id	sid	tid	token	lemma	pos
iajs-759	1	1	ibn	ibn	PROPN
iajs-759	1	2	alhaitham	alhaitham	NOUN
iajs-759	1	3	j.	j.	PROPN
iajs-759	1	4	for	for	ADP
iajs-759	1	5	pure	pure	ADJ
iajs-759	1	6	&	&	CCONJ
iajs-759	1	7	appl	appl	PROPN
iajs-759	1	8	.	.	PUNCT
iajs-759	2	1	sci	sci	PROPN
iajs-759	2	2	.	.	PUNCT
iajs-759	2	3	vol.24	vol.24	NOUN
iajs-759	2	4	(	(	PUNCT
iajs-759	2	5	2	2	NUM
iajs-759	2	6	)	)	PUNCT
iajs-759	2	7	2011	2011	NUM
iajs-759	2	8	open	open	PROPN
iajs-759	2	9	newton	newton	PROPN
iajs-759	2	10	contes	contes	PROPN
iajs-759	2	11	formula	formula	NOUN
iajs-759	2	12	for	for	ADP
iajs-759	2	13	solving	solve	VERB
iajs-759	2	14	linear	linear	PROPN
iajs-759	2	15	voltera	voltera	PROPN
iajs-759	2	16	integro	integro	ADJ
iajs-759	2	17	-	-	PUNCT
iajs-759	2	18	differential	differential	NOUN
iajs-759	2	19	equation	equation	NOUN
iajs-759	2	20	of	of	ADP
iajs-759	2	21	the	the	DET
iajs-759	2	22	first	first	ADJ
iajs-759	2	23	order	order	NOUN
iajs-759	2	24	a.	a.	NOUN
iajs-759	2	25	j.	j.	PROPN
iajs-759	2	26	saleh	saleh	PROPN
iajs-759	2	27	department	department	PROPN
iajs-759	2	28	of	of	ADP
iajs-759	2	29	mathematics	mathematics	PROPN
iajs-759	2	30	,	,	PUNCT
iajs-759	2	31	college	college	NOUN
iajs-759	2	32	of	of	ADP
iajs-759	2	33	basic	basic	ADJ
iajs-759	2	34	education	education	NOUN
iajs-759	2	35	,	,	PUNCT
iajs-759	2	36	al	al	PROPN
iajs-759	2	37	-	-	PUNCT
iajs-759	2	38	mustansiriyah	mustansiriyah	PROPN
iajs-759	2	39	university	university	NOUN
iajs-759	2	40	received	receive	VERB
iajs-759	2	41	in	in	ADP
iajs-759	2	42	:	:	PUNCT
iajs-759	2	43	17	17	NUM
iajs-759	2	44	,	,	PUNCT
iajs-759	2	45	january	january	PROPN
iajs-759	2	46	,	,	PUNCT
iajs-759	2	47	2010	2010	NUM
iajs-759	2	48	accepted	accept	VERB
iajs-759	2	49	in	in	ADP
iajs-759	2	50	:	:	PUNCT
iajs-759	2	51	17	17	NUM
iajs-759	2	52	,	,	PUNCT
iajs-759	2	53	june	june	PROPN
iajs-759	2	54	,	,	PUNCT
iajs-759	2	55	2010	2010	NUM
iajs-759	2	56	abstract	abstract	NOUN
iajs-759	2	57	in	in	ADP
iajs-759	2	58	this	this	DET
iajs-759	2	59	work	work	NOUN
iajs-759	2	60	,	,	PUNCT
iajs-759	2	61	some	some	PRON
iajs-759	2	62	of	of	ADP
iajs-759	2	63	numerical	numerical	ADJ
iajs-759	2	64	methods	method	NOUN
iajs-759	2	65	for	for	ADP
iajs-759	2	66	solving	solve	VERB
iajs-759	2	67	first	first	ADJ
iajs-759	2	68	order	order	NOUN
iajs-759	2	69	linear	linear	PROPN
iajs-759	2	70	volterra	volterra	PROPN
iajs-759	2	71	integrodifferential	integrodifferential	ADJ
iajs-759	2	72	equations	equation	NOUN
iajs-759	2	73	are	be	AUX
iajs-759	2	74	presented	present	VERB
iajs-759	2	75	.	.	PUNCT
iajs-759	3	1	the	the	DET
iajs-759	3	2	numerical	numerical	ADJ
iajs-759	3	3	solution	solution	NOUN
iajs-759	3	4	of	of	ADP
iajs-759	3	5	these	these	DET
iajs-759	3	6	equations	equation	NOUN
iajs-759	3	7	is	be	AUX
iajs-759	3	8	obtained	obtain	VERB
iajs-759	3	9	by	by	ADP
iajs-759	3	10	using	use	VERB
iajs-759	3	11	open	open	ADJ
iajs-759	3	12	newton	newton	PROPN
iajs-759	3	13	cotes	cotes	PROPN
iajs-759	3	14	formula	formula	NOUN
iajs-759	3	15	.	.	PUNCT
iajs-759	4	1	the	the	DET
iajs-759	4	2	open	open	PROPN
iajs-759	4	3	newton	newton	PROPN
iajs-759	4	4	cotes	cotes	PROPN
iajs-759	4	5	formula	formula	NOUN
iajs-759	4	6	is	be	AUX
iajs-759	4	7	applied	apply	VERB
iajs-759	4	8	to	to	PART
iajs-759	4	9	find	find	VERB
iajs-759	4	10	the	the	DET
iajs-759	4	11	optimum	optimum	ADJ
iajs-759	4	12	solution	solution	NOUN
iajs-759	4	13	for	for	ADP
iajs-759	4	14	this	this	DET
iajs-759	4	15	equation	equation	NOUN
iajs-759	4	16	.	.	PUNCT
iajs-759	5	1	the	the	DET
iajs-759	5	2	computer	computer	NOUN
iajs-759	5	3	program	program	NOUN
iajs-759	5	4	is	be	AUX
iajs-759	5	5	written	write	VERB
iajs-759	5	6	in	in	ADP
iajs-759	5	7	(	(	PUNCT
iajs-759	5	8	matlab	matlab	PROPN
iajs-759	5	9	)	)	PUNCT
iajs-759	5	10	language	language	NOUN
iajs-759	5	11	(	(	PUNCT
iajs-759	5	12	version	version	NOUN
iajs-759	5	13	6	6	NUM
iajs-759	5	14	)	)	PUNCT
iajs-759	5	15	key	key	ADJ
iajs-759	5	16	word	word	NOUN
iajs-759	5	17	:	:	PUNCT
iajs-759	5	18	voltera	voltera	NOUN
iajs-759	5	19	integrodifferential	integrodifferential	ADJ
iajs-759	5	20	equation	equation	NOUN
iajs-759	5	21	,	,	PUNCT
iajs-759	5	22	open	open	ADJ
iajs-759	5	23	newton	newton	PROPN
iajs-759	5	24	cotes	cotes	PROPN
iajs-759	5	25	formula	formula	NOUN
iajs-759	5	26	introduction	introduction	NOUN
iajs-759	5	27	in	in	ADP
iajs-759	5	28	this	this	DET
iajs-759	5	29	search	search	NOUN
iajs-759	5	30	we	we	PRON
iajs-759	5	31	first	first	ADV
iajs-759	5	32	present	present	VERB
iajs-759	5	33	the	the	DET
iajs-759	5	34	most	most	ADV
iajs-759	5	35	familiar	familiar	ADJ
iajs-759	5	36	formula	formula	NOUN
iajs-759	5	37	of	of	ADP
iajs-759	5	38	numerical	numerical	ADJ
iajs-759	5	39	integration	integration	NOUN
iajs-759	5	40	:	:	PUNCT
iajs-759	5	41	the	the	DET
iajs-759	5	42	open	open	PROPN
iajs-759	5	43	newton	newton	PROPN
iajs-759	5	44	cotes	cotes	PROPN
iajs-759	5	45	formula	formula	NOUN
iajs-759	5	46	(	(	PUNCT
iajs-759	5	47	o	o	NOUN
iajs-759	5	48	-	-	NOUN
iajs-759	5	49	n	n	NUM
iajs-759	5	50	)	)	PUNCT
iajs-759	5	51	.	.	PUNCT
iajs-759	6	1	and	and	CCONJ
iajs-759	6	2	then	then	ADV
iajs-759	6	3	we	we	PRON
iajs-759	6	4	illustrate	illustrate	VERB
iajs-759	6	5	primarily	primarily	ADV
iajs-759	6	6	the	the	DET
iajs-759	6	7	use	use	NOUN
iajs-759	6	8	of	of	ADP
iajs-759	6	9	these	these	DET
iajs-759	6	10	rules	rule	NOUN
iajs-759	6	11	for	for	ADP
iajs-759	6	12	evaluating	evaluate	VERB
iajs-759	6	13	integrals	integral	NOUN
iajs-759	6	14	and	and	CCONJ
iajs-759	6	15	show	show	VERB
iajs-759	6	16	how	how	SCONJ
iajs-759	6	17	the	the	DET
iajs-759	6	18	linear	linear	ADJ
iajs-759	6	19	vides	vide	NOUN
iajs-759	6	20	of	of	ADP
iajs-759	6	21	first	first	ADJ
iajs-759	6	22	order	order	NOUN
iajs-759	6	23	is	be	AUX
iajs-759	6	24	reduced	reduce	VERB
iajs-759	6	25	to	to	ADP
iajs-759	6	26	system	system	NOUN
iajs-759	6	27	of	of	ADP
iajs-759	6	28	(	(	PUNCT
iajs-759	6	29	n	n	CCONJ
iajs-759	6	30	)	)	PUNCT
iajs-759	6	31	equations	equation	NOUN
iajs-759	6	32	in	in	ADP
iajs-759	6	33	the	the	DET
iajs-759	6	34	(	(	PUNCT
iajs-759	6	35	n	n	CCONJ
iajs-759	6	36	)	)	PUNCT
iajs-759	6	37	unknowns	unknown	NOUN
iajs-759	6	38	of	of	ADP
iajs-759	6	39	the	the	DET
iajs-759	6	40	solution	solution	NOUN
iajs-759	6	41	sample	sample	NOUN
iajs-759	6	42	values	value	NOUN
iajs-759	6	43	u(xi	u(xi	PROPN
iajs-759	6	44	)	)	PUNCT
iajs-759	6	45	,	,	PUNCT
iajs-759	6	46	i=0,1,2,	i=0,1,2,	NOUN
iajs-759	6	47	…	…	PUNCT
iajs-759	6	48	n.	n.	NOUN
iajs-759	6	49	the	the	DET
iajs-759	6	50	procedure	procedure	NOUN
iajs-759	6	51	of	of	ADP
iajs-759	6	52	the	the	DET
iajs-759	6	53	previous	previous	ADJ
iajs-759	6	54	technique	technique	NOUN
iajs-759	6	55	is	be	AUX
iajs-759	6	56	called	call	VERB
iajs-759	6	57	the	the	DET
iajs-759	6	58	open	open	ADJ
iajs-759	6	59	newton	newton	PROPN
iajs-759	6	60	cotes	cotes	PROPN
iajs-759	6	61	formula	formula	NOUN
iajs-759	6	62	.	.	PUNCT
iajs-759	7	1	in	in	ADP
iajs-759	7	2	addition	addition	NOUN
iajs-759	7	3	a	a	DET
iajs-759	7	4	computer	computer	NOUN
iajs-759	7	5	program	program	NOUN
iajs-759	7	6	is	be	AUX
iajs-759	7	7	written	write	VERB
iajs-759	7	8	,	,	PUNCT
iajs-759	7	9	examples	example	NOUN
iajs-759	7	10	with	with	ADP
iajs-759	7	11	satisfactory	satisfactory	ADJ
iajs-759	7	12	results	result	NOUN
iajs-759	7	13	are	be	AUX
iajs-759	7	14	given	give	VERB
iajs-759	7	15	.	.	PUNCT
iajs-759	8	1	1	1	X
iajs-759	8	2	.	.	X
iajs-759	8	3	classification	classification	NOUN
iajs-759	8	4	of	of	ADP
iajs-759	8	5	integral	integral	ADJ
iajs-759	8	6	equations	equation	NOUN
iajs-759	8	7	:	:	PUNCT
iajs-759	8	8	any	any	DET
iajs-759	8	9	functional	functional	ADJ
iajs-759	8	10	equation	equation	NOUN
iajs-759	8	11	in	in	ADP
iajs-759	8	12	which	which	PRON
iajs-759	8	13	the	the	DET
iajs-759	8	14	unknown	unknown	ADJ
iajs-759	8	15	function	function	NOUN
iajs-759	8	16	appears	appear	VERB
iajs-759	8	17	under	under	ADP
iajs-759	8	18	the	the	DET
iajs-759	8	19	sign	sign	NOUN
iajs-759	8	20	of	of	ADP
iajs-759	8	21	integrations	integration	NOUN
iajs-759	8	22	is	be	AUX
iajs-759	8	23	called	call	VERB
iajs-759	8	24	an	an	DET
iajs-759	8	25	integral	integral	ADJ
iajs-759	8	26	equation	equation	NOUN
iajs-759	8	27	[	[	X
iajs-759	8	28	1	1	NUM
iajs-759	8	29	]	]	PUNCT
iajs-759	8	30	.	.	PUNCT
iajs-759	9	1	the	the	DET
iajs-759	9	2	general	general	ADJ
iajs-759	9	3	non	non	ADJ
iajs-759	9	4	-	-	ADJ
iajs-759	9	5	linear	linear	ADJ
iajs-759	9	6	integral	integral	ADJ
iajs-759	9	7	equation	equation	NOUN
iajs-759	9	8	can	can	AUX
iajs-759	9	9	be	be	AUX
iajs-759	9	10	presented	present	VERB
iajs-759	9	11	in	in	ADP
iajs-759	9	12	the	the	DET
iajs-759	9	13	form	form	NOUN
iajs-759	9	14	.	.	PUNCT
iajs-759	10	1			ADV
iajs-759	10	2	)	)	PUNCT
iajs-759	10	3	(	(	PUNCT
iajs-759	10	4	)	)	PUNCT
iajs-759	10	5	)	)	PUNCT
iajs-759	10	6	(	(	PUNCT
iajs-759	10	7	,	,	PUNCT
iajs-759	10	8	,	,	PUNCT
iajs-759	10	9	(	(	PUNCT
iajs-759	10	10	)	)	PUNCT
iajs-759	10	11	(	(	PUNCT
iajs-759	10	12	)	)	PUNCT
iajs-759	10	13	(	(	PUNCT
iajs-759	10	14	)	)	PUNCT
iajs-759	10	15	(	(	PUNCT
iajs-759	10	16	xb	xb	PROPN
iajs-759	10	17	a	a	DET
iajs-759	10	18	dttutxkxfxuxh	dttutxkxfxuxh	ADJ
iajs-759	10	19			X
iajs-759	10	20	…	…	PUNCT
iajs-759	10	21	(	(	PUNCT
iajs-759	10	22	1.1	1.1	NUM
iajs-759	10	23	)	)	PUNCT
iajs-759	10	24	and	and	CCONJ
iajs-759	10	25	if	if	SCONJ
iajs-759	10	26	)	)	PUNCT
iajs-759	10	27	(	(	PUNCT
iajs-759	10	28	)	)	PUNCT
iajs-759	10	29	,	,	PUNCT
iajs-759	10	30	(	(	PUNCT
iajs-759	10	31	)	)	PUNCT
iajs-759	10	32	)	)	PUNCT
iajs-759	10	33	(	(	PUNCT
iajs-759	10	34	,	,	PUNCT
iajs-759	10	35	,	,	PUNCT
iajs-759	10	36	(	(	PUNCT
iajs-759	10	37	tutxktutxk	tutxktutxk	NOUN
iajs-759	10	38			ADV
iajs-759	10	39	then	then	ADV
iajs-759	10	40	(	(	PUNCT
iajs-759	10	41	1.1	1.1	NUM
iajs-759	10	42	)	)	PUNCT
iajs-759	10	43	is	be	AUX
iajs-759	10	44	called	call	VERB
iajs-759	10	45	linear	linear	ADJ
iajs-759	10	46	integral	integral	ADJ
iajs-759	10	47	equation	equation	NOUN
iajs-759	10	48	having	have	VERB
iajs-759	10	49	the	the	DET
iajs-759	10	50	form	form	NOUN
iajs-759	10	51			ADV
iajs-759	10	52	)	)	PUNCT
iajs-759	10	53	(	(	PUNCT
iajs-759	10	54	)	)	PUNCT
iajs-759	10	55	(	(	PUNCT
iajs-759	10	56	)	)	PUNCT
iajs-759	10	57	,	,	PUNCT
iajs-759	10	58	(	(	PUNCT
iajs-759	10	59	)	)	PUNCT
iajs-759	10	60	(	(	PUNCT
iajs-759	10	61	)	)	PUNCT
iajs-759	10	62	(	(	PUNCT
iajs-759	10	63	)	)	PUNCT
iajs-759	10	64	(	(	PUNCT
iajs-759	10	65	xb	xb	PROPN
iajs-759	10	66	a	a	DET
iajs-759	10	67	dttutxkxfxuxh	dttutxkxfxuxh	ADJ
