id	sid	tid	token	lemma	pos
iajs-763	1	1	ibn	ibn	PROPN
iajs-763	1	2	alhaitham	alhaitham	NOUN
iajs-763	1	3	j.	j.	PROPN
iajs-763	1	4	for	for	ADP
iajs-763	1	5	pure	pure	ADJ
iajs-763	1	6	&	&	CCONJ
iajs-763	1	7	appl	appl	PROPN
iajs-763	1	8	.	.	PUNCT
iajs-763	2	1	sci	sci	PROPN
iajs-763	2	2	.	.	PUNCT
iajs-763	2	3	vol.24	vol.24	NOUN
iajs-763	2	4	(	(	PUNCT
iajs-763	2	5	2	2	NUM
iajs-763	2	6	)	)	PUNCT
iajs-763	2	7	2011	2011	NUM
iajs-763	2	8	solving	solving	NOUN
iajs-763	2	9	system	system	NOUN
iajs-763	2	10	of	of	ADP
iajs-763	2	11	linear	linear	ADJ
iajs-763	2	12	fredholm	fredholm	ADJ
iajs-763	2	13	integral	integral	ADJ
iajs-763	2	14	equations	equation	NOUN
iajs-763	2	15	of	of	ADP
iajs-763	2	16	second	second	ADJ
iajs-763	2	17	kind	kind	NOUN
iajs-763	2	18	using	use	VERB
iajs-763	2	19	open	open	ADJ
iajs-763	2	20	newton	newton	PROPN
iajs-763	2	21	-	-	PUNCT
iajs-763	2	22	cotes	cote	NOUN
iajs-763	2	23	formulas	formula	NOUN
iajs-763	2	24	g.	g.	PROPN
iajs-763	2	25	h.	h.	PROPN
iajs-763	2	26	ibraheem	ibraheem	PROPN
iajs-763	2	27	department	department	PROPN
iajs-763	2	28	of	of	ADP
iajs-763	2	29	mathematics	mathematics	PROPN
iajs-763	2	30	,	,	PUNCT
iajs-763	2	31	college	college	NOUN
iajs-763	2	32	of	of	ADP
iajs-763	2	33	education	education	NOUN
iajs-763	2	34	,	,	PUNCT
iajs-763	2	35	ibn	ibn	PROPN
iajs-763	2	36	-	-	PUNCT
iajs-763	2	37	al	al	PROPN
iajs-763	2	38	-	-	PUNCT
iajs-763	2	39	haitham	haitham	PROPN
iajs-763	2	40	,	,	PUNCT
iajs-763	2	41	university	university	PROPN
iajs-763	2	42	of	of	ADP
iajs-763	2	43	baghdad	baghdad	PROPN
iajs-763	2	44	received	receive	VERB
iajs-763	2	45	in	in	ADP
iajs-763	2	46	:	:	PUNCT
iajs-763	2	47	27,october	27,october	NUM
iajs-763	2	48	,	,	PUNCT
iajs-763	2	49	2010	2010	NUM
iajs-763	2	50	accepted	accept	VERB
iajs-763	2	51	in	in	ADP
iajs-763	2	52	:	:	PUNCT
iajs-763	2	53	28	28	NUM
iajs-763	2	54	,	,	PUNCT
iajs-763	2	55	february	february	PROPN
iajs-763	2	56	,	,	PUNCT
iajs-763	2	57	2011	2011	NUM
iajs-763	2	58	abstract	abstract	NOUN
iajs-763	2	59	in	in	ADP
iajs-763	2	60	this	this	DET
iajs-763	2	61	paper	paper	NOUN
iajs-763	2	62	,	,	PUNCT
iajs-763	2	63	the	the	DET
iajs-763	2	64	linear	linear	ADJ
iajs-763	2	65	system	system	NOUN
iajs-763	2	66	of	of	ADP
iajs-763	2	67	fredholm	fredholm	ADJ
iajs-763	2	68	integral	integral	ADJ
iajs-763	2	69	equations	equation	NOUN
iajs-763	2	70	is	be	AUX
iajs-763	2	71	solving	solve	VERB
iajs-763	2	72	using	use	VERB
iajs-763	2	73	open	open	ADJ
iajs-763	2	74	newton	newton	PROPN
iajs-763	2	75	-	-	PUNCT
iajs-763	2	76	cotes	cote	NOUN
iajs-763	2	77	formula	formula	NOUN
iajs-763	2	78	,	,	PUNCT
iajs-763	2	79	which	which	PRON
iajs-763	2	80	we	we	PRON
iajs-763	2	81	use	use	VERB
iajs-763	2	82	five	five	NUM
iajs-763	2	83	different	different	ADJ
iajs-763	2	84	types	type	NOUN
iajs-763	2	85	of	of	ADP
iajs-763	2	86	open	open	ADJ
iajs-763	2	87	newton	newton	PROPN
iajs-763	2	88	-	-	PUNCT
iajs-763	2	89	cotes	cote	NOUN
iajs-763	2	90	formula	formula	NOUN
iajs-763	2	91	to	to	PART
iajs-763	2	92	solve	solve	VERB
iajs-763	2	93	this	this	DET
iajs-763	2	94	system	system	NOUN
iajs-763	2	95	.	.	PUNCT
iajs-763	3	1	compare	compare	VERB
iajs-763	3	2	the	the	DET
iajs-763	3	3	results	result	NOUN
iajs-763	3	4	of	of	ADP
iajs-763	3	5	suggested	suggest	VERB
iajs-763	3	6	method	method	NOUN
iajs-763	3	7	with	with	ADP
iajs-763	3	8	the	the	DET
iajs-763	3	9	results	result	NOUN
iajs-763	3	10	of	of	ADP
iajs-763	3	11	another	another	DET
iajs-763	3	12	method	method	NOUN
iajs-763	3	13	(	(	PUNCT
iajs-763	3	14	closed	closed	ADJ
iajs-763	3	15	newton	newton	PROPN
iajs-763	3	16	-	-	PUNCT
iajs-763	3	17	cotes	cote	NOUN
iajs-763	3	18	formula	formula	NOUN
iajs-763	3	19	)	)	PUNCT
iajs-763	3	20	finally	finally	ADV
iajs-763	3	21	,	,	PUNCT
iajs-763	3	22	at	at	ADP
iajs-763	3	23	the	the	DET
iajs-763	3	24	end	end	NOUN
iajs-763	3	25	of	of	ADP
iajs-763	3	26	each	each	DET
iajs-763	3	27	method	method	NOUN
iajs-763	3	28	,	,	PUNCT
iajs-763	3	29	algorithms	algorithm	NOUN
iajs-763	3	30	and	and	CCONJ
iajs-763	3	31	programs	program	NOUN
iajs-763	3	32	developed	develop	VERB
iajs-763	3	33	and	and	CCONJ
iajs-763	3	34	written	write	VERB
iajs-763	3	35	in	in	ADP
iajs-763	3	36	matlab	matlab	PROPN
iajs-763	3	37	(	(	PUNCT
iajs-763	3	38	version	version	NOUN
iajs-763	3	39	7.0	7.0	NUM
iajs-763	3	40	)	)	PUNCT
iajs-763	3	41	and	and	CCONJ
iajs-763	3	42	we	we	PRON
iajs-763	3	43	give	give	VERB
iajs-763	3	44	some	some	DET
iajs-763	3	45	numerical	numerical	ADJ
iajs-763	3	46	examples	example	NOUN
iajs-763	3	47	,	,	PUNCT
iajs-763	3	48	illustrate	illustrate	VERB
iajs-763	3	49	suggested	suggest	VERB
iajs-763	3	50	method	method	NOUN
iajs-763	3	51	.	.	PUNCT
iajs-763	4	1	keyword	keyword	NOUN
iajs-763	4	2	:	:	PUNCT
iajs-763	4	3	open	open	PROPN
iajs-763	4	4	newton	newton	PROPN
iajs-763	4	5	–	–	PUNCT
iajs-763	4	6	cotes	cote	NOUN
iajs-763	4	7	formula	formula	NOUN
iajs-763	4	8	,	,	PUNCT
iajs-763	4	9	closed	close	VERB
iajs-763	4	10	newton	newton	PROPN
iajs-763	4	11	-	-	PUNCT
iajs-763	4	12	cotes	cote	NOUN
iajs-763	4	13	formula	formula	NOUN
iajs-763	4	14	,	,	PUNCT
iajs-763	4	15	system	system	NOUN
iajs-763	4	16	of	of	ADP
iajs-763	4	17	linear	linear	ADJ
iajs-763	4	18	fredholm	fredholm	ADJ
iajs-763	4	19	integral	integral	ADJ
iajs-763	4	20	equation	equation	NOUN
iajs-763	4	21	.	.	PUNCT
iajs-763	5	1	introduction	introduction	NOUN
iajs-763	5	2	the	the	DET
iajs-763	5	3	problem	problem	NOUN
iajs-763	5	4	of	of	ADP
iajs-763	5	5	newton	newton	PROPN
iajs-763	5	6	-	-	PUNCT
iajs-763	5	7	cotes	cote	NOUN
iajs-763	5	8	formula	formula	NOUN
iajs-763	5	9	arises	arise	VERB
iajs-763	5	10	when	when	SCONJ
iajs-763	5	11	the	the	DET
iajs-763	5	12	integration	integration	NOUN
iajs-763	5	13	can	can	AUX
iajs-763	5	14	not	not	PART
iajs-763	5	15	be	be	AUX
iajs-763	5	16	carried	carry	VERB
iajs-763	5	17	out	out	ADP
iajs-763	5	18	exactly	exactly	ADV
iajs-763	5	19	or	or	CCONJ
iajs-763	5	20	when	when	SCONJ
iajs-763	5	21	the	the	DET
iajs-763	5	22	function	function	NOUN
iajs-763	5	23	is	be	AUX
iajs-763	5	24	known	know	VERB
iajs-763	5	25	only	only	ADV
iajs-763	5	26	at	at	ADP
iajs-763	5	27	a	a	DET
iajs-763	5	28	finite	finite	ADJ
iajs-763	5	29	number	number	NOUN
iajs-763	5	30	of	of	ADP
iajs-763	5	31	data	datum	NOUN
iajs-763	5	32	.	.	PUNCT
iajs-763	6	1	furthermore	furthermore	ADV
iajs-763	6	2	,	,	PUNCT
iajs-763	6	3	newtoncotes	newtoncote	VERB
iajs-763	6	4	rules	rule	NOUN
iajs-763	6	5	are	be	AUX
iajs-763	6	6	primary	primary	ADJ
iajs-763	6	7	tool	tool	NOUN
iajs-763	6	8	used	use	VERB
iajs-763	6	9	by	by	ADP
iajs-763	6	10	engineers	engineer	NOUN
iajs-763	6	11	and	and	CCONJ
iajs-763	6	12	scientists	scientist	NOUN
iajs-763	6	13	to	to	PART
iajs-763	6	14	obtain	obtain	VERB
iajs-763	6	15	approximate	approximate	ADJ
iajs-763	6	16	answers	answer	NOUN
iajs-763	6	17	for	for	ADP
iajs-763	6	18	definite	definite	ADJ
iajs-763	6	19	integrals	integral	NOUN
iajs-763	6	20	that	that	PRON
iajs-763	6	21	can	can	AUX
iajs-763	6	22	not	not	PART
iajs-763	6	23	be	be	AUX
iajs-763	6	24	solved	solve	VERB
iajs-763	6	25	analytically	analytically	ADV
iajs-763	6	26	.	.	PUNCT
iajs-763	7	1	[	[	PUNCT
iajs-763	7	2	1	1	X
iajs-763	7	3	]	]	PUNCT
iajs-763	7	4	this	this	DET
iajs-763	7	5	paper	paper	NOUN
iajs-763	7	6	is	be	AUX
iajs-763	7	7	organized	organize	VERB
iajs-763	7	8	as	as	SCONJ
iajs-763	7	9	follows	follow	VERB
iajs-763	7	10	:	:	PUNCT
iajs-763	7	11	in	in	ADP
iajs-763	7	12	section	section	NOUN
iajs-763	7	13	2	2	NUM
iajs-763	7	14	,	,	PUNCT
iajs-763	7	15	we	we	PRON
iajs-763	7	16	introduce	introduce	VERB
iajs-763	7	17	a	a	DET
iajs-763	7	18	brief	brief	ADJ
iajs-763	7	19	introduction	introduction	NOUN
iajs-763	7	20	to	to	ADP
iajs-763	7	21	the	the	DET
iajs-763	7	22	open	open	PROPN
iajs-763	7	23	newton	newton	PROPN
iajs-763	7	24	-	-	PUNCT
iajs-763	7	25	cotes	cotes	PROPN
iajs-763	7	26	and	and	CCONJ
iajs-763	7	27	some	some	DET
iajs-763	7	28	basic	basic	ADJ
iajs-763	7	29	definitions	definition	NOUN
iajs-763	7	30	for	for	ADP
iajs-763	7	31	integral	integral	ADJ
iajs-763	7	32	equation	equation	NOUN
iajs-763	7	33	.	.	PUNCT
iajs-763	8	1	in	in	ADP
iajs-763	8	2	section	section	NOUN
iajs-763	8	3	3	3	NUM
iajs-763	8	4	,	,	PUNCT
iajs-763	8	5	we	we	PRON
iajs-763	8	6	construct	construct	VERB
iajs-763	8	7	our	our	PRON
iajs-763	8	8	methods	method	NOUN
iajs-763	8	9	to	to	PART
iajs-763	8	10	approximate	approximate	VERB
iajs-763	8	11	the	the	DET
iajs-763	8	12	solution	solution	NOUN
iajs-763	8	13	of	of	ADP
iajs-763	8	14	linear	linear	ADJ
iajs-763	8	15	system	system	NOUN
iajs-763	8	16	of	of	ADP
iajs-763	8	17	fredholm	fredholm	ADJ
iajs-763	8	18	integral	integral	ADJ
iajs-763	8	19	equations	equation	NOUN
iajs-763	8	20	.	.	PUNCT
iajs-763	9	1	numerical	numerical	ADJ
iajs-763	9	2	examples	example	NOUN
iajs-763	9	3	are	be	AUX
iajs-763	9	4	given	give	VERB
iajs-763	9	5	in	in	ADP
iajs-763	9	6	section	section	NOUN
iajs-763	9	7	4	4	NUM
iajs-763	9	8	.	.	PUNCT
iajs-763	10	1	1review	1review	NUM
iajs-763	10	2	and	and	CCONJ
iajs-763	10	3	background	background	NOUN
iajs-763	10	4	1.1	1.1	NUM
iajs-763	10	5	some	some	DET
iajs-763	10	6	definitions	definition	NOUN
iajs-763	10	7	of	of	ADP
iajs-763	10	8	integral	integral	ADJ
iajs-763	10	9	equation	equation	NOUN
iajs-763	10	10	definition	definition	NOUN
iajs-763	10	11	1	1	NUM
iajs-763	10	12	-	-	SYM
iajs-763	10	13	1	1	NUM
iajs-763	10	14	:	:	PUNCT
iajs-763	10	15	[	[	PUNCT
iajs-763	10	16	2	2	X
iajs-763	10	17	]	]	PUNCT
iajs-763	10	18	integral	integral	ADJ
iajs-763	10	19	equation	equation	NOUN
iajs-763	10	20	is	be	AUX
iajs-763	10	21	an	an	DET
iajs-763	10	22	equation	equation	NOUN
iajs-763	10	23	in	in	ADP
iajs-763	10	24	which	which	PRON
iajs-763	10	25	the	the	DET
iajs-763	10	26	unknown	unknown	ADJ
iajs-763	10	27	function	function	NOUN
iajs-763	10	28	appears	appear	VERB
iajs-763	10	29	under	under	ADP
iajs-763	10	30	an	an	DET
iajs-763	10	31	integral	integral	ADJ
iajs-763	10	32	sign	sign	NOUN
iajs-763	10	33	.	.	PUNCT
iajs-763	11	1	a	a	DET
iajs-763	11	2	general	general	ADJ
iajs-763	11	3	form	form	NOUN
iajs-763	11	4	of	of	ADP
iajs-763	11	5	linear	linear	ADJ
iajs-763	11	6	integral	integral	ADJ
iajs-763	11	7	equations	equation	NOUN
iajs-763	11	8	may	may	AUX
iajs-763	11	9	be	be	AUX
iajs-763	11	10	written	write	VERB
iajs-763	11	11	as	as	SCONJ
iajs-763	11	12	follows	follow	VERB
iajs-763	11	13	:	:	PUNCT
iajs-763	11	14	ibn	ibn	NOUN
iajs-763	11	15	alhaitham	alhaitham	NOUN
iajs-763	11	16	j.	j.	PROPN
iajs-763	11	17	for	for	ADP
iajs-763	11	18	pure	pure	ADJ
iajs-763	11	19	&	&	CCONJ
iajs-763	11	20	appl	appl	PROPN
iajs-763	11	21	.	.	PUNCT
iajs-763	12	1	sci	sci	PROPN
iajs-763	12	2	.	.	PUNCT
iajs-763	12	3	vol.24	vol.24	NOUN
iajs-763	12	4	(	(	PUNCT
iajs-763	12	5	2	2	NUM
iajs-763	12	6	)	)	PUNCT
iajs-763	12	7	2011	2011	NUM
iajs-763	12	8	bxadttutxkxfxuxh	bxadttutxkxfxuxh	NOUN
iajs-763	12	9	xb	xb	X
iajs-763	12	10	a	a	DET
iajs-763	12	11			NOUN
iajs-763	12	12			X
iajs-763	12	13	)	)	PUNCT
iajs-763	12	14	(	(	PUNCT
iajs-763	12	15	)	)	PUNCT
iajs-763	12	16	(	(	PUNCT
iajs-763	12	17	)	)	PUNCT
iajs-763	12	18	,	,	PUNCT
iajs-763	12	19	(	(	PUNCT
iajs-763	12	20	)	)	PUNCT
iajs-763	12	21	(	(	PUNCT
iajs-763	12	22	)	)	PUNCT
iajs-763	12	23	(	(	PUNCT
iajs-763	12	24	)	)	PUNCT
iajs-763	12	25	(	(	PUNCT
iajs-763	12	26			X
iajs-763	12	27	…	…	NUM
iajs-763	12	28	…	…	SYM
iajs-763	12	29	…	…	PUNCT
iajs-763	12	30	…	…	PUNCT
iajs-763	12	31	…	…	PUNCT
iajs-763	12	32	…	…	PUNCT
iajs-763	12	33	..	..	PUNCT
iajs-763	12	34	(	(	PUNCT
iajs-763	12	35	1	1	X
iajs-763	12	36	)	)	PUNCT
iajs-763	12	37	where	where	SCONJ
iajs-763	12	38	h(x	h(x	PROPN
iajs-763	12	39	)	)	PUNCT
iajs-763	12	40	and	and	CCONJ
iajs-763	12	41	f(x)are	f(x)are	VERB
iajs-763	12	42	given	give	VERB
iajs-763	12	43	function	function	NOUN
iajs-763	12	44	of	of	ADP
iajs-763	12	45	x	x	PROPN
iajs-763	12	46	,	,	PUNCT
iajs-763	12	47	t)k(x	t)k(x	PROPN
iajs-763	12	48	,	,	PUNCT
iajs-763	12	49	is	be	AUX
iajs-763	12	50	a	a	DET
iajs-763	12	51	function	function	NOUN
iajs-763	12	52	of	of	ADP
iajs-763	12	53	two	two	NUM
iajs-763	12	54	variables	variable	NOUN
iajs-763	12	55	x	x	PUNCT
iajs-763	12	56	and	and	CCONJ
iajs-763	12	57	t	t	PROPN
iajs-763	12	58	called	call	VERB
iajs-763	12	59	kernel	kernel	NOUN
iajs-763	12	60	of	of	ADP
iajs-763	12	61	integral	integral	ADJ
iajs-763	12	62	equation	equation	NOUN
iajs-763	12	63	which	which	PRON
iajs-763	12	64	are	be	AUX
iajs-763	12	65	also	also	ADV
iajs-763	12	66	known	know	VERB
iajs-763	12	67	,	,	PUNCT
iajs-763	12	68	while	while	SCONJ
iajs-763	12	69	u(x	u(x	NOUN
iajs-763	12	70	)	)	PUNCT
iajs-763	12	71	is	be	AUX
iajs-763	12	72	to	to	PART
iajs-763	12	73	be	be	AUX
iajs-763	12	74	determined	determine	VERB
iajs-763	12	75	and	and	CCONJ
iajs-763	12	76			ADJ
iajs-763	12	77	is	be	AUX
iajs-763	12	78	a	a	DET
iajs-763	12	79	scalar	scalar	ADJ
iajs-763	12	80	parameter	parameter	NOUN
iajs-763	12	81	[	[	X
iajs-763	12	82	in	in	ADP
iajs-763	12	83	this	this	DET
iajs-763	12	84	paper	paper	NOUN
iajs-763	12	85	we	we	PRON
iajs-763	12	86	take	take	VERB
iajs-763	12	87	1	1	NUM
iajs-763	12	88	]	]	PUNCT
iajs-763	12	89	.	.	PUNCT
iajs-763	13	1	definition	definition	NOUN
iajs-763	13	2	1	1	NUM
iajs-763	13	3	-	-	SYM
iajs-763	13	4	2	2	NUM
iajs-763	13	5	:	:	PUNCT
iajs-763	13	6	[	[	PUNCT
iajs-763	13	7	2	2	X
iajs-763	13	8	]	]	PUNCT
iajs-763	13	9	if	if	SCONJ
iajs-763	13	10	the	the	DET
iajs-763	13	11	function	function	NOUN
iajs-763	13	12	h(x	h(x	PROPN
iajs-763	13	13	)	)	PUNCT
iajs-763	14	1	=	=	NOUN
iajs-763	14	2	1	1	NUM
iajs-763	14	3	,	,	PUNCT
iajs-763	14	4	then	then	ADV
iajs-763	14	5	the	the	DET
iajs-763	14	6	linear	linear	ADJ
iajs-763	14	7	integral	integral	ADJ
iajs-763	14	8	equation	equation	NOUN
iajs-763	14	9	(	(	PUNCT
iajs-763	14	10	1	1	X
iajs-763	14	11	)	)	PUNCT
iajs-763	14	12	is	be	AUX
iajs-763	14	13	said	say	VERB
iajs-763	14	14	to	to	PART
iajs-763	14	15	be	be	AUX
iajs-763	14	16	an	an	DET
iajs-763	14	17	equation	equation	NOUN
iajs-763	14	18	of	of	ADP
iajs-763	14	19	the	the	DET
iajs-763	14	20	second	second	ADJ
iajs-763	14	21	kind	kind	NOUN
iajs-763	14	22	(	(	PUNCT
iajs-763	14	23	i.e.	i.e.	X
iajs-763	14	24	)	)	PUNCT
iajs-763	14	25	bxadttutxkxfxu	bxadttutxkxfxu	NOUN
iajs-763	14	26	xb	xb	PROPN
iajs-763	15	1	a	a	DET
iajs-763	15	2			PROPN
iajs-763	15	3			X
iajs-763	15	4	)	)	PUNCT
iajs-763	15	5	(	(	PUNCT
iajs-763	15	6	)	)	PUNCT
iajs-763	15	7	(	(	PUNCT
iajs-763	15	8	)	)	PUNCT
iajs-763	15	9	,	,	PUNCT
iajs-763	15	10	(	(	PUNCT
iajs-763	15	11	)	)	PUNCT
iajs-763	15	12	(	(	PUNCT
iajs-763	15	13	)	)	PUNCT
iajs-763	15	14	(	(	PUNCT
iajs-763	15	15	…	…	PUNCT
iajs-763	15	16	…	…	PUNCT
iajs-763	15	17	…	…	PUNCT
iajs-763	15	18	…	…	PUNCT
iajs-763	15	19	…	…	PUNCT
iajs-763	15	20	…	…	PUNCT
iajs-763	15	21	…	…	PUNCT
iajs-763	15	22	…	…	PUNCT
iajs-763	15	23	..	..	PUNCT
iajs-763	15	24	(	(	PUNCT
iajs-763	15	25	2	2	X
iajs-763	15	26	)	)	PUNCT
iajs-763	15	27	definition	definition	NOUN
iajs-763	15	28	1	1	NUM
iajs-763	15	29	-	-	SYM
iajs-763	15	30	3	3	NUM
iajs-763	15	31	:	:	PUNCT
iajs-763	15	32	[	[	PUNCT
iajs-763	15	33	2	2	X
iajs-763	15	34	]	]	PUNCT
iajs-763	15	35	the	the	DET
iajs-763	15	36	integral	integral	ADJ
iajs-763	15	37	equation	equation	NOUN
iajs-763	15	38	(	(	PUNCT
iajs-763	15	39	1	1	X
iajs-763	15	40	)	)	PUNCT
iajs-763	15	41	is	be	AUX
iajs-763	15	42	called	call	VERB
iajs-763	15	43	fredholm	fredholm	ADJ
iajs-763	15	44	integral	integral	ADJ
iajs-763	15	45	equation	equation	NOUN
iajs-763	15	46	(	(	PUNCT
iajs-763	15	47	fie	fie	X
iajs-763	15	48	)	)	PUNCT
iajs-763	15	49	if	if	SCONJ
iajs-763	15	50	b	b	NOUN
iajs-763	15	51	b(x	b(x	NOUN
iajs-763	15	52	)	)	PUNCT
iajs-763	16	1			NOUN
iajs-763	16	2	,	,	PUNCT
iajs-763	16	3	where	where	SCONJ
iajs-763	16	4	b	b	NOUN
iajs-763	16	5	is	be	AUX
iajs-763	16	6	constant	constant	ADJ
iajs-763	16	7	such	such	ADJ
iajs-763	16	8	that	that	SCONJ
iajs-763	16	9	ab	ab	PROPN
iajs-763	16	10			NUM
iajs-763	16	11	.	.	PUNCT
iajs-763	17	1	therefore	therefore	ADV
iajs-763	17	2	,	,	PUNCT
iajs-763	17	3	the	the	DET
iajs-763	17	4	integral	integral	ADJ
iajs-763	17	5	equations	equation	NOUN
iajs-763	17	6			PUNCT
iajs-763	18	1			PROPN
iajs-763	18	2	b	b	PROPN
iajs-763	18	3	a	a	DET
iajs-763	18	4	bxadttutxkxf	bxadttutxkxf	NOUN
iajs-763	18	5	)	)	PUNCT
iajs-763	18	6	(	(	PUNCT
iajs-763	18	7	)	)	PUNCT
iajs-763	18	8	,	,	PUNCT
iajs-763	18	9	(	(	PUNCT
iajs-763	18	10	)	)	PUNCT
iajs-763	18	11	(	(	PUNCT
iajs-763	18	12	bxadttutxkxfxu	bxadttutxkxfxu	PROPN
iajs-763	18	13	b	b	PROPN
iajs-763	18	14	a	a	DET
iajs-763	18	15			NOUN
iajs-763	18	16			X
iajs-763	18	17	)	)	PUNCT
iajs-763	18	18	(	(	PUNCT
iajs-763	18	19	)	)	PUNCT
iajs-763	18	20	,	,	PUNCT
iajs-763	18	21	(	(	PUNCT
iajs-763	18	22	)	)	PUNCT
iajs-763	18	23	(	(	PUNCT
iajs-763	18	24	)	)	PUNCT
iajs-763	18	25	(	(	PUNCT
iajs-763	18	26	represent	represent	VERB
iajs-763	18	27	the	the	DET
iajs-763	18	28	one	one	NUM
iajs-763	18	29	-	-	PUNCT
iajs-763	18	30	dimensional	dimensional	ADJ
iajs-763	18	31	fredholm	fredholm	NOUN
iajs-763	18	32	integral	integral	ADJ
iajs-763	18	33	equation	equation	NOUN
iajs-763	18	34	of	of	ADP
iajs-763	18	35	the	the	DET
iajs-763	18	36	first	first	ADJ
iajs-763	18	37	and	and	CCONJ
iajs-763	18	38	second	second	ADJ
iajs-763	18	39	kind	kind	NOUN
iajs-763	18	40	respectively	respectively	ADV
iajs-763	18	41	.	.	PUNCT
iajs-763	19	1	1.2	1.2	NUM
iajs-763	19	2	open	open	ADJ
iajs-763	19	3	newton	newton	PROPN
iajs-763	19	4	-	-	PUNCT
iajs-763	19	5	cotes	cote	NOUN
iajs-763	19	6	formula	formula	NOUN
iajs-763	19	7	in	in	ADP
iajs-763	19	8	numerical	numerical	ADJ
iajs-763	19	9	analysis	analysis	NOUN
iajs-763	19	10	,	,	PUNCT
iajs-763	19	11	the	the	DET
iajs-763	19	12	newton	newton	PROPN
iajs-763	19	13	-	-	PUNCT
iajs-763	19	14	cotes	cotes	PROPN
iajs-763	19	15	(	(	PUNCT
iajs-763	19	16	n	n	CCONJ
iajs-763	19	17	-	-	PUNCT
iajs-763	19	18	c	c	NOUN
iajs-763	19	19	)	)	PUNCT
iajs-763	19	20	formulas	formula	NOUN
iajs-763	19	21	are	be	AUX
iajs-763	19	22	a	a	DET
iajs-763	19	23	group	group	NOUN
iajs-763	19	24	of	of	ADP
iajs-763	19	25	formulas	formula	NOUN
iajs-763	19	26	of	of	ADP
iajs-763	19	27	numerical	numerical	ADJ
iajs-763	19	28	integration	integration	NOUN
iajs-763	19	29	based	base	VERB
iajs-763	19	30	on	on	ADP
iajs-763	19	31	evaluating	evaluate	VERB
iajs-763	19	32	the	the	DET
iajs-763	19	33	integrand	integrand	NOUN
iajs-763	19	34	at	at	ADP
iajs-763	19	35	equallyspaced	equallyspace	VERB
iajs-763	19	36	points	point	NOUN
iajs-763	19	37	.	.	PUNCT
iajs-763	20	1	they	they	PRON
iajs-763	20	2	are	be	AUX
iajs-763	20	3	named	name	VERB
iajs-763	20	4	after	after	ADP
iajs-763	20	5	isaac	isaac	PROPN
iajs-763	20	6	newton	newton	PROPN
iajs-763	20	7	and	and	CCONJ
iajs-763	20	8	roger	roger	PROPN
iajs-763	20	9	cotes	cotes	PROPN
iajs-763	20	10	[	[	PUNCT
iajs-763	20	11	3	3	NUM
iajs-763	20	12	]	]	PUNCT
iajs-763	20	13	.	.	PUNCT
iajs-763	21	1	there	there	PRON
iajs-763	21	2	are	be	VERB
iajs-763	21	3	two	two	NUM
iajs-763	21	4	types	type	NOUN
iajs-763	21	5	of	of	ADP
iajs-763	21	6	n	n	NOUN
iajs-763	21	7	-	-	PUNCT
iajs-763	21	8	c	c	NOUN
iajs-763	21	9	formulas	formula	NOUN
iajs-763	21	10	:	:	PUNCT
iajs-763	21	11	the	the	DET
iajs-763	21	12	(	(	PUNCT
iajs-763	21	13	closed	closed	ADJ
iajs-763	21	14	)	)	PUNCT
iajs-763	21	15	type	type	NOUN
iajs-763	21	16	which	which	PRON
iajs-763	21	17	uses	use	VERB
iajs-763	21	18	the	the	DET
iajs-763	21	19	function	function	NOUN
iajs-763	21	20	value	value	NOUN
iajs-763	21	21	at	at	ADV
iajs-763	21	22	all	all	DET
iajs-763	21	23	point	point	NOUN
iajs-763	21	24	in	in	ADP
iajs-763	21	25	the	the	DET
iajs-763	21	26	domain	domain	NOUN
iajs-763	21	27	.	.	PUNCT
iajs-763	22	1	the	the	DET
iajs-763	22	2	(	(	PUNCT
iajs-763	22	3	open	open	ADJ
iajs-763	22	4	)	)	PUNCT
iajs-763	22	5	type	type	NOUN
iajs-763	22	6	which	which	PRON
iajs-763	22	7	does	do	AUX
iajs-763	22	8	not	not	PART
iajs-763	22	9	use	use	VERB
iajs-763	22	10	the	the	DET
iajs-763	22	11	function	function	NOUN
iajs-763	22	12	value	value	NOUN
iajs-763	22	13	at	at	ADP
iajs-763	22	14	the	the	DET
iajs-763	22	15	initial	initial	ADJ
iajs-763	22	16	and	and	CCONJ
iajs-763	22	17	end	end	NOUN
iajs-763	22	18	point	point	NOUN
iajs-763	22	19	of	of	ADP
iajs-763	22	20	the	the	DET
iajs-763	22	21	domain	domain	NOUN
iajs-763	22	22	.	.	PUNCT
iajs-763	23	1	numerical	numerical	ADJ
iajs-763	23	2	integration	integration	NOUN
iajs-763	23	3	formulas	formula	NOUN
iajs-763	23	4	of	of	ADP
iajs-763	23	5	the	the	DET
iajs-763	23	6	form	form	NOUN
iajs-763	23	7	)	)	PUNCT
iajs-763	23	8	(	(	PUNCT
iajs-763	23	9	)	)	PUNCT
iajs-763	23	10	(	(	PUNCT
iajs-763	23	11	)	)	PUNCT
iajs-763	23	12	(	(	PUNCT
iajs-763	23	13	)	)	PUNCT
iajs-763	23	14	(	(	PUNCT
iajs-763	23	15	00	00	NUM
iajs-763	23	16	fexfwdxxfdxxf	fexfwdxxfdxxf	NOUN
iajs-763	23	17	b	b	PROPN
iajs-763	24	1	a	a	DET
iajs-763	24	2	n	n	NOUN
iajs-763	24	3	i	i	NOUN
iajs-763	24	4	x	x	PROPN
iajs-763	24	5	x	x	SYM
iajs-763	24	6	ii	ii	PROPN
iajs-763	24	7	n	n	ADV
iajs-763	24	8			NUM
iajs-763	25	1			ADV
iajs-763	26	1			NUM
iajs-763	26	2			PUNCT
iajs-763	27	1	where	where	SCONJ
iajs-763	27	2	)	)	PUNCT
iajs-763	27	3	(	(	PUNCT
iajs-763	27	4	fe	fe	X
iajs-763	27	5	is	be	AUX
iajs-763	27	6	the	the	DET
iajs-763	27	7	error	error	NOUN
iajs-763	27	8	,	,	PUNCT
iajs-763	27	9	niforhixxi	niforhixxi	NOUN
iajs-763	27	10	,	,	PUNCT
iajs-763	27	11	...	...	PUNCT
iajs-763	27	12	,	,	PUNCT
iajs-763	27	13	1,0	1,0	NUM
iajs-763	27	14	*	*	SYM
iajs-763	27	15	0	0	NUM
iajs-763	27	16			NOUN
iajs-763	27	17	,	,	PUNCT
iajs-763	27	18	and	and	CCONJ
iajs-763	27	19	niwi	niwi	NOUN
iajs-763	27	20	,	,	PUNCT
iajs-763	27	21	...	...	PUNCT
iajs-763	27	22	,	,	PUNCT
iajs-763	27	23	1,0	1,0	PRON
iajs-763	27	24	are	be	AUX
iajs-763	27	25	the	the	DET
iajs-763	27	26	weights	weight	NOUN
iajs-763	27	27	,	,	PUNCT
iajs-763	27	28	is	be	AUX
iajs-763	27	29	called	call	VERB
iajs-763	27	30	closed	closed	ADJ
iajs-763	27	31	newton	newton	PROPN
iajs-763	27	32	-	-	PUNCT
iajs-763	27	33	cotes	cote	NOUN
iajs-763	27	34	formulas	formula	NOUN
iajs-763	27	35	some	some	PRON
iajs-763	27	36	of	of	ADP
iajs-763	27	37	the	the	DET
iajs-763	27	38	common	common	ADJ
iajs-763	27	39	closed	closed	ADJ
iajs-763	27	40	n	n	CCONJ
iajs-763	27	41	-	-	PUNCT
iajs-763	27	42	c	c	NOUN
iajs-763	27	43	formulas	formula	NOUN
iajs-763	27	44	are	be	AUX
iajs-763	27	45	as	as	SCONJ
iajs-763	27	46	follows	follow	VERB
iajs-763	27	47	:	:	PUNCT
iajs-763	27	48	trapezoidal	trapezoidal	ADJ
iajs-763	27	49	rule	rule	NOUN
iajs-763	27	50	,	,	PUNCT
iajs-763	27	51	simpson	simpson	PROPN
iajs-763	27	52	1/3	1/3	NUM
iajs-763	27	53	rule	rule	NOUN
iajs-763	27	54	and	and	CCONJ
iajs-763	27	55	simpson	simpson	NOUN
iajs-763	27	56	3/8	3/8	NUM
iajs-763	27	57	rule	rule	NOUN
iajs-763	27	58	ibn	ibn	PROPN
iajs-763	27	59	alhaitham	alhaitham	NOUN
iajs-763	27	60	j.	j.	PROPN
iajs-763	27	61	for	for	ADP
iajs-763	27	62	pure	pure	ADJ
iajs-763	27	63	&	&	CCONJ
iajs-763	27	64	appl	appl	PROPN
iajs-763	27	65	.	.	PUNCT
iajs-763	28	1	sci	sci	PROPN
iajs-763	28	2	.	.	PUNCT
iajs-763	28	3	vol.24	vol.24	NOUN
iajs-763	28	4	(	(	PUNCT
iajs-763	28	5	2	2	NUM
iajs-763	28	6	)	)	PUNCT
iajs-763	28	7	2011	2011	NUM
iajs-763	28	8	numerical	numerical	ADJ
iajs-763	28	9	integration	integration	NOUN
iajs-763	28	10	formulas	formula	NOUN
iajs-763	28	11	of	of	ADP
iajs-763	28	12	the	the	DET
iajs-763	28	13	form	form	NOUN
iajs-763	28	14	)	)	PUNCT
iajs-763	28	15	(	(	PUNCT
iajs-763	28	16	)	)	PUNCT
iajs-763	28	17	(	(	PUNCT
iajs-763	28	18	)	)	PUNCT
iajs-763	28	19	(	(	PUNCT
iajs-763	28	20	)	)	PUNCT
iajs-763	28	21	(	(	PUNCT
iajs-763	28	22	0	0	NUM
iajs-763	28	23	1	1	NUM
iajs-763	28	24	1	1	NUM
iajs-763	28	25	fexfwdxxfdxxf	fexfwdxxfdxxf	NOUN
iajs-763	28	26	b	b	PROPN
iajs-763	28	27	a	a	PRON
iajs-763	28	28	n	n	NOUN
iajs-763	28	29	i	i	NOUN
iajs-763	28	30	x	x	PROPN
iajs-763	28	31	x	x	SYM
iajs-763	28	32	ii	ii	PROPN
iajs-763	28	33	n	n	ADV
iajs-763	28	34			NUM
iajs-763	29	1			ADV
iajs-763	29	2			ADV
iajs-763	29	3			ADP
iajs-763	29	4			PUNCT
iajs-763	29	5			PROPN
iajs-763	29	6	where	where	SCONJ
iajs-763	29	7	)	)	PUNCT
iajs-763	29	8	(	(	PUNCT
iajs-763	29	9	fe	fe	X
iajs-763	29	10	is	be	AUX
iajs-763	29	11	the	the	DET
iajs-763	29	12	error	error	NOUN
iajs-763	29	13	,	,	PUNCT
iajs-763	29	14	1,	1,	NUM
iajs-763	29	15	...	...	PUNCT
iajs-763	30	1	,0,1*)1(0	,0,1*)1(0	PUNCT
iajs-763	30	2			NOUN
iajs-763	30	3	niforhixxi	niforhixxi	NOUN
iajs-763	30	4	,	,	PUNCT
iajs-763	30	5	and	and	CCONJ
iajs-763	30	6	niwi	niwi	NOUN
iajs-763	30	7	,	,	PUNCT
iajs-763	30	8	...	...	PUNCT
iajs-763	30	9	,	,	PUNCT
iajs-763	30	10	1,0	1,0	PRON
iajs-763	30	11	are	be	AUX
iajs-763	30	12	the	the	DET
iajs-763	30	13	weights	weight	NOUN
iajs-763	30	14	,	,	PUNCT
iajs-763	30	15	is	be	AUX
iajs-763	30	16	called	call	VERB
iajs-763	30	17	open	open	ADJ
iajs-763	30	18	newton	newton	PROPN
iajs-763	30	19	-	-	PUNCT
iajs-763	30	20	cotes	cote	NOUN
iajs-763	30	21	formulas	formula	NOUN
iajs-763	30	22	.	.	PUNCT
iajs-763	31	1	some	some	PRON
iajs-763	31	2	of	of	ADP
iajs-763	31	3	the	the	DET
iajs-763	31	4	common	common	ADJ
iajs-763	31	5	open	open	ADJ
iajs-763	31	6	n	n	CCONJ
iajs-763	31	7	-	-	PUNCT
iajs-763	31	8	c	c	NOUN
iajs-763	31	9	formulas	formula	NOUN
iajs-763	31	10	with	with	ADP
iajs-763	31	11	their	their	PRON
iajs-763	31	12	error	error	NOUN
iajs-763	31	13	terms	term	NOUN
iajs-763	31	14	are	be	AUX
iajs-763	31	15	a	a	DET
iajs-763	31	16	follows	follow	NOUN
iajs-763	31	17	:	:	PUNCT
iajs-763	31	18	[	[	PUNCT
iajs-763	31	19	1	1	X
iajs-763	31	20	]	]	PUNCT
iajs-763	31	21	n=0	n=0	NUM
iajs-763	31	22	m	m	VERB
iajs-763	31	23	idpoint	idpoint	NOUN
iajs-763	31	24	rule	rule	NOUN
iajs-763	31	25	)	)	PUNCT
iajs-763	31	26	,	,	PUNCT
iajs-763	31	27	(	(	PUNCT
iajs-763	31	28	)	)	PUNCT
iajs-763	31	29	(	(	PUNCT
iajs-763	31	30	3	3	X
iajs-763	31	31	)	)	PUNCT
iajs-763	31	32	(	(	PUNCT
iajs-763	31	33	2	2	NUM
iajs-763	31	34	)	)	PUNCT
iajs-763	31	35	(	(	PUNCT
iajs-763	31	36	11	11	NUM
iajs-763	31	37	3	3	NUM
iajs-763	31	38	0	0	NUM
iajs-763	31	39	1	1	NUM
iajs-763	31	40	1	1	NUM
iajs-763	31	41	xxwheref	xxwheref	NOUN
iajs-763	31	42	h	h	NOUN
iajs-763	31	43	xhfdxxf	xhfdxxf	PROPN
iajs-763	32	1	x	x	PUNCT
iajs-763	32	2	x	x	SYM
iajs-763	32	3			PROPN
iajs-763	32	4			NOUN
iajs-763	32	5			NOUN
iajs-763	32	6			ADP
iajs-763	32	7	n=1	n=1	PROPN
iajs-763	32	8	)	)	PUNCT
iajs-763	32	9	,	,	PUNCT
iajs-763	32	10	(	(	PUNCT
iajs-763	32	11	)	)	PUNCT
iajs-763	32	12	(	(	PUNCT
iajs-763	32	13	4	4	NUM
iajs-763	32	14	3	3	NUM
iajs-763	32	15	)	)	PUNCT
iajs-763	32	16	]	]	PUNCT
iajs-763	32	17	(	(	PUNCT
iajs-763	32	18	)	)	PUNCT
iajs-763	32	19	(	(	PUNCT
iajs-763	32	20	[	[	PUNCT
iajs-763	32	21	2	2	NUM
iajs-763	32	22	3	3	NUM
iajs-763	32	23	)	)	PUNCT
iajs-763	32	24	(	(	PUNCT
iajs-763	32	25	21	21	NUM
iajs-763	32	26	3	3	NUM
iajs-763	32	27	10	10	NUM
iajs-763	32	28	2	2	NUM
iajs-763	32	29	1	1	NUM
iajs-763	32	30	xxwheref	xxwheref	NOUN
iajs-763	32	31	h	h	PROPN
iajs-763	33	1	xfxf	xfxf	PROPN
iajs-763	33	2	h	h	PROPN
iajs-763	33	3	dxxf	dxxf	NOUN
iajs-763	33	4	x	x	PUNCT
iajs-763	34	1	x	x	PUNCT
iajs-763	34	2			PROPN
iajs-763	34	3			NOUN
iajs-763	34	4			NOUN
iajs-763	34	5			ADP
iajs-763	34	6	n=2	n=2	ADV
iajs-763	34	7	)	)	PUNCT
iajs-763	34	8	,	,	PUNCT
iajs-763	34	9	(	(	PUNCT
iajs-763	34	10	)	)	PUNCT
iajs-763	34	11	(	(	PUNCT
iajs-763	34	12	45	45	NUM
iajs-763	34	13	14	14	NUM
iajs-763	34	14	)	)	PUNCT
iajs-763	35	1	]	]	X
iajs-763	35	2	(	(	PUNCT
iajs-763	35	3	2)()(2	2)()(2	NUM
iajs-763	35	4	[	[	PUNCT
iajs-763	35	5	3	3	NUM
iajs-763	35	6	4	4	NUM
iajs-763	35	7	)	)	PUNCT
iajs-763	35	8	(	(	PUNCT
iajs-763	35	9	31	31	NUM
iajs-763	35	10	)	)	SYM
iajs-763	35	11	4	4	NUM
iajs-763	35	12	(	(	PUNCT
iajs-763	35	13	5	5	NUM
iajs-763	35	14	210	210	NUM
iajs-763	35	15	3	3	NUM
iajs-763	35	16	1	1	NUM
iajs-763	35	17	xxwheref	xxwheref	NOUN
iajs-763	35	18	h	h	PROPN
iajs-763	35	19	xfxfxf	xfxfxf	PROPN
iajs-763	36	1	h	h	NOUN
iajs-763	36	2	dxxf	dxxf	NOUN
iajs-763	36	3	x	x	PUNCT
iajs-763	37	1	x	x	X
iajs-763	37	2			PROPN
iajs-763	37	3			NOUN
iajs-763	37	4			VERB
iajs-763	37	5			PROPN
iajs-763	37	6	n=3	n=3	PUNCT
iajs-763	37	7	)	)	PUNCT
iajs-763	37	8	,	,	PUNCT
iajs-763	37	9	(	(	PUNCT
iajs-763	37	10	)	)	PUNCT
iajs-763	37	11	(	(	PUNCT
iajs-763	37	12	144	144	NUM
iajs-763	37	13	95	95	NUM
iajs-763	37	14	)	)	PUNCT
iajs-763	37	15	]	]	PUNCT
iajs-763	37	16	(	(	PUNCT
iajs-763	37	17	11)()()(11	11)()()(11	NUM
iajs-763	37	18	[	[	PUNCT
iajs-763	37	19	24	24	NUM
iajs-763	37	20	5	5	NUM
iajs-763	37	21	)	)	PUNCT
iajs-763	37	22	(	(	PUNCT
iajs-763	37	23	41	41	NUM
iajs-763	37	24	)	)	SYM
iajs-763	37	25	4	4	NUM
iajs-763	37	26	(	(	PUNCT
iajs-763	37	27	5	5	NUM
iajs-763	37	28	3210	3210	NUM
iajs-763	37	29	4	4	NUM
iajs-763	37	30	1	1	NUM
iajs-763	37	31	xxwheref	xxwheref	NOUN
iajs-763	37	32	h	h	NOUN
iajs-763	37	33	xfxfxfxf	xfxfxfxf	PROPN
iajs-763	38	1	h	h	PROPN
iajs-763	38	2	dxxf	dxxf	NOUN
iajs-763	38	3	x	x	PUNCT
iajs-763	39	1	x	x	PUNCT
iajs-763	39	2			PROPN
iajs-763	39	3			PROPN
iajs-763	39	4			PROPN
iajs-763	39	5			PROPN
iajs-763	39	6	n=4	n=4	X
iajs-763	39	7	)	)	PUNCT
iajs-763	39	8	,	,	PUNCT
iajs-763	39	9	(	(	PUNCT
iajs-763	39	10	)	)	PUNCT
iajs-763	39	11	(	(	PUNCT
iajs-763	39	12	1404	1404	NUM
iajs-763	39	13	4	4	NUM
iajs-763	39	14	)	)	PUNCT
iajs-763	39	15	]	]	X
iajs-763	39	16	(	(	PUNCT
iajs-763	39	17	11)(14)(26)(14)(11	11)(14)(26)(14)(11	NUM
iajs-763	39	18	[	[	PUNCT
iajs-763	39	19	10	10	NUM
iajs-763	39	20	3	3	NUM
iajs-763	39	21	)	)	PUNCT
iajs-763	39	22	(	(	PUNCT
iajs-763	39	23	51	51	NUM
iajs-763	39	24	)	)	SYM
iajs-763	39	25	6	6	NUM
iajs-763	39	26	(	(	PUNCT
iajs-763	39	27	7	7	NUM
iajs-763	39	28	43210	43210	NUM
iajs-763	39	29	5	5	NUM
iajs-763	39	30	1	1	NUM
iajs-763	39	31	xxwheref	xxwheref	NOUN
iajs-763	39	32	h	h	NOUN
iajs-763	39	33	xfxfxfxfxf	xfxfxfxfxf	PROPN
iajs-763	40	1	h	h	PROPN
iajs-763	40	2	dxxf	dxxf	NOUN
iajs-763	40	3	x	x	PUNCT
iajs-763	41	1	x	x	X
iajs-763	41	2			PROPN
iajs-763	41	3			VERB
iajs-763	41	4			PRON
