id	sid	tid	token	lemma	pos
ejpam-6763	1	1	european	european	PROPN
ejpam-6763	1	2	journal	journal	PROPN
ejpam-6763	1	3	of	of	ADP
ejpam-6763	1	4	pure	pure	ADJ
ejpam-6763	1	5	and	and	CCONJ
ejpam-6763	1	6	applied	applied	ADJ
ejpam-6763	1	7	mathematics	mathematic	NOUN
ejpam-6763	1	8	2025	2025	NUM
ejpam-6763	1	9	,	,	PUNCT
ejpam-6763	1	10	vol	vol	NOUN
ejpam-6763	1	11	.	.	PROPN
ejpam-6763	1	12	18	18	NUM
ejpam-6763	1	13	,	,	PUNCT
ejpam-6763	1	14	issue	issue	NOUN
ejpam-6763	1	15	4	4	NUM
ejpam-6763	1	16	,	,	PUNCT
ejpam-6763	1	17	article	article	NOUN
ejpam-6763	1	18	number	number	NOUN
ejpam-6763	1	19	6763	6763	NUM
ejpam-6763	1	20	issn	issn	VERB
ejpam-6763	1	21	1307	1307	NUM
ejpam-6763	1	22	-	-	SYM
ejpam-6763	1	23	5543	5543	NUM
ejpam-6763	1	24	–	–	PUNCT
ejpam-6763	1	25	ejpam.com	ejpam.com	X
ejpam-6763	1	26	published	publish	VERB
ejpam-6763	1	27	by	by	ADP
ejpam-6763	1	28	new	new	PROPN
ejpam-6763	1	29	york	york	PROPN
ejpam-6763	1	30	business	business	PROPN
ejpam-6763	1	31	global	global	ADJ
ejpam-6763	1	32	employing	employ	VERB
ejpam-6763	1	33	cubic	cubic	ADJ
ejpam-6763	1	34	b	b	PROPN
ejpam-6763	1	35	-	-	PUNCT
ejpam-6763	1	36	spline	spline	NOUN
ejpam-6763	1	37	functions	function	NOUN
ejpam-6763	1	38	to	to	PART
ejpam-6763	1	39	solve	solve	VERB
ejpam-6763	1	40	linear	linear	ADJ
ejpam-6763	1	41	systems	system	NOUN
ejpam-6763	1	42	of	of	ADP
ejpam-6763	1	43	volterra	volterra	PROPN
ejpam-6763	1	44	integro	integro	PROPN
ejpam-6763	1	45	-	-	PUNCT
ejpam-6763	1	46	fractional	fractional	ADJ
ejpam-6763	1	47	differential	differential	ADJ
ejpam-6763	1	48	equations	equation	NOUN
ejpam-6763	1	49	with	with	ADP
ejpam-6763	1	50	variable	variable	ADJ
ejpam-6763	1	51	coefficients	coefficient	NOUN
ejpam-6763	1	52	diar	diar	PROPN
ejpam-6763	1	53	kh	kh	PROPN
ejpam-6763	1	54	.	.	PUNCT
ejpam-6763	1	55	abdullah1,∗	abdullah1,∗	NOUN
ejpam-6763	1	56	,	,	PUNCT
ejpam-6763	1	57	shazad	shazad	VERB
ejpam-6763	1	58	sh	sh	PROPN
ejpam-6763	1	59	.	.	PROPN
ejpam-6763	1	60	ahmed1	ahmed1	PROPN
ejpam-6763	1	61	,	,	PUNCT
ejpam-6763	1	62	karwan	karwan	PROPN
ejpam-6763	1	63	h.	h.	PROPN
ejpam-6763	1	64	f.	f.	PROPN
ejpam-6763	1	65	jwamer1	jwamer1	PROPN
ejpam-6763	1	66	1	1	NUM
ejpam-6763	1	67	mathematics	mathematics	PROPN
ejpam-6763	1	68	department	department	NOUN
ejpam-6763	1	69	,	,	PUNCT
ejpam-6763	1	70	college	college	NOUN
ejpam-6763	1	71	of	of	ADP
ejpam-6763	1	72	science	science	NOUN
ejpam-6763	1	73	,	,	PUNCT
ejpam-6763	1	74	university	university	NOUN
ejpam-6763	1	75	of	of	ADP
ejpam-6763	1	76	sulaimani	sulaimani	PROPN
ejpam-6763	1	77	,	,	PUNCT
ejpam-6763	1	78	sulaimanyah	sulaimanyah	NOUN
ejpam-6763	1	79	,	,	PUNCT
ejpam-6763	1	80	iraq	iraq	PROPN
ejpam-6763	1	81	abstract	abstract	NOUN
ejpam-6763	1	82	.	.	PUNCT
ejpam-6763	2	1	in	in	ADP
ejpam-6763	2	2	this	this	DET
ejpam-6763	2	3	study	study	NOUN
ejpam-6763	2	4	,	,	PUNCT
ejpam-6763	2	5	we	we	PRON
ejpam-6763	2	6	present	present	VERB
ejpam-6763	2	7	a	a	DET
ejpam-6763	2	8	collocation	collocation	NOUN
ejpam-6763	2	9	method	method	NOUN
ejpam-6763	2	10	based	base	VERB
ejpam-6763	2	11	on	on	ADP
ejpam-6763	2	12	cubic	cubic	ADJ
ejpam-6763	2	13	b	b	PROPN
ejpam-6763	2	14	-	-	PUNCT
ejpam-6763	2	15	spline	spline	NOUN
ejpam-6763	2	16	functions	function	NOUN
ejpam-6763	2	17	for	for	ADP
ejpam-6763	2	18	solving	solve	VERB
ejpam-6763	2	19	systems	system	NOUN
ejpam-6763	2	20	of	of	ADP
ejpam-6763	2	21	volterra	volterra	PROPN
ejpam-6763	2	22	integro	integro	PROPN
ejpam-6763	2	23	-	-	PUNCT
ejpam-6763	2	24	differential	differential	NOUN
ejpam-6763	2	25	equations	equation	NOUN
ejpam-6763	2	26	involving	involve	VERB
ejpam-6763	2	27	both	both	CCONJ
ejpam-6763	2	28	classical	classical	ADJ
ejpam-6763	2	29	and	and	CCONJ
ejpam-6763	2	30	fractional	fractional	ADJ
ejpam-6763	2	31	derivatives	derivative	NOUN
ejpam-6763	2	32	in	in	ADP
ejpam-6763	2	33	the	the	DET
ejpam-6763	2	34	caputo	caputo	PROPN
ejpam-6763	2	35	sense	sense	NOUN
ejpam-6763	2	36	(	(	PUNCT
ejpam-6763	2	37	lsvides	lsvide	NOUN
ejpam-6763	2	38	-	-	PUNCT
ejpam-6763	2	39	cf	cf	NOUN
ejpam-6763	2	40	)	)	PUNCT
ejpam-6763	2	41	.	.	PUNCT
ejpam-6763	3	1	the	the	DET
ejpam-6763	3	2	approach	approach	NOUN
ejpam-6763	3	3	begins	begin	VERB
ejpam-6763	3	4	by	by	ADP
ejpam-6763	3	5	dividing	divide	VERB
ejpam-6763	3	6	the	the	DET
ejpam-6763	3	7	problem	problem	NOUN
ejpam-6763	3	8	domain	domain	NOUN
ejpam-6763	3	9	into	into	ADP
ejpam-6763	3	10	a	a	DET
ejpam-6763	3	11	finite	finite	ADJ
ejpam-6763	3	12	number	number	NOUN
ejpam-6763	3	13	of	of	ADP
ejpam-6763	3	14	subintervals	subinterval	NOUN
ejpam-6763	3	15	,	,	PUNCT
ejpam-6763	3	16	followed	follow	VERB
ejpam-6763	3	17	by	by	ADP
ejpam-6763	3	18	the	the	DET
ejpam-6763	3	19	construction	construction	NOUN
ejpam-6763	3	20	of	of	ADP
ejpam-6763	3	21	cubic	cubic	ADJ
ejpam-6763	3	22	b	b	PROPN
ejpam-6763	3	23	-	-	PUNCT
ejpam-6763	3	24	spline	spline	NOUN
ejpam-6763	3	25	basis	basis	NOUN
ejpam-6763	3	26	functions	function	NOUN
ejpam-6763	3	27	within	within	ADP
ejpam-6763	3	28	each	each	DET
ejpam-6763	3	29	segment	segment	NOUN
ejpam-6763	3	30	.	.	PUNCT
ejpam-6763	4	1	control	control	NOUN
ejpam-6763	4	2	points	point	NOUN
ejpam-6763	4	3	are	be	AUX
ejpam-6763	4	4	introduced	introduce	VERB
ejpam-6763	4	5	as	as	ADP
ejpam-6763	4	6	the	the	DET
ejpam-6763	4	7	unknowns	unknown	NOUN
ejpam-6763	4	8	in	in	ADP
ejpam-6763	4	9	the	the	DET
ejpam-6763	4	10	approximate	approximate	ADJ
ejpam-6763	4	11	numerical	numerical	ADJ
ejpam-6763	4	12	solution	solution	NOUN
ejpam-6763	4	13	,	,	PUNCT
ejpam-6763	4	14	which	which	PRON
ejpam-6763	4	15	is	be	AUX
ejpam-6763	4	16	expressed	express	VERB
ejpam-6763	4	17	as	as	ADP
ejpam-6763	4	18	a	a	DET
ejpam-6763	4	19	cubic	cubic	ADJ
ejpam-6763	4	20	combination	combination	NOUN
ejpam-6763	4	21	of	of	ADP
ejpam-6763	4	22	these	these	DET
ejpam-6763	4	23	basis	basis	NOUN
ejpam-6763	4	24	functions	function	NOUN
ejpam-6763	4	25	.	.	PUNCT
ejpam-6763	5	1	the	the	DET
ejpam-6763	5	2	given	give	VERB
ejpam-6763	5	3	system	system	NOUN
ejpam-6763	5	4	of	of	ADP
ejpam-6763	5	5	vifdes	vifde	NOUN
ejpam-6763	5	6	-	-	PUNCT
ejpam-6763	5	7	cf	cf	NOUN
ejpam-6763	5	8	is	be	AUX
ejpam-6763	5	9	then	then	ADV
ejpam-6763	5	10	reduced	reduce	VERB
ejpam-6763	5	11	to	to	ADP
ejpam-6763	5	12	a	a	DET
ejpam-6763	5	13	system	system	NOUN
ejpam-6763	5	14	of	of	ADP
ejpam-6763	5	15	algebraic	algebraic	ADJ
ejpam-6763	5	16	equations	equation	NOUN
ejpam-6763	5	17	,	,	PUNCT
ejpam-6763	5	18	which	which	PRON
ejpam-6763	5	19	are	be	AUX
ejpam-6763	5	20	efficiently	efficiently	ADV
ejpam-6763	5	21	solved	solve	VERB
ejpam-6763	5	22	using	use	VERB
ejpam-6763	5	23	the	the	DET
ejpam-6763	5	24	jacobian	jacobian	ADJ
ejpam-6763	5	25	matrix	matrix	NOUN
ejpam-6763	5	26	method	method	NOUN
ejpam-6763	5	27	.	.	PUNCT
ejpam-6763	6	1	in	in	ADP
ejpam-6763	6	2	practice	practice	NOUN
ejpam-6763	6	3	,	,	PUNCT
ejpam-6763	6	4	the	the	DET
ejpam-6763	6	5	integrals	integral	NOUN
ejpam-6763	6	6	are	be	AUX
ejpam-6763	6	7	approximated	approximate	VERB
ejpam-6763	6	8	using	use	VERB
ejpam-6763	6	9	the	the	DET
ejpam-6763	6	10	clenshaw	clenshaw	ADJ
ejpam-6763	6	11	–	–	PUNCT
ejpam-6763	6	12	curtis	curtis	NOUN
ejpam-6763	6	13	quadrature	quadrature	NOUN
ejpam-6763	6	14	rule	rule	NOUN
ejpam-6763	6	15	.	.	PUNCT
ejpam-6763	7	1	the	the	DET
ejpam-6763	7	2	implementation	implementation	NOUN
ejpam-6763	7	3	of	of	ADP
ejpam-6763	7	4	this	this	DET
ejpam-6763	7	5	method	method	NOUN
ejpam-6763	7	6	is	be	AUX
ejpam-6763	7	7	supported	support	VERB
ejpam-6763	7	8	by	by	ADP
ejpam-6763	7	9	python	python	PROPN
ejpam-6763	7	10	software	software	NOUN
ejpam-6763	7	11	,	,	PUNCT
ejpam-6763	7	12	ensuring	ensure	VERB
ejpam-6763	7	13	effective	effective	ADJ
ejpam-6763	7	14	computational	computational	ADJ
ejpam-6763	7	15	processing	processing	NOUN
ejpam-6763	7	16	.	.	PUNCT
ejpam-6763	8	1	numerical	numerical	ADJ
ejpam-6763	8	2	examples	example	NOUN
ejpam-6763	8	3	are	be	AUX
ejpam-6763	8	4	provided	provide	VERB
ejpam-6763	8	5	to	to	PART
ejpam-6763	8	6	demonstrate	demonstrate	VERB
ejpam-6763	8	7	the	the	DET
ejpam-6763	8	8	efficiency	efficiency	NOUN
ejpam-6763	8	9	of	of	ADP
ejpam-6763	8	10	the	the	DET
ejpam-6763	8	11	proposed	propose	VERB
ejpam-6763	8	12	method	method	NOUN
ejpam-6763	8	13	.	.	PUNCT
ejpam-6763	9	1	an	an	DET
ejpam-6763	9	2	itemized	itemize	VERB
ejpam-6763	9	3	version	version	NOUN
ejpam-6763	9	4	of	of	ADP
ejpam-6763	9	5	the	the	DET
ejpam-6763	9	6	algorithm	algorithm	NOUN
ejpam-6763	9	7	is	be	AUX
ejpam-6763	9	8	also	also	ADV
ejpam-6763	9	9	presented	present	VERB
ejpam-6763	9	10	to	to	PART
ejpam-6763	9	11	facilitate	facilitate	VERB
ejpam-6763	9	12	its	its	PRON
ejpam-6763	9	13	implementation	implementation	NOUN
ejpam-6763	9	14	.	.	PUNCT
ejpam-6763	10	1	2020	2020	NUM
ejpam-6763	10	2	mathematics	mathematic	NOUN
ejpam-6763	10	3	subject	subject	NOUN
ejpam-6763	10	4	classifications	classification	NOUN
ejpam-6763	10	5	:	:	PUNCT
ejpam-6763	10	6	65r20	65r20	NUM
ejpam-6763	10	7	,	,	PUNCT
ejpam-6763	10	8	65m70	65m70	NUM
ejpam-6763	10	9	,	,	PUNCT
ejpam-6763	10	10	34a08	34a08	NUM
ejpam-6763	10	11	,	,	PUNCT
ejpam-6763	10	12	45j05	45j05	ADJ
ejpam-6763	10	13	key	key	ADJ
ejpam-6763	10	14	words	word	NOUN
ejpam-6763	10	15	and	and	CCONJ
ejpam-6763	10	16	phrases	phrase	NOUN
ejpam-6763	10	17	:	:	PUNCT
ejpam-6763	10	18	system	system	NOUN
ejpam-6763	10	19	of	of	ADP
ejpam-6763	10	20	volterra	volterra	PROPN
ejpam-6763	10	21	integro	integro	PROPN
ejpam-6763	10	22	-	-	PUNCT
ejpam-6763	10	23	fractional	fractional	ADJ
ejpam-6763	10	24	differential	differential	ADJ
ejpam-6763	10	25	equations	equation	NOUN
ejpam-6763	10	26	,	,	PUNCT
ejpam-6763	10	27	cubic	cubic	ADJ
ejpam-6763	10	28	b	b	X
ejpam-6763	10	29	-	-	PUNCT
ejpam-6763	10	30	spline	spline	NOUN
ejpam-6763	10	31	function	function	NOUN
ejpam-6763	10	32	,	,	PUNCT
ejpam-6763	10	33	collocation	collocation	NOUN
ejpam-6763	10	34	method	method	NOUN
ejpam-6763	10	35	,	,	PUNCT
ejpam-6763	10	36	jacobian	jacobian	ADJ
ejpam-6763	10	37	matrix	matrix	NOUN
ejpam-6763	10	38	algorithm	algorithm	NOUN
ejpam-6763	10	39	,	,	PUNCT
ejpam-6763	10	40	clenshaw	clenshaw	ADJ
ejpam-6763	10	41	-	-	PUNCT
ejpam-6763	10	42	curtis	curtis	NOUN
ejpam-6763	10	43	quadrature	quadrature	NOUN
ejpam-6763	10	44	rule	rule	VERB
ejpam-6763	10	45	1	1	NUM
ejpam-6763	10	46	.	.	PUNCT
ejpam-6763	11	1	introduction	introduction	NOUN
ejpam-6763	11	2	integro	integro	ADJ
ejpam-6763	11	3	-	-	PUNCT
ejpam-6763	11	4	differential	differential	NOUN
ejpam-6763	11	5	equations	equation	NOUN
ejpam-6763	11	6	(	(	PUNCT
ejpam-6763	11	7	ides	ide	NOUN
ejpam-6763	11	8	)	)	PUNCT
ejpam-6763	11	9	are	be	AUX
ejpam-6763	11	10	widely	widely	ADV
ejpam-6763	11	11	used	use	VERB
ejpam-6763	11	12	in	in	ADP
ejpam-6763	11	13	mathematical	mathematical	ADJ
ejpam-6763	11	14	modeling	modeling	NOUN
ejpam-6763	11	15	because	because	SCONJ
ejpam-6763	11	16	they	they	PRON
ejpam-6763	11	17	combine	combine	VERB
ejpam-6763	11	18	integration	integration	NOUN
ejpam-6763	11	19	and	and	CCONJ
ejpam-6763	11	20	differentiation	differentiation	NOUN
ejpam-6763	11	21	of	of	ADP
ejpam-6763	11	22	an	an	DET
ejpam-6763	11	23	unknown	unknown	ADJ
ejpam-6763	11	24	function	function	NOUN
ejpam-6763	11	25	.	.	PUNCT
ejpam-6763	12	1	scholars	scholar	NOUN
ejpam-6763	12	2	such	such	ADJ
ejpam-6763	12	3	as	as	ADP
ejpam-6763	12	4	volterra	volterra	NOUN
ejpam-6763	12	5	,	,	PUNCT
ejpam-6763	12	6	fredholm	fredholm	NOUN
ejpam-6763	12	7	,	,	PUNCT
ejpam-6763	12	8	malthus	malthus	PROPN
ejpam-6763	12	9	,	,	PUNCT
ejpam-6763	12	10	verhulst	verhulst	PROPN
ejpam-6763	12	11	,	,	PUNCT
ejpam-6763	12	12	abel	abel	PROPN
ejpam-6763	12	13	,	,	PUNCT
ejpam-6763	12	14	and	and	CCONJ
ejpam-6763	12	15	lotka	lotka	PROPN
ejpam-6763	12	16	have	have	AUX
ejpam-6763	12	17	employed	employ	VERB
ejpam-6763	12	18	ides	ide	NOUN
ejpam-6763	12	19	to	to	PART
ejpam-6763	12	20	study	study	VERB
ejpam-6763	12	21	problems	problem	NOUN
ejpam-6763	12	22	in	in	ADP
ejpam-6763	12	23	fields	field	NOUN
ejpam-6763	12	24	including	include	VERB
ejpam-6763	12	25	mathematical	mathematical	ADJ
ejpam-6763	12	26	biology	biology	NOUN
ejpam-6763	12	27	,	,	PUNCT
ejpam-6763	12	28	physics	physics	NOUN
ejpam-6763	12	29	,	,	PUNCT
ejpam-6763	12	30	and	and	CCONJ
ejpam-6763	12	31	economics	economic	NOUN
ejpam-6763	13	1	[	[	X
ejpam-6763	13	2	1	1	NUM
ejpam-6763	13	3	]	]	PUNCT
ejpam-6763	13	4	.	.	PUNCT
ejpam-6763	14	1	over	over	ADP
ejpam-6763	14	2	the	the	DET
ejpam-6763	14	3	past	past	ADJ
ejpam-6763	14	4	several	several	ADJ
ejpam-6763	14	5	decades	decade	NOUN
ejpam-6763	14	6	,	,	PUNCT
ejpam-6763	14	7	extensive	extensive	ADJ
ejpam-6763	14	8	research	research	NOUN
ejpam-6763	14	9	has	have	AUX
ejpam-6763	14	10	been	be	AUX
ejpam-6763	14	11	conducted	conduct	VERB
ejpam-6763	14	12	on	on	ADP
ejpam-6763	14	13	ides	ide	NOUN
ejpam-6763	14	14	,	,	PUNCT
ejpam-6763	14	15	resulting	result	VERB
ejpam-6763	14	16	in	in	ADP
ejpam-6763	14	17	numerous	numerous	ADJ
ejpam-6763	14	18	publications	publication	NOUN
ejpam-6763	14	19	and	and	CCONJ
ejpam-6763	14	20	theoretical	theoretical	ADJ
ejpam-6763	14	21	advancements	advancement	NOUN
ejpam-6763	14	22	.	.	PUNCT
ejpam-6763	15	1	one	one	NUM
ejpam-6763	15	2	notable	notable	ADJ
ejpam-6763	15	3	application	application	NOUN
ejpam-6763	15	4	of	of	ADP
ejpam-6763	15	5	ides	ide	NOUN
ejpam-6763	15	6	is	be	AUX
ejpam-6763	15	7	in	in	ADP
ejpam-6763	15	8	∗corresponding	∗corresponde	VERB
ejpam-6763	15	9	author	author	NOUN
ejpam-6763	15	10	.	.	PUNCT
ejpam-6763	16	1	doi	doi	NOUN
ejpam-6763	16	2	:	:	PUNCT
ejpam-6763	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6763	https://doi.org/10.29020/nybg.ejpam.v18i4.6763	ADJ
ejpam-6763	16	4	email	email	NOUN
ejpam-6763	16	5	addresses	address	NOUN
ejpam-6763	16	6	:	:	PUNCT
ejpam-6763	16	7	diar.khalid85@gmail.com	diar.khalid85@gmail.com	X
ejpam-6763	16	8	(	(	PUNCT
ejpam-6763	16	9	d.	d.	PROPN
ejpam-6763	16	10	kh	kh	PROPN
ejpam-6763	16	11	.	.	PUNCT
ejpam-6763	17	1	abdullah	abdullah	PROPN
ejpam-6763	17	2	)	)	PUNCT
ejpam-6763	17	3	,	,	PUNCT
ejpam-6763	17	4	shazad.ahmed@univsul.edu.iq	shazad.ahmed@univsul.edu.iq	NOUN
ejpam-6763	17	5	(	(	PUNCT
ejpam-6763	17	6	sh	sh	PROPN
ejpam-6763	17	7	.	.	PROPN
ejpam-6763	17	8	sh	sh	PROPN
ejpam-6763	17	9	.	.	PROPN
ejpam-6763	17	10	ahmed	ahmed	PROPN
ejpam-6763	17	11	)	)	PUNCT
ejpam-6763	17	12	,	,	PUNCT
ejpam-6763	17	13	karwan.jwamer@univsul.edu.iq	karwan.jwamer@univsul.edu.iq	PROPN
ejpam-6763	17	14	(	(	PUNCT
ejpam-6763	17	15	k.	k.	PROPN
ejpam-6763	17	16	h.	h.	PROPN
ejpam-6763	17	17	f.	f.	PROPN
ejpam-6763	17	18	jwamer	jwamer	PROPN
ejpam-6763	17	19	)	)	PUNCT
ejpam-6763	17	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6763	18	1	1	1	NUM
ejpam-6763	18	2	copyright	copyright	NOUN
ejpam-6763	18	3	:	:	PUNCT
ejpam-6763	18	4	©	©	PROPN
ejpam-6763	18	5	2025	2025	NUM
ejpam-6763	18	6	the	the	DET
ejpam-6763	18	7	author(s	author(s	NOUN
ejpam-6763	18	8	)	)	PUNCT
ejpam-6763	18	9	.	.	PUNCT
ejpam-6763	19	1	(	(	PUNCT
ejpam-6763	19	2	cc	cc	NOUN
ejpam-6763	19	3	by	by	ADP
ejpam-6763	19	4	-	-	PUNCT
ejpam-6763	19	5	nc	nc	PROPN
ejpam-6763	19	6	4.0	4.0	NUM
ejpam-6763	19	7	)	)	PUNCT
ejpam-6763	19	8	d.	d.	PROPN
ejpam-6763	19	9	kh	kh	PROPN
ejpam-6763	19	10	.	.	PUNCT
ejpam-6763	20	1	abdullah	abdullah	PROPN
ejpam-6763	20	2	,	,	PUNCT
ejpam-6763	20	3	sh	sh	PROPN
ejpam-6763	20	4	.	.	PROPN
ejpam-6763	20	5	sh	sh	PROPN
ejpam-6763	20	6	.	.	PROPN
ejpam-6763	20	7	ahmed	ahmed	PROPN
ejpam-6763	20	8	,	,	PUNCT
ejpam-6763	20	9	k.	k.	PROPN
ejpam-6763	20	10	h.	h.	PROPN
ejpam-6763	20	11	f.	f.	PROPN
ejpam-6763	20	12	jwamer	jwamer	PROPN
ejpam-6763	20	13	/	/	SYM
ejpam-6763	20	14	eur	eur	PROPN
ejpam-6763	20	15	.	.	PUNCT
ejpam-6763	21	1	j.	j.	PROPN
ejpam-6763	21	2	pure	pure	PROPN
ejpam-6763	21	3	appl	appl	PROPN
ejpam-6763	21	4	.	.	PROPN
ejpam-6763	21	5	math	math	PROPN
ejpam-6763	21	6	,	,	PUNCT
ejpam-6763	21	7	18	18	NUM
ejpam-6763	21	8	(	(	PUNCT
ejpam-6763	21	9	4	4	NUM
ejpam-6763	21	10	)	)	PUNCT
ejpam-6763	21	11	(	(	PUNCT
ejpam-6763	21	12	2025	2025	NUM
ejpam-6763	21	13	)	)	PUNCT
ejpam-6763	21	14	,	,	PUNCT
ejpam-6763	21	15	6763	6763	NUM
ejpam-6763	21	16	2	2	NUM
ejpam-6763	21	17	of	of	ADP
ejpam-6763	21	18	40	40	NUM
ejpam-6763	21	19	modeling	model	VERB
ejpam-6763	21	20	the	the	DET
ejpam-6763	21	21	dynamic	dynamic	ADJ
ejpam-6763	21	22	spread	spread	NOUN
ejpam-6763	21	23	of	of	ADP
ejpam-6763	21	24	viruses	virus	NOUN
ejpam-6763	21	25	using	use	VERB
ejpam-6763	21	26	statistical	statistical	ADJ
ejpam-6763	21	27	methods	method	NOUN
ejpam-6763	21	28	[	[	X
ejpam-6763	21	29	2	2	NUM
ejpam-6763	21	30	,	,	PUNCT
ejpam-6763	21	31	3	3	NUM
ejpam-6763	21	32	]	]	PUNCT
ejpam-6763	21	33	.	.	PUNCT
ejpam-6763	22	1	fractional	fractional	ADJ
ejpam-6763	22	2	integrodifferential	integrodifferential	ADJ
ejpam-6763	22	3	equations	equation	NOUN
ejpam-6763	22	4	,	,	PUNCT
ejpam-6763	22	5	in	in	ADP
ejpam-6763	22	6	particular	particular	ADJ
ejpam-6763	22	7	,	,	PUNCT
ejpam-6763	22	8	have	have	AUX
ejpam-6763	22	9	gained	gain	VERB
ejpam-6763	22	10	attention	attention	NOUN
ejpam-6763	22	11	due	due	ADP
ejpam-6763	22	12	to	to	ADP
ejpam-6763	22	13	their	their	PRON
ejpam-6763	22	14	ability	ability	NOUN
ejpam-6763	22	15	to	to	PART
ejpam-6763	22	16	represent	represent	VERB
ejpam-6763	22	17	memory	memory	NOUN
ejpam-6763	22	18	effects	effect	NOUN
ejpam-6763	22	19	and	and	CCONJ
ejpam-6763	22	20	hereditary	hereditary	ADJ
ejpam-6763	22	21	behavior	behavior	NOUN
ejpam-6763	22	22	in	in	ADP
ejpam-6763	22	23	complicated	complicated	ADJ
ejpam-6763	22	24	systems	system	NOUN
ejpam-6763	22	25	,	,	PUNCT
ejpam-6763	22	26	and	and	CCONJ
ejpam-6763	22	27	hence	hence	ADV
ejpam-6763	22	28	,	,	PUNCT
ejpam-6763	22	29	the	the	DET
ejpam-6763	22	30	search	search	NOUN
ejpam-6763	22	31	for	for	ADP
ejpam-6763	22	32	correct	correct	ADJ
ejpam-6763	22	33	approximate	approximate	ADJ
ejpam-6763	22	34	solutions	solution	NOUN
ejpam-6763	22	35	has	have	AUX
ejpam-6763	22	36	developed	develop	VERB
ejpam-6763	22	37	into	into	ADP
ejpam-6763	22	38	one	one	NUM
ejpam-6763	22	39	of	of	ADP
ejpam-6763	22	40	the	the	DET
ejpam-6763	22	41	central	central	ADJ
ejpam-6763	22	42	fields	field	NOUN
ejpam-6763	22	43	of	of	ADP
ejpam-6763	22	44	study	study	NOUN
ejpam-6763	22	45	in	in	ADP
ejpam-6763	22	46	numerical	numerical	ADJ
ejpam-6763	22	47	analysis	analysis	NOUN
ejpam-6763	22	48	,	,	PUNCT
ejpam-6763	22	49	which	which	PRON
ejpam-6763	22	50	led	lead	VERB
ejpam-6763	22	51	to	to	ADP
ejpam-6763	22	52	significant	significant	ADJ
ejpam-6763	22	53	results	result	NOUN
