id	sid	tid	token	lemma	pos
ejpam-6734	1	1	european	european	PROPN
ejpam-6734	1	2	journal	journal	PROPN
ejpam-6734	1	3	of	of	ADP
ejpam-6734	1	4	pure	pure	ADJ
ejpam-6734	1	5	and	and	CCONJ
ejpam-6734	1	6	applied	applied	ADJ
ejpam-6734	1	7	mathematics	mathematic	NOUN
ejpam-6734	1	8	2025	2025	NUM
ejpam-6734	1	9	,	,	PUNCT
ejpam-6734	1	10	vol	vol	NOUN
ejpam-6734	1	11	.	.	PROPN
ejpam-6734	1	12	18	18	NUM
ejpam-6734	1	13	,	,	PUNCT
ejpam-6734	1	14	issue	issue	NOUN
ejpam-6734	1	15	4	4	NUM
ejpam-6734	1	16	,	,	PUNCT
ejpam-6734	1	17	article	article	NOUN
ejpam-6734	1	18	number	number	NOUN
ejpam-6734	1	19	6734	6734	NUM
ejpam-6734	1	20	issn	issn	PROPN
ejpam-6734	1	21	1307	1307	NUM
ejpam-6734	1	22	-	-	SYM
ejpam-6734	1	23	5543	5543	NUM
ejpam-6734	1	24	–	–	PUNCT
ejpam-6734	1	25	ejpam.com	ejpam.com	X
ejpam-6734	1	26	published	publish	VERB
ejpam-6734	1	27	by	by	ADP
ejpam-6734	1	28	new	new	PROPN
ejpam-6734	1	29	york	york	PROPN
ejpam-6734	1	30	business	business	PROPN
ejpam-6734	1	31	global	global	ADJ
ejpam-6734	1	32	comparative	comparative	ADJ
ejpam-6734	1	33	analysis	analysis	NOUN
ejpam-6734	1	34	of	of	ADP
ejpam-6734	1	35	the	the	DET
ejpam-6734	1	36	differential	differential	ADJ
ejpam-6734	1	37	transform	transform	NOUN
ejpam-6734	1	38	method	method	NOUN
ejpam-6734	1	39	and	and	CCONJ
ejpam-6734	1	40	generalized	generalized	ADJ
ejpam-6734	1	41	fibonacci	fibonacci	NOUN
ejpam-6734	1	42	collocation	collocation	NOUN
ejpam-6734	1	43	method	method	NOUN
ejpam-6734	1	44	for	for	ADP
ejpam-6734	1	45	solving	solve	VERB
ejpam-6734	1	46	differential	differential	ADJ
ejpam-6734	1	47	equations	equation	NOUN
ejpam-6734	1	48	maha	maha	PROPN
ejpam-6734	1	49	abdalla	abdalla	PROPN
ejpam-6734	2	1	abdou1	abdou1	PROPN
ejpam-6734	2	2	,	,	PUNCT
ejpam-6734	2	3	amany	amany	PROPN
ejpam-6734	2	4	saad	saad	PROPN
ejpam-6734	2	5	mohamed2,∗	mohamed2,∗	PROPN
ejpam-6734	2	6	1	1	NUM
ejpam-6734	2	7	department	department	NOUN
ejpam-6734	2	8	of	of	ADP
ejpam-6734	2	9	mathematics	mathematic	NOUN
ejpam-6734	2	10	,	,	PUNCT
ejpam-6734	2	11	faculty	faculty	NOUN
ejpam-6734	2	12	of	of	ADP
ejpam-6734	2	13	education	education	NOUN
ejpam-6734	2	14	,	,	PUNCT
ejpam-6734	2	15	international	international	ADJ
ejpam-6734	2	16	university	university	PROPN
ejpam-6734	2	17	of	of	ADP
ejpam-6734	2	18	islamic	islamic	ADJ
ejpam-6734	2	19	and	and	CCONJ
ejpam-6734	2	20	linguistic	linguistic	ADJ
ejpam-6734	2	21	sciences	science	NOUN
ejpam-6734	2	22	,	,	PUNCT
ejpam-6734	2	23	postgraduate	postgraduate	ADJ
ejpam-6734	2	24	studies	study	NOUN
ejpam-6734	2	25	2	2	NUM
ejpam-6734	2	26	department	department	NOUN
ejpam-6734	2	27	of	of	ADP
ejpam-6734	2	28	mathematics	mathematic	NOUN
ejpam-6734	2	29	,	,	PUNCT
ejpam-6734	2	30	faculty	faculty	NOUN
ejpam-6734	2	31	of	of	ADP
ejpam-6734	2	32	science	science	NOUN
ejpam-6734	2	33	,	,	PUNCT
ejpam-6734	2	34	helwan	helwan	PROPN
ejpam-6734	2	35	university	university	PROPN
ejpam-6734	2	36	,	,	PUNCT
ejpam-6734	2	37	cairo	cairo	PROPN
ejpam-6734	2	38	,	,	PUNCT
ejpam-6734	2	39	egypt	egypt	PROPN
ejpam-6734	2	40	abstract	abstract	PROPN
ejpam-6734	2	41	.	.	PUNCT
ejpam-6734	3	1	this	this	DET
ejpam-6734	3	2	study	study	NOUN
ejpam-6734	3	3	investigates	investigate	VERB
ejpam-6734	3	4	two	two	NUM
ejpam-6734	3	5	ways	way	NOUN
ejpam-6734	3	6	of	of	ADP
ejpam-6734	3	7	discussing	discuss	VERB
ejpam-6734	3	8	the	the	DET
ejpam-6734	3	9	solution	solution	NOUN
ejpam-6734	3	10	of	of	ADP
ejpam-6734	3	11	linear	linear	ADJ
ejpam-6734	3	12	,	,	PUNCT
ejpam-6734	3	13	mixed	mixed	ADJ
ejpam-6734	3	14	,	,	PUNCT
ejpam-6734	3	15	and	and	CCONJ
ejpam-6734	3	16	special	special	ADJ
ejpam-6734	3	17	nonlinear	nonlinear	ADJ
ejpam-6734	3	18	models	model	NOUN
ejpam-6734	3	19	of	of	ADP
ejpam-6734	3	20	second	second	ADJ
ejpam-6734	3	21	-	-	PUNCT
ejpam-6734	3	22	order	order	NOUN
ejpam-6734	3	23	differential	differential	ADJ
ejpam-6734	3	24	equations	equation	NOUN
ejpam-6734	3	25	:	:	PUNCT
ejpam-6734	3	26	the	the	DET
ejpam-6734	3	27	differential	differential	ADJ
ejpam-6734	3	28	transform	transform	NOUN
ejpam-6734	3	29	method	method	NOUN
ejpam-6734	3	30	and	and	CCONJ
ejpam-6734	3	31	the	the	DET
ejpam-6734	3	32	generalized	generalize	VERB
ejpam-6734	3	33	fibonacci	fibonacci	NOUN
ejpam-6734	3	34	collocation	collocation	NOUN
ejpam-6734	3	35	method	method	NOUN
ejpam-6734	3	36	.	.	PUNCT
ejpam-6734	4	1	the	the	DET
ejpam-6734	4	2	differential	differential	ADJ
ejpam-6734	4	3	transform	transform	NOUN
ejpam-6734	4	4	method	method	NOUN
ejpam-6734	4	5	uses	use	VERB
ejpam-6734	4	6	a	a	DET
ejpam-6734	4	7	stepby	stepby	ADJ
ejpam-6734	4	8	-	-	PUNCT
ejpam-6734	4	9	step	step	NOUN
ejpam-6734	4	10	approach	approach	NOUN
ejpam-6734	4	11	to	to	PART
ejpam-6734	4	12	convert	convert	VERB
ejpam-6734	4	13	differential	differential	ADJ
ejpam-6734	4	14	equations	equation	NOUN
ejpam-6734	4	15	and	and	CCONJ
ejpam-6734	4	16	their	their	PRON
ejpam-6734	4	17	conditions	condition	NOUN
ejpam-6734	4	18	into	into	ADP
ejpam-6734	4	19	power	power	NOUN
ejpam-6734	4	20	series	series	NOUN
ejpam-6734	4	21	,	,	PUNCT
ejpam-6734	4	22	giving	give	VERB
ejpam-6734	4	23	an	an	DET
ejpam-6734	4	24	exact	exact	ADJ
ejpam-6734	4	25	or	or	CCONJ
ejpam-6734	4	26	highly	highly	ADV
ejpam-6734	4	27	accurate	accurate	ADJ
ejpam-6734	4	28	solution	solution	NOUN
ejpam-6734	4	29	.	.	PUNCT
ejpam-6734	5	1	on	on	ADP
ejpam-6734	5	2	the	the	DET
ejpam-6734	5	3	other	other	ADJ
ejpam-6734	5	4	hand	hand	NOUN
ejpam-6734	5	5	,	,	PUNCT
ejpam-6734	5	6	the	the	DET
ejpam-6734	5	7	generalized	generalize	VERB
ejpam-6734	5	8	fibonacci	fibonacci	NOUN
ejpam-6734	5	9	collocation	collocation	NOUN
ejpam-6734	5	10	method	method	NOUN
ejpam-6734	5	11	transforms	transform	VERB
ejpam-6734	5	12	the	the	DET
ejpam-6734	5	13	problem	problem	NOUN
ejpam-6734	5	14	into	into	ADP
ejpam-6734	5	15	a	a	DET
ejpam-6734	5	16	system	system	NOUN
ejpam-6734	5	17	of	of	ADP
ejpam-6734	5	18	equations	equation	NOUN
ejpam-6734	5	19	with	with	ADP
ejpam-6734	5	20	unknown	unknown	ADJ
ejpam-6734	5	21	coefficients	coefficient	NOUN
ejpam-6734	5	22	,	,	PUNCT
ejpam-6734	5	23	which	which	PRON
ejpam-6734	5	24	are	be	AUX
ejpam-6734	5	25	determined	determine	VERB
ejpam-6734	5	26	by	by	ADP
ejpam-6734	5	27	solving	solve	VERB
ejpam-6734	5	28	this	this	DET
ejpam-6734	5	29	system	system	NOUN
ejpam-6734	5	30	using	use	VERB
ejpam-6734	5	31	matrix	matrix	NOUN
ejpam-6734	5	32	operations	operation	NOUN
ejpam-6734	5	33	.	.	PUNCT
ejpam-6734	6	1	it	it	PRON
ejpam-6734	6	2	yields	yield	VERB
ejpam-6734	6	3	a	a	DET
ejpam-6734	6	4	numerical	numerical	ADJ
ejpam-6734	6	5	solution	solution	NOUN
ejpam-6734	6	6	.	.	PUNCT
ejpam-6734	7	1	we	we	PRON
ejpam-6734	7	2	discuss	discuss	VERB
ejpam-6734	7	3	convergence	convergence	NOUN
ejpam-6734	7	4	and	and	CCONJ
ejpam-6734	7	5	error	error	NOUN
ejpam-6734	7	6	bounds	bound	NOUN
ejpam-6734	7	7	of	of	ADP
ejpam-6734	7	8	generalized	generalized	ADJ
ejpam-6734	7	9	fibonacci	fibonacci	NOUN
ejpam-6734	7	10	polynomials	polynomial	NOUN
ejpam-6734	7	11	in	in	ADP
ejpam-6734	7	12	detail	detail	NOUN
ejpam-6734	7	13	.	.	PUNCT
ejpam-6734	8	1	this	this	DET
ejpam-6734	8	2	study	study	NOUN
ejpam-6734	8	3	evaluates	evaluate	VERB
ejpam-6734	8	4	the	the	DET
ejpam-6734	8	5	solutions	solution	NOUN
ejpam-6734	8	6	of	of	ADP
ejpam-6734	8	7	four	four	NUM
ejpam-6734	8	8	different	different	ADJ
ejpam-6734	8	9	problems	problem	NOUN
ejpam-6734	8	10	,	,	PUNCT
ejpam-6734	8	11	focusing	focus	VERB
ejpam-6734	8	12	on	on	ADP
ejpam-6734	8	13	their	their	PRON
ejpam-6734	8	14	reliability	reliability	NOUN
ejpam-6734	8	15	and	and	CCONJ
ejpam-6734	8	16	accuracy	accuracy	NOUN
ejpam-6734	8	17	.	.	PUNCT
ejpam-6734	9	1	this	this	DET
ejpam-6734	9	2	comparison	comparison	NOUN
ejpam-6734	9	3	shows	show	VERB
ejpam-6734	9	4	that	that	SCONJ
ejpam-6734	9	5	our	our	PRON
ejpam-6734	9	6	algorithms	algorithm	NOUN
ejpam-6734	9	7	are	be	AUX
ejpam-6734	9	8	efficient	efficient	ADJ
ejpam-6734	9	9	.	.	PUNCT
ejpam-6734	10	1	2020	2020	NUM
ejpam-6734	10	2	mathematics	mathematic	NOUN
ejpam-6734	10	3	subject	subject	NOUN
ejpam-6734	10	4	classifications	classification	NOUN
ejpam-6734	10	5	:	:	PUNCT
ejpam-6734	10	6	65l05	65l05	NUM
ejpam-6734	10	7	,	,	PUNCT
ejpam-6734	10	8	65l70	65l70	NUM
ejpam-6734	10	9	,	,	PUNCT
ejpam-6734	10	10	34a34	34a34	NUM
ejpam-6734	10	11	,	,	PUNCT
ejpam-6734	10	12	41a10	41a10	NUM
ejpam-6734	10	13	key	key	ADJ
ejpam-6734	10	14	words	word	NOUN
ejpam-6734	10	15	and	and	CCONJ
ejpam-6734	10	16	phrases	phrase	NOUN
ejpam-6734	10	17	:	:	PUNCT
ejpam-6734	10	18	differential	differential	ADJ
ejpam-6734	10	19	transform	transform	NOUN
ejpam-6734	10	20	method	method	NOUN
ejpam-6734	10	21	,	,	PUNCT
ejpam-6734	10	22	generalized	generalized	ADJ
ejpam-6734	10	23	fibonacci	fibonacci	NOUN
ejpam-6734	10	24	polynomials	polynomial	NOUN
ejpam-6734	10	25	,	,	PUNCT
ejpam-6734	10	26	collocation	collocation	NOUN
ejpam-6734	10	27	method	method	NOUN
ejpam-6734	10	28	,	,	PUNCT
ejpam-6734	10	29	convergence	convergence	NOUN
ejpam-6734	10	30	and	and	CCONJ
ejpam-6734	10	31	error	error	NOUN
ejpam-6734	10	32	analysis	analysis	NOUN
ejpam-6734	10	33	1	1	NUM
ejpam-6734	10	34	.	.	X
ejpam-6734	10	35	introduction	introduction	NOUN
ejpam-6734	10	36	a	a	DET
ejpam-6734	10	37	wide	wide	ADJ
ejpam-6734	10	38	range	range	NOUN
ejpam-6734	10	39	of	of	ADP
ejpam-6734	10	40	challenges	challenge	NOUN
ejpam-6734	10	41	can	can	AUX
ejpam-6734	10	42	be	be	AUX
ejpam-6734	10	43	modeled	model	VERB
ejpam-6734	10	44	in	in	ADP
ejpam-6734	10	45	mathematics	mathematic	NOUN
ejpam-6734	10	46	,	,	PUNCT
ejpam-6734	10	47	physics	physics	NOUN
ejpam-6734	10	48	,	,	PUNCT
ejpam-6734	10	49	chemistry	chemistry	NOUN
ejpam-6734	10	50	,	,	PUNCT
ejpam-6734	10	51	and	and	CCONJ
ejpam-6734	10	52	related	relate	VERB
ejpam-6734	10	53	scientific	scientific	ADJ
ejpam-6734	10	54	fields	field	NOUN
ejpam-6734	10	55	using	use	VERB
ejpam-6734	10	56	differential	differential	NOUN
ejpam-6734	10	57	or	or	CCONJ
ejpam-6734	10	58	partial	partial	ADJ
ejpam-6734	10	59	differential	differential	ADJ
ejpam-6734	10	60	equations	equation	NOUN
ejpam-6734	10	61	.	.	PUNCT
ejpam-6734	11	1	these	these	DET
ejpam-6734	11	2	equations	equation	NOUN
ejpam-6734	11	3	,	,	PUNCT
ejpam-6734	11	4	which	which	PRON
ejpam-6734	11	5	may	may	AUX
ejpam-6734	11	6	exhibit	exhibit	VERB
ejpam-6734	11	7	linear	linear	ADJ
ejpam-6734	11	8	or	or	CCONJ
ejpam-6734	11	9	non	non	ADJ
ejpam-6734	11	10	-	-	ADJ
ejpam-6734	11	11	linear	linear	ADJ
ejpam-6734	11	12	behavior	behavior	NOUN
ejpam-6734	11	13	depending	depend	VERB
ejpam-6734	11	14	on	on	ADP
ejpam-6734	11	15	the	the	DET
ejpam-6734	11	16	characteristics	characteristic	NOUN
ejpam-6734	11	17	of	of	ADP
ejpam-6734	11	18	the	the	DET
ejpam-6734	11	19	system	system	NOUN
ejpam-6734	11	20	,	,	PUNCT
ejpam-6734	11	21	often	often	ADV
ejpam-6734	11	22	pose	pose	VERB
ejpam-6734	11	23	significant	significant	ADJ
ejpam-6734	11	24	difficulties	difficulty	NOUN
ejpam-6734	11	25	when	when	SCONJ
ejpam-6734	11	26	seeking	seek	VERB
ejpam-6734	11	27	exact	exact	ADJ
ejpam-6734	11	28	analytical	analytical	ADJ
ejpam-6734	11	29	solutions	solution	NOUN
ejpam-6734	11	30	,	,	PUNCT
ejpam-6734	11	31	particularly	particularly	ADV
ejpam-6734	11	32	in	in	ADP
ejpam-6734	11	33	practical	practical	ADJ
ejpam-6734	11	34	,	,	PUNCT
ejpam-6734	11	35	real	real	ADJ
ejpam-6734	11	36	-	-	PUNCT
ejpam-6734	11	37	world	world	NOUN
ejpam-6734	11	38	contexts	contexts	NOUN
ejpam-6734	11	39	.	.	PUNCT
ejpam-6734	12	1	as	as	ADP
ejpam-6734	12	2	a	a	DET
ejpam-6734	12	3	result	result	NOUN
ejpam-6734	12	4	,	,	PUNCT
ejpam-6734	12	5	numerical	numerical	ADJ
ejpam-6734	12	6	and	and	CCONJ
ejpam-6734	12	7	semi	semi	ADJ
ejpam-6734	12	8	-	-	ADJ
ejpam-6734	12	9	analytical	analytical	ADJ
ejpam-6734	12	10	approaches	approach	NOUN
ejpam-6734	12	11	have	have	AUX
ejpam-6734	12	12	become	become	VERB
ejpam-6734	12	13	essential	essential	ADJ
ejpam-6734	12	14	methodologies	methodology	NOUN
ejpam-6734	12	15	for	for	ADP
ejpam-6734	12	16	obtaining	obtain	VERB
ejpam-6734	12	17	approximate	approximate	ADJ
ejpam-6734	12	18	solutions	solution	NOUN
ejpam-6734	12	19	to	to	ADP
ejpam-6734	12	20	these	these	DET
ejpam-6734	12	21	complex	complex	ADJ
ejpam-6734	12	22	problems	problem	NOUN
ejpam-6734	12	23	.	.	PUNCT
ejpam-6734	13	1	the	the	DET
ejpam-6734	13	2	differential	differential	ADJ
ejpam-6734	13	3	transform	transform	NOUN
ejpam-6734	13	4	method	method	NOUN
ejpam-6734	13	5	(	(	PUNCT
ejpam-6734	13	6	dtm	dtm	NOUN
ejpam-6734	13	7	)	)	PUNCT
ejpam-6734	13	8	is	be	AUX
ejpam-6734	13	9	much	much	ADV
ejpam-6734	13	10	easier	easy	ADJ
ejpam-6734	13	11	to	to	PART
ejpam-6734	13	12	use	use	VERB
ejpam-6734	13	13	compared	compare	VERB
ejpam-6734	13	14	to	to	ADP
ejpam-6734	13	15	the	the	DET
ejpam-6734	13	16	typical	typical	ADJ
ejpam-6734	13	17	higher	high	ADJ
ejpam-6734	13	18	-	-	PUNCT
ejpam-6734	13	19	order	order	NOUN
ejpam-6734	13	20	taylor	taylor	PROPN
ejpam-6734	13	21	series	series	PROPN
ejpam-6734	13	22	method	method	PROPN
ejpam-6734	13	23	,	,	PUNCT
ejpam-6734	13	24	which	which	PRON
ejpam-6734	13	25	requires	require	VERB
ejpam-6734	13	26	a	a	DET
ejpam-6734	13	27	lot	lot	NOUN
ejpam-6734	13	28	of	of	ADP
ejpam-6734	13	29	symbolic	symbolic	ADJ
ejpam-6734	13	30	math	math	NOUN
ejpam-6734	13	31	for	for	ADP
ejpam-6734	13	32	derivatives	derivative	NOUN
ejpam-6734	13	33	.	.	PUNCT
ejpam-6734	14	1	∗corresponding	∗corresponde	VERB
ejpam-6734	14	2	author	author	NOUN
ejpam-6734	14	3	.	.	PUNCT
ejpam-6734	15	1	doi	doi	NOUN
ejpam-6734	15	2	:	:	PUNCT
ejpam-6734	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6734	https://doi.org/10.29020/nybg.ejpam.v18i4.6734	PROPN
ejpam-6734	15	4	email	email	NOUN
ejpam-6734	15	5	address	address	NOUN
ejpam-6734	15	6	:	:	PUNCT
ejpam-6734	15	7	amany.saad78@yahoo.com	amany.saad78@yahoo.com	X
ejpam-6734	15	8	(	(	PUNCT
ejpam-6734	15	9	a.	a.	PROPN
ejpam-6734	15	10	s.	s.	PROPN
ejpam-6734	15	11	mohamed	mohamed	PROPN
ejpam-6734	15	12	)	)	PUNCT
ejpam-6734	15	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6734	16	1	1	1	NUM
ejpam-6734	16	2	copyright	copyright	NOUN
ejpam-6734	16	3	:	:	PUNCT
ejpam-6734	16	4	©	©	PROPN
ejpam-6734	16	5	2025	2025	NUM
ejpam-6734	16	6	the	the	DET
ejpam-6734	16	7	author(s	author(s	NOUN
ejpam-6734	16	8	)	)	PUNCT
ejpam-6734	16	9	.	.	PUNCT
ejpam-6734	17	1	(	(	PUNCT
ejpam-6734	17	2	cc	cc	NOUN
ejpam-6734	17	3	by	by	ADP
ejpam-6734	17	4	-	-	PUNCT
ejpam-6734	17	5	nc	nc	PROPN
ejpam-6734	17	6	4.0	4.0	NUM
ejpam-6734	17	7	)	)	PUNCT
ejpam-6734	17	8	m.	m.	NOUN
ejpam-6734	17	9	a.	a.	PROPN
ejpam-6734	17	10	abdou	abdou	PROPN
ejpam-6734	17	11	,	,	PUNCT
ejpam-6734	17	12	a.	a.	PROPN
ejpam-6734	17	13	s.	s.	PROPN
ejpam-6734	17	14	mohamed	mohamed	PROPN
ejpam-6734	17	15	/	/	SYM
ejpam-6734	17	16	eur	eur	PROPN
ejpam-6734	17	17	.	.	PUNCT
ejpam-6734	18	1	j.	j.	PROPN
ejpam-6734	18	2	pure	pure	PROPN
ejpam-6734	18	3	appl	appl	PROPN
ejpam-6734	18	4	.	.	PROPN
ejpam-6734	18	5	math	math	PROPN
ejpam-6734	18	6	,	,	PUNCT
ejpam-6734	18	7	18	18	NUM
ejpam-6734	18	8	(	(	PUNCT
ejpam-6734	18	9	4	4	NUM
ejpam-6734	18	10	)	)	PUNCT
ejpam-6734	18	11	(	(	PUNCT
ejpam-6734	18	12	2025	2025	NUM
ejpam-6734	18	13	)	)	PUNCT
ejpam-6734	18	14	,	,	PUNCT
ejpam-6734	18	15	6734	6734	NUM
ejpam-6734	18	16	2	2	NUM
ejpam-6734	18	17	of	of	ADP
ejpam-6734	18	18	20	20	NUM
ejpam-6734	18	19	although	although	SCONJ
ejpam-6734	18	20	taylor	taylor	PROPN
ejpam-6734	18	21	series	series	PROPN
ejpam-6734	18	22	can	can	AUX
ejpam-6734	18	23	get	get	VERB
ejpam-6734	18	24	complicated	complicated	ADJ
ejpam-6734	18	25	and	and	CCONJ
ejpam-6734	18	26	demand	demand	VERB
ejpam-6734	18	27	more	more	ADJ
ejpam-6734	18	28	resources	resource	NOUN
ejpam-6734	18	29	as	as	SCONJ
ejpam-6734	18	30	you	you	PRON
ejpam-6734	18	31	go	go	VERB
ejpam-6734	18	32	higher	higher	ADV
ejpam-6734	18	33	in	in	ADP
ejpam-6734	18	34	order	order	NOUN
ejpam-6734	18	35	,	,	PUNCT
ejpam-6734	18	36	it	it	PRON
ejpam-6734	18	37	offers	offer	VERB
ejpam-6734	18	38	a	a	DET
ejpam-6734	18	39	simpler	simple	ADJ
ejpam-6734	18	40	and	and	CCONJ
ejpam-6734	18	41	more	more	ADV
ejpam-6734	18	42	efficient	efficient	ADJ
ejpam-6734	18	43	way	way	NOUN
ejpam-6734	18	44	to	to	PART
ejpam-6734	18	45	find	find	VERB
ejpam-6734	18	46	analytic	analytic	ADJ
ejpam-6734	18	47	solutions	solution	NOUN
ejpam-6734	18	48	.	.	PUNCT
ejpam-6734	19	1	in	in	ADP
ejpam-6734	19	2	addition	addition	NOUN
ejpam-6734	19	3	,	,	PUNCT
ejpam-6734	19	4	it	it	PRON
ejpam-6734	19	5	works	work	VERB
ejpam-6734	19	6	well	well	ADV
ejpam-6734	19	7	with	with	ADP
ejpam-6734	19	8	different	different	ADJ
ejpam-6734	19	9	types	type	NOUN
ejpam-6734	19	10	of	of	ADP
ejpam-6734	19	11	differential	differential	ADJ
ejpam-6734	19	12	equations	equation	NOUN
ejpam-6734	19	13	(	(	PUNCT
ejpam-6734	19	14	ordinary	ordinary	ADJ
ejpam-6734	19	15	,	,	PUNCT
ejpam-6734	19	16	partial	partial	ADJ
ejpam-6734	19	17	fractional	fractional	NOUN
ejpam-6734	19	18	)	)	PUNCT
ejpam-6734	19	19	,	,	PUNCT
ejpam-6734	19	20	which	which	PRON
ejpam-6734	19	21	can	can	AUX
ejpam-6734	19	22	be	be	AUX
ejpam-6734	19	23	sorted	sort	VERB
ejpam-6734	19	24	into	into	ADP
ejpam-6734	19	25	various	various	ADJ
ejpam-6734	19	26	categories	category	NOUN
ejpam-6734	19	27	.	.	PUNCT
ejpam-6734	20	1	different	different	ADJ
ejpam-6734	20	2	problems	problem	NOUN
ejpam-6734	20	3	were	be	AUX
ejpam-6734	20	4	discussed	discuss	VERB
ejpam-6734	20	5	using	use	VERB
ejpam-6734	20	6	this	this	DET
ejpam-6734	20	7	method	method	NOUN
ejpam-6734	20	8	in	in	ADP
ejpam-6734	20	9	various	various	ADJ
ejpam-6734	20	10	studies	study	NOUN
ejpam-6734	20	11	.	.	PUNCT
ejpam-6734	21	1	for	for	ADP
ejpam-6734	21	2	example	example	NOUN
ejpam-6734	21	3	,	,	PUNCT
ejpam-6734	21	4	to	to	PART
ejpam-6734	21	5	solve	solve	VERB
ejpam-6734	21	6	rlc	rlc	PROPN
ejpam-6734	21	7	circuits	circuit	VERB
ejpam-6734	21	8	problems	problem	NOUN
ejpam-6734	21	9	,	,	PUNCT
ejpam-6734	21	10	linear	linear	ADJ
ejpam-6734	21	11	and	and	CCONJ
ejpam-6734	21	12	nonlinear	nonlinear	ADJ
ejpam-6734	21	13	pantograph	pantograph	NOUN
ejpam-6734	21	14	equation	equation	NOUN
ejpam-6734	21	15	,	,	PUNCT
ejpam-6734	21	16	non	non	ADJ
ejpam-6734	21	17	-	-	ADJ
ejpam-6734	21	18	linear	linear	ADJ
ejpam-6734	21	19	oscillatory	oscillatory	ADJ
ejpam-6734	21	20	systems	system	NOUN
ejpam-6734	21	21	[	[	X
ejpam-6734	21	22	1–3	1–3	NOUN
ejpam-6734	21	23	]	]	X
ejpam-6734	21	24	.	.	PUNCT
ejpam-6734	22	1	it	it	PRON
ejpam-6734	22	2	is	be	AUX
ejpam-6734	22	3	used	use	VERB
ejpam-6734	22	4	to	to	PART
ejpam-6734	22	5	solve	solve	VERB
ejpam-6734	22	6	non	non	ADJ
ejpam-6734	22	7	-	-	ADJ
ejpam-6734	22	8	linear	linear	ADJ
ejpam-6734	22	9	and	and	CCONJ
ejpam-6734	22	10	system	system	NOUN
ejpam-6734	22	11	of	of	ADP
ejpam-6734	22	12	partial	partial	ADJ
ejpam-6734	22	13	differential	differential	ADJ
ejpam-6734	22	14	equations	equation	NOUN
ejpam-6734	22	15	[	[	X
ejpam-6734	22	16	4	4	NUM
ejpam-6734	22	17	,	,	PUNCT
ejpam-6734	22	18	5	5	NUM
ejpam-6734	22	19	]	]	PUNCT
ejpam-6734	22	20	.	.	PUNCT
ejpam-6734	23	1	linear	linear	PROPN
ejpam-6734	23	2	and	and	CCONJ
ejpam-6734	23	3	non	non	ADJ
ejpam-6734	23	4	-	-	ADJ
ejpam-6734	23	5	linear	linear	ADJ
ejpam-6734	23	6	fractional	fractional	ADJ
ejpam-6734	23	7	ordinary	ordinary	ADJ
ejpam-6734	23	8	differential	differential	ADJ
ejpam-6734	23	9	equations	equation	NOUN
ejpam-6734	23	10	have	have	AUX
ejpam-6734	23	11	also	also	ADV
ejpam-6734	23	12	been	be	AUX
ejpam-6734	23	13	investigated	investigate	VERB
ejpam-6734	23	14	using	use	VERB
ejpam-6734	23	15	the	the	DET
ejpam-6734	23	16	dtm	dtm	NOUN
ejpam-6734	23	17	under	under	ADP
ejpam-6734	23	18	different	different	ADJ
ejpam-6734	23	19	conditions	condition	NOUN
ejpam-6734	24	1	[	[	X
ejpam-6734	24	2	6	6	NUM
ejpam-6734	24	3	,	,	PUNCT
ejpam-6734	24	4	7	7	NUM
ejpam-6734	24	5	]	]	PUNCT
ejpam-6734	24	6	.	.	PUNCT
ejpam-6734	25	1	using	use	VERB
ejpam-6734	25	2	this	this	DET
ejpam-6734	25	3	method	method	NOUN
ejpam-6734	25	4	to	to	PART
ejpam-6734	25	5	solve	solve	VERB
ejpam-6734	25	6	non	non	ADJ
ejpam-6734	25	7	-	-	ADJ
ejpam-6734	25	8	linear	linear	ADJ
ejpam-6734	25	9	and	and	CCONJ
ejpam-6734	25	10	multi	multi	ADJ
ejpam-6734	25	11	-	-	ADJ
ejpam-6734	25	12	term	term	ADJ
ejpam-6734	25	13	time	time	NOUN
ejpam-6734	25	14	fractional	fractional	ADJ
ejpam-6734	25	15	partial	partial	ADJ
ejpam-6734	25	16	differential	differential	NOUN
ejpam-6734	25	17	equations	equation	NOUN
ejpam-6734	25	18	[	[	X
ejpam-6734	25	19	8	8	NUM
ejpam-6734	25	20	,	,	PUNCT
ejpam-6734	25	21	9	9	NUM
ejpam-6734	25	22	]	]	PUNCT
ejpam-6734	25	23	.	.	PUNCT
ejpam-6734	26	1	in	in	ADP
ejpam-6734	26	2	the	the	DET
ejpam-6734	26	3	last	last	ADJ
ejpam-6734	26	4	few	few	ADJ
ejpam-6734	26	5	years	year	NOUN
ejpam-6734	26	6	,	,	PUNCT
ejpam-6734	26	7	spectral	spectral	ADJ
ejpam-6734	26	8	methods	method	NOUN
ejpam-6734	26	9	have	have	AUX
ejpam-6734	26	10	become	become	VERB
ejpam-6734	26	11	popular	popular	ADJ
ejpam-6734	26	12	for	for	ADP
ejpam-6734	26	13	solving	solve	VERB
ejpam-6734	26	14	differential	differential	ADJ
ejpam-6734	26	15	equations	equation	NOUN
ejpam-6734	26	16	because	because	SCONJ
ejpam-6734	26	17	they	they	PRON
ejpam-6734	26	18	’re	’re	VERB
ejpam-6734	26	19	accurate	accurate	ADJ
ejpam-6734	26	20	and	and	CCONJ
ejpam-6734	26	21	only	only	ADV
ejpam-6734	26	22	need	need	VERB
ejpam-6734	26	23	to	to	PART
ejpam-6734	26	24	deal	deal	VERB
ejpam-6734	26	25	with	with	ADP
ejpam-6734	26	26	a	a	DET
ejpam-6734	26	27	few	few	ADJ
ejpam-6734	26	28	unknowns	unknown	NOUN
ejpam-6734	26	29	.	.	PUNCT
ejpam-6734	27	1	for	for	ADP
ejpam-6734	27	2	example	example	NOUN
ejpam-6734	27	3	,	,	PUNCT
ejpam-6734	27	4	using	use	VERB
ejpam-6734	27	5	telephone	telephone	NOUN
ejpam-6734	27	6	polynomials	polynomial	NOUN
ejpam-6734	27	7	for	for	ADP
ejpam-6734	27	8	solving	solve	VERB
ejpam-6734	27	9	high	high	ADJ
ejpam-6734	27	10	-	-	PUNCT
ejpam-6734	27	11	order	order	NOUN
ejpam-6734	27	12	linear	linear	NOUN
ejpam-6734	27	13	,	,	PUNCT
ejpam-6734	27	14	non	non	ADJ
ejpam-6734	27	15	-	-	ADJ
ejpam-6734	27	16	linear	linear	ADJ
ejpam-6734	27	17	ordinary	ordinary	ADJ
ejpam-6734	27	18	differential	differential	ADJ
ejpam-6734	27	19	equations	equation	NOUN
ejpam-6734	27	20	and	and	CCONJ
ejpam-6734	27	21	systems	system	NOUN
ejpam-6734	27	22	,	,	PUNCT
ejpam-6734	27	23	with	with	ADP
ejpam-6734	27	24	homogeneous	homogeneous	ADJ
ejpam-6734	27	25	and	and	CCONJ
ejpam-6734	27	26	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6734	27	27	initial	initial	ADJ
ejpam-6734	27	28	conditions	condition	NOUN
ejpam-6734	27	29	[	[	X
ejpam-6734	27	30	10	10	NUM
ejpam-6734	27	31	]	]	PUNCT
ejpam-6734	27	32	.	.	PUNCT
ejpam-6734	28	1	treatment	treatment	NOUN
ejpam-6734	28	2	of	of	ADP
ejpam-6734	28	3	the	the	DET
ejpam-6734	28	4	tricomi	tricomi	NOUN
ejpam-6734	28	5	-	-	PUNCT
ejpam-6734	28	6	type	type	NOUN
ejpam-6734	28	7	time	time	NOUN
ejpam-6734	28	8	fractional	fractional	ADJ
ejpam-6734	28	9	equation	equation	NOUN
ejpam-6734	28	10	using	use	VERB
ejpam-6734	28	11	jacobi	jacobi	PROPN
ejpam-6734	28	12	shifted	shift	VERB
ejpam-6734	28	13	polynomials	polynomial	NOUN
ejpam-6734	28	14	[	[	X
ejpam-6734	28	15	11	11	NUM
ejpam-6734	28	16	]	]	PUNCT
ejpam-6734	28	17	.	.	PUNCT
ejpam-6734	29	1	using	use	VERB
ejpam-6734	29	2	fibonacci	fibonacci	NOUN
ejpam-6734	29	3	polynomials	polynomial	NOUN
ejpam-6734	29	4	for	for	ADP
ejpam-6734	29	5	solving	solve	VERB
ejpam-6734	29	6	second	second	ADJ
ejpam-6734	29	7	-	-	PUNCT
ejpam-6734	29	8	order	order	NOUN
ejpam-6734	29	9	linear	linear	ADJ
ejpam-6734	29	10	differential	differential	NOUN
ejpam-6734	29	11	equations	equation	NOUN
ejpam-6734	29	12	and	and	CCONJ
ejpam-6734	29	13	nonlinear	nonlinear	ADJ
ejpam-6734	29	14	pantograph	pantograph	NOUN
ejpam-6734	29	15	differential	differential	PROPN
ejpam-6734	29	16	equations	equation	NOUN
ejpam-6734	29	17	[	[	X
ejpam-6734	29	18	12–14	12–14	NUM
ejpam-6734	29	19	]	]	X
ejpam-6734	29	20	.	.	PUNCT
ejpam-6734	30	1	a	a	DET
ejpam-6734	30	2	system	system	NOUN
ejpam-6734	30	3	of	of	ADP
ejpam-6734	30	4	ordinary	ordinary	ADJ
ejpam-6734	30	5	and	and	CCONJ
ejpam-6734	30	6	fractional	fractional	ADJ
ejpam-6734	30	7	order	order	NOUN
ejpam-6734	30	8	differential	differential	NOUN
ejpam-6734	30	9	equations	equation	NOUN
ejpam-6734	30	10	can	can	AUX
ejpam-6734	30	11	be	be	AUX
ejpam-6734	30	12	solved	solve	VERB
ejpam-6734	30	13	by	by	ADP
ejpam-6734	30	14	lucas	lucas	PROPN
ejpam-6734	30	15	polynomials	polynomial	NOUN
ejpam-6734	30	16	[	[	X
ejpam-6734	30	17	15	15	NUM
ejpam-6734	30	18	,	,	PUNCT
ejpam-6734	30	19	16	16	NUM
ejpam-6734	30	20	]	]	PUNCT
ejpam-6734	30	21	.	.	PUNCT
ejpam-6734	31	1	discussion	discussion	NOUN
ejpam-6734	31	2	of	of	ADP
ejpam-6734	31	3	the	the	DET
ejpam-6734	31	4	time	time	NOUN
ejpam-6734	31	5	-	-	PUNCT
ejpam-6734	31	6	fractional	fractional	ADJ
ejpam-6734	31	7	fitzhugh	fitzhugh	PROPN
ejpam-6734	31	8	-	-	PUNCT
ejpam-6734	31	9	nagumo	nagumo	ADJ
ejpam-6734	31	10	differential	differential	ADJ
ejpam-6734	31	11	equation	equation	NOUN
ejpam-6734	31	12	using	use	VERB
ejpam-6734	31	13	lucas	lucas	NOUN
ejpam-6734	31	14	polynomials	polynomial	NOUN
ejpam-6734	31	15	shifted	shift	VERB
ejpam-6734	31	16	[	[	X
ejpam-6734	31	17	17	17	NUM
ejpam-6734	31	18	]	]	PUNCT
ejpam-6734	31	19	.	.	PUNCT
ejpam-6734	32	1	in	in	ADP
ejpam-6734	32	2	addition	addition	NOUN
ejpam-6734	32	3	,	,	PUNCT
ejpam-6734	32	4	fibonacci	fibonacci	NOUN
ejpam-6734	32	5	polynomials	polynomial	NOUN
ejpam-6734	32	6	solved	solve	VERB
ejpam-6734	32	7	different	different	ADJ
ejpam-6734	32	8	kinds	kind	NOUN
ejpam-6734	32	9	of	of	ADP
ejpam-6734	32	10	fractional	fractional	ADJ
ejpam-6734	32	11	,	,	PUNCT
ejpam-6734	32	12	multiterm	multiterm	ADJ
ejpam-6734	32	13	fractional	fractional	ADJ
ejpam-6734	32	14	initial	initial	ADJ
ejpam-6734	32	15	value	value	NOUN
ejpam-6734	32	16	problems	problem	NOUN
ejpam-6734	32	17	,	,	PUNCT
ejpam-6734	32	18	and	and	CCONJ
ejpam-6734	32	19	fractional	fractional	ADJ
ejpam-6734	32	20	integro	integro	ADJ
ejpam-6734	32	21	-	-	PUNCT
ejpam-6734	32	22	differential	differential	NOUN
ejpam-6734	32	23	equations[18	equations[18	PROPN
ejpam-6734	32	24	–	–	PUNCT
ejpam-6734	32	25	20	20	NUM
ejpam-6734	32	26	]	]	PUNCT
ejpam-6734	32	27	.	.	PUNCT
ejpam-6734	33	1	while	while	SCONJ
ejpam-6734	33	2	,	,	PUNCT
ejpam-6734	33	3	generalized	generalized	ADJ
ejpam-6734	33	4	fibonacci	fibonacci	NOUN
ejpam-6734	33	5	polynomials	polynomial	NOUN
ejpam-6734	33	6	solved	solve	VERB
ejpam-6734	33	7	fractional	fractional	ADJ
ejpam-6734	33	8	bagley	bagley	NOUN
ejpam-6734	33	9	-	-	PUNCT
ejpam-6734	33	10	torvik	torvik	NOUN
ejpam-6734	33	11	equation	equation	NOUN
ejpam-6734	33	12	and	and	CCONJ
ejpam-6734	33	13	time	time	NOUN
ejpam-6734	33	14	-	-	PUNCT
ejpam-6734	33	15	fractional	fractional	ADJ
ejpam-6734	33	16	kuramoto	kuramoto	NOUN
ejpam-6734	33	17	–	–	PUNCT
ejpam-6734	33	18	sivashinsky	sivashinsky	ADJ
ejpam-6734	33	19	equation	equation	NOUN
ejpam-6734	33	20	[	[	X
ejpam-6734	33	21	21	21	NUM
ejpam-6734	33	22	,	,	PUNCT
ejpam-6734	33	23	22	22	NUM
ejpam-6734	33	24	]	]	PUNCT
ejpam-6734	33	25	.	.	PUNCT
ejpam-6734	34	1	using	use	VERB
ejpam-6734	34	2	special	special	ADJ
ejpam-6734	34	3	cases	case	NOUN
ejpam-6734	34	4	of	of	ADP
ejpam-6734	34	5	generalized	generalized	ADJ
ejpam-6734	34	6	lucas	lucas	NOUN
ejpam-6734	34	7	and	and	CCONJ
ejpam-6734	34	8	fibonacci	fibonacci	NOUN
ejpam-6734	34	9	such	such	ADJ
ejpam-6734	34	10	as	as	ADP
ejpam-6734	34	11	:	:	PUNCT
ejpam-6734	34	12	fermat	fermat	PROPN
ejpam-6734	34	13	polynomials	polynomial	VERB
ejpam-6734	34	14	for	for	ADP
ejpam-6734	34	15	solving	solve	VERB
ejpam-6734	34	16	the	the	DET
ejpam-6734	34	17	fractional	fractional	ADJ
ejpam-6734	34	18	burgers	burger	NOUN
ejpam-6734	34	19	’	'	PUNCT
ejpam-6734	34	20	equation	equation	NOUN
ejpam-6734	34	21	[	[	X
ejpam-6734	34	22	23	23	NUM
ejpam-6734	34	23	]	]	PUNCT
ejpam-6734	34	24	.	.	PUNCT
ejpam-6734	35	1	additionally	additionally	ADV
ejpam-6734	35	2	,	,	PUNCT
ejpam-6734	35	3	second	second	ADJ
ejpam-6734	35	4	kind	kind	NOUN
ejpam-6734	35	5	chebyshev	chebyshev	NOUN
ejpam-6734	35	6	collocation	collocation	NOUN
ejpam-6734	35	7	method	method	NOUN
ejpam-6734	35	8	for	for	ADP
ejpam-6734	35	9	solving	solve	VERB
ejpam-6734	35	10	linear	linear	NOUN
ejpam-6734	35	11	and	and	CCONJ
ejpam-6734	35	12	nonlinear	nonlinear	ADJ
ejpam-6734	35	13	ordinary	ordinary	ADJ
ejpam-6734	35	14	differential	differential	ADJ
ejpam-6734	35	15	equations	equation	NOUN
ejpam-6734	35	16	then	then	ADV
ejpam-6734	35	17	comparing	compare	VERB
ejpam-6734	35	18	with	with	ADP
ejpam-6734	35	19	the	the	DET
ejpam-6734	35	20	differential	differential	ADJ
ejpam-6734	35	21	transform	transform	NOUN
ejpam-6734	35	22	method	method	NOUN
ejpam-6734	35	23	[	[	X
ejpam-6734	35	24	24	24	NUM
ejpam-6734	35	25	]	]	PUNCT
ejpam-6734	35	26	.	.	PUNCT
ejpam-6734	36	1	chebyshev	chebyshev	PROPN
ejpam-6734	36	2	polynomials	polynomial	NOUN
ejpam-6734	36	3	with	with	ADP
ejpam-6734	36	4	different	different	ADJ
ejpam-6734	36	5	kinds	kind	NOUN
ejpam-6734	36	6	use	use	VERB
ejpam-6734	36	7	for	for	ADP
ejpam-6734	36	8	solving	solve	VERB
ejpam-6734	36	9	various	various	ADJ
ejpam-6734	36	10	forms	form	NOUN
ejpam-6734	36	11	for	for	ADP
ejpam-6734	36	12	differential	differential	ADJ
ejpam-6734	36	13	equations	equation	NOUN
ejpam-6734	36	14	for	for	ADP
ejpam-6734	36	15	example	example	NOUN
ejpam-6734	36	16	:	:	PUNCT
ejpam-6734	36	17	third	third	ADJ
ejpam-6734	36	18	kind	kind	NOUN
ejpam-6734	36	19	discussed	discuss	VERB
ejpam-6734	36	20	the	the	DET
ejpam-6734	36	21	solution	solution	NOUN
ejpam-6734	36	22	of	of	ADP
ejpam-6734	36	23	highorder	highorder	NOUN
ejpam-6734	36	24	emden	emden	PROPN
ejpam-6734	36	25	–	–	PUNCT
ejpam-6734	36	26	fowler	fowler	PROPN
ejpam-6734	36	27	equations	equation	NOUN
ejpam-6734	37	1	[	[	X
ejpam-6734	37	2	25	25	NUM
ejpam-6734	37	3	]	]	PUNCT
ejpam-6734	37	4	.	.	PUNCT
ejpam-6734	38	1	solving	solve	VERB
ejpam-6734	38	2	the	the	DET
ejpam-6734	38	3	time	time	NOUN
ejpam-6734	38	4	fractional	fractional	ADJ
ejpam-6734	38	5	diffusion	diffusion	NOUN
ejpam-6734	38	6	wave	wave	NOUN
ejpam-6734	38	7	equation	equation	NOUN
ejpam-6734	38	8	using	use	VERB
ejpam-6734	38	9	shifted	shift	VERB
ejpam-6734	38	10	fourth	fourth	ADJ
ejpam-6734	38	11	-	-	PUNCT
ejpam-6734	38	12	kind	kind	NOUN
ejpam-6734	38	13	[	[	X
ejpam-6734	38	14	26	26	NUM
ejpam-6734	38	15	]	]	PUNCT
ejpam-6734	38	16	.	.	PUNCT
ejpam-6734	39	1	using	use	VERB
ejpam-6734	39	2	the	the	DET
ejpam-6734	39	3	seventh	seventh	ADJ
ejpam-6734	39	4	kind	kind	NOUN
ejpam-6734	39	5	chebyshev	chebyshev	NOUN
ejpam-6734	39	6	polynomials	polynomial	NOUN
ejpam-6734	39	7	for	for	ADP
ejpam-6734	39	8	discussing	discuss	VERB
ejpam-6734	39	9	the	the	DET
ejpam-6734	39	10	fractional	fractional	ADJ
ejpam-6734	39	11	delay	delay	NOUN
ejpam-6734	39	12	differential	differential	ADJ
ejpam-6734	39	13	equation	equation	NOUN
ejpam-6734	39	14	[	[	X
ejpam-6734	39	15	27	27	NUM
ejpam-6734	39	16	]	]	PUNCT
ejpam-6734	39	17	.	.	PUNCT
ejpam-6734	40	1	as	as	SCONJ
ejpam-6734	40	2	,	,	PUNCT
ejpam-6734	40	3	eighth	eighth	ADJ
ejpam-6734	40	4	-	-	PUNCT
ejpam-6734	40	5	kind	kind	NOUN
