id	sid	tid	token	lemma	pos
ejpam-5049	1	1	european	european	PROPN
ejpam-5049	1	2	journal	journal	PROPN
ejpam-5049	1	3	of	of	ADP
ejpam-5049	1	4	pure	pure	ADJ
ejpam-5049	1	5	and	and	CCONJ
ejpam-5049	1	6	applied	apply	VERB
ejpam-5049	1	7	mathematics	mathematic	NOUN
ejpam-5049	1	8	vol	vol	NOUN
ejpam-5049	1	9	.	.	PROPN
ejpam-5049	2	1	17	17	NUM
ejpam-5049	2	2	,	,	PUNCT
ejpam-5049	2	3	no	no	INTJ
ejpam-5049	2	4	.	.	NOUN
ejpam-5049	2	5	1	1	NUM
ejpam-5049	2	6	,	,	PUNCT
ejpam-5049	2	7	2024	2024	NUM
ejpam-5049	2	8	,	,	PUNCT
ejpam-5049	2	9	477	477	NUM
ejpam-5049	2	10	-	-	SYM
ejpam-5049	2	11	503	503	NUM
ejpam-5049	2	12	issn	issn	PROPN
ejpam-5049	2	13	1307	1307	NUM
ejpam-5049	2	14	-	-	SYM
ejpam-5049	2	15	5543	5543	NUM
ejpam-5049	2	16	–	–	PUNCT
ejpam-5049	3	1	ejpam.com	ejpam.com	X
ejpam-5049	3	2	published	publish	VERB
ejpam-5049	3	3	by	by	ADP
ejpam-5049	3	4	new	new	PROPN
ejpam-5049	3	5	york	york	PROPN
ejpam-5049	3	6	business	business	PROPN
ejpam-5049	3	7	global	global	PROPN
ejpam-5049	3	8	a	a	DET
ejpam-5049	3	9	spectral	spectral	ADJ
ejpam-5049	3	10	collocation	collocation	NOUN
ejpam-5049	3	11	method	method	NOUN
ejpam-5049	3	12	for	for	ADP
ejpam-5049	3	13	solving	solve	VERB
ejpam-5049	3	14	caputo	caputo	PROPN
ejpam-5049	3	15	-	-	PUNCT
ejpam-5049	3	16	liouville	liouville	VERB
ejpam-5049	3	17	fractional	fractional	ADJ
ejpam-5049	3	18	order	order	NOUN
ejpam-5049	3	19	fredholm	fredholm	NOUN
ejpam-5049	3	20	integro	integro	ADJ
ejpam-5049	3	21	-	-	PUNCT
ejpam-5049	3	22	differential	differential	NOUN
ejpam-5049	3	23	equations	equation	NOUN
ejpam-5049	3	24	khaled	khaled	PROPN
ejpam-5049	3	25	m.	m.	PROPN
ejpam-5049	3	26	saad1,2	saad1,2	PROPN
ejpam-5049	3	27	,	,	PUNCT
ejpam-5049	3	28	m.	m.	PROPN
ejpam-5049	3	29	q.	q.	PROPN
ejpam-5049	3	30	khirallah1,3,∗	khirallah1,3,∗	PROPN
ejpam-5049	3	31	1	1	NUM
ejpam-5049	3	32	department	department	NOUN
ejpam-5049	3	33	of	of	ADP
ejpam-5049	3	34	mathematics	mathematic	NOUN
ejpam-5049	3	35	,	,	PUNCT
ejpam-5049	3	36	college	college	NOUN
ejpam-5049	3	37	of	of	ADP
ejpam-5049	3	38	sciences	science	NOUN
ejpam-5049	3	39	and	and	CCONJ
ejpam-5049	3	40	arts	art	NOUN
ejpam-5049	3	41	,	,	PUNCT
ejpam-5049	3	42	najran	najran	ADJ
ejpam-5049	3	43	university	university	NOUN
ejpam-5049	3	44	,	,	PUNCT
ejpam-5049	3	45	najran	najran	NOUN
ejpam-5049	3	46	,	,	PUNCT
ejpam-5049	3	47	state	state	NOUN
ejpam-5049	3	48	,	,	PUNCT
ejpam-5049	3	49	saudi	saudi	PROPN
ejpam-5049	3	50	arabia	arabia	PROPN
ejpam-5049	3	51	2	2	NUM
ejpam-5049	3	52	department	department	NOUN
ejpam-5049	3	53	of	of	ADP
ejpam-5049	3	54	mathematics	mathematic	NOUN
ejpam-5049	3	55	,	,	PUNCT
ejpam-5049	3	56	faculty	faculty	NOUN
ejpam-5049	3	57	of	of	ADP
ejpam-5049	3	58	applied	apply	VERB
ejpam-5049	3	59	science	science	NOUN
ejpam-5049	3	60	,	,	PUNCT
ejpam-5049	3	61	taiz	taiz	PROPN
ejpam-5049	3	62	university	university	NOUN
ejpam-5049	3	63	,	,	PUNCT
ejpam-5049	3	64	taiz	taiz	PROPN
ejpam-5049	3	65	,	,	PUNCT
ejpam-5049	3	66	yemen	yemen	PROPN
ejpam-5049	3	67	3	3	NUM
ejpam-5049	3	68	department	department	NOUN
ejpam-5049	3	69	of	of	ADP
ejpam-5049	3	70	mathematics	mathematic	NOUN
ejpam-5049	3	71	and	and	CCONJ
ejpam-5049	3	72	computer	computer	NOUN
ejpam-5049	3	73	science	science	NOUN
ejpam-5049	3	74	,	,	PUNCT
ejpam-5049	3	75	faculty	faculty	NOUN
ejpam-5049	3	76	of	of	ADP
ejpam-5049	3	77	science	science	NOUN
ejpam-5049	3	78	,	,	PUNCT
ejpam-5049	3	79	ibb	ibb	PROPN
ejpam-5049	3	80	university	university	NOUN
ejpam-5049	3	81	,	,	PUNCT
ejpam-5049	3	82	ibb	ibb	NOUN
ejpam-5049	3	83	,	,	PUNCT
ejpam-5049	3	84	yemen	yemen	PROPN
ejpam-5049	3	85	abstract	abstract	NOUN
ejpam-5049	3	86	.	.	PUNCT
ejpam-5049	4	1	in	in	ADP
ejpam-5049	4	2	this	this	DET
ejpam-5049	4	3	paper	paper	NOUN
ejpam-5049	4	4	,	,	PUNCT
ejpam-5049	4	5	a	a	DET
ejpam-5049	4	6	numerical	numerical	ADJ
ejpam-5049	4	7	method	method	NOUN
ejpam-5049	4	8	for	for	ADP
ejpam-5049	4	9	solving	solve	VERB
ejpam-5049	4	10	the	the	DET
ejpam-5049	4	11	fractional	fractional	ADJ
ejpam-5049	4	12	order	order	NOUN
ejpam-5049	4	13	fredholm	fredholm	NOUN
ejpam-5049	4	14	integrodifferential	integrodifferential	ADJ
ejpam-5049	4	15	equations	equation	NOUN
ejpam-5049	4	16	via	via	ADP
ejpam-5049	4	17	the	the	DET
ejpam-5049	4	18	caputo	caputo	PROPN
ejpam-5049	4	19	-	-	PUNCT
ejpam-5049	4	20	liouville	liouville	PROPN
ejpam-5049	4	21	derivative	derivative	NOUN
ejpam-5049	4	22	is	be	AUX
ejpam-5049	4	23	presented	present	VERB
ejpam-5049	4	24	.	.	PUNCT
ejpam-5049	5	1	the	the	DET
ejpam-5049	5	2	method	method	NOUN
ejpam-5049	5	3	uses	use	VERB
ejpam-5049	5	4	the	the	DET
ejpam-5049	5	5	wellknown	wellknown	NOUN
ejpam-5049	5	6	shifted	shift	VERB
ejpam-5049	5	7	chebyshev	chebyshev	NOUN
ejpam-5049	5	8	expansion	expansion	NOUN
ejpam-5049	5	9	and	and	CCONJ
ejpam-5049	5	10	a	a	DET
ejpam-5049	5	11	truncated	truncated	ADJ
ejpam-5049	5	12	series	series	NOUN
ejpam-5049	5	13	to	to	PART
ejpam-5049	5	14	represent	represent	VERB
ejpam-5049	5	15	the	the	DET
ejpam-5049	5	16	unknown	unknown	ADJ
ejpam-5049	5	17	function	function	NOUN
ejpam-5049	5	18	.	.	PUNCT
ejpam-5049	6	1	it	it	PRON
ejpam-5049	6	2	also	also	ADV
ejpam-5049	6	3	incorporates	incorporate	VERB
ejpam-5049	6	4	numerical	numerical	ADJ
ejpam-5049	6	5	integration	integration	NOUN
ejpam-5049	6	6	techniques	technique	NOUN
ejpam-5049	6	7	like	like	ADP
ejpam-5049	6	8	the	the	DET
ejpam-5049	6	9	trapezoidal	trapezoidal	NOUN
ejpam-5049	6	10	,	,	PUNCT
ejpam-5049	6	11	simpson	simpson	PROPN
ejpam-5049	6	12	’s	’s	PART
ejpam-5049	6	13	1/3	1/3	NUM
ejpam-5049	6	14	,	,	PUNCT
ejpam-5049	6	15	and	and	CCONJ
ejpam-5049	6	16	simpson	simpson	PROPN
ejpam-5049	6	17	’s	’s	PART
ejpam-5049	6	18	8/3	8/3	NUM
ejpam-5049	6	19	methods	method	NOUN
ejpam-5049	6	20	.	.	PUNCT
ejpam-5049	7	1	the	the	DET
ejpam-5049	7	2	paper	paper	NOUN
ejpam-5049	7	3	also	also	ADV
ejpam-5049	7	4	provides	provide	VERB
ejpam-5049	7	5	an	an	DET
ejpam-5049	7	6	approximation	approximation	NOUN
ejpam-5049	7	7	for	for	ADP
ejpam-5049	7	8	the	the	DET
ejpam-5049	7	9	derivative	derivative	NOUN
ejpam-5049	7	10	of	of	ADP
ejpam-5049	7	11	an	an	DET
ejpam-5049	7	12	integer	integer	NOUN
ejpam-5049	7	13	.	.	PUNCT
ejpam-5049	8	1	the	the	DET
ejpam-5049	8	2	procedure	procedure	NOUN
ejpam-5049	8	3	converts	convert	VERB
ejpam-5049	8	4	the	the	DET
ejpam-5049	8	5	provided	provide	VERB
ejpam-5049	8	6	problem	problem	NOUN
ejpam-5049	8	7	into	into	ADP
ejpam-5049	8	8	a	a	DET
ejpam-5049	8	9	system	system	NOUN
ejpam-5049	8	10	of	of	ADP
ejpam-5049	8	11	algebraic	algebraic	ADJ
ejpam-5049	8	12	equations	equation	NOUN
ejpam-5049	8	13	using	use	VERB
ejpam-5049	8	14	shifted	shift	VERB
ejpam-5049	8	15	chebyshev	chebyshev	NOUN
ejpam-5049	8	16	coefficients	coefficient	NOUN
ejpam-5049	8	17	and	and	CCONJ
ejpam-5049	8	18	collocation	collocation	NOUN
ejpam-5049	8	19	points	point	NOUN
ejpam-5049	8	20	.	.	PUNCT
ejpam-5049	9	1	the	the	DET
ejpam-5049	9	2	coefficients	coefficient	NOUN
ejpam-5049	9	3	are	be	AUX
ejpam-5049	9	4	found	find	VERB
ejpam-5049	9	5	by	by	ADP
ejpam-5049	9	6	solving	solve	VERB
ejpam-5049	9	7	this	this	DET
ejpam-5049	9	8	system	system	NOUN
ejpam-5049	9	9	using	use	VERB
ejpam-5049	9	10	well	well	ADV
ejpam-5049	9	11	-	-	PUNCT
ejpam-5049	9	12	known	know	VERB
ejpam-5049	9	13	techniques	technique	NOUN
ejpam-5049	9	14	like	like	ADP
ejpam-5049	9	15	newton	newton	PROPN
ejpam-5049	9	16	’s	’s	PART
ejpam-5049	9	17	method	method	PROPN
ejpam-5049	9	18	.	.	PUNCT
ejpam-5049	10	1	numerical	numerical	ADJ
ejpam-5049	10	2	results	result	NOUN
ejpam-5049	10	3	are	be	AUX
ejpam-5049	10	4	presented	present	VERB
ejpam-5049	10	5	graphycally	graphycally	ADV
ejpam-5049	10	6	to	to	PART
ejpam-5049	10	7	illustrate	illustrate	VERB
ejpam-5049	10	8	the	the	DET
ejpam-5049	10	9	applicability	applicability	NOUN
ejpam-5049	10	10	,	,	PUNCT
ejpam-5049	10	11	efficacy	efficacy	NOUN
ejpam-5049	10	12	,	,	PUNCT
ejpam-5049	10	13	and	and	CCONJ
ejpam-5049	10	14	accuracy	accuracy	NOUN
ejpam-5049	10	15	of	of	ADP
ejpam-5049	10	16	the	the	DET
ejpam-5049	10	17	approach	approach	NOUN
ejpam-5049	10	18	presented	present	VERB
ejpam-5049	10	19	in	in	ADP
ejpam-5049	10	20	this	this	DET
ejpam-5049	10	21	work	work	NOUN
ejpam-5049	10	22	.	.	PUNCT
ejpam-5049	11	1	all	all	DET
ejpam-5049	11	2	calculations	calculation	NOUN
ejpam-5049	11	3	in	in	ADP
ejpam-5049	11	4	this	this	DET
ejpam-5049	11	5	study	study	NOUN
ejpam-5049	11	6	were	be	AUX
ejpam-5049	11	7	performed	perform	VERB
ejpam-5049	11	8	using	use	VERB
ejpam-5049	11	9	the	the	DET
ejpam-5049	11	10	mathematica	mathematica	PROPN
ejpam-5049	11	11	software	software	PROPN
ejpam-5049	11	12	program	program	PROPN
ejpam-5049	11	13	.	.	PUNCT
ejpam-5049	12	1	2020	2020	NUM
ejpam-5049	12	2	mathematics	mathematics	PROPN
ejpam-5049	12	3	subject	subject	NOUN
ejpam-5049	12	4	classifications	classification	NOUN
ejpam-5049	12	5	:	:	PUNCT
ejpam-5049	12	6	74sxx	74sxx	NOUN
ejpam-5049	12	7	,	,	PUNCT
ejpam-5049	12	8	97nxx	97nxx	VERB
ejpam-5049	12	9	key	key	ADJ
ejpam-5049	12	10	words	word	NOUN
ejpam-5049	12	11	and	and	CCONJ
ejpam-5049	12	12	phrases	phrase	NOUN
ejpam-5049	12	13	:	:	PUNCT
ejpam-5049	12	14	fractional	fractional	ADJ
ejpam-5049	12	15	order	order	NOUN
ejpam-5049	12	16	integro	integro	ADJ
ejpam-5049	12	17	-	-	PUNCT
ejpam-5049	12	18	differential	differential	NOUN
ejpam-5049	12	19	equations	equation	NOUN
ejpam-5049	12	20	,	,	PUNCT
ejpam-5049	12	21	caputo	caputo	PROPN
ejpam-5049	12	22	type	type	NOUN
ejpam-5049	12	23	fractional	fractional	PROPN
ejpam-5049	12	24	derivative	derivative	NOUN
ejpam-5049	12	25	,	,	PUNCT
ejpam-5049	12	26	the	the	DET
ejpam-5049	12	27	shifted	shift	VERB
ejpam-5049	12	28	chebyshev	chebyshev	PROPN
ejpam-5049	12	29	spectral	spectral	ADJ
ejpam-5049	12	30	collocation	collocation	NOUN
ejpam-5049	12	31	method	method	NOUN
ejpam-5049	12	32	,	,	PUNCT
ejpam-5049	12	33	trapezoidal	trapezoidal	NOUN
ejpam-5049	12	34	,	,	PUNCT
ejpam-5049	12	35	simpson	simpson	PROPN
ejpam-5049	12	36	1	1	NUM
ejpam-5049	12	37	.	.	PUNCT
ejpam-5049	12	38	introduction	introduction	NOUN
ejpam-5049	12	39	a	a	DET
ejpam-5049	12	40	subfield	subfield	NOUN
ejpam-5049	12	41	of	of	ADP
ejpam-5049	12	42	mathematics	mathematic	NOUN
ejpam-5049	12	43	known	know	VERB
ejpam-5049	12	44	as	as	ADP
ejpam-5049	12	45	fractional	fractional	ADJ
ejpam-5049	12	46	calculus	calculus	NOUN
ejpam-5049	12	47	extends	extend	VERB
ejpam-5049	12	48	the	the	DET
ejpam-5049	12	49	idea	idea	NOUN
ejpam-5049	12	50	of	of	ADP
ejpam-5049	12	51	derivatives	derivative	NOUN
ejpam-5049	12	52	and	and	CCONJ
ejpam-5049	12	53	integrals	integral	NOUN
ejpam-5049	12	54	to	to	ADP
ejpam-5049	12	55	non	non	ADJ
ejpam-5049	12	56	-	-	ADJ
ejpam-5049	12	57	integer	integer	ADJ
ejpam-5049	12	58	orders	order	NOUN
ejpam-5049	12	59	.	.	PUNCT
ejpam-5049	13	1	fractional	fractional	ADJ
ejpam-5049	13	2	calculus	calculus	NOUN
ejpam-5049	13	3	uses	use	VERB
ejpam-5049	13	4	fractional	fractional	ADJ
ejpam-5049	13	5	or	or	CCONJ
ejpam-5049	13	6	real	real	ADJ
ejpam-5049	13	7	numbers	number	NOUN
ejpam-5049	13	8	for	for	ADP
ejpam-5049	13	9	the	the	DET
ejpam-5049	13	10	order	order	NOUN
ejpam-5049	13	11	of	of	ADP
ejpam-5049	13	12	differentiation	differentiation	NOUN
ejpam-5049	13	13	or	or	CCONJ
ejpam-5049	13	14	integration	integration	NOUN
ejpam-5049	13	15	rather	rather	ADV
ejpam-5049	13	16	than	than	ADP
ejpam-5049	13	17	whole	whole	ADJ
ejpam-5049	13	18	numbers	number	NOUN
ejpam-5049	13	19	.	.	PUNCT
ejpam-5049	14	1	fractional	fractional	ADJ
ejpam-5049	14	2	derivatives	derivative	NOUN
ejpam-5049	14	3	and	and	CCONJ
ejpam-5049	14	4	fractional	fractional	ADJ
ejpam-5049	14	5	integrals	integral	NOUN
ejpam-5049	14	6	are	be	AUX
ejpam-5049	14	7	two	two	NUM
ejpam-5049	14	8	important	important	ADJ
ejpam-5049	14	9	ideas	idea	NOUN
ejpam-5049	14	10	in	in	ADP
ejpam-5049	14	11	fractional	fractional	ADJ
ejpam-5049	14	12	calculus	calculus	NOUN
ejpam-5049	14	13	.	.	PUNCT
ejpam-5049	15	1	the	the	DET
ejpam-5049	15	2	rate	rate	NOUN
ejpam-5049	15	3	at	at	ADP
ejpam-5049	15	4	which	which	PRON
ejpam-5049	15	5	a	a	DET
ejpam-5049	15	6	function	function	NOUN
ejpam-5049	15	7	changes	change	VERB
ejpam-5049	15	8	in	in	ADP
ejpam-5049	15	9	relation	relation	NOUN
ejpam-5049	15	10	to	to	ADP
ejpam-5049	15	11	a	a	DET
ejpam-5049	15	12	variable	variable	NOUN
ejpam-5049	15	13	of	of	ADP
ejpam-5049	15	14	order	order	NOUN
ejpam-5049	15	15	α	α	NOUN
ejpam-5049	15	16	is	be	AUX
ejpam-5049	15	17	represented	represent	VERB
ejpam-5049	15	18	by	by	ADP
ejpam-5049	15	19	dα	dα	NOUN
ejpam-5049	15	20	,	,	PUNCT
ejpam-5049	15	21	the	the	DET
ejpam-5049	15	22	fractional	fractional	ADJ
ejpam-5049	15	23	derivative	derivative	NOUN
ejpam-5049	15	24	of	of	ADP
ejpam-5049	15	25	the	the	DET
ejpam-5049	15	26	function	function	NOUN
ejpam-5049	15	27	.	.	PUNCT
ejpam-5049	16	1	similar	similar	ADJ
ejpam-5049	16	2	to	to	ADP
ejpam-5049	16	3	this	this	PRON
ejpam-5049	16	4	,	,	PUNCT
ejpam-5049	16	5	a	a	DET
ejpam-5049	16	6	generalization	generalization	NOUN
ejpam-5049	16	7	of	of	ADP
ejpam-5049	16	8	integration	integration	NOUN
ejpam-5049	16	9	is	be	AUX
ejpam-5049	16	10	∗corresponding	∗corresponde	VERB
ejpam-5049	16	11	author	author	NOUN
ejpam-5049	16	12	.	.	PUNCT
ejpam-5049	17	1	doi	doi	NOUN
ejpam-5049	17	2	:	:	PUNCT
ejpam-5049	17	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5049	https://doi.org/10.29020/nybg.ejpam.v17i1.5049	NUM
ejpam-5049	17	4	email	email	NOUN
ejpam-5049	17	5	addresses	address	VERB
ejpam-5049	17	6	:	:	PUNCT
ejpam-5049	18	1	khaledmasd@hotmail.com	khaledmasd@hotmail.com	PROPN
ejpam-5049	18	2	(	(	PUNCT
ejpam-5049	18	3	k.m.saad	k.m.saad	PROPN
ejpam-5049	18	4	)	)	PUNCT
ejpam-5049	18	5	,	,	PUNCT
ejpam-5049	18	6	mqm73@yahoo.com	mqm73@yahoo.com	X
ejpam-5049	18	7	(	(	PUNCT
ejpam-5049	18	8	m.q.khirallah	m.q.khirallah	PROPN
ejpam-5049	18	9	)	)	PUNCT
ejpam-5049	18	10	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5049	18	11	477	477	NUM
ejpam-5049	18	12	©	©	ADP
ejpam-5049	18	13	2024	2024	NUM
ejpam-5049	18	14	ejpam	ejpam	NOUN
ejpam-5049	18	15	all	all	DET
ejpam-5049	18	16	rights	right	NOUN
ejpam-5049	18	17	reserved	reserve	VERB
ejpam-5049	18	18	.	.	PUNCT
ejpam-5049	19	1	khaled	khaled	PROPN
ejpam-5049	19	2	m.	m.	PROPN
ejpam-5049	19	3	saad	saad	PROPN
ejpam-5049	19	4	,	,	PUNCT
ejpam-5049	19	5	m.	m.	NOUN
ejpam-5049	19	6	q.	q.	PROPN
ejpam-5049	19	7	khirallah	khirallah	PROPN
ejpam-5049	19	8	/	/	SYM
ejpam-5049	19	9	eur	eur	PROPN
ejpam-5049	19	10	.	.	PUNCT
ejpam-5049	20	1	j.	j.	PROPN
ejpam-5049	20	2	pure	pure	PROPN
ejpam-5049	20	3	appl	appl	PROPN
ejpam-5049	20	4	.	.	PROPN
ejpam-5049	20	5	math	math	PROPN
ejpam-5049	20	6	,	,	PUNCT
ejpam-5049	20	7	17	17	NUM
ejpam-5049	20	8	(	(	PUNCT
ejpam-5049	20	9	1	1	NUM
ejpam-5049	20	10	)	)	PUNCT
ejpam-5049	20	11	(	(	PUNCT
ejpam-5049	20	12	2024	2024	NUM
ejpam-5049	20	13	)	)	PUNCT
ejpam-5049	20	14	,	,	PUNCT
ejpam-5049	20	15	477	477	NUM
ejpam-5049	20	16	-	-	SYM
ejpam-5049	20	17	503	503	NUM
ejpam-5049	20	18	478	478	NUM
ejpam-5049	20	19	represented	represent	VERB
ejpam-5049	20	20	by	by	ADP
ejpam-5049	20	21	the	the	DET
ejpam-5049	20	22	fractional	fractional	ADJ
ejpam-5049	20	23	integral	integral	NOUN
ejpam-5049	20	24	of	of	ADP
ejpam-5049	20	25	a	a	DET
ejpam-5049	20	26	function	function	NOUN
ejpam-5049	20	27	with	with	ADP
ejpam-5049	20	28	regard	regard	NOUN
ejpam-5049	20	29	to	to	ADP
ejpam-5049	20	30	a	a	DET
ejpam-5049	20	31	variable	variable	NOUN
ejpam-5049	20	32	of	of	ADP
ejpam-5049	20	33	order	order	NOUN
ejpam-5049	20	34	d−α	d−α	NOUN
ejpam-5049	20	35	(	(	PUNCT
ejpam-5049	20	36	[	[	X
ejpam-5049	20	37	18	18	NUM
ejpam-5049	20	38	]	]	PUNCT
ejpam-5049	20	39	,	,	PUNCT
ejpam-5049	21	1	[	[	X
ejpam-5049	21	2	17	17	NUM
ejpam-5049	21	3	]	]	PUNCT
ejpam-5049	21	4	,	,	PUNCT
ejpam-5049	21	5	[	[	X
ejpam-5049	21	6	13	13	NUM
ejpam-5049	21	7	]	]	NUM
ejpam-5049	21	8	)	)	PUNCT
ejpam-5049	21	9	.	.	PUNCT
ejpam-5049	22	1	numerous	numerous	ADJ
ejpam-5049	22	2	areas	area	NOUN
ejpam-5049	22	3	of	of	ADP
ejpam-5049	22	4	mathematical	mathematical	ADJ
ejpam-5049	22	5	physics	physics	NOUN
ejpam-5049	22	6	and	and	CCONJ
ejpam-5049	22	7	engineering	engineering	NOUN
ejpam-5049	22	8	applications	application	NOUN
ejpam-5049	22	9	deal	deal	VERB
ejpam-5049	22	10	with	with	ADP
ejpam-5049	22	11	fractional	fractional	ADJ
ejpam-5049	22	12	integral	integral	ADJ
ejpam-5049	22	13	-	-	PUNCT
ejpam-5049	22	14	differential	differential	NOUN
ejpam-5049	22	15	equations	equation	NOUN
ejpam-5049	22	16	.	.	PUNCT
ejpam-5049	23	1	a	a	DET
ejpam-5049	23	2	great	great	ADJ
ejpam-5049	23	3	deal	deal	NOUN
ejpam-5049	23	4	of	of	ADP
ejpam-5049	23	5	attention	attention	NOUN
ejpam-5049	23	6	has	have	AUX
ejpam-5049	23	7	been	be	AUX
ejpam-5049	23	8	focused	focus	VERB
ejpam-5049	23	9	on	on	ADP
ejpam-5049	23	10	developing	develop	VERB
ejpam-5049	23	11	efficient	efficient	ADJ
ejpam-5049	23	12	techniques	technique	NOUN
ejpam-5049	23	13	for	for	ADP
ejpam-5049	23	14	getting	get	VERB
ejpam-5049	23	15	approximate	approximate	ADJ
ejpam-5049	23	16	or	or	CCONJ
ejpam-5049	23	17	numerical	numerical	ADJ
ejpam-5049	23	18	solutions	solution	NOUN
ejpam-5049	23	19	for	for	ADP
ejpam-5049	23	20	both	both	CCONJ
ejpam-5049	23	21	linear	linear	ADJ
ejpam-5049	23	22	and	and	CCONJ
ejpam-5049	23	23	nonlinear	nonlinear	ADJ
ejpam-5049	23	24	fractional	fractional	ADJ
ejpam-5049	23	25	integro	integro	ADJ
ejpam-5049	23	26	-	-	PUNCT
ejpam-5049	23	27	differential	differential	NOUN
ejpam-5049	23	28	equations	equation	NOUN
ejpam-5049	23	29	because	because	SCONJ
ejpam-5049	23	30	of	of	ADP
ejpam-5049	23	31	the	the	DET
ejpam-5049	23	32	difficulties	difficulty	NOUN
ejpam-5049	23	33	in	in	ADP
ejpam-5049	23	34	obtaining	obtain	VERB
ejpam-5049	23	35	analytical	analytical	ADJ
ejpam-5049	23	36	solutions	solution	NOUN
ejpam-5049	23	37	for	for	ADP
ejpam-5049	23	38	these	these	DET
ejpam-5049	23	39	problems	problem	NOUN
ejpam-5049	23	40	.	.	PUNCT
ejpam-5049	24	1	furthermore	furthermore	ADV
ejpam-5049	24	2	,	,	PUNCT
ejpam-5049	24	3	using	use	VERB
ejpam-5049	24	4	numerical	numerical	ADJ
ejpam-5049	24	5	or	or	CCONJ
ejpam-5049	24	6	approximating	approximate	VERB
ejpam-5049	24	7	methods	method	NOUN
ejpam-5049	24	8	to	to	PART
ejpam-5049	24	9	solve	solve	VERB
ejpam-5049	24	10	fractional	fractional	ADJ
ejpam-5049	24	11	integro	integro	ADJ
ejpam-5049	24	12	-	-	PUNCT
ejpam-5049	24	13	differential	differential	NOUN
ejpam-5049	24	14	equations	equation	NOUN
ejpam-5049	24	15	containing	contain	VERB
ejpam-5049	24	16	realistic	realistic	ADJ
ejpam-5049	24	17	nonlinear	nonlinear	ADJ
ejpam-5049	24	18	elements	element	NOUN
ejpam-5049	24	19	is	be	AUX
ejpam-5049	24	20	still	still	ADV
ejpam-5049	24	21	a	a	DET
ejpam-5049	24	22	challenging	challenging	ADJ
ejpam-5049	24	23	undertaking	undertaking	NOUN
ejpam-5049	24	24	.	.	PUNCT
ejpam-5049	25	1	integrals	integral	NOUN
ejpam-5049	25	2	and	and	CCONJ
ejpam-5049	25	3	derivatives	derivative	NOUN
ejpam-5049	25	4	of	of	ADP
ejpam-5049	25	5	an	an	DET
ejpam-5049	25	6	unknown	unknown	ADJ
ejpam-5049	25	7	function	function	NOUN
ejpam-5049	25	8	are	be	AUX
ejpam-5049	25	9	combined	combine	VERB
ejpam-5049	25	10	in	in	ADP
ejpam-5049	25	11	the	the	DET
ejpam-5049	25	12	integro	integro	ADJ
ejpam-5049	25	13	-	-	PUNCT
ejpam-5049	25	14	differential	differential	NOUN
ejpam-5049	25	15	equation	equation	NOUN
ejpam-5049	25	16	.	.	PUNCT
ejpam-5049	26	1	different	different	ADJ
ejpam-5049	26	2	kinds	kind	NOUN
ejpam-5049	26	3	of	of	ADP
ejpam-5049	26	4	functional	functional	ADJ
ejpam-5049	26	5	equations	equation	NOUN
ejpam-5049	26	6	,	,	PUNCT
ejpam-5049	26	7	such	such	ADJ
ejpam-5049	26	8	as	as	ADP
ejpam-5049	26	9	integral	integral	ADJ
ejpam-5049	26	10	and	and	CCONJ
ejpam-5049	26	11	integro	integro	ADJ
ejpam-5049	26	12	-	-	PUNCT
ejpam-5049	26	13	differential	differential	NOUN
ejpam-5049	26	14	equations	equation	NOUN
ejpam-5049	26	15	,	,	PUNCT
ejpam-5049	26	16	stochastic	stochastic	ADJ
ejpam-5049	26	17	equations	equation	NOUN
ejpam-5049	26	18	,	,	PUNCT
ejpam-5049	26	19	and	and	CCONJ
ejpam-5049	26	20	ordinary	ordinary	ADJ
ejpam-5049	26	21	or	or	CCONJ
ejpam-5049	26	22	partial	partial	ADJ
ejpam-5049	26	23	differential	differential	NOUN
ejpam-5049	26	24	equations	equation	NOUN
ejpam-5049	26	25	,	,	PUNCT
ejpam-5049	26	26	arise	arise	VERB
ejpam-5049	26	27	when	when	SCONJ
ejpam-5049	26	28	real	real	ADJ
ejpam-5049	26	29	-	-	PUNCT
ejpam-5049	26	30	world	world	NOUN
ejpam-5049	26	31	issues	issue	NOUN
ejpam-5049	26	32	are	be	AUX
ejpam-5049	26	33	mathematically	mathematically	ADV
ejpam-5049	26	34	modeled	model	VERB
ejpam-5049	26	35	.	.	PUNCT
ejpam-5049	27	1	in	in	ADP
ejpam-5049	27	2	many	many	ADJ
ejpam-5049	27	3	different	different	ADJ
ejpam-5049	27	4	domains	domain	NOUN
ejpam-5049	27	5	,	,	PUNCT
ejpam-5049	27	6	including	include	VERB
ejpam-5049	27	7	physics	physics	NOUN
ejpam-5049	27	8	,	,	PUNCT
ejpam-5049	27	9	astronomy	astronomy	NOUN
ejpam-5049	27	10	,	,	PUNCT
ejpam-5049	27	11	potential	potential	ADJ
ejpam-5049	27	12	theory	theory	NOUN
ejpam-5049	27	13	,	,	PUNCT
ejpam-5049	27	14	fluid	fluid	ADJ
ejpam-5049	27	15	dynamics	dynamic	NOUN
ejpam-5049	27	16	,	,	PUNCT
ejpam-5049	27	17	biological	biological	ADJ
ejpam-5049	27	18	models	model	NOUN
ejpam-5049	27	19	,	,	PUNCT
ejpam-5049	27	20	and	and	CCONJ
ejpam-5049	27	21	chemical	chemical	NOUN
ejpam-5049	27	22	kinetics	kinetic	NOUN
ejpam-5049	27	23	,	,	PUNCT
ejpam-5049	27	24	fractional	fractional	ADJ
ejpam-5049	27	25	integral	integral	ADJ
ejpam-5049	27	26	-	-	PUNCT
ejpam-5049	27	27	differential	differential	NOUN
ejpam-5049	27	28	equations	equation	NOUN
ejpam-5049	27	29	are	be	AUX
ejpam-5049	27	30	used	use	VERB
ejpam-5049	27	31	to	to	PART
ejpam-5049	27	32	mathematically	mathematically	ADV
ejpam-5049	27	33	formulate	formulate	VERB
ejpam-5049	27	34	physical	physical	ADJ
ejpam-5049	27	35	processes	process	NOUN
ejpam-5049	27	36	.	.	PUNCT
ejpam-5049	28	1	fractional	fractional	ADJ
ejpam-5049	28	2	integro	integro	ADJ
ejpam-5049	28	3	-	-	PUNCT
ejpam-5049	28	4	differential	differential	NOUN
ejpam-5049	28	5	equations	equation	NOUN
ejpam-5049	28	6	are	be	AUX
ejpam-5049	28	7	sometimes	sometimes	ADV
ejpam-5049	28	8	difficult	difficult	ADJ
ejpam-5049	28	9	to	to	PART
ejpam-5049	28	10	solve	solve	VERB
ejpam-5049	28	11	analytically	analytically	ADV
ejpam-5049	28	12	,	,	PUNCT
ejpam-5049	28	13	requiring	require	VERB
ejpam-5049	28	14	the	the	DET
ejpam-5049	28	15	construction	construction	NOUN
ejpam-5049	28	16	of	of	ADP
ejpam-5049	28	17	effective	effective	ADJ
ejpam-5049	28	18	approximation	approximation	NOUN
ejpam-5049	28	19	solutions	solution	NOUN
ejpam-5049	28	20	.	.	PUNCT
ejpam-5049	29	1	the	the	DET
ejpam-5049	29	2	jacobi	jacobi	PROPN
ejpam-5049	29	3	spectral	spectral	PROPN
ejpam-5049	29	4	method	method	NOUN
ejpam-5049	29	5	[	[	X
ejpam-5049	29	6	20	20	NUM
ejpam-5049	29	7	]	]	PUNCT
ejpam-5049	29	8	,	,	PUNCT
ejpam-5049	29	9	runge	runge	VERB
ejpam-5049	29	10	kutta	kutta	NOUN
ejpam-5049	29	11	method	method	NOUN
ejpam-5049	29	12	[	[	X
ejpam-5049	29	13	24	24	NUM
ejpam-5049	29	14	]	]	PUNCT
ejpam-5049	29	15	,	,	PUNCT
ejpam-5049	29	16	chebyshev	chebyshev	NOUN
ejpam-5049	29	17	collocation	collocation	NOUN
ejpam-5049	29	18	method	method	NOUN
ejpam-5049	29	19	[	[	X
ejpam-5049	29	20	3	3	NUM
ejpam-5049	29	21	]	]	PUNCT
ejpam-5049	29	22	,	,	PUNCT
ejpam-5049	29	23	laplace	laplace	NOUN
ejpam-5049	29	24	power	power	NOUN
ejpam-5049	29	25	series	series	PROPN
ejpam-5049	29	26	method	method	NOUN
ejpam-5049	29	27	[	[	X
ejpam-5049	29	28	1	1	NUM
ejpam-5049	29	29	]	]	PUNCT
ejpam-5049	29	30	,	,	PUNCT
ejpam-5049	29	31	rationalized	rationalize	VERB
ejpam-5049	29	32	haar	haar	NOUN
ejpam-5049	29	33	functions	function	NOUN
ejpam-5049	29	34	method	method	NOUN
ejpam-5049	29	35	[	[	X
ejpam-5049	29	36	15	15	NUM
ejpam-5049	29	37	]	]	X
ejpam-5049	29	38	,	,	PUNCT
ejpam-5049	29	39	galerkin	galerkin	ADJ
ejpam-5049	29	40	methods	method	NOUN
ejpam-5049	29	41	with	with	ADP
ejpam-5049	29	42	hybrid	hybrid	ADJ
ejpam-5049	29	43	functions[14	functions[14	PROPN
ejpam-5049	29	44	]	]	PUNCT
ejpam-5049	29	45	and	and	CCONJ
ejpam-5049	29	46	laguerre	laguerre	NOUN
ejpam-5049	29	47	collocation	collocation	NOUN
ejpam-5049	29	48	method	method	NOUN
ejpam-5049	29	49	[	[	X
ejpam-5049	29	50	5	5	NUM
ejpam-5049	29	51	]	]	PUNCT
ejpam-5049	29	52	are	be	AUX
ejpam-5049	29	53	just	just	ADV
ejpam-5049	29	54	a	a	DET
ejpam-5049	29	55	few	few	ADJ
ejpam-5049	29	56	of	of	ADP
ejpam-5049	29	57	the	the	DET
ejpam-5049	29	58	numerical	numerical	ADJ
ejpam-5049	29	59	techniques	technique	NOUN
ejpam-5049	29	60	that	that	PRON
ejpam-5049	29	61	have	have	AUX
ejpam-5049	29	62	been	be	AUX
ejpam-5049	29	63	used	use	VERB
ejpam-5049	29	64	to	to	PART
ejpam-5049	29	65	solve	solve	VERB
ejpam-5049	29	66	such	such	ADJ
ejpam-5049	29	67	equations	equation	NOUN
ejpam-5049	29	68	.	.	PUNCT
ejpam-5049	30	1	numerous	numerous	ADJ
ejpam-5049	30	2	applications	application	NOUN
ejpam-5049	30	3	can	can	AUX
ejpam-5049	30	4	be	be	AUX
ejpam-5049	30	5	also	also	ADV
ejpam-5049	30	6	found	find	VERB
ejpam-5049	30	7	for	for	ADP
ejpam-5049	30	8	the	the	DET
ejpam-5049	30	9	well	well	ADV
ejpam-5049	30	10	-	-	PUNCT
ejpam-5049	30	11	known	know	VERB
ejpam-5049	30	12	set	set	NOUN
ejpam-5049	30	13	of	of	ADP
ejpam-5049	30	14	orthogonal	orthogonal	ADJ
ejpam-5049	30	15	polynomials	polynomial	NOUN
ejpam-5049	30	16	defined	define	VERB
ejpam-5049	30	17	on	on	ADP
ejpam-5049	30	18	the	the	DET
ejpam-5049	30	19	interval	interval	NOUN
ejpam-5049	30	20	[	[	X
ejpam-5049	30	21	−1	−1	NOUN
ejpam-5049	30	22	,	,	PUNCT
ejpam-5049	30	23	1	1	NUM
ejpam-5049	30	24	]	]	PUNCT
ejpam-5049	30	25	,	,	PUNCT
ejpam-5049	30	26	known	know	VERB
ejpam-5049	30	27	as	as	ADP
ejpam-5049	30	28	chebyshev	chebyshev	NOUN
ejpam-5049	30	29	polynomials	polynomial	NOUN
ejpam-5049	30	30	[	[	X
ejpam-5049	30	31	11	11	NUM
ejpam-5049	30	32	,	,	PUNCT
ejpam-5049	30	33	19	19	NUM
ejpam-5049	30	34	]	]	PUNCT
ejpam-5049	30	35	.	.	PUNCT
ejpam-5049	31	1	their	their	PRON
ejpam-5049	31	2	advantageous	advantageous	ADJ
ejpam-5049	31	3	qualities	quality	NOUN
ejpam-5049	31	4	in	in	ADP
ejpam-5049	31	5	function	function	NOUN
ejpam-5049	31	6	approximation	approximation	NOUN
ejpam-5049	31	7	are	be	AUX
ejpam-5049	31	8	the	the	DET
ejpam-5049	31	9	reason	reason	NOUN
ejpam-5049	31	10	for	for	ADP
ejpam-5049	31	11	their	their	PRON
ejpam-5049	31	12	extensive	extensive	ADJ
ejpam-5049	31	13	use	use	NOUN
ejpam-5049	31	14	.	.	PUNCT
ejpam-5049	32	1	when	when	SCONJ
ejpam-5049	32	2	it	it	PRON
ejpam-5049	32	3	comes	come	VERB
ejpam-5049	32	4	to	to	ADP
ejpam-5049	32	5	chebyshev	chebyshev	NOUN
ejpam-5049	32	6	polynomials	polynomial	NOUN
ejpam-5049	32	7	,	,	PUNCT
ejpam-5049	32	8	the	the	DET
ejpam-5049	32	9	wide	wide	ADJ
ejpam-5049	32	10	range	range	NOUN
ejpam-5049	32	11	of	of	ADP
ejpam-5049	32	12	qualities	quality	NOUN
ejpam-5049	32	13	that	that	SCONJ
ejpam-5049	32	14	orthogonal	orthogonal	ADJ
ejpam-5049	32	15	polynomials	polynomial	NOUN
ejpam-5049	32	16	have	have	AUX
ejpam-5049	32	17	is	be	AUX
ejpam-5049	32	18	especially	especially	ADV
ejpam-5049	32	19	concise	concise	ADJ
ejpam-5049	32	20	,	,	PUNCT
ejpam-5049	32	21	which	which	PRON
ejpam-5049	32	22	makes	make	VERB
ejpam-5049	32	23	them	they	PRON
ejpam-5049	32	24	stand	stand	VERB
ejpam-5049	32	25	out	out	ADP
ejpam-5049	32	26	above	above	ADP
ejpam-5049	32	27	other	other	ADJ
ejpam-5049	32	28	orthogonal	orthogonal	ADJ
ejpam-5049	32	29	polynomials	polynomial	NOUN
ejpam-5049	32	30	.	.	PUNCT
ejpam-5049	33	1	these	these	DET
ejpam-5049	33	2	polynomials	polynomial	NOUN
ejpam-5049	33	3	are	be	AUX
ejpam-5049	33	4	members	member	NOUN
ejpam-5049	33	5	of	of	ADP
ejpam-5049	33	6	the	the	DET
ejpam-5049	33	7	unique	unique	ADJ
ejpam-5049	33	8	class	class	NOUN
ejpam-5049	33	9	of	of	ADP
ejpam-5049	33	10	orthogonal	orthogonal	ADJ
ejpam-5049	33	11	polynomials	polynomial	NOUN
ejpam-5049	33	12	called	call	VERB
ejpam-5049	33	13	jacobi	jacobi	PROPN
ejpam-5049	33	14	polynomials	polynomial	NOUN
ejpam-5049	33	15	.	.	PUNCT
ejpam-5049	34	1	chebyshev	chebyshev	PROPN
ejpam-5049	34	2	polynomials	polynomial	NOUN
ejpam-5049	34	3	offer	offer	VERB
ejpam-5049	34	4	advantages	advantage	NOUN
ejpam-5049	34	5	in	in	ADP
ejpam-5049	34	6	terms	term	NOUN
ejpam-5049	34	7	of	of	ADP
ejpam-5049	34	8	orthogonality	orthogonality	NOUN
ejpam-5049	34	9	,	,	PUNCT
ejpam-5049	34	10	error	error	NOUN
ejpam-5049	34	11	minimization	minimization	NOUN
ejpam-5049	34	12	,	,	PUNCT
ejpam-5049	34	13	and	and	CCONJ
ejpam-5049	34	14	convergence	convergence	NOUN
ejpam-5049	34	15	properties	property	NOUN
ejpam-5049	34	16	within	within	ADP
ejpam-5049	34	17	specific	specific	ADJ
ejpam-5049	34	18	intervals	interval	NOUN
ejpam-5049	34	19	.	.	PUNCT
ejpam-5049	35	1	however	however	ADV
ejpam-5049	35	2	,	,	PUNCT
ejpam-5049	35	3	their	their	PRON
ejpam-5049	35	4	limited	limited	ADJ
ejpam-5049	35	5	applicability	applicability	NOUN
ejpam-5049	35	6	outside	outside	ADP
ejpam-5049	35	7	these	these	DET
ejpam-5049	35	8	intervals	interval	NOUN
ejpam-5049	35	9	and	and	CCONJ
ejpam-5049	35	10	challenges	challenge	NOUN
ejpam-5049	35	11	in	in	ADP
ejpam-5049	35	12	certain	certain	ADJ
ejpam-5049	35	13	mathematical	mathematical	ADJ
ejpam-5049	35	14	operations	operation	NOUN
ejpam-5049	35	15	may	may	AUX
ejpam-5049	35	16	be	be	AUX
ejpam-5049	35	17	considered	consider	VERB
ejpam-5049	35	18	disadvantages	disadvantage	NOUN
ejpam-5049	35	19	in	in	ADP
ejpam-5049	35	20	certain	certain	ADJ
ejpam-5049	35	21	contexts	context	NOUN
ejpam-5049	35	22	.	.	PUNCT
ejpam-5049	36	1	jacobi	jacobi	PROPN
ejpam-5049	36	2	polynomials	polynomial	NOUN
ejpam-5049	36	3	are	be	AUX
ejpam-5049	36	4	solutions	solution	NOUN
ejpam-5049	36	5	to	to	ADP
ejpam-5049	36	6	sturm	sturm	PROPN
ejpam-5049	36	7	-	-	PUNCT
ejpam-5049	36	8	liouville	liouville	NOUN
ejpam-5049	36	9	equations	equation	NOUN
ejpam-5049	36	10	and	and	CCONJ
ejpam-5049	36	11	correspond	correspond	VERB
ejpam-5049	36	12	to	to	ADP
ejpam-5049	36	13	weight	weight	NOUN
ejpam-5049	36	14	functions	function	NOUN
ejpam-5049	36	15	of	of	ADP
ejpam-5049	36	16	the	the	DET
ejpam-5049	36	17	kind	kind	NOUN
ejpam-5049	36	18	(	(	PUNCT
ejpam-5049	36	19	1−	1−	NUM
ejpam-5049	36	20	β)α(1	β)α(1	PROPN
ejpam-5049	36	21	+	+	X
ejpam-5049	36	22	β)α	β)α	PUNCT
ejpam-5049	37	1	[	[	X
ejpam-5049	37	2	16	16	NUM
ejpam-5049	37	3	]	]	PUNCT
ejpam-5049	37	4	.	.	PUNCT
ejpam-5049	38	1	for	for	ADP
ejpam-5049	38	2	instance	instance	NOUN
ejpam-5049	38	3	,	,	PUNCT
ejpam-5049	38	4	the	the	DET
ejpam-5049	38	5	orthogonality	orthogonality	NOUN
ejpam-5049	38	6	condition	condition	NOUN
ejpam-5049	38	7	of	of	ADP
ejpam-5049	38	8	the	the	DET
ejpam-5049	38	9	chebyshev	chebyshev	NOUN
ejpam-5049	38	10	polynomials	polynomial	NOUN
ejpam-5049	38	11	is	be	AUX
ejpam-5049	38	12	utilized	utilize	VERB
ejpam-5049	38	13	to	to	PART
ejpam-5049	38	14	approximate	approximate	VERB
ejpam-5049	38	15	the	the	DET
ejpam-5049	38	16	functions	function	NOUN
ejpam-5049	38	17	of	of	ADP
ejpam-5049	38	18	the	the	DET
ejpam-5049	38	19	period	period	NOUN
ejpam-5049	38	20	[	[	X
ejpam-5049	38	21	a	a	X
ejpam-5049	38	22	,	,	PUNCT
ejpam-5049	38	23	b	b	NOUN
ejpam-5049	38	24	]	]	X
ejpam-5049	38	25	.	.	PUNCT
ejpam-5049	39	1	in	in	ADP
ejpam-5049	39	2	these	these	DET
ejpam-5049	39	3	techniques	technique	NOUN
ejpam-5049	39	4	,	,	PUNCT
ejpam-5049	39	5	which	which	PRON
ejpam-5049	39	6	strongly	strongly	ADV
ejpam-5049	39	7	rely	rely	VERB
ejpam-5049	39	8	on	on	ADP
ejpam-5049	39	9	polynomials	polynomial	NOUN
ejpam-5049	39	10	,	,	PUNCT
ejpam-5049	39	11	(	(	PUNCT
ejpam-5049	39	12	see	see	VERB
ejpam-5049	39	13	(	(	PUNCT
ejpam-5049	39	14	[	[	X
ejpam-5049	39	15	21	21	NUM
ejpam-5049	39	16	]	]	PUNCT
ejpam-5049	39	17	)	)	PUNCT
ejpam-5049	39	18	)	)	PUNCT
ejpam-5049	39	19	.	.	PUNCT
ejpam-5049	40	1	there	there	PRON
ejpam-5049	40	2	are	be	VERB
ejpam-5049	40	3	several	several	ADJ
ejpam-5049	40	4	advantages	advantage	NOUN
ejpam-5049	40	5	to	to	ADP
ejpam-5049	40	6	employee	employee	NOUN
ejpam-5049	40	7	shifted	shift	VERB
ejpam-5049	40	8	chebyshev	chebyshev	NOUN
ejpam-5049	40	9	polynomials	polynomial	NOUN
ejpam-5049	40	10	:	:	PUNCT
ejpam-5049	40	11	chebyshev	chebyshev	PROPN
ejpam-5049	40	12	polynomial	polynomial	PROPN
ejpam-5049	40	13	exhibit	exhibit	VERB
ejpam-5049	40	14	a	a	DET
ejpam-5049	40	15	multitude	multitude	NOUN
ejpam-5049	40	16	of	of	ADP
ejpam-5049	40	17	intriguing	intriguing	ADJ
ejpam-5049	40	18	and	and	CCONJ
ejpam-5049	40	19	beneficial	beneficial	ADJ
ejpam-5049	40	20	properties	property	NOUN
ejpam-5049	40	21	.	.	PUNCT
ejpam-5049	41	1	utilizing	utilize	VERB
ejpam-5049	41	2	chebyshev	chebyshev	NOUN
ejpam-5049	41	3	polynomials	polynomial	NOUN
ejpam-5049	41	4	as	as	SCONJ
ejpam-5049	41	5	fundamental	fundamental	ADJ
ejpam-5049	41	6	functions	function	NOUN
ejpam-5049	41	7	yields	yield	VERB
ejpam-5049	41	8	highly	highly	ADV
ejpam-5049	41	9	precise	precise	ADJ
ejpam-5049	41	10	solutions	solution	NOUN
ejpam-5049	41	11	.	.	PUNCT
ejpam-5049	42	1	the	the	DET
ejpam-5049	42	2	utilization	utilization	NOUN
ejpam-5049	42	3	of	of	ADP
ejpam-5049	42	4	chebyshev	chebyshev	NOUN
ejpam-5049	42	5	polynomials	polynomial	NOUN
ejpam-5049	42	6	in	in	ADP
ejpam-5049	42	7	research	research	NOUN
ejpam-5049	42	8	contributions	contribution	NOUN
ejpam-5049	42	9	is	be	AUX
ejpam-5049	42	10	comparatively	comparatively	ADV
ejpam-5049	42	11	limited	limited	ADJ
ejpam-5049	42	12	in	in	ADP
ejpam-5049	42	13	comparison	comparison	NOUN
ejpam-5049	42	14	to	to	ADP
ejpam-5049	42	15	other	other	ADJ
ejpam-5049	42	16	polynomial	polynomial	ADJ
ejpam-5049	42	17	types	type	NOUN
ejpam-5049	42	18	.	.	PUNCT
ejpam-5049	43	1	by	by	ADP
ejpam-5049	43	2	selecting	select	VERB
ejpam-5049	43	3	the	the	DET
ejpam-5049	43	4	modified	modify	VERB
ejpam-5049	43	5	set	set	NOUN
ejpam-5049	43	6	of	of	ADP
ejpam-5049	43	7	shifted	shift	VERB
ejpam-5049	43	8	chebyshev	chebyshev	NOUN
ejpam-5049	43	9	polynomials	polynomial	NOUN
ejpam-5049	43	10	as	as	ADP
ejpam-5049	43	11	the	the	DET
ejpam-5049	43	12	basis	basis	NOUN
ejpam-5049	43	13	functions	function	NOUN
ejpam-5049	43	14	and	and	CCONJ
ejpam-5049	43	15	retaining	retain	VERB
ejpam-5049	43	16	only	only	ADV
ejpam-5049	43	17	a	a	DET
ejpam-5049	43	18	few	few	ADJ
ejpam-5049	43	19	terms	term	NOUN
ejpam-5049	43	20	of	of	ADP
ejpam-5049	43	21	the	the	DET
ejpam-5049	43	22	modes	mode	NOUN
ejpam-5049	43	23	,	,	PUNCT
ejpam-5049	43	24	it	it	PRON
ejpam-5049	43	25	becomes	become	VERB
ejpam-5049	43	26	feasible	feasible	ADJ
ejpam-5049	43	27	to	to	PART
ejpam-5049	43	28	generate	generate	VERB
ejpam-5049	43	29	highly	highly	ADV
ejpam-5049	43	30	accurate	accurate	ADJ
ejpam-5049	43	31	approximations	approximation	NOUN
ejpam-5049	43	32	with	with	ADP
ejpam-5049	43	33	reduced	reduced	ADJ
