id	sid	tid	token	lemma	pos
ejpam-5704	1	1	european	european	PROPN
ejpam-5704	1	2	journal	journal	PROPN
ejpam-5704	1	3	of	of	ADP
ejpam-5704	1	4	pure	pure	ADJ
ejpam-5704	1	5	and	and	CCONJ
ejpam-5704	1	6	applied	applied	ADJ
ejpam-5704	1	7	mathematics	mathematic	NOUN
ejpam-5704	1	8	2025	2025	NUM
ejpam-5704	1	9	,	,	PUNCT
ejpam-5704	1	10	vol	vol	NOUN
ejpam-5704	1	11	.	.	PROPN
ejpam-5704	1	12	18	18	NUM
ejpam-5704	1	13	,	,	PUNCT
ejpam-5704	1	14	issue	issue	NOUN
ejpam-5704	1	15	2	2	NUM
ejpam-5704	1	16	,	,	PUNCT
ejpam-5704	1	17	article	article	NOUN
ejpam-5704	1	18	number	number	NOUN
ejpam-5704	1	19	5704	5704	NUM
ejpam-5704	1	20	issn	issn	PROPN
ejpam-5704	1	21	1307	1307	NUM
ejpam-5704	1	22	-	-	SYM
ejpam-5704	1	23	5543	5543	NUM
ejpam-5704	1	24	–	–	PUNCT
ejpam-5704	1	25	ejpam.com	ejpam.com	X
ejpam-5704	1	26	published	publish	VERB
ejpam-5704	1	27	by	by	ADP
ejpam-5704	1	28	new	new	PROPN
ejpam-5704	1	29	york	york	PROPN
ejpam-5704	1	30	business	business	PROPN
ejpam-5704	1	31	global	global	PROPN
ejpam-5704	1	32	development	development	NOUN
ejpam-5704	1	33	of	of	ADP
ejpam-5704	1	34	the	the	DET
ejpam-5704	1	35	nyström	nyström	NOUN
ejpam-5704	1	36	method	method	NOUN
ejpam-5704	1	37	for	for	ADP
ejpam-5704	1	38	weakly	weakly	ADJ
ejpam-5704	1	39	singular	singular	ADJ
ejpam-5704	1	40	functional	functional	ADJ
ejpam-5704	1	41	integral	integral	ADJ
ejpam-5704	1	42	equations	equation	NOUN
ejpam-5704	1	43	b.	b.	PROPN
ejpam-5704	1	44	h.	h.	PROPN
ejpam-5704	1	45	alrikabi1	alrikabi1	PROPN
ejpam-5704	1	46	,	,	PUNCT
ejpam-5704	1	47	p.	p.	NOUN
ejpam-5704	1	48	darania1,∗	darania1,∗	NOUN
ejpam-5704	1	49	,	,	PUNCT
ejpam-5704	1	50	s.	s.	PROPN
ejpam-5704	1	51	pishbin1	pishbin1	PROPN
ejpam-5704	1	52	1	1	NUM
ejpam-5704	1	53	department	department	NOUN
ejpam-5704	1	54	of	of	ADP
ejpam-5704	1	55	mathematics	mathematic	NOUN
ejpam-5704	1	56	,	,	PUNCT
ejpam-5704	1	57	faculty	faculty	NOUN
ejpam-5704	1	58	of	of	ADP
ejpam-5704	1	59	science	science	NOUN
ejpam-5704	1	60	,	,	PUNCT
ejpam-5704	1	61	urmia	urmia	PROPN
ejpam-5704	1	62	university	university	PROPN
ejpam-5704	1	63	,	,	PUNCT
ejpam-5704	1	64	p.o.box	p.o.box	PROPN
ejpam-5704	1	65	165	165	NUM
ejpam-5704	1	66	,	,	PUNCT
ejpam-5704	1	67	urmia	urmia	NOUN
ejpam-5704	1	68	-	-	PUNCT
ejpam-5704	1	69	iran	iran	PROPN
ejpam-5704	1	70	abstract	abstract	NOUN
ejpam-5704	1	71	.	.	PUNCT
ejpam-5704	2	1	in	in	ADP
ejpam-5704	2	2	this	this	DET
ejpam-5704	2	3	research	research	NOUN
ejpam-5704	2	4	,	,	PUNCT
ejpam-5704	2	5	we	we	PRON
ejpam-5704	2	6	apply	apply	VERB
ejpam-5704	2	7	the	the	DET
ejpam-5704	2	8	standard	standard	ADJ
ejpam-5704	2	9	product	product	NOUN
ejpam-5704	2	10	integration	integration	NOUN
ejpam-5704	2	11	method	method	NOUN
ejpam-5704	2	12	(	(	PUNCT
ejpam-5704	2	13	nyström	nyström	DET
ejpam-5704	2	14	method	method	NOUN
ejpam-5704	2	15	)	)	PUNCT
ejpam-5704	2	16	for	for	ADP
ejpam-5704	2	17	solving	solve	VERB
ejpam-5704	2	18	the	the	DET
ejpam-5704	2	19	delay	delay	NOUN
ejpam-5704	2	20	nonlinear	nonlinear	ADJ
ejpam-5704	2	21	weakly	weakly	ADJ
ejpam-5704	2	22	singular	singular	PROPN
ejpam-5704	2	23	volterra	volterra	PROPN
ejpam-5704	2	24	integral	integral	ADJ
ejpam-5704	2	25	equations	equation	NOUN
ejpam-5704	2	26	.	.	PUNCT
ejpam-5704	3	1	typically	typically	ADV
ejpam-5704	3	2	,	,	PUNCT
ejpam-5704	3	3	in	in	ADP
ejpam-5704	3	4	weakly	weakly	ADJ
ejpam-5704	3	5	singular	singular	ADJ
ejpam-5704	3	6	integral	integral	ADJ
ejpam-5704	3	7	equations	equation	NOUN
ejpam-5704	3	8	,	,	PUNCT
ejpam-5704	3	9	the	the	DET
ejpam-5704	3	10	singularity	singularity	NOUN
ejpam-5704	3	11	of	of	ADP
ejpam-5704	3	12	the	the	DET
ejpam-5704	3	13	kernel	kernel	NOUN
ejpam-5704	3	14	leads	lead	VERB
ejpam-5704	3	15	to	to	ADP
ejpam-5704	3	16	the	the	DET
ejpam-5704	3	17	derivatives	derivative	NOUN
ejpam-5704	3	18	of	of	ADP
ejpam-5704	3	19	the	the	DET
ejpam-5704	3	20	solution	solution	NOUN
ejpam-5704	3	21	becoming	become	VERB
ejpam-5704	3	22	singular	singular	ADJ
ejpam-5704	3	23	at	at	ADP
ejpam-5704	3	24	the	the	DET
ejpam-5704	3	25	boundary	boundary	NOUN
ejpam-5704	3	26	of	of	ADP
ejpam-5704	3	27	the	the	DET
ejpam-5704	3	28	domain	domain	NOUN
ejpam-5704	3	29	.	.	PUNCT
ejpam-5704	4	1	the	the	DET
ejpam-5704	4	2	chelyshkov	chelyshkov	NOUN
ejpam-5704	4	3	polynomials	polynomial	NOUN
ejpam-5704	4	4	serving	serve	VERB
ejpam-5704	4	5	as	as	ADP
ejpam-5704	4	6	orthogonal	orthogonal	ADJ
ejpam-5704	4	7	polynomials	polynomial	NOUN
ejpam-5704	4	8	,	,	PUNCT
ejpam-5704	4	9	find	find	VERB
ejpam-5704	4	10	application	application	NOUN
ejpam-5704	4	11	in	in	ADP
ejpam-5704	4	12	numerical	numerical	ADJ
ejpam-5704	4	13	integration	integration	NOUN
ejpam-5704	4	14	.	.	PUNCT
ejpam-5704	5	1	here	here	ADV
ejpam-5704	5	2	,	,	PUNCT
ejpam-5704	5	3	we	we	PRON
ejpam-5704	5	4	use	use	VERB
ejpam-5704	5	5	roots	root	NOUN
ejpam-5704	5	6	of	of	ADP
ejpam-5704	5	7	these	these	DET
ejpam-5704	5	8	polynomials	polynomial	NOUN
ejpam-5704	5	9	to	to	PART
ejpam-5704	5	10	make	make	VERB
ejpam-5704	5	11	lagrange	lagrange	NOUN
ejpam-5704	5	12	interpolating	interpolate	VERB
ejpam-5704	5	13	polynomial	polynomial	ADJ
ejpam-5704	5	14	for	for	ADP
ejpam-5704	5	15	approximating	approximate	VERB
ejpam-5704	5	16	the	the	DET
ejpam-5704	5	17	kernel	kernel	NOUN
ejpam-5704	5	18	functions	function	NOUN
ejpam-5704	5	19	in	in	ADP
ejpam-5704	5	20	weakly	weakly	ADJ
ejpam-5704	5	21	singular	singular	ADJ
ejpam-5704	5	22	functional	functional	ADJ
ejpam-5704	5	23	integral	integral	ADJ
ejpam-5704	5	24	equation	equation	NOUN
ejpam-5704	5	25	.	.	PUNCT
ejpam-5704	6	1	the	the	DET
ejpam-5704	6	2	proposed	propose	VERB
ejpam-5704	6	3	method	method	NOUN
ejpam-5704	6	4	’s	’s	PART
ejpam-5704	6	5	convergence	convergence	NOUN
ejpam-5704	6	6	analysis	analysis	NOUN
ejpam-5704	6	7	is	be	AUX
ejpam-5704	6	8	developed	develop	VERB
ejpam-5704	6	9	,	,	PUNCT
ejpam-5704	6	10	and	and	CCONJ
ejpam-5704	6	11	numerical	numerical	ADJ
ejpam-5704	6	12	examples	example	NOUN
ejpam-5704	6	13	demonstrate	demonstrate	VERB
ejpam-5704	6	14	the	the	DET
ejpam-5704	6	15	method	method	NOUN
ejpam-5704	6	16	’s	’s	PART
ejpam-5704	6	17	reliability	reliability	NOUN
ejpam-5704	6	18	and	and	CCONJ
ejpam-5704	6	19	efficiency	efficiency	NOUN
ejpam-5704	6	20	.	.	PUNCT
ejpam-5704	7	1	2020	2020	NUM
ejpam-5704	7	2	mathematics	mathematic	NOUN
ejpam-5704	7	3	subject	subject	NOUN
ejpam-5704	7	4	classifications	classification	NOUN
ejpam-5704	7	5	:	:	PUNCT
ejpam-5704	7	6	65r20	65r20	NUM
ejpam-5704	7	7	,	,	PUNCT
ejpam-5704	7	8	65l20	65l20	NUM
ejpam-5704	7	9	,	,	PUNCT
ejpam-5704	7	10	65l80	65l80	NUM
ejpam-5704	7	11	,	,	PUNCT
ejpam-5704	7	12	34k28	34k28	NUM
ejpam-5704	7	13	key	key	ADJ
ejpam-5704	7	14	words	word	NOUN
ejpam-5704	7	15	and	and	CCONJ
ejpam-5704	7	16	phrases	phrase	NOUN
ejpam-5704	7	17	:	:	PUNCT
ejpam-5704	7	18	functional	functional	ADJ
ejpam-5704	7	19	equations	equation	NOUN
ejpam-5704	7	20	,	,	PUNCT
ejpam-5704	7	21	nyström	nyström	DET
ejpam-5704	7	22	method	method	NOUN
ejpam-5704	7	23	,	,	PUNCT
ejpam-5704	7	24	non	non	ADJ
ejpam-5704	7	25	-	-	ADJ
ejpam-5704	7	26	vanishing	vanishing	ADJ
ejpam-5704	7	27	delays	delay	NOUN
ejpam-5704	7	28	,	,	PUNCT
ejpam-5704	7	29	vanishing	vanish	VERB
ejpam-5704	7	30	delays	delay	NOUN
ejpam-5704	7	31	,	,	PUNCT
ejpam-5704	7	32	convergence	convergence	NOUN
ejpam-5704	7	33	1	1	NUM
ejpam-5704	7	34	.	.	PUNCT
ejpam-5704	8	1	introduction	introduction	NOUN
ejpam-5704	8	2	the	the	DET
ejpam-5704	8	3	focal	focal	ADJ
ejpam-5704	8	4	issue	issue	NOUN
ejpam-5704	8	5	involves	involve	VERB
ejpam-5704	8	6	delay	delay	VERB
ejpam-5704	8	7	nonlinear	nonlinear	ADJ
ejpam-5704	8	8	weakly	weakly	ADJ
ejpam-5704	8	9	singular	singular	PROPN
ejpam-5704	8	10	volterra	volterra	PROPN
ejpam-5704	8	11	integral	integral	ADJ
ejpam-5704	8	12	equations	equation	NOUN
ejpam-5704	8	13	{	{	PUNCT
ejpam-5704	8	14	y(t	y(t	NOUN
ejpam-5704	8	15	)	)	PUNCT
ejpam-5704	8	16	=	=	SYM
ejpam-5704	8	17	f(t	f(t	NOUN
ejpam-5704	8	18	)	)	PUNCT
ejpam-5704	9	1	+	+	CCONJ
ejpam-5704	9	2	(	(	PUNCT
ejpam-5704	9	3	vαy)(t	vαy)(t	ADJ
ejpam-5704	9	4	)	)	PUNCT
ejpam-5704	9	5	+	+	CCONJ
ejpam-5704	9	6	(	(	PUNCT
ejpam-5704	9	7	vα	vα	INTJ
ejpam-5704	9	8	,	,	PUNCT
ejpam-5704	9	9	θy)(t	θy)(t	PROPN
ejpam-5704	9	10	)	)	PUNCT
ejpam-5704	9	11	,	,	PUNCT
ejpam-5704	9	12	t	t	PROPN
ejpam-5704	9	13	∈	∈	PROPN
ejpam-5704	9	14	(	(	PUNCT
ejpam-5704	9	15	t0	t0	PROPN
ejpam-5704	9	16	,	,	PUNCT
ejpam-5704	9	17	t	t	X
ejpam-5704	9	18	]	]	PUNCT
ejpam-5704	9	19	,	,	PUNCT
ejpam-5704	9	20	y(t	y(t	NUM
ejpam-5704	9	21	)	)	PUNCT
ejpam-5704	9	22	=	=	SYM
ejpam-5704	10	1	ϕ(t	ϕ(t	NUM
ejpam-5704	10	2	)	)	PUNCT
ejpam-5704	10	3	,	,	PUNCT
ejpam-5704	10	4	t	t	PROPN
ejpam-5704	10	5	∈	∈	PROPN
ejpam-5704	11	1	[	[	X
ejpam-5704	11	2	θ(t0	θ(t0	NOUN
ejpam-5704	11	3	)	)	PUNCT
ejpam-5704	11	4	,	,	PUNCT
ejpam-5704	11	5	t0	t0	PROPN
ejpam-5704	11	6	]	]	PUNCT
ejpam-5704	11	7	.	.	PUNCT
ejpam-5704	12	1	(	(	PUNCT
ejpam-5704	12	2	1	1	X
ejpam-5704	12	3	)	)	PUNCT
ejpam-5704	12	4	where	where	SCONJ
ejpam-5704	12	5	(	(	PUNCT
ejpam-5704	12	6	vαy)(t	vαy)(t	ADJ
ejpam-5704	12	7	)	)	PUNCT
ejpam-5704	12	8	=	=	SYM
ejpam-5704	13	1	∫	∫	PROPN
ejpam-5704	13	2	t	t	PROPN
ejpam-5704	13	3	t0	t0	PROPN
ejpam-5704	13	4	p1,h(t	p1,h(t	PROPN
ejpam-5704	13	5	,	,	PUNCT
ejpam-5704	13	6	w)k1(t	w)k1(t	PROPN
ejpam-5704	13	7	,	,	PUNCT
ejpam-5704	13	8	w	w	PROPN
ejpam-5704	13	9	,	,	PUNCT
ejpam-5704	13	10	y(w))dw	y(w))dw	PROPN
ejpam-5704	13	11	,	,	PUNCT
ejpam-5704	13	12	(	(	PUNCT
ejpam-5704	13	13	2	2	X
ejpam-5704	13	14	)	)	PUNCT
ejpam-5704	13	15	with	with	ADP
ejpam-5704	13	16	k1	k1	PROPN
ejpam-5704	13	17	∈	∈	PROPN
ejpam-5704	13	18	c(d	c(d	NOUN
ejpam-5704	13	19	×	×	NOUN
ejpam-5704	13	20	r	r	NOUN
ejpam-5704	13	21	)	)	PUNCT
ejpam-5704	13	22	,	,	PUNCT
ejpam-5704	13	23	d	d	NOUN
ejpam-5704	13	24	=	=	PRON
ejpam-5704	13	25	{	{	PUNCT
ejpam-5704	13	26	(	(	PUNCT
ejpam-5704	13	27	t	t	PROPN
ejpam-5704	13	28	,	,	PUNCT
ejpam-5704	13	29	w	w	PROPN
ejpam-5704	13	30	)	)	PUNCT
ejpam-5704	13	31	:	:	PUNCT
ejpam-5704	13	32	t0	t0	NOUN
ejpam-5704	13	33	≤	≤	NUM
ejpam-5704	13	34	w	w	PROPN
ejpam-5704	13	35	≤	≤	PROPN
ejpam-5704	13	36	t	t	NOUN
ejpam-5704	13	37	≤	≤	NUM
ejpam-5704	13	38	t	t	PROPN
ejpam-5704	13	39	}	}	PUNCT
ejpam-5704	13	40	,	,	PUNCT
ejpam-5704	13	41	k2	k2	PROPN
ejpam-5704	13	42	∈	∈	PROPN
ejpam-5704	13	43	c(dθ	c(dθ	PROPN
ejpam-5704	13	44	×	×	NOUN
ejpam-5704	13	45	r	r	NOUN
ejpam-5704	13	46	)	)	PUNCT
ejpam-5704	13	47	,	,	PUNCT
ejpam-5704	13	48	dθ	dθ	PROPN
ejpam-5704	13	49	=	=	PRON
ejpam-5704	13	50	{	{	PUNCT
ejpam-5704	13	51	(	(	PUNCT
ejpam-5704	13	52	t	t	PROPN
ejpam-5704	13	53	,	,	PUNCT
ejpam-5704	13	54	w	w	NOUN
ejpam-5704	13	55	)	)	PUNCT
ejpam-5704	13	56	:	:	PUNCT
ejpam-5704	13	57	θ(t0	θ(t0	NOUN
ejpam-5704	13	58	)	)	PUNCT
ejpam-5704	13	59	≤	≤	NUM
ejpam-5704	13	60	w	w	NOUN
ejpam-5704	13	61	≤	≤	PROPN
ejpam-5704	13	62	θ(t	θ(t	NOUN
ejpam-5704	13	63	)	)	PUNCT
ejpam-5704	13	64	}	}	PUNCT
ejpam-5704	13	65	and	and	CCONJ
ejpam-5704	13	66	(	(	PUNCT
ejpam-5704	13	67	vα	vα	INTJ
ejpam-5704	13	68	,	,	PUNCT
ejpam-5704	13	69	θy)(t	θy)(t	PROPN
ejpam-5704	13	70	)	)	PUNCT
ejpam-5704	14	1	=	=	SYM
ejpam-5704	15	1	∫	∫	PROPN
ejpam-5704	15	2	θ(t	θ(t	PROPN
ejpam-5704	15	3	)	)	PUNCT
ejpam-5704	15	4	t0	t0	PROPN
ejpam-5704	15	5	p2,h(t	p2,h(t	NOUN
ejpam-5704	15	6	,	,	PUNCT
ejpam-5704	15	7	w)k2(t	w)k2(t	PROPN
ejpam-5704	15	8	,	,	PUNCT
ejpam-5704	15	9	w	w	PROPN
ejpam-5704	15	10	,	,	PUNCT
ejpam-5704	15	11	y(w))dw	y(w))dw	PROPN
ejpam-5704	15	12	,	,	PUNCT
ejpam-5704	15	13	(	(	PUNCT
ejpam-5704	15	14	3	3	X
ejpam-5704	15	15	)	)	PUNCT
ejpam-5704	15	16	∗corresponding	∗corresponde	VERB
ejpam-5704	15	17	author	author	NOUN
ejpam-5704	15	18	.	.	PUNCT
ejpam-5704	16	1	doi	doi	NOUN
ejpam-5704	16	2	:	:	PUNCT
ejpam-5704	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5704	https://doi.org/10.29020/nybg.ejpam.v18i2.5704	VERB
ejpam-5704	16	4	email	email	NOUN
ejpam-5704	16	5	addresses	address	NOUN
ejpam-5704	16	6	:	:	PUNCT
ejpam-5704	17	1	bahaahussainmath@gmail.com	bahaahussainmath@gmail.com	X
ejpam-5704	17	2	(	(	PUNCT
ejpam-5704	17	3	b.	b.	PROPN
ejpam-5704	17	4	h.	h.	PROPN
ejpam-5704	17	5	alrikabi	alrikabi	PROPN
ejpam-5704	17	6	)	)	PUNCT
ejpam-5704	17	7	,	,	PUNCT
ejpam-5704	17	8	p.darania@urmia.ac.ir	p.darania@urmia.ac.ir	PROPN
ejpam-5704	17	9	(	(	PUNCT
ejpam-5704	17	10	p.	p.	NOUN
ejpam-5704	17	11	darania	darania	PROPN
ejpam-5704	17	12	)	)	PUNCT
ejpam-5704	17	13	,	,	PUNCT
ejpam-5704	17	14	s.pishbin@urmia.ac.ir	s.pishbin@urmia.ac.ir	PROPN
ejpam-5704	17	15	(	(	PUNCT
ejpam-5704	17	16	s.	s.	PROPN
ejpam-5704	17	17	pishbin	pishbin	PROPN
ejpam-5704	17	18	)	)	PUNCT
ejpam-5704	17	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5704	18	1	1	1	NUM
ejpam-5704	18	2	copyright	copyright	NOUN
ejpam-5704	18	3	:	:	PUNCT
ejpam-5704	18	4	©	©	PROPN
ejpam-5704	18	5	2025	2025	NUM
ejpam-5704	18	6	the	the	DET
ejpam-5704	18	7	author(s	author(s	NOUN
ejpam-5704	18	8	)	)	PUNCT
ejpam-5704	18	9	.	.	PUNCT
ejpam-5704	19	1	(	(	PUNCT
ejpam-5704	19	2	cc	cc	NOUN
ejpam-5704	19	3	by	by	ADP
ejpam-5704	19	4	-	-	PUNCT
ejpam-5704	19	5	nc	nc	PROPN
ejpam-5704	19	6	4.0	4.0	NUM
ejpam-5704	19	7	)	)	PUNCT
ejpam-5704	19	8	b.	b.	PROPN
ejpam-5704	19	9	h.	h.	PROPN
ejpam-5704	19	10	alrikabi	alrikabi	PROPN
ejpam-5704	19	11	,	,	PUNCT
ejpam-5704	19	12	p.	p.	PROPN
ejpam-5704	19	13	darania	darania	PROPN
ejpam-5704	19	14	,	,	PUNCT
ejpam-5704	19	15	s.pishbin	s.pishbin	PROPN
ejpam-5704	19	16	/	/	SYM
ejpam-5704	19	17	eur	eur	PROPN
ejpam-5704	19	18	.	.	PUNCT
ejpam-5704	20	1	j.	j.	PROPN
ejpam-5704	20	2	pure	pure	PROPN
ejpam-5704	20	3	appl	appl	PROPN
ejpam-5704	20	4	.	.	PROPN
ejpam-5704	20	5	math	math	PROPN
ejpam-5704	20	6	,	,	PUNCT
ejpam-5704	20	7	18	18	NUM
ejpam-5704	20	8	(	(	PUNCT
ejpam-5704	20	9	2	2	NUM
ejpam-5704	20	10	)	)	PUNCT
ejpam-5704	20	11	(	(	PUNCT
ejpam-5704	20	12	2025	2025	NUM
ejpam-5704	20	13	)	)	PUNCT
ejpam-5704	20	14	,	,	PUNCT
ejpam-5704	20	15	5704	5704	NUM
ejpam-5704	20	16	2	2	NUM
ejpam-5704	20	17	of	of	ADP
ejpam-5704	20	18	19	19	NUM
ejpam-5704	20	19	ϕ	ϕ	NOUN
ejpam-5704	20	20	,	,	PUNCT
ejpam-5704	20	21	f	f	PROPN
ejpam-5704	20	22	as	as	SCONJ
ejpam-5704	20	23	given	give	VERB
ejpam-5704	20	24	functions	function	NOUN
ejpam-5704	20	25	are	be	AUX
ejpam-5704	20	26	at	at	ADP
ejpam-5704	20	27	least	least	ADJ
ejpam-5704	20	28	continuous	continuous	ADJ
ejpam-5704	20	29	on	on	ADP
ejpam-5704	20	30	their	their	PRON
ejpam-5704	20	31	respective	respective	ADJ
ejpam-5704	20	32	domains	domain	NOUN
ejpam-5704	20	33	.	.	PUNCT
ejpam-5704	21	1	normal	normal	ADJ
ejpam-5704	21	2	forms	form	NOUN
ejpam-5704	21	3	of	of	ADP
ejpam-5704	21	4	weakly	weakly	ADJ
ejpam-5704	21	5	singular	singular	ADJ
ejpam-5704	21	6	kernels	kernel	NOUN
ejpam-5704	21	7	p.	p.	PROPN
ejpam-5704	21	8	,h(t	,h(t	PUNCT
ejpam-5704	21	9	,	,	PUNCT
ejpam-5704	21	10	w	w	PROPN
ejpam-5704	21	11	)	)	PUNCT
ejpam-5704	21	12	,	,	PUNCT
ejpam-5704	21	13	are	be	AUX
ejpam-5704	21	14	p.	p.	NOUN
ejpam-5704	21	15	,h(t	,h(t	PUNCT
ejpam-5704	21	16	,	,	PUNCT
ejpam-5704	21	17	w	w	NOUN
ejpam-5704	21	18	)	)	PUNCT
ejpam-5704	21	19	=	=	PUNCT
ejpam-5704	22	1			PUNCT
ejpam-5704	22	2	1	1	NUM
ejpam-5704	22	3	|t−w|µ	|t−w|µ	NUM
ejpam-5704	22	4	,	,	PUNCT
ejpam-5704	22	5	0	0	PUNCT
ejpam-5704	22	6	<	<	X
ejpam-5704	22	7	µ	µ	X
ejpam-5704	22	8	<	<	X
ejpam-5704	22	9	1	1	NUM
ejpam-5704	22	10	,	,	PUNCT
ejpam-5704	22	11	h	h	NOUN
ejpam-5704	22	12	=	=	SYM
ejpam-5704	22	13	1	1	NUM
ejpam-5704	22	14	,	,	PUNCT
ejpam-5704	22	15	log	log	VERB
ejpam-5704	22	16	|t−	|t−	PROPN
ejpam-5704	22	17	w|	w|	NOUN
ejpam-5704	22	18	,	,	PUNCT
ejpam-5704	22	19	h	h	NOUN
ejpam-5704	23	1	=	=	NOUN
ejpam-5704	23	2	2	2	X
ejpam-5704	23	3	.	.	PUNCT
ejpam-5704	23	4	(	(	PUNCT
ejpam-5704	23	5	4	4	X
ejpam-5704	23	6	)	)	PUNCT
ejpam-5704	23	7	here	here	ADV
ejpam-5704	23	8	,	,	PUNCT
ejpam-5704	23	9	the	the	DET
ejpam-5704	23	10	delay	delay	NOUN
ejpam-5704	23	11	function	function	VERB
ejpam-5704	23	12	θ	θ	PROPN
ejpam-5704	23	13	will	will	AUX
ejpam-5704	23	14	be	be	AUX
ejpam-5704	23	15	constrained	constrain	VERB
ejpam-5704	23	16	by	by	ADP
ejpam-5704	23	17	the	the	DET
ejpam-5704	23	18	following	following	ADJ
ejpam-5704	23	19	conditions	condition	NOUN
ejpam-5704	23	20	:	:	PUNCT
ejpam-5704	23	21	(	(	PUNCT
ejpam-5704	23	22	o1	o1	NOUN
ejpam-5704	23	23	)	)	PUNCT
ejpam-5704	23	24	θ(t	θ(t	PROPN
ejpam-5704	23	25	)	)	PUNCT
ejpam-5704	23	26	=	=	PUNCT
ejpam-5704	23	27	t−	t−	PROPN
ejpam-5704	23	28	η(t	η(t	NOUN
ejpam-5704	23	29	)	)	PUNCT
ejpam-5704	23	30	,	,	PUNCT
ejpam-5704	23	31	τ	τ	PROPN
ejpam-5704	23	32	∈	∈	PROPN
ejpam-5704	23	33	cν(i	cν(i	NOUN
ejpam-5704	23	34	)	)	PUNCT
ejpam-5704	23	35	,	,	PUNCT
ejpam-5704	23	36	i	i	PRON
ejpam-5704	23	37	=	=	PUNCT
ejpam-5704	24	1	[	[	X
ejpam-5704	24	2	t0	t0	PROPN
ejpam-5704	24	3	,	,	PUNCT
ejpam-5704	24	4	t	t	X
ejpam-5704	24	5	]	]	PUNCT
ejpam-5704	24	6	,	,	PUNCT
ejpam-5704	24	7	for	for	ADP
ejpam-5704	24	8	some	some	DET
ejpam-5704	24	9	ν	ν	NOUN
ejpam-5704	24	10	≥	≥	NOUN
ejpam-5704	24	11	0	0	NUM
ejpam-5704	24	12	,	,	PUNCT
ejpam-5704	24	13	(	(	PUNCT
ejpam-5704	24	14	o2	o2	PROPN
ejpam-5704	24	15	)	)	PUNCT
ejpam-5704	24	16			PUNCT
ejpam-5704	24	17	for	for	ADP
ejpam-5704	24	18	vanishing	vanish	VERB
ejpam-5704	24	19	delay	delay	NOUN
ejpam-5704	24	20	:	:	PUNCT
ejpam-5704	24	21	η(t0	η(t0	NOUN
ejpam-5704	24	22	)	)	PUNCT
ejpam-5704	24	23	=	=	SYM
ejpam-5704	24	24	0	0	NUM
ejpam-5704	24	25	,	,	PUNCT
ejpam-5704	24	26	and	and	CCONJ
ejpam-5704	24	27	η(t	η(t	NOUN
ejpam-5704	24	28	)	)	PUNCT
ejpam-5704	24	29	>	>	PUNCT
ejpam-5704	24	30	t0	t0	X
ejpam-5704	24	31	>	>	X
ejpam-5704	24	32	0	0	NUM
ejpam-5704	24	33	,	,	PUNCT
ejpam-5704	24	34	for	for	ADP
ejpam-5704	24	35	t0	t0	PROPN
ejpam-5704	24	36	<	<	X
ejpam-5704	24	37	t	t	PROPN
ejpam-5704	24	38	≤	≤	PROPN
ejpam-5704	24	39	t	t	PROPN
ejpam-5704	24	40	,	,	PUNCT
ejpam-5704	24	41	for	for	ADP
ejpam-5704	24	42	non	non	ADJ
ejpam-5704	24	43	-	-	ADJ
ejpam-5704	24	44	vanishing	vanishing	ADJ
ejpam-5704	24	45	delay	delay	NOUN
ejpam-5704	24	46	:	:	PUNCT
ejpam-5704	24	47	η(t	η(t	NOUN
ejpam-5704	24	48	)	)	PUNCT
ejpam-5704	24	49	≥	≥	NOUN
ejpam-5704	24	50	η0	η0	NOUN
ejpam-5704	24	51	>	>	X
ejpam-5704	24	52	0	0	NUM
ejpam-5704	24	53	,	,	PUNCT
ejpam-5704	24	54	for	for	ADP
ejpam-5704	24	55	all	all	DET
ejpam-5704	24	56	t	t	NOUN
ejpam-5704	24	57	∈	∈	PROPN
ejpam-5704	25	1	i	i	PRON
ejpam-5704	25	2	,	,	PUNCT
ejpam-5704	25	3	(	(	PUNCT
ejpam-5704	25	4	o3	o3	PROPN
ejpam-5704	25	5	)	)	PUNCT
ejpam-5704	25	6	θ	θ	PROPN
ejpam-5704	25	7	is	be	AUX
ejpam-5704	25	8	strictly	strictly	ADV
ejpam-5704	25	9	increasing	increase	VERB
ejpam-5704	25	10	on	on	ADP
ejpam-5704	25	11	i.	i.	NOUN
ejpam-5704	25	12	due	due	ADP
ejpam-5704	25	13	to	to	ADP
ejpam-5704	25	14	the	the	DET
ejpam-5704	25	15	assumption	assumption	NOUN
ejpam-5704	25	16	(	(	PUNCT
ejpam-5704	25	17	o2	o2	PROPN
ejpam-5704	25	18	)	)	PUNCT
ejpam-5704	25	19	that	that	SCONJ
ejpam-5704	25	20	the	the	DET
ejpam-5704	25	21	delay	delay	NOUN
ejpam-5704	25	22	η(t	η(t	NOUN
ejpam-5704	25	23	)	)	PUNCT
ejpam-5704	25	24	does	do	AUX
ejpam-5704	25	25	not	not	PART
ejpam-5704	25	26	become	become	VERB
ejpam-5704	25	27	zero	zero	NUM
ejpam-5704	25	28	on	on	ADP
ejpam-5704	25	29	i	i	PRON
ejpam-5704	25	30	,	,	PUNCT
ejpam-5704	25	31	having	have	VERB
ejpam-5704	25	32	smooth	smooth	ADJ
ejpam-5704	25	33	data	datum	NOUN
ejpam-5704	25	34	in	in	ADP
ejpam-5704	25	35	(	(	PUNCT
ejpam-5704	25	36	1	1	X
ejpam-5704	25	37	)	)	PUNCT
ejpam-5704	25	38	typically	typically	ADV
ejpam-5704	25	39	does	do	AUX
ejpam-5704	25	40	not	not	PART
ejpam-5704	25	41	result	result	VERB
ejpam-5704	25	42	in	in	ADP
ejpam-5704	25	43	a	a	DET
ejpam-5704	25	44	solution	solution	NOUN
ejpam-5704	25	45	y	y	PROPN
ejpam-5704	25	46	that	that	PRON
ejpam-5704	25	47	is	be	AUX
ejpam-5704	25	48	globally	globally	ADV
ejpam-5704	25	49	smooth	smooth	ADJ
ejpam-5704	25	50	.	.	PUNCT
ejpam-5704	26	1	it	it	PRON
ejpam-5704	26	2	is	be	AUX
ejpam-5704	26	3	widely	widely	ADV
ejpam-5704	26	4	recognized	recognize	VERB
ejpam-5704	26	5	that	that	SCONJ
ejpam-5704	26	6	these	these	DET
ejpam-5704	26	7	equations	equation	NOUN
ejpam-5704	26	8	often	often	ADV
ejpam-5704	26	9	exhibit	exhibit	VERB
ejpam-5704	26	10	discontinuity	discontinuity	NOUN
ejpam-5704	26	11	in	in	ADP
ejpam-5704	26	12	the	the	DET
ejpam-5704	26	13	solution	solution	NOUN
ejpam-5704	26	14	or	or	CCONJ
ejpam-5704	26	15	its	its	PRON
ejpam-5704	26	16	derivatives	derivative	NOUN
ejpam-5704	26	17	at	at	ADP
ejpam-5704	26	18	the	the	DET
ejpam-5704	26	19	initial	initial	ADJ
ejpam-5704	26	20	point	point	NOUN
ejpam-5704	26	21	of	of	ADP
ejpam-5704	26	22	the	the	DET
ejpam-5704	26	23	integration	integration	NOUN
ejpam-5704	26	24	domain	domain	NOUN
ejpam-5704	26	25	.	.	PUNCT
ejpam-5704	27	1	this	this	DET
ejpam-5704	27	2	discontinuity	discontinuity	NOUN
ejpam-5704	27	3	propagates	propagate	VERB
ejpam-5704	27	4	along	along	ADP
ejpam-5704	27	5	the	the	DET
ejpam-5704	27	6	integration	integration	NOUN
ejpam-5704	27	7	interval	interval	NOUN
ejpam-5704	27	8	,	,	PUNCT
ejpam-5704	27	9	giving	give	VERB
ejpam-5704	27	10	rise	rise	NOUN
ejpam-5704	27	11	to	to	ADP
ejpam-5704	27	12	subsequent	subsequent	ADJ
ejpam-5704	27	13	points	point	NOUN
ejpam-5704	27	14	referred	refer	VERB
ejpam-5704	27	15	to	to	ADP
ejpam-5704	27	16	as	as	ADP
ejpam-5704	27	17	singular	singular	ADJ
ejpam-5704	27	18	points	point	NOUN
ejpam-5704	27	19	.	.	PUNCT
ejpam-5704	28	1	determining	determine	VERB
ejpam-5704	28	2	these	these	DET
ejpam-5704	28	3	singular	singular	ADJ
ejpam-5704	28	4	points	point	NOUN
ejpam-5704	28	5	in	in	ADP
ejpam-5704	28	6	advance	advance	NOUN
ejpam-5704	28	7	is	be	AUX
ejpam-5704	28	8	challenging	challenging	ADJ
ejpam-5704	28	9	,	,	PUNCT
ejpam-5704	28	10	and	and	CCONJ
ejpam-5704	28	11	the	the	DET
ejpam-5704	28	12	solution	solution	NOUN
ejpam-5704	28	13	derivatives	derivative	NOUN
ejpam-5704	28	14	at	at	ADP
ejpam-5704	28	15	these	these	DET
ejpam-5704	28	16	points	point	NOUN
ejpam-5704	28	17	tend	tend	VERB
ejpam-5704	28	18	to	to	PART
ejpam-5704	28	19	smooth	smooth	VERB
ejpam-5704	28	20	out	out	ADP
ejpam-5704	28	21	along	along	ADP
ejpam-5704	28	22	the	the	DET
ejpam-5704	28	23	interval	interval	NOUN
ejpam-5704	28	24	.	.	PUNCT
ejpam-5704	29	1	many	many	ADJ
ejpam-5704	29	2	existing	exist	VERB
ejpam-5704	29	3	numerical	numerical	ADJ
ejpam-5704	29	4	methods	method	NOUN
ejpam-5704	29	5	for	for	ADP
ejpam-5704	29	6	such	such	ADJ
ejpam-5704	29	7	equations	equation	NOUN
ejpam-5704	29	8	are	be	AUX
ejpam-5704	29	9	highly	highly	ADV
ejpam-5704	29	10	sensitive	sensitive	ADJ
ejpam-5704	29	11	to	to	ADP
ejpam-5704	29	12	these	these	DET
ejpam-5704	29	13	singular	singular	ADJ
ejpam-5704	29	14	points	point	NOUN
ejpam-5704	29	15	.	.	PUNCT
ejpam-5704	30	1	therefore	therefore	ADV
ejpam-5704	30	2	,	,	PUNCT
ejpam-5704	30	3	it	it	PRON
ejpam-5704	30	4	is	be	AUX
ejpam-5704	30	5	crucial	crucial	ADJ
ejpam-5704	30	6	for	for	SCONJ
ejpam-5704	30	7	these	these	DET
ejpam-5704	30	8	methods	method	NOUN
ejpam-5704	30	9	to	to	PART
ejpam-5704	30	10	incorporate	incorporate	VERB
ejpam-5704	30	11	a	a	DET
ejpam-5704	30	12	process	process	NOUN
ejpam-5704	30	13	that	that	PRON
ejpam-5704	30	14	detects	detect	NOUN
ejpam-5704	30	15	and	and	CCONJ
ejpam-5704	30	16	includes	include	VERB
ejpam-5704	30	17	these	these	DET
ejpam-5704	30	18	points	point	NOUN
ejpam-5704	30	19	in	in	ADP
ejpam-5704	30	20	the	the	DET
ejpam-5704	30	21	mesh	mesh	NOUN
ejpam-5704	30	22	to	to	PART
ejpam-5704	30	23	ensure	ensure	VERB
ejpam-5704	30	24	the	the	DET
ejpam-5704	30	25	desired	desire	VERB
ejpam-5704	30	26	accuracy	accuracy	NOUN
ejpam-5704	30	27	(	(	PUNCT
ejpam-5704	30	28	for	for	ADP
ejpam-5704	30	29	further	further	ADJ
ejpam-5704	30	30	details	detail	NOUN
ejpam-5704	30	31	see	see	VERB
ejpam-5704	30	32	[	[	X
ejpam-5704	30	33	1	1	NUM
ejpam-5704	30	34	]	]	PUNCT
ejpam-5704	30	35	.	.	PUNCT
ejpam-5704	30	36	)	)	PUNCT
ejpam-5704	30	37	by	by	ADP
ejpam-5704	30	38	virtue	virtue	NOUN
ejpam-5704	30	39	of	of	ADP
ejpam-5704	30	40	volterra	volterra	PROPN
ejpam-5704	30	41	integral	integral	ADJ
ejpam-5704	30	42	equations	equation	NOUN
ejpam-5704	30	43	and	and	CCONJ
ejpam-5704	30	44	also	also	ADV
ejpam-5704	30	45	their	their	PRON
ejpam-5704	30	46	functional	functional	ADJ
ejpam-5704	30	47	counterparts	counterpart	NOUN
ejpam-5704	30	48	along	along	ADP
ejpam-5704	30	49	with	with	ADP
ejpam-5704	30	50	delay	delay	NOUN
ejpam-5704	30	51	terms	term	NOUN
ejpam-5704	30	52	whether	whether	SCONJ
ejpam-5704	30	53	vanishing	vanish	VERB
ejpam-5704	30	54	or	or	CCONJ
ejpam-5704	30	55	non	non	ADJ
ejpam-5704	30	56	-	-	ADJ
ejpam-5704	30	57	vanishing	vanishing	ADJ
ejpam-5704	30	58	,	,	PUNCT
ejpam-5704	30	59	a	a	DET
ejpam-5704	30	60	wide	wide	ADJ
ejpam-5704	30	61	spectrum	spectrum	NOUN
ejpam-5704	30	62	of	of	ADP
ejpam-5704	30	63	science	science	NOUN
ejpam-5704	30	64	subjects	subject	NOUN
ejpam-5704	30	65	,	,	PUNCT
ejpam-5704	30	66	namely	namely	ADV
ejpam-5704	30	67	in	in	ADP
ejpam-5704	30	68	biology	biology	NOUN
ejpam-5704	30	69	,	,	PUNCT
ejpam-5704	30	70	ecology	ecology	NOUN
ejpam-5704	30	71	,	,	PUNCT
ejpam-5704	30	72	physics	physics	NOUN
ejpam-5704	30	73	,	,	PUNCT
ejpam-5704	30	74	and	and	CCONJ
ejpam-5704	30	75	chemistry	chemistry	NOUN
ejpam-5704	30	76	have	have	AUX
ejpam-5704	30	77	been	be	AUX
ejpam-5704	30	78	mathematically	mathematically	ADV
ejpam-5704	30	79	well	well	ADV
ejpam-5704	30	80	-	-	PUNCT
ejpam-5704	30	81	formulated	formulate	VERB
ejpam-5704	30	82	in	in	ADP
ejpam-5704	30	83	order	order	NOUN
ejpam-5704	30	84	to	to	PART
ejpam-5704	30	85	analyse	analyse	VERB
ejpam-5704	30	86	and	and	CCONJ
ejpam-5704	30	87	study	study	VERB
ejpam-5704	30	88	underlying	underlie	VERB
ejpam-5704	30	89	phenomena	phenomenon	NOUN
ejpam-5704	30	90	.	.	PUNCT
ejpam-5704	31	1	particularly	particularly	ADV
ejpam-5704	31	2	,	,	PUNCT
ejpam-5704	31	3	these	these	DET
ejpam-5704	31	4	classes	class	NOUN
ejpam-5704	31	5	of	of	ADP
ejpam-5704	31	6	mathematical	mathematical	ADJ
ejpam-5704	31	7	modellings	modelling	NOUN
ejpam-5704	31	8	can	can	AUX
ejpam-5704	31	9	be	be	AUX
ejpam-5704	31	10	found	find	VERB
ejpam-5704	31	11	in	in	ADP
ejpam-5704	31	12	fluid	fluid	ADJ
ejpam-5704	31	13	dynamics	dynamic	NOUN
ejpam-5704	31	14	,	,	PUNCT
ejpam-5704	31	15	viscoelasticity	viscoelasticity	NOUN
ejpam-5704	31	16	of	of	ADP
ejpam-5704	31	17	materials	material	NOUN
ejpam-5704	31	18	,	,	PUNCT
ejpam-5704	31	19	population	population	NOUN
ejpam-5704	31	20	growth	growth	NOUN
ejpam-5704	31	21	dynamics	dynamic	NOUN
ejpam-5704	31	22	,	,	PUNCT
ejpam-5704	31	23	heat	heat	NOUN
ejpam-5704	31	24	conduction	conduction	NOUN
ejpam-5704	31	25	,	,	PUNCT
ejpam-5704	31	26	epidemiology	epidemiology	NOUN
ejpam-5704	31	27	,	,	PUNCT
ejpam-5704	31	28	controlled	control	VERB
ejpam-5704	31	29	liquidation	liquidation	NOUN
ejpam-5704	31	30	in	in	ADP
ejpam-5704	31	31	obsolete	obsolete	ADJ
ejpam-5704	31	32	production	production	NOUN
ejpam-5704	31	33	units	unit	NOUN
ejpam-5704	31	34	,	,	PUNCT
ejpam-5704	31	35	and	and	CCONJ
ejpam-5704	31	36	renovation	renovation	NOUN
ejpam-5704	31	37	in	in	ADP
ejpam-5704	31	38	economic	economic	ADJ
ejpam-5704	31	39	systems	system	NOUN
ejpam-5704	31	40	,	,	PUNCT
ejpam-5704	31	41	see	see	VERB
ejpam-5704	31	42	[	[	X
ejpam-5704	31	43	2–6	2–6	NOUN
ejpam-5704	31	44	]	]	X
ejpam-5704	31	45	and	and	CCONJ
ejpam-5704	31	46	references	reference	NOUN
ejpam-5704	31	47	therein	therein	ADV
ejpam-5704	31	48	.	.	PUNCT
ejpam-5704	32	1	some	some	DET
ejpam-5704	32	2	numerical	numerical	ADJ
ejpam-5704	32	3	methods	method	NOUN
ejpam-5704	32	4	have	have	AUX
ejpam-5704	32	5	been	be	AUX
ejpam-5704	32	6	proposed	propose	VERB
ejpam-5704	32	7	to	to	PART
ejpam-5704	32	8	obtain	obtain	VERB
ejpam-5704	32	9	approximate	approximate	ADJ
ejpam-5704	32	10	solutions	solution	NOUN
ejpam-5704	32	11	of	of	ADP
ejpam-5704	32	12	weakly	weakly	ADJ
ejpam-5704	32	13	singular	singular	PROPN
ejpam-5704	32	14	volterra	volterra	PROPN
ejpam-5704	32	15	integral	integral	ADJ
ejpam-5704	32	16	equation	equation	NOUN
ejpam-5704	32	17	,	,	PUNCT
ejpam-5704	32	18	such	such	ADJ
ejpam-5704	32	19	as	as	ADP
ejpam-5704	32	20	spectral	spectral	ADJ
ejpam-5704	32	21	method	method	NOUN
ejpam-5704	32	22	[	[	X
ejpam-5704	32	23	7–9	7–9	NOUN
ejpam-5704	32	24	]	]	X
ejpam-5704	32	25	,	,	PUNCT
ejpam-5704	32	26	collocation	collocation	NOUN
ejpam-5704	32	27	method	method	NOUN
ejpam-5704	32	28	[	[	X
ejpam-5704	32	29	10	10	NUM
ejpam-5704	32	30	,	,	PUNCT
ejpam-5704	32	31	11	11	NUM
ejpam-5704	32	32	]	]	PUNCT
ejpam-5704	32	33	,	,	PUNCT
ejpam-5704	32	34	radial	radial	ADJ
ejpam-5704	32	35	basis	basis	NOUN
ejpam-5704	32	36	function	function	NOUN
ejpam-5704	32	37	method	method	NOUN
ejpam-5704	32	38	[	[	X
ejpam-5704	32	39	12	12	NUM
ejpam-5704	32	40	]	]	PUNCT
ejpam-5704	32	41	,	,	PUNCT
ejpam-5704	32	42	bernstein	bernstein	PROPN
ejpam-5704	32	43	and	and	CCONJ
ejpam-5704	32	44	genocchi	genocchi	PROPN
ejpam-5704	32	45	polynomial	polynomial	ADJ
ejpam-5704	32	46	method	method	NOUN
ejpam-5704	32	47	[	[	X
ejpam-5704	32	48	13	13	NUM
ejpam-5704	32	49	,	,	PUNCT
ejpam-5704	32	50	14	14	NUM
ejpam-5704	32	51	]	]	PUNCT
ejpam-5704	32	52	and	and	CCONJ
ejpam-5704	32	53	successive	successive	ADJ
ejpam-5704	32	54	approximation	approximation	NOUN
ejpam-5704	32	55	method	method	NOUN
ejpam-5704	32	56	[	[	X
ejpam-5704	32	57	15	15	NUM
ejpam-5704	32	58	]	]	PUNCT
ejpam-5704	32	59	.	.	PUNCT
ejpam-5704	33	1	delay	delay	NOUN
ejpam-5704	33	2	ies	ie	NOUN
ejpam-5704	33	3	have	have	AUX
ejpam-5704	33	4	been	be	AUX
ejpam-5704	33	5	solved	solve	VERB
ejpam-5704	33	6	approximately	approximately	ADV
ejpam-5704	33	7	by	by	ADP
ejpam-5704	33	8	many	many	ADJ
ejpam-5704	33	9	authors	author	NOUN
ejpam-5704	33	10	,	,	PUNCT
ejpam-5704	33	11	such	such	ADJ
ejpam-5704	33	12	as	as	ADP
ejpam-5704	33	13	,	,	PUNCT
ejpam-5704	33	14	spectral	spectral	ADJ
ejpam-5704	33	15	methods	method	NOUN
ejpam-5704	33	16	[	[	X
ejpam-5704	33	17	16	16	NUM
ejpam-5704	33	18	]	]	PUNCT
ejpam-5704	33	19	,	,	PUNCT
ejpam-5704	33	20	two	two	NUM
ejpam-5704	33	21	-	-	PUNCT
ejpam-5704	33	22	point	point	NOUN
ejpam-5704	33	23	multistep	multistep	ADJ
ejpam-5704	33	24	block	block	NOUN
ejpam-5704	33	25	method	method	NOUN
ejpam-5704	33	26	with	with	ADP
ejpam-5704	33	27	constant	constant	ADJ
ejpam-5704	33	28	step	step	NOUN
ejpam-5704	33	29	-	-	PUNCT
ejpam-5704	33	30	size	size	NOUN
ejpam-5704	33	31	[	[	X
ejpam-5704	33	32	17	17	NUM
ejpam-5704	33	33	]	]	PUNCT
ejpam-5704	33	34	,	,	PUNCT
ejpam-5704	33	35	collocation	collocation	NOUN
ejpam-5704	33	36	and	and	CCONJ
ejpam-5704	33	37	continuous	continuous	ADJ
ejpam-5704	33	38	implicit	implicit	ADJ
ejpam-5704	33	39	runge	runge	NOUN
ejpam-5704	33	40	-	-	PUNCT
ejpam-5704	33	41	kutta	kutta	NOUN
ejpam-5704	33	42	methods	method	NOUN
ejpam-5704	33	43	[	[	X
ejpam-5704	33	44	18	18	NUM
ejpam-5704	33	45	]	]	PUNCT
ejpam-5704	33	46	,	,	PUNCT
ejpam-5704	33	47	spline	spline	NOUN
ejpam-5704	33	48	collocation	collocation	NOUN
ejpam-5704	33	49	method	method	NOUN
ejpam-5704	33	50	[	[	X
ejpam-5704	33	51	19	19	NUM
ejpam-5704	33	52	,	,	PUNCT
ejpam-5704	33	53	20	20	NUM
ejpam-5704	33	54	]	]	PUNCT
ejpam-5704	33	55	,	,	PUNCT
ejpam-5704	33	56	piecewise	piecewise	NOUN
ejpam-5704	33	57	collocation	collocation	NOUN
ejpam-5704	33	58	method	method	NOUN
ejpam-5704	33	59	[	[	X
ejpam-5704	33	60	21	21	NUM
ejpam-5704	33	61	]	]	PUNCT
ejpam-5704	33	62	,	,	PUNCT
ejpam-5704	33	63	and	and	CCONJ
ejpam-5704	33	64	linear	linear	ADJ
ejpam-5704	33	65	multistep	multistep	ADJ
ejpam-5704	33	66	methods	method	NOUN
ejpam-5704	33	67	[	[	X
ejpam-5704	33	68	22	22	NUM
ejpam-5704	33	69	]	]	PUNCT
ejpam-5704	33	70	.	.	PUNCT
ejpam-5704	34	1	also	also	ADV
ejpam-5704	34	2	,	,	PUNCT
ejpam-5704	34	3	onestep	onestep	NOUN
ejpam-5704	34	4	polynomial	polynomial	ADJ
ejpam-5704	34	5	collocation	collocation	NOUN
ejpam-5704	34	6	method	method	NOUN
ejpam-5704	34	7	[	[	X
ejpam-5704	34	8	1	1	X
ejpam-5704	34	9	]	]	PUNCT