ejpam-6763	22	54	in	in	ADP
ejpam-6763	22	55	the	the	DET
ejpam-6763	22	56	numerical	numerical	ADJ
ejpam-6763	22	57	solution	solution	NOUN
ejpam-6763	22	58	of	of	ADP
ejpam-6763	22	59	linear	linear	ADJ
ejpam-6763	22	60	types	type	NOUN
ejpam-6763	22	61	of	of	ADP
ejpam-6763	22	62	these	these	DET
ejpam-6763	22	63	equations	equation	NOUN
ejpam-6763	23	1	[	[	X
ejpam-6763	23	2	4	4	NUM
ejpam-6763	23	3	]	]	PUNCT
ejpam-6763	23	4	.	.	PUNCT
ejpam-6763	24	1	various	various	ADJ
ejpam-6763	24	2	kinds	kind	NOUN
ejpam-6763	24	3	of	of	ADP
ejpam-6763	24	4	fractional	fractional	ADJ
ejpam-6763	24	5	integral	integral	ADJ
ejpam-6763	24	6	equations	equation	NOUN
ejpam-6763	24	7	have	have	AUX
ejpam-6763	24	8	been	be	AUX
ejpam-6763	24	9	resolved	resolve	VERB
ejpam-6763	24	10	successfully	successfully	ADV
ejpam-6763	24	11	by	by	ADP
ejpam-6763	24	12	building	build	VERB
ejpam-6763	24	13	various	various	ADJ
ejpam-6763	24	14	approaches	approach	NOUN
ejpam-6763	24	15	in	in	ADP
ejpam-6763	24	16	recent	recent	ADJ
ejpam-6763	24	17	times	time	NOUN
ejpam-6763	25	1	[	[	X
ejpam-6763	25	2	5	5	NUM
ejpam-6763	25	3	]	]	PUNCT
ejpam-6763	25	4	.	.	PUNCT
ejpam-6763	26	1	for	for	ADP
ejpam-6763	26	2	such	such	ADJ
ejpam-6763	26	3	complex	complex	ADJ
ejpam-6763	26	4	systems	system	NOUN
ejpam-6763	26	5	,	,	PUNCT
ejpam-6763	26	6	reliable	reliable	ADJ
ejpam-6763	26	7	numerical	numerical	ADJ
ejpam-6763	26	8	methods	method	NOUN
ejpam-6763	26	9	are	be	AUX
ejpam-6763	26	10	necessary	necessary	ADJ
ejpam-6763	26	11	to	to	PART
ejpam-6763	26	12	avoid	avoid	VERB
ejpam-6763	26	13	misleading	mislead	VERB
ejpam-6763	26	14	predictions	prediction	NOUN
ejpam-6763	26	15	.	.	PUNCT
ejpam-6763	27	1	the	the	DET
ejpam-6763	27	2	flexibility	flexibility	NOUN
ejpam-6763	27	3	of	of	ADP
ejpam-6763	27	4	the	the	DET
ejpam-6763	27	5	cubic	cubic	ADJ
ejpam-6763	27	6	b	b	PROPN
ejpam-6763	27	7	-	-	PUNCT
ejpam-6763	27	8	spline	spline	NOUN
ejpam-6763	27	9	collocation	collocation	NOUN
ejpam-6763	27	10	method	method	NOUN
ejpam-6763	27	11	is	be	AUX
ejpam-6763	27	12	that	that	SCONJ
ejpam-6763	27	13	it	it	PRON
ejpam-6763	27	14	can	can	AUX
ejpam-6763	27	15	be	be	AUX
ejpam-6763	27	16	effectively	effectively	ADV
ejpam-6763	27	17	applied	apply	VERB
ejpam-6763	27	18	to	to	ADP
ejpam-6763	27	19	both	both	CCONJ
ejpam-6763	27	20	linear	linear	ADJ
ejpam-6763	27	21	and	and	CCONJ
ejpam-6763	27	22	nonlinear	nonlinear	ADJ
ejpam-6763	27	23	fides	fide	NOUN
ejpam-6763	27	24	,	,	PUNCT
ejpam-6763	27	25	arising	arise	VERB
ejpam-6763	27	26	in	in	ADP
ejpam-6763	27	27	viscoelasticity	viscoelasticity	NOUN
ejpam-6763	27	28	and	and	CCONJ
ejpam-6763	27	29	population	population	NOUN
ejpam-6763	27	30	control	control	NOUN
ejpam-6763	27	31	,	,	PUNCT
ejpam-6763	27	32	demonstrating	demonstrate	VERB
ejpam-6763	27	33	its	its	PRON
ejpam-6763	27	34	usefulness	usefulness	NOUN
ejpam-6763	27	35	in	in	ADP
ejpam-6763	27	36	applications	application	NOUN
ejpam-6763	27	37	[	[	X
ejpam-6763	27	38	6]-[7	6]-[7	NOUN
ejpam-6763	27	39	]	]	X
ejpam-6763	27	40	.	.	PUNCT
ejpam-6763	28	1	current	current	ADJ
ejpam-6763	28	2	research	research	NOUN
ejpam-6763	28	3	has	have	AUX
ejpam-6763	28	4	been	be	AUX
ejpam-6763	28	5	towards	towards	ADP
ejpam-6763	28	6	the	the	DET
ejpam-6763	28	7	development	development	NOUN
ejpam-6763	28	8	of	of	ADP
ejpam-6763	28	9	numerical	numerical	ADJ
ejpam-6763	28	10	methods	method	NOUN
ejpam-6763	28	11	that	that	PRON
ejpam-6763	28	12	can	can	AUX
ejpam-6763	28	13	provide	provide	VERB
ejpam-6763	28	14	precise	precise	ADJ
ejpam-6763	28	15	approximations	approximation	NOUN
ejpam-6763	28	16	of	of	ADP
ejpam-6763	28	17	the	the	DET
ejpam-6763	28	18	solutions	solution	NOUN
ejpam-6763	28	19	of	of	ADP
ejpam-6763	28	20	fides	fide	NOUN
ejpam-6763	28	21	.	.	PUNCT
ejpam-6763	29	1	among	among	ADP
ejpam-6763	29	2	them	they	PRON
ejpam-6763	29	3	,	,	PUNCT
ejpam-6763	29	4	the	the	DET
ejpam-6763	29	5	cubic	cubic	ADJ
ejpam-6763	29	6	b	b	PROPN
ejpam-6763	29	7	-	-	PUNCT
ejpam-6763	29	8	spline	spline	NOUN
ejpam-6763	29	9	collocation	collocation	NOUN
ejpam-6763	29	10	technique	technique	NOUN
ejpam-6763	29	11	was	be	AUX
ejpam-6763	29	12	recently	recently	ADV
ejpam-6763	29	13	popularized	popularize	VERB
ejpam-6763	29	14	,	,	PUNCT
ejpam-6763	29	15	as	as	SCONJ
ejpam-6763	29	16	cubic	cubic	ADJ
ejpam-6763	29	17	b	b	NOUN
ejpam-6763	29	18	-	-	PUNCT
ejpam-6763	29	19	splines	spline	NOUN
ejpam-6763	29	20	inherently	inherently	ADV
ejpam-6763	29	21	possess	possess	VERB
ejpam-6763	29	22	the	the	DET
ejpam-6763	29	23	flexibility	flexibility	NOUN
ejpam-6763	29	24	and	and	CCONJ
ejpam-6763	29	25	smoothness	smoothness	NOUN
ejpam-6763	29	26	that	that	PRON
ejpam-6763	29	27	would	would	AUX
ejpam-6763	29	28	be	be	AUX
ejpam-6763	29	29	suitable	suitable	ADJ
ejpam-6763	29	30	for	for	ADP
ejpam-6763	29	31	approximating	approximate	VERB
ejpam-6763	29	32	fractional	fractional	ADJ
ejpam-6763	29	33	derivative	derivative	ADJ
ejpam-6763	29	34	functions	function	NOUN
ejpam-6763	29	35	[	[	X
ejpam-6763	29	36	8	8	NUM
ejpam-6763	29	37	]	]	PUNCT
ejpam-6763	29	38	.	.	PUNCT
ejpam-6763	30	1	some	some	DET
ejpam-6763	30	2	researchers	researcher	NOUN
ejpam-6763	30	3	have	have	AUX
ejpam-6763	30	4	presented	present	VERB
ejpam-6763	30	5	extremely	extremely	ADV
ejpam-6763	30	6	powerful	powerful	ADJ
ejpam-6763	30	7	methods	method	NOUN
ejpam-6763	30	8	to	to	PART
ejpam-6763	30	9	derive	derive	VERB
ejpam-6763	30	10	efficient	efficient	ADJ
ejpam-6763	30	11	and	and	CCONJ
ejpam-6763	30	12	viable	viable	ADJ
ejpam-6763	30	13	approximate	approximate	ADJ
ejpam-6763	30	14	solutions	solution	NOUN
ejpam-6763	30	15	of	of	ADP
ejpam-6763	30	16	these	these	DET
ejpam-6763	30	17	equations	equation	NOUN
ejpam-6763	30	18	.	.	PUNCT
ejpam-6763	31	1	yi	yi	PROPN
ejpam-6763	31	2	et	et	PROPN
ejpam-6763	31	3	al	al	PROPN
ejpam-6763	31	4	.	.	PROPN
ejpam-6763	31	5	presented	present	VERB
ejpam-6763	31	6	a	a	DET
ejpam-6763	31	7	graphical	graphical	ADJ
ejpam-6763	31	8	illustration	illustration	NOUN
ejpam-6763	31	9	of	of	ADP
ejpam-6763	31	10	the	the	DET
ejpam-6763	31	11	cas	cas	PROPN
ejpam-6763	31	12	wavelet	wavelet	PROPN
ejpam-6763	31	13	method	method	NOUN
ejpam-6763	31	14	for	for	ADP
ejpam-6763	31	15	solving	solve	VERB
ejpam-6763	31	16	fides	fide	NOUN
ejpam-6763	31	17	[	[	X
ejpam-6763	31	18	9	9	NUM
ejpam-6763	31	19	]	]	PUNCT
ejpam-6763	31	20	.	.	PUNCT
ejpam-6763	32	1	quantic	quantic	PROPN
ejpam-6763	32	2	b	b	PROPN
ejpam-6763	32	3	-	-	PUNCT
ejpam-6763	32	4	spline	spline	NOUN
ejpam-6763	32	5	techniques	technique	NOUN
ejpam-6763	32	6	were	be	AUX
ejpam-6763	32	7	proposed	propose	VERB
ejpam-6763	32	8	by	by	ADP
ejpam-6763	32	9	raslan	raslan	NOUN
ejpam-6763	32	10	et	et	PROPN
ejpam-6763	32	11	al	al	PROPN
ejpam-6763	32	12	.	.	PROPN
ejpam-6763	32	13	and	and	CCONJ
ejpam-6763	32	14	fazal	fazal	PROPN
ejpam-6763	32	15	et	et	PROPN
ejpam-6763	32	16	al	al	PROPN
ejpam-6763	32	17	.	.	PROPN
ejpam-6763	33	1	see	see	VERB
ejpam-6763	33	2	[	[	X
ejpam-6763	33	3	10	10	NUM
ejpam-6763	33	4	,	,	PUNCT
ejpam-6763	33	5	11	11	NUM
ejpam-6763	33	6	]	]	PUNCT
ejpam-6763	33	7	.	.	PUNCT
ejpam-6763	34	1	diar	diar	NOUN
ejpam-6763	34	2	et	et	PROPN
ejpam-6763	34	3	al	al	PROPN
ejpam-6763	34	4	.	.	PROPN
ejpam-6763	34	5	illustrated	illustrate	VERB
ejpam-6763	34	6	quadratic	quadratic	ADJ
ejpam-6763	34	7	and	and	CCONJ
ejpam-6763	34	8	linear	linear	ADJ
ejpam-6763	34	9	spline	spline	NOUN
ejpam-6763	34	10	functions	function	NOUN
ejpam-6763	34	11	,	,	PUNCT
ejpam-6763	34	12	see	see	VERB
ejpam-6763	34	13	[	[	X
ejpam-6763	34	14	7	7	NUM
ejpam-6763	34	15	,	,	PUNCT
ejpam-6763	34	16	12	12	NUM
ejpam-6763	34	17	]	]	PUNCT
ejpam-6763	34	18	.	.	PUNCT
ejpam-6763	35	1	while	while	SCONJ
ejpam-6763	35	2	mohammad	mohammad	PROPN
ejpam-6763	35	3	et	et	PROPN
ejpam-6763	35	4	al	al	PROPN
ejpam-6763	35	5	.	.	PROPN
ejpam-6763	35	6	demonstrated	demonstrate	VERB
ejpam-6763	35	7	the	the	DET
ejpam-6763	35	8	spline	spline	NOUN
ejpam-6763	35	9	collocation	collocation	NOUN
ejpam-6763	35	10	method	method	NOUN
ejpam-6763	35	11	[	[	X
ejpam-6763	35	12	13	13	NUM
ejpam-6763	35	13	]	]	PUNCT
ejpam-6763	35	14	.	.	PUNCT
ejpam-6763	36	1	abbas	abbas	PROPN
ejpam-6763	36	2	et	et	PROPN
ejpam-6763	36	3	al	al	PROPN
ejpam-6763	36	4	.	.	PROPN
ejpam-6763	36	5	introduced	introduce	VERB
ejpam-6763	36	6	an	an	DET
ejpam-6763	36	7	efficient	efficient	ADJ
ejpam-6763	36	8	spline	spline	NOUN
ejpam-6763	36	9	technique	technique	NOUN
ejpam-6763	36	10	for	for	ADP
ejpam-6763	36	11	solving	solve	VERB
ejpam-6763	36	12	time	time	NOUN
ejpam-6763	36	13	-	-	PUNCT
ejpam-6763	36	14	fractional	fractional	ADJ
ejpam-6763	36	15	problems	problem	NOUN
ejpam-6763	36	16	[	[	X
ejpam-6763	36	17	14	14	NUM
ejpam-6763	36	18	]	]	PUNCT
ejpam-6763	36	19	.	.	PUNCT
ejpam-6763	37	1	ghosh	ghosh	PROPN
ejpam-6763	37	2	et	et	PROPN
ejpam-6763	37	3	al	al	PROPN
ejpam-6763	37	4	.	.	PROPN
ejpam-6763	37	5	presented	present	VERB
ejpam-6763	37	6	an	an	DET
ejpam-6763	37	7	iterative	iterative	NOUN
ejpam-6763	37	8	difference	difference	NOUN
ejpam-6763	37	9	scheme	scheme	NOUN
ejpam-6763	37	10	[	[	X
ejpam-6763	37	11	15	15	NUM
ejpam-6763	37	12	]	]	PUNCT
ejpam-6763	37	13	.	.	PUNCT
ejpam-6763	38	1	masti	masti	PROPN
ejpam-6763	38	2	et	et	PROPN
ejpam-6763	38	3	al	al	PROPN
ejpam-6763	38	4	.	.	PROPN
ejpam-6763	38	5	worked	work	VERB
ejpam-6763	38	6	on	on	ADP
ejpam-6763	38	7	the	the	DET
ejpam-6763	38	8	collocationgalerkin	collocationgalerkin	NOUN
ejpam-6763	38	9	method	method	NOUN
ejpam-6763	39	1	[	[	X
ejpam-6763	39	2	16	16	NUM
ejpam-6763	39	3	]	]	PUNCT
ejpam-6763	39	4	.	.	PUNCT
ejpam-6763	40	1	khan	khan	PROPN
ejpam-6763	40	2	et	et	PROPN
ejpam-6763	40	3	al	al	PROPN
ejpam-6763	40	4	.	.	PROPN
ejpam-6763	40	5	applied	apply	VERB
ejpam-6763	40	6	the	the	DET
ejpam-6763	40	7	ladm	ladm	ADJ
ejpam-6763	40	8	procedure	procedure	NOUN
ejpam-6763	40	9	[	[	X
ejpam-6763	40	10	17	17	NUM
ejpam-6763	40	11	]	]	PUNCT
ejpam-6763	40	12	.	.	PUNCT
ejpam-6763	41	1	khader	khader	PROPN
ejpam-6763	41	2	et	et	PROPN
ejpam-6763	41	3	al	al	PROPN
ejpam-6763	41	4	.	.	PROPN
ejpam-6763	41	5	used	use	VERB
ejpam-6763	41	6	the	the	DET
ejpam-6763	41	7	chebyshev	chebyshev	NOUN
ejpam-6763	41	8	pseudo	pseudo	NOUN
ejpam-6763	41	9	-	-	ADJ
ejpam-6763	41	10	spectral	spectral	ADJ
ejpam-6763	41	11	method	method	NOUN
ejpam-6763	41	12	[	[	X
ejpam-6763	41	13	18	18	NUM
ejpam-6763	41	14	]	]	PUNCT
ejpam-6763	41	15	.	.	PUNCT
ejpam-6763	42	1	huang	huang	PROPN
ejpam-6763	42	2	et	et	PROPN
ejpam-6763	42	3	al	al	PROPN
ejpam-6763	42	4	.	.	PROPN
ejpam-6763	42	5	presented	present	VERB
ejpam-6763	42	6	the	the	DET
ejpam-6763	42	7	taylor	taylor	PROPN
ejpam-6763	42	8	expansion	expansion	NOUN
ejpam-6763	42	9	method	method	NOUN
ejpam-6763	42	10	[	[	X
ejpam-6763	42	11	19	19	NUM
ejpam-6763	42	12	]	]	PUNCT
ejpam-6763	42	13	.	.	PUNCT
ejpam-6763	43	1	yn	yn	INTJ
ejpam-6763	43	2	h	h	NOUN
ejpam-6763	43	3	et	et	PROPN
ejpam-6763	43	4	al	al	PROPN
ejpam-6763	43	5	.	.	PROPN
ejpam-6763	43	6	demonstrated	demonstrate	VERB
ejpam-6763	43	7	the	the	DET
ejpam-6763	43	8	taylor	taylor	PROPN
ejpam-6763	43	9	series	series	PROPN
ejpam-6763	43	10	method	method	NOUN
ejpam-6763	43	11	[	[	X
ejpam-6763	43	12	20	20	NUM
ejpam-6763	43	13	]	]	PUNCT
ejpam-6763	43	14	.	.	PUNCT
ejpam-6763	44	1	singh	singh	PROPN
ejpam-6763	44	2	et	et	PROPN
ejpam-6763	44	3	al	al	PROPN
ejpam-6763	44	4	.	.	PROPN
ejpam-6763	44	5	applied	apply	VERB
ejpam-6763	44	6	the	the	DET
ejpam-6763	44	7	adaptive	adaptive	ADJ
ejpam-6763	44	8	mesh	mesh	NOUN
ejpam-6763	44	9	method	method	NOUN
ejpam-6763	44	10	[	[	X
ejpam-6763	44	11	21	21	NUM
ejpam-6763	44	12	]	]	X
ejpam-6763	44	13	,	,	PUNCT
ejpam-6763	44	14	li	li	PROPN
ejpam-6763	44	15	et	et	PROPN
ejpam-6763	44	16	al	al	PROPN
ejpam-6763	44	17	.	.	PROPN
ejpam-6763	44	18	explored	explore	VERB
ejpam-6763	44	19	deep	deep	ADJ
ejpam-6763	44	20	learning	learning	NOUN
ejpam-6763	44	21	techniques	technique	NOUN
ejpam-6763	45	1	[	[	X
ejpam-6763	45	2	22	22	NUM
ejpam-6763	45	3	]	]	PUNCT
ejpam-6763	45	4	,	,	PUNCT
ejpam-6763	45	5	and	and	CCONJ
ejpam-6763	45	6	shazad	shazad	VERB
ejpam-6763	45	7	worked	work	VERB
ejpam-6763	45	8	on	on	ADP
ejpam-6763	45	9	the	the	DET
ejpam-6763	45	10	system	system	NOUN
ejpam-6763	45	11	of	of	ADP
ejpam-6763	45	12	linear	linear	PROPN
ejpam-6763	45	13	volterra	volterra	PROPN
ejpam-6763	45	14	integro	integro	PROPN
ejpam-6763	45	15	-	-	PUNCT
ejpam-6763	45	16	fractional	fractional	ADJ
ejpam-6763	45	17	differential	differential	ADJ
ejpam-6763	45	18	equations	equation	NOUN
ejpam-6763	45	19	[	[	X
ejpam-6763	45	20	23	23	NUM
ejpam-6763	45	21	]	]	PUNCT
ejpam-6763	45	22	.	.	PUNCT
ejpam-6763	46	1	in	in	ADP
ejpam-6763	46	2	this	this	DET
ejpam-6763	46	3	paper	paper	NOUN
ejpam-6763	46	4	,	,	PUNCT
ejpam-6763	46	5	our	our	PRON
ejpam-6763	46	6	focus	focus	NOUN
ejpam-6763	46	7	is	be	AUX
ejpam-6763	46	8	on	on	ADP
ejpam-6763	46	9	approximating	approximate	VERB
ejpam-6763	46	10	a	a	DET
ejpam-6763	46	11	(	(	PUNCT
ejpam-6763	46	12	svide’s	svide’s	NOUN
ejpam-6763	46	13	-	-	PUNCT
ejpam-6763	46	14	cf	cf	NOUN
ejpam-6763	46	15	)	)	PUNCT
ejpam-6763	46	16	using	use	VERB
ejpam-6763	46	17	a	a	DET
ejpam-6763	46	18	new	new	ADJ
ejpam-6763	46	19	extended	extended	ADJ
ejpam-6763	46	20	cubic	cubic	ADJ
ejpam-6763	46	21	b	b	NOUN
ejpam-6763	46	22	-	-	PUNCT
ejpam-6763	46	23	spline	spline	NOUN
ejpam-6763	46	24	based	base	VERB
ejpam-6763	46	25	collocation	collocation	NOUN
ejpam-6763	46	26	method	method	NOUN
ejpam-6763	46	27	.	.	PUNCT
ejpam-6763	47	1	the	the	DET
ejpam-6763	47	2	target	target	NOUN
ejpam-6763	47	3	(	(	PUNCT
ejpam-6763	47	4	svide’s	svide’s	NOUN
ejpam-6763	47	5	-	-	PUNCT
ejpam-6763	47	6	cf	cf	NOUN
ejpam-6763	47	7	)	)	PUNCT
ejpam-6763	47	8	with	with	ADP
ejpam-6763	47	9	the	the	DET
ejpam-6763	47	10	general	general	ADJ
ejpam-6763	47	11	forms	form	NOUN
ejpam-6763	47	12	defined	define	VERB
ejpam-6763	47	13	on	on	ADP
ejpam-6763	47	14	any	any	DET
ejpam-6763	47	15	closed	closed	ADJ
ejpam-6763	47	16	-	-	PUNCT
ejpam-6763	47	17	bounded	bound	VERB
ejpam-6763	47	18	interval	interval	NOUN
ejpam-6763	47	19	[	[	X
ejpam-6763	47	20	a	a	X
ejpam-6763	47	21	,	,	PUNCT
ejpam-6763	47	22	b	b	NOUN
ejpam-6763	47	23	]	]	PUNCT
ejpam-6763	47	24	is	be	AUX
ejpam-6763	47	25	described	describe	VERB
ejpam-6763	47	26	by	by	ADP
ejpam-6763	47	27	the	the	DET
ejpam-6763	47	28	equations	equation	NOUN
ejpam-6763	47	29	:	:	PUNCT
ejpam-6763	47	30	pi(x)y	pi(x)y	PROPN
ejpam-6763	47	31	′	′	NUM
ejpam-6763	47	32	i(x	i(x	NOUN
ejpam-6763	47	33	)	)	PUNCT
ejpam-6763	48	1	+	+	X
ejpam-6763	48	2	ai0(x	ai0(x	NOUN
ejpam-6763	48	3	)	)	PUNCT
ejpam-6763	48	4	c	c	NOUN
ejpam-6763	48	5	adσi0	adσi0	NOUN
ejpam-6763	48	6	x	x	X
ejpam-6763	48	7	yi(x	yi(x	NUM
ejpam-6763	48	8	)	)	PUNCT
ejpam-6763	49	1	+	+	CCONJ
ejpam-6763	49	2	ai1(x)yi(x	ai1(x)yi(x	NOUN
ejpam-6763	49	3	)	)	PUNCT
ejpam-6763	49	4	=	=	SYM
ejpam-6763	50	1	fi(x	fi(x	X
ejpam-6763	50	2	)	)	PUNCT
ejpam-6763	51	1	+	+	CCONJ
ejpam-6763	51	2	m∑	m∑	CCONJ
ejpam-6763	51	3	j=0	j=0	PROPN
ejpam-6763	51	4	ωij	ωij	PROPN
ejpam-6763	51	5	∫	∫	PROPN
ejpam-6763	51	6	x	x	X
ejpam-6763	51	7	a	a	DET
ejpam-6763	51	8	kij(x	kij(x	PROPN
ejpam-6763	51	9	,	,	PUNCT
ejpam-6763	51	10	s	s	PART
ejpam-6763	51	11	)	)	PUNCT
ejpam-6763	51	12	c	c	NOUN
ejpam-6763	51	13	ad	ad	NOUN
ejpam-6763	51	14	βij	βij	NOUN
ejpam-6763	51	15	s	s	PART
ejpam-6763	51	16	yj(s	yj(s	NOUN
ejpam-6763	51	17	)	)	PUNCT
ejpam-6763	51	18	ds	ds	NOUN
ejpam-6763	51	19	.	.	PUNCT
ejpam-6763	52	1	(	(	PUNCT
ejpam-6763	52	2	1	1	NUM
ejpam-6763	52	3	)	)	PUNCT
ejpam-6763	52	4	under	under	ADP
ejpam-6763	52	5	the	the	DET
ejpam-6763	52	6	following	following	ADJ
ejpam-6763	52	7	conditions	condition	NOUN
ejpam-6763	52	8	:	:	PUNCT
ejpam-6763	52	9	[	[	PUNCT
ejpam-6763	52	10	dki	dki	NOUN
ejpam-6763	52	11	x	x	SYM
ejpam-6763	52	12	yi(x	yi(x	PROPN
ejpam-6763	52	13	)	)	PUNCT
ejpam-6763	52	14	]	]	PUNCT
ejpam-6763	53	1	x	x	X
ejpam-6763	53	2	=	=	NOUN
ejpam-6763	53	3	a	a	X
ejpam-6763	53	4	=	=	X
ejpam-6763	53	5	ϑiki	ϑiki	ADJ
ejpam-6763	53	6	,	,	PUNCT
ejpam-6763	53	7	∀ki	∀ki	NOUN
ejpam-6763	53	8	=	=	SYM
ejpam-6763	53	9	0	0	NUM
ejpam-6763	53	10	,	,	PUNCT
ejpam-6763	53	11	1	1	NUM
ejpam-6763	53	12	,	,	PUNCT
ejpam-6763	53	13	.	.	PUNCT
ejpam-6763	53	14	.	.	PUNCT
ejpam-6763	53	15	.	.	PUNCT
ejpam-6763	54	1	,	,	PUNCT
ejpam-6763	54	2	µi	µi	ADP
ejpam-6763	54	3	−	−	PROPN
ejpam-6763	54	4	1	1	NUM
ejpam-6763	54	5	,	,	PUNCT
ejpam-6763	54	6	and	and	CCONJ
ejpam-6763	54	7	i	i	NOUN
ejpam-6763	54	8	=	=	NOUN
ejpam-6763	54	9	0	0	NUM
ejpam-6763	54	10	,	,	PUNCT
ejpam-6763	54	11	1	1	NUM
ejpam-6763	54	12	,	,	PUNCT
ejpam-6763	54	13	.	.	PUNCT
ejpam-6763	54	14	.	.	PUNCT
ejpam-6763	55	1	.	.	PUNCT
ejpam-6763	56	1	,	,	PUNCT
ejpam-6763	56	2	m.	m.	NOUN
ejpam-6763	56	3	(	(	PUNCT
ejpam-6763	56	4	2	2	X
ejpam-6763	56	5	)	)	PUNCT
ejpam-6763	56	6	the	the	DET
ejpam-6763	56	7	variable	variable	ADJ
ejpam-6763	56	8	coefficients	coefficient	VERB
ejpam-6763	56	9	pi(x)(6≡	pi(x)(6≡	PROPN
ejpam-6763	56	10	0	0	NUM
ejpam-6763	56	11	)	)	PUNCT
ejpam-6763	56	12	,	,	PUNCT
ejpam-6763	56	13	ai0(x	ai0(x	PROPN
ejpam-6763	56	14	)	)	PUNCT
ejpam-6763	56	15	and	and	CCONJ
ejpam-6763	56	16	ai1(x	ai1(x	NOUN
ejpam-6763	56	17	)	)	PUNCT
ejpam-6763	56	18	∈	∈	PROPN
ejpam-6763	56	19	c([a	c([a	PROPN
ejpam-6763	56	20	,	,	PUNCT
ejpam-6763	56	21	b],r	b],r	NOUN
ejpam-6763	56	22	)	)	PUNCT
ejpam-6763	56	23	and	and	CCONJ
ejpam-6763	56	24	kij	kij	PROPN
ejpam-6763	56	25	∈	∈	PROPN
ejpam-6763	56	26	c(θ	c(θ	PROPN
ejpam-6763	56	27	,	,	PUNCT
ejpam-6763	56	28	r),θ	r),θ	NOUN
ejpam-6763	56	29	=	=	SYM
ejpam-6763	56	30	{	{	PUNCT
ejpam-6763	56	31	(	(	PUNCT
ejpam-6763	56	32	x	x	NOUN
ejpam-6763	56	33	,	,	PUNCT
ejpam-6763	56	34	s	s	PART
ejpam-6763	56	35	)	)	PUNCT
ejpam-6763	56	36	:	:	PUNCT
ejpam-6763	56	37	a	a	DET
ejpam-6763	56	38	≤	≤	NUM
ejpam-6763	56	39	s	s	PART
ejpam-6763	56	40	<	<	X
ejpam-6763	56	41	x	x	PROPN
ejpam-6763	56	42	≤	≤	NUM
ejpam-6763	56	43	b	b	NOUN
ejpam-6763	56	44	}	}	PUNCT
ejpam-6763	56	45	,	,	PUNCT
ejpam-6763	56	46	for	for	ADP
ejpam-6763	56	47	each	each	DET
ejpam-6763	56	48	i	i	PROPN
ejpam-6763	56	49	,	,	PUNCT
ejpam-6763	56	50	j	j	PROPN
ejpam-6763	56	51	=	=	SYM
ejpam-6763	56	52	0	0	NUM
ejpam-6763	56	53	,	,	PUNCT
ejpam-6763	56	54	1	1	NUM
ejpam-6763	56	55	,	,	PUNCT
ejpam-6763	56	56	.	.	PUNCT
ejpam-6763	56	57	.	.	PUNCT
ejpam-6763	56	58	.	.	PUNCT
ejpam-6763	57	1	,	,	PUNCT
ejpam-6763	57	2	m	m	PROPN
ejpam-6763	57	3	,	,	PUNCT
ejpam-6763	57	4	with	with	ADP
ejpam-6763	57	5	fractional	fractional	ADJ
ejpam-6763	57	6	orders	order	NOUN
ejpam-6763	57	7	:	:	PUNCT
