id	sid	tid	token	lemma	pos
ejpam-4384	1	1	european	european	PROPN
ejpam-4384	1	2	journal	journal	PROPN
ejpam-4384	1	3	of	of	ADP
ejpam-4384	1	4	pure	pure	ADJ
ejpam-4384	1	5	and	and	CCONJ
ejpam-4384	1	6	applied	apply	VERB
ejpam-4384	1	7	mathematics	mathematic	NOUN
ejpam-4384	1	8	vol	vol	NOUN
ejpam-4384	1	9	.	.	PROPN
ejpam-4384	2	1	15	15	NUM
ejpam-4384	2	2	,	,	PUNCT
ejpam-4384	2	3	no	no	INTJ
ejpam-4384	2	4	.	.	NOUN
ejpam-4384	2	5	2	2	NUM
ejpam-4384	2	6	,	,	PUNCT
ejpam-4384	2	7	2022	2022	NUM
ejpam-4384	2	8	,	,	PUNCT
ejpam-4384	2	9	796	796	NUM
ejpam-4384	2	10	-	-	SYM
ejpam-4384	2	11	809	809	NUM
ejpam-4384	2	12	issn	issn	PROPN
ejpam-4384	2	13	1307	1307	NUM
ejpam-4384	2	14	-	-	SYM
ejpam-4384	2	15	5543	5543	NUM
ejpam-4384	2	16	–	–	PUNCT
ejpam-4384	2	17	ejpam.com	ejpam.com	X
ejpam-4384	2	18	published	publish	VERB
ejpam-4384	2	19	by	by	ADP
ejpam-4384	2	20	new	new	PROPN
ejpam-4384	2	21	york	york	PROPN
ejpam-4384	2	22	business	business	PROPN
ejpam-4384	2	23	global	global	PROPN
ejpam-4384	2	24	toeplitz	toeplitz	PROPN
ejpam-4384	2	25	matrix	matrix	NOUN
ejpam-4384	2	26	and	and	CCONJ
ejpam-4384	2	27	nyström	nyström	DET
ejpam-4384	2	28	method	method	NOUN
ejpam-4384	2	29	for	for	ADP
ejpam-4384	2	30	solving	solve	VERB
ejpam-4384	2	31	linear	linear	ADJ
ejpam-4384	2	32	fractional	fractional	ADJ
ejpam-4384	2	33	integro	integro	ADJ
ejpam-4384	2	34	-	-	PUNCT
ejpam-4384	2	35	differential	differential	NOUN
ejpam-4384	2	36	equation	equation	NOUN
ejpam-4384	2	37	sammeha	sammeha	PROPN
ejpam-4384	2	38	raad1,∗	raad1,∗	NOUN
ejpam-4384	2	39	,	,	PUNCT
ejpam-4384	2	40	khawlah	khawlah	VERB
ejpam-4384	2	41	alqurashi1	alqurashi1	PROPN
ejpam-4384	2	42	1	1	NUM
ejpam-4384	2	43	mathematical	mathematical	ADJ
ejpam-4384	2	44	sciences	science	NOUN
ejpam-4384	2	45	,	,	PUNCT
ejpam-4384	2	46	applied	apply	VERB
ejpam-4384	2	47	sciences	science	NOUN
ejpam-4384	2	48	,	,	PUNCT
ejpam-4384	2	49	umm	umm	INTJ
ejpam-4384	2	50	al	al	PROPN
ejpam-4384	2	51	-	-	PUNCT
ejpam-4384	2	52	qura	qura	PROPN
ejpam-4384	2	53	university	university	PROPN
ejpam-4384	2	54	,	,	PUNCT
ejpam-4384	2	55	makkah	makkah	PROPN
ejpam-4384	2	56	,	,	PUNCT
ejpam-4384	2	57	saudi	saudi	PROPN
ejpam-4384	2	58	arabia	arabia	PROPN
ejpam-4384	2	59	abstract	abstract	NOUN
ejpam-4384	2	60	.	.	PUNCT
ejpam-4384	3	1	in	in	ADP
ejpam-4384	3	2	this	this	DET
ejpam-4384	3	3	paper	paper	NOUN
ejpam-4384	3	4	,	,	PUNCT
ejpam-4384	3	5	the	the	DET
ejpam-4384	3	6	volterra	volterra	NOUN
ejpam-4384	3	7	-	-	PUNCT
ejpam-4384	3	8	fredholm	fredholm	NOUN
ejpam-4384	3	9	integral	integral	ADJ
ejpam-4384	3	10	equation	equation	NOUN
ejpam-4384	3	11	is	be	AUX
ejpam-4384	3	12	derived	derive	VERB
ejpam-4384	3	13	from	from	ADP
ejpam-4384	3	14	a	a	DET
ejpam-4384	3	15	linear	linear	ADJ
ejpam-4384	3	16	integrodifferential	integrodifferential	ADJ
ejpam-4384	3	17	equation	equation	NOUN
ejpam-4384	3	18	with	with	ADP
ejpam-4384	3	19	a	a	DET
ejpam-4384	3	20	fractional	fractional	ADJ
ejpam-4384	3	21	order	order	NOUN
ejpam-4384	3	22	0	0	PUNCT
ejpam-4384	3	23	<	<	X
ejpam-4384	3	24	α	α	X
ejpam-4384	3	25	<	<	X
ejpam-4384	3	26	1	1	NUM
ejpam-4384	3	27	using	use	VERB
ejpam-4384	3	28	riemann	riemann	PROPN
ejpam-4384	3	29	–	–	PUNCT
ejpam-4384	3	30	liouville	liouville	VERB
ejpam-4384	3	31	fractional	fractional	ADJ
ejpam-4384	3	32	integral	integral	ADJ
ejpam-4384	3	33	.	.	PUNCT
ejpam-4384	4	1	the	the	DET
ejpam-4384	4	2	existence	existence	NOUN
ejpam-4384	4	3	and	and	CCONJ
ejpam-4384	4	4	uniqueness	uniqueness	NOUN
ejpam-4384	4	5	of	of	ADP
ejpam-4384	4	6	the	the	DET
ejpam-4384	4	7	solution	solution	NOUN
ejpam-4384	4	8	are	be	AUX
ejpam-4384	4	9	proved	prove	VERB
ejpam-4384	4	10	using	use	VERB
ejpam-4384	4	11	the	the	DET
ejpam-4384	4	12	picard	picard	NOUN
ejpam-4384	4	13	method	method	NOUN
ejpam-4384	4	14	.	.	PUNCT
ejpam-4384	5	1	popular	popular	ADJ
ejpam-4384	5	2	numerical	numerical	ADJ
ejpam-4384	5	3	methods	method	NOUN
ejpam-4384	5	4	;	;	PUNCT
ejpam-4384	5	5	the	the	DET
ejpam-4384	5	6	toeplitz	toeplitz	NOUN
ejpam-4384	5	7	matrix	matrix	NOUN
ejpam-4384	5	8	,	,	PUNCT
ejpam-4384	5	9	and	and	CCONJ
ejpam-4384	5	10	the	the	DET
ejpam-4384	5	11	product	product	NOUN
ejpam-4384	5	12	nyström	nyström	NOUN
ejpam-4384	5	13	are	be	AUX
ejpam-4384	5	14	used	use	VERB
ejpam-4384	5	15	in	in	ADP
ejpam-4384	5	16	the	the	DET
ejpam-4384	5	17	solution	solution	NOUN
ejpam-4384	5	18	.	.	PUNCT
ejpam-4384	6	1	these	these	DET
ejpam-4384	6	2	methods	method	NOUN
ejpam-4384	6	3	will	will	AUX
ejpam-4384	6	4	prove	prove	VERB
ejpam-4384	6	5	their	their	PRON
ejpam-4384	6	6	effective	effective	ADJ
ejpam-4384	6	7	in	in	ADP
ejpam-4384	6	8	solving	solve	VERB
ejpam-4384	6	9	this	this	DET
ejpam-4384	6	10	type	type	NOUN
ejpam-4384	6	11	of	of	ADP
ejpam-4384	6	12	equation	equation	NOUN
ejpam-4384	6	13	.	.	PUNCT
ejpam-4384	7	1	two	two	NUM
ejpam-4384	7	2	examples	example	NOUN
ejpam-4384	7	3	are	be	AUX
ejpam-4384	7	4	solved	solve	VERB
ejpam-4384	7	5	using	use	VERB
ejpam-4384	7	6	the	the	DET
ejpam-4384	7	7	mentioned	mention	VERB
ejpam-4384	7	8	methods	method	NOUN
ejpam-4384	7	9	and	and	CCONJ
ejpam-4384	7	10	the	the	DET
ejpam-4384	7	11	estimation	estimation	NOUN
ejpam-4384	7	12	error	error	NOUN
ejpam-4384	7	13	is	be	AUX
ejpam-4384	7	14	calculated	calculate	VERB
ejpam-4384	7	15	.	.	PUNCT
ejpam-4384	8	1	finally	finally	ADV
ejpam-4384	8	2	,	,	PUNCT
ejpam-4384	8	3	a	a	DET
ejpam-4384	8	4	comparison	comparison	NOUN
ejpam-4384	8	5	between	between	ADP
ejpam-4384	8	6	the	the	DET
ejpam-4384	8	7	numerical	numerical	ADJ
ejpam-4384	8	8	results	result	NOUN
ejpam-4384	8	9	is	be	AUX
ejpam-4384	8	10	made	make	VERB
ejpam-4384	8	11	.	.	PUNCT
ejpam-4384	9	1	2020	2020	NUM
ejpam-4384	9	2	mathematics	mathematic	NOUN
ejpam-4384	9	3	subject	subject	NOUN
ejpam-4384	9	4	classifications	classification	NOUN
ejpam-4384	9	5	:	:	PUNCT
ejpam-4384	9	6	45f15	45f15	NUM
ejpam-4384	9	7	,	,	PUNCT
ejpam-4384	9	8	45k05	45k05	NOUN
ejpam-4384	9	9	,	,	PUNCT
ejpam-4384	9	10	45e10	45e10	NUM
ejpam-4384	9	11	,	,	PUNCT
ejpam-4384	9	12	74h15	74h15	ADJ
ejpam-4384	9	13	key	key	ADJ
ejpam-4384	9	14	words	word	NOUN
ejpam-4384	9	15	and	and	CCONJ
ejpam-4384	9	16	phrases	phrase	NOUN
ejpam-4384	9	17	:	:	PUNCT
ejpam-4384	9	18	systems	system	NOUN
ejpam-4384	9	19	of	of	ADP
ejpam-4384	9	20	linear	linear	PROPN
ejpam-4384	9	21	abel	abel	PROPN
ejpam-4384	9	22	equations	equations	PROPN
ejpam-4384	9	23	,	,	PUNCT
ejpam-4384	9	24	integro	integro	ADJ
ejpam-4384	9	25	-	-	PUNCT
ejpam-4384	9	26	partial	partial	ADJ
ejpam-4384	9	27	differential	differential	NOUN
ejpam-4384	9	28	equations	equation	NOUN
ejpam-4384	9	29	,	,	PUNCT
ejpam-4384	9	30	picard	picard	NOUN
ejpam-4384	9	31	method	method	NOUN
ejpam-4384	9	32	;	;	PUNCT
ejpam-4384	9	33	toeplitz	toeplitz	NOUN
ejpam-4384	9	34	matrix	matrix	NOUN
ejpam-4384	9	35	,	,	PUNCT
ejpam-4384	9	36	nyström	nyström	PRON
ejpam-4384	9	37	method	method	NOUN
ejpam-4384	9	38	.	.	PUNCT
ejpam-4384	10	1	1	1	X
ejpam-4384	10	2	.	.	X
ejpam-4384	10	3	introduction	introduction	NOUN
ejpam-4384	10	4	the	the	DET
ejpam-4384	10	5	wide	wide	ADJ
ejpam-4384	10	6	range	range	NOUN
ejpam-4384	10	7	of	of	ADP
ejpam-4384	10	8	applications	application	NOUN
ejpam-4384	10	9	for	for	ADP
ejpam-4384	10	10	fractional	fractional	ADJ
ejpam-4384	10	11	equations	equation	NOUN
ejpam-4384	10	12	has	have	AUX
ejpam-4384	10	13	led	lead	VERB
ejpam-4384	10	14	to	to	ADP
ejpam-4384	10	15	increased	increase	VERB
ejpam-4384	10	16	interest	interest	NOUN
ejpam-4384	10	17	in	in	ADP
ejpam-4384	10	18	recent	recent	ADJ
ejpam-4384	10	19	years	year	NOUN
ejpam-4384	10	20	.	.	PUNCT
ejpam-4384	11	1	the	the	DET
ejpam-4384	11	2	list	list	NOUN
ejpam-4384	11	3	of	of	ADP
ejpam-4384	11	4	applications	application	NOUN
ejpam-4384	11	5	has	have	AUX
ejpam-4384	11	6	expanded	expand	VERB
ejpam-4384	11	7	and	and	CCONJ
ejpam-4384	11	8	become	become	VERB
ejpam-4384	11	9	more	more	ADV
ejpam-4384	11	10	diverse	diverse	ADJ
ejpam-4384	11	11	in	in	ADP
ejpam-4384	11	12	a	a	DET
ejpam-4384	11	13	short	short	ADJ
ejpam-4384	11	14	period	period	NOUN
ejpam-4384	11	15	of	of	ADP
ejpam-4384	11	16	time	time	NOUN
ejpam-4384	11	17	.	.	PUNCT
ejpam-4384	12	1	one	one	NUM
ejpam-4384	12	2	example	example	NOUN
ejpam-4384	12	3	of	of	ADP
ejpam-4384	12	4	such	such	ADJ
ejpam-4384	12	5	uses	use	NOUN
ejpam-4384	12	6	is	be	AUX
ejpam-4384	12	7	electromagnetic	electromagnetic	ADJ
ejpam-4384	12	8	fields	field	NOUN
ejpam-4384	12	9	.	.	PUNCT
ejpam-4384	13	1	[	[	X
ejpam-4384	13	2	17	17	NUM
ejpam-4384	13	3	]	]	PUNCT
ejpam-4384	13	4	constructed	construct	VERB
ejpam-4384	13	5	fractional	fractional	ADJ
ejpam-4384	13	6	integro	integro	ADJ
ejpam-4384	13	7	-	-	PUNCT
ejpam-4384	13	8	differential	differential	NOUN
ejpam-4384	13	9	equations	equation	NOUN
ejpam-4384	13	10	(	(	PUNCT
ejpam-4384	13	11	fi	fi	NOUN
ejpam-4384	13	12	-	-	NOUN
ejpam-4384	13	13	des	de	NOUN
ejpam-4384	13	14	)	)	PUNCT
ejpam-4384	13	15	from	from	ADP
ejpam-4384	13	16	electromagnetic	electromagnetic	ADJ
ejpam-4384	13	17	waves	wave	NOUN
ejpam-4384	13	18	in	in	ADP
ejpam-4384	13	19	a	a	DET
ejpam-4384	13	20	dielectric	dielectric	ADJ
ejpam-4384	13	21	material	material	NOUN
ejpam-4384	13	22	.	.	PUNCT
ejpam-4384	14	1	the	the	DET
ejpam-4384	14	2	existence	existence	NOUN
ejpam-4384	14	3	,	,	PUNCT
ejpam-4384	14	4	uniqueness	uniqueness	NOUN
ejpam-4384	14	5	and	and	CCONJ
ejpam-4384	14	6	the	the	DET
ejpam-4384	14	7	convergence	convergence	NOUN
ejpam-4384	14	8	of	of	ADP
ejpam-4384	14	9	the	the	DET
ejpam-4384	14	10	solution	solution	NOUN
ejpam-4384	14	11	of	of	ADP
ejpam-4384	14	12	fi	fi	NOUN
ejpam-4384	14	13	-	-	NOUN
ejpam-4384	14	14	des	de	NOUN
ejpam-4384	14	15	by	by	ADP
ejpam-4384	14	16	using	use	VERB
ejpam-4384	14	17	the	the	DET
ejpam-4384	14	18	picard	picard	NOUN
ejpam-4384	14	19	method	method	NOUN
ejpam-4384	14	20	were	be	AUX
ejpam-4384	14	21	discussed	discuss	VERB
ejpam-4384	14	22	in	in	ADP
ejpam-4384	14	23	[	[	X
ejpam-4384	14	24	9	9	NUM
ejpam-4384	14	25	]	]	PUNCT
ejpam-4384	14	26	.	.	PUNCT
ejpam-4384	15	1	the	the	DET
ejpam-4384	15	2	existence	existence	NOUN
ejpam-4384	15	3	and	and	CCONJ
ejpam-4384	15	4	uniqueness	uniqueness	NOUN
ejpam-4384	15	5	of	of	ADP
ejpam-4384	15	6	the	the	DET
ejpam-4384	15	7	solution	solution	NOUN
ejpam-4384	15	8	of	of	ADP
ejpam-4384	15	9	the	the	DET
ejpam-4384	15	10	linear	linear	PROPN
ejpam-4384	15	11	fractional	fractional	PROPN
ejpam-4384	15	12	volterra	volterra	PROPN
ejpam-4384	15	13	i	i	PROPN
ejpam-4384	15	14	-	-	PUNCT
ejpam-4384	15	15	des	des	PROPN
ejpam-4384	15	16	with	with	ADP
ejpam-4384	15	17	initial	initial	ADJ
ejpam-4384	15	18	conditions	condition	NOUN
ejpam-4384	15	19	relied	rely	VERB
ejpam-4384	15	20	on	on	ADP
ejpam-4384	15	21	applying	apply	VERB
ejpam-4384	15	22	the	the	DET
ejpam-4384	15	23	picard	picard	NOUN
ejpam-4384	15	24	iteration	iteration	NOUN
ejpam-4384	15	25	method	method	NOUN
ejpam-4384	15	26	to	to	PART
ejpam-4384	15	27	obtain	obtain	VERB
ejpam-4384	15	28	uniformly	uniformly	ADV
ejpam-4384	15	29	convergent	convergent	ADJ
ejpam-4384	15	30	series	series	NOUN
ejpam-4384	15	31	for	for	ADP
ejpam-4384	15	32	the	the	DET
ejpam-4384	15	33	exact	exact	ADJ
ejpam-4384	15	34	solution	solution	NOUN
ejpam-4384	15	35	were	be	AUX
ejpam-4384	15	36	discussed	discuss	VERB
ejpam-4384	15	37	by	by	ADP
ejpam-4384	15	38	[	[	X
ejpam-4384	15	39	13	13	NUM
ejpam-4384	15	40	]	]	PUNCT
ejpam-4384	15	41	.	.	PUNCT
ejpam-4384	16	1	the	the	DET
ejpam-4384	16	2	existence	existence	NOUN
ejpam-4384	16	3	and	and	CCONJ
ejpam-4384	16	4	uniqueness	uniqueness	NOUN
ejpam-4384	16	5	of	of	ADP
ejpam-4384	16	6	mild	mild	ADJ
ejpam-4384	16	7	solutions	solution	NOUN
ejpam-4384	16	8	for	for	ADP
ejpam-4384	16	9	fi	fi	NOUN
ejpam-4384	16	10	-	-	NOUN
ejpam-4384	16	11	des	des	X
ejpam-4384	16	12	were	be	AUX
ejpam-4384	16	13	investigated	investigate	VERB
ejpam-4384	16	14	by	by	ADP
ejpam-4384	16	15	using	use	VERB
ejpam-4384	16	16	holder	holder	NOUN
ejpam-4384	16	17	’s	’s	PART
ejpam-4384	16	18	inequality	inequality	NOUN
ejpam-4384	16	19	,	,	PUNCT
ejpam-4384	16	20	p	p	NOUN
ejpam-4384	16	21	-	-	PUNCT
ejpam-4384	16	22	mean	mean	NOUN
ejpam-4384	16	23	continuity	continuity	NOUN
ejpam-4384	16	24	,	,	PUNCT
ejpam-4384	16	25	and	and	CCONJ
ejpam-4384	16	26	schauder	schauder	NOUN
ejpam-4384	16	27	’s	’s	PART
ejpam-4384	16	28	fixed	fix	VERB
ejpam-4384	16	29	point	point	NOUN
ejpam-4384	16	30	theorem	theorem	VERB
ejpam-4384	16	31	in	in	ADP
ejpam-4384	16	32	banach	banach	NOUN
ejpam-4384	16	33	spaces	space	NOUN
ejpam-4384	16	34	in	in	ADP
ejpam-4384	16	35	[	[	X
ejpam-4384	16	36	3	3	NUM
ejpam-4384	16	37	]	]	PUNCT
ejpam-4384	16	38	.	.	PUNCT
ejpam-4384	17	1	several	several	ADJ
ejpam-4384	17	2	authors	author	NOUN
ejpam-4384	17	3	are	be	AUX
ejpam-4384	17	4	interested	interested	ADJ
ejpam-4384	17	5	in	in	ADP
ejpam-4384	17	6	solving	solve	VERB
ejpam-4384	17	7	fi	fi	NOUN
ejpam-4384	17	8	-	-	NOUN
ejpam-4384	17	9	des	des	X
ejpam-4384	17	10	by	by	ADP
ejpam-4384	17	11	analytical	analytical	ADJ
ejpam-4384	17	12	methods	method	NOUN
ejpam-4384	17	13	.	.	PUNCT
ejpam-4384	18	1	furthermore	furthermore	ADV
ejpam-4384	18	2	,	,	PUNCT
ejpam-4384	18	3	numerical	numerical	ADJ
ejpam-4384	18	4	methods	method	NOUN
ejpam-4384	18	5	are	be	AUX
ejpam-4384	18	6	used	use	VERB
ejpam-4384	18	7	to	to	PART
ejpam-4384	18	8	approximate	approximate	VERB
ejpam-4384	18	9	the	the	DET
ejpam-4384	18	10	solutions	solution	NOUN
ejpam-4384	18	11	.	.	PUNCT
ejpam-4384	19	1	in	in	ADP
ejpam-4384	19	2	[	[	X
ejpam-4384	19	3	12	12	NUM
ejpam-4384	19	4	]	]	PUNCT
ejpam-4384	19	5	introduced	introduce	VERB
ejpam-4384	19	6	the	the	DET
ejpam-4384	19	7	generalized	generalized	ADJ
ejpam-4384	19	8	hat	hat	NOUN
ejpam-4384	19	9	functions	function	NOUN
ejpam-4384	19	10	and	and	CCONJ
ejpam-4384	19	11	operational	operational	ADJ
ejpam-4384	19	12	matrix	matrix	NOUN
ejpam-4384	19	13	of	of	ADP
ejpam-4384	19	14	the	the	DET
ejpam-4384	19	15	fractional	fractional	ADJ
ejpam-4384	19	16	integration	integration	NOUN
ejpam-4384	19	17	to	to	PART
ejpam-4384	19	18	solve	solve	VERB
ejpam-4384	19	19	the	the	DET
ejpam-4384	19	20	fi	fi	NOUN
ejpam-4384	19	21	-	-	NOUN
ejpam-4384	19	22	des	des	X
ejpam-4384	19	23	of	of	ADP
ejpam-4384	19	24	bratu	bratu	NOUN
ejpam-4384	19	25	-	-	PUNCT
ejpam-4384	19	26	type	type	NOUN
ejpam-4384	19	27	numerically	numerically	ADV
ejpam-4384	19	28	.	.	PUNCT
ejpam-4384	20	1	the	the	DET
ejpam-4384	20	2	decomposition	decomposition	NOUN
ejpam-4384	20	3	∗corresponding	∗corresponde	VERB
ejpam-4384	20	4	author	author	NOUN
ejpam-4384	20	5	.	.	PUNCT
ejpam-4384	21	1	doi	doi	NOUN
ejpam-4384	21	2	:	:	PUNCT
ejpam-4384	21	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4384	https://doi.org/10.29020/nybg.ejpam.v15i2.4384	PROPN
ejpam-4384	21	4	email	email	NOUN
ejpam-4384	21	5	addresses	address	VERB
ejpam-4384	21	6	:	:	PUNCT
ejpam-4384	21	7	saraad@uqu.edu.sa	saraad@uqu.edu.sa	PROPN
ejpam-4384	21	8	(	(	PUNCT
ejpam-4384	21	9	s.	s.	PROPN
ejpam-4384	21	10	raad	raad	PROPN
ejpam-4384	21	11	)	)	PUNCT
ejpam-4384	21	12	,	,	PUNCT
ejpam-4384	21	13	s44180462@st.uqu.edu.sa	s44180462@st.uqu.edu.sa	PROPN
ejpam-4384	21	14	(	(	PUNCT
ejpam-4384	21	15	k.	k.	PROPN
ejpam-4384	21	16	alqurashi	alqurashi	PROPN
ejpam-4384	21	17	)	)	PUNCT
ejpam-4384	21	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4384	22	1	796	796	NUM
ejpam-4384	22	2	©	©	PROPN
ejpam-4384	22	3	2022	2022	NUM
ejpam-4384	22	4	ejpam	ejpam	VERB
ejpam-4384	22	5	all	all	DET
ejpam-4384	22	6	rights	right	NOUN
ejpam-4384	22	7	reserved	reserve	VERB
ejpam-4384	22	8	.	.	PUNCT
ejpam-4384	23	1	s.	s.	PROPN
ejpam-4384	23	2	raad	raad	PROPN
ejpam-4384	23	3	,	,	PUNCT
ejpam-4384	23	4	k.	k.	PROPN
ejpam-4384	23	5	alqurashi	alqurashi	PROPN
ejpam-4384	23	6	/	/	SYM
ejpam-4384	23	7	eur	eur	PROPN
ejpam-4384	23	8	.	.	PUNCT
ejpam-4384	24	1	j.	j.	PROPN
ejpam-4384	24	2	pure	pure	PROPN
ejpam-4384	24	3	appl	appl	PROPN
ejpam-4384	24	4	.	.	PROPN
ejpam-4384	24	5	math	math	PROPN
ejpam-4384	24	6	,	,	PUNCT
ejpam-4384	24	7	15	15	NUM
ejpam-4384	24	8	(	(	PUNCT
ejpam-4384	24	9	2	2	NUM
ejpam-4384	24	10	)	)	PUNCT
ejpam-4384	24	11	(	(	PUNCT
ejpam-4384	24	12	2022	2022	NUM
ejpam-4384	24	13	)	)	PUNCT
ejpam-4384	24	14	,	,	PUNCT
ejpam-4384	24	15	796	796	NUM
ejpam-4384	24	16	-	-	SYM
ejpam-4384	24	17	809	809	NUM
ejpam-4384	24	18	797	797	NUM
ejpam-4384	24	19	method	method	NOUN
ejpam-4384	24	20	for	for	ADP
ejpam-4384	24	21	approximating	approximate	VERB
ejpam-4384	24	22	the	the	DET
ejpam-4384	24	23	solution	solution	NOUN
ejpam-4384	24	24	of	of	ADP
ejpam-4384	24	25	fi	fi	NOUN
ejpam-4384	24	26	-	-	ADJ
ejpam-4384	24	27	des	des	ADJ
ejpam-4384	24	28	systems	system	NOUN
ejpam-4384	24	29	was	be	AUX
ejpam-4384	24	30	implemented	implement	VERB
ejpam-4384	24	31	by	by	ADP
ejpam-4384	24	32	[	[	X
ejpam-4384	24	33	11	11	NUM
ejpam-4384	24	34	]	]	PUNCT
ejpam-4384	24	35	.	.	PUNCT
ejpam-4384	25	1	in	in	ADP
ejpam-4384	25	2	[	[	X
ejpam-4384	25	3	15	15	NUM
ejpam-4384	25	4	]	]	PUNCT
ejpam-4384	25	5	applied	apply	VERB
ejpam-4384	25	6	the	the	DET
ejpam-4384	25	7	legendre	legendre	PROPN
ejpam-4384	25	8	wavelets	wavelets	PROPN
ejpam-4384	25	9	method	method	VERB
ejpam-4384	25	10	to	to	PART
ejpam-4384	25	11	approximate	approximate	VERB
ejpam-4384	25	12	the	the	DET
ejpam-4384	25	13	solution	solution	NOUN
ejpam-4384	25	14	of	of	ADP
ejpam-4384	25	15	fi	fi	NOUN
ejpam-4384	25	16	-	-	PROPN
ejpam-4384	25	17	des	des	X
ejpam-4384	25	18	.	.	PUNCT
ejpam-4384	26	1	in	in	ADP
ejpam-4384	26	2	[	[	X
ejpam-4384	26	3	5	5	NUM
ejpam-4384	26	4	]	]	PUNCT
ejpam-4384	26	5	,	,	PUNCT
ejpam-4384	26	6	sinc	sinc	ADJ
ejpam-4384	26	7	-	-	PUNCT
ejpam-4384	26	8	collocation	collocation	NOUN
ejpam-4384	26	9	method	method	NOUN
ejpam-4384	26	10	was	be	AUX
ejpam-4384	26	11	introduced	introduce	VERB
ejpam-4384	26	12	to	to	PART
ejpam-4384	26	13	solve	solve	VERB
ejpam-4384	26	14	volterra	volterra	NOUN
ejpam-4384	26	15	-	-	PUNCT
ejpam-4384	26	16	fredholm	fredholm	NOUN
ejpam-4384	26	17	fi	fi	NOUN
ejpam-4384	26	18	-	-	NOUN
ejpam-4384	26	19	des	des	PROPN
ejpam-4384	26	20	.	.	PROPN
ejpam-4384	26	21	numerical	numerical	PROPN
ejpam-4384	26	22	solutions	solution	NOUN
ejpam-4384	26	23	of	of	ADP
ejpam-4384	26	24	linear	linear	PROPN
ejpam-4384	26	25	fredholm	fredholm	NOUN
ejpam-4384	26	26	-	-	PUNCT
ejpam-4384	26	27	volterra	volterra	NOUN
ejpam-4384	26	28	fi	fi	NOUN
ejpam-4384	26	29	-	-	NOUN
ejpam-4384	26	30	des	des	ADJ
ejpam-4384	26	31	using	use	VERB
ejpam-4384	26	32	laguerre	laguerre	NOUN
ejpam-4384	26	33	polynomials	polynomial	NOUN
ejpam-4384	26	34	were	be	AUX
ejpam-4384	26	35	investigated	investigate	VERB
ejpam-4384	26	36	by	by	ADP
ejpam-4384	26	37	[	[	X
ejpam-4384	26	38	6	6	NUM
ejpam-4384	26	39	]	]	PUNCT
ejpam-4384	26	40	.	.	PUNCT
ejpam-4384	27	1	chebyshev	chebyshev	PROPN
ejpam-4384	27	2	polynomials	polynomial	NOUN
ejpam-4384	27	3	were	be	AUX
ejpam-4384	27	4	used	use	VERB
ejpam-4384	27	5	to	to	PART
ejpam-4384	27	6	solve	solve	VERB
ejpam-4384	27	7	the	the	DET
ejpam-4384	27	8	fredholm	fredholm	NOUN
ejpam-4384	27	9	and	and	CCONJ
ejpam-4384	27	10	volterra	volterra	NOUN
ejpam-4384	27	11	integro	integro	PROPN
ejpam-4384	27	12	-	-	PUNCT
ejpam-4384	27	13	differential	differential	NOUN
ejpam-4384	27	14	equations	equation	NOUN
ejpam-4384	27	15	in	in	ADP
ejpam-4384	27	16	[	[	X
ejpam-4384	27	17	7	7	NUM
ejpam-4384	27	18	]	]	PUNCT
ejpam-4384	27	19	.	.	PUNCT
ejpam-4384	28	1	using	use	VERB
ejpam-4384	28	2	coupled	couple	VERB
ejpam-4384	28	3	mathematical	mathematical	ADJ
ejpam-4384	28	4	solutions	solution	NOUN
ejpam-4384	28	5	,	,	PUNCT
ejpam-4384	28	6	the	the	DET
ejpam-4384	28	7	generalized	generalize	VERB
ejpam-4384	28	8	monotone	monotone	ADJ
ejpam-4384	28	9	iterative	iterative	NOUN
ejpam-4384	28	10	technique	technique	NOUN
ejpam-4384	28	11	was	be	AUX
ejpam-4384	28	12	developed	develop	VERB
ejpam-4384	28	13	to	to	PART
ejpam-4384	28	14	solve	solve	VERB
ejpam-4384	28	15	the	the	DET
ejpam-4384	28	16	caputo	caputo	PROPN
ejpam-4384	28	17	fi	fi	PROPN
ejpam-4384	28	18	-	-	PROPN
ejpam-4384	28	19	des	de	NOUN
ejpam-4384	28	20	of	of	ADP
ejpam-4384	28	21	order	order	NOUN
ejpam-4384	28	22	q[8	q[8	X
ejpam-4384	28	23	]	]	X
ejpam-4384	28	24	.	.	PUNCT
ejpam-4384	29	1	2	2	X
ejpam-4384	29	2	.	.	X
ejpam-4384	29	3	the	the	DET
ejpam-4384	29	4	linear	linear	ADJ
ejpam-4384	29	5	fractional	fractional	ADJ
ejpam-4384	29	6	integro	integro	ADJ
ejpam-4384	29	7	-	-	PUNCT
ejpam-4384	29	8	differential	differential	NOUN
ejpam-4384	29	9	equation	equation	NOUN
ejpam-4384	29	10	consider	consider	VERB
ejpam-4384	29	11	the	the	DET
ejpam-4384	29	12	linear	linear	ADJ
ejpam-4384	29	13	fractional	fractional	ADJ
ejpam-4384	29	14	integro	integro	ADJ
ejpam-4384	29	15	-	-	PUNCT
ejpam-4384	29	16	differential	differential	NOUN
ejpam-4384	29	17	equation	equation	NOUN
ejpam-4384	29	18	(	(	PUNCT
ejpam-4384	29	19	lfi	lfi	NOUN
ejpam-4384	29	20	-	-	PUNCT
ejpam-4384	29	21	de	de	NOUN
ejpam-4384	29	22	)	)	PUNCT
ejpam-4384	29	23	∂αu(x	∂αu(x	PROPN
ejpam-4384	29	24	,	,	PUNCT
ejpam-4384	29	25	t	t	NOUN
ejpam-4384	29	26	)	)	PUNCT
ejpam-4384	29	27	∂tα	∂tα	PROPN
ejpam-4384	29	28	=	=	SYM
ejpam-4384	29	29	f(x	f(x	PROPN
ejpam-4384	29	30	,	,	PUNCT
ejpam-4384	29	31	t	t	PROPN
ejpam-4384	29	32	)	)	PUNCT
ejpam-4384	30	1	+	+	CCONJ
ejpam-4384	30	2	λ	λ	PROPN
ejpam-4384	30	3	∫	∫	PROPN
ejpam-4384	30	4	b	b	PROPN
ejpam-4384	30	5	a	a	DET
ejpam-4384	30	6	k(x	k(x	PROPN
ejpam-4384	30	7	,	,	PUNCT
ejpam-4384	30	8	y)u(y	y)u(y	NOUN
ejpam-4384	30	9	,	,	PUNCT
ejpam-4384	30	10	t)dy	t)dy	PROPN
ejpam-4384	30	11	,	,	PUNCT
ejpam-4384	30	12	(	(	PUNCT
ejpam-4384	30	13	0	0	X
