id	sid	tid	token	lemma	pos
ejpam-304	1	1	10_304_abdulwaki.dvi	10_304_abdulwaki.dvi	NUM
ejpam-304	1	2	european	european	ADJ
ejpam-304	1	3	journal	journal	PROPN
ejpam-304	1	4	of	of	ADP
ejpam-304	1	5	pure	pure	ADJ
ejpam-304	1	6	and	and	CCONJ
ejpam-304	1	7	applied	apply	VERB
ejpam-304	1	8	mathematics	mathematic	NOUN
ejpam-304	1	9	vol	vol	NOUN
ejpam-304	1	10	.	.	PROPN
ejpam-304	1	11	2	2	NUM
ejpam-304	1	12	,	,	PUNCT
ejpam-304	1	13	no	no	INTJ
ejpam-304	1	14	.	.	NOUN
ejpam-304	1	15	3	3	NUM
ejpam-304	1	16	,	,	PUNCT
ejpam-304	1	17	2009	2009	NUM
ejpam-304	1	18	,	,	PUNCT
ejpam-304	1	19	(	(	PUNCT
ejpam-304	1	20	462	462	NUM
ejpam-304	1	21	-	-	NOUN
ejpam-304	1	22	472	472	NUM
ejpam-304	1	23	)	)	PUNCT
ejpam-304	1	24	issn	issn	PROPN
ejpam-304	1	25	1307	1307	NUM
ejpam-304	1	26	-	-	SYM
ejpam-304	1	27	5543	5543	NUM
ejpam-304	1	28	–	–	PUNCT
ejpam-304	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-304	1	30	on	on	ADP
ejpam-304	1	31	the	the	DET
ejpam-304	1	32	semi	semi	ADJ
ejpam-304	1	33	-	-	ADJ
ejpam-304	1	34	bounded	bounded	ADJ
ejpam-304	1	35	solution	solution	NOUN
ejpam-304	1	36	of	of	ADP
ejpam-304	1	37	cauchy	cauchy	PROPN
ejpam-304	1	38	type	type	NOUN
ejpam-304	1	39	singular	singular	ADJ
ejpam-304	1	40	integral	integral	ADJ
ejpam-304	1	41	equations	equation	NOUN
ejpam-304	1	42	of	of	ADP
ejpam-304	1	43	the	the	DET
ejpam-304	1	44	first	first	ADJ
ejpam-304	1	45	kind	kind	NOUN
ejpam-304	1	46	m.	m.	PROPN
ejpam-304	1	47	abdulkawi∗	abdulkawi∗	PROPN
ejpam-304	1	48	,	,	PUNCT
ejpam-304	1	49	z.	z.	PROPN
ejpam-304	1	50	k.	k.	PROPN
ejpam-304	1	51	eshkuvatov	eshkuvatov	PROPN
ejpam-304	1	52	,	,	PUNCT
ejpam-304	1	53	and	and	CCONJ
ejpam-304	1	54	n.	n.	PROPN
ejpam-304	1	55	m.	m.	PROPN
ejpam-304	1	56	a.	a.	PROPN
ejpam-304	1	57	nik	nik	PROPN
ejpam-304	1	58	long	long	PROPN
ejpam-304	1	59	department	department	PROPN
ejpam-304	1	60	of	of	ADP
ejpam-304	1	61	mathematics	mathematic	NOUN
ejpam-304	1	62	,	,	PUNCT
ejpam-304	1	63	faculty	faculty	NOUN
ejpam-304	1	64	of	of	ADP
ejpam-304	1	65	science	science	NOUN
ejpam-304	1	66	,	,	PUNCT
ejpam-304	1	67	university	university	NOUN
ejpam-304	1	68	putra	putra	PROPN
ejpam-304	1	69	malaysia	malaysia	PROPN
ejpam-304	1	70	,	,	PUNCT
ejpam-304	1	71	43400	43400	NUM
ejpam-304	1	72	serdang	serdang	PROPN
ejpam-304	1	73	,	,	PUNCT
ejpam-304	1	74	selangor	selangor	PROPN
ejpam-304	1	75	,	,	PUNCT
ejpam-304	1	76	malaysia	malaysia	PROPN
ejpam-304	1	77	abstract	abstract	NOUN
ejpam-304	1	78	.	.	PUNCT
ejpam-304	2	1	this	this	DET
ejpam-304	2	2	paper	paper	NOUN
ejpam-304	2	3	presents	present	VERB
ejpam-304	2	4	an	an	DET
ejpam-304	2	5	efficient	efficient	ADJ
ejpam-304	2	6	approximate	approximate	ADJ
ejpam-304	2	7	method	method	NOUN
ejpam-304	2	8	to	to	PART
ejpam-304	2	9	obtain	obtain	VERB
ejpam-304	2	10	a	a	DET
ejpam-304	2	11	numerical	numerical	ADJ
ejpam-304	2	12	solution	solution	NOUN
ejpam-304	2	13	,	,	PUNCT
ejpam-304	2	14	which	which	PRON
ejpam-304	2	15	is	be	AUX
ejpam-304	2	16	bounded	bound	VERB
ejpam-304	2	17	at	at	ADP
ejpam-304	2	18	the	the	DET
ejpam-304	2	19	end	end	NOUN
ejpam-304	2	20	point	point	NOUN
ejpam-304	2	21	x	x	X
ejpam-304	2	22	=	=	SYM
ejpam-304	2	23	−1	−1	NOUN
ejpam-304	2	24	,	,	PUNCT
ejpam-304	2	25	for	for	ADP
ejpam-304	2	26	cauchy	cauchy	ADJ
ejpam-304	2	27	type	type	NOUN
ejpam-304	2	28	singular	singular	ADJ
ejpam-304	2	29	integral	integral	ADJ
ejpam-304	2	30	equations	equation	NOUN
ejpam-304	2	31	of	of	ADP
ejpam-304	2	32	the	the	DET
ejpam-304	2	33	first	first	ADJ
ejpam-304	2	34	kind	kind	NOUN
ejpam-304	2	35	on	on	ADP
ejpam-304	2	36	the	the	DET
ejpam-304	2	37	interval	interval	NOUN
ejpam-304	2	38	[	[	X
ejpam-304	2	39	−1,1	−1,1	X
ejpam-304	2	40	]	]	X
ejpam-304	2	41	.	.	PUNCT
ejpam-304	3	1	the	the	DET
ejpam-304	3	2	solution	solution	NOUN
ejpam-304	3	3	is	be	AUX
ejpam-304	3	4	derived	derive	VERB
ejpam-304	3	5	by	by	ADP
ejpam-304	3	6	approximating	approximate	VERB
ejpam-304	3	7	the	the	DET
ejpam-304	3	8	unknown	unknown	ADJ
ejpam-304	3	9	density	density	NOUN
ejpam-304	3	10	function	function	NOUN
ejpam-304	3	11	using	use	VERB
ejpam-304	3	12	the	the	DET
ejpam-304	3	13	weighted	weight	VERB
ejpam-304	3	14	chebyshev	chebyshev	NOUN
ejpam-304	3	15	polynomials	polynomial	NOUN
ejpam-304	3	16	of	of	ADP
ejpam-304	3	17	the	the	DET
ejpam-304	3	18	third	third	ADJ
ejpam-304	3	19	kind	kind	NOUN
ejpam-304	3	20	,	,	PUNCT
ejpam-304	3	21	and	and	CCONJ
ejpam-304	3	22	then	then	ADV
ejpam-304	3	23	computing	compute	VERB
ejpam-304	3	24	the	the	DET
ejpam-304	3	25	cauchy	cauchy	ADJ
ejpam-304	3	26	singular	singular	PROPN
ejpam-304	3	27	integral	integral	ADJ
ejpam-304	3	28	which	which	PRON
ejpam-304	3	29	is	be	AUX
ejpam-304	3	30	obtained	obtain	VERB
ejpam-304	3	31	analytically	analytically	ADV
ejpam-304	3	32	.	.	PUNCT
ejpam-304	4	1	the	the	DET
ejpam-304	4	2	known	know	VERB
ejpam-304	4	3	force	force	NOUN
ejpam-304	4	4	function	function	NOUN
ejpam-304	4	5	is	be	AUX
ejpam-304	4	6	interpolated	interpolate	VERB
ejpam-304	4	7	using	use	VERB
ejpam-304	4	8	the	the	DET
ejpam-304	4	9	chebyshev	chebyshev	NOUN
ejpam-304	4	10	polynomials	polynomial	NOUN
ejpam-304	4	11	of	of	ADP
ejpam-304	4	12	the	the	DET
ejpam-304	4	13	fourth	fourth	ADJ
ejpam-304	4	14	kind	kind	NOUN
ejpam-304	4	15	.	.	PUNCT
ejpam-304	5	1	the	the	DET
ejpam-304	5	2	exactness	exactness	NOUN
ejpam-304	5	3	of	of	ADP
ejpam-304	5	4	this	this	DET
ejpam-304	5	5	approximate	approximate	ADJ
ejpam-304	5	6	method	method	NOUN
ejpam-304	5	7	is	be	AUX
ejpam-304	5	8	shown	show	VERB
ejpam-304	5	9	for	for	ADP
ejpam-304	5	10	characteristic	characteristic	ADJ
ejpam-304	5	11	equation	equation	NOUN
ejpam-304	5	12	when	when	SCONJ
ejpam-304	5	13	the	the	DET
ejpam-304	5	14	force	force	NOUN
ejpam-304	5	15	function	function	NOUN
ejpam-304	5	16	is	be	AUX
ejpam-304	5	17	a	a	DET
ejpam-304	5	18	cubic	cubic	ADJ
ejpam-304	5	19	.	.	PUNCT
ejpam-304	6	1	particular	particular	ADJ
ejpam-304	6	2	result	result	NOUN
ejpam-304	6	3	is	be	AUX
ejpam-304	6	4	also	also	ADV
ejpam-304	6	5	given	give	VERB
ejpam-304	6	6	to	to	PART
ejpam-304	6	7	show	show	VERB
ejpam-304	6	8	the	the	DET
ejpam-304	6	9	exactness	exactness	NOUN
ejpam-304	6	10	of	of	ADP
ejpam-304	6	11	this	this	DET
ejpam-304	6	12	method	method	NOUN
ejpam-304	6	13	.	.	PUNCT
ejpam-304	7	1	2000	2000	NUM
ejpam-304	7	2	mathematics	mathematic	NOUN
ejpam-304	7	3	subject	subject	NOUN
ejpam-304	7	4	classifications	classification	NOUN
ejpam-304	7	5	:	:	PUNCT
ejpam-304	7	6	65r20	65r20	NUM
ejpam-304	7	7	,	,	PUNCT
ejpam-304	7	8	45e05	45e05	NUM
ejpam-304	7	9	key	key	ADJ
ejpam-304	7	10	words	word	NOUN
ejpam-304	7	11	and	and	CCONJ
ejpam-304	7	12	phrases	phrase	NOUN
ejpam-304	7	13	:	:	PUNCT
ejpam-304	7	14	integral	integral	ADJ
ejpam-304	7	15	equations	equation	NOUN
ejpam-304	7	16	,	,	PUNCT
ejpam-304	7	17	cauchy	cauchy	ADJ
ejpam-304	7	18	singular	singular	ADJ
ejpam-304	7	19	kernel	kernel	PROPN
ejpam-304	7	20	,	,	PUNCT
ejpam-304	7	21	chebyshev	chebyshev	NOUN
ejpam-304	7	22	polynomials	polynomial	NOUN
ejpam-304	7	23	,	,	PUNCT
ejpam-304	7	24	approximation	approximation	NOUN
ejpam-304	7	25	.	.	PUNCT
ejpam-304	8	1	∗corresponding	∗corresponde	VERB
ejpam-304	8	2	author	author	NOUN
ejpam-304	8	3	.	.	PUNCT
ejpam-304	9	1	email	email	NOUN
ejpam-304	9	2	address	address	NOUN
ejpam-304	9	3	:	:	PUNCT
ejpam-304	9	4	akawi�math.upm.edu.my	akawi�math.upm.edu.my	PROPN
ejpam-304	9	5	(	(	PUNCT
ejpam-304	9	6	m.	m.	NOUN
ejpam-304	9	7	abdulkawi	abdulkawi	PROPN
ejpam-304	9	8	)	)	PUNCT
ejpam-304	9	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-304	10	1	462	462	NUM
ejpam-304	11	1	c	c	X
ejpam-304	11	2	©	©	PROPN
ejpam-304	11	3	2009	2009	NUM
ejpam-304	11	4	ejpam	ejpam	NOUN
ejpam-304	11	5	all	all	DET
ejpam-304	11	6	rights	right	NOUN
ejpam-304	11	7	reserved	reserve	VERB
ejpam-304	11	8	.	.	PUNCT
ejpam-304	12	1	m.	m.	NOUN
ejpam-304	12	2	abdulkawi	abdulkawi	PROPN
ejpam-304	12	3	,	,	PUNCT
ejpam-304	12	4	z.	z.	PROPN
ejpam-304	12	5	eshkuvatov	eshkuvatov	PROPN
ejpam-304	12	6	,	,	PUNCT
ejpam-304	12	7	and	and	CCONJ
ejpam-304	12	8	n.	n.	NOUN
ejpam-304	12	9	nik	nik	PROPN
ejpam-304	12	10	long	long	ADJ
ejpam-304	12	11	/	/	SYM
ejpam-304	12	12	eur	eur	PROPN
ejpam-304	12	13	.	.	PUNCT
ejpam-304	13	1	j.	j.	PROPN
ejpam-304	13	2	pure	pure	PROPN
ejpam-304	13	3	appl	appl	PROPN
ejpam-304	13	4	.	.	PROPN
ejpam-304	13	5	math	math	PROPN
ejpam-304	13	6	,	,	PUNCT
ejpam-304	13	7	2	2	NUM
ejpam-304	13	8	(	(	PUNCT
ejpam-304	13	9	2009	2009	NUM
ejpam-304	13	10	)	)	PUNCT
ejpam-304	13	11	,	,	PUNCT
ejpam-304	13	12	(	(	PUNCT
ejpam-304	13	13	462	462	NUM
ejpam-304	13	14	-	-	NOUN
ejpam-304	13	15	472	472	NUM
ejpam-304	13	16	)	)	PUNCT
ejpam-304	13	17	463	463	NUM
ejpam-304	13	18	1	1	NUM
ejpam-304	13	19	.	.	PUNCT
ejpam-304	14	1	introduction	introduction	NOUN
ejpam-304	14	2	let	let	VERB
ejpam-304	14	3	us	we	PRON
ejpam-304	14	4	consider	consider	VERB
ejpam-304	14	5	the	the	DET
ejpam-304	14	6	cauchy	cauchy	ADJ
ejpam-304	14	7	type	type	NOUN
ejpam-304	14	8	singular	singular	ADJ
ejpam-304	14	9	integral	integral	ADJ
ejpam-304	14	10	equations	equation	NOUN
ejpam-304	14	11	of	of	ADP
ejpam-304	14	12	the	the	DET
ejpam-304	14	13	first	first	ADJ
ejpam-304	14	14	kind	kind	NOUN
ejpam-304	14	15	∫	∫	PROPN
ejpam-304	14	16	1	1	NUM
ejpam-304	14	17	−1	−1	NOUN
ejpam-304	14	18	ϕ(t	ϕ(t	NUM
ejpam-304	14	19	)	)	PUNCT
ejpam-304	15	1	t	t	NOUN
ejpam-304	15	2	−	−	NOUN
ejpam-304	16	1	x	x	SYM
ejpam-304	16	2	d	d	X
ejpam-304	16	3	t	t	PROPN
ejpam-304	16	4	+	+	CCONJ
ejpam-304	16	5	∫	∫	PROPN
ejpam-304	16	6	1	1	NUM
ejpam-304	16	7	−1	−1	NOUN
ejpam-304	16	8	k(x	k(x	PROPN
ejpam-304	16	9	,	,	PUNCT
ejpam-304	16	10	t)ϕ(t	t)ϕ(t	NOUN
ejpam-304	16	11	)	)	PUNCT
ejpam-304	16	12	d	d	NOUN
ejpam-304	16	13	t	t	NOUN
ejpam-304	16	14	=	=	SYM
ejpam-304	16	15	f	f	PROPN
ejpam-304	16	16	(	(	PUNCT
ejpam-304	16	17	x	x	NOUN
ejpam-304	16	18	)	)	PUNCT
ejpam-304	16	19	,	,	PUNCT
ejpam-304	16	20	−1	−1	NOUN
ejpam-304	16	21	<	<	X
ejpam-304	16	22	x	x	X
ejpam-304	16	23	<	<	X
ejpam-304	16	24	1	1	NUM
ejpam-304	16	25	,	,	PUNCT
ejpam-304	16	26	(	(	PUNCT
ejpam-304	16	27	1.1	1.1	NUM
ejpam-304	16	28	)	)	PUNCT
ejpam-304	16	29	where	where	SCONJ
ejpam-304	16	30	k	k	PROPN
ejpam-304	16	31	and	and	CCONJ
ejpam-304	16	32	f	f	PROPN
ejpam-304	16	33	are	be	AUX
ejpam-304	16	34	assumed	assume	VERB
ejpam-304	16	35	to	to	PART
ejpam-304	16	36	be	be	AUX
ejpam-304	16	37	real	real	ADV
ejpam-304	16	38	-	-	PUNCT
ejpam-304	16	39	valued	value	VERB
ejpam-304	16	40	functions	function	NOUN
ejpam-304	16	41	belong	belong	VERB
ejpam-304	16	42	to	to	ADP
ejpam-304	16	43	the	the	DET
ejpam-304	16	44	class	class	NOUN
ejpam-304	16	45	of	of	ADP
ejpam-304	16	46	hölder	hölder	NOUN
ejpam-304	16	47	continues	continue	VERB
ejpam-304	16	48	functions	function	NOUN
ejpam-304	16	49	on	on	ADP
ejpam-304	16	50	the	the	DET
ejpam-304	16	51	sets	set	NOUN
ejpam-304	16	52	[	[	X
ejpam-304	16	53	−1	−1	NOUN
ejpam-304	16	54	,	,	PUNCT
ejpam-304	16	55	1]×	1]×	NUM
ejpam-304	16	56	[	[	X
ejpam-304	16	57	−1	−1	NOUN
ejpam-304	16	58	,	,	PUNCT
ejpam-304	16	59	1	1	NUM
ejpam-304	16	60	]	]	PUNCT
ejpam-304	16	61	and	and	CCONJ
ejpam-304	16	62	[	[	X
ejpam-304	16	63	−1	−1	NOUN
ejpam-304	16	64	,	,	PUNCT
ejpam-304	16	65	1	1	NUM
ejpam-304	16	66	]	]	PUNCT
ejpam-304	16	67	,	,	PUNCT
ejpam-304	16	68	respectively	respectively	ADV
ejpam-304	16	69	.	.	PUNCT
ejpam-304	17	1	ϕ	ϕ	PROPN
ejpam-304	17	2	is	be	AUX
ejpam-304	17	3	unknown	unknown	ADJ
ejpam-304	17	4	function	function	NOUN
ejpam-304	17	5	to	to	PART
ejpam-304	17	6	be	be	AUX
ejpam-304	17	7	determined	determine	VERB
ejpam-304	17	8	.	.	PUNCT
ejpam-304	18	1	the	the	DET
ejpam-304	18	2	singular	singular	ADJ
ejpam-304	18	3	integral	integral	ADJ
ejpam-304	18	4	equations	equation	NOUN
ejpam-304	18	5	have	have	AUX
ejpam-304	18	6	been	be	AUX
ejpam-304	18	7	widely	widely	ADV
ejpam-304	18	8	used	use	VERB
ejpam-304	18	9	[	[	X
ejpam-304	18	10	1–4	1–4	NOUN
ejpam-304	18	11	]	]	X
ejpam-304	18	12	in	in	ADP
ejpam-304	18	13	solving	solve	VERB
ejpam-304	18	14	problems	problem	NOUN
ejpam-304	18	15	associated	associate	VERB
ejpam-304	18	16	with	with	ADP
ejpam-304	18	17	aerodynamic	aerodynamic	ADJ
ejpam-304	18	18	,	,	PUNCT
ejpam-304	18	19	hydrodynamic	hydrodynamic	ADJ
ejpam-304	18	20	and	and	CCONJ
ejpam-304	18	21	elasticity	elasticity	NOUN
ejpam-304	18	22	.	.	PUNCT
ejpam-304	19	1	the	the	DET
ejpam-304	19	2	characteristic	characteristic	ADJ
ejpam-304	19	3	singular	singular	ADJ
ejpam-304	19	4	integral	integral	ADJ
ejpam-304	19	5	equation	equation	NOUN
ejpam-304	19	6	of	of	ADP
ejpam-304	19	7	equation	equation	NOUN
ejpam-304	19	8	(	(	PUNCT
ejpam-304	19	9	1.1	1.1	NUM
ejpam-304	19	10	)	)	PUNCT
ejpam-304	19	11	is	be	AUX
ejpam-304	19	12	of	of	ADP
ejpam-304	19	13	the	the	DET
ejpam-304	19	14	form	form	NOUN
ejpam-304	19	15	∫	∫	PROPN
ejpam-304	19	16	1	1	NUM
ejpam-304	19	17	−1	−1	NOUN
ejpam-304	19	18	ϕ(t	ϕ(t	NUM
ejpam-304	19	19	)	)	PUNCT
ejpam-304	20	1	t	t	NOUN
ejpam-304	20	2	−	−	NOUN
ejpam-304	21	1	x	x	SYM
ejpam-304	21	2	d	d	X
ejpam-304	21	3	t	t	PROPN
ejpam-304	21	4	=	=	SYM
ejpam-304	21	5	f	f	PROPN
ejpam-304	21	6	(	(	PUNCT
ejpam-304	21	7	x	x	NOUN
ejpam-304	21	8	)	)	PUNCT
ejpam-304	21	9	,	,	PUNCT
ejpam-304	21	10	−1	−1	NOUN
ejpam-304	21	11	<	<	X
ejpam-304	21	12	x	x	X
ejpam-304	21	13	<	<	X
ejpam-304	21	14	1	1	NUM
ejpam-304	21	15	.	.	PUNCT