ejpam-6763	57	8	σi1	σi1	X
ejpam-6763	57	9	>	>	X
ejpam-6763	57	10	σi0	σi0	NOUN
ejpam-6763	57	11	>	>	X
ejpam-6763	57	12	0	0	PUNCT
ejpam-6763	57	13	and	and	CCONJ
ejpam-6763	57	14	βim	βim	NOUN
ejpam-6763	57	15	>	>	PUNCT
ejpam-6763	57	16	βi(m−1	βi(m−1	PROPN
ejpam-6763	57	17	)	)	PUNCT
ejpam-6763	57	18	>	>	X
ejpam-6763	57	19	·	·	PUNCT
ejpam-6763	58	1	·	·	PUNCT
ejpam-6763	58	2	·	·	PUNCT
ejpam-6763	58	3	>	>	PUNCT
ejpam-6763	58	4	βi1	βi1	PROPN
ejpam-6763	58	5	>	>	X
ejpam-6763	58	6	βi0	βi0	PUNCT
ejpam-6763	59	1	=	=	SYM
ejpam-6763	59	2	0	0	NUM
ejpam-6763	59	3	,	,	PUNCT
ejpam-6763	59	4	and	and	CCONJ
ejpam-6763	59	5	for	for	ADP
ejpam-6763	59	6	all	all	DET
ejpam-6763	59	7	i	i	PROPN
ejpam-6763	59	8	,	,	PUNCT
ejpam-6763	59	9	j	j	PROPN
ejpam-6763	59	10	=	=	SYM
ejpam-6763	59	11	0	0	NUM
ejpam-6763	59	12	,	,	PUNCT
ejpam-6763	59	13	1	1	NUM
ejpam-6763	59	14	,	,	PUNCT
ejpam-6763	59	15	.	.	PUNCT
ejpam-6763	59	16	.	.	PUNCT
ejpam-6763	60	1	.	.	PUNCT
ejpam-6763	61	1	,	,	PUNCT
ejpam-6763	61	2	m.	m.	NOUN
ejpam-6763	61	3	furthermore	furthermore	ADV
ejpam-6763	61	4	,	,	PUNCT
ejpam-6763	61	5	the	the	DET
ejpam-6763	61	6	µi	µi	PROPN
ejpam-6763	61	7	=	=	PUNCT
ejpam-6763	61	8	max	max	PROPN
ejpam-6763	61	9	{	{	PUNCT
ejpam-6763	61	10	1,mβ	1,mβ	NUM
ejpam-6763	62	1	i	i	PRON
ejpam-6763	62	2	m	m	VERB
ejpam-6763	62	3	}	}	PUNCT
ejpam-6763	62	4	for	for	ADP
ejpam-6763	62	5	all	all	PRON
ejpam-6763	62	6	i	i	PRON
ejpam-6763	62	7	=	=	NOUN
ejpam-6763	62	8	0	0	NUM
ejpam-6763	62	9	,	,	PUNCT
ejpam-6763	62	10	1	1	NUM
ejpam-6763	62	11	,	,	PUNCT
ejpam-6763	62	12	.	.	PUNCT
ejpam-6763	62	13	.	.	PUNCT
ejpam-6763	62	14	.	.	PUNCT
ejpam-6763	63	1	,	,	PUNCT
ejpam-6763	63	2	m	m	PROPN
ejpam-6763	63	3	,	,	PUNCT
ejpam-6763	63	4	where	where	SCONJ
ejpam-6763	63	5	mβ	mβ	AUX
ejpam-6763	63	6	ij−1	ij−1	VERB
ejpam-6763	63	7	<	<	X
ejpam-6763	63	8	βij	βij	NOUN
ejpam-6763	63	9	≤	≤	PUNCT
ejpam-6763	64	1	mβ	mβ	INTJ
ejpam-6763	64	2	ij	ij	INTJ
ejpam-6763	64	3	,	,	PUNCT
ejpam-6763	64	4	m	m	VERB
ejpam-6763	64	5	β	β	NOUN
ejpam-6763	64	6	ij	ij	NOUN
ejpam-6763	65	1	=	=	NOUN
ejpam-6763	65	2	dβije	dβije	NOUN
ejpam-6763	65	3	,	,	PUNCT
ejpam-6763	65	4	ωij	ωij	INTJ
ejpam-6763	65	5	∈	∈	PROPN
ejpam-6763	65	6	r	r	NOUN
ejpam-6763	65	7	also	also	ADV
ejpam-6763	65	8	for	for	ADP
ejpam-6763	65	9	all	all	DET
ejpam-6763	65	10	i	i	PROPN
ejpam-6763	65	11	,	,	PUNCT
ejpam-6763	65	12	j	j	PROPN
ejpam-6763	65	13	=	=	SYM
ejpam-6763	65	14	0	0	NUM
ejpam-6763	65	15	,	,	PUNCT
ejpam-6763	65	16	1	1	NUM
ejpam-6763	65	17	,	,	PUNCT
ejpam-6763	65	18	.	.	PUNCT
ejpam-6763	65	19	.	.	PUNCT
ejpam-6763	65	20	.	.	PUNCT
ejpam-6763	66	1	,	,	PUNCT
ejpam-6763	66	2	m.	m.	NOUN
ejpam-6763	66	3	in	in	ADP
ejpam-6763	66	4	this	this	DET
ejpam-6763	66	5	work	work	NOUN
ejpam-6763	66	6	,	,	PUNCT
ejpam-6763	66	7	we	we	PRON
ejpam-6763	66	8	examined	examine	VERB
ejpam-6763	66	9	and	and	CCONJ
ejpam-6763	66	10	assessed	assess	VERB
ejpam-6763	66	11	a	a	DET
ejpam-6763	66	12	system	system	NOUN
ejpam-6763	66	13	of	of	ADP
ejpam-6763	66	14	d.	d.	PROPN
ejpam-6763	66	15	kh	kh	PROPN
ejpam-6763	66	16	.	.	PUNCT
ejpam-6763	67	1	abdullah	abdullah	PROPN
ejpam-6763	67	2	,	,	PUNCT
ejpam-6763	67	3	sh	sh	PROPN
ejpam-6763	67	4	.	.	PROPN
ejpam-6763	67	5	sh	sh	PROPN
ejpam-6763	67	6	.	.	PROPN
ejpam-6763	67	7	ahmed	ahmed	PROPN
ejpam-6763	67	8	,	,	PUNCT
ejpam-6763	67	9	k.	k.	PROPN
ejpam-6763	67	10	h.	h.	PROPN
ejpam-6763	67	11	f.	f.	PROPN
ejpam-6763	67	12	jwamer	jwamer	PROPN
ejpam-6763	67	13	/	/	SYM
ejpam-6763	67	14	eur	eur	PROPN
ejpam-6763	67	15	.	.	PUNCT
ejpam-6763	68	1	j.	j.	PROPN
ejpam-6763	68	2	pure	pure	PROPN
ejpam-6763	68	3	appl	appl	PROPN
ejpam-6763	68	4	.	.	PROPN
ejpam-6763	68	5	math	math	PROPN
ejpam-6763	68	6	,	,	PUNCT
ejpam-6763	68	7	18	18	NUM
ejpam-6763	68	8	(	(	PUNCT
ejpam-6763	68	9	4	4	NUM
ejpam-6763	68	10	)	)	PUNCT
ejpam-6763	68	11	(	(	PUNCT
ejpam-6763	68	12	2025	2025	NUM
ejpam-6763	68	13	)	)	PUNCT
ejpam-6763	68	14	,	,	PUNCT
ejpam-6763	68	15	6763	6763	NUM
ejpam-6763	68	16	3	3	NUM
ejpam-6763	68	17	of	of	ADP
ejpam-6763	68	18	40	40	NUM
ejpam-6763	68	19	volterra	volterra	NOUN
ejpam-6763	68	20	integro	integro	PROPN
ejpam-6763	68	21	-	-	PUNCT
ejpam-6763	68	22	differential	differential	NOUN
ejpam-6763	68	23	equations	equation	NOUN
ejpam-6763	68	24	for	for	ADP
ejpam-6763	68	25	classical	classical	ADJ
ejpam-6763	68	26	and	and	CCONJ
ejpam-6763	68	27	fractional	fractional	ADJ
ejpam-6763	68	28	orders	order	NOUN
ejpam-6763	68	29	(	(	PUNCT
ejpam-6763	68	30	svide’s	svide’s	NOUN
ejpam-6763	68	31	-	-	PUNCT
ejpam-6763	68	32	cf	cf	NOUN
ejpam-6763	68	33	)	)	PUNCT
ejpam-6763	68	34	,	,	PUNCT
ejpam-6763	68	35	using	use	VERB
ejpam-6763	68	36	quadrature	quadrature	NOUN
ejpam-6763	68	37	techniques	technique	NOUN
ejpam-6763	68	38	in	in	ADP
ejpam-6763	68	39	conjunction	conjunction	NOUN
ejpam-6763	68	40	with	with	ADP
ejpam-6763	68	41	cubic	cubic	ADJ
ejpam-6763	68	42	b	b	PROPN
ejpam-6763	68	43	-	-	PUNCT
ejpam-6763	68	44	spline	spline	NOUN
ejpam-6763	68	45	functions	function	NOUN
ejpam-6763	68	46	.	.	PUNCT
ejpam-6763	69	1	the	the	DET
ejpam-6763	69	2	information	information	NOUN
ejpam-6763	69	3	was	be	AUX
ejpam-6763	69	4	summarized	summarize	VERB
ejpam-6763	69	5	by	by	ADP
ejpam-6763	69	6	an	an	DET
ejpam-6763	69	7	algorithm	algorithm	NOUN
ejpam-6763	69	8	,	,	PUNCT
ejpam-6763	69	9	and	and	CCONJ
ejpam-6763	69	10	we	we	PRON
ejpam-6763	69	11	later	later	ADV
ejpam-6763	69	12	produced	produce	VERB
ejpam-6763	69	13	python	python	NOUN
ejpam-6763	69	14	software	software	NOUN
ejpam-6763	69	15	to	to	PART
ejpam-6763	69	16	implement	implement	VERB
ejpam-6763	69	17	the	the	DET
ejpam-6763	69	18	method	method	NOUN
ejpam-6763	69	19	and	and	CCONJ
ejpam-6763	69	20	a	a	DET
ejpam-6763	69	21	few	few	ADJ
ejpam-6763	69	22	test	test	NOUN
ejpam-6763	69	23	instances	instance	NOUN
ejpam-6763	69	24	that	that	PRON
ejpam-6763	69	25	were	be	AUX
ejpam-6763	69	26	resolved	resolve	VERB
ejpam-6763	69	27	with	with	ADP
ejpam-6763	69	28	the	the	DET
ejpam-6763	69	29	help	help	NOUN
ejpam-6763	69	30	of	of	ADP
ejpam-6763	69	31	these	these	DET
ejpam-6763	69	32	algorithms	algorithm	NOUN
ejpam-6763	69	33	.	.	PUNCT
ejpam-6763	70	1	this	this	DET
ejpam-6763	70	2	paper	paper	NOUN
ejpam-6763	70	3	is	be	AUX
ejpam-6763	70	4	structured	structure	VERB
ejpam-6763	70	5	in	in	ADP
ejpam-6763	70	6	the	the	DET
ejpam-6763	70	7	following	following	ADJ
ejpam-6763	70	8	manner	manner	NOUN
ejpam-6763	70	9	:	:	PUNCT
ejpam-6763	70	10	section	section	NOUN
ejpam-6763	70	11	2	2	NUM
ejpam-6763	70	12	presents	present	VERB
ejpam-6763	70	13	background	background	NOUN
ejpam-6763	70	14	information	information	NOUN
ejpam-6763	70	15	on	on	ADP
ejpam-6763	70	16	fractional	fractional	ADJ
ejpam-6763	70	17	calculus	calculus	NOUN
ejpam-6763	70	18	and	and	CCONJ
ejpam-6763	70	19	highlights	highlight	NOUN
ejpam-6763	70	20	its	its	PRON
ejpam-6763	70	21	key	key	ADJ
ejpam-6763	70	22	features	feature	NOUN
ejpam-6763	70	23	.	.	PUNCT
ejpam-6763	71	1	section	section	NOUN
ejpam-6763	71	2	3	3	NUM
ejpam-6763	71	3	discusses	discuss	VERB
ejpam-6763	71	4	the	the	DET
ejpam-6763	71	5	materials	material	NOUN
ejpam-6763	71	6	used	use	VERB
ejpam-6763	71	7	and	and	CCONJ
ejpam-6763	71	8	introduces	introduce	VERB
ejpam-6763	71	9	cubic	cubic	ADJ
ejpam-6763	71	10	b	b	PROPN
ejpam-6763	71	11	-	-	PUNCT
ejpam-6763	71	12	spline	spline	NOUN
ejpam-6763	71	13	functions	function	NOUN
ejpam-6763	71	14	along	along	ADP
ejpam-6763	71	15	with	with	ADP
ejpam-6763	71	16	new	new	ADJ
ejpam-6763	71	17	lemmas	lemma	NOUN
ejpam-6763	71	18	.	.	PUNCT
ejpam-6763	72	1	section	section	NOUN
ejpam-6763	72	2	4	4	NUM
ejpam-6763	72	3	explores	explore	VERB
ejpam-6763	72	4	the	the	DET
ejpam-6763	72	5	derivation	derivation	NOUN
ejpam-6763	72	6	of	of	ADP
ejpam-6763	72	7	the	the	DET
ejpam-6763	72	8	proposed	propose	VERB
ejpam-6763	72	9	method	method	NOUN
ejpam-6763	72	10	.	.	PUNCT
ejpam-6763	73	1	section	section	NOUN
ejpam-6763	73	2	5	5	NUM
ejpam-6763	73	3	provides	provide	VERB
ejpam-6763	73	4	the	the	DET
ejpam-6763	73	5	algorithms	algorithm	NOUN
ejpam-6763	73	6	.	.	PUNCT
ejpam-6763	74	1	section	section	NOUN
ejpam-6763	74	2	6	6	NUM
ejpam-6763	74	3	compares	compare	VERB
ejpam-6763	74	4	the	the	DET
ejpam-6763	74	5	numerical	numerical	ADJ
ejpam-6763	74	6	results	result	NOUN
ejpam-6763	74	7	with	with	ADP
ejpam-6763	74	8	those	those	PRON
ejpam-6763	74	9	from	from	ADP
ejpam-6763	74	10	existing	exist	VERB
ejpam-6763	74	11	methods	method	NOUN
ejpam-6763	74	12	.	.	PUNCT
ejpam-6763	75	1	finally	finally	ADV
ejpam-6763	75	2	,	,	PUNCT
ejpam-6763	75	3	section	section	NOUN
ejpam-6763	75	4	7	7	NUM
ejpam-6763	75	5	offers	offer	VERB
ejpam-6763	75	6	a	a	DET
ejpam-6763	75	7	concise	concise	ADJ
ejpam-6763	75	8	summary	summary	NOUN
ejpam-6763	75	9	of	of	ADP
ejpam-6763	75	10	the	the	DET
ejpam-6763	75	11	study	study	NOUN
ejpam-6763	75	12	’s	’s	PART
ejpam-6763	75	13	findings	finding	NOUN
ejpam-6763	75	14	.	.	PUNCT
ejpam-6763	76	1	2	2	X
ejpam-6763	76	2	.	.	X
ejpam-6763	76	3	basic	basic	ADJ
ejpam-6763	76	4	definitions	definition	NOUN
ejpam-6763	76	5	of	of	ADP
ejpam-6763	76	6	fractional	fractional	ADJ
ejpam-6763	76	7	derivatives	derivative	NOUN
ejpam-6763	76	8	this	this	DET
ejpam-6763	76	9	section	section	NOUN
ejpam-6763	76	10	discusses	discuss	VERB
ejpam-6763	76	11	fractional	fractional	ADJ
ejpam-6763	76	12	calculus	calculus	NOUN
ejpam-6763	76	13	and	and	CCONJ
ejpam-6763	76	14	its	its	PRON
ejpam-6763	76	15	properties	property	NOUN
ejpam-6763	76	16	and	and	CCONJ
ejpam-6763	76	17	defines	define	VERB
ejpam-6763	76	18	the	the	DET
ejpam-6763	76	19	numerical	numerical	ADJ
ejpam-6763	76	20	integration	integration	NOUN
ejpam-6763	76	21	as	as	ADP
ejpam-6763	76	22	the	the	DET
ejpam-6763	76	23	clenshaw	clenshaw	ADJ
ejpam-6763	76	24	-	-	PUNCT
ejpam-6763	76	25	curtis	curtis	NOUN
ejpam-6763	76	26	quadrature	quadrature	NOUN
ejpam-6763	76	27	rule	rule	NOUN
ejpam-6763	76	28	:	:	PUNCT
ejpam-6763	76	29	definition	definition	NOUN
ejpam-6763	76	30	1	1	NUM
ejpam-6763	76	31	.	.	PUNCT
ejpam-6763	77	1	(	(	PUNCT
ejpam-6763	77	2	[	[	X
ejpam-6763	77	3	3	3	NUM
ejpam-6763	77	4	]	]	PUNCT
ejpam-6763	77	5	,	,	PUNCT
ejpam-6763	77	6	[	[	X
ejpam-6763	77	7	24	24	NUM
ejpam-6763	77	8	]	]	PUNCT
ejpam-6763	77	9	)	)	PUNCT
ejpam-6763	77	10	.	.	PUNCT
ejpam-6763	78	1	the	the	DET
ejpam-6763	78	2	fractional	fractional	PROPN
ejpam-6763	78	3	operators	operators	PROPN
ejpam-6763	78	4	aj	aj	PROPN
ejpam-6763	78	5	α	α	PROPN
ejpam-6763	78	6	x	x	X
ejpam-6763	78	7	and	and	CCONJ
ejpam-6763	78	8	r	r	X
ejpam-6763	78	9	a	a	DET
ejpam-6763	78	10	dα	dα	ADJ
ejpam-6763	78	11	x	x	PUNCT
ejpam-6763	78	12	of	of	ADP
ejpam-6763	78	13	order	order	NOUN
ejpam-6763	78	14	α	α	NOUN
ejpam-6763	78	15	for	for	ADP
ejpam-6763	78	16	a	a	DET
ejpam-6763	78	17	function	function	NOUN
ejpam-6763	78	18	y(x	y(x	NOUN
ejpam-6763	78	19	)	)	PUNCT
ejpam-6763	78	20	are	be	AUX
ejpam-6763	78	21	called	call	VERB
ejpam-6763	78	22	the	the	DET
ejpam-6763	78	23	riemann	riemann	PROPN
ejpam-6763	78	24	-	-	PUNCT
ejpam-6763	78	25	liouville	liouville	VERB
ejpam-6763	78	26	fractional	fractional	ADJ
ejpam-6763	78	27	integral	integral	ADJ
ejpam-6763	78	28	and	and	CCONJ
ejpam-6763	78	29	differential	differential	ADJ
ejpam-6763	78	30	operators	operator	NOUN
ejpam-6763	78	31	,	,	PUNCT
ejpam-6763	78	32	respectively	respectively	ADV
ejpam-6763	78	33	,	,	PUNCT
ejpam-6763	78	34	for	for	ADP
ejpam-6763	78	35	all	all	DET
ejpam-6763	78	36	n−	n−	NOUN
ejpam-6763	78	37	1	1	NUM
ejpam-6763	78	38	<	<	X
ejpam-6763	78	39	α	α	PROPN
ejpam-6763	78	40	≤	≤	PUNCT
ejpam-6763	79	1	n	n	CCONJ
ejpam-6763	79	2	(	(	PUNCT
ejpam-6763	79	3	n	n	CCONJ
ejpam-6763	79	4	∈	∈	PROPN
ejpam-6763	79	5	z+	z+	NUM
ejpam-6763	79	6	,	,	PUNCT
ejpam-6763	79	7	α	α	PROPN
ejpam-6763	79	8	∈	∈	PROPN
ejpam-6763	79	9	r+	r+	NOUN
ejpam-6763	79	10	)	)	PUNCT
ejpam-6763	79	11	.	.	PUNCT
ejpam-6763	80	1	aj	aj	PROPN
ejpam-6763	80	2	α	α	PROPN
ejpam-6763	80	3	x	x	PROPN
ejpam-6763	80	4	y(x	y(x	PROPN
ejpam-6763	80	5	)	)	PUNCT
ejpam-6763	80	6	=	=	SYM
ejpam-6763	80	7	1	1	NUM
ejpam-6763	80	8	γ(α	γ(α	NOUN
ejpam-6763	80	9	)	)	PUNCT
ejpam-6763	80	10	∫	∫	PROPN
ejpam-6763	80	11	x	x	X
ejpam-6763	80	12	a	a	DET
ejpam-6763	80	13	y(s	y(s	PROPN
ejpam-6763	80	14	)	)	PUNCT
ejpam-6763	80	15	(	(	PUNCT
ejpam-6763	80	16	x−	x−	PROPN
ejpam-6763	80	17	s)1−α	s)1−α	PROPN
ejpam-6763	80	18	ds	ds	PROPN
ejpam-6763	80	19	;	;	PUNCT
ejpam-6763	80	20	aj	aj	PROPN
ejpam-6763	80	21	0	0	NUM
ejpam-6763	80	22	xy(x	xy(x	NUM
ejpam-6763	80	23	)	)	PUNCT
ejpam-6763	80	24	=	=	SYM
ejpam-6763	80	25	y(x	y(x	PROPN
ejpam-6763	80	26	)	)	PUNCT
ejpam-6763	80	27	,	,	PUNCT
ejpam-6763	80	28	x	x	X
ejpam-6763	80	29	>	>	X
ejpam-6763	80	30	a	a	DET
ejpam-6763	80	31	(	(	PUNCT
ejpam-6763	80	32	3	3	NUM
ejpam-6763	80	33	)	)	PUNCT
ejpam-6763	80	34	r	r	NOUN
ejpam-6763	80	35	a	a	DET
ejpam-6763	80	36	dα	dα	NOUN
ejpam-6763	80	37	xy(x	xy(x	NOUN
ejpam-6763	80	38	)	)	PUNCT
ejpam-6763	81	1	=	=	SYM
ejpam-6763	81	2	dn	dn	PROPN
ejpam-6763	81	3	dxn	dxn	PROPN
ejpam-6763	81	4	(	(	PUNCT
ejpam-6763	81	5	aj	aj	PROPN
ejpam-6763	81	6	n−α	n−α	PROPN
ejpam-6763	81	7	x	x	SYM
ejpam-6763	81	8	y(x	y(x	PROPN
ejpam-6763	81	9	)	)	PUNCT
ejpam-6763	81	10	)	)	PUNCT
ejpam-6763	82	1	=	=	SYM
ejpam-6763	82	2	1	1	NUM
ejpam-6763	82	3	γ(n−	γ(n−	PROPN
ejpam-6763	82	4	α	α	NOUN
ejpam-6763	82	5	)	)	PUNCT
ejpam-6763	82	6	dn	dn	NOUN
ejpam-6763	82	7	dxn	dxn	PROPN
ejpam-6763	82	8	∫	∫	PROPN
ejpam-6763	82	9	x	x	X
ejpam-6763	82	10	a	a	DET
ejpam-6763	82	11	y(s	y(s	PROPN
ejpam-6763	82	12	)	)	PUNCT
ejpam-6763	82	13	(	(	PUNCT
ejpam-6763	82	14	x−	x−	PROPN
ejpam-6763	82	15	s)α+1−n	s)α+1−n	PROPN
ejpam-6763	82	16	ds	ds	PROPN
ejpam-6763	82	17	,	,	PUNCT
ejpam-6763	82	18	x	x	X
ejpam-6763	82	19	>	>	X
ejpam-6763	82	20	a	a	DET
ejpam-6763	82	21	(	(	PUNCT
ejpam-6763	82	22	4	4	NUM
ejpam-6763	82	23	)	)	PUNCT
ejpam-6763	82	24	definition	definition	NOUN
ejpam-6763	82	25	2	2	NUM
ejpam-6763	82	26	.	.	PUNCT
ejpam-6763	83	1	(	(	PUNCT
ejpam-6763	83	2	[	[	X
ejpam-6763	83	3	3	3	NUM
ejpam-6763	83	4	]	]	PUNCT
ejpam-6763	83	5	,	,	PUNCT
ejpam-6763	83	6	[	[	X
ejpam-6763	83	7	24	24	NUM
ejpam-6763	83	8	]	]	PUNCT
ejpam-6763	83	9	)	)	PUNCT
ejpam-6763	83	10	.	.	PUNCT
ejpam-6763	84	1	the	the	DET
ejpam-6763	84	2	fractional	fractional	ADJ
ejpam-6763	84	3	operator	operator	NOUN
ejpam-6763	84	4	c	c	PROPN
ejpam-6763	84	5	adα	adα	NOUN
ejpam-6763	84	6	x	x	X
ejpam-6763	84	7	of	of	ADP
ejpam-6763	84	8	order	order	NOUN
ejpam-6763	84	9	α	α	NOUN
ejpam-6763	84	10	for	for	ADP
ejpam-6763	84	11	a	a	DET
ejpam-6763	84	12	function	function	NOUN
ejpam-6763	84	13	y(x	y(x	NOUN
ejpam-6763	84	14	)	)	PUNCT
ejpam-6763	84	15	is	be	AUX
ejpam-6763	84	16	called	call	VERB
ejpam-6763	84	17	the	the	DET
ejpam-6763	84	18	caputo	caputo	PROPN
ejpam-6763	84	19	fractional	fractional	PROPN
ejpam-6763	84	20	differential	differential	NOUN
ejpam-6763	84	21	operator	operator	NOUN
ejpam-6763	84	22	,	,	PUNCT
ejpam-6763	84	23	for	for	ADP
ejpam-6763	84	24	all	all	DET
ejpam-6763	84	25	n−1	n−1	PROPN
ejpam-6763	84	26	<	<	X
ejpam-6763	84	27	α	α	PROPN
ejpam-6763	84	28	≤	≤	PUNCT
ejpam-6763	84	29	n	n	CCONJ
ejpam-6763	84	30	(	(	PUNCT
ejpam-6763	84	31	n	n	CCONJ
ejpam-6763	84	32	∈	∈	PROPN
ejpam-6763	84	33	z+	z+	NUM
ejpam-6763	84	34	,	,	PUNCT
ejpam-6763	84	35	α	α	PROPN
ejpam-6763	84	36	∈	∈	PROPN
ejpam-6763	84	37	r+	r+	PRON
ejpam-6763	84	38	)	)	PUNCT
ejpam-6763	84	39	,	,	PUNCT
ejpam-6763	84	40	and	and	CCONJ
ejpam-6763	84	41	is	be	AUX
ejpam-6763	84	42	defined	define	VERB
ejpam-6763	84	43	as	as	ADP
ejpam-6763	84	44	:	:	PUNCT
ejpam-6763	84	45	c	c	PROPN
ejpam-6763	84	46	adα	adα	PROPN
ejpam-6763	84	47	xy(x	xy(x	PUNCT
ejpam-6763	84	48	)	)	PUNCT
ejpam-6763	85	1	=	=	SYM
ejpam-6763	85	2	aj	aj	ADJ
ejpam-6763	85	3	n−α	n−α	NUM
ejpam-6763	85	4	x	x	INTJ
ejpam-6763	85	5	(	(	PUNCT
ejpam-6763	85	6	dn	dn	INTJ
ejpam-6763	85	7	dxn	dxn	PROPN
ejpam-6763	85	8	y(x	y(x	NOUN
ejpam-6763	85	9	)	)	PUNCT
ejpam-6763	85	10	)	)	PUNCT
ejpam-6763	86	1	=	=	SYM
ejpam-6763	86	2	1	1	NUM
ejpam-6763	86	3	γ(n−	γ(n−	PROPN
ejpam-6763	86	4	α	α	NOUN
ejpam-6763	86	5	)	)	PUNCT
ejpam-6763	86	6	∫	∫	PROPN
ejpam-6763	86	7	x	x	X
ejpam-6763	86	8	a	a	DET
ejpam-6763	86	9	y(n)(s	y(n)(s	NUM
ejpam-6763	86	10	)	)	PUNCT
ejpam-6763	86	11	(	(	PUNCT
ejpam-6763	86	12	x−	x−	PROPN
ejpam-6763	86	13	s)α+1−n	s)α+1−n	PROPN
ejpam-6763	86	14	ds	ds	PROPN
ejpam-6763	86	15	,	,	PUNCT
ejpam-6763	86	16	x	x	X
ejpam-6763	86	17	>	>	X
ejpam-6763	86	18	a	a	DET
ejpam-6763	86	19	(	(	PUNCT
ejpam-6763	86	20	5	5	NUM
ejpam-6763	86	21	)	)	PUNCT
ejpam-6763	86	22	the	the	DET
ejpam-6763	86	23	following	follow	VERB
ejpam-6763	86	24	are	be	AUX
ejpam-6763	86	25	some	some	DET
ejpam-6763	86	26	interesting	interesting	ADJ
ejpam-6763	86	27	properties	property	NOUN
ejpam-6763	86	28	of	of	ADP
ejpam-6763	86	29	the	the	DET
ejpam-6763	86	30	operator	operator	NOUN
ejpam-6763	86	31	c	c	PROPN
ejpam-6763	86	32	adα	adα	NOUN
ejpam-6763	86	33	x	x	X
ejpam-6763	86	34	:	:	PUNCT
ejpam-6763	86	35	•	•	NOUN
ejpam-6763	86	36	for	for	ADP
ejpam-6763	86	37	n	n	NOUN
ejpam-6763	86	38	=	=	SYM
ejpam-6763	86	39	α	α	NOUN
ejpam-6763	86	40	,	,	PUNCT
ejpam-6763	86	41	we	we	PRON
ejpam-6763	86	42	have	have	VERB
ejpam-6763	86	43	c	c	PROPN
ejpam-6763	86	44	adα	adα	PROPN
ejpam-6763	86	45	xy(x	xy(x	PUNCT
ejpam-6763	86	46	)	)	PUNCT
ejpam-6763	87	1	=	=	SYM
ejpam-6763	87	2	dn	dn	PROPN
ejpam-6763	87	3	dxn	dxn	PROPN
ejpam-6763	87	4	y(x	y(x	NOUN
ejpam-6763	87	5	)	)	PUNCT
ejpam-6763	87	6	.	.	PUNCT
ejpam-6763	88	1	•	•	NUM
ejpam-6763	88	2	the	the	DET
ejpam-6763	88	3	operator	operator	NOUN
ejpam-6763	88	4	c	c	NOUN
ejpam-6763	88	5	ad	ad	NOUN
ejpam-6763	88	6	α	α	NOUN
ejpam-6763	88	7	x	x	VERB
ejpam-6763	88	8	is	be	AUX
ejpam-6763	88	9	linear	linear	ADJ
ejpam-6763	88	10	,	,	PUNCT
ejpam-6763	88	11	i.e.	i.e.	X
ejpam-6763	88	12	,	,	PUNCT
ejpam-6763	88	13	for	for	ADP
ejpam-6763	88	14	any	any	DET
ejpam-6763	88	15	ϕ1	ϕ1	NOUN
ejpam-6763	88	16	,	,	PUNCT
ejpam-6763	88	17	ϕ2	ϕ2	ADV
ejpam-6763	88	18	∈	∈	PROPN
ejpam-6763	88	19	r	r	NOUN
ejpam-6763	88	20	,	,	PUNCT
ejpam-6763	88	21	c	c	PROPN
ejpam-6763	88	22	adα	adα	NOUN
ejpam-6763	88	23	x	x	PUNCT
ejpam-6763	89	1	[	[	X
ejpam-6763	89	2	ϕ1y1(x)±	ϕ1y1(x)±	PROPN
ejpam-6763	89	3	ϕ2y2(x	ϕ2y2(x	PROPN
ejpam-6763	89	4	)	)	PUNCT
ejpam-6763	89	5	]	]	PUNCT
ejpam-6763	90	1	=	=	PUNCT
ejpam-6763	90	2	ϕ1	ϕ1	PROPN
ejpam-6763	90	3	c	c	PROPN
ejpam-6763	90	4	adα	adα	PROPN
ejpam-6763	90	5	t	t	PROPN
ejpam-6763	90	6	y1(x)±	y1(x)±	PROPN
ejpam-6763	90	7	ϕ2	ϕ2	ADV
ejpam-6763	90	8	c	c	PROPN
ejpam-6763	90	9	adα	adα	PROPN
ejpam-6763	90	10	xy2(x	xy2(x	PROPN