iajs-759	10	68			X
iajs-759	10	69	…	…	PUNCT
iajs-759	10	70	(	(	PUNCT
iajs-759	10	71	1.2	1.2	NUM
iajs-759	10	72	)	)	PUNCT
iajs-759	10	73	here	here	ADV
iajs-759	10	74	the	the	DET
iajs-759	10	75	function	function	NOUN
iajs-759	10	76	h(x	h(x	PROPN
iajs-759	10	77	)	)	PUNCT
iajs-759	10	78	,	,	PUNCT
iajs-759	10	79	f(x	f(x	PROPN
iajs-759	10	80	)	)	PUNCT
iajs-759	10	81	and	and	CCONJ
iajs-759	10	82	the	the	DET
iajs-759	10	83	kernel	kernel	PROPN
iajs-759	10	84	function	function	PROPN
iajs-759	10	85	k(x	k(x	PROPN
iajs-759	10	86	,	,	PUNCT
iajs-759	10	87	t	t	PROPN
iajs-759	10	88	)	)	PUNCT
iajs-759	10	89	are	be	AUX
iajs-759	10	90	prescribed	prescribe	VERB
iajs-759	10	91	,	,	PUNCT
iajs-759	10	92	while	while	SCONJ
iajs-759	10	93	u(x	u(x	NOUN
iajs-759	10	94	)	)	PUNCT
iajs-759	10	95	is	be	AUX
iajs-759	10	96	the	the	DET
iajs-759	10	97	unknown	unknown	ADJ
iajs-759	10	98	function	function	NOUN
iajs-759	10	99	to	to	PART
iajs-759	10	100	be	be	AUX
iajs-759	10	101	determined	determine	VERB
iajs-759	10	102	and	and	CCONJ
iajs-759	10	103			ADJ
iajs-759	10	104	is	be	AUX
iajs-759	10	105	a	a	DET
iajs-759	10	106	scalar	scalar	ADJ
iajs-759	10	107	parameter[2,3	parameter[2,3	NOUN
iajs-759	10	108	]	]	PUNCT
iajs-759	10	109	if	if	SCONJ
iajs-759	10	110	in	in	ADP
iajs-759	10	111	equation	equation	NOUN
iajs-759	10	112	(	(	PUNCT
iajs-759	10	113	1.1	1.1	NUM
iajs-759	10	114	)	)	PUNCT
iajs-759	10	115	and	and	CCONJ
iajs-759	10	116	equation	equation	NOUN
iajs-759	10	117	(	(	PUNCT
iajs-759	10	118	1.2	1.2	NUM
iajs-759	10	119	)	)	PUNCT
iajs-759	10	120	,	,	PUNCT
iajs-759	10	121	f(x)=0	f(x)=0	PUNCT
iajs-759	10	122	the	the	DET
iajs-759	10	123	integral	integral	ADJ
iajs-759	10	124	equations	equation	NOUN
iajs-759	10	125	are	be	AUX
iajs-759	10	126	said	say	VERB
iajs-759	10	127	to	to	PART
iajs-759	10	128	be	be	AUX
iajs-759	10	129	homogeneous	homogeneous	ADJ
iajs-759	10	130	integral	integral	ADJ
iajs-759	10	131	equations	equation	NOUN
iajs-759	10	132	otherwise	otherwise	ADV
iajs-759	10	133	,	,	PUNCT
iajs-759	10	134	they	they	PRON
iajs-759	10	135	are	be	AUX
iajs-759	10	136	non	non	X
iajs-759	10	137	homogeneous	homogeneous	ADJ
iajs-759	10	138	[	[	X
iajs-759	10	139	4	4	NUM
iajs-759	10	140	]	]	PUNCT
iajs-759	10	141	.	.	PUNCT
iajs-759	11	1	in	in	ADP
iajs-759	11	2	the	the	DET
iajs-759	11	3	classical	classical	ADJ
iajs-759	11	4	theory	theory	NOUN
iajs-759	11	5	of	of	ADP
iajs-759	11	6	integral	integral	ADJ
iajs-759	11	7	equations	equation	NOUN
iajs-759	11	8	one	one	NUM
iajs-759	11	9	distinguishes	distinguish	VERB
iajs-759	11	10	between	between	ADP
iajs-759	11	11	volterra	volterra	NOUN
iajs-759	11	12	equations	equation	NOUN
iajs-759	11	13	and	and	CCONJ
iajs-759	11	14	fredholm	fredholm	NOUN
iajs-759	11	15	equations	equation	NOUN
iajs-759	11	16	in	in	ADP
iajs-759	11	17	a	a	DET
iajs-759	11	18	fredholm	fredholm	ADJ
iajs-759	11	19	integral	integral	ADJ
iajs-759	11	20	equation	equation	NOUN
iajs-759	11	21	the	the	DET
iajs-759	11	22	region	region	NOUN
iajs-759	11	23	of	of	ADP
iajs-759	11	24	integration	integration	NOUN
iajs-759	11	25	is	be	AUX
iajs-759	11	26	fixed	fix	VERB
iajs-759	11	27	i.e.	i.e.	X
iajs-759	11	28	b(x)=b	b(x)=b	ADJ
iajs-759	11	29	,	,	PUNCT
iajs-759	11	30	where	where	SCONJ
iajs-759	11	31	as	as	ADP
iajs-759	11	32	in	in	ADP
iajs-759	11	33	volterra	volterra	NOUN
iajs-759	11	34	integral	integral	ADJ
iajs-759	11	35	equation	equation	NOUN
iajs-759	11	36	the	the	DET
iajs-759	11	37	region	region	NOUN
iajs-759	11	38	is	be	AUX
iajs-759	11	39	variable	variable	ADJ
iajs-759	11	40	[	[	X
iajs-759	11	41	5	5	NUM
iajs-759	11	42	]	]	PUNCT
iajs-759	11	43	.	.	PUNCT
iajs-759	12	1	thus	thus	ADV
iajs-759	12	2	,	,	PUNCT
iajs-759	12	3	the	the	DET
iajs-759	12	4	equation	equation	NOUN
iajs-759	12	5			ADV
iajs-759	12	6	b	b	PROPN
iajs-759	12	7	a	a	DET
iajs-759	12	8	dttutxkxfxuxh	dttutxkxfxuxh	NOUN
iajs-759	12	9	)	)	PUNCT
iajs-759	12	10	(	(	PUNCT
iajs-759	12	11	)	)	PUNCT
iajs-759	12	12	,	,	PUNCT
iajs-759	12	13	(	(	PUNCT
iajs-759	12	14	)	)	PUNCT
iajs-759	12	15	(	(	PUNCT
iajs-759	12	16	)	)	PUNCT
iajs-759	12	17	(	(	PUNCT
iajs-759	12	18	)	)	PUNCT
iajs-759	12	19	(	(	PUNCT
iajs-759	12	20			X
iajs-759	12	21	,	,	PUNCT
iajs-759	12	22	bxa	bxa	NOUN
iajs-759	12	23			NOUN
iajs-759	12	24	…	…	PUNCT
iajs-759	12	25	(	(	PUNCT
iajs-759	12	26	1.3	1.3	NUM
iajs-759	12	27	)	)	PUNCT
iajs-759	12	28	is	be	AUX
iajs-759	12	29	an	an	DET
iajs-759	12	30	example	example	NOUN
iajs-759	12	31	of	of	ADP
iajs-759	12	32	a	a	DET
iajs-759	12	33	linear	linear	ADJ
iajs-759	12	34	fredholm	fredholm	NOUN
iajs-759	12	35	integral	integral	ADJ
iajs-759	12	36	equation	equation	NOUN
iajs-759	12	37	and	and	CCONJ
iajs-759	12	38	the	the	DET
iajs-759	12	39	equation	equation	NOUN
iajs-759	12	40	ibn	ibn	PROPN
iajs-759	12	41	alhaitham	alhaitham	PROPN
iajs-759	12	42	j.	j.	PROPN
iajs-759	12	43	for	for	ADP
iajs-759	12	44	pure	pure	ADJ
iajs-759	12	45	&	&	CCONJ
iajs-759	12	46	appl	appl	PROPN
iajs-759	12	47	.	.	PUNCT
iajs-759	13	1	sci	sci	PROPN
iajs-759	13	2	.	.	PUNCT
iajs-759	13	3	vol.24	vol.24	NOUN
iajs-759	13	4	(	(	PUNCT
iajs-759	13	5	2	2	NUM
iajs-759	13	6	)	)	PUNCT
iajs-759	13	7	2011	2011	NUM
iajs-759	13	8			ADV
iajs-759	13	9	x	x	SYM
iajs-759	13	10	a	a	DET
iajs-759	13	11	dttutxkxfxuxh	dttutxkxfxuxh	NOUN
iajs-759	13	12	)	)	PUNCT
iajs-759	13	13	(	(	PUNCT
iajs-759	13	14	)	)	PUNCT
iajs-759	13	15	,	,	PUNCT
iajs-759	13	16	(	(	PUNCT
iajs-759	13	17	)	)	PUNCT
iajs-759	13	18	(	(	PUNCT
iajs-759	13	19	)	)	PUNCT
iajs-759	13	20	(	(	PUNCT
iajs-759	13	21	)	)	PUNCT
iajs-759	13	22	(	(	PUNCT
iajs-759	13	23			X
iajs-759	13	24	,	,	PUNCT
iajs-759	13	25	xa	xa	X
iajs-759	13	26	…	…	PUNCT
iajs-759	13	27	(	(	PUNCT
iajs-759	13	28	1.4	1.4	NUM
iajs-759	13	29	)	)	PUNCT
iajs-759	13	30	is	be	AUX
iajs-759	13	31	an	an	DET
iajs-759	13	32	example	example	NOUN
iajs-759	13	33	of	of	ADP
iajs-759	13	34	a	a	DET
iajs-759	13	35	linear	linear	PROPN
iajs-759	13	36	volterra	volterra	NOUN
iajs-759	13	37	integral	integral	ADJ
iajs-759	13	38	equation	equation	NOUN
iajs-759	13	39	.	.	PUNCT
iajs-759	14	1	1.1	1.1	NUM
iajs-759	14	2	voltera	voltera	NUM
iajs-759	14	3	integral	integral	ADJ
iajs-759	14	4	equations	equation	NOUN
iajs-759	14	5	:	:	PUNCT
iajs-759	14	6	a	a	DET
iajs-759	14	7	linear	linear	PROPN
iajs-759	14	8	volterra	volterra	NOUN
iajs-759	14	9	integral	integral	ADJ
iajs-759	14	10	equation	equation	NOUN
iajs-759	14	11	of	of	ADP
iajs-759	14	12	the	the	DET
iajs-759	14	13	first	first	ADJ
iajs-759	14	14	and	and	CCONJ
iajs-759	14	15	second	second	ADJ
iajs-759	14	16	kind	kind	NOUN
iajs-759	14	17	is	be	AUX
iajs-759	14	18	defined	define	VERB
iajs-759	14	19	as	as	ADP
iajs-759	14	20	in	in	ADP
iajs-759	14	21	equation	equation	NOUN
iajs-759	14	22	(	(	PUNCT
iajs-759	14	23	1.4	1.4	NUM
iajs-759	14	24	)	)	PUNCT
iajs-759	14	25	by	by	ADP
iajs-759	14	26	letting	let	VERB
iajs-759	14	27	h(x)=0	h(x)=0	ADJ
iajs-759	14	28	and	and	CCONJ
iajs-759	14	29	h(x)=1	h(x)=1	NOUN
iajs-759	14	30	,	,	PUNCT
iajs-759	14	31	[	[	X
iajs-759	14	32	6,1	6,1	NUM
iajs-759	14	33	]	]	X
iajs-759	14	34			NOUN
iajs-759	14	35	x	x	PUNCT
iajs-759	14	36	a	a	DET
iajs-759	14	37	dttutxkxf	dttutxkxf	NOUN
iajs-759	14	38	)	)	PUNCT
iajs-759	14	39	(	(	PUNCT
iajs-759	14	40	)	)	PUNCT
iajs-759	14	41	,	,	PUNCT
iajs-759	14	42	(	(	PUNCT
iajs-759	14	43	)	)	PUNCT
iajs-759	14	44	(	(	PUNCT
iajs-759	14	45			X
iajs-759	14	46	,	,	PUNCT
iajs-759	14	47	xa	xa	X
iajs-759	14	48	…	…	PUNCT
iajs-759	14	49	(	(	PUNCT
iajs-759	14	50	1.5	1.5	NUM
iajs-759	14	51	)	)	PUNCT
iajs-759	14	52			ADV
iajs-759	14	53	x	x	SYM
iajs-759	14	54	a	a	DET
iajs-759	14	55	dttutxkxfxu	dttutxkxfxu	NOUN
iajs-759	14	56	)	)	PUNCT
iajs-759	14	57	(	(	PUNCT
iajs-759	14	58	)	)	PUNCT
iajs-759	14	59	,	,	PUNCT
iajs-759	14	60	(	(	PUNCT
iajs-759	14	61	)	)	PUNCT
iajs-759	14	62	(	(	PUNCT
iajs-759	14	63	)	)	PUNCT
iajs-759	14	64	(	(	PUNCT
iajs-759	14	65			X
iajs-759	14	66	,	,	PUNCT
iajs-759	14	67	xa	xa	X
iajs-759	14	68	…	…	PUNCT
iajs-759	14	69	(	(	PUNCT
iajs-759	14	70	1.6	1.6	NUM
iajs-759	14	71	)	)	PUNCT
iajs-759	14	72	a	a	DET
iajs-759	14	73	volterra	volterra	NOUN
iajs-759	14	74	equation	equation	NOUN
iajs-759	14	75	can	can	AUX
iajs-759	14	76	be	be	AUX
iajs-759	14	77	looked	look	VERB
iajs-759	14	78	at	at	ADP
iajs-759	14	79	as	as	ADP
iajs-759	14	80	an	an	DET
iajs-759	14	81	important	important	ADJ
iajs-759	14	82	special	special	ADJ
iajs-759	14	83	case	case	NOUN
iajs-759	14	84	of	of	ADP
iajs-759	14	85	a	a	DET
iajs-759	14	86	fredholm	fredholm	NOUN
iajs-759	14	87	equation	equation	NOUN
iajs-759	14	88	which	which	PRON
iajs-759	14	89	arises	arise	VERB
iajs-759	14	90	when	when	SCONJ
iajs-759	14	91	k(x	k(x	PROPN
iajs-759	14	92	,	,	PUNCT
iajs-759	14	93	t)=0	t)=0	PROPN
iajs-759	14	94	for	for	ADP
iajs-759	14	95	t	t	PROPN
iajs-759	14	96	>	>	PUNCT
iajs-759	14	97	x.	x.	NOUN
iajs-759	15	1	the	the	DET
iajs-759	15	2	distinction	distinction	NOUN
iajs-759	15	3	between	between	ADP
iajs-759	15	4	fredholm	fredholm	NOUN
iajs-759	15	5	and	and	CCONJ
iajs-759	15	6	volterra	volterra	NOUN
iajs-759	15	7	equation	equation	NOUN
iajs-759	15	8	is	be	AUX
iajs-759	15	9	analogous	analogous	ADJ
iajs-759	15	10	to	to	ADP
iajs-759	15	11	the	the	DET
iajs-759	15	12	distinction	distinction	NOUN
iajs-759	15	13	between	between	ADP
iajs-759	15	14	boundary	boundary	ADJ
iajs-759	15	15	and	and	CCONJ
iajs-759	15	16	initial	initial	ADJ
iajs-759	15	17	value	value	NOUN
iajs-759	15	18	problems	problem	NOUN
iajs-759	15	19	in	in	ADP
iajs-759	15	20	ordinary	ordinary	ADJ
iajs-759	15	21	differential	differential	ADJ
iajs-759	15	22	equations	equation	NOUN
iajs-759	15	23	[	[	X
iajs-759	15	24	6,1	6,1	NUM
iajs-759	15	25	]	]	PUNCT
iajs-759	15	26	.	.	PUNCT
iajs-759	16	1	definition	definition	NOUN
iajs-759	16	2	1.1	1.1	NUM
iajs-759	16	3	:	:	PUNCT
iajs-759	16	4	an	an	DET
iajs-759	16	5	integral	integral	ADJ
iajs-759	16	6	equation	equation	NOUN
iajs-759	16	7	is	be	AUX
iajs-759	16	8	termed	term	VERB
iajs-759	16	9	linear	linear	PROPN
iajs-759	16	10	if	if	SCONJ
iajs-759	16	11	it	it	PRON
iajs-759	16	12	involves	involve	VERB
iajs-759	16	13	the	the	DET
iajs-759	16	14	integral	integral	ADJ
iajs-759	16	15	operator	operator	NOUN
iajs-759	16	16			NOUN
iajs-759	16	17	)	)	PUNCT
iajs-759	16	18	(	(	PUNCT
iajs-759	16	19	)	)	PUNCT
iajs-759	16	20	,	,	PUNCT
iajs-759	16	21	(	(	PUNCT
iajs-759	16	22	xb	xb	X
iajs-759	16	23	a	a	DET
iajs-759	16	24	dttxkl	dttxkl	NOUN
iajs-759	16	25			X
iajs-759	16	26	which	which	PRON
iajs-759	16	27	satisfies	satisfy	VERB
iajs-759	16	28	the	the	DET