ejpam-304	21	16	(	(	PUNCT
ejpam-304	21	17	1.2	1.2	NUM
ejpam-304	21	18	)	)	PUNCT
ejpam-304	21	19	eshkovatov	eshkovatov	NOUN
ejpam-304	21	20	et	et	PROPN
ejpam-304	21	21	al	al	PROPN
ejpam-304	21	22	.	.	PUNCT
ejpam-304	22	1	[	[	X
ejpam-304	22	2	5	5	NUM
ejpam-304	22	3	]	]	PUNCT
ejpam-304	22	4	discussed	discuss	VERB
ejpam-304	22	5	the	the	DET
ejpam-304	22	6	efficient	efficient	ADJ
ejpam-304	22	7	approximate	approximate	ADJ
ejpam-304	22	8	method	method	NOUN
ejpam-304	22	9	to	to	PART
ejpam-304	22	10	solve	solve	VERB
ejpam-304	22	11	characteristic	characteristic	ADJ
ejpam-304	22	12	equation	equation	NOUN
ejpam-304	22	13	(	(	PUNCT
ejpam-304	22	14	1.2	1.2	NUM
ejpam-304	22	15	)	)	PUNCT
ejpam-304	22	16	using	use	VERB
ejpam-304	22	17	chebyshev	chebyshev	NOUN
ejpam-304	22	18	polynomial	polynomial	ADJ
ejpam-304	22	19	approximations	approximation	NOUN
ejpam-304	22	20	of	of	ADP
ejpam-304	22	21	the	the	DET
ejpam-304	22	22	first	first	ADJ
ejpam-304	22	23	,	,	PUNCT
ejpam-304	22	24	second	second	ADJ
ejpam-304	22	25	,	,	PUNCT
ejpam-304	22	26	third	third	ADJ
ejpam-304	22	27	,	,	PUNCT
ejpam-304	22	28	and	and	CCONJ
ejpam-304	22	29	fourth	fourth	ADJ
ejpam-304	22	30	kinds	kind	NOUN
ejpam-304	22	31	with	with	ADP
ejpam-304	22	32	corresponding	correspond	VERB
ejpam-304	22	33	weight	weight	NOUN
ejpam-304	22	34	functions	function	NOUN
ejpam-304	22	35	for	for	ADP
ejpam-304	22	36	four	four	NUM
ejpam-304	22	37	cases	case	NOUN
ejpam-304	22	38	.	.	PUNCT
ejpam-304	23	1	the	the	DET
ejpam-304	23	2	collocation	collocation	NOUN
ejpam-304	23	3	points	point	NOUN
ejpam-304	23	4	are	be	AUX
ejpam-304	23	5	chosen	choose	VERB
ejpam-304	23	6	to	to	PART
ejpam-304	23	7	be	be	AUX
ejpam-304	23	8	the	the	DET
ejpam-304	23	9	zeros	zero	NOUN
ejpam-304	23	10	of	of	ADP
ejpam-304	23	11	chebyshev	chebyshev	NOUN
ejpam-304	23	12	polynomials	polynomial	NOUN
ejpam-304	23	13	.	.	PUNCT
ejpam-304	24	1	they	they	PRON
ejpam-304	24	2	showed	show	VERB
ejpam-304	24	3	that	that	SCONJ
ejpam-304	24	4	,	,	PUNCT
ejpam-304	24	5	the	the	DET
ejpam-304	24	6	approximate	approximate	ADJ
ejpam-304	24	7	method	method	NOUN
ejpam-304	24	8	gives	give	VERB
ejpam-304	24	9	exact	exact	ADJ
ejpam-304	24	10	solution	solution	NOUN
ejpam-304	24	11	when	when	SCONJ
ejpam-304	24	12	the	the	DET
ejpam-304	24	13	force	force	NOUN
ejpam-304	24	14	function	function	VERB
ejpam-304	24	15	f	f	PROPN
ejpam-304	24	16	is	be	AUX
ejpam-304	24	17	a	a	DET
ejpam-304	24	18	linear	linear	NOUN
ejpam-304	24	19	.	.	PUNCT
ejpam-304	25	1	abdulkawi	abdulkawi	PROPN
ejpam-304	25	2	et	et	PROPN
ejpam-304	25	3	al	al	PROPN
ejpam-304	25	4	.	.	PUNCT
ejpam-304	26	1	[	[	X
ejpam-304	26	2	6	6	NUM
ejpam-304	26	3	]	]	PUNCT
ejpam-304	26	4	presented	present	VERB
ejpam-304	26	5	a	a	DET
ejpam-304	26	6	numerical	numerical	ADJ
ejpam-304	26	7	solution	solution	NOUN
ejpam-304	26	8	of	of	ADP
ejpam-304	26	9	equation	equation	NOUN
ejpam-304	26	10	(	(	PUNCT
ejpam-304	26	11	1.1	1.1	NUM
ejpam-304	26	12	)	)	PUNCT
ejpam-304	26	13	,	,	PUNCT
ejpam-304	26	14	which	which	PRON
ejpam-304	26	15	is	be	AUX
ejpam-304	26	16	bounded	bound	VERB
ejpam-304	26	17	at	at	ADP
ejpam-304	26	18	the	the	DET
ejpam-304	26	19	end	end	NOUN
ejpam-304	26	20	points	point	NOUN
ejpam-304	26	21	x	x	SYM
ejpam-304	26	22	±	±	NUM
ejpam-304	26	23	1	1	NUM
ejpam-304	26	24	.	.	PUNCT
ejpam-304	27	1	they	they	PRON
ejpam-304	27	2	used	use	VERB
ejpam-304	27	3	chebyshev	chebyshev	NOUN
ejpam-304	27	4	polynomials	polynomial	NOUN
ejpam-304	27	5	of	of	ADP
ejpam-304	27	6	the	the	DET
ejpam-304	27	7	second	second	ADJ
ejpam-304	27	8	kind	kind	NOUN
ejpam-304	27	9	with	with	ADP
ejpam-304	27	10	the	the	DET
ejpam-304	27	11	corresponding	corresponding	ADJ
ejpam-304	27	12	weight	weight	NOUN
ejpam-304	27	13	function	function	NOUN
ejpam-304	27	14	to	to	PART
ejpam-304	27	15	approximate	approximate	VERB
ejpam-304	27	16	the	the	DET
ejpam-304	27	17	density	density	NOUN
ejpam-304	27	18	function	function	NOUN
ejpam-304	27	19	and	and	CCONJ
ejpam-304	27	20	the	the	DET
ejpam-304	27	21	chebyshev	chebyshev	NOUN
ejpam-304	27	22	polynomials	polynomial	NOUN
ejpam-304	27	23	of	of	ADP
ejpam-304	27	24	the	the	DET
ejpam-304	27	25	first	first	ADJ
ejpam-304	27	26	kind	kind	NOUN
ejpam-304	27	27	to	to	PART
ejpam-304	27	28	approximate	approximate	VERB
ejpam-304	27	29	the	the	DET
ejpam-304	27	30	force	force	NOUN
ejpam-304	27	31	function	function	NOUN
ejpam-304	27	32	.	.	PUNCT
ejpam-304	28	1	they	they	PRON
ejpam-304	28	2	showed	show	VERB
ejpam-304	28	3	that	that	SCONJ
ejpam-304	28	4	the	the	DET
ejpam-304	28	5	numerical	numerical	ADJ
ejpam-304	28	6	solution	solution	NOUN
ejpam-304	28	7	of	of	ADP
ejpam-304	28	8	characteristic	characteristic	ADJ
ejpam-304	28	9	equation	equation	NOUN
ejpam-304	28	10	is	be	AUX
ejpam-304	28	11	identical	identical	ADJ
ejpam-304	28	12	to	to	ADP
ejpam-304	28	13	the	the	DET
ejpam-304	28	14	exact	exact	ADJ
ejpam-304	28	15	solution	solution	NOUN
ejpam-304	28	16	when	when	SCONJ
ejpam-304	28	17	the	the	DET
ejpam-304	28	18	force	force	NOUN
ejpam-304	28	19	function	function	NOUN
ejpam-304	28	20	is	be	AUX
ejpam-304	28	21	a	a	DET
ejpam-304	28	22	cubic	cubic	NOUN
ejpam-304	28	23	.	.	PUNCT
ejpam-304	29	1	it	it	PRON
ejpam-304	29	2	is	be	AUX
ejpam-304	29	3	well	well	ADV
ejpam-304	29	4	known	know	VERB
ejpam-304	29	5	that	that	SCONJ
ejpam-304	29	6	the	the	DET
ejpam-304	29	7	analytical	analytical	ADJ
ejpam-304	29	8	solution	solution	NOUN
ejpam-304	29	9	of	of	ADP
ejpam-304	29	10	characteristic	characteristic	ADJ
ejpam-304	29	11	equation	equation	NOUN
ejpam-304	29	12	(	(	PUNCT
ejpam-304	29	13	1.2	1.2	NUM
ejpam-304	29	14	)	)	PUNCT
ejpam-304	29	15	,	,	PUNCT
ejpam-304	29	16	which	which	DET
ejpam-304	29	17	m.	m.	NOUN
ejpam-304	29	18	abdulkawi	abdulkawi	PROPN
ejpam-304	29	19	,	,	PUNCT
ejpam-304	29	20	z.	z.	PROPN
ejpam-304	29	21	eshkuvatov	eshkuvatov	PROPN
ejpam-304	29	22	,	,	PUNCT
ejpam-304	29	23	and	and	CCONJ
ejpam-304	29	24	n.	n.	NOUN
ejpam-304	29	25	nik	nik	PROPN
ejpam-304	29	26	long	long	ADJ
ejpam-304	29	27	/	/	SYM
ejpam-304	29	28	eur	eur	PROPN
ejpam-304	29	29	.	.	PUNCT
ejpam-304	30	1	j.	j.	PROPN
ejpam-304	30	2	pure	pure	PROPN
ejpam-304	30	3	appl	appl	PROPN
ejpam-304	30	4	.	.	PROPN
ejpam-304	30	5	math	math	PROPN
ejpam-304	30	6	,	,	PUNCT
ejpam-304	30	7	2	2	NUM
ejpam-304	30	8	(	(	PUNCT
ejpam-304	30	9	2009	2009	NUM
ejpam-304	30	10	)	)	PUNCT
ejpam-304	30	11	,	,	PUNCT
ejpam-304	30	12	(	(	PUNCT
ejpam-304	30	13	462	462	NUM
ejpam-304	30	14	-	-	NOUN
ejpam-304	30	15	472	472	NUM
ejpam-304	30	16	)	)	PUNCT
ejpam-304	30	17	464	464	NUM
ejpam-304	30	18	is	be	AUX
ejpam-304	30	19	bounded	bound	VERB
ejpam-304	30	20	at	at	ADP
ejpam-304	30	21	the	the	DET
ejpam-304	30	22	end	end	NOUN
ejpam-304	30	23	point	point	NOUN
ejpam-304	30	24	x	x	PUNCT
ejpam-304	31	1	=	=	SYM
ejpam-304	31	2	−1	−1	NOUN
ejpam-304	31	3	,	,	PUNCT
ejpam-304	31	4	is	be	AUX
ejpam-304	31	5	given	give	VERB
ejpam-304	31	6	by	by	ADP
ejpam-304	31	7	the	the	DET
ejpam-304	31	8	following	follow	VERB
ejpam-304	31	9	formula	formula	NOUN
ejpam-304	31	10	ϕ(x	ϕ(x	X
ejpam-304	31	11	)	)	PUNCT
ejpam-304	31	12	=	=	SYM
ejpam-304	32	1	−	−	PROPN
ejpam-304	32	2	1	1	NUM
ejpam-304	32	3	π2	π2	NOUN
ejpam-304	32	4	r	r	NOUN
ejpam-304	32	5	1	1	NUM
ejpam-304	32	6	+	+	NOUN
ejpam-304	32	7	x	x	SYM
ejpam-304	32	8	1−	1−	NUM
ejpam-304	32	9	x	x	SYM
ejpam-304	32	10	∫	∫	PROPN
ejpam-304	32	11	1	1	NUM
ejpam-304	32	12	−1	−1	NOUN
ejpam-304	32	13	r	r	NOUN
ejpam-304	32	14	1−	1−	NUM
ejpam-304	32	15	t	t	NOUN
ejpam-304	32	16	1	1	NUM
ejpam-304	32	17	+	+	NUM
ejpam-304	32	18	t	t	X
ejpam-304	32	19	f	f	X
ejpam-304	32	20	(	(	PUNCT
ejpam-304	32	21	t	t	PROPN
ejpam-304	32	22	)	)	PUNCT
ejpam-304	32	23	t	t	NOUN
ejpam-304	32	24	−	−	NOUN
ejpam-304	33	1	x	x	SYM
ejpam-304	33	2	d	d	X
ejpam-304	33	3	t	t	PROPN
ejpam-304	33	4	.	.	PUNCT
ejpam-304	34	1	(	(	PUNCT
ejpam-304	34	2	1.3	1.3	NUM
ejpam-304	34	3	)	)	PUNCT
ejpam-304	34	4	by	by	ADP
ejpam-304	34	5	solving	solve	VERB
ejpam-304	34	6	equation	equation	NOUN
ejpam-304	34	7	(	(	PUNCT
ejpam-304	34	8	1.1	1.1	NUM
ejpam-304	34	9	)	)	PUNCT
ejpam-304	34	10	with	with	ADP
ejpam-304	34	11	respect	respect	NOUN
ejpam-304	34	12	to	to	ADP
ejpam-304	34	13	its	its	PRON
ejpam-304	34	14	characteristic	characteristic	ADJ
ejpam-304	34	15	part	part	NOUN
ejpam-304	34	16	,	,	PUNCT
ejpam-304	34	17	we	we	PRON
ejpam-304	34	18	will	will	AUX
ejpam-304	34	19	find	find	VERB
ejpam-304	34	20	that	that	SCONJ
ejpam-304	34	21	it	it	PRON
ejpam-304	34	22	is	be	AUX
ejpam-304	34	23	equivalent	equivalent	ADJ
ejpam-304	34	24	to	to	ADP
ejpam-304	34	25	the	the	DET
ejpam-304	34	26	fredholm	fredholm	NOUN
ejpam-304	34	27	equation	equation	NOUN
ejpam-304	34	28	type	type	NOUN
ejpam-304	34	29	of	of	ADP
ejpam-304	34	30	the	the	DET
ejpam-304	34	31	second	second	ADJ
ejpam-304	34	32	kind	kind	NOUN
ejpam-304	35	1	[	[	X
ejpam-304	35	2	7	7	X
ejpam-304	35	3	]	]	X
ejpam-304	35	4	ϕ(t)+	ϕ(t)+	PROPN
ejpam-304	35	5	∫	∫	PROPN
ejpam-304	35	6	1	1	NUM
ejpam-304	35	7	−1	−1	NOUN
ejpam-304	35	8	n(t	n(t	PROPN
ejpam-304	35	9	,	,	PUNCT
ejpam-304	35	10	τ)ϕ(τ	τ)ϕ(τ	NOUN
ejpam-304	35	11	)	)	PUNCT
ejpam-304	35	12	dτ	dτ	NOUN
ejpam-304	35	13	=	=	SYM
ejpam-304	35	14	f(t	f(t	PROPN
ejpam-304	35	15	)	)	PUNCT
ejpam-304	35	16	,	,	PUNCT
ejpam-304	35	17	n(t	n(t	PROPN
ejpam-304	35	18	,	,	PUNCT
ejpam-304	35	19	τ	τ	PROPN
ejpam-304	35	20	)	)	PUNCT
ejpam-304	35	21	=	=	SYM
ejpam-304	36	1	−	−	PROPN
ejpam-304	36	2	1	1	NUM
ejpam-304	36	3	π2	π2	NOUN
ejpam-304	36	4	r	r	NOUN
ejpam-304	36	5	1	1	NUM
ejpam-304	36	6	+	+	NUM
ejpam-304	36	7	t	t	NOUN
ejpam-304	36	8	1−	1−	NUM
ejpam-304	37	1	t	t	NOUN
ejpam-304	37	2	∫	∫	PROPN
ejpam-304	37	3	1	1	NUM
ejpam-304	37	4	−1	−1	NOUN
ejpam-304	37	5	r	r	NOUN
ejpam-304	37	6	1−	1−	NUM
ejpam-304	37	7	x	x	SYM
ejpam-304	37	8	1	1	NUM
ejpam-304	37	9	+	+	CCONJ
ejpam-304	37	10	x	x	SYM
ejpam-304	37	11	k(x	k(x	PROPN
ejpam-304	37	12	,	,	PUNCT
ejpam-304	37	13	τ	τ	X
ejpam-304	37	14	)	)	PUNCT
ejpam-304	37	15	x	x	X
ejpam-304	38	1	−	−	PROPN
ejpam-304	38	2	t	t	NOUN
ejpam-304	38	3	d	d	X
ejpam-304	38	4	x	x	X
ejpam-304	38	5	,	,	PUNCT
ejpam-304	38	6	f(t	f(t	PROPN
ejpam-304	38	7	)	)	PUNCT
ejpam-304	39	1	=	=	SYM
ejpam-304	39	2	−	−	PROPN
ejpam-304	39	3	1	1	NUM
ejpam-304	39	4	π2	π2	NOUN
ejpam-304	39	5	r	r	NOUN
ejpam-304	39	6	1	1	NUM
ejpam-304	39	7	+	+	NUM
ejpam-304	39	8	t	t	NOUN
ejpam-304	39	9	1−	1−	NUM
ejpam-304	39	10	t	t	NOUN
ejpam-304	39	11	∫	∫	PROPN
ejpam-304	39	12	1	1	NUM
ejpam-304	39	13	−1	−1	NOUN
ejpam-304	39	14	r	r	NOUN
ejpam-304	39	15	1−	1−	NUM
ejpam-304	39	16	x	x	SYM
ejpam-304	39	17	1	1	NUM
ejpam-304	39	18	+	+	NUM
ejpam-304	39	19	x	x	SYM
ejpam-304	39	20	f	f	X
ejpam-304	39	21	(	(	PUNCT
ejpam-304	39	22	x	x	X
ejpam-304	39	23	)	)	PUNCT
ejpam-304	39	24	x	x	X
ejpam-304	39	25	−	−	PROPN
ejpam-304	40	1	t	t	NOUN
ejpam-304	40	2	d	d	X
ejpam-304	40	3	x	x	PROPN
ejpam-304	40	4	.	.	PUNCT
ejpam-304	41	1			PROPN
ejpam-304	41	2			PROPN
ejpam-304	41	3			PROPN
ejpam-304	41	4			PROPN
ejpam-304	41	5			PROPN
ejpam-304	41	6			PROPN
ejpam-304	41	7			PROPN
ejpam-304	41	8			PROPN
ejpam-304	41	9			ADJ
ejpam-304	41	10			PROPN
ejpam-304	41	11			PROPN
ejpam-304	41	12			PROPN
ejpam-304	41	13			PROPN
ejpam-304	41	14			PROPN
ejpam-304	41	15			NOUN
ejpam-304	41	16	(	(	PUNCT
ejpam-304	41	17	1.4	1.4	NUM
ejpam-304	41	18	)	)	PUNCT
ejpam-304	41	19	in	in	ADP
ejpam-304	41	20	the	the	DET
ejpam-304	41	21	sense	sense	NOUN
ejpam-304	41	22	of	of	ADP
ejpam-304	41	23	obtaining	obtain	VERB
ejpam-304	41	24	the	the	DET
ejpam-304	41	25	solution	solution	NOUN
ejpam-304	41	26	which	which	PRON
ejpam-304	41	27	one	one	PRON
ejpam-304	41	28	can	can	AUX
ejpam-304	41	29	apply	apply	VERB
ejpam-304	41	30	the	the	DET
ejpam-304	41	31	fredholm	fredholm	NOUN
ejpam-304	41	32	’s	’s	PART
ejpam-304	41	33	theorems	theorem	NOUN
ejpam-304	41	34	.	.	PUNCT
ejpam-304	42	1	in	in	ADP
ejpam-304	42	2	this	this	DET
ejpam-304	42	3	paper	paper	NOUN
ejpam-304	42	4	,	,	PUNCT
ejpam-304	42	5	we	we	PRON
ejpam-304	42	6	present	present	VERB
ejpam-304	42	7	an	an	DET
ejpam-304	42	8	approximate	approximate	ADJ
ejpam-304	42	9	solution	solution	NOUN
ejpam-304	42	10	for	for	ADP
ejpam-304	42	11	equation	equation	NOUN
ejpam-304	42	12	(	(	PUNCT
ejpam-304	42	13	1.1	1.1	NUM
ejpam-304	42	14	)	)	PUNCT
ejpam-304	42	15	which	which	PRON
ejpam-304	42	16	is	be	AUX
ejpam-304	42	17	bounded	bound	VERB
ejpam-304	42	18	at	at	ADP
ejpam-304	42	19	the	the	DET
ejpam-304	42	20	end	end	NOUN
ejpam-304	42	21	point	point	NOUN
ejpam-304	42	22	x	x	X
ejpam-304	42	23	=	=	SYM
ejpam-304	42	24	−1	−1	NOUN
ejpam-304	42	25	.	.	PUNCT
ejpam-304	43	1	2	2	X
ejpam-304	43	2	.	.	NUM
ejpam-304	43	3	approximate	approximate	ADJ
ejpam-304	43	4	solution	solution	NOUN
ejpam-304	43	5	of	of	ADP
ejpam-304	43	6	equation	equation	NOUN
ejpam-304	43	7	(	(	PUNCT
ejpam-304	43	8	1.1	1.1	NUM
ejpam-304	43	9	)	)	PUNCT
ejpam-304	43	10	guiding	guiding	NOUN
ejpam-304	43	11	by	by	ADP
ejpam-304	43	12	the	the	DET
ejpam-304	43	13	analytic	analytic	ADJ
ejpam-304	43	14	solutions	solution	NOUN
ejpam-304	43	15	of	of	ADP
ejpam-304	43	16	characteristic	characteristic	ADJ
ejpam-304	43	17	equation	equation	NOUN
ejpam-304	43	18	given	give	VERB
ejpam-304	43	19	by	by	ADP
ejpam-304	43	20	(	(	PUNCT
ejpam-304	43	21	1.3	1.3	NUM
ejpam-304	43	22	)	)	PUNCT
ejpam-304	43	23	,	,	PUNCT