ejpam-5704	34	10	has	have	AUX
ejpam-5704	34	11	been	be	AUX
ejpam-5704	34	12	applied	apply	VERB
ejpam-5704	34	13	to	to	PART
ejpam-5704	34	14	find	find	VERB
ejpam-5704	34	15	numerical	numerical	ADJ
ejpam-5704	34	16	solution	solution	NOUN
ejpam-5704	34	17	of	of	ADP
ejpam-5704	34	18	delay	delay	NOUN
ejpam-5704	34	19	ies	ie	NOUN
ejpam-5704	34	20	and	and	CCONJ
ejpam-5704	34	21	delay	delay	VERB
ejpam-5704	34	22	weakly	weakly	ADJ
ejpam-5704	34	23	singular	singular	ADJ
ejpam-5704	34	24	ies	ie	NOUN
ejpam-5704	34	25	.	.	PUNCT
ejpam-5704	35	1	in	in	ADP
ejpam-5704	35	2	[	[	X
ejpam-5704	35	3	23	23	NUM
ejpam-5704	35	4	]	]	PUNCT
ejpam-5704	35	5	,	,	PUNCT
ejpam-5704	35	6	a	a	DET
ejpam-5704	35	7	category	category	NOUN
ejpam-5704	35	8	of	of	ADP
ejpam-5704	35	9	volterra	volterra	PROPN
ejpam-5704	35	10	delay	delay	VERB
ejpam-5704	35	11	integral	integral	ADJ
ejpam-5704	35	12	equations	equation	NOUN
ejpam-5704	35	13	(	(	PUNCT
ejpam-5704	35	14	vdies	vdie	NOUN
ejpam-5704	35	15	)	)	PUNCT
ejpam-5704	35	16	involving	involve	VERB
ejpam-5704	35	17	noncompact	noncompact	NOUN
ejpam-5704	35	18	operators	operator	NOUN
ejpam-5704	35	19	is	be	AUX
ejpam-5704	35	20	estimated	estimate	VERB
ejpam-5704	35	21	using	use	VERB
ejpam-5704	35	22	collocation	collocation	NOUN
ejpam-5704	35	23	methods	method	NOUN
ejpam-5704	35	24	.	.	PUNCT
ejpam-5704	36	1	the	the	DET
ejpam-5704	36	2	study	study	NOUN
ejpam-5704	36	3	explores	explore	VERB
ejpam-5704	36	4	b.	b.	PROPN
ejpam-5704	36	5	h.	h.	PROPN
ejpam-5704	36	6	alrikabi	alrikabi	PROPN
ejpam-5704	36	7	,	,	PUNCT
ejpam-5704	36	8	p.	p.	PROPN
ejpam-5704	36	9	darania	darania	PROPN
ejpam-5704	36	10	,	,	PUNCT
ejpam-5704	36	11	s.pishbin	s.pishbin	PROPN
ejpam-5704	36	12	/	/	SYM
ejpam-5704	36	13	eur	eur	PROPN
ejpam-5704	36	14	.	.	PUNCT
ejpam-5704	37	1	j.	j.	PROPN
ejpam-5704	37	2	pure	pure	PROPN
ejpam-5704	37	3	appl	appl	PROPN
ejpam-5704	37	4	.	.	PROPN
ejpam-5704	37	5	math	math	PROPN
ejpam-5704	37	6	,	,	PUNCT
ejpam-5704	37	7	18	18	NUM
ejpam-5704	37	8	(	(	PUNCT
ejpam-5704	37	9	2	2	NUM
ejpam-5704	37	10	)	)	PUNCT
ejpam-5704	37	11	(	(	PUNCT
ejpam-5704	37	12	2025	2025	NUM
ejpam-5704	37	13	)	)	PUNCT
ejpam-5704	37	14	,	,	PUNCT
ejpam-5704	37	15	5704	5704	NUM
ejpam-5704	37	16	3	3	NUM
ejpam-5704	37	17	of	of	ADP
ejpam-5704	37	18	19	19	NUM
ejpam-5704	37	19	the	the	DET
ejpam-5704	37	20	characteristics	characteristic	NOUN
ejpam-5704	37	21	of	of	ADP
ejpam-5704	37	22	the	the	DET
ejpam-5704	37	23	associated	associated	ADJ
ejpam-5704	37	24	operators	operator	NOUN
ejpam-5704	37	25	and	and	CCONJ
ejpam-5704	37	26	delves	delf	NOUN
ejpam-5704	37	27	into	into	ADP
ejpam-5704	37	28	the	the	DET
ejpam-5704	37	29	discussions	discussion	NOUN
ejpam-5704	37	30	regarding	regard	VERB
ejpam-5704	37	31	the	the	DET
ejpam-5704	37	32	existence	existence	NOUN
ejpam-5704	37	33	,	,	PUNCT
ejpam-5704	37	34	uniqueness	uniqueness	NOUN
ejpam-5704	37	35	,	,	PUNCT
ejpam-5704	37	36	and	and	CCONJ
ejpam-5704	37	37	regularity	regularity	NOUN
ejpam-5704	37	38	of	of	ADP
ejpam-5704	37	39	the	the	DET
ejpam-5704	37	40	exact	exact	ADJ
ejpam-5704	37	41	solution	solution	NOUN
ejpam-5704	37	42	.	.	PUNCT
ejpam-5704	38	1	the	the	DET
ejpam-5704	38	2	paper	paper	NOUN
ejpam-5704	38	3	establishes	establish	VERB
ejpam-5704	38	4	the	the	DET
ejpam-5704	38	5	existence	existence	NOUN
ejpam-5704	38	6	and	and	CCONJ
ejpam-5704	38	7	uniqueness	uniqueness	NOUN
ejpam-5704	38	8	of	of	ADP
ejpam-5704	38	9	collocation	collocation	NOUN
ejpam-5704	38	10	solutions	solution	NOUN
ejpam-5704	38	11	,	,	PUNCT
ejpam-5704	38	12	specifically	specifically	ADV
ejpam-5704	38	13	under	under	ADP
ejpam-5704	38	14	two	two	NUM
ejpam-5704	38	15	distinct	distinct	ADJ
ejpam-5704	38	16	graded	grade	VERB
ejpam-5704	38	17	meshes	mesh	NOUN
ejpam-5704	38	18	.	.	PUNCT
ejpam-5704	39	1	additionally	additionally	ADV
ejpam-5704	39	2	,	,	PUNCT
ejpam-5704	39	3	the	the	DET
ejpam-5704	39	4	convergence	convergence	NOUN
ejpam-5704	39	5	conditions	condition	NOUN
ejpam-5704	39	6	and	and	CCONJ
ejpam-5704	39	7	order	order	NOUN
ejpam-5704	39	8	of	of	ADP
ejpam-5704	39	9	convergence	convergence	NOUN
ejpam-5704	39	10	are	be	AUX
ejpam-5704	39	11	presented	present	VERB
ejpam-5704	39	12	.	.	PUNCT
ejpam-5704	40	1	to	to	PART
ejpam-5704	40	2	validate	validate	VERB
ejpam-5704	40	3	the	the	DET
ejpam-5704	40	4	theoretical	theoretical	ADJ
ejpam-5704	40	5	orders	order	NOUN
ejpam-5704	40	6	of	of	ADP
ejpam-5704	40	7	convergence	convergence	NOUN
ejpam-5704	40	8	,	,	PUNCT
ejpam-5704	40	9	numerical	numerical	ADJ
ejpam-5704	40	10	examples	example	NOUN
ejpam-5704	40	11	are	be	AUX
ejpam-5704	40	12	provided	provide	VERB
ejpam-5704	40	13	.	.	PUNCT
ejpam-5704	41	1	the	the	DET
ejpam-5704	41	2	paper	paper	NOUN
ejpam-5704	41	3	is	be	AUX
ejpam-5704	41	4	organized	organize	VERB
ejpam-5704	41	5	as	as	SCONJ
ejpam-5704	41	6	follows	follow	VERB
ejpam-5704	41	7	:	:	PUNCT
ejpam-5704	41	8	section	section	NOUN
ejpam-5704	41	9	2	2	NUM
ejpam-5704	41	10	is	be	AUX
ejpam-5704	41	11	dedicated	dedicate	VERB
ejpam-5704	41	12	to	to	ADP
ejpam-5704	41	13	proposing	propose	VERB
ejpam-5704	41	14	some	some	DET
ejpam-5704	41	15	preliminaries	preliminary	NOUN
ejpam-5704	41	16	about	about	ADP
ejpam-5704	41	17	the	the	DET
ejpam-5704	41	18	product	product	NOUN
ejpam-5704	41	19	rules	rule	NOUN
ejpam-5704	41	20	using	use	VERB
ejpam-5704	41	21	the	the	DET
ejpam-5704	41	22	roots	root	NOUN
ejpam-5704	41	23	of	of	ADP
ejpam-5704	41	24	certain	certain	ADJ
ejpam-5704	41	25	types	type	NOUN
ejpam-5704	41	26	of	of	ADP
ejpam-5704	41	27	generalized	generalized	ADJ
ejpam-5704	41	28	jacobi	jacobi	PROPN
ejpam-5704	41	29	orthogonal	orthogonal	ADJ
ejpam-5704	41	30	polynomials	polynomial	NOUN
ejpam-5704	41	31	and	and	CCONJ
ejpam-5704	41	32	specific	specific	ADJ
ejpam-5704	41	33	properties	property	NOUN
ejpam-5704	41	34	of	of	ADP
ejpam-5704	41	35	orthogonal	orthogonal	ADJ
ejpam-5704	41	36	polynomials	polynomial	NOUN
ejpam-5704	41	37	.	.	PUNCT
ejpam-5704	42	1	in	in	ADP
ejpam-5704	42	2	section	section	NOUN
ejpam-5704	42	3	3	3	NUM
ejpam-5704	42	4	,	,	PUNCT
ejpam-5704	42	5	we	we	PRON
ejpam-5704	42	6	construct	construct	VERB
ejpam-5704	42	7	and	and	CCONJ
ejpam-5704	42	8	analyze	analyze	VERB
ejpam-5704	42	9	the	the	DET
ejpam-5704	42	10	product	product	NOUN
ejpam-5704	42	11	integration	integration	NOUN
ejpam-5704	42	12	method	method	NOUN
ejpam-5704	42	13	to	to	PART
ejpam-5704	42	14	solve	solve	VERB
ejpam-5704	42	15	the	the	DET
ejpam-5704	42	16	equation	equation	NOUN
ejpam-5704	42	17	(	(	PUNCT
ejpam-5704	42	18	1	1	X
ejpam-5704	42	19	)	)	PUNCT
ejpam-5704	42	20	numerically	numerically	ADV
ejpam-5704	42	21	and	and	CCONJ
ejpam-5704	42	22	in	in	ADP
ejpam-5704	42	23	section	section	NOUN
ejpam-5704	42	24	4	4	NUM
ejpam-5704	42	25	convergence	convergence	NOUN
ejpam-5704	42	26	of	of	ADP
ejpam-5704	42	27	numerical	numerical	ADJ
ejpam-5704	42	28	solutions	solution	NOUN
ejpam-5704	42	29	is	be	AUX
ejpam-5704	42	30	investigated	investigate	VERB
ejpam-5704	42	31	.	.	PUNCT
ejpam-5704	43	1	this	this	PRON
ejpam-5704	43	2	is	be	AUX
ejpam-5704	43	3	succeeded	succeed	VERB
ejpam-5704	43	4	by	by	ADP
ejpam-5704	43	5	the	the	DET
ejpam-5704	43	6	discussion	discussion	NOUN
ejpam-5704	43	7	of	of	ADP
ejpam-5704	43	8	three	three	NUM
ejpam-5704	43	9	test	test	NOUN
ejpam-5704	43	10	problems	problem	NOUN
ejpam-5704	43	11	in	in	ADP
ejpam-5704	43	12	section	section	NOUN
ejpam-5704	43	13	5	5	NUM
ejpam-5704	43	14	to	to	PART
ejpam-5704	43	15	validate	validate	VERB
ejpam-5704	43	16	the	the	DET
ejpam-5704	43	17	theoretical	theoretical	ADJ
ejpam-5704	43	18	results	result	NOUN
ejpam-5704	43	19	.	.	PUNCT
ejpam-5704	44	1	finally	finally	ADV
ejpam-5704	44	2	,	,	PUNCT
ejpam-5704	44	3	in	in	ADP
ejpam-5704	44	4	section	section	NOUN
ejpam-5704	44	5	6	6	NUM
ejpam-5704	44	6	,	,	PUNCT
ejpam-5704	44	7	we	we	PRON
ejpam-5704	44	8	conclude	conclude	VERB
ejpam-5704	44	9	the	the	DET
ejpam-5704	44	10	paper	paper	NOUN
ejpam-5704	44	11	and	and	CCONJ
ejpam-5704	44	12	suggest	suggest	VERB
ejpam-5704	44	13	potential	potential	ADJ
ejpam-5704	44	14	future	future	ADJ
ejpam-5704	44	15	avenues	avenue	NOUN
ejpam-5704	44	16	for	for	ADP
ejpam-5704	44	17	research	research	NOUN
ejpam-5704	44	18	,	,	PUNCT
ejpam-5704	44	19	which	which	PRON
ejpam-5704	44	20	are	be	AUX
ejpam-5704	44	21	currently	currently	ADV
ejpam-5704	44	22	less	less	ADV
ejpam-5704	44	23	explored	explore	VERB
ejpam-5704	44	24	.	.	PUNCT
ejpam-5704	45	1	2	2	X
ejpam-5704	45	2	.	.	X
ejpam-5704	45	3	preliminaries	preliminary	NOUN
ejpam-5704	45	4	consider	consider	VERB
ejpam-5704	45	5	the	the	DET
ejpam-5704	45	6	product	product	NOUN
ejpam-5704	45	7	rules∫	rules∫	VERB
ejpam-5704	45	8	1	1	NUM
ejpam-5704	45	9	0	0	NUM
ejpam-5704	45	10	p.	p.	NOUN
ejpam-5704	45	11	,h(t	,h(t	PUNCT
ejpam-5704	45	12	,	,	PUNCT
ejpam-5704	45	13	w)g(w)dw	w)g(w)dw	PROPN
ejpam-5704	46	1	≈	≈	PROPN
ejpam-5704	46	2	m∑	m∑	INTJ
ejpam-5704	46	3	i=1	i=1	PROPN
ejpam-5704	46	4	wm	wm	PROPN
ejpam-5704	46	5	,	,	PUNCT
ejpam-5704	46	6	i(t)g(tm	i(t)g(tm	PROPN
ejpam-5704	46	7	,	,	PUNCT
ejpam-5704	46	8	i	i	NOUN
ejpam-5704	46	9	)	)	PUNCT
ejpam-5704	46	10	=	=	NOUN
ejpam-5704	46	11	in	in	ADP
ejpam-5704	46	12	(	(	PUNCT
ejpam-5704	46	13	g	g	PROPN
ejpam-5704	46	14	,	,	PUNCT
ejpam-5704	46	15	t	t	PROPN
ejpam-5704	46	16	)	)	PUNCT
ejpam-5704	46	17	,	,	PUNCT
ejpam-5704	46	18	(	(	PUNCT
ejpam-5704	46	19	5	5	X
ejpam-5704	46	20	)	)	PUNCT
ejpam-5704	46	21	derived	derive	VERB
ejpam-5704	46	22	from	from	ADP
ejpam-5704	46	23	the	the	DET
ejpam-5704	46	24	roots	root	NOUN
ejpam-5704	46	25	of	of	ADP
ejpam-5704	46	26	particular	particular	ADJ
ejpam-5704	46	27	classes	class	NOUN
ejpam-5704	46	28	of	of	ADP
ejpam-5704	46	29	generalized	generalized	ADJ
ejpam-5704	46	30	jacobi	jacobi	PROPN
ejpam-5704	46	31	orthogonal	orthogonal	ADJ
ejpam-5704	46	32	polynomials	polynomial	NOUN
ejpam-5704	46	33	.	.	PUNCT
ejpam-5704	47	1	we	we	PRON
ejpam-5704	47	2	can	can	AUX
ejpam-5704	47	3	consider	consider	VERB
ejpam-5704	47	4	the	the	DET
ejpam-5704	47	5	error	error	NOUN
ejpam-5704	47	6	term	term	NOUN
ejpam-5704	47	7	of	of	ADP
ejpam-5704	47	8	(	(	PUNCT
ejpam-5704	47	9	5	5	NUM
ejpam-5704	47	10	)	)	PUNCT
ejpam-5704	47	11	as	as	ADP
ejpam-5704	47	12	rn	rn	PROPN
ejpam-5704	47	13	(	(	PUNCT
ejpam-5704	47	14	g	g	PROPN
ejpam-5704	47	15	;	;	PUNCT
ejpam-5704	47	16	t	t	PROPN
ejpam-5704	47	17	)	)	PUNCT
ejpam-5704	47	18	=	=	SYM
ejpam-5704	48	1	∫	∫	PROPN
ejpam-5704	48	2	1	1	NUM
ejpam-5704	48	3	0	0	NUM
ejpam-5704	49	1	p.	p.	NOUN
ejpam-5704	49	2	,h(t	,h(t	PUNCT
ejpam-5704	49	3	,	,	PUNCT
ejpam-5704	49	4	w)g(w)dw	w)g(w)dw	NOUN
ejpam-5704	49	5	−	−	PROPN
ejpam-5704	49	6	in	in	ADP
ejpam-5704	49	7	(	(	PUNCT
ejpam-5704	49	8	g	g	PROPN
ejpam-5704	49	9	,	,	PUNCT
ejpam-5704	49	10	t	t	PROPN
ejpam-5704	49	11	)	)	PUNCT
ejpam-5704	49	12	.	.	PUNCT
ejpam-5704	50	1	(	(	PUNCT
ejpam-5704	50	2	6	6	NUM
ejpam-5704	50	3	)	)	PUNCT
ejpam-5704	50	4	from[24	from[24	NOUN
ejpam-5704	50	5	,	,	PUNCT
ejpam-5704	50	6	25	25	NUM
ejpam-5704	50	7	]	]	PUNCT
ejpam-5704	50	8	,	,	PUNCT
ejpam-5704	50	9	we	we	PRON
ejpam-5704	50	10	have	have	VERB
ejpam-5704	50	11	rn	rn	PROPN
ejpam-5704	50	12	(	(	PUNCT
ejpam-5704	50	13	g	g	PROPN
ejpam-5704	50	14	,	,	PUNCT
ejpam-5704	50	15	t	t	PROPN
ejpam-5704	50	16	)	)	PUNCT
ejpam-5704	50	17	=	=	SYM
ejpam-5704	50	18	o(n−m	o(n−m	PROPN
ejpam-5704	50	19	)	)	PUNCT
ejpam-5704	50	20	when	when	SCONJ
ejpam-5704	50	21	g	g	PROPN
ejpam-5704	50	22	∈	∈	PROPN
ejpam-5704	50	23	cm[0	cm[0	PROPN
ejpam-5704	50	24	,	,	PUNCT
ejpam-5704	50	25	1	1	NUM
ejpam-5704	50	26	]	]	PUNCT
ejpam-5704	50	27	.	.	PUNCT
ejpam-5704	51	1	if	if	SCONJ
ejpam-5704	51	2	g	g	PROPN
ejpam-5704	51	3	is	be	AUX
ejpam-5704	51	4	a	a	DET
ejpam-5704	51	5	polynomial	polynomial	NOUN
ejpam-5704	51	6	of	of	ADP
ejpam-5704	51	7	degree	degree	NOUN
ejpam-5704	51	8	n	n	NOUN
ejpam-5704	51	9	,	,	PUNCT
ejpam-5704	51	10	then	then	ADV
ejpam-5704	51	11	rn	rn	PROPN
ejpam-5704	51	12	(	(	PUNCT
ejpam-5704	51	13	g	g	PROPN
ejpam-5704	51	14	,	,	PUNCT
ejpam-5704	51	15	t	t	PROPN
ejpam-5704	51	16	)	)	PUNCT
ejpam-5704	51	17	=	=	SYM
ejpam-5704	51	18	0	0	NUM
ejpam-5704	51	19	,	,	PUNCT
ejpam-5704	51	20	so	so	ADV
ejpam-5704	51	21	from	from	ADP
ejpam-5704	51	22	[	[	X
ejpam-5704	51	23	24	24	NUM
ejpam-5704	51	24	]	]	PUNCT
ejpam-5704	51	25	,	,	PUNCT
ejpam-5704	51	26	for	for	ADP
ejpam-5704	51	27	all	all	DET
ejpam-5704	51	28	polynomial	polynomial	ADJ
ejpam-5704	51	29	pn	pn	PROPN
ejpam-5704	51	30	of	of	ADP
ejpam-5704	51	31	degree	degree	NOUN
ejpam-5704	51	32	n	n	NOUN
ejpam-5704	51	33	,	,	PUNCT
ejpam-5704	51	34	we	we	PRON
ejpam-5704	51	35	have	have	VERB
ejpam-5704	51	36	rn	rn	PROPN
ejpam-5704	51	37	(	(	PUNCT
ejpam-5704	51	38	g	g	PROPN
ejpam-5704	51	39	,	,	PUNCT
ejpam-5704	51	40	t	t	PROPN
ejpam-5704	51	41	)	)	PUNCT
ejpam-5704	51	42	=	=	SYM
ejpam-5704	52	1	∫	∫	PROPN
ejpam-5704	52	2	1	1	NUM
ejpam-5704	52	3	0	0	NUM
ejpam-5704	53	1	p.	p.	NOUN
ejpam-5704	53	2	,h(t	,h(t	PUNCT
ejpam-5704	53	3	,	,	PUNCT
ejpam-5704	53	4	w)(g(w)−	w)(g(w)−	PROPN
ejpam-5704	53	5	pn	pn	X
ejpam-5704	53	6	(	(	PUNCT
ejpam-5704	53	7	w))dw	w))dw	NOUN
ejpam-5704	54	1	−	−	PROPN
ejpam-5704	54	2	∫	∫	PROPN
ejpam-5704	54	3	1	1	NUM
ejpam-5704	54	4	0	0	NUM
ejpam-5704	54	5	p.	p.	NOUN
ejpam-5704	54	6	,h(t	,h(t	PUNCT
ejpam-5704	54	7	,	,	PUNCT
ejpam-5704	54	8	w)ωn	w)ωn	PROPN
ejpam-5704	54	9	(	(	PUNCT
ejpam-5704	54	10	g−	g−	PROPN
ejpam-5704	54	11	pn	pn	PROPN
ejpam-5704	54	12	,	,	PUNCT
ejpam-5704	54	13	w)dw	w)dw	PROPN
ejpam-5704	54	14	,	,	PUNCT
ejpam-5704	54	15	where	where	SCONJ
ejpam-5704	54	16	ωn	ωn	X
ejpam-5704	54	17	(	(	PUNCT
ejpam-5704	54	18	g	g	PROPN
ejpam-5704	54	19	,	,	PUNCT
ejpam-5704	54	20	t	t	PROPN
ejpam-5704	54	21	)	)	PUNCT
ejpam-5704	54	22	represents	represent	VERB
ejpam-5704	54	23	the	the	DET
ejpam-5704	54	24	lagrange	lagrange	PROPN
ejpam-5704	54	25	interpolation	interpolation	NOUN
ejpam-5704	54	26	polynomial	polynomial	NOUN
ejpam-5704	54	27	that	that	PRON
ejpam-5704	54	28	interpolates	interpolate	VERB
ejpam-5704	54	29	g	g	NOUN
ejpam-5704	54	30	at	at	ADP
ejpam-5704	54	31	the	the	DET
ejpam-5704	54	32	points	point	NOUN
ejpam-5704	54	33	{	{	PUNCT
ejpam-5704	54	34	ti}ni=0	ti}ni=0	PROPN
ejpam-5704	54	35	,	,	PUNCT
ejpam-5704	54	36	the	the	DET
ejpam-5704	54	37	expression	expression	NOUN
ejpam-5704	54	38	is	be	AUX
ejpam-5704	54	39	defined	define	VERB
ejpam-5704	54	40	as	as	SCONJ
ejpam-5704	54	41	follows	follow	VERB
ejpam-5704	54	42	:	:	PUNCT
ejpam-5704	54	43	ωn	ωn	ADP
ejpam-5704	54	44	(	(	PUNCT
ejpam-5704	54	45	g	g	PROPN
ejpam-5704	54	46	,	,	PUNCT
ejpam-5704	54	47	t	t	PROPN
ejpam-5704	54	48	)	)	PUNCT
ejpam-5704	54	49	=	=	SYM
ejpam-5704	54	50	n∑	n∑	PROPN
ejpam-5704	54	51	i=0	i=0	PROPN
ejpam-5704	54	52	g(ti)ln	g(ti)ln	NOUN
ejpam-5704	54	53	,	,	PUNCT
ejpam-5704	54	54	j(t	j(t	PROPN
ejpam-5704	54	55	)	)	PUNCT
ejpam-5704	54	56	,	,	PUNCT
ejpam-5704	54	57	where	where	SCONJ
ejpam-5704	54	58	ln	ln	ADJ
ejpam-5704	54	59	,	,	PUNCT
ejpam-5704	54	60	j(t	j(t	PROPN
ejpam-5704	54	61	)	)	PUNCT
ejpam-5704	54	62	=	=	PUNCT
ejpam-5704	54	63	n∏	n∏	PROPN
ejpam-5704	54	64	i=0	i=0	PROPN
ejpam-5704	54	65	i	i	PRON
ejpam-5704	54	66	̸=j	̸=j	VERB
ejpam-5704	54	67	t−	t−	PRON
ejpam-5704	54	68	ti	ti	NOUN
ejpam-5704	54	69	tj	tj	NOUN
ejpam-5704	54	70	−	−	PROPN
ejpam-5704	54	71	ti	ti	PROPN
ejpam-5704	54	72	,	,	PUNCT
ejpam-5704	54	73	j	j	PROPN
ejpam-5704	54	74	=	=	SYM
ejpam-5704	54	75	0	0	NUM
ejpam-5704	54	76	,	,	PUNCT
ejpam-5704	54	77	1	1	NUM
ejpam-5704	54	78	,	,	PUNCT
ejpam-5704	54	79	...	...	PUNCT
ejpam-5704	54	80	,	,	PUNCT
ejpam-5704	54	81	n.	n.	NOUN
ejpam-5704	54	82	(	(	PUNCT
ejpam-5704	54	83	7	7	NUM
ejpam-5704	54	84	)	)	PUNCT
ejpam-5704	54	85	b.	b.	PROPN
ejpam-5704	54	86	h.	h.	PROPN
ejpam-5704	54	87	alrikabi	alrikabi	PROPN
ejpam-5704	54	88	,	,	PUNCT
ejpam-5704	54	89	p.	p.	PROPN
ejpam-5704	54	90	darania	darania	PROPN
ejpam-5704	54	91	,	,	PUNCT
ejpam-5704	54	92	s.pishbin	s.pishbin	PROPN
ejpam-5704	54	93	/	/	SYM
ejpam-5704	54	94	eur	eur	PROPN
ejpam-5704	54	95	.	.	PUNCT
ejpam-5704	55	1	j.	j.	PROPN
ejpam-5704	55	2	pure	pure	PROPN
ejpam-5704	55	3	appl	appl	PROPN
ejpam-5704	55	4	.	.	PROPN
ejpam-5704	55	5	math	math	PROPN
ejpam-5704	55	6	,	,	PUNCT
ejpam-5704	55	7	18	18	NUM
ejpam-5704	55	8	(	(	PUNCT
ejpam-5704	55	9	2	2	NUM
ejpam-5704	55	10	)	)	PUNCT
ejpam-5704	55	11	(	(	PUNCT
ejpam-5704	55	12	2025	2025	NUM
ejpam-5704	55	13	)	)	PUNCT
ejpam-5704	55	14	,	,	PUNCT
ejpam-5704	55	15	5704	5704	NUM
ejpam-5704	55	16	4	4	NUM
ejpam-5704	55	17	of	of	ADP
ejpam-5704	55	18	19	19	NUM
ejpam-5704	55	19	with	with	ADP
ejpam-5704	55	20	a	a	DET
ejpam-5704	55	21	careful	careful	ADJ
ejpam-5704	55	22	selection	selection	NOUN
ejpam-5704	55	23	of	of	ADP
ejpam-5704	55	24	the	the	DET
ejpam-5704	55	25	polynomial	polynomial	ADJ
ejpam-5704	55	26	sequence	sequence	NOUN
ejpam-5704	55	27	{	{	PUNCT
ejpam-5704	55	28	ωn	ωn	PROPN
ejpam-5704	55	29	}	}	PUNCT
ejpam-5704	55	30	,	,	PUNCT
ejpam-5704	55	31	it	it	PRON
ejpam-5704	55	32	becomes	become	VERB
ejpam-5704	55	33	possible	possible	ADJ
ejpam-5704	55	34	to	to	PART
ejpam-5704	55	35	establish	establish	VERB
ejpam-5704	55	36	upper	upper	ADJ
ejpam-5704	55	37	bounds	bound	NOUN
ejpam-5704	55	38	as	as	ADP
ejpam-5704	55	39	:	:	PUNCT
ejpam-5704	55	40	r1,n	r1,n	PROPN
ejpam-5704	55	41	(	(	PUNCT
ejpam-5704	55	42	g	g	PROPN
ejpam-5704	55	43	,	,	PUNCT
ejpam-5704	55	44	t	t	PROPN
ejpam-5704	55	45	)	)	PUNCT
ejpam-5704	55	46	=	=	SYM
ejpam-5704	56	1	∫	∫	PROPN
ejpam-5704	56	2	1	1	NUM
ejpam-5704	56	3	0	0	NUM
ejpam-5704	57	1	|	|	ADV
ejpam-5704	57	2	p.	p.	NOUN
ejpam-5704	57	3	,h(t	,h(t	PUNCT
ejpam-5704	57	4	,	,	PUNCT
ejpam-5704	57	5	w	w	PROPN
ejpam-5704	57	6	)	)	PUNCT
ejpam-5704	57	7	||	||	PUNCT
ejpam-5704	58	1	g(w)−	g(w)−	PRON
ejpam-5704	58	2	pn	pn	X
ejpam-5704	58	3	(	(	PUNCT
ejpam-5704	58	4	w	w	NOUN
ejpam-5704	58	5	)	)	PUNCT
ejpam-5704	58	6	|	|	ADV
ejpam-5704	58	7	dw	dw	PROPN
ejpam-5704	58	8	,	,	PUNCT
ejpam-5704	58	9	r2,n	r2,n	PROPN
ejpam-5704	58	10	(	(	PUNCT
ejpam-5704	58	11	g	g	PROPN
ejpam-5704	58	12	,	,	PUNCT
ejpam-5704	58	13	t	t	PROPN
ejpam-5704	58	14	)	)	PUNCT
ejpam-5704	58	15	=	=	SYM
ejpam-5704	59	1	∫	∫	PROPN
ejpam-5704	59	2	1	1	NUM
ejpam-5704	59	3	0	0	NUM
ejpam-5704	60	1	|	|	ADV
ejpam-5704	60	2	p.	p.	NOUN
ejpam-5704	60	3	,h(t	,h(t	PUNCT
ejpam-5704	60	4	,	,	PUNCT
ejpam-5704	60	5	w	w	PROPN
ejpam-5704	60	6	)	)	PUNCT
ejpam-5704	60	7	||	||	PUNCT
ejpam-5704	61	1	ωn	ωn	X
ejpam-5704	61	2	(	(	PUNCT
ejpam-5704	61	3	g−	g−	PROPN
ejpam-5704	61	4	pn	pn	PROPN
ejpam-5704	61	5	,	,	PUNCT
ejpam-5704	61	6	w	w	PROPN
ejpam-5704	61	7	)	)	PUNCT
ejpam-5704	61	8	|	|	ADV
ejpam-5704	61	9	dw	dw	NOUN
ejpam-5704	61	10	,	,	PUNCT
ejpam-5704	61	11	where	where	SCONJ
ejpam-5704	61	12	p.	p.	PROPN
ejpam-5704	61	13	,h(t	,h(t	PUNCT
ejpam-5704	61	14	,	,	PUNCT
ejpam-5704	61	15	w	w	PROPN
ejpam-5704	61	16	)	)	PUNCT
ejpam-5704	61	17	is	be	AUX
ejpam-5704	61	18	defined	define	VERB
ejpam-5704	61	19	in	in	ADP
ejpam-5704	61	20	(	(	PUNCT
ejpam-5704	61	21	4	4	NUM
ejpam-5704	61	22	)	)	PUNCT
ejpam-5704	61	23	.	.	PUNCT
ejpam-5704	62	1	theorem	theorem	VERB
ejpam-5704	62	2	2.1	2.1	NUM
ejpam-5704	62	3	.	.	PUNCT
ejpam-5704	63	1	(	(	PUNCT
ejpam-5704	63	2	from	from	ADP
ejpam-5704	63	3	[	[	X
ejpam-5704	63	4	8	8	NUM
ejpam-5704	63	5	]	]	PUNCT
ejpam-5704	63	6	)	)	PUNCT
ejpam-5704	63	7	assume	assume	VERB
ejpam-5704	63	8	that	that	SCONJ
ejpam-5704	63	9	g(t	g(t	PROPN
ejpam-5704	63	10	)	)	PUNCT
ejpam-5704	64	1	=	=	PUNCT
ejpam-5704	64	2	(	(	PUNCT
ejpam-5704	64	3	1−	1−	NUM
ejpam-5704	64	4	t)µ	t)µ	NOUN
ejpam-5704	64	5	where	where	SCONJ
ejpam-5704	64	6	µ	µ	X
ejpam-5704	64	7	>	>	X
ejpam-5704	64	8	−1	−1	NOUN
ejpam-5704	64	9	is	be	AUX
ejpam-5704	64	10	not	not	PART
ejpam-5704	64	11	an	an	DET
ejpam-5704	64	12	integer	integer	NOUN
ejpam-5704	64	13	and	and	CCONJ
ejpam-5704	64	14	τ	τ	PROPN
ejpam-5704	64	15	>	>	X
ejpam-5704	64	16	−1	−1	NOUN
ejpam-5704	64	17	,	,	PUNCT
ejpam-5704	64	18	with	with	ADP
ejpam-5704	64	19	µ+	µ+	X
ejpam-5704	64	20	τ	τ	PROPN
ejpam-5704	64	21	>	>	X
ejpam-5704	64	22	−1	−1	NOUN
ejpam-5704	64	23	,	,	PUNCT
ejpam-5704	64	24	then∫	then∫	NOUN
ejpam-5704	64	25	1	1	NUM
ejpam-5704	64	26	0	0	NUM
ejpam-5704	65	1	|	|	ADV
ejpam-5704	65	2	g(t)−	g(t)−	PROPN
ejpam-5704	65	3	ωn	ωn	ADP
ejpam-5704	65	4	(	(	PUNCT
ejpam-5704	65	5	g	g	PROPN
ejpam-5704	65	6	,	,	PUNCT
ejpam-5704	65	7	t	t	PROPN
ejpam-5704	65	8	)	)	PUNCT
ejpam-5704	65	9	||	||	NOUN
ejpam-5704	66	1	t−	t−	PROPN
ejpam-5704	66	2	w	w	PROPN
ejpam-5704	66	3	|τ	|τ	ADJ
ejpam-5704	66	4	dt	dt	X
ejpam-5704	66	5	≤	≤	PROPN
ejpam-5704	66	6	c	c	X
ejpam-5704	66	7	{	{	PUNCT
ejpam-5704	66	8	n−2−2µ−2τ	n−2−2µ−2τ	PROPN
ejpam-5704	66	9	logn	logn	VERB
ejpam-5704	66	10	,	,	PUNCT
ejpam-5704	66	11	|	|	ADV
ejpam-5704	66	12	w	w	NOUN
ejpam-5704	66	13	|≤	|≤	PROPN
ejpam-5704	66	14	1	1	NUM
ejpam-5704	66	15	,	,	PUNCT
ejpam-5704	66	16	τ	τ	X
ejpam-5704	66	17	<	<	X
ejpam-5704	66	18	0	0	PROPN
ejpam-5704	66	19	,	,	PUNCT
ejpam-5704	66	20	n−2−2µ	n−2−2µ	PROPN
ejpam-5704	66	21	logn	logn	VERB
ejpam-5704	66	22	,	,	PUNCT
ejpam-5704	67	1	|	|	ADV
ejpam-5704	67	2	w	w	NOUN
ejpam-5704	67	3	|≤	|≤	PROPN
ejpam-5704	67	4	1	1	NUM
ejpam-5704	67	5	,	,	PUNCT
ejpam-5704	67	6	τ	τ	PROPN
ejpam-5704	67	7	≥	≥	NOUN
ejpam-5704	67	8	0	0	NUM
ejpam-5704	67	9	,	,	PUNCT
ejpam-5704	67	10	(	(	PUNCT
ejpam-5704	67	11	8)	8)	NUM
ejpam-5704	67	12	such	such	ADJ
ejpam-5704	67	13	that	that	SCONJ
ejpam-5704	67	14	c	c	PROPN
ejpam-5704	67	15	represents	represent	VERB
ejpam-5704	67	16	a	a	DET
ejpam-5704	67	17	constant	constant	ADJ
ejpam-5704	67	18	that	that	PRON
ejpam-5704	67	19	remains	remain	VERB
ejpam-5704	67	20	unaffected	unaffected	ADJ
ejpam-5704	67	21	by	by	ADP
ejpam-5704	67	22	both	both	DET
ejpam-5704	67	23	w	w	NOUN
ejpam-5704	67	24	and	and	CCONJ
ejpam-5704	67	25	n	n	ADV
ejpam-5704	67	26	.	.	PUNCT
ejpam-5704	68	1	corollary	corollary	ADJ
ejpam-5704	68	2	2.2	2.2	NUM
ejpam-5704	68	3	.	.	PUNCT
ejpam-5704	69	1	(	(	PUNCT
ejpam-5704	69	2	from	from	ADP
ejpam-5704	69	3	[	[	X
ejpam-5704	69	4	8	8	NUM
ejpam-5704	69	5	]	]	PUNCT
ejpam-5704	69	6	)	)	PUNCT
ejpam-5704	69	7	assume	assume	VERB
ejpam-5704	69	8	that	that	SCONJ
ejpam-5704	69	9	g(t	g(t	PROPN
ejpam-5704	69	10	)	)	PUNCT
ejpam-5704	70	1	=	=	PUNCT
ejpam-5704	70	2	(	(	PUNCT
ejpam-5704	70	3	1−	1−	NUM
ejpam-5704	70	4	t)µ	t)µ	NOUN
ejpam-5704	70	5	where	where	SCONJ
ejpam-5704	70	6	µ	µ	X
ejpam-5704	70	7	>	>	X
ejpam-5704	70	8	0	0	NUM
ejpam-5704	70	9	,	,	PUNCT
ejpam-5704	70	10	is	be	AUX
ejpam-5704	70	11	not	not	PART
ejpam-5704	70	12	an	an	DET
ejpam-5704	70	13	integer	integer	NOUN
ejpam-5704	70	14	,	,	PUNCT
ejpam-5704	70	15	then	then	ADV
ejpam-5704	70	16	we	we	PRON
ejpam-5704	70	17	have∫	have∫	VERB
ejpam-5704	70	18	1	1	NUM
ejpam-5704	70	19	0	0	NUM
ejpam-5704	71	1	|	|	ADV
ejpam-5704	71	2	g(t)−	g(t)−	PROPN
ejpam-5704	71	3	ωn	ωn	ADP
ejpam-5704	71	4	(	(	PUNCT
ejpam-5704	71	5	g	g	PROPN
ejpam-5704	71	6	,	,	PUNCT
ejpam-5704	71	7	t	t	PROPN
ejpam-5704	71	8	)	)	PUNCT
ejpam-5704	71	9	||	||	NOUN
ejpam-5704	71	10	log	log	NOUN
ejpam-5704	72	1	|	|	ADV
ejpam-5704	72	2	t−	t−	PROPN
ejpam-5704	72	3	w	w	PROPN
ejpam-5704	72	4	||	||	NOUN
ejpam-5704	73	1	dt	dt	X
ejpam-5704	74	1	≤	≤	NUM
ejpam-5704	74	2	c	c	NOUN
ejpam-5704	74	3			PUNCT
ejpam-5704	74	4	n−2−2µ	n−2−2µ	PROPN
ejpam-5704	74	5	log2n	log2n	PROPN
ejpam-5704	74	6	,	,	PUNCT
ejpam-5704	74	7	|	|	ADV
ejpam-5704	74	8	w	w	NOUN
ejpam-5704	74	9	|≤	|≤	PROPN
ejpam-5704	74	10	1	1	NUM
ejpam-5704	74	11	,	,	PUNCT
ejpam-5704	74	12	n−2−2µ	n−2−2µ	PROPN
ejpam-5704	74	13	logn	logn	NOUN
ejpam-5704	74	14	,	,	PUNCT
ejpam-5704	74	15	0	0	NUM
ejpam-5704	74	16	≤	≤	NUM
ejpam-5704	75	1	w	w	ADP
ejpam-5704	75	2	<	<	X
ejpam-5704	75	3	1	1	NUM
ejpam-5704	75	4	,	,	PUNCT
ejpam-5704	75	5	(	(	PUNCT
ejpam-5704	75	6	9	9	X
ejpam-5704	75	7	)	)	PUNCT
ejpam-5704	75	8	where	where	SCONJ
ejpam-5704	75	9	c	c	NOUN
ejpam-5704	75	10	represents	represent	VERB
ejpam-5704	75	11	a	a	DET
ejpam-5704	75	12	constant	constant	ADJ
ejpam-5704	75	13	that	that	PRON
ejpam-5704	75	14	remains	remain	VERB
ejpam-5704	75	15	unaffected	unaffected	ADJ
ejpam-5704	75	16	by	by	ADP
ejpam-5704	75	17	both	both	DET
ejpam-5704	75	18	w	w	NOUN
ejpam-5704	75	19	and	and	CCONJ
ejpam-5704	75	20	n	n	NOUN
ejpam-5704	75	21	.	.	PUNCT
ejpam-5704	76	1	2.1	2.1	NUM
ejpam-5704	76	2	.	.	PUNCT
ejpam-5704	76	3	orthogonal	orthogonal	ADJ
ejpam-5704	76	4	polynomials	polynomial	NOUN
ejpam-5704	76	5	chelyshkov	chelyshkov	NOUN
ejpam-5704	76	6	has	have	AUX
ejpam-5704	76	7	introduced	introduce	VERB
ejpam-5704	76	8	polynomials	polynomial	NOUN
ejpam-5704	76	9	in	in	ADP
ejpam-5704	76	10	[	[	X
ejpam-5704	76	11	26	26	NUM
ejpam-5704	76	12	]	]	X
ejpam-5704	76	13	,	,	PUNCT
ejpam-5704	76	14	specifically	specifically	ADV
ejpam-5704	76	15	designed	design	VERB
ejpam-5704	76	16	to	to	PART
ejpam-5704	76	17	be	be	AUX
ejpam-5704	76	18	orthogonal	orthogonal	ADJ
ejpam-5704	76	19	over	over	ADP
ejpam-5704	76	20	the	the	DET
ejpam-5704	76	21	interval	interval	NOUN
ejpam-5704	76	22	[	[	X
ejpam-5704	76	23	0	0	NUM
ejpam-5704	76	24	,	,	PUNCT
ejpam-5704	76	25	1	1	NUM
ejpam-5704	76	26	]	]	PUNCT
ejpam-5704	76	27	which	which	PRON
ejpam-5704	76	28	the	the	DET
ejpam-5704	76	29	rodrigues	rodrigues	PROPN
ejpam-5704	76	30	type	type	NOUN
ejpam-5704	76	31	representation	representation	NOUN
ejpam-5704	76	32	as	as	ADP
ejpam-5704	76	33	pn	pn	PROPN
ejpam-5704	76	34	,	,	PUNCT
ejpam-5704	76	35	l(t	l(t	PROPN
ejpam-5704	76	36	)	)	PUNCT
ejpam-5704	76	37	=	=	SYM
ejpam-5704	76	38	1	1	NUM
ejpam-5704	76	39	(	(	PUNCT
ejpam-5704	76	40	n−	n−	NOUN
ejpam-5704	76	41	l	l	NOUN
ejpam-5704	76	42	)	)	PUNCT
ejpam-5704	76	43	!	!	PUNCT
ejpam-5704	77	1	1	1	NUM
ejpam-5704	78	1	tl+1	tl+1	NUM
ejpam-5704	78	2	dn−l	dn−l	PROPN
ejpam-5704	78	3	dtn−l	dtn−l	PROPN
ejpam-5704	78	4	(	(	PUNCT
ejpam-5704	78	5	tn+l+1(1−	tn+l+1(1−	NOUN
ejpam-5704	78	6	t)n−l	t)n−l	NOUN
ejpam-5704	78	7	)	)	PUNCT
ejpam-5704	78	8	,	,	PUNCT
ejpam-5704	78	9	l	l	NOUN
ejpam-5704	78	10	=	=	SYM
ejpam-5704	78	11	0	0	NUM
ejpam-5704	78	12	,	,	PUNCT
ejpam-5704	78	13	1	1	NUM
ejpam-5704	78	14	,	,	PUNCT
ejpam-5704	78	15	.	.	PUNCT
ejpam-5704	78	16	.	.	PUNCT
ejpam-5704	79	1	.	.	PUNCT
ejpam-5704	80	1	,	,	PUNCT
ejpam-5704	80	2	n	n	CCONJ
ejpam-5704	80	3	,	,	PUNCT
ejpam-5704	80	4	and	and	CCONJ
ejpam-5704	80	5	are	be	AUX
ejpam-5704	80	6	explicitly	explicitly	ADV
ejpam-5704	80	7	characterized	characterize	VERB
ejpam-5704	80	8	by	by	ADP
ejpam-5704	80	9	pn	pn	PROPN
ejpam-5704	80	10	,	,	PUNCT
ejpam-5704	80	11	l(t	l(t	PROPN
ejpam-5704	80	12	)	)	PUNCT
ejpam-5704	81	1	=	=	SYM
ejpam-5704	81	2	n−l∑	n−l∑	X
ejpam-5704	81	3	j=0	j=0	PROPN
ejpam-5704	81	4	(	(	PUNCT
ejpam-5704	81	5	−1)j	−1)j	X
ejpam-5704	81	6	(	(	PUNCT
ejpam-5704	81	7	n−	n−	NOUN
ejpam-5704	81	8	l	l	NOUN
ejpam-5704	81	9	j	j	PROPN
ejpam-5704	81	10	)	)	PUNCT
ejpam-5704	81	11	(	(	PUNCT
ejpam-5704	81	12	n+	n+	NUM
ejpam-5704	81	13	l	l	NOUN
ejpam-5704	81	14	+	+	CCONJ
ejpam-5704	81	15	1	1	NUM
ejpam-5704	81	16	+	+	NUM
ejpam-5704	81	17	j	j	PROPN
ejpam-5704	81	18	n−	n−	PROPN
ejpam-5704	81	19	l	l	NOUN
ejpam-5704	81	20	)	)	PUNCT
ejpam-5704	81	21	tl+j	tl+j	VERB
ejpam-5704	81	22	,	,	PUNCT
ejpam-5704	81	23	l	l	NOUN
ejpam-5704	81	24	=	=	SYM
ejpam-5704	81	25	0	0	NUM
ejpam-5704	81	26	,	,	PUNCT
ejpam-5704	81	27	1	1	NUM
ejpam-5704	81	28	,	,	PUNCT
ejpam-5704	81	29	...	...	PUNCT
ejpam-5704	81	30	,	,	PUNCT
ejpam-5704	81	31	n.	n.	NOUN
ejpam-5704	81	32	(	(	PUNCT
ejpam-5704	81	33	10	10	NUM
ejpam-5704	81	34	)	)	PUNCT
ejpam-5704	81	35	given	give	VERB
ejpam-5704	81	36	a	a	DET
ejpam-5704	81	37	fixed	fix	VERB
ejpam-5704	81	38	value	value	NOUN
ejpam-5704	81	39	for	for	ADP
ejpam-5704	81	40	n	n	CCONJ
ejpam-5704	81	41	,	,	PUNCT
ejpam-5704	81	42	the	the	DET
ejpam-5704	81	43	orthogonality	orthogonality	NOUN
ejpam-5704	81	44	property	property	NOUN
ejpam-5704	81	45	within	within	ADP
ejpam-5704	81	46	the	the	DET
ejpam-5704	81	47	interval	interval	NOUN
ejpam-5704	81	48	[	[	X
ejpam-5704	81	49	0	0	NUM
ejpam-5704	81	50	,	,	PUNCT
ejpam-5704	81	51	1	1	NUM
ejpam-5704	81	52	]	]	PUNCT
ejpam-5704	81	53	establishes	establish	VERB
ejpam-5704	81	54	an	an	DET
ejpam-5704	81	55	immediate	immediate	ADJ
ejpam-5704	81	56	link	link	NOUN
ejpam-5704	81	57	between	between	ADP
ejpam-5704	81	58	the	the	DET
ejpam-5704	81	59	polynomials	polynomial	NOUN
ejpam-5704	81	60	pn	pn	PROPN
ejpam-5704	81	61	,	,	PUNCT
ejpam-5704	81	62	l(t	l(t	PROPN
ejpam-5704	81	63	)	)	PUNCT
ejpam-5704	81	64	and	and	CCONJ
ejpam-5704	81	65	a	a	DET
ejpam-5704	81	66	set	set	NOUN
ejpam-5704	81	67	of	of	ADP
ejpam-5704	81	68	jacobi	jacobi	PROPN
ejpam-5704	81	69	polynomials	polynomial	VERB
ejpam-5704	81	70	p	p	PROPN
ejpam-5704	81	71	(	(	PUNCT
ejpam-5704	81	72	α	α	X
ejpam-5704	81	73	,	,	PUNCT
ejpam-5704	81	74	β	β	NOUN
ejpam-5704	81	75	)	)	PUNCT
ejpam-5704	81	76	m	m	VERB
ejpam-5704	81	77	(	(	PUNCT
ejpam-5704	81	78	t	t	PROPN
ejpam-5704	81	79	)	)	PUNCT
ejpam-5704	82	1	[	[	X
ejpam-5704	82	2	26	26	NUM
ejpam-5704	82	3	]	]	PUNCT
ejpam-5704	82	4	as	as	ADP
ejpam-5704	82	5	:	:	PUNCT
ejpam-5704	82	6	pn	pn	NOUN
ejpam-5704	82	7	,	,	PUNCT
ejpam-5704	82	8	l(t	l(t	PROPN
ejpam-5704	82	9	)	)	PUNCT
ejpam-5704	82	10	=	=	SYM
ejpam-5704	82	11	(	(	PUNCT
ejpam-5704	82	12	−1)n−ltlp	−1)n−ltlp	PROPN
ejpam-5704	82	13	(	(	PUNCT
ejpam-5704	82	14	0,2l+1	0,2l+1	NOUN
ejpam-5704	82	15	)	)	PUNCT
ejpam-5704	82	16	n−l	n−l	NOUN
ejpam-5704	82	17	(	(	PUNCT
ejpam-5704	82	18	2t−	2t−	NOUN
ejpam-5704	82	19	1	1	NUM
ejpam-5704	82	20	)	)	PUNCT
ejpam-5704	82	21	,	,	PUNCT
ejpam-5704	82	22	l	l	NOUN
ejpam-5704	82	23	=	=	SYM
ejpam-5704	82	24	0	0	NUM
ejpam-5704	82	25	,	,	PUNCT
ejpam-5704	82	26	1	1	NUM
ejpam-5704	82	27	,	,	PUNCT
ejpam-5704	82	28	.	.	PUNCT
ejpam-5704	82	29	.	.	PUNCT
ejpam-5704	83	1	.	.	PUNCT
ejpam-5704	84	1	,	,	PUNCT
ejpam-5704	84	2	n.	n.	NOUN
ejpam-5704	84	3	(	(	PUNCT
ejpam-5704	84	4	11	11	NUM
ejpam-5704	84	5	)	)	PUNCT
ejpam-5704	84	6	b.	b.	PROPN
ejpam-5704	84	7	h.	h.	PROPN
ejpam-5704	84	8	alrikabi	alrikabi	PROPN
ejpam-5704	84	9	,	,	PUNCT
ejpam-5704	84	10	p.	p.	PROPN
ejpam-5704	84	11	darania	darania	PROPN
ejpam-5704	84	12	,	,	PUNCT
ejpam-5704	84	13	s.pishbin	s.pishbin	PROPN
ejpam-5704	84	14	/	/	SYM
ejpam-5704	84	15	eur	eur	PROPN
ejpam-5704	84	16	.	.	PUNCT
ejpam-5704	85	1	j.	j.	PROPN
ejpam-5704	85	2	pure	pure	PROPN
ejpam-5704	85	3	appl	appl	PROPN
ejpam-5704	85	4	.	.	PROPN
ejpam-5704	85	5	math	math	PROPN
ejpam-5704	85	6	,	,	PUNCT
ejpam-5704	85	7	18	18	NUM
ejpam-5704	85	8	(	(	PUNCT
ejpam-5704	85	9	2	2	NUM
ejpam-5704	85	10	)	)	PUNCT
ejpam-5704	85	11	(	(	PUNCT
ejpam-5704	85	12	2025	2025	NUM
ejpam-5704	85	13	)	)	PUNCT
ejpam-5704	85	14	,	,	PUNCT
ejpam-5704	85	15	5704	5704	NUM
ejpam-5704	85	16	5	5	NUM
ejpam-5704	85	17	of	of	ADP
ejpam-5704	85	18	19	19	NUM
ejpam-5704	85	19	from	from	ADP
ejpam-5704	85	20	[	[	X
ejpam-5704	85	21	27	27	NUM
ejpam-5704	85	22	]	]	PUNCT
ejpam-5704	85	23	,	,	PUNCT
ejpam-5704	85	24	jacobi	jacobi	PROPN
ejpam-5704	85	25	polynomials	polynomial	NOUN
ejpam-5704	85	26	are	be	AUX
ejpam-5704	85	27	the	the	DET
ejpam-5704	85	28	polynomial	polynomial	ADJ
ejpam-5704	85	29	eigenfunctions	eigenfunction	NOUN
ejpam-5704	85	30	of	of	ADP
ejpam-5704	85	31	the	the	DET
ejpam-5704	85	32	singular	singular	PROPN
ejpam-5704	85	33	sturmliouville	sturmliouville	PROPN
ejpam-5704	85	34	problem	problem	NOUN
ejpam-5704	85	35	.	.	PUNCT
ejpam-5704	86	1	an	an	DET
ejpam-5704	86	2	explicit	explicit	ADJ
ejpam-5704	86	3	formula	formula	NOUN
ejpam-5704	86	4	is	be	AUX
ejpam-5704	86	5	given	give	VERB
ejpam-5704	86	6	by	by	ADP
ejpam-5704	86	7	p	p	PROPN
ejpam-5704	86	8	(	(	PUNCT
ejpam-5704	86	9	α	α	X
ejpam-5704	86	10	,	,	PUNCT
ejpam-5704	86	11	β	β	NOUN
ejpam-5704	86	12	)	)	PUNCT
ejpam-5704	86	13	m	m	VERB
ejpam-5704	86	14	(	(	PUNCT
ejpam-5704	86	15	t	t	PROPN
ejpam-5704	86	16	)	)	PUNCT
ejpam-5704	86	17	=	=	SYM
ejpam-5704	86	18	1	1	NUM
ejpam-5704	86	19	2	2	NUM
ejpam-5704	86	20	m	m	NOUN
ejpam-5704	86	21	m∑	m∑	NOUN
ejpam-5704	86	22	j=0	j=0	PROPN
ejpam-5704	86	23	(	(	PUNCT
ejpam-5704	86	24	m+	m+	NOUN