ejpam-6763	90	11	)	)	PUNCT
ejpam-6763	90	12	.	.	PUNCT
ejpam-6763	91	1	•	•	NOUN
ejpam-6763	91	2	for	for	ADP
ejpam-6763	91	3	any	any	DET
ejpam-6763	91	4	constant	constant	ADJ
ejpam-6763	91	5	ϕ	ϕ	PROPN
ejpam-6763	91	6	∈	∈	PROPN
ejpam-6763	91	7	r	r	PROPN
ejpam-6763	91	8	,	,	PUNCT
ejpam-6763	91	9	c	c	PROPN
ejpam-6763	91	10	adα	adα	PROPN
ejpam-6763	91	11	xϕ	xϕ	PUNCT
ejpam-6763	92	1	=	=	SYM
ejpam-6763	92	2	0	0	PROPN
ejpam-6763	92	3	.	.	PUNCT
ejpam-6763	93	1	d.	d.	PROPN
ejpam-6763	93	2	kh	kh	PROPN
ejpam-6763	93	3	.	.	PUNCT
ejpam-6763	94	1	abdullah	abdullah	PROPN
ejpam-6763	94	2	,	,	PUNCT
ejpam-6763	94	3	sh	sh	PROPN
ejpam-6763	94	4	.	.	PROPN
ejpam-6763	94	5	sh	sh	PROPN
ejpam-6763	94	6	.	.	PROPN
ejpam-6763	94	7	ahmed	ahmed	PROPN
ejpam-6763	94	8	,	,	PUNCT
ejpam-6763	94	9	k.	k.	PROPN
ejpam-6763	94	10	h.	h.	PROPN
ejpam-6763	94	11	f.	f.	PROPN
ejpam-6763	94	12	jwamer	jwamer	PROPN
ejpam-6763	94	13	/	/	SYM
ejpam-6763	94	14	eur	eur	PROPN
ejpam-6763	94	15	.	.	PUNCT
ejpam-6763	95	1	j.	j.	PROPN
ejpam-6763	95	2	pure	pure	PROPN
ejpam-6763	95	3	appl	appl	PROPN
ejpam-6763	95	4	.	.	PROPN
ejpam-6763	95	5	math	math	PROPN
ejpam-6763	95	6	,	,	PUNCT
ejpam-6763	95	7	18	18	NUM
ejpam-6763	95	8	(	(	PUNCT
ejpam-6763	95	9	4	4	NUM
ejpam-6763	95	10	)	)	PUNCT
ejpam-6763	95	11	(	(	PUNCT
ejpam-6763	95	12	2025	2025	NUM
ejpam-6763	95	13	)	)	PUNCT
ejpam-6763	95	14	,	,	PUNCT
ejpam-6763	95	15	6763	6763	NUM
ejpam-6763	95	16	4	4	NUM
ejpam-6763	95	17	of	of	ADP
ejpam-6763	95	18	40	40	NUM
ejpam-6763	95	19	•	•	NOUN
ejpam-6763	95	20	if	if	SCONJ
ejpam-6763	95	21	y(x	y(x	NOUN
ejpam-6763	95	22	)	)	PUNCT
ejpam-6763	95	23	=	=	SYM
ejpam-6763	95	24	(	(	PUNCT
ejpam-6763	95	25	x−	x−	PROPN
ejpam-6763	95	26	a)p	a)p	PROPN
ejpam-6763	95	27	,	,	PUNCT
ejpam-6763	95	28	then	then	ADV
ejpam-6763	95	29	:	:	PUNCT
ejpam-6763	95	30	c	c	PROPN
ejpam-6763	95	31	adα	adα	PROPN
ejpam-6763	95	32	x	x	SYM
ejpam-6763	95	33	(	(	PUNCT
ejpam-6763	95	34	x−	x−	PROPN
ejpam-6763	95	35	a)p	a)p	X
ejpam-6763	95	36	=	=	PUNCT
ejpam-6763	95	37			PUNCT
ejpam-6763	95	38	γ(p+	γ(p+	PROPN
ejpam-6763	95	39	1	1	NUM
ejpam-6763	95	40	)	)	PUNCT
ejpam-6763	95	41	γ(p−	γ(p−	X
ejpam-6763	95	42	α+	α+	X
ejpam-6763	95	43	1	1	NUM
ejpam-6763	95	44	)	)	PUNCT
ejpam-6763	95	45	(	(	PUNCT
ejpam-6763	95	46	x−	x−	PROPN
ejpam-6763	95	47	a)p−α	a)p−α	PROPN
ejpam-6763	95	48	,	,	PUNCT
ejpam-6763	95	49	if	if	SCONJ
ejpam-6763	95	50	p	p	PROPN
ejpam-6763	95	51	∈	∈	PROPN
ejpam-6763	95	52	n	n	CCONJ
ejpam-6763	95	53	,	,	PUNCT
ejpam-6763	95	54	p	p	PRON
ejpam-6763	95	55	≥	≥	NOUN
ejpam-6763	95	56	dαe	dαe	NOUN
ejpam-6763	95	57	or	or	CCONJ
ejpam-6763	95	58	p	p	NOUN
ejpam-6763	95	59	/∈	/∈	PROPN
ejpam-6763	95	60	n	n	CCONJ
ejpam-6763	95	61	,	,	PUNCT
ejpam-6763	95	62	p	p	X
ejpam-6763	95	63	>	>	X
ejpam-6763	95	64	dαe	dαe	NOUN
ejpam-6763	95	65	−	−	NOUN
ejpam-6763	95	66	1	1	NUM
ejpam-6763	95	67	0	0	NUM
ejpam-6763	95	68	,	,	PUNCT
ejpam-6763	95	69	if	if	SCONJ
ejpam-6763	95	70	p	p	X
ejpam-6763	95	71	∈	∈	PROPN
ejpam-6763	95	72	{	{	PUNCT
ejpam-6763	95	73	0	0	NUM
ejpam-6763	95	74	,	,	PUNCT
ejpam-6763	95	75	1	1	NUM
ejpam-6763	95	76	,	,	PUNCT
ejpam-6763	95	77	2	2	NUM
ejpam-6763	95	78	,	,	PUNCT
ejpam-6763	95	79	.	.	PUNCT
ejpam-6763	95	80	.	.	PUNCT
ejpam-6763	95	81	.	.	PUNCT
ejpam-6763	96	1	,	,	PUNCT
ejpam-6763	96	2	dαe	dαe	VERB
ejpam-6763	96	3	−	−	NUM
ejpam-6763	96	4	1	1	NUM
ejpam-6763	96	5	}	}	PUNCT
ejpam-6763	96	6	definition	definition	NOUN
ejpam-6763	96	7	3	3	NUM
ejpam-6763	96	8	.	.	PUNCT
ejpam-6763	97	1	(	(	PUNCT
ejpam-6763	97	2	[	[	X
ejpam-6763	97	3	12	12	NUM
ejpam-6763	97	4	]	]	PUNCT
ejpam-6763	97	5	,	,	PUNCT
ejpam-6763	97	6	[	[	X
ejpam-6763	97	7	25	25	NUM
ejpam-6763	97	8	]	]	PUNCT
ejpam-6763	97	9	,	,	PUNCT
ejpam-6763	98	1	[	[	X
ejpam-6763	98	2	26	26	NUM
ejpam-6763	98	3	]	]	PUNCT
ejpam-6763	98	4	)	)	PUNCT
ejpam-6763	98	5	.	.	PUNCT
ejpam-6763	99	1	clenshaw	clenshaw	ADJ
ejpam-6763	99	2	and	and	CCONJ
ejpam-6763	99	3	curtis	curtis	PROPN
ejpam-6763	99	4	established	establish	VERB
ejpam-6763	99	5	a	a	DET
ejpam-6763	99	6	method	method	NOUN
ejpam-6763	99	7	for	for	ADP
ejpam-6763	99	8	approximating	approximate	VERB
ejpam-6763	99	9	a	a	DET
ejpam-6763	99	10	definite	definite	ADJ
ejpam-6763	99	11	integral	integral	ADJ
ejpam-6763	99	12	by	by	ADP
ejpam-6763	99	13	expressing	express	VERB
ejpam-6763	99	14	the	the	DET
ejpam-6763	99	15	integrand	integrand	NOUN
ejpam-6763	99	16	as	as	ADP
ejpam-6763	99	17	a	a	DET
ejpam-6763	99	18	finite	finite	ADJ
ejpam-6763	99	19	chebyshev	chebyshev	PROPN
ejpam-6763	99	20	series	series	NOUN
ejpam-6763	99	21	.	.	PUNCT
ejpam-6763	100	1	this	this	DET
ejpam-6763	100	2	approach	approach	NOUN
ejpam-6763	100	3	is	be	AUX
ejpam-6763	100	4	especially	especially	ADV
ejpam-6763	100	5	effective	effective	ADJ
ejpam-6763	100	6	when	when	SCONJ
ejpam-6763	100	7	applied	apply	VERB
ejpam-6763	100	8	to	to	ADP
ejpam-6763	100	9	integral	integral	ADJ
ejpam-6763	100	10	equations	equation	NOUN
ejpam-6763	100	11	.	.	PUNCT
ejpam-6763	101	1	∫	∫	PROPN
ejpam-6763	101	2	1	1	NUM
ejpam-6763	101	3	−1	−1	NOUN
ejpam-6763	101	4	y(x	y(x	NOUN
ejpam-6763	101	5	)	)	PUNCT
ejpam-6763	101	6	dx	dx	PROPN
ejpam-6763	101	7	≈	≈	PROPN
ejpam-6763	101	8	n∑	n∑	PROPN
ejpam-6763	101	9	r=0	r=0	PROPN
ejpam-6763	101	10	,	,	PUNCT
ejpam-6763	101	11	even	even	ADV
ejpam-6763	101	12	′′	′′	PROPN
ejpam-6763	101	13	(	(	PUNCT
ejpam-6763	101	14	2	2	NUM
ejpam-6763	101	15	n	n	NUM
ejpam-6763	101	16	n∑	n∑	PROPN
ejpam-6763	101	17	k=0	k=0	PROPN
ejpam-6763	101	18	cos	cos	PROPN
ejpam-6763	101	19	(	(	PUNCT
ejpam-6763	101	20	rkπ	rkπ	PROPN
ejpam-6763	101	21	n	n	X
ejpam-6763	101	22	)	)	PUNCT
ejpam-6763	101	23	y	y	PROPN
ejpam-6763	101	24	(	(	PUNCT
ejpam-6763	101	25	cos	cos	PROPN
ejpam-6763	101	26	(	(	PUNCT
ejpam-6763	101	27	kπ	kπ	PROPN
ejpam-6763	101	28	n	n	PROPN
ejpam-6763	101	29	)	)	PUNCT
ejpam-6763	101	30	)	)	PUNCT
ejpam-6763	101	31	)	)	PUNCT
ejpam-6763	101	32	,	,	PUNCT
ejpam-6763	101	33	k	k	X
ejpam-6763	102	1	=	=	SYM
ejpam-6763	102	2	0	0	NUM
ejpam-6763	102	3	,	,	PUNCT
ejpam-6763	102	4	1	1	NUM
ejpam-6763	102	5	,	,	PUNCT
ejpam-6763	102	6	.	.	PUNCT
ejpam-6763	102	7	.	.	PUNCT
ejpam-6763	103	1	.	.	PUNCT
ejpam-6763	104	1	,	,	PUNCT
ejpam-6763	104	2	n	n	X
ejpam-6763	104	3	.	.	PUNCT
ejpam-6763	105	1	(	(	PUNCT
ejpam-6763	105	2	6	6	X
ejpam-6763	105	3	)	)	PUNCT
ejpam-6763	105	4	remark	remark	NOUN
ejpam-6763	105	5	2.1	2.1	NUM
ejpam-6763	105	6	(	(	PUNCT
ejpam-6763	105	7	[	[	X
ejpam-6763	105	8	26	26	NUM
ejpam-6763	105	9	]	]	NUM
ejpam-6763	105	10	)	)	PUNCT
ejpam-6763	105	11	.	.	PUNCT
ejpam-6763	106	1	the	the	DET
ejpam-6763	106	2	following	follow	VERB
ejpam-6763	106	3	observations	observation	NOUN
ejpam-6763	106	4	can	can	AUX
ejpam-6763	106	5	be	be	AUX
ejpam-6763	106	6	made	make	VERB
ejpam-6763	106	7	:	:	PUNCT
ejpam-6763	106	8	•	•	ADP
ejpam-6763	106	9	the	the	DET
ejpam-6763	106	10	notation	notation	NOUN
ejpam-6763	106	11	∑′′	∑′′	ADJ
ejpam-6763	106	12	indicates	indicate	VERB
ejpam-6763	106	13	that	that	SCONJ
ejpam-6763	106	14	the	the	DET
ejpam-6763	106	15	first	first	ADJ
ejpam-6763	106	16	and	and	CCONJ
ejpam-6763	106	17	last	last	ADJ
ejpam-6763	106	18	terms	term	NOUN
ejpam-6763	106	19	in	in	ADP
ejpam-6763	106	20	the	the	DET
ejpam-6763	106	21	summation	summation	NOUN
ejpam-6763	106	22	are	be	AUX
ejpam-6763	106	23	to	to	PART
ejpam-6763	106	24	be	be	AUX
ejpam-6763	106	25	halved	halve	VERB
ejpam-6763	106	26	.	.	PUNCT
ejpam-6763	107	1	•	•	NUM
ejpam-6763	107	2	the	the	DET
ejpam-6763	107	3	transformation	transformation	NOUN
ejpam-6763	107	4	x	x	PUNCT
ejpam-6763	107	5	=	=	PUNCT
ejpam-6763	107	6	b−	b−	PROPN
ejpam-6763	107	7	a	a	DET
ejpam-6763	107	8	2	2	NUM
ejpam-6763	107	9	t+	t+	NOUN
ejpam-6763	107	10	b+	b+	ADJ
ejpam-6763	107	11	a	a	DET
ejpam-6763	107	12	2	2	NUM
ejpam-6763	107	13	maps	map	NOUN
ejpam-6763	107	14	x	x	X
ejpam-6763	107	15	∈	∈	PROPN
ejpam-6763	108	1	[	[	X
ejpam-6763	108	2	−1	−1	NOUN
ejpam-6763	108	3	,	,	PUNCT
ejpam-6763	108	4	1	1	NUM
ejpam-6763	108	5	]	]	PUNCT
ejpam-6763	108	6	to	to	ADP
ejpam-6763	108	7	t	t	PROPN
ejpam-6763	108	8	∈	∈	PROPN
ejpam-6763	108	9	[	[	X
ejpam-6763	108	10	a	a	X
ejpam-6763	108	11	,	,	PUNCT
ejpam-6763	108	12	b	b	NOUN
ejpam-6763	108	13	]	]	X
ejpam-6763	108	14	.	.	PUNCT
ejpam-6763	109	1	3	3	X
ejpam-6763	109	2	.	.	X
ejpam-6763	109	3	materials	material	NOUN
ejpam-6763	109	4	and	and	CCONJ
ejpam-6763	109	5	cubic	cubic	ADJ
ejpam-6763	109	6	b	b	PROPN
ejpam-6763	109	7	-	-	PUNCT
ejpam-6763	109	8	spline	spline	NOUN
ejpam-6763	109	9	function	function	NOUN
ejpam-6763	109	10	in	in	ADP
ejpam-6763	109	11	this	this	DET
ejpam-6763	109	12	section	section	NOUN
ejpam-6763	109	13	,	,	PUNCT
ejpam-6763	109	14	we	we	PRON
ejpam-6763	109	15	will	will	AUX
ejpam-6763	109	16	define	define	VERB
ejpam-6763	109	17	the	the	DET
ejpam-6763	109	18	cubic	cubic	ADJ
ejpam-6763	109	19	b	b	PROPN
ejpam-6763	109	20	-	-	PUNCT
ejpam-6763	109	21	spline	spline	NOUN
ejpam-6763	109	22	function	function	NOUN
ejpam-6763	109	23	,	,	PUNCT
ejpam-6763	109	24	the	the	DET
ejpam-6763	109	25	b	b	NOUN
ejpam-6763	109	26	-	-	PUNCT
ejpam-6763	109	27	spline	spline	NOUN
ejpam-6763	109	28	curve	curve	NOUN
ejpam-6763	109	29	and	and	CCONJ
ejpam-6763	109	30	knot	knot	ADJ
ejpam-6763	109	31	vectors	vector	NOUN
ejpam-6763	109	32	,	,	PUNCT
ejpam-6763	109	33	starting	start	VERB
ejpam-6763	109	34	with	with	ADP
ejpam-6763	109	35	the	the	DET
ejpam-6763	109	36	definition	definition	NOUN
ejpam-6763	109	37	of	of	ADP
ejpam-6763	109	38	a	a	DET
ejpam-6763	109	39	b	b	NOUN
ejpam-6763	109	40	-	-	PUNCT
ejpam-6763	109	41	spline	spline	NOUN
ejpam-6763	109	42	of	of	ADP
ejpam-6763	109	43	degree	degree	NOUN
ejpam-6763	109	44	k.	k.	PROPN
ejpam-6763	109	45	definition	definition	NOUN
ejpam-6763	109	46	4	4	NUM
ejpam-6763	109	47	.	.	PUNCT
ejpam-6763	110	1	(	(	PUNCT
ejpam-6763	110	2	[	[	X
ejpam-6763	110	3	27	27	NUM
ejpam-6763	110	4	]	]	PUNCT
ejpam-6763	110	5	,	,	PUNCT
ejpam-6763	110	6	[	[	X
ejpam-6763	110	7	28	28	NUM
ejpam-6763	110	8	]	]	PUNCT
ejpam-6763	110	9	)	)	PUNCT
ejpam-6763	110	10	.	.	PUNCT
ejpam-6763	111	1	let	let	VERB
ejpam-6763	111	2	tn	tn	NOUN
ejpam-6763	111	3	=	=	SYM
ejpam-6763	111	4	{	{	PUNCT
ejpam-6763	111	5	x0	x0	PROPN
ejpam-6763	111	6	,	,	PUNCT
ejpam-6763	111	7	x1	x1	PROPN
ejpam-6763	111	8	,	,	PUNCT
ejpam-6763	111	9	.	.	PUNCT
ejpam-6763	111	10	.	.	PUNCT
ejpam-6763	112	1	.	.	PUNCT
ejpam-6763	113	1	,	,	PUNCT
ejpam-6763	113	2	xn	xn	X
ejpam-6763	113	3	}	}	PUNCT
ejpam-6763	113	4	be	be	VERB
ejpam-6763	113	5	a	a	DET
ejpam-6763	113	6	uniform	uniform	ADJ
ejpam-6763	113	7	or	or	CCONJ
ejpam-6763	113	8	non	non	ADJ
ejpam-6763	113	9	-	-	ADJ
ejpam-6763	113	10	uniform	uniform	ADJ
ejpam-6763	113	11	partition	partition	NOUN
ejpam-6763	113	12	of	of	ADP
ejpam-6763	113	13	the	the	DET
ejpam-6763	113	14	interval	interval	NOUN
ejpam-6763	113	15	[	[	X
ejpam-6763	113	16	a	a	X
ejpam-6763	113	17	,	,	PUNCT
ejpam-6763	113	18	b	b	NOUN
ejpam-6763	113	19	]	]	X
ejpam-6763	113	20	.	.	PUNCT
ejpam-6763	114	1	the	the	DET
ejpam-6763	114	2	k	k	NOUN
ejpam-6763	114	3	-	-	PUNCT
ejpam-6763	114	4	degree	degree	NOUN
ejpam-6763	114	5	b	b	NOUN
ejpam-6763	114	6	-	-	PUNCT
ejpam-6763	114	7	spline	spline	NOUN
ejpam-6763	114	8	basis	basis	NOUN
ejpam-6763	114	9	function	function	NOUN
ejpam-6763	114	10	bk	bk	ADP
ejpam-6763	114	11	r	r	NOUN
ejpam-6763	114	12	(	(	PUNCT
ejpam-6763	114	13	x	x	NOUN
ejpam-6763	114	14	)	)	PUNCT
ejpam-6763	114	15	,	,	PUNCT
ejpam-6763	114	16	for	for	ADP
ejpam-6763	114	17	r	r	PROPN
ejpam-6763	114	18	≥	≥	NOUN
ejpam-6763	114	19	0	0	NUM
ejpam-6763	114	20	,	,	PUNCT
ejpam-6763	114	21	is	be	AUX
ejpam-6763	114	22	defined	define	VERB
ejpam-6763	114	23	recursively	recursively	ADV
ejpam-6763	114	24	as	as	ADP
ejpam-6763	114	25	:	:	PUNCT
ejpam-6763	114	26	bk	bk	INTJ
ejpam-6763	114	27	r	r	NOUN
ejpam-6763	114	28	(	(	PUNCT
ejpam-6763	114	29	x	x	NOUN
ejpam-6763	114	30	)	)	PUNCT
ejpam-6763	114	31	=	=	SYM
ejpam-6763	114	32	x−	x−	PROPN
ejpam-6763	114	33	xr	xr	PROPN
ejpam-6763	114	34	xr+k	xr+k	PROPN
ejpam-6763	115	1	−	−	PROPN
ejpam-6763	115	2	xr	xr	PROPN
ejpam-6763	116	1	bk−1	bk−1	ADJ
ejpam-6763	116	2	r	r	NOUN
ejpam-6763	116	3	(	(	PUNCT
ejpam-6763	116	4	x	x	NOUN
ejpam-6763	116	5	)	)	PUNCT
ejpam-6763	116	6	+	+	NUM
ejpam-6763	116	7	xr+k+1	xr+k+1	NUM
ejpam-6763	117	1	−	−	NOUN
ejpam-6763	117	2	x	x	SYM
ejpam-6763	117	3	xr+k+1	xr+k+1	NUM
ejpam-6763	117	4	−	−	PROPN
ejpam-6763	118	1	xr+1	xr+1	PROPN
ejpam-6763	119	1	bk−1	bk−1	VERB
ejpam-6763	119	2	r+1	r+1	PROPN
ejpam-6763	119	3	(	(	PUNCT
ejpam-6763	119	4	x	x	X
ejpam-6763	119	5	)	)	PUNCT
ejpam-6763	119	6	(	(	PUNCT
ejpam-6763	119	7	7	7	X
ejpam-6763	119	8	)	)	PUNCT
ejpam-6763	119	9	remark	remark	NOUN
ejpam-6763	119	10	1	1	NUM
ejpam-6763	119	11	(	(	PUNCT
ejpam-6763	119	12	[	[	X
ejpam-6763	119	13	29	29	NUM
ejpam-6763	119	14	]	]	NUM
ejpam-6763	119	15	)	)	PUNCT
ejpam-6763	119	16	.	.	PUNCT
ejpam-6763	120	1	we	we	PRON
ejpam-6763	120	2	note	note	VERB
ejpam-6763	120	3	the	the	DET
ejpam-6763	120	4	following	follow	VERB
ejpam-6763	120	5	facts	fact	NOUN
ejpam-6763	120	6	about	about	ADP
ejpam-6763	120	7	the	the	DET
ejpam-6763	120	8	b	b	NOUN
ejpam-6763	120	9	-	-	PUNCT
ejpam-6763	120	10	spline	spline	NOUN
ejpam-6763	120	11	basis	basis	NOUN
ejpam-6763	120	12	functions	function	NOUN
ejpam-6763	120	13	:	:	PUNCT
ejpam-6763	120	14	•	•	NUM
ejpam-6763	120	15	local	local	ADJ
ejpam-6763	120	16	support	support	NOUN
ejpam-6763	120	17	:	:	PUNCT
ejpam-6763	120	18	bk	bk	PRON
ejpam-6763	120	19	r	r	NOUN
ejpam-6763	120	20	(	(	PUNCT
ejpam-6763	120	21	x	x	NOUN
ejpam-6763	120	22	)	)	PUNCT
ejpam-6763	120	23	=	=	SYM
ejpam-6763	120	24	0	0	NUM
ejpam-6763	120	25	for	for	ADP
ejpam-6763	120	26	all	all	PRON
ejpam-6763	120	27	x	x	NOUN
ejpam-6763	120	28	/∈	/∈	PUNCT
ejpam-6763	121	1	[	[	X
ejpam-6763	121	2	xr	xr	X
ejpam-6763	121	3	,	,	PUNCT
ejpam-6763	121	4	xr+k+1	xr+k+1	NUM
ejpam-6763	121	5	)	)	PUNCT
ejpam-6763	121	6	.	.	PUNCT
ejpam-6763	122	1	•	•	NUM
ejpam-6763	122	2	nonnegativity	nonnegativity	NOUN
ejpam-6763	122	3	:	:	PUNCT
ejpam-6763	122	4	bk	bk	INTJ
ejpam-6763	122	5	r	r	NOUN
ejpam-6763	122	6	(	(	PUNCT
ejpam-6763	122	7	x	x	NOUN
ejpam-6763	122	8	)	)	PUNCT
ejpam-6763	122	9	>	>	X
ejpam-6763	122	10	0	0	PUNCT
ejpam-6763	122	11	for	for	ADP
ejpam-6763	122	12	all	all	DET
ejpam-6763	122	13	x	x	SYM
ejpam-6763	122	14	∈	∈	PROPN
ejpam-6763	122	15	[	[	X
ejpam-6763	122	16	xr	xr	NOUN
ejpam-6763	122	17	,	,	PUNCT
ejpam-6763	122	18	xr+k+1	xr+k+1	NUM
ejpam-6763	122	19	)	)	PUNCT
ejpam-6763	122	20	.	.	PUNCT
ejpam-6763	123	1	remark	remark	NOUN
ejpam-6763	123	2	2	2	NUM
ejpam-6763	123	3	(	(	PUNCT
ejpam-6763	123	4	[	[	X
ejpam-6763	123	5	27	27	NUM
ejpam-6763	123	6	]	]	PUNCT
ejpam-6763	123	7	,	,	PUNCT
ejpam-6763	123	8	[	[	X
ejpam-6763	123	9	30	30	NUM
ejpam-6763	123	10	]	]	PUNCT
ejpam-6763	123	11	)	)	PUNCT
ejpam-6763	123	12	.	.	PUNCT
ejpam-6763	124	1	in	in	ADP
ejpam-6763	124	2	the	the	DET
ejpam-6763	124	3	context	context	NOUN
ejpam-6763	124	4	of	of	ADP
ejpam-6763	124	5	b	b	NOUN
ejpam-6763	124	6	-	-	PUNCT
ejpam-6763	124	7	spline	spline	NOUN
ejpam-6763	124	8	curves	curve	NOUN
ejpam-6763	124	9	,	,	PUNCT
ejpam-6763	124	10	the	the	DET
ejpam-6763	124	11	knot	knot	NOUN
ejpam-6763	124	12	vector	vector	NOUN
ejpam-6763	124	13	t	t	NOUN
ejpam-6763	124	14	=	=	PUNCT
ejpam-6763	124	15	{	{	PUNCT
ejpam-6763	124	16	x0	x0	PROPN
ejpam-6763	124	17	,	,	PUNCT
ejpam-6763	124	18	x1	x1	PROPN
ejpam-6763	124	19	,	,	PUNCT
ejpam-6763	124	20	x2	x2	PROPN
ejpam-6763	124	21	,	,	PUNCT
ejpam-6763	124	22	.	.	PUNCT
ejpam-6763	124	23	.	.	PUNCT
ejpam-6763	124	24	.	.	PUNCT
ejpam-6763	125	1	,	,	PUNCT
ejpam-6763	125	2	xm	xm	PROPN
ejpam-6763	125	3	}	}	PUNCT
ejpam-6763	125	4	plays	play	VERB
ejpam-6763	125	5	a	a	DET
ejpam-6763	125	6	crucial	crucial	ADJ
ejpam-6763	125	7	role	role	NOUN
ejpam-6763	125	8	in	in	ADP
ejpam-6763	125	9	determining	determine	VERB
ejpam-6763	125	10	the	the	DET
ejpam-6763	125	11	shape	shape	NOUN
ejpam-6763	125	12	of	of	ADP
ejpam-6763	125	13	the	the	DET
ejpam-6763	125	14	curve	curve	NOUN
ejpam-6763	125	15	.	.	PUNCT
ejpam-6763	126	1	d.	d.	PROPN
ejpam-6763	126	2	kh	kh	PROPN
ejpam-6763	126	3	.	.	PUNCT
ejpam-6763	127	1	abdullah	abdullah	PROPN
ejpam-6763	127	2	,	,	PUNCT
ejpam-6763	127	3	sh	sh	PROPN
ejpam-6763	127	4	.	.	PROPN
ejpam-6763	127	5	sh	sh	PROPN
ejpam-6763	127	6	.	.	PROPN
ejpam-6763	127	7	ahmed	ahmed	PROPN
ejpam-6763	127	8	,	,	PUNCT
ejpam-6763	127	9	k.	k.	PROPN
ejpam-6763	127	10	h.	h.	PROPN
ejpam-6763	127	11	f.	f.	PROPN
ejpam-6763	127	12	jwamer	jwamer	PROPN
ejpam-6763	127	13	/	/	SYM
ejpam-6763	127	14	eur	eur	PROPN
ejpam-6763	127	15	.	.	PUNCT
ejpam-6763	128	1	j.	j.	PROPN
ejpam-6763	128	2	pure	pure	PROPN
ejpam-6763	128	3	appl	appl	PROPN
ejpam-6763	128	4	.	.	PROPN
ejpam-6763	128	5	math	math	PROPN
ejpam-6763	128	6	,	,	PUNCT
ejpam-6763	128	7	18	18	NUM
ejpam-6763	128	8	(	(	PUNCT
ejpam-6763	128	9	4	4	NUM
ejpam-6763	128	10	)	)	PUNCT
ejpam-6763	128	11	(	(	PUNCT
ejpam-6763	128	12	2025	2025	NUM
ejpam-6763	128	13	)	)	PUNCT
ejpam-6763	128	14	,	,	PUNCT
ejpam-6763	128	15	6763	6763	NUM
ejpam-6763	128	16	5	5	NUM
ejpam-6763	128	17	of	of	ADP
ejpam-6763	128	18	40	40	NUM
ejpam-6763	128	19	definition	definition	NOUN
ejpam-6763	128	20	5	5	NUM
ejpam-6763	128	21	.	.	PUNCT
ejpam-6763	129	1	(	(	PUNCT
ejpam-6763	129	2	[	[	X
ejpam-6763	129	3	27	27	NUM
ejpam-6763	129	4	]	]	PUNCT
ejpam-6763	129	5	,	,	PUNCT
ejpam-6763	129	6	[	[	X
ejpam-6763	129	7	30	30	NUM
ejpam-6763	129	8	]	]	NUM
ejpam-6763	129	9	)	)	PUNCT
ejpam-6763	129	10	.	.	PUNCT
ejpam-6763	130	1	an	an	DET
ejpam-6763	130	2	open	open	ADJ
ejpam-6763	130	3	uniform	uniform	ADJ
ejpam-6763	130	4	knot	knot	NOUN
ejpam-6763	130	5	vector	vector	NOUN
ejpam-6763	130	6	is	be	AUX
ejpam-6763	130	7	a	a	DET
ejpam-6763	130	8	knot	knot	ADJ
ejpam-6763	130	9	vector	vector	NOUN
ejpam-6763	130	10	that	that	PRON
ejpam-6763	130	11	contains	contain	VERB
ejpam-6763	130	12	k	k	PROPN
ejpam-6763	130	13	equal	equal	ADJ
ejpam-6763	130	14	knot	knot	NOUN
ejpam-6763	130	15	values	value	NOUN
ejpam-6763	130	16	at	at	ADP
ejpam-6763	130	17	each	each	DET
ejpam-6763	130	18	end	end	NOUN
ejpam-6763	130	19	.	.	PUNCT
ejpam-6763	131	1	the	the	DET
ejpam-6763	131	2	parametric	parametric	ADJ
ejpam-6763	131	3	knot	knot	NOUN
ejpam-6763	131	4	values	value	VERB
ejpam-6763	131	5	xr	xr	PROPN
ejpam-6763	131	6	for	for	ADP
ejpam-6763	131	7	an	an	DET
ejpam-6763	131	8	open	open	ADJ
ejpam-6763	131	9	curve	curve	NOUN
ejpam-6763	131	10	are	be	AUX
ejpam-6763	131	11	given	give	VERB
ejpam-6763	131	12	by	by	ADP
ejpam-6763	131	13	:	:	PUNCT
ejpam-6763	131	14	xr	xr	PROPN
ejpam-6763	131	15	=	=	SYM