ejpam-304	43	24	using	use	VERB
ejpam-304	43	25	the	the	DET
ejpam-304	43	26	chebyshev	chebyshev	NOUN
ejpam-304	43	27	interpolation	interpolation	NOUN
ejpam-304	43	28	polynomials	polynomial	NOUN
ejpam-304	43	29	of	of	ADP
ejpam-304	43	30	third	third	ADJ
ejpam-304	43	31	kind	kind	NOUN
ejpam-304	43	32	vi	vi	PROPN
ejpam-304	43	33	and	and	CCONJ
ejpam-304	43	34	fourth	fourth	ADJ
ejpam-304	43	35	kind	kind	NOUN
ejpam-304	43	36	wi	wi	PROPN
ejpam-304	43	37	with	with	ADP
ejpam-304	43	38	corresponding	correspond	VERB
ejpam-304	43	39	weight	weight	NOUN
ejpam-304	43	40	functions	function	NOUN
ejpam-304	43	41	ω1	ω1	PROPN
ejpam-304	43	42	and	and	CCONJ
ejpam-304	43	43	ω2	ω2	ADJ
ejpam-304	43	44	[	[	X
ejpam-304	43	45	8	8	NUM
ejpam-304	43	46	]	]	PUNCT
ejpam-304	43	47	;	;	PUNCT
ejpam-304	43	48	vi(x	vi(x	NUM
ejpam-304	43	49	)	)	PUNCT
ejpam-304	44	1	=	=	SYM
ejpam-304	44	2	cos	cos	PROPN
ejpam-304	44	3	�	�	PROPN
ejpam-304	44	4	2i	2i	PROPN
ejpam-304	44	5	+	+	CCONJ
ejpam-304	44	6	1	1	NUM
ejpam-304	44	7	2	2	NUM
ejpam-304	44	8	cos−1	cos−1	PROPN
ejpam-304	44	9	x	x	SYM
ejpam-304	44	10	�	�	PROPN
ejpam-304	44	11	cos	cos	PROPN
ejpam-304	44	12	�	�	PROPN
ejpam-304	44	13	1	1	NUM
ejpam-304	44	14	2	2	NUM
ejpam-304	44	15	cos−1	cos−1	PROPN
ejpam-304	44	16	x	x	SYM
ejpam-304	44	17	�	�	PROPN
ejpam-304	44	18	,	,	PUNCT
ejpam-304	44	19	ω1(x	ω1(x	NUM
ejpam-304	44	20	)	)	PUNCT
ejpam-304	44	21	=	=	SYM
ejpam-304	44	22	r	r	NOUN
ejpam-304	44	23	1	1	NUM
ejpam-304	44	24	+	+	NOUN
ejpam-304	44	25	x	x	SYM
ejpam-304	44	26	1−	1−	NUM
ejpam-304	44	27	x	x	NOUN
ejpam-304	44	28	,	,	PUNCT
ejpam-304	44	29	wi(x	wi(x	NOUN
ejpam-304	44	30	)	)	PUNCT
ejpam-304	44	31	=	=	PUNCT
ejpam-304	44	32	sin	sin	NOUN
ejpam-304	44	33	�	�	PROPN
ejpam-304	44	34	2i	2i	NOUN
ejpam-304	44	35	+	+	CCONJ
ejpam-304	44	36	1	1	NUM
ejpam-304	44	37	2	2	NUM
ejpam-304	44	38	cos−1	cos−1	NOUN
ejpam-304	44	39	x	x	SYM
ejpam-304	44	40	�	�	PROPN
ejpam-304	44	41	sin	sin	PROPN
ejpam-304	44	42	�	�	PROPN
ejpam-304	44	43	1	1	NUM
ejpam-304	44	44	2	2	NUM
ejpam-304	44	45	cos−1	cos−1	PROPN
ejpam-304	44	46	x	x	SYM
ejpam-304	44	47	�	�	PROPN
ejpam-304	44	48	,	,	PUNCT
ejpam-304	44	49	ω2(x	ω2(x	PROPN
ejpam-304	44	50	)	)	PUNCT
ejpam-304	44	51	=	=	SYM
ejpam-304	44	52	r	r	NOUN
ejpam-304	44	53	1−	1−	NUM
ejpam-304	44	54	x	x	SYM
ejpam-304	44	55	1	1	NUM
ejpam-304	44	56	+	+	NUM
ejpam-304	44	57	x	x	PUNCT
ejpam-304	44	58	.	.	PUNCT
ejpam-304	45	1			PROPN
ejpam-304	45	2			PROPN
ejpam-304	45	3			PROPN
ejpam-304	45	4			PROPN
ejpam-304	45	5			PROPN
ejpam-304	45	6			PROPN
ejpam-304	45	7			PROPN
ejpam-304	45	8			PROPN
ejpam-304	45	9			ADJ
ejpam-304	45	10			PROPN
ejpam-304	45	11			PROPN
ejpam-304	45	12			PROPN
ejpam-304	45	13			PROPN
ejpam-304	45	14			PROPN
ejpam-304	45	15			NOUN
ejpam-304	45	16	,	,	PUNCT
ejpam-304	45	17	(	(	PUNCT
ejpam-304	45	18	2.1	2.1	NUM
ejpam-304	45	19	)	)	PUNCT
ejpam-304	45	20	and	and	CCONJ
ejpam-304	45	21	helping	help	VERB
ejpam-304	45	22	of	of	ADP
ejpam-304	45	23	the	the	DET
ejpam-304	45	24	following	follow	VERB
ejpam-304	45	25	important	important	ADJ
ejpam-304	45	26	formula	formula	NOUN
ejpam-304	45	27	for	for	ADP
ejpam-304	45	28	singular	singular	ADJ
ejpam-304	45	29	integrals	integral	NOUN
ejpam-304	45	30	with	with	ADP
ejpam-304	45	31	the	the	DET
ejpam-304	45	32	cauchy	cauchy	ADJ
ejpam-304	45	33	kernel	kernel	PROPN
ejpam-304	45	34	∫	∫	PROPN
ejpam-304	46	1	1	1	NUM
ejpam-304	46	2	−1	−1	NOUN
ejpam-304	46	3	r	r	NOUN
ejpam-304	46	4	1	1	NUM
ejpam-304	46	5	+	+	NUM
ejpam-304	46	6	t	t	NOUN
ejpam-304	46	7	1−	1−	NUM
ejpam-304	46	8	t	t	NOUN
ejpam-304	46	9	vi(t	vi(t	PUNCT
ejpam-304	46	10	)	)	PUNCT
ejpam-304	46	11	t	t	NOUN
ejpam-304	46	12	−	−	NOUN
ejpam-304	47	1	x	x	SYM
ejpam-304	47	2	d	d	X
ejpam-304	47	3	t	t	PROPN
ejpam-304	47	4	=	=	PUNCT
ejpam-304	47	5	πwi(x	πwi(x	PROPN
ejpam-304	47	6	)	)	PUNCT
ejpam-304	47	7	,	,	PUNCT
ejpam-304	48	1	−1	−1	NOUN
ejpam-304	48	2	<	<	X
ejpam-304	48	3	x	x	X
ejpam-304	48	4	<	<	X
ejpam-304	48	5	1	1	NUM
ejpam-304	48	6	,	,	PUNCT
ejpam-304	48	7	i	i	PRON
ejpam-304	48	8	=	=	NOUN
ejpam-304	48	9	0	0	NUM
ejpam-304	48	10	,	,	PUNCT
ejpam-304	48	11	1	1	NUM
ejpam-304	48	12	,	,	PUNCT
ejpam-304	48	13	...	...	PUNCT
ejpam-304	48	14	,	,	PUNCT
ejpam-304	48	15	n	n	CCONJ
ejpam-304	48	16	,	,	PUNCT
ejpam-304	48	17	(	(	PUNCT
ejpam-304	48	18	2.2	2.2	NUM
ejpam-304	48	19	)	)	PUNCT
ejpam-304	48	20	m.	m.	NOUN
ejpam-304	48	21	abdulkawi	abdulkawi	PROPN
ejpam-304	48	22	,	,	PUNCT
ejpam-304	48	23	z.	z.	PROPN
ejpam-304	48	24	eshkuvatov	eshkuvatov	PROPN
ejpam-304	48	25	,	,	PUNCT
ejpam-304	48	26	and	and	CCONJ
ejpam-304	48	27	n.	n.	NOUN
ejpam-304	48	28	nik	nik	PROPN
ejpam-304	48	29	long	long	ADJ
ejpam-304	48	30	/	/	SYM
ejpam-304	48	31	eur	eur	PROPN
ejpam-304	48	32	.	.	PUNCT
ejpam-304	49	1	j.	j.	PROPN
ejpam-304	49	2	pure	pure	PROPN
ejpam-304	49	3	appl	appl	PROPN
ejpam-304	49	4	.	.	PROPN
ejpam-304	49	5	math	math	PROPN
ejpam-304	49	6	,	,	PUNCT
ejpam-304	49	7	2	2	NUM
ejpam-304	49	8	(	(	PUNCT
ejpam-304	49	9	2009	2009	NUM
ejpam-304	49	10	)	)	PUNCT
ejpam-304	49	11	,	,	PUNCT
ejpam-304	49	12	(	(	PUNCT
ejpam-304	49	13	462	462	NUM
ejpam-304	49	14	-	-	NOUN
ejpam-304	49	15	472	472	NUM
ejpam-304	49	16	)	)	PUNCT
ejpam-304	49	17	465	465	NUM
ejpam-304	49	18	the	the	DET
ejpam-304	49	19	approximate	approximate	ADJ
ejpam-304	49	20	solution	solution	NOUN
ejpam-304	49	21	,	,	PUNCT
ejpam-304	49	22	which	which	PRON
ejpam-304	49	23	is	be	AUX
ejpam-304	49	24	bounded	bound	VERB
ejpam-304	49	25	at	at	ADP
ejpam-304	49	26	the	the	DET
ejpam-304	49	27	end	end	NOUN
ejpam-304	49	28	point	point	NOUN
ejpam-304	49	29	x	x	X
ejpam-304	49	30	=	=	SYM
ejpam-304	49	31	−1	−1	NOUN
ejpam-304	49	32	,	,	PUNCT
ejpam-304	49	33	of	of	ADP
ejpam-304	49	34	equation	equation	NOUN
ejpam-304	49	35	(	(	PUNCT
ejpam-304	49	36	1.1	1.1	NUM
ejpam-304	49	37	)	)	PUNCT
ejpam-304	49	38	is	be	AUX
ejpam-304	49	39	obtained	obtain	VERB
ejpam-304	49	40	.	.	PUNCT
ejpam-304	50	1	we	we	PRON
ejpam-304	50	2	will	will	AUX
ejpam-304	50	3	interpolate	interpolate	VERB
ejpam-304	50	4	the	the	DET
ejpam-304	50	5	known	know	VERB
ejpam-304	50	6	function	function	NOUN
ejpam-304	50	7	f	f	PROPN
ejpam-304	50	8	(	(	PUNCT
ejpam-304	50	9	x	x	X
ejpam-304	50	10	)	)	PUNCT
ejpam-304	50	11	by	by	ADP
ejpam-304	50	12	using	use	VERB
ejpam-304	50	13	the	the	DET
ejpam-304	50	14	chebyshev	chebyshev	NOUN
ejpam-304	50	15	orthogonal	orthogonal	ADJ
ejpam-304	50	16	polynomial	polynomial	NOUN
ejpam-304	50	17	of	of	ADP
ejpam-304	50	18	the	the	DET
ejpam-304	50	19	fourth	fourth	ADJ
ejpam-304	50	20	kind	kind	NOUN
ejpam-304	50	21	fn(x	fn(x	ADP
ejpam-304	50	22	)	)	PUNCT
ejpam-304	50	23	of	of	ADP
ejpam-304	50	24	degree	degree	NOUN
ejpam-304	50	25	n	n	PRON
ejpam-304	50	26	as	as	ADP
ejpam-304	50	27	f	f	PROPN
ejpam-304	50	28	(	(	PUNCT
ejpam-304	50	29	x)≈	x)≈	X
ejpam-304	50	30	fn(x	fn(x	X
ejpam-304	50	31	)	)	PUNCT
ejpam-304	50	32	=	=	SYM
ejpam-304	51	1	n	n	PROPN
ejpam-304	51	2	∑	∑	ADP
ejpam-304	51	3	k=0	k=0	PROPN
ejpam-304	51	4	fk	fk	INTJ
ejpam-304	51	5	wk(x	wk(x	NOUN
ejpam-304	51	6	)	)	PUNCT
ejpam-304	51	7	(	(	PUNCT
ejpam-304	51	8	2.3	2.3	NUM
ejpam-304	51	9	)	)	PUNCT
ejpam-304	51	10	where	where	SCONJ
ejpam-304	51	11	fk	fk	INTJ
ejpam-304	51	12	=	=	SYM
ejpam-304	51	13	1	1	NUM
ejpam-304	51	14	π	π	NOUN
ejpam-304	51	15	∫	∫	PROPN
ejpam-304	51	16	1	1	NUM
ejpam-304	51	17	−1	−1	NOUN
ejpam-304	51	18	r	r	NOUN
ejpam-304	51	19	1−	1−	NUM
ejpam-304	51	20	t	t	NOUN
ejpam-304	51	21	1	1	NUM
ejpam-304	51	22	+	+	NUM
ejpam-304	51	23	t	t	X
ejpam-304	51	24	f	f	X
ejpam-304	51	25	(	(	PUNCT
ejpam-304	51	26	t)wk(t	t)wk(t	NOUN
ejpam-304	51	27	)	)	PUNCT
ejpam-304	51	28	d	d	NOUN
ejpam-304	51	29	t	t	PROPN
ejpam-304	51	30	.	.	PUNCT
ejpam-304	52	1	(	(	PUNCT
ejpam-304	52	2	2.4	2.4	NUM
ejpam-304	52	3	)	)	PUNCT
ejpam-304	52	4	approximating	approximate	VERB
ejpam-304	52	5	the	the	DET
ejpam-304	52	6	unknown	unknown	ADJ
ejpam-304	52	7	function	function	NOUN
ejpam-304	52	8	ϕ	ϕ	NOUN
ejpam-304	52	9	by	by	ADP
ejpam-304	52	10	ϕn	ϕn	PRON
ejpam-304	52	11	which	which	PRON
ejpam-304	52	12	is	be	AUX
ejpam-304	52	13	defined	define	VERB
ejpam-304	52	14	as	as	ADP
ejpam-304	52	15	ϕn(x	ϕn(x	PRON
ejpam-304	52	16	)	)	PUNCT
ejpam-304	52	17	=	=	SYM
ejpam-304	52	18	r	r	AUX
ejpam-304	52	19	1	1	NUM
ejpam-304	52	20	+	+	NOUN
ejpam-304	52	21	x	x	SYM
ejpam-304	52	22	1−	1−	NUM
ejpam-304	52	23	x	x	SYM
ejpam-304	52	24	n	n	CCONJ
ejpam-304	52	25	∑	∑	ADV
ejpam-304	52	26	j=0	j=0	PROPN
ejpam-304	52	27	a	a	DET
ejpam-304	52	28	j	j	PROPN
ejpam-304	52	29	vj(x	vj(x	PUNCT
ejpam-304	52	30	)	)	PUNCT
ejpam-304	52	31	(	(	PUNCT
ejpam-304	52	32	2.5	2.5	NUM
ejpam-304	52	33	)	)	PUNCT
ejpam-304	52	34	where	where	SCONJ
ejpam-304	52	35	the	the	DET
ejpam-304	52	36	unknown	unknown	ADJ
ejpam-304	52	37	coefficients	coefficient	NOUN
ejpam-304	52	38	¦	¦	PROPN
ejpam-304	52	39	a	a	DET
ejpam-304	52	40	j	j	PROPN
ejpam-304	52	41	©	©	PROPN
ejpam-304	52	42	n	n	PROPN
ejpam-304	52	43	0	0	NUM
ejpam-304	52	44	are	be	AUX
ejpam-304	52	45	to	to	PART
ejpam-304	52	46	be	be	AUX
ejpam-304	52	47	determined	determine	VERB
ejpam-304	52	48	.	.	PUNCT
ejpam-304	53	1	substituting	substitute	VERB
ejpam-304	53	2	(	(	PUNCT
ejpam-304	53	3	2.5	2.5	NUM
ejpam-304	53	4	)	)	PUNCT
ejpam-304	53	5	into	into	ADP
ejpam-304	53	6	(	(	PUNCT
ejpam-304	53	7	1.1	1.1	NUM
ejpam-304	53	8	)	)	PUNCT
ejpam-304	53	9	we	we	PRON
ejpam-304	53	10	obtain	obtain	VERB
ejpam-304	53	11	n	n	AUX
ejpam-304	53	12	∑	∑	ADV
ejpam-304	53	13	j=0	j=0	PROPN
ejpam-304	53	14	a	a	DET
ejpam-304	53	15	j	j	PROPN
ejpam-304	53	16	∫	∫	PROPN
ejpam-304	53	17	1	1	NUM
ejpam-304	53	18	−1	−1	NOUN
ejpam-304	53	19	r	r	NOUN
ejpam-304	53	20	1	1	NUM
ejpam-304	53	21	+	+	NUM
ejpam-304	53	22	t	t	NOUN
ejpam-304	53	23	1−	1−	NUM
ejpam-304	53	24	t	t	PROPN
ejpam-304	53	25	vj(t	vj(t	NUM
ejpam-304	53	26	)	)	PUNCT
ejpam-304	53	27	t	t	NOUN
ejpam-304	53	28	−	−	NOUN
ejpam-304	54	1	x	x	SYM
ejpam-304	55	1	d	d	X
ejpam-304	55	2	t	t	NOUN
ejpam-304	55	3	+	+	CCONJ
ejpam-304	55	4	n	n	CCONJ
ejpam-304	55	5	∑	∑	ADV
ejpam-304	55	6	j=0	j=0	PROPN
ejpam-304	55	7	a	a	DET
ejpam-304	55	8	j	j	PROPN
ejpam-304	55	9	∫	∫	PROPN
ejpam-304	55	10	1	1	NUM
ejpam-304	55	11	−1	−1	NOUN
ejpam-304	55	12	r	r	NOUN
ejpam-304	55	13	1	1	NUM
ejpam-304	55	14	+	+	NUM
ejpam-304	55	15	t	t	NOUN
ejpam-304	55	16	1−	1−	NUM
ejpam-304	55	17	t	t	PROPN
ejpam-304	55	18	k(x	k(x	PROPN
ejpam-304	55	19	,	,	PUNCT
ejpam-304	55	20	t)vj(t	t)vj(t	PROPN
ejpam-304	55	21	)	)	PUNCT
ejpam-304	56	1	d	d	NOUN
ejpam-304	56	2	t	t	NOUN
ejpam-304	56	3	=	=	SYM
ejpam-304	56	4	f	f	PROPN
ejpam-304	56	5	(	(	PUNCT
ejpam-304	56	6	x	x	NOUN
ejpam-304	56	7	)	)	PUNCT
ejpam-304	56	8	.	.	PUNCT
ejpam-304	57	1	(	(	PUNCT
ejpam-304	57	2	2.6	2.6	NUM
ejpam-304	57	3	)	)	PUNCT
ejpam-304	57	4	using	use	VERB
ejpam-304	57	5	(	(	PUNCT
ejpam-304	57	6	2.2	2.2	NUM
ejpam-304	57	7	)	)	PUNCT
ejpam-304	57	8	into	into	ADP
ejpam-304	57	9	(	(	PUNCT
ejpam-304	57	10	2.6	2.6	NUM
ejpam-304	57	11	)	)	PUNCT
ejpam-304	57	12	we	we	PRON
ejpam-304	57	13	obtain	obtain	VERB
ejpam-304	57	14	π	π	PROPN
ejpam-304	57	15	n	n	CCONJ
ejpam-304	57	16	∑	∑	ADV
ejpam-304	57	17	j=0	j=0	PROPN
ejpam-304	57	18	a	a	DET
ejpam-304	57	19	j	j	NOUN
ejpam-304	57	20	wj(x	wj(x	PUNCT
ejpam-304	57	21	)	)	PUNCT
ejpam-304	58	1	+	+	CCONJ
ejpam-304	58	2	n	n	CCONJ
ejpam-304	58	3	∑	∑	ADV
ejpam-304	58	4	j=0	j=0	PROPN
ejpam-304	58	5	a	a	DET
ejpam-304	58	6	j	j	PROPN
ejpam-304	58	7	ζ	ζ	PROPN
ejpam-304	58	8	j(x	j(x	PROPN
ejpam-304	58	9	)	)	PUNCT
ejpam-304	59	1	=	=	SYM
ejpam-304	59	2	f	f	PROPN
ejpam-304	59	3	(	(	PUNCT
ejpam-304	59	4	x	x	X
ejpam-304	59	5	)	)	PUNCT
ejpam-304	59	6	(	(	PUNCT
ejpam-304	59	7	2.7	2.7	NUM
ejpam-304	59	8	)	)	PUNCT
ejpam-304	59	9	where	where	SCONJ
ejpam-304	59	10	ζ	ζ	NOUN
ejpam-304	59	11	j(x	j(x	PROPN
ejpam-304	59	12	)	)	PUNCT
ejpam-304	59	13	=	=	SYM
ejpam-304	60	1	∫	∫	PROPN
ejpam-304	60	2	1	1	NUM
ejpam-304	60	3	−1	−1	NOUN
ejpam-304	60	4	r	r	NOUN
ejpam-304	60	5	1	1	NUM
ejpam-304	60	6	+	+	NUM
ejpam-304	60	7	t	t	NOUN
ejpam-304	60	8	1−	1−	NUM
ejpam-304	60	9	t	t	PROPN
ejpam-304	60	10	k(x	k(x	PROPN
ejpam-304	60	11	,	,	PUNCT
ejpam-304	60	12	t)vj	t)vj	PROPN
ejpam-304	60	13	(	(	PUNCT
ejpam-304	60	14	t	t	NOUN
ejpam-304	60	15	)	)	PUNCT
ejpam-304	60	16	d	d	PROPN
ejpam-304	60	17	t	t	PROPN
ejpam-304	60	18	.	.	PUNCT
ejpam-304	61	1	(	(	PUNCT
ejpam-304	61	2	2.8	2.8	NUM
ejpam-304	61	3	)	)	PUNCT
ejpam-304	61	4	interpolating	interpolate	VERB
ejpam-304	61	5	the	the	DET
ejpam-304	61	6	function	function	NOUN
ejpam-304	61	7	ζ	ζ	PROPN
ejpam-304	61	8	j(x	j(x	PROPN
ejpam-304	61	9	)	)	PUNCT
ejpam-304	61	10	by	by	ADP
ejpam-304	61	11	using	use	VERB
ejpam-304	61	12	the	the	DET
ejpam-304	61	13	chebyshev	chebyshev	NOUN
ejpam-304	61	14	orthogonal	orthogonal	ADJ
ejpam-304	61	15	polynomial	polynomial	NOUN
ejpam-304	61	16	of	of	ADP
ejpam-304	61	17	the	the	DET
ejpam-304	61	18	fourth	fourth	ADJ
ejpam-304	61	19	kind	kind	NOUN
ejpam-304	61	20	as	as	SCONJ
ejpam-304	61	21	follows	follow	VERB
ejpam-304	61	22	ζ	ζ	NOUN
ejpam-304	61	23	j(x)≈	j(x)≈	NOUN
ejpam-304	61	24	n	n	CCONJ
ejpam-304	61	25	∑	∑	ADP
ejpam-304	61	26	k=0	k=0	PROPN
ejpam-304	61	27	µ	µ	PROPN
ejpam-304	61	28	j	j	PROPN
ejpam-304	61	29	,	,	PUNCT
ejpam-304	61	30	k	k	PROPN
ejpam-304	61	31	wk(x	wk(x	X
ejpam-304	61	32	)	)	PUNCT
ejpam-304	61	33	(	(	PUNCT
ejpam-304	61	34	2.9	2.9	NUM
ejpam-304	61	35	)	)	PUNCT