iajs-759	16	29	linearity	linearity	NOUN
iajs-759	16	30	condition	condition	NOUN
iajs-759	16	31	)	)	PUNCT
iajs-759	16	32	]	]	PUNCT
iajs-759	16	33	(	(	PUNCT
iajs-759	16	34	[	[	X
iajs-759	16	35	)	)	PUNCT
iajs-759	16	36	]	]	PUNCT
iajs-759	16	37	(	(	PUNCT
iajs-759	16	38	[	[	X
iajs-759	16	39	)	)	PUNCT
iajs-759	16	40	]	]	X
iajs-759	16	41	(	(	PUNCT
iajs-759	16	42	)	)	PUNCT
iajs-759	16	43	(	(	PUNCT
iajs-759	16	44	[	[	PUNCT
iajs-759	16	45	22112211	22112211	NUM
iajs-759	16	46	tulctulctuctucl	tulctulctuctucl	NOUN
iajs-759	16	47			PROPN
iajs-759	16	48	where	where	SCONJ
iajs-759	16	49	,	,	PUNCT
iajs-759	16	50	)	)	PUNCT
iajs-759	16	51	,	,	PUNCT
iajs-759	16	52	(	(	PUNCT
iajs-759	16	53	)	)	PUNCT
iajs-759	16	54	]	]	PUNCT
iajs-759	16	55	(	(	PUNCT
iajs-759	16	56	[	[	PUNCT
iajs-759	16	57	)	)	PUNCT
iajs-759	16	58	(	(	PUNCT
iajs-759	16	59			PROPN
iajs-759	16	60	xb	xb	PROPN
iajs-759	16	61	a	a	DET
iajs-759	16	62	dttxktul	dttxktul	NOUN
iajs-759	16	63			ADJ
iajs-759	16	64	and	and	CCONJ
iajs-759	16	65	c1	c1	PROPN
iajs-759	16	66	,	,	PUNCT
iajs-759	16	67	c2	c2	PROPN
iajs-759	16	68	are	be	AUX
iajs-759	16	69	constants	constant	NOUN
iajs-759	16	70	[	[	X
iajs-759	16	71	1,7	1,7	NUM
iajs-759	16	72	]	]	PUNCT
iajs-759	16	73	.	.	PUNCT
iajs-759	17	1	definition	definition	NOUN
iajs-759	17	2	1.2	1.2	NUM
iajs-759	17	3	:	:	PUNCT
iajs-759	17	4	the	the	DET
iajs-759	17	5	equation	equation	NOUN
iajs-759	17	6	(	(	PUNCT
iajs-759	17	7	1.1	1.1	NUM
iajs-759	17	8	)	)	PUNCT
iajs-759	17	9	is	be	AUX
iajs-759	17	10	said	say	VERB
iajs-759	17	11	to	to	PART
iajs-759	17	12	be	be	AUX
iajs-759	17	13	linear	linear	ADJ
iajs-759	17	14	integral	integral	ADJ
iajs-759	17	15	equation	equation	NOUN
iajs-759	17	16	of	of	ADP
iajs-759	17	17	the	the	DET
iajs-759	17	18	first	first	ADJ
iajs-759	17	19	kind	kind	NOUN
iajs-759	17	20	,	,	PUNCT
iajs-759	17	21	if	if	SCONJ
iajs-759	17	22	the	the	DET
iajs-759	17	23	unknown	unknown	ADJ
iajs-759	17	24	function	function	NOUN
iajs-759	17	25	is	be	AUX
iajs-759	17	26	present	present	ADJ
iajs-759	17	27	under	under	ADP
iajs-759	17	28	the	the	DET
iajs-759	17	29	integral	integral	ADJ
iajs-759	17	30	sign	sign	NOUN
iajs-759	17	31	only	only	ADV
iajs-759	17	32	,	,	PUNCT
iajs-759	17	33	i.e.	i.e.	X
iajs-759	17	34	0	0	NUM
iajs-759	17	35	)	)	PUNCT
iajs-759	17	36	(	(	PUNCT
iajs-759	17	37	xh	xh	VERB
iajs-759	17	38	;	;	PUNCT
iajs-759	17	39	linear	linear	ADJ
iajs-759	17	40	integral	integral	ADJ
iajs-759	17	41	equation	equation	NOUN
iajs-759	17	42	of	of	ADP
iajs-759	17	43	the	the	DET
iajs-759	17	44	second	second	ADJ
iajs-759	17	45	kind	kind	NOUN
iajs-759	17	46	also	also	ADV
iajs-759	17	47	has	have	VERB
iajs-759	17	48	the	the	DET
iajs-759	17	49	unknown	unknown	ADJ
iajs-759	17	50	function	function	NOUN
iajs-759	17	51	outside	outside	ADP
iajs-759	17	52	the	the	DET
iajs-759	17	53	integral	integral	ADJ
iajs-759	17	54	,	,	PUNCT
iajs-759	17	55	i.e.	i.e.	X
iajs-759	17	56	0	0	NUM
iajs-759	17	57	)	)	PUNCT
iajs-759	17	58	(	(	PUNCT
iajs-759	17	59	xh	xh	PROPN
iajs-759	17	60	for	for	ADP
iajs-759	17	61	bxa	bxa	NOUN
iajs-759	17	62			NOUN
iajs-759	17	63	;	;	PUNCT
iajs-759	17	64	and	and	CCONJ
iajs-759	17	65	if	if	SCONJ
iajs-759	17	66	h(x	h(x	PROPN
iajs-759	17	67	)	)	PUNCT
iajs-759	17	68	vanishes	vanish	VERB
iajs-759	17	69	somewhere	somewhere	ADV
iajs-759	17	70	but	but	CCONJ
iajs-759	17	71	not	not	PART
iajs-759	17	72	identically	identically	ADV
iajs-759	17	73	,	,	PUNCT
iajs-759	17	74	the	the	DET
iajs-759	17	75	equation	equation	NOUN
iajs-759	17	76	is	be	AUX
iajs-759	17	77	of	of	ADP
iajs-759	17	78	third	third	ADJ
iajs-759	17	79	kind	kind	NOUN
iajs-759	18	1	[	[	X
iajs-759	18	2	8	8	NUM
iajs-759	18	3	]	]	PUNCT
iajs-759	18	4	.	.	PUNCT
iajs-759	19	1	1.2	1.2	NUM
iajs-759	19	2	s	s	PART
iajs-759	19	3	ingular	ingular	ADJ
iajs-759	19	4	and	and	CCONJ
iajs-759	19	5	weakly	weakly	ADJ
iajs-759	19	6	s	s	PART
iajs-759	19	7	ingular	ingular	ADJ
iajs-759	19	8	equations	equation	NOUN
iajs-759	19	9	:	:	PUNCT
iajs-759	19	10	an	an	DET
iajs-759	19	11	integral	integral	ADJ
iajs-759	19	12	equation	equation	NOUN
iajs-759	19	13	may	may	AUX
iajs-759	19	14	be	be	AUX
iajs-759	19	15	called	call	VERB
iajs-759	19	16	singular	singular	ADJ
iajs-759	19	17	if	if	SCONJ
iajs-759	19	18	either	either	CCONJ
iajs-759	19	19	(	(	PUNCT
iajs-759	19	20	a	a	X
iajs-759	19	21	)	)	PUNCT
iajs-759	19	22	its	its	PRON
iajs-759	19	23	kernel	kernel	PROPN
iajs-759	19	24	k(x	k(x	PROPN
iajs-759	19	25	,	,	PUNCT
iajs-759	19	26	y	y	NOUN
iajs-759	19	27	)	)	PUNCT
iajs-759	19	28	is	be	AUX
iajs-759	19	29	not	not	PART
iajs-759	19	30	bounded	bound	VERB
iajs-759	19	31	(	(	PUNCT
iajs-759	19	32	b	b	NOUN
iajs-759	19	33	)	)	PUNCT
iajs-759	19	34	the	the	DET
iajs-759	19	35	range	range	NOUN
iajs-759	19	36	of	of	ADP
iajs-759	19	37	integration	integration	NOUN
iajs-759	19	38	is	be	AUX
iajs-759	19	39	infinite	infinite	ADJ
iajs-759	19	40	e.g.	e.g.	ADV
iajs-759	19	41	,	,	PUNCT
iajs-759	19	42	x0	x0	PROPN
iajs-759	19	43	or	or	CCONJ
iajs-759	19	44			NUM
iajs-759	19	45	x	x	X
iajs-759	19	46	.	.	PUNCT
iajs-759	20	1	and	and	CCONJ
iajs-759	20	2	it	it	PRON
iajs-759	20	3	is	be	AUX
iajs-759	20	4	said	say	VERB
iajs-759	20	5	to	to	PART
iajs-759	20	6	be	be	AUX
iajs-759	20	7	weakly	weakly	ADV
iajs-759	20	8	-	-	PUNCT
iajs-759	20	9	singular	singular	ADJ
iajs-759	20	10	if	if	SCONJ
iajs-759	20	11	the	the	DET
iajs-759	20	12	kernel	kernel	NOUN
iajs-759	20	13	becomes	become	VERB
iajs-759	20	14	infinite	infinite	ADJ
iajs-759	20	15	at	at	ADP
iajs-759	20	16	y	y	NOUN
iajs-759	20	17	=	=	NOUN
iajs-759	20	18	x.	x.	NOUN
iajs-759	21	1	[	[	X
iajs-759	21	2	9,10	9,10	NUM
iajs-759	21	3	]	]	SYM
iajs-759	21	4	2.3	2.3	NUM
iajs-759	21	5	structure	structure	NOUN
iajs-759	21	6	of	of	ADP
iajs-759	21	7	kernel	kernel	NOUN
iajs-759	21	8	:	:	PUNCT
iajs-759	21	9	(	(	PUNCT
iajs-759	21	10	a	a	X
iajs-759	21	11	)	)	PUNCT
iajs-759	21	12	linear	linear	ADJ
iajs-759	21	13	integral	integral	ADJ
iajs-759	21	14	equation	equation	NOUN
iajs-759	21	15	with	with	ADP
iajs-759	21	16	a	a	DET
iajs-759	21	17	kernel	kernel	NOUN
iajs-759	21	18	k(x	k(x	PROPN
iajs-759	21	19	,	,	PUNCT
iajs-759	21	20	t)=k(t	t)=k(t	PROPN
iajs-759	21	21	,	,	PUNCT
iajs-759	21	22	x	x	PRON
iajs-759	21	23	)	)	PUNCT
iajs-759	21	24	is	be	AUX
iajs-759	21	25	said	say	VERB
iajs-759	21	26	to	to	PART
iajs-759	21	27	be	be	AUX
iajs-759	21	28	symmetric	symmetric	ADJ
iajs-759	21	29	.	.	PUNCT
iajs-759	22	1	this	this	DET
iajs-759	22	2	property	property	NOUN
iajs-759	22	3	plays	play	VERB
iajs-759	22	4	a	a	DET
iajs-759	22	5	key	key	ADJ
iajs-759	22	6	role	role	NOUN
iajs-759	22	7	in	in	ADP
iajs-759	22	8	the	the	DET
iajs-759	22	9	theory	theory	NOUN
iajs-759	22	10	of	of	ADP
iajs-759	22	11	fredholm	fredholm	ADJ
iajs-759	22	12	integral	integral	ADJ
iajs-759	22	13	equations	equation	NOUN
iajs-759	22	14	.	.	PUNCT
iajs-759	23	1	(	(	PUNCT
iajs-759	23	2	b	b	X
iajs-759	23	3	)	)	PUNCT
iajs-759	23	4	if	if	SCONJ
iajs-759	23	5	k(x	k(x	PROPN
iajs-759	23	6	,	,	PUNCT
iajs-759	23	7	t)=k(a+	t)=k(a+	NOUN
iajs-759	23	8	bx	bx	NOUN
iajs-759	23	9	,	,	PUNCT
iajs-759	23	10	a+	a+	PUNCT
iajs-759	23	11	bt	bt	NOUN
iajs-759	23	12	)	)	PUNCT
iajs-759	23	13	in	in	ADP
iajs-759	23	14	linear	linear	ADJ
iajs-759	23	15	integral	integral	ADJ
iajs-759	23	16	equation	equation	NOUN
iajs-759	23	17	,	,	PUNCT
iajs-759	23	18	the	the	DET
iajs-759	23	19	kernel	kernel	NOUN
iajs-759	23	20	is	be	AUX
iajs-759	23	21	called	call	VERB
iajs-759	23	22	contersymmetric	contersymmetric	ADJ
iajs-759	23	23	.	.	PUNCT
iajs-759	24	1	(	(	PUNCT
iajs-759	24	2	c	c	X
iajs-759	24	3	)	)	PUNCT
iajs-759	24	4	if	if	SCONJ
iajs-759	24	5	k(x	k(x	PROPN
iajs-759	24	6	,	,	PUNCT
iajs-759	24	7	t	t	PROPN
iajs-759	24	8	)	)	PUNCT
iajs-759	24	9	in	in	ADP
iajs-759	24	10	(	(	PUNCT
iajs-759	24	11	1.1)and	1.1)and	NUM
iajs-759	24	12	(	(	PUNCT
iajs-759	24	13	1.2	1.2	NUM
iajs-759	24	14	)	)	PUNCT
iajs-759	24	15	depends	depend	VERB
iajs-759	24	16	only	only	ADV
iajs-759	24	17	on	on	ADP
iajs-759	24	18	the	the	DET
iajs-759	24	19	difference	difference	NOUN
iajs-759	24	20	(	(	PUNCT
iajs-759	24	21	x	x	NOUN
iajs-759	24	22	-	-	NOUN
iajs-759	24	23	t	t	NOUN
iajs-759	24	24	)	)	PUNCT
iajs-759	24	25	i.e.	i.e.	X
iajs-759	24	26	if	if	SCONJ
iajs-759	24	27	the	the	DET
iajs-759	24	28	kernel	kernel	NOUN
iajs-759	24	29	is	be	AUX
iajs-759	24	30	of	of	ADP
iajs-759	24	31	the	the	DET
iajs-759	24	32	form	form	NOUN
iajs-759	24	33	k(x	k(x	PROPN
iajs-759	24	34	,	,	PUNCT
iajs-759	24	35	t)=k(x	t)=k(x	PROPN
iajs-759	24	36	-	-	PUNCT
iajs-759	24	37	t).such	t).such	PROPN
iajs-759	24	38	a	a	DET
iajs-759	24	39	kernel	kernel	NOUN
iajs-759	24	40	is	be	AUX
iajs-759	24	41	called	call	VERB
iajs-759	24	42	difference	difference	NOUN
iajs-759	24	43	kernel	kernel	NOUN
iajs-759	24	44	and	and	CCONJ
iajs-759	24	45	the	the	DET
iajs-759	24	46	integral	integral	ADJ
iajs-759	24	47	equation	equation	NOUN
iajs-759	24	48	is	be	AUX
iajs-759	24	49	called	call	VERB
iajs-759	24	50	integral	integral	ADJ
iajs-759	24	51	equation	equation	NOUN
iajs-759	24	52	of	of	ADP
iajs-759	24	53	convolution	convolution	NOUN
iajs-759	24	54	type	type	NOUN
iajs-759	24	55	which	which	PRON
iajs-759	24	56	has	have	VERB
iajs-759	24	57	the	the	DET
iajs-759	24	58	form	form	NOUN
iajs-759	24	59	[	[	X
iajs-759	24	60	1,11	1,11	X
iajs-759	24	61	]	]	X
iajs-759	24	62	:	:	PUNCT
iajs-759	24	63			X
iajs-759	24	64			X
iajs-759	24	65	)	)	PUNCT
iajs-759	24	66	(	(	PUNCT
iajs-759	24	67	)	)	PUNCT
iajs-759	24	68	(	(	PUNCT
iajs-759	24	69	)	)	PUNCT
iajs-759	24	70	(	(	PUNCT
iajs-759	24	71	)	)	PUNCT
iajs-759	24	72	(	(	PUNCT
iajs-759	24	73	)	)	PUNCT
iajs-759	24	74	(	(	PUNCT
iajs-759	24	75	)	)	PUNCT
iajs-759	24	76	(	(	PUNCT
iajs-759	24	77	xb	xb	PROPN
iajs-759	24	78	a	a	DET
iajs-759	24	79	dttutxkxfxuxh	dttutxkxfxuxh	ADJ
iajs-759	24	80			X
iajs-759	24	81	…	…	PUNCT
iajs-759	24	82	(	(	PUNCT
iajs-759	24	83	1.7	1.7	NUM
iajs-759	24	84	)	)	PUNCT
iajs-759	24	85	(	(	PUNCT
iajs-759	24	86	d	d	X
iajs-759	24	87	)	)	PUNCT
iajs-759	24	88	in	in	ADP
iajs-759	24	89	equation	equation	NOUN
iajs-759	24	90	(	(	PUNCT
iajs-759	24	91	1.1	1.1	NUM
iajs-759	24	92	)	)	PUNCT
iajs-759	24	93	,	,	PUNCT
iajs-759	24	94	k(x	k(x	PROPN
iajs-759	24	95	,	,	PUNCT
iajs-759	24	96	t	t	PROPN
iajs-759	24	97	)	)	PUNCT
iajs-759	24	98	is	be	AUX
iajs-759	24	99	called	call	VERB
iajs-759	24	100	separable	separable	ADJ
iajs-759	24	101	or	or	CCONJ
iajs-759	24	102	degenerate	degenerate	ADJ
iajs-759	24	103	kernel	kernel	NOUN
iajs-759	24	104	of	of	ADP
iajs-759	24	105	rank	rank	NOUN