iajs-763	41	5			PROPN
iajs-763	41	6	2solution	2solution	NUM
iajs-763	41	7	of	of	ADP
iajs-763	41	8	a	a	DET
iajs-763	41	9	system	system	NOUN
iajs-763	41	10	of	of	ADP
iajs-763	41	11	linear	linear	ADJ
iajs-763	41	12	fredholm	fredholm	ADJ
iajs-763	41	13	integral	integral	ADJ
iajs-763	41	14	equations	equation	NOUN
iajs-763	41	15	of	of	ADP
iajs-763	41	16	the	the	DET
iajs-763	41	17	second	second	ADJ
iajs-763	41	18	kind	kind	NOUN
iajs-763	41	19	using	use	VERB
iajs-763	41	20	open	open	ADJ
iajs-763	41	21	n	n	CCONJ
iajs-763	41	22	-	-	PUNCT
iajs-763	41	23	c	c	NOUN
iajs-763	41	24	formulas	formula	NOUN
iajs-763	41	25	in	in	ADP
iajs-763	41	26	this	this	DET
iajs-763	41	27	section	section	NOUN
iajs-763	41	28	,	,	PUNCT
iajs-763	41	29	we	we	PRON
iajs-763	41	30	use	use	VERB
iajs-763	41	31	the	the	DET
iajs-763	41	32	common	common	ADJ
iajs-763	41	33	formula	formula	NOUN
iajs-763	41	34	of	of	ADP
iajs-763	41	35	open	open	ADJ
iajs-763	41	36	n	n	CCONJ
iajs-763	41	37	-	-	PUNCT
iajs-763	41	38	c	c	NOUN
iajs-763	41	39	to	to	PART
iajs-763	41	40	solve	solve	VERB
iajs-763	41	41	the	the	DET
iajs-763	41	42	system	system	NOUN
iajs-763	41	43	of	of	ADP
iajs-763	41	44	linear	linear	ADJ
iajs-763	41	45	fredholm	fredholm	ADJ
iajs-763	41	46	integral	integral	ADJ
iajs-763	41	47	equations	equation	NOUN
iajs-763	41	48	of	of	ADP
iajs-763	41	49	the	the	DET
iajs-763	41	50	second	second	ADJ
iajs-763	41	51	kind	kind	NOUN
iajs-763	41	52	.	.	PUNCT
iajs-763	42	1	consider	consider	VERB
iajs-763	42	2	the	the	DET
iajs-763	42	3	system	system	NOUN
iajs-763	42	4	of	of	ADP
iajs-763	42	5	linear	linear	ADJ
iajs-763	42	6	fredholm	fredholm	ADJ
iajs-763	42	7	integral	integral	ADJ
iajs-763	42	8	equations	equation	NOUN
iajs-763	42	9	of	of	ADP
iajs-763	42	10	the	the	DET
iajs-763	42	11	second	second	ADJ
iajs-763	42	12	kind	kind	NOUN
iajs-763	42	13	nrdtxutxkxfxu	nrdtxutxkxfxu	PROPN
iajs-763	42	14	s	s	PART
iajs-763	42	15	n	n	PROPN
iajs-763	42	16	s	s	PROPN
iajs-763	42	17	b	b	PROPN
iajs-763	42	18	a	a	DET
iajs-763	42	19	rsrr	rsrr	NOUN
iajs-763	42	20	,	,	PUNCT
iajs-763	42	21	...	...	PUNCT
iajs-763	42	22	,	,	PUNCT
iajs-763	42	23	2,1	2,1	NUM
iajs-763	42	24	,	,	PUNCT
iajs-763	42	25	)	)	PUNCT
iajs-763	42	26	(	(	PUNCT
iajs-763	42	27	)	)	PUNCT
iajs-763	42	28	,	,	PUNCT
iajs-763	42	29	(	(	PUNCT
iajs-763	42	30	)	)	PUNCT
iajs-763	42	31	(	(	PUNCT
iajs-763	42	32	)	)	PUNCT
iajs-763	42	33	(	(	PUNCT
iajs-763	42	34	1	1	NUM
iajs-763	42	35			NOUN
iajs-763	42	36			X
iajs-763	42	37			PUNCT
iajs-763	42	38			NUM
iajs-763	42	39	…	…	PUNCT
iajs-763	42	40	…	…	PUNCT
iajs-763	42	41	(	(	PUNCT
iajs-763	42	42	3	3	NUM
iajs-763	42	43	)	)	PUNCT
iajs-763	42	44	where	where	SCONJ
iajs-763	42	45	nsrkfnn	nsrkfnn	PROPN
iajs-763	42	46	rsr	rsr	NOUN
iajs-763	42	47	,	,	PUNCT
iajs-763	42	48	...	...	PUNCT
iajs-763	42	49	,	,	PUNCT
iajs-763	42	50	2,1	2,1	NUM
iajs-763	42	51	,	,	PUNCT
iajs-763	42	52	,	,	PUNCT
iajs-763	42	53	,	,	PUNCT
iajs-763	42	54	,	,	PUNCT
iajs-763	42	55			X
iajs-763	42	56	are	be	AUX
iajs-763	42	57	assumed	assume	VERB
iajs-763	42	58	to	to	PART
iajs-763	42	59	be	be	AUX
iajs-763	42	60	continuous	continuous	ADJ
iajs-763	42	61	function	function	NOUN
iajs-763	42	62	.	.	PUNCT
iajs-763	43	1	suppose	suppose	VERB
iajs-763	43	2	that	that	SCONJ
iajs-763	43	3	the	the	DET
iajs-763	43	4	interval	interval	NOUN
iajs-763	43	5	[	[	X
iajs-763	43	6	a	a	X
iajs-763	43	7	,	,	PUNCT
iajs-763	43	8	b	b	NOUN
iajs-763	43	9	]	]	X
iajs-763	43	10	is	be	AUX
iajs-763	43	11	divided	divide	VERB
iajs-763	43	12	into	into	ADP
iajs-763	43	13	n+2	n+2	NUM
iajs-763	43	14	equal	equal	ADJ
iajs-763	43	15	subintervals	subinterval	NOUN
iajs-763	43	16	of	of	ADP
iajs-763	43	17	length	length	NOUN
iajs-763	43	18	2	2	NUM
iajs-763	43	19			NOUN
iajs-763	43	20			PROPN
iajs-763	43	21	n	n	CCONJ
iajs-763	43	22	ab	ab	NOUN
iajs-763	43	23	h	h	NOUN
iajs-763	43	24	,	,	PUNCT
iajs-763	43	25	such	such	ADJ
iajs-763	43	26	that	that	SCONJ
iajs-763	43	27	1,1	1,1	NUM
iajs-763	43	28	,	,	PUNCT
iajs-763	43	29			NOUN
iajs-763	43	30			NUM
iajs-763	43	31	n	n	DET
iajs-763	43	32	xbxa	xbxa	NOUN
iajs-763	43	33	with	with	ADP
iajs-763	43	34	nihiαx	nihiαx	PROPN
iajs-763	43	35	i	i	PROPN
iajs-763	43	36	,	,	PUNCT
iajs-763	43	37	...	...	PUNCT
iajs-763	43	38	,	,	PUNCT
iajs-763	43	39	1,0	1,0	NUM
iajs-763	43	40	,	,	PUNCT
iajs-763	43	41	*	*	PUNCT
iajs-763	43	42			NOUN
iajs-763	43	43	this	this	PRON
iajs-763	43	44	implies	imply	VERB
iajs-763	43	45	that	that	SCONJ
iajs-763	43	46	hax	hax	NOUN
iajs-763	43	47	0	0	PROPN
iajs-763	43	48	and	and	CCONJ
iajs-763	43	49	hbxn	hbxn	NOUN
iajs-763	43	50			NOUN
iajs-763	43	51	and	and	CCONJ
iajs-763	43	52	)	)	PUNCT
iajs-763	43	53	(	(	PUNCT
iajs-763	43	54	ir	ir	PROPN
iajs-763	43	55	xu	xu	PROPN
iajs-763	43	56	for	for	ADP
iajs-763	43	57	nrni	nrni	PROPN
iajs-763	43	58	,	,	PUNCT
iajs-763	43	59	...	...	PUNCT
iajs-763	43	60	,	,	PUNCT
iajs-763	43	61	2,1,,	2,1,,	NUM
iajs-763	43	62	...	...	PUNCT
iajs-763	43	63	,1,0	,1,0	PUNCT
iajs-763	43	64			NUM
iajs-763	43	65	can	can	AUX
iajs-763	43	66	be	be	AUX
iajs-763	43	67	determined	determine	VERB
iajs-763	43	68	by	by	ADP
iajs-763	43	69	:	:	PUNCT
iajs-763	43	70	nrnidttutxkxfxu	nrnidttutxkxfxu	NOUN
iajs-763	43	71	n	n	PROPN
iajs-763	43	72	s	s	PROPN
iajs-763	43	73	b	b	NOUN
iajs-763	43	74	a	a	DET
iajs-763	43	75	sirsirir	sirsirir	NOUN
iajs-763	43	76	,	,	PUNCT
iajs-763	43	77	,	,	PUNCT
iajs-763	43	78	2,1,,,1,0	2,1,,,1,0	NUM
iajs-763	43	79	,	,	PUNCT
iajs-763	43	80	)	)	PUNCT
iajs-763	43	81	(	(	PUNCT
iajs-763	43	82	)	)	PUNCT
iajs-763	43	83	,	,	PUNCT
iajs-763	43	84	(	(	PUNCT
iajs-763	43	85	)	)	PUNCT
iajs-763	43	86	(	(	PUNCT
iajs-763	43	87	)	)	PUNCT
iajs-763	43	88	(	(	PUNCT
iajs-763	43	89	1	1	NUM
iajs-763	43	90			NOUN
iajs-763	43	91			NUM
iajs-763	43	92			NOUN
iajs-763	43	93			NUM
iajs-763	43	94	…	…	PUNCT
iajs-763	43	95	…	…	PUNCT
iajs-763	43	96	…	…	PUNCT
iajs-763	43	97	…	…	PUNCT
iajs-763	43	98	.(4	.(4	NUM
iajs-763	43	99	)	)	PUNCT
iajs-763	43	100	thus	thus	ADV
iajs-763	43	101	,	,	PUNCT
iajs-763	43	102	we	we	PRON
iajs-763	43	103	are	be	AUX
iajs-763	43	104	approximating	approximate	VERB
iajs-763	43	105	each	each	DET
iajs-763	43	106	integral	integral	ADJ
iajs-763	43	107	term	term	NOUN
iajs-763	43	108	by	by	ADP
iajs-763	43	109	the	the	DET
iajs-763	43	110	open	open	ADJ
iajs-763	43	111	n	n	CCONJ
iajs-763	43	112	-	-	PUNCT
iajs-763	43	113	c	c	NOUN
iajs-763	43	114	formulas	formula	NOUN
iajs-763	43	115	.	.	PUNCT
iajs-763	44	1	2.1	2.1	NUM
iajs-763	44	2	using	use	VERB
iajs-763	44	3	open	open	ADJ
iajs-763	44	4	n	n	CCONJ
iajs-763	44	5	-	-	PUNCT
iajs-763	44	6	c	c	NOUN
iajs-763	44	7	:	:	PUNCT
iajs-763	44	8	with	with	ADP
iajs-763	44	9	n=0	n=0	NUM
iajs-763	44	10	(	(	PUNCT
iajs-763	44	11	midpoint	midpoint	NOUN
iajs-763	44	12	rule	rule	NOUN
iajs-763	44	13	)	)	PUNCT
iajs-763	44	14	we	we	PRON
iajs-763	44	15	replace	replace	VERB
iajs-763	44	16	the	the	DET
iajs-763	44	17	integral	integral	ADJ
iajs-763	44	18	term	term	NOUN
iajs-763	44	19	that	that	PRON
iajs-763	44	20	appeared	appear	VERB
iajs-763	44	21	in	in	ADP
iajs-763	44	22	the	the	DET
iajs-763	44	23	right	right	ADJ
iajs-763	44	24	hand	hand	NOUN
iajs-763	44	25	side	side	NOUN
iajs-763	44	26	of	of	ADP
iajs-763	44	27	the	the	DET
iajs-763	44	28	above	above	ADJ
iajs-763	44	29	equation	equation	NOUN
iajs-763	44	30	by	by	ADP
iajs-763	44	31	the	the	DET
iajs-763	44	32	composite	composite	ADJ
iajs-763	44	33	midpoint	midpoint	NOUN
iajs-763	44	34	rule	rule	NOUN
iajs-763	44	35	which	which	PRON
iajs-763	44	36	illustrate	illustrate	VERB
iajs-763	44	37	in	in	ADP
iajs-763	44	38	the	the	DET
iajs-763	44	39	following	following	NOUN
iajs-763	44	40	theorem	theorem	NOUN
iajs-763	44	41	:	:	PUNCT
iajs-763	44	42	[	[	PUNCT
iajs-763	44	43	4	4	NUM
iajs-763	44	44	]	]	PUNCT
iajs-763	44	45	ibn	ibn	PROPN
iajs-763	44	46	alhaitham	alhaitham	NOUN
iajs-763	44	47	j.	j.	PROPN
iajs-763	44	48	for	for	ADP
iajs-763	44	49	pure	pure	ADJ
iajs-763	44	50	&	&	CCONJ
iajs-763	44	51	appl	appl	PROPN
iajs-763	44	52	.	.	PUNCT
iajs-763	45	1	sci	sci	PROPN
iajs-763	45	2	.	.	PUNCT
iajs-763	45	3	vol.24	vol.24	NOUN
iajs-763	45	4	(	(	PUNCT
iajs-763	45	5	2	2	NUM
iajs-763	45	6	)	)	PUNCT
iajs-763	45	7	2011	2011	NUM
iajs-763	45	8	theorem	theorem	VERB
iajs-763	45	9	:	:	PUNCT
iajs-763	45	10	let	let	VERB
iajs-763	45	11	]	]	PUNCT
iajs-763	45	12	,	,	PUNCT
iajs-763	45	13	[	[	X
iajs-763	45	14	2	2	NUM
iajs-763	45	15	bacf	bacf	NOUN
iajs-763	45	16			NOUN
iajs-763	45	17	.	.	PUNCT
iajs-763	46	1	with	with	ADP
iajs-763	46	2	)	)	PUNCT
iajs-763	46	3	22/	22/	NUM
iajs-763	46	4	(	(	PUNCT
iajs-763	46	5	)	)	PUNCT
iajs-763	46	6	(	(	PUNCT
iajs-763	46	7			X
iajs-763	46	8	mabh	mabh	PROPN
iajs-763	46	9	and	and	CCONJ
iajs-763	46	10	hjαxj	hjαxj	NOUN
iajs-763	46	11	)	)	PUNCT
iajs-763	46	12	1	1	NUM
iajs-763	46	13	(	(	PUNCT
iajs-763	46	14			NOUN
iajs-763	46	15	12,	12,	NUM
iajs-763	46	16	...	...	PUNCT
iajs-763	46	17	,0,1	,0,1	NOUN
iajs-763	46	18	,	,	PUNCT
iajs-763	46	19			PROPN
iajs-763	46	20	mj	mj	INTJ
iajs-763	46	21	,	,	PUNCT
iajs-763	46	22	the	the	DET
iajs-763	46	23	midpoint	midpoint	NOUN
iajs-763	46	24	rule	rule	NOUN
iajs-763	46	25	for	for	ADP
iajs-763	46	26	n=2	n=2	NOUN
iajs-763	46	27	m	m	PROPN
iajs-763	46	28	subintervals	subinterval	NOUN
iajs-763	46	29	is	be	AUX
iajs-763	46	30	:	:	PUNCT
iajs-763	46	31	)	)	PUNCT
iajs-763	46	32	(	(	PUNCT
iajs-763	46	33	6	6	NUM
iajs-763	46	34	)	)	PUNCT
iajs-763	46	35	(	(	PUNCT
iajs-763	46	36	2	2	NUM
iajs-763	46	37	)	)	PUNCT
iajs-763	46	38	(	(	PUNCT
iajs-763	46	39	20	20	NUM
iajs-763	46	40	0	0	NUM
iajs-763	46	41	2	2	NUM
iajs-763	46	42	fh	fh	NOUN
iajs-763	46	43	ab	ab	PROPN
iajs-763	46	44	xfhdxxf	xfhdxxf	PROPN
iajs-763	47	1	b	b	PROPN
iajs-763	47	2	a	a	DET
iajs-763	47	3	m	m	PROPN
iajs-763	47	4	j	j	PROPN
iajs-763	47	5	j	j	PROPN
iajs-763	47	6			PROPN
iajs-763	47	7			PROPN
iajs-763	47	8			PROPN
iajs-763	47	9			X
iajs-763	47	10			NOUN
iajs-763	47	11	for	for	ADP
iajs-763	47	12	some	some	PRON
iajs-763	47	13	)	)	PUNCT
iajs-763	47	14	,	,	PUNCT
iajs-763	47	15	(	(	PUNCT
iajs-763	47	16	ba	ba	ADV
iajs-763	47	17	.	.	PUNCT
iajs-763	48	1	if	if	SCONJ
iajs-763	48	2	the	the	DET
iajs-763	48	3	number	number	NOUN
iajs-763	48	4	of	of	ADP
iajs-763	48	5	subinterval	subinterval	NOUN
iajs-763	48	6	is	be	AUX
iajs-763	48	7	even	even	ADV
iajs-763	48	8	we	we	PRON
iajs-763	48	9	apply	apply	VERB
iajs-763	48	10	open	open	ADJ
iajs-763	48	11	n	n	CCONJ
iajs-763	48	12	-	-	PUNCT
iajs-763	48	13	c	c	NOUN
iajs-763	48	14	with	with	ADP
iajs-763	48	15	(	(	PUNCT
iajs-763	48	16	n=1	n=1	NOUN
iajs-763	48	17	)	)	PUNCT
iajs-763	48	18	rule	rule	NOUN
iajs-763	48	19	.	.	PUNCT
iajs-763	49	1	therefore	therefore	ADV
iajs-763	49	2	2/,,1,0,,,2,1	2/,,1,0,,,2,1	NUM
iajs-763	49	3	,	,	PUNCT
iajs-763	49	4	2	2	NUM
iajs-763	49	5	nmwhereminru	nmwhereminru	NOUN
iajs-763	49	6	ir	ir	PROPN
iajs-763	49	7			VERB
iajs-763	49	8			NOUN
iajs-763	49	9	are	be	AUX
iajs-763	49	10	obtained	obtain	VERB
iajs-763	49	11	by	by	ADP
iajs-763	49	12	solving	solve	VERB
iajs-763	49	13	the	the	DET
iajs-763	49	14	equation	equation	NOUN
iajs-763	49	15	:	:	PUNCT
iajs-763	49	16			ADJ
iajs-763	49	17			ADP
iajs-763	49	18	nsnrniuxxkhfu	nsnrniuxxkhfu	NOUN
iajs-763	49	19	jii	jii	PROPN
iajs-763	49	20	s	s	PART
iajs-763	49	21	n	n	PRON
iajs-763	49	22	j	j	PROPN
iajs-763	49	23	jirsrr	jirsrr	ADV
iajs-763	49	24	,	,	PUNCT
iajs-763	49	25	,	,	PUNCT
iajs-763	49	26	2,1,,,2,1	2,1,,,2,1	NUM
iajs-763	49	27	,	,	PUNCT
iajs-763	49	28	2	2	NUM
iajs-763	49	29	,	,	PUNCT
iajs-763	49	30	,	,	PUNCT
iajs-763	49	31	1,0,),(2	1,0,),(2	NUM
iajs-763	49	32	2	2	NUM
iajs-763	49	33	2/	2/	NUM
iajs-763	49	34	0	0	NUM
iajs-763	49	35	22	22	NUM
iajs-763	49	36			PROPN
iajs-763	49	37			PROPN
iajs-763	49	38			X
iajs-763	49	39			NUM
iajs-763	49	40	)	)	PUNCT
iajs-763	49	41	5(	5(	NUM
iajs-763	49	42	where	where	SCONJ
iajs-763	49	43	ir	ir	PROPN
iajs-763	49	44	u	u	NOUN
iajs-763	49	45	2	2	NUM
iajs-763	49	46	denote	denote	VERB
iajs-763	49	47	the	the	DET
iajs-763	49	48	numerical	numerical	ADJ
iajs-763	49	49	solution	solution	NOUN
iajs-763	49	50	at	at	ADP
iajs-763	49	51	,	,	PUNCT
iajs-763	49	52	m	m	VERB
iajs-763	49	53	=	=	NOUN
iajs-763	49	54	n/2	n/2	NOUN
iajs-763	49	55	,	,	PUNCT
iajs-763	49	56	transform	transform	VERB
iajs-763	49	57	all	all	DET
iajs-763	49	58	the	the	DET
iajs-763	49	59	terms	term	NOUN
iajs-763	49	60	involving	involve	VERB
iajs-763	49	61	the	the	DET
iajs-763	49	62	solution	solution	NOUN
iajs-763	49	63	ir	ir	NOUN
iajs-763	49	64	u	u	PROPN
iajs-763	49	65	2	2	NUM
iajs-763	49	66	2/,,1,0,,,2,1	2/,,1,0,,,2,1	NUM
iajs-763	49	67	,	,	PUNCT
iajs-763	49	68	nminr	nminr	PROPN
iajs-763	49	69			VERB
iajs-763	49	70			ADV
iajs-763	49	71	to	to	PART
iajs-763	49	72	left	left	VERB
iajs-763	49	73	side	side	NOUN
iajs-763	49	74	of	of	ADP
iajs-763	49	75	the	the	DET
iajs-763	49	76	equation	equation	NOUN
iajs-763	49	77	(	(	PUNCT
iajs-763	49	78	5	5	NUM
iajs-763	49	79	)	)	PUNCT
iajs-763	49	80	and	and	CCONJ
iajs-763	49	81	irf	irf	PROPN
iajs-763	49	82	2	2	NUM
iajs-763	49	83	to	to	ADP
iajs-763	49	84	the	the	DET
iajs-763	49	85	right	right	ADJ
iajs-763	49	86	side	side	NOUN
iajs-763	49	87	.	.	PUNCT
iajs-763	50	1			NOUN
iajs-763	51	1			PROPN
iajs-763	52	1			PUNCT
iajs-763	53	1			PUNCT
iajs-763	54	1			PUNCT
iajs-763	55	1			PUNCT
iajs-763	56	1			PUNCT
iajs-763	57	1			PUNCT
iajs-763	58	1			NOUN
iajs-763	59	1			PUNCT
iajs-763	60	1			NOUN
iajs-763	60	2			PROPN
iajs-763	60	3			PROPN
iajs-763	60	4			X
iajs-763	60	5			NOUN
iajs-763	60	6			NOUN
iajs-763	60	7			NOUN
iajs-763	60	8			NOUN
iajs-763	60	9			NOUN
iajs-763	60	10			NOUN
iajs-763	60	11			NOUN
iajs-763	60	12			NOUN
iajs-763	60	13			NOUN
iajs-763	60	14			NOUN
iajs-763	60	15			NOUN
iajs-763	60	16			NOUN
iajs-763	60	17			VERB
iajs-763	60	18			PROPN
iajs-763	60	19			NOUN
iajs-763	60	20			NOUN
iajs-763	60	21			NOUN
iajs-763	60	22			NOUN
iajs-763	60	23			NOUN
iajs-763	60	24			NOUN
iajs-763	60	25	)	)	PUNCT
iajs-763	60	26	,	,	PUNCT
iajs-763	60	27	(	(	PUNCT
iajs-763	60	28	21),(2),(2),(2),(2),(2	21),(2),(2),(2),(2),(2	NUM
iajs-763	60	29	)	)	PUNCT
iajs-763	60	30	,	,	PUNCT
iajs-763	60	31	(	(	PUNCT
iajs-763	60	32	2),(21),(2),(2),(2),(2	2),(21),(2),(2),(2),(2	NUM
iajs-763	60	33	)	)	PUNCT
iajs-763	60	34	,	,	PUNCT
iajs-763	60	35	(	(	PUNCT
iajs-763	60	36	2),(2),(21),(2),(2),(2	2),(2),(21),(2),(2),(2	NUM
iajs-763	60	37	)	)	PUNCT
iajs-763	60	38	,	,	PUNCT
iajs-763	60	39	(	(	PUNCT
iajs-763	60	40	2),(2),(2),(21),(2),(2	2),(2),(2),(21),(2),(2	NUM
iajs-763	60	41	)	)	PUNCT
iajs-763	60	42	,	,	PUNCT
iajs-763	60	43	(	(	PUNCT
iajs-763	60	44	2),(2),(2),(2),(21),(2	2),(2),(2),(2),(21),(2	NUM
iajs-763	60	45	)	)	PUNCT
iajs-763	60	46	,	,	PUNCT
iajs-763	60	47	(	(	PUNCT
iajs-763	60	48	2),(2),(2),(2),(2),(21	2),(2),(2),(2),(2),(21	NUM
iajs-763	60	49	1011101	1011101	NUM
iajs-763	60	50	1110111111011	1110111111011	NUM
iajs-763	60	51	0100001101001	0100001101001	NUM
iajs-763	60	52	111011	111011	NUM
iajs-763	60	53	111	111	NUM
iajs-763	60	54	101	101	NUM
iajs-763	60	55	1	1	NUM
iajs-763	60	56	1111101111	1111101111	NUM
iajs-763	60	57	1111	1111	NUM
iajs-763	60	58	1011	1011	NUM
iajs-763	60	59	1	1	NUM
iajs-763	60	60	0110100101	0110100101	NUM
iajs-763	60	61	1101	1101	NUM
iajs-763	60	62	1001	1001	NUM
iajs-763	60	63	1	1	NUM
iajs-763	60	64	mmnnmnnmnnmmnmnmn	mmnnmnnmnnmmnmnmn	NOUN
iajs-763	60	65	mnnnnnnmnnn	mnnnnnnmnnn	NOUN
iajs-763	60	66	mnnnnnnmnnn	mnnnnnnmnnn	NOUN
iajs-763	60	67	mmnmnmnmmmm	mmnmnmnmmmm	PROPN
iajs-763	60	68	mnnnm	mnnnm	ADJ
iajs-763	60	69	mnnnm	mnnnm	ADJ
iajs-763	60	70	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	NOUN
iajs-763	60	71	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	60	72	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	60	73	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	60	74	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	60	75	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	61	1			PROPN
iajs-763	61	2			VERB
iajs-763	61	3			PROPN
iajs-763	61	4			PROPN
iajs-763	61	5			NUM
iajs-763	61	6			PROPN
iajs-763	61	7			VERB
iajs-763	61	8			PROPN
iajs-763	61	9			PROPN
iajs-763	61	10			PROPN
iajs-763	61	11			PROPN
iajs-763	62	1			PUNCT
iajs-763	62	2			PUNCT
iajs-763	63	1			PUNCT
iajs-763	64	1			PUNCT
iajs-763	65	1			PUNCT
iajs-763	66	1			PUNCT
iajs-763	67	1			PUNCT
iajs-763	68	1			PUNCT
iajs-763	69	1			PUNCT
iajs-763	70	1			PUNCT
iajs-763	71	1			PUNCT
iajs-763	72	1			PUNCT
iajs-763	73	1			PUNCT
iajs-763	74	1			PUNCT
iajs-763	75	1			NOUN
iajs-763	76	1			PUNCT
iajs-763	77	1			NOUN
iajs-763	77	2			PROPN
iajs-763	77	3			PROPN
iajs-763	77	4			X
iajs-763	77	5			NOUN
iajs-763	77	6			NOUN
iajs-763	77	7			NOUN
iajs-763	77	8			NOUN
iajs-763	77	9			NOUN
iajs-763	77	10			NOUN
iajs-763	77	11			NOUN
iajs-763	77	12			NOUN
iajs-763	77	13			NOUN
iajs-763	77	14			NOUN
iajs-763	77	15			NOUN
iajs-763	77	16			NOUN
iajs-763	77	17			NOUN
iajs-763	77	18			NOUN
iajs-763	77	19			NOUN
iajs-763	77	20			NOUN
iajs-763	77	21			NOUN
iajs-763	77	22			NOUN
iajs-763	77	23			NOUN
iajs-763	77	24			NOUN
iajs-763	77	25			NOUN
iajs-763	77	26			PROPN
iajs-763	78	1			ADJ
iajs-763	78	2			PROPN
iajs-763	78	3			PROPN
iajs-763	79	1			PUNCT
iajs-763	80	1			PUNCT
iajs-763	81	1			PUNCT
iajs-763	82	1			PUNCT
iajs-763	83	1			PUNCT
iajs-763	84	1			PUNCT
iajs-763	85	1			PUNCT
iajs-763	86	1			PUNCT
iajs-763	87	1			PUNCT
iajs-763	88	1			PUNCT
iajs-763	89	1			PUNCT
iajs-763	90	1			PUNCT
iajs-763	91	1			PUNCT
iajs-763	92	1			PUNCT
iajs-763	93	1			NOUN
iajs-763	94	1			PUNCT
iajs-763	95	1			NOUN
iajs-763	95	2			PROPN
iajs-763	95	3			PROPN
iajs-763	95	4			X
iajs-763	95	5			NOUN
iajs-763	95	6			NOUN
iajs-763	95	7			NOUN
iajs-763	95	8			NOUN
iajs-763	95	9			NOUN
iajs-763	95	10			NOUN
iajs-763	95	11			NOUN
iajs-763	95	12			NOUN
iajs-763	95	13			NOUN
iajs-763	95	14			NOUN
iajs-763	95	15			NOUN
iajs-763	95	16			NOUN
iajs-763	95	17			NOUN
iajs-763	95	18			NOUN
iajs-763	95	19			NOUN
iajs-763	95	20			NOUN
iajs-763	95	21			NOUN
iajs-763	95	22			NOUN
iajs-763	95	23			NOUN
iajs-763	95	24			NOUN
iajs-763	95	25			NOUN
iajs-763	95	26			PROPN
iajs-763	95	27	nm	nm	INTJ
iajs-763	95	28	m	m	VERB
iajs-763	95	29	m	m	VERB
iajs-763	95	30	n	n	PRON
iajs-763	95	31	nm	nm	ADV
iajs-763	95	32	m	m	VERB
iajs-763	95	33	m	m	VERB
iajs-763	95	34	n	n	PRON
iajs-763	95	35	f	f	NOUN
iajs-763	96	1	f	f	PROPN
iajs-763	97	1	f	f	PROPN
iajs-763	98	1	f	f	PROPN
iajs-763	98	2	f	f	PROPN
iajs-763	98	3	f	f	X
iajs-763	98	4	u	u	X
iajs-763	98	5	u	u	VERB
iajs-763	98	6	u	u	X
iajs-763	98	7	u	u	X
iajs-763	98	8	u	u	X
iajs-763	98	9	u	u	NOUN
iajs-763	98	10			VERB
iajs-763	98	11			NUM
iajs-763	98	12			PROPN
iajs-763	98	13			PROPN
iajs-763	98	14			VERB
iajs-763	98	15			NUM
iajs-763	98	16	2	2	NUM
iajs-763	98	17	1	1	NUM
iajs-763	98	18	1	1	NUM
iajs-763	98	19	21	21	NUM
iajs-763	98	20	11	11	NUM
iajs-763	98	21	2	2	NUM
iajs-763	98	22	1	1	NUM
iajs-763	98	23	1	1	NUM
iajs-763	98	24	21	21	NUM
iajs-763	98	25	11	11	NUM
iajs-763	98	26	…	…	PUNCT
iajs-763	98	27	(	(	PUNCT
iajs-763	98	28	6	6	NUM
iajs-763	98	29	)	)	PUNCT
iajs-763	98	30	remark	remark	NOUN
iajs-763	98	31	:	:	PUNCT
iajs-763	98	32	equation	equation	NOUN
iajs-763	98	33	(	(	PUNCT
iajs-763	98	34	6	6	NUM
iajs-763	98	35	)	)	PUNCT
iajs-763	98	36	has	have	VERB
iajs-763	98	37	unique	unique	ADJ
iajs-763	98	38	solution	solution	NOUN
iajs-763	98	39	if	if	SCONJ
iajs-763	98	40	the	the	DET
iajs-763	98	41	determent	determent	NOUN
iajs-763	98	42	of	of	ADP
iajs-763	98	43	the	the	DET
iajs-763	98	44	matrix	matrix	NOUN
iajs-763	98	45	k	k	NOUN
iajs-763	98	46	not	not	PART
iajs-763	98	47	equal	equal	ADJ
iajs-763	98	48	to	to	ADP
iajs-763	98	49	zero	zero	NUM
iajs-763	98	50	also	also	ADV
iajs-763	98	51	,	,	PUNCT
iajs-763	98	52	if	if	SCONJ
iajs-763	98	53	the	the	DET
iajs-763	98	54	number	number	NOUN
iajs-763	98	55	of	of	ADP
iajs-763	98	56	subintervals	subinterval	NOUN
iajs-763	98	57	is	be	AUX
iajs-763	98	58	odd	odd	ADJ
iajs-763	98	59	,	,	PUNCT
iajs-763	98	60	we	we	PRON
iajs-763	98	61	get	get	VERB
iajs-763	98	62	combination	combination	NOUN
iajs-763	98	63	between	between	ADP
iajs-763	98	64	open	open	ADJ
iajs-763	98	65	n	n	CCONJ
iajs-763	98	66	-	-	PUNCT
iajs-763	98	67	c	c	NOUN
iajs-763	98	68	:	:	PUNCT
iajs-763	98	69	n=1	n=1	PROPN
iajs-763	98	70	and	and	CCONJ
iajs-763	98	71	open	open	ADJ
iajs-763	98	72	n	n	CCONJ
iajs-763	98	73	-	-	PUNCT
iajs-763	98	74	c	c	NOUN
iajs-763	98	75	:	:	PUNCT
iajs-763	98	76	n=0	n=0	NUM
iajs-763	98	77	:	:	PUNCT
iajs-763	98	78	midpoint	midpoint	NOUN
iajs-763	98	79	rules	rule	NOUN
iajs-763	98	80	.	.	PUNCT
iajs-763	99	1	therefore	therefore	ADV
iajs-763	99	2	mninru	mninru	VERB
iajs-763	99	3	ir	ir	PROPN
iajs-763	99	4			PRON
iajs-763	99	5	)	)	PUNCT
iajs-763	99	6	2(,,2,1,,,2,1	2(,,2,1,,,2,1	NUM
iajs-763	99	7	,	,	PUNCT
iajs-763	99	8			ADJ
iajs-763	99	9	where	where	SCONJ
iajs-763	99	10	2/)1	2/)1	NOUN
iajs-763	99	11	(	(	PUNCT
iajs-763	99	12			ADJ
iajs-763	99	13	nm	nm	SCONJ
iajs-763	99	14	are	be	AUX
iajs-763	99	15	obtained	obtain	VERB
iajs-763	99	16	by	by	ADP
iajs-763	99	17	solving	solve	VERB
iajs-763	99	18	the	the	DET
iajs-763	99	19	equations	equation	NOUN
iajs-763	99	20	:	:	PUNCT
iajs-763	99	21	2/)1()2(,,2,1,,,2,1,,,2,1	2/)1()2(,,2,1,,,2,1,,,2,1	NUM
iajs-763	99	22	2	2	NUM
iajs-763	99	23	2	2	NUM
iajs-763	99	24	3	3	NUM
iajs-763	99	25	2	2	NUM
iajs-763	99	26	3	3	NUM
iajs-763	99	27	)	)	PUNCT
iajs-763	99	28	2	2	NUM
iajs-763	99	29	(	(	PUNCT
iajs-763	99	30	3	3	NUM
iajs-763	99	31	2211	2211	NUM
iajs-763	99	32			ADJ
iajs-763	99	33			NOUN
iajs-763	99	34			PROPN
iajs-763	100	1			PROPN
iajs-763	100	2			PROPN
iajs-763	100	3	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	100	4	ukhuk	ukhuk	ADJ
iajs-763	100	5	h	h	PROPN
iajs-763	100	6	uk	uk	PROPN
iajs-763	100	7	h	h	PROPN
iajs-763	100	8	fu	fu	PROPN
iajs-763	101	1	mn	mn	PROPN
iajs-763	101	2	j	j	PROPN
iajs-763	101	3	srssrssrsrr	srssrssrsrr	ADV
iajs-763	101	4	jijiiii	jijiiii	VERB
iajs-763	101	5			PROPN
iajs-763	101	6	…	…	PUNCT
iajs-763	101	7	…	…	PUNCT
iajs-763	101	8	(	(	PUNCT
iajs-763	101	9	7	7	X
iajs-763	101	10	)	)	PUNCT
iajs-763	101	11	transform	transform	VERB
iajs-763	101	12	all	all	DET
iajs-763	101	13	the	the	DET
iajs-763	101	14	terms	term	NOUN
iajs-763	101	15	involving	involve	VERB
iajs-763	101	16	the	the	DET
iajs-763	101	17	solution	solution	NOUN
iajs-763	101	18	mninru	mninru	NOUN
iajs-763	101	19	ir	ir	NOUN
iajs-763	101	20			PROPN
iajs-763	101	21	)	)	PUNCT
iajs-763	101	22	2(,,2,1,,,2,1	2(,,2,1,,,2,1	NUM
iajs-763	101	23	,	,	PUNCT
iajs-763	101	24			ADJ
iajs-763	101	25	where	where	SCONJ
iajs-763	101	26	2/)1	2/)1	NOUN
iajs-763	101	27	(	(	PUNCT
iajs-763	101	28			ADJ
iajs-763	101	29	nm	nm	ADP
iajs-763	101	30	to	to	PART
iajs-763	101	31	left	left	VERB
iajs-763	101	32	side	side	NOUN
iajs-763	101	33	of	of	ADP
iajs-763	101	34	the	the	DET
iajs-763	101	35	equation	equation	NOUN
iajs-763	101	36	(	(	PUNCT
iajs-763	101	37	7	7	NUM
iajs-763	101	38	)	)	PUNCT
iajs-763	101	39	and	and	CCONJ
iajs-763	101	40	ir	ir	PROPN
iajs-763	101	41	f	f	X
iajs-763	101	42	to	to	ADP
iajs-763	101	43	the	the	DET
iajs-763	101	44	right	right	ADJ
iajs-763	101	45	side	side	NOUN
iajs-763	101	46	.	.	PUNCT
iajs-763	102	1	ibn	ibn	PROPN
iajs-763	102	2	alhaitham	alhaitham	PROPN
iajs-763	102	3	j.	j.	PROPN
iajs-763	102	4	for	for	ADP
iajs-763	102	5	pure	pure	ADJ
iajs-763	102	6	&	&	CCONJ
iajs-763	102	7	appl	appl	PROPN
iajs-763	102	8	.	.	PUNCT
iajs-763	103	1	sci	sci	PROPN
iajs-763	103	2	.	.	PUNCT
iajs-763	103	3	vol.24	vol.24	NOUN
iajs-763	103	4	(	(	PUNCT
iajs-763	103	5	2	2	NUM
iajs-763	103	6	)	)	PUNCT
iajs-763	103	7	2011	2011	NUM
iajs-763	103	8	finally	finally	ADV
iajs-763	103	9	,	,	PUNCT
iajs-763	103	10	each	each	PRON
iajs-763	103	11	of	of	ADP
iajs-763	103	12	system	system	NOUN
iajs-763	103	13	in	in	ADP
iajs-763	103	14	equations	equation	NOUN
iajs-763	103	15	(	(	PUNCT
iajs-763	103	16	6	6	NUM
iajs-763	103	17	)	)	PUNCT
iajs-763	103	18	and	and	CCONJ
iajs-763	103	19	(	(	PUNCT
iajs-763	103	20	7	7	X
iajs-763	103	21	)	)	PUNCT
iajs-763	103	22	can	can	AUX
iajs-763	103	23	be	be	AUX
iajs-763	103	24	written	write	VERB
iajs-763	103	25	in	in	ADP
iajs-763	103	26	matrix	matrix	NOUN
iajs-763	103	27	form	form	NOUN
iajs-763	103	28	as	as	ADP
iajs-763	103	29	fku	fku	PROPN
iajs-763	103	30			PROPN
iajs-763	103	31	where	where	SCONJ
iajs-763	103	32	k	k	PROPN
iajs-763	103	33	is	be	AUX
iajs-763	103	34	the	the	DET
iajs-763	103	35	matrix	matrix	NOUN
iajs-763	103	36	of	of	ADP
iajs-763	103	37	the	the	DET
iajs-763	103	38	coefficients	coefficient	NOUN
iajs-763	103	39	,	,	PUNCT
iajs-763	103	40	u	u	NOUN
iajs-763	103	41	is	be	AUX
iajs-763	103	42	the	the	DET
iajs-763	103	43	matrix	matrix	NOUN
iajs-763	103	44	of	of	ADP
iajs-763	103	45	solution	solution	NOUN
iajs-763	103	46	and	and	CCONJ
iajs-763	103	47	f	f	PROPN
iajs-763	103	48	is	be	AUX
iajs-763	103	49	the	the	DET
iajs-763	103	50	matrix	matrix	NOUN
iajs-763	103	51	of	of	ADP
iajs-763	103	52	non	non	ADJ
iajs-763	103	53	-	-	ADJ
iajs-763	103	54	homogeneous	homogeneous	ADJ
iajs-763	103	55	part	part	NOUN
iajs-763	103	56	.	.	PUNCT
iajs-763	104	1	to	to	PART
iajs-763	104	2	find	find	VERB
iajs-763	104	3	the	the	DET
iajs-763	104	4	approximate	approximate	ADJ
iajs-763	104	5	solution	solution	NOUN
iajs-763	104	6	nru	nru	PROPN
iajs-763	104	7	ir	ir	PROPN
iajs-763	104	8	,	,	PUNCT
iajs-763	104	9	,	,	PUNCT
iajs-763	104	10	2,1	2,1	NUM
iajs-763	104	11	,	,	PUNCT
iajs-763	104	12			NUM
iajs-763	104	13	we	we	PRON
iajs-763	104	14	find	find	VERB
iajs-763	104	15	fku	fku	PROPN
iajs-763	104	16	1	1	NUM
iajs-763	104	17	.	.	PUNCT
iajs-763	105	1	the	the	DET
iajs-763	105	2	algorithm	algorithm	NOUN
iajs-763	105	3	of	of	ADP
iajs-763	105	4	numerical	numerical	ADJ
iajs-763	105	5	solution	solution	NOUN
iajs-763	105	6	of	of	ADP
iajs-763	105	7	a	a	DET
iajs-763	105	8	s	s	NOUN
iajs-763	105	9	ystem	ystem	NOUN
iajs-763	105	10	of	of	ADP
iajs-763	105	11	linear	linear	PROPN
iajs-763	105	12	fredholm	fredholm	NOUN
iajs-763	105	13	integral	integral	ADJ
iajs-763	105	14	equations	equation	NOUN
iajs-763	105	15	using	use	VERB
iajs-763	105	16	open	open	ADJ
iajs-763	105	17	n	n	CCONJ
iajs-763	105	18	-	-	PUNCT
iajs-763	105	19	c	c	NOUN
iajs-763	105	20	:	:	PUNCT
iajs-763	105	21	{	{	PUNCT
iajs-763	105	22	n=0	n=0	X
iajs-763	105	23	}	}	PUNCT
iajs-763	105	24	(	(	PUNCT
iajs-763	105	25	soncn0	soncn0	NOUN
iajs-763	105	26	)	)	PUNCT
iajs-763	105	27	step	step	NOUN
iajs-763	105	28	1	1	NUM
iajs-763	105	29	:	:	PUNCT
iajs-763	105	30	compute	compute	VERB
iajs-763	105	31	2	2	NUM
iajs-763	105	32			PROPN
iajs-763	105	33			PROPN
iajs-763	105	34	n	n	CCONJ
iajs-763	105	35	ab	ab	NOUN
iajs-763	105	36	h	h	NOUN
iajs-763	105	37	,	,	PUNCT
iajs-763	105	38	nn	nn	ADJ
iajs-763	105	39	step	step	NOUN
iajs-763	105	40	2	2	NUM
iajs-763	105	41	:	:	PUNCT
iajs-763	105	42			PROPN
iajs-763	105	43	compute	compute	PROPN
iajs-763	105	44	2/,,1,0,,,2,1	2/,,1,0,,,2,1	NUM
iajs-763	105	45	,	,	PUNCT
iajs-763	105	46	2	2	NUM
iajs-763	105	47	nminru	nminru	NOUN
iajs-763	105	48	ir	ir	PROPN
iajs-763	105	49			VERB
iajs-763	105	50			ADV
iajs-763	105	51	,	,	PUNCT
iajs-763	105	52	using	use	VERB
iajs-763	105	53	equation	equation	NOUN
iajs-763	105	54	(	(	PUNCT
iajs-763	105	55	6	6	NUM
iajs-763	105	56	)	)	PUNCT
iajs-763	105	57	when	when	SCONJ
iajs-763	105	58	the	the	DET
iajs-763	105	59	number	number	NOUN
iajs-763	105	60	of	of	ADP
iajs-763	105	61	subintervals	subinterval	NOUN
iajs-763	105	62	is	be	AUX
iajs-763	105	63	even	even	ADV
iajs-763	105	64	.	.	PUNCT
iajs-763	106	1			PROPN
iajs-763	106	2	compute	compute	PROPN
iajs-763	106	3	mninru	mninru	NOUN
iajs-763	106	4	ir	ir	PROPN
iajs-763	106	5			PROPN
iajs-763	106	6	)	)	PUNCT
iajs-763	106	7	2(,,2,1,,,2,1	2(,,2,1,,,2,1	NUM
iajs-763	106	8	,	,	PUNCT
iajs-763	106	9			ADJ
iajs-763	106	10	where	where	SCONJ
iajs-763	106	11	2/)1	2/)1	NOUN
iajs-763	106	12	(	(	PUNCT
iajs-763	106	13			ADJ
iajs-763	106	14	nm	nm	NOUN
iajs-763	106	15	,	,	PUNCT
iajs-763	106	16	using	use	VERB
iajs-763	106	17	equation	equation	NOUN
iajs-763	106	18	(	(	PUNCT
iajs-763	106	19	7	7	NUM
iajs-763	106	20	)	)	PUNCT
iajs-763	106	21	when	when	SCONJ
iajs-763	106	22	the	the	DET
iajs-763	106	23	number	number	NOUN
iajs-763	106	24	of	of	ADP
iajs-763	106	25	subintervals	subinterval	NOUN
iajs-763	106	26	is	be	AUX
iajs-763	106	27	odd	odd	ADJ
iajs-763	106	28	.	.	PUNCT
iajs-763	107	1	step	step	NOUN
iajs-763	107	2	3	3	NUM
iajs-763	107	3	:	:	PUNCT
iajs-763	107	4	solve	solve	VERB
iajs-763	107	5	the	the	DET
iajs-763	107	6	resulting	result	VERB
iajs-763	107	7	system	system	NOUN
iajs-763	107	8	by	by	ADP
iajs-763	107	9	multiplication	multiplication	NOUN
iajs-763	107	10	it	it	PRON
iajs-763	107	11	with	with	ADP
iajs-763	107	12	k-1	k-1	PROPN
iajs-763	107	13	.	.	PUNCT
iajs-763	108	1	2.2	2.2	NUM
iajs-763	108	2	using	use	VERB
iajs-763	108	3	open	open	ADJ
iajs-763	108	4	n	n	CCONJ
iajs-763	108	5	-	-	PUNCT
iajs-763	108	6	c	c	NOUN
iajs-763	108	7	:	:	PUNCT
iajs-763	108	8	n=1	n=1	NOUN
iajs-763	108	9	rule	rule	NOUN
iajs-763	108	10	by	by	ADP
iajs-763	108	11	the	the	DET
iajs-763	108	12	same	same	ADJ
iajs-763	108	13	steps	step	NOUN
iajs-763	108	14	of	of	ADP
iajs-763	108	15	condition	condition	NOUN
iajs-763	108	16	on	on	ADP
iajs-763	108	17	equation	equation	NOUN
iajs-763	108	18	(	(	PUNCT
iajs-763	108	19	4	4	NUM
iajs-763	108	20	)	)	PUNCT
iajs-763	108	21	,	,	PUNCT
iajs-763	108	22	use	use	VERB
iajs-763	108	23	the	the	DET
iajs-763	108	24	open	open	ADJ
iajs-763	108	25	n	n	CCONJ
iajs-763	108	26	-	-	PUNCT
iajs-763	108	27	c	c	NOUN
iajs-763	108	28	where	where	SCONJ
iajs-763	108	29	n=1	n=1	PUNCT
iajs-763	108	30	formula	formula	NOUN
iajs-763	108	31	to	to	PART
iajs-763	108	32	approximate	approximate	VERB
iajs-763	108	33	each	each	DET
iajs-763	108	34	integral	integral	ADJ
iajs-763	108	35	term	term	NOUN
iajs-763	108	36	in	in	ADP
iajs-763	108	37	equation	equation	NOUN
iajs-763	108	38	(	(	PUNCT
iajs-763	108	39	4	4	NUM