ejpam-304	61	36	where	where	SCONJ
ejpam-304	61	37	µ	µ	PROPN
ejpam-304	61	38	j	j	PROPN
ejpam-304	61	39	,	,	PUNCT
ejpam-304	61	40	k	k	PROPN
ejpam-304	61	41	=	=	SYM
ejpam-304	61	42	1	1	NUM
ejpam-304	61	43	π	π	NOUN
ejpam-304	61	44	∫	∫	PROPN
ejpam-304	61	45	1	1	NUM
ejpam-304	61	46	−1	−1	NOUN
ejpam-304	61	47	r	r	NOUN
ejpam-304	61	48	1−	1−	NUM
ejpam-304	61	49	x	x	SYM
ejpam-304	61	50	1	1	NUM
ejpam-304	61	51	+	+	CCONJ
ejpam-304	61	52	x	x	SYM
ejpam-304	61	53	∫	∫	PROPN
ejpam-304	61	54	1	1	NUM
ejpam-304	61	55	−1	−1	NOUN
ejpam-304	61	56	r	r	NOUN
ejpam-304	61	57	1	1	NUM
ejpam-304	61	58	+	+	NUM
ejpam-304	61	59	t	t	NOUN
ejpam-304	61	60	1−	1−	NUM
ejpam-304	61	61	t	t	PROPN
ejpam-304	61	62	k(x	k(x	PROPN
ejpam-304	61	63	,	,	PUNCT
ejpam-304	61	64	t)vj(t)wk(x	t)vj(t)wk(x	PROPN
ejpam-304	61	65	)	)	PUNCT
ejpam-304	61	66	d	d	NOUN
ejpam-304	61	67	t	t	PROPN
ejpam-304	62	1	d	d	X
ejpam-304	62	2	x	x	X
ejpam-304	62	3	.	.	PUNCT
ejpam-304	63	1	(	(	PUNCT
ejpam-304	63	2	2.10	2.10	NUM
ejpam-304	63	3	)	)	PUNCT
ejpam-304	63	4	m.	m.	NOUN
ejpam-304	63	5	abdulkawi	abdulkawi	PROPN
ejpam-304	63	6	,	,	PUNCT
ejpam-304	63	7	z.	z.	PROPN
ejpam-304	63	8	eshkuvatov	eshkuvatov	PROPN
ejpam-304	63	9	,	,	PUNCT
ejpam-304	63	10	and	and	CCONJ
ejpam-304	63	11	n.	n.	NOUN
ejpam-304	63	12	nik	nik	PROPN
ejpam-304	63	13	long	long	ADJ
ejpam-304	63	14	/	/	SYM
ejpam-304	63	15	eur	eur	PROPN
ejpam-304	63	16	.	.	PUNCT
ejpam-304	64	1	j.	j.	PROPN
ejpam-304	64	2	pure	pure	PROPN
ejpam-304	64	3	appl	appl	PROPN
ejpam-304	64	4	.	.	PROPN
ejpam-304	64	5	math	math	PROPN
ejpam-304	64	6	,	,	PUNCT
ejpam-304	64	7	2	2	NUM
ejpam-304	64	8	(	(	PUNCT
ejpam-304	64	9	2009	2009	NUM
ejpam-304	64	10	)	)	PUNCT
ejpam-304	64	11	,	,	PUNCT
ejpam-304	64	12	(	(	PUNCT
ejpam-304	64	13	462	462	NUM
ejpam-304	64	14	-	-	NOUN
ejpam-304	64	15	472	472	NUM
ejpam-304	64	16	)	)	PUNCT
ejpam-304	64	17	466	466	NUM
ejpam-304	64	18	due	due	ADJ
ejpam-304	64	19	to	to	ADP
ejpam-304	64	20	(	(	PUNCT
ejpam-304	64	21	2.3	2.3	NUM
ejpam-304	64	22	-	-	SYM
ejpam-304	64	23	2.4	2.4	NUM
ejpam-304	64	24	)	)	PUNCT
ejpam-304	64	25	and	and	CCONJ
ejpam-304	64	26	(	(	PUNCT
ejpam-304	64	27	2.9	2.9	NUM
ejpam-304	64	28	-	-	SYM
ejpam-304	64	29	2.10	2.10	NUM
ejpam-304	64	30	)	)	PUNCT
ejpam-304	64	31	,	,	PUNCT
ejpam-304	64	32	equation	equation	NOUN
ejpam-304	64	33	(	(	PUNCT
ejpam-304	64	34	2.7	2.7	NUM
ejpam-304	64	35	)	)	PUNCT
ejpam-304	64	36	becomes	become	VERB
ejpam-304	64	37	n	n	ADV
ejpam-304	64	38	∑	∑	ADV
ejpam-304	64	39	j=0	j=0	PROPN
ejpam-304	64	40	a	a	DET
ejpam-304	64	41	j	j	PROPN
ejpam-304	64	42	wj(x	wj(x	PUNCT
ejpam-304	64	43	)	)	PUNCT
ejpam-304	65	1	+	+	CCONJ
ejpam-304	65	2	1	1	NUM
ejpam-304	65	3	π	π	NOUN
ejpam-304	65	4	n	n	NUM
ejpam-304	65	5	∑	∑	ADP
ejpam-304	65	6	k=0	k=0	PROPN
ejpam-304	65	7	n	n	CCONJ
ejpam-304	65	8	∑	∑	ADV
ejpam-304	65	9	j=0	j=0	PROPN
ejpam-304	65	10	a	a	DET
ejpam-304	65	11	j	j	PROPN
ejpam-304	65	12	µ	µ	PROPN
ejpam-304	65	13	j	j	PROPN
ejpam-304	65	14	,	,	PUNCT
ejpam-304	65	15	k	k	PROPN
ejpam-304	65	16	wk(x	wk(x	X
ejpam-304	65	17	)	)	PUNCT
ejpam-304	65	18	=	=	SYM
ejpam-304	65	19	1	1	NUM
ejpam-304	65	20	π	π	PROPN
ejpam-304	65	21	n	n	X
ejpam-304	65	22	∑	∑	ADP
ejpam-304	65	23	k=0	k=0	PROPN
ejpam-304	65	24	fk	fk	INTJ
ejpam-304	65	25	wk(x	wk(x	NOUN
ejpam-304	65	26	)	)	PUNCT
ejpam-304	65	27	.	.	PUNCT
ejpam-304	66	1	(	(	PUNCT
ejpam-304	66	2	2.11	2.11	NUM
ejpam-304	66	3	)	)	PUNCT
ejpam-304	66	4	the	the	DET
ejpam-304	66	5	unknown	unknown	ADJ
ejpam-304	66	6	coefficients	coefficient	NOUN
ejpam-304	66	7	¦	¦	PROPN
ejpam-304	66	8	a	a	DET
ejpam-304	66	9	j	j	PROPN
ejpam-304	66	10	©	©	PROPN
ejpam-304	66	11	n	n	PROPN
ejpam-304	66	12	0	0	NUM
ejpam-304	66	13	are	be	AUX
ejpam-304	66	14	determined	determine	VERB
ejpam-304	66	15	by	by	ADP
ejpam-304	66	16	solving	solve	VERB
ejpam-304	66	17	the	the	DET
ejpam-304	66	18	system	system	NOUN
ejpam-304	66	19	of	of	ADP
ejpam-304	66	20	linear	linear	PROPN
ejpam-304	66	21	equations	equation	NOUN
ejpam-304	66	22	obtained	obtain	VERB
ejpam-304	66	23	by	by	ADP
ejpam-304	66	24	comparing	compare	VERB
ejpam-304	66	25	the	the	DET
ejpam-304	66	26	coefficients	coefficient	NOUN
ejpam-304	66	27	of	of	ADP
ejpam-304	66	28	wj	wj	PROPN
ejpam-304	66	29	,	,	PUNCT
ejpam-304	66	30	j	j	PROPN
ejpam-304	66	31	=	=	SYM
ejpam-304	66	32	0	0	NUM
ejpam-304	66	33	,	,	PUNCT
ejpam-304	66	34	1	1	NUM
ejpam-304	66	35	,	,	PUNCT
ejpam-304	66	36	2	2	NUM
ejpam-304	66	37	,	,	PUNCT
ejpam-304	66	38	...	...	PUNCT
ejpam-304	66	39	,	,	PUNCT
ejpam-304	66	40	n	n	CCONJ
ejpam-304	66	41	in	in	ADP
ejpam-304	66	42	both	both	DET
ejpam-304	66	43	sides	side	NOUN
ejpam-304	66	44	of	of	ADP
ejpam-304	66	45	equation	equation	NOUN
ejpam-304	66	46	(	(	PUNCT
ejpam-304	66	47	2.11	2.11	NUM
ejpam-304	66	48	)	)	PUNCT
ejpam-304	66	49	which	which	PRON
ejpam-304	66	50	is	be	AUX
ejpam-304	66	51	a0	a0	PROPN
ejpam-304	66	52	+	+	CCONJ
ejpam-304	66	53	1	1	NUM
ejpam-304	66	54	π	π	PROPN
ejpam-304	66	55	n	n	CCONJ
ejpam-304	66	56	∑	∑	ADV
ejpam-304	66	57	j=0	j=0	PROPN
ejpam-304	66	58	a	a	DET
ejpam-304	66	59	j	j	PROPN
ejpam-304	66	60	µ	µ	PROPN
ejpam-304	66	61	j	j	PROPN
ejpam-304	66	62	,	,	PUNCT
ejpam-304	66	63	0	0	NUM
ejpam-304	67	1	=	=	SYM
ejpam-304	67	2	1	1	NUM
ejpam-304	67	3	π	π	PROPN
ejpam-304	67	4	f0	f0	PROPN
ejpam-304	67	5	,	,	PUNCT
ejpam-304	67	6	a1	a1	PROPN
ejpam-304	67	7	+	+	CCONJ
ejpam-304	67	8	1	1	NUM
ejpam-304	67	9	π	π	PROPN
ejpam-304	67	10	n	n	CCONJ
ejpam-304	67	11	∑	∑	ADV
ejpam-304	67	12	j=0	j=0	PROPN
ejpam-304	67	13	a	a	DET
ejpam-304	67	14	j	j	PROPN
ejpam-304	67	15	µ	µ	PROPN
ejpam-304	67	16	j	j	PROPN
ejpam-304	67	17	,	,	PUNCT
ejpam-304	67	18	1	1	NUM
ejpam-304	67	19	=	=	SYM
ejpam-304	67	20	1	1	NUM
ejpam-304	67	21	π	π	NOUN
ejpam-304	67	22	f1	f1	NOUN
ejpam-304	67	23	,	,	PUNCT
ejpam-304	67	24	.	.	PUNCT
ejpam-304	67	25	.	.	PUNCT
ejpam-304	67	26	.	.	PUNCT
ejpam-304	67	27	.	.	PUNCT
ejpam-304	67	28	.	.	PUNCT
ejpam-304	67	29	.	.	PUNCT
ejpam-304	67	30	.	.	PUNCT
ejpam-304	67	31	.	.	PUNCT
ejpam-304	67	32	.	.	PUNCT
ejpam-304	67	33	...	...	PUNCT
ejpam-304	67	34	...	...	PUNCT
ejpam-304	67	35	...	...	PUNCT
ejpam-304	67	36	.	.	PUNCT
ejpam-304	67	37	.	.	PUNCT
ejpam-304	67	38	.	.	PUNCT
ejpam-304	67	39	.	.	PUNCT
ejpam-304	67	40	.	.	PUNCT
ejpam-304	67	41	.	.	PUNCT
ejpam-304	67	42	.	.	PUNCT
ejpam-304	67	43	.	.	PUNCT
ejpam-304	67	44	.	.	PUNCT
ejpam-304	68	1	an+	an+	PROPN
ejpam-304	68	2	1	1	NUM
ejpam-304	68	3	π	π	PROPN
ejpam-304	68	4	n	n	CCONJ
ejpam-304	68	5	∑	∑	ADV
ejpam-304	68	6	j=0	j=0	PROPN
ejpam-304	68	7	a	a	DET
ejpam-304	68	8	j	j	PROPN
ejpam-304	68	9	µ	µ	PROPN
ejpam-304	68	10	j	j	PROPN
ejpam-304	68	11	,	,	PUNCT
ejpam-304	68	12	n	n	NOUN
ejpam-304	68	13	=	=	SYM
ejpam-304	68	14	1	1	NUM
ejpam-304	68	15	π	π	PROPN
ejpam-304	68	16	fn	fn	PROPN
ejpam-304	68	17	.	.	PUNCT
ejpam-304	69	1			PROPN
ejpam-304	69	2			PROPN
ejpam-304	69	3			PROPN
ejpam-304	69	4			PROPN
ejpam-304	69	5			PROPN
ejpam-304	69	6			PROPN
ejpam-304	69	7			PROPN
ejpam-304	69	8			PROPN
ejpam-304	69	9			PROPN
ejpam-304	69	10			PROPN
ejpam-304	69	11			PROPN
ejpam-304	69	12			PROPN
ejpam-304	69	13			PROPN
ejpam-304	69	14			PROPN
ejpam-304	69	15			PROPN
ejpam-304	69	16			PROPN
ejpam-304	69	17			PROPN
ejpam-304	69	18			ADJ
ejpam-304	69	19			PROPN
ejpam-304	69	20			PROPN
ejpam-304	69	21			PROPN
ejpam-304	69	22			PROPN
ejpam-304	69	23			PROPN
ejpam-304	69	24			PROPN
ejpam-304	69	25			PROPN
ejpam-304	69	26			PROPN
ejpam-304	69	27			PROPN
ejpam-304	69	28			PROPN
ejpam-304	69	29			PROPN
ejpam-304	69	30			PROPN
ejpam-304	69	31			PROPN
ejpam-304	69	32			PROPN
ejpam-304	69	33			NOUN
ejpam-304	69	34	(	(	PUNCT
ejpam-304	69	35	2.12	2.12	NUM
ejpam-304	69	36	)	)	PUNCT
ejpam-304	69	37	where	where	SCONJ
ejpam-304	69	38	the	the	DET
ejpam-304	69	39	coefficients	coefficient	NOUN
ejpam-304	69	40	�	�	PROPN
ejpam-304	69	41	fk	fk	INTJ
ejpam-304	69	42	and	and	CCONJ
ejpam-304	69	43	¦	¦	PROPN
ejpam-304	69	44	µ	µ	PROPN
ejpam-304	69	45	j	j	PROPN
ejpam-304	69	46	,	,	PUNCT
ejpam-304	69	47	k	k	PROPN
ejpam-304	69	48	©	©	PROPN
ejpam-304	69	49	are	be	AUX
ejpam-304	69	50	given	give	VERB
ejpam-304	69	51	by	by	ADP
ejpam-304	69	52	(	(	PUNCT
ejpam-304	69	53	2.4	2.4	NUM
ejpam-304	69	54	)	)	PUNCT
ejpam-304	69	55	and	and	CCONJ
ejpam-304	69	56	(	(	PUNCT
ejpam-304	69	57	2.10	2.10	NUM
ejpam-304	69	58	)	)	PUNCT
ejpam-304	69	59	,	,	PUNCT
ejpam-304	69	60	respectively	respectively	ADV
ejpam-304	69	61	.	.	PUNCT
ejpam-304	70	1	3	3	X
ejpam-304	70	2	.	.	NOUN
ejpam-304	70	3	approximate	approximate	ADJ
ejpam-304	70	4	solution	solution	NOUN
ejpam-304	70	5	of	of	ADP
ejpam-304	70	6	the	the	DET
ejpam-304	70	7	characteristic	characteristic	ADJ
ejpam-304	70	8	equation	equation	NOUN
ejpam-304	70	9	(	(	PUNCT
ejpam-304	70	10	1.2	1.2	NUM
ejpam-304	70	11	)	)	PUNCT
ejpam-304	70	12	theorem	theorem	VERB
ejpam-304	70	13	3.1	3.1	NUM
ejpam-304	70	14	.	.	PUNCT
ejpam-304	71	1	if	if	SCONJ
ejpam-304	71	2	f	f	PROPN
ejpam-304	71	3	(	(	PUNCT
ejpam-304	71	4	x	x	X
ejpam-304	71	5	)	)	PUNCT
ejpam-304	71	6	in	in	ADP
ejpam-304	71	7	characteristic	characteristic	ADJ
ejpam-304	71	8	equation	equation	NOUN
ejpam-304	71	9	(	(	PUNCT
ejpam-304	71	10	1.2	1.2	NUM
ejpam-304	71	11	)	)	PUNCT
ejpam-304	71	12	is	be	AUX
ejpam-304	71	13	a	a	DET
ejpam-304	71	14	cubic	cubic	ADJ
ejpam-304	71	15	function	function	NOUN
ejpam-304	71	16	,	,	PUNCT
ejpam-304	71	17	then	then	ADV
ejpam-304	71	18	the	the	DET
ejpam-304	71	19	approximate	approximate	ADJ
ejpam-304	71	20	solution	solution	NOUN
ejpam-304	71	21	(	(	PUNCT
ejpam-304	71	22	2.5	2.5	NUM
ejpam-304	71	23	)	)	PUNCT
ejpam-304	71	24	is	be	AUX
ejpam-304	71	25	identical	identical	ADJ
ejpam-304	71	26	to	to	ADP
ejpam-304	71	27	the	the	DET
ejpam-304	71	28	exact	exact	ADJ
ejpam-304	71	29	solution	solution	NOUN
ejpam-304	71	30	.	.	PUNCT
ejpam-304	72	1	proof	proof	NOUN
ejpam-304	72	2	.	.	PUNCT
ejpam-304	73	1	let	let	VERB
ejpam-304	73	2	us	we	PRON
ejpam-304	73	3	consider	consider	VERB
ejpam-304	73	4	the	the	DET
ejpam-304	73	5	characteristic	characteristic	ADJ
ejpam-304	73	6	singular	singular	ADJ
ejpam-304	73	7	integral	integral	ADJ
ejpam-304	73	8	equation	equation	NOUN
ejpam-304	73	9	∫	∫	PROPN
ejpam-304	73	10	1	1	NUM
ejpam-304	73	11	−1	−1	NOUN
ejpam-304	73	12	ϕ(t	ϕ(t	NUM
ejpam-304	73	13	)	)	PUNCT
ejpam-304	74	1	t	t	NOUN
ejpam-304	74	2	−	−	NOUN
ejpam-304	75	1	x	x	SYM
ejpam-304	75	2	d	d	X
ejpam-304	75	3	t	t	PROPN
ejpam-304	75	4	=	=	SYM
ejpam-304	75	5	f	f	PROPN
ejpam-304	75	6	(	(	PUNCT
ejpam-304	75	7	x	x	NOUN
ejpam-304	75	8	)	)	PUNCT
ejpam-304	75	9	,	,	PUNCT
ejpam-304	75	10	−1	−1	NOUN
ejpam-304	75	11	<	<	X
ejpam-304	75	12	x	x	X
ejpam-304	75	13	<	<	X
ejpam-304	75	14	1	1	NUM
ejpam-304	75	15	.	.	PUNCT
ejpam-304	75	16	(	(	PUNCT
ejpam-304	75	17	3.1	3.1	NUM
ejpam-304	75	18	)	)	PUNCT
ejpam-304	75	19	let	let	VERB
ejpam-304	75	20	f	f	PROPN
ejpam-304	75	21	(	(	PUNCT
ejpam-304	75	22	x	x	X
ejpam-304	75	23	)	)	PUNCT
ejpam-304	75	24	in	in	ADP
ejpam-304	75	25	(	(	PUNCT
ejpam-304	75	26	3.1	3.1	NUM
ejpam-304	75	27	)	)	PUNCT
ejpam-304	75	28	be	be	AUX
ejpam-304	75	29	a	a	DET
ejpam-304	75	30	cubic	cubic	ADJ
ejpam-304	75	31	function	function	NOUN
ejpam-304	75	32	i.e	i.e	X
ejpam-304	75	33	f	f	X
ejpam-304	75	34	(	(	PUNCT
ejpam-304	75	35	x	x	NOUN
ejpam-304	75	36	)	)	PUNCT
ejpam-304	75	37	=	=	SYM
ejpam-304	75	38	c0	c0	X
ejpam-304	75	39	+	+	X
ejpam-304	75	40	c1	c1	NOUN
ejpam-304	75	41	x	x	PUNCT
ejpam-304	76	1	+	+	CCONJ
ejpam-304	76	2	c2	c2	PROPN
ejpam-304	76	3	x2	x2	PROPN
ejpam-304	76	4	+	+	CCONJ
ejpam-304	76	5	c3	c3	NOUN
ejpam-304	76	6	x3	x3	PROPN
ejpam-304	76	7	,	,	PUNCT
ejpam-304	76	8	−1	−1	NOUN
ejpam-304	76	9	<	<	X
ejpam-304	76	10	x	x	X
ejpam-304	76	11	<	<	X
ejpam-304	76	12	1	1	NUM
ejpam-304	76	13	.	.	PUNCT
ejpam-304	76	14	(	(	PUNCT
ejpam-304	76	15	3.2	3.2	NUM
ejpam-304	76	16	)	)	PUNCT
ejpam-304	76	17	m.	m.	NOUN
ejpam-304	76	18	abdulkawi	abdulkawi	PROPN
ejpam-304	76	19	,	,	PUNCT
ejpam-304	76	20	z.	z.	PROPN
ejpam-304	76	21	eshkuvatov	eshkuvatov	PROPN
ejpam-304	76	22	,	,	PUNCT
ejpam-304	76	23	and	and	CCONJ
ejpam-304	76	24	n.	n.	NOUN
ejpam-304	76	25	nik	nik	PROPN
ejpam-304	76	26	long	long	ADJ
ejpam-304	76	27	/	/	SYM
ejpam-304	76	28	eur	eur	PROPN
ejpam-304	76	29	.	.	PUNCT
ejpam-304	77	1	j.	j.	PROPN
ejpam-304	77	2	pure	pure	PROPN
ejpam-304	77	3	appl	appl	PROPN
ejpam-304	77	4	.	.	PROPN
ejpam-304	77	5	math	math	PROPN
ejpam-304	77	6	,	,	PUNCT
ejpam-304	77	7	2	2	NUM
ejpam-304	77	8	(	(	PUNCT
ejpam-304	77	9	2009	2009	NUM
ejpam-304	77	10	)	)	PUNCT
ejpam-304	77	11	,	,	PUNCT
ejpam-304	77	12	(	(	PUNCT
ejpam-304	77	13	462	462	NUM
ejpam-304	77	14	-	-	NOUN
ejpam-304	77	15	472	472	NUM
ejpam-304	77	16	)	)	PUNCT
ejpam-304	77	17	467	467	NUM
ejpam-304	77	18	substituting	substitute	VERB
ejpam-304	77	19	(	(	PUNCT
ejpam-304	77	20	3.2	3.2	NUM
ejpam-304	77	21	)	)	PUNCT
ejpam-304	77	22	into	into	ADP
ejpam-304	77	23	(	(	PUNCT
ejpam-304	77	24	2.4	2.4	NUM
ejpam-304	77	25	)	)	PUNCT
ejpam-304	77	26	yields	yield	NOUN
ejpam-304	77	27	fk	fk	INTJ
ejpam-304	78	1	=	=	SYM
ejpam-304	78	2	1	1	NUM
ejpam-304	78	3	π	π	NOUN
ejpam-304	78	4	∫	∫	PROPN
ejpam-304	78	5	1	1	NUM
ejpam-304	78	6	−1	−1	NOUN
ejpam-304	78	7	r	r	NOUN
ejpam-304	78	8	1−	1−	NUM
ejpam-304	78	9	t	t	NOUN
ejpam-304	78	10	1	1	NUM
ejpam-304	78	11	+	+	NUM
ejpam-304	78	12	t	t	PROPN
ejpam-304	78	13	�	�	PROPN
