUN american_scientific_journal-1305 69 31 csc csc PROPN american_scientific_journal-1305 69 32 𝛼𝑑𝑑 𝛼𝑑𝑑 PROPN american_scientific_journal-1305 69 33 𝑖𝑓 𝑖𝑓 NUM american_scientific_journal-1305 69 34 𝛼 𝛼 PROPN american_scientific_journal-1305 69 35 𝑖𝑠 𝑖𝑠 NOUN american_scientific_journal-1305 69 36 π‘›π‘œπ‘‘ π‘›π‘œπ‘‘ NOUN american_scientific_journal-1305 70 1 π‘Ž π‘Ž NOUN american_scientific_journal-1305 70 2 π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ NOUN american_scientific_journal-1305 70 3 π‘œπ‘“ π‘œπ‘“ ADP american_scientific_journal-1305 70 4 πœ‹ πœ‹ NOUN american_scientific_journal-1305 70 5 ∞ ∞ PROPN american_scientific_journal-1305 70 6 βˆ’βˆž βˆ’βˆž ADP american_scientific_journal-1305 70 7 π‘₯(𝑑 π‘₯(𝑑 NOUN american_scientific_journal-1305 70 8 ) ) PUNCT american_scientific_journal-1305 70 9 𝑖𝑓 𝑖𝑓 VERB american_scientific_journal-1305 70 10 𝛼 𝛼 NOUN american_scientific_journal-1305 70 11 𝑖𝑠 𝑖𝑠 NOUN american_scientific_journal-1305 70 12 π‘›π‘œπ‘‘ π‘›π‘œπ‘‘ NOUN american_scientific_journal-1305 70 13 π‘Ž π‘Ž NOUN american_scientific_journal-1305 70 14 π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ NOUN american_scientific_journal-1305 70 15 π‘œπ‘“ π‘œπ‘“ ADP american_scientific_journal-1305 70 16 2πœ‹ 2πœ‹ NOUN american_scientific_journal-1305 70 17 π‘₯(βˆ’π‘‘ π‘₯(βˆ’π‘‘ ADV american_scientific_journal-1305 70 18 ) ) PUNCT american_scientific_journal-1305 71 1 𝑖𝑓 𝑖𝑓 VERB american_scientific_journal-1305 72 1 𝛼 𝛼 NOUN american_scientific_journal-1305 72 2 + + CCONJ american_scientific_journal-1305 72 3 πœ‹ πœ‹ NOUN american_scientific_journal-1305 72 4 𝑖𝑠 𝑖𝑠 NOUN american_scientific_journal-1305 72 5 π‘›π‘œπ‘‘ π‘›π‘œπ‘‘ NOUN american_scientific_journal-1305 73 1 π‘Ž π‘Ž NOUN american_scientific_journal-1305 73 2 π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’ NOUN american_scientific_journal-1305 73 3 π‘œπ‘“ π‘œπ‘“ ADP american_scientific_journal-1305 73 4 2πœ‹ 2πœ‹ NOUN american_scientific_journal-1305 73 5 ( ( PUNCT american_scientific_journal-1305 73 6 4 4 NUM american_scientific_journal-1305 73 7 ) ) PUNCT american_scientific_journal-1305 73 8 where where SCONJ american_scientific_journal-1305 73 9 𝑒 𝑒 X american_scientific_journal-1305 73 10 ≑ ≑ PROPN american_scientific_journal-1305 73 11 πœ” πœ” X american_scientific_journal-1305 73 12 ( ( PUNCT american_scientific_journal-1305 73 13 the the DET american_scientific_journal-1305 73 14 angular angular ADJ american_scientific_journal-1305 73 15 frequency frequency NOUN american_scientific_journal-1305 73 16 ) ) PUNCT american_scientific_journal-1305 73 17 . . PUNCT american_scientific_journal-1305 74 1 we we PRON american_scientific_journal-1305 74 2 assume assume VERB american_scientific_journal-1305 74 3 frft frft ADJ american_scientific_journal-1305 74 4 equivalent equivalent ADJ american_scientific_journal-1305 74 5 to to ADP american_scientific_journal-1305 74 6 𝐻𝑛𝑓(π‘₯)𝑒π‘₯𝑝 𝐻𝑛𝑓(π‘₯)𝑒π‘₯𝑝 ADV american_scientific_journal-1305 74 7 οΏ½ οΏ½ PROPN american_scientific_journal-1305 74 8 βˆ’ βˆ’ PROPN american_scientific_journal-1305 74 9 π‘₯2 π‘₯2 NOUN american_scientific_journal-1305 74 10 2 2 NUM american_scientific_journal-1305 74 11 οΏ½ οΏ½ NOUN american_scientific_journal-1305 74 12 and and CCONJ american_scientific_journal-1305 74 13 time time NOUN american_scientific_journal-1305 74 14 periodic periodic ADJ american_scientific_journal-1305 74 15 signal signal NOUN american_scientific_journal-1305 74 16 π‘₯ π‘₯ NOUN american_scientific_journal-1305 74 17 = = SYM american_scientific_journal-1305 74 18 𝐴 𝐴 PROPN american_scientific_journal-1305 74 19 sinπœ”πœŠ sinπœ”πœŠ VERB american_scientific_journal-1305 74 20 as as ADP american_scientific_journal-1305 74 21 gaussian gaussian NOUN american_scientific_journal-1305 74 22 and and CCONJ american_scientific_journal-1305 74 23 exponentially exponentially ADV american_scientific_journal-1305 74 24 correlated correlate VERB american_scientific_journal-1305 74 25 . . PUNCT american_scientific_journal-1305 75 1 a a PRON american_scientific_journal-1305 75 2 is be AUX american_scientific_journal-1305 75 3 real real ADV american_scientific_journal-1305 75 4 constant constant ADJ american_scientific_journal-1305 75 5 in in ADP american_scientific_journal-1305 75 6 π‘₯(𝑑 π‘₯(𝑑 NOUN american_scientific_journal-1305 75 7 ) ) PUNCT american_scientific_journal-1305 75 8 while while SCONJ american_scientific_journal-1305 75 9 𝐻𝑛𝑓(π‘₯ 𝐻𝑛𝑓(π‘₯ NOUN american_scientific_journal-1305 75 10 ) ) PUNCT american_scientific_journal-1305 75 11 is be AUX american_scientific_journal-1305 75 12 a a DET american_scientific_journal-1305 75 13 hermite hermite ADJ american_scientific_journal-1305 75 14 polynomial polynomial NOUN american_scientific_journal-1305 75 15 for for ADP american_scientific_journal-1305 75 16 𝑛𝑓 𝑛𝑓 PROPN american_scientific_journal-1305 75 17 exponents exponent NOUN american_scientific_journal-1305 75 18 ( ( PUNCT american_scientific_journal-1305 75 19 usually usually ADV american_scientific_journal-1305 75 20 termed term VERB american_scientific_journal-1305 75 21 as as ADP american_scientific_journal-1305 75 22 lyapunov lyapunov ADJ american_scientific_journal-1305 75 23 exponents exponent NOUN american_scientific_journal-1305 75 24 ) ) PUNCT american_scientific_journal-1305 75 25 . . PUNCT american_scientific_journal-1305 76 1 the the DET american_scientific_journal-1305 76 2 exponent exponent NOUN american_scientific_journal-1305 76 3 of of ADP american_scientific_journal-1305 76 4 𝑋𝛼(𝑒 𝑋𝛼(𝑒 PROPN american_scientific_journal-1305 76 5 ≑ ≑ PROPN american_scientific_journal-1305 76 6 πœ” πœ” PRON american_scientific_journal-1305 76 7 ) ) PUNCT american_scientific_journal-1305 76 8 in in ADP american_scientific_journal-1305 76 9 eq eq NOUN american_scientific_journal-1305 76 10 ( ( PUNCT american_scientific_journal-1305 76 11 4 4 NUM american_scientific_journal-1305 76 12 ) ) PUNCT american_scientific_journal-1305 76 13 is be AUX american_scientific_journal-1305 76 14 𝛼. 𝛼. NOUN american_scientific_journal-1305 76 15 we we PRON american_scientific_journal-1305 76 16 assume assume VERB american_scientific_journal-1305 76 17 the the DET american_scientific_journal-1305 76 18 exponent exponent NOUN american_scientific_journal-1305 76 19 𝛼 𝛼 NOUN american_scientific_journal-1305 76 20 of of ADP american_scientific_journal-1305 76 21 𝑋𝛼(𝑒 𝑋𝛼(𝑒 NOUN american_scientific_journal-1305 76 22 ) ) PUNCT american_scientific_journal-1305 76 23 to to PART american_scientific_journal-1305 76 24 become become VERB american_scientific_journal-1305 76 25 lyapunov lyapunov ADJ american_scientific_journal-1305 76 26 exponents exponent NOUN american_scientific_journal-1305 76 27 𝑋𝛼(𝑒 𝑋𝛼(𝑒 PROPN american_scientific_journal-1305 76 28 ≑ ≑ PROPN american_scientific_journal-1305 76 29 πœ” πœ” PRON american_scientific_journal-1305 76 30 ) ) PUNCT american_scientific_journal-1305 76 31 ~𝐻𝑛𝑓(π‘₯)exp ~𝐻𝑛𝑓(π‘₯)exp NOUN american_scientific_journal-1305 76 32 ( ( PUNCT american_scientific_journal-1305 76 33 βˆ’π‘₯2 βˆ’π‘₯2 NOUN american_scientific_journal-1305 76 34 2 2 NUM american_scientific_journal-1305 76 35 ) ) PUNCT american_scientific_journal-1305 76 36 β€˜ ' PUNCT american_scientific_journal-1305 76 37 ( ( PUNCT american_scientific_journal-1305 76 38 5 5 NUM american_scientific_journal-1305 76 39 ) ) PUNCT american_scientific_journal-1305 76 40 where where SCONJ american_scientific_journal-1305 76 41 𝛼 𝛼 NOUN american_scientific_journal-1305 76 42 = = PUNCT american_scientific_journal-1305 76 43 π‘Ž π‘Ž X american_scientific_journal-1305 76 44 πœ‹ πœ‹ NOUN american_scientific_journal-1305 76 45 2 2 NUM american_scientific_journal-1305 76 46 . . PUNCT american_scientific_journal-1305 77 1 using use VERB american_scientific_journal-1305 77 2 our our PRON american_scientific_journal-1305 77 3 recent recent ADJ american_scientific_journal-1305 77 4 results result NOUN american_scientific_journal-1305 77 5 on on ADP american_scientific_journal-1305 77 6 how how SCONJ american_scientific_journal-1305 77 7 fractional fractional ADJ american_scientific_journal-1305 77 8 charge charge NOUN american_scientific_journal-1305 77 9 on on ADP american_scientific_journal-1305 77 10 an an DET american_scientific_journal-1305 77 11 electron electron NOUN american_scientific_journal-1305 77 12 in in ADP american_scientific_journal-1305 77 13 the the DET american_scientific_journal-1305 77 14 momentum momentum NOUN american_scientific_journal-1305 77 15 space space NOUN american_scientific_journal-1305 77 16 is be AUX american_scientific_journal-1305 77 17 quantized quantize VERB american_scientific_journal-1305 77 18 ? ? PUNCT american_scientific_journal-1305 78 1 [ [ X american_scientific_journal-1305 78 2 27 27 NUM american_scientific_journal-1305 78 3 ] ] PUNCT american_scientific_journal-1305 78 4 , , PUNCT american_scientific_journal-1305 78 5 we we PRON american_scientific_journal-1305 78 6 find find VERB american_scientific_journal-1305 78 7 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ NOUN american_scientific_journal-1305 78 8 ) ) PUNCT american_scientific_journal-1305 79 1 = = SYM american_scientific_journal-1305 79 2 2𝑛𝑓 2𝑛𝑓 NOUN american_scientific_journal-1305 79 3 ( ( PUNCT american_scientific_journal-1305 79 4 6 6 NUM american_scientific_journal-1305 79 5 ) ) PUNCT american_scientific_journal-1305 79 6 where where SCONJ american_scientific_journal-1305 79 7 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ NOUN american_scientific_journal-1305 79 8 ) ) PUNCT american_scientific_journal-1305 79 9 are be AUX american_scientific_journal-1305 79 10 polynomials polynomial NOUN american_scientific_journal-1305 79 11 with with ADP american_scientific_journal-1305 79 12 𝑛𝑓 𝑛𝑓 PROPN american_scientific_journal-1305 79 13 , , PUNCT american_scientific_journal-1305 79 14 lyaponov lyaponov PROPN american_scientific_journal-1305 79 15 exponent exponent NOUN american_scientific_journal-1305 79 16 of of ADP american_scientific_journal-1305 79 17 2 2 NUM american_scientific_journal-1305 79 18 . . PUNCT american_scientific_journal-1305 79 19 eq eq X american_scientific_journal-1305 79 20 ( ( PUNCT american_scientific_journal-1305 79 21 6 6 NUM american_scientific_journal-1305 79 22 ) ) PUNCT american_scientific_journal-1305 79 23 is be AUX american_scientific_journal-1305 79 24 consistent consistent ADJ american_scientific_journal-1305 79 25 with with ADP american_scientific_journal-1305 79 26 the the DET american_scientific_journal-1305 79 27 following follow VERB american_scientific_journal-1305 79 28 definition definition NOUN american_scientific_journal-1305 79 29 of of ADP american_scientific_journal-1305 79 30 hermite hermite ADJ american_scientific_journal-1305 79 31 polynomials polynomial NOUN american_scientific_journal-1305 79 32 : : PUNCT american_scientific_journal-1305 79 33 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ NOUN american_scientific_journal-1305 79 34 ) ) PUNCT american_scientific_journal-1305 79 35 = = PUNCT american_scientific_journal-1305 80 1 ( ( PUNCT american_scientific_journal-1305 80 2 βˆ’1)π‘›π‘“π‘’πœ‰2 βˆ’1)π‘›π‘“π‘’πœ‰2 DET american_scientific_journal-1305 80 3 𝑑𝑛𝑓 𝑑𝑛𝑓 NOUN american_scientific_journal-1305 80 4 π‘‘πœ‰π‘›π‘“ π‘‘πœ‰π‘›π‘“ NOUN american_scientific_journal-1305 80 5 π‘’βˆ’πœ‰2 π‘’βˆ’πœ‰2 PROPN american_scientific_journal-1305 80 6 ( ( PUNCT american_scientific_journal-1305 80 7 7 7 NUM american_scientific_journal-1305 80 8 ) ) PUNCT american_scientific_journal-1305 80 9 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ PROPN american_scientific_journal-1305 80 10 ) ) PUNCT american_scientific_journal-1305 80 11 = = PUNCT american_scientific_journal-1305 81 1 ( ( PUNCT american_scientific_journal-1305 81 2 βˆ’1)π‘›π‘“π‘’πœ‰2 βˆ’1)π‘›π‘“π‘’πœ‰2 DET american_scientific_journal-1305 81 3 οΏ½ οΏ½ NOUN american_scientific_journal-1305 81 4 πœ‰ πœ‰ PART american_scientific_journal-1305 81 5 βˆ’ βˆ’ PROPN american_scientific_journal-1305 81 6 𝑑 𝑑 PROPN american_scientific_journal-1305 81 7 π‘‘πœ‰ π‘‘πœ‰ ADP american_scientific_journal-1305 81 8 οΏ½ οΏ½ PROPN american_scientific_journal-1305 81 9 𝑛𝑓 𝑛𝑓 PROPN american_scientific_journal-1305 81 10 π‘’βˆ’πœ‰2 π‘’βˆ’πœ‰2 X american_scientific_journal-1305 81 11 ( ( PUNCT american_scientific_journal-1305 81 12 8) 8) NUM american_scientific_journal-1305 81 13 eqs eqs X american_scientific_journal-1305 81 14 ( ( PUNCT american_scientific_journal-1305 81 15 7 7 NUM american_scientific_journal-1305 81 16 ) ) PUNCT american_scientific_journal-1305 81 17 and and CCONJ american_scientific_journal-1305 81 18 ( ( PUNCT american_scientific_journal-1305 81 19 8) 8) NUM american_scientific_journal-1305 81 20 show show VERB american_scientific_journal-1305 81 21 fractional fractional ADJ american_scientific_journal-1305 81 22 exponents exponent NOUN american_scientific_journal-1305 81 23 of of ADP american_scientific_journal-1305 81 24 𝑑 𝑑 PROPN american_scientific_journal-1305 81 25 π‘‘πœ‰ π‘‘πœ‰ PROPN american_scientific_journal-1305 81 26 and and CCONJ american_scientific_journal-1305 81 27 οΏ½ οΏ½ PROPN american_scientific_journal-1305 81 28 πœ‰ πœ‰ PART american_scientific_journal-1305 81 29 βˆ’ βˆ’ PROPN american_scientific_journal-1305 