ejpam-5704	86	25	α	α	PROPN
ejpam-5704	86	26	j	j	PROPN
ejpam-5704	86	27	)	)	PUNCT
ejpam-5704	86	28	(	(	PUNCT
ejpam-5704	86	29	m+	m+	NUM
ejpam-5704	86	30	β	β	X
ejpam-5704	86	31	m−	m−	PROPN
ejpam-5704	86	32	j	j	PROPN
ejpam-5704	86	33	)	)	PUNCT
ejpam-5704	86	34	(	(	PUNCT
ejpam-5704	86	35	t−	t−	PROPN
ejpam-5704	86	36	1)m−j(t+	1)m−j(t+	NOUN
ejpam-5704	86	37	1)j	1)j	NUM
ejpam-5704	86	38	.	.	PUNCT
ejpam-5704	87	1	an	an	DET
ejpam-5704	87	2	important	important	ADJ
ejpam-5704	87	3	consequence	consequence	NOUN
ejpam-5704	87	4	of	of	ADP
ejpam-5704	87	5	the	the	DET
ejpam-5704	87	6	symmetry	symmetry	NOUN
ejpam-5704	87	7	of	of	ADP
ejpam-5704	87	8	the	the	DET
ejpam-5704	87	9	weight	weight	NOUN
ejpam-5704	87	10	function	function	NOUN
ejpam-5704	87	11	w(t	w(t	PROPN
ejpam-5704	87	12	)	)	PUNCT
ejpam-5704	87	13	=	=	PUNCT
ejpam-5704	87	14	(	(	PUNCT
ejpam-5704	87	15	1−	1−	NUM
ejpam-5704	87	16	t)α(1	t)α(1	NOUN
ejpam-5704	87	17	+	+	CCONJ
ejpam-5704	87	18	t)β	t)β	NOUN
ejpam-5704	87	19	,	,	PUNCT
ejpam-5704	87	20	and	and	CCONJ
ejpam-5704	87	21	the	the	DET
ejpam-5704	87	22	orthogonality	orthogonality	NOUN
ejpam-5704	87	23	of	of	ADP
ejpam-5704	87	24	the	the	DET
ejpam-5704	87	25	jacobi	jacobi	PROPN
ejpam-5704	87	26	polynomials	polynomial	NOUN
ejpam-5704	87	27	,	,	PUNCT
ejpam-5704	87	28	is	be	AUX
ejpam-5704	87	29	the	the	DET
ejpam-5704	87	30	symmetry	symmetry	NOUN
ejpam-5704	87	31	relation	relation	NOUN
ejpam-5704	87	32	p	p	PROPN
ejpam-5704	87	33	(	(	PUNCT
ejpam-5704	87	34	α	α	X
ejpam-5704	87	35	,	,	PUNCT
ejpam-5704	87	36	β	β	NOUN
ejpam-5704	87	37	)	)	PUNCT
ejpam-5704	87	38	m	m	VERB
ejpam-5704	87	39	(	(	PUNCT
ejpam-5704	87	40	t	t	PROPN
ejpam-5704	87	41	)	)	PUNCT
ejpam-5704	87	42	=	=	SYM
ejpam-5704	88	1	(	(	PUNCT
ejpam-5704	88	2	−1)mp	−1)mp	PROPN
ejpam-5704	88	3	(	(	PUNCT
ejpam-5704	88	4	α	α	NOUN
ejpam-5704	88	5	,	,	PUNCT
ejpam-5704	88	6	β	β	NOUN
ejpam-5704	88	7	)	)	PUNCT
ejpam-5704	88	8	m	m	PROPN
ejpam-5704	88	9	(	(	PUNCT
ejpam-5704	88	10	−t	−t	NOUN
ejpam-5704	88	11	)	)	PUNCT
ejpam-5704	88	12	.	.	PUNCT
ejpam-5704	89	1	the	the	DET
ejpam-5704	89	2	ultraspherical	ultraspherical	ADJ
ejpam-5704	89	3	polynomials	polynomial	NOUN
ejpam-5704	89	4	are	be	AUX
ejpam-5704	89	5	simply	simply	ADV
ejpam-5704	89	6	jacobi	jacobi	PROPN
ejpam-5704	89	7	polynomials	polynomial	NOUN
ejpam-5704	89	8	with	with	ADP
ejpam-5704	89	9	α	α	NOUN
ejpam-5704	89	10	=	=	SYM
ejpam-5704	89	11	β	β	NOUN
ejpam-5704	89	12	,	,	PUNCT
ejpam-5704	89	13	and	and	CCONJ
ejpam-5704	89	14	normalized	normalize	VERB
ejpam-5704	89	15	differently	differently	ADV
ejpam-5704	89	16	:	:	PUNCT
ejpam-5704	89	17	p	p	X
ejpam-5704	89	18	(	(	PUNCT
ejpam-5704	89	19	α	α	NOUN
ejpam-5704	89	20	)	)	PUNCT
ejpam-5704	89	21	m	m	PROPN
ejpam-5704	89	22	(	(	PUNCT
ejpam-5704	89	23	t	t	PROPN
ejpam-5704	89	24	)	)	PUNCT
ejpam-5704	89	25	=	=	PUNCT
ejpam-5704	90	1	γ(α+	γ(α+	PRON
ejpam-5704	90	2	1)γ(m+	1)γ(m+	NUM
ejpam-5704	90	3	2α+	2α+	NUM
ejpam-5704	90	4	1	1	NUM
ejpam-5704	90	5	)	)	PUNCT
ejpam-5704	90	6	γ(2α+	γ(2α+	NOUN
ejpam-5704	90	7	1)γ(m+	1)γ(m+	NUM
ejpam-5704	90	8	α+	α+	NOUN
ejpam-5704	90	9	1	1	NUM
ejpam-5704	90	10	)	)	PUNCT
ejpam-5704	90	11	p	p	NOUN
ejpam-5704	90	12	(	(	PUNCT
ejpam-5704	90	13	α	α	NOUN
ejpam-5704	90	14	,	,	PUNCT
ejpam-5704	90	15	α	α	NOUN
ejpam-5704	90	16	)	)	PUNCT
ejpam-5704	90	17	m	m	PROPN
ejpam-5704	90	18	(	(	PUNCT
ejpam-5704	90	19	t	t	PROPN
ejpam-5704	90	20	)	)	PUNCT
ejpam-5704	90	21	,	,	PUNCT
ejpam-5704	90	22	where	where	SCONJ
ejpam-5704	90	23	γ	γ	X
ejpam-5704	90	24	(	(	PUNCT
ejpam-5704	90	25	·	·	PUNCT
ejpam-5704	90	26	)	)	PUNCT
ejpam-5704	90	27	is	be	AUX
ejpam-5704	90	28	the	the	DET
ejpam-5704	90	29	gamma	gamma	PROPN
ejpam-5704	90	30	function	function	NOUN
ejpam-5704	90	31	.	.	PUNCT
ejpam-5704	91	1	the	the	DET
ejpam-5704	91	2	relation	relation	NOUN
ejpam-5704	91	3	between	between	ADP
ejpam-5704	91	4	legendre	legendre	PROPN
ejpam-5704	91	5	and	and	CCONJ
ejpam-5704	91	6	chebyshev	chebyshev	PROPN
ejpam-5704	91	7	polynomials	polynomial	NOUN
ejpam-5704	91	8	with	with	ADP
ejpam-5704	91	9	the	the	DET
ejpam-5704	91	10	ultraspherical	ultraspherical	ADJ
ejpam-5704	91	11	polynomials	polynomial	NOUN
ejpam-5704	91	12	is	be	AUX
ejpam-5704	91	13	pm(t	pm(t	NOUN
ejpam-5704	91	14	)	)	PUNCT
ejpam-5704	92	1	=	=	SYM
ejpam-5704	92	2	p	p	X
ejpam-5704	92	3	(	(	PUNCT
ejpam-5704	92	4	0	0	NUM
ejpam-5704	92	5	)	)	PUNCT
ejpam-5704	92	6	m	m	PROPN
ejpam-5704	92	7	(	(	PUNCT
ejpam-5704	92	8	t	t	PROPN
ejpam-5704	92	9	)	)	PUNCT
ejpam-5704	92	10	,	,	PUNCT
ejpam-5704	92	11	tm(t	tm(t	NOUN
ejpam-5704	92	12	)	)	PUNCT
ejpam-5704	93	1	=	=	SYM
ejpam-5704	93	2	p	p	X
ejpam-5704	93	3	(	(	PUNCT
ejpam-5704	93	4	−	−	PROPN
ejpam-5704	93	5	1	1	NUM
ejpam-5704	93	6	2	2	NUM
ejpam-5704	93	7	,	,	PUNCT
ejpam-5704	93	8	−	−	PROPN
ejpam-5704	93	9	1	1	NUM
ejpam-5704	93	10	2	2	NUM
ejpam-5704	93	11	)	)	PUNCT
ejpam-5704	93	12	m	m	PROPN
ejpam-5704	93	13	(	(	PUNCT
ejpam-5704	93	14	t	t	PROPN
ejpam-5704	93	15	)	)	PUNCT
ejpam-5704	93	16	p	p	NOUN
ejpam-5704	93	17	(	(	PUNCT
ejpam-5704	93	18	−	−	PROPN
ejpam-5704	93	19	1	1	NUM
ejpam-5704	93	20	2	2	NUM
ejpam-5704	93	21	,	,	PUNCT
ejpam-5704	93	22	−	−	PROPN
ejpam-5704	93	23	1	1	NUM
ejpam-5704	93	24	2	2	NUM
ejpam-5704	93	25	)	)	PUNCT
ejpam-5704	93	26	m	m	VERB
ejpam-5704	93	27	(	(	PUNCT
ejpam-5704	93	28	1	1	NUM
ejpam-5704	93	29	)	)	PUNCT
ejpam-5704	93	30	.	.	PUNCT
ejpam-5704	94	1	also	also	ADV
ejpam-5704	94	2	for	for	ADP
ejpam-5704	94	3	considering	consider	VERB
ejpam-5704	94	4	the	the	DET
ejpam-5704	94	5	other	other	ADJ
ejpam-5704	94	6	orthogonal	orthogonal	ADJ
ejpam-5704	94	7	polynomials	polynomial	NOUN
ejpam-5704	94	8	,	,	PUNCT
ejpam-5704	94	9	we	we	PRON
ejpam-5704	94	10	can	can	AUX
ejpam-5704	94	11	refer	refer	VERB
ejpam-5704	94	12	to	to	ADP
ejpam-5704	94	13	[	[	X
ejpam-5704	94	14	28	28	NUM
ejpam-5704	94	15	,	,	PUNCT
ejpam-5704	94	16	29	29	NUM
ejpam-5704	94	17	]	]	PUNCT
ejpam-5704	94	18	.	.	PUNCT
ejpam-5704	95	1	according	accord	VERB
ejpam-5704	95	2	to	to	ADP
ejpam-5704	95	3	[	[	X
ejpam-5704	95	4	26	26	NUM
ejpam-5704	95	5	]	]	PUNCT
ejpam-5704	95	6	,	,	PUNCT
ejpam-5704	95	7	for	for	ADP
ejpam-5704	95	8	each	each	DET
ejpam-5704	95	9	value	value	NOUN
ejpam-5704	95	10	of	of	ADP
ejpam-5704	95	11	n	n	CCONJ
ejpam-5704	95	12	,	,	PUNCT
ejpam-5704	95	13	the	the	DET
ejpam-5704	95	14	polynomial	polynomial	ADJ
ejpam-5704	95	15	pn,0(t	pn,0(t	PROPN
ejpam-5704	95	16	)	)	PUNCT
ejpam-5704	95	17	has	have	VERB
ejpam-5704	95	18	precisely	precisely	ADV
ejpam-5704	95	19	n	n	CCONJ
ejpam-5704	95	20	distinct	distinct	ADJ
ejpam-5704	95	21	roots	root	NOUN
ejpam-5704	95	22	within	within	ADP
ejpam-5704	95	23	the	the	DET
ejpam-5704	95	24	interval	interval	NOUN
ejpam-5704	95	25	(	(	PUNCT
ejpam-5704	95	26	0	0	NUM
ejpam-5704	95	27	,	,	PUNCT
ejpam-5704	95	28	1	1	NUM
ejpam-5704	95	29	)	)	PUNCT
ejpam-5704	95	30	and	and	CCONJ
ejpam-5704	95	31	this	this	DET
ejpam-5704	95	32	set	set	NOUN
ejpam-5704	95	33	of	of	ADP
ejpam-5704	95	34	polynomials	polynomial	NOUN
ejpam-5704	95	35	exhibits	exhibit	VERB
ejpam-5704	95	36	all	all	DET
ejpam-5704	95	37	the	the	DET
ejpam-5704	95	38	typical	typical	ADJ
ejpam-5704	95	39	characteristics	characteristic	NOUN
ejpam-5704	95	40	found	find	VERB
ejpam-5704	95	41	in	in	ADP
ejpam-5704	95	42	other	other	ADJ
ejpam-5704	95	43	widely	widely	ADV
ejpam-5704	95	44	recognized	recognize	VERB
ejpam-5704	95	45	orthogonal	orthogonal	ADJ
ejpam-5704	95	46	polynomial	polynomial	ADJ
ejpam-5704	95	47	families	family	NOUN
ejpam-5704	95	48	such	such	ADJ
ejpam-5704	95	49	as	as	ADP
ejpam-5704	95	50	legendre	legendre	PROPN
ejpam-5704	95	51	or	or	CCONJ
ejpam-5704	95	52	chebyshev	chebyshev	NOUN
ejpam-5704	95	53	polynomials	polynomial	NOUN
ejpam-5704	95	54	.	.	PUNCT
ejpam-5704	96	1	yon	yon	PROPN
ejpam-5704	96	2	can	can	AUX
ejpam-5704	96	3	see	see	VERB
ejpam-5704	96	4	that	that	DET
ejpam-5704	96	5	distribution	distribution	NOUN
ejpam-5704	96	6	of	of	ADP
ejpam-5704	96	7	roots	root	NOUN
ejpam-5704	96	8	of	of	ADP
ejpam-5704	96	9	these	these	DET
ejpam-5704	96	10	polynomials	polynomial	NOUN
ejpam-5704	96	11	in	in	ADP
ejpam-5704	96	12	fig	fig	NOUN
ejpam-5704	96	13	.	.	PUNCT
ejpam-5704	97	1	1	1	NUM
ejpam-5704	97	2	and	and	CCONJ
ejpam-5704	97	3	fig	fig	NOUN
ejpam-5704	97	4	.	.	PUNCT
ejpam-5704	98	1	2	2	NUM
ejpam-5704	98	2	.	.	X
ejpam-5704	98	3	3	3	NUM
ejpam-5704	98	4	.	.	X
ejpam-5704	99	1	nyström	nyström	PRON
ejpam-5704	99	2	method	method	NOUN
ejpam-5704	99	3	here	here	ADV
ejpam-5704	99	4	,	,	PUNCT
ejpam-5704	99	5	we	we	PRON
ejpam-5704	99	6	outline	outline	VERB
ejpam-5704	99	7	the	the	DET
ejpam-5704	99	8	nyström	nyström	NOUN
ejpam-5704	99	9	method	method	NOUN
ejpam-5704	99	10	employed	employ	VERB
ejpam-5704	99	11	for	for	ADP
ejpam-5704	99	12	the	the	DET
ejpam-5704	99	13	numerical	numerical	ADJ
ejpam-5704	99	14	solution	solution	NOUN
ejpam-5704	99	15	of	of	ADP
ejpam-5704	99	16	equation	equation	NOUN
ejpam-5704	99	17	(	(	PUNCT
ejpam-5704	99	18	1	1	NUM
ejpam-5704	99	19	)	)	PUNCT
ejpam-5704	99	20	.	.	PUNCT
ejpam-5704	100	1	in	in	ADP
ejpam-5704	100	2	equation	equation	NOUN
ejpam-5704	100	3	(	(	PUNCT
ejpam-5704	100	4	1	1	NUM
ejpam-5704	100	5	)	)	PUNCT
ejpam-5704	100	6	,	,	PUNCT
ejpam-5704	100	7	for	for	ADP
ejpam-5704	100	8	the	the	DET
ejpam-5704	100	9	sake	sake	NOUN
ejpam-5704	100	10	of	of	ADP
ejpam-5704	100	11	convenience	convenience	NOUN
ejpam-5704	100	12	and	and	CCONJ
ejpam-5704	100	13	without	without	ADP
ejpam-5704	100	14	any	any	DET
ejpam-5704	100	15	loss	loss	NOUN
ejpam-5704	100	16	of	of	ADP
ejpam-5704	100	17	generality	generality	NOUN
ejpam-5704	100	18	,	,	PUNCT
ejpam-5704	100	19	we	we	PRON
ejpam-5704	100	20	assume	assume	VERB
ejpam-5704	100	21	certain	certain	ADJ
ejpam-5704	100	22	conditions	conditions	NUM
ejpam-5704	100	23	y(t	y(t	NUM
ejpam-5704	100	24	)	)	PUNCT
ejpam-5704	101	1	=	=	SYM
ejpam-5704	101	2	f(t	f(t	NOUN
ejpam-5704	101	3	)	)	PUNCT
ejpam-5704	102	1	+	+	CCONJ
ejpam-5704	102	2	(	(	PUNCT
ejpam-5704	102	3	vαy)(t	vαy)(t	ADJ
ejpam-5704	102	4	)	)	PUNCT
ejpam-5704	102	5	+	+	CCONJ
ejpam-5704	102	6	(	(	PUNCT
ejpam-5704	102	7	vα	vα	INTJ
ejpam-5704	102	8	,	,	PUNCT
ejpam-5704	102	9	θy)(t	θy)(t	PROPN
ejpam-5704	102	10	)	)	PUNCT
ejpam-5704	102	11	,	,	PUNCT
ejpam-5704	102	12	t	t	PROPN
ejpam-5704	102	13	∈	∈	PROPN
ejpam-5704	102	14	(	(	PUNCT
ejpam-5704	102	15	0	0	NUM
ejpam-5704	102	16	,	,	PUNCT
ejpam-5704	102	17	1	1	NUM
ejpam-5704	102	18	]	]	PUNCT
ejpam-5704	102	19	,	,	PUNCT
ejpam-5704	102	20	y(t	y(t	NUM
ejpam-5704	102	21	)	)	PUNCT
ejpam-5704	102	22	=	=	SYM
ejpam-5704	103	1	ϕ(t	ϕ(t	NUM
ejpam-5704	103	2	)	)	PUNCT
ejpam-5704	103	3	,	,	PUNCT
ejpam-5704	103	4	t	t	PROPN
ejpam-5704	103	5	∈	∈	PROPN
ejpam-5704	104	1	[	[	X
ejpam-5704	104	2	θ(0	θ(0	PROPN
ejpam-5704	104	3	)	)	PUNCT
ejpam-5704	104	4	,	,	PUNCT
ejpam-5704	104	5	0	0	NUM
ejpam-5704	104	6	]	]	PUNCT
ejpam-5704	104	7	.	.	PUNCT
ejpam-5704	105	1	(	(	PUNCT
ejpam-5704	105	2	12	12	NUM
ejpam-5704	105	3	)	)	PUNCT
ejpam-5704	105	4	by	by	ADP
ejpam-5704	105	5	chosen	choose	VERB
ejpam-5704	105	6	(	(	PUNCT
ejpam-5704	105	7	n	n	X
ejpam-5704	105	8	+	+	CCONJ
ejpam-5704	105	9	1	1	X
ejpam-5704	105	10	)	)	PUNCT
ejpam-5704	105	11	distinct	distinct	ADJ
ejpam-5704	105	12	points	point	NOUN
ejpam-5704	105	13	{	{	PUNCT
ejpam-5704	105	14	ti}ni=1	ti}ni=1	PROPN
ejpam-5704	105	15	⋃	⋃	PROPN
ejpam-5704	105	16	{	{	PUNCT
ejpam-5704	105	17	t0	t0	NOUN
ejpam-5704	105	18	=	=	PUNCT
ejpam-5704	105	19	0	0	NUM
ejpam-5704	105	20	}	}	PUNCT
ejpam-5704	105	21	,	,	PUNCT
ejpam-5704	105	22	in	in	ADP
ejpam-5704	105	23	the	the	DET
ejpam-5704	105	24	interval	interval	NOUN
ejpam-5704	105	25	ih	ih	NOUN
ejpam-5704	105	26	⊆	⊆	NUM
ejpam-5704	105	27	[	[	X
ejpam-5704	105	28	0	0	NUM
ejpam-5704	105	29	,	,	PUNCT
ejpam-5704	105	30	1	1	NUM
ejpam-5704	105	31	]	]	PUNCT
ejpam-5704	105	32	and	and	CCONJ
ejpam-5704	105	33	collocate	collocate	VERB
ejpam-5704	105	34	the	the	DET
ejpam-5704	105	35	equation	equation	NOUN
ejpam-5704	105	36	(	(	PUNCT
ejpam-5704	105	37	12	12	NUM
ejpam-5704	105	38	)	)	PUNCT
ejpam-5704	105	39	at	at	ADP
ejpam-5704	105	40	the	the	DET
ejpam-5704	105	41	underlying	underlie	VERB
ejpam-5704	105	42	local	local	ADJ
ejpam-5704	105	43	mesh	mesh	NOUN
ejpam-5704	105	44	{	{	PUNCT
ejpam-5704	105	45	ti}ni=0	ti}ni=0	NOUN
ejpam-5704	105	46	,	,	PUNCT
ejpam-5704	105	47	we	we	PRON
ejpam-5704	105	48	have	have	VERB
ejpam-5704	105	49	y(ti	y(ti	NUM
ejpam-5704	105	50	)	)	PUNCT
ejpam-5704	105	51	=	=	SYM
ejpam-5704	105	52	f(ti	f(ti	NOUN
ejpam-5704	105	53	)	)	PUNCT
ejpam-5704	106	1	+	+	CCONJ
ejpam-5704	106	2	(	(	PUNCT
ejpam-5704	106	3	vαy)(ti	vαy)(ti	NOUN
ejpam-5704	106	4	)	)	PUNCT
ejpam-5704	106	5	+	+	CCONJ
ejpam-5704	106	6	(	(	PUNCT
ejpam-5704	106	7	vα	vα	INTJ
ejpam-5704	106	8	,	,	PUNCT
ejpam-5704	106	9	θy)(ti	θy)(ti	NOUN
ejpam-5704	106	10	)	)	PUNCT
ejpam-5704	106	11	,	,	PUNCT
ejpam-5704	106	12	i	i	PRON
ejpam-5704	106	13	=	=	NOUN
ejpam-5704	106	14	0	0	NUM
ejpam-5704	106	15	,	,	PUNCT
ejpam-5704	106	16	1	1	NUM
ejpam-5704	106	17	,	,	PUNCT
ejpam-5704	106	18	...	...	PUNCT
ejpam-5704	106	19	,	,	PUNCT
ejpam-5704	106	20	n	n	CCONJ
ejpam-5704	106	21	,	,	PUNCT
ejpam-5704	106	22	(	(	PUNCT
ejpam-5704	106	23	13	13	NUM
ejpam-5704	106	24	)	)	PUNCT
ejpam-5704	106	25	where	where	SCONJ
ejpam-5704	106	26	(	(	PUNCT
ejpam-5704	106	27	vαy)(ti	vαy)(ti	NOUN
ejpam-5704	106	28	)	)	PUNCT
ejpam-5704	106	29	=	=	SYM
ejpam-5704	106	30	∫	∫	PROPN
ejpam-5704	106	31	ti	ti	PROPN
ejpam-5704	106	32	0	0	PROPN
ejpam-5704	106	33	p1,h(ti	p1,h(ti	PROPN
ejpam-5704	106	34	,	,	PUNCT
ejpam-5704	106	35	w)k1(ti	w)k1(ti	PROPN
ejpam-5704	106	36	,	,	PUNCT
ejpam-5704	106	37	w	w	PROPN
ejpam-5704	106	38	,	,	PUNCT
ejpam-5704	106	39	y(w))dw	y(w))dw	PROPN
ejpam-5704	106	40	,	,	PUNCT
ejpam-5704	106	41	(	(	PUNCT
ejpam-5704	106	42	14	14	NUM
ejpam-5704	106	43	)	)	PUNCT
ejpam-5704	106	44	b.	b.	PROPN
ejpam-5704	106	45	h.	h.	PROPN
ejpam-5704	106	46	alrikabi	alrikabi	PROPN
ejpam-5704	106	47	,	,	PUNCT
ejpam-5704	106	48	p.	p.	PROPN
ejpam-5704	106	49	darania	darania	PROPN
ejpam-5704	106	50	,	,	PUNCT
ejpam-5704	106	51	s.pishbin	s.pishbin	PROPN
ejpam-5704	106	52	/	/	SYM
ejpam-5704	106	53	eur	eur	PROPN
ejpam-5704	106	54	.	.	PUNCT
ejpam-5704	107	1	j.	j.	PROPN
ejpam-5704	107	2	pure	pure	PROPN
ejpam-5704	107	3	appl	appl	PROPN
ejpam-5704	107	4	.	.	PROPN
ejpam-5704	107	5	math	math	PROPN
ejpam-5704	107	6	,	,	PUNCT
ejpam-5704	107	7	18	18	NUM
ejpam-5704	107	8	(	(	PUNCT
ejpam-5704	107	9	2	2	NUM
ejpam-5704	107	10	)	)	PUNCT
ejpam-5704	107	11	(	(	PUNCT
ejpam-5704	107	12	2025	2025	NUM
ejpam-5704	107	13	)	)	PUNCT
ejpam-5704	107	14	,	,	PUNCT
ejpam-5704	107	15	5704	5704	NUM
ejpam-5704	107	16	6	6	NUM
ejpam-5704	107	17	of	of	ADP
ejpam-5704	107	18	19	19	NUM
ejpam-5704	107	19	0.0	0.0	NUM
ejpam-5704	107	20	0.2	0.2	NUM
ejpam-5704	107	21	0.4	0.4	NUM
ejpam-5704	107	22	0.6	0.6	NUM
ejpam-5704	107	23	0.8	0.8	NUM
ejpam-5704	107	24	0.00	0.00	NUM
ejpam-5704	107	25	0.05	0.05	NUM
ejpam-5704	107	26	0.10	0.10	NUM
ejpam-5704	107	27	0.15	0.15	NUM
ejpam-5704	107	28	0.20	0.20	NUM
ejpam-5704	107	29	roots	root	NOUN
ejpam-5704	107	30	of	of	ADP
ejpam-5704	107	31	chebyshev	chebyshev	NOUN
ejpam-5704	107	32	polynomial	polynomial	ADJ
ejpam-5704	107	33	roots	root	NOUN
ejpam-5704	107	34	of	of	ADP
ejpam-5704	107	35	legendre	legendre	PROPN
ejpam-5704	107	36	polynomial	polynomial	ADJ
ejpam-5704	107	37	roots	root	NOUN
ejpam-5704	107	38	of	of	ADP
ejpam-5704	107	39	chelyshkov	chelyshkov	ADJ
ejpam-5704	107	40	polynomial	polynomial	ADJ
ejpam-5704	107	41	figure	figure	NOUN
ejpam-5704	107	42	1	1	NUM
ejpam-5704	107	43	:	:	PUNCT
ejpam-5704	107	44	plot	plot	NOUN
ejpam-5704	107	45	of	of	ADP
ejpam-5704	107	46	distribution	distribution	NOUN
ejpam-5704	107	47	of	of	ADP
ejpam-5704	107	48	roots	root	NOUN
ejpam-5704	107	49	of	of	ADP
ejpam-5704	107	50	chelyshkov	chelyshkov	NOUN
ejpam-5704	107	51	,	,	PUNCT
ejpam-5704	107	52	legendre	legendre	PROPN
ejpam-5704	107	53	and	and	CCONJ
ejpam-5704	107	54	chebyshev	chebyshev	PROPN
ejpam-5704	107	55	polynomials	polynomial	NOUN
ejpam-5704	107	56	with	with	ADP
ejpam-5704	107	57	m	m	NOUN
ejpam-5704	107	58	=	=	SYM
ejpam-5704	107	59	4	4	NUM
ejpam-5704	107	60	.	.	NOUN
ejpam-5704	107	61	0.0	0.0	NUM
ejpam-5704	107	62	0.2	0.2	NUM
ejpam-5704	107	63	0.4	0.4	NUM
ejpam-5704	107	64	0.6	0.6	NUM
ejpam-5704	107	65	0.8	0.8	NUM
ejpam-5704	107	66	0.00	0.00	NUM
ejpam-5704	107	67	0.05	0.05	NUM
ejpam-5704	107	68	0.10	0.10	NUM
ejpam-5704	107	69	0.15	0.15	NUM
ejpam-5704	107	70	0.20	0.20	NUM
ejpam-5704	107	71	roots	root	NOUN
ejpam-5704	107	72	of	of	ADP
ejpam-5704	107	73	chebyshev	chebyshev	NOUN
ejpam-5704	107	74	polynomial	polynomial	ADJ
ejpam-5704	107	75	roots	root	NOUN
ejpam-5704	107	76	of	of	ADP
ejpam-5704	107	77	legendre	legendre	PROPN
ejpam-5704	107	78	polynomial	polynomial	ADJ
ejpam-5704	107	79	roots	root	NOUN
ejpam-5704	107	80	of	of	ADP
ejpam-5704	107	81	chelyshkov	chelyshkov	ADJ
ejpam-5704	107	82	polynomial	polynomial	ADJ
ejpam-5704	107	83	figure	figure	NOUN
ejpam-5704	107	84	2	2	NUM
ejpam-5704	107	85	:	:	PUNCT
ejpam-5704	107	86	plot	plot	NOUN
ejpam-5704	107	87	of	of	ADP
ejpam-5704	107	88	distribution	distribution	NOUN
ejpam-5704	107	89	of	of	ADP
ejpam-5704	107	90	roots	root	NOUN
ejpam-5704	107	91	of	of	ADP
ejpam-5704	107	92	chelyshkov	chelyshkov	NOUN
ejpam-5704	107	93	,	,	PUNCT
ejpam-5704	107	94	legendre	legendre	PROPN
ejpam-5704	107	95	and	and	CCONJ
ejpam-5704	107	96	chebyshev	chebyshev	PROPN
ejpam-5704	107	97	polynomials	polynomial	NOUN
ejpam-5704	107	98	with	with	ADP
ejpam-5704	107	99	m	m	PROPN
ejpam-5704	107	100	=	=	SYM
ejpam-5704	107	101	6	6	NUM
ejpam-5704	107	102	.	.	PUNCT
ejpam-5704	108	1	(	(	PUNCT
ejpam-5704	108	2	vα	vα	PROPN
ejpam-5704	108	3	,	,	PUNCT
ejpam-5704	108	4	θy)(ti	θy)(ti	NOUN
ejpam-5704	108	5	)	)	PUNCT
ejpam-5704	108	6	=	=	SYM
ejpam-5704	108	7	∫	∫	PROPN
ejpam-5704	108	8	θ(ti	θ(ti	NOUN
ejpam-5704	108	9	)	)	PUNCT
ejpam-5704	108	10	0	0	PUNCT
ejpam-5704	109	1	p2,h(ti	p2,h(ti	PROPN
ejpam-5704	109	2	,	,	PUNCT
ejpam-5704	109	3	w)k2(ti	w)k2(ti	PROPN
ejpam-5704	109	4	,	,	PUNCT
ejpam-5704	109	5	w	w	PROPN
ejpam-5704	109	6	,	,	PUNCT
ejpam-5704	109	7	y(w))dw	y(w))dw	PROPN
ejpam-5704	109	8	.	.	PUNCT
ejpam-5704	110	1	(	(	PUNCT
ejpam-5704	110	2	15	15	NUM
ejpam-5704	110	3	)	)	PUNCT
ejpam-5704	110	4	b.	b.	PROPN
ejpam-5704	110	5	h.	h.	PROPN
ejpam-5704	110	6	alrikabi	alrikabi	PROPN
ejpam-5704	110	7	,	,	PUNCT
ejpam-5704	110	8	p.	p.	PROPN
ejpam-5704	110	9	darania	darania	PROPN
ejpam-5704	110	10	,	,	PUNCT
ejpam-5704	110	11	s.pishbin	s.pishbin	PROPN
ejpam-5704	110	12	/	/	SYM
ejpam-5704	110	13	eur	eur	PROPN
ejpam-5704	110	14	.	.	PUNCT
ejpam-5704	111	1	j.	j.	PROPN
ejpam-5704	111	2	pure	pure	PROPN
ejpam-5704	111	3	appl	appl	PROPN
ejpam-5704	111	4	.	.	PROPN
ejpam-5704	111	5	math	math	PROPN
ejpam-5704	111	6	,	,	PUNCT
ejpam-5704	111	7	18	18	NUM
ejpam-5704	111	8	(	(	PUNCT
ejpam-5704	111	9	2	2	NUM
ejpam-5704	111	10	)	)	PUNCT
ejpam-5704	111	11	(	(	PUNCT
ejpam-5704	111	12	2025	2025	NUM
ejpam-5704	111	13	)	)	PUNCT
ejpam-5704	111	14	,	,	PUNCT
ejpam-5704	111	15	5704	5704	NUM
ejpam-5704	111	16	7	7	NUM
ejpam-5704	111	17	of	of	ADP
ejpam-5704	111	18	19	19	NUM
ejpam-5704	111	19	subsequently	subsequently	ADV
ejpam-5704	111	20	,	,	PUNCT
ejpam-5704	111	21	we	we	PRON
ejpam-5704	111	22	employ	employ	VERB
ejpam-5704	111	23	the	the	DET
ejpam-5704	111	24	lagrange	lagrange	PROPN
ejpam-5704	111	25	interpolation	interpolation	NOUN
ejpam-5704	111	26	polynomial	polynomial	NOUN
ejpam-5704	111	27	ωn	ωn	ADP
ejpam-5704	111	28	(	(	PUNCT
ejpam-5704	111	29	kh	kh	PROPN
ejpam-5704	111	30	,	,	PUNCT
ejpam-5704	111	31	w	w	PROPN
ejpam-5704	111	32	)	)	PUNCT
ejpam-5704	111	33	=	=	SYM
ejpam-5704	111	34	n∑	n∑	NOUN
ejpam-5704	111	35	j=0	j=0	PROPN
ejpam-5704	111	36	ln	ln	PROPN
ejpam-5704	111	37	,	,	PUNCT
ejpam-5704	111	38	j(w)kh(ti	j(w)kh(ti	NOUN
ejpam-5704	111	39	,	,	PUNCT
ejpam-5704	111	40	tj	tj	PROPN
ejpam-5704	111	41	,	,	PUNCT
ejpam-5704	111	42	y(tj	y(tj	PROPN
ejpam-5704	111	43	)	)	PUNCT
ejpam-5704	111	44	)	)	PUNCT
ejpam-5704	111	45	,	,	PUNCT
ejpam-5704	111	46	h	h	NOUN
ejpam-5704	112	1	=	=	NOUN
ejpam-5704	112	2	1	1	NUM
ejpam-5704	112	3	,	,	PUNCT
ejpam-5704	112	4	2	2	NUM
ejpam-5704	112	5	,	,	PUNCT
ejpam-5704	112	6	(	(	PUNCT
ejpam-5704	112	7	16	16	NUM
ejpam-5704	112	8	)	)	PUNCT
ejpam-5704	113	1	to	to	PART
ejpam-5704	113	2	approximate	approximate	VERB
ejpam-5704	113	3	kh(ti	kh(ti	PROPN
ejpam-5704	113	4	,	,	PUNCT
ejpam-5704	113	5	w	w	PROPN
ejpam-5704	113	6	,	,	PUNCT
ejpam-5704	113	7	y(w	y(w	NOUN
ejpam-5704	113	8	)	)	PUNCT
ejpam-5704	113	9	)	)	PUNCT
ejpam-5704	113	10	and	and	CCONJ
ejpam-5704	113	11	get	get	VERB
ejpam-5704	113	12	yn	yn	PROPN
ejpam-5704	113	13	(	(	PUNCT
ejpam-5704	113	14	ti	ti	NOUN
ejpam-5704	113	15	)	)	PUNCT
ejpam-5704	113	16	=	=	SYM
ejpam-5704	113	17	f(ti	f(ti	NOUN
ejpam-5704	113	18	)	)	PUNCT
ejpam-5704	114	1	+	+	CCONJ
ejpam-5704	114	2	n∑	n∑	DET
ejpam-5704	114	3	j=0	j=0	PROPN
ejpam-5704	114	4	[	[	PUNCT
ejpam-5704	114	5	w1,i	w1,i	PROPN
ejpam-5704	114	6	,	,	PUNCT
ejpam-5704	114	7	j	j	PROPN
ejpam-5704	114	8	k1(ti	k1(ti	PROPN
ejpam-5704	114	9	,	,	PUNCT
ejpam-5704	114	10	tj	tj	X
ejpam-5704	114	11	,	,	PUNCT
ejpam-5704	114	12	yn	yn	PROPN
ejpam-5704	114	13	(	(	PUNCT
ejpam-5704	114	14	tj	tj	NOUN
ejpam-5704	114	15	)	)	PUNCT
ejpam-5704	114	16	)	)	PUNCT
ejpam-5704	114	17	+	+	CCONJ
ejpam-5704	114	18	w2,i	w2,i	PROPN
ejpam-5704	114	19	,	,	PUNCT
ejpam-5704	114	20	j	j	PROPN
ejpam-5704	114	21	k2(ti	k2(ti	PROPN
ejpam-5704	114	22	,	,	PUNCT
ejpam-5704	114	23	tj	tj	PROPN
ejpam-5704	114	24	,	,	PUNCT
ejpam-5704	114	25	yn	yn	PROPN
ejpam-5704	114	26	(	(	PUNCT
ejpam-5704	114	27	tj	tj	NOUN
ejpam-5704	114	28	)	)	PUNCT
ejpam-5704	114	29	)	)	PUNCT
ejpam-5704	114	30	]	]	PUNCT
ejpam-5704	114	31	,	,	PUNCT
ejpam-5704	114	32	(	(	PUNCT
ejpam-5704	114	33	17	17	NUM
ejpam-5704	114	34	)	)	PUNCT
ejpam-5704	114	35	with	with	ADP
ejpam-5704	114	36	w1,i	w1,i	PROPN
ejpam-5704	114	37	,	,	PUNCT
ejpam-5704	114	38	j	j	PROPN
ejpam-5704	114	39	=	=	SYM
ejpam-5704	114	40	∫	∫	PROPN
ejpam-5704	114	41	ti	ti	PROPN
ejpam-5704	114	42	0	0	PROPN
ejpam-5704	114	43	p1,h(ti	p1,h(ti	PROPN
ejpam-5704	114	44	,	,	PUNCT
ejpam-5704	114	45	w)ln	w)ln	PROPN
ejpam-5704	114	46	,	,	PUNCT
ejpam-5704	114	47	j(w)dw	j(w)dw	PROPN
ejpam-5704	114	48	,	,	PUNCT
ejpam-5704	114	49	w2,i	w2,i	PROPN
ejpam-5704	114	50	,	,	PUNCT
ejpam-5704	114	51	j	j	PROPN
ejpam-5704	114	52	=	=	SYM
ejpam-5704	114	53	∫	∫	PROPN
ejpam-5704	114	54	θ(ti	θ(ti	NOUN
ejpam-5704	114	55	)	)	PUNCT
ejpam-5704	114	56	0	0	PUNCT
ejpam-5704	115	1	p2,h(ti	p2,h(ti	PROPN
ejpam-5704	115	2	,	,	PUNCT
ejpam-5704	115	3	w)ln	w)ln	PROPN
ejpam-5704	115	4	,	,	PUNCT
ejpam-5704	115	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	115	6	,	,	PUNCT
ejpam-5704	115	7	i	i	PRON
ejpam-5704	115	8	,	,	PUNCT
ejpam-5704	115	9	j	j	PROPN
ejpam-5704	115	10	=	=	SYM
ejpam-5704	115	11	0	0	NUM
ejpam-5704	115	12	,	,	PUNCT
ejpam-5704	115	13	1	1	NUM
ejpam-5704	115	14	,	,	PUNCT
ejpam-5704	115	15	2	2	NUM
ejpam-5704	115	16	,	,	PUNCT
ejpam-5704	115	17	·	·	PUNCT
ejpam-5704	115	18	·	·	PUNCT
ejpam-5704	115	19	·	·	PUNCT
ejpam-5704	115	20	,	,	PUNCT
ejpam-5704	115	21	n.	n.	PROPN
ejpam-5704	115	22	(	(	PUNCT
ejpam-5704	115	23	18	18	NUM
ejpam-5704	115	24	)	)	PUNCT
ejpam-5704	115	25	note	note	NOUN
ejpam-5704	115	26	that	that	SCONJ
ejpam-5704	115	27	the	the	DET
ejpam-5704	115	28	relationship	relationship	NOUN
ejpam-5704	115	29	given	give	VERB
ejpam-5704	115	30	in	in	ADP
ejpam-5704	115	31	equation	equation	NOUN
ejpam-5704	115	32	(	(	PUNCT
ejpam-5704	115	33	17	17	NUM
ejpam-5704	115	34	)	)	PUNCT
ejpam-5704	115	35	constitutes	constitute	VERB
ejpam-5704	115	36	a	a	DET
ejpam-5704	115	37	nonlinear	nonlinear	ADJ
ejpam-5704	115	38	system	system	NOUN
ejpam-5704	115	39	of	of	ADP
ejpam-5704	115	40	equations	equation	NOUN
ejpam-5704	115	41	with	with	ADP
ejpam-5704	115	42	dimensions	dimension	NOUN
ejpam-5704	115	43	(	(	PUNCT
ejpam-5704	115	44	n	n	NOUN
ejpam-5704	115	45	+	+	CCONJ
ejpam-5704	115	46	1	1	NUM
ejpam-5704	115	47	)	)	PUNCT
ejpam-5704	115	48	×	×	NOUN
ejpam-5704	115	49	(	(	PUNCT
ejpam-5704	115	50	n	n	NOUN
ejpam-5704	115	51	+	+	NOUN
ejpam-5704	115	52	1	1	NUM
ejpam-5704	115	53	)	)	PUNCT
ejpam-5704	115	54	.	.	PUNCT
ejpam-5704	116	1	this	this	DET
ejpam-5704	116	2	system	system	NOUN
ejpam-5704	116	3	possesses	possess	VERB
ejpam-5704	116	4	a	a	DET
ejpam-5704	116	5	unique	unique	ADJ
ejpam-5704	116	6	solution	solution	NOUN
ejpam-5704	116	7	,	,	PUNCT
ejpam-5704	116	8	as	as	SCONJ
ejpam-5704	116	9	demonstrated	demonstrate	VERB
ejpam-5704	116	10	in	in	ADP
ejpam-5704	116	11	sources	source	NOUN
ejpam-5704	116	12	such	such	ADJ
ejpam-5704	116	13	as	as	ADP
ejpam-5704	116	14	[	[	X
ejpam-5704	116	15	30	30	NUM
ejpam-5704	116	16	]	]	PUNCT
ejpam-5704	116	17	and	and	CCONJ
ejpam-5704	116	18	[	[	X
ejpam-5704	116	19	31	31	NUM
ejpam-5704	116	20	]	]	PUNCT
ejpam-5704	116	21	.	.	PUNCT
ejpam-5704	117	1	the	the	DET
ejpam-5704	117	2	resolution	resolution	NOUN
ejpam-5704	117	3	of	of	ADP
ejpam-5704	117	4	this	this	DET
ejpam-5704	117	5	nonlinear	nonlinear	ADJ
ejpam-5704	117	6	system	system	NOUN
ejpam-5704	117	7	yields	yield	VERB
ejpam-5704	117	8	the	the	DET
ejpam-5704	117	9	values	value	NOUN
ejpam-5704	117	10	of	of	ADP
ejpam-5704	117	11	yn	yn	PROPN
ejpam-5704	117	12	(	(	PUNCT
ejpam-5704	117	13	ti	ti	NOUN
ejpam-5704	117	14	)	)	PUNCT
ejpam-5704	117	15	for	for	ADP
ejpam-5704	117	16	i	i	PROPN
ejpam-5704	117	17	=	=	SYM
ejpam-5704	117	18	0	0	NUM
ejpam-5704	117	19	,	,	PUNCT
ejpam-5704	117	20	1	1	NUM
ejpam-5704	117	21	,	,	PUNCT
ejpam-5704	117	22	2	2	NUM
ejpam-5704	117	23	,	,	PUNCT
ejpam-5704	117	24	...	...	PUNCT
ejpam-5704	117	25	,	,	PUNCT
ejpam-5704	117	26	n	n	X
ejpam-5704	117	27	,	,	PUNCT
ejpam-5704	117	28	representing	represent	VERB
ejpam-5704	117	29	the	the	DET
ejpam-5704	117	30	solutions	solution	NOUN
ejpam-5704	117	31	of	of	ADP
ejpam-5704	117	32	(	(	PUNCT
ejpam-5704	117	33	12	12	NUM
ejpam-5704	117	34	)	)	PUNCT
ejpam-5704	117	35	at	at	ADP
ejpam-5704	117	36	the	the	DET
ejpam-5704	117	37	points	point	NOUN
ejpam-5704	117	38	{	{	PUNCT
ejpam-5704	117	39	ti}ni=0	ti}ni=0	NOUN
ejpam-5704	117	40	.	.	PROPN
ejpam-5704	117	41	remark	remark	PROPN
ejpam-5704	117	42	3.1	3.1	NUM
ejpam-5704	117	43	.	.	PUNCT
ejpam-5704	118	1	using	use	VERB
ejpam-5704	118	2	the	the	DET
ejpam-5704	118	3	relation	relation	NOUN
ejpam-5704	118	4	(	(	PUNCT
ejpam-5704	118	5	16	16	NUM
ejpam-5704	118	6	)	)	PUNCT
ejpam-5704	118	7	,	,	PUNCT
ejpam-5704	118	8	approximate	approximate	VERB
ejpam-5704	118	9	the	the	DET
ejpam-5704	118	10	integrals	integral	NOUN
ejpam-5704	118	11	in	in	ADP
ejpam-5704	118	12	(	(	PUNCT
ejpam-5704	118	13	12	12	NUM
ejpam-5704	118	14	)	)	PUNCT
ejpam-5704	118	15	,	,	PUNCT
ejpam-5704	118	16	obtaining	obtain	VERB
ejpam-5704	118	17	a	a	DET
ejpam-5704	118	18	new	new	ADJ
ejpam-5704	118	19	equation	equation	NOUN
ejpam-5704	118	20	:	:	PUNCT
ejpam-5704	118	21	yn	yn	PROPN
ejpam-5704	118	22	(	(	PUNCT
ejpam-5704	118	23	t	t	PROPN
ejpam-5704	118	24	)	)	PUNCT
ejpam-5704	118	25	=	=	SYM
ejpam-5704	118	26	f(t	f(t	NOUN
ejpam-5704	118	27	)	)	PUNCT
ejpam-5704	119	1	+	+	CCONJ
ejpam-5704	119	2	n∑	n∑	X
ejpam-5704	119	3	j=0	j=0	PROPN
ejpam-5704	119	4	(	(	PUNCT
ejpam-5704	119	5	w1,t	w1,t	PROPN
ejpam-5704	119	6	,	,	PUNCT
ejpam-5704	119	7	j	j	PROPN
ejpam-5704	119	8	k1(t	k1(t	PROPN
ejpam-5704	119	9	,	,	PUNCT
ejpam-5704	119	10	tj	tj	X
ejpam-5704	119	11	,	,	PUNCT
ejpam-5704	119	12	yn	yn	PROPN
ejpam-5704	119	13	(	(	PUNCT
ejpam-5704	119	14	tj	tj	NOUN
ejpam-5704	119	15	)	)	PUNCT
ejpam-5704	119	16	)	)	PUNCT
ejpam-5704	120	1	+	+	VERB
ejpam-5704	120	2	w2,t	w2,t	PROPN
ejpam-5704	120	3	,	,	PUNCT
ejpam-5704	120	4	j	j	PROPN
ejpam-5704	120	5	k2(t	k2(t	PROPN
ejpam-5704	120	6	,	,	PUNCT
ejpam-5704	120	7	tj	tj	PROPN
ejpam-5704	120	8	,	,	PUNCT
ejpam-5704	120	9	yn	yn	PROPN
ejpam-5704	120	10	(	(	PUNCT
ejpam-5704	120	11	tj	tj	NOUN
ejpam-5704	120	12	)	)	PUNCT
ejpam-5704	120	13	)	)	PUNCT
ejpam-5704	120	14	)	)	PUNCT
ejpam-5704	120	15	,	,	PUNCT
ejpam-5704	120	16	(	(	PUNCT
ejpam-5704	120	17	19	19	NUM
ejpam-5704	120	18	)	)	PUNCT
ejpam-5704	120	19	where	where	SCONJ
ejpam-5704	120	20	for	for	ADP
ejpam-5704	120	21	j	j	PROPN
ejpam-5704	120	22	=	=	SYM
ejpam-5704	120	23	0	0	PROPN
ejpam-5704	120	24	,	,	PUNCT
ejpam-5704	120	25	1	1	NUM
ejpam-5704	120	26	,	,	PUNCT
ejpam-5704	120	27	2	2	NUM
ejpam-5704	120	28	,	,	PUNCT
ejpam-5704	120	29	.	.	PUNCT
ejpam-5704	120	30	.	.	PUNCT
ejpam-5704	120	31	.	.	PUNCT
ejpam-5704	121	1	,	,	PUNCT
ejpam-5704	121	2	n	n	X
ejpam-5704	121	3	,	,	PUNCT
ejpam-5704	121	4	w1,t	w1,t	PROPN
ejpam-5704	121	5	,	,	PUNCT
ejpam-5704	121	6	j	j	PROPN
ejpam-5704	121	7	=	=	SYM
ejpam-5704	121	8	∫	∫	PROPN
ejpam-5704	122	1	t	t	PROPN
ejpam-5704	122	2	0	0	NUM
ejpam-5704	122	3	p1,h(t	p1,h(t	NOUN
ejpam-5704	122	4	,	,	PUNCT
ejpam-5704	122	5	w)ln	w)ln	PROPN
ejpam-5704	122	6	,	,	PUNCT
ejpam-5704	122	7	j(w)dw	j(w)dw	PROPN
ejpam-5704	122	8	,	,	PUNCT
ejpam-5704	122	9	w2,t	w2,t	PROPN
ejpam-5704	122	10	,	,	PUNCT
ejpam-5704	122	11	j	j	PROPN
ejpam-5704	122	12	=	=	SYM
ejpam-5704	122	13	∫	∫	PROPN
ejpam-5704	122	14	θ(t	θ(t	PROPN
ejpam-5704	122	15	)	)	PUNCT
ejpam-5704	122	16	0	0	NUM
ejpam-5704	123	1	p2,h(t	p2,h(t	NOUN
ejpam-5704	123	2	,	,	PUNCT
ejpam-5704	123	3	w)ln	w)ln	PROPN
ejpam-5704	123	4	,	,	PUNCT
ejpam-5704	123	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	123	6	,	,	PUNCT
ejpam-5704	123	7	we	we	PRON
ejpam-5704	123	8	write	write	VERB
ejpam-5704	123	9	this	this	PRON
ejpam-5704	123	10	as	as	ADP
ejpam-5704	123	11	an	an	DET
ejpam-5704	123	12	exact	exact	ADJ
ejpam-5704	123	13	equation	equation	NOUN
ejpam-5704	123	14	with	with	ADP
ejpam-5704	123	15	a	a	DET
ejpam-5704	123	16	new	new	ADJ
ejpam-5704	123	17	unknown	unknown	ADJ
ejpam-5704	123	18	function	function	NOUN
ejpam-5704	123	19	yn	yn	PROPN
ejpam-5704	123	20	(	(	PUNCT
ejpam-5704	123	21	t	t	PROPN
ejpam-5704	123	22	)	)	PUNCT
ejpam-5704	123	23	.	.	PUNCT
ejpam-5704	124	1	to	to	PART
ejpam-5704	124	2	find	find	VERB
ejpam-5704	124	3	the	the	DET
ejpam-5704	124	4	solution	solution	NOUN
ejpam-5704	124	5	at	at	ADP
ejpam-5704	124	6	the	the	DET
ejpam-5704	124	7	node	node	NOUN
ejpam-5704	124	8	points	point	NOUN
ejpam-5704	124	9	,	,	PUNCT
ejpam-5704	124	10	let	let	VERB
ejpam-5704	124	11	y(t	y(t	NUM
ejpam-5704	124	12	)	)	PUNCT
ejpam-5704	124	13	run	run	VERB
ejpam-5704	124	14	through	through	ADP
ejpam-5704	124	15	the	the	DET
ejpam-5704	124	16	quadrature	quadrature	NOUN
ejpam-5704	124	17	node	node	NOUN
ejpam-5704	124	18	points	point	NOUN
ejpam-5704	124	19	ti	ti	NOUN
ejpam-5704	124	20	.	.	PUNCT
ejpam-5704	125	1	this	this	PRON
ejpam-5704	125	2	yields	yield	VERB
ejpam-5704	125	3	the	the	DET
ejpam-5704	125	4	nonlinear	nonlinear	ADJ
ejpam-5704	125	5	system	system	NOUN
ejpam-5704	125	6	(	(	PUNCT
ejpam-5704	125	7	17	17	NUM
ejpam-5704	125	8	)	)	PUNCT
ejpam-5704	125	9	of	of	ADP
ejpam-5704	125	10	order	order	NOUN
ejpam-5704	125	11	n+1	n+1	PROPN
ejpam-5704	125	12	.	.	PUNCT
ejpam-5704	126	1	each	each	DET
ejpam-5704	126	2	solution	solution	NOUN
ejpam-5704	126	3	yn	yn	PROPN
ejpam-5704	126	4	(	(	PUNCT
ejpam-5704	126	5	t	t	PROPN
ejpam-5704	126	6	)	)	PUNCT
ejpam-5704	126	7	of	of	ADP
ejpam-5704	126	8	(	(	PUNCT
ejpam-5704	126	9	19	19	NUM
ejpam-5704	126	10	)	)	PUNCT
ejpam-5704	126	11	furnishes	furnish	VERB
ejpam-5704	126	12	a	a	DET
ejpam-5704	126	13	solution	solution	NOUN
ejpam-5704	126	14	to	to	ADP
ejpam-5704	126	15	(	(	PUNCT
ejpam-5704	126	16	17	17	NUM
ejpam-5704	126	17	):	):	PUNCT
ejpam-5704	126	18	merely	merely	ADV
ejpam-5704	126	19	evaluate	evaluate	VERB
ejpam-5704	126	20	yn	yn	PROPN
ejpam-5704	126	21	(	(	PUNCT
ejpam-5704	126	22	t	t	PROPN
ejpam-5704	126	23	)	)	PUNCT
ejpam-5704	126	24	at	at	ADP
ejpam-5704	126	25	the	the	DET
ejpam-5704	126	26	node	node	NOUN
ejpam-5704	126	27	points	point	NOUN
ejpam-5704	126	28	.	.	PUNCT
ejpam-5704	127	1	the	the	DET
ejpam-5704	127	2	converse	converse	NOUN
ejpam-5704	127	3	is	be	AUX