ejpam-6734	40	6	solved	solve	VERB
ejpam-6734	40	7	the	the	DET
ejpam-6734	40	8	nonlinear	nonlinear	ADJ
ejpam-6734	40	9	time	time	NOUN
ejpam-6734	40	10	-	-	PUNCT
ejpam-6734	40	11	fractional	fractional	ADJ
ejpam-6734	40	12	generalized	generalized	ADJ
ejpam-6734	40	13	kawahara	kawahara	NOUN
ejpam-6734	40	14	equation	equation	NOUN
ejpam-6734	40	15	[	[	X
ejpam-6734	40	16	28	28	NUM
ejpam-6734	40	17	]	]	PUNCT
ejpam-6734	40	18	.	.	PUNCT
ejpam-6734	41	1	solving	solve	VERB
ejpam-6734	41	2	time	time	NOUN
ejpam-6734	41	3	-	-	PUNCT
ejpam-6734	41	4	fractional	fractional	ADJ
ejpam-6734	41	5	heat	heat	NOUN
ejpam-6734	41	6	equation	equation	NOUN
ejpam-6734	41	7	with	with	ADP
ejpam-6734	41	8	nonlocal	nonlocal	ADJ
ejpam-6734	41	9	conditions	condition	NOUN
ejpam-6734	41	10	using	use	VERB
ejpam-6734	41	11	rectified	rectified	ADJ
ejpam-6734	41	12	chebyshev	chebyshev	NOUN
ejpam-6734	42	1	[	[	X
ejpam-6734	42	2	29	29	NUM
ejpam-6734	42	3	]	]	PUNCT
ejpam-6734	42	4	.	.	PUNCT
ejpam-6734	43	1	in	in	ADP
ejpam-6734	43	2	summary	summary	NOUN
ejpam-6734	43	3	,	,	PUNCT
ejpam-6734	43	4	numerical	numerical	ADJ
ejpam-6734	43	5	methods	method	NOUN
ejpam-6734	43	6	provide	provide	VERB
ejpam-6734	43	7	reliable	reliable	ADJ
ejpam-6734	43	8	and	and	CCONJ
ejpam-6734	43	9	computationally	computationally	ADV
ejpam-6734	43	10	efficient	efficient	ADJ
ejpam-6734	43	11	strategies	strategy	NOUN
ejpam-6734	43	12	for	for	ADP
ejpam-6734	43	13	addressing	address	VERB
ejpam-6734	43	14	diverse	diverse	ADJ
ejpam-6734	43	15	types	type	NOUN
ejpam-6734	43	16	of	of	ADP
ejpam-6734	43	17	differential	differential	ADJ
ejpam-6734	43	18	equations	equation	NOUN
ejpam-6734	43	19	,	,	PUNCT
ejpam-6734	43	20	particularly	particularly	ADV
ejpam-6734	43	21	in	in	ADP
ejpam-6734	43	22	scenarios	scenario	NOUN
ejpam-6734	43	23	where	where	SCONJ
ejpam-6734	43	24	obtaining	obtain	VERB
ejpam-6734	43	25	exact	exact	ADJ
ejpam-6734	43	26	analytical	analytical	ADJ
ejpam-6734	43	27	solutions	solution	NOUN
ejpam-6734	43	28	is	be	AUX
ejpam-6734	43	29	infeasible	infeasible	ADJ
ejpam-6734	43	30	or	or	CCONJ
ejpam-6734	43	31	analytically	analytically	ADV
ejpam-6734	43	32	intractable	intractable	ADJ
ejpam-6734	43	33	.	.	PUNCT
ejpam-6734	44	1	in	in	ADP
ejpam-6734	44	2	this	this	DET
ejpam-6734	44	3	article	article	NOUN
ejpam-6734	44	4	,	,	PUNCT
ejpam-6734	44	5	we	we	PRON
ejpam-6734	44	6	solve	solve	VERB
ejpam-6734	44	7	linear	linear	ADJ
ejpam-6734	44	8	and	and	CCONJ
ejpam-6734	44	9	nonlinear	nonlinear	ADJ
ejpam-6734	44	10	second	second	ADJ
ejpam-6734	44	11	-	-	PUNCT
ejpam-6734	44	12	order	order	NOUN
ejpam-6734	44	13	differential	differential	ADJ
ejpam-6734	44	14	equations	equation	NOUN
ejpam-6734	44	15	using	use	VERB
ejpam-6734	44	16	dtm	dtm	PROPN
ejpam-6734	44	17	and	and	CCONJ
ejpam-6734	44	18	the	the	DET
ejpam-6734	44	19	generalized	generalize	VERB
ejpam-6734	44	20	fibonacci	fibonacci	NOUN
ejpam-6734	44	21	collocation	collocation	NOUN
ejpam-6734	44	22	method	method	NOUN
ejpam-6734	44	23	(	(	PUNCT
ejpam-6734	44	24	gfcm	gfcm	PROPN
ejpam-6734	44	25	)	)	PUNCT
ejpam-6734	44	26	.	.	PUNCT
ejpam-6734	45	1	the	the	DET
ejpam-6734	45	2	dtm	dtm	PROPN
ejpam-6734	45	3	is	be	AUX
ejpam-6734	45	4	simple	simple	ADJ
ejpam-6734	45	5	to	to	PART
ejpam-6734	45	6	apply	apply	VERB
ejpam-6734	45	7	and	and	CCONJ
ejpam-6734	45	8	works	work	VERB
ejpam-6734	45	9	well	well	ADV
ejpam-6734	45	10	because	because	SCONJ
ejpam-6734	45	11	it	it	PRON
ejpam-6734	45	12	skips	skip	VERB
ejpam-6734	45	13	complicated	complicated	ADJ
ejpam-6734	45	14	algebra	algebra	NOUN
ejpam-6734	45	15	.	.	PUNCT
ejpam-6734	46	1	it	it	PRON
ejpam-6734	46	2	provides	provide	VERB
ejpam-6734	46	3	accurate	accurate	ADJ
ejpam-6734	46	4	results	result	NOUN
ejpam-6734	46	5	with	with	ADP
ejpam-6734	46	6	fewer	few	ADJ
ejpam-6734	46	7	calculations	calculation	NOUN
ejpam-6734	46	8	,	,	PUNCT
ejpam-6734	46	9	especially	especially	ADV
ejpam-6734	46	10	for	for	ADP
ejpam-6734	46	11	linear	linear	PROPN
ejpam-6734	46	12	differential	differential	ADJ
ejpam-6734	46	13	equations	equation	NOUN
ejpam-6734	46	14	,	,	PUNCT
ejpam-6734	46	15	by	by	ADP
ejpam-6734	46	16	creating	create	VERB
ejpam-6734	46	17	short	short	ADJ
ejpam-6734	46	18	series	series	NOUN
ejpam-6734	46	19	that	that	PRON
ejpam-6734	46	20	maintain	maintain	VERB
ejpam-6734	46	21	accuracy	accuracy	NOUN
ejpam-6734	46	22	.	.	PUNCT
ejpam-6734	47	1	it	it	PRON
ejpam-6734	47	2	can	can	AUX
ejpam-6734	47	3	handle	handle	VERB
ejpam-6734	47	4	both	both	CCONJ
ejpam-6734	47	5	initial	initial	ADJ
ejpam-6734	47	6	and	and	CCONJ
ejpam-6734	47	7	boundary	boundary	ADJ
ejpam-6734	47	8	-	-	PUNCT
ejpam-6734	47	9	value	value	NOUN
ejpam-6734	47	10	problems	problem	NOUN
ejpam-6734	47	11	,	,	PUNCT
ejpam-6734	47	12	often	often	ADV
ejpam-6734	47	13	reaching	reach	VERB
ejpam-6734	47	14	quick	quick	ADJ
ejpam-6734	47	15	answers	answer	NOUN
ejpam-6734	47	16	with	with	ADP
ejpam-6734	47	17	just	just	ADV
ejpam-6734	47	18	a	a	DET
ejpam-6734	47	19	few	few	ADJ
ejpam-6734	47	20	attempts	attempt	NOUN
ejpam-6734	47	21	.	.	PUNCT
ejpam-6734	48	1	it	it	PRON
ejpam-6734	48	2	may	may	AUX
ejpam-6734	48	3	face	face	VERB
ejpam-6734	48	4	convergence	convergence	NOUN
ejpam-6734	48	5	restrictions	restriction	NOUN
ejpam-6734	48	6	for	for	ADP
ejpam-6734	48	7	strongly	strongly	ADV
ejpam-6734	48	8	nonlinear	nonlinear	ADJ
ejpam-6734	48	9	problems	problem	NOUN
ejpam-6734	48	10	or	or	CCONJ
ejpam-6734	48	11	large	large	ADJ
ejpam-6734	48	12	domains	domain	NOUN
ejpam-6734	48	13	.	.	PUNCT
ejpam-6734	49	1	on	on	ADP
ejpam-6734	49	2	the	the	DET
ejpam-6734	49	3	other	other	ADJ
ejpam-6734	49	4	hand	hand	NOUN
ejpam-6734	49	5	,	,	PUNCT
ejpam-6734	49	6	the	the	DET
ejpam-6734	49	7	gfcm	gfcm	PROPN
ejpam-6734	49	8	with	with	ADP
ejpam-6734	49	9	m.	m.	PROPN
ejpam-6734	49	10	a.	a.	PROPN
ejpam-6734	49	11	abdou	abdou	PROPN
ejpam-6734	49	12	,	,	PUNCT
ejpam-6734	49	13	a.	a.	PROPN
ejpam-6734	49	14	s.	s.	PROPN
ejpam-6734	49	15	mohamed	mohamed	PROPN
ejpam-6734	49	16	/	/	SYM
ejpam-6734	49	17	eur	eur	PROPN
ejpam-6734	49	18	.	.	PUNCT
ejpam-6734	50	1	j.	j.	PROPN
ejpam-6734	50	2	pure	pure	PROPN
ejpam-6734	50	3	appl	appl	PROPN
ejpam-6734	50	4	.	.	PROPN
ejpam-6734	50	5	math	math	PROPN
ejpam-6734	50	6	,	,	PUNCT
ejpam-6734	50	7	18	18	NUM
ejpam-6734	50	8	(	(	PUNCT
ejpam-6734	50	9	4	4	NUM
ejpam-6734	50	10	)	)	PUNCT
ejpam-6734	50	11	(	(	PUNCT
ejpam-6734	50	12	2025	2025	NUM
ejpam-6734	50	13	)	)	PUNCT
ejpam-6734	50	14	,	,	PUNCT
ejpam-6734	50	15	6734	6734	NUM
ejpam-6734	50	16	3	3	NUM
ejpam-6734	50	17	of	of	ADP
ejpam-6734	50	18	20	20	NUM
ejpam-6734	50	19	the	the	DET
ejpam-6734	50	20	generalized	generalize	VERB
ejpam-6734	50	21	fibonacci	fibonacci	NOUN
ejpam-6734	50	22	polynomials	polynomial	NOUN
ejpam-6734	50	23	(	(	PUNCT
ejpam-6734	50	24	gfps	gfps	NOUN
ejpam-6734	50	25	)	)	PUNCT
ejpam-6734	50	26	,	,	PUNCT
ejpam-6734	50	27	as	as	SCONJ
ejpam-6734	50	28	basis	basis	NOUN
ejpam-6734	50	29	functions	function	NOUN
ejpam-6734	50	30	to	to	PART
ejpam-6734	50	31	give	give	VERB
ejpam-6734	50	32	accurate	accurate	ADJ
ejpam-6734	50	33	results	result	NOUN
ejpam-6734	50	34	,	,	PUNCT
ejpam-6734	50	35	especially	especially	ADV
ejpam-6734	50	36	for	for	ADP
ejpam-6734	50	37	problems	problem	NOUN
ejpam-6734	50	38	with	with	ADP
ejpam-6734	50	39	smooth	smooth	ADJ
ejpam-6734	50	40	solutions	solution	NOUN
ejpam-6734	50	41	.	.	PUNCT
ejpam-6734	51	1	it	it	PRON
ejpam-6734	51	2	can	can	AUX
ejpam-6734	51	3	solve	solve	VERB
ejpam-6734	51	4	different	different	ADJ
ejpam-6734	51	5	kinds	kind	NOUN
ejpam-6734	51	6	of	of	ADP
ejpam-6734	51	7	differential	differential	ADJ
ejpam-6734	51	8	equation	equation	NOUN
ejpam-6734	51	9	,	,	PUNCT
ejpam-6734	51	10	and	and	CCONJ
ejpam-6734	51	11	the	the	DET
ejpam-6734	51	12	error	error	NOUN
ejpam-6734	51	13	decreases	decrease	VERB
ejpam-6734	51	14	quickly	quickly	ADV
ejpam-6734	51	15	when	when	SCONJ
ejpam-6734	51	16	the	the	DET
ejpam-6734	51	17	collocation	collocation	NOUN
ejpam-6734	51	18	points	point	NOUN
ejpam-6734	51	19	are	be	AUX
ejpam-6734	51	20	added	add	VERB
ejpam-6734	51	21	.	.	PUNCT
ejpam-6734	52	1	in	in	ADP
ejpam-6734	52	2	addition	addition	NOUN
ejpam-6734	52	3	,	,	PUNCT
ejpam-6734	52	4	it	it	PRON
ejpam-6734	52	5	requires	require	VERB
ejpam-6734	52	6	careful	careful	ADJ
ejpam-6734	52	7	selection	selection	NOUN
ejpam-6734	52	8	of	of	ADP
ejpam-6734	52	9	collocation	collocation	NOUN
ejpam-6734	52	10	points	point	NOUN
ejpam-6734	52	11	and	and	CCONJ
ejpam-6734	52	12	may	may	AUX
ejpam-6734	52	13	involve	involve	VERB
ejpam-6734	52	14	a	a	DET
ejpam-6734	52	15	higher	high	ADJ
ejpam-6734	52	16	computational	computational	ADJ
ejpam-6734	52	17	cost	cost	NOUN
ejpam-6734	52	18	when	when	SCONJ
ejpam-6734	52	19	very	very	ADV
ejpam-6734	52	20	high	high	ADJ
ejpam-6734	52	21	accuracy	accuracy	NOUN
ejpam-6734	52	22	is	be	AUX
ejpam-6734	52	23	required	require	VERB
ejpam-6734	52	24	.	.	PUNCT
ejpam-6734	53	1	in	in	ADP
ejpam-6734	53	2	this	this	DET
ejpam-6734	53	3	study	study	NOUN
ejpam-6734	53	4	,	,	PUNCT
ejpam-6734	53	5	we	we	PRON
ejpam-6734	53	6	use	use	VERB
ejpam-6734	53	7	the	the	DET
ejpam-6734	53	8	dtm	dtm	NOUN
ejpam-6734	53	9	to	to	PART
ejpam-6734	53	10	find	find	VERB
ejpam-6734	53	11	exact	exact	ADJ
ejpam-6734	53	12	solutions	solution	NOUN
ejpam-6734	53	13	for	for	ADP
ejpam-6734	53	14	specific	specific	ADJ
ejpam-6734	53	15	second	second	ADJ
ejpam-6734	53	16	-	-	PUNCT
ejpam-6734	53	17	order	order	NOUN
ejpam-6734	53	18	differential	differential	ADJ
ejpam-6734	53	19	equations	equation	NOUN
ejpam-6734	53	20	,	,	PUNCT
ejpam-6734	53	21	including	include	VERB
ejpam-6734	53	22	some	some	DET
ejpam-6734	53	23	challenging	challenging	ADJ
ejpam-6734	53	24	ones	one	NOUN
ejpam-6734	53	25	,	,	PUNCT
ejpam-6734	53	26	such	such	ADJ
ejpam-6734	53	27	as	as	ADP
ejpam-6734	53	28	the	the	DET
ejpam-6734	53	29	singular	singular	NOUN
ejpam-6734	53	30	and	and	CCONJ
ejpam-6734	53	31	nonlinear	nonlinear	ADJ
ejpam-6734	53	32	bratu	bratu	PROPN
ejpam-6734	53	33	problem	problem	NOUN
ejpam-6734	53	34	.	.	PUNCT
ejpam-6734	54	1	these	these	DET
ejpam-6734	54	2	methods	method	NOUN
ejpam-6734	54	3	can	can	AUX
ejpam-6734	54	4	be	be	AUX
ejpam-6734	54	5	used	use	VERB
ejpam-6734	54	6	for	for	ADP
ejpam-6734	54	7	different	different	ADJ
ejpam-6734	54	8	branches	branch	NOUN
ejpam-6734	54	9	of	of	ADP
ejpam-6734	54	10	science	science	NOUN
ejpam-6734	54	11	and	and	CCONJ
ejpam-6734	54	12	engineering	engineering	NOUN
ejpam-6734	54	13	.	.	PUNCT
ejpam-6734	55	1	differential	differential	ADJ
ejpam-6734	55	2	equations	equation	NOUN
ejpam-6734	55	3	are	be	AUX
ejpam-6734	55	4	very	very	ADV
ejpam-6734	55	5	useful	useful	ADJ
ejpam-6734	55	6	.	.	PUNCT
ejpam-6734	56	1	they	they	PRON
ejpam-6734	56	2	appear	appear	VERB
ejpam-6734	56	3	all	all	DET
ejpam-6734	56	4	the	the	DET
ejpam-6734	56	5	time	time	NOUN
ejpam-6734	56	6	when	when	SCONJ
ejpam-6734	56	7	we	we	PRON
ejpam-6734	56	8	’re	’re	AUX
ejpam-6734	56	9	trying	try	VERB
ejpam-6734	56	10	to	to	PART
ejpam-6734	56	11	understand	understand	VERB
ejpam-6734	56	12	how	how	SCONJ
ejpam-6734	56	13	things	thing	NOUN
ejpam-6734	56	14	change	change	VERB
ejpam-6734	56	15	,	,	PUNCT
ejpam-6734	56	16	such	such	ADJ
ejpam-6734	56	17	as	as	ADP
ejpam-6734	56	18	velocity	velocity	NOUN
ejpam-6734	56	19	movement	movement	NOUN
ejpam-6734	56	20	,	,	PUNCT
ejpam-6734	56	21	heat	heat	NOUN
ejpam-6734	56	22	flow	flow	NOUN
ejpam-6734	56	23	,	,	PUNCT
ejpam-6734	56	24	or	or	CCONJ
ejpam-6734	56	25	circuits	circuit	NOUN
ejpam-6734	56	26	.	.	PUNCT
ejpam-6734	57	1	they	they	PRON
ejpam-6734	57	2	can	can	AUX
ejpam-6734	57	3	even	even	ADV
ejpam-6734	57	4	handle	handle	VERB
ejpam-6734	57	5	some	some	DET
ejpam-6734	57	6	tricky	tricky	ADJ
ejpam-6734	57	7	nonlinear	nonlinear	ADJ
ejpam-6734	57	8	things	thing	NOUN
ejpam-6734	57	9	.	.	PUNCT
ejpam-6734	58	1	this	this	DET
ejpam-6734	58	2	paper	paper	NOUN
ejpam-6734	58	3	discussed	discuss	VERB
ejpam-6734	58	4	general	general	ADJ
ejpam-6734	58	5	nonlinear	nonlinear	ADJ
ejpam-6734	58	6	second	second	ADJ
ejpam-6734	58	7	-	-	PUNCT
ejpam-6734	58	8	order	order	NOUN
ejpam-6734	58	9	equations	equation	NOUN
ejpam-6734	58	10	of	of	ADP
ejpam-6734	58	11	the	the	DET
ejpam-6734	58	12	form	form	NOUN
ejpam-6734	58	13	(	(	PUNCT
ejpam-6734	58	14	1	1	NUM
ejpam-6734	58	15	)	)	PUNCT
ejpam-6734	58	16	,	,	PUNCT
ejpam-6734	58	17	which	which	PRON
ejpam-6734	58	18	involve	involve	VERB
ejpam-6734	58	19	variable	variable	ADJ
ejpam-6734	58	20	coefficients	coefficient	NOUN
ejpam-6734	58	21	and	and	CCONJ
ejpam-6734	58	22	mixed	mixed	ADJ
ejpam-6734	58	23	nonlinear	nonlinear	ADJ
ejpam-6734	58	24	terms	term	NOUN
ejpam-6734	58	25	.	.	PUNCT
ejpam-6734	59	1	υ1(ω)ζ	υ1(ω)ζ	PROPN
ejpam-6734	59	2	′′(ω	′′(ω	PROPN
ejpam-6734	59	3	)	)	PUNCT
ejpam-6734	60	1	+	+	CCONJ
ejpam-6734	60	2	υ2(ω)ζ	υ2(ω)ζ	PROPN
ejpam-6734	60	3	′(ω	′(ω	NOUN
ejpam-6734	60	4	)	)	PUNCT
ejpam-6734	60	5	+	+	CCONJ
ejpam-6734	60	6	υ3(ω)ζ	υ3(ω)ζ	NUM
ejpam-6734	61	1	′2(ω	′2(ω	NUM
ejpam-6734	61	2	)	)	PUNCT
ejpam-6734	62	1	+	+	CCONJ
ejpam-6734	62	2	υ4(ω)ζ(ω	υ4(ω)ζ(ω	NOUN
ejpam-6734	62	3	)	)	PUNCT
ejpam-6734	62	4	=	=	SYM
ejpam-6734	62	5	ξ(ω	ξ(ω	NOUN
ejpam-6734	62	6	)	)	PUNCT
ejpam-6734	62	7	,	,	PUNCT
ejpam-6734	62	8	(	(	PUNCT
ejpam-6734	62	9	1	1	X
ejpam-6734	62	10	)	)	PUNCT
ejpam-6734	62	11	or	or	CCONJ
ejpam-6734	62	12	special	special	ADJ
ejpam-6734	62	13	non	non	ADJ
ejpam-6734	62	14	-	-	ADJ
ejpam-6734	62	15	linear	linear	ADJ
ejpam-6734	62	16	models	model	NOUN
ejpam-6734	62	17	of	of	ADP
ejpam-6734	62	18	the	the	DET
ejpam-6734	62	19	form	form	NOUN
ejpam-6734	62	20	(	(	PUNCT
ejpam-6734	62	21	2	2	NUM
ejpam-6734	62	22	)	)	PUNCT
ejpam-6734	62	23	,	,	PUNCT
ejpam-6734	62	24	ζ	ζ	PROPN
ejpam-6734	62	25	′′(ω	′′(ω	NOUN
ejpam-6734	62	26	)	)	PUNCT
ejpam-6734	62	27	+	+	CCONJ
ejpam-6734	62	28	f(ζ	f(ζ	NOUN
ejpam-6734	62	29	)	)	PUNCT
ejpam-6734	63	1	=	=	SYM
ejpam-6734	63	2	0	0	NUM
ejpam-6734	63	3	,	,	PUNCT
ejpam-6734	63	4	(	(	PUNCT
ejpam-6734	63	5	2	2	X
ejpam-6734	63	6	)	)	PUNCT
ejpam-6734	63	7	with	with	ADP
ejpam-6734	63	8	the	the	DET
ejpam-6734	63	9	conditions	condition	NOUN
ejpam-6734	63	10	:	:	PUNCT
ejpam-6734	63	11	ζ(0	ζ(0	NOUN
ejpam-6734	63	12	)	)	PUNCT
ejpam-6734	63	13	=	=	SYM
ejpam-6734	63	14	m1	m1	NOUN
ejpam-6734	63	15	,	,	PUNCT
ejpam-6734	63	16	ζ	ζ	PROPN
ejpam-6734	63	17	′(0	′(0	PROPN
ejpam-6734	63	18	)	)	PUNCT
ejpam-6734	64	1	=	=	SYM
ejpam-6734	64	2	m2	m2	PROPN
ejpam-6734	64	3	,	,	PUNCT
ejpam-6734	64	4	(	(	PUNCT
ejpam-6734	64	5	3	3	NUM
ejpam-6734	64	6	)	)	PUNCT
ejpam-6734	64	7	or	or	CCONJ
ejpam-6734	64	8	ζ(0	ζ(0	NOUN
ejpam-6734	64	9	)	)	PUNCT
ejpam-6734	64	10	=	=	SYM
ejpam-6734	64	11	m1	m1	NOUN
ejpam-6734	64	12	,	,	PUNCT
ejpam-6734	64	13	ζ(1	ζ(1	PROPN
ejpam-6734	64	14	)	)	PUNCT
ejpam-6734	64	15	=	=	SYM
ejpam-6734	64	16	m3	m3	PROPN
ejpam-6734	64	17	.	.	PUNCT
ejpam-6734	65	1	(	(	PUNCT
ejpam-6734	65	2	4	4	X
ejpam-6734	65	3	)	)	PUNCT
ejpam-6734	65	4	we	we	PRON
ejpam-6734	65	5	wrote	write	VERB
ejpam-6734	65	6	out	out	ADP
ejpam-6734	65	7	eq	eq	ADP
ejpam-6734	65	8	.	.	PUNCT
ejpam-6734	66	1	(	(	PUNCT
ejpam-6734	66	2	2	2	NUM
ejpam-6734	66	3	)	)	PUNCT
ejpam-6734	66	4	to	to	PART
ejpam-6734	66	5	show	show	VERB
ejpam-6734	66	6	that	that	SCONJ
ejpam-6734	66	7	our	our	PRON
ejpam-6734	66	8	methods	method	NOUN
ejpam-6734	66	9	are	be	AUX
ejpam-6734	66	10	n’t	not	PART
ejpam-6734	66	11	just	just	ADV
ejpam-6734	66	12	for	for	ADP
ejpam-6734	66	13	the	the	DET
ejpam-6734	66	14	most	most	ADV
ejpam-6734	66	15	general	general	ADJ
ejpam-6734	66	16	situation	situation	NOUN
ejpam-6734	66	17	.	.	PUNCT
ejpam-6734	67	1	they	they	PRON
ejpam-6734	67	2	also	also	ADV
ejpam-6734	67	3	work	work	VERB
ejpam-6734	67	4	for	for	ADP
ejpam-6734	67	5	some	some	DET
ejpam-6734	67	6	important	important	ADJ
ejpam-6734	67	7	specific	specific	ADJ
ejpam-6734	67	8	situations	situation	NOUN
ejpam-6734	67	9	.	.	PUNCT
ejpam-6734	68	1	this	this	DET
ejpam-6734	68	2	split	split	NOUN
ejpam-6734	68	3	makes	make	VERB
ejpam-6734	68	4	section	section	NOUN
ejpam-6734	68	5	4	4	NUM
ejpam-6734	68	6	easier	easy	ADJ
ejpam-6734	68	7	to	to	PART
ejpam-6734	68	8	follow	follow	VERB
ejpam-6734	68	9	.	.	PUNCT
ejpam-6734	69	1	some	some	DET
ejpam-6734	69	2	problems	problem	NOUN
ejpam-6734	69	3	just	just	ADV
ejpam-6734	69	4	naturally	naturally	ADV
ejpam-6734	69	5	fit	fit	ADJ
ejpam-6734	69	6	eq	eq	ADP
ejpam-6734	69	7	.	.	PUNCT
ejpam-6734	70	1	(	(	PUNCT
ejpam-6734	70	2	1	1	NUM
ejpam-6734	70	3	)	)	PUNCT
ejpam-6734	70	4	,	,	PUNCT
ejpam-6734	70	5	but	but	CCONJ
ejpam-6734	70	6	others	other	NOUN
ejpam-6734	70	7	are	be	AUX
ejpam-6734	70	8	better	well	ADV
ejpam-6734	70	9	suited	suited	ADJ
ejpam-6734	70	10	for	for	ADP
ejpam-6734	70	11	eq	eq	PROPN
ejpam-6734	70	12	.	.	PUNCT
ejpam-6734	71	1	(	(	PUNCT
ejpam-6734	71	2	2	2	NUM
ejpam-6734	71	3	)	)	PUNCT
ejpam-6734	71	4	.	.	PUNCT
ejpam-6734	72	1	where	where	SCONJ
ejpam-6734	72	2	ζ(ω	ζ(ω	PROPN
ejpam-6734	72	3	)	)	PUNCT
ejpam-6734	72	4	is	be	AUX
ejpam-6734	72	5	the	the	DET
ejpam-6734	72	6	unknown	unknown	ADJ
ejpam-6734	72	7	function	function	NOUN
ejpam-6734	72	8	and	and	CCONJ
ejpam-6734	72	9	m1,m2	m1,m2	PROPN
ejpam-6734	72	10	,	,	PUNCT
ejpam-6734	72	11	m3	m3	PROPN
ejpam-6734	72	12	are	be	AUX
ejpam-6734	72	13	arbitrary	arbitrary	ADJ
ejpam-6734	72	14	real	real	ADJ
ejpam-6734	72	15	constants	constant	NOUN
ejpam-6734	72	16	.	.	PUNCT
ejpam-6734	73	1	with	with	ADP
ejpam-6734	73	2	υj(ω)(j	υj(ω)(j	NOUN
ejpam-6734	73	3	=	=	SYM
ejpam-6734	73	4	1	1	NUM
ejpam-6734	73	5	,	,	PUNCT
ejpam-6734	73	6	...	...	PUNCT
ejpam-6734	73	7	4	4	NUM
ejpam-6734	73	8	)	)	PUNCT
ejpam-6734	73	9	,	,	PUNCT
ejpam-6734	73	10	f(ζ	f(ζ	PROPN
ejpam-6734	73	11	)	)	PUNCT
ejpam-6734	73	12	,	,	PUNCT
ejpam-6734	73	13	ξ(ω	ξ(ω	NOUN
ejpam-6734	73	14	)	)	PUNCT
ejpam-6734	73	15	are	be	AUX
ejpam-6734	73	16	known	know	VERB
ejpam-6734	73	17	and	and	CCONJ
ejpam-6734	73	18	continuous	continuous	ADJ
ejpam-6734	73	19	on	on	ADP
ejpam-6734	73	20	the	the	DET
ejpam-6734	73	21	interval	interval	NOUN
ejpam-6734	73	22	[	[	X
ejpam-6734	73	23	0	0	NUM
ejpam-6734	73	24	,	,	PUNCT
ejpam-6734	73	25	1	1	NUM
ejpam-6734	73	26	]	]	PUNCT
ejpam-6734	73	27	.	.	PUNCT
ejpam-6734	74	1	with	with	ADP
ejpam-6734	74	2	υ1(ω	υ1(ω	NOUN
ejpam-6734	74	3	)	)	PUNCT
ejpam-6734	74	4	̸=	̸=	PROPN
ejpam-6734	74	5	0	0	NUM
ejpam-6734	74	6	the	the	DET
ejpam-6734	74	7	paper	paper	NOUN
ejpam-6734	74	8	is	be	AUX
ejpam-6734	74	9	organized	organize	VERB
ejpam-6734	74	10	as	as	SCONJ
ejpam-6734	74	11	follows	follow	VERB
ejpam-6734	74	12	:	:	PUNCT
ejpam-6734	74	13	section	section	NOUN
ejpam-6734	74	14	2	2	NUM
ejpam-6734	74	15	presents	present	VERB
ejpam-6734	74	16	the	the	DET
ejpam-6734	74	17	important	important	ADJ
ejpam-6734	74	18	relations	relation	NOUN
ejpam-6734	74	19	for	for	ADP
ejpam-6734	74	20	the	the	DET
ejpam-6734	74	21	dtm	dtm	PROPN
ejpam-6734	74	22	,	,	PUNCT
ejpam-6734	74	23	the	the	DET
ejpam-6734	74	24	fcm	fcm	X
ejpam-6734	74	25	,	,	PUNCT
ejpam-6734	74	26	and	and	CCONJ
ejpam-6734	74	27	the	the	DET
ejpam-6734	74	28	algorithm	algorithm	NOUN
ejpam-6734	74	29	of	of	ADP
ejpam-6734	74	30	the	the	DET
ejpam-6734	74	31	methods	method	NOUN
ejpam-6734	74	32	that	that	PRON
ejpam-6734	74	33	are	be	AUX
ejpam-6734	74	34	useful	useful	ADJ
ejpam-6734	74	35	in	in	ADP
ejpam-6734	74	36	the	the	DET
ejpam-6734	74	37	next	next	ADJ
ejpam-6734	74	38	sections	section	NOUN
ejpam-6734	74	39	.	.	PUNCT
ejpam-6734	75	1	the	the	DET
ejpam-6734	75	2	convergence	convergence	NOUN
ejpam-6734	75	3	is	be	AUX
ejpam-6734	75	4	discussed	discuss	VERB
ejpam-6734	75	5	in	in	ADP
ejpam-6734	75	6	section	section	NOUN
ejpam-6734	75	7	3	3	NUM
ejpam-6734	75	8	.	.	PUNCT
ejpam-6734	76	1	we	we	PRON
ejpam-6734	76	2	give	give	VERB
ejpam-6734	76	3	some	some	DET
ejpam-6734	76	4	numerical	numerical	ADJ
ejpam-6734	76	5	examples	example	NOUN
ejpam-6734	76	6	and	and	CCONJ
ejpam-6734	76	7	compare	compare	VERB
ejpam-6734	76	8	them	they	PRON
ejpam-6734	76	9	with	with	ADP
ejpam-6734	76	10	others	other	NOUN
ejpam-6734	76	11	in	in	ADP
ejpam-6734	76	12	section	section	NOUN
ejpam-6734	76	13	4	4	NUM
ejpam-6734	76	14	,	,	PUNCT
ejpam-6734	76	15	the	the	DET
ejpam-6734	76	16	results	result	NOUN
ejpam-6734	76	17	show	show	VERB
ejpam-6734	76	18	the	the	DET
ejpam-6734	76	19	efficiency	efficiency	NOUN
ejpam-6734	76	20	of	of	ADP
ejpam-6734	76	21	the	the	DET
ejpam-6734	76	22	methods	method	NOUN
ejpam-6734	76	23	.	.	PUNCT
ejpam-6734	77	1	in	in	ADP
ejpam-6734	77	2	section	section	NOUN
ejpam-6734	77	3	5	5	NUM
ejpam-6734	77	4	,	,	PUNCT
ejpam-6734	77	5	we	we	PRON
ejpam-6734	77	6	introduce	introduce	VERB
ejpam-6734	77	7	some	some	DET
ejpam-6734	77	8	conclusions	conclusion	NOUN
ejpam-6734	77	9	.	.	PUNCT
ejpam-6734	78	1	2	2	X
ejpam-6734	78	2	.	.	X
ejpam-6734	78	3	description	description	NOUN
ejpam-6734	78	4	of	of	ADP
ejpam-6734	78	5	the	the	DET
ejpam-6734	78	6	methods	method	NOUN
ejpam-6734	78	7	this	this	DET
ejpam-6734	78	8	section	section	NOUN
ejpam-6734	78	9	describes	describe	VERB
ejpam-6734	78	10	the	the	DET
ejpam-6734	78	11	properties	property	NOUN
ejpam-6734	78	12	and	and	CCONJ
ejpam-6734	78	13	important	important	ADJ
ejpam-6734	78	14	relations	relation	NOUN
ejpam-6734	78	15	between	between	ADP
ejpam-6734	78	16	the	the	DET
ejpam-6734	78	17	dtm	dtm	PROPN
ejpam-6734	78	18	and	and	CCONJ
ejpam-6734	78	19	the	the	DET
ejpam-6734	78	20	gfcm	gfcm	PROPN
ejpam-6734	78	21	,	,	PUNCT
ejpam-6734	78	22	which	which	PRON
ejpam-6734	78	23	are	be	AUX
ejpam-6734	78	24	used	use	VERB
ejpam-6734	78	25	in	in	ADP
ejpam-6734	78	26	the	the	DET
ejpam-6734	78	27	following	follow	VERB
ejpam-6734	78	28	sections	section	NOUN
ejpam-6734	78	29	.	.	PUNCT
ejpam-6734	79	1	m.	m.	NOUN
ejpam-6734	79	2	a.	a.	PROPN
ejpam-6734	79	3	abdou	abdou	PROPN
ejpam-6734	79	4	,	,	PUNCT
ejpam-6734	79	5	a.	a.	PROPN
ejpam-6734	79	6	s.	s.	PROPN
ejpam-6734	79	7	mohamed	mohamed	PROPN
ejpam-6734	79	8	/	/	SYM
ejpam-6734	79	9	eur	eur	PROPN
ejpam-6734	79	10	.	.	PUNCT
ejpam-6734	80	1	j.	j.	PROPN
ejpam-6734	80	2	pure	pure	PROPN
ejpam-6734	80	3	appl	appl	PROPN
ejpam-6734	80	4	.	.	PROPN
ejpam-6734	80	5	math	math	PROPN
ejpam-6734	80	6	,	,	PUNCT
ejpam-6734	80	7	18	18	NUM
ejpam-6734	80	8	(	(	PUNCT
ejpam-6734	80	9	4	4	NUM
ejpam-6734	80	10	)	)	PUNCT
ejpam-6734	80	11	(	(	PUNCT
ejpam-6734	80	12	2025	2025	NUM
ejpam-6734	80	13	)	)	PUNCT
ejpam-6734	80	14	,	,	PUNCT
ejpam-6734	80	15	6734	6734	NUM
ejpam-6734	80	16	4	4	NUM
ejpam-6734	80	17	of	of	ADP
ejpam-6734	80	18	20	20	NUM
ejpam-6734	80	19	2.1	2.1	NUM
ejpam-6734	80	20	.	.	PUNCT
ejpam-6734	81	1	the	the	DET
ejpam-6734	81	2	dtm	dtm	PROPN
ejpam-6734	81	3	this	this	DET
ejpam-6734	81	4	method	method	NOUN
ejpam-6734	81	5	is	be	AUX
ejpam-6734	81	6	an	an	DET
ejpam-6734	81	7	expansion	expansion	NOUN
ejpam-6734	81	8	of	of	ADP
ejpam-6734	81	9	a	a	DET
ejpam-6734	81	10	function	function	NOUN
ejpam-6734	81	11	into	into	ADP
ejpam-6734	81	12	the	the	DET
ejpam-6734	81	13	taylor	taylor	PROPN
ejpam-6734	81	14	series	series	PROPN
ejpam-6734	81	15	.	.	PUNCT
ejpam-6734	82	1	the	the	DET
ejpam-6734	82	2	differential	differential	ADJ
ejpam-6734	82	3	transform	transform	NOUN
ejpam-6734	82	4	of	of	ADP
ejpam-6734	82	5	a	a	DET
ejpam-6734	82	6	function	function	NOUN
ejpam-6734	82	7	ζ(ω	ζ(ω	PROPN
ejpam-6734	82	8	)	)	PUNCT
ejpam-6734	82	9	is	be	AUX
ejpam-6734	82	10	defined	define	VERB
ejpam-6734	82	11	as	as	SCONJ
ejpam-6734	82	12	follows	follow	VERB
ejpam-6734	82	13	ψ(i	ψ(i	NOUN
ejpam-6734	82	14	)	)	PUNCT
ejpam-6734	83	1	=	=	SYM
ejpam-6734	83	2	1	1	NUM
ejpam-6734	83	3	i	i	NOUN
ejpam-6734	83	4	!	!	PUNCT
ejpam-6734	84	1	[	[	PUNCT
ejpam-6734	84	2	diζ(ω	diζ(ω	PROPN
ejpam-6734	84	3	)	)	PUNCT
ejpam-6734	84	4	dωi	dωi	NOUN
ejpam-6734	84	5	]	]	X
ejpam-6734	84	6	ω=0	ω=0	X
ejpam-6734	84	7	.	.	PUNCT
ejpam-6734	85	1	(	(	PUNCT
ejpam-6734	85	2	5	5	NUM
ejpam-6734	85	3	)	)	PUNCT
ejpam-6734	85	4	then	then	ADV
ejpam-6734	85	5	the	the	DET
ejpam-6734	85	6	inverse	inverse	NOUN
ejpam-6734	85	7	differential	differential	NOUN
ejpam-6734	85	8	transform	transform	NOUN
ejpam-6734	85	9	is	be	AUX
ejpam-6734	85	10	:	:	PUNCT
ejpam-6734	85	11	ζ(ω	ζ(ω	PROPN
ejpam-6734	85	12	)	)	PUNCT
ejpam-6734	85	13	=	=	PUNCT
ejpam-6734	86	1	∞∑	∞∑	NUM
ejpam-6734	86	2	i=0	i=0	ADJ
ejpam-6734	86	3	ψ(i	ψ(i	NOUN
ejpam-6734	86	4	)	)	PUNCT
ejpam-6734	86	5	ωi	ωi	X
ejpam-6734	86	6	.	.	PUNCT
ejpam-6734	87	1	(	(	PUNCT
ejpam-6734	87	2	6	6	NUM
ejpam-6734	87	3	)	)	PUNCT
ejpam-6734	87	4	the	the	DET
ejpam-6734	87	5	important	important	ADJ
ejpam-6734	87	6	relations	relation	NOUN
ejpam-6734	87	7	for	for	ADP
ejpam-6734	87	8	dtm	dtm	PROPN
ejpam-6734	87	9	are	be	AUX
ejpam-6734	87	10	:	:	PUNCT
ejpam-6734	87	11	if	if	SCONJ
ejpam-6734	87	12	ζ(ω	ζ(ω	PRON
ejpam-6734	87	13	)	)	PUNCT
ejpam-6734	87	14	=	=	PUNCT
ejpam-6734	88	1	sin(b1ω	sin(b1ω	PROPN
ejpam-6734	88	2	+	+	NUM
ejpam-6734	88	3	b2	b2	NOUN
ejpam-6734	88	4	)	)	PUNCT
ejpam-6734	88	5	,	,	PUNCT
ejpam-6734	88	6	then	then	ADV
ejpam-6734	88	7	ψ(i	ψ(i	PROPN
ejpam-6734	88	8	)	)	PUNCT
ejpam-6734	89	1	=	=	SYM
ejpam-6734	89	2	bi1	bi1	NOUN
ejpam-6734	90	1	i	i	PRON
ejpam-6734	90	2	!	!	PUNCT
ejpam-6734	91	1	sin	sin	NOUN
ejpam-6734	91	2	(	(	PUNCT
ejpam-6734	91	3	i	i	NOUN
ejpam-6734	91	4	π	π	PROPN
ejpam-6734	91	5	2	2	NUM
ejpam-6734	91	6	+	+	CCONJ
ejpam-6734	91	7	b2	b2	NOUN
ejpam-6734	91	8	)	)	PUNCT
ejpam-6734	91	9	.	.	PUNCT
ejpam-6734	92	1	(	(	PUNCT
ejpam-6734	92	2	7	7	X
ejpam-6734	92	3	)	)	PUNCT
ejpam-6734	92	4	if	if	SCONJ
ejpam-6734	92	5	ζ(ω	ζ(ω	NOUN
ejpam-6734	92	6	)	)	PUNCT
ejpam-6734	92	7	=	=	SYM
ejpam-6734	92	8	ωm	ωm	PROPN
ejpam-6734	92	9	,	,	PUNCT
ejpam-6734	92	10	then	then	ADV
ejpam-6734	92	11	ψ(i	ψ(i	NOUN
ejpam-6734	92	12	)	)	PUNCT
ejpam-6734	92	13	=	=	PUNCT
ejpam-6734	92	14	δ(i−m	δ(i−m	PROPN
ejpam-6734	92	15	)	)	PUNCT
ejpam-6734	92	16	=	=	PRON
ejpam-6734	92	17	{	{	PUNCT
ejpam-6734	92	18	1	1	NUM
ejpam-6734	92	19	i	i	NOUN
ejpam-6734	92	20	=	=	NOUN
ejpam-6734	92	21	m	m	VERB
ejpam-6734	92	22	0	0	NUM
ejpam-6734	93	1	i	i	PRON
ejpam-6734	93	2	̸=	̸=	PROPN
ejpam-6734	93	3	m	m	VERB
ejpam-6734	93	4	(	(	PUNCT
ejpam-6734	93	5	8)	8)	NUM
ejpam-6734	93	6	if	if	SCONJ
ejpam-6734	93	7	κ(ζ	κ(ζ	NOUN
ejpam-6734	93	8	)	)	PUNCT
ejpam-6734	93	9	=	=	SYM
ejpam-6734	93	10	ζ(n)(ω	ζ(n)(ω	NUM
ejpam-6734	93	11	)	)	PUNCT
ejpam-6734	93	12	,	,	PUNCT
ejpam-6734	93	13	then	then	ADV
ejpam-6734	93	14	χ(i	χ(i	PROPN
ejpam-6734	93	15	)	)	PUNCT
ejpam-6734	93	16	=	=	PUNCT
ejpam-6734	94	1	(	(	PUNCT
ejpam-6734	94	2	i+	i+	NOUN
ejpam-6734	94	3	1	1	NUM
ejpam-6734	94	4	)	)	PUNCT
ejpam-6734	94	5	(	(	PUNCT
ejpam-6734	94	6	i+	i+	NUM
ejpam-6734	94	7	2)	2)	NUM
ejpam-6734	94	8	....	....	PUNCT
ejpam-6734	94	9	(i+	(i+	PROPN
ejpam-6734	94	10	n)ψ(i+	n)ψ(i+	PROPN
ejpam-6734	94	11	n	n	CCONJ
ejpam-6734	94	12	)	)	PUNCT
ejpam-6734	94	13	.	.	PUNCT
ejpam-6734	95	1	(	(	PUNCT
ejpam-6734	95	2	9	9	X
ejpam-6734	95	3	)	)	PUNCT
ejpam-6734	95	4	if	if	SCONJ
ejpam-6734	95	5	κ(ζ	κ(ζ	NOUN
ejpam-6734	95	6	)	)	PUNCT
ejpam-6734	95	7	=	=	SYM
ejpam-6734	95	8	ecζ(ω	ecζ(ω	PROPN
ejpam-6734	95	9	)	)	PUNCT
ejpam-6734	95	10	,	,	PUNCT
ejpam-6734	95	11	then	then	ADV
ejpam-6734	95	12	χ(i	χ(i	PROPN
ejpam-6734	95	13	)	)	PUNCT
ejpam-6734	96	1	=	=	PRON
ejpam-6734	96	2	{	{	PUNCT
ejpam-6734	96	3	ecψ(0	ecψ(0	NOUN
ejpam-6734	96	4	)	)	PUNCT
ejpam-6734	96	5	,	,	PUNCT
ejpam-6734	97	1	i	i	PRON
ejpam-6734	97	2	=	=	NOUN
ejpam-6734	97	3	0	0	PROPN
ejpam-6734	97	4	c	c	NOUN
ejpam-6734	97	5	∑i−1	∑i−1	PROPN
ejpam-6734	98	1	k=0	k=0	PROPN
ejpam-6734	98	2	k+1	k+1	X
ejpam-6734	99	1	i	i	PRON
ejpam-6734	99	2	ψ(k	ψ(k	PROPN
ejpam-6734	99	3	+	+	CCONJ
ejpam-6734	99	4	1	1	X
ejpam-6734	99	5	)	)	PUNCT
ejpam-6734	99	6	χ(i−	χ(i−	NUM
ejpam-6734	100	1	k	k	NOUN
ejpam-6734	100	2	−	−	PROPN
ejpam-6734	101	1	1	1	NUM
ejpam-6734	101	2	)	)	PUNCT
ejpam-6734	101	3	,	,	PUNCT
ejpam-6734	101	4	i	i	PRON
ejpam-6734	101	5	≥	≥	VERB
ejpam-6734	101	6	1	1	NUM
ejpam-6734	101	7	(	(	PUNCT
ejpam-6734	101	8	10	10	NUM
ejpam-6734	101	9	)	)	PUNCT
ejpam-6734	101	10	if	if	SCONJ
ejpam-6734	101	11	κ(ω	κ(ω	PROPN
ejpam-6734	101	12	)	)	PUNCT
ejpam-6734	101	13	=	=	SYM
ejpam-6734	101	14	ζ1(ω	ζ1(ω	NUM
ejpam-6734	101	15	)	)	PUNCT
ejpam-6734	101	16	ζ2(ω	ζ2(ω	NUM
ejpam-6734	101	17	)	)	PUNCT
ejpam-6734	101	18	,	,	PUNCT
ejpam-6734	101	19	then	then	ADV
ejpam-6734	101	20	χ(i	χ(i	PROPN
ejpam-6734	101	21	)	)	PUNCT
ejpam-6734	102	1	=	=	SYM
ejpam-6734	102	2	i∑	i∑	PROPN
ejpam-6734	102	3	k=0	k=0	PROPN
ejpam-6734	102	4	ψ1(k	ψ1(k	PART
ejpam-6734	102	5	)	)	PUNCT
ejpam-6734	102	6	ψ2(i−	ψ2(i−	NOUN
ejpam-6734	103	1	k	k	X
ejpam-6734	103	2	)	)	PUNCT
ejpam-6734	103	3	.	.	PUNCT
ejpam-6734	104	1	(	(	PUNCT
ejpam-6734	104	2	11	11	NUM
ejpam-6734	104	3	)	)	PUNCT
ejpam-6734	104	4	2.2	2.2	NUM
ejpam-6734	104	5	.	.	PUNCT
ejpam-6734	105	1	the	the	DET
ejpam-6734	105	2	gfcm	gfcm	PROPN
ejpam-6734	105	3	in	in	ADP
ejpam-6734	105	4	this	this	DET
ejpam-6734	105	5	part	part	NOUN
ejpam-6734	105	6	,	,	PUNCT
ejpam-6734	105	7	we	we	PRON
ejpam-6734	105	8	display	display	VERB
ejpam-6734	105	9	the	the	DET
ejpam-6734	105	10	important	important	ADJ
ejpam-6734	105	11	relations	relation	NOUN
ejpam-6734	105	12	between	between	ADP
ejpam-6734	105	13	the	the	DET
ejpam-6734	105	14	gfps	gfps	NOUN
ejpam-6734	105	15	,	,	PUNCT
ejpam-6734	105	16	ϕλ1,λ2	ϕλ1,λ2	VERB
ejpam-6734	105	17	i	i	PRON
ejpam-6734	105	18	(	(	PUNCT
ejpam-6734	105	19	ω	ω	NOUN
ejpam-6734	105	20	)	)	PUNCT
ejpam-6734	105	21	of	of	ADP
ejpam-6734	105	22	degree	degree	NOUN
ejpam-6734	105	23	i	i	PRON
ejpam-6734	105	24	,	,	PUNCT
ejpam-6734	105	25	and	and	CCONJ
ejpam-6734	105	26	the	the	DET
ejpam-6734	105	27	algorithm	algorithm	NOUN
ejpam-6734	105	28	of	of	ADP
ejpam-6734	105	29	these	these	DET
ejpam-6734	105	30	polynomials	polynomial	NOUN
ejpam-6734	105	31	.	.	PUNCT
ejpam-6734	106	1	the	the	DET
ejpam-6734	106	2	basis	basis	NOUN
ejpam-6734	106	3	used	use	VERB
ejpam-6734	106	4	in	in	ADP
ejpam-6734	106	5	this	this	DET
ejpam-6734	106	6	paper	paper	NOUN
ejpam-6734	106	7	is	be	AUX
ejpam-6734	106	8	the	the	DET
ejpam-6734	106	9	generalized	generalized	ADJ
ejpam-6734	106	10	fibonacci	fibonacci	NOUN
ejpam-6734	106	11	polynomials	polynomial	NOUN
ejpam-6734	106	12	.	.	PUNCT
ejpam-6734	107	1	these	these	DET
ejpam-6734	107	2	polynomials	polynomial	NOUN
ejpam-6734	107	3	involve	involve	VERB
ejpam-6734	107	4	important	important	ADJ
ejpam-6734	107	5	particular	particular	ADJ
ejpam-6734	107	6	polynomials	polynomial	NOUN
ejpam-6734	107	7	,	,	PUNCT
ejpam-6734	107	8	such	such	ADJ
ejpam-6734	107	9	as	as	ADP
ejpam-6734	107	10	fibonacci	fibonacci	NOUN
ejpam-6734	107	11	,	,	PUNCT
ejpam-6734	107	12	pell	pell	INTJ
ejpam-6734	107	13	,	,	PUNCT
ejpam-6734	107	14	chebyshev	chebyshev	NOUN
ejpam-6734	107	15	polynomials	polynomial	NOUN
ejpam-6734	107	16	of	of	ADP
ejpam-6734	107	17	the	the	DET
ejpam-6734	107	18	second	second	ADJ
ejpam-6734	107	19	kind	kind	NOUN
ejpam-6734	107	20	,	,	PUNCT
ejpam-6734	107	21	fermat	fermat	ADJ
ejpam-6734	107	22	and	and	CCONJ
ejpam-6734	107	23	second	second	ADJ
ejpam-6734	107	24	kind	kind	NOUN
ejpam-6734	107	25	dickson	dickson	PROPN
ejpam-6734	107	26	depend	depend	VERB
ejpam-6734	107	27	on	on	ADP
ejpam-6734	107	28	λ1	λ1	ADJ
ejpam-6734	107	29	,	,	PUNCT
ejpam-6734	107	30	and	and	CCONJ