ejpam-4384	30	14	<	<	X
ejpam-4384	30	15	α	α	X
ejpam-4384	30	16	<	<	X
ejpam-4384	30	17	1	1	NUM
ejpam-4384	30	18	)	)	PUNCT
ejpam-4384	30	19	(	(	PUNCT
ejpam-4384	30	20	1	1	X
ejpam-4384	30	21	)	)	PUNCT
ejpam-4384	30	22	with	with	ADP
ejpam-4384	30	23	the	the	DET
ejpam-4384	30	24	initial	initial	ADJ
ejpam-4384	30	25	condition	condition	NOUN
ejpam-4384	30	26	u(x	u(x	NOUN
ejpam-4384	30	27	,	,	PUNCT
ejpam-4384	30	28	0	0	NUM
ejpam-4384	30	29	)	)	PUNCT
ejpam-4384	30	30	=	=	SYM
ejpam-4384	30	31	u0(x	u0(x	NOUN
ejpam-4384	30	32	)	)	PUNCT
ejpam-4384	30	33	.	.	PUNCT
ejpam-4384	31	1	in	in	ADP
ejpam-4384	31	2	(	(	PUNCT
ejpam-4384	31	3	1	1	X
ejpam-4384	31	4	)	)	PUNCT
ejpam-4384	31	5	the	the	DET
ejpam-4384	31	6	unknown	unknown	ADJ
ejpam-4384	31	7	function	function	NOUN
ejpam-4384	31	8	appears	appear	VERB
ejpam-4384	31	9	on	on	ADP
ejpam-4384	31	10	one	one	NUM
ejpam-4384	31	11	side	side	NOUN
ejpam-4384	31	12	of	of	ADP
ejpam-4384	31	13	the	the	DET
ejpam-4384	31	14	equation	equation	NOUN
ejpam-4384	31	15	under	under	ADP
ejpam-4384	31	16	the	the	DET
ejpam-4384	31	17	fractional	fractional	ADJ
ejpam-4384	31	18	order	order	NOUN
ejpam-4384	31	19	derivative	derivative	NOUN
ejpam-4384	31	20	and	and	CCONJ
ejpam-4384	31	21	appears	appear	VERB
ejpam-4384	31	22	on	on	ADP
ejpam-4384	31	23	the	the	DET
ejpam-4384	31	24	other	other	ADJ
ejpam-4384	31	25	side	side	NOUN
ejpam-4384	31	26	under	under	ADP
ejpam-4384	31	27	integration	integration	NOUN
ejpam-4384	31	28	.	.	PUNCT
ejpam-4384	32	1	definition	definition	NOUN
ejpam-4384	32	2	1	1	NUM
ejpam-4384	32	3	.	.	PUNCT
ejpam-4384	33	1	[	[	X
ejpam-4384	33	2	16	16	NUM
ejpam-4384	33	3	]	]	PUNCT
ejpam-4384	33	4	for	for	ADP
ejpam-4384	33	5	all	all	DET
ejpam-4384	33	6	t	t	NOUN
ejpam-4384	33	7	∈	∈	PROPN
ejpam-4384	33	8	[	[	X
ejpam-4384	33	9	a	a	X
ejpam-4384	33	10	,	,	PUNCT
ejpam-4384	33	11	b	b	NOUN
ejpam-4384	33	12	]	]	X
ejpam-4384	33	13	the	the	DET
ejpam-4384	33	14	left	leave	VERB
ejpam-4384	33	15	riemann	riemann	PROPN
ejpam-4384	33	16	-	-	PUNCT
ejpam-4384	33	17	liouville	liouville	VERB
ejpam-4384	33	18	fractional	fractional	ADJ
ejpam-4384	33	19	integral	integral	ADJ
ejpam-4384	33	20	of	of	ADP
ejpam-4384	33	21	order	order	NOUN
ejpam-4384	33	22	α	α	X
ejpam-4384	33	23	>	>	X
ejpam-4384	33	24	0	0	NUM
ejpam-4384	33	25	,	,	PUNCT
ejpam-4384	33	26	of	of	ADP
ejpam-4384	33	27	the	the	DET
ejpam-4384	33	28	function	function	NOUN
ejpam-4384	33	29	ϕ	ϕ	NOUN
ejpam-4384	33	30	:	:	PUNCT
ejpam-4384	33	31	(	(	PUNCT
ejpam-4384	33	32	0,∞	0,∞	NOUN
ejpam-4384	33	33	)	)	PUNCT
ejpam-4384	34	1	→	→	PUNCT
ejpam-4384	34	2	r	r	NOUN
ejpam-4384	34	3	is	be	AUX
ejpam-4384	34	4	defined	define	VERB
ejpam-4384	34	5	as	as	ADP
ejpam-4384	34	6	ai	ai	PROPN
ejpam-4384	34	7	α	α	X
ejpam-4384	34	8	t	t	NOUN
ejpam-4384	34	9	ϕ(t	ϕ(t	NUM
ejpam-4384	34	10	)	)	PUNCT
ejpam-4384	35	1	=	=	SYM
ejpam-4384	35	2	1	1	NUM
ejpam-4384	35	3	γ(α	γ(α	NOUN
ejpam-4384	35	4	)	)	PUNCT
ejpam-4384	35	5	∫	∫	PROPN
ejpam-4384	36	1	t	t	PROPN
ejpam-4384	36	2	a	a	DET
ejpam-4384	36	3	(	(	PUNCT
ejpam-4384	36	4	t−	t−	PROPN
ejpam-4384	36	5	τ)α−1ϕ(τ)dτ	τ)α−1ϕ(τ)dτ	NOUN
ejpam-4384	36	6	,	,	PUNCT
ejpam-4384	36	7	t	t	X
ejpam-4384	36	8	>	>	X
ejpam-4384	36	9	a.	a.	NOUN
ejpam-4384	36	10	(	(	PUNCT
ejpam-4384	36	11	2	2	X
ejpam-4384	36	12	)	)	PUNCT
ejpam-4384	36	13	applying	apply	VERB
ejpam-4384	36	14	relation	relation	NOUN
ejpam-4384	36	15	(	(	PUNCT
ejpam-4384	36	16	2	2	NUM
ejpam-4384	36	17	)	)	PUNCT
ejpam-4384	36	18	to	to	ADP
ejpam-4384	36	19	equation	equation	NOUN
ejpam-4384	36	20	(	(	PUNCT
ejpam-4384	36	21	1	1	NUM
ejpam-4384	36	22	)	)	PUNCT
ejpam-4384	36	23	,	,	PUNCT
ejpam-4384	36	24	we	we	PRON
ejpam-4384	36	25	obtain	obtain	VERB
ejpam-4384	36	26	u(x	u(x	NOUN
ejpam-4384	36	27	,	,	PUNCT
ejpam-4384	36	28	t	t	NOUN
ejpam-4384	36	29	)	)	PUNCT
ejpam-4384	36	30	=	=	SYM
ejpam-4384	36	31	η(x	η(x	PROPN
ejpam-4384	36	32	,	,	PUNCT
ejpam-4384	36	33	t	t	PROPN
ejpam-4384	36	34	)	)	PUNCT
ejpam-4384	36	35	+	+	NUM
ejpam-4384	36	36	λ	λ	PROPN
ejpam-4384	36	37	γ(α	γ(α	NOUN
ejpam-4384	36	38	)	)	PUNCT
ejpam-4384	37	1	∫	∫	PROPN
ejpam-4384	38	1	t	t	PROPN
ejpam-4384	38	2	0	0	NUM
ejpam-4384	38	3	∫	∫	PROPN
ejpam-4384	39	1	b	b	PROPN
ejpam-4384	39	2	a	a	PRON
ejpam-4384	39	3	(	(	PUNCT
ejpam-4384	39	4	t−	t−	PROPN
ejpam-4384	39	5	s)α−1k(x	s)α−1k(x	NOUN
ejpam-4384	39	6	,	,	PUNCT
ejpam-4384	39	7	y)u(y	y)u(y	NOUN
ejpam-4384	39	8	,	,	PUNCT
ejpam-4384	39	9	s)dyds	s)dyds	PROPN
ejpam-4384	39	10	,	,	PUNCT
ejpam-4384	39	11	(	(	PUNCT
ejpam-4384	39	12	3	3	X
ejpam-4384	39	13	)	)	PUNCT
ejpam-4384	39	14	where	where	SCONJ
ejpam-4384	39	15	η(x	η(x	NOUN
ejpam-4384	39	16	,	,	PUNCT
ejpam-4384	39	17	t	t	PROPN
ejpam-4384	39	18	)	)	PUNCT
ejpam-4384	39	19	=	=	SYM
ejpam-4384	39	20	u0(x	u0(x	NOUN
ejpam-4384	39	21	)	)	PUNCT
ejpam-4384	39	22	+	+	CCONJ
ejpam-4384	39	23	1	1	NUM
ejpam-4384	39	24	γ(α	γ(α	NOUN
ejpam-4384	39	25	)	)	PUNCT
ejpam-4384	39	26	∫	∫	PROPN
ejpam-4384	40	1	t	t	PROPN
ejpam-4384	40	2	0	0	NUM
ejpam-4384	40	3	(	(	PUNCT
ejpam-4384	40	4	t−	t−	PROPN
ejpam-4384	40	5	s)α−1f(x	s)α−1f(x	NOUN
ejpam-4384	40	6	,	,	PUNCT
ejpam-4384	40	7	s)ds	s)ds	PROPN
ejpam-4384	40	8	,	,	PUNCT
ejpam-4384	40	9	(	(	PUNCT
ejpam-4384	40	10	4	4	X
ejpam-4384	40	11	)	)	PUNCT
ejpam-4384	40	12	equation	equation	NOUN
ejpam-4384	40	13	(	(	PUNCT
ejpam-4384	40	14	3	3	X
ejpam-4384	40	15	)	)	PUNCT
ejpam-4384	40	16	is	be	AUX
ejpam-4384	40	17	a	a	DET
ejpam-4384	40	18	singular	singular	ADJ
ejpam-4384	40	19	volterra	volterra	NOUN
ejpam-4384	40	20	-	-	PUNCT
ejpam-4384	40	21	fredholm	fredholm	NOUN
ejpam-4384	40	22	integral	integral	ADJ
ejpam-4384	40	23	equation	equation	NOUN
ejpam-4384	40	24	(	(	PUNCT
ejpam-4384	40	25	v	v	NOUN
ejpam-4384	40	26	-	-	PUNCT
ejpam-4384	40	27	fie	fie	NOUN
ejpam-4384	40	28	)	)	PUNCT
ejpam-4384	40	29	of	of	ADP
ejpam-4384	40	30	abel	abel	PROPN
ejpam-4384	40	31	’s	’s	PART
ejpam-4384	40	32	type	type	NOUN
ejpam-4384	40	33	.	.	PUNCT
ejpam-4384	41	1	it	it	PRON
ejpam-4384	41	2	is	be	AUX
ejpam-4384	41	3	clear	clear	ADJ
ejpam-4384	41	4	that	that	SCONJ
ejpam-4384	41	5	equation	equation	NOUN
ejpam-4384	41	6	(	(	PUNCT
ejpam-4384	41	7	3	3	X
ejpam-4384	41	8	)	)	PUNCT
ejpam-4384	41	9	is	be	AUX
ejpam-4384	41	10	equivalent	equivalent	ADJ
ejpam-4384	41	11	to	to	ADP
ejpam-4384	41	12	equation	equation	NOUN
ejpam-4384	41	13	(	(	PUNCT
ejpam-4384	41	14	1	1	NUM
ejpam-4384	41	15	)	)	PUNCT
ejpam-4384	41	16	.	.	PUNCT
ejpam-4384	42	1	3	3	X
ejpam-4384	42	2	.	.	X
ejpam-4384	42	3	picard	picard	NOUN
ejpam-4384	42	4	method	method	NOUN
ejpam-4384	42	5	for	for	ADP
ejpam-4384	42	6	singularv	singularv	NOUN
ejpam-4384	42	7	-	-	PUNCT
ejpam-4384	42	8	fie	fie	NOUN
ejpam-4384	43	1	[	[	X
ejpam-4384	43	2	1	1	NUM
ejpam-4384	43	3	]	]	PUNCT
ejpam-4384	43	4	in	in	ADP
ejpam-4384	43	5	this	this	DET
ejpam-4384	43	6	section	section	NOUN
ejpam-4384	43	7	,	,	PUNCT
ejpam-4384	43	8	the	the	DET
ejpam-4384	43	9	picard	picard	NOUN
ejpam-4384	43	10	method	method	NOUN
ejpam-4384	43	11	is	be	AUX
ejpam-4384	43	12	used	use	VERB
ejpam-4384	43	13	to	to	PART
ejpam-4384	43	14	prove	prove	VERB
ejpam-4384	43	15	the	the	DET
ejpam-4384	43	16	existence	existence	NOUN
ejpam-4384	43	17	of	of	ADP
ejpam-4384	43	18	a	a	DET
ejpam-4384	43	19	unique	unique	ADJ
ejpam-4384	43	20	solution	solution	NOUN
ejpam-4384	43	21	to	to	PART
ejpam-4384	43	22	singular	singular	VERB
ejpam-4384	43	23	v	v	NOUN
ejpam-4384	43	24	-	-	PUNCT
ejpam-4384	43	25	fie	fie	NOUN
ejpam-4384	43	26	(	(	PUNCT
ejpam-4384	43	27	3	3	NUM
ejpam-4384	43	28	)	)	PUNCT
ejpam-4384	43	29	where	where	SCONJ
ejpam-4384	43	30	f	f	PROPN
ejpam-4384	43	31	(	(	PUNCT
ejpam-4384	43	32	t	t	PROPN
ejpam-4384	43	33	,	,	PUNCT
ejpam-4384	43	34	s	s	NOUN
ejpam-4384	43	35	)	)	PUNCT
ejpam-4384	44	1	=	=	SYM
ejpam-4384	44	2	(	(	PUNCT
ejpam-4384	44	3	t−	t−	PROPN
ejpam-4384	44	4	s)α−1	s)α−1	NOUN
ejpam-4384	44	5	.	.	PUNCT
ejpam-4384	45	1	for	for	ADP
ejpam-4384	45	2	this	this	DET
ejpam-4384	45	3	goal	goal	NOUN
ejpam-4384	45	4	,	,	PUNCT
ejpam-4384	45	5	consider	consider	VERB
ejpam-4384	45	6	the	the	DET
ejpam-4384	45	7	following	follow	VERB
ejpam-4384	45	8	conditions	condition	NOUN
ejpam-4384	45	9	:	:	PUNCT
ejpam-4384	45	10	s.	s.	PROPN
ejpam-4384	45	11	raad	raad	PROPN
ejpam-4384	45	12	,	,	PUNCT
ejpam-4384	45	13	k.	k.	PROPN
ejpam-4384	45	14	alqurashi	alqurashi	PROPN
ejpam-4384	45	15	/	/	SYM
ejpam-4384	45	16	eur	eur	PROPN
ejpam-4384	45	17	.	.	PUNCT
ejpam-4384	46	1	j.	j.	PROPN
ejpam-4384	46	2	pure	pure	PROPN
ejpam-4384	46	3	appl	appl	PROPN
ejpam-4384	46	4	.	.	PROPN
ejpam-4384	46	5	math	math	PROPN
ejpam-4384	46	6	,	,	PUNCT
ejpam-4384	46	7	15	15	NUM
ejpam-4384	46	8	(	(	PUNCT
ejpam-4384	46	9	2	2	NUM
ejpam-4384	46	10	)	)	PUNCT
ejpam-4384	46	11	(	(	PUNCT
ejpam-4384	46	12	2022	2022	NUM
ejpam-4384	46	13	)	)	PUNCT
ejpam-4384	46	14	,	,	PUNCT
ejpam-4384	46	15	796	796	NUM
ejpam-4384	46	16	-	-	SYM
ejpam-4384	46	17	809	809	NUM
ejpam-4384	46	18	798	798	NUM
ejpam-4384	46	19	(	(	PUNCT
ejpam-4384	46	20	i	i	NOUN
ejpam-4384	46	21	)	)	PUNCT
ejpam-4384	46	22	volterra	volterra	PROPN
ejpam-4384	46	23	integral	integral	PROPN
ejpam-4384	46	24	’s	’s	PART
ejpam-4384	47	1	kernel	kernel	PROPN
ejpam-4384	47	2	f	f	PROPN
ejpam-4384	47	3	(	(	PUNCT
ejpam-4384	47	4	t	t	PROPN
ejpam-4384	47	5	,	,	PUNCT
ejpam-4384	47	6	s	s	PART
ejpam-4384	47	7	)	)	PUNCT
ejpam-4384	47	8	satisfies	satisfy	VERB
ejpam-4384	47	9	the	the	DET
ejpam-4384	47	10	discontinuity	discontinuity	NOUN
ejpam-4384	47	11	condition	condition	NOUN
ejpam-4384	47	12	[	[	PUNCT
ejpam-4384	47	13	∫	∫	PROPN
ejpam-4384	47	14	t	t	PROPN
ejpam-4384	47	15	0	0	NUM
ejpam-4384	47	16	∫	∫	PROPN
ejpam-4384	47	17	t	t	PROPN
ejpam-4384	47	18	0	0	NUM
ejpam-4384	47	19	|f	|f	PROPN
ejpam-4384	47	20	(	(	PUNCT
ejpam-4384	47	21	t	t	PROPN
ejpam-4384	47	22	,	,	PUNCT
ejpam-4384	47	23	s)|2dsdt	s)|2dsdt	X
ejpam-4384	47	24	]	]	PUNCT
ejpam-4384	47	25	1	1	NUM
ejpam-4384	47	26	2	2	NUM
ejpam-4384	47	27	=	=	SYM
ejpam-4384	47	28	q	q	NOUN
ejpam-4384	47	29	,	,	PUNCT
ejpam-4384	47	30	(	(	PUNCT
ejpam-4384	47	31	q	q	X
ejpam-4384	47	32	is	be	AUX
ejpam-4384	47	33	a	a	DET
ejpam-4384	47	34	constant	constant	ADJ
ejpam-4384	47	35	)	)	PUNCT
ejpam-4384	47	36	.	.	PUNCT
ejpam-4384	48	1	(	(	PUNCT
ejpam-4384	48	2	ii	ii	X
ejpam-4384	48	3	)	)	PUNCT
ejpam-4384	48	4	the	the	DET
ejpam-4384	48	5	kernel	kernel	NOUN
ejpam-4384	48	6	of	of	ADP
ejpam-4384	48	7	fredholm	fredholm	PROPN
ejpam-4384	48	8	k(x	k(x	PROPN
ejpam-4384	48	9	,	,	PUNCT
ejpam-4384	48	10	y	y	NOUN
ejpam-4384	48	11	)	)	PUNCT
ejpam-4384	48	12	belongs	belong	VERB
ejpam-4384	48	13	to	to	ADP
ejpam-4384	48	14	the	the	DET
ejpam-4384	48	15	class	class	NOUN
ejpam-4384	48	16	c[a	c[a	NOUN
ejpam-4384	48	17	,	,	PUNCT
ejpam-4384	48	18	b	b	NOUN
ejpam-4384	48	19	]	]	X
ejpam-4384	48	20	,	,	PUNCT
ejpam-4384	48	21	and	and	CCONJ
ejpam-4384	48	22	it	it	PRON
ejpam-4384	48	23	is	be	AUX
ejpam-4384	48	24	bounded	bound	VERB
ejpam-4384	48	25	,	,	PUNCT
ejpam-4384	48	26	i.e.	i.e.	X
ejpam-4384	48	27	|k(x	|k(x	PROPN
ejpam-4384	48	28	,	,	PUNCT
ejpam-4384	49	1	y)|	y)|	PROPN
ejpam-4384	49	2	≤	≤	PROPN
ejpam-4384	49	3	b	b	PROPN
ejpam-4384	49	4	,	,	PUNCT
ejpam-4384	49	5	∀x	∀x	X
ejpam-4384	49	6	,	,	PUNCT
ejpam-4384	49	7	y	y	PROPN
ejpam-4384	49	8	∈	∈	PROPN
ejpam-4384	50	1	[	[	X
ejpam-4384	50	2	a	a	X
ejpam-4384	50	3	,	,	PUNCT
ejpam-4384	50	4	b	b	NOUN
ejpam-4384	50	5	]	]	X
ejpam-4384	50	6	,	,	PUNCT
ejpam-4384	50	7	(	(	PUNCT
ejpam-4384	50	8	b	b	NOUN
ejpam-4384	50	9	is	be	AUX
ejpam-4384	50	10	a	a	DET
ejpam-4384	50	11	constant	constant	ADJ
ejpam-4384	50	12	)	)	PUNCT
ejpam-4384	50	13	.	.	PUNCT
ejpam-4384	51	1	(	(	PUNCT
ejpam-4384	51	2	iii	iii	X
ejpam-4384	51	3	)	)	PUNCT
ejpam-4384	51	4	the	the	DET
ejpam-4384	51	5	function	function	NOUN
ejpam-4384	51	6	f(x	f(x	PROPN
ejpam-4384	51	7	,	,	PUNCT
ejpam-4384	51	8	t	t	PROPN
ejpam-4384	51	9	)	)	PUNCT
ejpam-4384	51	10	,	,	PUNCT
ejpam-4384	51	11	and	and	CCONJ
ejpam-4384	51	12	its	its	PRON
ejpam-4384	51	13	partial	partial	ADJ
ejpam-4384	51	14	derivatives	derivative	NOUN
ejpam-4384	51	15	with	with	ADP
ejpam-4384	51	16	respect	respect	NOUN
ejpam-4384	51	17	to	to	ADP
ejpam-4384	51	18	x	x	PROPN
ejpam-4384	51	19	and	and	CCONJ
ejpam-4384	51	20	t	t	PROPN
ejpam-4384	51	21	,	,	PUNCT
ejpam-4384	51	22	are	be	AUX
ejpam-4384	51	23	continuous	continuous	ADJ
ejpam-4384	51	24	in	in	ADP
ejpam-4384	51	25	the	the	DET
ejpam-4384	51	26	banach	banach	NOUN
ejpam-4384	51	27	space	space	NOUN
ejpam-4384	51	28	l2[0	l2[0	PROPN
ejpam-4384	51	29	,	,	PUNCT
ejpam-4384	51	30	t	t	X
ejpam-4384	51	31	]	]	X
ejpam-4384	51	32	×	×	NOUN
ejpam-4384	51	33	c[a	c[a	NOUN
ejpam-4384	51	34	,	,	PUNCT
ejpam-4384	51	35	b	b	NOUN
ejpam-4384	51	36	]	]	X
ejpam-4384	51	37	,	,	PUNCT
ejpam-4384	51	38	t	t	X
ejpam-4384	51	39	<	<	X
ejpam-4384	51	40	1	1	NUM
ejpam-4384	51	41	.	.	PUNCT
ejpam-4384	52	1	its	its	PRON
ejpam-4384	52	2	norm	norm	NOUN
ejpam-4384	52	3	is	be	AUX
ejpam-4384	52	4	defined	define	VERB
ejpam-4384	52	5	as	as	ADP
ejpam-4384	52	6	||f(x	||f(x	NOUN
ejpam-4384	52	7	,	,	PUNCT
ejpam-4384	52	8	t)||	t)||	PROPN
ejpam-4384	52	9	=	=	PROPN
ejpam-4384	52	10	max	max	PROPN
ejpam-4384	52	11	a≤x≤b	a≤x≤b	X
ejpam-4384	52	12	∣∣∣	∣∣∣	PROPN
ejpam-4384	52	13	∫	∫	PROPN
ejpam-4384	52	14	x	x	X
ejpam-4384	53	1	a	a	PRON
ejpam-4384	53	2	[	[	PUNCT
ejpam-4384	53	3	∫	∫	PROPN
ejpam-4384	53	4	t	t	PROPN
ejpam-4384	53	5	0	0	X
ejpam-4384	53	6	|f(x	|f(x	PROPN
ejpam-4384	53	7	,	,	PUNCT
ejpam-4384	53	8	s)|2ds	s)|2ds	VERB
ejpam-4384	53	9	]	]	PUNCT
ejpam-4384	53	10	1	1	NUM
ejpam-4384	53	11	2	2	NUM
ejpam-4384	53	12	dy	dy	NOUN
ejpam-4384	53	13	∣∣∣	∣∣∣	NOUN
ejpam-4384	53	14	=	=	SYM
ejpam-4384	53	15	h	h	NOUN
ejpam-4384	53	16	,	,	PUNCT
ejpam-4384	53	17	(	(	PUNCT
ejpam-4384	53	18	h	h	NOUN
ejpam-4384	53	19	is	be	AUX
ejpam-4384	53	20	a	a	DET
ejpam-4384	53	21	constant	constant	ADJ
ejpam-4384	53	22	)	)	PUNCT
ejpam-4384	53	23	.	.	PUNCT
ejpam-4384	54	1	(	(	PUNCT
ejpam-4384	54	2	iv	iv	X
ejpam-4384	54	3	)	)	PUNCT
ejpam-4384	54	4	the	the	DET
ejpam-4384	54	5	function	function	NOUN
ejpam-4384	54	6	u0(x	u0(x	NOUN
ejpam-4384	54	7	)	)	PUNCT
ejpam-4384	54	8	belongs	belong	VERB
ejpam-4384	54	9	to	to	ADP
ejpam-4384	54	10	the	the	DET
ejpam-4384	54	11	space	space	NOUN
ejpam-4384	54	12	c[a	c[a	NOUN
ejpam-4384	54	13	,	,	PUNCT
ejpam-4384	54	14	b	b	NOUN
ejpam-4384	54	15	]	]	PUNCT
ejpam-4384	54	16	and	and	CCONJ
ejpam-4384	54	17	has	have	VERB
ejpam-4384	54	18	the	the	DET
ejpam-4384	54	19	norm	norm	NOUN
ejpam-4384	54	20	||u0(x)||	||u0(x)||	NOUN
ejpam-4384	54	21	=	=	PROPN
ejpam-4384	54	22	max	max	PROPN
ejpam-4384	54	23	a≤x≤b	a≤x≤b	PUNCT
ejpam-4384	54	24	|u0(x)|	|u0(x)|	PUNCT
ejpam-4384	55	1	=	=	PUNCT
ejpam-4384	55	2	a	a	X
ejpam-4384	55	3	,	,	PUNCT
ejpam-4384	55	4	(	(	PUNCT
ejpam-4384	55	5	a	a	PRON
ejpam-4384	55	6	is	be	AUX
ejpam-4384	55	7	a	a	DET
ejpam-4384	55	8	constant	constant	ADJ
ejpam-4384	55	9	)	)	PUNCT
ejpam-4384	55	10	.	.	PUNCT
ejpam-4384	56	1	theorem	theorem	ADJ
ejpam-4384	56	2	1	1	NUM
ejpam-4384	56	3	.	.	PUNCT
ejpam-4384	56	4	equation	equation	NOUN
ejpam-4384	56	5	(	(	PUNCT
ejpam-4384	56	6	3	3	X
ejpam-4384	56	7	)	)	PUNCT
ejpam-4384	56	8	has	have	VERB
ejpam-4384	56	9	a	a	DET
ejpam-4384	56	10	unique	unique	ADJ
ejpam-4384	56	11	solution	solution	NOUN
ejpam-4384	56	12	in	in	ADP
ejpam-4384	56	13	the	the	DET
ejpam-4384	56	14	banach	banach	NOUN
ejpam-4384	56	15	space	space	NOUN
ejpam-4384	56	16	l2[0	l2[0	PROPN
ejpam-4384	56	17	,	,	PUNCT
ejpam-4384	56	18	t	t	X
ejpam-4384	56	19	]	]	PUNCT
ejpam-4384	56	20	×	×	PROPN
ejpam-4384	56	21	c[a	c[a	NUM
ejpam-4384	56	22	,	,	PUNCT
ejpam-4384	56	23	b	b	NOUN
ejpam-4384	56	24	]	]	X
ejpam-4384	56	25	,	,	PUNCT
ejpam-4384	56	26	under	under	ADP
ejpam-4384	56	27	the	the	DET
ejpam-4384	56	28	condition	condition	NOUN
ejpam-4384	56	29	λ(b−	λ(b−	X
ejpam-4384	56	30	a)bq	a)bq	PROPN
ejpam-4384	56	31	<	<	X
ejpam-4384	56	32	γ(α	γ(α	PROPN
ejpam-4384	56	33	)	)	PUNCT
ejpam-4384	56	34	.	.	PUNCT
ejpam-4384	57	1	proof	proof	NOUN
ejpam-4384	57	2	.	.	PUNCT
ejpam-4384	58	1	the	the	DET
ejpam-4384	58	2	existence	existence	NOUN
ejpam-4384	58	3	of	of	ADP
ejpam-4384	58	4	a	a	DET
ejpam-4384	58	5	unique	unique	ADJ
ejpam-4384	58	6	solution	solution	NOUN
ejpam-4384	58	7	of	of	ADP
ejpam-4384	58	8	equation	equation	NOUN
ejpam-4384	58	9	(	(	PUNCT
ejpam-4384	58	10	3	3	X
ejpam-4384	58	11	)	)	PUNCT
ejpam-4384	58	12	can	can	AUX
ejpam-4384	58	13	be	be	AUX
ejpam-4384	58	14	proved	prove	VERB
ejpam-4384	58	15	by	by	ADP
ejpam-4384	58	16	using	use	VERB
ejpam-4384	58	17	the	the	DET
ejpam-4384	58	18	method	method	NOUN
ejpam-4384	58	19	of	of	ADP
ejpam-4384	58	20	successive	successive	ADJ
ejpam-4384	58	21	approximations	approximation	NOUN
ejpam-4384	58	22	which	which	PRON
ejpam-4384	58	23	is	be	AUX
ejpam-4384	58	24	also	also	ADV
ejpam-4384	58	25	called	call	VERB
ejpam-4384	58	26	”	"	PUNCT
ejpam-4384	58	27	picard	picard	PROPN
ejpam-4384	58	28	’s	’s	PART
ejpam-4384	58	29	method	method	NOUN
ejpam-4384	58	30	”	"	PUNCT
ejpam-4384	58	31	.	.	PUNCT
ejpam-4384	59	1	this	this	DET
ejpam-4384	59	2	method	method	NOUN
ejpam-4384	59	3	consists	consist	VERB
ejpam-4384	59	4	of	of	ADP
ejpam-4384	59	5	the	the	DET
ejpam-4384	59	6	following	follow	VERB
ejpam-4384	59	7	simple	simple	ADJ
ejpam-4384	59	8	iteration	iteration	NOUN
ejpam-4384	59	9	.	.	PUNCT
ejpam-4384	60	1	un(x	un(x	PROPN
ejpam-4384	60	2	,	,	PUNCT
ejpam-4384	60	3	t	t	PROPN
ejpam-4384	60	4	)	)	PUNCT
ejpam-4384	60	5	=	=	SYM
ejpam-4384	61	1	η(x	η(x	PROPN
ejpam-4384	61	2	,	,	PUNCT
ejpam-4384	61	3	t	t	PROPN
ejpam-4384	61	4	)	)	PUNCT
ejpam-4384	61	5	+	+	NUM
ejpam-4384	61	6	λ	λ	PROPN
ejpam-4384	61	7	γ(α	γ(α	NOUN
ejpam-4384	61	8	)	)	PUNCT
ejpam-4384	62	1	∫	∫	PROPN
ejpam-4384	63	1	t	t	PROPN
ejpam-4384	63	2	0	0	NUM
ejpam-4384	63	3	∫	∫	PROPN
ejpam-4384	64	1	b	b	PROPN
ejpam-4384	64	2	a	a	DET
ejpam-4384	64	3	f	f	PROPN
ejpam-4384	64	4	(	(	PUNCT
ejpam-4384	64	5	t	t	PROPN
ejpam-4384	64	6	,	,	PUNCT
ejpam-4384	64	7	s)k(x	s)k(x	PROPN
ejpam-4384	64	8	,	,	PUNCT
ejpam-4384	64	9	y)un−1(y	y)un−1(y	PROPN
ejpam-4384	64	10	,	,	PUNCT
ejpam-4384	64	11	s)dyds	s)dyds	PROPN
ejpam-4384	64	12	,	,	PUNCT
ejpam-4384	64	13	(	(	PUNCT
ejpam-4384	64	14	n	n	CCONJ
ejpam-4384	64	15	≥	≥	NOUN
ejpam-4384	64	16	1	1	NUM
ejpam-4384	64	17	)	)	PUNCT
ejpam-4384	64	18	,	,	PUNCT
ejpam-4384	64	19	(	(	PUNCT
ejpam-4384	64	20	5	5	X
ejpam-4384	64	21	)	)	PUNCT
ejpam-4384	64	22	with	with	ADP
ejpam-4384	64	23	u0(x	u0(x	SYM
ejpam-4384	64	24	,	,	PUNCT
ejpam-4384	64	25	t	t	PROPN
ejpam-4384	64	26	)	)	PUNCT
ejpam-4384	64	27	=	=	SYM
ejpam-4384	65	1	η(x	η(x	PROPN
ejpam-4384	65	2	,	,	PUNCT
ejpam-4384	65	3	t	t	PROPN
ejpam-4384	65	4	)	)	PUNCT
ejpam-4384	65	5	.	.	PUNCT
ejpam-4384	66	1	for	for	ADP
ejpam-4384	66	2	ease	ease	NOUN
ejpam-4384	66	3	manipulation	manipulation	NOUN
ejpam-4384	66	4	it	it	PRON
ejpam-4384	66	5	is	be	AUX
ejpam-4384	66	6	convenient	convenient	ADJ
ejpam-4384	66	7	to	to	PART
ejpam-4384	66	8	introduce	introduce	VERB
ejpam-4384	66	9	ξn	ξn	NOUN
ejpam-4384	66	10	=	=	SYM
ejpam-4384	66	11	un(x	un(x	X
ejpam-4384	66	12	,	,	PUNCT
ejpam-4384	66	13	t)−	t)−	PROPN
ejpam-4384	66	14	un−1(x	un−1(x	NOUN
ejpam-4384	66	15	,	,	PUNCT
ejpam-4384	66	16	t	t	PROPN
ejpam-4384	66	17	)	)	PUNCT
ejpam-4384	66	18	(	(	PUNCT
ejpam-4384	66	19	6	6	NUM
ejpam-4384	66	20	)	)	PUNCT
ejpam-4384	67	1	where	where	SCONJ
ejpam-4384	67	2	un(x	un(x	NUM
ejpam-4384	67	3	,	,	PUNCT
ejpam-4384	67	4	t	t	PROPN
ejpam-4384	67	5	)	)	PUNCT
ejpam-4384	67	6	=	=	SYM
ejpam-4384	67	7	n∑	n∑	PROPN
ejpam-4384	67	8	i=0	i=0	PROPN
ejpam-4384	67	9	ξi(x	ξi(x	NUM
ejpam-4384	67	10	,	,	PUNCT
ejpam-4384	67	11	t	t	PROPN
ejpam-4384	67	12	)	)	PUNCT
ejpam-4384	67	13	,	,	PUNCT
ejpam-4384	67	14	ξ0(x	ξ0(x	PROPN
ejpam-4384	67	15	,	,	PUNCT
ejpam-4384	67	16	t	t	PROPN
ejpam-4384	67	17	)	)	PUNCT
ejpam-4384	67	18	=	=	SYM
ejpam-4384	67	19	η(x	η(x	PROPN
ejpam-4384	67	20	,	,	PUNCT
ejpam-4384	67	21	t	t	PROPN
ejpam-4384	67	22	)	)	PUNCT
ejpam-4384	67	23	,	,	PUNCT
ejpam-4384	67	24	(	(	PUNCT
ejpam-4384	67	25	7	7	X
ejpam-4384	67	26	)	)	PUNCT
ejpam-4384	67	27	subtracting	subtract	VERB
ejpam-4384	67	28	from	from	ADP
ejpam-4384	67	29	equation	equation	NOUN
ejpam-4384	67	30	(	(	PUNCT
ejpam-4384	67	31	5	5	NUM
ejpam-4384	67	32	)	)	PUNCT
ejpam-4384	67	33	a	a	DET
ejpam-4384	67	34	similar	similar	ADJ
ejpam-4384	67	35	equation	equation	NOUN
ejpam-4384	67	36	with	with	ADP
ejpam-4384	67	37	n	n	CCONJ
ejpam-4384	67	38	replaced	replace	VERB
ejpam-4384	67	39	by	by	ADP
ejpam-4384	67	40	n−	n−	PROPN
ejpam-4384	67	41	1	1	NUM
ejpam-4384	67	42	,	,	PUNCT
ejpam-4384	67	43	we	we	PRON
ejpam-4384	67	44	get	get	VERB
ejpam-4384	67	45	un(x	un(x	NOUN
ejpam-4384	67	46	,	,	PUNCT
ejpam-4384	67	47	t)−	t)−	PROPN
ejpam-4384	67	48	un−1(x	un−1(x	NOUN
ejpam-4384	67	49	,	,	PUNCT
ejpam-4384	67	50	t	t	PROPN
ejpam-4384	67	51	)	)	PUNCT
ejpam-4384	68	1	=	=	SYM
ejpam-4384	68	2	λ	λ	PROPN
ejpam-4384	68	3	γ(α	γ(α	PROPN
ejpam-4384	68	4	)	)	PUNCT
ejpam-4384	68	5	∫	∫	PROPN
ejpam-4384	69	1	t	t	PROPN
ejpam-4384	69	2	0	0	NUM
ejpam-4384	69	3	∫	∫	PROPN
ejpam-4384	70	1	b	b	PROPN
ejpam-4384	70	2	a	a	DET
ejpam-4384	70	3	f	f	PROPN
ejpam-4384	70	4	(	(	PUNCT
ejpam-4384	70	5	t	t	PROPN
ejpam-4384	70	6	,	,	PUNCT
ejpam-4384	70	7	s)k(x	s)k(x	PROPN
ejpam-4384	70	8	,	,	PUNCT
ejpam-4384	70	9	y)[un−1(y	y)[un−1(y	PROPN
ejpam-4384	70	10	,	,	PUNCT
ejpam-4384	70	11	s)−	s)−	PROPN
ejpam-4384	70	12	un−2(y	un−2(y	PROPN
ejpam-4384	70	13	,	,	PUNCT
ejpam-4384	70	14	s)]dyds	s)]dyds	PROPN
ejpam-4384	70	15	,	,	PUNCT
ejpam-4384	70	16	(	(	PUNCT
ejpam-4384	70	17	8)	8)	NUM
ejpam-4384	70	18	s.	s.	PROPN
ejpam-4384	70	19	raad	raad	PROPN
ejpam-4384	70	20	,	,	PUNCT
ejpam-4384	70	21	k.	k.	PROPN