ejpam-5704	127	4	also	also	ADV
ejpam-5704	127	5	true	true	ADJ
ejpam-5704	127	6	.	.	PUNCT
ejpam-5704	128	1	to	to	ADP
ejpam-5704	128	2	each	each	DET
ejpam-5704	128	3	solution	solution	NOUN
ejpam-5704	128	4	(	(	PUNCT
ejpam-5704	128	5	yn	yn	PROPN
ejpam-5704	128	6	(	(	PUNCT
ejpam-5704	128	7	t0	t0	PROPN
ejpam-5704	128	8	)	)	PUNCT
ejpam-5704	128	9	,	,	PUNCT
ejpam-5704	128	10	.	.	PUNCT
ejpam-5704	128	11	.	.	PUNCT
ejpam-5704	129	1	.	.	PUNCT
ejpam-5704	130	1	,	,	PUNCT
ejpam-5704	130	2	yn	yn	PROPN
ejpam-5704	130	3	(	(	PUNCT
ejpam-5704	130	4	tn	tn	PROPN
ejpam-5704	130	5	)	)	PUNCT
ejpam-5704	130	6	)	)	PUNCT
ejpam-5704	131	1	t	t	NOUN
ejpam-5704	131	2	of	of	ADP
ejpam-5704	131	3	(	(	PUNCT
ejpam-5704	131	4	17	17	NUM
ejpam-5704	131	5	)	)	PUNCT
ejpam-5704	131	6	,	,	PUNCT
ejpam-5704	131	7	there	there	PRON
ejpam-5704	131	8	is	be	VERB
ejpam-5704	131	9	a	a	DET
ejpam-5704	131	10	unique	unique	ADJ
ejpam-5704	131	11	solution	solution	NOUN
ejpam-5704	131	12	of	of	ADP
ejpam-5704	131	13	(	(	PUNCT
ejpam-5704	131	14	19	19	NUM
ejpam-5704	131	15	)	)	PUNCT
ejpam-5704	131	16	.	.	PUNCT
ejpam-5704	132	1	therefore	therefore	ADV
ejpam-5704	132	2	,	,	PUNCT
ejpam-5704	132	3	by	by	ADP
ejpam-5704	132	4	inserting	insert	VERB
ejpam-5704	132	5	(	(	PUNCT
ejpam-5704	132	6	yn	yn	PROPN
ejpam-5704	132	7	(	(	PUNCT
ejpam-5704	132	8	t0	t0	PROPN
ejpam-5704	132	9	)	)	PUNCT
ejpam-5704	132	10	,	,	PUNCT
ejpam-5704	132	11	.	.	PUNCT
ejpam-5704	132	12	.	.	PUNCT
ejpam-5704	132	13	.	.	PUNCT
ejpam-5704	133	1	,	,	PUNCT
ejpam-5704	133	2	yn	yn	PROPN
ejpam-5704	133	3	(	(	PUNCT
ejpam-5704	133	4	tn	tn	PROPN
ejpam-5704	133	5	)	)	PUNCT
ejpam-5704	133	6	)	)	PUNCT
ejpam-5704	133	7	t	t	NOUN
ejpam-5704	133	8	in	in	ADP
ejpam-5704	133	9	(	(	PUNCT
ejpam-5704	133	10	19	19	NUM
ejpam-5704	133	11	)	)	PUNCT
ejpam-5704	133	12	,	,	PUNCT
ejpam-5704	133	13	we	we	PRON
ejpam-5704	133	14	can	can	AUX
ejpam-5704	133	15	obtain	obtain	VERB
ejpam-5704	133	16	the	the	DET
ejpam-5704	133	17	approximate	approximate	ADJ
ejpam-5704	133	18	solution	solution	NOUN
ejpam-5704	133	19	in	in	ADP
ejpam-5704	133	20	each	each	DET
ejpam-5704	133	21	desired	desire	VERB
ejpam-5704	133	22	point	point	NOUN
ejpam-5704	133	23	t.	t.	PROPN
ejpam-5704	133	24	in	in	ADP
ejpam-5704	133	25	fact	fact	NOUN
ejpam-5704	133	26	,	,	PUNCT
ejpam-5704	133	27	the	the	DET
ejpam-5704	133	28	relation	relation	NOUN
ejpam-5704	133	29	(	(	PUNCT
ejpam-5704	133	30	19	19	NUM
ejpam-5704	133	31	)	)	PUNCT
ejpam-5704	133	32	is	be	AUX
ejpam-5704	133	33	the	the	DET
ejpam-5704	133	34	nyström	nyström	PRON
ejpam-5704	133	35	interpolation	interpolation	NOUN
ejpam-5704	133	36	formula	formula	NOUN
ejpam-5704	133	37	.	.	PUNCT
ejpam-5704	134	1	b.	b.	PROPN
ejpam-5704	134	2	h.	h.	PROPN
ejpam-5704	134	3	alrikabi	alrikabi	PROPN
ejpam-5704	134	4	,	,	PUNCT
ejpam-5704	134	5	p.	p.	PROPN
ejpam-5704	134	6	darania	darania	PROPN
ejpam-5704	134	7	,	,	PUNCT
ejpam-5704	134	8	s.pishbin	s.pishbin	PROPN
ejpam-5704	134	9	/	/	SYM
ejpam-5704	134	10	eur	eur	PROPN
ejpam-5704	134	11	.	.	PUNCT
ejpam-5704	135	1	j.	j.	PROPN
ejpam-5704	135	2	pure	pure	PROPN
ejpam-5704	135	3	appl	appl	PROPN
ejpam-5704	135	4	.	.	PROPN
ejpam-5704	135	5	math	math	PROPN
ejpam-5704	135	6	,	,	PUNCT
ejpam-5704	135	7	18	18	NUM
ejpam-5704	135	8	(	(	PUNCT
ejpam-5704	135	9	2	2	NUM
ejpam-5704	135	10	)	)	PUNCT
ejpam-5704	135	11	(	(	PUNCT
ejpam-5704	135	12	2025	2025	NUM
ejpam-5704	135	13	)	)	PUNCT
ejpam-5704	135	14	,	,	PUNCT
ejpam-5704	135	15	5704	5704	NUM
ejpam-5704	135	16	8	8	NUM
ejpam-5704	135	17	of	of	ADP
ejpam-5704	135	18	19	19	NUM
ejpam-5704	135	19	with	with	ADP
ejpam-5704	135	20	these	these	DET
ejpam-5704	135	21	symbols	symbol	NOUN
ejpam-5704	135	22	in	in	ADP
ejpam-5704	135	23	place	place	NOUN
ejpam-5704	135	24	,	,	PUNCT
ejpam-5704	135	25	we	we	PRON
ejpam-5704	135	26	can	can	AUX
ejpam-5704	135	27	encapsulate	encapsulate	VERB
ejpam-5704	135	28	the	the	DET
ejpam-5704	135	29	steps	step	NOUN
ejpam-5704	135	30	in	in	ADP
ejpam-5704	135	31	the	the	DET
ejpam-5704	135	32	following	following	ADJ
ejpam-5704	135	33	algorithm	algorithm	NOUN
ejpam-5704	135	34	:	:	PUNCT
ejpam-5704	135	35	algorithm	algorithm	NOUN
ejpam-5704	135	36	1	1	NUM
ejpam-5704	135	37	.	.	PUNCT
ejpam-5704	136	1	input	input	NOUN
ejpam-5704	136	2	:	:	PUNCT
ejpam-5704	136	3	n	n	CCONJ
ejpam-5704	136	4	;	;	PUNCT
ejpam-5704	136	5	begin	begin	VERB
ejpam-5704	136	6	for	for	ADP
ejpam-5704	136	7	l=0,1,2	l=0,1,2	NUM
ejpam-5704	136	8	.	.	PUNCT
ejpam-5704	136	9	.	.	PUNCT
ejpam-5704	136	10	.	.	PUNCT
ejpam-5704	137	1	,	,	PUNCT
ejpam-5704	137	2	n	n	CCONJ
ejpam-5704	137	3	:	:	PUNCT
ejpam-5704	137	4	compute	compute	VERB
ejpam-5704	137	5	tl	tl	PROPN
ejpam-5704	137	6	as	as	ADP
ejpam-5704	137	7	simple	simple	ADJ
ejpam-5704	137	8	roots	root	NOUN
ejpam-5704	137	9	of	of	ADP
ejpam-5704	137	10	n	n	PROPN
ejpam-5704	137	11	+	+	CCONJ
ejpam-5704	137	12	1	1	NUM
ejpam-5704	137	13	st	st	ADJ
ejpam-5704	137	14	-	-	PUNCT
ejpam-5704	137	15	degree	degree	NOUN
ejpam-5704	137	16	orthogonal	orthogonal	ADJ
ejpam-5704	137	17	polynomial	polynomial	NOUN
ejpam-5704	137	18	in	in	ADP
ejpam-5704	137	19	[	[	X
ejpam-5704	137	20	0	0	NUM
ejpam-5704	137	21	,	,	PUNCT
ejpam-5704	137	22	1	1	NUM
ejpam-5704	137	23	]	]	PUNCT
ejpam-5704	137	24	;	;	PUNCT
ejpam-5704	137	25	for	for	ADP
ejpam-5704	137	26	i=0,1	i=0,1	NOUN
ejpam-5704	137	27	.	.	PUNCT
ejpam-5704	137	28	.	.	PUNCT
ejpam-5704	137	29	.	.	PUNCT
ejpam-5704	138	1	,	,	PUNCT
ejpam-5704	139	1	n	n	CCONJ
ejpam-5704	139	2	:	:	PUNCT
ejpam-5704	139	3	for	for	ADP
ejpam-5704	139	4	j=0,1	j=0,1	ADV
ejpam-5704	139	5	,	,	PUNCT
ejpam-5704	139	6	.	.	PUNCT
ejpam-5704	139	7	.	.	PUNCT
ejpam-5704	140	1	.	.	PUNCT
ejpam-5704	141	1	,	,	PUNCT
ejpam-5704	141	2	n	n	CCONJ
ejpam-5704	141	3	:	:	PUNCT
ejpam-5704	141	4	for	for	ADP
ejpam-5704	141	5	r=1,2	r=1,2	ADJ
ejpam-5704	141	6	:	:	PUNCT
ejpam-5704	141	7	compute	compute	PROPN
ejpam-5704	141	8	wr	wr	PROPN
ejpam-5704	141	9	,	,	PUNCT
ejpam-5704	141	10	i	i	PRON
ejpam-5704	141	11	,	,	PUNCT
ejpam-5704	141	12	j	j	PROPN
ejpam-5704	141	13	from	from	ADP
ejpam-5704	141	14	(	(	PUNCT
ejpam-5704	141	15	18	18	NUM
ejpam-5704	141	16	)	)	PUNCT
ejpam-5704	141	17	;	;	PUNCT
ejpam-5704	141	18	solve	solve	VERB
ejpam-5704	141	19	nonlinear	nonlinear	ADJ
ejpam-5704	141	20	system	system	NOUN
ejpam-5704	141	21	(	(	PUNCT
ejpam-5704	141	22	17	17	NUM
ejpam-5704	141	23	)	)	PUNCT
ejpam-5704	141	24	and	and	CCONJ
ejpam-5704	141	25	compute	compute	VERB
ejpam-5704	141	26	yn	yn	PROPN
ejpam-5704	141	27	(	(	PUNCT
ejpam-5704	141	28	ti	ti	NOUN
ejpam-5704	141	29	)	)	PUNCT
ejpam-5704	141	30	;	;	PUNCT
ejpam-5704	141	31	end	end	NOUN
ejpam-5704	141	32	.	.	PUNCT
ejpam-5704	142	1	4	4	X
ejpam-5704	142	2	.	.	X
ejpam-5704	142	3	convergence	convergence	NOUN
ejpam-5704	142	4	theorem	theorem	VERB
ejpam-5704	142	5	here	here	ADV
ejpam-5704	142	6	,	,	PUNCT
ejpam-5704	142	7	we	we	PRON
ejpam-5704	142	8	investigate	investigate	VERB
ejpam-5704	142	9	the	the	DET
ejpam-5704	142	10	convergence	convergence	NOUN
ejpam-5704	142	11	analysis	analysis	NOUN
ejpam-5704	142	12	of	of	ADP
ejpam-5704	142	13	the	the	DET
ejpam-5704	142	14	equation	equation	NOUN
ejpam-5704	142	15	y(t	y(t	NUM
ejpam-5704	142	16	)	)	PUNCT
ejpam-5704	143	1	=	=	SYM
ejpam-5704	143	2	f(t	f(t	NOUN
ejpam-5704	143	3	)	)	PUNCT
ejpam-5704	144	1	+	+	CCONJ
ejpam-5704	144	2	(	(	PUNCT
ejpam-5704	144	3	vαy)(t	vαy)(t	ADJ
ejpam-5704	144	4	)	)	PUNCT
ejpam-5704	144	5	+	+	CCONJ
ejpam-5704	144	6	(	(	PUNCT
ejpam-5704	144	7	vα	vα	INTJ
ejpam-5704	144	8	,	,	PUNCT
ejpam-5704	144	9	θy)(t	θy)(t	PROPN
ejpam-5704	144	10	)	)	PUNCT
ejpam-5704	144	11	,	,	PUNCT
ejpam-5704	144	12	t	t	PROPN
ejpam-5704	144	13	∈	∈	PROPN
ejpam-5704	145	1	[	[	X
ejpam-5704	145	2	0	0	NUM
ejpam-5704	145	3	,	,	PUNCT
ejpam-5704	145	4	1	1	NUM
ejpam-5704	145	5	]	]	PUNCT
ejpam-5704	145	6	.	.	PUNCT
ejpam-5704	146	1	(	(	PUNCT
ejpam-5704	146	2	20	20	NUM
ejpam-5704	146	3	)	)	PUNCT
ejpam-5704	146	4	where	where	SCONJ
ejpam-5704	146	5	(	(	PUNCT
ejpam-5704	146	6	vαy)(t	vαy)(t	ADJ
ejpam-5704	146	7	)	)	PUNCT
ejpam-5704	146	8	=	=	SYM
ejpam-5704	147	1	∫	∫	PROPN
ejpam-5704	147	2	t	t	PROPN
ejpam-5704	147	3	0	0	NUM
ejpam-5704	147	4	p1(t	p1(t	PROPN
ejpam-5704	147	5	,	,	PUNCT
ejpam-5704	147	6	s)k1(t	s)k1(t	X
ejpam-5704	147	7	,	,	PUNCT
ejpam-5704	147	8	s)y(s)ds	s)y(s)ds	NOUN
ejpam-5704	147	9	,	,	PUNCT
ejpam-5704	147	10	(	(	PUNCT
ejpam-5704	147	11	vα	vα	INTJ
ejpam-5704	147	12	,	,	PUNCT
ejpam-5704	147	13	θy)(t	θy)(t	PROPN
ejpam-5704	147	14	)	)	PUNCT
ejpam-5704	148	1	=	=	SYM
ejpam-5704	148	2	∫	∫	PROPN
ejpam-5704	148	3	θ(t	θ(t	PROPN
ejpam-5704	148	4	)	)	PUNCT
ejpam-5704	148	5	0	0	NUM
ejpam-5704	149	1	p2(t	p2(t	PROPN
ejpam-5704	149	2	,	,	PUNCT
ejpam-5704	149	3	s)k2(t	s)k2(t	PROPN
ejpam-5704	149	4	,	,	PUNCT
ejpam-5704	149	5	s)y(s)ds	s)y(s)ds	NOUN
ejpam-5704	149	6	.	.	PUNCT
ejpam-5704	150	1	(	(	PUNCT
ejpam-5704	150	2	21	21	NUM
ejpam-5704	150	3	)	)	PUNCT
ejpam-5704	150	4	assuming	assume	VERB
ejpam-5704	150	5	that	that	SCONJ
ejpam-5704	150	6	the	the	DET
ejpam-5704	150	7	function	function	NOUN
ejpam-5704	150	8	f(t	f(t	PROPN
ejpam-5704	150	9	)	)	PUNCT
ejpam-5704	150	10	belongs	belong	VERB
ejpam-5704	150	11	to	to	ADP
ejpam-5704	150	12	the	the	DET
ejpam-5704	150	13	space	space	NOUN
ejpam-5704	150	14	c([0	c([0	NOUN
ejpam-5704	150	15	,	,	PUNCT
ejpam-5704	150	16	1	1	NUM
ejpam-5704	150	17	]	]	PUNCT
ejpam-5704	150	18	)	)	PUNCT
ejpam-5704	150	19	and	and	CCONJ
ejpam-5704	150	20	the	the	DET
ejpam-5704	150	21	kernels	kernel	NOUN
ejpam-5704	150	22	ph	ph	VERB
ejpam-5704	150	23	,	,	PUNCT
ejpam-5704	150	24	where	where	SCONJ
ejpam-5704	150	25	h	h	NOUN
ejpam-5704	150	26	=	=	NOUN
ejpam-5704	150	27	1	1	NUM
ejpam-5704	150	28	,	,	PUNCT
ejpam-5704	150	29	2	2	NUM
ejpam-5704	150	30	,	,	PUNCT
ejpam-5704	150	31	exhibit	exhibit	VERB
ejpam-5704	150	32	weak	weak	ADJ
ejpam-5704	150	33	singularity	singularity	NOUN
ejpam-5704	150	34	in	in	ADP
ejpam-5704	150	35	the	the	DET
ejpam-5704	150	36	forms	form	NOUN
ejpam-5704	150	37	(	(	PUNCT
ejpam-5704	150	38	4	4	NUM
ejpam-5704	150	39	)	)	PUNCT
ejpam-5704	150	40	,	,	PUNCT
ejpam-5704	150	41	the	the	DET
ejpam-5704	150	42	equation	equation	NOUN
ejpam-5704	150	43	(	(	PUNCT
ejpam-5704	150	44	20	20	NUM
ejpam-5704	150	45	)	)	PUNCT
ejpam-5704	150	46	possesses	possess	VERB
ejpam-5704	150	47	a	a	DET
ejpam-5704	150	48	distinct	distinct	ADJ
ejpam-5704	150	49	solution	solution	NOUN
ejpam-5704	150	50	y	y	PROPN
ejpam-5704	150	51	in	in	ADP
ejpam-5704	150	52	the	the	DET
ejpam-5704	150	53	interval	interval	NOUN
ejpam-5704	150	54	c[0	c[0	PROPN
ejpam-5704	150	55	,	,	PUNCT
ejpam-5704	150	56	1	1	NUM
ejpam-5704	150	57	]	]	PUNCT
ejpam-5704	150	58	.	.	PUNCT
ejpam-5704	151	1	it	it	PRON
ejpam-5704	151	2	is	be	AUX
ejpam-5704	151	3	anticipated	anticipate	VERB
ejpam-5704	151	4	that	that	SCONJ
ejpam-5704	151	5	this	this	DET
ejpam-5704	151	6	solution	solution	NOUN
ejpam-5704	151	7	may	may	AUX
ejpam-5704	151	8	have	have	VERB
ejpam-5704	151	9	unbounded	unbounded	ADJ
ejpam-5704	151	10	derivatives	derivative	NOUN
ejpam-5704	151	11	at	at	ADP
ejpam-5704	151	12	the	the	DET
ejpam-5704	151	13	endpoints	endpoint	NOUN
ejpam-5704	151	14	.	.	PUNCT
ejpam-5704	152	1	if	if	SCONJ
ejpam-5704	152	2	we	we	PRON
ejpam-5704	152	3	utilize	utilize	VERB
ejpam-5704	152	4	the	the	DET
ejpam-5704	152	5	method	method	NOUN
ejpam-5704	152	6	(	(	PUNCT
ejpam-5704	152	7	17	17	NUM
ejpam-5704	152	8	)	)	PUNCT
ejpam-5704	152	9	on	on	ADP
ejpam-5704	152	10	the	the	DET
ejpam-5704	152	11	test	test	NOUN
ejpam-5704	152	12	problem	problem	NOUN
ejpam-5704	152	13	(	(	PUNCT
ejpam-5704	152	14	20	20	NUM
ejpam-5704	152	15	)	)	PUNCT
ejpam-5704	152	16	for	for	ADP
ejpam-5704	152	17	a	a	DET
ejpam-5704	152	18	given	give	VERB
ejpam-5704	152	19	mesh	mesh	NOUN
ejpam-5704	152	20	{	{	PUNCT
ejpam-5704	152	21	ti}ni=1	ti}ni=1	NOUN
ejpam-5704	152	22	⋃	⋃	PROPN
ejpam-5704	152	23	{	{	PUNCT
ejpam-5704	152	24	0	0	NUM
ejpam-5704	152	25	}	}	PUNCT
ejpam-5704	152	26	,	,	PUNCT
ejpam-5704	152	27	the	the	DET
ejpam-5704	152	28	resulting	result	VERB
ejpam-5704	152	29	approximate	approximate	ADJ
ejpam-5704	152	30	solution	solution	NOUN
ejpam-5704	152	31	yn	yn	PROPN
ejpam-5704	152	32	(	(	PUNCT
ejpam-5704	152	33	t	t	PROPN
ejpam-5704	152	34	)	)	PUNCT
ejpam-5704	152	35	takes	take	VERB
ejpam-5704	152	36	the	the	DET
ejpam-5704	152	37	following	follow	VERB
ejpam-5704	152	38	form	form	NOUN
ejpam-5704	152	39	yn	yn	PROPN
ejpam-5704	152	40	(	(	PUNCT
ejpam-5704	152	41	t	t	PROPN
ejpam-5704	152	42	)	)	PUNCT
ejpam-5704	152	43	=	=	SYM
ejpam-5704	152	44	f(t	f(t	NOUN
ejpam-5704	152	45	)	)	PUNCT
ejpam-5704	153	1	+	+	CCONJ
ejpam-5704	153	2	n∑	n∑	PROPN
ejpam-5704	153	3	j=0	j=0	PROPN
ejpam-5704	153	4	(	(	PUNCT
ejpam-5704	153	5	ω1,j(p1,h	ω1,j(p1,h	NOUN
ejpam-5704	153	6	,	,	PUNCT
ejpam-5704	153	7	t	t	PROPN
ejpam-5704	153	8	)	)	PUNCT
ejpam-5704	153	9	+	+	CCONJ
ejpam-5704	153	10	ω2,j(p2,h	ω2,j(p2,h	ADP
ejpam-5704	153	11	,	,	PUNCT
ejpam-5704	153	12	θ(t)))yn	θ(t)))yn	NOUN
ejpam-5704	153	13	(	(	PUNCT
ejpam-5704	153	14	tj	tj	NOUN
ejpam-5704	153	15	)	)	PUNCT
ejpam-5704	153	16	,	,	PUNCT
ejpam-5704	153	17	(	(	PUNCT
ejpam-5704	153	18	22	22	NUM
ejpam-5704	153	19	)	)	PUNCT
ejpam-5704	153	20	where	where	SCONJ
ejpam-5704	153	21	ω1,j(p1,h	ω1,j(p1,h	NOUN
ejpam-5704	153	22	,	,	PUNCT
ejpam-5704	153	23	t	t	PROPN
ejpam-5704	153	24	)	)	PUNCT
ejpam-5704	153	25	=	=	SYM
ejpam-5704	153	26	∫	∫	PROPN
ejpam-5704	153	27	t	t	PROPN
ejpam-5704	153	28	0	0	NUM
ejpam-5704	153	29	p1,h(ti	p1,h(ti	PROPN
ejpam-5704	153	30	,	,	PUNCT
ejpam-5704	153	31	w)ln	w)ln	PROPN
ejpam-5704	153	32	,	,	PUNCT
ejpam-5704	153	33	j(w)dw	j(w)dw	PROPN
ejpam-5704	153	34	,	,	PUNCT
ejpam-5704	153	35	ω2,j(p2,h	ω2,j(p2,h	PROPN
ejpam-5704	153	36	,	,	PUNCT
ejpam-5704	153	37	θ(t	θ(t	PROPN
ejpam-5704	153	38	)	)	PUNCT
ejpam-5704	153	39	)	)	PUNCT
ejpam-5704	154	1	=	=	SYM
ejpam-5704	154	2	∫	∫	PROPN
ejpam-5704	154	3	θ(t	θ(t	PROPN
ejpam-5704	154	4	)	)	PUNCT
ejpam-5704	154	5	0	0	PUNCT
ejpam-5704	155	1	p2,h(ti	p2,h(ti	PROPN
ejpam-5704	155	2	,	,	PUNCT
ejpam-5704	155	3	w)ln	w)ln	PROPN
ejpam-5704	155	4	,	,	PUNCT
ejpam-5704	155	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	155	6	.	.	PUNCT
ejpam-5704	156	1	(	(	PUNCT
ejpam-5704	156	2	23	23	NUM
ejpam-5704	156	3	)	)	PUNCT
ejpam-5704	156	4	b.	b.	PROPN
ejpam-5704	156	5	h.	h.	PROPN
ejpam-5704	156	6	alrikabi	alrikabi	PROPN
ejpam-5704	156	7	,	,	PUNCT
ejpam-5704	156	8	p.	p.	PROPN
ejpam-5704	156	9	darania	darania	PROPN
ejpam-5704	156	10	,	,	PUNCT
ejpam-5704	156	11	s.pishbin	s.pishbin	PROPN
ejpam-5704	156	12	/	/	SYM
ejpam-5704	156	13	eur	eur	PROPN
ejpam-5704	156	14	.	.	PUNCT
ejpam-5704	157	1	j.	j.	PROPN
ejpam-5704	157	2	pure	pure	PROPN
ejpam-5704	157	3	appl	appl	PROPN
ejpam-5704	157	4	.	.	PROPN
ejpam-5704	157	5	math	math	PROPN
ejpam-5704	157	6	,	,	PUNCT
ejpam-5704	157	7	18	18	NUM
ejpam-5704	157	8	(	(	PUNCT
ejpam-5704	157	9	2	2	NUM
ejpam-5704	157	10	)	)	PUNCT
ejpam-5704	157	11	(	(	PUNCT
ejpam-5704	157	12	2025	2025	NUM
ejpam-5704	157	13	)	)	PUNCT
ejpam-5704	157	14	,	,	PUNCT
ejpam-5704	157	15	5704	5704	NUM
ejpam-5704	157	16	9	9	NUM
ejpam-5704	157	17	of	of	ADP
ejpam-5704	157	18	19	19	NUM
ejpam-5704	157	19	to	to	PART
ejpam-5704	157	20	assess	assess	VERB
ejpam-5704	157	21	the	the	DET
ejpam-5704	157	22	uniform	uniform	ADJ
ejpam-5704	157	23	convergence	convergence	NOUN
ejpam-5704	157	24	of	of	ADP
ejpam-5704	157	25	yn	yn	PROPN
ejpam-5704	157	26	(	(	PUNCT
ejpam-5704	157	27	t	t	PROPN
ejpam-5704	157	28	)	)	PUNCT
ejpam-5704	157	29	to	to	ADP
ejpam-5704	157	30	y(t	y(t	PROPN
ejpam-5704	157	31	)	)	PUNCT
ejpam-5704	157	32	as	as	ADP
ejpam-5704	157	33	solution	solution	NOUN
ejpam-5704	157	34	of	of	ADP
ejpam-5704	157	35	(	(	PUNCT
ejpam-5704	157	36	20	20	NUM
ejpam-5704	157	37	)	)	PUNCT
ejpam-5704	158	1	,	,	PUNCT
ejpam-5704	158	2	we	we	PRON
ejpam-5704	158	3	rewrite	rewrite	VERB
ejpam-5704	158	4	y(t)−	y(t)−	PROPN
ejpam-5704	158	5	yn	yn	PROPN
ejpam-5704	158	6	(	(	PUNCT
ejpam-5704	158	7	t	t	PROPN
ejpam-5704	158	8	)	)	PUNCT
ejpam-5704	158	9	=	=	SYM
ejpam-5704	159	1	n∑	n∑	X
ejpam-5704	159	2	j=0	j=0	PROPN
ejpam-5704	159	3	ω1,j(p1,h	ω1,j(p1,h	NOUN
ejpam-5704	159	4	,	,	PUNCT
ejpam-5704	159	5	t)(y(tj)−	t)(y(tj)−	NUM
ejpam-5704	159	6	yn	yn	PROPN
ejpam-5704	159	7	(	(	PUNCT
ejpam-5704	159	8	tj	tj	NOUN
ejpam-5704	159	9	)	)	PUNCT
ejpam-5704	159	10	)	)	PUNCT
ejpam-5704	160	1	+	+	CCONJ
ejpam-5704	160	2	n∑	n∑	DET
ejpam-5704	160	3	j=0	j=0	PROPN
ejpam-5704	160	4	ω2,j(p2,h	ω2,j(p2,h	PART
ejpam-5704	160	5	,	,	PUNCT
ejpam-5704	160	6	θ(t))(y(tj)−	θ(t))(y(tj)−	ADJ
ejpam-5704	160	7	yn	yn	PROPN
ejpam-5704	160	8	(	(	PUNCT
ejpam-5704	160	9	tj	tj	NOUN
ejpam-5704	160	10	)	)	PUNCT
ejpam-5704	160	11	)	)	PUNCT
ejpam-5704	161	1	+	+	X
ejpam-5704	161	2	t1,n	t1,n	PROPN
ejpam-5704	161	3	(	(	PUNCT
ejpam-5704	161	4	p1,h	p1,h	PROPN
ejpam-5704	161	5	,	,	PUNCT
ejpam-5704	161	6	y	y	PROPN
ejpam-5704	161	7	;	;	PUNCT
ejpam-5704	161	8	t	t	PROPN
ejpam-5704	161	9	)	)	PUNCT
ejpam-5704	161	10	+	+	CCONJ
ejpam-5704	162	1	t2,n	t2,n	PROPN
ejpam-5704	162	2	(	(	PUNCT
ejpam-5704	162	3	p2,h	p2,h	PROPN
ejpam-5704	162	4	,	,	PUNCT
ejpam-5704	162	5	y	y	PROPN
ejpam-5704	162	6	;	;	PUNCT
ejpam-5704	162	7	θ(t	θ(t	PROPN
ejpam-5704	162	8	)	)	PUNCT
ejpam-5704	162	9	)	)	PUNCT
ejpam-5704	162	10	,	,	PUNCT
ejpam-5704	162	11	(	(	PUNCT
ejpam-5704	162	12	24	24	NUM
ejpam-5704	162	13	)	)	PUNCT
ejpam-5704	162	14	where	where	SCONJ
ejpam-5704	162	15	t1,n	t1,n	PROPN
ejpam-5704	162	16	(	(	PUNCT
ejpam-5704	162	17	p1,h	p1,h	PROPN
ejpam-5704	162	18	,	,	PUNCT
ejpam-5704	162	19	y	y	PROPN
ejpam-5704	162	20	;	;	PUNCT
ejpam-5704	162	21	t	t	PROPN
ejpam-5704	162	22	)	)	PUNCT
ejpam-5704	162	23	=	=	SYM
ejpam-5704	163	1	∫	∫	PROPN
ejpam-5704	163	2	t	t	PROPN
ejpam-5704	163	3	0	0	NUM
ejpam-5704	163	4	p1,h(t	p1,h(t	NOUN
ejpam-5704	163	5	,	,	PUNCT
ejpam-5704	163	6	w)y(w)dw	w)y(w)dw	NOUN
ejpam-5704	163	7	−	−	PROPN
ejpam-5704	163	8	n∑	n∑	PROPN
ejpam-5704	163	9	j=0	j=0	PROPN
ejpam-5704	163	10	ω1,j(p1,h	ω1,j(p1,h	NOUN
ejpam-5704	163	11	,	,	PUNCT
ejpam-5704	163	12	t)y(tj	t)y(tj	NUM
ejpam-5704	163	13	)	)	PUNCT
ejpam-5704	163	14	,	,	PUNCT
ejpam-5704	163	15	t2,n	t2,n	PROPN
ejpam-5704	163	16	(	(	PUNCT
ejpam-5704	163	17	p2,h	p2,h	PROPN
ejpam-5704	163	18	,	,	PUNCT
ejpam-5704	163	19	y	y	PROPN
ejpam-5704	163	20	;	;	PUNCT
ejpam-5704	163	21	θ(t	θ(t	PROPN
ejpam-5704	163	22	)	)	PUNCT
ejpam-5704	163	23	)	)	PUNCT
ejpam-5704	164	1	=	=	SYM
ejpam-5704	164	2	∫	∫	PROPN
ejpam-5704	164	3	θ(t	θ(t	PROPN
ejpam-5704	164	4	)	)	PUNCT
ejpam-5704	164	5	0	0	NUM
ejpam-5704	164	6	p2,h(t	p2,h(t	NOUN
ejpam-5704	164	7	,	,	PUNCT
ejpam-5704	164	8	w)y(w)dw	w)y(w)dw	NOUN
ejpam-5704	164	9	−	−	PROPN
ejpam-5704	164	10	n∑	n∑	PROPN
ejpam-5704	164	11	j=0	j=0	PROPN
ejpam-5704	164	12	ω2,j(p2,h	ω2,j(p2,h	PROPN
ejpam-5704	164	13	,	,	PUNCT
ejpam-5704	164	14	θ(t))y(tj	θ(t))y(tj	PROPN
ejpam-5704	164	15	)	)	PUNCT
ejpam-5704	164	16	.	.	PUNCT
ejpam-5704	165	1	(	(	PUNCT
ejpam-5704	165	2	25	25	NUM
ejpam-5704	165	3	)	)	PUNCT
ejpam-5704	165	4	if	if	SCONJ
ejpam-5704	165	5	we	we	PRON
ejpam-5704	165	6	set	set	VERB
ejpam-5704	165	7	ωj(p1,h	ωj(p1,h	NOUN
ejpam-5704	165	8	,	,	PUNCT
ejpam-5704	165	9	p2,h	p2,h	PROPN
ejpam-5704	165	10	;	;	PUNCT
ejpam-5704	165	11	t	t	PROPN
ejpam-5704	165	12	,	,	PUNCT
ejpam-5704	165	13	θ(t	θ(t	PROPN
ejpam-5704	165	14	)	)	PUNCT
ejpam-5704	165	15	)	)	PUNCT
ejpam-5704	166	1	=	=	PUNCT
ejpam-5704	166	2	ω1,j(p1,h	ω1,j(p1,h	NOUN
ejpam-5704	166	3	,	,	PUNCT
ejpam-5704	166	4	t	t	PROPN
ejpam-5704	166	5	)	)	PUNCT
ejpam-5704	166	6	+	+	CCONJ
ejpam-5704	166	7	ω2,j(p2,h	ω2,j(p2,h	ADP
ejpam-5704	166	8	,	,	PUNCT
ejpam-5704	166	9	θ(t	θ(t	PROPN
ejpam-5704	166	10	)	)	PUNCT
ejpam-5704	166	11	)	)	PUNCT
ejpam-5704	166	12	,	,	PUNCT
ejpam-5704	166	13	tn	tn	PROPN
ejpam-5704	166	14	(	(	PUNCT
ejpam-5704	166	15	p1,h	p1,h	PROPN
ejpam-5704	166	16	,	,	PUNCT
ejpam-5704	166	17	p2,h	p2,h	PROPN
ejpam-5704	166	18	,	,	PUNCT
ejpam-5704	166	19	y	y	PROPN
ejpam-5704	166	20	;	;	PUNCT
ejpam-5704	166	21	t	t	PROPN
ejpam-5704	166	22	,	,	PUNCT
ejpam-5704	166	23	θ(t	θ(t	PROPN
ejpam-5704	166	24	)	)	PUNCT
ejpam-5704	166	25	)	)	PUNCT
ejpam-5704	167	1	=	=	SYM
ejpam-5704	167	2	t1,n	t1,n	PROPN
ejpam-5704	167	3	(	(	PUNCT
ejpam-5704	167	4	p1,h	p1,h	PROPN
ejpam-5704	167	5	,	,	PUNCT
ejpam-5704	167	6	y	y	PROPN
ejpam-5704	167	7	;	;	PUNCT
ejpam-5704	167	8	t	t	PROPN
ejpam-5704	167	9	)	)	PUNCT
ejpam-5704	167	10	+	+	CCONJ
ejpam-5704	167	11	t2,n	t2,n	PROPN
ejpam-5704	167	12	(	(	PUNCT
ejpam-5704	167	13	p2,h	p2,h	PROPN
ejpam-5704	167	14	,	,	PUNCT
ejpam-5704	167	15	y	y	PROPN
ejpam-5704	167	16	;	;	PUNCT
ejpam-5704	167	17	θ(t	θ(t	PROPN
ejpam-5704	167	18	)	)	PUNCT
ejpam-5704	167	19	)	)	PUNCT
ejpam-5704	167	20	,	,	PUNCT
ejpam-5704	167	21	(	(	PUNCT
ejpam-5704	167	22	26	26	NUM
ejpam-5704	167	23	)	)	PUNCT
ejpam-5704	167	24	then	then	ADV
ejpam-5704	167	25	equation	equation	NOUN
ejpam-5704	167	26	(	(	PUNCT
ejpam-5704	167	27	24	24	NUM
ejpam-5704	167	28	)	)	PUNCT
ejpam-5704	167	29	reduces	reduce	VERB
ejpam-5704	167	30	to	to	ADP
ejpam-5704	167	31	the	the	DET
ejpam-5704	167	32	following	follow	VERB
ejpam-5704	167	33	equation	equation	NOUN
ejpam-5704	167	34	y(t)−	y(t)−	PROPN
ejpam-5704	167	35	yn	yn	PROPN
ejpam-5704	167	36	(	(	PUNCT
ejpam-5704	167	37	t	t	PROPN
ejpam-5704	167	38	)	)	PUNCT
ejpam-5704	167	39	=	=	SYM
ejpam-5704	167	40	n∑	n∑	PROPN
ejpam-5704	167	41	j=0	j=0	PROPN
ejpam-5704	167	42	ωj(p1,h	ωj(p1,h	PROPN
ejpam-5704	167	43	,	,	PUNCT
ejpam-5704	167	44	p2,h	p2,h	PROPN
ejpam-5704	167	45	;	;	PUNCT
ejpam-5704	167	46	t	t	PROPN
ejpam-5704	167	47	,	,	PUNCT
ejpam-5704	167	48	θ(t))(y(tj)−	θ(t))(y(tj)−	PROPN
ejpam-5704	167	49	yn	yn	PROPN
ejpam-5704	167	50	(	(	PUNCT
ejpam-5704	167	51	tj	tj	NOUN
ejpam-5704	167	52	)	)	PUNCT
ejpam-5704	167	53	)	)	PUNCT
ejpam-5704	168	1	+	+	NOUN
ejpam-5704	168	2	tn	tn	PROPN
ejpam-5704	168	3	(	(	PUNCT
ejpam-5704	168	4	p1,h	p1,h	PROPN
ejpam-5704	168	5	,	,	PUNCT
ejpam-5704	168	6	p2,h	p2,h	PROPN
ejpam-5704	168	7	,	,	PUNCT
ejpam-5704	168	8	y	y	PROPN
ejpam-5704	168	9	;	;	PUNCT
ejpam-5704	168	10	t	t	PROPN
ejpam-5704	168	11	,	,	PUNCT
ejpam-5704	168	12	θ(t	θ(t	PROPN
ejpam-5704	168	13	)	)	PUNCT
ejpam-5704	168	14	)	)	PUNCT
ejpam-5704	168	15	.	.	PUNCT
ejpam-5704	169	1	(	(	PUNCT
ejpam-5704	169	2	27	27	NUM
ejpam-5704	169	3	)	)	PUNCT
ejpam-5704	169	4	now	now	ADV
ejpam-5704	169	5	,	,	PUNCT
ejpam-5704	169	6	define	define	VERB
ejpam-5704	169	7	linear	linear	ADJ
ejpam-5704	169	8	operator	operator	NOUN
ejpam-5704	169	9	an	an	DET
ejpam-5704	169	10	as:	as:	NOUN
ejpam-5704	169	11	an	an	DET
ejpam-5704	169	12	:	:	PUNCT
ejpam-5704	169	13	c[0	c[0	PROPN
ejpam-5704	169	14	,	,	PUNCT
ejpam-5704	169	15	1	1	NUM
ejpam-5704	169	16	]	]	X
ejpam-5704	169	17	−→	−→	ADJ
ejpam-5704	169	18	c[0	c[0	PROPN
ejpam-5704	169	19	,	,	PUNCT
ejpam-5704	169	20	1	1	X
ejpam-5704	169	21	]	]	PUNCT
ejpam-5704	169	22	an	an	DET
ejpam-5704	169	23	(	(	PUNCT
ejpam-5704	169	24	f(t	f(t	PROPN
ejpam-5704	169	25	)	)	PUNCT
ejpam-5704	169	26	)	)	PUNCT
ejpam-5704	170	1	=	=	PUNCT
ejpam-5704	170	2	n∑	n∑	PROPN
ejpam-5704	170	3	j=0	j=0	PROPN
ejpam-5704	170	4	ωj(p1,h	ωj(p1,h	PROPN
ejpam-5704	170	5	,	,	PUNCT
ejpam-5704	170	6	p2,h	p2,h	PROPN
ejpam-5704	170	7	;	;	PUNCT
ejpam-5704	170	8	t	t	PROPN
ejpam-5704	170	9	,	,	PUNCT
ejpam-5704	170	10	θ(t))f(tj	θ(t))f(tj	PROPN
ejpam-5704	170	11	)	)	PUNCT
ejpam-5704	170	12	,	,	PUNCT
ejpam-5704	170	13	f	f	PROPN
ejpam-5704	170	14	∈	∈	PROPN
ejpam-5704	170	15	c[0	c[0	PROPN
ejpam-5704	170	16	,	,	PUNCT
ejpam-5704	170	17	1	1	NUM
ejpam-5704	170	18	]	]	PUNCT
ejpam-5704	170	19	,	,	PUNCT
ejpam-5704	170	20	(	(	PUNCT
ejpam-5704	170	21	28	28	NUM
ejpam-5704	170	22	)	)	PUNCT
ejpam-5704	170	23	then	then	ADV
ejpam-5704	170	24	∥	∥	NUM
ejpam-5704	170	25	y(t)−	y(t)−	PROPN
ejpam-5704	170	26	yn	yn	PROPN
ejpam-5704	170	27	(	(	PUNCT
ejpam-5704	170	28	t	t	PROPN
ejpam-5704	170	29	)	)	PUNCT
ejpam-5704	170	30	∥∞=	∥∞=	VERB
ejpam-5704	170	31	∥	∥	PUNCT
ejpam-5704	170	32	an(y(t)−	an(y(t)−	PROPN
ejpam-5704	170	33	yn	yn	PROPN
ejpam-5704	170	34	(	(	PUNCT
ejpam-5704	170	35	t))+	t))+	PROPN
ejpam-5704	170	36	tn	tn	PROPN
ejpam-5704	170	37	(	(	PUNCT
ejpam-5704	170	38	p1,h	p1,h	PROPN
ejpam-5704	170	39	,	,	PUNCT
ejpam-5704	170	40	p2,h	p2,h	PROPN
ejpam-5704	170	41	,	,	PUNCT
ejpam-5704	170	42	y	y	PROPN
ejpam-5704	170	43	;	;	PUNCT
ejpam-5704	170	44	t	t	PROPN
ejpam-5704	170	45	,	,	PUNCT
ejpam-5704	170	46	θ(t	θ(t	PROPN
ejpam-5704	170	47	)	)	PUNCT
ejpam-5704	170	48	)	)	PUNCT
ejpam-5704	171	1	∥∞	∥∞	ADJ
ejpam-5704	171	2	≤	≤	NOUN
ejpam-5704	171	3	∥	∥	PUNCT
ejpam-5704	171	4	an	an	DET
ejpam-5704	171	5	∥∞∥	∥∞∥	NUM
ejpam-5704	171	6	y(t)−	y(t)−	PROPN
ejpam-5704	171	7	yn	yn	PROPN
ejpam-5704	171	8	(	(	PUNCT
ejpam-5704	171	9	t	t	NOUN
ejpam-5704	171	10	)	)	PUNCT
ejpam-5704	171	11	∥∞	∥∞	NOUN
ejpam-5704	171	12	+	+	CCONJ
ejpam-5704	171	13	∥	∥	PROPN
ejpam-5704	171	14	tn	tn	NOUN
ejpam-5704	171	15	(	(	PUNCT
ejpam-5704	171	16	p1,h	p1,h	PROPN
ejpam-5704	171	17	,	,	PUNCT
ejpam-5704	171	18	p2,h	p2,h	PROPN
ejpam-5704	171	19	,	,	PUNCT
ejpam-5704	171	20	y	y	PROPN
ejpam-5704	171	21	;	;	PUNCT
ejpam-5704	171	22	t	t	PROPN
ejpam-5704	171	23	,	,	PUNCT
ejpam-5704	171	24	θ(t	θ(t	PROPN
ejpam-5704	171	25	)	)	PUNCT
ejpam-5704	171	26	)	)	PUNCT
ejpam-5704	172	1	∥∞	∥∞	PROPN
ejpam-5704	172	2	,	,	PUNCT
ejpam-5704	172	3	(	(	PUNCT
ejpam-5704	172	4	29	29	NUM
ejpam-5704	172	5	)	)	PUNCT
ejpam-5704	172	6	b.	b.	PROPN
ejpam-5704	172	7	h.	h.	PROPN
ejpam-5704	172	8	alrikabi	alrikabi	PROPN
ejpam-5704	172	9	,	,	PUNCT
ejpam-5704	172	10	p.	p.	PROPN
ejpam-5704	172	11	darania	darania	PROPN
ejpam-5704	172	12	,	,	PUNCT
ejpam-5704	172	13	s.pishbin	s.pishbin	PROPN
ejpam-5704	172	14	/	/	SYM
ejpam-5704	172	15	eur	eur	PROPN
ejpam-5704	172	16	.	.	PUNCT
ejpam-5704	173	1	j.	j.	PROPN
ejpam-5704	173	2	pure	pure	PROPN
ejpam-5704	173	3	appl	appl	PROPN
ejpam-5704	173	4	.	.	PROPN
ejpam-5704	173	5	math	math	PROPN
ejpam-5704	173	6	,	,	PUNCT
ejpam-5704	173	7	18	18	NUM
ejpam-5704	173	8	(	(	PUNCT
ejpam-5704	173	9	2	2	NUM
ejpam-5704	173	10	)	)	PUNCT
ejpam-5704	173	11	(	(	PUNCT
ejpam-5704	173	12	2025	2025	NUM
ejpam-5704	173	13	)	)	PUNCT
ejpam-5704	173	14	,	,	PUNCT
ejpam-5704	173	15	5704	5704	NUM
ejpam-5704	173	16	10	10	NUM
ejpam-5704	173	17	of	of	ADP
ejpam-5704	173	18	19	19	NUM
ejpam-5704	173	19	and	and	CCONJ
ejpam-5704	173	20	by	by	ADP
ejpam-5704	173	21	considering	consider	VERB
ejpam-5704	173	22	(	(	PUNCT
ejpam-5704	173	23	27	27	NUM
ejpam-5704	173	24	)	)	PUNCT
ejpam-5704	173	25	,	,	PUNCT
ejpam-5704	173	26	we	we	PRON
ejpam-5704	173	27	have	have	VERB
ejpam-5704	173	28	∥	∥	NUM
ejpam-5704	173	29	y(t)−	y(t)−	PROPN
ejpam-5704	173	30	yn	yn	PROPN
ejpam-5704	173	31	(	(	PUNCT
ejpam-5704	173	32	t	t	PROPN
ejpam-5704	173	33	)	)	PUNCT
ejpam-5704	173	34	∥∞≤∥	∥∞≤∥	PUNCT
ejpam-5704	174	1	(	(	PUNCT
ejpam-5704	174	2	i	i	PROPN
ejpam-5704	174	3	−an	−an	PROPN
ejpam-5704	174	4	)	)	PUNCT
ejpam-5704	174	5	−1	−1	NOUN
ejpam-5704	174	6	∥∞∥	∥∞∥	ADJ
ejpam-5704	174	7	tn	tn	NOUN
ejpam-5704	175	1	∥∞	∥∞	ADJ
ejpam-5704	175	2	.	.	PUNCT
ejpam-5704	176	1	(	(	PUNCT
ejpam-5704	176	2	30	30	NUM
ejpam-5704	176	3	)	)	PUNCT
ejpam-5704	176	4	our	our	PRON
ejpam-5704	176	5	ultimate	ultimate	ADJ
ejpam-5704	176	6	objective	objective	NOUN
ejpam-5704	176	7	is	be	AUX
ejpam-5704	176	8	to	to	PART
ejpam-5704	176	9	establish	establish	VERB
ejpam-5704	176	10	an	an	DET
ejpam-5704	176	11	upper	upper	ADJ
ejpam-5704	176	12	bound	bind	VERB
ejpam-5704	176	13	for	for	ADP
ejpam-5704	176	14	(	(	PUNCT
ejpam-5704	176	15	30	30	NUM
ejpam-5704	176	16	)	)	PUNCT
ejpam-5704	176	17	.	.	PUNCT
ejpam-5704	177	1	we	we	PRON
ejpam-5704	177	2	begin	begin	VERB
ejpam-5704	177	3	by	by	ADP
ejpam-5704	177	4	preparing	prepare	VERB
ejpam-5704	177	5	a	a	DET
ejpam-5704	177	6	set	set	NOUN
ejpam-5704	177	7	of	of	ADP
ejpam-5704	177	8	auxiliary	auxiliary	ADJ
ejpam-5704	177	9	theorems	theorem	NOUN
ejpam-5704	177	10	and	and	CCONJ
ejpam-5704	177	11	lemmas	lemmas	PROPN
ejpam-5704	177	12	concerning	concern	VERB
ejpam-5704	177	13	kernels	kernel	NOUN
ejpam-5704	177	14	of	of	ADP
ejpam-5704	177	15	types	type	NOUN
ejpam-5704	177	16	(	(	PUNCT
ejpam-5704	177	17	4	4	NUM
ejpam-5704	177	18	)	)	PUNCT
ejpam-5704	177	19	.	.	PUNCT
ejpam-5704	178	1	theorem	theorem	NOUN
ejpam-5704	178	2	1	1	X
ejpam-5704	178	3	.	.	X
ejpam-5704	179	1	consider	consider	VERB
ejpam-5704	179	2	{	{	PUNCT
ejpam-5704	179	3	ti}ni=0	ti}ni=0	VERB
ejpam-5704	179	4	as	as	ADP
ejpam-5704	179	5	the	the	DET
ejpam-5704	179	6	zeros	zero	NOUN
ejpam-5704	179	7	of	of	ADP
ejpam-5704	179	8	the	the	DET
ejpam-5704	179	9	(	(	PUNCT
ejpam-5704	179	10	n	n	PROPN
ejpam-5704	179	11	+	+	CCONJ
ejpam-5704	179	12	1)-th	1)-th	NUM
ejpam-5704	179	13	-	-	PUNCT
ejpam-5704	179	14	degree	degree	NOUN
ejpam-5704	179	15	member	member	NOUN
ejpam-5704	179	16	of	of	ADP
ejpam-5704	179	17	a	a	DET
ejpam-5704	179	18	set	set	NOUN
ejpam-5704	179	19	of	of	ADP
ejpam-5704	179	20	polynomials	polynomial	NOUN
ejpam-5704	179	21	that	that	PRON
ejpam-5704	179	22	are	be	AUX
ejpam-5704	179	23	orthogonal	orthogonal	ADJ
ejpam-5704	179	24	on	on	ADP
ejpam-5704	179	25	ih	ih	PRON
ejpam-5704	179	26	⊆	⊆	NUM
ejpam-5704	179	27	[	[	X
ejpam-5704	179	28	0	0	NUM
ejpam-5704	179	29	,	,	PUNCT
ejpam-5704	179	30	1	1	NUM
ejpam-5704	179	31	]	]	PUNCT
ejpam-5704	179	32	with	with	ADP
ejpam-5704	179	33	respect	respect	NOUN
ejpam-5704	179	34	to	to	ADP
ejpam-5704	179	35	the	the	DET
ejpam-5704	179	36	weight	weight	NOUN
ejpam-5704	179	37	function	function	NOUN
ejpam-5704	179	38	w	w	PROPN
ejpam-5704	179	39	(	(	PUNCT
ejpam-5704	179	40	t	t	PROPN
ejpam-5704	179	41	)	)	PUNCT
ejpam-5704	179	42	=	=	NOUN
ejpam-5704	180	1	g(t)(1−	g(t)(1−	VERB
ejpam-5704	180	2	t)µ̄(1	t)µ̄(1	NOUN
ejpam-5704	180	3	+	+	X
ejpam-5704	180	4	t)ν̄	t)ν̄	INTJ
ejpam-5704	180	5	,	,	PUNCT
ejpam-5704	180	6	−1	−1	NOUN
ejpam-5704	180	7	<	<	X
ejpam-5704	180	8	µ̄	µ̄	PROPN
ejpam-5704	180	9	≤	≤	ADV
ejpam-5704	180	10	3	3	NUM
ejpam-5704	180	11	2	2	NUM
ejpam-5704	180	12	,	,	PUNCT
ejpam-5704	180	13	ν̄	ν̄	NOUN
ejpam-5704	180	14	≥	≥	NUM
ejpam-5704	180	15	−1	−1	NOUN
ejpam-5704	180	16	2	2	NUM
ejpam-5704	180	17	,	,	PUNCT
ejpam-5704	180	18	(	(	PUNCT
ejpam-5704	180	19	31	31	NUM
ejpam-5704	180	20	)	)	PUNCT
ejpam-5704	180	21	where	where	SCONJ
ejpam-5704	180	22	g(t	g(t	PROPN
ejpam-5704	180	23	)	)	PUNCT
ejpam-5704	180	24	is	be	AUX
ejpam-5704	180	25	a	a	DET
ejpam-5704	180	26	positive	positive	ADJ
ejpam-5704	180	27	and	and	CCONJ
ejpam-5704	180	28	continuous	continuous	ADJ
ejpam-5704	180	29	function	function	NOUN
ejpam-5704	180	30	within	within	ADP
ejpam-5704	180	31	the	the	DET
ejpam-5704	180	32	interval	interval	NOUN
ejpam-5704	180	33	ih	ih	NOUN
ejpam-5704	180	34	,	,	PUNCT
ejpam-5704	180	35	and	and	CCONJ
ejpam-5704	180	36	the	the	DET
ejpam-5704	180	37	modulus	modulus	NOUN
ejpam-5704	180	38	of	of	ADP
ejpam-5704	180	39	continuity	continuity	NOUN
ejpam-5704	180	40	u	u	NOUN
ejpam-5704	180	41	for	for	ADP
ejpam-5704	180	42	g	g	PROPN
ejpam-5704	180	43	fulfills	fulfill	VERB
ejpam-5704	180	44	the	the	DET
ejpam-5704	180	45	condition	condition	NOUN
ejpam-5704	180	46	∫	∫	PROPN
ejpam-5704	180	47	1	1	NUM
ejpam-5704	180	48	0	0	NUM
ejpam-5704	180	49	u(g	u(g	PROPN
ejpam-5704	180	50	,	,	PUNCT
ejpam-5704	180	51	s	s	X
ejpam-5704	180	52	)	)	PUNCT
ejpam-5704	180	53	ds	ds	NOUN
ejpam-5704	180	54	s	s	X
ejpam-5704	180	55	<	<	X
ejpam-5704	180	56	∞.	∞.	PROPN
ejpam-5704	180	57	also	also	ADV
ejpam-5704	180	58	,	,	PUNCT
ejpam-5704	180	59	let	let	VERB
ejpam-5704	180	60	ωn	ωn	VERB
ejpam-5704	180	61	(	(	PUNCT
ejpam-5704	180	62	y	y	PROPN
ejpam-5704	180	63	,	,	PUNCT
ejpam-5704	180	64	w	w	PROPN
ejpam-5704	180	65	)	)	PUNCT
ejpam-5704	180	66	represent	represent	VERB
ejpam-5704	180	67	the	the	DET
ejpam-5704	180	68	interpolating	interpolate	VERB
ejpam-5704	180	69	polynomial	polynomial	NOUN
ejpam-5704	180	70	of	of	ADP
ejpam-5704	180	71	degree	degree	NOUN
ejpam-5704	180	72	at	at	ADP
ejpam-5704	180	73	most	most	ADJ
ejpam-5704	180	74	n	n	NOUN
ejpam-5704	180	75	that	that	PRON
ejpam-5704	180	76	matches	match	VERB