81 30 𝑑 𝑑 PROPN american_scientific_journal-1305 81 31 π‘‘πœ‰ π‘‘πœ‰ ADP american_scientific_journal-1305 81 32 οΏ½ οΏ½ PROPN american_scientific_journal-1305 81 33 . . PUNCT american_scientific_journal-1305 82 1 the the DET american_scientific_journal-1305 82 2 fractional fractional ADJ american_scientific_journal-1305 82 3 exponents exponent NOUN american_scientific_journal-1305 82 4 , , PUNCT american_scientific_journal-1305 82 5 𝑛𝑓 𝑛𝑓 PROPN american_scientific_journal-1305 82 6 can can AUX american_scientific_journal-1305 82 7 be be AUX american_scientific_journal-1305 82 8 envisaged envisage VERB american_scientific_journal-1305 82 9 285 285 NUM american_scientific_journal-1305 82 10 american american ADJ american_scientific_journal-1305 82 11 scientific scientific ADJ american_scientific_journal-1305 82 12 research research NOUN american_scientific_journal-1305 82 13 journal journal NOUN american_scientific_journal-1305 82 14 for for ADP american_scientific_journal-1305 82 15 engineering engineering NOUN american_scientific_journal-1305 82 16 , , PUNCT american_scientific_journal-1305 82 17 technology technology NOUN american_scientific_journal-1305 82 18 , , PUNCT american_scientific_journal-1305 82 19 and and CCONJ american_scientific_journal-1305 82 20 sciences science NOUN american_scientific_journal-1305 82 21 ( ( PUNCT american_scientific_journal-1305 82 22 asrjets asrjet NOUN american_scientific_journal-1305 82 23 ) ) PUNCT american_scientific_journal-1305 82 24 ( ( PUNCT american_scientific_journal-1305 82 25 2016 2016 NUM american_scientific_journal-1305 82 26 ) ) PUNCT american_scientific_journal-1305 82 27 volume volume NOUN american_scientific_journal-1305 82 28 15 15 NUM american_scientific_journal-1305 82 29 , , PUNCT american_scientific_journal-1305 82 30 no no DET american_scientific_journal-1305 82 31 1 1 NUM american_scientific_journal-1305 82 32 , , PUNCT american_scientific_journal-1305 82 33 pp pp ADV american_scientific_journal-1305 82 34 282 282 NUM american_scientific_journal-1305 82 35 - - SYM american_scientific_journal-1305 82 36 289 289 NUM american_scientific_journal-1305 82 37 with with ADP american_scientific_journal-1305 82 38 lyapunov lyapunov ADJ american_scientific_journal-1305 82 39 exponents exponent NOUN american_scientific_journal-1305 82 40 for for ADP american_scientific_journal-1305 82 41 attractors attractor NOUN american_scientific_journal-1305 82 42 . . PUNCT american_scientific_journal-1305 83 1 the the DET american_scientific_journal-1305 83 2 lyaponov lyaponov PROPN american_scientific_journal-1305 83 3 exponents exponent NOUN american_scientific_journal-1305 83 4 are be AUX american_scientific_journal-1305 83 5 both both ADV american_scientific_journal-1305 83 6 positive positive ADJ american_scientific_journal-1305 83 7 and and CCONJ american_scientific_journal-1305 83 8 negative negative ADJ american_scientific_journal-1305 83 9 fractional fractional ADJ american_scientific_journal-1305 83 10 exponents exponent NOUN american_scientific_journal-1305 83 11 . . PUNCT american_scientific_journal-1305 84 1 hence hence ADV american_scientific_journal-1305 84 2 , , PUNCT american_scientific_journal-1305 84 3 eq(6 eq(6 PROPN american_scientific_journal-1305 84 4 ) ) PUNCT american_scientific_journal-1305 84 5 is be AUX american_scientific_journal-1305 84 6 modified modify VERB american_scientific_journal-1305 84 7 as as ADP american_scientific_journal-1305 84 8 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ NOUN american_scientific_journal-1305 84 9 ) ) PUNCT american_scientific_journal-1305 85 1 = = SYM american_scientific_journal-1305 85 2 2±𝑛𝑓 2±𝑛𝑓 NUM american_scientific_journal-1305 85 3 ( ( PUNCT american_scientific_journal-1305 85 4 9 9 NUM american_scientific_journal-1305 85 5 ) ) PUNCT american_scientific_journal-1305 85 6 with with ADP american_scientific_journal-1305 85 7 the the DET american_scientific_journal-1305 85 8 hermite hermite PROPN american_scientific_journal-1305 85 9 generating generating NOUN american_scientific_journal-1305 85 10 function function NOUN american_scientific_journal-1305 85 11 , , PUNCT american_scientific_journal-1305 85 12 𝐺(πœ‰ 𝐺(πœ‰ NOUN american_scientific_journal-1305 85 13 , , PUNCT american_scientific_journal-1305 85 14 𝑠 𝑠 NOUN american_scientific_journal-1305 85 15 ) ) PUNCT american_scientific_journal-1305 85 16 = = PUNCT american_scientific_journal-1305 86 1 π‘’βˆ’π‘ 2 π‘’βˆ’π‘ 2 PRON american_scientific_journal-1305 86 2 + + NOUN american_scientific_journal-1305 86 3 2π‘ πœ‰ 2π‘ πœ‰ ADJ american_scientific_journal-1305 86 4 βˆ‘ βˆ‘ ADV american_scientific_journal-1305 86 5 𝐻𝑛𝑓+1(πœ‰)𝑠𝑛 𝐻𝑛𝑓+1(πœ‰)𝑠𝑛 PROPN american_scientific_journal-1305 86 6 𝑛 𝑛 PROPN american_scientific_journal-1305 86 7 ! ! PUNCT american_scientific_journal-1305 86 8 ∞ ∞ NUM american_scientific_journal-1305 87 1 𝑛=0 𝑛=0 NOUN american_scientific_journal-1305 87 2 ( ( PUNCT american_scientific_journal-1305 87 3 10 10 NUM american_scientific_journal-1305 87 4 ) ) PUNCT american_scientific_journal-1305 87 5 and and CCONJ american_scientific_journal-1305 87 6 for for ADP american_scientific_journal-1305 87 7 𝑛 𝑛 PROPN american_scientific_journal-1305 87 8 = = SYM american_scientific_journal-1305 87 9 0 0 NUM american_scientific_journal-1305 87 10 , , PUNCT american_scientific_journal-1305 87 11 we we PRON american_scientific_journal-1305 87 12 can can AUX american_scientific_journal-1305 87 13 prove prove VERB american_scientific_journal-1305 87 14 that that SCONJ american_scientific_journal-1305 87 15 the the DET american_scientific_journal-1305 87 16 hermite hermite ADJ american_scientific_journal-1305 87 17 polynomials polynomial NOUN american_scientific_journal-1305 87 18 satisfy satisfy VERB american_scientific_journal-1305 87 19 the the DET american_scientific_journal-1305 87 20 recursion recursion NOUN american_scientific_journal-1305 87 21 relations relation NOUN american_scientific_journal-1305 87 22 : : PUNCT american_scientific_journal-1305 87 23 οΏ½ οΏ½ PROPN american_scientific_journal-1305 87 24 𝐻𝑛𝑓+1(πœ‰ 𝐻𝑛𝑓+1(πœ‰ PROPN american_scientific_journal-1305 87 25 ) ) PUNCT american_scientific_journal-1305 87 26 βˆ’ βˆ’ PROPN american_scientific_journal-1305 87 27 2πœ‰π»π‘›π‘“ 2πœ‰π»π‘›π‘“ PROPN american_scientific_journal-1305 87 28 + + CCONJ american_scientific_journal-1305 87 29 π»π‘›π‘“βˆ’1(πœ‰ π»π‘›π‘“βˆ’1(πœ‰ X american_scientific_journal-1305 87 30 ) ) PUNCT american_scientific_journal-1305 87 31 = = SYM american_scientific_journal-1305 88 1 0 0 NUM american_scientific_journal-1305 88 2 𝑑 𝑑 PROPN american_scientific_journal-1305 88 3 π‘‘πœ‰ π‘‘πœ‰ ADP american_scientific_journal-1305 88 4 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ PROPN american_scientific_journal-1305 88 5 ) ) PUNCT american_scientific_journal-1305 88 6 = = SYM american_scientific_journal-1305 88 7 2π‘›π‘“π»π‘›π‘“βˆ’1(πœ‰ 2π‘›π‘“π»π‘›π‘“βˆ’1(πœ‰ NUM american_scientific_journal-1305 88 8 ) ) PUNCT american_scientific_journal-1305 88 9 ( ( PUNCT american_scientific_journal-1305 88 10 11 11 NUM american_scientific_journal-1305 88 11 ) ) PUNCT american_scientific_journal-1305 88 12 eq(10 eq(10 PROPN american_scientific_journal-1305 88 13 ) ) PUNCT american_scientific_journal-1305 88 14 shows show VERB american_scientific_journal-1305 88 15 that that SCONJ american_scientific_journal-1305 88 16 if if SCONJ american_scientific_journal-1305 88 17 the the DET american_scientific_journal-1305 88 18 function function NOUN american_scientific_journal-1305 88 19 π‘’βˆ’π‘ 2 π‘’βˆ’π‘ 2 PRON american_scientific_journal-1305 88 20 + + NOUN american_scientific_journal-1305 88 21 2π‘ πœ‰ 2π‘ πœ‰ ADJ american_scientific_journal-1305 88 22 is be AUX american_scientific_journal-1305 88 23 expanded expand VERB american_scientific_journal-1305 88 24 in in ADP american_scientific_journal-1305 88 25 a a DET american_scientific_journal-1305 88 26 power power NOUN american_scientific_journal-1305 88 27 series series NOUN american_scientific_journal-1305 88 28 in in ADP american_scientific_journal-1305 88 29 𝑠 𝑠 PROPN american_scientific_journal-1305 88 30 , , PUNCT american_scientific_journal-1305 88 31 the the DET american_scientific_journal-1305 88 32 coefficients coefficient NOUN american_scientific_journal-1305 88 33 of of ADP american_scientific_journal-1305 88 34 successive successive ADJ american_scientific_journal-1305 88 35 powers power NOUN american_scientific_journal-1305 88 36 of of ADP american_scientific_journal-1305 88 37 𝑠 𝑠 PROPN american_scientific_journal-1305 88 38 are be AUX american_scientific_journal-1305 88 39 just just ADV american_scientific_journal-1305 88 40 1 1 NUM american_scientific_journal-1305 88 41 𝑛 𝑛 NOUN american_scientific_journal-1305 88 42 ! ! NOUN american_scientific_journal-1305 88 43 times time NOUN american_scientific_journal-1305 88 44 the the DET american_scientific_journal-1305 88 45 hermite hermite ADJ american_scientific_journal-1305 88 46 polynomials polynomial NOUN american_scientific_journal-1305 88 47 , , PUNCT american_scientific_journal-1305 88 48 𝐻𝑛𝑓. 𝐻𝑛𝑓. PROPN american_scientific_journal-1305 88 49 using use VERB american_scientific_journal-1305 88 50 eq(11 eq(11 NOUN american_scientific_journal-1305 88 51 ) ) PUNCT american_scientific_journal-1305 88 52 for for ADP american_scientific_journal-1305 88 53 each each PRON american_scientific_journal-1305 88 54 of of ADP american_scientific_journal-1305 88 55 the the DET american_scientific_journal-1305 88 56 fractional fractional ADJ american_scientific_journal-1305 88 57 exponents,𝑛𝑓 exponents,𝑛𝑓 PROPN american_scientific_journal-1305 88 58 on on ADP american_scientific_journal-1305 88 59 πœ†π‘“ πœ†π‘“ ADP american_scientific_journal-1305 89 1 = = PUNCT american_scientific_journal-1305 89 2 2𝑛𝑓+1 2𝑛𝑓+1 NUM american_scientific_journal-1305 89 3 for for ADP american_scientific_journal-1305 89 4 𝐸𝑛𝑓 𝐸𝑛𝑓 PROPN american_scientific_journal-1305 89 5 = = SYM american_scientific_journal-1305 89 6 οΏ½ οΏ½ PROPN american_scientific_journal-1305 90 1 𝑛𝑓 𝑛𝑓 NOUN american_scientific_journal-1305 90 2 + + NOUN american_scientific_journal-1305 90 3 1 1 NUM american_scientific_journal-1305 90 4 2 2 NUM american_scientific_journal-1305 90 5 οΏ½ οΏ½ NOUN american_scientific_journal-1305 90 6 β„πœ” β„πœ” ADJ american_scientific_journal-1305 90 7 , , PUNCT american_scientific_journal-1305 90 8 there there PRON american_scientific_journal-1305 90 9 is be VERB american_scientific_journal-1305 90 10 only only ADV american_scientific_journal-1305 90 11 one one NUM american_scientific_journal-1305 90 12 physically physically ADV american_scientific_journal-1305 90 13 acceptable acceptable ADJ american_scientific_journal-1305 90 14 solution solution NOUN american_scientific_journal-1305 90 15 for for ADP american_scientific_journal-1305 90 16 energy energy NOUN american_scientific_journal-1305 90 17 profile profile NOUN american_scientific_journal-1305 90 18 of of ADP american_scientific_journal-1305 90 19 the the DET american_scientific_journal-1305 90 20 attractor attractor NOUN american_scientific_journal-1305 90 21 πœ“π‘›π‘“(πœ‰ πœ“π‘›π‘“(πœ‰ PROPN american_scientific_journal-1305 90 22 ) ) PUNCT american_scientific_journal-1305 91 1 = = SYM american_scientific_journal-1305 91 2 𝑁𝑛𝑓𝑒 𝑁𝑛𝑓𝑒 PROPN american_scientific_journal-1305 91 3 βˆ’π›Ό2πœ‰ βˆ’π›Ό2πœ‰ NUM american_scientific_journal-1305 91 4 2 2 NUM american_scientific_journal-1305 91 5 2 2 NUM american_scientific_journal-1305 91 6 𝐻𝑛𝑓(πœ‰ 𝐻𝑛𝑓(πœ‰ NOUN american_scientific_journal-1305 91 7 ) ) PUNCT american_scientific_journal-1305 91 8 ( ( PUNCT american_scientific_journal-1305 91 9 12 12 NUM american_scientific_journal-1305 91 10 ) ) PUNCT american_scientific_journal-1305 91 11 where where SCONJ american_scientific_journal-1305 91 12 πœ‰ πœ‰ X american_scientific_journal-1305 91 13 ≑ ≑ PROPN american_scientific_journal-1305 91 14 π‘₯(𝑑 π‘₯(𝑑 PROPN american_scientific_journal-1305 91 15 ) ) PUNCT american_scientific_journal-1305 91 16 and and CCONJ american_scientific_journal-1305 91 17 𝑠 𝑠 PROPN american_scientific_journal-1305 91 18 ≑ ≑ PROPN american_scientific_journal-1305 91 19 πœ” πœ” ADP american_scientific_journal-1305 91 20 this this PRON american_scientific_journal-1305 91 21 implies imply VERB american_scientific_journal-1305 91 22 that that SCONJ american_scientific_journal-1305 91 23 𝑑~π›Όπœ‰. 