id	sid	tid	token	lemma	pos
ejpam-5456	1	1	european	european	PROPN
ejpam-5456	1	2	journal	journal	PROPN
ejpam-5456	1	3	of	of	ADP
ejpam-5456	1	4	pure	pure	ADJ
ejpam-5456	1	5	and	and	CCONJ
ejpam-5456	1	6	applied	apply	VERB
ejpam-5456	1	7	mathematics	mathematic	NOUN
ejpam-5456	1	8	vol	vol	NOUN
ejpam-5456	1	9	.	.	PROPN
ejpam-5456	2	1	17	17	NUM
ejpam-5456	2	2	,	,	PUNCT
ejpam-5456	2	3	no	no	INTJ
ejpam-5456	2	4	.	.	NOUN
ejpam-5456	2	5	4	4	NUM
ejpam-5456	2	6	,	,	PUNCT
ejpam-5456	2	7	2024	2024	NUM
ejpam-5456	2	8	,	,	PUNCT
ejpam-5456	2	9	3464	3464	NUM
ejpam-5456	2	10	-	-	SYM
ejpam-5456	2	11	3491	3491	NUM
ejpam-5456	2	12	issn	issn	PROPN
ejpam-5456	2	13	1307	1307	NUM
ejpam-5456	2	14	-	-	SYM
ejpam-5456	2	15	5543	5543	NUM
ejpam-5456	2	16	–	–	PUNCT
ejpam-5456	3	1	ejpam.com	ejpam.com	X
ejpam-5456	3	2	published	publish	VERB
ejpam-5456	3	3	by	by	ADP
ejpam-5456	3	4	new	new	PROPN
ejpam-5456	3	5	york	york	PROPN
ejpam-5456	3	6	business	business	PROPN
ejpam-5456	3	7	global	global	ADJ
ejpam-5456	3	8	conformable	conformable	ADJ
ejpam-5456	3	9	sumudu	sumudu	NOUN
ejpam-5456	3	10	transform	transform	NOUN
ejpam-5456	3	11	based	base	VERB
ejpam-5456	3	12	adomian	adomian	NOUN
ejpam-5456	3	13	decomposition	decomposition	NOUN
ejpam-5456	3	14	method	method	NOUN
ejpam-5456	3	15	for	for	ADP
ejpam-5456	3	16	linear	linear	ADJ
ejpam-5456	3	17	and	and	CCONJ
ejpam-5456	3	18	nonlinear	nonlinear	ADJ
ejpam-5456	3	19	fractional	fractional	ADJ
ejpam-5456	3	20	-	-	PUNCT
ejpam-5456	3	21	order	order	NOUN
ejpam-5456	3	22	schrödinger	schrödinger	NOUN
ejpam-5456	3	23	equations	equation	NOUN
ejpam-5456	3	24	muhammad	muhammad	PROPN
ejpam-5456	3	25	imran	imran	PROPN
ejpam-5456	3	26	liaqat1,2,∗	liaqat1,2,∗	PROPN
ejpam-5456	3	27	,	,	PUNCT
ejpam-5456	3	28	hussam	hussam	PROPN
ejpam-5456	3	29	aljarrah3	aljarrah3	PROPN
ejpam-5456	3	30	1	1	NUM
ejpam-5456	3	31	abdus	abdus	NOUN
ejpam-5456	3	32	salam	salam	PROPN
ejpam-5456	3	33	school	school	PROPN
ejpam-5456	3	34	of	of	ADP
ejpam-5456	3	35	mathematical	mathematical	ADJ
ejpam-5456	3	36	sciences	science	NOUN
ejpam-5456	3	37	,	,	PUNCT
ejpam-5456	3	38	government	government	NOUN
ejpam-5456	3	39	college	college	NOUN
ejpam-5456	3	40	university	university	PROPN
ejpam-5456	3	41	,	,	PUNCT
ejpam-5456	3	42	lahore	lahore	PROPN
ejpam-5456	3	43	54600	54600	NUM
ejpam-5456	3	44	,	,	PUNCT
ejpam-5456	3	45	pakistan	pakistan	PROPN
ejpam-5456	3	46	2	2	NUM
ejpam-5456	3	47	national	national	PROPN
ejpam-5456	3	48	college	college	PROPN
ejpam-5456	3	49	of	of	ADP
ejpam-5456	3	50	business	business	PROPN
ejpam-5456	3	51	administration	administration	PROPN
ejpam-5456	3	52	&	&	CCONJ
ejpam-5456	3	53	economics	economic	NOUN
ejpam-5456	3	54	,	,	PUNCT
ejpam-5456	3	55	54000	54000	NUM
ejpam-5456	3	56	lahore	lahore	NOUN
ejpam-5456	3	57	,	,	PUNCT
ejpam-5456	3	58	pakistan	pakistan	PROPN
ejpam-5456	3	59	3	3	NUM
ejpam-5456	3	60	ahmed	ahmed	PROPN
ejpam-5456	3	61	bin	bin	PROPN
ejpam-5456	3	62	mohammed	mohammed	PROPN
ejpam-5456	3	63	military	military	PROPN
ejpam-5456	3	64	college	college	PROPN
ejpam-5456	3	65	,	,	PUNCT
ejpam-5456	3	66	p.o	p.o	PROPN
ejpam-5456	3	67	.	.	PROPN
ejpam-5456	3	68	box	box	PROPN
ejpam-5456	3	69	22988	22988	NUM
ejpam-5456	3	70	,	,	PUNCT
ejpam-5456	3	71	doha	doha	PROPN
ejpam-5456	3	72	,	,	PUNCT
ejpam-5456	3	73	qatar	qatar	PROPN
ejpam-5456	3	74	abstract	abstract	NOUN
ejpam-5456	3	75	.	.	PUNCT
ejpam-5456	4	1	fractional	fractional	ADJ
ejpam-5456	4	2	-	-	PUNCT
ejpam-5456	4	3	order	order	NOUN
ejpam-5456	4	4	schrödinger	schrödinger	NOUN
ejpam-5456	4	5	differential	differential	ADJ
ejpam-5456	4	6	equations	equation	NOUN
ejpam-5456	4	7	extend	extend	VERB
ejpam-5456	4	8	the	the	DET
ejpam-5456	4	9	classical	classical	ADJ
ejpam-5456	4	10	schrödinger	schrödinger	NOUN
ejpam-5456	4	11	equation	equation	NOUN
ejpam-5456	4	12	by	by	ADP
ejpam-5456	4	13	incorporating	incorporate	VERB
ejpam-5456	4	14	fractional	fractional	ADJ
ejpam-5456	4	15	calculus	calculus	NOUN
ejpam-5456	4	16	to	to	PART
ejpam-5456	4	17	describe	describe	VERB
ejpam-5456	4	18	more	more	ADV
ejpam-5456	4	19	complex	complex	ADJ
ejpam-5456	4	20	physical	physical	ADJ
ejpam-5456	4	21	phenomena	phenomenon	NOUN
ejpam-5456	4	22	.	.	PUNCT
ejpam-5456	5	1	in	in	ADP
ejpam-5456	5	2	the	the	DET
ejpam-5456	5	3	literature	literature	NOUN
ejpam-5456	5	4	,	,	PUNCT
ejpam-5456	5	5	the	the	DET
ejpam-5456	5	6	schrödinger	schrödinger	NOUN
ejpam-5456	5	7	equation	equation	NOUN
ejpam-5456	5	8	is	be	AUX
ejpam-5456	5	9	mostly	mostly	ADV
ejpam-5456	5	10	solved	solve	VERB
ejpam-5456	5	11	using	use	VERB
ejpam-5456	5	12	fractional	fractional	ADJ
ejpam-5456	5	13	derivatives	derivative	NOUN
ejpam-5456	5	14	expressed	express	VERB
ejpam-5456	5	15	through	through	ADP
ejpam-5456	5	16	the	the	DET
ejpam-5456	5	17	caputo	caputo	PROPN
ejpam-5456	5	18	derivative	derivative	NOUN
ejpam-5456	5	19	.	.	PUNCT
ejpam-5456	6	1	however	however	ADV
ejpam-5456	6	2	,	,	PUNCT
ejpam-5456	6	3	there	there	PRON
ejpam-5456	6	4	is	be	VERB
ejpam-5456	6	5	limited	limited	ADJ
ejpam-5456	6	6	research	research	NOUN
ejpam-5456	6	7	on	on	ADP
ejpam-5456	6	8	exact	exact	ADJ
ejpam-5456	6	9	and	and	CCONJ
ejpam-5456	6	10	approximate	approximate	ADJ
ejpam-5456	6	11	solutions	solution	NOUN
ejpam-5456	6	12	involving	involve	VERB
ejpam-5456	6	13	conformable	conformable	ADJ
ejpam-5456	6	14	fractional	fractional	ADJ
ejpam-5456	6	15	derivatives	derivative	NOUN
ejpam-5456	6	16	.	.	PUNCT
ejpam-5456	7	1	this	this	DET
ejpam-5456	7	2	study	study	NOUN
ejpam-5456	7	3	aims	aim	VERB
ejpam-5456	7	4	to	to	PART
ejpam-5456	7	5	fill	fill	VERB
ejpam-5456	7	6	this	this	DET
ejpam-5456	7	7	gap	gap	NOUN
ejpam-5456	7	8	by	by	ADP
ejpam-5456	7	9	employing	employ	VERB
ejpam-5456	7	10	a	a	DET
ejpam-5456	7	11	hybrid	hybrid	ADJ
ejpam-5456	7	12	approach	approach	NOUN
ejpam-5456	7	13	that	that	PRON
ejpam-5456	7	14	combines	combine	VERB
ejpam-5456	7	15	the	the	DET
ejpam-5456	7	16	sumudu	sumudu	NOUN
ejpam-5456	7	17	transform	transform	NOUN
ejpam-5456	7	18	with	with	ADP
ejpam-5456	7	19	the	the	DET
ejpam-5456	7	20	decomposition	decomposition	NOUN
ejpam-5456	7	21	technique	technique	NOUN
ejpam-5456	7	22	to	to	PART
ejpam-5456	7	23	solve	solve	VERB
ejpam-5456	7	24	the	the	DET
ejpam-5456	7	25	schrödinger	schrödinger	NOUN
ejpam-5456	7	26	equation	equation	NOUN
ejpam-5456	7	27	with	with	ADP
ejpam-5456	7	28	conformable	conformable	ADJ
ejpam-5456	7	29	fractional	fractional	ADJ
ejpam-5456	7	30	derivatives	derivative	NOUN
ejpam-5456	7	31	,	,	PUNCT
ejpam-5456	7	32	considering	consider	VERB
ejpam-5456	7	33	zero	zero	NUM
ejpam-5456	7	34	and	and	CCONJ
ejpam-5456	7	35	nonzero	nonzero	NOUN
ejpam-5456	7	36	trapping	trap	VERB
ejpam-5456	7	37	potentials	potential	NOUN
ejpam-5456	7	38	.	.	PUNCT
ejpam-5456	8	1	the	the	DET
ejpam-5456	8	2	efficiency	efficiency	NOUN
ejpam-5456	8	3	of	of	ADP
ejpam-5456	8	4	this	this	DET
ejpam-5456	8	5	approach	approach	NOUN
ejpam-5456	8	6	is	be	AUX
ejpam-5456	8	7	evaluated	evaluate	VERB
ejpam-5456	8	8	through	through	ADP
ejpam-5456	8	9	the	the	DET
ejpam-5456	8	10	analysis	analysis	NOUN
ejpam-5456	8	11	of	of	ADP
ejpam-5456	8	12	relative	relative	ADJ
ejpam-5456	8	13	and	and	CCONJ
ejpam-5456	8	14	absolute	absolute	ADJ
ejpam-5456	8	15	errors	error	NOUN
ejpam-5456	8	16	,	,	PUNCT
ejpam-5456	8	17	confirming	confirm	VERB
ejpam-5456	8	18	its	its	PRON
ejpam-5456	8	19	accuracy	accuracy	NOUN
ejpam-5456	8	20	.	.	PUNCT
ejpam-5456	9	1	moreover	moreover	ADV
ejpam-5456	9	2	,	,	PUNCT
ejpam-5456	9	3	the	the	DET
ejpam-5456	9	4	obtained	obtain	VERB
ejpam-5456	9	5	results	result	NOUN
ejpam-5456	9	6	are	be	AUX
ejpam-5456	9	7	compared	compare	VERB
ejpam-5456	9	8	with	with	ADP
ejpam-5456	9	9	other	other	ADJ
ejpam-5456	9	10	techniques	technique	NOUN
ejpam-5456	9	11	,	,	PUNCT
ejpam-5456	9	12	including	include	VERB
ejpam-5456	9	13	the	the	DET
ejpam-5456	9	14	homotopy	homotopy	NOUN
ejpam-5456	9	15	analysis	analysis	NOUN
ejpam-5456	9	16	method	method	NOUN
ejpam-5456	9	17	(	(	PUNCT
ejpam-5456	9	18	ham	ham	NOUN
ejpam-5456	9	19	)	)	PUNCT
ejpam-5456	9	20	and	and	CCONJ
ejpam-5456	9	21	the	the	DET
ejpam-5456	9	22	residual	residual	ADJ
ejpam-5456	9	23	power	power	NOUN
ejpam-5456	9	24	series	series	NOUN
ejpam-5456	9	25	method	method	NOUN
ejpam-5456	9	26	(	(	PUNCT
ejpam-5456	9	27	rpsm	rpsm	PROPN
ejpam-5456	9	28	)	)	PUNCT
ejpam-5456	9	29	.	.	PUNCT
ejpam-5456	10	1	the	the	DET
ejpam-5456	10	2	comparison	comparison	NOUN
ejpam-5456	10	3	demonstrates	demonstrate	VERB
ejpam-5456	10	4	strong	strong	ADJ
ejpam-5456	10	5	consistency	consistency	NOUN
ejpam-5456	10	6	with	with	ADP
ejpam-5456	10	7	these	these	DET
ejpam-5456	10	8	methods	method	NOUN
ejpam-5456	10	9	,	,	PUNCT
ejpam-5456	10	10	suggesting	suggest	VERB
ejpam-5456	10	11	that	that	SCONJ
ejpam-5456	10	12	our	our	PRON
ejpam-5456	10	13	approach	approach	NOUN
ejpam-5456	10	14	is	be	AUX
ejpam-5456	10	15	a	a	DET
ejpam-5456	10	16	viable	viable	ADJ
ejpam-5456	10	17	alternative	alternative	NOUN
ejpam-5456	10	18	to	to	ADP
ejpam-5456	10	19	caputo	caputo	PROPN
ejpam-5456	10	20	derivative	derivative	PROPN
ejpam-5456	10	21	-	-	PUNCT
ejpam-5456	10	22	based	base	VERB
ejpam-5456	10	23	methods	method	NOUN
ejpam-5456	10	24	for	for	ADP
ejpam-5456	10	25	solving	solve	VERB
ejpam-5456	10	26	time	time	NOUN
ejpam-5456	10	27	-	-	PUNCT
ejpam-5456	10	28	fractional	fractional	ADJ
ejpam-5456	10	29	schrödinger	schrödinger	NOUN
ejpam-5456	10	30	equations	equation	NOUN
ejpam-5456	10	31	.	.	PUNCT
ejpam-5456	11	1	furthermore	furthermore	ADV
ejpam-5456	11	2	,	,	PUNCT
ejpam-5456	11	3	we	we	PRON
ejpam-5456	11	4	can	can	AUX
ejpam-5456	11	5	conclude	conclude	VERB
ejpam-5456	11	6	that	that	SCONJ
ejpam-5456	11	7	the	the	DET
ejpam-5456	11	8	conformable	conformable	ADJ
ejpam-5456	11	9	fractional	fractional	ADJ
ejpam-5456	11	10	derivative	derivative	NOUN
ejpam-5456	11	11	serves	serve	NOUN
ejpam-5456	11	12	as	as	ADP
ejpam-5456	11	13	a	a	DET
ejpam-5456	11	14	suitable	suitable	ADJ
ejpam-5456	11	15	substitute	substitute	NOUN
ejpam-5456	11	16	for	for	ADP
ejpam-5456	11	17	the	the	DET
ejpam-5456	11	18	caputo	caputo	PROPN
ejpam-5456	11	19	derivative	derivative	NOUN
ejpam-5456	11	20	in	in	ADP
ejpam-5456	11	21	modeling	modeling	NOUN
ejpam-5456	11	22	schrödinger	schrödinger	NOUN
ejpam-5456	11	23	equations	equation	NOUN
ejpam-5456	11	24	.	.	PUNCT
ejpam-5456	12	1	2020	2020	NUM
ejpam-5456	12	2	mathematics	mathematic	NOUN
ejpam-5456	12	3	subject	subject	NOUN
ejpam-5456	12	4	classifications	classification	NOUN
ejpam-5456	12	5	:	:	PUNCT
ejpam-5456	12	6	74s40	74s40	NUM
ejpam-5456	12	7	,	,	PUNCT
ejpam-5456	12	8	65d15	65d15	NUM
ejpam-5456	12	9	key	key	ADJ
ejpam-5456	12	10	words	word	NOUN
ejpam-5456	12	11	and	and	CCONJ
ejpam-5456	12	12	phrases	phrase	NOUN
ejpam-5456	12	13	:	:	PUNCT
ejpam-5456	12	14	fractional	fractional	ADJ
ejpam-5456	12	15	calculus	calculus	NOUN
ejpam-5456	12	16	,	,	PUNCT
ejpam-5456	12	17	approximate	approximate	ADJ
ejpam-5456	12	18	solutions	solution	NOUN
ejpam-5456	12	19	,	,	PUNCT
ejpam-5456	12	20	exact	exact	ADJ
ejpam-5456	12	21	solutions	solution	NOUN
ejpam-5456	12	22	,	,	PUNCT
ejpam-5456	12	23	conformable	conformable	ADJ
ejpam-5456	12	24	fractional	fractional	ADJ
ejpam-5456	12	25	derivatives	derivative	NOUN
ejpam-5456	12	26	1	1	NUM
ejpam-5456	12	27	.	.	PUNCT
ejpam-5456	13	1	introduction	introduction	NOUN
ejpam-5456	13	2	fractional	fractional	ADJ
ejpam-5456	13	3	derivatives	derivative	NOUN
ejpam-5456	13	4	form	form	VERB
ejpam-5456	13	5	the	the	DET
ejpam-5456	13	6	foundation	foundation	NOUN
ejpam-5456	13	7	of	of	ADP
ejpam-5456	13	8	fractional	fractional	ADJ
ejpam-5456	13	9	calculus	calculus	NOUN
ejpam-5456	13	10	(	(	PUNCT
ejpam-5456	13	11	fc	fc	PROPN
ejpam-5456	13	12	)	)	PUNCT
ejpam-5456	13	13	,	,	PUNCT
ejpam-5456	13	14	providing	provide	VERB
ejpam-5456	13	15	an	an	DET
ejpam-5456	13	16	effective	effective	ADJ
ejpam-5456	13	17	means	mean	NOUN
ejpam-5456	13	18	to	to	PART
ejpam-5456	13	19	describe	describe	VERB
ejpam-5456	13	20	and	and	CCONJ
ejpam-5456	13	21	analyze	analyze	VERB
ejpam-5456	13	22	systems	system	NOUN
ejpam-5456	13	23	with	with	ADP
ejpam-5456	13	24	non	non	ADJ
ejpam-5456	13	25	-	-	ADJ
ejpam-5456	13	26	local	local	ADJ
ejpam-5456	13	27	or	or	CCONJ
ejpam-5456	13	28	memory	memory	NOUN
ejpam-5456	13	29	-	-	PUNCT
ejpam-5456	13	30	driven	drive	VERB
ejpam-5456	13	31	behaviors	behavior	NOUN
ejpam-5456	13	32	.	.	PUNCT
ejpam-5456	14	1	in	in	ADP
ejpam-5456	14	2	contrast	contrast	NOUN
ejpam-5456	14	3	to	to	ADP
ejpam-5456	14	4	integer	integer	NOUN
ejpam-5456	14	5	-	-	PUNCT
ejpam-5456	14	6	order	order	NOUN
ejpam-5456	14	7	derivatives	derivative	NOUN
ejpam-5456	14	8	,	,	PUNCT
ejpam-5456	14	9	which	which	PRON
ejpam-5456	14	10	focus	focus	VERB
ejpam-5456	14	11	solely	solely	ADV
ejpam-5456	14	12	on	on	ADP
ejpam-5456	14	13	the	the	DET
ejpam-5456	14	14	instantaneous	instantaneous	ADJ
ejpam-5456	14	15	rate	rate	NOUN
ejpam-5456	14	16	∗corresponding	∗corresponde	VERB
ejpam-5456	14	17	author	author	NOUN
ejpam-5456	14	18	.	.	PUNCT
ejpam-5456	15	1	doi	doi	NOUN
ejpam-5456	15	2	:	:	PUNCT
ejpam-5456	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5456	https://doi.org/10.29020/nybg.ejpam.v17i4.5456	PROPN
ejpam-5456	15	4	email	email	NOUN
ejpam-5456	15	5	addresses	address	VERB
ejpam-5456	15	6	:	:	PUNCT
ejpam-5456	15	7	imran	imran	PROPN
ejpam-5456	15	8	liaqat	liaqat	PROPN
ejpam-5456	15	9	22@sms.edu.pk	22@sms.edu.pk	PROPN
ejpam-5456	15	10	(	(	PUNCT
ejpam-5456	15	11	m.	m.	NOUN
ejpam-5456	15	12	i.	i.	PROPN
ejpam-5456	15	13	liaqat	liaqat	PROPN
ejpam-5456	15	14	)	)	PUNCT
ejpam-5456	15	15	,	,	PUNCT
ejpam-5456	15	16	hussam	hussam	PROPN
ejpam-5456	15	17	aljarrah@abmmc.edu.qa	aljarrah@abmmc.edu.qa	PROPN
ejpam-5456	15	18	(	(	PUNCT
ejpam-5456	15	19	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	15	20	)	)	PUNCT
ejpam-5456	15	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5456	15	22	3464	3464	NUM
ejpam-5456	15	23	copyright	copyright	NOUN
ejpam-5456	15	24	:	:	PUNCT
ejpam-5456	15	25	©	©	PROPN
ejpam-5456	15	26	2024	2024	NUM
ejpam-5456	15	27	the	the	DET
ejpam-5456	15	28	author(s	author(s	NOUN
ejpam-5456	15	29	)	)	PUNCT
ejpam-5456	15	30	.	.	PUNCT
ejpam-5456	16	1	(	(	PUNCT
ejpam-5456	16	2	cc	cc	NOUN
ejpam-5456	16	3	by	by	ADP
ejpam-5456	16	4	-	-	PUNCT
ejpam-5456	16	5	nc	nc	PROPN
ejpam-5456	16	6	4.0	4.0	NUM
ejpam-5456	16	7	)	)	PUNCT
ejpam-5456	16	8	m.i	m.i	PROPN
ejpam-5456	16	9	.	.	PROPN
ejpam-5456	16	10	liaqat	liaqat	PROPN
ejpam-5456	16	11	,	,	PUNCT
ejpam-5456	16	12	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	16	13	/	/	SYM
ejpam-5456	16	14	eur	eur	PROPN
ejpam-5456	16	15	.	.	PUNCT
ejpam-5456	17	1	j.	j.	PROPN
ejpam-5456	17	2	pure	pure	PROPN
ejpam-5456	17	3	appl	appl	PROPN
ejpam-5456	17	4	.	.	PROPN
ejpam-5456	17	5	math	math	PROPN
ejpam-5456	17	6	,	,	PUNCT
ejpam-5456	17	7	17	17	NUM
ejpam-5456	17	8	(	(	PUNCT
ejpam-5456	17	9	4	4	NUM
ejpam-5456	17	10	)	)	PUNCT
ejpam-5456	17	11	(	(	PUNCT
ejpam-5456	17	12	2024	2024	NUM
ejpam-5456	17	13	)	)	PUNCT
ejpam-5456	17	14	,	,	PUNCT
ejpam-5456	17	15	3464	3464	NUM
ejpam-5456	17	16	-	-	SYM
ejpam-5456	17	17	3491	3491	NUM
ejpam-5456	17	18	3465	3465	NUM
ejpam-5456	17	19	of	of	ADP
ejpam-5456	17	20	change	change	NOUN
ejpam-5456	17	21	at	at	ADP
ejpam-5456	17	22	a	a	DET
ejpam-5456	17	23	single	single	ADJ
ejpam-5456	17	24	point	point	NOUN
ejpam-5456	17	25	,	,	PUNCT
ejpam-5456	17	26	fractional	fractional	ADJ
ejpam-5456	17	27	derivatives	derivative	NOUN
ejpam-5456	17	28	account	account	VERB
ejpam-5456	17	29	for	for	ADP
ejpam-5456	17	30	the	the	DET
ejpam-5456	17	31	function	function	NOUN
ejpam-5456	17	32	’s	’s	PART
ejpam-5456	17	33	behavior	behavior	NOUN
ejpam-5456	17	34	over	over	ADP
ejpam-5456	17	35	an	an	DET
ejpam-5456	17	36	interval	interval	NOUN
ejpam-5456	17	37	,	,	PUNCT
ejpam-5456	17	38	thereby	thereby	ADV
ejpam-5456	17	39	incorporating	incorporate	VERB
ejpam-5456	17	40	memory	memory	NOUN
ejpam-5456	17	41	into	into	ADP
ejpam-5456	17	42	the	the	DET
ejpam-5456	17	43	system	system	NOUN
ejpam-5456	17	44	’s	’s	PART
ejpam-5456	17	45	dynamics	dynamic	NOUN
ejpam-5456	17	46	.	.	PUNCT
ejpam-5456	18	1	there	there	PRON
ejpam-5456	18	2	are	be	VERB
ejpam-5456	18	3	several	several	ADJ
ejpam-5456	18	4	forms	form	NOUN
ejpam-5456	18	5	of	of	ADP
ejpam-5456	18	6	fractional	fractional	ADJ
ejpam-5456	18	7	-	-	PUNCT
ejpam-5456	18	8	order	order	NOUN
ejpam-5456	18	9	derivatives	derivative	NOUN
ejpam-5456	18	10	,	,	PUNCT
ejpam-5456	18	11	each	each	PRON
ejpam-5456	18	12	defined	define	VERB
ejpam-5456	18	13	and	and	CCONJ
ejpam-5456	18	14	characterized	characterize	VERB
ejpam-5456	18	15	in	in	ADP
ejpam-5456	18	16	its	its	PRON
ejpam-5456	18	17	own	own	ADJ
ejpam-5456	18	18	way	way	NOUN
ejpam-5456	18	19	.	.	PUNCT
ejpam-5456	19	1	some	some	PRON
ejpam-5456	19	2	of	of	ADP
ejpam-5456	19	3	the	the	DET
ejpam-5456	19	4	commonly	commonly	ADV
ejpam-5456	19	5	used	use	VERB
ejpam-5456	19	6	types	type	NOUN
ejpam-5456	19	7	include	include	VERB
ejpam-5456	19	8	the	the	DET
ejpam-5456	19	9	riemann	riemann	PROPN
ejpam-5456	19	10	–	–	PUNCT
ejpam-5456	19	11	liouville	liouville	PROPN
ejpam-5456	19	12	,	,	PUNCT
ejpam-5456	19	13	caputo	caputo	PROPN
ejpam-5456	19	14	,	,	PUNCT
ejpam-5456	19	15	grünwald	grünwald	ADJ
ejpam-5456	19	16	–	–	PUNCT
ejpam-5456	19	17	letnikov	letnikov	ADJ
ejpam-5456	19	18	,	,	PUNCT
ejpam-5456	19	19	caputo	caputo	PROPN
ejpam-5456	19	20	-	-	PUNCT
ejpam-5456	19	21	fabrizio	fabrizio	PROPN
ejpam-5456	19	22	,	,	PUNCT
ejpam-5456	19	23	and	and	CCONJ
ejpam-5456	19	24	conformable	conformable	ADJ
ejpam-5456	19	25	fractional	fractional	ADJ
ejpam-5456	19	26	operators	operator	NOUN
ejpam-5456	19	27	[	[	X
ejpam-5456	19	28	1	1	NUM
ejpam-5456	19	29	,	,	PUNCT
ejpam-5456	19	30	4	4	NUM
ejpam-5456	19	31	,	,	PUNCT
ejpam-5456	19	32	16	16	NUM
ejpam-5456	19	33	,	,	PUNCT
ejpam-5456	19	34	19	19	NUM
ejpam-5456	19	35	,	,	PUNCT
ejpam-5456	19	36	32	32	NUM
ejpam-5456	19	37	,	,	PUNCT
ejpam-5456	19	38	34	34	NUM
ejpam-5456	19	39	]	]	PUNCT
ejpam-5456	19	40	.	.	PUNCT
ejpam-5456	20	1	the	the	DET
ejpam-5456	20	2	choice	choice	NOUN
ejpam-5456	20	3	of	of	ADP
ejpam-5456	20	4	which	which	DET
ejpam-5456	20	5	definition	definition	NOUN
ejpam-5456	20	6	to	to	ADP
ejpam-5456	20	7	use	use	NOUN
ejpam-5456	20	8	depends	depend	VERB
ejpam-5456	20	9	on	on	ADP
ejpam-5456	20	10	the	the	DET
ejpam-5456	20	11	specific	specific	ADJ
ejpam-5456	20	12	problem	problem	NOUN
ejpam-5456	20	13	at	at	ADP
ejpam-5456	20	14	hand	hand	NOUN
ejpam-5456	20	15	and	and	CCONJ
ejpam-5456	20	16	the	the	DET
ejpam-5456	20	17	desired	desire	VERB
ejpam-5456	20	18	mathematical	mathematical	ADJ
ejpam-5456	20	19	properties	property	NOUN
ejpam-5456	20	20	of	of	ADP
ejpam-5456	20	21	the	the	DET
ejpam-5456	20	22	derivative	derivative	NOUN
ejpam-5456	20	23	.	.	PUNCT
ejpam-5456	21	1	recently	recently	ADV
ejpam-5456	21	2	,	,	PUNCT
ejpam-5456	21	3	a	a	DET
ejpam-5456	21	4	large	large	ADJ
ejpam-5456	21	5	number	number	NOUN
ejpam-5456	21	6	of	of	ADP
ejpam-5456	21	7	scholars	scholar	NOUN
ejpam-5456	21	8	have	have	AUX
ejpam-5456	21	9	been	be	AUX
ejpam-5456	21	10	actively	actively	ADV
ejpam-5456	21	11	investigating	investigate	VERB
ejpam-5456	21	12	different	different	ADJ
ejpam-5456	21	13	kinds	kind	NOUN
ejpam-5456	21	14	of	of	ADP
ejpam-5456	21	15	fractional	fractional	ADJ
ejpam-5456	21	16	-	-	PUNCT
ejpam-5456	21	17	order	order	NOUN
ejpam-5456	21	18	derivatives	derivative	NOUN
ejpam-5456	21	19	.	.	PUNCT
ejpam-5456	22	1	in	in	ADP
ejpam-5456	22	2	the	the	DET
ejpam-5456	22	3	context	context	NOUN
ejpam-5456	22	4	of	of	ADP
ejpam-5456	22	5	caputo	caputo	PROPN
ejpam-5456	22	6	-	-	PUNCT
ejpam-5456	22	7	fabrizio	fabrizio	PROPN
ejpam-5456	22	8	,	,	PUNCT
ejpam-5456	22	9	for	for	ADP
ejpam-5456	22	10	instance	instance	NOUN
ejpam-5456	22	11	,	,	PUNCT
ejpam-5456	22	12	the	the	DET
ejpam-5456	22	13	authors	author	NOUN
ejpam-5456	22	14	[	[	X
ejpam-5456	22	15	30	30	NUM
ejpam-5456	22	16	,	,	PUNCT
ejpam-5456	22	17	31	31	NUM
ejpam-5456	22	18	]	]	PUNCT
ejpam-5456	22	19	established	establish	VERB
ejpam-5456	22	20	highly	highly	ADV
ejpam-5456	22	21	significant	significant	ADJ
ejpam-5456	22	22	results	result	NOUN
ejpam-5456	22	23	.	.	PUNCT
ejpam-5456	23	1	conformable	conformable	ADJ
ejpam-5456	23	2	fractional	fractional	ADJ
ejpam-5456	23	3	operators	operator	NOUN
ejpam-5456	23	4	are	be	AUX
ejpam-5456	23	5	a	a	DET
ejpam-5456	23	6	novel	novel	ADJ
ejpam-5456	23	7	method	method	NOUN
ejpam-5456	23	8	for	for	ADP
ejpam-5456	23	9	solving	solve	VERB
ejpam-5456	23	10	fractional	fractional	ADJ
ejpam-5456	23	11	-	-	PUNCT
ejpam-5456	23	12	order	order	NOUN
ejpam-5456	23	13	differential	differential	ADJ
ejpam-5456	23	14	equations	equation	NOUN
ejpam-5456	23	15	(	(	PUNCT
ejpam-5456	23	16	fodes	fode	NOUN
ejpam-5456	23	17	)	)	PUNCT
ejpam-5456	23	18	that	that	PRON
ejpam-5456	23	19	was	be	AUX
ejpam-5456	23	20	presented	present	VERB
ejpam-5456	23	21	by	by	ADP
ejpam-5456	23	22	the	the	DET
ejpam-5456	23	23	authors	author	NOUN
ejpam-5456	23	24	[	[	X
ejpam-5456	23	25	17	17	NUM
ejpam-5456	23	26	]	]	PUNCT
ejpam-5456	23	27	.	.	PUNCT
ejpam-5456	24	1	zhang	zhang	PROPN
ejpam-5456	24	2	et	et	PROPN
ejpam-5456	24	3	al	al	PROPN
ejpam-5456	24	4	.	.	PUNCT
ejpam-5456	25	1	[	[	X
ejpam-5456	25	2	33	33	NUM
ejpam-5456	25	3	]	]	PUNCT
ejpam-5456	25	4	developed	develop	VERB
ejpam-5456	25	5	solutions	solution	NOUN
ejpam-5456	25	6	to	to	PART
ejpam-5456	25	7	differential	differential	VERB
ejpam-5456	25	8	equations	equation	NOUN
ejpam-5456	25	9	(	(	PUNCT
ejpam-5456	25	10	des	des	PROPN
ejpam-5456	25	11	)	)	PUNCT
ejpam-5456	25	12	within	within	ADP
ejpam-5456	25	13	the	the	DET
ejpam-5456	25	14	framework	framework	NOUN
ejpam-5456	25	15	of	of	ADP
ejpam-5456	25	16	caputo	caputo	PROPN
ejpam-5456	25	17	fractional	fractional	PROPN
ejpam-5456	25	18	derivatives	derivative	NOUN
ejpam-5456	25	19	(	(	PUNCT
ejpam-5456	25	20	cap	cap	NOUN
ejpam-5456	25	21	-	-	PUNCT
ejpam-5456	25	22	fd	fd	NOUN
ejpam-5456	25	23	)	)	PUNCT
ejpam-5456	25	24	.	.	PUNCT
ejpam-5456	26	1	using	use	VERB
ejpam-5456	26	2	the	the	DET
ejpam-5456	26	3	framework	framework	NOUN
ejpam-5456	26	4	of	of	ADP
ejpam-5456	26	5	the	the	DET
ejpam-5456	26	6	caputo	caputo	PROPN
ejpam-5456	26	7	derivative	derivative	PROPN
ejpam-5456	26	8	,	,	PUNCT
ejpam-5456	26	9	zhang	zhang	PROPN
ejpam-5456	26	10	and	and	CCONJ
ejpam-5456	26	11	xiong	xiong	PROPN
ejpam-5456	27	1	[	[	X
ejpam-5456	27	2	35	35	NUM
ejpam-5456	27	3	]	]	PUNCT
ejpam-5456	27	4	showed	show	VERB
ejpam-5456	27	5	that	that	SCONJ
ejpam-5456	27	6	the	the	DET
ejpam-5456	27	7	periodic	periodic	ADJ
ejpam-5456	27	8	solution	solution	NOUN
ejpam-5456	27	9	of	of	ADP
ejpam-5456	27	10	fodes	fode	NOUN
ejpam-5456	27	11	with	with	ADP
ejpam-5456	27	12	semilinear	semilinear	ADJ
ejpam-5456	27	13	impulses	impulse	NOUN
ejpam-5456	27	14	has	have	VERB
ejpam-5456	27	15	unique	unique	ADJ
ejpam-5456	27	16	solutions	solution	NOUN
ejpam-5456	27	17	and	and	CCONJ
ejpam-5456	27	18	global	global	ADJ
ejpam-5456	27	19	exponential	exponential	ADJ
ejpam-5456	27	20	stability	stability	NOUN
ejpam-5456	27	21	.	.	PUNCT
ejpam-5456	28	1	atanganabaleanu	atanganabaleanu	PROPN
ejpam-5456	28	2	derivatives	derivative	NOUN
ejpam-5456	28	3	are	be	AUX
ejpam-5456	28	4	used	use	VERB
ejpam-5456	28	5	by	by	ADP
ejpam-5456	28	6	syam	syam	NOUN
ejpam-5456	28	7	and	and	CCONJ
ejpam-5456	28	8	al	al	PROPN
ejpam-5456	28	9	-	-	PUNCT
ejpam-5456	28	10	refai	refai	PRON
ejpam-5456	29	1	[	[	X
ejpam-5456	29	2	24	24	NUM
ejpam-5456	29	3	]	]	PUNCT
ejpam-5456	29	4	to	to	PART
ejpam-5456	29	5	obtain	obtain	VERB
ejpam-5456	29	6	numerous	numerous	ADJ
ejpam-5456	29	7	valuable	valuable	ADJ
ejpam-5456	29	8	results	result	NOUN
ejpam-5456	29	9	about	about	ADP
ejpam-5456	29	10	solutions	solution	NOUN
ejpam-5456	29	11	to	to	ADP
ejpam-5456	29	12	fodes	fode	NOUN
ejpam-5456	29	13	.	.	PUNCT
ejpam-5456	30	1	using	use	VERB
ejpam-5456	30	2	grünwald	grünwald	ADJ
ejpam-5456	30	3	-	-	ADJ
ejpam-5456	30	4	letnikov	letnikov	ADJ
ejpam-5456	30	5	fractional	fractional	ADJ
ejpam-5456	30	6	derivatives	derivative	NOUN
ejpam-5456	30	7	,	,	PUNCT
ejpam-5456	30	8	li	li	PROPN
ejpam-5456	30	9	and	and	CCONJ
ejpam-5456	30	10	wang	wang	PROPN
ejpam-5456	31	1	[	[	X
ejpam-5456	31	2	27	27	NUM
ejpam-5456	31	3	]	]	PUNCT
ejpam-5456	31	4	discovered	discover	VERB
ejpam-5456	31	5	solutions	solution	NOUN
ejpam-5456	31	6	to	to	ADP
ejpam-5456	31	7	fractional	fractional	ADJ
ejpam-5456	31	8	rössler	rössler	NOUN
ejpam-5456	31	9	chaotic	chaotic	ADJ
ejpam-5456	31	10	systems	system	NOUN
ejpam-5456	31	11	.	.	PUNCT
ejpam-5456	32	1	for	for	ADP
ejpam-5456	32	2	more	more	ADJ
ejpam-5456	32	3	study	study	NOUN
ejpam-5456	32	4	,	,	PUNCT
ejpam-5456	32	5	refer	refer	VERB
ejpam-5456	32	6	to	to	ADP
ejpam-5456	32	7	[	[	X
ejpam-5456	32	8	6	6	NUM
ejpam-5456	32	9	,	,	PUNCT
ejpam-5456	32	10	9	9	NUM
ejpam-5456	32	11	,	,	PUNCT
ejpam-5456	32	12	20	20	NUM
ejpam-5456	32	13	,	,	PUNCT
ejpam-5456	32	14	21	21	NUM
ejpam-5456	32	15	]	]	PUNCT
ejpam-5456	32	16	.	.	PUNCT
ejpam-5456	33	1	conformable	conformable	ADJ
ejpam-5456	33	2	fractional	fractional	ADJ
ejpam-5456	33	3	derivatives	derivative	NOUN
ejpam-5456	33	4	(	(	PUNCT
ejpam-5456	33	5	con	con	NOUN
ejpam-5456	33	6	-	-	PUNCT
ejpam-5456	33	7	frd	frd	ADJ
ejpam-5456	33	8	)	)	PUNCT
ejpam-5456	33	9	provide	provide	VERB
ejpam-5456	33	10	a	a	DET
ejpam-5456	33	11	useful	useful	ADJ
ejpam-5456	33	12	and	and	CCONJ
ejpam-5456	33	13	intuitive	intuitive	ADJ
ejpam-5456	33	14	way	way	NOUN
ejpam-5456	33	15	to	to	PART
ejpam-5456	33	16	incorporate	incorporate	VERB
ejpam-5456	33	17	memory	memory	NOUN
ejpam-5456	33	18	effects	effect	NOUN
ejpam-5456	33	19	into	into	ADP
ejpam-5456	33	20	differential	differential	ADJ
ejpam-5456	33	21	equations	equation	NOUN
ejpam-5456	33	22	(	(	PUNCT
ejpam-5456	33	23	des	des	PROPN
ejpam-5456	33	24	)	)	PUNCT
ejpam-5456	33	25	.	.	PUNCT
ejpam-5456	34	1	con	con	ADJ
ejpam-5456	34	2	-	-	PUNCT
ejpam-5456	34	3	frd	frd	NOUN
ejpam-5456	34	4	retains	retain	VERB
ejpam-5456	34	5	many	many	ADJ
ejpam-5456	34	6	properties	property	NOUN
ejpam-5456	34	7	of	of	ADP
ejpam-5456	34	8	classical	classical	ADJ
ejpam-5456	34	9	derivatives	derivative	NOUN
ejpam-5456	34	10	,	,	PUNCT
ejpam-5456	34	11	making	make	VERB
ejpam-5456	34	12	it	it	PRON
ejpam-5456	34	13	easier	easy	ADJ
ejpam-5456	34	14	to	to	PART
ejpam-5456	34	15	work	work	VERB
ejpam-5456	34	16	with	with	ADP
ejpam-5456	34	17	while	while	SCONJ
ejpam-5456	34	18	offering	offer	VERB
ejpam-5456	34	19	the	the	DET
ejpam-5456	34	20	flexibility	flexibility	NOUN
ejpam-5456	34	21	of	of	ADP
ejpam-5456	34	22	fc	fc	PROPN
ejpam-5456	34	23	.	.	PUNCT
ejpam-5456	35	1	for	for	ADP
ejpam-5456	35	2	this	this	DET
ejpam-5456	35	3	reason	reason	NOUN
ejpam-5456	35	4	,	,	PUNCT
ejpam-5456	35	5	con	con	NOUN
ejpam-5456	35	6	-	-	PUNCT
ejpam-5456	35	7	frd	frd	ADJ
ejpam-5456	35	8	is	be	AUX
ejpam-5456	35	9	very	very	ADV
ejpam-5456	35	10	useful	useful	ADJ
ejpam-5456	35	11	for	for	ADP
ejpam-5456	35	12	simulating	simulate	VERB
ejpam-5456	35	13	real	real	ADJ
ejpam-5456	35	14	-	-	PUNCT
ejpam-5456	35	15	world	world	NOUN
ejpam-5456	35	16	phenomena	phenomenon	NOUN
ejpam-5456	35	17	in	in	ADP
ejpam-5456	35	18	physics	physics	PROPN
ejpam-5456	35	19	,	,	PUNCT
ejpam-5456	35	20	engineering	engineering	NOUN
ejpam-5456	35	21	,	,	PUNCT
ejpam-5456	35	22	control	control	NOUN
ejpam-5456	35	23	systems	system	NOUN
ejpam-5456	35	24	,	,	PUNCT
ejpam-5456	35	25	biology	biology	NOUN
ejpam-5456	35	26	,	,	PUNCT
ejpam-5456	35	27	and	and	CCONJ
ejpam-5456	35	28	other	other	ADJ
ejpam-5456	35	29	fields	field	NOUN
ejpam-5456	35	30	.	.	PUNCT
ejpam-5456	36	1	the	the	DET
ejpam-5456	36	2	con	con	NOUN
ejpam-5456	36	3	-	-	PUNCT
ejpam-5456	36	4	frd	frd	NOUN
ejpam-5456	36	5	of	of	ADP
ejpam-5456	36	6	a	a	DET
ejpam-5456	36	7	function	function	NOUN
ejpam-5456	36	8	δ(φ	δ(φ	NOUN
ejpam-5456	36	9	)	)	PUNCT
ejpam-5456	36	10	of	of	ADP
ejpam-5456	36	11	order	order	NOUN
ejpam-5456	36	12	µ	µ	NOUN
ejpam-5456	36	13	is	be	AUX
ejpam-5456	36	14	defined	define	VERB
ejpam-5456	36	15	as	as	ADP
ejpam-5456	36	16	[	[	X
ejpam-5456	36	17	12	12	NUM
ejpam-5456	36	18	]	]	X
ejpam-5456	36	19	:	:	PUNCT
ejpam-5456	36	20	tµ	tµ	NOUN
ejpam-5456	36	21	φδ(φ	φδ(φ	NUM
ejpam-5456	36	22	)	)	PUNCT
ejpam-5456	37	1	=	=	SYM
ejpam-5456	37	2	lim	lim	PROPN
ejpam-5456	37	3	ϵ→0	ϵ→0	X
ejpam-5456	37	4	δ⌈µ⌉−1(φ+	δ⌈µ⌉−1(φ+	NOUN
ejpam-5456	37	5	ϵφ⌈µ⌉−µ)−	ϵφ⌈µ⌉−µ)−	NUM
ejpam-5456	37	6	δ⌈µ⌉−1(φ	δ⌈µ⌉−1(φ	NOUN
ejpam-5456	37	7	)	)	PUNCT
ejpam-5456	37	8	ϵ	ϵ	NOUN
ejpam-5456	37	9	,	,	PUNCT
ejpam-5456	37	10	(	(	PUNCT
ejpam-5456	37	11	1	1	X
ejpam-5456	37	12	)	)	PUNCT
ejpam-5456	38	1	where	where	SCONJ
ejpam-5456	38	2	the	the	DET
ejpam-5456	38	3	con	con	NOUN
ejpam-5456	38	4	-	-	PUNCT
ejpam-5456	38	5	frd	frd	NOUN
ejpam-5456	38	6	with	with	ADP
ejpam-5456	38	7	regard	regard	NOUN
ejpam-5456	38	8	to	to	ADP
ejpam-5456	38	9	time	time	NOUN
ejpam-5456	38	10	is	be	AUX
ejpam-5456	38	11	denoted	denote	VERB
ejpam-5456	38	12	by	by	ADP
ejpam-5456	38	13	tµ	tµ	PRON
ejpam-5456	38	14	φ	φ	NUM
ejpam-5456	38	15	,	,	PUNCT
ejpam-5456	38	16	and	and	CCONJ
ejpam-5456	38	17	the	the	DET
ejpam-5456	38	18	smallest	small	ADJ
ejpam-5456	38	19	integer	integer	NOUN
ejpam-5456	38	20	that	that	PRON
ejpam-5456	38	21	is	be	AUX
ejpam-5456	38	22	equal	equal	ADJ
ejpam-5456	38	23	to	to	ADP
ejpam-5456	38	24	or	or	CCONJ
ejpam-5456	38	25	greater	great	ADJ
ejpam-5456	38	26	than	than	ADP
ejpam-5456	38	27	µ	µ	NOUN
ejpam-5456	38	28	is	be	AUX
ejpam-5456	38	29	⌈µ⌉	⌈µ⌉	NOUN
ejpam-5456	38	30	,	,	PUNCT
ejpam-5456	38	31	κ	κ	PROPN
ejpam-5456	38	32	∈	∈	PROPN
ejpam-5456	38	33	n	n	CCONJ
ejpam-5456	38	34	,	,	PUNCT
ejpam-5456	38	35	and	and	CCONJ
ejpam-5456	38	36	κ	κ	X
ejpam-5456	38	37	−	−	PROPN
ejpam-5456	38	38	1	1	NUM
ejpam-5456	38	39	<	<	X
ejpam-5456	38	40	µ	µ	X
ejpam-5456	38	41	≤	≤	NUM
ejpam-5456	38	42	κ	κ	PROPN
ejpam-5456	38	43	,	,	PUNCT
ejpam-5456	38	44	φ	φ	X
ejpam-5456	38	45	>	>	X
ejpam-5456	38	46	0	0	PROPN
ejpam-5456	38	47	.	.	PUNCT
ejpam-5456	39	1	in	in	ADP
ejpam-5456	39	2	the	the	DET
ejpam-5456	39	3	specific	specific	ADJ
ejpam-5456	39	4	case	case	NOUN
ejpam-5456	39	5	where	where	SCONJ
ejpam-5456	39	6	0	0	NUM
ejpam-5456	39	7	<	<	X
ejpam-5456	39	8	µ	µ	X
ejpam-5456	39	9	≤	≤	NUM
ejpam-5456	39	10	1	1	NUM
ejpam-5456	39	11	,	,	PUNCT
ejpam-5456	39	12	we	we	PRON
ejpam-5456	39	13	obtain	obtain	VERB
ejpam-5456	39	14	the	the	DET
ejpam-5456	39	15	following	following	NOUN
ejpam-5456	39	16	[	[	X
ejpam-5456	39	17	18	18	NUM
ejpam-5456	39	18	]	]	X
ejpam-5456	39	19	:	:	PUNCT
ejpam-5456	39	20	tµ	tµ	NOUN
ejpam-5456	39	21	φδ(φ	φδ(φ	NUM
ejpam-5456	39	22	)	)	PUNCT
ejpam-5456	39	23	=	=	SYM
ejpam-5456	39	24	lim	lim	PROPN
ejpam-5456	39	25	ϵ→0	ϵ→0	PROPN
ejpam-5456	39	26	δ(φ+	δ(φ+	PROPN
ejpam-5456	39	27	ϵφ1−µ)−	ϵφ1−µ)−	NOUN
ejpam-5456	39	28	δ(φ	δ(φ	NOUN
ejpam-5456	39	29	)	)	PUNCT
ejpam-5456	39	30	ϵ	ϵ	X
ejpam-5456	39	31	,	,	PUNCT
ejpam-5456	39	32	φ	φ	PROPN
ejpam-5456	39	33	>	>	X
ejpam-5456	39	34	0	0	PROPN
ejpam-5456	39	35	.	.	PUNCT
ejpam-5456	40	1	(	(	PUNCT
ejpam-5456	40	2	2	2	X
ejpam-5456	40	3	)	)	PUNCT
ejpam-5456	40	4	the	the	DET
ejpam-5456	40	5	conformable	conformable	ADJ
ejpam-5456	40	6	fractional	fractional	ADJ
ejpam-5456	40	7	integral	integral	ADJ
ejpam-5456	40	8	is	be	AUX
ejpam-5456	40	9	defined	define	VERB
ejpam-5456	40	10	as	as	SCONJ
ejpam-5456	40	11	follows	follow	VERB
ejpam-5456	40	12	:	:	PUNCT
ejpam-5456	40	13	iα̃µ(δ)(φ	iα̃µ(δ)(φ	NOUN
ejpam-5456	40	14	)	)	PUNCT
ejpam-5456	41	1	=	=	SYM
ejpam-5456	41	2	∫	∫	PROPN
ejpam-5456	41	3	φ	φ	NUM
ejpam-5456	41	4	α̃	α̃	PROPN
ejpam-5456	41	5	δ(℘	δ(℘	NOUN
ejpam-5456	41	6	)	)	PUNCT
ejpam-5456	41	7	(	(	PUNCT
ejpam-5456	41	8	℘−	℘−	NOUN
ejpam-5456	41	9	α̃	α̃	PROPN
ejpam-5456	41	10	)	)	PUNCT
ejpam-5456	41	11	1−µd℘	1−µd℘	NUM
ejpam-5456	41	12	,	,	PUNCT
ejpam-5456	41	13	µ	µ	X
ejpam-5456	41	14	∈	∈	NOUN
ejpam-5456	41	15	(	(	PUNCT
ejpam-5456	41	16	0	0	NUM
ejpam-5456	41	17	,	,	PUNCT
ejpam-5456	41	18	1	1	NUM
ejpam-5456	41	19	]	]	PUNCT
ejpam-5456	41	20	.	.	PUNCT
ejpam-5456	42	1	(	(	PUNCT
ejpam-5456	42	2	3	3	X
ejpam-5456	42	3	)	)	PUNCT
ejpam-5456	42	4	con	con	NOUN
ejpam-5456	42	5	-	-	PUNCT
ejpam-5456	42	6	frd	frd	NOUN
ejpam-5456	42	7	provides	provide	VERB
ejpam-5456	42	8	an	an	DET
ejpam-5456	42	9	alternative	alternative	ADJ
ejpam-5456	42	10	framework	framework	NOUN
ejpam-5456	42	11	for	for	ADP
ejpam-5456	42	12	fractional	fractional	ADJ
ejpam-5456	42	13	differentiation	differentiation	NOUN
ejpam-5456	42	14	that	that	PRON
ejpam-5456	42	15	simplifies	simplify	VERB
ejpam-5456	42	16	the	the	DET
ejpam-5456	42	17	computation	computation	NOUN
ejpam-5456	42	18	of	of	ADP
ejpam-5456	42	19	fractional	fractional	ADJ
ejpam-5456	42	20	derivatives	derivative	NOUN
ejpam-5456	42	21	and	and	CCONJ
ejpam-5456	42	22	maintains	maintain	VERB
ejpam-5456	42	23	some	some	DET
ejpam-5456	42	24	key	key	ADJ
ejpam-5456	42	25	properties	property	NOUN
ejpam-5456	42	26	of	of	ADP
ejpam-5456	42	27	classical	classical	ADJ
ejpam-5456	42	28	derivatives	derivative	NOUN
ejpam-5456	42	29	.	.	PUNCT
ejpam-5456	43	1	the	the	DET
ejpam-5456	43	2	con	con	ADJ
ejpam-5456	43	3	-	-	PUNCT
ejpam-5456	43	4	frd	frd	NOUN
ejpam-5456	43	5	offers	offer	VERB
ejpam-5456	43	6	several	several	ADJ
ejpam-5456	43	7	advantages	advantage	NOUN
ejpam-5456	43	8	compared	compare	VERB
ejpam-5456	43	9	to	to	ADP
ejpam-5456	43	10	other	other	ADJ
ejpam-5456	43	11	types	type	NOUN
ejpam-5456	43	12	of	of	ADP
ejpam-5456	43	13	fractional	fractional	ADJ
ejpam-5456	43	14	derivatives	derivative	NOUN
ejpam-5456	43	15	.	.	PUNCT
ejpam-5456	44	1	here	here	ADV
ejpam-5456	44	2	are	be	AUX
ejpam-5456	44	3	some	some	PRON
ejpam-5456	44	4	of	of	ADP
ejpam-5456	44	5	the	the	DET
ejpam-5456	44	6	key	key	ADJ
ejpam-5456	44	7	benefits	benefit	NOUN
ejpam-5456	44	8	[	[	X
ejpam-5456	44	9	5	5	NUM
ejpam-5456	44	10	,	,	PUNCT
ejpam-5456	44	11	15	15	NUM
ejpam-5456	44	12	,	,	PUNCT
ejpam-5456	44	13	26	26	NUM
ejpam-5456	44	14	,	,	PUNCT
ejpam-5456	44	15	28	28	NUM
ejpam-5456	44	16	]	]	SYM
ejpam-5456	44	17	:	:	PUNCT
ejpam-5456	44	18	m.i	m.i	PROPN
ejpam-5456	44	19	.	.	PROPN
ejpam-5456	44	20	liaqat	liaqat	PROPN
ejpam-5456	44	21	,	,	PUNCT
ejpam-5456	44	22	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	44	23	/	/	SYM
ejpam-5456	44	24	eur	eur	PROPN
ejpam-5456	44	25	.	.	PUNCT
ejpam-5456	45	1	j.	j.	PROPN
ejpam-5456	45	2	pure	pure	PROPN
ejpam-5456	45	3	appl	appl	PROPN
ejpam-5456	45	4	.	.	PROPN
ejpam-5456	45	5	math	math	PROPN
ejpam-5456	45	6	,	,	PUNCT
ejpam-5456	45	7	17	17	NUM
ejpam-5456	45	8	(	(	PUNCT
ejpam-5456	45	9	4	4	NUM
ejpam-5456	45	10	)	)	PUNCT
ejpam-5456	45	11	(	(	PUNCT
ejpam-5456	45	12	2024	2024	NUM
ejpam-5456	45	13	)	)	PUNCT
ejpam-5456	45	14	,	,	PUNCT
ejpam-5456	45	15	3464	3464	NUM
ejpam-5456	45	16	-	-	SYM
ejpam-5456	45	17	3491	3491	NUM
ejpam-5456	45	18	3466	3466	NUM
ejpam-5456	45	19	i.	i.	NOUN
ejpam-5456	45	20	simplicity	simplicity	NOUN
ejpam-5456	45	21	and	and	CCONJ
ejpam-5456	45	22	intuition	intuition	NOUN
ejpam-5456	45	23	:	:	PUNCT
ejpam-5456	45	24	con	con	ADJ
ejpam-5456	45	25	-	-	PUNCT
ejpam-5456	45	26	frd	frd	NOUN
ejpam-5456	45	27	are	be	AUX
ejpam-5456	45	28	designed	design	VERB
ejpam-5456	45	29	to	to	PART
ejpam-5456	45	30	be	be	AUX
ejpam-5456	45	31	a	a	DET
ejpam-5456	45	32	straightforward	straightforward	ADJ
ejpam-5456	45	33	generalization	generalization	NOUN
ejpam-5456	45	34	of	of	ADP
ejpam-5456	45	35	the	the	DET
ejpam-5456	45	36	classical	classical	ADJ
ejpam-5456	45	37	derivative	derivative	NOUN
ejpam-5456	45	38	,	,	PUNCT
ejpam-5456	45	39	making	make	VERB
ejpam-5456	45	40	them	they	PRON
ejpam-5456	45	41	easier	easy	ADJ
ejpam-5456	45	42	to	to	PART
ejpam-5456	45	43	understand	understand	VERB
ejpam-5456	45	44	and	and	CCONJ
ejpam-5456	45	45	apply	apply	VERB
ejpam-5456	45	46	.	.	PUNCT
ejpam-5456	46	1	they	they	PRON
ejpam-5456	46	2	retain	retain	VERB
ejpam-5456	46	3	many	many	ADJ
ejpam-5456	46	4	of	of	ADP
ejpam-5456	46	5	the	the	DET
ejpam-5456	46	6	properties	property	NOUN
ejpam-5456	46	7	of	of	ADP
ejpam-5456	46	8	integer	integer	NOUN
ejpam-5456	46	9	-	-	PUNCT
ejpam-5456	46	10	order	order	NOUN
ejpam-5456	46	11	derivatives	derivative	NOUN
ejpam-5456	46	12	,	,	PUNCT
ejpam-5456	46	13	which	which	PRON
ejpam-5456	46	14	can	can	AUX
ejpam-5456	46	15	simplify	simplify	VERB
ejpam-5456	46	16	the	the	DET
ejpam-5456	46	17	transition	transition	NOUN
ejpam-5456	46	18	from	from	ADP
ejpam-5456	46	19	classical	classical	ADJ
ejpam-5456	46	20	to	to	ADP
ejpam-5456	46	21	fc	fc	PROPN
ejpam-5456	46	22	.	.	PUNCT
ejpam-5456	46	23	ii	ii	PROPN
ejpam-5456	46	24	.	.	PUNCT
ejpam-5456	46	25	consistency	consistency	NOUN
ejpam-5456	46	26	with	with	ADP
ejpam-5456	46	27	classical	classical	ADJ
ejpam-5456	46	28	calculus	calculus	NOUN
ejpam-5456	46	29	:	:	PUNCT
ejpam-5456	46	30	unlike	unlike	ADP
ejpam-5456	46	31	some	some	DET
ejpam-5456	46	32	other	other	ADJ
ejpam-5456	46	33	fractional	fractional	ADJ
ejpam-5456	46	34	derivatives	derivative	NOUN
ejpam-5456	46	35	,	,	PUNCT
ejpam-5456	46	36	the	the	DET
ejpam-5456	46	37	conformable	conformable	ADJ
ejpam-5456	46	38	derivative	derivative	NOUN
ejpam-5456	46	39	maintains	maintain	VERB
ejpam-5456	46	40	a	a	DET
ejpam-5456	46	41	closer	close	ADJ
ejpam-5456	46	42	relationship	relationship	NOUN
ejpam-5456	46	43	to	to	ADP
ejpam-5456	46	44	classical	classical	ADJ
ejpam-5456	46	45	calculus	calculus	NOUN
ejpam-5456	46	46	.	.	PUNCT
ejpam-5456	47	1	it	it	PRON
ejpam-5456	47	2	satisfies	satisfy	VERB
ejpam-5456	47	3	properties	property	NOUN
ejpam-5456	47	4	like	like	ADP
ejpam-5456	47	5	the	the	DET
ejpam-5456	47	6	product	product	NOUN
ejpam-5456	47	7	rule	rule	NOUN
ejpam-5456	47	8	,	,	PUNCT
ejpam-5456	47	9	chain	chain	NOUN
ejpam-5456	47	10	rule	rule	NOUN
ejpam-5456	47	11	,	,	PUNCT
ejpam-5456	47	12	and	and	CCONJ
ejpam-5456	47	13	power	power	NOUN
ejpam-5456	47	14	rule	rule	NOUN
ejpam-5456	47	15	in	in	ADP
ejpam-5456	47	16	a	a	DET
ejpam-5456	47	17	manner	manner	NOUN
ejpam-5456	47	18	that	that	PRON
ejpam-5456	47	19	is	be	AUX
ejpam-5456	47	20	more	more	ADV
ejpam-5456	47	21	consistent	consistent	ADJ
ejpam-5456	47	22	with	with	ADP
ejpam-5456	47	23	classical	classical	ADJ
ejpam-5456	47	24	derivatives	derivative	NOUN
ejpam-5456	47	25	,	,	PUNCT
ejpam-5456	47	26	making	make	VERB
ejpam-5456	47	27	it	it	PRON
ejpam-5456	47	28	more	more	ADV
ejpam-5456	47	29	intuitive	intuitive	ADJ
ejpam-5456	47	30	for	for	ADP
ejpam-5456	47	31	those	those	PRON
ejpam-5456	47	32	familiar	familiar	ADJ
ejpam-5456	47	33	with	with	ADP
ejpam-5456	47	34	traditional	traditional	ADJ
ejpam-5456	47	35	calculus	calculus	NOUN
ejpam-5456	47	36	.	.	PUNCT
ejpam-5456	48	1	iii	iii	X
ejpam-5456	48	2	.	.	PUNCT
ejpam-5456	49	1	clear	clear	ADJ
ejpam-5456	49	2	physical	physical	ADJ
ejpam-5456	49	3	interpretation	interpretation	NOUN
ejpam-5456	49	4	:	:	PUNCT
ejpam-5456	49	5	conformable	conformable	ADJ
ejpam-5456	49	6	derivatives	derivative	NOUN
ejpam-5456	49	7	offer	offer	VERB
ejpam-5456	49	8	a	a	DET
ejpam-5456	49	9	clearer	clear	ADJ
ejpam-5456	49	10	physical	physical	ADJ
ejpam-5456	49	11	interpretation	interpretation	NOUN
ejpam-5456	49	12	compared	compare	VERB
ejpam-5456	49	13	to	to	ADP
ejpam-5456	49	14	some	some	DET
ejpam-5456	49	15	other	other	ADJ
ejpam-5456	49	16	fractional	fractional	ADJ
ejpam-5456	49	17	derivatives	derivative	NOUN
ejpam-5456	49	18	,	,	PUNCT
ejpam-5456	49	19	as	as	SCONJ
ejpam-5456	49	20	they	they	PRON
ejpam-5456	49	21	are	be	AUX
ejpam-5456	49	22	often	often	ADV
ejpam-5456	49	23	more	more	ADV
ejpam-5456	49	24	closely	closely	ADV
ejpam-5456	49	25	related	relate	VERB
ejpam-5456	49	26	to	to	ADP
ejpam-5456	49	27	the	the	DET
ejpam-5456	49	28	original	original	ADJ
ejpam-5456	49	29	physical	physical	ADJ
ejpam-5456	49	30	quantities	quantity	NOUN
ejpam-5456	49	31	and	and	CCONJ
ejpam-5456	49	32	processes	process	NOUN
ejpam-5456	49	33	.	.	PUNCT
ejpam-5456	50	1	this	this	PRON
ejpam-5456	50	2	makes	make	VERB
ejpam-5456	50	3	them	they	PRON
ejpam-5456	50	4	useful	useful	ADJ
ejpam-5456	50	5	in	in	ADP
ejpam-5456	50	6	modeling	model	VERB
ejpam-5456	50	7	real	real	ADJ
ejpam-5456	50	8	-	-	PUNCT
ejpam-5456	50	9	world	world	NOUN
ejpam-5456	50	10	phenomena	phenomenon	NOUN
ejpam-5456	50	11	where	where	SCONJ
ejpam-5456	50	12	a	a	DET
ejpam-5456	50	13	straightforward	straightforward	ADJ
ejpam-5456	50	14	interpretation	interpretation	NOUN
ejpam-5456	50	15	is	be	AUX
ejpam-5456	50	16	desired	desire	VERB
ejpam-5456	50	17	.	.	PUNCT
ejpam-5456	51	1	iv	iv	X
ejpam-5456	51	2	.	.	PUNCT
ejpam-5456	51	3	ease	ease	NOUN
ejpam-5456	51	4	of	of	ADP
ejpam-5456	51	5	application	application	NOUN
ejpam-5456	51	6	:	:	PUNCT
ejpam-5456	51	7	due	due	ADP
ejpam-5456	51	8	to	to	ADP
ejpam-5456	51	9	their	their	PRON
ejpam-5456	51	10	simpler	simple	ADJ
ejpam-5456	51	11	form	form	NOUN
ejpam-5456	51	12	and	and	CCONJ
ejpam-5456	51	13	consistency	consistency	NOUN
ejpam-5456	51	14	with	with	ADP
ejpam-5456	51	15	classical	classical	ADJ
ejpam-5456	51	16	calculus	calculus	NOUN
ejpam-5456	51	17	rules	rule	NOUN
ejpam-5456	51	18	,	,	PUNCT
ejpam-5456	51	19	con	con	NOUN
ejpam-5456	51	20	-	-	PUNCT
ejpam-5456	51	21	frd	frd	ADJ
ejpam-5456	51	22	are	be	AUX
ejpam-5456	51	23	often	often	ADV
ejpam-5456	51	24	easier	easy	ADJ
ejpam-5456	51	25	to	to	PART
ejpam-5456	51	26	apply	apply	VERB
ejpam-5456	51	27	in	in	ADP
ejpam-5456	51	28	various	various	ADJ
ejpam-5456	51	29	mathematical	mathematical	ADJ
ejpam-5456	51	30	and	and	CCONJ
ejpam-5456	51	31	engineering	engineering	NOUN
ejpam-5456	51	32	problems	problem	NOUN
ejpam-5456	51	33	.	.	PUNCT
ejpam-5456	52	1	they	they	PRON
ejpam-5456	52	2	can	can	AUX
ejpam-5456	52	3	be	be	AUX
ejpam-5456	52	4	used	use	VERB
ejpam-5456	52	5	in	in	ADP
ejpam-5456	52	6	solving	solve	VERB
ejpam-5456	52	7	des	des	PROPN
ejpam-5456	52	8	,	,	PUNCT
ejpam-5456	52	9	modeling	modeling	NOUN
ejpam-5456	52	10	systems	system	NOUN
ejpam-5456	52	11	,	,	PUNCT
ejpam-5456	52	12	and	and	CCONJ
ejpam-5456	52	13	analyzing	analyze	VERB
ejpam-5456	52	14	dynamic	dynamic	ADJ
ejpam-5456	52	15	behaviors	behavior	NOUN
ejpam-5456	52	16	without	without	ADP
ejpam-5456	52	17	requiring	require	VERB
ejpam-5456	52	18	complex	complex	ADJ
ejpam-5456	52	19	modifications	modification	NOUN
ejpam-5456	52	20	to	to	ADP
ejpam-5456	52	21	existing	exist	VERB
ejpam-5456	52	22	methods	method	NOUN
ejpam-5456	52	23	.	.	PUNCT
ejpam-5456	53	1	v.	v.	ADP
ejpam-5456	53	2	flexibility	flexibility	NOUN
ejpam-5456	53	3	in	in	ADP
ejpam-5456	53	4	modeling	modeling	NOUN
ejpam-5456	53	5	:	:	PUNCT
ejpam-5456	53	6	conformable	conformable	ADJ
ejpam-5456	53	7	derivatives	derivative	NOUN
ejpam-5456	53	8	provide	provide	VERB
ejpam-5456	53	9	a	a	DET
ejpam-5456	53	10	flexible	flexible	ADJ
ejpam-5456	53	11	framework	framework	NOUN
ejpam-5456	53	12	for	for	ADP
ejpam-5456	53	13	modeling	modeling	NOUN
ejpam-5456	53	14	systems	system	NOUN
ejpam-5456	53	15	that	that	PRON
ejpam-5456	53	16	exhibit	exhibit	VERB
ejpam-5456	53	17	non	non	ADJ
ejpam-5456	53	18	-	-	ADJ
ejpam-5456	53	19	integer	integer	ADJ
ejpam-5456	53	20	order	order	NOUN
ejpam-5456	53	21	dynamics	dynamic	NOUN
ejpam-5456	53	22	,	,	PUNCT
ejpam-5456	53	23	such	such	ADJ
ejpam-5456	53	24	as	as	ADP
ejpam-5456	53	25	memory	memory	NOUN
ejpam-5456	53	26	effects	effect	NOUN
ejpam-5456	53	27	or	or	CCONJ
ejpam-5456	53	28	anomalous	anomalous	ADJ
ejpam-5456	53	29	diffusion	diffusion	NOUN
ejpam-5456	53	30	,	,	PUNCT
ejpam-5456	53	31	without	without	ADP
ejpam-5456	53	32	the	the	DET
ejpam-5456	53	33	complexity	complexity	NOUN
ejpam-5456	53	34	that	that	PRON
ejpam-5456	53	35	comes	come	VERB
ejpam-5456	53	36	with	with	ADP
ejpam-5456	53	37	some	some	DET
ejpam-5456	53	38	other	other	ADJ
ejpam-5456	53	39	fractional	fractional	ADJ
ejpam-5456	53	40	derivatives	derivative	NOUN
ejpam-5456	53	41	.	.	PUNCT
ejpam-5456	54	1	this	this	PRON
ejpam-5456	54	2	makes	make	VERB
ejpam-5456	54	3	them	they	PRON
ejpam-5456	54	4	a	a	DET
ejpam-5456	54	5	practical	practical	ADJ
ejpam-5456	54	6	choice	choice	NOUN
ejpam-5456	54	7	for	for	ADP
ejpam-5456	54	8	applications	application	NOUN
ejpam-5456	54	9	in	in	ADP
ejpam-5456	54	10	physics	physics	NOUN
ejpam-5456	54	11	,	,	PUNCT
ejpam-5456	54	12	engineering	engineering	NOUN
ejpam-5456	54	13	,	,	PUNCT
ejpam-5456	54	14	biology	biology	NOUN
ejpam-5456	54	15	,	,	PUNCT
ejpam-5456	54	16	and	and	CCONJ
ejpam-5456	54	17	finance	finance	NOUN
ejpam-5456	54	18	.	.	PUNCT
ejpam-5456	55	1	vi	vi	X
ejpam-5456	55	2	.	.	PUNCT
ejpam-5456	55	3	compatibility	compatibility	NOUN
ejpam-5456	55	4	with	with	ADP
ejpam-5456	55	5	numerical	numerical	ADJ
ejpam-5456	55	6	methods	method	NOUN
ejpam-5456	55	7	:	:	PUNCT
ejpam-5456	55	8	the	the	DET
ejpam-5456	55	9	simpler	simple	ADJ
ejpam-5456	55	10	and	and	CCONJ
ejpam-5456	55	11	more	more	ADV
ejpam-5456	55	12	intuitive	intuitive	ADJ
ejpam-5456	55	13	nature	nature	NOUN
ejpam-5456	55	14	of	of	ADP
ejpam-5456	55	15	conformable	conformable	ADJ
ejpam-5456	55	16	derivatives	derivative	NOUN
ejpam-5456	55	17	often	often	ADV
ejpam-5456	55	18	leads	lead	VERB
ejpam-5456	55	19	to	to	ADP
ejpam-5456	55	20	easier	easy	ADJ
ejpam-5456	55	21	implementation	implementation	NOUN
ejpam-5456	55	22	in	in	ADP
ejpam-5456	55	23	numerical	numerical	ADJ
ejpam-5456	55	24	methods	method	NOUN
ejpam-5456	55	25	.	.	PUNCT
ejpam-5456	56	1	this	this	PRON
ejpam-5456	56	2	can	can	AUX
ejpam-5456	56	3	be	be	AUX
ejpam-5456	56	4	beneficial	beneficial	ADJ
ejpam-5456	56	5	for	for	ADP
ejpam-5456	56	6	computational	computational	ADJ
ejpam-5456	56	7	modeling	modeling	NOUN
ejpam-5456	56	8	and	and	CCONJ
ejpam-5456	56	9	simulation	simulation	NOUN
ejpam-5456	56	10	,	,	PUNCT
ejpam-5456	56	11	where	where	SCONJ
ejpam-5456	56	12	the	the	DET
ejpam-5456	56	13	goal	goal	NOUN
ejpam-5456	56	14	is	be	AUX
ejpam-5456	56	15	to	to	PART
ejpam-5456	56	16	approximate	approximate	VERB
ejpam-5456	56	17	solutions	solution	NOUN
ejpam-5456	56	18	to	to	ADP
ejpam-5456	56	19	fodes	fode	NOUN
ejpam-5456	56	20	.	.	PUNCT
ejpam-5456	57	1	the	the	DET
ejpam-5456	57	2	fodes	fode	NOUN
ejpam-5456	57	3	are	be	AUX
ejpam-5456	57	4	an	an	DET
ejpam-5456	57	5	advanced	advanced	ADJ
ejpam-5456	57	6	mathematical	mathematical	ADJ
ejpam-5456	57	7	tool	tool	NOUN
ejpam-5456	57	8	that	that	PRON
ejpam-5456	57	9	extends	extend	VERB
ejpam-5456	57	10	the	the	DET
ejpam-5456	57	11	concept	concept	NOUN
ejpam-5456	57	12	of	of	ADP
ejpam-5456	57	13	traditional	traditional	ADJ
ejpam-5456	57	14	des	des	X
ejpam-5456	57	15	to	to	ADP
ejpam-5456	57	16	non	non	ADJ
ejpam-5456	57	17	-	-	ADJ
ejpam-5456	57	18	integer	integer	ADJ
ejpam-5456	57	19	orders	order	NOUN
ejpam-5456	57	20	of	of	ADP
ejpam-5456	57	21	differentiation	differentiation	NOUN
ejpam-5456	57	22	and	and	CCONJ
ejpam-5456	57	23	integration	integration	NOUN
ejpam-5456	57	24	.	.	PUNCT
ejpam-5456	58	1	this	this	DET
ejpam-5456	58	2	generalization	generalization	NOUN
ejpam-5456	58	3	provides	provide	VERB
ejpam-5456	58	4	a	a	DET
ejpam-5456	58	5	more	more	ADV
ejpam-5456	58	6	flexible	flexible	ADJ
ejpam-5456	58	7	and	and	CCONJ
ejpam-5456	58	8	accurate	accurate	ADJ
ejpam-5456	58	9	framework	framework	NOUN
ejpam-5456	58	10	for	for	ADP
ejpam-5456	58	11	modeling	model	VERB
ejpam-5456	58	12	complex	complex	ADJ