ejpam-6734	107	31	λ2	λ2	NOUN
ejpam-6734	107	32	.	.	PUNCT
ejpam-6734	108	1	we	we	PRON
ejpam-6734	108	2	used	use	VERB
ejpam-6734	108	3	the	the	DET
ejpam-6734	108	4	first	first	ADJ
ejpam-6734	108	5	four	four	NUM
ejpam-6734	108	6	polynomials	polynomial	NOUN
ejpam-6734	108	7	only	only	ADV
ejpam-6734	108	8	.	.	PUNCT
ejpam-6734	109	1	the	the	DET
ejpam-6734	109	2	recurrence	recurrence	NOUN
ejpam-6734	109	3	relations	relation	NOUN
ejpam-6734	109	4	of	of	ADP
ejpam-6734	109	5	generalized	generalized	ADJ
ejpam-6734	109	6	fibonacci	fibonacci	NOUN
ejpam-6734	109	7	polynomials	polynomial	NOUN
ejpam-6734	109	8	have	have	VERB
ejpam-6734	109	9	the	the	DET
ejpam-6734	109	10	following	follow	VERB
ejpam-6734	109	11	form	form	NOUN
ejpam-6734	109	12	[	[	X
ejpam-6734	109	13	30	30	NUM
ejpam-6734	109	14	]	]	X
ejpam-6734	109	15	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	110	1	i	i	PRON
ejpam-6734	110	2	(	(	PUNCT
ejpam-6734	110	3	ω	ω	NOUN
ejpam-6734	110	4	)	)	PUNCT
ejpam-6734	110	5	=	=	PUNCT
ejpam-6734	110	6	λ1ωϕ	λ1ωϕ	PUNCT
ejpam-6734	111	1	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	111	2	i−1	i−1	PROPN
ejpam-6734	111	3	(	(	PUNCT
ejpam-6734	111	4	ω	ω	NOUN
ejpam-6734	111	5	)	)	PUNCT
ejpam-6734	111	6	+	+	CCONJ
ejpam-6734	111	7	λ2ϕ	λ2ϕ	X
ejpam-6734	111	8	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	111	9	i−2	i−2	PROPN
ejpam-6734	111	10	(	(	PUNCT
ejpam-6734	111	11	ω	ω	NOUN
ejpam-6734	111	12	)	)	PUNCT
ejpam-6734	111	13	,	,	PUNCT
ejpam-6734	111	14	i	i	PRON
ejpam-6734	111	15	≥	≥	VERB
ejpam-6734	111	16	2	2	NUM
ejpam-6734	111	17	.	.	PUNCT
ejpam-6734	111	18	(	(	PUNCT
ejpam-6734	111	19	12	12	NUM
ejpam-6734	111	20	)	)	PUNCT
ejpam-6734	111	21	m.	m.	NOUN
ejpam-6734	111	22	a.	a.	PROPN
ejpam-6734	111	23	abdou	abdou	PROPN
ejpam-6734	111	24	,	,	PUNCT
ejpam-6734	111	25	a.	a.	PROPN
ejpam-6734	111	26	s.	s.	PROPN
ejpam-6734	111	27	mohamed	mohamed	PROPN
ejpam-6734	111	28	/	/	SYM
ejpam-6734	111	29	eur	eur	PROPN
ejpam-6734	111	30	.	.	PUNCT
ejpam-6734	112	1	j.	j.	PROPN
ejpam-6734	112	2	pure	pure	PROPN
ejpam-6734	112	3	appl	appl	PROPN
ejpam-6734	112	4	.	.	PROPN
ejpam-6734	112	5	math	math	PROPN
ejpam-6734	112	6	,	,	PUNCT
ejpam-6734	112	7	18	18	NUM
ejpam-6734	112	8	(	(	PUNCT
ejpam-6734	112	9	4	4	NUM
ejpam-6734	112	10	)	)	PUNCT
ejpam-6734	112	11	(	(	PUNCT
ejpam-6734	112	12	2025	2025	NUM
ejpam-6734	112	13	)	)	PUNCT
ejpam-6734	112	14	,	,	PUNCT
ejpam-6734	112	15	6734	6734	NUM
ejpam-6734	112	16	5	5	NUM
ejpam-6734	112	17	of	of	ADP
ejpam-6734	112	18	20	20	NUM
ejpam-6734	112	19	with	with	ADP
ejpam-6734	112	20	initial	initial	ADJ
ejpam-6734	112	21	values	value	NOUN
ejpam-6734	112	22	:	:	PUNCT
ejpam-6734	112	23	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	112	24	0	0	PUNCT
ejpam-6734	113	1	(	(	PUNCT
ejpam-6734	113	2	ω	ω	NOUN
ejpam-6734	113	3	)	)	PUNCT
ejpam-6734	113	4	=	=	SYM
ejpam-6734	113	5	1	1	NUM
ejpam-6734	113	6	,	,	PUNCT
ejpam-6734	113	7	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	113	8	1	1	NUM
ejpam-6734	113	9	(	(	PUNCT
ejpam-6734	113	10	ω	ω	NOUN
ejpam-6734	113	11	)	)	PUNCT
ejpam-6734	113	12	=	=	SYM
ejpam-6734	113	13	λ1ω	λ1ω	NOUN
ejpam-6734	113	14	.	.	PUNCT
ejpam-6734	114	1	it	it	PRON
ejpam-6734	114	2	has	have	VERB
ejpam-6734	114	3	the	the	DET
ejpam-6734	114	4	binet	binet	NOUN
ejpam-6734	114	5	’s	’s	PART
ejpam-6734	114	6	form	form	NOUN
ejpam-6734	114	7	[	[	X
ejpam-6734	114	8	30	30	NUM
ejpam-6734	114	9	]	]	X
ejpam-6734	114	10	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	114	11	i	i	PRON
ejpam-6734	114	12	(	(	PUNCT
ejpam-6734	114	13	ω	ω	NOUN
ejpam-6734	114	14	)	)	PUNCT
ejpam-6734	114	15	=	=	SYM
ejpam-6734	114	16	(	(	PUNCT
ejpam-6734	115	1	λ1ω	λ1ω	X
ejpam-6734	115	2	+	+	CCONJ
ejpam-6734	115	3	√	√	NUM
ejpam-6734	115	4	λ2	λ2	NOUN
ejpam-6734	115	5	1ω	1ω	NUM
ejpam-6734	115	6	2	2	NUM
ejpam-6734	115	7	+	+	NUM
ejpam-6734	115	8	4λ2	4λ2	NUM
ejpam-6734	115	9	)	)	PUNCT
ejpam-6734	116	1	i	i	PRON
ejpam-6734	116	2	−	−	PROPN
ejpam-6734	117	1	(	(	PUNCT
ejpam-6734	118	1	λ1ω	λ1ω	X
ejpam-6734	118	2	+	+	CCONJ
ejpam-6734	118	3	√	√	NUM
ejpam-6734	118	4	λ2	λ2	NOUN
ejpam-6734	118	5	1ω	1ω	NUM
ejpam-6734	118	6	2	2	NUM
ejpam-6734	118	7	+	+	NUM
ejpam-6734	118	8	4λ2	4λ2	NUM
ejpam-6734	118	9	)	)	PUNCT
ejpam-6734	119	1	i	i	PRON
ejpam-6734	119	2	2i	2i	VERB
ejpam-6734	119	3	√	√	NUM
ejpam-6734	119	4	λ2	λ2	NOUN
ejpam-6734	119	5	1ω	1ω	PROPN
ejpam-6734	119	6	2	2	NUM
ejpam-6734	119	7	+	+	NUM
ejpam-6734	119	8	4λ2	4λ2	NUM
ejpam-6734	119	9	,	,	PUNCT
ejpam-6734	119	10	(	(	PUNCT
ejpam-6734	119	11	13	13	NUM
ejpam-6734	119	12	)	)	PUNCT
ejpam-6734	119	13	and	and	CCONJ
ejpam-6734	119	14	the	the	DET
ejpam-6734	119	15	analytic	analytic	ADJ
ejpam-6734	119	16	form	form	NOUN
ejpam-6734	119	17	is	be	AUX
ejpam-6734	119	18	[	[	X
ejpam-6734	119	19	30	30	NUM
ejpam-6734	119	20	]	]	X
ejpam-6734	119	21	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	119	22	i	i	PRON
ejpam-6734	119	23	(	(	PUNCT
ejpam-6734	119	24	ω	ω	NOUN
ejpam-6734	119	25	)	)	PUNCT
ejpam-6734	119	26	=	=	PUNCT
ejpam-6734	120	1	⌊	⌊	VERB
ejpam-6734	120	2	i	i	PRON
ejpam-6734	120	3	2	2	NUM
ejpam-6734	120	4	⌋∑	⌋∑	NOUN
ejpam-6734	120	5	k=0	k=0	PROPN
ejpam-6734	120	6	(	(	PUNCT
ejpam-6734	120	7	i−k	i−k	VERB
ejpam-6734	120	8	k	k	PROPN
ejpam-6734	120	9	)	)	PUNCT
ejpam-6734	120	10	λk	λk	ADP
ejpam-6734	120	11	2	2	NUM
ejpam-6734	120	12	(	(	PUNCT
ejpam-6734	120	13	λ1ω	λ1ω	NOUN
ejpam-6734	120	14	)	)	PUNCT
ejpam-6734	120	15	i−2k	i−2k	NOUN
ejpam-6734	120	16	.	.	PUNCT
ejpam-6734	121	1	(	(	PUNCT
ejpam-6734	121	2	14	14	NUM
ejpam-6734	121	3	)	)	PUNCT
ejpam-6734	121	4	we	we	PRON
ejpam-6734	121	5	expand	expand	VERB
ejpam-6734	121	6	the	the	DET
ejpam-6734	121	7	function	function	NOUN
ejpam-6734	121	8	in	in	ADP
ejpam-6734	121	9	terms	term	NOUN
ejpam-6734	121	10	of	of	ADP
ejpam-6734	121	11	the	the	DET
ejpam-6734	121	12	gfps	gfps	NOUN
ejpam-6734	121	13	:	:	PUNCT
ejpam-6734	121	14	ζ(ω	ζ(ω	PROPN
ejpam-6734	121	15	)	)	PUNCT
ejpam-6734	121	16	=	=	PUNCT
ejpam-6734	122	1	∞∑	∞∑	NUM
ejpam-6734	122	2	i=0	i=0	ADJ
ejpam-6734	122	3	aiϕ	aiϕ	NOUN
ejpam-6734	122	4	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	122	5	i	i	PROPN
ejpam-6734	122	6	(	(	PUNCT
ejpam-6734	122	7	ω	ω	NOUN
ejpam-6734	122	8	)	)	PUNCT
ejpam-6734	122	9	.	.	PUNCT
ejpam-6734	123	1	(	(	PUNCT
ejpam-6734	123	2	15	15	NUM
ejpam-6734	123	3	)	)	PUNCT
ejpam-6734	123	4	the	the	DET
ejpam-6734	123	5	approximate	approximate	ADJ
ejpam-6734	123	6	solution	solution	NOUN
ejpam-6734	123	7	has	have	VERB
ejpam-6734	123	8	the	the	DET
ejpam-6734	123	9	following	follow	VERB
ejpam-6734	123	10	form	form	NOUN
ejpam-6734	123	11	:	:	PUNCT
ejpam-6734	123	12	ζ(ω	ζ(ω	PROPN
ejpam-6734	123	13	)	)	PUNCT
ejpam-6734	124	1	≈	≈	PROPN
ejpam-6734	124	2	ζk(ω	ζk(ω	NOUN
ejpam-6734	124	3	)	)	PUNCT
ejpam-6734	124	4	=	=	VERB
ejpam-6734	125	1	l∑	l∑	PROPN
ejpam-6734	126	1	i=0	i=0	PROPN
ejpam-6734	126	2	ai	ai	AUX
ejpam-6734	126	3	ϕ	ϕ	PROPN
ejpam-6734	126	4	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	126	5	i	i	PROPN
ejpam-6734	126	6	(	(	PUNCT
ejpam-6734	126	7	ω	ω	NOUN
ejpam-6734	126	8	)	)	PUNCT
ejpam-6734	126	9	=	=	PUNCT
ejpam-6734	126	10	at	at	ADP
ejpam-6734	126	11	φ(ω	φ(ω	PROPN
ejpam-6734	126	12	)	)	PUNCT
ejpam-6734	126	13	,	,	PUNCT
ejpam-6734	126	14	(	(	PUNCT
ejpam-6734	126	15	16	16	NUM
ejpam-6734	126	16	)	)	PUNCT
ejpam-6734	126	17	where	where	SCONJ
ejpam-6734	126	18	φ(ω	φ(ω	ADV
ejpam-6734	126	19	)	)	PUNCT
ejpam-6734	127	1	=	=	PUNCT
ejpam-6734	127	2	[	[	PUNCT
ejpam-6734	127	3	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	127	4	0	0	NUM
ejpam-6734	127	5	(	(	PUNCT
ejpam-6734	127	6	ω	ω	NOUN
ejpam-6734	127	7	)	)	PUNCT
ejpam-6734	127	8	,	,	PUNCT
ejpam-6734	127	9	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	127	10	1	1	NUM
ejpam-6734	127	11	(	(	PUNCT
ejpam-6734	127	12	ω	ω	NOUN
ejpam-6734	127	13	)	)	PUNCT
ejpam-6734	127	14	,	,	PUNCT
ejpam-6734	127	15	...	...	PUNCT
ejpam-6734	127	16	,	,	PUNCT
ejpam-6734	127	17	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	127	18	l	l	NOUN
ejpam-6734	127	19	(	(	PUNCT
ejpam-6734	127	20	ω	ω	NOUN
ejpam-6734	127	21	)	)	PUNCT
ejpam-6734	127	22	]	]	X
ejpam-6734	127	23	t	t	NOUN
ejpam-6734	127	24	,	,	PUNCT
ejpam-6734	127	25	(	(	PUNCT
ejpam-6734	127	26	17	17	NUM
ejpam-6734	127	27	)	)	PUNCT
ejpam-6734	127	28	and	and	CCONJ
ejpam-6734	127	29	the	the	DET
ejpam-6734	127	30	coefficients	coefficient	NOUN
ejpam-6734	127	31	at	at	ADP
ejpam-6734	127	32	=	=	PROPN
ejpam-6734	128	1	[	[	X
ejpam-6734	128	2	a0	a0	PROPN
ejpam-6734	128	3	,	,	PUNCT
ejpam-6734	128	4	a1	a1	NOUN
ejpam-6734	128	5	,	,	PUNCT
ejpam-6734	128	6	...	...	PUNCT
ejpam-6734	128	7	,	,	PUNCT
ejpam-6734	128	8	al	al	PROPN
ejpam-6734	128	9	]	]	X
ejpam-6734	128	10	,	,	PUNCT
ejpam-6734	128	11	(	(	PUNCT
ejpam-6734	128	12	18	18	NUM
ejpam-6734	128	13	)	)	PUNCT
ejpam-6734	128	14	must	must	AUX
ejpam-6734	128	15	be	be	AUX
ejpam-6734	128	16	determined	determine	VERB
ejpam-6734	128	17	.	.	PUNCT
ejpam-6734	129	1	the	the	DET
ejpam-6734	129	2	first	first	ADJ
ejpam-6734	129	3	and	and	CCONJ
ejpam-6734	129	4	the	the	DET
ejpam-6734	129	5	second	second	ADJ
ejpam-6734	129	6	derivatives	derivative	NOUN
ejpam-6734	129	7	of	of	ADP
ejpam-6734	129	8	φ(ω	φ(ω	NOUN
ejpam-6734	129	9	)	)	PUNCT
ejpam-6734	129	10	are	be	AUX
ejpam-6734	129	11	in	in	ADP
ejpam-6734	129	12	the	the	DET
ejpam-6734	129	13	following	follow	VERB
ejpam-6734	129	14	forms	form	NOUN
ejpam-6734	129	15	[	[	X
ejpam-6734	129	16	30	30	NUM
ejpam-6734	129	17	]	]	PUNCT
ejpam-6734	129	18	dφ(ω	dφ(ω	NUM
ejpam-6734	129	19	)	)	PUNCT
ejpam-6734	129	20	dω	dω	ADP
ejpam-6734	129	21	=	=	PUNCT
ejpam-6734	129	22	h(1)φ(ω	h(1)φ(ω	NOUN
ejpam-6734	129	23	)	)	PUNCT
ejpam-6734	130	1	=	=	PRON
ejpam-6734	130	2	(	(	PUNCT
ejpam-6734	130	3	h	h	NOUN
ejpam-6734	130	4	(	(	PUNCT
ejpam-6734	130	5	1	1	NUM
ejpam-6734	130	6	)	)	PUNCT
ejpam-6734	130	7	αβ	αβ	NOUN
ejpam-6734	130	8	)	)	PUNCT
ejpam-6734	130	9	φ(ω	φ(ω	NOUN
ejpam-6734	130	10	)	)	PUNCT
ejpam-6734	130	11	,	,	PUNCT
ejpam-6734	130	12	and	and	CCONJ
ejpam-6734	130	13	d2φ(ω	d2φ(ω	PROPN
ejpam-6734	130	14	)	)	PUNCT
ejpam-6734	130	15	dω2	dω2	NOUN
ejpam-6734	130	16	=	=	SYM
ejpam-6734	130	17	h(2)φ(ω	h(2)φ(ω	NUM
ejpam-6734	130	18	)	)	PUNCT
ejpam-6734	131	1	=	=	PRON
ejpam-6734	131	2	(	(	PUNCT
ejpam-6734	131	3	h	h	NOUN
ejpam-6734	131	4	(	(	PUNCT
ejpam-6734	131	5	1	1	NUM
ejpam-6734	131	6	)	)	PUNCT
ejpam-6734	131	7	αβ	αβ	NOUN
ejpam-6734	131	8	)	)	PUNCT
ejpam-6734	131	9	2	2	NUM
ejpam-6734	131	10	φ(ω	φ(ω	NOUN
ejpam-6734	131	11	)	)	PUNCT
ejpam-6734	131	12	.	.	PUNCT
ejpam-6734	132	1	where	where	SCONJ
ejpam-6734	132	2	h	h	NOUN
ejpam-6734	132	3	(	(	PUNCT
ejpam-6734	132	4	1	1	X
ejpam-6734	132	5	)	)	PUNCT
ejpam-6734	132	6	αβ	αβ	PRON
ejpam-6734	132	7	is	be	AUX
ejpam-6734	132	8	(	(	PUNCT
ejpam-6734	132	9	l+	l+	PROPN
ejpam-6734	132	10	1)×	1)×	NUM
ejpam-6734	132	11	(	(	PUNCT
ejpam-6734	132	12	l+	l+	NOUN
ejpam-6734	132	13	1	1	NUM
ejpam-6734	132	14	)	)	PUNCT
ejpam-6734	132	15	operational	operational	ADJ
ejpam-6734	132	16	matrix	matrix	NOUN
ejpam-6734	132	17	.	.	PUNCT
ejpam-6734	133	1	it	it	PRON
ejpam-6734	133	2	has	have	VERB
ejpam-6734	133	3	the	the	DET
ejpam-6734	133	4	following	follow	VERB
ejpam-6734	133	5	form	form	NOUN
ejpam-6734	133	6	h	h	NOUN
ejpam-6734	133	7	(	(	PUNCT
ejpam-6734	133	8	1	1	NUM
ejpam-6734	133	9	)	)	PUNCT
ejpam-6734	133	10	αβ	αβ	NOUN
ejpam-6734	133	11	=	=	PRON
ejpam-6734	133	12	{	{	PUNCT
ejpam-6734	133	13	(	(	PUNCT
ejpam-6734	133	14	−1	−1	NOUN
ejpam-6734	133	15	)	)	PUNCT
ejpam-6734	133	16	α−β−1	α−β−1	NUM
ejpam-6734	133	17	2	2	NUM
ejpam-6734	133	18	(	(	PUNCT
ejpam-6734	133	19	β	β	X
ejpam-6734	133	20	+	+	X
ejpam-6734	133	21	1)λ1	1)λ1	NUM
ejpam-6734	133	22	λ	λ	NOUN
ejpam-6734	133	23	α−β−1	α−β−1	NUM
ejpam-6734	133	24	2	2	NUM
ejpam-6734	133	25	2	2	NUM
ejpam-6734	133	26	,	,	PUNCT
ejpam-6734	133	27	α	α	X
ejpam-6734	133	28	>	>	X
ejpam-6734	133	29	β	β	X
ejpam-6734	133	30	,	,	PUNCT
ejpam-6734	133	31	(	(	PUNCT
ejpam-6734	133	32	α+	α+	X
ejpam-6734	133	33	β	β	NOUN
ejpam-6734	133	34	)	)	PUNCT
ejpam-6734	133	35	odd	odd	ADJ
ejpam-6734	133	36	,	,	PUNCT
ejpam-6734	133	37	0	0	NUM
ejpam-6734	133	38	,	,	PUNCT
ejpam-6734	133	39	otherwise	otherwise	ADV
ejpam-6734	133	40	.	.	PUNCT
ejpam-6734	134	1	m.	m.	NOUN
ejpam-6734	134	2	a.	a.	PROPN
ejpam-6734	134	3	abdou	abdou	PROPN
ejpam-6734	134	4	,	,	PUNCT
ejpam-6734	134	5	a.	a.	PROPN
ejpam-6734	134	6	s.	s.	PROPN
ejpam-6734	134	7	mohamed	mohamed	PROPN
ejpam-6734	134	8	/	/	SYM
ejpam-6734	134	9	eur	eur	PROPN
ejpam-6734	134	10	.	.	PUNCT
ejpam-6734	135	1	j.	j.	PROPN
ejpam-6734	135	2	pure	pure	PROPN
ejpam-6734	135	3	appl	appl	PROPN
ejpam-6734	135	4	.	.	PROPN
ejpam-6734	135	5	math	math	PROPN
ejpam-6734	135	6	,	,	PUNCT
ejpam-6734	135	7	18	18	NUM
ejpam-6734	135	8	(	(	PUNCT
ejpam-6734	135	9	4	4	NUM
ejpam-6734	135	10	)	)	PUNCT
ejpam-6734	135	11	(	(	PUNCT
ejpam-6734	135	12	2025	2025	NUM
ejpam-6734	135	13	)	)	PUNCT
ejpam-6734	135	14	,	,	PUNCT
ejpam-6734	135	15	6734	6734	NUM
ejpam-6734	135	16	6	6	NUM
ejpam-6734	135	17	of	of	ADP
ejpam-6734	135	18	20	20	NUM
ejpam-6734	135	19	if	if	SCONJ
ejpam-6734	135	20	α	α	PRON
ejpam-6734	135	21	=	=	X
ejpam-6734	135	22	β	β	X
ejpam-6734	135	23	=	=	SYM
ejpam-6734	135	24	4	4	NUM
ejpam-6734	135	25	,	,	PUNCT
ejpam-6734	135	26	then	then	ADV
ejpam-6734	135	27	h(1	h(1	PROPN
ejpam-6734	135	28	)	)	PUNCT
ejpam-6734	135	29	can	can	AUX
ejpam-6734	135	30	be	be	AUX
ejpam-6734	135	31	written	write	VERB
ejpam-6734	135	32	in	in	ADP
ejpam-6734	135	33	the	the	DET
ejpam-6734	135	34	form	form	NOUN
ejpam-6734	135	35	h(1	h(1	PROPN
ejpam-6734	135	36	)	)	PUNCT
ejpam-6734	135	37	=	=	PUNCT
ejpam-6734	135	38			NOUN
ejpam-6734	135	39	0	0	NUM
ejpam-6734	135	40	0	0	NUM
ejpam-6734	135	41	0	0	NUM
ejpam-6734	135	42	0	0	NUM
ejpam-6734	135	43	0	0	NUM
ejpam-6734	136	1	λ1	λ1	ADJ
ejpam-6734	136	2	0	0	NUM
ejpam-6734	136	3	0	0	NUM
ejpam-6734	136	4	0	0	NUM
ejpam-6734	136	5	0	0	NUM
ejpam-6734	136	6	0	0	NUM
ejpam-6734	136	7	2λ1	2λ1	NUM
ejpam-6734	136	8	0	0	NUM
ejpam-6734	136	9	0	0	NUM
ejpam-6734	136	10	0	0	NUM
ejpam-6734	137	1	−λ1λ2	−λ1λ2	NOUN
ejpam-6734	137	2	0	0	NUM
ejpam-6734	137	3	3λ1	3λ1	NUM
ejpam-6734	137	4	0	0	NUM
ejpam-6734	137	5	0	0	NUM
ejpam-6734	137	6	0	0	PUNCT
ejpam-6734	138	1	−2λ1λ2	−2λ1λ2	VERB
ejpam-6734	138	2	0	0	NUM
ejpam-6734	138	3	4λ1	4λ1	NUM
ejpam-6734	138	4	0	0	NUM
ejpam-6734	138	5			NOUN
ejpam-6734	138	6	.	.	PUNCT
ejpam-6734	139	1	from	from	ADP
ejpam-6734	139	2	eq	eq	ADP
ejpam-6734	139	3	.	.	PUNCT
ejpam-6734	140	1	(	(	PUNCT
ejpam-6734	140	2	12	12	NUM
ejpam-6734	140	3	)	)	PUNCT
ejpam-6734	140	4	and	and	CCONJ
ejpam-6734	140	5	its	its	PRON
ejpam-6734	140	6	initial	initial	ADJ
ejpam-6734	140	7	values	value	NOUN
ejpam-6734	140	8	,	,	PUNCT
ejpam-6734	140	9	φ(ω	φ(ω	PROPN
ejpam-6734	140	10	)	)	PUNCT
ejpam-6734	140	11	can	can	AUX
ejpam-6734	140	12	be	be	AUX
ejpam-6734	140	13	written	write	VERB
ejpam-6734	140	14	in	in	ADP
ejpam-6734	140	15	the	the	DET
ejpam-6734	140	16	form	form	NOUN
ejpam-6734	140	17	φ(ω	φ(ω	NOUN
ejpam-6734	140	18	)	)	PUNCT
ejpam-6734	141	1	=	=	SYM
ejpam-6734	141	2			ADJ
ejpam-6734	142	1	1	1	NUM
ejpam-6734	142	2	λ1ω	λ1ω	NOUN
ejpam-6734	142	3	λ2	λ2	NOUN
ejpam-6734	142	4	1ω	1ω	NOUN
ejpam-6734	142	5	2	2	NUM
ejpam-6734	142	6	+	+	NUM
ejpam-6734	142	7	λ2	λ2	PROPN
ejpam-6734	142	8	λ3	λ3	PROPN
ejpam-6734	142	9	1ω	1ω	PROPN
ejpam-6734	142	10	3	3	NUM
ejpam-6734	142	11	+	+	NUM
ejpam-6734	142	12	2λ1λ2ω	2λ1λ2ω	NUM
ejpam-6734	142	13	λ4	λ4	PROPN
ejpam-6734	142	14	1ω	1ω	ADJ
ejpam-6734	142	15	4	4	NUM
ejpam-6734	142	16	+	+	SYM
ejpam-6734	142	17	3λ2	3λ2	NUM
ejpam-6734	142	18	1λ2ω	1λ2ω	ADJ
ejpam-6734	142	19	2	2	NUM
ejpam-6734	142	20	+	+	NUM
ejpam-6734	142	21	λ2	λ2	NOUN
ejpam-6734	142	22	2	2	NUM
ejpam-6734	142	23			NOUN
ejpam-6734	142	24	.	.	PUNCT
ejpam-6734	143	1	from	from	ADP
ejpam-6734	143	2	eq	eq	ADP
ejpam-6734	143	3	.	.	PUNCT
ejpam-6734	144	1	(	(	PUNCT
ejpam-6734	144	2	16	16	NUM
ejpam-6734	144	3	)	)	PUNCT
ejpam-6734	144	4	into	into	ADP
ejpam-6734	144	5	eq	eq	NOUN
ejpam-6734	144	6	.	.	PUNCT
ejpam-6734	145	1	(	(	PUNCT
ejpam-6734	145	2	1	1	NUM
ejpam-6734	145	3	)	)	PUNCT
ejpam-6734	145	4	,	,	PUNCT
ejpam-6734	145	5	we	we	PRON
ejpam-6734	145	6	have	have	VERB
ejpam-6734	145	7	υ1(ω	υ1(ω	VERB
ejpam-6734	145	8	)	)	PUNCT
ejpam-6734	145	9	l∑	l∑	PUNCT
ejpam-6734	146	1	i=0	i=0	PROPN
ejpam-6734	146	2	ai	ai	INTJ
ejpam-6734	146	3	(	(	PUNCT
ejpam-6734	146	4	h	h	NOUN
ejpam-6734	146	5	(	(	PUNCT
ejpam-6734	146	6	1	1	NUM
ejpam-6734	146	7	)	)	PUNCT
ejpam-6734	146	8	αβ	αβ	NOUN
ejpam-6734	146	9	)	)	PUNCT
ejpam-6734	146	10	2	2	NUM
ejpam-6734	146	11	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	146	12	i	i	NOUN
ejpam-6734	146	13	(	(	PUNCT
ejpam-6734	146	14	ω	ω	NOUN
ejpam-6734	146	15	)	)	PUNCT
ejpam-6734	146	16	+	+	PUNCT
ejpam-6734	146	17	υ2(ω	υ2(ω	X
ejpam-6734	146	18	)	)	PUNCT
ejpam-6734	146	19	l∑	l∑	PUNCT
ejpam-6734	147	1	i=0	i=0	PROPN
ejpam-6734	147	2	ai	ai	VERB
ejpam-6734	147	3	h	h	NOUN
ejpam-6734	147	4	(	(	PUNCT
ejpam-6734	147	5	1	1	NUM
ejpam-6734	147	6	)	)	PUNCT
ejpam-6734	147	7	mnϕ	mnϕ	NOUN
ejpam-6734	147	8	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	147	9	i	i	PROPN
ejpam-6734	147	10	(	(	PUNCT
ejpam-6734	147	11	ω	ω	NOUN
ejpam-6734	147	12	)	)	PUNCT
ejpam-6734	147	13	+	+	PUNCT
ejpam-6734	147	14	υ3(ω	υ3(ω	NOUN
ejpam-6734	147	15	)	)	PUNCT
ejpam-6734	147	16	l∑	l∑	AUX
ejpam-6734	148	1	i=0	i=0	PROPN
ejpam-6734	148	2	ai	ai	INTJ
ejpam-6734	148	3	(	(	PUNCT
ejpam-6734	148	4	h	h	NOUN
ejpam-6734	148	5	(	(	PUNCT
ejpam-6734	148	6	1	1	NUM
ejpam-6734	148	7	)	)	PUNCT
ejpam-6734	148	8	mnϕ	mnϕ	NOUN
ejpam-6734	148	9	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	148	10	i	i	PROPN
ejpam-6734	148	11	(	(	PUNCT
ejpam-6734	148	12	ω))2	ω))2	PROPN
ejpam-6734	148	13	+	+	NUM
ejpam-6734	148	14	υ4(ω	υ4(ω	PROPN
ejpam-6734	148	15	)	)	PUNCT
ejpam-6734	148	16	l∑	l∑	PUNCT
ejpam-6734	149	1	i=0	i=0	PROPN
ejpam-6734	149	2	ai	ai	VERB
ejpam-6734	149	3	ϕ	ϕ	PROPN
ejpam-6734	149	4	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	149	5	i	i	PROPN
ejpam-6734	149	6	(	(	PUNCT
ejpam-6734	149	7	ω	ω	NOUN
ejpam-6734	149	8	)	)	PUNCT
ejpam-6734	149	9	=	=	SYM
ejpam-6734	149	10	ξ(ω	ξ(ω	NOUN
ejpam-6734	149	11	)	)	PUNCT
ejpam-6734	149	12	.	.	PUNCT
ejpam-6734	150	1	(	(	PUNCT
ejpam-6734	150	2	19	19	NUM
ejpam-6734	150	3	)	)	PUNCT
ejpam-6734	150	4	let	let	VERB
ejpam-6734	150	5	θi	θi	X
ejpam-6734	150	6	(	(	PUNCT
ejpam-6734	150	7	ω	ω	NOUN
ejpam-6734	150	8	)	)	PUNCT
ejpam-6734	150	9	=	=	PUNCT
ejpam-6734	151	1	υ1(ω	υ1(ω	NOUN
ejpam-6734	151	2	)	)	PUNCT
ejpam-6734	151	3	(	(	PUNCT
ejpam-6734	151	4	h	h	NOUN
ejpam-6734	151	5	(	(	PUNCT
ejpam-6734	151	6	1	1	NUM
ejpam-6734	151	7	)	)	PUNCT
ejpam-6734	151	8	αβ	αβ	NOUN
ejpam-6734	151	9	)	)	PUNCT
ejpam-6734	151	10	2	2	NUM
ejpam-6734	151	11	ϕλ1,λ2	ϕλ1,λ2	NOUN
ejpam-6734	152	1	i	i	NOUN
ejpam-6734	152	2	(	(	PUNCT
ejpam-6734	152	3	ω)+υ2(ω	ω)+υ2(ω	ADJ
ejpam-6734	152	4	)	)	PUNCT
ejpam-6734	152	5	h	h	NOUN
ejpam-6734	152	6	(	(	PUNCT
ejpam-6734	152	7	1	1	NUM
ejpam-6734	152	8	)	)	PUNCT
ejpam-6734	152	9	mnϕ	mnϕ	NOUN
ejpam-6734	152	10	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	152	11	i	i	PROPN
ejpam-6734	152	12	(	(	PUNCT
ejpam-6734	152	13	ω)+υ3(ω	ω)+υ3(ω	X
ejpam-6734	152	14	)	)	PUNCT
ejpam-6734	152	15	(	(	PUNCT
ejpam-6734	152	16	h	h	NOUN
ejpam-6734	152	17	(	(	PUNCT
ejpam-6734	152	18	1	1	NUM
ejpam-6734	152	19	)	)	PUNCT
ejpam-6734	152	20	mnϕ	mnϕ	NOUN
ejpam-6734	152	21	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	152	22	i	i	PROPN
ejpam-6734	152	23	(	(	PUNCT
ejpam-6734	152	24	ω))2+υ4(ω)ϕ	ω))2+υ4(ω)ϕ	NUM
ejpam-6734	152	25	λ1,λ2	λ1,λ2	PROPN
ejpam-6734	152	26	i	i	PROPN
ejpam-6734	152	27	(	(	PUNCT
ejpam-6734	152	28	ω	ω	NOUN
ejpam-6734	152	29	)	)	PUNCT
ejpam-6734	152	30	,	,	PUNCT
ejpam-6734	152	31	then	then	ADV
ejpam-6734	152	32	eq	eq	ADP
ejpam-6734	152	33	.	.	PUNCT
ejpam-6734	153	1	(	(	PUNCT
ejpam-6734	153	2	19	19	NUM
ejpam-6734	153	3	)	)	PUNCT
ejpam-6734	153	4	has	have	VERB
ejpam-6734	153	5	the	the	DET
ejpam-6734	153	6	form	form	NOUN
ejpam-6734	153	7	l∑	l∑	PUNCT
ejpam-6734	154	1	i=0	i=0	PROPN
ejpam-6734	154	2	ai	ai	VERB
ejpam-6734	154	3	θi	θi	PROPN
ejpam-6734	154	4	(	(	PUNCT
ejpam-6734	154	5	ω	ω	NOUN
ejpam-6734	154	6	)	)	PUNCT
ejpam-6734	154	7	=	=	SYM
ejpam-6734	154	8	ξ(ω	ξ(ω	NOUN
ejpam-6734	154	9	)	)	PUNCT
ejpam-6734	154	10	.	.	PUNCT
ejpam-6734	155	1	(	(	PUNCT
ejpam-6734	155	2	20	20	NUM
ejpam-6734	155	3	)	)	PUNCT
ejpam-6734	155	4	the	the	DET
ejpam-6734	155	5	collocation	collocation	NOUN
ejpam-6734	155	6	points	point	NOUN
ejpam-6734	155	7	are	be	AUX
ejpam-6734	155	8	taken	take	VERB
ejpam-6734	155	9	as	as	ADP
ejpam-6734	155	10	the	the	DET
ejpam-6734	155	11	roots	root	NOUN
ejpam-6734	155	12	of	of	ADP
ejpam-6734	155	13	the	the	DET
ejpam-6734	155	14	generalized	generalize	VERB
ejpam-6734	155	15	fibonacci	fibonacci	NOUN
ejpam-6734	155	16	polynomial	polynomial	ADJ
ejpam-6734	155	17	of	of	ADP
ejpam-6734	155	18	degree	degree	NOUN
ejpam-6734	155	19	l+1	l+1	PROPN
ejpam-6734	155	20	,	,	PUNCT
ejpam-6734	155	21	in	in	ADP
ejpam-6734	155	22	order	order	NOUN
ejpam-6734	155	23	to	to	PART
ejpam-6734	155	24	guarantee	guarantee	VERB
ejpam-6734	155	25	accuracy	accuracy	NOUN
ejpam-6734	155	26	and	and	CCONJ
ejpam-6734	155	27	numerical	numerical	ADJ
ejpam-6734	155	28	stability	stability	NOUN
ejpam-6734	155	29	.	.	PUNCT
ejpam-6734	156	1	so	so	ADV
ejpam-6734	156	2	we	we	PRON
ejpam-6734	156	3	have	have	VERB
ejpam-6734	156	4	a	a	DET
ejpam-6734	156	5	system	system	NOUN
ejpam-6734	156	6	of	of	ADP
ejpam-6734	156	7	equations	equation	NOUN
ejpam-6734	156	8	l∑	l∑	PUNCT
ejpam-6734	157	1	i=0	i=0	PROPN
ejpam-6734	157	2	ai	ai	VERB
ejpam-6734	157	3	θi	θi	ADJ
ejpam-6734	157	4	(	(	PUNCT
ejpam-6734	157	5	ωℓ	ωℓ	NOUN
ejpam-6734	157	6	)	)	PUNCT
ejpam-6734	157	7	=	=	SYM
ejpam-6734	157	8	ξ(ωℓ	ξ(ωℓ	PROPN
ejpam-6734	157	9	)	)	PUNCT
ejpam-6734	157	10	,	,	PUNCT
ejpam-6734	157	11	i	i	PRON
ejpam-6734	157	12	,	,	PUNCT
ejpam-6734	157	13	ℓ	ℓ	PROPN
ejpam-6734	157	14	=	=	SYM
ejpam-6734	157	15	0	0	NUM
ejpam-6734	157	16	,	,	PUNCT
ejpam-6734	157	17	1	1	NUM
ejpam-6734	157	18	,	,	PUNCT
ejpam-6734	157	19	...	...	PUNCT
ejpam-6734	157	20	,	,	PUNCT
ejpam-6734	157	21	l.	l.	PROPN
ejpam-6734	158	1	so	so	ADV
ejpam-6734	158	2	,	,	PUNCT
ejpam-6734	158	3	the	the	DET
ejpam-6734	158	4	matrix	matrix	NOUN
ejpam-6734	158	5	form	form	NOUN
ejpam-6734	158	6	is	be	AUX
ejpam-6734	158	7	:	:	PUNCT
ejpam-6734	158	8	θt	θt	PROPN
ejpam-6734	158	9	a	a	DET
ejpam-6734	158	10	=	=	SYM
ejpam-6734	158	11	ξ	ξ	PROPN
ejpam-6734	158	12	,	,	PUNCT
ejpam-6734	158	13	where	where	SCONJ
ejpam-6734	158	14	θ	θ	PROPN
ejpam-6734	158	15	=	=	SYM
ejpam-6734	158	16	(	(	PUNCT
ejpam-6734	158	17	θi	θi	X
ejpam-6734	158	18	(	(	PUNCT
ejpam-6734	158	19	ωℓ	ωℓ	NOUN
ejpam-6734	158	20	)	)	PUNCT
ejpam-6734	158	21	)	)	PUNCT
ejpam-6734	158	22	,	,	PUNCT
ejpam-6734	158	23	i	i	PRON
ejpam-6734	158	24	,	,	PUNCT
ejpam-6734	158	25	ℓ	ℓ	PROPN
ejpam-6734	158	26	=	=	SYM
ejpam-6734	158	27	0	0	NUM
ejpam-6734	158	28	,	,	PUNCT
ejpam-6734	158	29	1	1	NUM
ejpam-6734	158	30	,	,	PUNCT
ejpam-6734	158	31	....	....	PUNCT
ejpam-6734	159	1	l	l	NOUN
ejpam-6734	159	2	,	,	PUNCT
ejpam-6734	159	3	and	and	CCONJ
ejpam-6734	159	4	ξ	ξ	X
ejpam-6734	159	5	=	=	SYM
ejpam-6734	160	1	[	[	X
ejpam-6734	160	2	ξ(ω0	ξ(ω0	NOUN
ejpam-6734	160	3	)	)	PUNCT
ejpam-6734	160	4	,	,	PUNCT
ejpam-6734	160	5	ξ(ω1	ξ(ω1	NUM
ejpam-6734	160	6	)	)	PUNCT
ejpam-6734	160	7	,	,	PUNCT
ejpam-6734	160	8	...	...	PUNCT
ejpam-6734	160	9	,	,	PUNCT
ejpam-6734	160	10	ξ(ωl	ξ(ωl	PROPN
ejpam-6734	160	11	)	)	PUNCT
ejpam-6734	160	12	]	]	PUNCT
ejpam-6734	161	1	t	t	PROPN
ejpam-6734	161	2	.	.	PUNCT
ejpam-6734	162	1	m.	m.	NOUN
ejpam-6734	162	2	a.	a.	PROPN
ejpam-6734	162	3	abdou	abdou	PROPN
ejpam-6734	162	4	,	,	PUNCT
ejpam-6734	162	5	a.	a.	PROPN
ejpam-6734	162	6	s.	s.	PROPN
ejpam-6734	162	7	mohamed	mohamed	PROPN
ejpam-6734	162	8	/	/	SYM
ejpam-6734	162	9	eur	eur	PROPN
ejpam-6734	162	10	.	.	PUNCT
ejpam-6734	163	1	j.	j.	PROPN
ejpam-6734	163	2	pure	pure	PROPN
ejpam-6734	163	3	appl	appl	PROPN
ejpam-6734	163	4	.	.	PROPN
ejpam-6734	163	5	math	math	PROPN
ejpam-6734	163	6	,	,	PUNCT
ejpam-6734	163	7	18	18	NUM
ejpam-6734	163	8	(	(	PUNCT
ejpam-6734	163	9	4	4	NUM
ejpam-6734	163	10	)	)	PUNCT
ejpam-6734	163	11	(	(	PUNCT
ejpam-6734	163	12	2025	2025	NUM
ejpam-6734	163	13	)	)	PUNCT
ejpam-6734	163	14	,	,	PUNCT
ejpam-6734	163	15	6734	6734	NUM
ejpam-6734	163	16	7	7	NUM
ejpam-6734	163	17	of	of	ADP
ejpam-6734	163	18	20	20	NUM
ejpam-6734	163	19	finally	finally	ADV
ejpam-6734	163	20	,	,	PUNCT
ejpam-6734	163	21	the	the	DET
ejpam-6734	163	22	constants	constant	NOUN
ejpam-6734	163	23	can	can	AUX
ejpam-6734	163	24	be	be	AUX
ejpam-6734	163	25	evaluated	evaluate	VERB
ejpam-6734	163	26	by	by	ADP
ejpam-6734	163	27	the	the	DET
ejpam-6734	163	28	following	follow	VERB
ejpam-6734	163	29	equation	equation	NOUN
ejpam-6734	163	30	:	:	PUNCT
ejpam-6734	163	31	a	a	PRON
ejpam-6734	163	32	=	=	X
ejpam-6734	163	33	(	(	PUNCT
ejpam-6734	163	34	θt	θt	NOUN
ejpam-6734	163	35	)	)	PUNCT
ejpam-6734	163	36	−1ξ	−1ξ	PROPN
ejpam-6734	163	37	,	,	PUNCT
ejpam-6734	163	38	(	(	PUNCT
ejpam-6734	163	39	21	21	NUM
ejpam-6734	163	40	)	)	PUNCT
ejpam-6734	163	41	using	use	VERB
ejpam-6734	163	42	the	the	DET
ejpam-6734	163	43	following	following	ADJ
ejpam-6734	163	44	conditions	condition	NOUN
ejpam-6734	163	45	:	:	PUNCT
ejpam-6734	163	46	atφ(0	atφ(0	PROPN
ejpam-6734	163	47	)	)	PUNCT
ejpam-6734	164	1	=	=	SYM
ejpam-6734	164	2	m1	m1	NOUN
ejpam-6734	164	3	,	,	PUNCT
ejpam-6734	164	4	atφ′(0	atφ′(0	PROPN
ejpam-6734	164	5	)	)	PUNCT
ejpam-6734	164	6	=	=	SYM
ejpam-6734	164	7	m2	m2	PROPN
ejpam-6734	164	8	,	,	PUNCT
ejpam-6734	164	9	or	or	CCONJ
ejpam-6734	164	10	atφ(0	atφ(0	NOUN
ejpam-6734	164	11	)	)	PUNCT
ejpam-6734	165	1	=	=	SYM
ejpam-6734	165	2	m1	m1	NOUN
ejpam-6734	165	3	,	,	PUNCT
ejpam-6734	165	4	atφ(1	atφ(1	NOUN
ejpam-6734	165	5	)	)	PUNCT
ejpam-6734	165	6	=	=	SYM
ejpam-6734	165	7	m3	m3	PROPN
ejpam-6734	165	8	.	.	PUNCT
ejpam-6734	166	1	now	now	ADV
ejpam-6734	166	2	we	we	PRON
ejpam-6734	166	3	summarize	summarize	VERB
ejpam-6734	166	4	the	the	DET
ejpam-6734	166	5	steps	step	NOUN
ejpam-6734	166	6	of	of	ADP
ejpam-6734	166	7	our	our	PRON
ejpam-6734	166	8	scheme	scheme	NOUN
ejpam-6734	166	9	in	in	ADP
ejpam-6734	166	10	algorithm	algorithm	NOUN
ejpam-6734	166	11	1	1	NUM
ejpam-6734	166	12	below	below	ADP
ejpam-6734	166	13	algorithm	algorithm	NOUN
ejpam-6734	166	14	1	1	NUM
ejpam-6734	166	15	coding	code	VERB
ejpam-6734	166	16	algorithm	algorithm	NOUN
ejpam-6734	166	17	for	for	ADP
ejpam-6734	166	18	the	the	DET
ejpam-6734	166	19	proposed	propose	VERB
ejpam-6734	166	20	scheme	scheme	NOUN
ejpam-6734	166	21	input	input	NOUN
ejpam-6734	166	22	υ1(ω	υ1(ω	NOUN
ejpam-6734	166	23	)	)	PUNCT
ejpam-6734	166	24	,	,	PUNCT
ejpam-6734	166	25	υ2(ω	υ2(ω	PROPN
ejpam-6734	166	26	)	)	PUNCT
ejpam-6734	166	27	,	,	PUNCT
ejpam-6734	166	28	υ3(ω	υ3(ω	NOUN
ejpam-6734	166	29	)	)	PUNCT
ejpam-6734	166	30	,	,	PUNCT
ejpam-6734	166	31	υ4(ω	υ4(ω	PROPN
ejpam-6734	166	32	)	)	PUNCT
ejpam-6734	166	33	,	,	PUNCT
ejpam-6734	166	34	ξ(ω	ξ(ω	NOUN
ejpam-6734	166	35	)	)	PUNCT
ejpam-6734	166	36	,	,	PUNCT
ejpam-6734	166	37	f(ζ	f(ζ	PROPN
ejpam-6734	166	38	)	)	PUNCT
ejpam-6734	166	39	,	,	PUNCT
ejpam-6734	166	40	and	and	CCONJ
ejpam-6734	166	41	ζ(ω	ζ(ω	PROPN
ejpam-6734	166	42	)	)	PUNCT
ejpam-6734	166	43	.	.	PUNCT
ejpam-6734	167	1	step	step	NOUN
ejpam-6734	167	2	1	1	NUM
ejpam-6734	167	3	.	.	PUNCT
ejpam-6734	167	4	define	define	VERB
ejpam-6734	167	5	generalized	generalized	ADJ
ejpam-6734	167	6	fibonacci	fibonacci	NOUN
ejpam-6734	167	7	polynomials	polynomial	NOUN
ejpam-6734	167	8	by	by	ADP
ejpam-6734	167	9	(	(	PUNCT
ejpam-6734	167	10	13	13	NUM
ejpam-6734	167	11	)	)	PUNCT
ejpam-6734	167	12	.	.	PUNCT
ejpam-6734	168	1	step	step	NOUN
ejpam-6734	168	2	2	2	NUM
ejpam-6734	168	3	.	.	PUNCT
ejpam-6734	168	4	compute	compute	VERB
ejpam-6734	168	5	the	the	DET
ejpam-6734	168	6	basis	basis	NOUN
ejpam-6734	168	7	function	function	NOUN
ejpam-6734	168	8	of	of	ADP
ejpam-6734	168	9	generalized	generalized	ADJ
ejpam-6734	168	10	fibonacci	fibonacci	NOUN
ejpam-6734	168	11	polynomials	polynomial	NOUN
ejpam-6734	168	12	by	by	ADP
ejpam-6734	168	13	(	(	PUNCT
ejpam-6734	168	14	16	16	NUM
ejpam-6734	168	15	)	)	PUNCT
ejpam-6734	168	16	.	.	PUNCT
ejpam-6734	169	1	step	step	NOUN
ejpam-6734	169	2	3	3	NUM
ejpam-6734	169	3	.	.	PUNCT
ejpam-6734	170	1	define	define	VERB
ejpam-6734	170	2	the	the	DET
ejpam-6734	170	3	basis	basis	NOUN
ejpam-6734	170	4	function	function	NOUN
ejpam-6734	170	5	vector	vector	NOUN
ejpam-6734	170	6	φ(ω	φ(ω	PROPN
ejpam-6734	170	7	)	)	PUNCT
ejpam-6734	170	8	by	by	ADP
ejpam-6734	170	9	(	(	PUNCT
ejpam-6734	170	10	17	17	NUM
ejpam-6734	170	11	)	)	PUNCT
ejpam-6734	170	12	.	.	PUNCT
ejpam-6734	171	1	step	step	NOUN
ejpam-6734	171	2	4	4	NUM
ejpam-6734	171	3	.	.	PUNCT
ejpam-6734	171	4	differentiate	differentiate	VERB
ejpam-6734	171	5	eq	eq	ADP
ejpam-6734	171	6	.	.	PUNCT
ejpam-6734	172	1	(	(	PUNCT
ejpam-6734	172	2	16	16	NUM
ejpam-6734	172	3	)	)	PUNCT
ejpam-6734	172	4	.	.	PUNCT
ejpam-6734	173	1	step	step	NOUN
ejpam-6734	173	2	5	5	NUM
ejpam-6734	173	3	.	.	PUNCT
ejpam-6734	174	1	substituting	substitute	VERB
ejpam-6734	174	2	eq	eq	ADP
ejpam-6734	174	3	.	.	PUNCT
ejpam-6734	175	1	(	(	PUNCT
ejpam-6734	175	2	16	16	NUM
ejpam-6734	175	3	)	)	PUNCT
ejpam-6734	175	4	and	and	CCONJ
ejpam-6734	175	5	its	its	PRON
ejpam-6734	175	6	differentiation	differentiation	NOUN
ejpam-6734	175	7	into	into	ADP
ejpam-6734	175	8	eq	eq	NOUN
ejpam-6734	175	9	.	.	PUNCT
ejpam-6734	176	1	(	(	PUNCT
ejpam-6734	176	2	1	1	NUM
ejpam-6734	176	3	)	)	PUNCT
ejpam-6734	176	4	.	.	PUNCT
ejpam-6734	177	1	step	step	NOUN
ejpam-6734	177	2	6	6	NUM
ejpam-6734	177	3	.	.	PUNCT
ejpam-6734	178	1	collocating	collocate	VERB
ejpam-6734	178	2	eq	eq	PROPN
ejpam-6734	178	3	.	.	PUNCT
ejpam-6734	179	1	(	(	PUNCT
ejpam-6734	179	2	19	19	NUM
ejpam-6734	179	3	)	)	PUNCT
ejpam-6734	179	4	in	in	ADP
ejpam-6734	179	5	(	(	PUNCT
ejpam-6734	179	6	l	l	NOUN
ejpam-6734	179	7	+	+	NOUN
ejpam-6734	179	8	1	1	X
ejpam-6734	179	9	)	)	PUNCT
ejpam-6734	179	10	×	×	NOUN
ejpam-6734	179	11	(	(	PUNCT
ejpam-6734	179	12	l	l	NOUN
ejpam-6734	179	13	+	+	NOUN
ejpam-6734	179	14	1	1	X
ejpam-6734	179	15	)	)	PUNCT
ejpam-6734	179	16	roots	root	NOUN
ejpam-6734	179	17	of	of	ADP
ejpam-6734	179	18	the	the	DET
ejpam-6734	179	19	generalized	generalized	ADJ
ejpam-6734	179	20	fibonacci	fibonacci	NOUN
ejpam-6734	179	21	polynomials	polynomial	NOUN
ejpam-6734	179	22	.	.	PUNCT
ejpam-6734	180	1	step	step	NOUN
ejpam-6734	180	2	7	7	NUM
ejpam-6734	180	3	.	.	PUNCT
ejpam-6734	180	4	evaluate	evaluate	VERB
ejpam-6734	180	5	the	the	DET
ejpam-6734	180	6	residue	residue	NOUN
ejpam-6734	180	7	of	of	ADP
ejpam-6734	180	8	eq	eq	NOUN
ejpam-6734	180	9	.	.	PUNCT
ejpam-6734	181	1	(	(	PUNCT
ejpam-6734	181	2	1	1	NUM
ejpam-6734	181	3	)	)	PUNCT
ejpam-6734	181	4	.	.	PUNCT
ejpam-6734	182	1	step	step	NOUN
ejpam-6734	182	2	8	8	NUM
ejpam-6734	182	3	.	.	PUNCT
ejpam-6734	183	1	compute	compute	VERB
ejpam-6734	183	2	the	the	DET
ejpam-6734	183	3	matrix	matrix	NOUN
ejpam-6734	183	4	ξ(ω	ξ(ω	NOUN
ejpam-6734	183	5	)	)	PUNCT
ejpam-6734	183	6	using	use	VERB
ejpam-6734	183	7	(	(	PUNCT
ejpam-6734	183	8	19	19	NUM