ejpam-5049	43	34	computational	computational	ADJ
ejpam-5049	43	35	effort	effort	NOUN
ejpam-5049	43	36	.	.	PUNCT
ejpam-5049	44	1	furthermore	furthermore	ADV
ejpam-5049	44	2	,	,	PUNCT
ejpam-5049	44	3	khaled	khaled	PROPN
ejpam-5049	44	4	m.	m.	PROPN
ejpam-5049	44	5	saad	saad	PROPN
ejpam-5049	44	6	,	,	PUNCT
ejpam-5049	44	7	m.	m.	NOUN
ejpam-5049	44	8	q.	q.	PROPN
ejpam-5049	44	9	khirallah	khirallah	PROPN
ejpam-5049	44	10	/	/	SYM
ejpam-5049	44	11	eur	eur	PROPN
ejpam-5049	44	12	.	.	PUNCT
ejpam-5049	45	1	j.	j.	PROPN
ejpam-5049	45	2	pure	pure	PROPN
ejpam-5049	45	3	appl	appl	PROPN
ejpam-5049	45	4	.	.	PROPN
ejpam-5049	45	5	math	math	PROPN
ejpam-5049	45	6	,	,	PUNCT
ejpam-5049	45	7	17	17	NUM
ejpam-5049	45	8	(	(	PUNCT
ejpam-5049	45	9	1	1	NUM
ejpam-5049	45	10	)	)	PUNCT
ejpam-5049	45	11	(	(	PUNCT
ejpam-5049	45	12	2024	2024	NUM
ejpam-5049	45	13	)	)	PUNCT
ejpam-5049	45	14	,	,	PUNCT
ejpam-5049	45	15	477	477	NUM
ejpam-5049	45	16	-	-	SYM
ejpam-5049	45	17	503	503	NUM
ejpam-5049	45	18	479	479	NUM
ejpam-5049	45	19	the	the	DET
ejpam-5049	45	20	associated	associated	ADJ
ejpam-5049	45	21	errors	error	NOUN
ejpam-5049	45	22	are	be	AUX
ejpam-5049	45	23	minimal	minimal	ADJ
ejpam-5049	45	24	.	.	PUNCT
ejpam-5049	46	1	the	the	DET
ejpam-5049	46	2	structure	structure	NOUN
ejpam-5049	46	3	of	of	ADP
ejpam-5049	46	4	this	this	DET
ejpam-5049	46	5	study	study	NOUN
ejpam-5049	46	6	is	be	AUX
ejpam-5049	46	7	as	as	SCONJ
ejpam-5049	46	8	follows	follow	VERB
ejpam-5049	46	9	.	.	PUNCT
ejpam-5049	47	1	the	the	DET
ejpam-5049	47	2	definitions	definition	NOUN
ejpam-5049	47	3	of	of	ADP
ejpam-5049	47	4	the	the	DET
ejpam-5049	47	5	fractional	fractional	ADJ
ejpam-5049	47	6	derivatives	derivative	NOUN
ejpam-5049	47	7	and	and	CCONJ
ejpam-5049	47	8	shifting	shift	VERB
ejpam-5049	47	9	chebyshev	chebyshev	NOUN
ejpam-5049	47	10	polynomials	polynomial	NOUN
ejpam-5049	47	11	are	be	AUX
ejpam-5049	47	12	briefly	briefly	ADV
ejpam-5049	47	13	discussed	discuss	VERB
ejpam-5049	47	14	in	in	ADP
ejpam-5049	47	15	section	section	NOUN
ejpam-5049	47	16	2	2	NUM
ejpam-5049	47	17	as	as	ADV
ejpam-5049	47	18	well	well	ADV
ejpam-5049	47	19	as	as	ADP
ejpam-5049	47	20	some	some	DET
ejpam-5049	47	21	preliminary	preliminary	ADJ
ejpam-5049	47	22	remarks	remark	NOUN
ejpam-5049	47	23	.	.	PUNCT
ejpam-5049	48	1	we	we	PRON
ejpam-5049	48	2	demonstrate	demonstrate	VERB
ejpam-5049	48	3	the	the	DET
ejpam-5049	48	4	numerical	numerical	ADJ
ejpam-5049	48	5	application	application	NOUN
ejpam-5049	48	6	of	of	ADP
ejpam-5049	48	7	the	the	DET
ejpam-5049	48	8	suggested	suggest	VERB
ejpam-5049	48	9	method	method	NOUN
ejpam-5049	48	10	and	and	CCONJ
ejpam-5049	48	11	applications	application	NOUN
ejpam-5049	48	12	in	in	ADP
ejpam-5049	48	13	sections	section	NOUN
ejpam-5049	48	14	3	3	NUM
ejpam-5049	48	15	and	and	CCONJ
ejpam-5049	48	16	4	4	NUM
ejpam-5049	48	17	.	.	X
ejpam-5049	48	18	section	section	NOUN
ejpam-5049	48	19	5	5	NUM
ejpam-5049	48	20	provides	provide	VERB
ejpam-5049	48	21	the	the	DET
ejpam-5049	48	22	conclusion	conclusion	NOUN
ejpam-5049	48	23	.	.	PUNCT
ejpam-5049	49	1	2	2	X
ejpam-5049	49	2	.	.	NUM
ejpam-5049	49	3	preliminaries	preliminary	NOUN
ejpam-5049	49	4	and	and	CCONJ
ejpam-5049	49	5	notations	notation	NOUN
ejpam-5049	49	6	2.1	2.1	NUM
ejpam-5049	49	7	.	.	PUNCT
ejpam-5049	50	1	some	some	DET
ejpam-5049	50	2	definitions	definition	NOUN
ejpam-5049	50	3	of	of	ADP
ejpam-5049	50	4	fractional	fractional	ADJ
ejpam-5049	50	5	derivatives	derivative	NOUN
ejpam-5049	50	6	definition	definition	NOUN
ejpam-5049	50	7	1	1	NUM
ejpam-5049	50	8	.	.	PUNCT
ejpam-5049	51	1	the	the	DET
ejpam-5049	51	2	fractional	fractional	ADJ
ejpam-5049	51	3	derivative	derivative	NOUN
ejpam-5049	51	4	of	of	ADP
ejpam-5049	51	5	order	order	NOUN
ejpam-5049	51	6	0	0	PUNCT
ejpam-5049	51	7	<	<	X
ejpam-5049	51	8	α	α	PROPN
ejpam-5049	51	9	≤	≤	ADV
ejpam-5049	51	10	1	1	NUM
ejpam-5049	51	11	in	in	ADP
ejpam-5049	51	12	the	the	DET
ejpam-5049	51	13	caputo	caputo	PROPN
ejpam-5049	51	14	sense	sense	NOUN
ejpam-5049	51	15	is	be	AUX
ejpam-5049	51	16	provided	provide	VERB
ejpam-5049	51	17	for	for	ADP
ejpam-5049	51	18	ϕ(β	ϕ(β	PROPN
ejpam-5049	51	19	)	)	PUNCT
ejpam-5049	51	20	∈	∈	PROPN
ejpam-5049	51	21	h1(0	h1(0	PROPN
ejpam-5049	51	22	,	,	PUNCT
ejpam-5049	51	23	b	b	NOUN
ejpam-5049	51	24	)	)	PUNCT
ejpam-5049	51	25	by	by	ADP
ejpam-5049	51	26	:	:	PUNCT
ejpam-5049	51	27	cdαϕ(β	cdαϕ(β	NOUN
ejpam-5049	51	28	)	)	PUNCT
ejpam-5049	51	29	=	=	SYM
ejpam-5049	51	30	1	1	NUM
ejpam-5049	51	31	γ(1−	γ(1−	NOUN
ejpam-5049	51	32	α	α	NUM
ejpam-5049	51	33	)	)	PUNCT
ejpam-5049	51	34	∫	∫	PROPN
ejpam-5049	51	35	β	β	X
ejpam-5049	51	36	0	0	NUM
ejpam-5049	52	1	ϕ	ϕ	NOUN
ejpam-5049	52	2	′	′	NUM
ejpam-5049	52	3	(	(	PUNCT
ejpam-5049	52	4	τ	τ	X
ejpam-5049	52	5	)	)	PUNCT
ejpam-5049	52	6	(	(	PUNCT
ejpam-5049	52	7	β	β	NOUN
ejpam-5049	52	8	−	−	NOUN
ejpam-5049	52	9	τ)ν	τ)ν	SYM
ejpam-5049	52	10	dτ	dτ	NOUN
ejpam-5049	52	11	,	,	PUNCT
ejpam-5049	52	12	β	β	X
ejpam-5049	52	13	>	>	X
ejpam-5049	52	14	0	0	PROPN
ejpam-5049	52	15	,	,	PUNCT
ejpam-5049	52	16	definition	definition	NOUN
ejpam-5049	52	17	2	2	NUM
ejpam-5049	52	18	.	.	PUNCT
ejpam-5049	52	19	where	where	SCONJ
ejpam-5049	52	20	h1(0	h1(0	PROPN
ejpam-5049	52	21	,	,	PUNCT
ejpam-5049	52	22	b	b	PROPN
ejpam-5049	52	23	)	)	PUNCT
ejpam-5049	52	24	is	be	AUX
ejpam-5049	52	25	the	the	DET
ejpam-5049	52	26	sobolev	sobolev	ADJ
ejpam-5049	52	27	space	space	NOUN
ejpam-5049	52	28	and	and	CCONJ
ejpam-5049	52	29	is	be	AUX
ejpam-5049	52	30	given	give	VERB
ejpam-5049	52	31	by	by	ADP
ejpam-5049	52	32	h1(0	h1(0	PROPN
ejpam-5049	52	33	,	,	PUNCT
ejpam-5049	52	34	b	b	NOUN
ejpam-5049	52	35	)	)	PUNCT
ejpam-5049	52	36	=	=	PRON
ejpam-5049	52	37	{	{	PUNCT
ejpam-5049	52	38	ϕ	ϕ	PROPN
ejpam-5049	52	39	∈	∈	PROPN
ejpam-5049	52	40	l2(0	l2(0	NOUN
ejpam-5049	52	41	,	,	PUNCT
ejpam-5049	52	42	b	b	NOUN
ejpam-5049	52	43	)	)	PUNCT
ejpam-5049	52	44	:	:	PUNCT
ejpam-5049	52	45	dϕ	dϕ	VERB
ejpam-5049	52	46	dβ	dβ	PROPN
ejpam-5049	52	47	∈	∈	PROPN
ejpam-5049	52	48	l2(0	l2(0	NOUN
ejpam-5049	52	49	,	,	PUNCT
ejpam-5049	52	50	b	b	NOUN
ejpam-5049	52	51	)	)	PUNCT
ejpam-5049	52	52	,	,	PUNCT
ejpam-5049	52	53	l2(0	l2(0	NOUN
ejpam-5049	52	54	,	,	PUNCT
ejpam-5049	52	55	b	b	NOUN
ejpam-5049	52	56	)	)	PUNCT
ejpam-5049	52	57	=	=	SYM
ejpam-5049	52	58	{	{	PUNCT
ejpam-5049	52	59	ϕ(β	ϕ(β	PROPN
ejpam-5049	52	60	)	)	PUNCT
ejpam-5049	52	61	:	:	PUNCT
ejpam-5049	53	1	(	(	PUNCT
ejpam-5049	53	2	∫	∫	PROPN
ejpam-5049	53	3	b	b	PROPN
ejpam-5049	53	4	0	0	NUM
ejpam-5049	53	5	ϕ(β)2dβ	ϕ(β)2dβ	ADJ
ejpam-5049	53	6	)	)	PUNCT
ejpam-5049	53	7	1	1	NUM
ejpam-5049	53	8	2	2	NUM
ejpam-5049	53	9	<	<	X
ejpam-5049	53	10	∞	∞	NUM
ejpam-5049	53	11	}	}	PUNCT
ejpam-5049	53	12	,	,	PUNCT
ejpam-5049	53	13	}	}	PUNCT
ejpam-5049	53	14	dαβm	dαβm	NOUN
ejpam-5049	53	15	=	=	SYM
ejpam-5049	53	16	{	{	PUNCT
ejpam-5049	53	17	0	0	NUM
ejpam-5049	53	18	,	,	PUNCT
ejpam-5049	53	19	m	m	PROPN
ejpam-5049	53	20	∈	∈	NOUN
ejpam-5049	53	21	{	{	PUNCT
ejpam-5049	53	22	0	0	NUM
ejpam-5049	53	23	,	,	PUNCT
ejpam-5049	53	24	1	1	NUM
ejpam-5049	53	25	,	,	PUNCT
ejpam-5049	53	26	2	2	NUM
ejpam-5049	53	27	,	,	PUNCT
ejpam-5049	53	28	.	.	PUNCT
ejpam-5049	53	29	.	.	PUNCT
ejpam-5049	53	30	.	.	PUNCT
ejpam-5049	54	1	,	,	PUNCT
ejpam-5049	54	2	⌈α⌉	⌈α⌉	ADP
ejpam-5049	54	3	−	−	NOUN
ejpam-5049	54	4	1	1	NUM
ejpam-5049	54	5	}	}	PUNCT
ejpam-5049	54	6	,	,	PUNCT
ejpam-5049	54	7	γ(m+1	γ(m+1	PUNCT
ejpam-5049	54	8	)	)	PUNCT
ejpam-5049	55	1	γ(m+1−α)β	γ(m+1−α)β	NOUN
ejpam-5049	55	2	m−α	m−α	PROPN
ejpam-5049	55	3	,	,	PUNCT
ejpam-5049	55	4	m	m	PROPN
ejpam-5049	55	5	∈	∈	PROPN
ejpam-5049	55	6	n	n	PRON
ejpam-5049	55	7	∧m	∧m	PROPN
ejpam-5049	55	8	≥	≥	NOUN
ejpam-5049	55	9	⌈α⌉	⌈α⌉	NOUN
ejpam-5049	55	10	,	,	PUNCT
ejpam-5049	55	11	where	where	SCONJ
ejpam-5049	55	12	⌈α⌉	⌈α⌉	ADP
ejpam-5049	55	13	the	the	DET
ejpam-5049	55	14	ceiling	ceiling	NOUN
ejpam-5049	55	15	function	function	NOUN
ejpam-5049	55	16	of	of	ADP
ejpam-5049	55	17	α	α	PROPN
ejpam-5049	55	18	and	and	CCONJ
ejpam-5049	55	19	n	n	CCONJ
ejpam-5049	55	20	=	=	SYM
ejpam-5049	55	21	1	1	NUM
ejpam-5049	55	22	,	,	PUNCT
ejpam-5049	55	23	2	2	NUM
ejpam-5049	55	24	,	,	PUNCT
ejpam-5049	55	25	3	3	NUM
ejpam-5049	55	26	,	,	PUNCT
ejpam-5049	55	27	·	·	PUNCT
ejpam-5049	55	28	·	·	PUNCT
ejpam-5049	55	29	·	·	PUNCT
ejpam-5049	55	30	.	.	PUNCT
ejpam-5049	56	1	2.2	2.2	NUM
ejpam-5049	56	2	.	.	PUNCT
ejpam-5049	57	1	the	the	DET
ejpam-5049	57	2	shifting	shift	VERB
ejpam-5049	57	3	chebyshev	chebyshev	NOUN
ejpam-5049	57	4	polynomials	polynomial	NOUN
ejpam-5049	57	5	and	and	CCONJ
ejpam-5049	57	6	function	function	NOUN
ejpam-5049	57	7	approximations	approximation	NOUN
ejpam-5049	57	8	in	in	ADP
ejpam-5049	57	9	this	this	DET
ejpam-5049	57	10	section	section	NOUN
ejpam-5049	57	11	,	,	PUNCT
ejpam-5049	57	12	we	we	PRON
ejpam-5049	57	13	give	give	VERB
ejpam-5049	57	14	the	the	DET
ejpam-5049	57	15	definitions	definition	NOUN
ejpam-5049	57	16	of	of	ADP
ejpam-5049	57	17	the	the	DET
ejpam-5049	57	18	shifted	shift	VERB
ejpam-5049	57	19	chebyshev	chebyshev	NOUN
ejpam-5049	57	20	polynomials	polynomial	NOUN
ejpam-5049	57	21	(	(	PUNCT
ejpam-5049	57	22	cps	cps	PROPN
ejpam-5049	57	23	)	)	PUNCT
ejpam-5049	57	24	,	,	PUNCT
ejpam-5049	57	25	their	their	PRON
ejpam-5049	57	26	notations	notation	NOUN
ejpam-5049	57	27	,	,	PUNCT
ejpam-5049	57	28	and	and	CCONJ
ejpam-5049	57	29	their	their	PRON
ejpam-5049	57	30	properties	property	NOUN
ejpam-5049	57	31	.	.	PUNCT
ejpam-5049	58	1	the	the	DET
ejpam-5049	58	2	majority	majority	NOUN
ejpam-5049	58	3	of	of	ADP
ejpam-5049	58	4	our	our	PRON
ejpam-5049	58	5	studies	study	NOUN
ejpam-5049	58	6	have	have	AUX
ejpam-5049	58	7	concentrated	concentrate	VERB
ejpam-5049	58	8	on	on	ADP
ejpam-5049	58	9	an	an	DET
ejpam-5049	58	10	orthogonal	orthogonal	ADJ
ejpam-5049	58	11	polynomial	polynomial	ADJ
ejpam-5049	58	12	class	class	NOUN
ejpam-5049	58	13	.	.	PUNCT
ejpam-5049	59	1	the	the	DET
ejpam-5049	59	2	recurrence	recurrence	NOUN
ejpam-5049	59	3	relations	relation	NOUN
ejpam-5049	59	4	and	and	CCONJ
ejpam-5049	59	5	analytical	analytical	ADJ
ejpam-5049	59	6	equations	equation	NOUN
ejpam-5049	59	7	of	of	ADP
ejpam-5049	59	8	these	these	DET
ejpam-5049	59	9	polynomials	polynomial	NOUN
ejpam-5049	59	10	can	can	AUX
ejpam-5049	59	11	be	be	AUX
ejpam-5049	59	12	used	use	VERB
ejpam-5049	59	13	to	to	PART
ejpam-5049	59	14	construct	construct	VERB
ejpam-5049	59	15	a	a	DET
ejpam-5049	59	16	family	family	NOUN
ejpam-5049	59	17	of	of	ADP
ejpam-5049	59	18	orthogonal	orthogonal	ADJ
ejpam-5049	59	19	polynomials	polynomial	NOUN
ejpam-5049	59	20	called	call	VERB
ejpam-5049	59	21	chebyshev	chebyshev	NOUN
ejpam-5049	59	22	polynomials	polynomial	NOUN
ejpam-5049	59	23	.	.	PUNCT
ejpam-5049	60	1	now	now	ADV
ejpam-5049	60	2	,	,	PUNCT
ejpam-5049	60	3	we	we	PRON
ejpam-5049	60	4	will	will	AUX
ejpam-5049	60	5	provide	provide	VERB
ejpam-5049	60	6	a	a	DET
ejpam-5049	60	7	quick	quick	ADJ
ejpam-5049	60	8	review	review	NOUN
ejpam-5049	60	9	of	of	ADP
ejpam-5049	60	10	the	the	DET
ejpam-5049	60	11	definitions	definition	NOUN
ejpam-5049	60	12	and	and	CCONJ
ejpam-5049	60	13	formulas	formula	NOUN
ejpam-5049	60	14	related	relate	VERB
ejpam-5049	60	15	to	to	ADP
ejpam-5049	60	16	the	the	DET
ejpam-5049	60	17	first	first	ADJ
ejpam-5049	60	18	-	-	PUNCT
ejpam-5049	60	19	type	type	NOUN
ejpam-5049	60	20	chebyshev	chebyshev	NOUN
ejpam-5049	60	21	polynomials	polynomial	NOUN
ejpam-5049	60	22	in	in	ADP
ejpam-5049	60	23	this	this	DET
ejpam-5049	60	24	section	section	NOUN
ejpam-5049	60	25	.	.	PUNCT
ejpam-5049	61	1	it	it	PRON
ejpam-5049	61	2	is	be	AUX
ejpam-5049	61	3	well	well	ADV
ejpam-5049	61	4	-	-	PUNCT
ejpam-5049	61	5	known	know	VERB
ejpam-5049	61	6	that	that	SCONJ
ejpam-5049	61	7	the	the	DET
ejpam-5049	61	8	first	first	ADJ
ejpam-5049	61	9	-	-	PUNCT
ejpam-5049	61	10	kind	kind	NOUN
ejpam-5049	61	11	chebyshev	chebyshev	NOUN
ejpam-5049	61	12	polynomials	polynomial	NOUN
ejpam-5049	61	13	are	be	AUX
ejpam-5049	61	14	defined	define	VERB
ejpam-5049	61	15	on	on	ADP
ejpam-5049	61	16	the	the	DET
ejpam-5049	61	17	interval	interval	NOUN
ejpam-5049	61	18	[	[	X
ejpam-5049	61	19	−1	−1	NOUN
ejpam-5049	61	20	,	,	PUNCT
ejpam-5049	61	21	1	1	NUM
ejpam-5049	61	22	]	]	PUNCT
ejpam-5049	61	23	as	as	SCONJ
ejpam-5049	61	24	follows	follow	VERB
ejpam-5049	61	25	(	(	PUNCT
ejpam-5049	61	26	see	see	VERB
ejpam-5049	61	27	,	,	PUNCT
ejpam-5049	61	28	for	for	ADP
ejpam-5049	61	29	details	detail	NOUN
ejpam-5049	61	30	,	,	PUNCT
ejpam-5049	61	31	[	[	X
ejpam-5049	61	32	16	16	NUM
ejpam-5049	61	33	,	,	PUNCT
ejpam-5049	61	34	23	23	NUM
ejpam-5049	61	35	]	]	PUNCT
ejpam-5049	61	36	;	;	PUNCT
ejpam-5049	61	37	see	see	VERB
ejpam-5049	61	38	also	also	ADV
ejpam-5049	61	39	the	the	DET
ejpam-5049	61	40	recently	recently	ADV
ejpam-5049	61	41	-	-	PUNCT
ejpam-5049	61	42	published	publish	VERB
ejpam-5049	61	43	survey	survey	NOUN
ejpam-5049	61	44	-	-	PUNCT
ejpam-5049	61	45	cumexpository	cumexpository	NOUN
ejpam-5049	61	46	review	review	NOUN
ejpam-5049	61	47	article	article	NOUN
ejpam-5049	61	48	[	[	X
ejpam-5049	61	49	9	9	X
ejpam-5049	61	50	]	]	PUNCT
ejpam-5049	61	51	on	on	ADP
ejpam-5049	61	52	the	the	DET
ejpam-5049	61	53	chebyshev	chebyshev	NOUN
ejpam-5049	61	54	and	and	CCONJ
ejpam-5049	61	55	related	related	ADJ
ejpam-5049	61	56	orthogonal	orthogonal	ADJ
ejpam-5049	61	57	polynomials	polynomial	NOUN
ejpam-5049	61	58	):	):	PUNCT
ejpam-5049	61	59	the	the	DET
ejpam-5049	61	60	range	range	NOUN
ejpam-5049	61	61	[	[	X
ejpam-5049	61	62	−1	−1	NOUN
ejpam-5049	61	63	,	,	PUNCT
ejpam-5049	61	64	1	1	NUM
ejpam-5049	61	65	]	]	PUNCT
ejpam-5049	61	66	is	be	AUX
ejpam-5049	61	67	where	where	SCONJ
ejpam-5049	61	68	the	the	DET
ejpam-5049	61	69	first	first	ADJ
ejpam-5049	61	70	-	-	PUNCT
ejpam-5049	61	71	type	type	NOUN
ejpam-5049	61	72	chebyshev	chebyshev	NOUN
ejpam-5049	61	73	polynomials	polynomial	NOUN
ejpam-5049	61	74	are	be	AUX
ejpam-5049	61	75	typically	typically	ADV
ejpam-5049	61	76	defined	define	VERB
ejpam-5049	61	77	,	,	PUNCT
ejpam-5049	61	78	as	as	SCONJ
ejpam-5049	61	79	follows	follow	VERB
ejpam-5049	61	80	(	(	PUNCT
ejpam-5049	61	81	see	see	VERB
ejpam-5049	61	82	[	[	X
ejpam-5049	61	83	16	16	NUM
ejpam-5049	61	84	,	,	PUNCT
ejpam-5049	61	85	23	23	NUM
ejpam-5049	61	86	]	]	PUNCT
ejpam-5049	61	87	for	for	ADP
ejpam-5049	61	88	more	more	ADJ
ejpam-5049	61	89	details	detail	NOUN
ejpam-5049	61	90	;	;	PUNCT
ejpam-5049	61	91	additionally	additionally	ADV
ejpam-5049	61	92	,	,	PUNCT
ejpam-5049	61	93	see	see	VERB
ejpam-5049	61	94	the	the	DET
ejpam-5049	61	95	recently	recently	ADV
ejpam-5049	61	96	published	publish	VERB
ejpam-5049	61	97	survey	survey	NOUN
ejpam-5049	61	98	and	and	CCONJ
ejpam-5049	61	99	expository	expository	ADJ
ejpam-5049	61	100	review	review	NOUN
ejpam-5049	61	101	in	in	ADP
ejpam-5049	61	102	[	[	X
ejpam-5049	61	103	9	9	NUM
ejpam-5049	61	104	]	]	PUNCT
ejpam-5049	61	105	on	on	ADP
ejpam-5049	61	106	chebyshev	chebyshev	PROPN
ejpam-5049	61	107	and	and	CCONJ
ejpam-5049	61	108	similar	similar	ADJ
ejpam-5049	61	109	orthogonal	orthogonal	ADJ
ejpam-5049	61	110	polynomials	polynomial	NOUN
ejpam-5049	61	111	)	)	PUNCT
ejpam-5049	61	112	.	.	PUNCT
ejpam-5049	62	1	khaled	khaled	PROPN
ejpam-5049	62	2	m.	m.	PROPN
ejpam-5049	62	3	saad	saad	PROPN
ejpam-5049	62	4	,	,	PUNCT
ejpam-5049	62	5	m.	m.	NOUN
ejpam-5049	62	6	q.	q.	PROPN
ejpam-5049	62	7	khirallah	khirallah	PROPN
ejpam-5049	62	8	/	/	SYM
ejpam-5049	62	9	eur	eur	PROPN
ejpam-5049	62	10	.	.	PUNCT
ejpam-5049	63	1	j.	j.	PROPN
ejpam-5049	63	2	pure	pure	PROPN
ejpam-5049	63	3	appl	appl	PROPN
ejpam-5049	63	4	.	.	PROPN
ejpam-5049	63	5	math	math	PROPN
ejpam-5049	63	6	,	,	PUNCT
ejpam-5049	63	7	17	17	NUM
ejpam-5049	63	8	(	(	PUNCT
ejpam-5049	63	9	1	1	NUM
ejpam-5049	63	10	)	)	PUNCT
ejpam-5049	63	11	(	(	PUNCT
ejpam-5049	63	12	2024	2024	NUM
ejpam-5049	63	13	)	)	PUNCT
ejpam-5049	63	14	,	,	PUNCT
ejpam-5049	63	15	477	477	NUM
ejpam-5049	63	16	-	-	SYM
ejpam-5049	63	17	503	503	NUM
ejpam-5049	63	18	480	480	NUM
ejpam-5049	63	19	ψn(γ	ψn(γ	NOUN
ejpam-5049	63	20	)	)	PUNCT
ejpam-5049	63	21	=	=	SYM
ejpam-5049	63	22	cos(nθ	cos(nθ	NOUN
ejpam-5049	63	23	)	)	PUNCT
ejpam-5049	63	24	(	(	PUNCT
ejpam-5049	63	25	n	n	CCONJ
ejpam-5049	63	26	∈	∈	PROPN
ejpam-5049	63	27	n0	n0	NOUN
ejpam-5049	63	28	:	:	PUNCT
ejpam-5049	63	29	=	=	NOUN
ejpam-5049	63	30	n	n	CCONJ
ejpam-5049	63	31	∪	∪	X
ejpam-5049	63	32	{	{	PUNCT
ejpam-5049	63	33	0	0	NUM
ejpam-5049	63	34	}	}	PUNCT
ejpam-5049	63	35	=	=	SYM
ejpam-5049	63	36	0	0	NUM
ejpam-5049	63	37	,	,	PUNCT
ejpam-5049	63	38	1	1	NUM
ejpam-5049	63	39	,	,	PUNCT
ejpam-5049	63	40	2	2	NUM
ejpam-5049	63	41	,	,	PUNCT
ejpam-5049	63	42	·	·	PUNCT
ejpam-5049	63	43	·	·	PUNCT
ejpam-5049	63	44	·	·	PUNCT
ejpam-5049	63	45	)	)	PUNCT
ejpam-5049	63	46	,	,	PUNCT
ejpam-5049	63	47	(	(	PUNCT
ejpam-5049	63	48	1	1	X
ejpam-5049	63	49	)	)	PUNCT
ejpam-5049	63	50	where	where	SCONJ
ejpam-5049	63	51	γ	γ	X
ejpam-5049	63	52	=	=	SYM
ejpam-5049	63	53	cos(θ	cos(θ	PROPN
ejpam-5049	63	54	)	)	PUNCT
ejpam-5049	63	55	.	.	PUNCT
ejpam-5049	64	1	the	the	DET
ejpam-5049	64	2	chebyshev	chebyshev	NOUN
ejpam-5049	64	3	polynomials	polynomial	NOUN
ejpam-5049	64	4	{	{	PUNCT
ejpam-5049	64	5	ψn(γ)}n∈n0	ψn(γ)}n∈n0	PUNCT
ejpam-5049	64	6	can	can	AUX
ejpam-5049	64	7	be	be	AUX
ejpam-5049	64	8	obtained	obtain	VERB
ejpam-5049	64	9	from	from	ADP
ejpam-5049	64	10	the	the	DET
ejpam-5049	64	11	following	follow	VERB
ejpam-5049	64	12	recurrence	recurrence	NOUN
ejpam-5049	64	13	relation	relation	NOUN
ejpam-5049	64	14	:	:	PUNCT
ejpam-5049	64	15	ψn+1(γ	ψn+1(γ	ADV
ejpam-5049	64	16	)	)	PUNCT
ejpam-5049	65	1	=	=	SYM
ejpam-5049	65	2	2γψn(γ)−ψn−1(γ	2γψn(γ)−ψn−1(γ	NUM
ejpam-5049	65	3	)	)	PUNCT
ejpam-5049	65	4	(	(	PUNCT
ejpam-5049	65	5	n	n	CCONJ
ejpam-5049	65	6	∈	∈	PROPN
ejpam-5049	65	7	n	n	CCONJ
ejpam-5049	65	8	)	)	PUNCT
ejpam-5049	65	9	(	(	PUNCT
ejpam-5049	65	10	ψ0(γ	ψ0(γ	X
ejpam-5049	65	11	)	)	PUNCT
ejpam-5049	65	12	=	=	SYM
ejpam-5049	65	13	1	1	NUM
ejpam-5049	65	14	;	;	PUNCT
ejpam-5049	65	15	ψ1(γ	ψ1(γ	X
ejpam-5049	65	16	)	)	PUNCT
ejpam-5049	65	17	=	=	SYM
ejpam-5049	65	18	γ	γ	PROPN
ejpam-5049	65	19	)	)	PUNCT
ejpam-5049	65	20	.	.	PUNCT
ejpam-5049	66	1	(	(	PUNCT
ejpam-5049	66	2	2	2	X
ejpam-5049	66	3	)	)	PUNCT
ejpam-5049	66	4	the	the	DET
ejpam-5049	66	5	chebyshev	chebyshev	NOUN
ejpam-5049	66	6	polynomials	polynomial	NOUN
ejpam-5049	66	7	{	{	PUNCT
ejpam-5049	66	8	ψn(γ)}n∈n0	ψn(γ)}n∈n0	PRON
ejpam-5049	66	9	are	be	AUX
ejpam-5049	66	10	orthogonal	orthogonal	ADJ
ejpam-5049	66	11	over	over	ADP
ejpam-5049	66	12	the	the	DET
ejpam-5049	66	13	interval	interval	NOUN
ejpam-5049	67	1	[	[	X
ejpam-5049	67	2	−1	−1	NOUN
ejpam-5049	67	3	,	,	PUNCT
ejpam-5049	67	4	1	1	NUM
ejpam-5049	67	5	]	]	PUNCT
ejpam-5049	67	6	with	with	ADP
ejpam-5049	67	7	the	the	DET
ejpam-5049	67	8	weight	weight	NOUN
ejpam-5049	67	9	function	function	NOUN
ejpam-5049	67	10	(	(	PUNCT
ejpam-5049	67	11	1−	1−	NUM
ejpam-5049	67	12	γ2)−	γ2)−	NUM
ejpam-5049	67	13	1	1	NUM
ejpam-5049	67	14	2	2	NUM
ejpam-5049	67	15	and	and	CCONJ
ejpam-5049	67	16	we	we	PRON
ejpam-5049	67	17	have	have	VERB
ejpam-5049	67	18	the	the	DET
ejpam-5049	67	19	following	follow	VERB
ejpam-5049	67	20	orthogonality	orthogonality	NOUN
ejpam-5049	67	21	property:∫	property:∫	NOUN
ejpam-5049	67	22	1	1	NUM
ejpam-5049	67	23	−1	−1	NOUN
ejpam-5049	67	24	(	(	PUNCT
ejpam-5049	67	25	1−	1−	NUM
ejpam-5049	67	26	γ2)−	γ2)−	NUM
ejpam-5049	67	27	1	1	NUM
ejpam-5049	67	28	2	2	NUM
ejpam-5049	67	29	ψi(γ)ψj(γ	ψi(γ)ψj(γ	NOUN
ejpam-5049	67	30	)	)	PUNCT
ejpam-5049	67	31	dξ	dξ	PROPN
ejpam-5049	67	32	=	=	PUNCT
ejpam-5049	67	33			X
ejpam-5049	67	34	0	0	NUM
ejpam-5049	68	1	(	(	PUNCT
ejpam-5049	68	2	i	i	PRON
ejpam-5049	68	3	̸=	̸=	PROPN
ejpam-5049	68	4	j	j	PROPN
ejpam-5049	68	5	)	)	PUNCT
ejpam-5049	68	6	π	π	PROPN
ejpam-5049	68	7	2	2	NUM
ejpam-5049	68	8	(	(	PUNCT
ejpam-5049	68	9	i	i	NOUN
ejpam-5049	68	10	=	=	SYM
ejpam-5049	68	11	j	j	PROPN
ejpam-5049	68	12	̸=	̸=	PROPN
ejpam-5049	68	13	0	0	NUM
ejpam-5049	68	14	)	)	PUNCT
ejpam-5049	68	15	π	π	NOUN
ejpam-5049	68	16	(	(	PUNCT
ejpam-5049	68	17	i	i	NOUN
ejpam-5049	68	18	=	=	SYM
ejpam-5049	68	19	j	j	PROPN
ejpam-5049	68	20	=	=	PUNCT
ejpam-5049	68	21	0	0	NUM
ejpam-5049	68	22	)	)	PUNCT
ejpam-5049	68	23	.	.	PUNCT
ejpam-5049	69	1	(	(	PUNCT
ejpam-5049	69	2	3	3	X
ejpam-5049	69	3	)	)	PUNCT
ejpam-5049	69	4	the	the	DET
ejpam-5049	69	5	following	follow	VERB
ejpam-5049	69	6	is	be	AUX
ejpam-5049	69	7	the	the	DET
ejpam-5049	69	8	exact	exact	ADJ
ejpam-5049	69	9	formula	formula	NOUN
ejpam-5049	69	10	for	for	ADP
ejpam-5049	69	11	the	the	DET
ejpam-5049	69	12	chebyshev	chebyshev	NOUN
ejpam-5049	69	13	polynomial	polynomial	NOUN
ejpam-5049	69	14	:	:	PUNCT
ejpam-5049	69	15	ψn(γ	ψn(γ	X
ejpam-5049	69	16	)	)	PUNCT
ejpam-5049	70	1	=	=	SYM
ejpam-5049	70	2	n	n	PRON
ejpam-5049	70	3	2	2	NUM
ejpam-5049	70	4	[	[	X
ejpam-5049	70	5	n/2]∑	n/2]∑	ADJ
ejpam-5049	70	6	i=0	i=0	PROPN
ejpam-5049	70	7	(	(	PUNCT
ejpam-5049	70	8	−1)i	−1)i	X
ejpam-5049	70	9	(	(	PUNCT
ejpam-5049	70	10	n−	n−	NOUN
ejpam-5049	70	11	i−	i−	PROPN
ejpam-5049	70	12	1	1	NUM
ejpam-5049	70	13	)	)	PUNCT
ejpam-5049	70	14	!	!	PUNCT
ejpam-5049	71	1	(	(	PUNCT
ejpam-5049	71	2	i	i	NOUN
ejpam-5049	71	3	)	)	PUNCT
ejpam-5049	71	4	!	!	PUNCT
ejpam-5049	72	1	(	(	PUNCT
ejpam-5049	72	2	n−	n−	NOUN
ejpam-5049	72	3	2i	2i	NUM
ejpam-5049	72	4	)	)	PUNCT
ejpam-5049	72	5	!	!	PUNCT
ejpam-5049	73	1	(	(	PUNCT
ejpam-5049	73	2	2γ)n−2i	2γ)n−2i	NUM
ejpam-5049	73	3	.	.	PUNCT
ejpam-5049	74	1	(	(	PUNCT
ejpam-5049	74	2	4	4	X
ejpam-5049	74	3	)	)	PUNCT
ejpam-5049	74	4	we	we	PRON
ejpam-5049	74	5	define	define	VERB
ejpam-5049	74	6	the	the	DET
ejpam-5049	74	7	shifted	shift	VERB
ejpam-5049	74	8	chebyshev	chebyshev	NOUN
ejpam-5049	74	9	polynomials	polynomial	NOUN
ejpam-5049	74	10	on	on	ADP
ejpam-5049	74	11	the	the	DET
ejpam-5049	74	12	interval	interval	NOUN
ejpam-5049	74	13	[	[	X
ejpam-5049	74	14	0	0	NUM
ejpam-5049	74	15	,	,	PUNCT
ejpam-5049	74	16	1	1	NUM
ejpam-5049	74	17	]	]	PUNCT
ejpam-5049	74	18	by	by	ADP
ejpam-5049	74	19	setting	set	VERB
ejpam-5049	74	20	the	the	DET
ejpam-5049	74	21	variable	variable	ADJ
ejpam-5049	74	22	γ	γ	X
ejpam-5049	74	23	=	=	NOUN
ejpam-5049	74	24	2β	2β	NOUN
ejpam-5049	74	25	−	−	NOUN
ejpam-5049	74	26	1	1	NUM
ejpam-5049	74	27	.	.	PUNCT
ejpam-5049	75	1	the	the	DET
ejpam-5049	75	2	following	follow	VERB
ejpam-5049	75	3	expressions	expression	NOUN
ejpam-5049	75	4	describe	describe	VERB
ejpam-5049	75	5	these	these	DET
ejpam-5049	75	6	polynomials	polynomial	NOUN
ejpam-5049	75	7	:	:	PUNCT
ejpam-5049	75	8	φs(β	φs(β	PUNCT
ejpam-5049	75	9	)	)	PUNCT
ejpam-5049	75	10	=	=	PUNCT
ejpam-5049	75	11	φs(2β	φs(2β	NUM
ejpam-5049	75	12	−	−	NOUN
ejpam-5049	75	13	1	1	NUM
ejpam-5049	75	14	)	)	PUNCT
ejpam-5049	75	15	=	=	SYM
ejpam-5049	75	16	β2s	β2s	X
ejpam-5049	75	17	(	(	PUNCT
ejpam-5049	75	18	√	√	NUM
ejpam-5049	75	19	β	β	X
ejpam-5049	75	20	)	)	PUNCT
ejpam-5049	75	21	,	,	PUNCT
ejpam-5049	75	22	where	where	SCONJ
ejpam-5049	75	23	a	a	DET
ejpam-5049	75	24	set	set	NOUN
ejpam-5049	75	25	of	of	ADP
ejpam-5049	75	26	orthogonal	orthogonal	ADJ
ejpam-5049	75	27	chebyshev	chebyshev	NOUN
ejpam-5049	75	28	polynomials	polynomial	NOUN
ejpam-5049	75	29	over	over	ADP
ejpam-5049	75	30	the	the	DET
ejpam-5049	75	31	range	range	NOUN
ejpam-5049	75	32	[	[	X
ejpam-5049	75	33	0	0	NUM
ejpam-5049	75	34	,	,	PUNCT
ejpam-5049	75	35	1	1	NUM
ejpam-5049	75	36	]	]	PUNCT
ejpam-5049	75	37	is	be	AUX
ejpam-5049	75	38	generated	generate	VERB
ejpam-5049	75	39	by	by	ADP
ejpam-5049	75	40	the	the	DET
ejpam-5049	75	41	polynomial	polynomial	ADJ
ejpam-5049	75	42	collection	collection	NOUN
ejpam-5049	75	43	{	{	PUNCT
ejpam-5049	75	44	φ2s(β)}s∈n0	φ2s(β)}s∈n0	X
ejpam-5049	75	45	.	.	PUNCT
ejpam-5049	76	1	calculating	calculate	VERB
ejpam-5049	76	2	the	the	DET
ejpam-5049	76	3	specific	specific	ADJ
ejpam-5049	76	4	expression	expression	NOUN
ejpam-5049	76	5	of	of	ADP
ejpam-5049	76	6	the	the	DET
ejpam-5049	76	7	shifted	shift	VERB
ejpam-5049	76	8	chebyshev	chebyshev	NOUN
ejpam-5049	76	9	polynomial	polynomial	NOUN
ejpam-5049	76	10	is	be	AUX
ejpam-5049	76	11	a	a	DET
ejpam-5049	76	12	straightforward	straightforward	ADJ
ejpam-5049	76	13	task	task	NOUN
ejpam-5049	76	14	.	.	PUNCT
ejpam-5049	77	1	t̄s(ζ	t̄s(ζ	NOUN
ejpam-5049	77	2	)	)	PUNCT
ejpam-5049	77	3	of	of	ADP
ejpam-5049	77	4	degree	degree	NOUN
ejpam-5049	77	5	s	s	PRON
ejpam-5049	77	6	as	as	SCONJ
ejpam-5049	77	7	follows	follow	VERB
ejpam-5049	77	8	(	(	PUNCT
ejpam-5049	77	9	see	see	VERB
ejpam-5049	77	10	[	[	X
ejpam-5049	77	11	16	16	NUM
ejpam-5049	77	12	]	]	SYM
ejpam-5049	77	13	):	):	PUNCT
ejpam-5049	77	14	φs(β	φs(β	PUNCT
ejpam-5049	77	15	)	)	PUNCT
ejpam-5049	77	16	=	=	SYM
ejpam-5049	77	17	s	s	VERB
ejpam-5049	77	18	s∑	s∑	PROPN
ejpam-5049	77	19	k=0	k=0	PROPN
ejpam-5049	77	20	(	(	PUNCT
ejpam-5049	77	21	−1)s−k	−1)s−k	NOUN
ejpam-5049	77	22	22k	22k	NOUN
ejpam-5049	77	23	(	(	PUNCT
ejpam-5049	77	24	s+	s+	ADV
ejpam-5049	77	25	k	k	PROPN
ejpam-5049	77	26	−	−	PROPN
ejpam-5049	77	27	1	1	NUM
ejpam-5049	77	28	)	)	PUNCT
ejpam-5049	77	29	!	!	PUNCT
ejpam-5049	78	1	(	(	PUNCT
ejpam-5049	78	2	2k	2k	NUM
ejpam-5049	78	3	)	)	PUNCT
ejpam-5049	78	4	!	!	PUNCT
ejpam-5049	79	1	(	(	PUNCT
ejpam-5049	79	2	s−	s−	PROPN
ejpam-5049	79	3	k	k	PROPN
ejpam-5049	79	4	)	)	PUNCT
ejpam-5049	79	5	!	!	PUNCT
ejpam-5049	80	1	βk	βk	NOUN
ejpam-5049	80	2	,	,	PUNCT
ejpam-5049	80	3	(	(	PUNCT
ejpam-5049	80	4	5	5	NUM
ejpam-5049	80	5	)	)	PUNCT
ejpam-5049	80	6	where	where	SCONJ
ejpam-5049	80	7	φ0(β	φ0(β	ADJ
ejpam-5049	80	8	)	)	PUNCT
ejpam-5049	80	9	=	=	SYM
ejpam-5049	80	10	1	1	NUM
ejpam-5049	80	11	and	and	CCONJ
ejpam-5049	80	12	φ1(β	φ1(β	NUM
ejpam-5049	80	13	)	)	PUNCT
ejpam-5049	80	14	=	=	NOUN
ejpam-5049	81	1	2β	2β	NOUN
ejpam-5049	81	2	−	−	NOUN
ejpam-5049	81	3	1	1	NUM
ejpam-5049	81	4	.	.	PUNCT
ejpam-5049	82	1	using	use	VERB
ejpam-5049	82	2	a	a	DET
ejpam-5049	82	3	linear	linear	ADJ
ejpam-5049	82	4	combination	combination	NOUN
ejpam-5049	82	5	of	of	ADP
ejpam-5049	82	6	the	the	DET
ejpam-5049	82	7	first	first	ADJ
ejpam-5049	82	8	(	(	PUNCT
ejpam-5049	82	9	m	m	VERB
ejpam-5049	82	10	+	+	ADJ
ejpam-5049	82	11	1	1	NUM
ejpam-5049	82	12	)	)	PUNCT
ejpam-5049	82	13	terms	term	NOUN
ejpam-5049	82	14	of	of	ADP
ejpam-5049	82	15	φs	φs	PROPN
ejpam-5049	82	16	,	,	PUNCT
ejpam-5049	82	17	we	we	PRON
ejpam-5049	82	18	expand	expand	VERB
ejpam-5049	82	19	and	and	CCONJ
ejpam-5049	82	20	evaluate	evaluate	VERB
ejpam-5049	82	21	the	the	DET
ejpam-5049	82	22	function	function	NOUN
ejpam-5049	82	23	ω(β	ω(β	NOUN
ejpam-5049	82	24	)	)	PUNCT
ejpam-5049	82	25	spanning	span	VERB
ejpam-5049	82	26	the	the	DET
ejpam-5049	82	27	interval	interval	NOUN
ejpam-5049	82	28	[	[	X
ejpam-5049	82	29	0	0	NUM
ejpam-5049	82	30	,	,	PUNCT
ejpam-5049	82	31	1	1	NUM
ejpam-5049	82	32	]	]	PUNCT
ejpam-5049	82	33	.	.	PUNCT
ejpam-5049	83	1	we	we	PRON
ejpam-5049	83	2	find	find	VERB
ejpam-5049	83	3	that	that	SCONJ
ejpam-5049	83	4	:	:	PUNCT
ejpam-5049	83	5	ω(β	ω(β	NOUN
ejpam-5049	83	6	)	)	PUNCT
ejpam-5049	83	7	≃	≃	NOUN
ejpam-5049	83	8	ωm(β	ωm(β	NOUN
ejpam-5049	83	9	)	)	PUNCT
ejpam-5049	83	10	=	=	SYM
ejpam-5049	83	11	m∑	m∑	CCONJ
ejpam-5049	83	12	i=0	i=0	ADJ
ejpam-5049	83	13	aiφi(β	aiφi(β	NOUN
ejpam-5049	83	14	)	)	PUNCT
ejpam-5049	83	15	.	.	PUNCT
ejpam-5049	84	1	(	(	PUNCT
ejpam-5049	84	2	6	6	X
ejpam-5049	84	3	)	)	PUNCT
ejpam-5049	84	4	khaled	khale	VERB
ejpam-5049	84	5	m.	m.	NOUN
ejpam-5049	84	6	saad	saad	PROPN
ejpam-5049	84	7	,	,	PUNCT
ejpam-5049	84	8	m.	m.	NOUN
ejpam-5049	84	9	q.	q.	PROPN
ejpam-5049	84	10	khirallah	khirallah	PROPN
ejpam-5049	84	11	/	/	SYM
ejpam-5049	84	12	eur	eur	PROPN
ejpam-5049	84	13	.	.	PUNCT
ejpam-5049	85	1	j.	j.	PROPN
ejpam-5049	85	2	pure	pure	PROPN
ejpam-5049	85	3	appl	appl	PROPN
ejpam-5049	85	4	.	.	PROPN
ejpam-5049	85	5	math	math	PROPN
ejpam-5049	85	6	,	,	PUNCT
ejpam-5049	85	7	17	17	NUM
ejpam-5049	85	8	(	(	PUNCT
ejpam-5049	85	9	1	1	NUM
ejpam-5049	85	10	)	)	PUNCT
ejpam-5049	85	11	(	(	PUNCT
ejpam-5049	85	12	2024	2024	NUM
ejpam-5049	85	13	)	)	PUNCT
ejpam-5049	85	14	,	,	PUNCT
ejpam-5049	85	15	477	477	NUM
ejpam-5049	85	16	-	-	SYM
ejpam-5049	85	17	503	503	NUM
ejpam-5049	85	18	481	481	NUM
ejpam-5049	85	19	the	the	DET
ejpam-5049	85	20	coefficients	coefficient	NOUN
ejpam-5049	85	21	ai	ai	VERB
ejpam-5049	85	22	are	be	AUX
ejpam-5049	85	23	determined	determine	VERB
ejpam-5049	85	24	by	by	ADP
ejpam-5049	85	25	:	:	PUNCT
ejpam-5049	85	26	ai	ai	VERB
ejpam-5049	85	27	=	=	PUNCT
ejpam-5049	85	28			NOUN
ejpam-5049	86	1	1	1	NUM
ejpam-5049	86	2	π	π	NOUN
ejpam-5049	86	3	∫	∫	PROPN
ejpam-5049	86	4	1	1	NUM
ejpam-5049	86	5	0	0	NUM
ejpam-5049	86	6	ω(η	ω(η	PROPN
ejpam-5049	86	7	)	)	PUNCT
ejpam-5049	86	8	φi(β)√	φi(β)√	NOUN
ejpam-5049	87	1	β	β	NOUN
ejpam-5049	87	2	−	−	NOUN
ejpam-5049	87	3	β2	β2	VERB
ejpam-5049	87	4	dβ	dβ	ADP
ejpam-5049	87	5	(	(	PUNCT
ejpam-5049	87	6	i	i	NOUN
ejpam-5049	87	7	=	=	NOUN
ejpam-5049	87	8	0	0	NUM
ejpam-5049	87	9	)	)	PUNCT
ejpam-5049	87	10	2	2	NUM
ejpam-5049	87	11	π	π	NOUN
ejpam-5049	87	12	∫	∫	PROPN
ejpam-5049	87	13	1	1	NUM
ejpam-5049	87	14	0	0	NUM
ejpam-5049	87	15	ω(β)φi(β)√	ω(β)φi(β)√	PROPN
ejpam-5049	87	16	β−β2	β−β2	NOUN
ejpam-5049	87	17	dβ	dβ	ADJ
ejpam-5049	87	18	(	(	PUNCT
ejpam-5049	87	19	i	i	NOUN
ejpam-5049	87	20	∈	∈	PROPN
ejpam-5049	87	21	n	n	CCONJ
ejpam-5049	87	22	)	)	PUNCT
ejpam-5049	87	23	.	.	PUNCT
ejpam-5049	88	1	(	(	PUNCT
ejpam-5049	88	2	7	7	X
ejpam-5049	88	3	)	)	PUNCT
ejpam-5049	88	4	the	the	DET
ejpam-5049	88	5	primary	primary	ADJ
ejpam-5049	88	6	approximate	approximate	ADJ
ejpam-5049	88	7	expression	expression	NOUN
ejpam-5049	88	8	for	for	ADP
ejpam-5049	88	9	the	the	DET
ejpam-5049	88	10	derivative	derivative	NOUN
ejpam-5049	88	11	of	of	ADP
ejpam-5049	88	12	ϕm(β	ϕm(β	NOUN
ejpam-5049	88	13	)	)	PUNCT
ejpam-5049	88	14	is	be	AUX
ejpam-5049	88	15	provided	provide	VERB
ejpam-5049	88	16	in	in	ADP
ejpam-5049	88	17	the	the	DET
ejpam-5049	88	18	theorem	theorem	NOUN
ejpam-5049	88	19	that	that	PRON
ejpam-5049	88	20	follows	follow	VERB
ejpam-5049	88	21	.	.	PUNCT
ejpam-5049	89	1	theorem	theorem	NOUN
ejpam-5049	89	2	1	1	NUM
ejpam-5049	89	3	.	.	PUNCT
ejpam-5049	90	1	[	[	X
ejpam-5049	90	2	10	10	NUM
ejpam-5049	90	3	,	,	PUNCT
ejpam-5049	90	4	22	22	NUM
ejpam-5049	90	5	]	]	PUNCT
ejpam-5049	90	6	in	in	ADP
ejpam-5049	90	7	eq	eq	ADP
ejpam-5049	90	8	.	.	PUNCT
ejpam-5049	91	1	(	(	PUNCT
ejpam-5049	91	2	6	6	NUM
ejpam-5049	91	3	)	)	PUNCT
ejpam-5049	91	4	,	,	PUNCT
ejpam-5049	91	5	the	the	DET
ejpam-5049	91	6	approximate	approximate	ADJ
ejpam-5049	91	7	solution	solution	NOUN
ejpam-5049	91	8	of	of	ADP
ejpam-5049	91	9	the	the	DET
ejpam-5049	91	10	main	main	ADJ
ejpam-5049	91	11	problem	problem	NOUN
ejpam-5049	91	12	is	be	AUX
ejpam-5049	91	13	given	give	VERB
ejpam-5049	91	14	in	in	ADP
ejpam-5049	91	15	terms	term	NOUN
ejpam-5049	91	16	of	of	ADP
ejpam-5049	91	17	shifted	shift	VERB
ejpam-5049	91	18	chebyshev	chebyshev	NOUN
ejpam-5049	91	19	polynomials	polynomial	NOUN
ejpam-5049	91	20	polynomials	polynomial	NOUN
ejpam-5049	91	21	.	.	PUNCT
ejpam-5049	92	1	following	follow	VERB
ejpam-5049	92	2	that	that	PRON
ejpam-5049	92	3	,	,	PUNCT
ejpam-5049	92	4	the	the	DET
ejpam-5049	92	5	fractional	fractional	ADJ
ejpam-5049	92	6	-	-	PUNCT
ejpam-5049	92	7	order	order	NOUN
ejpam-5049	92	8	terms	term	NOUN
ejpam-5049	92	9	can	can	AUX
ejpam-5049	92	10	be	be	AUX
ejpam-5049	92	11	changed	change	VERB
ejpam-5049	92	12	into	into	ADP
ejpam-5049	92	13	the	the	DET
ejpam-5049	92	14	following	follow	VERB
ejpam-5049	92	15	algebraic	algebraic	ADJ
ejpam-5049	92	16	equations	equation	NOUN
ejpam-5049	92	17	:	:	PUNCT
ejpam-5049	92	18	dα	dα	PROPN
ejpam-5049	92	19	(	(	PUNCT
ejpam-5049	92	20	ωm(β	ωm(β	NOUN
ejpam-5049	92	21	)	)	PUNCT
ejpam-5049	92	22	)	)	PUNCT
ejpam-5049	93	1	=	=	PUNCT
ejpam-5049	93	2	m∑	m∑	CCONJ
ejpam-5049	93	3	i=⌈α⌉	i=⌈α⌉	PROPN
ejpam-5049	93	4	i−⌈α⌉∑	i−⌈α⌉∑	NOUN
ejpam-5049	93	5	k=0	k=0	PROPN
ejpam-5049	93	6	ciχ	ciχ	PROPN
ejpam-5049	93	7	(	(	PUNCT
ejpam-5049	93	8	α	α	NOUN
ejpam-5049	93	9	)	)	PUNCT
ejpam-5049	93	10	i	i	PRON
ejpam-5049	93	11	,	,	PUNCT
ejpam-5049	93	12	k	k	PROPN
ejpam-5049	93	13	β	β	X
ejpam-5049	93	14	i−k−α	i−k−α	PROPN
ejpam-5049	93	15	,	,	PUNCT
ejpam-5049	93	16	(	(	PUNCT
ejpam-5049	93	17	8)	8)	NUM
ejpam-5049	93	18	χ	χ	NOUN
ejpam-5049	93	19	(	(	PUNCT
ejpam-5049	93	20	α	α	NOUN
ejpam-5049	93	21	)	)	PUNCT
ejpam-5049	93	22	i	i	PRON
ejpam-5049	93	23	,	,	PUNCT
ejpam-5049	93	24	k	k	PROPN
ejpam-5049	93	25	=	=	PRON
ejpam-5049	93	26	(	(	PUNCT
ejpam-5049	93	27	−1)k	−1)k	PROPN
ejpam-5049	93	28	4i−k2iγ(2i−	4i−k2iγ(2i−	NUM
ejpam-5049	93	29	k)γ(i−	k)γ(i−	PROPN
ejpam-5049	94	1	k	k	PROPN
ejpam-5049	95	1	+	+	CCONJ
ejpam-5049	95	2	1	1	X
ejpam-5049	95	3	)	)	PUNCT
ejpam-5049	95	4	γ(k	γ(k	NOUN
ejpam-5049	95	5	+	+	PROPN
ejpam-5049	96	1	1)γ(2i−	1)γ(2i−	NUM
ejpam-5049	96	2	2k	2k	NUM
ejpam-5049	96	3	+	+	CCONJ
ejpam-5049	96	4	1)γ(i−	1)γ(i−	NUM
ejpam-5049	97	1	k	k	NOUN
ejpam-5049	98	1	+	+	CCONJ
ejpam-5049	98	2	1−	1−	NUM
ejpam-5049	98	3	α	α	NOUN
ejpam-5049	98	4	)	)	PUNCT
ejpam-5049	98	5	,	,	PUNCT
ejpam-5049	98	6	(	(	PUNCT
ejpam-5049	98	7	9	9	X
ejpam-5049	98	8	)	)	PUNCT
ejpam-5049	98	9	where	where	SCONJ
ejpam-5049	98	10	γ	γ	X
ejpam-5049	98	11	(	(	PUNCT
ejpam-5049	98	12	.	.	PUNCT
ejpam-5049	98	13	)	)	PUNCT
ejpam-5049	98	14	is	be	AUX
ejpam-5049	98	15	the	the	DET
ejpam-5049	98	16	gamma	gamma	PROPN
ejpam-5049	98	17	function	function	NOUN
ejpam-5049	98	18	.	.	PUNCT
ejpam-5049	99	1	2.3	2.3	NUM
ejpam-5049	99	2	.	.	PUNCT
ejpam-5049	100	1	error	error	NOUN
ejpam-5049	100	2	analysis	analysis	NOUN
ejpam-5049	100	3	this	this	DET
ejpam-5049	100	4	section	section	NOUN
ejpam-5049	100	5	focuses	focus	VERB
ejpam-5049	100	6	specifically	specifically	ADV
ejpam-5049	100	7	on	on	ADP
ejpam-5049	100	8	introducing	introduce	VERB
ejpam-5049	100	9	the	the	DET
ejpam-5049	100	10	convergence	convergence	NOUN
ejpam-5049	100	11	analysis	analysis	NOUN
ejpam-5049	100	12	and	and	CCONJ
ejpam-5049	100	13	assessing	assess	VERB
ejpam-5049	100	14	the	the	DET
ejpam-5049	100	15	upper	upper	ADJ
ejpam-5049	100	16	limit	limit	NOUN
ejpam-5049	100	17	of	of	ADP
ejpam-5049	100	18	the	the	DET
ejpam-5049	100	19	error	error	NOUN
ejpam-5049	100	20	associated	associate	VERB
ejpam-5049	100	21	with	with	ADP
ejpam-5049	100	22	the	the	DET
ejpam-5049	100	23	proposed	propose	VERB
ejpam-5049	100	24	formula	formula	NOUN
ejpam-5049	100	25	.	.	PUNCT
ejpam-5049	101	1	theorem	theorem	NOUN
ejpam-5049	101	2	2	2	NUM
ejpam-5049	101	3	.	.	PUNCT
ejpam-5049	102	1	[	[	X
ejpam-5049	102	2	7	7	X
ejpam-5049	102	3	]	]	PUNCT
ejpam-5049	102	4	suppose	suppose	VERB
ejpam-5049	102	5	that	that	SCONJ
ejpam-5049	102	6	the	the	DET
ejpam-5049	102	7	function	function	NOUN
ejpam-5049	102	8	ω(β	ω(β	NOUN
ejpam-5049	102	9	)	)	PUNCT
ejpam-5049	102	10	is	be	AUX
ejpam-5049	102	11	so	so	ADV
ejpam-5049	102	12	constrained	constrain	VERB
ejpam-5049	102	13	that	that	SCONJ