ejpam-4384	70	22	alqurashi	alqurashi	PROPN
ejpam-4384	70	23	/	/	SYM
ejpam-4384	70	24	eur	eur	PROPN
ejpam-4384	70	25	.	.	PUNCT
ejpam-4384	71	1	j.	j.	PROPN
ejpam-4384	71	2	pure	pure	PROPN
ejpam-4384	71	3	appl	appl	PROPN
ejpam-4384	71	4	.	.	PROPN
ejpam-4384	71	5	math	math	PROPN
ejpam-4384	71	6	,	,	PUNCT
ejpam-4384	71	7	15	15	NUM
ejpam-4384	71	8	(	(	PUNCT
ejpam-4384	71	9	2	2	NUM
ejpam-4384	71	10	)	)	PUNCT
ejpam-4384	71	11	(	(	PUNCT
ejpam-4384	71	12	2022	2022	NUM
ejpam-4384	71	13	)	)	PUNCT
ejpam-4384	71	14	,	,	PUNCT
ejpam-4384	71	15	796	796	NUM
ejpam-4384	71	16	-	-	SYM
ejpam-4384	71	17	809	809	NUM
ejpam-4384	71	18	799	799	NUM
ejpam-4384	71	19	inserting	inserting	NOUN
ejpam-4384	71	20	(	(	PUNCT
ejpam-4384	71	21	6	6	NUM
ejpam-4384	71	22	)	)	PUNCT
ejpam-4384	71	23	in	in	ADP
ejpam-4384	71	24	(	(	PUNCT
ejpam-4384	71	25	8)	8)	NUM
ejpam-4384	71	26	,	,	PUNCT
ejpam-4384	71	27	we	we	PRON
ejpam-4384	71	28	have	have	VERB
ejpam-4384	71	29	|ξn(x	|ξn(x	NUM
ejpam-4384	71	30	,	,	PUNCT
ejpam-4384	71	31	t)|	t)|	NOUN
ejpam-4384	71	32	=	=	SYM
ejpam-4384	71	33	|λ|	|λ|	PROPN
ejpam-4384	71	34	γ(α	γ(α	PROPN
ejpam-4384	71	35	)	)	PUNCT
ejpam-4384	72	1	∫	∫	PROPN
ejpam-4384	73	1	t	t	PROPN
ejpam-4384	73	2	0	0	NUM
ejpam-4384	73	3	∫	∫	PROPN
ejpam-4384	74	1	b	b	PROPN
ejpam-4384	74	2	a	a	PRON
ejpam-4384	74	3	|f	|f	PROPN
ejpam-4384	74	4	(	(	PUNCT
ejpam-4384	74	5	t	t	PROPN
ejpam-4384	74	6	,	,	PUNCT
ejpam-4384	74	7	s)||k(x	s)||k(x	PROPN
ejpam-4384	74	8	,	,	PUNCT
ejpam-4384	74	9	y)||ξn−1(y	y)||ξn−1(y	PROPN
ejpam-4384	74	10	,	,	PUNCT
ejpam-4384	74	11	s)|dyds	s)|dyds	PROPN
ejpam-4384	74	12	,	,	PUNCT
ejpam-4384	74	13	(	(	PUNCT
ejpam-4384	74	14	9	9	X
ejpam-4384	74	15	)	)	PUNCT
ejpam-4384	74	16	using	use	VERB
ejpam-4384	74	17	condition	condition	NOUN
ejpam-4384	74	18	(	(	PUNCT
ejpam-4384	74	19	ii	ii	NOUN
ejpam-4384	74	20	)	)	PUNCT
ejpam-4384	74	21	,	,	PUNCT
ejpam-4384	74	22	then	then	ADV
ejpam-4384	74	23	applying	apply	VERB
ejpam-4384	74	24	cauchy	cauchy	NOUN
ejpam-4384	74	25	-	-	PUNCT
ejpam-4384	74	26	schwarz	schwarz	PROPN
ejpam-4384	74	27	inequality	inequality	NOUN
ejpam-4384	74	28	,	,	PUNCT
ejpam-4384	74	29	we	we	PRON
ejpam-4384	74	30	obtain	obtain	VERB
ejpam-4384	74	31	||ξn(x	||ξn(x	PROPN
ejpam-4384	74	32	,	,	PUNCT
ejpam-4384	74	33	t)||	t)||	NOUN
ejpam-4384	74	34	≤	≤	PROPN
ejpam-4384	74	35	|λ|b	|λ|b	PROPN
ejpam-4384	74	36	γ(α	γ(α	PROPN
ejpam-4384	74	37	)	)	PUNCT
ejpam-4384	75	1	(	(	PUNCT
ejpam-4384	75	2	∫	∫	PROPN
ejpam-4384	75	3	t	t	PROPN
ejpam-4384	75	4	0	0	NUM
ejpam-4384	75	5	∫	∫	PROPN
ejpam-4384	75	6	t	t	PROPN
ejpam-4384	75	7	0	0	NUM
ejpam-4384	75	8	|f	|f	PROPN
ejpam-4384	75	9	(	(	PUNCT
ejpam-4384	75	10	t	t	PROPN
ejpam-4384	75	11	,	,	PUNCT
ejpam-4384	75	12	s)|2dsdt	s)|2dsdt	X
ejpam-4384	75	13	)	)	PUNCT
ejpam-4384	75	14	1	1	NUM
ejpam-4384	75	15	2	2	NUM
ejpam-4384	75	16	max	max	PROPN
ejpam-4384	75	17	a≤x≤b	a≤x≤b	X
ejpam-4384	75	18	∣∣∣	∣∣∣	PROPN
ejpam-4384	75	19	∫	∫	PROPN
ejpam-4384	75	20	x	x	X
ejpam-4384	75	21	a	a	PRON
ejpam-4384	75	22	(	(	PUNCT
ejpam-4384	75	23	∫	∫	PROPN
ejpam-4384	75	24	t	t	PROPN
ejpam-4384	75	25	0	0	NUM
ejpam-4384	75	26	|ξn−1(y	|ξn−1(y	ADJ
ejpam-4384	75	27	,	,	PUNCT
ejpam-4384	75	28	s)|2ds	s)|2ds	VERB
ejpam-4384	75	29	)	)	PUNCT
ejpam-4384	75	30	1	1	NUM
ejpam-4384	75	31	2	2	NUM
ejpam-4384	75	32	dy	dy	NOUN
ejpam-4384	75	33	∣∣∣	∣∣∣	PROPN
ejpam-4384	75	34	∫	∫	PROPN
ejpam-4384	75	35	b	b	PROPN
ejpam-4384	75	36	a	a	DET
ejpam-4384	75	37	dy	dy	NOUN
ejpam-4384	75	38	,	,	PUNCT
ejpam-4384	75	39	in	in	ADP
ejpam-4384	75	40	view	view	NOUN
ejpam-4384	75	41	of	of	ADP
ejpam-4384	75	42	condition	condition	NOUN
ejpam-4384	75	43	(	(	PUNCT
ejpam-4384	75	44	i	i	NOUN
ejpam-4384	75	45	)	)	PUNCT
ejpam-4384	75	46	,	,	PUNCT
ejpam-4384	75	47	we	we	PRON
ejpam-4384	75	48	get	get	VERB
ejpam-4384	75	49	||ξn(x	||ξn(x	PROPN
ejpam-4384	75	50	,	,	PUNCT
ejpam-4384	75	51	t)||	t)||	NOUN
ejpam-4384	75	52	≤	≤	PROPN
ejpam-4384	75	53	|λ|bq(b−	|λ|bq(b−	X
ejpam-4384	75	54	a	a	PRON
ejpam-4384	75	55	)	)	PUNCT
ejpam-4384	75	56	γ(α	γ(α	NOUN
ejpam-4384	75	57	)	)	PUNCT
ejpam-4384	75	58	||ξn−1(x	||ξn−1(x	NUM
ejpam-4384	75	59	,	,	PUNCT
ejpam-4384	75	60	t)||	t)||	NOUN
ejpam-4384	75	61	.	.	PUNCT
ejpam-4384	76	1	(	(	PUNCT
ejpam-4384	76	2	10	10	NUM
ejpam-4384	76	3	)	)	PUNCT
ejpam-4384	76	4	inequality	inequality	NOUN
ejpam-4384	76	5	(	(	PUNCT
ejpam-4384	76	6	10	10	NUM
ejpam-4384	76	7	)	)	PUNCT
ejpam-4384	76	8	for	for	ADP
ejpam-4384	76	9	n	n	NOUN
ejpam-4384	76	10	=	=	SYM
ejpam-4384	76	11	1	1	NUM
ejpam-4384	76	12	,	,	PUNCT
ejpam-4384	76	13	yields	yield	NOUN
ejpam-4384	76	14	||ξ1(x	||ξ1(x	NOUN
ejpam-4384	76	15	,	,	PUNCT
ejpam-4384	76	16	t)||	t)||	NOUN
ejpam-4384	76	17	≤	≤	NUM
ejpam-4384	76	18	σ||ξ0(x	σ||ξ0(x	NOUN
ejpam-4384	76	19	,	,	PUNCT
ejpam-4384	76	20	t)||	t)||	NOUN
ejpam-4384	76	21	;	;	PUNCT
ejpam-4384	76	22	(	(	PUNCT
ejpam-4384	76	23	σ	σ	NOUN
ejpam-4384	76	24	=	=	PUNCT
ejpam-4384	76	25	|λ|bq(b−	|λ|bq(b−	NOUN
ejpam-4384	76	26	a	a	PRON
ejpam-4384	76	27	)	)	PUNCT
ejpam-4384	76	28	γ(α	γ(α	NOUN
ejpam-4384	76	29	)	)	PUNCT
ejpam-4384	76	30	)	)	PUNCT
ejpam-4384	76	31	,	,	PUNCT
ejpam-4384	76	32	(	(	PUNCT
ejpam-4384	76	33	11	11	NUM
ejpam-4384	76	34	)	)	PUNCT
ejpam-4384	76	35	from	from	ADP
ejpam-4384	76	36	(	(	PUNCT
ejpam-4384	76	37	4	4	NUM
ejpam-4384	76	38	)	)	PUNCT
ejpam-4384	76	39	and	and	CCONJ
ejpam-4384	76	40	(	(	PUNCT
ejpam-4384	76	41	7	7	NUM
ejpam-4384	76	42	)	)	PUNCT
ejpam-4384	76	43	,	,	PUNCT
ejpam-4384	76	44	we	we	PRON
ejpam-4384	76	45	have	have	VERB
ejpam-4384	76	46	|ξ0(x	|ξ0(x	NUM
ejpam-4384	76	47	,	,	PUNCT
ejpam-4384	76	48	t)|	t)|	ADJ
ejpam-4384	76	49	≤	≤	ADJ
ejpam-4384	76	50	|u0(x)|+	|u0(x)|+	PROPN
ejpam-4384	76	51	1	1	NUM
ejpam-4384	76	52	γ(α	γ(α	NOUN
ejpam-4384	76	53	)	)	PUNCT
ejpam-4384	76	54	∫	∫	PROPN
ejpam-4384	77	1	t	t	PROPN
ejpam-4384	77	2	0	0	NUM
ejpam-4384	77	3	|f	|f	PROPN
ejpam-4384	77	4	(	(	PUNCT
ejpam-4384	77	5	t	t	PROPN
ejpam-4384	77	6	,	,	PUNCT
ejpam-4384	77	7	s)||f(x	s)||f(x	NOUN
ejpam-4384	77	8	,	,	PUNCT
ejpam-4384	77	9	s)|ds	s)|ds	NOUN
ejpam-4384	77	10	,	,	PUNCT
ejpam-4384	77	11	after	after	ADP
ejpam-4384	77	12	applying	apply	VERB
ejpam-4384	77	13	cauchy	cauchy	NOUN
ejpam-4384	77	14	-	-	PUNCT
ejpam-4384	77	15	schwarz	schwarz	PROPN
ejpam-4384	77	16	inequality	inequality	NOUN
ejpam-4384	77	17	,	,	PUNCT
ejpam-4384	77	18	we	we	PRON
ejpam-4384	77	19	get	get	VERB
ejpam-4384	77	20	||ξ0(x	||ξ0(x	NOUN
ejpam-4384	77	21	,	,	PUNCT
ejpam-4384	78	1	t)||	t)||	NOUN
ejpam-4384	78	2	≤	≤	ADJ
ejpam-4384	78	3	max	max	PROPN
ejpam-4384	78	4	a≤x≤b	a≤x≤b	PROPN
ejpam-4384	78	5	|u0(x)|+	|u0(x)|+	PROPN
ejpam-4384	78	6	1	1	NUM
ejpam-4384	78	7	γ(α	γ(α	NOUN
ejpam-4384	78	8	)	)	PUNCT
ejpam-4384	79	1	(	(	PUNCT
ejpam-4384	79	2	∫	∫	PROPN
ejpam-4384	79	3	t	t	PROPN
ejpam-4384	79	4	0	0	NUM
ejpam-4384	79	5	∫	∫	PROPN
ejpam-4384	79	6	t	t	PROPN
ejpam-4384	79	7	0	0	NUM
ejpam-4384	79	8	|f	|f	PROPN
ejpam-4384	79	9	(	(	PUNCT
ejpam-4384	79	10	t	t	PROPN
ejpam-4384	79	11	,	,	PUNCT
ejpam-4384	79	12	s)|2dsdt	s)|2dsdt	X
ejpam-4384	79	13	)	)	PUNCT
ejpam-4384	79	14	1	1	NUM
ejpam-4384	79	15	2	2	NUM
ejpam-4384	79	16	max	max	PROPN
ejpam-4384	79	17	a≤x≤b	a≤x≤b	X
ejpam-4384	79	18	∣∣∣	∣∣∣	PROPN
ejpam-4384	80	1	∫	∫	PROPN
ejpam-4384	81	1	x	x	X
ejpam-4384	82	1	a	a	PRON
ejpam-4384	82	2	(	(	PUNCT
ejpam-4384	82	3	∫	∫	PROPN
ejpam-4384	82	4	t	t	PROPN
ejpam-4384	82	5	0	0	X
ejpam-4384	82	6	|f(x	|f(x	PROPN
ejpam-4384	82	7	,	,	PUNCT
ejpam-4384	82	8	s)|2ds	s)|2ds	VERB
ejpam-4384	82	9	)	)	PUNCT
ejpam-4384	82	10	1	1	NUM
ejpam-4384	82	11	2	2	NUM
ejpam-4384	82	12	dy	dy	NOUN
ejpam-4384	82	13	∣∣∣	∣∣∣	NOUN
ejpam-4384	82	14	,	,	PUNCT
ejpam-4384	82	15	using	use	VERB
ejpam-4384	82	16	conditions	condition	NOUN
ejpam-4384	82	17	(	(	PUNCT
ejpam-4384	82	18	i	i	NOUN
ejpam-4384	82	19	)	)	PUNCT
ejpam-4384	82	20	,	,	PUNCT
ejpam-4384	82	21	(	(	PUNCT
ejpam-4384	82	22	iii	iii	NOUN
ejpam-4384	82	23	)	)	PUNCT
ejpam-4384	82	24	and	and	CCONJ
ejpam-4384	82	25	(	(	PUNCT
ejpam-4384	82	26	iv	iv	X
ejpam-4384	82	27	)	)	PUNCT
ejpam-4384	82	28	,	,	PUNCT
ejpam-4384	82	29	the	the	DET
ejpam-4384	82	30	above	above	ADJ
ejpam-4384	82	31	inequality	inequality	NOUN
ejpam-4384	82	32	takes	take	VERB
ejpam-4384	82	33	the	the	DET
ejpam-4384	82	34	form	form	NOUN
ejpam-4384	82	35	||ξ0(x	||ξ0(x	NOUN
ejpam-4384	82	36	,	,	PUNCT
ejpam-4384	82	37	t)||	t)||	NOUN
ejpam-4384	82	38	≤	≤	NOUN
ejpam-4384	82	39	g	g	NOUN
ejpam-4384	82	40	;	;	PUNCT
ejpam-4384	82	41	(	(	PUNCT
ejpam-4384	82	42	g	g	NOUN
ejpam-4384	82	43	=	=	SYM
ejpam-4384	82	44	a+	a+	PUNCT
ejpam-4384	82	45	qh	qh	PROPN
ejpam-4384	82	46	γ(α	γ(α	PROPN
ejpam-4384	82	47	)	)	PUNCT
ejpam-4384	82	48	is	be	AUX
ejpam-4384	82	49	a	a	DET
ejpam-4384	82	50	constant	constant	ADJ
ejpam-4384	82	51	)	)	PUNCT
ejpam-4384	82	52	.	.	PUNCT
ejpam-4384	83	1	(	(	PUNCT
ejpam-4384	83	2	12	12	X
ejpam-4384	83	3	)	)	PUNCT
ejpam-4384	83	4	introducing	introduce	VERB
ejpam-4384	83	5	(	(	PUNCT
ejpam-4384	83	6	11	11	NUM
ejpam-4384	83	7	)	)	PUNCT
ejpam-4384	83	8	in	in	ADP
ejpam-4384	83	9	(	(	PUNCT
ejpam-4384	83	10	12	12	NUM
ejpam-4384	83	11	)	)	PUNCT
ejpam-4384	83	12	,	,	PUNCT
ejpam-4384	83	13	we	we	PRON
ejpam-4384	83	14	have	have	VERB
ejpam-4384	83	15	||ξ1(x	||ξ1(x	NOUN
ejpam-4384	83	16	,	,	PUNCT
ejpam-4384	83	17	t)||	t)||	ADJ
ejpam-4384	83	18	≤	≤	NOUN
ejpam-4384	83	19	σg	σg	NOUN
ejpam-4384	83	20	,	,	PUNCT
ejpam-4384	83	21	by	by	ADP
ejpam-4384	83	22	induction	induction	NOUN
ejpam-4384	83	23	,	,	PUNCT
ejpam-4384	83	24	we	we	PRON
ejpam-4384	83	25	can	can	AUX
ejpam-4384	83	26	prove	prove	VERB
ejpam-4384	83	27	that	that	SCONJ
ejpam-4384	83	28	||ξn(x	||ξn(x	PROPN
ejpam-4384	83	29	,	,	PUNCT
ejpam-4384	83	30	t)||	t)||	NOUN
ejpam-4384	83	31	≤	≤	ADJ
ejpam-4384	83	32	σng	σng	NOUN
ejpam-4384	83	33	;	;	PUNCT
ejpam-4384	83	34	n	n	PROPN
ejpam-4384	83	35	=	=	SYM
ejpam-4384	83	36	0	0	NUM
ejpam-4384	83	37	,	,	PUNCT
ejpam-4384	83	38	1	1	NUM
ejpam-4384	83	39	,	,	PUNCT
ejpam-4384	83	40	2	2	NUM
ejpam-4384	83	41	,	,	PUNCT
ejpam-4384	83	42	....	....	PUNCT
ejpam-4384	83	43	(	(	PUNCT
ejpam-4384	83	44	13	13	NUM
ejpam-4384	83	45	)	)	PUNCT
ejpam-4384	83	46	since	since	SCONJ
ejpam-4384	83	47	(	(	PUNCT
ejpam-4384	83	48	13	13	NUM
ejpam-4384	83	49	)	)	PUNCT
ejpam-4384	83	50	is	be	AUX
ejpam-4384	83	51	obviously	obviously	ADV
ejpam-4384	83	52	true	true	ADJ
ejpam-4384	83	53	for	for	ADP
ejpam-4384	83	54	n	n	NOUN
ejpam-4384	83	55	=	=	SYM
ejpam-4384	83	56	0	0	NUM
ejpam-4384	83	57	,	,	PUNCT
ejpam-4384	83	58	1	1	NUM
ejpam-4384	83	59	,	,	PUNCT
ejpam-4384	83	60	then	then	ADV
ejpam-4384	83	61	it	it	PRON
ejpam-4384	83	62	holds	hold	VERB
ejpam-4384	83	63	for	for	ADP
ejpam-4384	83	64	all	all	DET
ejpam-4384	83	65	n.	n.	NOUN
ejpam-4384	83	66	this	this	PRON
ejpam-4384	83	67	bound	bind	VERB
ejpam-4384	83	68	makes	make	VERB
ejpam-4384	83	69	the	the	DET
ejpam-4384	83	70	sequence	sequence	NOUN
ejpam-4384	83	71	{	{	PUNCT
ejpam-4384	83	72	ξn(x	ξn(x	X
ejpam-4384	83	73	,	,	PUNCT
ejpam-4384	83	74	t	t	PROPN
ejpam-4384	83	75	)	)	PUNCT
ejpam-4384	83	76	}	}	PUNCT
ejpam-4384	83	77	converges	converge	VERB
ejpam-4384	83	78	under	under	ADP
ejpam-4384	83	79	the	the	DET
ejpam-4384	83	80	condition	condition	NOUN
ejpam-4384	83	81	σ	σ	X
ejpam-4384	83	82	<	<	X
ejpam-4384	83	83	1	1	NUM
ejpam-4384	83	84	,	,	PUNCT
ejpam-4384	83	85	and	and	CCONJ
ejpam-4384	83	86	therefore	therefore	ADV
ejpam-4384	83	87	the	the	DET
ejpam-4384	83	88	sequence	sequence	NOUN
ejpam-4384	83	89	{	{	PUNCT
ejpam-4384	83	90	un(x	un(x	PROPN
ejpam-4384	83	91	,	,	PUNCT
ejpam-4384	83	92	t	t	PROPN
ejpam-4384	83	93	)	)	PUNCT
ejpam-4384	83	94	}	}	PUNCT
ejpam-4384	83	95	in	in	ADP
ejpam-4384	83	96	(	(	PUNCT
ejpam-4384	83	97	7	7	X
ejpam-4384	83	98	)	)	PUNCT
ejpam-4384	83	99	converges	converge	NOUN
ejpam-4384	83	100	.	.	PUNCT
ejpam-4384	84	1	hence	hence	ADV
ejpam-4384	84	2	we	we	PRON
ejpam-4384	84	3	can	can	AUX
ejpam-4384	84	4	write	write	VERB
ejpam-4384	84	5	u(x	u(x	NOUN
ejpam-4384	84	6	,	,	PUNCT
ejpam-4384	84	7	t	t	NOUN
ejpam-4384	84	8	)	)	PUNCT
ejpam-4384	84	9	=	=	PUNCT
ejpam-4384	85	1	∞∑	∞∑	NUM
ejpam-4384	85	2	i=0	i=0	PROPN
ejpam-4384	85	3	ξi(x	ξi(x	NUM
ejpam-4384	85	4	,	,	PUNCT
ejpam-4384	85	5	t	t	PROPN
ejpam-4384	85	6	)	)	PUNCT
ejpam-4384	85	7	,	,	PUNCT
ejpam-4384	85	8	(	(	PUNCT
ejpam-4384	85	9	14	14	X
ejpam-4384	85	10	)	)	PUNCT
ejpam-4384	85	11	s.	s.	PROPN
ejpam-4384	85	12	raad	raad	PROPN
ejpam-4384	85	13	,	,	PUNCT
ejpam-4384	85	14	k.	k.	PROPN
ejpam-4384	85	15	alqurashi	alqurashi	PROPN
ejpam-4384	85	16	/	/	SYM
ejpam-4384	85	17	eur	eur	PROPN
ejpam-4384	85	18	.	.	PUNCT
ejpam-4384	86	1	j.	j.	PROPN
ejpam-4384	86	2	pure	pure	PROPN
ejpam-4384	86	3	appl	appl	PROPN
ejpam-4384	86	4	.	.	PROPN
ejpam-4384	86	5	math	math	PROPN
ejpam-4384	86	6	,	,	PUNCT
ejpam-4384	86	7	15	15	NUM
ejpam-4384	86	8	(	(	PUNCT
ejpam-4384	86	9	2	2	NUM
ejpam-4384	86	10	)	)	PUNCT
ejpam-4384	86	11	(	(	PUNCT
ejpam-4384	86	12	2022	2022	NUM
ejpam-4384	86	13	)	)	PUNCT
ejpam-4384	86	14	,	,	PUNCT
ejpam-4384	86	15	796	796	NUM
ejpam-4384	86	16	-	-	SYM
ejpam-4384	86	17	809	809	NUM
ejpam-4384	86	18	800	800	NUM
ejpam-4384	86	19	the	the	DET
ejpam-4384	86	20	series	series	NOUN
ejpam-4384	86	21	(	(	PUNCT
ejpam-4384	86	22	14	14	NUM
ejpam-4384	86	23	)	)	PUNCT
ejpam-4384	86	24	is	be	AUX
ejpam-4384	86	25	uniformly	uniformly	ADV
ejpam-4384	86	26	convergent	convergent	NOUN
ejpam-4384	86	27	since	since	SCONJ
ejpam-4384	86	28	the	the	DET
ejpam-4384	86	29	terms	term	NOUN
ejpam-4384	86	30	ξi(x	ξi(x	NUM
ejpam-4384	86	31	,	,	PUNCT
ejpam-4384	86	32	t	t	PROPN
ejpam-4384	86	33	)	)	PUNCT
ejpam-4384	86	34	are	be	AUX
ejpam-4384	86	35	limited	limit	VERB
ejpam-4384	86	36	by	by	ADP
ejpam-4384	86	37	σi	σi	X
ejpam-4384	86	38	.	.	PUNCT
ejpam-4384	87	1	to	to	PART
ejpam-4384	87	2	prove	prove	VERB
ejpam-4384	87	3	that	that	SCONJ
ejpam-4384	87	4	u(x	u(x	NOUN
ejpam-4384	87	5	,	,	PUNCT
ejpam-4384	87	6	t	t	PROPN
ejpam-4384	87	7	)	)	PUNCT
ejpam-4384	87	8	defined	define	VERB
ejpam-4384	87	9	by	by	ADP
ejpam-4384	87	10	(	(	PUNCT
ejpam-4384	87	11	14	14	NUM
ejpam-4384	87	12	)	)	PUNCT
ejpam-4384	87	13	satisfies	satisfy	VERB
ejpam-4384	87	14	equation	equation	NOUN
ejpam-4384	87	15	(	(	PUNCT
ejpam-4384	87	16	3	3	NUM
ejpam-4384	87	17	)	)	PUNCT
ejpam-4384	87	18	,	,	PUNCT
ejpam-4384	87	19	set	set	VERB
ejpam-4384	87	20	u(x	u(x	PROPN
ejpam-4384	87	21	,	,	PUNCT
ejpam-4384	87	22	t	t	PROPN
ejpam-4384	87	23	)	)	PUNCT
ejpam-4384	87	24	=	=	SYM
ejpam-4384	87	25	un(x	un(x	X
ejpam-4384	87	26	,	,	PUNCT
ejpam-4384	87	27	t	t	PROPN
ejpam-4384	87	28	)	)	PUNCT
ejpam-4384	88	1	+	+	CCONJ
ejpam-4384	88	2	∆n(x	∆n(x	PROPN
ejpam-4384	88	3	,	,	PUNCT
ejpam-4384	88	4	t	t	PROPN
ejpam-4384	88	5	)	)	PUNCT
ejpam-4384	88	6	,	,	PUNCT
ejpam-4384	88	7	(	(	PUNCT
ejpam-4384	88	8	∆n(x	∆n(x	PROPN
ejpam-4384	88	9	,	,	PUNCT
ejpam-4384	88	10	t	t	PROPN
ejpam-4384	88	11	)	)	PUNCT
ejpam-4384	88	12	→	→	SYM
ejpam-4384	88	13	0	0	NUM
ejpam-4384	88	14	as	as	ADP
ejpam-4384	88	15	n→	n→	ADV
ejpam-4384	88	16	∞	∞	PROPN
ejpam-4384	88	17	)	)	PUNCT
ejpam-4384	88	18	,	,	PUNCT
ejpam-4384	88	19	(	(	PUNCT
ejpam-4384	88	20	15	15	NUM
ejpam-4384	88	21	)	)	PUNCT
ejpam-4384	88	22	from	from	ADP
ejpam-4384	88	23	equation	equation	NOUN
ejpam-4384	88	24	(	(	PUNCT
ejpam-4384	88	25	3	3	NUM
ejpam-4384	88	26	)	)	PUNCT
ejpam-4384	88	27	,	,	PUNCT
ejpam-4384	88	28	we	we	PRON
ejpam-4384	88	29	get	get	VERB
ejpam-4384	88	30	u(x	u(x	NOUN
ejpam-4384	88	31	,	,	PUNCT
ejpam-4384	88	32	t)−∆n(x	t)−∆n(x	NUM
ejpam-4384	88	33	,	,	PUNCT
ejpam-4384	88	34	t	t	PROPN
ejpam-4384	88	35	)	)	PUNCT
ejpam-4384	88	36	=	=	SYM
ejpam-4384	88	37	η(x	η(x	PROPN
ejpam-4384	88	38	,	,	PUNCT
ejpam-4384	88	39	t	t	PROPN
ejpam-4384	88	40	)	)	PUNCT
ejpam-4384	88	41	+	+	NUM
ejpam-4384	88	42	λ	λ	PROPN
ejpam-4384	88	43	γ(α	γ(α	NOUN
ejpam-4384	88	44	)	)	PUNCT
ejpam-4384	89	1	∫	∫	PROPN
ejpam-4384	90	1	t	t	PROPN
ejpam-4384	90	2	0	0	NUM
ejpam-4384	90	3	∫	∫	PROPN
ejpam-4384	91	1	b	b	PROPN
ejpam-4384	91	2	a	a	DET
ejpam-4384	91	3	f	f	PROPN
ejpam-4384	91	4	(	(	PUNCT
ejpam-4384	91	5	t	t	PROPN
ejpam-4384	91	6	,	,	PUNCT
ejpam-4384	91	7	s)k(x	s)k(x	PROPN
ejpam-4384	91	8	,	,	PUNCT
ejpam-4384	91	9	y)[u(y	y)[u(y	PROPN
ejpam-4384	91	10	,	,	PUNCT
ejpam-4384	91	11	s)−∆n−1(y	s)−∆n−1(y	PROPN
ejpam-4384	91	12	,	,	PUNCT
ejpam-4384	91	13	s)]dyds	s)]dyds	PROPN
ejpam-4384	91	14	,	,	PUNCT
ejpam-4384	91	15	therefore	therefore	ADV
ejpam-4384	91	16	,	,	PUNCT
ejpam-4384	91	17	we	we	PRON
ejpam-4384	91	18	have∣∣∣u(x	have∣∣∣u(x	VERB
ejpam-4384	91	19	,	,	PUNCT
ejpam-4384	91	20	t)−	t)−	PROPN
ejpam-4384	91	21	η(x	η(x	PROPN
ejpam-4384	91	22	,	,	PUNCT
ejpam-4384	91	23	t)−	t)−	PROPN
ejpam-4384	91	24	λ	λ	PROPN
ejpam-4384	91	25	γ(α	γ(α	PROPN
ejpam-4384	91	26	)	)	PUNCT
ejpam-4384	92	1	∫	∫	PROPN
ejpam-4384	93	1	t	t	PROPN
ejpam-4384	93	2	0	0	NUM
ejpam-4384	93	3	∫	∫	PROPN
ejpam-4384	94	1	b	b	PROPN
ejpam-4384	94	2	a	a	DET
ejpam-4384	94	3	f	f	PROPN
ejpam-4384	94	4	(	(	PUNCT
ejpam-4384	94	5	t	t	PROPN
ejpam-4384	94	6	,	,	PUNCT
ejpam-4384	94	7	s)k(x	s)k(x	PROPN
ejpam-4384	94	8	,	,	PUNCT
ejpam-4384	94	9	y)u(y	y)u(y	PROPN
ejpam-4384	94	10	,	,	PUNCT
ejpam-4384	94	11	s)dyds	s)dyds	NOUN
ejpam-4384	94	12	∣∣∣	∣∣∣	NOUN
ejpam-4384	94	13	≤	≤	NOUN
ejpam-4384	94	14	∣∣∆n(y	∣∣∆n(y	PROPN
ejpam-4384	94	15	,	,	PUNCT
ejpam-4384	94	16	s	s	X
ejpam-4384	94	17	)	)	PUNCT
ejpam-4384	94	18	∣∣+	∣∣+	PROPN
ejpam-4384	94	19	|λ|	|λ|	PROPN
ejpam-4384	94	20	γ(α	γ(α	PROPN
ejpam-4384	94	21	)	)	PUNCT
ejpam-4384	95	1	∫	∫	PROPN
ejpam-4384	96	1	t	t	PROPN
ejpam-4384	96	2	0	0	NUM
ejpam-4384	96	3	∫	∫	PROPN
ejpam-4384	97	1	b	b	PROPN
ejpam-4384	97	2	a	a	DET
ejpam-4384	97	3	|f	|f	PROPN
ejpam-4384	97	4	(	(	PUNCT
ejpam-4384	97	5	t	t	PROPN
ejpam-4384	97	6	,	,	PUNCT
ejpam-4384	97	7	s)||k(x	s)||k(x	PROPN
ejpam-4384	97	8	,	,	PUNCT
ejpam-4384	97	9	y)||∆n−1(y	y)||∆n−1(y	PROPN
ejpam-4384	97	10	,	,	PUNCT
ejpam-4384	97	11	s)|dyds	s)|dyds	NOUN
ejpam-4384	97	12	,	,	PUNCT
ejpam-4384	97	13	using	use	VERB
ejpam-4384	97	14	condition	condition	NOUN
ejpam-4384	97	15	(	(	PUNCT
ejpam-4384	97	16	ii	ii	NOUN
ejpam-4384	97	17	)	)	PUNCT
ejpam-4384	97	18	,	,	PUNCT
ejpam-4384	97	19	then	then	ADV
ejpam-4384	97	20	applying	apply	VERB
ejpam-4384	97	21	cauchy	cauchy	NOUN
ejpam-4384	97	22	-	-	PUNCT
ejpam-4384	97	23	schwarz	schwarz	PROPN
ejpam-4384	97	24	inequality	inequality	NOUN
ejpam-4384	97	25	to	to	ADP
ejpam-4384	97	26	the	the	DET
ejpam-4384	97	27	integral	integral	ADJ
ejpam-4384	97	28	term	term	NOUN
ejpam-4384	97	29	in	in	ADP
ejpam-4384	97	30	the	the	DET
ejpam-4384	97	31	right	right	ADJ
ejpam-4384	97	32	-	-	PUNCT
ejpam-4384	97	33	hand	hand	NOUN
ejpam-4384	97	34	side	side	NOUN
ejpam-4384	97	35	and	and	CCONJ
ejpam-4384	97	36	in	in	ADP
ejpam-4384	97	37	view	view	NOUN
ejpam-4384	97	38	of	of	ADP
ejpam-4384	97	39	condition	condition	NOUN
ejpam-4384	97	40	(	(	PUNCT
ejpam-4384	97	41	i	i	NOUN
ejpam-4384	97	42	)	)	PUNCT
ejpam-4384	97	43	,	,	PUNCT
ejpam-4384	97	44	we	we	PRON
ejpam-4384	97	45	get	get	VERB
ejpam-4384	97	46	||u(x	||u(x	NOUN
ejpam-4384	97	47	,	,	PUNCT
ejpam-4384	97	48	t)−	t)−	PROPN
ejpam-4384	97	49	η(x	η(x	PROPN
ejpam-4384	97	50	,	,	PUNCT
ejpam-4384	97	51	t)−	t)−	PROPN
ejpam-4384	97	52	λ	λ	PROPN
ejpam-4384	97	53	γ(α	γ(α	PROPN
ejpam-4384	97	54	)	)	PUNCT
ejpam-4384	98	1	∫	∫	PROPN
ejpam-4384	99	1	t	t	PROPN
ejpam-4384	99	2	0	0	NUM
ejpam-4384	99	3	∫	∫	PROPN
ejpam-4384	100	1	b	b	PROPN
ejpam-4384	100	2	a	a	DET
ejpam-4384	100	3	f	f	PROPN
ejpam-4384	100	4	(	(	PUNCT
ejpam-4384	100	5	t	t	PROPN
ejpam-4384	100	6	,	,	PUNCT
ejpam-4384	100	7	s)k(x	s)k(x	PROPN
ejpam-4384	100	8	,	,	PUNCT
ejpam-4384	100	9	y)u(y	y)u(y	NOUN
ejpam-4384	100	10	,	,	PUNCT
ejpam-4384	100	11	s)dyds||	s)dyds||	VERB
ejpam-4384	100	12	≤	≤	ADJ
ejpam-4384	100	13	||∆n(x	||∆n(x	NOUN
ejpam-4384	100	14	,	,	PUNCT
ejpam-4384	100	15	t)||+	t)||+	NUM
ejpam-4384	100	16	σ||∆n−1(x	σ||∆n−1(x	NOUN
ejpam-4384	100	17	,	,	PUNCT
ejpam-4384	100	18	t)||	t)||	NOUN
ejpam-4384	100	19	,	,	PUNCT
ejpam-4384	100	20	(	(	PUNCT
ejpam-4384	100	21	16	16	NUM
ejpam-4384	100	22	)	)	PUNCT
ejpam-4384	100	23	by	by	ADP
ejpam-4384	100	24	taking	take	VERB
ejpam-4384	100	25	n	n	CCONJ
ejpam-4384	100	26	large	large	ADJ
ejpam-4384	100	27	enough	enough	ADV
ejpam-4384	100	28	,	,	PUNCT
ejpam-4384	100	29	the	the	DET
ejpam-4384	100	30	right	right	ADJ
ejpam-4384	100	31	-	-	PUNCT
ejpam-4384	100	32	hand	hand	NOUN
ejpam-4384	100	33	side	side	NOUN
ejpam-4384	100	34	of	of	ADP
ejpam-4384	100	35	(	(	PUNCT
ejpam-4384	100	36	16	16	NUM
ejpam-4384	100	37	)	)	PUNCT
ejpam-4384	100	38	can	can	AUX
ejpam-4384	100	39	be	be	AUX
ejpam-4384	100	40	made	make	VERB
ejpam-4384	100	41	as	as	ADV
ejpam-4384	100	42	small	small	ADJ
ejpam-4384	100	43	as	as	SCONJ
ejpam-4384	100	44	desired	desire	VERB
ejpam-4384	100	45	.	.	PUNCT
ejpam-4384	101	1	consequently	consequently	ADV
ejpam-4384	101	2	,	,	PUNCT
ejpam-4384	101	3	the	the	DET
ejpam-4384	101	4	function	function	NOUN
ejpam-4384	101	5	u(x	u(x	NOUN
ejpam-4384	101	6	,	,	PUNCT
ejpam-4384	101	7	t	t	NOUN
ejpam-4384	101	8	)	)	PUNCT
ejpam-4384	101	9	defined	define	VERB
ejpam-4384	101	10	by	by	ADP
ejpam-4384	101	11	(	(	PUNCT
ejpam-4384	101	12	15	15	NUM
ejpam-4384	101	13	)	)	PUNCT
ejpam-4384	101	14	satisfies	satisfie	NOUN
ejpam-4384	101	15	u(x	u(x	NOUN
ejpam-4384	101	16	,	,	PUNCT
ejpam-4384	101	17	t	t	PROPN
ejpam-4384	101	18	)	)	PUNCT
ejpam-4384	101	19	=	=	SYM
ejpam-4384	101	20	η(x	η(x	PROPN
ejpam-4384	101	21	,	,	PUNCT
ejpam-4384	101	22	t	t	PROPN
ejpam-4384	101	23	)	)	PUNCT
ejpam-4384	101	24	+	+	NUM
ejpam-4384	101	25	λ	λ	PROPN
ejpam-4384	101	26	γ(α	γ(α	NOUN
ejpam-4384	101	27	)	)	PUNCT
ejpam-4384	102	1	∫	∫	PROPN
ejpam-4384	103	1	t	t	PROPN
ejpam-4384	103	2	0	0	NUM
ejpam-4384	103	3	∫	∫	PROPN