ejpam-6763	131	16			PROPN
ejpam-6763	131	17	0	0	NUM
ejpam-6763	131	18	,	,	PUNCT
ejpam-6763	131	19	r	r	NOUN
ejpam-6763	131	20	<	<	X
ejpam-6763	131	21	k	k	X
ejpam-6763	132	1	+	+	CCONJ
ejpam-6763	132	2	1	1	NUM
ejpam-6763	132	3	r	r	NOUN
ejpam-6763	132	4	−	−	PROPN
ejpam-6763	132	5	k	k	NOUN
ejpam-6763	132	6	,	,	PUNCT
ejpam-6763	132	7	k	k	PROPN
ejpam-6763	132	8	+	+	CCONJ
ejpam-6763	132	9	1	1	NUM
ejpam-6763	132	10	≤	≤	NUM
ejpam-6763	132	11	r	r	NOUN
ejpam-6763	132	12	≤	≤	NOUN
ejpam-6763	132	13	n	n	NUM
ejpam-6763	132	14	n−	n−	NOUN
ejpam-6763	132	15	k	k	NOUN
ejpam-6763	133	1	+	+	CCONJ
ejpam-6763	133	2	1	1	NUM
ejpam-6763	133	3	,	,	PUNCT
ejpam-6763	133	4	r	r	NOUN
ejpam-6763	133	5	>	>	X
ejpam-6763	133	6	n	n	PROPN
ejpam-6763	133	7	(	(	PUNCT
ejpam-6763	133	8	8)	8)	NUM
ejpam-6763	133	9	where	where	SCONJ
ejpam-6763	133	10	0	0	NUM
ejpam-6763	133	11	≤	≤	NUM
ejpam-6763	133	12	r	r	NOUN
ejpam-6763	133	13	≤	≤	NUM
ejpam-6763	133	14	n+	n+	PUNCT
ejpam-6763	134	1	k	k	X
ejpam-6763	135	1	+	+	CCONJ
ejpam-6763	135	2	1	1	NUM
ejpam-6763	135	3	,	,	PUNCT
ejpam-6763	135	4	and	and	CCONJ
ejpam-6763	135	5	the	the	DET
ejpam-6763	135	6	parameter	parameter	NOUN
ejpam-6763	135	7	x	x	PROPN
ejpam-6763	135	8	lies	lie	VERB
ejpam-6763	135	9	in	in	ADP
ejpam-6763	135	10	the	the	DET
ejpam-6763	135	11	range	range	NOUN
ejpam-6763	135	12	0	0	NUM
ejpam-6763	135	13	≤	≤	NUM
ejpam-6763	135	14	x	x	SYM
ejpam-6763	136	1	≤	≤	NUM
ejpam-6763	136	2	n−	n−	NOUN
ejpam-6763	136	3	k	k	PROPN
ejpam-6763	137	1	+	+	CCONJ
ejpam-6763	137	2	1	1	X
ejpam-6763	137	3	.	.	X
ejpam-6763	137	4	definition	definition	NOUN
ejpam-6763	137	5	6	6	NUM
ejpam-6763	137	6	.	.	PUNCT
ejpam-6763	138	1	(	(	PUNCT
ejpam-6763	138	2	[	[	X
ejpam-6763	138	3	27	27	NUM
ejpam-6763	138	4	]	]	NUM
ejpam-6763	138	5	)	)	PUNCT
ejpam-6763	138	6	.	.	PUNCT
ejpam-6763	139	1	a	a	DET
ejpam-6763	139	2	b	b	X
ejpam-6763	139	3	-	-	PUNCT
ejpam-6763	139	4	spline	spline	NOUN
ejpam-6763	139	5	curve	curve	NOUN
ejpam-6763	139	6	is	be	AUX
ejpam-6763	139	7	a	a	DET
ejpam-6763	139	8	piecewise	piecewise	NOUN
ejpam-6763	139	9	-	-	PUNCT
ejpam-6763	139	10	defined	define	VERB
ejpam-6763	139	11	polynomial	polynomial	ADJ
ejpam-6763	139	12	curve	curve	NOUN
ejpam-6763	139	13	.	.	PUNCT
ejpam-6763	140	1	mathematically	mathematically	ADV
ejpam-6763	140	2	,	,	PUNCT
ejpam-6763	140	3	a	a	DET
ejpam-6763	140	4	b	b	X
ejpam-6763	140	5	-	-	PUNCT
ejpam-6763	140	6	spline	spline	NOUN
ejpam-6763	140	7	curve	curve	NOUN
ejpam-6763	140	8	b(k	b(k	PROPN
ejpam-6763	140	9	,	,	PUNCT
ejpam-6763	140	10	n)(x	n)(x	PROPN
ejpam-6763	140	11	)	)	PUNCT
ejpam-6763	140	12	of	of	ADP
ejpam-6763	140	13	degree	degree	NOUN
ejpam-6763	140	14	k	k	PROPN
ejpam-6763	140	15	,	,	PUNCT
ejpam-6763	140	16	with	with	ADP
ejpam-6763	140	17	control	control	NOUN
ejpam-6763	140	18	points	point	NOUN
ejpam-6763	140	19	{	{	PUNCT
ejpam-6763	140	20	ϑ0	ϑ0	NOUN
ejpam-6763	140	21	,	,	PUNCT
ejpam-6763	140	22	ϑ1	ϑ1	PROPN
ejpam-6763	140	23	,	,	PUNCT
ejpam-6763	140	24	.	.	PUNCT
ejpam-6763	140	25	.	.	PUNCT
ejpam-6763	140	26	.	.	PUNCT
ejpam-6763	141	1	,	,	PUNCT
ejpam-6763	141	2	ϑn	ϑn	NOUN
ejpam-6763	141	3	}	}	PUNCT
ejpam-6763	141	4	and	and	CCONJ
ejpam-6763	141	5	a	a	DET
ejpam-6763	141	6	non	non	ADJ
ejpam-6763	141	7	-	-	ADJ
ejpam-6763	141	8	decreasing	decrease	VERB
ejpam-6763	141	9	knot	knot	NOUN
ejpam-6763	141	10	vector	vector	NOUN
ejpam-6763	141	11	t	t	NOUN
ejpam-6763	141	12	=	=	PUNCT
ejpam-6763	141	13	{	{	PUNCT
ejpam-6763	141	14	x0	x0	PROPN
ejpam-6763	141	15	,	,	PUNCT
ejpam-6763	141	16	x1	x1	PROPN
ejpam-6763	141	17	,	,	PUNCT
ejpam-6763	141	18	x2	x2	PROPN
ejpam-6763	141	19	,	,	PUNCT
ejpam-6763	141	20	.	.	PUNCT
ejpam-6763	141	21	.	.	PUNCT
ejpam-6763	142	1	.	.	PUNCT
ejpam-6763	143	1	,	,	PUNCT
ejpam-6763	143	2	xm	xm	PROPN
ejpam-6763	143	3	}	}	PUNCT
ejpam-6763	143	4	,	,	PUNCT
ejpam-6763	143	5	is	be	AUX
ejpam-6763	143	6	defined	define	VERB
ejpam-6763	143	7	as	as	ADP
ejpam-6763	143	8	:	:	PUNCT
ejpam-6763	143	9	b{k	b{k	ADJ
ejpam-6763	143	10	,	,	PUNCT
ejpam-6763	143	11	n}(x	n}(x	PROPN
ejpam-6763	143	12	)	)	PUNCT
ejpam-6763	143	13	=	=	SYM
ejpam-6763	144	1	n∑	n∑	NOUN
ejpam-6763	144	2	z=0	z=0	NUM
ejpam-6763	144	3	ϑz	ϑz	ADP
ejpam-6763	144	4	bk	bk	PROPN
ejpam-6763	144	5	z	z	PROPN
ejpam-6763	144	6	(	(	PUNCT
ejpam-6763	144	7	x	x	NOUN
ejpam-6763	144	8	)	)	PUNCT
ejpam-6763	144	9	,	,	PUNCT
ejpam-6763	144	10	x0	x0	PROPN
ejpam-6763	144	11	≤	≤	NUM
ejpam-6763	144	12	x	x	PUNCT
ejpam-6763	144	13	≤	≤	NUM
ejpam-6763	144	14	xm	xm	PROPN
ejpam-6763	144	15	(	(	PUNCT
ejpam-6763	144	16	9	9	NUM
ejpam-6763	144	17	)	)	PUNCT
ejpam-6763	144	18	here	here	ADV
ejpam-6763	144	19	,	,	PUNCT
ejpam-6763	144	20	ϑz	ϑz	PROPN
ejpam-6763	144	21	are	be	AUX
ejpam-6763	144	22	the	the	DET
ejpam-6763	144	23	control	control	NOUN
ejpam-6763	144	24	points	point	NOUN
ejpam-6763	144	25	that	that	PRON
ejpam-6763	144	26	influence	influence	VERB
ejpam-6763	144	27	the	the	DET
ejpam-6763	144	28	shape	shape	NOUN
ejpam-6763	144	29	of	of	ADP
ejpam-6763	144	30	the	the	DET
ejpam-6763	144	31	curve	curve	NOUN
ejpam-6763	144	32	,	,	PUNCT
ejpam-6763	144	33	and	and	CCONJ
ejpam-6763	144	34	bk	bk	VERB
ejpam-6763	144	35	z	z	NOUN
ejpam-6763	144	36	(	(	PUNCT
ejpam-6763	144	37	x	x	X
ejpam-6763	144	38	)	)	PUNCT
ejpam-6763	144	39	are	be	AUX
ejpam-6763	144	40	the	the	DET
ejpam-6763	144	41	b	b	NUM
ejpam-6763	144	42	-	-	PUNCT
ejpam-6763	144	43	spline	spline	NOUN
ejpam-6763	144	44	basis	basis	NOUN
ejpam-6763	144	45	functions	function	NOUN
ejpam-6763	144	46	of	of	ADP
ejpam-6763	144	47	degree	degree	NOUN
ejpam-6763	144	48	k	k	PROPN
ejpam-6763	144	49	,	,	PUNCT
ejpam-6763	144	50	which	which	PRON
ejpam-6763	144	51	are	be	AUX
ejpam-6763	144	52	defined	define	VERB
ejpam-6763	144	53	recursively	recursively	ADV
ejpam-6763	144	54	and	and	CCONJ
ejpam-6763	144	55	determine	determine	VERB
ejpam-6763	144	56	the	the	DET
ejpam-6763	144	57	influence	influence	NOUN
ejpam-6763	144	58	of	of	ADP
ejpam-6763	144	59	each	each	DET
ejpam-6763	144	60	control	control	NOUN
ejpam-6763	144	61	point	point	NOUN
ejpam-6763	144	62	on	on	ADP
ejpam-6763	144	63	the	the	DET
ejpam-6763	144	64	curve	curve	NOUN
ejpam-6763	144	65	for	for	ADP
ejpam-6763	144	66	any	any	DET
ejpam-6763	144	67	parameter	parameter	NOUN
ejpam-6763	144	68	value	value	NOUN
ejpam-6763	144	69	x.	x.	NOUN
ejpam-6763	144	70	lemma	lemma	PROPN
ejpam-6763	145	1	1	1	X
ejpam-6763	145	2	.	.	PUNCT
ejpam-6763	145	3	general	general	ADJ
ejpam-6763	145	4	expression	expression	NOUN
ejpam-6763	145	5	of	of	ADP
ejpam-6763	145	6	a	a	DET
ejpam-6763	145	7	cubic	cubic	ADJ
ejpam-6763	145	8	b	b	NOUN
ejpam-6763	145	9	-	-	PUNCT
ejpam-6763	145	10	spline	spline	NOUN
ejpam-6763	145	11	curve	curve	NOUN
ejpam-6763	145	12	.	.	PUNCT
ejpam-6763	146	1	let	let	VERB
ejpam-6763	146	2	ϑ0	ϑ0	NOUN
ejpam-6763	146	3	,	,	PUNCT
ejpam-6763	146	4	ϑ1	ϑ1	NOUN
ejpam-6763	146	5	,	,	PUNCT
ejpam-6763	146	6	ϑ2	ϑ2	NOUN
ejpam-6763	146	7	,	,	PUNCT
ejpam-6763	146	8	and	and	CCONJ
ejpam-6763	146	9	ϑ3	ϑ3	NOUN
ejpam-6763	146	10	be	be	VERB
ejpam-6763	146	11	four	four	NUM
ejpam-6763	146	12	consecutive	consecutive	ADJ
ejpam-6763	146	13	control	control	NOUN
ejpam-6763	146	14	points	point	NOUN
ejpam-6763	146	15	of	of	ADP
ejpam-6763	146	16	a	a	DET
ejpam-6763	146	17	third	third	ADJ
ejpam-6763	146	18	-	-	PUNCT
ejpam-6763	146	19	degree	degree	NOUN
ejpam-6763	146	20	b	b	NOUN
ejpam-6763	146	21	-	-	PUNCT
ejpam-6763	146	22	spline	spline	NOUN
ejpam-6763	146	23	curve	curve	NOUN
ejpam-6763	146	24	defined	define	VERB
ejpam-6763	146	25	on	on	ADP
ejpam-6763	146	26	the	the	DET
ejpam-6763	146	27	interval	interval	NOUN
ejpam-6763	146	28	[	[	X
ejpam-6763	146	29	a	a	X
ejpam-6763	146	30	,	,	PUNCT
ejpam-6763	146	31	b	b	NOUN
ejpam-6763	146	32	]	]	X
ejpam-6763	146	33	.	.	PUNCT
ejpam-6763	147	1	then	then	ADV
ejpam-6763	147	2	,	,	PUNCT
ejpam-6763	147	3	the	the	DET
ejpam-6763	147	4	curve	curve	NOUN
ejpam-6763	147	5	is	be	AUX
ejpam-6763	147	6	given	give	VERB
ejpam-6763	147	7	by	by	ADP
ejpam-6763	147	8	:	:	PUNCT
ejpam-6763	147	9	b{k	b{k	ADJ
ejpam-6763	147	10	,	,	PUNCT
ejpam-6763	147	11	n}(x	n}(x	PROPN
ejpam-6763	147	12	?	?	PUNCT
ejpam-6763	147	13	)	)	PUNCT
ejpam-6763	148	1	=	=	SYM
ejpam-6763	148	2	ϑ0	ϑ0	NOUN
ejpam-6763	148	3	(	(	PUNCT
ejpam-6763	148	4	b−	b−	NOUN
ejpam-6763	148	5	x	x	NOUN
ejpam-6763	148	6	?	?	PUNCT
ejpam-6763	148	7	b−	b−	PROPN
ejpam-6763	148	8	a	a	PRON
ejpam-6763	148	9	)	)	PUNCT
ejpam-6763	148	10	3	3	NUM
ejpam-6763	148	11	+	+	SYM
ejpam-6763	148	12	3ϑ1	3ϑ1	NUM
ejpam-6763	148	13	(	(	PUNCT
ejpam-6763	148	14	x	x	NOUN
ejpam-6763	148	15	?	?	PUNCT
ejpam-6763	148	16	−	−	PROPN
ejpam-6763	149	1	a	a	DET
ejpam-6763	149	2	b−	b−	NOUN
ejpam-6763	149	3	a	a	PRON
ejpam-6763	149	4	)	)	PUNCT
ejpam-6763	149	5	(	(	PUNCT
ejpam-6763	149	6	b−	b−	NOUN
ejpam-6763	149	7	x	x	NOUN
ejpam-6763	149	8	?	?	PUNCT
ejpam-6763	150	1	b−	b−	PROPN
ejpam-6763	150	2	a	a	PRON
ejpam-6763	150	3	)	)	PUNCT
ejpam-6763	150	4	2	2	NUM
ejpam-6763	150	5	+	+	SYM
ejpam-6763	150	6	3ϑ2	3ϑ2	NUM
ejpam-6763	150	7	(	(	PUNCT
ejpam-6763	150	8	x	x	X
ejpam-6763	150	9	?	?	PUNCT
ejpam-6763	150	10	−	−	PROPN
ejpam-6763	150	11	a	a	DET
ejpam-6763	150	12	b−	b−	NOUN
ejpam-6763	150	13	a	a	PRON
ejpam-6763	150	14	)	)	PUNCT
ejpam-6763	150	15	2(b−	2(b−	NUM
ejpam-6763	150	16	x	x	SYM
ejpam-6763	150	17	?	?	PUNCT
ejpam-6763	151	1	b−	b−	PROPN
ejpam-6763	151	2	a	a	PRON
ejpam-6763	151	3	)	)	PUNCT
ejpam-6763	152	1	+	+	NUM
ejpam-6763	152	2	ϑ3	ϑ3	NOUN
ejpam-6763	152	3	(	(	PUNCT
ejpam-6763	152	4	x	x	NOUN
ejpam-6763	152	5	?	?	PUNCT
ejpam-6763	152	6	−	−	PROPN
ejpam-6763	153	1	a	a	DET
ejpam-6763	153	2	b−	b−	NOUN
ejpam-6763	153	3	a	a	PRON
ejpam-6763	153	4	)	)	PUNCT
ejpam-6763	153	5	3	3	NUM
ejpam-6763	153	6	,	,	PUNCT
ejpam-6763	153	7	x	x	X
ejpam-6763	153	8	?	?	PUNCT
ejpam-6763	154	1	∈	∈	PROPN
ejpam-6763	155	1	[	[	X
ejpam-6763	155	2	a	a	X
ejpam-6763	155	3	,	,	PUNCT
ejpam-6763	155	4	b	b	NOUN
ejpam-6763	155	5	]	]	X
ejpam-6763	155	6	(	(	PUNCT
ejpam-6763	155	7	10	10	NUM
ejpam-6763	155	8	)	)	PUNCT
ejpam-6763	155	9	proof	proof	NOUN
ejpam-6763	155	10	.	.	PUNCT
ejpam-6763	156	1	first	first	ADV
ejpam-6763	156	2	,	,	PUNCT
ejpam-6763	156	3	we	we	PRON
ejpam-6763	156	4	convert	convert	VERB
ejpam-6763	156	5	the	the	DET
ejpam-6763	156	6	given	give	VERB
ejpam-6763	156	7	knots	knot	NOUN
ejpam-6763	156	8	xr	xr	PROPN
ejpam-6763	156	9	∈	∈	PROPN
ejpam-6763	156	10	t	t	PROPN
ejpam-6763	156	11	,	,	PUNCT
ejpam-6763	156	12	defined	define	VERB
ejpam-6763	156	13	on	on	ADP
ejpam-6763	156	14	the	the	DET
ejpam-6763	156	15	original	original	ADJ
ejpam-6763	156	16	interval	interval	NOUN
ejpam-6763	156	17	0	0	NUM
ejpam-6763	156	18	≤	≤	NUM
ejpam-6763	156	19	x	x	X
ejpam-6763	156	20	≤	≤	NUM
ejpam-6763	156	21	n−k+1	n−k+1	VERB
ejpam-6763	156	22	as	as	ADP
ejpam-6763	156	23	in	in	ADP
ejpam-6763	156	24	(	(	PUNCT
ejpam-6763	156	25	8)	8)	NUM
ejpam-6763	156	26	,	,	PUNCT
ejpam-6763	156	27	to	to	ADP
ejpam-6763	156	28	a	a	DET
ejpam-6763	156	29	new	new	ADJ
ejpam-6763	156	30	knot	knot	NOUN
ejpam-6763	156	31	vector	vector	NOUN
ejpam-6763	156	32	x?r	x?r	PROPN
ejpam-6763	156	33	∈	∈	PROPN
ejpam-6763	156	34	t	t	PROPN
ejpam-6763	156	35	?	?	PUNCT
ejpam-6763	157	1	defined	define	VERB
ejpam-6763	157	2	on	on	ADP
ejpam-6763	157	3	a	a	DET
ejpam-6763	157	4	new	new	ADJ
ejpam-6763	157	5	interval	interval	NOUN
ejpam-6763	157	6	x	x	PUNCT
ejpam-6763	157	7	?	?	PUNCT
ejpam-6763	158	1	∈	∈	PROPN
ejpam-6763	159	1	[	[	X
ejpam-6763	159	2	a	a	X
ejpam-6763	159	3	,	,	PUNCT
ejpam-6763	159	4	b	b	NOUN
ejpam-6763	159	5	]	]	X
ejpam-6763	159	6	.	.	PUNCT
ejpam-6763	160	1	this	this	PRON
ejpam-6763	160	2	is	be	AUX
ejpam-6763	160	3	achieved	achieve	VERB
ejpam-6763	160	4	by	by	ADP
ejpam-6763	160	5	applying	apply	VERB
ejpam-6763	160	6	the	the	DET
ejpam-6763	160	7	following	follow	VERB
ejpam-6763	160	8	linear	linear	ADJ
ejpam-6763	160	9	transformation	transformation	NOUN
ejpam-6763	160	10	to	to	ADP
ejpam-6763	160	11	each	each	DET
ejpam-6763	160	12	element	element	NOUN
ejpam-6763	160	13	of	of	ADP
ejpam-6763	160	14	the	the	DET
ejpam-6763	160	15	original	original	ADJ
ejpam-6763	160	16	knot	knot	NOUN
ejpam-6763	160	17	vector	vector	NOUN
ejpam-6763	160	18	t	t	NOUN
ejpam-6763	160	19	=	=	PUNCT
ejpam-6763	160	20	{	{	PUNCT
ejpam-6763	160	21	x0	x0	PROPN
ejpam-6763	160	22	,	,	PUNCT
ejpam-6763	160	23	x1	x1	PROPN
ejpam-6763	160	24	,	,	PUNCT
ejpam-6763	160	25	x2	x2	PROPN
ejpam-6763	160	26	,	,	PUNCT
ejpam-6763	160	27	.	.	PUNCT
ejpam-6763	160	28	.	.	PUNCT
ejpam-6763	161	1	.	.	PUNCT
ejpam-6763	162	1	,	,	PUNCT
ejpam-6763	162	2	xm	xm	PROPN
ejpam-6763	162	3	}	}	PUNCT
ejpam-6763	162	4	,	,	PUNCT
ejpam-6763	162	5	yielding	yield	VERB
ejpam-6763	162	6	a	a	DET
ejpam-6763	162	7	new	new	ADJ
ejpam-6763	162	8	knot	knot	NOUN
ejpam-6763	162	9	vector	vector	NOUN
ejpam-6763	162	10	t	t	NOUN
ejpam-6763	162	11	?	?	PUNCT
ejpam-6763	163	1	=	=	PRON
ejpam-6763	163	2	{	{	PUNCT
ejpam-6763	163	3	x?0	x?0	PROPN
ejpam-6763	163	4	,	,	PUNCT
ejpam-6763	163	5	x?1	x?1	PROPN
ejpam-6763	163	6	,	,	PUNCT
ejpam-6763	163	7	.	.	PUNCT
ejpam-6763	163	8	.	.	PUNCT
ejpam-6763	163	9	.	.	PUNCT
ejpam-6763	164	1	,	,	PUNCT
ejpam-6763	164	2	x?m	x?m	NUM
ejpam-6763	164	3	}	}	PUNCT
ejpam-6763	164	4	:	:	PUNCT
ejpam-6763	164	5	x?r	x?r	X
ejpam-6763	164	6	=	=	SYM
ejpam-6763	164	7	a+	a+	PUNCT
ejpam-6763	164	8	(	(	PUNCT
ejpam-6763	164	9	b−	b−	NOUN
ejpam-6763	164	10	a	a	DET
ejpam-6763	164	11	n−	n−	NOUN
ejpam-6763	164	12	k	k	NOUN
ejpam-6763	165	1	+	+	CCONJ
ejpam-6763	165	2	1	1	X
ejpam-6763	165	3	)	)	PUNCT
ejpam-6763	165	4	xr	xr	PROPN
ejpam-6763	165	5	(	(	PUNCT
ejpam-6763	165	6	11	11	NUM
ejpam-6763	165	7	)	)	PUNCT
ejpam-6763	165	8	by	by	ADP
ejpam-6763	165	9	applying	apply	VERB
ejpam-6763	165	10	the	the	DET
ejpam-6763	165	11	transformation	transformation	NOUN
ejpam-6763	165	12	defined	define	VERB
ejpam-6763	165	13	in	in	ADP
ejpam-6763	165	14	(	(	PUNCT
ejpam-6763	165	15	11	11	NUM
ejpam-6763	165	16	)	)	PUNCT
ejpam-6763	165	17	to	to	ADP
ejpam-6763	165	18	each	each	DET
ejpam-6763	165	19	case	case	NOUN
ejpam-6763	165	20	in	in	ADP
ejpam-6763	165	21	(	(	PUNCT
ejpam-6763	165	22	8)	8)	NUM
ejpam-6763	165	23	,	,	PUNCT
ejpam-6763	165	24	we	we	PRON
ejpam-6763	165	25	obtain	obtain	VERB
ejpam-6763	165	26	:	:	PUNCT
ejpam-6763	165	27	x?r	x?r	X
ejpam-6763	165	28	=	=	PUNCT
ejpam-6763	166	1			PROPN
ejpam-6763	167	1	a	a	X
ejpam-6763	167	2	,	,	PUNCT
ejpam-6763	167	3	r	r	NOUN
ejpam-6763	167	4	<	<	X
ejpam-6763	167	5	k	k	X
ejpam-6763	168	1	+	+	PROPN
ejpam-6763	168	2	1	1	NUM
ejpam-6763	168	3	a+	a+	PUNCT
ejpam-6763	168	4	(	(	PUNCT
ejpam-6763	168	5	b−	b−	PROPN
ejpam-6763	168	6	a	a	DET
ejpam-6763	168	7	n−	n−	NOUN
ejpam-6763	168	8	k	k	NOUN
ejpam-6763	169	1	+	+	PROPN
ejpam-6763	169	2	1	1	X
ejpam-6763	169	3	)	)	PUNCT
ejpam-6763	169	4	(	(	PUNCT
ejpam-6763	169	5	r	r	NOUN
ejpam-6763	169	6	−	−	PROPN
ejpam-6763	169	7	k	k	NOUN
ejpam-6763	169	8	)	)	PUNCT
ejpam-6763	169	9	,	,	PUNCT
ejpam-6763	170	1	k	k	PROPN
ejpam-6763	170	2	+	+	CCONJ
ejpam-6763	170	3	1	1	NUM
ejpam-6763	170	4	≤	≤	NUM
ejpam-6763	170	5	r	r	NOUN
ejpam-6763	170	6	≤	≤	NUM
ejpam-6763	170	7	n	n	PRON
ejpam-6763	170	8	b	b	NOUN
ejpam-6763	170	9	,	,	PUNCT
ejpam-6763	170	10	r	r	NOUN
ejpam-6763	170	11	>	>	X
ejpam-6763	170	12	n	n	PROPN
ejpam-6763	170	13	(	(	PUNCT
ejpam-6763	170	14	12	12	NUM
ejpam-6763	170	15	)	)	PUNCT
ejpam-6763	171	1	where	where	SCONJ
ejpam-6763	171	2	:	:	PUNCT
ejpam-6763	171	3	d.	d.	PROPN
ejpam-6763	171	4	kh	kh	PROPN
ejpam-6763	171	5	.	.	PUNCT
ejpam-6763	172	1	abdullah	abdullah	PROPN
ejpam-6763	172	2	,	,	PUNCT
ejpam-6763	172	3	sh	sh	PROPN
ejpam-6763	172	4	.	.	PROPN
ejpam-6763	172	5	sh	sh	PROPN
ejpam-6763	172	6	.	.	PROPN
ejpam-6763	172	7	ahmed	ahmed	PROPN
ejpam-6763	172	8	,	,	PUNCT
ejpam-6763	172	9	k.	k.	PROPN
ejpam-6763	172	10	h.	h.	PROPN
ejpam-6763	172	11	f.	f.	PROPN
ejpam-6763	172	12	jwamer	jwamer	PROPN
ejpam-6763	172	13	/	/	SYM
ejpam-6763	172	14	eur	eur	PROPN
ejpam-6763	172	15	.	.	PUNCT
ejpam-6763	173	1	j.	j.	PROPN
ejpam-6763	173	2	pure	pure	PROPN
ejpam-6763	173	3	appl	appl	PROPN
ejpam-6763	173	4	.	.	PROPN
ejpam-6763	173	5	math	math	PROPN
ejpam-6763	173	6	,	,	PUNCT
ejpam-6763	173	7	18	18	NUM
ejpam-6763	173	8	(	(	PUNCT
ejpam-6763	173	9	4	4	NUM
ejpam-6763	173	10	)	)	PUNCT
ejpam-6763	173	11	(	(	PUNCT
ejpam-6763	173	12	2025	2025	NUM
ejpam-6763	173	13	)	)	PUNCT
ejpam-6763	173	14	,	,	PUNCT
ejpam-6763	173	15	6763	6763	NUM
ejpam-6763	173	16	6	6	NUM
ejpam-6763	173	17	of	of	ADP
ejpam-6763	173	18	40	40	NUM
ejpam-6763	173	19	•	•	NOUN
ejpam-6763	173	20	for	for	ADP
ejpam-6763	173	21	r	r	NOUN
ejpam-6763	173	22	<	<	X
ejpam-6763	173	23	k	k	X
ejpam-6763	174	1	+	+	PROPN
ejpam-6763	174	2	1	1	NUM
ejpam-6763	174	3	,	,	PUNCT
ejpam-6763	174	4	xr	xr	PROPN
ejpam-6763	174	5	=	=	SYM
ejpam-6763	174	6	0	0	NUM
ejpam-6763	174	7	implies	imply	VERB
ejpam-6763	174	8	x?r	x?r	X
ejpam-6763	174	9	=	=	PUNCT
ejpam-6763	174	10	a	a	DET
ejpam-6763	174	11	•	•	NOUN
ejpam-6763	174	12	for	for	ADP
ejpam-6763	174	13	k	k	PROPN
ejpam-6763	174	14	+	+	CCONJ
ejpam-6763	174	15	1	1	NUM
ejpam-6763	174	16	≤	≤	NUM
ejpam-6763	174	17	r	r	NOUN
ejpam-6763	174	18	≤	≤	NUM
ejpam-6763	174	19	n	n	CCONJ
ejpam-6763	174	20	,	,	PUNCT
ejpam-6763	174	21	xr	xr	PROPN
ejpam-6763	175	1	=	=	SYM
ejpam-6763	175	2	r	r	NOUN
ejpam-6763	175	3	−	−	NOUN
ejpam-6763	175	4	k	k	PROPN
ejpam-6763	175	5	implies	imply	VERB
ejpam-6763	175	6	x?r	x?r	X
ejpam-6763	175	7	=	=	SYM
ejpam-6763	175	8	a+	a+	PUNCT
ejpam-6763	175	9	(	(	PUNCT
ejpam-6763	175	10	b−	b−	NOUN
ejpam-6763	175	11	a	a	DET
ejpam-6763	175	12	n−	n−	NOUN
ejpam-6763	175	13	k	k	NOUN
ejpam-6763	176	1	+	+	PROPN
ejpam-6763	176	2	1	1	X
ejpam-6763	176	3	)	)	PUNCT
ejpam-6763	176	4	(	(	PUNCT
ejpam-6763	176	5	r	r	NOUN
ejpam-6763	176	6	−	−	PROPN
ejpam-6763	176	7	k	k	NOUN
ejpam-6763	176	8	)	)	PUNCT
ejpam-6763	176	9	•	•	NOUN
ejpam-6763	176	10	for	for	ADP
ejpam-6763	176	11	r	r	NOUN
ejpam-6763	176	12	>	>	PUNCT
ejpam-6763	176	13	n	n	CCONJ
ejpam-6763	176	14	,	,	PUNCT
ejpam-6763	176	15	xr	xr	PROPN
ejpam-6763	177	1	=	=	SYM
ejpam-6763	177	2	n−	n−	PROPN
ejpam-6763	177	3	k	k	NOUN
ejpam-6763	178	1	+	+	CCONJ
ejpam-6763	178	2	1	1	NUM
ejpam-6763	178	3	implies	imply	VERB
ejpam-6763	178	4	x?r	x?r	X
ejpam-6763	179	1	=	=	SYM
ejpam-6763	179	2	b	b	PROPN
ejpam-6763	179	3	substituting	substitute	VERB
ejpam-6763	179	4	k	k	PROPN
ejpam-6763	179	5	=	=	SYM
ejpam-6763	179	6	3	3	NUM
ejpam-6763	179	7	(	(	PUNCT
ejpam-6763	179	8	cubic	cubic	ADJ
ejpam-6763	179	9	b	b	NOUN
ejpam-6763	179	10	-	-	PUNCT
ejpam-6763	179	11	spline	spline	NOUN
ejpam-6763	179	12	)	)	PUNCT
ejpam-6763	179	13	into	into	ADP