ejpam-304	78	14	c0	c0	PROPN
ejpam-304	78	15	+	+	PROPN
ejpam-304	78	16	c1	c1	PROPN
ejpam-304	78	17	t	t	PROPN
ejpam-304	78	18	+	+	CCONJ
ejpam-304	78	19	c2	c2	PROPN
ejpam-304	78	20	t2	t2	PROPN
ejpam-304	78	21	+	+	CCONJ
ejpam-304	78	22	c3	c3	PROPN
ejpam-304	78	23	t3	t3	PROPN
ejpam-304	78	24	�	�	PROPN
ejpam-304	78	25	wk(t	wk(t	PUNCT
ejpam-304	78	26	)	)	PUNCT
ejpam-304	78	27	d	d	PROPN
ejpam-304	78	28	t	t	PROPN
ejpam-304	78	29	.	.	PUNCT
ejpam-304	79	1	(	(	PUNCT
ejpam-304	79	2	3.3	3.3	NUM
ejpam-304	79	3	)	)	PUNCT
ejpam-304	79	4	using	use	VERB
ejpam-304	79	5	the	the	DET
ejpam-304	79	6	following	follow	VERB
ejpam-304	79	7	chebyshev	chebyshev	NOUN
ejpam-304	79	8	recurrence	recurrence	NOUN
ejpam-304	79	9	relations	relation	NOUN
ejpam-304	79	10	of	of	ADP
ejpam-304	79	11	the	the	DET
ejpam-304	79	12	third	third	ADJ
ejpam-304	79	13	and	and	CCONJ
ejpam-304	79	14	fourth	fourth	ADJ
ejpam-304	79	15	kinds	kind	NOUN
ejpam-304	79	16	,	,	PUNCT
ejpam-304	79	17	respectively	respectively	ADV
ejpam-304	79	18	,	,	PUNCT
ejpam-304	79	19	v0(x	v0(x	X
ejpam-304	79	20	)	)	PUNCT
ejpam-304	79	21	=	=	NOUN
ejpam-304	79	22	1	1	NUM
ejpam-304	79	23	,	,	PUNCT
ejpam-304	79	24	v1(x	v1(x	NUM
ejpam-304	79	25	)	)	PUNCT
ejpam-304	79	26	=	=	PUNCT
ejpam-304	80	1	2x	2x	NUM
ejpam-304	80	2	−	−	NOUN
ejpam-304	80	3	1	1	NUM
ejpam-304	80	4	,	,	PUNCT
ejpam-304	80	5	vn(x	vn(x	X
ejpam-304	80	6	)	)	PUNCT
ejpam-304	80	7	=	=	PUNCT
ejpam-304	81	1	2x	2x	NUM
ejpam-304	81	2	vn−1(x)−	vn−1(x)−	PROPN
ejpam-304	81	3	vn−2(x	vn−2(x	NOUN
ejpam-304	81	4	)	)	PUNCT
ejpam-304	81	5	,	,	PUNCT
ejpam-304	81	6	n	n	PRON
ejpam-304	81	7	≥	≥	NOUN
ejpam-304	81	8	2	2	NUM
ejpam-304	81	9	.	.	PUNCT
ejpam-304	82	1			PROPN
ejpam-304	82	2			PROPN
ejpam-304	82	3			NOUN
ejpam-304	82	4	,	,	PUNCT
ejpam-304	82	5	(	(	PUNCT
ejpam-304	82	6	3.4	3.4	NUM
ejpam-304	82	7	)	)	PUNCT
ejpam-304	82	8	w0(x	w0(x	NOUN
ejpam-304	82	9	)	)	PUNCT
ejpam-304	82	10	=	=	SYM
ejpam-304	82	11	1	1	NUM
ejpam-304	82	12	,	,	PUNCT
ejpam-304	82	13	w1(x	w1(x	NUM
ejpam-304	82	14	)	)	PUNCT
ejpam-304	82	15	=	=	PUNCT
ejpam-304	83	1	2x	2x	NOUN
ejpam-304	83	2	+	+	CCONJ
ejpam-304	83	3	1	1	NUM
ejpam-304	83	4	,	,	PUNCT
ejpam-304	83	5	wn(x	wn(x	NUM
ejpam-304	83	6	)	)	PUNCT
ejpam-304	83	7	=	=	SYM
ejpam-304	83	8	2x	2x	NUM
ejpam-304	83	9	wn−1(x)−wn−2(x	wn−1(x)−wn−2(x	NOUN
ejpam-304	83	10	)	)	PUNCT
ejpam-304	83	11	,	,	PUNCT
ejpam-304	83	12	n	n	PRON
ejpam-304	83	13	≥	≥	NOUN
ejpam-304	83	14	2	2	NUM
ejpam-304	83	15	.	.	PUNCT
ejpam-304	84	1			PROPN
ejpam-304	84	2			PROPN
ejpam-304	84	3			NOUN
ejpam-304	84	4	.	.	PUNCT
ejpam-304	85	1	(	(	PUNCT
ejpam-304	85	2	3.5	3.5	NUM
ejpam-304	85	3	)	)	PUNCT
ejpam-304	85	4	we	we	PRON
ejpam-304	85	5	have	have	VERB
ejpam-304	85	6	t3	t3	NOUN
ejpam-304	85	7	=	=	SYM
ejpam-304	85	8	1	1	NUM
ejpam-304	85	9	8	8	NUM
ejpam-304	85	10	�	�	PROPN
ejpam-304	85	11	v3	v3	PROPN
ejpam-304	85	12	(	(	PUNCT
ejpam-304	85	13	t	t	PROPN
ejpam-304	85	14	)	)	PUNCT
ejpam-304	86	1	+	+	CCONJ
ejpam-304	86	2	v2	v2	PROPN
ejpam-304	86	3	(	(	PUNCT
ejpam-304	86	4	t	t	NOUN
ejpam-304	86	5	)	)	PUNCT
ejpam-304	86	6	+	+	CCONJ
ejpam-304	86	7	3	3	NUM
ejpam-304	86	8	(	(	PUNCT
ejpam-304	86	9	v1	v1	PROPN
ejpam-304	86	10	(	(	PUNCT
ejpam-304	86	11	t	t	PROPN
ejpam-304	86	12	)	)	PUNCT
ejpam-304	86	13	+	+	CCONJ
ejpam-304	86	14	v0	v0	PROPN
ejpam-304	86	15	(	(	PUNCT
ejpam-304	86	16	t	t	NOUN
ejpam-304	86	17	)	)	PUNCT
ejpam-304	86	18	)	)	PUNCT
ejpam-304	86	19	�	�	PROPN
ejpam-304	87	1	=	=	SYM
ejpam-304	87	2	1	1	NUM
ejpam-304	87	3	8	8	NUM
ejpam-304	87	4	�	�	PROPN
ejpam-304	87	5	w3	w3	PROPN
ejpam-304	87	6	(	(	PUNCT
ejpam-304	87	7	t)−w2	t)−w2	PROPN
ejpam-304	87	8	(	(	PUNCT
ejpam-304	87	9	t	t	NOUN
ejpam-304	87	10	)	)	PUNCT
ejpam-304	87	11	+	+	CCONJ
ejpam-304	87	12	3	3	NUM
ejpam-304	87	13	(	(	PUNCT
ejpam-304	87	14	w1	w1	NOUN
ejpam-304	87	15	(	(	PUNCT
ejpam-304	87	16	t)−w0	t)−w0	X
ejpam-304	87	17	(	(	PUNCT
ejpam-304	87	18	t	t	NOUN
ejpam-304	87	19	)	)	PUNCT
ejpam-304	87	20	)	)	PUNCT
ejpam-304	87	21	�	�	PROPN
ejpam-304	87	22	,	,	PUNCT
ejpam-304	87	23	t2	t2	NOUN
ejpam-304	87	24	=	=	SYM
ejpam-304	87	25	1	1	NUM
ejpam-304	87	26	4	4	NUM
ejpam-304	87	27	�	�	NOUN
ejpam-304	87	28	v2	v2	PROPN
ejpam-304	87	29	(	(	PUNCT
ejpam-304	87	30	t	t	NOUN
ejpam-304	87	31	)	)	PUNCT
ejpam-304	87	32	+	+	NUM
ejpam-304	87	33	v1	v1	PROPN
ejpam-304	87	34	(	(	PUNCT
ejpam-304	87	35	t	t	NOUN
ejpam-304	87	36	)	)	PUNCT
ejpam-304	87	37	+	+	CCONJ
ejpam-304	87	38	2	2	NUM
ejpam-304	87	39	v0	v0	NOUN
ejpam-304	87	40	(	(	PUNCT
ejpam-304	87	41	t	t	NOUN
ejpam-304	87	42	)	)	PUNCT
ejpam-304	87	43	�	�	PROPN
ejpam-304	87	44	=	=	NOUN
ejpam-304	87	45	1	1	NUM
ejpam-304	87	46	4	4	NUM
ejpam-304	87	47	�	�	PROPN
ejpam-304	87	48	w2	w2	NOUN
ejpam-304	87	49	(	(	PUNCT
ejpam-304	87	50	t)−	t)−	PROPN
ejpam-304	87	51	w1	w1	NOUN
ejpam-304	87	52	(	(	PUNCT
ejpam-304	87	53	t	t	PROPN
ejpam-304	87	54	)	)	PUNCT
ejpam-304	87	55	+	+	NUM
ejpam-304	87	56	2w0	2w0	NUM
ejpam-304	87	57	(	(	PUNCT
ejpam-304	87	58	t	t	NOUN
ejpam-304	87	59	)	)	PUNCT
ejpam-304	87	60	�	�	PROPN
ejpam-304	87	61	,	,	PUNCT
ejpam-304	87	62	t	t	PROPN
ejpam-304	87	63	=	=	SYM
ejpam-304	87	64	1	1	NUM
ejpam-304	87	65	2	2	NUM
ejpam-304	87	66	�	�	NOUN
ejpam-304	87	67	v1	v1	NOUN
ejpam-304	87	68	(	(	PUNCT
ejpam-304	87	69	t	t	PROPN
ejpam-304	87	70	)	)	PUNCT
ejpam-304	87	71	+	+	CCONJ
ejpam-304	87	72	v0	v0	PROPN
ejpam-304	87	73	(	(	PUNCT
ejpam-304	87	74	t	t	PROPN
ejpam-304	87	75	)	)	PUNCT
ejpam-304	87	76	�	�	PROPN
ejpam-304	87	77	=	=	NOUN
ejpam-304	87	78	1	1	NUM
ejpam-304	87	79	2	2	NUM
ejpam-304	87	80	�	�	PROPN
ejpam-304	87	81	w1	w1	NOUN
ejpam-304	87	82	(	(	PUNCT
ejpam-304	87	83	t)−w0	t)−w0	X
ejpam-304	87	84	(	(	PUNCT
ejpam-304	87	85	t	t	NOUN
ejpam-304	87	86	)	)	PUNCT
ejpam-304	87	87	�	�	PROPN
ejpam-304	87	88	.	.	PUNCT
ejpam-304	88	1			PROPN
ejpam-304	88	2			PROPN
ejpam-304	88	3			PROPN
ejpam-304	88	4			PROPN
ejpam-304	88	5			PROPN
ejpam-304	88	6			PROPN
ejpam-304	88	7			PROPN
ejpam-304	88	8			PROPN
ejpam-304	88	9			PROPN
ejpam-304	88	10			PROPN
ejpam-304	88	11			PROPN
ejpam-304	88	12			PROPN
ejpam-304	88	13			PROPN
ejpam-304	88	14			PROPN
ejpam-304	88	15			PROPN
ejpam-304	88	16			ADJ
ejpam-304	88	17			PROPN
ejpam-304	88	18			PROPN
ejpam-304	88	19			PROPN
ejpam-304	88	20			PROPN
ejpam-304	88	21			PROPN
ejpam-304	88	22			PROPN
ejpam-304	88	23			PROPN
ejpam-304	88	24			PROPN
ejpam-304	88	25			PROPN
ejpam-304	88	26			PROPN
ejpam-304	88	27			PROPN
ejpam-304	88	28			PROPN
ejpam-304	88	29			NOUN
ejpam-304	88	30	(	(	PUNCT
ejpam-304	88	31	3.6	3.6	NUM
ejpam-304	88	32	)	)	PUNCT
ejpam-304	88	33	it	it	PRON
ejpam-304	88	34	is	be	AUX
ejpam-304	88	35	known	know	VERB
ejpam-304	88	36	that	that	SCONJ
ejpam-304	88	37	[	[	X
ejpam-304	88	38	8	8	NUM
ejpam-304	88	39	]	]	SYM
ejpam-304	88	40	∫	∫	PROPN
ejpam-304	88	41	1	1	NUM
ejpam-304	88	42	−1	−1	NOUN
ejpam-304	88	43	r	r	NOUN
ejpam-304	88	44	1	1	NUM
ejpam-304	88	45	+	+	NUM
ejpam-304	88	46	t	t	PROPN
ejpam-304	88	47	1−	1−	NUM
ejpam-304	88	48	t	t	NOUN
ejpam-304	88	49	vm(t)vn	vm(t)vn	ADP
ejpam-304	88	50	(	(	PUNCT
ejpam-304	88	51	t	t	NOUN
ejpam-304	88	52	)	)	PUNCT
ejpam-304	88	53	d	d	NOUN
ejpam-304	88	54	t	t	NOUN
ejpam-304	88	55	=	=	PUNCT
ejpam-304	88	56			PROPN
ejpam-304	88	57			PRON
ejpam-304	88	58			NOUN
ejpam-304	88	59	0	0	NUM
ejpam-304	88	60	,	,	PUNCT
ejpam-304	88	61	n	n	PROPN
ejpam-304	88	62	6=	6=	NUM
ejpam-304	88	63	m	m	PROPN
ejpam-304	88	64	,	,	PUNCT
ejpam-304	88	65	π	π	PROPN
ejpam-304	88	66	,	,	PUNCT
ejpam-304	88	67	n	n	NOUN
ejpam-304	88	68	=	=	NOUN
ejpam-304	88	69	m.	m.	NOUN
ejpam-304	88	70	(	(	PUNCT
ejpam-304	88	71	3.7	3.7	NUM
ejpam-304	88	72	)	)	PUNCT
ejpam-304	88	73	and	and	CCONJ
ejpam-304	88	74	∫	∫	PROPN
ejpam-304	88	75	1	1	NUM
ejpam-304	88	76	−1	−1	NOUN
ejpam-304	88	77	r	r	NOUN
ejpam-304	88	78	1−	1−	NUM
ejpam-304	88	79	t	t	NOUN
ejpam-304	88	80	1	1	NUM
ejpam-304	88	81	+	+	NUM
ejpam-304	88	82	t	t	PROPN
ejpam-304	88	83	wm(t)wn	wm(t)wn	VERB
ejpam-304	88	84	(	(	PUNCT
ejpam-304	88	85	t	t	NOUN
ejpam-304	88	86	)	)	PUNCT
ejpam-304	88	87	d	d	NOUN
ejpam-304	88	88	t	t	NOUN
ejpam-304	88	89	=	=	PUNCT
ejpam-304	88	90			PROPN
ejpam-304	88	91			PRON
ejpam-304	88	92			NOUN
ejpam-304	88	93	0	0	NUM
ejpam-304	88	94	,	,	PUNCT
ejpam-304	88	95	n	n	PROPN
ejpam-304	88	96	6=	6=	NUM
ejpam-304	88	97	m	m	PROPN
ejpam-304	88	98	,	,	PUNCT
ejpam-304	88	99	π	π	PROPN
ejpam-304	88	100	,	,	PUNCT
ejpam-304	88	101	n=	n=	ADJ
ejpam-304	88	102	m.	m.	NOUN
ejpam-304	88	103	(	(	PUNCT
ejpam-304	88	104	3.8	3.8	NUM
ejpam-304	88	105	)	)	PUNCT
ejpam-304	88	106	m.	m.	NOUN
ejpam-304	88	107	abdulkawi	abdulkawi	PROPN
ejpam-304	88	108	,	,	PUNCT
ejpam-304	88	109	z.	z.	PROPN
ejpam-304	88	110	eshkuvatov	eshkuvatov	PROPN
ejpam-304	88	111	,	,	PUNCT
ejpam-304	88	112	and	and	CCONJ
ejpam-304	88	113	n.	n.	NOUN
ejpam-304	88	114	nik	nik	PROPN
ejpam-304	88	115	long	long	ADJ
ejpam-304	88	116	/	/	SYM
ejpam-304	88	117	eur	eur	PROPN
ejpam-304	88	118	.	.	PUNCT
ejpam-304	89	1	j.	j.	PROPN
ejpam-304	89	2	pure	pure	PROPN
ejpam-304	89	3	appl	appl	PROPN
ejpam-304	89	4	.	.	PROPN
ejpam-304	89	5	math	math	PROPN
ejpam-304	89	6	,	,	PUNCT
ejpam-304	89	7	2	2	NUM
ejpam-304	89	8	(	(	PUNCT
ejpam-304	89	9	2009	2009	NUM
ejpam-304	89	10	)	)	PUNCT
ejpam-304	89	11	,	,	PUNCT
ejpam-304	89	12	(	(	PUNCT
ejpam-304	89	13	462	462	NUM
ejpam-304	89	14	-	-	NOUN
ejpam-304	89	15	472	472	NUM
ejpam-304	89	16	)	)	PUNCT
ejpam-304	89	17	468	468	NUM
ejpam-304	89	18	due	due	ADP
ejpam-304	89	19	to	to	ADP
ejpam-304	89	20	(	(	PUNCT
ejpam-304	89	21	3.3	3.3	NUM
ejpam-304	89	22	)	)	PUNCT
ejpam-304	89	23	,	,	PUNCT
ejpam-304	89	24	(	(	PUNCT
ejpam-304	89	25	3.6	3.6	NUM
ejpam-304	89	26	)	)	PUNCT
ejpam-304	89	27	and	and	CCONJ
ejpam-304	89	28	(	(	PUNCT
ejpam-304	89	29	3.8	3.8	NUM
ejpam-304	89	30	)	)	PUNCT
ejpam-304	90	1	,	,	PUNCT
ejpam-304	90	2	we	we	PRON
ejpam-304	90	3	obtain	obtain	VERB
ejpam-304	90	4	f0	f0	PROPN
ejpam-304	90	5	=	=	SYM
ejpam-304	90	6	c0	c0	PROPN
ejpam-304	90	7	−	−	PROPN
ejpam-304	90	8	c1−	c1−	PROPN
ejpam-304	90	9	c2	c2	PROPN
ejpam-304	90	10	2	2	NUM
ejpam-304	90	11	−	−	PROPN
ejpam-304	90	12	3	3	NUM
ejpam-304	90	13	c3	c3	NOUN
ejpam-304	90	14	8	8	NUM
ejpam-304	90	15	,	,	PUNCT
ejpam-304	90	16	f1	f1	NOUN
ejpam-304	90	17	=	=	SYM
ejpam-304	90	18	2	2	NUM
ejpam-304	90	19	c1	c1	NOUN
ejpam-304	90	20	−	−	PROPN
ejpam-304	90	21	c2	c2	PROPN
ejpam-304	90	22	4	4	NUM
ejpam-304	90	23	+	+	SYM
ejpam-304	90	24	3	3	NUM
ejpam-304	90	25	c3	c3	X
ejpam-304	90	26	8	8	NUM
ejpam-304	90	27	,	,	PUNCT
ejpam-304	90	28	f2	f2	ADJ
ejpam-304	90	29	=	=	SYM
ejpam-304	90	30	2	2	NUM
ejpam-304	90	31	c2	c2	PROPN
ejpam-304	90	32	−	−	PROPN
ejpam-304	90	33	c3	c3	PROPN
ejpam-304	90	34	8	8	NUM
ejpam-304	90	35	,	,	PUNCT
ejpam-304	90	36	f3	f3	NOUN
ejpam-304	90	37	=	=	SYM
ejpam-304	90	38	c3	c3	PROPN
ejpam-304	90	39	8	8	NUM
ejpam-304	90	40	.	.	PUNCT
ejpam-304	91	1			PROPN
ejpam-304	91	2			PROPN
ejpam-304	91	3			PROPN
ejpam-304	91	4			PROPN
ejpam-304	91	5			PROPN
ejpam-304	91	6			PROPN
ejpam-304	91	7			PROPN
ejpam-304	91	8			PROPN
ejpam-304	91	9			PROPN
ejpam-304	91	10			ADJ
ejpam-304	91	11			PROPN
ejpam-304	91	12			PROPN
ejpam-304	91	13			PROPN
ejpam-304	91	14			PROPN
ejpam-304	91	15			PROPN
ejpam-304	91	16			PROPN
ejpam-304	91	17			NOUN
ejpam-304	91	18	(	(	PUNCT
ejpam-304	91	19	3.9	3.9	NUM
ejpam-304	91	20	)	)	PUNCT
ejpam-304	91	21	from	from	ADP
ejpam-304	91	22	(	(	PUNCT
ejpam-304	91	23	2.12	2.12	NUM
ejpam-304	91	24	)	)	PUNCT
ejpam-304	91	25	when	when	SCONJ
ejpam-304	91	26	k(x	k(x	PROPN
ejpam-304	91	27	,	,	PUNCT
ejpam-304	91	28	t	t	PROPN
ejpam-304	91	29	)	)	PUNCT
ejpam-304	91	30	=	=	SYM
ejpam-304	91	31	0	0	NUM
ejpam-304	91	32	,	,	PUNCT
ejpam-304	91	33	yields	yield	VERB
ejpam-304	91	34	a	a	DET
ejpam-304	91	35	j	j	NOUN
ejpam-304	91	36	=	=	SYM
ejpam-304	91	37	1	1	NUM
ejpam-304	91	38	π	π	PROPN
ejpam-304	91	39	f	f	PROPN
ejpam-304	91	40	j	j	PROPN
ejpam-304	91	41	,	,	PUNCT
ejpam-304	91	42	j	j	PROPN
ejpam-304	91	43	=	=	SYM
ejpam-304	91	44	0	0	PROPN
ejpam-304	91	45	,	,	PUNCT
ejpam-304	91	46	...	...	PUNCT
ejpam-304	91	47	,	,	PUNCT
ejpam-304	91	48	n.	n.	PROPN
ejpam-304	91	49	(	(	PUNCT
ejpam-304	91	50	3.10	3.10	NUM
ejpam-304	91	51	)	)	PUNCT
ejpam-304	91	52	the	the	DET
ejpam-304	91	53	approximate	approximate	ADJ
ejpam-304	91	54	solution	solution	NOUN
ejpam-304	91	55	(	(	PUNCT
ejpam-304	91	56	2.5	2.5	NUM
ejpam-304	91	57	)	)	PUNCT
ejpam-304	91	58	with	with	ADP
ejpam-304	91	59	n=	n=	ADJ
ejpam-304	91	60	3	3	NUM
ejpam-304	91	61	becomes	become	VERB
ejpam-304	91	62	ϕn(x	ϕn(x	PRON
ejpam-304	91	63	)	)	PUNCT
ejpam-304	91	64	=	=	SYM
ejpam-304	91	65	1	1	NUM
ejpam-304	91	66	π	π	NOUN
ejpam-304	91	67	r	r	NOUN
ejpam-304	91	68	1	1	NUM
ejpam-304	91	69	+	+	NOUN
ejpam-304	91	70	x	x	SYM
ejpam-304	91	71	1−	1−	NUM
ejpam-304	91	72	x	x	SYM
ejpam-304	91	73	�	�	PROPN
ejpam-304	91	74	f0	f0	PROPN
ejpam-304	91	75	+	+	CCONJ
ejpam-304	91	76	f1v1(x	f1v1(x	NOUN
ejpam-304	91	77	)	)	PUNCT
ejpam-304	92	1	+	+	CCONJ
ejpam-304	92	2	f2v2	f2v2	X
ejpam-304	92	3	(	(	PUNCT
ejpam-304	92	4	x	x	X
ejpam-304	92	5	)	)	PUNCT
ejpam-304	93	1	+	+	CCONJ
ejpam-304	93	2	f3v3	f3v3	X
ejpam-304	93	3	(	(	PUNCT
ejpam-304	93	4	x	x	NOUN
ejpam-304	93	5	)	)	PUNCT
ejpam-304	93	6	�	�	PROPN
ejpam-304	93	7	.	.	PUNCT
ejpam-304	94	1	(	(	PUNCT
ejpam-304	94	2	3.11	3.11	NUM
ejpam-304	94	3	)	)	PUNCT
ejpam-304	94	4	substituting	substituting	NOUN