ejpam-4384	104	1	b	b	PROPN
ejpam-4384	104	2	a	a	DET
ejpam-4384	104	3	f	f	PROPN
ejpam-4384	104	4	(	(	PUNCT
ejpam-4384	104	5	t	t	PROPN
ejpam-4384	104	6	,	,	PUNCT
ejpam-4384	104	7	s)k(x	s)k(x	PROPN
ejpam-4384	104	8	,	,	PUNCT
ejpam-4384	104	9	y)u(y	y)u(y	NOUN
ejpam-4384	104	10	,	,	PUNCT
ejpam-4384	104	11	s)dyds	s)dyds	PROPN
ejpam-4384	104	12	,	,	PUNCT
ejpam-4384	105	1	and	and	CCONJ
ejpam-4384	105	2	is	be	AUX
ejpam-4384	105	3	therefore	therefore	ADV
ejpam-4384	105	4	the	the	DET
ejpam-4384	105	5	solution	solution	NOUN
ejpam-4384	105	6	to	to	ADP
ejpam-4384	105	7	equation	equation	NOUN
ejpam-4384	105	8	(	(	PUNCT
ejpam-4384	105	9	3	3	NUM
ejpam-4384	105	10	)	)	PUNCT
ejpam-4384	105	11	.	.	PUNCT
ejpam-4384	106	1	to	to	PART
ejpam-4384	106	2	show	show	VERB
ejpam-4384	106	3	that	that	SCONJ
ejpam-4384	106	4	u(x	u(x	NOUN
ejpam-4384	106	5	,	,	PUNCT
ejpam-4384	106	6	t	t	PROPN
ejpam-4384	106	7	)	)	PUNCT
ejpam-4384	106	8	is	be	AUX
ejpam-4384	106	9	the	the	DET
ejpam-4384	106	10	only	only	ADJ
ejpam-4384	106	11	solution	solution	NOUN
ejpam-4384	106	12	of	of	ADP
ejpam-4384	106	13	equation	equation	NOUN
ejpam-4384	106	14	(	(	PUNCT
ejpam-4384	106	15	3	3	NUM
ejpam-4384	106	16	)	)	PUNCT
ejpam-4384	106	17	,	,	PUNCT
ejpam-4384	106	18	we	we	PRON
ejpam-4384	106	19	assume	assume	VERB
ejpam-4384	106	20	the	the	DET
ejpam-4384	106	21	existence	existence	NOUN
ejpam-4384	106	22	of	of	ADP
ejpam-4384	106	23	another	another	DET
ejpam-4384	106	24	solution	solution	NOUN
ejpam-4384	106	25	ũ(x	ũ(x	PROPN
ejpam-4384	106	26	,	,	PUNCT
ejpam-4384	106	27	t	t	PROPN
ejpam-4384	106	28	)	)	PUNCT
ejpam-4384	106	29	,	,	PUNCT
ejpam-4384	106	30	then	then	ADV
ejpam-4384	106	31	|u(x	|u(x	PROPN
ejpam-4384	106	32	,	,	PUNCT
ejpam-4384	106	33	t)−	t)−	PROPN
ejpam-4384	106	34	ũ(x	ũ(x	PROPN
ejpam-4384	106	35	,	,	PUNCT
ejpam-4384	106	36	t)|	t)|	ADJ
ejpam-4384	106	37	≤	≤	NUM
ejpam-4384	106	38	|λ|	|λ|	PROPN
ejpam-4384	106	39	γ(α	γ(α	PROPN
ejpam-4384	106	40	)	)	PUNCT
ejpam-4384	107	1	∫	∫	PROPN
ejpam-4384	108	1	t	t	PROPN
ejpam-4384	108	2	0	0	NUM
ejpam-4384	108	3	∫	∫	PROPN
ejpam-4384	109	1	b	b	PROPN
ejpam-4384	109	2	a	a	PRON
ejpam-4384	109	3	|f	|f	PROPN
ejpam-4384	109	4	(	(	PUNCT
ejpam-4384	109	5	t	t	PROPN
ejpam-4384	109	6	,	,	PUNCT
ejpam-4384	109	7	s)||k(x	s)||k(x	PROPN
ejpam-4384	109	8	,	,	PUNCT
ejpam-4384	109	9	y)||u(y	y)||u(y	NOUN
ejpam-4384	109	10	,	,	PUNCT
ejpam-4384	109	11	s)−	s)−	PROPN
ejpam-4384	109	12	ũ(y	ũ(y	PROPN
ejpam-4384	109	13	,	,	PUNCT
ejpam-4384	109	14	s)|dyds	s)|dyds	NOUN
ejpam-4384	109	15	,	,	PUNCT
ejpam-4384	109	16	using	use	VERB
ejpam-4384	109	17	condition	condition	NOUN
ejpam-4384	109	18	(	(	PUNCT
ejpam-4384	109	19	ii	ii	NOUN
ejpam-4384	109	20	)	)	PUNCT
ejpam-4384	109	21	,	,	PUNCT
ejpam-4384	109	22	then	then	ADV
ejpam-4384	109	23	applying	apply	VERB
ejpam-4384	109	24	cauchy	cauchy	NOUN
ejpam-4384	109	25	-	-	PUNCT
ejpam-4384	109	26	schwarz	schwarz	PROPN
ejpam-4384	109	27	inequality	inequality	NOUN
ejpam-4384	109	28	and	and	CCONJ
ejpam-4384	109	29	finally	finally	ADV
ejpam-4384	109	30	in	in	ADP
ejpam-4384	109	31	view	view	NOUN
ejpam-4384	109	32	of	of	ADP
ejpam-4384	109	33	condition	condition	NOUN
ejpam-4384	109	34	(	(	PUNCT
ejpam-4384	109	35	i	i	NOUN
ejpam-4384	109	36	)	)	PUNCT
ejpam-4384	109	37	,	,	PUNCT
ejpam-4384	109	38	we	we	PRON
ejpam-4384	109	39	deduce	deduce	VERB
ejpam-4384	109	40	that	that	SCONJ
ejpam-4384	109	41	||u(x	||u(x	NOUN
ejpam-4384	109	42	,	,	PUNCT
ejpam-4384	109	43	t)−	t)−	PROPN
ejpam-4384	109	44	ũ(x	ũ(x	PROPN
ejpam-4384	109	45	,	,	PUNCT
ejpam-4384	109	46	t)||	t)||	PROPN
ejpam-4384	109	47	≤	≤	X
ejpam-4384	109	48	σ||u(x	σ||u(x	NOUN
ejpam-4384	109	49	,	,	PUNCT
ejpam-4384	109	50	t)−	t)−	PROPN
ejpam-4384	109	51	ũ(x	ũ(x	PROPN
ejpam-4384	109	52	,	,	PUNCT
ejpam-4384	109	53	t)||	t)||	NOUN
ejpam-4384	109	54	,	,	PUNCT
ejpam-4384	109	55	(	(	PUNCT
ejpam-4384	109	56	17	17	NUM
ejpam-4384	109	57	)	)	PUNCT
ejpam-4384	109	58	because	because	SCONJ
ejpam-4384	109	59	of	of	ADP
ejpam-4384	109	60	σ	σ	X
ejpam-4384	109	61	<	<	X
ejpam-4384	109	62	1	1	NUM
ejpam-4384	109	63	,	,	PUNCT
ejpam-4384	109	64	this	this	PRON
ejpam-4384	109	65	can	can	AUX
ejpam-4384	109	66	be	be	AUX
ejpam-4384	109	67	true	true	ADJ
ejpam-4384	109	68	if	if	SCONJ
ejpam-4384	109	69	u(x	u(x	NOUN
ejpam-4384	109	70	,	,	PUNCT
ejpam-4384	109	71	t	t	NOUN
ejpam-4384	109	72	)	)	PUNCT
ejpam-4384	109	73	=	=	SYM
ejpam-4384	110	1	ũ(x	ũ(x	PROPN
ejpam-4384	110	2	,	,	PUNCT
ejpam-4384	110	3	t	t	PROPN
ejpam-4384	110	4	)	)	PUNCT
ejpam-4384	110	5	;	;	PUNCT
ejpam-4384	110	6	that	that	PRON
ejpam-4384	110	7	is	is	ADV
ejpam-4384	110	8	,	,	PUNCT
ejpam-4384	110	9	the	the	DET
ejpam-4384	110	10	solution	solution	NOUN
ejpam-4384	110	11	of	of	ADP
ejpam-4384	110	12	equation	equation	NOUN
ejpam-4384	110	13	(	(	PUNCT
ejpam-4384	110	14	3	3	X
ejpam-4384	110	15	)	)	PUNCT
ejpam-4384	110	16	is	be	AUX
ejpam-4384	110	17	unique	unique	ADJ
ejpam-4384	110	18	.	.	PUNCT
ejpam-4384	111	1	s.	s.	PROPN
ejpam-4384	111	2	raad	raad	PROPN
ejpam-4384	111	3	,	,	PUNCT
ejpam-4384	111	4	k.	k.	PROPN
ejpam-4384	111	5	alqurashi	alqurashi	PROPN
ejpam-4384	111	6	/	/	SYM
ejpam-4384	111	7	eur	eur	PROPN
ejpam-4384	111	8	.	.	PUNCT
ejpam-4384	112	1	j.	j.	PROPN
ejpam-4384	112	2	pure	pure	PROPN
ejpam-4384	112	3	appl	appl	PROPN
ejpam-4384	112	4	.	.	PROPN
ejpam-4384	112	5	math	math	PROPN
ejpam-4384	112	6	,	,	PUNCT
ejpam-4384	112	7	15	15	NUM
ejpam-4384	112	8	(	(	PUNCT
ejpam-4384	112	9	2	2	NUM
ejpam-4384	112	10	)	)	PUNCT
ejpam-4384	112	11	(	(	PUNCT
ejpam-4384	112	12	2022	2022	NUM
ejpam-4384	112	13	)	)	PUNCT
ejpam-4384	112	14	,	,	PUNCT
ejpam-4384	112	15	796	796	NUM
ejpam-4384	112	16	-	-	SYM
ejpam-4384	112	17	809	809	NUM
ejpam-4384	112	18	801	801	NUM
ejpam-4384	112	19	4	4	NUM
ejpam-4384	112	20	.	.	PUNCT
ejpam-4384	113	1	a	a	DET
ejpam-4384	113	2	system	system	NOUN
ejpam-4384	113	3	of	of	ADP
ejpam-4384	113	4	volterra	volterra	PROPN
ejpam-4384	113	5	integral	integral	ADJ
ejpam-4384	113	6	equations	equation	NOUN
ejpam-4384	113	7	[	[	X
ejpam-4384	113	8	1	1	NUM
ejpam-4384	113	9	,	,	PUNCT
ejpam-4384	113	10	2	2	NUM
ejpam-4384	113	11	]	]	PUNCT
ejpam-4384	113	12	in	in	ADP
ejpam-4384	113	13	this	this	DET
ejpam-4384	113	14	section	section	NOUN
ejpam-4384	113	15	,	,	PUNCT
ejpam-4384	113	16	the	the	DET
ejpam-4384	113	17	v	v	NOUN
ejpam-4384	113	18	-	-	PUNCT
ejpam-4384	113	19	fie	fie	NOUN
ejpam-4384	113	20	will	will	AUX
ejpam-4384	113	21	be	be	AUX
ejpam-4384	113	22	converted	convert	VERB
ejpam-4384	113	23	to	to	ADP
ejpam-4384	113	24	a	a	DET
ejpam-4384	113	25	system	system	NOUN
ejpam-4384	113	26	of	of	ADP
ejpam-4384	113	27	volterra	volterra	PROPN
ejpam-4384	113	28	integral	integral	ADJ
ejpam-4384	113	29	equation	equation	NOUN
ejpam-4384	113	30	by	by	ADP
ejpam-4384	113	31	dividing	divide	VERB
ejpam-4384	113	32	the	the	DET
ejpam-4384	113	33	interval	interval	NOUN
ejpam-4384	113	34	[	[	X
ejpam-4384	113	35	a	a	X
ejpam-4384	113	36	,	,	PUNCT
ejpam-4384	113	37	b	b	NOUN
ejpam-4384	113	38	]	]	X
ejpam-4384	113	39	,	,	PUNCT
ejpam-4384	113	40	into	into	ADP
ejpam-4384	113	41	m	m	PROPN
ejpam-4384	113	42	subintervals	subinterval	NOUN
ejpam-4384	113	43	,	,	PUNCT
ejpam-4384	113	44	such	such	ADJ
ejpam-4384	113	45	that	that	SCONJ
ejpam-4384	113	46	a	a	DET
ejpam-4384	113	47	=	=	X
ejpam-4384	113	48	x0	x0	PROPN
ejpam-4384	113	49	<	<	X
ejpam-4384	114	1	x1	x1	X
ejpam-4384	114	2	<	<	X
ejpam-4384	114	3	x2	x2	X
ejpam-4384	114	4	<	<	X
ejpam-4384	114	5	......	......	PUNCT
ejpam-4384	115	1	<	<	X
ejpam-4384	115	2	xm	xm	X
ejpam-4384	115	3	<	<	X
ejpam-4384	115	4	......	......	PUNCT
ejpam-4384	116	1	<	<	X
ejpam-4384	116	2	xm	xm	PROPN
ejpam-4384	116	3	=	=	SYM
ejpam-4384	116	4	b	b	PROPN
ejpam-4384	116	5	where	where	SCONJ
ejpam-4384	116	6	x	x	X
ejpam-4384	116	7	=	=	SYM
ejpam-4384	116	8	xm	xm	PROPN
ejpam-4384	116	9	,	,	PUNCT
ejpam-4384	116	10	m	m	VERB
ejpam-4384	116	11	=	=	NOUN
ejpam-4384	116	12	0	0	NUM
ejpam-4384	116	13	,	,	PUNCT
ejpam-4384	116	14	1	1	NUM
ejpam-4384	116	15	,	,	PUNCT
ejpam-4384	116	16	2	2	NUM
ejpam-4384	116	17	...	...	PUNCT
ejpam-4384	116	18	,m	,m	PUNCT
ejpam-4384	116	19	.	.	PUNCT
ejpam-4384	117	1	equation	equation	NOUN
ejpam-4384	117	2	(	(	PUNCT
ejpam-4384	117	3	3	3	X
ejpam-4384	117	4	)	)	PUNCT
ejpam-4384	117	5	becomes	become	VERB
ejpam-4384	117	6	um(t	um(t	NOUN
ejpam-4384	117	7	)	)	PUNCT
ejpam-4384	117	8	=	=	SYM
ejpam-4384	117	9	ηm(t	ηm(t	NOUN
ejpam-4384	117	10	)	)	PUNCT
ejpam-4384	118	1	+	+	CCONJ
ejpam-4384	118	2	λ	λ	PROPN
ejpam-4384	118	3	γ(α	γ(α	NOUN
ejpam-4384	118	4	)	)	PUNCT
ejpam-4384	118	5	∫	∫	PROPN
ejpam-4384	119	1	t	t	PROPN
ejpam-4384	119	2	0	0	NUM
ejpam-4384	119	3	(	(	PUNCT
ejpam-4384	119	4	t−	t−	PROPN
ejpam-4384	119	5	s)α−1	s)α−1	PROPN
ejpam-4384	119	6	∫	∫	PROPN
ejpam-4384	119	7	b	b	PROPN
ejpam-4384	119	8	a	a	DET
ejpam-4384	119	9	k(xm	k(xm	PROPN
ejpam-4384	119	10	,	,	PUNCT
ejpam-4384	119	11	y)u(y	y)u(y	NOUN
ejpam-4384	119	12	,	,	PUNCT
ejpam-4384	119	13	s)dyds	s)dyds	NOUN
ejpam-4384	119	14	(	(	PUNCT
ejpam-4384	119	15	18	18	NUM
ejpam-4384	119	16	)	)	PUNCT
ejpam-4384	119	17	the	the	DET
ejpam-4384	119	18	fredholm	fredholm	ADJ
ejpam-4384	119	19	integral	integral	ADJ
ejpam-4384	119	20	part	part	NOUN
ejpam-4384	119	21	of	of	ADP
ejpam-4384	119	22	equation	equation	NOUN
ejpam-4384	119	23	(	(	PUNCT
ejpam-4384	119	24	18	18	NUM
ejpam-4384	119	25	)	)	PUNCT
ejpam-4384	119	26	,	,	PUNCT
ejpam-4384	119	27	after	after	ADP
ejpam-4384	119	28	using	use	VERB
ejpam-4384	119	29	the	the	DET
ejpam-4384	119	30	quadrature	quadrature	NOUN
ejpam-4384	119	31	formula	formula	NOUN
ejpam-4384	119	32	,	,	PUNCT
ejpam-4384	119	33	takes	take	VERB
ejpam-4384	119	34	the	the	DET
ejpam-4384	119	35	form	form	NOUN
ejpam-4384	119	36	∫	∫	PROPN
ejpam-4384	119	37	b	b	PROPN
ejpam-4384	119	38	a	a	DET
ejpam-4384	119	39	k(xm	k(xm	PROPN
ejpam-4384	119	40	,	,	PUNCT
ejpam-4384	119	41	y)u(y	y)u(y	NOUN
ejpam-4384	119	42	,	,	PUNCT
ejpam-4384	119	43	s)dy	s)dy	PROPN
ejpam-4384	119	44	=	=	SYM
ejpam-4384	119	45	m∑	m∑	PROPN
ejpam-4384	119	46	l=0	l=0	PROPN
ejpam-4384	119	47	wlk(xm	wlk(xm	PROPN
ejpam-4384	119	48	,	,	PUNCT
ejpam-4384	119	49	xl)u(xl	xl)u(xl	NUM
ejpam-4384	119	50	,	,	PUNCT
ejpam-4384	119	51	s	s	PART
ejpam-4384	119	52	)	)	PUNCT
ejpam-4384	119	53	,	,	PUNCT
ejpam-4384	119	54	l	l	NOUN
ejpam-4384	119	55	=	=	SYM
ejpam-4384	119	56	0	0	NUM
ejpam-4384	119	57	,	,	PUNCT
ejpam-4384	119	58	1	1	NUM
ejpam-4384	119	59	,	,	PUNCT
ejpam-4384	119	60	.....	.....	PUNCT
ejpam-4384	120	1	m	m	PROPN
ejpam-4384	120	2	(	(	PUNCT
ejpam-4384	120	3	19	19	NUM
ejpam-4384	120	4	)	)	PUNCT
ejpam-4384	120	5	using	use	VERB
ejpam-4384	120	6	(	(	PUNCT
ejpam-4384	120	7	19	19	NUM
ejpam-4384	120	8	)	)	PUNCT
ejpam-4384	120	9	in	in	ADP
ejpam-4384	120	10	(	(	PUNCT
ejpam-4384	120	11	18	18	NUM
ejpam-4384	120	12	)	)	PUNCT
ejpam-4384	120	13	,	,	PUNCT
ejpam-4384	120	14	we	we	PRON
ejpam-4384	120	15	have	have	VERB
ejpam-4384	120	16	the	the	DET
ejpam-4384	120	17	following	follow	VERB
ejpam-4384	120	18	volterra	volterra	NOUN
ejpam-4384	120	19	integral	integral	ADJ
ejpam-4384	120	20	equations	equation	NOUN
ejpam-4384	120	21	system	system	NOUN
ejpam-4384	120	22	um(t	um(t	NOUN
ejpam-4384	120	23	)	)	PUNCT
ejpam-4384	120	24	=	=	SYM
ejpam-4384	120	25	ηm(t	ηm(t	NOUN
ejpam-4384	120	26	)	)	PUNCT
ejpam-4384	121	1	+	+	CCONJ
ejpam-4384	121	2	λ	λ	X
ejpam-4384	121	3	γ(α	γ(α	NOUN
ejpam-4384	121	4	)	)	PUNCT
ejpam-4384	121	5	m∑	m∑	VERB
ejpam-4384	122	1	l=0	l=0	PROPN
ejpam-4384	122	2	wlkm	wlkm	VERB
ejpam-4384	122	3	,	,	PUNCT
ejpam-4384	122	4	l	l	PROPN
ejpam-4384	122	5	∫	∫	PROPN
ejpam-4384	122	6	t	t	PROPN
ejpam-4384	122	7	0	0	NUM
ejpam-4384	122	8	(	(	PUNCT
ejpam-4384	122	9	t−	t−	PROPN
ejpam-4384	122	10	s)α−1ul(s)ds	s)α−1ul(s)ds	PROPN
ejpam-4384	122	11	.	.	PUNCT
ejpam-4384	123	1	(	(	PUNCT
ejpam-4384	123	2	20	20	NUM
ejpam-4384	123	3	)	)	PUNCT
ejpam-4384	123	4	where	where	SCONJ
ejpam-4384	123	5	um(t	um(t	NUM
ejpam-4384	123	6	)	)	PUNCT
ejpam-4384	123	7	=	=	SYM
ejpam-4384	123	8	u(xm	u(xm	PROPN
ejpam-4384	123	9	,	,	PUNCT
ejpam-4384	123	10	t	t	PROPN
ejpam-4384	123	11	)	)	PUNCT
ejpam-4384	123	12	,	,	PUNCT
ejpam-4384	123	13	ηm(t	ηm(t	NOUN
ejpam-4384	123	14	)	)	PUNCT
ejpam-4384	123	15	=	=	SYM
ejpam-4384	123	16	η(xm	η(xm	PROPN
ejpam-4384	123	17	,	,	PUNCT
ejpam-4384	123	18	t	t	PROPN
ejpam-4384	123	19	)	)	PUNCT
ejpam-4384	123	20	,	,	PUNCT
ejpam-4384	123	21	km	km	NOUN
ejpam-4384	123	22	,	,	PUNCT
ejpam-4384	123	23	l	l	NOUN
ejpam-4384	123	24	=	=	SYM
ejpam-4384	123	25	k(xm	k(xm	PROPN
ejpam-4384	123	26	,	,	PUNCT
ejpam-4384	123	27	xl	xl	PROPN
ejpam-4384	123	28	)	)	PUNCT
ejpam-4384	123	29	,	,	PUNCT
ejpam-4384	123	30	w0	w0	PROPN
ejpam-4384	123	31	=	=	SYM
ejpam-4384	123	32	wm	wm	PROPN
ejpam-4384	123	33	=	=	SYM
ejpam-4384	123	34	1	1	NUM
ejpam-4384	123	35	2h0	2h0	NUM
ejpam-4384	123	36	,	,	PUNCT
ejpam-4384	123	37	wr	wr	PROPN
ejpam-4384	123	38	=	=	SYM
ejpam-4384	123	39	hr	hr	NOUN
ejpam-4384	123	40	,	,	PUNCT
ejpam-4384	123	41	(	(	PUNCT
ejpam-4384	123	42	r	r	NOUN
ejpam-4384	123	43	̸=	̸=	PROPN
ejpam-4384	123	44	0,m	0,m	NUM
ejpam-4384	123	45	)	)	PUNCT
ejpam-4384	123	46	.	.	PUNCT
ejpam-4384	124	1	5	5	X
ejpam-4384	124	2	.	.	X
ejpam-4384	124	3	numerical	numerical	ADJ
ejpam-4384	124	4	methods	method	NOUN
ejpam-4384	124	5	to	to	PART
ejpam-4384	124	6	solve	solve	VERB
ejpam-4384	124	7	singular	singular	PROPN
ejpam-4384	124	8	volterra	volterra	PROPN
ejpam-4384	124	9	integral	integral	ADJ
ejpam-4384	124	10	equation	equation	NOUN
ejpam-4384	124	11	5.1	5.1	NUM
ejpam-4384	124	12	.	.	PUNCT
ejpam-4384	125	1	the	the	DET
ejpam-4384	125	2	toeplitz	toeplitz	NOUN
ejpam-4384	125	3	matrix	matrix	NOUN
ejpam-4384	125	4	method	method	NOUN
ejpam-4384	125	5	[	[	X
ejpam-4384	125	6	2	2	NUM
ejpam-4384	125	7	,	,	PUNCT
ejpam-4384	125	8	4	4	NUM
ejpam-4384	125	9	]	]	PUNCT
ejpam-4384	125	10	consider	consider	VERB
ejpam-4384	125	11	the	the	DET
ejpam-4384	125	12	volterra	volterra	NOUN
ejpam-4384	125	13	integral	integral	ADJ
ejpam-4384	125	14	equation	equation	NOUN
ejpam-4384	125	15	:	:	PUNCT
ejpam-4384	125	16	u∗(t)−	u∗(t)−	PUNCT
ejpam-4384	125	17	λ	λ	X
ejpam-4384	125	18	∫	∫	PROPN
ejpam-4384	125	19	t	t	PROPN
ejpam-4384	125	20	0	0	NUM
ejpam-4384	125	21	(	(	PUNCT
ejpam-4384	125	22	t−	t−	PROPN
ejpam-4384	125	23	s)(α−1)u∗(s)ds	s)(α−1)u∗(s)ds	PROPN
ejpam-4384	125	24	=	=	PUNCT
ejpam-4384	125	25	f∗(t	f∗(t	PROPN
ejpam-4384	125	26	)	)	PUNCT
ejpam-4384	125	27	,	,	PUNCT
ejpam-4384	125	28	(	(	PUNCT
ejpam-4384	125	29	21	21	NUM
ejpam-4384	125	30	)	)	PUNCT
ejpam-4384	125	31	write	write	VERB
ejpam-4384	125	32	the	the	DET
ejpam-4384	125	33	integral	integral	ADJ
ejpam-4384	125	34	term	term	NOUN
ejpam-4384	125	35	in	in	ADP
ejpam-4384	125	36	the	the	DET
ejpam-4384	125	37	form∫	form∫	ADJ
ejpam-4384	125	38	t	t	NOUN
ejpam-4384	125	39	0	0	NUM
ejpam-4384	126	1	(	(	PUNCT
ejpam-4384	126	2	t−	t−	PROPN
ejpam-4384	126	3	s)(α−1)u∗(s)ds	s)(α−1)u∗(s)ds	PROPN
ejpam-4384	126	4	=	=	PROPN
ejpam-4384	126	5	n−1∑	n−1∑	PROPN
ejpam-4384	126	6	n=0	n=0	NUM
ejpam-4384	126	7	∫	∫	PROPN
ejpam-4384	127	1	nh+h	nh+h	PROPN
ejpam-4384	127	2	nh	nh	PROPN
ejpam-4384	127	3	(	(	PUNCT
ejpam-4384	127	4	t−	t−	PROPN
ejpam-4384	127	5	s)(α−1)u∗(s)ds	s)(α−1)u∗(s)ds	PROPN
ejpam-4384	127	6	,	,	PUNCT
ejpam-4384	127	7	(	(	PUNCT
ejpam-4384	127	8	h	h	NOUN
ejpam-4384	127	9	=	=	SYM
ejpam-4384	127	10	t	t	PROPN
ejpam-4384	127	11	n	n	PROPN
ejpam-4384	127	12	)	)	PUNCT
ejpam-4384	127	13	,	,	PUNCT
ejpam-4384	127	14	(	(	PUNCT
ejpam-4384	127	15	22	22	NUM
ejpam-4384	127	16	)	)	PUNCT
ejpam-4384	127	17	approximate	approximate	NOUN
ejpam-4384	127	18	the	the	DET
ejpam-4384	127	19	integral	integral	NOUN
ejpam-4384	127	20	in	in	ADP
ejpam-4384	127	21	the	the	DET
ejpam-4384	127	22	right	right	ADJ
ejpam-4384	127	23	hand	hand	NOUN
ejpam-4384	127	24	side	side	NOUN
ejpam-4384	127	25	of	of	ADP
ejpam-4384	127	26	equation	equation	NOUN
ejpam-4384	127	27	(	(	PUNCT
ejpam-4384	127	28	22	22	NUM
ejpam-4384	127	29	)	)	PUNCT
ejpam-4384	127	30	by∫	by∫	PROPN
ejpam-4384	127	31	nh+h	nh+h	PROPN
ejpam-4384	127	32	nh	nh	PROPN
ejpam-4384	127	33	(	(	PUNCT
ejpam-4384	127	34	t−	t−	PROPN
ejpam-4384	127	35	s)(α−1)u∗(s)ds	s)(α−1)u∗(s)ds	PROPN
ejpam-4384	127	36	=	=	SYM
ejpam-4384	127	37	an(t)u	an(t)u	NUM
ejpam-4384	127	38	∗(nh	∗(nh	PROPN
ejpam-4384	127	39	)	)	PUNCT
ejpam-4384	128	1	+	+	ADP
ejpam-4384	128	2	bn(t)u	bn(t)u	PROPN
ejpam-4384	128	3	∗(nh+	∗(nh+	NUM
ejpam-4384	128	4	h	h	NOUN
ejpam-4384	128	5	)	)	PUNCT
ejpam-4384	128	6	,	,	PUNCT
ejpam-4384	128	7	(	(	PUNCT
ejpam-4384	128	8	23	23	NUM
ejpam-4384	128	9	)	)	PUNCT
ejpam-4384	128	10	where	where	SCONJ
ejpam-4384	128	11	an(t	an(t	NOUN
ejpam-4384	128	12	)	)	PUNCT
ejpam-4384	128	13	=	=	SYM
ejpam-4384	128	14	1	1	NUM
ejpam-4384	128	15	h	h	NOUN
ejpam-4384	128	16	[	[	X
ejpam-4384	128	17	(	(	PUNCT
ejpam-4384	128	18	nh+	nh+	NOUN
ejpam-4384	128	19	h)i(t)−	h)i(t)−	PROPN
ejpam-4384	128	20	j(t	j(t	PROPN
ejpam-4384	128	21	)	)	PUNCT
ejpam-4384	128	22	]	]	X
ejpam-4384	128	23	,	,	PUNCT
ejpam-4384	128	24	bn(t	bn(t	PUNCT
ejpam-4384	128	25	)	)	PUNCT
ejpam-4384	128	26	=	=	SYM
ejpam-4384	128	27	1	1	NUM
ejpam-4384	128	28	h	h	NOUN
ejpam-4384	129	1	[	[	X
ejpam-4384	129	2	j(t)−	j(t)−	PROPN
ejpam-4384	129	3	nhi(t	nhi(t	PROPN
ejpam-4384	129	4	)	)	PUNCT
ejpam-4384	129	5	]	]	PUNCT
ejpam-4384	129	6	,	,	PUNCT
ejpam-4384	129	7	(	(	PUNCT
ejpam-4384	129	8	24	24	NUM
ejpam-4384	129	9	)	)	PUNCT
ejpam-4384	129	10	s.	s.	PROPN
ejpam-4384	129	11	raad	raad	PROPN
ejpam-4384	129	12	,	,	PUNCT
ejpam-4384	129	13	k.	k.	PROPN
ejpam-4384	129	14	alqurashi	alqurashi	PROPN
ejpam-4384	129	15	/	/	SYM
ejpam-4384	129	16	eur	eur	PROPN
ejpam-4384	129	17	.	.	PUNCT
ejpam-4384	130	1	j.	j.	PROPN
ejpam-4384	130	2	pure	pure	PROPN
ejpam-4384	130	3	appl	appl	PROPN
ejpam-4384	130	4	.	.	PROPN
ejpam-4384	130	5	math	math	PROPN
ejpam-4384	130	6	,	,	PUNCT
ejpam-4384	130	7	15	15	NUM
ejpam-4384	130	8	(	(	PUNCT
ejpam-4384	130	9	2	2	NUM
ejpam-4384	130	10	)	)	PUNCT
ejpam-4384	130	11	(	(	PUNCT
ejpam-4384	130	12	2022	2022	NUM
ejpam-4384	130	13	)	)	PUNCT
ejpam-4384	130	14	,	,	PUNCT
ejpam-4384	130	15	796	796	NUM
ejpam-4384	130	16	-	-	SYM
ejpam-4384	130	17	809	809	NUM
ejpam-4384	130	18	802	802	NUM
ejpam-4384	130	19	i(x	i(x	NOUN
ejpam-4384	130	20	)	)	PUNCT
ejpam-4384	130	21	=	=	SYM
ejpam-4384	131	1	∫	∫	PROPN
ejpam-4384	131	2	nh+h	nh+h	PROPN
ejpam-4384	131	3	nh	nh	PROPN
ejpam-4384	131	4	(	(	PUNCT
ejpam-4384	131	5	t−	t−	PROPN
ejpam-4384	131	6	s)(α−1)ds	s)(α−1)ds	PROPN
ejpam-4384	131	7	,	,	PUNCT
ejpam-4384	131	8	j(x	j(x	PROPN
ejpam-4384	131	9	)	)	PUNCT
ejpam-4384	131	10	=	=	SYM
ejpam-4384	132	1	∫	∫	PROPN
ejpam-4384	132	2	nh+h	nh+h	PROPN
ejpam-4384	132	3	nh	nh	PROPN
ejpam-4384	132	4	s(t−	s(t−	PROPN
ejpam-4384	132	5	s)(α−1)ds	s)(α−1)ds	PROPN
ejpam-4384	132	6	.	.	PROPN
ejpam-4384	133	1	(	(	PUNCT
ejpam-4384	133	2	25	25	NUM
ejpam-4384	133	3	)	)	PUNCT
ejpam-4384	133	4	if	if	SCONJ
ejpam-4384	133	5	we	we	PRON
ejpam-4384	133	6	set	set	VERB
ejpam-4384	133	7	t	t	NOUN
ejpam-4384	133	8	=	=	SYM
ejpam-4384	133	9	ph	ph	PROPN
ejpam-4384	133	10	,	,	PUNCT
ejpam-4384	133	11	the	the	DET
ejpam-4384	133	12	integral	integral	ADJ
ejpam-4384	133	13	equation	equation	NOUN
ejpam-4384	133	14	(	(	PUNCT
ejpam-4384	133	15	21	21	NUM
ejpam-4384	133	16	)	)	PUNCT
ejpam-4384	133	17	becomes	become	VERB
ejpam-4384	133	18	u∗(ph)−	u∗(ph)−	NOUN
ejpam-4384	133	19	λdn	λdn	NOUN
ejpam-4384	133	20	,	,	PUNCT
ejpam-4384	133	21	pu	pu	PROPN
ejpam-4384	133	22	∗(nh	∗(nh	PROPN
ejpam-4384	133	23	)	)	PUNCT
ejpam-4384	134	1	=	=	SYM
ejpam-4384	134	2	f∗(ph	f∗(ph	ADV
ejpam-4384	134	3	)	)	PUNCT
ejpam-4384	135	1	,	,	PUNCT
ejpam-4384	135	2	(	(	PUNCT
ejpam-4384	135	3	26	26	NUM
ejpam-4384	135	4	)	)	PUNCT
ejpam-4384	135	5	or	or	CCONJ
ejpam-4384	135	6	by	by	ADP
ejpam-4384	135	7	the	the	DET
ejpam-4384	135	8	matrix	matrix	NOUN
ejpam-4384	135	9	expression	expression	NOUN
ejpam-4384	136	1	[	[	X
ejpam-4384	136	2	i	i	PRON
ejpam-4384	136	3	−	−	VERB
ejpam-4384	136	4	λd]u∗	λd]u∗	NOUN
ejpam-4384	137	1	=	=	SYM
ejpam-4384	137	2	f	f	PROPN
ejpam-4384	137	3	∗	∗	NOUN
ejpam-4384	137	4	(	(	PUNCT
ejpam-4384	137	5	27	27	NUM
ejpam-4384	137	6	)	)	PUNCT
ejpam-4384	137	7	the	the	DET
ejpam-4384	137	8	function	function	NOUN
ejpam-4384	137	9	f	f	PROPN
ejpam-4384	137	10	∗	∗	NOUN
ejpam-4384	137	11	is	be	AUX
ejpam-4384	137	12	a	a	DET
ejpam-4384	137	13	vector	vector	NOUN
ejpam-4384	137	14	of	of	ADP
ejpam-4384	137	15	n	n	DET
ejpam-4384	137	16	+1	+1	ADJ
ejpam-4384	137	17	elements	element	NOUN
ejpam-4384	137	18	,	,	PUNCT
ejpam-4384	137	19	but	but	CCONJ
ejpam-4384	137	20	d	d	NOUN
ejpam-4384	137	21	is	be	AUX
ejpam-4384	137	22	a	a	DET
ejpam-4384	137	23	matrix	matrix	NOUN
ejpam-4384	137	24	whose	whose	DET
ejpam-4384	137	25	elements	element	NOUN
ejpam-4384	137	26	are	be	AUX
ejpam-4384	137	27	given	give	VERB
ejpam-4384	137	28	by	by	ADP
ejpam-4384	137	29	dn	dn	PROPN
ejpam-4384	137	30	,	,	PUNCT
ejpam-4384	137	31	p	p	NOUN
ejpam-4384	137	32	=	=	NOUN
ejpam-4384	137	33	an	an	NOUN
ejpam-4384	137	34	,	,	PUNCT
ejpam-4384	137	35	p	p	NOUN
ejpam-4384	137	36	+	+	X
ejpam-4384	137	37	a′n	a′n	NOUN
ejpam-4384	137	38	,	,	PUNCT
ejpam-4384	137	39	p	p	NOUN
ejpam-4384	137	40	the	the	DET
ejpam-4384	137	41	matrix	matrix	NOUN
ejpam-4384	137	42	an	an	DET
ejpam-4384	137	43	,	,	PUNCT
ejpam-4384	137	44	p	p	NOUN
ejpam-4384	137	45	=	=	PROPN
ejpam-4384	137	46	an(ph)+bn−1(ph	an(ph)+bn−1(ph	PROPN
ejpam-4384	137	47	)	)	PUNCT
ejpam-4384	137	48	is	be	AUX
ejpam-4384	137	49	the	the	DET
ejpam-4384	137	50	toeplitz	toeplitz	NOUN
ejpam-4384	137	51	matrix	matrix	NOUN
ejpam-4384	137	52	of	of	ADP
ejpam-4384	137	53	order	order	NOUN
ejpam-4384	137	54	n+1	n+1	ADV