ejpam-6763	179	14	the	the	DET
ejpam-6763	179	15	recurrence	recurrence	NOUN
ejpam-6763	179	16	relation	relation	NOUN
ejpam-6763	179	17	from	from	ADP
ejpam-6763	179	18	(	(	PUNCT
ejpam-6763	179	19	7	7	NUM
ejpam-6763	179	20	)	)	PUNCT
ejpam-6763	179	21	,	,	PUNCT
ejpam-6763	179	22	we	we	PRON
ejpam-6763	179	23	obtain	obtain	VERB
ejpam-6763	179	24	the	the	DET
ejpam-6763	179	25	cubic	cubic	ADJ
ejpam-6763	179	26	b	b	NOUN
ejpam-6763	179	27	-	-	PUNCT
ejpam-6763	179	28	spline	spline	NOUN
ejpam-6763	179	29	basis	basis	NOUN
ejpam-6763	179	30	functions	function	NOUN
ejpam-6763	179	31	used	use	VERB
ejpam-6763	179	32	in	in	ADP
ejpam-6763	179	33	the	the	DET
ejpam-6763	179	34	expression	expression	NOUN
ejpam-6763	179	35	above	above	ADV
ejpam-6763	179	36	.	.	PUNCT
ejpam-6763	180	1	b3	b3	PROPN
ejpam-6763	180	2	r(x	r(x	PROPN
ejpam-6763	180	3	?	?	PUNCT
ejpam-6763	180	4	)	)	PUNCT
ejpam-6763	181	1	=	=	PUNCT
ejpam-6763	182	1	x	x	X
ejpam-6763	182	2	?	?	PUNCT
ejpam-6763	182	3	−	−	PROPN
ejpam-6763	182	4	x?r	x?r	PROPN
ejpam-6763	182	5	x?r+3	x?r+3	PROPN
ejpam-6763	182	6	−	−	PROPN
ejpam-6763	182	7	x?r	x?r	PROPN
ejpam-6763	182	8	b2	b2	PROPN
ejpam-6763	182	9	r(x	r(x	PROPN
ejpam-6763	182	10	?	?	PUNCT
ejpam-6763	182	11	)	)	PUNCT
ejpam-6763	183	1	+	+	CCONJ
ejpam-6763	183	2	x?r+4	x?r+4	ADJ
ejpam-6763	183	3	−	−	PROPN
ejpam-6763	183	4	x	x	NOUN
ejpam-6763	183	5	?	?	PUNCT
ejpam-6763	184	1	x?r+4	x?r+4	PROPN
ejpam-6763	185	1	−	−	PROPN
ejpam-6763	185	2	x?r+1	x?r+1	PROPN
ejpam-6763	185	3	b2	b2	PROPN
ejpam-6763	185	4	r+1(x	r+1(x	NOUN
ejpam-6763	185	5	?	?	PUNCT
ejpam-6763	185	6	)	)	PUNCT
ejpam-6763	186	1	(	(	PUNCT
ejpam-6763	186	2	13	13	X
ejpam-6763	186	3	)	)	PUNCT
ejpam-6763	186	4	we	we	PRON
ejpam-6763	186	5	substitute	substitute	VERB
ejpam-6763	186	6	the	the	DET
ejpam-6763	186	7	expressions	expression	NOUN
ejpam-6763	186	8	for	for	ADP
ejpam-6763	186	9	b2	b2	NOUN
ejpam-6763	186	10	r(x	r(x	PROPN
ejpam-6763	186	11	?	?	PUNCT
ejpam-6763	186	12	)	)	PUNCT
ejpam-6763	186	13	and	and	CCONJ
ejpam-6763	186	14	b2	b2	PROPN
ejpam-6763	186	15	r+1(x	r+1(x	NOUN
ejpam-6763	186	16	?	?	PUNCT
ejpam-6763	186	17	)	)	PUNCT
ejpam-6763	186	18	,	,	PUNCT
ejpam-6763	186	19	which	which	PRON
ejpam-6763	186	20	are	be	AUX
ejpam-6763	186	21	computed	compute	VERB
ejpam-6763	186	22	using	use	VERB
ejpam-6763	186	23	the	the	DET
ejpam-6763	186	24	first	first	ADJ
ejpam-6763	186	25	and	and	CCONJ
ejpam-6763	186	26	zero	zero	NUM
ejpam-6763	186	27	degree	degree	NOUN
ejpam-6763	186	28	b	b	X
ejpam-6763	186	29	-	-	PUNCT
ejpam-6763	186	30	spline	spline	NOUN
ejpam-6763	186	31	basis	basis	NOUN
ejpam-6763	186	32	functions	function	NOUN
ejpam-6763	186	33	.	.	PUNCT
ejpam-6763	187	1	after	after	ADP
ejpam-6763	187	2	simplification	simplification	NOUN
ejpam-6763	187	3	and	and	CCONJ
ejpam-6763	187	4	substitution	substitution	NOUN
ejpam-6763	187	5	,	,	PUNCT
ejpam-6763	187	6	we	we	PRON
ejpam-6763	187	7	obtain	obtain	VERB
ejpam-6763	187	8	:	:	PUNCT
ejpam-6763	187	9	b3	b3	PROPN
ejpam-6763	187	10	r(x	r(x	PROPN
ejpam-6763	187	11	?	?	PUNCT
ejpam-6763	187	12	)	)	PUNCT
ejpam-6763	188	1	=	=	SYM
ejpam-6763	188	2			PRON
ejpam-6763	188	3	(	(	PUNCT
ejpam-6763	188	4	x	x	NOUN
ejpam-6763	188	5	?	?	PUNCT
ejpam-6763	188	6	−	−	PROPN
ejpam-6763	188	7	x?r	x?r	NOUN
ejpam-6763	188	8	)	)	PUNCT
ejpam-6763	188	9	3	3	NUM
ejpam-6763	188	10	(	(	PUNCT
ejpam-6763	188	11	x?r+3	x?r+3	NOUN
ejpam-6763	188	12	−	−	NOUN
ejpam-6763	188	13	x?r)(x	x?r)(x	PROPN
ejpam-6763	188	14	?	?	PUNCT
ejpam-6763	189	1	r+2	r+2	NUM
ejpam-6763	190	1	−	−	NOUN
ejpam-6763	190	2	x?r)(x	x?r)(x	PROPN
ejpam-6763	190	3	?	?	PUNCT
ejpam-6763	191	1	r+1	r+1	PROPN
ejpam-6763	192	1	−	−	PROPN
ejpam-6763	192	2	x?r	x?r	PROPN
ejpam-6763	192	3	)	)	PUNCT
ejpam-6763	192	4	,	,	PUNCT
ejpam-6763	192	5	if	if	SCONJ
ejpam-6763	192	6	x?r	x?r	PROPN
ejpam-6763	192	7	≤	≤	NUM
ejpam-6763	193	1	x	x	X
ejpam-6763	193	2	?	?	PUNCT
ejpam-6763	194	1	<	<	X
ejpam-6763	194	2	x?r+1	x?r+1	INTJ
ejpam-6763	194	3	(	(	PUNCT
ejpam-6763	194	4	x	x	NOUN
ejpam-6763	194	5	?	?	PUNCT
ejpam-6763	194	6	−	−	PROPN
ejpam-6763	194	7	x?r	x?r	NOUN
ejpam-6763	194	8	)	)	PUNCT
ejpam-6763	194	9	2(x?r+2	2(x?r+2	NUM
ejpam-6763	195	1	−	−	NOUN
ejpam-6763	195	2	x	x	SYM
ejpam-6763	195	3	?	?	PUNCT
ejpam-6763	195	4	)	)	PUNCT
ejpam-6763	196	1	(	(	PUNCT
ejpam-6763	196	2	x?r+3	x?r+3	NOUN
ejpam-6763	196	3	−	−	NOUN
ejpam-6763	196	4	x?r)(x	x?r)(x	PROPN
ejpam-6763	196	5	?	?	PUNCT
ejpam-6763	197	1	r+2	r+2	NUM
ejpam-6763	198	1	−	−	NOUN
ejpam-6763	198	2	x?r)(x	x?r)(x	PROPN
ejpam-6763	198	3	?	?	PUNCT
ejpam-6763	199	1	r+2	r+2	NUM
ejpam-6763	200	1	−	−	PROPN
ejpam-6763	200	2	x?r+1	x?r+1	PROPN
ejpam-6763	200	3	)	)	PUNCT
ejpam-6763	201	1	+	+	CCONJ
ejpam-6763	201	2	(	(	PUNCT
ejpam-6763	201	3	x	x	X
ejpam-6763	201	4	?	?	PUNCT
ejpam-6763	201	5	−	−	PROPN
ejpam-6763	201	6	x?r)(x	x?r)(x	PROPN
ejpam-6763	201	7	?	?	PUNCT
ejpam-6763	202	1	r+3	r+3	NOUN
ejpam-6763	202	2	−	−	PROPN
ejpam-6763	202	3	x?)(x	x?)(x	PROPN
ejpam-6763	202	4	?	?	PUNCT
ejpam-6763	203	1	−	−	PROPN
ejpam-6763	203	2	x?r+1	x?r+1	NUM
ejpam-6763	203	3	)	)	PUNCT
ejpam-6763	204	1	(	(	PUNCT
ejpam-6763	204	2	x?r+3	x?r+3	NOUN
ejpam-6763	204	3	−	−	NOUN
ejpam-6763	204	4	x?r)(x	x?r)(x	PROPN
ejpam-6763	204	5	?	?	PUNCT
ejpam-6763	205	1	r+3	r+3	NOUN
ejpam-6763	205	2	−	−	NOUN
ejpam-6763	205	3	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	205	4	?	?	PUNCT
ejpam-6763	206	1	r+2	r+2	NUM
ejpam-6763	207	1	−	−	PROPN
ejpam-6763	207	2	x?r+1	x?r+1	PROPN
ejpam-6763	207	3	)	)	PUNCT
ejpam-6763	208	1	+	+	CCONJ
ejpam-6763	208	2	(	(	PUNCT
ejpam-6763	208	3	x?r+4	x?r+4	PROPN
ejpam-6763	208	4	−	−	PROPN
ejpam-6763	208	5	x?)(x	x?)(x	PROPN
ejpam-6763	208	6	?	?	PUNCT
ejpam-6763	209	1	−	−	PROPN
ejpam-6763	209	2	x?r+1	x?r+1	NUM
ejpam-6763	209	3	)	)	PUNCT
ejpam-6763	209	4	2	2	NUM
ejpam-6763	209	5	(	(	PUNCT
ejpam-6763	209	6	x?r+4	x?r+4	ADJ
ejpam-6763	209	7	−	−	PROPN
ejpam-6763	209	8	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	209	9	?	?	PUNCT
ejpam-6763	210	1	r+3	r+3	NOUN
ejpam-6763	210	2	−	−	PROPN
ejpam-6763	210	3	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	210	4	?	?	PUNCT
ejpam-6763	211	1	r+2	r+2	NUM
ejpam-6763	212	1	−	−	PROPN
ejpam-6763	212	2	x?r+1	x?r+1	PROPN
ejpam-6763	212	3	)	)	PUNCT
ejpam-6763	212	4	if	if	SCONJ
ejpam-6763	212	5	x?r+1	x?r+1	PROPN
ejpam-6763	212	6	≤	≤	PROPN
ejpam-6763	213	1	x	x	X
ejpam-6763	213	2	?	?	PUNCT
ejpam-6763	213	3	<	<	X
ejpam-6763	213	4	x?r+2	x?r+2	PROPN
ejpam-6763	214	1	(	(	PUNCT
ejpam-6763	214	2	x?r+3	x?r+3	NOUN
ejpam-6763	214	3	−	−	PROPN
ejpam-6763	214	4	x?)2(x	x?)2(x	PROPN
ejpam-6763	214	5	?	?	PUNCT
ejpam-6763	215	1	−	−	PROPN
ejpam-6763	215	2	x?r	x?r	PROPN
ejpam-6763	215	3	)	)	PUNCT
ejpam-6763	215	4	(	(	PUNCT
ejpam-6763	215	5	x?r+3	x?r+3	NOUN
ejpam-6763	215	6	−	−	NOUN
ejpam-6763	215	7	x?r)(x	x?r)(x	PROPN
ejpam-6763	215	8	?	?	PUNCT
ejpam-6763	216	1	r+3	r+3	NOUN
ejpam-6763	216	2	−	−	NOUN
ejpam-6763	216	3	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	216	4	?	?	PUNCT
ejpam-6763	217	1	r+3	r+3	NOUN
ejpam-6763	217	2	−	−	PROPN
ejpam-6763	217	3	x?r+2	x?r+2	PROPN
ejpam-6763	217	4	)	)	PUNCT
ejpam-6763	218	1	+	+	CCONJ
ejpam-6763	218	2	(	(	PUNCT
ejpam-6763	218	3	x?r+4	x?r+4	PROPN
ejpam-6763	218	4	−	−	PROPN
ejpam-6763	218	5	x?)(x	x?)(x	PROPN
ejpam-6763	218	6	?	?	PUNCT
ejpam-6763	219	1	−	−	NOUN
ejpam-6763	219	2	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	219	3	?	?	PUNCT
ejpam-6763	220	1	r+3	r+3	NOUN
ejpam-6763	220	2	−	−	PUNCT
ejpam-6763	220	3	x	x	NOUN
ejpam-6763	220	4	?	?	PUNCT
ejpam-6763	220	5	)	)	PUNCT
ejpam-6763	221	1	(	(	PUNCT
ejpam-6763	221	2	x?r+4	x?r+4	ADJ
ejpam-6763	221	3	−	−	PROPN
ejpam-6763	221	4	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	221	5	?	?	PUNCT
ejpam-6763	222	1	r+3	r+3	NOUN
ejpam-6763	222	2	−	−	PROPN
ejpam-6763	222	3	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	222	4	?	?	PUNCT
ejpam-6763	223	1	r+3	r+3	NOUN
ejpam-6763	223	2	−	−	PROPN
ejpam-6763	223	3	x?r+2	x?r+2	PROPN
ejpam-6763	223	4	)	)	PUNCT
ejpam-6763	224	1	+	+	CCONJ
ejpam-6763	224	2	(	(	PUNCT
ejpam-6763	224	3	x?r+4	x?r+4	ADJ
ejpam-6763	224	4	−	−	PROPN
ejpam-6763	224	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	224	6	?	?	PUNCT
ejpam-6763	225	1	−	−	PROPN
ejpam-6763	225	2	x?r+2	x?r+2	PROPN
ejpam-6763	225	3	)	)	PUNCT
ejpam-6763	225	4	(	(	PUNCT
ejpam-6763	225	5	x?r+4	x?r+4	NOUN
ejpam-6763	225	6	−	−	PROPN
ejpam-6763	225	7	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	225	8	?	?	PUNCT
ejpam-6763	226	1	r+4	r+4	NUM
ejpam-6763	226	2	−	−	NOUN
ejpam-6763	226	3	x?r+2)(x	x?r+2)(x	PROPN
ejpam-6763	226	4	?	?	PUNCT
ejpam-6763	227	1	r+3	r+3	NOUN
ejpam-6763	227	2	−	−	PROPN
ejpam-6763	227	3	x?r+2	x?r+2	PROPN
ejpam-6763	227	4	)	)	PUNCT
ejpam-6763	227	5	if	if	SCONJ
ejpam-6763	227	6	x?r+2	x?r+2	PROPN
ejpam-6763	227	7	≤	≤	ADV
ejpam-6763	228	1	x	x	X
ejpam-6763	228	2	?	?	PUNCT
ejpam-6763	229	1	<	<	X
ejpam-6763	229	2	x?r+3	x?r+3	PROPN
ejpam-6763	229	3	(	(	PUNCT
ejpam-6763	229	4	x?r+4	x?r+4	PROPN
ejpam-6763	229	5	−	−	PROPN
ejpam-6763	229	6	x?)3	x?)3	PROPN
ejpam-6763	229	7	(	(	PUNCT
ejpam-6763	229	8	x?r+4	x?r+4	ADJ
ejpam-6763	229	9	−	−	PROPN
ejpam-6763	229	10	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	229	11	?	?	PUNCT
ejpam-6763	230	1	r+4	r+4	NUM
ejpam-6763	231	1	−	−	NOUN
ejpam-6763	231	2	x?r+2)(x	x?r+2)(x	PROPN
ejpam-6763	231	3	?	?	PUNCT
ejpam-6763	232	1	r+4	r+4	NUM
ejpam-6763	233	1	−	−	NUM
ejpam-6763	233	2	x?r+3	x?r+3	PROPN
ejpam-6763	233	3	)	)	PUNCT
ejpam-6763	233	4	,	,	PUNCT
ejpam-6763	233	5	if	if	SCONJ
ejpam-6763	233	6	x?r+3	x?r+3	VERB
ejpam-6763	233	7	≤	≤	ADJ
ejpam-6763	233	8	x	x	X
ejpam-6763	233	9	?	?	PUNCT
ejpam-6763	234	1	<	<	X
ejpam-6763	234	2	x?r+4	x?r+4	PROPN
ejpam-6763	234	3	0	0	NUM
ejpam-6763	234	4	,	,	PUNCT
ejpam-6763	234	5	otherwise	otherwise	ADV
ejpam-6763	234	6	(	(	PUNCT
ejpam-6763	234	7	14	14	NUM
ejpam-6763	234	8	)	)	PUNCT
ejpam-6763	234	9	now	now	ADV
ejpam-6763	234	10	,	,	PUNCT
ejpam-6763	234	11	if	if	SCONJ
ejpam-6763	234	12	we	we	PRON
ejpam-6763	234	13	set	set	VERB
ejpam-6763	234	14	k	k	PROPN
ejpam-6763	234	15	=	=	PUNCT
ejpam-6763	234	16	3	3	NUM
ejpam-6763	234	17	and	and	CCONJ
ejpam-6763	234	18	n	n	NOUN
ejpam-6763	234	19	=	=	SYM
ejpam-6763	234	20	3	3	NUM
ejpam-6763	234	21	,	,	PUNCT
ejpam-6763	234	22	then	then	ADV
ejpam-6763	234	23	from	from	ADP
ejpam-6763	234	24	(	(	PUNCT
ejpam-6763	234	25	12	12	NUM
ejpam-6763	234	26	)	)	PUNCT
ejpam-6763	234	27	,	,	PUNCT
ejpam-6763	234	28	we	we	PRON
ejpam-6763	234	29	obtain	obtain	VERB
ejpam-6763	234	30	the	the	DET
ejpam-6763	234	31	open	open	ADJ
ejpam-6763	234	32	uniform	uniform	ADJ
ejpam-6763	234	33	knot	knot	NOUN
ejpam-6763	234	34	vector	vector	NOUN
ejpam-6763	234	35	:	:	PUNCT
ejpam-6763	234	36	t	t	NOUN
ejpam-6763	234	37	?	?	PUNCT
ejpam-6763	235	1	=	=	PRON
ejpam-6763	235	2	{	{	PUNCT
ejpam-6763	235	3	a	a	X
ejpam-6763	235	4	,	,	PUNCT
ejpam-6763	235	5	a	a	PRON
ejpam-6763	235	6	,	,	PUNCT
ejpam-6763	235	7	a	a	PRON
ejpam-6763	235	8	,	,	PUNCT
ejpam-6763	235	9	a	a	PRON
ejpam-6763	235	10	,	,	PUNCT
ejpam-6763	235	11	b	b	PROPN
ejpam-6763	235	12	,	,	PUNCT
ejpam-6763	235	13	b	b	PROPN
ejpam-6763	235	14	,	,	PUNCT
ejpam-6763	235	15	b	b	PROPN
ejpam-6763	235	16	,	,	PUNCT
ejpam-6763	235	17	b	b	NOUN
ejpam-6763	235	18	}	}	PUNCT
ejpam-6763	235	19	.	.	PUNCT
ejpam-6763	236	1	the	the	DET
ejpam-6763	236	2	parameter	parameter	NOUN
ejpam-6763	236	3	x	x	PROPN
ejpam-6763	236	4	?	?	PROPN
ejpam-6763	236	5	lies	lie	VERB
ejpam-6763	236	6	in	in	ADP
ejpam-6763	236	7	the	the	DET
ejpam-6763	236	8	range	range	NOUN
ejpam-6763	236	9	:	:	PUNCT
ejpam-6763	237	1	x	x	X
ejpam-6763	237	2	?	?	PUNCT
ejpam-6763	237	3	∈	∈	PROPN
ejpam-6763	238	1	[	[	X
ejpam-6763	238	2	a	a	X
ejpam-6763	238	3	,	,	PUNCT
ejpam-6763	238	4	b	b	NOUN
ejpam-6763	238	5	]	]	X
ejpam-6763	238	6	.	.	PUNCT
ejpam-6763	239	1	since	since	SCONJ
ejpam-6763	239	2	the	the	DET
ejpam-6763	239	3	knot	knot	NOUN
ejpam-6763	239	4	vector	vector	NOUN
ejpam-6763	239	5	is	be	AUX
ejpam-6763	239	6	uniform	uniform	ADJ
ejpam-6763	239	7	and	and	CCONJ
ejpam-6763	239	8	open	open	ADJ
ejpam-6763	239	9	,	,	PUNCT
ejpam-6763	239	10	x?r	x?r	PROPN
ejpam-6763	239	11	∈	∈	PROPN
ejpam-6763	239	12	t	t	NOUN
ejpam-6763	239	13	?	?	PUNCT
ejpam-6763	240	1	for	for	ADP
ejpam-6763	240	2	r	r	NOUN
ejpam-6763	240	3	=	=	SYM
ejpam-6763	240	4	0	0	NUM
ejpam-6763	240	5	,	,	PUNCT
ejpam-6763	240	6	.	.	PUNCT
ejpam-6763	240	7	.	.	PUNCT
ejpam-6763	240	8	.	.	PUNCT
ejpam-6763	241	1	,	,	PUNCT
ejpam-6763	241	2	n.	n.	NOUN
ejpam-6763	241	3	substituting	substituting	NOUN
ejpam-6763	241	4	into	into	ADP
ejpam-6763	241	5	(	(	PUNCT
ejpam-6763	241	6	9	9	NUM
ejpam-6763	241	7	)	)	PUNCT
ejpam-6763	241	8	and	and	CCONJ
ejpam-6763	241	9	using	use	VERB
ejpam-6763	241	10	the	the	DET
ejpam-6763	241	11	basis	basis	NOUN
ejpam-6763	241	12	functions	function	NOUN
ejpam-6763	241	13	from	from	ADP
ejpam-6763	241	14	(	(	PUNCT
ejpam-6763	241	15	13	13	NUM
ejpam-6763	241	16	)	)	PUNCT
ejpam-6763	241	17	,	,	PUNCT
ejpam-6763	241	18	we	we	PRON
ejpam-6763	241	19	get	get	VERB
ejpam-6763	241	20	:	:	PUNCT
ejpam-6763	241	21	b{k	b{k	ADJ
ejpam-6763	241	22	,	,	PUNCT
ejpam-6763	241	23	n}(x	n}(x	PROPN
ejpam-6763	241	24	?	?	PUNCT
ejpam-6763	241	25	)	)	PUNCT
ejpam-6763	242	1	=	=	PUNCT
ejpam-6763	242	2	3∑	3∑	NUM
ejpam-6763	242	3	z=0	z=0	NUM
ejpam-6763	242	4	ϑz	ϑz	PRON
ejpam-6763	242	5	b3	b3	PROPN
ejpam-6763	242	6	z(x	z(x	NUM
ejpam-6763	242	7	?	?	PUNCT
ejpam-6763	242	8	)	)	PUNCT
ejpam-6763	243	1	d.	d.	PROPN
ejpam-6763	243	2	kh	kh	PROPN
ejpam-6763	243	3	.	.	PUNCT
ejpam-6763	244	1	abdullah	abdullah	PROPN
ejpam-6763	244	2	,	,	PUNCT
ejpam-6763	244	3	sh	sh	PROPN
ejpam-6763	244	4	.	.	PROPN
ejpam-6763	244	5	sh	sh	PROPN
ejpam-6763	244	6	.	.	PROPN
ejpam-6763	244	7	ahmed	ahmed	PROPN
ejpam-6763	244	8	,	,	PUNCT
ejpam-6763	244	9	k.	k.	PROPN
ejpam-6763	244	10	h.	h.	PROPN
ejpam-6763	244	11	f.	f.	PROPN
ejpam-6763	244	12	jwamer	jwamer	PROPN
ejpam-6763	244	13	/	/	SYM
ejpam-6763	244	14	eur	eur	PROPN
ejpam-6763	244	15	.	.	PUNCT
ejpam-6763	245	1	j.	j.	PROPN
ejpam-6763	245	2	pure	pure	PROPN
ejpam-6763	245	3	appl	appl	PROPN
ejpam-6763	245	4	.	.	PROPN
ejpam-6763	245	5	math	math	PROPN
ejpam-6763	245	6	,	,	PUNCT
ejpam-6763	245	7	18	18	NUM
ejpam-6763	245	8	(	(	PUNCT
ejpam-6763	245	9	4	4	NUM
ejpam-6763	245	10	)	)	PUNCT
ejpam-6763	245	11	(	(	PUNCT
ejpam-6763	245	12	2025	2025	NUM
ejpam-6763	245	13	)	)	PUNCT
ejpam-6763	245	14	,	,	PUNCT
ejpam-6763	245	15	6763	6763	NUM
ejpam-6763	245	16	7	7	NUM
ejpam-6763	245	17	of	of	ADP
ejpam-6763	245	18	40	40	NUM
ejpam-6763	245	19	=	=	SYM
ejpam-6763	245	20	ϑ0b3	ϑ0b3	X
ejpam-6763	245	21	0(x	0(x	NOUN
ejpam-6763	245	22	?	?	PUNCT
ejpam-6763	245	23	)	)	PUNCT
ejpam-6763	246	1	+	+	CCONJ
ejpam-6763	246	2	ϑ1b3	ϑ1b3	ADP
ejpam-6763	246	3	1(x	1(x	NUM
ejpam-6763	246	4	?	?	PUNCT
ejpam-6763	246	5	)	)	PUNCT
ejpam-6763	247	1	+	+	CCONJ
ejpam-6763	247	2	ϑ2b3	ϑ2b3	NOUN
ejpam-6763	247	3	2(x	2(x	NUM
ejpam-6763	247	4	?	?	PUNCT
ejpam-6763	247	5	)	)	PUNCT
ejpam-6763	248	1	+	+	CCONJ
ejpam-6763	248	2	ϑ3b3	ϑ3b3	X
ejpam-6763	248	3	3(x	3(x	NUM
ejpam-6763	248	4	?	?	PUNCT
ejpam-6763	248	5	)	)	PUNCT
ejpam-6763	248	6	(	(	PUNCT
ejpam-6763	248	7	15	15	NUM
ejpam-6763	248	8	)	)	PUNCT
ejpam-6763	248	9	that	that	PRON
ejpam-6763	248	10	is	be	AUX
ejpam-6763	248	11	:	:	PUNCT
ejpam-6763	248	12	b{k	b{k	ADJ
ejpam-6763	248	13	,	,	PUNCT
ejpam-6763	248	14	n}(x	n}(x	PROPN
ejpam-6763	248	15	?	?	PUNCT
ejpam-6763	248	16	)	)	PUNCT
ejpam-6763	249	1	=	=	SYM
ejpam-6763	249	2	ϑ0	ϑ0	NOUN
ejpam-6763	249	3	·	·	PUNCT
ejpam-6763	249	4			PUNCT
ejpam-6763	249	5	(	(	PUNCT
ejpam-6763	249	6	x	x	X
ejpam-6763	249	7	?	?	PUNCT
ejpam-6763	249	8	−	−	PROPN
ejpam-6763	249	9	x?0	x?0	PROPN
ejpam-6763	249	10	)	)	PUNCT
ejpam-6763	249	11	3	3	NUM
ejpam-6763	249	12	(	(	PUNCT
ejpam-6763	249	13	x?3	x?3	PROPN
ejpam-6763	249	14	−	−	PROPN
ejpam-6763	249	15	x?0)(x	x?0)(x	PUNCT
ejpam-6763	249	16	?	?	PUNCT
ejpam-6763	250	1	2	2	NUM
ejpam-6763	250	2	−	−	NOUN
ejpam-6763	250	3	x?0)(x	x?0)(x	PUNCT
ejpam-6763	250	4	?	?	PUNCT
ejpam-6763	251	1	1	1	NUM
ejpam-6763	251	2	−	−	NUM
ejpam-6763	251	3	x?0	x?0	NUM
ejpam-6763	251	4	)	)	PUNCT
ejpam-6763	251	5	,	,	PUNCT
ejpam-6763	251	6	if	if	SCONJ
ejpam-6763	251	7	x?0	x?0	ADP
ejpam-6763	251	8	≤	≤	NOUN
ejpam-6763	251	9	x	x	X
ejpam-6763	251	10	?	?	PUNCT
ejpam-6763	252	1	<	<	X
ejpam-6763	252	2	x?1	x?1	PROPN
ejpam-6763	253	1	(	(	PUNCT
ejpam-6763	253	2	x	x	NOUN
ejpam-6763	253	3	?	?	PUNCT
ejpam-6763	253	4	−	−	PROPN
ejpam-6763	253	5	x?0	x?0	PROPN
ejpam-6763	253	6	)	)	PUNCT
ejpam-6763	254	1	2(x?2	2(x?2	NUM
ejpam-6763	254	2	−	−	NOUN
ejpam-6763	254	3	x	x	NOUN
ejpam-6763	254	4	?	?	PUNCT
ejpam-6763	254	5	)	)	PUNCT
ejpam-6763	254	6	(	(	PUNCT
ejpam-6763	254	7	x?3	x?3	PROPN
ejpam-6763	254	8	−	−	PROPN
ejpam-6763	254	9	x?0)(x	x?0)(x	PUNCT
ejpam-6763	254	10	?	?	PUNCT
ejpam-6763	255	1	2	2	NUM
ejpam-6763	255	2	−	−	NOUN
ejpam-6763	255	3	x?0)(x	x?0)(x	PUNCT
ejpam-6763	255	4	?	?	PUNCT
ejpam-6763	256	1	2	2	NUM
ejpam-6763	256	2	−	−	NUM
ejpam-6763	256	3	x?1	x?1	NOUN
ejpam-6763	256	4	)	)	PUNCT
ejpam-6763	256	5	+	+	CCONJ
ejpam-6763	256	6	(	(	PUNCT
ejpam-6763	256	7	x	x	X
ejpam-6763	256	8	?	?	PUNCT
ejpam-6763	256	9	−	−	PROPN
ejpam-6763	256	10	x?0)(x	x?0)(x	PUNCT
ejpam-6763	256	11	?	?	PUNCT
ejpam-6763	257	1	3	3	NUM
ejpam-6763	257	2	−	−	PROPN
ejpam-6763	257	3	x?)(x	x?)(x	PROPN
ejpam-6763	257	4	?	?	PUNCT
ejpam-6763	257	5	−	−	PROPN
ejpam-6763	258	1	x?1	x?1	NUM
ejpam-6763	258	2	)	)	PUNCT
ejpam-6763	258	3	(	(	PUNCT
ejpam-6763	258	4	x?3	x?3	PROPN
ejpam-6763	258	5	−	−	PROPN
ejpam-6763	258	6	x?0)(x	x?0)(x	PUNCT
ejpam-6763	258	7	?	?	PUNCT
ejpam-6763	259	1	3	3	NUM
ejpam-6763	259	2	−	−	NOUN
ejpam-6763	259	3	x?1)(x	x?1)(x	PUNCT
ejpam-6763	259	4	?	?	PUNCT
ejpam-6763	260	1	2	2	NUM
ejpam-6763	260	2	−	−	NUM
ejpam-6763	260	3	x?1	x?1	NOUN
ejpam-6763	260	4	)	)	PUNCT
ejpam-6763	260	5	+	+	CCONJ
ejpam-6763	260	6	(	(	PUNCT
ejpam-6763	260	7	x?4	x?4	NOUN
ejpam-6763	260	8	−	−	PROPN
ejpam-6763	260	9	x?)(x	x?)(x	PROPN
ejpam-6763	260	10	?	?	PUNCT
ejpam-6763	260	11	−	−	PROPN
ejpam-6763	261	1	x?1	x?1	NOUN
ejpam-6763	261	2	)	)	PUNCT
ejpam-6763	261	3	2	2	NUM
ejpam-6763	261	4	(	(	PUNCT
ejpam-6763	261	5	x?4	x?4	NOUN
ejpam-6763	261	6	−	−	PROPN
ejpam-6763	261	7	x?1)(x	x?1)(x	PUNCT
ejpam-6763	261	8	?	?	PUNCT
ejpam-6763	262	1	3	3	NUM
ejpam-6763	262	2	−	−	NOUN
ejpam-6763	262	3	x?1)(x	x?1)(x	PUNCT
ejpam-6763	262	4	?	?	PUNCT
ejpam-6763	263	1	2	2	NUM
ejpam-6763	263	2	−	−	NUM
ejpam-6763	263	3	x?1	x?1	NOUN
ejpam-6763	263	4	)	)	PUNCT
ejpam-6763	263	5	if	if	SCONJ
ejpam-6763	263	6	x?1	x?1	ADJ
ejpam-6763	263	7	≤	≤	NUM