iajs-763	108	40	)	)	PUNCT
iajs-763	108	41	.	.	PUNCT
iajs-763	109	1	if	if	SCONJ
iajs-763	109	2	the	the	DET
iajs-763	109	3	number	number	NOUN
iajs-763	109	4	of	of	ADP
iajs-763	109	5	subintervals	subinterval	NOUN
iajs-763	109	6	is	be	AUX
iajs-763	109	7	(	(	PUNCT
iajs-763	109	8	a	a	DET
iajs-763	109	9	multiple	multiple	NOUN
iajs-763	109	10	of	of	ADP
iajs-763	109	11	three	three	NUM
iajs-763	109	12	)	)	PUNCT
iajs-763	109	13	.	.	PUNCT
iajs-763	110	1	therefore	therefore	ADV
iajs-763	110	2	mninru	mninru	VERB
iajs-763	110	3	ir	ir	PROPN
iajs-763	110	4			PRON
iajs-763	110	5	)	)	PUNCT
iajs-763	110	6	2(,,2,1,,,2,1	2(,,2,1,,,2,1	NUM
iajs-763	110	7	,	,	PUNCT
iajs-763	110	8			ADJ
iajs-763	110	9	where	where	SCONJ
iajs-763	110	10	3/)2	3/)2	NOUN
iajs-763	110	11	(	(	PUNCT
iajs-763	110	12			ADJ
iajs-763	110	13	nm	nm	SCONJ
iajs-763	110	14	are	be	AUX
iajs-763	110	15	obtained	obtain	VERB
iajs-763	110	16	by	by	ADP
iajs-763	110	17	solving	solve	VERB
iajs-763	110	18	the	the	DET
iajs-763	110	19	equations	equation	NOUN
iajs-763	110	20	:	:	PUNCT
iajs-763	110	21	we	we	PRON
iajs-763	110	22	apply	apply	VERB
iajs-763	110	23	open	open	ADJ
iajs-763	110	24	n	n	CCONJ
iajs-763	110	25	-	-	PUNCT
iajs-763	110	26	c	c	NOUN
iajs-763	110	27	with	with	ADP
iajs-763	110	28	(	(	PUNCT
iajs-763	110	29	n=1	n=1	PROPN
iajs-763	110	30	)	)	PUNCT
iajs-763	110	31	.	.	PUNCT
iajs-763	111	1	therefore	therefore	ADV
iajs-763	111	2	nru	nru	PROPN
iajs-763	111	3	ir	ir	PROPN
iajs-763	111	4	,	,	PUNCT
iajs-763	111	5	,	,	PUNCT
iajs-763	111	6	2,1	2,1	NUM
iajs-763	111	7	,	,	PUNCT
iajs-763	111	8			PUNCT
iajs-763	111	9	mni	mni	X
iajs-763	111	10			PROPN
iajs-763	111	11	)	)	PUNCT
iajs-763	111	12	2(,,2,1	2(,,2,1	NUM
iajs-763	111	13	,	,	PUNCT
iajs-763	111	14			NOUN
iajs-763	111	15	,	,	PUNCT
iajs-763	111	16	where	where	SCONJ
iajs-763	111	17	3/)2	3/)2	NOUN
iajs-763	111	18	(	(	PUNCT
iajs-763	111	19			ADJ
iajs-763	111	20	nm	nm	SCONJ
iajs-763	111	21	are	be	AUX
iajs-763	111	22	obtained	obtain	VERB
iajs-763	111	23	by	by	ADP
iajs-763	111	24	solving	solve	VERB
iajs-763	111	25	the	the	DET
iajs-763	111	26	equations	equation	NOUN
iajs-763	111	27	:	:	PUNCT
iajs-763	112	1	where	where	SCONJ
iajs-763	112	2	3/)2	3/)2	NOUN
iajs-763	112	3	(	(	PUNCT
iajs-763	112	4			ADJ
iajs-763	112	5	nm	nm	ADV
iajs-763	112	6			NOUN
iajs-763	112	7			PROPN
iajs-763	112	8	nsnrmniuxxk	nsnrmniuxxk	PROPN
iajs-763	112	9	h	h	PROPN
iajs-763	112	10	fu	fu	PROPN
iajs-763	112	11	jii	jii	PROPN
iajs-763	112	12	s	s	PROPN
iajs-763	112	13	mn	mn	PROPN
iajs-763	112	14	j	j	PROPN
iajs-763	112	15	jirsrr	jirsrr	ADV
iajs-763	112	16	,	,	PUNCT
iajs-763	112	17	,	,	PUNCT
iajs-763	112	18	2,1,,,2,1,)2(,,2,1	2,1,,,2,1,)2(,,2,1	NUM
iajs-763	112	19	,	,	PUNCT
iajs-763	112	20	)	)	PUNCT
iajs-763	112	21	,	,	PUNCT
iajs-763	112	22	(	(	PUNCT
iajs-763	112	23	2	2	NUM
iajs-763	112	24	3	3	NUM
iajs-763	112	25	)	)	PUNCT
iajs-763	112	26	2	2	NUM
iajs-763	112	27	(	(	PUNCT
iajs-763	112	28	1	1	NUM
iajs-763	112	29			PROPN
iajs-763	112	30			PROPN
iajs-763	112	31			X
iajs-763	112	32			NOUN
iajs-763	112	33			NUM
iajs-763	112	34	…	…	PUNCT
iajs-763	112	35	..	..	PUNCT
iajs-763	112	36	(	(	PUNCT
iajs-763	112	37	8)	8)	NUM
iajs-763	112	38	where	where	SCONJ
iajs-763	112	39	ir	ir	PUNCT
iajs-763	112	40	u	u	PROPN
iajs-763	112	41	denote	denote	VERB
iajs-763	112	42	the	the	DET
iajs-763	112	43	numerical	numerical	ADJ
iajs-763	112	44	solution	solution	NOUN
iajs-763	112	45	at	at	ADP
iajs-763	112	46	,	,	PUNCT
iajs-763	112	47	3/)2	3/)2	PROPN
iajs-763	112	48	(	(	PUNCT
iajs-763	112	49			ADJ
iajs-763	112	50	nmwhere	nmwhere	ADJ
iajs-763	112	51	transform	transform	VERB
iajs-763	112	52	all	all	DET
iajs-763	112	53	the	the	DET
iajs-763	112	54	terms	term	NOUN
iajs-763	112	55	involving	involve	VERB
iajs-763	112	56	the	the	DET
iajs-763	112	57	solution	solution	NOUN
iajs-763	112	58	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	112	59	…	…	SYM
iajs-763	112	60	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	112	61	,	,	PUNCT
iajs-763	112	62	nru	nru	PROPN
iajs-763	112	63	ir	ir	PROPN
iajs-763	112	64			NUM
iajs-763	112	65	to	to	AUX
iajs-763	112	66	left	left	ADJ
iajs-763	112	67	side	side	NOUN
iajs-763	112	68	of	of	ADP
iajs-763	112	69	the	the	DET
iajs-763	112	70	equation	equation	NOUN
iajs-763	112	71	(	(	PUNCT
iajs-763	112	72	8)	8)	NUM
iajs-763	112	73	and	and	CCONJ
iajs-763	112	74	i	i	PRON
iajs-763	112	75	fr	fr	INTJ
iajs-763	112	76	to	to	ADP
iajs-763	112	77	the	the	DET
iajs-763	112	78	right	right	ADJ
iajs-763	112	79	side	side	NOUN
iajs-763	112	80	.	.	PUNCT
iajs-763	113	1	ibn	ibn	PROPN
iajs-763	113	2	alhaitham	alhaitham	PROPN
iajs-763	113	3	j.	j.	PROPN
iajs-763	113	4	for	for	ADP
iajs-763	113	5	pure	pure	ADJ
iajs-763	113	6	&	&	CCONJ
iajs-763	113	7	appl	appl	PROPN
iajs-763	113	8	.	.	PUNCT
iajs-763	114	1	sci	sci	PROPN
iajs-763	114	2	.	.	PUNCT
iajs-763	114	3	vol.24	vol.24	NOUN
iajs-763	114	4	(	(	PUNCT
iajs-763	114	5	2	2	NUM
iajs-763	114	6	)	)	PUNCT
iajs-763	114	7	2011	2011	NUM
iajs-763	114	8			NOUN
iajs-763	115	1			PUNCT
iajs-763	115	2			PUNCT
iajs-763	116	1			PUNCT
iajs-763	117	1			PUNCT
iajs-763	118	1			PUNCT
iajs-763	119	1			PUNCT
iajs-763	120	1			PUNCT
iajs-763	121	1			PUNCT
iajs-763	122	1			PUNCT
iajs-763	123	1			PUNCT
iajs-763	124	1			PUNCT
iajs-763	125	1			PUNCT
iajs-763	126	1			PUNCT
iajs-763	127	1			PUNCT
iajs-763	128	1			PUNCT
iajs-763	129	1			NOUN
iajs-763	130	1			PUNCT
iajs-763	131	1			NOUN
iajs-763	131	2			PROPN
iajs-763	131	3			PROPN
iajs-763	131	4			X
iajs-763	131	5			NOUN
iajs-763	131	6			NOUN
iajs-763	131	7			NOUN
iajs-763	131	8			NOUN
iajs-763	131	9			NOUN
iajs-763	131	10			NOUN
iajs-763	131	11			NOUN
iajs-763	131	12			NOUN
iajs-763	131	13			NOUN
iajs-763	131	14			NOUN
iajs-763	131	15			NOUN
iajs-763	131	16			NOUN
iajs-763	131	17			NOUN
iajs-763	131	18			NOUN
iajs-763	131	19			NOUN
iajs-763	131	20			NOUN
iajs-763	131	21			NOUN
iajs-763	131	22			NOUN
iajs-763	131	23			NOUN
iajs-763	131	24			NOUN
iajs-763	131	25			VERB
iajs-763	131	26			PROPN
iajs-763	131	27			NOUN
iajs-763	131	28			NOUN
iajs-763	131	29			NOUN
iajs-763	131	30			NOUN
iajs-763	131	31			NOUN
iajs-763	131	32			NOUN
iajs-763	131	33	)	)	PUNCT
iajs-763	131	34	,	,	PUNCT
iajs-763	131	35	(	(	PUNCT
iajs-763	131	36	2	2	NUM
iajs-763	131	37	3	3	NUM
iajs-763	131	38	1	1	NUM
iajs-763	131	39	)	)	PUNCT
iajs-763	131	40	,	,	PUNCT
iajs-763	131	41	(	(	PUNCT
iajs-763	131	42	2	2	NUM
iajs-763	131	43	3	3	NUM
iajs-763	131	44	)	)	PUNCT
iajs-763	131	45	,	,	PUNCT
iajs-763	131	46	(	(	PUNCT
iajs-763	131	47	2	2	NUM
iajs-763	131	48	3	3	NUM
iajs-763	131	49	)	)	PUNCT
iajs-763	131	50	,	,	PUNCT
iajs-763	131	51	(	(	PUNCT
iajs-763	131	52	2	2	NUM
iajs-763	131	53	3	3	NUM
iajs-763	131	54	)	)	PUNCT
iajs-763	131	55	,	,	PUNCT
iajs-763	131	56	(	(	PUNCT
iajs-763	131	57	2	2	NUM
iajs-763	131	58	3	3	NUM
iajs-763	131	59	)	)	PUNCT
iajs-763	131	60	,	,	PUNCT
iajs-763	131	61	(	(	PUNCT
iajs-763	131	62	2	2	NUM
iajs-763	131	63	3	3	NUM
iajs-763	131	64	)	)	PUNCT
iajs-763	131	65	,	,	PUNCT
iajs-763	131	66	(	(	PUNCT
iajs-763	131	67	2	2	NUM
iajs-763	131	68	3	3	NUM
iajs-763	131	69	)	)	PUNCT
iajs-763	131	70	,	,	PUNCT
iajs-763	131	71	(	(	PUNCT
iajs-763	131	72	2	2	NUM
iajs-763	131	73	3	3	NUM
iajs-763	131	74	1	1	NUM
iajs-763	131	75	)	)	PUNCT
iajs-763	131	76	,	,	PUNCT
iajs-763	131	77	(	(	PUNCT
iajs-763	131	78	2	2	NUM
iajs-763	131	79	3	3	NUM
iajs-763	131	80	)	)	PUNCT
iajs-763	131	81	,	,	PUNCT
iajs-763	131	82	(	(	PUNCT
iajs-763	131	83	2	2	NUM
iajs-763	131	84	3	3	NUM
iajs-763	131	85	)	)	PUNCT
iajs-763	131	86	,	,	PUNCT
iajs-763	131	87	(	(	PUNCT
iajs-763	131	88	2	2	NUM
iajs-763	131	89	3	3	NUM
iajs-763	131	90	)	)	PUNCT
iajs-763	131	91	,	,	PUNCT
iajs-763	131	92	(	(	PUNCT
iajs-763	131	93	2	2	NUM
iajs-763	131	94	3	3	NUM
iajs-763	131	95	)	)	PUNCT
iajs-763	131	96	,	,	PUNCT
iajs-763	131	97	(	(	PUNCT
iajs-763	131	98	2	2	NUM
iajs-763	131	99	3	3	NUM
iajs-763	131	100	)	)	PUNCT
iajs-763	131	101	,	,	PUNCT
iajs-763	131	102	(	(	PUNCT
iajs-763	131	103	2	2	NUM
iajs-763	131	104	3	3	NUM
iajs-763	131	105	)	)	PUNCT
iajs-763	131	106	,	,	PUNCT
iajs-763	131	107	(	(	PUNCT
iajs-763	131	108	2	2	NUM
iajs-763	131	109	3	3	NUM
iajs-763	131	110	1	1	NUM
iajs-763	131	111	)	)	PUNCT
iajs-763	131	112	,	,	PUNCT
iajs-763	131	113	(	(	PUNCT
iajs-763	131	114	2	2	NUM
iajs-763	131	115	3	3	NUM
iajs-763	131	116	)	)	PUNCT
iajs-763	131	117	,	,	PUNCT
iajs-763	131	118	(	(	PUNCT
iajs-763	131	119	2	2	NUM
iajs-763	131	120	3	3	NUM
iajs-763	131	121	)	)	PUNCT
iajs-763	131	122	,	,	PUNCT
iajs-763	131	123	(	(	PUNCT
iajs-763	131	124	2	2	NUM
iajs-763	131	125	3	3	NUM
iajs-763	131	126	)	)	PUNCT
iajs-763	131	127	,	,	PUNCT
iajs-763	131	128	(	(	PUNCT
iajs-763	131	129	2	2	NUM
iajs-763	131	130	3	3	NUM
iajs-763	131	131	)	)	PUNCT
iajs-763	131	132	,	,	PUNCT
iajs-763	131	133	(	(	PUNCT
iajs-763	131	134	2	2	NUM
iajs-763	131	135	3	3	NUM
iajs-763	131	136	)	)	PUNCT
iajs-763	131	137	,	,	PUNCT
iajs-763	131	138	(	(	PUNCT
iajs-763	131	139	2	2	NUM
iajs-763	131	140	3	3	NUM
iajs-763	131	141	)	)	PUNCT
iajs-763	131	142	,	,	PUNCT
iajs-763	131	143	(	(	PUNCT
iajs-763	131	144	2	2	NUM
iajs-763	131	145	3	3	NUM
iajs-763	131	146	1	1	NUM
iajs-763	131	147	)	)	PUNCT
iajs-763	131	148	,	,	PUNCT
iajs-763	131	149	(	(	PUNCT
iajs-763	131	150	2	2	NUM
iajs-763	131	151	3	3	NUM
iajs-763	131	152	)	)	PUNCT
iajs-763	131	153	,	,	PUNCT
iajs-763	131	154	(	(	PUNCT
iajs-763	131	155	2	2	NUM
iajs-763	131	156	3	3	NUM
iajs-763	131	157	)	)	PUNCT
iajs-763	131	158	,	,	PUNCT
iajs-763	131	159	(	(	PUNCT
iajs-763	131	160	2	2	NUM
iajs-763	131	161	3	3	NUM
iajs-763	131	162	)	)	PUNCT
iajs-763	131	163	,	,	PUNCT
iajs-763	131	164	(	(	PUNCT
iajs-763	131	165	2	2	NUM
iajs-763	131	166	3	3	NUM
iajs-763	131	167	)	)	PUNCT
iajs-763	131	168	,	,	PUNCT
iajs-763	131	169	(	(	PUNCT
iajs-763	131	170	2	2	NUM
iajs-763	131	171	3	3	NUM
iajs-763	131	172	)	)	PUNCT
iajs-763	131	173	,	,	PUNCT
iajs-763	131	174	(	(	PUNCT
iajs-763	131	175	2	2	NUM
iajs-763	131	176	3	3	NUM
iajs-763	131	177	)	)	PUNCT
iajs-763	131	178	,	,	PUNCT
iajs-763	131	179	(	(	PUNCT
iajs-763	131	180	2	2	NUM
iajs-763	131	181	3	3	NUM
iajs-763	131	182	1	1	NUM
iajs-763	131	183	)	)	PUNCT
iajs-763	131	184	,	,	PUNCT
iajs-763	131	185	(	(	PUNCT
iajs-763	131	186	2	2	NUM
iajs-763	131	187	3	3	NUM
iajs-763	131	188	)	)	PUNCT
iajs-763	131	189	,	,	PUNCT
iajs-763	131	190	(	(	PUNCT
iajs-763	131	191	2	2	NUM
iajs-763	131	192	3	3	NUM
iajs-763	131	193	)	)	PUNCT
iajs-763	131	194	,	,	PUNCT
iajs-763	131	195	(	(	PUNCT
iajs-763	131	196	2	2	NUM
iajs-763	131	197	3	3	NUM
iajs-763	131	198	)	)	PUNCT
iajs-763	131	199	,	,	PUNCT
iajs-763	131	200	(	(	PUNCT
iajs-763	131	201	2	2	NUM
iajs-763	131	202	3	3	NUM
iajs-763	131	203	)	)	PUNCT
iajs-763	131	204	,	,	PUNCT
iajs-763	131	205	(	(	PUNCT
iajs-763	131	206	2	2	NUM
iajs-763	131	207	3	3	NUM
iajs-763	131	208	)	)	PUNCT
iajs-763	131	209	,	,	PUNCT
iajs-763	131	210	(	(	PUNCT
iajs-763	131	211	2	2	NUM
iajs-763	131	212	3	3	NUM
iajs-763	131	213	)	)	PUNCT
iajs-763	131	214	,	,	PUNCT
iajs-763	131	215	(	(	PUNCT
iajs-763	131	216	2	2	NUM
iajs-763	131	217	3	3	NUM
iajs-763	131	218	1	1	NUM
iajs-763	131	219	2112111	2112111	NUM
iajs-763	131	220	2221221221121	2221221221121	NUM
iajs-763	131	221	1211111211111	1211111211111	NUM
iajs-763	131	222	1211111211111	1211111211111	NUM
iajs-763	131	223	2122112121122111211	2122112121122111211	NUM
iajs-763	131	224	1121111111121111111	1121111111121111111	NUM
iajs-763	131	225	mmnnmnnmnnmmnmnmn	mmnnmnnmnnmmnmnmn	PROPN
iajs-763	131	226	mnnnnnnmnnn	mnnnnnnmnnn	NOUN
iajs-763	131	227	mnnnnnnmnnn	mnnnnnnmnnn	NOUN
iajs-763	131	228	mmnmnmnmmmm	mmnmnmnmmmm	PROPN
iajs-763	131	229	mnnnm	mnnnm	ADJ
iajs-763	131	230	mnnnm	mnnnm	ADJ
iajs-763	131	231	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	NOUN
iajs-763	131	232	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	131	233	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	131	234	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	131	235	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	131	236	xxhkxxhkxxhkxxhkxxhkxxhk	xxhkxxhkxxhkxxhkxxhkxxhk	PROPN
iajs-763	132	1			PROPN
iajs-763	132	2			VERB
iajs-763	132	3			PROPN
iajs-763	132	4			PROPN
iajs-763	132	5			NUM
iajs-763	132	6			PROPN
iajs-763	132	7			VERB
iajs-763	132	8			PROPN
iajs-763	132	9			PROPN
iajs-763	132	10			PROPN
iajs-763	132	11			PROPN
iajs-763	133	1			PUNCT
iajs-763	133	2			PUNCT
iajs-763	134	1			PUNCT
iajs-763	135	1			PUNCT
iajs-763	136	1			PUNCT
iajs-763	137	1			PUNCT
iajs-763	138	1			PUNCT
iajs-763	139	1			PUNCT
iajs-763	140	1			PUNCT
iajs-763	141	1			PUNCT
iajs-763	142	1			PUNCT
iajs-763	143	1			PUNCT
iajs-763	144	1			PUNCT
iajs-763	145	1			PUNCT
iajs-763	146	1			NOUN
iajs-763	147	1			PUNCT
iajs-763	148	1			NOUN
iajs-763	148	2			PROPN
iajs-763	148	3			PROPN
iajs-763	148	4			X
iajs-763	148	5			NOUN
iajs-763	148	6			NOUN
iajs-763	148	7			NOUN
iajs-763	148	8			NOUN
iajs-763	148	9			NOUN
iajs-763	148	10			NOUN
iajs-763	148	11			NOUN
iajs-763	148	12			NOUN
iajs-763	148	13			NOUN
iajs-763	148	14			NOUN
iajs-763	148	15			NOUN
iajs-763	148	16			NOUN
iajs-763	148	17			NOUN
iajs-763	148	18			NOUN
iajs-763	148	19			NOUN
iajs-763	148	20			NOUN
iajs-763	148	21			NOUN
iajs-763	148	22			NOUN
iajs-763	148	23			NOUN
iajs-763	148	24			NOUN
iajs-763	148	25			NOUN
iajs-763	148	26			PROPN
iajs-763	149	1			ADJ
iajs-763	149	2			PROPN
iajs-763	149	3			PROPN
iajs-763	150	1			PUNCT
iajs-763	151	1			PUNCT
iajs-763	152	1			PUNCT
iajs-763	153	1			PUNCT
iajs-763	154	1			PUNCT
iajs-763	155	1			PUNCT
iajs-763	156	1			PUNCT
iajs-763	157	1			PUNCT
iajs-763	158	1			PUNCT
iajs-763	159	1			PUNCT
iajs-763	160	1			PUNCT
iajs-763	161	1			PUNCT
iajs-763	162	1			PUNCT
iajs-763	163	1			PUNCT
iajs-763	164	1			NOUN
iajs-763	165	1			PUNCT
iajs-763	166	1			NOUN
iajs-763	166	2			PROPN
iajs-763	166	3			PROPN
iajs-763	166	4			X
iajs-763	166	5			NOUN
iajs-763	166	6			NOUN
iajs-763	166	7			NOUN
iajs-763	166	8			NOUN
iajs-763	166	9			NOUN
iajs-763	166	10			NOUN
iajs-763	166	11			NOUN
iajs-763	166	12			NOUN
iajs-763	166	13			NOUN
iajs-763	166	14			NOUN
iajs-763	166	15			NOUN
iajs-763	166	16			NOUN
iajs-763	166	17			NOUN
iajs-763	166	18			NOUN
iajs-763	166	19			NOUN
iajs-763	166	20			NOUN
iajs-763	166	21			NOUN
iajs-763	166	22			NOUN
iajs-763	166	23			NOUN
iajs-763	166	24			NOUN
iajs-763	166	25			NOUN
iajs-763	166	26			PROPN
iajs-763	166	27	nm	nm	INTJ
iajs-763	166	28	m	m	VERB
iajs-763	166	29	m	m	VERB
iajs-763	166	30	n	n	PRON
iajs-763	166	31	nm	nm	ADV
iajs-763	166	32	m	m	VERB
iajs-763	166	33	m	m	VERB
iajs-763	166	34	n	n	PRON
iajs-763	166	35	f	f	NOUN
iajs-763	167	1	f	f	PROPN
iajs-763	168	1	f	f	PROPN
iajs-763	169	1	f	f	PROPN
iajs-763	169	2	f	f	PROPN
iajs-763	169	3	f	f	X
iajs-763	169	4	u	u	X
iajs-763	169	5	u	u	VERB
iajs-763	169	6	u	u	X
iajs-763	169	7	u	u	X
iajs-763	169	8	u	u	X
iajs-763	169	9	u	u	NOUN
iajs-763	169	10			VERB
iajs-763	169	11			NUM
iajs-763	169	12			PROPN
iajs-763	169	13			PROPN
iajs-763	169	14			VERB
iajs-763	169	15			NUM
iajs-763	169	16	2	2	NUM
iajs-763	169	17	1	1	NUM
iajs-763	169	18	1	1	NUM
iajs-763	169	19	21	21	NUM
iajs-763	169	20	11	11	NUM
iajs-763	169	21	2	2	NUM
iajs-763	169	22	1	1	NUM
iajs-763	169	23	1	1	NUM
iajs-763	169	24	21	21	NUM
iajs-763	169	25	11	11	NUM
iajs-763	169	26	…	…	PUNCT
iajs-763	169	27	.....	.....	PUNCT
iajs-763	169	28	(	(	PUNCT
iajs-763	169	29	9	9	NUM
iajs-763	169	30	)	)	PUNCT
iajs-763	169	31	also	also	ADV
iajs-763	169	32	,	,	PUNCT
iajs-763	169	33	if	if	SCONJ
iajs-763	169	34	the	the	DET
iajs-763	169	35	number	number	NOUN
iajs-763	169	36	of	of	ADP
iajs-763	169	37	subintervals	subinterval	NOUN
iajs-763	169	38	is	be	AUX
iajs-763	169	39	(	(	PUNCT
iajs-763	169	40	a	a	DET
iajs-763	169	41	multiple	multiple	NOUN
iajs-763	169	42	of	of	ADP
iajs-763	169	43	three	three	NUM
iajs-763	169	44	+1	+1	PROPN
iajs-763	169	45	)	)	PUNCT
iajs-763	169	46	,	,	PUNCT
iajs-763	169	47	we	we	PRON
iajs-763	169	48	get	get	VERB
iajs-763	169	49	combination	combination	NOUN
iajs-763	169	50	between	between	ADP
iajs-763	169	51	open	open	ADJ
iajs-763	169	52	n	n	CCONJ
iajs-763	169	53	-	-	PUNCT
iajs-763	169	54	c	c	NOUN
iajs-763	169	55	:	:	PUNCT
iajs-763	169	56	n=0	n=0	NUM
iajs-763	169	57	midpoint	midpoint	NOUN
iajs-763	169	58	and	and	CCONJ
iajs-763	169	59	open	open	ADJ
iajs-763	169	60	n	n	CCONJ
iajs-763	169	61	-	-	PUNCT
iajs-763	169	62	c	c	NOUN
iajs-763	169	63	:	:	PUNCT
iajs-763	169	64	n=1	n=1	NOUN
iajs-763	169	65	rules	rule	NOUN
iajs-763	169	66	.	.	PUNCT
iajs-763	170	1	therefore	therefore	ADV
iajs-763	170	2	mninru	mninru	VERB
iajs-763	170	3	ir	ir	PROPN
iajs-763	170	4			PRON
iajs-763	170	5	)	)	PUNCT
iajs-763	170	6	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	170	7	,	,	PUNCT
iajs-763	170	8			ADJ
iajs-763	170	9	where	where	SCONJ
iajs-763	170	10	3/)1	3/)1	NUM
iajs-763	170	11	(	(	PUNCT
iajs-763	170	12			ADJ
iajs-763	170	13	nm	nm	SCONJ
iajs-763	170	14	are	be	AUX
iajs-763	170	15	obtained	obtain	VERB
iajs-763	170	16	by	by	ADP
iajs-763	170	17	solving	solve	VERB
iajs-763	170	18	the	the	DET
iajs-763	170	19	equation	equation	NOUN
iajs-763	170	20	:	:	PUNCT
iajs-763	171	1	3/)1()2(,,2,1,,,2,1,,,2,1	3/)1()2(,,2,1,,,2,1,,,2,1	NUM
iajs-763	171	2	2	2	NUM
iajs-763	171	3	3	3	NUM
iajs-763	171	4	2	2	NUM
iajs-763	171	5	)	)	PUNCT
iajs-763	171	6	2	2	NUM
iajs-763	171	7	(	(	PUNCT
iajs-763	171	8	2	2	NUM
iajs-763	171	9	11	11	NUM
iajs-763	171	10			NOUN
iajs-763	171	11			NOUN
iajs-763	171	12			X
iajs-763	172	1			NOUN
iajs-763	172	2			NUM
iajs-763	172	3	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	172	4	uk	uk	PROPN
iajs-763	172	5	h	h	PROPN
iajs-763	172	6	uhkfu	uhkfu	PROPN
iajs-763	172	7	mn	mn	PROPN
iajs-763	172	8	j	j	PROPN
iajs-763	172	9	srssrsrr	srssrsrr	PROPN
iajs-763	172	10	jijiii	jijiii	VERB
iajs-763	172	11			PROPN
iajs-763	172	12	…	…	PUNCT
iajs-763	172	13	…	…	PUNCT
iajs-763	172	14	.(10	.(10	NUM
iajs-763	172	15	)	)	PUNCT
iajs-763	172	16	transform	transform	VERB
iajs-763	172	17	all	all	DET
iajs-763	172	18	the	the	DET
iajs-763	172	19	terms	term	NOUN
iajs-763	172	20	involving	involve	VERB
iajs-763	172	21	the	the	DET
iajs-763	172	22	solution	solution	NOUN
iajs-763	172	23	mninru	mninru	NOUN
iajs-763	172	24	ir	ir	NOUN
iajs-763	172	25			PRON
iajs-763	172	26	)	)	PUNCT
iajs-763	172	27	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	172	28	,	,	PUNCT
iajs-763	172	29			NOUN
iajs-763	172	30	,	,	PUNCT
iajs-763	172	31	where	where	SCONJ
iajs-763	172	32	3/)1	3/)1	NUM
iajs-763	172	33	(	(	PUNCT
iajs-763	172	34			ADJ
iajs-763	172	35	nm	nm	ADP
iajs-763	172	36	to	to	PART
iajs-763	172	37	left	left	VERB
iajs-763	172	38	side	side	NOUN
iajs-763	172	39	of	of	ADP
iajs-763	172	40	the	the	DET
iajs-763	172	41	equation	equation	NOUN
iajs-763	172	42	(	(	PUNCT
iajs-763	172	43	10	10	NUM
iajs-763	172	44	)	)	PUNCT
iajs-763	172	45	and	and	CCONJ
iajs-763	172	46	ir	ir	PROPN
iajs-763	172	47	f	f	X
iajs-763	172	48	to	to	ADP
iajs-763	172	49	the	the	DET
iajs-763	172	50	right	right	ADJ
iajs-763	172	51	side	side	NOUN
iajs-763	172	52	.	.	PUNCT
iajs-763	173	1	if	if	SCONJ
iajs-763	173	2	the	the	DET
iajs-763	173	3	number	number	NOUN
iajs-763	173	4	of	of	ADP
iajs-763	173	5	subintervals	subinterval	NOUN
iajs-763	173	6	is	be	AUX
iajs-763	173	7	(	(	PUNCT
iajs-763	173	8	a	a	DET
iajs-763	173	9	multiple	multiple	NOUN
iajs-763	173	10	of	of	ADP
iajs-763	173	11	three	three	NUM
iajs-763	173	12	+2	+2	NOUN
iajs-763	173	13	)	)	PUNCT
iajs-763	173	14	,	,	PUNCT
iajs-763	173	15	we	we	PRON
iajs-763	173	16	get	get	VERB
iajs-763	173	17	combination	combination	NOUN
iajs-763	173	18	between	between	ADP
iajs-763	173	19	open	open	ADJ
iajs-763	173	20	nc	nc	PROPN
iajs-763	173	21	:	:	PUNCT
iajs-763	173	22	n=0	n=0	NUM
iajs-763	173	23	(	(	PUNCT
iajs-763	173	24	midpoint	midpoint	NOUN
iajs-763	173	25	method	method	NOUN
iajs-763	173	26	)	)	PUNCT
iajs-763	173	27	and	and	CCONJ
iajs-763	173	28	open	open	ADJ
iajs-763	173	29	n	n	CCONJ
iajs-763	173	30	-	-	SYM
iajs-763	173	31	c	c	NOUN
iajs-763	173	32	:	:	PUNCT
iajs-763	173	33	n=1	n=1	NOUN
iajs-763	173	34	rules	rule	NOUN
iajs-763	173	35	.	.	PUNCT
iajs-763	174	1	therefore	therefore	ADV
iajs-763	174	2	mninru	mninru	VERB
iajs-763	174	3	ir	ir	PROPN
iajs-763	174	4			PRON
iajs-763	174	5	)	)	PUNCT
iajs-763	174	6	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	174	7	,	,	PUNCT
iajs-763	174	8			NOUN
iajs-763	174	9	,	,	PUNCT
iajs-763	174	10	where	where	SCONJ
iajs-763	174	11	3	3	NUM
iajs-763	174	12	/	/	SYM
iajs-763	174	13	nm	nm	NOUN
iajs-763	174	14	are	be	AUX
iajs-763	174	15	obtained	obtain	VERB
iajs-763	174	16	by	by	ADP
iajs-763	174	17	solving	solve	VERB
iajs-763	174	18	the	the	DET
iajs-763	174	19	equation	equation	NOUN
iajs-763	174	20	:	:	PUNCT
iajs-763	174	21	3/)1(,,2,1,,,2,1,,,2,1	3/)1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	174	22	2	2	NUM
iajs-763	174	23	3	3	NUM
iajs-763	174	24	22	22	NUM
iajs-763	174	25	)	)	PUNCT
iajs-763	174	26	2	2	NUM
iajs-763	174	27	(	(	PUNCT
iajs-763	174	28	3	3	NUM
iajs-763	174	29	2211	2211	NUM
iajs-763	174	30	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	174	31	uk	uk	PROPN
iajs-763	174	32	h	h	PROPN
iajs-763	174	33	uhkuhkfu	uhkuhkfu	PROPN
iajs-763	174	34	mn	mn	PROPN
iajs-763	174	35	j	j	PROPN
iajs-763	174	36	srssrssrsrr	srssrssrsrr	ADV
iajs-763	174	37	jijiiii	jijiiii	VERB
iajs-763	174	38			PROPN
iajs-763	174	39			NOUN
iajs-763	174	40			X
iajs-763	175	1			PROPN
iajs-763	175	2			PROPN
iajs-763	175	3			PROPN
iajs-763	175	4	…	…	PUNCT
iajs-763	175	5	…	…	PUNCT
iajs-763	175	6	…	…	SYM
iajs-763	175	7	.(11	.(11	NUM
iajs-763	175	8	)	)	PUNCT
iajs-763	175	9	transform	transform	VERB
iajs-763	175	10	all	all	DET
iajs-763	175	11	the	the	DET
iajs-763	175	12	terms	term	NOUN
iajs-763	175	13	involving	involve	VERB
iajs-763	175	14	the	the	DET
iajs-763	175	15	solution	solution	NOUN
iajs-763	175	16	mninru	mninru	NOUN
iajs-763	175	17	ir	ir	NOUN
iajs-763	175	18			PRON
iajs-763	175	19	)	)	PUNCT
iajs-763	175	20	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	175	21	,	,	PUNCT
iajs-763	175	22			ADJ
iajs-763	175	23	where	where	SCONJ
iajs-763	175	24	3	3	NUM
iajs-763	175	25	/	/	SYM
iajs-763	175	26	nm	nm	NOUN
iajs-763	175	27	to	to	PART
iajs-763	175	28	left	left	VERB
iajs-763	175	29	side	side	NOUN
iajs-763	175	30	of	of	ADP
iajs-763	175	31	the	the	DET
iajs-763	175	32	equation	equation	NOUN
iajs-763	175	33	(	(	PUNCT
iajs-763	175	34	11	11	NUM
iajs-763	175	35	)	)	PUNCT
iajs-763	175	36	and	and	CCONJ
iajs-763	175	37	ir	ir	PROPN
iajs-763	175	38	f	f	X
iajs-763	175	39	to	to	ADP
iajs-763	175	40	the	the	DET
iajs-763	175	41	right	right	ADJ
iajs-763	175	42	side	side	NOUN
iajs-763	175	43	.	.	PUNCT
iajs-763	176	1	finally	finally	ADV
iajs-763	176	2	,	,	PUNCT
iajs-763	176	3	each	each	DET
iajs-763	176	4	system	system	NOUN
iajs-763	176	5	in	in	ADP
iajs-763	176	6	equations	equation	NOUN
iajs-763	176	7	(	(	PUNCT
iajs-763	176	8	9	9	NUM
iajs-763	176	9	)	)	PUNCT
iajs-763	176	10	,	,	PUNCT
iajs-763	176	11	(	(	PUNCT
iajs-763	176	12	10	10	NUM
iajs-763	176	13	)	)	PUNCT
iajs-763	176	14	and	and	CCONJ
iajs-763	176	15	(	(	PUNCT
iajs-763	176	16	11	11	NUM
iajs-763	176	17	)	)	PUNCT
iajs-763	176	18	can	can	AUX
iajs-763	176	19	be	be	AUX
iajs-763	176	20	written	write	VERB
iajs-763	176	21	in	in	ADP
iajs-763	176	22	a	a	DET
iajs-763	176	23	matrix	matrix	NOUN
iajs-763	176	24	form	form	NOUN
iajs-763	176	25	as	as	ADP
iajs-763	176	26	fku	fku	PROPN
iajs-763	176	27			PROPN
iajs-763	176	28	where	where	SCONJ
iajs-763	176	29	k	k	PROPN
iajs-763	176	30	is	be	AUX
iajs-763	176	31	the	the	DET
iajs-763	176	32	matrix	matrix	NOUN
iajs-763	176	33	of	of	ADP
iajs-763	176	34	the	the	DET
iajs-763	176	35	coefficients	coefficient	NOUN
iajs-763	176	36	,	,	PUNCT
iajs-763	176	37	u	u	NOUN
iajs-763	176	38	is	be	AUX
iajs-763	176	39	the	the	DET
iajs-763	176	40	matrix	matrix	NOUN
iajs-763	176	41	of	of	ADP
iajs-763	176	42	solution	solution	NOUN
iajs-763	176	43	and	and	CCONJ
iajs-763	176	44	f	f	PROPN
iajs-763	176	45	is	be	AUX
iajs-763	176	46	the	the	DET
iajs-763	176	47	matrix	matrix	NOUN
iajs-763	176	48	of	of	ADP
iajs-763	176	49	non	non	ADJ
iajs-763	176	50	-	-	ADJ
iajs-763	176	51	homogeneous	homogeneous	ADJ
iajs-763	176	52	part	part	NOUN
iajs-763	176	53	.	.	PUNCT
iajs-763	177	1	to	to	PART
iajs-763	177	2	find	find	VERB
iajs-763	177	3	the	the	DET
iajs-763	177	4	approximate	approximate	ADJ
iajs-763	177	5	solution	solution	NOUN
iajs-763	177	6	nrur	nrur	VERB
iajs-763	177	7	i	i	PRON
iajs-763	177	8	,	,	PUNCT
iajs-763	177	9	,	,	PUNCT
iajs-763	177	10	2,1	2,1	NUM
iajs-763	177	11	,	,	PUNCT
iajs-763	177	12			NUM
iajs-763	177	13	we	we	PRON
iajs-763	177	14	find	find	VERB
iajs-763	177	15	fku	fku	PROPN
iajs-763	177	16	1	1	NUM
iajs-763	177	17	the	the	DET
iajs-763	177	18	algorithm	algorithm	NOUN
iajs-763	177	19	of	of	ADP
iajs-763	177	20	open	open	ADJ
iajs-763	177	21	n	n	CCONJ
iajs-763	177	22	-	-	PUNCT
iajs-763	177	23	c	c	NOUN
iajs-763	177	24	{	{	PUNCT
iajs-763	177	25	n=1	n=1	PROPN
iajs-763	177	26	}	}	PUNCT
iajs-763	177	27	(	(	PUNCT
iajs-763	177	28	soncn1	soncn1	NOUN
iajs-763	177	29	)	)	PUNCT
iajs-763	177	30	ibn	ibn	PROPN
iajs-763	177	31	alhaitham	alhaitham	NOUN
iajs-763	177	32	j.	j.	PROPN
iajs-763	177	33	for	for	ADP
iajs-763	177	34	pure	pure	ADJ
iajs-763	177	35	&	&	CCONJ
iajs-763	177	36	appl	appl	PROPN
iajs-763	177	37	.	.	PUNCT
iajs-763	178	1	sci	sci	PROPN
iajs-763	178	2	.	.	PUNCT
iajs-763	178	3	vol.24	vol.24	NOUN
iajs-763	178	4	(	(	PUNCT
iajs-763	178	5	2	2	NUM
iajs-763	178	6	)	)	PUNCT
iajs-763	178	7	2011	2011	NUM
iajs-763	178	8	step	step	NOUN
iajs-763	178	9	1	1	NUM
iajs-763	178	10	:	:	PUNCT
iajs-763	178	11	compute	compute	VERB
iajs-763	178	12	2	2	NUM
iajs-763	178	13			PROPN
iajs-763	178	14			PROPN
iajs-763	178	15	n	n	CCONJ
iajs-763	178	16	ab	ab	NOUN
iajs-763	178	17	h	h	NOUN
iajs-763	178	18	,	,	PUNCT
iajs-763	178	19	nn	nn	ADJ
iajs-763	178	20	step	step	NOUN
iajs-763	178	21	2	2	NUM
iajs-763	178	22	:	:	PUNCT
iajs-763	178	23			PROPN
iajs-763	178	24	compute	compute	NOUN
iajs-763	178	25	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	178	26	…	…	SYM
iajs-763	178	27	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	178	28	,	,	PUNCT
iajs-763	178	29	nru	nru	PROPN
iajs-763	178	30	ir	ir	PROPN
iajs-763	178	31			NUM
iajs-763	178	32	where	where	SCONJ
iajs-763	178	33	3/)2	3/)2	NOUN
iajs-763	178	34	(	(	PUNCT
iajs-763	178	35			ADV
iajs-763	178	36	nm	nm	NOUN
iajs-763	178	37	,	,	PUNCT
iajs-763	178	38	using	use	VERB
iajs-763	178	39	equation	equation	NOUN
iajs-763	178	40	(	(	PUNCT
iajs-763	178	41	9	9	NUM
iajs-763	178	42	)	)	PUNCT
iajs-763	178	43	when	when	SCONJ
iajs-763	178	44	the	the	DET
iajs-763	178	45	number	number	NOUN
iajs-763	178	46	of	of	ADP
iajs-763	178	47	subintervals	subinterval	NOUN
iajs-763	178	48	is	be	AUX
iajs-763	178	49	(	(	PUNCT
iajs-763	178	50	a	a	DET
iajs-763	178	51	multiple	multiple	NOUN
iajs-763	178	52	of	of	ADP
iajs-763	178	53	3	3	NUM
iajs-763	178	54	)	)	PUNCT
iajs-763	178	55	.	.	PUNCT
iajs-763	179	1			PROPN
iajs-763	179	2	compute	compute	PROPN
iajs-763	179	3	mninru	mninru	NOUN
iajs-763	179	4	ir	ir	PROPN
iajs-763	179	5			PRON
iajs-763	179	6	)	)	PUNCT
iajs-763	179	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	179	8	,	,	PUNCT
iajs-763	179	9			ADJ
iajs-763	179	10	where	where	SCONJ
iajs-763	179	11	3/)1	3/)1	NUM
iajs-763	179	12	(	(	PUNCT
iajs-763	179	13			ADJ
iajs-763	179	14	nm	nm	NOUN
iajs-763	179	15	,	,	PUNCT
iajs-763	179	16	using	use	VERB
iajs-763	179	17	equation	equation	NOUN
iajs-763	179	18	(	(	PUNCT
iajs-763	179	19	10	10	NUM
iajs-763	179	20	)	)	PUNCT
iajs-763	179	21	when	when	SCONJ
iajs-763	179	22	the	the	DET
iajs-763	179	23	number	number	NOUN
iajs-763	179	24	of	of	ADP
iajs-763	179	25	subintervals	subinterval	NOUN
iajs-763	179	26	is	be	AUX
iajs-763	179	27	(	(	PUNCT
iajs-763	179	28	a	a	DET
iajs-763	179	29	multiple	multiple	NOUN
iajs-763	179	30	of	of	ADP
iajs-763	179	31	3	3	NUM
iajs-763	179	32	+1	+1	NOUN
iajs-763	179	33	)	)	PUNCT
iajs-763	179	34	.	.	PUNCT
iajs-763	180	1			PROPN
iajs-763	180	2	compute	compute	PROPN
iajs-763	180	3	mninru	mninru	NOUN
iajs-763	180	4	ir	ir	PROPN
iajs-763	180	5			PRON
iajs-763	180	6	)	)	PUNCT
iajs-763	180	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	180	8	,	,	PUNCT
iajs-763	180	9			ADJ
iajs-763	180	10	where	where	SCONJ
iajs-763	180	11	3	3	NUM
iajs-763	180	12	/	/	SYM
iajs-763	180	13	nm	nm	NOUN
iajs-763	180	14	,	,	PUNCT
iajs-763	180	15	using	use	VERB
iajs-763	180	16	equation	equation	NOUN
iajs-763	180	17	(	(	PUNCT
iajs-763	180	18	11	11	NUM
iajs-763	180	19	)	)	PUNCT
iajs-763	180	20	when	when	SCONJ
iajs-763	180	21	the	the	DET
iajs-763	180	22	number	number	NOUN
iajs-763	180	23	of	of	ADP
iajs-763	180	24	subintervals	subinterval	NOUN
iajs-763	180	25	is	be	AUX
iajs-763	180	26	(	(	PUNCT
iajs-763	180	27	a	a	DET
iajs-763	180	28	multiple	multiple	NOUN
iajs-763	180	29	of	of	ADP
iajs-763	180	30	3	3	NUM
iajs-763	180	31	+2	+2	NOUN
iajs-763	180	32	)	)	PUNCT
iajs-763	180	33	.	.	PUNCT
iajs-763	181	1	step	step	NOUN
iajs-763	181	2	3	3	NUM
iajs-763	181	3	:	:	PUNCT
iajs-763	181	4	solve	solve	VERB
iajs-763	181	5	the	the	DET
iajs-763	181	6	resulting	result	VERB
iajs-763	181	7	system	system	NOUN
iajs-763	181	8	by	by	ADP
iajs-763	181	9	multiplication	multiplication	NOUN
iajs-763	181	10	it	it	PRON
iajs-763	181	11	with	with	ADP
iajs-763	181	12	k	k	PROPN
iajs-763	181	13	-1	-1	PROPN
iajs-763	181	14	.	.	PUNCT
iajs-763	182	1	2.3	2.3	NUM
iajs-763	182	2	using	use	VERB
iajs-763	182	3	open	open	ADJ
iajs-763	182	4	n	n	CCONJ
iajs-763	182	5	-	-	PUNCT
iajs-763	182	6	c	c	NOUN
iajs-763	182	7	:	:	PUNCT
iajs-763	182	8	n=2	n=2	PRON
iajs-763	182	9	rule	rule	VERB
iajs-763	182	10	the	the	DET
iajs-763	182	11	open	open	ADJ
iajs-763	182	12	n	n	CCONJ
iajs-763	182	13	-	-	PUNCT
iajs-763	182	14	c	c	NOUN
iajs-763	182	15	:	:	PUNCT
iajs-763	182	16	n=2	n=2	PRON