ejpam-4384	137	55	,	,	PUNCT
ejpam-4384	137	56	0	0	NUM
ejpam-4384	137	57	≤	≤	NUM
ejpam-4384	137	58	n	n	CCONJ
ejpam-4384	137	59	,	,	PUNCT
ejpam-4384	137	60	p	p	NOUN
ejpam-4384	137	61	≤	≤	NOUN
ejpam-4384	137	62	n	n	NOUN
ejpam-4384	137	63	.	.	PUNCT
ejpam-4384	138	1	whereas	whereas	SCONJ
ejpam-4384	138	2	,	,	PUNCT
ejpam-4384	138	3	the	the	DET
ejpam-4384	138	4	elements	element	NOUN
ejpam-4384	138	5	of	of	ADP
ejpam-4384	138	6	the	the	DET
ejpam-4384	138	7	second	second	ADJ
ejpam-4384	138	8	matrix	matrix	NOUN
ejpam-4384	138	9	a′n	a′n	ADP
ejpam-4384	138	10	,	,	PUNCT
ejpam-4384	138	11	p	p	NOUN
ejpam-4384	138	12	are	be	AUX
ejpam-4384	138	13	zeros	zero	NOUN
ejpam-4384	138	14	except	except	SCONJ
ejpam-4384	138	15	for	for	ADP
ejpam-4384	138	16	a0,p	a0,p	PROPN
ejpam-4384	138	17	=	=	SYM
ejpam-4384	138	18	b1(ph	b1(ph	PROPN
ejpam-4384	138	19	)	)	PUNCT
ejpam-4384	138	20	and	and	CCONJ
ejpam-4384	138	21	ap−1,p	ap−1,p	NOUN
ejpam-4384	138	22	=	=	PUNCT
ejpam-4384	138	23	bp(ph	bp(ph	NOUN
ejpam-4384	138	24	)	)	PUNCT
ejpam-4384	138	25	.	.	PUNCT
ejpam-4384	139	1	therefore	therefore	ADV
ejpam-4384	139	2	,	,	PUNCT
ejpam-4384	139	3	the	the	DET
ejpam-4384	139	4	solution	solution	NOUN
ejpam-4384	139	5	of	of	ADP
ejpam-4384	139	6	the	the	DET
ejpam-4384	139	7	formula	formula	NOUN
ejpam-4384	139	8	(	(	PUNCT
ejpam-4384	139	9	27	27	NUM
ejpam-4384	139	10	)	)	PUNCT
ejpam-4384	139	11	will	will	AUX
ejpam-4384	139	12	take	take	VERB
ejpam-4384	139	13	the	the	DET
ejpam-4384	139	14	form	form	NOUN
ejpam-4384	139	15	u∗	u∗	ADV
ejpam-4384	139	16	=	=	PUNCT
ejpam-4384	140	1	[	[	X
ejpam-4384	140	2	i	i	PRON
ejpam-4384	140	3	−	−	PROPN
ejpam-4384	140	4	λd]−1f	λd]−1f	NOUN
ejpam-4384	140	5	∗	∗	NOUN
ejpam-4384	140	6	,	,	PUNCT
ejpam-4384	140	7	|i	|i	VERB
ejpam-4384	140	8	−	−	PROPN
ejpam-4384	140	9	λd|	λd|	NOUN
ejpam-4384	140	10	=	=	SYM
ejpam-4384	140	11	̸	̸	NUM
ejpam-4384	140	12	0	0	NUM
ejpam-4384	140	13	.	.	PUNCT
ejpam-4384	141	1	(	(	PUNCT
ejpam-4384	141	2	i	i	PRON
ejpam-4384	141	3	is	be	AUX
ejpam-4384	141	4	the	the	DET
ejpam-4384	141	5	identity	identity	NOUN
ejpam-4384	141	6	matrix	matrix	NOUN
ejpam-4384	141	7	.	.	PUNCT
ejpam-4384	141	8	)	)	PUNCT
ejpam-4384	142	1	(	(	PUNCT
ejpam-4384	142	2	28	28	NUM
ejpam-4384	142	3	)	)	PUNCT
ejpam-4384	142	4	5.2	5.2	NUM
ejpam-4384	142	5	.	.	PUNCT
ejpam-4384	143	1	the	the	DET
ejpam-4384	143	2	product	product	NOUN
ejpam-4384	143	3	nyström	nyström	PRON
ejpam-4384	143	4	method	method	NOUN
ejpam-4384	143	5	[	[	X
ejpam-4384	143	6	1	1	NUM
ejpam-4384	143	7	,	,	PUNCT
ejpam-4384	143	8	10	10	NUM
ejpam-4384	143	9	,	,	PUNCT
ejpam-4384	143	10	14	14	NUM
ejpam-4384	143	11	]	]	PUNCT
ejpam-4384	143	12	assume	assume	VERB
ejpam-4384	143	13	the	the	DET
ejpam-4384	143	14	volterra	volterra	NOUN
ejpam-4384	143	15	integral	integral	ADJ
ejpam-4384	143	16	equation	equation	NOUN
ejpam-4384	143	17	can	can	AUX
ejpam-4384	143	18	be	be	AUX
ejpam-4384	143	19	written	write	VERB
ejpam-4384	143	20	in	in	ADP
ejpam-4384	143	21	the	the	DET
ejpam-4384	143	22	form	form	NOUN
ejpam-4384	144	1	u∗(t)−	u∗(t)−	PROPN
ejpam-4384	144	2	λ	λ	PROPN
ejpam-4384	144	3	∫	∫	PROPN
ejpam-4384	144	4	t	t	PROPN
ejpam-4384	144	5	0	0	NUM
ejpam-4384	144	6	p(x	p(x	PROPN
ejpam-4384	144	7	,	,	PUNCT
ejpam-4384	144	8	y)k(x	y)k(x	NOUN
ejpam-4384	144	9	,	,	PUNCT
ejpam-4384	144	10	y)u∗(s)ds	y)u∗(s)ds	PROPN
ejpam-4384	144	11	=	=	PUNCT
ejpam-4384	144	12	f∗(t	f∗(t	PROPN
ejpam-4384	144	13	)	)	PUNCT
ejpam-4384	144	14	,	,	PUNCT
ejpam-4384	144	15	(	(	PUNCT
ejpam-4384	144	16	29	29	NUM
ejpam-4384	144	17	)	)	PUNCT
ejpam-4384	144	18	where	where	SCONJ
ejpam-4384	144	19	p(x	p(x	PROPN
ejpam-4384	144	20	,	,	PUNCT
ejpam-4384	144	21	y	y	NOUN
ejpam-4384	144	22	)	)	PUNCT
ejpam-4384	144	23	=	=	PUNCT
ejpam-4384	144	24	(	(	PUNCT
ejpam-4384	144	25	t	t	PROPN
ejpam-4384	144	26	−	−	PROPN
ejpam-4384	144	27	s)α−1	s)α−1	NOUN
ejpam-4384	144	28	and	and	CCONJ
ejpam-4384	144	29	k(x	k(x	PROPN
ejpam-4384	144	30	,	,	PUNCT
ejpam-4384	144	31	y	y	NOUN
ejpam-4384	144	32	)	)	PUNCT
ejpam-4384	144	33	are	be	AUX
ejpam-4384	144	34	‘	'	PUNCT
ejpam-4384	144	35	badly	badly	ADV
ejpam-4384	144	36	behaved	behave	VERB
ejpam-4384	144	37	‘	'	PUNCT
ejpam-4384	144	38	and	and	CCONJ
ejpam-4384	144	39	‘	'	PUNCT
ejpam-4384	144	40	well	well	ADV
ejpam-4384	144	41	behaved	behave	VERB
ejpam-4384	144	42	‘	'	PUNCT
ejpam-4384	144	43	of	of	ADP
ejpam-4384	144	44	their	their	PRON
ejpam-4384	144	45	arguments	argument	NOUN
ejpam-4384	144	46	,	,	PUNCT
ejpam-4384	144	47	respectively	respectively	ADV
ejpam-4384	144	48	.	.	PUNCT
ejpam-4384	145	1	equation	equation	NOUN
ejpam-4384	145	2	(	(	PUNCT
ejpam-4384	145	3	29	29	NUM
ejpam-4384	145	4	)	)	PUNCT
ejpam-4384	145	5	can	can	AUX
ejpam-4384	145	6	be	be	AUX
ejpam-4384	145	7	written	write	VERB
ejpam-4384	145	8	in	in	ADP
ejpam-4384	145	9	the	the	DET
ejpam-4384	145	10	form	form	NOUN
ejpam-4384	145	11	u∗(ti)−	u∗(ti)−	PROPN
ejpam-4384	145	12	λ	λ	PROPN
ejpam-4384	145	13	i∑	i∑	VERB
ejpam-4384	145	14	j=0	j=0	PROPN
ejpam-4384	145	15	wij(ti	wij(ti	NOUN
ejpam-4384	145	16	−	−	PROPN
ejpam-4384	145	17	s)α−1u∗(si	s)α−1u∗(si	PROPN
ejpam-4384	145	18	)	)	PUNCT
ejpam-4384	146	1	=	=	SYM
ejpam-4384	146	2	f∗(ti	f∗(ti	NOUN
ejpam-4384	146	3	)	)	PUNCT
ejpam-4384	146	4	,	,	PUNCT
ejpam-4384	146	5	(	(	PUNCT
ejpam-4384	146	6	30	30	NUM
ejpam-4384	146	7	)	)	PUNCT
ejpam-4384	146	8	here	here	ADV
ejpam-4384	146	9	xi	xi	AUX
ejpam-4384	146	10	=	=	SYM
ejpam-4384	146	11	yi	yi	PROPN
ejpam-4384	147	1	=	=	PUNCT
ejpam-4384	147	2	a	a	PRON
ejpam-4384	148	1	+	+	X
ejpam-4384	148	2	ih	ih	X
ejpam-4384	148	3	,	,	PUNCT
ejpam-4384	148	4	i	i	PRON
ejpam-4384	148	5	=	=	NOUN
ejpam-4384	148	6	0	0	NUM
ejpam-4384	148	7	,	,	PUNCT
ejpam-4384	148	8	1	1	NUM
ejpam-4384	148	9	,	,	PUNCT
ejpam-4384	148	10	..	..	PUNCT
ejpam-4384	148	11	,	,	PUNCT
ejpam-4384	148	12	n	n	CCONJ
ejpam-4384	148	13	with	with	ADP
ejpam-4384	148	14	h	h	NOUN
ejpam-4384	148	15	=	=	SYM
ejpam-4384	148	16	t	t	PROPN
ejpam-4384	148	17	n	n	NOUN
ejpam-4384	148	18	,	,	PUNCT
ejpam-4384	148	19	n	n	PRON
ejpam-4384	148	20	must	must	AUX
ejpam-4384	148	21	be	be	AUX
ejpam-4384	148	22	even	even	ADV
ejpam-4384	148	23	,	,	PUNCT
ejpam-4384	148	24	and	and	CCONJ
ejpam-4384	148	25	wij	wij	PROPN
ejpam-4384	148	26	are	be	AUX
ejpam-4384	148	27	the	the	DET
ejpam-4384	148	28	weights	weight	NOUN
ejpam-4384	148	29	to	to	PART
ejpam-4384	148	30	be	be	AUX
ejpam-4384	148	31	determined	determine	VERB
ejpam-4384	148	32	.	.	PUNCT
ejpam-4384	149	1	if	if	SCONJ
ejpam-4384	149	2	we	we	PRON
ejpam-4384	149	3	approximate	approximate	VERB
ejpam-4384	149	4	the	the	DET
ejpam-4384	149	5	nonsingular	nonsingular	ADJ
ejpam-4384	149	6	part	part	NOUN
ejpam-4384	149	7	by	by	ADP
ejpam-4384	149	8	the	the	DET
ejpam-4384	149	9	second	second	ADJ
ejpam-4384	149	10	degree	degree	NOUN
ejpam-4384	149	11	of	of	ADP
ejpam-4384	149	12	lagrange	lagrange	NOUN
ejpam-4384	149	13	interpolation	interpolation	NOUN
ejpam-4384	149	14	polynomial	polynomial	NOUN
ejpam-4384	149	15	,	,	PUNCT
ejpam-4384	149	16	therefore	therefore	ADV
ejpam-4384	149	17	,	,	PUNCT
ejpam-4384	149	18	ωi,0	ωi,0	PROPN
ejpam-4384	149	19	=	=	SYM
ejpam-4384	149	20	β1(yi	β1(yi	PROPN
ejpam-4384	149	21	)	)	PUNCT
ejpam-4384	149	22	,	,	PUNCT
ejpam-4384	149	23	ωi,2j+1	ωi,2j+1	PROPN
ejpam-4384	149	24	=	=	PUNCT
ejpam-4384	149	25	2γj+1(yi	2γj+1(yi	NUM
ejpam-4384	149	26	)	)	PUNCT
ejpam-4384	149	27	,	,	PUNCT
ejpam-4384	149	28	ωi,2j	ωi,2j	NUM
ejpam-4384	149	29	=	=	SYM
ejpam-4384	149	30	ζj(yi	ζj(yi	PROPN
ejpam-4384	149	31	)	)	PUNCT
ejpam-4384	150	1	+	+	CCONJ
ejpam-4384	150	2	βj+1(yi	βj+1(yi	NUM
ejpam-4384	150	3	)	)	PUNCT
ejpam-4384	150	4	,	,	PUNCT
ejpam-4384	150	5	ωi	ωi	NOUN
ejpam-4384	150	6	,	,	PUNCT
ejpam-4384	150	7	n	n	CCONJ
ejpam-4384	150	8	(	(	PUNCT
ejpam-4384	150	9	yi	yi	NOUN
ejpam-4384	150	10	)	)	PUNCT
ejpam-4384	150	11	=	=	NOUN
ejpam-4384	150	12	ζn	ζn	PRON
ejpam-4384	150	13	2	2	NUM
ejpam-4384	150	14	(	(	PUNCT
ejpam-4384	150	15	yi	yi	NOUN
ejpam-4384	150	16	)	)	PUNCT
ejpam-4384	150	17	(	(	PUNCT
ejpam-4384	150	18	31	31	NUM
ejpam-4384	150	19	)	)	PUNCT
ejpam-4384	150	20	assume	assume	VERB
ejpam-4384	150	21	v	v	X
ejpam-4384	150	22	=	=	SYM
ejpam-4384	150	23	i−	i−	ADJ
ejpam-4384	150	24	2j	2j	NOUN
ejpam-4384	150	25	+	+	CCONJ
ejpam-4384	150	26	2	2	NUM
ejpam-4384	150	27	,	,	PUNCT
ejpam-4384	150	28	then	then	ADV
ejpam-4384	150	29	ζj(yi	ζj(yi	PROPN
ejpam-4384	150	30	)	)	PUNCT
ejpam-4384	151	1	=	=	SYM
ejpam-4384	151	2	h	h	NOUN
ejpam-4384	151	3	2	2	NUM
ejpam-4384	151	4	∫	∫	NOUN
ejpam-4384	151	5	2	2	NUM
ejpam-4384	151	6	0	0	NUM
ejpam-4384	151	7	ρ(ρ−	ρ(ρ−	PROPN
ejpam-4384	151	8	1)(vh−	1)(vh−	NOUN
ejpam-4384	151	9	ρh)(α−1)dρ	ρh)(α−1)dρ	NOUN
ejpam-4384	151	10	,	,	PUNCT
ejpam-4384	151	11	βj(yi	βj(yi	PUNCT
ejpam-4384	151	12	)	)	PUNCT
ejpam-4384	151	13	=	=	SYM
ejpam-4384	152	1	h	h	NOUN
ejpam-4384	152	2	2	2	NUM
ejpam-4384	152	3	∫	∫	NOUN
ejpam-4384	152	4	2	2	NUM
ejpam-4384	152	5	0	0	NUM
ejpam-4384	152	6	(	(	PUNCT
ejpam-4384	152	7	ρ−	ρ−	NOUN
ejpam-4384	152	8	1)(ρ−	1)(ρ−	NUM
ejpam-4384	152	9	2)(vh−	2)(vh−	NOUN
ejpam-4384	152	10	ρh)(α−1)dρ	ρh)(α−1)dρ	NOUN
ejpam-4384	152	11	,	,	PUNCT
ejpam-4384	152	12	γj(yi	γj(yi	NOUN
ejpam-4384	152	13	)	)	PUNCT
ejpam-4384	153	1	=	=	SYM
ejpam-4384	153	2	h	h	NOUN
ejpam-4384	154	1	2	2	NUM
ejpam-4384	154	2	∫	∫	NOUN
ejpam-4384	154	3	2	2	NUM
ejpam-4384	154	4	0	0	NUM
ejpam-4384	154	5	ρ(2−	ρ(2−	NOUN
ejpam-4384	154	6	ρ)(vh−	ρ)(vh−	NOUN
ejpam-4384	154	7	ρh)(α−1)dρ	ρh)(α−1)dρ	NOUN
ejpam-4384	154	8	.	.	PUNCT
ejpam-4384	155	1	(	(	PUNCT
ejpam-4384	155	2	32	32	NUM
ejpam-4384	155	3	)	)	PUNCT
ejpam-4384	155	4	s.	s.	PROPN
ejpam-4384	155	5	raad	raad	PROPN
ejpam-4384	155	6	,	,	PUNCT
ejpam-4384	155	7	k.	k.	PROPN
ejpam-4384	155	8	alqurashi	alqurashi	PROPN
ejpam-4384	155	9	/	/	SYM
ejpam-4384	155	10	eur	eur	PROPN
ejpam-4384	155	11	.	.	PUNCT
ejpam-4384	156	1	j.	j.	PROPN
ejpam-4384	156	2	pure	pure	PROPN
ejpam-4384	156	3	appl	appl	PROPN
ejpam-4384	156	4	.	.	PROPN
ejpam-4384	156	5	math	math	PROPN
ejpam-4384	156	6	,	,	PUNCT
ejpam-4384	156	7	15	15	NUM
ejpam-4384	156	8	(	(	PUNCT
ejpam-4384	156	9	2	2	NUM
ejpam-4384	156	10	)	)	PUNCT
ejpam-4384	156	11	(	(	PUNCT
ejpam-4384	156	12	2022	2022	NUM
ejpam-4384	156	13	)	)	PUNCT
ejpam-4384	156	14	,	,	PUNCT
ejpam-4384	156	15	796	796	NUM
ejpam-4384	156	16	-	-	SYM
ejpam-4384	156	17	809	809	NUM
ejpam-4384	156	18	803	803	NUM
ejpam-4384	156	19	now	now	ADV
ejpam-4384	156	20	,	,	PUNCT
ejpam-4384	156	21	ψi	ψi	ADP
ejpam-4384	156	22	=	=	SYM
ejpam-4384	156	23	∫	∫	PROPN
ejpam-4384	157	1	2	2	NUM
ejpam-4384	157	2	0	0	NUM
ejpam-4384	157	3	ρi(vh−	ρi(vh−	NOUN
ejpam-4384	157	4	ρh)(α−1)dρ	ρh)(α−1)dρ	NOUN
ejpam-4384	157	5	,	,	PUNCT
ejpam-4384	157	6	equation	equation	NOUN
ejpam-4384	157	7	(	(	PUNCT
ejpam-4384	157	8	31	31	NUM
ejpam-4384	157	9	)	)	PUNCT
ejpam-4384	157	10	becomes	become	VERB
ejpam-4384	157	11	ωi,0	ωi,0	PROPN
ejpam-4384	157	12	=	=	PUNCT
ejpam-4384	157	13	h	h	NOUN
ejpam-4384	157	14	2	2	NUM
ejpam-4384	158	1	[	[	X
ejpam-4384	158	2	2ψ0(v)−	2ψ0(v)−	NUM
ejpam-4384	158	3	3ψ1(v	3ψ1(v	NUM
ejpam-4384	158	4	)	)	PUNCT
ejpam-4384	158	5	+	+	NUM
ejpam-4384	158	6	ψ2(v	ψ2(v	X
ejpam-4384	158	7	)	)	PUNCT
ejpam-4384	158	8	]	]	PUNCT
ejpam-4384	158	9	,	,	PUNCT
ejpam-4384	158	10	v	v	X
ejpam-4384	158	11	=	=	SYM
ejpam-4384	158	12	i	i	PRON
ejpam-4384	158	13	ωi,2j	ωi,2j	NUM
ejpam-4384	158	14	=	=	SYM
ejpam-4384	158	15	h	h	NOUN
ejpam-4384	158	16	2	2	NUM
ejpam-4384	159	1	[	[	X
ejpam-4384	159	2	ψ2(v)−	ψ2(v)−	X
ejpam-4384	159	3	ψ1(v	ψ1(v	ADJ
ejpam-4384	159	4	)	)	PUNCT
ejpam-4384	160	1	+	+	CCONJ
ejpam-4384	160	2	2ψ0(v	2ψ0(v	NUM
ejpam-4384	160	3	−	−	NOUN
ejpam-4384	160	4	2)−	2)−	NUM
ejpam-4384	160	5	3ψ1(v	3ψ1(v	NUM
ejpam-4384	160	6	−	−	NOUN
ejpam-4384	160	7	2	2	NUM
ejpam-4384	160	8	)	)	PUNCT
ejpam-4384	160	9	+	+	PRON
ejpam-4384	160	10	ψ2(v	ψ2(v	PROPN
ejpam-4384	160	11	−	−	NOUN
ejpam-4384	160	12	2	2	NUM
ejpam-4384	160	13	)	)	PUNCT
ejpam-4384	160	14	]	]	PUNCT
ejpam-4384	160	15	,	,	PUNCT
ejpam-4384	160	16	v	v	X
ejpam-4384	160	17	=	=	SYM
ejpam-4384	160	18	i−	i−	ADJ
ejpam-4384	160	19	2j	2j	NOUN
ejpam-4384	160	20	+	+	CCONJ
ejpam-4384	160	21	2	2	NUM
ejpam-4384	160	22	ωi,2j+1	ωi,2j+1	NUM
ejpam-4384	160	23	=	=	PUNCT
ejpam-4384	160	24	h[2ψ1(v)−	h[2ψ1(v)−	NOUN
ejpam-4384	160	25	ψ2(v	ψ2(v	PROPN
ejpam-4384	160	26	)	)	PUNCT
ejpam-4384	160	27	]	]	PUNCT
ejpam-4384	160	28	,	,	PUNCT
ejpam-4384	160	29	v	v	X
ejpam-4384	160	30	=	=	SYM
ejpam-4384	160	31	i−	i−	ADJ
ejpam-4384	160	32	2j	2j	X
ejpam-4384	160	33	ωi	ωi	NOUN
ejpam-4384	160	34	,	,	PUNCT
ejpam-4384	160	35	n	n	NOUN
ejpam-4384	160	36	=	=	NOUN
ejpam-4384	160	37	h	h	NOUN
ejpam-4384	160	38	2	2	NUM
ejpam-4384	161	1	[	[	X
ejpam-4384	161	2	ψ2(v)−	ψ2(v)−	X
ejpam-4384	161	3	ψ1(v	ψ1(v	PROPN
ejpam-4384	161	4	)	)	PUNCT
ejpam-4384	161	5	]	]	PUNCT
ejpam-4384	161	6	,	,	PUNCT
ejpam-4384	161	7	v	v	X
ejpam-4384	161	8	=	=	NOUN
ejpam-4384	161	9	i−n	i−n	NOUN
ejpam-4384	161	10	+	+	CCONJ
ejpam-4384	161	11	2	2	NUM
ejpam-4384	161	12	(	(	PUNCT
ejpam-4384	161	13	33	33	NUM
ejpam-4384	161	14	)	)	PUNCT
ejpam-4384	161	15	therefore	therefore	ADV
ejpam-4384	161	16	,	,	PUNCT
ejpam-4384	161	17	the	the	DET
ejpam-4384	161	18	integral	integral	ADJ
ejpam-4384	161	19	equation	equation	NOUN
ejpam-4384	161	20	(	(	PUNCT
ejpam-4384	161	21	29	29	NUM
ejpam-4384	161	22	)	)	PUNCT
ejpam-4384	161	23	is	be	AUX
ejpam-4384	161	24	reduced	reduce	VERB
ejpam-4384	161	25	to	to	ADP
ejpam-4384	161	26	a	a	DET
ejpam-4384	161	27	system	system	NOUN
ejpam-4384	161	28	of	of	ADP
ejpam-4384	161	29	linear	linear	PROPN
ejpam-4384	161	30	algebraic	algebraic	ADJ
ejpam-4384	161	31	equations	equation	NOUN
ejpam-4384	161	32	(	(	PUNCT
ejpam-4384	161	33	i	i	PRON
ejpam-4384	161	34	−	−	VERB
ejpam-4384	161	35	λw	λw	X
ejpam-4384	161	36	)	)	PUNCT
ejpam-4384	161	37	u∗	u∗	PROPN
ejpam-4384	161	38	=	=	SYM
ejpam-4384	161	39	f	f	PROPN
ejpam-4384	161	40	,	,	PUNCT
ejpam-4384	161	41	f	f	PROPN
ejpam-4384	161	42	=	=	PRON
ejpam-4384	161	43	f∗i	f∗i	PRON
ejpam-4384	161	44	=	=	SYM
ejpam-4384	161	45	f∗(ti	f∗(ti	NOUN
ejpam-4384	161	46	)	)	PUNCT
ejpam-4384	161	47	;	;	PUNCT
ejpam-4384	162	1	i	i	NOUN
ejpam-4384	162	2	=	=	NOUN
ejpam-4384	162	3	0	0	NUM
ejpam-4384	162	4	,	,	PUNCT
ejpam-4384	162	5	1	1	NUM
ejpam-4384	162	6	,	,	PUNCT
ejpam-4384	162	7	2	2	NUM
ejpam-4384	162	8	,	,	PUNCT
ejpam-4384	162	9	.....	.....	PUNCT
ejpam-4384	162	10	,	,	PUNCT
ejpam-4384	162	11	n	n	CCONJ
ejpam-4384	162	12	(	(	PUNCT
ejpam-4384	162	13	34	34	NUM
ejpam-4384	162	14	)	)	PUNCT
ejpam-4384	162	15	which	which	PRON
ejpam-4384	162	16	has	have	VERB
ejpam-4384	162	17	the	the	DET
ejpam-4384	162	18	solution	solution	NOUN
ejpam-4384	162	19	u∗	u∗	ADV
ejpam-4384	162	20	=	=	PUNCT
ejpam-4384	163	1	[	[	X
ejpam-4384	163	2	i	i	PRON
ejpam-4384	163	3	−	−	VERB
ejpam-4384	163	4	λw	λw	X
ejpam-4384	163	5	]	]	PUNCT
ejpam-4384	163	6	−1f	−1f	PROPN
ejpam-4384	163	7	,	,	PUNCT
ejpam-4384	163	8	|i	|i	VERB
ejpam-4384	163	9	−	−	PROPN
ejpam-4384	163	10	λw	λw	ADP
ejpam-4384	163	11	|	|	NOUN
ejpam-4384	163	12	=	=	NOUN
ejpam-4384	163	13	̸	̸	NUM
ejpam-4384	163	14	0	0	PUNCT
ejpam-4384	164	1	(	(	PUNCT
ejpam-4384	164	2	i	i	PRON
ejpam-4384	164	3	is	be	AUX
ejpam-4384	164	4	the	the	DET
ejpam-4384	164	5	identity	identity	NOUN
ejpam-4384	164	6	matrix	matrix	NOUN
ejpam-4384	164	7	.	.	PUNCT
ejpam-4384	164	8	)	)	PUNCT
ejpam-4384	165	1	(	(	PUNCT
ejpam-4384	165	2	35	35	NUM
ejpam-4384	165	3	)	)	PUNCT
ejpam-4384	165	4	6	6	NUM
ejpam-4384	165	5	.	.	PUNCT
ejpam-4384	165	6	numerical	numerical	ADJ
ejpam-4384	165	7	results	result	NOUN
ejpam-4384	165	8	in	in	ADP
ejpam-4384	165	9	this	this	DET
ejpam-4384	165	10	section	section	NOUN
ejpam-4384	165	11	,	,	PUNCT
ejpam-4384	165	12	the	the	DET
ejpam-4384	165	13	fractional	fractional	ADJ
ejpam-4384	165	14	integro	integro	ADJ
ejpam-4384	165	15	-	-	PUNCT
ejpam-4384	165	16	differential	differential	NOUN
ejpam-4384	165	17	equation	equation	NOUN
ejpam-4384	165	18	will	will	AUX
ejpam-4384	165	19	be	be	AUX
ejpam-4384	165	20	solved	solve	VERB
ejpam-4384	165	21	using	use	VERB
ejpam-4384	165	22	the	the	DET
ejpam-4384	165	23	toeplitz	toeplitz	NOUN
ejpam-4384	165	24	matrix	matrix	NOUN
ejpam-4384	165	25	and	and	CCONJ
ejpam-4384	165	26	the	the	DET
ejpam-4384	165	27	product	product	NOUN
ejpam-4384	166	1	nyström	nyström	DET
ejpam-4384	166	2	methods	method	NOUN
ejpam-4384	166	3	.	.	PUNCT
ejpam-4384	167	1	the	the	DET
ejpam-4384	167	2	results	result	NOUN
ejpam-4384	167	3	are	be	AUX
ejpam-4384	167	4	calculated	calculate	VERB
ejpam-4384	167	5	at	at	ADP
ejpam-4384	167	6	t	t	NOUN
ejpam-4384	167	7	=	=	PUNCT
ejpam-4384	167	8	0.009	0.009	NUM
ejpam-4384	167	9	,	,	PUNCT
ejpam-4384	167	10	0.05	0.05	NUM
ejpam-4384	167	11	,	,	PUNCT
ejpam-4384	167	12	0.2	0.2	NUM
ejpam-4384	167	13	,	,	PUNCT
ejpam-4384	167	14	and	and	CCONJ
ejpam-4384	167	15	α	α	NOUN
ejpam-4384	167	16	=	=	SYM
ejpam-4384	167	17	0.6	0.6	NUM
ejpam-4384	167	18	,	,	PUNCT
ejpam-4384	167	19	0.75	0.75	NUM
ejpam-4384	167	20	,	,	PUNCT
ejpam-4384	167	21	0.9	0.9	NUM
ejpam-4384	167	22	.	.	PUNCT
ejpam-4384	168	1	maple	maple	NOUN
ejpam-4384	168	2	18	18	NUM
ejpam-4384	168	3	software	software	NOUN
ejpam-4384	168	4	will	will	AUX
ejpam-4384	168	5	be	be	AUX
ejpam-4384	168	6	used	use	VERB
ejpam-4384	168	7	in	in	ADP
ejpam-4384	168	8	programming	programming	NOUN
ejpam-4384	168	9	.	.	PUNCT
ejpam-4384	169	1	example	example	NOUN
ejpam-4384	170	1	1	1	NUM
ejpam-4384	170	2	.	.	X
ejpam-4384	170	3	consider	consider	VERB
ejpam-4384	170	4	the	the	DET
ejpam-4384	170	5	fi	fi	NOUN
ejpam-4384	170	6	-	-	ADJ
ejpam-4384	170	7	de	de	X
ejpam-4384	170	8	∂αu(x	∂αu(x	PROPN
ejpam-4384	170	9	,	,	PUNCT
ejpam-4384	170	10	t	t	NOUN
ejpam-4384	170	11	)	)	PUNCT
ejpam-4384	170	12	∂tα	∂tα	PROPN
ejpam-4384	170	13	=	=	PUNCT
ejpam-4384	171	1	x	x	PUNCT
ejpam-4384	171	2	t1−α	t1−α	PROPN
ejpam-4384	171	3	γ(2−	γ(2−	NOUN
ejpam-4384	171	4	α	α	NOUN
ejpam-4384	171	5	)	)	PUNCT
ejpam-4384	171	6	−	−	PROPN
ejpam-4384	171	7	2t2−α	2t2−α	NUM
ejpam-4384	171	8	γ(3−	γ(3−	ADP
ejpam-4384	171	9	α	α	NUM
ejpam-4384	171	10	)	)	PUNCT
ejpam-4384	171	11	−λx(t−t2e+t2)+λ	−λx(t−t2e+t2)+λ	PROPN
ejpam-4384	171	12	∫	∫	PROPN
ejpam-4384	171	13	1	1	NUM
ejpam-4384	171	14	0	0	NUM
ejpam-4384	171	15	xeyu(y	xeyu(y	NUM
ejpam-4384	171	16	,	,	PUNCT
ejpam-4384	171	17	t)dy	t)dy	PROPN
ejpam-4384	171	18	,	,	PUNCT
ejpam-4384	171	19	u0(x	u0(x	NOUN
ejpam-4384	171	20	)	)	PUNCT
ejpam-4384	171	21	=	=	SYM
ejpam-4384	171	22	0	0	NUM
ejpam-4384	171	23	,	,	PUNCT
ejpam-4384	171	24	(	(	PUNCT
ejpam-4384	171	25	36	36	NUM
ejpam-4384	171	26	)	)	PUNCT
ejpam-4384	171	27	after	after	ADP
ejpam-4384	171	28	using	use	VERB
ejpam-4384	171	29	the	the	DET
ejpam-4384	171	30	riemann	riemann	PROPN
ejpam-4384	171	31	-	-	PUNCT
ejpam-4384	171	32	liouville	liouville	VERB
ejpam-4384	171	33	fractional	fractional	ADJ
ejpam-4384	171	34	integral	integral	ADJ
ejpam-4384	171	35	to	to	ADP
ejpam-4384	171	36	the	the	DET
ejpam-4384	171	37	equation	equation	NOUN
ejpam-4384	171	38	(	(	PUNCT
ejpam-4384	171	39	36	36	NUM
ejpam-4384	171	40	)	)	PUNCT
ejpam-4384	171	41	,	,	PUNCT
ejpam-4384	171	42	we	we	PRON
ejpam-4384	171	43	obtain	obtain	VERB
ejpam-4384	171	44	u(x	u(x	NOUN
ejpam-4384	171	45	,	,	PUNCT
ejpam-4384	171	46	t	t	NOUN
ejpam-4384	171	47	)	)	PUNCT
ejpam-4384	171	48	=	=	SYM
ejpam-4384	171	49	η(x	η(x	PROPN
ejpam-4384	171	50	,	,	PUNCT
ejpam-4384	171	51	t	t	PROPN
ejpam-4384	171	52	)	)	PUNCT
ejpam-4384	171	53	+	+	NUM
ejpam-4384	171	54	λ	λ	PROPN
ejpam-4384	171	55	γ(α	γ(α	NOUN
ejpam-4384	171	56	)	)	PUNCT
ejpam-4384	172	1	∫	∫	PROPN
ejpam-4384	173	1	t	t	PROPN
ejpam-4384	173	2	0	0	NUM
ejpam-4384	173	3	∫	∫	PROPN
ejpam-4384	173	4	1	1	NUM
ejpam-4384	173	5	0	0	NUM
ejpam-4384	173	6	(	(	PUNCT
ejpam-4384	173	7	t−	t−	PROPN
ejpam-4384	173	8	s)α−1xeyu(y	s)α−1xeyu(y	PROPN
ejpam-4384	173	9	,	,	PUNCT
ejpam-4384	173	10	s)dyds	s)dyds	PROPN
ejpam-4384	173	11	,	,	PUNCT
ejpam-4384	173	12	(	(	PUNCT
ejpam-4384	173	13	37	37	NUM
ejpam-4384	173	14	)	)	PUNCT
ejpam-4384	173	15	where	where	SCONJ
ejpam-4384	173	16	η(x	η(x	NOUN
ejpam-4384	173	17	,	,	PUNCT
ejpam-4384	173	18	t	t	PROPN
ejpam-4384	173	19	)	)	PUNCT
ejpam-4384	173	20	=	=	SYM
ejpam-4384	174	1	xt−	xt−	PUNCT
ejpam-4384	174	2	t2	t2	PROPN
ejpam-4384	174	3	−	−	PROPN
ejpam-4384	174	4	λx	λx	PROPN
ejpam-4384	174	5	[	[	PUNCT
ejpam-4384	174	6	t1+α	t1+α	PROPN
ejpam-4384	174	7	γ(2	γ(2	PROPN
ejpam-4384	174	8	+	+	CCONJ
ejpam-4384	174	9	α	α	X
ejpam-4384	174	10	)	)	PUNCT
ejpam-4384	175	1	+	+	NUM
ejpam-4384	175	2	2t2+α	2t2+α	NUM
ejpam-4384	175	3	γ(3	γ(3	NOUN
ejpam-4384	175	4	+	+	CCONJ
ejpam-4384	175	5	α	α	X
ejpam-4384	175	6	)	)	PUNCT
ejpam-4384	175	7	(	(	PUNCT
ejpam-4384	175	8	1−	1−	NUM
ejpam-4384	175	9	e	e	NOUN
ejpam-4384	175	10	)	)	PUNCT
ejpam-4384	175	11	]	]	PUNCT
ejpam-4384	175	12	.	.	PUNCT
ejpam-4384	176	1	(	(	PUNCT
ejpam-4384	176	2	38	38	NUM
ejpam-4384	176	3	)	)	PUNCT
ejpam-4384	176	4	applying	apply	VERB
ejpam-4384	176	5	the	the	DET
ejpam-4384	176	6	toeplitz	toeplitz	NOUN
ejpam-4384	176	7	matrix	matrix	NOUN
ejpam-4384	176	8	and	and	CCONJ
ejpam-4384	176	9	the	the	DET
ejpam-4384	176	10	product	product	NOUN
ejpam-4384	176	11	nyström	nyström	NOUN
ejpam-4384	176	12	methods	method	NOUN
ejpam-4384	176	13	to	to	ADP
ejpam-4384	176	14	equation	equation	NOUN
ejpam-4384	176	15	(	(	PUNCT
ejpam-4384	176	16	37	37	NUM
ejpam-4384	176	17	)	)	PUNCT
ejpam-4384	176	18	,	,	PUNCT
ejpam-4384	176	19	the	the	DET
ejpam-4384	176	20	numerical	numerical	ADJ
ejpam-4384	176	21	results	result	NOUN
ejpam-4384	176	22	are	be	AUX
ejpam-4384	176	23	shown	show	VERB
ejpam-4384	176	24	in	in	ADP
ejpam-4384	176	25	the	the	DET
ejpam-4384	176	26	following	follow	VERB