ejpam-304	94	5	(	(	PUNCT
ejpam-304	94	6	3.9	3.9	NUM
ejpam-304	94	7	)	)	PUNCT
ejpam-304	94	8	and	and	CCONJ
ejpam-304	94	9	(	(	PUNCT
ejpam-304	94	10	3.10	3.10	NUM
ejpam-304	94	11	)	)	PUNCT
ejpam-304	94	12	into	into	ADP
ejpam-304	94	13	(	(	PUNCT
ejpam-304	94	14	3.11	3.11	NUM
ejpam-304	94	15	)	)	PUNCT
ejpam-304	94	16	,	,	PUNCT
ejpam-304	94	17	we	we	PRON
ejpam-304	94	18	obtain	obtain	VERB
ejpam-304	94	19	the	the	DET
ejpam-304	94	20	approximate	approximate	ADJ
ejpam-304	94	21	solutions	solution	NOUN
ejpam-304	94	22	of	of	ADP
ejpam-304	94	23	characteristic	characteristic	ADJ
ejpam-304	94	24	equation	equation	NOUN
ejpam-304	94	25	(	(	PUNCT
ejpam-304	94	26	3.1	3.1	NUM
ejpam-304	94	27	)	)	PUNCT
ejpam-304	94	28	which	which	PRON
ejpam-304	94	29	is	be	AUX
ejpam-304	94	30	ϕn(x	ϕn(x	PRON
ejpam-304	94	31	)	)	PUNCT
ejpam-304	94	32	=	=	SYM
ejpam-304	95	1	1	1	NUM
ejpam-304	95	2	π	π	NOUN
ejpam-304	95	3	r	r	NOUN
ejpam-304	95	4	1	1	NUM
ejpam-304	95	5	+	+	NOUN
ejpam-304	95	6	x	x	SYM
ejpam-304	95	7	1−	1−	NUM
ejpam-304	95	8	x	x	SYM
ejpam-304	95	9	p	p	X
ejpam-304	95	10	(	(	PUNCT
ejpam-304	95	11	x	x	NOUN
ejpam-304	95	12	)	)	PUNCT
ejpam-304	95	13	,	,	PUNCT
ejpam-304	95	14	p(x	p(x	PROPN
ejpam-304	95	15	)	)	PUNCT
ejpam-304	95	16	=	=	SYM
ejpam-304	95	17	c0−	c0−	NOUN
ejpam-304	95	18	c1	c1	NOUN
ejpam-304	95	19	+	+	CCONJ
ejpam-304	95	20	1	1	NUM
ejpam-304	95	21	2	2	NUM
ejpam-304	95	22	(	(	PUNCT
ejpam-304	95	23	c2	c2	PROPN
ejpam-304	95	24	−	−	PROPN
ejpam-304	95	25	c3	c3	PROPN
ejpam-304	95	26	)	)	PUNCT
ejpam-304	95	27	+	+	CCONJ
ejpam-304	95	28	(	(	PUNCT
ejpam-304	95	29	c1	c1	PROPN
ejpam-304	95	30	−	−	PROPN
ejpam-304	95	31	c2	c2	PROPN
ejpam-304	95	32	+	+	CCONJ
ejpam-304	95	33	1	1	NUM
ejpam-304	95	34	2	2	NUM
ejpam-304	95	35	c3)x	c3)x	NOUN
ejpam-304	95	36	+	+	X
ejpam-304	95	37	(	(	PUNCT
ejpam-304	95	38	c2−	c2−	NOUN
ejpam-304	95	39	c3)x	c3)x	NOUN
ejpam-304	95	40	2	2	NUM
ejpam-304	95	41	+	+	NUM
ejpam-304	95	42	c3	c3	NOUN
ejpam-304	95	43	x3	x3	PROPN
ejpam-304	95	44	.	.	PUNCT
ejpam-304	96	1			PROPN
ejpam-304	96	2			PROPN
ejpam-304	96	3			PROPN
ejpam-304	96	4			ADJ
ejpam-304	96	5			NOUN
ejpam-304	96	6	(	(	PUNCT
ejpam-304	96	7	3.12	3.12	NUM
ejpam-304	96	8	)	)	PUNCT
ejpam-304	96	9	in	in	ADP
ejpam-304	96	10	order	order	NOUN
ejpam-304	96	11	to	to	PART
ejpam-304	96	12	obtain	obtain	VERB
ejpam-304	96	13	the	the	DET
ejpam-304	96	14	exact	exact	ADJ
ejpam-304	96	15	solution	solution	NOUN
ejpam-304	96	16	of	of	ADP
ejpam-304	96	17	equation	equation	NOUN
ejpam-304	96	18	(	(	PUNCT
ejpam-304	96	19	3.1	3.1	NUM
ejpam-304	96	20	)	)	PUNCT
ejpam-304	96	21	,	,	PUNCT
ejpam-304	96	22	we	we	PRON
ejpam-304	96	23	substitute	substitute	VERB
ejpam-304	96	24	(	(	PUNCT
ejpam-304	96	25	3.2	3.2	NUM
ejpam-304	96	26	)	)	PUNCT
ejpam-304	96	27	into	into	ADP
ejpam-304	96	28	(	(	PUNCT
ejpam-304	96	29	1.3	1.3	NUM
ejpam-304	96	30	)	)	PUNCT
ejpam-304	96	31	which	which	PRON
ejpam-304	96	32	gives	give	VERB
ejpam-304	96	33	ϕ(x	ϕ(x	PRON
ejpam-304	96	34	)	)	PUNCT
ejpam-304	96	35	=	=	PUNCT
ejpam-304	97	1	−	−	PROPN
ejpam-304	97	2	1	1	NUM
ejpam-304	97	3	π2	π2	NOUN
ejpam-304	97	4	r	r	NOUN
ejpam-304	97	5	1	1	NUM
ejpam-304	97	6	+	+	NOUN
ejpam-304	97	7	x	x	SYM
ejpam-304	97	8	1−	1−	NUM
ejpam-304	97	9	x	x	SYM
ejpam-304	97	10	∫	∫	PROPN
ejpam-304	97	11	1	1	NUM
ejpam-304	97	12	−1	−1	NOUN
ejpam-304	97	13	r	r	NOUN
ejpam-304	97	14	1−	1−	NUM
ejpam-304	97	15	t	t	NOUN
ejpam-304	97	16	1	1	NUM
ejpam-304	97	17	+	+	NUM
ejpam-304	97	18	t	t	PROPN
ejpam-304	97	19	c0	c0	NOUN
ejpam-304	97	20	+	+	CCONJ
ejpam-304	97	21	c1	c1	PROPN
ejpam-304	97	22	t	t	PROPN
ejpam-304	97	23	+	+	CCONJ
ejpam-304	97	24	c2	c2	PROPN
ejpam-304	97	25	t2	t2	PROPN
ejpam-304	97	26	+	+	CCONJ
ejpam-304	97	27	c3	c3	PROPN
ejpam-304	97	28	t3	t3	PROPN
ejpam-304	97	29	t	t	PROPN
ejpam-304	98	1	−	−	NOUN
ejpam-304	99	1	x	x	PUNCT
ejpam-304	100	1	d	d	X
ejpam-304	100	2	t	t	PROPN
ejpam-304	100	3	.	.	PUNCT
ejpam-304	101	1	(	(	PUNCT
ejpam-304	101	2	3.13	3.13	NUM
ejpam-304	101	3	)	)	PUNCT
ejpam-304	101	4	m.	m.	NOUN
ejpam-304	101	5	abdulkawi	abdulkawi	PROPN
ejpam-304	101	6	,	,	PUNCT
ejpam-304	101	7	z.	z.	PROPN
ejpam-304	101	8	eshkuvatov	eshkuvatov	PROPN
ejpam-304	101	9	,	,	PUNCT
ejpam-304	101	10	and	and	CCONJ
ejpam-304	101	11	n.	n.	NOUN
ejpam-304	101	12	nik	nik	PROPN
ejpam-304	101	13	long	long	ADJ
ejpam-304	101	14	/	/	SYM
ejpam-304	101	15	eur	eur	PROPN
ejpam-304	101	16	.	.	PUNCT
ejpam-304	102	1	j.	j.	PROPN
ejpam-304	102	2	pure	pure	PROPN
ejpam-304	102	3	appl	appl	PROPN
ejpam-304	102	4	.	.	PROPN
ejpam-304	102	5	math	math	PROPN
ejpam-304	102	6	,	,	PUNCT
ejpam-304	102	7	2	2	NUM
ejpam-304	102	8	(	(	PUNCT
ejpam-304	102	9	2009	2009	NUM
ejpam-304	102	10	)	)	PUNCT
ejpam-304	102	11	,	,	PUNCT
ejpam-304	102	12	(	(	PUNCT
ejpam-304	102	13	462	462	NUM
ejpam-304	102	14	-	-	NOUN
ejpam-304	102	15	472	472	NUM
ejpam-304	102	16	)	)	PUNCT
ejpam-304	102	17	469	469	NUM
ejpam-304	102	18	it	it	PRON
ejpam-304	102	19	is	be	AUX
ejpam-304	102	20	easy	easy	ADJ
ejpam-304	102	21	to	to	PART
ejpam-304	102	22	see	see	VERB
ejpam-304	102	23	that	that	DET
ejpam-304	102	24	∫	∫	PROPN
ejpam-304	102	25	1	1	NUM
ejpam-304	102	26	−1	−1	NOUN
ejpam-304	102	27	r	r	NOUN
ejpam-304	102	28	1−	1−	NUM
ejpam-304	102	29	t	t	NOUN
ejpam-304	102	30	1	1	NUM
ejpam-304	102	31	+	+	SYM
ejpam-304	102	32	t	t	PROPN
ejpam-304	102	33	1	1	NUM
ejpam-304	102	34	t	t	NOUN
ejpam-304	102	35	−	−	NOUN
ejpam-304	103	1	x	x	PUNCT
ejpam-304	104	1	d	d	X
ejpam-304	104	2	t	t	PROPN
ejpam-304	104	3	=	=	SYM
ejpam-304	104	4	−π	−π	PROPN
ejpam-304	104	5	,	,	PUNCT
ejpam-304	104	6	∫	∫	PROPN
ejpam-304	104	7	1	1	NUM
ejpam-304	104	8	−1	−1	NOUN
ejpam-304	104	9	r	r	NOUN
ejpam-304	104	10	1−	1−	NUM
ejpam-304	104	11	t	t	NOUN
ejpam-304	104	12	1	1	NUM
ejpam-304	104	13	+	+	NUM
ejpam-304	104	14	t	t	PROPN
ejpam-304	104	15	t	t	X
ejpam-304	104	16	t	t	NOUN
ejpam-304	104	17	−	−	NOUN
ejpam-304	105	1	x	x	PUNCT
ejpam-304	105	2	d	d	X
ejpam-304	105	3	t	t	PROPN
ejpam-304	105	4	=	=	NOUN
ejpam-304	105	5	−π(x	−π(x	NOUN
ejpam-304	105	6	−	−	NOUN
ejpam-304	105	7	1	1	NUM
ejpam-304	105	8	)	)	PUNCT
ejpam-304	105	9	,	,	PUNCT
ejpam-304	105	10	∫	∫	PROPN
ejpam-304	106	1	1	1	NUM
ejpam-304	106	2	−1	−1	NOUN
ejpam-304	106	3	r	r	NOUN
ejpam-304	106	4	1−	1−	NUM
ejpam-304	106	5	t	t	NOUN
ejpam-304	106	6	1	1	NUM
ejpam-304	106	7	+	+	PROPN
ejpam-304	106	8	t	t	NOUN
ejpam-304	106	9	t2	t2	NOUN
ejpam-304	106	10	t	t	PROPN
ejpam-304	106	11	−	−	NOUN
ejpam-304	106	12	x	x	SYM
ejpam-304	107	1	d	d	X
ejpam-304	107	2	t	t	PROPN
ejpam-304	107	3	=	=	SYM
ejpam-304	107	4	−π(x2−	−π(x2−	PROPN
ejpam-304	107	5	x	x	PUNCT
ejpam-304	107	6	+	+	NUM
ejpam-304	107	7	0.5	0.5	NUM
ejpam-304	107	8	)	)	PUNCT
ejpam-304	107	9	,	,	PUNCT
ejpam-304	107	10	∫	∫	PROPN
ejpam-304	107	11	1	1	NUM
ejpam-304	107	12	−1	−1	NOUN
ejpam-304	107	13	r	r	NOUN
ejpam-304	107	14	1−	1−	NUM
ejpam-304	107	15	t	t	NOUN
ejpam-304	107	16	1	1	NUM
ejpam-304	107	17	+	+	NUM
ejpam-304	107	18	t	t	PROPN
ejpam-304	107	19	t3	t3	PROPN
ejpam-304	107	20	t	t	PROPN
ejpam-304	108	1	−	−	NOUN
ejpam-304	108	2	x	x	PUNCT
ejpam-304	109	1	d	d	X
ejpam-304	109	2	t	t	NOUN
ejpam-304	109	3	=	=	PRON
ejpam-304	109	4	−π(x3−	−π(x3−	PROPN
ejpam-304	109	5	x2	x2	NOUN
ejpam-304	109	6	+	+	NUM
ejpam-304	109	7	0.5	0.5	NUM
ejpam-304	109	8	x	x	SYM
ejpam-304	109	9	−	−	PROPN
ejpam-304	109	10	0.5	0.5	NUM
ejpam-304	109	11	)	)	PUNCT
ejpam-304	109	12	.	.	PUNCT
ejpam-304	110	1			PROPN
ejpam-304	110	2			PROPN
ejpam-304	110	3			PROPN
ejpam-304	110	4			PROPN
ejpam-304	110	5			PROPN
ejpam-304	110	6			PROPN
ejpam-304	110	7			PROPN
ejpam-304	110	8			PROPN
ejpam-304	110	9			PROPN
ejpam-304	110	10			PROPN
ejpam-304	110	11			PROPN
ejpam-304	110	12			PROPN
ejpam-304	110	13			PROPN
ejpam-304	110	14			ADJ
ejpam-304	110	15			PROPN
ejpam-304	110	16			PROPN
ejpam-304	110	17			PROPN
ejpam-304	110	18			PROPN
ejpam-304	110	19			PROPN
ejpam-304	110	20			PROPN
ejpam-304	110	21			PROPN
ejpam-304	110	22			PROPN
ejpam-304	110	23			PROPN
ejpam-304	110	24			PROPN
ejpam-304	110	25			NOUN
ejpam-304	110	26	(	(	PUNCT
ejpam-304	110	27	3.14	3.14	NUM
ejpam-304	110	28	)	)	PUNCT
ejpam-304	110	29	using	use	VERB
ejpam-304	110	30	(	(	PUNCT
ejpam-304	110	31	3.14	3.14	NUM
ejpam-304	110	32	)	)	PUNCT
ejpam-304	110	33	into	into	ADP
ejpam-304	110	34	(	(	PUNCT
ejpam-304	110	35	3.13	3.13	NUM
ejpam-304	110	36	)	)	PUNCT
ejpam-304	110	37	,	,	PUNCT
ejpam-304	110	38	we	we	PRON
ejpam-304	110	39	obtain	obtain	VERB
ejpam-304	110	40	the	the	DET
ejpam-304	110	41	exact	exact	ADJ
ejpam-304	110	42	solution	solution	NOUN
ejpam-304	110	43	of	of	ADP
ejpam-304	110	44	equation	equation	NOUN
ejpam-304	110	45	(	(	PUNCT
ejpam-304	110	46	3.1	3.1	NUM
ejpam-304	110	47	)	)	PUNCT
ejpam-304	110	48	which	which	PRON
ejpam-304	110	49	is	be	AUX
ejpam-304	110	50	identical	identical	ADJ
ejpam-304	110	51	to	to	ADP
ejpam-304	110	52	the	the	DET
ejpam-304	110	53	approximate	approximate	ADJ
ejpam-304	110	54	solutions	solution	NOUN
ejpam-304	110	55	(	(	PUNCT
ejpam-304	110	56	3.12	3.12	NUM
ejpam-304	110	57	)	)	PUNCT
ejpam-304	110	58	.	.	PUNCT
ejpam-304	111	1	4	4	X
ejpam-304	111	2	.	.	X
ejpam-304	111	3	particular	particular	ADJ
ejpam-304	111	4	result	result	NOUN
ejpam-304	111	5	let	let	VERB
ejpam-304	111	6	us	we	PRON
ejpam-304	111	7	consider	consider	VERB
ejpam-304	111	8	the	the	DET
ejpam-304	111	9	integral	integral	ADJ
ejpam-304	111	10	equation	equation	NOUN
ejpam-304	111	11	∫	∫	PROPN
ejpam-304	111	12	1	1	NUM
ejpam-304	111	13	−1	−1	NOUN
ejpam-304	111	14	ϕ(t	ϕ(t	NUM
ejpam-304	111	15	)	)	PUNCT
ejpam-304	112	1	t	t	NOUN
ejpam-304	112	2	−	−	NOUN
ejpam-304	113	1	x	x	SYM
ejpam-304	113	2	d	d	X
ejpam-304	113	3	t	t	PROPN
ejpam-304	113	4	+	+	CCONJ
ejpam-304	113	5	∫	∫	PROPN
ejpam-304	113	6	1	1	NUM
ejpam-304	113	7	−1	−1	NOUN
ejpam-304	113	8	(	(	PUNCT
ejpam-304	113	9	x3	x3	ADJ
ejpam-304	113	10	+	+	X
ejpam-304	113	11	t3)ϕ(t	t3)ϕ(t	NOUN
ejpam-304	113	12	)	)	PUNCT
ejpam-304	113	13	d	d	NOUN
ejpam-304	113	14	t	t	NOUN
ejpam-304	113	15	=	=	SYM
ejpam-304	113	16	3x3	3x3	NUM
ejpam-304	113	17	+	+	NUM
ejpam-304	113	18	2x2	2x2	NUM
ejpam-304	113	19	+	+	CCONJ
ejpam-304	113	20	x	x	NOUN
ejpam-304	113	21	,	,	PUNCT
ejpam-304	113	22	−1	−1	NOUN
ejpam-304	113	23	<	<	X
ejpam-304	113	24	x	x	X
ejpam-304	113	25	<	<	X
ejpam-304	113	26	1	1	NUM
ejpam-304	113	27	(	(	PUNCT
ejpam-304	113	28	4.1	4.1	NUM
ejpam-304	113	29	)	)	PUNCT
ejpam-304	113	30	and	and	CCONJ
ejpam-304	113	31	we	we	PRON
ejpam-304	113	32	seek	seek	VERB
ejpam-304	113	33	the	the	DET
ejpam-304	113	34	solution	solution	NOUN
ejpam-304	113	35	of	of	ADP
ejpam-304	113	36	this	this	DET
ejpam-304	113	37	equation	equation	NOUN
ejpam-304	113	38	which	which	PRON
ejpam-304	113	39	is	be	AUX
ejpam-304	113	40	bounded	bound	VERB
ejpam-304	113	41	at	at	ADP
ejpam-304	113	42	x	x	X
ejpam-304	113	43	=	=	NOUN
ejpam-304	113	44	−1	−1	NOUN
ejpam-304	113	45	.	.	PUNCT
ejpam-304	114	1	from	from	ADP
ejpam-304	114	2	(	(	PUNCT
ejpam-304	114	3	2.4	2.4	NUM
ejpam-304	114	4	)	)	PUNCT
ejpam-304	114	5	and	and	CCONJ
ejpam-304	114	6	(	(	PUNCT
ejpam-304	114	7	3.6	3.6	NUM
ejpam-304	114	8	)	)	PUNCT
ejpam-304	114	9	yields	yield	NOUN
ejpam-304	114	10	fk	fk	INTJ
ejpam-304	114	11	=	=	SYM
ejpam-304	114	12	1	1	NUM
ejpam-304	114	13	π	π	NOUN
ejpam-304	114	14	∫	∫	PROPN
ejpam-304	114	15	1	1	NUM
ejpam-304	114	16	−1	−1	NOUN
ejpam-304	114	17	r	r	NOUN
ejpam-304	114	18	1−	1−	NUM
ejpam-304	114	19	x	x	SYM
ejpam-304	114	20	1	1	NUM
ejpam-304	114	21	+	+	CCONJ
ejpam-304	114	22	x	x	PART
ejpam-304	114	23	�	�	NOUN
ejpam-304	114	24	3t3	3t3	NUM
ejpam-304	114	25	+	+	NOUN
ejpam-304	114	26	2t2	2t2	NUM
ejpam-304	114	27	+	+	NUM
ejpam-304	114	28	t	t	PROPN
ejpam-304	114	29	�	�	PROPN
ejpam-304	114	30	wk(t	wk(t	PUNCT
ejpam-304	114	31	)	)	PUNCT
ejpam-304	114	32	d	d	NOUN
ejpam-304	114	33	t	t	NOUN
ejpam-304	114	34	=	=	SYM
ejpam-304	114	35	1	1	NUM
ejpam-304	114	36	π	π	NOUN
ejpam-304	114	37	∫	∫	PROPN
ejpam-304	114	38	1	1	NUM
ejpam-304	114	39	−1	−1	NOUN
ejpam-304	114	40	r	r	NOUN
ejpam-304	114	41	1−	1−	NUM
ejpam-304	114	42	x	x	SYM
ejpam-304	114	43	1	1	NUM
ejpam-304	114	44	+	+	CCONJ
ejpam-304	114	45	x	x	PART
ejpam-304	114	46	�	�	PROPN
ejpam-304	114	47	3	3	NUM
ejpam-304	114	48	8	8	NUM
ejpam-304	114	49	w3(t	w3(t	NUM
ejpam-304	114	50	)	)	PUNCT
ejpam-304	115	1	+	+	CCONJ
ejpam-304	115	2	1	1	NUM
ejpam-304	115	3	8	8	NUM
ejpam-304	115	4	w2(t)+	w2(t)+	PROPN
ejpam-304	115	5	9	9	NUM
ejpam-304	115	6	8	8	NUM
ejpam-304	115	7	w1(t)−	w1(t)−	SYM
ejpam-304	115	8	5	5	NUM
ejpam-304	115	9	8	8	NUM
ejpam-304	115	10	w0(t	w0(t	PROPN
ejpam-304	115	11	)	)	PUNCT
ejpam-304	115	12	�	�	PROPN
ejpam-304	116	1	wk(t)d	wk(t)d	PUNCT
ejpam-304	116	2	t	t	PROPN
ejpam-304	116	3	.	.	PUNCT
ejpam-304	117	1			PROPN
ejpam-304	117	2			PROPN
ejpam-304	117	3			PROPN
ejpam-304	117	4			PROPN
ejpam-304	117	5			ADJ
ejpam-304	117	6			ADJ
ejpam-304	117	7			NOUN
ejpam-304	117	8	(	(	PUNCT
ejpam-304	117	9	4.2	4.2	NUM
ejpam-304	117	10	)	)	PUNCT
ejpam-304	117	11	using	use	VERB
ejpam-304	117	12	(	(	PUNCT
ejpam-304	117	13	3.8	3.8	NUM
ejpam-304	117	14	)	)	PUNCT
ejpam-304	117	15	into	into	ADP
ejpam-304	117	16	(	(	PUNCT
ejpam-304	117	17	4.2	4.2	NUM
ejpam-304	117	18	)	)	PUNCT
ejpam-304	117	19	,	,	PUNCT
ejpam-304	117	20	we	we	PRON
ejpam-304	117	21	have	have	VERB
ejpam-304	117	22	�	�	PROPN
ejpam-304	117	23	f0	f0	PROPN
ejpam-304	118	1	=	=	NOUN