𝑑~π›Όπœ‰. NOUN american_scientific_journal-1305 91 24 considering consider VERB american_scientific_journal-1305 91 25 the the DET american_scientific_journal-1305 91 26 hermite hermite PROPN american_scientific_journal-1305 91 27 generating generating NOUN american_scientific_journal-1305 91 28 function function NOUN american_scientific_journal-1305 91 29 eq(10 eq(10 PROPN american_scientific_journal-1305 91 30 ) ) PUNCT american_scientific_journal-1305 91 31 and and CCONJ american_scientific_journal-1305 91 32 equating equate VERB american_scientific_journal-1305 91 33 the the DET american_scientific_journal-1305 91 34 t t PROPN american_scientific_journal-1305 91 35 coefficient coefficient NOUN american_scientific_journal-1305 91 36 of of ADP american_scientific_journal-1305 91 37 equal equal ADJ american_scientific_journal-1305 91 38 parts part NOUN american_scientific_journal-1305 91 39 of of ADP american_scientific_journal-1305 91 40 𝑠 𝑠 PROPN american_scientific_journal-1305 91 41 ≑ ≑ PROPN american_scientific_journal-1305 91 42 πœ” πœ” PROPN american_scientific_journal-1305 91 43 and and CCONJ american_scientific_journal-1305 91 44 𝑑~π›Όπœ‰ 𝑑~π›Όπœ‰ INTJ american_scientific_journal-1305 91 45 , , PUNCT american_scientific_journal-1305 91 46 the the DET american_scientific_journal-1305 91 47 normalized normalize VERB american_scientific_journal-1305 91 48 eigen eigen PROPN american_scientific_journal-1305 91 49 functions function NOUN american_scientific_journal-1305 91 50 for for ADP american_scientific_journal-1305 91 51 lyaponov lyaponov NOUN american_scientific_journal-1305 91 52 exponents exponent NOUN american_scientific_journal-1305 91 53 are be AUX american_scientific_journal-1305 91 54 given give VERB american_scientific_journal-1305 91 55 by by ADP american_scientific_journal-1305 91 56 πœ“π‘›π‘“ πœ“π‘›π‘“ PROPN american_scientific_journal-1305 91 57 οΏ½ οΏ½ PROPN american_scientific_journal-1305 91 58 π‘₯(𝑑 π‘₯(𝑑 PROPN american_scientific_journal-1305 91 59 ) ) PUNCT american_scientific_journal-1305 91 60 οΏ½ οΏ½ PROPN american_scientific_journal-1305 91 61 = = SYM american_scientific_journal-1305 91 62 οΏ½ οΏ½ PROPN american_scientific_journal-1305 91 63 𝛼 𝛼 PROPN american_scientific_journal-1305 91 64 βˆšπœ‹2 βˆšπœ‹2 PROPN american_scientific_journal-1305 91 65 𝑛𝑓𝑛 𝑛𝑓𝑛 PROPN american_scientific_journal-1305 91 66 ! ! PUNCT american_scientific_journal-1305 92 1 οΏ½ οΏ½ NOUN american_scientific_journal-1305 92 2 1 1 NUM american_scientific_journal-1305 92 3 2 2 NUM american_scientific_journal-1305 92 4 π‘’βˆ’ π‘’βˆ’ NOUN american_scientific_journal-1305 92 5 𝛼2π‘₯2(𝑑 𝛼2π‘₯2(𝑑 NOUN american_scientific_journal-1305 92 6 ) ) PUNCT american_scientific_journal-1305 92 7 2 2 NUM american_scientific_journal-1305 92 8 𝐻𝑛𝑓(π›Όπœ‰ 𝐻𝑛𝑓(π›Όπœ‰ PROPN american_scientific_journal-1305 92 9 ) ) PUNCT american_scientific_journal-1305 92 10 ( ( PUNCT american_scientific_journal-1305 92 11 13 13 NUM american_scientific_journal-1305 92 12 ) ) PUNCT american_scientific_journal-1305 92 13 for for ADP american_scientific_journal-1305 92 14 lyaponov lyaponov PROPN american_scientific_journal-1305 92 15 exponents exponent NOUN american_scientific_journal-1305 92 16 , , PUNCT american_scientific_journal-1305 92 17 ±𝑛𝑓 ±𝑛𝑓 ADJ american_scientific_journal-1305 92 18 , , PUNCT american_scientific_journal-1305 92 19 𝛼 𝛼 PROPN american_scientific_journal-1305 92 20 = = X american_scientific_journal-1305 92 21 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 92 22 , , PUNCT american_scientific_journal-1305 92 23 𝑛 𝑛 PROPN american_scientific_journal-1305 92 24 ! ! PUNCT american_scientific_journal-1305 92 25 = = NOUN american_scientific_journal-1305 93 1 0 0 X american_scientific_journal-1305 93 2 ! ! PUNCT american_scientific_journal-1305 93 3 = = SYM american_scientific_journal-1305 93 4 1 1 NUM american_scientific_journal-1305 93 5 and and CCONJ american_scientific_journal-1305 93 6 π‘₯(𝑑 π‘₯(𝑑 NUM american_scientific_journal-1305 93 7 ) ) PUNCT american_scientific_journal-1305 93 8 = = SYM american_scientific_journal-1305 93 9 𝐴 𝐴 PROPN american_scientific_journal-1305 93 10 sinπœ”πœŠπ‘‘ sinπœ”πœŠπ‘‘ VERB american_scientific_journal-1305 93 11 as as ADP american_scientific_journal-1305 93 12 gaussian gaussian NOUN american_scientific_journal-1305 93 13 , , PUNCT american_scientific_journal-1305 93 14 using use VERB american_scientific_journal-1305 93 15 eq(9 eq(9 PROPN american_scientific_journal-1305 93 16 ) ) PUNCT american_scientific_journal-1305 93 17 in in ADP american_scientific_journal-1305 93 18 eq(13 eq(13 NOUN american_scientific_journal-1305 93 19 ) ) PUNCT american_scientific_journal-1305 93 20 . . PUNCT american_scientific_journal-1305 94 1 eq eq X american_scientific_journal-1305 94 2 ( ( PUNCT american_scientific_journal-1305 94 3 13 13 NUM american_scientific_journal-1305 94 4 ) ) PUNCT american_scientific_journal-1305 94 5 is be AUX american_scientific_journal-1305 94 6 modified modify VERB american_scientific_journal-1305 94 7 as as ADP american_scientific_journal-1305 94 8 πœ“π‘›π‘“(𝐴 πœ“π‘›π‘“(𝐴 NUM american_scientific_journal-1305 94 9 sinπœ”πœŠπ‘‘ sinπœ”πœŠπ‘‘ ADV american_scientific_journal-1305 94 10 ) ) PUNCT american_scientific_journal-1305 94 11 = = SYM american_scientific_journal-1305 94 12 οΏ½ οΏ½ PROPN american_scientific_journal-1305 94 13 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 95 1 βˆšπœ‹2 βˆšπœ‹2 PROPN american_scientific_journal-1305 95 2 ±𝑛𝑓 ±𝑛𝑓 PROPN american_scientific_journal-1305 95 3 οΏ½ οΏ½ PROPN american_scientific_journal-1305 95 4 1 1 NUM american_scientific_journal-1305 95 5 2 2 NUM american_scientific_journal-1305 95 6 π‘’βˆ’ π‘’βˆ’ NOUN american_scientific_journal-1305 95 7 𝛼2(𝐴sinπœ”πœŠπ‘‘)2 𝛼2(𝐴sinπœ”πœŠπ‘‘)2 ADJ american_scientific_journal-1305 95 8 2 2 NUM american_scientific_journal-1305 95 9 Γ— Γ— NOUN american_scientific_journal-1305 95 10 2±𝑛𝑓 2±𝑛𝑓 NUM american_scientific_journal-1305 95 11 = = SYM american_scientific_journal-1305 95 12 οΏ½ οΏ½ PROPN american_scientific_journal-1305 95 13 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 96 1 βˆšπœ‹2 βˆšπœ‹2 PROPN american_scientific_journal-1305 96 2 ±𝑛𝑓 ±𝑛𝑓 PROPN american_scientific_journal-1305 96 3 οΏ½ οΏ½ PROPN american_scientific_journal-1305 96 4 1 1 NUM american_scientific_journal-1305 96 5 2 2 NUM american_scientific_journal-1305 96 6 2 2 NUM american_scientific_journal-1305 96 7 ±𝑛𝑓 ±𝑛𝑓 NOUN american_scientific_journal-1305 96 8 2 2 NUM american_scientific_journal-1305 96 9 π‘’βˆ’π›Ό π‘’βˆ’π›Ό PROPN american_scientific_journal-1305 96 10 2 2 NUM american_scientific_journal-1305 96 11 οΏ½ οΏ½ PROPN american_scientific_journal-1305 96 12 𝐴sinπœ”πœŠπ‘‘ 𝐴sinπœ”πœŠπ‘‘ PROPN american_scientific_journal-1305 96 13 √2 √2 PROPN american_scientific_journal-1305 96 14 οΏ½ οΏ½ PROPN american_scientific_journal-1305 96 15 2 2 NUM american_scientific_journal-1305 96 16 ( ( PUNCT american_scientific_journal-1305 96 17 14 14 NUM american_scientific_journal-1305 96 18 ) ) PUNCT american_scientific_journal-1305 96 19 the the DET american_scientific_journal-1305 96 20 term term NOUN american_scientific_journal-1305 96 21 π‘’βˆ’ π‘’βˆ’ NOUN american_scientific_journal-1305 96 22 𝛼2(𝐴sinπœ”πœŠπ‘‘)2 𝛼2(𝐴sinπœ”πœŠπ‘‘)2 ADJ american_scientific_journal-1305 96 23 2 2 NUM american_scientific_journal-1305 96 24 ~π‘’βˆ’ ~π‘’βˆ’ ADP american_scientific_journal-1305 96 25 οΏ½ οΏ½ NUM american_scientific_journal-1305 96 26 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ VERB american_scientific_journal-1305 96 27 𝐴sinπœ”πœŠπ‘‘ 𝐴sinπœ”πœŠπ‘‘ PROPN american_scientific_journal-1305 96 28 √2 √2 PROPN american_scientific_journal-1305 96 29 οΏ½ οΏ½ PROPN american_scientific_journal-1305 96 30 2 2 NUM american_scientific_journal-1305 96 31 is be AUX american_scientific_journal-1305 96 32 a a DET american_scientific_journal-1305 96 33 convergent convergent NOUN american_scientific_journal-1305 96 34 series series NOUN american_scientific_journal-1305 96 35 and and CCONJ american_scientific_journal-1305 96 36 tends tend VERB american_scientific_journal-1305 96 37 to to PART american_scientific_journal-1305 96 38 unity unity NOUN american_scientific_journal-1305 96 39 in in ADP american_scientific_journal-1305 96 40 eq eq NOUN american_scientific_journal-1305 96 41 ( ( PUNCT american_scientific_journal-1305 96 42 14 14 NUM american_scientific_journal-1305 96 43 ) ) PUNCT american_scientific_journal-1305 96 44 . . PUNCT american_scientific_journal-1305 97 1 with with ADP american_scientific_journal-1305 97 2 sinπœ”πœŠπ‘‘~πœ”πœŠπ‘‘ sinπœ”πœŠπ‘‘~πœ”πœŠπ‘‘ PROPN american_scientific_journal-1305 97 3 = = SYM american_scientific_journal-1305 97 4 𝛼 𝛼 NOUN american_scientific_journal-1305 97 5 , , PUNCT american_scientific_journal-1305 97 6 eq eq X american_scientific_journal-1305 97 7 ( ( PUNCT american_scientific_journal-1305 97 8 14 14 NUM american_scientific_journal-1305 97 9 ) ) PUNCT american_scientific_journal-1305 97 10 becomes become VERB american_scientific_journal-1305 97 11 286 286 NUM american_scientific_journal-1305 97 12 american american ADJ american_scientific_journal-1305 97 13 scientific scientific ADJ american_scientific_journal-1305 97 14 research research NOUN american_scientific_journal-1305 97 15 journal journal NOUN american_scientific_journal-1305 97 16 for for ADP american_scientific_journal-1305 97 17 engineering engineering NOUN american_scientific_journal-1305 97 18 , , PUNCT american_scientific_journal-1305 97 19 technology technology NOUN american_scientific_journal-1305 97 20 , , PUNCT american_scientific_journal-1305 97 21 and and CCONJ american_scientific_journal-1305 97 22 sciences science NOUN american_scientific_journal-1305 97 23 ( ( PUNCT american_scientific_journal-1305 97 24 asrjets asrjet NOUN american_scientific_journal-1305 97 25 ) ) PUNCT american_scientific_journal-1305 97 26 ( ( PUNCT american_scientific_journal-1305 97 27 2016 2016 NUM american_scientific_journal-1305 97 28 ) ) PUNCT american_scientific_journal-1305 97 29 volume volume NOUN american_scientific_journal-1305 97 30 15 15 NUM american_scientific_journal-1305 97 31 , , PUNCT american_scientific_journal-1305 97 32 no no DET american_scientific_journal-1305 97 33 1 1 NUM american_scientific_journal-1305 97 34 , , PUNCT american_scientific_journal-1305 97 35 pp pp ADV american_scientific_journal-1305 97 36 282 282 NUM american_scientific_journal-1305 97 37 - - SYM american_scientific_journal-1305 97 38 289 289 NUM american_scientific_journal-1305 97 39 πœ“π‘›π‘“(πœ”πœŠπ‘‘ πœ“π‘›π‘“(πœ”πœŠπ‘‘ ADP american_scientific_journal-1305 97 40 ) ) PUNCT american_scientific_journal-1305 97 41 = = SYM american_scientific_journal-1305 97 42 οΏ½ οΏ½ PROPN american_scientific_journal-1305 97 43 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 97 44 βˆšπœ‹ βˆšπœ‹ X american_scientific_journal-1305 97 45 οΏ½ οΏ½ PROPN american_scientific_journal-1305 97 46 1 1 NUM american_scientific_journal-1305 97 47 2 2 NUM american_scientific_journal-1305 97 48 2 2 NUM american_scientific_journal-1305 97 49 ±𝑛𝑓 ±𝑛𝑓 NOUN american_scientific_journal-1305 97 50 2 2 NUM american_scientific_journal-1305 97 51 ( ( PUNCT american_scientific_journal-1305 97 52 15 15 NUM american_scientific_journal-1305 97 53 ) ) PUNCT american_scientific_journal-1305 97 54 in in ADP american_scientific_journal-1305 97 55 a a DET american_scientific_journal-1305 97 56 time time NOUN american_scientific_journal-1305 97 57 series series NOUN american_scientific_journal-1305 97 58 following follow VERB american_scientific_journal-1305 97 59 aperiodic aperiodic ADJ american_scientific_journal-1305 97 60 stable stable ADJ american_scientific_journal-1305 97 61 chaos chaos NOUN american_scientific_journal-1305 97 62 ( ( PUNCT american_scientific_journal-1305 97 63 stationary stationary ADJ american_scientific_journal-1305 97 64 stochastic stochastic ADJ american_scientific_journal-1305 97 65 process process NOUN american_scientific_journal-1305 97 66 ) ) PUNCT american_scientific_journal-1305 97 67 , , PUNCT american_scientific_journal-1305 97 68 the the DET american_scientific_journal-1305 97 69 coefficient coefficient NOUN american_scientific_journal-1305 97 70 𝐴 𝐴 PROPN american_scientific_journal-1305 97 71 of of ADP american_scientific_journal-1305 97 72 sinπœ”πœŠπ‘‘ sinπœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 97 73 is be AUX american_scientific_journal-1305 97 74 a a DET american_scientific_journal-1305 97 75 real real ADJ american_scientific_journal-1305 97 76 constant constant ADJ american_scientific_journal-1305 97 77 for for ADP american_scientific_journal-1305 97 78 an an DET american_scientific_journal-1305 97 79 attractor attractor NOUN american_scientific_journal-1305 97 80 with with ADP american_scientific_journal-1305 97 81 frequencyπœ”πœŠ. frequencyπœ”πœŠ. NOUN american_scientific_journal-1305 97 82 at at ADP american_scientific_journal-1305 97 83 any any DET american_scientific_journal-1305 97 84 time time NOUN american_scientific_journal-1305 97 85 in in ADP american_scientific_journal-1305 97 86 a a DET american_scientific_journal-1305 97 87 time time NOUN american_scientific_journal-1305 97 88 series series NOUN american_scientific_journal-1305 97 89 in in ADP american_scientific_journal-1305 97 90 the the DET american_scientific_journal-1305 97 91 plane plane NOUN american_scientific_journal-1305 97 92 ( ( PUNCT american_scientific_journal-1305 97 93 𝑑,πœ” 𝑑,πœ” PROPN american_scientific_journal-1305 97 94 ) ) PUNCT american_scientific_journal-1305 98 1 [ [ X american_scientific_journal-1305 98 2 wiener wiener NOUN american_scientific_journal-1305 98 3 space space NOUN american_scientific_journal-1305 98 4 ] ] PUNCT american_scientific_journal-1305 98 5 , , PUNCT american_scientific_journal-1305 98 6 .i.e .i.e PUNCT american_scientific_journal-1305 98 7 . . PUNCT american_scientific_journal-1305 98 8 , , PUNCT american_scientific_journal-1305 98 9 𝑑 𝑑 PROPN american_scientific_journal-1305 98 10 = = VERB american_scientific_journal-1305 98 11 π‘‘π‘Žπ‘‘π‘‘ π‘‘π‘Žπ‘‘π‘‘ ADJ american_scientific_journal-1305 