ejpam-5456	58	13	systems	system	NOUN
ejpam-5456	58	14	that	that	PRON
ejpam-5456	58	15	exhibit	exhibit	VERB
ejpam-5456	58	16	memory	memory	NOUN
ejpam-5456	58	17	,	,	PUNCT
ejpam-5456	58	18	hereditary	hereditary	ADJ
ejpam-5456	58	19	properties	property	NOUN
ejpam-5456	58	20	,	,	PUNCT
ejpam-5456	58	21	or	or	CCONJ
ejpam-5456	58	22	anomalous	anomalous	ADJ
ejpam-5456	58	23	diffusion	diffusion	NOUN
ejpam-5456	58	24	,	,	PUNCT
ejpam-5456	58	25	which	which	PRON
ejpam-5456	58	26	are	be	AUX
ejpam-5456	58	27	not	not	PART
ejpam-5456	58	28	adequately	adequately	ADV
ejpam-5456	58	29	captured	capture	VERB
ejpam-5456	58	30	by	by	ADP
ejpam-5456	58	31	traditional	traditional	ADJ
ejpam-5456	58	32	integer	integer	NOUN
ejpam-5456	58	33	-	-	PUNCT
ejpam-5456	58	34	order	order	NOUN
ejpam-5456	58	35	models	model	NOUN
ejpam-5456	58	36	.	.	PUNCT
ejpam-5456	59	1	the	the	DET
ejpam-5456	59	2	power	power	NOUN
ejpam-5456	59	3	of	of	ADP
ejpam-5456	59	4	fodes	fode	NOUN
ejpam-5456	59	5	lies	lie	VERB
ejpam-5456	59	6	in	in	ADP
ejpam-5456	59	7	their	their	PRON
ejpam-5456	59	8	ability	ability	NOUN
ejpam-5456	59	9	to	to	PART
ejpam-5456	59	10	model	model	VERB
ejpam-5456	59	11	processes	process	NOUN
ejpam-5456	59	12	where	where	SCONJ
ejpam-5456	59	13	the	the	DET
ejpam-5456	59	14	rate	rate	NOUN
ejpam-5456	59	15	of	of	ADP
ejpam-5456	59	16	change	change	NOUN
ejpam-5456	59	17	is	be	AUX
ejpam-5456	59	18	not	not	PART
ejpam-5456	59	19	merely	merely	ADV
ejpam-5456	59	20	dependent	dependent	ADJ
ejpam-5456	59	21	on	on	ADP
ejpam-5456	59	22	the	the	DET
ejpam-5456	59	23	current	current	ADJ
ejpam-5456	59	24	state	state	NOUN
ejpam-5456	59	25	but	but	CCONJ
ejpam-5456	59	26	also	also	ADV
ejpam-5456	59	27	influenced	influence	VERB
ejpam-5456	59	28	by	by	ADP
ejpam-5456	59	29	the	the	DET
ejpam-5456	59	30	history	history	NOUN
ejpam-5456	59	31	of	of	ADP
ejpam-5456	59	32	the	the	DET
ejpam-5456	59	33	system	system	NOUN
ejpam-5456	59	34	.	.	PUNCT
ejpam-5456	60	1	this	this	PRON
ejpam-5456	60	2	is	be	AUX
ejpam-5456	60	3	particularly	particularly	ADV
ejpam-5456	60	4	relevant	relevant	ADJ
ejpam-5456	60	5	in	in	ADP
ejpam-5456	60	6	fields	field	NOUN
ejpam-5456	60	7	like	like	ADP
ejpam-5456	60	8	physics	physics	NOUN
ejpam-5456	60	9	,	,	PUNCT
ejpam-5456	60	10	engineering	engineering	NOUN
ejpam-5456	60	11	,	,	PUNCT
ejpam-5456	60	12	biology	biology	NOUN
ejpam-5456	60	13	,	,	PUNCT
ejpam-5456	60	14	and	and	CCONJ
ejpam-5456	60	15	finance	finance	NOUN
ejpam-5456	60	16	,	,	PUNCT
ejpam-5456	60	17	where	where	SCONJ
ejpam-5456	60	18	systems	system	NOUN
ejpam-5456	60	19	often	often	ADV
ejpam-5456	60	20	have	have	VERB
ejpam-5456	60	21	memory	memory	NOUN
ejpam-5456	60	22	effects	effect	NOUN
ejpam-5456	60	23	,	,	PUNCT
ejpam-5456	60	24	such	such	ADJ
ejpam-5456	60	25	as	as	ADP
ejpam-5456	60	26	viscoelastic	viscoelastic	ADJ
ejpam-5456	60	27	materials	material	NOUN
ejpam-5456	60	28	,	,	PUNCT
ejpam-5456	60	29	anomalous	anomalous	ADJ
ejpam-5456	60	30	transport	transport	NOUN
ejpam-5456	60	31	phenomena	phenomenon	NOUN
ejpam-5456	60	32	,	,	PUNCT
ejpam-5456	60	33	and	and	CCONJ
ejpam-5456	60	34	financial	financial	ADJ
ejpam-5456	60	35	markets	market	NOUN
ejpam-5456	60	36	with	with	ADP
ejpam-5456	60	37	long	long	ADJ
ejpam-5456	60	38	-	-	PUNCT
ejpam-5456	60	39	term	term	NOUN
ejpam-5456	60	40	dependencies	dependency	NOUN
ejpam-5456	60	41	.	.	PUNCT
ejpam-5456	61	1	in	in	ADP
ejpam-5456	61	2	the	the	DET
ejpam-5456	61	3	field	field	NOUN
ejpam-5456	61	4	of	of	ADP
ejpam-5456	61	5	fodes	fode	NOUN
ejpam-5456	61	6	,	,	PUNCT
ejpam-5456	61	7	several	several	ADJ
ejpam-5456	61	8	well	well	ADV
ejpam-5456	61	9	-	-	PUNCT
ejpam-5456	61	10	known	know	VERB
ejpam-5456	61	11	models	model	NOUN
ejpam-5456	61	12	have	have	AUX
ejpam-5456	61	13	been	be	AUX
ejpam-5456	61	14	developed	develop	VERB
ejpam-5456	61	15	to	to	PART
ejpam-5456	61	16	describe	describe	VERB
ejpam-5456	61	17	complex	complex	ADJ
ejpam-5456	61	18	systems	system	NOUN
ejpam-5456	61	19	with	with	ADP
ejpam-5456	61	20	memory	memory	NOUN
ejpam-5456	61	21	and	and	CCONJ
ejpam-5456	61	22	hereditary	hereditary	ADJ
ejpam-5456	61	23	properties	property	NOUN
ejpam-5456	61	24	.	.	PUNCT
ejpam-5456	62	1	among	among	ADP
ejpam-5456	62	2	these	these	DET
ejpam-5456	62	3	models	model	NOUN
ejpam-5456	62	4	,	,	PUNCT
ejpam-5456	62	5	the	the	DET
ejpam-5456	62	6	fractional	fractional	ADJ
ejpam-5456	62	7	schrödinger	schrödinger	NOUN
ejpam-5456	62	8	differential	differential	ADJ
ejpam-5456	62	9	equation	equation	NOUN
ejpam-5456	62	10	(	(	PUNCT
ejpam-5456	62	11	fsdes	fsdes	PROPN
ejpam-5456	62	12	)	)	PUNCT
ejpam-5456	62	13	stands	stand	VERB
ejpam-5456	62	14	out	out	ADP
ejpam-5456	62	15	as	as	ADP
ejpam-5456	62	16	particularly	particularly	ADV
ejpam-5456	62	17	important	important	ADJ
ejpam-5456	62	18	.	.	PUNCT
ejpam-5456	63	1	m.i	m.i	PROPN
ejpam-5456	63	2	.	.	PROPN
ejpam-5456	63	3	liaqat	liaqat	PROPN
ejpam-5456	63	4	,	,	PUNCT
ejpam-5456	63	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	63	6	/	/	SYM
ejpam-5456	63	7	eur	eur	PROPN
ejpam-5456	63	8	.	.	PUNCT
ejpam-5456	64	1	j.	j.	PROPN
ejpam-5456	64	2	pure	pure	PROPN
ejpam-5456	64	3	appl	appl	PROPN
ejpam-5456	64	4	.	.	PROPN
ejpam-5456	64	5	math	math	PROPN
ejpam-5456	64	6	,	,	PUNCT
ejpam-5456	64	7	17	17	NUM
ejpam-5456	64	8	(	(	PUNCT
ejpam-5456	64	9	4	4	NUM
ejpam-5456	64	10	)	)	PUNCT
ejpam-5456	64	11	(	(	PUNCT
ejpam-5456	64	12	2024	2024	NUM
ejpam-5456	64	13	)	)	PUNCT
ejpam-5456	64	14	,	,	PUNCT
ejpam-5456	64	15	3464	3464	NUM
ejpam-5456	64	16	-	-	SYM
ejpam-5456	64	17	3491	3491	NUM
ejpam-5456	64	18	3467	3467	NUM
ejpam-5456	64	19	this	this	DET
ejpam-5456	64	20	equation	equation	NOUN
ejpam-5456	64	21	extends	extend	VERB
ejpam-5456	64	22	the	the	DET
ejpam-5456	64	23	classical	classical	ADJ
ejpam-5456	64	24	schrödinger	schrödinger	NOUN
ejpam-5456	64	25	differential	differential	ADJ
ejpam-5456	64	26	equation	equation	NOUN
ejpam-5456	64	27	(	(	PUNCT
ejpam-5456	64	28	sde	sde	PROPN
ejpam-5456	64	29	)	)	PUNCT
ejpam-5456	64	30	by	by	ADP
ejpam-5456	64	31	incorporating	incorporate	VERB
ejpam-5456	64	32	fc	fc	PROPN
ejpam-5456	64	33	,	,	PUNCT
ejpam-5456	64	34	allowing	allow	VERB
ejpam-5456	64	35	for	for	ADP
ejpam-5456	64	36	a	a	DET
ejpam-5456	64	37	more	more	ADV
ejpam-5456	64	38	accurate	accurate	ADJ
ejpam-5456	64	39	description	description	NOUN
ejpam-5456	64	40	of	of	ADP
ejpam-5456	64	41	quantum	quantum	NOUN
ejpam-5456	64	42	systems	system	NOUN
ejpam-5456	64	43	with	with	ADP
ejpam-5456	64	44	anomalous	anomalous	ADJ
ejpam-5456	64	45	diffusion	diffusion	NOUN
ejpam-5456	64	46	and	and	CCONJ
ejpam-5456	64	47	other	other	ADJ
ejpam-5456	64	48	non	non	ADJ
ejpam-5456	64	49	-	-	ADJ
ejpam-5456	64	50	standard	standard	ADJ
ejpam-5456	64	51	behaviors	behavior	NOUN
ejpam-5456	64	52	.	.	PUNCT
ejpam-5456	65	1	typically	typically	ADV
ejpam-5456	65	2	,	,	PUNCT
ejpam-5456	65	3	the	the	DET
ejpam-5456	65	4	fractional	fractional	ADJ
ejpam-5456	65	5	derivative	derivative	NOUN
ejpam-5456	65	6	is	be	AUX
ejpam-5456	65	7	introduced	introduce	VERB
ejpam-5456	65	8	into	into	ADP
ejpam-5456	65	9	either	either	CCONJ
ejpam-5456	65	10	the	the	DET
ejpam-5456	65	11	time	time	NOUN
ejpam-5456	65	12	or	or	CCONJ
ejpam-5456	65	13	spatial	spatial	ADJ
ejpam-5456	65	14	components	component	NOUN
ejpam-5456	65	15	of	of	ADP
ejpam-5456	65	16	the	the	DET
ejpam-5456	65	17	sde	sde	PROPN
ejpam-5456	65	18	,	,	PUNCT
ejpam-5456	65	19	leading	lead	VERB
ejpam-5456	65	20	to	to	ADP
ejpam-5456	65	21	modifications	modification	NOUN
ejpam-5456	65	22	in	in	ADP
ejpam-5456	65	23	the	the	DET
ejpam-5456	65	24	wave	wave	NOUN
ejpam-5456	65	25	function	function	NOUN
ejpam-5456	65	26	’s	’s	PART
ejpam-5456	65	27	behavior	behavior	NOUN
ejpam-5456	65	28	,	,	PUNCT
ejpam-5456	65	29	with	with	ADP
ejpam-5456	65	30	potential	potential	ADJ
ejpam-5456	65	31	applications	application	NOUN
ejpam-5456	65	32	in	in	ADP
ejpam-5456	65	33	quantum	quantum	ADJ
ejpam-5456	65	34	mechanics	mechanic	NOUN
ejpam-5456	65	35	and	and	CCONJ
ejpam-5456	65	36	other	other	ADJ
ejpam-5456	65	37	fields	field	NOUN
ejpam-5456	65	38	such	such	ADJ
ejpam-5456	65	39	as	as	ADP
ejpam-5456	65	40	statistical	statistical	ADJ
ejpam-5456	65	41	mechanics	mechanic	NOUN
ejpam-5456	65	42	and	and	CCONJ
ejpam-5456	65	43	condensed	condense	VERB
ejpam-5456	65	44	matter	matter	NOUN
ejpam-5456	65	45	physics	physic	NOUN
ejpam-5456	65	46	.	.	PUNCT
ejpam-5456	66	1	fsdes	fsde	NOUN
ejpam-5456	66	2	have	have	VERB
ejpam-5456	66	3	diverse	diverse	ADJ
ejpam-5456	66	4	applications	application	NOUN
ejpam-5456	66	5	in	in	ADP
ejpam-5456	66	6	various	various	ADJ
ejpam-5456	66	7	fields	field	NOUN
ejpam-5456	66	8	of	of	ADP
ejpam-5456	66	9	science	science	NOUN
ejpam-5456	66	10	and	and	CCONJ
ejpam-5456	66	11	engineering	engineering	NOUN
ejpam-5456	66	12	,	,	PUNCT
ejpam-5456	66	13	primarily	primarily	ADV
ejpam-5456	66	14	due	due	ADP
ejpam-5456	66	15	to	to	ADP
ejpam-5456	66	16	their	their	PRON
ejpam-5456	66	17	ability	ability	NOUN
ejpam-5456	66	18	to	to	PART
ejpam-5456	66	19	model	model	VERB
ejpam-5456	66	20	systems	system	NOUN
ejpam-5456	66	21	with	with	ADP
ejpam-5456	66	22	memory	memory	NOUN
ejpam-5456	66	23	and	and	CCONJ
ejpam-5456	66	24	non	non	ADJ
ejpam-5456	66	25	-	-	ADJ
ejpam-5456	66	26	local	local	ADJ
ejpam-5456	66	27	interactions	interaction	NOUN
ejpam-5456	66	28	.	.	PUNCT
ejpam-5456	67	1	some	some	PRON
ejpam-5456	67	2	of	of	ADP
ejpam-5456	67	3	the	the	DET
ejpam-5456	67	4	key	key	ADJ
ejpam-5456	67	5	applications	application	NOUN
ejpam-5456	67	6	include	include	VERB
ejpam-5456	67	7	[	[	X
ejpam-5456	67	8	8	8	NUM
ejpam-5456	67	9	,	,	PUNCT
ejpam-5456	67	10	23	23	NUM
ejpam-5456	67	11	]	]	NUM
ejpam-5456	67	12	:	:	PUNCT
ejpam-5456	67	13	i.	i.	PROPN
ejpam-5456	67	14	quantum	quantum	PROPN
ejpam-5456	67	15	mechanics	mechanic	NOUN
ejpam-5456	67	16	:	:	PUNCT
ejpam-5456	67	17	fsdes	fsde	NOUN
ejpam-5456	67	18	are	be	AUX
ejpam-5456	67	19	used	use	VERB
ejpam-5456	67	20	to	to	PART
ejpam-5456	67	21	model	model	VERB
ejpam-5456	67	22	quantum	quantum	NOUN
ejpam-5456	67	23	systems	system	NOUN
ejpam-5456	67	24	where	where	SCONJ
ejpam-5456	67	25	the	the	DET
ejpam-5456	67	26	standard	standard	ADJ
ejpam-5456	67	27	sdes	sde	NOUN
ejpam-5456	67	28	may	may	AUX
ejpam-5456	67	29	not	not	PART
ejpam-5456	67	30	be	be	AUX
ejpam-5456	67	31	sufficient	sufficient	ADJ
ejpam-5456	67	32	,	,	PUNCT
ejpam-5456	67	33	such	such	ADJ
ejpam-5456	67	34	as	as	ADP
ejpam-5456	67	35	systems	system	NOUN
ejpam-5456	67	36	with	with	ADP
ejpam-5456	67	37	fractal	fractal	ADJ
ejpam-5456	67	38	geometries	geometry	NOUN
ejpam-5456	67	39	,	,	PUNCT
ejpam-5456	67	40	complex	complex	ADJ
ejpam-5456	67	41	potentials	potential	NOUN
ejpam-5456	67	42	,	,	PUNCT
ejpam-5456	67	43	or	or	CCONJ
ejpam-5456	67	44	in	in	ADP
ejpam-5456	67	45	scenarios	scenario	NOUN
ejpam-5456	67	46	involving	involve	VERB
ejpam-5456	67	47	anomalous	anomalous	ADJ
ejpam-5456	67	48	diffusion	diffusion	NOUN
ejpam-5456	67	49	.	.	PUNCT
ejpam-5456	68	1	they	they	PRON
ejpam-5456	68	2	help	help	VERB
ejpam-5456	68	3	in	in	ADP
ejpam-5456	68	4	understanding	understand	VERB
ejpam-5456	68	5	the	the	DET
ejpam-5456	68	6	quantum	quantum	ADJ
ejpam-5456	68	7	behavior	behavior	NOUN
ejpam-5456	68	8	in	in	ADP
ejpam-5456	68	9	disordered	disordered	ADJ
ejpam-5456	68	10	or	or	CCONJ
ejpam-5456	68	11	complex	complex	ADJ
ejpam-5456	68	12	materials	material	NOUN
ejpam-5456	68	13	.	.	PUNCT
ejpam-5456	69	1	ii	ii	PROPN
ejpam-5456	69	2	.	.	PROPN
ejpam-5456	70	1	condensed	condense	VERB
ejpam-5456	70	2	matter	matter	NOUN
ejpam-5456	70	3	physics	physics	NOUN
ejpam-5456	70	4	:	:	PUNCT
ejpam-5456	70	5	in	in	ADP
ejpam-5456	70	6	systems	system	NOUN
ejpam-5456	70	7	with	with	ADP
ejpam-5456	70	8	fractal	fractal	ADJ
ejpam-5456	70	9	or	or	CCONJ
ejpam-5456	70	10	irregular	irregular	ADJ
ejpam-5456	70	11	structures	structure	NOUN
ejpam-5456	70	12	,	,	PUNCT
ejpam-5456	70	13	like	like	ADP
ejpam-5456	70	14	certain	certain	ADJ
ejpam-5456	70	15	types	type	NOUN
ejpam-5456	70	16	of	of	ADP
ejpam-5456	70	17	semiconductors	semiconductor	NOUN
ejpam-5456	70	18	,	,	PUNCT
ejpam-5456	70	19	polymers	polymer	NOUN
ejpam-5456	70	20	,	,	PUNCT
ejpam-5456	70	21	or	or	CCONJ
ejpam-5456	70	22	amorphous	amorphous	ADJ
ejpam-5456	70	23	materials	material	NOUN
ejpam-5456	70	24	,	,	PUNCT
ejpam-5456	70	25	fsdes	fsde	NOUN
ejpam-5456	70	26	can	can	AUX
ejpam-5456	70	27	provide	provide	VERB
ejpam-5456	70	28	more	more	ADV
ejpam-5456	70	29	accurate	accurate	ADJ
ejpam-5456	70	30	descriptions	description	NOUN
ejpam-5456	70	31	of	of	ADP
ejpam-5456	70	32	the	the	DET
ejpam-5456	70	33	electronic	electronic	ADJ
ejpam-5456	70	34	properties	property	NOUN
ejpam-5456	70	35	,	,	PUNCT
ejpam-5456	70	36	enabling	enable	VERB
ejpam-5456	70	37	better	well	ADJ
ejpam-5456	70	38	predictions	prediction	NOUN
ejpam-5456	70	39	of	of	ADP
ejpam-5456	70	40	material	material	NOUN
ejpam-5456	70	41	behavior	behavior	NOUN
ejpam-5456	70	42	.	.	PUNCT
ejpam-5456	71	1	iii	iii	X
ejpam-5456	71	2	.	.	PUNCT
ejpam-5456	71	3	quantum	quantum	ADJ
ejpam-5456	71	4	optics	optic	NOUN
ejpam-5456	71	5	:	:	PUNCT
ejpam-5456	71	6	fsdes	fsde	NOUN
ejpam-5456	71	7	are	be	AUX
ejpam-5456	71	8	applied	apply	VERB
ejpam-5456	71	9	in	in	ADP
ejpam-5456	71	10	the	the	DET
ejpam-5456	71	11	study	study	NOUN
ejpam-5456	71	12	of	of	ADP
ejpam-5456	71	13	light	light	ADJ
ejpam-5456	71	14	-	-	PUNCT
ejpam-5456	71	15	matter	matter	NOUN
ejpam-5456	71	16	interactions	interaction	NOUN
ejpam-5456	71	17	,	,	PUNCT
ejpam-5456	71	18	particularly	particularly	ADV
ejpam-5456	71	19	in	in	ADP
ejpam-5456	71	20	media	medium	NOUN
ejpam-5456	71	21	with	with	ADP
ejpam-5456	71	22	non	non	ADJ
ejpam-5456	71	23	-	-	ADJ
ejpam-5456	71	24	standard	standard	ADJ
ejpam-5456	71	25	refractive	refractive	ADJ
ejpam-5456	71	26	indices	index	NOUN
ejpam-5456	71	27	or	or	CCONJ
ejpam-5456	71	28	in	in	ADP
ejpam-5456	71	29	systems	system	NOUN
ejpam-5456	71	30	exhibiting	exhibit	VERB
ejpam-5456	71	31	anomalous	anomalous	ADJ
ejpam-5456	71	32	dispersion	dispersion	NOUN
ejpam-5456	71	33	.	.	PUNCT
ejpam-5456	72	1	this	this	PRON
ejpam-5456	72	2	can	can	AUX
ejpam-5456	72	3	lead	lead	VERB
ejpam-5456	72	4	to	to	ADP
ejpam-5456	72	5	new	new	ADJ
ejpam-5456	72	6	insights	insight	NOUN
ejpam-5456	72	7	into	into	ADP
ejpam-5456	72	8	photon	photon	NOUN
ejpam-5456	72	9	transport	transport	NOUN
ejpam-5456	72	10	and	and	CCONJ
ejpam-5456	72	11	light	light	ADJ
ejpam-5456	72	12	localization	localization	NOUN
ejpam-5456	72	13	.	.	PUNCT
ejpam-5456	73	1	iv	iv	X
ejpam-5456	73	2	.	.	PUNCT
ejpam-5456	73	3	statistical	statistical	ADJ
ejpam-5456	73	4	mechanics	mechanic	NOUN
ejpam-5456	73	5	:	:	PUNCT
ejpam-5456	73	6	in	in	ADP
ejpam-5456	73	7	statistical	statistical	ADJ
ejpam-5456	73	8	mechanics	mechanic	NOUN
ejpam-5456	73	9	,	,	PUNCT
ejpam-5456	73	10	fsdes	fsde	VERB
ejpam-5456	73	11	describe	describe	VERB
ejpam-5456	73	12	systems	system	NOUN
ejpam-5456	73	13	with	with	ADP
ejpam-5456	73	14	longrange	longrange	PROPN
ejpam-5456	73	15	interactions	interaction	NOUN
ejpam-5456	73	16	or	or	CCONJ
ejpam-5456	73	17	memory	memory	NOUN
ejpam-5456	73	18	effects	effect	NOUN
ejpam-5456	73	19	.	.	PUNCT
ejpam-5456	74	1	this	this	PRON
ejpam-5456	74	2	is	be	AUX
ejpam-5456	74	3	particularly	particularly	ADV
ejpam-5456	74	4	useful	useful	ADJ
ejpam-5456	74	5	in	in	ADP
ejpam-5456	74	6	modeling	model	VERB
ejpam-5456	74	7	complex	complex	ADJ
ejpam-5456	74	8	systems	system	NOUN
ejpam-5456	74	9	like	like	ADP
ejpam-5456	74	10	glasses	glass	NOUN
ejpam-5456	74	11	,	,	PUNCT
ejpam-5456	74	12	spin	spin	NOUN
ejpam-5456	74	13	systems	system	NOUN
ejpam-5456	74	14	,	,	PUNCT
ejpam-5456	74	15	or	or	CCONJ
ejpam-5456	74	16	in	in	ADP
ejpam-5456	74	17	understanding	understand	VERB
ejpam-5456	74	18	anomalous	anomalous	ADJ
ejpam-5456	74	19	transport	transport	NOUN
ejpam-5456	74	20	phenomena	phenomenon	NOUN
ejpam-5456	74	21	.	.	PUNCT
ejpam-5456	75	1	v.	v.	ADP
ejpam-5456	75	2	signal	signal	ADJ
ejpam-5456	75	3	processing	processing	NOUN
ejpam-5456	75	4	and	and	CCONJ
ejpam-5456	75	5	image	image	NOUN
ejpam-5456	75	6	analysis	analysis	NOUN
ejpam-5456	75	7	:	:	PUNCT
ejpam-5456	75	8	fsdes	fsde	NOUN
ejpam-5456	75	9	have	have	AUX
ejpam-5456	75	10	been	be	AUX
ejpam-5456	75	11	employed	employ	VERB
ejpam-5456	75	12	in	in	ADP
ejpam-5456	75	13	signal	signal	NOUN
ejpam-5456	75	14	processing	processing	NOUN
ejpam-5456	75	15	,	,	PUNCT
ejpam-5456	75	16	particularly	particularly	ADV
ejpam-5456	75	17	in	in	ADP
ejpam-5456	75	18	the	the	DET
ejpam-5456	75	19	analysis	analysis	NOUN
ejpam-5456	75	20	of	of	ADP
ejpam-5456	75	21	signals	signal	NOUN
ejpam-5456	75	22	with	with	ADP
ejpam-5456	75	23	fractal	fractal	ADJ
ejpam-5456	75	24	characteristics	characteristic	NOUN
ejpam-5456	75	25	or	or	CCONJ
ejpam-5456	75	26	in	in	ADP
ejpam-5456	75	27	the	the	DET
ejpam-5456	75	28	context	context	NOUN
ejpam-5456	75	29	of	of	ADP
ejpam-5456	75	30	time	time	NOUN
ejpam-5456	75	31	-	-	PUNCT
ejpam-5456	75	32	series	series	NOUN
ejpam-5456	75	33	analysis	analysis	NOUN
ejpam-5456	75	34	.	.	PUNCT
ejpam-5456	76	1	similarly	similarly	ADV
ejpam-5456	76	2	,	,	PUNCT
ejpam-5456	76	3	they	they	PRON
ejpam-5456	76	4	are	be	AUX
ejpam-5456	76	5	used	use	VERB
ejpam-5456	76	6	in	in	ADP
ejpam-5456	76	7	image	image	NOUN
ejpam-5456	76	8	processing	processing	NOUN
ejpam-5456	76	9	,	,	PUNCT
ejpam-5456	76	10	especially	especially	ADV
ejpam-5456	76	11	for	for	ADP
ejpam-5456	76	12	edge	edge	NOUN
ejpam-5456	76	13	detection	detection	NOUN
ejpam-5456	76	14	or	or	CCONJ
ejpam-5456	76	15	texture	texture	ADJ
ejpam-5456	76	16	analysis	analysis	NOUN
ejpam-5456	76	17	in	in	ADP
ejpam-5456	76	18	images	image	NOUN
ejpam-5456	76	19	with	with	ADP
ejpam-5456	76	20	irregular	irregular	ADJ
ejpam-5456	76	21	patterns	pattern	NOUN
ejpam-5456	76	22	.	.	PUNCT
ejpam-5456	77	1	vi	vi	X
ejpam-5456	77	2	.	.	X
ejpam-5456	77	3	biophysics	biophysic	NOUN
ejpam-5456	77	4	:	:	PUNCT
ejpam-5456	77	5	in	in	ADP
ejpam-5456	77	6	biological	biological	ADJ
ejpam-5456	77	7	systems	system	NOUN
ejpam-5456	77	8	where	where	SCONJ
ejpam-5456	77	9	anomalous	anomalous	ADJ
ejpam-5456	77	10	diffusion	diffusion	NOUN
ejpam-5456	77	11	or	or	CCONJ
ejpam-5456	77	12	memory	memory	NOUN
ejpam-5456	77	13	effects	effect	NOUN
ejpam-5456	77	14	are	be	AUX
ejpam-5456	77	15	present	present	ADJ
ejpam-5456	77	16	,	,	PUNCT
ejpam-5456	77	17	such	such	ADJ
ejpam-5456	77	18	as	as	ADP
ejpam-5456	77	19	in	in	ADP
ejpam-5456	77	20	the	the	DET
ejpam-5456	77	21	transport	transport	NOUN
ejpam-5456	77	22	of	of	ADP
ejpam-5456	77	23	molecules	molecule	NOUN
ejpam-5456	77	24	within	within	ADP
ejpam-5456	77	25	cellular	cellular	ADJ
ejpam-5456	77	26	environments	environment	NOUN
ejpam-5456	77	27	or	or	CCONJ
ejpam-5456	77	28	in	in	ADP
ejpam-5456	77	29	modeling	model	VERB
ejpam-5456	77	30	neuron	neuron	NOUN
ejpam-5456	77	31	dynamics	dynamic	NOUN
ejpam-5456	77	32	,	,	PUNCT
ejpam-5456	77	33	fsdes	fsde	NOUN
ejpam-5456	77	34	can	can	AUX
ejpam-5456	77	35	provide	provide	VERB
ejpam-5456	77	36	more	more	ADJ
ejpam-5456	77	37	accurate	accurate	ADJ
ejpam-5456	77	38	models	model	NOUN
ejpam-5456	77	39	.	.	PUNCT
ejpam-5456	78	1	vii	vii	PROPN
ejpam-5456	78	2	.	.	PROPN
ejpam-5456	78	3	financial	financial	ADJ
ejpam-5456	78	4	mathematics	mathematic	NOUN
ejpam-5456	78	5	:	:	PUNCT
ejpam-5456	78	6	fractional	fractional	ADJ
ejpam-5456	78	7	order	order	NOUN
ejpam-5456	78	8	models	model	NOUN
ejpam-5456	78	9	,	,	PUNCT
ejpam-5456	78	10	including	include	VERB
ejpam-5456	78	11	those	those	PRON
ejpam-5456	78	12	derived	derive	VERB
ejpam-5456	78	13	from	from	ADP
ejpam-5456	78	14	the	the	DET
ejpam-5456	78	15	sdes	sde	NOUN
ejpam-5456	78	16	,	,	PUNCT
ejpam-5456	78	17	are	be	AUX
ejpam-5456	78	18	used	use	VERB
ejpam-5456	78	19	in	in	ADP
ejpam-5456	78	20	financial	financial	ADJ
ejpam-5456	78	21	mathematics	mathematic	NOUN
ejpam-5456	78	22	to	to	PART
ejpam-5456	78	23	describe	describe	VERB
ejpam-5456	78	24	markets	market	NOUN
ejpam-5456	78	25	with	with	ADP
ejpam-5456	78	26	memory	memory	NOUN
ejpam-5456	78	27	or	or	CCONJ
ejpam-5456	78	28	to	to	PART
ejpam-5456	78	29	model	model	VERB
ejpam-5456	78	30	the	the	DET
ejpam-5456	78	31	dynamics	dynamic	NOUN
ejpam-5456	78	32	of	of	ADP
ejpam-5456	78	33	prices	price	NOUN
ejpam-5456	78	34	and	and	CCONJ
ejpam-5456	78	35	options	option	NOUN
ejpam-5456	78	36	in	in	ADP
ejpam-5456	78	37	more	more	ADV
ejpam-5456	78	38	complex	complex	ADJ
ejpam-5456	78	39	financial	financial	ADJ
ejpam-5456	78	40	environments	environment	NOUN
ejpam-5456	78	41	.	.	PUNCT
ejpam-5456	79	1	the	the	DET
ejpam-5456	79	2	solutions	solution	NOUN
ejpam-5456	79	3	to	to	ADP
ejpam-5456	79	4	fsdes	fsde	NOUN
ejpam-5456	79	5	are	be	AUX
ejpam-5456	79	6	crucial	crucial	ADJ
ejpam-5456	79	7	for	for	ADP
ejpam-5456	79	8	understanding	understanding	NOUN
ejpam-5456	79	9	,	,	PUNCT
ejpam-5456	79	10	modeling	modeling	NOUN
ejpam-5456	79	11	,	,	PUNCT
ejpam-5456	79	12	and	and	CCONJ
ejpam-5456	79	13	predicting	predict	VERB
ejpam-5456	79	14	the	the	DET
ejpam-5456	79	15	behavior	behavior	NOUN
ejpam-5456	79	16	of	of	ADP
ejpam-5456	79	17	complex	complex	ADJ
ejpam-5456	79	18	systems	system	NOUN
ejpam-5456	79	19	that	that	PRON
ejpam-5456	79	20	exhibit	exhibit	VERB
ejpam-5456	79	21	memory	memory	NOUN
ejpam-5456	79	22	effects	effect	NOUN
ejpam-5456	79	23	,	,	PUNCT
ejpam-5456	79	24	non	non	ADJ
ejpam-5456	79	25	-	-	ADJ
ejpam-5456	79	26	local	local	ADJ
ejpam-5456	79	27	interactions	interaction	NOUN
ejpam-5456	79	28	,	,	PUNCT
ejpam-5456	79	29	anomalous	anomalous	ADJ
ejpam-5456	79	30	diffusion	diffusion	NOUN
ejpam-5456	79	31	,	,	PUNCT
ejpam-5456	79	32	and	and	CCONJ
ejpam-5456	79	33	other	other	ADJ
ejpam-5456	79	34	phenomena	phenomenon	NOUN
ejpam-5456	79	35	.	.	PUNCT
ejpam-5456	80	1	in	in	ADP
ejpam-5456	80	2	the	the	DET
ejpam-5456	80	3	literature	literature	NOUN
ejpam-5456	80	4	,	,	PUNCT
ejpam-5456	80	5	the	the	DET
ejpam-5456	80	6	sde	sde	PROPN
ejpam-5456	80	7	has	have	AUX
ejpam-5456	80	8	been	be	AUX
ejpam-5456	80	9	solved	solve	VERB
ejpam-5456	80	10	using	use	VERB
ejpam-5456	80	11	fractional	fractional	ADJ
ejpam-5456	80	12	derivatives	derivative	NOUN
ejpam-5456	80	13	represented	represent	VERB
ejpam-5456	80	14	in	in	ADP
ejpam-5456	80	15	the	the	DET
ejpam-5456	80	16	form	form	NOUN
ejpam-5456	80	17	of	of	ADP
ejpam-5456	80	18	the	the	DET
ejpam-5456	80	19	cap	cap	NOUN
ejpam-5456	80	20	-	-	PUNCT
ejpam-5456	80	21	fd	fd	NOUN
ejpam-5456	80	22	.	.	PUNCT
ejpam-5456	81	1	for	for	ADP
ejpam-5456	81	2	example	example	NOUN
ejpam-5456	81	3	,	,	PUNCT
ejpam-5456	81	4	fsdes	fsde	NOUN
ejpam-5456	81	5	have	have	VERB
ejpam-5456	81	6	m.i	m.i	PROPN
ejpam-5456	81	7	.	.	PROPN
ejpam-5456	81	8	liaqat	liaqat	PROPN
ejpam-5456	81	9	,	,	PUNCT
ejpam-5456	81	10	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	81	11	/	/	SYM
ejpam-5456	81	12	eur	eur	PROPN
ejpam-5456	81	13	.	.	PUNCT
ejpam-5456	82	1	j.	j.	PROPN
ejpam-5456	82	2	pure	pure	PROPN
ejpam-5456	82	3	appl	appl	PROPN
ejpam-5456	82	4	.	.	PROPN
ejpam-5456	82	5	math	math	PROPN
ejpam-5456	82	6	,	,	PUNCT
ejpam-5456	82	7	17	17	NUM
ejpam-5456	82	8	(	(	PUNCT
ejpam-5456	82	9	4	4	NUM
ejpam-5456	82	10	)	)	PUNCT
ejpam-5456	82	11	(	(	PUNCT
ejpam-5456	82	12	2024	2024	NUM
ejpam-5456	82	13	)	)	PUNCT
ejpam-5456	82	14	,	,	PUNCT
ejpam-5456	82	15	3464	3464	NUM
ejpam-5456	82	16	-	-	SYM
ejpam-5456	82	17	3491	3491	NUM
ejpam-5456	82	18	3468	3468	NUM
ejpam-5456	82	19	been	be	AUX
ejpam-5456	82	20	solved	solve	VERB
ejpam-5456	82	21	using	use	VERB
ejpam-5456	82	22	various	various	ADJ
ejpam-5456	82	23	methods	method	NOUN
ejpam-5456	82	24	[	[	X
ejpam-5456	82	25	7	7	NUM
ejpam-5456	82	26	,	,	PUNCT
ejpam-5456	82	27	11	11	NUM
ejpam-5456	82	28	,	,	PUNCT
ejpam-5456	82	29	13	13	NUM
ejpam-5456	82	30	,	,	PUNCT
ejpam-5456	82	31	22	22	NUM
ejpam-5456	82	32	,	,	PUNCT
ejpam-5456	82	33	25	25	NUM
ejpam-5456	82	34	,	,	PUNCT
ejpam-5456	82	35	29	29	NUM
ejpam-5456	82	36	,	,	PUNCT
ejpam-5456	82	37	36	36	NUM
ejpam-5456	82	38	]	]	PUNCT
ejpam-5456	82	39	.	.	PUNCT
ejpam-5456	83	1	however	however	ADV
ejpam-5456	83	2	,	,	PUNCT
ejpam-5456	83	3	the	the	DET
ejpam-5456	83	4	algorithms	algorithm	NOUN
ejpam-5456	83	5	of	of	ADP
ejpam-5456	83	6	each	each	PRON
ejpam-5456	83	7	of	of	ADP
ejpam-5456	83	8	these	these	DET
ejpam-5456	83	9	methods	method	NOUN
ejpam-5456	83	10	have	have	AUX
ejpam-5456	83	11	been	be	AUX
ejpam-5456	83	12	applied	apply	VERB
ejpam-5456	83	13	in	in	ADP
ejpam-5456	83	14	the	the	DET
ejpam-5456	83	15	sense	sense	NOUN
ejpam-5456	83	16	of	of	ADP
ejpam-5456	83	17	caputo	caputo	PROPN
ejpam-5456	83	18	derivatives	derivative	NOUN
ejpam-5456	83	19	.	.	PUNCT
ejpam-5456	84	1	no	no	DET
ejpam-5456	84	2	research	research	NOUN
ejpam-5456	84	3	work	work	NOUN
ejpam-5456	84	4	has	have	AUX
ejpam-5456	84	5	yet	yet	ADV
ejpam-5456	84	6	solved	solve	VERB
ejpam-5456	84	7	fsdes	fsde	NOUN
ejpam-5456	84	8	using	use	VERB
ejpam-5456	84	9	the	the	DET
ejpam-5456	84	10	adomian	adomian	NOUN
ejpam-5456	84	11	decomposition	decomposition	NOUN
ejpam-5456	84	12	method	method	NOUN
ejpam-5456	84	13	(	(	PUNCT
ejpam-5456	84	14	adm	adm	PROPN
ejpam-5456	84	15	)	)	PUNCT
ejpam-5456	84	16	with	with	ADP
ejpam-5456	84	17	the	the	DET
ejpam-5456	84	18	sumudu	sumudu	NOUN
ejpam-5456	84	19	transform	transform	NOUN
ejpam-5456	84	20	(	(	PUNCT
ejpam-5456	84	21	st	st	NOUN
ejpam-5456	84	22	)	)	PUNCT
ejpam-5456	84	23	in	in	ADP
ejpam-5456	84	24	the	the	DET
ejpam-5456	84	25	sense	sense	NOUN
ejpam-5456	84	26	of	of	ADP
ejpam-5456	84	27	con	con	NOUN
ejpam-5456	84	28	-	-	PUNCT
ejpam-5456	84	29	frd	frd	ADJ
ejpam-5456	84	30	.	.	PUNCT
ejpam-5456	85	1	in	in	ADP
ejpam-5456	85	2	this	this	DET
ejpam-5456	85	3	research	research	NOUN
ejpam-5456	85	4	,	,	PUNCT
ejpam-5456	85	5	we	we	PRON
ejpam-5456	85	6	addressed	address	VERB
ejpam-5456	85	7	this	this	DET
ejpam-5456	85	8	gap	gap	NOUN
ejpam-5456	85	9	by	by	ADP
ejpam-5456	85	10	solving	solve	VERB
ejpam-5456	85	11	linear	linear	NOUN
ejpam-5456	85	12	and	and	CCONJ
ejpam-5456	85	13	nonlinear	nonlinear	ADJ
ejpam-5456	85	14	fsdes	fsde	NOUN
ejpam-5456	85	15	using	use	VERB
ejpam-5456	85	16	a	a	DET
ejpam-5456	85	17	hybrid	hybrid	ADJ
ejpam-5456	85	18	approach	approach	NOUN
ejpam-5456	85	19	that	that	PRON
ejpam-5456	85	20	combines	combine	VERB
ejpam-5456	85	21	adm	adm	PROPN
ejpam-5456	85	22	and	and	CCONJ
ejpam-5456	85	23	st	st	PROPN
ejpam-5456	85	24	,	,	PUNCT
ejpam-5456	85	25	applied	apply	VERB
ejpam-5456	85	26	in	in	ADP
ejpam-5456	85	27	the	the	DET
ejpam-5456	85	28	sense	sense	NOUN
ejpam-5456	85	29	of	of	ADP
ejpam-5456	85	30	con	con	NOUN
ejpam-5456	85	31	-	-	PUNCT
ejpam-5456	85	32	frd	frd	ADJ
ejpam-5456	85	33	.	.	PUNCT
ejpam-5456	86	1	we	we	PRON
ejpam-5456	86	2	refer	refer	VERB
ejpam-5456	86	3	to	to	ADP
ejpam-5456	86	4	it	it	PRON
ejpam-5456	86	5	as	as	ADP
ejpam-5456	86	6	the	the	DET
ejpam-5456	86	7	sumudu	sumudu	NOUN
ejpam-5456	86	8	adomian	adomian	NOUN
ejpam-5456	86	9	decomposition	decomposition	NOUN
ejpam-5456	86	10	method	method	NOUN
ejpam-5456	86	11	(	(	PUNCT
ejpam-5456	86	12	sadm	sadm	ADJ
ejpam-5456	86	13	)	)	PUNCT
ejpam-5456	86	14	.	.	PUNCT
ejpam-5456	87	1	moreover	moreover	ADV
ejpam-5456	87	2	,	,	PUNCT
ejpam-5456	87	3	the	the	DET
ejpam-5456	87	4	correctness	correctness	NOUN
ejpam-5456	87	5	of	of	ADP
ejpam-5456	87	6	sadm	sadm	ADJ
ejpam-5456	87	7	is	be	AUX
ejpam-5456	87	8	assessed	assess	VERB
ejpam-5456	87	9	through	through	ADP
ejpam-5456	87	10	an	an	DET
ejpam-5456	87	11	examination	examination	NOUN
ejpam-5456	87	12	of	of	ADP
ejpam-5456	87	13	absolute	absolute	ADJ
ejpam-5456	87	14	errors	error	NOUN
ejpam-5456	87	15	(	(	PUNCT
ejpam-5456	87	16	abs	ab	NOUN
ejpam-5456	87	17	-	-	PUNCT
ejpam-5456	87	18	e	e	NOUN
ejpam-5456	87	19	)	)	PUNCT
ejpam-5456	87	20	and	and	CCONJ
ejpam-5456	87	21	relative	relative	ADJ
ejpam-5456	87	22	errors	error	NOUN
ejpam-5456	87	23	(	(	PUNCT
ejpam-5456	87	24	rel	rel	NOUN
ejpam-5456	87	25	-	-	PUNCT
ejpam-5456	87	26	e	e	NOUN
ejpam-5456	87	27	)	)	PUNCT
ejpam-5456	87	28	presented	present	VERB
ejpam-5456	87	29	in	in	ADP
ejpam-5456	87	30	both	both	CCONJ
ejpam-5456	87	31	numerical	numerical	ADJ
ejpam-5456	87	32	and	and	CCONJ
ejpam-5456	87	33	graphical	graphical	ADJ
ejpam-5456	87	34	representations	representation	NOUN
ejpam-5456	87	35	.	.	PUNCT
ejpam-5456	88	1	it	it	PRON
ejpam-5456	88	2	is	be	AUX
ejpam-5456	88	3	observed	observe	VERB
ejpam-5456	88	4	that	that	SCONJ
ejpam-5456	88	5	the	the	DET
ejpam-5456	88	6	approximate	approximate	ADJ
ejpam-5456	88	7	solution	solution	NOUN
ejpam-5456	88	8	(	(	PUNCT
ejpam-5456	88	9	app	app	PROPN
ejpam-5456	88	10	-	-	PUNCT
ejpam-5456	88	11	s	s	NOUN
ejpam-5456	88	12	)	)	PUNCT
ejpam-5456	88	13	rapidly	rapidly	ADV
ejpam-5456	88	14	approaches	approach	VERB
ejpam-5456	88	15	the	the	DET
ejpam-5456	88	16	exact	exact	ADJ
ejpam-5456	88	17	solution	solution	NOUN
ejpam-5456	88	18	(	(	PUNCT
ejpam-5456	88	19	ex	ex	NOUN
ejpam-5456	88	20	-	-	NOUN
ejpam-5456	88	21	s	s	NOUN
ejpam-5456	88	22	)	)	PUNCT
ejpam-5456	88	23	,	,	PUNCT
ejpam-5456	88	24	as	as	SCONJ
ejpam-5456	88	25	evidenced	evidence	VERB
ejpam-5456	88	26	by	by	ADP
ejpam-5456	88	27	the	the	DET
ejpam-5456	88	28	evaluation	evaluation	NOUN
ejpam-5456	88	29	of	of	ADP
ejpam-5456	88	30	2d	2d	NUM
ejpam-5456	88	31	and	and	CCONJ
ejpam-5456	88	32	3d	3d	NUM
ejpam-5456	88	33	graphs	graph	NOUN
ejpam-5456	88	34	across	across	ADP
ejpam-5456	88	35	various	various	ADJ
ejpam-5456	88	36	fractional	fractional	ADJ
ejpam-5456	88	37	-	-	PUNCT
ejpam-5456	88	38	order	order	NOUN
ejpam-5456	88	39	values	value	NOUN
ejpam-5456	88	40	.	.	PUNCT
ejpam-5456	89	1	the	the	DET
ejpam-5456	89	2	numerical	numerical	ADJ
ejpam-5456	89	3	and	and	CCONJ
ejpam-5456	89	4	graphical	graphical	ADJ
ejpam-5456	89	5	findings	finding	NOUN
ejpam-5456	89	6	confirm	confirm	VERB
ejpam-5456	89	7	the	the	DET
ejpam-5456	89	8	notable	notable	ADJ
ejpam-5456	89	9	precision	precision	NOUN
ejpam-5456	89	10	and	and	CCONJ
ejpam-5456	89	11	effectiveness	effectiveness	NOUN
ejpam-5456	89	12	of	of	ADP
ejpam-5456	89	13	sadm	sadm	ADJ
ejpam-5456	89	14	.	.	PUNCT
ejpam-5456	90	1	in	in	ADP
ejpam-5456	90	2	addition	addition	NOUN
ejpam-5456	90	3	,	,	PUNCT
ejpam-5456	90	4	the	the	DET
ejpam-5456	90	5	results	result	NOUN
ejpam-5456	90	6	obtained	obtain	VERB
ejpam-5456	90	7	using	use	VERB
ejpam-5456	90	8	sadm	sadm	ADV
ejpam-5456	90	9	are	be	AUX
ejpam-5456	90	10	compared	compare	VERB
ejpam-5456	90	11	with	with	ADP
ejpam-5456	90	12	other	other	ADJ
ejpam-5456	90	13	methods	method	NOUN
ejpam-5456	90	14	,	,	PUNCT
ejpam-5456	90	15	such	such	ADJ
ejpam-5456	90	16	as	as	ADP
ejpam-5456	90	17	the	the	DET
ejpam-5456	90	18	rpsm	rpsm	NOUN
ejpam-5456	90	19	[	[	X
ejpam-5456	90	20	37	37	NUM
ejpam-5456	90	21	]	]	PUNCT
ejpam-5456	90	22	and	and	CCONJ
ejpam-5456	90	23	ham	ham	NOUN
ejpam-5456	91	1	[	[	X
ejpam-5456	91	2	14	14	NUM
ejpam-5456	91	3	]	]	PUNCT
ejpam-5456	91	4	.	.	PUNCT
ejpam-5456	92	1	the	the	DET
ejpam-5456	92	2	comparison	comparison	NOUN
ejpam-5456	92	3	shows	show	VERB
ejpam-5456	92	4	excellent	excellent	ADJ
ejpam-5456	92	5	agreement	agreement	NOUN
ejpam-5456	92	6	with	with	ADP
ejpam-5456	92	7	these	these	DET
ejpam-5456	92	8	methods	method	NOUN
ejpam-5456	92	9	,	,	PUNCT
ejpam-5456	92	10	indicating	indicate	VERB
ejpam-5456	92	11	that	that	SCONJ
ejpam-5456	92	12	sadm	sadm	ADJ
ejpam-5456	92	13	is	be	AUX
ejpam-5456	92	14	a	a	DET
ejpam-5456	92	15	suitable	suitable	ADJ
ejpam-5456	92	16	alternative	alternative	NOUN
ejpam-5456	92	17	to	to	ADP
ejpam-5456	92	18	cap	cap	NOUN
ejpam-5456	92	19	-	-	PUNCT
ejpam-5456	92	20	fd	fd	NOUN
ejpam-5456	92	21	-	-	PUNCT
ejpam-5456	92	22	based	base	VERB
ejpam-5456	92	23	approaches	approach	NOUN
ejpam-5456	92	24	for	for	ADP
ejpam-5456	92	25	solving	solve	VERB
ejpam-5456	92	26	fsdes	fsde	NOUN
ejpam-5456	92	27	.	.	PUNCT
ejpam-5456	93	1	furthermore	furthermore	ADV
ejpam-5456	93	2	,	,	PUNCT
ejpam-5456	93	3	we	we	PRON
ejpam-5456	93	4	can	can	AUX
ejpam-5456	93	5	conclude	conclude	VERB
ejpam-5456	93	6	that	that	SCONJ
ejpam-5456	93	7	con	con	PROPN
ejpam-5456	93	8	-	-	PUNCT
ejpam-5456	93	9	fd	fd	PROPN
ejpam-5456	93	10	is	be	AUX
ejpam-5456	93	11	a	a	DET
ejpam-5456	93	12	suitable	suitable	ADJ
ejpam-5456	93	13	alternative	alternative	NOUN
ejpam-5456	93	14	to	to	ADP
ejpam-5456	93	15	cap	cap	NOUN
ejpam-5456	93	16	-	-	PUNCT
ejpam-5456	93	17	fd	fd	NOUN
ejpam-5456	93	18	in	in	ADP
ejpam-5456	93	19	modeling	modeling	NOUN
ejpam-5456	93	20	fsdes	fsde	NOUN
ejpam-5456	93	21	.	.	PUNCT
ejpam-5456	94	1	our	our	PRON
ejpam-5456	94	2	method	method	NOUN
ejpam-5456	94	3	also	also	ADV
ejpam-5456	94	4	has	have	VERB
ejpam-5456	94	5	an	an	DET
ejpam-5456	94	6	assumption	assumption	NOUN
ejpam-5456	94	7	.	.	PUNCT
ejpam-5456	95	1	to	to	PART
ejpam-5456	95	2	obtain	obtain	VERB
ejpam-5456	95	3	the	the	DET
ejpam-5456	95	4	solution	solution	NOUN
ejpam-5456	95	5	in	in	ADP
ejpam-5456	95	6	the	the	DET
ejpam-5456	95	7	original	original	ADJ
ejpam-5456	95	8	space	space	NOUN
ejpam-5456	95	9	,	,	PUNCT
ejpam-5456	95	10	sadm	sadm	ADJ
ejpam-5456	95	11	first	first	ADV
ejpam-5456	95	12	requires	require	VERB
ejpam-5456	95	13	finding	find	VERB
ejpam-5456	95	14	the	the	DET
ejpam-5456	95	15	st	st	PROPN
ejpam-5456	95	16	of	of	ADP
ejpam-5456	95	17	the	the	DET
ejpam-5456	95	18	target	target	NOUN
ejpam-5456	95	19	equations	equation	NOUN
ejpam-5456	95	20	and	and	CCONJ
ejpam-5456	95	21	then	then	ADV
ejpam-5456	95	22	performing	perform	VERB
ejpam-5456	95	23	the	the	DET
ejpam-5456	95	24	inverse	inverse	NOUN
ejpam-5456	95	25	st	st	PROPN
ejpam-5456	95	26	.	.	PROPN
ejpam-5456	95	27	consequently	consequently	ADV
ejpam-5456	95	28	,	,	PUNCT
ejpam-5456	95	29	for	for	ADP
ejpam-5456	95	30	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5456	95	31	equations	equation	NOUN
ejpam-5456	95	32	,	,	PUNCT
ejpam-5456	95	33	the	the	DET
ejpam-5456	95	34	source	source	NOUN
ejpam-5456	95	35	functions	function	NOUN
ejpam-5456	95	36	must	must	AUX
ejpam-5456	95	37	be	be	AUX
ejpam-5456	95	38	piecewise	piecewise	NOUN
ejpam-5456	95	39	continuous	continuous	ADJ
ejpam-5456	95	40	and	and	CCONJ
ejpam-5456	95	41	of	of	ADP
ejpam-5456	95	42	exponential	exponential	ADJ
ejpam-5456	95	43	order	order	NOUN
ejpam-5456	95	44	,	,	PUNCT
ejpam-5456	95	45	and	and	CCONJ
ejpam-5456	95	46	the	the	DET
ejpam-5456	95	47	inverse	inverse	NOUN
ejpam-5456	95	48	st	st	PROPN
ejpam-5456	95	49	must	must	AUX
ejpam-5456	95	50	exist	exist	VERB
ejpam-5456	95	51	after	after	ADP
ejpam-5456	95	52	computations	computation	NOUN
ejpam-5456	95	53	.	.	PUNCT
ejpam-5456	96	1	the	the	DET
ejpam-5456	96	2	st	st	PROPN
ejpam-5456	96	3	is	be	AUX
ejpam-5456	96	4	defined	define	VERB
ejpam-5456	96	5	for	for	ADP
ejpam-5456	96	6	exponentially	exponentially	ADV
ejpam-5456	96	7	ordered	order	VERB
ejpam-5456	96	8	functions	function	NOUN
ejpam-5456	96	9	.	.	PUNCT
ejpam-5456	97	1	we	we	PRON
ejpam-5456	97	2	examine	examine	VERB
ejpam-5456	97	3	functions	function	NOUN
ejpam-5456	97	4	that	that	PRON
ejpam-5456	97	5	are	be	AUX
ejpam-5456	97	6	defined	define	VERB
ejpam-5456	97	7	within	within	ADP
ejpam-5456	97	8	the	the	DET
ejpam-5456	97	9	set	set	NOUN
ejpam-5456	97	10	q.	q.	NOUN
ejpam-5456	97	11	q	q	PROPN
ejpam-5456	98	1	=	=	PUNCT
ejpam-5456	98	2	{	{	PUNCT
ejpam-5456	98	3	δ(φ)|∃p	δ(φ)|∃p	PROPN
ejpam-5456	98	4	,	,	PUNCT
ejpam-5456	98	5	h1,h2	h1,h2	PROPN
ejpam-5456	98	6	>	>	X
ejpam-5456	98	7	0	0	PROPN
ejpam-5456	98	8	,	,	PUNCT
ejpam-5456	98	9	|δ(φ	|δ(φ	PROPN
ejpam-5456	98	10	)	)	PUNCT
ejpam-5456	98	11	<	<	X
ejpam-5456	98	12	p	p	X
ejpam-5456	98	13	exp	exp	NOUN
ejpam-5456	98	14	|φ|	|φ|	PROPN
ejpam-5456	98	15	hℓ	hℓ	INTJ
ejpam-5456	98	16	if	if	SCONJ
ejpam-5456	98	17	δ	δ	PROPN
ejpam-5456	98	18	∈	∈	PROPN
ejpam-5456	98	19	(	(	PUNCT
ejpam-5456	98	20	−1)ℓ	−1)ℓ	X
ejpam-5456	98	21	×	×	NOUN
ejpam-5456	98	22	[	[	X
ejpam-5456	98	23	0,∞	0,∞	NOUN
ejpam-5456	98	24	)	)	PUNCT
ejpam-5456	98	25	}	}	PUNCT
ejpam-5456	98	26	.	.	PUNCT
ejpam-5456	99	1	the	the	DET
ejpam-5456	99	2	constant	constant	ADJ
ejpam-5456	99	3	p	p	NOUN
ejpam-5456	99	4	for	for	ADP
ejpam-5456	99	5	a	a	DET
ejpam-5456	99	6	given	give	VERB
ejpam-5456	99	7	function	function	NOUN
ejpam-5456	99	8	in	in	ADP
ejpam-5456	99	9	the	the	DET
ejpam-5456	99	10	set	set	NOUN
ejpam-5456	99	11	q	q	PROPN
ejpam-5456	99	12	must	must	AUX
ejpam-5456	99	13	be	be	AUX
ejpam-5456	99	14	a	a	DET
ejpam-5456	99	15	finite	finite	ADJ
ejpam-5456	99	16	value	value	NOUN
ejpam-5456	99	17	.	.	PUNCT
ejpam-5456	100	1	the	the	DET
ejpam-5456	100	2	st	st	PROPN
ejpam-5456	100	3	is	be	AUX
ejpam-5456	100	4	defined	define	VERB
ejpam-5456	100	5	as	as	SCONJ
ejpam-5456	100	6	follows	follow	VERB
ejpam-5456	100	7	[	[	X
ejpam-5456	100	8	10	10	NUM
ejpam-5456	100	9	]	]	X
ejpam-5456	100	10	:	:	PUNCT
ejpam-5456	100	11	sµ[δ(φ	sµ[δ(φ	PROPN
ejpam-5456	100	12	)	)	PUNCT
ejpam-5456	100	13	]	]	PUNCT
ejpam-5456	101	1	=	=	PUNCT
ejpam-5456	101	2	δ∗(ω	δ∗(ω	PROPN
ejpam-5456	101	3	)	)	PUNCT
ejpam-5456	101	4	=	=	SYM
ejpam-5456	101	5	1	1	NUM
ejpam-5456	101	6	ω	ω	NUM
ejpam-5456	101	7	∫	∫	PROPN
ejpam-5456	101	8	∞	∞	PROPN
ejpam-5456	101	9	0	0	NUM
ejpam-5456	102	1	δ(φ	δ(φ	NOUN
ejpam-5456	102	2	)	)	PUNCT
ejpam-5456	102	3	exp	exp	NOUN
ejpam-5456	102	4	−φµ	−φµ	PROPN
ejpam-5456	102	5	µω	µω	PROPN
ejpam-5456	102	6	dµφ	dµφ	PROPN
ejpam-5456	102	7	,	,	PUNCT
ejpam-5456	102	8	ω	ω	PROPN
ejpam-5456	102	9	∈	∈	PROPN
ejpam-5456	102	10	(	(	PUNCT
ejpam-5456	102	11	−h1,h2	−h1,h2	PROPN
ejpam-5456	102	12	)	)	PUNCT
ejpam-5456	102	13	.	.	PUNCT
ejpam-5456	103	1	the	the	DET
ejpam-5456	103	2	adm	adm	PROPN
ejpam-5456	103	3	is	be	AUX
ejpam-5456	103	4	a	a	DET
ejpam-5456	103	5	powerful	powerful	ADJ
ejpam-5456	103	6	technique	technique	NOUN
ejpam-5456	103	7	for	for	ADP
ejpam-5456	103	8	solving	solve	VERB
ejpam-5456	103	9	des	des	PROPN
ejpam-5456	103	10	,	,	PUNCT
ejpam-5456	103	11	including	include	VERB
ejpam-5456	103	12	fodes	fode	NOUN
ejpam-5456	103	13	.	.	PUNCT
ejpam-5456	104	1	it	it	PRON
ejpam-5456	104	2	is	be	AUX
ejpam-5456	104	3	particularly	particularly	ADV
ejpam-5456	104	4	useful	useful	ADJ
ejpam-5456	104	5	for	for	ADP
ejpam-5456	104	6	handling	handle	VERB
ejpam-5456	104	7	non	non	ADJ
ejpam-5456	104	8	-	-	ADJ
ejpam-5456	104	9	linear	linear	ADJ
ejpam-5456	104	10	des	de	NOUN
ejpam-5456	104	11	and	and	CCONJ
ejpam-5456	104	12	can	can	AUX
ejpam-5456	104	13	be	be	AUX
ejpam-5456	104	14	adapted	adapt	VERB
ejpam-5456	104	15	to	to	ADP
ejpam-5456	104	16	the	the	DET
ejpam-5456	104	17	fractional	fractional	ADJ
ejpam-5456	104	18	-	-	PUNCT
ejpam-5456	104	19	order	order	NOUN
ejpam-5456	104	20	case	case	NOUN
ejpam-5456	104	21	.	.	PUNCT
ejpam-5456	105	1	adm	adm	NOUN
ejpam-5456	105	2	involves	involve	VERB
ejpam-5456	105	3	decomposing	decompose	VERB
ejpam-5456	105	4	the	the	DET
ejpam-5456	105	5	solution	solution	NOUN
ejpam-5456	105	6	of	of	ADP
ejpam-5456	105	7	a	a	DET
ejpam-5456	105	8	de	de	NOUN
ejpam-5456	105	9	into	into	ADP
ejpam-5456	105	10	a	a	DET
ejpam-5456	105	11	series	series	NOUN
ejpam-5456	105	12	of	of	ADP
ejpam-5456	105	13	simpler	simple	ADJ
ejpam-5456	105	14	functions	function	NOUN
ejpam-5456	105	15	,	,	PUNCT
ejpam-5456	105	16	making	make	VERB
ejpam-5456	105	17	it	it	PRON
ejpam-5456	105	18	easier	easy	ADJ
ejpam-5456	105	19	to	to	PART
ejpam-5456	105	20	solve	solve	VERB
ejpam-5456	105	21	the	the	DET
ejpam-5456	105	22	equation	equation	NOUN
ejpam-5456	105	23	iteratively	iteratively	ADV
ejpam-5456	105	24	.	.	PUNCT
ejpam-5456	106	1	the	the	DET
ejpam-5456	106	2	main	main	ADJ
ejpam-5456	106	3	idea	idea	NOUN
ejpam-5456	106	4	is	be	AUX
ejpam-5456	106	5	to	to	PART
ejpam-5456	106	6	break	break	VERB
ejpam-5456	106	7	down	down	ADP
ejpam-5456	106	8	the	the	DET
ejpam-5456	106	9	problem	problem	NOUN
ejpam-5456	106	10	into	into	ADP
ejpam-5456	106	11	manageable	manageable	ADJ
ejpam-5456	106	12	components	component	NOUN
ejpam-5456	106	13	.	.	PUNCT
ejpam-5456	107	1	the	the	DET
ejpam-5456	107	2	adm	adm	PROPN
ejpam-5456	107	3	holds	hold	VERB
ejpam-5456	107	4	significant	significant	ADJ
ejpam-5456	107	5	importance	importance	NOUN
ejpam-5456	107	6	in	in	ADP
ejpam-5456	107	7	solving	solve	VERB
ejpam-5456	107	8	fodes	fode	NOUN
ejpam-5456	107	9	due	due	ADJ
ejpam-5456	107	10	to	to	ADP
ejpam-5456	107	11	several	several	ADJ
ejpam-5456	107	12	key	key	ADJ
ejpam-5456	107	13	advantages	advantage	NOUN
ejpam-5456	107	14	and	and	CCONJ
ejpam-5456	107	15	features	feature	NOUN
ejpam-5456	107	16	.	.	PUNCT
ejpam-5456	108	1	fodes	fode	NOUN
ejpam-5456	108	2	often	often	ADV
ejpam-5456	108	3	include	include	VERB
ejpam-5456	108	4	non	non	ADJ
ejpam-5456	108	5	-	-	ADJ
ejpam-5456	108	6	linear	linear	ADJ
ejpam-5456	108	7	terms	term	NOUN
ejpam-5456	108	8	that	that	PRON
ejpam-5456	108	9	can	can	AUX
ejpam-5456	108	10	be	be	AUX
ejpam-5456	108	11	challenging	challenge	VERB
ejpam-5456	108	12	to	to	PART
ejpam-5456	108	13	solve	solve	VERB
ejpam-5456	108	14	using	use	VERB
ejpam-5456	108	15	traditional	traditional	ADJ
ejpam-5456	108	16	methods	method	NOUN
ejpam-5456	108	17	.	.	PUNCT
ejpam-5456	109	1	adm	adm	PROPN
ejpam-5456	109	2	effectively	effectively	ADV
ejpam-5456	109	3	decomposes	decompose	VERB
ejpam-5456	109	4	these	these	DET
ejpam-5456	109	5	non	non	ADJ
ejpam-5456	109	6	-	-	ADJ
ejpam-5456	109	7	linear	linear	ADJ
ejpam-5456	109	8	terms	term	NOUN
ejpam-5456	109	9	into	into	ADP
ejpam-5456	109	10	simpler	simple	ADJ
ejpam-5456	109	11	components	component	NOUN
ejpam-5456	109	12	using	use	VERB
ejpam-5456	109	13	adomian	adomian	NOUN
ejpam-5456	109	14	polynomials	polynomial	NOUN
ejpam-5456	109	15	,	,	PUNCT
ejpam-5456	109	16	making	make	VERB
ejpam-5456	109	17	it	it	PRON
ejpam-5456	109	18	easier	easy	ADJ
ejpam-5456	109	19	to	to	PART
ejpam-5456	109	20	find	find	VERB
ejpam-5456	109	21	solutions	solution	NOUN
ejpam-5456	109	22	even	even	ADV
ejpam-5456	109	23	when	when	SCONJ
ejpam-5456	109	24	the	the	DET
ejpam-5456	109	25	equations	equation	NOUN
ejpam-5456	109	26	are	be	AUX
ejpam-5456	109	27	highly	highly	ADV
ejpam-5456	109	28	non	non	ADJ
ejpam-5456	109	29	-	-	ADJ
ejpam-5456	109	30	linear	linear	ADJ
ejpam-5456	109	31	.	.	PUNCT
ejpam-5456	110	1	adm	adm	PROPN
ejpam-5456	110	2	provides	provide	VERB
ejpam-5456	110	3	a	a	DET
ejpam-5456	110	4	systematic	systematic	ADJ
ejpam-5456	110	5	framework	framework	NOUN
ejpam-5456	110	6	for	for	ADP
ejpam-5456	110	7	solving	solve	VERB
ejpam-5456	110	8	fodes	fode	NOUN
ejpam-5456	110	9	by	by	ADP
ejpam-5456	110	10	breaking	break	VERB
ejpam-5456	110	11	down	down	ADP
ejpam-5456	110	12	the	the	DET
ejpam-5456	110	13	problem	problem	NOUN
ejpam-5456	110	14	into	into	ADP
ejpam-5456	110	15	a	a	DET
ejpam-5456	110	16	series	series	NOUN
ejpam-5456	110	17	of	of	ADP
ejpam-5456	110	18	simpler	simple	ADJ
ejpam-5456	110	19	problems	problem	NOUN
ejpam-5456	110	20	.	.	PUNCT
ejpam-5456	111	1	this	this	DET
ejpam-5456	111	2	approach	approach	NOUN
ejpam-5456	111	3	allows	allow	VERB
ejpam-5456	111	4	for	for	ADP
ejpam-5456	111	5	an	an	DET
ejpam-5456	111	6	iterative	iterative	NOUN
ejpam-5456	111	7	solution	solution	NOUN
ejpam-5456	111	8	where	where	SCONJ
ejpam-5456	111	9	each	each	DET
ejpam-5456	111	10	term	term	NOUN
ejpam-5456	111	11	in	in	ADP
ejpam-5456	111	12	the	the	DET
ejpam-5456	111	13	series	series	NOUN
ejpam-5456	111	14	is	be	AUX
ejpam-5456	111	15	computed	compute	VERB
ejpam-5456	111	16	sequentially	sequentially	ADV
ejpam-5456	111	17	,	,	PUNCT
ejpam-5456	111	18	making	make	VERB
ejpam-5456	111	19	it	it	PRON
ejpam-5456	111	20	easier	easy	ADJ
ejpam-5456	111	21	to	to	PART
ejpam-5456	111	22	handle	handle	VERB
ejpam-5456	111	23	complex	complex	ADJ
ejpam-5456	111	24	des	des	PROPN
ejpam-5456	111	25	.	.	PUNCT
ejpam-5456	112	1	the	the	DET
ejpam-5456	112	2	method	method	NOUN
ejpam-5456	112	3	is	be	AUX
ejpam-5456	112	4	flexible	flexible	ADJ
ejpam-5456	112	5	and	and	CCONJ
ejpam-5456	112	6	can	can	AUX
ejpam-5456	112	7	be	be	AUX
ejpam-5456	112	8	applied	apply	VERB
ejpam-5456	112	9	to	to	ADP
ejpam-5456	112	10	a	a	DET
ejpam-5456	112	11	wide	wide	ADJ
ejpam-5456	112	12	range	range	NOUN
ejpam-5456	112	13	of	of	ADP
ejpam-5456	112	14	fodes	fode	NOUN
ejpam-5456	112	15	,	,	PUNCT
ejpam-5456	112	16	including	include	VERB
ejpam-5456	112	17	those	those	PRON
ejpam-5456	112	18	with	with	ADP
ejpam-5456	112	19	complex	complex	ADJ
ejpam-5456	112	20	boundary	boundary	ADJ
ejpam-5456	112	21	m.i	m.i	PROPN
ejpam-5456	112	22	.	.	PROPN
ejpam-5456	112	23	liaqat	liaqat	PROPN
ejpam-5456	112	24	,	,	PUNCT
ejpam-5456	112	25	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	112	26	/	/	SYM
ejpam-5456	112	27	eur	eur	PROPN
ejpam-5456	112	28	.	.	PUNCT
ejpam-5456	113	1	j.	j.	PROPN
ejpam-5456	113	2	pure	pure	PROPN
ejpam-5456	113	3	appl	appl	PROPN
ejpam-5456	113	4	.	.	PROPN
ejpam-5456	113	5	math	math	PROPN
ejpam-5456	113	6	,	,	PUNCT
ejpam-5456	113	7	17	17	NUM
ejpam-5456	113	8	(	(	PUNCT
ejpam-5456	113	9	4	4	NUM
ejpam-5456	113	10	)	)	PUNCT
ejpam-5456	113	11	(	(	PUNCT
ejpam-5456	113	12	2024	2024	NUM
ejpam-5456	113	13	)	)	PUNCT
ejpam-5456	113	14	,	,	PUNCT
ejpam-5456	113	15	3464	3464	NUM
ejpam-5456	113	16	-	-	SYM
ejpam-5456	113	17	3491	3491	NUM
ejpam-5456	113	18	3469	3469	NUM
ejpam-5456	113	19	conditions	condition	NOUN
ejpam-5456	113	20	and	and	CCONJ
ejpam-5456	113	21	variable	variable	ADJ
ejpam-5456	113	22	coefficients	coefficient	NOUN
ejpam-5456	113	23	.	.	PUNCT
ejpam-5456	114	1	this	this	DET
ejpam-5456	114	2	adaptability	adaptability	NOUN
ejpam-5456	114	3	makes	make	VERB
ejpam-5456	114	4	adm	adm	PROPN
ejpam-5456	114	5	suitable	suitable	ADJ
ejpam-5456	114	6	for	for	ADP
ejpam-5456	114	7	a	a	DET
ejpam-5456	114	8	diverse	diverse	ADJ
ejpam-5456	114	9	set	set	NOUN
ejpam-5456	114	10	of	of	ADP
ejpam-5456	114	11	problems	problem	NOUN
ejpam-5456	114	12	across	across	ADP
ejpam-5456	114	13	different	different	ADJ
ejpam-5456	114	14	scientific	scientific	ADJ
ejpam-5456	114	15	and	and	CCONJ
ejpam-5456	114	16	engineering	engineering	NOUN
ejpam-5456	114	17	disciplines	discipline	NOUN
ejpam-5456	114	18	.	.	PUNCT
ejpam-5456	115	1	we	we	PRON
ejpam-5456	115	2	take	take	VERB
ejpam-5456	115	3	into	into	ADP
ejpam-5456	115	4	account	account	NOUN
ejpam-5456	115	5	the	the	DET
ejpam-5456	115	6	following	following	NOUN
ejpam-5456	115	7	:	:	PUNCT
ejpam-5456	115	8	nonlinear	nonlinear	PROPN
ejpam-5456	115	9	sde	sde	PROPN
ejpam-5456	115	10	with	with	ADP
ejpam-5456	115	11	respect	respect	NOUN
ejpam-5456	115	12	to	to	ADP
ejpam-5456	115	13	a	a	DET
ejpam-5456	115	14	conformable	conformable	ADJ
ejpam-5456	115	15	operator	operator	NOUN
ejpam-5456	115	16	and	and	CCONJ
ejpam-5456	115	17	a	a	DET
ejpam-5456	115	18	non	non	ADJ
ejpam-5456	115	19	-	-	ADJ
ejpam-5456	115	20	zero	zero	ADJ
ejpam-5456	115	21	trapping	trap	VERB
ejpam-5456	115	22	potential	potential	NOUN
ejpam-5456	115	23	that	that	PRON
ejpam-5456	115	24	is	be	AUX
ejpam-5456	115	25	time	time	NOUN
ejpam-5456	115	26	-	-	PUNCT
ejpam-5456	115	27	fractional	fractional	ADJ
ejpam-5456	115	28	.	.	PUNCT
ejpam-5456	116	1	ιtµ	ιtµ	PROPN
ejpam-5456	116	2	φδ(ϱ	φδ(ϱ	X
ejpam-5456	116	3	,	,	PUNCT
ejpam-5456	116	4	φ	φ	NUM
ejpam-5456	116	5	)	)	PUNCT
ejpam-5456	116	6	+	+	CCONJ
ejpam-5456	116	7	ζδϱϱ(ϱ	ζδϱϱ(ϱ	PROPN
ejpam-5456	116	8	,	,	PUNCT
ejpam-5456	116	9	φ	φ	NUM