ejpam-6734	183	9	)	)	PUNCT
ejpam-6734	183	10	.	.	PUNCT
ejpam-6734	184	1	step	step	NOUN
ejpam-6734	184	2	9	9	NUM
ejpam-6734	184	3	.	.	PUNCT
ejpam-6734	185	1	define	define	VERB
ejpam-6734	185	2	the	the	DET
ejpam-6734	185	3	(	(	PUNCT
ejpam-6734	185	4	l+	l+	PROPN
ejpam-6734	185	5	1)×	1)×	NUM
ejpam-6734	185	6	(	(	PUNCT
ejpam-6734	185	7	l+	l+	NOUN
ejpam-6734	185	8	1	1	X
ejpam-6734	185	9	)	)	PUNCT
ejpam-6734	185	10	unknown	unknown	ADJ
ejpam-6734	185	11	vectors	vector	NOUN
ejpam-6734	185	12	at	at	ADP
ejpam-6734	185	13	.	.	PUNCT
ejpam-6734	186	1	step	step	NOUN
ejpam-6734	186	2	10	10	NUM
ejpam-6734	186	3	.	.	PUNCT
ejpam-6734	187	1	use	use	VERB
ejpam-6734	187	2	findroot	findroot	NOUN
ejpam-6734	187	3	command	command	NOUN
ejpam-6734	187	4	to	to	PART
ejpam-6734	187	5	solve	solve	VERB
ejpam-6734	187	6	the	the	DET
ejpam-6734	187	7	system	system	NOUN
ejpam-6734	187	8	θt	θt	PROPN
ejpam-6734	187	9	c	c	NOUN
ejpam-6734	187	10	=	=	SYM
ejpam-6734	187	11	ξ	ξ	PROPN
ejpam-6734	187	12	.	.	PUNCT
ejpam-6734	187	13	step	step	NOUN
ejpam-6734	187	14	11	11	NUM
ejpam-6734	187	15	.	.	PUNCT
ejpam-6734	188	1	evaluate	evaluate	VERB
ejpam-6734	188	2	timeused	timeuse	VERB
ejpam-6734	188	3	for	for	ADP
ejpam-6734	188	4	the	the	DET
ejpam-6734	188	5	program	program	NOUN
ejpam-6734	188	6	.	.	PUNCT
ejpam-6734	189	1	step	step	NOUN
ejpam-6734	189	2	12	12	NUM
ejpam-6734	189	3	.	.	PUNCT
ejpam-6734	190	1	plot	plot	VERB
ejpam-6734	190	2	the	the	DET
ejpam-6734	190	3	absolute	absolute	ADJ
ejpam-6734	190	4	error	error	NOUN
ejpam-6734	190	5	.	.	PUNCT
ejpam-6734	191	1	output	output	VERB
ejpam-6734	191	2	the	the	DET
ejpam-6734	191	3	absolute	absolute	ADJ
ejpam-6734	191	4	error	error	NOUN
ejpam-6734	191	5	gi	gi	NOUN
ejpam-6734	191	6	and	and	CCONJ
ejpam-6734	191	7	approximate	approximate	ADJ
ejpam-6734	191	8	solution	solution	NOUN
ejpam-6734	191	9	φ(ω	φ(ω	NOUN
ejpam-6734	191	10	)	)	PUNCT
ejpam-6734	192	1	=	=	SYM
ejpam-6734	192	2	atθ	atθ	PROPN
ejpam-6734	192	3	.	.	PUNCT
ejpam-6734	193	1	3	3	X
ejpam-6734	193	2	.	.	X
ejpam-6734	193	3	the	the	DET
ejpam-6734	193	4	convergence	convergence	NOUN
ejpam-6734	193	5	and	and	CCONJ
ejpam-6734	193	6	error	error	NOUN
ejpam-6734	193	7	analysis	analysis	NOUN
ejpam-6734	193	8	in	in	ADP
ejpam-6734	193	9	this	this	DET
ejpam-6734	193	10	section	section	NOUN
ejpam-6734	193	11	,	,	PUNCT
ejpam-6734	193	12	we	we	PRON
ejpam-6734	193	13	evaluate	evaluate	VERB
ejpam-6734	193	14	the	the	DET
ejpam-6734	193	15	truncation	truncation	NOUN
ejpam-6734	193	16	error	error	NOUN
ejpam-6734	193	17	with	with	ADP
ejpam-6734	193	18	a	a	DET
ejpam-6734	193	19	generalized	generalized	ADJ
ejpam-6734	193	20	fibonacci	fibonacci	NOUN
ejpam-6734	193	21	expansion	expansion	NOUN
ejpam-6734	193	22	for	for	ADP
ejpam-6734	193	23	the	the	DET
ejpam-6734	193	24	equation	equation	NOUN
ejpam-6734	193	25	.	.	PUNCT
ejpam-6734	194	1	(	(	PUNCT
ejpam-6734	194	2	1	1	NUM
ejpam-6734	194	3	)	)	PUNCT
ejpam-6734	194	4	.	.	PUNCT
ejpam-6734	195	1	theorem	theorem	NOUN
ejpam-6734	195	2	1	1	NUM
ejpam-6734	195	3	.	.	PUNCT
ejpam-6734	196	1	let	let	VERB
ejpam-6734	196	2	gl(ω	gl(ω	X
ejpam-6734	196	3	)	)	PUNCT
ejpam-6734	196	4	=	=	SYM
ejpam-6734	196	5	∣∣υ1(ω)ζ	∣∣υ1(ω)ζ	PROPN
ejpam-6734	196	6	′′l(ω	′′l(ω	NOUN
ejpam-6734	196	7	)	)	PUNCT
ejpam-6734	197	1	+	+	CCONJ
ejpam-6734	197	2	υ2(ω)ζ	υ2(ω)ζ	NOUN
ejpam-6734	197	3	′	′	NUM
ejpam-6734	198	1	l(ω	l(ω	PROPN
ejpam-6734	198	2	)	)	PUNCT
ejpam-6734	199	1	+	+	CCONJ
ejpam-6734	199	2	υ3(ω)ζ	υ3(ω)ζ	NUM
ejpam-6734	199	3	′2	′2	X
ejpam-6734	199	4	l	l	X
ejpam-6734	199	5	(	(	PUNCT
ejpam-6734	199	6	ω	ω	NOUN
ejpam-6734	199	7	)	)	PUNCT
ejpam-6734	199	8	+	+	CCONJ
ejpam-6734	199	9	υ4(ω)ζl(ω)−	υ4(ω)ζl(ω)−	NOUN
ejpam-6734	199	10	ξ(ω	ξ(ω	NOUN
ejpam-6734	199	11	)	)	PUNCT
ejpam-6734	199	12	∣∣	∣∣	NUM
ejpam-6734	199	13	,	,	PUNCT
ejpam-6734	199	14	ğl	ğl	X
ejpam-6734	199	15	=	=	SYM
ejpam-6734	199	16	max	max	PROPN
ejpam-6734	199	17	0≤ω≤ϱ	0≤ω≤ϱ	PROPN
ejpam-6734	199	18	gl(ω	gl(ω	PROPN
ejpam-6734	199	19	)	)	PUNCT
ejpam-6734	199	20	,	,	PUNCT
ejpam-6734	199	21	ϱ	ϱ	ADP
ejpam-6734	199	22	≥	≥	NOUN
ejpam-6734	199	23	0	0	NUM
ejpam-6734	199	24	,	,	PUNCT
ejpam-6734	199	25	and	and	CCONJ
ejpam-6734	199	26	if	if	SCONJ
ejpam-6734	199	27	|υj(ω)|	|υj(ω)|	PRON
ejpam-6734	199	28	≤	≤	PUNCT
ejpam-6734	199	29	nj	nj	PROPN
ejpam-6734	199	30	.	.	PUNCT
ejpam-6734	200	1	where	where	SCONJ
ejpam-6734	200	2	nj	nj	PROPN
ejpam-6734	200	3	are	be	AUX
ejpam-6734	200	4	positive	positive	ADJ
ejpam-6734	200	5	constants	constant	NOUN
ejpam-6734	200	6	for	for	ADP
ejpam-6734	200	7	0	0	NUM
ejpam-6734	200	8	≤	≤	NUM
ejpam-6734	200	9	j	j	PROPN
ejpam-6734	200	10	≤	≤	ADV
ejpam-6734	200	11	4	4	NUM
ejpam-6734	200	12	.	.	PUNCT
ejpam-6734	201	1	then	then	ADV
ejpam-6734	201	2	we	we	PRON
ejpam-6734	201	3	have	have	VERB
ejpam-6734	201	4	the	the	DET
ejpam-6734	201	5	following	follow	VERB
ejpam-6734	201	6	truncation	truncation	NOUN
ejpam-6734	201	7	error	error	NOUN
ejpam-6734	201	8	:	:	PUNCT
ejpam-6734	201	9	ğl	ğl	X
ejpam-6734	201	10	≤	≤	NUM
ejpam-6734	201	11	4nρ2	4nρ2	NUM
ejpam-6734	201	12	{	{	PUNCT
ejpam-6734	201	13	w	w	PROPN
ejpam-6734	201	14	2+l	2+l	NUM
ejpam-6734	201	15	(	(	PUNCT
ejpam-6734	201	16	1	1	NUM
ejpam-6734	201	17	+	+	NUM
ejpam-6734	201	18	l	l	NOUN
ejpam-6734	201	19	)	)	PUNCT
ejpam-6734	201	20	(	(	PUNCT
ejpam-6734	201	21	γ	γ	X
ejpam-6734	201	22	(	(	PUNCT
ejpam-6734	201	23	1	1	NUM
ejpam-6734	201	24	+	+	NUM
ejpam-6734	201	25	l))2	l))2	PROPN
ejpam-6734	201	26	{	{	PUNCT
ejpam-6734	201	27	eww	eww	PROPN
ejpam-6734	201	28	(	(	PUNCT
ejpam-6734	201	29	1	1	NUM
ejpam-6734	201	30	+	+	NOUN
ejpam-6734	201	31	w	w	NOUN
ejpam-6734	201	32	)	)	PUNCT
ejpam-6734	202	1	+	+	CCONJ
ejpam-6734	202	2	(	(	PUNCT
ejpam-6734	202	3	1	1	NUM
ejpam-6734	202	4	+	+	NUM
ejpam-6734	202	5	l)(1	l)(1	X
ejpam-6734	203	1	+	+	CCONJ
ejpam-6734	203	2	l+w	l+w	X
ejpam-6734	203	3	)	)	PUNCT
ejpam-6734	203	4	}	}	PUNCT
ejpam-6734	203	5	×	×	NOUN
ejpam-6734	203	6	{	{	PUNCT
ejpam-6734	203	7	−w	−w	ADV
ejpam-6734	203	8	2+l(1	2+l(1	NUM
ejpam-6734	203	9	+	+	NUM
ejpam-6734	203	10	l+w	l+w	X
ejpam-6734	203	11	)	)	PUNCT
ejpam-6734	204	1	+	+	CCONJ
ejpam-6734	204	2	(	(	PUNCT
ejpam-6734	204	3	1	1	NUM
ejpam-6734	204	4	+	+	NUM
ejpam-6734	204	5	2eww	2eww	NOUN
ejpam-6734	204	6	2	2	NUM
ejpam-6734	204	7	(	(	PUNCT
ejpam-6734	204	8	1	1	NUM
ejpam-6734	204	9	+	+	NOUN
ejpam-6734	204	10	w	w	NOUN
ejpam-6734	204	11	)	)	PUNCT
ejpam-6734	204	12	)	)	PUNCT
ejpam-6734	204	13	γ	γ	X
ejpam-6734	204	14	(	(	PUNCT
ejpam-6734	204	15	1	1	NUM
ejpam-6734	204	16	+	+	NUM
ejpam-6734	204	17	l	l	NOUN
ejpam-6734	204	18	)	)	PUNCT
ejpam-6734	204	19	}	}	PUNCT
ejpam-6734	205	1	+	+	CCONJ
ejpam-6734	205	2	w	w	X
ejpam-6734	205	3	ewp	ewp	PROPN
ejpam-6734	205	4	(	(	PUNCT
ejpam-6734	205	5	wp	wp	NOUN
ejpam-6734	205	6	)	)	PUNCT
ejpam-6734	205	7	l	l	NOUN
ejpam-6734	205	8	γ	γ	X
ejpam-6734	205	9	(	(	PUNCT
ejpam-6734	205	10	l	l	NOUN
ejpam-6734	205	11	)	)	PUNCT
ejpam-6734	205	12	}	}	PUNCT
ejpam-6734	205	13	.	.	PUNCT
ejpam-6734	206	1	m.	m.	NOUN
ejpam-6734	206	2	a.	a.	PROPN
ejpam-6734	206	3	abdou	abdou	PROPN
ejpam-6734	206	4	,	,	PUNCT
ejpam-6734	206	5	a.	a.	PROPN
ejpam-6734	206	6	s.	s.	PROPN
ejpam-6734	206	7	mohamed	mohamed	PROPN
ejpam-6734	206	8	/	/	SYM
ejpam-6734	206	9	eur	eur	PROPN
ejpam-6734	206	10	.	.	PUNCT
ejpam-6734	207	1	j.	j.	PROPN
ejpam-6734	207	2	pure	pure	PROPN
ejpam-6734	207	3	appl	appl	PROPN
ejpam-6734	207	4	.	.	PROPN
ejpam-6734	207	5	math	math	PROPN
ejpam-6734	207	6	,	,	PUNCT
ejpam-6734	207	7	18	18	NUM
ejpam-6734	207	8	(	(	PUNCT
ejpam-6734	207	9	4	4	NUM
ejpam-6734	207	10	)	)	PUNCT
ejpam-6734	207	11	(	(	PUNCT
ejpam-6734	207	12	2025	2025	NUM
ejpam-6734	207	13	)	)	PUNCT
ejpam-6734	207	14	,	,	PUNCT
ejpam-6734	207	15	6734	6734	NUM
ejpam-6734	207	16	8	8	NUM
ejpam-6734	207	17	of	of	ADP
ejpam-6734	207	18	20	20	NUM
ejpam-6734	207	19	proof	proof	NOUN
ejpam-6734	207	20	.	.	PUNCT
ejpam-6734	208	1	from	from	ADP
ejpam-6734	208	2	eq	eq	ADP
ejpam-6734	208	3	.	.	PUNCT
ejpam-6734	209	1	(	(	PUNCT
ejpam-6734	209	2	1	1	NUM
ejpam-6734	209	3	)	)	PUNCT
ejpam-6734	209	4	,	,	PUNCT
ejpam-6734	209	5	we	we	PRON
ejpam-6734	209	6	have	have	VERB
ejpam-6734	209	7	ξ(ω	ξ(ω	NOUN
ejpam-6734	209	8	)	)	PUNCT
ejpam-6734	210	1	=	=	SYM
ejpam-6734	210	2	υ1(ω)ζ	υ1(ω)ζ	PROPN
ejpam-6734	210	3	′′(ω	′′(ω	PROPN
ejpam-6734	210	4	)	)	PUNCT
ejpam-6734	211	1	+	+	CCONJ
ejpam-6734	211	2	υ2(ω)ζ	υ2(ω)ζ	PROPN
ejpam-6734	211	3	′(ω	′(ω	NOUN
ejpam-6734	211	4	)	)	PUNCT
ejpam-6734	211	5	+	+	CCONJ
ejpam-6734	211	6	υ3(ω)ζ	υ3(ω)ζ	NUM
ejpam-6734	212	1	′2(ω	′2(ω	NUM
ejpam-6734	212	2	)	)	PUNCT
ejpam-6734	213	1	+	+	CCONJ
ejpam-6734	213	2	υ4(ω)ζ(ω	υ4(ω)ζ(ω	NOUN
ejpam-6734	213	3	)	)	PUNCT
ejpam-6734	213	4	.	.	PUNCT
ejpam-6734	214	1	from	from	ADP
ejpam-6734	214	2	the	the	DET
ejpam-6734	214	3	hypotheses	hypothesis	NOUN
ejpam-6734	214	4	of	of	ADP
ejpam-6734	214	5	the	the	DET
ejpam-6734	214	6	theorem	theorem	NOUN
ejpam-6734	214	7	,	,	PUNCT
ejpam-6734	214	8	we	we	PRON
ejpam-6734	214	9	obtain	obtain	VERB
ejpam-6734	214	10	gl(ω	gl(ω	X
ejpam-6734	214	11	)	)	PUNCT
ejpam-6734	214	12	≤	≤	NUM
ejpam-6734	214	13	n1	n1	ADJ
ejpam-6734	214	14	∣∣ζ	∣∣ζ	PROPN
ejpam-6734	214	15	′′(ω)−	′′(ω)−	PROPN
ejpam-6734	214	16	ζ	ζ	PROPN
ejpam-6734	214	17	′′l(ω	′′l(ω	NOUN
ejpam-6734	214	18	)	)	PUNCT
ejpam-6734	214	19	∣∣+n2	∣∣+n2	NUM
ejpam-6734	215	1	∣∣∣ζ	∣∣∣ζ	PROPN
ejpam-6734	215	2	′	′	NOUN
ejpam-6734	216	1	(	(	PUNCT
ejpam-6734	216	2	ω)−	ω)−	NOUN
ejpam-6734	216	3	ζ	ζ	NOUN
ejpam-6734	216	4	′	′	NUM
ejpam-6734	216	5	l(ω	l(ω	PROPN
ejpam-6734	216	6	)	)	PUNCT
ejpam-6734	216	7	∣∣∣+n3	∣∣∣+n3	NOUN
ejpam-6734	216	8	∣∣ζ	∣∣ζ	PROPN
ejpam-6734	216	9	′2(ω)−	′2(ω)−	PROPN
ejpam-6734	216	10	ζ	ζ	PROPN
ejpam-6734	216	11	′2l	′2l	PROPN
ejpam-6734	216	12	(	(	PUNCT
ejpam-6734	216	13	ω	ω	NOUN
ejpam-6734	216	14	)	)	PUNCT
ejpam-6734	216	15	∣∣+n4	∣∣+n4	ADP
ejpam-6734	216	16	|ζ(ω)−	|ζ(ω)−	PROPN
ejpam-6734	216	17	ζl(ω)|	ζl(ω)|	PUNCT
ejpam-6734	216	18	.	.	PUNCT
ejpam-6734	217	1	from	from	ADP
ejpam-6734	217	2	theorems	theorem	NOUN
ejpam-6734	217	3	(	(	PUNCT
ejpam-6734	217	4	5	5	NUM
ejpam-6734	217	5	)	)	PUNCT
ejpam-6734	217	6	and	and	CCONJ
ejpam-6734	217	7	(	(	PUNCT
ejpam-6734	217	8	6	6	NUM
ejpam-6734	217	9	)	)	PUNCT
ejpam-6734	217	10	[	[	X
ejpam-6734	217	11	30	30	NUM
ejpam-6734	217	12	]	]	PUNCT
ejpam-6734	217	13	|ai|	|ai|	PROPN
ejpam-6734	217	14	≤	≤	NUM
ejpam-6734	217	15	ρ	ρ	PROPN
ejpam-6734	217	16	w	w	PROPN
ejpam-6734	217	17	i+1	i+1	NOUN
ejpam-6734	217	18	i	i	PRON
ejpam-6734	217	19	!	!	PUNCT
ejpam-6734	217	20	,	,	PUNCT
ejpam-6734	217	21	∣∣ζ	∣∣ζ	PROPN
ejpam-6734	217	22	′′(ω)−	′′(ω)−	PROPN
ejpam-6734	217	23	ζ	ζ	NOUN
ejpam-6734	217	24	′′l(ω	′′l(ω	NOUN
ejpam-6734	217	25	)	)	PUNCT
ejpam-6734	217	26	∣∣	∣∣	NUM
ejpam-6734	217	27	≤	≤	NOUN
ejpam-6734	218	1	∞∑	∞∑	NUM
ejpam-6734	218	2	i	i	PRON
ejpam-6734	218	3	=	=	NOUN
ejpam-6734	218	4	l+1	l+1	ADJ
ejpam-6734	218	5	|ai|	|ai|	ADJ
ejpam-6734	218	6	∣∣∣(ϕλ1,λ2	∣∣∣(ϕλ1,λ2	PROPN
ejpam-6734	218	7	i	i	PROPN
ejpam-6734	218	8	(	(	PUNCT
ejpam-6734	218	9	ω))′′	ω))′′	INTJ
ejpam-6734	218	10	∣∣∣	∣∣∣	NOUN
ejpam-6734	218	11	.	.	PUNCT
ejpam-6734	219	1	where	where	SCONJ
ejpam-6734	219	2	∣∣ζ(i)(0)∣∣	∣∣ζ(i)(0)∣∣	ADP
ejpam-6734	219	3	=	=	SYM
ejpam-6734	219	4	qi	qi	PROPN
ejpam-6734	219	5	,	,	PUNCT
ejpam-6734	219	6	w	w	PROPN
ejpam-6734	219	7	=	=	PUNCT
ejpam-6734	219	8	q	q	X
ejpam-6734	220	1	|λ1|	|λ1|	NOUN
ejpam-6734	220	2	,	,	PUNCT
ejpam-6734	220	3	ρ	ρ	PROPN
ejpam-6734	220	4	=	=	NOUN
ejpam-6734	220	5	6|λ2|	6|λ2|	NUM
ejpam-6734	220	6	q|λ1|	q|λ1|	NOUN
ejpam-6734	220	7	w	w	ADP
ejpam-6734	220	8	2p	2p	NUM
ejpam-6734	220	9	2li6	2li6	NUM
ejpam-6734	220	10	(	(	PUNCT
ejpam-6734	220	11	λ2	λ2	NOUN
ejpam-6734	220	12	1w	1w	VERB
ejpam-6734	220	13	2p	2p	NUM
ejpam-6734	220	14	2	2	NUM
ejpam-6734	220	15	3|λ2|	3|λ2|	NUM
ejpam-6734	220	16	)	)	PUNCT
ejpam-6734	221	1	cosh(2q	cosh(2q	ADJ
ejpam-6734	221	2	√	√	VERB
ejpam-6734	221	3	λ2	λ2	NOUN
ejpam-6734	221	4	|λ1|	|λ1|	NOUN
ejpam-6734	221	5	)	)	PUNCT
ejpam-6734	221	6	.	.	PUNCT
ejpam-6734	222	1	from	from	ADP
ejpam-6734	222	2	lemma	lemma	PROPN
ejpam-6734	222	3	(	(	PUNCT
ejpam-6734	222	4	1	1	NUM
ejpam-6734	222	5	)	)	PUNCT
ejpam-6734	222	6	[	[	X
ejpam-6734	222	7	31	31	NUM
ejpam-6734	222	8	]	]	PUNCT
ejpam-6734	222	9	,	,	PUNCT
ejpam-6734	222	10	we	we	PRON
ejpam-6734	222	11	obtain∣∣∣(ϕλ1,λ2	obtain∣∣∣(ϕλ1,λ2	VERB
ejpam-6734	222	12	i	i	PRON
ejpam-6734	222	13	(	(	PUNCT
ejpam-6734	222	14	ω))′′	ω))′′	CCONJ
ejpam-6734	222	15	∣∣∣	∣∣∣	ADJ
ejpam-6734	222	16	≤	≤	NUM
ejpam-6734	222	17	i2	i2	PROPN
ejpam-6734	222	18	.	.	PUNCT
ejpam-6734	223	1	then	then	ADV
ejpam-6734	223	2	we	we	PRON
ejpam-6734	223	3	have	have	VERB
ejpam-6734	223	4	∣∣ζ	∣∣ζ	VERB
ejpam-6734	223	5	′′(ω)−	′′(ω)−	PROPN
ejpam-6734	223	6	ζ	ζ	NOUN
ejpam-6734	223	7	′′l(ω	′′l(ω	NOUN
ejpam-6734	223	8	)	)	PUNCT
ejpam-6734	223	9	∣∣	∣∣	X
ejpam-6734	224	1	=	=	SYM
ejpam-6734	224	2	∣∣∣ζ	∣∣∣ζ	NOUN
ejpam-6734	224	3	′	′	NOUN
ejpam-6734	225	1	(	(	PUNCT
ejpam-6734	225	2	ω)−	ω)−	NOUN
ejpam-6734	225	3	ζ	ζ	NOUN
ejpam-6734	225	4	′	′	NUM
ejpam-6734	225	5	l(ω	l(ω	PROPN
ejpam-6734	225	6	)	)	PUNCT
ejpam-6734	225	7	∣∣∣	∣∣∣	ADJ
ejpam-6734	225	8	≤	≤	NUM
ejpam-6734	225	9	ρ	ρ	NOUN
ejpam-6734	225	10	∞∑	∞∑	NUM
ejpam-6734	225	11	i	i	NOUN
ejpam-6734	225	12	=	=	NOUN
ejpam-6734	225	13	l+1	l+1	NOUN
ejpam-6734	225	14	w	w	ADP
ejpam-6734	225	15	i+1	i+1	NUM
ejpam-6734	225	16	i	i	PRON
ejpam-6734	225	17	!	!	PUNCT
ejpam-6734	226	1	i2	i2	PROPN
ejpam-6734	226	2	,	,	PUNCT
ejpam-6734	226	3	and	and	CCONJ
ejpam-6734	226	4	∣∣ζ	∣∣ζ	VERB
ejpam-6734	226	5	′2(ω)−	′2(ω)−	PROPN
ejpam-6734	226	6	ζ	ζ	PROPN
ejpam-6734	226	7	′2l	′2l	PROPN
ejpam-6734	226	8	(	(	PUNCT
ejpam-6734	226	9	ω	ω	NOUN
ejpam-6734	226	10	)	)	PUNCT
ejpam-6734	226	11	∣∣	∣∣	PROPN
ejpam-6734	226	12	≤	≤	NUM
ejpam-6734	226	13	∣∣ζ	∣∣ζ	PROPN
ejpam-6734	226	14	′(ω)−	′(ω)−	PROPN
ejpam-6734	226	15	ζ	ζ	ADJ
ejpam-6734	226	16	′l(ω	′l(ω	NOUN
ejpam-6734	226	17	)	)	PUNCT
ejpam-6734	226	18	∣∣2	∣∣2	PROPN
ejpam-6734	226	19	+	+	CCONJ
ejpam-6734	226	20	2	2	NUM
ejpam-6734	226	21	∣∣∣ζ	∣∣∣ζ	NOUN
ejpam-6734	226	22	′	′	NUM
ejpam-6734	226	23	l(ω	l(ω	PROPN
ejpam-6734	226	24	)	)	PUNCT
ejpam-6734	226	25	∣∣∣	∣∣∣	NOUN
ejpam-6734	226	26	∣∣∣ζ	∣∣∣ζ	PROPN
ejpam-6734	226	27	′	′	NUM
ejpam-6734	227	1	(	(	PUNCT
ejpam-6734	227	2	ω)−	ω)−	NOUN
ejpam-6734	227	3	ζ	ζ	NOUN
ejpam-6734	227	4	′	′	NUM
ejpam-6734	227	5	l(ω	l(ω	PROPN
ejpam-6734	227	6	)	)	PUNCT
ejpam-6734	227	7	∣∣∣	∣∣∣	NOUN
ejpam-6734	227	8	.	.	PUNCT
ejpam-6734	228	1	from	from	ADP
ejpam-6734	228	2	the	the	DET
ejpam-6734	228	3	pervious	pervious	ADJ
ejpam-6734	228	4	steps	step	NOUN
ejpam-6734	228	5	,	,	PUNCT
ejpam-6734	228	6	we	we	PRON
ejpam-6734	228	7	obtain	obtain	VERB
ejpam-6734	228	8	gl(ω	gl(ω	NOUN
ejpam-6734	228	9	)	)	PUNCT
ejpam-6734	228	10	≤	≤	NUM
ejpam-6734	228	11	ρ	ρ	NOUN
ejpam-6734	228	12	{	{	PUNCT
ejpam-6734	228	13	(	(	PUNCT
ejpam-6734	228	14	n1	n1	PROPN
ejpam-6734	228	15	+	+	CCONJ
ejpam-6734	228	16	n2	n2	ADJ
ejpam-6734	228	17	)	)	PUNCT
ejpam-6734	228	18	+	+	CCONJ
ejpam-6734	228	19	n3ρ	n3ρ	PRON
ejpam-6734	228	20	(	(	PUNCT
ejpam-6734	228	21	∞∑	∞∑	NUM
ejpam-6734	228	22	i	i	NOUN
ejpam-6734	228	23	=	=	NOUN
ejpam-6734	228	24	l+1	l+1	NOUN
ejpam-6734	228	25	w	w	ADP
ejpam-6734	228	26	i+1	i+1	ADJ
ejpam-6734	228	27	i	i	PRON
ejpam-6734	228	28	!	!	PUNCT
ejpam-6734	229	1	i2	i2	PROPN
ejpam-6734	229	2	+	+	CCONJ
ejpam-6734	229	3	2	2	NUM
ejpam-6734	229	4	l∑	l∑	NOUN
ejpam-6734	229	5	i=0	i=0	PROPN
ejpam-6734	229	6	w	w	ADP
ejpam-6734	229	7	i+1	i+1	NUM
ejpam-6734	229	8	i	i	PRON
ejpam-6734	229	9	!	!	PUNCT
ejpam-6734	229	10	i2	i2	PROPN
ejpam-6734	229	11	)	)	PUNCT
ejpam-6734	229	12	}	}	PUNCT
ejpam-6734	229	13	(	(	PUNCT
ejpam-6734	229	14	∞∑	∞∑	NUM
ejpam-6734	229	15	i	i	NOUN
ejpam-6734	229	16	=	=	NOUN
ejpam-6734	229	17	l+1	l+1	NOUN
ejpam-6734	229	18	w	w	ADP
ejpam-6734	229	19	i+1	i+1	NUM
ejpam-6734	230	1	i	i	PRON
ejpam-6734	230	2	!	!	PUNCT
ejpam-6734	231	1	i2	i2	PROPN
ejpam-6734	231	2	)	)	PUNCT
ejpam-6734	232	1	+	+	NOUN
ejpam-6734	232	2	ρ	ρ	X
ejpam-6734	232	3	n4w	n4w	X
ejpam-6734	232	4	ewp	ewp	X
ejpam-6734	232	5	(	(	PUNCT
ejpam-6734	232	6	wp	wp	NOUN
ejpam-6734	232	7	)	)	PUNCT
ejpam-6734	232	8	l	l	NOUN
ejpam-6734	232	9	(	(	PUNCT
ejpam-6734	232	10	l−	l−	NOUN
ejpam-6734	232	11	1	1	NUM
ejpam-6734	232	12	)	)	PUNCT
ejpam-6734	232	13	!	!	PUNCT
ejpam-6734	232	14	.	.	PUNCT
ejpam-6734	233	1	where	where	SCONJ
ejpam-6734	233	2	p	p	NOUN
ejpam-6734	233	3	=	=	NOUN
ejpam-6734	233	4	√	√	NUM
ejpam-6734	233	5	λ2	λ2	NOUN
ejpam-6734	233	6	1	1	NUM
ejpam-6734	233	7	ϱ2	ϱ2	NOUN
ejpam-6734	233	8	+	+	CCONJ
ejpam-6734	233	9	2	2	NUM
ejpam-6734	233	10	|λ2|	|λ2|	NOUN
ejpam-6734	233	11	,	,	PUNCT
ejpam-6734	233	12	if	if	SCONJ
ejpam-6734	233	13	n	n	NOUN
ejpam-6734	233	14	=	=	SYM
ejpam-6734	233	15	max(n1	max(n1	ADJ
ejpam-6734	233	16	,	,	PUNCT
ejpam-6734	233	17	n2	n2	ADJ
ejpam-6734	233	18	,	,	PUNCT
ejpam-6734	233	19	n3	n3	PROPN
ejpam-6734	233	20	,	,	PUNCT
ejpam-6734	233	21	n4	n4	PROPN
ejpam-6734	233	22	)	)	PUNCT
ejpam-6734	233	23	,	,	PUNCT
ejpam-6734	233	24	by	by	ADP
ejpam-6734	233	25	simplifying	simplify	VERB
ejpam-6734	233	26	,	,	PUNCT
ejpam-6734	233	27	we	we	PRON
ejpam-6734	233	28	obtain	obtain	VERB
ejpam-6734	233	29	gl(ω	gl(ω	X
ejpam-6734	233	30	)	)	PUNCT
ejpam-6734	233	31	≤	≤	NOUN
ejpam-6734	233	32	4nρ2	4nρ2	NUM
ejpam-6734	233	33	{	{	PUNCT
ejpam-6734	234	1	1	1	NUM
ejpam-6734	234	2	+	+	CCONJ
ejpam-6734	234	3	w	w	PROPN
ejpam-6734	234	4	2	2	NUM
ejpam-6734	234	5	γ	γ	X
ejpam-6734	234	6	(	(	PUNCT
ejpam-6734	234	7	1	1	NUM
ejpam-6734	234	8	+	+	NUM
ejpam-6734	234	9	l	l	NOUN
ejpam-6734	234	10	)	)	PUNCT
ejpam-6734	234	11	(	(	PUNCT
ejpam-6734	234	12	−wl	−wl	X
ejpam-6734	234	13	(	(	PUNCT
ejpam-6734	234	14	1	1	NUM
ejpam-6734	234	15	+	+	NOUN
ejpam-6734	234	16	w	w	NOUN
ejpam-6734	234	17	+	+	NUM
ejpam-6734	234	18	l	l	NOUN
ejpam-6734	234	19	)	)	PUNCT
ejpam-6734	235	1	+	+	CCONJ
ejpam-6734	235	2	ew	ew	INTJ
ejpam-6734	235	3	(	(	PUNCT
ejpam-6734	235	4	1	1	NUM
ejpam-6734	235	5	+	+	NOUN
ejpam-6734	235	6	w	w	NOUN
ejpam-6734	235	7	)	)	PUNCT
ejpam-6734	235	8	(	(	PUNCT
ejpam-6734	235	9	γ	γ	X
ejpam-6734	235	10	(	(	PUNCT
ejpam-6734	235	11	1	1	NUM
ejpam-6734	235	12	+	+	NUM
ejpam-6734	235	13	l	l	NOUN
ejpam-6734	235	14	)	)	PUNCT
ejpam-6734	236	1	+	+	CCONJ
ejpam-6734	236	2	γ	γ	X
ejpam-6734	236	3	(	(	PUNCT
ejpam-6734	236	4	1	1	NUM
ejpam-6734	236	5	+	+	NUM
ejpam-6734	236	6	l	l	NOUN
ejpam-6734	236	7	,	,	PUNCT
ejpam-6734	236	8	w	w	NOUN
ejpam-6734	236	9	)	)	PUNCT
ejpam-6734	236	10	)	)	PUNCT
ejpam-6734	236	11	)	)	PUNCT
ejpam-6734	236	12	}	}	PUNCT
ejpam-6734	236	13	×	×	PROPN
ejpam-6734	236	14	w	w	PROPN
ejpam-6734	236	15	2	2	NUM
ejpam-6734	236	16	γ	γ	X
ejpam-6734	236	17	(	(	PUNCT
ejpam-6734	236	18	1	1	NUM
ejpam-6734	236	19	+	+	NUM
ejpam-6734	236	20	l	l	NOUN
ejpam-6734	236	21	)	)	PUNCT
ejpam-6734	236	22	(	(	PUNCT
ejpam-6734	236	23	−wl	−wl	X
ejpam-6734	236	24	(	(	PUNCT
ejpam-6734	236	25	1	1	NUM
ejpam-6734	236	26	+	+	NOUN
ejpam-6734	236	27	w	w	NOUN
ejpam-6734	236	28	+	+	NUM
ejpam-6734	236	29	l	l	NOUN
ejpam-6734	236	30	)	)	PUNCT
ejpam-6734	237	1	+	+	CCONJ
ejpam-6734	237	2	ew	ew	INTJ
ejpam-6734	237	3	(	(	PUNCT
ejpam-6734	237	4	1	1	NUM
ejpam-6734	237	5	+	+	NOUN
ejpam-6734	237	6	w	w	NOUN
ejpam-6734	237	7	)	)	PUNCT
ejpam-6734	237	8	(	(	PUNCT
ejpam-6734	237	9	γ	γ	X
ejpam-6734	237	10	(	(	PUNCT
ejpam-6734	237	11	1	1	NUM
ejpam-6734	237	12	+	+	CCONJ
ejpam-6734	237	13	l)−	l)−	PROPN
ejpam-6734	237	14	γ	γ	X
ejpam-6734	237	15	(	(	PUNCT
ejpam-6734	237	16	1	1	NUM
ejpam-6734	237	17	+	+	NUM
ejpam-6734	237	18	l	l	NOUN
ejpam-6734	237	19	,	,	PUNCT
ejpam-6734	237	20	w	w	NOUN
ejpam-6734	237	21	)	)	PUNCT
ejpam-6734	237	22	)	)	PUNCT
ejpam-6734	237	23	)	)	PUNCT
ejpam-6734	238	1	+	+	NOUN
ejpam-6734	238	2	ρ	ρ	PROPN
ejpam-6734	238	3	nw	nw	PROPN
ejpam-6734	238	4	ewp	ewp	PROPN
ejpam-6734	238	5	(	(	PUNCT
ejpam-6734	238	6	wp	wp	PROPN
ejpam-6734	238	7	)	)	PUNCT
ejpam-6734	238	8	l	l	NOUN
ejpam-6734	238	9	(	(	PUNCT
ejpam-6734	238	10	l−	l−	NOUN
ejpam-6734	238	11	1	1	NUM
ejpam-6734	238	12	)	)	PUNCT
ejpam-6734	238	13	!	!	PUNCT
ejpam-6734	238	14	.	.	PUNCT
ejpam-6734	239	1	where	where	SCONJ
ejpam-6734	239	2	γ	γ	X
ejpam-6734	239	3	(	(	PUNCT
ejpam-6734	239	4	.	.	PUNCT
ejpam-6734	239	5	)	)	PUNCT
ejpam-6734	239	6	and	and	CCONJ
ejpam-6734	239	7	γ	γ	X
ejpam-6734	239	8	(	(	PUNCT
ejpam-6734	239	9	.	.	PUNCT
ejpam-6734	239	10	,	,	PUNCT
ejpam-6734	239	11	.	.	PUNCT
ejpam-6734	239	12	)	)	PUNCT
ejpam-6734	239	13	are	be	AUX
ejpam-6734	239	14	gamma	gamma	NOUN
ejpam-6734	239	15	and	and	CCONJ
ejpam-6734	239	16	incomplete	incomplete	ADJ
ejpam-6734	239	17	gamma	gamma	NOUN
ejpam-6734	239	18	functions	function	NOUN
ejpam-6734	239	19	respectively	respectively	ADV
ejpam-6734	239	20	.	.	PUNCT
ejpam-6734	240	1	so	so	ADV
ejpam-6734	240	2	γ	γ	X
ejpam-6734	240	3	(	(	PUNCT
ejpam-6734	240	4	1	1	NUM
ejpam-6734	240	5	+	+	CCONJ
ejpam-6734	240	6	l)−	l)−	PROPN
ejpam-6734	240	7	γ	γ	X
ejpam-6734	240	8	(	(	PUNCT
ejpam-6734	240	9	1	1	NUM
ejpam-6734	240	10	+	+	NUM
ejpam-6734	240	11	l	l	NOUN
ejpam-6734	240	12	,	,	PUNCT
ejpam-6734	240	13	w	w	NOUN
ejpam-6734	240	14	)	)	PUNCT
ejpam-6734	240	15	≤	≤	NUM
ejpam-6734	240	16	w∫	w∫	VERB
ejpam-6734	240	17	0	0	PUNCT
ejpam-6734	240	18	ωdω	ωdω	VERB
ejpam-6734	240	19	=	=	SYM
ejpam-6734	240	20	w	w	PROPN
ejpam-6734	240	21	1+l	1+l	NUM
ejpam-6734	240	22	1	1	NUM
ejpam-6734	240	23	+	+	NUM
ejpam-6734	240	24	l	l	NOUN
ejpam-6734	240	25	,	,	PUNCT
ejpam-6734	240	26	m.	m.	NOUN
ejpam-6734	240	27	a.	a.	PROPN
ejpam-6734	240	28	abdou	abdou	PROPN
ejpam-6734	240	29	,	,	PUNCT
ejpam-6734	240	30	a.	a.	PROPN
ejpam-6734	240	31	s.	s.	PROPN
ejpam-6734	240	32	mohamed	mohamed	PROPN
ejpam-6734	240	33	/	/	SYM
ejpam-6734	240	34	eur	eur	PROPN
ejpam-6734	240	35	.	.	PUNCT
ejpam-6734	241	1	j.	j.	PROPN
ejpam-6734	241	2	pure	pure	PROPN
ejpam-6734	241	3	appl	appl	PROPN
ejpam-6734	241	4	.	.	PROPN
ejpam-6734	241	5	math	math	PROPN
ejpam-6734	241	6	,	,	PUNCT
ejpam-6734	241	7	18	18	NUM
ejpam-6734	241	8	(	(	PUNCT
ejpam-6734	241	9	4	4	NUM
ejpam-6734	241	10	)	)	PUNCT
ejpam-6734	241	11	(	(	PUNCT
ejpam-6734	241	12	2025	2025	NUM
ejpam-6734	241	13	)	)	PUNCT
ejpam-6734	241	14	,	,	PUNCT
ejpam-6734	241	15	6734	6734	NUM
ejpam-6734	241	16	9	9	NUM
ejpam-6734	241	17	of	of	ADP
ejpam-6734	241	18	20	20	NUM
ejpam-6734	241	19	and	and	CCONJ
ejpam-6734	241	20	γ	γ	X
ejpam-6734	241	21	(	(	PUNCT
ejpam-6734	241	22	1	1	NUM
ejpam-6734	241	23	+	+	NUM
ejpam-6734	241	24	l	l	NOUN
ejpam-6734	241	25	)	)	PUNCT
ejpam-6734	242	1	+	+	CCONJ
ejpam-6734	242	2	γ	γ	X
ejpam-6734	242	3	(	(	PUNCT
ejpam-6734	242	4	1	1	NUM
ejpam-6734	242	5	+	+	NUM
ejpam-6734	242	6	l	l	NOUN
ejpam-6734	242	7	,	,	PUNCT
ejpam-6734	242	8	w	w	NOUN
ejpam-6734	242	9	)	)	PUNCT
ejpam-6734	242	10	≤	≤	NOUN
ejpam-6734	242	11	2γ	2γ	NOUN
ejpam-6734	242	12	(	(	PUNCT
ejpam-6734	242	13	1	1	NUM
ejpam-6734	242	14	+	+	NUM
ejpam-6734	242	15	l	l	NOUN
ejpam-6734	242	16	)	)	PUNCT
ejpam-6734	242	17	.	.	PUNCT
ejpam-6734	243	1	then	then	ADV
ejpam-6734	243	2	,	,	PUNCT
ejpam-6734	243	3	we	we	PRON
ejpam-6734	243	4	have	have	VERB
ejpam-6734	243	5	gl(ω	gl(ω	NOUN
ejpam-6734	243	6	)	)	PUNCT
ejpam-6734	243	7	≤	≤	NOUN
ejpam-6734	244	1	4nρ2w	4nρ2w	NUM
ejpam-6734	244	2	2+l	2+l	NUM
ejpam-6734	244	3	(	(	PUNCT
ejpam-6734	244	4	1	1	NUM
ejpam-6734	244	5	+	+	NUM
ejpam-6734	244	6	l	l	NOUN
ejpam-6734	244	7	)	)	PUNCT
ejpam-6734	244	8	(	(	PUNCT
ejpam-6734	244	9	γ	γ	X
ejpam-6734	244	10	(	(	PUNCT
ejpam-6734	244	11	1	1	NUM
ejpam-6734	244	12	+	+	NUM
ejpam-6734	244	13	l))2	l))2	PROPN
ejpam-6734	244	14	{	{	PUNCT
ejpam-6734	244	15	eww	eww	PROPN
ejpam-6734	244	16	(	(	PUNCT
ejpam-6734	244	17	1	1	NUM
ejpam-6734	244	18	+	+	NOUN
ejpam-6734	244	19	w	w	NOUN
ejpam-6734	244	20	)	)	PUNCT
ejpam-6734	245	1	+	+	CCONJ
ejpam-6734	245	2	(	(	PUNCT
ejpam-6734	245	3	1	1	NUM
ejpam-6734	245	4	+	+	NUM
ejpam-6734	245	5	l)(1	l)(1	X
ejpam-6734	246	1	+	+	CCONJ
ejpam-6734	246	2	l+w	l+w	X
ejpam-6734	246	3	)	)	PUNCT
ejpam-6734	246	4	}	}	PUNCT
ejpam-6734	246	5	×	×	NOUN
ejpam-6734	246	6	{	{	PUNCT
ejpam-6734	246	7	−w	−w	ADV
ejpam-6734	246	8	2+l(1	2+l(1	NUM
ejpam-6734	246	9	+	+	NUM
ejpam-6734	246	10	l+w	l+w	X
ejpam-6734	246	11	)	)	PUNCT
ejpam-6734	247	1	+	+	CCONJ
ejpam-6734	247	2	(	(	PUNCT
ejpam-6734	247	3	1	1	NUM
ejpam-6734	247	4	+	+	NUM
ejpam-6734	247	5	2eww	2eww	NOUN
ejpam-6734	247	6	2	2	NUM
ejpam-6734	247	7	(	(	PUNCT
ejpam-6734	247	8	1	1	NUM
ejpam-6734	247	9	+	+	NOUN
ejpam-6734	247	10	w	w	NOUN
ejpam-6734	247	11	)	)	PUNCT
ejpam-6734	247	12	)	)	PUNCT
ejpam-6734	247	13	γ	γ	X
ejpam-6734	247	14	(	(	PUNCT
ejpam-6734	247	15	1	1	NUM
ejpam-6734	247	16	+	+	NUM
ejpam-6734	247	17	l	l	NOUN
ejpam-6734	247	18	)	)	PUNCT
ejpam-6734	247	19	}	}	PUNCT
ejpam-6734	248	1	+	+	CCONJ
ejpam-6734	248	2	ρ	ρ	PROPN
ejpam-6734	248	3	nw	nw	PROPN
ejpam-6734	248	4	ewp	ewp	PROPN
ejpam-6734	248	5	(	(	PUNCT
ejpam-6734	248	6	wp	wp	NOUN
ejpam-6734	248	7	)	)	PUNCT
ejpam-6734	248	8	l	l	NOUN
ejpam-6734	248	9	γ	γ	X
ejpam-6734	248	10	(	(	PUNCT
ejpam-6734	248	11	l	l	NOUN
ejpam-6734	248	12	)	)	PUNCT
ejpam-6734	248	13	.	.	PUNCT
ejpam-6734	249	1	so	so	ADV
ejpam-6734	249	2	,	,	PUNCT
ejpam-6734	249	3	the	the	DET
ejpam-6734	249	4	result	result	NOUN
ejpam-6734	249	5	is	be	AUX
ejpam-6734	249	6	verified	verify	VERB
ejpam-6734	249	7	.	.	PUNCT
ejpam-6734	250	1	for	for	ADP
ejpam-6734	250	2	the	the	DET
ejpam-6734	250	3	general	general	ADJ
ejpam-6734	250	4	second	second	ADJ
ejpam-6734	250	5	-	-	PUNCT
ejpam-6734	250	6	order	order	NOUN
ejpam-6734	250	7	problem	problem	NOUN
ejpam-6734	250	8	(	(	PUNCT
ejpam-6734	250	9	1	1	NUM
ejpam-6734	250	10	)	)	PUNCT
ejpam-6734	250	11	with	with	ADP
ejpam-6734	250	12	initial	initial	ADJ
ejpam-6734	250	13	conditions	condition	NOUN
ejpam-6734	250	14	(	(	PUNCT
ejpam-6734	250	15	3	3	NUM
ejpam-6734	250	16	)	)	PUNCT
ejpam-6734	250	17	or	or	CCONJ
ejpam-6734	250	18	boundary	boundary	ADJ
ejpam-6734	250	19	conditions	condition	NOUN
ejpam-6734	250	20	(	(	PUNCT
ejpam-6734	250	21	4	4	NUM
ejpam-6734	250	22	)	)	PUNCT
ejpam-6734	250	23	,	,	PUNCT
ejpam-6734	250	24	the	the	DET
ejpam-6734	250	25	existence	existence	NOUN
ejpam-6734	250	26	and	and	CCONJ
ejpam-6734	250	27	uniqueness	uniqueness	NOUN
ejpam-6734	250	28	can	can	AUX
ejpam-6734	250	29	be	be	AUX
ejpam-6734	250	30	established	establish	VERB
ejpam-6734	250	31	if	if	SCONJ
ejpam-6734	250	32	υ1(ω	υ1(ω	NOUN
ejpam-6734	250	33	)	)	PUNCT
ejpam-6734	250	34	̸=	̸=	PROPN
ejpam-6734	250	35	0	0	NUM
ejpam-6734	250	36	and	and	CCONJ
ejpam-6734	250	37	is	be	AUX
ejpam-6734	250	38	continuous	continuous	ADJ
ejpam-6734	250	39	on	on	ADP
ejpam-6734	250	40	the	the	DET
ejpam-6734	250	41	interval	interval	NOUN
ejpam-6734	250	42	of	of	ADP
ejpam-6734	250	43	interest	interest	NOUN
ejpam-6734	250	44	.	.	PUNCT
ejpam-6734	251	1	where	where	SCONJ
ejpam-6734	251	2	ζ	ζ	PROPN
ejpam-6734	251	3	′′(ω	′′(ω	NOUN
ejpam-6734	251	4	)	)	PUNCT
ejpam-6734	251	5	depends	depend	VERB
ejpam-6734	251	6	on	on	ADP
ejpam-6734	251	7	a	a	DET
ejpam-6734	251	8	continuous	continuous	ADJ
ejpam-6734	251	9	function	function	NOUN
ejpam-6734	251	10	,	,	PUNCT
ejpam-6734	251	11	which	which	PRON
ejpam-6734	251	12	satisfies	satisfy	VERB
ejpam-6734	251	13	a	a	DET
ejpam-6734	251	14	lipschitz	lipschitz	NOUN
ejpam-6734	251	15	condition	condition	NOUN
ejpam-6734	251	16	in	in	ADP
ejpam-6734	251	17	ζ	ζ	PROPN
ejpam-6734	251	18	′(ω	′(ω	NOUN
ejpam-6734	251	19	)	)	PUNCT
ejpam-6734	251	20	and	and	CCONJ
ejpam-6734	251	21	ζ(ω	ζ(ω	NOUN
ejpam-6734	251	22	)	)	PUNCT
ejpam-6734	251	23	4	4	NUM
ejpam-6734	251	24	.	.	PUNCT
ejpam-6734	251	25	numerical	numerical	ADJ
ejpam-6734	251	26	examples	example	NOUN
ejpam-6734	251	27	this	this	DET
ejpam-6734	251	28	section	section	NOUN
ejpam-6734	251	29	presents	present	VERB
ejpam-6734	251	30	a	a	DET
ejpam-6734	251	31	series	series	NOUN
ejpam-6734	251	32	of	of	ADP
ejpam-6734	251	33	problem	problem	NOUN
ejpam-6734	251	34	solving	solve	VERB
ejpam-6734	251	35	applications	application	NOUN
ejpam-6734	251	36	using	use	VERB
ejpam-6734	251	37	dtm	dtm	PROPN
ejpam-6734	251	38	and	and	CCONJ
ejpam-6734	251	39	gfcm	gfcm	PROPN
ejpam-6734	251	40	,	,	PUNCT
ejpam-6734	251	41	aimed	aim	VERB
ejpam-6734	251	42	at	at	ADP
ejpam-6734	251	43	demonstrating	demonstrate	VERB
ejpam-6734	251	44	their	their	PRON
ejpam-6734	251	45	practical	practical	ADJ
ejpam-6734	251	46	implementation	implementation	NOUN
ejpam-6734	251	47	.	.	PUNCT
ejpam-6734	252	1	by	by	ADP
ejpam-6734	252	2	systematically	systematically	ADV
ejpam-6734	252	3	comparing	compare	VERB
ejpam-6734	252	4	the	the	DET
ejpam-6734	252	5	results	result	NOUN
ejpam-6734	252	6	with	with	ADP
ejpam-6734	252	7	those	those	PRON
ejpam-6734	252	8	from	from	ADP
ejpam-6734	252	9	established	establish	VERB
ejpam-6734	252	10	numerical	numerical	ADJ
ejpam-6734	252	11	methods	method	NOUN
ejpam-6734	252	12	,	,	PUNCT
ejpam-6734	252	13	we	we	PRON
ejpam-6734	252	14	provide	provide	VERB
ejpam-6734	252	15	evidence	evidence	NOUN
ejpam-6734	252	16	of	of	ADP
ejpam-6734	252	17	the	the	DET
ejpam-6734	252	18	enhanced	enhance	VERB
ejpam-6734	252	19	performance	performance	NOUN
ejpam-6734	252	20	of	of	ADP
ejpam-6734	252	21	dtm	dtm	PROPN
ejpam-6734	252	22	and	and	CCONJ
ejpam-6734	252	23	gfcm	gfcm	PROPN
ejpam-6734	252	24	in	in	ADP
ejpam-6734	252	25	terms	term	NOUN
ejpam-6734	252	26	of	of	ADP
ejpam-6734	252	27	solution	solution	NOUN
ejpam-6734	252	28	accuracy	accuracy	NOUN
ejpam-6734	252	29	and	and	CCONJ
ejpam-6734	252	30	computational	computational	ADJ
ejpam-6734	252	31	efficiency	efficiency	NOUN
ejpam-6734	252	32	.	.	PUNCT
ejpam-6734	253	1	example	example	NOUN
ejpam-6734	254	1	1	1	NUM
ejpam-6734	254	2	.	.	X
ejpam-6734	254	3	consider	consider	VERB
ejpam-6734	254	4	the	the	DET
ejpam-6734	254	5	following	follow	VERB
ejpam-6734	254	6	linear	linear	ADJ
ejpam-6734	254	7	second	second	ADJ
ejpam-6734	254	8	-	-	PUNCT
ejpam-6734	254	9	order	order	NOUN
ejpam-6734	254	10	boundary	boundary	ADJ
ejpam-6734	254	11	value	value	NOUN
ejpam-6734	254	12	problem:[32	problem:[32	PROPN
ejpam-6734	254	13	]	]	PUNCT
ejpam-6734	254	14	if	if	SCONJ
ejpam-6734	254	15	υ1(ω	υ1(ω	NOUN
ejpam-6734	254	16	)	)	PUNCT
ejpam-6734	254	17	=	=	SYM
ejpam-6734	254	18	1	1	NUM
ejpam-6734	254	19	,	,	PUNCT
ejpam-6734	254	20	υ2(ω	υ2(ω	NOUN
ejpam-6734	254	21	)	)	PUNCT
ejpam-6734	254	22	=	=	SYM
ejpam-6734	255	1	1−ω	1−ω	PROPN
ejpam-6734	255	2	,	,	PUNCT
ejpam-6734	255	3	υ3(ω	υ3(ω	NUM
ejpam-6734	255	4	)	)	PUNCT
ejpam-6734	255	5	=	=	SYM
ejpam-6734	255	6	0	0	NUM
ejpam-6734	255	7	,	,	PUNCT
ejpam-6734	255	8	υ4(ω	υ4(ω	PROPN
ejpam-6734	255	9	)	)	PUNCT
ejpam-6734	255	10	=	=	SYM
ejpam-6734	255	11	2	2	NUM
ejpam-6734	255	12	,	,	PUNCT
ejpam-6734	255	13	ξ(ω	ξ(ω	NOUN
ejpam-6734	255	14	)	)	PUNCT
ejpam-6734	255	15	=	=	PUNCT
ejpam-6734	255	16	(	(	PUNCT
ejpam-6734	255	17	1	1	NUM
ejpam-6734	255	18	+	+	NOUN
ejpam-6734	255	19	2ω−ω2	2ω−ω2	NUM
ejpam-6734	255	20	)	)	PUNCT
ejpam-6734	255	21	sin(ω	sin(ω	PROPN
ejpam-6734	255	22	)	)	PUNCT
ejpam-6734	255	23	,	,	PUNCT
ejpam-6734	255	24	m1	m1	PROPN
ejpam-6734	255	25	=	=	SYM
ejpam-6734	255	26	1	1	NUM
ejpam-6734	255	27	,	,	PUNCT
ejpam-6734	255	28	m3	m3	PROPN
ejpam-6734	255	29	=	=	SYM
ejpam-6734	255	30	0	0	PROPN
ejpam-6734	255	31	.	.	PUNCT
ejpam-6734	256	1	so	so	ADV
ejpam-6734	256	2	,	,	PUNCT
ejpam-6734	256	3	eq	eq	NOUN
ejpam-6734	256	4	.	.	PUNCT