ejpam-4384	176	27	tables	table	NOUN
ejpam-4384	176	28	.	.	PUNCT
ejpam-4384	177	1	s.	s.	PROPN
ejpam-4384	177	2	raad	raad	PROPN
ejpam-4384	177	3	,	,	PUNCT
ejpam-4384	177	4	k.	k.	PROPN
ejpam-4384	177	5	alqurashi	alqurashi	PROPN
ejpam-4384	177	6	/	/	SYM
ejpam-4384	177	7	eur	eur	PROPN
ejpam-4384	177	8	.	.	PUNCT
ejpam-4384	178	1	j.	j.	PROPN
ejpam-4384	178	2	pure	pure	PROPN
ejpam-4384	178	3	appl	appl	PROPN
ejpam-4384	178	4	.	.	PROPN
ejpam-4384	178	5	math	math	PROPN
ejpam-4384	178	6	,	,	PUNCT
ejpam-4384	178	7	15	15	NUM
ejpam-4384	178	8	(	(	PUNCT
ejpam-4384	178	9	2	2	NUM
ejpam-4384	178	10	)	)	PUNCT
ejpam-4384	178	11	(	(	PUNCT
ejpam-4384	178	12	2022	2022	NUM
ejpam-4384	178	13	)	)	PUNCT
ejpam-4384	178	14	,	,	PUNCT
ejpam-4384	178	15	796	796	NUM
ejpam-4384	178	16	-	-	SYM
ejpam-4384	178	17	809	809	NUM
ejpam-4384	178	18	804	804	NUM
ejpam-4384	178	19	table	table	NOUN
ejpam-4384	178	20	1	1	NUM
ejpam-4384	178	21	:	:	PUNCT
ejpam-4384	178	22	the	the	DET
ejpam-4384	178	23	numerical	numerical	ADJ
ejpam-4384	178	24	solution	solution	NOUN
ejpam-4384	178	25	at	at	ADP
ejpam-4384	178	26	α	α	NOUN
ejpam-4384	178	27	=	=	SYM
ejpam-4384	178	28	0.6	0.6	NUM
ejpam-4384	178	29	and	and	CCONJ
ejpam-4384	178	30	t	t	NOUN
ejpam-4384	178	31	=	=	NOUN
ejpam-4384	178	32	0.009	0.009	NUM
ejpam-4384	178	33	.	.	PUNCT
ejpam-4384	179	1	t	t	PROPN
ejpam-4384	179	2	exact	exact	ADJ
ejpam-4384	179	3	solution	solution	NOUN
ejpam-4384	179	4	toeplitz	toeplitz	NOUN
ejpam-4384	179	5	solution	solution	NOUN
ejpam-4384	179	6	error	error	NOUN
ejpam-4384	179	7	nyström	nyström	NOUN
ejpam-4384	179	8	solution	solution	NOUN
ejpam-4384	179	9	error	error	NOUN
ejpam-4384	179	10	0	0	NUM
ejpam-4384	179	11	0	0	NUM
ejpam-4384	179	12	0	0	NUM
ejpam-4384	179	13	0	0	NUM
ejpam-4384	179	14	0	0	NUM
ejpam-4384	179	15	0	0	NUM
ejpam-4384	179	16	0.0018	0.0018	NUM
ejpam-4384	179	17	1.7968×	1.7968×	NUM
ejpam-4384	179	18	10−3	10−3	NUM
ejpam-4384	179	19	1.7969×	1.7969×	NUM
ejpam-4384	179	20	10−3	10−3	NUM
ejpam-4384	179	21	1.0585×	1.0585×	NUM
ejpam-4384	179	22	10−7	10−7	NUM
ejpam-4384	179	23	1.7961×	1.7961×	NUM
ejpam-4384	179	24	10−3	10−3	NUM
ejpam-4384	179	25	1.9918×	1.9918×	NUM
ejpam-4384	179	26	10−7	10−7	NUM
ejpam-4384	179	27	0.0036	0.0036	NUM
ejpam-4384	179	28	3.5870×	3.5870×	NUM
ejpam-4384	179	29	10−3	10−3	NUM
ejpam-4384	179	30	3.5880×	3.5880×	NOUN
ejpam-4384	179	31	10−3	10−3	NUM
ejpam-4384	179	32	9.6681×	9.6681×	NUM
ejpam-4384	179	33	10−7	10−7	NUM
ejpam-4384	179	34	3.5882×	3.5882×	NUM
ejpam-4384	179	35	10−3	10−3	NUM
ejpam-4384	179	36	1.1977×	1.1977×	NUM
ejpam-4384	179	37	10−6	10−6	NUM
ejpam-4384	179	38	0.0054	0.0054	NUM
ejpam-4384	179	39	5.3708×	5.3708×	NUM
ejpam-4384	179	40	10−3	10−3	NUM
ejpam-4384	179	41	5.3731×	5.3731×	NUM
ejpam-4384	179	42	10−3	10−3	NUM
ejpam-4384	179	43	3.1263×	3.1263×	NUM
ejpam-4384	179	44	10−6	10−6	NUM
ejpam-4384	179	45	5.3743×	5.3743×	NUM
ejpam-4384	179	46	10−3	10−3	NUM
ejpam-4384	179	47	3.4511×	3.4511×	NUM
ejpam-4384	179	48	10−6	10−6	NUM
ejpam-4384	179	49	0.0072	0.0072	NUM
ejpam-4384	179	50	7.1482×	7.1482×	NUM
ejpam-4384	179	51	10−3	10−3	NUM
ejpam-4384	179	52	7.1553×	7.1553×	NOUN
ejpam-4384	179	53	10−3	10−3	NUM
ejpam-4384	179	54	7.1190×	7.1190×	NUM
ejpam-4384	179	55	10−6	10−6	NUM
ejpam-4384	179	56	7.1555×	7.1555×	NOUN
ejpam-4384	179	57	10−3	10−3	NUM
ejpam-4384	179	58	7.3083×	7.3083×	NOUN
ejpam-4384	179	59	10−6	10−6	NUM
ejpam-4384	179	60	0.0090	0.0090	NUM
ejpam-4384	179	61	8.9190×	8.9190×	NUM
ejpam-4384	179	62	10−3	10−3	NUM
ejpam-4384	179	63	8.9346×	8.9346×	NUM
ejpam-4384	179	64	10−3	10−3	NUM
ejpam-4384	179	65	1.5609×	1.5609×	NUM
ejpam-4384	179	66	10−5	10−5	NUM
ejpam-4384	179	67	8.9321×	8.9321×	NUM
ejpam-4384	179	68	10−3	10−3	NUM
ejpam-4384	179	69	1.3067×	1.3067×	NUM
ejpam-4384	179	70	10−5	10−5	NUM
ejpam-4384	179	71	table	table	NOUN
ejpam-4384	179	72	2	2	NUM
ejpam-4384	179	73	:	:	PUNCT
ejpam-4384	179	74	the	the	DET
ejpam-4384	179	75	numerical	numerical	ADJ
ejpam-4384	179	76	solution	solution	NOUN
ejpam-4384	179	77	at	at	ADP
ejpam-4384	179	78	α	α	NOUN
ejpam-4384	179	79	=	=	SYM
ejpam-4384	179	80	0.9	0.9	NUM
ejpam-4384	179	81	and	and	CCONJ
ejpam-4384	179	82	t	t	NOUN
ejpam-4384	179	83	=	=	NUM
ejpam-4384	179	84	0.009	0.009	NUM
ejpam-4384	179	85	.	.	PUNCT
ejpam-4384	180	1	t	t	PROPN
ejpam-4384	180	2	exact	exact	ADJ
ejpam-4384	180	3	solution	solution	NOUN
ejpam-4384	180	4	toeplitz	toeplitz	NOUN
ejpam-4384	180	5	solution	solution	NOUN
ejpam-4384	180	6	error	error	NOUN
ejpam-4384	180	7	nyström	nyström	NOUN
ejpam-4384	180	8	solution	solution	NOUN
ejpam-4384	180	9	error	error	NOUN
ejpam-4384	180	10	0	0	NUM
ejpam-4384	180	11	0	0	NUM
ejpam-4384	180	12	0	0	NUM
ejpam-4384	180	13	0	0	NUM
ejpam-4384	180	14	0	0	NUM
ejpam-4384	180	15	0	0	NUM
ejpam-4384	180	16	0.0018	0.0018	NUM
ejpam-4384	180	17	1.7968×	1.7968×	NUM
ejpam-4384	180	18	10−3	10−3	NUM
ejpam-4384	180	19	1.7968×	1.7968×	NUM
ejpam-4384	180	20	10−3	10−3	NUM
ejpam-4384	180	21	2.5004×	2.5004×	NUM
ejpam-4384	180	22	10−8	10−8	NUM
ejpam-4384	180	23	1.7968×	1.7968×	NUM
ejpam-4384	180	24	10−3	10−3	NUM
ejpam-4384	180	25	2.8887×	2.8887×	NUM
ejpam-4384	180	26	10−8	10−8	NUM
ejpam-4384	180	27	0.0036	0.0036	NUM
ejpam-4384	180	28	3.5870×	3.5870×	NUM
ejpam-4384	180	29	10−3	10−3	NUM
ejpam-4384	180	30	3.5872×	3.5872×	NUM
ejpam-4384	180	31	10−3	10−3	NUM
ejpam-4384	180	32	1.8726×	1.8726×	NUM
ejpam-4384	180	33	10−7	10−7	NUM
ejpam-4384	180	34	3.5872×	3.5872×	NUM
ejpam-4384	180	35	10−3	10−3	NUM
ejpam-4384	180	36	1.9739×	1.9739×	NUM
ejpam-4384	180	37	10−7	10−7	NUM
ejpam-4384	180	38	0.0054	0.0054	NUM
ejpam-4384	180	39	5.3708×	5.3708×	NUM
ejpam-4384	180	40	10−3	10−3	NUM
ejpam-4384	180	41	5.3715×	5.3715×	NOUN
ejpam-4384	180	42	10−3	10−3	NUM
ejpam-4384	180	43	6.1311×	6.1311×	NOUN
ejpam-4384	180	44	10−7	10−7	NUM
ejpam-4384	180	45	5.3715×	5.3715×	NUM
ejpam-4384	180	46	10−3	10−3	NUM
ejpam-4384	180	47	6.2659×	6.2659×	NOUN
ejpam-4384	180	48	10−7	10−7	NUM
ejpam-4384	180	49	0.0072	0.0072	NUM
ejpam-4384	180	50	7.1482×	7.1482×	NUM
ejpam-4384	180	51	10−3	10−3	NUM
ejpam-4384	180	52	7.1496×	7.1496×	NUM
ejpam-4384	180	53	10−3	10−3	NUM
ejpam-4384	180	54	1.4257×	1.4257×	NUM
ejpam-4384	180	55	10−6	10−6	NUM
ejpam-4384	180	56	7.1496×	7.1496×	NUM
ejpam-4384	180	57	10−3	10−3	NUM
ejpam-4384	180	58	1.4294×	1.4294×	NUM
ejpam-4384	180	59	10−6	10−6	NUM
ejpam-4384	180	60	0.0090	0.0090	NUM
ejpam-4384	180	61	8.9190×	8.9190×	NUM
ejpam-4384	180	62	10−3	10−3	NUM
ejpam-4384	180	63	8.9218×	8.9218×	NUM
ejpam-4384	180	64	10−3	10−3	NUM
ejpam-4384	180	65	2.7961×	2.7961×	NUM
ejpam-4384	180	66	10−6	10−6	NUM
ejpam-4384	180	67	8.9217×	8.9217×	NUM
ejpam-4384	180	68	10−3	10−3	NUM
ejpam-4384	180	69	2.7133×	2.7133×	NUM
ejpam-4384	180	70	10−6	10−6	NUM
ejpam-4384	180	71	table	table	NOUN
ejpam-4384	180	72	3	3	NUM
ejpam-4384	180	73	:	:	PUNCT
ejpam-4384	180	74	the	the	DET
ejpam-4384	180	75	numerical	numerical	ADJ
ejpam-4384	180	76	solution	solution	NOUN
ejpam-4384	180	77	at	at	ADP
ejpam-4384	180	78	α	α	NOUN
ejpam-4384	180	79	=	=	SYM
ejpam-4384	180	80	0.6	0.6	NUM
ejpam-4384	180	81	and	and	CCONJ
ejpam-4384	180	82	t	t	NOUN
ejpam-4384	180	83	=	=	NUM
ejpam-4384	180	84	0.2	0.2	NUM
ejpam-4384	180	85	.	.	PUNCT
ejpam-4384	181	1	t	t	PROPN
ejpam-4384	181	2	exact	exact	ADJ
ejpam-4384	181	3	solution	solution	NOUN
ejpam-4384	181	4	toeplitz	toeplitz	NOUN
ejpam-4384	181	5	solution	solution	NOUN
ejpam-4384	181	6	error	error	NOUN
ejpam-4384	181	7	nyström	nyström	NOUN
ejpam-4384	181	8	solution	solution	NOUN
ejpam-4384	181	9	error	error	NOUN
ejpam-4384	181	10	0	0	NUM
ejpam-4384	181	11	0	0	NUM
ejpam-4384	181	12	0	0	NUM
ejpam-4384	181	13	0	0	NUM
ejpam-4384	181	14	0	0	NUM
ejpam-4384	181	15	0	0	NUM
ejpam-4384	181	16	0.04	0.04	NUM
ejpam-4384	181	17	3.84×	3.84×	NUM
ejpam-4384	181	18	10−2	10−2	NUM
ejpam-4384	181	19	3.8413×	3.8413×	NUM
ejpam-4384	181	20	10−2	10−2	NUM
ejpam-4384	181	21	1.3325×	1.3325×	NUM
ejpam-4384	181	22	10−5	10−5	NUM
ejpam-4384	181	23	3.8426×	3.8426×	NUM
ejpam-4384	181	24	10−2	10−2	NUM
ejpam-4384	181	25	2.6277×	2.6277×	NUM
ejpam-4384	181	26	10−5	10−5	NUM
ejpam-4384	181	27	0.08	0.08	NUM
ejpam-4384	181	28	7.36×	7.36×	NUM
ejpam-4384	181	29	10−2	10−2	NUM
ejpam-4384	181	30	7.3717×	7.3717×	NUM
ejpam-4384	181	31	10−2	10−2	NUM
ejpam-4384	181	32	1.1738×	1.1738×	NUM
ejpam-4384	181	33	10−4	10−4	NUM
ejpam-4384	181	34	7.3748×	7.3748×	NUM
ejpam-4384	181	35	10−2	10−2	NUM
ejpam-4384	181	36	1.4837×	1.4837×	NUM
ejpam-4384	181	37	10−4	10−4	NUM
ejpam-4384	181	38	0.12	0.12	NUM
ejpam-4384	181	39	1.056×	1.056×	PROPN
ejpam-4384	181	40	10−1	10−1	PROPN
ejpam-4384	181	41	1.0596×	1.0596×	NUM
ejpam-4384	181	42	10−1	10−1	PROPN
ejpam-4384	181	43	3.5658×	3.5658×	NUM
ejpam-4384	181	44	10−4	10−4	PROPN
ejpam-4384	181	45	1.0591×	1.0591×	NUM
ejpam-4384	181	46	10−1	10−1	NUM
ejpam-4384	181	47	3.9846×	3.9846×	NUM
ejpam-4384	181	48	10−4	10−4	NUM
ejpam-4384	181	49	0.16	0.16	NUM
ejpam-4384	181	50	1.344×	1.344×	NUM
ejpam-4384	181	51	10−1	10−1	NUM
ejpam-4384	181	52	1.3516×	1.3516×	NUM
ejpam-4384	181	53	10−1	10−1	PROPN
ejpam-4384	181	54	7.5928×	7.5928×	NUM
ejpam-4384	181	55	10−4	10−4	NUM
ejpam-4384	181	56	1.3518×	1.3518×	NUM
ejpam-4384	181	57	10−1	10−1	NUM
ejpam-4384	181	58	7.8131×	7.8131×	NUM
ejpam-4384	181	59	10−4	10−4	NUM
ejpam-4384	181	60	0.20	0.20	NUM
ejpam-4384	181	61	1.60×	1.60×	NUM
ejpam-4384	181	62	10−1	10−1	PROPN
ejpam-4384	181	63	1.6162×	1.6162×	NUM
ejpam-4384	181	64	10−1	10−1	PROPN
ejpam-4384	181	65	1.6062×	1.6062×	NUM
ejpam-4384	181	66	10−3	10−3	NUM
ejpam-4384	181	67	1.6128×	1.6128×	NUM
ejpam-4384	181	68	10−1	10−1	NUM
ejpam-4384	181	69	1.2842×	1.2842×	NUM
ejpam-4384	181	70	10−3	10−3	NUM
ejpam-4384	181	71	table	table	NOUN
ejpam-4384	181	72	4	4	NUM
ejpam-4384	181	73	:	:	PUNCT
ejpam-4384	181	74	the	the	DET
ejpam-4384	181	75	numerical	numerical	ADJ
ejpam-4384	181	76	solution	solution	NOUN
ejpam-4384	181	77	at	at	ADP
ejpam-4384	181	78	α	α	NOUN
ejpam-4384	181	79	=	=	SYM
ejpam-4384	181	80	0.9	0.9	NUM
ejpam-4384	181	81	and	and	CCONJ
ejpam-4384	181	82	t	t	NOUN
ejpam-4384	181	83	=	=	NUM
ejpam-4384	181	84	0.2	0.2	NUM
ejpam-4384	181	85	.	.	PUNCT
ejpam-4384	182	1	t	t	PROPN
ejpam-4384	182	2	exact	exact	ADJ
ejpam-4384	182	3	solution	solution	NOUN
ejpam-4384	182	4	toeplitz	toeplitz	NOUN
ejpam-4384	182	5	solution	solution	NOUN
ejpam-4384	182	6	error	error	NOUN
ejpam-4384	182	7	nyström	nyström	NOUN
ejpam-4384	182	8	solution	solution	NOUN
ejpam-4384	182	9	error	error	NOUN
ejpam-4384	182	10	0	0	NUM
ejpam-4384	182	11	0	0	NUM
ejpam-4384	182	12	0	0	NUM
ejpam-4384	182	13	0	0	NUM
ejpam-4384	182	14	0	0	NUM
ejpam-4384	182	15	0	0	NUM
ejpam-4384	182	16	0.04	0.04	NUM
ejpam-4384	182	17	3.84×	3.84×	NUM
ejpam-4384	182	18	10−2	10−2	NUM
ejpam-4384	182	19	3.8408×	3.8408×	NUM
ejpam-4384	182	20	10−2	10−2	NUM
ejpam-4384	182	21	8.2129×	8.2129×	SYM
ejpam-4384	182	22	10−6	10−6	NUM
ejpam-4384	182	23	3.8401×	3.8401×	NUM
ejpam-4384	182	24	10−2	10−2	NUM
ejpam-4384	182	25	9.5921×	9.5921×	NUM
ejpam-4384	182	26	10−6	10−6	NUM
ejpam-4384	182	27	0.08	0.08	NUM
ejpam-4384	182	28	7.36×	7.36×	NUM
ejpam-4384	182	29	10−2	10−2	NUM
ejpam-4384	182	30	7.3658×	7.3658×	NOUN
ejpam-4384	182	31	10−2	10−2	NUM
ejpam-4384	182	32	5.7747×	5.7747×	NUM
ejpam-4384	182	33	10−5	10−5	NUM
ejpam-4384	182	34	7.3661×	7.3661×	NUM
ejpam-4384	182	35	10−2	10−2	NUM
ejpam-4384	182	36	6.1222×	6.1222×	NUM
ejpam-4384	182	37	10−5	10−5	NUM
ejpam-4384	182	38	0.12	0.12	NUM
ejpam-4384	182	39	1.056×	1.056×	PROPN
ejpam-4384	183	1	10−1	10−1	PROPN
ejpam-4384	183	2	1.0578×	1.0578×	NUM
ejpam-4384	183	3	10−1	10−1	NUM
ejpam-4384	183	4	1.7594×	1.7594×	NUM
ejpam-4384	183	5	10−4	10−4	NUM
ejpam-4384	183	6	1.0578×	1.0578×	NUM
ejpam-4384	183	7	10−1	10−1	NUM
ejpam-4384	183	8	1.8036×	1.8036×	NOUN
ejpam-4384	183	9	10−4	10−4	NUM
ejpam-4384	183	10	0.16	0.16	NUM
ejpam-4384	183	11	1.344×	1.344×	NUM
ejpam-4384	183	12	10−1	10−1	PROPN
ejpam-4384	183	13	1.3478×	1.3478×	NUM
ejpam-4384	183	14	10−1	10−1	PROPN
ejpam-4384	183	15	3.7816×	3.7816×	X
ejpam-4384	183	16	10−4	10−4	NUM
ejpam-4384	183	17	1.3478×	1.3478×	NUM
ejpam-4384	183	18	10−1	10−1	NUM
ejpam-4384	183	19	3.7916×	3.7916×	NUM
ejpam-4384	183	20	10−4	10−4	NUM
ejpam-4384	183	21	0.20	0.20	NUM
ejpam-4384	183	22	1.60×	1.60×	NUM
ejpam-4384	183	23	10−1	10−1	NUM
ejpam-4384	183	24	1.6068×	1.6068×	NUM
ejpam-4384	183	25	10−1	10−1	NUM
ejpam-4384	183	26	6.8461×	6.8461×	NUM
ejpam-4384	183	27	10−4	10−4	NUM
ejpam-4384	183	28	1.6066×	1.6066×	PROPN
ejpam-4384	183	29	10−1	10−1	PROPN
ejpam-4384	183	30	6.5791×	6.5791×	NUM
ejpam-4384	183	31	10−4	10−4	NUM
ejpam-4384	183	32	s.	s.	PROPN
ejpam-4384	183	33	raad	raad	PROPN
ejpam-4384	183	34	,	,	PUNCT
ejpam-4384	183	35	k.	k.	PROPN
ejpam-4384	183	36	alqurashi	alqurashi	PROPN
ejpam-4384	183	37	/	/	SYM
ejpam-4384	183	38	eur	eur	PROPN
ejpam-4384	183	39	.	.	PUNCT
ejpam-4384	184	1	j.	j.	PROPN
ejpam-4384	184	2	pure	pure	PROPN
ejpam-4384	184	3	appl	appl	PROPN
ejpam-4384	184	4	.	.	PROPN
ejpam-4384	184	5	math	math	PROPN
ejpam-4384	184	6	,	,	PUNCT
ejpam-4384	184	7	15	15	NUM
ejpam-4384	184	8	(	(	PUNCT
ejpam-4384	184	9	2	2	NUM
ejpam-4384	184	10	)	)	PUNCT
ejpam-4384	184	11	(	(	PUNCT
ejpam-4384	184	12	2022	2022	NUM
ejpam-4384	184	13	)	)	PUNCT
ejpam-4384	184	14	,	,	PUNCT
ejpam-4384	184	15	796	796	NUM
ejpam-4384	184	16	-	-	SYM
ejpam-4384	184	17	809	809	NUM
ejpam-4384	184	18	805	805	NUM
ejpam-4384	184	19	figure	figure	NOUN
ejpam-4384	184	20	1	1	NUM
ejpam-4384	184	21	:	:	PUNCT
ejpam-4384	184	22	the	the	DET
ejpam-4384	184	23	error	error	NOUN
ejpam-4384	184	24	by	by	ADP
ejpam-4384	184	25	toeplitz	toeplitz	NOUN
ejpam-4384	184	26	matrix	matrix	NOUN
ejpam-4384	184	27	and	and	CCONJ
ejpam-4384	184	28	nyström	nyström	DET
ejpam-4384	184	29	product	product	NOUN
ejpam-4384	184	30	methods	method	NOUN
ejpam-4384	184	31	at	at	ADP
ejpam-4384	184	32	various	various	ADJ
ejpam-4384	184	33	values	value	NOUN
ejpam-4384	184	34	for	for	ADP
ejpam-4384	184	35	α	α	NOUN
ejpam-4384	184	36	=	=	SYM
ejpam-4384	184	37	0.6	0.6	NUM
ejpam-4384	184	38	,	,	PUNCT
ejpam-4384	184	39	0.75	0.75	NUM
ejpam-4384	184	40	,	,	PUNCT
ejpam-4384	184	41	0.9	0.9	NUM
ejpam-4384	184	42	and	and	CCONJ
ejpam-4384	184	43	at	at	ADP
ejpam-4384	184	44	t	t	NOUN
ejpam-4384	184	45	=	=	SYM
ejpam-4384	184	46	0.009	0.009	NUM
ejpam-4384	184	47	,	,	PUNCT
ejpam-4384	184	48	0.05	0.05	NUM
ejpam-4384	184	49	,	,	PUNCT
ejpam-4384	184	50	0.2	0.2	NUM
ejpam-4384	184	51	.	.	PUNCT
ejpam-4384	185	1	tables	table	NOUN
ejpam-4384	185	2	and	and	CCONJ
ejpam-4384	185	3	the	the	DET
ejpam-4384	185	4	figures	figure	NOUN
ejpam-4384	185	5	show	show	VERB
ejpam-4384	185	6	that	that	SCONJ
ejpam-4384	185	7	the	the	DET
ejpam-4384	185	8	maximum	maximum	ADJ
ejpam-4384	185	9	error	error	NOUN
ejpam-4384	185	10	by	by	ADP
ejpam-4384	185	11	toeplitz	toeplitz	NOUN
ejpam-4384	185	12	matrix	matrix	NOUN
ejpam-4384	185	13	is	be	AUX
ejpam-4384	185	14	1.6062×10−3	1.6062×10−3	NUM
ejpam-4384	185	15	and	and	CCONJ
ejpam-4384	185	16	by	by	ADP
ejpam-4384	185	17	nyström	nyström	DET
ejpam-4384	185	18	method	method	NOUN
ejpam-4384	185	19	is	be	AUX
ejpam-4384	185	20	1.2842×	1.2842×	NUM
ejpam-4384	185	21	10−3	10−3	NUM
ejpam-4384	185	22	both	both	PRON
ejpam-4384	185	23	at	at	ADP
ejpam-4384	185	24	α	α	NOUN
ejpam-4384	185	25	=	=	SYM
ejpam-4384	185	26	0.6	0.6	NUM
ejpam-4384	185	27	and	and	CCONJ
ejpam-4384	185	28	t	t	NOUN
ejpam-4384	185	29	=	=	NUM
ejpam-4384	185	30	0.2	0.2	NUM
ejpam-4384	185	31	example	example	NOUN
ejpam-4384	185	32	2	2	NUM
ejpam-4384	185	33	.	.	X
ejpam-4384	185	34	consider	consider	VERB
ejpam-4384	185	35	the	the	DET
ejpam-4384	185	36	fi	fi	NOUN
ejpam-4384	185	37	-	-	ADJ
ejpam-4384	185	38	de	de	X
ejpam-4384	185	39	∂αu(x	∂αu(x	PROPN
ejpam-4384	185	40	,	,	PUNCT
ejpam-4384	185	41	t	t	NOUN
ejpam-4384	185	42	)	)	PUNCT
ejpam-4384	185	43	∂tα	∂tα	PROPN
ejpam-4384	185	44	=	=	SYM
ejpam-4384	185	45	x2	x2	PROPN
ejpam-4384	185	46	2t2−α	2t2−α	PROPN
ejpam-4384	185	47	γ(3−	γ(3−	ADP
ejpam-4384	185	48	α	α	NUM
ejpam-4384	185	49	)	)	PUNCT
ejpam-4384	185	50	−	−	PROPN
ejpam-4384	186	1	λt2	λt2	PROPN
ejpam-4384	186	2	(	(	PUNCT
ejpam-4384	186	3	x	x	SYM
ejpam-4384	186	4	4	4	NUM
ejpam-4384	186	5	+	+	NUM
ejpam-4384	186	6	x2	x2	PROPN
ejpam-4384	186	7	5	5	NUM
ejpam-4384	186	8	)	)	PUNCT
ejpam-4384	186	9	+	+	CCONJ
ejpam-4384	187	1	λ	λ	X
ejpam-4384	187	2	∫	∫	PROPN
ejpam-4384	187	3	1	1	NUM
ejpam-4384	187	4	0	0	NUM
ejpam-4384	188	1	(	(	PUNCT
ejpam-4384	188	2	xy	xy	PROPN
ejpam-4384	189	1	+	+	SYM
ejpam-4384	189	2	x2y2)u(y	x2y2)u(y	PROPN
ejpam-4384	189	3	,	,	PUNCT
ejpam-4384	189	4	t)dy	t)dy	PROPN
ejpam-4384	189	5	,	,	PUNCT
ejpam-4384	189	6	u0(x	u0(x	NOUN
ejpam-4384	189	7	)	)	PUNCT
ejpam-4384	189	8	=	=	SYM
ejpam-4384	189	9	0	0	NUM
ejpam-4384	189	10	(	(	PUNCT
ejpam-4384	189	11	39	39	NUM
ejpam-4384	189	12	)	)	PUNCT
ejpam-4384	189	13	applying	apply	VERB
ejpam-4384	189	14	the	the	DET
ejpam-4384	189	15	riemann	riemann	PROPN
ejpam-4384	189	16	-	-	PUNCT
ejpam-4384	189	17	liouville	liouville	VERB
ejpam-4384	189	18	fractional	fractional	ADJ
ejpam-4384	189	19	integral	integral	ADJ
ejpam-4384	189	20	to	to	ADP
ejpam-4384	189	21	equation	equation	NOUN
ejpam-4384	189	22	(	(	PUNCT
ejpam-4384	189	23	39	39	NUM
ejpam-4384	189	24	)	)	PUNCT
ejpam-4384	189	25	,	,	PUNCT
ejpam-4384	189	26	we	we	PRON
ejpam-4384	189	27	get	get	VERB
ejpam-4384	189	28	u(x	u(x	NOUN
ejpam-4384	189	29	,	,	PUNCT
ejpam-4384	189	30	t	t	NOUN
ejpam-4384	189	31	)	)	PUNCT
ejpam-4384	189	32	=	=	SYM
ejpam-4384	190	1	η(x	η(x	PROPN
ejpam-4384	190	2	,	,	PUNCT
ejpam-4384	190	3	t	t	PROPN
ejpam-4384	190	4	)	)	PUNCT
ejpam-4384	190	5	+	+	NUM
ejpam-4384	190	6	λ	λ	PROPN
ejpam-4384	190	7	γ(α	γ(α	NOUN
ejpam-4384	190	8	)	)	PUNCT
ejpam-4384	191	1	∫	∫	PROPN
ejpam-4384	191	2	t	t	PROPN
ejpam-4384	191	3	0	0	NUM
ejpam-4384	191	4	∫	∫	PROPN
ejpam-4384	191	5	1	1	NUM
ejpam-4384	191	6	0	0	NUM
ejpam-4384	191	7	(	(	PUNCT
ejpam-4384	191	8	t−	t−	PROPN
ejpam-4384	191	9	s)α−1(xy	s)α−1(xy	NOUN
ejpam-4384	191	10	+	+	CCONJ
ejpam-4384	191	11	x2y2)u(y	x2y2)u(y	PROPN
ejpam-4384	191	12	,	,	PUNCT
ejpam-4384	191	13	s)dyds	s)dyds	PROPN
ejpam-4384	191	14	,	,	PUNCT
ejpam-4384	191	15	(	(	PUNCT
ejpam-4384	191	16	40	40	NUM
ejpam-4384	191	17	)	)	PUNCT
ejpam-4384	191	18	and	and	CCONJ
ejpam-4384	191	19	η(x	η(x	PROPN
ejpam-4384	191	20	,	,	PUNCT
ejpam-4384	191	21	t	t	PROPN
ejpam-4384	191	22	)	)	PUNCT
ejpam-4384	192	1	=	=	PUNCT
ejpam-4384	192	2	x2t2	x2t2	PUNCT
ejpam-4384	193	1	−	−	NOUN
ejpam-4384	193	2	λx2	λx2	NOUN
ejpam-4384	193	3	2t2+α	2t2+α	NUM
ejpam-4384	193	4	5γ(3	5γ(3	NUM
ejpam-4384	193	5	+	+	CCONJ
ejpam-4384	193	6	α	α	X
ejpam-4384	193	7	)	)	PUNCT
ejpam-4384	193	8	−	−	PROPN
ejpam-4384	193	9	λx	λx	NOUN
ejpam-4384	193	10	2t2+α	2t2+α	NUM
ejpam-4384	193	11	4γ(3	4γ(3	PRON
ejpam-4384	193	12	+	+	CCONJ
ejpam-4384	193	13	α	α	X
ejpam-4384	193	14	)	)	PUNCT
ejpam-4384	193	15	.	.	PUNCT
ejpam-4384	194	1	(	(	PUNCT
ejpam-4384	194	2	41	41	NUM
ejpam-4384	194	3	)	)	PUNCT
ejpam-4384	194	4	the	the	DET
ejpam-4384	194	5	numerical	numerical	ADJ
ejpam-4384	194	6	results	result	NOUN
ejpam-4384	194	7	after	after	ADP
ejpam-4384	194	8	using	use	VERB
ejpam-4384	194	9	the	the	DET
ejpam-4384	194	10	toeplitz	toeplitz	NOUN
ejpam-4384	194	11	matrix	matrix	NOUN
ejpam-4384	194	12	and	and	CCONJ
ejpam-4384	194	13	the	the	DET
ejpam-4384	194	14	product	product	NOUN
ejpam-4384	194	15	nyström	nyström	NOUN
ejpam-4384	194	16	methods	method	NOUN
ejpam-4384	194	17	to	to	ADP
ejpam-4384	194	18	equation	equation	NOUN
ejpam-4384	194	19	(	(	PUNCT
ejpam-4384	194	20	40	40	NUM
ejpam-4384	194	21	)	)	PUNCT
ejpam-4384	194	22	are	be	AUX
ejpam-4384	194	23	demonstrated	demonstrate	VERB
ejpam-4384	194	24	in	in	ADP
ejpam-4384	194	25	the	the	DET
ejpam-4384	194	26	following	follow	VERB
ejpam-4384	194	27	tables	table	NOUN
ejpam-4384	194	28	.	.	PUNCT
ejpam-4384	195	1	table	table	NOUN
ejpam-4384	195	2	5	5	NUM
ejpam-4384	195	3	:	:	PUNCT
ejpam-4384	195	4	the	the	DET
ejpam-4384	195	5	numerical	numerical	ADJ
ejpam-4384	195	6	results	result	NOUN
ejpam-4384	195	7	at	at	ADP
ejpam-4384	195	8	α	α	NOUN
ejpam-4384	195	9	=	=	SYM
ejpam-4384	195	10	0.6	0.6	NUM
ejpam-4384	195	11	and	and	CCONJ
ejpam-4384	195	12	t	t	NOUN
ejpam-4384	195	13	=	=	SYM
ejpam-4384	196	1	0.009	0.009	NUM
ejpam-4384	196	2	t	t	NOUN
ejpam-4384	196	3	exact	exact	ADJ
ejpam-4384	196	4	solution	solution	NOUN
ejpam-4384	196	5	toeplitz	toeplitz	NOUN
ejpam-4384	196	6	solution	solution	NOUN
ejpam-4384	196	7	error	error	NOUN
ejpam-4384	196	8	nyström	nyström	NOUN
ejpam-4384	196	9	solution	solution	NOUN
ejpam-4384	196	10	error	error	NOUN
ejpam-4384	196	11	0	0	NUM
ejpam-4384	196	12	0	0	NUM
ejpam-4384	196	13	0	0	NUM
ejpam-4384	196	14	0	0	NUM
ejpam-4384	196	15	0	0	NUM
ejpam-4384	196	16	0	0	NUM
ejpam-4384	196	17	0.0018	0.0018	NUM
ejpam-4384	196	18	3.24×	3.24×	NUM
ejpam-4384	196	19	10−6	10−6	NUM
ejpam-4384	196	20	3.2400×	3.2400×	NUM
ejpam-4384	196	21	10−6	10−6	NUM
ejpam-4384	196	22	3.0434×	3.0434×	NUM
ejpam-4384	196	23	10−11	10−11	NUM
ejpam-4384	196	24	3.2401×	3.2401×	NUM
ejpam-4384	196	25	10−6	10−6	NUM
ejpam-4384	196	26	1.2663×	1.2663×	NUM
ejpam-4384	196	27	10−10	10−10	NUM
ejpam-4384	196	28	0.0036	0.0036	NUM
ejpam-4384	196	29	1.296×	1.296×	NUM
ejpam-4384	196	30	10−5	10−5	NUM
ejpam-4384	196	31	1.2961×	1.2961×	NUM
ejpam-4384	196	32	10−5	10−5	NUM
ejpam-4384	196	33	7.1041×	7.1041×	NOUN
ejpam-4384	197	1	10−10	10−10	NUM
ejpam-4384	197	2	1.2961×	1.2961×	NUM
ejpam-4384	197	3	10−5	10−5	NUM
ejpam-4384	197	4	1.2172×	1.2172×	NUM
ejpam-4384	197	5	10−9	10−9	NUM
ejpam-4384	197	6	0.0054	0.0054	NUM
ejpam-4384	197	7	2.916×	2.916×	PROPN
ejpam-4384	197	8	10−5	10−5	NUM
ejpam-4384	197	9	2.9164×	2.9164×	NUM