ejpam-5456	116	10	)	)	PUNCT
ejpam-5456	117	1	+	+	NUM
ejpam-5456	117	2	ℶ(ϱ)δ(ϱ	ℶ(ϱ)δ(ϱ	NUM
ejpam-5456	117	3	,	,	PUNCT
ejpam-5456	117	4	φ	φ	NUM
ejpam-5456	117	5	)	)	PUNCT
ejpam-5456	117	6	+	+	NUM
ejpam-5456	117	7	ℵ|δ(ϱ	ℵ|δ(ϱ	NOUN
ejpam-5456	117	8	,	,	PUNCT
ejpam-5456	117	9	φ)|2δ(ϱ	φ)|2δ(ϱ	X
ejpam-5456	117	10	,	,	PUNCT
ejpam-5456	117	11	φ	φ	NUM
ejpam-5456	117	12	)	)	PUNCT
ejpam-5456	118	1	=	=	SYM
ejpam-5456	118	2	0	0	NUM
ejpam-5456	118	3	,	,	PUNCT
ejpam-5456	118	4	(	(	PUNCT
ejpam-5456	118	5	4	4	NUM
ejpam-5456	118	6	)	)	PUNCT
ejpam-5456	118	7	with	with	ADP
ejpam-5456	118	8	the	the	DET
ejpam-5456	118	9	initial	initial	ADJ
ejpam-5456	118	10	condition	condition	NOUN
ejpam-5456	118	11	(	(	PUNCT
ejpam-5456	118	12	i	i	NOUN
ejpam-5456	118	13	-	-	PUNCT
ejpam-5456	118	14	c	c	NOUN
ejpam-5456	118	15	):	):	PUNCT
ejpam-5456	118	16	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	118	17	,	,	PUNCT
ejpam-5456	118	18	0	0	NUM
ejpam-5456	118	19	)	)	PUNCT
ejpam-5456	118	20	=	=	SYM
ejpam-5456	119	1	δ0(ϱ	δ0(ϱ	PROPN
ejpam-5456	119	2	)	)	PUNCT
ejpam-5456	119	3	,	,	PUNCT
ejpam-5456	119	4	(	(	PUNCT
ejpam-5456	119	5	5	5	X
ejpam-5456	119	6	)	)	PUNCT
ejpam-5456	119	7	here	here	ADV
ejpam-5456	119	8	ζ,ℵ	ζ,ℵ	VERB
ejpam-5456	119	9	∈	∈	PROPN
ejpam-5456	119	10	r	r	NOUN
ejpam-5456	119	11	,	,	PUNCT
ejpam-5456	119	12	0	0	PUNCT
ejpam-5456	119	13	<	<	X
ejpam-5456	119	14	µ	µ	X
ejpam-5456	119	15	≤	≤	NUM
ejpam-5456	119	16	1	1	NUM
ejpam-5456	119	17	,	,	PUNCT
ejpam-5456	119	18	ι2	ι2	PROPN
ejpam-5456	119	19	=	=	SYM
ejpam-5456	119	20	−1	−1	NOUN
ejpam-5456	119	21	;	;	PUNCT
ejpam-5456	119	22	tµ	tµ	PROPN
ejpam-5456	119	23	φ	φ	PROPN
ejpam-5456	119	24	is	be	AUX
ejpam-5456	119	25	con	con	NOUN
ejpam-5456	119	26	-	-	PUNCT
ejpam-5456	119	27	frd	frd	ADJ
ejpam-5456	119	28	;	;	PUNCT
ejpam-5456	119	29	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	119	30	,	,	PUNCT
ejpam-5456	119	31	φ	φ	NOUN
ejpam-5456	119	32	)	)	PUNCT
ejpam-5456	119	33	complex	complex	NOUN
ejpam-5456	119	34	-	-	PUNCT
ejpam-5456	119	35	valued	value	VERB
ejpam-5456	119	36	function	function	NOUN
ejpam-5456	119	37	,	,	PUNCT
ejpam-5456	119	38	ϱ	ϱ	PROPN
ejpam-5456	119	39	∈	∈	PROPN
ejpam-5456	119	40	r	r	NOUN
ejpam-5456	119	41	;	;	PUNCT
ejpam-5456	119	42	φ	φ	PROPN
ejpam-5456	119	43	≥	≥	NOUN
ejpam-5456	119	44	0	0	NUM
ejpam-5456	119	45	;	;	PUNCT
ejpam-5456	119	46	ℶ(ϱ	ℶ(ϱ	PROPN
ejpam-5456	119	47	)	)	PUNCT
ejpam-5456	119	48	represents	represent	VERB
ejpam-5456	119	49	trapping	trap	VERB
ejpam-5456	119	50	potential	potential	NOUN
ejpam-5456	119	51	;	;	PUNCT
ejpam-5456	119	52	|δ(ϱ	|δ(ϱ	NOUN
ejpam-5456	119	53	,	,	PUNCT
ejpam-5456	119	54	φ)|	φ)|	NOUN
ejpam-5456	119	55	is	be	AUX
ejpam-5456	119	56	the	the	DET
ejpam-5456	119	57	modulus	modulus	NOUN
ejpam-5456	119	58	of	of	ADP
ejpam-5456	119	59	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	119	60	,	,	PUNCT
ejpam-5456	119	61	φ	φ	NUM
ejpam-5456	119	62	)	)	PUNCT
ejpam-5456	119	63	.	.	PUNCT
ejpam-5456	120	1	the	the	DET
ejpam-5456	120	2	subsequent	subsequent	ADJ
ejpam-5456	120	3	sections	section	NOUN
ejpam-5456	120	4	are	be	AUX
ejpam-5456	120	5	structured	structure	VERB
ejpam-5456	120	6	as	as	SCONJ
ejpam-5456	120	7	follows	follow	VERB
ejpam-5456	120	8	:	:	PUNCT
ejpam-5456	120	9	section	section	NOUN
ejpam-5456	120	10	2	2	NUM
ejpam-5456	120	11	presents	present	VERB
ejpam-5456	120	12	the	the	DET
ejpam-5456	120	13	main	main	ADJ
ejpam-5456	120	14	characteristics	characteristic	NOUN
ejpam-5456	120	15	and	and	CCONJ
ejpam-5456	120	16	results	result	NOUN
ejpam-5456	120	17	that	that	PRON
ejpam-5456	120	18	form	form	VERB
ejpam-5456	120	19	the	the	DET
ejpam-5456	120	20	foundation	foundation	NOUN
ejpam-5456	120	21	of	of	ADP
ejpam-5456	120	22	our	our	PRON
ejpam-5456	120	23	study	study	NOUN
ejpam-5456	120	24	.	.	PUNCT
ejpam-5456	121	1	section	section	NOUN
ejpam-5456	121	2	3	3	NUM
ejpam-5456	121	3	provides	provide	VERB
ejpam-5456	121	4	the	the	DET
ejpam-5456	121	5	algorithm	algorithm	NOUN
ejpam-5456	121	6	of	of	ADP
ejpam-5456	121	7	the	the	DET
ejpam-5456	121	8	sadm	sadm	ADJ
ejpam-5456	121	9	.	.	PUNCT
ejpam-5456	122	1	in	in	ADP
ejpam-5456	122	2	section	section	NOUN
ejpam-5456	122	3	4	4	NUM
ejpam-5456	122	4	,	,	PUNCT
ejpam-5456	122	5	we	we	PRON
ejpam-5456	122	6	solve	solve	VERB
ejpam-5456	122	7	three	three	NUM
ejpam-5456	122	8	types	type	NOUN
ejpam-5456	122	9	of	of	ADP
ejpam-5456	122	10	fsdes	fsde	NOUN
ejpam-5456	122	11	using	use	VERB
ejpam-5456	122	12	the	the	DET
ejpam-5456	122	13	sadm	sadm	ADJ
ejpam-5456	122	14	.	.	PUNCT
ejpam-5456	123	1	in	in	ADP
ejpam-5456	123	2	section	section	NOUN
ejpam-5456	123	3	5	5	NUM
ejpam-5456	123	4	,	,	PUNCT
ejpam-5456	123	5	we	we	PRON
ejpam-5456	123	6	discuss	discuss	VERB
ejpam-5456	123	7	the	the	DET
ejpam-5456	123	8	results	result	NOUN
ejpam-5456	123	9	obtained	obtain	VERB
ejpam-5456	123	10	in	in	ADP
ejpam-5456	123	11	section	section	NOUN
ejpam-5456	123	12	4	4	NUM
ejpam-5456	123	13	through	through	ADP
ejpam-5456	123	14	graphical	graphical	ADJ
ejpam-5456	123	15	and	and	CCONJ
ejpam-5456	123	16	numerical	numerical	ADJ
ejpam-5456	123	17	outcomes	outcome	NOUN
ejpam-5456	123	18	and	and	CCONJ
ejpam-5456	123	19	analyze	analyze	VERB
ejpam-5456	123	20	the	the	DET
ejpam-5456	123	21	correctness	correctness	NOUN
ejpam-5456	123	22	of	of	ADP
ejpam-5456	123	23	our	our	PRON
ejpam-5456	123	24	approach	approach	NOUN
ejpam-5456	123	25	.	.	PUNCT
ejpam-5456	124	1	finally	finally	ADV
ejpam-5456	124	2	,	,	PUNCT
ejpam-5456	124	3	section	section	NOUN
ejpam-5456	124	4	6	6	NUM
ejpam-5456	124	5	presents	present	VERB
ejpam-5456	124	6	the	the	DET
ejpam-5456	124	7	conclusion	conclusion	NOUN
ejpam-5456	124	8	.	.	PUNCT
ejpam-5456	125	1	2	2	X
ejpam-5456	125	2	.	.	X
ejpam-5456	125	3	preliminaries	preliminary	NOUN
ejpam-5456	125	4	in	in	ADP
ejpam-5456	125	5	this	this	DET
ejpam-5456	125	6	section	section	NOUN
ejpam-5456	125	7	,	,	PUNCT
ejpam-5456	125	8	we	we	PRON
ejpam-5456	125	9	go	go	VERB
ejpam-5456	125	10	over	over	ADP
ejpam-5456	125	11	some	some	DET
ejpam-5456	125	12	useful	useful	ADJ
ejpam-5456	125	13	characteristics	characteristic	NOUN
ejpam-5456	125	14	of	of	ADP
ejpam-5456	125	15	con	con	NOUN
ejpam-5456	125	16	-	-	PUNCT
ejpam-5456	125	17	frd	frd	ADJ
ejpam-5456	125	18	and	and	CCONJ
ejpam-5456	125	19	st	st	PROPN
ejpam-5456	125	20	that	that	PRON
ejpam-5456	125	21	will	will	AUX
ejpam-5456	125	22	be	be	AUX
ejpam-5456	125	23	useful	useful	ADJ
ejpam-5456	125	24	in	in	ADP
ejpam-5456	125	25	this	this	DET
ejpam-5456	125	26	paper	paper	NOUN
ejpam-5456	125	27	.	.	PUNCT
ejpam-5456	126	1	theorem	theorem	NOUN
ejpam-5456	126	2	1	1	NUM
ejpam-5456	126	3	.	.	PUNCT
ejpam-5456	127	1	[	[	X
ejpam-5456	127	2	2	2	X
ejpam-5456	127	3	]	]	PUNCT
ejpam-5456	127	4	let	let	VERB
ejpam-5456	127	5	0	0	PUNCT
ejpam-5456	127	6	<	<	X
ejpam-5456	127	7	µ	µ	X
ejpam-5456	127	8	≤	≤	NUM
ejpam-5456	127	9	1	1	NUM
ejpam-5456	127	10	,	,	PUNCT
ejpam-5456	127	11	a1(ϱ	a1(ϱ	PROPN
ejpam-5456	127	12	,	,	PUNCT
ejpam-5456	127	13	φ	φ	NUM
ejpam-5456	127	14	)	)	PUNCT
ejpam-5456	127	15	and	and	CCONJ
ejpam-5456	127	16	a2(ϱ	a2(ϱ	PROPN
ejpam-5456	127	17	,	,	PUNCT
ejpam-5456	127	18	φ	φ	NUM
ejpam-5456	127	19	)	)	PUNCT
ejpam-5456	127	20	be	be	AUX
ejpam-5456	127	21	µ-differentiable	µ-differentiable	ADJ
ejpam-5456	127	22	at	at	ADP
ejpam-5456	127	23	a	a	DET
ejpam-5456	127	24	point	point	NOUN
ejpam-5456	127	25	φ	φ	X
ejpam-5456	127	26	>	>	X
ejpam-5456	127	27	0	0	PROPN
ejpam-5456	127	28	.	.	PUNCT
ejpam-5456	128	1	then	then	ADV
ejpam-5456	128	2	,	,	PUNCT
ejpam-5456	128	3	i.	i.	PROPN
ejpam-5456	128	4	tµ	tµ	PROPN
ejpam-5456	128	5	φ(ν1a1(ϱ	φ(ν1a1(ϱ	PROPN
ejpam-5456	128	6	,	,	PUNCT
ejpam-5456	128	7	φ	φ	NUM
ejpam-5456	128	8	)	)	PUNCT
ejpam-5456	129	1	+	+	CCONJ
ejpam-5456	129	2	ν2a2(ϱ	ν2a2(ϱ	PROPN
ejpam-5456	129	3	,	,	PUNCT
ejpam-5456	129	4	φ	φ	NOUN
ejpam-5456	129	5	)	)	PUNCT
ejpam-5456	129	6	)	)	PUNCT
ejpam-5456	130	1	=	=	SYM
ejpam-5456	130	2	ν1	ν1	PROPN
ejpam-5456	130	3	t	t	PROPN
ejpam-5456	130	4	µ	µ	PROPN
ejpam-5456	130	5	φa1(ϱ	φa1(ϱ	PROPN
ejpam-5456	130	6	,	,	PUNCT
ejpam-5456	130	7	φ	φ	NUM
ejpam-5456	130	8	)	)	PUNCT
ejpam-5456	131	1	+	+	SYM
ejpam-5456	131	2	ν2	ν2	PROPN
ejpam-5456	131	3	t	t	PROPN
ejpam-5456	131	4	µ	µ	PRON
ejpam-5456	131	5	φa2(ϱ	φa2(ϱ	PROPN
ejpam-5456	131	6	,	,	PUNCT
ejpam-5456	131	7	φ	φ	NUM
ejpam-5456	131	8	)	)	PUNCT
ejpam-5456	131	9	,	,	PUNCT
ejpam-5456	131	10	∀	∀	NOUN
ejpam-5456	131	11	ν1	ν1	NOUN
ejpam-5456	131	12	,	,	PUNCT
ejpam-5456	131	13	ν2	ν2	PROPN
ejpam-5456	131	14	∈	∈	PROPN
ejpam-5456	131	15	r.	r.	PROPN
ejpam-5456	131	16	ii	ii	PROPN
ejpam-5456	131	17	.	.	PUNCT
ejpam-5456	132	1	tµ	tµ	PRON
ejpam-5456	132	2	φ(φν	φ(φν	ADJ
ejpam-5456	132	3	)	)	PUNCT
ejpam-5456	133	1	=	=	SYM
ejpam-5456	133	2	νφν−µ	νφν−µ	NOUN
ejpam-5456	133	3	,	,	PUNCT
ejpam-5456	133	4	∀	∀	X
ejpam-5456	133	5	ν	ν	X
ejpam-5456	133	6	∈	∈	PROPN
ejpam-5456	133	7	r.	r.	PROPN
ejpam-5456	133	8	iii	iii	PROPN
ejpam-5456	133	9	.	.	PUNCT
ejpam-5456	134	1	tµ	tµ	PROPN
ejpam-5456	134	2	φ(ν	φ(ν	PROPN
ejpam-5456	134	3	)	)	PUNCT
ejpam-5456	134	4	=	=	SYM
ejpam-5456	135	1	0	0	NUM
ejpam-5456	135	2	,	,	PUNCT
ejpam-5456	135	3	ν	ν	PROPN
ejpam-5456	135	4	∈	∈	PROPN
ejpam-5456	135	5	r.	r.	PROPN
ejpam-5456	135	6	iv	iv	PROPN
ejpam-5456	135	7	.	.	PUNCT
ejpam-5456	136	1	tµ	tµ	PROPN
ejpam-5456	136	2	φa1(ϱ	φa1(ϱ	PROPN
ejpam-5456	136	3	,	,	PUNCT
ejpam-5456	136	4	φ)a2(ϱ	φ)a2(ϱ	PROPN
ejpam-5456	136	5	,	,	PUNCT
ejpam-5456	136	6	φ	φ	NOUN
ejpam-5456	136	7	)	)	PUNCT
ejpam-5456	136	8	)	)	PUNCT
ejpam-5456	137	1	=	=	SYM
ejpam-5456	137	2	a1(ϱ	a1(ϱ	PROPN
ejpam-5456	137	3	,	,	PUNCT
ejpam-5456	137	4	φ)t	φ)t	ADJ
ejpam-5456	137	5	µ	µ	PROPN
ejpam-5456	137	6	φa2(ϱ	φa2(ϱ	PROPN
ejpam-5456	137	7	,	,	PUNCT
ejpam-5456	137	8	φ	φ	NUM
ejpam-5456	137	9	)	)	PUNCT
ejpam-5456	137	10	+	+	CCONJ
ejpam-5456	137	11	a2(ϱ	a2(ϱ	PROPN
ejpam-5456	137	12	,	,	PUNCT
ejpam-5456	137	13	φ)t	φ)t	ADJ
ejpam-5456	137	14	µ	µ	PRON
ejpam-5456	137	15	φa1(ϱ	φa1(ϱ	PROPN
ejpam-5456	137	16	,	,	PUNCT
ejpam-5456	137	17	φ	φ	NUM
ejpam-5456	137	18	)	)	PUNCT
ejpam-5456	137	19	.	.	PUNCT
ejpam-5456	138	1	v.	v.	ADP
ejpam-5456	138	2	tµ	tµ	PRON
ejpam-5456	138	3	φ	φ	PROPN
ejpam-5456	138	4	a1(ϱ	a1(ϱ	PROPN
ejpam-5456	138	5	,	,	PUNCT
ejpam-5456	138	6	φ	φ	NOUN
ejpam-5456	138	7	)	)	PUNCT
ejpam-5456	138	8	a2(ϱ	a2(ϱ	PROPN
ejpam-5456	138	9	,	,	PUNCT
ejpam-5456	138	10	φ	φ	NUM
ejpam-5456	138	11	)	)	PUNCT
ejpam-5456	138	12	=	=	SYM
ejpam-5456	138	13	a2(ϱ	a2(ϱ	PROPN
ejpam-5456	138	14	,	,	PUNCT
ejpam-5456	138	15	φ)t	φ)t	ADJ
ejpam-5456	138	16	µ	µ	PRON
ejpam-5456	138	17	φa1(ϱ	φa1(ϱ	NOUN
ejpam-5456	138	18	,	,	PUNCT
ejpam-5456	138	19	φ)−	φ)−	PROPN
ejpam-5456	138	20	a1(ϱ	a1(ϱ	PROPN
ejpam-5456	138	21	,	,	PUNCT
ejpam-5456	138	22	φ)t	φ)t	ADJ
ejpam-5456	138	23	µ	µ	PRON
ejpam-5456	138	24	φa2(φ	φa2(φ	PROPN
ejpam-5456	138	25	)	)	PUNCT
ejpam-5456	138	26	a2	a2	PROPN
ejpam-5456	138	27	2(φ	2(φ	NUM
ejpam-5456	138	28	)	)	PUNCT
ejpam-5456	138	29	.	.	PUNCT
ejpam-5456	139	1	lemma	lemma	PROPN
ejpam-5456	139	2	1	1	NUM
ejpam-5456	139	3	.	.	PUNCT
ejpam-5456	140	1	[	[	X
ejpam-5456	140	2	3	3	X
ejpam-5456	140	3	]	]	PUNCT
ejpam-5456	140	4	assume	assume	VERB
ejpam-5456	140	5	that	that	SCONJ
ejpam-5456	140	6	a1(ϱ	a1(ϱ	PROPN
ejpam-5456	140	7	,	,	PUNCT
ejpam-5456	140	8	φ	φ	NUM
ejpam-5456	140	9	)	)	PUNCT
ejpam-5456	140	10	and	and	CCONJ
ejpam-5456	140	11	a2(ϱ	a2(ϱ	PROPN
ejpam-5456	140	12	,	,	PUNCT
ejpam-5456	140	13	φ	φ	NUM
ejpam-5456	140	14	)	)	PUNCT
ejpam-5456	140	15	satisfies	satisfy	VERB
ejpam-5456	140	16	the	the	DET
ejpam-5456	140	17	axioms	axiom	NOUN
ejpam-5456	140	18	of	of	ADP
ejpam-5456	140	19	existence	existence	NOUN
ejpam-5456	140	20	of	of	ADP
ejpam-5456	140	21	st	st	PROPN
ejpam-5456	140	22	,	,	PUNCT
ejpam-5456	140	23	sµ[a1(ϱ	sµ[a1(ϱ	PROPN
ejpam-5456	140	24	,	,	PUNCT
ejpam-5456	140	25	φ	φ	NOUN
ejpam-5456	140	26	)	)	PUNCT
ejpam-5456	140	27	]	]	PUNCT
ejpam-5456	141	1	=	=	SYM
ejpam-5456	141	2	a∗	a∗	PROPN
ejpam-5456	141	3	1(ϱ,ω),sµ[a2(ϱ	1(ϱ,ω),sµ[a2(ϱ	NUM
ejpam-5456	141	4	,	,	PUNCT
ejpam-5456	141	5	φ	φ	NOUN
ejpam-5456	141	6	)	)	PUNCT
ejpam-5456	141	7	]	]	PUNCT
ejpam-5456	141	8	=	=	SYM
ejpam-5456	141	9	a∗	a∗	PROPN
ejpam-5456	141	10	2(ϱ,ω	2(ϱ,ω	NUM
ejpam-5456	141	11	)	)	PUNCT
ejpam-5456	141	12	and	and	CCONJ
ejpam-5456	141	13	b1,b2	b1,b2	PROPN
ejpam-5456	141	14	are	be	AUX
ejpam-5456	141	15	constants	constant	NOUN
ejpam-5456	141	16	.	.	PUNCT
ejpam-5456	142	1	then	then	ADV
ejpam-5456	142	2	,	,	PUNCT
ejpam-5456	142	3	the	the	DET
ejpam-5456	142	4	following	following	ADJ
ejpam-5456	142	5	axioms	axiom	NOUN
ejpam-5456	142	6	hold	hold	VERB
ejpam-5456	142	7	:	:	PUNCT
ejpam-5456	142	8	i.	i.	PROPN
ejpam-5456	142	9	sµ[b1a1(ϱ	sµ[b1a1(ϱ	PROPN
ejpam-5456	142	10	,	,	PUNCT
ejpam-5456	142	11	φ	φ	NUM
ejpam-5456	142	12	)	)	PUNCT
ejpam-5456	143	1	+	+	ADJ
ejpam-5456	143	2	b2a2(ϱ	b2a2(ϱ	NOUN
ejpam-5456	143	3	,	,	PUNCT
ejpam-5456	143	4	φ	φ	NOUN
ejpam-5456	143	5	)	)	PUNCT
ejpam-5456	143	6	]	]	PUNCT
ejpam-5456	144	1	=	=	SYM
ejpam-5456	144	2	b1a∗	b1a∗	NOUN
ejpam-5456	144	3	1(ϱ,ω	1(ϱ,ω	NUM
ejpam-5456	144	4	)	)	PUNCT
ejpam-5456	145	1	+	+	ADJ
ejpam-5456	145	2	b2a∗	b2a∗	PROPN
ejpam-5456	145	3	2(ϱ,ω	2(ϱ,ω	NUM
ejpam-5456	145	4	)	)	PUNCT
ejpam-5456	145	5	.	.	PUNCT
ejpam-5456	146	1	ii	ii	X
ejpam-5456	146	2	.	.	PUNCT
ejpam-5456	147	1	s−1	s−1	PROPN
ejpam-5456	147	2	µ	µ	X
ejpam-5456	147	3	[	[	X
ejpam-5456	147	4	b1a∗	b1a∗	NOUN
ejpam-5456	147	5	1(ϱ,ω	1(ϱ,ω	NUM
ejpam-5456	147	6	)	)	PUNCT
ejpam-5456	148	1	+	+	ADJ
ejpam-5456	148	2	b2a∗	b2a∗	PROPN
ejpam-5456	148	3	2(ϱ,ω	2(ϱ,ω	NUM
ejpam-5456	148	4	)	)	PUNCT
ejpam-5456	148	5	]	]	PUNCT
ejpam-5456	149	1	=	=	SYM
ejpam-5456	149	2	b1a1(ϱ	b1a1(ϱ	NUM
ejpam-5456	149	3	,	,	PUNCT
ejpam-5456	149	4	φ	φ	NOUN
ejpam-5456	149	5	)	)	PUNCT
ejpam-5456	149	6	+	+	ADJ
ejpam-5456	149	7	b2a2(ϱ	b2a2(ϱ	NOUN
ejpam-5456	149	8	,	,	PUNCT
ejpam-5456	149	9	φ	φ	NUM
ejpam-5456	149	10	)	)	PUNCT
ejpam-5456	149	11	.	.	PUNCT
ejpam-5456	150	1	iii	iii	X
ejpam-5456	150	2	.	.	PUNCT
ejpam-5456	151	1	sµ[tµ	sµ[tµ	NOUN
ejpam-5456	151	2	φa(ϱ	φa(ϱ	NUM
ejpam-5456	151	3	,	,	PUNCT
ejpam-5456	151	4	φ	φ	NUM
ejpam-5456	151	5	)	)	PUNCT
ejpam-5456	151	6	]	]	PUNCT
ejpam-5456	152	1	=	=	PUNCT
ejpam-5456	152	2	s[a(ϱ,φ	s[a(ϱ,φ	NOUN
ejpam-5456	152	3	)	)	PUNCT
ejpam-5456	152	4	]	]	PUNCT
ejpam-5456	153	1	ω	ω	X
ejpam-5456	153	2	−	−	PROPN
ejpam-5456	153	3	a(ϱ,0	a(ϱ,0	PROPN
ejpam-5456	153	4	)	)	PUNCT
ejpam-5456	153	5	ω	ω	PROPN
ejpam-5456	153	6	.	.	PUNCT
ejpam-5456	154	1	iv	iv	X
ejpam-5456	154	2	.	.	PUNCT
ejpam-5456	154	3	sµ[tnµ	sµ[tnµ	PROPN
ejpam-5456	154	4	φ	φ	PROPN
ejpam-5456	154	5	a(ϱ	a(ϱ	PROPN
ejpam-5456	154	6	,	,	PUNCT
ejpam-5456	154	7	φ	φ	NOUN
ejpam-5456	154	8	)	)	PUNCT
ejpam-5456	154	9	]	]	PUNCT
ejpam-5456	155	1	=	=	PUNCT
ejpam-5456	155	2	s[a(ϱ,φ	s[a(ϱ,φ	PROPN
ejpam-5456	155	3	)	)	PUNCT
ejpam-5456	155	4	]	]	PUNCT
ejpam-5456	156	1	ωn	ωn	ADP
ejpam-5456	156	2	−	−	PROPN
ejpam-5456	156	3	a(ϱ,0	a(ϱ,0	PROPN
ejpam-5456	156	4	)	)	PUNCT
ejpam-5456	156	5	ωn	ωn	PRON
ejpam-5456	156	6	.	.	PUNCT
ejpam-5456	156	7	m.i	m.i	PROPN
ejpam-5456	156	8	.	.	PROPN
ejpam-5456	156	9	liaqat	liaqat	PROPN
ejpam-5456	156	10	,	,	PUNCT
ejpam-5456	156	11	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	156	12	/	/	SYM
ejpam-5456	156	13	eur	eur	PROPN
ejpam-5456	156	14	.	.	PUNCT
ejpam-5456	157	1	j.	j.	PROPN
ejpam-5456	157	2	pure	pure	PROPN
ejpam-5456	157	3	appl	appl	PROPN
ejpam-5456	157	4	.	.	PROPN
ejpam-5456	157	5	math	math	PROPN
ejpam-5456	157	6	,	,	PUNCT
ejpam-5456	157	7	17	17	NUM
ejpam-5456	157	8	(	(	PUNCT
ejpam-5456	157	9	4	4	NUM
ejpam-5456	157	10	)	)	PUNCT
ejpam-5456	157	11	(	(	PUNCT
ejpam-5456	157	12	2024	2024	NUM
ejpam-5456	157	13	)	)	PUNCT
ejpam-5456	157	14	,	,	PUNCT
ejpam-5456	157	15	3464	3464	NUM
ejpam-5456	157	16	-	-	SYM
ejpam-5456	157	17	3491	3491	NUM
ejpam-5456	157	18	3470	3470	NUM
ejpam-5456	157	19	3	3	NUM
ejpam-5456	157	20	.	.	PUNCT
ejpam-5456	158	1	analysis	analysis	NOUN
ejpam-5456	158	2	of	of	ADP
ejpam-5456	158	3	the	the	DET
ejpam-5456	158	4	sadm	sadm	ADJ
ejpam-5456	158	5	this	this	DET
ejpam-5456	158	6	section	section	NOUN
ejpam-5456	158	7	presents	present	VERB
ejpam-5456	158	8	the	the	DET
ejpam-5456	158	9	main	main	ADJ
ejpam-5456	158	10	steps	step	NOUN
ejpam-5456	158	11	for	for	ADP
ejpam-5456	158	12	solving	solve	VERB
ejpam-5456	158	13	fsdes	fsde	NOUN
ejpam-5456	158	14	using	use	VERB
ejpam-5456	158	15	st	st	PROPN
ejpam-5456	158	16	and	and	CCONJ
ejpam-5456	158	17	adm	adm	PROPN
ejpam-5456	158	18	.	.	PUNCT
ejpam-5456	159	1	we	we	PRON
ejpam-5456	159	2	apply	apply	VERB
ejpam-5456	159	3	these	these	DET
ejpam-5456	159	4	steps	step	NOUN
ejpam-5456	159	5	to	to	PART
ejpam-5456	159	6	solve	solve	VERB
ejpam-5456	159	7	fsdes	fsde	NOUN
ejpam-5456	159	8	in	in	ADP
ejpam-5456	159	9	the	the	DET
ejpam-5456	159	10	standard	standard	ADJ
ejpam-5456	159	11	structure	structure	NOUN
ejpam-5456	159	12	.	.	PUNCT
ejpam-5456	160	1	for	for	ADP
ejpam-5456	160	2	this	this	PRON
ejpam-5456	160	3	,	,	PUNCT
ejpam-5456	160	4	take	take	VERB
ejpam-5456	160	5	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	160	6	,	,	PUNCT
ejpam-5456	160	7	φ	φ	NUM
ejpam-5456	160	8	)	)	PUNCT
ejpam-5456	160	9	=	=	SYM
ejpam-5456	160	10	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	160	11	,	,	PUNCT
ejpam-5456	160	12	φ	φ	NUM
ejpam-5456	160	13	)	)	PUNCT
ejpam-5456	161	1	+	+	CCONJ
ejpam-5456	161	2	ιδ2(ϱ	ιδ2(ϱ	PROPN
ejpam-5456	161	3	,	,	PUNCT
ejpam-5456	161	4	φ	φ	NUM
ejpam-5456	161	5	)	)	PUNCT
ejpam-5456	161	6	in	in	ADP
ejpam-5456	161	7	eq	eq	ADP
ejpam-5456	161	8	.	.	PUNCT
ejpam-5456	162	1	(	(	PUNCT
ejpam-5456	162	2	4	4	NUM
ejpam-5456	162	3	)	)	PUNCT
ejpam-5456	162	4	and	and	CCONJ
ejpam-5456	162	5	we	we	PRON
ejpam-5456	162	6	get	get	VERB
ejpam-5456	162	7	:	:	PUNCT
ejpam-5456	162	8	tµ	tµ	PRON
ejpam-5456	162	9	φδ1(ϱ	φδ1(ϱ	NUM
ejpam-5456	162	10	,	,	PUNCT
ejpam-5456	162	11	φ	φ	NOUN
ejpam-5456	162	12	)	)	PUNCT
ejpam-5456	163	1	=	=	NOUN
ejpam-5456	163	2	−	−	NOUN
ejpam-5456	163	3	ζdϱϱδ2(ϱ	ζdϱϱδ2(ϱ	NOUN
ejpam-5456	163	4	,	,	PUNCT
ejpam-5456	163	5	φ)−	φ)−	PROPN
ejpam-5456	163	6	ℶ(ϱ)δ2(ϱ	ℶ(ϱ)δ2(ϱ	PROPN
ejpam-5456	163	7	,	,	PUNCT
ejpam-5456	163	8	φ)−	φ)−	PROPN
ejpam-5456	163	9	ℵ	ℵ	X
ejpam-5456	163	10	(	(	PUNCT
ejpam-5456	163	11	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	163	12	,	,	PUNCT
ejpam-5456	163	13	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	163	14	,	,	PUNCT
ejpam-5456	163	15	φ	φ	NUM
ejpam-5456	163	16	)	)	PUNCT
ejpam-5456	163	17	+	+	CCONJ
ejpam-5456	163	18	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	163	19	,	,	PUNCT
ejpam-5456	163	20	φ	φ	NUM
ejpam-5456	163	21	)	)	PUNCT
ejpam-5456	163	22	)	)	PUNCT
ejpam-5456	163	23	,	,	PUNCT
ejpam-5456	163	24	tµ	tµ	NOUN
ejpam-5456	163	25	φδ2(ϱ	φδ2(ϱ	PROPN
ejpam-5456	163	26	,	,	PUNCT
ejpam-5456	163	27	φ	φ	NUM
ejpam-5456	163	28	)	)	PUNCT
ejpam-5456	163	29	=	=	SYM
ejpam-5456	163	30	ζdϱϱδ1(ϱ	ζdϱϱδ1(ϱ	PROPN
ejpam-5456	163	31	,	,	PUNCT
ejpam-5456	163	32	φ	φ	NUM
ejpam-5456	163	33	)	)	PUNCT
ejpam-5456	163	34	+	+	CCONJ
ejpam-5456	163	35	ℶ(ϱ)δ1(ϱ	ℶ(ϱ)δ1(ϱ	PROPN
ejpam-5456	163	36	,	,	PUNCT
ejpam-5456	163	37	φ	φ	NOUN
ejpam-5456	163	38	)	)	PUNCT
ejpam-5456	163	39	+	+	NUM
ejpam-5456	163	40	ℵ	ℵ	ADJ
ejpam-5456	163	41	(	(	PUNCT
ejpam-5456	163	42	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	163	43	,	,	PUNCT
ejpam-5456	163	44	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	163	45	,	,	PUNCT
ejpam-5456	163	46	φ	φ	NUM
ejpam-5456	163	47	)	)	PUNCT
ejpam-5456	163	48	+	+	SYM
ejpam-5456	163	49	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	163	50	,	,	PUNCT
ejpam-5456	163	51	φ	φ	NOUN
ejpam-5456	163	52	)	)	PUNCT
ejpam-5456	163	53	)	)	PUNCT
ejpam-5456	163	54	,	,	PUNCT
ejpam-5456	163	55	(	(	PUNCT
ejpam-5456	163	56	6	6	NUM
ejpam-5456	163	57	)	)	PUNCT
ejpam-5456	163	58	with	with	ADP
ejpam-5456	163	59	i	i	PROPN
ejpam-5456	163	60	-	-	PUNCT
ejpam-5456	163	61	cs	cs	PROPN
ejpam-5456	163	62	:	:	PUNCT
ejpam-5456	163	63	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	163	64	,	,	PUNCT
ejpam-5456	163	65	0	0	NUM
ejpam-5456	163	66	)	)	PUNCT
ejpam-5456	163	67	=	=	SYM
ejpam-5456	163	68	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	163	69	)	)	PUNCT
ejpam-5456	163	70	,	,	PUNCT
ejpam-5456	163	71	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	163	72	,	,	PUNCT
ejpam-5456	163	73	0	0	NUM
ejpam-5456	163	74	)	)	PUNCT
ejpam-5456	163	75	=	=	SYM
ejpam-5456	163	76	δ2,0(ϱ	δ2,0(ϱ	NOUN
ejpam-5456	163	77	)	)	PUNCT
ejpam-5456	163	78	,	,	PUNCT
ejpam-5456	163	79	(	(	PUNCT
ejpam-5456	163	80	7	7	X
ejpam-5456	163	81	)	)	PUNCT
ejpam-5456	163	82	here	here	ADV
ejpam-5456	163	83	,	,	PUNCT
ejpam-5456	163	84	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	163	85	,	,	PUNCT
ejpam-5456	163	86	0	0	NUM
ejpam-5456	163	87	)	)	PUNCT
ejpam-5456	163	88	=	=	SYM
ejpam-5456	163	89	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	163	90	)	)	PUNCT
ejpam-5456	163	91	+	+	CCONJ
ejpam-5456	163	92	ιδ2,0(ϱ	ιδ2,0(ϱ	PROPN
ejpam-5456	163	93	)	)	PUNCT
ejpam-5456	163	94	.	.	PUNCT
ejpam-5456	164	1	by	by	ADP
ejpam-5456	164	2	applying	apply	VERB
ejpam-5456	164	3	sµ	sµ	NOUN
ejpam-5456	164	4	on	on	ADP
ejpam-5456	164	5	the	the	DET
ejpam-5456	164	6	above	above	ADJ
ejpam-5456	164	7	system	system	NOUN
ejpam-5456	164	8	.	.	PUNCT
ejpam-5456	165	1	sµ[tµ	sµ[tµ	PROPN
ejpam-5456	166	1	φδ1(ϱ	φδ1(ϱ	NUM
ejpam-5456	166	2	,	,	PUNCT
ejpam-5456	166	3	φ	φ	NOUN
ejpam-5456	166	4	)	)	PUNCT
ejpam-5456	166	5	]	]	PUNCT
ejpam-5456	167	1	=	=	NOUN
ejpam-5456	167	2	−	−	PROPN
ejpam-5456	167	3	sµ	sµ	PROPN
ejpam-5456	167	4	[	[	PUNCT
ejpam-5456	167	5	ζdϱϱδ2(ϱ	ζdϱϱδ2(ϱ	PROPN
ejpam-5456	167	6	,	,	PUNCT
ejpam-5456	167	7	φ	φ	NUM
ejpam-5456	167	8	)	)	PUNCT
ejpam-5456	167	9	+	+	CCONJ
ejpam-5456	167	10	ℶ(ϱ)δ2(ϱ	ℶ(ϱ)δ2(ϱ	PROPN
ejpam-5456	167	11	,	,	PUNCT
ejpam-5456	167	12	φ)+	φ)+	PROPN
ejpam-5456	167	13	ℵ	ℵ	PROPN
ejpam-5456	167	14	(	(	PUNCT
ejpam-5456	167	15	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	167	16	,	,	PUNCT
ejpam-5456	167	17	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	167	18	,	,	PUNCT
ejpam-5456	167	19	φ	φ	NUM
ejpam-5456	167	20	)	)	PUNCT
ejpam-5456	167	21	+	+	CCONJ
ejpam-5456	167	22	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	167	23	,	,	PUNCT
ejpam-5456	167	24	φ	φ	NUM
ejpam-5456	167	25	)	)	PUNCT
ejpam-5456	167	26	)	)	PUNCT
ejpam-5456	167	27	]	]	PUNCT
ejpam-5456	167	28	,	,	PUNCT
ejpam-5456	167	29	sµ[tµ	sµ[tµ	PUNCT
ejpam-5456	167	30	φδ2(ϱ	φδ2(ϱ	PROPN
ejpam-5456	167	31	,	,	PUNCT
ejpam-5456	167	32	φ	φ	NOUN
ejpam-5456	167	33	)	)	PUNCT
ejpam-5456	167	34	]	]	PUNCT
ejpam-5456	168	1	=	=	X
ejpam-5456	168	2	sµ	sµ	X
ejpam-5456	168	3	[	[	PUNCT
ejpam-5456	168	4	ζdϱϱδ1(ϱ	ζdϱϱδ1(ϱ	PROPN
ejpam-5456	168	5	,	,	PUNCT
ejpam-5456	168	6	φ	φ	NUM
ejpam-5456	168	7	)	)	PUNCT
ejpam-5456	168	8	+	+	SYM
ejpam-5456	168	9	ℶ(ϱ)δ1(ϱ	ℶ(ϱ)δ1(ϱ	PROPN
ejpam-5456	168	10	,	,	PUNCT
ejpam-5456	168	11	φ)+	φ)+	PROPN
ejpam-5456	168	12	ℵ	ℵ	PROPN
ejpam-5456	168	13	(	(	PUNCT
ejpam-5456	168	14	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	168	15	,	,	PUNCT
ejpam-5456	168	16	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	168	17	,	,	PUNCT
ejpam-5456	168	18	φ	φ	NUM
ejpam-5456	168	19	)	)	PUNCT
ejpam-5456	168	20	+	+	SYM
ejpam-5456	168	21	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	168	22	,	,	PUNCT
ejpam-5456	168	23	φ	φ	NOUN
ejpam-5456	168	24	)	)	PUNCT
ejpam-5456	168	25	)	)	PUNCT
ejpam-5456	168	26	]	]	PUNCT
ejpam-5456	168	27	.	.	PUNCT
ejpam-5456	169	1	(	(	PUNCT
ejpam-5456	169	2	8)	8)	NUM
ejpam-5456	169	3	through	through	ADP
ejpam-5456	169	4	lemma	lemma	PROPN
ejpam-5456	169	5	1(iii	1(iii	NUM
ejpam-5456	169	6	)	)	PUNCT
ejpam-5456	169	7	and	and	CCONJ
ejpam-5456	169	8	performing	perform	VERB
ejpam-5456	169	9	various	various	ADJ
ejpam-5456	169	10	computations	computation	NOUN
ejpam-5456	169	11	,	,	PUNCT
ejpam-5456	169	12	we	we	PRON
ejpam-5456	169	13	acquire	acquire	VERB
ejpam-5456	169	14	the	the	DET
ejpam-5456	169	15	following	following	NOUN
ejpam-5456	169	16	:	:	PUNCT
ejpam-5456	169	17	sµ[δ1(ϱ	sµ[δ1(ϱ	ADJ
ejpam-5456	169	18	,	,	PUNCT
ejpam-5456	169	19	φ	φ	NOUN
ejpam-5456	169	20	)	)	PUNCT
ejpam-5456	169	21	]	]	PUNCT
ejpam-5456	170	1	=	=	NUM
ejpam-5456	170	2	δ1(0)−	δ1(0)−	PROPN
ejpam-5456	170	3	ωsµ	ωsµ	PROPN
ejpam-5456	170	4	[	[	PUNCT
ejpam-5456	170	5	ζdϱϱδ2(ϱ	ζdϱϱδ2(ϱ	PROPN
ejpam-5456	170	6	,	,	PUNCT
ejpam-5456	170	7	φ	φ	NUM
ejpam-5456	170	8	)	)	PUNCT
ejpam-5456	170	9	]	]	PUNCT
ejpam-5456	170	10	−	−	PROPN
ejpam-5456	170	11	ωsµ	ωsµ	PROPN
ejpam-5456	170	12	[	[	PUNCT
ejpam-5456	170	13	ℶ(ϱ)δ2(ϱ	ℶ(ϱ)δ2(ϱ	PROPN
ejpam-5456	170	14	,	,	PUNCT
ejpam-5456	170	15	φ	φ	NUM
ejpam-5456	170	16	)	)	PUNCT
ejpam-5456	170	17	]	]	PUNCT
ejpam-5456	170	18	−	−	PROPN
ejpam-5456	170	19	ωsµ	ωsµ	PROPN
ejpam-5456	170	20	[	[	PUNCT
ejpam-5456	170	21	ℵ	ℵ	X
ejpam-5456	170	22	(	(	PUNCT
ejpam-5456	170	23	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	170	24	,	,	PUNCT
ejpam-5456	170	25	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	170	26	,	,	PUNCT
ejpam-5456	170	27	φ	φ	NUM
ejpam-5456	170	28	)	)	PUNCT
ejpam-5456	171	1	+	+	CCONJ
ejpam-5456	171	2	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	171	3	,	,	PUNCT
ejpam-5456	171	4	φ	φ	NUM
ejpam-5456	171	5	)	)	PUNCT
ejpam-5456	171	6	)	)	PUNCT
ejpam-5456	171	7	]	]	PUNCT
ejpam-5456	171	8	,	,	PUNCT
ejpam-5456	171	9	sµ[δ2(ϱ	sµ[δ2(ϱ	PROPN
ejpam-5456	171	10	,	,	PUNCT
ejpam-5456	171	11	φ	φ	NOUN
ejpam-5456	171	12	)	)	PUNCT
ejpam-5456	171	13	]	]	PUNCT
ejpam-5456	172	1	=	=	X
ejpam-5456	172	2	δ2(0	δ2(0	NOUN
ejpam-5456	172	3	)	)	PUNCT
ejpam-5456	173	1	+	+	CCONJ
ejpam-5456	173	2	ωsµ	ωsµ	ADJ
ejpam-5456	173	3	[	[	PUNCT
ejpam-5456	173	4	ζdϱϱδ1(ϱ	ζdϱϱδ1(ϱ	PROPN
ejpam-5456	173	5	,	,	PUNCT
ejpam-5456	173	6	φ	φ	NUM
ejpam-5456	173	7	)	)	PUNCT
ejpam-5456	173	8	]	]	PUNCT
ejpam-5456	174	1	+	+	X
ejpam-5456	174	2	ωsµ	ωsµ	X
ejpam-5456	174	3	[	[	PUNCT
ejpam-5456	174	4	ℶ(ϱ)δ1(ϱ	ℶ(ϱ)δ1(ϱ	PROPN
ejpam-5456	174	5	,	,	PUNCT
ejpam-5456	174	6	φ	φ	NUM
ejpam-5456	174	7	)	)	PUNCT
ejpam-5456	174	8	]	]	PUNCT
ejpam-5456	175	1	+	+	PUNCT
ejpam-5456	175	2	ωsµ	ωsµ	ADJ
ejpam-5456	175	3	[	[	PUNCT
ejpam-5456	175	4	ℵ	ℵ	X
ejpam-5456	175	5	(	(	PUNCT
ejpam-5456	175	6	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	175	7	,	,	PUNCT
ejpam-5456	175	8	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	175	9	,	,	PUNCT
ejpam-5456	175	10	φ	φ	NUM
ejpam-5456	175	11	)	)	PUNCT
ejpam-5456	175	12	+	+	SYM
ejpam-5456	175	13	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	175	14	,	,	PUNCT
ejpam-5456	175	15	φ	φ	NOUN
ejpam-5456	175	16	)	)	PUNCT
ejpam-5456	175	17	)	)	PUNCT
ejpam-5456	175	18	]	]	PUNCT
ejpam-5456	175	19	.	.	PUNCT
ejpam-5456	176	1	(	(	PUNCT
ejpam-5456	176	2	9	9	X
ejpam-5456	176	3	)	)	PUNCT
ejpam-5456	176	4	implementing	implement	VERB
ejpam-5456	176	5	the	the	DET
ejpam-5456	176	6	s−1	s−1	PROPN
ejpam-5456	176	7	µ	µ	NOUN
ejpam-5456	176	8	on	on	ADP
ejpam-5456	176	9	the	the	DET
ejpam-5456	176	10	system	system	NOUN
ejpam-5456	176	11	mentioned	mention	VERB
ejpam-5456	176	12	above	above	ADV
ejpam-5456	176	13	:	:	PUNCT
ejpam-5456	176	14	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	176	15	,	,	PUNCT
ejpam-5456	176	16	φ	φ	NUM
ejpam-5456	176	17	)	)	PUNCT
ejpam-5456	177	1	=	=	NOUN
ejpam-5456	177	2	s−1	s−1	NOUN
ejpam-5456	177	3	µ	µ	NOUN
ejpam-5456	177	4	[	[	PUNCT
ejpam-5456	177	5	δ1(0	δ1(0	PROPN
ejpam-5456	177	6	)	)	PUNCT
ejpam-5456	177	7	]	]	PUNCT
ejpam-5456	178	1	−	−	PROPN
ejpam-5456	178	2	s−1	s−1	PROPN
ejpam-5456	178	3	µ	µ	X
ejpam-5456	178	4	[	[	PUNCT
ejpam-5456	178	5	ωsµ	ωsµ	PROPN
ejpam-5456	178	6	[	[	PUNCT
ejpam-5456	178	7	ζdϱϱδ2(ϱ	ζdϱϱδ2(ϱ	PROPN
ejpam-5456	178	8	,	,	PUNCT
ejpam-5456	178	9	φ	φ	PROPN
ejpam-5456	178	10	)	)	PUNCT
ejpam-5456	178	11	]	]	X
ejpam-5456	178	12	]	]	X
ejpam-5456	178	13	−	−	PROPN
ejpam-5456	178	14	s−1	s−1	PROPN
ejpam-5456	178	15	µ	µ	X
ejpam-5456	178	16	[	[	PUNCT
ejpam-5456	178	17	ωsµ	ωsµ	X
ejpam-5456	178	18	[	[	PUNCT
ejpam-5456	178	19	ℶ(ϱ)δ2(ϱ	ℶ(ϱ)δ2(ϱ	PROPN
ejpam-5456	178	20	,	,	PUNCT
ejpam-5456	178	21	φ	φ	NUM
ejpam-5456	178	22	)	)	PUNCT
ejpam-5456	178	23	]	]	X
ejpam-5456	178	24	]	]	X
ejpam-5456	178	25	−	−	PROPN
ejpam-5456	178	26	s−1	s−1	PROPN
ejpam-5456	178	27	µ	µ	X
ejpam-5456	178	28	[	[	PUNCT
ejpam-5456	178	29	ωsµ	ωsµ	NOUN
ejpam-5456	178	30	[	[	PUNCT
ejpam-5456	178	31	ℵ	ℵ	X
ejpam-5456	178	32	(	(	PUNCT
ejpam-5456	178	33	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	178	34	,	,	PUNCT
ejpam-5456	178	35	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	178	36	,	,	PUNCT
ejpam-5456	178	37	φ	φ	NUM
ejpam-5456	178	38	)	)	PUNCT
ejpam-5456	179	1	+	+	CCONJ
ejpam-5456	179	2	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	179	3	,	,	PUNCT
ejpam-5456	179	4	φ	φ	NUM
ejpam-5456	179	5	)	)	PUNCT
ejpam-5456	179	6	)	)	PUNCT
ejpam-5456	180	1	]	]	PUNCT
ejpam-5456	180	2	]	]	X
ejpam-5456	180	3	,	,	PUNCT
ejpam-5456	180	4	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	180	5	,	,	PUNCT
ejpam-5456	180	6	φ	φ	NOUN
ejpam-5456	180	7	)	)	PUNCT
ejpam-5456	180	8	=	=	NOUN
ejpam-5456	180	9	s−1	s−1	PROPN
ejpam-5456	180	10	µ	µ	X
ejpam-5456	180	11	[	[	PUNCT
ejpam-5456	180	12	δ2(0	δ2(0	NOUN
ejpam-5456	180	13	)	)	PUNCT
ejpam-5456	180	14	]	]	PUNCT
ejpam-5456	181	1	+	+	CCONJ
ejpam-5456	181	2	s−1	s−1	PROPN
ejpam-5456	181	3	µ	µ	X
ejpam-5456	181	4	[	[	PUNCT
ejpam-5456	181	5	ωsµ	ωsµ	NOUN
ejpam-5456	181	6	[	[	PUNCT
ejpam-5456	181	7	ζdϱϱδ1(ϱ	ζdϱϱδ1(ϱ	PROPN
ejpam-5456	181	8	,	,	PUNCT
ejpam-5456	181	9	φ	φ	NUM
ejpam-5456	181	10	)	)	PUNCT
ejpam-5456	181	11	]	]	PUNCT
ejpam-5456	181	12	]	]	X
ejpam-5456	182	1	+	+	CCONJ
ejpam-5456	182	2	s−1	s−1	PROPN
ejpam-5456	182	3	µ	µ	X
ejpam-5456	182	4	[	[	PUNCT
ejpam-5456	182	5	ωsµ	ωsµ	X
ejpam-5456	182	6	[	[	PUNCT
ejpam-5456	182	7	ℶ(ϱ)δ1(ϱ	ℶ(ϱ)δ1(ϱ	PROPN
ejpam-5456	182	8	,	,	PUNCT
ejpam-5456	182	9	φ	φ	NUM
ejpam-5456	182	10	)	)	PUNCT
ejpam-5456	182	11	]	]	PUNCT
ejpam-5456	182	12	]	]	X
ejpam-5456	183	1	+	+	CCONJ
ejpam-5456	183	2	s−1	s−1	PROPN
ejpam-5456	183	3	µ	µ	X
ejpam-5456	183	4	[	[	PUNCT
ejpam-5456	183	5	ωsµ	ωsµ	NOUN
ejpam-5456	183	6	[	[	PUNCT
ejpam-5456	183	7	ℵ	ℵ	X
ejpam-5456	183	8	(	(	PUNCT
ejpam-5456	183	9	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	183	10	,	,	PUNCT
ejpam-5456	183	11	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	183	12	,	,	PUNCT
ejpam-5456	183	13	φ	φ	NUM
ejpam-5456	183	14	)	)	PUNCT
ejpam-5456	183	15	+	+	SYM
ejpam-5456	183	16	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	183	17	,	,	PUNCT
ejpam-5456	183	18	φ	φ	NOUN
ejpam-5456	183	19	)	)	PUNCT
ejpam-5456	183	20	)	)	PUNCT
ejpam-5456	183	21	)	)	PUNCT
ejpam-5456	183	22	]	]	PUNCT
ejpam-5456	183	23	.	.	PUNCT
ejpam-5456	184	1	(	(	PUNCT
ejpam-5456	184	2	10	10	NUM
ejpam-5456	184	3	)	)	PUNCT
ejpam-5456	184	4	consider	consider	VERB
ejpam-5456	184	5	the	the	DET
ejpam-5456	184	6	solution	solution	NOUN
ejpam-5456	184	7	of	of	ADP
ejpam-5456	184	8	eq	eq	PROPN
ejpam-5456	184	9	.	.	PUNCT
ejpam-5456	185	1	(	(	PUNCT
ejpam-5456	185	2	6	6	NUM
ejpam-5456	185	3	)	)	PUNCT
ejpam-5456	185	4	in	in	ADP
ejpam-5456	185	5	the	the	DET
ejpam-5456	185	6	following	follow	VERB
ejpam-5456	185	7	fractional	fractional	ADJ
ejpam-5456	185	8	power	power	NOUN
ejpam-5456	185	9	series	series	PROPN
ejpam-5456	185	10	(	(	PUNCT
ejpam-5456	185	11	fps	fps	PROPN
ejpam-5456	185	12	)	)	PUNCT
ejpam-5456	185	13	using	use	VERB
ejpam-5456	185	14	the	the	DET
ejpam-5456	185	15	idea	idea	NOUN
ejpam-5456	185	16	of	of	ADP
ejpam-5456	185	17	adm	adm	PROPN
ejpam-5456	185	18	.	.	PUNCT
ejpam-5456	186	1	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	186	2	,	,	PUNCT
ejpam-5456	186	3	φ	φ	NUM
ejpam-5456	186	4	)	)	PUNCT
ejpam-5456	187	1	=	=	PUNCT
ejpam-5456	187	2	∞∑	∞∑	NUM
ejpam-5456	187	3	ρ=0	ρ=0	NUM
ejpam-5456	187	4	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	187	5	,	,	PUNCT
ejpam-5456	187	6	φ	φ	NOUN
ejpam-5456	187	7	)	)	PUNCT
ejpam-5456	187	8	,	,	PUNCT
ejpam-5456	187	9	δ2(ϱ	δ2(ϱ	PRON
ejpam-5456	187	10	,	,	PUNCT
ejpam-5456	187	11	φ	φ	NOUN
ejpam-5456	187	12	)	)	PUNCT
ejpam-5456	187	13	=	=	PUNCT
ejpam-5456	188	1	∞∑	∞∑	NUM
ejpam-5456	188	2	ρ=0	ρ=0	NUM
ejpam-5456	188	3	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	188	4	,	,	PUNCT
ejpam-5456	188	5	φ	φ	NOUN
ejpam-5456	188	6	)	)	PUNCT
ejpam-5456	188	7	.	.	PUNCT
ejpam-5456	189	1	(	(	PUNCT
ejpam-5456	189	2	11	11	NUM
ejpam-5456	189	3	)	)	PUNCT
ejpam-5456	189	4	m.i	m.i	PROPN
ejpam-5456	189	5	.	.	PROPN
ejpam-5456	189	6	liaqat	liaqat	PROPN
ejpam-5456	189	7	,	,	PUNCT
ejpam-5456	189	8	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	189	9	/	/	SYM
ejpam-5456	189	10	eur	eur	PROPN
ejpam-5456	189	11	.	.	PUNCT
ejpam-5456	190	1	j.	j.	PROPN
ejpam-5456	190	2	pure	pure	PROPN
ejpam-5456	190	3	appl	appl	PROPN
ejpam-5456	190	4	.	.	PROPN
ejpam-5456	190	5	math	math	PROPN
ejpam-5456	190	6	,	,	PUNCT
ejpam-5456	190	7	17	17	NUM
ejpam-5456	190	8	(	(	PUNCT
ejpam-5456	190	9	4	4	NUM
ejpam-5456	190	10	)	)	PUNCT
ejpam-5456	190	11	(	(	PUNCT
ejpam-5456	190	12	2024	2024	NUM
ejpam-5456	190	13	)	)	PUNCT
ejpam-5456	190	14	,	,	PUNCT
ejpam-5456	190	15	3464	3464	NUM
ejpam-5456	190	16	-	-	SYM
ejpam-5456	190	17	3491	3491	NUM
ejpam-5456	190	18	3471	3471	NUM
ejpam-5456	190	19	the	the	DET
ejpam-5456	190	20	nonlinear	nonlinear	ADJ
ejpam-5456	190	21	terms	term	NOUN
ejpam-5456	190	22	z1(δ1	z1(δ1	NOUN
ejpam-5456	190	23	,	,	PUNCT
ejpam-5456	190	24	δ2	δ2	ADJ
ejpam-5456	190	25	)	)	PUNCT
ejpam-5456	190	26	and	and	CCONJ
ejpam-5456	190	27	z2(δ1	z2(δ1	NOUN
ejpam-5456	190	28	,	,	PUNCT
ejpam-5456	190	29	δ2	δ2	PROPN
ejpam-5456	190	30	)	)	PUNCT
ejpam-5456	190	31	represented	represent	VERB
ejpam-5456	190	32	as	as	ADP
ejpam-5456	190	33	z1(δ1	z1(δ1	NOUN
ejpam-5456	190	34	,	,	PUNCT
ejpam-5456	190	35	δ2	δ2	ADJ
ejpam-5456	190	36	)	)	PUNCT
ejpam-5456	190	37	=	=	PUNCT
ejpam-5456	191	1	∞∑	∞∑	NUM
ejpam-5456	191	2	ρ=0	ρ=0	PROPN
ejpam-5456	191	3	a1,ρ(δ1	a1,ρ(δ1	NOUN
ejpam-5456	191	4	,	,	PUNCT
ejpam-5456	191	5	δ2	δ2	PROPN
ejpam-5456	191	6	)	)	PUNCT
ejpam-5456	191	7	,	,	PUNCT
ejpam-5456	191	8	z2(δ1	z2(δ1	PROPN
ejpam-5456	191	9	,	,	PUNCT
ejpam-5456	191	10	δ2	δ2	ADV
ejpam-5456	191	11	)	)	PUNCT
ejpam-5456	191	12	=	=	PUNCT
ejpam-5456	191	13	∞∑	∞∑	NUM
ejpam-5456	191	14	ρ=0	ρ=0	NUM
ejpam-5456	191	15	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	191	16	,	,	PUNCT
ejpam-5456	191	17	δ2	δ2	PROPN
ejpam-5456	191	18	)	)	PUNCT
ejpam-5456	191	19	,	,	PUNCT
ejpam-5456	191	20	(	(	PUNCT
ejpam-5456	191	21	12	12	NUM
ejpam-5456	191	22	)	)	PUNCT
ejpam-5456	191	23	here	here	ADV
ejpam-5456	191	24	,	,	PUNCT
ejpam-5456	191	25	a1,ρ(δ1	a1,ρ(δ1	PROPN
ejpam-5456	191	26	,	,	PUNCT
ejpam-5456	191	27	δ2	δ2	PROPN
ejpam-5456	191	28	)	)	PUNCT
ejpam-5456	191	29	and	and	CCONJ
ejpam-5456	191	30	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	191	31	,	,	PUNCT
ejpam-5456	191	32	δ2	δ2	VERB
ejpam-5456	191	33	)	)	PUNCT
ejpam-5456	191	34	are	be	AUX
ejpam-5456	191	35	the	the	DET
ejpam-5456	191	36	adomian	adomian	NOUN
ejpam-5456	191	37	polynomials	polynomial	NOUN
ejpam-5456	191	38	(	(	PUNCT
ejpam-5456	191	39	a	a	DET
ejpam-5456	191	40	-	-	PUNCT
ejpam-5456	191	41	ps	ps	NOUN
ejpam-5456	191	42	)	)	PUNCT
ejpam-5456	191	43	for	for	ADP
ejpam-5456	191	44	the	the	DET
ejpam-5456	191	45	nonlinear	nonlinear	ADJ
ejpam-5456	191	46	term	term	NOUN
ejpam-5456	191	47	.	.	PUNCT
ejpam-5456	192	1	a1,ρ(δ1	a1,ρ(δ1	NOUN
ejpam-5456	192	2	,	,	PUNCT
ejpam-5456	192	3	δ2	δ2	ADJ
ejpam-5456	192	4	)	)	PUNCT
ejpam-5456	192	5	=	=	SYM
ejpam-5456	192	6	1	1	NUM
ejpam-5456	192	7	γ(ρ+	γ(ρ+	NUM
ejpam-5456	192	8	1	1	NUM
ejpam-5456	192	9	)	)	PUNCT
ejpam-5456	192	10	∂ρ	∂ρ	PROPN
ejpam-5456	192	11	∂χρ	∂χρ	PROPN
ejpam-5456	192	12	[	[	PUNCT
ejpam-5456	192	13	z1	z1	X
ejpam-5456	192	14	(	(	PUNCT
ejpam-5456	192	15	ρ∑	ρ∑	NOUN
ejpam-5456	192	16	σ=0	σ=0	PROPN
ejpam-5456	192	17	χσδ1,σ(ϱ	χσδ1,σ(ϱ	ADV
ejpam-5456	192	18	,	,	PUNCT
ejpam-5456	192	19	φ	φ	NUM
ejpam-5456	192	20	)	)	PUNCT
ejpam-5456	192	21	)	)	PUNCT
ejpam-5456	192	22	]	]	PUNCT
ejpam-5456	193	1	χ=0	χ=0	X
ejpam-5456	193	2	,	,	PUNCT
ejpam-5456	193	3	ρ	ρ	PROPN
ejpam-5456	193	4	=	=	SYM
ejpam-5456	193	5	0	0	NUM
ejpam-5456	193	6	,	,	PUNCT
ejpam-5456	193	7	1	1	NUM
ejpam-5456	193	8	,	,	PUNCT
ejpam-5456	193	9	2	2	NUM
ejpam-5456	193	10	,	,	PUNCT
ejpam-5456	193	11	.	.	PUNCT
ejpam-5456	193	12	.	.	PUNCT
ejpam-5456	194	1	.	.	PUNCT
ejpam-5456	195	1	,	,	PUNCT
ejpam-5456	195	2	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	195	3	,	,	PUNCT
ejpam-5456	195	4	δ2	δ2	ADJ
ejpam-5456	195	5	)	)	PUNCT
ejpam-5456	195	6	=	=	SYM
ejpam-5456	195	7	1	1	NUM
ejpam-5456	195	8	γ(ρ+	γ(ρ+	NUM
ejpam-5456	195	9	1	1	NUM
ejpam-5456	195	10	)	)	PUNCT
ejpam-5456	195	11	∂ρ	∂ρ	PROPN
ejpam-5456	196	1	∂χρ	∂χρ	PROPN
ejpam-5456	196	2	[	[	PUNCT
ejpam-5456	196	3	z2	z2	PROPN
ejpam-5456	196	4	(	(	PUNCT
ejpam-5456	196	5	ρ∑	ρ∑	PROPN
ejpam-5456	196	6	σ=0	σ=0	PROPN
ejpam-5456	196	7	χσδ2,σ(ϱ	χσδ2,σ(ϱ	PROPN
ejpam-5456	196	8	,	,	PUNCT
ejpam-5456	196	9	φ	φ	NUM
ejpam-5456	196	10	)	)	PUNCT
ejpam-5456	196	11	)	)	PUNCT
ejpam-5456	196	12	]	]	PUNCT
ejpam-5456	197	1	χ=0	χ=0	X
ejpam-5456	197	2	,	,	PUNCT
ejpam-5456	197	3	ρ	ρ	PROPN
ejpam-5456	197	4	=	=	SYM
ejpam-5456	197	5	0	0	NUM
ejpam-5456	197	6	,	,	PUNCT
ejpam-5456	197	7	1	1	NUM
ejpam-5456	197	8	,	,	PUNCT
ejpam-5456	197	9	2	2	NUM
ejpam-5456	197	10	,	,	PUNCT
ejpam-5456	197	11	.	.	PUNCT
ejpam-5456	197	12	.	.	PUNCT
ejpam-5456	197	13	.	.	PUNCT
ejpam-5456	197	14	.	.	PUNCT
ejpam-5456	198	1	(	(	PUNCT
ejpam-5456	198	2	13	13	NUM
ejpam-5456	198	3	)	)	PUNCT
ejpam-5456	198	4	from	from	ADP
ejpam-5456	198	5	eqs	eqs	PROPN
ejpam-5456	198	6	.	.	PUNCT
ejpam-5456	199	1	(	(	PUNCT
ejpam-5456	199	2	11	11	NUM
ejpam-5456	199	3	)	)	PUNCT
ejpam-5456	199	4	,	,	PUNCT
ejpam-5456	199	5	(	(	PUNCT
ejpam-5456	199	6	12	12	NUM
ejpam-5456	199	7	)	)	PUNCT
ejpam-5456	199	8	,	,	PUNCT
ejpam-5456	199	9	and	and	CCONJ
ejpam-5456	199	10	(	(	PUNCT
ejpam-5456	199	11	10	10	NUM
ejpam-5456	199	12	)	)	PUNCT
ejpam-5456	199	13	.	.	PUNCT
ejpam-5456	200	1	∞∑	∞∑	NUM
ejpam-5456	200	2	ρ=0	ρ=0	PUNCT
ejpam-5456	200	3	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	200	4	,	,	PUNCT
ejpam-5456	200	5	φ	φ	NUM
ejpam-5456	200	6	)	)	PUNCT
ejpam-5456	200	7	=	=	NOUN
ejpam-5456	200	8	s−1	s−1	NOUN
ejpam-5456	200	9	µ	µ	NOUN
ejpam-5456	200	10	[	[	PUNCT
ejpam-5456	200	11	δ1(0	δ1(0	PROPN
ejpam-5456	200	12	)	)	PUNCT
ejpam-5456	200	13	]	]	PUNCT
ejpam-5456	201	1	−	−	PROPN
ejpam-5456	201	2	s−1	s−1	PROPN
ejpam-5456	201	3	µ	µ	X
ejpam-5456	201	4	[	[	PUNCT
ejpam-5456	201	5	ωsµ	ωsµ	NOUN
ejpam-5456	201	6	[	[	PUNCT
ejpam-5456	201	7	ζdϱϱ	ζdϱϱ	NOUN
ejpam-5456	201	8	∞∑	∞∑	NUM
ejpam-5456	201	9	ρ=0	ρ=0	PROPN
ejpam-5456	201	10	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	201	11	,	,	PUNCT
ejpam-5456	201	12	φ	φ	NUM
ejpam-5456	201	13	)	)	PUNCT
ejpam-5456	201	14	]	]	X
ejpam-5456	201	15	]	]	PUNCT
ejpam-5456	202	1	−	−	PROPN
ejpam-5456	202	2	ℵ−1	ℵ−1	ADP
ejpam-5456	202	3	ϖ	ϖ	X
ejpam-5456	202	4	[	[	PUNCT
ejpam-5456	202	5	ωℵϖ	ωℵϖ	X
ejpam-5456	202	6	[	[	PUNCT
ejpam-5456	202	7	ℶ(ϱ	ℶ(ϱ	NOUN
ejpam-5456	202	8	)	)	PUNCT
ejpam-5456	202	9	∞∑	∞∑	NUM
ejpam-5456	202	10	ρ=0	ρ=0	NUM
ejpam-5456	202	11	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	202	12	,	,	PUNCT
ejpam-5456	202	13	φ	φ	NUM
ejpam-5456	202	14	)	)	PUNCT
ejpam-5456	202	15	]	]	X
ejpam-5456	202	16	]	]	X
ejpam-5456	202	17	−	−	PROPN
ejpam-5456	202	18	s−1	s−1	PROPN
ejpam-5456	202	19	µ	µ	X
ejpam-5456	202	20	[	[	PUNCT
ejpam-5456	202	21	ωsµ	ωsµ	NOUN
ejpam-5456	202	22	[	[	PUNCT
ejpam-5456	202	23	ℵ	ℵ	ADP
ejpam-5456	202	24	∞∑	∞∑	PROPN
ejpam-5456	202	25	ρ=0	ρ=0	PROPN
ejpam-5456	202	26	a1,ρ(δ1	a1,ρ(δ1	NOUN
ejpam-5456	202	27	,	,	PUNCT
ejpam-5456	202	28	δ2	δ2	PROPN
ejpam-5456	202	29	)	)	PUNCT
ejpam-5456	202	30	]	]	PUNCT
ejpam-5456	202	31	,	,	PUNCT
ejpam-5456	202	32	∞∑	∞∑	NUM
ejpam-5456	202	33	ρ=0	ρ=0	NUM
ejpam-5456	202	34	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	202	35	,	,	PUNCT
ejpam-5456	202	36	φ	φ	NUM
ejpam-5456	202	37	)	)	PUNCT
ejpam-5456	202	38	=	=	NOUN
ejpam-5456	202	39	s−1	s−1	PROPN
ejpam-5456	202	40	µ	µ	X
ejpam-5456	202	41	[	[	PUNCT
ejpam-5456	202	42	δ2(0	δ2(0	NOUN
ejpam-5456	202	43	)	)	PUNCT
ejpam-5456	202	44	]	]	PUNCT
ejpam-5456	203	1	+	+	CCONJ
ejpam-5456	203	2	s−1	s−1	PROPN
ejpam-5456	203	3	µ	µ	X
ejpam-5456	203	4	[	[	PUNCT
ejpam-5456	203	5	ωsµ	ωsµ	NOUN
ejpam-5456	203	6	[	[	PUNCT
ejpam-5456	203	7	ζdϱϱ	ζdϱϱ	NOUN
ejpam-5456	203	8	∞∑	∞∑	PROPN
ejpam-5456	203	9	ρ=0	ρ=0	PROPN
ejpam-5456	203	10	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	203	11	,	,	PUNCT
ejpam-5456	203	12	φ	φ	NUM
ejpam-5456	203	13	)	)	PUNCT
ejpam-5456	203	14	]	]	PUNCT
ejpam-5456	203	15	]	]	X
ejpam-5456	204	1	+	+	CCONJ
ejpam-5456	204	2	s−1	s−1	PROPN
ejpam-5456	204	3	µ	µ	X
ejpam-5456	204	4	[	[	PUNCT
ejpam-5456	204	5	ωsµ	ωsµ	PROPN
ejpam-5456	204	6	[	[	PUNCT
ejpam-5456	204	7	ℶ(ϱ	ℶ(ϱ	NOUN
ejpam-5456	204	8	)	)	PUNCT
ejpam-5456	204	9	∞∑	∞∑	NUM
ejpam-5456	204	10	ρ=0	ρ=0	PUNCT
ejpam-5456	204	11	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	204	12	,	,	PUNCT
ejpam-5456	204	13	φ	φ	NUM
ejpam-5456	204	14	)	)	PUNCT
ejpam-5456	204	15	]	]	PUNCT
ejpam-5456	204	16	]	]	X
ejpam-5456	204	17	+	+	CCONJ
ejpam-5456	204	18	s−1	s−1	PROPN
ejpam-5456	204	19	µ	µ	X
ejpam-5456	204	20	[	[	PUNCT
ejpam-5456	204	21	ωsµ	ωsµ	NOUN
ejpam-5456	204	22	[	[	PUNCT
ejpam-5456	204	23	ℵ	ℵ	ADP
ejpam-5456	204	24	∞∑	∞∑	PROPN
ejpam-5456	204	25	ρ=0	ρ=0	PROPN
ejpam-5456	204	26	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	204	27	,	,	PUNCT
ejpam-5456	204	28	δ2	δ2	ADJ
ejpam-5456	204	29	)	)	PUNCT
ejpam-5456	204	30	]	]	PUNCT
ejpam-5456	204	31	.	.	PUNCT
ejpam-5456	205	1	(	(	PUNCT
ejpam-5456	205	2	14	14	NUM
ejpam-5456	205	3	)	)	PUNCT
ejpam-5456	205	4	from	from	ADP
ejpam-5456	205	5	eq	eq	ADP
ejpam-5456	205	6	.	.	PUNCT
ejpam-5456	206	1	(	(	PUNCT
ejpam-5456	206	2	14	14	NUM
ejpam-5456	206	3	)	)	PUNCT
ejpam-5456	206	4	,	,	PUNCT
ejpam-5456	206	5	we	we	PRON
ejpam-5456	206	6	have	have	VERB
ejpam-5456	206	7	as	as	ADP
ejpam-5456	206	8	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	206	9	,	,	PUNCT
ejpam-5456	206	10	φ	φ	NUM
ejpam-5456	206	11	)	)	PUNCT
ejpam-5456	207	1	=	=	SYM
ejpam-5456	207	2	s−1	s−1	PROPN
ejpam-5456	207	3	µ	µ	X
ejpam-5456	207	4	[	[	PUNCT
ejpam-5456	207	5	δ1(0	δ1(0	PROPN
ejpam-5456	207	6	)	)	PUNCT
ejpam-5456	207	7	]	]	PUNCT
ejpam-5456	207	8	,	,	PUNCT
ejpam-5456	207	9	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	207	10	,	,	PUNCT
ejpam-5456	207	11	φ	φ	NOUN
ejpam-5456	207	12	)	)	PUNCT
ejpam-5456	208	1	=	=	SYM
ejpam-5456	208	2	s−1	s−1	PROPN
ejpam-5456	208	3	µ	µ	X
ejpam-5456	208	4	[	[	PUNCT
ejpam-5456	208	5	δ2(0	δ2(0	NOUN
ejpam-5456	208	6	)	)	PUNCT
ejpam-5456	208	7	]	]	PUNCT
ejpam-5456	208	8	.	.	PUNCT
ejpam-5456	209	1	(	(	PUNCT
ejpam-5456	209	2	15	15	NUM
ejpam-5456	209	3	)	)	PUNCT
ejpam-5456	209	4	the	the	DET
ejpam-5456	209	5	2nd	2nd	ADJ
ejpam-5456	209	6	term	term	NOUN
ejpam-5456	209	7	of	of	ADP
ejpam-5456	209	8	the	the	DET
ejpam-5456	209	9	fps	fps	NOUN
ejpam-5456	209	10	is	be	AUX
ejpam-5456	209	11	as	as	ADP
ejpam-5456	209	12	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	209	13	,	,	PUNCT
ejpam-5456	209	14	φ	φ	NOUN
ejpam-5456	209	15	)	)	PUNCT
ejpam-5456	210	1	=	=	NOUN
ejpam-5456	210	2	−	−	PROPN
ejpam-5456	210	3	s−1	s−1	PROPN
ejpam-5456	210	4	µ	µ	X
ejpam-5456	210	5	[	[	PUNCT
ejpam-5456	210	6	ωsµ	ωsµ	ADJ
ejpam-5456	210	7	[	[	PUNCT
ejpam-5456	210	8	ζdϱϱδ2,0(ϱ	ζdϱϱδ2,0(ϱ	NOUN
ejpam-5456	210	9	,	,	PUNCT
ejpam-5456	210	10	φ	φ	NOUN
ejpam-5456	210	11	)	)	PUNCT
ejpam-5456	210	12	]	]	X
ejpam-5456	210	13	]	]	X
ejpam-5456	210	14	−	−	PROPN
ejpam-5456	210	15	s−1	s−1	PROPN
ejpam-5456	210	16	µ	µ	X
ejpam-5456	210	17	[	[	PUNCT
ejpam-5456	210	18	ωsµ	ωsµ	X
ejpam-5456	210	19	[	[	PUNCT
ejpam-5456	210	20	ℶ(ϱ)δ2,0(ϱ	ℶ(ϱ)δ2,0(ϱ	PROPN
ejpam-5456	210	21	,	,	PUNCT
ejpam-5456	210	22	φ	φ	NUM
ejpam-5456	210	23	)	)	PUNCT
ejpam-5456	210	24	]	]	X
ejpam-5456	210	25	]	]	X
ejpam-5456	210	26	−	−	PROPN
ejpam-5456	210	27	s−1	s−1	PROPN
ejpam-5456	210	28	µ	µ	X
ejpam-5456	210	29	[	[	PUNCT
ejpam-5456	210	30	ωsµ	ωsµ	ADJ
ejpam-5456	210	31	[	[	PUNCT
ejpam-5456	210	32	ℵa1,0(δ1	ℵa1,0(δ1	ADJ
ejpam-5456	210	33	,	,	PUNCT
ejpam-5456	210	34	δ2	δ2	ADJ
ejpam-5456	210	35	)	)	PUNCT
ejpam-5456	210	36	]	]	PUNCT
ejpam-5456	210	37	,	,	PUNCT
ejpam-5456	210	38	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	210	39	,	,	PUNCT
ejpam-5456	210	40	φ	φ	NOUN
ejpam-5456	210	41	)	)	PUNCT
ejpam-5456	211	1	=	=	NOUN
ejpam-5456	211	2	s−1	s−1	PROPN
ejpam-5456	211	3	µ	µ	X
ejpam-5456	211	4	[	[	PUNCT
ejpam-5456	211	5	ωsµ	ωsµ	ADJ
ejpam-5456	211	6	[	[	PUNCT
ejpam-5456	211	7	ζdϱϱδ1,0(ϱ	ζdϱϱδ1,0(ϱ	NOUN
ejpam-5456	211	8	,	,	PUNCT
ejpam-5456	211	9	φ	φ	NOUN
ejpam-5456	211	10	)	)	PUNCT
ejpam-5456	211	11	]	]	PUNCT
ejpam-5456	211	12	]	]	X
ejpam-5456	212	1	+	+	CCONJ
ejpam-5456	212	2	s−1	s−1	PROPN
ejpam-5456	212	3	µ	µ	X
ejpam-5456	212	4	[	[	PUNCT
ejpam-5456	212	5	ωsµ	ωsµ	X
ejpam-5456	212	6	[	[	PUNCT
ejpam-5456	212	7	ℶ(ϱ)δ1,0(ϱ	ℶ(ϱ)δ1,0(ϱ	PROPN
ejpam-5456	212	8	,	,	PUNCT
ejpam-5456	212	9	φ	φ	NUM
ejpam-5456	212	10	)	)	PUNCT
ejpam-5456	212	11	]	]	PUNCT
ejpam-5456	212	12	]	]	X
ejpam-5456	213	1	+	+	CCONJ
ejpam-5456	213	2	s−1	s−1	PROPN
ejpam-5456	213	3	µ	µ	X
ejpam-5456	213	4	[	[	PUNCT
ejpam-5456	213	5	ωsµ	ωsµ	X
ejpam-5456	213	6	[	[	PUNCT
ejpam-5456	213	7	ℵa2,0(δ1	ℵa2,0(δ1	X
ejpam-5456	213	8	,	,	PUNCT
ejpam-5456	213	9	δ2	δ2	ADJ
ejpam-5456	213	10	)	)	PUNCT
ejpam-5456	213	11	]	]	PUNCT
ejpam-5456	213	12	.	.	PUNCT
ejpam-5456	214	1	(	(	PUNCT
ejpam-5456	214	2	16	16	NUM
ejpam-5456	214	3	)	)	PUNCT
ejpam-5456	214	4	the	the	DET
ejpam-5456	214	5	following	follow	VERB
ejpam-5456	214	6	are	be	AUX
ejpam-5456	214	7	the	the	DET
ejpam-5456	214	8	3rd	3rd	ADJ
ejpam-5456	214	9	and	and	CCONJ
ejpam-5456	214	10	4th	4th	ADJ
ejpam-5456	214	11	terms	term	NOUN
ejpam-5456	214	12	of	of	ADP
ejpam-5456	214	13	the	the	DET
ejpam-5456	214	14	fps	fps	PROPN
ejpam-5456	214	15	:	:	PUNCT
ejpam-5456	214	16	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	214	17	,	,	PUNCT
ejpam-5456	214	18	φ	φ	NOUN
ejpam-5456	214	19	)	)	PUNCT
ejpam-5456	214	20	=	=	NOUN
ejpam-5456	214	21	−	−	PROPN
ejpam-5456	214	22	s−1	s−1	PROPN
ejpam-5456	214	23	µ	µ	X
ejpam-5456	214	24	[	[	PUNCT
ejpam-5456	214	25	ωsϱ	ωsϱ	X
ejpam-5456	214	26	[	[	PUNCT
ejpam-5456	214	27	ζdϱϱδ2,1(ϱ	ζdϱϱδ2,1(ϱ	PROPN
ejpam-5456	214	28	,	,	PUNCT
ejpam-5456	214	29	φ	φ	NUM
ejpam-5456	214	30	)	)	PUNCT
ejpam-5456	214	31	]	]	X
ejpam-5456	214	32	]	]	X
ejpam-5456	214	33	−	−	PROPN
ejpam-5456	214	34	s−1	s−1	PROPN
ejpam-5456	214	35	µ	µ	X
ejpam-5456	214	36	[	[	PUNCT
ejpam-5456	214	37	ωsµ	ωsµ	X
ejpam-5456	214	38	[	[	PUNCT
ejpam-5456	214	39	ℶ(ϱ)δ2,1(ϱ	ℶ(ϱ)δ2,1(ϱ	PROPN
ejpam-5456	214	40	,	,	PUNCT
ejpam-5456	214	41	φ	φ	NUM
ejpam-5456	214	42	)	)	PUNCT
ejpam-5456	214	43	]	]	X
ejpam-5456	214	44	]	]	X
ejpam-5456	214	45	−	−	PROPN
ejpam-5456	214	46	m.i	m.i	PROPN
ejpam-5456	214	47	.	.	PROPN
ejpam-5456	214	48	liaqat	liaqat	PROPN
ejpam-5456	214	49	,	,	PUNCT
ejpam-5456	214	50	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	214	51	/	/	SYM
ejpam-5456	214	52	eur	eur	PROPN
ejpam-5456	214	53	.	.	PUNCT
ejpam-5456	215	1	j.	j.	PROPN
ejpam-5456	215	2	pure	pure	PROPN
ejpam-5456	215	3	appl	appl	PROPN
ejpam-5456	215	4	.	.	PROPN
ejpam-5456	215	5	math	math	PROPN
ejpam-5456	215	6	,	,	PUNCT
ejpam-5456	215	7	17	17	NUM
ejpam-5456	215	8	(	(	PUNCT
ejpam-5456	215	9	4	4	NUM
ejpam-5456	215	10	)	)	PUNCT