98 12 ( ( PUNCT american_scientific_journal-1305 98 13 time time NOUN american_scientific_journal-1305 98 14 of of ADP american_scientific_journal-1305 98 15 flight flight NOUN american_scientific_journal-1305 98 16 for for ADP american_scientific_journal-1305 98 17 an an DET american_scientific_journal-1305 98 18 attractor attractor NOUN american_scientific_journal-1305 98 19 ) ) PUNCT american_scientific_journal-1305 98 20 , , PUNCT american_scientific_journal-1305 98 21 a a DET american_scientific_journal-1305 98 22 phase phase NOUN american_scientific_journal-1305 98 23 change change NOUN american_scientific_journal-1305 98 24 of of ADP american_scientific_journal-1305 98 25 πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ NOUN american_scientific_journal-1305 98 26 will will AUX american_scientific_journal-1305 98 27 cause cause VERB american_scientific_journal-1305 98 28 a a DET american_scientific_journal-1305 98 29 change change NOUN american_scientific_journal-1305 98 30 in in ADP american_scientific_journal-1305 98 31 energy energy NOUN american_scientific_journal-1305 98 32 profile profile NOUN american_scientific_journal-1305 98 33 and and CCONJ american_scientific_journal-1305 98 34 hence hence ADV american_scientific_journal-1305 98 35 an an DET american_scientific_journal-1305 98 36 aperiodic aperiodic ADJ american_scientific_journal-1305 98 37 stable stable ADJ american_scientific_journal-1305 98 38 chaotic chaotic ADJ american_scientific_journal-1305 98 39 attractors attractor NOUN american_scientific_journal-1305 98 40 will will AUX american_scientific_journal-1305 98 41 be be AUX american_scientific_journal-1305 98 42 produced produce VERB american_scientific_journal-1305 98 43 on on ADP american_scientific_journal-1305 98 44 a a DET american_scientific_journal-1305 98 45 time time NOUN american_scientific_journal-1305 98 46 series series NOUN american_scientific_journal-1305 98 47 . . PUNCT american_scientific_journal-1305 99 1 the the DET american_scientific_journal-1305 99 2 coefficient coefficient PROPN american_scientific_journal-1305 99 3 𝐴 𝐴 PROPN american_scientific_journal-1305 99 4 , , PUNCT american_scientific_journal-1305 99 5 being be AUX american_scientific_journal-1305 99 6 a a DET american_scientific_journal-1305 99 7 real real ADV american_scientific_journal-1305 99 8 constant constant ADJ american_scientific_journal-1305 99 9 , , PUNCT american_scientific_journal-1305 99 10 can can AUX american_scientific_journal-1305 99 11 be be AUX american_scientific_journal-1305 99 12 quantized quantize VERB american_scientific_journal-1305 99 13 with with ADP american_scientific_journal-1305 99 14 simulation simulation NOUN american_scientific_journal-1305 99 15 . . PUNCT american_scientific_journal-1305 100 1 equation equation NOUN american_scientific_journal-1305 100 2 ( ( PUNCT american_scientific_journal-1305 100 3 15 15 NUM american_scientific_journal-1305 100 4 ) ) PUNCT american_scientific_journal-1305 100 5 can can AUX american_scientific_journal-1305 100 6 be be AUX american_scientific_journal-1305 100 7 modified modify VERB american_scientific_journal-1305 100 8 as as ADP american_scientific_journal-1305 100 9 πœ“Β±π‘›π‘“(Β±πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ πœ“Β±π‘›π‘“(Β±πœ”πœŠπ‘‘π‘Žπ‘‘π‘‘ PROPN american_scientific_journal-1305 100 10 ) ) PUNCT american_scientific_journal-1305 100 11 = = SYM american_scientific_journal-1305 100 12 οΏ½ οΏ½ PROPN american_scientific_journal-1305 100 13 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 100 14 βˆšπœ‹ βˆšπœ‹ X american_scientific_journal-1305 100 15 οΏ½ οΏ½ PROPN american_scientific_journal-1305 100 16 1 1 NUM american_scientific_journal-1305 100 17 2 2 NUM american_scientific_journal-1305 100 18 2 2 NUM american_scientific_journal-1305 100 19 ±𝑛𝑓 ±𝑛𝑓 NOUN american_scientific_journal-1305 100 20 2 2 NUM american_scientific_journal-1305 100 21 ( ( PUNCT american_scientific_journal-1305 100 22 16 16 NUM american_scientific_journal-1305 100 23 ) ) PUNCT american_scientific_journal-1305 100 24 where where SCONJ american_scientific_journal-1305 100 25 πœ‹ πœ‹ NOUN american_scientific_journal-1305 100 26 2 2 NUM american_scientific_journal-1305 100 27 < < X american_scientific_journal-1305 100 28 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ X american_scientific_journal-1305 100 29 ≀ ≀ ADJ american_scientific_journal-1305 100 30 2πœ‹ 2πœ‹ NOUN american_scientific_journal-1305 100 31 and and CCONJ american_scientific_journal-1305 100 32 0 0 NUM american_scientific_journal-1305 100 33 ≀ ≀ NUM american_scientific_journal-1305 100 34 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ VERB american_scientific_journal-1305 100 35 < < X american_scientific_journal-1305 100 36 πœ‹ πœ‹ X american_scientific_journal-1305 100 37 2 2 NUM american_scientific_journal-1305 100 38 , , PUNCT american_scientific_journal-1305 100 39 .i.e .i.e PUNCT american_scientific_journal-1305 100 40 . . PUNCT american_scientific_journal-1305 100 41 , , PUNCT american_scientific_journal-1305 100 42 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ VERB american_scientific_journal-1305 101 1 = = PUNCT american_scientific_journal-1305 101 2 𝛼 𝛼 PROPN american_scientific_journal-1305 101 3 β‰  β‰  PROPN american_scientific_journal-1305 101 4 πœ‹ πœ‹ PROPN american_scientific_journal-1305 101 5 2 2 NUM american_scientific_journal-1305 101 6 eq(16 eq(16 NOUN american_scientific_journal-1305 101 7 ) ) PUNCT american_scientific_journal-1305 101 8 represents represent VERB american_scientific_journal-1305 101 9 shape shape NOUN american_scientific_journal-1305 101 10 of of ADP american_scientific_journal-1305 101 11 profile profile NOUN american_scientific_journal-1305 101 12 for for ADP american_scientific_journal-1305 101 13 aperiodic aperiodic ADJ american_scientific_journal-1305 101 14 stable stable ADJ american_scientific_journal-1305 101 15 attractors attractor NOUN american_scientific_journal-1305 101 16 with with ADP american_scientific_journal-1305 101 17 lyapunov lyapunov ADJ american_scientific_journal-1305 101 18 exponents exponent NOUN american_scientific_journal-1305 101 19 , , PUNCT american_scientific_journal-1305 101 20 ±𝑛𝑓. ±𝑛𝑓. PROPN american_scientific_journal-1305 101 21 the the DET american_scientific_journal-1305 101 22 periodic periodic ADJ american_scientific_journal-1305 101 23 unstable unstable ADJ american_scientific_journal-1305 101 24 attractors attractor NOUN american_scientific_journal-1305 101 25 at at ADP american_scientific_journal-1305 101 26 𝛼 𝛼 NOUN american_scientific_journal-1305 101 27 = = NOUN american_scientific_journal-1305 101 28 πœ”πœŠπ‘‘ πœ”πœŠπ‘‘ NOUN american_scientific_journal-1305 102 1 = = PUNCT american_scientific_journal-1305 102 2 πœ‹ πœ‹ PRON american_scientific_journal-1305 102 3 2 2 NUM american_scientific_journal-1305 102 4 will will AUX american_scientific_journal-1305 102 5 be be AUX american_scientific_journal-1305 102 6 produced produce VERB american_scientific_journal-1305 102 7 following follow VERB american_scientific_journal-1305 102 8 the the DET american_scientific_journal-1305 102 9 ft ft NOUN american_scientific_journal-1305 102 10 . . PUNCT american_scientific_journal-1305 102 11 eq eq NOUN american_scientific_journal-1305 103 1 ( ( PUNCT american_scientific_journal-1305 103 2 16 16 NUM american_scientific_journal-1305 103 3 ) ) PUNCT american_scientific_journal-1305 103 4 obeys obey NOUN american_scientific_journal-1305 103 5 wd wd PROPN american_scientific_journal-1305 103 6 and and CCONJ american_scientific_journal-1305 103 7 ws ws PROPN american_scientific_journal-1305 103 8 in in ADP american_scientific_journal-1305 103 9 ( ( PUNCT american_scientific_journal-1305 103 10 𝑑,πœ” 𝑑,πœ” PROPN american_scientific_journal-1305 103 11 ) ) PUNCT american_scientific_journal-1305 103 12 plane plane NOUN american_scientific_journal-1305 103 13 . . PUNCT american_scientific_journal-1305 104 1 all all DET american_scientific_journal-1305 104 2 attractors attractor NOUN american_scientific_journal-1305 104 3 whether whether SCONJ american_scientific_journal-1305 104 4 periodic periodic ADJ american_scientific_journal-1305 104 5 or or CCONJ american_scientific_journal-1305 104 6 aperiodic aperiodic ADJ american_scientific_journal-1305 104 7 are be AUX american_scientific_journal-1305 104 8 , , PUNCT american_scientific_journal-1305 104 9 in in ADP american_scientific_journal-1305 104 10 fact fact NOUN american_scientific_journal-1305 104 11 , , PUNCT american_scientific_journal-1305 104 12 the the DET american_scientific_journal-1305 104 13 manifestation manifestation NOUN american_scientific_journal-1305 104 14 of of ADP american_scientific_journal-1305 104 15 lyaponov lyaponov PROPN american_scientific_journal-1305 104 16 exponents exponent NOUN american_scientific_journal-1305 104 17 . . PUNCT american_scientific_journal-1305 105 1 3 3 X american_scientific_journal-1305 105 2 . . X american_scientific_journal-1305 105 3 conclusion conclusion VERB american_scientific_journal-1305 105 4 the the DET american_scientific_journal-1305 105 5 shape shape NOUN american_scientific_journal-1305 105 6 of of ADP american_scientific_journal-1305 105 7 energy energy NOUN american_scientific_journal-1305 105 8 profile profile NOUN american_scientific_journal-1305 105 9 for for ADP american_scientific_journal-1305 105 10 aperiodic aperiodic ADJ american_scientific_journal-1305 105 11 stable stable ADJ american_scientific_journal-1305 105 12 attractors attractor NOUN american_scientific_journal-1305 105 13 with with ADP american_scientific_journal-1305 105 14 lyaponov lyaponov PROPN american_scientific_journal-1305 105 15 exponents exponent NOUN american_scientific_journal-1305 105 16 ±𝑛𝑓 ±𝑛𝑓 ADJ american_scientific_journal-1305 105 17 is be AUX american_scientific_journal-1305 105 18 determined determine VERB american_scientific_journal-1305 105 19 by by ADP american_scientific_journal-1305 105 20 using use VERB american_scientific_journal-1305 105 21 fractional fractional ADJ american_scientific_journal-1305 105 22 fourier fourier NOUN american_scientific_journal-1305 105 23 transform transform NOUN american_scientific_journal-1305 105 24 . . PUNCT american_scientific_journal-1305 106 1 the the DET american_scientific_journal-1305 106 2 formula formula NOUN american_scientific_journal-1305 106 3 aperiodic aperiodic ADJ american_scientific_journal-1305 106 4 stable stable ADJ american_scientific_journal-1305 106 5 attractors attractor NOUN american_scientific_journal-1305 106 6 eq eq ADP american_scientific_journal-1305 106 7 ( ( PUNCT american_scientific_journal-1305 106 8 16 16 NUM american_scientific_journal-1305 106 9 ) ) PUNCT american_scientific_journal-1305 106 10 is be AUX american_scientific_journal-1305 106 11 established establish VERB american_scientific_journal-1305 106 12 . . PUNCT american_scientific_journal-1305 107 1 withπœ”πœŠπ‘‘ withπœ”πœŠπ‘‘ VERB american_scientific_journal-1305 108 1 = = PUNCT american_scientific_journal-1305 108 2 πœ‹ πœ‹ X american_scientific_journal-1305 108 3 2 2 NUM american_scientific_journal-1305 108 4 , , PUNCT american_scientific_journal-1305 108 5 it it PRON american_scientific_journal-1305 108 6 is be AUX american_scientific_journal-1305 108 7 found find VERB american_scientific_journal-1305 108 8 that that SCONJ american_scientific_journal-1305 108 9 the the DET american_scientific_journal-1305 108 10 enegy enegy PROPN american_scientific_journal-1305 108 11 profile profile NOUN american_scientific_journal-1305 108 12 exists exist VERB american_scientific_journal-1305 108 13 for for ADP american_scientific_journal-1305 108 14 periodic periodic ADJ american_scientific_journal-1305 108 15 unstable unstable ADJ american_scientific_journal-1305 108 16 attractors attractor NOUN american_scientific_journal-1305 108 17 at at ADP american_scientific_journal-1305 108 18 different different ADJ american_scientific_journal-1305 108 19 values value NOUN american_scientific_journal-1305 108 20 of of ADP american_scientific_journal-1305 108 21 lyaponov lyaponov PROPN american_scientific_journal-1305 108 22 exponents exponent NOUN american_scientific_journal-1305 108 23 , , PUNCT american_scientific_journal-1305 108 24 𝑛𝑓.critical 𝑛𝑓.critical ADJ american_scientific_journal-1305 108 25 analysis analysis NOUN american_scientific_journal-1305 108 26 about about ADP american_scientific_journal-1305 108 27 chaos chaos NOUN american_scientific_journal-1305 108 28 is be AUX american_scientific_journal-1305 108 29 revisited revisit VERB american_scientific_journal-1305 108 30 with with ADP american_scientific_journal-1305 108 31 emphasis emphasis NOUN american_scientific_journal-1305 108 32 on on ADP american_scientific_journal-1305 108 33 time time NOUN american_scientific_journal-1305 108 34 series series PROPN american_scientific_journal-1305 108 35 modeling modeling PROPN american_scientific_journal-1305 108 36 . . PUNCT american_scientific_journal-1305 109 1 references reference NOUN american_scientific_journal-1305 109 2 [ [ X american_scientific_journal-1305 109 3 1 1 X american_scientific_journal-1305 109 4 ] ] PUNCT american_scientific_journal-1305 