iajs-763	182	17	formula	formula	NOUN
iajs-763	182	18	can	can	AUX
iajs-763	182	19	be	be	AUX
iajs-763	182	20	used	use	VERB
iajs-763	182	21	to	to	PART
iajs-763	182	22	approximate	approximate	VERB
iajs-763	182	23	equation	equation	NOUN
iajs-763	182	24	(	(	PUNCT
iajs-763	182	25	4	4	NUM
iajs-763	182	26	)	)	PUNCT
iajs-763	182	27	such	such	ADJ
iajs-763	182	28	that	that	SCONJ
iajs-763	182	29	:	:	PUNCT
iajs-763	182	30	if	if	SCONJ
iajs-763	182	31	the	the	DET
iajs-763	182	32	number	number	NOUN
iajs-763	182	33	of	of	ADP
iajs-763	182	34	subintervals	subinterval	NOUN
iajs-763	182	35	is	be	AUX
iajs-763	182	36	(	(	PUNCT
iajs-763	182	37	a	a	DET
iajs-763	182	38	multiple	multiple	NOUN
iajs-763	182	39	of	of	ADP
iajs-763	182	40	four	four	NUM
iajs-763	182	41	)	)	PUNCT
iajs-763	182	42	,	,	PUNCT
iajs-763	182	43	we	we	PRON
iajs-763	182	44	apply	apply	VERB
iajs-763	182	45	the	the	DET
iajs-763	182	46	open	open	ADJ
iajs-763	182	47	n	n	CCONJ
iajs-763	182	48	-	-	PUNCT
iajs-763	182	49	c	c	NOUN
iajs-763	182	50	:	:	PUNCT
iajs-763	182	51	n=2	n=2	PRON
iajs-763	182	52	formula	formula	NOUN
iajs-763	182	53	to	to	ADP
iajs-763	182	54	each	each	DET
iajs-763	182	55	integral	integral	ADJ
iajs-763	182	56	term	term	NOUN
iajs-763	182	57	in	in	ADP
iajs-763	182	58	equation	equation	NOUN
iajs-763	182	59	(	(	PUNCT
iajs-763	182	60	4	4	NUM
iajs-763	182	61	)	)	PUNCT
iajs-763	182	62	as	as	ADP
iajs-763	182	63	the	the	DET
iajs-763	182	64	form	form	NOUN
iajs-763	182	65	:	:	PUNCT
iajs-763	182	66			ADJ
iajs-763	182	67			ADP
iajs-763	182	68	4/)2()2(,,2,1,,,2,1,,,2,1	4/)2()2(,,2,1,,,2,1,,,2,1	PROPN
iajs-763	182	69	2222	2222	NUM
iajs-763	182	70	3	3	NUM
iajs-763	182	71	4	4	NUM
iajs-763	182	72	)	)	PUNCT
iajs-763	182	73	2())2(()1())1((44332211	2())2(()1())1((44332211	NUM
iajs-763	182	74			NOUN
iajs-763	182	75			PROPN
iajs-763	182	76			NOUN
iajs-763	182	77	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	182	78	ukukukukukuk	ukukukukukuk	ADJ
iajs-763	182	79	h	h	PROPN
iajs-763	182	80	fu	fu	PROPN
iajs-763	182	81	mnmnimnmniiiiiii	mnmnimnmniiiiiii	VERB
iajs-763	182	82	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	182	83			PROPN
iajs-763	182	84			NOUN
iajs-763	182	85	…	…	PUNCT
iajs-763	182	86	…	…	PUNCT
iajs-763	182	87	(	(	PUNCT
iajs-763	182	88	12	12	NUM
iajs-763	182	89	)	)	PUNCT
iajs-763	182	90	transform	transform	VERB
iajs-763	182	91	all	all	DET
iajs-763	182	92	the	the	DET
iajs-763	182	93	terms	term	NOUN
iajs-763	182	94	involving	involve	VERB
iajs-763	182	95	the	the	DET
iajs-763	182	96	solution	solution	NOUN
iajs-763	182	97	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	182	98	…	…	SYM
iajs-763	182	99	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	182	100	,	,	PUNCT
iajs-763	182	101	nru	nru	PROPN
iajs-763	182	102	ir	ir	PROPN
iajs-763	182	103			NUM
iajs-763	182	104	where	where	SCONJ
iajs-763	182	105	4/)2	4/)2	NOUN
iajs-763	182	106	(	(	PUNCT
iajs-763	182	107			ADJ
iajs-763	182	108	nm	nm	INTJ
iajs-763	182	109	to	to	ADP
iajs-763	182	110	the	the	DET
iajs-763	182	111	left	left	ADJ
iajs-763	182	112	side	side	NOUN
iajs-763	182	113	of	of	ADP
iajs-763	182	114	the	the	DET
iajs-763	182	115	equation	equation	NOUN
iajs-763	182	116	(	(	PUNCT
iajs-763	182	117	12	12	NUM
iajs-763	182	118	)	)	PUNCT
iajs-763	182	119	and	and	CCONJ
iajs-763	182	120	ir	ir	PROPN
iajs-763	182	121	f	f	X
iajs-763	182	122	to	to	ADP
iajs-763	182	123	the	the	DET
iajs-763	182	124	right	right	ADJ
iajs-763	182	125	side	side	NOUN
iajs-763	182	126	.	.	PUNCT
iajs-763	183	1	also	also	ADV
iajs-763	183	2	,	,	PUNCT
iajs-763	183	3	if	if	SCONJ
iajs-763	183	4	the	the	DET
iajs-763	183	5	number	number	NOUN
iajs-763	183	6	of	of	ADP
iajs-763	183	7	subintervals	subinterval	NOUN
iajs-763	183	8	(	(	PUNCT
iajs-763	183	9	n+2	n+2	NUM
iajs-763	183	10	)	)	PUNCT
iajs-763	183	11	is	be	AUX
iajs-763	183	12	(	(	PUNCT
iajs-763	183	13	a	a	DET
iajs-763	183	14	multiple	multiple	NOUN
iajs-763	183	15	of	of	ADP
iajs-763	183	16	four	four	NUM
iajs-763	183	17	+1	+1	PROPN
iajs-763	183	18	)	)	PUNCT
iajs-763	183	19	,	,	PUNCT
iajs-763	183	20	we	we	PRON
iajs-763	183	21	get	get	VERB
iajs-763	183	22	combination	combination	NOUN
iajs-763	183	23	between	between	ADP
iajs-763	183	24	open	open	ADJ
iajs-763	183	25	n	n	CCONJ
iajs-763	183	26	-	-	PUNCT
iajs-763	183	27	c	c	NOUN
iajs-763	183	28	:	:	PUNCT
iajs-763	183	29	n=0	n=0	NUM
iajs-763	183	30	,	,	PUNCT
iajs-763	183	31	open	open	ADJ
iajs-763	183	32	n	n	CCONJ
iajs-763	183	33	-	-	PUNCT
iajs-763	183	34	c	c	NOUN
iajs-763	183	35	:	:	PUNCT
iajs-763	183	36	n=1	n=1	PROPN
iajs-763	183	37	and	and	CCONJ
iajs-763	183	38	open	open	ADJ
iajs-763	183	39	n	n	CCONJ
iajs-763	183	40	-	-	PUNCT
iajs-763	183	41	c	c	NOUN
iajs-763	183	42	:	:	PUNCT
iajs-763	183	43	n=2	n=2	X
iajs-763	183	44	rules	rule	NOUN
iajs-763	183	45	and	and	CCONJ
iajs-763	183	46	mnimru	mnimru	VERB
iajs-763	183	47	ir	ir	PROPN
iajs-763	183	48			PRON
iajs-763	183	49	)	)	PUNCT
iajs-763	183	50	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	183	51	,	,	PUNCT
iajs-763	183	52			ADP
iajs-763	183	53	where	where	SCONJ
iajs-763	183	54	4/)1	4/)1	PROPN
iajs-763	183	55	(	(	PUNCT
iajs-763	183	56			ADJ
iajs-763	183	57	nm	nm	SCONJ
iajs-763	183	58	are	be	AUX
iajs-763	183	59	obtained	obtain	VERB
iajs-763	183	60	by	by	ADP
iajs-763	183	61	solving	solve	VERB
iajs-763	183	62	the	the	DET
iajs-763	183	63	system	system	NOUN
iajs-763	183	64	of	of	ADP
iajs-763	183	65	equations	equation	NOUN
iajs-763	183	66	:	:	PUNCT
iajs-763	184	1	4/)1()1(,,2,1,,,2,1,,,2,1	4/)1()1(,,2,1,,,2,1,,,2,1	X
iajs-763	184	2	]	]	SYM
iajs-763	184	3	22	22	NUM
iajs-763	184	4	[	[	PUNCT
iajs-763	184	5	3	3	NUM
iajs-763	184	6	4	4	NUM
iajs-763	184	7	2	2	NUM
iajs-763	184	8	3	3	NUM
iajs-763	184	9	2	2	NUM
iajs-763	184	10	3	3	NUM
iajs-763	184	11	2	2	NUM
iajs-763	184	12	)	)	PUNCT
iajs-763	184	13	1())1(()(5544332211	1())1(()(5544332211	PROPN
iajs-763	184	14			ADJ
iajs-763	184	15			PROPN
iajs-763	184	16			NOUN
iajs-763	184	17	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	184	18	ukukukuk	ukukukuk	PROPN
iajs-763	184	19	h	h	PROPN
iajs-763	184	20	uk	uk	PROPN
iajs-763	184	21	h	h	PROPN
iajs-763	184	22	uk	uk	PROPN
iajs-763	184	23	h	h	PROPN
iajs-763	184	24	uhkfu	uhkfu	PROPN
iajs-763	184	25	mnmnimnmniiiiiiii	mnmnimnmniiiiiiii	PROPN
iajs-763	184	26	srssrssrssrssrssrssrsrr	srssrssrssrssrssrssrsrr	VERB
iajs-763	184	27			PROPN
iajs-763	184	28			NOUN
iajs-763	184	29	...	...	PUNCT
iajs-763	184	30	(	(	PUNCT
iajs-763	184	31	13	13	X
iajs-763	184	32	)	)	PUNCT
iajs-763	184	33	transform	transform	VERB
iajs-763	184	34	all	all	DET
iajs-763	184	35	the	the	DET
iajs-763	184	36	terms	term	NOUN
iajs-763	184	37	involving	involve	VERB
iajs-763	184	38	the	the	DET
iajs-763	184	39	solution	solution	NOUN
iajs-763	184	40	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	184	41	…	…	SYM
iajs-763	184	42	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	184	43	,	,	PUNCT
iajs-763	184	44	nru	nru	PROPN
iajs-763	184	45	ir	ir	PROPN
iajs-763	184	46			NUM
iajs-763	184	47	,	,	PUNCT
iajs-763	184	48	where	where	SCONJ
iajs-763	184	49	4/)1	4/)1	PROPN
iajs-763	184	50	(	(	PUNCT
iajs-763	184	51			ADV
iajs-763	184	52	nm	nm	NOUN
iajs-763	184	53	to	to	ADP
iajs-763	184	54	the	the	DET
iajs-763	184	55	left	left	ADJ
iajs-763	184	56	side	side	NOUN
iajs-763	184	57	of	of	ADP
iajs-763	184	58	the	the	DET
iajs-763	184	59	equation	equation	NOUN
iajs-763	184	60	(	(	PUNCT
iajs-763	184	61	13	13	NUM
iajs-763	184	62	)	)	PUNCT
iajs-763	184	63	and	and	CCONJ
iajs-763	184	64	ir	ir	PROPN
iajs-763	184	65	f	f	X
iajs-763	184	66	to	to	ADP
iajs-763	184	67	the	the	DET
iajs-763	184	68	right	right	ADJ
iajs-763	184	69	side	side	NOUN
iajs-763	184	70	.	.	PUNCT
iajs-763	185	1	if	if	SCONJ
iajs-763	185	2	the	the	DET
iajs-763	185	3	number	number	NOUN
iajs-763	185	4	of	of	ADP
iajs-763	185	5	subintervals	subinterval	NOUN
iajs-763	185	6	(	(	PUNCT
iajs-763	185	7	n+2	n+2	NUM
iajs-763	185	8	)	)	PUNCT
iajs-763	185	9	is	be	AUX
iajs-763	185	10	(	(	PUNCT
iajs-763	185	11	a	a	DET
iajs-763	185	12	multiple	multiple	NOUN
iajs-763	185	13	of	of	ADP
iajs-763	185	14	four	four	NUM
iajs-763	185	15	+2	+2	NOUN
iajs-763	185	16	)	)	PUNCT
iajs-763	185	17	,	,	PUNCT
iajs-763	185	18	we	we	PRON
iajs-763	185	19	get	get	VERB
iajs-763	185	20	combination	combination	NOUN
iajs-763	185	21	between	between	ADP
iajs-763	185	22	open	open	ADJ
iajs-763	185	23	n	n	CCONJ
iajs-763	185	24	-	-	PUNCT
iajs-763	185	25	c	c	NOUN
iajs-763	185	26	:	:	PUNCT
iajs-763	185	27	n=0	n=0	NUM
iajs-763	185	28	and	and	CCONJ
iajs-763	185	29	open	open	ADJ
iajs-763	185	30	n	n	CCONJ
iajs-763	185	31	-	-	PUNCT
iajs-763	185	32	c	c	NOUN
iajs-763	185	33	:	:	PUNCT
iajs-763	185	34	n=2	n=2	X
iajs-763	185	35	rules	rule	NOUN
iajs-763	185	36	and	and	CCONJ
iajs-763	185	37	mnimru	mnimru	VERB
iajs-763	185	38	ir	ir	PROPN
iajs-763	185	39			PRON
iajs-763	185	40	)	)	PUNCT
iajs-763	185	41	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	185	42	,	,	PUNCT
iajs-763	185	43			NOUN
iajs-763	185	44	,	,	PUNCT
iajs-763	185	45	where	where	SCONJ
iajs-763	185	46	4	4	NUM
iajs-763	185	47	/	/	SYM
iajs-763	185	48	nm	nm	NOUN
iajs-763	185	49	are	be	AUX
iajs-763	185	50	obtained	obtain	VERB
iajs-763	185	51	by	by	ADP
iajs-763	185	52	solving	solve	VERB
iajs-763	185	53	the	the	DET
iajs-763	185	54	system	system	NOUN
iajs-763	185	55	of	of	ADP
iajs-763	185	56	equations	equation	NOUN
iajs-763	185	57	.	.	PUNCT
iajs-763	186	1	4/)1(,,2,1,,,2,1,,,2,1	4/)1(,,2,1,,,2,1,,,2,1	PRON
iajs-763	186	2	]	]	SYM
iajs-763	186	3	222	222	NUM
iajs-763	186	4	[	[	PUNCT
iajs-763	186	5	3	3	NUM
iajs-763	186	6	4	4	NUM
iajs-763	186	7	2	2	NUM
iajs-763	186	8	)	)	PUNCT
iajs-763	186	9	1())1(()(44332211	1())1(()(44332211	NOUN
iajs-763	186	10	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	186	11	ukukukukuk	ukukukukuk	ADJ
iajs-763	186	12	h	h	PROPN
iajs-763	186	13	uhkfu	uhkfu	PROPN
iajs-763	186	14	mnmnimnmniiiiiii	mnmnimnmniiiiiii	PROPN
iajs-763	186	15	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	186	16			PROPN
iajs-763	186	17			NOUN
iajs-763	186	18			NOUN
iajs-763	186	19			PROPN
iajs-763	186	20			NOUN
iajs-763	186	21	…	…	PUNCT
iajs-763	186	22	…	…	PUNCT
iajs-763	186	23	…	…	PUNCT
iajs-763	186	24	…	…	PUNCT
iajs-763	186	25	.(14	.(14	X
iajs-763	186	26	)	)	PUNCT
iajs-763	186	27	transform	transform	VERB
iajs-763	186	28	all	all	DET
iajs-763	186	29	the	the	DET
iajs-763	186	30	terms	term	NOUN
iajs-763	186	31	involving	involve	VERB
iajs-763	186	32	the	the	DET
iajs-763	186	33	solution	solution	NOUN
iajs-763	186	34	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	186	35	…	…	SYM
iajs-763	186	36	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	186	37	,	,	PUNCT
iajs-763	186	38	nru	nru	PROPN
iajs-763	186	39	ir	ir	PROPN
iajs-763	186	40			NUM
iajs-763	186	41	where	where	SCONJ
iajs-763	186	42	4	4	NUM
iajs-763	186	43	/	/	SYM
iajs-763	186	44	nm	nm	NOUN
iajs-763	186	45			NOUN
iajs-763	186	46	to	to	ADP
iajs-763	186	47	the	the	DET
iajs-763	186	48	left	left	ADJ
iajs-763	186	49	side	side	NOUN
iajs-763	186	50	of	of	ADP
iajs-763	186	51	the	the	DET
iajs-763	186	52	equation	equation	NOUN
iajs-763	186	53	(	(	PUNCT
iajs-763	186	54	14	14	NUM
iajs-763	186	55	)	)	PUNCT
iajs-763	186	56	and	and	CCONJ
iajs-763	186	57	ir	ir	PROPN
iajs-763	186	58	f	f	X
iajs-763	186	59	to	to	ADP
iajs-763	186	60	the	the	DET
iajs-763	186	61	right	right	ADJ
iajs-763	186	62	side	side	NOUN
iajs-763	186	63	.	.	PUNCT
iajs-763	187	1	ibn	ibn	PROPN
iajs-763	187	2	alhaitham	alhaitham	PROPN
iajs-763	187	3	j.	j.	PROPN
iajs-763	187	4	for	for	ADP
iajs-763	187	5	pure	pure	ADJ
iajs-763	187	6	&	&	CCONJ
iajs-763	187	7	appl	appl	PROPN
iajs-763	187	8	.	.	PUNCT
iajs-763	188	1	sci	sci	PROPN
iajs-763	188	2	.	.	PUNCT
iajs-763	188	3	vol.24	vol.24	NOUN
iajs-763	188	4	(	(	PUNCT
iajs-763	188	5	2	2	NUM
iajs-763	188	6	)	)	PUNCT
iajs-763	188	7	2011	2011	NUM
iajs-763	188	8	]	]	PUNCT
iajs-763	188	9	also	also	ADV
iajs-763	188	10	,	,	PUNCT
iajs-763	188	11	if	if	SCONJ
iajs-763	188	12	the	the	DET
iajs-763	188	13	number	number	NOUN
iajs-763	188	14	of	of	ADP
iajs-763	188	15	subintervals	subinterval	NOUN
iajs-763	188	16	(	(	PUNCT
iajs-763	188	17	n+2	n+2	NUM
iajs-763	188	18	)	)	PUNCT
iajs-763	188	19	is	be	AUX
iajs-763	188	20	(	(	PUNCT
iajs-763	188	21	a	a	DET
iajs-763	188	22	multiple	multiple	NOUN
iajs-763	188	23	of	of	ADP
iajs-763	188	24	four	four	NUM
iajs-763	188	25	+3	+3	NOUN
iajs-763	188	26	)	)	PUNCT
iajs-763	188	27	we	we	PRON
iajs-763	188	28	get	get	VERB
iajs-763	188	29	combination	combination	NOUN
iajs-763	188	30	between	between	ADP
iajs-763	188	31	open	open	ADJ
iajs-763	188	32	n	n	CCONJ
iajs-763	188	33	-	-	PUNCT
iajs-763	188	34	c	c	NOUN
iajs-763	188	35	:	:	PUNCT
iajs-763	188	36	n=1	n=1	PROPN
iajs-763	188	37	and	and	CCONJ
iajs-763	188	38	open	open	ADJ
iajs-763	188	39	n	n	CCONJ
iajs-763	188	40	-	-	PUNCT
iajs-763	188	41	c	c	NOUN
iajs-763	188	42	:	:	PUNCT
iajs-763	188	43	n=2	n=2	X
iajs-763	188	44	rules	rule	NOUN
iajs-763	188	45	and	and	CCONJ
iajs-763	188	46	mnimru	mnimru	VERB
iajs-763	188	47	ir	ir	PROPN
iajs-763	188	48			PRON
iajs-763	188	49	)	)	PUNCT
iajs-763	188	50	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	188	51	,	,	PUNCT
iajs-763	188	52			NOUN
iajs-763	188	53	,	,	PUNCT
iajs-763	188	54	where	where	SCONJ
iajs-763	188	55	4/)1	4/)1	PROPN
iajs-763	188	56	(	(	PUNCT
iajs-763	188	57			ADJ
iajs-763	188	58	nm	nm	NOUN
iajs-763	188	59	are	be	AUX
iajs-763	188	60	obtained	obtain	VERB
iajs-763	188	61	by	by	ADP
iajs-763	188	62	solving	solve	VERB
iajs-763	188	63	the	the	DET
iajs-763	188	64	system	system	NOUN
iajs-763	188	65	of	of	ADP
iajs-763	188	66	equations	equation	NOUN
iajs-763	188	67	.	.	PUNCT
iajs-763	189	1	4/)1()1(,,2,1,,,2,1,,,2,1	4/)1()1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	189	2	]	]	SYM
iajs-763	189	3	22	22	NUM
iajs-763	189	4	[	[	PUNCT
iajs-763	189	5	3	3	NUM
iajs-763	189	6	4	4	NUM
iajs-763	189	7	2	2	NUM
iajs-763	189	8	3	3	NUM
iajs-763	189	9	2	2	NUM
iajs-763	189	10	3	3	NUM
iajs-763	189	11	)	)	PUNCT
iajs-763	190	1	1())1(()(44332211	1())1(()(44332211	NUM
iajs-763	190	2			ADJ
iajs-763	190	3			NOUN
iajs-763	190	4			ADV
iajs-763	190	5	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	190	6	ukukukuk	ukukukuk	PROPN
iajs-763	190	7	h	h	PROPN
iajs-763	190	8	uk	uk	PROPN
iajs-763	190	9	h	h	PROPN
iajs-763	190	10	uhk	uhk	PROPN
iajs-763	190	11	h	h	PROPN
iajs-763	190	12	fu	fu	PROPN
iajs-763	190	13	mnmnimnmniiiiirsii	mnmnimnmniiiiirsii	NOUN
iajs-763	190	14	srssrssrssrssrssrr	srssrssrssrssrssrr	VERB
iajs-763	190	15			PROPN
iajs-763	190	16			NOUN
iajs-763	190	17	…	…	PUNCT
iajs-763	190	18	..	..	PUNCT
iajs-763	190	19	…	…	PUNCT
iajs-763	190	20	.(15	.(15	X
iajs-763	190	21	)	)	PUNCT
iajs-763	190	22	transform	transform	VERB
iajs-763	190	23	all	all	DET
iajs-763	190	24	the	the	DET
iajs-763	190	25	terms	term	NOUN
iajs-763	190	26	involving	involve	VERB
iajs-763	190	27	the	the	DET
iajs-763	190	28	solution	solution	NOUN
iajs-763	190	29	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	190	30	…	…	SYM
iajs-763	190	31	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	190	32	,	,	PUNCT
iajs-763	190	33	nru	nru	PROPN
iajs-763	190	34	ir	ir	PROPN
iajs-763	190	35			NUM
iajs-763	190	36	where	where	SCONJ
iajs-763	190	37	4/)1	4/)1	PROPN
iajs-763	190	38	(	(	PUNCT
iajs-763	190	39			ADJ
iajs-763	190	40	nm	nm	ADV
iajs-763	190	41	to	to	ADP
iajs-763	190	42	the	the	DET
iajs-763	190	43	left	left	ADJ
iajs-763	190	44	side	side	NOUN
iajs-763	190	45	of	of	ADP
iajs-763	190	46	the	the	DET
iajs-763	190	47	equation	equation	NOUN
iajs-763	190	48	(	(	PUNCT
iajs-763	190	49	15	15	NUM
iajs-763	190	50	)	)	PUNCT
iajs-763	190	51	and	and	CCONJ
iajs-763	190	52	ir	ir	PROPN
iajs-763	190	53	f	f	X
iajs-763	190	54	to	to	ADP
iajs-763	190	55	the	the	DET
iajs-763	190	56	right	right	ADJ
iajs-763	190	57	side	side	NOUN
iajs-763	190	58	.	.	PUNCT
iajs-763	191	1	finally	finally	ADV
iajs-763	191	2	,	,	PUNCT
iajs-763	191	3	each	each	DET
iajs-763	191	4	system	system	NOUN
iajs-763	191	5	in	in	ADP
iajs-763	191	6	equations	equation	NOUN
iajs-763	191	7	(	(	PUNCT
iajs-763	191	8	12	12	NUM
iajs-763	191	9	)	)	PUNCT
iajs-763	191	10	,	,	PUNCT
iajs-763	191	11	(	(	PUNCT
iajs-763	191	12	13	13	NUM
iajs-763	191	13	)	)	PUNCT
iajs-763	191	14	,	,	PUNCT
iajs-763	191	15	(	(	PUNCT
iajs-763	191	16	14	14	NUM
iajs-763	191	17	)	)	PUNCT
iajs-763	191	18	and	and	CCONJ
iajs-763	191	19	(	(	PUNCT
iajs-763	191	20	15	15	NUM
iajs-763	191	21	)	)	PUNCT
iajs-763	191	22	can	can	AUX
iajs-763	191	23	be	be	AUX
iajs-763	191	24	written	write	VERB
iajs-763	191	25	in	in	ADP
iajs-763	191	26	a	a	DET
iajs-763	191	27	matrix	matrix	NOUN
iajs-763	191	28	form	form	NOUN
iajs-763	191	29	as	as	ADP
iajs-763	191	30	fku	fku	PROPN
iajs-763	191	31			PROPN
iajs-763	191	32	,	,	PUNCT
iajs-763	191	33	where	where	SCONJ
iajs-763	191	34	k	k	PROPN
iajs-763	191	35	is	be	AUX
iajs-763	191	36	the	the	DET
iajs-763	191	37	matrix	matrix	NOUN
iajs-763	191	38	of	of	ADP
iajs-763	191	39	the	the	DET
iajs-763	191	40	coefficients	coefficient	NOUN
iajs-763	191	41	,	,	PUNCT
iajs-763	191	42	u	u	NOUN
iajs-763	191	43	is	be	AUX
iajs-763	191	44	the	the	DET
iajs-763	191	45	matrix	matrix	NOUN
iajs-763	191	46	of	of	ADP
iajs-763	191	47	solution	solution	NOUN
iajs-763	191	48	and	and	CCONJ
iajs-763	191	49	f	f	PROPN
iajs-763	191	50	is	be	AUX
iajs-763	191	51	the	the	DET
iajs-763	191	52	matrix	matrix	NOUN
iajs-763	191	53	of	of	ADP
iajs-763	191	54	non	non	ADJ
iajs-763	191	55	-	-	ADJ
iajs-763	191	56	homogeneous	homogeneous	ADJ
iajs-763	191	57	part	part	NOUN
iajs-763	191	58	.	.	PUNCT
iajs-763	192	1	to	to	PART
iajs-763	192	2	find	find	VERB
iajs-763	192	3	the	the	DET
iajs-763	192	4	approximate	approximate	ADJ
iajs-763	192	5	solution	solution	NOUN
iajs-763	192	6	nru	nru	PROPN
iajs-763	192	7	ir	ir	PROPN
iajs-763	192	8	,	,	PUNCT
iajs-763	192	9	,	,	PUNCT
iajs-763	192	10	2,1	2,1	NUM
iajs-763	192	11	,	,	PUNCT
iajs-763	192	12			NUM
iajs-763	192	13	,	,	PUNCT
iajs-763	192	14	we	we	PRON
iajs-763	192	15	find	find	VERB
iajs-763	192	16	fku	fku	PROPN
iajs-763	192	17	1	1	NUM
iajs-763	192	18	the	the	DET
iajs-763	192	19	algorithm	algorithm	NOUN
iajs-763	192	20	of	of	ADP
iajs-763	192	21	open	open	ADJ
iajs-763	192	22	n	n	CCONJ
iajs-763	192	23	-	-	PUNCT
iajs-763	192	24	c:{n=2	c:{n=2	PRON
iajs-763	192	25	}	}	PUNCT
iajs-763	192	26	(	(	PUNCT
iajs-763	192	27	soncn2	soncn2	NOUN
iajs-763	192	28	)	)	PUNCT
iajs-763	192	29	step	step	NOUN
iajs-763	192	30	1	1	NUM
iajs-763	192	31	:	:	PUNCT
iajs-763	192	32	compute	compute	VERB
iajs-763	192	33	2	2	NUM
iajs-763	192	34			PROPN
iajs-763	192	35			PROPN
iajs-763	192	36	n	n	CCONJ
iajs-763	192	37	ab	ab	NOUN
iajs-763	192	38	h	h	NOUN
iajs-763	192	39	,	,	PUNCT
iajs-763	192	40	nn	nn	ADJ
iajs-763	192	41	step	step	NOUN
iajs-763	192	42	2	2	NUM
iajs-763	192	43	:	:	PUNCT
iajs-763	192	44			PROPN
iajs-763	192	45	compute	compute	NOUN
iajs-763	192	46	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	192	47	…	…	SYM
iajs-763	192	48	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	192	49	,	,	PUNCT
iajs-763	192	50	nru	nru	PROPN
iajs-763	192	51	ir	ir	PROPN
iajs-763	192	52			NUM
iajs-763	192	53	where	where	SCONJ
iajs-763	192	54	4/)2	4/)2	NOUN
iajs-763	192	55	(	(	PUNCT
iajs-763	192	56			ADV
iajs-763	192	57	nm	nm	NOUN
iajs-763	192	58	,	,	PUNCT
iajs-763	192	59	using	use	VERB
iajs-763	192	60	equation	equation	NOUN
iajs-763	192	61	(	(	PUNCT
iajs-763	192	62	12	12	NUM
iajs-763	192	63	)	)	PUNCT
iajs-763	192	64	when	when	SCONJ
iajs-763	192	65	the	the	DET
iajs-763	192	66	number	number	NOUN
iajs-763	192	67	of	of	ADP
iajs-763	192	68	subintervals	subinterval	NOUN
iajs-763	192	69	is	be	AUX
iajs-763	192	70	(	(	PUNCT
iajs-763	192	71	a	a	DET
iajs-763	192	72	multiple	multiple	NOUN
iajs-763	192	73	of	of	ADP
iajs-763	192	74	4	4	NUM
iajs-763	192	75	)	)	PUNCT
iajs-763	192	76	.	.	PUNCT
iajs-763	193	1			PROPN
iajs-763	193	2	compute	compute	PROPN
iajs-763	193	3	mninru	mninru	NOUN
iajs-763	193	4	ir	ir	PROPN
iajs-763	193	5			PRON
iajs-763	193	6	)	)	PUNCT
iajs-763	193	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	193	8	,	,	PUNCT
iajs-763	193	9			ADP
iajs-763	193	10	where	where	SCONJ
iajs-763	193	11	4/)1	4/)1	PROPN
iajs-763	193	12	(	(	PUNCT
iajs-763	193	13			ADJ
iajs-763	193	14	nm	nm	NOUN
iajs-763	193	15	,	,	PUNCT
iajs-763	193	16	using	use	VERB
iajs-763	193	17	equation	equation	NOUN
iajs-763	193	18	(	(	PUNCT
iajs-763	193	19	13	13	NUM
iajs-763	193	20	)	)	PUNCT
iajs-763	193	21	when	when	SCONJ
iajs-763	193	22	the	the	DET
iajs-763	193	23	number	number	NOUN
iajs-763	193	24	of	of	ADP
iajs-763	193	25	subintervals	subinterval	NOUN
iajs-763	193	26	is	be	AUX
iajs-763	193	27	(	(	PUNCT
iajs-763	193	28	a	a	DET
iajs-763	193	29	multiple	multiple	NOUN
iajs-763	193	30	of	of	ADP
iajs-763	193	31	4	4	NUM
iajs-763	193	32	+1	+1	NOUN
iajs-763	193	33	)	)	PUNCT
iajs-763	193	34	.	.	PUNCT
iajs-763	194	1			PROPN
iajs-763	194	2	compute	compute	PROPN
iajs-763	194	3	mninru	mninru	NOUN
iajs-763	194	4	ir	ir	PROPN
iajs-763	194	5			PRON
iajs-763	194	6	)	)	PUNCT
iajs-763	194	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	194	8	,	,	PUNCT
iajs-763	194	9			ADJ
iajs-763	194	10	where	where	SCONJ
iajs-763	194	11	4	4	NUM
iajs-763	194	12	/	/	SYM
iajs-763	194	13	nm	nm	NOUN
iajs-763	194	14			NOUN
iajs-763	194	15	,	,	PUNCT
iajs-763	194	16	using	use	VERB
iajs-763	194	17	equation	equation	NOUN
iajs-763	194	18	(	(	PUNCT
iajs-763	194	19	14	14	NUM
iajs-763	194	20	)	)	PUNCT
iajs-763	194	21	when	when	SCONJ
iajs-763	194	22	the	the	DET
iajs-763	194	23	number	number	NOUN
iajs-763	194	24	of	of	ADP
iajs-763	194	25	subintervals	subinterval	NOUN
iajs-763	194	26	is	be	AUX
iajs-763	194	27	(	(	PUNCT
iajs-763	194	28	a	a	DET
iajs-763	194	29	multiple	multiple	NOUN
iajs-763	194	30	of	of	ADP
iajs-763	194	31	4	4	NUM
iajs-763	194	32	+2	+2	NOUN
iajs-763	194	33	)	)	PUNCT
iajs-763	194	34	.	.	PUNCT
iajs-763	195	1			PROPN
iajs-763	195	2	compute	compute	PROPN
iajs-763	195	3	mninru	mninru	NOUN
iajs-763	195	4	ir	ir	PROPN
iajs-763	195	5			PRON
iajs-763	195	6	)	)	PUNCT
iajs-763	195	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	195	8	,	,	PUNCT
iajs-763	195	9			ADP
iajs-763	195	10	where	where	SCONJ
iajs-763	195	11	4/)1	4/)1	PROPN
iajs-763	195	12	(	(	PUNCT
iajs-763	195	13			ADJ
iajs-763	195	14	nm	nm	NOUN
iajs-763	195	15	,	,	PUNCT
iajs-763	195	16	using	use	VERB
iajs-763	195	17	equation	equation	NOUN
iajs-763	195	18	(	(	PUNCT
iajs-763	195	19	15	15	NUM
iajs-763	195	20	)	)	PUNCT
iajs-763	195	21	when	when	SCONJ
iajs-763	195	22	the	the	DET
iajs-763	195	23	number	number	NOUN
iajs-763	195	24	of	of	ADP
iajs-763	195	25	subintervals	subinterval	NOUN
iajs-763	195	26	is	be	AUX
iajs-763	195	27	(	(	PUNCT
iajs-763	195	28	a	a	DET
iajs-763	195	29	multiple	multiple	NOUN
iajs-763	195	30	of	of	ADP
iajs-763	195	31	4	4	NUM
iajs-763	195	32	+3	+3	NOUN
iajs-763	195	33	)	)	PUNCT
iajs-763	195	34	.	.	PUNCT
iajs-763	196	1	step	step	NOUN
iajs-763	196	2	3	3	NUM
iajs-763	196	3	:	:	PUNCT
iajs-763	196	4	solve	solve	VERB
iajs-763	196	5	the	the	DET
iajs-763	196	6	resulting	result	VERB
iajs-763	196	7	system	system	NOUN
iajs-763	196	8	by	by	ADP
iajs-763	196	9	multiplication	multiplication	NOUN
iajs-763	196	10	it	it	PRON
iajs-763	196	11	with	with	ADP
iajs-763	196	12	k	k	PROPN
iajs-763	196	13	-1	-1	PROPN
iajs-763	196	14	.	.	PUNCT
iajs-763	197	1	2.4	2.4	NUM
iajs-763	197	2	using	use	VERB
iajs-763	197	3	open	open	ADJ
iajs-763	197	4	n	n	CCONJ
iajs-763	197	5	-	-	PUNCT
iajs-763	197	6	c	c	NOUN
iajs-763	197	7	:	:	PUNCT
iajs-763	197	8	n=3	n=3	PUNCT
iajs-763	197	9	rule	rule	VERB
iajs-763	197	10	the	the	DET
iajs-763	197	11	open	open	ADJ
iajs-763	197	12	n	n	CCONJ
iajs-763	197	13	-	-	PUNCT
iajs-763	197	14	c	c	NOUN
iajs-763	197	15	:	:	PUNCT
iajs-763	197	16	n=3	n=3	PUNCT
iajs-763	197	17	formula	formula	NOUN
iajs-763	197	18	can	can	AUX
iajs-763	197	19	be	be	AUX
iajs-763	197	20	used	use	VERB
iajs-763	197	21	to	to	PART
iajs-763	197	22	approximate	approximate	VERB
iajs-763	197	23	equation	equation	NOUN
iajs-763	197	24	(	(	PUNCT
iajs-763	197	25	4	4	NUM
iajs-763	197	26	)	)	PUNCT
iajs-763	197	27	such	such	ADJ
iajs-763	197	28	that	that	SCONJ
iajs-763	197	29	:	:	PUNCT
iajs-763	197	30	if	if	SCONJ
iajs-763	197	31	the	the	DET
iajs-763	197	32	number	number	NOUN
iajs-763	197	33	of	of	ADP
iajs-763	197	34	subintervals	subinterval	NOUN
iajs-763	197	35	is	be	AUX
iajs-763	197	36	(	(	PUNCT
iajs-763	197	37	a	a	DET
iajs-763	197	38	multiple	multiple	NOUN
iajs-763	197	39	of	of	ADP
iajs-763	197	40	five	five	NUM
iajs-763	197	41	)	)	PUNCT
iajs-763	197	42	we	we	PRON
iajs-763	197	43	apply	apply	VERB
iajs-763	197	44	the	the	DET
iajs-763	197	45	open	open	ADJ
iajs-763	197	46	n	n	CCONJ
iajs-763	197	47	-	-	PUNCT
iajs-763	197	48	c	c	NOUN
iajs-763	197	49	:	:	PUNCT
iajs-763	197	50	n=3	n=3	PUNCT
iajs-763	197	51	formula	formula	NOUN
iajs-763	197	52	to	to	ADP
iajs-763	197	53	each	each	DET
iajs-763	197	54	integral	integral	ADJ
iajs-763	197	55	term	term	NOUN
iajs-763	197	56	in	in	ADP
iajs-763	197	57	equation	equation	NOUN
iajs-763	197	58	(	(	PUNCT
iajs-763	197	59	4	4	NUM
iajs-763	197	60	)	)	PUNCT
iajs-763	197	61	as	as	ADP
iajs-763	197	62	the	the	DET
iajs-763	197	63	form	form	NOUN
iajs-763	197	64	:	:	PUNCT
iajs-763	197	65			ADJ
iajs-763	197	66			PROPN
iajs-763	197	67	5/)2()2(,,2,1,,,2,1,,,2,1	5/)2()2(,,2,1,,,2,1,,,2,1	PROPN
iajs-763	197	68	111111	111111	NUM
iajs-763	197	69	24	24	NUM
iajs-763	197	70	5	5	NUM
iajs-763	197	71	)	)	PUNCT
iajs-763	197	72	2())2(()1())1((44332211	2())2(()1())1((44332211	NUM
iajs-763	197	73			NOUN
iajs-763	197	74			NOUN
iajs-763	197	75			NOUN
iajs-763	197	76	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	197	77	ukukukukukuk	ukukukukukuk	ADJ
iajs-763	197	78	h	h	PROPN
iajs-763	197	79	fu	fu	PROPN
iajs-763	197	80	mnmnimnmniiiiiii	mnmnimnmniiiiiii	VERB
iajs-763	197	81	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	197	82			PROPN
iajs-763	197	83			NOUN
iajs-763	197	84	…	…	PUNCT
iajs-763	197	85	…	…	SYM
iajs-763	197	86	…	…	SYM
iajs-763	197	87	.(16	.(16	NUM
iajs-763	197	88	)	)	PUNCT
iajs-763	197	89	transform	transform	VERB
iajs-763	197	90	all	all	DET
iajs-763	197	91	the	the	DET
iajs-763	197	92	terms	term	NOUN
iajs-763	197	93	involving	involve	VERB
iajs-763	197	94	the	the	DET
iajs-763	197	95	solution	solution	NOUN
iajs-763	197	96	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	197	97	…	…	SYM
iajs-763	197	98	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	197	99	,	,	PUNCT
iajs-763	197	100	nru	nru	PROPN
iajs-763	197	101	ir	ir	PROPN
iajs-763	197	102			NUM
iajs-763	197	103	,	,	PUNCT
iajs-763	197	104	where	where	SCONJ
iajs-763	197	105	5/)2	5/)2	NOUN
iajs-763	197	106	(	(	PUNCT
iajs-763	197	107			ADJ
iajs-763	197	108	nm	nm	INTJ
iajs-763	197	109	to	to	ADP
iajs-763	197	110	the	the	DET
iajs-763	197	111	left	left	ADJ
iajs-763	197	112	side	side	NOUN
iajs-763	197	113	of	of	ADP
iajs-763	197	114	the	the	DET
iajs-763	197	115	equation	equation	NOUN
iajs-763	197	116	(	(	PUNCT
iajs-763	197	117	16	16	NUM
iajs-763	197	118	)	)	PUNCT
iajs-763	197	119	and	and	CCONJ
iajs-763	197	120	ir	ir	PROPN
iajs-763	197	121	f	f	X
iajs-763	197	122	to	to	ADP
iajs-763	197	123	the	the	DET
iajs-763	197	124	right	right	ADJ
iajs-763	197	125	side	side	NOUN
iajs-763	197	126	.	.	PUNCT
iajs-763	198	1	ibn	ibn	PROPN
iajs-763	198	2	alhaitham	alhaitham	PROPN
iajs-763	198	3	j.	j.	PROPN
iajs-763	198	4	for	for	ADP
iajs-763	198	5	pure	pure	ADJ
iajs-763	198	6	&	&	CCONJ
iajs-763	198	7	appl	appl	PROPN
iajs-763	198	8	.	.	PUNCT
iajs-763	199	1	sci	sci	PROPN
iajs-763	199	2	.	.	PUNCT
iajs-763	199	3	vol.24	vol.24	NOUN
iajs-763	199	4	(	(	PUNCT
iajs-763	199	5	2	2	NUM
iajs-763	199	6	)	)	PUNCT
iajs-763	199	7	2011	2011	NUM
iajs-763	199	8	also	also	ADV
iajs-763	199	9	,	,	PUNCT
iajs-763	199	10	if	if	SCONJ
iajs-763	199	11	the	the	DET
iajs-763	199	12	number	number	NOUN
iajs-763	199	13	of	of	ADP
iajs-763	199	14	subintervals	subinterval	NOUN
iajs-763	199	15	(	(	PUNCT
iajs-763	199	16	n+2	n+2	NUM
iajs-763	199	17	)	)	PUNCT
iajs-763	199	18	is	be	AUX
iajs-763	199	19	(	(	PUNCT
iajs-763	199	20	a	a	DET
iajs-763	199	21	multiple	multiple	NOUN
iajs-763	199	22	of	of	ADP
iajs-763	199	23	five	five	NUM
iajs-763	199	24	+1	+1	NOUN
iajs-763	199	25	)	)	PUNCT
iajs-763	199	26	we	we	PRON
iajs-763	199	27	get	get	VERB
iajs-763	199	28	combination	combination	NOUN
iajs-763	199	29	between	between	ADP
iajs-763	199	30	open	open	ADJ
iajs-763	199	31	n	n	CCONJ
iajs-763	199	32	-	-	PUNCT
iajs-763	199	33	c	c	NOUN
iajs-763	199	34	:	:	PUNCT
iajs-763	199	35	n=1	n=1	PROPN
iajs-763	199	36	and	and	CCONJ
iajs-763	199	37	open	open	ADJ
iajs-763	199	38	n	n	CCONJ
iajs-763	199	39	-	-	PUNCT
iajs-763	199	40	c	c	NOUN
iajs-763	199	41	:	:	PUNCT
iajs-763	199	42	n=3	n=3	PUNCT
iajs-763	199	43	rules	rule	NOUN
iajs-763	199	44	and	and	CCONJ
iajs-763	199	45	mnimru	mnimru	VERB
iajs-763	199	46	ir	ir	PROPN
iajs-763	199	47			PRON
iajs-763	199	48	)	)	PUNCT
iajs-763	199	49	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	199	50	,	,	PUNCT
iajs-763	199	51			NOUN
iajs-763	199	52	,	,	PUNCT
iajs-763	199	53	where	where	SCONJ
iajs-763	199	54	5/)1	5/)1	PROPN
iajs-763	199	55	(	(	PUNCT
iajs-763	199	56			ADJ
iajs-763	199	57	nm	nm	SCONJ
iajs-763	199	58	are	be	AUX
iajs-763	199	59	obtained	obtain	VERB
iajs-763	199	60	by	by	ADP
iajs-763	199	61	solving	solve	VERB
iajs-763	199	62	the	the	DET
iajs-763	199	63	system	system	NOUN
iajs-763	199	64	of	of	ADP
iajs-763	199	65	equations	equation	NOUN
iajs-763	199	66	.	.	PUNCT
iajs-763	200	1	5/)1()1(,,2,1,,,2,1,,,2,1	5/)1()1(,,2,1,,,2,1,,,2,1	PRON
iajs-763	200	2	]	]	SYM
iajs-763	200	3	1111	1111	NUM
iajs-763	200	4	[	[	PUNCT
iajs-763	200	5	24	24	NUM
iajs-763	200	6	5	5	NUM
iajs-763	200	7	2	2	NUM
iajs-763	200	8	3	3	NUM
iajs-763	200	9	2	2	NUM
iajs-763	200	10	3	3	NUM