ejpam-5456	215	11	(	(	PUNCT
ejpam-5456	215	12	2024	2024	NUM
ejpam-5456	215	13	)	)	PUNCT
ejpam-5456	215	14	,	,	PUNCT
ejpam-5456	215	15	3464	3464	NUM
ejpam-5456	215	16	-	-	SYM
ejpam-5456	215	17	3491	3491	NUM
ejpam-5456	215	18	3472	3472	NUM
ejpam-5456	215	19	s−1	s−1	PROPN
ejpam-5456	215	20	µ	µ	X
ejpam-5456	215	21	[	[	PUNCT
ejpam-5456	215	22	ωsµ	ωsµ	ADJ
ejpam-5456	215	23	[	[	PUNCT
ejpam-5456	215	24	ℵa1,1(δ1	ℵa1,1(δ1	ADJ
ejpam-5456	215	25	,	,	PUNCT
ejpam-5456	215	26	δ2	δ2	ADJ
ejpam-5456	215	27	)	)	PUNCT
ejpam-5456	215	28	]	]	PUNCT
ejpam-5456	215	29	,	,	PUNCT
ejpam-5456	215	30	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	215	31	,	,	PUNCT
ejpam-5456	215	32	φ	φ	NUM
ejpam-5456	215	33	)	)	PUNCT
ejpam-5456	215	34	=	=	NOUN
ejpam-5456	215	35	s−1	s−1	PROPN
ejpam-5456	215	36	µ	µ	X
ejpam-5456	215	37	[	[	PUNCT
ejpam-5456	215	38	ωsµ	ωsµ	NOUN
ejpam-5456	215	39	[	[	PUNCT
ejpam-5456	215	40	ζdϱϱδ1,1(ϱ	ζdϱϱδ1,1(ϱ	PROPN
ejpam-5456	215	41	,	,	PUNCT
ejpam-5456	215	42	φ	φ	NUM
ejpam-5456	215	43	)	)	PUNCT
ejpam-5456	215	44	]	]	PUNCT
ejpam-5456	215	45	]	]	X
ejpam-5456	216	1	+	+	CCONJ
ejpam-5456	216	2	s−1	s−1	PROPN
ejpam-5456	216	3	µ	µ	X
ejpam-5456	216	4	[	[	PUNCT
ejpam-5456	216	5	ωsµ	ωsµ	X
ejpam-5456	216	6	[	[	PUNCT
ejpam-5456	216	7	ℶ(ϱ)δ1,1(ϱ	ℶ(ϱ)δ1,1(ϱ	PROPN
ejpam-5456	216	8	,	,	PUNCT
ejpam-5456	216	9	φ	φ	NOUN
ejpam-5456	216	10	)	)	PUNCT
ejpam-5456	216	11	]	]	PUNCT
ejpam-5456	216	12	]	]	X
ejpam-5456	217	1	+	+	CCONJ
ejpam-5456	217	2	s−1	s−1	PROPN
ejpam-5456	217	3	µ	µ	X
ejpam-5456	217	4	[	[	PUNCT
ejpam-5456	217	5	ωsµ	ωsµ	X
ejpam-5456	217	6	[	[	PUNCT
ejpam-5456	217	7	ℵa2,1(δ1	ℵa2,1(δ1	X
ejpam-5456	217	8	,	,	PUNCT
ejpam-5456	217	9	δ2	δ2	ADJ
ejpam-5456	217	10	)	)	PUNCT
ejpam-5456	217	11	]	]	PUNCT
ejpam-5456	217	12	.	.	PUNCT
ejpam-5456	218	1	(	(	PUNCT
ejpam-5456	218	2	17	17	NUM
ejpam-5456	218	3	)	)	PUNCT
ejpam-5456	218	4	δ1,3(ϱ	δ1,3(ϱ	PROPN
ejpam-5456	218	5	,	,	PUNCT
ejpam-5456	218	6	φ	φ	NOUN
ejpam-5456	218	7	)	)	PUNCT
ejpam-5456	219	1	=	=	NOUN
ejpam-5456	219	2	−	−	PROPN
ejpam-5456	219	3	s−1	s−1	PROPN
ejpam-5456	219	4	µ	µ	X
ejpam-5456	219	5	[	[	PUNCT
ejpam-5456	219	6	ωsµ	ωsµ	ADJ
ejpam-5456	219	7	[	[	PUNCT
ejpam-5456	219	8	ζdϱϱδ2,2(ϱ	ζdϱϱδ2,2(ϱ	NOUN
ejpam-5456	219	9	,	,	PUNCT
ejpam-5456	219	10	φ	φ	NUM
ejpam-5456	219	11	)	)	PUNCT
ejpam-5456	219	12	]	]	X
ejpam-5456	219	13	]	]	X
ejpam-5456	219	14	−	−	PROPN
ejpam-5456	219	15	s−1	s−1	PROPN
ejpam-5456	219	16	µ	µ	X
ejpam-5456	219	17	[	[	PUNCT
ejpam-5456	219	18	ωsµ	ωsµ	X
ejpam-5456	219	19	[	[	PUNCT
ejpam-5456	219	20	ℶ(ϱ)δ2,2(ϱ	ℶ(ϱ)δ2,2(ϱ	NOUN
ejpam-5456	219	21	,	,	PUNCT
ejpam-5456	219	22	φ	φ	NUM
ejpam-5456	219	23	)	)	PUNCT
ejpam-5456	219	24	]	]	X
ejpam-5456	219	25	]	]	X
ejpam-5456	219	26	−	−	PROPN
ejpam-5456	219	27	s−1	s−1	PROPN
ejpam-5456	219	28	µ	µ	X
ejpam-5456	219	29	[	[	PUNCT
ejpam-5456	219	30	ωsµ	ωsµ	NOUN
ejpam-5456	219	31	[	[	PUNCT
ejpam-5456	219	32	ℵa1,2(δ1	ℵa1,2(δ1	NOUN
ejpam-5456	219	33	,	,	PUNCT
ejpam-5456	219	34	δ2	δ2	ADJ
ejpam-5456	219	35	)	)	PUNCT
ejpam-5456	219	36	]	]	PUNCT
ejpam-5456	219	37	,	,	PUNCT
ejpam-5456	219	38	δ2,3(ϱ	δ2,3(ϱ	PROPN
ejpam-5456	219	39	,	,	PUNCT
ejpam-5456	219	40	φ	φ	NOUN
ejpam-5456	219	41	)	)	PUNCT
ejpam-5456	220	1	=	=	NOUN
ejpam-5456	220	2	s−1	s−1	PROPN
ejpam-5456	220	3	µ	µ	X
ejpam-5456	220	4	[	[	PUNCT
ejpam-5456	220	5	ωsµ	ωsµ	PROPN
ejpam-5456	220	6	[	[	PUNCT
ejpam-5456	220	7	ζdϱϱδ1,2(ϱ	ζdϱϱδ1,2(ϱ	PROPN
ejpam-5456	220	8	,	,	PUNCT
ejpam-5456	220	9	φ	φ	PROPN
ejpam-5456	220	10	)	)	PUNCT
ejpam-5456	220	11	]	]	PUNCT
ejpam-5456	220	12	]	]	X
ejpam-5456	221	1	+	+	CCONJ
ejpam-5456	221	2	s−1	s−1	PROPN
ejpam-5456	221	3	µ	µ	X
ejpam-5456	221	4	[	[	PUNCT
ejpam-5456	221	5	ωsµ	ωsµ	X
ejpam-5456	221	6	[	[	PUNCT
ejpam-5456	221	7	ℶ(ϱ)δ1,2(ϱ	ℶ(ϱ)δ1,2(ϱ	PROPN
ejpam-5456	221	8	,	,	PUNCT
ejpam-5456	221	9	φ	φ	NUM
ejpam-5456	221	10	)	)	PUNCT
ejpam-5456	221	11	]	]	PUNCT
ejpam-5456	221	12	]	]	X
ejpam-5456	222	1	+	+	CCONJ
ejpam-5456	222	2	s−1	s−1	PROPN
ejpam-5456	222	3	µ	µ	X
ejpam-5456	222	4	[	[	PUNCT
ejpam-5456	222	5	ωsµ	ωsµ	NOUN
ejpam-5456	222	6	[	[	PUNCT
ejpam-5456	222	7	ℵa2,2(δ1	ℵa2,2(δ1	PROPN
ejpam-5456	222	8	,	,	PUNCT
ejpam-5456	222	9	δ2	δ2	ADJ
ejpam-5456	222	10	)	)	PUNCT
ejpam-5456	222	11	]	]	PUNCT
ejpam-5456	222	12	.	.	PUNCT
ejpam-5456	223	1	(	(	PUNCT
ejpam-5456	223	2	18	18	NUM
ejpam-5456	223	3	)	)	PUNCT
ejpam-5456	223	4	by	by	ADP
ejpam-5456	223	5	making	make	VERB
ejpam-5456	223	6	generalizing	generalize	VERB
ejpam-5456	223	7	we	we	PRON
ejpam-5456	223	8	get	get	VERB
ejpam-5456	223	9	the	the	DET
ejpam-5456	223	10	following	following	NOUN
ejpam-5456	223	11	:	:	PUNCT
ejpam-5456	223	12	δ1,ρ+1(ϱ	δ1,ρ+1(ϱ	ADJ
ejpam-5456	223	13	,	,	PUNCT
ejpam-5456	223	14	φ	φ	NOUN
ejpam-5456	223	15	)	)	PUNCT
ejpam-5456	224	1	=	=	NOUN
ejpam-5456	224	2	−	−	PROPN
ejpam-5456	224	3	s−1	s−1	PROPN
ejpam-5456	224	4	µ	µ	X
ejpam-5456	224	5	[	[	PUNCT
ejpam-5456	224	6	ωsµ	ωsµ	X
ejpam-5456	224	7	[	[	PUNCT
ejpam-5456	224	8	ζdϱϱδ2,ρ(ϱ	ζdϱϱδ2,ρ(ϱ	PROPN
ejpam-5456	224	9	,	,	PUNCT
ejpam-5456	224	10	φ	φ	NOUN
ejpam-5456	224	11	)	)	PUNCT
ejpam-5456	224	12	]	]	X
ejpam-5456	224	13	]	]	X
ejpam-5456	224	14	−	−	PROPN
ejpam-5456	224	15	s−1	s−1	PROPN
ejpam-5456	224	16	µ	µ	X
ejpam-5456	224	17	[	[	PUNCT
ejpam-5456	224	18	ωsµ	ωsµ	X
ejpam-5456	224	19	[	[	PUNCT
ejpam-5456	224	20	ℶ(ϱ)δ2,ρ(ϱ	ℶ(ϱ)δ2,ρ(ϱ	PROPN
ejpam-5456	224	21	,	,	PUNCT
ejpam-5456	224	22	φ	φ	NUM
ejpam-5456	224	23	)	)	PUNCT
ejpam-5456	224	24	]	]	X
ejpam-5456	224	25	]	]	X
ejpam-5456	224	26	−	−	PROPN
ejpam-5456	224	27	s−1	s−1	PROPN
ejpam-5456	224	28	µ	µ	X
ejpam-5456	224	29	[	[	PUNCT
ejpam-5456	224	30	ωsµ	ωsµ	NOUN
ejpam-5456	224	31	[	[	PUNCT
ejpam-5456	224	32	ℵa1,ρ(δ1	ℵa1,ρ(δ1	NOUN
ejpam-5456	224	33	,	,	PUNCT
ejpam-5456	224	34	δ2	δ2	ADJ
ejpam-5456	224	35	)	)	PUNCT
ejpam-5456	224	36	]	]	PUNCT
ejpam-5456	224	37	,	,	PUNCT
ejpam-5456	224	38	δ2,ρ+1(ϱ	δ2,ρ+1(ϱ	PROPN
ejpam-5456	224	39	,	,	PUNCT
ejpam-5456	224	40	φ	φ	NOUN
ejpam-5456	224	41	)	)	PUNCT
ejpam-5456	225	1	=	=	NOUN
ejpam-5456	225	2	s−1	s−1	PROPN
ejpam-5456	225	3	µ	µ	X
ejpam-5456	225	4	[	[	PUNCT
ejpam-5456	225	5	ωsµ	ωsµ	X
ejpam-5456	225	6	[	[	PUNCT
ejpam-5456	225	7	ζdϱϱδ1,ρ(ϱ	ζdϱϱδ1,ρ(ϱ	PROPN
ejpam-5456	225	8	,	,	PUNCT
ejpam-5456	225	9	φ	φ	NUM
ejpam-5456	225	10	)	)	PUNCT
ejpam-5456	225	11	]	]	PUNCT
ejpam-5456	225	12	]	]	X
ejpam-5456	226	1	+	+	CCONJ
ejpam-5456	226	2	s−1	s−1	PROPN
ejpam-5456	226	3	µ	µ	X
ejpam-5456	226	4	[	[	PUNCT
ejpam-5456	226	5	ωsµ	ωsµ	X
ejpam-5456	226	6	[	[	PUNCT
ejpam-5456	226	7	ℶ(ϱ)δ1,ρ(ϱ	ℶ(ϱ)δ1,ρ(ϱ	PROPN
ejpam-5456	226	8	,	,	PUNCT
ejpam-5456	226	9	φ	φ	NUM
ejpam-5456	226	10	)	)	PUNCT
ejpam-5456	226	11	]	]	PUNCT
ejpam-5456	226	12	]	]	X
ejpam-5456	227	1	+	+	CCONJ
ejpam-5456	227	2	s−1	s−1	PROPN
ejpam-5456	227	3	µ	µ	X
ejpam-5456	227	4	[	[	PUNCT
ejpam-5456	227	5	ωsµ	ωsµ	NOUN
ejpam-5456	227	6	[	[	PUNCT
ejpam-5456	227	7	ℵa2,ρ(δ1	ℵa2,ρ(δ1	ADJ
ejpam-5456	227	8	,	,	PUNCT
ejpam-5456	227	9	δ2	δ2	PROPN
ejpam-5456	227	10	)	)	PUNCT
ejpam-5456	227	11	]	]	PUNCT
ejpam-5456	227	12	.	.	PUNCT
ejpam-5456	228	1	(	(	PUNCT
ejpam-5456	228	2	19	19	NUM
ejpam-5456	228	3	)	)	PUNCT
ejpam-5456	228	4	lastly	lastly	ADV
ejpam-5456	228	5	,	,	PUNCT
ejpam-5456	228	6	the	the	DET
ejpam-5456	228	7	fps	fps	NOUN
ejpam-5456	228	8	is	be	AUX
ejpam-5456	228	9	obtained	obtain	VERB
ejpam-5456	228	10	in	in	ADP
ejpam-5456	228	11	the	the	DET
ejpam-5456	228	12	following	following	ADJ
ejpam-5456	228	13	ways	way	NOUN
ejpam-5456	228	14	:	:	PUNCT
ejpam-5456	228	15	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	228	16	,	,	PUNCT
ejpam-5456	228	17	φ	φ	NUM
ejpam-5456	228	18	)	)	PUNCT
ejpam-5456	229	1	=	=	VERB
ejpam-5456	229	2	lim	lim	PROPN
ejpam-5456	229	3	σ→∞	σ→∞	NUM
ejpam-5456	229	4	σ∑	σ∑	PROPN
ejpam-5456	229	5	ρ=0	ρ=0	PROPN
ejpam-5456	229	6	δ1,ρ(ϱ	δ1,ρ(ϱ	PROPN
ejpam-5456	229	7	,	,	PUNCT
ejpam-5456	229	8	φ	φ	NOUN
ejpam-5456	229	9	)	)	PUNCT
ejpam-5456	229	10	,	,	PUNCT
ejpam-5456	229	11	δ2(ϱ	δ2(ϱ	PRON
ejpam-5456	229	12	,	,	PUNCT
ejpam-5456	229	13	φ	φ	NOUN
ejpam-5456	229	14	)	)	PUNCT
ejpam-5456	230	1	=	=	VERB
ejpam-5456	230	2	lim	lim	PROPN
ejpam-5456	230	3	σ→∞	σ→∞	NUM
ejpam-5456	230	4	σ∑	σ∑	PROPN
ejpam-5456	230	5	ρ=0	ρ=0	PROPN
ejpam-5456	230	6	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	230	7	,	,	PUNCT
ejpam-5456	230	8	φ	φ	NOUN
ejpam-5456	230	9	)	)	PUNCT
ejpam-5456	230	10	.	.	PUNCT
ejpam-5456	231	1	(	(	PUNCT
ejpam-5456	231	2	20	20	NUM
ejpam-5456	231	3	)	)	SYM
ejpam-5456	231	4	4	4	NUM
ejpam-5456	231	5	.	.	PUNCT
ejpam-5456	231	6	numerical	numerical	ADJ
ejpam-5456	231	7	problems	problem	NOUN
ejpam-5456	231	8	using	use	VERB
ejpam-5456	231	9	the	the	DET
ejpam-5456	231	10	method	method	NOUN
ejpam-5456	231	11	outlined	outline	VERB
ejpam-5456	231	12	in	in	ADP
ejpam-5456	231	13	the	the	DET
ejpam-5456	231	14	preceding	precede	VERB
ejpam-5456	231	15	section	section	NOUN
ejpam-5456	231	16	,	,	PUNCT
ejpam-5456	231	17	we	we	PRON
ejpam-5456	231	18	find	find	VERB
ejpam-5456	231	19	the	the	DET
ejpam-5456	231	20	app	app	NOUN
ejpam-5456	231	21	-	-	PUNCT
ejpam-5456	231	22	ss	ss	PROPN
ejpam-5456	231	23	and	and	CCONJ
ejpam-5456	231	24	ex	ex	NOUN
ejpam-5456	231	25	-	-	NOUN
ejpam-5456	231	26	ss	ss	NOUN
ejpam-5456	231	27	of	of	ADP
ejpam-5456	231	28	linear	linear	PROPN
ejpam-5456	231	29	and	and	CCONJ
ejpam-5456	231	30	nonlinear	nonlinear	ADJ
ejpam-5456	231	31	fsdes	fsde	NOUN
ejpam-5456	231	32	in	in	ADP
ejpam-5456	231	33	this	this	DET
ejpam-5456	231	34	section	section	NOUN
ejpam-5456	231	35	.	.	PUNCT
ejpam-5456	232	1	the	the	DET
ejpam-5456	232	2	solutions	solution	NOUN
ejpam-5456	232	3	to	to	ADP
ejpam-5456	232	4	the	the	DET
ejpam-5456	232	5	schrödinger	schrödinger	NOUN
ejpam-5456	232	6	equations	equation	NOUN
ejpam-5456	232	7	encompass	encompass	VERB
ejpam-5456	232	8	a	a	DET
ejpam-5456	232	9	wealth	wealth	NOUN
ejpam-5456	232	10	of	of	ADP
ejpam-5456	232	11	information	information	NOUN
ejpam-5456	232	12	regarding	regard	VERB
ejpam-5456	232	13	the	the	DET
ejpam-5456	232	14	probabilistic	probabilistic	ADJ
ejpam-5456	232	15	nature	nature	NOUN
ejpam-5456	232	16	of	of	ADP
ejpam-5456	232	17	quantum	quantum	NOUN
ejpam-5456	232	18	systems	system	NOUN
ejpam-5456	232	19	,	,	PUNCT
ejpam-5456	232	20	their	their	PRON
ejpam-5456	232	21	energy	energy	NOUN
ejpam-5456	232	22	states	state	NOUN
ejpam-5456	232	23	,	,	PUNCT
ejpam-5456	232	24	and	and	CCONJ
ejpam-5456	232	25	their	their	PRON
ejpam-5456	232	26	dynamic	dynamic	ADJ
ejpam-5456	232	27	behavior	behavior	NOUN
ejpam-5456	232	28	.	.	PUNCT
ejpam-5456	233	1	this	this	DET
ejpam-5456	233	2	information	information	NOUN
ejpam-5456	233	3	is	be	AUX
ejpam-5456	233	4	foundational	foundational	ADJ
ejpam-5456	233	5	for	for	ADP
ejpam-5456	233	6	understanding	understand	VERB
ejpam-5456	233	7	the	the	DET
ejpam-5456	233	8	principles	principle	NOUN
ejpam-5456	233	9	of	of	ADP
ejpam-5456	233	10	quantum	quantum	ADJ
ejpam-5456	233	11	mechanics	mechanic	NOUN
ejpam-5456	233	12	and	and	CCONJ
ejpam-5456	233	13	their	their	PRON
ejpam-5456	233	14	applications	application	NOUN
ejpam-5456	233	15	in	in	ADP
ejpam-5456	233	16	various	various	ADJ
ejpam-5456	233	17	fields	field	NOUN
ejpam-5456	233	18	,	,	PUNCT
ejpam-5456	233	19	including	include	VERB
ejpam-5456	233	20	quantum	quantum	ADJ
ejpam-5456	233	21	chemistry	chemistry	NOUN
ejpam-5456	233	22	,	,	PUNCT
ejpam-5456	233	23	condensed	condense	VERB
ejpam-5456	233	24	matter	matter	NOUN
ejpam-5456	233	25	physics	physics	NOUN
ejpam-5456	233	26	,	,	PUNCT
ejpam-5456	233	27	and	and	CCONJ
ejpam-5456	233	28	quantum	quantum	NOUN
ejpam-5456	233	29	information	information	NOUN
ejpam-5456	233	30	science	science	NOUN
ejpam-5456	233	31	.	.	PUNCT
ejpam-5456	234	1	problem	problem	NOUN
ejpam-5456	234	2	4.1	4.1	NUM
ejpam-5456	234	3	.	.	PUNCT
ejpam-5456	235	1	examine	examine	VERB
ejpam-5456	235	2	the	the	DET
ejpam-5456	235	3	subsequent	subsequent	ADJ
ejpam-5456	235	4	linear	linear	ADJ
ejpam-5456	235	5	fsdes	fsde	NOUN
ejpam-5456	235	6	:	:	PUNCT
ejpam-5456	235	7	ιtµ	ιtµ	NOUN
ejpam-5456	235	8	φδ(ϱ	φδ(ϱ	NOUN
ejpam-5456	235	9	,	,	PUNCT
ejpam-5456	235	10	φ	φ	NUM
ejpam-5456	235	11	)	)	PUNCT
ejpam-5456	236	1	+	+	CCONJ
ejpam-5456	237	1	dϱϱδ(ϱ	dϱϱδ(ϱ	PROPN
ejpam-5456	237	2	,	,	PUNCT
ejpam-5456	237	3	φ	φ	NUM
ejpam-5456	237	4	)	)	PUNCT
ejpam-5456	237	5	=	=	SYM
ejpam-5456	237	6	0	0	PROPN
ejpam-5456	237	7	,	,	PUNCT
ejpam-5456	237	8	φ	φ	PROPN
ejpam-5456	237	9	≥	≥	PROPN
ejpam-5456	237	10	0	0	NUM
ejpam-5456	237	11	,	,	PUNCT
ejpam-5456	237	12	0	0	PUNCT
ejpam-5456	237	13	<	<	X
ejpam-5456	237	14	µ	µ	X
ejpam-5456	237	15	≤	≤	NUM
ejpam-5456	237	16	1	1	NUM
ejpam-5456	237	17	,	,	PUNCT
ejpam-5456	237	18	(	(	PUNCT
ejpam-5456	237	19	21	21	NUM
ejpam-5456	237	20	)	)	PUNCT
ejpam-5456	237	21	with	with	ADP
ejpam-5456	237	22	the	the	DET
ejpam-5456	237	23	i	i	PROPN
ejpam-5456	237	24	-	-	PUNCT
ejpam-5456	237	25	c	c	NOUN
ejpam-5456	237	26	:	:	PUNCT
ejpam-5456	237	27	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	237	28	,	,	PUNCT
ejpam-5456	237	29	0	0	NUM
ejpam-5456	237	30	)	)	PUNCT
ejpam-5456	237	31	=	=	SYM
ejpam-5456	237	32	1	1	NUM
ejpam-5456	238	1	+	+	CCONJ
ejpam-5456	238	2	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	238	3	)	)	PUNCT
ejpam-5456	238	4	,	,	PUNCT
ejpam-5456	238	5	ϱ	ϱ	PROPN
ejpam-5456	238	6	∈	∈	PROPN
ejpam-5456	238	7	r.	r.	NOUN
ejpam-5456	238	8	by	by	ADP
ejpam-5456	238	9	utilizing	utilize	VERB
ejpam-5456	238	10	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	238	11	,	,	PUNCT
ejpam-5456	238	12	φ	φ	NUM
ejpam-5456	238	13	)	)	PUNCT
ejpam-5456	238	14	=	=	SYM
ejpam-5456	238	15	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	238	16	,	,	PUNCT
ejpam-5456	238	17	φ	φ	NUM
ejpam-5456	238	18	)	)	PUNCT
ejpam-5456	239	1	+	+	CCONJ
ejpam-5456	239	2	ιδ2(ϱ	ιδ2(ϱ	PROPN
ejpam-5456	239	3	,	,	PUNCT
ejpam-5456	239	4	φ	φ	NUM
ejpam-5456	239	5	)	)	PUNCT
ejpam-5456	239	6	and	and	CCONJ
ejpam-5456	239	7	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	239	8	,	,	PUNCT
ejpam-5456	239	9	0	0	NUM
ejpam-5456	239	10	)	)	PUNCT
ejpam-5456	239	11	=	=	SYM
ejpam-5456	239	12	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	239	13	)	)	PUNCT
ejpam-5456	239	14	+	+	CCONJ
ejpam-5456	239	15	ιδ2,0(ϱ	ιδ2,0(ϱ	PROPN
ejpam-5456	239	16	)	)	PUNCT
ejpam-5456	239	17	,	,	PUNCT
ejpam-5456	239	18	we	we	PRON
ejpam-5456	239	19	have	have	VERB
ejpam-5456	239	20	the	the	DET
ejpam-5456	239	21	following	following	NOUN
ejpam-5456	239	22	:	:	PUNCT
ejpam-5456	239	23	tµ	tµ	PRON
ejpam-5456	239	24	φδ1(ϱ	φδ1(ϱ	NUM
ejpam-5456	239	25	,	,	PUNCT
ejpam-5456	239	26	φ	φ	NUM
ejpam-5456	239	27	)	)	PUNCT
ejpam-5456	239	28	=	=	SYM
ejpam-5456	239	29	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	239	30	,	,	PUNCT
ejpam-5456	239	31	φ	φ	NOUN
ejpam-5456	239	32	)	)	PUNCT
ejpam-5456	239	33	,	,	PUNCT
ejpam-5456	239	34	m.i	m.i	PROPN
ejpam-5456	239	35	.	.	PROPN
ejpam-5456	239	36	liaqat	liaqat	PROPN
ejpam-5456	239	37	,	,	PUNCT
ejpam-5456	239	38	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	239	39	/	/	SYM
ejpam-5456	239	40	eur	eur	PROPN
ejpam-5456	239	41	.	.	PUNCT
ejpam-5456	240	1	j.	j.	PROPN
ejpam-5456	240	2	pure	pure	PROPN
ejpam-5456	240	3	appl	appl	PROPN
ejpam-5456	240	4	.	.	PROPN
ejpam-5456	240	5	math	math	PROPN
ejpam-5456	240	6	,	,	PUNCT
ejpam-5456	240	7	17	17	NUM
ejpam-5456	240	8	(	(	PUNCT
ejpam-5456	240	9	4	4	NUM
ejpam-5456	240	10	)	)	PUNCT
ejpam-5456	240	11	(	(	PUNCT
ejpam-5456	240	12	2024	2024	NUM
ejpam-5456	240	13	)	)	PUNCT
ejpam-5456	240	14	,	,	PUNCT
ejpam-5456	240	15	3464	3464	NUM
ejpam-5456	240	16	-	-	SYM
ejpam-5456	240	17	3491	3491	NUM
ejpam-5456	240	18	3473	3473	NUM
ejpam-5456	240	19	tµ	tµ	NOUN
ejpam-5456	240	20	φδ2(ϱ	φδ2(ϱ	PROPN
ejpam-5456	240	21	,	,	PUNCT
ejpam-5456	240	22	φ	φ	NOUN
ejpam-5456	240	23	)	)	PUNCT
ejpam-5456	241	1	=	=	NOUN
ejpam-5456	241	2	−	−	PROPN
ejpam-5456	241	3	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	241	4	,	,	PUNCT
ejpam-5456	241	5	φ	φ	NOUN
ejpam-5456	241	6	)	)	PUNCT
ejpam-5456	241	7	,	,	PUNCT
ejpam-5456	241	8	(	(	PUNCT
ejpam-5456	241	9	22	22	NUM
ejpam-5456	241	10	)	)	PUNCT
ejpam-5456	241	11	with	with	ADP
ejpam-5456	241	12	i	i	PROPN
ejpam-5456	241	13	-	-	PUNCT
ejpam-5456	241	14	cs	cs	ADJ
ejpam-5456	241	15	:	:	PUNCT
ejpam-5456	241	16	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	241	17	,	,	PUNCT
ejpam-5456	241	18	0	0	NUM
ejpam-5456	241	19	)	)	PUNCT
ejpam-5456	241	20	=	=	SYM
ejpam-5456	241	21	1	1	NUM
ejpam-5456	241	22	+	+	CCONJ
ejpam-5456	241	23	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	241	24	)	)	PUNCT
ejpam-5456	241	25	,	,	PUNCT
ejpam-5456	241	26	δ2,0(ϱ	δ2,0(ϱ	NOUN
ejpam-5456	241	27	,	,	PUNCT
ejpam-5456	241	28	0	0	NUM
ejpam-5456	241	29	)	)	PUNCT
ejpam-5456	241	30	=	=	NOUN
ejpam-5456	241	31	0	0	NUM
ejpam-5456	241	32	.	.	PUNCT
ejpam-5456	242	1	(	(	PUNCT
ejpam-5456	242	2	23	23	NUM
ejpam-5456	242	3	)	)	PUNCT
ejpam-5456	242	4	by	by	ADP
ejpam-5456	242	5	applying	apply	VERB
ejpam-5456	242	6	sµ	sµ	NOUN
ejpam-5456	242	7	to	to	ADP
ejpam-5456	242	8	the	the	DET
ejpam-5456	242	9	above	above	ADJ
ejpam-5456	242	10	system	system	NOUN
ejpam-5456	242	11	and	and	CCONJ
ejpam-5456	242	12	implementing	implement	VERB
ejpam-5456	242	13	some	some	DET
ejpam-5456	242	14	calculations	calculation	NOUN
ejpam-5456	242	15	,	,	PUNCT
ejpam-5456	242	16	we	we	PRON
ejpam-5456	242	17	get	get	VERB
ejpam-5456	242	18	the	the	DET
ejpam-5456	242	19	subsequent	subsequent	ADJ
ejpam-5456	242	20	:	:	PUNCT
ejpam-5456	242	21	sµ[δ1(ϱ	sµ[δ1(ϱ	ADJ
ejpam-5456	242	22	,	,	PUNCT
ejpam-5456	242	23	φ	φ	NOUN
ejpam-5456	242	24	)	)	PUNCT
ejpam-5456	242	25	]	]	PUNCT
ejpam-5456	243	1	=	=	PUNCT
ejpam-5456	243	2	δ1(0	δ1(0	PROPN
ejpam-5456	243	3	)	)	PUNCT
ejpam-5456	244	1	+	+	SYM
ejpam-5456	244	2	ωsµ	ωsµ	ADJ
ejpam-5456	244	3	[	[	PUNCT
ejpam-5456	244	4	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	244	5	,	,	PUNCT
ejpam-5456	244	6	φ	φ	NOUN
ejpam-5456	244	7	)	)	PUNCT
ejpam-5456	244	8	]	]	PUNCT
ejpam-5456	244	9	,	,	PUNCT
ejpam-5456	244	10	sµ[δ2(ϱ	sµ[δ2(ϱ	VERB
ejpam-5456	244	11	,	,	PUNCT
ejpam-5456	244	12	φ	φ	NOUN
ejpam-5456	244	13	)	)	PUNCT
ejpam-5456	244	14	]	]	PUNCT
ejpam-5456	245	1	=	=	SYM
ejpam-5456	245	2	δ2(0)−	δ2(0)−	X
ejpam-5456	245	3	ωsµ	ωsµ	PROPN
ejpam-5456	245	4	[	[	PUNCT
ejpam-5456	245	5	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	245	6	,	,	PUNCT
ejpam-5456	245	7	φ	φ	NOUN
ejpam-5456	245	8	)	)	PUNCT
ejpam-5456	245	9	]	]	PUNCT
ejpam-5456	245	10	.	.	PUNCT
ejpam-5456	246	1	(	(	PUNCT
ejpam-5456	246	2	24	24	NUM
ejpam-5456	246	3	)	)	PUNCT
ejpam-5456	246	4	taking	take	VERB
ejpam-5456	246	5	s−1	s−1	PROPN
ejpam-5456	246	6	µ	µ	NOUN
ejpam-5456	246	7	.	.	PUNCT
ejpam-5456	247	1	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	247	2	,	,	PUNCT
ejpam-5456	247	3	φ	φ	NUM
ejpam-5456	247	4	)	)	PUNCT
ejpam-5456	248	1	=	=	NOUN
ejpam-5456	248	2	s−1	s−1	NOUN
ejpam-5456	248	3	µ	µ	NOUN
ejpam-5456	248	4	[	[	PUNCT
ejpam-5456	248	5	δ1(0	δ1(0	PROPN
ejpam-5456	248	6	)	)	PUNCT
ejpam-5456	248	7	]	]	PUNCT
ejpam-5456	249	1	+	+	CCONJ
ejpam-5456	249	2	s−1	s−1	PROPN
ejpam-5456	249	3	µ	µ	X
ejpam-5456	249	4	[	[	PUNCT
ejpam-5456	249	5	ωsµ	ωsµ	X
ejpam-5456	249	6	[	[	PUNCT
ejpam-5456	249	7	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	249	8	,	,	PUNCT
ejpam-5456	249	9	φ	φ	NOUN
ejpam-5456	249	10	)	)	PUNCT
ejpam-5456	249	11	]	]	X
ejpam-5456	249	12	]	]	X
ejpam-5456	249	13	,	,	PUNCT
ejpam-5456	249	14	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	249	15	,	,	PUNCT
ejpam-5456	249	16	φ	φ	NOUN
ejpam-5456	249	17	)	)	PUNCT
ejpam-5456	249	18	=	=	NOUN
ejpam-5456	249	19	s−1	s−1	PROPN
ejpam-5456	249	20	µ	µ	X
ejpam-5456	249	21	[	[	PUNCT
ejpam-5456	249	22	δ2(0	δ2(0	NOUN
ejpam-5456	249	23	)	)	PUNCT
ejpam-5456	249	24	]	]	PUNCT
ejpam-5456	250	1	−	−	PROPN
ejpam-5456	250	2	s−1	s−1	PROPN
ejpam-5456	250	3	µ	µ	X
ejpam-5456	250	4	[	[	PUNCT
ejpam-5456	250	5	ωsµ	ωsµ	NOUN
ejpam-5456	250	6	[	[	PUNCT
ejpam-5456	250	7	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	250	8	,	,	PUNCT
ejpam-5456	250	9	φ	φ	NOUN
ejpam-5456	250	10	)	)	PUNCT
ejpam-5456	250	11	]	]	X
ejpam-5456	250	12	]	]	PUNCT
ejpam-5456	250	13	.	.	PUNCT
ejpam-5456	251	1	(	(	PUNCT
ejpam-5456	251	2	25	25	NUM
ejpam-5456	251	3	)	)	PUNCT
ejpam-5456	251	4	we	we	PRON
ejpam-5456	251	5	derive	derive	VERB
ejpam-5456	251	6	the	the	DET
ejpam-5456	251	7	following	follow	VERB
ejpam-5456	251	8	result	result	NOUN
ejpam-5456	251	9	:	:	PUNCT
ejpam-5456	251	10	∞∑	∞∑	NUM
ejpam-5456	251	11	ρ=0	ρ=0	PUNCT
ejpam-5456	251	12	δ1,ρ(ϱ	δ1,ρ(ϱ	ADP
ejpam-5456	251	13	,	,	PUNCT
ejpam-5456	251	14	φ	φ	NUM
ejpam-5456	251	15	)	)	PUNCT
ejpam-5456	251	16	=	=	NOUN
ejpam-5456	251	17	s−1	s−1	NOUN
ejpam-5456	251	18	µ	µ	NOUN
ejpam-5456	251	19	[	[	PUNCT
ejpam-5456	251	20	δ1(0	δ1(0	PROPN
ejpam-5456	251	21	)	)	PUNCT
ejpam-5456	251	22	]	]	PUNCT
ejpam-5456	252	1	+	+	CCONJ
ejpam-5456	252	2	s−1	s−1	PROPN
ejpam-5456	252	3	µ	µ	X
ejpam-5456	252	4	[	[	PUNCT
ejpam-5456	252	5	ωsµ	ωsµ	NOUN
ejpam-5456	252	6	[	[	PUNCT
ejpam-5456	252	7	dϱϱ	dϱϱ	NOUN
ejpam-5456	252	8	∞∑	∞∑	NUM
ejpam-5456	252	9	ρ=0	ρ=0	PUNCT
ejpam-5456	252	10	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	252	11	,	,	PUNCT
ejpam-5456	252	12	φ	φ	NUM
ejpam-5456	252	13	)	)	PUNCT
ejpam-5456	252	14	]	]	X
ejpam-5456	252	15	]	]	X
ejpam-5456	252	16	,	,	PUNCT
ejpam-5456	252	17	∞∑	∞∑	NUM
ejpam-5456	252	18	ρ=0	ρ=0	NUM
ejpam-5456	252	19	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	252	20	,	,	PUNCT
ejpam-5456	252	21	φ	φ	NUM
ejpam-5456	252	22	)	)	PUNCT
ejpam-5456	252	23	=	=	NOUN
ejpam-5456	252	24	s−1	s−1	PROPN
ejpam-5456	252	25	µ	µ	X
ejpam-5456	252	26	[	[	PUNCT
ejpam-5456	252	27	δ2(0	δ2(0	NOUN
ejpam-5456	252	28	)	)	PUNCT
ejpam-5456	252	29	]	]	PUNCT
ejpam-5456	252	30	−	−	PROPN
ejpam-5456	253	1	s−1	s−1	PROPN
ejpam-5456	253	2	µ	µ	X
ejpam-5456	253	3	[	[	PUNCT
ejpam-5456	253	4	ωsµ	ωsµ	NOUN
ejpam-5456	253	5	[	[	PUNCT
ejpam-5456	253	6	dϱϱ	dϱϱ	NOUN
ejpam-5456	253	7	∞∑	∞∑	PROPN
ejpam-5456	253	8	ρ=0	ρ=0	PROPN
ejpam-5456	253	9	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	253	10	,	,	PUNCT
ejpam-5456	253	11	φ	φ	NUM
ejpam-5456	253	12	)	)	PUNCT
ejpam-5456	253	13	]	]	X
ejpam-5456	253	14	]	]	PUNCT
ejpam-5456	253	15	.	.	PUNCT
ejpam-5456	254	1	(	(	PUNCT
ejpam-5456	254	2	26	26	NUM
ejpam-5456	254	3	)	)	PUNCT
ejpam-5456	254	4	we	we	PRON
ejpam-5456	254	5	extract	extract	VERB
ejpam-5456	254	6	the	the	DET
ejpam-5456	254	7	following	following	NOUN
ejpam-5456	254	8	from	from	ADP
ejpam-5456	254	9	the	the	DET
ejpam-5456	254	10	above	above	ADJ
ejpam-5456	254	11	:	:	PUNCT
ejpam-5456	254	12	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	254	13	,	,	PUNCT
ejpam-5456	254	14	φ	φ	NUM
ejpam-5456	254	15	)	)	PUNCT
ejpam-5456	255	1	=	=	NOUN
ejpam-5456	255	2	s−1	s−1	PROPN
ejpam-5456	255	3	µ	µ	X
ejpam-5456	255	4	[	[	PUNCT
ejpam-5456	255	5	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	255	6	,	,	PUNCT
ejpam-5456	255	7	0	0	NUM
ejpam-5456	255	8	)	)	PUNCT
ejpam-5456	255	9	]	]	PUNCT
ejpam-5456	255	10	,	,	PUNCT
ejpam-5456	255	11	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	255	12	,	,	PUNCT
ejpam-5456	255	13	φ	φ	NOUN
ejpam-5456	255	14	)	)	PUNCT
ejpam-5456	256	1	=	=	NOUN
ejpam-5456	256	2	s−1	s−1	PROPN
ejpam-5456	256	3	µ	µ	NOUN
ejpam-5456	256	4	[	[	PUNCT
ejpam-5456	256	5	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	256	6	,	,	PUNCT
ejpam-5456	256	7	0	0	NUM
ejpam-5456	256	8	)	)	PUNCT
ejpam-5456	256	9	]	]	PUNCT
ejpam-5456	256	10	.	.	PUNCT
ejpam-5456	257	1	(	(	PUNCT
ejpam-5456	257	2	27	27	NUM
ejpam-5456	257	3	)	)	PUNCT
ejpam-5456	257	4	below	below	ADV
ejpam-5456	257	5	is	be	AUX
ejpam-5456	257	6	the	the	DET
ejpam-5456	257	7	first	first	ADJ
ejpam-5456	257	8	term	term	NOUN
ejpam-5456	257	9	:	:	PUNCT
ejpam-5456	257	10	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	257	11	,	,	PUNCT
ejpam-5456	257	12	φ	φ	NUM
ejpam-5456	257	13	)	)	PUNCT
ejpam-5456	258	1	=	=	NOUN
ejpam-5456	258	2	1	1	NUM
ejpam-5456	258	3	+	+	CCONJ
ejpam-5456	258	4	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	258	5	)	)	PUNCT
ejpam-5456	258	6	,	,	PUNCT
ejpam-5456	258	7	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	258	8	,	,	PUNCT
ejpam-5456	258	9	φ	φ	NOUN
ejpam-5456	258	10	)	)	PUNCT
ejpam-5456	258	11	=	=	NOUN
ejpam-5456	258	12	0	0	NUM
ejpam-5456	258	13	.	.	PUNCT
ejpam-5456	259	1	(	(	PUNCT
ejpam-5456	259	2	28	28	NUM
ejpam-5456	259	3	)	)	PUNCT
ejpam-5456	259	4	the	the	DET
ejpam-5456	259	5	next	next	ADJ
ejpam-5456	259	6	term	term	NOUN
ejpam-5456	259	7	expressions	expression	NOUN
ejpam-5456	259	8	are	be	AUX
ejpam-5456	259	9	as	as	SCONJ
ejpam-5456	259	10	follows	follow	VERB
ejpam-5456	259	11	:	:	PUNCT
ejpam-5456	259	12	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	259	13	,	,	PUNCT
ejpam-5456	259	14	φ	φ	NUM
ejpam-5456	259	15	)	)	PUNCT
ejpam-5456	260	1	=	=	NOUN
ejpam-5456	260	2	s−1	s−1	PROPN
ejpam-5456	260	3	µ	µ	X
ejpam-5456	260	4	[	[	PUNCT
ejpam-5456	260	5	ωsµ	ωsµ	ADJ
ejpam-5456	260	6	[	[	PUNCT
ejpam-5456	260	7	dϱϱδ2,0(ϱ	dϱϱδ2,0(ϱ	NOUN
ejpam-5456	260	8	,	,	PUNCT
ejpam-5456	260	9	φ	φ	NOUN
ejpam-5456	260	10	)	)	PUNCT
ejpam-5456	260	11	]	]	X
ejpam-5456	260	12	]	]	PUNCT
ejpam-5456	260	13	,	,	PUNCT
ejpam-5456	260	14	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	260	15	,	,	PUNCT
ejpam-5456	260	16	φ	φ	NOUN
ejpam-5456	260	17	)	)	PUNCT
ejpam-5456	260	18	=	=	NOUN
ejpam-5456	260	19	s−1	s−1	PROPN
ejpam-5456	260	20	µ	µ	X
ejpam-5456	260	21	[	[	PUNCT
ejpam-5456	260	22	ωsµ	ωsµ	ADJ
ejpam-5456	260	23	[	[	PUNCT
ejpam-5456	260	24	dϱϱδ1,0(ϱ	dϱϱδ1,0(ϱ	NOUN
ejpam-5456	260	25	,	,	PUNCT
ejpam-5456	260	26	φ	φ	NUM
ejpam-5456	260	27	)	)	PUNCT
ejpam-5456	260	28	]	]	PUNCT
ejpam-5456	260	29	]	]	PUNCT
ejpam-5456	260	30	.	.	PUNCT
ejpam-5456	261	1	(	(	PUNCT
ejpam-5456	261	2	29	29	NUM
ejpam-5456	261	3	)	)	PUNCT
ejpam-5456	261	4	from	from	ADP
ejpam-5456	261	5	the	the	DET
ejpam-5456	261	6	above	above	ADJ
ejpam-5456	261	7	system	system	NOUN
ejpam-5456	261	8	,	,	PUNCT
ejpam-5456	261	9	we	we	PRON
ejpam-5456	261	10	have	have	VERB
ejpam-5456	261	11	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	261	12	,	,	PUNCT
ejpam-5456	261	13	φ	φ	NUM
ejpam-5456	261	14	)	)	PUNCT
ejpam-5456	262	1	=	=	NOUN
ejpam-5456	262	2	s−1	s−1	PROPN
ejpam-5456	262	3	µ	µ	X
ejpam-5456	262	4	[	[	PUNCT
ejpam-5456	262	5	ωsµ	ωsµ	NOUN
ejpam-5456	262	6	[	[	PUNCT
ejpam-5456	262	7	dϱϱ(0	dϱϱ(0	NOUN
ejpam-5456	262	8	)	)	PUNCT
ejpam-5456	262	9	]	]	PUNCT
ejpam-5456	262	10	]	]	X
ejpam-5456	262	11	,	,	PUNCT
ejpam-5456	262	12	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	262	13	,	,	PUNCT
ejpam-5456	262	14	φ	φ	NOUN
ejpam-5456	262	15	)	)	PUNCT
ejpam-5456	262	16	=	=	NOUN
ejpam-5456	262	17	s−1	s−1	PROPN
ejpam-5456	262	18	µ	µ	X
ejpam-5456	262	19	[	[	PUNCT
ejpam-5456	262	20	ωsµ	ωsµ	ADJ
ejpam-5456	262	21	[	[	PUNCT
ejpam-5456	262	22	dϱϱ(1	dϱϱ(1	NOUN
ejpam-5456	262	23	+	+	CCONJ
ejpam-5456	262	24	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	262	25	)	)	PUNCT
ejpam-5456	262	26	)	)	PUNCT
ejpam-5456	263	1	]	]	PUNCT
ejpam-5456	263	2	]	]	PUNCT
ejpam-5456	263	3	.	.	PUNCT
ejpam-5456	264	1	(	(	PUNCT
ejpam-5456	264	2	30	30	X
ejpam-5456	264	3	)	)	PUNCT
ejpam-5456	264	4	m.i	m.i	PROPN
ejpam-5456	264	5	.	.	PROPN
ejpam-5456	264	6	liaqat	liaqat	PROPN
ejpam-5456	264	7	,	,	PUNCT
ejpam-5456	264	8	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	264	9	/	/	SYM
ejpam-5456	264	10	eur	eur	PROPN
ejpam-5456	264	11	.	.	PUNCT
ejpam-5456	265	1	j.	j.	PROPN
ejpam-5456	265	2	pure	pure	PROPN
ejpam-5456	265	3	appl	appl	PROPN
ejpam-5456	265	4	.	.	PROPN
ejpam-5456	265	5	math	math	PROPN
ejpam-5456	265	6	,	,	PUNCT
ejpam-5456	265	7	17	17	NUM
ejpam-5456	265	8	(	(	PUNCT
ejpam-5456	265	9	4	4	NUM
ejpam-5456	265	10	)	)	PUNCT
ejpam-5456	265	11	(	(	PUNCT
ejpam-5456	265	12	2024	2024	NUM
ejpam-5456	265	13	)	)	PUNCT
ejpam-5456	265	14	,	,	PUNCT
ejpam-5456	265	15	3464	3464	NUM
ejpam-5456	265	16	-	-	SYM
ejpam-5456	265	17	3491	3491	NUM
ejpam-5456	265	18	3474	3474	NUM
ejpam-5456	265	19	as	as	ADP
ejpam-5456	265	20	a	a	DET
ejpam-5456	265	21	result	result	NOUN
ejpam-5456	265	22	,	,	PUNCT
ejpam-5456	265	23	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	265	24	,	,	PUNCT
ejpam-5456	265	25	φ	φ	NUM
ejpam-5456	265	26	)	)	PUNCT
ejpam-5456	265	27	=	=	NOUN
ejpam-5456	265	28	0	0	NUM
ejpam-5456	265	29	,	,	PUNCT
ejpam-5456	265	30	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	265	31	,	,	PUNCT
ejpam-5456	265	32	φ	φ	NOUN
ejpam-5456	265	33	)	)	PUNCT
ejpam-5456	266	1	=	=	NOUN
ejpam-5456	266	2	−	−	PROPN
ejpam-5456	266	3	4	4	NUM
ejpam-5456	266	4	γ(2	γ(2	NOUN
ejpam-5456	266	5	)	)	PUNCT
ejpam-5456	266	6	cosh(2ϱ	cosh(2ϱ	PROPN
ejpam-5456	266	7	)	)	PUNCT
ejpam-5456	266	8	φµ	φµ	ADP
ejpam-5456	266	9	µ	µ	NUM
ejpam-5456	266	10	.	.	PUNCT
ejpam-5456	267	1	(	(	PUNCT
ejpam-5456	267	2	31	31	NUM
ejpam-5456	267	3	)	)	PUNCT
ejpam-5456	267	4	the	the	DET
ejpam-5456	267	5	third	third	ADJ
ejpam-5456	267	6	-	-	PUNCT
ejpam-5456	267	7	term	term	NOUN
ejpam-5456	267	8	expressions	expression	NOUN
ejpam-5456	267	9	are	be	AUX
ejpam-5456	267	10	as	as	SCONJ
ejpam-5456	267	11	follows	follow	VERB
ejpam-5456	267	12	:	:	PUNCT
ejpam-5456	267	13	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	267	14	,	,	PUNCT
ejpam-5456	267	15	φ	φ	NUM
ejpam-5456	267	16	)	)	PUNCT
ejpam-5456	267	17	=	=	NOUN
ejpam-5456	267	18	s−1	s−1	PROPN
ejpam-5456	267	19	µ	µ	X
ejpam-5456	267	20	[	[	PUNCT
ejpam-5456	267	21	ωsµ	ωsµ	NOUN
ejpam-5456	267	22	[	[	PUNCT
ejpam-5456	267	23	dϱϱδ2,1(ϱ	dϱϱδ2,1(ϱ	NOUN
ejpam-5456	267	24	,	,	PUNCT
ejpam-5456	267	25	φ	φ	NUM
ejpam-5456	267	26	)	)	PUNCT
ejpam-5456	267	27	]	]	X
ejpam-5456	267	28	]	]	X
ejpam-5456	267	29	,	,	PUNCT
ejpam-5456	267	30	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	267	31	,	,	PUNCT
ejpam-5456	267	32	φ	φ	NUM
ejpam-5456	267	33	)	)	PUNCT
ejpam-5456	268	1	=	=	NOUN
ejpam-5456	268	2	s−1	s−1	PROPN
ejpam-5456	268	3	µ	µ	X
ejpam-5456	268	4	[	[	PUNCT
ejpam-5456	268	5	ωsµ	ωsµ	X
ejpam-5456	268	6	[	[	PUNCT
ejpam-5456	268	7	dϱϱδ1,1(ϱ	dϱϱδ1,1(ϱ	PROPN
ejpam-5456	268	8	,	,	PUNCT
ejpam-5456	268	9	φ	φ	NUM
ejpam-5456	268	10	)	)	PUNCT
ejpam-5456	268	11	]	]	X
ejpam-5456	268	12	]	]	PUNCT
ejpam-5456	268	13	.	.	PUNCT
ejpam-5456	269	1	(	(	PUNCT
ejpam-5456	269	2	32	32	NUM
ejpam-5456	269	3	)	)	PUNCT
ejpam-5456	269	4	we	we	PRON
ejpam-5456	269	5	have	have	VERB
ejpam-5456	269	6	the	the	DET
ejpam-5456	269	7	following	following	NOUN
ejpam-5456	269	8	from	from	ADP
ejpam-5456	269	9	above	above	ADV
ejpam-5456	269	10	:	:	PUNCT
ejpam-5456	269	11	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	269	12	,	,	PUNCT
ejpam-5456	269	13	φ	φ	NUM
ejpam-5456	269	14	)	)	PUNCT
ejpam-5456	269	15	=	=	NOUN
ejpam-5456	269	16	s−1	s−1	PROPN
ejpam-5456	269	17	µ	µ	X
ejpam-5456	269	18	[	[	PUNCT
ejpam-5456	269	19	ωsµ	ωsµ	NOUN
ejpam-5456	269	20	[	[	PUNCT
ejpam-5456	269	21	dϱϱ	dϱϱ	NOUN
ejpam-5456	269	22	(	(	PUNCT
ejpam-5456	269	23	4	4	NUM
ejpam-5456	269	24	γ(2	γ(2	NOUN
ejpam-5456	269	25	)	)	PUNCT
ejpam-5456	269	26	cosh(2ϱ	cosh(2ϱ	PROPN
ejpam-5456	269	27	)	)	PUNCT
ejpam-5456	269	28	φµ	φµ	ADP
ejpam-5456	269	29	µ	µ	PROPN
ejpam-5456	269	30	)	)	PUNCT
ejpam-5456	269	31	]	]	PUNCT
ejpam-5456	269	32	]	]	X
ejpam-5456	269	33	,	,	PUNCT
ejpam-5456	269	34	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	269	35	,	,	PUNCT
ejpam-5456	269	36	φ	φ	NUM
ejpam-5456	269	37	)	)	PUNCT
ejpam-5456	270	1	=	=	NOUN
ejpam-5456	270	2	s−1	s−1	PROPN
ejpam-5456	270	3	µ	µ	X
ejpam-5456	270	4	[	[	PUNCT
ejpam-5456	270	5	ωsµ	ωsµ	NOUN
ejpam-5456	270	6	[	[	PUNCT
ejpam-5456	270	7	dϱϱ(0	dϱϱ(0	NOUN
ejpam-5456	270	8	)	)	PUNCT
ejpam-5456	270	9	]	]	PUNCT
ejpam-5456	270	10	]	]	PUNCT
ejpam-5456	270	11	.	.	PUNCT
ejpam-5456	271	1	(	(	PUNCT
ejpam-5456	271	2	33	33	NUM
ejpam-5456	271	3	)	)	PUNCT
ejpam-5456	271	4	the	the	DET
ejpam-5456	271	5	third	third	ADJ
ejpam-5456	271	6	term	term	NOUN
ejpam-5456	271	7	is	be	AUX
ejpam-5456	271	8	as	as	SCONJ
ejpam-5456	271	9	follows	follow	VERB
ejpam-5456	271	10	:	:	PUNCT
ejpam-5456	271	11	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	271	12	,	,	PUNCT
ejpam-5456	271	13	φ	φ	NOUN
ejpam-5456	271	14	)	)	PUNCT
ejpam-5456	271	15	=	=	NOUN
ejpam-5456	271	16	−	−	PROPN
ejpam-5456	271	17	8	8	NUM
ejpam-5456	271	18	γ(3	γ(3	PROPN
ejpam-5456	271	19	)	)	PUNCT
ejpam-5456	271	20	cosh(2ϱ	cosh(2ϱ	PROPN
ejpam-5456	271	21	)	)	PUNCT
ejpam-5456	271	22	φ2µ	φ2µ	PROPN
ejpam-5456	271	23	µ2	µ2	PROPN
ejpam-5456	271	24	,	,	PUNCT
ejpam-5456	271	25	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	271	26	,	,	PUNCT
ejpam-5456	271	27	φ	φ	NOUN
ejpam-5456	271	28	)	)	PUNCT
ejpam-5456	271	29	=	=	NOUN
ejpam-5456	271	30	0	0	NUM
ejpam-5456	271	31	.	.	PUNCT
ejpam-5456	272	1	(	(	PUNCT
ejpam-5456	272	2	34	34	NUM
ejpam-5456	272	3	)	)	PUNCT
ejpam-5456	272	4	the	the	DET
ejpam-5456	272	5	next	next	ADJ
ejpam-5456	272	6	terms	term	NOUN
ejpam-5456	272	7	are	be	AUX
ejpam-5456	272	8	as	as	SCONJ
ejpam-5456	272	9	follows	follow	VERB
ejpam-5456	272	10	:	:	PUNCT
ejpam-5456	273	1	δ1,3(ϱ	δ1,3(ϱ	PROPN
ejpam-5456	273	2	,	,	PUNCT
ejpam-5456	273	3	φ	φ	NOUN
ejpam-5456	273	4	)	)	PUNCT
ejpam-5456	273	5	=	=	SYM
ejpam-5456	273	6	0	0	NUM
ejpam-5456	273	7	,	,	PUNCT
ejpam-5456	273	8	δ2,3(ϱ	δ2,3(ϱ	PROPN
ejpam-5456	273	9	,	,	PUNCT
ejpam-5456	273	10	φ	φ	NOUN
ejpam-5456	273	11	)	)	PUNCT
ejpam-5456	273	12	=	=	SYM
ejpam-5456	273	13	64	64	NUM
ejpam-5456	273	14	γ(4	γ(4	ADJ
ejpam-5456	273	15	)	)	PUNCT
ejpam-5456	273	16	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	273	17	)	)	PUNCT
ejpam-5456	273	18	φ3µ	φ3µ	NOUN
ejpam-5456	273	19	µ3	µ3	NOUN
ejpam-5456	273	20	.	.	PUNCT
ejpam-5456	274	1	(	(	PUNCT
ejpam-5456	274	2	35	35	NUM
ejpam-5456	274	3	)	)	PUNCT
ejpam-5456	274	4	δ1,4(ϱ	δ1,4(ϱ	PROPN
ejpam-5456	274	5	,	,	PUNCT
ejpam-5456	274	6	φ	φ	NOUN
ejpam-5456	274	7	)	)	PUNCT
ejpam-5456	274	8	=	=	PROPN
ejpam-5456	274	9	256	256	NUM
ejpam-5456	274	10	γ(5	γ(5	NOUN
ejpam-5456	274	11	)	)	PUNCT
ejpam-5456	274	12	cosh(2ϱ	cosh(2ϱ	PROPN
ejpam-5456	274	13	)	)	PUNCT
ejpam-5456	274	14	φ4µ	φ4µ	PROPN
ejpam-5456	274	15	µ4	µ4	PROPN
ejpam-5456	274	16	,	,	PUNCT
ejpam-5456	274	17	δ2,4(ϱ	δ2,4(ϱ	PROPN
ejpam-5456	274	18	,	,	PUNCT
ejpam-5456	274	19	φ	φ	NOUN
ejpam-5456	274	20	)	)	PUNCT
ejpam-5456	274	21	=	=	NOUN
ejpam-5456	274	22	0	0	NUM
ejpam-5456	274	23	.	.	PUNCT
ejpam-5456	275	1	(	(	PUNCT
ejpam-5456	275	2	36	36	NUM
ejpam-5456	275	3	)	)	PUNCT
ejpam-5456	275	4	the	the	DET
ejpam-5456	275	5	procedure	procedure	NOUN
ejpam-5456	275	6	is	be	AUX
ejpam-5456	275	7	repeated	repeat	VERB
ejpam-5456	275	8	to	to	PART
ejpam-5456	275	9	achieve	achieve	VERB
ejpam-5456	275	10	the	the	DET
ejpam-5456	275	11	results	result	NOUN
ejpam-5456	275	12	for	for	ADP
ejpam-5456	275	13	the	the	DET
ejpam-5456	275	14	sixth	sixth	ADJ
ejpam-5456	275	15	term	term	NOUN
ejpam-5456	275	16	.	.	PUNCT
ejpam-5456	276	1	δ1,5(ϱ	δ1,5(ϱ	PROPN
ejpam-5456	276	2	,	,	PUNCT
ejpam-5456	276	3	φ	φ	NOUN
ejpam-5456	276	4	)	)	PUNCT
ejpam-5456	276	5	=	=	NOUN
ejpam-5456	276	6	0	0	NUM
ejpam-5456	276	7	,	,	PUNCT
ejpam-5456	276	8	δ2,5(ϱ	δ2,5(ϱ	PROPN
ejpam-5456	276	9	,	,	PUNCT
ejpam-5456	276	10	φ	φ	NOUN
ejpam-5456	276	11	)	)	PUNCT
ejpam-5456	276	12	=	=	NOUN
ejpam-5456	276	13	−	−	PROPN
ejpam-5456	276	14	1024	1024	NUM
ejpam-5456	276	15	γ(6	γ(6	NOUN
ejpam-5456	276	16	)	)	PUNCT
ejpam-5456	276	17	cosh(2ϱ	cosh(2ϱ	PROPN
ejpam-5456	276	18	)	)	PUNCT
ejpam-5456	276	19	φ5µ	φ5µ	NOUN
ejpam-5456	276	20	µ5	µ5	PROPN
ejpam-5456	276	21	.	.	PUNCT
ejpam-5456	277	1	(	(	PUNCT
ejpam-5456	277	2	37	37	NUM
ejpam-5456	277	3	)	)	PUNCT
ejpam-5456	277	4	as	as	ADP
ejpam-5456	277	5	a	a	DET
ejpam-5456	277	6	result	result	NOUN
ejpam-5456	277	7	,	,	PUNCT
ejpam-5456	277	8	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	277	9	,	,	PUNCT
ejpam-5456	277	10	φ	φ	NUM
ejpam-5456	277	11	)	)	PUNCT
ejpam-5456	277	12	=	=	SYM
ejpam-5456	278	1	1	1	NUM
ejpam-5456	278	2	+	+	CCONJ
ejpam-5456	278	3	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	278	4	)	)	PUNCT
ejpam-5456	278	5	(	(	PUNCT
ejpam-5456	278	6	∞∑	∞∑	NUM
ejpam-5456	278	7	ρ=0	ρ=0	NUM
ejpam-5456	278	8	(	(	PUNCT
ejpam-5456	278	9	−1)ρ	−1)ρ	NOUN
ejpam-5456	278	10	γ(2ρ+	γ(2ρ+	VERB
ejpam-5456	278	11	1	1	NUM
ejpam-5456	278	12	)	)	PUNCT
ejpam-5456	278	13	(	(	PUNCT
ejpam-5456	278	14	4φµ	4φµ	NOUN
ejpam-5456	278	15	µ	µ	X
ejpam-5456	278	16	)	)	PUNCT
ejpam-5456	278	17	2ρ	2ρ	NOUN
ejpam-5456	278	18	−	−	PROPN
ejpam-5456	279	1	ι	ι	PROPN
ejpam-5456	279	2	∞∑	∞∑	PRON
ejpam-5456	279	3	ρ=0	ρ=0	PROPN
ejpam-5456	279	4	(	(	PUNCT
ejpam-5456	279	5	−1)ρ	−1)ρ	NOUN
ejpam-5456	279	6	γ(2ρ+	γ(2ρ+	VERB
ejpam-5456	279	7	2	2	NUM
ejpam-5456	279	8	)	)	PUNCT
ejpam-5456	279	9	(	(	PUNCT
ejpam-5456	279	10	4φµ	4φµ	ADJ
ejpam-5456	279	11	µ	µ	X
ejpam-5456	279	12	)	)	PUNCT
ejpam-5456	279	13	2ρ+1	2ρ+1	PROPN
ejpam-5456	279	14	)	)	PUNCT
ejpam-5456	279	15	.	.	PUNCT
ejpam-5456	280	1	(	(	PUNCT
ejpam-5456	280	2	38	38	NUM
ejpam-5456	280	3	)	)	PUNCT
ejpam-5456	280	4	m.i	m.i	PROPN
ejpam-5456	280	5	.	.	PROPN
ejpam-5456	280	6	liaqat	liaqat	PROPN
ejpam-5456	280	7	,	,	PUNCT
ejpam-5456	280	8	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	280	9	/	/	SYM
ejpam-5456	280	10	eur	eur	PROPN
ejpam-5456	280	11	.	.	PUNCT
ejpam-5456	281	1	j.	j.	PROPN
ejpam-5456	281	2	pure	pure	PROPN
ejpam-5456	281	3	appl	appl	PROPN
ejpam-5456	281	4	.	.	PROPN
ejpam-5456	281	5	math	math	PROPN
ejpam-5456	281	6	,	,	PUNCT
ejpam-5456	281	7	17	17	NUM
ejpam-5456	281	8	(	(	PUNCT
ejpam-5456	281	9	4	4	NUM
ejpam-5456	281	10	)	)	PUNCT
ejpam-5456	281	11	(	(	PUNCT
ejpam-5456	281	12	2024	2024	NUM
ejpam-5456	281	13	)	)	PUNCT
ejpam-5456	281	14	,	,	PUNCT
ejpam-5456	281	15	3464	3464	NUM
ejpam-5456	281	16	-	-	SYM
ejpam-5456	281	17	3491	3491	NUM
ejpam-5456	281	18	3475	3475	NUM
ejpam-5456	281	19	the	the	DET
ejpam-5456	281	20	ex	ex	NOUN
ejpam-5456	281	21	-	-	PROPN
ejpam-5456	281	22	s	s	PRON
ejpam-5456	281	23	when	when	SCONJ
ejpam-5456	281	24	µ	µ	X
ejpam-5456	281	25	=	=	SYM
ejpam-5456	281	26	1.0	1.0	NUM
ejpam-5456	281	27	is	be	AUX
ejpam-5456	281	28	1	1	NUM
ejpam-5456	281	29	+	+	CCONJ
ejpam-5456	281	30	cosh(2ϱ	cosh(2ϱ	ADJ
ejpam-5456	281	31	)	)	PUNCT
ejpam-5456	281	32	exp−4ιφ	exp−4ιφ	PROPN
ejpam-5456	281	33	.	.	PUNCT
ejpam-5456	282	1	a	a	DET
ejpam-5456	282	2	similar	similar	ADJ
ejpam-5456	282	3	result	result	NOUN
ejpam-5456	282	4	was	be	AUX
ejpam-5456	282	5	obtained	obtain	VERB
ejpam-5456	282	6	by	by	ADP
ejpam-5456	282	7	[	[	X
ejpam-5456	282	8	10	10	NUM
ejpam-5456	282	9	]	]	PUNCT
ejpam-5456	282	10	.	.	PUNCT
ejpam-5456	283	1	problem	problem	NOUN
ejpam-5456	283	2	4.2	4.2	NUM
ejpam-5456	283	3	.	.	PUNCT
ejpam-5456	284	1	take	take	VERB
ejpam-5456	284	2	into	into	ADP
ejpam-5456	284	3	consideration	consideration	NOUN
ejpam-5456	284	4	the	the	DET
ejpam-5456	284	5	subsequent	subsequent	ADJ
ejpam-5456	284	6	nonlinear	nonlinear	ADJ
ejpam-5456	284	7	fsde	fsde	NOUN
ejpam-5456	284	8	:	:	PUNCT
ejpam-5456	284	9	ιtµ	ιtµ	PROPN
ejpam-5456	284	10	φδ(ϱ	φδ(ϱ	NOUN
ejpam-5456	284	11	,	,	PUNCT
ejpam-5456	284	12	φ	φ	NUM
ejpam-5456	284	13	)	)	PUNCT
ejpam-5456	284	14	+	+	SYM
ejpam-5456	284	15	δϱϱ(ϱ	δϱϱ(ϱ	PROPN
ejpam-5456	284	16	,	,	PUNCT
ejpam-5456	284	17	φ	φ	NUM
ejpam-5456	284	18	)	)	PUNCT
ejpam-5456	284	19	+	+	NUM
ejpam-5456	284	20	2|δ(ϱ	2|δ(ϱ	NOUN
ejpam-5456	284	21	,	,	PUNCT
ejpam-5456	284	22	φ)|2δ(ϱ	φ)|2δ(ϱ	PROPN
ejpam-5456	284	23	,	,	PUNCT
ejpam-5456	284	24	φ	φ	NUM
ejpam-5456	284	25	)	)	PUNCT
ejpam-5456	284	26	=	=	SYM
ejpam-5456	284	27	0	0	NUM
ejpam-5456	284	28	,	,	PUNCT
ejpam-5456	284	29	(	(	PUNCT
ejpam-5456	284	30	39	39	NUM
ejpam-5456	284	31	)	)	PUNCT
ejpam-5456	284	32	with	with	ADP
ejpam-5456	284	33	the	the	DET
ejpam-5456	284	34	i	i	PROPN
ejpam-5456	284	35	-	-	PUNCT
ejpam-5456	284	36	c	c	NOUN
ejpam-5456	284	37	:	:	PUNCT
ejpam-5456	284	38	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	284	39	,	,	PUNCT
ejpam-5456	284	40	0	0	NUM
ejpam-5456	284	41	)	)	PUNCT
ejpam-5456	284	42	=	=	SYM
ejpam-5456	284	43	expiϱ	expiϱ	PROPN
ejpam-5456	284	44	,	,	PUNCT
ejpam-5456	284	45	ϱ	ϱ	PROPN
ejpam-5456	284	46	∈	∈	PROPN
ejpam-5456	284	47	r.	r.	PROPN
ejpam-5456	284	48	(	(	PUNCT
ejpam-5456	284	49	40	40	NUM
ejpam-5456	284	50	)	)	PUNCT
ejpam-5456	284	51	suppose	suppose	VERB
ejpam-5456	284	52	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	284	53	,	,	PUNCT
ejpam-5456	284	54	φ	φ	NUM
ejpam-5456	284	55	)	)	PUNCT
ejpam-5456	284	56	=	=	SYM
ejpam-5456	284	57	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	284	58	,	,	PUNCT
ejpam-5456	284	59	φ	φ	NUM
ejpam-5456	284	60	)	)	PUNCT
ejpam-5456	284	61	+	+	CCONJ
ejpam-5456	284	62	ιδ2(ϱ	ιδ2(ϱ	PROPN
ejpam-5456	284	63	,	,	PUNCT
ejpam-5456	284	64	φ	φ	NOUN
ejpam-5456	284	65	)	)	PUNCT
ejpam-5456	284	66	so	so	SCONJ
ejpam-5456	284	67	that	that	SCONJ
ejpam-5456	284	68	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	284	69	,	,	PUNCT
ejpam-5456	284	70	0	0	NUM
ejpam-5456	284	71	)	)	PUNCT
ejpam-5456	284	72	=	=	SYM
ejpam-5456	284	73	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	284	74	)	)	PUNCT
ejpam-5456	285	1	+	+	CCONJ
ejpam-5456	285	2	ιδ2,0(ϱ	ιδ2,0(ϱ	PROPN
ejpam-5456	285	3	)	)	PUNCT
ejpam-5456	285	4	.	.	PUNCT
ejpam-5456	286	1	as	as	ADP
ejpam-5456	286	2	a	a	DET
ejpam-5456	286	3	result	result	NOUN
ejpam-5456	286	4	,	,	PUNCT
ejpam-5456	286	5	tµ	tµ	PRON
ejpam-5456	286	6	φδ1(ϱ	φδ1(ϱ	NUM
ejpam-5456	286	7	,	,	PUNCT
ejpam-5456	286	8	φ	φ	NUM
ejpam-5456	286	9	)	)	PUNCT
ejpam-5456	286	10	=	=	PUNCT
ejpam-5456	286	11	−dϱϱδ2(ϱ	−dϱϱδ2(ϱ	ADV
ejpam-5456	286	12	,	,	PUNCT
ejpam-5456	286	13	φ)−	φ)−	PROPN
ejpam-5456	286	14	2	2	NUM
ejpam-5456	286	15	(	(	PUNCT
ejpam-5456	286	16	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	286	17	,	,	PUNCT
ejpam-5456	286	18	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	286	19	,	,	PUNCT
ejpam-5456	286	20	φ	φ	NUM
ejpam-5456	286	21	)	)	PUNCT
ejpam-5456	286	22	+	+	CCONJ
ejpam-5456	286	23	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	286	24	,	,	PUNCT
ejpam-5456	286	25	φ	φ	NUM
ejpam-5456	286	26	)	)	PUNCT
ejpam-5456	286	27	)	)	PUNCT
ejpam-5456	286	28	,	,	PUNCT
ejpam-5456	286	29	tµ	tµ	PROPN
ejpam-5456	286	30	τ	τ	PROPN
ejpam-5456	286	31	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	286	32	,	,	PUNCT
ejpam-5456	286	33	φ	φ	NUM
ejpam-5456	286	34	)	)	PUNCT
ejpam-5456	286	35	=	=	PUNCT
ejpam-5456	286	36	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	286	37	,	,	PUNCT
ejpam-5456	286	38	φ	φ	NOUN
ejpam-5456	286	39	)	)	PUNCT
ejpam-5456	286	40	+	+	CCONJ
ejpam-5456	286	41	2	2	NUM
ejpam-5456	286	42	(	(	PUNCT
ejpam-5456	286	43	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	286	44	,	,	PUNCT
ejpam-5456	286	45	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	286	46	,	,	PUNCT
ejpam-5456	286	47	φ	φ	NUM
ejpam-5456	286	48	)	)	PUNCT
ejpam-5456	286	49	+	+	SYM
ejpam-5456	286	50	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	286	51	,	,	PUNCT
ejpam-5456	286	52	φ	φ	NOUN
ejpam-5456	286	53	)	)	PUNCT
ejpam-5456	286	54	)	)	PUNCT
ejpam-5456	286	55	.	.	PUNCT
ejpam-5456	287	1	(	(	PUNCT
ejpam-5456	287	2	41	41	NUM
ejpam-5456	287	3	)	)	PUNCT
ejpam-5456	287	4	with	with	ADP
ejpam-5456	287	5	the	the	DET
ejpam-5456	287	6	i.cs	i.cs	NOUN
ejpam-5456	287	7	:	:	PUNCT
ejpam-5456	287	8	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	287	9	,	,	PUNCT
ejpam-5456	287	10	0	0	NUM
ejpam-5456	287	11	)	)	PUNCT
ejpam-5456	287	12	=	=	SYM
ejpam-5456	287	13	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	287	14	)	)	PUNCT
ejpam-5456	287	15	,	,	PUNCT
ejpam-5456	287	16	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	287	17	,	,	PUNCT
ejpam-5456	287	18	0	0	NUM
ejpam-5456	287	19	)	)	PUNCT
ejpam-5456	287	20	=	=	SYM
ejpam-5456	287	21	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	287	22	)	)	PUNCT
ejpam-5456	287	23	,	,	PUNCT
ejpam-5456	287	24	(	(	PUNCT
ejpam-5456	287	25	42	42	X
ejpam-5456	287	26	)	)	PUNCT
ejpam-5456	287	27	applying	apply	VERB
ejpam-5456	287	28	st	st	PROPN
ejpam-5456	287	29	to	to	ADP
ejpam-5456	287	30	eq	eq	PROPN
ejpam-5456	287	31	.	.	PUNCT
ejpam-5456	288	1	(	(	PUNCT
ejpam-5456	288	2	41	41	NUM
ejpam-5456	288	3	)	)	PUNCT
ejpam-5456	288	4	,	,	PUNCT
ejpam-5456	288	5	using	use	VERB
ejpam-5456	288	6	the	the	DET
ejpam-5456	288	7	linear	linear	ADJ
ejpam-5456	288	8	property	property	NOUN
ejpam-5456	288	9	of	of	ADP
ejpam-5456	288	10	st	st	PROPN
ejpam-5456	288	11	and	and	CCONJ
ejpam-5456	288	12	lemma	lemma	PROPN
ejpam-5456	288	13	1(iii	1(iii	NUM
ejpam-5456	288	14	)	)	PUNCT
ejpam-5456	288	15	and	and	CCONJ
ejpam-5456	288	16	making	make	VERB
ejpam-5456	288	17	some	some	DET
ejpam-5456	288	18	calculations	calculation	NOUN
ejpam-5456	288	19	,	,	PUNCT
ejpam-5456	288	20	we	we	PRON
ejpam-5456	288	21	get	get	VERB
ejpam-5456	288	22	sµ[δ1(ϱ	sµ[δ1(ϱ	ADJ
ejpam-5456	288	23	,	,	PUNCT
ejpam-5456	288	24	φ	φ	NOUN
ejpam-5456	288	25	)	)	PUNCT
ejpam-5456	288	26	]	]	PUNCT
ejpam-5456	289	1	=	=	NUM
ejpam-5456	289	2	δ1(0)−	δ1(0)−	PROPN
ejpam-5456	289	3	ωsµ	ωsµ	PROPN
ejpam-5456	289	4	[	[	PUNCT
ejpam-5456	289	5	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	289	6	,	,	PUNCT
ejpam-5456	289	7	φ	φ	NOUN
ejpam-5456	289	8	)	)	PUNCT
ejpam-5456	289	9	]	]	PUNCT
ejpam-5456	289	10	−	−	PROPN
ejpam-5456	289	11	ωsµ	ωsµ	X
ejpam-5456	289	12	[	[	PUNCT
ejpam-5456	289	13	2	2	NUM
ejpam-5456	289	14	(	(	PUNCT
ejpam-5456	289	15	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	289	16	,	,	PUNCT
ejpam-5456	289	17	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	289	18	,	,	PUNCT
ejpam-5456	289	19	φ	φ	NUM
ejpam-5456	289	20	)	)	PUNCT
ejpam-5456	289	21	+	+	CCONJ
ejpam-5456	289	22	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	289	23	,	,	PUNCT
ejpam-5456	289	24	φ	φ	NUM
ejpam-5456	289	25	)	)	PUNCT
ejpam-5456	289	26	)	)	PUNCT
ejpam-5456	289	27	]	]	PUNCT
ejpam-5456	289	28	,	,	PUNCT
ejpam-5456	289	29	sµ[δ2(ϱ	sµ[δ2(ϱ	PROPN
ejpam-5456	289	30	,	,	PUNCT
ejpam-5456	289	31	φ	φ	NOUN
ejpam-5456	289	32	)	)	PUNCT
ejpam-5456	289	33	]	]	PUNCT
ejpam-5456	290	1	=	=	X
ejpam-5456	290	2	δ2(0	δ2(0	NOUN
ejpam-5456	290	3	)	)	PUNCT
ejpam-5456	291	1	+	+	CCONJ
ejpam-5456	291	2	ωsµ	ωsµ	NOUN
ejpam-5456	291	3	[	[	PUNCT
ejpam-5456	291	4	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	291	5	,	,	PUNCT
ejpam-5456	291	6	φ	φ	NOUN
ejpam-5456	291	7	)	)	PUNCT
ejpam-5456	291	8	]	]	PUNCT
ejpam-5456	292	1	+	+	PUNCT
ejpam-5456	292	2	ωsµ	ωsµ	ADJ
ejpam-5456	292	3	[	[	PUNCT
ejpam-5456	292	4	2	2	NUM
ejpam-5456	292	5	(	(	PUNCT
ejpam-5456	292	6	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	292	7	,	,	PUNCT
ejpam-5456	292	8	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	292	9	,	,	PUNCT
ejpam-5456	292	10	φ	φ	NUM
ejpam-5456	292	11	)	)	PUNCT
ejpam-5456	292	12	+	+	SYM
ejpam-5456	292	13	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	292	14	,	,	PUNCT
ejpam-5456	292	15	φ	φ	NOUN
ejpam-5456	292	16	)	)	PUNCT
ejpam-5456	292	17	)	)	PUNCT
ejpam-5456	292	18	]	]	PUNCT
ejpam-5456	292	19	.	.	PUNCT
ejpam-5456	293	1	(	(	PUNCT
ejpam-5456	293	2	43	43	NUM
ejpam-5456	293	3	)	)	PUNCT
ejpam-5456	293	4	through	through	ADP
ejpam-5456	293	5	s−1	s−1	PROPN
ejpam-5456	293	6	µ	µ	NOUN
ejpam-5456	293	7	on	on	ADP
ejpam-5456	293	8	the	the	DET
ejpam-5456	293	9	system	system	NOUN
ejpam-5456	293	10	mentioned	mention	VERB
ejpam-5456	293	11	before	before	ADV
ejpam-5456	293	12	.	.	PUNCT
ejpam-5456	294	1	δ1(υ	δ1(υ	PROPN
ejpam-5456	294	2	,	,	PUNCT
ejpam-5456	294	3	τ	τ	X
ejpam-5456	294	4	)	)	PUNCT
ejpam-5456	295	1	=	=	NOUN