109 5 j. j. PROPN american_scientific_journal-1305 109 6 jimenez jimenez PROPN american_scientific_journal-1305 109 7 , , PUNCT american_scientific_journal-1305 109 8 j.a j.a PROPN american_scientific_journal-1305 109 9 . . PROPN american_scientific_journal-1305 109 10 moreno moreno PROPN american_scientific_journal-1305 109 11 , , PUNCT american_scientific_journal-1305 109 12 and and CCONJ american_scientific_journal-1305 109 13 g.j g.j PROPN american_scientific_journal-1305 109 14 . . PROPN american_scientific_journal-1305 109 15 ruggieri ruggieri PROPN american_scientific_journal-1305 109 16 , , PUNCT american_scientific_journal-1305 109 17 β€œ " PUNCT american_scientific_journal-1305 109 18 forecasting forecast VERB american_scientific_journal-1305 109 19 on on ADP american_scientific_journal-1305 109 20 chaotic chaotic ADJ american_scientific_journal-1305 109 21 time time NOUN american_scientific_journal-1305 109 22 series series NOUN american_scientific_journal-1305 109 23 : : PUNCT american_scientific_journal-1305 109 24 a a DET american_scientific_journal-1305 109 25 local local ADJ american_scientific_journal-1305 109 26 optimal optimal ADJ american_scientific_journal-1305 109 27 linear linear ADJ american_scientific_journal-1305 109 28 reconstruction reconstruction NOUN american_scientific_journal-1305 109 29 method method NOUN american_scientific_journal-1305 109 30 , , PUNCT american_scientific_journal-1305 109 31 ” " PUNCT american_scientific_journal-1305 109 32 phy.rev.a phy.rev.a NOUN american_scientific_journal-1305 109 33 . . PUNCT american_scientific_journal-1305 109 34 , , PUNCT american_scientific_journal-1305 109 35 vol vol NOUN american_scientific_journal-1305 109 36 . . PROPN american_scientific_journal-1305 109 37 45 45 NUM american_scientific_journal-1305 109 38 , , PUNCT american_scientific_journal-1305 109 39 no no INTJ american_scientific_journal-1305 109 40 . . NOUN american_scientific_journal-1305 109 41 6 6 NUM american_scientific_journal-1305 109 42 , , PUNCT american_scientific_journal-1305 109 43 pp pp ADJ american_scientific_journal-1305 109 44 . . PUNCT american_scientific_journal-1305 110 1 3553–3558 3553–3558 NUM american_scientific_journal-1305 110 2 , , PUNCT american_scientific_journal-1305 110 3 1992 1992 NUM american_scientific_journal-1305 110 4 . . PUNCT american_scientific_journal-1305 111 1 [ [ X american_scientific_journal-1305 111 2 2 2 X american_scientific_journal-1305 111 3 ] ] X american_scientific_journal-1305 111 4 j.h j.h PROPN american_scientific_journal-1305 111 5 lefebvre lefebvre PROPN american_scientific_journal-1305 111 6 , , PUNCT american_scientific_journal-1305 111 7 d.a d.a PROPN american_scientific_journal-1305 111 8 . . PROPN american_scientific_journal-1305 111 9 goodings gooding NOUN american_scientific_journal-1305 111 10 , , PUNCT american_scientific_journal-1305 111 11 m.v m.v PROPN american_scientific_journal-1305 111 12 . . PROPN american_scientific_journal-1305 111 13 kannath kannath PROPN american_scientific_journal-1305 111 14 , , PUNCT american_scientific_journal-1305 111 15 and and CCONJ american_scientific_journal-1305 111 16 e.l e.l PROPN american_scientific_journal-1305 111 17 . . PROPN american_scientific_journal-1305 111 18 fallen fall VERB american_scientific_journal-1305 111 19 , , PUNCT american_scientific_journal-1305 111 20 β€œ " PUNCT american_scientific_journal-1305 111 21 predictability predictability NOUN american_scientific_journal-1305 111 22 of of ADP american_scientific_journal-1305 111 23 normal normal ADJ american_scientific_journal-1305 111 24 heart heart NOUN american_scientific_journal-1305 111 25 rhythms rhythm NOUN american_scientific_journal-1305 111 26 and and CCONJ american_scientific_journal-1305 111 27 deterministic deterministic ADJ american_scientific_journal-1305 111 28 chaos chaos NOUN american_scientific_journal-1305 111 29 , , PUNCT american_scientific_journal-1305 111 30 ” " PUNCT american_scientific_journal-1305 111 31 chaos chaos NOUN american_scientific_journal-1305 111 32 , , PUNCT american_scientific_journal-1305 111 33 vol vol NOUN american_scientific_journal-1305 111 34 . . PROPN american_scientific_journal-1305 112 1 3 3 NUM american_scientific_journal-1305 112 2 , , PUNCT american_scientific_journal-1305 112 3 pp pp ADJ american_scientific_journal-1305 112 4 . . PUNCT american_scientific_journal-1305 113 1 267–277 267–277 NUM american_scientific_journal-1305 113 2 , , PUNCT american_scientific_journal-1305 113 3 1993 1993 NUM american_scientific_journal-1305 113 4 . . PUNCT american_scientific_journal-1305 114 1 [ [ X american_scientific_journal-1305 114 2 3 3 X american_scientific_journal-1305 114 3 ] ] X american_scientific_journal-1305 114 4 d.m d.m PROPN american_scientific_journal-1305 114 5 . . PUNCT american_scientific_journal-1305 114 6 rubin rubin PROPN american_scientific_journal-1305 114 7 , , PUNCT american_scientific_journal-1305 114 8 β€œ " PUNCT american_scientific_journal-1305 114 9 use use NOUN american_scientific_journal-1305 114 10 of of ADP american_scientific_journal-1305 114 11 forecasting forecast VERB american_scientific_journal-1305 114 12 signatures signature NOUN american_scientific_journal-1305 114 13 to to PART american_scientific_journal-1305 114 14 help help VERB american_scientific_journal-1305 114 15 distinguish distinguish VERB american_scientific_journal-1305 114 16 periodicity periodicity NOUN american_scientific_journal-1305 114 17 , , PUNCT american_scientific_journal-1305 114 18 randomness randomness NOUN american_scientific_journal-1305 114 19 , , PUNCT american_scientific_journal-1305 114 20 and and CCONJ american_scientific_journal-1305 114 21 chaos chaos NOUN american_scientific_journal-1305 114 22 in in ADP american_scientific_journal-1305 114 23 ripples ripple NOUN american_scientific_journal-1305 114 24 and and CCONJ american_scientific_journal-1305 114 25 other other ADJ american_scientific_journal-1305 114 26 spatial spatial ADJ american_scientific_journal-1305 114 27 patterns pattern NOUN american_scientific_journal-1305 114 28 ” " PUNCT american_scientific_journal-1305 114 29 chaos chaos NOUN american_scientific_journal-1305 114 30 , , PUNCT american_scientific_journal-1305 114 31 vol vol NOUN american_scientific_journal-1305 114 32 . . PROPN american_scientific_journal-1305 114 33 2 2 NUM american_scientific_journal-1305 114 34 , , PUNCT american_scientific_journal-1305 114 35 pp pp ADJ american_scientific_journal-1305 114 36 . . PUNCT american_scientific_journal-1305 115 1 525–535 525–535 NUM american_scientific_journal-1305 115 2 , , PUNCT american_scientific_journal-1305 115 3 1992 1992 NUM american_scientific_journal-1305 115 4 . . PUNCT american_scientific_journal-1305 116 1 [ [ X american_scientific_journal-1305 116 2 4 4 NUM american_scientific_journal-1305 116 3 ] ] X american_scientific_journal-1305 116 4 j.d.berger j.d.berger NOUN american_scientific_journal-1305 116 5 , , PUNCT american_scientific_journal-1305 116 6 β€œ " PUNCT american_scientific_journal-1305 116 7 statirstical statirstical ADJ american_scientific_journal-1305 116 8 decision decision NOUN american_scientific_journal-1305 116 9 theory theory NOUN american_scientific_journal-1305 116 10 and and CCONJ american_scientific_journal-1305 116 11 [ [ X american_scientific_journal-1305 116 12 4bayesian 4bayesian NUM american_scientific_journal-1305 116 13 analysis analysis NOUN american_scientific_journal-1305 116 14 , , PUNCT american_scientific_journal-1305 116 15 ” " PUNCT american_scientific_journal-1305 116 16 springer springer NOUN american_scientific_journal-1305 116 17 verlag verlag PROPN american_scientific_journal-1305 116 18 , , PUNCT american_scientific_journal-1305 116 19 berlin berlin PROPN american_scientific_journal-1305 116 20 , , PUNCT american_scientific_journal-1305 116 21 1982 1982 NUM american_scientific_journal-1305 116 22 . . PUNCT american_scientific_journal-1305 117 1 [ [ X american_scientific_journal-1305 117 2 5 5 NUM american_scientific_journal-1305 117 3 ] ] PUNCT american_scientific_journal-1305 117 4 m. m. NOUN american_scientific_journal-1305 117 5 casdagli casdagli NOUN american_scientific_journal-1305 117 6 and and CCONJ american_scientific_journal-1305 117 7 j. j. PROPN american_scientific_journal-1305 117 8 roy roy PROPN american_scientific_journal-1305 117 9 , , PUNCT american_scientific_journal-1305 117 10 β€œ " PUNCT american_scientific_journal-1305 117 11 chaos chaos NOUN american_scientific_journal-1305 117 12 and and CCONJ american_scientific_journal-1305 117 13 deterministic deterministic ADJ american_scientific_journal-1305 117 14 versus versus ADP american_scientific_journal-1305 117 15 stochastic stochastic ADJ american_scientific_journal-1305 117 16 nonlinear nonlinear ADJ american_scientific_journal-1305 117 17 modeling modeling NOUN american_scientific_journal-1305 117 18 , , PUNCT american_scientific_journal-1305 117 19 ” " PUNCT american_scientific_journal-1305 117 20 stat stat NOUN american_scientific_journal-1305 117 21 . . PUNCT american_scientific_journal-1305 118 1 soc soc PROPN american_scientific_journal-1305 118 2 , , PUNCT american_scientific_journal-1305 118 3 b. b. PROPN american_scientific_journal-1305 118 4 , , PUNCT american_scientific_journal-1305 118 5 vol vol NOUN american_scientific_journal-1305 118 6 . . PROPN american_scientific_journal-1305 118 7 54 54 NUM american_scientific_journal-1305 118 8 , , PUNCT american_scientific_journal-1305 118 9 pp pp ADJ american_scientific_journal-1305 118 10 . . PUNCT american_scientific_journal-1305 119 1 303–328 303–328 NUM american_scientific_journal-1305 119 2 , , PUNCT american_scientific_journal-1305 119 3 1991 1991 NUM american_scientific_journal-1305 119 4 . . PUNCT american_scientific_journal-1305 120 1 287 287 NUM american_scientific_journal-1305 120 2 american american ADJ american_scientific_journal-1305 120 3 scientific scientific ADJ american_scientific_journal-1305 120 4 research research NOUN american_scientific_journal-1305 120 5 journal journal NOUN american_scientific_journal-1305 120 6 for for ADP american_scientific_journal-1305 120 7 engineering engineering NOUN american_scientific_journal-1305 120 8 , , PUNCT american_scientific_journal-1305 120 9 technology technology NOUN american_scientific_journal-1305 120 10 , , PUNCT american_scientific_journal-1305 120 11 and and CCONJ american_scientific_journal-1305 120 12 sciences science NOUN american_scientific_journal-1305 120 13 ( ( PUNCT american_scientific_journal-1305 120 14 asrjets asrjet NOUN american_scientific_journal-1305 120 15 ) ) PUNCT american_scientific_journal-1305 120 16 ( ( PUNCT american_scientific_journal-1305 120 17 2016 2016 NUM american_scientific_journal-1305 120 18 ) ) PUNCT american_scientific_journal-1305 120 19 volume volume NOUN american_scientific_journal-1305 120 20 15 15 NUM american_scientific_journal-1305 120 21 , , PUNCT american_scientific_journal-1305 120 22 no no DET american_scientific_journal-1305 120 23 1 1 NUM american_scientific_journal-1305 120 24 , , PUNCT american_scientific_journal-1305 120 25 pp pp ADV american_scientific_journal-1305 120 26 282 282 NUM american_scientific_journal-1305 120 27 - - SYM american_scientific_journal-1305 120 28 289 289 NUM american_scientific_journal-1305 120 29 [ [ X american_scientific_journal-1305 120 30 6 6 NUM american_scientific_journal-1305 120 31 ] ] X american_scientific_journal-1305 120 32 y.z y.z PROPN american_scientific_journal-1305 120 33 . . PROPN american_scientific_journal-1305 120 34 jafri jafri PROPN american_scientific_journal-1305 120 35 , , PUNCT american_scientific_journal-1305 120 36 β€œ " PUNCT american_scientific_journal-1305 120 37 is be AUX american_scientific_journal-1305 120 38 chaotic chaotic ADJ american_scientific_journal-1305 120 39 time time NOUN american_scientific_journal-1305 120 40 series series NOUN american_scientific_journal-1305 120 41 deterministic deterministic ADJ american_scientific_journal-1305 120 42 ? ? PUNCT american_scientific_journal-1305 120 43 ” " PUNCT american_scientific_journal-1305 121 1 sci sci PROPN american_scientific_journal-1305 121 2 international international PROPN american_scientific_journal-1305 121 3 ( ( PUNCT american_scientific_journal-1305 121 4 lhr lhr PROPN american_scientific_journal-1305 121 5 ) ) PUNCT american_scientific_journal-1305 121 6 , , PUNCT american_scientific_journal-1305 121 7 vol vol NOUN american_scientific_journal-1305 121 8 . . PROPN american_scientific_journal-1305 121 9 8 8 NUM american_scientific_journal-1305 121 10 , , PUNCT american_scientific_journal-1305 121 11 no.1 no.1 NUM american_scientific_journal-1305 121 12 , , PUNCT american_scientific_journal-1305 121 13 pp pp ADJ american_scientific_journal-1305 121 14 . . PUNCT american_scientific_journal-1305 121 15 13–14 13–14 NUM american_scientific_journal-1305 121 16 , , PUNCT american_scientific_journal-1305 121 17 1996 1996 NUM american_scientific_journal-1305 121 18 . . PUNCT american_scientific_journal-1305 122 1 [ [ X american_scientific_journal-1305 122 2 7 7 X american_scientific_journal-1305 122 3 ] ] X american_scientific_journal-1305 122 4 h. h. PROPN american_scientific_journal-1305 