ejpam-6734	257	1	(	(	PUNCT
ejpam-6734	257	2	1	1	X
ejpam-6734	257	3	)	)	PUNCT
ejpam-6734	257	4	can	can	AUX
ejpam-6734	257	5	be	be	AUX
ejpam-6734	257	6	written	write	VERB
ejpam-6734	257	7	in	in	ADP
ejpam-6734	257	8	the	the	DET
ejpam-6734	257	9	form	form	NOUN
ejpam-6734	257	10	:	:	PUNCT
ejpam-6734	257	11	ζ	ζ	PROPN
ejpam-6734	257	12	′′	′′	PROPN
ejpam-6734	257	13	(	(	PUNCT
ejpam-6734	257	14	ω	ω	PROPN
ejpam-6734	257	15	)	)	PUNCT
ejpam-6734	257	16	+	+	CCONJ
ejpam-6734	257	17	(	(	PUNCT
ejpam-6734	257	18	1−	1−	NUM
ejpam-6734	257	19	ω)ζ	ω)ζ	PUNCT
ejpam-6734	257	20	′	′	NUM
ejpam-6734	257	21	(	(	PUNCT
ejpam-6734	257	22	ω	ω	NOUN
ejpam-6734	257	23	)	)	PUNCT
ejpam-6734	257	24	+	+	CCONJ
ejpam-6734	257	25	2ζ(ω	2ζ(ω	NUM
ejpam-6734	257	26	)	)	PUNCT
ejpam-6734	257	27	=	=	PUNCT
ejpam-6734	257	28	(	(	PUNCT
ejpam-6734	257	29	1	1	NUM
ejpam-6734	257	30	+	+	CCONJ
ejpam-6734	257	31	2ω	2ω	NUM
ejpam-6734	257	32	−	−	PROPN
ejpam-6734	257	33	ω2	ω2	NUM
ejpam-6734	257	34	)	)	PUNCT
ejpam-6734	257	35	sin(ω	sin(ω	PROPN
ejpam-6734	257	36	)	)	PUNCT
ejpam-6734	257	37	,	,	PUNCT
ejpam-6734	257	38	0	0	NUM
ejpam-6734	257	39	<	<	X
ejpam-6734	257	40	ω	ω	NUM
ejpam-6734	257	41	≤	≤	NUM
ejpam-6734	257	42	1	1	NUM
ejpam-6734	257	43	(	(	PUNCT
ejpam-6734	257	44	22	22	NUM
ejpam-6734	257	45	)	)	PUNCT
ejpam-6734	257	46	subject	subject	NOUN
ejpam-6734	257	47	to	to	ADP
ejpam-6734	257	48	the	the	DET
ejpam-6734	257	49	boundary	boundary	ADJ
ejpam-6734	257	50	conditions	condition	NOUN
ejpam-6734	257	51	(	(	PUNCT
ejpam-6734	257	52	4	4	NUM
ejpam-6734	257	53	)	)	PUNCT
ejpam-6734	257	54	ζ(0	ζ(0	NOUN
ejpam-6734	257	55	)	)	PUNCT
ejpam-6734	257	56	=	=	SYM
ejpam-6734	257	57	1	1	NUM
ejpam-6734	257	58	,	,	PUNCT
ejpam-6734	257	59	ζ(1	ζ(1	PROPN
ejpam-6734	257	60	)	)	PUNCT
ejpam-6734	257	61	=	=	NOUN
ejpam-6734	258	1	0	0	X
ejpam-6734	258	2	.	.	PUNCT
ejpam-6734	259	1	(	(	PUNCT
ejpam-6734	259	2	23	23	NUM
ejpam-6734	259	3	)	)	PUNCT
ejpam-6734	259	4	from	from	ADP
ejpam-6734	259	5	the	the	DET
ejpam-6734	259	6	definition	definition	NOUN
ejpam-6734	259	7	of	of	ADP
ejpam-6734	259	8	dtm	dtm	PROPN
ejpam-6734	259	9	,	,	PUNCT
ejpam-6734	259	10	eqs	eqs	X
ejpam-6734	259	11	.	.	PUNCT
ejpam-6734	260	1	(	(	PUNCT
ejpam-6734	260	2	7	7	NUM
ejpam-6734	260	3	)	)	PUNCT
ejpam-6734	260	4	,	,	PUNCT
ejpam-6734	260	5	(	(	PUNCT
ejpam-6734	260	6	8)	8)	NUM
ejpam-6734	260	7	,	,	PUNCT
ejpam-6734	260	8	(	(	PUNCT
ejpam-6734	260	9	9	9	NUM
ejpam-6734	260	10	)	)	PUNCT
ejpam-6734	260	11	,	,	PUNCT
ejpam-6734	260	12	and	and	CCONJ
ejpam-6734	260	13	(	(	PUNCT
ejpam-6734	260	14	11	11	NUM
ejpam-6734	260	15	)	)	PUNCT
ejpam-6734	260	16	.	.	PUNCT
ejpam-6734	261	1	so	so	ADV
ejpam-6734	261	2	,	,	PUNCT
ejpam-6734	261	3	eq.(22	eq.(22	NOUN
ejpam-6734	261	4	)	)	PUNCT
ejpam-6734	261	5	transforms	transform	VERB
ejpam-6734	261	6	to	to	ADP
ejpam-6734	261	7	:	:	PUNCT
ejpam-6734	261	8	ψ(i+	ψ(i+	NUM
ejpam-6734	261	9	2	2	X
ejpam-6734	261	10	)	)	PUNCT
ejpam-6734	261	11	=	=	SYM
ejpam-6734	261	12	1	1	NUM
ejpam-6734	261	13	(	(	PUNCT
ejpam-6734	261	14	i+	i+	NUM
ejpam-6734	261	15	1)(i+	1)(i+	NUM
ejpam-6734	261	16	2	2	NUM
ejpam-6734	261	17	)	)	PUNCT
ejpam-6734	261	18	{	{	PUNCT
ejpam-6734	261	19	−(i+	−(i+	PROPN
ejpam-6734	261	20	1)ψ(i+	1)ψ(i+	NUM
ejpam-6734	261	21	1	1	NUM
ejpam-6734	261	22	)	)	PUNCT
ejpam-6734	261	23	+	+	CCONJ
ejpam-6734	262	1	i∑	i∑	ADJ
ejpam-6734	262	2	k=0	k=0	PROPN
ejpam-6734	262	3	δ(k	δ(k	VERB
ejpam-6734	262	4	−	−	PROPN
ejpam-6734	262	5	1)(i−	1)(i−	NUM
ejpam-6734	262	6	k	k	NOUN
ejpam-6734	263	1	+	+	PROPN
ejpam-6734	263	2	1)ψ(i−	1)ψ(i−	NUM
ejpam-6734	263	3	k	k	X
ejpam-6734	264	1	+	+	PROPN
ejpam-6734	264	2	1)−	1)−	PROPN
ejpam-6734	264	3	2ψ(i)+	2ψ(i)+	NUM
ejpam-6734	264	4	1	1	NUM
ejpam-6734	265	1	i	i	NOUN
ejpam-6734	265	2	!	!	PUNCT
ejpam-6734	266	1	sin	sin	NOUN
ejpam-6734	266	2	(	(	PUNCT
ejpam-6734	266	3	πi	πi	ADV
ejpam-6734	266	4	2	2	NUM
ejpam-6734	266	5	)	)	PUNCT
ejpam-6734	266	6	+	+	CCONJ
ejpam-6734	266	7	2	2	NUM
ejpam-6734	266	8	i∑	i∑	ADJ
ejpam-6734	266	9	k=0	k=0	PROPN
ejpam-6734	266	10	δ(k	δ(k	NOUN
ejpam-6734	266	11	−	−	PROPN
ejpam-6734	266	12	1	1	NUM
ejpam-6734	266	13	)	)	PUNCT
ejpam-6734	266	14	(	(	PUNCT
ejpam-6734	266	15	i−	i−	PROPN
ejpam-6734	266	16	k	k	PROPN
ejpam-6734	266	17	)	)	PUNCT
ejpam-6734	266	18	!	!	PUNCT
ejpam-6734	267	1	sin	sin	NOUN
ejpam-6734	267	2	(	(	PUNCT
ejpam-6734	267	3	π(i−	π(i−	PROPN
ejpam-6734	267	4	k	k	NOUN
ejpam-6734	267	5	)	)	PUNCT
ejpam-6734	267	6	2	2	NUM
ejpam-6734	267	7	)	)	PUNCT
ejpam-6734	267	8	−	−	PROPN
ejpam-6734	267	9	i∑	i∑	CCONJ
ejpam-6734	267	10	k=0	k=0	PROPN
ejpam-6734	267	11	δ(k	δ(k	NOUN
ejpam-6734	267	12	−	−	PROPN
ejpam-6734	267	13	2	2	NUM
ejpam-6734	267	14	)	)	PUNCT
ejpam-6734	267	15	(	(	PUNCT
ejpam-6734	267	16	i−	i−	PROPN
ejpam-6734	267	17	k	k	PROPN
ejpam-6734	267	18	)	)	PUNCT
ejpam-6734	267	19	!	!	PUNCT
ejpam-6734	268	1	sin	sin	NOUN
ejpam-6734	268	2	(	(	PUNCT
ejpam-6734	268	3	π(i−	π(i−	PROPN
ejpam-6734	268	4	k	k	NOUN
ejpam-6734	268	5	)	)	PUNCT
ejpam-6734	268	6	2	2	NUM
ejpam-6734	268	7	)	)	PUNCT
ejpam-6734	268	8	}	}	PUNCT
ejpam-6734	268	9	,	,	PUNCT
ejpam-6734	268	10	(	(	PUNCT
ejpam-6734	268	11	24	24	NUM
ejpam-6734	268	12	)	)	PUNCT
ejpam-6734	268	13	m.	m.	NOUN
ejpam-6734	268	14	a.	a.	PROPN
ejpam-6734	268	15	abdou	abdou	PROPN
ejpam-6734	268	16	,	,	PUNCT
ejpam-6734	268	17	a.	a.	PROPN
ejpam-6734	268	18	s.	s.	PROPN
ejpam-6734	268	19	mohamed	mohamed	PROPN
ejpam-6734	268	20	/	/	SYM
ejpam-6734	268	21	eur	eur	PROPN
ejpam-6734	268	22	.	.	PUNCT
ejpam-6734	269	1	j.	j.	PROPN
ejpam-6734	269	2	pure	pure	PROPN
ejpam-6734	269	3	appl	appl	PROPN
ejpam-6734	269	4	.	.	PROPN
ejpam-6734	269	5	math	math	PROPN
ejpam-6734	269	6	,	,	PUNCT
ejpam-6734	269	7	18	18	NUM
ejpam-6734	269	8	(	(	PUNCT
ejpam-6734	269	9	4	4	NUM
ejpam-6734	269	10	)	)	PUNCT
ejpam-6734	269	11	(	(	PUNCT
ejpam-6734	269	12	2025	2025	NUM
ejpam-6734	269	13	)	)	PUNCT
ejpam-6734	269	14	,	,	PUNCT
ejpam-6734	269	15	6734	6734	NUM
ejpam-6734	269	16	10	10	NUM
ejpam-6734	269	17	of	of	ADP
ejpam-6734	269	18	20	20	NUM
ejpam-6734	269	19	with	with	ADP
ejpam-6734	269	20	the	the	DET
ejpam-6734	269	21	conditions	condition	NOUN
ejpam-6734	269	22	:	:	PUNCT
ejpam-6734	269	23	ψ(0	ψ(0	X
ejpam-6734	269	24	)	)	PUNCT
ejpam-6734	269	25	=	=	SYM
ejpam-6734	270	1	1	1	NUM
ejpam-6734	270	2	,	,	PUNCT
ejpam-6734	270	3	ψ(1	ψ(1	PROPN
ejpam-6734	270	4	)	)	PUNCT
ejpam-6734	270	5	=	=	SYM
ejpam-6734	270	6	a.	a.	NOUN
ejpam-6734	270	7	(	(	PUNCT
ejpam-6734	270	8	25	25	NUM
ejpam-6734	270	9	)	)	PUNCT
ejpam-6734	270	10	using	use	VERB
ejpam-6734	270	11	eqs	eqs	PROPN
ejpam-6734	270	12	.	.	PUNCT
ejpam-6734	270	13	(	(	PUNCT
ejpam-6734	270	14	24	24	NUM
ejpam-6734	270	15	)	)	PUNCT
ejpam-6734	270	16	,	,	PUNCT
ejpam-6734	270	17	and	and	CCONJ
ejpam-6734	270	18	(	(	PUNCT
ejpam-6734	270	19	25	25	NUM
ejpam-6734	270	20	)	)	PUNCT
ejpam-6734	270	21	.	.	PUNCT
ejpam-6734	271	1	when	when	SCONJ
ejpam-6734	271	2	i	i	PRON
ejpam-6734	271	3	=	=	NOUN
ejpam-6734	271	4	0	0	NUM
ejpam-6734	271	5	,	,	PUNCT
ejpam-6734	271	6	ψ(2	ψ(2	NOUN
ejpam-6734	271	7	)	)	PUNCT
ejpam-6734	271	8	=	=	SYM
ejpam-6734	272	1	−	−	PROPN
ejpam-6734	272	2	(	(	PUNCT
ejpam-6734	272	3	2+a	2+a	NUM
ejpam-6734	272	4	)	)	PUNCT
ejpam-6734	272	5	2	2	NUM
ejpam-6734	272	6	,	,	PUNCT
ejpam-6734	272	7	when	when	SCONJ
ejpam-6734	272	8	i	i	PRON
ejpam-6734	272	9	=	=	NOUN
ejpam-6734	272	10	1	1	NUM
ejpam-6734	272	11	,	,	PUNCT
ejpam-6734	272	12	then	then	ADV
ejpam-6734	272	13	ψ(3	ψ(3	PROPN
ejpam-6734	272	14	)	)	PUNCT
ejpam-6734	272	15	=	=	SYM
ejpam-6734	272	16	1	1	NUM
ejpam-6734	272	17	2	2	NUM
ejpam-6734	272	18	,	,	PUNCT
ejpam-6734	272	19	when	when	SCONJ
ejpam-6734	272	20	i	i	PRON
ejpam-6734	272	21	=	=	SYM
ejpam-6734	272	22	2	2	NUM
ejpam-6734	272	23	,	,	PUNCT
ejpam-6734	272	24	then	then	ADV
ejpam-6734	272	25	ψ(4	ψ(4	NOUN
ejpam-6734	272	26	)	)	PUNCT
ejpam-6734	272	27	=	=	SYM
ejpam-6734	272	28	−1	−1	NOUN
ejpam-6734	272	29	24	24	NUM
ejpam-6734	272	30	.	.	PUNCT
ejpam-6734	273	1	then	then	ADV
ejpam-6734	273	2	from	from	ADP
ejpam-6734	273	3	eq	eq	ADP
ejpam-6734	273	4	.	.	PUNCT
ejpam-6734	274	1	(	(	PUNCT
ejpam-6734	274	2	6	6	NUM
ejpam-6734	274	3	)	)	PUNCT
ejpam-6734	274	4	,	,	PUNCT
ejpam-6734	274	5	we	we	PRON
ejpam-6734	274	6	have	have	VERB
ejpam-6734	274	7	ζ(ω	ζ(ω	PROPN
ejpam-6734	274	8	)	)	PUNCT
ejpam-6734	274	9	=	=	SYM
ejpam-6734	275	1	1	1	NUM
ejpam-6734	275	2	+	+	CCONJ
ejpam-6734	275	3	aω	aω	ADJ
ejpam-6734	275	4	−	−	PROPN
ejpam-6734	275	5	(	(	PUNCT
ejpam-6734	275	6	2	2	NUM
ejpam-6734	275	7	+	+	CCONJ
ejpam-6734	275	8	a	a	X
ejpam-6734	275	9	)	)	PUNCT
ejpam-6734	275	10	2	2	NUM
ejpam-6734	276	1	ω2	ω2	NOUN
ejpam-6734	276	2	+	+	CCONJ
ejpam-6734	276	3	1	1	NUM
ejpam-6734	276	4	2	2	NUM
ejpam-6734	276	5	ω3	ω3	NOUN
ejpam-6734	276	6	+	+	CCONJ
ejpam-6734	276	7	1	1	NUM
ejpam-6734	276	8	24	24	NUM
ejpam-6734	276	9	ω4	ω4	NUM
ejpam-6734	276	10	−	−	PROPN
ejpam-6734	276	11	...	...	PUNCT
ejpam-6734	277	1	(	(	PUNCT
ejpam-6734	277	2	26	26	NUM
ejpam-6734	277	3	)	)	PUNCT
ejpam-6734	277	4	by	by	ADP
ejpam-6734	277	5	solving	solve	VERB
ejpam-6734	277	6	conditions	condition	NOUN
ejpam-6734	277	7	(	(	PUNCT
ejpam-6734	277	8	25	25	NUM
ejpam-6734	277	9	)	)	PUNCT
ejpam-6734	277	10	,	,	PUNCT
ejpam-6734	277	11	so	so	ADV
ejpam-6734	277	12	a	a	DET
ejpam-6734	277	13	=	=	NOUN
ejpam-6734	277	14	−1	−1	NOUN
ejpam-6734	277	15	.	.	PUNCT
ejpam-6734	278	1	then	then	ADV
ejpam-6734	278	2	eq.(26	eq.(26	ADV
ejpam-6734	278	3	)	)	PUNCT
ejpam-6734	278	4	has	have	VERB
ejpam-6734	278	5	the	the	DET
ejpam-6734	278	6	form	form	NOUN
ejpam-6734	278	7	ζ(ω	ζ(ω	PROPN
ejpam-6734	278	8	)	)	PUNCT
ejpam-6734	278	9	=	=	PUNCT
ejpam-6734	278	10	(	(	PUNCT
ejpam-6734	278	11	1−	1−	NUM
ejpam-6734	278	12	ω	ω	NUM
ejpam-6734	278	13	)	)	PUNCT
ejpam-6734	278	14	cos(ω	cos(ω	PROPN
ejpam-6734	278	15	)	)	PUNCT
ejpam-6734	278	16	.	.	PUNCT
ejpam-6734	279	1	which	which	PRON
ejpam-6734	279	2	is	be	AUX
ejpam-6734	279	3	the	the	DET
ejpam-6734	279	4	exact	exact	ADJ
ejpam-6734	279	5	solution	solution	NOUN
ejpam-6734	279	6	.	.	PUNCT
ejpam-6734	280	1	table	table	NOUN
ejpam-6734	280	2	1	1	NUM
ejpam-6734	280	3	compares	compare	VERB
ejpam-6734	280	4	the	the	DET
ejpam-6734	280	5	absolute	absolute	ADJ
ejpam-6734	280	6	errors	error	NOUN
ejpam-6734	280	7	resulting	result	VERB
ejpam-6734	280	8	from	from	ADP
ejpam-6734	280	9	the	the	DET
ejpam-6734	280	10	gfcm	gfcm	PROPN
ejpam-6734	280	11	and	and	CCONJ
ejpam-6734	280	12	those	those	PRON
ejpam-6734	280	13	obtained	obtain	VERB
ejpam-6734	280	14	using	use	VERB
ejpam-6734	280	15	the	the	DET
ejpam-6734	280	16	second	second	ADJ
ejpam-6734	280	17	-	-	PUNCT
ejpam-6734	280	18	kind	kind	NOUN
ejpam-6734	280	19	chebyshev	chebyshev	NOUN
ejpam-6734	280	20	wavelets	wavelet	NOUN
ejpam-6734	280	21	algorithm	algorithm	NOUN
ejpam-6734	280	22	[	[	X
ejpam-6734	280	23	32	32	NUM
ejpam-6734	280	24	]	]	PUNCT
ejpam-6734	280	25	at	at	ADP
ejpam-6734	280	26	i=3,4,5	i=3,4,5	NOUN
ejpam-6734	280	27	.	.	PUNCT
ejpam-6734	281	1	the	the	DET
ejpam-6734	281	2	data	datum	NOUN
ejpam-6734	281	3	indicate	indicate	VERB
ejpam-6734	281	4	that	that	SCONJ
ejpam-6734	281	5	our	our	PRON
ejpam-6734	281	6	method	method	NOUN
ejpam-6734	281	7	achieves	achieve	VERB
ejpam-6734	281	8	smaller	small	ADJ
ejpam-6734	281	9	absolute	absolute	ADJ
ejpam-6734	281	10	errors	error	NOUN
ejpam-6734	281	11	,	,	PUNCT
ejpam-6734	281	12	particularly	particularly	ADV
ejpam-6734	281	13	for	for	ADP
ejpam-6734	281	14	lower	low	ADJ
ejpam-6734	281	15	indices	index	NOUN
ejpam-6734	281	16	i	i	PRON
ejpam-6734	281	17	and	and	CCONJ
ejpam-6734	281	18	different	different	ADJ
ejpam-6734	281	19	values	value	NOUN
ejpam-6734	281	20	of	of	ADP
ejpam-6734	281	21	λ1	λ1	ADJ
ejpam-6734	281	22	and	and	CCONJ
ejpam-6734	281	23	λ2	λ2	NOUN
ejpam-6734	281	24	.	.	PUNCT
ejpam-6734	281	25	table	table	NOUN
ejpam-6734	281	26	2	2	NUM
ejpam-6734	281	27	provides	provide	VERB
ejpam-6734	281	28	the	the	DET
ejpam-6734	281	29	computation	computation	NOUN
ejpam-6734	281	30	times	time	NOUN
ejpam-6734	281	31	(	(	PUNCT
ejpam-6734	281	32	cpu	cpu	NOUN
ejpam-6734	281	33	time	time	NOUN
ejpam-6734	281	34	)	)	PUNCT
ejpam-6734	281	35	for	for	ADP
ejpam-6734	281	36	each	each	DET
ejpam-6734	281	37	method	method	NOUN
ejpam-6734	281	38	and	and	CCONJ
ejpam-6734	281	39	the	the	DET
ejpam-6734	281	40	changes	change	NOUN
ejpam-6734	281	41	in	in	ADP
ejpam-6734	281	42	error	error	NOUN
ejpam-6734	281	43	values	value	NOUN
ejpam-6734	281	44	between	between	ADP
ejpam-6734	281	45	consecutive	consecutive	ADJ
ejpam-6734	281	46	steps	step	NOUN
ejpam-6734	281	47	.	.	PUNCT
ejpam-6734	282	1	figure	figure	NOUN
ejpam-6734	282	2	1	1	NUM
ejpam-6734	282	3	visually	visually	ADV
ejpam-6734	282	4	represent	represent	VERB
ejpam-6734	282	5	the	the	DET
ejpam-6734	282	6	results	result	NOUN
ejpam-6734	282	7	corresponding	correspond	VERB
ejpam-6734	282	8	to	to	ADP
ejpam-6734	282	9	the	the	DET
ejpam-6734	282	10	same	same	ADJ
ejpam-6734	282	11	parameter	parameter	NOUN
ejpam-6734	282	12	values	value	NOUN
ejpam-6734	282	13	.	.	PUNCT
ejpam-6734	283	1	the	the	DET
ejpam-6734	283	2	graph	graph	NOUN
ejpam-6734	283	3	of	of	ADP
ejpam-6734	283	4	exact	exact	ADJ
ejpam-6734	283	5	and	and	CCONJ
ejpam-6734	283	6	approximate	approximate	ADJ
ejpam-6734	283	7	solutions	solution	NOUN
ejpam-6734	283	8	at	at	ADP
ejpam-6734	283	9	i=4	i=4	PROPN
ejpam-6734	283	10	is	be	AUX
ejpam-6734	283	11	plotted	plot	VERB
ejpam-6734	283	12	in	in	ADP
ejpam-6734	283	13	figure	figure	NOUN
ejpam-6734	283	14	2	2	NUM
ejpam-6734	283	15	.	.	PUNCT
ejpam-6734	283	16	table	table	NOUN
ejpam-6734	283	17	1	1	NUM
ejpam-6734	283	18	:	:	PUNCT
ejpam-6734	283	19	comparison	comparison	NOUN
ejpam-6734	283	20	between	between	ADP
ejpam-6734	283	21	the	the	DET
ejpam-6734	283	22	absolute	absolute	ADJ
ejpam-6734	283	23	errors	error	NOUN
ejpam-6734	283	24	for	for	ADP
ejpam-6734	283	25	example	example	NOUN
ejpam-6734	283	26	1	1	NUM
ejpam-6734	283	27	λ1	λ1	ADJ
ejpam-6734	283	28	λ2	λ2	NOUN
ejpam-6734	284	1	i	i	PRON
ejpam-6734	284	2	g	g	VERB
ejpam-6734	285	1	i	i	PRON
ejpam-6734	285	2	g	g	VERB
ejpam-6734	286	1	i	i	PRON
ejpam-6734	286	2	g	g	PROPN
ejpam-6734	286	3	1	1	NUM
ejpam-6734	286	4	1	1	NUM
ejpam-6734	286	5	3	3	NUM
ejpam-6734	286	6	1.89×	1.89×	NUM
ejpam-6734	286	7	10−3	10−3	NUM
ejpam-6734	286	8	4	4	NUM
ejpam-6734	286	9	2.59×	2.59×	NUM
ejpam-6734	286	10	10−4	10−4	NUM
ejpam-6734	286	11	5	5	NUM
ejpam-6734	286	12	9.08×	9.08×	NUM
ejpam-6734	286	13	10−6	10−6	NUM
ejpam-6734	286	14	2	2	NUM
ejpam-6734	286	15	1	1	NUM
ejpam-6734	286	16	1.89×	1.89×	NUM
ejpam-6734	286	17	10−3	10−3	NUM
ejpam-6734	286	18	2.59×	2.59×	NUM
ejpam-6734	286	19	10−4	10−4	NUM
ejpam-6734	286	20	9.08×	9.08×	NUM
ejpam-6734	286	21	10−6	10−6	NUM
ejpam-6734	286	22	2	2	NUM
ejpam-6734	286	23	−1	−1	NOUN
ejpam-6734	286	24	1.89×	1.89×	NUM
ejpam-6734	286	25	10−3	10−3	NUM
ejpam-6734	286	26	2.59×	2.59×	NUM
ejpam-6734	286	27	10−4	10−4	NUM
ejpam-6734	286	28	9.08×	9.08×	NUM
ejpam-6734	286	29	10−6	10−6	NUM
ejpam-6734	286	30	3	3	NUM
ejpam-6734	286	31	−2	−2	NOUN
ejpam-6734	286	32	1.89×	1.89×	NUM
ejpam-6734	286	33	10−3	10−3	NUM
ejpam-6734	286	34	2.59×	2.59×	NUM
ejpam-6734	286	35	10−4	10−4	NUM
ejpam-6734	286	36	9.08×	9.08×	NUM
ejpam-6734	286	37	10−6	10−6	NUM
ejpam-6734	286	38	method	method	NOUN
ejpam-6734	286	39	in	in	ADP
ejpam-6734	286	40	[	[	X
ejpam-6734	286	41	32	32	NUM
ejpam-6734	286	42	]	]	PUNCT
ejpam-6734	286	43	2.28×	2.28×	NUM
ejpam-6734	286	44	10−3	10−3	NUM
ejpam-6734	287	1	6.32×	6.32×	NUM
ejpam-6734	287	2	10−5	10−5	NUM
ejpam-6734	287	3	6.23×	6.23×	NUM
ejpam-6734	287	4	10−6	10−6	NUM
ejpam-6734	287	5	table	table	NOUN
ejpam-6734	287	6	2	2	NUM
ejpam-6734	287	7	:	:	PUNCT
ejpam-6734	287	8	the	the	DET
ejpam-6734	287	9	cpu	cpu	ADJ
ejpam-6734	287	10	time	time	NOUN
ejpam-6734	287	11	for	for	ADP
ejpam-6734	287	12	example	example	NOUN
ejpam-6734	287	13	1	1	NUM
ejpam-6734	287	14	cpu	cpu	NOUN
ejpam-6734	287	15	time	time	NOUN
ejpam-6734	287	16	gi	gi	VERB
ejpam-6734	287	17	0.25	0.25	NUM
ejpam-6734	287	18	1.63×	1.63×	NUM
ejpam-6734	287	19	10−3	10−3	NUM
ejpam-6734	287	20	0.282	0.282	NUM
ejpam-6734	287	21	2.50×	2.50×	NUM
ejpam-6734	287	22	10−4	10−4	NUM
ejpam-6734	287	23	0.297	0.297	NUM
ejpam-6734	287	24	6.62×	6.62×	NUM
ejpam-6734	287	25	10−6	10−6	NUM
ejpam-6734	287	26	example	example	NOUN
ejpam-6734	287	27	2	2	NUM
ejpam-6734	287	28	.	.	X
ejpam-6734	288	1	consider	consider	VERB
ejpam-6734	288	2	the	the	DET
ejpam-6734	288	3	following	follow	VERB
ejpam-6734	288	4	non	non	ADJ
ejpam-6734	288	5	-	-	ADJ
ejpam-6734	288	6	linear	linear	ADJ
ejpam-6734	288	7	second	second	ADJ
ejpam-6734	288	8	order	order	NOUN
ejpam-6734	288	9	boundary	boundary	ADJ
ejpam-6734	289	1	[	[	X
ejpam-6734	289	2	32	32	NUM
ejpam-6734	289	3	]	]	PUNCT
ejpam-6734	289	4	if	if	SCONJ
ejpam-6734	289	5	υ1(ω	υ1(ω	NOUN
ejpam-6734	289	6	)	)	PUNCT
ejpam-6734	289	7	=	=	SYM
ejpam-6734	289	8	4	4	NUM
ejpam-6734	289	9	,	,	PUNCT
ejpam-6734	289	10	υ2(ω	υ2(ω	PRON
ejpam-6734	289	11	)	)	PUNCT
ejpam-6734	289	12	=	=	SYM
ejpam-6734	289	13	0	0	NUM
ejpam-6734	289	14	,	,	PUNCT
ejpam-6734	289	15	υ3(ω	υ3(ω	PROPN
ejpam-6734	289	16	)	)	PUNCT
ejpam-6734	289	17	=	=	SYM
ejpam-6734	289	18	−2	−2	NOUN
ejpam-6734	289	19	,	,	PUNCT
ejpam-6734	289	20	υ4(ω	υ4(ω	PROPN
ejpam-6734	289	21	)	)	PUNCT
ejpam-6734	289	22	=	=	SYM
ejpam-6734	289	23	1	1	NUM
ejpam-6734	289	24	,	,	PUNCT
ejpam-6734	289	25	ξ(ω	ξ(ω	NOUN
ejpam-6734	289	26	)	)	PUNCT
ejpam-6734	289	27	=	=	SYM
ejpam-6734	289	28	0	0	NUM
ejpam-6734	289	29	,	,	PUNCT
ejpam-6734	289	30	m1	m1	PROPN
ejpam-6734	289	31	=	=	SYM
ejpam-6734	289	32	−1	−1	NOUN
ejpam-6734	289	33	,	,	PUNCT
ejpam-6734	289	34	m2	m2	PROPN
ejpam-6734	289	35	=	=	PROPN
ejpam-6734	289	36	0	0	PROPN
ejpam-6734	289	37	.	.	PUNCT
ejpam-6734	290	1	so	so	ADV
ejpam-6734	290	2	,	,	PUNCT
ejpam-6734	290	3	eq	eq	NOUN
ejpam-6734	290	4	.	.	PUNCT
ejpam-6734	291	1	(	(	PUNCT
ejpam-6734	291	2	1	1	X
ejpam-6734	291	3	)	)	PUNCT
ejpam-6734	291	4	can	can	AUX
ejpam-6734	291	5	be	be	AUX
ejpam-6734	291	6	written	write	VERB
ejpam-6734	291	7	in	in	ADP
ejpam-6734	291	8	the	the	DET
ejpam-6734	291	9	form	form	NOUN
ejpam-6734	291	10	:	:	PUNCT
ejpam-6734	291	11	4ζ	4ζ	NUM
ejpam-6734	291	12	′′(ω)−	′′(ω)−	PROPN
ejpam-6734	291	13	2(ζ	2(ζ	NUM
ejpam-6734	291	14	′(ω))2	′(ω))2	NOUN
ejpam-6734	291	15	+	+	CCONJ
ejpam-6734	291	16	ζ(ω	ζ(ω	NOUN
ejpam-6734	291	17	)	)	PUNCT
ejpam-6734	291	18	=	=	SYM
ejpam-6734	292	1	0	0	NUM
ejpam-6734	292	2	,	,	PUNCT
ejpam-6734	292	3	0	0	NUM
ejpam-6734	292	4	<	<	X
ejpam-6734	292	5	ω	ω	NUM
ejpam-6734	292	6	≤	≤	NUM
ejpam-6734	292	7	1	1	NUM
ejpam-6734	292	8	(	(	PUNCT
ejpam-6734	292	9	27	27	NUM
ejpam-6734	292	10	)	)	PUNCT
ejpam-6734	292	11	m.	m.	NOUN
ejpam-6734	292	12	a.	a.	PROPN
ejpam-6734	292	13	abdou	abdou	PROPN
ejpam-6734	292	14	,	,	PUNCT
ejpam-6734	292	15	a.	a.	PROPN
ejpam-6734	292	16	s.	s.	PROPN
ejpam-6734	292	17	mohamed	mohamed	PROPN
ejpam-6734	292	18	/	/	SYM
ejpam-6734	292	19	eur	eur	PROPN
ejpam-6734	292	20	.	.	PUNCT
ejpam-6734	293	1	j.	j.	PROPN
ejpam-6734	293	2	pure	pure	PROPN
ejpam-6734	293	3	appl	appl	PROPN
ejpam-6734	293	4	.	.	PROPN
ejpam-6734	293	5	math	math	PROPN
ejpam-6734	293	6	,	,	PUNCT
ejpam-6734	293	7	18	18	NUM
ejpam-6734	293	8	(	(	PUNCT
ejpam-6734	293	9	4	4	NUM
ejpam-6734	293	10	)	)	PUNCT
ejpam-6734	293	11	(	(	PUNCT
ejpam-6734	293	12	2025	2025	NUM
ejpam-6734	293	13	)	)	PUNCT
ejpam-6734	293	14	,	,	PUNCT
ejpam-6734	293	15	6734	6734	NUM
ejpam-6734	293	16	11	11	NUM
ejpam-6734	293	17	of	of	ADP
ejpam-6734	293	18	20	20	NUM
ejpam-6734	293	19	figure	figure	NOUN
ejpam-6734	293	20	1	1	NUM
ejpam-6734	293	21	:	:	PUNCT
ejpam-6734	293	22	graph	graph	NOUN
ejpam-6734	293	23	of	of	ADP
ejpam-6734	293	24	the	the	DET
ejpam-6734	293	25	error	error	NOUN
ejpam-6734	293	26	at	at	ADP
ejpam-6734	293	27	i=3	i=3	PROPN
ejpam-6734	293	28	,	,	PUNCT
ejpam-6734	293	29	4	4	NUM
ejpam-6734	293	30	,	,	PUNCT
ejpam-6734	293	31	and	and	CCONJ
ejpam-6734	293	32	5	5	NUM
ejpam-6734	293	33	for	for	ADP
ejpam-6734	293	34	example	example	NOUN
ejpam-6734	293	35	1	1	NUM
ejpam-6734	293	36	figure	figure	NOUN
ejpam-6734	293	37	2	2	NUM
ejpam-6734	293	38	:	:	PUNCT
ejpam-6734	293	39	approximate	approximate	ADJ
ejpam-6734	293	40	and	and	CCONJ
ejpam-6734	293	41	exact	exact	ADJ
ejpam-6734	293	42	solutions	solution	NOUN
ejpam-6734	293	43	at	at	ADP
ejpam-6734	293	44	i=4	i=4	NOUN
ejpam-6734	293	45	,	,	PUNCT
ejpam-6734	293	46	λ1	λ1	ADJ
ejpam-6734	293	47	=	=	SYM
ejpam-6734	293	48	3	3	NUM
ejpam-6734	293	49	,	,	PUNCT
ejpam-6734	293	50	λ2	λ2	NOUN
ejpam-6734	293	51	=	=	SYM
ejpam-6734	293	52	−2	−2	NOUN
ejpam-6734	293	53	for	for	ADP
ejpam-6734	293	54	example	example	NOUN
ejpam-6734	293	55	1	1	NUM
ejpam-6734	293	56	with	with	ADP
ejpam-6734	293	57	the	the	DET
ejpam-6734	293	58	conditions	condition	NOUN
ejpam-6734	293	59	(	(	PUNCT
ejpam-6734	293	60	3	3	X
ejpam-6734	293	61	)	)	PUNCT
ejpam-6734	293	62	ζ(0	ζ(0	NOUN
ejpam-6734	293	63	)	)	PUNCT
ejpam-6734	293	64	=	=	SYM
ejpam-6734	293	65	−1	−1	NOUN
ejpam-6734	293	66	,	,	PUNCT
ejpam-6734	293	67	ζ	ζ	PROPN
ejpam-6734	293	68	′(0	′(0	NOUN
ejpam-6734	293	69	)	)	PUNCT
ejpam-6734	293	70	=	=	SYM
ejpam-6734	294	1	0	0	X
ejpam-6734	294	2	.	.	PUNCT
ejpam-6734	295	1	(	(	PUNCT
ejpam-6734	295	2	28	28	NUM
ejpam-6734	295	3	)	)	PUNCT
ejpam-6734	295	4	from	from	ADP
ejpam-6734	295	5	the	the	DET
ejpam-6734	295	6	definition	definition	NOUN
ejpam-6734	295	7	of	of	ADP
ejpam-6734	295	8	dtm	dtm	PROPN
ejpam-6734	295	9	,	,	PUNCT
ejpam-6734	295	10	eqs	eqs	X
ejpam-6734	295	11	.	.	PUNCT
ejpam-6734	296	1	(	(	PUNCT
ejpam-6734	296	2	9	9	NUM
ejpam-6734	296	3	)	)	PUNCT
ejpam-6734	296	4	and	and	CCONJ
ejpam-6734	296	5	(	(	PUNCT
ejpam-6734	296	6	11	11	NUM
ejpam-6734	296	7	)	)	PUNCT
ejpam-6734	296	8	.	.	PUNCT
ejpam-6734	297	1	so	so	ADV
ejpam-6734	297	2	,	,	PUNCT
ejpam-6734	297	3	eq	eq	NOUN
ejpam-6734	297	4	.	.	PUNCT
ejpam-6734	298	1	(	(	PUNCT
ejpam-6734	298	2	27	27	NUM
ejpam-6734	298	3	)	)	PUNCT
ejpam-6734	298	4	transforms	transform	VERB
ejpam-6734	298	5	to	to	ADP
ejpam-6734	298	6	ψ(i+	ψ(i+	NUM
ejpam-6734	298	7	2	2	NUM
ejpam-6734	298	8	)	)	PUNCT
ejpam-6734	298	9	=	=	SYM
ejpam-6734	298	10	1	1	NUM
ejpam-6734	298	11	4(i+	4(i+	NUM
ejpam-6734	298	12	1)(i+	1)(i+	NUM
ejpam-6734	298	13	2	2	NUM
ejpam-6734	298	14	)	)	PUNCT
ejpam-6734	298	15	{	{	PUNCT
ejpam-6734	298	16	2	2	NUM
ejpam-6734	298	17	i∑	i∑	PROPN
ejpam-6734	298	18	k=0	k=0	PROPN
ejpam-6734	298	19	(	(	PUNCT
ejpam-6734	298	20	k	k	X
ejpam-6734	298	21	+	+	PROPN
ejpam-6734	299	1	1)(i−	1)(i−	NUM
ejpam-6734	299	2	k	k	NOUN
ejpam-6734	299	3	+	+	PUNCT
ejpam-6734	299	4	1)ψ(k	1)ψ(k	NUM
ejpam-6734	299	5	+	+	SYM
ejpam-6734	299	6	1)ψ(i−	1)ψ(i−	NUM
ejpam-6734	299	7	k	k	X
ejpam-6734	300	1	+	+	CCONJ
ejpam-6734	300	2	1)−ψ(i	1)−ψ(i	NUM
ejpam-6734	300	3	)	)	PUNCT
ejpam-6734	300	4	}	}	PUNCT
ejpam-6734	300	5	,	,	PUNCT
ejpam-6734	300	6	(	(	PUNCT
ejpam-6734	300	7	29	29	NUM
ejpam-6734	300	8	)	)	PUNCT
ejpam-6734	300	9	with	with	ADP
ejpam-6734	300	10	the	the	DET
ejpam-6734	300	11	conditions	condition	NOUN
ejpam-6734	300	12	.	.	PUNCT
ejpam-6734	301	1	ψ(0	ψ(0	VERB
ejpam-6734	301	2	)	)	PUNCT
ejpam-6734	301	3	=	=	SYM
ejpam-6734	301	4	−1	−1	NOUN
ejpam-6734	301	5	,	,	PUNCT
ejpam-6734	301	6	ψ(1	ψ(1	PROPN
ejpam-6734	301	7	)	)	PUNCT
ejpam-6734	301	8	=	=	SYM
ejpam-6734	301	9	0	0	X
ejpam-6734	301	10	.	.	PUNCT
ejpam-6734	301	11	(	(	PUNCT
ejpam-6734	301	12	30	30	NUM
ejpam-6734	301	13	)	)	PUNCT
ejpam-6734	301	14	from	from	ADP
ejpam-6734	301	15	eqs	eqs	PROPN
ejpam-6734	301	16	.	.	PUNCT
ejpam-6734	301	17	(	(	PUNCT
ejpam-6734	301	18	29	29	NUM
ejpam-6734	301	19	)	)	PUNCT
ejpam-6734	301	20	and	and	CCONJ
ejpam-6734	301	21	(	(	PUNCT
ejpam-6734	301	22	30	30	NUM
ejpam-6734	301	23	)	)	PUNCT
ejpam-6734	301	24	.	.	PUNCT
ejpam-6734	302	1	m.	m.	NOUN
ejpam-6734	302	2	a.	a.	PROPN
ejpam-6734	302	3	abdou	abdou	PROPN
ejpam-6734	302	4	,	,	PUNCT
ejpam-6734	302	5	a.	a.	PROPN
ejpam-6734	302	6	s.	s.	PROPN
ejpam-6734	302	7	mohamed	mohamed	PROPN
ejpam-6734	302	8	/	/	SYM
ejpam-6734	302	9	eur	eur	PROPN
ejpam-6734	302	10	.	.	PUNCT
ejpam-6734	303	1	j.	j.	PROPN
ejpam-6734	303	2	pure	pure	PROPN
ejpam-6734	303	3	appl	appl	PROPN
ejpam-6734	303	4	.	.	PROPN
ejpam-6734	303	5	math	math	PROPN
ejpam-6734	303	6	,	,	PUNCT
ejpam-6734	303	7	18	18	NUM
ejpam-6734	303	8	(	(	PUNCT
ejpam-6734	303	9	4	4	NUM
ejpam-6734	303	10	)	)	PUNCT
ejpam-6734	303	11	(	(	PUNCT
ejpam-6734	303	12	2025	2025	NUM
ejpam-6734	303	13	)	)	PUNCT
ejpam-6734	303	14	,	,	PUNCT
ejpam-6734	303	15	6734	6734	NUM
ejpam-6734	303	16	12	12	NUM
ejpam-6734	303	17	of	of	ADP
ejpam-6734	303	18	20	20	NUM
ejpam-6734	303	19	when	when	SCONJ
ejpam-6734	303	20	i	i	PRON
ejpam-6734	303	21	=	=	NOUN
ejpam-6734	303	22	0	0	NUM
ejpam-6734	303	23	,	,	PUNCT
ejpam-6734	303	24	then	then	ADV
ejpam-6734	303	25	ψ(2	ψ(2	NOUN
ejpam-6734	303	26	)	)	PUNCT
ejpam-6734	304	1	=	=	PUNCT
ejpam-6734	304	2	1	1	NUM
ejpam-6734	304	3	,	,	PUNCT
ejpam-6734	304	4	when	when	SCONJ
ejpam-6734	304	5	i	i	PRON
ejpam-6734	304	6	=	=	NOUN
ejpam-6734	304	7	1	1	NUM
ejpam-6734	304	8	,	,	PUNCT
ejpam-6734	304	9	then	then	ADV
ejpam-6734	304	10	ψ(3	ψ(3	PROPN
ejpam-6734	304	11	)	)	PUNCT
ejpam-6734	304	12	=	=	SYM
ejpam-6734	305	1	1	1	NUM
ejpam-6734	305	2	,	,	PUNCT
ejpam-6734	305	3	when	when	SCONJ
ejpam-6734	305	4	i	i	PRON
ejpam-6734	305	5	=	=	SYM
ejpam-6734	305	6	2	2	NUM
ejpam-6734	305	7	,	,	PUNCT
ejpam-6734	305	8	then	then	ADV
ejpam-6734	305	9	ψ(4	ψ(4	NOUN
ejpam-6734	305	10	)	)	PUNCT
ejpam-6734	305	11	=	=	SYM
ejpam-6734	305	12	0	0	NUM
ejpam-6734	305	13	,	,	PUNCT
ejpam-6734	305	14	when	when	SCONJ
ejpam-6734	305	15	i	i	PRON
ejpam-6734	305	16	=	=	SYM
ejpam-6734	305	17	3	3	NUM
ejpam-6734	305	18	,	,	PUNCT
ejpam-6734	305	19	then	then	ADV
ejpam-6734	305	20	ψ(5	ψ(5	PROPN
ejpam-6734	305	21	)	)	PUNCT
ejpam-6734	305	22	=	=	SYM
ejpam-6734	305	23	0	0	NUM
ejpam-6734	305	24	,	,	PUNCT
ejpam-6734	305	25	when	when	SCONJ
ejpam-6734	305	26	i	i	PRON
ejpam-6734	305	27	=	=	SYM
ejpam-6734	305	28	4	4	NUM
ejpam-6734	305	29	,	,	PUNCT
ejpam-6734	305	30	then	then	ADV
ejpam-6734	305	31	ψ(6	ψ(6	PROPN
ejpam-6734	305	32	)	)	PUNCT
ejpam-6734	306	1	=	=	PUNCT
ejpam-6734	307	1	0	0	X
ejpam-6734	307	2	.	.	PUNCT
ejpam-6734	308	1	then	then	ADV
ejpam-6734	308	2	from	from	ADP
ejpam-6734	308	3	eq	eq	ADP
ejpam-6734	308	4	.	.	PUNCT
ejpam-6734	309	1	(	(	PUNCT
ejpam-6734	309	2	6	6	NUM
ejpam-6734	309	3	)	)	PUNCT
ejpam-6734	309	4	,	,	PUNCT
ejpam-6734	309	5	we	we	PRON
ejpam-6734	309	6	have	have	VERB
ejpam-6734	309	7	ζ(ω	ζ(ω	PROPN
ejpam-6734	309	8	)	)	PUNCT
ejpam-6734	309	9	=	=	SYM
ejpam-6734	310	1	ω2	ω2	ADJ
ejpam-6734	310	2	8	8	NUM
ejpam-6734	310	3	−	−	PROPN
ejpam-6734	310	4	1	1	NUM
ejpam-6734	310	5	.	.	NOUN
ejpam-6734	310	6	which	which	PRON
ejpam-6734	310	7	is	be	AUX
ejpam-6734	310	8	the	the	DET
ejpam-6734	310	9	exact	exact	ADJ
ejpam-6734	310	10	solution	solution	NOUN
ejpam-6734	310	11	.	.	PUNCT
ejpam-6734	311	1	in	in	ADP
ejpam-6734	311	2	table	table	NOUN
ejpam-6734	311	3	3	3	NUM
ejpam-6734	311	4	,	,	PUNCT
ejpam-6734	311	5	we	we	PRON
ejpam-6734	311	6	compare	compare	VERB
ejpam-6734	311	7	the	the	DET
ejpam-6734	311	8	absolute	absolute	ADJ
ejpam-6734	311	9	errors	error	NOUN
ejpam-6734	311	10	generated	generate	VERB
ejpam-6734	311	11	by	by	ADP
ejpam-6734	311	12	the	the	DET
ejpam-6734	311	13	gfcm	gfcm	PROPN
ejpam-6734	311	14	for	for	ADP
ejpam-6734	311	15	i=2,3	i=2,3	NOUN
ejpam-6734	311	16	,	,	PUNCT
ejpam-6734	311	17	various	various	ADJ
ejpam-6734	311	18	values	value	NOUN
ejpam-6734	311	19	of	of	ADP
ejpam-6734	311	20	λ1	λ1	PROPN
ejpam-6734	311	21	and	and	CCONJ
ejpam-6734	311	22	λ2	λ2	NOUN
ejpam-6734	311	23	.	.	PUNCT
ejpam-6734	311	24	table	table	NOUN
ejpam-6734	311	25	4	4	NUM
ejpam-6734	311	26	provides	provide	VERB
ejpam-6734	311	27	the	the	DET
ejpam-6734	311	28	cpu	cpu	NOUN
ejpam-6734	311	29	times	time	NOUN
ejpam-6734	311	30	needed	need	VERB
ejpam-6734	311	31	for	for	ADP
ejpam-6734	311	32	the	the	DET
ejpam-6734	311	33	calculations	calculation	NOUN
ejpam-6734	311	34	.	.	PUNCT
ejpam-6734	312	1	the	the	DET
ejpam-6734	312	2	results	result	NOUN
ejpam-6734	312	3	show	show	VERB
ejpam-6734	312	4	that	that	SCONJ
ejpam-6734	312	5	the	the	DET
ejpam-6734	312	6	proposed	propose	VERB
ejpam-6734	312	7	method	method	NOUN
ejpam-6734	312	8	achieves	achieve	VERB
ejpam-6734	312	9	the	the	DET
ejpam-6734	312	10	best	good	ADJ
ejpam-6734	312	11	errors	error	NOUN
ejpam-6734	312	12	especially	especially	ADV
ejpam-6734	312	13	for	for	ADP
ejpam-6734	312	14	smaller	small	ADJ
ejpam-6734	312	15	values	value	NOUN
ejpam-6734	312	16	of	of	ADP
ejpam-6734	312	17	i.	i.	NOUN
ejpam-6734	312	18	figure	figure	NOUN
ejpam-6734	312	19	3	3	NUM
ejpam-6734	312	20	visualizes	visualize	VERB
ejpam-6734	312	21	our	our	PRON
ejpam-6734	312	22	results	result	NOUN
ejpam-6734	312	23	for	for	ADP
ejpam-6734	312	24	i=3,4	i=3,4	NOUN
ejpam-6734	312	25	,	,	PUNCT
ejpam-6734	312	26	and	and	CCONJ
ejpam-6734	313	1	λ1	λ1	ADJ
ejpam-6734	313	2	=	=	SYM
ejpam-6734	313	3	λ2	λ2	NOUN
ejpam-6734	313	4	=	=	SYM
ejpam-6734	313	5	1	1	NUM
ejpam-6734	313	6	.	.	PUNCT
ejpam-6734	314	1	the	the	DET
ejpam-6734	314	2	graph	graph	NOUN
ejpam-6734	314	3	of	of	ADP
ejpam-6734	314	4	exact	exact	ADJ
ejpam-6734	314	5	and	and	CCONJ
ejpam-6734	314	6	approximate	approximate	ADJ
ejpam-6734	314	7	solutions	solution	NOUN
ejpam-6734	314	8	at	at	ADP
ejpam-6734	314	9	i=5	i=5	ADV
ejpam-6734	314	10	is	be	AUX
ejpam-6734	314	11	plotted	plot	VERB
ejpam-6734	314	12	in	in	ADP
ejpam-6734	314	13	figure	figure	NOUN
ejpam-6734	314	14	4	4	NUM
ejpam-6734	314	15	.	.	PUNCT
ejpam-6734	314	16	table	table	NOUN
ejpam-6734	314	17	3	3	NUM
ejpam-6734	314	18	:	:	PUNCT
ejpam-6734	314	19	comparison	comparison	NOUN
ejpam-6734	314	20	between	between	ADP
ejpam-6734	314	21	the	the	DET
ejpam-6734	314	22	absolute	absolute	ADJ
ejpam-6734	314	23	errors	error	NOUN
ejpam-6734	314	24	for	for	ADP
ejpam-6734	314	25	example	example	NOUN
ejpam-6734	314	26	2	2	NUM
ejpam-6734	314	27	λ1	λ1	ADJ
ejpam-6734	314	28	λ2	λ2	NOUN
ejpam-6734	315	1	i	i	PRON
ejpam-6734	315	2	g	g	VERB
ejpam-6734	316	1	i	i	PRON
ejpam-6734	316	2	g	g	PROPN
ejpam-6734	316	3	1	1	NUM
ejpam-6734	316	4	1	1	NUM
ejpam-6734	316	5	2	2	NUM
ejpam-6734	316	6	0	0	NUM
ejpam-6734	316	7	3	3	NUM
ejpam-6734	316	8	2.3×	2.3×	NUM
ejpam-6734	316	9	10−17	10−17	NUM
ejpam-6734	316	10	2	2	NUM
ejpam-6734	316	11	1	1	NUM
ejpam-6734	316	12	0	0	NUM
ejpam-6734	316	13	2.5×	2.5×	NUM
ejpam-6734	316	14	10−18	10−18	NUM
ejpam-6734	316	15	2	2	NUM
ejpam-6734	316	16	−1	−1	NOUN
ejpam-6734	316	17	0	0	NUM
ejpam-6734	316	18	5.8×	5.8×	NUM
ejpam-6734	316	19	10−18	10−18	NUM
ejpam-6734	316	20	3	3	NUM
ejpam-6734	316	21	−2	−2	NOUN
ejpam-6734	316	22	0	0	NUM
ejpam-6734	316	23	8.7×	8.7×	NUM
ejpam-6734	316	24	10−18	10−18	NUM
ejpam-6734	316	25	table	table	NOUN
ejpam-6734	316	26	4	4	NUM
ejpam-6734	316	27	:	:	PUNCT
ejpam-6734	316	28	the	the	DET
ejpam-6734	316	29	cpu	cpu	ADJ
ejpam-6734	316	30	time	time	NOUN
ejpam-6734	316	31	for	for	ADP
ejpam-6734	316	32	example	example	NOUN
ejpam-6734	316	33	2	2	NUM
ejpam-6734	316	34	cpu	cpu	NOUN
ejpam-6734	316	35	time	time	NOUN
ejpam-6734	316	36	gi	gi	ADP
ejpam-6734	317	1	0.235	0.235	NUM
ejpam-6734	317	2	2.5×	2.5×	NUM
ejpam-6734	317	3	10−18	10−18	NUM
ejpam-6734	317	4	0.266	0.266	NUM
ejpam-6734	317	5	1.1×	1.1×	NUM