ejpam-5456	295	2	s−1	s−1	PROPN
ejpam-5456	295	3	µ	µ	NOUN
ejpam-5456	295	4	[	[	PUNCT
ejpam-5456	295	5	δ1(0	δ1(0	PROPN
ejpam-5456	295	6	)	)	PUNCT
ejpam-5456	295	7	]	]	PUNCT
ejpam-5456	296	1	−	−	PROPN
ejpam-5456	296	2	s−1	s−1	PROPN
ejpam-5456	296	3	µ	µ	X
ejpam-5456	296	4	[	[	PUNCT
ejpam-5456	296	5	ωsµ	ωsµ	X
ejpam-5456	296	6	[	[	PUNCT
ejpam-5456	296	7	dυυδ2(ϱ	dυυδ2(ϱ	PROPN
ejpam-5456	296	8	,	,	PUNCT
ejpam-5456	296	9	φ	φ	NUM
ejpam-5456	296	10	)	)	PUNCT
ejpam-5456	296	11	]	]	X
ejpam-5456	296	12	]	]	X
ejpam-5456	296	13	−	−	PROPN
ejpam-5456	296	14	s−1	s−1	PROPN
ejpam-5456	296	15	µ	µ	X
ejpam-5456	296	16	[	[	PUNCT
ejpam-5456	296	17	ωsµ	ωsµ	X
ejpam-5456	296	18	[	[	PUNCT
ejpam-5456	296	19	2	2	NUM
ejpam-5456	296	20	(	(	PUNCT
ejpam-5456	296	21	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	296	22	,	,	PUNCT
ejpam-5456	296	23	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	296	24	,	,	PUNCT
ejpam-5456	296	25	φ	φ	NUM
ejpam-5456	296	26	)	)	PUNCT
ejpam-5456	297	1	+	+	CCONJ
ejpam-5456	297	2	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	297	3	,	,	PUNCT
ejpam-5456	297	4	φ	φ	NUM
ejpam-5456	297	5	)	)	PUNCT
ejpam-5456	297	6	)	)	PUNCT
ejpam-5456	298	1	]	]	PUNCT
ejpam-5456	298	2	]	]	X
ejpam-5456	298	3	,	,	PUNCT
ejpam-5456	298	4	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	298	5	,	,	PUNCT
ejpam-5456	298	6	φ	φ	NOUN
ejpam-5456	298	7	)	)	PUNCT
ejpam-5456	298	8	=	=	NOUN
ejpam-5456	298	9	s−1	s−1	PROPN
ejpam-5456	298	10	µ	µ	X
ejpam-5456	298	11	[	[	PUNCT
ejpam-5456	298	12	δ2(0	δ2(0	NOUN
ejpam-5456	298	13	)	)	PUNCT
ejpam-5456	298	14	]	]	PUNCT
ejpam-5456	299	1	+	+	CCONJ
ejpam-5456	299	2	s−1	s−1	PROPN
ejpam-5456	299	3	µ	µ	X
ejpam-5456	299	4	[	[	PUNCT
ejpam-5456	299	5	ωsµ	ωsµ	NOUN
ejpam-5456	299	6	[	[	PUNCT
ejpam-5456	299	7	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	299	8	,	,	PUNCT
ejpam-5456	299	9	φ	φ	NOUN
ejpam-5456	299	10	)	)	PUNCT
ejpam-5456	299	11	]	]	PUNCT
ejpam-5456	299	12	]	]	X
ejpam-5456	300	1	+	+	CCONJ
ejpam-5456	300	2	s−1	s−1	PROPN
ejpam-5456	300	3	µ	µ	X
ejpam-5456	300	4	[	[	PUNCT
ejpam-5456	300	5	ωsµ	ωsµ	X
ejpam-5456	300	6	[	[	PUNCT
ejpam-5456	300	7	2	2	NUM
ejpam-5456	300	8	(	(	PUNCT
ejpam-5456	300	9	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	300	10	,	,	PUNCT
ejpam-5456	300	11	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	300	12	,	,	PUNCT
ejpam-5456	300	13	φ	φ	NUM
ejpam-5456	300	14	)	)	PUNCT
ejpam-5456	300	15	+	+	SYM
ejpam-5456	300	16	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	300	17	,	,	PUNCT
ejpam-5456	300	18	φ	φ	NOUN
ejpam-5456	300	19	)	)	PUNCT
ejpam-5456	300	20	)	)	PUNCT
ejpam-5456	300	21	]	]	PUNCT
ejpam-5456	300	22	.	.	PUNCT
ejpam-5456	301	1	(	(	PUNCT
ejpam-5456	301	2	44	44	NUM
ejpam-5456	301	3	)	)	PUNCT
ejpam-5456	301	4	we	we	PRON
ejpam-5456	301	5	get	get	VERB
ejpam-5456	301	6	the	the	DET
ejpam-5456	301	7	following	following	NOUN
ejpam-5456	301	8	:	:	PUNCT
ejpam-5456	301	9	∞∑	∞∑	NUM
ejpam-5456	301	10	ρ=0	ρ=0	PUNCT
ejpam-5456	301	11	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	301	12	,	,	PUNCT
ejpam-5456	301	13	φ	φ	NUM
ejpam-5456	301	14	)	)	PUNCT
ejpam-5456	301	15	=	=	NOUN
ejpam-5456	301	16	s−1	s−1	NOUN
ejpam-5456	301	17	µ	µ	NOUN
ejpam-5456	301	18	[	[	PUNCT
ejpam-5456	301	19	δ1(0	δ1(0	PROPN
ejpam-5456	301	20	)	)	PUNCT
ejpam-5456	301	21	]	]	PUNCT
ejpam-5456	301	22	−	−	PROPN
ejpam-5456	302	1	s−1	s−1	PROPN
ejpam-5456	302	2	µ	µ	X
ejpam-5456	302	3	[	[	PUNCT
ejpam-5456	302	4	ωsµ	ωsµ	NOUN
ejpam-5456	302	5	[	[	PUNCT
ejpam-5456	302	6	dϱϱ	dϱϱ	NOUN
ejpam-5456	302	7	∞∑	∞∑	NUM
ejpam-5456	302	8	ρ=0	ρ=0	PUNCT
ejpam-5456	302	9	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	302	10	,	,	PUNCT
ejpam-5456	302	11	φ	φ	NUM
ejpam-5456	302	12	)	)	PUNCT
ejpam-5456	302	13	]	]	X
ejpam-5456	302	14	]	]	X
ejpam-5456	302	15	−	−	PROPN
ejpam-5456	302	16	s−1	s−1	PROPN
ejpam-5456	302	17	µ	µ	X
ejpam-5456	302	18	[	[	PUNCT
ejpam-5456	302	19	ωsµ	ωsµ	X
ejpam-5456	302	20	[	[	PUNCT
ejpam-5456	302	21	2	2	NUM
ejpam-5456	302	22	∞∑	∞∑	NUM
ejpam-5456	302	23	ρ=0	ρ=0	PROPN
ejpam-5456	302	24	a1,ρ(δ1	a1,ρ(δ1	NOUN
ejpam-5456	302	25	,	,	PUNCT
ejpam-5456	302	26	δ2	δ2	PROPN
ejpam-5456	302	27	)	)	PUNCT
ejpam-5456	302	28	]	]	PUNCT
ejpam-5456	302	29	,	,	PUNCT
ejpam-5456	302	30	∞∑	∞∑	NUM
ejpam-5456	302	31	ρ=0	ρ=0	NUM
ejpam-5456	302	32	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	302	33	,	,	PUNCT
ejpam-5456	302	34	φ	φ	NUM
ejpam-5456	302	35	)	)	PUNCT
ejpam-5456	302	36	=	=	NOUN
ejpam-5456	302	37	s−1	s−1	PROPN
ejpam-5456	302	38	µ	µ	X
ejpam-5456	302	39	[	[	PUNCT
ejpam-5456	302	40	δ2(0	δ2(0	NOUN
ejpam-5456	302	41	)	)	PUNCT
ejpam-5456	302	42	]	]	PUNCT
ejpam-5456	303	1	+	+	CCONJ
ejpam-5456	303	2	s−1	s−1	PROPN
ejpam-5456	303	3	µ	µ	X
ejpam-5456	303	4	[	[	PUNCT
ejpam-5456	303	5	ωsµ	ωsµ	NOUN
ejpam-5456	303	6	[	[	PUNCT
ejpam-5456	303	7	dϱϱ	dϱϱ	NOUN
ejpam-5456	303	8	∞∑	∞∑	PROPN
ejpam-5456	303	9	ρ=0	ρ=0	PROPN
ejpam-5456	303	10	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	303	11	,	,	PUNCT
ejpam-5456	303	12	φ	φ	NUM
ejpam-5456	303	13	)	)	PUNCT
ejpam-5456	303	14	]	]	PUNCT
ejpam-5456	303	15	]	]	X
ejpam-5456	303	16	+	+	CCONJ
ejpam-5456	303	17	m.i	m.i	PROPN
ejpam-5456	303	18	.	.	PROPN
ejpam-5456	303	19	liaqat	liaqat	PROPN
ejpam-5456	303	20	,	,	PUNCT
ejpam-5456	303	21	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	303	22	/	/	SYM
ejpam-5456	303	23	eur	eur	PROPN
ejpam-5456	303	24	.	.	PUNCT
ejpam-5456	304	1	j.	j.	PROPN
ejpam-5456	304	2	pure	pure	PROPN
ejpam-5456	304	3	appl	appl	PROPN
ejpam-5456	304	4	.	.	PROPN
ejpam-5456	304	5	math	math	PROPN
ejpam-5456	304	6	,	,	PUNCT
ejpam-5456	304	7	17	17	NUM
ejpam-5456	304	8	(	(	PUNCT
ejpam-5456	304	9	4	4	NUM
ejpam-5456	304	10	)	)	PUNCT
ejpam-5456	304	11	(	(	PUNCT
ejpam-5456	304	12	2024	2024	NUM
ejpam-5456	304	13	)	)	PUNCT
ejpam-5456	304	14	,	,	PUNCT
ejpam-5456	304	15	3464	3464	NUM
ejpam-5456	304	16	-	-	SYM
ejpam-5456	304	17	3491	3491	NUM
ejpam-5456	304	18	3476	3476	NUM
ejpam-5456	304	19	s−1	s−1	PROPN
ejpam-5456	304	20	µ	µ	X
ejpam-5456	304	21	[	[	PUNCT
ejpam-5456	304	22	ωsµ	ωsµ	X
ejpam-5456	304	23	[	[	PUNCT
ejpam-5456	304	24	2	2	NUM
ejpam-5456	304	25	∞∑	∞∑	NUM
ejpam-5456	304	26	ρ=0	ρ=0	PUNCT
ejpam-5456	304	27	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	304	28	,	,	PUNCT
ejpam-5456	304	29	δ2	δ2	ADJ
ejpam-5456	304	30	)	)	PUNCT
ejpam-5456	304	31	]	]	PUNCT
ejpam-5456	304	32	.	.	PUNCT
ejpam-5456	305	1	(	(	PUNCT
ejpam-5456	305	2	45	45	NUM
ejpam-5456	305	3	)	)	PUNCT
ejpam-5456	305	4	from	from	ADP
ejpam-5456	305	5	the	the	DET
ejpam-5456	305	6	above	above	ADJ
ejpam-5456	305	7	system	system	NOUN
ejpam-5456	305	8	,	,	PUNCT
ejpam-5456	305	9	we	we	PRON
ejpam-5456	305	10	obtain	obtain	VERB
ejpam-5456	305	11	the	the	DET
ejpam-5456	305	12	first	first	ADJ
ejpam-5456	305	13	terms	term	NOUN
ejpam-5456	305	14	of	of	ADP
ejpam-5456	305	15	the	the	DET
ejpam-5456	305	16	fps	fps	PROPN
ejpam-5456	305	17	solutions	solution	NOUN
ejpam-5456	305	18	.	.	PUNCT
ejpam-5456	306	1	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	306	2	,	,	PUNCT
ejpam-5456	306	3	φ	φ	NUM
ejpam-5456	306	4	)	)	PUNCT
ejpam-5456	306	5	=	=	SYM
ejpam-5456	306	6	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	306	7	)	)	PUNCT
ejpam-5456	306	8	,	,	PUNCT
ejpam-5456	306	9	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	306	10	,	,	PUNCT
ejpam-5456	306	11	φ	φ	NOUN
ejpam-5456	306	12	)	)	PUNCT
ejpam-5456	306	13	=	=	SYM
ejpam-5456	306	14	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	306	15	)	)	PUNCT
ejpam-5456	306	16	.	.	PUNCT
ejpam-5456	307	1	(	(	PUNCT
ejpam-5456	307	2	46	46	X
ejpam-5456	307	3	)	)	PUNCT
ejpam-5456	307	4	we	we	PRON
ejpam-5456	307	5	extract	extract	VERB
ejpam-5456	307	6	the	the	DET
ejpam-5456	307	7	following	following	ADJ
ejpam-5456	307	8	terms	term	NOUN
ejpam-5456	307	9	of	of	ADP
ejpam-5456	307	10	the	the	DET
ejpam-5456	307	11	fps	fps	NOUN
ejpam-5456	307	12	as	as	SCONJ
ejpam-5456	307	13	follows	follow	VERB
ejpam-5456	307	14	:	:	PUNCT
ejpam-5456	307	15	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	307	16	,	,	PUNCT
ejpam-5456	307	17	φ	φ	NUM
ejpam-5456	307	18	)	)	PUNCT
ejpam-5456	307	19	=	=	SYM
ejpam-5456	307	20	−	−	PROPN
ejpam-5456	307	21	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	307	22	)	)	PUNCT
ejpam-5456	307	23	φµ	φµ	ADP
ejpam-5456	307	24	µγ(2	µγ(2	NOUN
ejpam-5456	307	25	)	)	PUNCT
ejpam-5456	307	26	,	,	PUNCT
ejpam-5456	307	27	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	307	28	,	,	PUNCT
ejpam-5456	307	29	φ	φ	NUM
ejpam-5456	307	30	)	)	PUNCT
ejpam-5456	307	31	=	=	SYM
ejpam-5456	307	32	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	307	33	)	)	PUNCT
ejpam-5456	307	34	φµ	φµ	ADP
ejpam-5456	307	35	µγ(2	µγ(2	NOUN
ejpam-5456	307	36	)	)	PUNCT
ejpam-5456	307	37	.	.	PUNCT
ejpam-5456	308	1	(	(	PUNCT
ejpam-5456	308	2	47	47	NUM
ejpam-5456	308	3	)	)	PUNCT
ejpam-5456	308	4	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	308	5	,	,	PUNCT
ejpam-5456	308	6	φ	φ	NOUN
ejpam-5456	308	7	)	)	PUNCT
ejpam-5456	308	8	=	=	SYM
ejpam-5456	308	9	−	−	PROPN
ejpam-5456	308	10	φ2µ	φ2µ	PROPN
ejpam-5456	308	11	µ22	µ22	PROPN
ejpam-5456	308	12	!	!	PUNCT
ejpam-5456	308	13	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	308	14	)	)	PUNCT
ejpam-5456	308	15	,	,	PUNCT
ejpam-5456	308	16	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	308	17	,	,	PUNCT
ejpam-5456	308	18	φ	φ	NOUN
ejpam-5456	308	19	)	)	PUNCT
ejpam-5456	308	20	=	=	SYM
ejpam-5456	308	21	−	−	PROPN
ejpam-5456	308	22	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	308	23	)	)	PUNCT
ejpam-5456	308	24	φ2µ	φ2µ	PROPN
ejpam-5456	308	25	µ2γ(3	µ2γ(3	PROPN
ejpam-5456	308	26	)	)	PUNCT
ejpam-5456	308	27	.	.	PUNCT
ejpam-5456	309	1	(	(	PUNCT
ejpam-5456	309	2	48	48	NUM
ejpam-5456	309	3	)	)	PUNCT
ejpam-5456	309	4	δ1,3(ϱ	δ1,3(ϱ	PROPN
ejpam-5456	309	5	,	,	PUNCT
ejpam-5456	309	6	φ	φ	NOUN
ejpam-5456	309	7	)	)	PUNCT
ejpam-5456	309	8	=	=	SYM
ejpam-5456	309	9	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	309	10	)	)	PUNCT
ejpam-5456	309	11	φ3µ	φ3µ	NOUN
ejpam-5456	309	12	µ3γ(4	µ3γ(4	PROPN
ejpam-5456	309	13	)	)	PUNCT
ejpam-5456	309	14	,	,	PUNCT
ejpam-5456	309	15	δ2,3(ϱ	δ2,3(ϱ	PROPN
ejpam-5456	309	16	,	,	PUNCT
ejpam-5456	309	17	φ	φ	NOUN
ejpam-5456	309	18	)	)	PUNCT
ejpam-5456	309	19	=	=	SYM
ejpam-5456	309	20	−	−	PROPN
ejpam-5456	309	21	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	309	22	)	)	PUNCT
ejpam-5456	309	23	φ3µ	φ3µ	NOUN
ejpam-5456	309	24	µ3γ(4	µ3γ(4	PROPN
ejpam-5456	309	25	)	)	PUNCT
ejpam-5456	309	26	.	.	PUNCT
ejpam-5456	310	1	(	(	PUNCT
ejpam-5456	310	2	49	49	X
ejpam-5456	310	3	)	)	PUNCT
ejpam-5456	310	4	δ1,4(ϱ	δ1,4(ϱ	PROPN
ejpam-5456	310	5	,	,	PUNCT
ejpam-5456	310	6	φ	φ	NOUN
ejpam-5456	310	7	)	)	PUNCT
ejpam-5456	310	8	=	=	SYM
ejpam-5456	310	9	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	310	10	)	)	PUNCT
ejpam-5456	310	11	φ3µ	φ3µ	NOUN
ejpam-5456	310	12	µ3γ(5	µ3γ(5	PROPN
ejpam-5456	310	13	)	)	PUNCT
ejpam-5456	310	14	,	,	PUNCT
ejpam-5456	310	15	δ2,4(ϱ	δ2,4(ϱ	PROPN
ejpam-5456	310	16	,	,	PUNCT
ejpam-5456	310	17	φ	φ	NOUN
ejpam-5456	310	18	)	)	PUNCT
ejpam-5456	310	19	=	=	SYM
ejpam-5456	310	20	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	310	21	)	)	PUNCT
ejpam-5456	310	22	φ3µ	φ3µ	NOUN
ejpam-5456	310	23	µ3γ(5	µ3γ(5	PROPN
ejpam-5456	310	24	)	)	PUNCT
ejpam-5456	310	25	.	.	PUNCT
ejpam-5456	311	1	(	(	PUNCT
ejpam-5456	311	2	50	50	NUM
ejpam-5456	311	3	)	)	PUNCT
ejpam-5456	311	4	the	the	DET
ejpam-5456	311	5	procedure	procedure	NOUN
ejpam-5456	311	6	is	be	AUX
ejpam-5456	311	7	repeated	repeat	VERB
ejpam-5456	311	8	to	to	PART
ejpam-5456	311	9	achieve	achieve	VERB
ejpam-5456	311	10	the	the	DET
ejpam-5456	311	11	results	result	NOUN
ejpam-5456	311	12	for	for	ADP
ejpam-5456	311	13	the	the	DET
ejpam-5456	311	14	sixth	sixth	ADJ
ejpam-5456	311	15	terms	term	NOUN
ejpam-5456	311	16	.	.	PUNCT
ejpam-5456	312	1	δ1,5(ϱ	δ1,5(ϱ	PROPN
ejpam-5456	312	2	,	,	PUNCT
ejpam-5456	312	3	φ	φ	NOUN
ejpam-5456	312	4	)	)	PUNCT
ejpam-5456	312	5	=	=	SYM
ejpam-5456	312	6	−	−	PROPN
ejpam-5456	312	7	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	312	8	)	)	PUNCT
ejpam-5456	312	9	φ5µ	φ5µ	NOUN
ejpam-5456	312	10	µ5γ(6	µ5γ(6	NOUN
ejpam-5456	312	11	)	)	PUNCT
ejpam-5456	312	12	,	,	PUNCT
ejpam-5456	312	13	δ2,5(ϱ	δ2,5(ϱ	PROPN
ejpam-5456	312	14	,	,	PUNCT
ejpam-5456	312	15	φ	φ	NUM
ejpam-5456	312	16	)	)	PUNCT
ejpam-5456	312	17	=	=	SYM
ejpam-5456	312	18	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	312	19	)	)	PUNCT
ejpam-5456	312	20	φ5µ	φ5µ	NOUN
ejpam-5456	312	21	µ5γ(6	µ5γ(6	NOUN
ejpam-5456	312	22	)	)	PUNCT
ejpam-5456	312	23	.	.	PUNCT
ejpam-5456	313	1	(	(	PUNCT
ejpam-5456	313	2	51	51	NUM
ejpam-5456	313	3	)	)	PUNCT
ejpam-5456	313	4	the	the	DET
ejpam-5456	313	5	fps	fps	PROPN
ejpam-5456	313	6	solution	solution	NOUN
ejpam-5456	313	7	is	be	AUX
ejpam-5456	313	8	as	as	SCONJ
ejpam-5456	313	9	follows	follow	VERB
ejpam-5456	313	10	:	:	PUNCT
ejpam-5456	313	11	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	313	12	,	,	PUNCT
ejpam-5456	313	13	φ	φ	NUM
ejpam-5456	313	14	)	)	PUNCT
ejpam-5456	313	15	=	=	SYM
ejpam-5456	313	16	(	(	PUNCT
ejpam-5456	313	17	cos(ϱ	cos(ϱ	PROPN
ejpam-5456	313	18	)	)	PUNCT
ejpam-5456	314	1	+	+	CCONJ
ejpam-5456	314	2	ι	ι	DET
ejpam-5456	314	3	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	314	4	)	)	PUNCT
ejpam-5456	314	5	)	)	PUNCT
ejpam-5456	315	1	(	(	PUNCT
ejpam-5456	315	2	∞∑	∞∑	NUM
ejpam-5456	315	3	ρ=0	ρ=0	NUM
ejpam-5456	315	4	1	1	NUM
ejpam-5456	315	5	γ(ρ+	γ(ρ+	NUM
ejpam-5456	315	6	1	1	NUM
ejpam-5456	315	7	)	)	PUNCT
ejpam-5456	315	8	(	(	PUNCT
ejpam-5456	315	9	ιφµ	ιφµ	NOUN
ejpam-5456	315	10	µ	µ	X
ejpam-5456	315	11	)	)	PUNCT
ejpam-5456	315	12	ρ	ρ	PROPN
ejpam-5456	315	13	)	)	PUNCT
ejpam-5456	315	14	.	.	PUNCT
ejpam-5456	316	1	(	(	PUNCT
ejpam-5456	316	2	52	52	NUM
ejpam-5456	316	3	)	)	PUNCT
ejpam-5456	316	4	m.i	m.i	PROPN
ejpam-5456	316	5	.	.	PROPN
ejpam-5456	316	6	liaqat	liaqat	PROPN
ejpam-5456	316	7	,	,	PUNCT
ejpam-5456	316	8	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	316	9	/	/	SYM
ejpam-5456	316	10	eur	eur	PROPN
ejpam-5456	316	11	.	.	PUNCT
ejpam-5456	317	1	j.	j.	PROPN
ejpam-5456	317	2	pure	pure	PROPN
ejpam-5456	317	3	appl	appl	PROPN
ejpam-5456	317	4	.	.	PROPN
ejpam-5456	317	5	math	math	PROPN
ejpam-5456	317	6	,	,	PUNCT
ejpam-5456	317	7	17	17	NUM
ejpam-5456	317	8	(	(	PUNCT
ejpam-5456	317	9	4	4	NUM
ejpam-5456	317	10	)	)	PUNCT
ejpam-5456	317	11	(	(	PUNCT
ejpam-5456	317	12	2024	2024	NUM
ejpam-5456	317	13	)	)	PUNCT
ejpam-5456	317	14	,	,	PUNCT
ejpam-5456	317	15	3464	3464	NUM
ejpam-5456	317	16	-	-	SYM
ejpam-5456	317	17	3491	3491	NUM
ejpam-5456	317	18	3477	3477	NUM
ejpam-5456	317	19	the	the	DET
ejpam-5456	317	20	ex	ex	NOUN
ejpam-5456	317	21	-	-	PROPN
ejpam-5456	317	22	s	s	PRON
ejpam-5456	317	23	when	when	SCONJ
ejpam-5456	317	24	µ	µ	X
ejpam-5456	317	25	=	=	SYM
ejpam-5456	317	26	1	1	NUM
ejpam-5456	317	27	is	be	AUX
ejpam-5456	317	28	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	317	29	,	,	PUNCT
ejpam-5456	317	30	φ	φ	NUM
ejpam-5456	317	31	)	)	PUNCT
ejpam-5456	317	32	=	=	SYM
ejpam-5456	318	1	expι	expι	NOUN
ejpam-5456	318	2	(	(	PUNCT
ejpam-5456	318	3	ϱ+φ	ϱ+φ	NUM
ejpam-5456	318	4	)	)	PUNCT
ejpam-5456	318	5	.	.	PUNCT
ejpam-5456	319	1	the	the	DET
ejpam-5456	319	2	same	same	ADJ
ejpam-5456	319	3	solution	solution	NOUN
ejpam-5456	319	4	was	be	AUX
ejpam-5456	319	5	achieved	achieve	VERB
ejpam-5456	319	6	by	by	ADP
ejpam-5456	319	7	[	[	X
ejpam-5456	319	8	2	2	NUM
ejpam-5456	319	9	]	]	PUNCT
ejpam-5456	319	10	.	.	PUNCT
ejpam-5456	320	1	problem	problem	NOUN
ejpam-5456	320	2	4.3	4.3	NUM
ejpam-5456	320	3	.	.	PUNCT
ejpam-5456	321	1	consider	consider	VERB
ejpam-5456	321	2	the	the	DET
ejpam-5456	321	3	following	follow	VERB
ejpam-5456	321	4	nonlinear	nonlinear	PROPN
ejpam-5456	321	5	fsde	fsde	PROPN
ejpam-5456	321	6	that	that	PRON
ejpam-5456	321	7	follows	follow	VERB
ejpam-5456	321	8	:	:	PUNCT
ejpam-5456	321	9	ιtµ	ιtµ	NOUN
ejpam-5456	321	10	φδ(ϱ	φδ(ϱ	NOUN
ejpam-5456	321	11	,	,	PUNCT
ejpam-5456	321	12	φ	φ	NUM
ejpam-5456	321	13	)	)	PUNCT
ejpam-5456	322	1	+	+	CCONJ
ejpam-5456	322	2	1	1	NUM
ejpam-5456	322	3	2	2	NUM
ejpam-5456	322	4	δϱϱ(ϱ	δϱϱ(ϱ	NOUN
ejpam-5456	322	5	,	,	PUNCT
ejpam-5456	322	6	φ)−	φ)−	PROPN
ejpam-5456	322	7	cos2(ϱ)δ(ϱ	cos2(ϱ)δ(ϱ	PROPN
ejpam-5456	322	8	,	,	PUNCT
ejpam-5456	322	9	φ)−	φ)−	PROPN
ejpam-5456	322	10	|δ(ϱ	|δ(ϱ	PROPN
ejpam-5456	322	11	,	,	PUNCT
ejpam-5456	322	12	φ)|2δ(ϱ	φ)|2δ(ϱ	X
ejpam-5456	322	13	,	,	PUNCT
ejpam-5456	322	14	φ	φ	NUM
ejpam-5456	322	15	)	)	PUNCT
ejpam-5456	322	16	=	=	SYM
ejpam-5456	322	17	0	0	NUM
ejpam-5456	322	18	,	,	PUNCT
ejpam-5456	322	19	(	(	PUNCT
ejpam-5456	322	20	53	53	NUM
ejpam-5456	322	21	)	)	PUNCT
ejpam-5456	322	22	with	with	ADP
ejpam-5456	322	23	the	the	DET
ejpam-5456	322	24	i	i	PROPN
ejpam-5456	322	25	-	-	PUNCT
ejpam-5456	322	26	c	c	NOUN
ejpam-5456	322	27	:	:	PUNCT
ejpam-5456	322	28	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	322	29	,	,	PUNCT
ejpam-5456	322	30	0	0	NUM
ejpam-5456	322	31	)	)	PUNCT
ejpam-5456	322	32	=	=	SYM
ejpam-5456	322	33	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	322	34	)	)	PUNCT
ejpam-5456	322	35	,	,	PUNCT
ejpam-5456	322	36	ϱ	ϱ	PROPN
ejpam-5456	322	37	∈	∈	PROPN
ejpam-5456	322	38	r.	r.	PROPN
ejpam-5456	322	39	(	(	PUNCT
ejpam-5456	322	40	54	54	NUM
ejpam-5456	322	41	)	)	PUNCT
ejpam-5456	322	42	suppose	suppose	VERB
ejpam-5456	322	43	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	322	44	,	,	PUNCT
ejpam-5456	322	45	φ	φ	NUM
ejpam-5456	322	46	)	)	PUNCT
ejpam-5456	322	47	=	=	SYM
ejpam-5456	322	48	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	322	49	,	,	PUNCT
ejpam-5456	322	50	φ	φ	NUM
ejpam-5456	322	51	)	)	PUNCT
ejpam-5456	322	52	+	+	CCONJ
ejpam-5456	322	53	ιδ2(ϱ	ιδ2(ϱ	PROPN
ejpam-5456	322	54	,	,	PUNCT
ejpam-5456	322	55	φ	φ	NUM
ejpam-5456	322	56	)	)	PUNCT
ejpam-5456	322	57	then	then	ADV
ejpam-5456	322	58	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	322	59	,	,	PUNCT
ejpam-5456	322	60	0	0	NUM
ejpam-5456	322	61	)	)	PUNCT
ejpam-5456	322	62	=	=	SYM
ejpam-5456	322	63	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	322	64	)	)	PUNCT
ejpam-5456	322	65	+	+	CCONJ
ejpam-5456	322	66	ιδ2,0(ϱ	ιδ2,0(ϱ	PROPN
ejpam-5456	322	67	)	)	PUNCT
ejpam-5456	322	68	.	.	PUNCT
ejpam-5456	323	1	as	as	ADP
ejpam-5456	323	2	a	a	DET
ejpam-5456	323	3	result	result	NOUN
ejpam-5456	323	4	,	,	PUNCT
ejpam-5456	323	5	tµ	tµ	PRON
ejpam-5456	323	6	φδ1(ϱ	φδ1(ϱ	NUM
ejpam-5456	323	7	,	,	PUNCT
ejpam-5456	323	8	φ	φ	NUM
ejpam-5456	323	9	)	)	PUNCT
ejpam-5456	323	10	=	=	NOUN
ejpam-5456	323	11	−	−	PROPN
ejpam-5456	323	12	1	1	NUM
ejpam-5456	323	13	2	2	NUM
ejpam-5456	323	14	dϱϱδ2(ϱ	dϱϱδ2(ϱ	ADV
ejpam-5456	323	15	,	,	PUNCT
ejpam-5456	323	16	φ	φ	NOUN
ejpam-5456	323	17	)	)	PUNCT
ejpam-5456	323	18	+	+	CCONJ
ejpam-5456	323	19	cos2(ϱ)δ2(ϱ	cos2(ϱ)δ2(ϱ	PROPN
ejpam-5456	323	20	,	,	PUNCT
ejpam-5456	323	21	φ	φ	NOUN
ejpam-5456	323	22	)	)	PUNCT
ejpam-5456	323	23	+	+	CCONJ
ejpam-5456	323	24	(	(	PUNCT
ejpam-5456	323	25	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	323	26	,	,	PUNCT
ejpam-5456	323	27	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	323	28	,	,	PUNCT
ejpam-5456	323	29	φ	φ	NUM
ejpam-5456	323	30	)	)	PUNCT
ejpam-5456	324	1	+	+	CCONJ
ejpam-5456	324	2	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	324	3	,	,	PUNCT
ejpam-5456	324	4	φ	φ	NUM
ejpam-5456	324	5	)	)	PUNCT
ejpam-5456	324	6	)	)	PUNCT
ejpam-5456	324	7	,	,	PUNCT
ejpam-5456	324	8	tµ	tµ	NOUN
ejpam-5456	324	9	φδ2(ϱ	φδ2(ϱ	PROPN
ejpam-5456	324	10	,	,	PUNCT
ejpam-5456	324	11	φ	φ	NUM
ejpam-5456	324	12	)	)	PUNCT
ejpam-5456	324	13	=	=	SYM
ejpam-5456	324	14	1	1	NUM
ejpam-5456	324	15	2	2	NUM
ejpam-5456	324	16	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	324	17	,	,	PUNCT
ejpam-5456	324	18	φ)−	φ)−	PROPN
ejpam-5456	324	19	cos2(ϱ)δ1(ϱ	cos2(ϱ)δ1(ϱ	PROPN
ejpam-5456	324	20	,	,	PUNCT
ejpam-5456	324	21	φ)−	φ)−	PROPN
ejpam-5456	324	22	(	(	PUNCT
ejpam-5456	324	23	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	324	24	,	,	PUNCT
ejpam-5456	324	25	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	324	26	,	,	PUNCT
ejpam-5456	324	27	φ	φ	NUM
ejpam-5456	324	28	)	)	PUNCT
ejpam-5456	324	29	+	+	SYM
ejpam-5456	324	30	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	324	31	,	,	PUNCT
ejpam-5456	324	32	φ	φ	NOUN
ejpam-5456	324	33	)	)	PUNCT
ejpam-5456	324	34	)	)	PUNCT
ejpam-5456	324	35	,	,	PUNCT
ejpam-5456	324	36	(	(	PUNCT
ejpam-5456	324	37	55	55	NUM
ejpam-5456	324	38	)	)	PUNCT
ejpam-5456	324	39	with	with	ADP
ejpam-5456	324	40	the	the	DET
ejpam-5456	324	41	i	i	PROPN
ejpam-5456	324	42	-	-	PUNCT
ejpam-5456	324	43	cs	cs	PROPN
ejpam-5456	324	44	:	:	PUNCT
ejpam-5456	324	45	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	324	46	,	,	PUNCT
ejpam-5456	324	47	0	0	NUM
ejpam-5456	324	48	)	)	PUNCT
ejpam-5456	324	49	=	=	SYM
ejpam-5456	324	50	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	324	51	)	)	PUNCT
ejpam-5456	324	52	,	,	PUNCT
ejpam-5456	324	53	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	324	54	,	,	PUNCT
ejpam-5456	324	55	0	0	NUM
ejpam-5456	324	56	)	)	PUNCT
ejpam-5456	324	57	=	=	NOUN
ejpam-5456	324	58	0	0	NUM
ejpam-5456	324	59	.	.	PUNCT
ejpam-5456	325	1	(	(	PUNCT
ejpam-5456	325	2	56	56	NUM
ejpam-5456	325	3	)	)	PUNCT
ejpam-5456	325	4	after	after	ADP
ejpam-5456	325	5	applying	apply	VERB
ejpam-5456	325	6	st	st	PROPN
ejpam-5456	325	7	to	to	ADP
ejpam-5456	325	8	eq	eq	PROPN
ejpam-5456	325	9	.	.	PUNCT
ejpam-5456	326	1	(	(	PUNCT
ejpam-5456	326	2	55	55	NUM
ejpam-5456	326	3	)	)	PUNCT
ejpam-5456	326	4	,	,	PUNCT
ejpam-5456	326	5	utilizing	utilize	VERB
ejpam-5456	326	6	lemma	lemma	PROPN
ejpam-5456	326	7	1(iii	1(iii	NUM
ejpam-5456	326	8	)	)	PUNCT
ejpam-5456	326	9	and	and	CCONJ
ejpam-5456	326	10	the	the	DET
ejpam-5456	326	11	linear	linear	ADJ
ejpam-5456	326	12	property	property	NOUN
ejpam-5456	326	13	of	of	ADP
ejpam-5456	326	14	st	st	PROPN
ejpam-5456	326	15	,	,	PUNCT
ejpam-5456	326	16	and	and	CCONJ
ejpam-5456	326	17	performing	perform	VERB
ejpam-5456	326	18	certain	certain	ADJ
ejpam-5456	326	19	computations	computation	NOUN
ejpam-5456	326	20	,	,	PUNCT
ejpam-5456	326	21	we	we	PRON
ejpam-5456	326	22	obtain	obtain	VERB
ejpam-5456	326	23	s[δ1(ϱ	s[δ1(ϱ	NOUN
ejpam-5456	326	24	,	,	PUNCT
ejpam-5456	326	25	φ	φ	NOUN
ejpam-5456	326	26	)	)	PUNCT
ejpam-5456	326	27	]	]	PUNCT
ejpam-5456	327	1	=	=	NUM
ejpam-5456	327	2	δ1(0)−	δ1(0)−	PROPN
ejpam-5456	327	3	ωsµ	ωsµ	ADJ
ejpam-5456	327	4	[	[	PUNCT
ejpam-5456	327	5	1	1	NUM
ejpam-5456	327	6	2	2	NUM
ejpam-5456	327	7	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	327	8	,	,	PUNCT
ejpam-5456	327	9	φ	φ	NOUN
ejpam-5456	327	10	)	)	PUNCT
ejpam-5456	327	11	]	]	PUNCT
ejpam-5456	328	1	+	+	X
ejpam-5456	328	2	ωsµ	ωsµ	X
ejpam-5456	328	3	[	[	PUNCT
ejpam-5456	328	4	cos2(ϱ)δ2(ϱ	cos2(ϱ)δ2(ϱ	PROPN
ejpam-5456	328	5	,	,	PUNCT
ejpam-5456	328	6	φ	φ	NUM
ejpam-5456	328	7	)	)	PUNCT
ejpam-5456	328	8	]	]	PUNCT
ejpam-5456	329	1	+	+	PUNCT
ejpam-5456	329	2	ωsµ	ωsµ	ADJ
ejpam-5456	329	3	[	[	X
ejpam-5456	329	4	(	(	PUNCT
ejpam-5456	329	5	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	329	6	,	,	PUNCT
ejpam-5456	329	7	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	329	8	,	,	PUNCT
ejpam-5456	329	9	φ	φ	NUM
ejpam-5456	329	10	)	)	PUNCT
ejpam-5456	329	11	+	+	CCONJ
ejpam-5456	329	12	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	329	13	,	,	PUNCT
ejpam-5456	329	14	φ	φ	NUM
ejpam-5456	329	15	)	)	PUNCT
ejpam-5456	329	16	)	)	PUNCT
ejpam-5456	329	17	]	]	PUNCT
ejpam-5456	329	18	,	,	PUNCT
ejpam-5456	329	19	sµ[δ2(ϱ	sµ[δ2(ϱ	PROPN
ejpam-5456	329	20	,	,	PUNCT
ejpam-5456	329	21	φ	φ	NOUN
ejpam-5456	329	22	)	)	PUNCT
ejpam-5456	329	23	]	]	PUNCT
ejpam-5456	329	24	=	=	X
ejpam-5456	329	25	δ2(0	δ2(0	NOUN
ejpam-5456	329	26	)	)	PUNCT
ejpam-5456	330	1	+	+	CCONJ
ejpam-5456	330	2	ωsµ	ωsµ	ADJ
ejpam-5456	330	3	[	[	X
ejpam-5456	330	4	1	1	NUM
ejpam-5456	330	5	2	2	NUM
ejpam-5456	330	6	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	330	7	,	,	PUNCT
ejpam-5456	330	8	φ	φ	NOUN
ejpam-5456	330	9	)	)	PUNCT
ejpam-5456	330	10	]	]	PUNCT
ejpam-5456	330	11	−	−	PROPN
ejpam-5456	330	12	ωsµ	ωsµ	PROPN
ejpam-5456	330	13	[	[	PUNCT
ejpam-5456	330	14	cos2(ϱ)δ1(ϱ	cos2(ϱ)δ1(ϱ	PROPN
ejpam-5456	330	15	,	,	PUNCT
ejpam-5456	330	16	φ	φ	NUM
ejpam-5456	330	17	)	)	PUNCT
ejpam-5456	330	18	]	]	PUNCT
ejpam-5456	331	1	−	−	PROPN
ejpam-5456	331	2	ωsµ	ωsµ	PROPN
ejpam-5456	331	3	[	[	X
ejpam-5456	331	4	(	(	PUNCT
ejpam-5456	331	5	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	331	6	,	,	PUNCT
ejpam-5456	331	7	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	331	8	,	,	PUNCT
ejpam-5456	331	9	φ	φ	NUM
ejpam-5456	331	10	)	)	PUNCT
ejpam-5456	331	11	+	+	SYM
ejpam-5456	331	12	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	331	13	,	,	PUNCT
ejpam-5456	331	14	φ	φ	NOUN
ejpam-5456	331	15	)	)	PUNCT
ejpam-5456	331	16	)	)	PUNCT
ejpam-5456	331	17	]	]	PUNCT
ejpam-5456	331	18	.	.	PUNCT
ejpam-5456	332	1	(	(	PUNCT
ejpam-5456	332	2	57	57	NUM
ejpam-5456	332	3	)	)	PUNCT
ejpam-5456	332	4	assess	assess	VERB
ejpam-5456	332	5	s−1	s−1	PROPN
ejpam-5456	332	6	µ	µ	NOUN
ejpam-5456	332	7	in	in	ADP
ejpam-5456	332	8	the	the	DET
ejpam-5456	332	9	system	system	NOUN
ejpam-5456	332	10	mentioned	mention	VERB
ejpam-5456	332	11	earlier	early	ADV
ejpam-5456	332	12	.	.	PUNCT
ejpam-5456	333	1	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	333	2	,	,	PUNCT
ejpam-5456	333	3	φ	φ	NUM
ejpam-5456	333	4	)	)	PUNCT
ejpam-5456	334	1	=	=	NOUN
ejpam-5456	334	2	s−1	s−1	NOUN
ejpam-5456	334	3	µ	µ	NOUN
ejpam-5456	334	4	[	[	PUNCT
ejpam-5456	334	5	δ1(0	δ1(0	PROPN
ejpam-5456	334	6	)	)	PUNCT
ejpam-5456	334	7	]	]	PUNCT
ejpam-5456	335	1	−	−	PROPN
ejpam-5456	335	2	s−1	s−1	PROPN
ejpam-5456	335	3	µ	µ	X
ejpam-5456	335	4	[	[	PUNCT
ejpam-5456	335	5	ωs	ωs	ADP
ejpam-5456	335	6	[	[	X
ejpam-5456	335	7	1	1	NUM
ejpam-5456	335	8	2	2	NUM
ejpam-5456	335	9	dϱϱδ2(ϱ	dϱϱδ2(ϱ	NOUN
ejpam-5456	335	10	,	,	PUNCT
ejpam-5456	335	11	φ	φ	NOUN
ejpam-5456	335	12	)	)	PUNCT
ejpam-5456	335	13	]	]	PUNCT
ejpam-5456	335	14	]	]	X
ejpam-5456	336	1	+	+	CCONJ
ejpam-5456	336	2	s−1	s−1	PROPN
ejpam-5456	336	3	[	[	PUNCT
ejpam-5456	336	4	ωs	ωs	X
ejpam-5456	336	5	[	[	PUNCT
ejpam-5456	336	6	cos2(ϱ)δ2(ϱ	cos2(ϱ)δ2(ϱ	PROPN
ejpam-5456	336	7	,	,	PUNCT
ejpam-5456	336	8	φ	φ	NOUN
ejpam-5456	336	9	)	)	PUNCT
ejpam-5456	336	10	]	]	PUNCT
ejpam-5456	336	11	]	]	X
ejpam-5456	337	1	+	+	CCONJ
ejpam-5456	337	2	s−1	s−1	PROPN
ejpam-5456	337	3	µ	µ	X
ejpam-5456	337	4	[	[	PUNCT
ejpam-5456	337	5	ωsµ	ωsµ	NOUN
ejpam-5456	337	6	[	[	X
ejpam-5456	337	7	(	(	PUNCT
ejpam-5456	337	8	δ21(ϱ	δ21(ϱ	NUM
ejpam-5456	337	9	,	,	PUNCT
ejpam-5456	337	10	φ)δ2(ϱ	φ)δ2(ϱ	NOUN
ejpam-5456	337	11	,	,	PUNCT
ejpam-5456	337	12	φ	φ	NUM
ejpam-5456	337	13	)	)	PUNCT
ejpam-5456	337	14	+	+	CCONJ
ejpam-5456	337	15	δ32(ϱ	δ32(ϱ	PROPN
ejpam-5456	337	16	,	,	PUNCT
ejpam-5456	337	17	φ	φ	NUM
ejpam-5456	337	18	)	)	PUNCT
ejpam-5456	337	19	)	)	PUNCT
ejpam-5456	338	1	]	]	PUNCT
ejpam-5456	338	2	]	]	X
ejpam-5456	338	3	,	,	PUNCT
ejpam-5456	338	4	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	338	5	,	,	PUNCT
ejpam-5456	338	6	φ	φ	NOUN
ejpam-5456	338	7	)	)	PUNCT
ejpam-5456	338	8	=	=	NOUN
ejpam-5456	338	9	s−1	s−1	PROPN
ejpam-5456	338	10	µ	µ	X
ejpam-5456	338	11	[	[	PUNCT
ejpam-5456	338	12	δ2(0	δ2(0	NOUN
ejpam-5456	338	13	)	)	PUNCT
ejpam-5456	338	14	]	]	PUNCT
ejpam-5456	339	1	+	+	CCONJ
ejpam-5456	339	2	s−1	s−1	PROPN
ejpam-5456	339	3	µ	µ	X
ejpam-5456	339	4	[	[	PUNCT
ejpam-5456	339	5	ωsµ	ωsµ	NOUN
ejpam-5456	339	6	[	[	X
ejpam-5456	339	7	1	1	NUM
ejpam-5456	339	8	2	2	NUM
ejpam-5456	339	9	dϱϱδ1(ϱ	dϱϱδ1(ϱ	NOUN
ejpam-5456	339	10	,	,	PUNCT
ejpam-5456	339	11	φ	φ	NOUN
ejpam-5456	339	12	)	)	PUNCT
ejpam-5456	339	13	]	]	X
ejpam-5456	339	14	]	]	X
ejpam-5456	339	15	−	−	PROPN
ejpam-5456	339	16	s−1	s−1	PROPN
ejpam-5456	339	17	µ	µ	X
ejpam-5456	339	18	[	[	PUNCT
ejpam-5456	339	19	ωsµ	ωsµ	X
ejpam-5456	339	20	[	[	PUNCT
ejpam-5456	339	21	cos2(ϱ)δ1(ϱ	cos2(ϱ)δ1(ϱ	PROPN
ejpam-5456	339	22	,	,	PUNCT
ejpam-5456	339	23	φ	φ	NUM
ejpam-5456	339	24	)	)	PUNCT
ejpam-5456	339	25	]	]	X
ejpam-5456	339	26	]	]	X
ejpam-5456	339	27	−	−	PROPN
ejpam-5456	339	28	s−1	s−1	PROPN
ejpam-5456	339	29	µ	µ	X
ejpam-5456	339	30	[	[	PUNCT
ejpam-5456	339	31	ωs	ωs	ADP
ejpam-5456	339	32	[	[	X
ejpam-5456	339	33	(	(	PUNCT
ejpam-5456	339	34	δ22(ϱ	δ22(ϱ	ADJ
ejpam-5456	339	35	,	,	PUNCT
ejpam-5456	339	36	φ)δ1(ϱ	φ)δ1(ϱ	NUM
ejpam-5456	339	37	,	,	PUNCT
ejpam-5456	339	38	φ	φ	NUM
ejpam-5456	339	39	)	)	PUNCT
ejpam-5456	339	40	+	+	SYM
ejpam-5456	339	41	δ31(ϱ	δ31(ϱ	PROPN
ejpam-5456	339	42	,	,	PUNCT
ejpam-5456	339	43	φ	φ	NOUN
ejpam-5456	339	44	)	)	PUNCT
ejpam-5456	339	45	)	)	PUNCT
ejpam-5456	340	1	]	]	PUNCT
ejpam-5456	340	2	]	]	PUNCT
ejpam-5456	340	3	.	.	PUNCT
ejpam-5456	341	1	(	(	PUNCT
ejpam-5456	341	2	58	58	X
ejpam-5456	341	3	)	)	PUNCT
ejpam-5456	341	4	using	use	VERB
ejpam-5456	341	5	the	the	DET
ejpam-5456	341	6	method	method	NOUN
ejpam-5456	341	7	outlined	outline	VERB
ejpam-5456	341	8	in	in	ADP
ejpam-5456	341	9	section	section	NOUN
ejpam-5456	341	10	3	3	NUM
ejpam-5456	341	11	,	,	PUNCT
ejpam-5456	341	12	we	we	PRON
ejpam-5456	341	13	derive	derive	VERB
ejpam-5456	341	14	the	the	DET
ejpam-5456	341	15	following	follow	VERB
ejpam-5456	341	16	result	result	NOUN
ejpam-5456	341	17	from	from	ADP
ejpam-5456	341	18	eq	eq	ADP
ejpam-5456	341	19	.	.	PUNCT
ejpam-5456	342	1	(	(	PUNCT
ejpam-5456	342	2	58	58	NUM
ejpam-5456	342	3	):	):	PUNCT
ejpam-5456	343	1	∞∑	∞∑	NUM
ejpam-5456	343	2	ρ=0	ρ=0	PUNCT
ejpam-5456	343	3	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	343	4	,	,	PUNCT
ejpam-5456	343	5	φ	φ	NUM
ejpam-5456	343	6	)	)	PUNCT
ejpam-5456	343	7	=	=	NOUN
ejpam-5456	343	8	s−1	s−1	NOUN
ejpam-5456	343	9	µ	µ	NOUN
ejpam-5456	343	10	[	[	PUNCT
ejpam-5456	343	11	δ1(0	δ1(0	PROPN
ejpam-5456	343	12	)	)	PUNCT
ejpam-5456	343	13	]	]	PUNCT
ejpam-5456	344	1	−	−	PROPN
ejpam-5456	344	2	s−1	s−1	PROPN
ejpam-5456	344	3	µ	µ	X
ejpam-5456	344	4	[	[	PUNCT
ejpam-5456	344	5	ωsµ	ωsµ	NOUN
ejpam-5456	344	6	[	[	PUNCT
ejpam-5456	344	7	1	1	NUM
ejpam-5456	344	8	2	2	NUM
ejpam-5456	344	9	dϱϱ	dϱϱ	NOUN
ejpam-5456	344	10	∞∑	∞∑	NUM
ejpam-5456	344	11	ρ=0	ρ=0	PUNCT
ejpam-5456	344	12	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	344	13	,	,	PUNCT
ejpam-5456	344	14	φ	φ	NUM
ejpam-5456	344	15	)	)	PUNCT
ejpam-5456	344	16	]	]	PUNCT
ejpam-5456	344	17	]	]	X
ejpam-5456	345	1	+	+	CCONJ
ejpam-5456	345	2	s−1	s−1	PROPN
ejpam-5456	345	3	µ	µ	X
ejpam-5456	345	4	[	[	PUNCT
ejpam-5456	345	5	ωsµ	ωsµ	NOUN
ejpam-5456	345	6	[	[	PUNCT
ejpam-5456	345	7	cos2(ϱ	cos2(ϱ	NOUN
ejpam-5456	345	8	)	)	PUNCT
ejpam-5456	345	9	∞∑	∞∑	NUM
ejpam-5456	345	10	ρ=0	ρ=0	NUM
ejpam-5456	345	11	δ2,ρ(ϱ	δ2,ρ(ϱ	NOUN
ejpam-5456	345	12	,	,	PUNCT
ejpam-5456	345	13	φ	φ	NUM
ejpam-5456	345	14	)	)	PUNCT
ejpam-5456	345	15	]	]	PUNCT
ejpam-5456	345	16	]	]	X
ejpam-5456	346	1	+	+	CCONJ
ejpam-5456	346	2	s−1	s−1	PROPN
ejpam-5456	346	3	µ	µ	X
ejpam-5456	346	4	[	[	PUNCT
ejpam-5456	346	5	ωsµ	ωsµ	X
ejpam-5456	346	6	[	[	PUNCT
ejpam-5456	346	7	∞∑	∞∑	PROPN
ejpam-5456	346	8	ρ=0	ρ=0	PROPN
ejpam-5456	346	9	a1,ρ(δ1	a1,ρ(δ1	NOUN
ejpam-5456	346	10	,	,	PUNCT
ejpam-5456	346	11	δ2	δ2	PROPN
ejpam-5456	346	12	)	)	PUNCT
ejpam-5456	346	13	]	]	PUNCT
ejpam-5456	346	14	,	,	PUNCT
ejpam-5456	346	15	m.i	m.i	PROPN
ejpam-5456	346	16	.	.	PROPN
ejpam-5456	346	17	liaqat	liaqat	PROPN
ejpam-5456	346	18	,	,	PUNCT
ejpam-5456	346	19	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	346	20	/	/	SYM
ejpam-5456	346	21	eur	eur	PROPN
ejpam-5456	346	22	.	.	PUNCT
ejpam-5456	347	1	j.	j.	PROPN
ejpam-5456	347	2	pure	pure	PROPN
ejpam-5456	347	3	appl	appl	PROPN
ejpam-5456	347	4	.	.	PROPN
ejpam-5456	347	5	math	math	PROPN
ejpam-5456	347	6	,	,	PUNCT
ejpam-5456	347	7	17	17	NUM
ejpam-5456	347	8	(	(	PUNCT
ejpam-5456	347	9	4	4	NUM
ejpam-5456	347	10	)	)	PUNCT
ejpam-5456	347	11	(	(	PUNCT
ejpam-5456	347	12	2024	2024	NUM
ejpam-5456	347	13	)	)	PUNCT
ejpam-5456	347	14	,	,	PUNCT
ejpam-5456	347	15	3464	3464	NUM
ejpam-5456	347	16	-	-	SYM
ejpam-5456	347	17	3491	3491	NUM
ejpam-5456	347	18	3478	3478	NUM
ejpam-5456	347	19	∞∑	∞∑	NUM
ejpam-5456	347	20	ρ=0	ρ=0	NUM
ejpam-5456	347	21	δ2,ρ(ϱ	δ2,ρ(ϱ	SYM
ejpam-5456	347	22	,	,	PUNCT
ejpam-5456	347	23	φ	φ	NUM
ejpam-5456	347	24	)	)	PUNCT
ejpam-5456	348	1	=	=	NOUN
ejpam-5456	348	2	s−1	s−1	PROPN
ejpam-5456	348	3	µ	µ	X
ejpam-5456	348	4	[	[	PUNCT
ejpam-5456	348	5	δ2(0	δ2(0	NOUN
ejpam-5456	348	6	)	)	PUNCT
ejpam-5456	348	7	]	]	PUNCT
ejpam-5456	349	1	+	+	CCONJ
ejpam-5456	349	2	s−1	s−1	PROPN
ejpam-5456	349	3	µ	µ	X
ejpam-5456	349	4	[	[	PUNCT
ejpam-5456	349	5	ωs	ωs	ADP
ejpam-5456	349	6	[	[	PUNCT
ejpam-5456	349	7	1	1	NUM
ejpam-5456	349	8	2	2	NUM
ejpam-5456	349	9	dϱϱ	dϱϱ	NOUN
ejpam-5456	349	10	∞∑	∞∑	NUM
ejpam-5456	349	11	ρ=0	ρ=0	PUNCT
ejpam-5456	349	12	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	349	13	,	,	PUNCT
ejpam-5456	349	14	φ	φ	NUM
ejpam-5456	349	15	)	)	PUNCT
ejpam-5456	349	16	]	]	X
ejpam-5456	349	17	]	]	X
ejpam-5456	349	18	−	−	PROPN
ejpam-5456	349	19	s−1	s−1	PROPN
ejpam-5456	349	20	µ	µ	X
ejpam-5456	349	21	[	[	PUNCT
ejpam-5456	349	22	ωsµ	ωsµ	NOUN
ejpam-5456	349	23	[	[	PUNCT
ejpam-5456	349	24	cos2(ϱ	cos2(ϱ	NOUN
ejpam-5456	349	25	)	)	PUNCT
ejpam-5456	349	26	∞∑	∞∑	NUM
ejpam-5456	349	27	ρ=0	ρ=0	PUNCT
ejpam-5456	349	28	δ1,ρ(ϱ	δ1,ρ(ϱ	NUM
ejpam-5456	349	29	,	,	PUNCT
ejpam-5456	349	30	φ	φ	NUM
ejpam-5456	349	31	)	)	PUNCT
ejpam-5456	349	32	]	]	X
ejpam-5456	349	33	]	]	X
ejpam-5456	349	34	−	−	PROPN
ejpam-5456	349	35	s−1	s−1	PROPN
ejpam-5456	349	36	µ	µ	X
ejpam-5456	349	37	[	[	PUNCT
ejpam-5456	349	38	ωsµ	ωsµ	X
ejpam-5456	349	39	[	[	PUNCT
ejpam-5456	349	40	∞∑	∞∑	PROPN
ejpam-5456	349	41	ρ=0	ρ=0	PUNCT
ejpam-5456	349	42	a2,ρ(δ1	a2,ρ(δ1	PROPN
ejpam-5456	349	43	,	,	PUNCT
ejpam-5456	349	44	δ2	δ2	ADJ
ejpam-5456	349	45	)	)	PUNCT
ejpam-5456	349	46	]	]	PUNCT
ejpam-5456	349	47	.	.	PUNCT
ejpam-5456	350	1	(	(	PUNCT
ejpam-5456	350	2	59	59	NUM
ejpam-5456	350	3	)	)	PUNCT
ejpam-5456	350	4	we	we	PRON
ejpam-5456	350	5	extracted	extract	VERB
ejpam-5456	350	6	the	the	DET
ejpam-5456	350	7	first	first	ADJ
ejpam-5456	350	8	term	term	NOUN
ejpam-5456	350	9	of	of	ADP
ejpam-5456	350	10	the	the	DET
ejpam-5456	350	11	fps	fps	NOUN
ejpam-5456	350	12	solution	solution	NOUN
ejpam-5456	350	13	for	for	ADP
ejpam-5456	350	14	the	the	DET
ejpam-5456	350	15	eq	eq	NOUN
ejpam-5456	350	16	.	.	PUNCT
ejpam-5456	351	1	(	(	PUNCT
ejpam-5456	351	2	55	55	NUM
ejpam-5456	351	3	)	)	PUNCT
ejpam-5456	351	4	via	via	ADP
ejpam-5456	351	5	the	the	DET
ejpam-5456	351	6	equivalent	equivalent	NOUN
ejpam-5456	351	7	on	on	ADP
ejpam-5456	351	8	the	the	DET
ejpam-5456	351	9	two	two	NUM
ejpam-5456	351	10	ends	end	NOUN
ejpam-5456	351	11	of	of	ADP
ejpam-5456	351	12	eq	eq	PROPN
ejpam-5456	351	13	.	.	PUNCT
ejpam-5456	352	1	(	(	PUNCT
ejpam-5456	352	2	59	59	NUM
ejpam-5456	352	3	)	)	PUNCT
ejpam-5456	352	4	.	.	PUNCT
ejpam-5456	353	1	δ1,0(ϱ	δ1,0(ϱ	PROPN
ejpam-5456	353	2	,	,	PUNCT
ejpam-5456	353	3	φ	φ	NUM
ejpam-5456	353	4	)	)	PUNCT
ejpam-5456	353	5	=	=	SYM
ejpam-5456	353	6	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	353	7	)	)	PUNCT
ejpam-5456	353	8	,	,	PUNCT
ejpam-5456	353	9	δ2,0(ϱ	δ2,0(ϱ	PROPN
ejpam-5456	353	10	,	,	PUNCT
ejpam-5456	353	11	φ	φ	NOUN
ejpam-5456	353	12	)	)	PUNCT
ejpam-5456	353	13	=	=	SYM
ejpam-5456	353	14	0	0	X
ejpam-5456	353	15	.	.	PUNCT
ejpam-5456	354	1	(	(	PUNCT
ejpam-5456	354	2	60	60	NUM
ejpam-5456	354	3	)	)	PUNCT
ejpam-5456	354	4	we	we	PRON
ejpam-5456	354	5	extract	extract	VERB
ejpam-5456	354	6	the	the	DET
ejpam-5456	354	7	following	follow	VERB
ejpam-5456	354	8	second	second	ADJ
ejpam-5456	354	9	term	term	NOUN
ejpam-5456	354	10	of	of	ADP
ejpam-5456	354	11	the	the	DET
ejpam-5456	354	12	fps	fps	PROPN
ejpam-5456	354	13	.	.	PUNCT
ejpam-5456	355	1	δ1,1(ϱ	δ1,1(ϱ	PROPN
ejpam-5456	355	2	,	,	PUNCT
ejpam-5456	355	3	φ	φ	NUM
ejpam-5456	355	4	)	)	PUNCT
ejpam-5456	355	5	=	=	SYM
ejpam-5456	355	6	0	0	NUM
ejpam-5456	355	7	,	,	PUNCT
ejpam-5456	355	8	δ2,1(ϱ	δ2,1(ϱ	PROPN
ejpam-5456	355	9	,	,	PUNCT
ejpam-5456	355	10	φ	φ	NOUN
ejpam-5456	355	11	)	)	PUNCT
ejpam-5456	355	12	=	=	SYM
ejpam-5456	356	1	−3	−3	PROPN
ejpam-5456	356	2	2	2	NUM
ejpam-5456	356	3	sin(ϱ	sin(ϱ	NOUN
ejpam-5456	356	4	)	)	PUNCT
ejpam-5456	356	5	φµ	φµ	ADP
ejpam-5456	356	6	µγ(2	µγ(2	NOUN
ejpam-5456	356	7	)	)	PUNCT
ejpam-5456	356	8	.	.	PUNCT
ejpam-5456	357	1	(	(	PUNCT
ejpam-5456	357	2	61	61	NUM
ejpam-5456	357	3	)	)	PUNCT
ejpam-5456	357	4	similarly	similarly	ADV
ejpam-5456	357	5	,	,	PUNCT
ejpam-5456	357	6	we	we	PRON
ejpam-5456	357	7	found	find	VERB
ejpam-5456	357	8	the	the	DET
ejpam-5456	357	9	third	third	ADJ
ejpam-5456	357	10	,	,	PUNCT
ejpam-5456	357	11	fourth	fourth	ADJ
ejpam-5456	357	12	,	,	PUNCT
ejpam-5456	357	13	and	and	CCONJ
ejpam-5456	357	14	fifth	fifth	ADJ
ejpam-5456	357	15	terms	term	NOUN
ejpam-5456	357	16	.	.	PUNCT
ejpam-5456	358	1	δ1,2(ϱ	δ1,2(ϱ	PROPN
ejpam-5456	358	2	,	,	PUNCT
ejpam-5456	358	3	φ	φ	NOUN
ejpam-5456	358	4	)	)	PUNCT
ejpam-5456	358	5	=	=	PUNCT
ejpam-5456	358	6	−9	−9	NOUN
ejpam-5456	358	7	4	4	NUM
ejpam-5456	358	8	sin(ϱ	sin(ϱ	NOUN
ejpam-5456	358	9	)	)	PUNCT
ejpam-5456	358	10	φ2µ	φ2µ	PROPN
ejpam-5456	358	11	µ2γ(3	µ2γ(3	PROPN
ejpam-5456	358	12	)	)	PUNCT
ejpam-5456	358	13	,	,	PUNCT
ejpam-5456	358	14	δ2,2(ϱ	δ2,2(ϱ	PROPN
ejpam-5456	358	15	,	,	PUNCT
ejpam-5456	358	16	φ	φ	NOUN
ejpam-5456	358	17	)	)	PUNCT
ejpam-5456	358	18	=	=	SYM
ejpam-5456	359	1	0	0	X
ejpam-5456	359	2	.	.	PUNCT
ejpam-5456	360	1	(	(	PUNCT
ejpam-5456	360	2	62	62	NUM
ejpam-5456	360	3	)	)	PUNCT
ejpam-5456	360	4	δ1,3(ϱ	δ1,3(ϱ	PROPN
ejpam-5456	360	5	,	,	PUNCT
ejpam-5456	360	6	φ	φ	NOUN
ejpam-5456	360	7	)	)	PUNCT
ejpam-5456	360	8	=	=	SYM
ejpam-5456	360	9	0	0	NUM
ejpam-5456	360	10	,	,	PUNCT
ejpam-5456	360	11	δ2,3(ϱ	δ2,3(ϱ	PROPN
ejpam-5456	360	12	,	,	PUNCT
ejpam-5456	360	13	φ	φ	NOUN
ejpam-5456	360	14	)	)	PUNCT
ejpam-5456	360	15	=	=	SYM
ejpam-5456	360	16	27	27	NUM
ejpam-5456	360	17	8	8	NUM
ejpam-5456	360	18	sin(ϱ	sin(ϱ	NOUN
ejpam-5456	360	19	)	)	PUNCT
ejpam-5456	360	20	φ3µ	φ3µ	NOUN
ejpam-5456	360	21	µ3γ(4	µ3γ(4	NOUN
ejpam-5456	360	22	)	)	PUNCT
ejpam-5456	360	23	.	.	PUNCT
ejpam-5456	361	1	(	(	PUNCT
ejpam-5456	361	2	63	63	NUM
ejpam-5456	361	3	)	)	PUNCT
ejpam-5456	361	4	δ1,4(ϱ	δ1,4(ϱ	PROPN
ejpam-5456	361	5	,	,	PUNCT
ejpam-5456	361	6	φ	φ	NOUN
ejpam-5456	361	7	)	)	PUNCT
ejpam-5456	361	8	=	=	SYM
ejpam-5456	362	1	81	81	NUM
ejpam-5456	362	2	16	16	NUM
ejpam-5456	362	3	sin(ϱ	sin(ϱ	NOUN
ejpam-5456	362	4	)	)	PUNCT
ejpam-5456	362	5	φ4µ	φ4µ	PROPN
ejpam-5456	362	6	µ4γ(5	µ4γ(5	PROPN
ejpam-5456	362	7	)	)	PUNCT
ejpam-5456	362	8	,	,	PUNCT
ejpam-5456	362	9	δ2,4(ϱ	δ2,4(ϱ	PROPN
ejpam-5456	362	10	,	,	PUNCT
ejpam-5456	362	11	φ	φ	NOUN
ejpam-5456	362	12	)	)	PUNCT
ejpam-5456	362	13	=	=	SYM
ejpam-5456	362	14	0	0	X
ejpam-5456	362	15	.	.	PUNCT
ejpam-5456	363	1	(	(	PUNCT
ejpam-5456	363	2	64	64	NUM
ejpam-5456	363	3	)	)	PUNCT
ejpam-5456	363	4	the	the	DET
ejpam-5456	363	5	procedure	procedure	NOUN
ejpam-5456	363	6	is	be	AUX
ejpam-5456	363	7	repeated	repeat	VERB
ejpam-5456	363	8	to	to	PART
ejpam-5456	363	9	achieve	achieve	VERB
ejpam-5456	363	10	the	the	DET
ejpam-5456	363	11	results	result	NOUN
ejpam-5456	363	12	for	for	ADP
ejpam-5456	363	13	the	the	DET
ejpam-5456	363	14	sixth	sixth	ADJ
ejpam-5456	363	15	term	term	NOUN
ejpam-5456	363	16	.	.	PUNCT
ejpam-5456	364	1	δ1,5(ϱ	δ1,5(ϱ	PROPN
ejpam-5456	364	2	,	,	PUNCT
ejpam-5456	364	3	φ	φ	NUM
ejpam-5456	364	4	)	)	PUNCT
ejpam-5456	364	5	=	=	SYM
ejpam-5456	364	6	0	0	NUM
ejpam-5456	364	7	,	,	PUNCT
ejpam-5456	364	8	δ2,5(ϱ	δ2,5(ϱ	PROPN
ejpam-5456	364	9	,	,	PUNCT
ejpam-5456	364	10	φ	φ	NOUN
ejpam-5456	364	11	)	)	PUNCT
ejpam-5456	364	12	=	=	SYM
ejpam-5456	364	13	−243	−243	NOUN
ejpam-5456	364	14	32	32	NUM
ejpam-5456	364	15	sin(ϱ	sin(ϱ	NOUN
ejpam-5456	364	16	)	)	PUNCT
ejpam-5456	364	17	φ5µ	φ5µ	NOUN
ejpam-5456	364	18	µ5γ(6	µ5γ(6	NOUN
ejpam-5456	364	19	)	)	PUNCT
ejpam-5456	364	20	.	.	PUNCT
ejpam-5456	365	1	(	(	PUNCT
ejpam-5456	365	2	65	65	NUM
ejpam-5456	365	3	)	)	PUNCT
ejpam-5456	365	4	hence	hence	ADV
ejpam-5456	365	5	,	,	PUNCT
ejpam-5456	365	6	the	the	DET
ejpam-5456	365	7	system	system	NOUN
ejpam-5456	365	8	described	describe	VERB
ejpam-5456	365	9	in	in	ADP
ejpam-5456	365	10	eq	eq	ADP
ejpam-5456	365	11	.	.	PUNCT
ejpam-5456	366	1	(	(	PUNCT
ejpam-5456	366	2	55	55	NUM
ejpam-5456	366	3	)	)	PUNCT
ejpam-5456	366	4	has	have	VERB
ejpam-5456	366	5	an	an	DET
ejpam-5456	366	6	fps	fps	NOUN
ejpam-5456	366	7	solution	solution	NOUN
ejpam-5456	366	8	,	,	PUNCT
ejpam-5456	366	9	which	which	PRON
ejpam-5456	366	10	is	be	AUX
ejpam-5456	366	11	outlined	outline	VERB
ejpam-5456	366	12	below	below	ADV
ejpam-5456	366	13	.	.	PUNCT
ejpam-5456	367	1	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	367	2	,	,	PUNCT
ejpam-5456	367	3	φ	φ	NUM
ejpam-5456	367	4	)	)	PUNCT
ejpam-5456	367	5	=	=	SYM
ejpam-5456	367	6	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	367	7	)	)	PUNCT
ejpam-5456	367	8	(	(	PUNCT
ejpam-5456	367	9	∞∑	∞∑	NUM
ejpam-5456	367	10	ρ=0	ρ=0	NUM
ejpam-5456	367	11	(	(	PUNCT
ejpam-5456	367	12	−1)ρ	−1)ρ	NOUN
ejpam-5456	367	13	γ(2ρ+	γ(2ρ+	VERB
ejpam-5456	367	14	1	1	NUM
ejpam-5456	367	15	)	)	PUNCT
ejpam-5456	367	16	(	(	PUNCT
ejpam-5456	367	17	3φµ	3φµ	NOUN
ejpam-5456	367	18	2µ	2µ	NUM
ejpam-5456	367	19	)	)	PUNCT
ejpam-5456	367	20	2ρ	2ρ	NOUN
ejpam-5456	368	1	−	−	PROPN
ejpam-5456	368	2	ι	ι	PROPN
ejpam-5456	368	3	∞∑	∞∑	PRON
ejpam-5456	368	4	ρ=0	ρ=0	PROPN
ejpam-5456	368	5	(	(	PUNCT
ejpam-5456	368	6	−1)ρ	−1)ρ	NOUN
ejpam-5456	368	7	γ(2ρ+	γ(2ρ+	VERB
ejpam-5456	368	8	2	2	NUM
ejpam-5456	368	9	)	)	PUNCT
ejpam-5456	368	10	(	(	PUNCT
ejpam-5456	368	11	3φµ	3φµ	NOUN
ejpam-5456	368	12	2µ	2µ	NUM
ejpam-5456	368	13	)	)	PUNCT
ejpam-5456	368	14	2ρ+1	2ρ+1	NUM
ejpam-5456	368	15	)	)	PUNCT
ejpam-5456	368	16	.	.	PUNCT
ejpam-5456	369	1	(	(	PUNCT
ejpam-5456	369	2	66	66	NUM
ejpam-5456	369	3	)	)	PUNCT
ejpam-5456	369	4	the	the	DET
ejpam-5456	369	5	ex	ex	PROPN
ejpam-5456	369	6	-	-	PROPN
ejpam-5456	369	7	s	s	PRON
ejpam-5456	369	8	when	when	SCONJ
ejpam-5456	369	9	µ	µ	X
ejpam-5456	369	10	=	=	SYM
ejpam-5456	369	11	1.0	1.0	NUM
ejpam-5456	369	12	is	be	AUX
ejpam-5456	369	13	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	369	14	,	,	PUNCT
ejpam-5456	369	15	φ	φ	NUM
ejpam-5456	369	16	)	)	PUNCT
ejpam-5456	369	17	=	=	SYM
ejpam-5456	369	18	sin(ϱ	sin(ϱ	PROPN
ejpam-5456	369	19	)	)	PUNCT
ejpam-5456	370	1	exp−	exp−	PROPN
ejpam-5456	370	2	3ιφ	3ιφ	NOUN
ejpam-5456	370	3	2	2	NUM
ejpam-5456	370	4	.	.	PUNCT
ejpam-5456	371	1	an	an	DET
ejpam-5456	371	2	identical	identical	ADJ
ejpam-5456	371	3	result	result	NOUN
ejpam-5456	371	4	was	be	AUX
ejpam-5456	371	5	obtained	obtain	VERB
ejpam-5456	371	6	by	by	ADP
ejpam-5456	371	7	[	[	X
ejpam-5456	371	8	10	10	NUM
ejpam-5456	371	9	]	]	PUNCT
ejpam-5456	371	10	.	.	PUNCT
ejpam-5456	372	1	m.i	m.i	PROPN
ejpam-5456	372	2	.	.	PROPN
ejpam-5456	372	3	liaqat	liaqat	PROPN
ejpam-5456	372	4	,	,	PUNCT
ejpam-5456	372	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	372	6	/	/	SYM
ejpam-5456	372	7	eur	eur	PROPN
ejpam-5456	372	8	.	.	PUNCT
ejpam-5456	373	1	j.	j.	PROPN
ejpam-5456	373	2	pure	pure	PROPN
ejpam-5456	373	3	appl	appl	PROPN
ejpam-5456	373	4	.	.	PROPN
ejpam-5456	373	5	math	math	PROPN
ejpam-5456	373	6	,	,	PUNCT
ejpam-5456	373	7	17	17	NUM
ejpam-5456	373	8	(	(	PUNCT
ejpam-5456	373	9	4	4	NUM
ejpam-5456	373	10	)	)	PUNCT
ejpam-5456	373	11	(	(	PUNCT
ejpam-5456	373	12	2024	2024	NUM
ejpam-5456	373	13	)	)	PUNCT
ejpam-5456	373	14	,	,	PUNCT
ejpam-5456	373	15	3464	3464	NUM
ejpam-5456	373	16	-	-	SYM
ejpam-5456	373	17	3491	3491	NUM
ejpam-5456	373	18	3479	3479	NUM
ejpam-5456	373	19	5	5	NUM
ejpam-5456	373	20	.	.	PUNCT
ejpam-5456	373	21	graphical	graphical	ADJ
ejpam-5456	373	22	and	and	CCONJ
ejpam-5456	373	23	numerical	numerical	ADJ
ejpam-5456	373	24	outcome	outcome	NOUN
ejpam-5456	373	25	in	in	ADP
ejpam-5456	373	26	this	this	DET
ejpam-5456	373	27	section	section	NOUN
ejpam-5456	373	28	,	,	PUNCT
ejpam-5456	373	29	we	we	PRON
ejpam-5456	373	30	analyze	analyze	VERB
ejpam-5456	373	31	the	the	DET
ejpam-5456	373	32	numerical	numerical	ADJ
ejpam-5456	373	33	and	and	CCONJ
ejpam-5456	373	34	graphical	graphical	ADJ
ejpam-5456	373	35	results	result	NOUN
ejpam-5456	373	36	of	of	ADP
ejpam-5456	373	37	the	the	DET
ejpam-5456	373	38	ex	ex	NOUN
ejpam-5456	373	39	-	-	NOUN
ejpam-5456	373	40	ss	ss	NOUN
ejpam-5456	373	41	and	and	CCONJ
ejpam-5456	373	42	appss	appss	ADV
ejpam-5456	373	43	for	for	ADP
ejpam-5456	373	44	the	the	DET
ejpam-5456	373	45	linear	linear	ADJ
ejpam-5456	373	46	and	and	CCONJ
ejpam-5456	373	47	nonlinear	nonlinear	ADJ
ejpam-5456	373	48	problems	problem	NOUN
ejpam-5456	373	49	presented	present	VERB
ejpam-5456	373	50	in	in	ADP
ejpam-5456	373	51	the	the	DET
ejpam-5456	373	52	fourth	fourth	ADJ
ejpam-5456	373	53	section	section	NOUN
ejpam-5456	373	54	of	of	ADP
ejpam-5456	373	55	this	this	DET
ejpam-5456	373	56	research	research	NOUN
ejpam-5456	373	57	study	study	NOUN
ejpam-5456	373	58	.	.	PUNCT
ejpam-5456	374	1	to	to	PART
ejpam-5456	374	2	assess	assess	VERB
ejpam-5456	374	3	the	the	DET
ejpam-5456	374	4	sadm	sadm	ADJ
ejpam-5456	374	5	’s	’s	PART
ejpam-5456	374	6	accuracy	accuracy	NOUN
ejpam-5456	374	7	,	,	PUNCT
ejpam-5456	374	8	we	we	PRON
ejpam-5456	374	9	use	use	VERB
ejpam-5456	374	10	two	two	NUM
ejpam-5456	374	11	error	error	NOUN
ejpam-5456	374	12	functions	function	NOUN
ejpam-5456	374	13	,	,	PUNCT
ejpam-5456	374	14	the	the	DET
ejpam-5456	374	15	abs	ab	NOUN
ejpam-5456	374	16	-	-	PUNCT
ejpam-5456	374	17	e	e	NOUN
ejpam-5456	374	18	and	and	CCONJ
ejpam-5456	374	19	rele	rele	PROPN
ejpam-5456	374	20	functions	function	NOUN
ejpam-5456	374	21	.	.	PUNCT
ejpam-5456	375	1	delineating	delineate	VERB
ejpam-5456	375	2	the	the	DET
ejpam-5456	375	3	errors	error	NOUN
ejpam-5456	375	4	in	in	ADP
ejpam-5456	375	5	the	the	DET
ejpam-5456	375	6	app	app	PROPN
ejpam-5456	375	7	-	-	PUNCT
ejpam-5456	375	8	ss	ss	PROPN
ejpam-5456	375	9	is	be	AUX
ejpam-5456	375	10	essential	essential	ADJ
ejpam-5456	375	11	since	since	SCONJ
ejpam-5456	375	12	sadm	sadm	ADV
ejpam-5456	375	13	provides	provide	VERB
ejpam-5456	375	14	an	an	DET
ejpam-5456	375	15	approximation	approximation	NOUN
ejpam-5456	375	16	expressed	express	VERB
ejpam-5456	375	17	in	in	ADP
ejpam-5456	375	18	terms	term	NOUN
ejpam-5456	375	19	of	of	ADP
ejpam-5456	375	20	an	an	DET
ejpam-5456	375	21	infinite	infinite	ADJ
ejpam-5456	375	22	fps	fps	PROPN
ejpam-5456	375	23	.	.	PUNCT
ejpam-5456	376	1	first	first	ADV
ejpam-5456	376	2	,	,	PUNCT
ejpam-5456	376	3	we	we	PRON
ejpam-5456	376	4	present	present	VERB
ejpam-5456	376	5	some	some	DET
ejpam-5456	376	6	useful	useful	ADJ
ejpam-5456	376	7	notation	notation	NOUN
ejpam-5456	376	8	for	for	ADP
ejpam-5456	376	9	ex	ex	NOUN
ejpam-5456	376	10	-	-	NOUN
ejpam-5456	376	11	s	s	X
ejpam-5456	376	12	and	and	CCONJ
ejpam-5456	376	13	app	app	PROPN
ejpam-5456	376	14	-	-	PUNCT
ejpam-5456	376	15	s	s	NOUN
ejpam-5456	376	16	,	,	PUNCT
ejpam-5456	376	17	along	along	ADP
ejpam-5456	376	18	with	with	ADP
ejpam-5456	376	19	formulas	formula	NOUN
ejpam-5456	376	20	for	for	ADP
ejpam-5456	376	21	error	error	NOUN
ejpam-5456	376	22	functions	function	NOUN
ejpam-5456	376	23	,	,	PUNCT
ejpam-5456	376	24	which	which	PRON
ejpam-5456	376	25	we	we	PRON
ejpam-5456	376	26	utilize	utilize	VERB