ejpam-5049	102	14	ω′′(β	ω′′(β	ADV
ejpam-5049	102	15	)	)	PUNCT
ejpam-5049	102	16	∈	∈	PROPN
ejpam-5049	102	17	l2[0	l2[0	PROPN
ejpam-5049	102	18	,	,	PUNCT
ejpam-5049	102	19	b	b	NOUN
ejpam-5049	102	20	]	]	PUNCT
ejpam-5049	102	21	and	and	CCONJ
ejpam-5049	102	22	|ω′′	|ω′′	ADP
ejpam-5049	102	23	(	(	PUNCT
ejpam-5049	103	1	β)|	β)|	PROPN
ejpam-5049	103	2	≦	≦	PROPN
ejpam-5049	103	3	c	c	NOUN
ejpam-5049	103	4	,	,	PUNCT
ejpam-5049	103	5	where	where	SCONJ
ejpam-5049	103	6	c	c	PROPN
ejpam-5049	103	7	is	be	AUX
ejpam-5049	103	8	a	a	DET
ejpam-5049	103	9	constant	constant	ADJ
ejpam-5049	103	10	.	.	PUNCT
ejpam-5049	104	1	then	then	ADV
ejpam-5049	104	2	the	the	DET
ejpam-5049	104	3	series	series	NOUN
ejpam-5049	104	4	(	(	PUNCT
ejpam-5049	104	5	6	6	NUM
ejpam-5049	104	6	)	)	PUNCT
ejpam-5049	104	7	of	of	ADP
ejpam-5049	104	8	the	the	DET
ejpam-5049	104	9	shifted	shift	VERB
ejpam-5049	104	10	chebyshev	chebyshev	NOUN
ejpam-5049	104	11	expansion	expansion	NOUN
ejpam-5049	104	12	is	be	AUX
ejpam-5049	104	13	uniformly	uniformly	ADV
ejpam-5049	104	14	convergent	convergent	ADJ
ejpam-5049	104	15	and	and	CCONJ
ejpam-5049	104	16	:	:	PUNCT
ejpam-5049	104	17	|aℓ|	|aℓ|	X
ejpam-5049	104	18	<	<	X
ejpam-5049	104	19	c	c	PROPN
ejpam-5049	104	20	ℓ2	ℓ2	PROPN
ejpam-5049	104	21	,	,	PUNCT
ejpam-5049	104	22	(	(	PUNCT
ejpam-5049	104	23	ℓ	ℓ	PROPN
ejpam-5049	104	24	∈	∈	PROPN
ejpam-5049	104	25	1	1	NUM
ejpam-5049	104	26	,	,	PUNCT
ejpam-5049	104	27	2	2	NUM
ejpam-5049	104	28	,	,	PUNCT
ejpam-5049	104	29	...	...	PUNCT
ejpam-5049	104	30	)	)	PUNCT
ejpam-5049	104	31	.	.	PUNCT
ejpam-5049	105	1	(	(	PUNCT
ejpam-5049	105	2	10	10	NUM
ejpam-5049	105	3	)	)	PUNCT
ejpam-5049	105	4	theorem	theorem	NOUN
ejpam-5049	105	5	3	3	NUM
ejpam-5049	105	6	.	.	PUNCT
ejpam-5049	106	1	[	[	X
ejpam-5049	106	2	7	7	X
ejpam-5049	106	3	]	]	PUNCT
ejpam-5049	106	4	suppose	suppose	VERB
ejpam-5049	106	5	that	that	SCONJ
ejpam-5049	106	6	ω(β	ω(β	NOUN
ejpam-5049	106	7	)	)	PUNCT
ejpam-5049	106	8	∈	∈	PROPN
ejpam-5049	106	9	cm[0	cm[0	PROPN
ejpam-5049	106	10	,	,	PUNCT
ejpam-5049	106	11	1	1	NUM
ejpam-5049	106	12	]	]	PUNCT
ejpam-5049	106	13	.	.	PUNCT
ejpam-5049	107	1	then	then	ADV
ejpam-5049	107	2	the	the	DET
ejpam-5049	107	3	error	error	NOUN
ejpam-5049	107	4	in	in	ADP
ejpam-5049	107	5	approximating	approximate	VERB
ejpam-5049	107	6	the	the	DET
ejpam-5049	107	7	function	function	NOUN
ejpam-5049	107	8	ω(β	ω(β	NOUN
ejpam-5049	107	9	)	)	PUNCT
ejpam-5049	107	10	by	by	ADP
ejpam-5049	107	11	ωm(β	ωm(β	NOUN
ejpam-5049	107	12	)	)	PUNCT
ejpam-5049	107	13	by	by	ADP
ejpam-5049	107	14	using	use	VERB
ejpam-5049	107	15	the	the	DET
ejpam-5049	107	16	formula	formula	NOUN
ejpam-5049	107	17	(	(	PUNCT
ejpam-5049	107	18	6	6	NUM
ejpam-5049	107	19	)	)	PUNCT
ejpam-5049	107	20	can	can	AUX
ejpam-5049	107	21	be	be	AUX
ejpam-5049	107	22	bounded	bound	VERB
ejpam-5049	107	23	by	by	ADP
ejpam-5049	107	24	:	:	PUNCT
ejpam-5049	107	25	∥ϕ(β)−	∥ϕ(β)−	PROPN
ejpam-5049	107	26	ϕm(β)∥	ϕm(β)∥	PROPN
ejpam-5049	107	27	≦	≦	VERB
ejpam-5049	107	28	℘∆m+1	℘∆m+1	PROPN
ejpam-5049	107	29	(	(	PUNCT
ejpam-5049	107	30	m+	m+	NOUN
ejpam-5049	107	31	1	1	NUM
ejpam-5049	107	32	)	)	PUNCT
ejpam-5049	107	33	!	!	PUNCT
ejpam-5049	108	1	√	√	NUM
ejpam-5049	109	1	π	π	NOUN
ejpam-5049	109	2	2	2	NUM
ejpam-5049	109	3	and	and	CCONJ
ejpam-5049	109	4	℘	℘	PROPN
ejpam-5049	109	5	=	=	SYM
ejpam-5049	109	6	maxt∈[0,1]ϕ	maxt∈[0,1]ϕ	X
ejpam-5049	109	7	(	(	PUNCT
ejpam-5049	109	8	m+1)(β	m+1)(β	NOUN
ejpam-5049	109	9	)	)	PUNCT
ejpam-5049	109	10	(	(	PUNCT
ejpam-5049	109	11	11	11	NUM
ejpam-5049	109	12	)	)	PUNCT
ejpam-5049	109	13	(	(	PUNCT
ejpam-5049	109	14	∆	∆	X
ejpam-5049	109	15	=	=	PUNCT
ejpam-5049	109	16	max{β0	max{β0	ADV
ejpam-5049	109	17	,	,	PUNCT
ejpam-5049	109	18	β	β	X
ejpam-5049	109	19	−	−	NOUN
ejpam-5049	109	20	β0	β0	PROPN
ejpam-5049	109	21	}	}	PUNCT
ejpam-5049	109	22	)	)	PUNCT
ejpam-5049	109	23	.	.	PUNCT
ejpam-5049	110	1	khaled	khaled	PROPN
ejpam-5049	110	2	m.	m.	PROPN
ejpam-5049	110	3	saad	saad	PROPN
ejpam-5049	110	4	,	,	PUNCT
ejpam-5049	110	5	m.	m.	NOUN
ejpam-5049	110	6	q.	q.	PROPN
ejpam-5049	110	7	khirallah	khirallah	PROPN
ejpam-5049	110	8	/	/	SYM
ejpam-5049	110	9	eur	eur	PROPN
ejpam-5049	110	10	.	.	PUNCT
ejpam-5049	111	1	j.	j.	PROPN
ejpam-5049	111	2	pure	pure	PROPN
ejpam-5049	111	3	appl	appl	PROPN
ejpam-5049	111	4	.	.	PROPN
ejpam-5049	111	5	math	math	PROPN
ejpam-5049	111	6	,	,	PUNCT
ejpam-5049	111	7	17	17	NUM
ejpam-5049	111	8	(	(	PUNCT
ejpam-5049	111	9	1	1	NUM
ejpam-5049	111	10	)	)	PUNCT
ejpam-5049	111	11	(	(	PUNCT
ejpam-5049	111	12	2024	2024	NUM
ejpam-5049	111	13	)	)	PUNCT
ejpam-5049	111	14	,	,	PUNCT
ejpam-5049	111	15	477	477	NUM
ejpam-5049	111	16	-	-	SYM
ejpam-5049	111	17	503	503	NUM
ejpam-5049	111	18	482	482	NUM
ejpam-5049	111	19	3	3	NUM
ejpam-5049	111	20	.	.	X
ejpam-5049	111	21	approach	approach	NOUN
ejpam-5049	111	22	to	to	ADP
ejpam-5049	111	23	fractional	fractional	ADJ
ejpam-5049	111	24	fredholm	fredholm	NOUN
ejpam-5049	111	25	integro	integro	ADJ
ejpam-5049	111	26	-	-	PUNCT
ejpam-5049	111	27	differential	differential	NOUN
ejpam-5049	111	28	equation	equation	NOUN
ejpam-5049	111	29	solving	solve	VERB
ejpam-5049	111	30	in	in	ADP
ejpam-5049	111	31	this	this	DET
ejpam-5049	111	32	section	section	NOUN
ejpam-5049	112	1	,	,	PUNCT
ejpam-5049	112	2	we	we	PRON
ejpam-5049	112	3	present	present	VERB
ejpam-5049	112	4	the	the	DET
ejpam-5049	112	5	schema	schema	NOUN
ejpam-5049	112	6	for	for	ADP
ejpam-5049	112	7	the	the	DET
ejpam-5049	112	8	following	follow	VERB
ejpam-5049	112	9	nonlinear	nonlinear	ADJ
ejpam-5049	112	10	fractional	fractional	ADJ
ejpam-5049	112	11	fredholm	fredholm	NOUN
ejpam-5049	112	12	integro	integro	ADJ
ejpam-5049	112	13	-	-	PUNCT
ejpam-5049	112	14	differential	differential	NOUN
ejpam-5049	112	15	equation	equation	NOUN
ejpam-5049	112	16	:	:	PUNCT
ejpam-5049	112	17	dαϕ(β	dαϕ(β	X
ejpam-5049	112	18	)	)	PUNCT
ejpam-5049	112	19	=	=	SYM
ejpam-5049	112	20	g	g	PROPN
ejpam-5049	112	21	(	(	PUNCT
ejpam-5049	112	22	β	β	X
ejpam-5049	112	23	,	,	PUNCT
ejpam-5049	112	24	ϕ(β	ϕ(β	PROPN
ejpam-5049	112	25	)	)	PUNCT
ejpam-5049	112	26	,	,	PUNCT
ejpam-5049	112	27	∫	∫	PROPN
ejpam-5049	112	28	1	1	NUM
ejpam-5049	112	29	0	0	NUM
ejpam-5049	112	30	h(β	h(β	PROPN
ejpam-5049	112	31	,	,	PUNCT
ejpam-5049	112	32	ϕ(β))dβ	ϕ(β))dβ	NOUN
ejpam-5049	112	33	)	)	PUNCT
ejpam-5049	112	34	,	,	PUNCT
ejpam-5049	112	35	0	0	PUNCT
ejpam-5049	112	36	<	<	X
ejpam-5049	112	37	β	β	X
ejpam-5049	112	38	≤	≤	ADV
ejpam-5049	112	39	1	1	NUM
ejpam-5049	112	40	,	,	PUNCT
ejpam-5049	112	41	n−	n−	NOUN
ejpam-5049	112	42	1	1	NUM
ejpam-5049	112	43	<	<	X
ejpam-5049	112	44	α	α	PROPN
ejpam-5049	112	45	≤	≤	PROPN
ejpam-5049	112	46	n.	n.	NOUN
ejpam-5049	112	47	(	(	PUNCT
ejpam-5049	112	48	12	12	NUM
ejpam-5049	112	49	)	)	PUNCT
ejpam-5049	112	50	here	here	ADV
ejpam-5049	112	51	,	,	PUNCT
ejpam-5049	112	52	we	we	PRON
ejpam-5049	112	53	use	use	VERB
ejpam-5049	112	54	the	the	DET
ejpam-5049	112	55	shifted	shift	VERB
ejpam-5049	112	56	chebyshev	chebyshev	NOUN
ejpam-5049	112	57	polynomials	polynomial	NOUN
ejpam-5049	112	58	collocation	collocation	NOUN
ejpam-5049	112	59	method	method	NOUN
ejpam-5049	112	60	and	and	CCONJ
ejpam-5049	112	61	theorem	theorem	VERB
ejpam-5049	112	62	1	1	NUM
ejpam-5049	112	63	to	to	PART
ejpam-5049	112	64	solve	solve	VERB
ejpam-5049	112	65	(	(	PUNCT
ejpam-5049	112	66	12	12	NUM
ejpam-5049	112	67	)	)	PUNCT
ejpam-5049	112	68	as	as	SCONJ
ejpam-5049	112	69	follows	follow	VERB
ejpam-5049	112	70	m∑	m∑	CCONJ
ejpam-5049	112	71	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	112	72	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	112	73	k=0	k=0	PROPN
ejpam-5049	112	74	cjχ	cjχ	PROPN
ejpam-5049	112	75	(	(	PUNCT
ejpam-5049	112	76	α	α	NOUN
ejpam-5049	112	77	)	)	PUNCT
ejpam-5049	112	78	j	j	PROPN
ejpam-5049	112	79	,	,	PUNCT
ejpam-5049	112	80	k	k	PROPN
ejpam-5049	112	81	β	β	X
ejpam-5049	112	82	j−k−α	j−k−α	NOUN
ejpam-5049	112	83	=	=	PUNCT
ejpam-5049	112	84	g	g	PROPN
ejpam-5049	112	85	β	β	PROPN
ejpam-5049	112	86	,	,	PUNCT
ejpam-5049	112	87	m∑	m∑	CCONJ
ejpam-5049	112	88	j=0	j=0	PROPN
ejpam-5049	112	89	cj	cj	PROPN
ejpam-5049	112	90	φj(β	φj(β	PROPN
ejpam-5049	112	91	)	)	PUNCT
ejpam-5049	112	92	,	,	PUNCT
ejpam-5049	112	93	∫	∫	PROPN
ejpam-5049	112	94	1	1	NUM
ejpam-5049	112	95	0	0	NUM
ejpam-5049	112	96	h	h	PROPN
ejpam-5049	112	97	β	β	NOUN
ejpam-5049	112	98	,	,	PUNCT
ejpam-5049	112	99	m∑	m∑	CCONJ
ejpam-5049	112	100	j=0	j=0	PROPN
ejpam-5049	112	101	cj	cj	PROPN
ejpam-5049	112	102	φj(β	φj(β	PROPN
ejpam-5049	112	103	)	)	PUNCT
ejpam-5049	113	1			PROPN
ejpam-5049	113	2	dβ	dβ	ADP
ejpam-5049	113	3			PROPN
ejpam-5049	113	4	.	.	PUNCT
ejpam-5049	114	1	(	(	PUNCT
ejpam-5049	114	2	13	13	NUM
ejpam-5049	114	3	)	)	PUNCT
ejpam-5049	114	4	therefore	therefore	ADV
ejpam-5049	114	5	,	,	PUNCT
ejpam-5049	114	6	we	we	PRON
ejpam-5049	114	7	use	use	VERB
ejpam-5049	114	8	the	the	DET
ejpam-5049	114	9	following	follow	VERB
ejpam-5049	114	10	numerical	numerical	ADJ
ejpam-5049	114	11	methods	method	NOUN
ejpam-5049	114	12	for	for	ADP
ejpam-5049	114	13	integration	integration	NOUN
ejpam-5049	114	14	to	to	PART
ejpam-5049	114	15	analyze	analyze	VERB
ejpam-5049	114	16	the	the	DET
ejpam-5049	114	17	system	system	NOUN
ejpam-5049	114	18	of	of	ADP
ejpam-5049	114	19	equations	equation	NOUN
ejpam-5049	114	20	given	give	VERB
ejpam-5049	114	21	in	in	ADP
ejpam-5049	114	22	equation	equation	NOUN
ejpam-5049	114	23	(	(	PUNCT
ejpam-5049	114	24	13	13	NUM
ejpam-5049	114	25	):	):	PUNCT
ejpam-5049	114	26	(	(	PUNCT
ejpam-5049	114	27	i	i	NOUN
ejpam-5049	114	28	)	)	PUNCT
ejpam-5049	114	29	trapezoidal	trapezoidal	NOUN
ejpam-5049	114	30	’s	’s	PART
ejpam-5049	114	31	method	method	NOUN
ejpam-5049	114	32	m∑	m∑	VERB
ejpam-5049	114	33	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	114	34	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	114	35	k=0	k=0	PROPN
ejpam-5049	114	36	cjχ	cjχ	PROPN
ejpam-5049	114	37	(	(	PUNCT
ejpam-5049	114	38	α	α	NOUN
ejpam-5049	114	39	)	)	PUNCT
ejpam-5049	114	40	j	j	PROPN
ejpam-5049	114	41	,	,	PUNCT
ejpam-5049	114	42	k	k	PROPN
ejpam-5049	114	43	β	β	X
ejpam-5049	114	44	j−k−α	j−k−α	NOUN
ejpam-5049	114	45	=	=	PUNCT
ejpam-5049	114	46	g	g	PROPN
ejpam-5049	114	47	β	β	PROPN
ejpam-5049	114	48	,	,	PUNCT
ejpam-5049	114	49	m∑	m∑	CCONJ
ejpam-5049	114	50	j=0	j=0	PROPN
ejpam-5049	114	51	cj	cj	PROPN
ejpam-5049	114	52	φj(β	φj(β	PROPN
ejpam-5049	114	53	)	)	PUNCT
ejpam-5049	114	54	,	,	PUNCT
ejpam-5049	114	55	h	h	NOUN
ejpam-5049	114	56	2	2	NUM
ejpam-5049	114	57	(	(	PUNCT
ejpam-5049	114	58	f	f	PROPN
ejpam-5049	114	59	(	(	PUNCT
ejpam-5049	114	60	β0	β0	PROPN
ejpam-5049	114	61	)	)	PUNCT
ejpam-5049	115	1	+	+	NUM
ejpam-5049	116	1	f	f	X
ejpam-5049	116	2	(	(	PUNCT
ejpam-5049	116	3	βl	βl	NOUN
ejpam-5049	116	4	)	)	PUNCT
ejpam-5049	116	5	+	+	CCONJ
ejpam-5049	116	6	2	2	NUM
ejpam-5049	116	7	l−1∑	l−1∑	NOUN
ejpam-5049	116	8	k=1	k=1	PROPN
ejpam-5049	116	9	f	f	PROPN
ejpam-5049	116	10	(	(	PUNCT
ejpam-5049	116	11	βk	βk	NOUN
ejpam-5049	116	12	)	)	PUNCT
ejpam-5049	116	13	)	)	PUNCT
ejpam-5049	117	1			PROPN
ejpam-5049	117	2	.	.	PUNCT
ejpam-5049	118	1	(	(	PUNCT
ejpam-5049	118	2	14	14	NUM
ejpam-5049	118	3	)	)	PUNCT
ejpam-5049	118	4	at	at	ADP
ejpam-5049	118	5	these	these	DET
ejpam-5049	118	6	points	point	NOUN
ejpam-5049	118	7	,	,	PUNCT
ejpam-5049	118	8	βs	βs	X
ejpam-5049	118	9	,	,	PUNCT
ejpam-5049	118	10	s	s	PART
ejpam-5049	118	11	=	=	NOUN
ejpam-5049	118	12	0	0	NUM
ejpam-5049	118	13	,	,	PUNCT
ejpam-5049	118	14	1	1	NUM
ejpam-5049	118	15	,	,	PUNCT
ejpam-5049	118	16	...	...	PUNCT
ejpam-5049	118	17	,	,	PUNCT
ejpam-5049	118	18	m−	m−	PROPN
ejpam-5049	118	19	α	α	INTJ
ejpam-5049	118	20	,	,	PUNCT
ejpam-5049	118	21	we	we	PRON
ejpam-5049	118	22	collocate	collocate	VERB
ejpam-5049	118	23	(	(	PUNCT
ejpam-5049	118	24	14	14	NUM
ejpam-5049	118	25	)	)	PUNCT
ejpam-5049	118	26	.	.	PUNCT
ejpam-5049	119	1	m∑	m∑	PRON
ejpam-5049	119	2	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	119	3	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	119	4	k=0	k=0	PROPN
ejpam-5049	119	5	cjχ	cjχ	PROPN
ejpam-5049	119	6	(	(	PUNCT
ejpam-5049	119	7	α	α	NOUN
ejpam-5049	119	8	)	)	PUNCT
ejpam-5049	119	9	j	j	PROPN
ejpam-5049	119	10	,	,	PUNCT
ejpam-5049	119	11	k	k	PROPN
ejpam-5049	119	12	β	β	X
ejpam-5049	120	1	j−k−α	j−k−α	NOUN
ejpam-5049	120	2	s	s	PART
ejpam-5049	120	3	=	=	PROPN
ejpam-5049	120	4	g	g	PROPN
ejpam-5049	120	5	βs	βs	NOUN
ejpam-5049	120	6	,	,	PUNCT
ejpam-5049	120	7	m∑	m∑	CCONJ
ejpam-5049	120	8	j=0	j=0	PROPN
ejpam-5049	120	9	cj	cj	NOUN
ejpam-5049	120	10	φj(βs	φj(β	NOUN
ejpam-5049	120	11	)	)	PUNCT
ejpam-5049	120	12	,	,	PUNCT
ejpam-5049	120	13	h	h	NOUN
ejpam-5049	120	14	2	2	NUM
ejpam-5049	120	15	(	(	PUNCT
ejpam-5049	120	16	f	f	PROPN
ejpam-5049	120	17	(	(	PUNCT
ejpam-5049	120	18	β0	β0	PROPN
ejpam-5049	120	19	)	)	PUNCT
ejpam-5049	121	1	+	+	NUM
ejpam-5049	122	1	f	f	X
ejpam-5049	122	2	(	(	PUNCT
ejpam-5049	122	3	βl	βl	NOUN
ejpam-5049	122	4	)	)	PUNCT
ejpam-5049	122	5	+	+	CCONJ
ejpam-5049	122	6	2	2	NUM
ejpam-5049	122	7	l−1∑	l−1∑	NOUN
ejpam-5049	122	8	k=1	k=1	PROPN
ejpam-5049	122	9	f	f	PROPN
ejpam-5049	122	10	(	(	PUNCT
ejpam-5049	122	11	βk	βk	NOUN
ejpam-5049	122	12	)	)	PUNCT
ejpam-5049	122	13	)	)	PUNCT
ejpam-5049	123	1			PROPN
ejpam-5049	123	2	,	,	PUNCT
ejpam-5049	123	3	(	(	PUNCT
ejpam-5049	123	4	15	15	NUM
ejpam-5049	123	5	)	)	PUNCT
ejpam-5049	124	1	where	where	SCONJ
ejpam-5049	124	2	f	f	PROPN
ejpam-5049	124	3	(	(	PUNCT
ejpam-5049	124	4	β	β	X
ejpam-5049	124	5	)	)	PUNCT
ejpam-5049	124	6	=	=	SYM
ejpam-5049	125	1	h	h	NOUN
ejpam-5049	125	2	(	(	PUNCT
ejpam-5049	125	3	β	β	X
ejpam-5049	125	4	,	,	PUNCT
ejpam-5049	125	5	∑m	∑m	PROPN
ejpam-5049	125	6	j=0	j=0	PROPN
ejpam-5049	125	7	cj	cj	PROPN
ejpam-5049	125	8	φj(β	φj(β	PROPN
ejpam-5049	125	9	)	)	PUNCT
ejpam-5049	125	10	)	)	PUNCT
ejpam-5049	125	11	.	.	PUNCT
ejpam-5049	126	1	(	(	PUNCT
ejpam-5049	126	2	ii	ii	X
ejpam-5049	126	3	)	)	PUNCT
ejpam-5049	126	4	simpson	simpson	PROPN
ejpam-5049	126	5	’s	’s	PART
ejpam-5049	126	6	1/3	1/3	NUM
ejpam-5049	126	7	method	method	NOUN
ejpam-5049	126	8	m∑	m∑	VERB
ejpam-5049	126	9	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	126	10	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	126	11	k=0	k=0	PROPN
ejpam-5049	126	12	ciχ	ciχ	PROPN
ejpam-5049	126	13	(	(	PUNCT
ejpam-5049	126	14	α	α	NOUN
ejpam-5049	126	15	)	)	PUNCT
ejpam-5049	126	16	i	i	PRON
ejpam-5049	126	17	,	,	PUNCT
ejpam-5049	126	18	k	k	PROPN
ejpam-5049	126	19	β	β	X
ejpam-5049	126	20	j−k−α	j−k−α	NOUN
ejpam-5049	126	21	=	=	PUNCT
ejpam-5049	126	22	g	g	PROPN
ejpam-5049	126	23	β	β	PROPN
ejpam-5049	126	24	,	,	PUNCT
ejpam-5049	126	25	m∑	m∑	CCONJ
ejpam-5049	126	26	j=0	j=0	PROPN
ejpam-5049	126	27	cj	cj	PROPN
ejpam-5049	126	28	φj(β	φj(β	PROPN
ejpam-5049	126	29	)	)	PUNCT
ejpam-5049	126	30	,	,	PUNCT
ejpam-5049	126	31	h	h	NOUN
ejpam-5049	126	32	2	2	NUM
ejpam-5049	126	33	(	(	PUNCT
ejpam-5049	126	34	f	f	PROPN
ejpam-5049	126	35	(	(	PUNCT
ejpam-5049	126	36	β0	β0	PROPN
ejpam-5049	126	37	)	)	PUNCT
ejpam-5049	127	1	+	+	NUM
ejpam-5049	127	2	f	f	X
ejpam-5049	127	3	(	(	PUNCT
ejpam-5049	127	4	βl	βl	NOUN
ejpam-5049	127	5	)	)	PUNCT
ejpam-5049	127	6	+	+	CCONJ
ejpam-5049	127	7	2	2	NUM
ejpam-5049	127	8	l	l	NOUN
ejpam-5049	127	9	2	2	X
ejpam-5049	127	10	−1∑	−1∑	NOUN
ejpam-5049	127	11	k=1	k=1	PROPN
ejpam-5049	127	12	f	f	PROPN
ejpam-5049	127	13	(	(	PUNCT
ejpam-5049	127	14	β2k	β2k	PUNCT
ejpam-5049	127	15	)	)	PUNCT
ejpam-5049	127	16	+	+	CCONJ
ejpam-5049	127	17	4	4	NUM
ejpam-5049	127	18	l	l	NOUN
ejpam-5049	128	1	2∑	2∑	X
ejpam-5049	129	1	k=1	k=1	X
ejpam-5049	130	1	f	f	X
ejpam-5049	131	1	(	(	PUNCT
ejpam-5049	132	1	β2k−1	β2k−1	PROPN
ejpam-5049	132	2	)	)	PUNCT
ejpam-5049	132	3	)	)	PUNCT
ejpam-5049	133	1			PROPN
ejpam-5049	133	2	.	.	PUNCT
ejpam-5049	134	1	(	(	PUNCT
ejpam-5049	134	2	16	16	NUM
ejpam-5049	134	3	)	)	PUNCT
ejpam-5049	134	4	khaled	khaled	PROPN
ejpam-5049	134	5	m.	m.	NOUN
ejpam-5049	134	6	saad	saad	PROPN
ejpam-5049	134	7	,	,	PUNCT
ejpam-5049	134	8	m.	m.	NOUN
ejpam-5049	134	9	q.	q.	PROPN
ejpam-5049	134	10	khirallah	khirallah	PROPN
ejpam-5049	134	11	/	/	SYM
ejpam-5049	134	12	eur	eur	PROPN
ejpam-5049	134	13	.	.	PUNCT
ejpam-5049	135	1	j.	j.	PROPN
ejpam-5049	135	2	pure	pure	PROPN
ejpam-5049	135	3	appl	appl	PROPN
ejpam-5049	135	4	.	.	PROPN
ejpam-5049	135	5	math	math	PROPN
ejpam-5049	135	6	,	,	PUNCT
ejpam-5049	135	7	17	17	NUM
ejpam-5049	135	8	(	(	PUNCT
ejpam-5049	135	9	1	1	NUM
ejpam-5049	135	10	)	)	PUNCT
ejpam-5049	135	11	(	(	PUNCT
ejpam-5049	135	12	2024	2024	NUM
ejpam-5049	135	13	)	)	PUNCT
ejpam-5049	135	14	,	,	PUNCT
ejpam-5049	135	15	477	477	NUM
ejpam-5049	135	16	-	-	SYM
ejpam-5049	135	17	503	503	NUM
ejpam-5049	135	18	483	483	NUM
ejpam-5049	135	19	at	at	ADP
ejpam-5049	135	20	these	these	DET
ejpam-5049	135	21	points	point	NOUN
ejpam-5049	135	22	,	,	PUNCT
ejpam-5049	135	23	βs	βs	X
ejpam-5049	135	24	,	,	PUNCT
ejpam-5049	135	25	s	s	PART
ejpam-5049	135	26	=	=	NOUN
ejpam-5049	135	27	0	0	NUM
ejpam-5049	135	28	,	,	PUNCT
ejpam-5049	135	29	1	1	NUM
ejpam-5049	135	30	,	,	PUNCT
ejpam-5049	135	31	...	...	PUNCT
ejpam-5049	135	32	,	,	PUNCT
ejpam-5049	135	33	m−	m−	PROPN
ejpam-5049	135	34	α	α	INTJ
ejpam-5049	135	35	,	,	PUNCT
ejpam-5049	135	36	we	we	PRON
ejpam-5049	135	37	collocate	collocate	VERB
ejpam-5049	135	38	(	(	PUNCT
ejpam-5049	135	39	16	16	NUM
ejpam-5049	135	40	)	)	PUNCT
ejpam-5049	135	41	.	.	PUNCT
ejpam-5049	136	1	m∑	m∑	PRON
ejpam-5049	136	2	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	136	3	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	136	4	k=0	k=0	PROPN
ejpam-5049	136	5	cjχ	cjχ	PROPN
ejpam-5049	136	6	(	(	PUNCT
ejpam-5049	136	7	α	α	NOUN
ejpam-5049	136	8	)	)	PUNCT
ejpam-5049	136	9	j	j	PROPN
ejpam-5049	136	10	,	,	PUNCT
ejpam-5049	136	11	k	k	PROPN
ejpam-5049	136	12	β	β	X
ejpam-5049	137	1	j−k−α	j−k−α	NOUN
ejpam-5049	137	2	s	s	PART
ejpam-5049	137	3	=	=	PROPN
ejpam-5049	137	4	g	g	PROPN
ejpam-5049	137	5	βs	βs	NOUN
ejpam-5049	137	6	,	,	PUNCT
ejpam-5049	137	7	m∑	m∑	CCONJ
ejpam-5049	137	8	j=0	j=0	PROPN
ejpam-5049	137	9	cj	cj	PROPN
ejpam-5049	137	10	φj(β	φj(β	PROPN
ejpam-5049	137	11	)	)	PUNCT
ejpam-5049	137	12	,	,	PUNCT
ejpam-5049	137	13	h	h	NOUN
ejpam-5049	137	14	2	2	NUM
ejpam-5049	137	15	(	(	PUNCT
ejpam-5049	137	16	f	f	PROPN
ejpam-5049	137	17	(	(	PUNCT
ejpam-5049	137	18	β0	β0	PROPN
ejpam-5049	137	19	)	)	PUNCT
ejpam-5049	138	1	+	+	NUM
ejpam-5049	138	2	f	f	X
ejpam-5049	138	3	(	(	PUNCT
ejpam-5049	138	4	βl	βl	NOUN
ejpam-5049	138	5	)	)	PUNCT
ejpam-5049	138	6	+	+	CCONJ
ejpam-5049	138	7	2	2	NUM
ejpam-5049	138	8	l	l	NOUN
ejpam-5049	138	9	2	2	X
ejpam-5049	138	10	−1∑	−1∑	NOUN
ejpam-5049	138	11	k=1	k=1	PROPN
ejpam-5049	138	12	f	f	PROPN
ejpam-5049	138	13	(	(	PUNCT
ejpam-5049	138	14	β2k	β2k	PUNCT
ejpam-5049	138	15	)	)	PUNCT
ejpam-5049	138	16	+	+	CCONJ
ejpam-5049	138	17	4	4	NUM
ejpam-5049	138	18	l	l	NOUN
ejpam-5049	139	1	2∑	2∑	X
ejpam-5049	140	1	k=1	k=1	X
ejpam-5049	141	1	f	f	X
ejpam-5049	142	1	(	(	PUNCT
ejpam-5049	143	1	β2k−1	β2k−1	PROPN
ejpam-5049	143	2	)	)	PUNCT
ejpam-5049	143	3	)	)	PUNCT
ejpam-5049	144	1			PROPN
ejpam-5049	144	2	,	,	PUNCT
ejpam-5049	144	3	(	(	PUNCT
ejpam-5049	144	4	17	17	NUM
ejpam-5049	144	5	)	)	PUNCT
ejpam-5049	145	1	where	where	SCONJ
ejpam-5049	145	2	f	f	PROPN
ejpam-5049	145	3	(	(	PUNCT
ejpam-5049	145	4	β	β	X
ejpam-5049	145	5	)	)	PUNCT
ejpam-5049	145	6	=	=	SYM
ejpam-5049	146	1	h	h	NOUN
ejpam-5049	146	2	(	(	PUNCT
ejpam-5049	146	3	β	β	X
ejpam-5049	146	4	,	,	PUNCT
ejpam-5049	146	5	∑m	∑m	PROPN
ejpam-5049	146	6	j=0	j=0	PROPN
ejpam-5049	146	7	cj	cj	PROPN
ejpam-5049	146	8	φj(β	φj(β	PROPN
ejpam-5049	146	9	)	)	PUNCT
ejpam-5049	146	10	)	)	PUNCT
ejpam-5049	146	11	.	.	PUNCT
ejpam-5049	147	1	(	(	PUNCT
ejpam-5049	147	2	iii	iii	X
ejpam-5049	147	3	)	)	PUNCT
ejpam-5049	147	4	simpson	simpson	PROPN
ejpam-5049	147	5	’s	’s	PART
ejpam-5049	147	6	3/8	3/8	NUM
ejpam-5049	147	7	method	method	NOUN
ejpam-5049	147	8	m∑	m∑	VERB
ejpam-5049	147	9	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	147	10	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	147	11	k=0	k=0	PROPN
ejpam-5049	147	12	cjχ	cjχ	PROPN
ejpam-5049	147	13	(	(	PUNCT
ejpam-5049	147	14	α	α	NOUN
ejpam-5049	147	15	)	)	PUNCT
ejpam-5049	147	16	j	j	PROPN
ejpam-5049	147	17	,	,	PUNCT
ejpam-5049	147	18	k	k	PROPN
ejpam-5049	147	19	β	β	X
ejpam-5049	147	20	j−k−α	j−k−α	NOUN
ejpam-5049	147	21	=	=	PUNCT
ejpam-5049	147	22	g	g	PROPN
ejpam-5049	147	23	(	(	PUNCT
ejpam-5049	147	24	β	β	X
ejpam-5049	147	25	,	,	PUNCT
ejpam-5049	147	26	m∑	m∑	CCONJ
ejpam-5049	147	27	j=0	j=0	PROPN
ejpam-5049	147	28	cj	cj	PROPN
ejpam-5049	147	29	φj(β	φj(β	PROPN
ejpam-5049	147	30	)	)	PUNCT
ejpam-5049	147	31	,	,	PUNCT
ejpam-5049	147	32	3h	3h	NUM
ejpam-5049	147	33	8	8	NUM
ejpam-5049	147	34	(	(	PUNCT
ejpam-5049	147	35	f	f	PROPN
ejpam-5049	147	36	(	(	PUNCT
ejpam-5049	147	37	β0	β0	PROPN
ejpam-5049	147	38	)	)	PUNCT
ejpam-5049	148	1	+	+	NUM
ejpam-5049	148	2	f	f	X
ejpam-5049	148	3	(	(	PUNCT
ejpam-5049	148	4	βl	βl	NOUN
ejpam-5049	148	5	)	)	PUNCT
ejpam-5049	148	6	+	+	CCONJ
ejpam-5049	148	7	3	3	NUM
ejpam-5049	148	8	l	l	NOUN
ejpam-5049	148	9	3∑	3∑	NUM
ejpam-5049	148	10	k=1	k=1	PUNCT
ejpam-5049	148	11	(	(	PUNCT
ejpam-5049	148	12	f	f	X
ejpam-5049	148	13	(	(	PUNCT
ejpam-5049	148	14	β3k−2	β3k−2	PROPN
ejpam-5049	148	15	)	)	PUNCT
ejpam-5049	149	1	+	+	NUM
ejpam-5049	149	2	f	f	X
ejpam-5049	149	3	(	(	PUNCT
ejpam-5049	149	4	β3k−1	β3k−1	PROPN
ejpam-5049	149	5	)	)	PUNCT
ejpam-5049	149	6	)	)	PUNCT
ejpam-5049	150	1	+2	+2	PROPN
ejpam-5049	150	2	n	n	CCONJ
ejpam-5049	150	3	3	3	NUM
ejpam-5049	150	4	−1∑	−1∑	NOUN
ejpam-5049	150	5	k=1	k=1	PROPN
ejpam-5049	150	6	f	f	PROPN
ejpam-5049	150	7	(	(	PUNCT
ejpam-5049	150	8	β3k	β3k	NOUN
ejpam-5049	150	9	)	)	PUNCT
ejpam-5049	150	10	)	)	PUNCT
ejpam-5049	150	11	)	)	PUNCT
ejpam-5049	150	12	.	.	PUNCT
ejpam-5049	151	1	(	(	PUNCT
ejpam-5049	151	2	18	18	NUM
ejpam-5049	151	3	)	)	PUNCT
ejpam-5049	151	4	at	at	ADP
ejpam-5049	151	5	these	these	DET
ejpam-5049	151	6	points	point	NOUN
ejpam-5049	151	7	,	,	PUNCT
ejpam-5049	151	8	βs	βs	X
ejpam-5049	151	9	,	,	PUNCT
ejpam-5049	151	10	s	s	PART
ejpam-5049	151	11	=	=	NOUN
ejpam-5049	151	12	0	0	NUM
ejpam-5049	151	13	,	,	PUNCT
ejpam-5049	151	14	1	1	NUM
ejpam-5049	151	15	,	,	PUNCT
ejpam-5049	151	16	...	...	PUNCT
ejpam-5049	151	17	,	,	PUNCT
ejpam-5049	151	18	m−	m−	PROPN
ejpam-5049	151	19	α	α	INTJ
ejpam-5049	151	20	,	,	PUNCT
ejpam-5049	151	21	we	we	PRON
ejpam-5049	151	22	collocate	collocate	VERB
ejpam-5049	151	23	(	(	PUNCT
ejpam-5049	151	24	18	18	NUM
ejpam-5049	151	25	)	)	PUNCT
ejpam-5049	151	26	.	.	PUNCT
ejpam-5049	152	1	m∑	m∑	PRON
ejpam-5049	152	2	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	152	3	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	152	4	k=0	k=0	PROPN
ejpam-5049	152	5	cjχ	cjχ	PROPN
ejpam-5049	152	6	(	(	PUNCT
ejpam-5049	152	7	α	α	NOUN
ejpam-5049	152	8	)	)	PUNCT
ejpam-5049	152	9	j	j	PROPN
ejpam-5049	152	10	,	,	PUNCT
ejpam-5049	152	11	k	k	PROPN
ejpam-5049	152	12	β	β	X
ejpam-5049	153	1	j−k−α	j−k−α	NOUN
ejpam-5049	153	2	s	s	PART
ejpam-5049	153	3	=	=	X
ejpam-5049	153	4	g	g	PROPN
ejpam-5049	153	5	(	(	PUNCT
ejpam-5049	153	6	βs	βs	INTJ
ejpam-5049	153	7	,	,	PUNCT
ejpam-5049	153	8	m∑	m∑	CCONJ
ejpam-5049	153	9	j=0	j=0	PROPN
ejpam-5049	153	10	cj	cj	PROPN
ejpam-5049	153	11	φj(β	φj(β	PROPN
ejpam-5049	153	12	)	)	PUNCT
ejpam-5049	153	13	,	,	PUNCT
ejpam-5049	153	14	3h	3h	NUM
ejpam-5049	153	15	8	8	NUM
ejpam-5049	153	16	(	(	PUNCT
ejpam-5049	153	17	f	f	PROPN
ejpam-5049	153	18	(	(	PUNCT
ejpam-5049	153	19	β0	β0	PROPN
ejpam-5049	153	20	)	)	PUNCT
ejpam-5049	153	21	+	+	NUM
ejpam-5049	153	22	f	f	X
ejpam-5049	153	23	(	(	PUNCT
ejpam-5049	153	24	βl	βl	NOUN
ejpam-5049	153	25	)	)	PUNCT
ejpam-5049	153	26	+	+	CCONJ
ejpam-5049	153	27	3	3	NUM
ejpam-5049	153	28	l	l	NOUN
ejpam-5049	153	29	3∑	3∑	NUM
ejpam-5049	153	30	k=1	k=1	PUNCT
ejpam-5049	153	31	(	(	PUNCT
ejpam-5049	153	32	f	f	X
ejpam-5049	153	33	(	(	PUNCT
ejpam-5049	153	34	β3k−2	β3k−2	PROPN
ejpam-5049	153	35	)	)	PUNCT
ejpam-5049	154	1	+	+	NUM
ejpam-5049	154	2	f	f	X
ejpam-5049	154	3	(	(	PUNCT
ejpam-5049	154	4	β3k−1	β3k−1	PROPN
ejpam-5049	154	5	)	)	PUNCT
ejpam-5049	154	6	)	)	PUNCT
ejpam-5049	155	1	+2	+2	NOUN
ejpam-5049	155	2	l	l	NOUN
ejpam-5049	156	1	3	3	X
ejpam-5049	156	2	−1∑	−1∑	INTJ
ejpam-5049	156	3	k=1	k=1	PROPN
ejpam-5049	156	4	f	f	PROPN
ejpam-5049	156	5	(	(	PUNCT
ejpam-5049	156	6	β3k	β3k	NOUN
ejpam-5049	156	7	)	)	PUNCT
ejpam-5049	156	8	)	)	PUNCT
ejpam-5049	156	9	)	)	PUNCT
ejpam-5049	156	10	,	,	PUNCT
ejpam-5049	156	11	(	(	PUNCT
ejpam-5049	156	12	19	19	NUM
ejpam-5049	156	13	)	)	PUNCT
ejpam-5049	157	1	where	where	SCONJ
ejpam-5049	157	2	f	f	PROPN
ejpam-5049	157	3	(	(	PUNCT
ejpam-5049	157	4	β	β	X
ejpam-5049	157	5	)	)	PUNCT
ejpam-5049	157	6	=	=	SYM
ejpam-5049	157	7	h	h	NOUN
ejpam-5049	157	8	(	(	PUNCT
ejpam-5049	157	9	β	β	X
ejpam-5049	157	10	,	,	PUNCT
ejpam-5049	157	11	∑m	∑m	PROPN
ejpam-5049	157	12	j=0	j=0	PROPN
ejpam-5049	157	13	cj	cj	PROPN
ejpam-5049	157	14	φj(β	φj(β	PROPN
ejpam-5049	157	15	)	)	PUNCT
ejpam-5049	157	16	)	)	PUNCT
ejpam-5049	158	1	.	.	PUNCT
ejpam-5049	159	1	the	the	DET
ejpam-5049	159	2	roots	root	NOUN
ejpam-5049	159	3	of	of	ADP
ejpam-5049	159	4	the	the	DET
ejpam-5049	159	5	shifted	shift	VERB
ejpam-5049	159	6	chebyshev	chebyshev	NOUN
ejpam-5049	159	7	polynomials	polynomial	NOUN
ejpam-5049	159	8	are	be	AUX
ejpam-5049	159	9	used	use	VERB
ejpam-5049	159	10	to	to	PART
ejpam-5049	159	11	find	find	VERB
ejpam-5049	159	12	appropriate	appropriate	ADJ
ejpam-5049	159	13	collocation	collocation	NOUN
ejpam-5049	159	14	locations	location	NOUN
ejpam-5049	159	15	φm+1−⌈α⌉.	φm+1−⌈α⌉.	NOUN
ejpam-5049	159	16	additionally	additionally	ADV
ejpam-5049	159	17	,	,	PUNCT
ejpam-5049	159	18	we	we	PRON
ejpam-5049	159	19	can	can	AUX
ejpam-5049	159	20	get	get	VERB
ejpam-5049	159	21	r	r	NOUN
ejpam-5049	159	22	equations	equation	NOUN
ejpam-5049	159	23	by	by	ADP
ejpam-5049	159	24	inserting	insert	VERB
ejpam-5049	159	25	(	(	PUNCT
ejpam-5049	159	26	6	6	NUM
ejpam-5049	159	27	)	)	PUNCT
ejpam-5049	159	28	in	in	ADP
ejpam-5049	159	29	the	the	DET
ejpam-5049	159	30	boundary	boundary	ADJ
ejpam-5049	159	31	conditions	condition	NOUN
ejpam-5049	159	32	.	.	PUNCT
ejpam-5049	160	1	equations	equation	NOUN
ejpam-5049	160	2	(	(	PUNCT
ejpam-5049	160	3	15	15	NUM
ejpam-5049	160	4	)	)	PUNCT
ejpam-5049	160	5	or	or	CCONJ
ejpam-5049	160	6	(	(	PUNCT
ejpam-5049	160	7	17	17	NUM
ejpam-5049	160	8	)	)	PUNCT
ejpam-5049	160	9	or	or	CCONJ
ejpam-5049	160	10	(	(	PUNCT
ejpam-5049	160	11	19	19	NUM
ejpam-5049	160	12	)	)	PUNCT
ejpam-5049	160	13	,	,	PUNCT
ejpam-5049	160	14	when	when	SCONJ
ejpam-5049	160	15	combined	combine	VERB
ejpam-5049	160	16	with	with	ADP
ejpam-5049	160	17	the	the	DET
ejpam-5049	160	18	r	r	NOUN
ejpam-5049	160	19	equations	equation	NOUN
ejpam-5049	160	20	of	of	ADP
ejpam-5049	160	21	the	the	DET
ejpam-5049	160	22	boundary	boundary	ADJ
ejpam-5049	160	23	conditions	condition	NOUN
ejpam-5049	160	24	,	,	PUNCT
ejpam-5049	160	25	gives	give	VERB
ejpam-5049	160	26	(	(	PUNCT
ejpam-5049	160	27	m	m	VERB
ejpam-5049	160	28	+	+	ADJ
ejpam-5049	160	29	1	1	NUM
ejpam-5049	160	30	)	)	PUNCT
ejpam-5049	160	31	of	of	ADP
ejpam-5049	160	32	an	an	DET
ejpam-5049	160	33	algebraic	algebraic	ADJ
ejpam-5049	160	34	equation	equation	NOUN
ejpam-5049	160	35	system	system	NOUN
ejpam-5049	160	36	that	that	PRON
ejpam-5049	160	37	can	can	AUX
ejpam-5049	160	38	be	be	AUX
ejpam-5049	160	39	solved	solve	VERB
ejpam-5049	160	40	using	use	VERB
ejpam-5049	160	41	the	the	DET
ejpam-5049	160	42	newton	newton	PROPN
ejpam-5049	160	43	iteration	iteration	NOUN
ejpam-5049	160	44	method	method	NOUN
ejpam-5049	160	45	for	for	ADP
ejpam-5049	160	46	the	the	DET
ejpam-5049	160	47	unknowns	unknown	NOUN
ejpam-5049	160	48	cj	cj	NOUN
ejpam-5049	160	49	,	,	PUNCT
ejpam-5049	160	50	j	j	PROPN
ejpam-5049	161	1	=	=	SYM
ejpam-5049	161	2	0	0	NUM
ejpam-5049	161	3	,	,	PUNCT
ejpam-5049	161	4	1	1	NUM
ejpam-5049	161	5	,	,	PUNCT
ejpam-5049	161	6	...	...	PUNCT
ejpam-5049	161	7	,	,	PUNCT
ejpam-5049	161	8	.,m	.,m	PROPN
ejpam-5049	161	9	.	.	PUNCT
ejpam-5049	162	1	khaled	khaled	PROPN
ejpam-5049	162	2	m.	m.	PROPN
ejpam-5049	162	3	saad	saad	PROPN
ejpam-5049	162	4	,	,	PUNCT
ejpam-5049	162	5	m.	m.	NOUN
ejpam-5049	162	6	q.	q.	PROPN
ejpam-5049	162	7	khirallah	khirallah	PROPN
ejpam-5049	162	8	/	/	SYM
ejpam-5049	162	9	eur	eur	PROPN
ejpam-5049	162	10	.	.	PUNCT
ejpam-5049	163	1	j.	j.	PROPN
ejpam-5049	163	2	pure	pure	PROPN
ejpam-5049	163	3	appl	appl	PROPN
ejpam-5049	163	4	.	.	PROPN
ejpam-5049	163	5	math	math	PROPN
ejpam-5049	163	6	,	,	PUNCT
ejpam-5049	163	7	17	17	NUM
ejpam-5049	163	8	(	(	PUNCT
ejpam-5049	163	9	1	1	NUM
ejpam-5049	163	10	)	)	PUNCT
ejpam-5049	163	11	(	(	PUNCT
ejpam-5049	163	12	2024	2024	NUM
ejpam-5049	163	13	)	)	PUNCT
ejpam-5049	163	14	,	,	PUNCT
ejpam-5049	163	15	477	477	NUM
ejpam-5049	163	16	-	-	SYM
ejpam-5049	163	17	503	503	NUM
ejpam-5049	163	18	484	484	NUM
ejpam-5049	163	19	4	4	NUM
ejpam-5049	163	20	.	.	PUNCT
ejpam-5049	163	21	numerical	numerical	ADJ
ejpam-5049	163	22	examples	example	NOUN
ejpam-5049	163	23	in	in	ADP
ejpam-5049	163	24	this	this	DET
ejpam-5049	163	25	section	section	NOUN
ejpam-5049	163	26	we	we	PRON
ejpam-5049	163	27	present	present	VERB
ejpam-5049	163	28	three	three	NUM
ejpam-5049	163	29	examples	example	NOUN
ejpam-5049	163	30	of	of	ADP
ejpam-5049	163	31	fractional	fractional	ADJ
ejpam-5049	163	32	fredholm	fredholm	NOUN
ejpam-5049	163	33	integro	integro	ADJ
ejpam-5049	163	34	-	-	PUNCT
ejpam-5049	163	35	differential	differential	NOUN
ejpam-5049	163	36	using	use	VERB
ejpam-5049	163	37	the	the	DET
ejpam-5049	163	38	proposed	propose	VERB
ejpam-5049	163	39	approach	approach	NOUN
ejpam-5049	163	40	.	.	PUNCT
ejpam-5049	164	1	example	example	NOUN
ejpam-5049	165	1	1	1	NUM
ejpam-5049	165	2	.	.	X
ejpam-5049	165	3	consider	consider	VERB
ejpam-5049	165	4	the	the	DET
ejpam-5049	165	5	following	follow	VERB
ejpam-5049	165	6	fractional	fractional	ADJ
ejpam-5049	165	7	fredholm	fredholm	NOUN
ejpam-5049	165	8	integro	integro	ADJ
ejpam-5049	165	9	-	-	PUNCT
ejpam-5049	165	10	differential	differential	NOUN
ejpam-5049	165	11	equation	equation	NOUN
ejpam-5049	165	12	[	[	X
ejpam-5049	165	13	8	8	X
ejpam-5049	165	14	]	]	SYM
ejpam-5049	165	15	dαϕ(β	dαϕ(β	PROPN
ejpam-5049	165	16	)	)	PUNCT
ejpam-5049	165	17	=	=	SYM
ejpam-5049	165	18	βeβ	βeβ	NOUN
ejpam-5049	165	19	+	+	CCONJ
ejpam-5049	165	20	eβ	eβ	VERB
ejpam-5049	165	21	−	−	PROPN
ejpam-5049	165	22	β	β	NOUN
ejpam-5049	166	1	+	+	CCONJ
ejpam-5049	166	2	∫	∫	PROPN
ejpam-5049	166	3	1	1	NUM
ejpam-5049	166	4	0	0	NUM
ejpam-5049	166	5	β	β	X
ejpam-5049	166	6	ϕ(β	ϕ(β	PROPN
ejpam-5049	166	7	)	)	PUNCT
ejpam-5049	166	8	dβ	dβ	ADJ
ejpam-5049	166	9	,	,	PUNCT
ejpam-5049	166	10	0	0	NUM
ejpam-5049	166	11	<	<	X
ejpam-5049	166	12	α	α	PROPN
ejpam-5049	166	13	≤	≤	NUM
ejpam-5049	166	14	1	1	NUM
ejpam-5049	166	15	,	,	PUNCT
ejpam-5049	166	16	(	(	PUNCT
ejpam-5049	166	17	20	20	NUM
ejpam-5049	166	18	)	)	PUNCT
ejpam-5049	166	19	subject	subject	NOUN
ejpam-5049	166	20	to	to	ADP
ejpam-5049	166	21	the	the	DET
ejpam-5049	166	22	initial	initial	ADJ
ejpam-5049	166	23	condition	condition	NOUN
ejpam-5049	166	24	ϕ(0	ϕ(0	NOUN
ejpam-5049	166	25	)	)	PUNCT
ejpam-5049	167	1	=	=	PUNCT
ejpam-5049	167	2	0	0	NUM
ejpam-5049	167	3	,	,	PUNCT
ejpam-5049	167	4	(	(	PUNCT
ejpam-5049	167	5	21	21	NUM
ejpam-5049	167	6	)	)	PUNCT
ejpam-5049	167	7	with	with	ADP
ejpam-5049	167	8	exact	exact	ADJ
ejpam-5049	167	9	solution	solution	NOUN
ejpam-5049	167	10	ϕ(β	ϕ(β	PROPN
ejpam-5049	167	11	)	)	PUNCT
ejpam-5049	167	12	=	=	SYM
ejpam-5049	168	1	βeβ	βeβ	INTJ
ejpam-5049	168	2	.	.	PUNCT
ejpam-5049	169	1	we	we	PRON
ejpam-5049	169	2	apply	apply	VERB
ejpam-5049	169	3	the	the	DET
ejpam-5049	169	4	provided	provide	VERB
ejpam-5049	169	5	procedure	procedure	NOUN
ejpam-5049	169	6	and	and	CCONJ
ejpam-5049	169	7	arrive	arrive	VERB
ejpam-5049	169	8	at	at	ADP
ejpam-5049	169	9	an	an	DET
ejpam-5049	169	10	approximation	approximation	NOUN
ejpam-5049	169	11	of	of	ADP
ejpam-5049	169	12	the	the	DET
ejpam-5049	169	13	solution	solution	NOUN
ejpam-5049	169	14	as	as	ADP
ejpam-5049	169	15	,	,	PUNCT
ejpam-5049	169	16	ϕm(β	ϕm(β	NUM
ejpam-5049	169	17	)	)	PUNCT
ejpam-5049	169	18	=	=	PUNCT
ejpam-5049	169	19	m∑	m∑	CCONJ
ejpam-5049	169	20	j=0	j=0	PROPN
ejpam-5049	169	21	cjφj(β	cjφj(β	PROPN
ejpam-5049	169	22	)	)	PUNCT
ejpam-5049	169	23	.	.	PUNCT
ejpam-5049	170	1	(	(	PUNCT
ejpam-5049	170	2	22	22	NUM
ejpam-5049	170	3	)	)	PUNCT
ejpam-5049	170	4	using	use	VERB
ejpam-5049	170	5	the	the	DET
ejpam-5049	170	6	equations	equation	NOUN
ejpam-5049	170	7	provided	provide	VERB
ejpam-5049	170	8	by	by	ADP
ejpam-5049	170	9	the	the	DET
ejpam-5049	170	10	trapezoidal	trapezoidal	ADJ
ejpam-5049	170	11	method	method	NOUN
ejpam-5049	170	12	(	(	PUNCT
ejpam-5049	170	13	15	15	NUM
ejpam-5049	170	14	)	)	PUNCT
ejpam-5049	170	15	,	,	PUNCT
ejpam-5049	170	16	simpson	simpson	PROPN
ejpam-5049	170	17	’s	’s	PART
ejpam-5049	170	18	method	method	NOUN
ejpam-5049	170	19	(	(	PUNCT
ejpam-5049	170	20	17	17	NUM
ejpam-5049	170	21	)	)	PUNCT
ejpam-5049	170	22	,	,	PUNCT
ejpam-5049	170	23	and	and	CCONJ
ejpam-5049	170	24	simpson	simpson	PROPN
ejpam-5049	170	25	’s	’s	PART
ejpam-5049	170	26	3/8	3/8	NUM
ejpam-5049	170	27	method	method	NOUN
ejpam-5049	170	28	(	(	PUNCT
ejpam-5049	170	29	19	19	NUM
ejpam-5049	170	30	)	)	PUNCT
ejpam-5049	170	31	,	,	PUNCT
ejpam-5049	170	32	we	we	PRON
ejpam-5049	170	33	construct	construct	VERB
ejpam-5049	170	34	the	the	DET
ejpam-5049	170	35	schema	schema	NOUN
ejpam-5049	170	36	as	as	SCONJ
ejpam-5049	170	37	follows	follow	VERB
ejpam-5049	170	38	:	:	PUNCT
ejpam-5049	170	39	(	(	PUNCT
ejpam-5049	170	40	i	i	NOUN
ejpam-5049	170	41	)	)	PUNCT
ejpam-5049	170	42	trapezoidal	trapezoidal	NOUN
ejpam-5049	170	43	’s	’s	PART
ejpam-5049	170	44	method	method	NOUN
ejpam-5049	170	45	using	use	VERB
ejpam-5049	170	46	(	(	PUNCT
ejpam-5049	170	47	14	14	NUM
ejpam-5049	170	48	)	)	PUNCT
ejpam-5049	170	49	and	and	CCONJ
ejpam-5049	170	50	(	(	PUNCT
ejpam-5049	170	51	15	15	NUM
ejpam-5049	170	52	)	)	PUNCT
ejpam-5049	170	53	,	,	PUNCT
ejpam-5049	170	54	we	we	PRON
ejpam-5049	170	55	obtain	obtain	VERB
ejpam-5049	170	56	m∑	m∑	PRON
ejpam-5049	170	57	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	170	58	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	170	59	k=0	k=0	PROPN
ejpam-5049	170	60	cjχ	cjχ	PROPN
ejpam-5049	170	61	(	(	PUNCT
ejpam-5049	170	62	α	α	NOUN
ejpam-5049	170	63	)	)	PUNCT
ejpam-5049	170	64	k	k	NOUN
ejpam-5049	170	65	βj−k−α	βj−k−α	NOUN
ejpam-5049	170	66	=	=	PUNCT
ejpam-5049	170	67	φ(β	φ(β	PROPN
ejpam-5049	170	68	)	)	PUNCT
ejpam-5049	171	1	+	+	CCONJ
ejpam-5049	171	2	h	h	NOUN
ejpam-5049	171	3	2	2	NUM
ejpam-5049	171	4	(	(	PUNCT
ejpam-5049	171	5	β0	β0	NOUN
ejpam-5049	171	6	m∑	m∑	CCONJ
ejpam-5049	171	7	j=0	j=0	PROPN