122 5 casdagli casdagli PROPN american_scientific_journal-1305 122 6 , , PUNCT american_scientific_journal-1305 122 7 β€œ " PUNCT american_scientific_journal-1305 122 8 a a DET american_scientific_journal-1305 122 9 dynamical dynamical ADJ american_scientific_journal-1305 122 10 system system NOUN american_scientific_journal-1305 122 11 approach approach NOUN american_scientific_journal-1305 122 12 to to ADP american_scientific_journal-1305 122 13 modeling model VERB american_scientific_journal-1305 122 14 input input NOUN american_scientific_journal-1305 122 15 - - PUNCT american_scientific_journal-1305 122 16 output output NOUN american_scientific_journal-1305 122 17 system system NOUN american_scientific_journal-1305 122 18 in in ADP american_scientific_journal-1305 122 19 non non ADJ american_scientific_journal-1305 122 20 - - ADJ american_scientific_journal-1305 122 21 linear linear ADJ american_scientific_journal-1305 122 22 modeling modeling NOUN american_scientific_journal-1305 122 23 and and CCONJ american_scientific_journal-1305 122 24 forecasting forecasting NOUN american_scientific_journal-1305 122 25 , , PUNCT american_scientific_journal-1305 122 26 ” " PUNCT american_scientific_journal-1305 122 27 sfi sfi NOUN american_scientific_journal-1305 122 28 ( ( PUNCT american_scientific_journal-1305 122 29 scientific scientific ADJ american_scientific_journal-1305 122 30 forum forum NOUN american_scientific_journal-1305 122 31 international international ADJ american_scientific_journal-1305 122 32 ) ) PUNCT american_scientific_journal-1305 122 33 studies study NOUN american_scientific_journal-1305 122 34 in in ADP american_scientific_journal-1305 122 35 the the DET american_scientific_journal-1305 122 36 series series NOUN american_scientific_journal-1305 122 37 of of ADP american_scientific_journal-1305 122 38 complexity complexity NOUN american_scientific_journal-1305 122 39 process process NOUN american_scientific_journal-1305 122 40 , , PUNCT american_scientific_journal-1305 122 41 vol vol NOUN american_scientific_journal-1305 122 42 . . PROPN american_scientific_journal-1305 122 43 12 12 NUM american_scientific_journal-1305 122 44 , , PUNCT american_scientific_journal-1305 122 45 pp pp ADJ american_scientific_journal-1305 122 46 . . PUNCT american_scientific_journal-1305 122 47 265 265 NUM american_scientific_journal-1305 122 48 – – PUNCT american_scientific_journal-1305 122 49 281 281 NUM american_scientific_journal-1305 122 50 , , PUNCT american_scientific_journal-1305 122 51 1992 1992 NUM american_scientific_journal-1305 122 52 . . PUNCT american_scientific_journal-1305 123 1 [ [ X american_scientific_journal-1305 123 2 8 8 X american_scientific_journal-1305 123 3 ] ] PUNCT american_scientific_journal-1305 123 4 s. s. PROPN american_scientific_journal-1305 123 5 neil neil PROPN american_scientific_journal-1305 123 6 rasband rasband PROPN american_scientific_journal-1305 123 7 , , PUNCT american_scientific_journal-1305 123 8 β€œ " PUNCT american_scientific_journal-1305 123 9 chaotic chaotic ADJ american_scientific_journal-1305 123 10 dynamics dynamic NOUN american_scientific_journal-1305 123 11 of of ADP american_scientific_journal-1305 123 12 non non ADJ american_scientific_journal-1305 123 13 - - ADJ american_scientific_journal-1305 123 14 linear linear ADJ american_scientific_journal-1305 123 15 systems system NOUN american_scientific_journal-1305 123 16 , , PUNCT american_scientific_journal-1305 123 17 ” " PUNCT american_scientific_journal-1305 123 18 wiley wiley NOUN american_scientific_journal-1305 123 19 , , PUNCT american_scientific_journal-1305 123 20 1997 1997 NUM american_scientific_journal-1305 123 21 [ [ X american_scientific_journal-1305 123 22 9 9 NUM american_scientific_journal-1305 123 23 ] ] SYM american_scientific_journal-1305 123 24 j.d j.d PROPN american_scientific_journal-1305 123 25 . . PROPN american_scientific_journal-1305 123 26 farmer farmer PROPN american_scientific_journal-1305 123 27 , , PUNCT american_scientific_journal-1305 123 28 β€œ " PUNCT american_scientific_journal-1305 123 29 chaotic chaotic ADJ american_scientific_journal-1305 123 30 attractors attractor NOUN american_scientific_journal-1305 123 31 of of ADP american_scientific_journal-1305 123 32 infinite infinite ADJ american_scientific_journal-1305 123 33 dimensional dimensional ADJ american_scientific_journal-1305 123 34 dynamic dynamic ADJ american_scientific_journal-1305 123 35 systems system NOUN american_scientific_journal-1305 123 36 , , PUNCT american_scientific_journal-1305 123 37 ” " PUNCT american_scientific_journal-1305 123 38 physica physica NOUN american_scientific_journal-1305 123 39 d d NOUN american_scientific_journal-1305 123 40 : : PUNCT american_scientific_journal-1305 123 41 nonlinear nonlinear ADJ american_scientific_journal-1305 123 42 phenomena phenomena NOUN american_scientific_journal-1305 123 43 vol vol NOUN american_scientific_journal-1305 123 44 , , PUNCT american_scientific_journal-1305 123 45 4 4 NUM american_scientific_journal-1305 123 46 . . PUNCT american_scientific_journal-1305 123 47 no.3 no.3 VERB american_scientific_journal-1305 123 48 pp pp ADV american_scientific_journal-1305 123 49 . . PUNCT american_scientific_journal-1305 124 1 366 366 NUM american_scientific_journal-1305 124 2 - - SYM american_scientific_journal-1305 124 3 393 393 NUM american_scientific_journal-1305 124 4 , , PUNCT american_scientific_journal-1305 124 5 1982 1982 NUM american_scientific_journal-1305 124 6 [ [ X american_scientific_journal-1305 124 7 10 10 NUM american_scientific_journal-1305 124 8 ] ] X american_scientific_journal-1305 124 9 e. e. PROPN american_scientific_journal-1305 124 10 canessa canessa PROPN american_scientific_journal-1305 124 11 and and CCONJ american_scientific_journal-1305 124 12 a. a. NOUN american_scientific_journal-1305 124 13 calmetta calmetta PROPN american_scientific_journal-1305 124 14 , , PUNCT american_scientific_journal-1305 124 15 β€œ " PUNCT american_scientific_journal-1305 124 16 physics physics NOUN american_scientific_journal-1305 124 17 of of ADP american_scientific_journal-1305 124 18 biological biological ADJ american_scientific_journal-1305 124 19 random random ADJ american_scientific_journal-1305 124 20 process process NOUN american_scientific_journal-1305 124 21 , , PUNCT american_scientific_journal-1305 124 22 ” " PUNCT american_scientific_journal-1305 124 23 phy phy NOUN american_scientific_journal-1305 124 24 rev.e.50 rev.e.50 PROPN american_scientific_journal-1305 124 25 , , PUNCT american_scientific_journal-1305 124 26 1994 1994 NUM american_scientific_journal-1305 124 27 . . PUNCT american_scientific_journal-1305 125 1 [ [ X american_scientific_journal-1305 125 2 11 11 NUM american_scientific_journal-1305 125 3 ] ] X american_scientific_journal-1305 125 4 p.v p.v PROPN american_scientific_journal-1305 125 5 . . PROPN american_scientific_journal-1305 125 6 baylay baylay NOUN american_scientific_journal-1305 125 7 and and CCONJ american_scientific_journal-1305 125 8 n.l n.l PROPN american_scientific_journal-1305 125 9 . . PROPN american_scientific_journal-1305 125 10 virgin virgin PROPN american_scientific_journal-1305 125 11 , , PUNCT american_scientific_journal-1305 125 12 β€œ " PUNCT american_scientific_journal-1305 125 13 practical practical ADJ american_scientific_journal-1305 125 14 considerations consideration NOUN american_scientific_journal-1305 125 15 in in ADP american_scientific_journal-1305 125 16 the the DET american_scientific_journal-1305 125 17 control control NOUN american_scientific_journal-1305 125 18 of of ADP american_scientific_journal-1305 125 19 chaos chaos NOUN american_scientific_journal-1305 125 20 , , PUNCT american_scientific_journal-1305 125 21 ” " PUNCT american_scientific_journal-1305 125 22 physical physical ADJ american_scientific_journal-1305 125 23 review review NOUN american_scientific_journal-1305 125 24 e e PROPN american_scientific_journal-1305 125 25 50 50 NUM american_scientific_journal-1305 125 26 , , PUNCT american_scientific_journal-1305 125 27 no no INTJ american_scientific_journal-1305 125 28 . . NOUN american_scientific_journal-1305 125 29 1 1 NUM american_scientific_journal-1305 125 30 , , PUNCT american_scientific_journal-1305 125 31 pp pp ADJ american_scientific_journal-1305 125 32 . . PUNCT american_scientific_journal-1305 126 1 604 604 NUM american_scientific_journal-1305 126 2 , , PUNCT american_scientific_journal-1305 126 3 1994 1994 NUM american_scientific_journal-1305 126 4 . . PUNCT american_scientific_journal-1305 127 1 [ [ X american_scientific_journal-1305 127 2 12 12 NUM american_scientific_journal-1305 127 3 ] ] X american_scientific_journal-1305 127 4 l.x l.x PROPN american_scientific_journal-1305 127 5 . . PUNCT american_scientific_journal-1305 127 6 wang wang PROPN american_scientific_journal-1305 127 7 , , PUNCT american_scientific_journal-1305 127 8 β€œ " PUNCT american_scientific_journal-1305 127 9 adaptive adaptive ADJ american_scientific_journal-1305 127 10 fuzzy fuzzy ADJ american_scientific_journal-1305 127 11 system system NOUN american_scientific_journal-1305 127 12 and and CCONJ american_scientific_journal-1305 127 13 control control NOUN american_scientific_journal-1305 127 14 , , PUNCT american_scientific_journal-1305 127 15 design design NOUN american_scientific_journal-1305 127 16 and and CCONJ american_scientific_journal-1305 127 17 stability stability NOUN american_scientific_journal-1305 127 18 analysis analysis NOUN american_scientific_journal-1305 127 19 , , PUNCT american_scientific_journal-1305 127 20 ” " PUNCT american_scientific_journal-1305 127 21 prentice prentice NOUN american_scientific_journal-1305 127 22 hall hall PROPN american_scientific_journal-1305 127 23 , , PUNCT american_scientific_journal-1305 127 24 englewoodcliffs englewoodcliff NOUN american_scientific_journal-1305 127 25 , , PUNCT american_scientific_journal-1305 127 26 1994 1994 NUM american_scientific_journal-1305 127 27 . . PUNCT american_scientific_journal-1305 128 1 [ [ X american_scientific_journal-1305 128 2 13 13 NUM american_scientific_journal-1305 128 3 ] ] X american_scientific_journal-1305 128 4 e. e. PROPN american_scientific_journal-1305 128 5 lorenz lorenz PROPN american_scientific_journal-1305 128 6 , , PUNCT american_scientific_journal-1305 128 7 β€œ " PUNCT american_scientific_journal-1305 128 8 deterministic deterministic VERB american_scientific_journal-1305 128 9 no no DET american_scientific_journal-1305 128 10 periodic periodic ADJ american_scientific_journal-1305 128 11 flow flow NOUN american_scientific_journal-1305 128 12 , , PUNCT american_scientific_journal-1305 128 13 ” " PUNCT american_scientific_journal-1305 128 14 atmospheric atmospheric ADJ american_scientific_journal-1305 128 15 science science NOUN american_scientific_journal-1305 128 16 , , PUNCT american_scientific_journal-1305 128 17 vol vol NOUN american_scientific_journal-1305 128 18 . . PROPN american_scientific_journal-1305 128 19 20 20 NUM american_scientific_journal-1305 128 20 , , PUNCT american_scientific_journal-1305 128 21 pp pp ADJ american_scientific_journal-1305 128 22 . . PUNCT american_scientific_journal-1305 128 23 130 130 NUM american_scientific_journal-1305 128 24 , , PUNCT american_scientific_journal-1305 128 25 1963 1963 NUM american_scientific_journal-1305 128 26 . . PUNCT american_scientific_journal-1305 129 1 [ [ X american_scientific_journal-1305 129 2 14 14 NUM american_scientific_journal-1305 129 3 ] ] X american_scientific_journal-1305 129 4 o.e o.e PROPN american_scientific_journal-1305 129 5 . . PROPN american_scientific_journal-1305 129 6 rossler rossler PROPN american_scientific_journal-1305 129 7 , , PUNCT american_scientific_journal-1305 129 8 β€œ " PUNCT american_scientific_journal-1305 129 9 an an DET american_scientific_journal-1305 129 10 equation equation NOUN american_scientific_journal-1305 129 11 for for ADP american_scientific_journal-1305 129 12 continuous continuous ADJ american_scientific_journal-1305 129 13 chaos chaos NOUN american_scientific_journal-1305 129 14 , , PUNCT american_scientific_journal-1305 129 15 ” " PUNCT american_scientific_journal-1305 129 16 physical physical ADJ american_scientific_journal-1305 129 17 review review NOUN american_scientific_journal-1305 129 18 letters letter NOUN american_scientific_journal-1305 129 19 , , PUNCT american_scientific_journal-1305 129 20 vol vol NOUN american_scientific_journal-1305 129 21 . . NOUN american_scientific_journal-1305 129 22 57a 57a NUM american_scientific_journal-1305 129 23 , , PUNCT american_scientific_journal-1305 129 24 pp pp ADP american_scientific_journal-1305 129 25 . . PUNCT american_scientific_journal-1305 130 1 397–398 397–398 NUM american_scientific_journal-1305 130 2 , , PUNCT american_scientific_journal-1305 130 3 1976 1976 NUM american_scientific_journal-1305 130 4 . . PUNCT american_scientific_journal-1305 131 1 [ [ X american_scientific_journal-1305 131 2 15 15 NUM american_scientific_journal-1305 131 3 ] ] X american_scientific_journal-1305 131 4 y.z y.z PROPN american_scientific_journal-1305 131 5 jafri jafri PROPN american_scientific_journal-1305 131 6 , , PUNCT american_scientific_journal-1305 