iajs-759	24	106	n	n	NOUN
iajs-759	24	107	if	if	SCONJ
iajs-759	24	108	it	it	PRON
iajs-759	24	109	is	be	AUX
iajs-759	24	110	of	of	ADP
iajs-759	24	111	the	the	DET
iajs-759	24	112	form	form	NOUN
iajs-759	24	113	:	:	PUNCT
iajs-759	24	114			X
iajs-759	25	1			NOUN
iajs-759	26	1			NOUN
iajs-759	27	1	n	n	PRON
iajs-759	27	2	r	r	NOUN
iajs-759	27	3	rr	rr	NOUN
iajs-759	27	4	tbxatxk	tbxatxk	NOUN
iajs-759	27	5	1	1	NUM
iajs-759	27	6	)	)	PUNCT
iajs-759	27	7	(	(	PUNCT
iajs-759	27	8	)	)	PUNCT
iajs-759	27	9	(	(	PUNCT
iajs-759	27	10	)	)	PUNCT
iajs-759	27	11	,	,	PUNCT
iajs-759	27	12	(	(	PUNCT
iajs-759	27	13	where	where	SCONJ
iajs-759	27	14	n	n	PRON
iajs-759	27	15	is	be	AUX
iajs-759	27	16	finite	finite	ADJ
iajs-759	27	17	,	,	PUNCT
iajs-759	27	18	it	it	PRON
iajs-759	27	19	is	be	AUX
iajs-759	27	20	assumed	assume	VERB
iajs-759	27	21	that	that	SCONJ
iajs-759	27	22	the	the	DET
iajs-759	27	23	functions	function	NOUN
iajs-759	27	24	{	{	PUNCT
iajs-759	27	25	ar	ar	NOUN
iajs-759	27	26	}	}	PUNCT
iajs-759	27	27	and	and	CCONJ
iajs-759	27	28	{	{	PUNCT
iajs-759	27	29	br	br	NOUN
iajs-759	27	30	}	}	PUNCT
iajs-759	27	31	are	be	AUX
iajs-759	27	32	sufficiently	sufficiently	ADV
iajs-759	27	33	smooth	smooth	ADJ
iajs-759	27	34	functions	function	NOUN
iajs-759	27	35	of	of	ADP
iajs-759	27	36	these	these	DET
iajs-759	27	37	arguments	argument	NOUN
iajs-759	27	38	[	[	X
iajs-759	27	39	11	11	NUM
iajs-759	27	40	]	]	PUNCT
iajs-759	27	41	.	.	PUNCT
iajs-759	28	1	ibn	ibn	PROPN
iajs-759	28	2	alhaitham	alhaitham	PROPN
iajs-759	28	3	j.	j.	PROPN
iajs-759	28	4	for	for	ADP
iajs-759	28	5	pure	pure	ADJ
iajs-759	28	6	&	&	CCONJ
iajs-759	28	7	appl	appl	PROPN
iajs-759	28	8	.	.	PUNCT
iajs-759	29	1	sci	sci	PROPN
iajs-759	29	2	.	.	PUNCT
iajs-759	29	3	vol.24	vol.24	NOUN
iajs-759	29	4	(	(	PUNCT
iajs-759	29	5	2	2	NUM
iajs-759	29	6	)	)	PUNCT
iajs-759	29	7	2011	2011	NUM
iajs-759	29	8	hence	hence	ADV
iajs-759	29	9	,	,	PUNCT
iajs-759	29	10	in	in	ADP
iajs-759	29	11	many	many	ADJ
iajs-759	29	12	cases	case	NOUN
iajs-759	29	13	a	a	DET
iajs-759	29	14	non	non	ADJ
iajs-759	29	15	degenerate	degenerate	ADJ
iajs-759	29	16	kernel	kernel	PROPN
iajs-759	29	17	k(x	k(x	PROPN
iajs-759	29	18	,	,	PUNCT
iajs-759	29	19	t	t	PROPN
iajs-759	29	20	)	)	PUNCT
iajs-759	29	21	may	may	AUX
iajs-759	29	22	be	be	AUX
iajs-759	29	23	approximated	approximate	VERB
iajs-759	29	24	by	by	ADP
iajs-759	29	25	a	a	DET
iajs-759	29	26	degenerate	degenerate	ADJ
iajs-759	29	27	kernel	kernel	NOUN
iajs-759	29	28	as	as	ADP
iajs-759	29	29	a	a	DET
iajs-759	29	30	partial	partial	ADJ
iajs-759	29	31	sum	sum	NOUN
iajs-759	29	32	of	of	ADP
iajs-759	29	33	taylor	taylor	PROPN
iajs-759	29	34	series	series	PROPN
iajs-759	29	35	expansion	expansion	NOUN
iajs-759	29	36	of	of	ADP
iajs-759	29	37	k(x	k(x	PROPN
iajs-759	29	38	,	,	PUNCT
iajs-759	29	39	t	t	PROPN
iajs-759	29	40	)	)	PUNCT
iajs-759	30	1	[	[	X
iajs-759	30	2	11	11	NUM
iajs-759	30	3	]	]	PUNCT
iajs-759	30	4	.	.	PUNCT
iajs-759	31	1	for	for	ADP
iajs-759	31	2	example	example	NOUN
iajs-759	31	3	,	,	PUNCT
iajs-759	31	4	consider	consider	VERB
iajs-759	31	5	the	the	DET
iajs-759	31	6	kernel	kernel	PROPN
iajs-759	31	7	xt	xt	PROPN
iajs-759	31	8	etxk	etxk	VERB
iajs-759	31	9			NUM
iajs-759	31	10	1	1	NUM
iajs-759	31	11	)	)	PUNCT
iajs-759	31	12	,	,	PUNCT
iajs-759	31	13	(	(	PUNCT
iajs-759	31	14	which	which	PRON
iajs-759	31	15	may	may	AUX
iajs-759	31	16	be	be	AUX
iajs-759	31	17	approximated	approximate	VERB
iajs-759	31	18	to	to	PART
iajs-759	31	19	be	be	AUX
iajs-759	31	20	finite	finite	ADJ
iajs-759	31	21	number	number	NOUN
iajs-759	31	22	of	of	ADP
iajs-759	31	23	terms	term	NOUN
iajs-759	31	24	of	of	ADP
iajs-759	31	25	its	its	PRON
iajs-759	31	26	taylor	taylor	PROPN
iajs-759	31	27	’s	’s	PART
iajs-759	31	28	series	series	NOUN
iajs-759	31	29	about	about	ADP
iajs-759	31	30	0,0	0,0	NOUN
iajs-759	31	31	00	00	NUM
iajs-759	31	32			NUM
iajs-759	31	33	yx	yx	ADP
iajs-759	31	34	i.e.	i.e.	X
iajs-759	31	35	]	]	PUNCT
iajs-759	31	36	!	!	PUNCT
iajs-759	32	1	3!2	3!2	NUM
iajs-759	32	2	1[11	1[11	NUM
iajs-759	32	3	3322	3322	NUM
iajs-759	32	4			PROPN
iajs-759	32	5	txtx	txtx	VERB
iajs-759	32	6	xte	xte	PROPN
iajs-759	32	7	xt	xt	PROPN
iajs-759	33	1	hence	hence	ADV
iajs-759	33	2	,	,	PUNCT
iajs-759	33	3	if	if	SCONJ
iajs-759	33	4	only	only	ADV
iajs-759	33	5	3	3	NUM
iajs-759	33	6	-	-	NOUN
iajs-759	33	7	terms	term	NOUN
iajs-759	33	8	of	of	ADP
iajs-759	33	9	the	the	DET
iajs-759	33	10	series	series	NOUN
iajs-759	33	11	are	be	AUX
iajs-759	33	12	considered	consider	VERB
iajs-759	33	13	,	,	PUNCT
iajs-759	33	14	we	we	PRON
iajs-759	33	15	have	have	VERB
iajs-759	33	16	a	a	DET
iajs-759	33	17	degenerate	degenerate	ADJ
iajs-759	33	18	kernel	kernel	NOUN
iajs-759	33	19	:	:	PUNCT
iajs-759	33	20			X
iajs-759	33	21			NUM
iajs-759	33	22			SYM
iajs-759	33	23	3	3	NUM
iajs-759	33	24	1	1	NUM
iajs-759	33	25	3322	3322	NUM
iajs-759	33	26	)	)	PUNCT
iajs-759	33	27	(	(	PUNCT
iajs-759	33	28	)	)	PUNCT
iajs-759	33	29	(	(	PUNCT
iajs-759	33	30	!	!	NOUN
iajs-759	33	31	3!2	3!2	NUM
iajs-759	33	32	)	)	PUNCT
iajs-759	33	33	,	,	PUNCT
iajs-759	33	34	(	(	PUNCT
iajs-759	33	35	r	r	NOUN
iajs-759	33	36	rr	rr	PROPN
iajs-759	33	37	tbxa	tbxa	NOUN
iajs-759	33	38	txtx	txtx	VERB
iajs-759	33	39	xttxk	xttxk	PROPN
iajs-759	34	1			PROPN
iajs-759	34	2	where	where	SCONJ
iajs-759	34	3	,	,	PUNCT
iajs-759	34	4	)	)	PUNCT
iajs-759	34	5	(	(	PUNCT
iajs-759	34	6	1	1	NUM
iajs-759	34	7	xxa	xxa	ADV
iajs-759	34	8			NUM
iajs-759	34	9	,	,	PUNCT
iajs-759	34	10	)	)	PUNCT
iajs-759	34	11	(	(	PUNCT
iajs-759	34	12	2	2	NUM
iajs-759	34	13	2	2	NUM
iajs-759	34	14	xxa	xxa	ADP
iajs-759	34	15			NUM
iajs-759	34	16	3	3	NUM
iajs-759	34	17	3	3	NUM
iajs-759	34	18	)	)	PUNCT
iajs-759	34	19	(	(	PUNCT
iajs-759	34	20	xxa	xxa	PROPN
iajs-759	34	21			NUM
iajs-759	34	22	,	,	PUNCT
iajs-759	34	23	)	)	PUNCT
iajs-759	34	24	(	(	PUNCT
iajs-759	34	25	1	1	NUM
iajs-759	34	26	ttb	ttb	PROPN
iajs-759	34	27			NUM
iajs-759	34	28	,	,	PUNCT
iajs-759	34	29	!	!	PUNCT
iajs-759	34	30	2	2	X
iajs-759	34	31	)	)	PUNCT
iajs-759	34	32	(	(	PUNCT
iajs-759	34	33	2	2	NUM
iajs-759	34	34	2	2	NUM
iajs-759	34	35	t	t	NOUN
iajs-759	34	36	tb	tb	ADP
iajs-759	34	37			NUM
iajs-759	34	38	!	!	PUNCT
iajs-759	34	39	3	3	X
iajs-759	34	40	)	)	PUNCT
iajs-759	34	41	(	(	PUNCT
iajs-759	34	42	3	3	NUM
iajs-759	34	43	3	3	NUM
iajs-759	34	44	t	t	NOUN
iajs-759	34	45	tb	tb	ADP
iajs-759	34	46			NUM
iajs-759	34	47	definition	definition	NOUN
iajs-759	34	48	1.3	1.3	NUM
iajs-759	34	49	:	:	PUNCT
iajs-759	34	50	an	an	DET
iajs-759	34	51	ordinary	ordinary	ADJ
iajs-759	34	52	differential	differential	ADJ
iajs-759	34	53	equation	equation	NOUN
iajs-759	34	54	is	be	AUX
iajs-759	34	55	an	an	DET
iajs-759	34	56	equation	equation	NOUN
iajs-759	34	57	that	that	PRON
iajs-759	34	58	involves	involve	VERB
iajs-759	34	59	at	at	ADP
iajs-759	34	60	most	most	ADV
iajs-759	34	61	the	the	DET
iajs-759	34	62	thn	thn	PROPN
iajs-759	34	63	derivative	derivative	NOUN
iajs-759	34	64	of	of	ADP
iajs-759	34	65	an	an	DET
iajs-759	34	66	unknown	unknown	ADJ
iajs-759	34	67	function	function	NOUN
iajs-759	34	68	[	[	X
iajs-759	34	69	13	13	NUM
iajs-759	34	70	]	]	PUNCT
iajs-759	34	71	.	.	PUNCT
iajs-759	35	1	i.e.	i.e.	X
iajs-759	35	2	if	if	SCONJ
iajs-759	35	3	the	the	DET
iajs-759	35	4	unknown	unknown	ADJ
iajs-759	35	5	function	function	NOUN
iajs-759	35	6	u	u	NOUN
iajs-759	35	7	is	be	AUX
iajs-759	35	8	a	a	DET
iajs-759	35	9	function	function	NOUN
iajs-759	35	10	of	of	ADP
iajs-759	35	11	x	x	PUNCT
iajs-759	35	12	then	then	ADV
iajs-759	35	13	we	we	PRON
iajs-759	35	14	write	write	VERB
iajs-759	35	15	the	the	DET
iajs-759	35	16	differential	differential	ADJ
iajs-759	35	17	equation	equation	NOUN
iajs-759	35	18	of	of	ADP
iajs-759	35	19	order	order	NOUN
iajs-759	35	20	n	n	PRON
iajs-759	35	21	as	as	ADP
iajs-759	35	22	:	:	PUNCT
iajs-759	35	23	)	)	PUNCT
iajs-759	35	24	,	,	PUNCT
iajs-759	35	25	.......	.......	PUNCT
iajs-759	35	26	,	,	PUNCT
iajs-759	35	27	,	,	PUNCT
iajs-759	35	28	,	,	PUNCT
iajs-759	35	29	,	,	PUNCT
iajs-759	35	30	(	(	PUNCT
iajs-759	35	31	)	)	PUNCT
iajs-759	35	32	(	(	PUNCT
iajs-759	35	33	)	)	PUNCT
iajs-759	35	34	1	1	NUM
iajs-759	35	35	(	(	PUNCT
iajs-759	35	36			NOUN
iajs-759	35	37	n	n	CCONJ
iajs-759	35	38	n	n	PROPN
iajs-759	35	39	n	n	PROPN
iajs-759	35	40	uuuuxg	uuuuxg	PROPN
iajs-759	35	41	dx	dx	PROPN
iajs-759	35	42	xud	xud	PROPN
iajs-759	35	43	where	where	SCONJ
iajs-759	35	44	g	g	PROPN
iajs-759	35	45	is	be	AUX
iajs-759	35	46	a	a	DET
iajs-759	35	47	given	give	VERB
iajs-759	35	48	function	function	NOUN
iajs-759	35	49	of	of	ADP
iajs-759	35	50	variable	variable	NOUN
iajs-759	35	51	)	)	PUNCT
iajs-759	35	52	1	1	NUM
iajs-759	35	53	(	(	PUNCT
iajs-759	35	54	,	,	PUNCT
iajs-759	35	55	.......	.......	PUNCT
iajs-759	35	56	,	,	PUNCT
iajs-759	35	57	,	,	PUNCT
iajs-759	35	58	,	,	PUNCT
iajs-759	35	59	,	,	PUNCT
iajs-759	35	60			NOUN
iajs-759	35	61	nuuuux	nuuuux	PROPN
iajs-759	35	62	1.4	1.4	NUM
iajs-759	35	63	integro	integro	ADJ
iajs-759	35	64	-	-	PUNCT
iajs-759	35	65	differential	differential	NOUN
iajs-759	35	66	equation	equation	NOUN
iajs-759	35	67	:	:	PUNCT
iajs-759	36	1	[	[	X
iajs-759	36	2	14,15	14,15	NUM
iajs-759	36	3	]	]	X
iajs-759	36	4	an	an	DET
iajs-759	36	5	integro	integro	ADJ
iajs-759	36	6	-	-	PUNCT
iajs-759	36	7	differential	differential	NOUN
iajs-759	36	8	equation	equation	NOUN
iajs-759	36	9	is	be	AUX
iajs-759	36	10	an	an	DET
iajs-759	36	11	equation	equation	NOUN
iajs-759	36	12	involving	involve	VERB
iajs-759	36	13	one	one	NUM
iajs-759	36	14	(	(	PUNCT
iajs-759	36	15	or	or	CCONJ
iajs-759	36	16	more	more	ADJ
iajs-759	36	17	)	)	PUNCT
iajs-759	36	18	unknown	unknown	ADJ
iajs-759	36	19	functions	function	NOUN
iajs-759	36	20	u(x	u(x	NOUN
iajs-759	36	21	)	)	PUNCT
iajs-759	36	22	,	,	PUNCT
iajs-759	36	23	together	together	ADV
iajs-759	36	24	with	with	ADP
iajs-759	36	25	both	both	CCONJ
iajs-759	36	26	differential	differential	ADJ
iajs-759	36	27	and	and	CCONJ
iajs-759	36	28	integral	integral	ADJ
iajs-759	36	29	operations	operation	NOUN
iajs-759	36	30	on	on	ADP
iajs-759	36	31	x.	x.	NOUN
iajs-759	36	32	a	a	DET
iajs-759	36	33	linear	linear	ADJ
iajs-759	36	34	integro	integro	ADJ
iajs-759	36	35	-	-	PUNCT
iajs-759	36	36	differential	differential	NOUN
iajs-759	36	37	equation	equation	NOUN
iajs-759	36	38	of	of	ADP
iajs-759	36	39	order	order	NOUN
iajs-759	36	40	n	n	X
iajs-759	36	41	is	be	AUX
iajs-759	36	42	an	an	DET
iajs-759	36	43	equation	equation	NOUN
iajs-759	36	44	of	of	ADP
iajs-759	36	45	the	the	DET
iajs-759	36	46	form	form	NOUN