ejpam-5704	180	77	the	the	DET
ejpam-5704	180	78	function	function	NOUN
ejpam-5704	180	79	y	y	PROPN
ejpam-5704	180	80	at	at	ADP
ejpam-5704	180	81	{	{	PUNCT
ejpam-5704	180	82	ti}ni=1∪{t0	ti}ni=1∪{t0	PROPN
ejpam-5704	180	83	=	=	PUNCT
ejpam-5704	181	1	0	0	NUM
ejpam-5704	181	2	}	}	PUNCT
ejpam-5704	181	3	.	.	PUNCT
ejpam-5704	182	1	additionally	additionally	ADV
ejpam-5704	182	2	,	,	PUNCT
ejpam-5704	182	3	assume	assume	VERB
ejpam-5704	182	4	that	that	SCONJ
ejpam-5704	182	5	p1,h(t	p1,h(t	ADP
ejpam-5704	182	6	,	,	PUNCT
ejpam-5704	182	7	w	w	NOUN
ejpam-5704	182	8	)	)	PUNCT
ejpam-5704	182	9	and	and	CCONJ
ejpam-5704	182	10	p2,h(t	p2,h(t	NOUN
ejpam-5704	182	11	,	,	PUNCT
ejpam-5704	182	12	w	w	NOUN
ejpam-5704	182	13	)	)	PUNCT
ejpam-5704	182	14	are	be	AUX
ejpam-5704	182	15	kernels	kernel	NOUN
ejpam-5704	182	16	of	of	ADP
ejpam-5704	182	17	type	type	NOUN
ejpam-5704	182	18	(	(	PUNCT
ejpam-5704	182	19	4	4	NUM
ejpam-5704	182	20	)	)	PUNCT
ejpam-5704	182	21	.	.	PUNCT
ejpam-5704	183	1	then	then	ADV
ejpam-5704	183	2	,	,	PUNCT
ejpam-5704	183	3	for	for	ADP
ejpam-5704	183	4	any	any	DET
ejpam-5704	183	5	function	function	NOUN
ejpam-5704	183	6	y	y	PROPN
ejpam-5704	183	7	∈	∈	PROPN
ejpam-5704	183	8	c(ih	c(ih	NOUN
ejpam-5704	183	9	)	)	PUNCT
ejpam-5704	183	10	,	,	PUNCT
ejpam-5704	183	11	we	we	PRON
ejpam-5704	183	12	have	have	VERB
ejpam-5704	183	13	lim	lim	PROPN
ejpam-5704	183	14	n→∞	n→∞	NUM
ejpam-5704	183	15	∥	∥	NUM
ejpam-5704	183	16	∫	∫	PROPN
ejpam-5704	183	17	t	t	PROPN
ejpam-5704	183	18	0	0	NUM
ejpam-5704	183	19	p1,h(t	p1,h(t	NOUN
ejpam-5704	183	20	,	,	PUNCT
ejpam-5704	183	21	w)(y(w)−	w)(y(w)−	NOUN
ejpam-5704	183	22	ωn	ωn	PROPN
ejpam-5704	183	23	(	(	PUNCT
ejpam-5704	183	24	y	y	PROPN
ejpam-5704	183	25	,	,	PUNCT
ejpam-5704	183	26	w))dw	w))dw	PROPN
ejpam-5704	183	27	+	+	CCONJ
ejpam-5704	183	28	∫	∫	PROPN
ejpam-5704	183	29	θ(t	θ(t	PROPN
ejpam-5704	183	30	)	)	PUNCT
ejpam-5704	183	31	0	0	NUM
ejpam-5704	183	32	p2,h(t	p2,h(t	NOUN
ejpam-5704	183	33	,	,	PUNCT
ejpam-5704	183	34	w)(y(w)−	w)(y(w)−	NOUN
ejpam-5704	183	35	ωn	ωn	PROPN
ejpam-5704	183	36	(	(	PUNCT
ejpam-5704	183	37	y	y	PROPN
ejpam-5704	183	38	,	,	PUNCT
ejpam-5704	183	39	w))dw∥	w))dw∥	X
ejpam-5704	183	40	=	=	PUNCT
ejpam-5704	184	1	0	0	X
ejpam-5704	184	2	.	.	PUNCT
ejpam-5704	185	1	(	(	PUNCT
ejpam-5704	185	2	32	32	NUM
ejpam-5704	185	3	)	)	PUNCT
ejpam-5704	185	4	especially	especially	ADV
ejpam-5704	185	5	,	,	PUNCT
ejpam-5704	185	6	for	for	ADP
ejpam-5704	185	7	0	0	NUM
ejpam-5704	185	8	<	<	X
ejpam-5704	185	9	µ	µ	X
ejpam-5704	185	10	<	<	X
ejpam-5704	185	11	1	1	NUM
ejpam-5704	185	12	,	,	PUNCT
ejpam-5704	185	13	the	the	DET
ejpam-5704	185	14	limits	limit	NOUN
ejpam-5704	185	15	are	be	AUX
ejpam-5704	185	16	as	as	SCONJ
ejpam-5704	185	17	follows	follow	VERB
ejpam-5704	185	18	∥tn	∥tn	NOUN
ejpam-5704	185	19	(	(	PUNCT
ejpam-5704	185	20	|t−	|t−	PROPN
ejpam-5704	185	21	w|−µ	w|−µ	PROPN
ejpam-5704	185	22	,	,	PUNCT
ejpam-5704	185	23	|t−	|t−	PROPN
ejpam-5704	185	24	w|−µ	w|−µ	PROPN
ejpam-5704	185	25	,	,	PUNCT
ejpam-5704	185	26	y	y	PROPN
ejpam-5704	185	27	;	;	PUNCT
ejpam-5704	185	28	t	t	PROPN
ejpam-5704	185	29	,	,	PUNCT
ejpam-5704	185	30	θ(t))∥∞	θ(t))∥∞	PROPN
ejpam-5704	185	31	=	=	SYM
ejpam-5704	185	32	o{h1	o{h1	NUM
ejpam-5704	185	33	}	}	PUNCT
ejpam-5704	185	34	,	,	PUNCT
ejpam-5704	185	35	(	(	PUNCT
ejpam-5704	185	36	33	33	NUM
ejpam-5704	185	37	)	)	PUNCT
ejpam-5704	185	38	∥tn	∥tn	NOUN
ejpam-5704	185	39	(	(	PUNCT
ejpam-5704	185	40	log	log	NOUN
ejpam-5704	185	41	|t−	|t−	PROPN
ejpam-5704	185	42	w|	w|	NOUN
ejpam-5704	185	43	,	,	PUNCT
ejpam-5704	185	44	log	log	NOUN
ejpam-5704	185	45	|t−	|t−	PROPN
ejpam-5704	185	46	w|	w|	NOUN
ejpam-5704	185	47	,	,	PUNCT
ejpam-5704	185	48	y	y	PROPN
ejpam-5704	185	49	;	;	PUNCT
ejpam-5704	185	50	t	t	PROPN
ejpam-5704	185	51	,	,	PUNCT
ejpam-5704	185	52	θ(t))∥∞	θ(t))∥∞	PROPN
ejpam-5704	185	53	=	=	SYM
ejpam-5704	185	54	o{h2	o{h2	PROPN
ejpam-5704	185	55	}	}	PUNCT
ejpam-5704	185	56	,	,	PUNCT
ejpam-5704	185	57	(	(	PUNCT
ejpam-5704	185	58	34	34	NUM
ejpam-5704	185	59	)	)	PUNCT
ejpam-5704	185	60	∥tn	∥tn	PROPN
ejpam-5704	185	61	(	(	PUNCT
ejpam-5704	185	62	|t−	|t−	PROPN
ejpam-5704	185	63	w|−µ	w|−µ	PROPN
ejpam-5704	185	64	,	,	PUNCT
ejpam-5704	185	65	log	log	VERB
ejpam-5704	185	66	|t−	|t−	PROPN
ejpam-5704	185	67	w|	w|	NOUN
ejpam-5704	185	68	,	,	PUNCT
ejpam-5704	185	69	y	y	PROPN
ejpam-5704	185	70	;	;	PUNCT
ejpam-5704	185	71	t	t	PROPN
ejpam-5704	185	72	,	,	PUNCT
ejpam-5704	185	73	θ(t))∥∞	θ(t))∥∞	PROPN
ejpam-5704	185	74	=	=	SYM
ejpam-5704	185	75	o{h3	o{h3	PROPN
ejpam-5704	185	76	}	}	PUNCT
ejpam-5704	185	77	,	,	PUNCT
ejpam-5704	185	78	(	(	PUNCT
ejpam-5704	185	79	35	35	NUM
ejpam-5704	185	80	)	)	PUNCT
ejpam-5704	185	81	where	where	SCONJ
ejpam-5704	185	82	h1	h1	NOUN
ejpam-5704	185	83	=	=	SYM
ejpam-5704	185	84	(	(	PUNCT
ejpam-5704	185	85	n+1)2µ−2κ−2	n+1)2µ−2κ−2	PROPN
ejpam-5704	185	86	log(n+1	log(n+1	PROPN
ejpam-5704	185	87	)	)	PUNCT
ejpam-5704	185	88	,	,	PUNCT
ejpam-5704	185	89	h2	h2	NOUN
ejpam-5704	185	90	=	=	SYM
ejpam-5704	185	91	(	(	PUNCT
ejpam-5704	185	92	n+1)−2−2κ	n+1)−2−2κ	X
ejpam-5704	185	93	log2(n+1	log2(n+1	NOUN
ejpam-5704	185	94	)	)	PUNCT
ejpam-5704	185	95	and	and	CCONJ
ejpam-5704	185	96	h3	h3	NOUN
ejpam-5704	185	97	=	=	SYM
ejpam-5704	185	98	min{h1	min{h1	ADJ
ejpam-5704	185	99	,	,	PUNCT
ejpam-5704	185	100	h2	h2	NOUN
ejpam-5704	185	101	}	}	PUNCT
ejpam-5704	185	102	.	.	PUNCT
ejpam-5704	186	1	b.	b.	PROPN
ejpam-5704	186	2	h.	h.	PROPN
ejpam-5704	186	3	alrikabi	alrikabi	PROPN
ejpam-5704	186	4	,	,	PUNCT
ejpam-5704	186	5	p.	p.	PROPN
ejpam-5704	186	6	darania	darania	PROPN
ejpam-5704	186	7	,	,	PUNCT
ejpam-5704	186	8	s.pishbin	s.pishbin	PROPN
ejpam-5704	186	9	/	/	SYM
ejpam-5704	186	10	eur	eur	PROPN
ejpam-5704	186	11	.	.	PUNCT
ejpam-5704	187	1	j.	j.	PROPN
ejpam-5704	187	2	pure	pure	PROPN
ejpam-5704	187	3	appl	appl	PROPN
ejpam-5704	187	4	.	.	PROPN
ejpam-5704	187	5	math	math	PROPN
ejpam-5704	187	6	,	,	PUNCT
ejpam-5704	187	7	18	18	NUM
ejpam-5704	187	8	(	(	PUNCT
ejpam-5704	187	9	2	2	NUM
ejpam-5704	187	10	)	)	PUNCT
ejpam-5704	187	11	(	(	PUNCT
ejpam-5704	187	12	2025	2025	NUM
ejpam-5704	187	13	)	)	PUNCT
ejpam-5704	187	14	,	,	PUNCT
ejpam-5704	187	15	5704	5704	NUM
ejpam-5704	187	16	11	11	NUM
ejpam-5704	187	17	of	of	ADP
ejpam-5704	187	18	19	19	NUM
ejpam-5704	187	19	proof	proof	NOUN
ejpam-5704	187	20	.	.	PUNCT
ejpam-5704	188	1	by	by	ADP
ejpam-5704	188	2	using	use	VERB
ejpam-5704	188	3	the	the	DET
ejpam-5704	188	4	equation	equation	NOUN
ejpam-5704	188	5	(	(	PUNCT
ejpam-5704	188	6	26	26	NUM
ejpam-5704	188	7	)	)	PUNCT
ejpam-5704	188	8	,	,	PUNCT
ejpam-5704	188	9	we	we	PRON
ejpam-5704	188	10	have	have	VERB
ejpam-5704	188	11	|	|	ADV
ejpam-5704	188	12	tn	tn	PROPN
ejpam-5704	188	13	(	(	PUNCT
ejpam-5704	188	14	p1,h	p1,h	PROPN
ejpam-5704	188	15	,	,	PUNCT
ejpam-5704	188	16	p2,h	p2,h	PROPN
ejpam-5704	188	17	,	,	PUNCT
ejpam-5704	188	18	y	y	PROPN
ejpam-5704	188	19	;	;	PUNCT
ejpam-5704	188	20	t	t	PROPN
ejpam-5704	188	21	,	,	PUNCT
ejpam-5704	188	22	θ(t	θ(t	PROPN
ejpam-5704	188	23	)	)	PUNCT
ejpam-5704	188	24	)	)	PUNCT
ejpam-5704	188	25	|=	|=	PUNCT
ejpam-5704	189	1	|	|	ADV
ejpam-5704	189	2	∫	∫	X
ejpam-5704	189	3	t	t	PROPN
ejpam-5704	189	4	0	0	NUM
ejpam-5704	189	5	p1,h(t	p1,h(t	NOUN
ejpam-5704	189	6	,	,	PUNCT
ejpam-5704	189	7	w)y(w)dw	w)y(w)dw	NOUN
ejpam-5704	189	8	−	−	PROPN
ejpam-5704	189	9	n∑	n∑	PROPN
ejpam-5704	189	10	j=0	j=0	PROPN
ejpam-5704	189	11	ω1j(p1,h	ω1j(p1,h	ADV
ejpam-5704	189	12	,	,	PUNCT
ejpam-5704	189	13	t)y(tj	t)y(tj	NUM
ejpam-5704	189	14	)	)	PUNCT
ejpam-5704	190	1	+	+	CCONJ
ejpam-5704	190	2	∫	∫	PROPN
ejpam-5704	190	3	θ(t	θ(t	PROPN
ejpam-5704	190	4	)	)	PUNCT
ejpam-5704	190	5	0	0	NUM
ejpam-5704	190	6	p2,h(t	p2,h(t	NOUN
ejpam-5704	190	7	,	,	PUNCT
ejpam-5704	190	8	w)y(w)dw	w)y(w)dw	NOUN
ejpam-5704	190	9	−	−	PROPN
ejpam-5704	190	10	n∑	n∑	PROPN
ejpam-5704	190	11	j=0	j=0	PROPN
ejpam-5704	190	12	ω2j(p2,h	ω2j(p2,h	NUM
ejpam-5704	190	13	,	,	PUNCT
ejpam-5704	190	14	θ(t))y(tj	θ(t))y(tj	NOUN
ejpam-5704	190	15	)	)	PUNCT
ejpam-5704	190	16	|	|	ADV
ejpam-5704	190	17	≤	≤	NUM
ejpam-5704	190	18	∫	∫	PROPN
ejpam-5704	190	19	t	t	NOUN
ejpam-5704	190	20	0	0	NUM
ejpam-5704	191	1	|	|	ADV
ejpam-5704	191	2	p1,h(t	p1,h(t	ADP
ejpam-5704	191	3	,	,	PUNCT
ejpam-5704	191	4	w	w	NOUN
ejpam-5704	191	5	)	)	PUNCT
ejpam-5704	191	6	||	||	PUNCT
ejpam-5704	192	1	y(w)−	y(w)−	INTJ
ejpam-5704	192	2	ωn	ωn	ADP
ejpam-5704	192	3	(	(	PUNCT
ejpam-5704	192	4	y	y	PROPN
ejpam-5704	192	5	,	,	PUNCT
ejpam-5704	192	6	w	w	NOUN
ejpam-5704	192	7	)	)	PUNCT
ejpam-5704	193	1	|	|	ADV
ejpam-5704	193	2	dw	dw	PROPN
ejpam-5704	193	3	+	+	CCONJ
ejpam-5704	193	4	∫	∫	PROPN
ejpam-5704	193	5	θ(t	θ(t	PROPN
ejpam-5704	193	6	)	)	PUNCT
ejpam-5704	193	7	0	0	PUNCT
ejpam-5704	194	1	|	|	CCONJ
ejpam-5704	194	2	p2,h(t	p2,h(t	NOUN
ejpam-5704	194	3	,	,	PUNCT
ejpam-5704	194	4	w	w	NOUN
ejpam-5704	194	5	)	)	PUNCT
ejpam-5704	194	6	||	||	PUNCT
ejpam-5704	195	1	y(w)−	y(w)−	INTJ
ejpam-5704	195	2	ωn	ωn	ADP
ejpam-5704	195	3	(	(	PUNCT
ejpam-5704	195	4	y	y	PROPN
ejpam-5704	195	5	,	,	PUNCT
ejpam-5704	195	6	w	w	NOUN
ejpam-5704	195	7	)	)	PUNCT
ejpam-5704	195	8	|	|	ADV
ejpam-5704	195	9	dw	dw	PROPN
ejpam-5704	195	10	≤	≤	NUM
ejpam-5704	195	11	∫	∫	PROPN
ejpam-5704	195	12	1	1	NUM
ejpam-5704	195	13	0	0	NUM
ejpam-5704	196	1	|	|	ADV
ejpam-5704	196	2	p1,h(t	p1,h(t	ADP
ejpam-5704	196	3	,	,	PUNCT
ejpam-5704	196	4	w	w	NOUN
ejpam-5704	196	5	)	)	PUNCT
ejpam-5704	196	6	||	||	PUNCT
ejpam-5704	197	1	y(w)−	y(w)−	INTJ
ejpam-5704	197	2	ωn	ωn	ADP
ejpam-5704	197	3	(	(	PUNCT
ejpam-5704	197	4	y	y	PROPN
ejpam-5704	197	5	,	,	PUNCT
ejpam-5704	197	6	w	w	NOUN
ejpam-5704	197	7	)	)	PUNCT
ejpam-5704	197	8	|	|	ADV
ejpam-5704	197	9	dw	dw	PROPN
ejpam-5704	198	1	+	+	CCONJ
ejpam-5704	198	2	∫	∫	PROPN
ejpam-5704	198	3	1	1	NUM
ejpam-5704	198	4	0	0	NUM
ejpam-5704	199	1	|	|	PRON
ejpam-5704	199	2	p2,h(t	p2,h(t	NOUN
ejpam-5704	199	3	,	,	PUNCT
ejpam-5704	199	4	w	w	NOUN
ejpam-5704	199	5	)	)	PUNCT
ejpam-5704	199	6	||	||	PUNCT
ejpam-5704	200	1	y(w)−	y(w)−	INTJ
ejpam-5704	200	2	ωn	ωn	ADP
ejpam-5704	200	3	(	(	PUNCT
ejpam-5704	200	4	y	y	PROPN
ejpam-5704	200	5	,	,	PUNCT
ejpam-5704	200	6	w	w	PROPN
ejpam-5704	200	7	)	)	PUNCT
ejpam-5704	200	8	|	|	ADV
ejpam-5704	200	9	dw	dw	PROPN
ejpam-5704	200	10	.	.	PROPN
ejpam-5704	201	1	(	(	PUNCT
ejpam-5704	201	2	36	36	NUM
ejpam-5704	201	3	)	)	PUNCT
ejpam-5704	201	4	the	the	DET
ejpam-5704	201	5	proof	proof	NOUN
ejpam-5704	201	6	is	be	AUX
ejpam-5704	201	7	readily	readily	ADV
ejpam-5704	201	8	derived	derive	VERB
ejpam-5704	201	9	from	from	ADP
ejpam-5704	201	10	an	an	DET
ejpam-5704	201	11	outcome	outcome	NOUN
ejpam-5704	201	12	of	of	ADP
ejpam-5704	201	13	theorem	theorem	NOUN
ejpam-5704	201	14	2.2	2.2	NUM
ejpam-5704	201	15	.	.	PUNCT
ejpam-5704	202	1	the	the	DET
ejpam-5704	202	2	inequalities	inequality	NOUN
ejpam-5704	202	3	(	(	PUNCT
ejpam-5704	202	4	33	33	NUM
ejpam-5704	202	5	)	)	PUNCT
ejpam-5704	202	6	and	and	CCONJ
ejpam-5704	202	7	(	(	PUNCT
ejpam-5704	202	8	35	35	NUM
ejpam-5704	202	9	)	)	PUNCT
ejpam-5704	202	10	provide	provide	VERB
ejpam-5704	202	11	a	a	DET
ejpam-5704	202	12	measure	measure	NOUN
ejpam-5704	202	13	of	of	ADP
ejpam-5704	202	14	the	the	DET
ejpam-5704	202	15	convergence	convergence	NOUN
ejpam-5704	202	16	rate	rate	NOUN
ejpam-5704	202	17	.	.	PUNCT
ejpam-5704	203	1	now	now	ADV
ejpam-5704	203	2	,	,	PUNCT
ejpam-5704	203	3	let	let	VERB
ejpam-5704	203	4	’s	’s	PRON
ejpam-5704	203	5	examine	examine	VERB
ejpam-5704	203	6	the	the	DET
ejpam-5704	203	7	characteristics	characteristic	NOUN
ejpam-5704	203	8	of	of	ADP
ejpam-5704	203	9	the	the	DET
ejpam-5704	203	10	initial	initial	ADJ
ejpam-5704	203	11	term	term	NOUN
ejpam-5704	203	12	∥	∥	NUM
ejpam-5704	203	13	(	(	PUNCT
ejpam-5704	203	14	i	i	PROPN
ejpam-5704	203	15	−an	−an	PROPN
ejpam-5704	203	16	)	)	PUNCT
ejpam-5704	203	17	−1	−1	NOUN
ejpam-5704	203	18	∥∞	∥∞	NOUN
ejpam-5704	203	19	theorem	theorem	NOUN
ejpam-5704	203	20	2	2	NUM
ejpam-5704	203	21	.	.	X
ejpam-5704	203	22	for	for	ADP
ejpam-5704	203	23	a	a	DET
ejpam-5704	203	24	given	give	VERB
ejpam-5704	203	25	set	set	NOUN
ejpam-5704	203	26	of	of	ADP
ejpam-5704	203	27	nodes	node	NOUN
ejpam-5704	203	28	{	{	PUNCT
ejpam-5704	203	29	ti}ni=0	ti}ni=0	ADJ
ejpam-5704	203	30	defined	define	VERB
ejpam-5704	203	31	as	as	ADP
ejpam-5704	203	32	theorem	theorem	NOUN
ejpam-5704	203	33	1	1	NUM
ejpam-5704	203	34	with	with	ADP
ejpam-5704	203	35	the	the	DET
ejpam-5704	203	36	restriction	restriction	NOUN
ejpam-5704	203	37	−1	−1	NOUN
ejpam-5704	203	38	2	2	NUM
ejpam-5704	203	39	<	<	X
ejpam-5704	203	40	µ̄	µ̄	PROPN
ejpam-5704	203	41	,	,	PUNCT
ejpam-5704	203	42	ν̄	ν̄	NOUN
ejpam-5704	203	43	<	<	X
ejpam-5704	203	44	3	3	NUM
ejpam-5704	203	45	2	2	NUM
ejpam-5704	203	46	,	,	PUNCT
ejpam-5704	203	47	let	let	VERB
ejpam-5704	203	48	ln	ln	ADJ
ejpam-5704	203	49	,	,	PUNCT
ejpam-5704	203	50	j(w	j(w	PROPN
ejpam-5704	203	51	)	)	PUNCT
ejpam-5704	203	52	show	show	VERB
ejpam-5704	203	53	the	the	DET
ejpam-5704	203	54	corresponding	correspond	VERB
ejpam-5704	203	55	j−th	j−th	PROPN
ejpam-5704	203	56	lagrange	lagrange	PROPN
ejpam-5704	203	57	polynomial	polynomial	NOUN
ejpam-5704	203	58	.	.	PUNCT
ejpam-5704	204	1	fix	fix	VERB
ejpam-5704	204	2	a	a	DET
ejpam-5704	204	3	subinterval	subinterval	NOUN
ejpam-5704	204	4	[	[	X
ejpam-5704	204	5	a	a	X
ejpam-5704	204	6	,	,	PUNCT
ejpam-5704	204	7	b	b	NOUN
ejpam-5704	204	8	]	]	X
ejpam-5704	204	9	⊆	⊆	NUM
ejpam-5704	204	10	[	[	X
ejpam-5704	204	11	0	0	NUM
ejpam-5704	204	12	,	,	PUNCT
ejpam-5704	204	13	1	1	NUM
ejpam-5704	204	14	]	]	PUNCT
ejpam-5704	204	15	.	.	PUNCT
ejpam-5704	205	1	then	then	ADV
ejpam-5704	205	2	,	,	PUNCT
ejpam-5704	205	3	there	there	PRON
ejpam-5704	205	4	is	be	VERB
ejpam-5704	205	5	a	a	DET
ejpam-5704	205	6	positive	positive	ADJ
ejpam-5704	205	7	number	number	NOUN
ejpam-5704	205	8	c	c	NOUN
ejpam-5704	205	9	and	and	CCONJ
ejpam-5704	205	10	a	a	DET
ejpam-5704	205	11	value	value	NOUN
ejpam-5704	205	12	of	of	ADP
ejpam-5704	205	13	q1	q1	NOUN
ejpam-5704	205	14	greater	great	ADJ
ejpam-5704	205	15	than	than	ADP
ejpam-5704	205	16	1	1	NUM
ejpam-5704	205	17	,	,	PUNCT
ejpam-5704	205	18	such	such	ADJ
ejpam-5704	205	19	that	that	DET
ejpam-5704	205	20	sup	sup	NOUN
ejpam-5704	205	21	n∑	n∑	PROPN
ejpam-5704	205	22	j=0	j=0	PROPN
ejpam-5704	206	1	|	|	ADV
ejpam-5704	206	2	∫	∫	PROPN
ejpam-5704	207	1	b	b	PROPN
ejpam-5704	207	2	a	a	DET
ejpam-5704	207	3	(	(	PUNCT
ejpam-5704	207	4	p1,h(b	p1,h(b	ADJ
ejpam-5704	207	5	,	,	PUNCT
ejpam-5704	207	6	w	w	NOUN
ejpam-5704	207	7	)	)	PUNCT
ejpam-5704	207	8	+	+	CCONJ
ejpam-5704	207	9	p2,h(b	p2,h(b	NOUN
ejpam-5704	207	10	,	,	PUNCT
ejpam-5704	207	11	w))ln	w))ln	PROPN
ejpam-5704	207	12	,	,	PUNCT
ejpam-5704	207	13	j(w)dw	j(w)dw	PROPN
ejpam-5704	207	14	|≤	|≤	PROPN
ejpam-5704	207	15	c(∥	c(∥	PROPN
ejpam-5704	207	16	p1,h(b	p1,h(b	PROPN
ejpam-5704	207	17	,	,	PUNCT
ejpam-5704	207	18	w	w	NOUN
ejpam-5704	207	19	)	)	PUNCT
ejpam-5704	207	20	∥q1	∥q1	NOUN
ejpam-5704	207	21	+	+	X
ejpam-5704	207	22	∥	∥	PUNCT
ejpam-5704	207	23	p2,h(b	p2,h(b	NOUN
ejpam-5704	207	24	,	,	PUNCT
ejpam-5704	207	25	w	w	NOUN
ejpam-5704	207	26	)	)	PUNCT
ejpam-5704	207	27	∥q1	∥q1	NOUN
ejpam-5704	207	28	)	)	PUNCT
ejpam-5704	207	29	,	,	PUNCT
ejpam-5704	207	30	(	(	PUNCT
ejpam-5704	207	31	37	37	NUM
ejpam-5704	207	32	)	)	PUNCT
ejpam-5704	207	33	for	for	ADP
ejpam-5704	207	34	all	all	DET
ejpam-5704	207	35	p.	p.	NOUN
ejpam-5704	207	36	,h	,h	PUNCT
ejpam-5704	208	1	∈	∈	PROPN
ejpam-5704	208	2	lq1	lq1	NOUN
ejpam-5704	208	3	with	with	ADP
ejpam-5704	208	4	∥	∥	PROPN
ejpam-5704	208	5	p.	p.	NOUN
ejpam-5704	208	6	,h	,h	PUNCT
ejpam-5704	208	7	∥q1=	∥q1=	VERB
ejpam-5704	208	8	(	(	PUNCT
ejpam-5704	208	9	∫	∫	PROPN
ejpam-5704	208	10	1	1	NUM
ejpam-5704	208	11	0	0	NUM
ejpam-5704	209	1	|	|	ADV
ejpam-5704	209	2	p.	p.	NOUN
ejpam-5704	209	3	,h(b	,h(b	PUNCT
ejpam-5704	209	4	,	,	PUNCT
ejpam-5704	209	5	w	w	NOUN
ejpam-5704	209	6	)	)	PUNCT
ejpam-5704	209	7	|q1	|q1	NOUN
ejpam-5704	209	8	dw	dw	PROPN
ejpam-5704	209	9	)	)	PUNCT
ejpam-5704	209	10	1	1	NUM
ejpam-5704	209	11	q1	q1	NOUN
ejpam-5704	209	12	.	.	PUNCT
ejpam-5704	210	1	proof	proof	NOUN
ejpam-5704	210	2	.	.	PUNCT
ejpam-5704	211	1	in	in	ADP
ejpam-5704	211	2	the	the	DET
ejpam-5704	211	3	same	same	ADJ
ejpam-5704	211	4	manner	manner	NOUN
ejpam-5704	211	5	in	in	ADP
ejpam-5704	211	6	[	[	X
ejpam-5704	211	7	32	32	NUM
ejpam-5704	211	8	]	]	PUNCT
ejpam-5704	211	9	,	,	PUNCT
ejpam-5704	211	10	we	we	PRON
ejpam-5704	211	11	set	set	VERB
ejpam-5704	211	12	b	b	NOUN
ejpam-5704	211	13	=	=	PRON
ejpam-5704	211	14	{	{	PUNCT
ejpam-5704	211	15	f	f	PROPN
ejpam-5704	211	16	∈	∈	PROPN
ejpam-5704	211	17	c[0	c[0	PROPN
ejpam-5704	211	18	,	,	PUNCT
ejpam-5704	211	19	1	1	NUM
ejpam-5704	211	20	]	]	PUNCT
ejpam-5704	211	21	:	:	PUNCT
ejpam-5704	211	22	∥f∥∞	∥f∥∞	X
ejpam-5704	211	23	=	=	SYM
ejpam-5704	211	24	1	1	NUM
ejpam-5704	211	25	}	}	PUNCT
ejpam-5704	211	26	.	.	PUNCT
ejpam-5704	212	1	then	then	ADV
ejpam-5704	212	2	we	we	PRON
ejpam-5704	212	3	b.	b.	PROPN
ejpam-5704	212	4	h.	h.	PROPN
ejpam-5704	212	5	alrikabi	alrikabi	PROPN
ejpam-5704	212	6	,	,	PUNCT
ejpam-5704	212	7	p.	p.	PROPN
ejpam-5704	212	8	darania	darania	PROPN
ejpam-5704	212	9	,	,	PUNCT
ejpam-5704	212	10	s.pishbin	s.pishbin	PROPN
ejpam-5704	212	11	/	/	SYM
ejpam-5704	212	12	eur	eur	PROPN
ejpam-5704	212	13	.	.	PUNCT
ejpam-5704	213	1	j.	j.	PROPN
ejpam-5704	213	2	pure	pure	PROPN
ejpam-5704	213	3	appl	appl	PROPN
ejpam-5704	213	4	.	.	PROPN
ejpam-5704	213	5	math	math	PROPN
ejpam-5704	213	6	,	,	PUNCT
ejpam-5704	213	7	18	18	NUM
ejpam-5704	213	8	(	(	PUNCT
ejpam-5704	213	9	2	2	NUM
ejpam-5704	213	10	)	)	PUNCT
ejpam-5704	213	11	(	(	PUNCT
ejpam-5704	213	12	2025	2025	NUM
ejpam-5704	213	13	)	)	PUNCT
ejpam-5704	213	14	,	,	PUNCT
ejpam-5704	213	15	5704	5704	NUM
ejpam-5704	213	16	12	12	NUM
ejpam-5704	213	17	of	of	ADP
ejpam-5704	213	18	19	19	NUM
ejpam-5704	213	19	have	have	AUX
ejpam-5704	213	20	n∑	n∑	PROPN
ejpam-5704	213	21	j=0	j=0	PROPN
ejpam-5704	214	1	|	|	ADV
ejpam-5704	214	2	∫	∫	PROPN
ejpam-5704	215	1	b	b	PROPN
ejpam-5704	215	2	a	a	DET
ejpam-5704	215	3	[	[	X
ejpam-5704	215	4	p1,h(b	p1,h(b	ADJ
ejpam-5704	215	5	,	,	PUNCT
ejpam-5704	215	6	w	w	NOUN
ejpam-5704	215	7	)	)	PUNCT
ejpam-5704	215	8	+	+	CCONJ
ejpam-5704	215	9	p2,h(b	p2,h(b	NOUN
ejpam-5704	215	10	,	,	PUNCT
ejpam-5704	215	11	w)]ln	w)]ln	NOUN
ejpam-5704	215	12	,	,	PUNCT
ejpam-5704	215	13	j(w)dw	j(w)dw	PROPN
ejpam-5704	216	1	|	|	ADV
ejpam-5704	216	2	=	=	PUNCT
ejpam-5704	216	3	sup	sup	NOUN
ejpam-5704	216	4	f∈b	f∈b	ADV
ejpam-5704	217	1	|	|	ADV
ejpam-5704	217	2	∫	∫	PROPN
ejpam-5704	218	1	b	b	PROPN
ejpam-5704	218	2	a	a	DET
ejpam-5704	218	3	n∑	n∑	PROPN
ejpam-5704	218	4	j=0	j=0	PROPN
ejpam-5704	218	5	(	(	PUNCT
ejpam-5704	218	6	p1,h(b	p1,h(b	NOUN
ejpam-5704	218	7	,	,	PUNCT
ejpam-5704	218	8	w	w	NOUN
ejpam-5704	218	9	)	)	PUNCT
ejpam-5704	218	10	+	+	CCONJ
ejpam-5704	218	11	p2,h(b	p2,h(b	NOUN
ejpam-5704	218	12	,	,	PUNCT
ejpam-5704	218	13	w))ln	w))ln	PROPN
ejpam-5704	218	14	,	,	PUNCT
ejpam-5704	218	15	j(w)f(tj)dw	j(w)f(tj)dw	PROPN
ejpam-5704	218	16	|	|	ADV
ejpam-5704	218	17	≤	≤	NUM
ejpam-5704	218	18	sup	sup	NOUN
ejpam-5704	218	19	f∈b	f∈b	ADJ
ejpam-5704	218	20	∫	∫	PROPN
ejpam-5704	219	1	b	b	PROPN
ejpam-5704	219	2	a	a	DET
ejpam-5704	219	3	|	|	ADV
ejpam-5704	219	4	n∑	n∑	PROPN
ejpam-5704	219	5	j=0	j=0	PROPN
ejpam-5704	219	6	lnj(w)f(tj	lnj(w)f(tj	PROPN
ejpam-5704	219	7	)	)	PUNCT
ejpam-5704	220	1	|	|	ADV
ejpam-5704	220	2	{	{	PUNCT
ejpam-5704	220	3	|	|	ADV
ejpam-5704	220	4	p1,h(b	p1,h(b	ADJ
ejpam-5704	220	5	,	,	PUNCT
ejpam-5704	220	6	w	w	NOUN
ejpam-5704	220	7	)	)	PUNCT
ejpam-5704	221	1	|	|	ADV
ejpam-5704	222	1	+	+	CCONJ
ejpam-5704	222	2	|	|	ADV
ejpam-5704	222	3	p2,h(b	p2,h(b	NOUN
ejpam-5704	222	4	,	,	PUNCT
ejpam-5704	222	5	w	w	NOUN
ejpam-5704	222	6	)	)	PUNCT
ejpam-5704	222	7	|}dw	|}dw	PROPN
ejpam-5704	222	8	≤	≤	PROPN
ejpam-5704	222	9	sup	sup	NOUN
ejpam-5704	222	10	f∈b	f∈b	NOUN
ejpam-5704	222	11	{	{	PUNCT
ejpam-5704	222	12	[	[	PUNCT
ejpam-5704	222	13	∫	∫	PROPN
ejpam-5704	222	14	b	b	PROPN
ejpam-5704	222	15	a	a	DET
ejpam-5704	222	16	|	|	ADV
ejpam-5704	222	17	n∑	n∑	PROPN
ejpam-5704	222	18	j=0	j=0	PROPN
ejpam-5704	222	19	lnj(w)f(tj	lnj(w)f(tj	PROPN
ejpam-5704	222	20	)	)	PUNCT
ejpam-5704	222	21	|q2	|q2	VERB
ejpam-5704	223	1	dw	dw	X
ejpam-5704	223	2	]	]	X
ejpam-5704	223	3	1	1	NUM
ejpam-5704	223	4	q2	q2	NOUN
ejpam-5704	223	5	{	{	PUNCT
ejpam-5704	223	6	[	[	PUNCT
ejpam-5704	223	7	∫	∫	PROPN
ejpam-5704	223	8	b	b	PROPN
ejpam-5704	223	9	a	a	PRON
ejpam-5704	223	10	|	|	ADV
ejpam-5704	223	11	p1,h(b	p1,h(b	ADJ
ejpam-5704	223	12	,	,	PUNCT
ejpam-5704	223	13	w	w	NOUN
ejpam-5704	223	14	)	)	PUNCT
ejpam-5704	223	15	|q1	|q1	NOUN
ejpam-5704	223	16	dw	dw	X
ejpam-5704	223	17	]	]	X
ejpam-5704	223	18	1	1	NUM
ejpam-5704	223	19	q1	q1	NOUN
ejpam-5704	223	20	+	+	CCONJ
ejpam-5704	223	21	[	[	PUNCT
ejpam-5704	223	22	∫	∫	PROPN
ejpam-5704	223	23	b	b	PROPN
ejpam-5704	223	24	a	a	DET
ejpam-5704	223	25	|	|	NOUN
ejpam-5704	223	26	p2,h(b	p2,h(b	NOUN
ejpam-5704	223	27	,	,	PUNCT
ejpam-5704	223	28	w	w	NOUN
ejpam-5704	223	29	)	)	PUNCT
ejpam-5704	223	30	|q1	|q1	NOUN
ejpam-5704	223	31	dw	dw	X
ejpam-5704	223	32	]	]	X
ejpam-5704	223	33	1	1	NUM
ejpam-5704	223	34	q1	q1	NOUN
ejpam-5704	223	35	}	}	PUNCT
ejpam-5704	223	36	}	}	PUNCT
ejpam-5704	223	37	≤	≤	NUM
ejpam-5704	223	38	sup	sup	NOUN
ejpam-5704	223	39	f∈b	f∈b	NOUN
ejpam-5704	223	40	{	{	PUNCT
ejpam-5704	223	41	[	[	PUNCT
ejpam-5704	223	42	∫	∫	PROPN
ejpam-5704	223	43	1	1	NUM
ejpam-5704	223	44	0	0	NUM
ejpam-5704	224	1	|	|	ADV
ejpam-5704	224	2	n∑	n∑	PROPN
ejpam-5704	224	3	j=0	j=0	PROPN
ejpam-5704	224	4	lnj(w)f(tj	lnj(w)f(tj	PROPN
ejpam-5704	224	5	)	)	PUNCT
ejpam-5704	224	6	|q2	|q2	VERB
ejpam-5704	224	7	dw	dw	X
ejpam-5704	224	8	]	]	X
ejpam-5704	224	9	1	1	NUM
ejpam-5704	224	10	q2	q2	NOUN
ejpam-5704	224	11	{	{	PUNCT
ejpam-5704	224	12	[	[	PUNCT
ejpam-5704	224	13	∫	∫	PROPN
ejpam-5704	224	14	b	b	PROPN
ejpam-5704	224	15	a	a	PRON
ejpam-5704	224	16	|	|	ADV
ejpam-5704	224	17	p1,h(b	p1,h(b	ADJ
ejpam-5704	224	18	,	,	PUNCT
ejpam-5704	224	19	w	w	NOUN
ejpam-5704	224	20	)	)	PUNCT
ejpam-5704	224	21	|q1	|q1	NOUN
ejpam-5704	224	22	dw	dw	X
ejpam-5704	224	23	]	]	X
ejpam-5704	224	24	1	1	NUM
ejpam-5704	224	25	q1	q1	NOUN
ejpam-5704	224	26	+	+	CCONJ
ejpam-5704	224	27	[	[	PUNCT
ejpam-5704	224	28	∫	∫	PROPN
ejpam-5704	224	29	b	b	PROPN
ejpam-5704	224	30	a	a	DET
ejpam-5704	224	31	|	|	NOUN
ejpam-5704	224	32	p2,h(b	p2,h(b	NOUN
ejpam-5704	224	33	,	,	PUNCT
ejpam-5704	224	34	w	w	NOUN
ejpam-5704	224	35	)	)	PUNCT
ejpam-5704	224	36	|q1	|q1	NOUN
ejpam-5704	224	37	dw	dw	X
ejpam-5704	224	38	]	]	X
ejpam-5704	224	39	1	1	NUM
ejpam-5704	224	40	q1	q1	NOUN
ejpam-5704	224	41	}	}	PUNCT
ejpam-5704	224	42	}	}	PUNCT
ejpam-5704	224	43	≤	≤	NUM
ejpam-5704	224	44	sup	sup	NOUN
ejpam-5704	224	45	f∈b	f∈b	NOUN
ejpam-5704	224	46	{	{	PUNCT
ejpam-5704	224	47	∥	∥	PROPN
ejpam-5704	224	48	n∑	n∑	X
ejpam-5704	224	49	j=0	j=0	PROPN
ejpam-5704	224	50	lnj(w)f(tj	lnj(w)f(tj	PROPN
ejpam-5704	224	51	)	)	PUNCT
ejpam-5704	224	52	∥q2	∥q2	PUNCT
ejpam-5704	225	1	[	[	X
ejpam-5704	225	2	∥	∥	X
ejpam-5704	225	3	p1,h(b	p1,h(b	ADJ
ejpam-5704	225	4	,	,	PUNCT
ejpam-5704	225	5	w	w	NOUN
ejpam-5704	225	6	)	)	PUNCT
ejpam-5704	225	7	∥q1	∥q1	NOUN
ejpam-5704	225	8	+	+	X
ejpam-5704	225	9	∥	∥	PUNCT
ejpam-5704	225	10	p2,h(b	p2,h(b	NOUN
ejpam-5704	225	11	,	,	PUNCT
ejpam-5704	225	12	w	w	NOUN
ejpam-5704	225	13	)	)	PUNCT
ejpam-5704	225	14	∥q1	∥q1	NOUN
ejpam-5704	225	15	]	]	PUNCT
ejpam-5704	225	16	}	}	PUNCT
ejpam-5704	225	17	,	,	PUNCT
ejpam-5704	225	18	(	(	PUNCT
ejpam-5704	225	19	38	38	NUM
ejpam-5704	225	20	)	)	PUNCT
ejpam-5704	225	21	for	for	ADP
ejpam-5704	225	22	all	all	DET
ejpam-5704	225	23	p.	p.	NOUN
ejpam-5704	225	24	,h	,h	PUNCT
ejpam-5704	226	1	∈	∈	PROPN
ejpam-5704	226	2	lq1	lq1	PROPN
ejpam-5704	226	3	,	,	PUNCT
ejpam-5704	226	4	h	h	NOUN
ejpam-5704	226	5	=	=	NOUN
ejpam-5704	226	6	1	1	NUM
ejpam-5704	226	7	,	,	PUNCT
ejpam-5704	226	8	2	2	NUM
ejpam-5704	226	9	with	with	ADP
ejpam-5704	226	10	q1	q1	PROPN
ejpam-5704	226	11	,	,	PUNCT
ejpam-5704	226	12	q2	q2	NOUN
ejpam-5704	226	13	>	>	X
ejpam-5704	226	14	1	1	NUM
ejpam-5704	226	15	such	such	ADJ
ejpam-5704	226	16	that	that	DET
ejpam-5704	226	17	1	1	NUM
ejpam-5704	226	18	q1	q1	NOUN
ejpam-5704	226	19	+	+	CCONJ
ejpam-5704	226	20	1	1	NUM
ejpam-5704	226	21	q2	q2	NOUN
ejpam-5704	226	22	=	=	SYM
ejpam-5704	226	23	1	1	X
ejpam-5704	226	24	.	.	PUNCT
ejpam-5704	227	1	now	now	ADV
ejpam-5704	227	2	,	,	PUNCT
ejpam-5704	227	3	from	from	ADP
ejpam-5704	227	4	[	[	X
ejpam-5704	227	5	25	25	NUM
ejpam-5704	227	6	]	]	PUNCT
ejpam-5704	227	7	,	,	PUNCT
ejpam-5704	227	8	given	give	VERB
ejpam-5704	227	9	the	the	DET
ejpam-5704	227	10	conditions	condition	NOUN
ejpam-5704	227	11	specified	specify	VERB
ejpam-5704	227	12	in	in	ADP
ejpam-5704	227	13	this	this	DET
ejpam-5704	227	14	theorem	theorem	NOUN
ejpam-5704	227	15	,	,	PUNCT
ejpam-5704	227	16	we	we	PRON
ejpam-5704	227	17	obtain	obtain	VERB
ejpam-5704	227	18	:	:	PUNCT
ejpam-5704	227	19	sup	sup	NOUN
ejpam-5704	227	20	f∈b	f∈b	NOUN
ejpam-5704	227	21	∥	∥	PUNCT
ejpam-5704	227	22	n∑	n∑	X
ejpam-5704	227	23	j=0	j=0	PROPN
ejpam-5704	228	1	ln	ln	PROPN
ejpam-5704	228	2	,	,	PUNCT
ejpam-5704	228	3	j(w)f(tj	j(w)f(tj	NOUN
ejpam-5704	228	4	)	)	PUNCT
ejpam-5704	229	1	∥q2≤	∥q2≤	ADP
ejpam-5704	229	2	c	c	NOUN
ejpam-5704	229	3	∥	∥	X
ejpam-5704	229	4	f	f	X
ejpam-5704	229	5	∥∞	∥∞	PROPN
ejpam-5704	229	6	,	,	PUNCT
ejpam-5704	229	7	(	(	PUNCT
ejpam-5704	229	8	39	39	NUM
ejpam-5704	229	9	)	)	PUNCT
ejpam-5704	229	10	for	for	ADP
ejpam-5704	229	11	any	any	DET
ejpam-5704	229	12	bounded	bounded	ADJ
ejpam-5704	229	13	function	function	NOUN
ejpam-5704	229	14	f	f	PROPN
ejpam-5704	229	15	and	and	CCONJ
ejpam-5704	229	16	0	0	NUM
ejpam-5704	229	17	<	<	X
ejpam-5704	229	18	q2	q2	PROPN
ejpam-5704	229	19	<	<	X
ejpam-5704	229	20	∞.	∞.	PROPN
ejpam-5704	229	21	hence	hence	ADV
ejpam-5704	229	22	,	,	PUNCT
ejpam-5704	229	23	the	the	DET
ejpam-5704	229	24	bound	bound	ADJ
ejpam-5704	229	25	(	(	PUNCT
ejpam-5704	229	26	37	37	NUM
ejpam-5704	229	27	)	)	PUNCT
ejpam-5704	229	28	follows	follow	VERB
ejpam-5704	229	29	.	.	PUNCT
ejpam-5704	230	1	lemma	lemma	PROPN
ejpam-5704	230	2	1	1	NUM
ejpam-5704	230	3	.	.	PUNCT
ejpam-5704	231	1	if	if	SCONJ
ejpam-5704	231	2	the	the	DET
ejpam-5704	231	3	kernels	kernel	NOUN
ejpam-5704	231	4	ph	ph	NOUN
ejpam-5704	231	5	satisfy	satisfy	NOUN
ejpam-5704	231	6	{	{	PUNCT
ejpam-5704	231	7	p.	p.	NOUN
ejpam-5704	231	8	,h	,h	PUNCT
ejpam-5704	231	9	∈	∈	PROPN
ejpam-5704	231	10	lq1	lq1	PROPN
ejpam-5704	231	11	,	,	PUNCT
ejpam-5704	231	12	q1	q1	VERB
ejpam-5704	231	13	>	>	X
ejpam-5704	231	14	1	1	NUM
ejpam-5704	231	15	,	,	PUNCT
ejpam-5704	231	16	h	h	NOUN
ejpam-5704	231	17	=	=	SYM
ejpam-5704	231	18	1	1	NUM
ejpam-5704	231	19	,	,	PUNCT
ejpam-5704	231	20	2	2	NUM
ejpam-5704	231	21	,	,	PUNCT
ejpam-5704	231	22	lim	lim	PROPN
ejpam-5704	231	23	t1→t	t1→t	PROPN
ejpam-5704	231	24	∥	∥	PROPN
ejpam-5704	231	25	p.	p.	NOUN
ejpam-5704	232	1	,h(t1	,h(t1	PUNCT
ejpam-5704	232	2	,	,	PUNCT
ejpam-5704	232	3	w)−	w)−	PROPN
ejpam-5704	232	4	p.	p.	NOUN
ejpam-5704	232	5	,h(t	,h(t	PUNCT
ejpam-5704	232	6	,	,	PUNCT
ejpam-5704	232	7	w	w	NOUN
ejpam-5704	232	8	)	)	PUNCT
ejpam-5704	232	9	∥q1=	∥q1=	VERB
ejpam-5704	232	10	0	0	NUM
ejpam-5704	232	11	,	,	PUNCT
ejpam-5704	232	12	∀t	∀t	PROPN
ejpam-5704	232	13	∈	∈	PROPN
ejpam-5704	232	14	ih	ih	X
ejpam-5704	232	15	.	.	PUNCT
ejpam-5704	233	1	(	(	PUNCT
ejpam-5704	233	2	40	40	NUM
ejpam-5704	233	3	)	)	PUNCT
ejpam-5704	233	4	then	then	ADV
ejpam-5704	233	5	lim	lim	PROPN
ejpam-5704	233	6	(	(	PUNCT
ejpam-5704	233	7	t1,θ(t1))→(t	t1,θ(t1))→(t	PROPN
ejpam-5704	233	8	,	,	PUNCT
ejpam-5704	233	9	θ(t	θ(t	PROPN
ejpam-5704	233	10	)	)	PUNCT
ejpam-5704	233	11	)	)	PUNCT
ejpam-5704	233	12	sup	sup	NOUN
ejpam-5704	233	13	n	n	CCONJ
ejpam-5704	233	14	n∑	n∑	PROPN
ejpam-5704	233	15	j=0	j=0	PROPN
ejpam-5704	233	16	|	|	ADV
ejpam-5704	233	17	ωj(p1,h	ωj(p1,h	NOUN
ejpam-5704	233	18	,	,	PUNCT
ejpam-5704	233	19	p2,h	p2,h	PROPN
ejpam-5704	233	20	;	;	PUNCT
ejpam-5704	233	21	t1	t1	NUM
ejpam-5704	233	22	,	,	PUNCT
ejpam-5704	233	23	θ(t1))−	θ(t1))−	VERB
ejpam-5704	233	24	ωj(p1,h	ωj(p1,h	NOUN
ejpam-5704	233	25	,	,	PUNCT
ejpam-5704	233	26	p2,h	p2,h	PROPN
ejpam-5704	233	27	;	;	PUNCT
ejpam-5704	233	28	t	t	PROPN
ejpam-5704	233	29	,	,	PUNCT
ejpam-5704	233	30	θ(t	θ(t	PROPN
ejpam-5704	233	31	)	)	PUNCT
ejpam-5704	233	32	)	)	PUNCT
ejpam-5704	233	33	|=	|=	X
ejpam-5704	233	34	0	0	NUM
ejpam-5704	233	35	,	,	PUNCT
ejpam-5704	233	36	(	(	PUNCT
ejpam-5704	233	37	41	41	NUM
ejpam-5704	233	38	)	)	PUNCT
ejpam-5704	233	39	for	for	ADP
ejpam-5704	233	40	all	all	DET
ejpam-5704	233	41	t	t	NOUN
ejpam-5704	233	42	∈	∈	PROPN
ejpam-5704	233	43	ih	ih	X
ejpam-5704	233	44	.	.	PUNCT
ejpam-5704	234	1	b.	b.	PROPN
ejpam-5704	234	2	h.	h.	PROPN
ejpam-5704	234	3	alrikabi	alrikabi	PROPN
ejpam-5704	234	4	,	,	PUNCT
ejpam-5704	234	5	p.	p.	PROPN
ejpam-5704	234	6	darania	darania	PROPN
ejpam-5704	234	7	,	,	PUNCT
ejpam-5704	234	8	s.pishbin	s.pishbin	PROPN
ejpam-5704	234	9	/	/	SYM
ejpam-5704	234	10	eur	eur	PROPN
ejpam-5704	234	11	.	.	PUNCT
ejpam-5704	235	1	j.	j.	PROPN
ejpam-5704	235	2	pure	pure	PROPN
ejpam-5704	235	3	appl	appl	PROPN
ejpam-5704	235	4	.	.	PROPN
ejpam-5704	235	5	math	math	PROPN
ejpam-5704	235	6	,	,	PUNCT
ejpam-5704	235	7	18	18	NUM
ejpam-5704	235	8	(	(	PUNCT
ejpam-5704	235	9	2	2	NUM
ejpam-5704	235	10	)	)	PUNCT
ejpam-5704	235	11	(	(	PUNCT
ejpam-5704	235	12	2025	2025	NUM
ejpam-5704	235	13	)	)	PUNCT
ejpam-5704	235	14	,	,	PUNCT
ejpam-5704	235	15	5704	5704	NUM
ejpam-5704	235	16	13	13	NUM
ejpam-5704	235	17	of	of	ADP
ejpam-5704	235	18	19	19	NUM
ejpam-5704	235	19	proof	proof	NOUN
ejpam-5704	235	20	.	.	PUNCT
ejpam-5704	236	1	by	by	ADP
ejpam-5704	236	2	using	use	VERB
ejpam-5704	236	3	ωj	ωj	ADP
ejpam-5704	236	4	=	=	PUNCT
ejpam-5704	236	5	ω1j	ω1j	PROPN
ejpam-5704	236	6	+	+	CCONJ
ejpam-5704	236	7	ω2j	ω2j	NUM
ejpam-5704	236	8	we	we	PRON
ejpam-5704	236	9	get	get	VERB
ejpam-5704	236	10	sup	sup	NOUN
ejpam-5704	236	11	n	n	CCONJ
ejpam-5704	236	12	{	{	PUNCT
ejpam-5704	236	13	n∑	n∑	NOUN
ejpam-5704	236	14	j=0	j=0	PROPN
ejpam-5704	236	15	|	|	ADV
ejpam-5704	236	16	ωj(p1,h	ωj(p1,h	NOUN
ejpam-5704	236	17	,	,	PUNCT
ejpam-5704	236	18	p2,h	p2,h	PROPN
ejpam-5704	236	19	;	;	PUNCT
ejpam-5704	236	20	t1	t1	NUM
ejpam-5704	236	21	,	,	PUNCT
ejpam-5704	236	22	θ(t1))−	θ(t1))−	VERB
ejpam-5704	236	23	ωj(p1,h	ωj(p1,h	NOUN
ejpam-5704	236	24	,	,	PUNCT
ejpam-5704	236	25	p2,h	p2,h	PROPN
ejpam-5704	236	26	;	;	PUNCT
ejpam-5704	236	27	t	t	PROPN
ejpam-5704	236	28	,	,	PUNCT
ejpam-5704	236	29	θ(t	θ(t	PROPN
ejpam-5704	236	30	)	)	PUNCT
ejpam-5704	236	31	)	)	PUNCT
ejpam-5704	237	1	|	|	ADV
ejpam-5704	237	2	}	}	PUNCT
ejpam-5704	237	3	=	=	PUNCT
ejpam-5704	237	4	sup	sup	NOUN
ejpam-5704	237	5	n	n	CCONJ
ejpam-5704	237	6	{	{	PUNCT
ejpam-5704	237	7	n∑	n∑	NOUN
ejpam-5704	237	8	j=0	j=0	PROPN
ejpam-5704	237	9	|	|	ADV
ejpam-5704	237	10	[	[	X
ejpam-5704	237	11	ω1j(p1,h	ω1j(p1,h	X
ejpam-5704	237	12	,	,	PUNCT
ejpam-5704	237	13	t1)−	t1)−	NOUN
ejpam-5704	237	14	ω1j(p1,h	ω1j(p1,h	X
ejpam-5704	237	15	,	,	PUNCT
ejpam-5704	237	16	t	t	PROPN
ejpam-5704	237	17	)	)	PUNCT
ejpam-5704	237	18	]	]	PUNCT
ejpam-5704	238	1	+	+	CCONJ
ejpam-5704	238	2	[	[	X
ejpam-5704	238	3	ω2j(p2,h	ω2j(p2,h	NUM
ejpam-5704	238	4	,	,	PUNCT
ejpam-5704	238	5	t1)−	t1)−	NOUN
ejpam-5704	238	6	ω2j(p2,h	ω2j(p2,h	NUM
ejpam-5704	238	7	,	,	PUNCT
ejpam-5704	238	8	t	t	PROPN
ejpam-5704	238	9	)	)	PUNCT
ejpam-5704	238	10	]	]	PUNCT
ejpam-5704	239	1	|	|	ADV
ejpam-5704	239	2	}	}	PUNCT
ejpam-5704	239	3	=	=	PUNCT
ejpam-5704	239	4	sup	sup	NOUN
ejpam-5704	239	5	n	n	CCONJ
ejpam-5704	239	6	{	{	PUNCT
ejpam-5704	239	7	n∑	n∑	NOUN
ejpam-5704	239	8	j=0	j=0	PROPN
ejpam-5704	239	9	|	|	ADV
ejpam-5704	239	10	∫	∫	PROPN
ejpam-5704	239	11	t1	t1	NOUN
ejpam-5704	239	12	0	0	NUM
ejpam-5704	240	1	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	240	2	,	,	PUNCT
ejpam-5704	240	3	w)ln	w)ln	PROPN
ejpam-5704	240	4	,	,	PUNCT