ejpam-304	118	2	−	−	PROPN
ejpam-304	118	3	5	5	NUM
ejpam-304	118	4	8	8	NUM
ejpam-304	118	5	,	,	PUNCT
ejpam-304	118	6	f1	f1	NOUN
ejpam-304	118	7	=	=	NOUN
ejpam-304	118	8	9	9	NUM
ejpam-304	118	9	8	8	NUM
ejpam-304	118	10	,	,	PUNCT
ejpam-304	118	11	f2	f2	ADJ
ejpam-304	118	12	=	=	NOUN
ejpam-304	118	13	1	1	NUM
ejpam-304	118	14	8	8	NUM
ejpam-304	118	15	,	,	PUNCT
ejpam-304	118	16	f3	f3	NOUN
ejpam-304	118	17	=	=	SYM
ejpam-304	118	18	3	3	NUM
ejpam-304	118	19	8	8	NUM
ejpam-304	118	20	�	�	PROPN
ejpam-304	118	21	.	.	PUNCT
ejpam-304	119	1	(	(	PUNCT
ejpam-304	119	2	4.3	4.3	NUM
ejpam-304	119	3	)	)	PUNCT
ejpam-304	119	4	due	due	ADP
ejpam-304	119	5	to	to	ADP
ejpam-304	119	6	(	(	PUNCT
ejpam-304	119	7	2.10	2.10	NUM
ejpam-304	119	8	)	)	PUNCT
ejpam-304	119	9	we	we	PRON
ejpam-304	119	10	get	get	VERB
ejpam-304	119	11	µ	µ	PRON
ejpam-304	119	12	j	j	PROPN
ejpam-304	119	13	,	,	PUNCT
ejpam-304	119	14	k	k	PROPN
ejpam-304	120	1	=	=	SYM
ejpam-304	120	2	1	1	NUM
ejpam-304	120	3	π	π	NOUN
ejpam-304	120	4	∫	∫	PROPN
ejpam-304	120	5	1	1	NUM
ejpam-304	120	6	−1	−1	NOUN
ejpam-304	120	7	r	r	NOUN
ejpam-304	120	8	1−	1−	NUM
ejpam-304	120	9	x	x	SYM
ejpam-304	120	10	1	1	NUM
ejpam-304	120	11	+	+	CCONJ
ejpam-304	120	12	x	x	SYM
ejpam-304	120	13	∫	∫	PROPN
ejpam-304	120	14	1	1	NUM
ejpam-304	120	15	−1	−1	NOUN
ejpam-304	120	16	r	r	NOUN
ejpam-304	120	17	1	1	NUM
ejpam-304	120	18	+	+	NUM
ejpam-304	120	19	t	t	NOUN
ejpam-304	120	20	1−	1−	NUM
ejpam-304	120	21	t	t	PROPN
ejpam-304	120	22	�	�	PROPN
ejpam-304	120	23	x3	x3	PROPN
ejpam-304	120	24	+	+	CCONJ
ejpam-304	120	25	t3	t3	PROPN
ejpam-304	120	26	�	�	PROPN
ejpam-304	120	27	vj(t)wk(x	vj(t)wk(x	ADP
ejpam-304	120	28	)	)	PUNCT
ejpam-304	121	1	d	d	NOUN
ejpam-304	121	2	t	t	PROPN
ejpam-304	121	3	d	d	X
ejpam-304	121	4	x	x	X
ejpam-304	121	5	.	.	PUNCT
ejpam-304	122	1	(	(	PUNCT
ejpam-304	122	2	4.4	4.4	NUM
ejpam-304	122	3	)	)	PUNCT
ejpam-304	122	4	m.	m.	NOUN
ejpam-304	122	5	abdulkawi	abdulkawi	PROPN
ejpam-304	122	6	,	,	PUNCT
ejpam-304	122	7	z.	z.	PROPN
ejpam-304	122	8	eshkuvatov	eshkuvatov	PROPN
ejpam-304	122	9	,	,	PUNCT
ejpam-304	122	10	and	and	CCONJ
ejpam-304	122	11	n.	n.	NOUN
ejpam-304	122	12	nik	nik	PROPN
ejpam-304	122	13	long	long	ADJ
ejpam-304	122	14	/	/	SYM
ejpam-304	122	15	eur	eur	PROPN
ejpam-304	122	16	.	.	PUNCT
ejpam-304	123	1	j.	j.	PROPN
ejpam-304	123	2	pure	pure	PROPN
ejpam-304	123	3	appl	appl	PROPN
ejpam-304	123	4	.	.	PROPN
ejpam-304	123	5	math	math	PROPN
ejpam-304	123	6	,	,	PUNCT
ejpam-304	123	7	2	2	NUM
ejpam-304	123	8	(	(	PUNCT
ejpam-304	123	9	2009	2009	NUM
ejpam-304	123	10	)	)	PUNCT
ejpam-304	123	11	,	,	PUNCT
ejpam-304	123	12	(	(	PUNCT
ejpam-304	123	13	462	462	NUM
ejpam-304	123	14	-	-	NOUN
ejpam-304	123	15	472	472	NUM
ejpam-304	123	16	)	)	PUNCT
ejpam-304	123	17	470	470	NUM
ejpam-304	123	18	using	use	VERB
ejpam-304	123	19	orthogonal	orthogonal	ADJ
ejpam-304	123	20	property	property	NOUN
ejpam-304	123	21	(	(	PUNCT
ejpam-304	123	22	3.7	3.7	NUM
ejpam-304	123	23	)	)	PUNCT
ejpam-304	123	24	into	into	ADP
ejpam-304	123	25	(	(	PUNCT
ejpam-304	123	26	4.4	4.4	NUM
ejpam-304	123	27	)	)	PUNCT
ejpam-304	123	28	we	we	PRON
ejpam-304	123	29	obtain	obtain	VERB
ejpam-304	123	30	µ0,k	µ0,k	NOUN
ejpam-304	123	31	=	=	SYM
ejpam-304	123	32	1	1	NUM
ejpam-304	123	33	π	π	NOUN
ejpam-304	123	34	∫	∫	PROPN
ejpam-304	123	35	1	1	NUM
ejpam-304	123	36	−1	−1	NOUN
ejpam-304	123	37	r	r	NOUN
ejpam-304	123	38	1−	1−	NUM
ejpam-304	123	39	x	x	SYM
ejpam-304	123	40	1	1	NUM
ejpam-304	123	41	+	+	NUM
ejpam-304	123	42	x	x	NOUN
ejpam-304	123	43			NOUN
ejpam-304	123	44	πx3	πx3	ADJ
ejpam-304	123	45	+	+	NUM
ejpam-304	123	46	∫	∫	PROPN
ejpam-304	123	47	1	1	NUM
ejpam-304	123	48	−1	−1	NOUN
ejpam-304	123	49	r	r	NOUN
ejpam-304	123	50	1	1	NUM
ejpam-304	123	51	+	+	NUM
ejpam-304	123	52	t	t	NOUN
ejpam-304	123	53	1−	1−	NUM
ejpam-304	123	54	t	t	PROPN
ejpam-304	123	55	t3	t3	PROPN
ejpam-304	123	56	v0	v0	PROPN
ejpam-304	123	57	d	d	PROPN
ejpam-304	123	58	t	t	PROPN
ejpam-304	123	59			PROPN
ejpam-304	123	60	wk(x	wk(x	PROPN
ejpam-304	123	61	)	)	PUNCT
ejpam-304	123	62	d	d	NOUN
ejpam-304	123	63	x	x	SYM
ejpam-304	123	64	(	(	PUNCT
ejpam-304	123	65	4.5	4.5	NUM
ejpam-304	123	66	)	)	PUNCT
ejpam-304	123	67	and	and	CCONJ
ejpam-304	123	68	µ	µ	PRON
ejpam-304	123	69	j	j	PROPN
ejpam-304	123	70	,	,	PUNCT
ejpam-304	123	71	k	k	PROPN
ejpam-304	123	72	=	=	SYM
ejpam-304	123	73	1	1	NUM
ejpam-304	123	74	π	π	NOUN
ejpam-304	123	75	∫	∫	PROPN
ejpam-304	123	76	1	1	NUM
ejpam-304	123	77	−1	−1	NOUN
ejpam-304	123	78	r	r	NOUN
ejpam-304	123	79	1−	1−	NUM
ejpam-304	123	80	x	x	SYM
ejpam-304	123	81	1	1	NUM
ejpam-304	123	82	+	+	NUM
ejpam-304	123	83	x	x	NOUN
ejpam-304	123	84			PROPN
ejpam-304	123	85			X
ejpam-304	123	86	∫	∫	PROPN
ejpam-304	123	87	1	1	NUM
ejpam-304	123	88	−1	−1	NOUN
ejpam-304	123	89	r	r	NOUN
ejpam-304	123	90	1	1	NUM
ejpam-304	123	91	+	+	NUM
ejpam-304	123	92	t	t	NOUN
ejpam-304	124	1	1−	1−	NUM
ejpam-304	124	2	t	t	PROPN
ejpam-304	124	3	t3	t3	PROPN
ejpam-304	124	4	vj	vj	PROPN
ejpam-304	124	5	d	d	PROPN
ejpam-304	124	6	t	t	PROPN
ejpam-304	124	7			PROPN
ejpam-304	124	8	wk(x	wk(x	PROPN
ejpam-304	124	9	)	)	PUNCT
ejpam-304	124	10	d	d	PROPN
ejpam-304	124	11	x	x	X
ejpam-304	124	12	,	,	PUNCT
ejpam-304	124	13	j	j	PROPN
ejpam-304	124	14	=	=	SYM
ejpam-304	124	15	1	1	NUM
ejpam-304	124	16	,	,	PUNCT
ejpam-304	124	17	2	2	NUM
ejpam-304	124	18	,	,	PUNCT
ejpam-304	124	19	...	...	PUNCT
ejpam-304	124	20	,	,	PUNCT
ejpam-304	124	21	n.	n.	NOUN
ejpam-304	124	22	(	(	PUNCT
ejpam-304	124	23	4.6	4.6	NUM
ejpam-304	124	24	)	)	PUNCT
ejpam-304	124	25	due	due	ADP
ejpam-304	124	26	to	to	ADP
ejpam-304	124	27	(	(	PUNCT
ejpam-304	124	28	3.6	3.6	NUM
ejpam-304	124	29	-	-	SYM
ejpam-304	124	30	3.7	3.7	NUM
ejpam-304	124	31	)	)	PUNCT
ejpam-304	124	32	,	,	PUNCT
ejpam-304	124	33	equation	equation	NOUN
ejpam-304	124	34	(	(	PUNCT
ejpam-304	124	35	4.5	4.5	NUM
ejpam-304	124	36	)	)	PUNCT
ejpam-304	124	37	becomes	become	VERB
ejpam-304	124	38	µ0,k	µ0,k	PROPN
ejpam-304	124	39	=	=	SYM
ejpam-304	124	40	∫	∫	PROPN
ejpam-304	124	41	1	1	NUM
ejpam-304	124	42	−1	−1	NOUN
ejpam-304	124	43	r	r	NOUN
ejpam-304	124	44	1−	1−	NUM
ejpam-304	124	45	x	x	SYM
ejpam-304	124	46	1	1	NUM
ejpam-304	124	47	+	+	CCONJ
ejpam-304	124	48	x	x	PART
ejpam-304	124	49	�	�	NOUN
ejpam-304	124	50	x3	x3	PROPN
ejpam-304	124	51	+	+	CCONJ
ejpam-304	124	52	3	3	NUM
ejpam-304	124	53	8	8	NUM
ejpam-304	124	54	�	�	PROPN
ejpam-304	124	55	wk(x	wk(x	NOUN
ejpam-304	124	56	)	)	PUNCT
ejpam-304	125	1	d	d	X
ejpam-304	125	2	x	x	SYM
ejpam-304	125	3	(	(	PUNCT
ejpam-304	125	4	4.7	4.7	NUM
ejpam-304	125	5	)	)	PUNCT
ejpam-304	125	6	which	which	PRON
ejpam-304	125	7	gives	give	VERB
ejpam-304	125	8	µ0,0	µ0,0	NOUN
ejpam-304	125	9	=	=	SYM
ejpam-304	125	10	0	0	NUM
ejpam-304	125	11	,	,	PUNCT
ejpam-304	125	12	µ0,1	µ0,1	ADP
ejpam-304	125	13	=	=	NOUN
ejpam-304	125	14	3π	3π	NUM
ejpam-304	125	15	8	8	NUM
ejpam-304	125	16	,	,	PUNCT
ejpam-304	125	17	µ0,2	µ0,2	PROPN
ejpam-304	125	18	=	=	SYM
ejpam-304	125	19	−	−	PROPN
ejpam-304	125	20	π	π	SYM
ejpam-304	125	21	8	8	NUM
ejpam-304	125	22	,	,	PUNCT
ejpam-304	125	23	µ0,3	µ0,3	ADV
ejpam-304	125	24	=	=	SYM
ejpam-304	125	25	π	π	SYM
ejpam-304	125	26	8	8	NUM
ejpam-304	125	27	.	.	PUNCT
ejpam-304	125	28	�	�	PROPN
ejpam-304	125	29	(	(	PUNCT
ejpam-304	125	30	4.8	4.8	NUM
ejpam-304	125	31	)	)	PUNCT
ejpam-304	125	32	from	from	ADP
ejpam-304	125	33	(	(	PUNCT
ejpam-304	125	34	4.6	4.6	NUM
ejpam-304	125	35	)	)	PUNCT
ejpam-304	125	36	with	with	ADP
ejpam-304	125	37	help	help	NOUN
ejpam-304	125	38	of	of	ADP
ejpam-304	125	39	(	(	PUNCT
ejpam-304	125	40	3.6	3.6	NUM
ejpam-304	125	41	-	-	SYM
ejpam-304	125	42	3.7	3.7	NUM
ejpam-304	125	43	)	)	PUNCT
ejpam-304	125	44	,	,	PUNCT
ejpam-304	125	45	yields	yield	VERB
ejpam-304	125	46	µ1,k	µ1,k	PROPN
ejpam-304	125	47	=	=	SYM
ejpam-304	125	48	3	3	NUM
ejpam-304	125	49	8	8	NUM
ejpam-304	125	50	∫	∫	NOUN
ejpam-304	125	51	1	1	NUM
ejpam-304	125	52	−1	−1	NOUN
ejpam-304	125	53	r	r	NOUN
ejpam-304	125	54	1−	1−	NUM
ejpam-304	125	55	x	x	SYM
ejpam-304	125	56	1	1	NUM
ejpam-304	125	57	+	+	NUM
ejpam-304	125	58	x	x	SYM
ejpam-304	125	59	wk(x	wk(x	NOUN
ejpam-304	125	60	)	)	PUNCT
ejpam-304	125	61	d	d	NOUN
ejpam-304	125	62	x	x	SYM
ejpam-304	125	63	(	(	PUNCT
ejpam-304	125	64	4.9	4.9	NUM
ejpam-304	125	65	)	)	PUNCT
ejpam-304	125	66	which	which	PRON
ejpam-304	125	67	gives	give	VERB
ejpam-304	125	68	µ1,0	µ1,0	NOUN
ejpam-304	125	69	=	=	NOUN
ejpam-304	125	70	3π	3π	NOUN
ejpam-304	125	71	8	8	NUM
ejpam-304	125	72	,	,	PUNCT
ejpam-304	125	73	µ1,k	µ1,k	PROPN
ejpam-304	125	74	=	=	SYM
ejpam-304	125	75	0	0	PROPN
ejpam-304	125	76	,	,	PUNCT
ejpam-304	125	77	k	k	NOUN
ejpam-304	125	78	=	=	SYM
ejpam-304	125	79	1	1	NUM
ejpam-304	125	80	,	,	PUNCT
ejpam-304	125	81	2	2	NUM
ejpam-304	125	82	,	,	PUNCT
ejpam-304	125	83	3	3	NUM
ejpam-304	125	84	.	.	X
ejpam-304	125	85	�	�	PROPN
ejpam-304	125	86	(	(	PUNCT
ejpam-304	125	87	4.10	4.10	NUM
ejpam-304	125	88	)	)	PUNCT
ejpam-304	125	89	similarly	similarly	ADV
ejpam-304	125	90	,	,	PUNCT
ejpam-304	125	91	we	we	PRON
ejpam-304	125	92	obtain	obtain	VERB
ejpam-304	125	93	µ2,0	µ2,0	X
ejpam-304	125	94	=	=	PUNCT
ejpam-304	125	95	µ3,0	µ3,0	PROPN
ejpam-304	125	96	=	=	PUNCT
ejpam-304	125	97	π	π	SYM
ejpam-304	125	98	8	8	NUM
ejpam-304	125	99	,	,	PUNCT
ejpam-304	125	100	µ2,k	µ2,k	PROPN
ejpam-304	125	101	=	=	SYM
ejpam-304	125	102	µ3,k	µ3,k	PROPN
ejpam-304	125	103	=	=	SYM
ejpam-304	125	104	0	0	NUM
ejpam-304	125	105	,	,	PUNCT
ejpam-304	125	106	k	k	NOUN
ejpam-304	125	107	=	=	SYM
ejpam-304	125	108	1	1	NUM
ejpam-304	125	109	,	,	PUNCT
ejpam-304	125	110	2	2	NUM
ejpam-304	125	111	,	,	PUNCT
ejpam-304	125	112	3	3	NUM
ejpam-304	125	113	.	.	X
ejpam-304	125	114	ª	ª	PROPN
ejpam-304	125	115	(	(	PUNCT
ejpam-304	125	116	4.11	4.11	NUM
ejpam-304	125	117	)	)	PUNCT
ejpam-304	125	118	due	due	ADP
ejpam-304	125	119	to	to	ADP
ejpam-304	125	120	(	(	PUNCT
ejpam-304	125	121	2.12	2.12	NUM
ejpam-304	125	122	)	)	PUNCT
ejpam-304	125	123	,	,	PUNCT
ejpam-304	125	124	(	(	PUNCT
ejpam-304	125	125	4.3	4.3	NUM
ejpam-304	125	126	)	)	PUNCT
ejpam-304	125	127	and	and	CCONJ
ejpam-304	125	128	(	(	PUNCT
ejpam-304	125	129	4.8	4.8	NUM
ejpam-304	125	130	,	,	PUNCT
ejpam-304	125	131	4.10	4.10	NUM
ejpam-304	125	132	-	-	SYM
ejpam-304	125	133	4.11	4.11	NUM
ejpam-304	125	134	)	)	PUNCT
ejpam-304	125	135	we	we	PRON
ejpam-304	125	136	have	have	VERB
ejpam-304	125	137	the	the	DET
ejpam-304	125	138	following	follow	VERB
ejpam-304	125	139	system	system	NOUN
ejpam-304	125	140	of	of	ADP
ejpam-304	125	141	linear	linear	PROPN
ejpam-304	125	142	equations	equation	NOUN
ejpam-304	125	143	ak	ak	PROPN
ejpam-304	126	1	+	+	CCONJ
ejpam-304	126	2	1	1	NUM
ejpam-304	126	3	π	π	PROPN
ejpam-304	126	4	3	3	NUM
ejpam-304	126	5	∑	∑	PUNCT
ejpam-304	126	6	j=0	j=0	PROPN
ejpam-304	126	7	a	a	DET
ejpam-304	126	8	j	j	PROPN
ejpam-304	126	9	µ	µ	PROPN
ejpam-304	126	10	j	j	PROPN
ejpam-304	126	11	,	,	PUNCT
ejpam-304	126	12	k	k	PROPN
ejpam-304	127	1	=	=	SYM
ejpam-304	127	2	1	1	NUM
ejpam-304	127	3	π	π	X
ejpam-304	127	4	fk	fk	INTJ
ejpam-304	127	5	,	,	PUNCT
ejpam-304	127	6	k	k	PROPN
ejpam-304	127	7	=	=	SYM
ejpam-304	127	8	0	0	NUM
ejpam-304	127	9	,	,	PUNCT
ejpam-304	127	10	1	1	NUM
ejpam-304	127	11	,	,	PUNCT
ejpam-304	127	12	2	2	NUM
ejpam-304	127	13	,	,	PUNCT
ejpam-304	127	14	3	3	NUM
ejpam-304	127	15	.	.	PUNCT
ejpam-304	127	16	(	(	PUNCT
ejpam-304	127	17	4.12	4.12	NUM
ejpam-304	127	18	)	)	PUNCT
ejpam-304	127	19	it	it	PRON
ejpam-304	127	20	is	be	AUX
ejpam-304	127	21	not	not	PART
ejpam-304	127	22	difficult	difficult	ADJ
ejpam-304	127	23	to	to	PART
ejpam-304	127	24	see	see	VERB
ejpam-304	127	25	that	that	SCONJ
ejpam-304	127	26	the	the	DET
ejpam-304	127	27	solution	solution	NOUN
ejpam-304	127	28	of	of	ADP
ejpam-304	127	29	the	the	DET
ejpam-304	127	30	system	system	NOUN
ejpam-304	127	31	(	(	PUNCT
ejpam-304	127	32	4.12	4.12	NUM
ejpam-304	127	33	)	)	PUNCT
ejpam-304	127	34	is	be	AUX
ejpam-304	127	35	a0	a0	NOUN
ejpam-304	127	36	=	=	PUNCT
ejpam-304	128	1	−	−	PROPN
ejpam-304	128	2	71	71	NUM
ejpam-304	128	3	55π	55π	NOUN
ejpam-304	128	4	,	,	PUNCT
ejpam-304	128	5	a1	a1	NOUN
ejpam-304	128	6	=	=	SYM
ejpam-304	128	7	177	177	NUM
ejpam-304	128	8	110π	110π	PROPN
ejpam-304	128	9	,	,	PUNCT
ejpam-304	128	10	a2	a2	PROPN
ejpam-304	128	11	=	=	PROPN
ejpam-304	128	12	−	−	PROPN
ejpam-304	128	13	2	2	NUM
ejpam-304	128	14	55π	55π	NOUN
ejpam-304	128	15	,	,	PUNCT
ejpam-304	128	16	a3	a3	NOUN
ejpam-304	128	17	=	=	NOUN
ejpam-304	128	18	59	59	NUM
ejpam-304	128	19	110π	110π	PROPN
ejpam-304	128	20	.	.	PUNCT
ejpam-304	129	1	�	�	PROPN
ejpam-304	129	2	(	(	PUNCT
ejpam-304	129	3	4.13	4.13	NUM
ejpam-304	129	4	)	)	PUNCT
ejpam-304	129	5	references	reference	NOUN
ejpam-304	129	6	471	471	NUM
ejpam-304	129	7	substituting	substitute	VERB
ejpam-304	129	8	the	the	DET
ejpam-304	129	9	values	value	NOUN
ejpam-304	129	10	of	of	ADP
ejpam-304	129	11	the	the	DET
ejpam-304	129	12	coefficients	coefficient	NOUN
ejpam-304	129	13	¦	¦	PROPN
ejpam-304	129	14	a	a	DET
ejpam-304	129	15	j	j	PROPN
ejpam-304	129	16	©	©	NOUN
ejpam-304	129	17	3	3	NUM
ejpam-304	129	18	0	0	NUM
ejpam-304	129	19	into	into	ADP
ejpam-304	129	20	(	(	PUNCT
ejpam-304	129	21	2.5	2.5	NUM
ejpam-304	129	22	)	)	PUNCT
ejpam-304	129	23	yields	yield	VERB
ejpam-304	129	24	the	the	DET
ejpam-304	129	25	approximate	approximate	ADJ