ejpam-6734	317	6	10−18	10−18	NOUN
ejpam-6734	317	7	example	example	NOUN
ejpam-6734	317	8	3	3	X
ejpam-6734	317	9	.	.	X
ejpam-6734	317	10	consider	consider	VERB
ejpam-6734	317	11	the	the	DET
ejpam-6734	317	12	non	non	ADJ
ejpam-6734	317	13	-	-	ADJ
ejpam-6734	317	14	linear	linear	ADJ
ejpam-6734	317	15	second	second	ADJ
ejpam-6734	317	16	-	-	PUNCT
ejpam-6734	317	17	order	order	NOUN
ejpam-6734	317	18	initial	initial	ADJ
ejpam-6734	317	19	value	value	NOUN
ejpam-6734	317	20	problem	problem	NOUN
ejpam-6734	317	21	:	:	PUNCT
ejpam-6734	318	1	[	[	X
ejpam-6734	318	2	33	33	NUM
ejpam-6734	318	3	]	]	PUNCT
ejpam-6734	318	4	if	if	SCONJ
ejpam-6734	318	5	f(ζ	f(ζ	PROPN
ejpam-6734	318	6	)	)	PUNCT
ejpam-6734	318	7	=	=	SYM
ejpam-6734	318	8	e−2ζ(ω	e−2ζ(ω	X
ejpam-6734	318	9	)	)	PUNCT
ejpam-6734	318	10	,	,	PUNCT
ejpam-6734	318	11	m1	m1	PROPN
ejpam-6734	318	12	=	=	SYM
ejpam-6734	318	13	1	1	NUM
ejpam-6734	318	14	,	,	PUNCT
ejpam-6734	318	15	m2	m2	PROPN
ejpam-6734	318	16	=	=	PROPN
ejpam-6734	318	17	1	1	NUM
ejpam-6734	318	18	e	e	NOUN
ejpam-6734	318	19	.	.	PUNCT
ejpam-6734	319	1	so	so	ADV
ejpam-6734	319	2	,	,	PUNCT
ejpam-6734	319	3	eq	eq	NOUN
ejpam-6734	319	4	.	.	PUNCT
ejpam-6734	320	1	(	(	PUNCT
ejpam-6734	320	2	2	2	X
ejpam-6734	320	3	)	)	PUNCT
ejpam-6734	320	4	can	can	AUX
ejpam-6734	320	5	be	be	AUX
ejpam-6734	320	6	written	write	VERB
ejpam-6734	320	7	in	in	ADP
ejpam-6734	320	8	the	the	DET
ejpam-6734	320	9	form	form	NOUN
ejpam-6734	320	10	:	:	PUNCT
ejpam-6734	320	11	ζ	ζ	NOUN
ejpam-6734	320	12	′′(ω	′′(ω	NOUN
ejpam-6734	320	13	)	)	PUNCT
ejpam-6734	320	14	+	+	CCONJ
ejpam-6734	320	15	e−2ζ(ω	e−2ζ(ω	NOUN
ejpam-6734	320	16	)	)	PUNCT
ejpam-6734	320	17	=	=	SYM
ejpam-6734	321	1	0	0	NUM
ejpam-6734	321	2	,	,	PUNCT
ejpam-6734	321	3	(	(	PUNCT
ejpam-6734	321	4	31	31	NUM
ejpam-6734	321	5	)	)	PUNCT
ejpam-6734	321	6	with	with	ADP
ejpam-6734	321	7	the	the	DET
ejpam-6734	321	8	conditions	condition	NOUN
ejpam-6734	321	9	(	(	PUNCT
ejpam-6734	321	10	3	3	X
ejpam-6734	321	11	)	)	PUNCT
ejpam-6734	321	12	ζ(0	ζ(0	NOUN
ejpam-6734	321	13	)	)	PUNCT
ejpam-6734	321	14	=	=	SYM
ejpam-6734	321	15	1	1	NUM
ejpam-6734	321	16	,	,	PUNCT
ejpam-6734	321	17	ζ	ζ	NOUN
ejpam-6734	321	18	′(0	′(0	NOUN
ejpam-6734	321	19	)	)	PUNCT
ejpam-6734	321	20	=	=	SYM
ejpam-6734	321	21	1	1	NUM
ejpam-6734	321	22	e	e	NOUN
ejpam-6734	321	23	.	.	PUNCT
ejpam-6734	322	1	(	(	PUNCT
ejpam-6734	322	2	32	32	NUM
ejpam-6734	322	3	)	)	PUNCT
ejpam-6734	322	4	from	from	ADP
ejpam-6734	322	5	the	the	DET
ejpam-6734	322	6	definition	definition	NOUN
ejpam-6734	322	7	of	of	ADP
ejpam-6734	322	8	dtm	dtm	PROPN
ejpam-6734	322	9	,	,	PUNCT
ejpam-6734	322	10	eqs	eqs	X
ejpam-6734	322	11	.	.	PUNCT
ejpam-6734	323	1	(	(	PUNCT
ejpam-6734	323	2	9	9	NUM
ejpam-6734	323	3	)	)	PUNCT
ejpam-6734	323	4	and	and	CCONJ
ejpam-6734	323	5	(	(	PUNCT
ejpam-6734	323	6	10	10	NUM
ejpam-6734	323	7	)	)	PUNCT
ejpam-6734	323	8	.	.	PUNCT
ejpam-6734	324	1	so	so	ADV
ejpam-6734	324	2	,	,	PUNCT
ejpam-6734	324	3	eq	eq	NOUN
ejpam-6734	324	4	.	.	PUNCT
ejpam-6734	325	1	(	(	PUNCT
ejpam-6734	325	2	32	32	NUM
ejpam-6734	325	3	)	)	PUNCT
ejpam-6734	325	4	transforms	transform	VERB
ejpam-6734	325	5	to	to	ADP
ejpam-6734	325	6	ψ(i+	ψ(i+	NUM
ejpam-6734	325	7	2	2	NUM
ejpam-6734	325	8	)	)	PUNCT
ejpam-6734	325	9	=	=	SYM
ejpam-6734	325	10	−1	−1	NOUN
ejpam-6734	325	11	(	(	PUNCT
ejpam-6734	325	12	i+	i+	NUM
ejpam-6734	325	13	1)(i+	1)(i+	NUM
ejpam-6734	325	14	2	2	NUM
ejpam-6734	325	15	)	)	PUNCT
ejpam-6734	325	16	f1(i	f1(i	NUM
ejpam-6734	325	17	)	)	PUNCT
ejpam-6734	325	18	,	,	PUNCT
ejpam-6734	325	19	(	(	PUNCT
ejpam-6734	325	20	33	33	NUM
ejpam-6734	325	21	)	)	PUNCT
ejpam-6734	325	22	where	where	SCONJ
ejpam-6734	325	23	f1(i	f1(i	X
ejpam-6734	325	24	)	)	PUNCT
ejpam-6734	325	25	is	be	AUX
ejpam-6734	325	26	the	the	DET
ejpam-6734	325	27	differential	differential	ADJ
ejpam-6734	325	28	transform	transform	NOUN
ejpam-6734	325	29	of	of	ADP
ejpam-6734	325	30	f(ζ	f(ζ	PROPN
ejpam-6734	325	31	)	)	PUNCT
ejpam-6734	325	32	,	,	PUNCT
ejpam-6734	325	33	using	use	VERB
ejpam-6734	325	34	the	the	DET
ejpam-6734	325	35	following	follow	VERB
ejpam-6734	325	36	conditions	condition	NOUN
ejpam-6734	325	37	ψ(0	ψ(0	PART
ejpam-6734	325	38	)	)	PUNCT
ejpam-6734	325	39	=	=	SYM
ejpam-6734	325	40	1	1	NUM
ejpam-6734	325	41	,	,	PUNCT
ejpam-6734	325	42	ψ(1	ψ(1	PROPN
ejpam-6734	325	43	)	)	PUNCT
ejpam-6734	325	44	=	=	SYM
ejpam-6734	325	45	1	1	NUM
ejpam-6734	325	46	e	e	NOUN
ejpam-6734	325	47	.	.	PUNCT
ejpam-6734	326	1	(	(	PUNCT
ejpam-6734	326	2	34	34	NUM
ejpam-6734	326	3	)	)	PUNCT
ejpam-6734	326	4	m.	m.	NOUN
ejpam-6734	326	5	a.	a.	PROPN
ejpam-6734	326	6	abdou	abdou	PROPN
ejpam-6734	326	7	,	,	PUNCT
ejpam-6734	326	8	a.	a.	PROPN
ejpam-6734	326	9	s.	s.	PROPN
ejpam-6734	326	10	mohamed	mohamed	PROPN
ejpam-6734	326	11	/	/	SYM
ejpam-6734	326	12	eur	eur	PROPN
ejpam-6734	326	13	.	.	PUNCT
ejpam-6734	327	1	j.	j.	PROPN
ejpam-6734	327	2	pure	pure	PROPN
ejpam-6734	327	3	appl	appl	PROPN
ejpam-6734	327	4	.	.	PROPN
ejpam-6734	327	5	math	math	PROPN
ejpam-6734	327	6	,	,	PUNCT
ejpam-6734	327	7	18	18	NUM
ejpam-6734	327	8	(	(	PUNCT
ejpam-6734	327	9	4	4	NUM
ejpam-6734	327	10	)	)	PUNCT
ejpam-6734	327	11	(	(	PUNCT
ejpam-6734	327	12	2025	2025	NUM
ejpam-6734	327	13	)	)	PUNCT
ejpam-6734	327	14	,	,	PUNCT
ejpam-6734	327	15	6734	6734	NUM
ejpam-6734	327	16	13	13	NUM
ejpam-6734	327	17	of	of	ADP
ejpam-6734	327	18	20	20	NUM
ejpam-6734	327	19	figure	figure	NOUN
ejpam-6734	327	20	3	3	NUM
ejpam-6734	327	21	:	:	PUNCT
ejpam-6734	327	22	graph	graph	NOUN
ejpam-6734	327	23	of	of	ADP
ejpam-6734	327	24	the	the	DET
ejpam-6734	327	25	error	error	NOUN
ejpam-6734	327	26	at	at	ADP
ejpam-6734	327	27	i=3	i=3	PROPN
ejpam-6734	327	28	,	,	PUNCT
ejpam-6734	327	29	4	4	NUM
ejpam-6734	327	30	,	,	PUNCT
ejpam-6734	327	31	and	and	CCONJ
ejpam-6734	327	32	λ1	λ1	ADJ
ejpam-6734	327	33	=	=	SYM
ejpam-6734	327	34	λ2	λ2	NOUN
ejpam-6734	327	35	=	=	SYM
ejpam-6734	327	36	1	1	NUM
ejpam-6734	327	37	for	for	ADP
ejpam-6734	327	38	example	example	NOUN
ejpam-6734	327	39	2	2	NUM
ejpam-6734	327	40	figure	figure	NOUN
ejpam-6734	327	41	4	4	NUM
ejpam-6734	327	42	:	:	PUNCT
ejpam-6734	327	43	approximate	approximate	ADJ
ejpam-6734	327	44	and	and	CCONJ
ejpam-6734	327	45	exact	exact	ADJ
ejpam-6734	327	46	solutions	solution	NOUN
ejpam-6734	327	47	at	at	ADP
ejpam-6734	327	48	i=5	i=5	PROPN
ejpam-6734	327	49	,	,	PUNCT
ejpam-6734	327	50	λ1	λ1	ADJ
ejpam-6734	327	51	=	=	SYM
ejpam-6734	327	52	λ2	λ2	NOUN
ejpam-6734	327	53	=	=	SYM
ejpam-6734	327	54	1	1	NUM
ejpam-6734	327	55	for	for	ADP
ejpam-6734	327	56	example	example	NOUN
ejpam-6734	327	57	2	2	NUM
ejpam-6734	327	58	from	from	ADP
ejpam-6734	327	59	eqs	eqs	PROPN
ejpam-6734	327	60	.	.	PUNCT
ejpam-6734	328	1	(	(	PUNCT
ejpam-6734	328	2	33	33	NUM
ejpam-6734	328	3	)	)	PUNCT
ejpam-6734	328	4	,	,	PUNCT
ejpam-6734	328	5	and	and	CCONJ
ejpam-6734	328	6	(	(	PUNCT
ejpam-6734	328	7	34	34	NUM
ejpam-6734	328	8	)	)	PUNCT
ejpam-6734	328	9	.	.	PUNCT
ejpam-6734	329	1	when	when	SCONJ
ejpam-6734	329	2	i	i	PRON
ejpam-6734	329	3	=	=	NOUN
ejpam-6734	329	4	0	0	NUM
ejpam-6734	329	5	,	,	PUNCT
ejpam-6734	329	6	then	then	ADV
ejpam-6734	329	7	ψ(2	ψ(2	NOUN
ejpam-6734	329	8	)	)	PUNCT
ejpam-6734	330	1	=	=	PUNCT
ejpam-6734	331	1	−	−	PROPN
ejpam-6734	331	2	e−2	e−2	PROPN
ejpam-6734	331	3	2	2	NUM
ejpam-6734	331	4	,	,	PUNCT
ejpam-6734	331	5	when	when	SCONJ
ejpam-6734	331	6	i	i	PRON
ejpam-6734	331	7	=	=	NOUN
ejpam-6734	331	8	1	1	NUM
ejpam-6734	331	9	,	,	PUNCT
ejpam-6734	331	10	then	then	ADV
ejpam-6734	331	11	ψ(3	ψ(3	PROPN
ejpam-6734	331	12	)	)	PUNCT
ejpam-6734	331	13	=	=	PUNCT
ejpam-6734	332	1	e−3	e−3	PROPN
ejpam-6734	332	2	3	3	NUM
ejpam-6734	332	3	,	,	PUNCT
ejpam-6734	332	4	when	when	SCONJ
ejpam-6734	332	5	i	i	PRON
ejpam-6734	332	6	=	=	SYM
ejpam-6734	332	7	2	2	NUM
ejpam-6734	332	8	,	,	PUNCT
ejpam-6734	332	9	then	then	ADV
ejpam-6734	332	10	ψ(4	ψ(4	PROPN
ejpam-6734	332	11	)	)	PUNCT
ejpam-6734	332	12	=	=	SYM
ejpam-6734	333	1	−e−4	−e−4	PROPN
ejpam-6734	333	2	4	4	NUM
ejpam-6734	333	3	,	,	PUNCT
ejpam-6734	333	4	when	when	SCONJ
ejpam-6734	333	5	j	j	PROPN
ejpam-6734	333	6	=	=	SYM
ejpam-6734	333	7	3	3	NUM
ejpam-6734	333	8	,	,	PUNCT
ejpam-6734	333	9	then	then	ADV
ejpam-6734	333	10	ψ(5	ψ(5	PROPN
ejpam-6734	333	11	)	)	PUNCT
ejpam-6734	333	12	=	=	SYM
ejpam-6734	334	1	e−5	e−5	PROPN
ejpam-6734	334	2	5	5	NUM
ejpam-6734	334	3	.	.	PUNCT
ejpam-6734	335	1	so	so	ADV
ejpam-6734	335	2	from	from	ADP
ejpam-6734	335	3	eq	eq	ADP
ejpam-6734	335	4	.	.	PUNCT
ejpam-6734	336	1	(	(	PUNCT
ejpam-6734	336	2	6	6	NUM
ejpam-6734	336	3	)	)	PUNCT
ejpam-6734	336	4	,	,	PUNCT
ejpam-6734	336	5	we	we	PRON
ejpam-6734	336	6	have	have	VERB
ejpam-6734	336	7	ζω	ζω	NOUN
ejpam-6734	336	8	)	)	PUNCT
ejpam-6734	336	9	=	=	SYM
ejpam-6734	336	10	ln(e+	ln(e+	PROPN
ejpam-6734	336	11	ω	ω	PROPN
ejpam-6734	336	12	)	)	PUNCT
ejpam-6734	336	13	.	.	PUNCT
ejpam-6734	337	1	which	which	PRON
ejpam-6734	337	2	is	be	AUX
ejpam-6734	337	3	the	the	DET
ejpam-6734	337	4	exact	exact	ADJ
ejpam-6734	337	5	solution	solution	NOUN
ejpam-6734	337	6	.	.	PUNCT
ejpam-6734	338	1	from	from	ADP
ejpam-6734	338	2	gfcm	gfcm	PROPN
ejpam-6734	338	3	,	,	PUNCT
ejpam-6734	338	4	table	table	NOUN
ejpam-6734	338	5	5	5	NUM
ejpam-6734	338	6	compares	compare	VERB
ejpam-6734	338	7	the	the	DET
ejpam-6734	338	8	absolute	absolute	ADJ
ejpam-6734	338	9	errors	error	NOUN
ejpam-6734	338	10	of	of	ADP
ejpam-6734	338	11	the	the	DET
ejpam-6734	338	12	proposed	propose	VERB
ejpam-6734	338	13	method	method	NOUN
ejpam-6734	338	14	with	with	ADP
ejpam-6734	338	15	m.	m.	NOUN
ejpam-6734	338	16	a.	a.	PROPN
ejpam-6734	338	17	abdou	abdou	PROPN
ejpam-6734	338	18	,	,	PUNCT
ejpam-6734	338	19	a.	a.	PROPN
ejpam-6734	338	20	s.	s.	PROPN
ejpam-6734	338	21	mohamed	mohamed	PROPN
ejpam-6734	338	22	/	/	SYM
ejpam-6734	338	23	eur	eur	PROPN
ejpam-6734	338	24	.	.	PUNCT
ejpam-6734	339	1	j.	j.	PROPN
ejpam-6734	339	2	pure	pure	PROPN
ejpam-6734	339	3	appl	appl	PROPN
ejpam-6734	339	4	.	.	PROPN
ejpam-6734	339	5	math	math	PROPN
ejpam-6734	339	6	,	,	PUNCT
ejpam-6734	339	7	18	18	NUM
ejpam-6734	339	8	(	(	PUNCT
ejpam-6734	339	9	4	4	NUM
ejpam-6734	339	10	)	)	PUNCT
ejpam-6734	339	11	(	(	PUNCT
ejpam-6734	339	12	2025	2025	NUM
ejpam-6734	339	13	)	)	PUNCT
ejpam-6734	339	14	,	,	PUNCT
ejpam-6734	339	15	6734	6734	NUM
ejpam-6734	339	16	14	14	NUM
ejpam-6734	339	17	of	of	ADP
ejpam-6734	339	18	20	20	NUM
ejpam-6734	339	19	modified	modify	VERB
ejpam-6734	339	20	adomian	adomian	NOUN
ejpam-6734	339	21	decomposition	decomposition	NOUN
ejpam-6734	339	22	method	method	NOUN
ejpam-6734	339	23	and	and	CCONJ
ejpam-6734	339	24	c2	c2	PROPN
ejpam-6734	339	25	-	-	PUNCT
ejpam-6734	339	26	spline	spline	NOUN
ejpam-6734	339	27	method	method	NOUN
ejpam-6734	339	28	[	[	X
ejpam-6734	339	29	33	33	NUM
ejpam-6734	339	30	]	]	PUNCT
ejpam-6734	339	31	.	.	PUNCT
ejpam-6734	340	1	the	the	DET
ejpam-6734	340	2	results	result	NOUN
ejpam-6734	340	3	at	at	ADP
ejpam-6734	340	4	i=14	i=14	PROPN
ejpam-6734	340	5	,	,	PUNCT
ejpam-6734	340	6	different	different	ADJ
ejpam-6734	340	7	values	value	NOUN
ejpam-6734	340	8	of	of	ADP
ejpam-6734	340	9	ω	ω	PROPN
ejpam-6734	340	10	,	,	PUNCT
ejpam-6734	340	11	λ1	λ1	ADJ
ejpam-6734	340	12	and	and	CCONJ
ejpam-6734	340	13	λ2	λ2	NOUN
ejpam-6734	340	14	.	.	PUNCT
ejpam-6734	341	1	the	the	DET
ejpam-6734	341	2	cpu	cpu	NOUN
ejpam-6734	341	3	times	time	NOUN
ejpam-6734	341	4	for	for	ADP
ejpam-6734	341	5	these	these	DET
ejpam-6734	341	6	methods	method	NOUN
ejpam-6734	341	7	are	be	AUX
ejpam-6734	341	8	provided	provide	VERB
ejpam-6734	341	9	in	in	ADP
ejpam-6734	341	10	table	table	NOUN
ejpam-6734	341	11	6	6	NUM
ejpam-6734	341	12	.	.	PUNCT
ejpam-6734	342	1	it	it	PRON
ejpam-6734	342	2	is	be	AUX
ejpam-6734	342	3	evident	evident	ADJ
ejpam-6734	342	4	that	that	SCONJ
ejpam-6734	342	5	the	the	DET
ejpam-6734	342	6	proposed	propose	VERB
ejpam-6734	342	7	method	method	NOUN
ejpam-6734	342	8	achieves	achieve	VERB
ejpam-6734	342	9	the	the	DET
ejpam-6734	342	10	lowest	low	ADJ
ejpam-6734	342	11	absolute	absolute	ADJ
ejpam-6734	342	12	errors	error	NOUN
ejpam-6734	342	13	.	.	PUNCT
ejpam-6734	343	1	these	these	DET
ejpam-6734	343	2	errors	error	NOUN
ejpam-6734	343	3	are	be	AUX
ejpam-6734	343	4	also	also	ADV
ejpam-6734	343	5	visually	visually	ADV
ejpam-6734	343	6	represented	represent	VERB
ejpam-6734	343	7	in	in	ADP
ejpam-6734	343	8	figure	figure	NOUN
ejpam-6734	343	9	5	5	NUM
ejpam-6734	343	10	.	.	PUNCT
ejpam-6734	344	1	the	the	DET
ejpam-6734	344	2	graph	graph	NOUN
ejpam-6734	344	3	of	of	ADP
ejpam-6734	344	4	exact	exact	ADJ
ejpam-6734	344	5	and	and	CCONJ
ejpam-6734	344	6	approximate	approximate	ADJ
ejpam-6734	344	7	solutions	solution	NOUN
ejpam-6734	344	8	at	at	ADP
ejpam-6734	344	9	i=8	i=8	ADV
ejpam-6734	344	10	is	be	AUX
ejpam-6734	344	11	plotted	plot	VERB
ejpam-6734	344	12	in	in	ADP
ejpam-6734	344	13	figure	figure	NOUN
ejpam-6734	344	14	6	6	NUM
ejpam-6734	344	15	.	.	PUNCT
ejpam-6734	344	16	table	table	NOUN
ejpam-6734	344	17	5	5	NUM
ejpam-6734	344	18	:	:	PUNCT
ejpam-6734	344	19	results	result	NOUN
ejpam-6734	344	20	of	of	ADP
ejpam-6734	344	21	absolute	absolute	ADJ
ejpam-6734	344	22	errors	error	NOUN
ejpam-6734	344	23	for	for	ADP
ejpam-6734	344	24	example	example	NOUN
ejpam-6734	344	25	3	3	NUM
ejpam-6734	344	26	ω	ω	NUM
ejpam-6734	344	27	modified	modify	VERB
ejpam-6734	344	28	adm	adm	PROPN
ejpam-6734	344	29	[	[	X
ejpam-6734	344	30	33	33	NUM
ejpam-6734	344	31	]	]	X
ejpam-6734	344	32	c2	c2	PROPN
ejpam-6734	344	33	-	-	PUNCT
ejpam-6734	344	34	spline	spline	NOUN
ejpam-6734	344	35	method	method	NOUN
ejpam-6734	344	36	[	[	X
ejpam-6734	344	37	33	33	NUM
ejpam-6734	344	38	]	]	SYM
ejpam-6734	344	39	0.2	0.2	NUM
ejpam-6734	344	40	3.91×	3.91×	NUM
ejpam-6734	344	41	10−11	10−11	NUM
ejpam-6734	344	42	2.04×	2.04×	NUM
ejpam-6734	344	43	10−14	10−14	NUM
ejpam-6734	344	44	0.4	0.4	NUM
ejpam-6734	344	45	1.66×	1.66×	NUM
ejpam-6734	344	46	10−9	10−9	NUM
ejpam-6734	344	47	4.99×	4.99×	NUM
ejpam-6734	344	48	10−14	10−14	NUM
ejpam-6734	344	49	0.6	0.6	NUM
ejpam-6734	344	50	1.30×	1.30×	NUM
ejpam-6734	344	51	10−8	10−8	NUM
ejpam-6734	344	52	8.50×	8.50×	NUM
ejpam-6734	344	53	10−14	10−14	NUM
ejpam-6734	344	54	0.8	0.8	NUM
ejpam-6734	344	55	3.17×	3.17×	NUM
ejpam-6734	344	56	10−7	10−7	NUM
ejpam-6734	344	57	1.25×	1.25×	NUM
ejpam-6734	344	58	10−13	10−13	NOUN
ejpam-6734	344	59	1	1	NUM
ejpam-6734	344	60	2.20×	2.20×	NUM
ejpam-6734	344	61	10−6	10−6	NUM
ejpam-6734	344	62	1.68×	1.68×	NUM
ejpam-6734	344	63	10−13	10−13	PROPN
ejpam-6734	344	64	ω	ω	PROPN
ejpam-6734	344	65	(	(	PUNCT
ejpam-6734	344	66	λ1	λ1	ADJ
ejpam-6734	344	67	,	,	PUNCT
ejpam-6734	344	68	λ2	λ2	NOUN
ejpam-6734	344	69	)	)	PUNCT
ejpam-6734	344	70	=	=	SYM
ejpam-6734	345	1	(	(	PUNCT
ejpam-6734	345	2	1	1	NUM
ejpam-6734	345	3	,	,	PUNCT
ejpam-6734	345	4	1	1	NUM
ejpam-6734	345	5	)	)	PUNCT
ejpam-6734	345	6	(	(	PUNCT
ejpam-6734	345	7	λ1	λ1	ADJ
ejpam-6734	345	8	,	,	PUNCT
ejpam-6734	345	9	λ2	λ2	NOUN
ejpam-6734	345	10	)	)	PUNCT
ejpam-6734	345	11	=	=	PUNCT
ejpam-6734	346	1	(	(	PUNCT
ejpam-6734	346	2	2	2	NUM
ejpam-6734	346	3	,	,	PUNCT
ejpam-6734	346	4	1	1	NUM
ejpam-6734	346	5	)	)	PUNCT
ejpam-6734	346	6	(	(	PUNCT
ejpam-6734	346	7	λ1	λ1	ADJ
ejpam-6734	346	8	,	,	PUNCT
ejpam-6734	346	9	λ2	λ2	NOUN
ejpam-6734	346	10	)	)	PUNCT
ejpam-6734	346	11	=	=	SYM
ejpam-6734	346	12	(	(	PUNCT
ejpam-6734	346	13	2,−1	2,−1	NUM
ejpam-6734	346	14	)	)	PUNCT
ejpam-6734	346	15	(	(	PUNCT
ejpam-6734	346	16	λ1	λ1	ADJ
ejpam-6734	346	17	,	,	PUNCT
ejpam-6734	346	18	λ2	λ2	NOUN
ejpam-6734	346	19	)	)	PUNCT
ejpam-6734	346	20	=	=	SYM
ejpam-6734	346	21	(	(	PUNCT
ejpam-6734	346	22	3,−2	3,−2	NUM
ejpam-6734	346	23	)	)	PUNCT
ejpam-6734	346	24	0.2	0.2	NUM
ejpam-6734	346	25	1.15×	1.15×	NUM
ejpam-6734	346	26	10−14	10−14	NUM
ejpam-6734	346	27	1.24×	1.24×	NUM
ejpam-6734	346	28	10−14	10−14	NUM
ejpam-6734	346	29	1.35×	1.35×	NUM
ejpam-6734	346	30	10−14	10−14	PROPN
ejpam-6734	347	1	1.11×	1.11×	NUM
ejpam-6734	347	2	10−14	10−14	NOUN
ejpam-6734	347	3	0.4	0.4	NUM
ejpam-6734	347	4	2.40×	2.40×	NUM
ejpam-6734	347	5	10−14	10−14	NUM
ejpam-6734	347	6	2.62×	2.62×	NUM
ejpam-6734	347	7	10−14	10−14	PROPN
ejpam-6734	347	8	2.84×	2.84×	NUM
ejpam-6734	347	9	10−14	10−14	NUM
ejpam-6734	347	10	2.35×	2.35×	NUM
ejpam-6734	347	11	10−14	10−14	NOUN
ejpam-6734	347	12	0.6	0.6	NUM
ejpam-6734	347	13	3.62×	3.62×	NUM
ejpam-6734	347	14	10−14	10−14	NUM
ejpam-6734	347	15	3.95×	3.95×	NUM
ejpam-6734	347	16	10−14	10−14	NUM
ejpam-6734	347	17	4.71×	4.71×	NUM
ejpam-6734	347	18	10−14	10−14	NUM
ejpam-6734	347	19	3.62×	3.62×	NUM
ejpam-6734	347	20	10−14	10−14	NUM
ejpam-6734	347	21	0.8	0.8	NUM
ejpam-6734	347	22	4.95×	4.95×	NUM
ejpam-6734	347	23	10−14	10−14	NUM
ejpam-6734	347	24	5.35×	5.35×	NUM
ejpam-6734	347	25	10−14	10−14	PROPN
ejpam-6734	347	26	5.84×	5.84×	NUM
ejpam-6734	347	27	10−14	10−14	NUM
ejpam-6734	347	28	4.91×	4.91×	NUM
ejpam-6734	347	29	10−14	10−14	NUM
ejpam-6734	347	30	1	1	NUM
ejpam-6734	347	31	6.17×	6.17×	NUM
ejpam-6734	347	32	10−14	10−14	NUM
ejpam-6734	348	1	6.73×	6.73×	NUM
ejpam-6734	348	2	10−14	10−14	NUM
ejpam-6734	348	3	7.39×	7.39×	NUM
ejpam-6734	348	4	10−14	10−14	NUM
ejpam-6734	348	5	6.44×	6.44×	NUM
ejpam-6734	348	6	10−14	10−14	NUM
ejpam-6734	348	7	table	table	NOUN
ejpam-6734	348	8	6	6	NUM
ejpam-6734	348	9	:	:	PUNCT
ejpam-6734	348	10	the	the	DET
ejpam-6734	348	11	cpu	cpu	ADJ
ejpam-6734	348	12	time	time	NOUN
ejpam-6734	348	13	for	for	ADP
ejpam-6734	348	14	example	example	NOUN
ejpam-6734	348	15	3	3	NUM
ejpam-6734	348	16	cpu	cpu	NOUN
ejpam-6734	348	17	time	time	NOUN
ejpam-6734	348	18	gi	gi	ADP
ejpam-6734	348	19	0.578	0.578	NUM
ejpam-6734	348	20	4.44×	4.44×	NUM
ejpam-6734	348	21	10−14	10−14	NUM
ejpam-6734	348	22	figure	figure	NOUN
ejpam-6734	348	23	5	5	NUM
ejpam-6734	348	24	:	:	PUNCT
ejpam-6734	348	25	graph	graph	NOUN
ejpam-6734	348	26	of	of	ADP
ejpam-6734	348	27	the	the	DET
ejpam-6734	348	28	error	error	NOUN
ejpam-6734	348	29	at	at	ADP
ejpam-6734	348	30	i=14	i=14	PROPN
ejpam-6734	348	31	,	,	PUNCT
ejpam-6734	348	32	different	different	ADJ
ejpam-6734	348	33	values	value	NOUN
ejpam-6734	348	34	of	of	ADP
ejpam-6734	348	35	λ1	λ1	ADJ
ejpam-6734	348	36	and	and	CCONJ
ejpam-6734	348	37	λ2	λ2	NOUN
ejpam-6734	348	38	for	for	ADP
ejpam-6734	348	39	example	example	NOUN
ejpam-6734	348	40	3	3	NUM
ejpam-6734	348	41	example	example	NOUN
ejpam-6734	348	42	4	4	NUM
ejpam-6734	348	43	.	.	PUNCT
ejpam-6734	348	44	consider	consider	VERB
ejpam-6734	348	45	the	the	DET
ejpam-6734	348	46	nonlinear	nonlinear	ADJ
ejpam-6734	348	47	second	second	ADJ
ejpam-6734	348	48	-	-	PUNCT
ejpam-6734	348	49	order	order	NOUN
ejpam-6734	348	50	bratu	bratu	NOUN
ejpam-6734	348	51	problem	problem	NOUN
ejpam-6734	348	52	[	[	X
ejpam-6734	348	53	34	34	NUM
ejpam-6734	348	54	]	]	PUNCT
ejpam-6734	348	55	if	if	SCONJ
ejpam-6734	348	56	f(ζ	f(ζ	PROPN
ejpam-6734	348	57	)	)	PUNCT
ejpam-6734	349	1	=	=	SYM
ejpam-6734	349	2	−2eζ(ω	−2eζ(ω	PROPN
ejpam-6734	349	3	)	)	PUNCT
ejpam-6734	349	4	,	,	PUNCT
ejpam-6734	349	5	m1	m1	PROPN
ejpam-6734	349	6	=	=	SYM
ejpam-6734	349	7	0	0	PROPN
ejpam-6734	349	8	,	,	PUNCT
ejpam-6734	349	9	m2	m2	PROPN
ejpam-6734	349	10	=	=	SYM
ejpam-6734	349	11	0	0	PROPN
ejpam-6734	349	12	.	.	PUNCT
ejpam-6734	349	13	m.	m.	PROPN
ejpam-6734	349	14	a.	a.	PROPN
ejpam-6734	349	15	abdou	abdou	PROPN
ejpam-6734	349	16	,	,	PUNCT
ejpam-6734	349	17	a.	a.	PROPN
ejpam-6734	349	18	s.	s.	PROPN
ejpam-6734	349	19	mohamed	mohamed	PROPN
ejpam-6734	349	20	/	/	SYM
ejpam-6734	349	21	eur	eur	PROPN
ejpam-6734	349	22	.	.	PUNCT
ejpam-6734	350	1	j.	j.	PROPN
ejpam-6734	350	2	pure	pure	PROPN
ejpam-6734	350	3	appl	appl	PROPN
ejpam-6734	350	4	.	.	PROPN
ejpam-6734	350	5	math	math	PROPN
ejpam-6734	350	6	,	,	PUNCT
ejpam-6734	350	7	18	18	NUM
ejpam-6734	350	8	(	(	PUNCT
ejpam-6734	350	9	4	4	NUM
ejpam-6734	350	10	)	)	PUNCT
ejpam-6734	350	11	(	(	PUNCT
ejpam-6734	350	12	2025	2025	NUM
ejpam-6734	350	13	)	)	PUNCT
ejpam-6734	350	14	,	,	PUNCT
ejpam-6734	350	15	6734	6734	NUM
ejpam-6734	350	16	15	15	NUM
ejpam-6734	350	17	of	of	ADP
ejpam-6734	350	18	20	20	NUM
ejpam-6734	350	19	figure	figure	NOUN
ejpam-6734	350	20	6	6	NUM
ejpam-6734	350	21	:	:	PUNCT
ejpam-6734	350	22	approximate	approximate	ADJ
ejpam-6734	350	23	and	and	CCONJ
ejpam-6734	350	24	exact	exact	ADJ
ejpam-6734	350	25	solutions	solution	NOUN
ejpam-6734	350	26	at	at	ADP
ejpam-6734	350	27	i=8	i=8	ADP
ejpam-6734	350	28	,	,	PUNCT
ejpam-6734	350	29	λ1	λ1	PROPN
ejpam-6734	350	30	=	=	SYM
ejpam-6734	350	31	2	2	NUM
ejpam-6734	350	32	,	,	PUNCT
ejpam-6734	350	33	λ2	λ2	NOUN
ejpam-6734	350	34	=	=	SYM
ejpam-6734	350	35	−1	−1	NOUN
ejpam-6734	350	36	for	for	ADP
ejpam-6734	350	37	example	example	NOUN
ejpam-6734	351	1	3	3	NUM
ejpam-6734	351	2	so	so	ADV
ejpam-6734	351	3	,	,	PUNCT
ejpam-6734	351	4	eq	eq	NOUN
ejpam-6734	351	5	.	.	PUNCT
ejpam-6734	352	1	(	(	PUNCT
ejpam-6734	352	2	2	2	X
ejpam-6734	352	3	)	)	PUNCT
ejpam-6734	352	4	can	can	AUX
ejpam-6734	352	5	be	be	AUX
ejpam-6734	352	6	written	write	VERB
ejpam-6734	352	7	in	in	ADP
ejpam-6734	352	8	the	the	DET
ejpam-6734	352	9	form	form	NOUN
ejpam-6734	352	10	:	:	PUNCT
ejpam-6734	352	11	ζ	ζ	NOUN
ejpam-6734	352	12	′′(ω)−	′′(ω)−	NOUN
ejpam-6734	352	13	2eζ(ω	2eζ(ω	NUM
ejpam-6734	352	14	)	)	PUNCT
ejpam-6734	353	1	=	=	SYM
ejpam-6734	353	2	0	0	NUM
ejpam-6734	353	3	,	,	PUNCT
ejpam-6734	353	4	(	(	PUNCT
ejpam-6734	353	5	35	35	NUM
ejpam-6734	353	6	)	)	PUNCT
ejpam-6734	353	7	with	with	ADP
ejpam-6734	353	8	the	the	DET
ejpam-6734	353	9	conditions	condition	NOUN
ejpam-6734	353	10	(	(	PUNCT
ejpam-6734	353	11	3	3	X
ejpam-6734	353	12	)	)	PUNCT
ejpam-6734	353	13	ζ(0	ζ(0	NOUN
ejpam-6734	353	14	)	)	PUNCT
ejpam-6734	353	15	=	=	SYM
ejpam-6734	353	16	0	0	NUM
ejpam-6734	353	17	,	,	PUNCT
ejpam-6734	353	18	ζ	ζ	NOUN
ejpam-6734	353	19	′(0	′(0	NOUN
ejpam-6734	353	20	)	)	PUNCT
ejpam-6734	353	21	=	=	SYM
ejpam-6734	354	1	0	0	X
ejpam-6734	354	2	.	.	PUNCT
ejpam-6734	355	1	(	(	PUNCT
ejpam-6734	355	2	36	36	NUM
ejpam-6734	355	3	)	)	PUNCT
ejpam-6734	355	4	from	from	ADP
ejpam-6734	355	5	the	the	DET
ejpam-6734	355	6	definition	definition	NOUN
ejpam-6734	355	7	of	of	ADP
ejpam-6734	355	8	dtm	dtm	PROPN
ejpam-6734	355	9	,	,	PUNCT
ejpam-6734	355	10	eqs	eqs	X
ejpam-6734	355	11	(	(	PUNCT
ejpam-6734	355	12	9	9	NUM
ejpam-6734	355	13	)	)	PUNCT
ejpam-6734	355	14	and	and	CCONJ
ejpam-6734	355	15	(	(	PUNCT
ejpam-6734	355	16	10	10	NUM
ejpam-6734	355	17	)	)	PUNCT
ejpam-6734	355	18	.	.	PUNCT
ejpam-6734	356	1	so	so	ADV
ejpam-6734	356	2	,	,	PUNCT
ejpam-6734	356	3	eq	eq	NOUN
ejpam-6734	356	4	.	.	PUNCT
ejpam-6734	357	1	(	(	PUNCT
ejpam-6734	357	2	35	35	NUM
ejpam-6734	357	3	)	)	PUNCT
ejpam-6734	357	4	transforms	transform	VERB
ejpam-6734	357	5	to	to	ADP
ejpam-6734	357	6	ψ(i+	ψ(i+	NUM
ejpam-6734	357	7	2	2	NUM
ejpam-6734	357	8	)	)	PUNCT
ejpam-6734	357	9	=	=	SYM
ejpam-6734	357	10	2	2	NUM
ejpam-6734	357	11	(	(	PUNCT
ejpam-6734	357	12	i+	i+	NUM
ejpam-6734	357	13	1)(i+	1)(i+	NUM
ejpam-6734	357	14	2	2	NUM
ejpam-6734	357	15	)	)	PUNCT
ejpam-6734	357	16	f2(i	f2(i	NOUN
ejpam-6734	357	17	)	)	PUNCT
ejpam-6734	357	18	,	,	PUNCT
ejpam-6734	357	19	(	(	PUNCT
ejpam-6734	357	20	37	37	NUM
ejpam-6734	357	21	)	)	PUNCT
ejpam-6734	357	22	where	where	SCONJ
ejpam-6734	357	23	f2(i	f2(i	X
ejpam-6734	357	24	)	)	PUNCT
ejpam-6734	357	25	is	be	AUX
ejpam-6734	357	26	the	the	DET
ejpam-6734	357	27	differential	differential	ADJ
ejpam-6734	357	28	transform	transform	NOUN
ejpam-6734	357	29	of	of	ADP
ejpam-6734	357	30	f(ζ	f(ζ	PROPN
ejpam-6734	357	31	)	)	PUNCT
ejpam-6734	357	32	,	,	PUNCT
ejpam-6734	357	33	with	with	ADP
ejpam-6734	357	34	the	the	DET
ejpam-6734	357	35	conditions	condition	NOUN
ejpam-6734	357	36	ψ(0	ψ(0	PART
ejpam-6734	357	37	)	)	PUNCT
ejpam-6734	357	38	=	=	SYM
ejpam-6734	358	1	1	1	NUM
ejpam-6734	358	2	,	,	PUNCT
ejpam-6734	358	3	ψ(1	ψ(1	PROPN
ejpam-6734	358	4	)	)	PUNCT
ejpam-6734	358	5	=	=	SYM
ejpam-6734	358	6	0	0	X
ejpam-6734	358	7	.	.	PUNCT
ejpam-6734	359	1	(	(	PUNCT
ejpam-6734	359	2	38	38	NUM
ejpam-6734	359	3	)	)	PUNCT
ejpam-6734	359	4	from	from	ADP
ejpam-6734	359	5	eqs	eqs	PROPN
ejpam-6734	359	6	.	.	PUNCT
ejpam-6734	360	1	(	(	PUNCT
ejpam-6734	360	2	37	37	NUM
ejpam-6734	360	3	)	)	PUNCT
ejpam-6734	360	4	,	,	PUNCT
ejpam-6734	360	5	and	and	CCONJ
ejpam-6734	360	6	(	(	PUNCT
ejpam-6734	360	7	38	38	NUM
ejpam-6734	360	8	)	)	PUNCT
ejpam-6734	360	9	.	.	PUNCT
ejpam-6734	361	1	when	when	SCONJ
ejpam-6734	361	2	i	i	PRON
ejpam-6734	361	3	=	=	NOUN
ejpam-6734	361	4	0	0	NUM
ejpam-6734	361	5	,	,	PUNCT
ejpam-6734	361	6	then	then	ADV
ejpam-6734	361	7	ψ(2	ψ(2	NOUN
ejpam-6734	361	8	)	)	PUNCT
ejpam-6734	361	9	=	=	PUNCT
ejpam-6734	362	1	1	1	NUM
ejpam-6734	362	2	,	,	PUNCT
ejpam-6734	362	3	when	when	SCONJ
ejpam-6734	362	4	i	i	PRON
ejpam-6734	362	5	=	=	NOUN
ejpam-6734	362	6	1	1	NUM
ejpam-6734	362	7	,	,	PUNCT
ejpam-6734	362	8	then	then	ADV
ejpam-6734	362	9	ψ(3	ψ(3	PROPN
ejpam-6734	362	10	)	)	PUNCT
ejpam-6734	362	11	=	=	SYM
ejpam-6734	363	1	0	0	NUM
ejpam-6734	363	2	,	,	PUNCT
ejpam-6734	363	3	when	when	SCONJ
ejpam-6734	363	4	i	i	PRON
ejpam-6734	363	5	=	=	SYM
ejpam-6734	363	6	2	2	NUM
ejpam-6734	363	7	,	,	PUNCT
ejpam-6734	363	8	then	then	ADV
ejpam-6734	363	9	ψ(4	ψ(4	NOUN
ejpam-6734	363	10	)	)	PUNCT
ejpam-6734	363	11	=	=	SYM
ejpam-6734	363	12	1	1	NUM
ejpam-6734	363	13	6	6	NUM
ejpam-6734	363	14	,	,	PUNCT
ejpam-6734	363	15	when	when	SCONJ
ejpam-6734	363	16	i	i	PRON
ejpam-6734	363	17	=	=	SYM
ejpam-6734	363	18	3	3	NUM
ejpam-6734	363	19	,	,	PUNCT
ejpam-6734	363	20	then	then	ADV
ejpam-6734	363	21	ψ(5	ψ(5	PROPN
ejpam-6734	363	22	)	)	PUNCT
ejpam-6734	363	23	=	=	SYM
ejpam-6734	363	24	0	0	NUM
ejpam-6734	363	25	,	,	PUNCT
ejpam-6734	363	26	when	when	SCONJ
ejpam-6734	363	27	i	i	PRON
ejpam-6734	363	28	=	=	SYM
ejpam-6734	363	29	4	4	NUM
ejpam-6734	363	30	,	,	PUNCT
ejpam-6734	363	31	then	then	ADV
ejpam-6734	363	32	ψ(6	ψ(6	PROPN
ejpam-6734	363	33	)	)	PUNCT
ejpam-6734	363	34	=	=	SYM
ejpam-6734	363	35	2	2	NUM
ejpam-6734	363	36	45	45	NUM
ejpam-6734	363	37	.	.	PUNCT
ejpam-6734	364	1	from	from	ADP
ejpam-6734	364	2	eq	eq	ADP
ejpam-6734	364	3	.	.	PUNCT
ejpam-6734	365	1	(	(	PUNCT
ejpam-6734	365	2	6	6	NUM
ejpam-6734	365	3	)	)	PUNCT
ejpam-6734	365	4	,	,	PUNCT
ejpam-6734	365	5	we	we	PRON
ejpam-6734	365	6	have	have	VERB
ejpam-6734	365	7	ζ(ω	ζ(ω	PROPN
ejpam-6734	365	8	)	)	PUNCT
ejpam-6734	366	1	=	=	SYM
ejpam-6734	366	2	−2	−2	NOUN
ejpam-6734	366	3	log(cos(ω	log(cos(ω	PROPN
ejpam-6734	366	4	)	)	PUNCT
ejpam-6734	366	5	)	)	PUNCT
ejpam-6734	366	6	.	.	PUNCT
ejpam-6734	367	1	which	which	PRON
ejpam-6734	367	2	is	be	AUX
ejpam-6734	367	3	the	the	DET
ejpam-6734	367	4	exact	exact	ADJ
ejpam-6734	367	5	solution	solution	NOUN
ejpam-6734	367	6	.	.	PUNCT
ejpam-6734	368	1	table	table	NOUN
ejpam-6734	368	2	7	7	NUM
ejpam-6734	368	3	shows	show	VERB
ejpam-6734	368	4	a	a	DET
ejpam-6734	368	5	comparison	comparison	NOUN
ejpam-6734	368	6	of	of	ADP
ejpam-6734	368	7	the	the	DET
ejpam-6734	368	8	absolute	absolute	ADJ
ejpam-6734	368	9	errors	error	NOUN
ejpam-6734	368	10	obtained	obtain	VERB
ejpam-6734	368	11	using	use	VERB
ejpam-6734	368	12	the	the	DET
ejpam-6734	368	13	proposed	propose	VERB
ejpam-6734	368	14	method	method	NOUN
ejpam-6734	368	15	and	and	CCONJ
ejpam-6734	368	16	the	the	DET
ejpam-6734	368	17	legendre	legendre	PROPN
ejpam-6734	368	18	wavelet	wavelet	PROPN
ejpam-6734	368	19	method	method	NOUN
ejpam-6734	368	20	[	[	X
ejpam-6734	368	21	34	34	NUM
ejpam-6734	368	22	]	]	PUNCT
ejpam-6734	368	23	at	at	ADP
ejpam-6734	368	24	i=10	i=10	NOUN
ejpam-6734	368	25	.	.	PUNCT
ejpam-6734	369	1	the	the	DET
ejpam-6734	369	2	associated	associated	PROPN
ejpam-6734	369	3	cpu	cpu	NOUN
ejpam-6734	369	4	times	time	NOUN
ejpam-6734	369	5	are	be	AUX
ejpam-6734	369	6	detailed	detail	VERB
ejpam-6734	369	7	in	in	ADP
ejpam-6734	369	8	table	table	NOUN
ejpam-6734	369	9	8	8	NUM
ejpam-6734	369	10	.	.	PUNCT
ejpam-6734	370	1	the	the	DET
ejpam-6734	370	2	data	datum	NOUN
ejpam-6734	370	3	indicate	indicate	VERB
ejpam-6734	370	4	that	that	SCONJ
ejpam-6734	370	5	the	the	DET
ejpam-6734	370	6	proposed	propose	VERB
ejpam-6734	370	7	method	method	NOUN
ejpam-6734	370	8	produces	produce	VERB
ejpam-6734	370	9	the	the	DET
ejpam-6734	370	10	lowest	low	ADJ
ejpam-6734	370	11	absolute	absolute	ADJ
ejpam-6734	370	12	errors	error	NOUN
ejpam-6734	370	13	m.	m.	NOUN
ejpam-6734	370	14	a.	a.	PROPN
ejpam-6734	370	15	abdou	abdou	PROPN
ejpam-6734	370	16	,	,	PUNCT
ejpam-6734	370	17	a.	a.	PROPN
ejpam-6734	370	18	s.	s.	PROPN
ejpam-6734	370	19	mohamed	mohamed	PROPN
ejpam-6734	370	20	/	/	SYM
ejpam-6734	370	21	eur	eur	PROPN
ejpam-6734	370	22	.	.	PUNCT
ejpam-6734	371	1	j.	j.	PROPN
ejpam-6734	371	2	pure	pure	PROPN
ejpam-6734	371	3	appl	appl	PROPN
ejpam-6734	371	4	.	.	PROPN
ejpam-6734	371	5	math	math	PROPN
ejpam-6734	371	6	,	,	PUNCT
ejpam-6734	371	7	18	18	NUM
ejpam-6734	371	8	(	(	PUNCT
ejpam-6734	371	9	4	4	NUM
ejpam-6734	371	10	)	)	PUNCT
ejpam-6734	371	11	(	(	PUNCT
ejpam-6734	371	12	2025	2025	NUM
ejpam-6734	371	13	)	)	PUNCT
ejpam-6734	371	14	,	,	PUNCT
ejpam-6734	371	15	6734	6734	NUM
ejpam-6734	371	16	16	16	NUM
ejpam-6734	371	17	of	of	ADP
ejpam-6734	371	18	20	20	NUM
ejpam-6734	371	19	at	at	ADP
ejpam-6734	371	20	different	different	ADJ
ejpam-6734	371	21	values	value	NOUN
ejpam-6734	371	22	of	of	ADP
ejpam-6734	371	23	ω	ω	PROPN
ejpam-6734	371	24	.	.	PUNCT
ejpam-6734	372	1	these	these	DET
ejpam-6734	372	2	results	result	NOUN
ejpam-6734	372	3	are	be	AUX
ejpam-6734	372	4	also	also	ADV
ejpam-6734	372	5	depicted	depict	VERB
ejpam-6734	372	6	graphically	graphically	ADV
ejpam-6734	372	7	in	in	ADP
ejpam-6734	372	8	figure	figure	NOUN
ejpam-6734	372	9	7	7	NUM
ejpam-6734	372	10	.	.	PUNCT
ejpam-6734	373	1	the	the	DET
ejpam-6734	373	2	graph	graph	NOUN
ejpam-6734	373	3	of	of	ADP
ejpam-6734	373	4	exact	exact	ADJ
ejpam-6734	373	5	and	and	CCONJ
ejpam-6734	373	6	approximate	approximate	ADJ
ejpam-6734	373	7	solutions	solution	NOUN
ejpam-6734	373	8	at	at	ADP
ejpam-6734	373	9	i=3	i=3	PROPN
ejpam-6734	373	10	is	be	AUX
ejpam-6734	373	11	plotted	plot	VERB
ejpam-6734	373	12	in	in	ADP
ejpam-6734	373	13	figure	figure	NOUN
ejpam-6734	373	14	8	8	NUM
ejpam-6734	373	15	.	.	PUNCT
ejpam-6734	373	16	table	table	NOUN
ejpam-6734	373	17	7	7	NUM
ejpam-6734	373	18	:	:	PUNCT
ejpam-6734	373	19	comparison	comparison	NOUN
ejpam-6734	373	20	between	between	ADP
ejpam-6734	373	21	the	the	DET
ejpam-6734	373	22	absolute	absolute	ADJ
ejpam-6734	373	23	errors	error	NOUN
ejpam-6734	373	24	for	for	ADP
ejpam-6734	373	25	example	example	NOUN
ejpam-6734	373	26	4	4	NUM
ejpam-6734	373	27	ω	ω	NOUN
ejpam-6734	373	28	(	(	PUNCT
ejpam-6734	373	29	λ1	λ1	ADJ
ejpam-6734	373	30	,	,	PUNCT
ejpam-6734	373	31	λ2	λ2	NOUN
ejpam-6734	373	32	)	)	PUNCT
ejpam-6734	373	33	=	=	SYM
ejpam-6734	373	34	(	(	PUNCT
ejpam-6734	373	35	1	1	NUM
ejpam-6734	373	36	,	,	PUNCT
ejpam-6734	373	37	1	1	NUM
ejpam-6734	373	38	)	)	PUNCT
ejpam-6734	373	39	(	(	PUNCT
ejpam-6734	373	40	λ1	λ1	ADJ
ejpam-6734	373	41	,	,	PUNCT
ejpam-6734	373	42	λ2	λ2	NOUN
ejpam-6734	373	43	)	)	PUNCT
ejpam-6734	373	44	=	=	PUNCT
ejpam-6734	373	45	(	(	PUNCT
ejpam-6734	373	46	2	2	NUM
ejpam-6734	373	47	,	,	PUNCT
ejpam-6734	373	48	1	1	NUM
ejpam-6734	373	49	)	)	PUNCT
ejpam-6734	373	50	(	(	PUNCT
ejpam-6734	373	51	λ1	λ1	ADJ
ejpam-6734	373	52	,	,	PUNCT
ejpam-6734	373	53	λ2	λ2	NOUN