iajs-763	200	11	2	2	NUM
iajs-763	200	12	3	3	NUM
iajs-763	200	13	2	2	NUM
iajs-763	200	14	3	3	NUM
iajs-763	200	15	)	)	PUNCT
iajs-763	200	16	1())1(()(5544332211	1())1(()(5544332211	PROPN
iajs-763	200	17			ADJ
iajs-763	200	18			NOUN
iajs-763	200	19			ADV
iajs-763	200	20	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	200	21	ukukuk	ukukuk	ADJ
iajs-763	200	22	h	h	PROPN
iajs-763	200	23	uk	uk	PROPN
iajs-763	200	24	h	h	PROPN
iajs-763	200	25	uk	uk	PROPN
iajs-763	200	26	h	h	PROPN
iajs-763	200	27	uk	uk	PROPN
iajs-763	200	28	h	h	PROPN
iajs-763	200	29	uhk	uhk	PROPN
iajs-763	200	30	h	h	PROPN
iajs-763	200	31	fu	fu	PROPN
iajs-763	200	32	mnmnimnmniiiiiiii	mnmnimnmniiiiiiii	PROPN
iajs-763	200	33	srssrssrssrssrssrssrsrr	srssrssrssrssrssrssrsrr	VERB
iajs-763	200	34			PROPN
iajs-763	200	35			NOUN
iajs-763	200	36	...	...	PUNCT
iajs-763	200	37	(	(	PUNCT
iajs-763	200	38	17	17	NUM
iajs-763	200	39	)	)	PUNCT
iajs-763	200	40	transform	transform	VERB
iajs-763	200	41	all	all	DET
iajs-763	200	42	the	the	DET
iajs-763	200	43	terms	term	NOUN
iajs-763	200	44	involving	involve	VERB
iajs-763	200	45	the	the	DET
iajs-763	200	46	solution	solution	NOUN
iajs-763	200	47	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	200	48	…	…	SYM
iajs-763	200	49	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	200	50	,	,	PUNCT
iajs-763	200	51	nru	nru	PROPN
iajs-763	200	52	ir	ir	PROPN
iajs-763	200	53			NUM
iajs-763	200	54	,	,	PUNCT
iajs-763	200	55	where	where	SCONJ
iajs-763	200	56	5/)1	5/)1	PROPN
iajs-763	200	57	(	(	PUNCT
iajs-763	200	58			ADJ
iajs-763	200	59	nm	nm	INTJ
iajs-763	200	60	to	to	ADP
iajs-763	200	61	the	the	DET
iajs-763	200	62	left	left	ADJ
iajs-763	200	63	side	side	NOUN
iajs-763	200	64	of	of	ADP
iajs-763	200	65	the	the	DET
iajs-763	200	66	equation	equation	NOUN
iajs-763	200	67	(	(	PUNCT
iajs-763	200	68	17	17	NUM
iajs-763	200	69	)	)	PUNCT
iajs-763	200	70	and	and	CCONJ
iajs-763	200	71	ir	ir	PROPN
iajs-763	200	72	f	f	X
iajs-763	200	73	to	to	ADP
iajs-763	200	74	the	the	DET
iajs-763	200	75	right	right	ADJ
iajs-763	200	76	side	side	NOUN
iajs-763	200	77	.	.	PUNCT
iajs-763	201	1	if	if	SCONJ
iajs-763	201	2	the	the	DET
iajs-763	201	3	number	number	NOUN
iajs-763	201	4	of	of	ADP
iajs-763	201	5	subintervals	subinterval	NOUN
iajs-763	201	6	(	(	PUNCT
iajs-763	201	7	n+2	n+2	NUM
iajs-763	201	8	)	)	PUNCT
iajs-763	201	9	is	be	AUX
iajs-763	201	10	(	(	PUNCT
iajs-763	201	11	a	a	DET
iajs-763	201	12	multiple	multiple	NOUN
iajs-763	201	13	of	of	ADP
iajs-763	201	14	five	five	NUM
iajs-763	201	15	+2	+2	NOUN
iajs-763	201	16	)	)	PUNCT
iajs-763	201	17	we	we	PRON
iajs-763	201	18	get	get	VERB
iajs-763	201	19	combination	combination	NOUN
iajs-763	201	20	between	between	ADP
iajs-763	201	21	open	open	ADJ
iajs-763	201	22	n	n	CCONJ
iajs-763	201	23	-	-	PUNCT
iajs-763	201	24	c	c	NOUN
iajs-763	201	25	:	:	PUNCT
iajs-763	201	26	n=0	n=0	NUM
iajs-763	201	27	and	and	CCONJ
iajs-763	201	28	open	open	ADJ
iajs-763	201	29	n	n	CCONJ
iajs-763	201	30	-	-	PUNCT
iajs-763	201	31	c	c	NOUN
iajs-763	201	32	:	:	PUNCT
iajs-763	201	33	n=3	n=3	PUNCT
iajs-763	201	34	rules	rule	NOUN
iajs-763	201	35	and	and	CCONJ
iajs-763	201	36	mnimru	mnimru	VERB
iajs-763	201	37	ir	ir	PROPN
iajs-763	201	38			PRON
iajs-763	201	39	)	)	PUNCT
iajs-763	201	40	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	201	41	,	,	PUNCT
iajs-763	201	42			NOUN
iajs-763	201	43	,	,	PUNCT
iajs-763	201	44	where	where	SCONJ
iajs-763	201	45	5	5	NUM
iajs-763	201	46	/	/	SYM
iajs-763	201	47	nm	nm	NOUN
iajs-763	201	48	are	be	AUX
iajs-763	201	49	obtained	obtain	VERB
iajs-763	201	50	by	by	ADP
iajs-763	201	51	solving	solve	VERB
iajs-763	201	52	the	the	DET
iajs-763	201	53	system	system	NOUN
iajs-763	201	54	of	of	ADP
iajs-763	201	55	equations	equation	NOUN
iajs-763	201	56	.	.	PUNCT
iajs-763	202	1	5/)1(,,2,1,,,2,1,,,2,1	5/)1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	202	2	]	]	SYM
iajs-763	202	3	1111	1111	NUM
iajs-763	202	4	[	[	PUNCT
iajs-763	202	5	24	24	NUM
iajs-763	202	6	5	5	NUM
iajs-763	202	7	2	2	NUM
iajs-763	202	8	)	)	PUNCT
iajs-763	202	9	1())1(()(44332211	1())1(()(44332211	NOUN
iajs-763	202	10	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	202	11	ukukukukuk	ukukukukuk	ADJ
iajs-763	202	12	h	h	PROPN
iajs-763	202	13	uhkfu	uhkfu	PROPN
iajs-763	202	14	mnmnimnmniiiiiii	mnmnimnmniiiiiii	PROPN
iajs-763	202	15	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	202	16			PROPN
iajs-763	202	17			VERB
iajs-763	202	18			X
iajs-763	202	19			PROPN
iajs-763	202	20			NOUN
iajs-763	202	21	…	…	PUNCT
iajs-763	202	22	…	…	SYM
iajs-763	202	23	.(18	.(18	PUNCT
iajs-763	202	24	)	)	PUNCT
iajs-763	202	25	transform	transform	VERB
iajs-763	202	26	all	all	DET
iajs-763	202	27	the	the	DET
iajs-763	202	28	terms	term	NOUN
iajs-763	202	29	involving	involve	VERB
iajs-763	202	30	the	the	DET
iajs-763	202	31	solution	solution	NOUN
iajs-763	202	32	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	202	33	…	…	SYM
iajs-763	202	34	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	202	35	,	,	PUNCT
iajs-763	202	36	nru	nru	PROPN
iajs-763	202	37	ir	ir	PROPN
iajs-763	202	38			NUM
iajs-763	202	39	where	where	SCONJ
iajs-763	202	40	5	5	NUM
iajs-763	202	41	/	/	SYM
iajs-763	202	42	nm	nm	NOUN
iajs-763	202	43			NOUN
iajs-763	202	44	to	to	ADP
iajs-763	202	45	the	the	DET
iajs-763	202	46	left	left	ADJ
iajs-763	202	47	side	side	NOUN
iajs-763	202	48	of	of	ADP
iajs-763	202	49	the	the	DET
iajs-763	202	50	equation	equation	NOUN
iajs-763	202	51	(	(	PUNCT
iajs-763	202	52	18	18	NUM
iajs-763	202	53	)	)	PUNCT
iajs-763	202	54	and	and	CCONJ
iajs-763	202	55	ir	ir	PROPN
iajs-763	202	56	f	f	X
iajs-763	202	57	to	to	ADP
iajs-763	202	58	the	the	DET
iajs-763	202	59	right	right	ADJ
iajs-763	202	60	side	side	NOUN
iajs-763	202	61	.	.	PUNCT
iajs-763	203	1	also	also	ADV
iajs-763	203	2	,	,	PUNCT
iajs-763	203	3	if	if	SCONJ
iajs-763	203	4	the	the	DET
iajs-763	203	5	number	number	NOUN
iajs-763	203	6	of	of	ADP
iajs-763	203	7	subintervals	subinterval	NOUN
iajs-763	203	8	(	(	PUNCT
iajs-763	203	9	n+2	n+2	NUM
iajs-763	203	10	)	)	PUNCT
iajs-763	203	11	is	be	AUX
iajs-763	203	12	(	(	PUNCT
iajs-763	203	13	a	a	DET
iajs-763	203	14	multiple	multiple	NOUN
iajs-763	203	15	of	of	ADP
iajs-763	203	16	five	five	NUM
iajs-763	203	17	+3	+3	NOUN
iajs-763	203	18	)	)	PUNCT
iajs-763	203	19	we	we	PRON
iajs-763	203	20	get	get	VERB
iajs-763	203	21	combination	combination	NOUN
iajs-763	203	22	between	between	ADP
iajs-763	203	23	open	open	ADJ
iajs-763	203	24	n	n	CCONJ
iajs-763	203	25	-	-	PUNCT
iajs-763	203	26	c	c	NOUN
iajs-763	203	27	:	:	PUNCT
iajs-763	203	28	n=1	n=1	PROPN
iajs-763	203	29	and	and	CCONJ
iajs-763	203	30	open	open	ADJ
iajs-763	203	31	n	n	CCONJ
iajs-763	203	32	-	-	PUNCT
iajs-763	203	33	c	c	NOUN
iajs-763	203	34	:	:	PUNCT
iajs-763	203	35	n=3	n=3	PUNCT
iajs-763	203	36	rules	rule	NOUN
iajs-763	203	37	and	and	CCONJ
iajs-763	203	38	mnimru	mnimru	VERB
iajs-763	203	39	ir	ir	PROPN
iajs-763	203	40			PRON
iajs-763	203	41	)	)	PUNCT
iajs-763	203	42	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	203	43	,	,	PUNCT
iajs-763	203	44			NOUN
iajs-763	203	45	,	,	PUNCT
iajs-763	203	46	where	where	SCONJ
iajs-763	203	47	5/)1	5/)1	NUM
iajs-763	203	48	(	(	PUNCT
iajs-763	203	49			ADJ
iajs-763	203	50	nm	nm	NOUN
iajs-763	203	51	are	be	AUX
iajs-763	203	52	obtained	obtain	VERB
iajs-763	203	53	by	by	ADP
iajs-763	203	54	solving	solve	VERB
iajs-763	203	55	the	the	DET
iajs-763	203	56	system	system	NOUN
iajs-763	203	57	of	of	ADP
iajs-763	203	58	equations	equation	NOUN
iajs-763	203	59	.	.	PUNCT
iajs-763	204	1	5/)1()1(,,2,1,,,2,1,,,2,1	5/)1()1(,,2,1,,,2,1,,,2,1	PRON
iajs-763	204	2	]	]	SYM
iajs-763	204	3	1111	1111	NUM
iajs-763	204	4	[	[	PUNCT
iajs-763	204	5	24	24	NUM
iajs-763	204	6	5	5	NUM
iajs-763	204	7	2	2	NUM
iajs-763	204	8	3	3	NUM
iajs-763	204	9	2	2	NUM
iajs-763	204	10	3	3	NUM
iajs-763	204	11	)	)	PUNCT
iajs-763	205	1	1())1(()(44332211	1())1(()(44332211	NOUN
iajs-763	205	2			ADJ
iajs-763	205	3			NOUN
iajs-763	205	4			NOUN
iajs-763	205	5	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	205	6	ukukukuk	ukukukuk	PROPN
iajs-763	205	7	h	h	PROPN
iajs-763	205	8	uk	uk	PROPN
iajs-763	205	9	h	h	PROPN
iajs-763	205	10	uhk	uhk	PROPN
iajs-763	205	11	h	h	PROPN
iajs-763	205	12	fu	fu	PROPN
iajs-763	205	13	mnmnimnmniiiiiii	mnmnimnmniiiiiii	INTJ
iajs-763	205	14	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	205	15			PROPN
iajs-763	205	16			NOUN
iajs-763	205	17	…	…	PUNCT
iajs-763	205	18	…	…	PUNCT
iajs-763	205	19	.(19	.(19	SYM
iajs-763	205	20	)	)	PUNCT
iajs-763	205	21	transform	transform	VERB
iajs-763	205	22	all	all	DET
iajs-763	205	23	the	the	DET
iajs-763	205	24	terms	term	NOUN
iajs-763	205	25	involving	involve	VERB
iajs-763	205	26	the	the	DET
iajs-763	205	27	solution	solution	NOUN
iajs-763	205	28	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	205	29	…	…	SYM
iajs-763	205	30	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	205	31	,	,	PUNCT
iajs-763	205	32	nru	nru	PROPN
iajs-763	205	33	ir	ir	PROPN
iajs-763	205	34			NUM
iajs-763	205	35	,	,	PUNCT
iajs-763	205	36	where	where	SCONJ
iajs-763	205	37	5/)1	5/)1	NUM
iajs-763	205	38	(	(	PUNCT
iajs-763	205	39			ADJ
iajs-763	205	40	nm	nm	ADV
iajs-763	205	41	to	to	ADP
iajs-763	205	42	the	the	DET
iajs-763	205	43	left	left	ADJ
iajs-763	205	44	side	side	NOUN
iajs-763	205	45	of	of	ADP
iajs-763	205	46	the	the	DET
iajs-763	205	47	equation	equation	NOUN
iajs-763	205	48	(	(	PUNCT
iajs-763	205	49	19	19	NUM
iajs-763	205	50	)	)	PUNCT
iajs-763	205	51	and	and	CCONJ
iajs-763	205	52	ir	ir	PROPN
iajs-763	205	53	f	f	X
iajs-763	205	54	to	to	ADP
iajs-763	205	55	the	the	DET
iajs-763	205	56	right	right	ADJ
iajs-763	205	57	side	side	NOUN
iajs-763	205	58	.	.	PUNCT
iajs-763	206	1	and	and	CCONJ
iajs-763	206	2	,	,	PUNCT
iajs-763	206	3	if	if	SCONJ
iajs-763	206	4	the	the	DET
iajs-763	206	5	number	number	NOUN
iajs-763	206	6	of	of	ADP
iajs-763	206	7	subintervals	subinterval	NOUN
iajs-763	206	8	(	(	PUNCT
iajs-763	206	9	n+2	n+2	NUM
iajs-763	206	10	)	)	PUNCT
iajs-763	206	11	is	be	AUX
iajs-763	206	12	(	(	PUNCT
iajs-763	206	13	a	a	DET
iajs-763	206	14	multiple	multiple	NOUN
iajs-763	206	15	of	of	ADP
iajs-763	206	16	five	five	NUM
iajs-763	206	17	+4	+4	NUM
iajs-763	206	18	)	)	PUNCT
iajs-763	206	19	we	we	PRON
iajs-763	206	20	get	get	VERB
iajs-763	206	21	combination	combination	NOUN
iajs-763	206	22	between	between	ADP
iajs-763	206	23	open	open	ADJ
iajs-763	206	24	n	n	CCONJ
iajs-763	206	25	-	-	PUNCT
iajs-763	206	26	c	c	NOUN
iajs-763	206	27	:	:	PUNCT
iajs-763	206	28	n=2	n=2	X
iajs-763	206	29	and	and	CCONJ
iajs-763	206	30	open	open	VERB
iajs-763	206	31	n	n	CCONJ
iajs-763	206	32	-	-	PUNCT
iajs-763	206	33	c	c	NOUN
iajs-763	206	34	:	:	PUNCT
iajs-763	206	35	n=3	n=3	PUNCT
iajs-763	206	36	rules	rule	NOUN
iajs-763	206	37	and	and	CCONJ
iajs-763	206	38	mnimru	mnimru	VERB
iajs-763	206	39	ir	ir	PROPN
iajs-763	206	40			PRON
iajs-763	206	41	)	)	PUNCT
iajs-763	206	42	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	206	43	,	,	PUNCT
iajs-763	206	44			NOUN
iajs-763	206	45	,	,	PUNCT
iajs-763	206	46	where	where	SCONJ
iajs-763	206	47	5/)2	5/)2	NOUN
iajs-763	206	48	(	(	PUNCT
iajs-763	206	49			ADJ
iajs-763	206	50	nm	nm	NOUN
iajs-763	206	51	are	be	AUX
iajs-763	206	52	obtained	obtain	VERB
iajs-763	206	53	by	by	ADP
iajs-763	206	54	solving	solve	VERB
iajs-763	206	55	the	the	DET
iajs-763	206	56	system	system	NOUN
iajs-763	206	57	of	of	ADP
iajs-763	206	58	equations	equation	NOUN
iajs-763	206	59	.	.	PUNCT
iajs-763	207	1	5/)2()1(,,2,1,,,2,1,,,2,1	5/)2()1(,,2,1,,,2,1,,,2,1	X
iajs-763	207	2	]	]	SYM
iajs-763	207	3	1111	1111	NUM
iajs-763	207	4	[	[	PUNCT
iajs-763	207	5	24	24	NUM
iajs-763	207	6	5	5	NUM
iajs-763	207	7	]	]	SYM
iajs-763	207	8	22	22	NUM
iajs-763	207	9	[	[	PUNCT
iajs-763	207	10	3	3	NUM
iajs-763	207	11	4	4	NUM
iajs-763	207	12	)	)	PUNCT
iajs-763	207	13	1())1(()(44332211	1())1(()(44332211	NOUN
iajs-763	207	14			ADJ
iajs-763	207	15			NOUN
iajs-763	207	16			NOUN
iajs-763	207	17	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	207	18	ukukuk	ukukuk	ADJ
iajs-763	207	19	h	h	PROPN
iajs-763	207	20	ukukuhk	ukukuhk	PROPN
iajs-763	207	21	h	h	PROPN
iajs-763	207	22	fu	fu	PROPN
iajs-763	207	23	mnmnimnmniiiiiii	mnmnimnmniiiiiii	VERB
iajs-763	207	24	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	207	25			PROPN
iajs-763	207	26			NOUN
iajs-763	207	27	…	…	PUNCT
iajs-763	207	28	(	(	PUNCT
iajs-763	207	29	20	20	NUM
iajs-763	207	30	)	)	PUNCT
iajs-763	207	31	transform	transform	VERB
iajs-763	207	32	all	all	DET
iajs-763	207	33	the	the	DET
iajs-763	207	34	terms	term	NOUN
iajs-763	207	35	involving	involve	VERB
iajs-763	207	36	the	the	DET
iajs-763	207	37	solution	solution	NOUN
iajs-763	207	38	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	207	39	…	…	SYM
iajs-763	207	40	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	207	41	,	,	PUNCT
iajs-763	207	42	nru	nru	PROPN
iajs-763	207	43	ir	ir	PROPN
iajs-763	207	44			NUM
iajs-763	207	45	,	,	PUNCT
iajs-763	207	46	where	where	SCONJ
iajs-763	207	47	5/)2	5/)2	NOUN
iajs-763	207	48	(	(	PUNCT
iajs-763	207	49			ADJ
iajs-763	207	50	nm	nm	ADV
iajs-763	207	51	to	to	ADP
iajs-763	207	52	the	the	DET
iajs-763	207	53	left	left	ADJ
iajs-763	207	54	side	side	NOUN
iajs-763	207	55	of	of	ADP
iajs-763	207	56	the	the	DET
iajs-763	207	57	equation	equation	NOUN
iajs-763	207	58	(	(	PUNCT
iajs-763	207	59	20	20	NUM
iajs-763	207	60	)	)	PUNCT
iajs-763	207	61	and	and	CCONJ
iajs-763	207	62	ir	ir	PROPN
iajs-763	207	63	f	f	X
iajs-763	207	64	to	to	ADP
iajs-763	207	65	the	the	DET
iajs-763	207	66	right	right	ADJ
iajs-763	207	67	side	side	NOUN
iajs-763	207	68	.	.	PUNCT
iajs-763	208	1	finally	finally	ADV
iajs-763	208	2	,	,	PUNCT
iajs-763	208	3	each	each	DET
iajs-763	208	4	system	system	NOUN
iajs-763	208	5	in	in	ADP
iajs-763	208	6	equations	equation	NOUN
iajs-763	208	7	(	(	PUNCT
iajs-763	208	8	16	16	NUM
iajs-763	208	9	)	)	PUNCT
iajs-763	208	10	,	,	PUNCT
iajs-763	208	11	(	(	PUNCT
iajs-763	208	12	17	17	NUM
iajs-763	208	13	)	)	PUNCT
iajs-763	208	14	,	,	PUNCT
iajs-763	208	15	(	(	PUNCT
iajs-763	208	16	18	18	NUM
iajs-763	208	17	)	)	PUNCT
iajs-763	208	18	,	,	PUNCT
iajs-763	208	19	(	(	PUNCT
iajs-763	208	20	19	19	NUM
iajs-763	208	21	)	)	PUNCT
iajs-763	208	22	and	and	CCONJ
iajs-763	208	23	(	(	PUNCT
iajs-763	208	24	20	20	NUM
iajs-763	208	25	)	)	PUNCT
iajs-763	208	26	can	can	AUX
iajs-763	208	27	be	be	AUX
iajs-763	208	28	written	write	VERB
iajs-763	208	29	in	in	ADP
iajs-763	208	30	a	a	DET
iajs-763	208	31	matrix	matrix	NOUN
iajs-763	208	32	form	form	NOUN
iajs-763	208	33	as	as	ADP
iajs-763	208	34	fku	fku	PROPN
iajs-763	208	35			PROPN
iajs-763	208	36	where	where	SCONJ
iajs-763	208	37	k	k	PROPN
iajs-763	208	38	is	be	AUX
iajs-763	208	39	the	the	DET
iajs-763	208	40	matrix	matrix	NOUN
iajs-763	208	41	of	of	ADP
iajs-763	208	42	the	the	DET
iajs-763	208	43	coefficients	coefficient	NOUN
iajs-763	208	44	,	,	PUNCT
iajs-763	208	45	u	u	NOUN
iajs-763	208	46	is	be	AUX
iajs-763	208	47	the	the	DET
iajs-763	208	48	matrix	matrix	NOUN
iajs-763	208	49	of	of	ADP
iajs-763	208	50	solution	solution	NOUN
iajs-763	208	51	and	and	CCONJ
iajs-763	208	52	f	f	PROPN
iajs-763	208	53	ibn	ibn	PROPN
iajs-763	208	54	alhaitham	alhaitham	PROPN
iajs-763	208	55	j.	j.	PROPN
iajs-763	208	56	for	for	ADP
iajs-763	208	57	pure	pure	ADJ
iajs-763	208	58	&	&	CCONJ
iajs-763	208	59	appl	appl	PROPN
iajs-763	208	60	.	.	PUNCT
iajs-763	209	1	sci	sci	PROPN
iajs-763	209	2	.	.	PUNCT
iajs-763	209	3	vol.24	vol.24	NOUN
iajs-763	209	4	(	(	PUNCT
iajs-763	209	5	2	2	NUM
iajs-763	209	6	)	)	PUNCT
iajs-763	209	7	2011	2011	NUM
iajs-763	209	8	is	be	AUX
iajs-763	209	9	the	the	DET
iajs-763	209	10	matrix	matrix	NOUN
iajs-763	209	11	of	of	ADP
iajs-763	209	12	non	non	ADJ
iajs-763	209	13	-	-	ADJ
iajs-763	209	14	homogeneous	homogeneous	ADJ
iajs-763	209	15	part	part	NOUN
iajs-763	209	16	.	.	PUNCT
iajs-763	210	1	to	to	PART
iajs-763	210	2	find	find	VERB
iajs-763	210	3	the	the	DET
iajs-763	210	4	approximate	approximate	ADJ
iajs-763	210	5	solution	solution	NOUN
iajs-763	210	6	nru	nru	PROPN
iajs-763	210	7	ir	ir	PROPN
iajs-763	210	8	,	,	PUNCT
iajs-763	210	9	,	,	PUNCT
iajs-763	210	10	2,1	2,1	NUM
iajs-763	210	11	,	,	PUNCT
iajs-763	210	12			NUM
iajs-763	210	13	we	we	PRON
iajs-763	210	14	find	find	VERB
iajs-763	210	15	fku	fku	PROPN
iajs-763	210	16	1	1	NUM
iajs-763	210	17	the	the	DET
iajs-763	210	18	algorithm	algorithm	NOUN
iajs-763	210	19	of	of	ADP
iajs-763	210	20	open	open	ADJ
iajs-763	210	21	n	n	CCONJ
iajs-763	210	22	-	-	PUNCT
iajs-763	210	23	c	c	NOUN
iajs-763	210	24	{	{	PUNCT
iajs-763	210	25	n=3	n=3	NOUN
iajs-763	210	26	}	}	PUNCT
iajs-763	210	27	(	(	PUNCT
iajs-763	210	28	soncn3	soncn3	NOUN
iajs-763	210	29	)	)	PUNCT
iajs-763	210	30	step	step	NOUN
iajs-763	210	31	1	1	NUM
iajs-763	210	32	:	:	PUNCT
iajs-763	210	33	compute	compute	VERB
iajs-763	210	34	2	2	NUM
iajs-763	210	35			PROPN
iajs-763	210	36			PROPN
iajs-763	210	37	n	n	CCONJ
iajs-763	210	38	ab	ab	NOUN
iajs-763	210	39	h	h	NOUN
iajs-763	210	40	,	,	PUNCT
iajs-763	210	41	nn	nn	ADJ
iajs-763	210	42	step	step	NOUN
iajs-763	210	43	2	2	NUM
iajs-763	210	44	:	:	PUNCT
iajs-763	210	45			PROPN
iajs-763	210	46	compute	compute	NOUN
iajs-763	210	47	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	210	48	…	…	SYM
iajs-763	210	49	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	210	50	,	,	PUNCT
iajs-763	210	51	nru	nru	PROPN
iajs-763	210	52	ir	ir	PROPN
iajs-763	210	53			NUM
iajs-763	210	54	where	where	SCONJ
iajs-763	210	55	5/)2	5/)2	NOUN
iajs-763	210	56	(	(	PUNCT
iajs-763	210	57			ADJ
iajs-763	210	58	nm	nm	NOUN
iajs-763	210	59	,	,	PUNCT
iajs-763	210	60	using	use	VERB
iajs-763	210	61	equation	equation	NOUN
iajs-763	210	62	(	(	PUNCT
iajs-763	210	63	16	16	NUM
iajs-763	210	64	)	)	PUNCT
iajs-763	210	65	when	when	SCONJ
iajs-763	210	66	the	the	DET
iajs-763	210	67	number	number	NOUN
iajs-763	210	68	of	of	ADP
iajs-763	210	69	subintervals	subinterval	NOUN
iajs-763	210	70	is	be	AUX
iajs-763	210	71	(	(	PUNCT
iajs-763	210	72	a	a	DET
iajs-763	210	73	multiple	multiple	NOUN
iajs-763	210	74	of	of	ADP
iajs-763	210	75	5	5	NUM
iajs-763	210	76	)	)	PUNCT
iajs-763	210	77	.	.	PUNCT
iajs-763	211	1			PROPN
iajs-763	211	2	compute	compute	PROPN
iajs-763	211	3	mninru	mninru	NOUN
iajs-763	211	4	ir	ir	PROPN
iajs-763	211	5			PRON
iajs-763	211	6	)	)	PUNCT
iajs-763	211	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	211	8	,	,	PUNCT
iajs-763	211	9			ADJ
iajs-763	211	10	where	where	SCONJ
iajs-763	211	11	5/)1	5/)1	PROPN
iajs-763	211	12	(	(	PUNCT
iajs-763	211	13			ADJ
iajs-763	211	14	nm	nm	NOUN
iajs-763	211	15	,	,	PUNCT
iajs-763	211	16	using	use	VERB
iajs-763	211	17	equation	equation	NOUN
iajs-763	211	18	(	(	PUNCT
iajs-763	211	19	17	17	NUM
iajs-763	211	20	)	)	PUNCT
iajs-763	211	21	when	when	SCONJ
iajs-763	211	22	the	the	DET
iajs-763	211	23	number	number	NOUN
iajs-763	211	24	of	of	ADP
iajs-763	211	25	subintervals	subinterval	NOUN
iajs-763	211	26	is	be	AUX
iajs-763	211	27	(	(	PUNCT
iajs-763	211	28	a	a	DET
iajs-763	211	29	multiple	multiple	NOUN
iajs-763	211	30	of	of	ADP
iajs-763	211	31	5	5	NUM
iajs-763	211	32	+1	+1	NOUN
iajs-763	211	33	)	)	PUNCT
iajs-763	211	34	.	.	PUNCT
iajs-763	212	1			PROPN
iajs-763	212	2	compute	compute	PROPN
iajs-763	212	3	mninru	mninru	NOUN
iajs-763	212	4	ir	ir	PROPN
iajs-763	212	5			PRON
iajs-763	212	6	)	)	PUNCT
iajs-763	212	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	212	8	,	,	PUNCT
iajs-763	212	9			ADJ
iajs-763	212	10	where	where	SCONJ
iajs-763	212	11	5	5	NUM
iajs-763	212	12	/	/	SYM
iajs-763	212	13	nm	nm	NOUN
iajs-763	212	14	,	,	PUNCT
iajs-763	212	15	using	use	VERB
iajs-763	212	16	equation	equation	NOUN
iajs-763	212	17	(	(	PUNCT
iajs-763	212	18	18	18	NUM
iajs-763	212	19	)	)	PUNCT
iajs-763	212	20	when	when	SCONJ
iajs-763	212	21	the	the	DET
iajs-763	212	22	number	number	NOUN
iajs-763	212	23	of	of	ADP
iajs-763	212	24	subintervals	subinterval	NOUN
iajs-763	212	25	is	be	AUX
iajs-763	212	26	(	(	PUNCT
iajs-763	212	27	a	a	DET
iajs-763	212	28	multiple	multiple	NOUN
iajs-763	212	29	of	of	ADP
iajs-763	212	30	5	5	NUM
iajs-763	212	31	+2	+2	NOUN
iajs-763	212	32	)	)	PUNCT
iajs-763	212	33	.	.	PUNCT
iajs-763	213	1			PROPN
iajs-763	213	2	compute	compute	PROPN
iajs-763	213	3	mninru	mninru	NOUN
iajs-763	213	4	ir	ir	PROPN
iajs-763	213	5			PRON
iajs-763	213	6	)	)	PUNCT
iajs-763	213	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	213	8	,	,	PUNCT
iajs-763	213	9			ADJ
iajs-763	213	10	where	where	SCONJ
iajs-763	213	11	5/)1	5/)1	NUM
iajs-763	213	12	(	(	PUNCT
iajs-763	213	13			ADJ
iajs-763	213	14	nm	nm	NOUN
iajs-763	213	15	,	,	PUNCT
iajs-763	213	16	using	use	VERB
iajs-763	213	17	equation	equation	NOUN
iajs-763	213	18	(	(	PUNCT
iajs-763	213	19	19	19	NUM
iajs-763	213	20	)	)	PUNCT
iajs-763	213	21	when	when	SCONJ
iajs-763	213	22	the	the	DET
iajs-763	213	23	number	number	NOUN
iajs-763	213	24	of	of	ADP
iajs-763	213	25	subintervals	subinterval	NOUN
iajs-763	213	26	is	be	AUX
iajs-763	213	27	(	(	PUNCT
iajs-763	213	28	a	a	DET
iajs-763	213	29	multiple	multiple	NOUN
iajs-763	213	30	of	of	ADP
iajs-763	213	31	5	5	NUM
iajs-763	213	32	+3	+3	NOUN
iajs-763	213	33	)	)	PUNCT
iajs-763	213	34	.	.	PUNCT
iajs-763	214	1			PROPN
iajs-763	214	2	compute	compute	PROPN
iajs-763	214	3	mninru	mninru	NOUN
iajs-763	214	4	ir	ir	PROPN
iajs-763	214	5			PRON
iajs-763	214	6	)	)	PUNCT
iajs-763	214	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	214	8	,	,	PUNCT
iajs-763	214	9			ADJ
iajs-763	214	10	where	where	SCONJ
iajs-763	214	11	5/)2	5/)2	NOUN
iajs-763	214	12	(	(	PUNCT
iajs-763	214	13			ADJ
iajs-763	214	14	nm	nm	NOUN
iajs-763	214	15	,	,	PUNCT
iajs-763	214	16	using	use	VERB
iajs-763	214	17	equation	equation	NOUN
iajs-763	214	18	(	(	PUNCT
iajs-763	214	19	20	20	NUM
iajs-763	214	20	)	)	PUNCT
iajs-763	214	21	when	when	SCONJ
iajs-763	214	22	the	the	DET
iajs-763	214	23	number	number	NOUN
iajs-763	214	24	of	of	ADP
iajs-763	214	25	subintervals	subinterval	NOUN
iajs-763	214	26	is	be	AUX
iajs-763	214	27	(	(	PUNCT
iajs-763	214	28	a	a	DET
iajs-763	214	29	multiple	multiple	NOUN
iajs-763	214	30	of	of	ADP
iajs-763	214	31	5	5	NUM
iajs-763	214	32	+4	+4	NUM
iajs-763	214	33	)	)	PUNCT
iajs-763	214	34	.	.	PUNCT
iajs-763	215	1	step	step	NOUN
iajs-763	215	2	3	3	NUM
iajs-763	215	3	:	:	PUNCT
iajs-763	215	4	solve	solve	VERB
iajs-763	215	5	the	the	DET
iajs-763	215	6	resulting	result	VERB
iajs-763	215	7	system	system	NOUN
iajs-763	215	8	by	by	ADP
iajs-763	215	9	multiplication	multiplication	NOUN
iajs-763	215	10	it	it	PRON
iajs-763	215	11	with	with	ADP
iajs-763	215	12	k	k	PROPN
iajs-763	215	13	-1	-1	PROPN
iajs-763	215	14	.	.	PUNCT
iajs-763	216	1	2.4	2.4	NUM
iajs-763	216	2	using	use	VERB
iajs-763	216	3	open	open	ADJ
iajs-763	216	4	n	n	CCONJ
iajs-763	216	5	-	-	PUNCT
iajs-763	216	6	c	c	NOUN
iajs-763	216	7	:	:	PUNCT
iajs-763	216	8	n=4	n=4	X
iajs-763	216	9	rule	rule	VERB
iajs-763	216	10	the	the	DET
iajs-763	216	11	open	open	ADJ
iajs-763	216	12	n	n	CCONJ
iajs-763	216	13	-	-	PUNCT
iajs-763	216	14	c	c	NOUN
iajs-763	216	15	:	:	PUNCT
iajs-763	216	16	n=4	n=4	ADJ
iajs-763	216	17	formula	formula	NOUN
iajs-763	216	18	can	can	AUX
iajs-763	216	19	be	be	AUX
iajs-763	216	20	used	use	VERB
iajs-763	216	21	to	to	PART
iajs-763	216	22	approximate	approximate	VERB
iajs-763	216	23	equation	equation	NOUN
iajs-763	216	24	(	(	PUNCT
iajs-763	216	25	4	4	NUM
iajs-763	216	26	)	)	PUNCT
iajs-763	216	27	such	such	ADJ
iajs-763	216	28	that	that	SCONJ
iajs-763	216	29	:	:	PUNCT
iajs-763	216	30	if	if	SCONJ
iajs-763	216	31	the	the	DET
iajs-763	216	32	number	number	NOUN
iajs-763	216	33	of	of	ADP
iajs-763	216	34	subintervals	subinterval	NOUN
iajs-763	216	35	is	be	AUX
iajs-763	216	36	(	(	PUNCT
iajs-763	216	37	a	a	DET
iajs-763	216	38	multiple	multiple	NOUN
iajs-763	216	39	of	of	ADP
iajs-763	216	40	six	six	NUM
iajs-763	216	41	)	)	PUNCT
iajs-763	216	42	we	we	PRON
iajs-763	216	43	apply	apply	VERB
iajs-763	216	44	the	the	DET
iajs-763	216	45	open	open	ADJ
iajs-763	216	46	n	n	CCONJ
iajs-763	216	47	-	-	PUNCT
iajs-763	216	48	c	c	NOUN
iajs-763	216	49	:	:	PUNCT
iajs-763	216	50	n=4	n=4	ADJ
iajs-763	216	51	formula	formula	NOUN
iajs-763	216	52	to	to	ADP
iajs-763	216	53	each	each	DET
iajs-763	216	54	integral	integral	ADJ
iajs-763	216	55	term	term	NOUN
iajs-763	216	56	in	in	ADP
iajs-763	216	57	equation	equation	NOUN
iajs-763	216	58	(	(	PUNCT
iajs-763	216	59	4	4	NUM
iajs-763	216	60	)	)	PUNCT
iajs-763	216	61	as	as	ADP
iajs-763	216	62	the	the	DET
iajs-763	216	63	form	form	NOUN
iajs-763	216	64	:	:	PUNCT
iajs-763	216	65			ADJ
iajs-763	216	66			ADP
iajs-763	216	67	6/)2()2(,,2,1,,,2,1,,,2,1	6/)2()2(,,2,1,,,2,1,,,2,1	NUM
iajs-763	216	68	11141114261411	11141114261411	NUM
iajs-763	216	69	10	10	NUM
iajs-763	216	70	3	3	NUM
iajs-763	216	71	)	)	PUNCT
iajs-763	216	72	2())2(()1())1((5544332211	2())2(()1())1((5544332211	NUM
iajs-763	216	73			NOUN
iajs-763	216	74			X
iajs-763	216	75			VERB
iajs-763	216	76	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	216	77	ukukukukukukuk	ukukukukukukuk	ADJ
iajs-763	216	78	h	h	PROPN
iajs-763	216	79	fu	fu	PROPN
iajs-763	216	80	mnmnimnmniiiiiiii	mnmnimnmniiiiiiii	PROPN
iajs-763	217	1	srssrssrssrssrssrssrsrr	srssrssrssrssrssrssrsrr	VERB
iajs-763	217	2			PROPN
iajs-763	217	3			NOUN
iajs-763	217	4	…	…	PUNCT
iajs-763	217	5	.(21	.(21	NUM
iajs-763	217	6	)	)	PUNCT
iajs-763	218	1	transform	transform	VERB
iajs-763	218	2	all	all	DET
iajs-763	218	3	the	the	DET
iajs-763	218	4	terms	term	NOUN
iajs-763	218	5	involving	involve	VERB
iajs-763	218	6	the	the	DET
iajs-763	218	7	solution	solution	NOUN
iajs-763	218	8	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	218	9	…	…	SYM
iajs-763	218	10	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	218	11	,	,	PUNCT
iajs-763	218	12	nru	nru	PROPN
iajs-763	218	13	ir	ir	PROPN
iajs-763	218	14			NUM
iajs-763	218	15	,	,	PUNCT
iajs-763	218	16	where	where	SCONJ
iajs-763	218	17	6/)2	6/)2	NOUN
iajs-763	218	18	(	(	PUNCT
iajs-763	218	19			ADV
iajs-763	218	20	nm	nm	INTJ
iajs-763	218	21	to	to	ADP
iajs-763	218	22	the	the	DET
iajs-763	218	23	left	left	ADJ
iajs-763	218	24	side	side	NOUN
iajs-763	218	25	of	of	ADP
iajs-763	218	26	the	the	DET
iajs-763	218	27	equation	equation	NOUN
iajs-763	218	28	(	(	PUNCT
iajs-763	218	29	21	21	NUM
iajs-763	218	30	)	)	PUNCT
iajs-763	218	31	and	and	CCONJ
iajs-763	218	32	ir	ir	PROPN
iajs-763	218	33	f	f	X
iajs-763	218	34	to	to	ADP
iajs-763	218	35	the	the	DET
iajs-763	218	36	right	right	ADJ
iajs-763	218	37	side	side	NOUN
iajs-763	218	38	.	.	PUNCT
iajs-763	219	1	also	also	ADV
iajs-763	219	2	,	,	PUNCT
iajs-763	219	3	if	if	SCONJ
iajs-763	219	4	the	the	DET
iajs-763	219	5	number	number	NOUN
iajs-763	219	6	of	of	ADP
iajs-763	219	7	subintervals	subinterval	NOUN
iajs-763	219	8	(	(	PUNCT
iajs-763	219	9	n+2	n+2	NUM
iajs-763	219	10	)	)	PUNCT
iajs-763	219	11	is	be	AUX
iajs-763	219	12	(	(	PUNCT
iajs-763	219	13	a	a	DET
iajs-763	219	14	multiple	multiple	NOUN
iajs-763	219	15	of	of	ADP
iajs-763	219	16	six	six	NUM
iajs-763	219	17	+1	+1	NOUN
iajs-763	219	18	)	)	PUNCT
iajs-763	219	19	we	we	PRON
iajs-763	219	20	get	get	VERB
iajs-763	219	21	combination	combination	NOUN
iajs-763	219	22	between	between	ADP
iajs-763	219	23	open	open	ADJ
iajs-763	219	24	n	n	CCONJ
iajs-763	219	25	-	-	PUNCT
iajs-763	219	26	c	c	NOUN
iajs-763	219	27	:	:	PUNCT
iajs-763	219	28	n=0	n=0	NUM
iajs-763	219	29	,	,	PUNCT
iajs-763	219	30	open	open	ADJ
iajs-763	219	31	n	n	CCONJ
iajs-763	219	32	-	-	PUNCT
iajs-763	219	33	c	c	NOUN
iajs-763	219	34	:	:	PUNCT
iajs-763	219	35	n=3	n=3	NOUN
iajs-763	219	36	,	,	PUNCT
iajs-763	219	37	and	and	CCONJ
iajs-763	219	38	open	open	ADJ
iajs-763	219	39	n	n	CCONJ
iajs-763	219	40	-	-	PUNCT
iajs-763	219	41	c	c	NOUN
iajs-763	219	42	:	:	PUNCT
iajs-763	219	43	n=4	n=4	ADJ
iajs-763	219	44	rules	rule	NOUN
iajs-763	219	45	and	and	CCONJ
iajs-763	219	46	mnimru	mnimru	VERB
iajs-763	219	47	ir	ir	PROPN
iajs-763	219	48			PRON
iajs-763	219	49	)	)	PUNCT
iajs-763	219	50	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	219	51	,	,	PUNCT
iajs-763	219	52			NOUN
iajs-763	219	53	,	,	PUNCT
iajs-763	219	54	where	where	SCONJ
iajs-763	219	55	6/)1	6/)1	X
iajs-763	219	56	(	(	PUNCT
iajs-763	219	57			ADJ
iajs-763	219	58	nm	nm	SCONJ
iajs-763	219	59	are	be	AUX
iajs-763	219	60	obtained	obtain	VERB
iajs-763	219	61	by	by	ADP
iajs-763	219	62	solving	solve	VERB
iajs-763	219	63	the	the	DET
iajs-763	219	64	system	system	NOUN
iajs-763	219	65	of	of	ADP
iajs-763	219	66	equations	equation	NOUN
iajs-763	219	67	.	.	PUNCT
iajs-763	220	1	5/)1()1(,,2,1,,,2,1,,,2,1	5/)1()1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	220	2	]	]	PUNCT
iajs-763	220	3	111411	111411	NUM
iajs-763	220	4	[	[	PUNCT
iajs-763	220	5	10	10	NUM
iajs-763	220	6	3	3	NUM
iajs-763	220	7	1111	1111	NUM
iajs-763	220	8	[	[	PUNCT
iajs-763	220	9	24	24	NUM
iajs-763	220	10	5	5	NUM
iajs-763	220	11	2	2	NUM
iajs-763	220	12	)	)	PUNCT
iajs-763	220	13	1())1(()(665544332211	1())1(()(665544332211	NOUN
iajs-763	220	14	]	]	PUNCT
iajs-763	220	15			NOUN
iajs-763	220	16			PROPN
iajs-763	220	17			ADV
iajs-763	220	18	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	220	19	ukukuk	ukukuk	ADJ
iajs-763	220	20	h	h	PROPN
iajs-763	220	21	ukukukuk	ukukukuk	PROPN
iajs-763	220	22	h	h	PROPN
iajs-763	220	23	uhkfu	uhkfu	PROPN
iajs-763	220	24	mnmnimnmniiiiiiiii	mnmnimnmniiiiiiiii	PROPN
iajs-763	220	25	srssrssrssrssrssrssrssrsrr	srssrssrssrssrssrssrssrsrr	NOUN
iajs-763	220	26			PROPN
iajs-763	220	27			NOUN
iajs-763	220	28	....	....	PUNCT
iajs-763	220	29	(	(	PUNCT
iajs-763	220	30	22	22	NUM
iajs-763	220	31	)	)	PUNCT
iajs-763	220	32	transform	transform	VERB
iajs-763	220	33	all	all	DET
iajs-763	220	34	the	the	DET
iajs-763	220	35	terms	term	NOUN
iajs-763	220	36	involving	involve	VERB