ejpam-5704	240	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	241	1	−	−	PROPN
ejpam-5704	241	2	∫	∫	PROPN
ejpam-5704	241	3	t	t	PROPN
ejpam-5704	241	4	0	0	NUM
ejpam-5704	241	5	p1,h(t	p1,h(t	NOUN
ejpam-5704	241	6	,	,	PUNCT
ejpam-5704	241	7	w)ln	w)ln	PROPN
ejpam-5704	241	8	,	,	PUNCT
ejpam-5704	241	9	j(w)dw	j(w)dw	PROPN
ejpam-5704	242	1	+	+	CCONJ
ejpam-5704	242	2	∫	∫	PROPN
ejpam-5704	242	3	θ(t1	θ(t1	NOUN
ejpam-5704	242	4	)	)	PUNCT
ejpam-5704	242	5	0	0	NUM
ejpam-5704	243	1	p2,h(t1	p2,h(t1	NUM
ejpam-5704	243	2	,	,	PUNCT
ejpam-5704	243	3	w)ln	w)ln	PROPN
ejpam-5704	243	4	,	,	PUNCT
ejpam-5704	243	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	243	6	−	−	PROPN
ejpam-5704	243	7	∫	∫	PROPN
ejpam-5704	243	8	θ(t	θ(t	PROPN
ejpam-5704	243	9	)	)	PUNCT
ejpam-5704	243	10	0	0	NUM
ejpam-5704	244	1	p2,h(t	p2,h(t	NOUN
ejpam-5704	244	2	,	,	PUNCT
ejpam-5704	244	3	w)ln	w)ln	PROPN
ejpam-5704	244	4	,	,	PUNCT
ejpam-5704	244	5	j(w)dw	j(w)dw	NOUN
ejpam-5704	244	6	|	|	ADJ
ejpam-5704	244	7	}	}	PUNCT
ejpam-5704	244	8	=	=	PUNCT
ejpam-5704	244	9	sup	sup	NOUN
ejpam-5704	244	10	n	n	CCONJ
ejpam-5704	244	11	{	{	PUNCT
ejpam-5704	244	12	n∑	n∑	NOUN
ejpam-5704	244	13	j=0	j=0	PROPN
ejpam-5704	245	1	|	|	ADV
ejpam-5704	245	2	∫	∫	PROPN
ejpam-5704	245	3	t	t	NOUN
ejpam-5704	245	4	0	0	NUM
ejpam-5704	246	1	[	[	X
ejpam-5704	246	2	p1,h(t1	p1,h(t1	NOUN
ejpam-5704	246	3	,	,	PUNCT
ejpam-5704	246	4	w)−	w)−	PROPN
ejpam-5704	246	5	p1,h(t	p1,h(t	NOUN
ejpam-5704	246	6	,	,	PUNCT
ejpam-5704	246	7	w)]ln	w)]ln	NOUN
ejpam-5704	246	8	,	,	PUNCT
ejpam-5704	246	9	j(w)dw	j(w)dw	PROPN
ejpam-5704	247	1	+	+	NUM
ejpam-5704	247	2	∫	∫	PROPN
ejpam-5704	247	3	t1	t1	PROPN
ejpam-5704	247	4	t	t	PROPN
ejpam-5704	247	5	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	247	6	,	,	PUNCT
ejpam-5704	247	7	w)ln	w)ln	PROPN
ejpam-5704	247	8	,	,	PUNCT
ejpam-5704	247	9	j(w)dw	j(w)dw	PROPN
ejpam-5704	248	1	+	+	CCONJ
ejpam-5704	248	2	∫	∫	PROPN
ejpam-5704	248	3	θ(t	θ(t	PROPN
ejpam-5704	248	4	)	)	PUNCT
ejpam-5704	248	5	0	0	PUNCT
ejpam-5704	249	1	[	[	X
ejpam-5704	249	2	p2,h(t1	p2,h(t1	X
ejpam-5704	249	3	,	,	PUNCT
ejpam-5704	249	4	w)−	w)−	PROPN
ejpam-5704	249	5	p2,h(t	p2,h(t	NOUN
ejpam-5704	249	6	,	,	PUNCT
ejpam-5704	249	7	w)]ln	w)]ln	NOUN
ejpam-5704	249	8	,	,	PUNCT
ejpam-5704	249	9	j(w)dw	j(w)dw	PROPN
ejpam-5704	250	1	+	+	CCONJ
ejpam-5704	250	2	∫	∫	PROPN
ejpam-5704	250	3	θ(t1	θ(t1	NOUN
ejpam-5704	250	4	)	)	PUNCT
ejpam-5704	250	5	θ(t	θ(t	PROPN
ejpam-5704	250	6	)	)	PUNCT
ejpam-5704	250	7	p2,h(t1	p2,h(t1	PROPN
ejpam-5704	250	8	,	,	PUNCT
ejpam-5704	250	9	w)ln	w)ln	PROPN
ejpam-5704	250	10	,	,	PUNCT
ejpam-5704	250	11	j(w)dw	j(w)dw	NOUN
ejpam-5704	250	12	|	|	ADV
ejpam-5704	250	13	}	}	PUNCT
ejpam-5704	250	14	≤	≤	NUM
ejpam-5704	250	15	sup	sup	NOUN
ejpam-5704	250	16	n	n	CCONJ
ejpam-5704	250	17	{	{	PUNCT
ejpam-5704	250	18	n∑	n∑	NOUN
ejpam-5704	250	19	j=0	j=0	PROPN
ejpam-5704	250	20	|	|	ADV
ejpam-5704	250	21	∫	∫	PROPN
ejpam-5704	251	1	t1	t1	NOUN
ejpam-5704	251	2	0	0	NUM
ejpam-5704	252	1	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	252	2	,	,	PUNCT
ejpam-5704	252	3	w)ln	w)ln	PROPN
ejpam-5704	252	4	,	,	PUNCT
ejpam-5704	252	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	253	1	|	|	ADV
ejpam-5704	253	2	−	−	PROPN
ejpam-5704	253	3	n∑	n∑	PROPN
ejpam-5704	253	4	j=0	j=0	PROPN
ejpam-5704	254	1	|	|	ADV
ejpam-5704	254	2	∫	∫	PROPN
ejpam-5704	254	3	t	t	PROPN
ejpam-5704	254	4	0	0	NUM
ejpam-5704	255	1	p1,h(t	p1,h(t	NOUN
ejpam-5704	255	2	,	,	PUNCT
ejpam-5704	255	3	w)ln	w)ln	PROPN
ejpam-5704	255	4	,	,	PUNCT
ejpam-5704	255	5	j(w)dw	j(w)dw	NOUN
ejpam-5704	256	1	|	|	ADV
ejpam-5704	257	1	+	+	CCONJ
ejpam-5704	257	2	n∑	n∑	PROPN
ejpam-5704	257	3	j=0	j=0	PROPN
ejpam-5704	257	4	|	|	ADV
ejpam-5704	257	5	∫	∫	PROPN
ejpam-5704	257	6	θ(t1	θ(t1	PART
ejpam-5704	257	7	)	)	PUNCT
ejpam-5704	257	8	0	0	NUM
ejpam-5704	258	1	p2,h(t1	p2,h(t1	NUM
ejpam-5704	258	2	,	,	PUNCT
ejpam-5704	258	3	w)ln	w)ln	PROPN
ejpam-5704	258	4	,	,	PUNCT
ejpam-5704	258	5	j(w)dw	j(w)dw	PROPN
ejpam-5704	259	1	|	|	ADV
ejpam-5704	259	2	−	−	PROPN
ejpam-5704	259	3	n∑	n∑	PROPN
ejpam-5704	259	4	j=0	j=0	PROPN
ejpam-5704	259	5	|	|	ADV
ejpam-5704	259	6	∫	∫	PROPN
ejpam-5704	259	7	θ(t	θ(t	PROPN
ejpam-5704	259	8	)	)	PUNCT
ejpam-5704	259	9	0	0	NUM
ejpam-5704	259	10	p2,h(t	p2,h(t	NOUN
ejpam-5704	259	11	,	,	PUNCT
ejpam-5704	259	12	w)ln	w)ln	PROPN
ejpam-5704	259	13	,	,	PUNCT
ejpam-5704	259	14	j(w)dw	j(w)dw	NOUN
ejpam-5704	259	15	|	|	ADV
ejpam-5704	259	16	}	}	PUNCT
ejpam-5704	259	17	≤	≤	NOUN
ejpam-5704	259	18	c	c	X
ejpam-5704	259	19	{	{	PUNCT
ejpam-5704	259	20	[	[	PUNCT
ejpam-5704	259	21	∫	∫	PROPN
ejpam-5704	259	22	t1	t1	NOUN
ejpam-5704	259	23	0	0	NUM
ejpam-5704	260	1	|	|	ADV
ejpam-5704	260	2	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	260	3	,	,	PUNCT
ejpam-5704	260	4	w)−	w)−	PROPN
ejpam-5704	260	5	p1,h(t	p1,h(t	NOUN
ejpam-5704	260	6	,	,	PUNCT
ejpam-5704	260	7	w	w	NOUN
ejpam-5704	260	8	)	)	PUNCT
ejpam-5704	260	9	|q1	|q1	NOUN
ejpam-5704	260	10	dw	dw	X
ejpam-5704	260	11	]	]	X
ejpam-5704	260	12	1	1	NUM
ejpam-5704	260	13	q1	q1	NOUN
ejpam-5704	260	14	+	+	CCONJ
ejpam-5704	260	15	[	[	PUNCT
ejpam-5704	260	16	∫	∫	PROPN
ejpam-5704	260	17	t1	t1	PROPN
ejpam-5704	260	18	t	t	PROPN
ejpam-5704	261	1	|	|	ADV
ejpam-5704	261	2	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	261	3	,	,	PUNCT
ejpam-5704	261	4	w	w	NOUN
ejpam-5704	261	5	)	)	PUNCT
ejpam-5704	261	6	|q1	|q1	NOUN
ejpam-5704	261	7	dw	dw	X
ejpam-5704	261	8	]	]	X
ejpam-5704	261	9	1	1	NUM
ejpam-5704	261	10	q1	q1	NOUN
ejpam-5704	261	11	+	+	PROPN
ejpam-5704	261	12	[	[	PUNCT
ejpam-5704	261	13	∫	∫	PROPN
ejpam-5704	261	14	t1	t1	NOUN
ejpam-5704	261	15	0	0	NUM
ejpam-5704	262	1	|	|	ADV
ejpam-5704	262	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	262	3	,	,	PUNCT
ejpam-5704	262	4	w)−	w)−	PROPN
ejpam-5704	262	5	p2,h(t	p2,h(t	NOUN
ejpam-5704	262	6	,	,	PUNCT
ejpam-5704	262	7	w	w	NOUN
ejpam-5704	262	8	)	)	PUNCT
ejpam-5704	262	9	|q1	|q1	NOUN
ejpam-5704	263	1	dw	dw	X
ejpam-5704	263	2	]	]	X
ejpam-5704	263	3	1	1	NUM
ejpam-5704	263	4	q1	q1	NOUN
ejpam-5704	263	5	+	+	CCONJ
ejpam-5704	263	6	[	[	PUNCT
ejpam-5704	263	7	∫	∫	PROPN
ejpam-5704	263	8	θ(t1	θ(t1	NOUN
ejpam-5704	263	9	)	)	PUNCT
ejpam-5704	263	10	θ(t	θ(t	PROPN
ejpam-5704	263	11	)	)	PUNCT
ejpam-5704	264	1	|	|	ADV
ejpam-5704	264	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	264	3	,	,	PUNCT
ejpam-5704	264	4	w	w	NOUN
ejpam-5704	264	5	)	)	PUNCT
ejpam-5704	264	6	|q1	|q1	NOUN
ejpam-5704	264	7	dw	dw	X
ejpam-5704	264	8	]	]	X
ejpam-5704	264	9	1	1	NUM
ejpam-5704	264	10	q1	q1	PROPN
ejpam-5704	264	11	}	}	PUNCT
ejpam-5704	264	12	≤	≤	NUM
ejpam-5704	265	1	c	c	X
ejpam-5704	265	2	{	{	PUNCT
ejpam-5704	265	3	[	[	PUNCT
ejpam-5704	265	4	∫	∫	PROPN
ejpam-5704	265	5	1	1	NUM
ejpam-5704	265	6	0	0	NUM
ejpam-5704	265	7	|	|	ADV
ejpam-5704	265	8	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	265	9	,	,	PUNCT
ejpam-5704	265	10	w)−	w)−	PROPN
ejpam-5704	265	11	p1,h(t	p1,h(t	NOUN
ejpam-5704	265	12	,	,	PUNCT
ejpam-5704	265	13	w	w	NOUN
ejpam-5704	265	14	)	)	PUNCT
ejpam-5704	265	15	|q1	|q1	NOUN
ejpam-5704	265	16	dw	dw	X
ejpam-5704	265	17	]	]	X
ejpam-5704	265	18	1	1	NUM
ejpam-5704	265	19	q1	q1	NOUN
ejpam-5704	265	20	+	+	CCONJ
ejpam-5704	265	21	[	[	PUNCT
ejpam-5704	265	22	∫	∫	PROPN
ejpam-5704	265	23	t1	t1	PROPN
ejpam-5704	265	24	t	t	PROPN
ejpam-5704	266	1	|	|	ADV
ejpam-5704	266	2	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	266	3	,	,	PUNCT
ejpam-5704	266	4	w	w	NOUN
ejpam-5704	266	5	)	)	PUNCT
ejpam-5704	266	6	|q1	|q1	NOUN
ejpam-5704	266	7	dw	dw	X
ejpam-5704	266	8	]	]	X
ejpam-5704	266	9	1	1	NUM
ejpam-5704	266	10	q1	q1	NOUN
ejpam-5704	266	11	+	+	PROPN
ejpam-5704	266	12	[	[	PUNCT
ejpam-5704	266	13	∫	∫	PROPN
ejpam-5704	266	14	1	1	NUM
ejpam-5704	266	15	0	0	NUM
ejpam-5704	267	1	|	|	ADV
ejpam-5704	267	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	267	3	,	,	PUNCT
ejpam-5704	267	4	w)−	w)−	PROPN
ejpam-5704	267	5	p2,h(t	p2,h(t	NOUN
ejpam-5704	267	6	,	,	PUNCT
ejpam-5704	267	7	w	w	NOUN
ejpam-5704	267	8	)	)	PUNCT
ejpam-5704	267	9	|q1	|q1	NOUN
ejpam-5704	267	10	dw	dw	X
ejpam-5704	267	11	]	]	X
ejpam-5704	267	12	1	1	NUM
ejpam-5704	267	13	q1	q1	NOUN
ejpam-5704	267	14	+	+	CCONJ
ejpam-5704	267	15	[	[	PUNCT
ejpam-5704	267	16	∫	∫	PROPN
ejpam-5704	267	17	θ(t1	θ(t1	NOUN
ejpam-5704	267	18	)	)	PUNCT
ejpam-5704	267	19	θ(t	θ(t	PROPN
ejpam-5704	267	20	)	)	PUNCT
ejpam-5704	268	1	|	|	ADV
ejpam-5704	268	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	268	3	,	,	PUNCT
ejpam-5704	268	4	w	w	NOUN
ejpam-5704	268	5	)	)	PUNCT
ejpam-5704	268	6	|q1	|q1	NOUN
ejpam-5704	268	7	dw	dw	X
ejpam-5704	268	8	]	]	X
ejpam-5704	268	9	1	1	NUM
ejpam-5704	268	10	q1	q1	PROPN
ejpam-5704	268	11	}	}	PUNCT
ejpam-5704	268	12	≤	≤	PUNCT
ejpam-5704	269	1	c{∥	c{∥	PROPN
ejpam-5704	269	2	p1,h(t1	p1,h(t1	PROPN
ejpam-5704	269	3	,	,	PUNCT
ejpam-5704	269	4	w)−	w)−	PROPN
ejpam-5704	269	5	p1,h(t	p1,h(t	NOUN
ejpam-5704	269	6	,	,	PUNCT
ejpam-5704	269	7	w	w	NOUN
ejpam-5704	269	8	)	)	PUNCT
ejpam-5704	269	9	∥q1	∥q1	VERB
ejpam-5704	270	1	+	+	NOUN
ejpam-5704	270	2	[	[	PUNCT
ejpam-5704	270	3	∫	∫	PROPN
ejpam-5704	270	4	θ(t1	θ(t1	NOUN
ejpam-5704	270	5	)	)	PUNCT
ejpam-5704	270	6	θ(t	θ(t	PROPN
ejpam-5704	270	7	)	)	PUNCT
ejpam-5704	271	1	|	|	ADV
ejpam-5704	271	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	271	3	,	,	PUNCT
ejpam-5704	271	4	w	w	NOUN
ejpam-5704	271	5	)	)	PUNCT
ejpam-5704	271	6	|q1	|q1	NOUN
ejpam-5704	271	7	dw	dw	X
ejpam-5704	271	8	]	]	X
ejpam-5704	271	9	1	1	NUM
ejpam-5704	271	10	q1	q1	NOUN
ejpam-5704	271	11	+	+	CCONJ
ejpam-5704	271	12	∥	∥	NOUN
ejpam-5704	271	13	p2,h(t1	p2,h(t1	NOUN
ejpam-5704	271	14	,	,	PUNCT
ejpam-5704	271	15	w)−	w)−	PROPN
ejpam-5704	271	16	p2,h(t	p2,h(t	NOUN
ejpam-5704	271	17	,	,	PUNCT
ejpam-5704	271	18	w	w	NOUN
ejpam-5704	271	19	)	)	PUNCT
ejpam-5704	271	20	∥q1	∥q1	VERB
ejpam-5704	272	1	+	+	NOUN
ejpam-5704	272	2	[	[	PUNCT
ejpam-5704	272	3	∫	∫	PROPN
ejpam-5704	272	4	θ(t1	θ(t1	NOUN
ejpam-5704	272	5	)	)	PUNCT
ejpam-5704	272	6	θ(t	θ(t	PROPN
ejpam-5704	272	7	)	)	PUNCT
ejpam-5704	273	1	|	|	ADV
ejpam-5704	273	2	p2,h(t1	p2,h(t1	NUM
ejpam-5704	273	3	,	,	PUNCT
ejpam-5704	273	4	w	w	NOUN
ejpam-5704	273	5	)	)	PUNCT
ejpam-5704	273	6	|q1	|q1	NOUN
ejpam-5704	273	7	dw	dw	X
ejpam-5704	273	8	]	]	X
ejpam-5704	273	9	1	1	NUM
ejpam-5704	273	10	q1	q1	NOUN
ejpam-5704	273	11	}	}	PUNCT
ejpam-5704	273	12	.	.	PUNCT
ejpam-5704	274	1	(	(	PUNCT
ejpam-5704	274	2	42	42	X
ejpam-5704	274	3	)	)	PUNCT
ejpam-5704	274	4	b.	b.	PROPN
ejpam-5704	274	5	h.	h.	PROPN
ejpam-5704	274	6	alrikabi	alrikabi	PROPN
ejpam-5704	274	7	,	,	PUNCT
ejpam-5704	274	8	p.	p.	PROPN
ejpam-5704	274	9	darania	darania	PROPN
ejpam-5704	274	10	,	,	PUNCT
ejpam-5704	274	11	s.pishbin	s.pishbin	PROPN
ejpam-5704	274	12	/	/	SYM
ejpam-5704	274	13	eur	eur	PROPN
ejpam-5704	274	14	.	.	PUNCT
ejpam-5704	275	1	j.	j.	PROPN
ejpam-5704	275	2	pure	pure	PROPN
ejpam-5704	275	3	appl	appl	PROPN
ejpam-5704	275	4	.	.	PROPN
ejpam-5704	275	5	math	math	PROPN
ejpam-5704	275	6	,	,	PUNCT
ejpam-5704	275	7	18	18	NUM
ejpam-5704	275	8	(	(	PUNCT
ejpam-5704	275	9	2	2	NUM
ejpam-5704	275	10	)	)	PUNCT
ejpam-5704	275	11	(	(	PUNCT
ejpam-5704	275	12	2025	2025	NUM
ejpam-5704	275	13	)	)	PUNCT
ejpam-5704	275	14	,	,	PUNCT
ejpam-5704	275	15	5704	5704	NUM
ejpam-5704	275	16	14	14	NUM
ejpam-5704	275	17	of	of	ADP
ejpam-5704	275	18	19	19	NUM
ejpam-5704	275	19	the	the	DET
ejpam-5704	275	20	lemma	lemma	PROPN
ejpam-5704	275	21	now	now	ADV
ejpam-5704	275	22	follow	follow	VERB
ejpam-5704	275	23	from	from	ADP
ejpam-5704	275	24	these	these	DET
ejpam-5704	275	25	statements	statement	NOUN
ejpam-5704	275	26	.	.	PUNCT
ejpam-5704	276	1	theorem	theorem	NOUN
ejpam-5704	276	2	3	3	X
ejpam-5704	276	3	.	.	PUNCT
ejpam-5704	276	4	consider	consider	VERB
ejpam-5704	276	5	the	the	DET
ejpam-5704	276	6	operator	operator	NOUN
ejpam-5704	276	7	an	an	DET
ejpam-5704	276	8	defined	define	VERB
ejpam-5704	276	9	as	as	ADP
ejpam-5704	276	10	in	in	ADP
ejpam-5704	276	11	(	(	PUNCT
ejpam-5704	276	12	28	28	NUM
ejpam-5704	276	13	)	)	PUNCT
ejpam-5704	276	14	,	,	PUNCT
ejpam-5704	276	15	and	and	CCONJ
ejpam-5704	276	16	let	let	VERB
ejpam-5704	276	17	the	the	DET
ejpam-5704	276	18	nodes	node	NOUN
ejpam-5704	276	19	{	{	PUNCT
ejpam-5704	276	20	ti}ni=0	ti}ni=0	NOUN
ejpam-5704	276	21	be	be	AUX
ejpam-5704	276	22	selected	select	VERB
ejpam-5704	276	23	as	as	SCONJ
ejpam-5704	276	24	outlined	outline	VERB
ejpam-5704	276	25	in	in	ADP
ejpam-5704	276	26	theorem	theorem	NOUN
ejpam-5704	276	27	1	1	NUM
ejpam-5704	276	28	.	.	PUNCT
ejpam-5704	277	1	if	if	SCONJ
ejpam-5704	277	2	conditions	condition	NOUN
ejpam-5704	277	3	(	(	PUNCT
ejpam-5704	277	4	32	32	NUM
ejpam-5704	277	5	)	)	PUNCT
ejpam-5704	277	6	,	,	PUNCT
ejpam-5704	277	7	(	(	PUNCT
ejpam-5704	277	8	37	37	NUM
ejpam-5704	277	9	)	)	PUNCT
ejpam-5704	277	10	,	,	PUNCT
ejpam-5704	277	11	and	and	CCONJ
ejpam-5704	277	12	(	(	PUNCT
ejpam-5704	277	13	41	41	NUM
ejpam-5704	277	14	)	)	PUNCT
ejpam-5704	277	15	are	be	AUX
ejpam-5704	277	16	satisfied	satisfied	ADJ
ejpam-5704	277	17	,	,	PUNCT
ejpam-5704	277	18	then	then	ADV
ejpam-5704	277	19	for	for	ADP
ejpam-5704	277	20	all	all	DET
ejpam-5704	277	21	sufficiently	sufficiently	ADV
ejpam-5704	277	22	large	large	ADJ
ejpam-5704	277	23	values	value	NOUN
ejpam-5704	277	24	of	of	ADP
ejpam-5704	277	25	n	n	NOUN
ejpam-5704	277	26	,	,	PUNCT
ejpam-5704	277	27	there	there	PRON
ejpam-5704	277	28	exists	exist	VERB
ejpam-5704	277	29	a	a	DET
ejpam-5704	277	30	constant	constant	ADJ
ejpam-5704	277	31	c	c	NOUN
ejpam-5704	277	32	>	>	X
ejpam-5704	277	33	0	0	NUM
ejpam-5704	277	34	that	that	PRON
ejpam-5704	277	35	is	be	AUX
ejpam-5704	277	36	independent	independent	ADJ
ejpam-5704	277	37	of	of	ADP
ejpam-5704	277	38	n	n	PROPN
ejpam-5704	277	39	,	,	PUNCT
ejpam-5704	277	40	so	so	SCONJ
ejpam-5704	277	41	that	that	SCONJ
ejpam-5704	277	42	∥	∥	NUM
ejpam-5704	277	43	(	(	PUNCT
ejpam-5704	277	44	i	i	PROPN
ejpam-5704	277	45	−an	−an	PROPN
ejpam-5704	277	46	)	)	PUNCT
ejpam-5704	277	47	−1	−1	NOUN
ejpam-5704	277	48	∥≤	∥≤	PROPN
ejpam-5704	277	49	c.	c.	NOUN
ejpam-5704	277	50	(	(	PUNCT
ejpam-5704	277	51	43	43	NUM
ejpam-5704	277	52	)	)	PUNCT
ejpam-5704	277	53	proof	proof	NOUN
ejpam-5704	277	54	.	.	PUNCT
ejpam-5704	278	1	the	the	DET
ejpam-5704	278	2	proof	proof	NOUN
ejpam-5704	278	3	immediately	immediately	ADV
ejpam-5704	278	4	stems	stem	VERB
ejpam-5704	278	5	from	from	ADP
ejpam-5704	278	6	an	an	DET
ejpam-5704	278	7	implication	implication	NOUN
ejpam-5704	278	8	of	of	ADP
ejpam-5704	278	9	theorem	theorem	NOUN
ejpam-5704	278	10	2	2	NUM
ejpam-5704	278	11	in	in	ADP
ejpam-5704	278	12	[	[	X
ejpam-5704	278	13	32	32	NUM
ejpam-5704	278	14	]	]	PUNCT
ejpam-5704	278	15	and	and	CCONJ
ejpam-5704	278	16	lemma	lemma	PROPN
ejpam-5704	278	17	1	1	NUM
ejpam-5704	278	18	in	in	ADP
ejpam-5704	278	19	[	[	X
ejpam-5704	278	20	33	33	NUM
ejpam-5704	278	21	]	]	PUNCT
ejpam-5704	278	22	.	.	PUNCT
ejpam-5704	279	1	the	the	DET
ejpam-5704	279	2	outcomes	outcome	NOUN
ejpam-5704	279	3	of	of	ADP
ejpam-5704	279	4	our	our	PRON
ejpam-5704	279	5	efforts	effort	NOUN
ejpam-5704	279	6	in	in	ADP
ejpam-5704	279	7	this	this	DET
ejpam-5704	279	8	section	section	NOUN
ejpam-5704	279	9	lead	lead	NOUN
ejpam-5704	279	10	to	to	ADP
ejpam-5704	279	11	the	the	DET
ejpam-5704	279	12	following	follow	VERB
ejpam-5704	279	13	principal	principal	NOUN
ejpam-5704	279	14	theorem	theorem	NOUN
ejpam-5704	279	15	:	:	PUNCT
ejpam-5704	279	16	theorem	theorem	ADJ
ejpam-5704	279	17	4	4	NUM
ejpam-5704	279	18	.	.	PUNCT
ejpam-5704	279	19	consider	consider	VERB
ejpam-5704	279	20	y(t	y(t	NUM
ejpam-5704	279	21	)	)	PUNCT
ejpam-5704	279	22	and	and	CCONJ
ejpam-5704	279	23	yn	yn	PROPN
ejpam-5704	279	24	(	(	PUNCT
ejpam-5704	279	25	t	t	PROPN
ejpam-5704	279	26	)	)	PUNCT
ejpam-5704	279	27	as	as	ADP
ejpam-5704	279	28	the	the	DET
ejpam-5704	279	29	exact	exact	ADJ
ejpam-5704	279	30	and	and	CCONJ
ejpam-5704	279	31	approximated	approximated	ADJ
ejpam-5704	279	32	solutions	solution	NOUN
ejpam-5704	279	33	,	,	PUNCT
ejpam-5704	279	34	respectively	respectively	ADV
ejpam-5704	279	35	,	,	PUNCT
ejpam-5704	279	36	to	to	ADP
ejpam-5704	279	37	the	the	DET
ejpam-5704	279	38	equation	equation	NOUN
ejpam-5704	279	39	(	(	PUNCT
ejpam-5704	279	40	20	20	NUM
ejpam-5704	279	41	)	)	PUNCT
ejpam-5704	279	42	.	.	PUNCT
ejpam-5704	280	1	these	these	DET
ejpam-5704	280	2	solutions	solution	NOUN
ejpam-5704	280	3	are	be	AUX
ejpam-5704	280	4	constructed	construct	VERB
ejpam-5704	280	5	based	base	VERB
ejpam-5704	280	6	on	on	ADP
ejpam-5704	280	7	a	a	DET
ejpam-5704	280	8	collection	collection	NOUN
ejpam-5704	280	9	of	of	ADP
ejpam-5704	280	10	distinct	distinct	ADJ
ejpam-5704	280	11	nodes	node	NOUN
ejpam-5704	280	12	{	{	PUNCT
ejpam-5704	280	13	ti}ni=1∪{t0	ti}ni=1∪{t0	PROPN
ejpam-5704	280	14	=	=	PUNCT
ejpam-5704	280	15	0	0	NUM
ejpam-5704	280	16	}	}	PUNCT
ejpam-5704	280	17	.	.	PUNCT
ejpam-5704	281	1	if	if	SCONJ
ejpam-5704	281	2	the	the	DET
ejpam-5704	281	3	nodes	node	NOUN
ejpam-5704	281	4	{	{	PUNCT
ejpam-5704	281	5	ti	ti	NOUN
ejpam-5704	281	6	}	}	PUNCT
ejpam-5704	281	7	are	be	AUX
ejpam-5704	281	8	the	the	DET
ejpam-5704	281	9	zeroes	zero	NOUN
ejpam-5704	281	10	of	of	ADP
ejpam-5704	281	11	the	the	DET
ejpam-5704	281	12	orthogonal	orthogonal	ADJ
ejpam-5704	281	13	polynomial	polynomial	NOUN
ejpam-5704	281	14	in	in	ADP
ejpam-5704	281	15	ih	ih	PROPN
ejpam-5704	281	16	and	and	CCONJ
ejpam-5704	281	17	ph(t	ph(t	PRON
ejpam-5704	281	18	,	,	PUNCT
ejpam-5704	281	19	w	w	NOUN
ejpam-5704	281	20	)	)	PUNCT
ejpam-5704	281	21	is	be	AUX
ejpam-5704	281	22	the	the	DET
ejpam-5704	281	23	kernel	kernel	PROPN
ejpam-5704	281	24	function	function	NOUN
ejpam-5704	281	25	of	of	ADP
ejpam-5704	281	26	the	the	DET
ejpam-5704	281	27	form	form	NOUN
ejpam-5704	281	28	(	(	PUNCT
ejpam-5704	281	29	4	4	NUM
ejpam-5704	281	30	)	)	PUNCT
ejpam-5704	281	31	,	,	PUNCT
ejpam-5704	281	32	then	then	ADV
ejpam-5704	281	33	yn	yn	PROPN
ejpam-5704	281	34	(	(	PUNCT
ejpam-5704	281	35	t	t	PROPN
ejpam-5704	281	36	)	)	PUNCT
ejpam-5704	281	37	converges	converge	VERB
ejpam-5704	281	38	uniformly	uniformly	ADV
ejpam-5704	281	39	to	to	ADP
ejpam-5704	281	40	y(t	y(t	PROPN
ejpam-5704	281	41	)	)	PUNCT
ejpam-5704	281	42	.	.	PUNCT
ejpam-5704	282	1	furthermore	furthermore	ADV
ejpam-5704	282	2	,	,	PUNCT
ejpam-5704	282	3	the	the	DET
ejpam-5704	282	4	convergence	convergence	NOUN
ejpam-5704	282	5	rate	rate	NOUN
ejpam-5704	282	6	aligns	align	VERB
ejpam-5704	282	7	with	with	ADP
ejpam-5704	282	8	the	the	DET
ejpam-5704	282	9	product	product	NOUN
ejpam-5704	282	10	integration	integration	NOUN
ejpam-5704	282	11	quadrature	quadrature	NOUN
ejpam-5704	282	12	that	that	PRON
ejpam-5704	282	13	we	we	PRON
ejpam-5704	282	14	select	select	VERB
ejpam-5704	282	15	to	to	PART
ejpam-5704	282	16	approximate	approximate	VERB
ejpam-5704	282	17	the	the	DET
ejpam-5704	282	18	integral	integral	ADJ
ejpam-5704	282	19	term	term	NOUN
ejpam-5704	282	20	(	(	PUNCT
ejpam-5704	282	21	20	20	NUM
ejpam-5704	282	22	)	)	PUNCT
ejpam-5704	282	23	.	.	PUNCT
ejpam-5704	283	1	5	5	X
ejpam-5704	283	2	.	.	X
ejpam-5704	283	3	numerical	numerical	ADJ
ejpam-5704	283	4	results	result	NOUN
ejpam-5704	283	5	in	in	ADP
ejpam-5704	283	6	this	this	DET
ejpam-5704	283	7	section	section	NOUN
ejpam-5704	283	8	,	,	PUNCT
ejpam-5704	283	9	we	we	PRON
ejpam-5704	283	10	present	present	VERB
ejpam-5704	283	11	the	the	DET
ejpam-5704	283	12	numerical	numerical	ADJ
ejpam-5704	283	13	outcomes	outcome	NOUN
ejpam-5704	283	14	of	of	ADP
ejpam-5704	283	15	various	various	ADJ
ejpam-5704	283	16	test	test	NOUN
ejpam-5704	283	17	problems	problem	NOUN
ejpam-5704	283	18	solved	solve	VERB
ejpam-5704	283	19	using	use	VERB
ejpam-5704	283	20	the	the	DET
ejpam-5704	283	21	method	method	NOUN
ejpam-5704	283	22	proposed	propose	VERB
ejpam-5704	283	23	in	in	ADP
ejpam-5704	283	24	this	this	DET
ejpam-5704	283	25	article	article	NOUN
ejpam-5704	283	26	.	.	PUNCT
ejpam-5704	284	1	different	different	ADJ
ejpam-5704	284	2	forms	form	NOUN
ejpam-5704	284	3	of	of	ADP
ejpam-5704	284	4	kernels	kernel	NOUN
ejpam-5704	284	5	are	be	AUX
ejpam-5704	284	6	taken	take	VERB
ejpam-5704	284	7	into	into	ADP
ejpam-5704	284	8	account	account	NOUN
ejpam-5704	284	9	for	for	ADP
ejpam-5704	284	10	computational	computational	ADJ
ejpam-5704	284	11	purposes	purpose	NOUN
ejpam-5704	284	12	in	in	ADP
ejpam-5704	284	13	the	the	DET
ejpam-5704	284	14	following	follow	VERB
ejpam-5704	284	15	test	test	NOUN
ejpam-5704	284	16	problems	problem	NOUN
ejpam-5704	284	17	.	.	PUNCT
ejpam-5704	285	1	the	the	DET
ejpam-5704	285	2	discretization	discretization	NOUN
ejpam-5704	285	3	algorithm	algorithm	NOUN
ejpam-5704	285	4	relies	rely	VERB
ejpam-5704	285	5	on	on	ADP
ejpam-5704	285	6	nodes	node	NOUN
ejpam-5704	285	7	that	that	PRON
ejpam-5704	285	8	coincide	coincide	VERB
ejpam-5704	285	9	with	with	ADP
ejpam-5704	285	10	the	the	DET
ejpam-5704	285	11	zeros	zero	NOUN
ejpam-5704	285	12	of	of	ADP
ejpam-5704	285	13	the	the	DET
ejpam-5704	285	14	specified	specified	ADJ
ejpam-5704	285	15	orthogonal	orthogonal	ADJ
ejpam-5704	285	16	polynomials	polynomial	NOUN
ejpam-5704	285	17	of	of	ADP
ejpam-5704	285	18	the	the	DET
ejpam-5704	285	19	(	(	PUNCT
ejpam-5704	285	20	n)-th	n)-th	NOUN
ejpam-5704	285	21	degree	degree	NOUN
ejpam-5704	285	22	,	,	PUNCT
ejpam-5704	285	23	along	along	ADP
ejpam-5704	285	24	with	with	ADP
ejpam-5704	285	25	t	t	NOUN
ejpam-5704	285	26	=	=	SYM
ejpam-5704	285	27	0	0	X
ejpam-5704	285	28	.	.	PUNCT
ejpam-5704	286	1	additionally	additionally	ADV
ejpam-5704	286	2	,	,	PUNCT
ejpam-5704	286	3	a	a	DET
ejpam-5704	286	4	product	product	NOUN
ejpam-5704	286	5	integration	integration	NOUN
ejpam-5704	286	6	method	method	NOUN
ejpam-5704	286	7	described	describe	VERB
ejpam-5704	286	8	in	in	ADP
ejpam-5704	286	9	section	section	NOUN
ejpam-5704	286	10	3	3	NUM
ejpam-5704	286	11	is	be	AUX
ejpam-5704	286	12	employed	employ	VERB
ejpam-5704	286	13	.	.	PUNCT
ejpam-5704	287	1	all	all	DET
ejpam-5704	287	2	calculations	calculation	NOUN
ejpam-5704	287	3	were	be	AUX
ejpam-5704	287	4	conducted	conduct	VERB
ejpam-5704	287	5	using	use	VERB
ejpam-5704	287	6	mathematica	mathematica	PROPN
ejpam-5704	287	7	software	software	PROPN
ejpam-5704	287	8	.	.	PUNCT
ejpam-5704	288	1	example	example	NOUN
ejpam-5704	288	2	5.1	5.1	NUM
ejpam-5704	288	3	.	.	PUNCT
ejpam-5704	289	1	the	the	DET
ejpam-5704	289	2	non	non	ADJ
ejpam-5704	289	3	-	-	ADJ
ejpam-5704	289	4	linear	linear	ADJ
ejpam-5704	289	5	,	,	PUNCT
ejpam-5704	289	6	weakly	weakly	ADJ
ejpam-5704	289	7	singular	singular	PROPN
ejpam-5704	289	8	volterra	volterra	PROPN
ejpam-5704	289	9	functional	functional	ADJ
ejpam-5704	289	10	integral	integral	ADJ
ejpam-5704	289	11	equation	equation	NOUN
ejpam-5704	289	12	y(t	y(t	NUM
ejpam-5704	289	13	)	)	PUNCT
ejpam-5704	290	1	=	=	SYM
ejpam-5704	290	2	f(t	f(t	NOUN
ejpam-5704	290	3	)	)	PUNCT
ejpam-5704	291	1	+	+	CCONJ
ejpam-5704	292	1	∫	∫	PROPN
ejpam-5704	292	2	t	t	NOUN
ejpam-5704	292	3	0	0	NUM
ejpam-5704	292	4	ln	ln	ADJ
ejpam-5704	292	5	|t−	|t−	PROPN
ejpam-5704	292	6	w|	w|	NOUN
ejpam-5704	292	7	(	(	PUNCT
ejpam-5704	292	8	tw2	tw2	PROPN
ejpam-5704	292	9	−	−	PROPN
ejpam-5704	292	10	y2(w))dw	y2(w))dw	NOUN
ejpam-5704	293	1	+	+	CCONJ
ejpam-5704	293	2	∫	∫	PROPN
ejpam-5704	293	3	t	t	PROPN
ejpam-5704	293	4	10	10	NUM
ejpam-5704	293	5	0	0	NUM
ejpam-5704	293	6	|t−	|t−	PROPN
ejpam-5704	293	7	w|−	w|−	NOUN
ejpam-5704	293	8	1	1	NUM
ejpam-5704	293	9	2	2	NUM
ejpam-5704	293	10	y2(w)dw	y2(w)dw	NOUN
ejpam-5704	293	11	,	,	PUNCT
ejpam-5704	293	12	t	t	PROPN
ejpam-5704	293	13	∈	∈	PROPN
ejpam-5704	294	1	[	[	X
ejpam-5704	294	2	0	0	NUM
ejpam-5704	294	3	,	,	PUNCT
ejpam-5704	294	4	1	1	NUM
ejpam-5704	294	5	]	]	PUNCT
ejpam-5704	294	6	with	with	ADP
ejpam-5704	294	7	f(t	f(t	NOUN
ejpam-5704	294	8	)	)	PUNCT
ejpam-5704	294	9	such	such	ADJ
ejpam-5704	294	10	that	that	PRON
ejpam-5704	294	11	possesses	possess	VERB
ejpam-5704	294	12	the	the	DET
ejpam-5704	294	13	exact	exact	ADJ
ejpam-5704	294	14	solution	solution	NOUN
ejpam-5704	294	15	y(t	y(t	NUM
ejpam-5704	294	16	)	)	PUNCT
ejpam-5704	294	17	=	=	PUNCT
ejpam-5704	294	18	t	t	PROPN
ejpam-5704	294	19	13	13	NUM
ejpam-5704	294	20	2	2	NUM
ejpam-5704	294	21	.	.	PUNCT
ejpam-5704	294	22	example	example	NOUN
ejpam-5704	295	1	5.2	5.2	NUM
ejpam-5704	295	2	.	.	PUNCT
ejpam-5704	296	1	the	the	DET
ejpam-5704	296	2	nonlinear	nonlinear	ADJ
ejpam-5704	296	3	weakly	weakly	ADJ
ejpam-5704	296	4	singular	singular	PROPN
ejpam-5704	296	5	volterra	volterra	PROPN
ejpam-5704	296	6	functional	functional	ADJ
ejpam-5704	296	7	integral	integral	ADJ
ejpam-5704	296	8	equation	equation	NOUN
ejpam-5704	296	9	in	in	ADP
ejpam-5704	296	10	[	[	X
ejpam-5704	296	11	0	0	NUM
ejpam-5704	296	12	,	,	PUNCT
ejpam-5704	296	13	1	1	NUM
ejpam-5704	296	14	]	]	SYM
ejpam-5704	296	15	y	y	PROPN
ejpam-5704	296	16	(	(	PUNCT
ejpam-5704	296	17	t	t	PROPN
ejpam-5704	296	18	)	)	PUNCT
ejpam-5704	296	19	=	=	SYM
ejpam-5704	297	1	f	f	PROPN
ejpam-5704	297	2	(	(	PUNCT
ejpam-5704	297	3	t	t	PROPN
ejpam-5704	297	4	)	)	PUNCT
ejpam-5704	298	1	+	+	CCONJ
ejpam-5704	298	2	∫	∫	PROPN
ejpam-5704	298	3	t	t	PROPN
ejpam-5704	298	4	0	0	NUM
ejpam-5704	298	5	|t−	|t−	PROPN
ejpam-5704	298	6	w|−	w|−	NOUN
ejpam-5704	298	7	1	1	NUM
ejpam-5704	298	8	2	2	NUM
ejpam-5704	298	9	y2	y2	NOUN
ejpam-5704	298	10	(	(	PUNCT
ejpam-5704	298	11	w	w	NOUN
ejpam-5704	298	12	)	)	PUNCT
ejpam-5704	298	13	dw	dw	NOUN
ejpam-5704	299	1	+	+	CCONJ
ejpam-5704	299	2	∫	∫	PROPN
ejpam-5704	299	3	t−	t−	PROPN
ejpam-5704	299	4	1	1	NUM
ejpam-5704	299	5	10	10	NUM
ejpam-5704	299	6	0	0	NUM
ejpam-5704	299	7	|t−	|t−	PROPN
ejpam-5704	299	8	w|−	w|−	NOUN
ejpam-5704	299	9	1	1	NUM
ejpam-5704	299	10	2	2	NUM
ejpam-5704	299	11	y2	y2	NOUN
ejpam-5704	299	12	(	(	PUNCT
ejpam-5704	299	13	w	w	NOUN
ejpam-5704	299	14	)	)	PUNCT
ejpam-5704	299	15	dw	dw	PROPN
ejpam-5704	299	16	,	,	PUNCT
ejpam-5704	299	17	with	with	ADP
ejpam-5704	299	18	f(t	f(t	NOUN
ejpam-5704	299	19	)	)	PUNCT
ejpam-5704	299	20	such	such	ADJ
ejpam-5704	299	21	that	that	PRON
ejpam-5704	299	22	possesses	possess	VERB
ejpam-5704	299	23	the	the	DET
ejpam-5704	299	24	analytical	analytical	ADJ
ejpam-5704	299	25	solution	solution	NOUN
ejpam-5704	299	26	y(t	y(t	NUM
ejpam-5704	299	27	)	)	PUNCT
ejpam-5704	300	1	=	=	SYM
ejpam-5704	300	2	e2	e2	PROPN
ejpam-5704	300	3	t.	t.	PROPN
ejpam-5704	300	4	we	we	PRON
ejpam-5704	300	5	consider	consider	VERB
ejpam-5704	300	6	the	the	DET
ejpam-5704	300	7	other	other	ADJ
ejpam-5704	300	8	example	example	NOUN
ejpam-5704	300	9	which	which	PRON
ejpam-5704	300	10	the	the	DET
ejpam-5704	300	11	exact	exact	ADJ
ejpam-5704	300	12	solution	solution	NOUN
ejpam-5704	300	13	has	have	VERB
ejpam-5704	300	14	the	the	DET
ejpam-5704	300	15	low	low	ADJ
ejpam-5704	300	16	regularity	regularity	NOUN
ejpam-5704	300	17	.	.	PUNCT
ejpam-5704	301	1	the	the	DET
ejpam-5704	301	2	exact	exact	ADJ
ejpam-5704	301	3	solution	solution	NOUN
ejpam-5704	301	4	is	be	AUX
ejpam-5704	301	5	y(t	y(t	PROPN
ejpam-5704	301	6	)	)	PUNCT
ejpam-5704	302	1	=	=	SYM
ejpam-5704	302	2	√	√	NUM
ejpam-5704	302	3	t	t	PROPN
ejpam-5704	302	4	,	,	PUNCT
ejpam-5704	302	5	then	then	ADV
ejpam-5704	302	6	derivative	derivative	ADJ
ejpam-5704	302	7	of	of	ADP
ejpam-5704	302	8	this	this	DET
ejpam-5704	302	9	solution	solution	NOUN
ejpam-5704	302	10	is	be	AUX
ejpam-5704	302	11	unbounded	unbounded	ADJ
ejpam-5704	302	12	at	at	ADP
ejpam-5704	302	13	t	t	NOUN
ejpam-5704	302	14	=	=	SYM
ejpam-5704	302	15	0	0	PUNCT
ejpam-5704	302	16	and	and	CCONJ
ejpam-5704	302	17	reflects	reflect	VERB
ejpam-5704	302	18	the	the	DET
ejpam-5704	302	19	general	general	ADJ
ejpam-5704	302	20	qualitative	qualitative	ADJ
ejpam-5704	302	21	regularity	regularity	NOUN
ejpam-5704	302	22	behaviour	behaviour	NOUN
ejpam-5704	302	23	of	of	ADP
ejpam-5704	302	24	the	the	DET
ejpam-5704	302	25	solution	solution	NOUN
ejpam-5704	302	26	near	near	ADP
ejpam-5704	302	27	t	t	PROPN
ejpam-5704	302	28	=	=	PUNCT
ejpam-5704	302	29	0	0	NUM
ejpam-5704	302	30	+	+	PROPN
ejpam-5704	302	31	.	.	PUNCT
ejpam-5704	302	32	b.	b.	PROPN
ejpam-5704	302	33	h.	h.	PROPN
ejpam-5704	302	34	alrikabi	alrikabi	PROPN
ejpam-5704	302	35	,	,	PUNCT
ejpam-5704	302	36	p.	p.	PROPN
ejpam-5704	302	37	darania	darania	PROPN
ejpam-5704	302	38	,	,	PUNCT
ejpam-5704	302	39	s.pishbin	s.pishbin	PROPN
ejpam-5704	302	40	/	/	SYM
ejpam-5704	302	41	eur	eur	PROPN
ejpam-5704	302	42	.	.	PUNCT
ejpam-5704	303	1	j.	j.	PROPN
ejpam-5704	303	2	pure	pure	PROPN
ejpam-5704	303	3	appl	appl	PROPN
ejpam-5704	303	4	.	.	PROPN
ejpam-5704	303	5	math	math	PROPN
ejpam-5704	303	6	,	,	PUNCT
ejpam-5704	303	7	18	18	NUM
ejpam-5704	303	8	(	(	PUNCT
ejpam-5704	303	9	2	2	NUM
ejpam-5704	303	10	)	)	PUNCT
ejpam-5704	303	11	(	(	PUNCT
ejpam-5704	303	12	2025	2025	NUM
ejpam-5704	303	13	)	)	PUNCT
ejpam-5704	303	14	,	,	PUNCT
ejpam-5704	303	15	5704	5704	NUM
ejpam-5704	303	16	15	15	NUM
ejpam-5704	303	17	of	of	ADP
ejpam-5704	303	18	19	19	NUM
ejpam-5704	303	19	n	n	NOUN
ejpam-5704	303	20	chelyshkov	chelyshkov	NOUN
ejpam-5704	303	21	polynomials	polynomial	NOUN
ejpam-5704	303	22	legendre	legendre	PROPN
ejpam-5704	303	23	polynomials	polynomials	PROPN
ejpam-5704	303	24	chebyshev	chebyshev	NOUN
ejpam-5704	303	25	polynomials	polynomial	NOUN
ejpam-5704	304	1	4	4	NUM
ejpam-5704	304	2	2.81×	2.81×	NUM
ejpam-5704	304	3	10−2	10−2	NUM
ejpam-5704	304	4	3.87×	3.87×	NUM
ejpam-5704	304	5	10−2	10−2	NUM
ejpam-5704	304	6	7.31×	7.31×	NUM
ejpam-5704	304	7	10−2	10−2	NUM
ejpam-5704	304	8	5	5	NUM
ejpam-5704	304	9	9.50×	9.50×	NUM
ejpam-5704	304	10	10−3	10−3	NUM
ejpam-5704	304	11	1.48×	1.48×	NUM
ejpam-5704	304	12	10−2	10−2	NUM
ejpam-5704	304	13	1.77×	1.77×	NUM
ejpam-5704	304	14	10−2	10−2	NUM
ejpam-5704	304	15	6	6	NUM
ejpam-5704	304	16	2.48×	2.48×	NUM
ejpam-5704	304	17	10−3	10−3	NUM
ejpam-5704	304	18	3.98×	3.98×	NUM
ejpam-5704	304	19	10−3	10−3	NUM
ejpam-5704	304	20	5.10×	5.10×	NUM
ejpam-5704	304	21	10−3	10−3	NUM
ejpam-5704	304	22	7	7	NUM
ejpam-5704	304	23	6.34×	6.34×	NUM
ejpam-5704	304	24	10−4	10−4	NUM
ejpam-5704	304	25	1.00×	1.00×	NUM
ejpam-5704	304	26	10−3	10−3	NUM
ejpam-5704	304	27	1.38×	1.38×	NUM
ejpam-5704	304	28	10−3	10−3	NUM
ejpam-5704	304	29	8	8	NUM
ejpam-5704	304	30	1.25×	1.25×	NUM
ejpam-5704	304	31	10−4	10−4	NUM
ejpam-5704	304	32	2.10×	2.10×	NUM
ejpam-5704	304	33	10−4	10−4	NUM
ejpam-5704	304	34	2.57×	2.57×	NUM
ejpam-5704	304	35	10−4	10−4	NUM
ejpam-5704	304	36	9	9	NUM
ejpam-5704	304	37	2.02×	2.02×	NUM
ejpam-5704	304	38	10−5	10−5	NUM
ejpam-5704	304	39	3.44×	3.44×	NUM
ejpam-5704	304	40	10−5	10−5	NUM
ejpam-5704	304	41	4.30×	4.30×	NUM
ejpam-5704	304	42	10−5	10−5	NUM
ejpam-5704	304	43	10	10	NUM
ejpam-5704	304	44	2.40×	2.40×	NUM
ejpam-5704	304	45	10−6	10−6	NUM
ejpam-5704	304	46	3.90×	3.90×	NUM
ejpam-5704	304	47	10−6	10−6	NUM
ejpam-5704	304	48	5.06×	5.06×	NUM
ejpam-5704	304	49	10−6	10−6	NUM
ejpam-5704	304	50	table	table	NOUN
ejpam-5704	304	51	1	1	NUM
ejpam-5704	304	52	:	:	PUNCT
ejpam-5704	304	53	maximum	maximum	ADJ
ejpam-5704	304	54	errors	error	NOUN
ejpam-5704	304	55	by	by	ADP
ejpam-5704	304	56	using	use	VERB
ejpam-5704	304	57	different	different	ADJ
ejpam-5704	304	58	types	type	NOUN
ejpam-5704	304	59	of	of	ADP
ejpam-5704	304	60	orthogonal	orthogonal	ADJ
ejpam-5704	304	61	polynomials	polynomial	NOUN
ejpam-5704	304	62	in	in	ADP
ejpam-5704	304	63	example	example	NOUN
ejpam-5704	304	64	5.1	5.1	NUM
ejpam-5704	304	65	.	.	PUNCT
ejpam-5704	305	1	n	n	PRON
ejpam-5704	305	2	chelyshkov	chelyshkov	NOUN
ejpam-5704	305	3	polynomials	polynomial	NOUN
ejpam-5704	305	4	legendre	legendre	PROPN
ejpam-5704	305	5	polynomials	polynomials	PROPN
ejpam-5704	305	6	chebyshev	chebyshev	NOUN
ejpam-5704	305	7	polynomials	polynomial	NOUN
ejpam-5704	305	8	4	4	NUM
ejpam-5704	305	9	1.70×	1.70×	NUM
ejpam-5704	305	10	10−2	10−2	NUM
ejpam-5704	305	11	1.72×	1.72×	NUM
ejpam-5704	305	12	10−2	10−2	NUM
ejpam-5704	305	13	2.13×	2.13×	NUM
ejpam-5704	305	14	10−2	10−2	NUM
ejpam-5704	305	15	5	5	NUM