iajs-759	36	47			PUNCT
iajs-759	37	1			NOUN
iajs-759	37	2			PROPN
iajs-759	37	3			NUM
iajs-759	37	4	)	)	PUNCT
iajs-759	37	5	(	(	PUNCT
iajs-759	37	6	1	1	NUM
iajs-759	37	7	0	0	NUM
iajs-759	37	8	)	)	PUNCT
iajs-759	37	9	(	(	PUNCT
iajs-759	37	10	)	)	PUNCT
iajs-759	37	11	(	(	PUNCT
iajs-759	37	12	)	)	PUNCT
iajs-759	37	13	(	(	PUNCT
iajs-759	37	14	)	)	PUNCT
iajs-759	37	15	,	,	PUNCT
iajs-759	37	16	(	(	PUNCT
iajs-759	37	17	)	)	PUNCT
iajs-759	37	18	(	(	PUNCT
iajs-759	37	19	)	)	PUNCT
iajs-759	37	20	(	(	PUNCT
iajs-759	37	21	)	)	PUNCT
iajs-759	37	22	(	(	PUNCT
iajs-759	37	23	)	)	PUNCT
iajs-759	37	24	(	(	PUNCT
iajs-759	37	25	xb	xb	X
iajs-759	37	26	a	a	PRON
iajs-759	37	27	n	n	NOUN
iajs-759	38	1	i	i	PRON
iajs-759	38	2	i	i	PRON
iajs-759	38	3	i	i	PRON
iajs-759	38	4	n	n	VERB
iajs-759	38	5	dttutxkxfxuxpxu	dttutxkxfxuxpxu	VERB
iajs-759	38	6			ADJ
iajs-759	38	7	here	here	ADV
iajs-759	38	8	,	,	PUNCT
iajs-759	38	9	)	)	PUNCT
iajs-759	38	10	1,	1,	NUM
iajs-759	38	11	......	......	PUNCT
iajs-759	38	12	,1,0	,1,0	PROPN
iajs-759	38	13	)	)	PUNCT
iajs-759	38	14	(	(	PUNCT
iajs-759	38	15	(	(	PUNCT
iajs-759	38	16	)	)	PUNCT
iajs-759	38	17	,	,	PUNCT
iajs-759	38	18	(	(	PUNCT
iajs-759	38	19	)	)	PUNCT
iajs-759	38	20	,	,	PUNCT
iajs-759	38	21	,	,	PUNCT
iajs-759	38	22	(	(	PUNCT
iajs-759	38	23			ADJ
iajs-759	38	24	nixpxftxk	nixpxftxk	NOUN
iajs-759	38	25	i	i	PRON
iajs-759	38	26	are	be	AUX
iajs-759	38	27	known	know	VERB
iajs-759	38	28	functions	function	NOUN
iajs-759	38	29	,	,	PUNCT
iajs-759	38	30	u(x	u(x	NOUN
iajs-759	38	31	)	)	PUNCT
iajs-759	38	32	is	be	AUX
iajs-759	38	33	the	the	DET
iajs-759	38	34	unknown	unknown	ADJ
iajs-759	38	35	function	function	NOUN
iajs-759	38	36	,	,	PUNCT
iajs-759	38	37	and	and	CCONJ
iajs-759	38	38			NOUN
iajs-759	38	39	is	be	AUX
iajs-759	38	40	a	a	DET
iajs-759	38	41	scalar	scalar	ADJ
iajs-759	38	42	parameter[11	parameter[11	NOUN
iajs-759	38	43	]	]	PUNCT
iajs-759	38	44	.	.	PUNCT
iajs-759	39	1	2	2	X
iajs-759	39	2	.	.	X
iajs-759	39	3	numerical	numerical	ADJ
iajs-759	39	4	solution	solution	NOUN
iajs-759	39	5	of	of	ADP
iajs-759	39	6	vide	vide	NOUN
iajs-759	39	7	using	use	VERB
iajs-759	39	8	open	open	ADJ
iajs-759	39	9	newton	newton	PROPN
iajs-759	39	10	cotes	cotes	PROPN
iajs-759	39	11	formula(o	formula(o	PROPN
iajs-759	39	12	-	-	PUNCT
iajs-759	39	13	n	n	CCONJ
iajs-759	39	14	)	)	PUNCT
iajs-759	39	15	.	.	PUNCT
iajs-759	40	1	in	in	ADP
iajs-759	40	2	this	this	DET
iajs-759	40	3	search	search	NOUN
iajs-759	40	4	,	,	PUNCT
iajs-759	40	5	we	we	PRON
iajs-759	40	6	use	use	VERB
iajs-759	40	7	open	open	ADJ
iajs-759	40	8	newton	newton	PROPN
iajs-759	40	9	cotes	cotes	PROPN
iajs-759	40	10	formula	formula	NOUN
iajs-759	40	11	(	(	PUNCT
iajs-759	40	12	o	o	NOUN
iajs-759	40	13	-	-	NOUN
iajs-759	40	14	n	n	CCONJ
iajs-759	40	15	)	)	PUNCT
iajs-759	40	16	to	to	PART
iajs-759	40	17	find	find	VERB
iajs-759	40	18	the	the	DET
iajs-759	40	19	numerical	numerical	ADJ
iajs-759	40	20	solution	solution	NOUN
iajs-759	40	21	of	of	ADP
iajs-759	40	22	1st	1st	ADJ
iajs-759	40	23	order	order	NOUN
iajs-759	40	24	linear	linear	PROPN
iajs-759	40	25	vide	vide	NOUN
iajs-759	40	26	,	,	PUNCT
iajs-759	40	27	in	in	ADP
iajs-759	40	28	the	the	DET
iajs-759	40	29	form	form	NOUN
iajs-759	40	30	:	:	PUNCT
iajs-759	40	31			PUNCT
iajs-759	40	32			NOUN
iajs-759	40	33	x	x	PUNCT
iajs-759	40	34	a	a	DET
iajs-759	40	35	baixdyyuyxkxfxuxpxu	baixdyyuyxkxfxuxpxu	NOUN
iajs-759	40	36	]	]	PUNCT
iajs-759	40	37	,	,	PUNCT
iajs-759	40	38	[	[	X
iajs-759	40	39	,	,	PUNCT
iajs-759	40	40	)	)	PUNCT
iajs-759	40	41	(	(	PUNCT
iajs-759	40	42	)	)	PUNCT
iajs-759	40	43	,	,	PUNCT
iajs-759	40	44	(	(	PUNCT
iajs-759	40	45	)	)	PUNCT
iajs-759	40	46	(	(	PUNCT
iajs-759	40	47	)	)	PUNCT
iajs-759	40	48	(	(	PUNCT
iajs-759	40	49	)	)	PUNCT
iajs-759	40	50	(	(	PUNCT
iajs-759	40	51	)	)	PUNCT
iajs-759	40	52	(	(	PUNCT
iajs-759	40	53	…	…	PUNCT
iajs-759	40	54	(	(	PUNCT
iajs-759	40	55	1.8	1.8	NUM
iajs-759	40	56	)	)	PUNCT
iajs-759	40	57	with	with	ADP
iajs-759	40	58	the	the	DET
iajs-759	40	59	initial	initial	ADJ
iajs-759	40	60	condition	condition	NOUN
iajs-759	40	61	,	,	PUNCT
iajs-759	40	62	)	)	PUNCT
iajs-759	40	63	(	(	PUNCT
iajs-759	40	64	0uau	0uau	NUM
iajs-759	40	65			NOUN
iajs-759	40	66	where	where	SCONJ
iajs-759	40	67	the	the	DET
iajs-759	40	68	functions	function	NOUN
iajs-759	40	69	f	f	PROPN
iajs-759	40	70	and	and	CCONJ
iajs-759	40	71	p	p	NOUN
iajs-759	40	72	are	be	AUX
iajs-759	40	73	assumed	assume	VERB
iajs-759	40	74	to	to	PART
iajs-759	40	75	be	be	AUX
iajs-759	40	76	continuous	continuous	ADJ
iajs-759	40	77	on	on	ADP
iajs-759	40	78	i	i	PRON
iajs-759	40	79	and	and	CCONJ
iajs-759	40	80	k	k	PROPN
iajs-759	40	81	denotes	denote	NOUN
iajs-759	40	82	given	give	VERB
iajs-759	40	83	continuous	continuous	ADJ
iajs-759	40	84	functions	function	NOUN
iajs-759	40	85	.	.	PUNCT
iajs-759	41	1	were	be	AUX
iajs-759	41	2	the	the	DET
iajs-759	41	3	interval	interval	NOUN
iajs-759	41	4	[	[	X
iajs-759	41	5	a	a	X
iajs-759	41	6	,	,	PUNCT
iajs-759	41	7	b	b	NOUN
iajs-759	41	8	]	]	X
iajs-759	41	9	is	be	AUX
iajs-759	41	10	divided	divide	VERB
iajs-759	41	11	in	in	ADP
iajs-759	41	12	to	to	ADP
iajs-759	41	13	n	n	CCONJ
iajs-759	41	14	equal	equal	ADJ
iajs-759	41	15	subintervals	subinterval	NOUN
iajs-759	41	16	,	,	PUNCT
iajs-759	41	17	where	where	SCONJ
iajs-759	41	18	h=(b	h=(b	NOUN
iajs-759	41	19	-	-	PUNCT
iajs-759	41	20	a)/n	a)/n	PROPN
iajs-759	41	21	,	,	PUNCT
iajs-759	41	22	byay	byay	NOUN
iajs-759	41	23	n	n	CCONJ
iajs-759	41	24			NUM
iajs-759	41	25	,	,	PUNCT
iajs-759	41	26	0	0	NUM
iajs-759	41	27	and	and	CCONJ
iajs-759	41	28	*	*	ADJ
iajs-759	41	29	,	,	PUNCT
iajs-759	41	30	0,1	0,1	NUM
iajs-759	41	31	,	,	PUNCT
iajs-759	41	32	,	,	PUNCT
iajs-759	41	33	.jy	.jy	PUNCT
iajs-759	42	1	a	a	DET
iajs-759	42	2	j	j	PROPN
iajs-759	42	3	h	h	NOUN
iajs-759	42	4	j	j	PROPN
iajs-759	42	5	n	n	PROPN
iajs-759	42	6			ADV
iajs-759	43	1			NOUN
iajs-759	43	2			NOUN
iajs-759	43	3	we	we	PRON
iajs-759	43	4	set	set	VERB
iajs-759	43	5	,	,	PUNCT
iajs-759	43	6	0,1	0,1	NUM
iajs-759	43	7	,	,	PUNCT
iajs-759	43	8	,	,	PUNCT
iajs-759	43	9	,	,	PUNCT
iajs-759	43	10	(	(	PUNCT
iajs-759	43	11	)	)	PUNCT
iajs-759	43	12	,	,	PUNCT
iajs-759	43	13	(	(	PUNCT
iajs-759	43	14	)	)	PUNCT
iajs-759	43	15	,	,	PUNCT
iajs-759	43	16	(	(	PUNCT
iajs-759	43	17	)	)	PUNCT
iajs-759	43	18	,	,	PUNCT
iajs-759	43	19	i	i	PRON
iajs-759	44	1	j	j	VERB
iajs-759	45	1	i	i	PRON
iajs-759	45	2	i	i	PRON
iajs-759	46	1	i	i	PRON
iajs-759	46	2	i	i	PRON
iajs-759	47	1	i	i	PRON
iajs-759	47	2	ix	ix	INTJ
iajs-759	47	3	y	y	PROPN
iajs-759	48	1	i	i	PRON
iajs-759	48	2	nu	nu	VERB
iajs-759	48	3	x	x	PUNCT
iajs-759	48	4	u	u	NOUN
iajs-759	48	5	p	p	NOUN
iajs-759	48	6	x	x	X
iajs-759	48	7	p	p	X
iajs-759	48	8	f	f	X
iajs-759	48	9	x	x	PUNCT
iajs-759	48	10	f	f	VERB
iajs-759	49	1			NUM
iajs-759	49	2			NUM
iajs-759	49	3			PROPN
iajs-759	49	4			PROPN
iajs-759	49	5	ii	ii	PROPN
iajs-759	49	6	uxu	uxu	NOUN
iajs-759	49	7			NOUN
iajs-759	49	8	)	)	PUNCT
iajs-759	49	9	(	(	PUNCT
iajs-759	49	10	and	and	CCONJ
iajs-759	49	11	.	.	PUNCT
iajs-759	49	12	)	)	PUNCT
iajs-759	50	1	,	,	PUNCT
iajs-759	50	2	(	(	PUNCT
iajs-759	50	3	ijji	ijji	PROPN
iajs-759	50	4	kyxk	kyxk	PROPN
iajs-759	50	5			NUM
iajs-759	50	6	2.1	2.1	NUM
iajs-759	50	7	open	open	ADJ
iajs-759	50	8	newton	newton	PROPN
iajs-759	50	9	cotes	cotes	PROPN
iajs-759	50	10	formula(o	formula(o	PROPN
iajs-759	50	11	-	-	PUNCT
iajs-759	50	12	n	n	CCONJ
iajs-759	50	13	)	)	PUNCT
iajs-759	50	14	.	.	PUNCT
iajs-759	51	1	open	open	PROPN
iajs-759	51	2	newton	newton	PROPN
iajs-759	51	3	cotes	cotes	PROPN
iajs-759	51	4	formula	formula	NOUN
iajs-759	51	5	is	be	AUX
iajs-759	51	6	used	use	VERB
iajs-759	51	7	with	with	ADP
iajs-759	51	8	n	n	NOUN
iajs-759	51	9	-	-	PUNCT
iajs-759	51	10	subinterval	subinterval	NOUN
iajs-759	51	11	to	to	PART
iajs-759	51	12	approximate	approximate	VERB
iajs-759	51	13	the	the	DET
iajs-759	51	14	integral	integral	ADJ
iajs-759	51	15	in	in	ADP
iajs-759	51	16	equation	equation	NOUN
iajs-759	51	17	(	(	PUNCT
iajs-759	51	18	1.6	1.6	NUM
iajs-759	51	19	)	)	PUNCT
iajs-759	51	20	,	,	PUNCT
iajs-759	51	21	hence	hence	ADV
iajs-759	51	22	if	if	SCONJ
iajs-759	51	23	n	n	PROPN
iajs-759	51	24	=	=	SYM
iajs-759	51	25	0	0	NUM
iajs-759	51	26	m	m	VERB
iajs-759	52	1	idpoint	idpoint	NOUN
iajs-759	52	2	m	m	VERB
iajs-759	52	3	ethod	ethod	NOUN
iajs-759	52	4	let	let	VERB
iajs-759	52	5	h	h	NOUN
iajs-759	52	6	=	=	PUNCT
iajs-759	52	7	(	(	PUNCT
iajs-759	52	8	b	b	X
iajs-759	52	9	-	-	PUNCT
iajs-759	52	10	a)/(2m+2	a)/(2m+2	NOUN
iajs-759	52	11	)	)	PUNCT
iajs-759	52	12	and	and	CCONJ
iajs-759	52	13	xj	xj	PROPN
iajs-759	52	14	=	=	PUNCT
iajs-759	53	1	a	a	PRON
iajs-759	53	2	+	+	X
iajs-759	53	3	(	(	PUNCT
iajs-759	53	4	j	j	PROPN
iajs-759	53	5	+	+	CCONJ
iajs-759	53	6	1)h	1)h	PROPN
iajs-759	53	7	for	for	ADP
iajs-759	53	8	j	j	PROPN
iajs-759	53	9	=	=	SYM
iajs-759	53	10	1,	1,	NUM
iajs-759	53	11	…	…	SYM
iajs-759	53	12	.,2m+1	.,2m+1	NOUN
iajs-759	53	13	for	for	ADP
iajs-759	53	14	n	n	NOUN
iajs-759	53	15	=	=	SYM
iajs-759	53	16	2	2	NUM
iajs-759	53	17	m	m	NOUN
iajs-759	53	18	subinterval	subinterval	NOUN
iajs-759	53	19	is	be	AUX
iajs-759	53	20	ibn	ibn	PROPN
iajs-759	53	21	alhaitham	alhaitham	NOUN
iajs-759	53	22	j.	j.	PROPN
iajs-759	53	23	for	for	ADP
iajs-759	53	24	pure	pure	ADJ
iajs-759	53	25	&	&	CCONJ
iajs-759	53	26	appl	appl	PROPN
iajs-759	53	27	.	.	PUNCT
iajs-759	54	1	sci	sci	PROPN
iajs-759	54	2	.	.	PUNCT
iajs-759	54	3	vol.24	vol.24	NOUN
iajs-759	54	4	(	(	PUNCT
iajs-759	54	5	2	2	NUM
iajs-759	54	6	)	)	PUNCT
iajs-759	54	7	2011	2011	NUM
iajs-759	54	8	)	)	PUNCT
iajs-759	54	9	,	,	PUNCT
iajs-759	54	10	(	(	PUNCT
iajs-759	54	11	)	)	PUNCT
iajs-759	54	12	(	(	PUNCT
iajs-759	54	13	6	6	NUM
iajs-759	54	14	)	)	PUNCT
iajs-759	54	15	(	(	PUNCT
iajs-759	54	16	2	2	NUM
iajs-759	54	17	)	)	PUNCT
iajs-759	54	18	(	(	PUNCT
iajs-759	54	19	0	0	NUM
iajs-759	54	20	2	2	NUM
iajs-759	54	21	2	2	NUM
iajs-759	54	22	baforsommmfh	baforsommmfh	NOUN
iajs-759	54	23	ab	ab	PROPN
iajs-759	54	24	xfhdxxf	xfhdxxf	PROPN
iajs-759	55	1	m	m	PROPN
iajs-759	56	1	j	j	PROPN
iajs-759	56	2	j	j	PROPN
iajs-759	56	3	b	b	PROPN
iajs-759	56	4	a	a	DET
iajs-759	56	5			ADJ
iajs-759	56	6			NOUN
iajs-759	56	7			ADJ
iajs-759	56	8			NUM
iajs-759	56	9			NOUN
iajs-759	56	10	…	…	PUNCT
iajs-759	56	11	(	(	PUNCT
iajs-759	56	12	1.9	1.9	NUM
iajs-759	56	13	)	)	PUNCT
iajs-759	56	14	]	]	PUNCT
iajs-759	56	15	2	2	X
iajs-759	56	16	.....	.....	SYM
iajs-759	56	17	2[2	2[2	NUM
iajs-759	56	18	111100	111100	NUM
iajs-759	56	19	iiiiiiiiiiii	iiiiiiiiiiii	X