iajs-763	220	37	the	the	DET
iajs-763	220	38	solution	solution	NOUN
iajs-763	220	39	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	220	40	…	…	SYM
iajs-763	220	41	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	220	42	,	,	PUNCT
iajs-763	220	43	nru	nru	PROPN
iajs-763	220	44	ir	ir	PROPN
iajs-763	220	45			NUM
iajs-763	220	46	,	,	PUNCT
iajs-763	220	47	where	where	SCONJ
iajs-763	220	48	6/)1	6/)1	X
iajs-763	220	49	(	(	PUNCT
iajs-763	220	50			ADJ
iajs-763	220	51	nm	nm	NOUN
iajs-763	220	52	to	to	ADP
iajs-763	220	53	the	the	DET
iajs-763	220	54	left	left	ADJ
iajs-763	220	55	side	side	NOUN
iajs-763	220	56	of	of	ADP
iajs-763	220	57	the	the	DET
iajs-763	220	58	equation	equation	NOUN
iajs-763	220	59	(	(	PUNCT
iajs-763	220	60	22	22	NUM
iajs-763	220	61	)	)	PUNCT
iajs-763	220	62	and	and	CCONJ
iajs-763	220	63	ir	ir	PROPN
iajs-763	220	64	f	f	X
iajs-763	220	65	to	to	ADP
iajs-763	220	66	the	the	DET
iajs-763	220	67	right	right	ADJ
iajs-763	220	68	side	side	NOUN
iajs-763	220	69	.	.	PUNCT
iajs-763	221	1	ibn	ibn	PROPN
iajs-763	221	2	alhaitham	alhaitham	PROPN
iajs-763	221	3	j.	j.	PROPN
iajs-763	221	4	for	for	ADP
iajs-763	221	5	pure	pure	ADJ
iajs-763	221	6	&	&	CCONJ
iajs-763	221	7	appl	appl	PROPN
iajs-763	221	8	.	.	PUNCT
iajs-763	222	1	sci	sci	PROPN
iajs-763	222	2	.	.	PUNCT
iajs-763	222	3	vol.24	vol.24	NOUN
iajs-763	222	4	(	(	PUNCT
iajs-763	222	5	2	2	NUM
iajs-763	222	6	)	)	PUNCT
iajs-763	222	7	2011	2011	NUM
iajs-763	222	8	if	if	SCONJ
iajs-763	222	9	the	the	DET
iajs-763	222	10	number	number	NOUN
iajs-763	222	11	of	of	ADP
iajs-763	222	12	subintervals	subinterval	NOUN
iajs-763	222	13	(	(	PUNCT
iajs-763	222	14	n+2	n+2	NUM
iajs-763	222	15	)	)	PUNCT
iajs-763	222	16	is	be	AUX
iajs-763	222	17	(	(	PUNCT
iajs-763	222	18	a	a	DET
iajs-763	222	19	multiple	multiple	NOUN
iajs-763	222	20	of	of	ADP
iajs-763	222	21	six	six	NUM
iajs-763	222	22	+2	+2	NOUN
iajs-763	222	23	)	)	PUNCT
iajs-763	222	24	we	we	PRON
iajs-763	222	25	get	get	VERB
iajs-763	222	26	combination	combination	NOUN
iajs-763	222	27	between	between	ADP
iajs-763	222	28	open	open	ADJ
iajs-763	222	29	n	n	CCONJ
iajs-763	222	30	-	-	PUNCT
iajs-763	222	31	c	c	NOUN
iajs-763	222	32	:	:	PUNCT
iajs-763	222	33	n=0	n=0	NUM
iajs-763	222	34	and	and	CCONJ
iajs-763	222	35	open	open	ADJ
iajs-763	222	36	n	n	CCONJ
iajs-763	222	37	-	-	PUNCT
iajs-763	222	38	c	c	NOUN
iajs-763	222	39	:	:	PUNCT
iajs-763	222	40	n=4	n=4	ADJ
iajs-763	222	41	rules	rule	NOUN
iajs-763	222	42	and	and	CCONJ
iajs-763	222	43	mnimru	mnimru	VERB
iajs-763	222	44	ir	ir	PROPN
iajs-763	222	45			PRON
iajs-763	222	46	)	)	PUNCT
iajs-763	222	47	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	222	48	,	,	PUNCT
iajs-763	222	49			ADJ
iajs-763	222	50	where	where	SCONJ
iajs-763	222	51	6	6	NUM
iajs-763	222	52	/	/	SYM
iajs-763	222	53	nm	nm	NOUN
iajs-763	222	54	are	be	AUX
iajs-763	222	55	obtained	obtain	VERB
iajs-763	222	56	by	by	ADP
iajs-763	222	57	solving	solve	VERB
iajs-763	222	58	the	the	DET
iajs-763	222	59	system	system	NOUN
iajs-763	222	60	of	of	ADP
iajs-763	222	61	equations	equation	NOUN
iajs-763	222	62	.	.	PUNCT
iajs-763	223	1	6/)1(,,2,1,,,2,1,,,2,1	6/)1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	223	2	]	]	PUNCT
iajs-763	223	3	1114261411	1114261411	NUM
iajs-763	223	4	[	[	PUNCT
iajs-763	223	5	10	10	NUM
iajs-763	223	6	3	3	NUM
iajs-763	223	7	2	2	NUM
iajs-763	223	8	)	)	PUNCT
iajs-763	223	9	1())1(()(44332211	1())1(()(44332211	NOUN
iajs-763	223	10	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	223	11	ukukukukuk	ukukukukuk	ADJ
iajs-763	223	12	h	h	PROPN
iajs-763	223	13	uhkfu	uhkfu	PROPN
iajs-763	223	14	mnmnimnmniiiiiii	mnmnimnmniiiiiii	PROPN
iajs-763	223	15	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	223	16			PROPN
iajs-763	223	17			NOUN
iajs-763	223	18			NOUN
iajs-763	223	19			PROPN
iajs-763	223	20			NOUN
iajs-763	223	21	.	.	PUNCT
iajs-763	223	22	…	…	PUNCT
iajs-763	223	23	.(23	.(23	NOUN
iajs-763	223	24	)	)	PUNCT
iajs-763	223	25	transform	transform	VERB
iajs-763	223	26	all	all	DET
iajs-763	223	27	the	the	DET
iajs-763	223	28	terms	term	NOUN
iajs-763	223	29	involving	involve	VERB
iajs-763	223	30	the	the	DET
iajs-763	223	31	solution	solution	NOUN
iajs-763	223	32	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	223	33	…	…	SYM
iajs-763	223	34	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	223	35	,	,	PUNCT
iajs-763	223	36	nru	nru	PROPN
iajs-763	223	37	ir	ir	PROPN
iajs-763	223	38			NUM
iajs-763	223	39	,	,	PUNCT
iajs-763	223	40	where	where	SCONJ
iajs-763	223	41	6	6	NUM
iajs-763	223	42	/	/	SYM
iajs-763	223	43	nm	nm	NOUN
iajs-763	223	44			NOUN
iajs-763	223	45	to	to	ADP
iajs-763	223	46	the	the	DET
iajs-763	223	47	left	left	ADJ
iajs-763	223	48	side	side	NOUN
iajs-763	223	49	of	of	ADP
iajs-763	223	50	the	the	DET
iajs-763	223	51	equation	equation	NOUN
iajs-763	223	52	(	(	PUNCT
iajs-763	223	53	23	23	NUM
iajs-763	223	54	)	)	PUNCT
iajs-763	223	55	and	and	CCONJ
iajs-763	223	56	ir	ir	PROPN
iajs-763	223	57	f	f	X
iajs-763	223	58	to	to	ADP
iajs-763	223	59	the	the	DET
iajs-763	223	60	right	right	ADJ
iajs-763	223	61	side	side	NOUN
iajs-763	223	62	.	.	PUNCT
iajs-763	224	1	also	also	ADV
iajs-763	224	2	,	,	PUNCT
iajs-763	224	3	if	if	SCONJ
iajs-763	224	4	the	the	DET
iajs-763	224	5	number	number	NOUN
iajs-763	224	6	of	of	ADP
iajs-763	224	7	subintervals	subinterval	NOUN
iajs-763	224	8	(	(	PUNCT
iajs-763	224	9	n+2	n+2	NUM
iajs-763	224	10	)	)	PUNCT
iajs-763	224	11	is	be	AUX
iajs-763	224	12	(	(	PUNCT
iajs-763	224	13	a	a	DET
iajs-763	224	14	multiple	multiple	NOUN
iajs-763	224	15	of	of	ADP
iajs-763	224	16	six	six	NUM
iajs-763	224	17	+3	+3	PROPN
iajs-763	224	18	)	)	PUNCT
iajs-763	224	19	we	we	PRON
iajs-763	224	20	get	get	VERB
iajs-763	224	21	combination	combination	NOUN
iajs-763	224	22	between	between	ADP
iajs-763	224	23	open	open	ADJ
iajs-763	224	24	n	n	CCONJ
iajs-763	224	25	-	-	PUNCT
iajs-763	224	26	c	c	NOUN
iajs-763	224	27	:	:	PUNCT
iajs-763	224	28	n=1	n=1	PROPN
iajs-763	224	29	and	and	CCONJ
iajs-763	224	30	open	open	ADJ
iajs-763	224	31	n	n	CCONJ
iajs-763	224	32	-	-	PUNCT
iajs-763	224	33	c	c	NOUN
iajs-763	224	34	:	:	PUNCT
iajs-763	224	35	n=4	n=4	ADJ
iajs-763	224	36	rules	rule	NOUN
iajs-763	224	37	and	and	CCONJ
iajs-763	224	38	mnimru	mnimru	VERB
iajs-763	224	39	ir	ir	PROPN
iajs-763	224	40			PRON
iajs-763	224	41	)	)	PUNCT
iajs-763	224	42	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	224	43	,	,	PUNCT
iajs-763	224	44			NOUN
iajs-763	224	45	,	,	PUNCT
iajs-763	224	46	where	where	SCONJ
iajs-763	224	47	6/)1	6/)1	NUM
iajs-763	224	48	(	(	PUNCT
iajs-763	224	49			ADJ
iajs-763	224	50	nm	nm	NOUN
iajs-763	224	51	are	be	AUX
iajs-763	224	52	obtained	obtain	VERB
iajs-763	224	53	by	by	ADP
iajs-763	224	54	solving	solve	VERB
iajs-763	224	55	the	the	DET
iajs-763	224	56	system	system	NOUN
iajs-763	224	57	of	of	ADP
iajs-763	224	58	equations	equation	NOUN
iajs-763	224	59	.	.	PUNCT
iajs-763	225	1	6/)1()1(,,2,1,,,2,1,,,2,1	6/)1()1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	225	2	]	]	SYM
iajs-763	225	3	11141411	11141411	NUM
iajs-763	225	4	[	[	PUNCT
iajs-763	225	5	10	10	NUM
iajs-763	225	6	3	3	NUM
iajs-763	225	7	2	2	NUM
iajs-763	225	8	3	3	NUM
iajs-763	225	9	2	2	NUM
iajs-763	225	10	3	3	NUM
iajs-763	225	11	)	)	PUNCT
iajs-763	225	12	1())1(()(44332211	1())1(()(44332211	NUM
iajs-763	225	13			ADJ
iajs-763	225	14			NOUN
iajs-763	225	15			ADV
iajs-763	225	16	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	225	17	ukukukuk	ukukukuk	PROPN
iajs-763	225	18	h	h	PROPN
iajs-763	225	19	uk	uk	PROPN
iajs-763	225	20	h	h	PROPN
iajs-763	225	21	uhk	uhk	PROPN
iajs-763	225	22	h	h	PROPN
iajs-763	225	23	fu	fu	PROPN
iajs-763	225	24	mnmnimnmniiiiiii	mnmnimnmniiiiiii	INTJ
iajs-763	225	25	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	225	26			PROPN
iajs-763	225	27			NOUN
iajs-763	225	28	…	…	PUNCT
iajs-763	225	29	.(24	.(24	X
iajs-763	225	30	)	)	PUNCT
iajs-763	225	31	transform	transform	VERB
iajs-763	225	32	all	all	DET
iajs-763	225	33	the	the	DET
iajs-763	225	34	terms	term	NOUN
iajs-763	225	35	involving	involve	VERB
iajs-763	225	36	the	the	DET
iajs-763	225	37	solution	solution	NOUN
iajs-763	225	38	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	225	39	…	…	SYM
iajs-763	225	40	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	225	41	,	,	PUNCT
iajs-763	225	42	nru	nru	PROPN
iajs-763	225	43	ir	ir	PROPN
iajs-763	225	44			NUM
iajs-763	225	45	where	where	SCONJ
iajs-763	225	46	6/)1	6/)1	NUM
iajs-763	225	47	(	(	PUNCT
iajs-763	225	48			PROPN
iajs-763	225	49	nm	nm	ADV
iajs-763	225	50	to	to	ADP
iajs-763	225	51	the	the	DET
iajs-763	225	52	left	left	ADJ
iajs-763	225	53	side	side	NOUN
iajs-763	225	54	of	of	ADP
iajs-763	225	55	the	the	DET
iajs-763	225	56	equation	equation	NOUN
iajs-763	225	57	(	(	PUNCT
iajs-763	225	58	24	24	NUM
iajs-763	225	59	)	)	PUNCT
iajs-763	225	60	and	and	CCONJ
iajs-763	225	61	ir	ir	PROPN
iajs-763	225	62	f	f	X
iajs-763	225	63	to	to	ADP
iajs-763	225	64	the	the	DET
iajs-763	225	65	right	right	ADJ
iajs-763	225	66	side	side	NOUN
iajs-763	225	67	.	.	PUNCT
iajs-763	226	1	if	if	SCONJ
iajs-763	226	2	the	the	DET
iajs-763	226	3	number	number	NOUN
iajs-763	226	4	of	of	ADP
iajs-763	226	5	subintervals	subinterval	NOUN
iajs-763	226	6	(	(	PUNCT
iajs-763	226	7	n+2	n+2	NUM
iajs-763	226	8	)	)	PUNCT
iajs-763	226	9	is	be	AUX
iajs-763	226	10	(	(	PUNCT
iajs-763	226	11	a	a	DET
iajs-763	226	12	multiple	multiple	NOUN
iajs-763	226	13	of	of	ADP
iajs-763	226	14	six	six	NUM
iajs-763	226	15	+4	+4	NUM
iajs-763	226	16	)	)	PUNCT
iajs-763	226	17	we	we	PRON
iajs-763	226	18	get	get	VERB
iajs-763	226	19	combination	combination	NOUN
iajs-763	226	20	between	between	ADP
iajs-763	226	21	open	open	ADJ
iajs-763	226	22	n	n	CCONJ
iajs-763	226	23	-	-	PUNCT
iajs-763	226	24	c	c	NOUN
iajs-763	226	25	:	:	PUNCT
iajs-763	226	26	n=2	n=2	X
iajs-763	226	27	and	and	CCONJ
iajs-763	226	28	open	open	VERB
iajs-763	226	29	n	n	CCONJ
iajs-763	226	30	-	-	PUNCT
iajs-763	226	31	c	c	NOUN
iajs-763	226	32	:	:	PUNCT
iajs-763	226	33	n=4	n=4	ADJ
iajs-763	226	34	rules	rule	NOUN
iajs-763	226	35	and	and	CCONJ
iajs-763	226	36	mnimru	mnimru	VERB
iajs-763	226	37	ir	ir	PROPN
iajs-763	226	38			PRON
iajs-763	226	39	)	)	PUNCT
iajs-763	226	40	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	226	41	,	,	PUNCT
iajs-763	226	42			NOUN
iajs-763	226	43	,	,	PUNCT
iajs-763	226	44	where	where	SCONJ
iajs-763	226	45	6/)2	6/)2	NOUN
iajs-763	226	46	(	(	PUNCT
iajs-763	226	47			ADJ
iajs-763	226	48	nm	nm	NOUN
iajs-763	226	49	are	be	AUX
iajs-763	226	50	obtained	obtain	VERB
iajs-763	226	51	by	by	ADP
iajs-763	226	52	solving	solve	VERB
iajs-763	226	53	the	the	DET
iajs-763	226	54	system	system	NOUN
iajs-763	226	55	of	of	ADP
iajs-763	226	56	equations	equation	NOUN
iajs-763	226	57	.	.	PUNCT
iajs-763	227	1	6/)2()1(,,2,1,,,2,1,,,2,1	6/)2()1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	227	2	]	]	SYM
iajs-763	227	3	111411	111411	NUM
iajs-763	227	4	[	[	PUNCT
iajs-763	227	5	10	10	NUM
iajs-763	227	6	3	3	NUM
iajs-763	227	7	]	]	SYM
iajs-763	227	8	22	22	NUM
iajs-763	227	9	[	[	PUNCT
iajs-763	227	10	3	3	NUM
iajs-763	227	11	4	4	NUM
iajs-763	227	12	)	)	PUNCT
iajs-763	227	13	1())1(()(44332211	1())1(()(44332211	NUM
iajs-763	227	14			ADJ
iajs-763	227	15			X
iajs-763	227	16			ADV
iajs-763	227	17	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	227	18	ukukuk	ukukuk	ADJ
iajs-763	227	19	h	h	PROPN
iajs-763	227	20	ukukuhk	ukukuhk	PROPN
iajs-763	227	21	h	h	PROPN
iajs-763	227	22	fu	fu	PROPN
iajs-763	227	23	mnmnimnmniiiiiii	mnmnimnmniiiiiii	VERB
iajs-763	227	24	srssrssrssrssrssrsrr	srssrssrssrssrssrsrr	PROPN
iajs-763	227	25			PROPN
iajs-763	227	26			NOUN
iajs-763	227	27	…	…	PUNCT
iajs-763	227	28	.(25	.(25	X
iajs-763	227	29	)	)	PUNCT
iajs-763	227	30	transform	transform	VERB
iajs-763	227	31	all	all	DET
iajs-763	227	32	the	the	DET
iajs-763	227	33	terms	term	NOUN
iajs-763	227	34	involving	involve	VERB
iajs-763	227	35	the	the	DET
iajs-763	227	36	solution	solution	NOUN
iajs-763	227	37	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	227	38	…	…	SYM
iajs-763	227	39	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	227	40	,	,	PUNCT
iajs-763	227	41	nru	nru	PROPN
iajs-763	227	42	ir	ir	PROPN
iajs-763	227	43			NUM
iajs-763	227	44	,	,	PUNCT
iajs-763	227	45	where	where	SCONJ
iajs-763	227	46	6/)2	6/)2	NOUN
iajs-763	227	47	(	(	PUNCT
iajs-763	227	48			PROPN
iajs-763	227	49	nm	nm	ADV
iajs-763	227	50	to	to	ADP
iajs-763	227	51	the	the	DET
iajs-763	227	52	left	left	ADJ
iajs-763	227	53	side	side	NOUN
iajs-763	227	54	of	of	ADP
iajs-763	227	55	the	the	DET
iajs-763	227	56	equation	equation	NOUN
iajs-763	227	57	(	(	PUNCT
iajs-763	227	58	25	25	NUM
iajs-763	227	59	)	)	PUNCT
iajs-763	227	60	and	and	CCONJ
iajs-763	227	61	ifr	ifr	PROPN
iajs-763	227	62	to	to	ADP
iajs-763	227	63	the	the	DET
iajs-763	227	64	right	right	ADJ
iajs-763	227	65	side	side	NOUN
iajs-763	227	66	.	.	PUNCT
iajs-763	228	1	also	also	ADV
iajs-763	228	2	,	,	PUNCT
iajs-763	228	3	if	if	SCONJ
iajs-763	228	4	the	the	DET
iajs-763	228	5	number	number	NOUN
iajs-763	228	6	of	of	ADP
iajs-763	228	7	subintervals	subinterval	NOUN
iajs-763	228	8	(	(	PUNCT
iajs-763	228	9	n+2	n+2	NUM
iajs-763	228	10	)	)	PUNCT
iajs-763	228	11	is	be	AUX
iajs-763	228	12	(	(	PUNCT
iajs-763	228	13	a	a	DET
iajs-763	228	14	multiple	multiple	NOUN
iajs-763	228	15	of	of	ADP
iajs-763	228	16	six	six	NUM
iajs-763	228	17	+5	+5	PROPN
iajs-763	228	18	)	)	PUNCT
iajs-763	228	19	we	we	PRON
iajs-763	228	20	get	get	VERB
iajs-763	228	21	combination	combination	NOUN
iajs-763	228	22	between	between	ADP
iajs-763	228	23	open	open	ADJ
iajs-763	228	24	n	n	CCONJ
iajs-763	228	25	-	-	PUNCT
iajs-763	228	26	c	c	NOUN
iajs-763	228	27	:	:	PUNCT
iajs-763	228	28	n=3	n=3	PUNCT
iajs-763	228	29	and	and	CCONJ
iajs-763	228	30	open	open	ADJ
iajs-763	228	31	n	n	CCONJ
iajs-763	228	32	-	-	PUNCT
iajs-763	228	33	c	c	NOUN
iajs-763	228	34	:	:	PUNCT
iajs-763	228	35	n=4	n=4	ADJ
iajs-763	228	36	rules	rule	NOUN
iajs-763	228	37	and	and	CCONJ
iajs-763	228	38	mnimru	mnimru	VERB
iajs-763	228	39	ir	ir	PROPN
iajs-763	228	40			PRON
iajs-763	228	41	)	)	PUNCT
iajs-763	228	42	1(,2,1,,,2,1	1(,2,1,,,2,1	NUM
iajs-763	228	43	,	,	PUNCT
iajs-763	228	44			NOUN
iajs-763	228	45	,	,	PUNCT
iajs-763	228	46	where	where	SCONJ
iajs-763	228	47	6/)3	6/)3	NOUN
iajs-763	228	48	(	(	PUNCT
iajs-763	228	49			ADJ
iajs-763	228	50	nm	nm	NOUN
iajs-763	228	51	are	be	AUX
iajs-763	228	52	obtained	obtain	VERB
iajs-763	228	53	by	by	ADP
iajs-763	228	54	solving	solve	VERB
iajs-763	228	55	the	the	DET
iajs-763	228	56	system	system	NOUN
iajs-763	228	57	of	of	ADP
iajs-763	228	58	equations	equation	NOUN
iajs-763	228	59	.	.	PUNCT
iajs-763	229	1	6/)3()1(,,2,1,,,2,1,,,2,1	6/)3()1(,,2,1,,,2,1,,,2,1	NUM
iajs-763	229	2	]	]	PUNCT
iajs-763	229	3	111411	111411	NUM
iajs-763	229	4	[	[	PUNCT
iajs-763	229	5	10	10	NUM
iajs-763	229	6	3	3	NUM
iajs-763	229	7	]	]	SYM
iajs-763	229	8	1111	1111	NUM
iajs-763	229	9	[	[	PUNCT
iajs-763	229	10	24	24	NUM
iajs-763	229	11	5	5	NUM
iajs-763	229	12	)	)	PUNCT
iajs-763	230	1	1())1(()(5544332211	1())1(()(5544332211	PROPN
iajs-763	230	2			PROPN
iajs-763	230	3			PROPN
iajs-763	230	4			ADV
iajs-763	230	5	nmwheremninsnrfor	nmwheremninsnrfor	ADP
iajs-763	230	6	ukukuk	ukukuk	ADJ
iajs-763	230	7	h	h	PROPN
iajs-763	230	8	ukukukuhk	ukukukuhk	PROPN
iajs-763	230	9	h	h	PROPN
iajs-763	230	10	fu	fu	PROPN
iajs-763	230	11	mnmnimnmniiiiiiii	mnmnimnmniiiiiiii	PROPN
iajs-763	230	12	srssrssrssrssrssrssrsrr	srssrssrssrssrssrssrsrr	VERB
iajs-763	230	13			PROPN
iajs-763	230	14			NOUN
iajs-763	230	15	....	....	PUNCT
iajs-763	230	16	(	(	PUNCT
iajs-763	230	17	26	26	NUM
iajs-763	230	18	)	)	PUNCT
iajs-763	230	19	transform	transform	VERB
iajs-763	230	20	all	all	DET
iajs-763	230	21	the	the	DET
iajs-763	230	22	terms	term	NOUN
iajs-763	230	23	involving	involve	VERB
iajs-763	230	24	the	the	DET
iajs-763	230	25	solution	solution	NOUN
iajs-763	230	26	m-1)+(n,	m-1)+(n,	NOUN
iajs-763	230	27	…	…	SYM
iajs-763	230	28	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	230	29	,	,	PUNCT
iajs-763	230	30	nru	nru	PROPN
iajs-763	230	31	ir	ir	PROPN
iajs-763	230	32			NUM
iajs-763	230	33	,	,	PUNCT
iajs-763	230	34	where	where	SCONJ
iajs-763	230	35	6/)3	6/)3	NOUN
iajs-763	230	36	(	(	PUNCT
iajs-763	230	37			ADJ
iajs-763	230	38	nm	nm	ADV
iajs-763	230	39	to	to	ADP
iajs-763	230	40	the	the	DET
iajs-763	230	41	left	left	ADJ
iajs-763	230	42	side	side	NOUN
iajs-763	230	43	of	of	ADP
iajs-763	230	44	the	the	DET
iajs-763	230	45	equation	equation	NOUN
iajs-763	230	46	(	(	PUNCT
iajs-763	230	47	26	26	NUM
iajs-763	230	48	)	)	PUNCT
iajs-763	230	49	and	and	CCONJ
iajs-763	230	50	ir	ir	PROPN
iajs-763	230	51	f	f	X
iajs-763	230	52	to	to	ADP
iajs-763	230	53	the	the	DET
iajs-763	230	54	right	right	ADJ
iajs-763	230	55	side	side	NOUN
iajs-763	230	56	.	.	PUNCT
iajs-763	231	1	finally	finally	ADV
iajs-763	231	2	,	,	PUNCT
iajs-763	231	3	each	each	DET
iajs-763	231	4	system	system	NOUN
iajs-763	231	5	in	in	ADP
iajs-763	231	6	equations	equation	NOUN
iajs-763	231	7	(	(	PUNCT
iajs-763	231	8	21	21	NUM
iajs-763	231	9	)	)	PUNCT
iajs-763	231	10	,	,	PUNCT
iajs-763	231	11	(	(	PUNCT
iajs-763	231	12	22	22	NUM
iajs-763	231	13	)	)	PUNCT
iajs-763	231	14	,	,	PUNCT
iajs-763	231	15	(	(	PUNCT
iajs-763	231	16	23	23	NUM
iajs-763	231	17	)	)	PUNCT
iajs-763	231	18	,	,	PUNCT
iajs-763	231	19	(	(	PUNCT
iajs-763	231	20	24	24	NUM
iajs-763	231	21	)	)	PUNCT
iajs-763	231	22	,	,	PUNCT
iajs-763	231	23	(	(	PUNCT
iajs-763	231	24	25	25	NUM
iajs-763	231	25	)	)	PUNCT
iajs-763	231	26	and	and	CCONJ
iajs-763	231	27	(	(	PUNCT
iajs-763	231	28	26	26	NUM
iajs-763	231	29	)	)	PUNCT
iajs-763	231	30	can	can	AUX
iajs-763	231	31	be	be	AUX
iajs-763	231	32	written	write	VERB
iajs-763	231	33	in	in	ADP
iajs-763	231	34	a	a	DET
iajs-763	231	35	matrix	matrix	NOUN
iajs-763	231	36	form	form	NOUN
iajs-763	231	37	as	as	ADP
iajs-763	231	38	fku	fku	PROPN
iajs-763	231	39			PROPN
iajs-763	231	40	where	where	SCONJ
iajs-763	231	41	k	k	PROPN
iajs-763	231	42	is	be	AUX
iajs-763	231	43	the	the	DET
iajs-763	231	44	matrix	matrix	NOUN
iajs-763	231	45	of	of	ADP
iajs-763	231	46	the	the	DET
iajs-763	231	47	coefficients	coefficient	NOUN
iajs-763	231	48	,	,	PUNCT
iajs-763	231	49	u	u	NOUN
iajs-763	231	50	is	be	AUX
iajs-763	231	51	the	the	DET
iajs-763	231	52	matrix	matrix	NOUN
iajs-763	231	53	of	of	ADP
iajs-763	231	54	solution	solution	NOUN
iajs-763	231	55	ibn	ibn	PROPN
iajs-763	231	56	alhaitham	alhaitham	PROPN
iajs-763	231	57	j.	j.	PROPN
iajs-763	231	58	for	for	ADP
iajs-763	231	59	pure	pure	ADJ
iajs-763	231	60	&	&	CCONJ
iajs-763	231	61	appl	appl	PROPN
iajs-763	231	62	.	.	PUNCT
iajs-763	232	1	sci	sci	PROPN
iajs-763	232	2	.	.	PUNCT
iajs-763	232	3	vol.24	vol.24	NOUN
iajs-763	232	4	(	(	PUNCT
iajs-763	232	5	2	2	NUM
iajs-763	232	6	)	)	PUNCT
iajs-763	232	7	2011	2011	NUM
iajs-763	232	8	and	and	CCONJ
iajs-763	232	9	f	f	PROPN
iajs-763	232	10	is	be	AUX
iajs-763	232	11	the	the	DET
iajs-763	232	12	matrix	matrix	NOUN
iajs-763	232	13	of	of	ADP
iajs-763	232	14	non	non	ADJ
iajs-763	232	15	-	-	ADJ
iajs-763	232	16	homogeneous	homogeneous	ADJ
iajs-763	232	17	part	part	NOUN
iajs-763	232	18	.	.	PUNCT
iajs-763	233	1	to	to	PART
iajs-763	233	2	find	find	VERB
iajs-763	233	3	the	the	DET
iajs-763	233	4	approximate	approximate	ADJ
iajs-763	233	5	solution	solution	NOUN
iajs-763	233	6	nru	nru	PROPN
iajs-763	233	7	ir	ir	PROPN
iajs-763	233	8	,	,	PUNCT
iajs-763	233	9	,	,	PUNCT
iajs-763	233	10	2,1	2,1	NUM
iajs-763	233	11	,	,	PUNCT
iajs-763	233	12			NUM
iajs-763	233	13	we	we	PRON
iajs-763	233	14	find	find	VERB
iajs-763	233	15	fku	fku	PROPN
iajs-763	233	16	1	1	NUM
iajs-763	233	17	the	the	DET
iajs-763	233	18	algorithm	algorithm	NOUN
iajs-763	233	19	of	of	ADP
iajs-763	233	20	open	open	ADJ
iajs-763	233	21	n	n	CCONJ
iajs-763	233	22	-	-	PUNCT
iajs-763	233	23	c	c	NOUN
iajs-763	233	24	{	{	PUNCT
iajs-763	233	25	n=4	n=4	NOUN
iajs-763	233	26	}	}	PUNCT
iajs-763	233	27	(	(	PUNCT
iajs-763	233	28	soncn4	soncn4	NOUN
iajs-763	233	29	)	)	PUNCT
iajs-763	233	30	step	step	NOUN
iajs-763	233	31	1	1	NUM
iajs-763	233	32	:	:	PUNCT
iajs-763	233	33	compute	compute	VERB
iajs-763	233	34	2	2	NUM
iajs-763	233	35			PROPN
iajs-763	233	36			PROPN
iajs-763	233	37	n	n	CCONJ
iajs-763	233	38	ab	ab	NOUN
iajs-763	233	39	h	h	NOUN
iajs-763	233	40	,	,	PUNCT
iajs-763	233	41	nn	nn	ADJ
iajs-763	233	42	step	step	NOUN
iajs-763	233	43	2	2	NUM
iajs-763	233	44	:	:	PUNCT
iajs-763	233	45			PROPN
iajs-763	233	46	compute	compute	NOUN
iajs-763	233	47	m-2)+(n,	m-2)+(n,	PROPN
iajs-763	233	48	…	…	SYM
iajs-763	233	49	1,2,=i,,,2,1	1,2,=i,,,2,1	NUM
iajs-763	233	50	,	,	PUNCT
iajs-763	233	51	nru	nru	PROPN
iajs-763	233	52	ir	ir	PROPN
iajs-763	233	53			NUM
iajs-763	233	54	where	where	SCONJ
iajs-763	233	55	6/)2	6/)2	NOUN
iajs-763	233	56	(	(	PUNCT
iajs-763	233	57			ADV
iajs-763	233	58	nm	nm	NOUN
iajs-763	233	59	,	,	PUNCT
iajs-763	233	60	using	use	VERB
iajs-763	233	61	equation	equation	NOUN
iajs-763	233	62	(	(	PUNCT
iajs-763	233	63	21	21	NUM
iajs-763	233	64	)	)	PUNCT
iajs-763	233	65	when	when	SCONJ
iajs-763	233	66	the	the	DET
iajs-763	233	67	number	number	NOUN
iajs-763	233	68	of	of	ADP
iajs-763	233	69	subintervals	subinterval	NOUN
iajs-763	233	70	is	be	AUX
iajs-763	233	71	(	(	PUNCT
iajs-763	233	72	a	a	DET
iajs-763	233	73	multiple	multiple	NOUN
iajs-763	233	74	of	of	ADP
iajs-763	233	75	6	6	NUM
iajs-763	233	76	)	)	PUNCT
iajs-763	233	77	.	.	PUNCT
iajs-763	234	1			PROPN
iajs-763	234	2	compute	compute	PROPN
iajs-763	234	3	mninru	mninru	NOUN
iajs-763	234	4	ir	ir	PROPN
iajs-763	234	5			PRON
iajs-763	234	6	)	)	PUNCT
iajs-763	234	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	234	8	,	,	PUNCT
iajs-763	234	9			ADJ
iajs-763	234	10	where	where	SCONJ
iajs-763	234	11	6/)1	6/)1	NOUN
iajs-763	234	12	(	(	PUNCT
iajs-763	234	13			ADJ
iajs-763	234	14	nm	nm	NOUN
iajs-763	234	15	,	,	PUNCT
iajs-763	234	16	using	use	VERB
iajs-763	234	17	equation	equation	NOUN
iajs-763	234	18	(	(	PUNCT
iajs-763	234	19	22	22	NUM
iajs-763	234	20	)	)	PUNCT
iajs-763	234	21	when	when	SCONJ
iajs-763	234	22	the	the	DET
iajs-763	234	23	number	number	NOUN
iajs-763	234	24	of	of	ADP
iajs-763	234	25	subintervals	subinterval	NOUN
iajs-763	234	26	is	be	AUX
iajs-763	234	27	(	(	PUNCT
iajs-763	234	28	a	a	DET
iajs-763	234	29	multiple	multiple	NOUN
iajs-763	234	30	of	of	ADP
iajs-763	234	31	6	6	NUM
iajs-763	234	32	+1	+1	NOUN
iajs-763	234	33	)	)	PUNCT
iajs-763	234	34	.	.	PUNCT
iajs-763	235	1			PROPN
iajs-763	235	2	compute	compute	PROPN
iajs-763	235	3	mninru	mninru	NOUN
iajs-763	235	4	ir	ir	PROPN
iajs-763	235	5			PRON
iajs-763	235	6	)	)	PUNCT
iajs-763	235	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	235	8	,	,	PUNCT
iajs-763	235	9			ADJ
iajs-763	235	10	where	where	SCONJ
iajs-763	235	11	5	5	NUM
iajs-763	235	12	/	/	SYM
iajs-763	235	13	nm	nm	NOUN
iajs-763	235	14	,	,	PUNCT
iajs-763	235	15	using	use	VERB
iajs-763	235	16	equation	equation	NOUN
iajs-763	235	17	(	(	PUNCT
iajs-763	235	18	23	23	NUM
iajs-763	235	19	)	)	PUNCT
iajs-763	235	20	when	when	SCONJ
iajs-763	235	21	the	the	DET
iajs-763	235	22	number	number	NOUN
iajs-763	235	23	of	of	ADP
iajs-763	235	24	subintervals	subinterval	NOUN
iajs-763	235	25	is	be	AUX
iajs-763	235	26	(	(	PUNCT
iajs-763	235	27	a	a	DET
iajs-763	235	28	multiple	multiple	NOUN
iajs-763	235	29	of	of	ADP
iajs-763	235	30	6	6	NUM
iajs-763	235	31	+2	+2	NOUN
iajs-763	235	32	)	)	PUNCT
iajs-763	235	33	.	.	PUNCT
iajs-763	236	1			PROPN
iajs-763	236	2	compute	compute	PROPN
iajs-763	236	3	mninru	mninru	NOUN
iajs-763	236	4	ir	ir	PROPN
iajs-763	236	5			PRON
iajs-763	236	6	)	)	PUNCT
iajs-763	236	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	236	8	,	,	PUNCT
iajs-763	236	9			ADJ
iajs-763	236	10	where	where	SCONJ
iajs-763	236	11	6/)1	6/)1	NOUN
iajs-763	236	12	(	(	PUNCT
iajs-763	236	13			ADJ
iajs-763	236	14	nm	nm	NOUN
iajs-763	236	15	,	,	PUNCT
iajs-763	236	16	using	use	VERB
iajs-763	236	17	equation	equation	NOUN
iajs-763	236	18	(	(	PUNCT
iajs-763	236	19	24	24	NUM
iajs-763	236	20	)	)	PUNCT
iajs-763	236	21	when	when	SCONJ
iajs-763	236	22	the	the	DET
iajs-763	236	23	number	number	NOUN
iajs-763	236	24	of	of	ADP
iajs-763	236	25	subintervals	subinterval	NOUN
iajs-763	236	26	is	be	AUX
iajs-763	236	27	(	(	PUNCT
iajs-763	236	28	a	a	DET
iajs-763	236	29	multiple	multiple	NOUN
iajs-763	236	30	of	of	ADP
iajs-763	236	31	6	6	NUM
iajs-763	236	32	+3	+3	NOUN
iajs-763	236	33	)	)	PUNCT
iajs-763	236	34	.	.	PUNCT
iajs-763	237	1			PROPN
iajs-763	237	2	compute	compute	PROPN
iajs-763	237	3	mninru	mninru	NOUN
iajs-763	237	4	ir	ir	PROPN
iajs-763	237	5			PRON
iajs-763	237	6	)	)	PUNCT
iajs-763	237	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	237	8	,	,	PUNCT
iajs-763	237	9			ADP
iajs-763	237	10	where	where	SCONJ
iajs-763	237	11	6/)2	6/)2	NOUN
iajs-763	237	12	(	(	PUNCT
iajs-763	237	13			ADJ
iajs-763	237	14	nm	nm	NOUN
iajs-763	237	15	,	,	PUNCT
iajs-763	237	16	using	use	VERB
iajs-763	237	17	equation	equation	NOUN
iajs-763	237	18	(	(	PUNCT
iajs-763	237	19	25	25	NUM
iajs-763	237	20	)	)	PUNCT
iajs-763	237	21	when	when	SCONJ
iajs-763	237	22	the	the	DET
iajs-763	237	23	number	number	NOUN
iajs-763	237	24	of	of	ADP
iajs-763	237	25	subintervals	subinterval	NOUN
iajs-763	237	26	is	be	AUX
iajs-763	237	27	(	(	PUNCT
iajs-763	237	28	a	a	DET
iajs-763	237	29	multiple	multiple	NOUN
iajs-763	237	30	of	of	ADP
iajs-763	237	31	6	6	NUM
iajs-763	237	32	+4	+4	NUM
iajs-763	237	33	)	)	PUNCT
iajs-763	237	34	.	.	PUNCT
iajs-763	238	1			PROPN
iajs-763	238	2	compute	compute	PROPN
iajs-763	238	3	mninru	mninru	NOUN
iajs-763	238	4	ir	ir	PROPN
iajs-763	238	5			PRON
iajs-763	238	6	)	)	PUNCT
iajs-763	238	7	1(,,2,1,,,2,1	1(,,2,1,,,2,1	NUM
iajs-763	238	8	,	,	PUNCT
iajs-763	238	9			ADP
iajs-763	238	10	where	where	SCONJ
iajs-763	238	11	6/)2	6/)2	NOUN
iajs-763	238	12	(	(	PUNCT
iajs-763	238	13			ADJ
iajs-763	238	14	nm	nm	NOUN
iajs-763	238	15	,	,	PUNCT
iajs-763	238	16	using	use	VERB
iajs-763	238	17	equation	equation	NOUN
iajs-763	238	18	(	(	PUNCT
iajs-763	238	19	26	26	NUM
iajs-763	238	20	)	)	PUNCT
iajs-763	238	21	when	when	SCONJ
iajs-763	238	22	the	the	DET
iajs-763	238	23	number	number	NOUN
iajs-763	238	24	of	of	ADP
iajs-763	238	25	subintervals	subinterval	NOUN
iajs-763	238	26	is	be	AUX
iajs-763	238	27	(	(	PUNCT
iajs-763	238	28	a	a	DET
iajs-763	238	29	multiple	multiple	NOUN
iajs-763	238	30	of	of	ADP
iajs-763	238	31	6	6	NUM
iajs-763	238	32	+5	+5	NUM
iajs-763	238	33	)	)	PUNCT
iajs-763	238	34	.	.	PUNCT
iajs-763	239	1	step	step	NOUN
iajs-763	239	2	3	3	NUM
iajs-763	239	3	:	:	PUNCT
iajs-763	239	4	solve	solve	VERB
iajs-763	239	5	the	the	DET
iajs-763	239	6	resulting	result	VERB
iajs-763	239	7	system	system	NOUN
iajs-763	239	8	by	by	ADP
iajs-763	239	9	multiplication	multiplication	NOUN
iajs-763	239	10	it	it	PRON
iajs-763	239	11	with	with	ADP
iajs-763	239	12	k	k	PROPN
iajs-763	239	13	-1	-1	PROPN
iajs-763	239	14	.	.	PUNCT
iajs-763	240	1	3numerical	3numerical	NUM
iajs-763	240	2	examples	example	NOUN
iajs-763	240	3	in	in	ADP
iajs-763	240	4	this	this	DET
iajs-763	240	5	section	section	NOUN
iajs-763	240	6	,	,	PUNCT
iajs-763	240	7	we	we	PRON
iajs-763	240	8	test	test	VERB
iajs-763	240	9	some	some	PRON
iajs-763	240	10	of	of	ADP
iajs-763	240	11	the	the	DET
iajs-763	240	12	numerical	numerical	ADJ
iajs-763	240	13	examples	example	NOUN
iajs-763	240	14	performed	perform	VERB
iajs-763	240	15	to	to	ADP
iajs-763	240	16	solving	solve	VERB
iajs-763	240	17	this	this	DET
iajs-763	240	18	linear	linear	ADJ
iajs-763	240	19	system	system	NOUN
iajs-763	240	20	of	of	ADP
iajs-763	240	21	fredholm	fredholm	ADJ
iajs-763	240	22	integral	integral	ADJ
iajs-763	240	23	equations	equation	NOUN
iajs-763	240	24	.	.	PUNCT
iajs-763	241	1	the	the	DET
iajs-763	241	2	exact	exact	ADJ
iajs-763	241	3	solution	solution	NOUN
iajs-763	241	4	is	be	AUX
iajs-763	241	5	used	use	VERB
iajs-763	241	6	only	only	ADV
iajs-763	241	7	to	to	PART
iajs-763	241	8	show	show	VERB
iajs-763	241	9	the	the	DET
iajs-763	241	10	accuracy	accuracy	NOUN
iajs-763	241	11	of	of	ADP
iajs-763	241	12	the	the	DET
iajs-763	241	13	numerical	numerical	ADJ
iajs-763	241	14	solution	solution	NOUN
iajs-763	241	15	which	which	PRON
iajs-763	241	16	obtained	obtain	VERB
iajs-763	241	17	with	with	ADP
iajs-763	241	18	our	our	PRON
iajs-763	241	19	method	method	NOUN
iajs-763	241	20	.	.	PUNCT
iajs-763	242	1	example	example	NOUN
iajs-763	242	2	(	(	PUNCT
iajs-763	242	3	1	1	NUM
iajs-763	242	4	):	):	PUNCT
iajs-763	242	5	consider	consider	VERB
iajs-763	242	6	the	the	DET
iajs-763	242	7	problem	problem	NOUN
iajs-763	242	8	:	:	PUNCT
iajs-763	242	9			NOUN
iajs-763	242	10			SYM
iajs-763	242	11			NOUN
iajs-763	242	12			PRON
iajs-763	242	13			PUNCT
iajs-763	243	1			PROPN
iajs-763	243	2			ADV
iajs-763	243	3			ADV
iajs-763	243	4			PUNCT
iajs-763	243	5	1	1	NUM
iajs-763	243	6	0	0	NUM
iajs-763	243	7	21	21	NUM
iajs-763	243	8	2	2	NUM
iajs-763	243	9	2	2	NUM
iajs-763	243	10	1	1	NUM
iajs-763	243	11	0	0	NUM
iajs-763	243	12	211	211	NUM
iajs-763	243	13	)	)	PUNCT
iajs-763	243	14	(	(	PUNCT
iajs-763	243	15	)	)	PUNCT
iajs-763	243	16	(	(	PUNCT
iajs-763	243	17	1	1	NUM
iajs-763	243	18	12	12	NUM
iajs-763	243	19	19	19	NUM
iajs-763	243	20	)	)	PUNCT
iajs-763	243	21	(	(	PUNCT
iajs-763	243	22	)	)	PUNCT
iajs-763	243	23	(	(	PUNCT
iajs-763	243	24	)	)	PUNCT
iajs-763	243	25	(	(	PUNCT
iajs-763	243	26	3	3	X
iajs-763	243	27	)	)	PUNCT
iajs-763	243	28	(	(	PUNCT
iajs-763	243	29	36	36	NUM
iajs-763	243	30	17	17	NUM
iajs-763	243	31	18	18	NUM
iajs-763	243	32	)	)	PUNCT
iajs-763	243	33	(	(	PUNCT
iajs-763	243	34	dttutuxtxxxu	dttutuxtxxxu	ADJ
iajs-763	243	35	dttutu	dttutu	NOUN
iajs-763	243	36	txx	txx	AUX
iajs-763	243	37	xu	xu	PROPN
iajs-763	243	38	which	which	PRON
iajs-763	243	39	is	be	AUX