ejpam-6763	263	8	x	x	X
ejpam-6763	263	9	?	?	PUNCT
ejpam-6763	264	1	<	<	X
ejpam-6763	264	2	x?2	x?2	PROPN
ejpam-6763	265	1	(	(	PUNCT
ejpam-6763	265	2	x?3	x?3	PROPN
ejpam-6763	265	3	−	−	PROPN
ejpam-6763	265	4	x?)2(x	x?)2(x	PROPN
ejpam-6763	265	5	?	?	PUNCT
ejpam-6763	266	1	−	−	PROPN
ejpam-6763	266	2	x?0	x?0	PROPN
ejpam-6763	266	3	)	)	PUNCT
ejpam-6763	267	1	(	(	PUNCT
ejpam-6763	267	2	x?3	x?3	PROPN
ejpam-6763	267	3	−	−	PROPN
ejpam-6763	267	4	x?0)(x	x?0)(x	PUNCT
ejpam-6763	267	5	?	?	PUNCT
ejpam-6763	268	1	3	3	NUM
ejpam-6763	268	2	−	−	NOUN
ejpam-6763	268	3	x?1)(x	x?1)(x	PUNCT
ejpam-6763	268	4	?	?	PUNCT
ejpam-6763	269	1	3	3	NUM
ejpam-6763	269	2	−	−	PROPN
ejpam-6763	269	3	x?2	x?2	PROPN
ejpam-6763	269	4	)	)	PUNCT
ejpam-6763	270	1	+	+	CCONJ
ejpam-6763	270	2	(	(	PUNCT
ejpam-6763	270	3	x?4	x?4	NOUN
ejpam-6763	270	4	−	−	PROPN
ejpam-6763	270	5	x?)(x	x?)(x	PROPN
ejpam-6763	270	6	?	?	PUNCT
ejpam-6763	271	1	−	−	PROPN
ejpam-6763	271	2	x?1)(x	x?1)(x	PUNCT
ejpam-6763	271	3	?	?	PUNCT
ejpam-6763	272	1	3	3	NUM
ejpam-6763	272	2	−	−	NOUN
ejpam-6763	272	3	x	x	NOUN
ejpam-6763	272	4	?	?	PUNCT
ejpam-6763	272	5	)	)	PUNCT
ejpam-6763	272	6	(	(	PUNCT
ejpam-6763	272	7	x?3	x?3	PROPN
ejpam-6763	272	8	−	−	PROPN
ejpam-6763	272	9	x?1	x?1	X
ejpam-6763	272	10	)	)	PUNCT
ejpam-6763	273	1	2(x?3	2(x?3	NUM
ejpam-6763	273	2	−	−	PROPN
ejpam-6763	273	3	x?2	x?2	PROPN
ejpam-6763	273	4	)	)	PUNCT
ejpam-6763	274	1	+	+	CCONJ
ejpam-6763	274	2	(	(	PUNCT
ejpam-6763	274	3	x?4	x?4	NOUN
ejpam-6763	274	4	−	−	PROPN
ejpam-6763	274	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	274	6	?	?	PUNCT
ejpam-6763	275	1	−	−	PROPN
ejpam-6763	275	2	x?2	x?2	PROPN
ejpam-6763	275	3	)	)	PUNCT
ejpam-6763	276	1	(	(	PUNCT
ejpam-6763	276	2	x?4	x?4	NOUN
ejpam-6763	276	3	−	−	PROPN
ejpam-6763	276	4	x?1)(x	x?1)(x	PUNCT
ejpam-6763	276	5	?	?	PUNCT
ejpam-6763	277	1	4	4	NUM
ejpam-6763	277	2	−	−	NOUN
ejpam-6763	277	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	277	4	?	?	PUNCT
ejpam-6763	278	1	3	3	NUM
ejpam-6763	278	2	−	−	PROPN
ejpam-6763	278	3	x?2	x?2	PROPN
ejpam-6763	278	4	)	)	PUNCT
ejpam-6763	278	5	if	if	SCONJ
ejpam-6763	278	6	x?2	x?2	PROPN
ejpam-6763	278	7	≤	≤	PROPN
ejpam-6763	278	8	x	x	X
ejpam-6763	278	9	?	?	PUNCT
ejpam-6763	278	10	<	<	X
ejpam-6763	278	11	x?3	x?3	NOUN
ejpam-6763	278	12	(	(	PUNCT
ejpam-6763	278	13	x?4	x?4	PROPN
ejpam-6763	278	14	−	−	PROPN
ejpam-6763	278	15	x?)3	x?)3	NOUN
ejpam-6763	278	16	(	(	PUNCT
ejpam-6763	278	17	x?4	x?4	PROPN
ejpam-6763	278	18	−	−	PROPN
ejpam-6763	278	19	x?1)(x	x?1)(x	PUNCT
ejpam-6763	278	20	?	?	PUNCT
ejpam-6763	279	1	4	4	NUM
ejpam-6763	279	2	−	−	NOUN
ejpam-6763	279	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	279	4	?	?	PUNCT
ejpam-6763	280	1	4	4	NUM
ejpam-6763	280	2	−	−	PROPN
ejpam-6763	280	3	x?3	x?3	NOUN
ejpam-6763	280	4	)	)	PUNCT
ejpam-6763	280	5	,	,	PUNCT
ejpam-6763	280	6	if	if	SCONJ
ejpam-6763	280	7	x?3	x?3	PROPN
ejpam-6763	280	8	≤	≤	NUM
ejpam-6763	280	9	x	x	X
ejpam-6763	280	10	?	?	PUNCT
ejpam-6763	280	11	<	<	X
ejpam-6763	281	1	x?4	x?4	PROPN
ejpam-6763	281	2	0	0	NUM
ejpam-6763	281	3	,	,	PUNCT
ejpam-6763	281	4	otherwise	otherwise	ADV
ejpam-6763	281	5	+	+	ADP
ejpam-6763	281	6	ϑ1	ϑ1	NOUN
ejpam-6763	281	7	·	·	PUNCT
ejpam-6763	281	8			X
ejpam-6763	281	9	(	(	PUNCT
ejpam-6763	281	10	x	x	X
ejpam-6763	281	11	?	?	PUNCT
ejpam-6763	281	12	−	−	VERB
ejpam-6763	281	13	x?1	x?1	NOUN
ejpam-6763	281	14	)	)	PUNCT
ejpam-6763	281	15	3	3	NUM
ejpam-6763	281	16	(	(	PUNCT
ejpam-6763	281	17	x?4	x?4	NOUN
ejpam-6763	281	18	−	−	PROPN
ejpam-6763	281	19	x?1)(x	x?1)(x	PUNCT
ejpam-6763	281	20	?	?	PUNCT
ejpam-6763	282	1	3	3	NUM
ejpam-6763	282	2	−	−	NOUN
ejpam-6763	282	3	x?1)(x	x?1)(x	PUNCT
ejpam-6763	282	4	?	?	PUNCT
ejpam-6763	283	1	2	2	NUM
ejpam-6763	283	2	−	−	NUM
ejpam-6763	283	3	x?1	x?1	NOUN
ejpam-6763	283	4	)	)	PUNCT
ejpam-6763	283	5	,	,	PUNCT
ejpam-6763	283	6	if	if	SCONJ
ejpam-6763	283	7	x?1	x?1	ADJ
ejpam-6763	283	8	≤	≤	NUM
ejpam-6763	283	9	x	x	X
ejpam-6763	283	10	?	?	PUNCT
ejpam-6763	284	1	<	<	X
ejpam-6763	284	2	x?2	x?2	PROPN
ejpam-6763	285	1	(	(	PUNCT
ejpam-6763	285	2	x	x	NOUN
ejpam-6763	285	3	?	?	PUNCT
ejpam-6763	285	4	−	−	VERB
ejpam-6763	285	5	x?1	x?1	NOUN
ejpam-6763	285	6	)	)	PUNCT
ejpam-6763	286	1	2(x?3	2(x?3	NUM
ejpam-6763	286	2	−	−	NOUN
ejpam-6763	286	3	x	x	NOUN
ejpam-6763	286	4	?	?	PUNCT
ejpam-6763	286	5	)	)	PUNCT
ejpam-6763	286	6	(	(	PUNCT
ejpam-6763	286	7	x?4	x?4	NOUN
ejpam-6763	286	8	−	−	PROPN
ejpam-6763	286	9	x?1)(x	x?1)(x	PUNCT
ejpam-6763	286	10	?	?	PUNCT
ejpam-6763	287	1	3	3	NUM
ejpam-6763	287	2	−	−	NOUN
ejpam-6763	287	3	x?1)(x	x?1)(x	PUNCT
ejpam-6763	287	4	?	?	PUNCT
ejpam-6763	288	1	3	3	NUM
ejpam-6763	288	2	−	−	PROPN
ejpam-6763	288	3	x?2	x?2	PROPN
ejpam-6763	288	4	)	)	PUNCT
ejpam-6763	289	1	+	+	CCONJ
ejpam-6763	289	2	(	(	PUNCT
ejpam-6763	289	3	x	x	X
ejpam-6763	289	4	?	?	PUNCT
ejpam-6763	289	5	−	−	PROPN
ejpam-6763	289	6	x?1)(x	x?1)(x	PUNCT
ejpam-6763	289	7	?	?	PUNCT
ejpam-6763	290	1	4	4	NUM
ejpam-6763	290	2	−	−	PROPN
ejpam-6763	290	3	x?)(x	x?)(x	PROPN
ejpam-6763	290	4	?	?	PUNCT
ejpam-6763	291	1	−	−	PROPN
ejpam-6763	291	2	x?2	x?2	PROPN
ejpam-6763	291	3	)	)	PUNCT
ejpam-6763	292	1	(	(	PUNCT
ejpam-6763	292	2	x?4	x?4	NOUN
ejpam-6763	292	3	−	−	PROPN
ejpam-6763	292	4	x?1)(x	x?1)(x	PUNCT
ejpam-6763	292	5	?	?	PUNCT
ejpam-6763	293	1	4	4	NUM
ejpam-6763	293	2	−	−	NOUN
ejpam-6763	293	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	293	4	?	?	PUNCT
ejpam-6763	294	1	3	3	NUM
ejpam-6763	294	2	−	−	PROPN
ejpam-6763	294	3	x?2	x?2	PROPN
ejpam-6763	294	4	)	)	PUNCT
ejpam-6763	295	1	+	+	CCONJ
ejpam-6763	295	2	(	(	PUNCT
ejpam-6763	295	3	x?5	x?5	PROPN
ejpam-6763	295	4	−	−	PROPN
ejpam-6763	295	5	x?)(x	x?)(x	PROPN
ejpam-6763	295	6	?	?	PUNCT
ejpam-6763	296	1	−	−	PROPN
ejpam-6763	296	2	x?2	x?2	PROPN
ejpam-6763	296	3	)	)	PUNCT
ejpam-6763	296	4	2	2	NUM
ejpam-6763	296	5	(	(	PUNCT
ejpam-6763	296	6	x?5	x?5	X
ejpam-6763	296	7	−	−	PROPN
ejpam-6763	296	8	x?2)(x	x?2)(x	PROPN
ejpam-6763	296	9	?	?	PUNCT
ejpam-6763	297	1	4	4	NUM
ejpam-6763	297	2	−	−	NOUN
ejpam-6763	297	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	297	4	?	?	PUNCT
ejpam-6763	298	1	3	3	NUM
ejpam-6763	298	2	−	−	PROPN
ejpam-6763	298	3	x?2	x?2	PROPN
ejpam-6763	298	4	)	)	PUNCT
ejpam-6763	298	5	if	if	SCONJ
ejpam-6763	298	6	x?2	x?2	PROPN
ejpam-6763	298	7	≤	≤	PROPN
ejpam-6763	298	8	x	x	X
ejpam-6763	298	9	?	?	PUNCT
ejpam-6763	298	10	<	<	X
ejpam-6763	298	11	x?3	x?3	PROPN
ejpam-6763	298	12	(	(	PUNCT
ejpam-6763	298	13	x?4	x?4	PROPN
ejpam-6763	298	14	−	−	PROPN
ejpam-6763	298	15	x?)2(x	x?)2(x	PROPN
ejpam-6763	298	16	?	?	PUNCT
ejpam-6763	299	1	−	−	PROPN
ejpam-6763	299	2	x?1	x?1	NUM
ejpam-6763	299	3	)	)	PUNCT
ejpam-6763	300	1	(	(	PUNCT
ejpam-6763	300	2	x?4	x?4	NOUN
ejpam-6763	300	3	−	−	PROPN
ejpam-6763	300	4	x?1)(x	x?1)(x	PUNCT
ejpam-6763	300	5	?	?	PUNCT
ejpam-6763	301	1	4	4	NUM
ejpam-6763	301	2	−	−	NOUN
ejpam-6763	301	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	301	4	?	?	PUNCT
ejpam-6763	302	1	4	4	NUM
ejpam-6763	302	2	−	−	NUM
ejpam-6763	302	3	x?3	x?3	NOUN
ejpam-6763	302	4	)	)	PUNCT
ejpam-6763	303	1	+	+	CCONJ
ejpam-6763	303	2	(	(	PUNCT
ejpam-6763	303	3	x?5	x?5	PROPN
ejpam-6763	303	4	−	−	PROPN
ejpam-6763	303	5	x?)(x	x?)(x	PROPN
ejpam-6763	303	6	?	?	PUNCT
ejpam-6763	304	1	−	−	PROPN
ejpam-6763	304	2	x?2)(x	x?2)(x	PROPN
ejpam-6763	304	3	?	?	PUNCT
ejpam-6763	305	1	4	4	NUM
ejpam-6763	305	2	−	−	NOUN
ejpam-6763	305	3	x	x	NOUN
ejpam-6763	305	4	?	?	PUNCT
ejpam-6763	305	5	)	)	PUNCT
ejpam-6763	305	6	(	(	PUNCT
ejpam-6763	305	7	x?5	x?5	X
ejpam-6763	305	8	−	−	PROPN
ejpam-6763	305	9	x?2)(x	x?2)(x	PROPN
ejpam-6763	305	10	?	?	PUNCT
ejpam-6763	306	1	4	4	NUM
ejpam-6763	306	2	−	−	NOUN
ejpam-6763	306	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	306	4	?	?	PUNCT
ejpam-6763	307	1	4	4	NUM
ejpam-6763	307	2	−	−	NUM
ejpam-6763	307	3	x?3	x?3	NOUN
ejpam-6763	307	4	)	)	PUNCT
ejpam-6763	308	1	+	+	CCONJ
ejpam-6763	308	2	(	(	PUNCT
ejpam-6763	308	3	x?5	x?5	PUNCT
ejpam-6763	308	4	−	−	PROPN
ejpam-6763	308	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	308	6	?	?	PUNCT
ejpam-6763	309	1	−	−	PROPN
ejpam-6763	309	2	x?3	x?3	NOUN
ejpam-6763	309	3	)	)	PUNCT
ejpam-6763	309	4	(	(	PUNCT
ejpam-6763	309	5	x?5	x?5	X
ejpam-6763	309	6	−	−	PROPN
ejpam-6763	309	7	x?2)(x	x?2)(x	PROPN
ejpam-6763	309	8	?	?	PUNCT
ejpam-6763	310	1	5	5	NUM
ejpam-6763	310	2	−	−	PROPN
ejpam-6763	310	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	310	4	?	?	PUNCT
ejpam-6763	311	1	4	4	NUM
ejpam-6763	311	2	−	−	PROPN
ejpam-6763	311	3	x?3	x?3	NOUN
ejpam-6763	311	4	)	)	PUNCT
ejpam-6763	311	5	if	if	SCONJ
ejpam-6763	311	6	x?3	x?3	PROPN
ejpam-6763	311	7	≤	≤	NUM
ejpam-6763	311	8	x	x	X
ejpam-6763	311	9	?	?	PUNCT
ejpam-6763	311	10	<	<	X
ejpam-6763	312	1	x?4	x?4	PROPN
ejpam-6763	312	2	(	(	PUNCT
ejpam-6763	312	3	x?5	x?5	X
ejpam-6763	312	4	−	−	PROPN
ejpam-6763	312	5	x?)3	x?)3	NOUN
ejpam-6763	312	6	(	(	PUNCT
ejpam-6763	312	7	x?5	x?5	PROPN
ejpam-6763	312	8	−	−	PROPN
ejpam-6763	312	9	x?2)(x	x?2)(x	PROPN
ejpam-6763	312	10	?	?	PUNCT
ejpam-6763	313	1	5	5	NUM
ejpam-6763	313	2	−	−	PROPN
ejpam-6763	313	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	313	4	?	?	PUNCT
ejpam-6763	314	1	5	5	NUM
ejpam-6763	314	2	−	−	NOUN
ejpam-6763	314	3	x?4	x?4	PROPN
ejpam-6763	314	4	)	)	PUNCT
ejpam-6763	314	5	,	,	PUNCT
ejpam-6763	314	6	if	if	SCONJ
ejpam-6763	314	7	x?4	x?4	PRON
ejpam-6763	314	8	≤	≤	NUM
ejpam-6763	314	9	x	x	X
ejpam-6763	314	10	?	?	PUNCT
ejpam-6763	314	11	<	<	X
ejpam-6763	314	12	x?5	x?5	PROPN
ejpam-6763	314	13	0	0	NUM
ejpam-6763	314	14	,	,	PUNCT
ejpam-6763	314	15	otherwise	otherwise	ADV
ejpam-6763	314	16	d.	d.	PROPN
ejpam-6763	314	17	kh	kh	PROPN
ejpam-6763	314	18	.	.	PUNCT
ejpam-6763	315	1	abdullah	abdullah	PROPN
ejpam-6763	315	2	,	,	PUNCT
ejpam-6763	315	3	sh	sh	PROPN
ejpam-6763	315	4	.	.	PROPN
ejpam-6763	315	5	sh	sh	PROPN
ejpam-6763	315	6	.	.	PROPN
ejpam-6763	315	7	ahmed	ahmed	PROPN
ejpam-6763	315	8	,	,	PUNCT
ejpam-6763	315	9	k.	k.	PROPN
ejpam-6763	315	10	h.	h.	PROPN
ejpam-6763	315	11	f.	f.	PROPN
ejpam-6763	315	12	jwamer	jwamer	PROPN
ejpam-6763	315	13	/	/	SYM
ejpam-6763	315	14	eur	eur	PROPN
ejpam-6763	315	15	.	.	PUNCT
ejpam-6763	316	1	j.	j.	PROPN
ejpam-6763	316	2	pure	pure	PROPN
ejpam-6763	316	3	appl	appl	PROPN
ejpam-6763	316	4	.	.	PROPN
ejpam-6763	316	5	math	math	PROPN
ejpam-6763	316	6	,	,	PUNCT
ejpam-6763	316	7	18	18	NUM
ejpam-6763	316	8	(	(	PUNCT
ejpam-6763	316	9	4	4	NUM
ejpam-6763	316	10	)	)	PUNCT
ejpam-6763	316	11	(	(	PUNCT
ejpam-6763	316	12	2025	2025	NUM
ejpam-6763	316	13	)	)	PUNCT
ejpam-6763	316	14	,	,	PUNCT
ejpam-6763	316	15	6763	6763	NUM
ejpam-6763	316	16	8	8	NUM
ejpam-6763	316	17	of	of	ADP
ejpam-6763	316	18	40	40	NUM
ejpam-6763	316	19	+	+	ADJ
ejpam-6763	316	20	ϑ2	ϑ2	NOUN
ejpam-6763	316	21	·	·	PUNCT
ejpam-6763	316	22			NUM
ejpam-6763	316	23	(	(	PUNCT
ejpam-6763	316	24	x	x	X
ejpam-6763	316	25	?	?	PUNCT
ejpam-6763	317	1	−	−	PROPN
ejpam-6763	317	2	x?2	x?2	PROPN
ejpam-6763	317	3	)	)	PUNCT
ejpam-6763	317	4	3	3	NUM
ejpam-6763	317	5	(	(	PUNCT
ejpam-6763	317	6	x?5	x?5	X
ejpam-6763	317	7	−	−	PROPN
ejpam-6763	317	8	x?2)(x	x?2)(x	PROPN
ejpam-6763	317	9	?	?	PUNCT
ejpam-6763	318	1	4	4	NUM
ejpam-6763	318	2	−	−	NOUN
ejpam-6763	318	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	318	4	?	?	PUNCT
ejpam-6763	319	1	3	3	NUM
ejpam-6763	319	2	−	−	PROPN
ejpam-6763	319	3	x?2	x?2	PROPN
ejpam-6763	319	4	)	)	PUNCT
ejpam-6763	319	5	,	,	PUNCT
ejpam-6763	319	6	if	if	SCONJ
ejpam-6763	319	7	x?2	x?2	PROPN
ejpam-6763	319	8	≤	≤	NOUN
ejpam-6763	319	9	x	x	X
ejpam-6763	319	10	?	?	PUNCT
ejpam-6763	319	11	<	<	X
ejpam-6763	320	1	x?3	x?3	PROPN
ejpam-6763	320	2	(	(	PUNCT
ejpam-6763	320	3	x	x	X
ejpam-6763	320	4	?	?	PUNCT
ejpam-6763	320	5	−	−	PROPN
ejpam-6763	320	6	x?2	x?2	PROPN
ejpam-6763	320	7	)	)	PUNCT
ejpam-6763	321	1	2(x?4	2(x?4	NUM
ejpam-6763	321	2	−	−	NOUN
ejpam-6763	321	3	x	x	NOUN
ejpam-6763	321	4	?	?	PUNCT
ejpam-6763	321	5	)	)	PUNCT
ejpam-6763	321	6	(	(	PUNCT
ejpam-6763	321	7	x?5	x?5	X
ejpam-6763	321	8	−	−	PROPN
ejpam-6763	321	9	x?2)(x	x?2)(x	PROPN
ejpam-6763	321	10	?	?	PUNCT
ejpam-6763	322	1	4	4	NUM
ejpam-6763	322	2	−	−	NOUN
ejpam-6763	322	3	x?2)(x	x?2)(x	PUNCT
ejpam-6763	322	4	?	?	PUNCT
ejpam-6763	323	1	4	4	NUM
ejpam-6763	323	2	−	−	NUM
ejpam-6763	323	3	x?3	x?3	NOUN
ejpam-6763	323	4	)	)	PUNCT
ejpam-6763	324	1	+	+	CCONJ
ejpam-6763	324	2	(	(	PUNCT
ejpam-6763	324	3	x	x	X
ejpam-6763	324	4	?	?	PUNCT
ejpam-6763	324	5	−	−	PROPN
ejpam-6763	324	6	x?2)(x	x?2)(x	PROPN
ejpam-6763	324	7	?	?	PUNCT
ejpam-6763	325	1	5	5	NUM
ejpam-6763	325	2	−	−	PROPN
ejpam-6763	325	3	x?)(x	x?)(x	PROPN
ejpam-6763	325	4	?	?	PUNCT
ejpam-6763	325	5	−	−	PROPN
ejpam-6763	325	6	x?3	x?3	NOUN
ejpam-6763	325	7	)	)	PUNCT
ejpam-6763	325	8	(	(	PUNCT
ejpam-6763	325	9	x?5	x?5	X
ejpam-6763	325	10	−	−	PROPN
ejpam-6763	325	11	x?2)(x	x?2)(x	PROPN
ejpam-6763	325	12	?	?	PUNCT
ejpam-6763	326	1	5	5	NUM
ejpam-6763	326	2	−	−	PROPN
ejpam-6763	326	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	326	4	?	?	PUNCT
ejpam-6763	327	1	4	4	NUM
ejpam-6763	327	2	−	−	NUM
ejpam-6763	327	3	x?3	x?3	NOUN
ejpam-6763	327	4	)	)	PUNCT
ejpam-6763	328	1	+	+	CCONJ
ejpam-6763	328	2	(	(	PUNCT
ejpam-6763	328	3	x?6	x?6	NOUN
ejpam-6763	328	4	−	−	PROPN
ejpam-6763	328	5	x?)(x	x?)(x	PROPN
ejpam-6763	328	6	?	?	PUNCT
ejpam-6763	329	1	−	−	PROPN
ejpam-6763	329	2	x?3	x?3	NOUN
ejpam-6763	329	3	)	)	PUNCT
ejpam-6763	329	4	2	2	NUM
ejpam-6763	329	5	(	(	PUNCT
ejpam-6763	329	6	x?6	x?6	X
ejpam-6763	329	7	−	−	PROPN
ejpam-6763	329	8	x?3)(x	x?3)(x	PROPN
ejpam-6763	329	9	?	?	PUNCT
ejpam-6763	330	1	5	5	NUM
ejpam-6763	330	2	−	−	NOUN
ejpam-6763	330	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	330	4	?	?	PUNCT
ejpam-6763	331	1	4	4	NUM
ejpam-6763	331	2	−	−	PROPN
ejpam-6763	331	3	x?3	x?3	NOUN
ejpam-6763	331	4	)	)	PUNCT
ejpam-6763	331	5	if	if	SCONJ
ejpam-6763	331	6	x?3	x?3	PROPN
ejpam-6763	331	7	≤	≤	NUM
ejpam-6763	331	8	x	x	X
ejpam-6763	331	9	?	?	PUNCT
ejpam-6763	331	10	<	<	X
ejpam-6763	332	1	x?4	x?4	PROPN
ejpam-6763	332	2	(	(	PUNCT
ejpam-6763	332	3	x?5	x?5	X
ejpam-6763	332	4	−	−	PROPN
ejpam-6763	332	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	332	6	?	?	PUNCT
ejpam-6763	333	1	−	−	PROPN
ejpam-6763	333	2	x?2	x?2	PROPN
ejpam-6763	333	3	)	)	PUNCT
ejpam-6763	333	4	(	(	PUNCT
ejpam-6763	333	5	x?5	x?5	X
ejpam-6763	333	6	−	−	PROPN
ejpam-6763	333	7	x?2)(x	x?2)(x	PROPN
ejpam-6763	333	8	?	?	PUNCT
ejpam-6763	334	1	5	5	NUM
ejpam-6763	334	2	−	−	PROPN
ejpam-6763	334	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	334	4	?	?	PUNCT
ejpam-6763	335	1	5	5	NUM
ejpam-6763	335	2	−	−	NOUN
ejpam-6763	335	3	x?4	x?4	PROPN
ejpam-6763	335	4	)	)	PUNCT
ejpam-6763	336	1	+	+	CCONJ
ejpam-6763	336	2	(	(	PUNCT
ejpam-6763	336	3	x?6	x?6	NOUN
ejpam-6763	336	4	−	−	PROPN
ejpam-6763	336	5	x?)(x	x?)(x	PROPN
ejpam-6763	336	6	?	?	PUNCT
ejpam-6763	337	1	−	−	PROPN
ejpam-6763	338	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	338	2	?	?	PUNCT
ejpam-6763	339	1	5	5	NUM
ejpam-6763	339	2	−	−	NOUN
ejpam-6763	339	3	x	x	NOUN
ejpam-6763	339	4	?	?	PUNCT
ejpam-6763	339	5	)	)	PUNCT
ejpam-6763	339	6	(	(	PUNCT
ejpam-6763	339	7	x?6	x?6	X
ejpam-6763	339	8	−	−	PROPN
ejpam-6763	340	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	340	2	?	?	PUNCT
ejpam-6763	341	1	5	5	NUM
ejpam-6763	341	2	−	−	NOUN
ejpam-6763	341	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	341	4	?	?	PUNCT
ejpam-6763	342	1	5	5	NUM
ejpam-6763	342	2	−	−	NOUN
ejpam-6763	342	3	x?4	x?4	PROPN
ejpam-6763	342	4	)	)	PUNCT
ejpam-6763	343	1	+	+	CCONJ
ejpam-6763	343	2	(	(	PUNCT
ejpam-6763	343	3	x?6	x?6	NOUN
ejpam-6763	343	4	−	−	NOUN
ejpam-6763	343	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	343	6	?	?	PUNCT
ejpam-6763	344	1	−	−	PROPN
ejpam-6763	344	2	x?4	x?4	PROPN
ejpam-6763	344	3	)	)	PUNCT
ejpam-6763	344	4	(	(	PUNCT
ejpam-6763	344	5	x?6	x?6	X
ejpam-6763	344	6	−	−	PROPN
ejpam-6763	345	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	345	2	?	?	PUNCT
ejpam-6763	346	1	6	6	NUM
ejpam-6763	346	2	−	−	PROPN
ejpam-6763	346	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	346	4	?	?	PUNCT
ejpam-6763	347	1	5	5	NUM
ejpam-6763	347	2	−	−	NOUN
ejpam-6763	347	3	x?4	x?4	PROPN
ejpam-6763	347	4	)	)	PUNCT
ejpam-6763	348	1	if	if	SCONJ
ejpam-6763	348	2	x?4	x?4	PROPN
ejpam-6763	348	3	≤	≤	NUM
ejpam-6763	349	1	x	x	X
ejpam-6763	349	2	?	?	PUNCT
ejpam-6763	349	3	<	<	X
ejpam-6763	349	4	x?5	x?5	PROPN
ejpam-6763	350	1	(	(	PUNCT
ejpam-6763	350	2	x?6	x?6	X
ejpam-6763	350	3	−	−	PROPN
ejpam-6763	351	1	x?)3	x?)3	NOUN
ejpam-6763	352	1	(	(	PUNCT
ejpam-6763	352	2	x?6	x?6	X
ejpam-6763	352	3	−	−	PROPN
ejpam-6763	353	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	353	2	?	?	PUNCT
ejpam-6763	354	1	6	6	NUM
ejpam-6763	354	2	−	−	PROPN
ejpam-6763	354	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	354	4	?	?	PUNCT
ejpam-6763	355	1	6	6	NUM
ejpam-6763	355	2	−	−	NUM
ejpam-6763	355	3	x?5	x?5	PROPN
ejpam-6763	355	4	)	)	PUNCT
ejpam-6763	355	5	,	,	PUNCT
ejpam-6763	355	6	if	if	SCONJ
ejpam-6763	355	7	x?5	x?5	PUNCT
ejpam-6763	355	8	≤	≤	NUM
ejpam-6763	355	9	x	x	X
ejpam-6763	355	10	?	?	PUNCT
ejpam-6763	355	11	<	<	X
ejpam-6763	355	12	x?6	x?6	PROPN
ejpam-6763	355	13	0	0	NUM
ejpam-6763	355	14	,	,	PUNCT
ejpam-6763	355	15	otherwise	otherwise	ADV
ejpam-6763	355	16	+	+	NOUN
ejpam-6763	355	17	ϑ3	ϑ3	NOUN
ejpam-6763	355	18	·	·	PUNCT
ejpam-6763	355	19			PUNCT
ejpam-6763	356	1	(	(	PUNCT
ejpam-6763	356	2	x	x	X
ejpam-6763	356	3	?	?	PUNCT
ejpam-6763	356	4	−	−	NOUN
ejpam-6763	356	5	x?3	x?3	NOUN
ejpam-6763	356	6	)	)	PUNCT
ejpam-6763	356	7	3	3	NUM
ejpam-6763	356	8	(	(	PUNCT
ejpam-6763	356	9	x?6	x?6	X
ejpam-6763	356	10	−	−	PROPN
ejpam-6763	357	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	357	2	?	?	PUNCT
ejpam-6763	358	1	5	5	NUM
ejpam-6763	358	2	−	−	NOUN
ejpam-6763	358	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	358	4	?	?	PUNCT
ejpam-6763	359	1	4	4	NUM
ejpam-6763	359	2	−	−	PROPN
ejpam-6763	359	3	x?3	x?3	NOUN
ejpam-6763	359	4	)	)	PUNCT
ejpam-6763	359	5	,	,	PUNCT
ejpam-6763	359	6	if	if	SCONJ
ejpam-6763	359	7	x?3	x?3	PROPN
ejpam-6763	359	8	≤	≤	NUM
ejpam-6763	359	9	x	x	X
ejpam-6763	359	10	?	?	PUNCT
ejpam-6763	360	1	<	<	X
ejpam-6763	360	2	x?4	x?4	PROPN
ejpam-6763	361	1	(	(	PUNCT
ejpam-6763	361	2	x	x	X
ejpam-6763	361	3	?	?	PUNCT
ejpam-6763	361	4	−	−	NOUN
ejpam-6763	361	5	x?3	x?3	NOUN
ejpam-6763	361	6	)	)	PUNCT
ejpam-6763	362	1	2(x?5	2(x?5	NUM
ejpam-6763	362	2	−	−	NOUN
ejpam-6763	362	3	x	x	NOUN
ejpam-6763	362	4	?	?	PUNCT
ejpam-6763	362	5	)	)	PUNCT
ejpam-6763	362	6	(	(	PUNCT
ejpam-6763	362	7	x?6	x?6	X