131 7 l. l. PROPN american_scientific_journal-1305 131 8 kamal kamal PROPN american_scientific_journal-1305 131 9 , , PUNCT american_scientific_journal-1305 131 10 and and CCONJ american_scientific_journal-1305 131 11 s. s. PROPN american_scientific_journal-1305 131 12 massod massod PROPN american_scientific_journal-1305 131 13 raza raza PROPN american_scientific_journal-1305 131 14 , , PUNCT american_scientific_journal-1305 131 15 β€œ " PUNCT american_scientific_journal-1305 131 16 chaotic chaotic ADJ american_scientific_journal-1305 131 17 time time NOUN american_scientific_journal-1305 131 18 series series NOUN american_scientific_journal-1305 131 19 prediction prediction NOUN american_scientific_journal-1305 131 20 and and CCONJ american_scientific_journal-1305 131 21 meckey meckey ADJ american_scientific_journal-1305 131 22 glass glass NOUN american_scientific_journal-1305 131 23 simulation simulation NOUN american_scientific_journal-1305 131 24 with with ADP american_scientific_journal-1305 131 25 fuzzy fuzzy ADJ american_scientific_journal-1305 131 26 logic logic NOUN american_scientific_journal-1305 131 27 , , PUNCT american_scientific_journal-1305 131 28 ” " PUNCT american_scientific_journal-1305 131 29 international international ADJ american_scientific_journal-1305 131 30 journal journal NOUN american_scientific_journal-1305 131 31 of of ADP american_scientific_journal-1305 131 32 the the DET american_scientific_journal-1305 131 33 physical physical ADJ american_scientific_journal-1305 131 34 sciences science NOUN american_scientific_journal-1305 131 35 , , PUNCT american_scientific_journal-1305 131 36 vol vol NOUN american_scientific_journal-1305 131 37 . . PROPN american_scientific_journal-1305 131 38 7 7 NUM american_scientific_journal-1305 131 39 , , PUNCT american_scientific_journal-1305 131 40 no no INTJ american_scientific_journal-1305 131 41 . . NOUN american_scientific_journal-1305 131 42 17 17 NUM american_scientific_journal-1305 131 43 , , PUNCT american_scientific_journal-1305 131 44 pp pp ADJ american_scientific_journal-1305 131 45 . . PUNCT american_scientific_journal-1305 131 46 2596–2606 2596–2606 NUM american_scientific_journal-1305 131 47 , , PUNCT american_scientific_journal-1305 131 48 2012 2012 NUM american_scientific_journal-1305 131 49 . . PUNCT american_scientific_journal-1305 132 1 [ [ X american_scientific_journal-1305 132 2 16 16 NUM american_scientific_journal-1305 132 3 ] ] X american_scientific_journal-1305 132 4 y.z y.z PROPN american_scientific_journal-1305 132 5 jafri jafri PROPN american_scientific_journal-1305 132 6 , , PUNCT american_scientific_journal-1305 132 7 l. l. PROPN american_scientific_journal-1305 132 8 kamal kamal PROPN american_scientific_journal-1305 132 9 , , PUNCT american_scientific_journal-1305 132 10 and and CCONJ american_scientific_journal-1305 132 11 s. s. PROPN american_scientific_journal-1305 132 12 massod massod PROPN american_scientific_journal-1305 132 13 raza raza PROPN american_scientific_journal-1305 132 14 , , PUNCT american_scientific_journal-1305 132 15 β€œ " PUNCT american_scientific_journal-1305 132 16 rule rule NOUN american_scientific_journal-1305 132 17 based base VERB american_scientific_journal-1305 132 18 fuzzy fuzzy ADJ american_scientific_journal-1305 132 19 logic logic NOUN american_scientific_journal-1305 132 20 time time NOUN american_scientific_journal-1305 132 21 series series PROPN american_scientific_journal-1305 132 22 prediction prediction PROPN american_scientific_journal-1305 132 23 , , PUNCT american_scientific_journal-1305 132 24 ” " PUNCT american_scientific_journal-1305 132 25 international international ADJ american_scientific_journal-1305 132 26 journal journal NOUN american_scientific_journal-1305 132 27 of of ADP american_scientific_journal-1305 132 28 the the DET american_scientific_journal-1305 132 29 physical physical ADJ american_scientific_journal-1305 132 30 sciences science NOUN american_scientific_journal-1305 132 31 , , PUNCT american_scientific_journal-1305 132 32 vol vol NOUN american_scientific_journal-1305 132 33 . . PROPN american_scientific_journal-1305 132 34 7 7 NUM american_scientific_journal-1305 132 35 , , PUNCT american_scientific_journal-1305 132 36 no no INTJ american_scientific_journal-1305 132 37 . . NOUN american_scientific_journal-1305 132 38 11 11 NUM american_scientific_journal-1305 132 39 , , PUNCT american_scientific_journal-1305 132 40 pp pp ADJ american_scientific_journal-1305 132 41 . . PUNCT american_scientific_journal-1305 132 42 1862–1873 1862–1873 NUM american_scientific_journal-1305 132 43 , , PUNCT american_scientific_journal-1305 132 44 2012 2012 NUM american_scientific_journal-1305 132 45 . . PUNCT american_scientific_journal-1305 133 1 [ [ X american_scientific_journal-1305 133 2 17 17 NUM american_scientific_journal-1305 133 3 ] ] SYM american_scientific_journal-1305 133 4 l.kamal l.kamal ADJ american_scientific_journal-1305 133 5 and and CCONJ american_scientific_journal-1305 133 6 y.z.jafri y.z.jafri ADJ american_scientific_journal-1305 133 7 , , PUNCT american_scientific_journal-1305 133 8 β€œ " PUNCT american_scientific_journal-1305 133 9 stochastic stochastic ADJ american_scientific_journal-1305 133 10 modelling modelling NOUN american_scientific_journal-1305 133 11 and and CCONJ american_scientific_journal-1305 133 12 generation generation NOUN american_scientific_journal-1305 133 13 of of ADP american_scientific_journal-1305 133 14 synthetic synthetic ADJ american_scientific_journal-1305 133 15 sequences sequence NOUN american_scientific_journal-1305 133 16 of of ADP american_scientific_journal-1305 133 17 hourly hourly ADJ american_scientific_journal-1305 133 18 global global ADJ american_scientific_journal-1305 133 19 solar solar ADJ american_scientific_journal-1305 133 20 radiation radiation NOUN american_scientific_journal-1305 133 21 at at ADP american_scientific_journal-1305 133 22 quetta quetta PROPN american_scientific_journal-1305 133 23 , , PUNCT american_scientific_journal-1305 133 24 pakistan pakistan PROPN american_scientific_journal-1305 133 25 , , PUNCT american_scientific_journal-1305 133 26 ” " PUNCT american_scientific_journal-1305 133 27 renewable renewable ADJ american_scientific_journal-1305 133 28 energy energy NOUN american_scientific_journal-1305 133 29 , , PUNCT american_scientific_journal-1305 133 30 vol vol NOUN american_scientific_journal-1305 133 31 . . PROPN american_scientific_journal-1305 133 32 18 18 NUM american_scientific_journal-1305 133 33 , , PUNCT american_scientific_journal-1305 133 34 pp pp ADJ american_scientific_journal-1305 133 35 . . PUNCT american_scientific_journal-1305 134 1 565–572 565–572 NUM american_scientific_journal-1305 134 2 , , PUNCT american_scientific_journal-1305 134 3 1999 1999 NUM american_scientific_journal-1305 134 4 . . PUNCT american_scientific_journal-1305 135 1 [ [ X american_scientific_journal-1305 135 2 18 18 NUM american_scientific_journal-1305 135 3 ] ] X american_scientific_journal-1305 135 4 l. l. PROPN american_scientific_journal-1305 135 5 kamal kamal PROPN american_scientific_journal-1305 135 6 and and CCONJ american_scientific_journal-1305 135 7 y.z y.z PROPN american_scientific_journal-1305 135 8 . . PROPN american_scientific_journal-1305 135 9 jafri jafri PROPN american_scientific_journal-1305 135 10 , , PUNCT american_scientific_journal-1305 135 11 β€œ " PUNCT american_scientific_journal-1305 135 12 time time NOUN american_scientific_journal-1305 135 13 series series NOUN american_scientific_journal-1305 135 14 models model NOUN american_scientific_journal-1305 135 15 to to PART american_scientific_journal-1305 135 16 simulate simulate VERB american_scientific_journal-1305 135 17 and and CCONJ american_scientific_journal-1305 135 18 forecast forecast VERB american_scientific_journal-1305 135 19 hourly hourly ADV american_scientific_journal-1305 135 20 averaged average VERB american_scientific_journal-1305 135 21 wind wind NOUN american_scientific_journal-1305 135 22 speed speed NOUN american_scientific_journal-1305 135 23 in in ADP american_scientific_journal-1305 135 24 quetta quetta PROPN american_scientific_journal-1305 135 25 , , PUNCT american_scientific_journal-1305 135 26 pakistan pakistan PROPN american_scientific_journal-1305 135 27 , , PUNCT american_scientific_journal-1305 135 28 ” " PUNCT american_scientific_journal-1305 135 29 renewable renewable ADJ american_scientific_journal-1305 135 30 energy energy NOUN american_scientific_journal-1305 135 31 , , PUNCT american_scientific_journal-1305 135 32 vol vol NOUN american_scientific_journal-1305 135 33 . . PROPN american_scientific_journal-1305 135 34 61 61 NUM american_scientific_journal-1305 135 35 , , PUNCT american_scientific_journal-1305 135 36 no no INTJ american_scientific_journal-1305 135 37 . . NOUN american_scientific_journal-1305 135 38 1 1 NUM american_scientific_journal-1305 135 39 , , PUNCT american_scientific_journal-1305 135 40 pp pp ADJ american_scientific_journal-1305 135 41 . . PUNCT american_scientific_journal-1305 136 1 23–32 23–32 NUM american_scientific_journal-1305 136 2 , , PUNCT american_scientific_journal-1305 136 3 1997 1997 NUM american_scientific_journal-1305 136 4 . . PUNCT american_scientific_journal-1305 137 1 [ [ X american_scientific_journal-1305 137 2 19 19 NUM american_scientific_journal-1305 137 3 ] ] PUNCT american_scientific_journal-1305 137 4 m. m. NOUN american_scientific_journal-1305 137 5 casdagli casdagli NOUN american_scientific_journal-1305 137 6 , , PUNCT american_scientific_journal-1305 137 7 j.and j.and PROPN american_scientific_journal-1305 137 8 roy roy PROPN american_scientific_journal-1305 137 9 , , PUNCT american_scientific_journal-1305 137 10 β€œ " PUNCT american_scientific_journal-1305 137 11 chaos chaos NOUN american_scientific_journal-1305 137 12 and and CCONJ american_scientific_journal-1305 137 13 deterministic deterministic ADJ american_scientific_journal-1305 137 14 versus versus ADP american_scientific_journal-1305 137 15 stochastic stochastic ADJ american_scientific_journal-1305 137 16 nonlinear nonlinear ADJ american_scientific_journal-1305 137 17 modeling modeling NOUN american_scientific_journal-1305 137 18 ” " PUNCT american_scientific_journal-1305 137 19 jr jr PROPN american_scientific_journal-1305 137 20 . . PROPN american_scientific_journal-1305 137 21 royal royal PROPN american_scientific_journal-1305 137 22 stat.soc.b stat.soc.b PROPN american_scientific_journal-1305 137 23 , , PUNCT american_scientific_journal-1305 137 24 vol vol NOUN american_scientific_journal-1305 137 25 . . PUNCT american_scientific_journal-1305 137 26 b54 b54 PROPN american_scientific_journal-1305 137 27 , , PUNCT american_scientific_journal-1305 137 28 pp pp ADP american_scientific_journal-1305 137 29 . . PUNCT american_scientific_journal-1305 138 1 303–328 303–328 NUM american_scientific_journal-1305 138 2 , , PUNCT american_scientific_journal-1305 138 3 1991 1991 NUM american_scientific_journal-1305 138 4 . . PUNCT american_scientific_journal-1305 139 1 [ [ X american_scientific_journal-1305 139 2 20 20 NUM american_scientific_journal-1305 139 3 ] ] PUNCT american_scientific_journal-1305 139 4 b. b. PROPN american_scientific_journal-1305 139 5 kosko kosko PROPN american_scientific_journal-1305 139 6 , , PUNCT american_scientific_journal-1305 139 7 β€œ " PUNCT american_scientific_journal-1305 139 8 fuzzy fuzzy ADJ american_scientific_journal-1305 139 9 engineering engineering NOUN american_scientific_journal-1305 139 10 , , PUNCT american_scientific_journal-1305 139 11 ” " PUNCT american_scientific_journal-1305 139 12 1997 1997 NUM american_scientific_journal-1305 139 13 . . PUNCT american_scientific_journal-1305 140 1 [ [ X american_scientific_journal-1305 140 2 21 21 NUM american_scientific_journal-1305 140 3 ] ] X american_scientific_journal-1305 140 4 y.z y.z PROPN american_scientific_journal-1305 140 5 jafri jafri PROPN american_scientific_journal-1305 140 6 , , PUNCT american_scientific_journal-1305 140 7 β€œ " PUNCT american_scientific_journal-1305 140 8 resents resent VERB american_scientific_journal-1305 140 9 trends trend NOUN american_scientific_journal-1305 140 10 in in ADP american_scientific_journal-1305 140 11 time time NOUN american_scientific_journal-1305 140 12 series series PROPN american_scientific_journal-1305 140 13 modelling modelling NOUN american_scientific_journal-1305 140 14 , , PUNCT american_scientific_journal-1305 140 15 simulation simulation NOUN american_scientific_journal-1305 140 16 and and CCONJ american_scientific_journal-1305 140 17 prediction prediction NOUN american_scientific_journal-1305 140 18 : : PUNCT american_scientific_journal-1305 140 19 statistical statistical ADJ american_scientific_journal-1305 140 20 and and CCONJ american_scientific_journal-1305 140 21 fuzzy fuzzy ADJ american_scientific_journal-1305 140 22 logic logic NOUN american_scientific_journal-1305 140 23 approach approach NOUN american_scientific_journal-1305 140 24 , , PUNCT american_scientific_journal-1305 140 25 ph.d ph.d PROPN american_scientific_journal-1305 140 26 thesis thesis NOUN american_scientific_journal-1305 140 27 , , PUNCT american_scientific_journal-1305 