iajs-763	243	40	a	a	DET
iajs-763	243	41	system	system	NOUN
iajs-763	243	42	of	of	ADP
iajs-763	243	43	two	two	NUM
iajs-763	243	44	linear	linear	ADJ
iajs-763	243	45	fie	fie	NOUN
iajs-763	243	46	's	's	PART
iajs-763	243	47	,	,	PUNCT
iajs-763	243	48	with	with	ADP
iajs-763	243	49	exact	exact	ADJ
iajs-763	243	50	solution	solution	NOUN
iajs-763	243	51	is	be	AUX
iajs-763	243	52	[	[	X
iajs-763	243	53	5	5	NUM
iajs-763	243	54	]	]	SYM
iajs-763	243	55	:	:	PUNCT
iajs-763	243	56	1)(,1	1)(,1	NUM
iajs-763	243	57	)	)	PUNCT
iajs-763	243	58	(	(	PUNCT
iajs-763	243	59	2	2	NUM
iajs-763	243	60	21	21	NUM
iajs-763	243	61			NOUN
iajs-763	243	62	xxuxxu	xxuxxu	ADJ
iajs-763	243	63	tables	table	NOUN
iajs-763	243	64	(	(	PUNCT
iajs-763	243	65	1	1	NUM
iajs-763	243	66	)	)	PUNCT
iajs-763	243	67	and	and	CCONJ
iajs-763	243	68	(	(	PUNCT
iajs-763	243	69	2	2	X
iajs-763	243	70	)	)	PUNCT
iajs-763	243	71	present	present	ADJ
iajs-763	243	72	a	a	DET
iajs-763	243	73	comparison	comparison	NOUN
iajs-763	243	74	between	between	ADP
iajs-763	243	75	the	the	DET
iajs-763	243	76	exact	exact	ADJ
iajs-763	243	77	and	and	CCONJ
iajs-763	243	78	numerical	numerical	ADJ
iajs-763	243	79	solution	solution	NOUN
iajs-763	243	80	of	of	ADP
iajs-763	243	81	four	four	NUM
iajs-763	243	82	types	type	NOUN
iajs-763	243	83	of	of	ADP
iajs-763	243	84	open	open	ADJ
iajs-763	243	85	newton	newton	PROPN
iajs-763	243	86	–	–	PUNCT
iajs-763	243	87	cotes	cote	NOUN
iajs-763	243	88	and	and	CCONJ
iajs-763	243	89	two	two	NUM
iajs-763	243	90	types	type	NOUN
iajs-763	243	91	of	of	ADP
iajs-763	243	92	closed	closed	ADJ
iajs-763	243	93	newton	newton	PROPN
iajs-763	243	94	–	–	PUNCT
iajs-763	243	95	cotes	cote	NOUN
iajs-763	243	96	for	for	ADP
iajs-763	243	97	u1	u1	NOUN
iajs-763	243	98	and	and	CCONJ
iajs-763	243	99	u2	u2	NOUN
iajs-763	243	100	respectively	respectively	ADV
iajs-763	243	101	depending	depend	VERB
iajs-763	243	102	on	on	ADP
iajs-763	243	103	least	least	ADJ
iajs-763	243	104	square	square	ADJ
iajs-763	243	105	error	error	NOUN
iajs-763	243	106	and	and	CCONJ
iajs-763	243	107	running	run	VERB
iajs-763	243	108	time	time	NOUN
iajs-763	243	109	with	with	ADP
iajs-763	243	110	h=1/16	h=1/16	PROPN
iajs-763	243	111	.	.	PUNCT
iajs-763	244	1	example	example	NOUN
iajs-763	244	2	(	(	PUNCT
iajs-763	244	3	2	2	NUM
iajs-763	244	4	):	):	PUNCT
iajs-763	244	5	consider	consider	VERB
iajs-763	244	6	the	the	DET
iajs-763	244	7	problem	problem	NOUN
iajs-763	244	8	:	:	PUNCT
iajs-763	245	1			PROPN
iajs-763	245	2			X
iajs-763	246	1			X
iajs-763	247	1			PROPN
iajs-763	247	2			PRON
iajs-763	248	1			NOUN
iajs-763	248	2	1	1	NUM
iajs-763	248	3	0	0	NUM
iajs-763	248	4	3	3	NUM
iajs-763	248	5	1	1	NUM
iajs-763	248	6	0	0	NUM
iajs-763	248	7	2	2	NUM
iajs-763	248	8	1	1	NUM
iajs-763	248	9	0	0	NUM
iajs-763	248	10	1	1	NUM
iajs-763	248	11	2	2	NUM
iajs-763	248	12	3	3	NUM
iajs-763	248	13	1	1	NUM
iajs-763	248	14	0	0	NUM
iajs-763	248	15	3	3	NUM
iajs-763	248	16	1	1	NUM
iajs-763	248	17	0	0	NUM
iajs-763	248	18	2	2	NUM
iajs-763	248	19	1	1	NUM
iajs-763	248	20	0	0	NUM
iajs-763	248	21	1	1	NUM
iajs-763	248	22	22	22	NUM
iajs-763	248	23	2	2	NUM
iajs-763	248	24	1	1	NUM
iajs-763	248	25	0	0	NUM
iajs-763	248	26	3	3	NUM
iajs-763	248	27	2	2	NUM
iajs-763	248	28	1	1	NUM
iajs-763	248	29	0	0	NUM
iajs-763	248	30	2	2	NUM
iajs-763	248	31	1	1	NUM
iajs-763	248	32	0	0	NUM
iajs-763	248	33	1	1	NUM
iajs-763	248	34	2	2	NUM
iajs-763	248	35	1	1	NUM
iajs-763	248	36	)	)	PUNCT
iajs-763	248	37	(	(	PUNCT
iajs-763	248	38	)	)	PUNCT
iajs-763	248	39	(	(	PUNCT
iajs-763	248	40	)	)	PUNCT
iajs-763	248	41	(	(	PUNCT
iajs-763	248	42	3)()1	3)()1	NUM
iajs-763	248	43	(	(	PUNCT
iajs-763	248	44	6	6	NUM
iajs-763	248	45	11	11	NUM
iajs-763	248	46	12	12	NUM
iajs-763	248	47	7	7	NUM
iajs-763	248	48	)	)	PUNCT
iajs-763	248	49	(	(	PUNCT
iajs-763	248	50	)	)	PUNCT
iajs-763	248	51	(	(	PUNCT
iajs-763	248	52	)	)	PUNCT
iajs-763	248	53	(	(	PUNCT
iajs-763	248	54	)	)	PUNCT
iajs-763	248	55	(	(	PUNCT
iajs-763	248	56	)	)	PUNCT
iajs-763	248	57	2	2	NUM
iajs-763	248	58	(	(	PUNCT
iajs-763	248	59	)	)	PUNCT
iajs-763	248	60	(	(	PUNCT
iajs-763	248	61	)	)	PUNCT
iajs-763	248	62	(	(	PUNCT
iajs-763	248	63	6	6	NUM
iajs-763	248	64	7	7	NUM
iajs-763	248	65	3	3	NUM
iajs-763	248	66	5	5	NUM
iajs-763	248	67	3	3	NUM
iajs-763	248	68	2	2	NUM
iajs-763	248	69	)	)	PUNCT
iajs-763	248	70	(	(	PUNCT
iajs-763	248	71	)	)	PUNCT
iajs-763	248	72	(	(	PUNCT
iajs-763	248	73	)	)	PUNCT
iajs-763	248	74	(	(	PUNCT
iajs-763	248	75	)	)	PUNCT
iajs-763	248	76	(	(	PUNCT
iajs-763	248	77	)	)	PUNCT
iajs-763	248	78	(	(	PUNCT
iajs-763	248	79	30	30	NUM
iajs-763	248	80	29	29	NUM
iajs-763	248	81	3	3	NUM
iajs-763	248	82	)	)	PUNCT
iajs-763	248	83	(	(	PUNCT
iajs-763	248	84	dttuxtdttudttuxxxxu	dttuxtdttudttuxxxxu	ADV
iajs-763	248	85	dttuxdttutdttuxxxxu	dttuxdttutdttuxxxxu	ADV
iajs-763	248	86	dttutdttutdttutx	dttutdttutdttutx	PROPN
iajs-763	248	87	x	x	PUNCT
iajs-763	248	88	xxu	xxu	PROPN
iajs-763	248	89	ibn	ibn	PROPN
iajs-763	248	90	alhaitham	alhaitham	NOUN
iajs-763	248	91	j.	j.	PROPN
iajs-763	248	92	for	for	ADP
iajs-763	248	93	pure	pure	ADJ
iajs-763	248	94	&	&	CCONJ
iajs-763	248	95	appl	appl	PROPN
iajs-763	248	96	.	.	PUNCT
iajs-763	249	1	sci	sci	PROPN
iajs-763	249	2	.	.	PUNCT
iajs-763	249	3	vol.24	vol.24	NOUN
iajs-763	249	4	(	(	PUNCT
iajs-763	249	5	2	2	NUM
iajs-763	249	6	)	)	PUNCT
iajs-763	249	7	2011	2011	NUM
iajs-763	249	8	which	which	PRON
iajs-763	249	9	is	be	AUX
iajs-763	249	10	a	a	DET
iajs-763	249	11	system	system	NOUN
iajs-763	249	12	of	of	ADP
iajs-763	249	13	three	three	NUM
iajs-763	249	14	linear	linear	ADJ
iajs-763	249	15	fie	fie	NOUN
iajs-763	249	16	's	's	PART
iajs-763	249	17	,	,	PUNCT
iajs-763	249	18	with	with	ADP
iajs-763	249	19	exact	exact	ADJ
iajs-763	249	20	solution	solution	NOUN
iajs-763	249	21	is	be	AUX
iajs-763	249	22	2	2	NUM
iajs-763	249	23	3	3	NUM
iajs-763	249	24	2	2	NUM
iajs-763	249	25	2	2	NUM
iajs-763	249	26	2	2	NUM
iajs-763	249	27	1	1	NUM
iajs-763	249	28	1	1	NUM
iajs-763	249	29	)	)	PUNCT
iajs-763	249	30	(	(	PUNCT
iajs-763	249	31	,	,	PUNCT
iajs-763	249	32	)	)	PUNCT
iajs-763	249	33	(	(	PUNCT
iajs-763	249	34	,	,	PUNCT
iajs-763	249	35	)	)	PUNCT
iajs-763	249	36	(	(	PUNCT
iajs-763	249	37	xxuxxxuxxu	xxuxxxuxxu	PROPN
iajs-763	249	38			NOUN
iajs-763	249	39	tables	table	NOUN
iajs-763	249	40	(	(	PUNCT
iajs-763	249	41	3)(5	3)(5	NUM
iajs-763	249	42	)	)	PUNCT
iajs-763	249	43	present	present	VERB
iajs-763	249	44	a	a	DET
iajs-763	249	45	comparison	comparison	NOUN
iajs-763	249	46	between	between	ADP
iajs-763	249	47	the	the	DET
iajs-763	249	48	exact	exact	ADJ
iajs-763	249	49	and	and	CCONJ
iajs-763	249	50	numerical	numerical	ADJ
iajs-763	249	51	solution	solution	NOUN
iajs-763	249	52	of	of	ADP
iajs-763	249	53	four	four	NUM
iajs-763	249	54	types	type	NOUN
iajs-763	249	55	of	of	ADP
iajs-763	249	56	open	open	ADJ
iajs-763	249	57	newton	newton	PROPN
iajs-763	249	58	–	–	PUNCT
iajs-763	249	59	cotes	cote	NOUN
iajs-763	249	60	and	and	CCONJ
iajs-763	249	61	three	three	NUM
iajs-763	249	62	types	type	NOUN
iajs-763	249	63	of	of	ADP
iajs-763	249	64	closed	closed	ADJ
iajs-763	249	65	newton	newton	PROPN
iajs-763	249	66	–	–	PUNCT
iajs-763	249	67	cotes	cote	NOUN
iajs-763	249	68	for	for	ADP
iajs-763	249	69	u1	u1	NOUN
iajs-763	249	70	,	,	PUNCT
iajs-763	249	71	u2	u2	NOUN
iajs-763	249	72	and	and	CCONJ
iajs-763	249	73	u3	u3	NOUN
iajs-763	249	74	respectively	respectively	ADV
iajs-763	249	75	depending	depend	VERB
iajs-763	249	76	on	on	ADP
iajs-763	249	77	least	least	ADJ
iajs-763	249	78	square	square	ADJ
iajs-763	249	79	error	error	NOUN
iajs-763	249	80	and	and	CCONJ
iajs-763	249	81	running	run	VERB
iajs-763	249	82	time	time	NOUN
iajs-763	249	83	with	with	ADP
iajs-763	249	84	h=	h=	NOUN
iajs-763	249	85	0.1	0.1	NUM
iajs-763	249	86	example	example	NOUN
iajs-763	249	87	(	(	PUNCT
iajs-763	249	88	3	3	NUM
iajs-763	249	89	):	):	PUNCT
iajs-763	249	90	consider	consider	VERB
iajs-763	249	91	the	the	DET
iajs-763	249	92	problem	problem	NOUN
iajs-763	249	93	:	:	PUNCT
iajs-763	249	94			ADJ
iajs-763	249	95			ADJ
iajs-763	249	96			NOUN
iajs-763	249	97			PROPN
iajs-763	250	1	1	1	NUM
iajs-763	250	2	0	0	NUM
iajs-763	250	3	2	2	NUM
iajs-763	250	4	2	2	NUM
iajs-763	250	5	1	1	NUM
iajs-763	250	6	0	0	NUM
iajs-763	250	7	1	1	NUM
iajs-763	250	8	24	24	NUM
iajs-763	250	9	2	2	NUM
iajs-763	250	10	1	1	NUM
iajs-763	250	11	0	0	NUM
iajs-763	250	12	2	2	NUM
iajs-763	250	13	2	2	NUM
iajs-763	250	14	1	1	NUM
iajs-763	250	15	0	0	NUM
iajs-763	250	16	1	1	NUM
iajs-763	250	17	2	2	NUM
iajs-763	250	18	1	1	NUM
iajs-763	250	19	)	)	PUNCT
iajs-763	250	20	(	(	PUNCT
iajs-763	250	21	)	)	PUNCT
iajs-763	250	22	(	(	PUNCT
iajs-763	250	23	)	)	PUNCT
iajs-763	250	24	(	(	PUNCT
iajs-763	250	25	12	12	NUM
iajs-763	250	26	7	7	NUM
iajs-763	250	27	5	5	NUM
iajs-763	250	28	1	1	NUM
iajs-763	250	29	)	)	PUNCT
iajs-763	250	30	(	(	PUNCT
iajs-763	250	31	)	)	PUNCT
iajs-763	250	32	(	(	PUNCT
iajs-763	250	33	)	)	PUNCT
iajs-763	250	34	(	(	PUNCT
iajs-763	250	35	)	)	PUNCT
iajs-763	250	36	1(1	1(1	NUM
iajs-763	250	37	12	12	NUM
iajs-763	250	38	25	25	NUM
iajs-763	250	39	6	6	NUM
iajs-763	250	40	5	5	NUM
iajs-763	250	41	)	)	PUNCT
iajs-763	250	42	(	(	PUNCT
iajs-763	250	43	dttuxtxdttuxtxxxxu	dttuxtxdttuxtxxxxu	ADV
iajs-763	250	44	dttutxdttutxxxxu	dttutxdttutxxxxu	ADV
iajs-763	250	45	which	which	PRON
iajs-763	250	46	is	be	AUX
iajs-763	250	47	a	a	DET
iajs-763	250	48	system	system	NOUN
iajs-763	250	49	of	of	ADP
iajs-763	250	50	two	two	NUM
iajs-763	250	51	linear	linear	ADJ
iajs-763	250	52	fie	fie	NOUN
iajs-763	250	53	's	's	PART
iajs-763	250	54	,	,	PUNCT
iajs-763	250	55	with	with	ADP
iajs-763	250	56	exact	exact	ADJ
iajs-763	250	57	solution	solution	NOUN
iajs-763	250	58	is	be	AUX
iajs-763	250	59	[	[	X
iajs-763	250	60	6	6	NUM
iajs-763	250	61	]	]	PUNCT
iajs-763	250	62	:	:	PUNCT
iajs-763	250	63	4	4	NUM
iajs-763	250	64	2	2	NUM
iajs-763	250	65	2	2	NUM
iajs-763	250	66	1	1	NUM
iajs-763	250	67	)	)	PUNCT
iajs-763	250	68	(	(	PUNCT
iajs-763	250	69	,	,	PUNCT
iajs-763	250	70	1	1	NUM
iajs-763	250	71	)	)	PUNCT
iajs-763	250	72	(	(	PUNCT
iajs-763	250	73	xxuxxu	xxuxxu	ADJ
iajs-763	250	74			NOUN
iajs-763	250	75	tables	table	NOUN
iajs-763	250	76	(	(	PUNCT
iajs-763	250	77	6	6	NUM
iajs-763	250	78	)	)	PUNCT
iajs-763	250	79	and	and	CCONJ
iajs-763	250	80	(	(	PUNCT
iajs-763	250	81	7	7	X
iajs-763	250	82	)	)	PUNCT
iajs-763	250	83	present	present	ADJ
iajs-763	250	84	a	a	DET
iajs-763	250	85	comparison	comparison	NOUN
iajs-763	250	86	between	between	ADP
iajs-763	250	87	the	the	DET
iajs-763	250	88	exact	exact	ADJ
iajs-763	250	89	and	and	CCONJ
iajs-763	250	90	numerical	numerical	ADJ
iajs-763	250	91	solution	solution	NOUN
iajs-763	250	92	of	of	ADP
iajs-763	250	93	four	four	NUM
iajs-763	250	94	types	type	NOUN
iajs-763	250	95	of	of	ADP
iajs-763	250	96	open	open	ADJ
iajs-763	250	97	newton	newton	PROPN
iajs-763	250	98	–	–	PUNCT
iajs-763	250	99	cotes	cote	NOUN
iajs-763	250	100	and	and	CCONJ
iajs-763	250	101	two	two	NUM
iajs-763	250	102	types	type	NOUN
iajs-763	250	103	of	of	ADP
iajs-763	250	104	closed	closed	ADJ
iajs-763	250	105	newton	newton	PROPN
iajs-763	250	106	–	–	PUNCT
iajs-763	250	107	cotes	cote	NOUN
iajs-763	250	108	for	for	ADP
iajs-763	250	109	u1	u1	NOUN
iajs-763	250	110	and	and	CCONJ
iajs-763	250	111	u2	u2	NOUN
iajs-763	250	112	respectively	respectively	ADV
iajs-763	250	113	depending	depend	VERB
iajs-763	250	114	on	on	ADP
iajs-763	250	115	least	least	ADJ
iajs-763	250	116	square	square	ADJ
iajs-763	250	117	error	error	NOUN
iajs-763	250	118	and	and	CCONJ
iajs-763	250	119	running	run	VERB
iajs-763	250	120	time	time	NOUN
iajs-763	250	121	with	with	ADP
iajs-763	250	122	h=1/18	h=1/18	NOUN
iajs-763	250	123	conclusion	conclusion	NOUN
iajs-763	250	124	in	in	ADP
iajs-763	250	125	this	this	DET
iajs-763	250	126	paper	paper	NOUN
iajs-763	250	127	we	we	PRON
iajs-763	250	128	suggest	suggest	VERB
iajs-763	250	129	open	open	ADJ
iajs-763	250	130	n	n	CCONJ
iajs-763	250	131	-	-	PUNCT
iajs-763	250	132	c	c	NOUN
iajs-763	250	133	formula	formula	NOUN
iajs-763	250	134	to	to	PART
iajs-763	250	135	solve	solve	VERB
iajs-763	250	136	system	system	NOUN
iajs-763	250	137	of	of	ADP
iajs-763	250	138	linear	linear	ADJ
iajs-763	250	139	fredholm	fredholm	ADJ
iajs-763	250	140	integral	integral	ADJ
iajs-763	250	141	equations	equation	NOUN
iajs-763	250	142	of	of	ADP
iajs-763	250	143	the	the	DET
iajs-763	250	144	second	second	ADJ
iajs-763	250	145	kind	kind	NOUN
iajs-763	250	146	and	and	CCONJ
iajs-763	250	147	we	we	PRON
iajs-763	250	148	obtain	obtain	VERB
iajs-763	250	149	the	the	DET
iajs-763	250	150	following	follow	VERB
iajs-763	250	151	results	result	NOUN
iajs-763	250	152	:	:	PUNCT
iajs-763	250	153	1the	1the	PRON
iajs-763	250	154	results	result	NOUN
iajs-763	250	155	obtained	obtain	VERB
iajs-763	250	156	using	use	VERB
iajs-763	250	157	open	open	ADJ
iajs-763	250	158	n	n	CCONJ
iajs-763	250	159	-	-	PUNCT
iajs-763	250	160	c	c	NOUN
iajs-763	250	161	formulas	formula	NOUN
iajs-763	250	162	are	be	AUX
iajs-763	250	163	more	more	ADV
iajs-763	250	164	accurate	accurate	ADJ
iajs-763	250	165	than	than	ADP
iajs-763	250	166	the	the	DET
iajs-763	250	167	results	result	NOUN
iajs-763	250	168	obtained	obtain	VERB
iajs-763	250	169	using	use	VERB
iajs-763	250	170	closed	closed	ADJ
iajs-763	250	171	n	n	CCONJ
iajs-763	250	172	-	-	PUNCT
iajs-763	250	173	c	c	NOUN
iajs-763	250	174	formulas	formula	NOUN
iajs-763	250	175	in	in	ADP
iajs-763	250	176	general	general	ADJ
iajs-763	250	177	.	.	PUNCT
iajs-763	251	1	2open	2open	NUM
iajs-763	251	2	n	n	CCONJ
iajs-763	251	3	-	-	PUNCT
iajs-763	251	4	c	c	NOUN
iajs-763	251	5	formulas	formula	NOUN
iajs-763	251	6	are	be	AUX
iajs-763	251	7	more	more	ADV
iajs-763	251	8	efficient	efficient	ADJ
iajs-763	251	9	than	than	ADP
iajs-763	251	10	closed	closed	ADJ
iajs-763	251	11	n	n	CCONJ
iajs-763	251	12	-	-	PUNCT
iajs-763	251	13	c	c	NOUN
iajs-763	251	14	formulas	formula	NOUN
iajs-763	251	15	since	since	SCONJ
iajs-763	251	16	the	the	DET
iajs-763	251	17	open	open	ADJ
iajs-763	251	18	n	n	CCONJ
iajs-763	251	19	-	-	PUNCT
iajs-763	251	20	c	c	NOUN
iajs-763	251	21	formulas	formula	NOUN
iajs-763	251	22	have	have	VERB
iajs-763	251	23	most	most	ADJ
iajs-763	251	24	results	result	NOUN
iajs-763	251	25	than	than	SCONJ
iajs-763	251	26	closed	closed	ADJ
iajs-763	251	27	n	n	CCONJ
iajs-763	251	28	-	-	PUNCT
iajs-763	251	29	c	c	NOUN
iajs-763	251	30	with	with	ADP
iajs-763	251	31	fewer	few	ADJ
iajs-763	251	32	nodes	node	NOUN
iajs-763	251	33	in	in	ADP
iajs-763	251	34	the	the	DET
iajs-763	251	35	open	open	ADJ
iajs-763	251	36	n	n	CCONJ
iajs-763	251	37	-	-	PUNCT
iajs-763	251	38	c	c	NOUN
iajs-763	251	39	formulas	formula	NOUN
iajs-763	251	40	.	.	PUNCT
iajs-763	252	1	3the	3the	DET
iajs-763	252	2	results	result	NOUN
iajs-763	252	3	obtained	obtain	VERB
iajs-763	252	4	in	in	ADP
iajs-763	252	5	open	open	ADJ
iajs-763	252	6	n	n	CCONJ
iajs-763	252	7	-	-	PUNCT
iajs-763	252	8	c	c	NOUN
iajs-763	252	9	formula	formula	NOUN
iajs-763	252	10	when	when	SCONJ
iajs-763	252	11	n=4	n=4	ADJ
iajs-763	252	12	or	or	CCONJ
iajs-763	252	13	multiple	multiple	NOUN
iajs-763	252	14	of	of	ADP
iajs-763	252	15	four	four	NUM
iajs-763	252	16	is	be	AUX
iajs-763	252	17	most	most	ADJ
iajs-763	252	18	of	of	ADP
iajs-763	252	19	the	the	DET
iajs-763	252	20	results	result	NOUN
iajs-763	252	21	in	in	ADP
iajs-763	252	22	a	a	DET
iajs-763	252	23	short	short	ADJ
iajs-763	252	24	time	time	NOUN
iajs-763	252	25	in	in	ADP
iajs-763	252	26	other	other	ADJ
iajs-763	252	27	open	open	ADJ
iajs-763	252	28	n	n	CCONJ
iajs-763	252	29	-	-	PUNCT
iajs-763	252	30	c	c	NOUN
iajs-763	252	31	formulas	formula	NOUN
iajs-763	252	32	.	.	PUNCT
iajs-763	253	1	references	reference	NOUN
iajs-763	253	2	1.mathews	1.mathews	NUM
iajs-763	253	3	,	,	PUNCT
iajs-763	253	4	j.h	j.h	PROPN
iajs-763	253	5	.	.	PROPN
iajs-763	253	6	and	and	CCONJ
iajs-763	253	7	fink	fink	PROPN
iajs-763	253	8	,	,	PUNCT
iajs-763	253	9	k.d	k.d	PROPN
iajs-763	253	10	.	.	PROPN
iajs-763	253	11	(	(	PUNCT
iajs-763	253	12	1999	1999	NUM
iajs-763	253	13	)	)	PUNCT
iajs-763	253	14	,	,	PUNCT
iajs-763	253	15	"	"	PUNCT
iajs-763	253	16	numerical	numerical	ADJ
iajs-763	253	17	methods	method	NOUN
iajs-763	253	18	using	use	VERB
iajs-763	253	19	matlab	matlab	PROPN
iajs-763	253	20	"	"	PUNCT
iajs-763	253	21	;	;	PUNCT
iajs-763	253	22	third	third	ADJ
iajs-763	253	23	edition	edition	NOUN
iajs-763	253	24	,	,	PUNCT
iajs-763	253	25	prenice	prenice	NOUN
iajs-763	253	26	-	-	PUNCT
iajs-763	253	27	hall	hall	PROPN
iajs-763	253	28	,	,	PUNCT
iajs-763	253	29	inc	inc	PROPN
iajs-763	253	30	.	.	PROPN
iajs-763	253	31	2.chambers	2.chambers	NUM
iajs-763	253	32	,	,	PUNCT
iajs-763	253	33	l.i.g	l.i.g	NOUN
iajs-763	253	34	.	.	PUNCT
iajs-763	253	35	(	(	PUNCT
iajs-763	253	36	1976	1976	NUM
iajs-763	253	37	)	)	PUNCT
iajs-763	253	38	,	,	PUNCT
iajs-763	253	39	“	"	PUNCT
iajs-763	253	40	integral	integral	ADJ
iajs-763	253	41	equation	equation	NOUN
iajs-763	253	42	:	:	PUNCT
iajs-763	253	43	a	a	DET
iajs-763	253	44	short	short	ADJ
iajs-763	253	45	course	course	NOUN
iajs-763	253	46	”	"	PUNCT
iajs-763	253	47	;	;	PUNCT
iajs-763	253	48	international	international	ADJ
iajs-763	253	49	textbook	textbook	NOUN
iajs-763	253	50	company	company	NOUN
iajs-763	253	51	limited	limit	VERB
iajs-763	253	52	.	.	PUNCT
iajs-763	254	1	3	3	X
iajs-763	254	2	.	.	X
iajs-763	254	3	lapidus	lapidus	PROPN
iajs-763	254	4	,	,	PUNCT
iajs-763	254	5	l.	l.	PROPN
iajs-763	254	6	and	and	CCONJ
iajs-763	254	7	seinfeld	seinfeld	PROPN
iajs-763	254	8	,	,	PUNCT
iajs-763	254	9	j.	j.	PROPN
iajs-763	254	10	h.	h.	PROPN
iajs-763	254	11	(	(	PUNCT
iajs-763	254	12	1971	1971	NUM
iajs-763	254	13	)	)	PUNCT
iajs-763	254	14	“	"	PUNCT
iajs-763	254	15	numerical	numerical	ADJ
iajs-763	254	16	solution	solution	NOUN
iajs-763	254	17	of	of	ADP
iajs-763	254	18	ordinary	ordinary	ADJ
iajs-763	254	19	differential	differential	ADJ
iajs-763	254	20	equations	equation	NOUN
iajs-763	254	21	”	"	PUNCT
iajs-763	254	22	;	;	PUNCT
iajs-763	254	23	academic	academic	ADJ
iajs-763	254	24	press	press	NOUN
iajs-763	254	25	new	new	ADJ
iajs-763	254	26	-	-	PUNCT
iajs-763	254	27	york	york	PROPN
iajs-763	254	28	and	and	CCONJ
iajs-763	254	29	london	london	PROPN
iajs-763	254	30	.	.	PUNCT
iajs-763	255	1	4.burden	4.burden	NUM
iajs-763	255	2	,	,	PUNCT
iajs-763	255	3	r.	r.	PROPN
iajs-763	255	4	l.	l.	PROPN
iajs-763	255	5	and	and	CCONJ
iajs-763	255	6	faires	faire	NOUN
iajs-763	255	7	,	,	PUNCT
iajs-763	255	8	j.	j.	PROPN
iajs-763	255	9	d.	d.	PROPN
iajs-763	255	10	(	(	PUNCT
iajs-763	255	11	2006	2006	NUM
iajs-763	255	12	)	)	PUNCT
iajs-763	255	13	,	,	PUNCT
iajs-763	255	14	“	"	PUNCT
iajs-763	255	15	numerical	numerical	ADJ
iajs-763	255	16	analysis	analysis	NOUN
iajs-763	255	17	”	"	PUNCT
iajs-763	255	18	;	;	PUNCT
iajs-763	255	19	eighth	eighth	ADJ
iajs-763	255	20	edition	edition	NOUN
iajs-763	255	21	,	,	PUNCT
iajs-763	255	22	an	an	DET
iajs-763	255	23	international	international	ADJ
iajs-763	255	24	thomson	thomson	NOUN
iajs-763	255	25	publishing	publishing	NOUN
iajs-763	255	26	company	company	NOUN
iajs-763	255	27	.	.	PUNCT
iajs-763	256	1	5.vahidi	5.vahidi	NUM
iajs-763	256	2	,	,	PUNCT
iajs-763	256	3	a.s	a.s	PROPN
iajs-763	256	4	.	.	PROPN
iajs-763	256	5	r.	r.	PROPN
iajs-763	256	6	and	and	CCONJ
iajs-763	256	7	mokhtari	mokhtari	PROPN
iajs-763	256	8	,	,	PUNCT
iajs-763	256	9	m.	m.	NOUN
iajs-763	256	10	(	(	PUNCT
iajs-763	256	11	2008	2008	NUM
iajs-763	256	12	)	)	PUNCT
iajs-763	256	13	,	,	PUNCT
iajs-763	256	14	“	"	PUNCT
iajs-763	256	15	on	on	ADP
iajs-763	256	16	the	the	DET
iajs-763	256	17	decomposition	decomposition	NOUN
iajs-763	256	18	method	method	NOUN
iajs-763	256	19	for	for	ADP
iajs-763	256	20	system	system	NOUN
iajs-763	256	21	of	of	ADP
iajs-763	256	22	linear	linear	ADJ
iajs-763	256	23	fredholm	fredholm	ADJ
iajs-763	256	24	integral	integral	ADJ
iajs-763	256	25	equations	equation	NOUN
iajs-763	256	26	of	of	ADP
iajs-763	256	27	the	the	DET
iajs-763	256	28	second	second	ADJ
iajs-763	256	29	kind	kind	NOUN
iajs-763	256	30	”	"	PUNCT
iajs-763	256	31	;	;	PUNCT
iajs-763	256	32	applied	apply	VERB
iajs-763	256	33	mathematical	mathematical	ADJ
iajs-763	256	34	sciences	sciences	PROPN
iajs-763	256	35	,	,	PUNCT
iajs-763	256	36	iran	iran	PROPN
iajs-763	256	37	,	,	PUNCT
iajs-763	256	38	2	2	NUM
iajs-763	256	39	:(	:(	SYM
iajs-763	256	40	2	2	NUM
iajs-763	256	41	)	)	PUNCT
iajs-763	256	42	57	57	NUM
iajs-763	256	43	-	-	SYM
iajs-763	256	44	62	62	NUM
iajs-763	256	45	.	.	PUNCT
iajs-763	257	1	6.al	6.al	X
iajs-763	257	2	-	-	PUNCT
iajs-763	257	3	dulaimi	dulaimi	ADJ
iajs-763	257	4	,	,	PUNCT
iajs-763	257	5	m.	m.	NOUN
iajs-763	257	6	y.	y.	PROPN
iajs-763	257	7	(	(	PUNCT
iajs-763	257	8	2008),”some	2008),”some	NUM
iajs-763	257	9	modified	modify	VERB
iajs-763	257	10	quadrature	quadrature	NOUN
iajs-763	257	11	rules	rule	NOUN
iajs-763	257	12	for	for	ADP
iajs-763	257	13	solving	solve	VERB
iajs-763	257	14	system	system	NOUN
iajs-763	257	15	of	of	ADP
iajs-763	257	16	fredholm	fredholm	ADJ
iajs-763	257	17	linear	linear	ADJ
iajs-763	257	18	integral	integral	ADJ
iajs-763	257	19	equations	equation	NOUN
iajs-763	257	20	”	"	PUNCT
iajs-763	257	21	;	;	PUNCT
iajs-763	258	1	m.sc	m.sc	PROPN
iajs-763	258	2	.	.	PUNCT
iajs-763	259	1	thesis	thesis	NOUN
iajs-763	259	2	,	,	PUNCT
iajs-763	259	3	university	university	NOUN
iajs-763	259	4	of	of	ADP
iajs-763	259	5	baghdad	baghdad	PROPN
iajs-763	259	6	,	,	PUNCT
iajs-763	259	7	ibn	ibn	PROPN
iajs-763	259	8	-	-	PUNCT
iajs-763	259	9	al	al	PROPN
iajs-763	259	10	-	-	PUNCT
iajs-763	259	11	haitham	haitham	PROPN
iajs-763	259	12	college	college	PROPN
iajs-763	259	13	of	of	ADP
iajs-763	259	14	education	education	NOUN
iajs-763	259	15	.	.	PUNCT
iajs-763	260	1	ibn	ibn	PROPN
iajs-763	260	2	alhaitham	alhaitham	PROPN
iajs-763	260	3	j.	j.	PROPN
iajs-763	260	4	for	for	ADP
iajs-763	260	5	pure	pure	ADJ
iajs-763	260	6	&	&	CCONJ
iajs-763	260	7	appl	appl	PROPN
iajs-763	260	8	.	.	PUNCT
iajs-763	261	1	sci	sci	PROPN
iajs-763	261	2	.	.	PUNCT
iajs-763	261	3	vol.24	vol.24	NOUN
iajs-763	261	4	(	(	PUNCT
iajs-763	261	5	2	2	NUM
iajs-763	261	6	)	)	PUNCT
iajs-763	261	7	2011	2011	NUM
iajs-763	261	8	table	table	NOUN
iajs-763	261	9	(	(	PUNCT
iajs-763	261	10	1	1	X
iajs-763	261	11	)	)	PUNCT
iajs-763	261	12	a	a	DET
iajs-763	261	13	comparison	comparison	NOUN
iajs-763	261	14	between	between	ADP
iajs-763	261	15	the	the	DET
iajs-763	261	16	exact	exact	ADJ
iajs-763	261	17	and	and	CCONJ
iajs-763	261	18	numerical	numerical	ADJ
iajs-763	261	19	solution	solution	NOUN
iajs-763	261	20	of	of	ADP
iajs-763	261	21	4	4	NUM
iajs-763	261	22	types	type	NOUN
iajs-763	261	23	of	of	ADP
iajs-763	261	24	open	open	ADJ
iajs-763	261	25	n	n	NOUN
iajs-763	261	26	–	–	PUNCT
iajs-763	261	27	c	c	NOUN
iajs-763	261	28	and	and	CCONJ
iajs-763	261	29	2	2	NUM
iajs-763	261	30	types	type	NOUN
iajs-763	261	31	of	of	ADP
iajs-763	261	32	closed	closed	ADJ
iajs-763	261	33	n	n	CCONJ
iajs-763	261	34	–	–	PUNCT
iajs-763	261	35	c	c	NOUN
iajs-763	261	36	for	for	ADP
iajs-763	261	37	u1	u1	NOUN
iajs-763	261	38	table	table	NOUN
iajs-763	261	39	(	(	PUNCT
iajs-763	261	40	2	2	NUM
iajs-763	261	41	)	)	PUNCT
iajs-763	261	42	a	a	DET
iajs-763	261	43	comparison	comparison	NOUN
iajs-763	261	44	between	between	ADP
iajs-763	261	45	the	the	DET
iajs-763	261	46	exact	exact	ADJ
iajs-763	261	47	and	and	CCONJ
iajs-763	261	48	numerical	numerical	ADJ
iajs-763	261	49	solution	solution	NOUN
iajs-763	261	50	of	of	ADP
iajs-763	261	51	4	4	NUM
iajs-763	261	52	types	type	NOUN
iajs-763	261	53	of	of	ADP
iajs-763	261	54	open	open	ADJ
iajs-763	261	55	n	n	NOUN
iajs-763	261	56	–	–	PUNCT
iajs-763	261	57	c	c	NOUN
iajs-763	261	58	and	and	CCONJ
iajs-763	261	59	2	2	NUM
iajs-763	261	60	types	type	NOUN
iajs-763	261	61	of	of	ADP
iajs-763	261	62	closed	closed	ADJ
iajs-763	261	63	n	n	CCONJ
iajs-763	261	64	–	–	PUNCT
iajs-763	261	65	c	c	NOUN
iajs-763	261	66	for	for	ADP
iajs-763	261	67	u2	u2	PROPN
iajs-763	261	68	closed	closed	ADJ
iajs-763	261	69	n	n	CCONJ
iajs-763	261	70	-	-	PUNCT
iajs-763	261	71	c	c	NOUN
iajs-763	261	72	simp	simp	ADJ
iajs-763	261	73	.	.	PROPN
iajs-763	261	74	3/8	3/8	NUM
iajs-763	261	75	closed	closed	ADJ
iajs-763	261	76	n	n	CCONJ
iajs-763	261	77	-	-	PUNCT
iajs-763	261	78	c	c	NOUN
iajs-763	261	79	trap	trap	NOUN
iajs-763	261	80	.	.	PUNCT
iajs-763	262	1	open	open	ADJ
iajs-763	262	2	n	n	CCONJ
iajs-763	262	3	-	-	PUNCT
iajs-763	262	4	c	c	NOUN
iajs-763	262	5	n=4	n=4	X
iajs-763	262	6	open	open	ADJ
iajs-763	262	7	n	n	CCONJ
iajs-763	262	8	-	-	PUNCT
iajs-763	262	9	c	c	NOUN
iajs-763	262	10	n=3	n=3	PUNCT
iajs-763	262	11	open	open	ADJ
iajs-763	262	12	n	n	CCONJ
iajs-763	262	13	-	-	PUNCT
iajs-763	262	14	c	c	NOUN
iajs-763	262	15	n=2	n=2	PRON
iajs-763	262	16	open	open	VERB
iajs-763	262	17	n	n	CCONJ
iajs-763	262	18	-	-	PUNCT
iajs-763	262	19	c	c	NOUN
iajs-763	262	20	n=1	n=1	PROPN
iajs-763	262	21	open	open	ADJ
iajs-763	262	22	n	n	CCONJ
iajs-763	262	23	-	-	PUNCT
iajs-763	262	24	c	c	NOUN
iajs-763	262	25	n=0	n=0	CCONJ
iajs-763	262	26	exact	exact	ADJ
iajs-763	262	27	u1	u1	NOUN
iajs-763	262	28	x	x	SYM
iajs-763	262	29	1.06254649	1.06254649	NUM
iajs-763	262	30	1.06408126	1.06408126	NUM
iajs-763	262	31	1.0625000	1.0625000	NUM
iajs-763	262	32	1.06135355	1.06135355	NUM
iajs-763	262	33	1.06250000	1.06250000	NUM
iajs-763	262	34	1.05802317	1.05802317	NUM
iajs-763	262	35	61.0593592	61.0593592	NUM
iajs-763	262	36	1.0625000	1.0625000	NUM
iajs-763	262	37	0.62500	0.62500	NUM
iajs-763	262	38	1.12505018	1.12505018	NUM
iajs-763	262	39	1.12668959	1.12668959	NUM
iajs-763	262	40	1.1250000	1.1250000	NUM
iajs-763	262	41	1.12376887	1.12376887	NUM
iajs-763	262	42	01.1250000	01.1250000	NUM
iajs-763	262	43	1.1250000	1.1250000	NUM
iajs-763	262	44	0.12500	0.12500	NUM
iajs-763	262	45	1.31256126	1.31256126	NUM
iajs-763	262	46	1.31451459	1.31451459	NUM
iajs-763	262	47	1.3750000	1.3750000	NUM
iajs-763	262	48	1.37500000	1.37500000	NUM
iajs-763	262	49	1.36899583	1.36899583	NUM
iajs-763	262	50	1.3750000	1.3750000	NUM
iajs-763	262	51	0.37500	0.37500	NUM
iajs-763	262	52	1.50007234	1.50007234	NUM
iajs-763	262	53	1.50233959	1.50233959	NUM
iajs-763	262	54	1.5000000	1.5000000	NUM
iajs-763	262	55	1.49826084	1.49826084	NUM
iajs-763	262	56	1.49338489	1.49338489	NUM
iajs-763	262	57	1.5000000	1.5000000	NUM
iajs-763	262	58	0.50000	0.50000	NUM
iajs-763	262	59	1.75008711	1.75008711	NUM
iajs-763	262	60	1.75277293	1.75277293	NUM
iajs-763	262	61	1.7500000	1.7500000	NUM
iajs-763	262	62	1.74792216	1.74792216	NUM
iajs-763	262	63	1.74216302	1.74216302	NUM
iajs-763	262	64	1.7500000	1.7500000	NUM
iajs-763	262	65	0.75000	0.75000	NUM
iajs-763	262	66	1.87509449	1.87509449	NUM
iajs-763	262	67	1.87798960	1.87798960	NUM
iajs-763	262	68	1.8750000	1.8750000	NUM
iajs-763	262	69	1.87275281	1.87275281	NUM
iajs-763	262	70	1.86655208	1.86655208	NUM
iajs-763	262	71	1.8750000	1.8750000	NUM
iajs-763	262	72	0.87500	0.87500	NUM
iajs-763	262	73	1.038e-008	1.038e-008	NUM
iajs-763	262	74	1.028e-005	1.028e-005	NUM
iajs-763	262	75	1.972e-031	1.972e-031	NUM
iajs-763	262	76	e-0065.437	e-0065.437	PROPN
iajs-763	262	77	e-0311.972	e-0311.972	PROPN
iajs-763	262	78	e-0057.662	e-0057.662	PROPN
iajs-763	262	79	e-0053.789	e-0053.789	PROPN
iajs-763	262	80	l.s.e	l.s.e	NOUN
iajs-763	262	81	.	.	PUNCT
iajs-763	262	82	0.297000	0.297000	NUM
iajs-763	263	1	0.31200	0.31200	NUM
iajs-763	263	2	0.18800	0.18800	NUM
iajs-763	263	3	0.172000	0.172000	NUM
iajs-763	263	4	0.203000	0.203000	NUM
iajs-763	263	5	0.12500	0.12500	NUM
iajs-763	263	6	0.07800	0.07800	NUM
iajs-763	263	7	time	time	NOUN
iajs-763	263	8	closed	closed	ADJ
iajs-763	263	9	n	n	CCONJ
iajs-763	263	10	-	-	PUNCT
iajs-763	263	11	c	c	NOUN
iajs-763	263	12	simp	simp	ADJ
iajs-763	263	13	.	.	PROPN
iajs-763	263	14	3/8	3/8	NUM
iajs-763	263	15	closed	closed	ADJ
iajs-763	263	16	n	n	CCONJ
iajs-763	263	17	-	-	PUNCT
iajs-763	263	18	c	c	NOUN
iajs-763	263	19	trap	trap	NOUN
iajs-763	263	20	.	.	PUNCT
iajs-763	264	1	open	open	ADJ
iajs-763	264	2	n	n	CCONJ
iajs-763	264	3	-	-	PUNCT
iajs-763	264	4	c	c	NOUN
iajs-763	264	5	n=4	n=4	X
iajs-763	264	6	open	open	ADJ
iajs-763	264	7	n	n	CCONJ
iajs-763	264	8	-	-	PUNCT
iajs-763	264	9	c	c	NOUN
iajs-763	264	10	n=3	n=3	PUNCT
iajs-763	264	11	open	open	ADJ
iajs-763	264	12	n	n	CCONJ
iajs-763	264	13	-	-	PUNCT
iajs-763	264	14	c	c	NOUN
iajs-763	264	15	n=2	n=2	PRON
iajs-763	264	16	open	open	VERB
iajs-763	264	17	n	n	CCONJ
iajs-763	264	18	-	-	PUNCT
iajs-763	264	19	c	c	NOUN
iajs-763	264	20	n=1	n=1	PROPN
iajs-763	264	21	open	open	ADJ
iajs-763	264	22	n	n	CCONJ
iajs-763	264	23	-	-	PUNCT
iajs-763	264	24	c	c	NOUN
iajs-763	264	25	n=0	n=0	CCONJ
iajs-763	264	26	exact	exact	ADJ
iajs-763	264	27	u2	u2	NOUN
iajs-763	264	28	x	x	NOUN
iajs-763	264	29	1.00391427	1.00391427	NUM
iajs-763	264	30	1.00418242	1.00418242	NUM
iajs-763	264	31	1.00390625	1.00390625	NUM
iajs-763	264	32	1.00370716	1.00370716	NUM
iajs-763	264	33	1.00390625	1.00390625	NUM
iajs-763	264	34	1.00312412	1.00312412	NUM
iajs-763	264	35	1.00335774	1.00335774	NUM
iajs-763	264	36	1.0039062	1.0039062	NUM
iajs-763	264	37	0.62500	0.62500	NUM
iajs-763	264	38	1.01564105	1.01564105	NUM
iajs-763	264	39	1.01617734	1.01617734	NUM
iajs-763	264	40	1.0156250	1.0156250	NUM
iajs-763	264	41	1.01522683	1.01522683	NUM
iajs-763	264	42	1.01562500	1.01562500	NUM
iajs-763	264	43	1.0156250	1.0156250	NUM
iajs-763	264	44	0.12500	0.12500	NUM
iajs-763	264	45	1.14067315	1.14067315	NUM
iajs-763	264	46	1.14228204	1.14228204	NUM
iajs-763	264	47	1.1406250	1.1406250	NUM
iajs-763	264	48	1.14062500	1.14062500	NUM
iajs-763	264	49	1.13593222	1.13593222	NUM
iajs-763	264	50	1.1406250	1.1406250	NUM
iajs-763	264	51	0.37500	0.37500	NUM
iajs-763	264	52	1.25006420	1.25006420	NUM
iajs-763	265	1	1.25220939	1.25220939	NUM
iajs-763	265	2	1.2500000	1.2500000	NUM
iajs-763	265	3	1.24840733	1.24840733	NUM
iajs-763	265	4	1.24374297	1.24374297	NUM