iajs-759	56	20	ukukukukhfupu	ukukukukhfupu	ADJ
iajs-759	56	21			PROPN
iajs-759	56	22			NUM
iajs-759	56	23	…	…	PUNCT
iajs-759	56	24	(	(	PUNCT
iajs-759	56	25	1.10	1.10	NUM
iajs-759	56	26	)	)	PUNCT
iajs-759	56	27	since	since	SCONJ
iajs-759	56	28	h	h	PROPN
iajs-759	56	29	xuxu	xuxu	PROPN
iajs-759	56	30	xu	xu	PROPN
iajs-759	56	31	ii	ii	PROPN
iajs-759	57	1	i	i	NOUN
iajs-759	57	2	)	)	PUNCT
iajs-759	57	3	(	(	PUNCT
iajs-759	57	4	)	)	PUNCT
iajs-759	57	5	(	(	PUNCT
iajs-759	57	6	)	)	PUNCT
iajs-759	57	7	(	(	PUNCT
iajs-759	57	8	1	1	NUM
iajs-759	57	9			NOUN
iajs-759	57	10	…	…	PUNCT
iajs-759	57	11	(	(	PUNCT
iajs-759	57	12	1.11	1.11	NUM
iajs-759	57	13	)	)	PUNCT
iajs-759	57	14	substituting	substitute	VERB
iajs-759	57	15	equation	equation	NOUN
iajs-759	57	16	(	(	PUNCT
iajs-759	57	17	1.11	1.11	NUM
iajs-759	57	18	)	)	PUNCT
iajs-759	57	19	into	into	ADP
iajs-759	57	20	equation	equation	NOUN
iajs-759	57	21	(	(	PUNCT
iajs-759	57	22	1.9	1.9	NUM
iajs-759	57	23	)	)	PUNCT
iajs-759	57	24	we	we	PRON
iajs-759	57	25	have	have	VERB
iajs-759	57	26	]	]	X
iajs-759	57	27	2	2	NUM
iajs-759	57	28	.....	.....	SYM
iajs-759	57	29	2[2	2[2	NUM
iajs-759	57	30	)	)	PUNCT
iajs-759	57	31	2	2	NUM
iajs-759	57	32	1	1	NUM
iajs-759	57	33	(	(	PUNCT
iajs-759	57	34	111100	111100	NUM
iajs-759	57	35	2	2	NUM
iajs-759	57	36	1	1	NUM
iajs-759	57	37	2	2	NUM
iajs-759	57	38			NOUN
iajs-759	57	39			NOUN
iajs-759	57	40	iiiiiiiiiii	iiiiiiiiiii	VERB
iajs-759	57	41	ukukukhhfuuk	ukukukhhfuuk	ADJ
iajs-759	57	42	h	h	NOUN
iajs-759	57	43	hp	hp	NOUN
iajs-759	57	44	…	…	PUNCT
iajs-759	57	45	(	(	PUNCT
iajs-759	57	46	1.12	1.12	NUM
iajs-759	57	47	)	)	PUNCT
iajs-759	57	48	which	which	PRON
iajs-759	57	49	are	be	AUX
iajs-759	57	50	(	(	PUNCT
iajs-759	57	51	n+1	n+1	NOUN
iajs-759	57	52	)	)	PUNCT
iajs-759	57	53	equation	equation	NOUN
iajs-759	57	54	in	in	ADP
iajs-759	57	55	ui	ui	PROPN
iajs-759	57	56	that	that	PRON
iajs-759	57	57	represents	represent	VERB
iajs-759	57	58	the	the	DET
iajs-759	57	59	approximate	approximate	ADJ
iajs-759	57	60	solution	solution	NOUN
iajs-759	57	61	to	to	ADP
iajs-759	57	62	equation	equation	NOUN
iajs-759	57	63	(	(	PUNCT
iajs-759	57	64	1.8	1.8	NUM
iajs-759	57	65	)	)	PUNCT
iajs-759	57	66	at	at	ADP
iajs-759	57	67	)	)	PUNCT
iajs-759	57	68	.,	.,	PUNCT
iajs-759	57	69	....	....	PUNCT
iajs-759	58	1	,1,0	,1,0	PROPN
iajs-759	58	2	(	(	PUNCT
iajs-759	58	3	,	,	PUNCT
iajs-759	58	4	*	*	PUNCT
iajs-759	58	5	nihiax	nihiax	NOUN
iajs-759	58	6			NOUN
iajs-759	58	7			PROPN
iajs-759	58	8			PROPN
iajs-759	59	1			PUNCT
iajs-759	59	2			NOUN
iajs-759	59	3			PROPN
iajs-759	59	4			PROPN
iajs-759	59	5			X
iajs-759	59	6			NOUN
iajs-759	59	7			NOUN
iajs-759	59	8			NOUN
iajs-759	59	9			NOUN
iajs-759	59	10			NOUN
iajs-759	59	11			NOUN
iajs-759	59	12			PROPN
iajs-759	59	13			VERB
iajs-759	59	14			ADJ
iajs-759	59	15			PROPN
iajs-759	59	16			NOUN
iajs-759	59	17			PROPN
iajs-759	59	18			PROPN
iajs-759	60	1			PUNCT
iajs-759	61	1			PUNCT
iajs-759	62	1			PUNCT
iajs-759	62	2			NOUN
iajs-759	63	1			PUNCT
iajs-759	63	2			NOUN
iajs-759	63	3			PROPN
iajs-759	63	4			PROPN
iajs-759	63	5			X
iajs-759	63	6			NOUN
iajs-759	63	7			NOUN
iajs-759	63	8			NOUN
iajs-759	63	9			NOUN
iajs-759	63	10			NOUN
iajs-759	63	11			NOUN
iajs-759	63	12			NOUN
iajs-759	63	13			NOUN
iajs-759	63	14			NOUN
iajs-759	63	15			VERB
iajs-759	63	16			NOUN
iajs-759	63	17			NOUN
iajs-759	63	18			PROPN
iajs-759	64	1			PUNCT
iajs-759	64	2			NOUN
iajs-759	64	3			PROPN
iajs-759	64	4			PROPN
iajs-759	64	5			X
iajs-759	64	6			NOUN
iajs-759	64	7			NOUN
iajs-759	64	8			NOUN
iajs-759	64	9			NOUN
iajs-759	64	10			NOUN
iajs-759	64	11			NOUN
iajs-759	64	12			PROPN
iajs-759	64	13			ADP
iajs-759	64	14			ADV
iajs-759	64	15			PROPN
iajs-759	64	16			VERB
iajs-759	64	17			VERB
iajs-759	64	18			NOUN
iajs-759	64	19			NOUN
iajs-759	64	20			ADJ
iajs-759	64	21			ADV
iajs-759	65	1	030	030	NUM
iajs-759	65	2	2	2	NUM
iajs-759	65	3	3	3	NUM
iajs-759	65	4	020	020	NUM
iajs-759	65	5	2	2	NUM
iajs-759	65	6	2	2	NUM
iajs-759	65	7	0010	0010	NUM
iajs-759	65	8	2	2	NUM
iajs-759	65	9	1	1	NUM
iajs-759	65	10	3	3	NUM
iajs-759	65	11	2	2	NUM
iajs-759	65	12	1	1	NUM
iajs-759	65	13	33	33	NUM
iajs-759	65	14	2	2	NUM
iajs-759	65	15	332	332	NUM
iajs-759	65	16	2	2	NUM
iajs-759	65	17	31	31	NUM
iajs-759	65	18	2	2	NUM
iajs-759	65	19	22	22	NUM
iajs-759	65	20	2	2	NUM
iajs-759	65	21	221	221	NUM
iajs-759	65	22	2	2	NUM
iajs-759	65	23	11	11	NUM
iajs-759	65	24	2	2	NUM
iajs-759	65	25	1	1	NUM
iajs-759	65	26	2	2	NUM
iajs-759	65	27	2	2	NUM
iajs-759	65	28	2	2	NUM
iajs-759	65	29	0021212	0021212	NUM
iajs-759	65	30	0002121	0002121	NUM
iajs-759	65	31	000021	000021	NUM
iajs-759	65	32	ukhhf	ukhhf	ADJ
iajs-759	65	33	ukhhf	ukhhf	NOUN
iajs-759	65	34	uukhhf	uukhhf	PROPN
iajs-759	65	35	u	u	NOUN
iajs-759	65	36	u	u	NOUN
iajs-759	65	37	u	u	NOUN
iajs-759	65	38	khhpkhkh	khhpkhkh	NOUN
iajs-759	65	39	khhpkh	khhpkh	PROPN
iajs-759	65	40	khhp	khhp	VERB
iajs-759	65	41	the	the	DET
iajs-759	65	42	algorithm	algorithm	NOUN
iajs-759	65	43	(	(	PUNCT
iajs-759	65	44	aq	aq	NOUN
iajs-759	65	45	)	)	PUNCT
iajs-759	65	46	the	the	DET
iajs-759	65	47	numerical	numerical	ADJ
iajs-759	65	48	solution	solution	NOUN
iajs-759	65	49	of	of	ADP
iajs-759	65	50	(	(	PUNCT
iajs-759	65	51	1	1	NUM
iajs-759	65	52	st	st	PROPN
iajs-759	65	53	order	order	NOUN
iajs-759	65	54	vides	vide	NOUN
iajs-759	65	55	)	)	PUNCT
iajs-759	65	56	,	,	PUNCT
iajs-759	65	57	by	by	ADP
iajs-759	65	58	using	use	VERB
iajs-759	65	59	open	open	ADJ
iajs-759	65	60	newton	newton	PROPN
iajs-759	65	61	cotes	cotes	PROPN
iajs-759	65	62	formula	formula	NOUN
iajs-759	65	63	(	(	PUNCT
iajs-759	65	64	on	on	ADP
iajs-759	65	65	)	)	PUNCT
iajs-759	65	66	,	,	PUNCT
iajs-759	65	67	is	be	AUX
iajs-759	65	68	obtained	obtain	VERB
iajs-759	65	69	as	as	ADP
iajs-759	65	70	follows	follow	VERB
iajs-759	65	71	:	:	PUNCT
iajs-759	65	72	step	step	NOUN
iajs-759	65	73	1	1	NUM
iajs-759	65	74	:	:	PUNCT
iajs-759	65	75	put	put	VERB
iajs-759	65	76	h=(b	h=(b	NOUN
iajs-759	65	77	-	-	PUNCT
iajs-759	65	78	a)/n	a)/n	PROPN
iajs-759	65	79	,	,	PUNCT
iajs-759	65	80	nn	nn	ADJ
iajs-759	65	81	step	step	NOUN
iajs-759	65	82	2	2	NUM
iajs-759	65	83	:	:	PUNCT
iajs-759	65	84	set	set	NOUN
iajs-759	65	85	)	)	PUNCT
iajs-759	65	86	(	(	PUNCT
iajs-759	65	87	0	0	PUNCT
iajs-759	65	88	auu	auu	PROPN
iajs-759	65	89			NOUN
iajs-759	65	90	(	(	PUNCT
iajs-759	65	91	which	which	PRON
iajs-759	65	92	is	be	AUX
iajs-759	65	93	the	the	DET
iajs-759	65	94	initial	initial	ADJ
iajs-759	65	95	condition	condition	NOUN
iajs-759	65	96	)	)	PUNCT
iajs-759	65	97	is	be	AUX
iajs-759	65	98	given	give	VERB
iajs-759	65	99	.	.	PUNCT
iajs-759	66	1	step	step	NOUN
iajs-759	66	2	3	3	NUM
iajs-759	66	3	:	:	PUNCT
iajs-759	66	4	compute	compute	VERB
iajs-759	66	5	iu	iu	ADP
iajs-759	66	6			ADV
iajs-759	66	7	by	by	ADP
iajs-759	66	8	using	use	VERB
iajs-759	66	9	h	h	NOUN
iajs-759	66	10	uu	uu	PROPN
iajs-759	66	11	u	u	NOUN
iajs-759	66	12	ii	ii	NOUN
iajs-759	67	1	i	i	PRON
iajs-759	67	2	1	1	NUM
iajs-759	67	3			NOUN
iajs-759	67	4	step	step	NOUN
iajs-759	67	5	4	4	NUM
iajs-759	67	6	:	:	PUNCT
iajs-759	67	7	use	use	VERB
iajs-759	67	8	step	step	NOUN
iajs-759	67	9	–	–	PUNCT
iajs-759	67	10	1	1	NUM
iajs-759	67	11	,	,	PUNCT
iajs-759	67	12	-2	-2	NOUN
iajs-759	67	13	and	and	CCONJ
iajs-759	67	14	–	–	PUNCT
iajs-759	67	15	3	3	NUM
iajs-759	67	16	in	in	ADP
iajs-759	67	17	equation	equation	NOUN
iajs-759	67	18	(	(	PUNCT
iajs-759	67	19	1.10	1.10	NUM
iajs-759	67	20	)	)	PUNCT
iajs-759	67	21	to	to	PART
iajs-759	67	22	find	find	VERB
iajs-759	67	23	)	)	PUNCT
iajs-759	67	24	,	,	PUNCT
iajs-759	67	25	......	......	PUNCT
iajs-759	67	26	,	,	PUNCT
iajs-759	67	27	2,1	2,1	NUM
iajs-759	67	28	(	(	PUNCT
iajs-759	67	29	,	,	PUNCT
iajs-759	67	30	niui	niui	PROPN
iajs-759	67	31			NUM
iajs-759	67	32	we	we	PRON
iajs-759	67	33	get	get	VERB
iajs-759	67	34	]	]	X
iajs-759	67	35	2	2	NUM
iajs-759	67	36	.....	.....	SYM
iajs-759	67	37	2[2)21	2[2)21	NOUN
iajs-759	67	38	(	(	PUNCT
iajs-759	67	39	111100	111100	NUM
iajs-759	67	40	2	2	NUM
iajs-759	67	41	1	1	NUM
iajs-759	67	42	2	2	NUM
iajs-759	67	43			NOUN
iajs-759	67	44			NOUN
iajs-759	67	45	iiiiiiiiiii	iiiiiiiiiii	VERB
iajs-759	67	46	ukukukhhfuukhhp	ukukukhhfuukhhp	NOUN
iajs-759	67	47	3	3	NUM
iajs-759	67	48	.	.	PUNCT
iajs-759	68	1	numerical	numerical	ADJ
iajs-759	68	2	examples	example	NOUN
iajs-759	68	3	:	:	PUNCT
iajs-759	68	4	example	example	NOUN
iajs-759	68	5	4.1	4.1	NUM
iajs-759	68	6	:	:	PUNCT
iajs-759	68	7	consider	consider	VERB
iajs-759	68	8	the	the	DET
iajs-759	68	9	following	follow	VERB
iajs-759	68	10	vide	vide	NOUN
iajs-759	68	11	:	:	PUNCT
iajs-759	68	12	.	.	PUNCT
iajs-759	69	1	0	0	NUM
iajs-759	69	2	1	1	NUM
iajs-759	69	3	5	5	NUM
iajs-759	69	4	(	(	PUNCT
iajs-759	69	5	)	)	PUNCT
iajs-759	69	6	(	(	PUNCT
iajs-759	69	7	1	1	X
iajs-759	69	8	)	)	PUNCT
iajs-759	69	9	(	(	PUNCT
iajs-759	69	10	)	)	PUNCT
iajs-759	69	11	,	,	PUNCT
iajs-759	69	12	0	0	NUM
iajs-759	69	13	1	1	NUM
iajs-759	69	14	2	2	NUM
iajs-759	69	15	6	6	NUM
iajs-759	69	16	x	x	SYM
iajs-759	69	17	u	u	NOUN
iajs-759	69	18	x	x	NOUN
iajs-759	69	19	x	x	X
iajs-759	69	20	xt	xt	ADP
iajs-759	69	21	u	u	NOUN
iajs-759	70	1	t	t	NOUN
iajs-759	70	2	dt	dt	X
iajs-759	70	3	x	x	PROPN
iajs-759	71	1			PROPN
iajs-759	71	2			PROPN
iajs-759	71	3			PROPN
iajs-759	71	4			PUNCT
iajs-759	71	5			PUNCT
iajs-759	71	6			NUM
iajs-759	71	7			VERB
iajs-759	71	8	the	the	DET
iajs-759	71	9	exact	exact	ADJ
iajs-759	71	10	solution	solution	NOUN
iajs-759	71	11	is	be	AUX
iajs-759	71	12	u(x	u(x	NOUN
iajs-759	71	13	)	)	PUNCT
iajs-759	71	14	=	=	SYM
iajs-759	72	1	1	1	NUM
iajs-759	72	2	+	+	CCONJ
iajs-759	72	3	x	x	SYM
iajs-759	72	4	,	,	PUNCT
iajs-759	72	5	[	[	X
iajs-759	72	6	16	16	NUM
iajs-759	72	7	]	]	PUNCT
iajs-759	72	8	.	.	PUNCT
iajs-759	73	1	take	take	VERB
iajs-759	73	2	n=10	n=10	PRON
iajs-759	73	3	h=0.1	h=0.1	NOUN
iajs-759	73	4	and	and	CCONJ
iajs-759	73	5	xi	xi	X
iajs-759	73	6	=	=	NOUN
iajs-759	73	7	a+ih	a+ih	PROPN
iajs-759	73	8	,	,	PUNCT
iajs-759	73	9	i=0	i=0	PROPN
iajs-759	73	10	,	,	PUNCT
iajs-759	73	11	1	1	NUM
iajs-759	73	12	,	,	PUNCT
iajs-759	73	13	…	…	PUNCT
iajs-759	73	14	.	.	NUM
iajs-759	73	15	,	,	PUNCT
iajs-759	73	16	n.	n.	NOUN
iajs-759	73	17	table	table	NOUN
iajs-759	73	18	(	(	PUNCT
iajs-759	73	19	1	1	X
iajs-759	73	20	)	)	PUNCT
iajs-759	73	21	illustrates	illustrate	VERB
iajs-759	73	22	the	the	DET
iajs-759	73	23	comparison	comparison	NOUN
iajs-759	73	24	between	between	ADP
iajs-759	73	25	the	the	DET
iajs-759	73	26	exact	exact	ADJ