140 28 ” " PUNCT american_scientific_journal-1305 140 29 ph ph VERB american_scientific_journal-1305 140 30 . . PUNCT american_scientific_journal-1305 141 1 d d X american_scientific_journal-1305 141 2 thesis thesis NOUN american_scientific_journal-1305 141 3 , , PUNCT american_scientific_journal-1305 141 4 university university NOUN american_scientific_journal-1305 141 5 of of ADP american_scientific_journal-1305 141 6 balochistan balochistan PROPN american_scientific_journal-1305 141 7 , , PUNCT american_scientific_journal-1305 141 8 quetta quetta PROPN american_scientific_journal-1305 141 9 , , PUNCT american_scientific_journal-1305 141 10 pakistan pakistan PROPN american_scientific_journal-1305 141 11 , , PUNCT american_scientific_journal-1305 141 12 2007 2007 NUM american_scientific_journal-1305 141 13 . . PUNCT american_scientific_journal-1305 142 1 288 288 NUM american_scientific_journal-1305 142 2 american american ADJ american_scientific_journal-1305 142 3 scientific scientific ADJ american_scientific_journal-1305 142 4 research research NOUN american_scientific_journal-1305 142 5 journal journal NOUN american_scientific_journal-1305 142 6 for for ADP american_scientific_journal-1305 142 7 engineering engineering NOUN american_scientific_journal-1305 142 8 , , PUNCT american_scientific_journal-1305 142 9 technology technology NOUN american_scientific_journal-1305 142 10 , , PUNCT american_scientific_journal-1305 142 11 and and CCONJ american_scientific_journal-1305 142 12 sciences science NOUN american_scientific_journal-1305 142 13 ( ( PUNCT american_scientific_journal-1305 142 14 asrjets asrjet NOUN american_scientific_journal-1305 142 15 ) ) PUNCT american_scientific_journal-1305 142 16 ( ( PUNCT american_scientific_journal-1305 142 17 2016 2016 NUM american_scientific_journal-1305 142 18 ) ) PUNCT american_scientific_journal-1305 142 19 volume volume NOUN american_scientific_journal-1305 142 20 15 15 NUM american_scientific_journal-1305 142 21 , , PUNCT american_scientific_journal-1305 142 22 no no DET american_scientific_journal-1305 142 23 1 1 NUM american_scientific_journal-1305 142 24 , , PUNCT american_scientific_journal-1305 142 25 pp pp ADV american_scientific_journal-1305 142 26 282 282 NUM american_scientific_journal-1305 142 27 - - SYM american_scientific_journal-1305 142 28 289 289 NUM american_scientific_journal-1305 143 1 [ [ X american_scientific_journal-1305 143 2 22 22 NUM american_scientific_journal-1305 143 3 ] ] PUNCT american_scientific_journal-1305 143 4 l. l. PROPN american_scientific_journal-1305 143 5 kamal kamal PROPN american_scientific_journal-1305 143 6 and and CCONJ american_scientific_journal-1305 143 7 y.z y.z PROPN american_scientific_journal-1305 143 8 . . PROPN american_scientific_journal-1305 143 9 jafri jafri PROPN american_scientific_journal-1305 143 10 , , PUNCT american_scientific_journal-1305 143 11 β€œ " PUNCT american_scientific_journal-1305 143 12 information information NOUN american_scientific_journal-1305 143 13 theory theory NOUN american_scientific_journal-1305 143 14 in in ADP american_scientific_journal-1305 143 15 stochastic stochastic ADJ american_scientific_journal-1305 143 16 process process NOUN american_scientific_journal-1305 143 17 , , PUNCT american_scientific_journal-1305 143 18 ” " PUNCT american_scientific_journal-1305 143 19 science science NOUN american_scientific_journal-1305 143 20 international international ADJ american_scientific_journal-1305 143 21 lahore lahore PROPN american_scientific_journal-1305 143 22 , , PUNCT american_scientific_journal-1305 143 23 vol vol NOUN american_scientific_journal-1305 143 24 . . PROPN american_scientific_journal-1305 143 25 9 9 NUM american_scientific_journal-1305 143 26 , , PUNCT american_scientific_journal-1305 143 27 no no INTJ american_scientific_journal-1305 143 28 . . NOUN american_scientific_journal-1305 143 29 3 3 NUM american_scientific_journal-1305 143 30 , , PUNCT american_scientific_journal-1305 143 31 pp pp ADJ american_scientific_journal-1305 143 32 . . PUNCT american_scientific_journal-1305 144 1 329–330 329–330 NUM american_scientific_journal-1305 144 2 , , PUNCT american_scientific_journal-1305 144 3 1997 1997 NUM american_scientific_journal-1305 144 4 . . PUNCT american_scientific_journal-1305 145 1 [ [ X american_scientific_journal-1305 145 2 23 23 NUM american_scientific_journal-1305 145 3 ] ] X american_scientific_journal-1305 145 4 l.e l.e AUX american_scientific_journal-1305 145 5 . . PROPN american_scientific_journal-1305 145 6 reided reide VERB american_scientific_journal-1305 145 7 , , PUNCT american_scientific_journal-1305 145 8 β€œ " PUNCT american_scientific_journal-1305 145 9 the the DET american_scientific_journal-1305 145 10 transition transition NOUN american_scientific_journal-1305 145 11 to to PART american_scientific_journal-1305 145 12 chaos chaos VERB american_scientific_journal-1305 145 13 , , PUNCT american_scientific_journal-1305 145 14 ” " PUNCT american_scientific_journal-1305 145 15 no no NOUN american_scientific_journal-1305 145 16 . . NOUN american_scientific_journal-1305 145 17 3 3 NUM american_scientific_journal-1305 145 18 , , PUNCT american_scientific_journal-1305 145 19 1992 1992 NUM american_scientific_journal-1305 145 20 . . PUNCT american_scientific_journal-1305 146 1 [ [ X american_scientific_journal-1305 146 2 24 24 NUM american_scientific_journal-1305 146 3 ] ] PUNCT american_scientific_journal-1305 146 4 l. l. PROPN american_scientific_journal-1305 146 5 kamal kamal PROPN american_scientific_journal-1305 146 6 and and CCONJ american_scientific_journal-1305 146 7 y.z y.z PROPN american_scientific_journal-1305 146 8 . . PROPN american_scientific_journal-1305 146 9 jafri jafri PROPN american_scientific_journal-1305 146 10 , , PUNCT american_scientific_journal-1305 146 11 β€œ " PUNCT american_scientific_journal-1305 146 12 disorder disorder NOUN american_scientific_journal-1305 146 13 in in ADP american_scientific_journal-1305 146 14 a a DET american_scientific_journal-1305 146 15 stochastic stochastic ADJ american_scientific_journal-1305 146 16 processes process NOUN american_scientific_journal-1305 146 17 , , PUNCT american_scientific_journal-1305 146 18 ” " PUNCT american_scientific_journal-1305 146 19 vol vol NOUN american_scientific_journal-1305 146 20 . . PROPN american_scientific_journal-1305 146 21 7 7 NUM american_scientific_journal-1305 146 22 , , PUNCT american_scientific_journal-1305 146 23 no no INTJ american_scientific_journal-1305 146 24 . . NOUN american_scientific_journal-1305 146 25 4 4 NUM american_scientific_journal-1305 146 26 , , PUNCT american_scientific_journal-1305 146 27 pp pp ADJ american_scientific_journal-1305 146 28 . . PUNCT american_scientific_journal-1305 147 1 465–467 465–467 NUM american_scientific_journal-1305 147 2 , , PUNCT american_scientific_journal-1305 147 3 1995 1995 NUM american_scientific_journal-1305 147 4 . . PUNCT american_scientific_journal-1305 148 1 [ [ X american_scientific_journal-1305 148 2 25 25 NUM american_scientific_journal-1305 148 3 ] ] X american_scientific_journal-1305 148 4 r.n r.n PROPN american_scientific_journal-1305 148 5 . . PROPN american_scientific_journal-1305 148 6 bracewell bracewell PROPN american_scientific_journal-1305 148 7 , , PUNCT american_scientific_journal-1305 148 8 β€œ " PUNCT american_scientific_journal-1305 148 9 the the DET american_scientific_journal-1305 148 10 fourier fourier NOUN american_scientific_journal-1305 148 11 transform transform NOUN american_scientific_journal-1305 148 12 , , PUNCT american_scientific_journal-1305 148 13 ” " PUNCT american_scientific_journal-1305 148 14 scientific scientific ADJ american_scientific_journal-1305 148 15 american american ADJ american_scientific_journal-1305 148 16 , , PUNCT american_scientific_journal-1305 148 17 vol vol NOUN american_scientific_journal-1305 148 18 . . PROPN american_scientific_journal-1305 148 19 260 260 NUM american_scientific_journal-1305 148 20 , , PUNCT american_scientific_journal-1305 148 21 no no INTJ american_scientific_journal-1305 148 22 . . NOUN american_scientific_journal-1305 148 23 6 6 NUM american_scientific_journal-1305 148 24 , , PUNCT american_scientific_journal-1305 148 25 pp pp ADJ american_scientific_journal-1305 148 26 . . PUNCT american_scientific_journal-1305 148 27 86–95 86–95 NOUN american_scientific_journal-1305 148 28 , , PUNCT american_scientific_journal-1305 148 29 2000 2000 NUM american_scientific_journal-1305 148 30 . . PUNCT american_scientific_journal-1305 149 1 [ [ X american_scientific_journal-1305 149 2 26 26 NUM american_scientific_journal-1305 149 3 ] ] X american_scientific_journal-1305 149 4 l.b.almeida l.b.almeida PROPN american_scientific_journal-1305 149 5 , , PUNCT american_scientific_journal-1305 149 6 β€œ " PUNCT american_scientific_journal-1305 149 7 the the DET american_scientific_journal-1305 149 8 fractional fractional ADJ american_scientific_journal-1305 149 9 fourier fourier NOUN american_scientific_journal-1305 149 10 transform transform NOUN american_scientific_journal-1305 149 11 and and CCONJ american_scientific_journal-1305 149 12 time time NOUN american_scientific_journal-1305 149 13 - - PUNCT american_scientific_journal-1305 149 14 frequency frequency NOUN american_scientific_journal-1305 149 15 representations representation NOUN american_scientific_journal-1305 149 16 , , PUNCT american_scientific_journal-1305 149 17 ” " PUNCT american_scientific_journal-1305 149 18 ieee ieee NOUN american_scientific_journal-1305 149 19 transactions transaction NOUN american_scientific_journal-1305 149 20 on on ADP american_scientific_journal-1305 149 21 signal signal ADJ american_scientific_journal-1305 149 22 processing processing NOUN american_scientific_journal-1305 149 23 , , PUNCT american_scientific_journal-1305 149 24 vol vol NOUN american_scientific_journal-1305 149 25 . . PROPN american_scientific_journal-1305 150 1 42 42 NUM american_scientific_journal-1305 150 2 , , PUNCT american_scientific_journal-1305 150 3 no no INTJ american_scientific_journal-1305 150 4 . . NOUN american_scientific_journal-1305 150 5 11 11 NUM american_scientific_journal-1305 150 6 , , PUNCT american_scientific_journal-1305 151 1 pp pp ADJ american_scientific_journal-1305 151 2 . . PUNCT american_scientific_journal-1305 152 1 3084–3091 3084–3091 NUM american_scientific_journal-1305 152 2 , , PUNCT american_scientific_journal-1305 152 3 1994 1994 NUM american_scientific_journal-1305 152 4 . . PUNCT american_scientific_journal-1305 153 1 [ [ X american_scientific_journal-1305 153 2 27 27 NUM american_scientific_journal-1305 153 3 ] ] X american_scientific_journal-1305 153 4 s. s. PROPN american_scientific_journal-1305 153 5 iqbal iqbal PROPN american_scientific_journal-1305 153 6 , , PUNCT american_scientific_journal-1305 153 7 f. f. PROPN american_scientific_journal-1305 153 8 sarwar sarwar PROPN american_scientific_journal-1305 153 9 , , PUNCT american_scientific_journal-1305 153 10 s.m.raza s.m.raza NOUN american_scientific_journal-1305 153 11 , , PUNCT american_scientific_journal-1305 153 12 a.rehman a.rehman ADJ american_scientific_journal-1305 153 13 β€œ " PUNCT american_scientific_journal-1305 153 14 how how SCONJ american_scientific_journal-1305 153 15 fractional fractional ADJ american_scientific_journal-1305 153 16 charge charge NOUN american_scientific_journal-1305 153 17 on on ADP american_scientific_journal-1305 153 18 an an DET american_scientific_journal-1305 153 19 electron electron NOUN american_scientific_journal-1305 153 20 in in ADP american_scientific_journal-1305 153 21 the the DET american_scientific_journal-1305 153 22 momentum momentum NOUN american_scientific_journal-1305 153 23 space space NOUN american_scientific_journal-1305 153 24 is be AUX american_scientific_journal-1305 153 25 quantized quantize VERB american_scientific_journal-1305 153 26 ? ? PUNCT american_scientific_journal-1305 154 1 american american ADJ american_scientific_journal-1305 154 2 scientific scientific ADJ american_scientific_journal-1305 154 3 research research PROPN american_scientific_journal-1305 154 4 journal journal NOUN american_scientific_journal-1305 154 5 for for ADP american_scientific_journal-1305 154 6 engineering engineering NOUN american_scientific_journal-1305 154 7 , , PUNCT american_scientific_journal-1305 154 8 technology technology NOUN american_scientific_journal-1305 154 9 , , PUNCT american_scientific_journal-1305 154 10 and and CCONJ american_scientific_journal-1305 154 11 sciences science NOUN american_scientific_journal-1305 154 12 vol vol NOUN american_scientific_journal-1305 154 13 . . PUNCT american_scientific_journal-1305 155 1 14(2 14(2 NUM american_scientific_journal-1305 155 2 ) ) PUNCT american_scientific_journal-1305 156 1 , , PUNCT american_scientific_journal-1305 156 2 pp.265 pp.265 NOUN american_scientific_journal-1305 156 3 - - PUNCT american_scientific_journal-1305 156 4 272 272 NUM american_scientific_journal-1305 156 5 , , PUNCT american_scientific_journal-1305 156 6 nov nov PROPN american_scientific_journal-1305 156 7 2015 2015 NUM american_scientific_journal-1305 156 8 . . PUNCT american_scientific_journal-1305 157 1 289 289 NUM