ejpam-5456	376	27	in	in	ADP
ejpam-5456	376	28	this	this	DET
ejpam-5456	376	29	section	section	NOUN
ejpam-5456	376	30	to	to	PART
ejpam-5456	376	31	analyze	analyze	VERB
ejpam-5456	376	32	the	the	DET
ejpam-5456	376	33	reliability	reliability	NOUN
ejpam-5456	376	34	and	and	CCONJ
ejpam-5456	376	35	correctness	correctness	NOUN
ejpam-5456	376	36	of	of	ADP
ejpam-5456	376	37	our	our	PRON
ejpam-5456	376	38	approach	approach	NOUN
ejpam-5456	376	39	.	.	PUNCT
ejpam-5456	377	1	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	377	2	,	,	PUNCT
ejpam-5456	377	3	φ	φ	NUM
ejpam-5456	377	4	)	)	PUNCT
ejpam-5456	377	5	≈δκ(ϱ	≈δκ(ϱ	NOUN
ejpam-5456	377	6	,	,	PUNCT
ejpam-5456	377	7	φ	φ	NOUN
ejpam-5456	377	8	)	)	PUNCT
ejpam-5456	377	9	,	,	PUNCT
ejpam-5456	377	10	κ	κ	X
ejpam-5456	377	11	=	=	SYM
ejpam-5456	377	12	1	1	NUM
ejpam-5456	377	13	,	,	PUNCT
ejpam-5456	377	14	2	2	NUM
ejpam-5456	377	15	,	,	PUNCT
ejpam-5456	377	16	3	3	NUM
ejpam-5456	377	17	,	,	PUNCT
ejpam-5456	377	18	·	·	PUNCT
ejpam-5456	377	19	·	·	PUNCT
ejpam-5456	377	20	·	·	PUNCT
ejpam-5456	377	21	,	,	PUNCT
ejpam-5456	377	22	where	where	SCONJ
ejpam-5456	377	23	δ(ϱ	δ(ϱ	NOUN
ejpam-5456	377	24	,	,	PUNCT
ejpam-5456	377	25	φ	φ	NUM
ejpam-5456	377	26	)	)	PUNCT
ejpam-5456	377	27	and	and	CCONJ
ejpam-5456	377	28	δκ(ϱ	δκ(ϱ	NUM
ejpam-5456	377	29	,	,	PUNCT
ejpam-5456	377	30	φ	φ	NUM
ejpam-5456	377	31	)	)	PUNCT
ejpam-5456	377	32	denote	denote	VERB
ejpam-5456	377	33	the	the	DET
ejpam-5456	377	34	ex	ex	NOUN
ejpam-5456	377	35	-	-	NOUN
ejpam-5456	377	36	s	s	X
ejpam-5456	377	37	and	and	CCONJ
ejpam-5456	377	38	app	app	PROPN
ejpam-5456	377	39	-	-	PUNCT
ejpam-5456	377	40	s	s	NOUN
ejpam-5456	377	41	of	of	ADP
ejpam-5456	377	42	the	the	DET
ejpam-5456	377	43	nonlinear	nonlinear	ADJ
ejpam-5456	377	44	problems	problem	NOUN
ejpam-5456	377	45	4.2	4.2	NUM
ejpam-5456	377	46	and	and	CCONJ
ejpam-5456	377	47	4.3	4.3	NUM
ejpam-5456	377	48	obtained	obtain	VERB
ejpam-5456	377	49	by	by	ADP
ejpam-5456	377	50	sadm	sadm	ADJ
ejpam-5456	377	51	.	.	PUNCT
ejpam-5456	378	1	abs	ab	NOUN
ejpam-5456	378	2	-	-	PUNCT
ejpam-5456	378	3	e	e	NOUN
ejpam-5456	378	4	plays	play	VERB
ejpam-5456	378	5	a	a	DET
ejpam-5456	378	6	crucial	crucial	ADJ
ejpam-5456	378	7	role	role	NOUN
ejpam-5456	378	8	in	in	ADP
ejpam-5456	378	9	quantifying	quantify	VERB
ejpam-5456	378	10	the	the	DET
ejpam-5456	378	11	accuracy	accuracy	NOUN
ejpam-5456	378	12	of	of	ADP
ejpam-5456	378	13	these	these	DET
ejpam-5456	378	14	app	app	NOUN
ejpam-5456	378	15	-	-	PUNCT
ejpam-5456	378	16	ss	ss	NOUN
ejpam-5456	378	17	and	and	CCONJ
ejpam-5456	378	18	is	be	AUX
ejpam-5456	378	19	indispensable	indispensable	ADJ
ejpam-5456	378	20	for	for	ADP
ejpam-5456	378	21	validating	validate	VERB
ejpam-5456	378	22	and	and	CCONJ
ejpam-5456	378	23	refining	refine	VERB
ejpam-5456	378	24	numerical	numerical	ADJ
ejpam-5456	378	25	techniques	technique	NOUN
ejpam-5456	378	26	.	.	PUNCT
ejpam-5456	379	1	the	the	DET
ejpam-5456	379	2	abs	ab	NOUN
ejpam-5456	379	3	-	-	PUNCT
ejpam-5456	379	4	e	e	NOUN
ejpam-5456	379	5	represents	represent	VERB
ejpam-5456	379	6	the	the	DET
ejpam-5456	379	7	magnitude	magnitude	NOUN
ejpam-5456	379	8	of	of	ADP
ejpam-5456	379	9	the	the	DET
ejpam-5456	379	10	absolute	absolute	ADJ
ejpam-5456	379	11	difference	difference	NOUN
ejpam-5456	379	12	between	between	ADP
ejpam-5456	379	13	the	the	DET
ejpam-5456	379	14	app	app	PROPN
ejpam-5456	379	15	-	-	PUNCT
ejpam-5456	379	16	s	s	X
ejpam-5456	379	17	(	(	PUNCT
ejpam-5456	379	18	δκ(ϱ	δκ(ϱ	NUM
ejpam-5456	379	19	,	,	PUNCT
ejpam-5456	379	20	φ	φ	NOUN
ejpam-5456	379	21	)	)	PUNCT
ejpam-5456	379	22	)	)	PUNCT
ejpam-5456	379	23	obtained	obtain	VERB
ejpam-5456	379	24	through	through	ADP
ejpam-5456	379	25	approximate	approximate	ADJ
ejpam-5456	379	26	methods	method	NOUN
ejpam-5456	379	27	and	and	CCONJ
ejpam-5456	379	28	the	the	DET
ejpam-5456	379	29	ex	ex	NOUN
ejpam-5456	379	30	-	-	PROPN
ejpam-5456	379	31	s	s	X
ejpam-5456	379	32	(	(	PUNCT
ejpam-5456	379	33	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	379	34	,	,	PUNCT
ejpam-5456	379	35	φ	φ	NOUN
ejpam-5456	379	36	)	)	PUNCT
ejpam-5456	379	37	)	)	PUNCT
ejpam-5456	379	38	,	,	PUNCT
ejpam-5456	379	39	if	if	SCONJ
ejpam-5456	379	40	available	available	ADJ
ejpam-5456	379	41	.	.	PUNCT
ejpam-5456	380	1	smaller	small	ADJ
ejpam-5456	380	2	abs	ab	NOUN
ejpam-5456	380	3	-	-	PUNCT
ejpam-5456	380	4	e	e	NOUN
ejpam-5456	380	5	values	value	NOUN
ejpam-5456	380	6	indicate	indicate	VERB
ejpam-5456	380	7	higher	high	ADJ
ejpam-5456	380	8	accuracy	accuracy	NOUN
ejpam-5456	380	9	in	in	ADP
ejpam-5456	380	10	the	the	DET
ejpam-5456	380	11	approximation	approximation	NOUN
ejpam-5456	380	12	.	.	PUNCT
ejpam-5456	381	1	the	the	DET
ejpam-5456	381	2	abs	ab	NOUN
ejpam-5456	381	3	-	-	PUNCT
ejpam-5456	381	4	e	e	NOUN
ejpam-5456	381	5	is	be	AUX
ejpam-5456	381	6	defined	define	VERB
ejpam-5456	381	7	as	as	SCONJ
ejpam-5456	381	8	follows	follow	VERB
ejpam-5456	381	9	:	:	PUNCT
ejpam-5456	381	10	abs.eκ(ϱ	abs.eκ(ϱ	NOUN
ejpam-5456	381	11	,	,	PUNCT
ejpam-5456	381	12	φ	φ	NUM
ejpam-5456	381	13	)	)	PUNCT
ejpam-5456	381	14	=	=	SYM
ejpam-5456	381	15	|δ(ϱ	|δ(ϱ	PROPN
ejpam-5456	381	16	,	,	PUNCT
ejpam-5456	381	17	φ)−	φ)−	PROPN
ejpam-5456	381	18	δκ(ϱ	δκ(ϱ	PUNCT
ejpam-5456	381	19	,	,	PUNCT
ejpam-5456	381	20	φ)|	φ)|	NOUN
ejpam-5456	381	21	,	,	PUNCT
ejpam-5456	381	22	κ	κ	X
ejpam-5456	381	23	=	=	SYM
ejpam-5456	381	24	1	1	NUM
ejpam-5456	381	25	,	,	PUNCT
ejpam-5456	381	26	2	2	NUM
ejpam-5456	381	27	,	,	PUNCT
ejpam-5456	381	28	3	3	NUM
ejpam-5456	381	29	,	,	PUNCT
ejpam-5456	381	30	·	·	PUNCT
ejpam-5456	381	31	·	·	PUNCT
ejpam-5456	381	32	·	·	PUNCT
ejpam-5456	381	33	,	,	PUNCT
ejpam-5456	381	34	when	when	SCONJ
ejpam-5456	381	35	κ	κ	PROPN
ejpam-5456	381	36	increases	increase	VERB
ejpam-5456	381	37	to	to	PART
ejpam-5456	381	38	infinity	infinity	NOUN
ejpam-5456	381	39	,	,	PUNCT
ejpam-5456	381	40	it	it	PRON
ejpam-5456	381	41	frequently	frequently	ADV
ejpam-5456	381	42	happens	happen	VERB
ejpam-5456	381	43	that	that	SCONJ
ejpam-5456	381	44	abs.eκ(ϱ	abs.eκ(ϱ	NOUN
ejpam-5456	381	45	,	,	PUNCT
ejpam-5456	381	46	φ	φ	NUM
ejpam-5456	381	47	)	)	PUNCT
ejpam-5456	381	48	gets	get	AUX
ejpam-5456	381	49	decreasing	decrease	VERB
ejpam-5456	381	50	,	,	PUNCT
ejpam-5456	381	51	eventually	eventually	ADV
ejpam-5456	381	52	decreasing	decrease	VERB
ejpam-5456	381	53	almost	almost	ADV
ejpam-5456	381	54	to	to	ADP
ejpam-5456	381	55	zero	zero	NUM
ejpam-5456	381	56	.	.	PUNCT
ejpam-5456	382	1	the	the	DET
ejpam-5456	382	2	rel	rel	PROPN
ejpam-5456	382	3	-	-	PUNCT
ejpam-5456	382	4	e	e	NOUN
ejpam-5456	382	5	serves	serve	VERB
ejpam-5456	382	6	as	as	ADP
ejpam-5456	382	7	a	a	DET
ejpam-5456	382	8	powerful	powerful	ADJ
ejpam-5456	382	9	tool	tool	NOUN
ejpam-5456	382	10	for	for	ADP
ejpam-5456	382	11	evaluating	evaluate	VERB
ejpam-5456	382	12	the	the	DET
ejpam-5456	382	13	effectiveness	effectiveness	NOUN
ejpam-5456	382	14	of	of	ADP
ejpam-5456	382	15	the	the	DET
ejpam-5456	382	16	approach	approach	NOUN
ejpam-5456	382	17	that	that	PRON
ejpam-5456	382	18	generates	generate	VERB
ejpam-5456	382	19	app	app	PROPN
ejpam-5456	382	20	-	-	PUNCT
ejpam-5456	382	21	ss	ss	NOUN
ejpam-5456	382	22	.	.	PUNCT
ejpam-5456	383	1	it	it	PRON
ejpam-5456	383	2	is	be	AUX
ejpam-5456	383	3	calculated	calculate	VERB
ejpam-5456	383	4	as	as	ADP
ejpam-5456	383	5	the	the	DET
ejpam-5456	383	6	ratio	ratio	NOUN
ejpam-5456	383	7	of	of	ADP
ejpam-5456	383	8	the	the	DET
ejpam-5456	383	9	abs	ab	NOUN
ejpam-5456	383	10	-	-	PUNCT
ejpam-5456	383	11	e	e	NOUN
ejpam-5456	383	12	to	to	ADP
ejpam-5456	383	13	the	the	DET
ejpam-5456	383	14	magnitude	magnitude	NOUN
ejpam-5456	383	15	of	of	ADP
ejpam-5456	383	16	the	the	DET
ejpam-5456	383	17	ex	ex	NOUN
ejpam-5456	383	18	-	-	NOUN
ejpam-5456	383	19	s	s	X
ejpam-5456	383	20	at	at	ADP
ejpam-5456	383	21	each	each	DET
ejpam-5456	383	22	point	point	NOUN
ejpam-5456	383	23	within	within	ADP
ejpam-5456	383	24	the	the	DET
ejpam-5456	383	25	solution	solution	NOUN
ejpam-5456	383	26	domain	domain	NOUN
ejpam-5456	383	27	.	.	PUNCT
ejpam-5456	384	1	this	this	PRON
ejpam-5456	384	2	provides	provide	VERB
ejpam-5456	384	3	valuable	valuable	ADJ
ejpam-5456	384	4	insights	insight	NOUN
ejpam-5456	384	5	into	into	ADP
ejpam-5456	384	6	the	the	DET
ejpam-5456	384	7	degree	degree	NOUN
ejpam-5456	384	8	of	of	ADP
ejpam-5456	384	9	alignment	alignment	NOUN
ejpam-5456	384	10	between	between	ADP
ejpam-5456	384	11	the	the	DET
ejpam-5456	384	12	app	app	PROPN
ejpam-5456	384	13	-	-	PUNCT
ejpam-5456	384	14	s	s	NOUN
ejpam-5456	384	15	and	and	CCONJ
ejpam-5456	384	16	the	the	DET
ejpam-5456	384	17	behavior	behavior	NOUN
ejpam-5456	384	18	of	of	ADP
ejpam-5456	384	19	the	the	DET
ejpam-5456	384	20	ex	ex	PROPN
ejpam-5456	384	21	-	-	PROPN
ejpam-5456	384	22	s.	s.	PROPN
ejpam-5456	384	23	a	a	DET
ejpam-5456	384	24	smaller	small	ADJ
ejpam-5456	384	25	rel	rel	NOUN
ejpam-5456	384	26	-	-	PUNCT
ejpam-5456	384	27	e	e	NOUN
ejpam-5456	384	28	indicates	indicate	VERB
ejpam-5456	384	29	higher	high	ADJ
ejpam-5456	384	30	accuracy	accuracy	NOUN
ejpam-5456	384	31	in	in	ADP
ejpam-5456	384	32	the	the	DET
ejpam-5456	384	33	approximation	approximation	NOUN
ejpam-5456	384	34	.	.	PUNCT
ejpam-5456	385	1	mathematically	mathematically	ADV
ejpam-5456	385	2	,	,	PUNCT
ejpam-5456	385	3	it	it	PRON
ejpam-5456	385	4	is	be	AUX
ejpam-5456	385	5	defined	define	VERB
ejpam-5456	385	6	as	as	SCONJ
ejpam-5456	385	7	follows	follow	VERB
ejpam-5456	385	8	:	:	PUNCT
ejpam-5456	385	9	rel.eκ(ϱ	rel.eκ(ϱ	NOUN
ejpam-5456	385	10	,	,	PUNCT
ejpam-5456	385	11	φ	φ	NUM
ejpam-5456	385	12	)	)	PUNCT
ejpam-5456	386	1	=	=	PUNCT
ejpam-5456	386	2	|δ(ϱ	|δ(ϱ	PROPN
ejpam-5456	386	3	,	,	PUNCT
ejpam-5456	386	4	φ)−	φ)−	PROPN
ejpam-5456	386	5	δκ(ϱ	δκ(ϱ	PUNCT
ejpam-5456	386	6	,	,	PUNCT
ejpam-5456	386	7	φ)|	φ)|	PROPN
ejpam-5456	386	8	|δ(ϱ	|δ(ϱ	PROPN
ejpam-5456	386	9	,	,	PUNCT
ejpam-5456	386	10	φ)|	φ)|	NOUN
ejpam-5456	386	11	,	,	PUNCT
ejpam-5456	386	12	κ	κ	X
ejpam-5456	386	13	=	=	SYM
ejpam-5456	386	14	1	1	NUM
ejpam-5456	386	15	,	,	PUNCT
ejpam-5456	386	16	2	2	NUM
ejpam-5456	386	17	,	,	PUNCT
ejpam-5456	386	18	3	3	NUM
ejpam-5456	386	19	,	,	PUNCT
ejpam-5456	386	20	·	·	PUNCT
ejpam-5456	386	21	·	·	PUNCT
ejpam-5456	386	22	·	·	PUNCT
ejpam-5456	386	23	,	,	PUNCT
ejpam-5456	386	24	where	where	SCONJ
ejpam-5456	386	25	the	the	DET
ejpam-5456	386	26	rel	rel	NOUN
ejpam-5456	386	27	-	-	PUNCT
ejpam-5456	386	28	e	e	NOUN
ejpam-5456	386	29	for	for	ADP
ejpam-5456	386	30	the	the	DET
ejpam-5456	386	31	κth	κth	NOUN
ejpam-5456	386	32	-	-	PUNCT
ejpam-5456	386	33	step	step	NOUN
ejpam-5456	386	34	app	app	NOUN
ejpam-5456	386	35	-	-	PUNCT
ejpam-5456	386	36	s	s	PART
ejpam-5456	386	37	is	be	AUX
ejpam-5456	386	38	represented	represent	VERB
ejpam-5456	386	39	by	by	ADP
ejpam-5456	386	40	rel.eκ(ϱ	rel.eκ(ϱ	PROPN
ejpam-5456	386	41	,	,	PUNCT
ejpam-5456	386	42	φ	φ	NOUN
ejpam-5456	386	43	)	)	PUNCT
ejpam-5456	386	44	for	for	ADP
ejpam-5456	386	45	the	the	DET
ejpam-5456	386	46	ex	ex	NOUN
ejpam-5456	386	47	-	-	PROPN
ejpam-5456	386	48	s	s	X
ejpam-5456	386	49	(	(	PUNCT
ejpam-5456	386	50	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	386	51	,	,	PUNCT
ejpam-5456	386	52	φ	φ	NOUN
ejpam-5456	386	53	)	)	PUNCT
ejpam-5456	386	54	)	)	PUNCT
ejpam-5456	386	55	.	.	PUNCT
ejpam-5456	387	1	in	in	ADP
ejpam-5456	387	2	fact	fact	NOUN
ejpam-5456	387	3	,	,	PUNCT
ejpam-5456	387	4	it	it	PRON
ejpam-5456	387	5	often	often	ADV
ejpam-5456	387	6	happens	happen	VERB
ejpam-5456	387	7	that	that	SCONJ
ejpam-5456	387	8	as	as	SCONJ
ejpam-5456	387	9	κ	κ	PROPN
ejpam-5456	387	10	goes	go	VERB
ejpam-5456	387	11	to	to	ADP
ejpam-5456	387	12	infinity	infinity	NOUN
ejpam-5456	387	13	,	,	PUNCT
ejpam-5456	387	14	rel.eκ(ϱ	rel.eκ(ϱ	NOUN
ejpam-5456	387	15	,	,	PUNCT
ejpam-5456	387	16	φ	φ	NUM
ejpam-5456	387	17	)	)	PUNCT
ejpam-5456	387	18	gets	get	VERB
ejpam-5456	387	19	ever	ever	ADV
ejpam-5456	387	20	smaller	small	ADJ
ejpam-5456	387	21	until	until	SCONJ
ejpam-5456	387	22	it	it	PRON
ejpam-5456	387	23	almost	almost	ADV
ejpam-5456	387	24	reaches	reach	VERB
ejpam-5456	387	25	zero	zero	NUM
ejpam-5456	387	26	.	.	PUNCT
ejpam-5456	388	1	in	in	ADP
ejpam-5456	388	2	figures	figure	NOUN
ejpam-5456	388	3	1	1	NUM
ejpam-5456	388	4	-	-	SYM
ejpam-5456	388	5	4	4	NUM
ejpam-5456	388	6	for	for	ADP
ejpam-5456	388	7	problems	problem	NOUN
ejpam-5456	388	8	4.2	4.2	NUM
ejpam-5456	388	9	and	and	CCONJ
ejpam-5456	388	10	4.3	4.3	NUM
ejpam-5456	388	11	,	,	PUNCT
ejpam-5456	388	12	2d	2d	NUM
ejpam-5456	388	13	curves	curve	NOUN
ejpam-5456	388	14	are	be	AUX
ejpam-5456	388	15	employed	employ	VERB
ejpam-5456	388	16	to	to	PART
ejpam-5456	388	17	compare	compare	VERB
ejpam-5456	388	18	the	the	DET
ejpam-5456	388	19	app	app	NOUN
ejpam-5456	388	20	-	-	PUNCT
ejpam-5456	388	21	ss	ss	PROPN
ejpam-5456	388	22	and	and	CCONJ
ejpam-5456	388	23	ex	ex	NOUN
ejpam-5456	388	24	-	-	NOUN
ejpam-5456	388	25	ss	ss	NOUN
ejpam-5456	388	26	in	in	ADP
ejpam-5456	388	27	terms	term	NOUN
ejpam-5456	388	28	of	of	ADP
ejpam-5456	388	29	rel	rel	NOUN
ejpam-5456	388	30	-	-	PUNCT
ejpam-5456	388	31	e	e	NOUN
ejpam-5456	388	32	and	and	CCONJ
ejpam-5456	388	33	abs	abs	PROPN
ejpam-5456	388	34	-	-	PUNCT
ejpam-5456	388	35	e.	e.	PROPN
ejpam-5456	388	36	the	the	DET
ejpam-5456	388	37	comparative	comparative	ADJ
ejpam-5456	388	38	analysis	analysis	NOUN
ejpam-5456	388	39	reveals	reveal	VERB
ejpam-5456	388	40	a	a	DET
ejpam-5456	388	41	high	high	ADJ
ejpam-5456	388	42	degree	degree	NOUN
ejpam-5456	388	43	of	of	ADP
ejpam-5456	388	44	similarity	similarity	NOUN
ejpam-5456	388	45	between	between	ADP
ejpam-5456	388	46	the	the	DET
ejpam-5456	388	47	fifth	fifth	ADJ
ejpam-5456	388	48	-	-	PUNCT
ejpam-5456	388	49	step	step	NOUN
ejpam-5456	388	50	app	app	NOUN
ejpam-5456	388	51	-	-	PUNCT
ejpam-5456	388	52	ss	ss	NOUN
ejpam-5456	388	53	and	and	CCONJ
ejpam-5456	388	54	the	the	DET
ejpam-5456	388	55	ex	ex	NOUN
ejpam-5456	388	56	-	-	PROPN
ejpam-5456	388	57	ss	ss	NOUN
ejpam-5456	388	58	.	.	PUNCT
ejpam-5456	389	1	the	the	DET
ejpam-5456	389	2	abs	ab	NOUN
ejpam-5456	389	3	-	-	PUNCT
ejpam-5456	389	4	e	e	NOUN
ejpam-5456	389	5	is	be	AUX
ejpam-5456	389	6	presented	present	VERB
ejpam-5456	389	7	on	on	ADP
ejpam-5456	389	8	the	the	DET
ejpam-5456	389	9	graphs	graph	NOUN
ejpam-5456	389	10	to	to	PART
ejpam-5456	389	11	demonstrate	demonstrate	VERB
ejpam-5456	389	12	the	the	DET
ejpam-5456	389	13	excellent	excellent	ADJ
ejpam-5456	389	14	precision	precision	NOUN
ejpam-5456	389	15	of	of	ADP
ejpam-5456	389	16	sadm	sadm	ADJ
ejpam-5456	389	17	.	.	PUNCT
ejpam-5456	390	1	the	the	DET
ejpam-5456	390	2	2d	2d	NUM
ejpam-5456	390	3	graphs	graph	NOUN
ejpam-5456	390	4	of	of	ADP
ejpam-5456	390	5	the	the	DET
ejpam-5456	390	6	app	app	PROPN
ejpam-5456	390	7	-	-	PUNCT
ejpam-5456	390	8	ss	ss	NOUN
ejpam-5456	390	9	obtained	obtain	VERB
ejpam-5456	390	10	from	from	ADP
ejpam-5456	390	11	five	five	NUM
ejpam-5456	390	12	iterations	iteration	NOUN
ejpam-5456	390	13	and	and	CCONJ
ejpam-5456	390	14	the	the	DET
ejpam-5456	390	15	ex	ex	NOUN
ejpam-5456	390	16	-	-	NOUN
ejpam-5456	390	17	ss	ss	NOUN
ejpam-5456	390	18	derived	derive	VERB
ejpam-5456	390	19	by	by	ADP
ejpam-5456	390	20	sadm	sadm	ADV
ejpam-5456	390	21	for	for	ADP
ejpam-5456	390	22	µ	µ	NOUN
ejpam-5456	390	23	=	=	SYM
ejpam-5456	390	24	0.6	0.6	NUM
ejpam-5456	390	25	,	,	PUNCT
ejpam-5456	390	26	0.7	0.7	NUM
ejpam-5456	390	27	,	,	PUNCT
ejpam-5456	390	28	0.8	0.8	NUM
ejpam-5456	390	29	,	,	PUNCT
ejpam-5456	390	30	0.9	0.9	NUM
ejpam-5456	390	31	,	,	PUNCT
ejpam-5456	390	32	and	and	CCONJ
ejpam-5456	390	33	1.0	1.0	NUM
ejpam-5456	390	34	are	be	AUX
ejpam-5456	390	35	depicted	depict	VERB
ejpam-5456	390	36	in	in	ADP
ejpam-5456	390	37	figures	figure	NOUN
ejpam-5456	390	38	5	5	NUM
ejpam-5456	390	39	and	and	CCONJ
ejpam-5456	390	40	6	6	NUM
ejpam-5456	390	41	for	for	ADP
ejpam-5456	390	42	problems	problem	NOUN
ejpam-5456	390	43	4.2	4.2	NUM
ejpam-5456	390	44	and	and	CCONJ
ejpam-5456	390	45	4.3	4.3	NUM
ejpam-5456	390	46	.	.	PUNCT
ejpam-5456	391	1	these	these	DET
ejpam-5456	391	2	graphs	graph	NOUN
ejpam-5456	391	3	illustrate	illustrate	VERB
ejpam-5456	391	4	how	how	SCONJ
ejpam-5456	391	5	,	,	PUNCT
ejpam-5456	391	6	as	as	ADP
ejpam-5456	391	7	µ	µ	X
ejpam-5456	391	8	→	→	SYM
ejpam-5456	391	9	1.0	1.0	NUM
ejpam-5456	391	10	,	,	PUNCT
ejpam-5456	391	11	the	the	DET
ejpam-5456	391	12	app	app	PROPN
ejpam-5456	391	13	-	-	PUNCT
ejpam-5456	391	14	ss	ss	NOUN
ejpam-5456	391	15	converge	converge	NOUN
ejpam-5456	391	16	to	to	ADP
ejpam-5456	391	17	the	the	DET
ejpam-5456	391	18	ex	ex	NOUN
ejpam-5456	391	19	-	-	NOUN
ejpam-5456	391	20	ss	ss	NOUN
ejpam-5456	391	21	.	.	PUNCT
ejpam-5456	392	1	the	the	DET
ejpam-5456	392	2	interaction	interaction	NOUN
ejpam-5456	392	3	between	between	ADP
ejpam-5456	392	4	the	the	DET
ejpam-5456	392	5	app	app	PROPN
ejpam-5456	392	6	-	-	PUNCT
ejpam-5456	392	7	ss	ss	PROPN
ejpam-5456	392	8	and	and	CCONJ
ejpam-5456	392	9	ex	ex	NOUN
ejpam-5456	392	10	-	-	NOUN
ejpam-5456	392	11	ss	ss	NOUN
ejpam-5456	392	12	when	when	SCONJ
ejpam-5456	392	13	µ	µ	X
ejpam-5456	392	14	=	=	SYM
ejpam-5456	392	15	1.0	1.0	NUM
ejpam-5456	392	16	demonstrates	demonstrate	VERB
ejpam-5456	392	17	the	the	DET
ejpam-5456	392	18	accuracy	accuracy	NOUN
ejpam-5456	392	19	of	of	ADP
ejpam-5456	392	20	the	the	DET
ejpam-5456	392	21	proposed	propose	VERB
ejpam-5456	392	22	approach	approach	NOUN
ejpam-5456	392	23	.	.	PUNCT
ejpam-5456	393	1	m.i	m.i	PROPN
ejpam-5456	393	2	.	.	PROPN
ejpam-5456	393	3	liaqat	liaqat	PROPN
ejpam-5456	393	4	,	,	PUNCT
ejpam-5456	393	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	393	6	/	/	SYM
ejpam-5456	393	7	eur	eur	PROPN
ejpam-5456	393	8	.	.	PUNCT
ejpam-5456	394	1	j.	j.	PROPN
ejpam-5456	394	2	pure	pure	PROPN
ejpam-5456	394	3	appl	appl	PROPN
ejpam-5456	394	4	.	.	PROPN
ejpam-5456	394	5	math	math	PROPN
ejpam-5456	394	6	,	,	PUNCT
ejpam-5456	394	7	17	17	NUM
ejpam-5456	394	8	(	(	PUNCT
ejpam-5456	394	9	4	4	NUM
ejpam-5456	394	10	)	)	PUNCT
ejpam-5456	394	11	(	(	PUNCT
ejpam-5456	394	12	2024	2024	NUM
ejpam-5456	394	13	)	)	PUNCT
ejpam-5456	394	14	,	,	PUNCT
ejpam-5456	394	15	3464	3464	NUM
ejpam-5456	394	16	-	-	SYM
ejpam-5456	394	17	3491	3491	NUM
ejpam-5456	394	18	3480	3480	NUM
ejpam-5456	394	19	figures	figure	NOUN
ejpam-5456	394	20	7	7	NUM
ejpam-5456	394	21	-	-	SYM
ejpam-5456	394	22	14	14	NUM
ejpam-5456	394	23	for	for	ADP
ejpam-5456	394	24	problems	problem	NOUN
ejpam-5456	394	25	4.2	4.2	NUM
ejpam-5456	394	26	and	and	CCONJ
ejpam-5456	394	27	4.3	4.3	NUM
ejpam-5456	394	28	display	display	NOUN
ejpam-5456	394	29	the	the	DET
ejpam-5456	394	30	3d	3d	NUM
ejpam-5456	394	31	graphs	graph	NOUN
ejpam-5456	394	32	of	of	ADP
ejpam-5456	394	33	the	the	DET
ejpam-5456	394	34	app	app	PROPN
ejpam-5456	394	35	-	-	PUNCT
ejpam-5456	394	36	ss	ss	NOUN
ejpam-5456	394	37	obtained	obtain	VERB
ejpam-5456	394	38	from	from	ADP
ejpam-5456	394	39	five	five	NUM
ejpam-5456	394	40	iterations	iteration	NOUN
ejpam-5456	394	41	and	and	CCONJ
ejpam-5456	394	42	the	the	DET
ejpam-5456	394	43	ex	ex	NOUN
ejpam-5456	394	44	-	-	NOUN
ejpam-5456	394	45	ss	ss	NOUN
ejpam-5456	394	46	determined	determine	VERB
ejpam-5456	394	47	by	by	ADP
ejpam-5456	394	48	sadm	sadm	ADV
ejpam-5456	394	49	for	for	ADP
ejpam-5456	394	50	µ	µ	NOUN
ejpam-5456	394	51	=	=	SYM
ejpam-5456	394	52	0.7	0.7	NUM
ejpam-5456	394	53	,	,	PUNCT
ejpam-5456	394	54	0.8	0.8	NUM
ejpam-5456	394	55	,	,	PUNCT
ejpam-5456	394	56	0.9	0.9	NUM
ejpam-5456	394	57	,	,	PUNCT
ejpam-5456	394	58	1.0	1.0	NUM
ejpam-5456	394	59	and	and	CCONJ
ejpam-5456	394	60	exss	exss	ADJ
ejpam-5456	394	61	.	.	PUNCT
ejpam-5456	395	1	these	these	DET
ejpam-5456	395	2	graphs	graph	NOUN
ejpam-5456	395	3	demonstrate	demonstrate	VERB
ejpam-5456	395	4	how	how	SCONJ
ejpam-5456	395	5	the	the	DET
ejpam-5456	395	6	app	app	PROPN
ejpam-5456	395	7	-	-	PUNCT
ejpam-5456	395	8	ss	ss	NOUN
ejpam-5456	395	9	converge	converge	NOUN
ejpam-5456	395	10	to	to	ADP
ejpam-5456	395	11	the	the	DET
ejpam-5456	395	12	ex	ex	NOUN
ejpam-5456	395	13	-	-	NOUN
ejpam-5456	395	14	ss	ss	NOUN
ejpam-5456	395	15	as	as	ADP
ejpam-5456	395	16	µ	µ	PRON
ejpam-5456	395	17	approaches	approach	VERB
ejpam-5456	395	18	1.0	1.0	NUM
ejpam-5456	395	19	.	.	PUNCT
ejpam-5456	396	1	the	the	DET
ejpam-5456	396	2	interaction	interaction	NOUN
ejpam-5456	396	3	between	between	ADP
ejpam-5456	396	4	the	the	DET
ejpam-5456	396	5	app	app	PROPN
ejpam-5456	396	6	-	-	PUNCT
ejpam-5456	396	7	ss	ss	PROPN
ejpam-5456	396	8	and	and	CCONJ
ejpam-5456	396	9	ex	ex	NOUN
ejpam-5456	396	10	-	-	NOUN
ejpam-5456	396	11	ss	ss	NOUN
ejpam-5456	396	12	when	when	SCONJ
ejpam-5456	396	13	µ	µ	X
ejpam-5456	396	14	=	=	SYM
ejpam-5456	396	15	1.0	1.0	NUM
ejpam-5456	396	16	illustrates	illustrate	VERB
ejpam-5456	396	17	the	the	DET
ejpam-5456	396	18	accuracy	accuracy	NOUN
ejpam-5456	396	19	of	of	ADP
ejpam-5456	396	20	the	the	DET
ejpam-5456	396	21	proposed	propose	VERB
ejpam-5456	396	22	method	method	NOUN
ejpam-5456	396	23	.	.	PUNCT
ejpam-5456	397	1	the	the	DET
ejpam-5456	397	2	abs	ab	NOUN
ejpam-5456	397	3	-	-	PUNCT
ejpam-5456	397	4	e	e	NOUN
ejpam-5456	397	5	and	and	CCONJ
ejpam-5456	397	6	rel	rel	NOUN
ejpam-5456	397	7	-	-	PUNCT
ejpam-5456	397	8	e	e	NOUN
ejpam-5456	397	9	for	for	ADP
ejpam-5456	397	10	specified	specified	ADJ
ejpam-5456	397	11	locations	location	NOUN
ejpam-5456	397	12	between	between	ADP
ejpam-5456	397	13	the	the	DET
ejpam-5456	397	14	ex	ex	NOUN
ejpam-5456	397	15	-	-	NOUN
ejpam-5456	397	16	ss	ss	NOUN
ejpam-5456	397	17	and	and	CCONJ
ejpam-5456	397	18	fifth	fifth	ADJ
ejpam-5456	397	19	-	-	PUNCT
ejpam-5456	397	20	order	order	NOUN
ejpam-5456	397	21	app	app	ADJ
ejpam-5456	397	22	-	-	PUNCT
ejpam-5456	397	23	ss	ss	NOUN
ejpam-5456	397	24	derived	derive	VERB
ejpam-5456	397	25	by	by	ADP
ejpam-5456	397	26	sadm	sadm	ADV
ejpam-5456	397	27	in	in	ADP
ejpam-5456	397	28	problems	problem	NOUN
ejpam-5456	397	29	4.2	4.2	NUM
ejpam-5456	397	30	and	and	CCONJ
ejpam-5456	397	31	4.3	4.3	NUM
ejpam-5456	397	32	at	at	ADP
ejpam-5456	397	33	µ	µ	X
ejpam-5456	397	34	=	=	SYM
ejpam-5456	397	35	1.0	1.0	NUM
ejpam-5456	397	36	are	be	AUX
ejpam-5456	397	37	presented	present	VERB
ejpam-5456	397	38	in	in	ADP
ejpam-5456	397	39	tables	table	NOUN
ejpam-5456	397	40	1	1	NUM
ejpam-5456	397	41	and	and	CCONJ
ejpam-5456	397	42	2	2	NUM
ejpam-5456	397	43	.	.	X
ejpam-5456	398	1	these	these	DET
ejpam-5456	398	2	tables	table	NOUN
ejpam-5456	398	3	demonstrate	demonstrate	VERB
ejpam-5456	398	4	that	that	SCONJ
ejpam-5456	398	5	the	the	DET
ejpam-5456	398	6	app	app	PROPN
ejpam-5456	398	7	-	-	PUNCT
ejpam-5456	398	8	ss	ss	PROPN
ejpam-5456	398	9	and	and	CCONJ
ejpam-5456	398	10	ex	ex	NOUN
ejpam-5456	398	11	-	-	NOUN
ejpam-5456	398	12	ss	ss	NOUN
ejpam-5456	398	13	are	be	AUX
ejpam-5456	398	14	nearly	nearly	ADV
ejpam-5456	398	15	in	in	ADP
ejpam-5456	398	16	agreement	agreement	NOUN
ejpam-5456	398	17	,	,	PUNCT
ejpam-5456	398	18	confirming	confirm	VERB
ejpam-5456	398	19	the	the	DET
ejpam-5456	398	20	accuracy	accuracy	NOUN
ejpam-5456	398	21	of	of	ADP
ejpam-5456	398	22	sadm	sadm	ADJ
ejpam-5456	398	23	.	.	PUNCT
ejpam-5456	399	1	from	from	ADP
ejpam-5456	399	2	these	these	DET
ejpam-5456	399	3	tables	table	NOUN
ejpam-5456	399	4	,	,	PUNCT
ejpam-5456	399	5	it	it	PRON
ejpam-5456	399	6	is	be	AUX
ejpam-5456	399	7	observed	observe	VERB
ejpam-5456	399	8	that	that	SCONJ
ejpam-5456	399	9	the	the	DET
ejpam-5456	399	10	abs	ab	NOUN
ejpam-5456	399	11	-	-	PUNCT
ejpam-5456	399	12	e	e	NOUN
ejpam-5456	399	13	and	and	CCONJ
ejpam-5456	399	14	rel	rel	NOUN
ejpam-5456	399	15	-	-	PUNCT
ejpam-5456	399	16	e	e	NOUN
ejpam-5456	399	17	for	for	ADP
ejpam-5456	399	18	all	all	DET
ejpam-5456	399	19	problems	problem	NOUN
ejpam-5456	399	20	in	in	ADP
ejpam-5456	399	21	the	the	DET
ejpam-5456	399	22	fifth	fifth	ADJ
ejpam-5456	399	23	-	-	PUNCT
ejpam-5456	399	24	step	step	NOUN
ejpam-5456	399	25	app	app	NOUN
ejpam-5456	399	26	-	-	PUNCT
ejpam-5456	399	27	ss	ss	NOUN
ejpam-5456	399	28	is	be	AUX
ejpam-5456	399	29	very	very	ADV
ejpam-5456	399	30	small	small	ADJ
ejpam-5456	399	31	.	.	PUNCT
ejpam-5456	400	1	the	the	DET
ejpam-5456	400	2	findings	finding	NOUN
ejpam-5456	400	3	presented	present	VERB
ejpam-5456	400	4	in	in	ADP
ejpam-5456	400	5	this	this	DET
ejpam-5456	400	6	section	section	NOUN
ejpam-5456	400	7	,	,	PUNCT
ejpam-5456	400	8	depicted	depict	VERB
ejpam-5456	400	9	in	in	ADP
ejpam-5456	400	10	both	both	DET
ejpam-5456	400	11	graphs	graph	NOUN
ejpam-5456	400	12	and	and	CCONJ
ejpam-5456	400	13	tables	table	NOUN
ejpam-5456	400	14	,	,	PUNCT
ejpam-5456	400	15	demonstrate	demonstrate	VERB
ejpam-5456	400	16	that	that	SCONJ
ejpam-5456	400	17	sadm	sadm	ADV
ejpam-5456	400	18	is	be	AUX
ejpam-5456	400	19	a	a	DET
ejpam-5456	400	20	useful	useful	ADJ
ejpam-5456	400	21	and	and	CCONJ
ejpam-5456	400	22	effective	effective	ADJ
ejpam-5456	400	23	technique	technique	NOUN
ejpam-5456	400	24	for	for	ADP
ejpam-5456	400	25	solving	solve	VERB
ejpam-5456	400	26	fsdes	fsde	NOUN
ejpam-5456	400	27	,	,	PUNCT
ejpam-5456	400	28	requiring	require	VERB
ejpam-5456	400	29	fewer	few	ADJ
ejpam-5456	400	30	calculations	calculation	NOUN
ejpam-5456	400	31	and	and	CCONJ
ejpam-5456	400	32	iterations	iteration	NOUN
ejpam-5456	400	33	.	.	PUNCT
ejpam-5456	401	1	0.0	0.0	NUM
ejpam-5456	401	2	0.1	0.1	NUM
ejpam-5456	401	3	0.2	0.2	NUM
ejpam-5456	401	4	0.3	0.3	NUM
ejpam-5456	401	5	0.4	0.4	NUM
ejpam-5456	401	6	0.5	0.5	NUM
ejpam-5456	401	7	0.000000	0.000000	NUM
ejpam-5456	401	8	5.×10	5.×10	NUM
ejpam-5456	401	9	-	-	SYM
ejpam-5456	401	10	6	6	NUM
ejpam-5456	401	11	0.000010	0.000010	NUM
ejpam-5456	401	12	0.000015	0.000015	NUM
ejpam-5456	401	13	φ	φ	NOUN
ejpam-5456	401	14	r	r	NOUN
ejpam-5456	401	15	el	el	PROPN
ejpam-5456	401	16	.e	.e	PROPN
ejpam-5456	402	1	r	r	NOUN
ejpam-5456	402	2	(	(	PUNCT
ejpam-5456	402	3	a	a	NOUN
ejpam-5456	402	4	)	)	PUNCT
ejpam-5456	402	5	0.0	0.0	NUM
ejpam-5456	402	6	0.1	0.1	NUM
ejpam-5456	402	7	0.2	0.2	NUM
ejpam-5456	402	8	0.3	0.3	NUM
ejpam-5456	402	9	0.4	0.4	NUM
ejpam-5456	402	10	0.5	0.5	NUM
ejpam-5456	402	11	0	0	NUM
ejpam-5456	402	12	1.×10	1.×10	NUM
ejpam-5456	402	13	-	-	SYM
ejpam-5456	402	14	6	6	NUM
ejpam-5456	402	15	2.×10	2.×10	NUM
ejpam-5456	402	16	-	-	SYM
ejpam-5456	402	17	6	6	NUM
ejpam-5456	402	18	3.×10	3.×10	NOUN
ejpam-5456	402	19	-	-	SYM
ejpam-5456	402	20	6	6	NUM
ejpam-5456	402	21	4.×10	4.×10	NOUN
ejpam-5456	402	22	-	-	SYM
ejpam-5456	402	23	6	6	NUM
ejpam-5456	402	24	φ	φ	NOUN
ejpam-5456	402	25	r	r	NOUN
ejpam-5456	402	26	el	el	PROPN
ejpam-5456	402	27	.e	.e	PROPN
ejpam-5456	403	1	r	r	NOUN
ejpam-5456	403	2	(	(	PUNCT
ejpam-5456	403	3	b	b	NOUN
ejpam-5456	403	4	)	)	PUNCT
ejpam-5456	403	5	figure	figure	NOUN
ejpam-5456	403	6	1	1	NUM
ejpam-5456	403	7	:	:	PUNCT
ejpam-5456	403	8	2d	2d	NUM
ejpam-5456	403	9	graphs	graph	NOUN
ejpam-5456	403	10	of	of	ADP
ejpam-5456	403	11	rel	rel	NOUN
ejpam-5456	403	12	-	-	PUNCT
ejpam-5456	403	13	e	e	NOUN
ejpam-5456	403	14	in	in	ADP
ejpam-5456	403	15	the	the	DET
ejpam-5456	403	16	range	range	NOUN
ejpam-5456	403	17	φ	φ	PROPN
ejpam-5456	403	18	∈	∈	PROPN
ejpam-5456	404	1	[	[	X
ejpam-5456	404	2	0	0	NUM
ejpam-5456	404	3	,	,	PUNCT
ejpam-5456	404	4	0.5	0.5	NUM
ejpam-5456	404	5	]	]	PUNCT
ejpam-5456	404	6	comparing	compare	VERB
ejpam-5456	404	7	the	the	DET
ejpam-5456	404	8	fifth	fifth	ADJ
ejpam-5456	404	9	-	-	PUNCT
ejpam-5456	404	10	step	step	NOUN
ejpam-5456	404	11	app	app	NOUN
ejpam-5456	404	12	-	-	PUNCT
ejpam-5456	404	13	s	s	NOUN
ejpam-5456	404	14	and	and	CCONJ
ejpam-5456	404	15	ex	ex	NOUN
ejpam-5456	404	16	-	-	NOUN
ejpam-5456	404	17	s	s	X
ejpam-5456	404	18	for	for	ADP
ejpam-5456	404	19	ϱ	ϱ	NOUN
ejpam-5456	404	20	=	=	SYM
ejpam-5456	404	21	0.1	0.1	NUM
ejpam-5456	404	22	with	with	ADP
ejpam-5456	404	23	µ	µ	NOUN
ejpam-5456	404	24	=	=	SYM
ejpam-5456	404	25	1.0	1.0	NUM
ejpam-5456	404	26	in	in	ADP
ejpam-5456	404	27	problem	problem	NOUN
ejpam-5456	404	28	4.2	4.2	NUM
ejpam-5456	404	29	:	:	PUNCT
ejpam-5456	404	30	(	(	PUNCT
ejpam-5456	404	31	a	a	X
ejpam-5456	404	32	)	)	PUNCT
ejpam-5456	404	33	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	404	34	,	,	PUNCT
ejpam-5456	404	35	φ	φ	NOUN
ejpam-5456	404	36	)	)	PUNCT
ejpam-5456	404	37	;	;	PUNCT
ejpam-5456	404	38	(	(	PUNCT
ejpam-5456	404	39	b	b	X
ejpam-5456	404	40	)	)	PUNCT
ejpam-5456	404	41	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	404	42	,	,	PUNCT
ejpam-5456	404	43	φ	φ	NOUN
ejpam-5456	404	44	)	)	PUNCT
ejpam-5456	404	45	.	.	PUNCT
ejpam-5456	405	1	0.0	0.0	NUM
ejpam-5456	405	2	0.1	0.1	NUM
ejpam-5456	405	3	0.2	0.2	NUM
ejpam-5456	405	4	0.3	0.3	NUM
ejpam-5456	405	5	0.4	0.4	NUM
ejpam-5456	405	6	0.5	0.5	NUM
ejpam-5456	405	7	0	0	NUM
ejpam-5456	405	8	5.×10	5.×10	NUM
ejpam-5456	405	9	-	-	SYM
ejpam-5456	405	10	12	12	NUM
ejpam-5456	405	11	1.×10	1.×10	NUM
ejpam-5456	405	12	-	-	SYM
ejpam-5456	405	13	11	11	NUM
ejpam-5456	405	14	1.5	1.5	NUM
ejpam-5456	405	15	×10	×10	NOUN
ejpam-5456	405	16	-	-	SYM
ejpam-5456	405	17	11	11	NUM
ejpam-5456	405	18	2.×10	2.×10	NUM
ejpam-5456	405	19	-	-	SYM
ejpam-5456	405	20	11	11	NUM
ejpam-5456	405	21	φ	φ	NOUN
ejpam-5456	405	22	r	r	NOUN
ejpam-5456	405	23	el	el	PROPN
ejpam-5456	405	24	.e	.e	PROPN
ejpam-5456	406	1	r	r	NOUN
ejpam-5456	406	2	(	(	PUNCT
ejpam-5456	406	3	a	a	NOUN
ejpam-5456	406	4	)	)	PUNCT
ejpam-5456	406	5	0.0	0.0	NUM
ejpam-5456	406	6	0.1	0.1	NUM
ejpam-5456	406	7	0.2	0.2	NUM
ejpam-5456	406	8	0.3	0.3	NUM
ejpam-5456	406	9	0.4	0.4	NUM
ejpam-5456	406	10	0.5	0.5	NUM
ejpam-5456	406	11	0	0	NUM
ejpam-5456	406	12	2.×10	2.×10	NUM
ejpam-5456	406	13	-	-	SYM
ejpam-5456	406	14	13	13	NUM
ejpam-5456	406	15	4.×10	4.×10	NOUN
ejpam-5456	406	16	-	-	SYM
ejpam-5456	406	17	13	13	NUM
ejpam-5456	406	18	6.×10	6.×10	NOUN
ejpam-5456	406	19	-	-	SYM
ejpam-5456	406	20	13	13	NUM
ejpam-5456	406	21	8.×10	8.×10	NUM
ejpam-5456	406	22	-	-	SYM
ejpam-5456	406	23	13	13	NUM
ejpam-5456	406	24	1.×10	1.×10	NUM
ejpam-5456	406	25	-	-	SYM
ejpam-5456	406	26	12	12	NUM
ejpam-5456	406	27	1.2	1.2	NUM
ejpam-5456	406	28	×10	×10	NOUN
ejpam-5456	406	29	-	-	PUNCT
ejpam-5456	406	30	12	12	NUM
ejpam-5456	406	31	φ	φ	NOUN
ejpam-5456	406	32	r	r	NOUN
ejpam-5456	406	33	el	el	PROPN
ejpam-5456	406	34	.e	.e	PROPN
ejpam-5456	407	1	r	r	NOUN
ejpam-5456	407	2	(	(	PUNCT
ejpam-5456	407	3	b	b	NOUN
ejpam-5456	407	4	)	)	PUNCT
ejpam-5456	407	5	figure	figure	NOUN
ejpam-5456	407	6	2	2	NUM
ejpam-5456	407	7	:	:	PUNCT
ejpam-5456	407	8	2d	2d	NUM
ejpam-5456	407	9	graphs	graph	NOUN
ejpam-5456	407	10	of	of	ADP
ejpam-5456	407	11	rel	rel	NOUN
ejpam-5456	407	12	-	-	PUNCT
ejpam-5456	407	13	e	e	NOUN
ejpam-5456	407	14	in	in	ADP
ejpam-5456	407	15	the	the	DET
ejpam-5456	407	16	range	range	NOUN
ejpam-5456	407	17	φ	φ	PROPN
ejpam-5456	407	18	∈	∈	PROPN
ejpam-5456	408	1	[	[	X
ejpam-5456	408	2	0	0	NUM
ejpam-5456	408	3	,	,	PUNCT
ejpam-5456	408	4	0.5	0.5	NUM
ejpam-5456	408	5	]	]	PUNCT
ejpam-5456	408	6	comparing	compare	VERB
ejpam-5456	408	7	the	the	DET
ejpam-5456	408	8	fifth	fifth	ADJ
ejpam-5456	408	9	-	-	PUNCT
ejpam-5456	408	10	step	step	NOUN
ejpam-5456	408	11	app	app	NOUN
ejpam-5456	408	12	-	-	PUNCT
ejpam-5456	408	13	s	s	NOUN
ejpam-5456	408	14	and	and	CCONJ
ejpam-5456	408	15	ex	ex	NOUN
ejpam-5456	408	16	-	-	NOUN
ejpam-5456	408	17	s	s	X
ejpam-5456	408	18	for	for	ADP
ejpam-5456	408	19	ϱ	ϱ	NOUN
ejpam-5456	408	20	=	=	SYM
ejpam-5456	408	21	0.1	0.1	NUM
ejpam-5456	408	22	with	with	ADP
ejpam-5456	408	23	µ	µ	NOUN
ejpam-5456	408	24	=	=	SYM
ejpam-5456	408	25	1.0	1.0	NUM
ejpam-5456	408	26	in	in	ADP
ejpam-5456	408	27	problem	problem	NOUN
ejpam-5456	408	28	4.3	4.3	NUM
ejpam-5456	408	29	:	:	PUNCT
ejpam-5456	408	30	(	(	PUNCT
ejpam-5456	408	31	a	a	X
ejpam-5456	408	32	)	)	PUNCT
ejpam-5456	408	33	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	408	34	,	,	PUNCT
ejpam-5456	408	35	φ	φ	NOUN
ejpam-5456	408	36	)	)	PUNCT
ejpam-5456	408	37	;	;	PUNCT
ejpam-5456	408	38	(	(	PUNCT
ejpam-5456	408	39	b	b	X
ejpam-5456	408	40	)	)	PUNCT
ejpam-5456	408	41	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	408	42	,	,	PUNCT
ejpam-5456	408	43	φ	φ	NUM
ejpam-5456	408	44	)	)	PUNCT
ejpam-5456	408	45	.	.	PUNCT
ejpam-5456	409	1	m.i	m.i	PROPN
ejpam-5456	409	2	.	.	PROPN
ejpam-5456	409	3	liaqat	liaqat	PROPN
ejpam-5456	409	4	,	,	PUNCT
ejpam-5456	409	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	409	6	/	/	SYM
ejpam-5456	409	7	eur	eur	PROPN
ejpam-5456	409	8	.	.	PUNCT
ejpam-5456	410	1	j.	j.	PROPN
ejpam-5456	410	2	pure	pure	PROPN
ejpam-5456	410	3	appl	appl	PROPN
ejpam-5456	410	4	.	.	PROPN
ejpam-5456	410	5	math	math	PROPN
ejpam-5456	410	6	,	,	PUNCT
ejpam-5456	410	7	17	17	NUM
ejpam-5456	410	8	(	(	PUNCT
ejpam-5456	410	9	4	4	NUM
ejpam-5456	410	10	)	)	PUNCT
ejpam-5456	410	11	(	(	PUNCT
ejpam-5456	410	12	2024	2024	NUM
ejpam-5456	410	13	)	)	PUNCT
ejpam-5456	410	14	,	,	PUNCT
ejpam-5456	410	15	3464	3464	NUM
ejpam-5456	410	16	-	-	SYM
ejpam-5456	410	17	3491	3491	NUM
ejpam-5456	410	18	3481	3481	NUM
ejpam-5456	410	19	0.0	0.0	NUM
ejpam-5456	410	20	0.1	0.1	NUM
ejpam-5456	410	21	0.2	0.2	NUM
ejpam-5456	410	22	0.3	0.3	NUM
ejpam-5456	410	23	0.4	0.4	NUM
ejpam-5456	410	24	0.5	0.5	NUM
ejpam-5456	410	25	0.000000	0.000000	NUM
ejpam-5456	410	26	2.×10	2.×10	NUM
ejpam-5456	410	27	-	-	SYM
ejpam-5456	410	28	6	6	NUM
ejpam-5456	410	29	4.×10	4.×10	NOUN
ejpam-5456	410	30	-	-	PUNCT
ejpam-5456	410	31	6	6	NUM
ejpam-5456	410	32	6.×10	6.×10	NOUN
ejpam-5456	410	33	-	-	SYM
ejpam-5456	410	34	6	6	NUM
ejpam-5456	410	35	8.×10	8.×10	NOUN
ejpam-5456	410	36	-	-	SYM
ejpam-5456	410	37	6	6	NUM
ejpam-5456	410	38	0.000010	0.000010	NUM
ejpam-5456	410	39	0.000012	0.000012	NUM
ejpam-5456	410	40	0.000014	0.000014	NUM
ejpam-5456	410	41	φ	φ	NOUN
ejpam-5456	410	42	a	a	DET
ejpam-5456	410	43	bs	bs	NOUN
ejpam-5456	410	44	.e	.e	NOUN
ejpam-5456	411	1	r	r	NOUN
ejpam-5456	411	2	(	(	PUNCT
ejpam-5456	411	3	a	a	NOUN
ejpam-5456	411	4	)	)	PUNCT
ejpam-5456	411	5	0.0	0.0	NUM
ejpam-5456	411	6	0.1	0.1	NUM
ejpam-5456	411	7	0.2	0.2	NUM
ejpam-5456	411	8	0.3	0.3	NUM
ejpam-5456	411	9	0.4	0.4	NUM
ejpam-5456	411	10	0.5	0.5	NUM
ejpam-5456	411	11	0	0	NUM
ejpam-5456	411	12	5.×10	5.×10	NUM
ejpam-5456	411	13	-	-	SYM
ejpam-5456	411	14	7	7	NUM
ejpam-5456	411	15	1.×10	1.×10	NUM
ejpam-5456	411	16	-	-	SYM
ejpam-5456	411	17	6	6	NUM
ejpam-5456	411	18	1.5	1.5	NUM
ejpam-5456	411	19	×10	×10	NOUN
ejpam-5456	411	20	-	-	SYM
ejpam-5456	411	21	6	6	NUM
ejpam-5456	411	22	2.×10	2.×10	NUM
ejpam-5456	411	23	-	-	SYM
ejpam-5456	411	24	6	6	NUM
ejpam-5456	411	25	φ	φ	NOUN
ejpam-5456	411	26	a	a	DET
ejpam-5456	411	27	bs	bs	NOUN
ejpam-5456	411	28	.e	.e	NOUN
ejpam-5456	412	1	r	r	NOUN
ejpam-5456	412	2	(	(	PUNCT
ejpam-5456	412	3	b	b	NOUN
ejpam-5456	412	4	)	)	PUNCT
ejpam-5456	412	5	figure	figure	NOUN
ejpam-5456	412	6	3	3	NUM
ejpam-5456	412	7	:	:	PUNCT
ejpam-5456	412	8	2d	2d	NUM
ejpam-5456	412	9	graphs	graph	NOUN
ejpam-5456	412	10	of	of	ADP
ejpam-5456	412	11	abs	ab	NOUN
ejpam-5456	412	12	-	-	PUNCT
ejpam-5456	412	13	e	e	NOUN
ejpam-5456	412	14	in	in	ADP
ejpam-5456	412	15	the	the	DET
ejpam-5456	412	16	range	range	NOUN
ejpam-5456	412	17	φ	φ	PROPN
ejpam-5456	412	18	∈	∈	PROPN
ejpam-5456	413	1	[	[	X
ejpam-5456	413	2	0	0	NUM
ejpam-5456	413	3	,	,	PUNCT
ejpam-5456	413	4	0.5	0.5	NUM
ejpam-5456	413	5	]	]	PUNCT
ejpam-5456	413	6	comparing	compare	VERB
ejpam-5456	413	7	the	the	DET
ejpam-5456	413	8	fifth	fifth	ADJ
ejpam-5456	413	9	-	-	PUNCT
ejpam-5456	413	10	step	step	NOUN
ejpam-5456	413	11	app	app	NOUN
ejpam-5456	413	12	-	-	PUNCT
ejpam-5456	413	13	s	s	NOUN
ejpam-5456	413	14	and	and	CCONJ
ejpam-5456	413	15	ex	ex	NOUN
ejpam-5456	413	16	-	-	NOUN
ejpam-5456	413	17	s	s	X
ejpam-5456	413	18	for	for	ADP
ejpam-5456	413	19	ϱ	ϱ	NOUN
ejpam-5456	413	20	=	=	SYM
ejpam-5456	413	21	0.1	0.1	NUM
ejpam-5456	413	22	with	with	ADP
ejpam-5456	413	23	µ	µ	NOUN
ejpam-5456	413	24	=	=	SYM
ejpam-5456	413	25	1.0	1.0	NUM
ejpam-5456	413	26	in	in	ADP
ejpam-5456	413	27	problem	problem	NOUN
ejpam-5456	413	28	4.2	4.2	NUM
ejpam-5456	413	29	:	:	PUNCT
ejpam-5456	413	30	(	(	PUNCT
ejpam-5456	413	31	a	a	X
ejpam-5456	413	32	)	)	PUNCT
ejpam-5456	413	33	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	413	34	,	,	PUNCT
ejpam-5456	413	35	φ	φ	NOUN
ejpam-5456	413	36	)	)	PUNCT
ejpam-5456	413	37	;	;	PUNCT
ejpam-5456	413	38	(	(	PUNCT
ejpam-5456	413	39	b	b	X
ejpam-5456	413	40	)	)	PUNCT
ejpam-5456	413	41	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	413	42	,	,	PUNCT
ejpam-5456	413	43	φ	φ	NOUN
ejpam-5456	413	44	)	)	PUNCT
ejpam-5456	413	45	.	.	PUNCT
ejpam-5456	414	1	0.0	0.0	NUM
ejpam-5456	414	2	0.1	0.1	NUM
ejpam-5456	414	3	0.2	0.2	NUM
ejpam-5456	414	4	0.3	0.3	NUM
ejpam-5456	414	5	0.4	0.4	NUM
ejpam-5456	414	6	0.5	0.5	NUM
ejpam-5456	414	7	0	0	NUM
ejpam-5456	414	8	2.×10	2.×10	NUM
ejpam-5456	414	9	-	-	SYM
ejpam-5456	414	10	13	13	NUM
ejpam-5456	414	11	4.×10	4.×10	NOUN
ejpam-5456	414	12	-	-	SYM
ejpam-5456	414	13	13	13	NUM
ejpam-5456	414	14	6.×10	6.×10	NOUN
ejpam-5456	414	15	-	-	SYM
ejpam-5456	414	16	13	13	NUM
ejpam-5456	414	17	8.×10	8.×10	NOUN
ejpam-5456	414	18	-	-	SYM
ejpam-5456	414	19	13	13	NUM
ejpam-5456	414	20	φ	φ	NOUN
ejpam-5456	414	21	a	a	DET
ejpam-5456	414	22	bs	bs	NOUN
ejpam-5456	414	23	.e	.e	NOUN
ejpam-5456	415	1	r	r	NOUN
ejpam-5456	415	2	(	(	PUNCT
ejpam-5456	415	3	a	a	NOUN
ejpam-5456	415	4	)	)	PUNCT
ejpam-5456	415	5	0.0	0.0	NUM
ejpam-5456	415	6	0.1	0.1	NUM
ejpam-5456	415	7	0.2	0.2	NUM
ejpam-5456	415	8	0.3	0.3	NUM
ejpam-5456	415	9	0.4	0.4	NUM
ejpam-5456	415	10	0.5	0.5	NUM
ejpam-5456	415	11	0	0	NUM
ejpam-5456	415	12	1.×10	1.×10	NUM
ejpam-5456	415	13	-	-	SYM
ejpam-5456	415	14	14	14	NUM
ejpam-5456	415	15	2.×10	2.×10	NUM
ejpam-5456	415	16	-	-	SYM
ejpam-5456	415	17	14	14	NUM
ejpam-5456	415	18	3.×10	3.×10	NOUN
ejpam-5456	415	19	-	-	SYM
ejpam-5456	415	20	14	14	NUM
ejpam-5456	415	21	φ	φ	NOUN
ejpam-5456	415	22	a	a	DET
ejpam-5456	415	23	bs	bs	NOUN
ejpam-5456	415	24	.e	.e	NOUN
ejpam-5456	416	1	r	r	NOUN
ejpam-5456	416	2	(	(	PUNCT
ejpam-5456	416	3	b	b	NOUN
ejpam-5456	416	4	)	)	PUNCT
ejpam-5456	416	5	figure	figure	NOUN
ejpam-5456	416	6	4	4	NUM
ejpam-5456	416	7	:	:	PUNCT
ejpam-5456	416	8	2d	2d	NUM
ejpam-5456	416	9	graphs	graph	NOUN
ejpam-5456	416	10	of	of	ADP
ejpam-5456	416	11	abs	ab	NOUN
ejpam-5456	416	12	-	-	PUNCT
ejpam-5456	416	13	e	e	NOUN
ejpam-5456	416	14	in	in	ADP
ejpam-5456	416	15	the	the	DET
ejpam-5456	416	16	range	range	NOUN
ejpam-5456	416	17	φ	φ	PROPN
ejpam-5456	416	18	∈	∈	PROPN
ejpam-5456	417	1	[	[	X
ejpam-5456	417	2	0	0	NUM
ejpam-5456	417	3	,	,	PUNCT
ejpam-5456	417	4	0.5	0.5	NUM
ejpam-5456	417	5	]	]	PUNCT
ejpam-5456	417	6	comparing	compare	VERB
ejpam-5456	417	7	the	the	DET
ejpam-5456	417	8	fifth	fifth	ADJ
ejpam-5456	417	9	-	-	PUNCT
ejpam-5456	417	10	step	step	NOUN
ejpam-5456	417	11	app	app	NOUN
ejpam-5456	417	12	-	-	PUNCT
ejpam-5456	417	13	s	s	NOUN
ejpam-5456	417	14	and	and	CCONJ
ejpam-5456	417	15	ex	ex	NOUN
ejpam-5456	417	16	-	-	NOUN
ejpam-5456	417	17	s	s	X
ejpam-5456	417	18	for	for	ADP
ejpam-5456	417	19	ϱ	ϱ	NOUN
ejpam-5456	417	20	=	=	SYM
ejpam-5456	417	21	0.1	0.1	NUM
ejpam-5456	417	22	with	with	ADP
ejpam-5456	417	23	µ	µ	NOUN
ejpam-5456	417	24	=	=	SYM
ejpam-5456	417	25	1.0	1.0	NUM
ejpam-5456	417	26	in	in	ADP
ejpam-5456	417	27	problem	problem	NOUN
ejpam-5456	417	28	4.3	4.3	NUM
ejpam-5456	417	29	:	:	PUNCT
ejpam-5456	417	30	(	(	PUNCT
ejpam-5456	417	31	a	a	X
ejpam-5456	417	32	)	)	PUNCT
ejpam-5456	417	33	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	417	34	,	,	PUNCT
ejpam-5456	417	35	φ	φ	NOUN
ejpam-5456	417	36	)	)	PUNCT
ejpam-5456	417	37	;	;	PUNCT
ejpam-5456	417	38	(	(	PUNCT
ejpam-5456	417	39	b	b	X
ejpam-5456	417	40	)	)	PUNCT
ejpam-5456	417	41	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	417	42	,	,	PUNCT
ejpam-5456	417	43	φ	φ	NOUN
ejpam-5456	417	44	)	)	PUNCT
ejpam-5456	417	45	.	.	PUNCT
ejpam-5456	418	1	0.0	0.0	NUM
ejpam-5456	418	2	0.2	0.2	NUM
ejpam-5456	418	3	0.4	0.4	NUM
ejpam-5456	418	4	0.6	0.6	NUM
ejpam-5456	418	5	0.8	0.8	NUM
ejpam-5456	418	6	1.0	1.0	NUM
ejpam-5456	418	7	-0.2	-0.2	NUM
ejpam-5456	418	8	0.0	0.0	NUM
ejpam-5456	418	9	0.2	0.2	NUM
ejpam-5456	418	10	0.4	0.4	NUM
ejpam-5456	418	11	0.6	0.6	NUM
ejpam-5456	418	12	0.8	0.8	NUM
ejpam-5456	418	13	1.0	1.0	NUM
ejpam-5456	418	14	φ	φ	NUM
ejpam-5456	418	15	δ	δ	PROPN
ejpam-5456	418	16	1	1	NUM
ejpam-5456	418	17	μ=0.6	μ=0.6	NOUN
ejpam-5456	418	18	μ=0.7	μ=0.7	NOUN
ejpam-5456	418	19	μ=0.8	μ=0.8	NOUN
ejpam-5456	418	20	μ=0.9	μ=0.9	NOUN
ejpam-5456	418	21	μ=1.0	μ=1.0	PRON
ejpam-5456	418	22	exact	exact	ADJ
ejpam-5456	418	23	(	(	PUNCT
ejpam-5456	418	24	a	a	X
ejpam-5456	418	25	)	)	PUNCT
ejpam-5456	418	26	0.0	0.0	NUM
ejpam-5456	418	27	0.2	0.2	NUM
ejpam-5456	418	28	0.4	0.4	NUM
ejpam-5456	418	29	0.6	0.6	NUM
ejpam-5456	418	30	0.8	0.8	NUM
ejpam-5456	418	31	1.0	1.0	NUM
ejpam-5456	418	32	0.0	0.0	NUM
ejpam-5456	418	33	0.2	0.2	NUM
ejpam-5456	418	34	0.4	0.4	NUM
ejpam-5456	418	35	0.6	0.6	NUM
ejpam-5456	418	36	0.8	0.8	NUM
ejpam-5456	418	37	1.0	1.0	NUM
ejpam-5456	418	38	φ	φ	NUM
ejpam-5456	418	39	δ	δ	PROPN
ejpam-5456	418	40	2	2	NUM
ejpam-5456	418	41	μ=0.6	μ=0.6	NOUN
ejpam-5456	418	42	μ=0.7	μ=0.7	NOUN
ejpam-5456	418	43	μ=0.8	μ=0.8	NOUN
ejpam-5456	418	44	μ=0.9	μ=0.9	NOUN
ejpam-5456	418	45	μ=1.0	μ=1.0	PRON
ejpam-5456	418	46	exact	exact	ADJ
ejpam-5456	418	47	(	(	PUNCT
ejpam-5456	418	48	b	b	NOUN
ejpam-5456	418	49	)	)	PUNCT
ejpam-5456	418	50	figure	figure	NOUN
ejpam-5456	418	51	5	5	NUM
ejpam-5456	418	52	:	:	PUNCT
ejpam-5456	418	53	for	for	ADP
ejpam-5456	418	54	problem	problem	NOUN
ejpam-5456	418	55	4.2	4.2	NUM
ejpam-5456	418	56	,	,	PUNCT
ejpam-5456	418	57	the	the	DET
ejpam-5456	418	58	2d	2d	NUM
ejpam-5456	418	59	diagrams	diagram	NOUN
ejpam-5456	418	60	of	of	ADP
ejpam-5456	418	61	app	app	PROPN
ejpam-5456	418	62	-	-	PUNCT
ejpam-5456	418	63	s	s	NOUN
ejpam-5456	418	64	for	for	ADP
ejpam-5456	418	65	various	various	ADJ
ejpam-5456	418	66	levels	level	NOUN
ejpam-5456	418	67	of	of	ADP
ejpam-5456	418	68	µ	µ	NOUN
ejpam-5456	418	69	and	and	CCONJ
ejpam-5456	418	70	ex	ex	NOUN
ejpam-5456	418	71	-	-	NOUN
ejpam-5456	418	72	s	s	X
ejpam-5456	418	73	in	in	ADP
ejpam-5456	418	74	the	the	DET
ejpam-5456	418	75	range	range	NOUN
ejpam-5456	418	76	φ	φ	PROPN
ejpam-5456	418	77	∈	∈	PROPN
ejpam-5456	419	1	[	[	X
ejpam-5456	419	2	0	0	NUM
ejpam-5456	419	3	,	,	PUNCT
ejpam-5456	419	4	1.0	1.0	NUM
ejpam-5456	419	5	]	]	PUNCT
ejpam-5456	419	6	at	at	ADP
ejpam-5456	419	7	ϱ	ϱ	NOUN
ejpam-5456	419	8	=	=	SYM
ejpam-5456	419	9	0.1	0.1	NUM
ejpam-5456	419	10	are	be	AUX
ejpam-5456	419	11	shown	show	VERB
ejpam-5456	419	12	for	for	ADP
ejpam-5456	419	13	:	:	PUNCT
ejpam-5456	419	14	(	(	PUNCT
ejpam-5456	419	15	a	a	X
ejpam-5456	419	16	)	)	PUNCT
ejpam-5456	419	17	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	419	18	,	,	PUNCT
ejpam-5456	419	19	φ	φ	NOUN
ejpam-5456	419	20	)	)	PUNCT
ejpam-5456	419	21	;	;	PUNCT
ejpam-5456	419	22	(	(	PUNCT
ejpam-5456	419	23	b	b	X
ejpam-5456	419	24	)	)	PUNCT
ejpam-5456	419	25	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	419	26	,	,	PUNCT
ejpam-5456	419	27	φ	φ	NUM
ejpam-5456	419	28	)	)	PUNCT
ejpam-5456	419	29	.	.	PUNCT
ejpam-5456	420	1	m.i	m.i	PROPN
ejpam-5456	420	2	.	.	PROPN
ejpam-5456	420	3	liaqat	liaqat	PROPN
ejpam-5456	420	4	,	,	PUNCT
ejpam-5456	420	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	420	6	/	/	SYM
ejpam-5456	420	7	eur	eur	PROPN
ejpam-5456	420	8	.	.	PUNCT
ejpam-5456	421	1	j.	j.	PROPN
ejpam-5456	421	2	pure	pure	PROPN
ejpam-5456	421	3	appl	appl	PROPN
ejpam-5456	421	4	.	.	PROPN
ejpam-5456	421	5	math	math	PROPN
ejpam-5456	421	6	,	,	PUNCT
ejpam-5456	421	7	17	17	NUM
ejpam-5456	421	8	(	(	PUNCT
ejpam-5456	421	9	4	4	NUM
ejpam-5456	421	10	)	)	PUNCT
ejpam-5456	421	11	(	(	PUNCT
ejpam-5456	421	12	2024	2024	NUM
ejpam-5456	421	13	)	)	PUNCT
ejpam-5456	421	14	,	,	PUNCT
ejpam-5456	421	15	3464	3464	NUM
ejpam-5456	421	16	-	-	SYM
ejpam-5456	421	17	3491	3491	NUM
ejpam-5456	421	18	3482	3482	NUM
ejpam-5456	421	19	0.0	0.0	NUM
ejpam-5456	421	20	0.2	0.2	NUM
ejpam-5456	421	21	0.4	0.4	NUM
ejpam-5456	421	22	0.6	0.6	NUM
ejpam-5456	421	23	0.8	0.8	NUM
ejpam-5456	421	24	1.0	1.0	NUM
ejpam-5456	421	25	-0.05	-0.05	NUM
ejpam-5456	421	26	0.00	0.00	NUM
ejpam-5456	421	27	0.05	0.05	NUM
ejpam-5456	421	28	0.10	0.10	NUM
ejpam-5456	421	29	φ	φ	NUM
ejpam-5456	421	30	δ	δ	PROPN
ejpam-5456	421	31	1	1	NUM
ejpam-5456	421	32	μ=0.6	μ=0.6	NOUN
ejpam-5456	421	33	μ=0.7	μ=0.7	NOUN
ejpam-5456	421	34	μ=0.8	μ=0.8	NOUN
ejpam-5456	421	35	μ=0.9	μ=0.9	NOUN
ejpam-5456	421	36	μ=1.0	μ=1.0	PRON
ejpam-5456	421	37	exact	exact	ADJ
ejpam-5456	421	38	(	(	PUNCT
ejpam-5456	421	39	a	a	X
ejpam-5456	421	40	)	)	PUNCT
ejpam-5456	421	41	0.0	0.0	NUM
ejpam-5456	421	42	0.2	0.2	NUM
ejpam-5456	421	43	0.4	0.4	NUM
ejpam-5456	421	44	0.6	0.6	NUM
ejpam-5456	421	45	0.8	0.8	NUM
ejpam-5456	421	46	1.0	1.0	NUM
ejpam-5456	421	47	-0.10	-0.10	NUM
ejpam-5456	421	48	-0.08	-0.08	NUM
ejpam-5456	421	49	-0.06	-0.06	NUM
ejpam-5456	421	50	-0.04	-0.04	NUM
ejpam-5456	421	51	-0.02	-0.02	NUM
ejpam-5456	421	52	0.00	0.00	NUM
ejpam-5456	421	53	φ	φ	NUM
ejpam-5456	421	54	δ	δ	PROPN
ejpam-5456	421	55	2	2	NUM
ejpam-5456	421	56	μ=0.6	μ=0.6	NOUN
ejpam-5456	421	57	μ=0.7	μ=0.7	NOUN
ejpam-5456	421	58	μ=0.8	μ=0.8	NOUN
ejpam-5456	421	59	μ=0.9	μ=0.9	NOUN
ejpam-5456	421	60	μ=1.0	μ=1.0	PRON
ejpam-5456	421	61	exact	exact	ADJ
ejpam-5456	421	62	(	(	PUNCT
ejpam-5456	421	63	b	b	NOUN
ejpam-5456	421	64	)	)	PUNCT
ejpam-5456	421	65	figure	figure	NOUN
ejpam-5456	421	66	6	6	NUM
ejpam-5456	421	67	:	:	PUNCT
ejpam-5456	421	68	for	for	ADP
ejpam-5456	421	69	problem	problem	NOUN
ejpam-5456	421	70	4.3	4.3	NUM
ejpam-5456	421	71	,	,	PUNCT
ejpam-5456	421	72	the	the	DET
ejpam-5456	421	73	2d	2d	NUM
ejpam-5456	421	74	diagrams	diagram	NOUN
ejpam-5456	421	75	of	of	ADP
ejpam-5456	421	76	app	app	PROPN
ejpam-5456	421	77	-	-	PUNCT
ejpam-5456	421	78	ss	ss	NOUN
ejpam-5456	421	79	for	for	ADP
ejpam-5456	421	80	various	various	ADJ
ejpam-5456	421	81	levels	level	NOUN
ejpam-5456	421	82	of	of	ADP
ejpam-5456	421	83	µ	µ	NOUN
ejpam-5456	421	84	and	and	CCONJ
ejpam-5456	421	85	ex	ex	NOUN
ejpam-5456	421	86	-	-	NOUN
ejpam-5456	421	87	ss	ss	NOUN
ejpam-5456	421	88	in	in	ADP
ejpam-5456	421	89	the	the	DET
ejpam-5456	421	90	range	range	NOUN
ejpam-5456	421	91	φ	φ	PROPN
ejpam-5456	421	92	∈	∈	PROPN
ejpam-5456	422	1	[	[	X
ejpam-5456	422	2	0	0	NUM
ejpam-5456	422	3	,	,	PUNCT
ejpam-5456	422	4	1.0	1.0	NUM
ejpam-5456	422	5	]	]	PUNCT
ejpam-5456	422	6	at	at	ADP
ejpam-5456	422	7	ϱ	ϱ	NOUN
ejpam-5456	422	8	=	=	SYM
ejpam-5456	422	9	0.1	0.1	NUM
ejpam-5456	422	10	are	be	AUX
ejpam-5456	422	11	shown	show	VERB
ejpam-5456	422	12	for	for	ADP
ejpam-5456	422	13	:	:	PUNCT
ejpam-5456	422	14	(	(	PUNCT
ejpam-5456	422	15	a	a	X
ejpam-5456	422	16	)	)	PUNCT
ejpam-5456	422	17	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	422	18	,	,	PUNCT
ejpam-5456	422	19	φ	φ	NOUN
ejpam-5456	422	20	)	)	PUNCT
ejpam-5456	422	21	;	;	PUNCT
ejpam-5456	422	22	(	(	PUNCT
ejpam-5456	422	23	b	b	X
ejpam-5456	422	24	)	)	PUNCT
ejpam-5456	422	25	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	422	26	,	,	PUNCT
ejpam-5456	422	27	φ	φ	NOUN
ejpam-5456	422	28	)	)	PUNCT
ejpam-5456	422	29	.	.	PUNCT
ejpam-5456	423	1	(	(	PUNCT
ejpam-5456	423	2	a	a	X
ejpam-5456	423	3	)	)	PUNCT
ejpam-5456	423	4	(	(	PUNCT
ejpam-5456	423	5	b	b	X
ejpam-5456	423	6	)	)	PUNCT
ejpam-5456	423	7	m.i	m.i	PROPN
ejpam-5456	423	8	.	.	PROPN
ejpam-5456	423	9	liaqat	liaqat	PROPN
ejpam-5456	423	10	,	,	PUNCT