iajs-763	265	5	1.2500000	1.2500000	NUM
iajs-763	265	6	0.50000	0.50000	NUM
iajs-763	265	7	1.56259630	1.56259630	NUM
iajs-763	265	8	1.56581408	1.56581408	NUM
iajs-763	265	9	1.5625000	1.5625000	NUM
iajs-763	265	10	1.56011100	1.56011100	NUM
iajs-763	265	11	1.55311445	1.55311445	NUM
iajs-763	265	12	1.5625000	1.5625000	NUM
iajs-763	265	13	0.75000	0.75000	NUM
iajs-763	265	14	1.76573735	1.76573735	NUM
iajs-763	265	15	1.76949143	1.76949143	NUM
iajs-763	265	16	1.7656250	1.7656250	NUM
iajs-763	265	17	1.76283783	1.76283783	NUM
iajs-763	265	18	1.76562500	1.76562500	NUM
iajs-763	265	19	1.75467520	1.75467520	NUM
iajs-763	265	20	1.7656250	1.7656250	NUM
iajs-763	265	21	0.87500	0.87500	NUM
iajs-763	265	22	1.648e-008	1.648e-008	NOUN
iajs-763	265	23	1.952e-005	1.952e-005	NUM
iajs-763	265	24	0	0	PUNCT
iajs-763	266	1	e-0068.917	e-0068.917	PROPN
iajs-763	266	2	e-0324.930	e-0324.930	PROPN
iajs-763	266	3	e-0041.376	e-0041.376	PROPN
iajs-763	266	4	e-0056.769	e-0056.769	PROPN
iajs-763	266	5	l.s.e	l.s.e	NOUN
iajs-763	266	6	.	.	PUNCT
iajs-763	267	1	0.297000	0.297000	NUM
iajs-763	267	2	0.31200	0.31200	NUM
iajs-763	267	3	0.18800	0.18800	NUM
iajs-763	267	4	0.172000	0.172000	NUM
iajs-763	267	5	0.203000	0.203000	NUM
iajs-763	267	6	0.12500	0.12500	NUM
iajs-763	267	7	0.07800	0.07800	NUM
iajs-763	267	8	time	time	NOUN
iajs-763	267	9	ibn	ibn	PROPN
iajs-763	267	10	alhaitham	alhaitham	NOUN
iajs-763	267	11	j.	j.	PROPN
iajs-763	267	12	for	for	ADP
iajs-763	267	13	pure	pure	ADJ
iajs-763	267	14	&	&	CCONJ
iajs-763	267	15	appl	appl	PROPN
iajs-763	267	16	.	.	PUNCT
iajs-763	268	1	sci	sci	PROPN
iajs-763	268	2	.	.	PUNCT
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iajs-763	268	4	(	(	PUNCT
iajs-763	268	5	2	2	NUM
iajs-763	268	6	)	)	PUNCT
iajs-763	268	7	2011	2011	NUM
iajs-763	268	8	table	table	NOUN
iajs-763	268	9	(	(	PUNCT
iajs-763	268	10	3	3	X
iajs-763	268	11	)	)	PUNCT
iajs-763	268	12	a	a	DET
iajs-763	268	13	comparison	comparison	NOUN
iajs-763	268	14	between	between	ADP
iajs-763	268	15	the	the	DET
iajs-763	268	16	exact	exact	ADJ
iajs-763	268	17	and	and	CCONJ
iajs-763	268	18	numerical	numerical	ADJ
iajs-763	268	19	solution	solution	NOUN
iajs-763	268	20	of	of	ADP
iajs-763	268	21	4	4	NUM
iajs-763	268	22	types	type	NOUN
iajs-763	268	23	of	of	ADP
iajs-763	268	24	open	open	ADJ
iajs-763	268	25	n	n	NOUN
iajs-763	268	26	–	–	PUNCT
iajs-763	268	27	c	c	NOUN
iajs-763	268	28	and	and	CCONJ
iajs-763	268	29	2	2	NUM
iajs-763	268	30	types	type	NOUN
iajs-763	268	31	of	of	ADP
iajs-763	268	32	closed	closed	ADJ
iajs-763	268	33	n	n	CCONJ
iajs-763	268	34	–	–	PUNCT
iajs-763	268	35	c	c	NOUN
iajs-763	268	36	for	for	ADP
iajs-763	268	37	u1	u1	NOUN
iajs-763	268	38	table	table	NOUN
iajs-763	268	39	(	(	PUNCT
iajs-763	268	40	4	4	NUM
iajs-763	268	41	)	)	PUNCT
iajs-763	268	42	a	a	DET
iajs-763	268	43	comparison	comparison	NOUN
iajs-763	268	44	between	between	ADP
iajs-763	268	45	the	the	DET
iajs-763	268	46	exact	exact	ADJ
iajs-763	268	47	and	and	CCONJ
iajs-763	268	48	numerical	numerical	ADJ
iajs-763	268	49	solution	solution	NOUN
iajs-763	268	50	of	of	ADP
iajs-763	268	51	4	4	NUM
iajs-763	268	52	types	type	NOUN
iajs-763	268	53	of	of	ADP
iajs-763	268	54	open	open	ADJ
iajs-763	268	55	n	n	NOUN
iajs-763	268	56	–	–	PUNCT
iajs-763	268	57	c	c	NOUN
iajs-763	268	58	and	and	CCONJ
iajs-763	268	59	2	2	NUM
iajs-763	268	60	types	type	NOUN
iajs-763	268	61	of	of	ADP
iajs-763	268	62	closed	closed	ADJ
iajs-763	268	63	n	n	CCONJ
iajs-763	268	64	–	–	PUNCT
iajs-763	268	65	c	c	NOUN
iajs-763	268	66	for	for	ADP
iajs-763	268	67	u2	u2	PROPN
iajs-763	268	68	closed	closed	ADJ
iajs-763	268	69	n	n	CCONJ
iajs-763	268	70	-	-	PUNCT
iajs-763	268	71	c	c	NOUN
iajs-763	268	72	simp	simp	ADJ
iajs-763	268	73	.	.	PROPN
iajs-763	268	74	3/8	3/8	NUM
iajs-763	268	75	closed	closed	ADJ
iajs-763	268	76	n	n	CCONJ
iajs-763	268	77	-	-	PUNCT
iajs-763	268	78	c	c	NOUN
iajs-763	268	79	trap	trap	NOUN
iajs-763	268	80	.	.	PUNCT
iajs-763	269	1	open	open	ADJ
iajs-763	269	2	n	n	CCONJ
iajs-763	269	3	-	-	PUNCT
iajs-763	269	4	c	c	NOUN
iajs-763	269	5	n=4	n=4	X
iajs-763	269	6	open	open	ADJ
iajs-763	269	7	n	n	CCONJ
iajs-763	269	8	-	-	PUNCT
iajs-763	269	9	c	c	NOUN
iajs-763	269	10	n=3	n=3	PUNCT
iajs-763	269	11	open	open	ADJ
iajs-763	269	12	n	n	CCONJ
iajs-763	269	13	-	-	PUNCT
iajs-763	269	14	c	c	NOUN
iajs-763	269	15	n=2	n=2	PRON
iajs-763	269	16	open	open	VERB
iajs-763	269	17	n	n	CCONJ
iajs-763	269	18	-	-	PUNCT
iajs-763	269	19	c	c	NOUN
iajs-763	269	20	n=1	n=1	PROPN
iajs-763	269	21	open	open	ADJ
iajs-763	269	22	n	n	CCONJ
iajs-763	269	23	-	-	PUNCT
iajs-763	269	24	c	c	NOUN
iajs-763	269	25	n=0	n=0	CCONJ
iajs-763	269	26	exact	exact	ADJ
iajs-763	269	27	u1	u1	NOUN
iajs-763	269	28	x	x	X
iajs-763	269	29	0.00853472	0.00853472	NUM
iajs-763	269	30	-0.0123549	-0.0123549	NOUN
iajs-763	270	1	0.00985664	0.00985664	NUM
iajs-763	270	2	0.00939200	0.00939200	NUM
iajs-763	270	3	0.01634641	0.01634641	NUM
iajs-763	270	4	0.07564343	0.07564343	NUM
iajs-763	270	5	0.05805579	0.05805579	NUM
iajs-763	270	6	0.010000	0.010000	NUM
iajs-763	270	7	0.1	0.1	NUM
iajs-763	270	8	0.08810184	0.08810184	NUM
iajs-763	270	9	0.06074898	0.06074898	NUM
iajs-763	270	10	0.08980885	0.08980885	NUM
iajs-763	270	11	0.08918933	0.08918933	NUM
iajs-763	270	12	0.09823966	0.09823966	NUM
iajs-763	270	13	0.17608013	0.17608013	NUM
iajs-763	270	14	0.15296328	0.15296328	NUM
iajs-763	270	15	0.090000	0.090000	NUM
iajs-763	270	16	0.3	0.3	NUM
iajs-763	270	17	0.24766898	0.24766898	NUM
iajs-763	270	18	0.21385289	0.21385289	NUM
iajs-763	270	19	0.24976106	0.24976106	NUM
iajs-763	270	20	0.26013291	0.26013291	NUM
iajs-763	270	21	0.35651683	0.35651683	NUM
iajs-763	270	22	0.32787077	0.32787077	NUM
iajs-763	270	23	0.250000	0.250000	NUM
iajs-763	270	24	0.5	0.5	NUM
iajs-763	270	25	0.48723610	0.48723610	NUM
iajs-763	270	26	0.44695676	0.44695676	NUM
iajs-763	270	27	0.48971327	0.48971327	NUM
iajs-763	270	28	0.48878400	0.48878400	NUM
iajs-763	270	29	0.50202615	0.50202615	NUM
iajs-763	270	30	0.58277826	0.58277826	NUM
iajs-763	270	31	0.490000	0.490000	NUM
iajs-763	270	32	0.7	0.7	NUM
iajs-763	270	33	0.80680323	0.80680323	NUM
iajs-763	270	34	0.76006071	0.76006071	NUM
iajs-763	270	35	0.80966549	0.80966549	NUM
iajs-763	270	36	0.80858133	0.80858133	NUM
iajs-763	270	37	0.82391940	0.82391940	NUM
iajs-763	270	38	0.95739024	0.95739024	NUM
iajs-763	270	39	0.91768575	0.91768575	NUM
iajs-763	270	40	0.810000	0.810000	NUM
iajs-763	270	41	0.9	0.9	NUM
iajs-763	270	42	1.16e-005	1.16e-005	NUM
iajs-763	270	43	0.00285	0.00285	NUM
iajs-763	270	44	1.118	1.118	NUM
iajs-763	270	45	e-007	e-007	CCONJ
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iajs-763	270	47	e-006	e-006	NOUN
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iajs-763	270	49	e-004	e-004	VERB
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iajs-763	270	52	l.s.e	l.s.e	NOUN
iajs-763	270	53	.	.	PUNCT
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iajs-763	270	56	0.15600	0.15600	NUM
iajs-763	270	57	0.1710000	0.1710000	NUM
iajs-763	270	58	0.110000	0.110000	NUM
iajs-763	270	59	0.110000	0.110000	NUM
iajs-763	270	60	0.078000	0.078000	NUM
iajs-763	270	61	time	time	NOUN
iajs-763	270	62	closed	closed	ADJ
iajs-763	270	63	n	n	CCONJ
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iajs-763	270	65	c	c	NOUN
iajs-763	270	66	simp	simp	ADJ
iajs-763	270	67	.	.	PROPN
iajs-763	270	68	3/8	3/8	NUM
iajs-763	270	69	closed	closed	ADJ
iajs-763	270	70	n	n	CCONJ
iajs-763	270	71	-	-	PUNCT
iajs-763	270	72	c	c	NOUN
iajs-763	270	73	trap	trap	NOUN
iajs-763	270	74	.	.	PUNCT
iajs-763	271	1	open	open	ADJ
iajs-763	271	2	n	n	CCONJ
iajs-763	271	3	-	-	PUNCT
iajs-763	271	4	c	c	NOUN
iajs-763	271	5	n=4	n=4	X
iajs-763	271	6	open	open	ADJ
iajs-763	271	7	n	n	CCONJ
iajs-763	271	8	-	-	PUNCT
iajs-763	271	9	c	c	NOUN
iajs-763	271	10	n=3	n=3	PUNCT
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iajs-763	271	12	n	n	CCONJ
iajs-763	271	13	-	-	PUNCT
iajs-763	271	14	c	c	NOUN
iajs-763	271	15	n=2	n=2	PRON
iajs-763	271	16	open	open	VERB
iajs-763	271	17	n	n	CCONJ
iajs-763	271	18	-	-	PUNCT
iajs-763	271	19	c	c	NOUN
iajs-763	271	20	n=1	n=1	PROPN
iajs-763	271	21	open	open	ADJ
iajs-763	271	22	n	n	CCONJ
iajs-763	271	23	-	-	PUNCT
iajs-763	271	24	c	c	NOUN
iajs-763	271	25	n=0	n=0	CCONJ
iajs-763	271	26	exact	exact	ADJ
iajs-763	271	27	u2	u2	NOUN
iajs-763	271	28	x	x	PUNCT
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iajs-763	271	30	0.12946933	0.12946933	NUM
iajs-763	271	31	0.11008521	0.11008521	NUM
iajs-763	271	32	0.11036142	0.11036142	NUM
iajs-763	271	33	0.10543206	0.10543206	NUM
iajs-763	271	34	0.05300473	0.05300473	NUM
iajs-763	271	35	0.06875521	0.06875521	NUM
iajs-763	271	36	0.11000	0.11000	NUM
iajs-763	271	37	0.1	0.1	NUM
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iajs-763	271	39	0.40942113	0.40942113	NUM
iajs-763	272	1	0.39010194	0.39010194	NUM
iajs-763	272	2	0.39043235	0.39043235	NUM
iajs-763	272	3	0.38528876	0.38528876	NUM
iajs-763	272	4	0.33304139	0.33304139	NUM
iajs-763	272	5	0.34870102	0.34870102	NUM
iajs-763	272	6	0.39000	0.39000	NUM
iajs-763	272	7	0.3	0.3	NUM
iajs-763	272	8	0.75092003	0.75092003	NUM
iajs-763	272	9	0.76661449	0.76661449	NUM
iajs-763	272	10	0.75009955	0.75009955	NUM
iajs-763	272	11	0.74590276	0.74590276	NUM
iajs-763	272	12	0.70125273	0.70125273	NUM
iajs-763	272	13	0.71460984	0.71460984	NUM
iajs-763	272	14	0.75000	0.75000	NUM
iajs-763	272	15	0.5	0.5	NUM
iajs-763	272	16	1.19061016	1.19061016	NUM
iajs-763	272	17	1.20104942	1.20104942	NUM
iajs-763	272	18	1.19007805	1.19007805	NUM
iajs-763	272	19	1.19033102	1.19033102	NUM
iajs-763	272	20	1.18727406	1.18727406	NUM
iajs-763	272	21	1.16648165	1.16648165	NUM
iajs-763	272	22	1.19000	1.19000	NUM
iajs-763	272	23	0.7	0.7	NUM
iajs-763	272	24	1.71012715	1.71012715	NUM
iajs-763	272	25	1.71272591	1.71272591	NUM
iajs-763	272	26	1.71003743	1.71003743	NUM
iajs-763	272	27	1.71015875	1.71015875	NUM
iajs-763	272	28	1.70940265	1.70940265	NUM
iajs-763	272	29	1.70219946	1.70219946	NUM
iajs-763	272	30	1.70431646	1.70431646	NUM
iajs-763	272	31	1.71000	1.71000	NUM
iajs-763	272	32	0.9	0.9	NUM
iajs-763	272	33	3.214e-008	3.214e-008	NUM
iajs-763	272	34	6.102e-006	6.102e-006	NUM
iajs-763	272	35	1.401	1.401	NUM
iajs-763	272	36	e-009	e-009	X
iajs-763	272	37	2.520	2.520	NUM
iajs-763	272	38	e-008	e-008	NOUN
iajs-763	272	39	3.568	3.568	NUM
iajs-763	272	40	e-007	e-007	CCONJ
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iajs-763	272	42	e-005	e-005	NUM
iajs-763	272	43	3.230	3.230	NUM
iajs-763	272	44	e-005	e-005	NUM
iajs-763	272	45	l.s.e	l.s.e	NOUN
iajs-763	272	46	.	.	PUNCT
iajs-763	272	47	1.172	1.172	NUM
iajs-763	272	48	1.188	1.188	NUM
iajs-763	272	49	0.15600	0.15600	NUM
iajs-763	272	50	0.1710000	0.1710000	NUM
iajs-763	272	51	0.110000	0.110000	NUM
iajs-763	272	52	0.110000	0.110000	NUM
iajs-763	272	53	0.078000	0.078000	NUM
iajs-763	272	54	time	time	NOUN
iajs-763	272	55	ibn	ibn	PROPN
iajs-763	272	56	alhaitham	alhaitham	NOUN
iajs-763	272	57	j.	j.	PROPN
iajs-763	272	58	for	for	ADP
iajs-763	272	59	pure	pure	ADJ
iajs-763	272	60	&	&	CCONJ
iajs-763	272	61	appl	appl	PROPN
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iajs-763	273	1	sci	sci	PROPN
iajs-763	273	2	.	.	PUNCT
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iajs-763	273	5	2	2	NUM
iajs-763	273	6	)	)	PUNCT
iajs-763	273	7	2011	2011	NUM
iajs-763	273	8	table	table	NOUN
iajs-763	273	9	(	(	PUNCT
iajs-763	273	10	5	5	NUM
iajs-763	273	11	)	)	PUNCT
iajs-763	273	12	a	a	DET
iajs-763	273	13	comparison	comparison	NOUN
iajs-763	273	14	between	between	ADP
iajs-763	273	15	the	the	DET
iajs-763	273	16	exact	exact	ADJ
iajs-763	273	17	and	and	CCONJ
iajs-763	273	18	numerical	numerical	ADJ
iajs-763	273	19	solution	solution	NOUN
iajs-763	273	20	of	of	ADP
iajs-763	273	21	4	4	NUM
iajs-763	273	22	types	type	NOUN
iajs-763	273	23	of	of	ADP
iajs-763	273	24	open	open	ADJ
iajs-763	273	25	n	n	NOUN
iajs-763	273	26	–	–	PUNCT
iajs-763	273	27	c	c	NOUN
iajs-763	273	28	and	and	CCONJ
iajs-763	273	29	2	2	NUM
iajs-763	273	30	types	type	NOUN
iajs-763	273	31	of	of	ADP
iajs-763	273	32	closed	closed	ADJ
iajs-763	273	33	n	n	CCONJ
iajs-763	273	34	–	–	PUNCT
iajs-763	273	35	c	c	NOUN
iajs-763	273	36	for	for	ADP
iajs-763	273	37	u3	u3	NOUN
iajs-763	273	38	table	table	NOUN
iajs-763	273	39	(	(	PUNCT
iajs-763	273	40	6	6	NUM
iajs-763	273	41	)	)	PUNCT
iajs-763	273	42	a	a	DET
iajs-763	273	43	comparison	comparison	NOUN
iajs-763	273	44	between	between	ADP
iajs-763	273	45	the	the	DET
iajs-763	273	46	exact	exact	ADJ
iajs-763	273	47	and	and	CCONJ
iajs-763	273	48	numerical	numerical	ADJ
iajs-763	273	49	solution	solution	NOUN
iajs-763	273	50	of	of	ADP
iajs-763	273	51	4	4	NUM
iajs-763	273	52	types	type	NOUN
iajs-763	273	53	of	of	ADP
iajs-763	273	54	open	open	ADJ
iajs-763	273	55	n	n	NOUN
iajs-763	273	56	–	–	PUNCT
iajs-763	273	57	c	c	NOUN
iajs-763	273	58	and	and	CCONJ
iajs-763	273	59	2	2	NUM
iajs-763	273	60	types	type	NOUN
iajs-763	273	61	of	of	ADP
iajs-763	273	62	closed	closed	ADJ
iajs-763	273	63	n	n	CCONJ
iajs-763	273	64	–	–	PUNCT
iajs-763	273	65	c	c	NOUN
iajs-763	273	66	for	for	ADP
iajs-763	273	67	u1	u1	NOUN
iajs-763	273	68	closed	close	VERB
iajs-763	273	69	n	n	CCONJ
iajs-763	273	70	-	-	PUNCT
iajs-763	273	71	c	c	NOUN
iajs-763	273	72	simp	simp	ADJ
iajs-763	273	73	.	.	PROPN
iajs-763	273	74	3/8	3/8	NUM
iajs-763	273	75	closed	closed	ADJ
iajs-763	273	76	n	n	CCONJ
iajs-763	273	77	-	-	PUNCT
iajs-763	273	78	c	c	NOUN
iajs-763	273	79	trap	trap	NOUN
iajs-763	273	80	.	.	PUNCT
iajs-763	274	1	open	open	ADJ
iajs-763	274	2	n	n	CCONJ
iajs-763	274	3	-	-	PUNCT
iajs-763	274	4	c	c	NOUN
iajs-763	274	5	n=4	n=4	X
iajs-763	274	6	open	open	ADJ
iajs-763	274	7	n	n	CCONJ
iajs-763	274	8	-	-	PUNCT
iajs-763	274	9	c	c	NOUN
iajs-763	274	10	n=3	n=3	PUNCT
iajs-763	274	11	open	open	ADJ
iajs-763	274	12	n	n	CCONJ
iajs-763	274	13	-	-	PUNCT
iajs-763	274	14	c	c	NOUN
iajs-763	274	15	n=2	n=2	PRON
iajs-763	274	16	open	open	VERB
iajs-763	274	17	n	n	CCONJ
iajs-763	274	18	-	-	PUNCT
iajs-763	274	19	c	c	NOUN
iajs-763	274	20	n=1	n=1	PROPN
iajs-763	274	21	open	open	ADJ
iajs-763	274	22	n	n	CCONJ
iajs-763	274	23	-	-	PUNCT
iajs-763	274	24	c	c	NOUN
iajs-763	274	25	n=0	n=0	SYM
iajs-763	274	26	exact	exact	ADJ
iajs-763	274	27	u3	u3	NOUN
iajs-763	274	28	x	x	SYM
iajs-763	274	29	0.99026659	0.99026659	NUM
iajs-763	274	30	0.99687951	0.99687951	NUM
iajs-763	274	31	0.98996416	0.98996416	NUM
iajs-763	274	32	0.98984800	0.98984800	NUM
iajs-763	274	33	0.98878499	0.98878499	NUM
iajs-763	274	34	0.97099871	0.97099871	NUM
iajs-763	274	35	0.99000000	0.99000000	NUM
iajs-763	274	36	0.99000	0.99000	NUM
iajs-763	274	37	0.1	0.1	NUM
iajs-763	274	38	0.90969268	0.90969268	NUM
iajs-763	274	39	0.90749750	0.90749750	NUM
iajs-763	274	40	0.90989248	0.90989248	NUM
iajs-763	274	41	0.90954400	0.90954400	NUM
iajs-763	274	42	0.91131067	0.91131067	NUM
iajs-763	274	43	0.91867773	0.91867773	NUM
iajs-763	274	44	0.91000000	0.91000000	NUM
iajs-763	274	45	0.91000	0.91000	NUM
iajs-763	274	46	0.3	0.3	NUM
iajs-763	274	47	0.74911876	0.74911876	NUM
iajs-763	274	48	0.73811548	0.73811548	NUM
iajs-763	274	49	0.74982080	0.74982080	NUM
iajs-763	274	50	0.75383634	0.75383634	NUM
iajs-763	274	51	0.78635675	0.78635675	NUM
iajs-763	274	52	0.75000000	0.75000000	NUM
iajs-763	274	53	0.75000	0.75000	NUM
iajs-763	274	54	0.5	0.5	NUM
iajs-763	274	55	0.50854484	0.50854484	NUM
iajs-763	274	56	0.51000000	0.51000000	NUM
iajs-763	274	57	0.50974912	0.50974912	NUM
iajs-763	274	58	0.50893600	0.50893600	NUM
iajs-763	274	59	0.51636201	0.51636201	NUM
iajs-763	274	60	0.51000000	0.51000000	NUM
iajs-763	274	61	0.51000	0.51000	NUM
iajs-763	274	62	0.7	0.7	NUM
iajs-763	274	63	0.18797093	0.18797093	NUM
iajs-763	274	64	0.19000000	0.19000000	NUM
iajs-763	274	65	0.18967744	0.18967744	NUM
iajs-763	274	66	0.18863200	0.18863200	NUM
iajs-763	274	67	0.19888768	0.19888768	NUM
iajs-763	274	68	0.28171479	0.28171479	NUM
iajs-763	274	69	0.19000000	0.19000000	NUM
iajs-763	274	70	0.19000	0.19000	NUM
iajs-763	274	71	0.9	0.9	NUM
iajs-763	274	72	5.36e-006	5.36e-006	NUM
iajs-763	274	73	0.0012	0.0012	NUM
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iajs-763	274	75	e-007	e-007	CCONJ
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iajs-763	274	77	e-006	e-006	ADJ
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iajs-763	274	79	e-005	e-005	NUM
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iajs-763	274	81	0.00450909	0.00450909	NUM
iajs-763	274	82	l.s.e	l.s.e	NOUN
iajs-763	274	83	.	.	PUNCT
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iajs-763	275	5	0.11000	0.11000	NUM
iajs-763	275	6	0.1100	0.1100	NUM
iajs-763	275	7	0.07800	0.07800	NUM
iajs-763	275	8	time	time	NOUN
iajs-763	275	9	closed	closed	ADJ
iajs-763	275	10	n	n	CCONJ
iajs-763	275	11	-	-	PUNCT
iajs-763	275	12	c	c	NOUN
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iajs-763	275	14	.	.	PROPN
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iajs-763	275	16	closed	closed	ADJ
iajs-763	275	17	n	n	CCONJ
iajs-763	275	18	-	-	PUNCT
iajs-763	275	19	c	c	NOUN
iajs-763	275	20	trap	trap	NOUN
iajs-763	275	21	.	.	PUNCT
iajs-763	276	1	open	open	ADJ
iajs-763	276	2	n	n	CCONJ
iajs-763	276	3	-	-	PUNCT
iajs-763	276	4	c	c	NOUN
iajs-763	276	5	n=4	n=4	X
iajs-763	276	6	open	open	ADJ
iajs-763	276	7	n	n	CCONJ
iajs-763	276	8	-	-	PUNCT
iajs-763	276	9	c	c	NOUN
iajs-763	276	10	n=3	n=3	PUNCT
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iajs-763	276	12	n	n	CCONJ
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iajs-763	276	14	c	c	NOUN
iajs-763	276	15	n=2	n=2	PRON
iajs-763	276	16	open	open	VERB
iajs-763	276	17	n	n	CCONJ
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iajs-763	276	19	c	c	NOUN
iajs-763	276	20	n=1	n=1	PROPN
iajs-763	276	21	open	open	ADJ
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iajs-763	276	24	c	c	NOUN
iajs-763	276	25	n=0	n=0	CCONJ
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iajs-763	276	28	x	x	SYM
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iajs-763	276	33	1.00299173	1.00299173	NUM
iajs-763	276	34	0.99935102	0.99935102	NUM
iajs-763	276	35	1.00056628	1.00056628	NUM
iajs-763	276	36	1.0030864	1.0030864	NUM
iajs-763	276	37	0.05556	0.05556	NUM
iajs-763	276	38	1.04939139	1.04939139	NUM
iajs-763	276	39	1.05476199	1.05476199	NUM
iajs-763	276	40	1.04938271	1.04938271	NUM
iajs-763	276	41	1.04847428	1.04847428	NUM
iajs-763	276	42	1.04899455	1.04899455	NUM
iajs-763	276	43	1.03397239	1.03397239	NUM
iajs-763	276	44	1.0493827	1.0493827	NUM
iajs-763	276	45	0.22222	0.22222	NUM
iajs-763	276	46	1.15125043	1.15125043	NUM
iajs-763	276	47	1.16093361	1.16093361	NUM
iajs-763	276	48	1.15123456	1.15123456	NUM
iajs-763	276	49	1.14960709	1.14960709	NUM
iajs-763	276	50	1.15053877	1.15053877	NUM
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iajs-763	276	52	1.13248750	1.13248750	NUM
iajs-763	276	53	1.1512345	1.1512345	NUM
iajs-763	276	54	0.38889	0.38889	NUM
iajs-763	276	55	1.30866561	1.30866561	NUM
iajs-763	276	56	1.32290534	1.32290534	NUM
iajs-763	276	57	1.30864197	1.30864197	NUM
iajs-763	276	58	1.30626312	1.30626312	NUM
iajs-763	276	59	1.26777251	1.26777251	NUM
iajs-763	276	60	1.3086419	1.3086419	NUM
iajs-763	276	61	0.55556	0.55556	NUM
iajs-763	276	62	1.52163693	1.52163693	NUM
iajs-763	276	63	1.54067718	1.54067718	NUM
iajs-763	276	64	1.52160493	1.52160493	NUM
iajs-763	276	65	1.52025143	1.52025143	NUM
iajs-763	276	66	1.46695127	1.46695127	NUM
iajs-763	276	67	1.48473476	1.48473476	NUM
iajs-763	276	68	1.5216049	1.5216049	NUM
iajs-763	276	69	0.72222	0.72222	NUM
iajs-763	276	70	1.79016439	1.79016439	NUM
iajs-763	276	71	1.81424913	1.81424913	NUM
iajs-763	276	72	1.79012345	1.79012345	NUM
iajs-763	276	73	1.78614486	1.78614486	NUM
iajs-763	276	74	1.78841988	1.78841988	NUM
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iajs-763	276	76	1.7901234	1.7901234	NUM
iajs-763	276	77	0.88889	0.88889	NUM
iajs-763	276	78	2.229e-009	2.229e-009	NUM
iajs-763	276	79	7.634e-004	7.634e-004	NUM
iajs-763	276	80	4.146e-029	4.146e-029	NOUN
iajs-763	276	81	e-0051.812	e-0051.812	PROPN
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iajs-763	277	3	0.281000	0.281000	NUM
iajs-763	277	4	0.203000	0.203000	NUM
iajs-763	277	5	0.188000	0.188000	NUM
iajs-763	277	6	0.157000	0.157000	NUM
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iajs-763	277	8	time	time	NOUN
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iajs-763	277	10	alhaitham	alhaitham	NOUN
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iajs-763	278	1	sci	sci	PROPN
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iajs-763	278	7	2011	2011	NUM
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iajs-763	278	11	)	)	PUNCT
iajs-763	278	12	a	a	DET
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iajs-763	278	30	types	type	NOUN
iajs-763	278	31	of	of	ADP
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iajs-763	278	42	simp	simp	ADJ
iajs-763	278	43	.	.	PROPN
iajs-763	278	44	3/8	3/8	NUM
iajs-763	278	45	closed	closed	ADJ
iajs-763	278	46	n	n	CCONJ
iajs-763	278	47	-	-	PUNCT
iajs-763	278	48	c	c	NOUN
iajs-763	278	49	trap	trap	NOUN
iajs-763	278	50	.	.	PUNCT
iajs-763	279	1	open	open	ADJ
iajs-763	279	2	n	n	CCONJ
iajs-763	279	3	-	-	PUNCT
iajs-763	279	4	c	c	NOUN
iajs-763	279	5	n=4	n=4	X
iajs-763	279	6	open	open	ADJ
iajs-763	279	7	n	n	CCONJ
iajs-763	279	8	-	-	PUNCT
iajs-763	279	9	c	c	NOUN
iajs-763	279	10	n=3	n=3	PUNCT
iajs-763	279	11	open	open	ADJ
iajs-763	279	12	n	n	CCONJ
iajs-763	279	13	-	-	PUNCT
iajs-763	279	14	c	c	NOUN
iajs-763	279	15	n=2	n=2	PRON
iajs-763	279	16	open	open	VERB
iajs-763	279	17	n	n	CCONJ
iajs-763	279	18	-	-	PUNCT
iajs-763	279	19	c	c	NOUN
iajs-763	279	20	n=1	n=1	PROPN
iajs-763	279	21	open	open	ADJ
iajs-763	279	22	n	n	CCONJ
iajs-763	279	23	-	-	PUNCT
iajs-763	279	24	c	c	NOUN
iajs-763	279	25	n=0	n=0	CCONJ
iajs-763	279	26	exact	exact	ADJ
iajs-763	279	27	u2	u2	NOUN
iajs-763	279	28	x	x	PUNCT
iajs-763	279	29	0.00000979	0.00000979	NUM
iajs-763	279	30	0.00031686	0.00031686	NUM
iajs-763	279	31	0.00000952	0.00000952	NUM
iajs-763	279	32	0.000045400.000013190.000865070.00058130.0000095	0.000045400.000013190.000865070.00058130.0000095	NUM
iajs-763	279	33	0.05556	0.05556	NUM
iajs-763	279	34	0.00243999	0.00243999	NUM
iajs-763	279	35	0.00387053	0.00387053	NUM
iajs-763	279	36	0.00243865	0.00243865	NUM
iajs-763	279	37	0.00219055	0.00219055	NUM
iajs-763	279	38	0.00233587	0.00233587	NUM
iajs-763	279	39	0.00164220	0.00164220	NUM
iajs-763	279	40	0.0024386	0.0024386	NUM
iajs-763	279	41	0.22222	0.22222	NUM
iajs-763	279	42	0.02287473	0.02287473	NUM
iajs-763	279	43	0.02573211	0.02573211	NUM
iajs-763	279	44	0.02287189	0.02287189	NUM
iajs-763	279	45	0.02238811	0.02238811	NUM
iajs-763	279	46	0.02267126	0.02267126	NUM
iajs-763	279	47	0.01471108	0.01471108	NUM
iajs-763	279	48	0.01736184	0.01736184	NUM
iajs-763	279	49	0.0228718	0.0228718	NUM
iajs-763	279	50	0.38889	0.38889	NUM
iajs-763	279	51	0.09526463	0.09526463	NUM
iajs-763	279	52	0.09985221	0.09985221	NUM
iajs-763	279	53	0.09525986	0.09525986	NUM
iajs-763	279	54	0.09449787	0.09449787	NUM
iajs-763	279	55	0.08214541	0.08214541	NUM
iajs-763	280	1	0.0952598	0.0952598	NUM
iajs-763	280	2	0.55556	0.55556	NUM
iajs-763	280	3	0.27207881	0.27207881	NUM
iajs-763	280	4	0.27869997	0.27869997	NUM
iajs-763	280	5	0.27207171	0.27207171	NUM
iajs-763	280	6	0.27162193	0.27162193	NUM
iajs-763	280	7	0.25312991	0.25312991	NUM
iajs-763	280	8	0.25928723	0.25928723	NUM
iajs-763	281	1	0.2720717	0.2720717	NUM
iajs-763	281	2	0.72222	0.72222	NUM
iajs-763	281	3	0.62430494	0.62430494	NUM
iajs-763	281	4	0.63326303	0.63326303	NUM
iajs-763	281	5	0.62429507	0.62429507	NUM
iajs-763	281	6	0.62284907	0.62284907	NUM
iajs-763	281	7	0.62369401	0.62369401	NUM
iajs-763	281	8	0.59865224	0.59865224	NUM
iajs-763	281	9	0.6242950	0.6242950	NUM
iajs-763	281	10	0.88889	0.88889	NUM
iajs-763	281	11	1.425e-010	1.425e-010	NUM
iajs-763	281	12	1.144e-004	1.144e-004	NUM
iajs-763	281	13	8.985e-030	8.985e-030	NUM
iajs-763	281	14	e-0062.485	e-0062.485	PROPN
iajs-763	281	15	e-0074.296	e-0074.296	ADJ
iajs-763	281	16	e-0047.879	e-0047.879	PROPN
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iajs-763	281	18	l.s.e	l.s.e	NOUN
iajs-763	281	19	.	.	PUNCT
iajs-763	282	1	0.391000	0.391000	NUM
iajs-763	282	2	0.359000	0.359000	NUM
iajs-763	282	3	0.281000	0.281000	NUM
iajs-763	282	4	0.203000	0.203000	NUM
iajs-763	282	5	0.188000	0.188000	NUM
iajs-763	282	6	0.157000	0.157000	NUM
iajs-763	282	7	0.094000	0.094000	NUM
iajs-763	282	8	time	time	NOUN
iajs-763	282	9	2011	2011	NUM
iajs-763	282	10	)	)	PUNCT
iajs-763	282	11	2	2	NUM
iajs-763	282	12	(	(	PUNCT
iajs-763	282	13	24والتطبیقیة	24والتطبیقیة	NUM
iajs-763	282	14	المجلدمجلة	المجلدمجلة	VERB
iajs-763	282	15	ابن	ابن	PROPN
iajs-763	282	16	الھیثم	الھیثم	PROPN
iajs-763	282	17	للعلوم	للعلوم	NOUN
iajs-763	282	18	الصرفة	الصرفة	PROPN
iajs-763	282	19	صیغ	صیغ	PROPN
iajs-763	282	20	عمالمنظومة	عمالمنظومة	NOUN
iajs-763	282	21	معادالت	معادالت	ADJ
iajs-763	282	22	فریدهوم	فریدهوم	PROPN
iajs-763	282	23	التكاملیة	التكاملیة	PROPN
iajs-763	282	24	الخطیة	الخطیة	VERB
iajs-763	282	25	من	من	PROPN
iajs-763	282	26	النوع	النوع	PROPN
iajs-763	282	27	الثاني	الثاني	PROPN
iajs-763	282	28	باستحل	باستحل	NOUN
iajs-763	282	29	كوتس	كوتس	PROPN
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iajs-763	282	31	–	–	PUNCT
iajs-763	282	32	نیوتن	نیوتن	PROPN
iajs-763	282	33	غادة	غادة	PROPN
iajs-763	282	34	حسن	حسن	PROPN
iajs-763	282	35	إبراهیم	إبراهیم	PROPN
iajs-763	282	36	جامعة	جامعة	PROPN
iajs-763	282	37	بغداد	بغداد	PROPN
iajs-763	282	38	،	،	PROPN
iajs-763	282	39	أبن	أبن	NOUN
iajs-763	282	40	الهیثم	الهیثم	ADJ
iajs-763	282	41	–	–	PUNCT
iajs-763	282	42	كلیة	كلیة	PROPN
iajs-763	282	43	التربیة	التربیة	NOUN
iajs-763	282	44	،	،	PROPN
iajs-763	283	1	قسم	قسم	PROPN
iajs-763	283	2	الریاضیات	الریاضیات	VERB
iajs-763	283	3	2010	2010	NUM
iajs-763	283	4	،	،	PROPN
iajs-763	283	5	تشرین	تشرین	PROPN
iajs-763	283	6	األول	األول	PROPN
iajs-763	283	7	،	،	PROPN
iajs-763	283	8	27	27	NUM
iajs-763	283	9	:	:	PUNCT
iajs-763	283	10	استلم	استلم	PROPN
iajs-763	283	11	البحث	البحث	VERB
iajs-763	283	12	في	في	X
iajs-763	283	13	,	,	PUNCT
iajs-763	283	14	2011شباط	2011شباط	NUM
iajs-763	283	15	،	،	NOUN
iajs-763	283	16	28	28	NUM
iajs-763	283	17	:	:	PUNCT
iajs-763	284	1	قبل	قبل	NOUN
iajs-763	284	2	البحث	البحث	VERB
iajs-763	284	3	في	في	ADP
iajs-763	284	4	الخالصة	الخالصة	PROPN
iajs-763	284	5	اذ	اذ	PROPN
iajs-763	284	6	،	،	PROPN
iajs-763	284	7	كوتس	كوتس	PROPN
iajs-763	284	8	المفتوحـة	المفتوحـة	PROPN
iajs-763	284	9	–	–	PUNCT
iajs-763	284	10	صیغ	صیغ	ADJ
iajs-763	284	11	نیوتن	نیوتن	NOUN
iajs-763	284	12	عمالالبحث	عمالالبحث	NOUN
iajs-763	285	1	حل	حل	VERB
iajs-763	285	2	منظومة	منظومة	INTJ
iajs-763	286	1	من	من	PRON
iajs-763	286	2	معادالت	معادالت	ADJ
iajs-763	286	3	فریدهوم	فریدهوم	PROPN
iajs-763	286	4	التكاملیة	التكاملیة	PROPN
iajs-763	286	5	الخطیة	الخطیة	PROPN
iajs-763	286	6	باست	باست	ADJ
iajs-763	286	7	هذا	هذا	NOUN
iajs-763	286	8	یتضمن	یتضمن	ADV
iajs-763	286	9	.	.	PUNCT
iajs-763	287	1	لحل	لحل	VERB
iajs-763	287	2	هذا	هذا	PROPN
iajs-763	287	3	النظام	النظام	PROPN
iajs-763	287	4	كوتس	كوتس	PROPN
iajs-763	287	5	المفتوحة	المفتوحة	PROPN
iajs-763	287	6	–	–	PUNCT
iajs-763	287	7	من	من	PRON
iajs-763	287	8	صیغ	صیغ	ADJ
iajs-763	287	9	نیوتن	نیوتن	NOUN
iajs-763	287	10	خمس	خمس	PROPN
iajs-763	287	11	صیغ	صیغ	PROPN
iajs-763	287	12	مختلفة	مختلفة	PROPN
iajs-763	287	13	عملنااست	عملنااست	PROPN
iajs-763	287	14	.كوتس	.كوتس	PUNCT
iajs-763	287	15	المغلقة	المغلقة	PROPN
iajs-763	287	16	–	–	PUNCT
iajs-763	287	17	ق	ق	PROPN
iajs-763	287	18	نیوتن	نیوتن	PROPN
iajs-763	287	19	ائق	ائق	PROPN
iajs-763	287	20	أخرى	أخرى	PROPN
iajs-763	287	21	مثل	مثل	NOUN
iajs-763	287	22	طر	طر	PRON
iajs-763	287	23	ائالبحث	ائالبحث	PROPN
iajs-763	287	24	مع	مع	ADP
iajs-763	287	25	نتائج	نتائج	PROPN
iajs-763	288	1	طر	طر	ADP
iajs-763	288	2	كذلك	كذلك	PROPN
iajs-763	288	3	قارنا	قارنا	PROPN
iajs-763	288	4	نتائج	نتائج	PROPN
iajs-763	288	5	الطریقة	الطریقة	PROPN
iajs-763	288	6	المقترحة	المقترحة	PROPN
iajs-763	288	7	في	في	ADP
iajs-763	288	8	هذا	هذا	NOUN
iajs-763	288	9	أیضا	أیضا	NOUN
iajs-763	288	10	)	)	PUNCT
iajs-763	288	11	matlab	matlab	PROPN
iajs-763	288	12	(	(	PUNCT
iajs-763	288	13	version	version	NOUN
iajs-763	288	14	7.0	7.0	NUM
iajs-763	288	15	)	)	PUNCT
iajs-763	288	16	(	(	PUNCT
iajs-763	288	17	را	را	INTJ
iajs-763	288	18	في	في	ADP
iajs-763	288	19	نهایة	نهایة	PROPN
iajs-763	288	20	كل	كل	PROPN
iajs-763	288	21	طریقة	طریقة	NOUN
iajs-763	288	22	ذكرنا	ذكرنا	ADV
iajs-763	288	23	الخوارزمیة	الخوارزمیة	PROPN
iajs-763	288	24	وبرنامج	وبرنامج	PROPN
iajs-763	288	25	للطریقة	للطریقة	PROPN
iajs-763	289	1	المقترحة	المقترحة	PROPN
iajs-763	289	2	للحل	للحل	PROPN
iajs-763	289	3	وبلغة	وبلغة	PROPN
iajs-763	289	4	أخی	أخی	PROPN
iajs-763	289	5	.وضحنا	.وضحنا	PUNCT
iajs-763	289	6	الطریقة	الطریقة	PROPN
iajs-763	289	7	المقترحة	المقترحة	PROPN
iajs-763	290	1	من	من	PROPN
iajs-763	290	2	خالل	خالل	PROPN
iajs-763	290	3	األمثلة	األمثلة	PROPN
iajs-763	290	4	العددیة	العددیة	VERB
iajs-763	290	5	كوتس	كوتس	PROPN
iajs-763	290	6	المغلقة	المغلقة	PROPN
iajs-763	290	7	،	،	PROPN
iajs-763	291	1	منظومة	منظومة	PROPN
iajs-763	291	2	معادالت	معادالت	PROPN
iajs-763	291	3	فریـدهولم	فریـدهولم	PROPN
iajs-763	291	4	التكاملیـة	التكاملیـة	ADJ
iajs-763	291	5	–	–	PUNCT
iajs-763	291	6	كوتس	كوتس	PROPN
iajs-763	291	7	المفتوحة	المفتوحة	PROPN
iajs-763	291	8	،	،	PROPN
iajs-763	291	9	صیغ	صیغ	PROPN
iajs-763	291	10	نیوتن	نیوتن	NOUN
iajs-763	291	11	–	–	PUNCT
iajs-763	291	12	صیغ	صیغ	ADJ
iajs-763	291	13	نیوتن	نیوتن	NOUN
iajs-763	291	14	:	:	PUNCT
iajs-763	291	15	الكلمات	الكلمات	VERB
iajs-763	291	16	المفتاحیة	المفتاحیة	ADV
iajs-763	291	17	.الخطیة	.الخطیة	PUNCT