ejpam-6734	373	54	)	)	PUNCT
ejpam-6734	373	55	=	=	SYM
ejpam-6734	373	56	(	(	PUNCT
ejpam-6734	373	57	2,−1	2,−1	NUM
ejpam-6734	373	58	)	)	PUNCT
ejpam-6734	373	59	(	(	PUNCT
ejpam-6734	373	60	λ1	λ1	ADJ
ejpam-6734	373	61	,	,	PUNCT
ejpam-6734	373	62	λ2	λ2	NOUN
ejpam-6734	373	63	)	)	PUNCT
ejpam-6734	373	64	=	=	SYM
ejpam-6734	373	65	(	(	PUNCT
ejpam-6734	373	66	3,−2	3,−2	NUM
ejpam-6734	373	67	)	)	PUNCT
ejpam-6734	374	1	0.2	0.2	NUM
ejpam-6734	374	2	1.62×	1.62×	NUM
ejpam-6734	374	3	10−5	10−5	NUM
ejpam-6734	374	4	1.62×	1.62×	NUM
ejpam-6734	374	5	10−5	10−5	NUM
ejpam-6734	374	6	1.62×	1.62×	NUM
ejpam-6734	374	7	10−5	10−5	NUM
ejpam-6734	374	8	1.62×	1.62×	NUM
ejpam-6734	374	9	10−5	10−5	NUM
ejpam-6734	374	10	0.4	0.4	NUM
ejpam-6734	374	11	3.57×	3.57×	NUM
ejpam-6734	374	12	10−5	10−5	NUM
ejpam-6734	374	13	3.57×	3.57×	NUM
ejpam-6734	374	14	10−5	10−5	NUM
ejpam-6734	374	15	3.57×	3.57×	NUM
ejpam-6734	374	16	10−5	10−5	NUM
ejpam-6734	374	17	3.57×	3.57×	NUM
ejpam-6734	374	18	10−5	10−5	NUM
ejpam-6734	374	19	0.6	0.6	NUM
ejpam-6734	374	20	5.86×	5.86×	NUM
ejpam-6734	374	21	10−5	10−5	NUM
ejpam-6734	374	22	5.86×	5.86×	NUM
ejpam-6734	374	23	10−5	10−5	NUM
ejpam-6734	374	24	5.86×	5.86×	NUM
ejpam-6734	374	25	10−5	10−5	NUM
ejpam-6734	374	26	5.86×	5.86×	NUM
ejpam-6734	374	27	10−5	10−5	NUM
ejpam-6734	374	28	0.8	0.8	NUM
ejpam-6734	374	29	8.88×	8.88×	NUM
ejpam-6734	374	30	10−5	10−5	NUM
ejpam-6734	374	31	8.88×	8.88×	NUM
ejpam-6734	374	32	10−5	10−5	NUM
ejpam-6734	375	1	8.88×	8.88×	NUM
ejpam-6734	375	2	10−5	10−5	NUM
ejpam-6734	376	1	8.88×	8.88×	NUM
ejpam-6734	376	2	10−5	10−5	NUM
ejpam-6734	376	3	1	1	NUM
ejpam-6734	376	4	1.29×	1.29×	NUM
ejpam-6734	376	5	10−4	10−4	NUM
ejpam-6734	376	6	1.29×	1.29×	NUM
ejpam-6734	376	7	10−4	10−4	NUM
ejpam-6734	376	8	1.29×	1.29×	NUM
ejpam-6734	376	9	10−4	10−4	NUM
ejpam-6734	376	10	1.29×	1.29×	NUM
ejpam-6734	376	11	10−4	10−4	NUM
ejpam-6734	376	12	lwm	lwm	NOUN
ejpam-6734	376	13	[	[	X
ejpam-6734	376	14	34	34	NUM
ejpam-6734	376	15	]	]	SYM
ejpam-6734	376	16	1.38×	1.38×	NUM
ejpam-6734	376	17	10−4	10−4	NUM
ejpam-6734	376	18	table	table	NOUN
ejpam-6734	376	19	8	8	NUM
ejpam-6734	376	20	:	:	PUNCT
ejpam-6734	376	21	the	the	DET
ejpam-6734	376	22	cpu	cpu	ADJ
ejpam-6734	376	23	time	time	NOUN
ejpam-6734	376	24	for	for	ADP
ejpam-6734	376	25	example	example	NOUN
ejpam-6734	376	26	4	4	NUM
ejpam-6734	376	27	cpu	cpu	NOUN
ejpam-6734	376	28	time	time	NOUN
ejpam-6734	376	29	gi	gi	ADP
ejpam-6734	376	30	0.484	0.484	NUM
ejpam-6734	376	31	7.75×	7.75×	NUM
ejpam-6734	376	32	10−5	10−5	NUM
ejpam-6734	376	33	figure	figure	NOUN
ejpam-6734	376	34	7	7	NUM
ejpam-6734	376	35	:	:	PUNCT
ejpam-6734	376	36	graph	graph	NOUN
ejpam-6734	376	37	of	of	ADP
ejpam-6734	376	38	the	the	DET
ejpam-6734	376	39	error	error	NOUN
ejpam-6734	376	40	at	at	ADP
ejpam-6734	376	41	at	at	ADP
ejpam-6734	376	42	i=10	i=10	NOUN
ejpam-6734	376	43	,	,	PUNCT
ejpam-6734	376	44	different	different	ADJ
ejpam-6734	376	45	values	value	NOUN
ejpam-6734	376	46	of	of	ADP
ejpam-6734	376	47	λ1	λ1	ADJ
ejpam-6734	376	48	and	and	CCONJ
ejpam-6734	376	49	λ2	λ2	NOUN
ejpam-6734	376	50	for	for	ADP
ejpam-6734	376	51	example	example	NOUN
ejpam-6734	376	52	4	4	NUM
ejpam-6734	376	53	5	5	NUM
ejpam-6734	376	54	.	.	PUNCT
ejpam-6734	376	55	conclusion	conclusion	NOUN
ejpam-6734	376	56	this	this	DET
ejpam-6734	376	57	research	research	NOUN
ejpam-6734	376	58	looked	look	VERB
ejpam-6734	376	59	at	at	ADP
ejpam-6734	376	60	solving	solve	VERB
ejpam-6734	376	61	differential	differential	ADJ
ejpam-6734	376	62	equations	equation	NOUN
ejpam-6734	376	63	using	use	VERB
ejpam-6734	376	64	two	two	NUM
ejpam-6734	376	65	main	main	ADJ
ejpam-6734	376	66	techniques	technique	NOUN
ejpam-6734	376	67	.	.	PUNCT
ejpam-6734	377	1	the	the	DET
ejpam-6734	377	2	useful	useful	ADJ
ejpam-6734	377	3	of	of	ADP
ejpam-6734	377	4	our	our	PRON
ejpam-6734	377	5	work	work	NOUN
ejpam-6734	377	6	is	be	AUX
ejpam-6734	377	7	that	that	SCONJ
ejpam-6734	377	8	we	we	PRON
ejpam-6734	377	9	’re	’re	AUX
ejpam-6734	377	10	making	make	VERB
ejpam-6734	377	11	better	well	ADJ
ejpam-6734	377	12	use	use	NOUN
ejpam-6734	377	13	of	of	ADP
ejpam-6734	377	14	the	the	DET
ejpam-6734	377	15	generalized	generalize	VERB
ejpam-6734	377	16	fibonacci	fibonacci	NOUN
ejpam-6734	377	17	polynomials	polynomial	NOUN
ejpam-6734	377	18	with	with	ADP
ejpam-6734	377	19	a	a	DET
ejpam-6734	377	20	collocation	collocation	NOUN
ejpam-6734	377	21	method	method	NOUN
ejpam-6734	377	22	.	.	PUNCT
ejpam-6734	378	1	we	we	PRON
ejpam-6734	378	2	’ve	’ve	AUX
ejpam-6734	378	3	also	also	ADV
ejpam-6734	378	4	got	get	VERB
ejpam-6734	378	5	some	some	DET
ejpam-6734	378	6	fresh	fresh	ADJ
ejpam-6734	378	7	ways	way	NOUN
ejpam-6734	378	8	to	to	PART
ejpam-6734	378	9	look	look	VERB
ejpam-6734	378	10	at	at	ADP
ejpam-6734	378	11	how	how	SCONJ
ejpam-6734	378	12	well	well	ADV
ejpam-6734	378	13	it	it	PRON
ejpam-6734	378	14	works	work	VERB
ejpam-6734	378	15	and	and	CCONJ
ejpam-6734	378	16	where	where	SCONJ
ejpam-6734	378	17	it	it	PRON
ejpam-6734	378	18	might	might	AUX
ejpam-6734	378	19	be	be	AUX
ejpam-6734	378	20	bad	bad	ADJ
ejpam-6734	378	21	.	.	PUNCT
ejpam-6734	379	1	plus	plus	CCONJ
ejpam-6734	379	2	,	,	PUNCT
ejpam-6734	379	3	we	we	PRON
ejpam-6734	379	4	’re	’re	AUX
ejpam-6734	379	5	putting	put	VERB
ejpam-6734	379	6	the	the	DET
ejpam-6734	379	7	different	different	ADJ
ejpam-6734	379	8	technique	technique	NOUN
ejpam-6734	379	9	,	,	PUNCT
ejpam-6734	379	10	dtm	dtm	PROPN
ejpam-6734	379	11	,	,	PUNCT
ejpam-6734	379	12	to	to	PART
ejpam-6734	379	13	tackle	tackle	VERB
ejpam-6734	379	14	all	all	DET
ejpam-6734	379	15	sorts	sort	NOUN
ejpam-6734	379	16	of	of	ADP
ejpam-6734	379	17	tricky	tricky	ADJ
ejpam-6734	379	18	math	math	NOUN
ejpam-6734	379	19	problems	problem	NOUN
ejpam-6734	379	20	–	–	PUNCT
ejpam-6734	379	21	straight	straight	ADJ
ejpam-6734	379	22	-	-	PUNCT
ejpam-6734	379	23	up	up	ADP
ejpam-6734	379	24	ones	one	NOUN
ejpam-6734	379	25	,	,	PUNCT
ejpam-6734	379	26	weird	weird	ADJ
ejpam-6734	379	27	ones	one	NOUN
ejpam-6734	379	28	,	,	PUNCT
ejpam-6734	379	29	and	and	CCONJ
ejpam-6734	379	30	even	even	ADV
ejpam-6734	379	31	those	those	PRON
ejpam-6734	379	32	with	with	ADP
ejpam-6734	379	33	singularities	singularity	NOUN
ejpam-6734	379	34	.	.	PUNCT
ejpam-6734	380	1	it	it	PRON
ejpam-6734	380	2	looks	look	VERB
ejpam-6734	380	3	like	like	SCONJ
ejpam-6734	380	4	our	our	PRON
ejpam-6734	380	5	approach	approach	NOUN
ejpam-6734	380	6	is	be	AUX
ejpam-6734	380	7	more	more	ADV
ejpam-6734	380	8	accurate	accurate	ADJ
ejpam-6734	380	9	and	and	CCONJ
ejpam-6734	380	10	faster	fast	ADJ
ejpam-6734	380	11	than	than	ADP
ejpam-6734	380	12	what	what	PRON
ejpam-6734	380	13	people	people	NOUN
ejpam-6734	380	14	are	be	AUX
ejpam-6734	380	15	already	already	ADV
ejpam-6734	380	16	doing	do	VERB
ejpam-6734	380	17	.	.	PUNCT
ejpam-6734	381	1	we	we	PRON
ejpam-6734	381	2	compared	compare	VERB
ejpam-6734	381	3	our	our	PRON
ejpam-6734	381	4	methods	method	NOUN
ejpam-6734	381	5	with	with	ADP
ejpam-6734	381	6	others	other	NOUN
ejpam-6734	381	7	,	,	PUNCT
ejpam-6734	381	8	which	which	PRON
ejpam-6734	381	9	showed	show	VERB
ejpam-6734	381	10	that	that	SCONJ
ejpam-6734	381	11	the	the	DET
ejpam-6734	381	12	accuracy	accuracy	NOUN
ejpam-6734	381	13	,	,	PUNCT
ejpam-6734	381	14	and	and	CCONJ
ejpam-6734	381	15	found	find	VERB
ejpam-6734	381	16	them	they	PRON
ejpam-6734	381	17	to	to	PART
ejpam-6734	381	18	be	be	AUX
ejpam-6734	381	19	effective	effective	ADJ
ejpam-6734	381	20	and	and	CCONJ
ejpam-6734	381	21	easy	easy	ADJ
ejpam-6734	381	22	to	to	PART
ejpam-6734	381	23	use	use	VERB
ejpam-6734	381	24	in	in	ADP
ejpam-6734	381	25	different	different	ADJ
ejpam-6734	381	26	types	type	NOUN
ejpam-6734	381	27	of	of	ADP
ejpam-6734	381	28	differential	differential	ADJ
ejpam-6734	381	29	equations	equation	NOUN
ejpam-6734	381	30	.	.	PUNCT
ejpam-6734	382	1	the	the	DET
ejpam-6734	382	2	truncation	truncation	NOUN
ejpam-6734	382	3	error	error	NOUN
ejpam-6734	382	4	of	of	ADP
ejpam-6734	382	5	the	the	DET
ejpam-6734	382	6	main	main	ADJ
ejpam-6734	382	7	equation	equation	NOUN
ejpam-6734	382	8	is	be	AUX
ejpam-6734	382	9	discussed	discuss	VERB
ejpam-6734	382	10	.	.	PUNCT
ejpam-6734	383	1	in	in	ADP
ejpam-6734	383	2	the	the	DET
ejpam-6734	383	3	future	future	ADJ
ejpam-6734	383	4	studies	study	NOUN
ejpam-6734	383	5	,	,	PUNCT
ejpam-6734	383	6	the	the	DET
ejpam-6734	383	7	proposed	propose	VERB
ejpam-6734	383	8	m.	m.	NOUN
ejpam-6734	383	9	a.	a.	PROPN
ejpam-6734	383	10	abdou	abdou	PROPN
ejpam-6734	383	11	,	,	PUNCT
ejpam-6734	383	12	a.	a.	PROPN
ejpam-6734	383	13	s.	s.	PROPN
ejpam-6734	383	14	mohamed	mohamed	PROPN
ejpam-6734	383	15	/	/	SYM
ejpam-6734	383	16	eur	eur	PROPN
ejpam-6734	383	17	.	.	PUNCT
ejpam-6734	384	1	j.	j.	PROPN
ejpam-6734	384	2	pure	pure	PROPN
ejpam-6734	384	3	appl	appl	PROPN
ejpam-6734	384	4	.	.	PROPN
ejpam-6734	384	5	math	math	PROPN
ejpam-6734	384	6	,	,	PUNCT
ejpam-6734	384	7	18	18	NUM
ejpam-6734	384	8	(	(	PUNCT
ejpam-6734	384	9	4	4	NUM
ejpam-6734	384	10	)	)	PUNCT
ejpam-6734	384	11	(	(	PUNCT
ejpam-6734	384	12	2025	2025	NUM
ejpam-6734	384	13	)	)	PUNCT
ejpam-6734	384	14	,	,	PUNCT
ejpam-6734	384	15	6734	6734	NUM
ejpam-6734	384	16	17	17	NUM
ejpam-6734	384	17	of	of	ADP
ejpam-6734	384	18	20	20	NUM
ejpam-6734	384	19	figure	figure	NOUN
ejpam-6734	384	20	8	8	NUM
ejpam-6734	384	21	:	:	PUNCT
ejpam-6734	384	22	approximate	approximate	ADJ
ejpam-6734	384	23	and	and	CCONJ
ejpam-6734	384	24	exact	exact	ADJ
ejpam-6734	384	25	solutions	solution	NOUN
ejpam-6734	384	26	at	at	ADP
ejpam-6734	384	27	i=3	i=3	PROPN
ejpam-6734	384	28	,	,	PUNCT
ejpam-6734	384	29	λ1	λ1	PROPN
ejpam-6734	384	30	=	=	SYM
ejpam-6734	384	31	2	2	NUM
ejpam-6734	384	32	,	,	PUNCT
ejpam-6734	384	33	λ2	λ2	NOUN
ejpam-6734	384	34	=	=	SYM
ejpam-6734	384	35	1	1	NUM
ejpam-6734	384	36	for	for	ADP
ejpam-6734	384	37	example	example	NOUN
ejpam-6734	384	38	4	4	NUM
ejpam-6734	384	39	methods	method	NOUN
ejpam-6734	384	40	may	may	AUX
ejpam-6734	384	41	solve	solve	VERB
ejpam-6734	384	42	higher	high	ADJ
ejpam-6734	384	43	-	-	PUNCT
ejpam-6734	384	44	order	order	NOUN
ejpam-6734	384	45	,	,	PUNCT
ejpam-6734	384	46	coupled	couple	VERB
ejpam-6734	384	47	,	,	PUNCT
ejpam-6734	384	48	and	and	CCONJ
ejpam-6734	384	49	fractional	fractional	ADJ
ejpam-6734	384	50	differential	differential	ADJ
ejpam-6734	384	51	equations	equation	NOUN
ejpam-6734	384	52	.	.	PUNCT
ejpam-6734	385	1	it	it	PRON
ejpam-6734	385	2	would	would	AUX
ejpam-6734	385	3	also	also	ADV
ejpam-6734	385	4	be	be	AUX
ejpam-6734	385	5	interesting	interesting	ADJ
ejpam-6734	385	6	to	to	PART
ejpam-6734	385	7	explore	explore	VERB
ejpam-6734	385	8	their	their	PRON
ejpam-6734	385	9	computational	computational	ADJ
ejpam-6734	385	10	efficiency	efficiency	NOUN
ejpam-6734	385	11	on	on	ADP
ejpam-6734	385	12	large	large	ADJ
ejpam-6734	385	13	-	-	PUNCT
ejpam-6734	385	14	scale	scale	NOUN
ejpam-6734	385	15	problems	problem	NOUN
ejpam-6734	385	16	and	and	CCONJ
ejpam-6734	385	17	to	to	PART
ejpam-6734	385	18	apply	apply	VERB
ejpam-6734	385	19	them	they	PRON
ejpam-6734	385	20	to	to	ADP
ejpam-6734	385	21	practical	practical	ADJ
ejpam-6734	385	22	models	model	NOUN
ejpam-6734	385	23	in	in	ADP
ejpam-6734	385	24	physics	physics	NOUN
ejpam-6734	385	25	and	and	CCONJ
ejpam-6734	385	26	engineering	engineering	NOUN
ejpam-6734	385	27	.	.	PUNCT
ejpam-6734	386	1	acknowledgements	acknowledgement	NOUN
ejpam-6734	386	2	the	the	DET
ejpam-6734	386	3	authors	author	NOUN
ejpam-6734	386	4	are	be	AUX
ejpam-6734	386	5	very	very	ADV
ejpam-6734	386	6	grateful	grateful	ADJ
ejpam-6734	386	7	to	to	ADP
ejpam-6734	386	8	the	the	DET
ejpam-6734	386	9	anonymous	anonymous	ADJ
ejpam-6734	386	10	referees	referee	NOUN
ejpam-6734	386	11	for	for	ADP
ejpam-6734	386	12	careful	careful	ADJ
ejpam-6734	386	13	reviewing	reviewing	NOUN
ejpam-6734	386	14	and	and	CCONJ
ejpam-6734	386	15	crucial	crucial	ADJ
ejpam-6734	386	16	comments	comment	NOUN
ejpam-6734	386	17	,	,	PUNCT
ejpam-6734	386	18	which	which	PRON
ejpam-6734	386	19	enabled	enable	VERB
ejpam-6734	386	20	us	we	PRON
ejpam-6734	386	21	to	to	PART
ejpam-6734	386	22	improve	improve	VERB
ejpam-6734	386	23	the	the	DET
ejpam-6734	386	24	manuscript	manuscript	NOUN
ejpam-6734	386	25	.	.	PUNCT
ejpam-6734	387	1	competing	compete	VERB
ejpam-6734	387	2	interests	interest	NOUN
ejpam-6734	387	3	the	the	DET
ejpam-6734	387	4	authors	author	NOUN
ejpam-6734	387	5	declares	declare	VERB
ejpam-6734	387	6	that	that	SCONJ
ejpam-6734	387	7	they	they	PRON
ejpam-6734	387	8	have	have	VERB
ejpam-6734	387	9	no	no	DET
ejpam-6734	387	10	competing	compete	VERB
ejpam-6734	387	11	interest	interest	NOUN
ejpam-6734	387	12	.	.	PUNCT
ejpam-6734	388	1	funding	fund	VERB
ejpam-6734	388	2	this	this	DET
ejpam-6734	388	3	research	research	NOUN
ejpam-6734	388	4	received	receive	VERB
ejpam-6734	388	5	no	no	DET
ejpam-6734	388	6	specific	specific	ADJ
ejpam-6734	388	7	grant	grant	NOUN
ejpam-6734	388	8	from	from	ADP
ejpam-6734	388	9	any	any	DET
ejpam-6734	388	10	funding	funding	NOUN
ejpam-6734	388	11	agency	agency	NOUN
ejpam-6734	388	12	in	in	ADP
ejpam-6734	388	13	the	the	DET
ejpam-6734	388	14	public	public	ADJ
ejpam-6734	388	15	,	,	PUNCT
ejpam-6734	388	16	commercial	commercial	ADJ
ejpam-6734	388	17	,	,	PUNCT
ejpam-6734	388	18	or	or	CCONJ
ejpam-6734	388	19	not	not	PART
ejpam-6734	388	20	-	-	PUNCT
ejpam-6734	388	21	for	for	ADP
ejpam-6734	388	22	-	-	PUNCT
ejpam-6734	388	23	profit	profit	NOUN
ejpam-6734	388	24	sectors	sector	NOUN
ejpam-6734	388	25	.	.	PUNCT
ejpam-6734	389	1	authors	author	NOUN
ejpam-6734	389	2	’	'	PUNCT
ejpam-6734	389	3	contributions	contribution	NOUN
ejpam-6734	389	4	the	the	DET
ejpam-6734	389	5	authors	author	NOUN
ejpam-6734	389	6	confirm	confirm	VERB
ejpam-6734	389	7	that	that	SCONJ
ejpam-6734	389	8	this	this	PRON
ejpam-6734	389	9	is	be	AUX
ejpam-6734	389	10	their	their	PRON
ejpam-6734	389	11	own	own	ADJ
ejpam-6734	389	12	work	work	NOUN
ejpam-6734	389	13	.	.	PUNCT
ejpam-6734	390	1	references	reference	NOUN
ejpam-6734	390	2	[	[	X
ejpam-6734	390	3	1	1	NUM
ejpam-6734	390	4	]	]	PUNCT
ejpam-6734	390	5	r.	r.	PROPN
ejpam-6734	390	6	a.	a.	PROPN
ejpam-6734	390	7	ibrahim	ibrahim	PROPN
ejpam-6734	390	8	and	and	CCONJ
ejpam-6734	390	9	m.	m.	PROPN
ejpam-6734	390	10	saad	saad	PROPN
ejpam-6734	390	11	.	.	PUNCT
ejpam-6734	391	1	application	application	NOUN
ejpam-6734	391	2	of	of	ADP
ejpam-6734	391	3	differential	differential	ADJ
ejpam-6734	391	4	transform	transform	NOUN
ejpam-6734	391	5	method	method	NOUN
ejpam-6734	391	6	with	with	ADP
ejpam-6734	391	7	a	a	DET
ejpam-6734	391	8	domain	domain	NOUN
ejpam-6734	391	9	polynomial	polynomial	NOUN
ejpam-6734	391	10	for	for	ADP
ejpam-6734	391	11	solving	solve	VERB
ejpam-6734	391	12	rlc	rlc	PROPN
ejpam-6734	391	13	circuits	circuit	NOUN
ejpam-6734	391	14	problems	problem	NOUN
ejpam-6734	391	15	and	and	CCONJ
ejpam-6734	391	16	higher	high	ADJ
ejpam-6734	391	17	order	order	NOUN
ejpam-6734	391	18	differential	differential	ADJ
ejpam-6734	391	19	equations	equation	NOUN
ejpam-6734	391	20	.	.	PUNCT
ejpam-6734	392	1	engineering	engineering	NOUN
ejpam-6734	392	2	research	research	NOUN
ejpam-6734	392	3	journal	journal	NOUN
ejpam-6734	392	4	,	,	PUNCT
ejpam-6734	392	5	51(4):89–95	51(4):89–95	NUM
ejpam-6734	392	6	,	,	PUNCT
ejpam-6734	392	7	2022	2022	NUM
ejpam-6734	392	8	.	.	PUNCT
ejpam-6734	393	1	m.	m.	NOUN
ejpam-6734	393	2	a.	a.	PROPN
ejpam-6734	393	3	abdou	abdou	PROPN
ejpam-6734	393	4	,	,	PUNCT
ejpam-6734	393	5	a.	a.	PROPN
ejpam-6734	393	6	s.	s.	PROPN
ejpam-6734	393	7	mohamed	mohamed	PROPN
ejpam-6734	393	8	/	/	SYM
ejpam-6734	393	9	eur	eur	PROPN
ejpam-6734	393	10	.	.	PUNCT
ejpam-6734	394	1	j.	j.	PROPN
ejpam-6734	394	2	pure	pure	PROPN
ejpam-6734	394	3	appl	appl	PROPN
ejpam-6734	394	4	.	.	PROPN
ejpam-6734	394	5	math	math	PROPN
ejpam-6734	394	6	,	,	PUNCT
ejpam-6734	394	7	18	18	NUM
ejpam-6734	394	8	(	(	PUNCT
ejpam-6734	394	9	4	4	NUM
ejpam-6734	394	10	)	)	PUNCT
ejpam-6734	394	11	(	(	PUNCT
ejpam-6734	394	12	2025	2025	NUM
ejpam-6734	394	13	)	)	PUNCT
ejpam-6734	394	14	,	,	PUNCT
ejpam-6734	394	15	6734	6734	NUM
ejpam-6734	394	16	18	18	NUM
ejpam-6734	394	17	of	of	ADP
ejpam-6734	394	18	20	20	NUM
ejpam-6734	394	19	[	[	SYM
ejpam-6734	394	20	2	2	NUM
ejpam-6734	394	21	]	]	PUNCT
ejpam-6734	394	22	s.	s.	PROPN
ejpam-6734	394	23	r.	r.	PROPN
ejpam-6734	394	24	m.	m.	PROPN
ejpam-6734	394	25	noori	noori	PROPN
ejpam-6734	394	26	and	and	CCONJ
ejpam-6734	394	27	n.	n.	PROPN
ejpam-6734	394	28	taghizaheh	taghizaheh	PROPN
ejpam-6734	394	29	.	.	PUNCT
ejpam-6734	395	1	modified	modify	VERB
ejpam-6734	395	2	differential	differential	ADJ
ejpam-6734	395	3	transform	transform	NOUN
ejpam-6734	395	4	method	method	NOUN
ejpam-6734	395	5	for	for	ADP
ejpam-6734	395	6	solving	solve	VERB
ejpam-6734	395	7	linear	linear	NOUN
ejpam-6734	395	8	and	and	CCONJ
ejpam-6734	395	9	nonlinear	nonlinear	ADJ
ejpam-6734	395	10	pantograph	pantograph	NOUN
ejpam-6734	395	11	type	type	NOUN
ejpam-6734	395	12	of	of	ADP
ejpam-6734	395	13	differential	differential	NOUN
ejpam-6734	395	14	and	and	CCONJ
ejpam-6734	395	15	volterra	volterra	PROPN
ejpam-6734	395	16	integro	integro	PROPN
ejpam-6734	395	17	-	-	PUNCT
ejpam-6734	395	18	differential	differential	NOUN
ejpam-6734	395	19	equations	equation	NOUN
ejpam-6734	395	20	with	with	ADP
ejpam-6734	395	21	proportional	proportional	ADJ
ejpam-6734	395	22	delays	delay	NOUN
ejpam-6734	395	23	.	.	PUNCT
ejpam-6734	396	1	advances	advance	NOUN
ejpam-6734	396	2	in	in	ADP
ejpam-6734	396	3	difference	difference	NOUN
ejpam-6734	396	4	equations	equation	NOUN
ejpam-6734	396	5	,	,	PUNCT
ejpam-6734	396	6	2020:649	2020:649	NOUN
ejpam-6734	396	7	,	,	PUNCT
ejpam-6734	396	8	2020	2020	NUM
ejpam-6734	396	9	.	.	PUNCT
ejpam-6734	397	1	[	[	X
ejpam-6734	397	2	3	3	X
ejpam-6734	397	3	]	]	X
ejpam-6734	397	4	m.	m.	NOUN
ejpam-6734	397	5	el	el	PROPN
ejpam-6734	397	6	-	-	PUNCT
ejpam-6734	397	7	shahed	shahed	ADJ
ejpam-6734	397	8	.	.	PUNCT
ejpam-6734	398	1	application	application	NOUN
ejpam-6734	398	2	of	of	ADP
ejpam-6734	398	3	differential	differential	ADJ
ejpam-6734	398	4	transform	transform	NOUN
ejpam-6734	398	5	method	method	NOUN
ejpam-6734	398	6	to	to	ADP
ejpam-6734	398	7	non	non	ADJ
ejpam-6734	398	8	-	-	ADJ
ejpam-6734	398	9	linear	linear	ADJ
ejpam-6734	398	10	oscillatory	oscillatory	ADJ
ejpam-6734	398	11	systems	system	NOUN
ejpam-6734	398	12	.	.	PUNCT
ejpam-6734	399	1	communications	communication	NOUN
ejpam-6734	399	2	in	in	ADP
ejpam-6734	399	3	nonlinear	nonlinear	ADJ
ejpam-6734	399	4	science	science	NOUN
ejpam-6734	399	5	and	and	CCONJ
ejpam-6734	399	6	numerical	numerical	PROPN
ejpam-6734	399	7	simulation	simulation	PROPN
ejpam-6734	399	8	,	,	PUNCT
ejpam-6734	399	9	13:1714	13:1714	NUM
ejpam-6734	399	10	–	–	PUNCT
ejpam-6734	399	11	1720	1720	NUM
ejpam-6734	399	12	,	,	PUNCT
ejpam-6734	399	13	2008	2008	NUM
ejpam-6734	399	14	.	.	PUNCT
ejpam-6734	400	1	[	[	X
ejpam-6734	400	2	4	4	X
ejpam-6734	400	3	]	]	PUNCT
ejpam-6734	400	4	h.	h.	PROPN
ejpam-6734	400	5	nayar	nayar	PROPN
ejpam-6734	400	6	and	and	CCONJ
ejpam-6734	400	7	p.	p.	NOUN
ejpam-6734	400	8	a.	a.	PROPN
ejpam-6734	400	9	anakira	anakira	PROPN
ejpam-6734	400	10	phiri	phiri	PROPN
ejpam-6734	400	11	.	.	PUNCT
ejpam-6734	401	1	modification	modification	NOUN
ejpam-6734	401	2	of	of	ADP
ejpam-6734	401	3	differential	differential	ADJ
ejpam-6734	401	4	transform	transform	NOUN
ejpam-6734	401	5	method	method	NOUN
ejpam-6734	401	6	with	with	ADP
ejpam-6734	401	7	search	search	NOUN
ejpam-6734	401	8	direction	direction	NOUN
ejpam-6734	401	9	along	along	ADP
ejpam-6734	401	10	the	the	DET
ejpam-6734	401	11	spatial	spatial	ADJ
ejpam-6734	401	12	axis	axis	NOUN
ejpam-6734	401	13	.	.	PUNCT
ejpam-6734	402	1	international	international	ADJ
ejpam-6734	402	2	journal	journal	PROPN
ejpam-6734	402	3	of	of	ADP
ejpam-6734	402	4	differential	differential	ADJ
ejpam-6734	402	5	equations	equation	NOUN
ejpam-6734	402	6	,	,	PUNCT
ejpam-6734	402	7	2024:22	2024:22	NUM
ejpam-6734	402	8	,	,	PUNCT
ejpam-6734	402	9	2024	2024	NUM
ejpam-6734	402	10	.	.	PUNCT
ejpam-6734	403	1	article	article	NOUN
ejpam-6734	403	2	i	i	PROPN
ejpam-6734	403	3	d	d	PROPN
ejpam-6734	403	4	6777175	6777175	NUM
ejpam-6734	403	5	.	.	PUNCT
ejpam-6734	404	1	[	[	X
ejpam-6734	404	2	5	5	NUM
ejpam-6734	404	3	]	]	PUNCT
ejpam-6734	404	4	c.	c.	PROPN
ejpam-6734	404	5	huang	huang	PROPN
ejpam-6734	404	6	,	,	PUNCT
ejpam-6734	404	7	j.	j.	PROPN
ejpam-6734	404	8	li	li	PROPN
ejpam-6734	404	9	,	,	PUNCT
ejpam-6734	404	10	and	and	CCONJ
ejpam-6734	404	11	f.	f.	PROPN
ejpam-6734	404	12	lin	lin	PROPN
ejpam-6734	404	13	.	.	PUNCT
ejpam-6734	405	1	a	a	DET
ejpam-6734	405	2	new	new	ADJ
ejpam-6734	405	3	algorithm	algorithm	NOUN
ejpam-6734	405	4	based	base	VERB
ejpam-6734	405	5	on	on	ADP
ejpam-6734	405	6	differential	differential	ADJ
ejpam-6734	405	7	transform	transform	NOUN
ejpam-6734	405	8	method	method	NOUN
ejpam-6734	405	9	for	for	ADP
ejpam-6734	405	10	solving	solve	VERB
ejpam-6734	405	11	partial	partial	ADJ
ejpam-6734	405	12	differential	differential	NOUN
ejpam-6734	405	13	equation	equation	NOUN
ejpam-6734	405	14	system	system	NOUN
ejpam-6734	405	15	with	with	ADP
ejpam-6734	405	16	initial	initial	ADJ
ejpam-6734	405	17	and	and	CCONJ
ejpam-6734	405	18	boundary	boundary	ADJ
ejpam-6734	405	19	conditions	condition	NOUN
ejpam-6734	405	20	.	.	PUNCT
ejpam-6734	406	1	advances	advance	NOUN
ejpam-6734	406	2	in	in	ADP
ejpam-6734	406	3	pure	pure	ADJ
ejpam-6734	406	4	mathematics	mathematic	NOUN
ejpam-6734	406	5	,	,	PUNCT
ejpam-6734	406	6	10:337–349	10:337–349	NUM
ejpam-6734	406	7	,	,	PUNCT
ejpam-6734	406	8	2020	2020	NUM
ejpam-6734	406	9	.	.	PUNCT
ejpam-6734	407	1	[	[	X
ejpam-6734	407	2	6	6	NUM
ejpam-6734	407	3	]	]	PUNCT
ejpam-6734	407	4	e.	e.	PROPN
ejpam-6734	407	5	demirci	demirci	PROPN
ejpam-6734	407	6	and	and	CCONJ
ejpam-6734	407	7	n.	n.	NOUN
ejpam-6734	407	8	ozalp	ozalp	NOUN
ejpam-6734	407	9	.	.	PUNCT
ejpam-6734	408	1	a	a	DET
ejpam-6734	408	2	method	method	NOUN
ejpam-6734	408	3	for	for	ADP
ejpam-6734	408	4	solving	solve	VERB
ejpam-6734	408	5	differential	differential	ADJ
ejpam-6734	408	6	equations	equation	NOUN
ejpam-6734	408	7	of	of	ADP
ejpam-6734	408	8	fractional	fractional	ADJ
ejpam-6734	408	9	order	order	NOUN
ejpam-6734	408	10	.	.	PUNCT
ejpam-6734	409	1	journal	journal	NOUN
ejpam-6734	409	2	of	of	ADP
ejpam-6734	409	3	computational	computational	ADJ
ejpam-6734	409	4	and	and	CCONJ
ejpam-6734	409	5	applied	applied	ADJ
ejpam-6734	409	6	mathematics	mathematic	NOUN
ejpam-6734	409	7	,	,	PUNCT
ejpam-6734	409	8	236:2754–2762	236:2754–2762	NUM
ejpam-6734	409	9	,	,	PUNCT
ejpam-6734	409	10	2012	2012	NUM
ejpam-6734	409	11	.	.	PUNCT
ejpam-6734	410	1	[	[	X
ejpam-6734	410	2	7	7	X
ejpam-6734	410	3	]	]	X
ejpam-6734	410	4	h.	h.	PROPN
ejpam-6734	410	5	k.	k.	PROPN
ejpam-6734	410	6	jassim	jassim	PROPN
ejpam-6734	410	7	and	and	CCONJ
ejpam-6734	410	8	m.	m.	PROPN
ejpam-6734	410	9	a.	a.	PROPN
ejpam-6734	410	10	hussein	hussein	PROPN
ejpam-6734	410	11	.	.	PUNCT
ejpam-6734	411	1	a	a	DET
ejpam-6734	411	2	new	new	ADJ
ejpam-6734	411	3	approach	approach	NOUN
ejpam-6734	411	4	for	for	ADP
ejpam-6734	411	5	solving	solve	VERB
ejpam-6734	411	6	nonlinear	nonlinear	ADJ
ejpam-6734	411	7	fractional	fractional	ADJ
ejpam-6734	411	8	ordinary	ordinary	ADJ
ejpam-6734	411	9	differential	differential	ADJ
ejpam-6734	411	10	equations	equation	NOUN
ejpam-6734	411	11	.	.	PUNCT
ejpam-6734	412	1	mathematics	mathematic	NOUN
ejpam-6734	412	2	,	,	PUNCT
ejpam-6734	412	3	11:1565	11:1565	ADV
ejpam-6734	412	4	,	,	PUNCT
ejpam-6734	412	5	2023	2023	NUM
ejpam-6734	412	6	.	.	PUNCT
ejpam-6734	413	1	[	[	X
ejpam-6734	413	2	8	8	NUM
ejpam-6734	413	3	]	]	X
ejpam-6734	413	4	a.	a.	NOUN
ejpam-6734	413	5	khalouta	khalouta	PROPN
ejpam-6734	413	6	.	.	PUNCT
ejpam-6734	414	1	closed	close	VERB
ejpam-6734	414	2	form	form	NOUN
ejpam-6734	414	3	solutions	solution	NOUN
ejpam-6734	414	4	to	to	ADP
ejpam-6734	414	5	some	some	DET
ejpam-6734	414	6	nonlinear	nonlinear	ADJ
ejpam-6734	414	7	fractional	fractional	ADJ
ejpam-6734	414	8	partial	partial	ADJ
ejpam-6734	414	9	differential	differential	NOUN
ejpam-6734	414	10	equations	equation	NOUN
ejpam-6734	414	11	arising	arise	VERB
ejpam-6734	414	12	in	in	ADP
ejpam-6734	414	13	mathematical	mathematical	ADJ
ejpam-6734	414	14	sciences	science	NOUN
ejpam-6734	414	15	.	.	PUNCT
ejpam-6734	415	1	palestine	palestine	PROPN
ejpam-6734	415	2	journal	journal	PROPN
ejpam-6734	415	3	of	of	ADP
ejpam-6734	415	4	mathematics	mathematic	NOUN
ejpam-6734	415	5	,	,	PUNCT
ejpam-6734	415	6	11:113	11:113	NUM
ejpam-6734	415	7	–	–	PUNCT
ejpam-6734	415	8	126	126	NUM
ejpam-6734	415	9	,	,	PUNCT
ejpam-6734	415	10	2022	2022	NUM
ejpam-6734	415	11	.	.	PUNCT
ejpam-6734	416	1	[	[	X
ejpam-6734	416	2	9	9	NUM
ejpam-6734	416	3	]	]	PUNCT
ejpam-6734	416	4	s.	s.	PROPN
ejpam-6734	416	5	abuasad	abuasad	PROPN
ejpam-6734	416	6	,	,	PUNCT
ejpam-6734	416	7	i.	i.	PROPN
ejpam-6734	416	8	hashim	hashim	PROPN
ejpam-6734	416	9	,	,	PUNCT
ejpam-6734	416	10	and	and	CCONJ
ejpam-6734	416	11	s.	s.	PROPN
ejpam-6734	416	12	a.	a.	PROPN
ejpam-6734	416	13	abdul	abdul	PROPN
ejpam-6734	416	14	karim	karim	PROPN
ejpam-6734	416	15	.	.	PUNCT
ejpam-6734	417	1	modified	modify	VERB
ejpam-6734	417	2	fractional	fractional	ADJ
ejpam-6734	417	3	differential	differential	NOUN
ejpam-6734	417	4	transform	transform	NOUN
ejpam-6734	417	5	method	method	NOUN
ejpam-6734	417	6	for	for	ADP
ejpam-6734	417	7	the	the	DET
ejpam-6734	417	8	solution	solution	NOUN
ejpam-6734	417	9	of	of	ADP
ejpam-6734	417	10	multi	multi	ADJ
ejpam-6734	417	11	-	-	ADJ
ejpam-6734	417	12	term	term	ADJ
ejpam-6734	417	13	time	time	NOUN
ejpam-6734	417	14	-	-	PUNCT
ejpam-6734	417	15	fractional	fractional	ADJ
ejpam-6734	417	16	diffusion	diffusion	NOUN
ejpam-6734	417	17	equations	equation	NOUN
ejpam-6734	417	18	.	.	PUNCT
ejpam-6734	418	1	advances	advance	NOUN
ejpam-6734	418	2	in	in	ADP
ejpam-6734	418	3	mathematical	mathematical	ADJ
ejpam-6734	418	4	physics	physics	NOUN
ejpam-6734	418	5	,	,	PUNCT
ejpam-6734	418	6	2019:14	2019:14	NUM
ejpam-6734	418	7	,	,	PUNCT
ejpam-6734	418	8	2019	2019	NUM
ejpam-6734	418	9	.	.	PUNCT
ejpam-6734	419	1	article	article	NOUN
ejpam-6734	419	2	i	i	PROPN
ejpam-6734	419	3	d	d	PROPN
ejpam-6734	419	4	5703916	5703916	NUM
ejpam-6734	419	5	.	.	PUNCT
ejpam-6734	420	1	[	[	X
ejpam-6734	420	2	10	10	NUM
ejpam-6734	420	3	]	]	X
ejpam-6734	420	4	ahmed	ahmed	PROPN
ejpam-6734	420	5	gamal	gamal	PROPN
ejpam-6734	420	6	atta	atta	PROPN
ejpam-6734	420	7	,	,	PUNCT
ejpam-6734	420	8	jomana	jomana	PROPN
ejpam-6734	420	9	farag	farag	PROPN
ejpam-6734	420	10	soliman	soliman	PROPN
ejpam-6734	420	11	,	,	PUNCT
ejpam-6734	420	12	elaf	elaf	PROPN
ejpam-6734	420	13	wael	wael	PROPN
ejpam-6734	420	14	elsaeed	elsaeed	PROPN
ejpam-6734	420	15	,	,	PUNCT
ejpam-6734	420	16	mostafa	mostafa	PROPN
ejpam-6734	420	17	wael	wael	PROPN
ejpam-6734	420	18	elsaeed	elsaeed	PROPN
ejpam-6734	420	19	,	,	PUNCT
ejpam-6734	420	20	and	and	CCONJ
ejpam-6734	420	21	youssri	youssri	PROPN
ejpam-6734	420	22	hassan	hassan	PROPN
ejpam-6734	420	23	youssri	youssri	PROPN
ejpam-6734	420	24	.	.	PUNCT
ejpam-6734	421	1	spectral	spectral	ADJ
ejpam-6734	421	2	collocation	collocation	NOUN
ejpam-6734	421	3	algorithm	algorithm	NOUN
ejpam-6734	421	4	for	for	ADP
ejpam-6734	421	5	the	the	DET
ejpam-6734	421	6	fractional	fractional	ADJ
ejpam-6734	421	7	bratu	bratu	NOUN
ejpam-6734	421	8	equation	equation	NOUN
ejpam-6734	421	9	via	via	ADP
ejpam-6734	421	10	hexic	hexic	PROPN
ejpam-6734	421	11	shifted	shift	VERB
ejpam-6734	421	12	chebyshev	chebyshev	NOUN
ejpam-6734	421	13	polynomials	polynomial	NOUN
ejpam-6734	421	14	.	.	PUNCT
ejpam-6734	422	1	computational	computational	ADJ
ejpam-6734	422	2	methods	method	NOUN
ejpam-6734	422	3	for	for	ADP
ejpam-6734	422	4	differential	differential	ADJ
ejpam-6734	422	5	equations	equation	NOUN
ejpam-6734	422	6	,	,	PUNCT
ejpam-6734	422	7	13(4):1102–1116	13(4):1102–1116	NUM
ejpam-6734	422	8	,	,	PUNCT
ejpam-6734	422	9	2025	2025	NUM
ejpam-6734	422	10	.	.	PUNCT
ejpam-6734	423	1	[	[	X
ejpam-6734	423	2	11	11	NUM
ejpam-6734	423	3	]	]	X
ejpam-6734	423	4	y.	y.	PROPN
ejpam-6734	423	5	h.	h.	PROPN
ejpam-6734	423	6	youssri	youssri	PROPN
ejpam-6734	423	7	,	,	PUNCT
ejpam-6734	423	8	r.	r.	PROPN
ejpam-6734	423	9	m.	m.	PROPN
ejpam-6734	423	10	hafez	hafez	PROPN
ejpam-6734	423	11	,	,	PUNCT
ejpam-6734	423	12	and	and	CCONJ
ejpam-6734	423	13	a.	a.	NOUN
ejpam-6734	423	14	g.	g.	PROPN
ejpam-6734	423	15	atta	atta	PROPN
ejpam-6734	423	16	.	.	PUNCT
ejpam-6734	424	1	an	an	DET
ejpam-6734	424	2	innovative	innovative	ADJ
ejpam-6734	424	3	pseudo	pseudo	NOUN
ejpam-6734	424	4	-	-	ADJ
ejpam-6734	424	5	spectral	spectral	ADJ
ejpam-6734	424	6	galerkin	galerkin	ADJ
ejpam-6734	424	7	algorithm	algorithm	NOUN
ejpam-6734	424	8	for	for	ADP
ejpam-6734	424	9	the	the	DET
ejpam-6734	424	10	time	time	NOUN
ejpam-6734	424	11	-	-	PUNCT
ejpam-6734	424	12	fractional	fractional	ADJ
ejpam-6734	424	13	tricomi	tricomi	NOUN
ejpam-6734	424	14	-	-	PUNCT
ejpam-6734	424	15	type	type	NOUN
ejpam-6734	424	16	equation	equation	NOUN
ejpam-6734	424	17	.	.	PUNCT
ejpam-6734	425	1	physica	physica	PROPN
ejpam-6734	425	2	scripta	scripta	PROPN
ejpam-6734	425	3	,	,	PUNCT
ejpam-6734	425	4	99(10):105238	99(10):105238	NUM
ejpam-6734	425	5	,	,	PUNCT
ejpam-6734	425	6	2013	2013	NUM
ejpam-6734	425	7	.	.	PUNCT
ejpam-6734	426	1	[	[	X
ejpam-6734	426	2	12	12	NUM
ejpam-6734	426	3	]	]	PUNCT
ejpam-6734	426	4	a.	a.	NOUN
ejpam-6734	426	5	kurt	kurt	PROPN
ejpam-6734	426	6	,	,	PUNCT
ejpam-6734	426	7	s.	s.	PROPN
ejpam-6734	426	8	yalcinbas	yalcinbas	PROPN
ejpam-6734	426	9	,	,	PUNCT
ejpam-6734	426	10	and	and	CCONJ
ejpam-6734	426	11	m.	m.	NOUN
ejpam-6734	426	12	sezer	sezer	PROPN
ejpam-6734	426	13	.	.	PUNCT
ejpam-6734	427	1	fibonacci	fibonacci	NOUN
ejpam-6734	427	2	collocation	collocation	NOUN
ejpam-6734	427	3	method	method	NOUN
ejpam-6734	427	4	for	for	ADP
ejpam-6734	427	5	solving	solve	VERB
ejpam-6734	427	6	linear	linear	PROPN
ejpam-6734	427	7	differential	differential	ADJ
ejpam-6734	427	8	difference	difference	NOUN
ejpam-6734	427	9	equations	equation	NOUN
ejpam-6734	427	10	.	.	PUNCT
ejpam-6734	428	1	mathematical	mathematical	ADJ
ejpam-6734	428	2	and	and	CCONJ
ejpam-6734	428	3	computational	computational	ADJ
ejpam-6734	428	4	applications	application	NOUN
ejpam-6734	428	5	,	,	PUNCT
ejpam-6734	428	6	18(3):448–458	18(3):448–458	NUM
ejpam-6734	428	7	,	,	PUNCT
ejpam-6734	428	8	2013	2013	NUM
ejpam-6734	428	9	.	.	PUNCT
ejpam-6734	429	1	[	[	X
ejpam-6734	429	2	13	13	NUM
ejpam-6734	429	3	]	]	PUNCT
ejpam-6734	429	4	a.	a.	PROPN
ejpam-6734	429	5	b.	b.	PROPN
ejpam-6734	429	6	m.	m.	PROPN
ejpam-6734	429	7	i.	i.	PROPN
ejpam-6734	429	8	koc	koc	PROPN
ejpam-6734	429	9	,	,	PUNCT
ejpam-6734	429	10	m.	m.	NOUN
ejpam-6734	429	11	cakmak	cakmak	PROPN
ejpam-6734	429	12	,	,	PUNCT
ejpam-6734	429	13	a.	a.	NOUN
ejpam-6734	429	14	kurnaz	kurnaz	PROPN
ejpam-6734	429	15	,	,	PUNCT
ejpam-6734	429	16	and	and	CCONJ
ejpam-6734	429	17	k.	k.	PROPN
ejpam-6734	429	18	uslu	uslu	PROPN
ejpam-6734	429	19	.	.	PUNCT
ejpam-6734	430	1	a	a	DET
ejpam-6734	430	2	new	new	ADJ
ejpam-6734	430	3	fibonacci	fibonacci	NOUN