ejpam-5456	423	11	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	423	12	/	/	SYM
ejpam-5456	423	13	eur	eur	PROPN
ejpam-5456	423	14	.	.	PUNCT
ejpam-5456	424	1	j.	j.	PROPN
ejpam-5456	424	2	pure	pure	PROPN
ejpam-5456	424	3	appl	appl	PROPN
ejpam-5456	424	4	.	.	PROPN
ejpam-5456	424	5	math	math	PROPN
ejpam-5456	424	6	,	,	PUNCT
ejpam-5456	424	7	17	17	NUM
ejpam-5456	424	8	(	(	PUNCT
ejpam-5456	424	9	4	4	NUM
ejpam-5456	424	10	)	)	PUNCT
ejpam-5456	424	11	(	(	PUNCT
ejpam-5456	424	12	2024	2024	NUM
ejpam-5456	424	13	)	)	PUNCT
ejpam-5456	424	14	,	,	PUNCT
ejpam-5456	424	15	3464	3464	NUM
ejpam-5456	424	16	-	-	SYM
ejpam-5456	424	17	3491	3491	NUM
ejpam-5456	424	18	3483	3483	NUM
ejpam-5456	424	19	(	(	PUNCT
ejpam-5456	424	20	c	c	NOUN
ejpam-5456	424	21	)	)	PUNCT
ejpam-5456	424	22	(	(	PUNCT
ejpam-5456	424	23	d	d	X
ejpam-5456	424	24	)	)	PUNCT
ejpam-5456	424	25	figure	figure	NOUN
ejpam-5456	424	26	7	7	NUM
ejpam-5456	424	27	:	:	PUNCT
ejpam-5456	424	28	the	the	DET
ejpam-5456	424	29	3d	3d	PROPN
ejpam-5456	424	30	diagrams	diagram	NOUN
ejpam-5456	424	31	of	of	ADP
ejpam-5456	424	32	app	app	PROPN
ejpam-5456	424	33	-	-	PUNCT
ejpam-5456	424	34	s	s	NOUN
ejpam-5456	424	35	for	for	ADP
ejpam-5456	424	36	various	various	ADJ
ejpam-5456	424	37	levels	level	NOUN
ejpam-5456	424	38	of	of	ADP
ejpam-5456	424	39	µ	µ	NOUN
ejpam-5456	424	40	in	in	ADP
ejpam-5456	424	41	the	the	DET
ejpam-5456	424	42	range	range	NOUN
ejpam-5456	424	43	φ	φ	PROPN
ejpam-5456	424	44	∈	∈	PROPN
ejpam-5456	425	1	[	[	X
ejpam-5456	425	2	0	0	NUM
ejpam-5456	425	3	,	,	PUNCT
ejpam-5456	425	4	2.0	2.0	NUM
ejpam-5456	425	5	]	]	PUNCT
ejpam-5456	425	6	and	and	CCONJ
ejpam-5456	425	7	−3π	−3π	NOUN
ejpam-5456	425	8	≤	≤	NUM
ejpam-5456	425	9	ϱ	ϱ	ADP
ejpam-5456	425	10	≤	≤	ADJ
ejpam-5456	425	11	3π	3π	NOUN
ejpam-5456	425	12	for	for	ADP
ejpam-5456	425	13	problem	problem	NOUN
ejpam-5456	425	14	4.2	4.2	NUM
ejpam-5456	425	15	of	of	ADP
ejpam-5456	425	16	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	425	17	,	,	PUNCT
ejpam-5456	425	18	φ	φ	NUM
ejpam-5456	425	19	)	)	PUNCT
ejpam-5456	425	20	are	be	AUX
ejpam-5456	425	21	as	as	SCONJ
ejpam-5456	425	22	follows	follow	VERB
ejpam-5456	425	23	:	:	PUNCT
ejpam-5456	425	24	(	(	PUNCT
ejpam-5456	425	25	a	a	X
ejpam-5456	425	26	)	)	PUNCT
ejpam-5456	425	27	µ	µ	X
ejpam-5456	425	28	=	=	SYM
ejpam-5456	425	29	0.7	0.7	NUM
ejpam-5456	425	30	;	;	PUNCT
ejpam-5456	425	31	(	(	PUNCT
ejpam-5456	425	32	b	b	X
ejpam-5456	425	33	)	)	PUNCT
ejpam-5456	425	34	µ	µ	NOUN
ejpam-5456	425	35	=	=	SYM
ejpam-5456	425	36	0.8	0.8	NUM
ejpam-5456	425	37	;	;	PUNCT
ejpam-5456	425	38	(	(	PUNCT
ejpam-5456	425	39	c	c	X
ejpam-5456	425	40	)	)	PUNCT
ejpam-5456	425	41	µ	µ	X
ejpam-5456	425	42	=	=	SYM
ejpam-5456	425	43	0.9	0.9	NUM
ejpam-5456	425	44	;	;	PUNCT
ejpam-5456	425	45	and	and	CCONJ
ejpam-5456	425	46	(	(	PUNCT
ejpam-5456	425	47	d	d	X
ejpam-5456	425	48	)	)	PUNCT
ejpam-5456	425	49	µ	µ	X
ejpam-5456	425	50	=	=	SYM
ejpam-5456	425	51	1.0	1.0	NUM
ejpam-5456	425	52	.	.	PUNCT
ejpam-5456	426	1	figure	figure	NOUN
ejpam-5456	426	2	8	8	NUM
ejpam-5456	426	3	:	:	PUNCT
ejpam-5456	426	4	for	for	ADP
ejpam-5456	426	5	problem	problem	NOUN
ejpam-5456	426	6	4.2	4.2	NUM
ejpam-5456	426	7	,	,	PUNCT
ejpam-5456	426	8	the	the	DET
ejpam-5456	426	9	3d	3d	PROPN
ejpam-5456	426	10	diagrams	diagram	NOUN
ejpam-5456	426	11	of	of	ADP
ejpam-5456	426	12	ex	ex	NOUN
ejpam-5456	426	13	-	-	NOUN
ejpam-5456	426	14	s	s	X
ejpam-5456	426	15	in	in	ADP
ejpam-5456	426	16	the	the	DET
ejpam-5456	426	17	range	range	NOUN
ejpam-5456	426	18	φ	φ	PROPN
ejpam-5456	426	19	∈	∈	PROPN
ejpam-5456	427	1	[	[	X
ejpam-5456	427	2	0	0	NUM
ejpam-5456	427	3	,	,	PUNCT
ejpam-5456	427	4	2.0	2.0	NUM
ejpam-5456	427	5	]	]	PUNCT
ejpam-5456	427	6	and	and	CCONJ
ejpam-5456	427	7	−3π	−3π	NOUN
ejpam-5456	427	8	≤	≤	NUM
ejpam-5456	427	9	ϱ	ϱ	ADP
ejpam-5456	427	10	≤	≤	ADJ
ejpam-5456	427	11	3π	3π	NOUN
ejpam-5456	427	12	for	for	ADP
ejpam-5456	427	13	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	427	14	,	,	PUNCT
ejpam-5456	427	15	φ	φ	NUM
ejpam-5456	427	16	)	)	PUNCT
ejpam-5456	427	17	are	be	AUX
ejpam-5456	427	18	shown	show	VERB
ejpam-5456	427	19	.	.	PUNCT
ejpam-5456	428	1	(	(	PUNCT
ejpam-5456	428	2	a	a	X
ejpam-5456	428	3	)	)	PUNCT
ejpam-5456	428	4	(	(	PUNCT
ejpam-5456	428	5	b	b	X
ejpam-5456	428	6	)	)	PUNCT
ejpam-5456	428	7	m.i	m.i	PROPN
ejpam-5456	428	8	.	.	PROPN
ejpam-5456	428	9	liaqat	liaqat	PROPN
ejpam-5456	428	10	,	,	PUNCT
ejpam-5456	428	11	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	428	12	/	/	SYM
ejpam-5456	428	13	eur	eur	PROPN
ejpam-5456	428	14	.	.	PUNCT
ejpam-5456	429	1	j.	j.	PROPN
ejpam-5456	429	2	pure	pure	PROPN
ejpam-5456	429	3	appl	appl	PROPN
ejpam-5456	429	4	.	.	PROPN
ejpam-5456	429	5	math	math	PROPN
ejpam-5456	429	6	,	,	PUNCT
ejpam-5456	429	7	17	17	NUM
ejpam-5456	429	8	(	(	PUNCT
ejpam-5456	429	9	4	4	NUM
ejpam-5456	429	10	)	)	PUNCT
ejpam-5456	429	11	(	(	PUNCT
ejpam-5456	429	12	2024	2024	NUM
ejpam-5456	429	13	)	)	PUNCT
ejpam-5456	429	14	,	,	PUNCT
ejpam-5456	429	15	3464	3464	NUM
ejpam-5456	429	16	-	-	SYM
ejpam-5456	429	17	3491	3491	NUM
ejpam-5456	429	18	3484	3484	NUM
ejpam-5456	429	19	(	(	PUNCT
ejpam-5456	429	20	c	c	NOUN
ejpam-5456	429	21	)	)	PUNCT
ejpam-5456	429	22	(	(	PUNCT
ejpam-5456	429	23	d	d	X
ejpam-5456	429	24	)	)	PUNCT
ejpam-5456	429	25	figure	figure	NOUN
ejpam-5456	429	26	9	9	NUM
ejpam-5456	429	27	:	:	PUNCT
ejpam-5456	429	28	the	the	DET
ejpam-5456	429	29	3d	3d	PROPN
ejpam-5456	429	30	diagrams	diagram	NOUN
ejpam-5456	429	31	of	of	ADP
ejpam-5456	429	32	app	app	PROPN
ejpam-5456	429	33	-	-	PUNCT
ejpam-5456	429	34	s	s	NOUN
ejpam-5456	429	35	for	for	ADP
ejpam-5456	429	36	various	various	ADJ
ejpam-5456	429	37	levels	level	NOUN
ejpam-5456	429	38	of	of	ADP
ejpam-5456	429	39	µ	µ	NOUN
ejpam-5456	429	40	in	in	ADP
ejpam-5456	429	41	the	the	DET
ejpam-5456	429	42	range	range	NOUN
ejpam-5456	429	43	φ	φ	PROPN
ejpam-5456	429	44	∈	∈	PROPN
ejpam-5456	430	1	[	[	X
ejpam-5456	430	2	0	0	NUM
ejpam-5456	430	3	,	,	PUNCT
ejpam-5456	430	4	2.0	2.0	NUM
ejpam-5456	430	5	]	]	PUNCT
ejpam-5456	430	6	and	and	CCONJ
ejpam-5456	430	7	−3π	−3π	NOUN
ejpam-5456	430	8	≤	≤	NUM
ejpam-5456	430	9	ϱ	ϱ	ADP
ejpam-5456	430	10	≤	≤	ADJ
ejpam-5456	430	11	3π	3π	NOUN
ejpam-5456	430	12	for	for	ADP
ejpam-5456	430	13	problem	problem	NOUN
ejpam-5456	430	14	4.2	4.2	NUM
ejpam-5456	430	15	of	of	ADP
ejpam-5456	430	16	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	430	17	,	,	PUNCT
ejpam-5456	430	18	φ	φ	NUM
ejpam-5456	430	19	)	)	PUNCT
ejpam-5456	430	20	are	be	AUX
ejpam-5456	430	21	as	as	SCONJ
ejpam-5456	430	22	follows	follow	VERB
ejpam-5456	430	23	:	:	PUNCT
ejpam-5456	430	24	(	(	PUNCT
ejpam-5456	430	25	a	a	X
ejpam-5456	430	26	)	)	PUNCT
ejpam-5456	430	27	µ	µ	X
ejpam-5456	430	28	=	=	SYM
ejpam-5456	430	29	0.7	0.7	NUM
ejpam-5456	430	30	;	;	PUNCT
ejpam-5456	430	31	(	(	PUNCT
ejpam-5456	430	32	b	b	X
ejpam-5456	430	33	)	)	PUNCT
ejpam-5456	430	34	µ	µ	NOUN
ejpam-5456	430	35	=	=	SYM
ejpam-5456	430	36	0.8	0.8	NUM
ejpam-5456	430	37	;	;	PUNCT
ejpam-5456	430	38	(	(	PUNCT
ejpam-5456	430	39	c	c	X
ejpam-5456	430	40	)	)	PUNCT
ejpam-5456	430	41	µ	µ	X
ejpam-5456	430	42	=	=	SYM
ejpam-5456	430	43	0.9	0.9	NUM
ejpam-5456	430	44	;	;	PUNCT
ejpam-5456	430	45	and	and	CCONJ
ejpam-5456	430	46	(	(	PUNCT
ejpam-5456	430	47	d	d	X
ejpam-5456	430	48	)	)	PUNCT
ejpam-5456	430	49	µ	µ	X
ejpam-5456	430	50	=	=	SYM
ejpam-5456	430	51	1.0	1.0	NUM
ejpam-5456	430	52	.	.	PUNCT
ejpam-5456	431	1	figure	figure	NOUN
ejpam-5456	431	2	10	10	NUM
ejpam-5456	431	3	:	:	PUNCT
ejpam-5456	431	4	for	for	ADP
ejpam-5456	431	5	problem	problem	NOUN
ejpam-5456	431	6	4.2	4.2	NUM
ejpam-5456	431	7	,	,	PUNCT
ejpam-5456	431	8	the	the	DET
ejpam-5456	431	9	3d	3d	PROPN
ejpam-5456	431	10	diagrams	diagram	NOUN
ejpam-5456	431	11	of	of	ADP
ejpam-5456	431	12	ex	ex	NOUN
ejpam-5456	431	13	-	-	NOUN
ejpam-5456	431	14	s	s	X
ejpam-5456	431	15	in	in	ADP
ejpam-5456	431	16	the	the	DET
ejpam-5456	431	17	range	range	NOUN
ejpam-5456	431	18	φ	φ	PROPN
ejpam-5456	431	19	∈	∈	PROPN
ejpam-5456	432	1	[	[	X
ejpam-5456	432	2	0	0	NUM
ejpam-5456	432	3	,	,	PUNCT
ejpam-5456	432	4	2.0	2.0	NUM
ejpam-5456	432	5	]	]	PUNCT
ejpam-5456	432	6	and	and	CCONJ
ejpam-5456	432	7	−3π	−3π	NOUN
ejpam-5456	432	8	≤	≤	NUM
ejpam-5456	432	9	ϱ	ϱ	ADP
ejpam-5456	432	10	≤	≤	ADJ
ejpam-5456	432	11	3π	3π	NOUN
ejpam-5456	432	12	for	for	ADP
ejpam-5456	432	13	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	432	14	,	,	PUNCT
ejpam-5456	432	15	φ	φ	NUM
ejpam-5456	432	16	)	)	PUNCT
ejpam-5456	432	17	are	be	AUX
ejpam-5456	432	18	shown	show	VERB
ejpam-5456	432	19	.	.	PUNCT
ejpam-5456	433	1	(	(	PUNCT
ejpam-5456	433	2	a	a	X
ejpam-5456	433	3	)	)	PUNCT
ejpam-5456	433	4	(	(	PUNCT
ejpam-5456	433	5	b	b	X
ejpam-5456	433	6	)	)	PUNCT
ejpam-5456	433	7	m.i	m.i	PROPN
ejpam-5456	433	8	.	.	PROPN
ejpam-5456	433	9	liaqat	liaqat	PROPN
ejpam-5456	433	10	,	,	PUNCT
ejpam-5456	433	11	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	433	12	/	/	SYM
ejpam-5456	433	13	eur	eur	PROPN
ejpam-5456	433	14	.	.	PUNCT
ejpam-5456	434	1	j.	j.	PROPN
ejpam-5456	434	2	pure	pure	PROPN
ejpam-5456	434	3	appl	appl	PROPN
ejpam-5456	434	4	.	.	PROPN
ejpam-5456	434	5	math	math	PROPN
ejpam-5456	434	6	,	,	PUNCT
ejpam-5456	434	7	17	17	NUM
ejpam-5456	434	8	(	(	PUNCT
ejpam-5456	434	9	4	4	NUM
ejpam-5456	434	10	)	)	PUNCT
ejpam-5456	434	11	(	(	PUNCT
ejpam-5456	434	12	2024	2024	NUM
ejpam-5456	434	13	)	)	PUNCT
ejpam-5456	434	14	,	,	PUNCT
ejpam-5456	434	15	3464	3464	NUM
ejpam-5456	434	16	-	-	SYM
ejpam-5456	434	17	3491	3491	NUM
ejpam-5456	434	18	3485	3485	NUM
ejpam-5456	434	19	(	(	PUNCT
ejpam-5456	434	20	c	c	NOUN
ejpam-5456	434	21	)	)	PUNCT
ejpam-5456	434	22	(	(	PUNCT
ejpam-5456	434	23	d	d	X
ejpam-5456	434	24	)	)	PUNCT
ejpam-5456	434	25	figure	figure	NOUN
ejpam-5456	434	26	11	11	NUM
ejpam-5456	434	27	:	:	PUNCT
ejpam-5456	434	28	the	the	DET
ejpam-5456	434	29	3d	3d	PROPN
ejpam-5456	434	30	diagrams	diagram	NOUN
ejpam-5456	434	31	of	of	ADP
ejpam-5456	434	32	app	app	PROPN
ejpam-5456	434	33	-	-	PUNCT
ejpam-5456	434	34	s	s	NOUN
ejpam-5456	434	35	for	for	ADP
ejpam-5456	434	36	various	various	ADJ
ejpam-5456	434	37	levels	level	NOUN
ejpam-5456	434	38	of	of	ADP
ejpam-5456	434	39	µ	µ	NOUN
ejpam-5456	434	40	in	in	ADP
ejpam-5456	434	41	the	the	DET
ejpam-5456	434	42	range	range	NOUN
ejpam-5456	434	43	φ	φ	PROPN
ejpam-5456	434	44	∈	∈	PROPN
ejpam-5456	435	1	[	[	X
ejpam-5456	435	2	0	0	NUM
ejpam-5456	435	3	,	,	PUNCT
ejpam-5456	435	4	2.0	2.0	NUM
ejpam-5456	435	5	]	]	PUNCT
ejpam-5456	435	6	and	and	CCONJ
ejpam-5456	435	7	−3π	−3π	NOUN
ejpam-5456	435	8	≤	≤	NUM
ejpam-5456	435	9	ϱ	ϱ	ADP
ejpam-5456	435	10	≤	≤	ADJ
ejpam-5456	435	11	3π	3π	NOUN
ejpam-5456	435	12	for	for	ADP
ejpam-5456	435	13	problem	problem	NOUN
ejpam-5456	435	14	4.3	4.3	NUM
ejpam-5456	435	15	of	of	ADP
ejpam-5456	435	16	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	435	17	,	,	PUNCT
ejpam-5456	435	18	φ	φ	NUM
ejpam-5456	435	19	)	)	PUNCT
ejpam-5456	435	20	are	be	AUX
ejpam-5456	435	21	as	as	SCONJ
ejpam-5456	435	22	follows	follow	VERB
ejpam-5456	435	23	:	:	PUNCT
ejpam-5456	435	24	(	(	PUNCT
ejpam-5456	435	25	a	a	X
ejpam-5456	435	26	)	)	PUNCT
ejpam-5456	435	27	µ	µ	X
ejpam-5456	435	28	=	=	SYM
ejpam-5456	435	29	0.7	0.7	NUM
ejpam-5456	435	30	;	;	PUNCT
ejpam-5456	435	31	(	(	PUNCT
ejpam-5456	435	32	b	b	X
ejpam-5456	435	33	)	)	PUNCT
ejpam-5456	435	34	µ	µ	NOUN
ejpam-5456	435	35	=	=	SYM
ejpam-5456	435	36	0.8	0.8	NUM
ejpam-5456	435	37	;	;	PUNCT
ejpam-5456	435	38	(	(	PUNCT
ejpam-5456	435	39	c	c	X
ejpam-5456	435	40	)	)	PUNCT
ejpam-5456	435	41	µ	µ	X
ejpam-5456	435	42	=	=	SYM
ejpam-5456	435	43	0.9	0.9	NUM
ejpam-5456	435	44	;	;	PUNCT
ejpam-5456	435	45	and	and	CCONJ
ejpam-5456	435	46	(	(	PUNCT
ejpam-5456	435	47	d	d	X
ejpam-5456	435	48	)	)	PUNCT
ejpam-5456	435	49	µ	µ	X
ejpam-5456	435	50	=	=	SYM
ejpam-5456	435	51	1.0	1.0	NUM
ejpam-5456	435	52	.	.	PUNCT
ejpam-5456	436	1	figure	figure	NOUN
ejpam-5456	436	2	12	12	NUM
ejpam-5456	436	3	:	:	PUNCT
ejpam-5456	436	4	for	for	ADP
ejpam-5456	436	5	problem	problem	NOUN
ejpam-5456	436	6	4.3	4.3	NUM
ejpam-5456	436	7	,	,	PUNCT
ejpam-5456	436	8	the	the	DET
ejpam-5456	436	9	3d	3d	PROPN
ejpam-5456	436	10	diagrams	diagram	NOUN
ejpam-5456	436	11	of	of	ADP
ejpam-5456	436	12	ex	ex	NOUN
ejpam-5456	436	13	-	-	NOUN
ejpam-5456	436	14	s	s	X
ejpam-5456	436	15	in	in	ADP
ejpam-5456	436	16	the	the	DET
ejpam-5456	436	17	range	range	NOUN
ejpam-5456	436	18	φ	φ	PROPN
ejpam-5456	436	19	∈	∈	PROPN
ejpam-5456	437	1	[	[	X
ejpam-5456	437	2	0	0	NUM
ejpam-5456	437	3	,	,	PUNCT
ejpam-5456	437	4	2.0	2.0	NUM
ejpam-5456	437	5	]	]	PUNCT
ejpam-5456	437	6	and	and	CCONJ
ejpam-5456	437	7	−3π	−3π	NOUN
ejpam-5456	437	8	≤	≤	NUM
ejpam-5456	437	9	ϱ	ϱ	ADP
ejpam-5456	437	10	≤	≤	ADJ
ejpam-5456	437	11	3π	3π	NOUN
ejpam-5456	437	12	for	for	ADP
ejpam-5456	437	13	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	437	14	,	,	PUNCT
ejpam-5456	437	15	φ	φ	NUM
ejpam-5456	437	16	)	)	PUNCT
ejpam-5456	437	17	are	be	AUX
ejpam-5456	437	18	shown	show	VERB
ejpam-5456	437	19	.	.	PUNCT
ejpam-5456	438	1	(	(	PUNCT
ejpam-5456	438	2	a	a	X
ejpam-5456	438	3	)	)	PUNCT
ejpam-5456	438	4	(	(	PUNCT
ejpam-5456	438	5	b	b	X
ejpam-5456	438	6	)	)	PUNCT
ejpam-5456	438	7	m.i	m.i	PROPN
ejpam-5456	438	8	.	.	PROPN
ejpam-5456	438	9	liaqat	liaqat	PROPN
ejpam-5456	438	10	,	,	PUNCT
ejpam-5456	438	11	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	438	12	/	/	SYM
ejpam-5456	438	13	eur	eur	PROPN
ejpam-5456	438	14	.	.	PUNCT
ejpam-5456	439	1	j.	j.	PROPN
ejpam-5456	439	2	pure	pure	PROPN
ejpam-5456	439	3	appl	appl	PROPN
ejpam-5456	439	4	.	.	PROPN
ejpam-5456	439	5	math	math	PROPN
ejpam-5456	439	6	,	,	PUNCT
ejpam-5456	439	7	17	17	NUM
ejpam-5456	439	8	(	(	PUNCT
ejpam-5456	439	9	4	4	NUM
ejpam-5456	439	10	)	)	PUNCT
ejpam-5456	439	11	(	(	PUNCT
ejpam-5456	439	12	2024	2024	NUM
ejpam-5456	439	13	)	)	PUNCT
ejpam-5456	439	14	,	,	PUNCT
ejpam-5456	439	15	3464	3464	NUM
ejpam-5456	439	16	-	-	SYM
ejpam-5456	439	17	3491	3491	NUM
ejpam-5456	439	18	3486	3486	NUM
ejpam-5456	439	19	(	(	PUNCT
ejpam-5456	439	20	c	c	NOUN
ejpam-5456	439	21	)	)	PUNCT
ejpam-5456	439	22	(	(	PUNCT
ejpam-5456	439	23	d	d	X
ejpam-5456	439	24	)	)	PUNCT
ejpam-5456	439	25	figure	figure	NOUN
ejpam-5456	439	26	13	13	NUM
ejpam-5456	439	27	:	:	PUNCT
ejpam-5456	439	28	the	the	DET
ejpam-5456	439	29	3d	3d	PROPN
ejpam-5456	439	30	diagrams	diagram	NOUN
ejpam-5456	439	31	of	of	ADP
ejpam-5456	439	32	app	app	PROPN
ejpam-5456	439	33	-	-	PUNCT
ejpam-5456	439	34	s	s	NOUN
ejpam-5456	439	35	for	for	ADP
ejpam-5456	439	36	various	various	ADJ
ejpam-5456	439	37	levels	level	NOUN
ejpam-5456	439	38	of	of	ADP
ejpam-5456	439	39	µ	µ	NOUN
ejpam-5456	439	40	in	in	ADP
ejpam-5456	439	41	the	the	DET
ejpam-5456	439	42	range	range	NOUN
ejpam-5456	439	43	φ	φ	PROPN
ejpam-5456	439	44	∈	∈	PROPN
ejpam-5456	440	1	[	[	X
ejpam-5456	440	2	0	0	NUM
ejpam-5456	440	3	,	,	PUNCT
ejpam-5456	440	4	2.0	2.0	NUM
ejpam-5456	440	5	]	]	PUNCT
ejpam-5456	440	6	and	and	CCONJ
ejpam-5456	440	7	−3π	−3π	NOUN
ejpam-5456	440	8	≤	≤	NUM
ejpam-5456	440	9	ϱ	ϱ	ADP
ejpam-5456	440	10	≤	≤	ADJ
ejpam-5456	440	11	3π	3π	NOUN
ejpam-5456	440	12	for	for	ADP
ejpam-5456	440	13	problem	problem	NOUN
ejpam-5456	440	14	4.3	4.3	NUM
ejpam-5456	440	15	of	of	ADP
ejpam-5456	440	16	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	440	17	,	,	PUNCT
ejpam-5456	440	18	φ	φ	NUM
ejpam-5456	440	19	)	)	PUNCT
ejpam-5456	440	20	are	be	AUX
ejpam-5456	440	21	as	as	SCONJ
ejpam-5456	440	22	follows	follow	VERB
ejpam-5456	440	23	:	:	PUNCT
ejpam-5456	440	24	(	(	PUNCT
ejpam-5456	440	25	a	a	X
ejpam-5456	440	26	)	)	PUNCT
ejpam-5456	440	27	µ	µ	X
ejpam-5456	440	28	=	=	SYM
ejpam-5456	440	29	0.7	0.7	NUM
ejpam-5456	440	30	;	;	PUNCT
ejpam-5456	440	31	(	(	PUNCT
ejpam-5456	440	32	b	b	X
ejpam-5456	440	33	)	)	PUNCT
ejpam-5456	440	34	µ	µ	NOUN
ejpam-5456	440	35	=	=	SYM
ejpam-5456	440	36	0.8	0.8	NUM
ejpam-5456	440	37	;	;	PUNCT
ejpam-5456	440	38	(	(	PUNCT
ejpam-5456	440	39	c	c	X
ejpam-5456	440	40	)	)	PUNCT
ejpam-5456	440	41	µ	µ	X
ejpam-5456	440	42	=	=	SYM
ejpam-5456	440	43	0.9	0.9	NUM
ejpam-5456	440	44	;	;	PUNCT
ejpam-5456	440	45	and	and	CCONJ
ejpam-5456	440	46	(	(	PUNCT
ejpam-5456	440	47	d	d	X
ejpam-5456	440	48	)	)	PUNCT
ejpam-5456	440	49	µ	µ	X
ejpam-5456	440	50	=	=	SYM
ejpam-5456	440	51	1.0	1.0	NUM
ejpam-5456	440	52	.	.	PUNCT
ejpam-5456	441	1	figure	figure	NOUN
ejpam-5456	441	2	14	14	NUM
ejpam-5456	441	3	:	:	PUNCT
ejpam-5456	441	4	for	for	ADP
ejpam-5456	441	5	problem	problem	NOUN
ejpam-5456	441	6	4.3	4.3	NUM
ejpam-5456	441	7	,	,	PUNCT
ejpam-5456	441	8	the	the	DET
ejpam-5456	441	9	3d	3d	PROPN
ejpam-5456	441	10	diagrams	diagram	NOUN
ejpam-5456	441	11	of	of	ADP
ejpam-5456	441	12	ex	ex	NOUN
ejpam-5456	441	13	-	-	NOUN
ejpam-5456	441	14	s	s	X
ejpam-5456	441	15	in	in	ADP
ejpam-5456	441	16	the	the	DET
ejpam-5456	441	17	range	range	NOUN
ejpam-5456	441	18	φ	φ	PROPN
ejpam-5456	441	19	∈	∈	PROPN
ejpam-5456	442	1	[	[	X
ejpam-5456	442	2	0	0	NUM
ejpam-5456	442	3	,	,	PUNCT
ejpam-5456	442	4	2.0	2.0	NUM
ejpam-5456	442	5	]	]	PUNCT
ejpam-5456	442	6	and	and	CCONJ
ejpam-5456	442	7	−3π	−3π	NOUN
ejpam-5456	442	8	≤	≤	NUM
ejpam-5456	442	9	ϱ	ϱ	ADP
ejpam-5456	442	10	≤	≤	ADJ
ejpam-5456	442	11	3π	3π	NOUN
ejpam-5456	442	12	for	for	ADP
ejpam-5456	442	13	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	442	14	,	,	PUNCT
ejpam-5456	442	15	φ	φ	NUM
ejpam-5456	442	16	)	)	PUNCT
ejpam-5456	442	17	are	be	AUX
ejpam-5456	442	18	shown	show	VERB
ejpam-5456	442	19	.	.	PUNCT
ejpam-5456	443	1	the	the	DET
ejpam-5456	443	2	numerical	numerical	ADJ
ejpam-5456	443	3	values	value	NOUN
ejpam-5456	443	4	of	of	ADP
ejpam-5456	443	5	abs	ab	NOUN
ejpam-5456	443	6	-	-	PUNCT
ejpam-5456	443	7	e	e	NOUN
ejpam-5456	443	8	and	and	CCONJ
ejpam-5456	443	9	rel	rel	PROPN
ejpam-5456	443	10	-	-	PUNCT
ejpam-5456	443	11	e	e	NOUN
ejpam-5456	443	12	are	be	AUX
ejpam-5456	443	13	shown	show	VERB
ejpam-5456	443	14	in	in	ADP
ejpam-5456	443	15	tables	table	NOUN
ejpam-5456	443	16	1	1	NUM
ejpam-5456	443	17	and	and	CCONJ
ejpam-5456	443	18	2	2	NUM
ejpam-5456	443	19	for	for	ADP
ejpam-5456	443	20	the	the	DET
ejpam-5456	443	21	5thstep	5thstep	NUM
ejpam-5456	443	22	app	app	NOUN
ejpam-5456	443	23	-	-	PUNCT
ejpam-5456	443	24	s	s	NOUN
ejpam-5456	443	25	and	and	CCONJ
ejpam-5456	443	26	ex	ex	NOUN
ejpam-5456	443	27	-	-	NOUN
ejpam-5456	443	28	s	s	X
ejpam-5456	443	29	of	of	ADP
ejpam-5456	443	30	the	the	DET
ejpam-5456	443	31	real	real	ADJ
ejpam-5456	443	32	(	(	PUNCT
ejpam-5456	443	33	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	443	34	,	,	PUNCT
ejpam-5456	443	35	φ	φ	NOUN
ejpam-5456	443	36	)	)	PUNCT
ejpam-5456	443	37	)	)	PUNCT
ejpam-5456	443	38	and	and	CCONJ
ejpam-5456	443	39	imaginary	imaginary	ADJ
ejpam-5456	443	40	(	(	PUNCT
ejpam-5456	443	41	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	443	42	,	,	PUNCT
ejpam-5456	443	43	φ	φ	NUM
ejpam-5456	443	44	)	)	PUNCT
ejpam-5456	443	45	)	)	PUNCT
ejpam-5456	443	46	parts	part	NOUN
ejpam-5456	443	47	of	of	ADP
ejpam-5456	443	48	δ(ϱ	δ(ϱ	PROPN
ejpam-5456	443	49	,	,	PUNCT
ejpam-5456	443	50	φ	φ	NUM
ejpam-5456	443	51	)	)	PUNCT
ejpam-5456	443	52	for	for	ADP
ejpam-5456	443	53	problems	problem	NOUN
ejpam-5456	443	54	4.2	4.2	NUM
ejpam-5456	443	55	and	and	CCONJ
ejpam-5456	443	56	4.3	4.3	NUM
ejpam-5456	443	57	,	,	PUNCT
ejpam-5456	443	58	respectively	respectively	ADV
ejpam-5456	443	59	,	,	PUNCT
ejpam-5456	443	60	with	with	ADP
ejpam-5456	443	61	µ	µ	NOUN
ejpam-5456	443	62	=	=	SYM
ejpam-5456	443	63	1	1	NUM
ejpam-5456	443	64	and	and	CCONJ
ejpam-5456	443	65	ϱ	ϱ	X
ejpam-5456	443	66	=	=	SYM
ejpam-5456	443	67	0.2	0.2	NUM
ejpam-5456	443	68	.	.	PUNCT
ejpam-5456	444	1	these	these	DET
ejpam-5456	444	2	tables	table	NOUN
ejpam-5456	444	3	demonstrate	demonstrate	VERB
ejpam-5456	444	4	that	that	SCONJ
ejpam-5456	444	5	the	the	DET
ejpam-5456	444	6	app	app	PROPN
ejpam-5456	444	7	-	-	PUNCT
ejpam-5456	444	8	ss	ss	PROPN
ejpam-5456	444	9	and	and	CCONJ
ejpam-5456	444	10	ex	ex	NOUN
ejpam-5456	444	11	-	-	NOUN
ejpam-5456	444	12	ss	ss	NOUN
ejpam-5456	444	13	are	be	AUX
ejpam-5456	444	14	nearly	nearly	ADV
ejpam-5456	444	15	in	in	ADP
ejpam-5456	444	16	agreement	agreement	NOUN
ejpam-5456	444	17	,	,	PUNCT
ejpam-5456	444	18	confirming	confirm	VERB
ejpam-5456	444	19	the	the	DET
ejpam-5456	444	20	accuracy	accuracy	NOUN
ejpam-5456	444	21	of	of	ADP
ejpam-5456	444	22	sadm	sadm	ADJ
ejpam-5456	444	23	.	.	PUNCT
ejpam-5456	445	1	m.i	m.i	PROPN
ejpam-5456	445	2	.	.	PROPN
ejpam-5456	445	3	liaqat	liaqat	PROPN
ejpam-5456	445	4	,	,	PUNCT
ejpam-5456	445	5	h.aljarrah	h.aljarrah	PROPN
ejpam-5456	445	6	/	/	SYM
ejpam-5456	445	7	eur	eur	PROPN
ejpam-5456	445	8	.	.	PUNCT
ejpam-5456	446	1	j.	j.	PROPN
ejpam-5456	446	2	pure	pure	PROPN
ejpam-5456	446	3	appl	appl	PROPN
ejpam-5456	446	4	.	.	PROPN
ejpam-5456	446	5	math	math	PROPN
ejpam-5456	446	6	,	,	PUNCT
ejpam-5456	446	7	17	17	NUM
ejpam-5456	446	8	(	(	PUNCT
ejpam-5456	446	9	4	4	NUM
ejpam-5456	446	10	)	)	PUNCT
ejpam-5456	446	11	(	(	PUNCT
ejpam-5456	446	12	2024	2024	NUM
ejpam-5456	446	13	)	)	PUNCT
ejpam-5456	446	14	,	,	PUNCT
ejpam-5456	446	15	3464	3464	NUM
ejpam-5456	446	16	-	-	SYM
ejpam-5456	446	17	3491	3491	NUM
ejpam-5456	446	18	3487	3487	NUM
ejpam-5456	446	19	table	table	NOUN
ejpam-5456	446	20	1	1	NUM
ejpam-5456	446	21	:	:	PUNCT
ejpam-5456	446	22	the	the	DET
ejpam-5456	446	23	abs	abs	NOUN
ejpam-5456	446	24	-	-	PUNCT
ejpam-5456	446	25	e	e	NOUN
ejpam-5456	446	26	and	and	CCONJ
ejpam-5456	446	27	rel	rel	NOUN
ejpam-5456	446	28	-	-	PUNCT
ejpam-5456	446	29	e	e	NOUN
ejpam-5456	446	30	for	for	ADP
ejpam-5456	446	31	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	446	32	,	,	PUNCT
ejpam-5456	446	33	φ	φ	NUM
ejpam-5456	446	34	)	)	PUNCT
ejpam-5456	446	35	and	and	CCONJ
ejpam-5456	446	36	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	446	37	,	,	PUNCT
ejpam-5456	446	38	φ	φ	NOUN
ejpam-5456	446	39	)	)	PUNCT
ejpam-5456	446	40	at	at	ADP
ejpam-5456	446	41	µ	µ	NOUN
ejpam-5456	446	42	=	=	SYM
ejpam-5456	446	43	1	1	NUM
ejpam-5456	446	44	for	for	ADP
ejpam-5456	446	45	problem	problem	NOUN
ejpam-5456	446	46	4.2	4.2	NUM
ejpam-5456	446	47	.	.	PUNCT
ejpam-5456	447	1	φ	φ	PROPN
ejpam-5456	447	2	|δ1	|δ1	PROPN
ejpam-5456	447	3	−	−	PROPN
ejpam-5456	447	4	δ51	δ51	NOUN
ejpam-5456	447	5	|	|	NOUN
ejpam-5456	447	6	|δ1−δ51	|δ1−δ51	NOUN
ejpam-5456	447	7	|	|	ADV
ejpam-5456	447	8	|δ1|	|δ1|	ADJ
ejpam-5456	447	9	|δ2	|δ2	NOUN
ejpam-5456	447	10	−	−	PROPN
ejpam-5456	447	11	δ52	δ52	NOUN
ejpam-5456	447	12	|	|	ADV
ejpam-5456	447	13	|δ2−δ52	|δ2−δ52	NUM
ejpam-5456	447	14	|	|	NOUN
ejpam-5456	447	15	|δ2|	|δ2|	NOUN
ejpam-5456	447	16	0.1	0.1	NUM
ejpam-5456	447	17	1.35702×	1.35702×	NUM
ejpam-5456	447	18	10−9	10−9	NUM
ejpam-5456	447	19	1.42046×	1.42046×	NUM
ejpam-5456	447	20	10−9	10−9	NUM
ejpam-5456	447	21	2.95323×	2.95323×	NUM
ejpam-5456	447	22	10−10	10−10	NUM
ejpam-5456	447	23	9.99334×	9.99334×	NUM
ejpam-5456	447	24	10−10	10−10	NUM
ejpam-5456	447	25	0.2	0.2	NUM
ejpam-5456	447	26	8.65506×	8.65506×	NUM
ejpam-5456	447	27	10−8	10−8	NUM
ejpam-5456	447	28	9.39683×	9.39683×	NUM
ejpam-5456	447	29	10−8	10−8	NUM
ejpam-5456	447	30	2.01346×	2.01346×	NUM
ejpam-5456	447	31	10−8	10−8	NUM
ejpam-5456	447	32	5.17042×	5.17042×	NUM
ejpam-5456	447	33	10−8	10−8	NUM
ejpam-5456	447	34	0.3	0.3	NUM
ejpam-5456	447	35	9.82114×	9.82114×	NUM
ejpam-5456	447	36	10−7	10−7	NUM
ejpam-5456	447	37	1.11911×	1.11911×	NUM
ejpam-5456	447	38	10−6	10−6	NUM
ejpam-5456	447	39	2.43305×	2.43305×	NUM
ejpam-5456	447	40	10−7	10−7	NUM
ejpam-5456	447	41	5.07492×	5.07492×	NUM
ejpam-5456	447	42	10−7	10−7	NUM
ejpam-5456	447	43	0.4	0.4	NUM
ejpam-5456	447	44	5.49515×	5.49515×	NUM
ejpam-5456	447	45	10−6	10−6	NUM
ejpam-5456	447	46	6.65808×	6.65808×	NUM
ejpam-5456	447	47	10−6	10−6	NUM
ejpam-5456	447	48	1.44488×	1.44488×	NUM
ejpam-5456	447	49	10−6	10−6	NUM
ejpam-5456	447	50	2.55892×	2.55892×	NUM
ejpam-5456	447	51	10−6	10−6	NUM
ejpam-5456	447	52	0.5	0.5	NUM
ejpam-5456	447	53	2.08672×	2.08672×	NUM
ejpam-5456	447	54	10−5	10−5	NUM
ejpam-5456	447	55	2.72831×	2.72831×	NUM
ejpam-5456	447	56	10−5	10−5	NUM
ejpam-5456	447	57	5.80614×	5.80614×	NUM
ejpam-5456	447	58	10−6	10−6	NUM
ejpam-5456	447	59	9.01270×	9.01270×	NUM
ejpam-5456	447	60	10−6	10−6	NUM
ejpam-5456	447	61	0.6	0.6	NUM
ejpam-5456	447	62	6.20037×	6.20037×	NOUN
ejpam-5456	448	1	10−5	10−5	NUM
ejpam-5456	448	2	8.89954×	8.89954×	NUM
ejpam-5456	448	3	10−5	10−5	NUM
ejpam-5456	448	4	1.82078×	1.82078×	NUM
ejpam-5456	448	5	10−5	10−5	NUM
ejpam-5456	448	6	2.53818×	2.53818×	NOUN
ejpam-5456	448	7	10−5	10−5	NUM
ejpam-5456	448	8	0.7	0.7	NUM
ejpam-5456	448	9	1.55526×	1.55526×	NUM
ejpam-5456	448	10	10−4	10−4	NUM
ejpam-5456	448	11	2.50199×	2.50199×	NUM
ejpam-5456	448	12	10−4	10−4	NUM
ejpam-5456	448	13	4.80863×	4.80863×	NUM
ejpam-5456	448	14	10−5	10−5	NUM
ejpam-5456	448	15	6.13872×	6.13872×	NOUN
ejpam-5456	449	1	10−6	10−6	NUM
ejpam-5456	449	2	0.8	0.8	NUM
ejpam-5456	449	3	3.44589×	3.44589×	NUM
ejpam-5456	449	4	10−4	10−4	NUM
ejpam-5456	449	5	6.37771×	6.37771×	NUM
ejpam-5456	449	6	10−4	10−4	NUM
ejpam-5456	449	7	1.11933×	1.11933×	NUM
ejpam-5456	449	8	10−4	10−4	NUM
ejpam-5456	449	9	1.33020×	1.33020×	NUM
ejpam-5456	449	10	10−4	10−4	NUM
ejpam-5456	449	11	0.9	0.9	NUM
ejpam-5456	449	12	6.94386×	6.94386×	NUM
ejpam-5456	449	13	10−4	10−4	NUM
ejpam-5456	449	14	1.53085×	1.53085×	NUM
ejpam-5456	449	15	10−3	10−3	NUM
ejpam-5456	449	16	2.36508×	2.36508×	NUM
ejpam-5456	449	17	10−4	10−4	NUM
ejpam-5456	449	18	2.65379×	2.65379×	NUM
ejpam-5456	449	19	10−4	10−4	NUM
ejpam-5456	449	20	1.0	1.0	NUM
ejpam-5456	449	21	1.29829×	1.29829×	NUM
ejpam-5456	449	22	10−3	10−3	NUM
ejpam-5456	449	23	3.58289×	3.58289×	NUM
ejpam-5456	449	24	10−3	10−3	NUM
ejpam-5456	449	25	4.62838×	4.62838×	NOUN
ejpam-5456	449	26	10−6	10−6	NUM
ejpam-5456	449	27	4.96586×	4.96586×	NUM
ejpam-5456	449	28	10−4	10−4	NUM
ejpam-5456	449	29	table	table	NOUN
ejpam-5456	449	30	2	2	NUM
ejpam-5456	449	31	:	:	PUNCT
ejpam-5456	449	32	the	the	DET
ejpam-5456	449	33	abs	abs	NOUN
ejpam-5456	449	34	-	-	PUNCT
ejpam-5456	449	35	e	e	NOUN
ejpam-5456	449	36	and	and	CCONJ
ejpam-5456	449	37	rel	rel	NOUN
ejpam-5456	449	38	-	-	PUNCT
ejpam-5456	449	39	e	e	NOUN
ejpam-5456	449	40	for	for	ADP
ejpam-5456	449	41	δ1(ϱ	δ1(ϱ	PROPN
ejpam-5456	449	42	,	,	PUNCT
ejpam-5456	449	43	φ	φ	NUM
ejpam-5456	449	44	)	)	PUNCT
ejpam-5456	449	45	and	and	CCONJ
ejpam-5456	449	46	δ2(ϱ	δ2(ϱ	PROPN
ejpam-5456	449	47	,	,	PUNCT
ejpam-5456	449	48	φ	φ	NOUN
ejpam-5456	449	49	)	)	PUNCT
ejpam-5456	449	50	at	at	ADP
ejpam-5456	449	51	µ	µ	NOUN
ejpam-5456	449	52	=	=	SYM
ejpam-5456	449	53	1	1	NUM
ejpam-5456	449	54	for	for	ADP
ejpam-5456	449	55	problem	problem	NOUN
ejpam-5456	449	56	4.3	4.3	NUM
ejpam-5456	449	57	.	.	PUNCT
ejpam-5456	450	1	φ	φ	PROPN
ejpam-5456	450	2	|δ1	|δ1	PROPN
ejpam-5456	450	3	−	−	PROPN
ejpam-5456	450	4	δ51	δ51	NOUN
ejpam-5456	450	5	|	|	NOUN
ejpam-5456	450	6	|δ1−δ51	|δ1−δ51	NOUN
ejpam-5456	450	7	|	|	ADV
ejpam-5456	450	8	|δ1|	|δ1|	ADJ
ejpam-5456	450	9	|δ2	|δ2	NOUN
ejpam-5456	450	10	−	−	PROPN
ejpam-5456	450	11	δ52	δ52	NOUN
ejpam-5456	450	12	|	|	ADV
ejpam-5456	450	13	|δ2−δ52	|δ2−δ52	NUM
ejpam-5456	450	14	|	|	NOUN
ejpam-5456	450	15	|δ2|	|δ2|	NOUN
ejpam-5456	450	16	0.1	0.1	NUM
ejpam-5456	451	1	2.77556×	2.77556×	NUM
ejpam-5456	451	2	10−17	10−17	NUM
ejpam-5456	451	3	1.41294×	1.41294×	NOUN
ejpam-5456	452	1	10−16	10−16	NOUN
ejpam-5456	452	2	3.46945×	3.46945×	NUM
ejpam-5456	452	3	10−18	10−18	NUM
ejpam-5456	452	4	1.16861×	1.16861×	NUM
ejpam-5456	452	5	10−16	10−16	NOUN
ejpam-5456	452	6	0.2	0.2	NUM
ejpam-5456	452	7	2.22045×	2.22045×	NUM
ejpam-5456	452	8	10−16	10−16	PROPN
ejpam-5456	452	9	1.16991×	1.16991×	NUM
ejpam-5456	452	10	10−15	10−15	PROPN
ejpam-5456	452	11	0.00000	0.00000	NUM
ejpam-5456	452	12	0.00000	0.00000	NUM
ejpam-5456	452	13	0.3	0.3	NUM
ejpam-5456	452	14	2.85605×	2.85605×	NOUN
ejpam-5456	453	1	10−14	10−14	NUM
ejpam-5456	453	2	1.59653×	1.59653×	NUM
ejpam-5456	453	3	10−13	10−13	NUM
ejpam-5456	453	4	9.99201×	9.99201×	NUM
ejpam-5456	453	5	10−16	10−16	NUM
ejpam-5456	453	6	1.15629×	1.15629×	NUM
ejpam-5456	453	7	10−14	10−14	NUM
ejpam-5456	453	8	0.4	0.4	NUM
ejpam-5456	453	9	9.01057×	9.01057×	NUM
ejpam-5456	453	10	10−13	10−13	NUM
ejpam-5456	453	11	5.49529×	5.49529×	NUM
ejpam-5456	453	12	10−12	10−12	NOUN
ejpam-5456	453	13	4.16195×	4.16195×	NOUN
ejpam-5456	453	14	10−14	10−14	PROPN
ejpam-5456	453	15	3.71016×	3.71016×	NUM
ejpam-5456	453	16	10−13	10−13	NUM
ejpam-5456	453	17	0.5	0.5	NUM
ejpam-5456	453	18	1.30975×	1.30975×	NUM
ejpam-5456	453	19	10−11	10−11	NUM
ejpam-5456	453	20	7.98778×	7.98778×	NUM
ejpam-5456	453	21	10−11	10−11	NUM
ejpam-5456	453	22	7.55923×	7.55923×	NUM
ejpam-5456	453	23	10−13	10−13	NOUN
ejpam-5456	453	24	5.58203×	5.58203×	NUM
ejpam-5456	453	25	10−12	10−12	NOUN
ejpam-5456	453	26	0.6	0.6	NUM
ejpam-5456	453	27	1.16620×	1.16620×	NUM
ejpam-5456	453	28	10−10	10−10	PROPN
ejpam-5456	453	29	9.44332×	9.44332×	NUM
ejpam-5456	453	30	10−10	10−10	NUM
ejpam-5456	453	31	8.07848×	8.07848×	NUM
ejpam-5456	453	32	10−12	10−12	NOUN
ejpam-5456	453	33	5.19106×	5.19106×	NOUN
ejpam-5456	453	34	10−11	10−11	NOUN
ejpam-5456	453	35	0.7	0.7	NUM
ejpam-5456	453	36	7.40353×	7.40353×	NUM
ejpam-5456	453	37	10−10	10−10	NUM
ejpam-5456	453	38	7.48950×	7.48950×	NOUN
ejpam-5456	453	39	10−9	10−9	NUM
ejpam-5456	453	40	5.98459×	5.98459×	NUM
ejpam-5456	453	41	10−11	10−11	NUM
ejpam-5456	453	42	3.47274×	3.47274×	NUM
ejpam-5456	453	43	10−10	10−10	NUM
ejpam-5456	453	44	0.8	0.8	NUM
ejpam-5456	453	45	3.66893×	3.66893×	NUM
ejpam-5456	453	46	10−9	10−9	NUM
ejpam-5456	453	47	5.09649×	5.09649×	NOUN
ejpam-5456	453	48	10−8	10−8	NUM
ejpam-5456	453	49	3.39027×	3.39027×	NUM
ejpam-5456	453	50	10−10	10−10	NUM
ejpam-5456	453	51	1.83092×	1.83092×	NUM
ejpam-5456	453	52	10−9	10−9	NUM
ejpam-5456	453	53	0.9	0.9	NUM
ejpam-5456	453	54	1.50474×	1.50474×	NUM
ejpam-5456	453	55	10−8	10−8	NUM
ejpam-5456	453	56	3.45838×	3.45838×	NUM
ejpam-5456	453	57	10−7	10−7	NUM
ejpam-5456	453	58	1.56469×	1.56469×	NUM
ejpam-5456	453	59	10−9	10−9	NUM
ejpam-5456	453	60	8.07183×	8.07183×	NUM
ejpam-5456	453	61	10−9	10−9	NUM
ejpam-5456	453	62	1.0	1.0	NUM
ejpam-5456	453	63	5.31541×	5.31541×	NOUN
ejpam-5456	453	64	10−8	10−8	NUM
ejpam-5456	453	65	3.78232×	3.78232×	NUM
ejpam-5456	453	66	10−6	10−6	NUM
ejpam-5456	453	67	6.14324×	6.14324×	NUM
ejpam-5456	453	68	10−9	10−9	NUM
ejpam-5456	453	69	3.09996×	3.09996×	NUM
ejpam-5456	453	70	10−8	10−8	NUM
ejpam-5456	453	71	6	6	NUM
ejpam-5456	453	72	.	.	PUNCT
ejpam-5456	453	73	conclusions	conclusion	NOUN
ejpam-5456	453	74	to	to	ADP
ejpam-5456	453	75	the	the	DET
ejpam-5456	453	76	best	good	ADJ
ejpam-5456	453	77	of	of	ADP
ejpam-5456	453	78	the	the	DET
ejpam-5456	453	79	authors	author	NOUN
ejpam-5456	453	80	’	’	PART
ejpam-5456	453	81	knowledge	knowledge	NOUN
ejpam-5456	453	82	,	,	PUNCT
ejpam-5456	453	83	no	no	DET
ejpam-5456	453	84	research	research	NOUN
ejpam-5456	453	85	has	have	AUX
ejpam-5456	453	86	yet	yet	ADV
ejpam-5456	453	87	solved	solve	VERB
ejpam-5456	453	88	fsdes	fsde	NOUN
ejpam-5456	453	89	using	use	VERB
ejpam-5456	453	90	the	the	DET
ejpam-5456	453	91	adm	adm	NOUN
ejpam-5456	453	92	with	with	ADP
ejpam-5456	453	93	the	the	DET
ejpam-5456	453	94	st	st	PROPN
ejpam-5456	453	95	in	in	ADP
ejpam-5456	453	96	the	the	DET
ejpam-5456	453	97	sense	sense	NOUN
ejpam-5456	453	98	of	of	ADP
ejpam-5456	453	99	con	con	NOUN
ejpam-5456	453	100	-	-	PUNCT
ejpam-5456	453	101	frd	frd	ADJ
ejpam-5456	453	102	.	.	PUNCT
ejpam-5456	454	1	in	in	ADP
ejpam-5456	454	2	this	this	DET
ejpam-5456	454	3	research	research	NOUN
ejpam-5456	454	4	,	,	PUNCT
ejpam-5456	454	5	we	we	PRON
ejpam-5456	454	6	addressed	address	VERB
ejpam-5456	454	7	this	this	DET
ejpam-5456	454	8	gap	gap	NOUN
ejpam-5456	454	9	by	by	ADP
ejpam-5456	454	10	solving	solve	VERB
ejpam-5456	454	11	linear	linear	NOUN
ejpam-5456	454	12	and	and	CCONJ
ejpam-5456	454	13	nonlinear	nonlinear	ADJ
ejpam-5456	454	14	fsdes	fsde	NOUN
ejpam-5456	454	15	using	use	VERB
ejpam-5456	454	16	a	a	DET
ejpam-5456	454	17	hybrid	hybrid	ADJ
ejpam-5456	454	18	approach	approach	NOUN
ejpam-5456	454	19	that	that	PRON
ejpam-5456	454	20	combines	combine	VERB
ejpam-5456	454	21	adm	adm	PROPN
ejpam-5456	454	22	and	and	CCONJ
ejpam-5456	454	23	st	st	PROPN
ejpam-5456	454	24	,	,	PUNCT
ejpam-5456	454	25	applied	apply	VERB
ejpam-5456	454	26	in	in	ADP
ejpam-5456	454	27	the	the	DET
ejpam-5456	454	28	sense	sense	NOUN
ejpam-5456	454	29	of	of	ADP
ejpam-5456	454	30	con	con	NOUN
ejpam-5456	454	31	-	-	PUNCT
ejpam-5456	454	32	frd	frd	ADJ
ejpam-5456	454	33	.	.	PUNCT
ejpam-5456	455	1	the	the	DET
ejpam-5456	455	2	effectiveness	effectiveness	NOUN
ejpam-5456	455	3	of	of	ADP
ejpam-5456	455	4	the	the	DET
ejpam-5456	455	5	sadm	sadm	ADJ
ejpam-5456	455	6	is	be	AUX
ejpam-5456	455	7	demonstrated	demonstrate	VERB
ejpam-5456	455	8	through	through	ADP
ejpam-5456	455	9	graphical	graphical	ADJ
ejpam-5456	455	10	and	and	CCONJ
ejpam-5456	455	11	numerical	numerical	ADJ
ejpam-5456	455	12	results	result	NOUN
ejpam-5456	455	13	,	,	PUNCT
ejpam-5456	455	14	showing	show	VERB
ejpam-5456	455	15	that	that	SCONJ
ejpam-5456	455	16	the	the	DET
ejpam-5456	455	17	app	app	PROPN
ejpam-5456	455	18	-	-	PUNCT
ejpam-5456	455	19	ss	ss	NOUN
ejpam-5456	455	20	obtained	obtain	VERB
ejpam-5456	455	21	via	via	ADP
ejpam-5456	455	22	the	the	DET
ejpam-5456	455	23	sadm	sadm	ADJ
ejpam-5456	455	24	are	be	AUX
ejpam-5456	455	25	in	in	ADP
ejpam-5456	455	26	complete	complete	ADJ
ejpam-5456	455	27	agreement	agreement	NOUN
ejpam-5456	455	28	with	with	ADP
ejpam-5456	455	29	the	the	DET
ejpam-5456	455	30	ex	ex	NOUN
ejpam-5456	455	31	-	-	NOUN
ejpam-5456	455	32	ss	ss	NOUN
ejpam-5456	455	33	.	.	PUNCT
ejpam-5456	455	34	tables	table	NOUN
ejpam-5456	455	35	1	1	NUM
ejpam-5456	455	36	and	and	CCONJ
ejpam-5456	455	37	2	2	NUM
ejpam-5456	455	38	provide	provide	VERB
ejpam-5456	455	39	numerical	numerical	ADJ
ejpam-5456	455	40	evidence	evidence	NOUN
ejpam-5456	455	41	of	of	ADP
ejpam-5456	455	42	the	the	DET
ejpam-5456	455	43	correctness	correctness	NOUN
ejpam-5456	455	44	of	of	ADP
ejpam-5456	455	45	our	our	PRON
ejpam-5456	455	46	approach	approach	NOUN
ejpam-5456	455	47	by	by	ADP
ejpam-5456	455	48	comparing	compare	VERB
ejpam-5456	455	49	the	the	DET
ejpam-5456	455	50	app	app	PROPN
ejpam-5456	455	51	-	-	PUNCT
ejpam-5456	455	52	ss	ss	PROPN
ejpam-5456	455	53	and	and	CCONJ
ejpam-5456	455	54	ex	ex	NOUN
ejpam-5456	455	55	-	-	NOUN
ejpam-5456	455	56	ss	ss	NOUN
ejpam-5456	455	57	through	through	ADP
ejpam-5456	455	58	abs	ab	NOUN
ejpam-5456	455	59	-	-	PUNCT
ejpam-5456	455	60	e	e	NOUN
ejpam-5456	455	61	and	and	CCONJ
ejpam-5456	455	62	rel	rel	PROPN
ejpam-5456	455	63	-	-	PROPN
ejpam-5456	455	64	e.	e.	PROPN
ejpam-5456	455	65	furthermore	furthermore	PROPN
ejpam-5456	455	66	,	,	PUNCT
ejpam-5456	455	67	a	a	DET
ejpam-5456	455	68	comparison	comparison	NOUN
ejpam-5456	455	69	is	be	AUX
ejpam-5456	455	70	made	make	VERB
ejpam-5456	455	71	between	between	ADP
ejpam-5456	455	72	the	the	DET
ejpam-5456	455	73	results	result	NOUN
ejpam-5456	455	74	obtained	obtain	VERB
ejpam-5456	455	75	from	from	ADP
ejpam-5456	455	76	sadm	sadm	ADV
ejpam-5456	455	77	and	and	CCONJ
ejpam-5456	455	78	those	those	PRON
ejpam-5456	455	79	from	from	ADP
ejpam-5456	455	80	alternative	alternative	ADJ
ejpam-5456	455	81	techniques	technique	NOUN
ejpam-5456	455	82	,	,	PUNCT
ejpam-5456	455	83	including	include	VERB
ejpam-5456	455	84	the	the	DET
ejpam-5456	455	85	ham	ham	NOUN
ejpam-5456	455	86	and	and	CCONJ
ejpam-5456	455	87	rpsm	rpsm	VERB
ejpam-5456	455	88	.	.	PUNCT
ejpam-5456	456	1	the	the	DET
ejpam-5456	456	2	comparison	comparison	NOUN
ejpam-5456	456	3	demonstrates	demonstrate	VERB
ejpam-5456	456	4	a	a	DET
ejpam-5456	456	5	high	high	ADJ
ejpam-5456	456	6	degree	degree	NOUN
ejpam-5456	456	7	of	of	ADP
ejpam-5456	456	8	agreement	agreement	NOUN
ejpam-5456	456	9	with	with	ADP
ejpam-5456	456	10	these	these	DET
ejpam-5456	456	11	techniques	technique	NOUN
ejpam-5456	456	12	,	,	PUNCT
ejpam-5456	456	13	suggesting	suggest	VERB
ejpam-5456	456	14	that	that	SCONJ
ejpam-5456	456	15	sadm	sadm	ADJ
ejpam-5456	456	16	is	be	AUX
ejpam-5456	456	17	a	a	DET
ejpam-5456	456	18	good	good	ADJ
ejpam-5456	456	19	substitute	substitute	NOUN
ejpam-5456	456	20	for	for	ADP
ejpam-5456	456	21	cap	cap	NOUN
ejpam-5456	456	22	-	-	PUNCT
ejpam-5456	456	23	fd	fd	NOUN
ejpam-5456	456	24	-	-	PUNCT
ejpam-5456	456	25	based	base	VERB
ejpam-5456	456	26	methods	method	NOUN
ejpam-5456	456	27	in	in	ADP
ejpam-5456	456	28	solving	solve	VERB
ejpam-5456	456	29	fsdes	fsde	NOUN
ejpam-5456	456	30	.	.	PUNCT
ejpam-5456	457	1	additionally	additionally	ADV
ejpam-5456	457	2	,	,	PUNCT
ejpam-5456	457	3	we	we	PRON
ejpam-5456	457	4	can	can	AUX
ejpam-5456	457	5	conclude	conclude	VERB
ejpam-5456	457	6	that	that	SCONJ
ejpam-5456	457	7	con	con	PROPN
ejpam-5456	457	8	-	-	PUNCT
ejpam-5456	457	9	fd	fd	PROPN
ejpam-5456	457	10	serves	serve	VERB
ejpam-5456	457	11	as	as	ADP
ejpam-5456	457	12	a	a	DET
ejpam-5456	457	13	suitable	suitable	ADJ
ejpam-5456	457	14	alternative	alternative	NOUN
ejpam-5456	457	15	to	to	ADP
ejpam-5456	457	16	cap	cap	NOUN
ejpam-5456	457	17	-	-	PUNCT
ejpam-5456	457	18	fd	fd	NOUN
ejpam-5456	457	19	for	for	ADP
ejpam-5456	457	20	modeling	modeling	NOUN
ejpam-5456	457	21	fsdes	fsde	NOUN
ejpam-5456	457	22	.	.	PUNCT
ejpam-5456	458	1	the	the	DET
ejpam-5456	458	2	key	key	ADJ
ejpam-5456	458	3	features	feature	NOUN
ejpam-5456	458	4	of	of	ADP
ejpam-5456	458	5	the	the	DET
ejpam-5456	458	6	sadm	sadm	ADJ
ejpam-5456	458	7	distinguish	distinguish	VERB
ejpam-5456	458	8	it	it	PRON
ejpam-5456	458	9	from	from	ADP
ejpam-5456	458	10	other	other	ADJ
ejpam-5456	458	11	methods	method	NOUN
ejpam-5456	458	12	that	that	PRON
ejpam-5456	458	13	provide	provide	VERB
ejpam-5456	458	14	approximate	approximate	ADJ
ejpam-5456	458	15	solutions	solution	NOUN
ejpam-5456	458	16	.	.	PUNCT
ejpam-5456	459	1	this	this	DET
ejpam-5456	459	2	method	method	NOUN
ejpam-5456	459	3	eliminates	eliminate	VERB
ejpam-5456	459	4	the	the	DET
ejpam-5456	459	5	need	need	NOUN
ejpam-5456	459	6	for	for	ADP
ejpam-5456	459	7	assumptions	assumption	NOUN
ejpam-5456	459	8	about	about	ADP
ejpam-5456	459	9	physical	physical	ADJ
ejpam-5456	459	10	parameters	parameter	NOUN
ejpam-5456	459	11	,	,	PUNCT
ejpam-5456	459	12	making	make	VERB
ejpam-5456	459	13	it	it	PRON
ejpam-5456	459	14	applicable	applicable	ADJ
ejpam-5456	459	15	to	to	ADP
ejpam-5456	459	16	both	both	CCONJ
ejpam-5456	459	17	weakly	weakly	ADJ
ejpam-5456	459	18	and	and	CCONJ
ejpam-5456	459	19	strongly	strongly	ADV
ejpam-5456	459	20	nonlinear	nonlinear	ADJ
ejpam-5456	459	21	problems	problem	NOUN
ejpam-5456	459	22	and	and	CCONJ
ejpam-5456	459	23	addressing	address	VERB
ejpam-5456	459	24	some	some	DET
ejpam-5456	459	25	limitations	limitation	NOUN
ejpam-5456	459	26	of	of	ADP
ejpam-5456	459	27	perturbation	perturbation	NOUN
ejpam-5456	459	28	techniques	technique	NOUN
ejpam-5456	459	29	.	.	PUNCT
ejpam-5456	460	1	the	the	DET
ejpam-5456	460	2	sadm	sadm	ADJ
ejpam-5456	460	3	allows	allow	VERB
ejpam-5456	460	4	for	for	ADP
ejpam-5456	460	5	the	the	DET
ejpam-5456	460	6	derivation	derivation	NOUN
ejpam-5456	460	7	references	reference	NOUN
ejpam-5456	460	8	3488	3488	NUM
ejpam-5456	460	9	of	of	ADP
ejpam-5456	460	10	fps	fps	PROPN
ejpam-5456	460	11	solutions	solution	NOUN
ejpam-5456	460	12	for	for	ADP
ejpam-5456	460	13	fodes	fode	NOUN
ejpam-5456	460	14	without	without	ADP
ejpam-5456	460	15	requiring	require	VERB
ejpam-5456	460	16	perturbation	perturbation	NOUN
ejpam-5456	460	17	,	,	PUNCT
ejpam-5456	460	18	linearization	linearization	NOUN
ejpam-5456	460	19	,	,	PUNCT
ejpam-5456	460	20	or	or	CCONJ
ejpam-5456	460	21	discretization	discretization	NOUN
ejpam-5456	460	22	,	,	PUNCT
ejpam-5456	460	23	unlike	unlike	ADP
ejpam-5456	460	24	other	other	ADJ
ejpam-5456	460	25	approximate	approximate	ADJ
ejpam-5456	460	26	solution	solution	NOUN
ejpam-5456	460	27	methods	method	NOUN
ejpam-5456	460	28	.	.	PUNCT
ejpam-5456	461	1	the	the	DET
ejpam-5456	461	2	efficiency	efficiency	NOUN
ejpam-5456	461	3	of	of	ADP
ejpam-5456	461	4	the	the	DET
ejpam-5456	461	5	sadm	sadm	ADJ
ejpam-5456	461	6	underscores	underscore	VERB
ejpam-5456	461	7	its	its	PRON
ejpam-5456	461	8	computational	computational	ADJ
ejpam-5456	461	9	strength	strength	NOUN
ejpam-5456	461	10	,	,	PUNCT
ejpam-5456	461	11	making	make	VERB
ejpam-5456	461	12	it	it	PRON
ejpam-5456	461	13	a	a	DET
ejpam-5456	461	14	valuable	valuable	ADJ
ejpam-5456	461	15	alternative	alternative	NOUN
ejpam-5456	461	16	to	to	ADP
ejpam-5456	461	17	cap	cap	NOUN
ejpam-5456	461	18	-	-	PUNCT
ejpam-5456	461	19	fd	fd	NOUN
ejpam-5456	461	20	-	-	PUNCT
ejpam-5456	461	21	based	base	VERB
ejpam-5456	461	22	methods	method	NOUN
ejpam-5456	461	23	for	for	ADP
ejpam-5456	461	24	solving	solve	VERB
ejpam-5456	461	25	fsdes	fsde	NOUN
ejpam-5456	461	26	.	.	PUNCT
ejpam-5456	462	1	we	we	PRON
ejpam-5456	462	2	also	also	ADV
ejpam-5456	462	3	found	find	VERB
ejpam-5456	462	4	that	that	SCONJ
ejpam-5456	462	5	the	the	DET
ejpam-5456	462	6	con	con	PROPN
ejpam-5456	462	7	-	-	PUNCT
ejpam-5456	462	8	fd	fd	VERB
ejpam-5456	462	9	effectively	effectively	ADV
ejpam-5456	462	10	replaces	replace	VERB
ejpam-5456	462	11	the	the	DET
ejpam-5456	462	12	cap	cap	NOUN
ejpam-5456	462	13	-	-	PUNCT
ejpam-5456	462	14	fd	fd	NOUN
ejpam-5456	462	15	for	for	ADP
ejpam-5456	462	16	modeling	model	VERB
ejpam-5456	462	17	time	time	NOUN
ejpam-5456	462	18	-	-	PUNCT
ejpam-5456	462	19	fsdes	fsde	NOUN
ejpam-5456	462	20	.	.	PUNCT
ejpam-5456	463	1	overall	overall	ADV
ejpam-5456	463	2	,	,	PUNCT
ejpam-5456	463	3	the	the	DET
ejpam-5456	463	4	sadm	sadm	ADJ
ejpam-5456	463	5	proves	prove	VERB
ejpam-5456	463	6	to	to	PART
ejpam-5456	463	7	be	be	AUX
ejpam-5456	463	8	user	user	NOUN
ejpam-5456	463	9	-	-	PUNCT
ejpam-5456	463	10	friendly	friendly	ADJ
ejpam-5456	463	11	,	,	PUNCT
ejpam-5456	463	12	accurate	accurate	ADJ
ejpam-5456	463	13	,	,	PUNCT
ejpam-5456	463	14	and	and	CCONJ
ejpam-5456	463	15	efficient	efficient	ADJ
ejpam-5456	463	16	.	.	PUNCT
ejpam-5456	464	1	moreover	moreover	ADV
ejpam-5456	464	2	,	,	PUNCT
ejpam-5456	464	3	this	this	DET
ejpam-5456	464	4	method	method	NOUN
ejpam-5456	464	5	is	be	AUX
ejpam-5456	464	6	versatile	versatile	ADJ
ejpam-5456	464	7	and	and	CCONJ
ejpam-5456	464	8	can	can	AUX
ejpam-5456	464	9	be	be	AUX
ejpam-5456	464	10	applied	apply	VERB
ejpam-5456	464	11	to	to	ADP
ejpam-5456	464	12	a	a	DET
ejpam-5456	464	13	range	range	NOUN
ejpam-5456	464	14	of	of	ADP
ejpam-5456	464	15	ordinary	ordinary	ADJ
ejpam-5456	464	16	and	and	CCONJ
ejpam-5456	464	17	partial	partial	ADJ
ejpam-5456	464	18	fodes	fode	NOUN
ejpam-5456	464	19	.	.	PUNCT
ejpam-5456	465	1	in	in	ADP
ejpam-5456	465	2	the	the	DET
ejpam-5456	465	3	future	future	NOUN
ejpam-5456	465	4	,	,	PUNCT
ejpam-5456	465	5	we	we	PRON
ejpam-5456	465	6	intend	intend	VERB
ejpam-5456	465	7	to	to	PART
ejpam-5456	465	8	employ	employ	VERB
ejpam-5456	465	9	sadm	sadm	ADV
ejpam-5456	465	10	to	to	PART
ejpam-5456	465	11	solve	solve	VERB
ejpam-5456	465	12	various	various	ADJ
ejpam-5456	465	13	nonlinear	nonlinear	ADJ
ejpam-5456	465	14	fractional	fractional	ADJ
ejpam-5456	465	15	models	model	NOUN
ejpam-5456	465	16	arising	arise	VERB
ejpam-5456	465	17	in	in	ADP
ejpam-5456	465	18	biological	biological	ADJ
ejpam-5456	465	19	systems	system	NOUN
ejpam-5456	465	20	.	.	PUNCT
ejpam-5456	466	1	acknowledgements	acknowledgement	NOUN
ejpam-5456	466	2	.	.	PUNCT
ejpam-5456	467	1	the	the	DET
ejpam-5456	467	2	authors	author	NOUN
ejpam-5456	467	3	express	express	VERB
ejpam-5456	467	4	their	their	PRON
ejpam-5456	467	5	gratitude	gratitude	NOUN
ejpam-5456	467	6	to	to	ADP
ejpam-5456	467	7	the	the	DET
ejpam-5456	467	8	editor	editor	NOUN
ejpam-5456	467	9	and	and	CCONJ
ejpam-5456	467	10	the	the	DET
ejpam-5456	467	11	reviewers	reviewer	NOUN
ejpam-5456	467	12	for	for	ADP
ejpam-5456	467	13	their	their	PRON
ejpam-5456	467	14	valuable	valuable	ADJ
ejpam-5456	467	15	comments	comment	NOUN
ejpam-5456	467	16	.	.	PUNCT
ejpam-5456	468	1	references	reference	NOUN
ejpam-5456	468	2	[	[	X
ejpam-5456	468	3	1	1	NUM
ejpam-5456	468	4	]	]	X
ejpam-5456	468	5	mohammed	mohammed	PROPN
ejpam-5456	468	6	-	-	PUNCT
ejpam-5456	468	7	salah	salah	PROPN
ejpam-5456	468	8	abdelouahab	abdelouahab	PROPN
ejpam-5456	468	9	and	and	CCONJ
ejpam-5456	468	10	nasr	nasr	PROPN
ejpam-5456	468	11	-	-	PUNCT
ejpam-5456	468	12	eddine	eddine	PROPN
ejpam-5456	468	13	hamri	hamri	NOUN
ejpam-5456	468	14	.	.	PUNCT
ejpam-5456	469	1	the	the	DET
ejpam-5456	469	2	grünwald	grünwald	ADJ
ejpam-5456	469	3	–	–	PUNCT
ejpam-5456	469	4	letnikov	letnikov	ADJ
ejpam-5456	469	5	fractional	fractional	ADJ
ejpam-5456	469	6	–	–	PUNCT
ejpam-5456	469	7	order	order	NOUN
ejpam-5456	469	8	derivative	derivative	NOUN
ejpam-5456	469	9	with	with	ADP
ejpam-5456	469	10	fixed	fix	VERB
ejpam-5456	469	11	memory	memory	NOUN
ejpam-5456	469	12	length	length	NOUN
ejpam-5456	469	13	.	.	PUNCT
ejpam-5456	470	1	mediterranean	mediterranean	PROPN
ejpam-5456	470	2	journal	journal	PROPN
ejpam-5456	470	3	of	of	ADP
ejpam-5456	470	4	mathematics	mathematic	NOUN
ejpam-5456	470	5	,	,	PUNCT
ejpam-5456	470	6	13(2):557–572	13(2):557–572	PROPN
ejpam-5456	470	7	,	,	PUNCT
ejpam-5456	470	8	2016	2016	NUM
ejpam-5456	470	9	.	.	PUNCT
ejpam-5456	471	1	[	[	X
ejpam-5456	471	2	2	2	X
ejpam-5456	471	3	]	]	PUNCT
ejpam-5456	471	4	shams	sham	VERB
ejpam-5456	471	5	a	a	DET
ejpam-5456	471	6	ahmed	ahmed	PROPN
ejpam-5456	471	7	.	.	PUNCT
ejpam-5456	472	1	an	an	DET
ejpam-5456	472	2	efficient	efficient	ADJ
ejpam-5456	472	3	new	new	ADJ
ejpam-5456	472	4	technique	technique	NOUN
ejpam-5456	472	5	for	for	ADP
ejpam-5456	472	6	solving	solve	VERB
ejpam-5456	472	7	nonlinear	nonlinear	ADJ
ejpam-5456	472	8	problems	problem	NOUN
ejpam-5456	472	9	involving	involve	VERB
ejpam-5456	472	10	the	the	DET
ejpam-5456	472	11	conformable	conformable	ADJ
ejpam-5456	472	12	fractional	fractional	ADJ
ejpam-5456	472	13	derivatives	derivative	NOUN
ejpam-5456	472	14	.	.	PUNCT
ejpam-5456	473	1	journal	journal	NOUN
ejpam-5456	473	2	of	of	ADP
ejpam-5456	473	3	applied	apply	VERB
ejpam-5456	473	4	mathematics	mathematic	NOUN
ejpam-5456	473	5	,	,	PUNCT
ejpam-5456	473	6	2024(1):5958560	2024(1):5958560	PROPN
ejpam-5456	473	7	,	,	PUNCT
ejpam-5456	473	8	2024	2024	NUM
ejpam-5456	473	9	.	.	PUNCT
ejpam-5456	474	1	[	[	X
ejpam-5456	474	2	3	3	X
ejpam-5456	474	3	]	]	PUNCT
ejpam-5456	474	4	zeyad	zeyad	PROPN
ejpam-5456	474	5	al	al	PROPN
ejpam-5456	474	6	-	-	PUNCT
ejpam-5456	474	7	zhour	zhour	PROPN
ejpam-5456	474	8	,	,	PUNCT
ejpam-5456	474	9	fatimah	fatimah	PROPN
ejpam-5456	474	10	alrawajeh	alrawajeh	PROPN
ejpam-5456	474	11	,	,	PUNCT
ejpam-5456	474	12	nouf	nouf	PROPN
ejpam-5456	474	13	al	al	PROPN
ejpam-5456	474	14	-	-	PUNCT
ejpam-5456	474	15	mutairi	mutairi	NOUN
ejpam-5456	474	16	,	,	PUNCT
ejpam-5456	474	17	and	and	CCONJ
ejpam-5456	474	18	raed	raed	NOUN
ejpam-5456	474	19	alkhasawneh	alkhasawneh	NOUN
ejpam-5456	474	20	.	.	PUNCT
ejpam-5456	475	1	new	new	ADJ
ejpam-5456	475	2	results	result	NOUN
ejpam-5456	475	3	on	on	ADP
ejpam-5456	475	4	the	the	DET
ejpam-5456	475	5	conformable	conformable	ADJ
ejpam-5456	475	6	fractional	fractional	ADJ
ejpam-5456	475	7	sumudu	sumudu	NOUN
ejpam-5456	475	8	transform	transform	NOUN
ejpam-5456	475	9	:	:	PUNCT