ejpam-5049	171	8	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	171	9	)	)	PUNCT
ejpam-5049	172	1	+	+	CCONJ
ejpam-5049	172	2	2	2	NUM
ejpam-5049	172	3	l−1∑	l−1∑	NOUN
ejpam-5049	172	4	k=1	k=1	PROPN
ejpam-5049	172	5	βk	βk	PROPN
ejpam-5049	172	6	m∑	m∑	VERB
ejpam-5049	172	7	j=0	j=0	PROPN
ejpam-5049	172	8	cjφj(βk	cjφj(βk	PROPN
ejpam-5049	172	9	)	)	PUNCT
ejpam-5049	172	10	+	+	SYM
ejpam-5049	172	11	βl	βl	PROPN
ejpam-5049	172	12	m∑	m∑	CCONJ
ejpam-5049	172	13	j=0	j=0	PROPN
ejpam-5049	172	14	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	172	15	)	)	PUNCT
ejpam-5049	172	16	)	)	PUNCT
ejpam-5049	172	17	,	,	PUNCT
ejpam-5049	172	18	(	(	PUNCT
ejpam-5049	172	19	23	23	NUM
ejpam-5049	172	20	)	)	PUNCT
ejpam-5049	172	21	where	where	SCONJ
ejpam-5049	172	22	φ(β	φ(β	NOUN
ejpam-5049	172	23	)	)	PUNCT
ejpam-5049	172	24	=	=	SYM
ejpam-5049	172	25	βeβ	βeβ	NOUN
ejpam-5049	173	1	+	+	CCONJ
ejpam-5049	173	2	eβ	eβ	VERB
ejpam-5049	173	3	−	−	PROPN
ejpam-5049	173	4	β	β	NOUN
ejpam-5049	173	5	,	,	PUNCT
ejpam-5049	173	6	and	and	CCONJ
ejpam-5049	173	7	m∑	m∑	CCONJ
ejpam-5049	173	8	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	173	9	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	173	10	k=0	k=0	PROPN
ejpam-5049	173	11	cjχ	cjχ	PROPN
ejpam-5049	173	12	(	(	PUNCT
ejpam-5049	173	13	α	α	NOUN
ejpam-5049	173	14	)	)	PUNCT
ejpam-5049	173	15	j	j	PROPN
ejpam-5049	173	16	,	,	PUNCT
ejpam-5049	173	17	k	k	PROPN
ejpam-5049	173	18	β	β	X
ejpam-5049	173	19	j−k−α	j−k−α	NOUN
ejpam-5049	173	20	s	s	PART
ejpam-5049	173	21	=	=	PUNCT
ejpam-5049	173	22	φ(β	φ(β	PROPN
ejpam-5049	173	23	)	)	PUNCT
ejpam-5049	174	1	+	+	CCONJ
ejpam-5049	174	2	h	h	NOUN
ejpam-5049	174	3	2	2	NUM
ejpam-5049	174	4	(	(	PUNCT
ejpam-5049	174	5	β0	β0	NOUN
ejpam-5049	174	6	m∑	m∑	CCONJ
ejpam-5049	174	7	j=0	j=0	PROPN
ejpam-5049	174	8	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	174	9	)	)	PUNCT
ejpam-5049	175	1	+	+	CCONJ
ejpam-5049	175	2	2	2	NUM
ejpam-5049	175	3	l−1∑	l−1∑	NOUN
ejpam-5049	175	4	k=1	k=1	PROPN
ejpam-5049	175	5	βk	βk	PROPN
ejpam-5049	175	6	m∑	m∑	VERB
ejpam-5049	175	7	j=0	j=0	PROPN
ejpam-5049	175	8	cjφj(βk	cjφj(βk	PROPN
ejpam-5049	175	9	)	)	PUNCT
ejpam-5049	175	10	khaled	khaled	PROPN
ejpam-5049	175	11	m.	m.	NOUN
ejpam-5049	175	12	saad	saad	PROPN
ejpam-5049	175	13	,	,	PUNCT
ejpam-5049	175	14	m.	m.	NOUN
ejpam-5049	175	15	q.	q.	PROPN
ejpam-5049	175	16	khirallah	khirallah	PROPN
ejpam-5049	175	17	/	/	SYM
ejpam-5049	175	18	eur	eur	PROPN
ejpam-5049	175	19	.	.	PUNCT
ejpam-5049	176	1	j.	j.	PROPN
ejpam-5049	176	2	pure	pure	PROPN
ejpam-5049	176	3	appl	appl	PROPN
ejpam-5049	176	4	.	.	PROPN
ejpam-5049	176	5	math	math	PROPN
ejpam-5049	176	6	,	,	PUNCT
ejpam-5049	176	7	17	17	NUM
ejpam-5049	176	8	(	(	PUNCT
ejpam-5049	176	9	1	1	NUM
ejpam-5049	176	10	)	)	PUNCT
ejpam-5049	176	11	(	(	PUNCT
ejpam-5049	176	12	2024	2024	NUM
ejpam-5049	176	13	)	)	PUNCT
ejpam-5049	176	14	,	,	PUNCT
ejpam-5049	176	15	477	477	NUM
ejpam-5049	176	16	-	-	SYM
ejpam-5049	176	17	503	503	NUM
ejpam-5049	176	18	485	485	NUM
ejpam-5049	176	19	+	+	NUM
ejpam-5049	176	20	βl	βl	NOUN
ejpam-5049	176	21	m∑	m∑	NOUN
ejpam-5049	176	22	j=0	j=0	PROPN
ejpam-5049	176	23	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	176	24	)	)	PUNCT
ejpam-5049	176	25	)	)	PUNCT
ejpam-5049	176	26	.	.	PUNCT
ejpam-5049	177	1	(	(	PUNCT
ejpam-5049	177	2	24	24	NUM
ejpam-5049	177	3	)	)	PUNCT
ejpam-5049	177	4	(	(	PUNCT
ejpam-5049	177	5	ii	ii	NOUN
ejpam-5049	177	6	)	)	PUNCT
ejpam-5049	177	7	simpson	simpson	PROPN
ejpam-5049	177	8	’s	’s	PART
ejpam-5049	177	9	1/3	1/3	NUM
ejpam-5049	177	10	method	method	NOUN
ejpam-5049	177	11	using	use	VERB
ejpam-5049	177	12	(	(	PUNCT
ejpam-5049	177	13	16	16	NUM
ejpam-5049	177	14	)	)	PUNCT
ejpam-5049	177	15	and	and	CCONJ
ejpam-5049	177	16	(	(	PUNCT
ejpam-5049	177	17	17	17	NUM
ejpam-5049	177	18	)	)	PUNCT
ejpam-5049	177	19	,	,	PUNCT
ejpam-5049	177	20	we	we	PRON
ejpam-5049	177	21	obtain	obtain	VERB
ejpam-5049	177	22	m∑	m∑	PRON
ejpam-5049	177	23	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	177	24	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	177	25	k=0	k=0	PROPN
ejpam-5049	177	26	cjχ	cjχ	PROPN
ejpam-5049	177	27	(	(	PUNCT
ejpam-5049	177	28	α	α	NOUN
ejpam-5049	177	29	)	)	PUNCT
ejpam-5049	177	30	j	j	PROPN
ejpam-5049	177	31	,	,	PUNCT
ejpam-5049	177	32	k	k	PROPN
ejpam-5049	177	33	β	β	X
ejpam-5049	177	34	j−k−α	j−k−α	NOUN
ejpam-5049	177	35	=	=	PUNCT
ejpam-5049	177	36	φ(β	φ(β	PROPN
ejpam-5049	177	37	)	)	PUNCT
ejpam-5049	178	1	+	+	NUM
ejpam-5049	178	2	h	h	NOUN
ejpam-5049	178	3	3	3	NUM
ejpam-5049	178	4	(	(	PUNCT
ejpam-5049	178	5	β0	β0	PROPN
ejpam-5049	178	6	m∑	m∑	CCONJ
ejpam-5049	178	7	j=0	j=0	PROPN
ejpam-5049	178	8	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	178	9	)	)	PUNCT
ejpam-5049	179	1	+	+	CCONJ
ejpam-5049	179	2	2	2	NUM
ejpam-5049	179	3	l	l	NOUN
ejpam-5049	179	4	2	2	NUM
ejpam-5049	179	5	−1∑	−1∑	PROPN
ejpam-5049	179	6	k=1	k=1	X
ejpam-5049	179	7	β2k	β2k	PUNCT
ejpam-5049	179	8	m∑	m∑	CCONJ
ejpam-5049	179	9	j=0	j=0	PROPN
ejpam-5049	179	10	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	179	11	)	)	PUNCT
ejpam-5049	179	12	+	+	CCONJ
ejpam-5049	179	13	4	4	NUM
ejpam-5049	179	14	l	l	NOUN
ejpam-5049	179	15	2∑	2∑	X
ejpam-5049	179	16	k=1	k=1	PUNCT
ejpam-5049	179	17	β2k−1	β2k−1	PROPN
ejpam-5049	179	18	m∑	m∑	PUNCT
ejpam-5049	179	19	j=0	j=0	PROPN
ejpam-5049	179	20	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	179	21	)	)	PUNCT
ejpam-5049	179	22	+	+	CCONJ
ejpam-5049	179	23	βl	βl	PROPN
ejpam-5049	179	24	m∑	m∑	CCONJ
ejpam-5049	179	25	j=0	j=0	PROPN
ejpam-5049	179	26	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	179	27	)	)	PUNCT
ejpam-5049	179	28	)	)	PUNCT
ejpam-5049	179	29	,	,	PUNCT
ejpam-5049	179	30	(	(	PUNCT
ejpam-5049	179	31	25	25	NUM
ejpam-5049	179	32	)	)	PUNCT
ejpam-5049	179	33	and	and	CCONJ
ejpam-5049	179	34	m∑	m∑	ADV
ejpam-5049	179	35	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	179	36	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	179	37	k=0	k=0	PROPN
ejpam-5049	179	38	cjχ	cjχ	PROPN
ejpam-5049	179	39	(	(	PUNCT
ejpam-5049	179	40	α	α	NOUN
ejpam-5049	179	41	)	)	PUNCT
ejpam-5049	179	42	j	j	PROPN
ejpam-5049	179	43	,	,	PUNCT
ejpam-5049	179	44	k	k	PROPN
ejpam-5049	179	45	β	β	X
ejpam-5049	179	46	j−k−α	j−k−α	NOUN
ejpam-5049	179	47	s	s	PART
ejpam-5049	179	48	=	=	PUNCT
ejpam-5049	179	49	φ(β	φ(β	PROPN
ejpam-5049	179	50	)	)	PUNCT
ejpam-5049	179	51	+	+	NUM
ejpam-5049	179	52	h	h	NOUN
ejpam-5049	179	53	3	3	NUM
ejpam-5049	180	1	(	(	PUNCT
ejpam-5049	180	2	β0	β0	PROPN
ejpam-5049	180	3	m∑	m∑	CCONJ
ejpam-5049	180	4	i=0	i=0	PROPN
ejpam-5049	180	5	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	180	6	)	)	PUNCT
ejpam-5049	181	1	+	+	CCONJ
ejpam-5049	181	2	2	2	NUM
ejpam-5049	181	3	l	l	NOUN
ejpam-5049	181	4	2	2	NUM
ejpam-5049	181	5	−1∑	−1∑	PROPN
ejpam-5049	181	6	k=1	k=1	X
ejpam-5049	181	7	β2k	β2k	PUNCT
ejpam-5049	181	8	m∑	m∑	CCONJ
ejpam-5049	181	9	j=0	j=0	PROPN
ejpam-5049	181	10	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	181	11	)	)	PUNCT
ejpam-5049	181	12	+	+	CCONJ
ejpam-5049	181	13	4	4	NUM
ejpam-5049	181	14	l	l	NOUN
ejpam-5049	181	15	2∑	2∑	X
ejpam-5049	181	16	k=1	k=1	PUNCT
ejpam-5049	181	17	β2k−1	β2k−1	PROPN
ejpam-5049	181	18	m∑	m∑	PUNCT
ejpam-5049	181	19	j=0	j=0	PROPN
ejpam-5049	181	20	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	181	21	)	)	PUNCT
ejpam-5049	181	22	+	+	CCONJ
ejpam-5049	181	23	βl	βl	PROPN
ejpam-5049	181	24	m∑	m∑	CCONJ
ejpam-5049	181	25	j=0	j=0	PROPN
ejpam-5049	181	26	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	181	27	)	)	PUNCT
ejpam-5049	181	28	)	)	PUNCT
ejpam-5049	181	29	.	.	PUNCT
ejpam-5049	182	1	(	(	PUNCT
ejpam-5049	182	2	26	26	NUM
ejpam-5049	182	3	)	)	PUNCT
ejpam-5049	182	4	(	(	PUNCT
ejpam-5049	182	5	iii	iii	X
ejpam-5049	182	6	)	)	PUNCT
ejpam-5049	182	7	simpson	simpson	PROPN
ejpam-5049	182	8	’s	’s	PART
ejpam-5049	182	9	3/8	3/8	NUM
ejpam-5049	182	10	method	method	NOUN
ejpam-5049	182	11	using	use	VERB
ejpam-5049	182	12	(	(	PUNCT
ejpam-5049	182	13	18	18	NUM
ejpam-5049	182	14	)	)	PUNCT
ejpam-5049	182	15	and	and	CCONJ
ejpam-5049	182	16	(	(	PUNCT
ejpam-5049	182	17	19	19	NUM
ejpam-5049	182	18	)	)	PUNCT
ejpam-5049	182	19	,	,	PUNCT
ejpam-5049	182	20	we	we	PRON
ejpam-5049	182	21	obtain	obtain	VERB
ejpam-5049	182	22	m∑	m∑	PRON
ejpam-5049	182	23	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	182	24	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	182	25	k=0	k=0	PROPN
ejpam-5049	182	26	cjχ	cjχ	PROPN
ejpam-5049	182	27	(	(	PUNCT
ejpam-5049	182	28	α	α	NOUN
ejpam-5049	182	29	)	)	PUNCT
ejpam-5049	182	30	j	j	PROPN
ejpam-5049	182	31	,	,	PUNCT
ejpam-5049	182	32	k	k	PROPN
ejpam-5049	182	33	β	β	X
ejpam-5049	182	34	j−k−α	j−k−α	NOUN
ejpam-5049	182	35	=	=	PUNCT
ejpam-5049	182	36	φ(β	φ(β	PROPN
ejpam-5049	182	37	)	)	PUNCT
ejpam-5049	183	1	+	+	CCONJ
ejpam-5049	183	2	3h	3h	NUM
ejpam-5049	183	3	8	8	NUM
ejpam-5049	183	4	(	(	PUNCT
ejpam-5049	183	5	β0	β0	NOUN
ejpam-5049	183	6	m∑	m∑	CCONJ
ejpam-5049	183	7	j=0	j=0	PROPN
ejpam-5049	183	8	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	183	9	)	)	PUNCT
ejpam-5049	184	1	+	+	CCONJ
ejpam-5049	184	2	3	3	NUM
ejpam-5049	184	3	l	l	NOUN
ejpam-5049	184	4	3∑	3∑	NUM
ejpam-5049	184	5	k=1	k=1	NOUN
ejpam-5049	184	6	(	(	PUNCT
ejpam-5049	184	7	β3k−2	β3k−2	PROPN
ejpam-5049	184	8	m∑	m∑	PUNCT
ejpam-5049	184	9	j=0	j=0	PROPN
ejpam-5049	184	10	ciφj(β3k−2	ciφj(β3k−2	PROPN
ejpam-5049	184	11	)	)	PUNCT
ejpam-5049	185	1	+	+	CCONJ
ejpam-5049	185	2	β3k−1	β3k−1	PROPN
ejpam-5049	185	3	m∑	m∑	CCONJ
ejpam-5049	185	4	j=0	j=0	PROPN
ejpam-5049	185	5	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	185	6	)	)	PUNCT
ejpam-5049	185	7	)	)	PUNCT
ejpam-5049	186	1	+	+	CCONJ
ejpam-5049	186	2	2	2	NUM
ejpam-5049	186	3	l	l	NOUN
ejpam-5049	186	4	3	3	NUM
ejpam-5049	186	5	−1∑	−1∑	INTJ
ejpam-5049	186	6	k=1	k=1	PUNCT
ejpam-5049	186	7	β3k	β3k	PROPN
ejpam-5049	186	8	m∑	m∑	VERB
ejpam-5049	186	9	j=0	j=0	PROPN
ejpam-5049	186	10	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	186	11	)	)	PUNCT
ejpam-5049	187	1	+	+	CCONJ
ejpam-5049	187	2	βl	βl	PROPN
ejpam-5049	187	3	m∑	m∑	NOUN
ejpam-5049	187	4	j=0	j=0	PROPN
ejpam-5049	187	5	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	187	6	)	)	PUNCT
ejpam-5049	187	7	)	)	PUNCT
ejpam-5049	187	8	,	,	PUNCT
ejpam-5049	187	9	(	(	PUNCT
ejpam-5049	187	10	27	27	NUM
ejpam-5049	187	11	)	)	PUNCT
ejpam-5049	187	12	and	and	CCONJ
ejpam-5049	187	13	m∑	m∑	CCONJ
ejpam-5049	187	14	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	187	15	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	187	16	k=0	k=0	PROPN
ejpam-5049	187	17	cjχ	cjχ	PROPN
ejpam-5049	187	18	(	(	PUNCT
ejpam-5049	187	19	α	α	NOUN
ejpam-5049	187	20	)	)	PUNCT
ejpam-5049	187	21	j	j	PROPN
ejpam-5049	187	22	,	,	PUNCT
ejpam-5049	187	23	k	k	PROPN
ejpam-5049	187	24	β	β	X
ejpam-5049	187	25	j−k−α	j−k−α	NOUN
ejpam-5049	187	26	s	s	PART
ejpam-5049	187	27	=	=	PUNCT
ejpam-5049	187	28	φ(β	φ(β	PROPN
ejpam-5049	187	29	)	)	PUNCT
ejpam-5049	188	1	+	+	NUM
ejpam-5049	188	2	h	h	NOUN
ejpam-5049	188	3	3	3	NUM
ejpam-5049	189	1	(	(	PUNCT
ejpam-5049	189	2	β0	β0	PROPN
ejpam-5049	189	3	m∑	m∑	CCONJ
ejpam-5049	189	4	j=0	j=0	PROPN
ejpam-5049	189	5	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	189	6	)	)	PUNCT
ejpam-5049	190	1	+	+	CCONJ
ejpam-5049	190	2	2	2	NUM
ejpam-5049	190	3	l	l	NOUN
ejpam-5049	190	4	2	2	NUM
ejpam-5049	190	5	−1∑	−1∑	PROPN
ejpam-5049	190	6	k=1	k=1	X
ejpam-5049	190	7	β2k	β2k	PUNCT
ejpam-5049	190	8	m∑	m∑	CCONJ
ejpam-5049	190	9	j=0	j=0	PROPN
ejpam-5049	190	10	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	190	11	)	)	PUNCT
ejpam-5049	190	12	khaled	khaled	PROPN
ejpam-5049	190	13	m.	m.	NOUN
ejpam-5049	190	14	saad	saad	PROPN
ejpam-5049	190	15	,	,	PUNCT
ejpam-5049	190	16	m.	m.	NOUN
ejpam-5049	190	17	q.	q.	PROPN
ejpam-5049	190	18	khirallah	khirallah	PROPN
ejpam-5049	190	19	/	/	SYM
ejpam-5049	190	20	eur	eur	PROPN
ejpam-5049	190	21	.	.	PUNCT
ejpam-5049	191	1	j.	j.	PROPN
ejpam-5049	191	2	pure	pure	PROPN
ejpam-5049	191	3	appl	appl	PROPN
ejpam-5049	191	4	.	.	PROPN
ejpam-5049	191	5	math	math	PROPN
ejpam-5049	191	6	,	,	PUNCT
ejpam-5049	191	7	17	17	NUM
ejpam-5049	191	8	(	(	PUNCT
ejpam-5049	191	9	1	1	NUM
ejpam-5049	191	10	)	)	PUNCT
ejpam-5049	191	11	(	(	PUNCT
ejpam-5049	191	12	2024	2024	NUM
ejpam-5049	191	13	)	)	PUNCT
ejpam-5049	191	14	,	,	PUNCT
ejpam-5049	191	15	477	477	NUM
ejpam-5049	191	16	-	-	SYM
ejpam-5049	191	17	503	503	NUM
ejpam-5049	191	18	486	486	NUM
ejpam-5049	191	19	+	+	CCONJ
ejpam-5049	191	20	4	4	NUM
ejpam-5049	191	21	l	l	NOUN
ejpam-5049	191	22	2∑	2∑	X
ejpam-5049	192	1	k=1	k=1	PUNCT
ejpam-5049	192	2	β2k−1	β2k−1	PROPN
ejpam-5049	192	3	m∑	m∑	PUNCT
ejpam-5049	192	4	j=0	j=0	PROPN
ejpam-5049	192	5	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	192	6	)	)	PUNCT
ejpam-5049	193	1	+	+	CCONJ
ejpam-5049	193	2	βl	βl	PROPN
ejpam-5049	193	3	m∑	m∑	CCONJ
ejpam-5049	193	4	j=0	j=0	PROPN
ejpam-5049	193	5	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	193	6	)	)	PUNCT
ejpam-5049	193	7	)	)	PUNCT
ejpam-5049	193	8	,	,	PUNCT
ejpam-5049	193	9	(	(	PUNCT
ejpam-5049	193	10	28	28	NUM
ejpam-5049	193	11	)	)	PUNCT
ejpam-5049	193	12	where	where	SCONJ
ejpam-5049	193	13	βs	βs	PRON
ejpam-5049	193	14	are	be	AUX
ejpam-5049	193	15	the	the	DET
ejpam-5049	193	16	roots	root	NOUN
ejpam-5049	193	17	of	of	ADP
ejpam-5049	193	18	the	the	DET
ejpam-5049	193	19	shifted	shift	VERB
ejpam-5049	193	20	chebyshev	chebyshev	NOUN
ejpam-5049	193	21	polynomial	polynomial	PROPN
ejpam-5049	193	22	and	and	CCONJ
ejpam-5049	193	23	s	s	NOUN
ejpam-5049	193	24	=	=	SYM
ejpam-5049	193	25	0	0	NUM
ejpam-5049	193	26	,	,	PUNCT
ejpam-5049	193	27	1	1	NUM
ejpam-5049	193	28	,	,	PUNCT
ejpam-5049	193	29	2	2	NUM
ejpam-5049	193	30	,	,	PUNCT
ejpam-5049	193	31	3	3	NUM
ejpam-5049	193	32	,	,	PUNCT
ejpam-5049	193	33	...	...	PUNCT
ejpam-5049	193	34	,	,	PUNCT
ejpam-5049	193	35	m.	m.	NOUN
ejpam-5049	193	36	the	the	DET
ejpam-5049	193	37	initial	initial	ADJ
ejpam-5049	193	38	condition	condition	NOUN
ejpam-5049	193	39	(	(	PUNCT
ejpam-5049	193	40	21	21	NUM
ejpam-5049	193	41	)	)	PUNCT
ejpam-5049	193	42	can	can	AUX
ejpam-5049	193	43	be	be	AUX
ejpam-5049	193	44	written	write	VERB
ejpam-5049	193	45	as	as	ADP
ejpam-5049	193	46	ϕm(0	ϕm(0	NOUN
ejpam-5049	193	47	)	)	PUNCT
ejpam-5049	193	48	=	=	PUNCT
ejpam-5049	193	49	m∑	m∑	CCONJ
ejpam-5049	193	50	j=0	j=0	PROPN
ejpam-5049	193	51	cjφj(0	cjφj(0	PROPN
ejpam-5049	193	52	)	)	PUNCT
ejpam-5049	194	1	=	=	PUNCT
ejpam-5049	194	2	m∑	m∑	CCONJ
ejpam-5049	194	3	j=0	j=0	PROPN
ejpam-5049	194	4	(	(	PUNCT
ejpam-5049	194	5	−1)jcj	−1)jcj	NOUN
ejpam-5049	194	6	=	=	NOUN
ejpam-5049	194	7	0	0	PROPN
ejpam-5049	194	8	.	.	PUNCT
ejpam-5049	195	1	(	(	PUNCT
ejpam-5049	195	2	29	29	NUM
ejpam-5049	195	3	)	)	PUNCT
ejpam-5049	195	4	to	to	PART
ejpam-5049	195	5	acquire	acquire	VERB
ejpam-5049	195	6	the	the	DET
ejpam-5049	195	7	coefficients	coefficient	NOUN
ejpam-5049	195	8	’	'	PUNCT
ejpam-5049	195	9	cj	cj	NOUN
ejpam-5049	195	10	’	'	PUNCT
ejpam-5049	195	11	in	in	ADP
ejpam-5049	195	12	the	the	DET
ejpam-5049	195	13	preceding	precede	VERB
ejpam-5049	195	14	three	three	NUM
ejpam-5049	195	15	cases	case	NOUN
ejpam-5049	195	16	,	,	PUNCT
ejpam-5049	195	17	one	one	PRON
ejpam-5049	195	18	can	can	AUX
ejpam-5049	195	19	solve	solve	VERB
ejpam-5049	195	20	algebraic	algebraic	ADJ
ejpam-5049	195	21	equations	equation	NOUN
ejpam-5049	195	22	(	(	PUNCT
ejpam-5049	195	23	24	24	NUM
ejpam-5049	195	24	)	)	PUNCT
ejpam-5049	195	25	,	,	PUNCT
ejpam-5049	195	26	(	(	PUNCT
ejpam-5049	195	27	26	26	NUM
ejpam-5049	195	28	)	)	PUNCT
ejpam-5049	195	29	and	and	CCONJ
ejpam-5049	195	30	(	(	PUNCT
ejpam-5049	195	31	28	28	NUM
ejpam-5049	195	32	)	)	PUNCT
ejpam-5049	195	33	,	,	PUNCT
ejpam-5049	195	34	corresponding	correspond	VERB
ejpam-5049	195	35	to	to	ADP
ejpam-5049	195	36	equation	equation	NOUN
ejpam-5049	195	37	(	(	PUNCT
ejpam-5049	195	38	29	29	NUM
ejpam-5049	195	39	)	)	PUNCT
ejpam-5049	195	40	in	in	ADP
ejpam-5049	195	41	each	each	DET
ejpam-5049	195	42	case	case	NOUN
ejpam-5049	195	43	.	.	PUNCT
ejpam-5049	196	1	ultimately	ultimately	ADV
ejpam-5049	196	2	,	,	PUNCT
ejpam-5049	196	3	by	by	ADP
ejpam-5049	196	4	replacing	replace	VERB
ejpam-5049	196	5	the	the	DET
ejpam-5049	196	6	coefficients	coefficient	NOUN
ejpam-5049	196	7	’	'	PUNCT
ejpam-5049	196	8	cj	cj	NOUN
ejpam-5049	196	9	’	'	PUNCT
ejpam-5049	196	10	in	in	ADP
ejpam-5049	196	11	equation	equation	NOUN
ejpam-5049	196	12	(	(	PUNCT
ejpam-5049	196	13	22	22	NUM
ejpam-5049	196	14	)	)	PUNCT
ejpam-5049	196	15	,	,	PUNCT
ejpam-5049	196	16	one	one	PRON
ejpam-5049	196	17	can	can	AUX
ejpam-5049	196	18	obtain	obtain	VERB
ejpam-5049	196	19	an	an	DET
ejpam-5049	196	20	approximate	approximate	ADJ
ejpam-5049	196	21	numerical	numerical	ADJ
ejpam-5049	196	22	solution	solution	NOUN
ejpam-5049	196	23	for	for	ADP
ejpam-5049	196	24	equation	equation	NOUN
ejpam-5049	196	25	(	(	PUNCT
ejpam-5049	196	26	20	20	NUM
ejpam-5049	196	27	)	)	PUNCT
ejpam-5049	196	28	.	.	PUNCT
ejpam-5049	197	1	now	now	ADV
ejpam-5049	197	2	,	,	PUNCT
ejpam-5049	197	3	we	we	PRON
ejpam-5049	197	4	present	present	VERB
ejpam-5049	197	5	various	various	ADJ
ejpam-5049	197	6	figures	figure	NOUN
ejpam-5049	197	7	to	to	PART
ejpam-5049	197	8	illustrate	illustrate	VERB
ejpam-5049	197	9	the	the	DET
ejpam-5049	197	10	numerical	numerical	ADJ
ejpam-5049	197	11	results	result	NOUN
ejpam-5049	197	12	.	.	PUNCT
ejpam-5049	198	1	a	a	DET
ejpam-5049	198	2	comparison	comparison	NOUN
ejpam-5049	198	3	of	of	ADP
ejpam-5049	198	4	the	the	DET
ejpam-5049	198	5	exact	exact	ADJ
ejpam-5049	198	6	and	and	CCONJ
ejpam-5049	198	7	approximate	approximate	ADJ
ejpam-5049	198	8	solutions	solution	NOUN
ejpam-5049	198	9	with	with	ADP
ejpam-5049	198	10	α	α	PROPN
ejpam-5049	198	11	=	=	PUNCT
ejpam-5049	198	12	0.8	0.8	NUM
ejpam-5049	198	13	,	,	PUNCT
ejpam-5049	198	14	0.9	0.9	NUM
ejpam-5049	198	15	,	,	PUNCT
ejpam-5049	198	16	1	1	NUM
ejpam-5049	198	17	and	and	CCONJ
ejpam-5049	198	18	m	m	VERB
ejpam-5049	198	19	=	=	NOUN
ejpam-5049	198	20	6	6	NUM
ejpam-5049	198	21	is	be	AUX
ejpam-5049	198	22	shown	show	VERB
ejpam-5049	198	23	in	in	ADP
ejpam-5049	198	24	figure	figure	NOUN
ejpam-5049	198	25	1(a	1(a	NUM
ejpam-5049	198	26	)	)	PUNCT
ejpam-5049	198	27	.	.	PUNCT
ejpam-5049	199	1	this	this	DET
ejpam-5049	199	2	comparison	comparison	NOUN
ejpam-5049	199	3	applies	apply	VERB
ejpam-5049	199	4	specifically	specifically	ADV
ejpam-5049	199	5	to	to	ADP
ejpam-5049	199	6	trapezoidal	trapezoidal	NOUN
ejpam-5049	199	7	’s	’s	PART
ejpam-5049	199	8	case	case	NOUN
ejpam-5049	199	9	,	,	PUNCT
ejpam-5049	199	10	while	while	SCONJ
ejpam-5049	199	11	the	the	DET
ejpam-5049	199	12	remaining	remain	VERB
ejpam-5049	199	13	two	two	NUM
ejpam-5049	199	14	cases	case	NOUN
ejpam-5049	199	15	exhibit	exhibit	VERB
ejpam-5049	199	16	identical	identical	ADJ
ejpam-5049	199	17	behavior	behavior	NOUN
ejpam-5049	199	18	.	.	PUNCT
ejpam-5049	200	1	in	in	ADP
ejpam-5049	200	2	this	this	DET
ejpam-5049	200	3	graphical	graphical	ADJ
ejpam-5049	200	4	representation	representation	NOUN
ejpam-5049	200	5	,	,	PUNCT
ejpam-5049	200	6	we	we	PRON
ejpam-5049	200	7	observe	observe	VERB
ejpam-5049	200	8	the	the	DET
ejpam-5049	200	9	trends	trend	NOUN
ejpam-5049	200	10	of	of	ADP
ejpam-5049	200	11	the	the	DET
ejpam-5049	200	12	approximate	approximate	ADJ
ejpam-5049	200	13	solutions	solution	NOUN
ejpam-5049	200	14	for	for	ADP
ejpam-5049	200	15	various	various	ADJ
ejpam-5049	200	16	α	α	NOUN
ejpam-5049	200	17	values	value	NOUN
ejpam-5049	200	18	.	.	PUNCT
ejpam-5049	201	1	these	these	DET
ejpam-5049	201	2	solutions	solution	NOUN
ejpam-5049	201	3	exhibit	exhibit	VERB
ejpam-5049	201	4	regular	regular	ADJ
ejpam-5049	201	5	behavior	behavior	NOUN
ejpam-5049	201	6	,	,	PUNCT
ejpam-5049	201	7	and	and	CCONJ
ejpam-5049	201	8	their	their	PRON
ejpam-5049	201	9	proximity	proximity	NOUN
ejpam-5049	201	10	increases	increase	VERB
ejpam-5049	201	11	as	as	ADP
ejpam-5049	201	12	α	α	NOUN
ejpam-5049	201	13	approaches	approach	NOUN
ejpam-5049	201	14	toward	toward	ADP
ejpam-5049	201	15	the	the	DET
ejpam-5049	201	16	integer	integer	NOUN
ejpam-5049	201	17	value	value	NOUN
ejpam-5049	201	18	.	.	PUNCT
ejpam-5049	202	1	the	the	DET
ejpam-5049	202	2	different	different	ADJ
ejpam-5049	202	3	value	value	NOUN
ejpam-5049	202	4	of	of	ADP
ejpam-5049	202	5	α	α	PROPN
ejpam-5049	202	6	is	be	AUX
ejpam-5049	202	7	highlighted	highlight	VERB
ejpam-5049	202	8	in	in	ADP
ejpam-5049	202	9	the	the	DET
ejpam-5049	202	10	figure	figure	NOUN
ejpam-5049	202	11	1(a	1(a	NUM
ejpam-5049	202	12	)	)	PUNCT
ejpam-5049	202	13	.	.	PUNCT
ejpam-5049	203	1	figure	figure	NOUN
ejpam-5049	203	2	1(b	1(b	NUM
ejpam-5049	203	3	)	)	PUNCT
ejpam-5049	203	4	illustrates	illustrate	VERB
ejpam-5049	203	5	the	the	DET
ejpam-5049	203	6	corresponding	corresponding	ADJ
ejpam-5049	203	7	absolute	absolute	ADJ
ejpam-5049	203	8	error	error	NOUN
ejpam-5049	203	9	for	for	ADP
ejpam-5049	203	10	the	the	DET
ejpam-5049	203	11	trapezoidal	trapezoidal	ADJ
ejpam-5049	203	12	,	,	PUNCT
ejpam-5049	203	13	simpson	simpson	PROPN
ejpam-5049	203	14	’	'	PUNCT
ejpam-5049	203	15	3/8	3/8	NUM
ejpam-5049	203	16	and	and	CCONJ
ejpam-5049	203	17	simpson	simpson	NOUN
ejpam-5049	203	18	’	'	PUNCT
ejpam-5049	203	19	1/3	1/3	NUM
ejpam-5049	203	20	methods	method	NOUN
ejpam-5049	203	21	.	.	PUNCT
ejpam-5049	204	1	to	to	PART
ejpam-5049	204	2	further	far	ADV
ejpam-5049	204	3	verify	verify	VERB
ejpam-5049	204	4	,	,	PUNCT
ejpam-5049	204	5	considering	consider	VERB
ejpam-5049	204	6	the	the	DET
ejpam-5049	204	7	absence	absence	NOUN
ejpam-5049	204	8	of	of	ADP
ejpam-5049	204	9	an	an	DET
ejpam-5049	204	10	exact	exact	ADJ
ejpam-5049	204	11	solution	solution	NOUN
ejpam-5049	204	12	in	in	ADP
ejpam-5049	204	13	the	the	DET
ejpam-5049	204	14	non	non	ADJ
ejpam-5049	204	15	-	-	ADJ
ejpam-5049	204	16	integer	integer	ADJ
ejpam-5049	204	17	case	case	NOUN
ejpam-5049	204	18	,	,	PUNCT
ejpam-5049	204	19	it	it	PRON
ejpam-5049	204	20	becomes	become	VERB
ejpam-5049	204	21	crucial	crucial	ADJ
ejpam-5049	204	22	to	to	PART
ejpam-5049	204	23	assess	assess	VERB
ejpam-5049	204	24	the	the	DET
ejpam-5049	204	25	error	error	NOUN
ejpam-5049	204	26	.	.	PUNCT
ejpam-5049	205	1	therefore	therefore	ADV
ejpam-5049	205	2	,	,	PUNCT
ejpam-5049	205	3	to	to	PART
ejpam-5049	205	4	confirm	confirm	VERB
ejpam-5049	205	5	the	the	DET
ejpam-5049	205	6	validity	validity	NOUN
ejpam-5049	205	7	of	of	ADP
ejpam-5049	205	8	our	our	PRON
ejpam-5049	205	9	approach	approach	NOUN
ejpam-5049	205	10	,	,	PUNCT
ejpam-5049	205	11	we	we	PRON
ejpam-5049	205	12	compute	compute	VERB
ejpam-5049	205	13	the	the	DET
ejpam-5049	205	14	absolute	absolute	ADJ
ejpam-5049	205	15	error	error	NOUN
ejpam-5049	205	16	in	in	ADP
ejpam-5049	205	17	a	a	DET
ejpam-5049	205	18	two	two	NUM
ejpam-5049	205	19	-	-	PUNCT
ejpam-5049	205	20	step	step	NOUN
ejpam-5049	205	21	process	process	NOUN
ejpam-5049	205	22	,	,	PUNCT
ejpam-5049	205	23	i.e.	i.e.	X
ejpam-5049	205	24	|ϕm+1(β)−	|ϕm+1(β)−	X
ejpam-5049	205	25	ϕm(β)|	ϕm(β)|	NOUN
ejpam-5049	205	26	.	.	PUNCT
ejpam-5049	206	1	the	the	DET
ejpam-5049	206	2	error	error	NOUN
ejpam-5049	206	3	in	in	ADP
ejpam-5049	206	4	a	a	DET
ejpam-5049	206	5	two	two	NUM
ejpam-5049	206	6	-	-	PUNCT
ejpam-5049	206	7	step	step	NOUN
ejpam-5049	206	8	process	process	NOUN
ejpam-5049	206	9	in	in	ADP
ejpam-5049	206	10	figure	figure	NOUN
ejpam-5049	206	11	1(c	1(c	NUM
ejpam-5049	206	12	)	)	PUNCT
ejpam-5049	206	13	is	be	AUX
ejpam-5049	206	14	plotted	plot	VERB
ejpam-5049	206	15	for	for	ADP
ejpam-5049	206	16	the	the	DET
ejpam-5049	206	17	same	same	ADJ
ejpam-5049	206	18	values	value	NOUN
ejpam-5049	206	19	as	as	ADP
ejpam-5049	206	20	in	in	ADP
ejpam-5049	206	21	figures	figure	NOUN
ejpam-5049	206	22	1(a	1(a	NUM
ejpam-5049	206	23	)	)	PUNCT
ejpam-5049	206	24	and	and	CCONJ
ejpam-5049	206	25	1(b	1(b	NUM
ejpam-5049	206	26	)	)	PUNCT
ejpam-5049	206	27	.	.	PUNCT
ejpam-5049	207	1	it	it	PRON
ejpam-5049	207	2	is	be	AUX
ejpam-5049	207	3	clear	clear	ADJ
ejpam-5049	207	4	from	from	ADP
ejpam-5049	207	5	these	these	DET
ejpam-5049	207	6	figures	figure	NOUN
ejpam-5049	207	7	that	that	SCONJ
ejpam-5049	207	8	the	the	DET
ejpam-5049	207	9	order	order	NOUN
ejpam-5049	207	10	of	of	ADP
ejpam-5049	207	11	the	the	DET
ejpam-5049	207	12	error	error	NOUN
ejpam-5049	207	13	is	be	AUX
ejpam-5049	207	14	very	very	ADV
ejpam-5049	207	15	small	small	ADJ
ejpam-5049	207	16	.	.	PUNCT
ejpam-5049	207	17	example	example	NOUN
ejpam-5049	208	1	2	2	NUM
ejpam-5049	208	2	.	.	X
ejpam-5049	208	3	consider	consider	VERB
ejpam-5049	208	4	the	the	DET
ejpam-5049	208	5	following	follow	VERB
ejpam-5049	208	6	fractional	fractional	ADJ
ejpam-5049	208	7	fredholm	fredholm	NOUN
ejpam-5049	208	8	integro	integro	ADJ
ejpam-5049	208	9	-	-	PUNCT
ejpam-5049	208	10	differential	differential	NOUN
ejpam-5049	208	11	equation	equation	NOUN
ejpam-5049	208	12	dαϕ(β	dαϕ(β	PROPN
ejpam-5049	208	13	)	)	PUNCT
ejpam-5049	208	14	=	=	PUNCT
ejpam-5049	209	1	2−	2−	NUM
ejpam-5049	209	2	7β2	7β2	NUM
ejpam-5049	209	3	3	3	NUM
ejpam-5049	209	4	+	+	CCONJ
ejpam-5049	209	5	2β	2β	NOUN
ejpam-5049	209	6	+	+	CCONJ
ejpam-5049	209	7	∫	∫	PROPN
ejpam-5049	209	8	1	1	NUM
ejpam-5049	209	9	0	0	NUM
ejpam-5049	209	10	β2	β2	PROPN
ejpam-5049	209	11	ϕ(β	ϕ(β	PROPN
ejpam-5049	209	12	)	)	PUNCT
ejpam-5049	209	13	dβ	dβ	ADJ
ejpam-5049	209	14	,	,	PUNCT
ejpam-5049	209	15	(	(	PUNCT
ejpam-5049	209	16	30	30	NUM
ejpam-5049	209	17	)	)	PUNCT
ejpam-5049	209	18	subject	subject	NOUN
ejpam-5049	209	19	to	to	ADP
ejpam-5049	209	20	the	the	DET
ejpam-5049	209	21	initial	initial	ADJ
ejpam-5049	209	22	condition	condition	NOUN
ejpam-5049	209	23	ϕ(0	ϕ(0	NOUN
ejpam-5049	209	24	)	)	PUNCT
ejpam-5049	209	25	=	=	PUNCT
ejpam-5049	210	1	1	1	X
ejpam-5049	210	2	.	.	PUNCT
ejpam-5049	210	3	(	(	PUNCT
ejpam-5049	210	4	31	31	NUM
ejpam-5049	210	5	)	)	PUNCT
ejpam-5049	210	6	using	use	VERB
ejpam-5049	210	7	the	the	DET
ejpam-5049	210	8	suggested	suggested	ADJ
ejpam-5049	210	9	approach	approach	NOUN
ejpam-5049	210	10	,	,	PUNCT
ejpam-5049	210	11	we	we	PRON
ejpam-5049	210	12	deduce	deduce	VERB
ejpam-5049	210	13	the	the	DET
ejpam-5049	210	14	following	follow	VERB
ejpam-5049	210	15	approximation	approximation	NOUN
ejpam-5049	210	16	for	for	ADP
ejpam-5049	210	17	the	the	DET
ejpam-5049	210	18	solution	solution	NOUN
ejpam-5049	210	19	:	:	PUNCT
ejpam-5049	210	20	ϕm(β	ϕm(β	X
ejpam-5049	210	21	)	)	PUNCT
ejpam-5049	210	22	=	=	PUNCT
ejpam-5049	210	23	m∑	m∑	CCONJ
ejpam-5049	210	24	j=0	j=0	PROPN
ejpam-5049	210	25	cjφj(β	cjφj(β	PROPN
ejpam-5049	210	26	)	)	PUNCT
ejpam-5049	210	27	.	.	PUNCT
ejpam-5049	211	1	(	(	PUNCT
ejpam-5049	211	2	32	32	NUM
ejpam-5049	211	3	)	)	PUNCT
ejpam-5049	211	4	khaled	khale	VERB
ejpam-5049	211	5	m.	m.	NOUN
ejpam-5049	211	6	saad	saad	PROPN
ejpam-5049	211	7	,	,	PUNCT
ejpam-5049	211	8	m.	m.	NOUN
ejpam-5049	211	9	q.	q.	PROPN
ejpam-5049	211	10	khirallah	khirallah	PROPN
ejpam-5049	211	11	/	/	SYM
ejpam-5049	211	12	eur	eur	PROPN
ejpam-5049	211	13	.	.	PUNCT
ejpam-5049	212	1	j.	j.	PROPN
ejpam-5049	212	2	pure	pure	PROPN
ejpam-5049	212	3	appl	appl	PROPN
ejpam-5049	212	4	.	.	PROPN
ejpam-5049	212	5	math	math	PROPN
ejpam-5049	212	6	,	,	PUNCT
ejpam-5049	212	7	17	17	NUM
ejpam-5049	212	8	(	(	PUNCT
ejpam-5049	212	9	1	1	NUM
ejpam-5049	212	10	)	)	PUNCT
ejpam-5049	212	11	(	(	PUNCT
ejpam-5049	212	12	2024	2024	NUM
ejpam-5049	212	13	)	)	PUNCT
ejpam-5049	212	14	,	,	PUNCT
ejpam-5049	212	15	477	477	NUM
ejpam-5049	212	16	-	-	SYM
ejpam-5049	212	17	503	503	NUM
ejpam-5049	212	18	487	487	NUM
ejpam-5049	212	19	using	use	VERB
ejpam-5049	212	20	the	the	DET
ejpam-5049	212	21	trapezoidal	trapezoidal	ADJ
ejpam-5049	212	22	method	method	NOUN
ejpam-5049	212	23	(	(	PUNCT
ejpam-5049	212	24	15	15	NUM
ejpam-5049	212	25	)	)	PUNCT
ejpam-5049	212	26	,	,	PUNCT
ejpam-5049	212	27	simpson	simpson	PROPN
ejpam-5049	212	28	’s	’s	PART
ejpam-5049	212	29	method	method	NOUN
ejpam-5049	212	30	(	(	PUNCT
ejpam-5049	212	31	17	17	NUM
ejpam-5049	212	32	)	)	PUNCT
ejpam-5049	212	33	,	,	PUNCT
ejpam-5049	212	34	and	and	CCONJ
ejpam-5049	212	35	simpson	simpson	PROPN
ejpam-5049	212	36	’s	’s	PART
ejpam-5049	212	37	3/8	3/8	NUM
ejpam-5049	212	38	method	method	NOUN
ejpam-5049	212	39	(	(	PUNCT
ejpam-5049	212	40	19	19	NUM
ejpam-5049	212	41	)	)	PUNCT
ejpam-5049	213	1	,	,	PUNCT
ejpam-5049	213	2	we	we	PRON
ejpam-5049	213	3	construct	construct	VERB
ejpam-5049	213	4	the	the	DET
ejpam-5049	213	5	schema	schema	NOUN
ejpam-5049	213	6	as	as	SCONJ
ejpam-5049	213	7	follows	follow	VERB
ejpam-5049	213	8	:	:	PUNCT
ejpam-5049	213	9	(	(	PUNCT
ejpam-5049	213	10	i	i	NOUN
ejpam-5049	213	11	)	)	PUNCT
ejpam-5049	213	12	trapezoidal	trapezoidal	NOUN
ejpam-5049	213	13	’s	’s	PART
ejpam-5049	213	14	method	method	NOUN
ejpam-5049	213	15	using	use	VERB
ejpam-5049	213	16	(	(	PUNCT
ejpam-5049	213	17	14	14	NUM
ejpam-5049	213	18	)	)	PUNCT
ejpam-5049	213	19	and	and	CCONJ
ejpam-5049	213	20	(	(	PUNCT
ejpam-5049	213	21	15	15	NUM
ejpam-5049	213	22	)	)	PUNCT
ejpam-5049	213	23	,	,	PUNCT
ejpam-5049	213	24	we	we	PRON
ejpam-5049	213	25	obtain	obtain	VERB
ejpam-5049	213	26	m∑	m∑	PRON
ejpam-5049	213	27	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	213	28	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	213	29	k=0	k=0	PROPN
ejpam-5049	213	30	cjχ	cjχ	PROPN
ejpam-5049	213	31	(	(	PUNCT
ejpam-5049	213	32	α	α	NOUN
ejpam-5049	213	33	)	)	PUNCT
ejpam-5049	213	34	j	j	PROPN
ejpam-5049	213	35	,	,	PUNCT
ejpam-5049	213	36	k	k	PROPN
ejpam-5049	213	37	β	β	X
ejpam-5049	213	38	j−k−α	j−k−α	NOUN
ejpam-5049	213	39	=	=	PUNCT
ejpam-5049	213	40	φ(β	φ(β	PROPN
ejpam-5049	213	41	)	)	PUNCT
ejpam-5049	214	1	+	+	CCONJ
ejpam-5049	214	2	h	h	NOUN
ejpam-5049	214	3	2	2	NUM
ejpam-5049	214	4	(	(	PUNCT
ejpam-5049	214	5	β2	β2	NOUN
ejpam-5049	214	6	0	0	PROPN
ejpam-5049	214	7	m∑	m∑	PROPN
ejpam-5049	214	8	j=0	j=0	PROPN
ejpam-5049	214	9	ciφj(β0	ciφj(β0	PROPN
ejpam-5049	214	10	)	)	PUNCT
ejpam-5049	215	1	+	+	CCONJ
ejpam-5049	215	2	2	2	NUM
ejpam-5049	215	3	l−1∑	l−1∑	NOUN
ejpam-5049	215	4	k=1	k=1	PROPN
ejpam-5049	215	5	β2	β2	PROPN
ejpam-5049	215	6	k	k	PROPN
ejpam-5049	215	7	m∑	m∑	CCONJ
ejpam-5049	215	8	j=0	j=0	PROPN
ejpam-5049	215	9	cjφj(βk	cjφj(βk	PROPN
ejpam-5049	215	10	)	)	PUNCT
ejpam-5049	215	11	+	+	NUM
ejpam-5049	215	12	β2	β2	NOUN
ejpam-5049	215	13	l	l	NOUN
ejpam-5049	215	14	m∑	m∑	PROPN
ejpam-5049	215	15	i=0	i=0	PROPN
ejpam-5049	215	16	ciφj(βl	ciφj(βl	PROPN
ejpam-5049	215	17	)	)	PUNCT
ejpam-5049	215	18	)	)	PUNCT
ejpam-5049	215	19	,	,	PUNCT
ejpam-5049	215	20	(	(	PUNCT
ejpam-5049	215	21	33	33	NUM
ejpam-5049	215	22	)	)	PUNCT
ejpam-5049	215	23	and	and	CCONJ
ejpam-5049	215	24	m∑	m∑	ADV
ejpam-5049	215	25	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	215	26	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	215	27	k=0	k=0	PROPN
ejpam-5049	215	28	cjχ	cjχ	PROPN
ejpam-5049	215	29	(	(	PUNCT
ejpam-5049	215	30	α	α	NOUN
ejpam-5049	215	31	)	)	PUNCT
ejpam-5049	215	32	j	j	PROPN
ejpam-5049	215	33	,	,	PUNCT
ejpam-5049	215	34	k	k	PROPN
ejpam-5049	215	35	β	β	X
ejpam-5049	215	36	j−k−α	j−k−α	NOUN
ejpam-5049	215	37	s	s	PART
ejpam-5049	215	38	=	=	PUNCT
ejpam-5049	215	39	φ(β	φ(β	PROPN
ejpam-5049	215	40	)	)	PUNCT
ejpam-5049	216	1	+	+	CCONJ
ejpam-5049	216	2	h	h	NOUN
ejpam-5049	216	3	2	2	NUM
ejpam-5049	216	4	(	(	PUNCT
ejpam-5049	216	5	β2	β2	NOUN
ejpam-5049	216	6	0	0	PROPN
ejpam-5049	216	7	m∑	m∑	PROPN
ejpam-5049	216	8	j=0	j=0	PROPN
ejpam-5049	216	9	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	216	10	)	)	PUNCT
ejpam-5049	217	1	+	+	CCONJ
ejpam-5049	217	2	2	2	NUM
ejpam-5049	217	3	l−1∑	l−1∑	NOUN
ejpam-5049	217	4	k=1	k=1	PROPN
ejpam-5049	217	5	β2	β2	PROPN
ejpam-5049	217	6	k	k	PROPN
ejpam-5049	217	7	m∑	m∑	CCONJ
ejpam-5049	217	8	j=0	j=0	PROPN
ejpam-5049	217	9	cjφj(βk	cjφj(βk	PROPN
ejpam-5049	217	10	)	)	PUNCT
ejpam-5049	217	11	+	+	NUM
ejpam-5049	217	12	β2	β2	NOUN
ejpam-5049	217	13	l	l	PROPN
ejpam-5049	217	14	m∑	m∑	VERB
ejpam-5049	217	15	j=0	j=0	PROPN
ejpam-5049	217	16	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	217	17	)	)	PUNCT
ejpam-5049	217	18	)	)	PUNCT
ejpam-5049	217	19	.	.	PUNCT
ejpam-5049	218	1	(	(	PUNCT
ejpam-5049	218	2	34	34	NUM
ejpam-5049	218	3	)	)	PUNCT
ejpam-5049	218	4	(	(	PUNCT
ejpam-5049	218	5	ii	ii	NOUN
ejpam-5049	218	6	)	)	PUNCT
ejpam-5049	218	7	simpson	simpson	PROPN
ejpam-5049	218	8	’s	’s	PART
ejpam-5049	218	9	1/3	1/3	NUM
ejpam-5049	218	10	method	method	NOUN
ejpam-5049	218	11	using	use	VERB
ejpam-5049	218	12	(	(	PUNCT
ejpam-5049	218	13	16	16	NUM
ejpam-5049	218	14	)	)	PUNCT
ejpam-5049	218	15	and	and	CCONJ
ejpam-5049	218	16	(	(	PUNCT
ejpam-5049	218	17	17	17	NUM
ejpam-5049	218	18	)	)	PUNCT
ejpam-5049	218	19	,	,	PUNCT
ejpam-5049	218	20	we	we	PRON
ejpam-5049	218	21	obtain	obtain	VERB
ejpam-5049	218	22	m∑	m∑	PRON
ejpam-5049	218	23	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	218	24	m−⌈α⌉∑	m−⌈α⌉∑	PROPN
ejpam-5049	218	25	k=0	k=0	PROPN
ejpam-5049	218	26	cjχ	cjχ	PROPN
ejpam-5049	218	27	(	(	PUNCT
ejpam-5049	218	28	α	α	NOUN
ejpam-5049	218	29	)	)	PUNCT
ejpam-5049	218	30	j	j	PROPN
ejpam-5049	218	31	,	,	PUNCT
ejpam-5049	218	32	k	k	PROPN
ejpam-5049	218	33	β	β	X
ejpam-5049	218	34	j−k−α	j−k−α	NOUN
ejpam-5049	218	35	=	=	PUNCT
ejpam-5049	218	36	φ(β	φ(β	PROPN
ejpam-5049	218	37	)	)	PUNCT
ejpam-5049	219	1	+	+	NUM
ejpam-5049	219	2	h	h	NOUN
ejpam-5049	219	3	3	3	NUM
ejpam-5049	219	4	(	(	PUNCT
ejpam-5049	219	5	β2	β2	NOUN
ejpam-5049	219	6	0	0	PROPN
ejpam-5049	219	7	m∑	m∑	PROPN
ejpam-5049	219	8	j=0	j=0	PROPN
ejpam-5049	219	9	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	219	10	)	)	PUNCT
ejpam-5049	220	1	+	+	CCONJ
ejpam-5049	220	2	2	2	NUM
ejpam-5049	220	3	l	l	NOUN
ejpam-5049	220	4	2	2	X
ejpam-5049	220	5	−1∑	−1∑	PROPN
ejpam-5049	220	6	k=1	k=1	PROPN
ejpam-5049	220	7	β2	β2	PROPN
ejpam-5049	220	8	2k	2k	PROPN
ejpam-5049	220	9	m∑	m∑	CCONJ
ejpam-5049	220	10	j=0	j=0	PROPN
ejpam-5049	220	11	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	220	12	)	)	PUNCT
ejpam-5049	221	1	+	+	CCONJ
ejpam-5049	221	2	4	4	NUM
ejpam-5049	221	3	l	l	NOUN
ejpam-5049	221	4	2∑	2∑	X
ejpam-5049	222	1	k=1	k=1	PUNCT
ejpam-5049	222	2	β2	β2	VERB
ejpam-5049	222	3	2k−1	2k−1	NUM
ejpam-5049	222	4	m∑	m∑	VERB
ejpam-5049	222	5	j=0	j=0	PROPN
ejpam-5049	222	6	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	222	7	)	)	PUNCT
ejpam-5049	223	1	+	+	NUM
ejpam-5049	223	2	β2	β2	NOUN
ejpam-5049	223	3	l	l	PROPN
ejpam-5049	223	4	m∑	m∑	CCONJ
ejpam-5049	223	5	j=0	j=0	PROPN
ejpam-5049	223	6	cjφj(j	cjφj(j	PROPN
ejpam-5049	223	7	,	,	PUNCT
ejpam-5049	223	8	βl	βl	NOUN
ejpam-5049	223	9	)	)	PUNCT
ejpam-5049	223	10	)	)	PUNCT
ejpam-5049	223	11	,	,	PUNCT
ejpam-5049	223	12	(	(	PUNCT
ejpam-5049	223	13	35	35	NUM
ejpam-5049	223	14	)	)	PUNCT
ejpam-5049	223	15	and	and	CCONJ
ejpam-5049	223	16	n∑	n∑	ADJ