ejpam-304	129	26	solution	solution	NOUN
ejpam-304	129	27	of	of	ADP
ejpam-304	129	28	equation	equation	NOUN
ejpam-304	129	29	(	(	PUNCT
ejpam-304	129	30	4.1	4.1	NUM
ejpam-304	129	31	)	)	PUNCT
ejpam-304	129	32	ϕn(x	ϕn(x	X
ejpam-304	129	33	)	)	PUNCT
ejpam-304	130	1	=	=	SYM
ejpam-304	130	2	1	1	NUM
ejpam-304	130	3	55π	55π	NOUN
ejpam-304	130	4	r	r	NOUN
ejpam-304	130	5	1	1	NUM
ejpam-304	130	6	+	+	NOUN
ejpam-304	130	7	x	x	SYM
ejpam-304	130	8	1−	1−	NUM
ejpam-304	130	9	x	x	SYM
ejpam-304	130	10	�	�	PROPN
ejpam-304	130	11	236	236	NUM
ejpam-304	130	12	x3	x3	NOUN
ejpam-304	130	13	−	−	PROPN
ejpam-304	130	14	126	126	NUM
ejpam-304	130	15	x2	x2	NOUN
ejpam-304	131	1	+	+	CCONJ
ejpam-304	131	2	63	63	NUM
ejpam-304	131	3	x	x	SYM
ejpam-304	131	4	−	−	PROPN
ejpam-304	131	5	128	128	NUM
ejpam-304	131	6	�	�	PROPN
ejpam-304	131	7	(	(	PUNCT
ejpam-304	131	8	4.14	4.14	NUM
ejpam-304	131	9	)	)	PUNCT
ejpam-304	131	10	which	which	PRON
ejpam-304	131	11	is	be	AUX
ejpam-304	131	12	identical	identical	ADJ
ejpam-304	131	13	to	to	ADP
ejpam-304	131	14	the	the	DET
ejpam-304	131	15	exact	exact	ADJ
ejpam-304	131	16	solution	solution	NOUN
ejpam-304	131	17	.	.	PUNCT
ejpam-304	132	1	5	5	X
ejpam-304	132	2	.	.	X
ejpam-304	132	3	conclusion	conclusion	VERB
ejpam-304	132	4	the	the	DET
ejpam-304	132	5	chebyshev	chebyshev	PROPN
ejpam-304	132	6	orthogonal	orthogonal	ADJ
ejpam-304	132	7	polynomials	polynomial	NOUN
ejpam-304	132	8	of	of	ADP
ejpam-304	132	9	the	the	DET
ejpam-304	132	10	third	third	ADJ
ejpam-304	132	11	and	and	CCONJ
ejpam-304	132	12	fourth	fourth	ADJ
ejpam-304	132	13	kinds	kind	NOUN
ejpam-304	132	14	are	be	AUX
ejpam-304	132	15	used	use	VERB
ejpam-304	132	16	to	to	PART
ejpam-304	132	17	approximate	approximate	VERB
ejpam-304	132	18	the	the	DET
ejpam-304	132	19	unknown	unknown	ADJ
ejpam-304	132	20	density	density	NOUN
ejpam-304	132	21	function	function	NOUN
ejpam-304	132	22	which	which	PRON
ejpam-304	132	23	is	be	AUX
ejpam-304	132	24	bounded	bound	VERB
ejpam-304	132	25	at	at	ADP
ejpam-304	132	26	the	the	DET
ejpam-304	132	27	end	end	NOUN
ejpam-304	132	28	point	point	NOUN
ejpam-304	132	29	x	x	X
ejpam-304	132	30	=	=	SYM
ejpam-304	132	31	−1	−1	NOUN
ejpam-304	132	32	,	,	PUNCT
ejpam-304	132	33	and	and	CCONJ
ejpam-304	132	34	the	the	DET
ejpam-304	132	35	known	know	VERB
ejpam-304	132	36	force	force	NOUN
ejpam-304	132	37	function	function	NOUN
ejpam-304	132	38	,	,	PUNCT
ejpam-304	132	39	respectively	respectively	ADV
ejpam-304	132	40	,	,	PUNCT
ejpam-304	132	41	for	for	ADP
ejpam-304	132	42	solving	solve	VERB
ejpam-304	132	43	the	the	DET
ejpam-304	132	44	cauchy	cauchy	ADJ
ejpam-304	132	45	type	type	NOUN
ejpam-304	132	46	singular	singular	ADJ
ejpam-304	132	47	integral	integral	ADJ
ejpam-304	132	48	equation	equation	NOUN
ejpam-304	132	49	of	of	ADP
ejpam-304	132	50	the	the	DET
ejpam-304	132	51	first	first	ADJ
ejpam-304	132	52	kind	kind	NOUN
ejpam-304	132	53	.	.	PUNCT
ejpam-304	133	1	theorem	theorem	VERB
ejpam-304	133	2	3.1	3.1	NUM
ejpam-304	133	3	shows	show	VERB
ejpam-304	133	4	the	the	DET
ejpam-304	133	5	exactness	exactness	NOUN
ejpam-304	133	6	of	of	ADP
ejpam-304	133	7	the	the	DET
ejpam-304	133	8	approximate	approximate	ADJ
ejpam-304	133	9	method	method	NOUN
ejpam-304	133	10	presented	present	VERB
ejpam-304	133	11	for	for	ADP
ejpam-304	133	12	characteristic	characteristic	ADJ
ejpam-304	133	13	equation	equation	NOUN
ejpam-304	133	14	when	when	SCONJ
ejpam-304	133	15	the	the	DET
ejpam-304	133	16	force	force	NOUN
ejpam-304	133	17	function	function	NOUN
ejpam-304	133	18	is	be	AUX
ejpam-304	133	19	a	a	DET
ejpam-304	133	20	cubic	cubic	ADJ
ejpam-304	133	21	.	.	PUNCT
ejpam-304	134	1	particular	particular	ADJ
ejpam-304	134	2	result	result	NOUN
ejpam-304	134	3	also	also	ADV
ejpam-304	134	4	shows	show	VERB
ejpam-304	134	5	that	that	SCONJ
ejpam-304	134	6	this	this	DET
ejpam-304	134	7	approximate	approximate	ADJ
ejpam-304	134	8	method	method	NOUN
ejpam-304	134	9	does	do	AUX
ejpam-304	134	10	not	not	PART
ejpam-304	134	11	only	only	ADV
ejpam-304	134	12	give	give	VERB
ejpam-304	134	13	the	the	DET
ejpam-304	134	14	exact	exact	ADJ
ejpam-304	134	15	solution	solution	NOUN
ejpam-304	134	16	for	for	ADP
ejpam-304	134	17	characteristic	characteristic	ADJ
ejpam-304	134	18	equation	equation	NOUN
ejpam-304	134	19	but	but	CCONJ
ejpam-304	134	20	also	also	ADV
ejpam-304	134	21	for	for	ADP
ejpam-304	134	22	other	other	ADJ
ejpam-304	134	23	cauchy	cauchy	ADJ
ejpam-304	134	24	type	type	NOUN
ejpam-304	134	25	singular	singular	ADJ
ejpam-304	134	26	integral	integral	ADJ
ejpam-304	134	27	equations	equation	NOUN
ejpam-304	134	28	of	of	ADP
ejpam-304	134	29	the	the	DET
ejpam-304	134	30	first	first	ADJ
ejpam-304	134	31	kind	kind	NOUN
ejpam-304	134	32	.	.	PUNCT
ejpam-304	135	1	acknowledgements	acknowledgement	NOUN
ejpam-304	135	2	this	this	DET
ejpam-304	135	3	work	work	NOUN
ejpam-304	135	4	was	be	AUX
ejpam-304	135	5	supported	support	VERB
ejpam-304	135	6	by	by	ADP
ejpam-304	135	7	university	university	NOUN
ejpam-304	135	8	putra	putra	PROPN
ejpam-304	135	9	malaysia	malaysia	PROPN
ejpam-304	135	10	under	under	ADP
ejpam-304	135	11	graduate	graduate	NOUN
ejpam-304	135	12	research	research	NOUN
ejpam-304	135	13	fellowship	fellowship	NOUN
ejpam-304	135	14	(	(	PUNCT
ejpam-304	135	15	grf	grf	NOUN
ejpam-304	135	16	)	)	PUNCT
ejpam-304	135	17	.	.	PUNCT
ejpam-304	136	1	references	reference	NOUN
ejpam-304	136	2	[	[	X
ejpam-304	136	3	1	1	NUM
ejpam-304	136	4	]	]	X
ejpam-304	136	5	gakhov	gakhov	PROPN
ejpam-304	136	6	,	,	PUNCT
ejpam-304	136	7	f.d	f.d	PROPN
ejpam-304	136	8	.	.	PUNCT
ejpam-304	136	9	:	:	PUNCT
ejpam-304	136	10	boundary	boundary	ADJ
ejpam-304	136	11	value	value	NOUN
ejpam-304	136	12	problems	problem	NOUN
ejpam-304	136	13	,	,	PUNCT
ejpam-304	136	14	translation	translation	NOUN
ejpam-304	136	15	edited	edit	VERB
ejpam-304	136	16	by	by	ADP
ejpam-304	136	17	sneddon	sneddon	PROPN
ejpam-304	136	18	,	,	PUNCT
ejpam-304	136	19	i.n	i.n	PROPN
ejpam-304	136	20	,	,	PUNCT
ejpam-304	136	21	pergamon	pergamon	PROPN
ejpam-304	136	22	press	press	PROPN
ejpam-304	136	23	ltd(1963	ltd(1963	PROPN
ejpam-304	136	24	)	)	PUNCT
ejpam-304	136	25	.	.	PUNCT
ejpam-304	137	1	[	[	X
ejpam-304	137	2	2	2	NUM
ejpam-304	137	3	]	]	X
ejpam-304	137	4	ladopoulos	ladopoulo	NOUN
ejpam-304	137	5	,	,	PUNCT
ejpam-304	137	6	e.g.	e.g.	ADV
ejpam-304	137	7	:	:	PUNCT
ejpam-304	137	8	singular	singular	ADJ
ejpam-304	137	9	integral	integral	ADJ
ejpam-304	137	10	equations	equation	NOUN
ejpam-304	137	11	,	,	PUNCT
ejpam-304	137	12	linear	linear	ADJ
ejpam-304	137	13	and	and	CCONJ
ejpam-304	137	14	non	non	ADJ
ejpam-304	137	15	-	-	ADJ
ejpam-304	137	16	linear	linear	ADJ
ejpam-304	137	17	,	,	PUNCT
ejpam-304	137	18	theory	theory	NOUN
ejpam-304	137	19	and	and	CCONJ
ejpam-304	137	20	its	its	PRON
ejpam-304	137	21	applications	application	NOUN
ejpam-304	137	22	in	in	ADP
ejpam-304	137	23	science	science	NOUN
ejpam-304	137	24	and	and	CCONJ
ejpam-304	137	25	engineering	engineering	NOUN
ejpam-304	137	26	,	,	PUNCT
ejpam-304	137	27	springer	springer	NOUN
ejpam-304	137	28	-	-	PUNCT
ejpam-304	137	29	verlag	verlag	PROPN
ejpam-304	137	30	(	(	PUNCT
ejpam-304	137	31	2000	2000	NUM
ejpam-304	137	32	)	)	PUNCT
ejpam-304	137	33	.	.	PUNCT
ejpam-304	138	1	references	reference	NOUN
ejpam-304	138	2	472	472	NUM
ejpam-304	139	1	[	[	X
ejpam-304	139	2	3	3	NUM
ejpam-304	139	3	]	]	X
ejpam-304	139	4	martin	martin	PROPN
ejpam-304	139	5	,	,	PUNCT
ejpam-304	139	6	p.a	p.a	PROPN
ejpam-304	139	7	.	.	PROPN
ejpam-304	139	8	and	and	CCONJ
ejpam-304	139	9	rizzo	rizzo	PROPN
ejpam-304	139	10	,	,	PUNCT
ejpam-304	139	11	f.j	f.j	PROPN
ejpam-304	139	12	.	.	PROPN
ejpam-304	139	13	:	:	PUNCT
ejpam-304	140	1	on	on	ADP
ejpam-304	140	2	boundary	boundary	ADJ
ejpam-304	140	3	integral	integral	ADJ
ejpam-304	140	4	equations	equation	NOUN
ejpam-304	140	5	for	for	ADP
ejpam-304	140	6	crack	crack	NOUN
ejpam-304	140	7	problems	problem	NOUN
ejpam-304	140	8	,	,	PUNCT
ejpam-304	140	9	proc	proc	PROPN
ejpam-304	140	10	.	.	PUNCT
ejpam-304	140	11	roy	roy	PROPN
ejpam-304	140	12	.	.	PROPN
ejpam-304	140	13	soc	soc	PROPN
ejpam-304	140	14	.	.	PUNCT
ejpam-304	141	1	a	a	DET
ejpam-304	141	2	,	,	PUNCT
ejpam-304	141	3	421	421	NUM
ejpam-304	141	4	,	,	PUNCT
ejpam-304	141	5	341	341	NUM
ejpam-304	141	6	-	-	SYM
ejpam-304	141	7	345	345	NUM
ejpam-304	141	8	(	(	PUNCT
ejpam-304	141	9	1989	1989	NUM
ejpam-304	141	10	)	)	PUNCT
ejpam-304	141	11	.	.	PUNCT
ejpam-304	142	1	[	[	X
ejpam-304	142	2	4	4	NUM
ejpam-304	142	3	]	]	X
ejpam-304	142	4	muskhelishvili	muskhelishvili	NOUN
ejpam-304	142	5	,	,	PUNCT
ejpam-304	142	6	n.i	n.i	PROPN
ejpam-304	142	7	.	.	PROPN
ejpam-304	142	8	:	:	PUNCT
ejpam-304	142	9	singular	singular	PROPN
ejpam-304	142	10	integral	integral	ADJ
ejpam-304	142	11	equations	equation	NOUN
ejpam-304	142	12	,	,	PUNCT
ejpam-304	142	13	edited	edit	VERB
ejpam-304	142	14	by	by	ADP
ejpam-304	142	15	j.r.m	j.r.m	PROPN
ejpam-304	142	16	.	.	PUNCT
ejpam-304	143	1	radok	radok	PROPN
ejpam-304	143	2	,	,	PUNCT
ejpam-304	143	3	noordhoff	noordhoff	PROPN
ejpam-304	143	4	international	international	PROPN
ejpam-304	143	5	publishing	publishing	PROPN
ejpam-304	143	6	leyden	leyden	PROPN
ejpam-304	143	7	(	(	PUNCT
ejpam-304	143	8	1977	1977	NUM
ejpam-304	143	9	)	)	PUNCT
ejpam-304	143	10	.	.	PUNCT
ejpam-304	144	1	[	[	X
ejpam-304	144	2	5	5	NUM
ejpam-304	144	3	]	]	X
ejpam-304	144	4	z.k	z.k	PROPN
ejpam-304	144	5	.	.	PROPN
ejpam-304	144	6	eshkuvatov	eshkuvatov	PROPN
ejpam-304	144	7	,	,	PUNCT
ejpam-304	144	8	,	,	PUNCT
ejpam-304	144	9	n.m.a	n.m.a	ADV
ejpam-304	144	10	.	.	PUNCT
ejpam-304	145	1	nik	nik	PROPN
ejpam-304	145	2	long	long	ADV
ejpam-304	145	3	,	,	PUNCT
ejpam-304	145	4	m.	m.	NOUN
ejpam-304	145	5	abdulkawi	abdulkawi	PROPN
ejpam-304	145	6	.	.	PUNCT
ejpam-304	146	1	approximate	approximate	ADJ
ejpam-304	146	2	solution	solution	NOUN
ejpam-304	146	3	of	of	ADP
ejpam-304	146	4	singular	singular	ADJ
ejpam-304	146	5	integral	integral	ADJ
ejpam-304	146	6	equations	equation	NOUN
ejpam-304	146	7	of	of	ADP
ejpam-304	146	8	the	the	DET
ejpam-304	146	9	first	first	ADJ
ejpam-304	146	10	kind	kind	NOUN
ejpam-304	146	11	with	with	ADP
ejpam-304	146	12	cauchy	cauchy	PROPN
ejpam-304	146	13	kernel	kernel	PROPN
ejpam-304	146	14	.	.	PUNCT
ejpam-304	147	1	appl	appl	PROPN
ejpam-304	147	2	.	.	PROPN
ejpam-304	147	3	math	math	PROPN
ejpam-304	147	4	.	.	PUNCT
ejpam-304	148	1	lett	lett	PROPN
ejpam-304	148	2	,	,	PUNCT
ejpam-304	148	3	22	22	NUM
ejpam-304	148	4	,	,	PUNCT
ejpam-304	148	5	651	651	NUM
ejpam-304	148	6	-	-	SYM
ejpam-304	148	7	657(2009	657(2009	NUM
ejpam-304	148	8	)	)	PUNCT
ejpam-304	148	9	.	.	PUNCT
ejpam-304	149	1	[	[	X
ejpam-304	149	2	6	6	NUM
ejpam-304	149	3	]	]	PUNCT
ejpam-304	149	4	m.	m.	NOUN
ejpam-304	149	5	abdulkawi	abdulkawi	PROPN
ejpam-304	149	6	,	,	PUNCT
ejpam-304	149	7	z.k	z.k	PROPN
ejpam-304	149	8	.	.	PROPN
ejpam-304	149	9	eshkuvatov	eshkuvatov	PROPN
ejpam-304	149	10	,	,	PUNCT
ejpam-304	149	11	n.m.a	n.m.a	NOUN
ejpam-304	149	12	.	.	PUNCT
ejpam-304	150	1	nik	nik	PROPN
ejpam-304	150	2	long	long	ADV
ejpam-304	150	3	.	.	PUNCT
ejpam-304	151	1	a	a	DET
ejpam-304	151	2	note	note	NOUN
ejpam-304	151	3	on	on	ADP
ejpam-304	151	4	the	the	DET
ejpam-304	151	5	numerical	numerical	ADJ
ejpam-304	151	6	solution	solution	NOUN
ejpam-304	151	7	of	of	ADP
ejpam-304	151	8	singular	singular	ADJ
ejpam-304	151	9	integral	integral	ADJ
ejpam-304	151	10	equations	equation	NOUN
ejpam-304	151	11	of	of	ADP
ejpam-304	151	12	cauchy	cauchy	PROPN
ejpam-304	151	13	type	type	NOUN
ejpam-304	151	14	.	.	PUNCT
ejpam-304	152	1	ijamc	ijamc	NOUN
ejpam-304	152	2	.	.	PUNCT
ejpam-304	153	1	5	5	NUM
ejpam-304	153	2	:	:	SYM
ejpam-304	153	3	2	2	NUM
ejpam-304	153	4	,	,	PUNCT
ejpam-304	153	5	90	90	NUM
ejpam-304	153	6	-	-	PUNCT
ejpam-304	153	7	93(2009	93(2009	NUM
ejpam-304	153	8	)	)	PUNCT
ejpam-304	153	9	.	.	PUNCT
ejpam-304	154	1	[	[	X
ejpam-304	154	2	7	7	NUM
ejpam-304	154	3	]	]	X
ejpam-304	154	4	lifanov	lifanov	PROPN
ejpam-304	154	5	,	,	PUNCT
ejpam-304	154	6	i.	i.	PROPN
ejpam-304	154	7	k.	k.	PROPN
ejpam-304	154	8	:	:	PUNCT
ejpam-304	154	9	singular	singular	PROPN
ejpam-304	154	10	integral	integral	ADJ
ejpam-304	154	11	equation	equation	NOUN
ejpam-304	154	12	and	and	CCONJ
ejpam-304	154	13	discrete	discrete	ADJ
ejpam-304	154	14	vortices	vortex	NOUN
ejpam-304	154	15	,	,	PUNCT
ejpam-304	154	16	vso	vso	PROPN
ejpam-304	154	17	,	,	PUNCT
ejpam-304	154	18	the	the	DET
ejpam-304	154	19	netherlands	netherlands	PROPN
ejpam-304	154	20	(	(	PUNCT
ejpam-304	154	21	1996	1996	NUM
ejpam-304	154	22	)	)	PUNCT
ejpam-304	154	23	.	.	PUNCT
ejpam-304	155	1	[	[	X
ejpam-304	155	2	8	8	NUM
ejpam-304	155	3	]	]	X
ejpam-304	155	4	mason	mason	PROPN
ejpam-304	155	5	,	,	PUNCT
ejpam-304	155	6	j.c	j.c	PROPN
ejpam-304	155	7	.	.	PROPN
ejpam-304	155	8	and	and	CCONJ
ejpam-304	155	9	handscomb	handscomb	NOUN
ejpam-304	155	10	,	,	PUNCT
ejpam-304	155	11	d.c	d.c	PROPN
ejpam-304	155	12	.	.	PUNCT
ejpam-304	155	13	:	:	PUNCT
ejpam-304	155	14	chebyshev	chebyshev	PROPN
ejpam-304	155	15	polynomials	polynomial	NOUN
ejpam-304	155	16	,	,	PUNCT
ejpam-304	155	17	crc	crc	PROPN
ejpam-304	155	18	press	press	PROPN
ejpam-304	155	19	llc	llc	PROPN
ejpam-304	155	20	(	(	PUNCT
ejpam-304	155	21	2003	2003	NUM
ejpam-304	155	22	)	)	PUNCT
ejpam-304	155	23	.	.	PUNCT