ejpam-5456	475	10	theories	theory	NOUN
ejpam-5456	475	11	and	and	CCONJ
ejpam-5456	475	12	applications	application	NOUN
ejpam-5456	475	13	.	.	PUNCT
ejpam-5456	476	1	international	international	ADJ
ejpam-5456	476	2	journal	journal	NOUN
ejpam-5456	476	3	of	of	ADP
ejpam-5456	476	4	analysis	analysis	NOUN
ejpam-5456	476	5	and	and	CCONJ
ejpam-5456	476	6	applications	application	NOUN
ejpam-5456	476	7	,	,	PUNCT
ejpam-5456	476	8	17(6):1019–1033	17(6):1019–1033	NUM
ejpam-5456	476	9	,	,	PUNCT
ejpam-5456	476	10	2019	2019	NUM
ejpam-5456	476	11	.	.	PUNCT
ejpam-5456	477	1	[	[	X
ejpam-5456	477	2	4	4	X
ejpam-5456	477	3	]	]	X
ejpam-5456	477	4	wedad	wedad	PROPN
ejpam-5456	477	5	albalawi	albalawi	PROPN
ejpam-5456	477	6	,	,	PUNCT
ejpam-5456	477	7	muhammad	muhammad	PROPN
ejpam-5456	477	8	imran	imran	PROPN
ejpam-5456	477	9	liaqat	liaqat	PROPN
ejpam-5456	477	10	,	,	PUNCT
ejpam-5456	477	11	fahim	fahim	PROPN
ejpam-5456	477	12	ud	ud	INTJ
ejpam-5456	477	13	din	din	PROPN
ejpam-5456	477	14	,	,	PUNCT
ejpam-5456	477	15	kottakkaran	kottakkaran	VERB
ejpam-5456	477	16	sooppy	sooppy	ADJ
ejpam-5456	477	17	nisar	nisar	PROPN
ejpam-5456	477	18	,	,	PUNCT
ejpam-5456	477	19	and	and	CCONJ
ejpam-5456	477	20	abdel	abdel	PROPN
ejpam-5456	477	21	-	-	PUNCT
ejpam-5456	477	22	haleem	haleem	PROPN
ejpam-5456	477	23	abdel	abdel	PROPN
ejpam-5456	477	24	-	-	PUNCT
ejpam-5456	477	25	aty	aty	PROPN
ejpam-5456	477	26	.	.	PUNCT
ejpam-5456	478	1	well	well	ADJ
ejpam-5456	478	2	-	-	PUNCT
ejpam-5456	478	3	posedness	posedness	NOUN
ejpam-5456	478	4	and	and	CCONJ
ejpam-5456	478	5	ulam	ulam	NOUN
ejpam-5456	478	6	-	-	PUNCT
ejpam-5456	478	7	hyers	hyer	NOUN
ejpam-5456	478	8	stability	stability	NOUN
ejpam-5456	478	9	results	result	NOUN
ejpam-5456	478	10	of	of	ADP
ejpam-5456	478	11	solutions	solution	NOUN
ejpam-5456	478	12	to	to	PART
ejpam-5456	478	13	pantograph	pantograph	VERB
ejpam-5456	478	14	fractional	fractional	ADJ
ejpam-5456	478	15	stochastic	stochastic	ADJ
ejpam-5456	478	16	differential	differential	ADJ
ejpam-5456	478	17	equations	equation	NOUN
ejpam-5456	478	18	in	in	ADP
ejpam-5456	478	19	the	the	DET
ejpam-5456	478	20	sense	sense	NOUN
ejpam-5456	478	21	of	of	ADP
ejpam-5456	478	22	conformable	conformable	ADJ
ejpam-5456	478	23	derivatives	derivative	NOUN
ejpam-5456	478	24	.	.	PUNCT
ejpam-5456	479	1	aims	aim	VERB
ejpam-5456	479	2	mathematics	mathematic	NOUN
ejpam-5456	479	3	,	,	PUNCT
ejpam-5456	479	4	9(5):12375–12398	9(5):12375–12398	NUM
ejpam-5456	479	5	,	,	PUNCT
ejpam-5456	479	6	2024	2024	NUM
ejpam-5456	479	7	.	.	PUNCT
ejpam-5456	480	1	[	[	X
ejpam-5456	480	2	5	5	NUM
ejpam-5456	480	3	]	]	PUNCT
ejpam-5456	480	4	sahar	sahar	X
ejpam-5456	480	5	albosaily	albosaily	ADV
ejpam-5456	480	6	,	,	PUNCT
ejpam-5456	480	7	elsayed	elsaye	VERB
ejpam-5456	480	8	m	m	AUX
ejpam-5456	480	9	elsayed	elsaye	VERB
ejpam-5456	480	10	,	,	PUNCT
ejpam-5456	480	11	m	m	VERB
ejpam-5456	480	12	daher	daher	NOUN
ejpam-5456	480	13	albalwi	albalwi	NOUN
ejpam-5456	480	14	,	,	PUNCT
ejpam-5456	480	15	meshari	meshari	ADJ
ejpam-5456	480	16	alesemi	alesemi	NOUN
ejpam-5456	480	17	,	,	PUNCT
ejpam-5456	480	18	and	and	CCONJ
ejpam-5456	480	19	wael	wael	PROPN
ejpam-5456	480	20	w	w	PROPN
ejpam-5456	480	21	mohammed	mohammed	PROPN
ejpam-5456	480	22	.	.	PUNCT
ejpam-5456	481	1	the	the	DET
ejpam-5456	481	2	analytical	analytical	ADJ
ejpam-5456	481	3	stochastic	stochastic	ADJ
ejpam-5456	481	4	solutions	solution	NOUN
ejpam-5456	481	5	for	for	ADP
ejpam-5456	481	6	the	the	DET
ejpam-5456	481	7	stochastic	stochastic	ADJ
ejpam-5456	481	8	potential	potential	ADJ
ejpam-5456	481	9	yu	yu	PROPN
ejpam-5456	481	10	–	–	PUNCT
ejpam-5456	481	11	toda	toda	PROPN
ejpam-5456	481	12	–	–	PUNCT
ejpam-5456	481	13	sasa	sasa	PROPN
ejpam-5456	481	14	–	–	PUNCT
ejpam-5456	481	15	fukuyama	fukuyama	PROPN
ejpam-5456	481	16	equation	equation	NOUN
ejpam-5456	481	17	with	with	ADP
ejpam-5456	481	18	conformable	conformable	ADJ
ejpam-5456	481	19	derivative	derivative	NOUN
ejpam-5456	481	20	using	use	VERB
ejpam-5456	481	21	different	different	ADJ
ejpam-5456	481	22	methods	method	NOUN
ejpam-5456	481	23	.	.	PUNCT
ejpam-5456	482	1	fractal	fractal	ADJ
ejpam-5456	482	2	and	and	CCONJ
ejpam-5456	482	3	fractional	fractional	ADJ
ejpam-5456	482	4	,	,	PUNCT
ejpam-5456	482	5	7(11):787	7(11):787	NUM
ejpam-5456	482	6	,	,	PUNCT
ejpam-5456	482	7	2023	2023	NUM
ejpam-5456	482	8	.	.	PUNCT
ejpam-5456	483	1	[	[	X
ejpam-5456	483	2	6	6	NUM
ejpam-5456	483	3	]	]	X
ejpam-5456	483	4	nidal	nidal	PROPN
ejpam-5456	483	5	anakira	anakira	PROPN
ejpam-5456	483	6	,	,	PUNCT
ejpam-5456	483	7	zinouba	zinouba	PROPN
ejpam-5456	483	8	chebana	chebana	PROPN
ejpam-5456	483	9	,	,	PUNCT
ejpam-5456	483	10	taki	taki	PROPN
ejpam-5456	483	11	-	-	PUNCT
ejpam-5456	483	12	eddine	eddine	NOUN
ejpam-5456	483	13	oussaeif	oussaeif	NOUN
ejpam-5456	483	14	,	,	PUNCT
ejpam-5456	483	15	iqbal	iqbal	PROPN
ejpam-5456	483	16	m	m	PROPN
ejpam-5456	483	17	batiha	batiha	VERB
ejpam-5456	483	18	,	,	PUNCT
ejpam-5456	483	19	and	and	CCONJ
ejpam-5456	483	20	adel	adel	PROPN
ejpam-5456	483	21	ouannas	ouannas	PROPN
ejpam-5456	483	22	.	.	PUNCT
ejpam-5456	484	1	a	a	DET
ejpam-5456	484	2	study	study	NOUN
ejpam-5456	484	3	of	of	ADP
ejpam-5456	484	4	a	a	DET
ejpam-5456	484	5	weak	weak	ADJ
ejpam-5456	484	6	solution	solution	NOUN
ejpam-5456	484	7	of	of	ADP
ejpam-5456	484	8	a	a	DET
ejpam-5456	484	9	diffusion	diffusion	NOUN
ejpam-5456	484	10	problem	problem	NOUN
ejpam-5456	484	11	for	for	ADP
ejpam-5456	484	12	a	a	DET
ejpam-5456	484	13	temporal	temporal	ADJ
ejpam-5456	484	14	fractional	fractional	ADJ
ejpam-5456	484	15	differential	differential	NOUN
ejpam-5456	484	16	equation	equation	NOUN
ejpam-5456	484	17	.	.	PUNCT
ejpam-5456	485	1	nonlinear	nonlinear	ADJ
ejpam-5456	485	2	functional	functional	ADJ
ejpam-5456	485	3	analysis	analysis	NOUN
ejpam-5456	485	4	and	and	CCONJ
ejpam-5456	485	5	applications	application	NOUN
ejpam-5456	485	6	,	,	PUNCT
ejpam-5456	485	7	pages	page	NOUN
ejpam-5456	485	8	679–689	679–689	NUM
ejpam-5456	485	9	,	,	PUNCT
ejpam-5456	485	10	2022	2022	NUM
ejpam-5456	485	11	.	.	PUNCT
ejpam-5456	486	1	references	reference	NOUN
ejpam-5456	486	2	3489	3489	NUM
ejpam-5456	486	3	[	[	X
ejpam-5456	486	4	7	7	NUM
ejpam-5456	486	5	]	]	X
ejpam-5456	486	6	k	k	PROPN
ejpam-5456	486	7	aruna	aruna	PROPN
ejpam-5456	486	8	and	and	CCONJ
ejpam-5456	486	9	asv	asv	PROPN
ejpam-5456	486	10	ravi	ravi	PROPN
ejpam-5456	486	11	kanth	kanth	PROPN
ejpam-5456	486	12	.	.	PUNCT
ejpam-5456	487	1	approximate	approximate	ADJ
ejpam-5456	487	2	solutions	solution	NOUN
ejpam-5456	487	3	of	of	ADP
ejpam-5456	487	4	non	non	ADJ
ejpam-5456	487	5	-	-	ADJ
ejpam-5456	487	6	linear	linear	ADJ
ejpam-5456	487	7	fractional	fractional	ADJ
ejpam-5456	487	8	schrodinger	schrodinger	NOUN
ejpam-5456	487	9	equation	equation	NOUN
ejpam-5456	487	10	via	via	ADP
ejpam-5456	487	11	differential	differential	ADJ
ejpam-5456	487	12	transform	transform	NOUN
ejpam-5456	487	13	method	method	NOUN
ejpam-5456	487	14	and	and	CCONJ
ejpam-5456	487	15	modified	modify	VERB
ejpam-5456	487	16	differential	differential	ADJ
ejpam-5456	487	17	transform	transform	NOUN
ejpam-5456	487	18	method	method	NOUN
ejpam-5456	487	19	.	.	PUNCT
ejpam-5456	488	1	national	national	PROPN
ejpam-5456	488	2	academy	academy	PROPN
ejpam-5456	488	3	science	science	PROPN
ejpam-5456	488	4	letters	letter	NOUN
ejpam-5456	488	5	,	,	PUNCT
ejpam-5456	488	6	36:201–213	36:201–213	PROPN
ejpam-5456	488	7	,	,	PUNCT
ejpam-5456	488	8	2013	2013	NUM
ejpam-5456	488	9	.	.	PUNCT
ejpam-5456	489	1	[	[	X
ejpam-5456	489	2	8	8	NUM
ejpam-5456	489	3	]	]	PUNCT
ejpam-5456	489	4	allaberen	allaberen	NOUN
ejpam-5456	490	1	ashyralyev	ashyralyev	CCONJ
ejpam-5456	490	2	and	and	CCONJ
ejpam-5456	490	3	betul	betul	PROPN
ejpam-5456	490	4	hicdurmaz	hicdurmaz	PROPN
ejpam-5456	490	5	.	.	PUNCT
ejpam-5456	491	1	a	a	DET
ejpam-5456	491	2	note	note	NOUN
ejpam-5456	491	3	on	on	ADP
ejpam-5456	491	4	the	the	DET
ejpam-5456	491	5	fractional	fractional	PROPN
ejpam-5456	491	6	schrödinger	schrödinger	NOUN
ejpam-5456	491	7	differential	differential	NOUN
ejpam-5456	491	8	equations	equation	NOUN
ejpam-5456	491	9	.	.	PUNCT
ejpam-5456	492	1	kybernetes	kybernete	NOUN
ejpam-5456	492	2	,	,	PUNCT
ejpam-5456	492	3	40(5/6):736–750	40(5/6):736–750	NUM
ejpam-5456	492	4	,	,	PUNCT
ejpam-5456	492	5	2011	2011	NUM
ejpam-5456	492	6	.	.	PUNCT
ejpam-5456	493	1	[	[	X
ejpam-5456	493	2	9	9	NUM
ejpam-5456	493	3	]	]	PUNCT
ejpam-5456	493	4	abdelhamid	abdelhamid	PROPN
ejpam-5456	493	5	mohammed	mohammed	PROPN
ejpam-5456	493	6	djaouti	djaouti	PROPN
ejpam-5456	493	7	,	,	PUNCT
ejpam-5456	493	8	zareen	zareen	X
ejpam-5456	493	9	a	a	DET
ejpam-5456	493	10	khan	khan	PROPN
ejpam-5456	493	11	,	,	PUNCT
ejpam-5456	493	12	muhammad	muhammad	PROPN
ejpam-5456	493	13	imran	imran	PROPN
ejpam-5456	493	14	liaqat	liaqat	PROPN
ejpam-5456	493	15	,	,	PUNCT
ejpam-5456	493	16	and	and	CCONJ
ejpam-5456	493	17	ashraf	ashraf	PROPN
ejpam-5456	493	18	al	al	PROPN
ejpam-5456	493	19	-	-	PUNCT
ejpam-5456	493	20	quran	quran	PROPN
ejpam-5456	493	21	.	.	PUNCT
ejpam-5456	494	1	a	a	DET
ejpam-5456	494	2	study	study	NOUN
ejpam-5456	494	3	of	of	ADP
ejpam-5456	494	4	some	some	DET
ejpam-5456	494	5	generalized	generalized	ADJ
ejpam-5456	494	6	results	result	NOUN
ejpam-5456	494	7	of	of	ADP
ejpam-5456	494	8	neutral	neutral	ADJ
ejpam-5456	494	9	stochastic	stochastic	ADJ
ejpam-5456	494	10	differential	differential	ADJ
ejpam-5456	494	11	equations	equation	NOUN
ejpam-5456	494	12	in	in	ADP
ejpam-5456	494	13	the	the	DET
ejpam-5456	494	14	framework	framework	NOUN
ejpam-5456	494	15	of	of	ADP
ejpam-5456	494	16	caputo	caputo	PROPN
ejpam-5456	494	17	–	–	PUNCT
ejpam-5456	494	18	katugampola	katugampola	ADJ
ejpam-5456	494	19	fractional	fractional	ADJ
ejpam-5456	494	20	derivatives	derivative	NOUN
ejpam-5456	494	21	.	.	PUNCT
ejpam-5456	495	1	mathematics	mathematic	NOUN
ejpam-5456	495	2	,	,	PUNCT
ejpam-5456	495	3	12(11):1654	12(11):1654	NUM
ejpam-5456	495	4	,	,	PUNCT
ejpam-5456	495	5	2024	2024	NUM
ejpam-5456	495	6	.	.	PUNCT
ejpam-5456	496	1	[	[	X
ejpam-5456	496	2	10	10	NUM
ejpam-5456	496	3	]	]	X
ejpam-5456	496	4	hassan	hassan	PROPN
ejpam-5456	496	5	eltayeb	eltayeb	PROPN
ejpam-5456	496	6	and	and	CCONJ
ejpam-5456	496	7	said	say	VERB
ejpam-5456	496	8	mesloub	mesloub	PROPN
ejpam-5456	496	9	.	.	PUNCT
ejpam-5456	497	1	application	application	NOUN
ejpam-5456	497	2	of	of	ADP
ejpam-5456	497	3	multi	multi	ADJ
ejpam-5456	497	4	-	-	ADJ
ejpam-5456	497	5	dimensional	dimensional	ADJ
ejpam-5456	497	6	of	of	ADP
ejpam-5456	497	7	conformable	conformable	ADJ
ejpam-5456	497	8	sumudu	sumudu	NOUN
ejpam-5456	497	9	decomposition	decomposition	NOUN
ejpam-5456	497	10	method	method	NOUN
ejpam-5456	497	11	for	for	ADP
ejpam-5456	497	12	solving	solve	VERB
ejpam-5456	497	13	conformable	conformable	ADJ
ejpam-5456	497	14	singular	singular	ADJ
ejpam-5456	497	15	fractional	fractional	ADJ
ejpam-5456	497	16	coupled	couple	VERB
ejpam-5456	497	17	burger	burger	NOUN
ejpam-5456	497	18	,	,	PUNCT
ejpam-5456	497	19	s	s	PART
ejpam-5456	497	20	equation	equation	NOUN
ejpam-5456	497	21	.	.	PUNCT
ejpam-5456	498	1	acta	acta	PROPN
ejpam-5456	498	2	mathematica	mathematica	PROPN
ejpam-5456	498	3	scientia	scientia	PROPN
ejpam-5456	498	4	,	,	PUNCT
ejpam-5456	498	5	41:1679–1698	41:1679–1698	PROPN
ejpam-5456	498	6	,	,	PUNCT
ejpam-5456	498	7	2021	2021	NUM
ejpam-5456	498	8	.	.	PUNCT
ejpam-5456	499	1	[	[	X
ejpam-5456	499	2	11	11	NUM
ejpam-5456	499	3	]	]	X
ejpam-5456	499	4	che	che	PROPN
ejpam-5456	499	5	haziqah	haziqah	PROPN
ejpam-5456	499	6	che	che	PROPN
ejpam-5456	499	7	hussin	hussin	PROPN
ejpam-5456	499	8	,	,	PUNCT
ejpam-5456	499	9	adem	adem	PROPN
ejpam-5456	499	10	kilicman	kilicman	PROPN
ejpam-5456	499	11	,	,	PUNCT
ejpam-5456	499	12	and	and	CCONJ
ejpam-5456	499	13	amirah	amirah	VERB
ejpam-5456	499	14	azmi	azmi	PROPN
ejpam-5456	499	15	.	.	PUNCT
ejpam-5456	500	1	analytical	analytical	ADJ
ejpam-5456	500	2	solutions	solution	NOUN
ejpam-5456	500	3	of	of	ADP
ejpam-5456	500	4	nonlinear	nonlinear	ADJ
ejpam-5456	500	5	schrodinger	schrodinger	PROPN
ejpam-5456	500	6	equations	equation	NOUN
ejpam-5456	500	7	using	use	VERB
ejpam-5456	500	8	multistep	multistep	ADV
ejpam-5456	500	9	modified	modify	VERB
ejpam-5456	500	10	reduced	reduce	VERB
ejpam-5456	500	11	differential	differential	NOUN
ejpam-5456	500	12	transform	transform	NOUN
ejpam-5456	500	13	method	method	NOUN
ejpam-5456	500	14	.	.	PUNCT
ejpam-5456	501	1	compusoft	compusoft	ADV
ejpam-5456	501	2	,	,	PUNCT
ejpam-5456	501	3	7(11):2939–2944	7(11):2939–2944	NUM
ejpam-5456	501	4	,	,	PUNCT
ejpam-5456	501	5	2018	2018	NUM
ejpam-5456	501	6	.	.	PUNCT
ejpam-5456	502	1	[	[	X
ejpam-5456	502	2	12	12	NUM
ejpam-5456	502	3	]	]	X
ejpam-5456	502	4	aziz	aziz	PROPN
ejpam-5456	502	5	khan	khan	PROPN
ejpam-5456	502	6	,	,	PUNCT
ejpam-5456	502	7	muhammad	muhammad	PROPN
ejpam-5456	502	8	imran	imran	PROPN
ejpam-5456	502	9	liaqat	liaqat	PROPN
ejpam-5456	502	10	,	,	PUNCT
ejpam-5456	502	11	manar	manar	VERB
ejpam-5456	502	12	a	a	DET
ejpam-5456	502	13	alqudah	alqudah	NOUN
ejpam-5456	502	14	,	,	PUNCT
ejpam-5456	502	15	and	and	CCONJ
ejpam-5456	502	16	thabet	thabet	ADJ
ejpam-5456	502	17	abdeljawad	abdeljawad	NOUN
ejpam-5456	502	18	.	.	PUNCT
ejpam-5456	503	1	analysis	analysis	NOUN
ejpam-5456	503	2	of	of	ADP
ejpam-5456	503	3	the	the	DET
ejpam-5456	503	4	conformable	conformable	ADJ
ejpam-5456	503	5	temporal	temporal	ADJ
ejpam-5456	503	6	-	-	PUNCT
ejpam-5456	503	7	fractional	fractional	ADJ
ejpam-5456	503	8	swift	swift	NOUN
ejpam-5456	503	9	–	–	PUNCT
ejpam-5456	503	10	hohenberg	hohenberg	NOUN
ejpam-5456	503	11	equation	equation	NOUN
ejpam-5456	503	12	using	use	VERB
ejpam-5456	503	13	a	a	DET
ejpam-5456	503	14	novel	novel	ADJ
ejpam-5456	503	15	computational	computational	ADJ
ejpam-5456	503	16	technique	technique	NOUN
ejpam-5456	503	17	.	.	PUNCT
ejpam-5456	504	1	fractals	fractal	NOUN
ejpam-5456	504	2	,	,	PUNCT
ejpam-5456	504	3	31(04):2340050	31(04):2340050	NUM
ejpam-5456	504	4	,	,	PUNCT
ejpam-5456	504	5	2023	2023	NUM
ejpam-5456	504	6	.	.	PUNCT
ejpam-5456	505	1	[	[	X
ejpam-5456	505	2	13	13	NUM
ejpam-5456	505	3	]	]	PUNCT
ejpam-5456	505	4	najeeb	najeeb	PROPN
ejpam-5456	505	5	alam	alam	PROPN
ejpam-5456	505	6	khan	khan	PROPN
ejpam-5456	505	7	,	,	PUNCT
ejpam-5456	505	8	muhammad	muhammad	PROPN
ejpam-5456	505	9	jamil	jamil	PROPN
ejpam-5456	505	10	,	,	PUNCT
ejpam-5456	505	11	and	and	CCONJ
ejpam-5456	505	12	asmat	asmat	PROPN
ejpam-5456	505	13	ara	ara	PROPN
ejpam-5456	505	14	.	.	PROPN
ejpam-5456	505	15	approximate	approximate	ADJ
ejpam-5456	505	16	solutions	solution	NOUN
ejpam-5456	505	17	to	to	ADP
ejpam-5456	505	18	time	time	NOUN
ejpam-5456	505	19	-	-	PUNCT
ejpam-5456	505	20	fractional	fractional	ADJ
ejpam-5456	505	21	schrödinger	schrödinger	NOUN
ejpam-5456	505	22	equation	equation	NOUN
ejpam-5456	505	23	via	via	ADP
ejpam-5456	505	24	homotopy	homotopy	NOUN
ejpam-5456	505	25	analysis	analysis	NOUN
ejpam-5456	505	26	method	method	NOUN
ejpam-5456	505	27	.	.	PUNCT
ejpam-5456	506	1	international	international	ADJ
ejpam-5456	506	2	scholarly	scholarly	ADJ
ejpam-5456	506	3	research	research	NOUN
ejpam-5456	506	4	notices	notice	NOUN
ejpam-5456	506	5	,	,	PUNCT
ejpam-5456	506	6	2012(1):197068	2012(1):197068	NUM
ejpam-5456	506	7	,	,	PUNCT
ejpam-5456	506	8	2012	2012	NUM
ejpam-5456	506	9	.	.	PUNCT
ejpam-5456	507	1	[	[	X
ejpam-5456	507	2	14	14	NUM
ejpam-5456	507	3	]	]	PUNCT
ejpam-5456	507	4	najeeb	najeeb	PROPN
ejpam-5456	507	5	alam	alam	PROPN
ejpam-5456	507	6	khan	khan	PROPN
ejpam-5456	507	7	,	,	PUNCT
ejpam-5456	507	8	muhammad	muhammad	PROPN
ejpam-5456	507	9	jamil	jamil	PROPN
ejpam-5456	507	10	,	,	PUNCT
ejpam-5456	507	11	and	and	CCONJ
ejpam-5456	507	12	asmat	asmat	PROPN
ejpam-5456	507	13	ara	ara	PROPN
ejpam-5456	507	14	.	.	PROPN
ejpam-5456	507	15	approximate	approximate	ADJ
ejpam-5456	507	16	solutions	solution	NOUN
ejpam-5456	507	17	to	to	ADP
ejpam-5456	507	18	time	time	NOUN
ejpam-5456	507	19	-	-	PUNCT
ejpam-5456	507	20	fractional	fractional	ADJ
ejpam-5456	507	21	schrödinger	schrödinger	NOUN
ejpam-5456	507	22	equation	equation	NOUN
ejpam-5456	507	23	via	via	ADP
ejpam-5456	507	24	homotopy	homotopy	NOUN
ejpam-5456	507	25	analysis	analysis	NOUN
ejpam-5456	507	26	method	method	NOUN
ejpam-5456	507	27	.	.	PUNCT
ejpam-5456	508	1	international	international	ADJ
ejpam-5456	508	2	scholarly	scholarly	ADJ
ejpam-5456	508	3	research	research	NOUN
ejpam-5456	508	4	notices	notice	NOUN
ejpam-5456	508	5	,	,	PUNCT
ejpam-5456	508	6	2012(1):197068	2012(1):197068	NUM
ejpam-5456	508	7	,	,	PUNCT
ejpam-5456	508	8	2012	2012	NUM
ejpam-5456	508	9	.	.	PUNCT
ejpam-5456	509	1	[	[	X
ejpam-5456	509	2	15	15	NUM
ejpam-5456	509	3	]	]	X
ejpam-5456	509	4	zeliha	zeliha	PROPN
ejpam-5456	509	5	korpinar	korpinar	NOUN
ejpam-5456	509	6	,	,	PUNCT
ejpam-5456	509	7	fairouz	fairouz	ADJ
ejpam-5456	509	8	tchier	tchier	NOUN
ejpam-5456	509	9	,	,	PUNCT
ejpam-5456	509	10	mustafa	mustafa	PROPN
ejpam-5456	509	11	inc	inc	PROPN
ejpam-5456	509	12	,	,	PUNCT
ejpam-5456	509	13	fatiha	fatiha	PROPN
ejpam-5456	509	14	bousbahi	bousbahi	NOUN
ejpam-5456	509	15	,	,	PUNCT
ejpam-5456	509	16	ferdous	ferdous	ADJ
ejpam-5456	509	17	mo	mo	PROPN
ejpam-5456	509	18	tawfiq	tawfiq	PROPN
ejpam-5456	509	19	,	,	PUNCT
ejpam-5456	509	20	and	and	CCONJ
ejpam-5456	509	21	mehmet	mehmet	PROPN
ejpam-5456	509	22	ali	ali	PROPN
ejpam-5456	509	23	akinlar	akinlar	PROPN
ejpam-5456	509	24	.	.	PUNCT
ejpam-5456	510	1	applicability	applicability	NOUN
ejpam-5456	510	2	of	of	ADP
ejpam-5456	510	3	time	time	NOUN
ejpam-5456	510	4	conformable	conformable	ADJ
ejpam-5456	510	5	derivative	derivative	NOUN
ejpam-5456	510	6	to	to	ADP
ejpam-5456	510	7	wickfractional	wickfractional	ADJ
ejpam-5456	510	8	–	–	PUNCT
ejpam-5456	510	9	stochastic	stochastic	ADJ
ejpam-5456	510	10	pdes	pde	NOUN
ejpam-5456	510	11	.	.	PUNCT
ejpam-5456	511	1	alexandria	alexandria	PROPN
ejpam-5456	511	2	engineering	engineering	PROPN
ejpam-5456	511	3	journal	journal	PROPN
ejpam-5456	511	4	,	,	PUNCT
ejpam-5456	511	5	59(3):1485–1493	59(3):1485–1493	NUM
ejpam-5456	511	6	,	,	PUNCT
ejpam-5456	511	7	2020	2020	NUM
ejpam-5456	511	8	.	.	PUNCT
ejpam-5456	512	1	[	[	X
ejpam-5456	512	2	16	16	NUM
ejpam-5456	512	3	]	]	X
ejpam-5456	512	4	césar	césar	PROPN
ejpam-5456	512	5	e	e	PROPN
ejpam-5456	512	6	torres	torre	VERB
ejpam-5456	512	7	ledesma	ledesma	PROPN
ejpam-5456	512	8	and	and	CCONJ
ejpam-5456	512	9	manuel	manuel	PROPN
ejpam-5456	512	10	c	c	PROPN
ejpam-5456	512	11	montalvo	montalvo	PROPN
ejpam-5456	512	12	bonilla	bonilla	PROPN
ejpam-5456	512	13	.	.	PUNCT
ejpam-5456	513	1	fractional	fractional	ADJ
ejpam-5456	513	2	sobolev	sobolev	PROPN
ejpam-5456	513	3	space	space	NOUN
ejpam-5456	513	4	with	with	ADP
ejpam-5456	513	5	riemann	riemann	PROPN
ejpam-5456	513	6	–	–	PUNCT
ejpam-5456	513	7	liouville	liouville	VERB
ejpam-5456	513	8	fractional	fractional	ADJ
ejpam-5456	513	9	derivative	derivative	NOUN
ejpam-5456	513	10	and	and	CCONJ
ejpam-5456	513	11	application	application	NOUN
ejpam-5456	513	12	to	to	ADP
ejpam-5456	513	13	a	a	DET
ejpam-5456	513	14	fractional	fractional	ADJ
ejpam-5456	513	15	concave	concave	ADJ
ejpam-5456	513	16	–	–	PUNCT
ejpam-5456	513	17	convex	convex	NOUN
ejpam-5456	513	18	problem	problem	NOUN
ejpam-5456	513	19	.	.	PUNCT
ejpam-5456	514	1	advances	advance	NOUN
ejpam-5456	514	2	in	in	ADP
ejpam-5456	514	3	operator	operator	NOUN
ejpam-5456	514	4	theory	theory	NOUN
ejpam-5456	514	5	,	,	PUNCT
ejpam-5456	514	6	6(4):65	6(4):65	NOUN
ejpam-5456	514	7	,	,	PUNCT
ejpam-5456	514	8	2021	2021	NUM
ejpam-5456	514	9	.	.	PUNCT
ejpam-5456	515	1	[	[	X
ejpam-5456	515	2	17	17	NUM
ejpam-5456	515	3	]	]	PUNCT
ejpam-5456	515	4	muhammad	muhammad	PROPN
ejpam-5456	515	5	imran	imran	PROPN
ejpam-5456	515	6	liaqat	liaqat	PROPN
ejpam-5456	515	7	,	,	PUNCT
ejpam-5456	515	8	ali	ali	PROPN
ejpam-5456	515	9	akgül	akgül	PROPN
ejpam-5456	515	10	,	,	PUNCT
ejpam-5456	515	11	manuel	manuel	PROPN
ejpam-5456	515	12	de	de	PROPN
ejpam-5456	515	13	la	la	PROPN
ejpam-5456	515	14	sen	sen	PROPN
ejpam-5456	515	15	,	,	PUNCT
ejpam-5456	515	16	and	and	CCONJ
ejpam-5456	515	17	mustafa	mustafa	PROPN
ejpam-5456	515	18	bayram	bayram	PROPN
ejpam-5456	515	19	.	.	PROPN
ejpam-5456	515	20	approximate	approximate	ADJ
ejpam-5456	515	21	and	and	CCONJ
ejpam-5456	515	22	exact	exact	ADJ
ejpam-5456	515	23	solutions	solution	NOUN
ejpam-5456	515	24	in	in	ADP
ejpam-5456	515	25	the	the	DET
ejpam-5456	515	26	sense	sense	NOUN
ejpam-5456	515	27	of	of	ADP
ejpam-5456	515	28	conformable	conformable	ADJ
ejpam-5456	515	29	derivatives	derivative	NOUN
ejpam-5456	515	30	of	of	ADP
ejpam-5456	515	31	quantum	quantum	ADJ
ejpam-5456	515	32	mechanics	mechanic	NOUN
ejpam-5456	515	33	models	model	NOUN
ejpam-5456	515	34	using	use	VERB
ejpam-5456	515	35	a	a	DET
ejpam-5456	515	36	novel	novel	ADJ
ejpam-5456	515	37	algorithm	algorithm	NOUN
ejpam-5456	515	38	.	.	PUNCT
ejpam-5456	516	1	symmetry	symmetry	NOUN
ejpam-5456	516	2	,	,	PUNCT
ejpam-5456	516	3	15(3):744	15(3):744	NUM
ejpam-5456	516	4	,	,	PUNCT
ejpam-5456	516	5	2023	2023	NUM
ejpam-5456	516	6	.	.	PUNCT
ejpam-5456	517	1	[	[	X
ejpam-5456	517	2	18	18	NUM
ejpam-5456	517	3	]	]	PUNCT
ejpam-5456	517	4	muhammad	muhammad	PROPN
ejpam-5456	517	5	imran	imran	PROPN
ejpam-5456	517	6	liaqat	liaqat	PROPN
ejpam-5456	517	7	,	,	PUNCT
ejpam-5456	517	8	aziz	aziz	PROPN
ejpam-5456	517	9	khan	khan	PROPN
ejpam-5456	517	10	,	,	PUNCT
ejpam-5456	517	11	manar	manar	PROPN
ejpam-5456	517	12	a	a	DET
ejpam-5456	517	13	alqudah	alqudah	NOUN
ejpam-5456	517	14	,	,	PUNCT
ejpam-5456	517	15	and	and	CCONJ
ejpam-5456	517	16	thabet	thabet	ADJ
ejpam-5456	517	17	abdeljawad	abdeljawad	NOUN
ejpam-5456	517	18	.	.	PUNCT
ejpam-5456	518	1	adapted	adapt	VERB
ejpam-5456	518	2	homotopy	homotopy	NOUN
ejpam-5456	518	3	perturbation	perturbation	NOUN
ejpam-5456	518	4	method	method	NOUN
ejpam-5456	518	5	with	with	ADP
ejpam-5456	518	6	shehu	shehu	NOUN
ejpam-5456	518	7	transform	transform	VERB
ejpam-5456	518	8	for	for	ADP
ejpam-5456	518	9	solving	solve	VERB
ejpam-5456	518	10	conformable	conformable	ADJ
ejpam-5456	518	11	fractional	fractional	ADJ
ejpam-5456	518	12	nonlinear	nonlinear	ADJ
ejpam-5456	518	13	partial	partial	ADJ
ejpam-5456	518	14	differential	differential	NOUN
ejpam-5456	518	15	equations	equation	NOUN
ejpam-5456	518	16	.	.	PUNCT
ejpam-5456	519	1	fractals	fractal	NOUN
ejpam-5456	519	2	,	,	PUNCT
ejpam-5456	519	3	31(02):2340027	31(02):2340027	NUM
ejpam-5456	519	4	,	,	PUNCT
ejpam-5456	519	5	2023	2023	NUM
ejpam-5456	519	6	.	.	PUNCT
ejpam-5456	520	1	references	reference	NOUN
ejpam-5456	520	2	3490	3490	NUM
ejpam-5456	520	3	[	[	X
ejpam-5456	520	4	19	19	NUM
ejpam-5456	520	5	]	]	X
ejpam-5456	520	6	huan	huan	PROPN
ejpam-5456	520	7	luo	luo	PROPN
ejpam-5456	520	8	and	and	CCONJ
ejpam-5456	520	9	tianwei	tianwei	PROPN
ejpam-5456	520	10	zhang	zhang	PROPN
ejpam-5456	520	11	.	.	PUNCT
ejpam-5456	520	12	equilibrium	equilibrium	NOUN
ejpam-5456	520	13	point	point	NOUN
ejpam-5456	520	14	,	,	PUNCT
ejpam-5456	520	15	exponential	exponential	ADJ
ejpam-5456	520	16	stability	stability	NOUN
ejpam-5456	520	17	and	and	CCONJ
ejpam-5456	520	18	synchronization	synchronization	NOUN
ejpam-5456	520	19	of	of	ADP
ejpam-5456	520	20	numerical	numerical	ADJ
ejpam-5456	520	21	fractional	fractional	ADJ
ejpam-5456	520	22	-	-	PUNCT
ejpam-5456	520	23	order	order	NOUN
ejpam-5456	520	24	shunting	shunt	VERB
ejpam-5456	520	25	inhibitory	inhibitory	ADJ
ejpam-5456	520	26	cellular	cellular	ADJ
ejpam-5456	520	27	neural	neural	ADJ
ejpam-5456	520	28	networks	network	NOUN
ejpam-5456	520	29	with	with	ADP
ejpam-5456	520	30	piecewise	piecewise	NOUN
ejpam-5456	520	31	feature	feature	NOUN
ejpam-5456	520	32	.	.	PUNCT
ejpam-5456	521	1	proceedings	proceeding	NOUN
ejpam-5456	521	2	of	of	ADP
ejpam-5456	521	3	the	the	DET
ejpam-5456	521	4	institution	institution	NOUN
ejpam-5456	521	5	of	of	ADP
ejpam-5456	521	6	mechanical	mechanical	ADJ
ejpam-5456	521	7	engineers	engineer	NOUN
ejpam-5456	521	8	,	,	PUNCT
ejpam-5456	521	9	part	part	NOUN
ejpam-5456	521	10	i	i	PRON
ejpam-5456	521	11	:	:	PUNCT
ejpam-5456	521	12	journal	journal	PROPN
ejpam-5456	521	13	of	of	ADP
ejpam-5456	521	14	systems	system	NOUN
ejpam-5456	521	15	and	and	CCONJ
ejpam-5456	521	16	control	control	PROPN
ejpam-5456	521	17	engineering	engineering	NOUN
ejpam-5456	521	18	,	,	PUNCT
ejpam-5456	521	19	236(10):1908–1921	236(10):1908–1921	NUM
ejpam-5456	521	20	,	,	PUNCT
ejpam-5456	521	21	2022	2022	NUM
ejpam-5456	521	22	.	.	PUNCT
ejpam-5456	522	1	[	[	X
ejpam-5456	522	2	20	20	NUM
ejpam-5456	522	3	]	]	PUNCT
ejpam-5456	522	4	wael	wael	PROPN
ejpam-5456	522	5	wmohammed	wmohammed	PROPN
ejpam-5456	522	6	,	,	PUNCT
ejpam-5456	522	7	clemente	clemente	PROPN
ejpam-5456	522	8	cesarano	cesarano	PROPN
ejpam-5456	522	9	,	,	PUNCT
ejpam-5456	522	10	naveed	naveed	PROPN
ejpam-5456	522	11	iqbal	iqbal	PROPN
ejpam-5456	522	12	,	,	PUNCT
ejpam-5456	522	13	rabeb	rabeb	NOUN
ejpam-5456	522	14	sidaoui	sidaoui	NOUN
ejpam-5456	522	15	,	,	PUNCT
ejpam-5456	522	16	and	and	CCONJ
ejpam-5456	522	17	ekram	ekram	PROPN
ejpam-5456	522	18	e	e	PROPN
ejpam-5456	522	19	ali	ali	PROPN
ejpam-5456	522	20	.	.	PUNCT
ejpam-5456	523	1	the	the	DET
ejpam-5456	523	2	exact	exact	ADJ
ejpam-5456	523	3	solutions	solution	NOUN
ejpam-5456	523	4	for	for	ADP
ejpam-5456	523	5	the	the	DET
ejpam-5456	523	6	fractional	fractional	ADJ
ejpam-5456	523	7	riemann	riemann	PROPN
ejpam-5456	523	8	wave	wave	NOUN
ejpam-5456	523	9	equation	equation	NOUN
ejpam-5456	523	10	in	in	ADP
ejpam-5456	523	11	quantum	quantum	ADJ
ejpam-5456	523	12	mechanics	mechanic	NOUN
ejpam-5456	523	13	and	and	CCONJ
ejpam-5456	523	14	optics	optic	NOUN
ejpam-5456	523	15	.	.	PUNCT
ejpam-5456	524	1	physica	physica	PROPN
ejpam-5456	524	2	scripta	scripta	PROPN
ejpam-5456	524	3	,	,	PUNCT
ejpam-5456	524	4	99(8):085245	99(8):085245	NUM
ejpam-5456	524	5	,	,	PUNCT
ejpam-5456	524	6	2024	2024	NUM
ejpam-5456	524	7	.	.	PUNCT
ejpam-5456	525	1	[	[	X
ejpam-5456	525	2	21	21	NUM
ejpam-5456	525	3	]	]	X
ejpam-5456	525	4	abdelhamid	abdelhamid	PROPN
ejpam-5456	525	5	mohammed	mohammed	PROPN
ejpam-5456	525	6	djaouti	djaouti	PROPN
ejpam-5456	525	7	and	and	CCONJ
ejpam-5456	525	8	muhammad	muhammad	PROPN
ejpam-5456	525	9	imran	imran	PROPN
ejpam-5456	525	10	liaqat	liaqat	PROPN
ejpam-5456	525	11	.	.	PUNCT
ejpam-5456	526	1	qualitative	qualitative	ADJ
ejpam-5456	526	2	analysis	analysis	NOUN
ejpam-5456	526	3	for	for	ADP
ejpam-5456	526	4	the	the	DET
ejpam-5456	526	5	solutions	solution	NOUN
ejpam-5456	526	6	of	of	ADP
ejpam-5456	526	7	fractional	fractional	ADJ
ejpam-5456	526	8	stochastic	stochastic	ADJ
ejpam-5456	526	9	differential	differential	ADJ
ejpam-5456	526	10	equations	equation	NOUN
ejpam-5456	526	11	.	.	PUNCT
ejpam-5456	527	1	axioms	axiom	NOUN
ejpam-5456	527	2	,	,	PUNCT
ejpam-5456	527	3	13(7):438	13(7):438	NOUN
ejpam-5456	527	4	,	,	PUNCT
ejpam-5456	527	5	2024	2024	NUM
ejpam-5456	527	6	.	.	PUNCT
ejpam-5456	528	1	[	[	X
ejpam-5456	528	2	22	22	NUM
ejpam-5456	528	3	]	]	PUNCT
ejpam-5456	528	4	a	a	DET
ejpam-5456	528	5	sadighi	sadighi	NOUN
ejpam-5456	528	6	and	and	CCONJ
ejpam-5456	528	7	dd	dd	VERB
ejpam-5456	528	8	ganji	ganji	X
ejpam-5456	528	9	.	.	PUNCT
ejpam-5456	529	1	analytic	analytic	ADJ
ejpam-5456	529	2	treatment	treatment	NOUN
ejpam-5456	529	3	of	of	ADP
ejpam-5456	529	4	linear	linear	PROPN
ejpam-5456	529	5	and	and	CCONJ
ejpam-5456	529	6	nonlinear	nonlinear	ADJ
ejpam-5456	529	7	schrödinger	schrödinger	NOUN
ejpam-5456	529	8	equations	equation	NOUN
ejpam-5456	529	9	:	:	PUNCT
ejpam-5456	529	10	a	a	DET
ejpam-5456	529	11	study	study	NOUN
ejpam-5456	529	12	with	with	ADP
ejpam-5456	529	13	homotopy	homotopy	NOUN
ejpam-5456	529	14	–	–	PUNCT
ejpam-5456	529	15	perturbation	perturbation	NOUN
ejpam-5456	529	16	and	and	CCONJ
ejpam-5456	529	17	adomian	adomian	NOUN
ejpam-5456	529	18	decomposition	decomposition	NOUN
ejpam-5456	529	19	methods	method	NOUN
ejpam-5456	529	20	.	.	PUNCT
ejpam-5456	530	1	physics	physics	NOUN
ejpam-5456	530	2	letters	letter	NOUN
ejpam-5456	530	3	a	a	DET
ejpam-5456	530	4	,	,	PUNCT
ejpam-5456	530	5	372(4):465–469	372(4):465–469	NOUN
ejpam-5456	530	6	,	,	PUNCT
ejpam-5456	530	7	2008	2008	NUM
ejpam-5456	530	8	.	.	PUNCT
ejpam-5456	531	1	[	[	X
ejpam-5456	531	2	23	23	NUM
ejpam-5456	531	3	]	]	X
ejpam-5456	531	4	babak	babak	NOUN
ejpam-5456	531	5	shiri	shiri	NOUN
ejpam-5456	531	6	and	and	CCONJ
ejpam-5456	531	7	dumitru	dumitru	PROPN
ejpam-5456	531	8	baleanu	baleanu	NOUN
ejpam-5456	531	9	.	.	PUNCT
ejpam-5456	531	10	system	system	NOUN
ejpam-5456	531	11	of	of	ADP
ejpam-5456	531	12	fractional	fractional	ADJ
ejpam-5456	531	13	differential	differential	ADJ
ejpam-5456	531	14	algebraic	algebraic	ADJ
ejpam-5456	531	15	equations	equation	NOUN
ejpam-5456	531	16	with	with	ADP
ejpam-5456	531	17	applications	application	NOUN
ejpam-5456	531	18	.	.	PUNCT
ejpam-5456	532	1	chaos	chaos	NOUN
ejpam-5456	532	2	,	,	PUNCT
ejpam-5456	532	3	solitons	soliton	NOUN
ejpam-5456	532	4	&	&	CCONJ
ejpam-5456	532	5	fractals	fractal	NOUN
ejpam-5456	532	6	,	,	PUNCT
ejpam-5456	532	7	120:203–212	120:203–212	NUM
ejpam-5456	532	8	,	,	PUNCT
ejpam-5456	532	9	2019	2019	NUM
ejpam-5456	532	10	.	.	PUNCT
ejpam-5456	533	1	[	[	X
ejpam-5456	533	2	24	24	NUM
ejpam-5456	533	3	]	]	SYM
ejpam-5456	533	4	mi	mi	PROPN
ejpam-5456	533	5	syam	syam	NOUN
ejpam-5456	533	6	and	and	CCONJ
ejpam-5456	533	7	mohammed	mohammed	PROPN
ejpam-5456	533	8	al	al	PROPN
ejpam-5456	533	9	-	-	PUNCT
ejpam-5456	533	10	refai	refai	PROPN
ejpam-5456	533	11	.	.	PUNCT
ejpam-5456	534	1	fractional	fractional	ADJ
ejpam-5456	534	2	differential	differential	ADJ
ejpam-5456	534	3	equations	equation	NOUN
ejpam-5456	534	4	with	with	ADP
ejpam-5456	534	5	atangana	atangana	PROPN
ejpam-5456	534	6	–	–	PUNCT
ejpam-5456	534	7	baleanu	baleanu	ADJ
ejpam-5456	534	8	fractional	fractional	ADJ
ejpam-5456	534	9	derivative	derivative	NOUN
ejpam-5456	534	10	:	:	PUNCT
ejpam-5456	534	11	analysis	analysis	NOUN
ejpam-5456	534	12	and	and	CCONJ
ejpam-5456	534	13	applications	application	NOUN
ejpam-5456	534	14	.	.	PUNCT
ejpam-5456	535	1	chaos	chaos	NOUN
ejpam-5456	535	2	,	,	PUNCT
ejpam-5456	535	3	solitons	soliton	NOUN
ejpam-5456	535	4	&	&	CCONJ
ejpam-5456	535	5	fractals	fractal	NOUN
ejpam-5456	535	6	:	:	PUNCT
ejpam-5456	535	7	x	x	NOUN
ejpam-5456	535	8	,	,	PUNCT
ejpam-5456	535	9	2:100013	2:100013	NUM
ejpam-5456	535	10	,	,	PUNCT
ejpam-5456	535	11	2019	2019	NUM
ejpam-5456	535	12	.	.	PUNCT
ejpam-5456	536	1	[	[	X
ejpam-5456	536	2	25	25	NUM
ejpam-5456	536	3	]	]	X
ejpam-5456	536	4	junjie	junjie	PROPN
ejpam-5456	536	5	wang	wang	PROPN
ejpam-5456	536	6	.	.	PUNCT
ejpam-5456	537	1	symplectic	symplectic	ADJ
ejpam-5456	537	2	-	-	PUNCT
ejpam-5456	537	3	preserving	preserve	VERB
ejpam-5456	537	4	fourier	fourier	NOUN
ejpam-5456	537	5	spectral	spectral	ADJ
ejpam-5456	537	6	scheme	scheme	NOUN
ejpam-5456	537	7	for	for	ADP
ejpam-5456	537	8	space	space	NOUN
ejpam-5456	537	9	fractional	fractional	PROPN
ejpam-5456	537	10	klein	klein	PROPN
ejpam-5456	537	11	–	–	PUNCT
ejpam-5456	537	12	gordon	gordon	PROPN
ejpam-5456	537	13	–	–	PUNCT
ejpam-5456	537	14	schrödinger	schrödinger	NOUN
ejpam-5456	537	15	equations	equation	NOUN
ejpam-5456	537	16	.	.	PUNCT
ejpam-5456	538	1	numerical	numerical	ADJ
ejpam-5456	538	2	methods	method	NOUN
ejpam-5456	538	3	for	for	ADP
ejpam-5456	538	4	partial	partial	ADJ
ejpam-5456	538	5	differential	differential	NOUN
ejpam-5456	538	6	equations	equation	NOUN
ejpam-5456	538	7	,	,	PUNCT
ejpam-5456	538	8	37(2):1030–1056	37(2):1030–1056	NUM
ejpam-5456	538	9	,	,	PUNCT
ejpam-5456	538	10	2021	2021	NUM
ejpam-5456	538	11	.	.	PUNCT
ejpam-5456	539	1	[	[	X
ejpam-5456	539	2	26	26	NUM
ejpam-5456	539	3	]	]	X
ejpam-5456	539	4	wen	wen	PROPN
ejpam-5456	539	5	-	-	PROPN
ejpam-5456	539	6	ze	ze	PROPN
ejpam-5456	539	7	wu	wu	PROPN
ejpam-5456	539	8	,	,	PUNCT
ejpam-5456	539	9	liang	liang	PROPN
ejpam-5456	539	10	zeng	zeng	PROPN
ejpam-5456	539	11	,	,	PUNCT
ejpam-5456	539	12	chong	chong	PROPN
ejpam-5456	539	13	liu	liu	PROPN
ejpam-5456	539	14	,	,	PUNCT
ejpam-5456	539	15	wanli	wanli	PROPN
ejpam-5456	539	16	xie	xie	PROPN
ejpam-5456	539	17	,	,	PUNCT
ejpam-5456	539	18	and	and	CCONJ
ejpam-5456	539	19	mark	mark	PROPN
ejpam-5456	539	20	goh	goh	PROPN
ejpam-5456	539	21	.	.	PUNCT
ejpam-5456	540	1	a	a	DET
ejpam-5456	540	2	time	time	NOUN
ejpam-5456	540	3	powerbased	powerbase	VERB
ejpam-5456	540	4	grey	grey	PROPN
ejpam-5456	540	5	model	model	NOUN
ejpam-5456	540	6	with	with	ADP
ejpam-5456	540	7	conformable	conformable	ADJ
ejpam-5456	540	8	fractional	fractional	ADJ
ejpam-5456	540	9	derivative	derivative	NOUN
ejpam-5456	540	10	and	and	CCONJ
ejpam-5456	540	11	its	its	PRON
ejpam-5456	540	12	applications	application	NOUN
ejpam-5456	540	13	.	.	PUNCT
ejpam-5456	541	1	chaos	chaos	NOUN
ejpam-5456	541	2	,	,	PUNCT
ejpam-5456	541	3	solitons	soliton	NOUN
ejpam-5456	541	4	&	&	CCONJ
ejpam-5456	541	5	fractals	fractal	NOUN
ejpam-5456	541	6	,	,	PUNCT
ejpam-5456	541	7	155:111657	155:111657	NUM
ejpam-5456	541	8	,	,	PUNCT
ejpam-5456	541	9	2022	2022	NUM
ejpam-5456	541	10	.	.	PUNCT
ejpam-5456	542	1	[	[	X
ejpam-5456	542	2	27	27	NUM
ejpam-5456	542	3	]	]	PUNCT
ejpam-5456	542	4	zichen	zichen	NOUN
ejpam-5456	542	5	yao	yao	PROPN
ejpam-5456	542	6	,	,	PUNCT
ejpam-5456	542	7	zhanwen	zhanwen	PROPN
ejpam-5456	542	8	yang	yang	PROPN
ejpam-5456	542	9	,	,	PUNCT
ejpam-5456	542	10	and	and	CCONJ
ejpam-5456	542	11	jianfang	jianfang	PROPN
ejpam-5456	542	12	gao	gao	PROPN
ejpam-5456	542	13	.	.	PUNCT
ejpam-5456	543	1	unconditional	unconditional	ADJ
ejpam-5456	543	2	stability	stability	NOUN
ejpam-5456	543	3	analysis	analysis	NOUN
ejpam-5456	543	4	of	of	ADP
ejpam-5456	543	5	grünwald	grünwald	ADJ
ejpam-5456	543	6	letnikov	letnikov	NOUN
ejpam-5456	543	7	method	method	NOUN
ejpam-5456	543	8	for	for	ADP
ejpam-5456	543	9	fractional	fractional	ADJ
ejpam-5456	543	10	-	-	PUNCT
ejpam-5456	543	11	order	order	NOUN
ejpam-5456	543	12	delay	delay	NOUN
ejpam-5456	543	13	differential	differential	ADJ
ejpam-5456	543	14	equations	equation	NOUN
ejpam-5456	543	15	.	.	PUNCT
ejpam-5456	544	1	chaos	chaos	NOUN
ejpam-5456	544	2	,	,	PUNCT
ejpam-5456	544	3	solitons	soliton	NOUN
ejpam-5456	544	4	&	&	CCONJ
ejpam-5456	544	5	fractals	fractal	NOUN
ejpam-5456	544	6	,	,	PUNCT
ejpam-5456	544	7	177:114193	177:114193	NUM
ejpam-5456	544	8	,	,	PUNCT
ejpam-5456	544	9	2023	2023	NUM
ejpam-5456	544	10	.	.	PUNCT
ejpam-5456	545	1	[	[	X
ejpam-5456	545	2	28	28	NUM
ejpam-5456	545	3	]	]	X
ejpam-5456	545	4	mina	mina	PROPN
ejpam-5456	545	5	yavari	yavari	PROPN
ejpam-5456	545	6	and	and	CCONJ
ejpam-5456	545	7	alireza	alireza	PROPN
ejpam-5456	545	8	nazemi	nazemi	PROPN
ejpam-5456	545	9	.	.	PUNCT
ejpam-5456	546	1	on	on	ADP
ejpam-5456	546	2	fractional	fractional	ADJ
ejpam-5456	546	3	infinite	infinite	NOUN
ejpam-5456	546	4	-	-	PUNCT
ejpam-5456	546	5	horizon	horizon	NOUN
ejpam-5456	546	6	optimal	optimal	ADJ
ejpam-5456	546	7	control	control	NOUN
ejpam-5456	546	8	problems	problem	NOUN
ejpam-5456	546	9	with	with	ADP
ejpam-5456	546	10	a	a	DET
ejpam-5456	546	11	combination	combination	NOUN
ejpam-5456	546	12	of	of	ADP
ejpam-5456	546	13	conformable	conformable	NOUN
ejpam-5456	546	14	and	and	CCONJ
ejpam-5456	546	15	caputo	caputo	PROPN
ejpam-5456	546	16	–	–	PUNCT
ejpam-5456	546	17	fabrizio	fabrizio	ADJ
ejpam-5456	546	18	fractional	fractional	ADJ
ejpam-5456	546	19	derivatives	derivative	NOUN
ejpam-5456	546	20	.	.	PUNCT
ejpam-5456	547	1	isa	isa	NOUN
ejpam-5456	547	2	transactions	transaction	NOUN
ejpam-5456	547	3	,	,	PUNCT
ejpam-5456	547	4	101:78–90	101:78–90	PROPN
ejpam-5456	547	5	,	,	PUNCT
ejpam-5456	547	6	2020	2020	NUM
ejpam-5456	547	7	.	.	PUNCT
ejpam-5456	548	1	[	[	X
ejpam-5456	548	2	29	29	NUM
ejpam-5456	548	3	]	]	X
ejpam-5456	548	4	ahmet	ahmet	PROPN
ejpam-5456	548	5	yildirim	yildirim	PROPN
ejpam-5456	548	6	.	.	PUNCT
ejpam-5456	549	1	an	an	DET
ejpam-5456	549	2	algorithm	algorithm	NOUN
ejpam-5456	549	3	for	for	ADP
ejpam-5456	549	4	solving	solve	VERB
ejpam-5456	549	5	the	the	DET
ejpam-5456	549	6	fractional	fractional	ADJ
ejpam-5456	549	7	nonlinear	nonlinear	NOUN
ejpam-5456	549	8	schrödinger	schrödinger	NOUN
ejpam-5456	549	9	equation	equation	NOUN
ejpam-5456	549	10	by	by	ADP
ejpam-5456	549	11	means	mean	NOUN
ejpam-5456	549	12	of	of	ADP
ejpam-5456	549	13	the	the	DET
ejpam-5456	549	14	homotopy	homotopy	NOUN
ejpam-5456	549	15	perturbation	perturbation	NOUN
ejpam-5456	549	16	method	method	NOUN
ejpam-5456	549	17	.	.	PUNCT
ejpam-5456	550	1	international	international	ADJ
ejpam-5456	550	2	journal	journal	PROPN
ejpam-5456	550	3	of	of	ADP
ejpam-5456	550	4	nonlinear	nonlinear	PROPN
ejpam-5456	550	5	sciences	sciences	PROPN
ejpam-5456	550	6	and	and	CCONJ
ejpam-5456	550	7	numerical	numerical	PROPN
ejpam-5456	550	8	simulation	simulation	PROPN
ejpam-5456	550	9	,	,	PUNCT
ejpam-5456	550	10	10(4):445–450	10(4):445–450	PROPN
ejpam-5456	550	11	,	,	PUNCT
ejpam-5456	550	12	2009	2009	NUM
ejpam-5456	550	13	.	.	PUNCT
ejpam-5456	551	1	[	[	X
ejpam-5456	551	2	30	30	NUM
ejpam-5456	551	3	]	]	X
ejpam-5456	551	4	tianwei	tianwei	PROPN
ejpam-5456	551	5	zhang	zhang	PROPN
ejpam-5456	551	6	and	and	CCONJ
ejpam-5456	551	7	yongkun	yongkun	PROPN
ejpam-5456	551	8	li	li	PROPN
ejpam-5456	551	9	.	.	PROPN
ejpam-5456	551	10	exponential	exponential	PROPN
ejpam-5456	551	11	euler	euler	PROPN
ejpam-5456	551	12	scheme	scheme	NOUN
ejpam-5456	551	13	of	of	ADP
ejpam-5456	551	14	multi	multi	ADJ
ejpam-5456	551	15	-	-	ADJ
ejpam-5456	551	16	delay	delay	ADJ
ejpam-5456	551	17	caputo	caputo	PROPN
ejpam-5456	551	18	–	–	PUNCT
ejpam-5456	551	19	fabrizio	fabrizio	ADJ
ejpam-5456	551	20	fractional	fractional	ADJ
ejpam-5456	551	21	-	-	PUNCT
ejpam-5456	551	22	order	order	NOUN
ejpam-5456	551	23	differential	differential	ADJ
ejpam-5456	551	24	equations	equation	NOUN
ejpam-5456	551	25	.	.	PUNCT
ejpam-5456	552	1	applied	apply	VERB
ejpam-5456	552	2	mathematics	mathematics	NOUN
ejpam-5456	552	3	letters	letter	NOUN
ejpam-5456	552	4	,	,	PUNCT
ejpam-5456	552	5	124:107709	124:107709	NUM
ejpam-5456	552	6	,	,	PUNCT
ejpam-5456	552	7	2022	2022	NUM
ejpam-5456	552	8	.	.	PUNCT
ejpam-5456	553	1	references	reference	NOUN
ejpam-5456	553	2	3491	3491	NUM
ejpam-5456	553	3	[	[	X
ejpam-5456	553	4	31	31	NUM
ejpam-5456	553	5	]	]	PUNCT
ejpam-5456	553	6	tianwei	tianwei	PROPN
ejpam-5456	553	7	zhang	zhang	PROPN
ejpam-5456	553	8	and	and	CCONJ
ejpam-5456	553	9	yongkun	yongkun	PROPN
ejpam-5456	553	10	li	li	PROPN
ejpam-5456	553	11	.	.	PROPN
ejpam-5456	553	12	global	global	ADJ
ejpam-5456	553	13	exponential	exponential	ADJ
ejpam-5456	553	14	stability	stability	NOUN
ejpam-5456	553	15	of	of	ADP
ejpam-5456	553	16	discrete	discrete	ADJ
ejpam-5456	553	17	–	–	PUNCT
ejpam-5456	553	18	time	time	NOUN
ejpam-5456	553	19	almost	almost	ADV
ejpam-5456	553	20	automorphic	automorphic	ADJ
ejpam-5456	553	21	caputo	caputo	PROPN
ejpam-5456	553	22	–	–	PUNCT
ejpam-5456	553	23	fabrizio	fabrizio	PROPN
ejpam-5456	553	24	bam	bam	NOUN
ejpam-5456	553	25	fuzzy	fuzzy	ADJ
ejpam-5456	553	26	neural	neural	ADJ
ejpam-5456	553	27	networks	network	NOUN
ejpam-5456	553	28	via	via	ADP
ejpam-5456	553	29	exponential	exponential	NOUN
ejpam-5456	553	30	euler	euler	NOUN
ejpam-5456	553	31	technique	technique	NOUN
ejpam-5456	553	32	.	.	PUNCT
ejpam-5456	554	1	knowledge	knowledge	NOUN
ejpam-5456	554	2	-	-	PUNCT
ejpam-5456	554	3	based	base	VERB
ejpam-5456	554	4	systems	system	NOUN
ejpam-5456	554	5	,	,	PUNCT
ejpam-5456	554	6	246:108675	246:108675	NUM
ejpam-5456	554	7	,	,	PUNCT
ejpam-5456	554	8	2022	2022	NUM
ejpam-5456	554	9	.	.	PUNCT
ejpam-5456	555	1	[	[	X
ejpam-5456	555	2	32	32	NUM
ejpam-5456	555	3	]	]	PUNCT
ejpam-5456	555	4	tianwei	tianwei	PROPN
ejpam-5456	555	5	zhang	zhang	PROPN
ejpam-5456	555	6	and	and	CCONJ
ejpam-5456	555	7	yongkun	yongkun	PROPN
ejpam-5456	555	8	li	li	PROPN
ejpam-5456	555	9	.	.	PROPN
ejpam-5456	555	10	s	s	PART
ejpam-5456	555	11	-	-	PUNCT
ejpam-5456	555	12	asymptotically	asymptotically	ADV
ejpam-5456	555	13	periodic	periodic	ADJ
ejpam-5456	555	14	fractional	fractional	ADJ
ejpam-5456	555	15	functional	functional	ADJ
ejpam-5456	555	16	differential	differential	ADJ
ejpam-5456	555	17	equations	equation	NOUN
ejpam-5456	555	18	with	with	ADP
ejpam-5456	555	19	off	off	ADP
ejpam-5456	555	20	-	-	PUNCT
ejpam-5456	555	21	diagonal	diagonal	ADJ
ejpam-5456	555	22	matrix	matrix	NOUN
ejpam-5456	555	23	mittag	mittag	ADJ
ejpam-5456	555	24	–	–	PUNCT
ejpam-5456	555	25	leffler	leffler	NOUN
ejpam-5456	555	26	function	function	NOUN
ejpam-5456	555	27	kernels	kernel	NOUN
ejpam-5456	555	28	.	.	PUNCT
ejpam-5456	556	1	mathematics	mathematic	NOUN
ejpam-5456	556	2	and	and	CCONJ
ejpam-5456	556	3	computers	computer	NOUN
ejpam-5456	556	4	in	in	ADP
ejpam-5456	556	5	simulation	simulation	NOUN
ejpam-5456	556	6	,	,	PUNCT
ejpam-5456	556	7	193:331–347	193:331–347	NUM
ejpam-5456	556	8	,	,	PUNCT
ejpam-5456	556	9	2022	2022	NUM
ejpam-5456	556	10	.	.	PUNCT
ejpam-5456	557	1	[	[	X
ejpam-5456	557	2	33	33	NUM
ejpam-5456	557	3	]	]	PUNCT
ejpam-5456	557	4	tianwei	tianwei	PROPN
ejpam-5456	557	5	zhang	zhang	PROPN
ejpam-5456	557	6	,	,	PUNCT
ejpam-5456	557	7	yongkun	yongkun	PROPN
ejpam-5456	557	8	li	li	PROPN
ejpam-5456	557	9	,	,	PUNCT
ejpam-5456	557	10	and	and	CCONJ
ejpam-5456	557	11	jianwen	jianwen	NOUN
ejpam-5456	557	12	zhou	zhou	PROPN
ejpam-5456	557	13	.	.	PUNCT
ejpam-5456	558	1	almost	almost	ADV
ejpam-5456	558	2	automorphic	automorphic	ADJ
ejpam-5456	558	3	strong	strong	ADJ
ejpam-5456	558	4	oscillation	oscillation	NOUN
ejpam-5456	558	5	in	in	ADP
ejpam-5456	558	6	time	time	NOUN
ejpam-5456	558	7	-	-	PUNCT
ejpam-5456	558	8	fractional	fractional	ADJ
ejpam-5456	558	9	parabolic	parabolic	NOUN
ejpam-5456	558	10	equations	equation	NOUN
ejpam-5456	558	11	.	.	PUNCT
ejpam-5456	559	1	fractal	fractal	PROPN
ejpam-5456	559	2	and	and	CCONJ
ejpam-5456	559	3	fractional	fractional	ADJ
ejpam-5456	559	4	,	,	PUNCT
ejpam-5456	559	5	7(1):88	7(1):88	NUM
ejpam-5456	559	6	,	,	PUNCT
ejpam-5456	559	7	2023	2023	NUM
ejpam-5456	559	8	.	.	PUNCT
ejpam-5456	560	1	[	[	X
ejpam-5456	560	2	34	34	NUM
ejpam-5456	560	3	]	]	PUNCT
ejpam-5456	560	4	tianwei	tianwei	PROPN
ejpam-5456	560	5	zhang	zhang	PROPN
ejpam-5456	560	6	,	,	PUNCT
ejpam-5456	560	7	huizhen	huizhen	PROPN
ejpam-5456	560	8	qu	qu	PROPN
ejpam-5456	560	9	,	,	PUNCT
ejpam-5456	560	10	and	and	CCONJ
ejpam-5456	560	11	jianwen	jianwen	PROPN
ejpam-5456	560	12	zhou	zhou	PROPN
ejpam-5456	560	13	.	.	PUNCT
ejpam-5456	561	1	asymptotically	asymptotically	ADV
ejpam-5456	561	2	almost	almost	ADV
ejpam-5456	561	3	periodic	periodic	ADJ
ejpam-5456	561	4	synchronization	synchronization	NOUN
ejpam-5456	561	5	in	in	ADP
ejpam-5456	561	6	fuzzy	fuzzy	ADJ
ejpam-5456	561	7	competitive	competitive	ADJ
ejpam-5456	561	8	neural	neural	ADJ
ejpam-5456	561	9	networks	network	NOUN
ejpam-5456	561	10	with	with	ADP
ejpam-5456	561	11	caputo	caputo	PROPN
ejpam-5456	561	12	-	-	PUNCT
ejpam-5456	561	13	fabrizio	fabrizio	PROPN
ejpam-5456	561	14	operator	operator	NOUN
ejpam-5456	561	15	.	.	PUNCT
ejpam-5456	562	1	fuzzy	fuzzy	ADJ
ejpam-5456	562	2	sets	set	NOUN
ejpam-5456	562	3	and	and	CCONJ
ejpam-5456	562	4	systems	system	NOUN
ejpam-5456	562	5	,	,	PUNCT
ejpam-5456	562	6	471:108676	471:108676	NUM
ejpam-5456	562	7	,	,	PUNCT
ejpam-5456	562	8	2023	2023	NUM
ejpam-5456	562	9	.	.	PUNCT
ejpam-5456	563	1	[	[	X
ejpam-5456	563	2	35	35	NUM
ejpam-5456	563	3	]	]	PUNCT
ejpam-5456	563	4	tianwei	tianwei	X
ejpam-5456	563	5	zhang	zhang	PROPN
ejpam-5456	563	6	and	and	CCONJ
ejpam-5456	563	7	lianglin	lianglin	PROPN
ejpam-5456	563	8	xiong	xiong	PROPN
ejpam-5456	563	9	.	.	PUNCT
ejpam-5456	564	1	periodic	periodic	ADJ
ejpam-5456	564	2	motion	motion	NOUN
ejpam-5456	564	3	for	for	ADP
ejpam-5456	564	4	impulsive	impulsive	ADJ
ejpam-5456	564	5	fractional	fractional	ADJ
ejpam-5456	564	6	functional	functional	ADJ
ejpam-5456	564	7	differential	differential	ADJ
ejpam-5456	564	8	equations	equation	NOUN
ejpam-5456	564	9	with	with	ADP
ejpam-5456	564	10	piecewise	piecewise	PROPN
ejpam-5456	564	11	caputo	caputo	PROPN
ejpam-5456	564	12	derivative	derivative	PROPN
ejpam-5456	564	13	.	.	PUNCT
ejpam-5456	565	1	applied	apply	VERB
ejpam-5456	565	2	mathematics	mathematics	NOUN
ejpam-5456	565	3	letters	letter	NOUN
ejpam-5456	565	4	,	,	PUNCT
ejpam-5456	565	5	101:106072	101:106072	NUM
ejpam-5456	565	6	,	,	PUNCT
ejpam-5456	565	7	2020	2020	NUM
ejpam-5456	565	8	.	.	PUNCT
ejpam-5456	566	1	[	[	X
ejpam-5456	566	2	36	36	NUM
ejpam-5456	566	3	]	]	X
ejpam-5456	566	4	yu	yu	PROPN
ejpam-5456	566	5	zhang	zhang	PROPN
ejpam-5456	566	6	,	,	PUNCT
ejpam-5456	566	7	amit	amit	PROPN
ejpam-5456	566	8	kumar	kumar	PROPN
ejpam-5456	566	9	,	,	PUNCT
ejpam-5456	566	10	sunil	sunil	PROPN
ejpam-5456	566	11	kumar	kumar	PROPN
ejpam-5456	566	12	,	,	PUNCT
ejpam-5456	566	13	dumitru	dumitru	PROPN
ejpam-5456	566	14	baleanu	baleanu	NOUN
ejpam-5456	566	15	,	,	PUNCT
ejpam-5456	566	16	and	and	CCONJ
ejpam-5456	566	17	xiao	xiao	PROPN
ejpam-5456	566	18	-	-	PUNCT
ejpam-5456	566	19	jun	jun	PROPN
ejpam-5456	566	20	yang	yang	PROPN
ejpam-5456	566	21	.	.	PUNCT
ejpam-5456	567	1	residual	residual	ADJ
ejpam-5456	567	2	power	power	NOUN
ejpam-5456	567	3	series	series	PROPN
ejpam-5456	567	4	method	method	NOUN
ejpam-5456	567	5	for	for	ADP
ejpam-5456	567	6	time	time	NOUN
ejpam-5456	567	7	–	–	PUNCT
ejpam-5456	567	8	fractional	fractional	ADJ
ejpam-5456	567	9	schrödinger	schrödinger	NOUN
ejpam-5456	567	10	equations	equation	NOUN
ejpam-5456	567	11	.	.	PUNCT
ejpam-5456	568	1	j.	j.	PROPN
ejpam-5456	568	2	nonlinear	nonlinear	PROPN
ejpam-5456	568	3	sci	sci	PROPN
ejpam-5456	568	4	.	.	PUNCT
ejpam-5456	568	5	appl	appl	PROPN
ejpam-5456	568	6	,	,	PUNCT
ejpam-5456	568	7	9(11):5821–5829	9(11):5821–5829	NUM
ejpam-5456	568	8	,	,	PUNCT
ejpam-5456	568	9	2016	2016	NUM
ejpam-5456	568	10	.	.	PUNCT
ejpam-5456	569	1	[	[	X
ejpam-5456	569	2	37	37	NUM
ejpam-5456	569	3	]	]	X
ejpam-5456	569	4	yu	yu	PROPN
ejpam-5456	569	5	zhang	zhang	PROPN
ejpam-5456	569	6	,	,	PUNCT
ejpam-5456	569	7	amit	amit	PROPN
ejpam-5456	569	8	kumar	kumar	PROPN
ejpam-5456	569	9	,	,	PUNCT
ejpam-5456	569	10	sunil	sunil	PROPN
ejpam-5456	569	11	kumar	kumar	PROPN
ejpam-5456	569	12	,	,	PUNCT
ejpam-5456	569	13	dumitru	dumitru	PROPN
ejpam-5456	569	14	baleanu	baleanu	NOUN
ejpam-5456	569	15	,	,	PUNCT
ejpam-5456	569	16	and	and	CCONJ
ejpam-5456	569	17	xiao	xiao	PROPN
ejpam-5456	569	18	-	-	PUNCT
ejpam-5456	569	19	jun	jun	PROPN
ejpam-5456	569	20	yang	yang	PROPN
ejpam-5456	569	21	.	.	PUNCT
ejpam-5456	570	1	residual	residual	ADJ
ejpam-5456	570	2	power	power	NOUN
ejpam-5456	570	3	series	series	PROPN
ejpam-5456	570	4	method	method	NOUN
ejpam-5456	570	5	for	for	ADP
ejpam-5456	570	6	time	time	NOUN
ejpam-5456	570	7	–	–	PUNCT
ejpam-5456	570	8	fractional	fractional	ADJ
ejpam-5456	570	9	schrödinger	schrödinger	NOUN
ejpam-5456	570	10	equations	equation	NOUN
ejpam-5456	570	11	.	.	PUNCT
ejpam-5456	571	1	j.	j.	PROPN
ejpam-5456	571	2	nonlinear	nonlinear	PROPN
ejpam-5456	571	3	sci	sci	PROPN
ejpam-5456	571	4	.	.	PUNCT
ejpam-5456	571	5	appl	appl	PROPN
ejpam-5456	571	6	,	,	PUNCT
ejpam-5456	571	7	9(11):5821–5829	9(11):5821–5829	NUM
ejpam-5456	571	8	,	,	PUNCT
ejpam-5456	571	9	2016	2016	NUM
ejpam-5456	571	10	.	.	PUNCT