ejpam-5049	223	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	223	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	223	19	k=0	k=0	PROPN
ejpam-5049	223	20	cjχ	cjχ	PROPN
ejpam-5049	223	21	(	(	PUNCT
ejpam-5049	223	22	α	α	NOUN
ejpam-5049	223	23	)	)	PUNCT
ejpam-5049	223	24	j	j	PROPN
ejpam-5049	223	25	,	,	PUNCT
ejpam-5049	223	26	k	k	PROPN
ejpam-5049	223	27	β	β	X
ejpam-5049	223	28	j−k−α	j−k−α	NOUN
ejpam-5049	223	29	s	s	PART
ejpam-5049	223	30	=	=	PUNCT
ejpam-5049	223	31	φ(β	φ(β	PROPN
ejpam-5049	223	32	)	)	PUNCT
ejpam-5049	224	1	+	+	NUM
ejpam-5049	224	2	h	h	NOUN
ejpam-5049	224	3	3	3	NUM
ejpam-5049	224	4	(	(	PUNCT
ejpam-5049	224	5	β2	β2	NOUN
ejpam-5049	224	6	0	0	PROPN
ejpam-5049	224	7	m∑	m∑	PROPN
ejpam-5049	224	8	j=0	j=0	PROPN
ejpam-5049	224	9	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	224	10	)	)	PUNCT
ejpam-5049	225	1	+	+	CCONJ
ejpam-5049	225	2	2	2	NUM
ejpam-5049	225	3	l	l	NOUN
ejpam-5049	225	4	2	2	X
ejpam-5049	225	5	−1∑	−1∑	PROPN
ejpam-5049	225	6	k=1	k=1	PROPN
ejpam-5049	225	7	β2	β2	PROPN
ejpam-5049	225	8	2k	2k	PROPN
ejpam-5049	225	9	m∑	m∑	CCONJ
ejpam-5049	225	10	j=0	j=0	PROPN
ejpam-5049	225	11	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	225	12	)	)	PUNCT
ejpam-5049	226	1	+	+	CCONJ
ejpam-5049	226	2	4	4	NUM
ejpam-5049	226	3	l	l	NOUN
ejpam-5049	226	4	2∑	2∑	X
ejpam-5049	227	1	k=1	k=1	PUNCT
ejpam-5049	227	2	β2	β2	VERB
ejpam-5049	227	3	2k−1	2k−1	NUM
ejpam-5049	227	4	m∑	m∑	VERB
ejpam-5049	227	5	j=0	j=0	PROPN
ejpam-5049	227	6	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	227	7	)	)	PUNCT
ejpam-5049	228	1	+	+	NUM
ejpam-5049	228	2	β2	β2	NOUN
ejpam-5049	228	3	l	l	PROPN
ejpam-5049	228	4	m∑	m∑	VERB
ejpam-5049	228	5	j=0	j=0	PROPN
ejpam-5049	228	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	228	7	)	)	PUNCT
ejpam-5049	228	8	)	)	PUNCT
ejpam-5049	228	9	.	.	PUNCT
ejpam-5049	229	1	(	(	PUNCT
ejpam-5049	229	2	36	36	NUM
ejpam-5049	229	3	)	)	PUNCT
ejpam-5049	229	4	(	(	PUNCT
ejpam-5049	229	5	iii	iii	X
ejpam-5049	229	6	)	)	PUNCT
ejpam-5049	229	7	simpson	simpson	PROPN
ejpam-5049	229	8	’s	’s	PART
ejpam-5049	229	9	3/8	3/8	NUM
ejpam-5049	229	10	method	method	NOUN
ejpam-5049	229	11	khaled	khaled	PROPN
ejpam-5049	229	12	m.	m.	NOUN
ejpam-5049	229	13	saad	saad	PROPN
ejpam-5049	229	14	,	,	PUNCT
ejpam-5049	229	15	m.	m.	NOUN
ejpam-5049	229	16	q.	q.	PROPN
ejpam-5049	229	17	khirallah	khirallah	PROPN
ejpam-5049	229	18	/	/	SYM
ejpam-5049	229	19	eur	eur	PROPN
ejpam-5049	229	20	.	.	PUNCT
ejpam-5049	230	1	j.	j.	PROPN
ejpam-5049	230	2	pure	pure	PROPN
ejpam-5049	230	3	appl	appl	PROPN
ejpam-5049	230	4	.	.	PROPN
ejpam-5049	230	5	math	math	PROPN
ejpam-5049	230	6	,	,	PUNCT
ejpam-5049	230	7	17	17	NUM
ejpam-5049	230	8	(	(	PUNCT
ejpam-5049	230	9	1	1	NUM
ejpam-5049	230	10	)	)	PUNCT
ejpam-5049	230	11	(	(	PUNCT
ejpam-5049	230	12	2024	2024	NUM
ejpam-5049	230	13	)	)	PUNCT
ejpam-5049	230	14	,	,	PUNCT
ejpam-5049	230	15	477	477	NUM
ejpam-5049	230	16	-	-	SYM
ejpam-5049	230	17	503	503	NUM
ejpam-5049	230	18	488	488	NUM
ejpam-5049	230	19	using	use	VERB
ejpam-5049	230	20	(	(	PUNCT
ejpam-5049	230	21	18	18	NUM
ejpam-5049	230	22	)	)	PUNCT
ejpam-5049	230	23	and	and	CCONJ
ejpam-5049	230	24	(	(	PUNCT
ejpam-5049	230	25	19	19	NUM
ejpam-5049	230	26	)	)	PUNCT
ejpam-5049	231	1	,	,	PUNCT
ejpam-5049	231	2	we	we	PRON
ejpam-5049	231	3	obtain	obtain	VERB
ejpam-5049	231	4	m∑	m∑	PRON
ejpam-5049	231	5	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	231	6	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	231	7	k=0	k=0	PROPN
ejpam-5049	231	8	cjχ	cjχ	PROPN
ejpam-5049	231	9	(	(	PUNCT
ejpam-5049	231	10	α	α	NOUN
ejpam-5049	231	11	)	)	PUNCT
ejpam-5049	231	12	j	j	PROPN
ejpam-5049	231	13	,	,	PUNCT
ejpam-5049	231	14	k	k	PROPN
ejpam-5049	231	15	β	β	X
ejpam-5049	231	16	j−k−α	j−k−α	NOUN
ejpam-5049	231	17	=	=	PUNCT
ejpam-5049	231	18	φ(β	φ(β	PROPN
ejpam-5049	231	19	)	)	PUNCT
ejpam-5049	231	20	+	+	CCONJ
ejpam-5049	231	21	3h	3h	NUM
ejpam-5049	231	22	8	8	NUM
ejpam-5049	231	23	(	(	PUNCT
ejpam-5049	231	24	β2	β2	NOUN
ejpam-5049	231	25	0	0	PROPN
ejpam-5049	231	26	m∑	m∑	CCONJ
ejpam-5049	231	27	j=0	j=0	PROPN
ejpam-5049	231	28	cjφj(j	cjφj(j	PROPN
ejpam-5049	231	29	,	,	PUNCT
ejpam-5049	231	30	β0	β0	PROPN
ejpam-5049	231	31	)	)	PUNCT
ejpam-5049	231	32	+	+	CCONJ
ejpam-5049	231	33	3	3	NUM
ejpam-5049	231	34	l	l	NOUN
ejpam-5049	231	35	3∑	3∑	NUM
ejpam-5049	231	36	k=1	k=1	NOUN
ejpam-5049	232	1	(	(	PUNCT
ejpam-5049	232	2	β2	β2	PROPN
ejpam-5049	232	3	3k−2	3k−2	PROPN
ejpam-5049	232	4	m∑	m∑	VERB
ejpam-5049	232	5	j=0	j=0	PROPN
ejpam-5049	232	6	cjφj(j	cjφj(j	PROPN
ejpam-5049	232	7	,	,	PUNCT
ejpam-5049	232	8	β3k−2	β3k−2	PROPN
ejpam-5049	232	9	)	)	PUNCT
ejpam-5049	233	1	+	+	CCONJ
ejpam-5049	233	2	β3k−1	β3k−1	PROPN
ejpam-5049	233	3	m∑	m∑	PUNCT
ejpam-5049	233	4	j=0	j=0	PROPN
ejpam-5049	233	5	cjφj(j	cjφj(j	NOUN
ejpam-5049	233	6	,	,	PUNCT
ejpam-5049	233	7	β3k−1	β3k−1	PROPN
ejpam-5049	233	8	)	)	PUNCT
ejpam-5049	233	9	)	)	PUNCT
ejpam-5049	234	1	+	+	CCONJ
ejpam-5049	234	2	2	2	NUM
ejpam-5049	234	3	l	l	NOUN
ejpam-5049	234	4	3	3	NUM
ejpam-5049	234	5	−1∑	−1∑	PROPN
ejpam-5049	234	6	k=1	k=1	PROPN
ejpam-5049	234	7	β2	β2	PROPN
ejpam-5049	234	8	3k	3k	PROPN
ejpam-5049	234	9	m∑	m∑	PUNCT
ejpam-5049	234	10	j=0	j=0	PROPN
ejpam-5049	234	11	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	234	12	)	)	PUNCT
ejpam-5049	235	1	+	+	NUM
ejpam-5049	235	2	β2	β2	NOUN
ejpam-5049	235	3	l	l	PROPN
ejpam-5049	235	4	m∑	m∑	VERB
ejpam-5049	235	5	j=0	j=0	PROPN
ejpam-5049	235	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	235	7	)	)	PUNCT
ejpam-5049	235	8	)	)	PUNCT
ejpam-5049	235	9	,	,	PUNCT
ejpam-5049	235	10	(	(	PUNCT
ejpam-5049	235	11	37	37	NUM
ejpam-5049	235	12	)	)	PUNCT
ejpam-5049	235	13	and	and	CCONJ
ejpam-5049	235	14	m∑	m∑	CCONJ
ejpam-5049	235	15	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	235	16	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	235	17	k=0	k=0	PROPN
ejpam-5049	235	18	cjχ	cjχ	PROPN
ejpam-5049	235	19	(	(	PUNCT
ejpam-5049	235	20	α	α	NOUN
ejpam-5049	235	21	)	)	PUNCT
ejpam-5049	235	22	j	j	PROPN
ejpam-5049	235	23	,	,	PUNCT
ejpam-5049	235	24	k	k	PROPN
ejpam-5049	235	25	β	β	X
ejpam-5049	235	26	j−k−α	j−k−α	NOUN
ejpam-5049	235	27	s	s	PART
ejpam-5049	235	28	=	=	PUNCT
ejpam-5049	235	29	φ(β	φ(β	PROPN
ejpam-5049	235	30	)	)	PUNCT
ejpam-5049	235	31	+	+	CCONJ
ejpam-5049	235	32	3h	3h	NUM
ejpam-5049	235	33	8	8	NUM
ejpam-5049	235	34	(	(	PUNCT
ejpam-5049	235	35	β2	β2	NOUN
ejpam-5049	235	36	0	0	PROPN
ejpam-5049	235	37	m∑	m∑	PROPN
ejpam-5049	235	38	j=0	j=0	PROPN
ejpam-5049	235	39	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	235	40	)	)	PUNCT
ejpam-5049	236	1	+	+	CCONJ
ejpam-5049	236	2	3	3	NUM
ejpam-5049	236	3	l	l	NOUN
ejpam-5049	236	4	3∑	3∑	NUM
ejpam-5049	236	5	k=1	k=1	NOUN
ejpam-5049	237	1	(	(	PUNCT
ejpam-5049	237	2	β2	β2	PROPN
ejpam-5049	237	3	3k−2	3k−2	PROPN
ejpam-5049	237	4	m∑	m∑	VERB
ejpam-5049	237	5	j=0	j=0	PROPN
ejpam-5049	237	6	cjφj(β3k−2	cjφj(β3k−2	PROPN
ejpam-5049	237	7	)	)	PUNCT
ejpam-5049	238	1	+	+	CCONJ
ejpam-5049	238	2	β3k−1	β3k−1	PROPN
ejpam-5049	238	3	m∑	m∑	CCONJ
ejpam-5049	238	4	j=0	j=0	PROPN
ejpam-5049	238	5	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	238	6	)	)	PUNCT
ejpam-5049	238	7	)	)	PUNCT
ejpam-5049	239	1	+	+	CCONJ
ejpam-5049	239	2	2	2	NUM
ejpam-5049	239	3	l	l	NOUN
ejpam-5049	239	4	3	3	NUM
ejpam-5049	239	5	−1∑	−1∑	PROPN
ejpam-5049	239	6	k=1	k=1	PROPN
ejpam-5049	239	7	β2	β2	PROPN
ejpam-5049	239	8	3k	3k	PROPN
ejpam-5049	239	9	m∑	m∑	PUNCT
ejpam-5049	239	10	j=0	j=0	PROPN
ejpam-5049	239	11	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	239	12	)	)	PUNCT
ejpam-5049	240	1	+	+	NUM
ejpam-5049	240	2	β2	β2	NOUN
ejpam-5049	240	3	l	l	PROPN
ejpam-5049	240	4	m∑	m∑	VERB
ejpam-5049	240	5	j=0	j=0	PROPN
ejpam-5049	240	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	240	7	)	)	PUNCT
ejpam-5049	240	8	)	)	PUNCT
ejpam-5049	240	9	.	.	PUNCT
ejpam-5049	241	1	(	(	PUNCT
ejpam-5049	241	2	38	38	NUM
ejpam-5049	241	3	)	)	PUNCT
ejpam-5049	241	4	we	we	PRON
ejpam-5049	241	5	follow	follow	VERB
ejpam-5049	241	6	the	the	DET
ejpam-5049	241	7	same	same	ADJ
ejpam-5049	241	8	procedure	procedure	NOUN
ejpam-5049	241	9	as	as	SCONJ
ejpam-5049	241	10	described	describe	VERB
ejpam-5049	241	11	in	in	ADP
ejpam-5049	241	12	example	example	NOUN
ejpam-5049	241	13	one	one	NUM
ejpam-5049	241	14	.	.	PUNCT
ejpam-5049	242	1	approximate	approximate	ADJ
ejpam-5049	242	2	solutions	solution	NOUN
ejpam-5049	242	3	for	for	ADP
ejpam-5049	242	4	a	a	DET
ejpam-5049	242	5	variety	variety	NOUN
ejpam-5049	242	6	of	of	ADP
ejpam-5049	242	7	α	α	PROPN
ejpam-5049	242	8	values	value	NOUN
ejpam-5049	242	9	are	be	AUX
ejpam-5049	242	10	shown	show	VERB
ejpam-5049	242	11	in	in	ADP
ejpam-5049	242	12	figure	figure	NOUN
ejpam-5049	242	13	3	3	NUM
ejpam-5049	242	14	(	(	PUNCT
ejpam-5049	242	15	a	a	NOUN
ejpam-5049	242	16	)	)	PUNCT
ejpam-5049	242	17	.	.	PUNCT
ejpam-5049	243	1	this	this	DET
ejpam-5049	243	2	comparison	comparison	NOUN
ejpam-5049	243	3	is	be	AUX
ejpam-5049	243	4	specifically	specifically	ADV
ejpam-5049	243	5	relevant	relevant	ADJ
ejpam-5049	243	6	to	to	ADP
ejpam-5049	243	7	the	the	DET
ejpam-5049	243	8	simpson	simpson	PROPN
ejpam-5049	243	9	’s	’s	PART
ejpam-5049	243	10	1/8	1/8	NUM
ejpam-5049	243	11	case	case	NOUN
ejpam-5049	243	12	,	,	PUNCT
ejpam-5049	243	13	while	while	SCONJ
ejpam-5049	243	14	the	the	DET
ejpam-5049	243	15	other	other	ADJ
ejpam-5049	243	16	two	two	NUM
ejpam-5049	243	17	cases	case	NOUN
ejpam-5049	243	18	demonstrate	demonstrate	VERB
ejpam-5049	243	19	similar	similar	ADJ
ejpam-5049	243	20	behavior	behavior	NOUN
ejpam-5049	243	21	.	.	PUNCT
ejpam-5049	244	1	the	the	DET
ejpam-5049	244	2	absolute	absolute	ADJ
ejpam-5049	244	3	error	error	NOUN
ejpam-5049	244	4	between	between	ADP
ejpam-5049	244	5	the	the	DET
ejpam-5049	244	6	approximate	approximate	ADJ
ejpam-5049	244	7	solutions	solution	NOUN
ejpam-5049	244	8	via	via	ADP
ejpam-5049	244	9	trapezoidal	trapezoidal	NOUN
ejpam-5049	244	10	,	,	PUNCT
ejpam-5049	244	11	simpson	simpson	PROPN
ejpam-5049	244	12	’	'	PUNCT
ejpam-5049	244	13	1/8	1/8	NUM
ejpam-5049	244	14	,	,	PUNCT
ejpam-5049	244	15	and	and	CCONJ
ejpam-5049	244	16	simpson	simpson	PROPN
ejpam-5049	244	17	’	'	PUNCT
ejpam-5049	244	18	1/3	1/3	NUM
ejpam-5049	244	19	methods	method	NOUN
ejpam-5049	244	20	and	and	CCONJ
ejpam-5049	244	21	the	the	DET
ejpam-5049	244	22	exact	exact	ADJ
ejpam-5049	244	23	solution	solution	NOUN
ejpam-5049	244	24	is	be	AUX
ejpam-5049	244	25	shown	show	VERB
ejpam-5049	244	26	in	in	ADP
ejpam-5049	244	27	figure	figure	NOUN
ejpam-5049	244	28	3	3	NUM
ejpam-5049	244	29	(	(	PUNCT
ejpam-5049	244	30	b	b	NOUN
ejpam-5049	244	31	)	)	PUNCT
ejpam-5049	244	32	.	.	PUNCT
ejpam-5049	245	1	in	in	ADP
ejpam-5049	245	2	figure	figure	NOUN
ejpam-5049	245	3	4	4	NUM
ejpam-5049	245	4	,	,	PUNCT
ejpam-5049	245	5	the	the	DET
ejpam-5049	245	6	absolute	absolute	ADJ
ejpam-5049	245	7	error	error	NOUN
ejpam-5049	245	8	between	between	ADP
ejpam-5049	245	9	each	each	DET
ejpam-5049	245	10	subsequent	subsequent	ADJ
ejpam-5049	245	11	step	step	NOUN
ejpam-5049	245	12	when	when	SCONJ
ejpam-5049	245	13	the	the	DET
ejpam-5049	245	14	non	non	ADJ
ejpam-5049	245	15	-	-	ADJ
ejpam-5049	245	16	integer	integer	ADJ
ejpam-5049	245	17	α	α	NOUN
ejpam-5049	245	18	values	value	NOUN
ejpam-5049	245	19	via	via	ADP
ejpam-5049	245	20	trapezoidal	trapezoidal	ADJ
ejpam-5049	245	21	,	,	PUNCT
ejpam-5049	245	22	simpson	simpson	PROPN
ejpam-5049	245	23	’	'	PUNCT
ejpam-5049	245	24	1/8	1/8	NUM
ejpam-5049	245	25	,	,	PUNCT
ejpam-5049	245	26	and	and	CCONJ
ejpam-5049	245	27	simpson	simpson	PROPN
ejpam-5049	245	28	’	'	PUNCT
ejpam-5049	246	1	1/3	1/3	NUM
ejpam-5049	246	2	methods	method	NOUN
ejpam-5049	246	3	are	be	AUX
ejpam-5049	246	4	applied	apply	VERB
ejpam-5049	246	5	is	be	AUX
ejpam-5049	246	6	shown	show	VERB
ejpam-5049	246	7	.	.	PUNCT
ejpam-5049	247	1	collectively	collectively	ADV
ejpam-5049	247	2	,	,	PUNCT
ejpam-5049	247	3	these	these	DET
ejpam-5049	247	4	numerical	numerical	ADJ
ejpam-5049	247	5	outcomes	outcome	NOUN
ejpam-5049	247	6	illustrate	illustrate	VERB
ejpam-5049	247	7	the	the	DET
ejpam-5049	247	8	precision	precision	NOUN
ejpam-5049	247	9	of	of	ADP
ejpam-5049	247	10	the	the	DET
ejpam-5049	247	11	approximations	approximation	NOUN
ejpam-5049	247	12	.	.	PUNCT
ejpam-5049	248	1	it	it	PRON
ejpam-5049	248	2	has	have	AUX
ejpam-5049	248	3	been	be	AUX
ejpam-5049	248	4	demonstrated	demonstrate	VERB
ejpam-5049	248	5	that	that	SCONJ
ejpam-5049	248	6	augmenting	augment	VERB
ejpam-5049	248	7	the	the	DET
ejpam-5049	248	8	number	number	NOUN
ejpam-5049	248	9	of	of	ADP
ejpam-5049	248	10	steps	step	NOUN
ejpam-5049	248	11	by	by	ADP
ejpam-5049	248	12	m	m	PROPN
ejpam-5049	248	13	enhances	enhance	NOUN
ejpam-5049	248	14	accuracy	accuracy	NOUN
ejpam-5049	248	15	.	.	PUNCT
ejpam-5049	249	1	example	example	NOUN
ejpam-5049	250	1	3	3	X
ejpam-5049	250	2	.	.	X
ejpam-5049	250	3	consider	consider	VERB
ejpam-5049	250	4	the	the	DET
ejpam-5049	250	5	following	follow	VERB
ejpam-5049	250	6	fractional	fractional	ADJ
ejpam-5049	250	7	fredholm	fredholm	NOUN
ejpam-5049	250	8	integro	integro	ADJ
ejpam-5049	250	9	-	-	PUNCT
ejpam-5049	250	10	differential	differential	NOUN
ejpam-5049	250	11	equation	equation	NOUN
ejpam-5049	250	12	[	[	X
ejpam-5049	250	13	4	4	NUM
ejpam-5049	250	14	]	]	PUNCT
ejpam-5049	250	15	dαϕ1(β	dαϕ1(β	NOUN
ejpam-5049	250	16	)	)	PUNCT
ejpam-5049	250	17	=	=	SYM
ejpam-5049	251	1	2	2	NUM
ejpam-5049	251	2	+	+	CCONJ
ejpam-5049	251	3	12	12	NUM
ejpam-5049	251	4	5	5	NUM
ejpam-5049	251	5	β	β	NOUN
ejpam-5049	251	6	−	−	PROPN
ejpam-5049	251	7	∫	∫	PROPN
ejpam-5049	251	8	1	1	NUM
ejpam-5049	251	9	0	0	NUM
ejpam-5049	251	10	β(ϕ2	β(ϕ2	NOUN
ejpam-5049	251	11	1(β	1(β	NUM
ejpam-5049	251	12	)	)	PUNCT
ejpam-5049	252	1	+	+	CCONJ
ejpam-5049	253	1	ϕ2(β	ϕ2(β	PROPN
ejpam-5049	253	2	)	)	PUNCT
ejpam-5049	253	3	2	2	NUM
ejpam-5049	253	4	)	)	PUNCT
ejpam-5049	253	5	)	)	PUNCT
ejpam-5049	253	6	,	,	PUNCT
ejpam-5049	253	7	dβ	dβ	NOUN
ejpam-5049	253	8	,	,	PUNCT
ejpam-5049	253	9	(	(	PUNCT
ejpam-5049	253	10	39	39	NUM
ejpam-5049	253	11	)	)	PUNCT
ejpam-5049	253	12	khaled	khale	VERB
ejpam-5049	253	13	m.	m.	NOUN
ejpam-5049	253	14	saad	saad	PROPN
ejpam-5049	253	15	,	,	PUNCT
ejpam-5049	253	16	m.	m.	NOUN
ejpam-5049	253	17	q.	q.	PROPN
ejpam-5049	253	18	khirallah	khirallah	PROPN
ejpam-5049	253	19	/	/	SYM
ejpam-5049	253	20	eur	eur	PROPN
ejpam-5049	253	21	.	.	PUNCT
ejpam-5049	254	1	j.	j.	PROPN
ejpam-5049	254	2	pure	pure	PROPN
ejpam-5049	254	3	appl	appl	PROPN
ejpam-5049	254	4	.	.	PROPN
ejpam-5049	254	5	math	math	PROPN
ejpam-5049	254	6	,	,	PUNCT
ejpam-5049	254	7	17	17	NUM
ejpam-5049	254	8	(	(	PUNCT
ejpam-5049	254	9	1	1	NUM
ejpam-5049	254	10	)	)	PUNCT
ejpam-5049	254	11	(	(	PUNCT
ejpam-5049	254	12	2024	2024	NUM
ejpam-5049	254	13	)	)	PUNCT
ejpam-5049	254	14	,	,	PUNCT
ejpam-5049	254	15	477	477	NUM
ejpam-5049	254	16	-	-	SYM
ejpam-5049	254	17	503	503	NUM
ejpam-5049	254	18	489	489	NUM
ejpam-5049	254	19	dαϕ2(β	dαϕ2(β	NOUN
ejpam-5049	254	20	)	)	PUNCT
ejpam-5049	254	21	=	=	SYM
ejpam-5049	255	1	−2	−2	NOUN
ejpam-5049	256	1	+	+	CCONJ
ejpam-5049	256	2	4	4	NUM
ejpam-5049	256	3	3	3	NUM
ejpam-5049	256	4	β	β	NOUN
ejpam-5049	256	5	−	−	PROPN
ejpam-5049	256	6	∫	∫	PROPN
ejpam-5049	256	7	1	1	NUM
ejpam-5049	256	8	0	0	NUM
ejpam-5049	256	9	β(ϕ2	β(ϕ2	NOUN
ejpam-5049	256	10	1(β)−	1(β)−	NUM
ejpam-5049	257	1	ϕ2(β	ϕ2(β	NUM
ejpam-5049	257	2	)	)	PUNCT
ejpam-5049	257	3	2	2	NUM
ejpam-5049	257	4	)	)	PUNCT
ejpam-5049	257	5	)	)	PUNCT
ejpam-5049	257	6	,	,	PUNCT
ejpam-5049	257	7	dβ	dβ	NOUN
ejpam-5049	257	8	,	,	PUNCT
ejpam-5049	257	9	(	(	PUNCT
ejpam-5049	257	10	40	40	NUM
ejpam-5049	257	11	)	)	PUNCT
ejpam-5049	257	12	0	0	PUNCT
ejpam-5049	258	1	<	<	X
ejpam-5049	258	2	α	α	PROPN
ejpam-5049	258	3	≤	≤	NUM
ejpam-5049	258	4	2	2	NUM
ejpam-5049	258	5	,	,	PUNCT
ejpam-5049	258	6	subject	subject	ADJ
ejpam-5049	258	7	to	to	ADP
ejpam-5049	258	8	the	the	DET
ejpam-5049	258	9	initial	initial	ADJ
ejpam-5049	258	10	conditions	condition	NOUN
ejpam-5049	258	11	ϕ1(0	ϕ1(0	PRON
ejpam-5049	258	12	)	)	PUNCT
ejpam-5049	258	13	=	=	SYM
ejpam-5049	259	1	1	1	NUM
ejpam-5049	259	2	,	,	PUNCT
ejpam-5049	259	3	ϕ	ϕ	NOUN
ejpam-5049	259	4	′	′	NOUN
ejpam-5049	259	5	1(0	1(0	NUM
ejpam-5049	259	6	)	)	PUNCT
ejpam-5049	260	1	=	=	SYM
ejpam-5049	260	2	0	0	NUM
ejpam-5049	260	3	,	,	PUNCT
ejpam-5049	260	4	ϕ2(0	ϕ2(0	NOUN
ejpam-5049	260	5	)	)	PUNCT
ejpam-5049	260	6	=	=	SYM
ejpam-5049	260	7	1	1	NUM
ejpam-5049	260	8	,	,	PUNCT
ejpam-5049	260	9	ϕ	ϕ	NOUN
ejpam-5049	260	10	′	′	NOUN
ejpam-5049	260	11	2(0	2(0	NUM
ejpam-5049	260	12	)	)	PUNCT
ejpam-5049	260	13	=	=	SYM
ejpam-5049	260	14	0	0	NUM
ejpam-5049	260	15	,	,	PUNCT
ejpam-5049	260	16	(	(	PUNCT
ejpam-5049	260	17	41	41	NUM
ejpam-5049	260	18	)	)	PUNCT
ejpam-5049	260	19	with	with	ADP
ejpam-5049	260	20	exact	exact	ADJ
ejpam-5049	260	21	solutions	solution	NOUN
ejpam-5049	260	22	ϕ1	ϕ1	NOUN
ejpam-5049	260	23	=	=	SYM
ejpam-5049	260	24	1	1	NUM
ejpam-5049	260	25	+	+	CCONJ
ejpam-5049	260	26	β2	β2	NOUN
ejpam-5049	260	27	and	and	CCONJ
ejpam-5049	260	28	ϕ1	ϕ1	NOUN
ejpam-5049	260	29	=	=	SYM
ejpam-5049	260	30	1−	1−	NUM
ejpam-5049	260	31	β2	β2	NOUN
ejpam-5049	260	32	(	(	PUNCT
ejpam-5049	260	33	i	i	NOUN
ejpam-5049	260	34	)	)	PUNCT
ejpam-5049	260	35	trapezoidal	trapezoidal	NOUN
ejpam-5049	260	36	’s	’s	PART
ejpam-5049	260	37	method	method	NOUN
ejpam-5049	260	38	using	use	VERB
ejpam-5049	260	39	(	(	PUNCT
ejpam-5049	260	40	14	14	NUM
ejpam-5049	260	41	)	)	PUNCT
ejpam-5049	260	42	,	,	PUNCT
ejpam-5049	260	43	we	we	PRON
ejpam-5049	260	44	get	get	VERB
ejpam-5049	260	45	m∑	m∑	PUNCT
ejpam-5049	261	1	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	261	2	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	261	3	k=0	k=0	PROPN
ejpam-5049	261	4	cjχ	cjχ	PROPN
ejpam-5049	261	5	(	(	PUNCT
ejpam-5049	261	6	α	α	NOUN
ejpam-5049	261	7	)	)	PUNCT
ejpam-5049	261	8	j	j	PROPN
ejpam-5049	261	9	,	,	PUNCT
ejpam-5049	261	10	k	k	PROPN
ejpam-5049	261	11	β	β	X
ejpam-5049	261	12	j−k−α	j−k−α	NOUN
ejpam-5049	261	13	=	=	PUNCT
ejpam-5049	261	14	φ1(β	φ1(β	PROPN
ejpam-5049	261	15	)	)	PUNCT
ejpam-5049	261	16	+	+	NUM
ejpam-5049	261	17	h	h	NOUN
ejpam-5049	261	18	2	2	NUM
ejpam-5049	261	19	(	(	PUNCT
ejpam-5049	261	20	β0	β0	PROPN
ejpam-5049	261	21	(	(	PUNCT
ejpam-5049	261	22	m∑	m∑	ADV
ejpam-5049	261	23	j=0	j=0	PROPN
ejpam-5049	261	24	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	261	25	)	)	PUNCT
ejpam-5049	261	26	)	)	PUNCT
ejpam-5049	261	27	2	2	X
ejpam-5049	262	1	+	+	CCONJ
ejpam-5049	262	2	β0	β0	ADJ
ejpam-5049	262	3	(	(	PUNCT
ejpam-5049	262	4	m∑	m∑	ADV
ejpam-5049	262	5	j=0	j=0	PROPN
ejpam-5049	262	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	262	7	)	)	PUNCT
ejpam-5049	262	8	)	)	PUNCT
ejpam-5049	263	1	2	2	NUM
ejpam-5049	263	2	+	+	SYM
ejpam-5049	263	3	2	2	NUM
ejpam-5049	263	4	l−1∑	l−1∑	NOUN
ejpam-5049	263	5	k=1	k=1	X
ejpam-5049	263	6	βk	βk	PROPN
ejpam-5049	263	7	(	(	PUNCT
ejpam-5049	263	8	m∑	m∑	CCONJ
ejpam-5049	263	9	j=0	j=0	PROPN
ejpam-5049	263	10	cjφj(βk	cjφj(βk	NOUN
ejpam-5049	263	11	)	)	PUNCT
ejpam-5049	263	12	)	)	PUNCT
ejpam-5049	264	1	2	2	NUM
ejpam-5049	264	2	+	+	SYM
ejpam-5049	264	3	2	2	NUM
ejpam-5049	264	4	l−1∑	l−1∑	NOUN
ejpam-5049	264	5	k=1	k=1	X
ejpam-5049	264	6	βk	βk	PROPN
ejpam-5049	264	7	(	(	PUNCT
ejpam-5049	264	8	m∑	m∑	CCONJ
ejpam-5049	264	9	j=0	j=0	PROPN
ejpam-5049	264	10	djφj(βk	djφj(βk	ADJ
ejpam-5049	264	11	)	)	PUNCT
ejpam-5049	264	12	)	)	PUNCT
ejpam-5049	264	13	2	2	NUM
ejpam-5049	265	1	+	+	NUM
ejpam-5049	265	2	βl	βl	NOUN
ejpam-5049	265	3	(	(	PUNCT
ejpam-5049	265	4	m∑	m∑	CCONJ
ejpam-5049	265	5	j=0	j=0	PROPN
ejpam-5049	265	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	265	7	)	)	PUNCT
ejpam-5049	265	8	)	)	PUNCT
ejpam-5049	265	9	2	2	X
ejpam-5049	266	1	+	+	NUM
ejpam-5049	266	2	βl	βl	NOUN
ejpam-5049	266	3	(	(	PUNCT
ejpam-5049	266	4	m∑	m∑	CCONJ
ejpam-5049	266	5	j=0	j=0	PROPN
ejpam-5049	266	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	266	7	)	)	PUNCT
ejpam-5049	266	8	)	)	PUNCT
ejpam-5049	266	9	2	2	NUM
ejpam-5049	266	10	)	)	PUNCT
ejpam-5049	266	11	,	,	PUNCT
ejpam-5049	266	12	(	(	PUNCT
ejpam-5049	266	13	42	42	NUM
ejpam-5049	266	14	)	)	PUNCT
ejpam-5049	266	15	and	and	CCONJ
ejpam-5049	266	16	m∑	m∑	CCONJ
ejpam-5049	266	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	266	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	266	19	k=0	k=0	PROPN
ejpam-5049	266	20	djχ	djχ	PROPN
ejpam-5049	266	21	(	(	PUNCT
ejpam-5049	266	22	α	α	NOUN
ejpam-5049	266	23	)	)	PUNCT
ejpam-5049	266	24	j	j	PROPN
ejpam-5049	266	25	,	,	PUNCT
ejpam-5049	266	26	k	k	PROPN
ejpam-5049	266	27	β	β	X
ejpam-5049	266	28	j−k−α	j−k−α	NOUN
ejpam-5049	266	29	=	=	PUNCT
ejpam-5049	266	30	φ1(β	φ1(β	PROPN
ejpam-5049	266	31	)	)	PUNCT
ejpam-5049	266	32	+	+	NUM
ejpam-5049	266	33	h	h	NOUN
ejpam-5049	266	34	2	2	NUM
ejpam-5049	266	35	(	(	PUNCT
ejpam-5049	266	36	β0	β0	PROPN
ejpam-5049	266	37	(	(	PUNCT
ejpam-5049	266	38	m∑	m∑	ADV
ejpam-5049	266	39	j=0	j=0	PROPN
ejpam-5049	266	40	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	266	41	)	)	PUNCT
ejpam-5049	266	42	)	)	PUNCT
ejpam-5049	267	1	2	2	NUM
ejpam-5049	267	2	−	−	NOUN
ejpam-5049	267	3	β0	β0	NOUN
ejpam-5049	267	4	(	(	PUNCT
ejpam-5049	267	5	m∑	m∑	ADV
ejpam-5049	267	6	j=0	j=0	PROPN
ejpam-5049	267	7	djφj(β0	djφj(β0	PROPN
ejpam-5049	267	8	)	)	PUNCT
ejpam-5049	267	9	)	)	PUNCT
ejpam-5049	267	10	2	2	NUM
ejpam-5049	268	1	+	+	SYM
ejpam-5049	268	2	2	2	NUM
ejpam-5049	268	3	l−1∑	l−1∑	NOUN
ejpam-5049	268	4	k=1	k=1	X
ejpam-5049	268	5	βk	βk	PROPN
ejpam-5049	268	6	(	(	PUNCT
ejpam-5049	268	7	m∑	m∑	CCONJ
ejpam-5049	268	8	j=0	j=0	PROPN
ejpam-5049	268	9	cjφj(βk	cjφj(βk	NOUN
ejpam-5049	268	10	)	)	PUNCT
ejpam-5049	268	11	)	)	PUNCT
ejpam-5049	269	1	2	2	NUM
ejpam-5049	269	2	−	−	NOUN
ejpam-5049	269	3	2	2	NUM
ejpam-5049	269	4	l−1∑	l−1∑	NOUN
ejpam-5049	269	5	k=1	k=1	X
ejpam-5049	269	6	βk	βk	PROPN
ejpam-5049	269	7	(	(	PUNCT
ejpam-5049	269	8	m∑	m∑	CCONJ
ejpam-5049	269	9	j=0	j=0	PROPN
ejpam-5049	269	10	djφj(βk	djφj(βk	ADJ
ejpam-5049	269	11	)	)	PUNCT
ejpam-5049	269	12	)	)	PUNCT
ejpam-5049	269	13	2	2	NUM
ejpam-5049	270	1	+	+	NUM
ejpam-5049	270	2	βl	βl	NOUN
ejpam-5049	270	3	(	(	PUNCT
ejpam-5049	270	4	m∑	m∑	CCONJ
ejpam-5049	270	5	j=0	j=0	PROPN
ejpam-5049	270	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	270	7	)	)	PUNCT
ejpam-5049	270	8	)	)	PUNCT
ejpam-5049	270	9	2	2	NUM
ejpam-5049	270	10	−	−	NOUN
ejpam-5049	270	11	βl	βl	NOUN
ejpam-5049	270	12	(	(	PUNCT
ejpam-5049	270	13	m∑	m∑	CCONJ
ejpam-5049	270	14	j=0	j=0	PROPN
ejpam-5049	270	15	djφj(βl	djφj(βl	PROPN
ejpam-5049	270	16	)	)	PUNCT
ejpam-5049	270	17	)	)	PUNCT
ejpam-5049	270	18	2	2	NUM
ejpam-5049	270	19	)	)	PUNCT
ejpam-5049	270	20	,	,	PUNCT
ejpam-5049	270	21	(	(	PUNCT
ejpam-5049	270	22	43	43	NUM
ejpam-5049	270	23	)	)	PUNCT
ejpam-5049	270	24	where	where	SCONJ
ejpam-5049	270	25	φ1(β	φ1(β	NOUN
ejpam-5049	270	26	)	)	PUNCT
ejpam-5049	270	27	=	=	SYM
ejpam-5049	270	28	2	2	NUM
ejpam-5049	270	29	+	+	CCONJ
ejpam-5049	270	30	12	12	NUM
ejpam-5049	270	31	5	5	NUM
ejpam-5049	270	32	β	β	NOUN
ejpam-5049	270	33	,	,	PUNCT
ejpam-5049	270	34	φ2(β	φ2(β	PROPN
ejpam-5049	270	35	)	)	PUNCT
ejpam-5049	270	36	=	=	SYM
ejpam-5049	270	37	−2	−2	NOUN
ejpam-5049	270	38	+	+	CCONJ
ejpam-5049	270	39	4	4	NUM
ejpam-5049	270	40	3	3	NUM
ejpam-5049	270	41	β	β	NOUN
ejpam-5049	270	42	.	.	PUNCT
ejpam-5049	271	1	using	use	VERB
ejpam-5049	271	2	(	(	PUNCT
ejpam-5049	271	3	15	15	NUM
ejpam-5049	271	4	)	)	PUNCT
ejpam-5049	271	5	,	,	PUNCT
ejpam-5049	271	6	we	we	PRON
ejpam-5049	271	7	get	get	VERB
ejpam-5049	271	8	m∑	m∑	PUNCT
ejpam-5049	272	1	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	272	2	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	272	3	k=0	k=0	PROPN
ejpam-5049	272	4	cjχ	cjχ	PROPN
ejpam-5049	272	5	(	(	PUNCT
ejpam-5049	272	6	α	α	NOUN
ejpam-5049	272	7	)	)	PUNCT
ejpam-5049	272	8	j	j	PROPN
ejpam-5049	272	9	,	,	PUNCT
ejpam-5049	272	10	k	k	PROPN
ejpam-5049	272	11	β	β	X
ejpam-5049	272	12	j−k−α	j−k−α	NOUN
ejpam-5049	272	13	s	s	PART
ejpam-5049	272	14	=	=	PUNCT
ejpam-5049	272	15	φ1(β	φ1(β	PROPN
ejpam-5049	272	16	)	)	PUNCT
ejpam-5049	272	17	+	+	NUM
ejpam-5049	272	18	h	h	NOUN
ejpam-5049	272	19	2	2	NUM
ejpam-5049	272	20	(	(	PUNCT
ejpam-5049	272	21	β0	β0	PROPN
ejpam-5049	272	22	(	(	PUNCT
ejpam-5049	272	23	m∑	m∑	ADV
ejpam-5049	272	24	j=0	j=0	PROPN
ejpam-5049	272	25	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	272	26	)	)	PUNCT
ejpam-5049	272	27	)	)	PUNCT
ejpam-5049	272	28	2	2	X
ejpam-5049	273	1	+	+	CCONJ
ejpam-5049	273	2	β0	β0	ADJ
ejpam-5049	273	3	(	(	PUNCT
ejpam-5049	273	4	m∑	m∑	ADV
ejpam-5049	273	5	j=0	j=0	PROPN
ejpam-5049	273	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	273	7	)	)	PUNCT
ejpam-5049	273	8	)	)	PUNCT
ejpam-5049	273	9	2	2	NUM
ejpam-5049	274	1	+	+	CCONJ
ejpam-5049	274	2	khaled	khaled	ADJ
ejpam-5049	274	3	m.	m.	NOUN
ejpam-5049	274	4	saad	saad	PROPN
ejpam-5049	274	5	,	,	PUNCT
ejpam-5049	274	6	m.	m.	NOUN
ejpam-5049	274	7	q.	q.	PROPN
ejpam-5049	274	8	khirallah	khirallah	PROPN
ejpam-5049	274	9	/	/	SYM
ejpam-5049	274	10	eur	eur	PROPN
ejpam-5049	274	11	.	.	PUNCT
ejpam-5049	275	1	j.	j.	PROPN
ejpam-5049	275	2	pure	pure	PROPN
ejpam-5049	275	3	appl	appl	PROPN
ejpam-5049	275	4	.	.	PROPN
ejpam-5049	275	5	math	math	PROPN
ejpam-5049	275	6	,	,	PUNCT
ejpam-5049	275	7	17	17	NUM
ejpam-5049	275	8	(	(	PUNCT
ejpam-5049	275	9	1	1	NUM
ejpam-5049	275	10	)	)	PUNCT
ejpam-5049	275	11	(	(	PUNCT
ejpam-5049	275	12	2024	2024	NUM
ejpam-5049	275	13	)	)	PUNCT
ejpam-5049	275	14	,	,	PUNCT
ejpam-5049	275	15	477	477	NUM
ejpam-5049	275	16	-	-	SYM
ejpam-5049	275	17	503	503	NUM
ejpam-5049	275	18	490	490	NUM
ejpam-5049	275	19	2	2	NUM
ejpam-5049	275	20	l−1∑	l−1∑	NOUN
ejpam-5049	275	21	k=1	k=1	X
ejpam-5049	275	22	βk	βk	PROPN
ejpam-5049	275	23	(	(	PUNCT
ejpam-5049	275	24	m∑	m∑	CCONJ
ejpam-5049	275	25	j=0	j=0	PROPN
ejpam-5049	275	26	cjφj(βk	cjφj(βk	NOUN
ejpam-5049	275	27	)	)	PUNCT
ejpam-5049	275	28	)	)	PUNCT
ejpam-5049	275	29	2	2	NUM
ejpam-5049	276	1	+	+	SYM
ejpam-5049	276	2	2	2	NUM
ejpam-5049	276	3	l−1∑	l−1∑	NOUN
ejpam-5049	276	4	k=1	k=1	X
ejpam-5049	276	5	βk	βk	PROPN
ejpam-5049	276	6	(	(	PUNCT
ejpam-5049	276	7	m∑	m∑	CCONJ
ejpam-5049	276	8	j=0	j=0	PROPN
ejpam-5049	276	9	djφj(βk	djφj(βk	ADJ
ejpam-5049	276	10	)	)	PUNCT
ejpam-5049	276	11	)	)	PUNCT
ejpam-5049	276	12	2	2	NUM
ejpam-5049	277	1	+	+	NUM
ejpam-5049	277	2	βl	βl	NOUN
ejpam-5049	277	3	(	(	PUNCT
ejpam-5049	277	4	m∑	m∑	CCONJ
ejpam-5049	277	5	j=0	j=0	PROPN
ejpam-5049	277	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	277	7	)	)	PUNCT
ejpam-5049	277	8	)	)	PUNCT
ejpam-5049	277	9	2	2	X
ejpam-5049	278	1	+	+	NUM
ejpam-5049	278	2	βl	βl	NOUN
ejpam-5049	278	3	(	(	PUNCT
ejpam-5049	278	4	m∑	m∑	CCONJ
ejpam-5049	278	5	j=0	j=0	PROPN
ejpam-5049	278	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	278	7	)	)	PUNCT
ejpam-5049	278	8	)	)	PUNCT
ejpam-5049	278	9	2	2	NUM
ejpam-5049	278	10	)	)	PUNCT
ejpam-5049	278	11	,	,	PUNCT
ejpam-5049	278	12	(	(	PUNCT
ejpam-5049	278	13	44	44	NUM
ejpam-5049	278	14	)	)	PUNCT
ejpam-5049	278	15	and	and	CCONJ
ejpam-5049	278	16	m∑	m∑	CCONJ
ejpam-5049	278	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	278	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	278	19	k=0	k=0	PROPN
ejpam-5049	278	20	djχ	djχ	PROPN
ejpam-5049	278	21	(	(	PUNCT
ejpam-5049	278	22	α	α	NOUN
ejpam-5049	278	23	)	)	PUNCT
ejpam-5049	278	24	j	j	PROPN
ejpam-5049	278	25	,	,	PUNCT
ejpam-5049	278	26	k	k	PROPN
ejpam-5049	278	27	β	β	X
ejpam-5049	278	28	j−k−α	j−k−α	NOUN
ejpam-5049	278	29	s	s	PART
ejpam-5049	278	30	=	=	PUNCT
ejpam-5049	278	31	φ1(β	φ1(β	PROPN
ejpam-5049	278	32	)	)	PUNCT
ejpam-5049	278	33	+	+	NUM
ejpam-5049	278	34	h	h	NOUN
ejpam-5049	278	35	2	2	NUM
ejpam-5049	278	36	(	(	PUNCT
ejpam-5049	278	37	β0	β0	PROPN
ejpam-5049	278	38	(	(	PUNCT
ejpam-5049	278	39	m∑	m∑	ADV
ejpam-5049	278	40	j=0	j=0	PROPN
ejpam-5049	278	41	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	278	42	)	)	PUNCT
ejpam-5049	278	43	)	)	PUNCT
ejpam-5049	278	44	2	2	NUM
ejpam-5049	278	45	−	−	NOUN
ejpam-5049	278	46	β0	β0	NOUN
ejpam-5049	278	47	(	(	PUNCT
ejpam-5049	278	48	m∑	m∑	ADV
ejpam-5049	278	49	j=0	j=0	PROPN
ejpam-5049	278	50	djφj(β0	djφj(β0	PROPN
ejpam-5049	278	51	)	)	PUNCT
ejpam-5049	278	52	)	)	PUNCT
ejpam-5049	278	53	2	2	NUM
ejpam-5049	279	1	+	+	SYM
ejpam-5049	279	2	2	2	NUM
ejpam-5049	279	3	l−1∑	l−1∑	NOUN
ejpam-5049	279	4	k=1	k=1	X
ejpam-5049	279	5	βk	βk	PROPN
ejpam-5049	279	6	(	(	PUNCT
ejpam-5049	279	7	m∑	m∑	CCONJ
ejpam-5049	279	8	j=0	j=0	PROPN
ejpam-5049	279	9	cjφj(βk	cjφj(βk	NOUN
ejpam-5049	279	10	)	)	PUNCT
ejpam-5049	279	11	)	)	PUNCT
ejpam-5049	280	1	2	2	NUM
ejpam-5049	280	2	−	−	NOUN
ejpam-5049	280	3	2	2	NUM
ejpam-5049	280	4	l−1∑	l−1∑	NOUN
ejpam-5049	280	5	k=1	k=1	X
ejpam-5049	280	6	βk	βk	PROPN
ejpam-5049	280	7	(	(	PUNCT
ejpam-5049	280	8	m∑	m∑	CCONJ
ejpam-5049	280	9	j=0	j=0	PROPN
ejpam-5049	280	10	djφj(βk	djφj(βk	ADJ
ejpam-5049	280	11	)	)	PUNCT
ejpam-5049	280	12	)	)	PUNCT
ejpam-5049	280	13	2	2	NUM
ejpam-5049	281	1	+	+	NUM
ejpam-5049	281	2	βl	βl	NOUN
ejpam-5049	281	3	(	(	PUNCT
ejpam-5049	281	4	m∑	m∑	CCONJ
ejpam-5049	281	5	j=0	j=0	PROPN
ejpam-5049	281	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	281	7	)	)	PUNCT
ejpam-5049	281	8	)	)	PUNCT
ejpam-5049	281	9	2	2	NUM
ejpam-5049	281	10	−	−	NOUN
ejpam-5049	281	11	βl	βl	NOUN
ejpam-5049	281	12	(	(	PUNCT
ejpam-5049	281	13	m∑	m∑	CCONJ
ejpam-5049	281	14	j=0	j=0	PROPN
ejpam-5049	281	15	djφj(βl	djφj(βl	PROPN
ejpam-5049	281	16	)	)	PUNCT
ejpam-5049	281	17	)	)	PUNCT
ejpam-5049	281	18	2	2	NUM
ejpam-5049	281	19	)	)	PUNCT
ejpam-5049	281	20	.	.	PUNCT
ejpam-5049	282	1	(	(	PUNCT
ejpam-5049	282	2	45	45	NUM
ejpam-5049	282	3	)	)	PUNCT
ejpam-5049	282	4	(	(	PUNCT
ejpam-5049	282	5	ii	ii	NOUN
ejpam-5049	282	6	)	)	PUNCT
ejpam-5049	282	7	simpson	simpson	PROPN
ejpam-5049	282	8	’s	’s	PART
ejpam-5049	282	9	1/3	1/3	NUM
ejpam-5049	282	10	method	method	NOUN
ejpam-5049	282	11	using	use	VERB
ejpam-5049	282	12	(	(	PUNCT
ejpam-5049	282	13	16	16	NUM
ejpam-5049	282	14	)	)	PUNCT
ejpam-5049	282	15	,	,	PUNCT
ejpam-5049	282	16	we	we	PRON
ejpam-5049	282	17	obtain	obtain	VERB
ejpam-5049	282	18	m∑	m∑	PRON
ejpam-5049	282	19	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	282	20	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	282	21	k=0	k=0	PROPN
ejpam-5049	282	22	cjχ	cjχ	PROPN
ejpam-5049	282	23	(	(	PUNCT
ejpam-5049	282	24	α	α	NOUN
ejpam-5049	282	25	)	)	PUNCT
ejpam-5049	282	26	j	j	PROPN
ejpam-5049	282	27	,	,	PUNCT
ejpam-5049	282	28	k	k	PROPN
ejpam-5049	282	29	β	β	X
ejpam-5049	282	30	j−k−α	j−k−α	NOUN
ejpam-5049	282	31	=	=	PUNCT
ejpam-5049	282	32	φ1(β	φ1(β	PROPN
ejpam-5049	282	33	)	)	PUNCT
ejpam-5049	283	1	+	+	NUM
ejpam-5049	283	2	h	h	NOUN
ejpam-5049	283	3	3	3	NUM
ejpam-5049	283	4	(	(	PUNCT
ejpam-5049	283	5	β0	β0	PROPN
ejpam-5049	283	6	(	(	PUNCT
ejpam-5049	283	7	m∑	m∑	ADV
ejpam-5049	283	8	j=0	j=0	PROPN
ejpam-5049	283	9	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	283	10	)	)	PUNCT
ejpam-5049	283	11	)	)	PUNCT
ejpam-5049	283	12	2	2	X
ejpam-5049	284	1	+	+	CCONJ
ejpam-5049	284	2	β0	β0	ADJ
ejpam-5049	284	3	(	(	PUNCT
ejpam-5049	284	4	m∑	m∑	ADV
ejpam-5049	284	5	j=0	j=0	PROPN
ejpam-5049	284	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	284	7	)	)	PUNCT
ejpam-5049	284	8	)	)	PUNCT
ejpam-5049	285	1	2	2	NUM
ejpam-5049	285	2	+	+	SYM
ejpam-5049	285	3	2	2	NUM
ejpam-5049	285	4	l	l	NOUN
ejpam-5049	285	5	2	2	NUM
ejpam-5049	285	6	−1∑	−1∑	PROPN
ejpam-5049	285	7	k=1	k=1	X
ejpam-5049	285	8	β2k	β2k	PUNCT
ejpam-5049	285	9	(	(	PUNCT
ejpam-5049	285	10	m∑	m∑	CCONJ
ejpam-5049	285	11	j=0	j=0	PROPN
ejpam-5049	285	12	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	285	13	)	)	PUNCT
ejpam-5049	285	14	)	)	PUNCT
ejpam-5049	285	15	2	2	NUM
ejpam-5049	286	1	+	+	SYM
ejpam-5049	286	2	2	2	NUM
ejpam-5049	286	3	l	l	NOUN
ejpam-5049	286	4	2	2	NUM
ejpam-5049	286	5	−1∑	−1∑	PROPN
ejpam-5049	286	6	k=1	k=1	X
ejpam-5049	286	7	β2k	β2k	PUNCT
ejpam-5049	286	8	(	(	PUNCT
ejpam-5049	286	9	m∑	m∑	CCONJ
ejpam-5049	286	10	j=0	j=0	ADJ
ejpam-5049	286	11	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	286	12	)	)	PUNCT
ejpam-5049	286	13	)	)	PUNCT
ejpam-5049	287	1	2	2	NUM
ejpam-5049	287	2	4	4	NUM
ejpam-5049	287	3	l	l	NOUN
ejpam-5049	287	4	2∑	2∑	X
ejpam-5049	288	1	k=1	k=1	PUNCT
ejpam-5049	288	2	β2k−1	β2k−1	PROPN
ejpam-5049	288	3	(	(	PUNCT
ejpam-5049	288	4	m∑	m∑	CCONJ
ejpam-5049	288	5	j=0	j=0	PROPN
ejpam-5049	288	6	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	288	7	)	)	PUNCT
ejpam-5049	288	8	)	)	PUNCT
ejpam-5049	288	9	2	2	NUM
ejpam-5049	289	1	+	+	CCONJ
ejpam-5049	289	2	4	4	NUM
ejpam-5049	289	3	l	l	NOUN
ejpam-5049	289	4	2∑	2∑	X
ejpam-5049	289	5	k=1	k=1	PUNCT
ejpam-5049	289	6	β2k	β2k	PUNCT
ejpam-5049	289	7	(	(	PUNCT
ejpam-5049	289	8	m∑	m∑	INTJ
ejpam-5049	289	9	i=0	i=0	PROPN
ejpam-5049	289	10	diφj(j	diφj(j	PROPN
ejpam-5049	289	11	,	,	PUNCT
ejpam-5049	289	12	β2k	β2k	PUNCT
ejpam-5049	289	13	)	)	PUNCT
ejpam-5049	289	14	)	)	PUNCT
ejpam-5049	290	1	2	2	X
ejpam-5049	291	1	+	+	NUM
ejpam-5049	291	2	βl	βl	NOUN
ejpam-5049	291	3	(	(	PUNCT
ejpam-5049	291	4	m∑	m∑	CCONJ
ejpam-5049	291	5	j=0	j=0	PROPN
ejpam-5049	291	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	291	7	)	)	PUNCT
ejpam-5049	291	8	)	)	PUNCT
ejpam-5049	291	9	2	2	X
ejpam-5049	292	1	+	+	NUM
ejpam-5049	292	2	βl	βl	NOUN
ejpam-5049	292	3	(	(	PUNCT
ejpam-5049	292	4	m∑	m∑	CCONJ
ejpam-5049	292	5	j=0	j=0	PROPN
ejpam-5049	292	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	292	7	)	)	PUNCT
ejpam-5049	292	8	)	)	PUNCT
ejpam-5049	292	9	2	2	NUM
ejpam-5049	292	10	)	)	PUNCT
ejpam-5049	292	11	,	,	PUNCT
ejpam-5049	292	12	(	(	PUNCT
ejpam-5049	292	13	46	46	NUM
ejpam-5049	292	14	)	)	PUNCT
ejpam-5049	292	15	and	and	CCONJ
ejpam-5049	292	16	m∑	m∑	CCONJ
ejpam-5049	292	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	292	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	292	19	k=0	k=0	PROPN
ejpam-5049	292	20	djχ	djχ	PROPN
ejpam-5049	292	21	(	(	PUNCT
ejpam-5049	292	22	α	α	NOUN
ejpam-5049	292	23	)	)	PUNCT
ejpam-5049	292	24	j	j	PROPN
ejpam-5049	292	25	,	,	PUNCT
ejpam-5049	292	26	k	k	PROPN
ejpam-5049	292	27	β	β	X
ejpam-5049	292	28	j−k−α	j−k−α	NOUN
ejpam-5049	292	29	=	=	PUNCT
ejpam-5049	292	30	φ2(β	φ2(β	PROPN
ejpam-5049	292	31	)	)	PUNCT
ejpam-5049	293	1	+	+	CCONJ
ejpam-5049	293	2	h	h	NOUN
ejpam-5049	293	3	3	3	NUM
ejpam-5049	294	1	(	(	PUNCT
ejpam-5049	294	2	β0	β0	PROPN
ejpam-5049	294	3	(	(	PUNCT
ejpam-5049	294	4	m∑	m∑	ADV
ejpam-5049	294	5	j=0	j=0	PROPN
ejpam-5049	294	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	294	7	)	)	PUNCT
ejpam-5049	294	8	)	)	PUNCT
ejpam-5049	295	1	2	2	NUM
ejpam-5049	295	2	−	−	NOUN
ejpam-5049	295	3	β0	β0	NOUN
ejpam-5049	295	4	(	(	PUNCT
ejpam-5049	295	5	m∑	m∑	ADV
ejpam-5049	295	6	j=0	j=0	PROPN
ejpam-5049	295	7	djφj(β0	djφj(β0	PROPN