ejpam-5704	305	16	4.28×	4.28×	NUM
ejpam-5704	305	17	10−3	10−3	NUM
ejpam-5704	305	18	4.42×	4.42×	NUM
ejpam-5704	305	19	10−3	10−3	NUM
ejpam-5704	305	20	5.20×	5.20×	NUM
ejpam-5704	305	21	10−3	10−3	NUM
ejpam-5704	305	22	6	6	NUM
ejpam-5704	305	23	8.35×	8.35×	NUM
ejpam-5704	305	24	10−4	10−4	NUM
ejpam-5704	305	25	8.90×	8.90×	NUM
ejpam-5704	305	26	10−4	10−4	NUM
ejpam-5704	305	27	9.93×	9.93×	NUM
ejpam-5704	305	28	10−4	10−4	NUM
ejpam-5704	305	29	7	7	NUM
ejpam-5704	305	30	1.30×	1.30×	NUM
ejpam-5704	305	31	10−4	10−4	NUM
ejpam-5704	305	32	1.45×	1.45×	NUM
ejpam-5704	305	33	10−4	10−4	PROPN
ejpam-5704	305	34	1.53×	1.53×	NUM
ejpam-5704	305	35	10−4	10−4	NUM
ejpam-5704	305	36	8	8	NUM
ejpam-5704	305	37	1.61×	1.61×	NUM
ejpam-5704	305	38	10−5	10−5	NUM
ejpam-5704	305	39	1.97×	1.97×	NUM
ejpam-5704	305	40	10−5	10−5	NUM
ejpam-5704	305	41	1.98×	1.98×	NUM
ejpam-5704	305	42	10−5	10−5	NUM
ejpam-5704	305	43	9	9	NUM
ejpam-5704	305	44	1.47×	1.47×	NUM
ejpam-5704	305	45	10−6	10−6	NUM
ejpam-5704	305	46	2.31×	2.31×	NUM
ejpam-5704	305	47	10−6	10−6	NUM
ejpam-5704	305	48	2.51×	2.51×	NUM
ejpam-5704	305	49	10−6	10−6	NUM
ejpam-5704	305	50	10	10	NUM
ejpam-5704	305	51	1.64×	1.64×	NUM
ejpam-5704	305	52	10−7	10−7	NUM
ejpam-5704	305	53	2.31×	2.31×	NUM
ejpam-5704	305	54	10−7	10−7	NUM
ejpam-5704	305	55	6.71×	6.71×	NUM
ejpam-5704	305	56	10−7	10−7	NUM
ejpam-5704	305	57	table	table	NOUN
ejpam-5704	305	58	2	2	NUM
ejpam-5704	305	59	:	:	PUNCT
ejpam-5704	305	60	maximum	maximum	ADJ
ejpam-5704	305	61	errors	error	NOUN
ejpam-5704	305	62	by	by	ADP
ejpam-5704	305	63	using	use	VERB
ejpam-5704	305	64	different	different	ADJ
ejpam-5704	305	65	types	type	NOUN
ejpam-5704	305	66	of	of	ADP
ejpam-5704	305	67	orthogonal	orthogonal	ADJ
ejpam-5704	305	68	polynomials	polynomial	NOUN
ejpam-5704	305	69	in	in	ADP
ejpam-5704	305	70	example	example	NOUN
ejpam-5704	305	71	5.2	5.2	NUM
ejpam-5704	305	72	.	.	PUNCT
ejpam-5704	305	73	example	example	NOUN
ejpam-5704	305	74	5.3	5.3	NUM
ejpam-5704	305	75	.	.	PUNCT
ejpam-5704	306	1	the	the	DET
ejpam-5704	306	2	non	non	ADJ
ejpam-5704	306	3	-	-	ADJ
ejpam-5704	306	4	linear	linear	ADJ
ejpam-5704	306	5	,	,	PUNCT
ejpam-5704	306	6	weakly	weakly	ADJ
ejpam-5704	306	7	singular	singular	PROPN
ejpam-5704	306	8	volterra	volterra	PROPN
ejpam-5704	306	9	functional	functional	ADJ
ejpam-5704	306	10	integral	integral	ADJ
ejpam-5704	306	11	equation	equation	NOUN
ejpam-5704	306	12	y(t	y(t	NUM
ejpam-5704	306	13	)	)	PUNCT
ejpam-5704	307	1	=	=	SYM
ejpam-5704	308	1	f(t)−	f(t)−	PROPN
ejpam-5704	308	2	∫	∫	PROPN
ejpam-5704	308	3	t	t	PROPN
ejpam-5704	308	4	0	0	NUM
ejpam-5704	308	5	|t−	|t−	PROPN
ejpam-5704	308	6	w|−	w|−	NOUN
ejpam-5704	308	7	1	1	NUM
ejpam-5704	308	8	2	2	NUM
ejpam-5704	308	9	y3(w)dw	y3(w)dw	NOUN
ejpam-5704	308	10	+	+	CCONJ
ejpam-5704	308	11	∫	∫	PROPN
ejpam-5704	308	12	0.9	0.9	NUM
ejpam-5704	308	13	t	t	NOUN
ejpam-5704	308	14	0	0	NUM
ejpam-5704	308	15	|t−	|t−	PROPN
ejpam-5704	308	16	w|−	w|−	NOUN
ejpam-5704	308	17	1	1	NUM
ejpam-5704	308	18	2	2	NUM
ejpam-5704	308	19	y2(w)dw	y2(w)dw	NOUN
ejpam-5704	308	20	,	,	PUNCT
ejpam-5704	308	21	t	t	PROPN
ejpam-5704	308	22	∈	∈	PROPN
ejpam-5704	309	1	[	[	X
ejpam-5704	309	2	0	0	NUM
ejpam-5704	309	3	,	,	PUNCT
ejpam-5704	309	4	1	1	NUM
ejpam-5704	309	5	]	]	PUNCT
ejpam-5704	309	6	with	with	ADP
ejpam-5704	309	7	f(t	f(t	NOUN
ejpam-5704	309	8	)	)	PUNCT
ejpam-5704	309	9	such	such	ADJ
ejpam-5704	309	10	that	that	PRON
ejpam-5704	309	11	possesses	possess	VERB
ejpam-5704	309	12	the	the	DET
ejpam-5704	309	13	exact	exact	ADJ
ejpam-5704	309	14	solution	solution	NOUN
ejpam-5704	309	15	y(t	y(t	NUM
ejpam-5704	309	16	)	)	PUNCT
ejpam-5704	309	17	=	=	SYM
ejpam-5704	309	18	t	t	PROPN
ejpam-5704	309	19	1	1	NUM
ejpam-5704	309	20	2	2	NUM
ejpam-5704	309	21	.	.	PUNCT
ejpam-5704	310	1	we	we	PRON
ejpam-5704	310	2	give	give	VERB
ejpam-5704	310	3	the	the	DET
ejpam-5704	310	4	numerical	numerical	ADJ
ejpam-5704	310	5	solution	solution	NOUN
ejpam-5704	310	6	of	of	ADP
ejpam-5704	310	7	the	the	DET
ejpam-5704	310	8	examples	example	NOUN
ejpam-5704	310	9	,	,	PUNCT
ejpam-5704	310	10	at	at	ADP
ejpam-5704	310	11	the	the	DET
ejpam-5704	310	12	root	root	NOUN
ejpam-5704	310	13	of	of	ADP
ejpam-5704	310	14	n	n	PRON
ejpam-5704	310	15	-st	-st	ADJ
ejpam-5704	310	16	-	-	PUNCT
ejpam-5704	310	17	degree	degree	NOUN
ejpam-5704	310	18	orthogonal	orthogonal	ADJ
ejpam-5704	310	19	polynomials	polynomial	NOUN
ejpam-5704	310	20	.	.	PUNCT
ejpam-5704	311	1	the	the	DET
ejpam-5704	311	2	maximum	maximum	ADJ
ejpam-5704	311	3	errors	error	NOUN
ejpam-5704	311	4	obtained	obtain	VERB
ejpam-5704	311	5	using	use	VERB
ejpam-5704	311	6	the	the	DET
ejpam-5704	311	7	presented	present	VERB
ejpam-5704	311	8	method	method	NOUN
ejpam-5704	311	9	are	be	AUX
ejpam-5704	311	10	compared	compare	VERB
ejpam-5704	311	11	with	with	ADP
ejpam-5704	311	12	the	the	DET
ejpam-5704	311	13	exact	exact	ADJ
ejpam-5704	311	14	solution	solution	NOUN
ejpam-5704	311	15	in	in	ADP
ejpam-5704	311	16	tables	table	NOUN
ejpam-5704	311	17	1	1	NUM
ejpam-5704	311	18	,	,	PUNCT
ejpam-5704	311	19	2	2	NUM
ejpam-5704	311	20	and	and	CCONJ
ejpam-5704	311	21	3	3	NUM
ejpam-5704	311	22	.	.	PUNCT
ejpam-5704	312	1	in	in	ADP
ejpam-5704	312	2	the	the	DET
ejpam-5704	312	3	case	case	NOUN
ejpam-5704	312	4	of	of	ADP
ejpam-5704	312	5	examples	example	NOUN
ejpam-5704	312	6	,	,	PUNCT
ejpam-5704	312	7	the	the	DET
ejpam-5704	312	8	obtained	obtain	VERB
ejpam-5704	312	9	nonlinear	nonlinear	ADJ
ejpam-5704	312	10	systems	system	NOUN
ejpam-5704	312	11	are	be	AUX
ejpam-5704	312	12	solved	solve	VERB
ejpam-5704	312	13	using	use	VERB
ejpam-5704	312	14	newton	newton	PROPN
ejpam-5704	312	15	’s	’s	PART
ejpam-5704	312	16	method	method	NOUN
ejpam-5704	312	17	.	.	PUNCT
ejpam-5704	313	1	n	n	PRON
ejpam-5704	313	2	chelyshkov	chelyshkov	NOUN
ejpam-5704	313	3	polynomials	polynomial	NOUN
ejpam-5704	313	4	legendre	legendre	PROPN
ejpam-5704	313	5	polynomials	polynomials	PROPN
ejpam-5704	313	6	chebyshev	chebyshev	NOUN
ejpam-5704	313	7	polynomials	polynomial	NOUN
ejpam-5704	313	8	4	4	NUM
ejpam-5704	313	9	6.16×	6.16×	NUM
ejpam-5704	313	10	10−4	10−4	NUM
ejpam-5704	313	11	6.69×	6.69×	NUM
ejpam-5704	313	12	10−4	10−4	NUM
ejpam-5704	313	13	1.16×	1.16×	PROPN
ejpam-5704	313	14	10−3	10−3	NUM
ejpam-5704	313	15	5	5	NUM
ejpam-5704	313	16	2.91×	2.91×	NUM
ejpam-5704	313	17	10−4	10−4	NUM
ejpam-5704	313	18	3.44×	3.44×	NUM
ejpam-5704	313	19	10−4	10−4	NUM
ejpam-5704	313	20	5.50×	5.50×	NUM
ejpam-5704	313	21	10−4	10−4	NUM
ejpam-5704	313	22	6	6	NUM
ejpam-5704	313	23	1.54×	1.54×	NUM
ejpam-5704	313	24	10−4	10−4	NUM
ejpam-5704	313	25	2.23×	2.23×	NUM
ejpam-5704	313	26	10−4	10−4	NUM
ejpam-5704	313	27	3.19×	3.19×	PROPN
ejpam-5704	313	28	10−4	10−4	NUM
ejpam-5704	313	29	7	7	NUM
ejpam-5704	313	30	8.87×	8.87×	NUM
ejpam-5704	313	31	10−5	10−5	NUM
ejpam-5704	313	32	1.44×	1.44×	NUM
ejpam-5704	313	33	10−4	10−4	NUM
ejpam-5704	313	34	2.06×	2.06×	NUM
ejpam-5704	313	35	10−4	10−4	NUM
ejpam-5704	313	36	8	8	NUM
ejpam-5704	313	37	5.45×	5.45×	NUM
ejpam-5704	313	38	10−5	10−5	NUM
ejpam-5704	313	39	1.00×	1.00×	NUM
ejpam-5704	313	40	10−4	10−4	PROPN
ejpam-5704	313	41	1.40×	1.40×	NUM
ejpam-5704	313	42	10−4	10−4	NUM
ejpam-5704	313	43	9	9	NUM
ejpam-5704	313	44	3.53×	3.53×	NUM
ejpam-5704	313	45	10−5	10−5	NUM
ejpam-5704	313	46	6.93×	6.93×	NUM
ejpam-5704	313	47	10−5	10−5	NUM
ejpam-5704	313	48	9.53×	9.53×	NUM
ejpam-5704	313	49	10−5	10−5	NUM
ejpam-5704	313	50	10	10	NUM
ejpam-5704	313	51	2.38×	2.38×	NUM
ejpam-5704	313	52	10−5	10−5	NUM
ejpam-5704	313	53	4.91×	4.91×	NUM
ejpam-5704	313	54	10−5	10−5	NUM
ejpam-5704	313	55	4.67×	4.67×	NUM
ejpam-5704	313	56	10−5	10−5	NUM
ejpam-5704	313	57	table	table	NOUN
ejpam-5704	313	58	3	3	NUM
ejpam-5704	313	59	:	:	PUNCT
ejpam-5704	313	60	maximum	maximum	ADJ
ejpam-5704	313	61	errors	error	NOUN
ejpam-5704	313	62	by	by	ADP
ejpam-5704	313	63	using	use	VERB
ejpam-5704	313	64	different	different	ADJ
ejpam-5704	313	65	types	type	NOUN
ejpam-5704	313	66	of	of	ADP
ejpam-5704	313	67	orthogonal	orthogonal	ADJ
ejpam-5704	313	68	polynomials	polynomial	NOUN
ejpam-5704	313	69	in	in	ADP
ejpam-5704	313	70	example	example	NOUN
ejpam-5704	313	71	5.3	5.3	NUM
ejpam-5704	313	72	.	.	PUNCT
ejpam-5704	314	1	b.	b.	PROPN
ejpam-5704	314	2	h.	h.	PROPN
ejpam-5704	314	3	alrikabi	alrikabi	PROPN
ejpam-5704	314	4	,	,	PUNCT
ejpam-5704	314	5	p.	p.	PROPN
ejpam-5704	314	6	darania	darania	PROPN
ejpam-5704	314	7	,	,	PUNCT
ejpam-5704	314	8	s.pishbin	s.pishbin	PROPN
ejpam-5704	314	9	/	/	SYM
ejpam-5704	314	10	eur	eur	PROPN
ejpam-5704	314	11	.	.	PUNCT
ejpam-5704	315	1	j.	j.	PROPN
ejpam-5704	315	2	pure	pure	PROPN
ejpam-5704	315	3	appl	appl	PROPN
ejpam-5704	315	4	.	.	PROPN
ejpam-5704	315	5	math	math	PROPN
ejpam-5704	315	6	,	,	PUNCT
ejpam-5704	315	7	18	18	NUM
ejpam-5704	315	8	(	(	PUNCT
ejpam-5704	315	9	2	2	NUM
ejpam-5704	315	10	)	)	PUNCT
ejpam-5704	315	11	(	(	PUNCT
ejpam-5704	315	12	2025	2025	NUM
ejpam-5704	315	13	)	)	PUNCT
ejpam-5704	315	14	,	,	PUNCT
ejpam-5704	315	15	5704	5704	NUM
ejpam-5704	315	16	16	16	NUM
ejpam-5704	315	17	of	of	ADP
ejpam-5704	315	18	19	19	NUM
ejpam-5704	315	19	n	n	NUM
ejpam-5704	315	20	example	example	NOUN
ejpam-5704	315	21	5.1	5.1	NUM
ejpam-5704	315	22	example	example	NOUN
ejpam-5704	315	23	5.2	5.2	NUM
ejpam-5704	315	24	example	example	NOUN
ejpam-5704	315	25	5.3	5.3	NUM
ejpam-5704	315	26	4	4	NUM
ejpam-5704	315	27	6.03×	6.03×	NUM
ejpam-5704	315	28	10−4	10−4	NUM
ejpam-5704	315	29	8.60×	8.60×	NUM
ejpam-5704	315	30	10−4	10−4	NUM
ejpam-5704	315	31	2.72×	2.72×	NUM
ejpam-5704	315	32	10−5	10−5	NUM
ejpam-5704	315	33	6	6	NUM
ejpam-5704	315	34	3.60×	3.60×	NUM
ejpam-5704	315	35	10−4	10−4	NUM
ejpam-5704	315	36	9.54×	9.54×	NUM
ejpam-5704	315	37	10−6	10−6	NUM
ejpam-5704	315	38	4.07×	4.07×	NUM
ejpam-5704	315	39	10−6	10−6	NUM
ejpam-5704	315	40	8	8	NUM
ejpam-5704	315	41	4.79×	4.79×	NUM
ejpam-5704	315	42	10−6	10−6	NUM
ejpam-5704	315	43	3.41×	3.41×	NUM
ejpam-5704	315	44	10−7	10−7	NUM
ejpam-5704	315	45	8.67×	8.67×	NUM
ejpam-5704	315	46	10−7	10−7	NUM
ejpam-5704	315	47	10	10	NUM
ejpam-5704	315	48	9.95×	9.95×	NUM
ejpam-5704	315	49	10−8	10−8	NUM
ejpam-5704	315	50	1.81×	1.81×	NUM
ejpam-5704	315	51	10−7	10−7	NUM
ejpam-5704	315	52	2.86×	2.86×	NUM
ejpam-5704	315	53	10−7	10−7	NUM
ejpam-5704	315	54	table	table	NOUN
ejpam-5704	315	55	4	4	NUM
ejpam-5704	315	56	:	:	PUNCT
ejpam-5704	315	57	absolute	absolute	ADJ
ejpam-5704	315	58	errors	error	NOUN
ejpam-5704	315	59	at	at	ADP
ejpam-5704	315	60	the	the	DET
ejpam-5704	315	61	point	point	NOUN
ejpam-5704	315	62	tn+1	tn+1	NOUN
ejpam-5704	315	63	=	=	SYM
ejpam-5704	315	64	1	1	NUM
ejpam-5704	315	65	for	for	ADP
ejpam-5704	315	66	different	different	ADJ
ejpam-5704	315	67	values	value	NOUN
ejpam-5704	315	68	of	of	ADP
ejpam-5704	315	69	n	n	PROPN
ejpam-5704	315	70	.	.	PUNCT
ejpam-5704	316	1	in	in	ADP
ejpam-5704	316	2	tables	table	NOUN
ejpam-5704	316	3	1	1	NUM
ejpam-5704	316	4	,	,	PUNCT
ejpam-5704	316	5	2	2	NUM
ejpam-5704	316	6	and	and	CCONJ
ejpam-5704	316	7	3	3	NUM
ejpam-5704	316	8	,	,	PUNCT
ejpam-5704	316	9	we	we	PRON
ejpam-5704	316	10	report	report	VERB
ejpam-5704	316	11	maximum	maximum	ADJ
ejpam-5704	316	12	errors	error	NOUN
ejpam-5704	316	13	in	in	ADP
ejpam-5704	316	14	examples	example	NOUN
ejpam-5704	316	15	5.1	5.1	NUM
ejpam-5704	316	16	,	,	PUNCT
ejpam-5704	316	17	5.2	5.2	NUM
ejpam-5704	316	18	and	and	CCONJ
ejpam-5704	316	19	5.3	5.3	NUM
ejpam-5704	316	20	.	.	PUNCT
ejpam-5704	317	1	we	we	PRON
ejpam-5704	317	2	consider	consider	VERB
ejpam-5704	317	3	chelyshkov	chelyshkov	NOUN
ejpam-5704	317	4	,	,	PUNCT
ejpam-5704	317	5	legendre	legendre	PROPN
ejpam-5704	317	6	and	and	CCONJ
ejpam-5704	317	7	chebyshev	chebyshev	PROPN
ejpam-5704	317	8	polynomials	polynomial	NOUN
ejpam-5704	317	9	as	as	ADP
ejpam-5704	317	10	orthogonal	orthogonal	ADJ
ejpam-5704	317	11	polynomials	polynomial	NOUN
ejpam-5704	317	12	and	and	CCONJ
ejpam-5704	317	13	observe	observe	VERB
ejpam-5704	317	14	that	that	SCONJ
ejpam-5704	317	15	our	our	PRON
ejpam-5704	317	16	proposed	propose	VERB
ejpam-5704	317	17	numerical	numerical	PROPN
ejpam-5704	317	18	method	method	PROPN
ejpam-5704	317	19	works	work	VERB
ejpam-5704	317	20	well	well	ADV
ejpam-5704	317	21	for	for	ADP
ejpam-5704	317	22	theses	these	VERB
ejpam-5704	317	23	different	different	ADJ
ejpam-5704	317	24	types	type	NOUN
ejpam-5704	317	25	of	of	ADP
ejpam-5704	317	26	orthogonal	orthogonal	ADJ
ejpam-5704	317	27	polynomials	polynomial	NOUN
ejpam-5704	317	28	.	.	PUNCT
ejpam-5704	318	1	also	also	ADV
ejpam-5704	318	2	,	,	PUNCT
ejpam-5704	318	3	according	accord	VERB
ejpam-5704	318	4	to	to	ADP
ejpam-5704	318	5	the	the	DET
ejpam-5704	318	6	dispersion	dispersion	NOUN
ejpam-5704	318	7	of	of	ADP
ejpam-5704	318	8	the	the	DET
ejpam-5704	318	9	roots	root	NOUN
ejpam-5704	318	10	of	of	ADP
ejpam-5704	318	11	these	these	DET
ejpam-5704	318	12	polynomials	polynomial	NOUN
ejpam-5704	318	13	,	,	PUNCT
ejpam-5704	318	14	it	it	PRON
ejpam-5704	318	15	seems	seem	VERB
ejpam-5704	318	16	that	that	SCONJ
ejpam-5704	318	17	the	the	DET
ejpam-5704	318	18	errors	error	NOUN
ejpam-5704	318	19	reported	report	VERB
ejpam-5704	318	20	by	by	ADP
ejpam-5704	318	21	chelyshkov	chelyshkov	NOUN
ejpam-5704	318	22	polynomials	polynomial	NOUN
ejpam-5704	318	23	is	be	AUX
ejpam-5704	318	24	slightly	slightly	ADV
ejpam-5704	318	25	better	well	ADJ
ejpam-5704	318	26	than	than	ADP
ejpam-5704	318	27	the	the	DET
ejpam-5704	318	28	other	other	ADJ
ejpam-5704	318	29	polynomials	polynomial	NOUN
ejpam-5704	318	30	.	.	PUNCT
ejpam-5704	319	1	remark	remark	PROPN
ejpam-5704	319	2	5.4	5.4	NUM
ejpam-5704	319	3	.	.	PUNCT
ejpam-5704	320	1	to	to	PART
ejpam-5704	320	2	get	get	VERB
ejpam-5704	320	3	the	the	DET
ejpam-5704	320	4	approximate	approximate	ADJ
ejpam-5704	320	5	solution	solution	NOUN
ejpam-5704	320	6	at	at	ADP
ejpam-5704	320	7	any	any	DET
ejpam-5704	320	8	given	give	VERB
ejpam-5704	320	9	point	point	NOUN
ejpam-5704	320	10	η	η	PROPN
ejpam-5704	320	11	within	within	ADP
ejpam-5704	320	12	the	the	DET
ejpam-5704	320	13	interval	interval	NOUN
ejpam-5704	320	14	ih	ih	NOUN
ejpam-5704	320	15	⊆	⊆	NUM
ejpam-5704	320	16	[	[	X
ejpam-5704	320	17	0	0	NUM
ejpam-5704	320	18	,	,	PUNCT
ejpam-5704	320	19	1	1	NUM
ejpam-5704	320	20	]	]	PUNCT
ejpam-5704	320	21	,	,	PUNCT
ejpam-5704	320	22	our	our	PRON
ejpam-5704	320	23	focus	focus	NOUN
ejpam-5704	320	24	lies	lie	VERB
ejpam-5704	320	25	on	on	ADP
ejpam-5704	320	26	a	a	DET
ejpam-5704	320	27	rule	rule	NOUN
ejpam-5704	320	28	that	that	PRON
ejpam-5704	320	29	relies	rely	VERB
ejpam-5704	320	30	on	on	ADP
ejpam-5704	320	31	both	both	CCONJ
ejpam-5704	320	32	β	β	X
ejpam-5704	320	33	and	and	CCONJ
ejpam-5704	320	34	y(η)∫	y(η)∫	PROPN
ejpam-5704	321	1	1	1	NUM
ejpam-5704	321	2	0	0	NUM
ejpam-5704	321	3	y(w)dw	y(w)dw	PROPN
ejpam-5704	321	4	≈	≈	PROPN
ejpam-5704	321	5	n∑	n∑	PROPN
ejpam-5704	321	6	j=0	j=0	PROPN
ejpam-5704	321	7	βjy(tj	βjy(tj	PUNCT
ejpam-5704	321	8	)	)	PUNCT
ejpam-5704	321	9	+	+	NUM
ejpam-5704	321	10	βy(η	βy(η	NUM
ejpam-5704	321	11	)	)	PUNCT
ejpam-5704	321	12	.	.	PUNCT
ejpam-5704	322	1	from	from	ADP
ejpam-5704	322	2	[	[	X
ejpam-5704	322	3	34	34	NUM
ejpam-5704	322	4	]	]	PUNCT
ejpam-5704	322	5	and	and	CCONJ
ejpam-5704	322	6	[	[	X
ejpam-5704	322	7	35	35	NUM
ejpam-5704	322	8	]	]	PUNCT
ejpam-5704	322	9	,	,	PUNCT
ejpam-5704	322	10	we	we	PRON
ejpam-5704	322	11	know	know	VERB
ejpam-5704	322	12	that	that	SCONJ
ejpam-5704	322	13	this	this	DET
ejpam-5704	322	14	method	method	NOUN
ejpam-5704	322	15	is	be	AUX
ejpam-5704	322	16	exact	exact	ADJ
ejpam-5704	322	17	for	for	ADP
ejpam-5704	322	18	all	all	DET
ejpam-5704	322	19	polynomials	polynomial	NOUN
ejpam-5704	322	20	whose	whose	DET
ejpam-5704	322	21	degree	degree	NOUN
ejpam-5704	322	22	does	do	AUX
ejpam-5704	322	23	not	not	PART
ejpam-5704	322	24	exceed	exceed	VERB
ejpam-5704	322	25	2n	2n	NUM
ejpam-5704	322	26	.	.	PUNCT
ejpam-5704	323	1	nevertheless	nevertheless	ADV
ejpam-5704	323	2	,	,	PUNCT
ejpam-5704	323	3	when	when	SCONJ
ejpam-5704	323	4	considering	consider	VERB
ejpam-5704	323	5	quadrature	quadrature	NOUN
ejpam-5704	323	6	rules	rule	NOUN
ejpam-5704	323	7	that	that	PRON
ejpam-5704	323	8	incorporate	incorporate	VERB
ejpam-5704	323	9	the	the	DET
ejpam-5704	323	10	point	point	NOUN
ejpam-5704	323	11	η	η	PROPN
ejpam-5704	323	12	as	as	ADP
ejpam-5704	323	13	one	one	NUM
ejpam-5704	323	14	of	of	ADP
ejpam-5704	323	15	their	their	PRON
ejpam-5704	323	16	nodes	node	NOUN
ejpam-5704	323	17	,	,	PUNCT
ejpam-5704	323	18	serving	serve	VERB
ejpam-5704	323	19	as	as	ADP
ejpam-5704	323	20	a	a	DET
ejpam-5704	323	21	collocation	collocation	NOUN
ejpam-5704	323	22	point	point	NOUN
ejpam-5704	323	23	,	,	PUNCT
ejpam-5704	323	24	we	we	PRON
ejpam-5704	323	25	will	will	AUX
ejpam-5704	323	26	be	be	AUX
ejpam-5704	323	27	faced	face	VERB
ejpam-5704	323	28	with	with	ADP
ejpam-5704	323	29	a	a	DET
ejpam-5704	323	30	nonlinear	nonlinear	ADJ
ejpam-5704	323	31	system	system	NOUN
ejpam-5704	323	32	of	of	ADP
ejpam-5704	323	33	equations	equation	NOUN
ejpam-5704	323	34	of	of	ADP
ejpam-5704	323	35	size	size	NOUN
ejpam-5704	323	36	(	(	PUNCT
ejpam-5704	323	37	n	n	NOUN
ejpam-5704	323	38	+	+	CCONJ
ejpam-5704	323	39	1	1	NUM
ejpam-5704	323	40	)	)	PUNCT
ejpam-5704	323	41	×	×	NOUN
ejpam-5704	323	42	(	(	PUNCT
ejpam-5704	323	43	n	n	NOUN
ejpam-5704	323	44	+	+	NOUN
ejpam-5704	323	45	1	1	NUM
ejpam-5704	323	46	)	)	PUNCT
ejpam-5704	323	47	.	.	PUNCT
ejpam-5704	324	1	the	the	DET
ejpam-5704	324	2	solutions	solution	NOUN
ejpam-5704	324	3	to	to	ADP
ejpam-5704	324	4	this	this	DET
ejpam-5704	324	5	system	system	NOUN
ejpam-5704	324	6	provide	provide	VERB
ejpam-5704	324	7	the	the	DET
ejpam-5704	324	8	values	value	NOUN
ejpam-5704	324	9	at	at	ADP
ejpam-5704	324	10	our	our	PRON
ejpam-5704	324	11	grid	grid	NOUN
ejpam-5704	324	12	points	point	NOUN
ejpam-5704	324	13	,	,	PUNCT
ejpam-5704	324	14	particularly	particularly	ADV
ejpam-5704	324	15	at	at	ADP
ejpam-5704	324	16	tn+1	tn+1	PROPN
ejpam-5704	324	17	=	=	SYM
ejpam-5704	324	18	η([8	η([8	PROPN
ejpam-5704	324	19	]	]	PUNCT
ejpam-5704	324	20	)	)	PUNCT
ejpam-5704	324	21	.	.	PUNCT
ejpam-5704	325	1	in	in	ADP
ejpam-5704	325	2	table	table	NOUN
ejpam-5704	325	3	4	4	NUM
ejpam-5704	325	4	,	,	PUNCT
ejpam-5704	325	5	we	we	PRON
ejpam-5704	325	6	set	set	VERB
ejpam-5704	325	7	tn+1	tn+1	NOUN
ejpam-5704	325	8	=	=	SYM
ejpam-5704	325	9	1	1	NUM
ejpam-5704	325	10	and	and	CCONJ
ejpam-5704	325	11	report	report	VERB
ejpam-5704	325	12	absolute	absolute	ADJ
ejpam-5704	325	13	value	value	NOUN
ejpam-5704	325	14	errors	error	NOUN
ejpam-5704	325	15	at	at	ADP
ejpam-5704	325	16	this	this	DET
ejpam-5704	325	17	points	point	NOUN
ejpam-5704	325	18	for	for	ADP
ejpam-5704	325	19	the	the	DET
ejpam-5704	325	20	examples	example	NOUN
ejpam-5704	325	21	5.1	5.1	NUM
ejpam-5704	325	22	,	,	PUNCT
ejpam-5704	325	23	5.2	5.2	NUM
ejpam-5704	325	24	and	and	CCONJ
ejpam-5704	325	25	5.3	5.3	NUM
ejpam-5704	325	26	.	.	NOUN
ejpam-5704	326	1	6	6	NUM
ejpam-5704	326	2	.	.	X
ejpam-5704	326	3	conclusion	conclusion	NOUN
ejpam-5704	326	4	using	use	VERB
ejpam-5704	326	5	incorporating	incorporate	VERB
ejpam-5704	326	6	the	the	DET
ejpam-5704	326	7	nyström	nyström	DET
ejpam-5704	326	8	method	method	NOUN
ejpam-5704	326	9	,	,	PUNCT
ejpam-5704	326	10	the	the	DET
ejpam-5704	326	11	non	non	ADJ
ejpam-5704	326	12	linear	linear	ADJ
ejpam-5704	326	13	weakly	weakly	ADJ
ejpam-5704	326	14	singular	singular	PROPN
ejpam-5704	326	15	volterra	volterra	PROPN
ejpam-5704	326	16	functional	functional	PROPN
ejpam-5704	326	17	can	can	AUX
ejpam-5704	326	18	be	be	AUX
ejpam-5704	326	19	converted	convert	VERB
ejpam-5704	326	20	into	into	ADP
ejpam-5704	326	21	a	a	DET
ejpam-5704	326	22	nonlinear	nonlinear	ADJ
ejpam-5704	326	23	system	system	NOUN
ejpam-5704	326	24	.	.	PUNCT
ejpam-5704	327	1	this	this	DET
ejpam-5704	327	2	system	system	NOUN
ejpam-5704	327	3	can	can	AUX
ejpam-5704	327	4	be	be	AUX
ejpam-5704	327	5	solved	solve	VERB
ejpam-5704	327	6	by	by	ADP
ejpam-5704	327	7	some	some	DET
ejpam-5704	327	8	classical	classical	ADJ
ejpam-5704	327	9	techniques	technique	NOUN
ejpam-5704	327	10	.	.	PUNCT
ejpam-5704	328	1	the	the	DET
ejpam-5704	328	2	method	method	NOUN
ejpam-5704	328	3	’s	’s	PART
ejpam-5704	328	4	effectiveness	effectiveness	NOUN
ejpam-5704	328	5	and	and	CCONJ
ejpam-5704	328	6	accuracy	accuracy	NOUN
ejpam-5704	328	7	in	in	ADP
ejpam-5704	328	8	solving	solve	VERB
ejpam-5704	328	9	nonlinear	nonlinear	ADJ
ejpam-5704	328	10	equations	equation	NOUN
ejpam-5704	328	11	have	have	AUX
ejpam-5704	328	12	been	be	AUX
ejpam-5704	328	13	assessed	assess	VERB
ejpam-5704	328	14	through	through	ADP
ejpam-5704	328	15	various	various	ADJ
ejpam-5704	328	16	problems	problem	NOUN
ejpam-5704	328	17	.	.	PUNCT
ejpam-5704	329	1	another	another	DET
ejpam-5704	329	2	significant	significant	ADJ
ejpam-5704	329	3	advantage	advantage	NOUN
ejpam-5704	329	4	of	of	ADP
ejpam-5704	329	5	the	the	DET
ejpam-5704	329	6	proposed	propose	VERB
ejpam-5704	329	7	method	method	NOUN
ejpam-5704	329	8	is	be	AUX
ejpam-5704	329	9	that	that	SCONJ
ejpam-5704	329	10	the	the	DET
ejpam-5704	329	11	unknown	unknown	ADJ
ejpam-5704	329	12	coefficients	coefficient	NOUN
ejpam-5704	329	13	can	can	AUX
ejpam-5704	329	14	be	be	AUX
ejpam-5704	329	15	determined	determine	VERB
ejpam-5704	329	16	quite	quite	ADV
ejpam-5704	329	17	easily	easily	ADV
ejpam-5704	329	18	using	use	VERB
ejpam-5704	329	19	computer	computer	NOUN
ejpam-5704	329	20	programs	program	NOUN
ejpam-5704	329	21	.	.	PUNCT
ejpam-5704	330	1	in	in	ADP
ejpam-5704	330	2	our	our	PRON
ejpam-5704	330	3	future	future	ADJ
ejpam-5704	330	4	work	work	NOUN
ejpam-5704	330	5	,	,	PUNCT
ejpam-5704	330	6	we	we	PRON
ejpam-5704	330	7	will	will	AUX
ejpam-5704	330	8	study	study	VERB
ejpam-5704	330	9	the	the	DET
ejpam-5704	330	10	nyström	nyström	NOUN
ejpam-5704	330	11	method	method	NOUN
ejpam-5704	330	12	to	to	PART
ejpam-5704	330	13	solve	solve	VERB
ejpam-5704	330	14	delay	delay	PROPN
ejpam-5704	330	15	b.	b.	PROPN
ejpam-5704	330	16	h.	h.	PROPN
ejpam-5704	330	17	alrikabi	alrikabi	PROPN
ejpam-5704	330	18	,	,	PUNCT
ejpam-5704	330	19	p.	p.	PROPN
ejpam-5704	330	20	darania	darania	PROPN
ejpam-5704	330	21	,	,	PUNCT
ejpam-5704	330	22	s.pishbin	s.pishbin	PROPN
ejpam-5704	330	23	/	/	SYM
ejpam-5704	330	24	eur	eur	PROPN
ejpam-5704	330	25	.	.	PUNCT
ejpam-5704	331	1	j.	j.	PROPN
ejpam-5704	331	2	pure	pure	PROPN
ejpam-5704	331	3	appl	appl	PROPN
ejpam-5704	331	4	.	.	PROPN
ejpam-5704	331	5	math	math	PROPN
ejpam-5704	331	6	,	,	PUNCT
ejpam-5704	331	7	18	18	NUM
ejpam-5704	331	8	(	(	PUNCT
ejpam-5704	331	9	2	2	NUM
ejpam-5704	331	10	)	)	PUNCT
ejpam-5704	331	11	(	(	PUNCT
ejpam-5704	331	12	2025	2025	NUM
ejpam-5704	331	13	)	)	PUNCT
ejpam-5704	331	14	,	,	PUNCT
ejpam-5704	331	15	5704	5704	NUM
ejpam-5704	331	16	17	17	NUM
ejpam-5704	331	17	of	of	ADP
ejpam-5704	331	18	19	19	NUM
ejpam-5704	331	19	weakly	weakly	ADJ
ejpam-5704	331	20	singular	singular	ADJ
ejpam-5704	331	21	integral	integral	ADJ
ejpam-5704	331	22	-	-	PUNCT
ejpam-5704	331	23	algebraic	algebraic	ADJ
ejpam-5704	331	24	equations	equation	NOUN
ejpam-5704	331	25	in	in	ADP
ejpam-5704	331	26	the	the	DET
ejpam-5704	331	27	following	follow	VERB
ejpam-5704	331	28	form	form	NOUN
ejpam-5704	331	29	:	:	PUNCT
ejpam-5704	331	30	b(t)x(t	b(t)x(t	NOUN
ejpam-5704	331	31	)	)	PUNCT
ejpam-5704	331	32	+	+	NUM
ejpam-5704	332	1	∫	∫	PROPN
ejpam-5704	332	2	t	t	PROPN
ejpam-5704	332	3	0	0	NUM
ejpam-5704	332	4	p1,h(t	p1,h(t	PROPN
ejpam-5704	332	5	,	,	PUNCT
ejpam-5704	332	6	s)k1(t	s)k1(t	ADJ
ejpam-5704	332	7	,	,	PUNCT
ejpam-5704	332	8	s)x(s)ds+	s)x(s)ds+	PROPN
ejpam-5704	332	9	∫	∫	PROPN
ejpam-5704	332	10	θ(t	θ(t	PROPN
ejpam-5704	332	11	)	)	PUNCT
ejpam-5704	332	12	0	0	NUM
ejpam-5704	333	1	p2,h(t	p2,h(t	NOUN
ejpam-5704	333	2	,	,	PUNCT
ejpam-5704	333	3	w)k2(t	w)k2(t	NOUN
ejpam-5704	333	4	,	,	PUNCT
ejpam-5704	333	5	s)x(s)ds	s)x(s)ds	NOUN
ejpam-5704	333	6	=	=	SYM
ejpam-5704	333	7	f	f	PROPN
ejpam-5704	333	8	(	(	PUNCT
ejpam-5704	333	9	t	t	PROPN
ejpam-5704	333	10	)	)	PUNCT
ejpam-5704	333	11	,	,	PUNCT
ejpam-5704	333	12	t	t	PROPN
ejpam-5704	333	13	∈	∈	PROPN
ejpam-5704	334	1	i	i	PRON
ejpam-5704	334	2	,	,	PUNCT
ejpam-5704	334	3	subject	subject	ADJ
ejpam-5704	334	4	to	to	ADP
ejpam-5704	334	5	det(b(t	det(b(t	NOUN
ejpam-5704	334	6	)	)	PUNCT
ejpam-5704	334	7	)	)	PUNCT
ejpam-5704	335	1	=	=	PUNCT
ejpam-5704	335	2	0	0	NUM
ejpam-5704	335	3	,	,	PUNCT
ejpam-5704	335	4	∀t	∀t	PROPN
ejpam-5704	335	5	∈	∈	PROPN
ejpam-5704	335	6	i.	i.	NOUN
ejpam-5704	335	7	references	reference	NOUN
ejpam-5704	335	8	[	[	X
ejpam-5704	335	9	1	1	NUM
ejpam-5704	335	10	]	]	PUNCT
ejpam-5704	335	11	h.	h.	PROPN
ejpam-5704	335	12	brunner	brunner	PROPN
ejpam-5704	335	13	.	.	PUNCT
ejpam-5704	336	1	collocation	collocation	NOUN
ejpam-5704	336	2	methods	method	NOUN
ejpam-5704	336	3	for	for	ADP
ejpam-5704	336	4	volterra	volterra	NOUN
ejpam-5704	336	5	integral	integral	ADJ
ejpam-5704	336	6	and	and	CCONJ
ejpam-5704	336	7	related	related	ADJ
ejpam-5704	336	8	functional	functional	ADJ
ejpam-5704	336	9	equations	equation	NOUN
ejpam-5704	336	10	.	.	PUNCT
ejpam-5704	337	1	cambridge	cambridge	PROPN
ejpam-5704	337	2	university	university	PROPN
ejpam-5704	337	3	press	press	PROPN
ejpam-5704	337	4	,	,	PUNCT
ejpam-5704	337	5	cambridge	cambridge	PROPN
ejpam-5704	337	6	,	,	PUNCT
ejpam-5704	337	7	2004	2004	NUM
ejpam-5704	337	8	.	.	PUNCT
ejpam-5704	338	1	[	[	X
ejpam-5704	338	2	2	2	X
ejpam-5704	338	3	]	]	PUNCT
ejpam-5704	338	4	h.	h.	PROPN
ejpam-5704	338	5	brunner	brunner	PROPN
ejpam-5704	338	6	and	and	CCONJ
ejpam-5704	338	7	y.	y.	PROPN
ejpam-5704	338	8	yatsenko	yatsenko	PROPN
ejpam-5704	338	9	.	.	PUNCT
ejpam-5704	339	1	spline	spline	NOUN
ejpam-5704	339	2	collocation	collocation	NOUN
ejpam-5704	339	3	methods	method	NOUN
ejpam-5704	339	4	for	for	ADP
ejpam-5704	339	5	nonlinear	nonlinear	PROPN
ejpam-5704	339	6	volterra	volterra	PROPN
ejpam-5704	339	7	integral	integral	ADJ
ejpam-5704	339	8	equations	equation	NOUN
ejpam-5704	339	9	with	with	ADP
ejpam-5704	339	10	unknown	unknown	ADJ
ejpam-5704	339	11	delay	delay	NOUN
ejpam-5704	339	12	.	.	PUNCT
ejpam-5704	340	1	journal	journal	NOUN
ejpam-5704	340	2	of	of	ADP
ejpam-5704	340	3	computational	computational	ADJ
ejpam-5704	340	4	and	and	CCONJ
ejpam-5704	340	5	applied	applied	ADJ
ejpam-5704	340	6	mathematics	mathematic	NOUN
ejpam-5704	340	7	,	,	PUNCT
ejpam-5704	340	8	71(1):67–81	71(1):67–81	NUM
ejpam-5704	340	9	,	,	PUNCT
ejpam-5704	340	10	1996	1996	NUM
ejpam-5704	340	11	.	.	PUNCT
ejpam-5704	341	1	[	[	X
ejpam-5704	341	2	3	3	NUM
ejpam-5704	341	3	]	]	PUNCT
ejpam-5704	341	4	a.	a.	NOUN
ejpam-5704	341	5	cardone	cardone	PROPN
ejpam-5704	341	6	and	and	CCONJ
ejpam-5704	341	7	d.	d.	PROPN
ejpam-5704	341	8	conte	conte	PROPN
ejpam-5704	341	9	.	.	PUNCT
ejpam-5704	342	1	multistep	multistep	ADJ
ejpam-5704	342	2	collocation	collocation	NOUN
ejpam-5704	342	3	methods	method	NOUN
ejpam-5704	342	4	for	for	ADP
ejpam-5704	342	5	volterra	volterra	PROPN
ejpam-5704	342	6	integrodifferential	integrodifferential	ADJ
ejpam-5704	342	7	equations	equation	NOUN
ejpam-5704	342	8	.	.	PUNCT
ejpam-5704	343	1	applied	apply	VERB
ejpam-5704	343	2	mathematics	mathematic	NOUN
ejpam-5704	343	3	and	and	CCONJ
ejpam-5704	343	4	computation	computation	NOUN
ejpam-5704	343	5	,	,	PUNCT
ejpam-5704	343	6	221:770–7856	221:770–7856	NUM
ejpam-5704	343	7	,	,	PUNCT
ejpam-5704	343	8	2013	2013	NUM
ejpam-5704	343	9	.	.	PUNCT
ejpam-5704	344	1	[	[	X
ejpam-5704	344	2	4	4	X
ejpam-5704	344	3	]	]	PUNCT
ejpam-5704	344	4	w.	w.	PROPN
ejpam-5704	344	5	ming	ming	PROPN
ejpam-5704	344	6	and	and	CCONJ
ejpam-5704	344	7	c.	c.	PROPN
ejpam-5704	344	8	huang	huang	PROPN
ejpam-5704	344	9	.	.	PROPN
ejpam-5704	344	10	collocation	collocation	NOUN
ejpam-5704	344	11	methods	method	NOUN
ejpam-5704	344	12	for	for	ADP
ejpam-5704	344	13	volterra	volterra	NOUN
ejpam-5704	344	14	functional	functional	ADJ
ejpam-5704	344	15	integral	integral	ADJ
ejpam-5704	344	16	equations	equation	NOUN
ejpam-5704	344	17	with	with	ADP
ejpam-5704	344	18	non	non	ADJ
ejpam-5704	344	19	-	-	ADJ
ejpam-5704	344	20	vanishing	vanishing	ADJ
ejpam-5704	344	21	delays	delay	NOUN
ejpam-5704	344	22	.	.	PUNCT
ejpam-5704	345	1	applied	apply	VERB
ejpam-5704	345	2	mathematics	mathematic	NOUN
ejpam-5704	345	3	and	and	CCONJ
ejpam-5704	345	4	computation	computation	NOUN
ejpam-5704	345	5	,	,	PUNCT
ejpam-5704	345	6	269:198–214	269:198–214	NUM
ejpam-5704	345	7	,	,	PUNCT
ejpam-5704	345	8	2017	2017	NUM
ejpam-5704	345	9	.	.	PUNCT
ejpam-5704	346	1	[	[	X
ejpam-5704	346	2	5	5	X
ejpam-5704	346	3	]	]	PUNCT
ejpam-5704	346	4	c.	c.	PROPN
ejpam-5704	346	5	huang	huang	PROPN
ejpam-5704	346	6	w.	w.	PROPN
ejpam-5704	346	7	ming	ming	PROPN
ejpam-5704	346	8	and	and	CCONJ
ejpam-5704	346	9	l.	l.	PROPN
ejpam-5704	346	10	zhao	zhao	PROPN
ejpam-5704	346	11	.	.	PUNCT
ejpam-5704	347	1	optimal	optimal	ADJ
ejpam-5704	347	2	superconvergence	superconvergence	NOUN
ejpam-5704	347	3	results	result	NOUN
ejpam-5704	347	4	for	for	ADP
ejpam-5704	347	5	volterra	volterra	NOUN
ejpam-5704	347	6	functional	functional	ADJ
ejpam-5704	347	7	integral	integral	ADJ
ejpam-5704	347	8	equations	equation	NOUN
ejpam-5704	347	9	with	with	ADP
ejpam-5704	347	10	proportional	proportional	ADJ
ejpam-5704	347	11	vanishing	vanishing	NOUN
ejpam-5704	347	12	delays	delay	NOUN
ejpam-5704	347	13	.	.	PUNCT
ejpam-5704	348	1	applied	apply	VERB
ejpam-5704	348	2	mathematics	mathematic	NOUN
ejpam-5704	348	3	and	and	CCONJ
ejpam-5704	348	4	computation	computation	NOUN
ejpam-5704	348	5	,	,	PUNCT
ejpam-5704	348	6	320:292–301	320:292–301	NUM
ejpam-5704	348	7	,	,	PUNCT
ejpam-5704	348	8	2018	2018	NUM
ejpam-5704	348	9	.	.	PUNCT
ejpam-5704	349	1	[	[	X
ejpam-5704	349	2	6	6	NUM
ejpam-5704	349	3	]	]	PUNCT
ejpam-5704	349	4	m.	m.	NOUN
ejpam-5704	349	5	wang	wang	PROPN
ejpam-5704	349	6	.	.	PUNCT
ejpam-5704	350	1	multistep	multistep	ADJ
ejpam-5704	350	2	collocation	collocation	NOUN
ejpam-5704	350	3	method	method	NOUN
ejpam-5704	350	4	for	for	ADP
ejpam-5704	350	5	fredholm	fredholm	ADJ
ejpam-5704	350	6	integral	integral	ADJ
ejpam-5704	350	7	equations	equation	NOUN
ejpam-5704	350	8	of	of	ADP
ejpam-5704	350	9	the	the	DET
ejpam-5704	350	10	second	second	ADJ
ejpam-5704	350	11	kind	kind	NOUN
ejpam-5704	350	12	.	.	PUNCT
ejpam-5704	351	1	applied	apply	VERB
ejpam-5704	351	2	mathematics	mathematic	NOUN
ejpam-5704	351	3	and	and	CCONJ
ejpam-5704	351	4	computation	computation	NOUN
ejpam-5704	351	5	,	,	PUNCT
ejpam-5704	351	6	420(126870):1–16	420(126870):1–16	NUM
ejpam-5704	351	7	,	,	PUNCT
ejpam-5704	351	8	2022	2022	NUM
ejpam-5704	351	9	.	.	PUNCT
ejpam-5704	352	1	[	[	X
ejpam-5704	352	2	7	7	X
ejpam-5704	352	3	]	]	X
ejpam-5704	352	4	t.	t.	PROPN
ejpam-5704	352	5	tang	tang	PROPN
ejpam-5704	352	6	c.	c.	PROPN
ejpam-5704	352	7	huang	huang	PROPN
ejpam-5704	352	8	and	and	CCONJ
ejpam-5704	352	9	z.	z.	PROPN
ejpam-5704	352	10	zhang	zhang	PROPN
ejpam-5704	352	11	.	.	PUNCT
ejpam-5704	353	1	supergeometric	supergeometric	ADJ
ejpam-5704	353	2	convergence	convergence	NOUN
ejpam-5704	353	3	of	of	ADP
ejpam-5704	353	4	spectral	spectral	ADJ
ejpam-5704	353	5	collocation	collocation	NOUN
ejpam-5704	353	6	methods	method	NOUN
ejpam-5704	353	7	for	for	ADP
ejpam-5704	353	8	weakly	weakly	ADJ
ejpam-5704	353	9	singular	singular	PROPN
ejpam-5704	353	10	volterra	volterra	NOUN
ejpam-5704	353	11	and	and	CCONJ
ejpam-5704	353	12	fredholm	fredholm	VERB
ejpam-5704	353	13	integral	integral	ADJ
ejpam-5704	353	14	equations	equation	NOUN
ejpam-5704	353	15	with	with	ADP
ejpam-5704	353	16	smooth	smooth	ADJ
ejpam-5704	353	17	solutions	solution	NOUN
ejpam-5704	353	18	.	.	PUNCT
ejpam-5704	354	1	journal	journal	NOUN
ejpam-5704	354	2	of	of	ADP
ejpam-5704	354	3	computational	computational	ADJ
ejpam-5704	354	4	mathematics	mathematic	NOUN
ejpam-5704	354	5	,	,	PUNCT
ejpam-5704	354	6	29(6):698–719	29(6):698–719	PROPN
ejpam-5704	354	7	,	,	PUNCT
ejpam-5704	354	8	2011	2011	NUM
ejpam-5704	354	9	.	.	PUNCT