iajs-759	73	27	and	and	CCONJ
iajs-759	73	28	numerical	numerical	ADJ
iajs-759	73	29	solution	solution	NOUN
iajs-759	73	30	depending	depend	VERB
iajs-759	73	31	on	on	ADP
iajs-759	73	32	the	the	DET
iajs-759	73	33	least	least	ADJ
iajs-759	73	34	square	square	ADJ
iajs-759	73	35	error	error	NOUN
iajs-759	73	36	and	and	CCONJ
iajs-759	73	37	running	running	NOUN
iajs-759	73	38	time	time	NOUN
iajs-759	73	39	.	.	PUNCT
iajs-759	74	1	ibn	ibn	PROPN
iajs-759	74	2	alhaitham	alhaitham	PROPN
iajs-759	74	3	j.	j.	PROPN
iajs-759	74	4	for	for	ADP
iajs-759	74	5	pure	pure	ADJ
iajs-759	74	6	&	&	CCONJ
iajs-759	74	7	appl	appl	PROPN
iajs-759	74	8	.	.	PUNCT
iajs-759	75	1	sci	sci	PROPN
iajs-759	75	2	.	.	PUNCT
iajs-759	75	3	vol.24	vol.24	NOUN
iajs-759	75	4	(	(	PUNCT
iajs-759	75	5	2	2	NUM
iajs-759	75	6	)	)	PUNCT
iajs-759	75	7	2011	2011	NUM
iajs-759	75	8	example	example	NOUN
iajs-759	75	9	4.2	4.2	NUM
iajs-759	75	10	:	:	PUNCT
iajs-759	75	11	consider	consider	VERB
iajs-759	75	12	the	the	DET
iajs-759	75	13	following	follow	VERB
iajs-759	75	14	voltera	voltera	NOUN
iajs-759	75	15	integro	integro	PROPN
iajs-759	75	16	-	-	PUNCT
iajs-759	75	17	differential	differential	NOUN
iajs-759	75	18	equation	equation	NOUN
iajs-759	75	19	:	:	PUNCT
iajs-759	75	20	0x	0x	NUM
iajs-759	75	21			PUNCT
iajs-759	76	1			NOUN
iajs-759	76	2	x	x	PRON
iajs-759	76	3	dttutxxxxu	dttutxxxxu	ADJ
iajs-759	76	4	0	0	NUM
iajs-759	76	5	4	4	NUM
iajs-759	76	6	)	)	PUNCT
iajs-759	76	7	(	(	PUNCT
iajs-759	76	8	)	)	PUNCT
iajs-759	76	9	2	2	NUM
iajs-759	76	10	(	(	PUNCT
iajs-759	76	11	6	6	NUM
iajs-759	76	12	5	5	NUM
iajs-759	76	13	2	2	NUM
iajs-759	76	14	)	)	PUNCT
iajs-759	76	15	(	(	PUNCT
iajs-759	76	16	'	'	PUNCT
iajs-759	76	17	table	table	NOUN
iajs-759	76	18	(	(	PUNCT
iajs-759	76	19	2	2	NUM
iajs-759	76	20	)	)	PUNCT
iajs-759	76	21	presents	present	VERB
iajs-759	76	22	results	result	NOUN
iajs-759	76	23	from	from	ADP
iajs-759	76	24	a	a	DET
iajs-759	76	25	computer	computer	NOUN
iajs-759	76	26	program	program	NOUN
iajs-759	76	27	that	that	PRON
iajs-759	76	28	solves	solve	VERB
iajs-759	76	29	this	this	DET
iajs-759	76	30	problem	problem	NOUN
iajs-759	76	31	over	over	ADP
iajs-759	76	32	the	the	DET
iajs-759	76	33	interval	interval	NOUN
iajs-759	76	34	x=0	x=0	PROPN
iajs-759	76	35	to	to	PART
iajs-759	76	36	x=1	x=1	PROPN
iajs-759	76	37	with	with	ADP
iajs-759	76	38	u(x	u(x	NOUN
iajs-759	76	39	)	)	PUNCT
iajs-759	76	40	=	=	SYM
iajs-759	76	41	x	x	SYM
iajs-759	76	42	2	2	NUM
iajs-759	76	43	for	for	ADP
iajs-759	76	44	which	which	PRON
iajs-759	76	45	the	the	DET
iajs-759	76	46	analytical	analytical	ADJ
iajs-759	76	47	solution	solution	NOUN
iajs-759	76	48	is	be	AUX
iajs-759	76	49	h=0.1	h=0.1	NOUN
iajs-759	76	50	,	,	PUNCT
iajs-759	77	1	[	[	X
iajs-759	77	2	16	16	NUM
iajs-759	77	3	]	]	PUNCT
iajs-759	77	4	.	.	PUNCT
iajs-759	78	1	4	4	X
iajs-759	78	2	.	.	X
iajs-759	78	3	discussion	discussion	NOUN
iajs-759	78	4	and	and	CCONJ
iajs-759	78	5	conclusion	conclusion	NOUN
iajs-759	78	6	.	.	PUNCT
iajs-759	79	1	the	the	DET
iajs-759	79	2	approximate	approximate	ADJ
iajs-759	79	3	solution	solution	NOUN
iajs-759	79	4	of	of	ADP
iajs-759	79	5	linear	linear	PROPN
iajs-759	79	6	voltera	voltera	PROPN
iajs-759	79	7	integro	integro	ADJ
iajs-759	79	8	-	-	PUNCT
iajs-759	79	9	differential	differential	NOUN
iajs-759	79	10	equation	equation	NOUN
iajs-759	79	11	(	(	PUNCT
iajs-759	79	12	1.8	1.8	NUM
iajs-759	79	13	)	)	PUNCT
iajs-759	79	14	is	be	AUX
iajs-759	79	15	given	give	VERB
iajs-759	79	16	using	use	VERB
iajs-759	79	17	the	the	DET
iajs-759	79	18	open	open	ADJ
iajs-759	79	19	newton	newton	PROPN
iajs-759	79	20	cotes	cotes	PROPN
iajs-759	79	21	formula	formula	NOUN
iajs-759	79	22	.	.	PUNCT
iajs-759	80	1	a	a	DET
iajs-759	80	2	computer	computer	NOUN
iajs-759	80	3	program	program	NOUN
iajs-759	80	4	was	be	AUX
iajs-759	80	5	written	write	VERB
iajs-759	80	6	and	and	CCONJ
iajs-759	80	7	several	several	ADJ
iajs-759	80	8	examples	example	NOUN
iajs-759	80	9	were	be	AUX
iajs-759	80	10	solved	solve	VERB
iajs-759	80	11	using	use	VERB
iajs-759	80	12	these	these	DET
iajs-759	80	13	method	method	NOUN
iajs-759	80	14	.	.	PUNCT
iajs-759	81	1	we	we	PRON
iajs-759	81	2	have	have	VERB
iajs-759	81	3	the	the	DET
iajs-759	81	4	option	option	NOUN
iajs-759	81	5	that	that	SCONJ
iajs-759	81	6	the	the	DET
iajs-759	81	7	result	result	NOUN
iajs-759	81	8	of	of	ADP
iajs-759	81	9	the	the	DET
iajs-759	81	10	o	o	NOUN
iajs-759	81	11	-	-	NOUN
iajs-759	81	12	n	n	PRON
iajs-759	81	13	formula	formula	NOUN
iajs-759	81	14	is	be	AUX
iajs-759	81	15	better	well	ADJ
iajs-759	81	16	than	than	ADP
iajs-759	81	17	the	the	DET
iajs-759	81	18	results	result	NOUN
iajs-759	81	19	of	of	ADP
iajs-759	81	20	homotopy	homotopy	NOUN
iajs-759	81	21	perturbation	perturbation	NOUN
iajs-759	81	22	method	method	NOUN
iajs-759	81	23	.	.	PUNCT
iajs-759	82	1	relying	rely	VERB
iajs-759	82	2	on	on	ADP
iajs-759	82	3	our	our	PRON
iajs-759	82	4	work	work	NOUN
iajs-759	82	5	the	the	DET
iajs-759	82	6	following	follow	VERB
iajs-759	82	7	notes	note	NOUN
iajs-759	82	8	are	be	AUX
iajs-759	82	9	drawn	draw	VERB
iajs-759	82	10	:	:	PUNCT
iajs-759	82	11	1.the	1.the	DET
iajs-759	82	12	number	number	NOUN
iajs-759	82	13	of	of	ADP
iajs-759	82	14	subintervals	subinterval	NOUN
iajs-759	82	15	n	n	PRON
iajs-759	82	16	is	be	AUX
iajs-759	82	17	restricted	restrict	VERB
iajs-759	82	18	to	to	PART
iajs-759	82	19	be	be	AUX
iajs-759	82	20	even	even	ADV
iajs-759	82	21	for	for	ADP
iajs-759	82	22	open	open	ADJ
iajs-759	82	23	newton	newton	PROPN
iajs-759	82	24	cotes	cotes	PROPN
iajs-759	82	25	formula	formula	NOUN
iajs-759	82	26	.	.	PUNCT
iajs-759	83	1	2.through	2.through	NUM
iajs-759	83	2	the	the	DET
iajs-759	83	3	solution	solution	NOUN
iajs-759	83	4	of	of	ADP
iajs-759	83	5	linear	linear	PROPN
iajs-759	83	6	voltera	voltera	PROPN
iajs-759	83	7	integro	integro	ADJ
iajs-759	83	8	-	-	PUNCT
iajs-759	83	9	differential	differential	NOUN
iajs-759	83	10	equations	equation	NOUN
iajs-759	83	11	of	of	ADP
iajs-759	83	12	the	the	DET
iajs-759	83	13	first	first	ADJ
iajs-759	83	14	order	order	NOUN
iajs-759	83	15	,	,	PUNCT
iajs-759	83	16	we	we	PRON
iajs-759	83	17	see	see	VERB
iajs-759	83	18	that	that	SCONJ
iajs-759	83	19	references	reference	NOUN
iajs-759	83	20	1	1	NUM
iajs-759	83	21	.	.	PUNCT
iajs-759	84	1	al	al	PROPN
iajs-759	84	2	-	-	PUNCT
iajs-759	84	3	rawi	rawi	PROPN
iajs-759	84	4	,	,	PUNCT
iajs-759	84	5	s.n	s.n	PROPN
iajs-759	84	6	.	.	PROPN
iajs-759	84	7	(	(	PUNCT
iajs-759	84	8	1995	1995	NUM
iajs-759	84	9	)	)	PUNCT
iajs-759	84	10	,	,	PUNCT
iajs-759	84	11	numerical	numerical	ADJ
iajs-759	84	12	solution	solution	NOUN
iajs-759	84	13	of	of	ADP
iajs-759	84	14	first	first	ADJ
iajs-759	84	15	kind	kind	ADJ
iajs-759	84	16	integral	integral	ADJ
iajs-759	84	17	equations	equation	NOUN
iajs-759	84	18	of	of	ADP
iajs-759	84	19	convolutions	convolution	NOUN
iajs-759	84	20	type	type	NOUN
iajs-759	84	21	;	;	PUNCT
iajs-759	84	22	m.sc	m.sc	PROPN
iajs-759	84	23	.	.	PUNCT
iajs-759	85	1	thesis	thesis	NOUN
iajs-759	85	2	,	,	PUNCT
iajs-759	85	3	university	university	NOUN
iajs-759	85	4	of	of	ADP
iajs-759	85	5	technology	technology	NOUN
iajs-759	85	6	.	.	PUNCT
iajs-759	86	1	2	2	X
iajs-759	86	2	.	.	X
iajs-759	86	3	al	al	PROPN
iajs-759	86	4	-	-	PUNCT
iajs-759	86	5	yacob	yacob	PROPN
iajs-759	86	6	,	,	PUNCT
iajs-759	86	7	l.a	l.a	PROPN
iajs-759	86	8	.	.	PROPN
iajs-759	86	9	(	(	PUNCT
iajs-759	86	10	2002	2002	NUM
iajs-759	86	11	)	)	PUNCT
iajs-759	86	12	,	,	PUNCT
iajs-759	86	13	approximate	approximate	ADJ
iajs-759	86	14	solution	solution	NOUN
iajs-759	86	15	of	of	ADP
iajs-759	86	16	volterra	volterra	PROPN
iajs-759	86	17	integral	integral	ADJ
iajs-759	86	18	equations	equation	NOUN
iajs-759	86	19	of	of	ADP
iajs-759	86	20	convolutions	convolution	NOUN
iajs-759	86	21	type	type	NOUN
iajs-759	86	22	;	;	PUNCT
iajs-759	86	23	m.sc	m.sc	PROPN
iajs-759	86	24	.	.	PUNCT
iajs-759	87	1	thesis	thesis	NOUN
iajs-759	87	2	,	,	PUNCT
iajs-759	87	3	university	university	NOUN
iajs-759	87	4	of	of	ADP
iajs-759	87	5	technology	technology	NOUN
iajs-759	87	6	.	.	PUNCT
iajs-759	88	1	3	3	X
iajs-759	88	2	.	.	X
iajs-759	88	3	barker	barker	PROPN
iajs-759	88	4	,	,	PUNCT
iajs-759	88	5	c.t.h	c.t.h	PROPN
iajs-759	88	6	.	.	PUNCT
iajs-759	88	7	(	(	PUNCT
iajs-759	88	8	1977	1977	NUM
iajs-759	88	9	)	)	PUNCT
iajs-759	88	10	the	the	DET
iajs-759	88	11	numerical	numerical	ADJ
iajs-759	88	12	treatment	treatment	NOUN
iajs-759	88	13	of	of	ADP
iajs-759	88	14	integral	integral	ADJ
iajs-759	88	15	equation	equation	NOUN
iajs-759	88	16	;	;	PUNCT
iajs-759	88	17	oxford	oxford	PROPN
iajs-759	88	18	university	university	NOUN
iajs-759	88	19	press	press	NOUN
iajs-759	88	20	.	.	PUNCT
iajs-759	89	1	4	4	X
iajs-759	89	2	.	.	X
iajs-759	89	3	al	al	PROPN
iajs-759	89	4	-	-	PUNCT
iajs-759	89	5	kachi	kachi	PROPN
iajs-759	89	6	,	,	PUNCT
iajs-759	89	7	a.m	a.m	PROPN
iajs-759	89	8	.	.	PUNCT
iajs-759	90	1	(	(	PUNCT
iajs-759	90	2	2000	2000	NUM
iajs-759	90	3	)	)	PUNCT
iajs-759	90	4	,	,	PUNCT
iajs-759	90	5	approximate	approximate	ADJ
iajs-759	90	6	method	method	NOUN
iajs-759	90	7	for	for	ADP
iajs-759	90	8	solving	solve	VERB
iajs-759	90	9	voltera	voltera	NOUN
iajs-759	90	10	integral	integral	ADJ
iajs-759	90	11	of	of	ADP
iajs-759	90	12	first	first	ADJ
iajs-759	90	13	kind	kind	NOUN
iajs-759	90	14	;	;	PUNCT
iajs-759	91	1	m.sc	m.sc	PROPN
iajs-759	91	2	.	.	PUNCT
iajs-759	92	1	thesis	thesis	NOUN
iajs-759	92	2	,	,	PUNCT
iajs-759	92	3	university	university	NOUN
iajs-759	92	4	of	of	ADP
iajs-759	92	5	technology	technology	NOUN
iajs-759	92	6	.	.	PUNCT
iajs-759	93	1	5	5	X
iajs-759	93	2	.	.	X
iajs-759	93	3	gerlach	gerlach	PROPN
iajs-759	93	4	,	,	PUNCT
iajs-759	93	5	u.	u.	PROPN
iajs-759	93	6	(	(	PUNCT
iajs-759	93	7	2002	2002	NUM
iajs-759	93	8	)	)	PUNCT
iajs-759	93	9	,	,	PUNCT
iajs-759	93	10	boundary	boundary	ADJ
iajs-759	93	11	value	value	NOUN
iajs-759	93	12	problem	problem	NOUN
iajs-759	93	13	via	via	ADP
iajs-759	93	14	green	green	PROPN
iajs-759	93	15	’s	’s	PART
iajs-759	93	16	function	function	NOUN
iajs-759	93	17	:	:	PUNCT
iajs-759	93	18	integral	integral	ADJ
iajs-759	93	19	equation	equation	NOUN
iajs-759	93	20	;	;	PUNCT
iajs-759	93	21	http	http	CCONJ
iajs-759	93	22	:	:	PUNCT
iajs-759	93	23	//www	//www	PROPN
iajs-759	93	24	.	.	PROPN
iajs-759	93	25	math	math	PROPN
iajs-759	93	26	.	.	PUNCT
iajs-759	94	1	ohio	ohio	PROPN
iajs-759	94	2	-	-	PUNCT
iajs-759	94	3	state	state	NOUN
iajs-759	94	4	.	.	PUNCT
iajs-759	95	1	edu	edu	PROPN
iajs-759	95	2	/~gerlach	/~gerlach	PUNCT