ejpam-5049	295	8	)	)	PUNCT
ejpam-5049	295	9	)	)	PUNCT
ejpam-5049	295	10	2	2	NUM
ejpam-5049	296	1	+	+	SYM
ejpam-5049	296	2	2	2	NUM
ejpam-5049	296	3	l	l	NOUN
ejpam-5049	296	4	2	2	NUM
ejpam-5049	296	5	−1∑	−1∑	PROPN
ejpam-5049	296	6	k=1	k=1	X
ejpam-5049	296	7	β2k	β2k	PUNCT
ejpam-5049	296	8	(	(	PUNCT
ejpam-5049	296	9	m∑	m∑	CCONJ
ejpam-5049	296	10	j=0	j=0	PROPN
ejpam-5049	296	11	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	296	12	)	)	PUNCT
ejpam-5049	296	13	)	)	PUNCT
ejpam-5049	297	1	2	2	NUM
ejpam-5049	297	2	−	−	NUM
ejpam-5049	297	3	2	2	NUM
ejpam-5049	297	4	l	l	NOUN
ejpam-5049	297	5	2	2	NUM
ejpam-5049	297	6	−1∑	−1∑	PROPN
ejpam-5049	297	7	k=1	k=1	X
ejpam-5049	297	8	β2k	β2k	PUNCT
ejpam-5049	297	9	(	(	PUNCT
ejpam-5049	297	10	m∑	m∑	CCONJ
ejpam-5049	297	11	j=0	j=0	ADJ
ejpam-5049	297	12	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	297	13	)	)	PUNCT
ejpam-5049	297	14	)	)	PUNCT
ejpam-5049	297	15	2	2	NUM
ejpam-5049	297	16	khaled	khale	VERB
ejpam-5049	297	17	m.	m.	NOUN
ejpam-5049	297	18	saad	saad	PROPN
ejpam-5049	297	19	,	,	PUNCT
ejpam-5049	297	20	m.	m.	NOUN
ejpam-5049	297	21	q.	q.	PROPN
ejpam-5049	297	22	khirallah	khirallah	PROPN
ejpam-5049	297	23	/	/	SYM
ejpam-5049	297	24	eur	eur	PROPN
ejpam-5049	297	25	.	.	PUNCT
ejpam-5049	298	1	j.	j.	PROPN
ejpam-5049	298	2	pure	pure	PROPN
ejpam-5049	298	3	appl	appl	PROPN
ejpam-5049	298	4	.	.	PROPN
ejpam-5049	298	5	math	math	PROPN
ejpam-5049	298	6	,	,	PUNCT
ejpam-5049	298	7	17	17	NUM
ejpam-5049	298	8	(	(	PUNCT
ejpam-5049	298	9	1	1	NUM
ejpam-5049	298	10	)	)	PUNCT
ejpam-5049	298	11	(	(	PUNCT
ejpam-5049	298	12	2024	2024	NUM
ejpam-5049	298	13	)	)	PUNCT
ejpam-5049	298	14	,	,	PUNCT
ejpam-5049	298	15	477	477	NUM
ejpam-5049	298	16	-	-	SYM
ejpam-5049	298	17	503	503	NUM
ejpam-5049	298	18	491	491	NUM
ejpam-5049	298	19	4	4	NUM
ejpam-5049	298	20	l	l	NOUN
ejpam-5049	298	21	2∑	2∑	X
ejpam-5049	299	1	k=1	k=1	PUNCT
ejpam-5049	299	2	β2k−1	β2k−1	PROPN
ejpam-5049	299	3	(	(	PUNCT
ejpam-5049	299	4	m∑	m∑	CCONJ
ejpam-5049	299	5	j=0	j=0	PROPN
ejpam-5049	299	6	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	299	7	)	)	PUNCT
ejpam-5049	299	8	)	)	PUNCT
ejpam-5049	299	9	2	2	NUM
ejpam-5049	299	10	−	−	NOUN
ejpam-5049	299	11	4	4	NUM
ejpam-5049	299	12	l	l	NOUN
ejpam-5049	299	13	2∑	2∑	X
ejpam-5049	299	14	k=1	k=1	PUNCT
ejpam-5049	299	15	β2k	β2k	PUNCT
ejpam-5049	299	16	(	(	PUNCT
ejpam-5049	299	17	m∑	m∑	CCONJ
ejpam-5049	299	18	j=0	j=0	ADJ
ejpam-5049	299	19	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	299	20	)	)	PUNCT
ejpam-5049	299	21	)	)	PUNCT
ejpam-5049	299	22	2	2	X
ejpam-5049	300	1	+	+	NUM
ejpam-5049	300	2	βl	βl	NOUN
ejpam-5049	300	3	(	(	PUNCT
ejpam-5049	300	4	m∑	m∑	CCONJ
ejpam-5049	300	5	j=0	j=0	PROPN
ejpam-5049	300	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	300	7	)	)	PUNCT
ejpam-5049	300	8	)	)	PUNCT
ejpam-5049	300	9	2	2	NUM
ejpam-5049	300	10	−	−	NOUN
ejpam-5049	300	11	βl	βl	NOUN
ejpam-5049	300	12	(	(	PUNCT
ejpam-5049	300	13	m∑	m∑	CCONJ
ejpam-5049	300	14	j=0	j=0	PROPN
ejpam-5049	300	15	djφj(βl	djφj(βl	PROPN
ejpam-5049	300	16	)	)	PUNCT
ejpam-5049	300	17	)	)	PUNCT
ejpam-5049	300	18	2	2	NUM
ejpam-5049	300	19	)	)	PUNCT
ejpam-5049	300	20	.	.	PUNCT
ejpam-5049	301	1	(	(	PUNCT
ejpam-5049	301	2	47	47	NUM
ejpam-5049	301	3	)	)	PUNCT
ejpam-5049	301	4	now	now	ADV
ejpam-5049	301	5	,	,	PUNCT
ejpam-5049	301	6	using	use	VERB
ejpam-5049	301	7	(	(	PUNCT
ejpam-5049	301	8	17	17	NUM
ejpam-5049	301	9	)	)	PUNCT
ejpam-5049	301	10	,	,	PUNCT
ejpam-5049	301	11	we	we	PRON
ejpam-5049	301	12	obtain	obtain	VERB
ejpam-5049	301	13	m∑	m∑	PRON
ejpam-5049	301	14	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	301	15	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	301	16	k=0	k=0	PROPN
ejpam-5049	301	17	cjχ	cjχ	PROPN
ejpam-5049	301	18	(	(	PUNCT
ejpam-5049	301	19	α	α	NOUN
ejpam-5049	301	20	)	)	PUNCT
ejpam-5049	301	21	j	j	PROPN
ejpam-5049	301	22	,	,	PUNCT
ejpam-5049	301	23	k	k	PROPN
ejpam-5049	301	24	β	β	X
ejpam-5049	301	25	j−k−α	j−k−α	NOUN
ejpam-5049	301	26	s	s	PART
ejpam-5049	301	27	=	=	PUNCT
ejpam-5049	301	28	φ1(βs	φ1(βs	PROPN
ejpam-5049	301	29	)	)	PUNCT
ejpam-5049	301	30	+	+	NUM
ejpam-5049	301	31	h	h	NOUN
ejpam-5049	301	32	3	3	NUM
ejpam-5049	302	1	(	(	PUNCT
ejpam-5049	302	2	β0	β0	PROPN
ejpam-5049	302	3	(	(	PUNCT
ejpam-5049	302	4	m∑	m∑	ADV
ejpam-5049	302	5	j=0	j=0	PROPN
ejpam-5049	302	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	302	7	)	)	PUNCT
ejpam-5049	302	8	)	)	PUNCT
ejpam-5049	302	9	2	2	X
ejpam-5049	303	1	+	+	CCONJ
ejpam-5049	303	2	β0	β0	ADJ
ejpam-5049	303	3	(	(	PUNCT
ejpam-5049	303	4	m∑	m∑	ADV
ejpam-5049	303	5	j=0	j=0	PROPN
ejpam-5049	303	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	303	7	)	)	PUNCT
ejpam-5049	303	8	)	)	PUNCT
ejpam-5049	304	1	2	2	NUM
ejpam-5049	304	2	+	+	SYM
ejpam-5049	304	3	2	2	NUM
ejpam-5049	304	4	l	l	NOUN
ejpam-5049	304	5	2	2	NUM
ejpam-5049	304	6	−1∑	−1∑	PROPN
ejpam-5049	304	7	k=1	k=1	X
ejpam-5049	304	8	β2k	β2k	PUNCT
ejpam-5049	304	9	(	(	PUNCT
ejpam-5049	304	10	m∑	m∑	CCONJ
ejpam-5049	304	11	j=0	j=0	PROPN
ejpam-5049	304	12	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	304	13	)	)	PUNCT
ejpam-5049	304	14	)	)	PUNCT
ejpam-5049	304	15	2	2	NUM
ejpam-5049	305	1	+	+	SYM
ejpam-5049	305	2	2	2	NUM
ejpam-5049	305	3	l	l	NOUN
ejpam-5049	305	4	2	2	NUM
ejpam-5049	305	5	−1∑	−1∑	PROPN
ejpam-5049	305	6	k=1	k=1	X
ejpam-5049	305	7	β2k	β2k	PUNCT
ejpam-5049	305	8	(	(	PUNCT
ejpam-5049	305	9	m∑	m∑	CCONJ
ejpam-5049	305	10	j=0	j=0	ADJ
ejpam-5049	305	11	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	305	12	)	)	PUNCT
ejpam-5049	305	13	)	)	PUNCT
ejpam-5049	306	1	2	2	NUM
ejpam-5049	306	2	4	4	NUM
ejpam-5049	306	3	l	l	NOUN
ejpam-5049	306	4	2∑	2∑	X
ejpam-5049	307	1	k=1	k=1	PUNCT
ejpam-5049	307	2	β2k−1	β2k−1	PROPN
ejpam-5049	307	3	(	(	PUNCT
ejpam-5049	307	4	m∑	m∑	CCONJ
ejpam-5049	307	5	j=0	j=0	PROPN
ejpam-5049	307	6	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	307	7	)	)	PUNCT
ejpam-5049	307	8	)	)	PUNCT
ejpam-5049	307	9	2	2	NUM
ejpam-5049	308	1	+	+	CCONJ
ejpam-5049	308	2	4	4	NUM
ejpam-5049	308	3	l	l	NOUN
ejpam-5049	308	4	2∑	2∑	X
ejpam-5049	308	5	k=1	k=1	PUNCT
ejpam-5049	308	6	β2k	β2k	PUNCT
ejpam-5049	308	7	(	(	PUNCT
ejpam-5049	308	8	m∑	m∑	CCONJ
ejpam-5049	308	9	j=0	j=0	ADJ
ejpam-5049	308	10	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	308	11	)	)	PUNCT
ejpam-5049	308	12	)	)	PUNCT
ejpam-5049	309	1	2	2	X
ejpam-5049	310	1	+	+	NUM
ejpam-5049	310	2	βl	βl	NOUN
ejpam-5049	310	3	(	(	PUNCT
ejpam-5049	310	4	m∑	m∑	CCONJ
ejpam-5049	310	5	j=0	j=0	PROPN
ejpam-5049	310	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	310	7	)	)	PUNCT
ejpam-5049	310	8	)	)	PUNCT
ejpam-5049	310	9	2	2	X
ejpam-5049	311	1	+	+	NUM
ejpam-5049	311	2	βl	βl	NOUN
ejpam-5049	311	3	(	(	PUNCT
ejpam-5049	311	4	m∑	m∑	CCONJ
ejpam-5049	311	5	j=0	j=0	PROPN
ejpam-5049	311	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	311	7	)	)	PUNCT
ejpam-5049	311	8	)	)	PUNCT
ejpam-5049	311	9	2	2	NUM
ejpam-5049	311	10	)	)	PUNCT
ejpam-5049	311	11	,	,	PUNCT
ejpam-5049	311	12	(	(	PUNCT
ejpam-5049	311	13	48	48	NUM
ejpam-5049	311	14	)	)	PUNCT
ejpam-5049	311	15	and	and	CCONJ
ejpam-5049	311	16	m∑	m∑	CCONJ
ejpam-5049	311	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	311	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	311	19	k=0	k=0	PROPN
ejpam-5049	311	20	djχ	djχ	PROPN
ejpam-5049	311	21	(	(	PUNCT
ejpam-5049	311	22	α	α	NOUN
ejpam-5049	311	23	)	)	PUNCT
ejpam-5049	311	24	j	j	PROPN
ejpam-5049	311	25	,	,	PUNCT
ejpam-5049	311	26	k	k	PROPN
ejpam-5049	311	27	β	β	X
ejpam-5049	311	28	j−k−α	j−k−α	NOUN
ejpam-5049	311	29	s	s	PART
ejpam-5049	311	30	=	=	SYM
ejpam-5049	311	31	φ2(βs	φ2(βs	PROPN
ejpam-5049	311	32	)	)	PUNCT
ejpam-5049	312	1	+	+	CCONJ
ejpam-5049	312	2	h	h	NOUN
ejpam-5049	312	3	3	3	NUM
ejpam-5049	313	1	(	(	PUNCT
ejpam-5049	313	2	β0	β0	PROPN
ejpam-5049	313	3	(	(	PUNCT
ejpam-5049	313	4	m∑	m∑	ADV
ejpam-5049	313	5	j=0	j=0	PROPN
ejpam-5049	313	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	313	7	)	)	PUNCT
ejpam-5049	313	8	)	)	PUNCT
ejpam-5049	314	1	2	2	NUM
ejpam-5049	314	2	−	−	NOUN
ejpam-5049	314	3	β0	β0	NOUN
ejpam-5049	314	4	(	(	PUNCT
ejpam-5049	314	5	m∑	m∑	ADV
ejpam-5049	314	6	j=0	j=0	PROPN
ejpam-5049	314	7	djφj(jβ0	djφj(jβ0	PROPN
ejpam-5049	314	8	)	)	PUNCT
ejpam-5049	314	9	)	)	PUNCT
ejpam-5049	314	10	2	2	NUM
ejpam-5049	315	1	+	+	SYM
ejpam-5049	315	2	2	2	NUM
ejpam-5049	315	3	l	l	NOUN
ejpam-5049	315	4	2	2	NUM
ejpam-5049	315	5	−1∑	−1∑	PROPN
ejpam-5049	315	6	k=1	k=1	X
ejpam-5049	315	7	β2k	β2k	PUNCT
ejpam-5049	315	8	(	(	PUNCT
ejpam-5049	315	9	m∑	m∑	CCONJ
ejpam-5049	315	10	j=0	j=0	PROPN
ejpam-5049	315	11	cjφj(β2k	cjφj(β2k	NOUN
ejpam-5049	315	12	)	)	PUNCT
ejpam-5049	315	13	)	)	PUNCT
ejpam-5049	316	1	2	2	NUM
ejpam-5049	316	2	−	−	NUM
ejpam-5049	316	3	2	2	NUM
ejpam-5049	316	4	l	l	NOUN
ejpam-5049	316	5	2	2	NUM
ejpam-5049	316	6	−1∑	−1∑	PROPN
ejpam-5049	316	7	k=1	k=1	X
ejpam-5049	316	8	β2k	β2k	PUNCT
ejpam-5049	316	9	(	(	PUNCT
ejpam-5049	316	10	m∑	m∑	CCONJ
ejpam-5049	316	11	j=0	j=0	ADJ
ejpam-5049	316	12	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	316	13	)	)	PUNCT
ejpam-5049	316	14	)	)	PUNCT
ejpam-5049	316	15	2	2	NUM
ejpam-5049	316	16	4	4	NUM
ejpam-5049	316	17	l	l	NOUN
ejpam-5049	316	18	2∑	2∑	X
ejpam-5049	316	19	k=1	k=1	PUNCT
ejpam-5049	316	20	β2k−1	β2k−1	PROPN
ejpam-5049	316	21	(	(	PUNCT
ejpam-5049	316	22	m∑	m∑	CCONJ
ejpam-5049	316	23	j=0	j=0	PROPN
ejpam-5049	316	24	cjφj(β2k−1	cjφj(β2k−1	PROPN
ejpam-5049	316	25	)	)	PUNCT
ejpam-5049	316	26	)	)	PUNCT
ejpam-5049	316	27	2	2	NUM
ejpam-5049	316	28	−	−	NOUN
ejpam-5049	316	29	4	4	NUM
ejpam-5049	316	30	l	l	NOUN
ejpam-5049	316	31	2∑	2∑	X
ejpam-5049	316	32	k=1	k=1	PUNCT
ejpam-5049	316	33	β2k	β2k	PUNCT
ejpam-5049	316	34	(	(	PUNCT
ejpam-5049	316	35	m∑	m∑	CCONJ
ejpam-5049	316	36	j=0	j=0	ADJ
ejpam-5049	316	37	djφj(β2k	djφj(β2k	PROPN
ejpam-5049	316	38	)	)	PUNCT
ejpam-5049	316	39	)	)	PUNCT
ejpam-5049	316	40	2	2	X
ejpam-5049	317	1	+	+	NUM
ejpam-5049	317	2	βl	βl	NOUN
ejpam-5049	317	3	(	(	PUNCT
ejpam-5049	317	4	m∑	m∑	CCONJ
ejpam-5049	317	5	j=0	j=0	PROPN
ejpam-5049	317	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	317	7	)	)	PUNCT
ejpam-5049	317	8	)	)	PUNCT
ejpam-5049	317	9	2	2	NUM
ejpam-5049	317	10	−	−	NOUN
ejpam-5049	317	11	βl	βl	NOUN
ejpam-5049	317	12	(	(	PUNCT
ejpam-5049	317	13	m∑	m∑	CCONJ
ejpam-5049	317	14	j=0	j=0	PROPN
ejpam-5049	317	15	djφj(βl	djφj(βl	PROPN
ejpam-5049	317	16	)	)	PUNCT
ejpam-5049	317	17	)	)	PUNCT
ejpam-5049	317	18	2	2	NUM
ejpam-5049	317	19	)	)	PUNCT
ejpam-5049	317	20	.	.	PUNCT
ejpam-5049	318	1	(	(	PUNCT
ejpam-5049	318	2	49	49	NUM
ejpam-5049	318	3	)	)	PUNCT
ejpam-5049	318	4	(	(	PUNCT
ejpam-5049	318	5	iii	iii	X
ejpam-5049	318	6	)	)	PUNCT
ejpam-5049	318	7	simpson	simpson	PROPN
ejpam-5049	318	8	’s	’s	PART
ejpam-5049	318	9	3/8	3/8	NUM
ejpam-5049	318	10	method	method	NOUN
ejpam-5049	318	11	using	use	VERB
ejpam-5049	318	12	(	(	PUNCT
ejpam-5049	318	13	18	18	NUM
ejpam-5049	318	14	)	)	PUNCT
ejpam-5049	318	15	,	,	PUNCT
ejpam-5049	318	16	we	we	PRON
ejpam-5049	318	17	obtain	obtain	VERB
ejpam-5049	318	18	m∑	m∑	PRON
ejpam-5049	318	19	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	318	20	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	318	21	k=0	k=0	PROPN
ejpam-5049	318	22	cjχ	cjχ	PROPN
ejpam-5049	318	23	(	(	PUNCT
ejpam-5049	318	24	α	α	NOUN
ejpam-5049	318	25	)	)	PUNCT
ejpam-5049	318	26	j	j	PROPN
ejpam-5049	318	27	,	,	PUNCT
ejpam-5049	318	28	k	k	PROPN
ejpam-5049	318	29	β	β	X
ejpam-5049	318	30	j−k−α	j−k−α	NOUN
ejpam-5049	318	31	=	=	PUNCT
ejpam-5049	318	32	φ1(β	φ1(β	PROPN
ejpam-5049	318	33	)	)	PUNCT
ejpam-5049	318	34	+	+	NUM
ejpam-5049	318	35	3h	3h	NUM
ejpam-5049	318	36	8	8	NUM
ejpam-5049	319	1	(	(	PUNCT
ejpam-5049	319	2	β0	β0	NOUN
ejpam-5049	319	3	(	(	PUNCT
ejpam-5049	319	4	m∑	m∑	ADV
ejpam-5049	319	5	j=0	j=0	PROPN
ejpam-5049	319	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	319	7	)	)	PUNCT
ejpam-5049	319	8	)	)	PUNCT
ejpam-5049	319	9	2	2	X
ejpam-5049	320	1	+	+	CCONJ
ejpam-5049	320	2	β0	β0	ADJ
ejpam-5049	320	3	(	(	PUNCT
ejpam-5049	320	4	m∑	m∑	ADV
ejpam-5049	320	5	j=0	j=0	PROPN
ejpam-5049	320	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	320	7	)	)	PUNCT
ejpam-5049	320	8	)	)	PUNCT
ejpam-5049	320	9	2	2	NUM
ejpam-5049	320	10	khaled	khale	VERB
ejpam-5049	320	11	m.	m.	NOUN
ejpam-5049	320	12	saad	saad	PROPN
ejpam-5049	320	13	,	,	PUNCT
ejpam-5049	320	14	m.	m.	NOUN
ejpam-5049	320	15	q.	q.	PROPN
ejpam-5049	320	16	khirallah	khirallah	PROPN
ejpam-5049	320	17	/	/	SYM
ejpam-5049	320	18	eur	eur	PROPN
ejpam-5049	320	19	.	.	PUNCT
ejpam-5049	321	1	j.	j.	PROPN
ejpam-5049	321	2	pure	pure	PROPN
ejpam-5049	321	3	appl	appl	PROPN
ejpam-5049	321	4	.	.	PROPN
ejpam-5049	321	5	math	math	PROPN
ejpam-5049	321	6	,	,	PUNCT
ejpam-5049	321	7	17	17	NUM
ejpam-5049	321	8	(	(	PUNCT
ejpam-5049	321	9	1	1	NUM
ejpam-5049	321	10	)	)	PUNCT
ejpam-5049	321	11	(	(	PUNCT
ejpam-5049	321	12	2024	2024	NUM
ejpam-5049	321	13	)	)	PUNCT
ejpam-5049	321	14	,	,	PUNCT
ejpam-5049	321	15	477	477	NUM
ejpam-5049	321	16	-	-	SYM
ejpam-5049	321	17	503	503	NUM
ejpam-5049	321	18	492	492	NUM
ejpam-5049	322	1	+	+	CCONJ
ejpam-5049	322	2	3	3	NUM
ejpam-5049	322	3	l	l	NOUN
ejpam-5049	322	4	3∑	3∑	NUM
ejpam-5049	322	5	k=1	k=1	X
ejpam-5049	323	1	β2k−2	β2k−2	PROPN
ejpam-5049	323	2	(	(	PUNCT
ejpam-5049	323	3	m∑	m∑	CCONJ
ejpam-5049	323	4	j=0	j=0	PROPN
ejpam-5049	323	5	cjφj(β2k−2	cjφj(β2k−2	PROPN
ejpam-5049	323	6	)	)	PUNCT
ejpam-5049	323	7	)	)	PUNCT
ejpam-5049	323	8	2	2	NUM
ejpam-5049	324	1	+	+	CCONJ
ejpam-5049	324	2	3	3	NUM
ejpam-5049	324	3	l	l	NOUN
ejpam-5049	324	4	3∑	3∑	NUM
ejpam-5049	324	5	k=1	k=1	X
ejpam-5049	325	1	β2k−2	β2k−2	PROPN
ejpam-5049	325	2	(	(	PUNCT
ejpam-5049	325	3	m∑	m∑	CCONJ
ejpam-5049	325	4	j=0	j=0	PROPN
ejpam-5049	325	5	djφj(β2k−2	djφj(β2k−2	PROPN
ejpam-5049	325	6	)	)	PUNCT
ejpam-5049	325	7	)	)	PUNCT
ejpam-5049	325	8	2	2	NUM
ejpam-5049	326	1	+	+	CCONJ
ejpam-5049	326	2	3	3	NUM
ejpam-5049	326	3	l	l	NOUN
ejpam-5049	326	4	3∑	3∑	NOUN
ejpam-5049	326	5	k=1	k=1	X
ejpam-5049	326	6	β3k−1	β3k−1	PROPN
ejpam-5049	326	7	(	(	PUNCT
ejpam-5049	326	8	m∑	m∑	CCONJ
ejpam-5049	326	9	j=0	j=0	PROPN
ejpam-5049	326	10	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	326	11	)	)	PUNCT
ejpam-5049	326	12	)	)	PUNCT
ejpam-5049	326	13	2	2	NUM
ejpam-5049	327	1	+	+	CCONJ
ejpam-5049	327	2	3	3	NUM
ejpam-5049	327	3	l	l	NOUN
ejpam-5049	327	4	3∑	3∑	NOUN
ejpam-5049	327	5	k=1	k=1	X
ejpam-5049	327	6	β3k−1	β3k−1	PROPN
ejpam-5049	327	7	(	(	PUNCT
ejpam-5049	327	8	m∑	m∑	CCONJ
ejpam-5049	327	9	j=0	j=0	PROPN
ejpam-5049	327	10	djφj(β3k−1	djφj(β3k−1	PROPN
ejpam-5049	327	11	)	)	PUNCT
ejpam-5049	327	12	)	)	PUNCT
ejpam-5049	327	13	2	2	NUM
ejpam-5049	327	14	2	2	NUM
ejpam-5049	327	15	l	l	NOUN
ejpam-5049	327	16	3	3	NUM
ejpam-5049	328	1	−1∑	−1∑	INTJ
ejpam-5049	328	2	k=1	k=1	X
ejpam-5049	328	3	β3k	β3k	X
ejpam-5049	328	4	(	(	PUNCT
ejpam-5049	328	5	m∑	m∑	CCONJ
ejpam-5049	328	6	j=0	j=0	PROPN
ejpam-5049	328	7	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	328	8	)	)	PUNCT
ejpam-5049	328	9	)	)	PUNCT
ejpam-5049	329	1	2	2	NUM
ejpam-5049	329	2	+	+	SYM
ejpam-5049	329	3	2	2	NUM
ejpam-5049	329	4	l	l	NOUN
ejpam-5049	329	5	2∑	2∑	X
ejpam-5049	330	1	k=1	k=1	PUNCT
ejpam-5049	330	2	β3k	β3k	X
ejpam-5049	330	3	(	(	PUNCT
ejpam-5049	330	4	m∑	m∑	CCONJ
ejpam-5049	330	5	j=0	j=0	PROPN
ejpam-5049	330	6	djφj(β3k	djφj(β3k	NOUN
ejpam-5049	330	7	)	)	PUNCT
ejpam-5049	330	8	)	)	PUNCT
ejpam-5049	330	9	2	2	X
ejpam-5049	331	1	+	+	NUM
ejpam-5049	331	2	βl	βl	NOUN
ejpam-5049	331	3	(	(	PUNCT
ejpam-5049	331	4	m∑	m∑	CCONJ
ejpam-5049	331	5	j=0	j=0	PROPN
ejpam-5049	331	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	331	7	)	)	PUNCT
ejpam-5049	331	8	)	)	PUNCT
ejpam-5049	331	9	2	2	X
ejpam-5049	332	1	+	+	NUM
ejpam-5049	332	2	βl	βl	NOUN
ejpam-5049	332	3	(	(	PUNCT
ejpam-5049	332	4	m∑	m∑	CCONJ
ejpam-5049	332	5	j=0	j=0	PROPN
ejpam-5049	332	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	332	7	)	)	PUNCT
ejpam-5049	332	8	)	)	PUNCT
ejpam-5049	332	9	2	2	NUM
ejpam-5049	332	10	)	)	PUNCT
ejpam-5049	332	11	,	,	PUNCT
ejpam-5049	332	12	(	(	PUNCT
ejpam-5049	332	13	50	50	NUM
ejpam-5049	332	14	)	)	PUNCT
ejpam-5049	332	15	and	and	CCONJ
ejpam-5049	332	16	m∑	m∑	CCONJ
ejpam-5049	332	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	332	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	332	19	k=0	k=0	PROPN
ejpam-5049	332	20	djχ	djχ	PROPN
ejpam-5049	332	21	(	(	PUNCT
ejpam-5049	332	22	α	α	NOUN
ejpam-5049	332	23	)	)	PUNCT
ejpam-5049	332	24	j	j	PROPN
ejpam-5049	332	25	,	,	PUNCT
ejpam-5049	332	26	k	k	PROPN
ejpam-5049	332	27	β	β	X
ejpam-5049	332	28	j−k−α	j−k−α	NOUN
ejpam-5049	332	29	=	=	PUNCT
ejpam-5049	332	30	φ2(β	φ2(β	PROPN
ejpam-5049	332	31	)	)	PUNCT
ejpam-5049	332	32	+	+	CCONJ
ejpam-5049	333	1	3h	3h	NUM
ejpam-5049	333	2	8	8	NUM
ejpam-5049	334	1	(	(	PUNCT
ejpam-5049	334	2	β0	β0	NOUN
ejpam-5049	334	3	(	(	PUNCT
ejpam-5049	334	4	m∑	m∑	ADV
ejpam-5049	334	5	j=0	j=0	PROPN
ejpam-5049	334	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	334	7	)	)	PUNCT
ejpam-5049	334	8	)	)	PUNCT
ejpam-5049	335	1	2	2	NUM
ejpam-5049	335	2	−	−	NOUN
ejpam-5049	335	3	β0	β0	NOUN
ejpam-5049	335	4	(	(	PUNCT
ejpam-5049	335	5	m∑	m∑	ADV
ejpam-5049	335	6	j=0	j=0	PROPN
ejpam-5049	335	7	djφj(β0	djφj(β0	PROPN
ejpam-5049	335	8	)	)	PUNCT
ejpam-5049	335	9	)	)	PUNCT
ejpam-5049	335	10	2	2	NUM
ejpam-5049	336	1	+	+	CCONJ
ejpam-5049	336	2	3	3	NUM
ejpam-5049	336	3	l	l	NOUN
ejpam-5049	336	4	3∑	3∑	NUM
ejpam-5049	336	5	k=1	k=1	X
ejpam-5049	337	1	β2k−2	β2k−2	PROPN
ejpam-5049	337	2	(	(	PUNCT
ejpam-5049	337	3	m∑	m∑	CCONJ
ejpam-5049	337	4	j=0	j=0	PROPN
ejpam-5049	337	5	cjφj(β2k−2	cjφj(β2k−2	PROPN
ejpam-5049	337	6	)	)	PUNCT
ejpam-5049	337	7	)	)	PUNCT
ejpam-5049	338	1	2	2	NUM
ejpam-5049	338	2	−	−	NOUN
ejpam-5049	338	3	3	3	NUM
ejpam-5049	338	4	l	l	NOUN
ejpam-5049	338	5	3∑	3∑	NUM
ejpam-5049	338	6	k=1	k=1	X
ejpam-5049	339	1	β2k−2	β2k−2	PROPN
ejpam-5049	339	2	(	(	PUNCT
ejpam-5049	339	3	m∑	m∑	CCONJ
ejpam-5049	339	4	j=0	j=0	PROPN
ejpam-5049	339	5	djφj(β2k−2	djφj(β2k−2	PROPN
ejpam-5049	339	6	)	)	PUNCT
ejpam-5049	339	7	)	)	PUNCT
ejpam-5049	339	8	2	2	NUM
ejpam-5049	340	1	+	+	CCONJ
ejpam-5049	340	2	3	3	NUM
ejpam-5049	340	3	l	l	NOUN
ejpam-5049	340	4	3∑	3∑	NOUN
ejpam-5049	340	5	k=1	k=1	X
ejpam-5049	340	6	β3k−1	β3k−1	PROPN
ejpam-5049	340	7	(	(	PUNCT
ejpam-5049	340	8	m∑	m∑	CCONJ
ejpam-5049	340	9	j=0	j=0	PROPN
ejpam-5049	340	10	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	340	11	)	)	PUNCT
ejpam-5049	340	12	)	)	PUNCT
ejpam-5049	341	1	2	2	NUM
ejpam-5049	341	2	−	−	NOUN
ejpam-5049	341	3	3	3	NUM
ejpam-5049	341	4	l	l	NOUN
ejpam-5049	341	5	3∑	3∑	NOUN
ejpam-5049	341	6	k=1	k=1	X
ejpam-5049	341	7	β3k−1	β3k−1	PROPN
ejpam-5049	341	8	(	(	PUNCT
ejpam-5049	341	9	m∑	m∑	CCONJ
ejpam-5049	341	10	j=0	j=0	PROPN
ejpam-5049	341	11	djφj(β3k−1	djφj(β3k−1	PROPN
ejpam-5049	341	12	)	)	PUNCT
ejpam-5049	341	13	)	)	PUNCT
ejpam-5049	341	14	2	2	NUM
ejpam-5049	341	15	2	2	NUM
ejpam-5049	341	16	l	l	NOUN
ejpam-5049	341	17	3	3	NUM
ejpam-5049	342	1	−1∑	−1∑	INTJ
ejpam-5049	343	1	k=1	k=1	X
ejpam-5049	344	1	β3k	β3k	X
ejpam-5049	344	2	(	(	PUNCT
ejpam-5049	344	3	m∑	m∑	CCONJ
ejpam-5049	344	4	j=0	j=0	PROPN
ejpam-5049	344	5	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	344	6	)	)	PUNCT
ejpam-5049	344	7	)	)	PUNCT
ejpam-5049	344	8	2	2	NUM
ejpam-5049	344	9	−	−	NUM
ejpam-5049	344	10	2	2	NUM
ejpam-5049	344	11	l	l	NOUN
ejpam-5049	344	12	2∑	2∑	X
ejpam-5049	345	1	k=1	k=1	PUNCT
ejpam-5049	345	2	β3k	β3k	X
ejpam-5049	345	3	(	(	PUNCT
ejpam-5049	345	4	m∑	m∑	CCONJ
ejpam-5049	345	5	j=0	j=0	PROPN
ejpam-5049	345	6	djφj(β3k	djφj(β3k	NOUN
ejpam-5049	345	7	)	)	PUNCT
ejpam-5049	345	8	)	)	PUNCT
ejpam-5049	345	9	2	2	X
ejpam-5049	346	1	+	+	NUM
ejpam-5049	346	2	βl	βl	NOUN
ejpam-5049	346	3	(	(	PUNCT
ejpam-5049	346	4	m∑	m∑	CCONJ
ejpam-5049	346	5	j=0	j=0	PROPN
ejpam-5049	346	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	346	7	)	)	PUNCT
ejpam-5049	346	8	)	)	PUNCT
ejpam-5049	346	9	2	2	NUM
ejpam-5049	346	10	−	−	NOUN
ejpam-5049	346	11	βl	βl	NOUN
ejpam-5049	346	12	(	(	PUNCT
ejpam-5049	346	13	m∑	m∑	CCONJ
ejpam-5049	346	14	j=0	j=0	PROPN
ejpam-5049	346	15	djφj(βl	djφj(βl	PROPN
ejpam-5049	346	16	)	)	PUNCT
ejpam-5049	346	17	)	)	PUNCT
ejpam-5049	346	18	2	2	NUM
ejpam-5049	346	19	)	)	PUNCT
ejpam-5049	346	20	.	.	PUNCT
ejpam-5049	347	1	(	(	PUNCT
ejpam-5049	347	2	51	51	NUM
ejpam-5049	347	3	)	)	PUNCT
ejpam-5049	347	4	using	use	VERB
ejpam-5049	347	5	(	(	PUNCT
ejpam-5049	347	6	19	19	NUM
ejpam-5049	347	7	)	)	PUNCT
ejpam-5049	347	8	,	,	PUNCT
ejpam-5049	347	9	we	we	PRON
ejpam-5049	347	10	obtain	obtain	VERB
ejpam-5049	347	11	m∑	m∑	PRON
ejpam-5049	347	12	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	347	13	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	347	14	k=0	k=0	PROPN
ejpam-5049	347	15	cjχ	cjχ	PROPN
ejpam-5049	347	16	(	(	PUNCT
ejpam-5049	347	17	α	α	NOUN
ejpam-5049	347	18	)	)	PUNCT
ejpam-5049	347	19	j	j	PROPN
ejpam-5049	347	20	,	,	PUNCT
ejpam-5049	347	21	k	k	PROPN
ejpam-5049	347	22	β	β	X
ejpam-5049	347	23	j−k−α	j−k−α	NOUN
ejpam-5049	347	24	s	s	PART
ejpam-5049	347	25	=	=	PUNCT
ejpam-5049	347	26	φ1(βs	φ1(βs	PROPN
ejpam-5049	347	27	)	)	PUNCT
ejpam-5049	348	1	+	+	CCONJ
ejpam-5049	348	2	3h	3h	NUM
ejpam-5049	348	3	8	8	NUM
ejpam-5049	349	1	(	(	PUNCT
ejpam-5049	349	2	β0	β0	NOUN
ejpam-5049	349	3	(	(	PUNCT
ejpam-5049	349	4	m∑	m∑	ADV
ejpam-5049	349	5	j=0	j=0	PROPN
ejpam-5049	349	6	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	349	7	)	)	PUNCT
ejpam-5049	349	8	)	)	PUNCT
ejpam-5049	349	9	2	2	X
ejpam-5049	350	1	+	+	CCONJ
ejpam-5049	350	2	β0	β0	ADJ
ejpam-5049	350	3	(	(	PUNCT
ejpam-5049	350	4	m∑	m∑	ADV
ejpam-5049	350	5	j=0	j=0	PROPN
ejpam-5049	350	6	djφj(β0	djφj(β0	PROPN
ejpam-5049	350	7	)	)	PUNCT
ejpam-5049	350	8	)	)	PUNCT
ejpam-5049	351	1	2	2	NUM
ejpam-5049	351	2	+	+	CCONJ
ejpam-5049	351	3	3	3	NUM
ejpam-5049	351	4	l	l	NOUN
ejpam-5049	351	5	3∑	3∑	NUM
ejpam-5049	351	6	k=1	k=1	X
ejpam-5049	352	1	β2k−2	β2k−2	PROPN
ejpam-5049	352	2	(	(	PUNCT
ejpam-5049	352	3	m∑	m∑	CCONJ
ejpam-5049	352	4	j=0	j=0	PROPN
ejpam-5049	352	5	cjφj(β2k−2	cjφj(β2k−2	PROPN
ejpam-5049	352	6	)	)	PUNCT
ejpam-5049	352	7	)	)	PUNCT
ejpam-5049	352	8	2	2	NUM
ejpam-5049	353	1	+	+	CCONJ
ejpam-5049	353	2	3	3	NUM
ejpam-5049	353	3	l	l	NOUN
ejpam-5049	353	4	3∑	3∑	NUM
ejpam-5049	353	5	k=1	k=1	X
ejpam-5049	354	1	β2k−2	β2k−2	PROPN
ejpam-5049	354	2	(	(	PUNCT
ejpam-5049	354	3	m∑	m∑	CCONJ
ejpam-5049	354	4	j=0	j=0	PROPN
ejpam-5049	354	5	djφj(β2k−2	djφj(β2k−2	PROPN
ejpam-5049	354	6	)	)	PUNCT
ejpam-5049	354	7	)	)	PUNCT
ejpam-5049	354	8	2	2	NUM
ejpam-5049	355	1	+	+	CCONJ
ejpam-5049	355	2	3	3	NUM
ejpam-5049	355	3	l	l	NOUN
ejpam-5049	355	4	3∑	3∑	NOUN
ejpam-5049	355	5	k=1	k=1	X
ejpam-5049	355	6	β3k−1	β3k−1	PROPN
ejpam-5049	355	7	(	(	PUNCT
ejpam-5049	355	8	m∑	m∑	CCONJ
ejpam-5049	355	9	j=0	j=0	PROPN
ejpam-5049	355	10	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	355	11	)	)	PUNCT
ejpam-5049	355	12	)	)	PUNCT
ejpam-5049	355	13	2	2	NUM
ejpam-5049	356	1	+	+	CCONJ
ejpam-5049	356	2	3	3	NUM
ejpam-5049	356	3	l	l	NOUN
ejpam-5049	356	4	3∑	3∑	NOUN
ejpam-5049	356	5	k=1	k=1	X
ejpam-5049	356	6	β3k−1	β3k−1	PROPN
ejpam-5049	356	7	(	(	PUNCT
ejpam-5049	356	8	m∑	m∑	CCONJ
ejpam-5049	356	9	j=0	j=0	PROPN
ejpam-5049	356	10	djφj(β3k−1	djφj(β3k−1	PROPN
ejpam-5049	356	11	)	)	PUNCT
ejpam-5049	356	12	)	)	PUNCT
ejpam-5049	356	13	2	2	NUM
ejpam-5049	356	14	khaled	khale	VERB
ejpam-5049	356	15	m.	m.	NOUN
ejpam-5049	356	16	saad	saad	PROPN
ejpam-5049	356	17	,	,	PUNCT
ejpam-5049	356	18	m.	m.	NOUN
ejpam-5049	356	19	q.	q.	PROPN
ejpam-5049	356	20	khirallah	khirallah	PROPN
ejpam-5049	356	21	/	/	SYM
ejpam-5049	356	22	eur	eur	PROPN
ejpam-5049	356	23	.	.	PUNCT
ejpam-5049	357	1	j.	j.	PROPN
ejpam-5049	357	2	pure	pure	PROPN
ejpam-5049	357	3	appl	appl	PROPN
ejpam-5049	357	4	.	.	PROPN
ejpam-5049	357	5	math	math	PROPN
ejpam-5049	357	6	,	,	PUNCT
ejpam-5049	357	7	17	17	NUM
ejpam-5049	357	8	(	(	PUNCT
ejpam-5049	357	9	1	1	NUM
ejpam-5049	357	10	)	)	PUNCT
ejpam-5049	357	11	(	(	PUNCT
ejpam-5049	357	12	2024	2024	NUM
ejpam-5049	357	13	)	)	PUNCT
ejpam-5049	357	14	,	,	PUNCT
ejpam-5049	357	15	477	477	NUM
ejpam-5049	357	16	-	-	SYM
ejpam-5049	357	17	503	503	NUM
ejpam-5049	357	18	493	493	NUM
ejpam-5049	357	19	2	2	NUM
ejpam-5049	357	20	l	l	NOUN
ejpam-5049	357	21	3	3	NUM
ejpam-5049	358	1	−1∑	−1∑	INTJ
ejpam-5049	358	2	k=1	k=1	X
ejpam-5049	358	3	β3k	β3k	X
ejpam-5049	358	4	(	(	PUNCT
ejpam-5049	358	5	m∑	m∑	CCONJ
ejpam-5049	358	6	j=0	j=0	PROPN
ejpam-5049	358	7	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	358	8	)	)	PUNCT
ejpam-5049	358	9	)	)	PUNCT
ejpam-5049	359	1	2	2	NUM
ejpam-5049	359	2	+	+	SYM
ejpam-5049	359	3	2	2	NUM
ejpam-5049	359	4	l	l	NOUN
ejpam-5049	359	5	2∑	2∑	X
ejpam-5049	360	1	k=1	k=1	PUNCT
ejpam-5049	360	2	β3k	β3k	X
ejpam-5049	360	3	(	(	PUNCT
ejpam-5049	360	4	m∑	m∑	CCONJ
ejpam-5049	360	5	j=0	j=0	PROPN
ejpam-5049	360	6	djφj(β3k	djφj(β3k	NOUN
ejpam-5049	360	7	)	)	PUNCT
ejpam-5049	360	8	)	)	PUNCT
ejpam-5049	360	9	2	2	X
ejpam-5049	361	1	+	+	NUM
ejpam-5049	361	2	βl	βl	NOUN
ejpam-5049	361	3	(	(	PUNCT
ejpam-5049	361	4	m∑	m∑	CCONJ
ejpam-5049	361	5	j=0	j=0	PROPN
ejpam-5049	361	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	361	7	)	)	PUNCT
ejpam-5049	361	8	)	)	PUNCT
ejpam-5049	361	9	2	2	X
ejpam-5049	362	1	+	+	NUM
ejpam-5049	362	2	βl	βl	NOUN
ejpam-5049	362	3	(	(	PUNCT
ejpam-5049	362	4	m∑	m∑	CCONJ
ejpam-5049	362	5	j=0	j=0	PROPN
ejpam-5049	362	6	djφj(βl	djφj(βl	PROPN
ejpam-5049	362	7	)	)	PUNCT
ejpam-5049	362	8	)	)	PUNCT
ejpam-5049	362	9	2	2	NUM
ejpam-5049	362	10	)	)	PUNCT
ejpam-5049	362	11	,	,	PUNCT
ejpam-5049	362	12	(	(	PUNCT
ejpam-5049	362	13	52	52	NUM
ejpam-5049	362	14	)	)	PUNCT
ejpam-5049	362	15	and	and	CCONJ
ejpam-5049	362	16	m∑	m∑	CCONJ
ejpam-5049	362	17	j=⌈α⌉	j=⌈α⌉	PROPN
ejpam-5049	362	18	j−⌈α⌉∑	j−⌈α⌉∑	PROPN
ejpam-5049	362	19	k=0	k=0	PROPN
ejpam-5049	362	20	djχ	djχ	PROPN
ejpam-5049	362	21	(	(	PUNCT
ejpam-5049	362	22	α	α	NOUN
ejpam-5049	362	23	)	)	PUNCT
ejpam-5049	362	24	j	j	PROPN
ejpam-5049	362	25	,	,	PUNCT
ejpam-5049	362	26	k	k	PROPN
ejpam-5049	362	27	β	β	X
ejpam-5049	362	28	j−k−α	j−k−α	NOUN
ejpam-5049	362	29	s	s	PART
ejpam-5049	362	30	=	=	SYM
ejpam-5049	362	31	φ2(βs	φ2(βs	PROPN
ejpam-5049	362	32	)	)	PUNCT
ejpam-5049	363	1	+	+	CCONJ
ejpam-5049	363	2	3h	3h	NUM
ejpam-5049	363	3	8	8	NUM
ejpam-5049	363	4	(	(	PUNCT
ejpam-5049	363	5	β0	β0	NOUN
ejpam-5049	363	6	(	(	PUNCT
ejpam-5049	363	7	m∑	m∑	ADV
ejpam-5049	363	8	j=0	j=0	PROPN
ejpam-5049	363	9	cjφj(β0	cjφj(β0	PROPN
ejpam-5049	363	10	)	)	PUNCT
ejpam-5049	363	11	)	)	PUNCT
ejpam-5049	364	1	2	2	NUM
ejpam-5049	364	2	−	−	NOUN
ejpam-5049	364	3	β0	β0	NOUN
ejpam-5049	364	4	(	(	PUNCT
ejpam-5049	364	5	m∑	m∑	ADV
ejpam-5049	364	6	j=0	j=0	PROPN
ejpam-5049	364	7	djφj(β0	djφj(β0	PROPN
ejpam-5049	364	8	)	)	PUNCT
ejpam-5049	364	9	)	)	PUNCT
ejpam-5049	364	10	2	2	NUM
ejpam-5049	365	1	+	+	CCONJ
ejpam-5049	365	2	3	3	NUM
ejpam-5049	365	3	l	l	NOUN
ejpam-5049	365	4	3∑	3∑	NUM
ejpam-5049	365	5	k=1	k=1	X
ejpam-5049	366	1	β2k−2	β2k−2	PROPN
ejpam-5049	366	2	(	(	PUNCT
ejpam-5049	366	3	m∑	m∑	CCONJ
ejpam-5049	366	4	j=0	j=0	PROPN
ejpam-5049	366	5	cjφj(β2k−2	cjφj(β2k−2	PROPN
ejpam-5049	366	6	)	)	PUNCT
ejpam-5049	366	7	)	)	PUNCT
ejpam-5049	367	1	2	2	NUM
ejpam-5049	367	2	−	−	NOUN
ejpam-5049	367	3	3	3	NUM
ejpam-5049	367	4	l	l	NOUN
ejpam-5049	367	5	3∑	3∑	NUM
ejpam-5049	367	6	k=1	k=1	X
ejpam-5049	368	1	β2k−2	β2k−2	PROPN
ejpam-5049	368	2	(	(	PUNCT
ejpam-5049	368	3	m∑	m∑	CCONJ
ejpam-5049	368	4	j=0	j=0	PROPN
ejpam-5049	368	5	djφj(β2k−2	djφj(β2k−2	PROPN
ejpam-5049	368	6	)	)	PUNCT
ejpam-5049	368	7	)	)	PUNCT
ejpam-5049	368	8	2	2	NUM
ejpam-5049	369	1	+	+	CCONJ
ejpam-5049	369	2	3	3	NUM
ejpam-5049	369	3	l	l	NOUN
ejpam-5049	369	4	3∑	3∑	NOUN
ejpam-5049	369	5	k=1	k=1	X
ejpam-5049	369	6	β3k−1	β3k−1	PROPN
ejpam-5049	369	7	(	(	PUNCT
ejpam-5049	369	8	m∑	m∑	CCONJ
ejpam-5049	369	9	j=0	j=0	PROPN
ejpam-5049	369	10	cjφj(β3k−1	cjφj(β3k−1	PROPN
ejpam-5049	369	11	)	)	PUNCT
ejpam-5049	369	12	)	)	PUNCT
ejpam-5049	370	1	2	2	NUM
ejpam-5049	370	2	−	−	NOUN
ejpam-5049	370	3	3	3	NUM
ejpam-5049	370	4	l	l	NOUN
ejpam-5049	370	5	3∑	3∑	NOUN
ejpam-5049	370	6	k=1	k=1	X
ejpam-5049	370	7	β3k−1	β3k−1	PROPN
ejpam-5049	370	8	(	(	PUNCT
ejpam-5049	370	9	m∑	m∑	CCONJ
ejpam-5049	370	10	j=0	j=0	PROPN
ejpam-5049	370	11	djφj(β3k−1	djφj(β3k−1	PROPN
ejpam-5049	370	12	)	)	PUNCT
ejpam-5049	370	13	)	)	PUNCT
ejpam-5049	370	14	2	2	NUM
ejpam-5049	370	15	2	2	NUM
ejpam-5049	370	16	l	l	NOUN
ejpam-5049	370	17	3	3	NUM
ejpam-5049	371	1	−1∑	−1∑	INTJ
ejpam-5049	372	1	k=1	k=1	X
ejpam-5049	373	1	β3k	β3k	X
ejpam-5049	373	2	(	(	PUNCT
ejpam-5049	373	3	m∑	m∑	CCONJ
ejpam-5049	373	4	j=0	j=0	PROPN
ejpam-5049	373	5	cjφj(β3k	cjφj(β3k	PROPN
ejpam-5049	373	6	)	)	PUNCT
ejpam-5049	373	7	)	)	PUNCT
ejpam-5049	373	8	2	2	NUM
ejpam-5049	373	9	−	−	NUM
ejpam-5049	373	10	2	2	NUM
ejpam-5049	373	11	l	l	NOUN
ejpam-5049	373	12	2∑	2∑	X
ejpam-5049	374	1	k=1	k=1	PUNCT
ejpam-5049	374	2	β3k	β3k	X
ejpam-5049	374	3	(	(	PUNCT
ejpam-5049	374	4	m∑	m∑	CCONJ
ejpam-5049	374	5	j=0	j=0	PROPN
ejpam-5049	374	6	djφj(β3k	djφj(β3k	NOUN
ejpam-5049	374	7	)	)	PUNCT
ejpam-5049	374	8	)	)	PUNCT
ejpam-5049	374	9	2	2	X
ejpam-5049	375	1	+	+	NUM
ejpam-5049	375	2	βl	βl	NOUN
ejpam-5049	375	3	(	(	PUNCT
ejpam-5049	375	4	m∑	m∑	CCONJ
ejpam-5049	375	5	j=0	j=0	PROPN
ejpam-5049	375	6	cjφj(βl	cjφj(βl	PROPN
ejpam-5049	375	7	)	)	PUNCT
ejpam-5049	375	8	)	)	PUNCT
ejpam-5049	375	9	2	2	NUM
ejpam-5049	375	10	−	−	NOUN
ejpam-5049	375	11	βl	βl	NOUN
ejpam-5049	375	12	(	(	PUNCT
ejpam-5049	375	13	m∑	m∑	INTJ
ejpam-5049	375	14	i=0	i=0	PROPN
ejpam-5049	375	15	diφj(βl	diφj(βl	PROPN
ejpam-5049	375	16	)	)	PUNCT
ejpam-5049	375	17	)	)	PUNCT
ejpam-5049	375	18	2	2	NUM
ejpam-5049	375	19	)	)	PUNCT
ejpam-5049	375	20	.	.	PUNCT
ejpam-5049	376	1	(	(	PUNCT
ejpam-5049	376	2	53	53	NUM
ejpam-5049	376	3	)	)	PUNCT
ejpam-5049	376	4	additionally	additionally	ADV
ejpam-5049	376	5	,	,	PUNCT
ejpam-5049	376	6	we	we	PRON
ejpam-5049	376	7	follow	follow	VERB
ejpam-5049	376	8	the	the	DET
ejpam-5049	376	9	same	same	ADJ
ejpam-5049	376	10	stages	stage	NOUN
ejpam-5049	376	11	outlined	outline	VERB
ejpam-5049	376	12	in	in	ADP
ejpam-5049	376	13	examples	example	NOUN
ejpam-5049	376	14	1	1	NUM
ejpam-5049	376	15	and	and	CCONJ
ejpam-5049	376	16	2	2	NUM
ejpam-5049	376	17	.	.	NUM
ejpam-5049	376	18	figures	figure	NOUN
ejpam-5049	376	19	5	5	NUM
ejpam-5049	376	20	(	(	PUNCT
ejpam-5049	376	21	a	a	NOUN
ejpam-5049	376	22	)	)	PUNCT
ejpam-5049	376	23	and	and	CCONJ
ejpam-5049	376	24	5	5	NUM
ejpam-5049	376	25	(	(	PUNCT
ejpam-5049	376	26	a	a	NOUN
ejpam-5049	376	27	)	)	PUNCT
ejpam-5049	376	28	show	show	VERB
ejpam-5049	376	29	the	the	DET
ejpam-5049	376	30	approximate	approximate	ADJ
ejpam-5049	376	31	solutions	solution	NOUN
ejpam-5049	376	32	and	and	CCONJ
ejpam-5049	376	33	how	how	SCONJ
ejpam-5049	376	34	they	they	PRON
ejpam-5049	376	35	coincide	coincide	VERB
ejpam-5049	376	36	with	with	ADP
ejpam-5049	376	37	the	the	DET
ejpam-5049	376	38	exact	exact	ADJ
ejpam-5049	376	39	solution	solution	NOUN
ejpam-5049	376	40	for	for	ADP
ejpam-5049	376	41	α	α	NOUN
ejpam-5049	376	42	=	=	SYM
ejpam-5049	376	43	0.8	0.8	NUM
ejpam-5049	376	44	,	,	PUNCT
ejpam-5049	376	45	0.9	0.9	NUM
ejpam-5049	376	46	and	and	CCONJ
ejpam-5049	376	47	α	α	NOUN
ejpam-5049	377	1	=	=	ADJ
ejpam-5049	377	2	1	1	X
ejpam-5049	377	3	.	.	PUNCT
ejpam-5049	378	1	the	the	DET
ejpam-5049	378	2	absolute	absolute	ADJ
ejpam-5049	378	3	error	error	NOUN
ejpam-5049	378	4	between	between	ADP
ejpam-5049	378	5	the	the	DET
ejpam-5049	378	6	approximate	approximate	ADJ
ejpam-5049	378	7	solutions	solution	NOUN
ejpam-5049	378	8	and	and	CCONJ
ejpam-5049	378	9	the	the	DET
ejpam-5049	378	10	exact	exact	ADJ
ejpam-5049	378	11	solution	solution	NOUN
ejpam-5049	378	12	is	be	AUX
ejpam-5049	378	13	shown	show	VERB
ejpam-5049	378	14	in	in	ADP
ejpam-5049	378	15	figures	figure	NOUN
ejpam-5049	378	16	5(b	5(b	NUM
ejpam-5049	378	17	)	)	PUNCT
ejpam-5049	378	18	and	and	CCONJ
ejpam-5049	378	19	6(b	6(b	NUM
ejpam-5049	378	20	)	)	PUNCT
ejpam-5049	378	21	.	.	PUNCT
ejpam-5049	379	1	when	when	SCONJ
ejpam-5049	379	2	the	the	DET
ejpam-5049	379	3	order	order	NOUN
ejpam-5049	379	4	of	of	ADP
ejpam-5049	379	5	the	the	DET
ejpam-5049	379	6	derivative	derivative	NOUN
ejpam-5049	379	7	becomes	become	VERB
ejpam-5049	379	8	close	close	ADJ
ejpam-5049	379	9	to	to	ADP
ejpam-5049	379	10	the	the	DET
ejpam-5049	379	11	integer	integer	NOUN
ejpam-5049	379	12	number	number	NOUN
ejpam-5049	379	13	,	,	PUNCT
ejpam-5049	379	14	the	the	DET
ejpam-5049	379	15	approximate	approximate	ADJ
ejpam-5049	379	16	solutions	solution	NOUN
ejpam-5049	379	17	approach	approach	NOUN
ejpam-5049	379	18	to	to	ADP
ejpam-5049	379	19	the	the	DET
ejpam-5049	379	20	exact	exact	ADJ
ejpam-5049	379	21	solution	solution	NOUN
ejpam-5049	379	22	.	.	PUNCT
ejpam-5049	380	1	in	in	ADP
ejpam-5049	380	2	this	this	DET
ejpam-5049	380	3	example	example	NOUN
ejpam-5049	380	4	,	,	PUNCT
ejpam-5049	380	5	the	the	DET
ejpam-5049	380	6	comparison	comparison	NOUN
ejpam-5049	380	7	applies	apply	VERB
ejpam-5049	380	8	specifically	specifically	ADV
ejpam-5049	380	9	to	to	ADP
ejpam-5049	380	10	simpson	simpson	PROPN
ejpam-5049	380	11	3/8	3/8	NUM
ejpam-5049	380	12	’s	’s	PART
ejpam-5049	380	13	case	case	NOUN
ejpam-5049	380	14	,	,	PUNCT
ejpam-5049	380	15	while	while	SCONJ
ejpam-5049	380	16	the	the	DET
ejpam-5049	380	17	remaining	remain	VERB
ejpam-5049	380	18	two	two	NUM
ejpam-5049	380	19	cases	case	NOUN
ejpam-5049	380	20	exhibit	exhibit	VERB
ejpam-5049	380	21	identical	identical	ADJ
ejpam-5049	380	22	behavior	behavior	NOUN
ejpam-5049	380	23	.	.	PUNCT
ejpam-5049	381	1	furthermore	furthermore	ADV
ejpam-5049	381	2	,	,	PUNCT
ejpam-5049	381	3	for	for	ADP
ejpam-5049	381	4	the	the	DET
ejpam-5049	381	5	non	non	ADJ
ejpam-5049	381	6	-	-	ADJ
ejpam-5049	381	7	integer	integer	ADJ
ejpam-5049	381	8	order	order	NOUN
ejpam-5049	381	9	in	in	ADP
ejpam-5049	381	10	two	two	NUM
ejpam-5049	381	11	sequential	sequential	ADJ
ejpam-5049	381	12	approximations	approximation	NOUN
ejpam-5049	381	13	,	,	PUNCT
ejpam-5049	381	14	figure	figure	NOUN
ejpam-5049	381	15	7	7	NUM
ejpam-5049	381	16	confirms	confirm	VERB
ejpam-5049	381	17	the	the	DET
ejpam-5049	381	18	accuracy	accuracy	NOUN
ejpam-5049	381	19	of	of	ADP
ejpam-5049	381	20	the	the	DET
ejpam-5049	381	21	approximate	approximate	ADJ
ejpam-5049	381	22	solutions	solution	NOUN
ejpam-5049	381	23	with	with	ADP
ejpam-5049	381	24	α	α	NOUN
ejpam-5049	381	25	=	=	SYM
ejpam-5049	381	26	0.8	0.8	NUM
ejpam-5049	381	27	and	and	CCONJ
ejpam-5049	381	28	m	m	VERB
ejpam-5049	381	29	=	=	NOUN
ejpam-5049	381	30	6	6	NUM
ejpam-5049	381	31	and	and	CCONJ
ejpam-5049	381	32	m	m	VERB
ejpam-5049	381	33	=	=	ADJ
ejpam-5049	381	34	7	7	NUM