ejpam-5704	355	1	[	[	X
ejpam-5704	355	2	8	8	NUM
ejpam-5704	355	3	]	]	PUNCT
ejpam-5704	355	4	m.	m.	NOUN
ejpam-5704	355	5	rasty	rasty	NOUN
ejpam-5704	355	6	and	and	CCONJ
ejpam-5704	355	7	m.	m.	NOUN
ejpam-5704	355	8	hadizadeh	hadizadeh	NOUN
ejpam-5704	355	9	.	.	PUNCT
ejpam-5704	356	1	a	a	DET
ejpam-5704	356	2	product	product	NOUN
ejpam-5704	356	3	integration	integration	NOUN
ejpam-5704	356	4	approach	approach	NOUN
ejpam-5704	356	5	on	on	ADP
ejpam-5704	356	6	new	new	ADJ
ejpam-5704	356	7	orthogonal	orthogonal	ADJ
ejpam-5704	356	8	polynomials	polynomial	NOUN
ejpam-5704	356	9	for	for	ADP
ejpam-5704	356	10	nonlinear	nonlinear	ADJ
ejpam-5704	356	11	weakly	weakly	ADJ
ejpam-5704	356	12	singular	singular	ADJ
ejpam-5704	356	13	integral	integral	ADJ
ejpam-5704	356	14	equations	equation	NOUN
ejpam-5704	356	15	.	.	PUNCT
ejpam-5704	357	1	acta	acta	PROPN
ejpam-5704	357	2	applicandae	applicandae	PROPN
ejpam-5704	357	3	mathematicae	mathematicae	PROPN
ejpam-5704	357	4	,	,	PUNCT
ejpam-5704	357	5	109:861–873	109:861–873	NUM
ejpam-5704	357	6	,	,	PUNCT
ejpam-5704	357	7	2010	2010	NUM
ejpam-5704	357	8	.	.	PUNCT
ejpam-5704	358	1	[	[	X
ejpam-5704	358	2	9	9	NUM
ejpam-5704	358	3	]	]	X
ejpam-5704	358	4	m.a	m.a	PROPN
ejpam-5704	358	5	.	.	PROPN
ejpam-5704	358	6	zaky	zaky	PROPN
ejpam-5704	358	7	and	and	CCONJ
ejpam-5704	358	8	i.	i.	PROPN
ejpam-5704	358	9	g.	g.	PROPN
ejpam-5704	358	10	ameen	ameen	PROPN
ejpam-5704	358	11	.	.	PUNCT
ejpam-5704	359	1	a	a	DET
ejpam-5704	359	2	novel	novel	ADJ
ejpam-5704	359	3	jacobi	jacobi	PROPN
ejpam-5704	359	4	spectral	spectral	ADJ
ejpam-5704	359	5	method	method	NOUN
ejpam-5704	359	6	for	for	ADP
ejpam-5704	359	7	multi	multi	ADJ
ejpam-5704	359	8	-	-	ADJ
ejpam-5704	359	9	dimensional	dimensional	ADJ
ejpam-5704	359	10	weakly	weakly	ADJ
ejpam-5704	359	11	singular	singular	ADJ
ejpam-5704	359	12	nonlinear	nonlinear	PROPN
ejpam-5704	359	13	volterra	volterra	PROPN
ejpam-5704	359	14	integral	integral	ADJ
ejpam-5704	359	15	equations	equation	NOUN
ejpam-5704	359	16	with	with	ADP
ejpam-5704	359	17	nonsmooth	nonsmooth	ADJ
ejpam-5704	359	18	solutions	solution	NOUN
ejpam-5704	359	19	.	.	PUNCT
ejpam-5704	360	1	engineering	engineer	VERB
ejpam-5704	360	2	with	with	ADP
ejpam-5704	360	3	computers	computer	NOUN
ejpam-5704	360	4	-	-	PUNCT
ejpam-5704	360	5	germany	germany	PROPN
ejpam-5704	360	6	,	,	PUNCT
ejpam-5704	360	7	37:2623–2631	37:2623–2631	NUM
ejpam-5704	360	8	,	,	PUNCT
ejpam-5704	360	9	2021	2021	NUM
ejpam-5704	360	10	.	.	PUNCT
ejpam-5704	361	1	[	[	X
ejpam-5704	361	2	10	10	NUM
ejpam-5704	361	3	]	]	X
ejpam-5704	361	4	h.	h.	PROPN
ejpam-5704	361	5	cai	cai	PROPN
ejpam-5704	361	6	and	and	CCONJ
ejpam-5704	361	7	y.	y.	PROPN
ejpam-5704	361	8	chen	chen	PROPN
ejpam-5704	361	9	.	.	PUNCT
ejpam-5704	362	1	a	a	DET
ejpam-5704	362	2	fractional	fractional	ADJ
ejpam-5704	362	3	order	order	NOUN
ejpam-5704	362	4	collocation	collocation	NOUN
ejpam-5704	362	5	method	method	NOUN
ejpam-5704	362	6	for	for	ADP
ejpam-5704	362	7	second	second	ADJ
ejpam-5704	362	8	kind	kind	X
ejpam-5704	362	9	volterra	volterra	PROPN
ejpam-5704	362	10	integral	integral	ADJ
ejpam-5704	362	11	equations	equation	NOUN
ejpam-5704	362	12	with	with	ADP
ejpam-5704	362	13	weakly	weakly	ADJ
ejpam-5704	362	14	singular	singular	ADJ
ejpam-5704	362	15	kernels	kernel	NOUN
ejpam-5704	362	16	.	.	PUNCT
ejpam-5704	363	1	journal	journal	PROPN
ejpam-5704	363	2	of	of	ADP
ejpam-5704	363	3	scientific	scientific	ADJ
ejpam-5704	363	4	computing	computing	NOUN
ejpam-5704	363	5	,	,	PUNCT
ejpam-5704	363	6	75:970–992	75:970–992	NUM
ejpam-5704	363	7	,	,	PUNCT
ejpam-5704	363	8	2018	2018	NUM
ejpam-5704	363	9	.	.	PUNCT
ejpam-5704	364	1	[	[	X
ejpam-5704	364	2	11	11	NUM
ejpam-5704	364	3	]	]	PUNCT
ejpam-5704	364	4	t.	t.	PROPN
ejpam-5704	364	5	herdman	herdman	PROPN
ejpam-5704	364	6	y.	y.	PROPN
ejpam-5704	364	7	cao	cao	PROPN
ejpam-5704	364	8	and	and	CCONJ
ejpam-5704	364	9	y.	y.	PROPN
ejpam-5704	364	10	xu	xu	PROPN
ejpam-5704	364	11	.	.	PUNCT
ejpam-5704	365	1	a	a	DET
ejpam-5704	365	2	hybrid	hybrid	ADJ
ejpam-5704	365	3	collocation	collocation	NOUN
ejpam-5704	365	4	method	method	NOUN
ejpam-5704	365	5	for	for	ADP
ejpam-5704	365	6	volterra	volterra	NOUN
ejpam-5704	365	7	integral	integral	ADJ
ejpam-5704	365	8	equations	equation	NOUN
ejpam-5704	365	9	with	with	ADP
ejpam-5704	365	10	weakly	weakly	ADJ
ejpam-5704	365	11	singular	singular	ADJ
ejpam-5704	365	12	kernels	kernel	NOUN
ejpam-5704	365	13	.	.	PUNCT
ejpam-5704	366	1	siam	siam	PROPN
ejpam-5704	366	2	journal	journal	PROPN
ejpam-5704	366	3	on	on	ADP
ejpam-5704	366	4	numerical	numerical	ADJ
ejpam-5704	366	5	analysis	analysis	NOUN
ejpam-5704	366	6	,	,	PUNCT
ejpam-5704	366	7	41:364	41:364	NUM
ejpam-5704	366	8	–	–	PUNCT
ejpam-5704	366	9	381	381	NUM
ejpam-5704	366	10	,	,	PUNCT
ejpam-5704	366	11	2003	2003	NUM
ejpam-5704	366	12	.	.	PUNCT
ejpam-5704	367	1	[	[	X
ejpam-5704	367	2	12	12	NUM
ejpam-5704	367	3	]	]	PUNCT
ejpam-5704	367	4	p.	p.	NOUN
ejpam-5704	367	5	assari	assari	NOUN
ejpam-5704	367	6	and	and	CCONJ
ejpam-5704	367	7	m.	m.	NOUN
ejpam-5704	367	8	dehghan	dehghan	PROPN
ejpam-5704	367	9	.	.	PUNCT
ejpam-5704	368	1	a	a	DET
ejpam-5704	368	2	meshless	meshless	ADJ
ejpam-5704	368	3	method	method	NOUN
ejpam-5704	368	4	for	for	ADP
ejpam-5704	368	5	the	the	DET
ejpam-5704	368	6	numerical	numerical	ADJ
ejpam-5704	368	7	solution	solution	NOUN
ejpam-5704	368	8	of	of	ADP
ejpam-5704	368	9	nonlinear	nonlinear	ADJ
ejpam-5704	368	10	weakly	weakly	ADJ
ejpam-5704	368	11	singular	singular	ADJ
ejpam-5704	368	12	integral	integral	ADJ
ejpam-5704	368	13	equations	equation	NOUN
ejpam-5704	368	14	using	use	VERB
ejpam-5704	368	15	radial	radial	ADJ
ejpam-5704	368	16	basis	basis	NOUN
ejpam-5704	368	17	functions	function	NOUN
ejpam-5704	368	18	.	.	PUNCT
ejpam-5704	369	1	the	the	DET
ejpam-5704	369	2	european	european	PROPN
ejpam-5704	369	3	physical	physical	PROPN
ejpam-5704	369	4	journal	journal	PROPN
ejpam-5704	369	5	plus	plus	CCONJ
ejpam-5704	369	6	,	,	PUNCT
ejpam-5704	369	7	132:1–23	132:1–23	NUM
ejpam-5704	369	8	,	,	PUNCT
ejpam-5704	369	9	2017	2017	NUM
ejpam-5704	369	10	.	.	PUNCT
ejpam-5704	370	1	[	[	X
ejpam-5704	370	2	13	13	NUM
ejpam-5704	370	3	]	]	PUNCT
ejpam-5704	370	4	m.	m.	NOUN
ejpam-5704	370	5	a.	a.	PROPN
ejpam-5704	370	6	ebadi	ebadi	PROPN
ejpam-5704	370	7	e.	e.	PROPN
ejpam-5704	370	8	hashemizadeh	hashemizadeh	PROPN
ejpam-5704	370	9	and	and	CCONJ
ejpam-5704	370	10	s.	s.	PROPN
ejpam-5704	370	11	noeiaghdam	noeiaghdam	PROPN
ejpam-5704	370	12	.	.	PUNCT
ejpam-5704	371	1	matrix	matrix	NOUN
ejpam-5704	371	2	method	method	NOUN
ejpam-5704	371	3	by	by	ADP
ejpam-5704	371	4	genocchi	genocchi	PROPN
ejpam-5704	371	5	polynomials	polynomial	NOUN
ejpam-5704	371	6	for	for	ADP
ejpam-5704	371	7	solving	solve	VERB
ejpam-5704	371	8	nonlinear	nonlinear	ADJ
ejpam-5704	371	9	volterra	volterra	PROPN
ejpam-5704	371	10	integral	integral	ADJ
ejpam-5704	371	11	equations	equation	NOUN
ejpam-5704	371	12	with	with	ADP
ejpam-5704	371	13	weakly	weakly	ADJ
ejpam-5704	371	14	singular	singular	ADJ
ejpam-5704	371	15	kernels	kernel	NOUN
ejpam-5704	371	16	.	.	PUNCT
ejpam-5704	372	1	symmetry	symmetry	PROPN
ejpam-5704	372	2	,	,	PUNCT
ejpam-5704	372	3	12:1–16	12:1–16	NUM
ejpam-5704	372	4	,	,	PUNCT
ejpam-5704	372	5	2020	2020	NUM
ejpam-5704	372	6	.	.	PUNCT
ejpam-5704	373	1	b.	b.	PROPN
ejpam-5704	373	2	h.	h.	PROPN
ejpam-5704	373	3	alrikabi	alrikabi	PROPN
ejpam-5704	373	4	,	,	PUNCT
ejpam-5704	373	5	p.	p.	PROPN
ejpam-5704	373	6	darania	darania	PROPN
ejpam-5704	373	7	,	,	PUNCT
ejpam-5704	373	8	s.pishbin	s.pishbin	PROPN
ejpam-5704	373	9	/	/	SYM
ejpam-5704	373	10	eur	eur	PROPN
ejpam-5704	373	11	.	.	PUNCT
ejpam-5704	374	1	j.	j.	PROPN
ejpam-5704	374	2	pure	pure	PROPN
ejpam-5704	374	3	appl	appl	PROPN
ejpam-5704	374	4	.	.	PROPN
ejpam-5704	374	5	math	math	PROPN
ejpam-5704	374	6	,	,	PUNCT
ejpam-5704	374	7	18	18	NUM
ejpam-5704	374	8	(	(	PUNCT
ejpam-5704	374	9	2	2	NUM
ejpam-5704	374	10	)	)	PUNCT
ejpam-5704	374	11	(	(	PUNCT
ejpam-5704	374	12	2025	2025	NUM
ejpam-5704	374	13	)	)	PUNCT
ejpam-5704	374	14	,	,	PUNCT
ejpam-5704	374	15	5704	5704	NUM
ejpam-5704	374	16	18	18	NUM
ejpam-5704	374	17	of	of	ADP
ejpam-5704	374	18	19	19	NUM
ejpam-5704	375	1	[	[	SYM
ejpam-5704	375	2	14	14	NUM
ejpam-5704	375	3	]	]	PUNCT
ejpam-5704	375	4	j.	j.	PROPN
ejpam-5704	375	5	huang	huang	PROPN
ejpam-5704	375	6	y.	y.	PROPN
ejpam-5704	375	7	b.	b.	PROPN
ejpam-5704	375	8	pan	pan	PROPN
ejpam-5704	375	9	and	and	CCONJ
ejpam-5704	375	10	y.y	y.y	PROPN
ejpam-5704	375	11	ma	ma	PROPN
ejpam-5704	375	12	.	.	PROPN
ejpam-5704	375	13	bernstein	bernstein	PROPN
ejpam-5704	375	14	series	series	PROPN
ejpam-5704	375	15	solutions	solution	NOUN
ejpam-5704	375	16	of	of	ADP
ejpam-5704	375	17	multidimensional	multidimensional	ADJ
ejpam-5704	375	18	linear	linear	NOUN
ejpam-5704	375	19	and	and	CCONJ
ejpam-5704	375	20	nonlinear	nonlinear	ADJ
ejpam-5704	375	21	volterra	volterra	PROPN
ejpam-5704	375	22	integral	integral	ADJ
ejpam-5704	375	23	equations	equation	NOUN
ejpam-5704	375	24	with	with	ADP
ejpam-5704	375	25	fractional	fractional	ADJ
ejpam-5704	375	26	order	order	NOUN
ejpam-5704	375	27	weakly	weakly	ADJ
ejpam-5704	375	28	singular	singular	ADJ
ejpam-5704	375	29	kernels	kernel	NOUN
ejpam-5704	375	30	.	.	PUNCT
ejpam-5704	376	1	applied	apply	VERB
ejpam-5704	376	2	mathematics	mathematic	NOUN
ejpam-5704	376	3	and	and	CCONJ
ejpam-5704	376	4	computation	computation	NOUN
ejpam-5704	376	5	,	,	PUNCT
ejpam-5704	376	6	374:149–161	374:149–161	NUM
ejpam-5704	376	7	,	,	PUNCT
ejpam-5704	376	8	2019	2019	NUM
ejpam-5704	376	9	.	.	PUNCT
ejpam-5704	377	1	[	[	X
ejpam-5704	377	2	15	15	NUM
ejpam-5704	377	3	]	]	PUNCT
ejpam-5704	377	4	a.	a.	NOUN
ejpam-5704	377	5	m.	m.	NOUN
ejpam-5704	377	6	wazwaz	wazwaz	PROPN
ejpam-5704	377	7	.	.	PUNCT
ejpam-5704	378	1	linear	linear	ADJ
ejpam-5704	378	2	and	and	CCONJ
ejpam-5704	378	3	nonlinear	nonlinear	ADJ
ejpam-5704	378	4	integral	integral	ADJ
ejpam-5704	378	5	equations	equation	NOUN
ejpam-5704	378	6	.	.	PUNCT
ejpam-5704	379	1	springer	springer	PROPN
ejpam-5704	379	2	,	,	PUNCT
ejpam-5704	379	3	heidelberg	heidelberg	PROPN
ejpam-5704	379	4	,	,	PUNCT
ejpam-5704	379	5	2011	2011	NUM
ejpam-5704	379	6	.	.	PUNCT
ejpam-5704	380	1	[	[	X
ejpam-5704	380	2	16	16	NUM
ejpam-5704	380	3	]	]	X
ejpam-5704	380	4	h.	h.	PROPN
ejpam-5704	380	5	brunner	brunner	PROPN
ejpam-5704	380	6	i.	i.	PROPN
ejpam-5704	380	7	ali	ali	PROPN
ejpam-5704	380	8	and	and	CCONJ
ejpam-5704	380	9	t.	t.	PROPN
ejpam-5704	380	10	tang	tang	PROPN
ejpam-5704	380	11	.	.	PUNCT
ejpam-5704	381	1	spectral	spectral	ADJ
ejpam-5704	381	2	methods	method	NOUN
ejpam-5704	381	3	for	for	ADP
ejpam-5704	381	4	pantograph	pantograph	NOUN
ejpam-5704	381	5	-	-	PUNCT
ejpam-5704	381	6	type	type	NOUN
ejpam-5704	381	7	differential	differential	NOUN
ejpam-5704	381	8	and	and	CCONJ
ejpam-5704	381	9	integral	integral	ADJ
ejpam-5704	381	10	equations	equation	NOUN
ejpam-5704	381	11	with	with	ADP
ejpam-5704	381	12	multiple	multiple	ADJ
ejpam-5704	381	13	delays	delay	NOUN
ejpam-5704	381	14	.	.	PUNCT
ejpam-5704	382	1	frontiers	frontier	NOUN
ejpam-5704	382	2	of	of	ADP
ejpam-5704	382	3	mathematics	mathematics	PROPN
ejpam-5704	382	4	in	in	ADP
ejpam-5704	382	5	china	china	PROPN
ejpam-5704	382	6	,	,	PUNCT
ejpam-5704	382	7	4:49–61	4:49–61	PROPN
ejpam-5704	382	8	,	,	PUNCT
ejpam-5704	382	9	2009	2009	NUM
ejpam-5704	382	10	.	.	PUNCT
ejpam-5704	383	1	[	[	X
ejpam-5704	383	2	17	17	NUM
ejpam-5704	383	3	]	]	X
ejpam-5704	383	4	n.	n.	PROPN
ejpam-5704	383	5	senu	senu	PROPN
ejpam-5704	383	6	n.	n.	PROPN
ejpam-5704	383	7	a.	a.	PROPN
ejpam-5704	383	8	baharum	baharum	PROPN
ejpam-5704	383	9	,	,	PUNCT
ejpam-5704	383	10	z.a	z.a	PROPN
ejpam-5704	383	11	.	.	PROPN
ejpam-5704	383	12	majid	majid	PROPN
ejpam-5704	383	13	and	and	CCONJ
ejpam-5704	383	14	h.	h.	PROPN
ejpam-5704	383	15	rosali	rosali	PROPN
ejpam-5704	383	16	.	.	PUNCT
ejpam-5704	384	1	numerical	numerical	ADJ
ejpam-5704	384	2	approach	approach	NOUN
ejpam-5704	384	3	for	for	ADP
ejpam-5704	384	4	delay	delay	PROPN
ejpam-5704	384	5	volterra	volterra	PROPN
ejpam-5704	384	6	integro	integro	PROPN
ejpam-5704	384	7	-	-	PUNCT
ejpam-5704	384	8	differential	differential	NOUN
ejpam-5704	384	9	equation	equation	NOUN
ejpam-5704	384	10	.	.	PUNCT
ejpam-5704	385	1	sains	sain	NOUN
ejpam-5704	385	2	malaysiana	malaysiana	PROPN
ejpam-5704	385	3	,	,	PUNCT
ejpam-5704	385	4	51(12):4125–4144	51(12):4125–4144	NUM
ejpam-5704	385	5	,	,	PUNCT
ejpam-5704	385	6	2002	2002	NUM
ejpam-5704	385	7	.	.	PUNCT
ejpam-5704	386	1	[	[	X
ejpam-5704	386	2	18	18	NUM
ejpam-5704	386	3	]	]	X
ejpam-5704	386	4	h.	h.	PROPN
ejpam-5704	386	5	brunner	brunner	PROPN
ejpam-5704	386	6	.	.	PUNCT
ejpam-5704	387	1	collocation	collocation	NOUN
ejpam-5704	387	2	and	and	CCONJ
ejpam-5704	387	3	continuous	continuous	ADJ
ejpam-5704	387	4	implicit	implicit	ADJ
ejpam-5704	387	5	runge	runge	NOUN
ejpam-5704	387	6	-	-	PUNCT
ejpam-5704	387	7	kutta	kutta	NOUN
ejpam-5704	387	8	methods	method	NOUN
ejpam-5704	387	9	for	for	ADP
ejpam-5704	387	10	a	a	DET
ejpam-5704	387	11	class	class	NOUN
ejpam-5704	387	12	of	of	ADP
ejpam-5704	387	13	delay	delay	PROPN
ejpam-5704	387	14	volterra	volterra	PROPN
ejpam-5704	387	15	integral	integral	ADJ
ejpam-5704	387	16	equations	equation	NOUN
ejpam-5704	387	17	.	.	PUNCT
ejpam-5704	388	1	journal	journal	NOUN
ejpam-5704	388	2	of	of	ADP
ejpam-5704	388	3	computational	computational	ADJ
ejpam-5704	388	4	and	and	CCONJ
ejpam-5704	388	5	applied	applied	ADJ
ejpam-5704	388	6	mathematics	mathematic	NOUN
ejpam-5704	388	7	,	,	PUNCT
ejpam-5704	388	8	53:61–72	53:61–72	NUM
ejpam-5704	388	9	,	,	PUNCT
ejpam-5704	388	10	1994	1994	NUM
ejpam-5704	388	11	.	.	PUNCT
ejpam-5704	389	1	[	[	X
ejpam-5704	389	2	19	19	NUM
ejpam-5704	389	3	]	]	X
ejpam-5704	389	4	e.	e.	PROPN
ejpam-5704	389	5	marchetti	marchetti	PROPN
ejpam-5704	389	6	f.	f.	PROPN
ejpam-5704	389	7	calio	calio	PROPN
ejpam-5704	389	8	and	and	CCONJ
ejpam-5704	389	9	r.	r.	PROPN
ejpam-5704	389	10	pavani	pavani	PROPN
ejpam-5704	389	11	.	.	PUNCT
ejpam-5704	390	1	about	about	ADP
ejpam-5704	390	2	the	the	DET
ejpam-5704	390	3	deficient	deficient	ADJ
ejpam-5704	390	4	spline	spline	NOUN
ejpam-5704	390	5	collocation	collocation	NOUN
ejpam-5704	390	6	method	method	NOUN
ejpam-5704	390	7	for	for	ADP
ejpam-5704	390	8	particular	particular	ADJ
ejpam-5704	390	9	differential	differential	NOUN
ejpam-5704	390	10	and	and	CCONJ
ejpam-5704	390	11	integral	integral	ADJ
ejpam-5704	390	12	equations	equation	NOUN
ejpam-5704	390	13	with	with	ADP
ejpam-5704	390	14	delay	delay	NOUN
ejpam-5704	390	15	.	.	PUNCT
ejpam-5704	391	1	rendiconti	rendiconti	PROPN
ejpam-5704	391	2	del	del	PROPN
ejpam-5704	391	3	seminario	seminario	PROPN
ejpam-5704	391	4	matematico	matematico	PROPN
ejpam-5704	391	5	politecnico	politecnico	PROPN
ejpam-5704	391	6	di	di	PROPN
ejpam-5704	391	7	torino	torino	PROPN
ejpam-5704	391	8	,	,	PUNCT
ejpam-5704	391	9	61:287–300	61:287–300	PROPN
ejpam-5704	391	10	,	,	PUNCT
ejpam-5704	391	11	2003	2003	NUM
ejpam-5704	391	12	.	.	PUNCT
ejpam-5704	392	1	[	[	X
ejpam-5704	392	2	20	20	NUM
ejpam-5704	392	3	]	]	PUNCT
ejpam-5704	392	4	r.	r.	PROPN
ejpam-5704	392	5	pavani	pavani	PROPN
ejpam-5704	392	6	f.	f.	PROPN
ejpam-5704	392	7	calio	calio	PROPN
ejpam-5704	392	8	,	,	PUNCT
ejpam-5704	392	9	e.	e.	PROPN
ejpam-5704	392	10	marchetti	marchetti	PROPN
ejpam-5704	392	11	and	and	CCONJ
ejpam-5704	392	12	g.	g.	PROPN
ejpam-5704	392	13	micula	micula	PROPN
ejpam-5704	392	14	.	.	PUNCT
ejpam-5704	393	1	about	about	ADP
ejpam-5704	393	2	some	some	DET
ejpam-5704	393	3	volterra	volterra	NOUN
ejpam-5704	393	4	problems	problem	NOUN
ejpam-5704	393	5	solved	solve	VERB
ejpam-5704	393	6	by	by	ADP
ejpam-5704	393	7	a	a	DET
ejpam-5704	393	8	particular	particular	ADJ
ejpam-5704	393	9	spline	spline	NOUN
ejpam-5704	393	10	collocation	collocation	NOUN
ejpam-5704	393	11	.	.	PUNCT
ejpam-5704	394	1	studia	studia	PROPN
ejpam-5704	394	2	universitatis	universitatis	PROPN
ejpam-5704	394	3	babes	babes	PROPN
ejpam-5704	394	4	-	-	PUNCT
ejpam-5704	394	5	bolyai	bolyai	NOUN
ejpam-5704	394	6	,	,	PUNCT
ejpam-5704	394	7	48:45–52	48:45–52	NUM
ejpam-5704	394	8	,	,	PUNCT
ejpam-5704	394	9	2003	2003	NUM
ejpam-5704	394	10	.	.	PUNCT
ejpam-5704	395	1	[	[	X
ejpam-5704	395	2	21	21	NUM
ejpam-5704	395	3	]	]	X
ejpam-5704	395	4	f.	f.	PROPN
ejpam-5704	395	5	ghoreishi	ghoreishi	PROPN
ejpam-5704	395	6	m.	m.	PROPN
ejpam-5704	395	7	khasi	khasi	PROPN
ejpam-5704	395	8	and	and	CCONJ
ejpam-5704	395	9	m.	m.	NOUN
ejpam-5704	395	10	hadizadeh	hadizadeh	PROPN
ejpam-5704	395	11	.	.	PUNCT
ejpam-5704	396	1	numerical	numerical	ADJ
ejpam-5704	396	2	analysis	analysis	NOUN
ejpam-5704	396	3	of	of	ADP
ejpam-5704	396	4	a	a	DET
ejpam-5704	396	5	high	high	ADJ
ejpam-5704	396	6	order	order	NOUN
ejpam-5704	396	7	method	method	NOUN
ejpam-5704	396	8	for	for	ADP
ejpam-5704	396	9	state	state	NOUN
ejpam-5704	396	10	-	-	PUNCT
ejpam-5704	396	11	dependent	dependent	ADJ
ejpam-5704	396	12	delay	delay	NOUN
ejpam-5704	396	13	integral	integral	ADJ
ejpam-5704	396	14	equations	equation	NOUN
ejpam-5704	396	15	.	.	PUNCT
ejpam-5704	397	1	numerical	numerical	ADJ
ejpam-5704	397	2	algorithms	algorithms	PROPN
ejpam-5704	397	3	,	,	PUNCT
ejpam-5704	397	4	66:177–201	66:177–201	PROPN
ejpam-5704	397	5	,	,	PUNCT
ejpam-5704	397	6	2013	2013	NUM
ejpam-5704	397	7	.	.	PUNCT
ejpam-5704	398	1	[	[	X
ejpam-5704	398	2	22	22	NUM
ejpam-5704	398	3	]	]	PUNCT
ejpam-5704	398	4	s.	s.	PROPN
ejpam-5704	398	5	gan	gan	PROPN
ejpam-5704	398	6	s.	s.	PROPN
ejpam-5704	398	7	wu	wu	PROPN
ejpam-5704	398	8	.	.	PUNCT
ejpam-5704	399	1	errors	error	NOUN
ejpam-5704	399	2	of	of	ADP
ejpam-5704	399	3	linear	linear	ADJ
ejpam-5704	399	4	multistep	multistep	ADJ
ejpam-5704	399	5	methods	method	NOUN
ejpam-5704	399	6	for	for	ADP
ejpam-5704	399	7	singularly	singularly	ADV
ejpam-5704	399	8	perturbed	perturb	VERB
ejpam-5704	399	9	volterra	volterra	PROPN
ejpam-5704	399	10	delay	delay	PROPN
ejpam-5704	399	11	integro	integro	PROPN
ejpam-5704	399	12	-	-	PUNCT
ejpam-5704	399	13	differential	differential	NOUN
ejpam-5704	399	14	equations	equation	NOUN
ejpam-5704	399	15	.	.	PUNCT
ejpam-5704	400	1	mathematics	mathematic	NOUN
ejpam-5704	400	2	and	and	CCONJ
ejpam-5704	400	3	computers	computer	NOUN
ejpam-5704	400	4	in	in	ADP
ejpam-5704	400	5	simulation	simulation	NOUN
ejpam-5704	400	6	,	,	PUNCT
ejpam-5704	400	7	79:3148–3159	79:3148–3159	NUM
ejpam-5704	400	8	,	,	PUNCT
ejpam-5704	400	9	2009	2009	NUM
ejpam-5704	400	10	.	.	PUNCT
ejpam-5704	401	1	[	[	X
ejpam-5704	401	2	23	23	NUM
ejpam-5704	401	3	]	]	X
ejpam-5704	401	4	y.	y.	PROPN
ejpam-5704	401	5	xiao	xiao	PROPN
ejpam-5704	401	6	h.	h.	PROPN
ejpam-5704	401	7	song	song	PROPN
ejpam-5704	401	8	and	and	CCONJ
ejpam-5704	401	9	m.	m.	PROPN
ejpam-5704	401	10	chen	chen	PROPN
ejpam-5704	401	11	.	.	PUNCT
ejpam-5704	402	1	collocation	collocation	NOUN
ejpam-5704	402	2	methods	method	NOUN
ejpam-5704	402	3	for	for	ADP
ejpam-5704	402	4	third	third	ADJ
ejpam-5704	402	5	-	-	PUNCT
ejpam-5704	402	6	kind	kind	NOUN
ejpam-5704	402	7	volterra	volterra	NOUN
ejpam-5704	402	8	integral	integral	ADJ
ejpam-5704	402	9	equations	equation	NOUN
ejpam-5704	402	10	with	with	ADP
ejpam-5704	402	11	proportional	proportional	ADJ
ejpam-5704	402	12	delays	delay	NOUN
ejpam-5704	402	13	.	.	PUNCT
ejpam-5704	403	1	applied	apply	VERB
ejpam-5704	403	2	mathematics	mathematic	NOUN
ejpam-5704	403	3	and	and	CCONJ
ejpam-5704	403	4	computation	computation	NOUN
ejpam-5704	403	5	,	,	PUNCT
ejpam-5704	403	6	388:1–11	388:1–11	NUM
ejpam-5704	403	7	,	,	PUNCT
ejpam-5704	403	8	2020	2020	NUM
ejpam-5704	403	9	.	.	PUNCT
ejpam-5704	404	1	[	[	X
ejpam-5704	404	2	24	24	NUM
ejpam-5704	404	3	]	]	X
ejpam-5704	404	4	g.	g.	PROPN
ejpam-5704	404	5	mastroianni	mastroianni	PROPN
ejpam-5704	404	6	g.	g.	PROPN
ejpam-5704	404	7	criscuolo	criscuolo	PROPN
ejpam-5704	404	8	and	and	CCONJ
ejpam-5704	404	9	g.	g.	PROPN
ejpam-5704	404	10	monegato	monegato	PROPN
ejpam-5704	404	11	.	.	PUNCT
ejpam-5704	405	1	convergence	convergence	NOUN
ejpam-5704	405	2	properties	property	NOUN
ejpam-5704	405	3	of	of	ADP
ejpam-5704	405	4	a	a	DET
ejpam-5704	405	5	class	class	NOUN
ejpam-5704	405	6	of	of	ADP
ejpam-5704	405	7	product	product	NOUN
ejpam-5704	405	8	formulas	formula	NOUN
ejpam-5704	405	9	for	for	ADP
ejpam-5704	405	10	weakly	weakly	ADJ
ejpam-5704	405	11	singular	singular	ADJ
ejpam-5704	405	12	integral	integral	ADJ
ejpam-5704	405	13	equations	equation	NOUN
ejpam-5704	405	14	.	.	PUNCT
ejpam-5704	406	1	mathematics	mathematic	NOUN
ejpam-5704	406	2	of	of	ADP
ejpam-5704	406	3	computation	computation	NOUN
ejpam-5704	406	4	,	,	PUNCT
ejpam-5704	406	5	55:213–230	55:213–230	NUM
ejpam-5704	406	6	,	,	PUNCT
ejpam-5704	406	7	1990	1990	NUM
ejpam-5704	406	8	.	.	PUNCT
ejpam-5704	407	1	[	[	X
ejpam-5704	407	2	25	25	NUM
ejpam-5704	407	3	]	]	PUNCT
ejpam-5704	407	4	p.	p.	NOUN
ejpam-5704	407	5	nevai	nevai	NOUN
ejpam-5704	407	6	.	.	PUNCT
ejpam-5704	408	1	mean	mean	ADJ
ejpam-5704	408	2	convergence	convergence	NOUN
ejpam-5704	408	3	of	of	ADP
ejpam-5704	408	4	lagrange	lagrange	NOUN
ejpam-5704	408	5	interpolation	interpolation	NOUN
ejpam-5704	408	6	.	.	PUNCT
ejpam-5704	409	1	trans	trans	AUX
ejpam-5704	409	2	.	.	PROPN
ejpam-5704	409	3	am	be	AUX
ejpam-5704	409	4	.	.	PUNCT
ejpam-5704	410	1	math	math	NOUN
ejpam-5704	410	2	.	.	PUNCT
ejpam-5704	411	1	soc	soc	PROPN
ejpam-5704	411	2	.	.	PUNCT
ejpam-5704	411	3	,	,	PUNCT
ejpam-5704	411	4	282:669–689	282:669–689	NUM
ejpam-5704	411	5	,	,	PUNCT
ejpam-5704	411	6	1984	1984	NUM
ejpam-5704	411	7	.	.	PUNCT
ejpam-5704	412	1	[	[	X
ejpam-5704	412	2	26	26	NUM
ejpam-5704	412	3	]	]	X
ejpam-5704	412	4	v.s.	v.s.	ADJ
ejpam-5704	412	5	chelyshkov	chelyshkov	NOUN
ejpam-5704	412	6	.	.	PUNCT
ejpam-5704	413	1	alternative	alternative	ADJ
ejpam-5704	413	2	orthogonal	orthogonal	ADJ
ejpam-5704	413	3	polynomials	polynomial	NOUN
ejpam-5704	413	4	and	and	CCONJ
ejpam-5704	413	5	quadratures	quadrature	NOUN
ejpam-5704	413	6	.	.	PUNCT
ejpam-5704	414	1	electronic	electronic	ADJ
ejpam-5704	414	2	transactions	transaction	NOUN
ejpam-5704	414	3	on	on	ADP
ejpam-5704	414	4	numerical	numerical	ADJ
ejpam-5704	414	5	analysis	analysis	NOUN
ejpam-5704	414	6	,	,	PUNCT
ejpam-5704	414	7	25(7):17–26	25(7):17–26	NUM
ejpam-5704	414	8	,	,	PUNCT
ejpam-5704	414	9	2006	2006	NUM
ejpam-5704	414	10	.	.	PUNCT
ejpam-5704	415	1	[	[	X
ejpam-5704	415	2	27	27	NUM
ejpam-5704	415	3	]	]	PUNCT
ejpam-5704	415	4	s.	s.	PROPN
ejpam-5704	415	5	gottlieb	gottlieb	PROPN
ejpam-5704	415	6	j.	j.	PROPN
ejpam-5704	415	7	hesthaven	hesthaven	PROPN
ejpam-5704	415	8	and	and	CCONJ
ejpam-5704	415	9	d.	d.	PROPN
ejpam-5704	415	10	gottlieb	gottlieb	PROPN
ejpam-5704	415	11	.	.	PUNCT
ejpam-5704	416	1	spectral	spectral	ADJ
ejpam-5704	416	2	methods	method	NOUN
ejpam-5704	416	3	for	for	ADP
ejpam-5704	416	4	time	time	NOUN
ejpam-5704	416	5	-	-	PUNCT
ejpam-5704	416	6	dependent	dependent	ADJ
ejpam-5704	416	7	problems	problem	NOUN
ejpam-5704	416	8	.	.	PUNCT
ejpam-5704	417	1	cambridge	cambridge	PROPN
ejpam-5704	417	2	university	university	PROPN
ejpam-5704	417	3	press	press	PROPN
ejpam-5704	417	4	,	,	PUNCT
ejpam-5704	417	5	cambridge	cambridge	PROPN
ejpam-5704	417	6	,	,	PUNCT
ejpam-5704	417	7	2007	2007	NUM
ejpam-5704	417	8	.	.	PUNCT
ejpam-5704	418	1	[	[	X
ejpam-5704	418	2	28	28	NUM
ejpam-5704	418	3	]	]	X
ejpam-5704	418	4	c.	c.	PROPN
ejpam-5704	418	5	cesarano	cesarano	PROPN
ejpam-5704	418	6	.	.	PUNCT
ejpam-5704	419	1	generalized	generalize	VERB
ejpam-5704	419	2	chebyshev	chebyshev	NOUN
ejpam-5704	419	3	polynomials	polynomial	NOUN
ejpam-5704	419	4	.	.	PUNCT
ejpam-5704	420	1	hacettepe	hacettepe	PROPN
ejpam-5704	420	2	journal	journal	PROPN
ejpam-5704	420	3	of	of	ADP
ejpam-5704	420	4	mathematics	mathematic	NOUN
ejpam-5704	420	5	and	and	CCONJ
ejpam-5704	420	6	statistics	statistic	NOUN
ejpam-5704	420	7	,	,	PUNCT
ejpam-5704	420	8	43(5):731–740	43(5):731–740	PROPN
ejpam-5704	420	9	,	,	PUNCT
ejpam-5704	420	10	2014	2014	NUM
ejpam-5704	420	11	.	.	PUNCT
ejpam-5704	421	1	[	[	X
ejpam-5704	421	2	29	29	NUM
ejpam-5704	421	3	]	]	PUNCT
ejpam-5704	421	4	b.	b.	PROPN
ejpam-5704	421	5	germano	germano	PROPN
ejpam-5704	421	6	c.	c.	PROPN
ejpam-5704	421	7	cesarano	cesarano	PROPN
ejpam-5704	421	8	and	and	CCONJ
ejpam-5704	421	9	p.e	p.e	PROPN
ejpam-5704	421	10	.	.	PROPN
ejpam-5704	421	11	ricci	ricci	PROPN
ejpam-5704	421	12	.	.	PUNCT
ejpam-5704	422	1	laguerre	laguerre	NOUN
ejpam-5704	422	2	-	-	PUNCT
ejpam-5704	422	3	type	type	NOUN
ejpam-5704	422	4	bessel	bessel	NOUN
ejpam-5704	422	5	functions	function	NOUN
ejpam-5704	422	6	.	.	PUNCT
ejpam-5704	423	1	integral	integral	ADJ
ejpam-5704	423	2	transforms	transform	NOUN
ejpam-5704	423	3	and	and	CCONJ
ejpam-5704	423	4	special	special	ADJ
ejpam-5704	423	5	functions	function	NOUN
ejpam-5704	423	6	,	,	PUNCT
ejpam-5704	423	7	16(4):315–322	16(4):315–322	PROPN
ejpam-5704	423	8	,	,	PUNCT
ejpam-5704	423	9	2005	2005	NUM
ejpam-5704	423	10	.	.	PUNCT
ejpam-5704	424	1	[	[	X
ejpam-5704	424	2	30	30	NUM
ejpam-5704	424	3	]	]	X
ejpam-5704	424	4	h.	h.	PROPN
ejpam-5704	424	5	kaneko	kaneko	PROPN
ejpam-5704	424	6	and	and	CCONJ
ejpam-5704	424	7	y.	y.	PROPN
ejpam-5704	424	8	xu	xu	PROPN
ejpam-5704	424	9	.	.	PUNCT
ejpam-5704	425	1	gauss	gauss	ADJ
ejpam-5704	425	2	-	-	PUNCT
ejpam-5704	425	3	type	type	NOUN
ejpam-5704	425	4	quadratures	quadrature	NOUN
ejpam-5704	425	5	for	for	ADP
ejpam-5704	425	6	weakly	weakly	ADJ
ejpam-5704	425	7	singular	singular	ADJ
ejpam-5704	425	8	integrals	integral	NOUN
ejpam-5704	425	9	and	and	CCONJ
ejpam-5704	425	10	their	their	PRON
ejpam-5704	425	11	application	application	NOUN
ejpam-5704	425	12	to	to	PART
ejpam-5704	425	13	fredholm	fredholm	VERB
ejpam-5704	425	14	integral	integral	ADJ
ejpam-5704	425	15	equations	equation	NOUN
ejpam-5704	425	16	of	of	ADP
ejpam-5704	425	17	second	second	ADJ
ejpam-5704	425	18	kind	kind	NOUN
ejpam-5704	425	19	.	.	PUNCT
ejpam-5704	426	1	mathematics	mathematic	NOUN
ejpam-5704	426	2	of	of	ADP
ejpam-5704	426	3	computation	computation	NOUN
ejpam-5704	426	4	,	,	PUNCT
ejpam-5704	426	5	62:739–753	62:739–753	PROPN
ejpam-5704	426	6	,	,	PUNCT
ejpam-5704	426	7	1994	1994	NUM
ejpam-5704	426	8	.	.	PUNCT
ejpam-5704	427	1	[	[	X
ejpam-5704	427	2	31	31	NUM
ejpam-5704	427	3	]	]	PUNCT
ejpam-5704	427	4	l.	l.	PROPN
ejpam-5704	427	5	tao	tao	PROPN
ejpam-5704	427	6	and	and	CCONJ
ejpam-5704	427	7	h.	h.	PROPN
ejpam-5704	427	8	yong	yong	PROPN
ejpam-5704	427	9	.	.	PUNCT
ejpam-5704	428	1	extrapolation	extrapolation	NOUN
ejpam-5704	428	2	method	method	NOUN
ejpam-5704	428	3	for	for	ADP
ejpam-5704	428	4	solving	solve	VERB
ejpam-5704	428	5	weakly	weakly	ADJ
ejpam-5704	428	6	singular	singular	ADJ
ejpam-5704	428	7	nonlinear	nonlinear	PROPN
ejpam-5704	428	8	volterra	volterra	PROPN
ejpam-5704	428	9	integral	integral	ADJ
ejpam-5704	428	10	equations	equation	NOUN
ejpam-5704	428	11	of	of	ADP
ejpam-5704	428	12	second	second	ADJ
ejpam-5704	428	13	kind	kind	NOUN
ejpam-5704	428	14	.	.	PUNCT
ejpam-5704	429	1	journal	journal	PROPN
ejpam-5704	429	2	of	of	ADP
ejpam-5704	429	3	mathematical	mathematical	ADJ
ejpam-5704	429	4	analysis	analysis	NOUN
ejpam-5704	429	5	and	and	CCONJ
ejpam-5704	429	6	b.	b.	PROPN
ejpam-5704	429	7	h.	h.	PROPN
ejpam-5704	429	8	alrikabi	alrikabi	PROPN
ejpam-5704	429	9	,	,	PUNCT
ejpam-5704	429	10	p.	p.	PROPN
ejpam-5704	429	11	darania	darania	PROPN
ejpam-5704	429	12	,	,	PUNCT
ejpam-5704	429	13	s.pishbin	s.pishbin	PROPN
ejpam-5704	429	14	/	/	SYM
ejpam-5704	429	15	eur	eur	PROPN
ejpam-5704	429	16	.	.	PUNCT
ejpam-5704	430	1	j.	j.	PROPN
ejpam-5704	430	2	pure	pure	PROPN
ejpam-5704	430	3	appl	appl	PROPN
ejpam-5704	430	4	.	.	PROPN
ejpam-5704	430	5	math	math	PROPN
ejpam-5704	430	6	,	,	PUNCT
ejpam-5704	430	7	18	18	NUM
ejpam-5704	430	8	(	(	PUNCT
ejpam-5704	430	9	2	2	NUM
ejpam-5704	430	10	)	)	PUNCT
ejpam-5704	430	11	(	(	PUNCT
ejpam-5704	430	12	2025	2025	NUM
ejpam-5704	430	13	)	)	PUNCT
ejpam-5704	430	14	,	,	PUNCT
ejpam-5704	430	15	5704	5704	NUM
ejpam-5704	430	16	19	19	NUM
ejpam-5704	430	17	of	of	ADP
ejpam-5704	430	18	19	19	NUM
ejpam-5704	430	19	applications	application	NOUN
ejpam-5704	430	20	,	,	PUNCT
ejpam-5704	430	21	324:225–237	324:225–237	NUM
ejpam-5704	430	22	,	,	PUNCT
ejpam-5704	430	23	2006	2006	NUM
ejpam-5704	430	24	.	.	PUNCT
ejpam-5704	431	1	[	[	X
ejpam-5704	431	2	32	32	NUM
ejpam-5704	431	3	]	]	X
ejpam-5704	431	4	a.p	a.p	PROPN
ejpam-5704	431	5	.	.	PROPN
ejpam-5704	431	6	orsi	orsi	PROPN
ejpam-5704	431	7	.	.	PUNCT
ejpam-5704	431	8	product	product	NOUN
ejpam-5704	431	9	integration	integration	NOUN
ejpam-5704	431	10	for	for	ADP
ejpam-5704	431	11	volterra	volterra	NOUN
ejpam-5704	431	12	integral	integral	ADJ
ejpam-5704	431	13	equations	equation	NOUN
ejpam-5704	431	14	of	of	ADP
ejpam-5704	431	15	the	the	DET
ejpam-5704	431	16	second	second	ADJ
ejpam-5704	431	17	kined	kine	VERB
ejpam-5704	431	18	with	with	ADP
ejpam-5704	431	19	weakly	weakly	ADJ
ejpam-5704	431	20	singular	singular	ADJ
ejpam-5704	431	21	kernels	kernel	NOUN
ejpam-5704	431	22	.	.	PUNCT
ejpam-5704	432	1	mathematics	mathematic	NOUN
ejpam-5704	432	2	of	of	ADP
ejpam-5704	432	3	computation	computation	NOUN
ejpam-5704	432	4	,	,	PUNCT
ejpam-5704	432	5	212:1201–1212	212:1201–1212	NUM
ejpam-5704	432	6	,	,	PUNCT
ejpam-5704	432	7	1996	1996	NUM
ejpam-5704	432	8	.	.	PUNCT
ejpam-5704	433	1	[	[	X
ejpam-5704	433	2	33	33	NUM
ejpam-5704	433	3	]	]	X
ejpam-5704	433	4	i.h	i.h	PROPN
ejpam-5704	433	5	.	.	PROPN
ejpam-5704	433	6	sloan	sloan	PROPN
ejpam-5704	433	7	.	.	PUNCT
ejpam-5704	434	1	analysis	analysis	NOUN
ejpam-5704	434	2	of	of	ADP
ejpam-5704	434	3	genral	genral	ADJ
ejpam-5704	434	4	quadrature	quadrature	NOUN
ejpam-5704	434	5	methods	method	NOUN
ejpam-5704	434	6	for	for	ADP
ejpam-5704	434	7	integral	integral	ADJ
ejpam-5704	434	8	equations	equation	NOUN
ejpam-5704	434	9	with	with	ADP
ejpam-5704	434	10	continuous	continuous	ADJ
ejpam-5704	434	11	or	or	CCONJ
ejpam-5704	434	12	discontinuous	discontinuous	ADJ
ejpam-5704	434	13	terms	term	NOUN
ejpam-5704	434	14	.	.	PUNCT
ejpam-5704	435	1	journal	journal	NOUN
ejpam-5704	435	2	of	of	ADP
ejpam-5704	435	3	the	the	DET
ejpam-5704	435	4	institute	institute	PROPN
ejpam-5704	435	5	of	of	ADP
ejpam-5704	435	6	mathematics	mathematics	PROPN
ejpam-5704	435	7	and	and	CCONJ
ejpam-5704	435	8	its	its	PRON
ejpam-5704	435	9	applications	application	NOUN
ejpam-5704	435	10	,	,	PUNCT
ejpam-5704	435	11	26:175–186	26:175–186	PROPN
ejpam-5704	435	12	,	,	PUNCT
ejpam-5704	435	13	1980	1980	NUM
ejpam-5704	435	14	.	.	PUNCT
ejpam-5704	436	1	[	[	X
ejpam-5704	436	2	34	34	NUM
ejpam-5704	436	3	]	]	X
ejpam-5704	436	4	v.i	v.i	PROPN
ejpam-5704	436	5	.	.	PROPN
ejpam-5704	436	6	krylov	krylov	PROPN
ejpam-5704	436	7	.	.	PUNCT
ejpam-5704	436	8	approximate	approximate	ADJ
ejpam-5704	436	9	calculation	calculation	NOUN
ejpam-5704	436	10	of	of	ADP
ejpam-5704	436	11	integrals	integral	NOUN
ejpam-5704	436	12	.	.	PUNCT
ejpam-5704	437	1	macmillan	macmillan	PROPN
ejpam-5704	437	2	company	company	PROPN
ejpam-5704	437	3	,	,	PUNCT
ejpam-5704	437	4	new	new	PROPN
ejpam-5704	437	5	york	york	PROPN
ejpam-5704	437	6	,	,	PUNCT
ejpam-5704	437	7	1962	1962	NUM
ejpam-5704	437	8	.	.	PUNCT
ejpam-5704	438	1	[	[	X
ejpam-5704	438	2	35	35	NUM
ejpam-5704	438	3	]	]	X
ejpam-5704	438	4	p.k	p.k	PROPN
ejpam-5704	438	5	.	.	PUNCT
ejpam-5704	439	1	kythe	kythe	PROPN
ejpam-5704	439	2	and	and	CCONJ
ejpam-5704	439	3	p.	p.	PROPN
ejpam-5704	439	4	puri	puri	PROPN
ejpam-5704	439	5	.	.	PUNCT
ejpam-5704	440	1	computational	computational	ADJ
ejpam-5704	440	2	methods	method	NOUN
ejpam-5704	440	3	for	for	ADP
ejpam-5704	440	4	linear	linear	ADJ
ejpam-5704	440	5	integral	integral	ADJ
ejpam-5704	440	6	equations	equation	NOUN
ejpam-5704	440	7	.	.	PUNCT
ejpam-5704	441	1	birkhuser	birkhuser	NOUN
ejpam-5704	441	2	,	,	PUNCT
ejpam-5704	441	3	boston	boston	PROPN
ejpam-5704	441	4	,	,	PUNCT
ejpam-5704	441	5	2002	2002	NUM
ejpam-5704	441	6	.	.	PUNCT