ejpam-4384	197	10	10−5	10−5	NUM
ejpam-4384	197	11	3.7224×	3.7224×	NUM
ejpam-4384	197	12	10−9	10−9	NUM
ejpam-4384	197	13	2.915×	2.915×	NUM
ejpam-4384	197	14	10−5	10−5	NUM
ejpam-4384	197	15	4.8778×	4.8778×	NUM
ejpam-4384	197	16	10−9	10−9	NUM
ejpam-4384	197	17	0.0072	0.0072	NUM
ejpam-4384	197	18	5.184×	5.184×	NUM
ejpam-4384	197	19	10−5	10−5	NUM
ejpam-4384	197	20	5.1852×	5.1852×	NOUN
ejpam-4384	197	21	10−5	10−5	NUM
ejpam-4384	197	22	1.1978×	1.1978×	NUM
ejpam-4384	197	23	10−8	10−8	NUM
ejpam-4384	197	24	5.1853×	5.1853×	ADV
ejpam-4384	197	25	10−5	10−5	NUM
ejpam-4384	197	26	1.3282×	1.3282×	NUM
ejpam-4384	197	27	10−8	10−8	NUM
ejpam-4384	197	28	0.0090	0.0090	NUM
ejpam-4384	197	29	8.1×	8.1×	PROPN
ejpam-4384	197	30	10−5	10−5	NUM
ejpam-4384	197	31	8.1039×	8.1039×	NUM
ejpam-4384	197	32	10−5	10−5	NUM
ejpam-4384	197	33	3.9302×	3.9302×	NUM
ejpam-4384	197	34	10−8	10−8	NUM
ejpam-4384	197	35	8.1029×	8.1029×	NUM
ejpam-4384	197	36	10−5	10−5	NUM
ejpam-4384	197	37	2.9079×	2.9079×	NUM
ejpam-4384	197	38	10−8	10−8	NUM
ejpam-4384	197	39	s.	s.	PROPN
ejpam-4384	197	40	raad	raad	PROPN
ejpam-4384	197	41	,	,	PUNCT
ejpam-4384	197	42	k.	k.	PROPN
ejpam-4384	197	43	alqurashi	alqurashi	PROPN
ejpam-4384	197	44	/	/	SYM
ejpam-4384	197	45	eur	eur	PROPN
ejpam-4384	197	46	.	.	PUNCT
ejpam-4384	198	1	j.	j.	PROPN
ejpam-4384	198	2	pure	pure	PROPN
ejpam-4384	198	3	appl	appl	PROPN
ejpam-4384	198	4	.	.	PROPN
ejpam-4384	198	5	math	math	PROPN
ejpam-4384	198	6	,	,	PUNCT
ejpam-4384	198	7	15	15	NUM
ejpam-4384	198	8	(	(	PUNCT
ejpam-4384	198	9	2	2	NUM
ejpam-4384	198	10	)	)	PUNCT
ejpam-4384	198	11	(	(	PUNCT
ejpam-4384	198	12	2022	2022	NUM
ejpam-4384	198	13	)	)	PUNCT
ejpam-4384	198	14	,	,	PUNCT
ejpam-4384	198	15	796	796	NUM
ejpam-4384	198	16	-	-	SYM
ejpam-4384	198	17	809	809	NUM
ejpam-4384	198	18	806	806	NUM
ejpam-4384	198	19	table	table	NOUN
ejpam-4384	198	20	6	6	NUM
ejpam-4384	198	21	:	:	PUNCT
ejpam-4384	198	22	the	the	DET
ejpam-4384	198	23	numerical	numerical	ADJ
ejpam-4384	198	24	results	result	NOUN
ejpam-4384	198	25	at	at	ADP
ejpam-4384	198	26	α	α	NOUN
ejpam-4384	198	27	=	=	SYM
ejpam-4384	198	28	0.9	0.9	NUM
ejpam-4384	198	29	and	and	CCONJ
ejpam-4384	198	30	t	t	NOUN
ejpam-4384	198	31	=	=	SYM
ejpam-4384	199	1	0.009	0.009	NUM
ejpam-4384	199	2	t	t	NOUN
ejpam-4384	199	3	exact	exact	ADJ
ejpam-4384	199	4	solution	solution	NOUN
ejpam-4384	199	5	toeplitz	toeplitz	NOUN
ejpam-4384	199	6	solution	solution	NOUN
ejpam-4384	199	7	error	error	NOUN
ejpam-4384	199	8	nyström	nyström	NOUN
ejpam-4384	199	9	solution	solution	NOUN
ejpam-4384	199	10	error	error	NOUN
ejpam-4384	199	11	0	0	NUM
ejpam-4384	199	12	0	0	NUM
ejpam-4384	199	13	0	0	NUM
ejpam-4384	199	14	0	0	NUM
ejpam-4384	199	15	0	0	NUM
ejpam-4384	199	16	0	0	NUM
ejpam-4384	199	17	0.0018	0.0018	NUM
ejpam-4384	199	18	3.24×	3.24×	NUM
ejpam-4384	199	19	10−6	10−6	NUM
ejpam-4384	199	20	3.2400×	3.2400×	NUM
ejpam-4384	199	21	10−6	10−6	NUM
ejpam-4384	199	22	1.5934×	1.5934×	NUM
ejpam-4384	199	23	10−11	10−11	NUM
ejpam-4384	199	24	3.2400×	3.2400×	NUM
ejpam-4384	199	25	10−6	10−6	NUM
ejpam-4384	199	26	1.8594×	1.8594×	NUM
ejpam-4384	199	27	10−11	10−11	NOUN
ejpam-4384	199	28	0.0036	0.0036	NUM
ejpam-4384	199	29	1.296×	1.296×	NUM
ejpam-4384	199	30	10−5	10−5	NUM
ejpam-4384	199	31	1.2962×	1.2962×	NUM
ejpam-4384	199	32	10−5	10−5	NUM
ejpam-4384	199	33	1.8965×	1.8965×	NUM
ejpam-4384	199	34	10−10	10−10	NUM
ejpam-4384	199	35	1.2960×	1.2960×	NUM
ejpam-4384	199	36	10−5	10−5	NUM
ejpam-4384	199	37	2.0850×	2.0850×	NUM
ejpam-4384	199	38	10−10	10−10	PROPN
ejpam-4384	199	39	0.0054	0.0054	NUM
ejpam-4384	199	40	2.916×	2.916×	PROPN
ejpam-4384	199	41	10−5	10−5	NUM
ejpam-4384	199	42	2.9161×	2.9161×	NUM
ejpam-4384	199	43	10−5	10−5	NUM
ejpam-4384	199	44	8.7897×	8.7897×	NUM
ejpam-4384	199	45	10−10	10−10	NUM
ejpam-4384	199	46	2.9161×	2.9161×	NUM
ejpam-4384	199	47	10−5	10−5	NUM
ejpam-4384	199	48	9.2193×	9.2193×	NOUN
ejpam-4384	200	1	10−10	10−10	NUM
ejpam-4384	200	2	0.0072	0.0072	NUM
ejpam-4384	200	3	5.184×	5.184×	NUM
ejpam-4384	200	4	10−5	10−5	NUM
ejpam-4384	200	5	5.1843×	5.1843×	NOUN
ejpam-4384	200	6	10−5	10−5	NUM
ejpam-4384	200	7	2.6682×	2.6682×	NUM
ejpam-4384	200	8	10−9	10−9	NUM
ejpam-4384	200	9	5.1843×	5.1843×	NOUN
ejpam-4384	200	10	10−5	10−5	NUM
ejpam-4384	200	11	2.7020×	2.7020×	NUM
ejpam-4384	200	12	10−9	10−9	NUM
ejpam-4384	200	13	0.0090	0.0090	NUM
ejpam-4384	200	14	8.1×	8.1×	PROPN
ejpam-4384	200	15	10−5	10−5	NUM
ejpam-4384	200	16	8.1007×	8.1007×	NUM
ejpam-4384	200	17	10−5	10−5	NUM
ejpam-4384	200	18	6.6027×	6.6027×	NUM
ejpam-4384	200	19	10−9	10−9	NUM
ejpam-4384	200	20	8.1006×	8.1006×	SYM
ejpam-4384	200	21	10−5	10−5	NUM
ejpam-4384	200	22	6.2751×	6.2751×	NUM
ejpam-4384	200	23	10−9	10−9	NUM
ejpam-4384	200	24	table	table	NOUN
ejpam-4384	200	25	7	7	NUM
ejpam-4384	200	26	:	:	PUNCT
ejpam-4384	200	27	the	the	DET
ejpam-4384	200	28	numerical	numerical	ADJ
ejpam-4384	200	29	results	result	NOUN
ejpam-4384	200	30	at	at	ADP
ejpam-4384	200	31	α	α	NOUN
ejpam-4384	200	32	=	=	SYM
ejpam-4384	200	33	0.6	0.6	NUM
ejpam-4384	200	34	and	and	CCONJ
ejpam-4384	200	35	t	t	NOUN
ejpam-4384	200	36	=	=	NUM
ejpam-4384	200	37	0.2	0.2	NUM
ejpam-4384	200	38	t	t	NOUN
ejpam-4384	200	39	exact	exact	ADJ
ejpam-4384	200	40	solution	solution	NOUN
ejpam-4384	200	41	toeplitz	toeplitz	NOUN
ejpam-4384	200	42	solution	solution	NOUN
ejpam-4384	200	43	error	error	NOUN
ejpam-4384	200	44	nyström	nyström	NOUN
ejpam-4384	200	45	solution	solution	NOUN
ejpam-4384	200	46	error	error	NOUN
ejpam-4384	200	47	0	0	NUM
ejpam-4384	200	48	0	0	NUM
ejpam-4384	200	49	0	0	NUM
ejpam-4384	200	50	0	0	NUM
ejpam-4384	200	51	0	0	NUM
ejpam-4384	200	52	0	0	NUM
ejpam-4384	200	53	0.04	0.04	NUM
ejpam-4384	200	54	1.6×	1.6×	NUM
ejpam-4384	200	55	10−3	10−3	NUM
ejpam-4384	200	56	1.6001×	1.6001×	NUM
ejpam-4384	200	57	10−3	10−3	NUM
ejpam-4384	200	58	9.6612×	9.6612×	NOUN
ejpam-4384	200	59	10−8	10−8	NUM
ejpam-4384	200	60	1.6004×	1.6004×	NUM
ejpam-4384	200	61	10−3	10−3	NUM
ejpam-4384	200	62	4.0211×	4.0211×	NUM
ejpam-4384	200	63	10−7	10−7	NUM
ejpam-4384	200	64	0.08	0.08	NUM
ejpam-4384	200	65	6.4×	6.4×	NUM
ejpam-4384	200	66	10−3	10−3	NUM
ejpam-4384	200	67	6.4023×	6.4023×	NOUN
ejpam-4384	200	68	10−3	10−3	NUM
ejpam-4384	200	69	2.2562×	2.2562×	NUM
ejpam-4384	200	70	10−6	10−6	NUM
ejpam-4384	200	71	6.4039×	6.4039×	NUM
ejpam-4384	200	72	10−3	10−3	NUM
ejpam-4384	200	73	3.8664×	3.8664×	NUM
ejpam-4384	200	74	10−6	10−6	NUM
ejpam-4384	200	75	0.12	0.12	NUM
ejpam-4384	200	76	1.44×	1.44×	NUM
ejpam-4384	200	77	10−2	10−2	NUM
ejpam-4384	200	78	1.4412×	1.4412×	NUM
ejpam-4384	200	79	10−2	10−2	NUM
ejpam-4384	200	80	1.1827×	1.1827×	NUM
ejpam-4384	200	81	10−5	10−5	NUM
ejpam-4384	200	82	1.4416×	1.4416×	NUM
ejpam-4384	200	83	10−2	10−2	NUM
ejpam-4384	200	84	1.5501×	1.5501×	NUM
ejpam-4384	200	85	10−5	10−5	NUM
ejpam-4384	200	86	0.16	0.16	NUM
ejpam-4384	200	87	2.56×	2.56×	NUM
ejpam-4384	200	88	10−2	10−2	NUM
ejpam-4384	200	89	2.5638×	2.5638×	NUM
ejpam-4384	200	90	10−2	10−2	NUM
ejpam-4384	200	91	3.8076×	3.8076×	NUM
ejpam-4384	200	92	10−5	10−5	NUM
ejpam-4384	200	93	2.5642×	2.5642×	NUM
ejpam-4384	200	94	10−2	10−2	NUM
ejpam-4384	200	95	4.2227×	4.2227×	NUM
ejpam-4384	200	96	10−5	10−5	NUM
ejpam-4384	200	97	0.20	0.20	NUM
ejpam-4384	200	98	4×	4×	NOUN
ejpam-4384	200	99	10−2	10−2	NUM
ejpam-4384	200	100	4.0125×	4.0125×	NUM
ejpam-4384	200	101	10−2	10−2	NUM
ejpam-4384	200	102	1.2499×	1.2499×	NUM
ejpam-4384	200	103	10−4	10−4	NUM
ejpam-4384	200	104	4.0093×	4.0093×	NUM
ejpam-4384	200	105	10−2	10−2	NUM
ejpam-4384	200	106	9.2503×	9.2503×	NUM
ejpam-4384	200	107	10−5	10−5	NUM
ejpam-4384	200	108	table	table	NOUN
ejpam-4384	200	109	8	8	NUM
ejpam-4384	200	110	:	:	PUNCT
ejpam-4384	200	111	the	the	DET
ejpam-4384	200	112	numerical	numerical	ADJ
ejpam-4384	200	113	results	result	NOUN
ejpam-4384	200	114	at	at	ADP
ejpam-4384	200	115	α	α	NOUN
ejpam-4384	200	116	=	=	SYM
ejpam-4384	200	117	0.9	0.9	NUM
ejpam-4384	200	118	and	and	CCONJ
ejpam-4384	200	119	t	t	NOUN
ejpam-4384	200	120	=	=	NUM
ejpam-4384	200	121	0.2	0.2	NUM
ejpam-4384	200	122	t	t	NOUN
ejpam-4384	200	123	exact	exact	ADJ
ejpam-4384	200	124	solution	solution	NOUN
ejpam-4384	200	125	toeplitz	toeplitz	NOUN
ejpam-4384	200	126	solution	solution	NOUN
ejpam-4384	200	127	error	error	NOUN
ejpam-4384	200	128	nyström	nyström	NOUN
ejpam-4384	200	129	solution	solution	NOUN
ejpam-4384	200	130	error	error	NOUN
ejpam-4384	200	131	0	0	NUM
ejpam-4384	200	132	0	0	NUM
ejpam-4384	200	133	0	0	NUM
ejpam-4384	200	134	0	0	NUM
ejpam-4384	200	135	0	0	NUM
ejpam-4384	200	136	0	0	NUM
ejpam-4384	200	137	0.04	0.04	NUM
ejpam-4384	200	138	1.6×	1.6×	NUM
ejpam-4384	200	139	10−3	10−3	NUM
ejpam-4384	200	140	1.6001×	1.6001×	NUM
ejpam-4384	200	141	10−3	10−3	NUM
ejpam-4384	200	142	1.2824×	1.2824×	NUM
ejpam-4384	200	143	10−7	10−7	NUM
ejpam-4384	200	144	1.6001×	1.6001×	NUM
ejpam-4384	200	145	10−3	10−3	NUM
ejpam-4384	200	146	1.4965×	1.4965×	NUM
ejpam-4384	200	147	10−7	10−7	NUM
ejpam-4384	200	148	0.08	0.08	NUM
ejpam-4384	200	149	6.4×	6.4×	NUM
ejpam-4384	200	150	10−3	10−3	NUM
ejpam-4384	200	151	6.4015×	6.4015×	NUM
ejpam-4384	200	152	10−3	10−3	NUM
ejpam-4384	200	153	1.5266×	1.5266×	NOUN
ejpam-4384	200	154	10−6	10−6	NUM
ejpam-4384	200	155	6.4017×	6.4017×	NUM
ejpam-4384	200	156	10−3	10−3	NUM
ejpam-4384	200	157	1.6784×	1.6784×	NUM
ejpam-4384	200	158	10−6	10−6	NUM
ejpam-4384	200	159	0.12	0.12	NUM
ejpam-4384	200	160	1.44×	1.44×	NUM
ejpam-4384	200	161	10−2	10−2	NUM
ejpam-4384	200	162	1.4407×	1.4407×	NUM
ejpam-4384	200	163	10−2	10−2	NUM
ejpam-4384	200	164	7.0765×	7.0765×	NOUN
ejpam-4384	200	165	10−6	10−6	NUM
ejpam-4384	200	166	1.4407×	1.4407×	NUM
ejpam-4384	200	167	10−2	10−2	NUM
ejpam-4384	200	168	7.4226×	7.4226×	NUM
ejpam-4384	200	169	10−6	10−6	NUM
ejpam-4384	200	170	0.16	0.16	NUM
ejpam-4384	200	171	2.56×	2.56×	NUM
ejpam-4384	200	172	10−2	10−2	NUM
ejpam-4384	200	173	2.5621×	2.5621×	NUM
ejpam-4384	200	174	10−2	10−2	NUM
ejpam-4384	200	175	2.1487×	2.1487×	NUM
ejpam-4384	200	176	10−5	10−5	NUM
ejpam-4384	200	177	2.5622×	2.5622×	NUM
ejpam-4384	200	178	10−2	10−2	NUM
ejpam-4384	200	179	2.1759×	2.1759×	NUM
ejpam-4384	200	180	10−5	10−5	NUM
ejpam-4384	200	181	0.20	0.20	NUM
ejpam-4384	200	182	4×	4×	NOUN
ejpam-4384	200	183	10−2	10−2	NUM
ejpam-4384	200	184	4.0053×	4.0053×	NUM
ejpam-4384	200	185	10−2	10−2	NUM
ejpam-4384	200	186	5.3186×	5.3186×	NUM
ejpam-4384	200	187	10−5	10−5	NUM
ejpam-4384	200	188	4.0051×	4.0051×	NUM
ejpam-4384	200	189	10−2	10−2	NUM
ejpam-4384	200	190	5.0548×	5.0548×	NOUN
ejpam-4384	200	191	10−5	10−5	NUM
ejpam-4384	200	192	s.	s.	PROPN
ejpam-4384	200	193	raad	raad	PROPN
ejpam-4384	200	194	,	,	PUNCT
ejpam-4384	200	195	k.	k.	PROPN
ejpam-4384	200	196	alqurashi	alqurashi	PROPN
ejpam-4384	200	197	/	/	SYM
ejpam-4384	200	198	eur	eur	PROPN
ejpam-4384	200	199	.	.	PUNCT
ejpam-4384	201	1	j.	j.	PROPN
ejpam-4384	201	2	pure	pure	PROPN
ejpam-4384	201	3	appl	appl	PROPN
ejpam-4384	201	4	.	.	PROPN
ejpam-4384	201	5	math	math	PROPN
ejpam-4384	201	6	,	,	PUNCT
ejpam-4384	201	7	15	15	NUM
ejpam-4384	201	8	(	(	PUNCT
ejpam-4384	201	9	2	2	NUM
ejpam-4384	201	10	)	)	PUNCT
ejpam-4384	201	11	(	(	PUNCT
ejpam-4384	201	12	2022	2022	NUM
ejpam-4384	201	13	)	)	PUNCT
ejpam-4384	201	14	,	,	PUNCT
ejpam-4384	201	15	796	796	NUM
ejpam-4384	201	16	-	-	SYM
ejpam-4384	201	17	809	809	NUM
ejpam-4384	201	18	807	807	NUM
ejpam-4384	201	19	figure	figure	NOUN
ejpam-4384	201	20	2	2	NUM
ejpam-4384	201	21	:	:	PUNCT
ejpam-4384	201	22	the	the	DET
ejpam-4384	201	23	error	error	NOUN
ejpam-4384	201	24	by	by	ADP
ejpam-4384	201	25	toeplitz	toeplitz	NOUN
ejpam-4384	201	26	matrix	matrix	NOUN
ejpam-4384	201	27	and	and	CCONJ
ejpam-4384	201	28	nyström	nyström	DET
ejpam-4384	201	29	product	product	NOUN
ejpam-4384	201	30	methods	method	NOUN
ejpam-4384	201	31	at	at	ADP
ejpam-4384	201	32	various	various	ADJ
ejpam-4384	201	33	values	value	NOUN
ejpam-4384	201	34	for	for	ADP
ejpam-4384	201	35	α	α	NOUN
ejpam-4384	201	36	=	=	SYM
ejpam-4384	201	37	0.6	0.6	NUM
ejpam-4384	201	38	,	,	PUNCT
ejpam-4384	201	39	0.75	0.75	NUM
ejpam-4384	201	40	,	,	PUNCT
ejpam-4384	201	41	0.9	0.9	NUM
ejpam-4384	201	42	and	and	CCONJ
ejpam-4384	201	43	at	at	ADP
ejpam-4384	201	44	t	t	NOUN
ejpam-4384	201	45	=	=	SYM
ejpam-4384	201	46	0.009	0.009	NUM
ejpam-4384	201	47	,	,	PUNCT
ejpam-4384	201	48	0.05	0.05	NUM
ejpam-4384	201	49	,	,	PUNCT
ejpam-4384	201	50	0.2	0.2	NUM
ejpam-4384	201	51	.	.	PUNCT
ejpam-4384	202	1	it	it	PRON
ejpam-4384	202	2	is	be	AUX
ejpam-4384	202	3	clear	clear	ADJ
ejpam-4384	202	4	the	the	DET
ejpam-4384	202	5	largest	large	ADJ
ejpam-4384	202	6	error	error	NOUN
ejpam-4384	202	7	by	by	ADP
ejpam-4384	202	8	toeplitz	toeplitz	NOUN
ejpam-4384	202	9	matrix	matrix	NOUN
ejpam-4384	202	10	and	and	CCONJ
ejpam-4384	202	11	nyström	nyström	PRON
ejpam-4384	202	12	product	product	NOUN
ejpam-4384	202	13	methods	method	NOUN
ejpam-4384	202	14	is	be	AUX
ejpam-4384	202	15	at	at	ADP
ejpam-4384	202	16	α	α	NOUN
ejpam-4384	202	17	=	=	SYM
ejpam-4384	202	18	0.6	0.6	NUM
ejpam-4384	202	19	and	and	CCONJ
ejpam-4384	202	20	t	t	NOUN
ejpam-4384	202	21	=	=	NUM
ejpam-4384	202	22	0.2	0.2	NUM
ejpam-4384	202	23	.	.	PUNCT
ejpam-4384	203	1	the	the	DET
ejpam-4384	203	2	largest	large	ADJ
ejpam-4384	203	3	error	error	NOUN
ejpam-4384	203	4	by	by	ADP
ejpam-4384	203	5	toeplitz	toeplitz	NOUN
ejpam-4384	203	6	matrix	matrix	NOUN
ejpam-4384	203	7	is	be	AUX
ejpam-4384	203	8	1.2499	1.2499	NUM
ejpam-4384	203	9	×	×	NOUN
ejpam-4384	203	10	10−4	10−4	NUM
ejpam-4384	203	11	,	,	PUNCT
ejpam-4384	203	12	where	where	SCONJ
ejpam-4384	203	13	as	as	SCONJ
ejpam-4384	203	14	it	it	PRON
ejpam-4384	203	15	by	by	ADP
ejpam-4384	203	16	nyström	nyström	DET
ejpam-4384	203	17	method	method	NOUN
ejpam-4384	203	18	is	be	AUX
ejpam-4384	203	19	9.2503×	9.2503×	NUM
ejpam-4384	203	20	10−5	10−5	NUM
ejpam-4384	203	21	notes	note	NOUN
ejpam-4384	203	22	through	through	ADP
ejpam-4384	203	23	the	the	DET
ejpam-4384	203	24	results	result	NOUN
ejpam-4384	203	25	given	give	VERB
ejpam-4384	203	26	in	in	ADP
ejpam-4384	203	27	the	the	DET
ejpam-4384	203	28	previous	previous	ADJ
ejpam-4384	203	29	tables	table	NOUN
ejpam-4384	203	30	,	,	PUNCT
ejpam-4384	203	31	we	we	PRON
ejpam-4384	203	32	note	note	VERB
ejpam-4384	203	33	that	that	SCONJ
ejpam-4384	203	34	both	both	CCONJ
ejpam-4384	203	35	the	the	DET
ejpam-4384	203	36	toeplitz	toeplitz	NOUN
ejpam-4384	203	37	matrix	matrix	NOUN
ejpam-4384	203	38	and	and	CCONJ
ejpam-4384	203	39	the	the	DET
ejpam-4384	203	40	nyström	nyström	NOUN
ejpam-4384	203	41	product	product	NOUN
ejpam-4384	203	42	methods	method	NOUN
ejpam-4384	203	43	are	be	AUX
ejpam-4384	203	44	effective	effective	ADJ
ejpam-4384	203	45	in	in	ADP
ejpam-4384	203	46	solving	solve	VERB
ejpam-4384	203	47	our	our	PRON
ejpam-4384	203	48	problem	problem	NOUN
ejpam-4384	203	49	.	.	PUNCT
ejpam-4384	204	1	the	the	DET
ejpam-4384	204	2	tables	table	NOUN
ejpam-4384	204	3	and	and	CCONJ
ejpam-4384	204	4	the	the	DET
ejpam-4384	204	5	figures	figure	NOUN
ejpam-4384	204	6	show	show	VERB
ejpam-4384	204	7	that	that	SCONJ
ejpam-4384	204	8	the	the	DET
ejpam-4384	204	9	numerical	numerical	ADJ
ejpam-4384	204	10	solutions	solution	NOUN
ejpam-4384	204	11	were	be	AUX
ejpam-4384	204	12	obtained	obtain	VERB
ejpam-4384	204	13	using	use	VERB
ejpam-4384	204	14	toeplitz	toeplitz	NOUN
ejpam-4384	204	15	matrix	matrix	NOUN
ejpam-4384	204	16	and	and	CCONJ
ejpam-4384	204	17	the	the	DET
ejpam-4384	204	18	product	product	NOUN
ejpam-4384	204	19	nyström	nyström	PRON
ejpam-4384	204	20	are	be	AUX
ejpam-4384	204	21	very	very	ADV
ejpam-4384	204	22	close	close	ADJ
ejpam-4384	204	23	to	to	ADP
ejpam-4384	204	24	the	the	DET
ejpam-4384	204	25	exact	exact	ADJ
ejpam-4384	204	26	solution	solution	NOUN
ejpam-4384	204	27	.	.	PUNCT
ejpam-4384	205	1	however	however	ADV
ejpam-4384	205	2	,	,	PUNCT
ejpam-4384	205	3	the	the	DET
ejpam-4384	205	4	results	result	NOUN
ejpam-4384	205	5	using	use	VERB
ejpam-4384	205	6	nyström	nyström	NOUN
ejpam-4384	205	7	are	be	AUX
ejpam-4384	205	8	better	well	ADJ
ejpam-4384	205	9	than	than	ADP
ejpam-4384	205	10	corvesponding	corvesponde	VERB
ejpam-4384	205	11	results	result	NOUN
ejpam-4384	205	12	by	by	ADP
ejpam-4384	205	13	toeplitz	toeplitz	NOUN
ejpam-4384	205	14	matrix	matrix	NOUN
ejpam-4384	205	15	.	.	PUNCT
ejpam-4384	206	1	also	also	ADV
ejpam-4384	206	2	,	,	PUNCT
ejpam-4384	206	3	for	for	ADP
ejpam-4384	206	4	any	any	DET
ejpam-4384	206	5	choice	choice	NOUN
ejpam-4384	206	6	of	of	ADP
ejpam-4384	206	7	the	the	DET
ejpam-4384	206	8	time	time	NOUN
ejpam-4384	206	9	value	value	NOUN
ejpam-4384	206	10	t	t	PROPN
ejpam-4384	206	11	,	,	PUNCT
ejpam-4384	206	12	there	there	PRON
ejpam-4384	206	13	is	be	VERB
ejpam-4384	206	14	a	a	DET
ejpam-4384	206	15	negative	negative	ADJ
ejpam-4384	206	16	proportionality	proportionality	NOUN
ejpam-4384	206	17	between	between	ADP
ejpam-4384	206	18	α	α	PROPN
ejpam-4384	206	19	and	and	CCONJ
ejpam-4384	206	20	the	the	DET
ejpam-4384	206	21	error	error	NOUN
ejpam-4384	206	22	,	,	PUNCT
ejpam-4384	206	23	i.e.	i.e.	X
ejpam-4384	206	24	the	the	PRON
ejpam-4384	206	25	higher	high	ADJ
ejpam-4384	206	26	the	the	DET
ejpam-4384	206	27	value	value	NOUN
ejpam-4384	206	28	of	of	ADP
ejpam-4384	206	29	α	α	NOUN
ejpam-4384	206	30	,	,	PUNCT
ejpam-4384	206	31	the	the	PRON
ejpam-4384	206	32	smaller	small	ADJ
ejpam-4384	206	33	the	the	DET
ejpam-4384	206	34	error	error	NOUN
ejpam-4384	206	35	.	.	PUNCT
ejpam-4384	207	1	we	we	PRON
ejpam-4384	207	2	also	also	ADV
ejpam-4384	207	3	note	note	VERB
ejpam-4384	207	4	that	that	SCONJ
ejpam-4384	207	5	with	with	ADP
ejpam-4384	207	6	increasing	increase	VERB
ejpam-4384	207	7	time	time	NOUN
ejpam-4384	207	8	values	value	NOUN
ejpam-4384	207	9	,	,	PUNCT
ejpam-4384	207	10	the	the	DET
ejpam-4384	207	11	error	error	NOUN
ejpam-4384	207	12	for	for	ADP
ejpam-4384	207	13	any	any	DET
ejpam-4384	207	14	values	value	NOUN
ejpam-4384	207	15	of	of	ADP
ejpam-4384	207	16	α	α	PRON
ejpam-4384	207	17	increases	increase	NOUN
ejpam-4384	207	18	.	.	PUNCT
ejpam-4384	208	1	7	7	X
ejpam-4384	208	2	.	.	X
ejpam-4384	208	3	conclusion	conclusion	NOUN
ejpam-4384	208	4	we	we	PRON
ejpam-4384	208	5	have	have	AUX
ejpam-4384	208	6	assumed	assume	VERB
ejpam-4384	208	7	a	a	DET
ejpam-4384	208	8	lfi	lfi	NOUN
ejpam-4384	208	9	-	-	PUNCT
ejpam-4384	208	10	de	de	X
ejpam-4384	208	11	with	with	ADP
ejpam-4384	208	12	a	a	DET
ejpam-4384	208	13	fractional	fractional	ADJ
ejpam-4384	208	14	-	-	PUNCT
ejpam-4384	208	15	order	order	NOUN
ejpam-4384	208	16	0	0	PUNCT
ejpam-4384	208	17	<	<	X
ejpam-4384	208	18	α	α	X
ejpam-4384	208	19	<	<	X
ejpam-4384	208	20	1	1	NUM
ejpam-4384	208	21	.	.	PUNCT
ejpam-4384	209	1	then	then	ADV
ejpam-4384	209	2	,	,	PUNCT
ejpam-4384	209	3	the	the	DET
ejpam-4384	209	4	riemannliouville	riemannliouville	NOUN
ejpam-4384	209	5	fractional	fractional	NOUN
ejpam-4384	209	6	integral	integral	ADJ
ejpam-4384	209	7	of	of	ADP
ejpam-4384	209	8	order	order	NOUN
ejpam-4384	209	9	α	α	PROPN
ejpam-4384	209	10	>	>	X
ejpam-4384	209	11	0	0	NUM
ejpam-4384	209	12	was	be	AUX
ejpam-4384	209	13	applied	apply	VERB
ejpam-4384	209	14	to	to	ADP
ejpam-4384	209	15	the	the	DET
ejpam-4384	209	16	fi	fi	NOUN
ejpam-4384	209	17	-	-	NOUN
ejpam-4384	209	18	de	de	NOUN
ejpam-4384	209	19	to	to	PART
ejpam-4384	209	20	convert	convert	VERB
ejpam-4384	209	21	it	it	PRON
ejpam-4384	209	22	to	to	ADP
ejpam-4384	209	23	a	a	DET
ejpam-4384	209	24	v	v	NOUN
ejpam-4384	209	25	-	-	NOUN
ejpam-4384	209	26	fie	fie	NOUN
ejpam-4384	209	27	with	with	ADP
ejpam-4384	209	28	abel	abel	PROPN
ejpam-4384	209	29	’s	’s	PART
ejpam-4384	209	30	kernel	kernel	PROPN
ejpam-4384	209	31	.	.	PUNCT
ejpam-4384	210	1	after	after	ADP
ejpam-4384	210	2	that	that	PRON
ejpam-4384	210	3	,	,	PUNCT
ejpam-4384	210	4	the	the	DET
ejpam-4384	210	5	uniqueness	uniqueness	NOUN
ejpam-4384	210	6	of	of	ADP
ejpam-4384	210	7	the	the	DET
ejpam-4384	210	8	solution	solution	NOUN
ejpam-4384	210	9	of	of	ADP
ejpam-4384	210	10	the	the	DET
ejpam-4384	210	11	v	v	NOUN
ejpam-4384	210	12	-	-	PUNCT
ejpam-4384	210	13	fie	fie	NOUN
ejpam-4384	210	14	,	,	PUNCT
ejpam-4384	210	15	which	which	PRON
ejpam-4384	210	16	is	be	AUX
ejpam-4384	210	17	equivalent	equivalent	ADJ
ejpam-4384	210	18	to	to	ADP
ejpam-4384	210	19	the	the	DET
ejpam-4384	210	20	lfi	lfi	NOUN
ejpam-4384	210	21	-	-	PUNCT
ejpam-4384	210	22	de	de	X
ejpam-4384	210	23	,	,	PUNCT
ejpam-4384	210	24	has	have	AUX
ejpam-4384	210	25	been	be	AUX
ejpam-4384	210	26	proved	prove	VERB
ejpam-4384	210	27	by	by	ADP
ejpam-4384	210	28	using	use	VERB
ejpam-4384	210	29	the	the	DET
ejpam-4384	210	30	picard	picard	NOUN
ejpam-4384	210	31	method	method	NOUN
ejpam-4384	210	32	.	.	PUNCT
ejpam-4384	211	1	finally	finally	ADV
ejpam-4384	211	2	,	,	PUNCT
ejpam-4384	211	3	two	two	NUM
ejpam-4384	211	4	numerical	numerical	ADJ
ejpam-4384	211	5	methods	method	NOUN
ejpam-4384	211	6	;	;	PUNCT
ejpam-4384	211	7	the	the	DET
ejpam-4384	211	8	toeplitz	toeplitz	NOUN
ejpam-4384	211	9	matrix	matrix	NOUN
ejpam-4384	211	10	and	and	CCONJ
ejpam-4384	211	11	product	product	NOUN
ejpam-4384	211	12	nyström	nyström	NOUN
ejpam-4384	211	13	methods	method	NOUN
ejpam-4384	211	14	were	be	AUX
ejpam-4384	211	15	used	use	VERB
ejpam-4384	211	16	to	to	PART
ejpam-4384	211	17	find	find	VERB
ejpam-4384	211	18	the	the	DET
ejpam-4384	211	19	numerical	numerical	ADJ
ejpam-4384	211	20	solution	solution	NOUN
ejpam-4384	211	21	.	.	PUNCT
ejpam-4384	212	1	the	the	DET
ejpam-4384	212	2	results	result	NOUN
ejpam-4384	212	3	showed	show	VERB
ejpam-4384	212	4	the	the	DET
ejpam-4384	212	5	efficiency	efficiency	NOUN