ejpam-5049	381	35	,	,	PUNCT
ejpam-5049	381	36	via	via	ADP
ejpam-5049	381	37	trapezoidal	trapezoidal	NOUN
ejpam-5049	381	38	,	,	PUNCT
ejpam-5049	381	39	simpson	simpson	PROPN
ejpam-5049	381	40	’	'	PUNCT
ejpam-5049	381	41	1/8	1/8	NUM
ejpam-5049	381	42	,	,	PUNCT
ejpam-5049	381	43	and	and	CCONJ
ejpam-5049	381	44	simpson	simpson	PROPN
ejpam-5049	381	45	’	'	PUNCT
ejpam-5049	381	46	1/3	1/3	NUM
ejpam-5049	381	47	methods	method	NOUN
ejpam-5049	381	48	.	.	PUNCT
ejpam-5049	382	1	in	in	ADP
ejpam-5049	382	2	the	the	DET
ejpam-5049	382	3	preceding	precede	VERB
ejpam-5049	382	4	three	three	NUM
ejpam-5049	382	5	examples	example	NOUN
ejpam-5049	382	6	,	,	PUNCT
ejpam-5049	382	7	we	we	PRON
ejpam-5049	382	8	observe	observe	VERB
ejpam-5049	382	9	a	a	DET
ejpam-5049	382	10	consistent	consistent	ADJ
ejpam-5049	382	11	pattern	pattern	NOUN
ejpam-5049	382	12	in	in	ADP
ejpam-5049	382	13	the	the	DET
ejpam-5049	382	14	behavior	behavior	NOUN
ejpam-5049	382	15	of	of	ADP
ejpam-5049	382	16	the	the	DET
ejpam-5049	382	17	approximate	approximate	ADJ
ejpam-5049	382	18	solutions	solution	NOUN
ejpam-5049	382	19	.	.	PUNCT
ejpam-5049	383	1	they	they	PRON
ejpam-5049	383	2	tend	tend	VERB
ejpam-5049	383	3	to	to	PART
ejpam-5049	383	4	converge	converge	VERB
ejpam-5049	383	5	towards	towards	ADP
ejpam-5049	383	6	the	the	DET
ejpam-5049	383	7	exact	exact	ADJ
ejpam-5049	383	8	solution	solution	NOUN
ejpam-5049	383	9	as	as	ADP
ejpam-5049	383	10	the	the	DET
ejpam-5049	383	11	order	order	NOUN
ejpam-5049	383	12	of	of	ADP
ejpam-5049	383	13	the	the	DET
ejpam-5049	383	14	non	non	ADJ
ejpam-5049	383	15	-	-	ADJ
ejpam-5049	383	16	integer	integer	ADJ
ejpam-5049	383	17	derivative	derivative	ADJ
ejpam-5049	383	18	approaches	approach	VERB
ejpam-5049	383	19	the	the	DET
ejpam-5049	383	20	integer	integer	NOUN
ejpam-5049	383	21	order	order	NOUN
ejpam-5049	383	22	.	.	PUNCT
ejpam-5049	384	1	this	this	DET
ejpam-5049	384	2	observation	observation	NOUN
ejpam-5049	384	3	contributes	contribute	VERB
ejpam-5049	384	4	positively	positively	ADV
ejpam-5049	384	5	to	to	ADP
ejpam-5049	384	6	the	the	DET
ejpam-5049	384	7	overall	overall	ADJ
ejpam-5049	384	8	presentation	presentation	NOUN
ejpam-5049	384	9	of	of	ADP
ejpam-5049	384	10	this	this	DET
ejpam-5049	384	11	work	work	NOUN
ejpam-5049	384	12	.	.	PUNCT
ejpam-5049	385	1	additionally	additionally	ADV
ejpam-5049	385	2	,	,	PUNCT
ejpam-5049	385	3	when	when	SCONJ
ejpam-5049	385	4	dealing	deal	VERB
ejpam-5049	385	5	with	with	ADP
ejpam-5049	385	6	an	an	DET
ejpam-5049	385	7	non	non	ADJ
ejpam-5049	385	8	-	-	ADJ
ejpam-5049	385	9	integer	integer	ADJ
ejpam-5049	385	10	order	order	NOUN
ejpam-5049	385	11	,	,	PUNCT
ejpam-5049	385	12	the	the	DET
ejpam-5049	385	13	absolute	absolute	ADJ
ejpam-5049	385	14	error	error	NOUN
ejpam-5049	385	15	between	between	ADP
ejpam-5049	385	16	successive	successive	ADJ
ejpam-5049	385	17	approximate	approximate	ADJ
ejpam-5049	385	18	solutions	solution	NOUN
ejpam-5049	385	19	for	for	ADP
ejpam-5049	385	20	various	various	ADJ
ejpam-5049	385	21	values	value	NOUN
ejpam-5049	385	22	of	of	ADP
ejpam-5049	385	23	m	m	VERB
ejpam-5049	385	24	yielded	yield	VERB
ejpam-5049	385	25	accurate	accurate	ADJ
ejpam-5049	385	26	results	result	NOUN
ejpam-5049	385	27	.	.	PUNCT
ejpam-5049	386	1	khaled	khaled	PROPN
ejpam-5049	386	2	m.	m.	PROPN
ejpam-5049	386	3	saad	saad	PROPN
ejpam-5049	386	4	,	,	PUNCT
ejpam-5049	386	5	m.	m.	NOUN
ejpam-5049	386	6	q.	q.	PROPN
ejpam-5049	386	7	khirallah	khirallah	PROPN
ejpam-5049	386	8	/	/	SYM
ejpam-5049	386	9	eur	eur	PROPN
ejpam-5049	386	10	.	.	PUNCT
ejpam-5049	387	1	j.	j.	PROPN
ejpam-5049	387	2	pure	pure	PROPN
ejpam-5049	387	3	appl	appl	PROPN
ejpam-5049	387	4	.	.	PROPN
ejpam-5049	387	5	math	math	PROPN
ejpam-5049	387	6	,	,	PUNCT
ejpam-5049	387	7	17	17	NUM
ejpam-5049	387	8	(	(	PUNCT
ejpam-5049	387	9	1	1	NUM
ejpam-5049	387	10	)	)	PUNCT
ejpam-5049	387	11	(	(	PUNCT
ejpam-5049	387	12	2024	2024	NUM
ejpam-5049	387	13	)	)	PUNCT
ejpam-5049	387	14	,	,	PUNCT
ejpam-5049	387	15	477	477	NUM
ejpam-5049	387	16	-	-	SYM
ejpam-5049	387	17	503	503	NUM
ejpam-5049	387	18	494	494	NUM
ejpam-5049	387	19	0.0	0.0	NUM
ejpam-5049	387	20	0.2	0.2	NUM
ejpam-5049	387	21	0.4	0.4	NUM
ejpam-5049	387	22	0.6	0.6	NUM
ejpam-5049	387	23	0.8	0.8	NUM
ejpam-5049	387	24	1.0	1.0	NUM
ejpam-5049	387	25	0.0	0.0	NUM
ejpam-5049	387	26	0.5	0.5	NUM
ejpam-5049	387	27	1.0	1.0	NUM
ejpam-5049	387	28	1.5	1.5	NUM
ejpam-5049	387	29	2.0	2.0	NUM
ejpam-5049	387	30	2.5	2.5	NUM
ejpam-5049	387	31	3.0	3.0	NUM
ejpam-5049	387	32	3.5	3.5	NUM
ejpam-5049	387	33	β	β	PROPN
ejpam-5049	387	34	φ	φ	PROPN
ejpam-5049	387	35	hβl	hβl	PROPN
ejpam-5049	387	36	hal	hal	PROPN
ejpam-5049	387	37	0.0	0.0	NUM
ejpam-5049	388	1	0.2	0.2	NUM
ejpam-5049	388	2	0.4	0.4	NUM
ejpam-5049	388	3	0.6	0.6	NUM
ejpam-5049	388	4	0.8	0.8	NUM
ejpam-5049	388	5	1.0	1.0	NUM
ejpam-5049	388	6	0.0000	0.0000	NUM
ejpam-5049	388	7	0.0001	0.0001	NUM
ejpam-5049	388	8	0.0002	0.0002	NUM
ejpam-5049	388	9	0.0003	0.0003	NUM
ejpam-5049	388	10	0.0004	0.0004	NUM
ejpam-5049	388	11	0.0005	0.0005	NUM
ejpam-5049	388	12	β	β	X
ejpam-5049	388	13	 	 	SPACE
ejpam-5049	388	14	φh	φh	VERB
ejpam-5049	388	15	β	β	X
ejpam-5049	388	16	l	l	X
ejpam-5049	388	17	-	-	PROPN
ejpam-5049	388	18	φ	φ	PROPN
ejpam-5049	388	19	7	7	NUM
ejpam-5049	388	20	hβl	hβl	NOUN
ejpam-5049	388	21	  	  	SPACE
ejpam-5049	388	22	hbl	hbl	PROPN
ejpam-5049	388	23	trapezoidal	trapezoidal	PROPN
ejpam-5049	388	24	simpson	simpson	PROPN
ejpam-5049	388	25	'	'	PART
ejpam-5049	388	26	3	3	NUM
ejpam-5049	388	27	8	8	NUM
ejpam-5049	388	28	simpson	simpson	PROPN
ejpam-5049	388	29	'	'	PART
ejpam-5049	388	30	1	1	NUM
ejpam-5049	388	31	3	3	NUM
ejpam-5049	388	32	figure	figure	NOUN
ejpam-5049	388	33	1	1	NUM
ejpam-5049	388	34	:	:	PUNCT
ejpam-5049	388	35	(	(	PUNCT
ejpam-5049	388	36	a	a	X
ejpam-5049	388	37	)	)	PUNCT
ejpam-5049	388	38	combining	combine	VERB
ejpam-5049	388	39	approximate	approximate	ADJ
ejpam-5049	388	40	solutions	solution	NOUN
ejpam-5049	388	41	with	with	ADP
ejpam-5049	388	42	the	the	DET
ejpam-5049	388	43	exact	exact	ADJ
ejpam-5049	388	44	solution	solution	NOUN
ejpam-5049	388	45	for	for	ADP
ejpam-5049	388	46	different	different	ADJ
ejpam-5049	388	47	values	value	NOUN
ejpam-5049	388	48	of	of	ADP
ejpam-5049	388	49	alpha	alpha	NOUN
ejpam-5049	388	50	for	for	ADP
ejpam-5049	388	51	example	example	NOUN
ejpam-5049	388	52	1	1	NUM
ejpam-5049	388	53	.	.	PUNCT
ejpam-5049	388	54	(	(	PUNCT
ejpam-5049	388	55	red	red	ADJ
ejpam-5049	388	56	solid	solid	ADJ
ejpam-5049	388	57	color	color	NOUN
ejpam-5049	388	58	:	:	PUNCT
ejpam-5049	388	59	α	α	NOUN
ejpam-5049	388	60	=	=	NOUN
ejpam-5049	388	61	0.8	0.8	NUM
ejpam-5049	388	62	;	;	PUNCT
ejpam-5049	388	63	blue	blue	ADJ
ejpam-5049	388	64	solid	solid	ADJ
ejpam-5049	388	65	color	color	NOUN
ejpam-5049	388	66	:	:	PUNCT
ejpam-5049	388	67	α	α	X
ejpam-5049	388	68	=	=	NOUN
ejpam-5049	388	69	0.9	0.9	NUM
ejpam-5049	388	70	;	;	PUNCT
ejpam-5049	388	71	black	black	ADJ
ejpam-5049	388	72	solid	solid	ADJ
ejpam-5049	388	73	color	color	NOUN
ejpam-5049	388	74	:	:	PUNCT
ejpam-5049	388	75	α	α	X
ejpam-5049	388	76	=	=	SYM
ejpam-5049	388	77	1	1	NUM
ejpam-5049	388	78	;	;	PUNCT
ejpam-5049	388	79	green	green	ADJ
ejpam-5049	388	80	dashed	dash	VERB
ejpam-5049	388	81	color	color	NOUN
ejpam-5049	388	82	:	:	PUNCT
ejpam-5049	388	83	exact	exact	ADJ
ejpam-5049	388	84	solution	solution	NOUN
ejpam-5049	388	85	)	)	PUNCT
ejpam-5049	388	86	.	.	PUNCT
ejpam-5049	389	1	(	(	PUNCT
ejpam-5049	389	2	b	b	X
ejpam-5049	389	3	)	)	PUNCT
ejpam-5049	389	4	the	the	DET
ejpam-5049	389	5	absolute	absolute	ADJ
ejpam-5049	389	6	error	error	NOUN
ejpam-5049	389	7	between	between	ADP
ejpam-5049	389	8	the	the	DET
ejpam-5049	389	9	approximate	approximate	ADJ
ejpam-5049	389	10	solutions	solution	NOUN
ejpam-5049	389	11	and	and	CCONJ
ejpam-5049	389	12	the	the	DET
ejpam-5049	389	13	analytical	analytical	ADJ
ejpam-5049	389	14	solution	solution	NOUN
ejpam-5049	389	15	for	for	ADP
ejpam-5049	389	16	example	example	NOUN
ejpam-5049	389	17	1	1	NUM
ejpam-5049	389	18	.	.	PUNCT
ejpam-5049	389	19	khaled	khaled	PROPN
ejpam-5049	389	20	m.	m.	PROPN
ejpam-5049	389	21	saad	saad	PROPN
ejpam-5049	389	22	,	,	PUNCT
ejpam-5049	389	23	m.	m.	NOUN
ejpam-5049	389	24	q.	q.	PROPN
ejpam-5049	389	25	khirallah	khirallah	PROPN
ejpam-5049	389	26	/	/	SYM
ejpam-5049	389	27	eur	eur	PROPN
ejpam-5049	389	28	.	.	PUNCT
ejpam-5049	390	1	j.	j.	PROPN
ejpam-5049	390	2	pure	pure	PROPN
ejpam-5049	390	3	appl	appl	PROPN
ejpam-5049	390	4	.	.	PROPN
ejpam-5049	390	5	math	math	PROPN
ejpam-5049	390	6	,	,	PUNCT
ejpam-5049	390	7	17	17	NUM
ejpam-5049	390	8	(	(	PUNCT
ejpam-5049	390	9	1	1	NUM
ejpam-5049	390	10	)	)	PUNCT
ejpam-5049	390	11	(	(	PUNCT
ejpam-5049	390	12	2024	2024	NUM
ejpam-5049	390	13	)	)	PUNCT
ejpam-5049	390	14	,	,	PUNCT
ejpam-5049	390	15	477	477	NUM
ejpam-5049	390	16	-	-	SYM
ejpam-5049	390	17	503	503	NUM
ejpam-5049	390	18	495	495	NUM
ejpam-5049	390	19	0.0	0.0	NUM
ejpam-5049	390	20	0.2	0.2	NUM
ejpam-5049	390	21	0.4	0.4	NUM
ejpam-5049	390	22	0.6	0.6	NUM
ejpam-5049	390	23	0.8	0.8	NUM
ejpam-5049	390	24	1.0	1.0	NUM
ejpam-5049	390	25	0.0000	0.0000	NUM
ejpam-5049	390	26	0.0005	0.0005	NUM
ejpam-5049	390	27	0.0010	0.0010	NUM
ejpam-5049	390	28	0.0015	0.0015	NUM
ejpam-5049	390	29	0.0020	0.0020	NUM
ejpam-5049	390	30	0.0025	0.0025	NUM
ejpam-5049	390	31	0.0030	0.0030	NUM
ejpam-5049	390	32	0.0035	0.0035	NUM
ejpam-5049	390	33	β	β	SYM
ejpam-5049	390	34	 	 	SPACE
ejpam-5049	390	35	φ	φ	PROPN
ejpam-5049	390	36	6	6	NUM
ejpam-5049	390	37	hβl	hβl	PROPN
ejpam-5049	390	38	φ	φ	PROPN
ejpam-5049	390	39	7	7	NUM
ejpam-5049	390	40	hβl	hβl	NOUN
ejpam-5049	390	41	  	  	SPACE
ejpam-5049	390	42	figure	figure	NOUN
ejpam-5049	390	43	2	2	NUM
ejpam-5049	390	44	:	:	PUNCT
ejpam-5049	390	45	plotting	plot	VERB
ejpam-5049	390	46	the	the	DET
ejpam-5049	390	47	difference	difference	NOUN
ejpam-5049	390	48	between	between	ADP
ejpam-5049	390	49	the	the	DET
ejpam-5049	390	50	two	two	NUM
ejpam-5049	390	51	step	step	NOUN
ejpam-5049	390	52	of	of	ADP
ejpam-5049	390	53	the	the	DET
ejpam-5049	390	54	approximate	approximate	ADJ
ejpam-5049	390	55	solutions	solution	NOUN
ejpam-5049	390	56	with	with	ADP
ejpam-5049	390	57	α	α	NOUN
ejpam-5049	390	58	=	=	SYM
ejpam-5049	390	59	0.8	0.8	NUM
ejpam-5049	390	60	and	and	CCONJ
ejpam-5049	390	61	m	m	VERB
ejpam-5049	390	62	=	=	NOUN
ejpam-5049	390	63	6	6	NUM
ejpam-5049	390	64	and	and	CCONJ
ejpam-5049	390	65	m	m	VERB
ejpam-5049	390	66	=	=	NOUN
ejpam-5049	390	67	7	7	NUM
ejpam-5049	390	68	for	for	ADP
ejpam-5049	390	69	example	example	NOUN
ejpam-5049	390	70	1	1	NUM
ejpam-5049	390	71	.	.	PUNCT
ejpam-5049	391	1	(	(	PUNCT
ejpam-5049	391	2	black	black	ADJ
ejpam-5049	391	3	dashed	dash	VERB
ejpam-5049	391	4	color	color	NOUN
ejpam-5049	391	5	:	:	PUNCT
ejpam-5049	391	6	trapezoidal	trapezoidal	ADJ
ejpam-5049	391	7	green	green	PROPN
ejpam-5049	391	8	dashed	dash	VERB
ejpam-5049	391	9	color	color	NOUN
ejpam-5049	391	10	:	:	PUNCT
ejpam-5049	392	1	simpson	simpson	PROPN
ejpam-5049	392	2	’	'	PUNCT
ejpam-5049	392	3	3/8	3/8	NUM
ejpam-5049	392	4	simpson	simpson	NOUN
ejpam-5049	392	5	’	'	PUNCT
ejpam-5049	392	6	1/3	1/3	PROPN
ejpam-5049	392	7	:	:	PUNCT
ejpam-5049	392	8	red	red	ADJ
ejpam-5049	392	9	solid	solid	ADJ
ejpam-5049	392	10	color	color	NOUN
ejpam-5049	392	11	)	)	PUNCT
ejpam-5049	392	12	.	.	PUNCT
ejpam-5049	393	1	khaled	khaled	PROPN
ejpam-5049	393	2	m.	m.	PROPN
ejpam-5049	393	3	saad	saad	PROPN
ejpam-5049	393	4	,	,	PUNCT
ejpam-5049	393	5	m.	m.	NOUN
ejpam-5049	393	6	q.	q.	PROPN
ejpam-5049	393	7	khirallah	khirallah	PROPN
ejpam-5049	393	8	/	/	SYM
ejpam-5049	393	9	eur	eur	PROPN
ejpam-5049	393	10	.	.	PUNCT
ejpam-5049	394	1	j.	j.	PROPN
ejpam-5049	394	2	pure	pure	PROPN
ejpam-5049	394	3	appl	appl	PROPN
ejpam-5049	394	4	.	.	PROPN
ejpam-5049	394	5	math	math	PROPN
ejpam-5049	394	6	,	,	PUNCT
ejpam-5049	394	7	17	17	NUM
ejpam-5049	394	8	(	(	PUNCT
ejpam-5049	394	9	1	1	NUM
ejpam-5049	394	10	)	)	PUNCT
ejpam-5049	394	11	(	(	PUNCT
ejpam-5049	394	12	2024	2024	NUM
ejpam-5049	394	13	)	)	PUNCT
ejpam-5049	394	14	,	,	PUNCT
ejpam-5049	394	15	477	477	NUM
ejpam-5049	394	16	-	-	SYM
ejpam-5049	394	17	503	503	NUM
ejpam-5049	394	18	496	496	NUM
ejpam-5049	394	19	0.0	0.0	NUM
ejpam-5049	394	20	0.2	0.2	NUM
ejpam-5049	394	21	0.4	0.4	NUM
ejpam-5049	394	22	0.6	0.6	NUM
ejpam-5049	394	23	0.8	0.8	NUM
ejpam-5049	394	24	1.0	1.0	NUM
ejpam-5049	394	25	1.0	1.0	NUM
ejpam-5049	394	26	1.5	1.5	NUM
ejpam-5049	394	27	2.0	2.0	NUM
ejpam-5049	394	28	2.5	2.5	NUM
ejpam-5049	394	29	3.0	3.0	NUM
ejpam-5049	394	30	3.5	3.5	NUM
ejpam-5049	394	31	4.0	4.0	NUM
ejpam-5049	394	32	4.5	4.5	NUM
ejpam-5049	394	33	β	β	PROPN
ejpam-5049	394	34	φ	φ	PROPN
ejpam-5049	394	35	hβl	hβl	PROPN
ejpam-5049	394	36	hal	hal	PROPN
ejpam-5049	394	37	0.0	0.0	NUM
ejpam-5049	395	1	0.2	0.2	NUM
ejpam-5049	395	2	0.4	0.4	NUM
ejpam-5049	395	3	0.6	0.6	NUM
ejpam-5049	395	4	0.8	0.8	NUM
ejpam-5049	395	5	1.0	1.0	NUM
ejpam-5049	395	6	0.00000	0.00000	NUM
ejpam-5049	395	7	0.00005	0.00005	NUM
ejpam-5049	395	8	0.00010	0.00010	NUM
ejpam-5049	395	9	0.00015	0.00015	NUM
ejpam-5049	395	10	0.00020	0.00020	NUM
ejpam-5049	395	11	0.00025	0.00025	NUM
ejpam-5049	395	12	0.00030	0.00030	NUM
ejpam-5049	395	13	0.00035	0.00035	NUM
ejpam-5049	395	14	β	β	PART
ejpam-5049	395	15	 	 	SPACE
ejpam-5049	395	16	φh	φh	VERB
ejpam-5049	395	17	β	β	X
ejpam-5049	395	18	l	l	X
ejpam-5049	395	19	-	-	PROPN
ejpam-5049	395	20	φ	φ	PROPN
ejpam-5049	395	21	7	7	NUM
ejpam-5049	395	22	hβl	hβl	NOUN
ejpam-5049	395	23	  	  	SPACE
ejpam-5049	395	24	hbl	hbl	PROPN
ejpam-5049	395	25	trapezoidal	trapezoidal	PROPN
ejpam-5049	395	26	simpson	simpson	PROPN
ejpam-5049	395	27	'	'	PART
ejpam-5049	395	28	3	3	NUM
ejpam-5049	395	29	8	8	NUM
ejpam-5049	395	30	simpson	simpson	PROPN
ejpam-5049	395	31	'	'	PART
ejpam-5049	395	32	1	1	NUM
ejpam-5049	395	33	3	3	NUM
ejpam-5049	395	34	figure	figure	NOUN
ejpam-5049	395	35	3	3	NUM
ejpam-5049	395	36	:	:	PUNCT
ejpam-5049	395	37	(	(	PUNCT
ejpam-5049	395	38	a	a	X
ejpam-5049	395	39	)	)	PUNCT
ejpam-5049	395	40	combining	combine	VERB
ejpam-5049	395	41	approximate	approximate	ADJ
ejpam-5049	395	42	solutions	solution	NOUN
ejpam-5049	395	43	with	with	ADP
ejpam-5049	395	44	the	the	DET
ejpam-5049	395	45	exact	exact	ADJ
ejpam-5049	395	46	solution	solution	NOUN
ejpam-5049	395	47	for	for	ADP
ejpam-5049	395	48	different	different	ADJ
ejpam-5049	395	49	values	value	NOUN
ejpam-5049	395	50	of	of	ADP
ejpam-5049	395	51	alpha	alpha	NOUN
ejpam-5049	395	52	for	for	ADP
ejpam-5049	395	53	example	example	NOUN
ejpam-5049	395	54	2	2	NUM
ejpam-5049	395	55	.	.	PUNCT
ejpam-5049	395	56	(	(	PUNCT
ejpam-5049	395	57	red	red	ADJ
ejpam-5049	395	58	solid	solid	ADJ
ejpam-5049	395	59	color	color	NOUN
ejpam-5049	395	60	:	:	PUNCT
ejpam-5049	395	61	α	α	NOUN
ejpam-5049	395	62	=	=	NOUN
ejpam-5049	395	63	0.8	0.8	NUM
ejpam-5049	395	64	;	;	PUNCT
ejpam-5049	395	65	blue	blue	ADJ
ejpam-5049	395	66	solid	solid	ADJ
ejpam-5049	395	67	color	color	NOUN
ejpam-5049	395	68	:	:	PUNCT
ejpam-5049	395	69	α	α	X
ejpam-5049	395	70	=	=	NOUN
ejpam-5049	395	71	0.9	0.9	NUM
ejpam-5049	395	72	;	;	PUNCT
ejpam-5049	395	73	black	black	ADJ
ejpam-5049	395	74	solid	solid	ADJ
ejpam-5049	395	75	color	color	NOUN
ejpam-5049	395	76	:	:	PUNCT
ejpam-5049	395	77	α	α	X
ejpam-5049	395	78	=	=	SYM
ejpam-5049	395	79	1	1	NUM
ejpam-5049	395	80	;	;	PUNCT
ejpam-5049	395	81	green	green	ADJ
ejpam-5049	395	82	dashed	dash	VERB
ejpam-5049	395	83	color	color	NOUN
ejpam-5049	395	84	:	:	PUNCT
ejpam-5049	395	85	exact	exact	ADJ
ejpam-5049	395	86	solution	solution	NOUN
ejpam-5049	395	87	)	)	PUNCT
ejpam-5049	395	88	.	.	PUNCT
ejpam-5049	396	1	(	(	PUNCT
ejpam-5049	396	2	b	b	X
ejpam-5049	396	3	)	)	PUNCT
ejpam-5049	396	4	the	the	DET
ejpam-5049	396	5	absolute	absolute	ADJ
ejpam-5049	396	6	error	error	NOUN
ejpam-5049	396	7	between	between	ADP
ejpam-5049	396	8	the	the	DET
ejpam-5049	396	9	approximate	approximate	ADJ
ejpam-5049	396	10	solutions	solution	NOUN
ejpam-5049	396	11	and	and	CCONJ
ejpam-5049	396	12	the	the	DET
ejpam-5049	396	13	analytical	analytical	ADJ
ejpam-5049	396	14	solution	solution	NOUN
ejpam-5049	396	15	for	for	ADP
ejpam-5049	396	16	example	example	NOUN
ejpam-5049	396	17	2	2	NUM
ejpam-5049	396	18	.	.	PUNCT
ejpam-5049	396	19	khaled	khaled	PROPN
ejpam-5049	396	20	m.	m.	PROPN
ejpam-5049	396	21	saad	saad	PROPN
ejpam-5049	396	22	,	,	PUNCT
ejpam-5049	396	23	m.	m.	NOUN
ejpam-5049	396	24	q.	q.	PROPN
ejpam-5049	396	25	khirallah	khirallah	PROPN
ejpam-5049	396	26	/	/	SYM
ejpam-5049	396	27	eur	eur	PROPN
ejpam-5049	396	28	.	.	PUNCT
ejpam-5049	397	1	j.	j.	PROPN
ejpam-5049	397	2	pure	pure	PROPN
ejpam-5049	397	3	appl	appl	PROPN
ejpam-5049	397	4	.	.	PROPN
ejpam-5049	397	5	math	math	PROPN
ejpam-5049	397	6	,	,	PUNCT
ejpam-5049	397	7	17	17	NUM
ejpam-5049	397	8	(	(	PUNCT
ejpam-5049	397	9	1	1	NUM
ejpam-5049	397	10	)	)	PUNCT
ejpam-5049	397	11	(	(	PUNCT
ejpam-5049	397	12	2024	2024	NUM
ejpam-5049	397	13	)	)	PUNCT
ejpam-5049	397	14	,	,	PUNCT
ejpam-5049	397	15	477	477	NUM
ejpam-5049	397	16	-	-	SYM
ejpam-5049	397	17	503	503	NUM
ejpam-5049	397	18	497	497	NUM
ejpam-5049	397	19	0.0	0.0	NUM
ejpam-5049	397	20	0.2	0.2	NUM
ejpam-5049	397	21	0.4	0.4	NUM
ejpam-5049	397	22	0.6	0.6	NUM
ejpam-5049	397	23	0.8	0.8	NUM
ejpam-5049	397	24	1.0	1.0	NUM
ejpam-5049	397	25	0.000	0.000	NUM
ejpam-5049	397	26	0.001	0.001	NUM
ejpam-5049	397	27	0.002	0.002	NUM
ejpam-5049	397	28	0.003	0.003	NUM
ejpam-5049	397	29	0.004	0.004	NUM
ejpam-5049	397	30	0.005	0.005	NUM
ejpam-5049	397	31	0.006	0.006	NUM
ejpam-5049	397	32	0.007	0.007	NUM
ejpam-5049	397	33	β	β	SYM
ejpam-5049	397	34	 	 	SPACE
ejpam-5049	397	35	φ	φ	PROPN
ejpam-5049	397	36	6	6	NUM
ejpam-5049	397	37	hβl	hβl	PROPN
ejpam-5049	397	38	φ	φ	PROPN
ejpam-5049	397	39	7	7	NUM
ejpam-5049	397	40	hβl	hβl	NOUN
ejpam-5049	397	41	  	  	SPACE
ejpam-5049	397	42	figure	figure	NOUN
ejpam-5049	397	43	4	4	NUM
ejpam-5049	397	44	:	:	PUNCT
ejpam-5049	397	45	plotting	plot	VERB
ejpam-5049	397	46	the	the	DET
ejpam-5049	397	47	difference	difference	NOUN
ejpam-5049	397	48	between	between	ADP
ejpam-5049	397	49	the	the	DET
ejpam-5049	397	50	two	two	NUM
ejpam-5049	397	51	step	step	NOUN
ejpam-5049	397	52	of	of	ADP
ejpam-5049	397	53	the	the	DET
ejpam-5049	397	54	approximate	approximate	ADJ
ejpam-5049	397	55	solutions	solution	NOUN
ejpam-5049	397	56	with	with	ADP
ejpam-5049	397	57	α	α	NOUN
ejpam-5049	397	58	=	=	SYM
ejpam-5049	397	59	0.8	0.8	NUM
ejpam-5049	397	60	and	and	CCONJ
ejpam-5049	397	61	m	m	VERB
ejpam-5049	397	62	=	=	NOUN
ejpam-5049	397	63	6	6	NUM
ejpam-5049	397	64	and	and	CCONJ
ejpam-5049	397	65	m	m	VERB
ejpam-5049	397	66	=	=	NOUN
ejpam-5049	397	67	7	7	NUM
ejpam-5049	397	68	for	for	ADP
ejpam-5049	397	69	example	example	NOUN
ejpam-5049	397	70	2	2	NUM
ejpam-5049	397	71	.	.	PUNCT
ejpam-5049	398	1	(	(	PUNCT
ejpam-5049	398	2	black	black	ADJ
ejpam-5049	398	3	dashed	dash	VERB
ejpam-5049	398	4	color	color	NOUN
ejpam-5049	398	5	:	:	PUNCT
ejpam-5049	398	6	trapezoidal	trapezoidal	ADJ
ejpam-5049	398	7	green	green	PROPN
ejpam-5049	398	8	dashed	dash	VERB
ejpam-5049	398	9	color	color	NOUN
ejpam-5049	398	10	:	:	PUNCT
ejpam-5049	399	1	simpson	simpson	PROPN
ejpam-5049	399	2	’	'	PUNCT
ejpam-5049	399	3	3/8	3/8	NUM
ejpam-5049	399	4	simpson	simpson	NOUN
ejpam-5049	399	5	’	'	PUNCT
ejpam-5049	399	6	1/3	1/3	PROPN
ejpam-5049	399	7	:	:	PUNCT
ejpam-5049	399	8	red	red	ADJ
ejpam-5049	399	9	solid	solid	ADJ
ejpam-5049	399	10	color	color	NOUN
ejpam-5049	399	11	)	)	PUNCT
ejpam-5049	399	12	.	.	PUNCT
ejpam-5049	400	1	khaled	khaled	PROPN
ejpam-5049	400	2	m.	m.	PROPN
ejpam-5049	400	3	saad	saad	PROPN
ejpam-5049	400	4	,	,	PUNCT
ejpam-5049	400	5	m.	m.	NOUN
ejpam-5049	400	6	q.	q.	PROPN
ejpam-5049	400	7	khirallah	khirallah	PROPN
ejpam-5049	400	8	/	/	SYM
ejpam-5049	400	9	eur	eur	PROPN
ejpam-5049	400	10	.	.	PUNCT
ejpam-5049	401	1	j.	j.	PROPN
ejpam-5049	401	2	pure	pure	PROPN
ejpam-5049	401	3	appl	appl	PROPN
ejpam-5049	401	4	.	.	PROPN
ejpam-5049	401	5	math	math	PROPN
ejpam-5049	401	6	,	,	PUNCT
ejpam-5049	401	7	17	17	NUM
ejpam-5049	401	8	(	(	PUNCT
ejpam-5049	401	9	1	1	NUM
ejpam-5049	401	10	)	)	PUNCT
ejpam-5049	401	11	(	(	PUNCT
ejpam-5049	401	12	2024	2024	NUM
ejpam-5049	401	13	)	)	PUNCT
ejpam-5049	401	14	,	,	PUNCT
ejpam-5049	401	15	477	477	NUM
ejpam-5049	401	16	-	-	SYM
ejpam-5049	401	17	503	503	NUM
ejpam-5049	401	18	498	498	NUM
ejpam-5049	401	19	0.0	0.0	NUM
ejpam-5049	401	20	0.2	0.2	NUM
ejpam-5049	401	21	0.4	0.4	NUM
ejpam-5049	401	22	0.6	0.6	NUM
ejpam-5049	401	23	0.8	0.8	NUM
ejpam-5049	401	24	1.0	1.0	NUM
ejpam-5049	401	25	1.0	1.0	NUM
ejpam-5049	401	26	1.2	1.2	NUM
ejpam-5049	401	27	1.4	1.4	NUM
ejpam-5049	401	28	1.6	1.6	NUM
ejpam-5049	401	29	1.8	1.8	NUM
ejpam-5049	401	30	2.0	2.0	NUM
ejpam-5049	401	31	β	β	X
ejpam-5049	401	32	φ	φ	X
ejpam-5049	401	33	1	1	NUM
ejpam-5049	401	34	hβl	hβl	PROPN
ejpam-5049	401	35	hal	hal	PROPN
ejpam-5049	401	36	0.0	0.0	NUM
ejpam-5049	401	37	0.2	0.2	NUM
ejpam-5049	401	38	0.4	0.4	NUM
ejpam-5049	401	39	0.6	0.6	NUM
ejpam-5049	401	40	0.8	0.8	NUM
ejpam-5049	401	41	1.0	1.0	NUM
ejpam-5049	401	42	0.0000	0.0000	NUM
ejpam-5049	401	43	0.00002	0.00002	NUM
ejpam-5049	401	44	0.00004	0.00004	NUM
ejpam-5049	401	45	0.00006	0.00006	NUM
ejpam-5049	401	46	0.00008	0.00008	NUM
ejpam-5049	401	47	0.0001	0.0001	NUM
ejpam-5049	401	48	β	β	NOUN
ejpam-5049	401	49	 	 	SPACE
ejpam-5049	401	50	φ	φ	PROPN
ejpam-5049	401	51	1	1	NUM
ejpam-5049	401	52	hβl	hβl	PROPN
ejpam-5049	401	53	φ	φ	PROPN
ejpam-5049	401	54	1	1	NUM
ejpam-5049	401	55	,	,	PUNCT
ejpam-5049	401	56	7	7	NUM
ejpam-5049	401	57	hβl	hβl	NOUN
ejpam-5049	401	58	  	  	SPACE
ejpam-5049	401	59	hbl	hbl	PROPN
ejpam-5049	401	60	trapezoidal	trapezoidal	PROPN
ejpam-5049	401	61	simpson	simpson	PROPN
ejpam-5049	401	62	'	'	PART
ejpam-5049	401	63	1	1	NUM
ejpam-5049	401	64	3	3	NUM
ejpam-5049	401	65	simpson	simpson	PROPN
ejpam-5049	401	66	'	'	PART
ejpam-5049	401	67	3	3	NUM
ejpam-5049	401	68	8	8	NUM
ejpam-5049	401	69	figure	figure	NOUN
ejpam-5049	401	70	5	5	NUM
ejpam-5049	401	71	:	:	PUNCT
ejpam-5049	401	72	(	(	PUNCT
ejpam-5049	401	73	a	a	X
ejpam-5049	401	74	)	)	PUNCT
ejpam-5049	401	75	combining	combine	VERB
ejpam-5049	401	76	approximate	approximate	ADJ
ejpam-5049	401	77	solutions	solution	NOUN
ejpam-5049	401	78	with	with	ADP
ejpam-5049	401	79	the	the	DET
ejpam-5049	401	80	exact	exact	ADJ
ejpam-5049	401	81	solution	solution	NOUN
ejpam-5049	401	82	for	for	ADP
ejpam-5049	401	83	different	different	ADJ
ejpam-5049	401	84	values	value	NOUN
ejpam-5049	401	85	of	of	ADP
ejpam-5049	401	86	alpha	alpha	NOUN
ejpam-5049	401	87	for	for	ADP
ejpam-5049	401	88	example	example	NOUN
ejpam-5049	401	89	3	3	NUM
ejpam-5049	401	90	.	.	PUNCT
ejpam-5049	401	91	(	(	PUNCT
ejpam-5049	401	92	red	red	ADJ
ejpam-5049	401	93	solid	solid	ADJ
ejpam-5049	401	94	color	color	NOUN
ejpam-5049	401	95	:	:	PUNCT
ejpam-5049	401	96	α	α	NOUN
ejpam-5049	401	97	=	=	NOUN
ejpam-5049	401	98	0.8	0.8	NUM
ejpam-5049	401	99	;	;	PUNCT
ejpam-5049	401	100	blue	blue	ADJ
ejpam-5049	401	101	solid	solid	ADJ
ejpam-5049	401	102	color	color	NOUN
ejpam-5049	401	103	:	:	PUNCT
ejpam-5049	401	104	α	α	X
ejpam-5049	401	105	=	=	NOUN
ejpam-5049	401	106	0.9	0.9	NUM
ejpam-5049	401	107	;	;	PUNCT
ejpam-5049	401	108	black	black	ADJ
ejpam-5049	401	109	solid	solid	ADJ
ejpam-5049	401	110	color	color	NOUN
ejpam-5049	401	111	:	:	PUNCT
ejpam-5049	401	112	α	α	X
ejpam-5049	401	113	=	=	SYM
ejpam-5049	401	114	1	1	NUM
ejpam-5049	401	115	;	;	PUNCT
ejpam-5049	401	116	green	green	ADJ
ejpam-5049	401	117	dashed	dash	VERB
ejpam-5049	401	118	color	color	NOUN
ejpam-5049	401	119	:	:	PUNCT
ejpam-5049	401	120	exact	exact	ADJ
ejpam-5049	401	121	solution	solution	NOUN
ejpam-5049	401	122	)	)	PUNCT
ejpam-5049	401	123	.	.	PUNCT
ejpam-5049	402	1	(	(	PUNCT
ejpam-5049	402	2	b	b	X
ejpam-5049	402	3	)	)	PUNCT
ejpam-5049	402	4	the	the	DET
ejpam-5049	402	5	absolute	absolute	ADJ
ejpam-5049	402	6	error	error	NOUN
ejpam-5049	402	7	between	between	ADP
ejpam-5049	402	8	the	the	DET
ejpam-5049	402	9	approximate	approximate	ADJ
ejpam-5049	402	10	solutions	solution	NOUN
ejpam-5049	402	11	and	and	CCONJ
ejpam-5049	402	12	the	the	DET
ejpam-5049	402	13	analytical	analytical	ADJ
ejpam-5049	402	14	solution	solution	NOUN
ejpam-5049	402	15	for	for	ADP
ejpam-5049	402	16	example	example	NOUN
ejpam-5049	402	17	3	3	NUM
ejpam-5049	402	18	.	.	PUNCT
ejpam-5049	402	19	khaled	khaled	PROPN
ejpam-5049	402	20	m.	m.	PROPN
ejpam-5049	402	21	saad	saad	PROPN
ejpam-5049	402	22	,	,	PUNCT
ejpam-5049	402	23	m.	m.	NOUN
ejpam-5049	402	24	q.	q.	PROPN
ejpam-5049	402	25	khirallah	khirallah	PROPN
ejpam-5049	402	26	/	/	SYM
ejpam-5049	402	27	eur	eur	PROPN
ejpam-5049	402	28	.	.	PUNCT
ejpam-5049	403	1	j.	j.	PROPN
ejpam-5049	403	2	pure	pure	PROPN
ejpam-5049	403	3	appl	appl	PROPN
ejpam-5049	403	4	.	.	PROPN
ejpam-5049	403	5	math	math	PROPN
ejpam-5049	403	6	,	,	PUNCT
ejpam-5049	403	7	17	17	NUM
ejpam-5049	403	8	(	(	PUNCT
ejpam-5049	403	9	1	1	NUM
ejpam-5049	403	10	)	)	PUNCT
ejpam-5049	403	11	(	(	PUNCT
ejpam-5049	403	12	2024	2024	NUM
ejpam-5049	403	13	)	)	PUNCT
ejpam-5049	403	14	,	,	PUNCT
ejpam-5049	403	15	477	477	NUM
ejpam-5049	403	16	-	-	SYM
ejpam-5049	403	17	503	503	NUM
ejpam-5049	403	18	499	499	NUM
ejpam-5049	403	19	0.0	0.0	NUM
ejpam-5049	403	20	0.2	0.2	NUM
ejpam-5049	403	21	0.4	0.4	NUM
ejpam-5049	403	22	0.6	0.6	NUM
ejpam-5049	403	23	0.8	0.8	NUM
ejpam-5049	403	24	1.0	1.0	NUM
ejpam-5049	403	25	-0.2	-0.2	NUM
ejpam-5049	403	26	0.0	0.0	NUM
ejpam-5049	403	27	0.2	0.2	NUM
ejpam-5049	403	28	0.4	0.4	NUM
ejpam-5049	403	29	0.6	0.6	NUM
ejpam-5049	403	30	0.8	0.8	NUM
ejpam-5049	403	31	1.0	1.0	NUM
ejpam-5049	403	32	β	β	X
ejpam-5049	403	33	φ	φ	X
ejpam-5049	403	34	2	2	NUM
ejpam-5049	403	35	hβl	hβl	NOUN
ejpam-5049	403	36	hbl	hbl	NOUN
ejpam-5049	403	37	0.0	0.0	NUM
ejpam-5049	403	38	0.2	0.2	NUM
ejpam-5049	403	39	0.4	0.4	NUM
ejpam-5049	403	40	0.6	0.6	NUM
ejpam-5049	403	41	0.8	0.8	NUM
ejpam-5049	403	42	1.0	1.0	NUM
ejpam-5049	403	43	0.00000	0.00000	NUM
ejpam-5049	403	44	0.00005	0.00005	NUM
ejpam-5049	403	45	0.00010	0.00010	NUM
ejpam-5049	403	46	0.00015	0.00015	NUM
ejpam-5049	403	47	0.00020	0.00020	NUM
ejpam-5049	403	48	β	β	X
ejpam-5049	403	49	 	 	SPACE
ejpam-5049	403	50	φ	φ	PROPN
ejpam-5049	403	51	2	2	NUM
ejpam-5049	403	52	hβl	hβl	X
ejpam-5049	403	53	φ	φ	PROPN
ejpam-5049	403	54	2	2	NUM
ejpam-5049	403	55	,	,	PUNCT
ejpam-5049	403	56	7	7	NUM
ejpam-5049	403	57	hβl	hβl	NOUN
ejpam-5049	403	58	  	  	SPACE
ejpam-5049	403	59	hbl	hbl	PROPN
ejpam-5049	403	60	trapezoidal	trapezoidal	PROPN
ejpam-5049	403	61	simpson	simpson	PROPN
ejpam-5049	403	62	'	'	PART
ejpam-5049	403	63	1	1	NUM
ejpam-5049	403	64	3	3	NUM
ejpam-5049	403	65	simpson	simpson	PROPN
ejpam-5049	403	66	'	'	PART
ejpam-5049	403	67	3	3	NUM
ejpam-5049	403	68	8	8	NUM
ejpam-5049	403	69	figure	figure	NOUN
ejpam-5049	403	70	6	6	NUM
ejpam-5049	403	71	:	:	PUNCT
ejpam-5049	403	72	(	(	PUNCT
ejpam-5049	403	73	a	a	X
ejpam-5049	403	74	)	)	PUNCT
ejpam-5049	403	75	combining	combine	VERB
ejpam-5049	403	76	approximate	approximate	ADJ
ejpam-5049	403	77	solutions	solution	NOUN
ejpam-5049	403	78	with	with	ADP
ejpam-5049	403	79	the	the	DET
ejpam-5049	403	80	exact	exact	ADJ
ejpam-5049	403	81	solution	solution	NOUN
ejpam-5049	403	82	for	for	ADP
ejpam-5049	403	83	different	different	ADJ
ejpam-5049	403	84	values	value	NOUN
ejpam-5049	403	85	of	of	ADP
ejpam-5049	403	86	alpha	alpha	NOUN
ejpam-5049	403	87	for	for	ADP
ejpam-5049	403	88	example	example	NOUN
ejpam-5049	403	89	3	3	NUM
ejpam-5049	403	90	.	.	PUNCT
ejpam-5049	403	91	(	(	PUNCT
ejpam-5049	403	92	red	red	ADJ
ejpam-5049	403	93	solid	solid	ADJ
ejpam-5049	403	94	color	color	NOUN
ejpam-5049	403	95	:	:	PUNCT
ejpam-5049	403	96	α	α	NOUN
ejpam-5049	403	97	=	=	NOUN
ejpam-5049	403	98	0.8	0.8	NUM
ejpam-5049	403	99	;	;	PUNCT
ejpam-5049	403	100	blue	blue	ADJ
ejpam-5049	403	101	solid	solid	ADJ
ejpam-5049	403	102	color	color	NOUN
ejpam-5049	403	103	:	:	PUNCT
ejpam-5049	403	104	α	α	X
ejpam-5049	403	105	=	=	NOUN
ejpam-5049	403	106	0.9	0.9	NUM
ejpam-5049	403	107	;	;	PUNCT
ejpam-5049	403	108	black	black	ADJ
ejpam-5049	403	109	solid	solid	ADJ
ejpam-5049	403	110	color	color	NOUN
ejpam-5049	403	111	:	:	PUNCT
ejpam-5049	403	112	α	α	X
ejpam-5049	403	113	=	=	SYM
ejpam-5049	403	114	1	1	NUM
ejpam-5049	403	115	;	;	PUNCT
ejpam-5049	403	116	green	green	ADJ
ejpam-5049	403	117	dashed	dash	VERB
ejpam-5049	403	118	color	color	NOUN
ejpam-5049	403	119	:	:	PUNCT
ejpam-5049	403	120	exact	exact	ADJ
ejpam-5049	403	121	solution	solution	NOUN
ejpam-5049	403	122	)	)	PUNCT
ejpam-5049	403	123	.	.	PUNCT
ejpam-5049	404	1	(	(	PUNCT
ejpam-5049	404	2	b	b	X
ejpam-5049	404	3	)	)	PUNCT
ejpam-5049	404	4	the	the	DET
ejpam-5049	404	5	absolute	absolute	ADJ
ejpam-5049	404	6	error	error	NOUN
ejpam-5049	404	7	between	between	ADP
ejpam-5049	404	8	the	the	DET
ejpam-5049	404	9	approximate	approximate	ADJ
ejpam-5049	404	10	solutions	solution	NOUN
ejpam-5049	404	11	and	and	CCONJ
ejpam-5049	404	12	the	the	DET
ejpam-5049	404	13	analytical	analytical	ADJ
ejpam-5049	404	14	solution	solution	NOUN
ejpam-5049	404	15	for	for	ADP
ejpam-5049	404	16	example	example	NOUN
ejpam-5049	404	17	3	3	NUM
ejpam-5049	404	18	.	.	PUNCT
ejpam-5049	404	19	khaled	khaled	PROPN
ejpam-5049	404	20	m.	m.	PROPN
ejpam-5049	404	21	saad	saad	PROPN
ejpam-5049	404	22	,	,	PUNCT
ejpam-5049	404	23	m.	m.	NOUN
ejpam-5049	404	24	q.	q.	PROPN
ejpam-5049	404	25	khirallah	khirallah	PROPN
ejpam-5049	404	26	/	/	SYM
ejpam-5049	404	27	eur	eur	PROPN
ejpam-5049	404	28	.	.	PUNCT
ejpam-5049	405	1	j.	j.	PROPN
ejpam-5049	405	2	pure	pure	PROPN
ejpam-5049	405	3	appl	appl	PROPN
ejpam-5049	405	4	.	.	PROPN
ejpam-5049	405	5	math	math	PROPN
ejpam-5049	405	6	,	,	PUNCT
ejpam-5049	405	7	17	17	NUM
ejpam-5049	405	8	(	(	PUNCT
ejpam-5049	405	9	1	1	NUM
ejpam-5049	405	10	)	)	PUNCT
ejpam-5049	405	11	(	(	PUNCT
ejpam-5049	405	12	2024	2024	NUM
ejpam-5049	405	13	)	)	PUNCT
ejpam-5049	405	14	,	,	PUNCT
ejpam-5049	405	15	477	477	NUM
ejpam-5049	405	16	-	-	SYM
ejpam-5049	405	17	503	503	NUM
ejpam-5049	405	18	500	500	NUM
ejpam-5049	405	19	0.0	0.0	NUM
ejpam-5049	405	20	0.2	0.2	NUM
ejpam-5049	405	21	0.4	0.4	NUM
ejpam-5049	405	22	0.6	0.6	NUM
ejpam-5049	405	23	0.8	0.8	NUM
ejpam-5049	405	24	1.0	1.0	NUM
ejpam-5049	405	25	0.0000	0.0000	NUM
ejpam-5049	405	26	0.0002	0.0002	NUM
ejpam-5049	405	27	0.0004	0.0004	NUM
ejpam-5049	405	28	0.0006	0.0006	NUM
ejpam-5049	405	29	0.0008	0.0008	NUM
ejpam-5049	405	30	0.0010	0.0010	NUM
ejpam-5049	405	31	0.0012	0.0012	NUM
ejpam-5049	405	32	0.0014	0.0014	NUM
ejpam-5049	405	33	β	β	SYM
ejpam-5049	405	34	 	 	SPACE
ejpam-5049	405	35	φ	φ	PROPN
ejpam-5049	405	36	1	1	NUM
ejpam-5049	405	37	,	,	PUNCT
ejpam-5049	405	38	6	6	NUM
ejpam-5049	405	39	hβl	hβl	NOUN
ejpam-5049	405	40	φ	φ	PROPN
ejpam-5049	405	41	1	1	NUM
ejpam-5049	405	42	,	,	PUNCT
ejpam-5049	405	43	7	7	NUM
ejpam-5049	405	44	hβl	hβl	NOUN
ejpam-5049	405	45	  	  	SPACE
ejpam-5049	405	46	hal	hal	NOUN
ejpam-5049	405	47	0.0	0.0	NUM
ejpam-5049	405	48	0.2	0.2	NUM
ejpam-5049	405	49	0.4	0.4	NUM
ejpam-5049	405	50	0.6	0.6	NUM
ejpam-5049	405	51	0.8	0.8	NUM
ejpam-5049	405	52	1.0	1.0	NUM
ejpam-5049	405	53	0.0000	0.0000	NUM
ejpam-5049	405	54	0.0005	0.0005	NUM
ejpam-5049	405	55	0.0010	0.0010	NUM
ejpam-5049	405	56	0.0015	0.0015	NUM
ejpam-5049	405	57	β	β	SYM
ejpam-5049	405	58	 	 	SPACE
ejpam-5049	405	59	φ	φ	PROPN
ejpam-5049	405	60	2	2	NUM
ejpam-5049	405	61	,	,	PUNCT
ejpam-5049	405	62	6	6	NUM
ejpam-5049	405	63	hβl	hβl	NOUN
ejpam-5049	405	64	φ	φ	PROPN
ejpam-5049	405	65	2	2	NUM
ejpam-5049	405	66	,	,	PUNCT
ejpam-5049	405	67	7	7	NUM
ejpam-5049	405	68	hβl	hβl	NOUN
ejpam-5049	405	69	  	  	SPACE
ejpam-5049	405	70	hbl	hbl	NOUN
ejpam-5049	405	71	figure	figure	NOUN
ejpam-5049	405	72	7	7	NUM
ejpam-5049	405	73	:	:	PUNCT
ejpam-5049	405	74	(	(	PUNCT
ejpam-5049	405	75	a	a	X
ejpam-5049	405	76	)	)	PUNCT
ejpam-5049	405	77	plotting	plot	VERB
ejpam-5049	405	78	the	the	DET
ejpam-5049	405	79	difference	difference	NOUN
ejpam-5049	405	80	between	between	ADP
ejpam-5049	405	81	the	the	DET
ejpam-5049	405	82	two	two	NUM
ejpam-5049	405	83	step	step	NOUN
ejpam-5049	405	84	of	of	ADP
ejpam-5049	405	85	the	the	DET
ejpam-5049	405	86	approximate	approximate	ADJ
ejpam-5049	405	87	solutions	solution	NOUN
ejpam-5049	405	88	u	u	NOUN
ejpam-5049	405	89	with	with	ADP
ejpam-5049	405	90	α	α	NOUN
ejpam-5049	405	91	=	=	SYM
ejpam-5049	405	92	0.8	0.8	NUM
ejpam-5049	405	93	and	and	CCONJ
ejpam-5049	405	94	m	m	VERB
ejpam-5049	405	95	=	=	NOUN
ejpam-5049	405	96	6	6	NUM
ejpam-5049	405	97	and	and	CCONJ
ejpam-5049	405	98	m	m	VERB
ejpam-5049	405	99	=	=	NOUN
ejpam-5049	405	100	7	7	NUM
ejpam-5049	405	101	for	for	ADP
ejpam-5049	405	102	example	example	NOUN
ejpam-5049	405	103	3	3	NUM
ejpam-5049	405	104	.	.	PUNCT
ejpam-5049	406	1	(	(	PUNCT
ejpam-5049	406	2	black	black	ADJ
ejpam-5049	406	3	dashed	dash	VERB
ejpam-5049	406	4	color	color	NOUN
ejpam-5049	406	5	:	:	PUNCT
ejpam-5049	406	6	trapezoidal	trapezoidal	ADJ
ejpam-5049	406	7	green	green	PROPN
ejpam-5049	406	8	dashed	dash	VERB
ejpam-5049	406	9	color	color	NOUN
ejpam-5049	406	10	:	:	PUNCT
ejpam-5049	407	1	simpson	simpson	PROPN
ejpam-5049	407	2	’	'	PUNCT
ejpam-5049	407	3	3/8	3/8	NUM
ejpam-5049	407	4	simpson	simpson	NOUN
ejpam-5049	407	5	’	'	PUNCT
ejpam-5049	407	6	1/3	1/3	PROPN
ejpam-5049	407	7	:	:	PUNCT
ejpam-5049	407	8	red	red	ADJ
ejpam-5049	407	9	solid	solid	ADJ
ejpam-5049	407	10	color	color	NOUN
ejpam-5049	407	11	)	)	PUNCT
ejpam-5049	407	12	.	.	PUNCT
ejpam-5049	408	1	(	(	PUNCT
ejpam-5049	408	2	b	b	X
ejpam-5049	408	3	)	)	PUNCT
ejpam-5049	408	4	plotting	plot	VERB
ejpam-5049	408	5	the	the	DET
ejpam-5049	408	6	difference	difference	NOUN
ejpam-5049	408	7	between	between	ADP
ejpam-5049	408	8	the	the	DET
ejpam-5049	408	9	two	two	NUM
ejpam-5049	408	10	step	step	NOUN
ejpam-5049	408	11	of	of	ADP
ejpam-5049	408	12	the	the	DET
ejpam-5049	408	13	approximate	approximate	ADJ
ejpam-5049	408	14	solutions	solution	NOUN
ejpam-5049	408	15	v	v	NOUN
ejpam-5049	408	16	with	with	ADP
ejpam-5049	408	17	α	α	NOUN
ejpam-5049	408	18	=	=	SYM
ejpam-5049	408	19	0.8	0.8	NUM
ejpam-5049	408	20	and	and	CCONJ
ejpam-5049	408	21	m	m	VERB
ejpam-5049	408	22	=	=	NOUN
ejpam-5049	408	23	6	6	NUM
ejpam-5049	408	24	and	and	CCONJ
ejpam-5049	408	25	m	m	VERB
ejpam-5049	408	26	=	=	NOUN
ejpam-5049	408	27	7	7	NUM
ejpam-5049	408	28	for	for	ADP
ejpam-5049	408	29	example	example	NOUN
ejpam-5049	408	30	3	3	NUM
ejpam-5049	408	31	.	.	PUNCT
ejpam-5049	409	1	(	(	PUNCT
ejpam-5049	409	2	black	black	ADJ
ejpam-5049	409	3	dashed	dash	VERB
ejpam-5049	409	4	color	color	NOUN
ejpam-5049	409	5	:	:	PUNCT
ejpam-5049	409	6	trapezoidal	trapezoidal	ADJ
ejpam-5049	409	7	green	green	PROPN
ejpam-5049	409	8	dashed	dash	VERB
ejpam-5049	409	9	color	color	NOUN
ejpam-5049	409	10	:	:	PUNCT
ejpam-5049	410	1	simpson	simpson	PROPN