iajs-759	96	1	/math	/math	PROPN
iajs-759	96	2	/	/	SYM
iajs-759	96	3	bv	bv	PROPN
iajs-759	96	4	typest	typest	NOUN
iajs-759	96	5	/	/	SYM
iajs-759	97	1	node76.html	node76.html	INTJ
iajs-759	97	2	.	.	PUNCT
iajs-759	98	1	6	6	NUM
iajs-759	98	2	.	.	X
iajs-759	98	3	linz	linz	PROPN
iajs-759	98	4	,	,	PUNCT
iajs-759	98	5	p.	p.	NOUN
iajs-759	98	6	(	(	PUNCT
iajs-759	98	7	1985	1985	NUM
iajs-759	98	8	)	)	PUNCT
iajs-759	98	9	,	,	PUNCT
iajs-759	98	10	analytical	analytical	ADJ
iajs-759	98	11	and	and	CCONJ
iajs-759	98	12	numerical	numerical	ADJ
iajs-759	98	13	methods	method	NOUN
iajs-759	98	14	for	for	ADP
iajs-759	98	15	voltera	voltera	NOUN
iajs-759	98	16	equations	equation	NOUN
iajs-759	98	17	;	;	PUNCT
iajs-759	98	18	siam	siam	PROPN
iajs-759	98	19	philadelphia	philadelphia	PROPN
iajs-759	98	20	.	.	PUNCT
iajs-759	99	1	7	7	X
iajs-759	99	2	.	.	X
iajs-759	99	3	kalwi	kalwi	PROPN
iajs-759	99	4	,	,	PUNCT
iajs-759	99	5	p.w	p.w	PROPN
iajs-759	99	6	.	.	PUNCT
iajs-759	99	7	(	(	PUNCT
iajs-759	99	8	1999	1999	NUM
iajs-759	99	9	)	)	PUNCT
iajs-759	99	10	,	,	PUNCT
iajs-759	99	11	numerical	numerical	ADJ
iajs-759	99	12	methods	method	NOUN
iajs-759	99	13	for	for	ADP
iajs-759	99	14	solving	solve	VERB
iajs-759	99	15	fredholm	fredholm	ADJ
iajs-759	99	16	integral	integral	ADJ
iajs-759	99	17	equations	equation	NOUN
iajs-759	99	18	of	of	ADP
iajs-759	99	19	the	the	DET
iajs-759	99	20	second	second	ADJ
iajs-759	99	21	kind	kind	NOUN
iajs-759	99	22	;	;	PUNCT
iajs-759	99	23	m.sc	m.sc	PROPN
iajs-759	99	24	.	.	PUNCT
iajs-759	100	1	thesis	thesis	NOUN
iajs-759	100	2	,	,	PUNCT
iajs-759	100	3	university	university	NOUN
iajs-759	100	4	of	of	ADP
iajs-759	100	5	technology	technology	NOUN
iajs-759	100	6	.	.	PUNCT
iajs-759	101	1	8	8	X
iajs-759	101	2	.	.	X
iajs-759	101	3	phillips	phillip	NOUN
iajs-759	101	4	,	,	PUNCT
iajs-759	101	5	david	david	PROPN
iajs-759	101	6	l.	l.	PROPN
iajs-759	101	7	(	(	PUNCT
iajs-759	101	8	1961	1961	NUM
iajs-759	101	9	)	)	PUNCT
iajs-759	101	10	,	,	PUNCT
iajs-759	101	11	a	a	DET
iajs-759	101	12	technique	technique	NOUN
iajs-759	101	13	for	for	ADP
iajs-759	101	14	the	the	DET
iajs-759	101	15	numerical	numerical	ADJ
iajs-759	101	16	solution	solution	NOUN
iajs-759	101	17	of	of	ADP
iajs-759	101	18	certain	certain	ADJ
iajs-759	101	19	integral	integral	ADJ
iajs-759	101	20	equation	equation	NOUN
iajs-759	101	21	of	of	ADP
iajs-759	101	22	the	the	DET
iajs-759	101	23	first	first	ADJ
iajs-759	101	24	kind	kind	NOUN
iajs-759	101	25	;	;	PUNCT
iajs-759	101	26	june	june	PROPN
iajs-759	101	27	.	.	PROPN
iajs-759	102	1	9	9	NUM
iajs-759	102	2	.	.	X
iajs-759	102	3	weisstein	weisstein	PROPN
iajs-759	102	4	,	,	PUNCT
iajs-759	102	5	e.w	e.w	PROPN
iajs-759	102	6	.	.	PROPN
iajs-759	102	7	(	(	PUNCT
iajs-759	102	8	2002	2002	NUM
iajs-759	102	9	)	)	PUNCT
iajs-759	102	10	,	,	PUNCT
iajs-759	102	11	integral	integral	ADJ
iajs-759	102	12	equation	equation	NOUN
iajs-759	102	13	,	,	PUNCT
iajs-759	102	14	www.marauder.tm/research/iamprey/a.pdf	www.marauder.tm/research/iamprey/a.pdf	PROPN
iajs-759	102	15	press	press	NOUN
iajs-759	102	16	.	.	PUNCT
iajs-759	103	1	10	10	NUM
iajs-759	103	2	.	.	X
iajs-759	103	3	r.s.k	r.s.k	NOUN
iajs-759	103	4	.	.	PUNCT
iajs-759	104	1	(	(	PUNCT
iajs-759	104	2	2002	2002	NUM
iajs-759	104	3	)	)	PUNCT
iajs-759	104	4	,	,	PUNCT
iajs-759	104	5	approximated	approximate	VERB
iajs-759	104	6	treatment	treatment	NOUN
iajs-759	104	7	of	of	ADP
iajs-759	104	8	higher	high	ADJ
iajs-759	104	9	-	-	PUNCT
iajs-759	104	10	order	order	NOUN
iajs-759	104	11	linear	linear	ADJ
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iajs-759	108	16	equations	equation	NOUN
iajs-759	108	17	;	;	PUNCT
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iajs-759	110	2	.	.	PUNCT
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iajs-759	111	5	2002	2002	NUM
iajs-759	111	6	)	)	PUNCT
iajs-759	111	7	,	,	PUNCT
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iajs-759	111	14	-	-	PUNCT
iajs-759	111	15	differential	differential	NOUN
iajs-759	111	16	equations	equation	NOUN
iajs-759	111	17	;	;	PUNCT
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iajs-759	113	2	.	.	X
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iajs-759	113	4	,	,	PUNCT
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iajs-759	113	8	)	)	PUNCT
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iajs-759	113	12	-	-	PUNCT
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iajs-759	113	15	equations	equation	NOUN
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iajs-759	116	13	.	.	PUNCT
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iajs-759	117	2	,	,	PUNCT
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iajs-759	117	18	equations	equation	NOUN
iajs-759	117	19	;	;	PUNCT
iajs-759	117	20	cambridge	cambridge	PROPN
iajs-759	117	21	university	university	PROPN
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iajs-759	117	23	.	.	PUNCT
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iajs-759	118	2	.	.	X
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iajs-759	119	10	differential	differential	ADJ
iajs-759	119	11	equation	equation	NOUN
iajs-759	119	12	;	;	PUNCT
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iajs-759	121	16	linear	linear	NOUN
iajs-759	121	17	system	system	NOUN
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iajs-759	121	21	differential	differential	NOUN
iajs-759	121	22	equations	equation	NOUN
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iajs-759	127	5	perturbation	perturbation	NOUN
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iajs-759	131	11	)	)	PUNCT
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iajs-759	131	25	example	example	NOUN
iajs-759	131	26	(	(	PUNCT
iajs-759	131	27	2	2	NUM
iajs-759	131	28	)	)	PUNCT
iajs-759	131	29	.	.	PUNCT
iajs-759	132	1	method	method	NOUN
iajs-759	132	2	nodes	node	NOUN
iajs-759	132	3	on	on	ADP
iajs-759	132	4	homotopy	homotopy	NOUN
iajs-759	132	5	perturbation	perturbation	NOUN
iajs-759	132	6	simpsons1/3	simpsons1/3	ADP
iajs-759	132	7	simpsons13/8	simpsons13/8	NOUN
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iajs-759	132	11	0.00000000000	0.00000000000	NUM
iajs-759	132	12	0.00000000000	0.00000000000	NUM
iajs-759	132	13	0.1	0.1	NUM
iajs-759	132	14	0.020112340710	0.020112340710	NUM
iajs-759	132	15	0.020112340710	0.020112340710	NUM
iajs-759	132	16	0.020021699215	0.020021699215	NUM
iajs-759	132	17	0.020021699215	0.020021699215	NUM
iajs-759	132	18	0.2	0.2	NUM
iajs-759	132	19	0.060870350306	0.060870350306	NUM
iajs-759	132	20	0.060870350306	0.060870350306	NUM
iajs-759	132	21	0.060115379036	0.060115379036	NUM
iajs-759	132	22	0.060115379036	0.060115379036	NUM
iajs-759	132	23	0.3	0.3	NUM
iajs-759	132	24	0.123471139122	0.123471139122	NUM
iajs-759	132	25	0.12347113912	0.12347113912	NUM
iajs-759	132	26	0.120446218308	0.120446218308	NUM
iajs-759	132	27	0.120432870642	0.120432870642	NUM
iajs-759	132	28	0.4	0.4	NUM
iajs-759	132	29	0.210064039206	0.210064039206	NUM
iajs-759	132	30	0.210064039206	0.210064039206	NUM
iajs-759	132	31	0.201204441266	0.201204441266	NUM
iajs-759	132	32	0.201205986374	0.201205986374	NUM
iajs-759	132	33	0.5	0.5	NUM
iajs-759	132	34	0.324135025802	0.324135025802	NUM
iajs-759	132	35	0.324135025802	0.324135025802	NUM
iajs-759	132	36	0.302718695118	0.302718695118	NUM
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iajs-759	132	45	0.658846458868	0.658846458868	NUM
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iajs-759	132	50	0.899428134734	0.899428134734	NUM
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iajs-759	132	60	1.617657119881	1.617657119881	NUM
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iajs-759	133	17	للعلوم	للعلوم	PROPN
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iajs-759	133	22	نیوتن	نیوتن	PROPN
iajs-759	133	23	كوتس	كوتس	PROPN
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iajs-759	133	27	التكاملیة	التكاملیة	VERB
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iajs-759	134	2	من	من	INTJ
iajs-759	135	1	الرتبة	الرتبة	PROPN
iajs-759	135	2	االولى	االولى	PROPN
iajs-759	135	3	عاطفة	عاطفة	NOUN
iajs-759	135	4	جلیل	جلیل	NOUN
iajs-759	135	5	صالح	صالح	NOUN
iajs-759	135	6	الجامعة	الجامعة	NOUN
iajs-759	135	7	المستنصریة،كلیة	المستنصریة،كلیة	X
iajs-759	135	8	التربیة	التربیة	NOUN
iajs-759	135	9	األساسیة	األساسیة	PROPN
iajs-759	135	10	،	،	PROPN
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iajs-759	136	2	الریاضیات	الریاضیات	VERB
iajs-759	136	3	2010	2010	NUM
iajs-759	136	4	،	،	NOUN
iajs-759	136	5	كانون	كانون	PROPN
iajs-759	136	6	الثاني	الثاني	PROPN
iajs-759	136	7	،	،	X
iajs-759	136	8	17	17	NUM
iajs-759	136	9	:	:	PUNCT
iajs-759	136	10	استلم	استلم	PROPN
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iajs-759	136	13	2010	2010	NUM
iajs-759	136	14	،	،	NOUN
iajs-759	136	15	حزیران	حزیران	X
iajs-759	136	16	،	،	NOUN
iajs-759	136	17	17	17	NUM
iajs-759	136	18	:	:	PUNCT
iajs-759	136	19	قبل	قبل	NOUN
iajs-759	136	20	البحث	البحث	VERB
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iajs-759	136	25	يالتفاضلیة	يالتفاضلیة	PROPN
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iajs-759	136	29	ق	ق	PROPN
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iajs-759	136	37	هذا	هذا	PROPN
iajs-759	136	38	العمل	العمل	PROPN
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iajs-759	136	43	معادالت	معادالت	PROPN
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iajs-759	136	47	بأستعمالالحلول	بأستعمالالحلول	PROPN
iajs-759	136	48	العددیة	العددیة	VERB
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iajs-759	137	6	المعادلةطریقة	المعادلةطریقة	PROPN
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iajs-759	137	8	كوتس	كوتس	PROPN
iajs-759	137	9	طبقت	طبقت	PROPN
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iajs-759	137	11	.version	.version	VERB
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iajs-759	138	3	قد	قد	PRON
iajs-759	138	4	كتبت	كتبت	ADJ
iajs-759	138	5	بلغة	بلغة	VERB
iajs-759	138	6	ماتالب	ماتالب	PROPN
iajs-759	138	7	كوتس	كوتس	PROPN
iajs-759	138	8	المفتوحة	المفتوحة	PROPN
iajs-759	138	9	-صیغ	-صیغ	PUNCT
iajs-759	138	10	نیوتن	نیوتن	PROPN
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iajs-759	138	13	معادالت	معادالت	ADJ
iajs-759	138	14	فولتیرا	فولتیرا	NOUN
iajs-759	138	15	التفاضلیة	التفاضلیة	NOUN
iajs-759	138	16	:	:	PUNCT
iajs-759	138	17	الكلمات	الكلمات	VERB
iajs-759	138	18	المفتاحیة	المفتاحیة	ADV