ejpam-4384	212	6	and	and	CCONJ
ejpam-4384	212	7	accuracy	accuracy	NOUN
ejpam-4384	212	8	of	of	ADP
ejpam-4384	212	9	the	the	DET
ejpam-4384	212	10	two	two	NUM
ejpam-4384	212	11	methods	method	NOUN
ejpam-4384	212	12	through	through	ADP
ejpam-4384	212	13	the	the	DET
ejpam-4384	212	14	multi	multi	NOUN
ejpam-4384	212	15	-	-	NOUN
ejpam-4384	212	16	values	value	NOUN
ejpam-4384	212	17	of	of	ADP
ejpam-4384	212	18	α	α	PROPN
ejpam-4384	212	19	and	and	CCONJ
ejpam-4384	212	20	t	t	PROPN
ejpam-4384	212	21	.	.	PUNCT
ejpam-4384	213	1	references	reference	NOUN
ejpam-4384	213	2	808	808	NUM
ejpam-4384	213	3	references	reference	NOUN
ejpam-4384	213	4	[	[	X
ejpam-4384	213	5	1	1	NUM
ejpam-4384	213	6	]	]	X
ejpam-4384	213	7	abdou	abdou	PROPN
ejpam-4384	213	8	m.	m.	PROPN
ejpam-4384	213	9	a.	a.	PROPN
ejpam-4384	213	10	,	,	PUNCT
ejpam-4384	213	11	el	el	PROPN
ejpam-4384	213	12	-	-	PUNCT
ejpam-4384	213	13	kojak	kojak	PROPN
ejpam-4384	213	14	,	,	PUNCT
ejpam-4384	213	15	m.	m.	NOUN
ejpam-4384	213	16	k.	k.	PROPN
ejpam-4384	213	17	,	,	PUNCT
ejpam-4384	213	18	and	and	CCONJ
ejpam-4384	213	19	s.	s.	PROPN
ejpam-4384	213	20	a.	a.	PROPN
ejpam-4384	213	21	raad	raad	PROPN
ejpam-4384	213	22	.	.	PUNCT
ejpam-4384	214	1	analytic	analytic	ADJ
ejpam-4384	214	2	and	and	CCONJ
ejpam-4384	214	3	numeric	numeric	ADJ
ejpam-4384	214	4	solution	solution	NOUN
ejpam-4384	214	5	of	of	ADP
ejpam-4384	214	6	linear	linear	ADJ
ejpam-4384	214	7	partial	partial	ADJ
ejpam-4384	214	8	differential	differential	NOUN
ejpam-4384	214	9	equation	equation	NOUN
ejpam-4384	214	10	of	of	ADP
ejpam-4384	214	11	fractional	fractional	ADJ
ejpam-4384	214	12	order	order	NOUN
ejpam-4384	214	13	.	.	PUNCT
ejpam-4384	215	1	global	global	ADJ
ejpam-4384	215	2	j.	j.	PROPN
ejpam-4384	215	3	and	and	CCONJ
ejpam-4384	215	4	decision	decision	NOUN
ejpam-4384	215	5	science	science	NOUN
ejpam-4384	215	6	.	.	PUNCT
ejpam-4384	216	1	ins.(usa	ins.(usa	VERB
ejpam-4384	216	2	)	)	PUNCT
ejpam-4384	216	3	,	,	PUNCT
ejpam-4384	216	4	13(3/10):57–71	13(3/10):57–71	NOUN
ejpam-4384	216	5	.	.	PUNCT
ejpam-4384	216	6	,	,	PUNCT
ejpam-4384	216	7	2013	2013	NUM
ejpam-4384	216	8	.	.	PUNCT
ejpam-4384	217	1	[	[	X
ejpam-4384	217	2	2	2	X
ejpam-4384	217	3	]	]	PUNCT
ejpam-4384	217	4	raad	raad	PROPN
ejpam-4384	217	5	s.	s.	PROPN
ejpam-4384	217	6	a.	a.	PROPN
ejpam-4384	217	7	,	,	PUNCT
ejpam-4384	217	8	abdou	abdou	PROPN
ejpam-4384	217	9	m.	m.	PROPN
ejpam-4384	217	10	a.	a.	PROPN
ejpam-4384	217	11	,	,	PUNCT
ejpam-4384	217	12	and	and	CCONJ
ejpam-4384	217	13	m.	m.	NOUN
ejpam-4384	217	14	m.	m.	PROPN
ejpam-4384	217	15	el	el	PROPN
ejpam-4384	217	16	-	-	PUNCT
ejpam-4384	217	17	kojok	kojok	PROPN
ejpam-4384	217	18	.	.	PUNCT
ejpam-4384	218	1	on	on	ADP
ejpam-4384	218	2	the	the	DET
ejpam-4384	218	3	solution	solution	NOUN
ejpam-4384	218	4	of	of	ADP
ejpam-4384	218	5	fredholm	fredholm	NOUN
ejpam-4384	218	6	-	-	PUNCT
ejpam-4384	218	7	volterra	volterra	NOUN
ejpam-4384	218	8	integral	integral	ADJ
ejpam-4384	218	9	equation	equation	NOUN
ejpam-4384	218	10	with	with	ADP
ejpam-4384	218	11	discontinuous	discontinuous	ADJ
ejpam-4384	218	12	kernel	kernel	NOUN
ejpam-4384	218	13	in	in	ADP
ejpam-4384	218	14	time	time	NOUN
ejpam-4384	218	15	.	.	PUNCT
ejpam-4384	219	1	journal	journal	NOUN
ejpam-4384	219	2	of	of	ADP
ejpam-4384	219	3	advances	advance	NOUN
ejpam-4384	219	4	in	in	ADP
ejpam-4384	219	5	mathematics	mathematic	NOUN
ejpam-4384	219	6	,	,	PUNCT
ejpam-4384	219	7	9(4):2553–2563	9(4):2553–2563	PROPN
ejpam-4384	219	8	,	,	PUNCT
ejpam-4384	219	9	2014	2014	NUM
ejpam-4384	219	10	.	.	PUNCT
ejpam-4384	220	1	[	[	X
ejpam-4384	220	2	3	3	NUM
ejpam-4384	220	3	]	]	PUNCT
ejpam-4384	220	4	mohamed	mohamed	PROPN
ejpam-4384	220	5	i	i	PROPN
ejpam-4384	220	6	abbas	abbas	PROPN
ejpam-4384	220	7	.	.	PUNCT
ejpam-4384	221	1	existence	existence	NOUN
ejpam-4384	221	2	and	and	CCONJ
ejpam-4384	221	3	uniqueness	uniqueness	NOUN
ejpam-4384	221	4	of	of	ADP
ejpam-4384	221	5	mittage	mittage	NOUN
ejpam-4384	221	6	-	-	PUNCT
ejpam-4384	221	7	leffler	leffler	NOUN
ejpam-4384	221	8	-	-	PUNCT
ejpam-4384	221	9	ulam	ulam	NOUN
ejpam-4384	221	10	stable	stable	ADJ
ejpam-4384	221	11	solution	solution	NOUN
ejpam-4384	221	12	for	for	ADP
ejpam-4384	221	13	fractional	fractional	ADJ
ejpam-4384	221	14	integrodifferential	integrodifferential	ADJ
ejpam-4384	221	15	equations	equation	NOUN
ejpam-4384	221	16	with	with	ADP
ejpam-4384	221	17	nonlocal	nonlocal	ADJ
ejpam-4384	221	18	initial	initial	ADJ
ejpam-4384	221	19	conditions	condition	NOUN
ejpam-4384	221	20	.	.	PUNCT
ejpam-4384	222	1	european	european	ADJ
ejpam-4384	222	2	journal	journal	PROPN
ejpam-4384	222	3	of	of	ADP
ejpam-4384	222	4	pure	pure	ADJ
ejpam-4384	222	5	and	and	CCONJ
ejpam-4384	222	6	applied	applied	ADJ
ejpam-4384	222	7	mathematics	mathematic	NOUN
ejpam-4384	222	8	,	,	PUNCT
ejpam-4384	222	9	8(4):478–498	8(4):478–498	NOUN
ejpam-4384	222	10	,	,	PUNCT
ejpam-4384	222	11	2015	2015	NUM
ejpam-4384	222	12	.	.	PUNCT
ejpam-4384	223	1	[	[	X
ejpam-4384	223	2	4	4	X
ejpam-4384	223	3	]	]	X
ejpam-4384	223	4	ma	ma	PROPN
ejpam-4384	223	5	abdou	abdou	PROPN
ejpam-4384	223	6	,	,	PUNCT
ejpam-4384	223	7	mm	mm	PROPN
ejpam-4384	223	8	el	el	PROPN
ejpam-4384	223	9	-	-	PUNCT
ejpam-4384	223	10	borai	borai	NOUN
ejpam-4384	223	11	,	,	PUNCT
ejpam-4384	223	12	and	and	CCONJ
ejpam-4384	223	13	mm	mm	PROPN
ejpam-4384	223	14	el	el	PROPN
ejpam-4384	223	15	-	-	PUNCT
ejpam-4384	223	16	kojok	kojok	PROPN
ejpam-4384	223	17	.	.	PUNCT
ejpam-4384	224	1	toeplitz	toeplitz	NOUN
ejpam-4384	224	2	matrix	matrix	NOUN
ejpam-4384	224	3	method	method	NOUN
ejpam-4384	224	4	and	and	CCONJ
ejpam-4384	224	5	nonlinear	nonlinear	ADJ
ejpam-4384	224	6	integral	integral	ADJ
ejpam-4384	224	7	equation	equation	NOUN
ejpam-4384	224	8	of	of	ADP
ejpam-4384	224	9	hammerstein	hammerstein	PROPN
ejpam-4384	224	10	type	type	PROPN
ejpam-4384	224	11	.	.	PUNCT
ejpam-4384	225	1	journal	journal	PROPN
ejpam-4384	225	2	of	of	ADP
ejpam-4384	225	3	computational	computational	ADJ
ejpam-4384	225	4	and	and	CCONJ
ejpam-4384	225	5	applied	applied	ADJ
ejpam-4384	225	6	mathematics	mathematic	NOUN
ejpam-4384	225	7	,	,	PUNCT
ejpam-4384	225	8	223(2):765–776	223(2):765–776	NUM
ejpam-4384	225	9	,	,	PUNCT
ejpam-4384	225	10	2009	2009	NUM
ejpam-4384	225	11	.	.	PUNCT
ejpam-4384	226	1	[	[	X
ejpam-4384	226	2	5	5	NUM
ejpam-4384	226	3	]	]	X
ejpam-4384	226	4	sertan	sertan	PROPN
ejpam-4384	226	5	alkan	alkan	PROPN
ejpam-4384	226	6	and	and	CCONJ
ejpam-4384	226	7	veysel	veysel	PROPN
ejpam-4384	226	8	fuat	fuat	PROPN
ejpam-4384	226	9	hatipoglu	hatipoglu	PROPN
ejpam-4384	226	10	.	.	PUNCT
ejpam-4384	227	1	approximate	approximate	ADJ
ejpam-4384	227	2	solutions	solution	NOUN
ejpam-4384	227	3	of	of	ADP
ejpam-4384	227	4	volterra	volterra	NOUN
ejpam-4384	227	5	-	-	PUNCT
ejpam-4384	227	6	fredholm	fredholm	NOUN
ejpam-4384	227	7	integro	integro	ADJ
ejpam-4384	227	8	-	-	PUNCT
ejpam-4384	227	9	differential	differential	NOUN
ejpam-4384	227	10	equations	equation	NOUN
ejpam-4384	227	11	of	of	ADP
ejpam-4384	227	12	fractional	fractional	ADJ
ejpam-4384	227	13	order	order	NOUN
ejpam-4384	227	14	.	.	PUNCT
ejpam-4384	228	1	tbilisi	tbilisi	PROPN
ejpam-4384	228	2	mathematical	mathematical	PROPN
ejpam-4384	228	3	journal	journal	PROPN
ejpam-4384	228	4	,	,	PUNCT
ejpam-4384	228	5	10(2):1–13	10(2):1–13	NUM
ejpam-4384	228	6	,	,	PUNCT
ejpam-4384	228	7	2017	2017	NUM
ejpam-4384	228	8	.	.	PUNCT
ejpam-4384	229	1	[	[	X
ejpam-4384	229	2	6	6	NUM
ejpam-4384	229	3	]	]	PUNCT
ejpam-4384	229	4	ayşegül	ayşegül	PROPN
ejpam-4384	229	5	daşcıoğlu	daşcıoğlu	PROPN
ejpam-4384	229	6	and	and	CCONJ
ejpam-4384	229	7	dilek	dilek	PROPN
ejpam-4384	229	8	varol	varol	PROPN
ejpam-4384	229	9	.	.	PUNCT
ejpam-4384	230	1	laguerre	laguerre	PROPN
ejpam-4384	230	2	polynomial	polynomial	ADJ
ejpam-4384	230	3	solutions	solution	NOUN
ejpam-4384	230	4	of	of	ADP
ejpam-4384	230	5	linear	linear	ADJ
ejpam-4384	230	6	fractional	fractional	ADJ
ejpam-4384	230	7	integro	integro	ADJ
ejpam-4384	230	8	-	-	PUNCT
ejpam-4384	230	9	differential	differential	NOUN
ejpam-4384	230	10	equations	equation	NOUN
ejpam-4384	230	11	.	.	PUNCT
ejpam-4384	231	1	mathematical	mathematical	ADJ
ejpam-4384	231	2	sciences	science	NOUN
ejpam-4384	231	3	,	,	PUNCT
ejpam-4384	231	4	15(1):47–54	15(1):47–54	NUM
ejpam-4384	231	5	,	,	PUNCT
ejpam-4384	231	6	2021	2021	NUM
ejpam-4384	231	7	.	.	PUNCT
ejpam-4384	232	1	[	[	X
ejpam-4384	232	2	7	7	X
ejpam-4384	232	3	]	]	X
ejpam-4384	232	4	mishra	mishra	PROPN
ejpam-4384	232	5	vn	vn	PROPN
ejpam-4384	232	6	deepmala	deepmala	PROPN
ejpam-4384	232	7	,	,	PUNCT
ejpam-4384	232	8	hr	hr	NOUN
ejpam-4384	232	9	marasi	marasi	NOUN
ejpam-4384	232	10	,	,	PUNCT
ejpam-4384	232	11	h	h	NOUN
ejpam-4384	232	12	shabanian	shabanian	ADJ
ejpam-4384	232	13	,	,	PUNCT
ejpam-4384	232	14	and	and	CCONJ
ejpam-4384	232	15	m	m	PROPN
ejpam-4384	232	16	nosraty	nosraty	NOUN
ejpam-4384	232	17	.	.	PUNCT
ejpam-4384	233	1	solution	solution	NOUN
ejpam-4384	233	2	of	of	ADP
ejpam-4384	233	3	voltrafredholm	voltrafredholm	ADJ
ejpam-4384	233	4	integro	integro	ADJ
ejpam-4384	233	5	-	-	PUNCT
ejpam-4384	233	6	differential	differential	NOUN
ejpam-4384	233	7	equations	equation	NOUN
ejpam-4384	233	8	using	use	VERB
ejpam-4384	233	9	chebyshev	chebyshev	NOUN
ejpam-4384	233	10	collocation	collocation	NOUN
ejpam-4384	233	11	method	method	NOUN
ejpam-4384	233	12	.	.	PUNCT
ejpam-4384	234	1	global	global	ADJ
ejpam-4384	234	2	journal	journal	PROPN
ejpam-4384	234	3	of	of	ADP
ejpam-4384	234	4	technology	technology	NOUN
ejpam-4384	234	5	and	and	CCONJ
ejpam-4384	234	6	optimization	optimization	NOUN
ejpam-4384	234	7	,	,	PUNCT
ejpam-4384	234	8	8(210):1–4	8(210):1–4	NUM
ejpam-4384	234	9	,	,	PUNCT
ejpam-4384	234	10	2017	2017	NUM
ejpam-4384	234	11	.	.	PUNCT
ejpam-4384	235	1	[	[	X
ejpam-4384	235	2	8	8	NUM
ejpam-4384	235	3	]	]	X
ejpam-4384	235	4	j	j	PROPN
ejpam-4384	235	5	vasundhara	vasundhara	PROPN
ejpam-4384	235	6	devi	devi	PROPN
ejpam-4384	235	7	and	and	CCONJ
ejpam-4384	235	8	chaduvula	chaduvula	PROPN
ejpam-4384	235	9	venkata	venkata	PROPN
ejpam-4384	235	10	sreedhar	sreedhar	PROPN
ejpam-4384	235	11	.	.	PUNCT
ejpam-4384	236	1	generalized	generalize	VERB
ejpam-4384	236	2	monotone	monotone	ADJ
ejpam-4384	236	3	iterative	iterative	NOUN
ejpam-4384	236	4	method	method	NOUN
ejpam-4384	236	5	for	for	ADP
ejpam-4384	236	6	caputo	caputo	PROPN
ejpam-4384	236	7	fractional	fractional	PROPN
ejpam-4384	236	8	integro	integro	PROPN
ejpam-4384	236	9	-	-	PUNCT
ejpam-4384	236	10	differential	differential	NOUN
ejpam-4384	236	11	equation	equation	NOUN
ejpam-4384	236	12	.	.	PUNCT
ejpam-4384	237	1	european	european	ADJ
ejpam-4384	237	2	journal	journal	PROPN
ejpam-4384	237	3	of	of	ADP
ejpam-4384	237	4	pure	pure	ADJ
ejpam-4384	237	5	and	and	CCONJ
ejpam-4384	237	6	applied	applied	ADJ
ejpam-4384	237	7	mathematics	mathematic	NOUN
ejpam-4384	237	8	,	,	PUNCT
ejpam-4384	237	9	9(4):346–359	9(4):346–359	ADJ
ejpam-4384	237	10	,	,	PUNCT
ejpam-4384	237	11	2016	2016	NUM
ejpam-4384	237	12	.	.	PUNCT
ejpam-4384	238	1	[	[	X
ejpam-4384	238	2	9	9	NUM
ejpam-4384	238	3	]	]	PUNCT
ejpam-4384	238	4	ama	ama	PROPN
ejpam-4384	238	5	el	el	PROPN
ejpam-4384	238	6	-	-	PUNCT
ejpam-4384	238	7	sayed	say	VERB
ejpam-4384	238	8	,	,	PUNCT
ejpam-4384	238	9	hhg	hhg	PROPN
ejpam-4384	238	10	hashem	hashem	PROPN
ejpam-4384	238	11	,	,	PUNCT
ejpam-4384	238	12	and	and	CCONJ
ejpam-4384	238	13	eaa	eaa	PROPN
ejpam-4384	238	14	ziada	ziada	PROPN
ejpam-4384	238	15	.	.	PUNCT
ejpam-4384	239	1	picard	picard	PROPN
ejpam-4384	239	2	and	and	CCONJ
ejpam-4384	239	3	adomian	adomian	NOUN
ejpam-4384	239	4	methods	method	NOUN
ejpam-4384	239	5	for	for	ADP
ejpam-4384	239	6	quadratic	quadratic	ADJ
ejpam-4384	239	7	integral	integral	ADJ
ejpam-4384	239	8	equation	equation	NOUN
ejpam-4384	239	9	.	.	PUNCT
ejpam-4384	240	1	computational	computational	ADJ
ejpam-4384	240	2	&	&	CCONJ
ejpam-4384	240	3	applied	applied	ADJ
ejpam-4384	240	4	mathematics	mathematic	NOUN
ejpam-4384	240	5	,	,	PUNCT
ejpam-4384	240	6	29(3):447–463	29(3):447–463	NUM
ejpam-4384	240	7	,	,	PUNCT
ejpam-4384	240	8	2010	2010	NUM
ejpam-4384	240	9	.	.	PUNCT
ejpam-4384	241	1	[	[	X
ejpam-4384	241	2	10	10	NUM
ejpam-4384	241	3	]	]	X
ejpam-4384	241	4	han	han	PROPN
ejpam-4384	241	5	guoqiang	guoqiang	PROPN
ejpam-4384	241	6	and	and	CCONJ
ejpam-4384	241	7	zhang	zhang	PROPN
ejpam-4384	241	8	liqing	liqing	PROPN
ejpam-4384	241	9	.	.	PUNCT
ejpam-4384	242	1	asymptotic	asymptotic	ADJ
ejpam-4384	242	2	expansion	expansion	NOUN
ejpam-4384	242	3	for	for	ADP
ejpam-4384	242	4	the	the	DET
ejpam-4384	242	5	trapezoidal	trapezoidal	ADJ
ejpam-4384	242	6	nyström	nyström	NOUN
ejpam-4384	242	7	method	method	NOUN
ejpam-4384	242	8	of	of	ADP
ejpam-4384	242	9	linear	linear	PROPN
ejpam-4384	242	10	volterra	volterra	PROPN
ejpam-4384	242	11	—	—	PUNCT
ejpam-4384	242	12	fredholm	fredholm	NOUN
ejpam-4384	242	13	equations	equation	NOUN
ejpam-4384	242	14	.	.	PUNCT
ejpam-4384	243	1	journal	journal	NOUN
ejpam-4384	243	2	of	of	ADP
ejpam-4384	243	3	computational	computational	ADJ
ejpam-4384	243	4	and	and	CCONJ
ejpam-4384	243	5	applied	applied	ADJ
ejpam-4384	243	6	mathematics	mathematic	NOUN
ejpam-4384	243	7	,	,	PUNCT
ejpam-4384	243	8	51(3):339–348	51(3):339–348	NOUN
ejpam-4384	243	9	,	,	PUNCT
ejpam-4384	243	10	1994	1994	NUM
ejpam-4384	243	11	.	.	PUNCT
ejpam-4384	244	1	[	[	X
ejpam-4384	244	2	11	11	NUM
ejpam-4384	244	3	]	]	SYM
ejpam-4384	244	4	shaher	shaher	ADJ
ejpam-4384	244	5	momani	momani	PROPN
ejpam-4384	244	6	and	and	CCONJ
ejpam-4384	244	7	rami	rami	PROPN
ejpam-4384	244	8	qaralleh	qaralleh	PROPN
ejpam-4384	244	9	.	.	PUNCT
ejpam-4384	245	1	an	an	DET
ejpam-4384	245	2	efficient	efficient	ADJ
ejpam-4384	245	3	method	method	NOUN
ejpam-4384	245	4	for	for	ADP
ejpam-4384	245	5	solving	solve	VERB
ejpam-4384	245	6	systems	system	NOUN
ejpam-4384	245	7	of	of	ADP
ejpam-4384	245	8	fractional	fractional	ADJ
ejpam-4384	245	9	integro	integro	ADJ
ejpam-4384	245	10	-	-	PUNCT
ejpam-4384	245	11	differential	differential	NOUN
ejpam-4384	245	12	equations	equation	NOUN
ejpam-4384	245	13	.	.	PUNCT
ejpam-4384	246	1	computers	computer	NOUN
ejpam-4384	246	2	&	&	CCONJ
ejpam-4384	246	3	mathematics	mathematics	PROPN
ejpam-4384	246	4	with	with	ADP
ejpam-4384	246	5	applications	application	NOUN
ejpam-4384	246	6	,	,	PUNCT
ejpam-4384	246	7	52(3	52(3	NUM
ejpam-4384	246	8	-	-	SYM
ejpam-4384	246	9	4):459–470	4):459–470	NUM
ejpam-4384	246	10	,	,	PUNCT
ejpam-4384	246	11	2006	2006	NUM
ejpam-4384	246	12	.	.	PUNCT
ejpam-4384	247	1	[	[	X
ejpam-4384	247	2	12	12	NUM
ejpam-4384	247	3	]	]	X
ejpam-4384	247	4	li	li	PROPN
ejpam-4384	247	5	mulin	mulin	PROPN
ejpam-4384	247	6	,	,	PUNCT
ejpam-4384	247	7	wang	wang	PROPN
ejpam-4384	247	8	lifeng	lifeng	PROPN
ejpam-4384	247	9	,	,	PUNCT
ejpam-4384	247	10	and	and	CCONJ
ejpam-4384	247	11	yu	yu	PROPN
ejpam-4384	247	12	liu	liu	PROPN
ejpam-4384	247	13	.	.	PUNCT
ejpam-4384	248	1	generalized	generalize	VERB
ejpam-4384	248	2	hat	hat	NOUN
ejpam-4384	248	3	functions	function	NOUN
ejpam-4384	248	4	method	method	NOUN
ejpam-4384	248	5	for	for	ADP
ejpam-4384	248	6	solving	solve	VERB
ejpam-4384	248	7	fractional	fractional	ADJ
ejpam-4384	248	8	integro	integro	ADJ
ejpam-4384	248	9	-	-	PUNCT
ejpam-4384	248	10	differential	differential	NOUN
ejpam-4384	248	11	equations	equation	NOUN
ejpam-4384	248	12	of	of	ADP
ejpam-4384	248	13	bratu	bratu	NOUN
ejpam-4384	248	14	-	-	PUNCT
ejpam-4384	248	15	type	type	NOUN
ejpam-4384	248	16	.	.	PUNCT
ejpam-4384	249	1	iaeng	iaeng	PROPN
ejpam-4384	249	2	international	international	PROPN
ejpam-4384	249	3	journal	journal	PROPN
ejpam-4384	249	4	of	of	ADP
ejpam-4384	249	5	computer	computer	NOUN
ejpam-4384	249	6	science	science	NOUN
ejpam-4384	249	7	,	,	PUNCT
ejpam-4384	249	8	44(1):105–111	44(1):105–111	PROPN
ejpam-4384	249	9	,	,	PUNCT
ejpam-4384	249	10	2017	2017	NUM
ejpam-4384	249	11	.	.	PUNCT
ejpam-4384	250	1	references	reference	NOUN
ejpam-4384	250	2	809	809	NUM
ejpam-4384	251	1	[	[	X
ejpam-4384	251	2	13	13	NUM
ejpam-4384	251	3	]	]	X
ejpam-4384	251	4	hasan	hasan	PROPN
ejpam-4384	251	5	n.	n.	PROPN
ejpam-4384	251	6	n.	n.	PROPN
ejpam-4384	251	7	and	and	CCONJ
ejpam-4384	251	8	hussien	hussien	PROPN
ejpam-4384	251	9	d.	d.	PROPN
ejpam-4384	251	10	a.	a.	PROPN
ejpam-4384	251	11	existence	existence	PROPN
ejpam-4384	251	12	and	and	CCONJ
ejpam-4384	251	13	uniqueness	uniqueness	ADJ
ejpam-4384	251	14	solution	solution	NOUN
ejpam-4384	251	15	of	of	ADP
ejpam-4384	251	16	linear	linear	PROPN
ejpam-4384	251	17	fractional	fractional	PROPN
ejpam-4384	251	18	volterra	volterra	PROPN
ejpam-4384	251	19	integro	integro	PROPN
ejpam-4384	251	20	-	-	PUNCT
ejpam-4384	251	21	differential	differential	NOUN
ejpam-4384	251	22	equations	equation	NOUN
ejpam-4384	251	23	.	.	PUNCT
ejpam-4384	252	1	journal	journal	PROPN
ejpam-4384	252	2	of	of	ADP
ejpam-4384	252	3	engineering	engineering	PROPN
ejpam-4384	252	4	&	&	CCONJ
ejpam-4384	252	5	applied	apply	VERB
ejpam-4384	252	6	sciences	science	NOUN
ejpam-4384	252	7	,	,	PUNCT
ejpam-4384	252	8	14:418–419	14:418–419	NUM
ejpam-4384	252	9	,	,	PUNCT
ejpam-4384	252	10	2019	2019	NUM
ejpam-4384	252	11	.	.	PUNCT
ejpam-4384	253	1	[	[	X
ejpam-4384	253	2	14	14	NUM
ejpam-4384	253	3	]	]	PUNCT
ejpam-4384	253	4	sameeha	sameeha	PROPN
ejpam-4384	253	5	ali	ali	PROPN
ejpam-4384	253	6	raad	raad	PROPN
ejpam-4384	253	7	and	and	CCONJ
ejpam-4384	253	8	mariam	mariam	PROPN
ejpam-4384	253	9	mohammed	mohammed	PROPN
ejpam-4384	253	10	al	al	PROPN
ejpam-4384	253	11	-	-	PUNCT
ejpam-4384	253	12	atawi	atawi	PROPN
ejpam-4384	253	13	.	.	PUNCT
ejpam-4384	254	1	nyström	nyström	PRON
ejpam-4384	254	2	method	method	NOUN
ejpam-4384	254	3	to	to	PART
ejpam-4384	254	4	solve	solve	VERB
ejpam-4384	254	5	twodimensional	twodimensional	ADJ
ejpam-4384	254	6	volterra	volterra	NOUN
ejpam-4384	254	7	integral	integral	ADJ
ejpam-4384	254	8	equation	equation	NOUN
ejpam-4384	254	9	with	with	ADP
ejpam-4384	254	10	discontinuous	discontinuous	ADJ
ejpam-4384	254	11	kernel	kernel	NOUN
ejpam-4384	254	12	.	.	PUNCT
ejpam-4384	255	1	journal	journal	PROPN
ejpam-4384	255	2	of	of	ADP
ejpam-4384	255	3	computational	computational	ADJ
ejpam-4384	255	4	and	and	CCONJ
ejpam-4384	255	5	theoretical	theoretical	ADJ
ejpam-4384	255	6	nanoscience	nanoscience	NOUN
ejpam-4384	255	7	,	,	PUNCT
ejpam-4384	255	8	18(4):1177–1184	18(4):1177–1184	NUM
ejpam-4384	255	9	,	,	PUNCT
ejpam-4384	255	10	2021	2021	NUM
ejpam-4384	255	11	.	.	PUNCT
ejpam-4384	256	1	[	[	X
ejpam-4384	256	2	15	15	NUM
ejpam-4384	256	3	]	]	SYM
ejpam-4384	256	4	ea	ea	NOUN
ejpam-4384	256	5	rawashdeh	rawashdeh	NOUN
ejpam-4384	256	6	.	.	PUNCT
ejpam-4384	257	1	legendre	legendre	PROPN
ejpam-4384	257	2	wavelets	wavelets	PROPN
ejpam-4384	257	3	method	method	NOUN
ejpam-4384	257	4	for	for	ADP
ejpam-4384	257	5	fractional	fractional	ADJ
ejpam-4384	257	6	integro	integro	ADJ
ejpam-4384	257	7	-	-	PUNCT
ejpam-4384	257	8	differential	differential	NOUN
ejpam-4384	257	9	equations	equation	NOUN
ejpam-4384	257	10	.	.	PUNCT
ejpam-4384	258	1	applied	apply	VERB
ejpam-4384	258	2	mathematical	mathematical	ADJ
ejpam-4384	258	3	sciences	sciences	PROPN
ejpam-4384	258	4	,	,	PUNCT
ejpam-4384	258	5	5(2):2467–2474	5(2):2467–2474	PROPN
ejpam-4384	258	6	,	,	PUNCT
ejpam-4384	258	7	2011	2011	NUM
ejpam-4384	258	8	.	.	PUNCT
ejpam-4384	259	1	[	[	X
ejpam-4384	259	2	16	16	NUM
ejpam-4384	259	3	]	]	PUNCT
ejpam-4384	259	4	n	n	CCONJ
ejpam-4384	259	5	singha	singha	PROPN
ejpam-4384	259	6	and	and	CCONJ
ejpam-4384	259	7	c	c	PROPN
ejpam-4384	259	8	nahak	nahak	PROPN
ejpam-4384	259	9	.	.	PUNCT
ejpam-4384	260	1	solutions	solution	NOUN
ejpam-4384	260	2	of	of	ADP
ejpam-4384	260	3	the	the	DET
ejpam-4384	260	4	generalized	generalized	ADJ
ejpam-4384	260	5	abel	abel	PROPN
ejpam-4384	260	6	’s	’s	PART
ejpam-4384	260	7	integral	integral	ADJ
ejpam-4384	260	8	equation	equation	NOUN
ejpam-4384	260	9	using	use	VERB
ejpam-4384	260	10	laguerre	laguerre	NOUN
ejpam-4384	260	11	orthogonal	orthogonal	ADJ
ejpam-4384	260	12	approximation	approximation	NOUN
ejpam-4384	260	13	.	.	PUNCT
ejpam-4384	261	1	applications	application	NOUN
ejpam-4384	261	2	and	and	CCONJ
ejpam-4384	261	3	applied	apply	VERB
ejpam-4384	261	4	mathematics	mathematic	NOUN
ejpam-4384	261	5	:	:	PUNCT
ejpam-4384	261	6	an	an	DET
ejpam-4384	261	7	international	international	ADJ
ejpam-4384	261	8	journal	journal	NOUN
ejpam-4384	261	9	(	(	PUNCT
ejpam-4384	261	10	aam	aam	PROPN
ejpam-4384	261	11	)	)	PUNCT
ejpam-4384	261	12	,	,	PUNCT
ejpam-4384	261	13	14(2):27	14(2):27	NUM
ejpam-4384	261	14	,	,	PUNCT
ejpam-4384	261	15	2019	2019	NUM
ejpam-4384	261	16	.	.	PUNCT
ejpam-4384	262	1	[	[	X
ejpam-4384	262	2	17	17	NUM
ejpam-4384	262	3	]	]	X
ejpam-4384	262	4	vasily	vasily	PROPN
ejpam-4384	262	5	e	e	NOUN
ejpam-4384	262	6	tarasov	tarasov	NOUN
ejpam-4384	262	7	.	.	PUNCT
ejpam-4384	263	1	fractional	fractional	ADJ
ejpam-4384	263	2	integro	integro	ADJ
ejpam-4384	263	3	-	-	PUNCT
ejpam-4384	263	4	differential	differential	NOUN
ejpam-4384	263	5	equations	equation	NOUN
ejpam-4384	263	6	for	for	ADP
ejpam-4384	263	7	electromagnetic	electromagnetic	ADJ
ejpam-4384	263	8	waves	wave	NOUN
ejpam-4384	263	9	in	in	ADP
ejpam-4384	263	10	dielectric	dielectric	ADJ
ejpam-4384	263	11	media	medium	NOUN
ejpam-4384	263	12	.	.	PUNCT
ejpam-4384	264	1	theoretical	theoretical	ADJ
ejpam-4384	264	2	and	and	CCONJ
ejpam-4384	264	3	mathematical	mathematical	ADJ
ejpam-4384	264	4	physics	physics	NOUN
ejpam-4384	264	5	,	,	PUNCT
ejpam-4384	264	6	158(3):355–359	158(3):355–359	PROPN
ejpam-4384	264	7	,	,	PUNCT
ejpam-4384	264	8	2009	2009	NUM
ejpam-4384	264	9	.	.	PUNCT