ejpam-5049	410	2	’	'	PUNCT
ejpam-5049	410	3	3/8	3/8	NUM
ejpam-5049	410	4	simpson	simpson	NOUN
ejpam-5049	410	5	’	'	PUNCT
ejpam-5049	410	6	1/3	1/3	PROPN
ejpam-5049	410	7	:	:	PUNCT
ejpam-5049	410	8	red	red	ADJ
ejpam-5049	410	9	solid	solid	ADJ
ejpam-5049	410	10	color	color	NOUN
ejpam-5049	410	11	)	)	PUNCT
ejpam-5049	410	12	.	.	PUNCT
ejpam-5049	411	1	references	reference	NOUN
ejpam-5049	411	2	501	501	NUM
ejpam-5049	411	3	5	5	NUM
ejpam-5049	411	4	.	.	PUNCT
ejpam-5049	412	1	conclusions	conclusion	NOUN
ejpam-5049	412	2	this	this	DET
ejpam-5049	412	3	study	study	NOUN
ejpam-5049	412	4	used	use	VERB
ejpam-5049	412	5	the	the	DET
ejpam-5049	412	6	caputo	caputo	PROPN
ejpam-5049	412	7	fractional	fractional	PROPN
ejpam-5049	412	8	derivative	derivative	NOUN
ejpam-5049	412	9	in	in	ADP
ejpam-5049	412	10	conjunction	conjunction	NOUN
ejpam-5049	412	11	with	with	ADP
ejpam-5049	412	12	the	the	DET
ejpam-5049	412	13	chebyshev	chebyshev	PROPN
ejpam-5049	412	14	spectral	spectral	ADJ
ejpam-5049	412	15	approach	approach	NOUN
ejpam-5049	412	16	to	to	PART
ejpam-5049	412	17	solve	solve	VERB
ejpam-5049	412	18	fractional	fractional	ADJ
ejpam-5049	412	19	integro	integro	ADJ
ejpam-5049	412	20	-	-	PUNCT
ejpam-5049	412	21	differential	differential	NOUN
ejpam-5049	412	22	equations	equation	NOUN
ejpam-5049	412	23	.	.	PUNCT
ejpam-5049	413	1	the	the	DET
ejpam-5049	413	2	trapezoidal	trapezoidal	NOUN
ejpam-5049	413	3	,	,	PUNCT
ejpam-5049	413	4	simpson	simpson	PROPN
ejpam-5049	413	5	’s	’s	PART
ejpam-5049	413	6	1/3	1/3	NUM
ejpam-5049	413	7	,	,	PUNCT
ejpam-5049	413	8	and	and	CCONJ
ejpam-5049	413	9	simpson	simpson	PROPN
ejpam-5049	413	10	’s	’s	PART
ejpam-5049	413	11	8/3	8/3	NUM
ejpam-5049	413	12	methods	method	NOUN
ejpam-5049	413	13	combined	combine	VERB
ejpam-5049	413	14	with	with	ADP
ejpam-5049	413	15	the	the	DET
ejpam-5049	413	16	properties	property	NOUN
ejpam-5049	413	17	of	of	ADP
ejpam-5049	413	18	chebyshev	chebyshev	NOUN
ejpam-5049	413	19	polynomials	polynomial	NOUN
ejpam-5049	413	20	to	to	PART
ejpam-5049	413	21	convert	convert	VERB
ejpam-5049	413	22	fractional	fractional	ADJ
ejpam-5049	413	23	integro	integro	ADJ
ejpam-5049	413	24	-	-	PUNCT
ejpam-5049	413	25	differential	differential	NOUN
ejpam-5049	413	26	equations	equation	NOUN
ejpam-5049	413	27	into	into	ADP
ejpam-5049	413	28	algebraic	algebraic	ADJ
ejpam-5049	413	29	equations	equation	NOUN
ejpam-5049	413	30	.	.	PUNCT
ejpam-5049	414	1	the	the	DET
ejpam-5049	414	2	resulting	result	VERB
ejpam-5049	414	3	equations	equation	NOUN
ejpam-5049	414	4	were	be	AUX
ejpam-5049	414	5	then	then	ADV
ejpam-5049	414	6	solved	solve	VERB
ejpam-5049	414	7	using	use	VERB
ejpam-5049	414	8	well	well	ADV
ejpam-5049	414	9	-	-	PUNCT
ejpam-5049	414	10	known	know	VERB
ejpam-5049	414	11	techniques	technique	NOUN
ejpam-5049	414	12	like	like	ADP
ejpam-5049	414	13	newton	newton	PROPN
ejpam-5049	414	14	’s	’s	PART
ejpam-5049	414	15	.	.	PUNCT
ejpam-5049	415	1	the	the	DET
ejpam-5049	415	2	numerical	numerical	ADJ
ejpam-5049	415	3	results	result	NOUN
ejpam-5049	415	4	was	be	AUX
ejpam-5049	415	5	carried	carry	VERB
ejpam-5049	415	6	out	out	ADP
ejpam-5049	415	7	using	use	VERB
ejpam-5049	415	8	the	the	DET
ejpam-5049	415	9	mathmetica	mathmetica	ADJ
ejpam-5049	415	10	soft	soft	ADJ
ejpam-5049	415	11	program	program	NOUN
ejpam-5049	415	12	.	.	PUNCT
ejpam-5049	416	1	we	we	PRON
ejpam-5049	416	2	suggest	suggest	AUX
ejpam-5049	416	3	emphasizing	emphasize	VERB
ejpam-5049	416	4	the	the	DET
ejpam-5049	416	5	incorporation	incorporation	NOUN
ejpam-5049	416	6	of	of	ADP
ejpam-5049	416	7	fractional	fractional	ADJ
ejpam-5049	416	8	space	space	NOUN
ejpam-5049	416	9	-	-	PUNCT
ejpam-5049	416	10	time	time	NOUN
ejpam-5049	416	11	derivatives	derivative	NOUN
ejpam-5049	416	12	in	in	ADP
ejpam-5049	416	13	our	our	PRON
ejpam-5049	416	14	forthcoming	forthcoming	ADJ
ejpam-5049	416	15	research	research	NOUN
ejpam-5049	416	16	.	.	PUNCT
ejpam-5049	417	1	additionally	additionally	ADV
ejpam-5049	417	2	,	,	PUNCT
ejpam-5049	417	3	we	we	PRON
ejpam-5049	417	4	plan	plan	VERB
ejpam-5049	417	5	to	to	PART
ejpam-5049	417	6	transform	transform	VERB
ejpam-5049	417	7	the	the	DET
ejpam-5049	417	8	fractional	fractional	ADJ
ejpam-5049	417	9	time	time	NOUN
ejpam-5049	417	10	derivative	derivative	ADJ
ejpam-5049	417	11	into	into	ADP
ejpam-5049	417	12	a	a	DET
ejpam-5049	417	13	discrete	discrete	ADJ
ejpam-5049	417	14	equation	equation	NOUN
ejpam-5049	417	15	using	use	VERB
ejpam-5049	417	16	unconventional	unconventional	ADJ
ejpam-5049	417	17	finite	finite	ADJ
ejpam-5049	417	18	-	-	PUNCT
ejpam-5049	417	19	difference	difference	NOUN
ejpam-5049	417	20	techniques	technique	NOUN
ejpam-5049	417	21	.	.	PUNCT
ejpam-5049	418	1	to	to	PART
ejpam-5049	418	2	streamline	streamline	VERB
ejpam-5049	418	3	intricate	intricate	ADJ
ejpam-5049	418	4	models	model	NOUN
ejpam-5049	418	5	into	into	ADP
ejpam-5049	418	6	a	a	DET
ejpam-5049	418	7	set	set	NOUN
ejpam-5049	418	8	of	of	ADP
ejpam-5049	418	9	solvable	solvable	ADJ
ejpam-5049	418	10	differential	differential	ADJ
ejpam-5049	418	11	equations	equation	NOUN
ejpam-5049	418	12	,	,	PUNCT
ejpam-5049	418	13	we	we	PRON
ejpam-5049	418	14	may	may	AUX
ejpam-5049	418	15	also	also	ADV
ejpam-5049	418	16	utilize	utilize	VERB
ejpam-5049	418	17	special	special	ADJ
ejpam-5049	418	18	additional	additional	ADJ
ejpam-5049	418	19	polynomial	polynomial	ADJ
ejpam-5049	418	20	functions	function	NOUN
ejpam-5049	418	21	[	[	X
ejpam-5049	418	22	2	2	NUM
ejpam-5049	418	23	,	,	PUNCT
ejpam-5049	418	24	6	6	NUM
ejpam-5049	418	25	,	,	PUNCT
ejpam-5049	418	26	12	12	NUM
ejpam-5049	418	27	]	]	PUNCT
ejpam-5049	418	28	.	.	PUNCT
ejpam-5049	419	1	references	reference	NOUN
ejpam-5049	419	2	[	[	X
ejpam-5049	419	3	1	1	NUM
ejpam-5049	419	4	]	]	PUNCT
ejpam-5049	419	5	a.	a.	NOUN
ejpam-5049	419	6	k.	k.	PROPN
ejpam-5049	419	7	alomari	alomari	PROPN
ejpam-5049	419	8	,	,	PUNCT
ejpam-5049	419	9	m.	m.	NOUN
ejpam-5049	419	10	alaroud	alaroud	PROPN
ejpam-5049	419	11	,	,	PUNCT
ejpam-5049	419	12	t.	t.	PROPN
ejpam-5049	419	13	n.	n.	PROPN
ejpam-5049	419	14	tahat	tahat	PROPN
ejpam-5049	419	15	,	,	PUNCT
ejpam-5049	419	16	and	and	CCONJ
ejpam-5049	419	17	a.	a.	NOUN
ejpam-5049	419	18	almalki	almalki	ADV
ejpam-5049	419	19	.	.	PUNCT
ejpam-5049	420	1	extended	extend	VERB
ejpam-5049	420	2	laplace	laplace	NOUN
ejpam-5049	420	3	power	power	NOUN
ejpam-5049	420	4	series	series	NOUN
ejpam-5049	420	5	method	method	NOUN
ejpam-5049	420	6	for	for	ADP
ejpam-5049	420	7	solving	solve	VERB
ejpam-5049	420	8	nonlinear	nonlinear	ADJ
ejpam-5049	420	9	caputo	caputo	PROPN
ejpam-5049	420	10	fractional	fractional	PROPN
ejpam-5049	420	11	volterra	volterra	PROPN
ejpam-5049	420	12	integro	integro	PROPN
ejpam-5049	420	13	-	-	PUNCT
ejpam-5049	420	14	differential	differential	NOUN
ejpam-5049	420	15	equations	equation	NOUN
ejpam-5049	420	16	.	.	PUNCT
ejpam-5049	421	1	symmetry	symmetry	NOUN
ejpam-5049	421	2	,	,	PUNCT
ejpam-5049	421	3	15:1296–1296	15:1296–1296	NUM
ejpam-5049	421	4	,	,	PUNCT
ejpam-5049	421	5	2023	2023	NUM
ejpam-5049	421	6	.	.	PUNCT
ejpam-5049	422	1	[	[	X
ejpam-5049	422	2	2	2	NUM
ejpam-5049	422	3	]	]	PUNCT
ejpam-5049	422	4	m.	m.	NOUN
ejpam-5049	422	5	asif	asif	PROPN
ejpam-5049	422	6	,	,	PUNCT
ejpam-5049	422	7	i.	i.	PROPN
ejpam-5049	422	8	khan	khan	PROPN
ejpam-5049	422	9	,	,	PUNCT
ejpam-5049	422	10	n.	n.	PROPN
ejpam-5049	422	11	haider	haider	PROPN
ejpam-5049	422	12	,	,	PUNCT
ejpam-5049	422	13	and	and	CCONJ
ejpam-5049	422	14	q.	q.	PROPN
ejpam-5049	422	15	al	al	PROPN
ejpam-5049	422	16	-	-	PUNCT
ejpam-5049	422	17	mdallal	mdallal	PROPN
ejpam-5049	422	18	.	.	PUNCT
ejpam-5049	423	1	legendre	legendre	PROPN
ejpam-5049	423	2	multi	multi	ADJ
ejpam-5049	423	3	-	-	ADJ
ejpam-5049	423	4	wavelets	wavelets	ADJ
ejpam-5049	423	5	collocation	collocation	NOUN
ejpam-5049	423	6	method	method	NOUN
ejpam-5049	423	7	for	for	ADP
ejpam-5049	423	8	numerical	numerical	ADJ
ejpam-5049	423	9	solution	solution	NOUN
ejpam-5049	423	10	of	of	ADP
ejpam-5049	423	11	linear	linear	PROPN
ejpam-5049	423	12	and	and	CCONJ
ejpam-5049	423	13	nonlinear	nonlinear	ADJ
ejpam-5049	423	14	integral	integral	ADJ
ejpam-5049	423	15	equations	equation	NOUN
ejpam-5049	423	16	.	.	PUNCT
ejpam-5049	424	1	alexandria	alexandria	PROPN
ejpam-5049	424	2	engineering	engineering	PROPN
ejpam-5049	424	3	journal	journal	PROPN
ejpam-5049	424	4	,	,	PUNCT
ejpam-5049	424	5	59:5099–5109	59:5099–5109	NUM
ejpam-5049	424	6	,	,	PUNCT
ejpam-5049	424	7	2020	2020	NUM
ejpam-5049	424	8	.	.	PUNCT
ejpam-5049	425	1	[	[	X
ejpam-5049	425	2	3	3	NUM
ejpam-5049	425	3	]	]	PUNCT
ejpam-5049	425	4	a.	a.	NOUN
ejpam-5049	425	5	g.	g.	PROPN
ejpam-5049	425	6	atta	atta	PROPN
ejpam-5049	425	7	and	and	CCONJ
ejpam-5049	425	8	y.	y.	PROPN
ejpam-5049	425	9	h.	h.	PROPN
ejpam-5049	425	10	youssri	youssri	PROPN
ejpam-5049	425	11	.	.	PUNCT
ejpam-5049	426	1	advanced	advanced	PROPN
ejpam-5049	426	2	shifted	shift	VERB
ejpam-5049	426	3	first	first	ADJ
ejpam-5049	426	4	-	-	PUNCT
ejpam-5049	426	5	kind	kind	NOUN
ejpam-5049	426	6	chebyshev	chebyshev	NOUN
ejpam-5049	426	7	collocation	collocation	NOUN
ejpam-5049	426	8	approach	approach	NOUN
ejpam-5049	426	9	for	for	ADP
ejpam-5049	426	10	solving	solve	VERB
ejpam-5049	426	11	the	the	DET
ejpam-5049	426	12	nonlinear	nonlinear	ADJ
ejpam-5049	426	13	time	time	NOUN
ejpam-5049	426	14	-	-	PUNCT
ejpam-5049	426	15	fractional	fractional	ADJ
ejpam-5049	426	16	partial	partial	ADJ
ejpam-5049	426	17	integro	integro	ADJ
ejpam-5049	426	18	-	-	PUNCT
ejpam-5049	426	19	differential	differential	NOUN
ejpam-5049	426	20	equation	equation	NOUN
ejpam-5049	426	21	with	with	ADP
ejpam-5049	426	22	a	a	DET
ejpam-5049	426	23	weakly	weakly	ADJ
ejpam-5049	426	24	singular	singular	ADJ
ejpam-5049	426	25	kernel	kernel	NOUN
ejpam-5049	426	26	.	.	PUNCT
ejpam-5049	427	1	computational	computational	ADJ
ejpam-5049	427	2	applied	apply	VERB
ejpam-5049	427	3	mathematics	mathematic	NOUN
ejpam-5049	427	4	,	,	PUNCT
ejpam-5049	427	5	41	41	NUM
ejpam-5049	427	6	,	,	PUNCT
ejpam-5049	427	7	2022	2022	NUM
ejpam-5049	427	8	.	.	PUNCT
ejpam-5049	428	1	[	[	X
ejpam-5049	428	2	4	4	X
ejpam-5049	428	3	]	]	PUNCT
ejpam-5049	428	4	h.	h.	PROPN
ejpam-5049	428	5	o.	o.	PROPN
ejpam-5049	428	6	bakodah	bakodah	PROPN
ejpam-5049	428	7	,	,	PUNCT
ejpam-5049	428	8	m.	m.	NOUN
ejpam-5049	428	9	al	al	PROPN
ejpam-5049	428	10	-	-	PUNCT
ejpam-5049	428	11	mazmumy	mazmumy	PROPN
ejpam-5049	428	12	,	,	PUNCT
ejpam-5049	428	13	and	and	CCONJ
ejpam-5049	428	14	s.	s.	PROPN
ejpam-5049	428	15	o.	o.	PROPN
ejpam-5049	428	16	almuhalbedi	almuhalbedi	PROPN
ejpam-5049	428	17	.	.	PUNCT
ejpam-5049	429	1	solving	solve	VERB
ejpam-5049	429	2	system	system	NOUN
ejpam-5049	429	3	of	of	ADP
ejpam-5049	429	4	integro	integro	PROPN
ejpam-5049	429	5	differential	differential	ADJ
ejpam-5049	429	6	equations	equation	NOUN
ejpam-5049	429	7	using	use	VERB
ejpam-5049	429	8	discrete	discrete	ADJ
ejpam-5049	429	9	adomian	adomian	NOUN
ejpam-5049	429	10	decomposition	decomposition	NOUN
ejpam-5049	429	11	method	method	NOUN
ejpam-5049	429	12	.	.	PUNCT
ejpam-5049	430	1	journal	journal	PROPN
ejpam-5049	430	2	of	of	ADP
ejpam-5049	430	3	taibah	taibah	PROPN
ejpam-5049	430	4	university	university	PROPN
ejpam-5049	430	5	for	for	ADP
ejpam-5049	430	6	science	science	NOUN
ejpam-5049	430	7	,	,	PUNCT
ejpam-5049	430	8	13:805–812	13:805–812	NUM
ejpam-5049	430	9	,	,	PUNCT
ejpam-5049	430	10	2019	2019	NUM
ejpam-5049	430	11	.	.	PUNCT
ejpam-5049	431	1	[	[	X
ejpam-5049	431	2	5	5	NUM
ejpam-5049	431	3	]	]	X
ejpam-5049	431	4	d.	d.	PROPN
ejpam-5049	431	5	v.	v.	PROPN
ejpam-5049	431	6	bayram	bayram	PROPN
ejpam-5049	431	7	and	and	CCONJ
ejpam-5049	431	8	a.	a.	PROPN
ejpam-5049	431	9	dascioglu	dascioglu	PROPN
ejpam-5049	431	10	.	.	PUNCT
ejpam-5049	432	1	a	a	DET
ejpam-5049	432	2	method	method	NOUN
ejpam-5049	432	3	for	for	ADP
ejpam-5049	432	4	fractional	fractional	PROPN
ejpam-5049	432	5	volterra	volterra	PROPN
ejpam-5049	432	6	integro	integro	PROPN
ejpam-5049	432	7	-	-	PUNCT
ejpam-5049	432	8	differential	differential	NOUN
ejpam-5049	432	9	equations	equation	NOUN
ejpam-5049	432	10	by	by	ADP
ejpam-5049	432	11	laguerre	laguerre	NOUN
ejpam-5049	432	12	polynomials	polynomial	NOUN
ejpam-5049	432	13	.	.	PUNCT
ejpam-5049	433	1	advances	advance	NOUN
ejpam-5049	433	2	in	in	ADP
ejpam-5049	433	3	difference	difference	NOUN
ejpam-5049	433	4	equations	equation	NOUN
ejpam-5049	433	5	,	,	PUNCT
ejpam-5049	433	6	2018	2018	NUM
ejpam-5049	433	7	,	,	PUNCT
ejpam-5049	433	8	2018	2018	NUM
ejpam-5049	433	9	.	.	PUNCT
ejpam-5049	434	1	[	[	X
ejpam-5049	434	2	6	6	NUM
ejpam-5049	434	3	]	]	SYM
ejpam-5049	434	4	ali	ali	PROPN
ejpam-5049	434	5	.	.	PUNCT
ejpam-5049	434	6	f.	f.	PROPN
ejpam-5049	434	7	jameel	jameel	PROPN
ejpam-5049	434	8	,	,	PUNCT
ejpam-5049	434	9	n.	n.	PROPN
ejpam-5049	434	10	r.	r.	PROPN
ejpam-5049	434	11	anakira	anakira	PROPN
ejpam-5049	434	12	,	,	PUNCT
ejpam-5049	434	13	a.	a.	PROPN
ejpam-5049	434	14	k.	k.	PROPN
ejpam-5049	434	15	alomari	alomari	PROPN
ejpam-5049	434	16	,	,	PUNCT
ejpam-5049	434	17	and	and	CCONJ
ejpam-5049	434	18	noraziah	noraziah	PROPN
ejpam-5049	434	19	h.	h.	PROPN
ejpam-5049	434	20	man	man	PROPN
ejpam-5049	434	21	.	.	PUNCT
ejpam-5049	435	1	solution	solution	NOUN
ejpam-5049	435	2	and	and	CCONJ
ejpam-5049	435	3	analysis	analysis	NOUN
ejpam-5049	435	4	of	of	ADP
ejpam-5049	435	5	the	the	DET
ejpam-5049	435	6	fuzzy	fuzzy	ADJ
ejpam-5049	435	7	volterra	volterra	NOUN
ejpam-5049	435	8	integral	integral	ADJ
ejpam-5049	435	9	equations	equation	NOUN
ejpam-5049	435	10	via	via	ADP
ejpam-5049	435	11	homotopy	homotopy	NOUN
ejpam-5049	435	12	analysis	analysis	NOUN
ejpam-5049	435	13	method	method	NOUN
ejpam-5049	435	14	.	.	PUNCT
ejpam-5049	436	1	computer	computer	NOUN
ejpam-5049	436	2	modeling	modeling	NOUN
ejpam-5049	436	3	in	in	ADP
ejpam-5049	436	4	engineering	engineering	NOUN
ejpam-5049	436	5	sciences	science	NOUN
ejpam-5049	436	6	,	,	PUNCT
ejpam-5049	436	7	127:875–899	127:875–899	NUM
ejpam-5049	436	8	,	,	PUNCT
ejpam-5049	436	9	2021	2021	NUM
ejpam-5049	436	10	.	.	PUNCT
ejpam-5049	437	1	[	[	X
ejpam-5049	437	2	7	7	X
ejpam-5049	437	3	]	]	X
ejpam-5049	437	4	w.	w.	PROPN
ejpam-5049	437	5	g	g	PROPN
ejpam-5049	437	6	and	and	CCONJ
ejpam-5049	437	7	m.	m.	PROPN
ejpam-5049	437	8	a.	a.	PROPN
ejpam-5049	437	9	snyder	snyder	PROPN
ejpam-5049	437	10	.	.	PUNCT
ejpam-5049	438	1	chebyshev	chebyshev	PROPN
ejpam-5049	438	2	methods	method	NOUN
ejpam-5049	438	3	in	in	ADP
ejpam-5049	438	4	numerical	numerical	ADJ
ejpam-5049	438	5	approximation	approximation	NOUN
ejpam-5049	438	6	.	.	PUNCT
ejpam-5049	439	1	mathematics	mathematic	NOUN
ejpam-5049	439	2	of	of	ADP
ejpam-5049	439	3	computation	computation	NOUN
ejpam-5049	439	4	,	,	PUNCT
ejpam-5049	439	5	22:894–894	22:894–894	PROPN
ejpam-5049	439	6	,	,	PUNCT
ejpam-5049	439	7	1968	1968	NUM
ejpam-5049	439	8	.	.	PUNCT
ejpam-5049	440	1	[	[	X
ejpam-5049	440	2	8	8	NUM
ejpam-5049	440	3	]	]	X
ejpam-5049	440	4	b.	b.	PROPN
ejpam-5049	440	5	d.	d.	PROPN
ejpam-5049	440	6	garba	garba	PROPN
ejpam-5049	440	7	and	and	CCONJ
ejpam-5049	440	8	s.	s.	PROPN
ejpam-5049	440	9	l.	l.	PROPN
ejpam-5049	440	10	bichi	bichi	PROPN
ejpam-5049	440	11	.	.	PUNCT
ejpam-5049	441	1	on	on	ADP
ejpam-5049	441	2	solving	solve	VERB
ejpam-5049	441	3	linear	linear	PROPN
ejpam-5049	441	4	fredholm	fredholm	NOUN
ejpam-5049	441	5	integro	integro	ADJ
ejpam-5049	441	6	-	-	PUNCT
ejpam-5049	441	7	differential	differential	NOUN
ejpam-5049	441	8	equations	equation	NOUN
ejpam-5049	441	9	via	via	ADP
ejpam-5049	441	10	finite	finite	ADJ
ejpam-5049	441	11	difference	difference	PROPN
ejpam-5049	441	12	-	-	PUNCT
ejpam-5049	441	13	simpson	simpson	PROPN
ejpam-5049	441	14	’s	’s	PART
ejpam-5049	441	15	approach	approach	NOUN
ejpam-5049	441	16	.	.	PUNCT
ejpam-5049	442	1	malaya	malaya	PROPN
ejpam-5049	442	2	journal	journal	PROPN
ejpam-5049	442	3	of	of	ADP
ejpam-5049	442	4	matematik	matematik	PROPN
ejpam-5049	442	5	,	,	PUNCT
ejpam-5049	442	6	8:469–472	8:469–472	NOUN
ejpam-5049	442	7	,	,	PUNCT
ejpam-5049	442	8	2020	2020	NUM
ejpam-5049	442	9	.	.	PUNCT
ejpam-5049	443	1	references	reference	NOUN
ejpam-5049	443	2	502	502	NUM
ejpam-5049	444	1	[	[	X
ejpam-5049	444	2	9	9	NUM
ejpam-5049	444	3	]	]	SYM
ejpam-5049	444	4	hari	hari	PROPN
ejpam-5049	444	5	mohan	mohan	PROPN
ejpam-5049	444	6	h.	h.	PROPN
ejpam-5049	444	7	m.	m.	PROPN
ejpam-5049	444	8	srivastava	srivastava	PROPN
ejpam-5049	444	9	.	.	PUNCT
ejpam-5049	445	1	a	a	DET
ejpam-5049	445	2	survey	survey	NOUN
ejpam-5049	445	3	of	of	ADP
ejpam-5049	445	4	some	some	DET
ejpam-5049	445	5	recent	recent	ADJ
ejpam-5049	445	6	developments	development	NOUN
ejpam-5049	445	7	on	on	ADP
ejpam-5049	445	8	higher	high	ADJ
ejpam-5049	445	9	transcendental	transcendental	ADJ
ejpam-5049	445	10	functions	function	NOUN
ejpam-5049	445	11	of	of	ADP
ejpam-5049	445	12	analytic	analytic	ADJ
ejpam-5049	445	13	number	number	NOUN
ejpam-5049	445	14	theory	theory	NOUN
ejpam-5049	445	15	and	and	CCONJ
ejpam-5049	445	16	applied	apply	VERB
ejpam-5049	445	17	mathematics	mathematic	NOUN
ejpam-5049	445	18	.	.	PUNCT
ejpam-5049	446	1	symmetry	symmetry	PROPN
ejpam-5049	446	2	,	,	PUNCT
ejpam-5049	446	3	13:2294	13:2294	NUM
ejpam-5049	446	4	,	,	PUNCT
ejpam-5049	446	5	2021	2021	NUM
ejpam-5049	446	6	.	.	PUNCT
ejpam-5049	447	1	[	[	X
ejpam-5049	447	2	10	10	NUM
ejpam-5049	447	3	]	]	PUNCT
ejpam-5049	447	4	m.	m.	NOUN
ejpam-5049	447	5	m.	m.	NOUN
ejpam-5049	447	6	khader	khader	PROPN
ejpam-5049	447	7	.	.	PUNCT
ejpam-5049	448	1	on	on	ADP
ejpam-5049	448	2	the	the	DET
ejpam-5049	448	3	numerical	numerical	ADJ
ejpam-5049	448	4	solutions	solution	NOUN
ejpam-5049	448	5	for	for	ADP
ejpam-5049	448	6	the	the	DET
ejpam-5049	448	7	fractional	fractional	ADJ
ejpam-5049	448	8	diffusion	diffusion	NOUN
ejpam-5049	448	9	equation	equation	NOUN
ejpam-5049	448	10	.	.	PUNCT
ejpam-5049	449	1	communications	communication	NOUN
ejpam-5049	449	2	in	in	ADP
ejpam-5049	449	3	nonlinear	nonlinear	ADJ
ejpam-5049	449	4	science	science	NOUN
ejpam-5049	449	5	and	and	CCONJ
ejpam-5049	449	6	numerical	numerical	PROPN
ejpam-5049	449	7	simulation	simulation	PROPN
ejpam-5049	449	8	,	,	PUNCT
ejpam-5049	449	9	16:2535–2542	16:2535–2542	NUM
ejpam-5049	449	10	,	,	PUNCT
ejpam-5049	449	11	2011	2011	NUM
ejpam-5049	449	12	.	.	PUNCT
ejpam-5049	450	1	[	[	X
ejpam-5049	450	2	11	11	NUM
ejpam-5049	450	3	]	]	PUNCT
ejpam-5049	450	4	m.	m.	NOUN
ejpam-5049	450	5	m.	m.	NOUN
ejpam-5049	450	6	khader	khader	PROPN
ejpam-5049	450	7	and	and	CCONJ
ejpam-5049	450	8	k.	k.	PROPN
ejpam-5049	450	9	m.	m.	PROPN
ejpam-5049	450	10	saad	saad	PROPN
ejpam-5049	450	11	.	.	PUNCT
ejpam-5049	451	1	on	on	ADP
ejpam-5049	451	2	the	the	DET
ejpam-5049	451	3	numerical	numerical	ADJ
ejpam-5049	451	4	evaluation	evaluation	NOUN
ejpam-5049	451	5	for	for	ADP
ejpam-5049	451	6	studying	study	VERB
ejpam-5049	451	7	the	the	DET
ejpam-5049	451	8	fractional	fractional	ADJ
ejpam-5049	451	9	kdv	kdv	NOUN
ejpam-5049	451	10	,	,	PUNCT
ejpam-5049	451	11	kdv	kdv	NOUN
ejpam-5049	451	12	-	-	PUNCT
ejpam-5049	451	13	burgers	burger	NOUN
ejpam-5049	451	14	and	and	CCONJ
ejpam-5049	451	15	burgers	burger	NOUN
ejpam-5049	451	16	equations	equation	NOUN
ejpam-5049	451	17	.	.	PUNCT
ejpam-5049	452	1	the	the	DET
ejpam-5049	452	2	european	european	PROPN
ejpam-5049	452	3	physical	physical	PROPN
ejpam-5049	452	4	journal	journal	PROPN
ejpam-5049	452	5	plus	plus	CCONJ
ejpam-5049	452	6	,	,	PUNCT
ejpam-5049	452	7	133	133	NUM
ejpam-5049	452	8	,	,	PUNCT
ejpam-5049	452	9	2018	2018	NUM
ejpam-5049	452	10	.	.	PUNCT
ejpam-5049	453	1	[	[	X
ejpam-5049	453	2	12	12	NUM
ejpam-5049	453	3	]	]	X
ejpam-5049	453	4	i.	i.	PROPN
ejpam-5049	453	5	khan	khan	PROPN
ejpam-5049	453	6	,	,	PUNCT
ejpam-5049	453	7	m.	m.	NOUN
ejpam-5049	453	8	asif	asif	PROPN
ejpam-5049	453	9	,	,	PUNCT
ejpam-5049	453	10	r.	r.	PROPN
ejpam-5049	453	11	amin	amin	PROPN
ejpam-5049	453	12	,	,	PUNCT
ejpam-5049	453	13	q.	q.	PROPN
ejpam-5049	453	14	al	al	PROPN
ejpam-5049	453	15	-	-	PUNCT
ejpam-5049	453	16	mdallal	mdallal	PROPN
ejpam-5049	453	17	,	,	PUNCT
ejpam-5049	453	18	and	and	CCONJ
ejpam-5049	453	19	f.	f.	PROPN
ejpam-5049	453	20	jarad	jarad	PROPN
ejpam-5049	453	21	.	.	PUNCT
ejpam-5049	454	1	on	on	ADP
ejpam-5049	454	2	a	a	DET
ejpam-5049	454	3	new	new	ADJ
ejpam-5049	454	4	method	method	NOUN
ejpam-5049	454	5	for	for	ADP
ejpam-5049	454	6	finding	find	VERB
ejpam-5049	454	7	numerical	numerical	ADJ
ejpam-5049	454	8	solutions	solution	NOUN
ejpam-5049	454	9	to	to	ADP
ejpam-5049	454	10	integro	integro	ADJ
ejpam-5049	454	11	-	-	PUNCT
ejpam-5049	454	12	differential	differential	NOUN
ejpam-5049	454	13	equations	equation	NOUN
ejpam-5049	454	14	based	base	VERB
ejpam-5049	454	15	on	on	ADP
ejpam-5049	454	16	legendre	legendre	PROPN
ejpam-5049	454	17	multi	multi	PROPN
ejpam-5049	454	18	-	-	ADJ
ejpam-5049	454	19	wavelets	wavelets	ADJ
ejpam-5049	454	20	collocation	collocation	NOUN
ejpam-5049	454	21	.	.	PUNCT
ejpam-5049	455	1	alexandria	alexandria	PROPN
ejpam-5049	455	2	engineering	engineering	PROPN
ejpam-5049	455	3	journal	journal	PROPN
ejpam-5049	455	4	,	,	PUNCT
ejpam-5049	455	5	61:3037–3049	61:3037–3049	NUM
ejpam-5049	455	6	,	,	PUNCT
ejpam-5049	455	7	2022	2022	NUM
ejpam-5049	455	8	.	.	PUNCT
ejpam-5049	456	1	[	[	X
ejpam-5049	456	2	13	13	NUM
ejpam-5049	456	3	]	]	PUNCT
ejpam-5049	456	4	a.	a.	NOUN
ejpam-5049	456	5	a.	a.	NOUN
ejpam-5049	456	6	kilbas	kilbas	PROPN
ejpam-5049	456	7	,	,	PUNCT
ejpam-5049	456	8	h.	h.	PROPN
ejpam-5049	456	9	m	m	PROPN
ejpam-5049	456	10	srivastava	srivastava	PROPN
ejpam-5049	456	11	,	,	PUNCT
ejpam-5049	456	12	and	and	CCONJ
ejpam-5049	456	13	j.	j.	PROPN
ejpam-5049	456	14	trujillo	trujillo	PROPN
ejpam-5049	456	15	.	.	PUNCT
ejpam-5049	456	16	theory	theory	NOUN
ejpam-5049	456	17	and	and	CCONJ
ejpam-5049	456	18	applications	application	NOUN
ejpam-5049	456	19	of	of	ADP
ejpam-5049	456	20	fractional	fractional	ADJ
ejpam-5049	456	21	differential	differential	ADJ
ejpam-5049	456	22	equations	equation	NOUN
ejpam-5049	456	23	.	.	PUNCT
ejpam-5049	457	1	north	north	NOUN
ejpam-5049	457	2	-	-	PUNCT
ejpam-5049	457	3	holland	holland	PROPN
ejpam-5049	457	4	mathematics	mathematics	PROPN
ejpam-5049	457	5	studies	study	NOUN
ejpam-5049	457	6	,	,	PUNCT
ejpam-5049	457	7	204	204	NUM
ejpam-5049	457	8	:	:	PUNCT
ejpam-5049	457	9	vii	vii	PROPN
ejpam-5049	457	10	–	–	PUNCT
ejpam-5049	457	11	x	x	NOUN
ejpam-5049	457	12	,	,	PUNCT
ejpam-5049	457	13	2006	2006	NUM
ejpam-5049	457	14	.	.	PUNCT
ejpam-5049	458	1	[	[	X
ejpam-5049	458	2	14	14	NUM
ejpam-5049	458	3	]	]	PUNCT
ejpam-5049	458	4	k.	k.	PROPN
ejpam-5049	458	5	maleknejad	maleknejad	PROPN
ejpam-5049	458	6	and	and	CCONJ
ejpam-5049	458	7	m.tavassoli	m.tavassoli	NOUN
ejpam-5049	458	8	kajani	kajani	NOUN
ejpam-5049	458	9	.	.	PUNCT
ejpam-5049	459	1	solving	solve	VERB
ejpam-5049	459	2	linear	linear	ADJ
ejpam-5049	459	3	integro	integro	ADJ
ejpam-5049	459	4	-	-	PUNCT
ejpam-5049	459	5	differential	differential	NOUN
ejpam-5049	459	6	equation	equation	NOUN
ejpam-5049	459	7	system	system	NOUN
ejpam-5049	459	8	by	by	ADP
ejpam-5049	459	9	galerkin	galerkin	ADJ
ejpam-5049	459	10	methods	method	NOUN
ejpam-5049	459	11	with	with	ADP
ejpam-5049	459	12	hybrid	hybrid	ADJ
ejpam-5049	459	13	functions	function	NOUN
ejpam-5049	459	14	.	.	PUNCT
ejpam-5049	460	1	applied	apply	VERB
ejpam-5049	460	2	mathematics	mathematic	NOUN
ejpam-5049	460	3	and	and	CCONJ
ejpam-5049	460	4	computation	computation	NOUN
ejpam-5049	460	5	,	,	PUNCT
ejpam-5049	460	6	159:603–612	159:603–612	NUM
ejpam-5049	460	7	,	,	PUNCT
ejpam-5049	460	8	2004	2004	NUM
ejpam-5049	460	9	.	.	PUNCT
ejpam-5049	461	1	[	[	X
ejpam-5049	461	2	15	15	NUM
ejpam-5049	461	3	]	]	X
ejpam-5049	461	4	k.	k.	PROPN
ejpam-5049	461	5	maleknejad	maleknejad	PROPN
ejpam-5049	461	6	,	,	PUNCT
ejpam-5049	461	7	f.	f.	PROPN
ejpam-5049	461	8	mirzaee	mirzaee	PROPN
ejpam-5049	461	9	,	,	PUNCT
ejpam-5049	461	10	and	and	CCONJ
ejpam-5049	461	11	s.	s.	PROPN
ejpam-5049	461	12	abbasbandy	abbasbandy	PROPN
ejpam-5049	461	13	.	.	PUNCT
ejpam-5049	462	1	solving	solve	VERB
ejpam-5049	462	2	linear	linear	ADJ
ejpam-5049	462	3	integro	integro	ADJ
ejpam-5049	462	4	-	-	PUNCT
ejpam-5049	462	5	differential	differential	NOUN
ejpam-5049	462	6	equations	equation	NOUN
ejpam-5049	462	7	system	system	NOUN
ejpam-5049	462	8	by	by	ADP
ejpam-5049	462	9	using	use	VERB
ejpam-5049	462	10	rationalized	rationalize	VERB
ejpam-5049	462	11	haar	haar	NOUN
ejpam-5049	462	12	functions	function	NOUN
ejpam-5049	462	13	method	method	NOUN
ejpam-5049	462	14	.	.	PUNCT
ejpam-5049	463	1	applied	apply	VERB
ejpam-5049	463	2	mathematics	mathematic	NOUN
ejpam-5049	463	3	and	and	CCONJ
ejpam-5049	463	4	computation	computation	NOUN
ejpam-5049	463	5	,	,	PUNCT
ejpam-5049	463	6	155:317–328	155:317–328	NUM
ejpam-5049	463	7	,	,	PUNCT
ejpam-5049	463	8	2004	2004	NUM
ejpam-5049	463	9	.	.	PUNCT
ejpam-5049	464	1	[	[	X
ejpam-5049	464	2	16	16	NUM
ejpam-5049	464	3	]	]	X
ejpam-5049	464	4	j.	j.	PROPN
ejpam-5049	464	5	c.	c.	PROPN
ejpam-5049	464	6	mason	mason	PROPN
ejpam-5049	464	7	and	and	CCONJ
ejpam-5049	464	8	d.	d.	PROPN
ejpam-5049	464	9	c.	c.	PROPN
ejpam-5049	464	10	handscomb	handscomb	PROPN
ejpam-5049	464	11	.	.	PUNCT
ejpam-5049	465	1	chebyshev	chebyshev	PROPN
ejpam-5049	465	2	polynomials	polynomial	NOUN
ejpam-5049	465	3	.	.	PUNCT
ejpam-5049	466	1	chapman	chapman	PROPN
ejpam-5049	466	2	hall	hall	PROPN
ejpam-5049	466	3	/	/	SYM
ejpam-5049	466	4	crc	crc	PROPN
ejpam-5049	466	5	,	,	PUNCT
ejpam-5049	466	6	2002	2002	NUM
ejpam-5049	466	7	.	.	PUNCT
ejpam-5049	467	1	[	[	X
ejpam-5049	467	2	17	17	NUM
ejpam-5049	467	3	]	]	PUNCT
ejpam-5049	467	4	k.	k.	PROPN
ejpam-5049	467	5	s.	s.	PROPN
ejpam-5049	467	6	miller	miller	PROPN
ejpam-5049	467	7	and	and	CCONJ
ejpam-5049	467	8	b.	b.	PROPN
ejpam-5049	467	9	ross	ross	PROPN
ejpam-5049	467	10	.	.	PUNCT
ejpam-5049	468	1	an	an	DET
ejpam-5049	468	2	introduction	introduction	NOUN
ejpam-5049	468	3	to	to	ADP
ejpam-5049	468	4	the	the	DET
ejpam-5049	468	5	fractional	fractional	ADJ
ejpam-5049	468	6	calculus	calculus	NOUN
ejpam-5049	468	7	and	and	CCONJ
ejpam-5049	468	8	fractional	fractional	ADJ
ejpam-5049	468	9	differential	differential	ADJ
ejpam-5049	468	10	equations	equation	NOUN
ejpam-5049	468	11	.	.	PUNCT
ejpam-5049	469	1	wiley	wiley	PROPN
ejpam-5049	469	2	,	,	PUNCT
ejpam-5049	469	3	1993	1993	NUM
ejpam-5049	469	4	.	.	PUNCT
ejpam-5049	470	1	[	[	X
ejpam-5049	470	2	18	18	NUM
ejpam-5049	470	3	]	]	PUNCT
ejpam-5049	470	4	i.	i.	NOUN
ejpam-5049	470	5	podlubny	podlubny	PROPN
ejpam-5049	470	6	.	.	PUNCT
ejpam-5049	471	1	fractional	fractional	ADJ
ejpam-5049	471	2	differential	differential	ADJ
ejpam-5049	471	3	equations	equation	NOUN
ejpam-5049	471	4	:	:	PUNCT
ejpam-5049	471	5	an	an	DET
ejpam-5049	471	6	introduction	introduction	NOUN
ejpam-5049	471	7	to	to	ADP
ejpam-5049	471	8	fractional	fractional	ADJ
ejpam-5049	471	9	derivatives	derivative	NOUN
ejpam-5049	471	10	,	,	PUNCT
ejpam-5049	471	11	fractional	fractional	ADJ
ejpam-5049	471	12	differential	differential	ADJ
ejpam-5049	471	13	equations	equation	NOUN
ejpam-5049	471	14	,	,	PUNCT
ejpam-5049	471	15	to	to	ADP
ejpam-5049	471	16	methods	method	NOUN
ejpam-5049	471	17	of	of	ADP
ejpam-5049	471	18	their	their	PRON
ejpam-5049	471	19	solution	solution	NOUN
ejpam-5049	471	20	and	and	CCONJ
ejpam-5049	471	21	some	some	PRON
ejpam-5049	471	22	of	of	ADP
ejpam-5049	471	23	their	their	PRON
ejpam-5049	471	24	applications	application	NOUN
ejpam-5049	471	25	.	.	PUNCT
ejpam-5049	472	1	academic	academic	ADJ
ejpam-5049	472	2	press	press	NOUN
ejpam-5049	472	3	,	,	PUNCT
ejpam-5049	472	4	1998	1998	NUM
ejpam-5049	472	5	.	.	PUNCT
ejpam-5049	473	1	[	[	X
ejpam-5049	473	2	19	19	NUM
ejpam-5049	473	3	]	]	PUNCT
ejpam-5049	473	4	k.	k.	PROPN
ejpam-5049	473	5	m.	m.	PROPN
ejpam-5049	473	6	saad	saad	PROPN
ejpam-5049	473	7	and	and	CCONJ
ejpam-5049	473	8	h.	h.	PROPN
ejpam-5049	473	9	m.	m.	PROPN
ejpam-5049	473	10	srivastava	srivastava	PROPN
ejpam-5049	473	11	.	.	PUNCT
ejpam-5049	474	1	numerical	numerical	ADJ
ejpam-5049	474	2	solutions	solution	NOUN
ejpam-5049	474	3	of	of	ADP
ejpam-5049	474	4	the	the	DET
ejpam-5049	474	5	multi	multi	ADJ
ejpam-5049	474	6	-	-	ADJ
ejpam-5049	474	7	space	space	ADJ
ejpam-5049	474	8	fractionalorder	fractionalorder	NOUN
ejpam-5049	474	9	coupled	couple	VERB
ejpam-5049	474	10	korteweg	korteweg	PROPN
ejpam-5049	474	11	–	–	PUNCT
ejpam-5049	474	12	de	de	PROPN
ejpam-5049	474	13	vries	vries	NOUN
ejpam-5049	474	14	equation	equation	NOUN
ejpam-5049	474	15	with	with	ADP
ejpam-5049	474	16	several	several	ADJ
ejpam-5049	474	17	different	different	ADJ
ejpam-5049	474	18	kernels	kernel	NOUN
ejpam-5049	474	19	.	.	PUNCT
ejpam-5049	475	1	fractal	fractal	PROPN
ejpam-5049	475	2	and	and	CCONJ
ejpam-5049	475	3	fractional	fractional	ADJ
ejpam-5049	475	4	,	,	PUNCT
ejpam-5049	475	5	7:716–716	7:716–716	NOUN
ejpam-5049	475	6	,	,	PUNCT
ejpam-5049	475	7	09	09	NUM
ejpam-5049	475	8	2023	2023	NUM
ejpam-5049	475	9	.	.	PUNCT
ejpam-5049	476	1	[	[	X
ejpam-5049	476	2	20	20	NUM
ejpam-5049	476	3	]	]	X
ejpam-5049	476	4	harendra	harendra	X
ejpam-5049	476	5	singh	singh	PROPN
ejpam-5049	476	6	and	and	CCONJ
ejpam-5049	476	7	ramta	ramta	PROPN
ejpam-5049	476	8	ram	ram	PROPN
ejpam-5049	476	9	pathak	pathak	PROPN
ejpam-5049	476	10	.	.	PUNCT
ejpam-5049	477	1	jacobi	jacobi	PROPN
ejpam-5049	477	2	spectral	spectral	PROPN
ejpam-5049	477	3	method	method	NOUN
ejpam-5049	477	4	for	for	ADP
ejpam-5049	477	5	the	the	DET
ejpam-5049	477	6	fractional	fractional	ADJ
ejpam-5049	477	7	reaction	reaction	NOUN
ejpam-5049	477	8	–	–	PUNCT
ejpam-5049	477	9	diffusion	diffusion	NOUN
ejpam-5049	477	10	equation	equation	NOUN
ejpam-5049	477	11	arising	arise	VERB
ejpam-5049	477	12	in	in	ADP
ejpam-5049	477	13	ecology	ecology	NOUN
ejpam-5049	477	14	.	.	PUNCT
ejpam-5049	478	1	mathematical	mathematical	ADJ
ejpam-5049	478	2	methods	method	NOUN
ejpam-5049	478	3	in	in	ADP
ejpam-5049	478	4	the	the	DET
ejpam-5049	478	5	applied	apply	VERB
ejpam-5049	478	6	sciences	science	NOUN
ejpam-5049	478	7	,	,	PUNCT
ejpam-5049	478	8	2024	2024	NUM
ejpam-5049	478	9	.	.	PUNCT
ejpam-5049	479	1	[	[	X
ejpam-5049	479	2	21	21	NUM
ejpam-5049	479	3	]	]	X
ejpam-5049	479	4	h.	h.	PROPN
ejpam-5049	479	5	m.	m.	PROPN
ejpam-5049	479	6	srivastava	srivastava	PROPN
ejpam-5049	479	7	,	,	PUNCT
ejpam-5049	479	8	k.	k.	PROPN
ejpam-5049	479	9	m.	m.	PROPN
ejpam-5049	479	10	saad	saad	PROPN
ejpam-5049	479	11	,	,	PUNCT
ejpam-5049	479	12	and	and	CCONJ
ejpam-5049	479	13	w.	w.	PROPN
ejpam-5049	479	14	m.	m.	PROPN
ejpam-5049	479	15	hamanah	hamanah	PROPN
ejpam-5049	479	16	.	.	PUNCT
ejpam-5049	480	1	certain	certain	ADJ
ejpam-5049	480	2	new	new	ADJ
ejpam-5049	480	3	models	model	NOUN
ejpam-5049	480	4	of	of	ADP
ejpam-5049	480	5	the	the	DET
ejpam-5049	480	6	multi	multi	ADJ
ejpam-5049	480	7	-	-	ADJ
ejpam-5049	480	8	space	space	ADJ
ejpam-5049	480	9	fractal	fractal	ADJ
ejpam-5049	480	10	-	-	PUNCT
ejpam-5049	480	11	fractional	fractional	ADJ
ejpam-5049	480	12	kuramoto	kuramoto	NOUN
ejpam-5049	480	13	-	-	PUNCT
ejpam-5049	480	14	sivashinsky	sivashinsky	NOUN
ejpam-5049	480	15	and	and	CCONJ
ejpam-5049	480	16	korteweg	korteweg	NOUN
ejpam-5049	480	17	-	-	PUNCT
ejpam-5049	480	18	de	de	NOUN
ejpam-5049	480	19	vries	vries	PROPN
ejpam-5049	480	20	equations	equation	NOUN
ejpam-5049	480	21	.	.	PUNCT
ejpam-5049	481	1	mathematics	mathematic	NOUN
ejpam-5049	481	2	,	,	PUNCT
ejpam-5049	481	3	10:1089	10:1089	NUM
ejpam-5049	481	4	,	,	PUNCT
ejpam-5049	481	5	2022	2022	NUM
ejpam-5049	481	6	.	.	PUNCT
ejpam-5049	482	1	references	reference	NOUN
ejpam-5049	482	2	503	503	NUM
ejpam-5049	482	3	[	[	X
ejpam-5049	482	4	22	22	NUM
ejpam-5049	482	5	]	]	X
ejpam-5049	482	6	n.	n.	PROPN
ejpam-5049	482	7	h.	h.	PROPN
ejpam-5049	482	8	sweilam	sweilam	PROPN
ejpam-5049	482	9	and	and	CCONJ
ejpam-5049	482	10	m.	m.	NOUN
ejpam-5049	482	11	m.	m.	NOUN
ejpam-5049	482	12	khader	khader	PROPN
ejpam-5049	482	13	.	.	PUNCT
ejpam-5049	483	1	a	a	DET
ejpam-5049	483	2	chebyshev	chebyshev	NOUN
ejpam-5049	483	3	pseudo	pseudo	NOUN
ejpam-5049	483	4	-	-	ADJ
ejpam-5049	483	5	spectral	spectral	ADJ
ejpam-5049	483	6	method	method	NOUN
ejpam-5049	483	7	for	for	ADP
ejpam-5049	483	8	solving	solve	VERB
ejpam-5049	483	9	fractional	fractional	ADJ
ejpam-5049	483	10	order	order	NOUN
ejpam-5049	483	11	integro	integro	ADJ
ejpam-5049	483	12	-	-	PUNCT
ejpam-5049	483	13	differential	differential	NOUN
ejpam-5049	483	14	equations	equation	NOUN
ejpam-5049	483	15	.	.	PUNCT
ejpam-5049	484	1	the	the	DET
ejpam-5049	484	2	anziam	anziam	PROPN
ejpam-5049	484	3	journal	journal	PROPN
ejpam-5049	484	4	,	,	PUNCT
ejpam-5049	484	5	51:464–475	51:464–475	PROPN
ejpam-5049	484	6	,	,	PUNCT
ejpam-5049	484	7	2010	2010	NUM
ejpam-5049	484	8	.	.	PUNCT
ejpam-5049	485	1	[	[	X
ejpam-5049	485	2	23	23	NUM
ejpam-5049	485	3	]	]	X
ejpam-5049	485	4	g.	g.	PROPN
ejpam-5049	485	5	szego	szego	PROPN
ejpam-5049	485	6	.	.	PUNCT
ejpam-5049	486	1	orthogonal	orthogonal	ADJ
ejpam-5049	486	2	polynomials	polynomial	NOUN
ejpam-5049	486	3	.	.	PUNCT
ejpam-5049	487	1	american	american	PROPN
ejpam-5049	487	2	mathematical	mathematical	PROPN
ejpam-5049	487	3	society	society	NOUN
ejpam-5049	487	4	,	,	PUNCT
ejpam-5049	487	5	2003	2003	NUM
ejpam-5049	487	6	.	.	PUNCT
ejpam-5049	488	1	[	[	X
ejpam-5049	488	2	24	24	NUM
ejpam-5049	488	3	]	]	X
ejpam-5049	488	4	g.	g.	PROPN
ejpam-5049	488	5	zhang	zhang	PROPN
ejpam-5049	488	6	and	and	CCONJ
ejpam-5049	488	7	r.	r.	PROPN
ejpam-5049	488	8	zhu	zhu	PROPN
ejpam-5049	488	9	.	.	PUNCT
ejpam-5049	489	1	runge	runge	PROPN
ejpam-5049	489	2	–	–	PUNCT
ejpam-5049	489	3	kutta	kutta	NOUN
ejpam-5049	489	4	convolution	convolution	NOUN
ejpam-5049	489	5	quadrature	quadrature	NOUN
ejpam-5049	489	6	methods	method	NOUN
ejpam-5049	489	7	with	with	ADP
ejpam-5049	489	8	convergence	convergence	NOUN
ejpam-5049	489	9	and	and	CCONJ
ejpam-5049	489	10	stability	stability	NOUN
ejpam-5049	489	11	analysis	analysis	NOUN
ejpam-5049	489	12	for	for	ADP
ejpam-5049	489	13	nonlinear	nonlinear	ADJ
ejpam-5049	489	14	singular	singular	ADJ
ejpam-5049	489	15	fractional	fractional	PROPN
ejpam-5049	489	16	integro	integro	PROPN
ejpam-5049	489	17	–	–	PUNCT
ejpam-5049	489	18	differential	differential	ADJ
ejpam-5049	489	19	equations	equation	NOUN
ejpam-5049	489	20	.	.	PUNCT
ejpam-5049	490	1	communications	communication	NOUN
ejpam-5049	490	2	in	in	ADP
ejpam-5049	490	3	nonlinear	nonlinear	ADJ
ejpam-5049	490	4	science	science	NOUN
ejpam-5049	490	5	and	and	CCONJ
ejpam-5049	490	6	numerical	numerical	PROPN
ejpam-5049	490	7	simulation	simulation	PROPN
ejpam-5049	490	8	,	,	PUNCT
ejpam-5049	490	9	84:105132	84:105132	NUM
ejpam-5049	490	10	–	–	PUNCT
ejpam-5049	490	11	105132	105132	NUM
ejpam-5049	490	12	,	,	PUNCT
ejpam-5049	490	13	2020	2020	NUM
ejpam-5049	490	14	.	.	PUNCT