ejpam-6734	430	4	type	type	NOUN
ejpam-6734	430	5	collocation	collocation	NOUN
ejpam-6734	430	6	procedure	procedure	NOUN
ejpam-6734	430	7	for	for	ADP
ejpam-6734	430	8	boundary	boundary	ADJ
ejpam-6734	430	9	value	value	NOUN
ejpam-6734	430	10	problems	problem	NOUN
ejpam-6734	430	11	.	.	PUNCT
ejpam-6734	431	1	advances	advance	NOUN
ejpam-6734	431	2	in	in	ADP
ejpam-6734	431	3	difference	difference	NOUN
ejpam-6734	431	4	equations	equation	NOUN
ejpam-6734	431	5	,	,	PUNCT
ejpam-6734	431	6	2013:262	2013:262	NUM
ejpam-6734	431	7	,	,	PUNCT
ejpam-6734	431	8	2013	2013	NUM
ejpam-6734	431	9	.	.	PUNCT
ejpam-6734	432	1	[	[	X
ejpam-6734	432	2	14	14	NUM
ejpam-6734	432	3	]	]	PUNCT
ejpam-6734	432	4	m.	m.	NOUN
ejpam-6734	432	5	cakmak	cakmak	PROPN
ejpam-6734	432	6	.	.	PUNCT
ejpam-6734	433	1	fibonacci	fibonacci	NOUN
ejpam-6734	433	2	collocation	collocation	NOUN
ejpam-6734	433	3	method	method	NOUN
ejpam-6734	433	4	for	for	ADP
ejpam-6734	433	5	solving	solve	VERB
ejpam-6734	433	6	a	a	DET
ejpam-6734	433	7	class	class	NOUN
ejpam-6734	433	8	of	of	ADP
ejpam-6734	433	9	nonlinear	nonlinear	ADJ
ejpam-6734	433	10	pantograph	pantograph	NOUN
ejpam-6734	433	11	differential	differential	PROPN
ejpam-6734	433	12	equations	equation	NOUN
ejpam-6734	433	13	.	.	PUNCT
ejpam-6734	434	1	mathematical	mathematical	ADJ
ejpam-6734	434	2	methods	method	NOUN
ejpam-6734	434	3	in	in	ADP
ejpam-6734	434	4	the	the	DET
ejpam-6734	434	5	applied	apply	VERB
ejpam-6734	434	6	sciences	science	NOUN
ejpam-6734	434	7	,	,	PUNCT
ejpam-6734	434	8	45:11962–11976	45:11962–11976	NOUN
ejpam-6734	434	9	,	,	PUNCT
ejpam-6734	434	10	2022	2022	NUM
ejpam-6734	434	11	.	.	PUNCT
ejpam-6734	435	1	[	[	X
ejpam-6734	435	2	15	15	NUM
ejpam-6734	435	3	]	]	X
ejpam-6734	435	4	m.	m.	NOUN
ejpam-6734	435	5	cetin	cetin	PROPN
ejpam-6734	435	6	,	,	PUNCT
ejpam-6734	435	7	m.	m.	NOUN
ejpam-6734	435	8	sezer	sezer	NOUN
ejpam-6734	435	9	,	,	PUNCT
ejpam-6734	435	10	and	and	CCONJ
ejpam-6734	435	11	c.	c.	PROPN
ejpam-6734	435	12	guler	guler	NOUN
ejpam-6734	435	13	.	.	PUNCT
ejpam-6734	436	1	lucas	lucas	PROPN
ejpam-6734	436	2	polynomials	polynomials	PROPN
ejpam-6734	436	3	approach	approach	VERB
ejpam-6734	436	4	for	for	ADP
ejpam-6734	436	5	system	system	NOUN
ejpam-6734	436	6	of	of	ADP
ejpam-6734	436	7	highorder	highorder	NOUN
ejpam-6734	436	8	linear	linear	PROPN
ejpam-6734	436	9	differential	differential	NOUN
ejpam-6734	436	10	equations	equation	NOUN
ejpam-6734	436	11	and	and	CCONJ
ejpam-6734	436	12	residual	residual	ADJ
ejpam-6734	436	13	error	error	NOUN
ejpam-6734	436	14	estimation	estimation	NOUN
ejpam-6734	436	15	.	.	PUNCT
ejpam-6734	437	1	mathematical	mathematical	ADJ
ejpam-6734	437	2	problems	problem	NOUN
ejpam-6734	437	3	in	in	ADP
ejpam-6734	437	4	engineering	engineering	NOUN
ejpam-6734	437	5	,	,	PUNCT
ejpam-6734	437	6	2015:14	2015:14	NUM
ejpam-6734	437	7	,	,	PUNCT
ejpam-6734	437	8	2015	2015	NUM
ejpam-6734	437	9	.	.	PUNCT
ejpam-6734	438	1	article	article	NOUN
ejpam-6734	438	2	i	i	PROPN
ejpam-6734	438	3	d	d	PROPN
ejpam-6734	438	4	625984	625984	NUM
ejpam-6734	438	5	.	.	PUNCT
ejpam-6734	439	1	[	[	X
ejpam-6734	439	2	16	16	NUM
ejpam-6734	439	3	]	]	X
ejpam-6734	439	4	w.	w.	PROPN
ejpam-6734	439	5	m.	m.	PROPN
ejpam-6734	439	6	abd	abd	PROPN
ejpam-6734	439	7	-	-	PUNCT
ejpam-6734	439	8	elhameed	elhameed	PROPN
ejpam-6734	439	9	and	and	CCONJ
ejpam-6734	439	10	y.	y.	PROPN
ejpam-6734	439	11	h.	h.	PROPN
ejpam-6734	439	12	youssri	youssri	PROPN
ejpam-6734	439	13	.	.	PUNCT
ejpam-6734	440	1	spectral	spectral	ADJ
ejpam-6734	440	2	solutions	solution	NOUN
ejpam-6734	440	3	for	for	ADP
ejpam-6734	440	4	fractional	fractional	ADJ
ejpam-6734	440	5	differential	differential	ADJ
ejpam-6734	440	6	equations	equation	NOUN
ejpam-6734	440	7	via	via	ADP
ejpam-6734	440	8	a	a	DET
ejpam-6734	440	9	novel	novel	ADJ
ejpam-6734	440	10	lucas	lucas	NOUN
ejpam-6734	440	11	operational	operational	ADJ
ejpam-6734	440	12	matrix	matrix	NOUN
ejpam-6734	440	13	of	of	ADP
ejpam-6734	440	14	fractional	fractional	ADJ
ejpam-6734	440	15	derivatives	derivative	NOUN
ejpam-6734	440	16	.	.	PUNCT
ejpam-6734	441	1	romanian	romanian	ADJ
ejpam-6734	441	2	m.	m.	PROPN
ejpam-6734	441	3	a.	a.	PROPN
ejpam-6734	441	4	abdou	abdou	PROPN
ejpam-6734	441	5	,	,	PUNCT
ejpam-6734	441	6	a.	a.	PROPN
ejpam-6734	441	7	s.	s.	PROPN
ejpam-6734	441	8	mohamed	mohamed	PROPN
ejpam-6734	441	9	/	/	SYM
ejpam-6734	441	10	eur	eur	PROPN
ejpam-6734	441	11	.	.	PUNCT
ejpam-6734	442	1	j.	j.	PROPN
ejpam-6734	442	2	pure	pure	PROPN
ejpam-6734	442	3	appl	appl	PROPN
ejpam-6734	442	4	.	.	PROPN
ejpam-6734	442	5	math	math	PROPN
ejpam-6734	442	6	,	,	PUNCT
ejpam-6734	442	7	18	18	NUM
ejpam-6734	442	8	(	(	PUNCT
ejpam-6734	442	9	4	4	NUM
ejpam-6734	442	10	)	)	PUNCT
ejpam-6734	442	11	(	(	PUNCT
ejpam-6734	442	12	2025	2025	NUM
ejpam-6734	442	13	)	)	PUNCT
ejpam-6734	442	14	,	,	PUNCT
ejpam-6734	442	15	6734	6734	NUM
ejpam-6734	442	16	19	19	NUM
ejpam-6734	442	17	of	of	ADP
ejpam-6734	442	18	20	20	NUM
ejpam-6734	442	19	journal	journal	NOUN
ejpam-6734	442	20	of	of	ADP
ejpam-6734	442	21	physics	physics	PROPN
ejpam-6734	442	22	,	,	PUNCT
ejpam-6734	442	23	61(5–6):795–818	61(5–6):795–818	PROPN
ejpam-6734	442	24	,	,	PUNCT
ejpam-6734	442	25	2016	2016	NUM
ejpam-6734	442	26	.	.	PUNCT
ejpam-6734	443	1	[	[	X
ejpam-6734	443	2	17	17	NUM
ejpam-6734	443	3	]	]	X
ejpam-6734	443	4	yh	yh	PROPN
ejpam-6734	443	5	youssri	youssri	PROPN
ejpam-6734	443	6	and	and	CCONJ
ejpam-6734	443	7	sm	sm	PROPN
ejpam-6734	443	8	sayed	say	VERB
ejpam-6734	443	9	.	.	PUNCT
ejpam-6734	444	1	efficient	efficient	ADJ
ejpam-6734	444	2	spectral	spectral	ADJ
ejpam-6734	444	3	collocation	collocation	NOUN
ejpam-6734	444	4	algorithm	algorithm	NOUN
ejpam-6734	444	5	for	for	ADP
ejpam-6734	444	6	pantograph	pantograph	NOUN
ejpam-6734	444	7	integro	integro	ADJ
ejpam-6734	444	8	-	-	PUNCT
ejpam-6734	444	9	differential	differential	NOUN
ejpam-6734	444	10	equations	equation	NOUN
ejpam-6734	444	11	involving	involve	VERB
ejpam-6734	444	12	delay	delay	NOUN
ejpam-6734	444	13	and	and	CCONJ
ejpam-6734	444	14	weakly	weakly	ADJ
ejpam-6734	444	15	singular	singular	ADJ
ejpam-6734	444	16	kernels	kernel	NOUN
ejpam-6734	444	17	.	.	PUNCT
ejpam-6734	445	1	journal	journal	PROPN
ejpam-6734	445	2	of	of	ADP
ejpam-6734	445	3	umm	umm	INTJ
ejpam-6734	445	4	al	al	PROPN
ejpam-6734	445	5	-	-	PUNCT
ejpam-6734	445	6	qura	qura	PROPN
ejpam-6734	445	7	university	university	NOUN
ejpam-6734	445	8	for	for	ADP
ejpam-6734	445	9	applied	apply	VERB
ejpam-6734	445	10	sciences	science	NOUN
ejpam-6734	445	11	,	,	PUNCT
ejpam-6734	445	12	pages	page	NOUN
ejpam-6734	445	13	1–15	1–15	NUM
ejpam-6734	445	14	,	,	PUNCT
ejpam-6734	445	15	2025	2025	NUM
ejpam-6734	445	16	.	.	PUNCT
ejpam-6734	446	1	[	[	X
ejpam-6734	446	2	18	18	NUM
ejpam-6734	446	3	]	]	X
ejpam-6734	446	4	w.	w.	PROPN
ejpam-6734	446	5	m.	m.	PROPN
ejpam-6734	446	6	abd	abd	PROPN
ejpam-6734	446	7	-	-	PUNCT
ejpam-6734	446	8	elhameed	elhameed	PROPN
ejpam-6734	446	9	and	and	CCONJ
ejpam-6734	446	10	y.	y.	PROPN
ejpam-6734	446	11	h.	h.	PROPN
ejpam-6734	446	12	youssri	youssri	PROPN
ejpam-6734	446	13	.	.	PUNCT
ejpam-6734	447	1	a	a	DET
ejpam-6734	447	2	novel	novel	ADJ
ejpam-6734	447	3	operational	operational	ADJ
ejpam-6734	447	4	matrix	matrix	NOUN
ejpam-6734	447	5	of	of	ADP
ejpam-6734	447	6	caputo	caputo	PROPN
ejpam-6734	447	7	fractional	fractional	ADJ
ejpam-6734	447	8	derivatives	derivative	NOUN
ejpam-6734	447	9	of	of	ADP
ejpam-6734	447	10	fibonacci	fibonacci	NOUN
ejpam-6734	447	11	polynomials	polynomial	NOUN
ejpam-6734	447	12	:	:	PUNCT
ejpam-6734	447	13	spectral	spectral	ADJ
ejpam-6734	447	14	solutions	solution	NOUN
ejpam-6734	447	15	of	of	ADP
ejpam-6734	447	16	fractional	fractional	ADJ
ejpam-6734	447	17	differential	differential	ADJ
ejpam-6734	447	18	equations	equation	NOUN
ejpam-6734	447	19	.	.	PUNCT
ejpam-6734	448	1	entropy	entropy	PROPN
ejpam-6734	448	2	,	,	PUNCT
ejpam-6734	448	3	18	18	NUM
ejpam-6734	448	4	,	,	PUNCT
ejpam-6734	448	5	2016	2016	NUM
ejpam-6734	448	6	.	.	PUNCT
ejpam-6734	449	1	[	[	X
ejpam-6734	449	2	19	19	NUM
ejpam-6734	449	3	]	]	X
ejpam-6734	449	4	y.	y.	PROPN
ejpam-6734	449	5	h.	h.	PROPN
ejpam-6734	449	6	youssri	youssri	PROPN
ejpam-6734	449	7	and	and	CCONJ
ejpam-6734	449	8	w.	w.	PROPN
ejpam-6734	449	9	m.	m.	PROPN
ejpam-6734	449	10	abd	abd	PROPN
ejpam-6734	449	11	-	-	PUNCT
ejpam-6734	449	12	elhameed	elhameed	NOUN
ejpam-6734	449	13	.	.	PUNCT
ejpam-6734	450	1	spectral	spectral	ADJ
ejpam-6734	450	2	solutions	solution	NOUN
ejpam-6734	450	3	for	for	ADP
ejpam-6734	450	4	multi	multi	ADJ
ejpam-6734	450	5	-	-	ADJ
ejpam-6734	450	6	term	term	ADJ
ejpam-6734	450	7	fractional	fractional	ADJ
ejpam-6734	450	8	initial	initial	ADJ
ejpam-6734	450	9	value	value	NOUN
ejpam-6734	450	10	problems	problem	NOUN
ejpam-6734	450	11	using	use	VERB
ejpam-6734	450	12	a	a	DET
ejpam-6734	450	13	new	new	ADJ
ejpam-6734	450	14	fibonacci	fibonacci	NOUN
ejpam-6734	450	15	operational	operational	ADJ
ejpam-6734	450	16	matrix	matrix	NOUN
ejpam-6734	450	17	of	of	ADP
ejpam-6734	450	18	fractional	fractional	ADJ
ejpam-6734	450	19	integration	integration	NOUN
ejpam-6734	450	20	.	.	PUNCT
ejpam-6734	451	1	progress	progress	NOUN
ejpam-6734	451	2	in	in	ADP
ejpam-6734	451	3	fractional	fractional	ADJ
ejpam-6734	451	4	differentiation	differentiation	NOUN
ejpam-6734	451	5	and	and	CCONJ
ejpam-6734	451	6	applications	application	NOUN
ejpam-6734	451	7	,	,	PUNCT
ejpam-6734	451	8	an	an	DET
ejpam-6734	451	9	international	international	ADJ
ejpam-6734	451	10	journal	journal	NOUN
ejpam-6734	451	11	,	,	PUNCT
ejpam-6734	451	12	2(2):141–151	2(2):141–151	NUM
ejpam-6734	451	13	,	,	PUNCT
ejpam-6734	451	14	2016	2016	NUM
ejpam-6734	451	15	.	.	PUNCT
ejpam-6734	452	1	[	[	X
ejpam-6734	452	2	20	20	NUM
ejpam-6734	452	3	]	]	X
ejpam-6734	453	1	y.	y.	PROPN
ejpam-6734	453	2	h.	h.	PROPN
ejpam-6734	453	3	youssri	youssri	PROPN
ejpam-6734	453	4	and	and	CCONJ
ejpam-6734	453	5	a.	a.	NOUN
ejpam-6734	453	6	g.	g.	PROPN
ejpam-6734	453	7	atta	atta	PROPN
ejpam-6734	453	8	.	.	PUNCT
ejpam-6734	454	1	fejér	fejér	NOUN
ejpam-6734	454	2	-	-	PUNCT
ejpam-6734	454	3	quadrature	quadrature	NOUN
ejpam-6734	454	4	collocation	collocation	NOUN
ejpam-6734	454	5	algorithm	algorithm	NOUN
ejpam-6734	454	6	for	for	ADP
ejpam-6734	454	7	solving	solve	VERB
ejpam-6734	454	8	fractional	fractional	ADJ
ejpam-6734	454	9	integro	integro	ADJ
ejpam-6734	454	10	-	-	PUNCT
ejpam-6734	454	11	differential	differential	NOUN
ejpam-6734	454	12	equations	equation	NOUN
ejpam-6734	454	13	via	via	ADP
ejpam-6734	454	14	fibonacci	fibonacci	NOUN
ejpam-6734	454	15	polynomials	polynomial	NOUN
ejpam-6734	454	16	.	.	PUNCT
ejpam-6734	455	1	contemporary	contemporary	ADJ
ejpam-6734	455	2	mathematics	mathematic	NOUN
ejpam-6734	455	3	,	,	PUNCT
ejpam-6734	455	4	5(1):296–308	5(1):296–308	NUM
ejpam-6734	455	5	,	,	PUNCT
ejpam-6734	455	6	2024	2024	NUM
ejpam-6734	455	7	.	.	PUNCT
ejpam-6734	456	1	[	[	X
ejpam-6734	456	2	21	21	NUM
ejpam-6734	456	3	]	]	PUNCT
ejpam-6734	456	4	a.	a.	NOUN
ejpam-6734	456	5	g.	g.	PROPN
ejpam-6734	456	6	atta	atta	PROPN
ejpam-6734	456	7	,	,	PUNCT
ejpam-6734	456	8	g.	g.	PROPN
ejpam-6734	456	9	m.	m.	PROPN
ejpam-6734	456	10	moatimid	moatimid	PROPN
ejpam-6734	456	11	,	,	PUNCT
ejpam-6734	456	12	and	and	CCONJ
ejpam-6734	456	13	y.	y.	PROPN
ejpam-6734	456	14	h.	h.	PROPN
ejpam-6734	456	15	youssri	youssri	PROPN
ejpam-6734	456	16	.	.	PUNCT
ejpam-6734	457	1	generalized	generalized	ADJ
ejpam-6734	457	2	fibonacci	fibonacci	PROPN
ejpam-6734	457	3	operational	operational	PROPN
ejpam-6734	457	4	tau	tau	PROPN
ejpam-6734	457	5	algorithm	algorithm	NOUN
ejpam-6734	457	6	for	for	ADP
ejpam-6734	457	7	fractional	fractional	ADJ
ejpam-6734	457	8	bagley	bagley	NOUN
ejpam-6734	457	9	-	-	PUNCT
ejpam-6734	457	10	torvik	torvik	NOUN
ejpam-6734	457	11	equation	equation	NOUN
ejpam-6734	457	12	.	.	PUNCT
ejpam-6734	458	1	progress	progress	NOUN
ejpam-6734	458	2	in	in	ADP
ejpam-6734	458	3	fractional	fractional	ADJ
ejpam-6734	458	4	differentiation	differentiation	NOUN
ejpam-6734	458	5	and	and	CCONJ
ejpam-6734	458	6	applications	application	NOUN
ejpam-6734	458	7	,	,	PUNCT
ejpam-6734	458	8	an	an	DET
ejpam-6734	458	9	international	international	ADJ
ejpam-6734	458	10	journal	journal	NOUN
ejpam-6734	458	11	,	,	PUNCT
ejpam-6734	458	12	6(3):215–224	6(3):215–224	NOUN
ejpam-6734	458	13	,	,	PUNCT
ejpam-6734	458	14	2020	2020	NUM
ejpam-6734	458	15	.	.	PUNCT
ejpam-6734	459	1	[	[	X
ejpam-6734	459	2	22	22	NUM
ejpam-6734	459	3	]	]	X
ejpam-6734	459	4	youssri	youssri	PROPN
ejpam-6734	459	5	hassan	hassan	PROPN
ejpam-6734	459	6	youssri	youssri	PROPN
ejpam-6734	459	7	and	and	CCONJ
ejpam-6734	459	8	ahmed	ahmed	PROPN
ejpam-6734	459	9	gamal	gamal	PROPN
ejpam-6734	459	10	atta	atta	PROPN
ejpam-6734	459	11	.	.	PUNCT
ejpam-6734	460	1	optimal	optimal	ADJ
ejpam-6734	460	2	third	third	ADJ
ejpam-6734	460	3	-	-	PUNCT
ejpam-6734	460	4	kind	kind	NOUN
ejpam-6734	460	5	chebyshev	chebyshev	NOUN
ejpam-6734	460	6	collocation	collocation	NOUN
ejpam-6734	460	7	algorithm	algorithm	NOUN
ejpam-6734	460	8	for	for	ADP
ejpam-6734	460	9	solving	solve	VERB
ejpam-6734	460	10	beam	beam	NOUN
ejpam-6734	460	11	-	-	PUNCT
ejpam-6734	460	12	type	type	NOUN
ejpam-6734	460	13	micro	micro	NOUN
ejpam-6734	460	14	-	-	ADJ
ejpam-6734	460	15	and	and	CCONJ
ejpam-6734	460	16	nanoscale	nanoscale	PROPN
ejpam-6734	460	17	bvps	bvps	PROPN
ejpam-6734	460	18	.	.	PROPN
ejpam-6734	461	1	journal	journal	PROPN
ejpam-6734	461	2	of	of	ADP
ejpam-6734	461	3	mathematical	mathematical	ADJ
ejpam-6734	461	4	modeling	modeling	NOUN
ejpam-6734	461	5	,	,	PUNCT
ejpam-6734	461	6	13(4):883–898	13(4):883–898	PROPN
ejpam-6734	461	7	,	,	PUNCT
ejpam-6734	461	8	2025	2025	NUM
ejpam-6734	461	9	.	.	PUNCT
ejpam-6734	462	1	[	[	X
ejpam-6734	462	2	23	23	NUM
ejpam-6734	462	3	]	]	X
ejpam-6734	462	4	shorouk	shorouk	PROPN
ejpam-6734	462	5	gamal	gamal	PROPN
ejpam-6734	462	6	kamel	kamel	PROPN
ejpam-6734	462	7	,	,	PUNCT
ejpam-6734	462	8	ahmed	ahmed	PROPN
ejpam-6734	462	9	gamal	gamal	PROPN
ejpam-6734	462	10	atta	atta	PROPN
ejpam-6734	462	11	,	,	PUNCT
ejpam-6734	462	12	and	and	CCONJ
ejpam-6734	462	13	youssri	youssri	PROPN
ejpam-6734	462	14	hassan	hassan	PROPN
ejpam-6734	462	15	youssri	youssri	PROPN
ejpam-6734	462	16	.	.	PUNCT
ejpam-6734	463	1	a	a	DET
ejpam-6734	463	2	spectral	spectral	ADJ
ejpam-6734	463	3	delannoy	delannoy	VERB
ejpam-6734	463	4	polynomial	polynomial	ADJ
ejpam-6734	463	5	-	-	PUNCT
ejpam-6734	463	6	based	base	VERB
ejpam-6734	463	7	computational	computational	ADJ
ejpam-6734	463	8	framework	framework	NOUN
ejpam-6734	463	9	for	for	ADP
ejpam-6734	463	10	fractional	fractional	ADJ
ejpam-6734	463	11	differential	differential	NOUN
ejpam-6734	463	12	problems	problem	NOUN
ejpam-6734	463	13	in	in	ADP
ejpam-6734	463	14	complex	complex	ADJ
ejpam-6734	463	15	systems	system	NOUN
ejpam-6734	463	16	.	.	PUNCT
ejpam-6734	464	1	international	international	ADJ
ejpam-6734	464	2	journal	journal	NOUN
ejpam-6734	464	3	of	of	ADP
ejpam-6734	464	4	modern	modern	ADJ
ejpam-6734	464	5	physics	physic	NOUN
ejpam-6734	464	6	c	c	NOUN
ejpam-6734	464	7	,	,	PUNCT
ejpam-6734	464	8	2025	2025	NUM
ejpam-6734	464	9	.	.	PUNCT
ejpam-6734	465	1	[	[	X
ejpam-6734	465	2	24	24	NUM
ejpam-6734	465	3	]	]	PUNCT
ejpam-6734	465	4	a.	a.	PROPN
ejpam-6734	465	5	s.	s.	PROPN
ejpam-6734	465	6	mohamed	mohamed	PROPN
ejpam-6734	465	7	.	.	PROPN
ejpam-6734	466	1	exact	exact	ADJ
ejpam-6734	466	2	differential	differential	ADJ
ejpam-6734	466	3	transform	transform	NOUN
ejpam-6734	466	4	method	method	NOUN
ejpam-6734	466	5	and	and	CCONJ
ejpam-6734	466	6	semi	semi	ADJ
ejpam-6734	466	7	-	-	ADJ
ejpam-6734	466	8	analytic	analytic	ADJ
ejpam-6734	466	9	chebyshev	chebyshev	NOUN
ejpam-6734	466	10	collocation	collocation	NOUN
ejpam-6734	466	11	method	method	NOUN
ejpam-6734	466	12	for	for	ADP
ejpam-6734	466	13	ordinary	ordinary	ADJ
ejpam-6734	466	14	differential	differential	ADJ
ejpam-6734	466	15	equations	equation	NOUN
ejpam-6734	466	16	.	.	PUNCT
ejpam-6734	467	1	boundary	boundary	ADJ
ejpam-6734	467	2	value	value	NOUN
ejpam-6734	467	3	problems	problem	NOUN
ejpam-6734	467	4	,	,	PUNCT
ejpam-6734	467	5	2025:36	2025:36	NUM
ejpam-6734	467	6	,	,	PUNCT
ejpam-6734	467	7	2025	2025	NUM
ejpam-6734	467	8	.	.	PUNCT
ejpam-6734	468	1	[	[	X
ejpam-6734	468	2	25	25	NUM
ejpam-6734	468	3	]	]	PUNCT
ejpam-6734	468	4	w.	w.	PROPN
ejpam-6734	468	5	m.	m.	PROPN
ejpam-6734	468	6	abd	abd	PROPN
ejpam-6734	468	7	-	-	PUNCT
ejpam-6734	468	8	elhameed	elhameed	PROPN
ejpam-6734	468	9	,	,	PUNCT
ejpam-6734	468	10	m.	m.	NOUN
ejpam-6734	468	11	s.	s.	PROPN
ejpam-6734	468	12	al	al	PROPN
ejpam-6734	468	13	-	-	PUNCT
ejpam-6734	468	14	harbi	harbi	PROPN
ejpam-6734	468	15	,	,	PUNCT
ejpam-6734	468	16	a.	a.	PROPN
ejpam-6734	468	17	k.	k.	PROPN
ejpam-6734	468	18	amin	amin	PROPN
ejpam-6734	468	19	,	,	PUNCT
ejpam-6734	468	20	and	and	CCONJ
ejpam-6734	468	21	h.	h.	PROPN
ejpam-6734	468	22	m.	m.	PROPN
ejpam-6734	468	23	ahmed	ahmed	PROPN
ejpam-6734	468	24	.	.	PUNCT
ejpam-6734	469	1	spectral	spectral	ADJ
ejpam-6734	469	2	treatment	treatment	NOUN
ejpam-6734	469	3	of	of	ADP
ejpam-6734	469	4	high	high	ADJ
ejpam-6734	469	5	-	-	PUNCT
ejpam-6734	469	6	order	order	NOUN
ejpam-6734	469	7	emden	emden	ADJ
ejpam-6734	469	8	–	–	PUNCT
ejpam-6734	469	9	fowler	fowler	PROPN
ejpam-6734	469	10	equations	equation	NOUN
ejpam-6734	469	11	based	base	VERB
ejpam-6734	469	12	on	on	ADP
ejpam-6734	469	13	modified	modify	VERB
ejpam-6734	469	14	chebyshev	chebyshev	NOUN
ejpam-6734	469	15	polynomials	polynomial	NOUN
ejpam-6734	469	16	.	.	PUNCT
ejpam-6734	470	1	axioms	axiom	NOUN
ejpam-6734	470	2	,	,	PUNCT
ejpam-6734	470	3	12(2):99	12(2):99	NUM
ejpam-6734	470	4	,	,	PUNCT
ejpam-6734	470	5	2023	2023	NUM
ejpam-6734	470	6	.	.	PUNCT
ejpam-6734	471	1	[	[	X
ejpam-6734	471	2	26	26	NUM
ejpam-6734	471	3	]	]	PUNCT
ejpam-6734	471	4	a.	a.	NOUN
ejpam-6734	471	5	g.	g.	PROPN
ejpam-6734	471	6	atta	atta	PROPN
ejpam-6734	471	7	.	.	PUNCT
ejpam-6734	472	1	approximate	approximate	ADJ
ejpam-6734	472	2	petrov	petrov	PROPN
ejpam-6734	472	3	–	–	PUNCT
ejpam-6734	472	4	galerkin	galerkin	ADJ
ejpam-6734	472	5	solution	solution	NOUN
ejpam-6734	472	6	for	for	ADP
ejpam-6734	472	7	the	the	DET
ejpam-6734	472	8	time	time	NOUN
ejpam-6734	472	9	fractional	fractional	ADJ
ejpam-6734	472	10	diffusion	diffusion	NOUN
ejpam-6734	472	11	wave	wave	NOUN
ejpam-6734	472	12	equation	equation	NOUN
ejpam-6734	472	13	.	.	PUNCT
ejpam-6734	473	1	mathematical	mathematical	ADJ
ejpam-6734	473	2	methods	method	NOUN
ejpam-6734	473	3	in	in	ADP
ejpam-6734	473	4	the	the	DET
ejpam-6734	473	5	applied	apply	VERB
ejpam-6734	473	6	sciences	science	NOUN
ejpam-6734	473	7	,	,	PUNCT
ejpam-6734	473	8	48(12):11670–11685	48(12):11670–11685	NUM
ejpam-6734	473	9	,	,	PUNCT
ejpam-6734	473	10	2025	2025	NUM
ejpam-6734	473	11	.	.	PUNCT
ejpam-6734	474	1	[	[	X
ejpam-6734	474	2	27	27	NUM
ejpam-6734	474	3	]	]	X
ejpam-6734	474	4	w.	w.	PROPN
ejpam-6734	474	5	m.	m.	PROPN
ejpam-6734	474	6	abd	abd	PROPN
ejpam-6734	474	7	-	-	PUNCT
ejpam-6734	474	8	elhameed	elhameed	PROPN
ejpam-6734	474	9	,	,	PUNCT
ejpam-6734	474	10	m.	m.	NOUN
ejpam-6734	474	11	s.	s.	PROPN
ejpam-6734	474	12	al	al	PROPN
ejpam-6734	474	13	-	-	PUNCT
ejpam-6734	474	14	harbi	harbi	PROPN
ejpam-6734	474	15	,	,	PUNCT
ejpam-6734	474	16	a.	a.	PROPN
ejpam-6734	474	17	k.	k.	PROPN
ejpam-6734	474	18	amin	amin	PROPN
ejpam-6734	474	19	,	,	PUNCT
ejpam-6734	474	20	and	and	CCONJ
ejpam-6734	474	21	h.	h.	PROPN
ejpam-6734	474	22	m.	m.	PROPN
ejpam-6734	474	23	ahmed	ahmed	PROPN
ejpam-6734	474	24	.	.	PUNCT
ejpam-6734	475	1	tau	tau	PROPN
ejpam-6734	475	2	algorithm	algorithm	PROPN
ejpam-6734	475	3	for	for	ADP
ejpam-6734	475	4	fractional	fractional	ADJ
ejpam-6734	475	5	delay	delay	NOUN
ejpam-6734	475	6	differential	differential	ADJ
ejpam-6734	475	7	equations	equation	NOUN
ejpam-6734	475	8	utilizing	utilize	VERB
ejpam-6734	475	9	seventh	seventh	ADJ
ejpam-6734	475	10	-	-	PUNCT
ejpam-6734	475	11	kind	kind	NOUN
ejpam-6734	475	12	chebyshev	chebyshev	NOUN
ejpam-6734	475	13	polynomials	polynomial	NOUN
ejpam-6734	475	14	.	.	PUNCT
ejpam-6734	476	1	journal	journal	PROPN
ejpam-6734	476	2	of	of	ADP
ejpam-6734	476	3	mathematical	mathematical	ADJ
ejpam-6734	476	4	modeling	modeling	NOUN
ejpam-6734	476	5	,	,	PUNCT
ejpam-6734	476	6	12(2):277–299	12(2):277–299	NOUN
ejpam-6734	476	7	,	,	PUNCT
ejpam-6734	476	8	2024	2024	NUM
ejpam-6734	476	9	.	.	PUNCT
ejpam-6734	477	1	[	[	X
ejpam-6734	477	2	28	28	NUM
ejpam-6734	477	3	]	]	X
ejpam-6734	477	4	w.	w.	PROPN
ejpam-6734	477	5	m.	m.	PROPN
ejpam-6734	477	6	abd	abd	PROPN
ejpam-6734	477	7	-	-	PUNCT
ejpam-6734	477	8	elhameed	elhameed	PROPN
ejpam-6734	477	9	,	,	PUNCT
ejpam-6734	477	10	y.	y.	PROPN
ejpam-6734	477	11	h.	h.	PROPN
ejpam-6734	477	12	youssri	youssri	PROPN
ejpam-6734	477	13	,	,	PUNCT
ejpam-6734	477	14	a.	a.	PROPN
ejpam-6734	477	15	k.	k.	PROPN
ejpam-6734	477	16	amin	amin	PROPN
ejpam-6734	477	17	,	,	PUNCT
ejpam-6734	477	18	and	and	CCONJ
ejpam-6734	477	19	a.	a.	NOUN
ejpam-6734	477	20	g.	g.	PROPN
ejpam-6734	477	21	atta	atta	PROPN
ejpam-6734	477	22	.	.	PUNCT
ejpam-6734	478	1	eighth	eighth	ADJ
ejpam-6734	478	2	-	-	PUNCT
ejpam-6734	478	3	kind	kind	NOUN
ejpam-6734	478	4	chebyshev	chebyshev	NOUN
ejpam-6734	478	5	polynomials	polynomial	NOUN
ejpam-6734	478	6	collocation	collocation	NOUN
ejpam-6734	478	7	algorithm	algorithm	NOUN
ejpam-6734	478	8	for	for	ADP
ejpam-6734	478	9	the	the	DET
ejpam-6734	478	10	nonlinear	nonlinear	ADJ
ejpam-6734	478	11	time	time	NOUN
ejpam-6734	478	12	-	-	PUNCT
ejpam-6734	478	13	fractional	fractional	ADJ
ejpam-6734	478	14	generalized	generalized	ADJ
ejpam-6734	478	15	kawahara	kawahara	NOUN
ejpam-6734	478	16	equation	equation	NOUN
ejpam-6734	478	17	.	.	PUNCT
ejpam-6734	479	1	fractal	fractal	PROPN
ejpam-6734	479	2	and	and	CCONJ
ejpam-6734	479	3	fractional	fractional	ADJ
ejpam-6734	479	4	,	,	PUNCT
ejpam-6734	479	5	7:652	7:652	NUM
ejpam-6734	479	6	,	,	PUNCT
ejpam-6734	479	7	2023	2023	NUM
ejpam-6734	479	8	.	.	PUNCT
ejpam-6734	480	1	[	[	X
ejpam-6734	480	2	29	29	NUM
ejpam-6734	480	3	]	]	X
ejpam-6734	480	4	y.	y.	PROPN
ejpam-6734	480	5	h.	h.	PROPN
ejpam-6734	480	6	youssri	youssri	PROPN
ejpam-6734	480	7	,	,	PUNCT
ejpam-6734	480	8	m.	m.	PROPN
ejpam-6734	480	9	i.	i.	PROPN
ejpam-6734	480	10	ismail	ismail	PROPN
ejpam-6734	480	11	,	,	PUNCT
ejpam-6734	480	12	and	and	CCONJ
ejpam-6734	480	13	a.	a.	NOUN
ejpam-6734	480	14	g.	g.	PROPN
ejpam-6734	480	15	atta	atta	PROPN
ejpam-6734	480	16	.	.	PUNCT
ejpam-6734	481	1	chebyshev	chebyshev	PROPN
ejpam-6734	481	2	petrov	petrov	PROPN
ejpam-6734	481	3	-	-	PUNCT
ejpam-6734	481	4	galerkin	galerkin	ADJ
ejpam-6734	481	5	procedure	procedure	NOUN
ejpam-6734	481	6	for	for	ADP
ejpam-6734	481	7	the	the	DET
ejpam-6734	481	8	time	time	NOUN
ejpam-6734	481	9	-	-	PUNCT
ejpam-6734	481	10	fractional	fractional	ADJ
ejpam-6734	481	11	heat	heat	NOUN
ejpam-6734	481	12	equation	equation	NOUN
ejpam-6734	481	13	with	with	ADP
ejpam-6734	481	14	nonlocal	nonlocal	ADJ
ejpam-6734	481	15	conditions	condition	NOUN
ejpam-6734	481	16	.	.	PUNCT
ejpam-6734	482	1	physica	physica	PROPN
ejpam-6734	482	2	scripta	scripta	PROPN
ejpam-6734	482	3	,	,	PUNCT
ejpam-6734	482	4	99(1):015251	99(1):015251	NUM
ejpam-6734	482	5	,	,	PUNCT
ejpam-6734	482	6	2023	2023	NUM
ejpam-6734	482	7	.	.	PUNCT
ejpam-6734	483	1	[	[	X
ejpam-6734	483	2	30	30	NUM
ejpam-6734	483	3	]	]	X
ejpam-6734	483	4	w.	w.	PROPN
ejpam-6734	483	5	m.	m.	PROPN
ejpam-6734	483	6	abd	abd	PROPN
ejpam-6734	483	7	-	-	PUNCT
ejpam-6734	483	8	elhameed	elhameed	PROPN
ejpam-6734	483	9	and	and	CCONJ
ejpam-6734	483	10	y.	y.	PROPN
ejpam-6734	483	11	h.	h.	PROPN
ejpam-6734	483	12	youssri	youssri	PROPN
ejpam-6734	483	13	.	.	PUNCT
ejpam-6734	484	1	spectral	spectral	ADJ
ejpam-6734	484	2	tau	tau	PROPN
ejpam-6734	484	3	algorithm	algorithm	NOUN
ejpam-6734	484	4	for	for	ADP
ejpam-6734	484	5	certain	certain	ADJ
ejpam-6734	484	6	coupled	couple	VERB
ejpam-6734	484	7	system	system	NOUN
ejpam-6734	484	8	of	of	ADP
ejpam-6734	484	9	fractional	fractional	ADJ
ejpam-6734	484	10	differential	differential	ADJ
ejpam-6734	484	11	equations	equation	NOUN
ejpam-6734	484	12	via	via	ADP
ejpam-6734	484	13	generalized	generalized	ADJ
ejpam-6734	484	14	fibonacci	fibonacci	NOUN
ejpam-6734	484	15	polynomial	polynomial	PROPN
ejpam-6734	484	16	m.	m.	PROPN
ejpam-6734	484	17	a.	a.	PROPN
ejpam-6734	484	18	abdou	abdou	PROPN
ejpam-6734	484	19	,	,	PUNCT
ejpam-6734	484	20	a.	a.	PROPN
ejpam-6734	484	21	s.	s.	PROPN
ejpam-6734	484	22	mohamed	mohamed	PROPN
ejpam-6734	484	23	/	/	SYM
ejpam-6734	484	24	eur	eur	PROPN
ejpam-6734	484	25	.	.	PUNCT
ejpam-6734	485	1	j.	j.	PROPN
ejpam-6734	485	2	pure	pure	PROPN
ejpam-6734	485	3	appl	appl	PROPN
ejpam-6734	485	4	.	.	PROPN
ejpam-6734	485	5	math	math	PROPN
ejpam-6734	485	6	,	,	PUNCT
ejpam-6734	485	7	18	18	NUM
ejpam-6734	485	8	(	(	PUNCT
ejpam-6734	485	9	4	4	NUM
ejpam-6734	485	10	)	)	PUNCT
ejpam-6734	485	11	(	(	PUNCT
ejpam-6734	485	12	2025	2025	NUM
ejpam-6734	485	13	)	)	PUNCT
ejpam-6734	485	14	,	,	PUNCT
ejpam-6734	485	15	6734	6734	NUM
ejpam-6734	485	16	20	20	NUM
ejpam-6734	485	17	of	of	ADP
ejpam-6734	485	18	20	20	NUM
ejpam-6734	485	19	sequence	sequence	NOUN
ejpam-6734	485	20	.	.	PUNCT
ejpam-6734	486	1	iranian	iranian	ADJ
ejpam-6734	486	2	journal	journal	PROPN
ejpam-6734	486	3	of	of	ADP
ejpam-6734	486	4	science	science	NOUN
ejpam-6734	486	5	and	and	CCONJ
ejpam-6734	486	6	technology	technology	NOUN
ejpam-6734	486	7	,	,	PUNCT
ejpam-6734	486	8	transaction	transaction	NOUN
ejpam-6734	486	9	a	a	DET
ejpam-6734	486	10	:	:	PUNCT
ejpam-6734	486	11	science	science	NOUN
ejpam-6734	486	12	,	,	PUNCT
ejpam-6734	486	13	2017	2017	NUM
ejpam-6734	486	14	.	.	PUNCT
ejpam-6734	487	1	[	[	X
ejpam-6734	487	2	31	31	NUM
ejpam-6734	487	3	]	]	PUNCT
ejpam-6734	487	4	a.	a.	PROPN
ejpam-6734	487	5	s.	s.	PROPN
ejpam-6734	487	6	mohamed	mohamed	PROPN
ejpam-6734	487	7	.	.	PUNCT
ejpam-6734	488	1	fibonacci	fibonacci	NOUN
ejpam-6734	488	2	collocation	collocation	NOUN
ejpam-6734	488	3	pseudo	pseudo	NOUN
ejpam-6734	488	4	-	-	ADJ
ejpam-6734	488	5	spectral	spectral	ADJ
ejpam-6734	488	6	method	method	NOUN
ejpam-6734	488	7	of	of	ADP
ejpam-6734	488	8	variable	variable	ADJ
ejpam-6734	488	9	-	-	PUNCT
ejpam-6734	488	10	order	order	NOUN
ejpam-6734	488	11	space	space	NOUN
ejpam-6734	488	12	-	-	PUNCT
ejpam-6734	488	13	fractional	fractional	ADJ
ejpam-6734	488	14	diffusion	diffusion	NOUN
ejpam-6734	488	15	equations	equation	NOUN
ejpam-6734	488	16	with	with	ADP
ejpam-6734	488	17	error	error	NOUN
ejpam-6734	488	18	analysis	analysis	NOUN
ejpam-6734	488	19	.	.	PUNCT
ejpam-6734	489	1	mathematics	mathematic	NOUN
ejpam-6734	489	2	,	,	PUNCT
ejpam-6734	489	3	7(8):14323	7(8):14323	NUM
ejpam-6734	489	4	–	–	PUNCT
ejpam-6734	489	5	14337	14337	NUM
ejpam-6734	489	6	,	,	PUNCT
ejpam-6734	489	7	2022	2022	NUM
ejpam-6734	489	8	.	.	PUNCT
ejpam-6734	490	1	[	[	X
ejpam-6734	490	2	32	32	NUM
ejpam-6734	490	3	]	]	PUNCT
ejpam-6734	490	4	w.	w.	PROPN
ejpam-6734	490	5	m.	m.	PROPN
ejpam-6734	490	6	abd	abd	PROPN
ejpam-6734	490	7	-	-	PUNCT
ejpam-6734	490	8	elhameed	elhameed	PROPN
ejpam-6734	490	9	,	,	PUNCT
ejpam-6734	490	10	e.	e.	PROPN
ejpam-6734	490	11	h.	h.	PROPN
ejpam-6734	490	12	doha	doha	PROPN
ejpam-6734	490	13	,	,	PUNCT
ejpam-6734	490	14	and	and	CCONJ
ejpam-6734	490	15	y.	y.	PROPN
ejpam-6734	490	16	h.	h.	PROPN
ejpam-6734	490	17	youssri	youssri	PROPN
ejpam-6734	490	18	.	.	PUNCT
ejpam-6734	491	1	new	new	ADJ
ejpam-6734	491	2	spectral	spectral	ADJ
ejpam-6734	491	3	second	second	ADJ
ejpam-6734	491	4	kind	kind	NOUN
ejpam-6734	491	5	chebyshev	chebyshev	NOUN
ejpam-6734	491	6	wavelets	wavelet	NOUN
ejpam-6734	491	7	algorithm	algorithm	NOUN
ejpam-6734	491	8	for	for	ADP
ejpam-6734	491	9	solving	solve	VERB
ejpam-6734	491	10	linear	linear	NOUN
ejpam-6734	491	11	and	and	CCONJ
ejpam-6734	491	12	nonlinear	nonlinear	ADJ
ejpam-6734	491	13	second	second	ADJ
ejpam-6734	491	14	-	-	PUNCT
ejpam-6734	491	15	order	order	NOUN
ejpam-6734	491	16	differential	differential	ADJ
ejpam-6734	491	17	equations	equation	NOUN
ejpam-6734	491	18	involving	involve	VERB
ejpam-6734	491	19	singular	singular	NOUN
ejpam-6734	491	20	and	and	CCONJ
ejpam-6734	491	21	bratu	bratu	NOUN
ejpam-6734	491	22	type	type	NOUN
ejpam-6734	491	23	equations	equation	NOUN
ejpam-6734	491	24	.	.	PUNCT
ejpam-6734	492	1	abstract	abstract	ADJ
ejpam-6734	492	2	and	and	CCONJ
ejpam-6734	492	3	applied	apply	VERB
ejpam-6734	492	4	analysis	analysis	NOUN
ejpam-6734	492	5	,	,	PUNCT
ejpam-6734	492	6	2013:9	2013:9	NUM
ejpam-6734	492	7	,	,	PUNCT
ejpam-6734	492	8	2013	2013	NUM
ejpam-6734	492	9	.	.	PUNCT
ejpam-6734	493	1	article	article	NOUN
ejpam-6734	493	2	i	i	PROPN
ejpam-6734	493	3	d	d	PROPN
ejpam-6734	493	4	715756	715756	NUM
ejpam-6734	493	5	.	.	PUNCT
ejpam-6734	494	1	[	[	X
ejpam-6734	494	2	33	33	NUM
ejpam-6734	494	3	]	]	PUNCT
ejpam-6734	494	4	k.	k.	PROPN
ejpam-6734	494	5	al	al	PROPN
ejpam-6734	494	6	-	-	PUNCT
ejpam-6734	494	7	khaled	khaled	PROPN
ejpam-6734	494	8	and	and	CCONJ
ejpam-6734	494	9	m.	m.	PROPN
ejpam-6734	494	10	n.	n.	PROPN
ejpam-6734	494	11	anwar	anwar	PROPN
ejpam-6734	494	12	.	.	PUNCT
ejpam-6734	495	1	numerical	numerical	PROPN
ejpam-6734	495	2	comparison	comparison	NOUN
ejpam-6734	495	3	of	of	ADP
ejpam-6734	495	4	methods	method	NOUN
ejpam-6734	495	5	for	for	ADP
ejpam-6734	495	6	solving	solve	VERB
ejpam-6734	495	7	secondorder	secondorder	ADJ
ejpam-6734	495	8	ordinary	ordinary	ADJ
ejpam-6734	495	9	initial	initial	ADJ
ejpam-6734	495	10	value	value	NOUN
ejpam-6734	495	11	problems	problem	NOUN
ejpam-6734	495	12	.	.	PUNCT
ejpam-6734	496	1	applied	apply	VERB
ejpam-6734	496	2	mathematical	mathematical	ADJ
ejpam-6734	496	3	modeling	modeling	NOUN
ejpam-6734	496	4	,	,	PUNCT
ejpam-6734	496	5	31:292–301	31:292–301	PROPN
ejpam-6734	496	6	,	,	PUNCT
ejpam-6734	496	7	2007	2007	NUM
ejpam-6734	496	8	.	.	PUNCT
ejpam-6734	497	1	[	[	X
ejpam-6734	497	2	34	34	NUM
ejpam-6734	497	3	]	]	X
ejpam-6734	497	4	s.	s.	PROPN
ejpam-6734	497	5	g.	g.	PROPN
ejpam-6734	497	6	venkatesh	venkatesh	PROPN
ejpam-6734	497	7	,	,	PUNCT
ejpam-6734	497	8	s.	s.	PROPN
ejpam-6734	497	9	k.	k.	PROPN
ejpam-6734	497	10	ayyaswamy	ayyaswamy	PROPN
ejpam-6734	497	11	,	,	PUNCT
ejpam-6734	497	12	and	and	CCONJ
ejpam-6734	497	13	s.	s.	PROPN
ejpam-6734	497	14	balachandar	balachandar	PROPN
ejpam-6734	497	15	.	.	PUNCT
ejpam-6734	498	1	the	the	DET
ejpam-6734	498	2	legendre	legendre	PROPN
ejpam-6734	498	3	wavelet	wavelet	PROPN
ejpam-6734	498	4	method	method	NOUN
ejpam-6734	498	5	for	for	ADP
ejpam-6734	498	6	solving	solve	VERB
ejpam-6734	498	7	initial	initial	ADJ
ejpam-6734	498	8	value	value	NOUN
ejpam-6734	498	9	problems	problem	NOUN
ejpam-6734	498	10	of	of	ADP
ejpam-6734	498	11	bratu	bratu	NOUN
ejpam-6734	498	12	-	-	PUNCT
ejpam-6734	498	13	type	type	NOUN
ejpam-6734	498	14	.	.	PUNCT
ejpam-6734	499	1	computers	computer	NOUN
ejpam-6734	499	2	and	and	CCONJ
ejpam-6734	499	3	mathematics	mathematic	NOUN
ejpam-6734	499	4	with	with	ADP
ejpam-6734	499	5	applications	application	NOUN
ejpam-6734	499	6	,	,	PUNCT
ejpam-6734	499	7	63:1287–1295	63:1287–1295	NUM
ejpam-6734	499	8	,	,	PUNCT
ejpam-6734	499	9	2012	2012	NUM
ejpam-6734	499	10	.	.	PUNCT