ejpam-6763	362	8	−	−	PROPN
ejpam-6763	363	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	363	2	?	?	PUNCT
ejpam-6763	364	1	5	5	NUM
ejpam-6763	364	2	−	−	NOUN
ejpam-6763	364	3	x?3)(x	x?3)(x	PUNCT
ejpam-6763	364	4	?	?	PUNCT
ejpam-6763	365	1	5	5	NUM
ejpam-6763	365	2	−	−	NOUN
ejpam-6763	365	3	x?4	x?4	PROPN
ejpam-6763	365	4	)	)	PUNCT
ejpam-6763	366	1	+	+	CCONJ
ejpam-6763	366	2	(	(	PUNCT
ejpam-6763	366	3	x	x	X
ejpam-6763	366	4	?	?	PUNCT
ejpam-6763	366	5	−	−	PROPN
ejpam-6763	366	6	x?3)(x	x?3)(x	PROPN
ejpam-6763	366	7	?	?	PUNCT
ejpam-6763	367	1	6	6	NUM
ejpam-6763	367	2	−	−	PROPN
ejpam-6763	367	3	x?)(x	x?)(x	PROPN
ejpam-6763	367	4	?	?	PUNCT
ejpam-6763	368	1	−	−	PROPN
ejpam-6763	368	2	x?4	x?4	PROPN
ejpam-6763	368	3	)	)	PUNCT
ejpam-6763	368	4	(	(	PUNCT
ejpam-6763	368	5	x?6	x?6	X
ejpam-6763	368	6	−	−	PROPN
ejpam-6763	369	1	x?3)(x	x?3)(x	PROPN
ejpam-6763	369	2	?	?	PUNCT
ejpam-6763	370	1	6	6	NUM
ejpam-6763	370	2	−	−	PROPN
ejpam-6763	370	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	370	4	?	?	PUNCT
ejpam-6763	371	1	5	5	NUM
ejpam-6763	371	2	−	−	NOUN
ejpam-6763	371	3	x?4	x?4	PROPN
ejpam-6763	371	4	)	)	PUNCT
ejpam-6763	372	1	+	+	CCONJ
ejpam-6763	372	2	(	(	PUNCT
ejpam-6763	372	3	x?7	x?7	PROPN
ejpam-6763	372	4	−	−	PROPN
ejpam-6763	373	1	x?)(x	x?)(x	PROPN
ejpam-6763	373	2	?	?	PUNCT
ejpam-6763	374	1	−	−	PROPN
ejpam-6763	374	2	x?4	x?4	PROPN
ejpam-6763	374	3	)	)	PUNCT
ejpam-6763	374	4	2	2	NUM
ejpam-6763	374	5	(	(	PUNCT
ejpam-6763	374	6	x?7	x?7	NOUN
ejpam-6763	375	1	−	−	PROPN
ejpam-6763	375	2	x?4)(x	x?4)(x	PUNCT
ejpam-6763	375	3	?	?	PUNCT
ejpam-6763	376	1	6	6	NUM
ejpam-6763	376	2	−	−	NOUN
ejpam-6763	376	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	376	4	?	?	PUNCT
ejpam-6763	377	1	5	5	NUM
ejpam-6763	377	2	−	−	NOUN
ejpam-6763	377	3	x?4	x?4	PROPN
ejpam-6763	377	4	)	)	PUNCT
ejpam-6763	378	1	if	if	SCONJ
ejpam-6763	378	2	x?4	x?4	PROPN
ejpam-6763	378	3	≤	≤	NUM
ejpam-6763	379	1	x	x	X
ejpam-6763	379	2	?	?	PUNCT
ejpam-6763	379	3	<	<	X
ejpam-6763	379	4	x?5	x?5	PROPN
ejpam-6763	380	1	(	(	PUNCT
ejpam-6763	380	2	x?6	x?6	X
ejpam-6763	380	3	−	−	PROPN
ejpam-6763	380	4	x?)2(x	x?)2(x	PROPN
ejpam-6763	380	5	?	?	PUNCT
ejpam-6763	381	1	−	−	PROPN
ejpam-6763	381	2	x?3	x?3	NOUN
ejpam-6763	381	3	)	)	PUNCT
ejpam-6763	381	4	(	(	PUNCT
ejpam-6763	381	5	x?6	x?6	X
ejpam-6763	381	6	−	−	PROPN
ejpam-6763	381	7	x?3)(x	x?3)(x	PROPN
ejpam-6763	381	8	?	?	PUNCT
ejpam-6763	382	1	6	6	NUM
ejpam-6763	382	2	−	−	PROPN
ejpam-6763	382	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	382	4	?	?	PUNCT
ejpam-6763	383	1	6	6	NUM
ejpam-6763	383	2	−	−	NUM
ejpam-6763	383	3	x?5	x?5	PUNCT
ejpam-6763	383	4	)	)	PUNCT
ejpam-6763	384	1	+	+	CCONJ
ejpam-6763	384	2	(	(	PUNCT
ejpam-6763	384	3	x?7	x?7	PROPN
ejpam-6763	384	4	−	−	PROPN
ejpam-6763	384	5	x?)(x	x?)(x	PROPN
ejpam-6763	384	6	?	?	PUNCT
ejpam-6763	385	1	−	−	PROPN
ejpam-6763	385	2	x?4)(x	x?4)(x	PUNCT
ejpam-6763	385	3	?	?	PUNCT
ejpam-6763	386	1	6	6	NUM
ejpam-6763	386	2	−	−	NOUN
ejpam-6763	386	3	x	x	NOUN
ejpam-6763	386	4	?	?	PUNCT
ejpam-6763	386	5	)	)	PUNCT
ejpam-6763	386	6	(	(	PUNCT
ejpam-6763	386	7	x?7	x?7	NOUN
ejpam-6763	386	8	−	−	PROPN
ejpam-6763	386	9	x?4)(x	x?4)(x	PUNCT
ejpam-6763	386	10	?	?	PUNCT
ejpam-6763	387	1	6	6	NUM
ejpam-6763	387	2	−	−	PROPN
ejpam-6763	387	3	x?4)(x	x?4)(x	PUNCT
ejpam-6763	387	4	?	?	PUNCT
ejpam-6763	388	1	6	6	NUM
ejpam-6763	388	2	−	−	NUM
ejpam-6763	388	3	x?5	x?5	PUNCT
ejpam-6763	388	4	)	)	PUNCT
ejpam-6763	389	1	+	+	CCONJ
ejpam-6763	389	2	(	(	PUNCT
ejpam-6763	389	3	x?7	x?7	PROPN
ejpam-6763	389	4	−	−	PROPN
ejpam-6763	389	5	x?)2(x	x?)2(x	PROPN
ejpam-6763	389	6	?	?	PUNCT
ejpam-6763	390	1	−	−	PROPN
ejpam-6763	390	2	x?5	x?5	PROPN
ejpam-6763	390	3	)	)	PUNCT
ejpam-6763	391	1	(	(	PUNCT
ejpam-6763	391	2	x?7	x?7	NOUN
ejpam-6763	392	1	−	−	PROPN
ejpam-6763	392	2	x?4)(x	x?4)(x	PUNCT
ejpam-6763	392	3	?	?	PUNCT
ejpam-6763	393	1	7	7	NUM
ejpam-6763	393	2	−	−	PROPN
ejpam-6763	393	3	x?5)(x	x?5)(x	PROPN
ejpam-6763	393	4	?	?	PUNCT
ejpam-6763	394	1	6	6	NUM
ejpam-6763	394	2	−	−	NUM
ejpam-6763	394	3	x?5	x?5	PUNCT
ejpam-6763	394	4	)	)	PUNCT
ejpam-6763	394	5	if	if	SCONJ
ejpam-6763	394	6	x?5	x?5	NOUN
ejpam-6763	394	7	≤	≤	NUM
ejpam-6763	394	8	x	x	X
ejpam-6763	394	9	?	?	PUNCT
ejpam-6763	394	10	<	<	X
ejpam-6763	394	11	x?6	x?6	PROPN
ejpam-6763	394	12	(	(	PUNCT
ejpam-6763	394	13	x?7	x?7	PROPN
ejpam-6763	395	1	−	−	PROPN
ejpam-6763	395	2	x?)3	x?)3	PROPN
ejpam-6763	395	3	(	(	PUNCT
ejpam-6763	395	4	x?7	x?7	PROPN
ejpam-6763	396	1	−	−	PROPN
ejpam-6763	396	2	x?4)(x	x?4)(x	PUNCT
ejpam-6763	396	3	?	?	PUNCT
ejpam-6763	397	1	7	7	NUM
ejpam-6763	397	2	−	−	NOUN
ejpam-6763	397	3	x?5)(x	x?5)(x	PROPN
ejpam-6763	397	4	?	?	PUNCT
ejpam-6763	398	1	7	7	NUM
ejpam-6763	398	2	−	−	NUM
ejpam-6763	398	3	x?6	x?6	NUM
ejpam-6763	398	4	)	)	PUNCT
ejpam-6763	398	5	,	,	PUNCT
ejpam-6763	398	6	if	if	SCONJ
ejpam-6763	398	7	x?6	x?6	PUNCT
ejpam-6763	398	8	≤	≤	NUM
ejpam-6763	399	1	x	x	X
ejpam-6763	399	2	?	?	PUNCT
ejpam-6763	399	3	<	<	X
ejpam-6763	399	4	x?7	x?7	PROPN
ejpam-6763	399	5	0	0	NUM
ejpam-6763	399	6	,	,	PUNCT
ejpam-6763	399	7	otherwise	otherwise	ADV
ejpam-6763	399	8	through	through	ADP
ejpam-6763	399	9	the	the	DET
ejpam-6763	399	10	utilization	utilization	NOUN
ejpam-6763	399	11	of	of	ADP
ejpam-6763	399	12	t	t	PROPN
ejpam-6763	399	13	?	?	PUNCT
ejpam-6763	400	1	and	and	CCONJ
ejpam-6763	400	2	carrying	carry	VERB
ejpam-6763	400	3	out	out	ADP
ejpam-6763	400	4	subsequent	subsequent	ADJ
ejpam-6763	400	5	computations	computation	NOUN
ejpam-6763	400	6	,	,	PUNCT
ejpam-6763	400	7	we	we	PRON
ejpam-6763	400	8	obtain	obtain	VERB
ejpam-6763	400	9	(	(	PUNCT
ejpam-6763	400	10	10	10	NUM
ejpam-6763	400	11	):	):	PUNCT
ejpam-6763	400	12	b{c,3}(x	b{c,3}(x	X
ejpam-6763	400	13	?	?	PUNCT
ejpam-6763	400	14	)	)	PUNCT
ejpam-6763	401	1	=	=	SYM
ejpam-6763	401	2			X
ejpam-6763	401	3	ϑ0(b−	ϑ0(b−	NOUN
ejpam-6763	401	4	x?)3	x?)3	NOUN
ejpam-6763	401	5	(	(	PUNCT
ejpam-6763	401	6	b−	b−	PROPN
ejpam-6763	401	7	a)3	a)3	VERB
ejpam-6763	401	8	+	+	CCONJ
ejpam-6763	401	9	3ϑ1(b−	3ϑ1(b−	NUM
ejpam-6763	401	10	x?)2(x	x?)2(x	NOUN
ejpam-6763	401	11	?	?	PUNCT
ejpam-6763	402	1	−	−	PROPN
ejpam-6763	402	2	a	a	X
ejpam-6763	402	3	)	)	PUNCT
ejpam-6763	402	4	(	(	PUNCT
ejpam-6763	402	5	b−	b−	NOUN
ejpam-6763	402	6	a)3	a)3	VERB
ejpam-6763	402	7	+	+	CCONJ
ejpam-6763	402	8	3ϑ2(x	3ϑ2(x	NUM
ejpam-6763	402	9	?	?	PUNCT
ejpam-6763	403	1	−	−	PUNCT
ejpam-6763	404	1	a)2(b−	a)2(b−	NOUN
ejpam-6763	404	2	x	x	X
ejpam-6763	404	3	?	?	PUNCT
ejpam-6763	404	4	)	)	PUNCT
ejpam-6763	404	5	(	(	PUNCT
ejpam-6763	404	6	b−	b−	NOUN
ejpam-6763	404	7	a)3	a)3	VERB
ejpam-6763	404	8	+	+	X
ejpam-6763	404	9	ϑ3(x	ϑ3(x	X
ejpam-6763	404	10	?	?	PUNCT
ejpam-6763	405	1	−	−	PROPN
ejpam-6763	406	1	a)3	a)3	ADV
ejpam-6763	406	2	(	(	PUNCT
ejpam-6763	406	3	b−	b−	PROPN
ejpam-6763	406	4	a)3	a)3	ADJ
ejpam-6763	406	5	if	if	SCONJ
ejpam-6763	406	6	a	a	DET
ejpam-6763	406	7	≤	≤	NUM
ejpam-6763	406	8	x	x	NOUN
ejpam-6763	406	9	?	?	PUNCT
ejpam-6763	406	10	≤	≤	NUM
ejpam-6763	406	11	b	b	NOUN
ejpam-6763	406	12	0	0	NUM
ejpam-6763	406	13	,	,	PUNCT
ejpam-6763	406	14	otherwise	otherwise	ADV
ejpam-6763	406	15	(	(	PUNCT
ejpam-6763	406	16	16	16	NUM
ejpam-6763	406	17	)	)	PUNCT
ejpam-6763	406	18	d.	d.	PROPN
ejpam-6763	406	19	kh	kh	PROPN
ejpam-6763	406	20	.	.	PUNCT
ejpam-6763	407	1	abdullah	abdullah	PROPN
ejpam-6763	407	2	,	,	PUNCT
ejpam-6763	407	3	sh	sh	PROPN
ejpam-6763	407	4	.	.	PROPN
ejpam-6763	407	5	sh	sh	PROPN
ejpam-6763	407	6	.	.	PROPN
ejpam-6763	407	7	ahmed	ahmed	PROPN
ejpam-6763	407	8	,	,	PUNCT
ejpam-6763	407	9	k.	k.	PROPN
ejpam-6763	407	10	h.	h.	PROPN
ejpam-6763	407	11	f.	f.	PROPN
ejpam-6763	407	12	jwamer	jwamer	PROPN
ejpam-6763	407	13	/	/	SYM
ejpam-6763	407	14	eur	eur	PROPN
ejpam-6763	407	15	.	.	PUNCT
ejpam-6763	408	1	j.	j.	PROPN
ejpam-6763	408	2	pure	pure	PROPN
ejpam-6763	408	3	appl	appl	PROPN
ejpam-6763	408	4	.	.	PROPN
ejpam-6763	408	5	math	math	PROPN
ejpam-6763	408	6	,	,	PUNCT
ejpam-6763	408	7	18	18	NUM
ejpam-6763	408	8	(	(	PUNCT
ejpam-6763	408	9	4	4	NUM
ejpam-6763	408	10	)	)	PUNCT
ejpam-6763	408	11	(	(	PUNCT
ejpam-6763	408	12	2025	2025	NUM
ejpam-6763	408	13	)	)	PUNCT
ejpam-6763	408	14	,	,	PUNCT
ejpam-6763	408	15	6763	6763	NUM
ejpam-6763	408	16	9	9	NUM
ejpam-6763	408	17	of	of	ADP
ejpam-6763	408	18	40	40	NUM
ejpam-6763	408	19	the	the	DET
ejpam-6763	408	20	proof	proof	NOUN
ejpam-6763	408	21	is	be	AUX
ejpam-6763	408	22	done	do	VERB
ejpam-6763	408	23	.	.	PUNCT
ejpam-6763	409	1	lemma	lemma	PROPN
ejpam-6763	409	2	2	2	X
ejpam-6763	409	3	.	.	PUNCT
ejpam-6763	409	4	let	let	VERB
ejpam-6763	409	5	b{c,3}(x	b{c,3}(x	NOUN
ejpam-6763	409	6	?	?	PUNCT
ejpam-6763	409	7	)	)	PUNCT
ejpam-6763	409	8	represent	represent	VERB
ejpam-6763	409	9	a	a	DET
ejpam-6763	409	10	cubic	cubic	ADJ
ejpam-6763	409	11	b	b	NOUN
ejpam-6763	409	12	-	-	PUNCT
ejpam-6763	409	13	spline	spline	NOUN
ejpam-6763	409	14	curve	curve	NOUN
ejpam-6763	409	15	defined	define	VERB
ejpam-6763	409	16	over	over	ADP
ejpam-6763	409	17	the	the	DET
ejpam-6763	409	18	closed	closed	ADJ
ejpam-6763	409	19	bounded	bounded	ADJ
ejpam-6763	409	20	interval	interval	NOUN
ejpam-6763	410	1	[	[	X
ejpam-6763	410	2	a	a	X
ejpam-6763	410	3	,	,	PUNCT
ejpam-6763	410	4	b	b	NOUN
ejpam-6763	410	5	]	]	X
ejpam-6763	410	6	with	with	ADP
ejpam-6763	410	7	control	control	NOUN
ejpam-6763	410	8	points	point	NOUN
ejpam-6763	410	9	ϑ0	ϑ0	PROPN
ejpam-6763	410	10	,	,	PUNCT
ejpam-6763	410	11	ϑ1	ϑ1	NOUN
ejpam-6763	410	12	,	,	PUNCT
ejpam-6763	410	13	ϑ2	ϑ2	NOUN
ejpam-6763	410	14	,	,	PUNCT
ejpam-6763	410	15	and	and	CCONJ
ejpam-6763	410	16	ϑ3	ϑ3	NOUN
ejpam-6763	410	17	being	be	AUX
ejpam-6763	410	18	four	four	NUM
ejpam-6763	410	19	consecutive	consecutive	ADJ
ejpam-6763	410	20	control	control	NOUN
ejpam-6763	410	21	points	point	NOUN
ejpam-6763	410	22	.	.	PUNCT
ejpam-6763	411	1	the	the	DET
ejpam-6763	411	2	α	α	PROPN
ejpam-6763	411	3	-	-	PUNCT
ejpam-6763	411	4	caputo	caputo	PROPN
ejpam-6763	411	5	fractional	fractional	PROPN
ejpam-6763	411	6	derivative	derivative	NOUN
ejpam-6763	411	7	of	of	ADP
ejpam-6763	411	8	b{c,3}(x	b{c,3}(x	NOUN
ejpam-6763	411	9	?	?	PUNCT
ejpam-6763	411	10	)	)	PUNCT
ejpam-6763	411	11	,	,	PUNCT
ejpam-6763	411	12	for	for	ADP
ejpam-6763	411	13	α	α	DET
ejpam-6763	411	14	∈	∈	PROPN
ejpam-6763	411	15	(	(	PUNCT
ejpam-6763	411	16	0	0	NUM
ejpam-6763	411	17	,	,	PUNCT
ejpam-6763	411	18	1	1	NUM
ejpam-6763	411	19	]	]	PUNCT
ejpam-6763	411	20	,	,	PUNCT
ejpam-6763	411	21	is	be	AUX
ejpam-6763	411	22	expressed	express	VERB
ejpam-6763	411	23	as	as	ADP
ejpam-6763	411	24	:	:	PUNCT
ejpam-6763	411	25	c	c	PROPN
ejpam-6763	411	26	adα	adα	PROPN
ejpam-6763	411	27	x?b{c,3}(x	x?b{c,3}(x	PROPN
ejpam-6763	411	28	?	?	PUNCT
ejpam-6763	411	29	)	)	PUNCT
ejpam-6763	412	1	=	=	PUNCT
ejpam-6763	412	2	3(x	3(x	NUM
ejpam-6763	412	3	?	?	PUNCT
ejpam-6763	413	1	−	−	PROPN
ejpam-6763	413	2	a)1−α	a)1−α	PROPN
ejpam-6763	413	3	(	(	PUNCT
ejpam-6763	413	4	nh)3	nh)3	PROPN
ejpam-6763	413	5	γ(4−	γ(4−	PROPN
ejpam-6763	413	6	α	α	X
ejpam-6763	413	7	)	)	PUNCT
ejpam-6763	413	8	[	[	PUNCT
ejpam-6763	413	9	ϑ0	ϑ0	NOUN
ejpam-6763	413	10	(	(	PUNCT
ejpam-6763	413	11	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	413	12	α)(x	α)(x	NOUN
ejpam-6763	413	13	?	?	PUNCT
ejpam-6763	414	1	−	−	PROPN
ejpam-6763	415	1	a)−	a)−	PROPN
ejpam-6763	415	2	(	(	PUNCT
ejpam-6763	415	3	nh)2(2−	nh)2(2−	PROPN
ejpam-6763	415	4	α)(3−	α)(3−	NUM
ejpam-6763	415	5	α	α	NOUN
ejpam-6763	415	6	)	)	PUNCT
ejpam-6763	415	7	−	−	PROPN
ejpam-6763	415	8	2(x	2(x	NUM
ejpam-6763	415	9	?	?	PUNCT
ejpam-6763	416	1	−	−	PROPN
ejpam-6763	416	2	a)2	a)2	PROPN
ejpam-6763	416	3	)	)	PUNCT
ejpam-6763	417	1	+	+	CCONJ
ejpam-6763	417	2	ϑ1	ϑ1	NOUN
ejpam-6763	417	3	(	(	PUNCT
ejpam-6763	417	4	(	(	PUNCT
ejpam-6763	417	5	nh)2(2−	nh)2(2−	PROPN
ejpam-6763	417	6	α)(3−	α)(3−	PROPN
ejpam-6763	417	7	α)−	α)−	PROPN
ejpam-6763	417	8	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	417	9	α)(x	α)(x	NOUN
ejpam-6763	417	10	?	?	PUNCT
ejpam-6763	418	1	−	−	PROPN
ejpam-6763	419	1	a	a	X
ejpam-6763	419	2	)	)	PUNCT
ejpam-6763	419	3	+	+	NOUN
ejpam-6763	419	4	6(x	6(x	NUM
ejpam-6763	419	5	?	?	PUNCT
ejpam-6763	420	1	−	−	PROPN
ejpam-6763	420	2	a)2	a)2	PROPN
ejpam-6763	420	3	)	)	PUNCT
ejpam-6763	421	1	+	+	CCONJ
ejpam-6763	421	2	ϑ2	ϑ2	PROPN
ejpam-6763	421	3	(	(	PUNCT
ejpam-6763	421	4	(	(	PUNCT
ejpam-6763	421	5	nh)(3−	nh)(3−	PROPN
ejpam-6763	421	6	α)(x	α)(x	PROPN
ejpam-6763	421	7	?	?	PUNCT
ejpam-6763	422	1	−	−	PROPN
ejpam-6763	423	1	a)−	a)−	ADV
ejpam-6763	423	2	6(x	6(x	NUM
ejpam-6763	423	3	?	?	PUNCT
ejpam-6763	424	1	−	−	PROPN
ejpam-6763	424	2	a)2	a)2	PROPN
ejpam-6763	424	3	)	)	PUNCT
ejpam-6763	425	1	+	+	CCONJ
ejpam-6763	426	1	2ϑ3(x	2ϑ3(x	NUM
ejpam-6763	426	2	?	?	PUNCT
ejpam-6763	427	1	−	−	PROPN
ejpam-6763	427	2	a)2	a)2	NOUN
ejpam-6763	427	3	]	]	PUNCT
ejpam-6763	427	4	(	(	PUNCT
ejpam-6763	427	5	17	17	NUM
ejpam-6763	427	6	)	)	PUNCT
ejpam-6763	427	7	proof	proof	NOUN
ejpam-6763	427	8	:	:	PUNCT
ejpam-6763	427	9	use	use	VERB
ejpam-6763	427	10	a	a	DET
ejpam-6763	427	11	general	general	ADJ
ejpam-6763	427	12	expression	expression	NOUN
ejpam-6763	427	13	of	of	ADP
ejpam-6763	427	14	a	a	DET
ejpam-6763	427	15	cubic	cubic	ADJ
ejpam-6763	427	16	b	b	NOUN
ejpam-6763	427	17	-	-	PUNCT
ejpam-6763	427	18	spline	spline	NOUN
ejpam-6763	427	19	curve	curve	NOUN
ejpam-6763	427	20	defined	define	VERB
ejpam-6763	427	21	on	on	ADP
ejpam-6763	427	22	the	the	DET
ejpam-6763	427	23	interval	interval	NOUN
ejpam-6763	427	24	x	x	X
ejpam-6763	427	25	?	?	PUNCT
ejpam-6763	428	1	∈	∈	PROPN
ejpam-6763	429	1	[	[	X
ejpam-6763	429	2	a	a	X
ejpam-6763	429	3	,	,	PUNCT
ejpam-6763	429	4	b	b	NOUN
ejpam-6763	429	5	]	]	X
ejpam-6763	429	6	.	.	PUNCT
ejpam-6763	430	1	from	from	ADP
ejpam-6763	430	2	equation	equation	NOUN
ejpam-6763	430	3	(	(	PUNCT
ejpam-6763	430	4	16	16	NUM
ejpam-6763	430	5	)	)	PUNCT
ejpam-6763	430	6	,	,	PUNCT
ejpam-6763	430	7	it	it	PRON
ejpam-6763	430	8	is	be	AUX
ejpam-6763	430	9	given	give	VERB
ejpam-6763	430	10	by	by	ADP
ejpam-6763	430	11	:	:	PUNCT
ejpam-6763	430	12	b{c,3}(x	b{c,3}(x	X
ejpam-6763	430	13	?	?	PUNCT
ejpam-6763	430	14	)	)	PUNCT
ejpam-6763	431	1	=	=	SYM
ejpam-6763	431	2	ϑ0	ϑ0	NOUN
ejpam-6763	431	3	(	(	PUNCT
ejpam-6763	431	4	b−	b−	NOUN
ejpam-6763	431	5	x	x	NOUN
ejpam-6763	431	6	?	?	PUNCT
ejpam-6763	431	7	b−	b−	PROPN
ejpam-6763	431	8	a	a	PRON
ejpam-6763	431	9	)	)	PUNCT
ejpam-6763	431	10	3	3	NUM
ejpam-6763	431	11	+	+	SYM
ejpam-6763	431	12	3ϑ1	3ϑ1	NUM
ejpam-6763	431	13	(	(	PUNCT
ejpam-6763	431	14	x	x	NOUN
ejpam-6763	431	15	?	?	PUNCT
ejpam-6763	431	16	−	−	PROPN
ejpam-6763	432	1	a	a	DET
ejpam-6763	432	2	b−	b−	NOUN
ejpam-6763	432	3	a	a	PRON
ejpam-6763	432	4	)	)	PUNCT
ejpam-6763	432	5	(	(	PUNCT
ejpam-6763	432	6	b−	b−	NOUN
ejpam-6763	432	7	x	x	NOUN
ejpam-6763	432	8	?	?	PUNCT
ejpam-6763	433	1	b−	b−	PROPN
ejpam-6763	433	2	a	a	PRON
ejpam-6763	433	3	)	)	PUNCT
ejpam-6763	433	4	2	2	NUM
ejpam-6763	433	5	+	+	SYM
ejpam-6763	433	6	3ϑ2	3ϑ2	NUM
ejpam-6763	433	7	(	(	PUNCT
ejpam-6763	433	8	x	x	X
ejpam-6763	433	9	?	?	PUNCT
ejpam-6763	433	10	−	−	PROPN
ejpam-6763	433	11	a	a	DET
ejpam-6763	433	12	b−	b−	NOUN
ejpam-6763	433	13	a	a	PRON
ejpam-6763	433	14	)	)	PUNCT
ejpam-6763	433	15	2(b−	2(b−	NUM
ejpam-6763	433	16	x	x	SYM
ejpam-6763	433	17	?	?	PUNCT
ejpam-6763	434	1	b−	b−	PROPN
ejpam-6763	434	2	a	a	PRON
ejpam-6763	434	3	)	)	PUNCT
ejpam-6763	435	1	+	+	NUM
ejpam-6763	435	2	ϑ3	ϑ3	NOUN
ejpam-6763	435	3	(	(	PUNCT
ejpam-6763	435	4	x	x	NOUN
ejpam-6763	435	5	?	?	PUNCT
ejpam-6763	435	6	−	−	PROPN
ejpam-6763	436	1	a	a	DET
ejpam-6763	436	2	b−	b−	NOUN
ejpam-6763	436	3	a	a	PRON
ejpam-6763	436	4	)	)	PUNCT
ejpam-6763	436	5	3	3	NUM
ejpam-6763	436	6	(	(	PUNCT
ejpam-6763	436	7	18	18	NUM
ejpam-6763	436	8	)	)	PUNCT
ejpam-6763	436	9	we	we	PRON
ejpam-6763	436	10	simplify	simplify	VERB
ejpam-6763	436	11	the	the	DET
ejpam-6763	436	12	given	give	VERB
ejpam-6763	436	13	expression	expression	NOUN
ejpam-6763	436	14	as	as	SCONJ
ejpam-6763	436	15	follows	follow	VERB
ejpam-6763	436	16	:	:	PUNCT
ejpam-6763	436	17	b{c,3}(x	b{c,3}(x	NOUN
ejpam-6763	436	18	?	?	PUNCT
ejpam-6763	436	19	)	)	PUNCT
ejpam-6763	437	1	=	=	SYM
ejpam-6763	437	2	ϑ0	ϑ0	NOUN
ejpam-6763	437	3	(	(	PUNCT
ejpam-6763	437	4	b−	b−	PROPN
ejpam-6763	437	5	a)3	a)3	ADJ
ejpam-6763	437	6	(	(	PUNCT
ejpam-6763	437	7	b−	b−	X
ejpam-6763	437	8	x?)3	x?)3	PROPN
ejpam-6763	437	9	+	+	CCONJ
ejpam-6763	437	10	3ϑ1	3ϑ1	NUM
ejpam-6763	437	11	(	(	PUNCT
ejpam-6763	437	12	b−	b−	PROPN
ejpam-6763	437	13	a)3	a)3	ADJ
ejpam-6763	437	14	(	(	PUNCT
ejpam-6763	437	15	x	x	X
ejpam-6763	437	16	?	?	PUNCT
ejpam-6763	438	1	−	−	NOUN
ejpam-6763	438	2	a)(b−	a)(b−	NOUN
ejpam-6763	438	3	x?)2	x?)2	PUNCT
ejpam-6763	439	1	+	+	CCONJ
ejpam-6763	439	2	3ϑ2	3ϑ2	NUM
ejpam-6763	439	3	(	(	PUNCT
ejpam-6763	439	4	b−	b−	PROPN
ejpam-6763	439	5	a)3	a)3	ADJ
ejpam-6763	439	6	(	(	PUNCT
ejpam-6763	439	7	x	x	X
ejpam-6763	439	8	?	?	PUNCT
ejpam-6763	439	9	−	−	PROPN
ejpam-6763	440	1	a)2(b−	a)2(b−	NOUN
ejpam-6763	440	2	x	x	NOUN
ejpam-6763	440	3	?	?	PUNCT
ejpam-6763	440	4	)	)	PUNCT
ejpam-6763	441	1	+	+	CCONJ
ejpam-6763	441	2	ϑ3	ϑ3	NOUN
ejpam-6763	441	3	(	(	PUNCT
ejpam-6763	441	4	b−	b−	PROPN
ejpam-6763	441	5	a)3	a)3	ADV
ejpam-6763	441	6	(	(	PUNCT
ejpam-6763	441	7	x	x	X
ejpam-6763	441	8	?	?	PUNCT
ejpam-6763	442	1	−	−	PROPN
ejpam-6763	443	1	a)3	a)3	ADV
ejpam-6763	443	2	(	(	PUNCT
ejpam-6763	443	3	19	19	NUM
ejpam-6763	443	4	)	)	PUNCT
ejpam-6763	443	5	from	from	ADP
ejpam-6763	443	6	the	the	DET
ejpam-6763	443	7	properties	property	NOUN
ejpam-6763	443	8	of	of	ADP
ejpam-6763	443	9	the	the	DET
ejpam-6763	443	10	caputo	caputo	PROPN
ejpam-6763	443	11	fractional	fractional	PROPN
ejpam-6763	443	12	derivative	derivative	NOUN
ejpam-6763	443	13	in	in	ADP
ejpam-6763	443	14	definition	definition	NOUN
ejpam-6763	443	15	2	2	NUM
ejpam-6763	443	16	,	,	PUNCT
ejpam-6763	443	17	for	for	ADP
ejpam-6763	443	18	α	α	DET
ejpam-6763	443	19	∈	∈	PROPN
ejpam-6763	443	20	(	(	PUNCT
ejpam-6763	443	21	0	0	NUM
ejpam-6763	443	22	,	,	PUNCT
ejpam-6763	443	23	1	1	NUM
ejpam-6763	443	24	]	]	PUNCT
ejpam-6763	443	25	,	,	PUNCT
ejpam-6763	443	26	we	we	PRON
ejpam-6763	443	27	can	can	AUX
ejpam-6763	443	28	express	express	VERB
ejpam-6763	443	29	the	the	DET
ejpam-6763	443	30	cubic	cubic	ADJ
ejpam-6763	443	31	b	b	PROPN
ejpam-6763	443	32	-	-	PUNCT
ejpam-6763	443	33	spline	spline	NOUN
ejpam-6763	443	34	curve	curve	NOUN
ejpam-6763	443	35	for	for	ADP
ejpam-6763	443	36	all	all	DET
ejpam-6763	443	37	x	x	NOUN
ejpam-6763	443	38	?	?	PUNCT
ejpam-6763	444	1	∈	∈	PROPN
ejpam-6763	445	1	[	[	X
ejpam-6763	445	2	a	a	X
ejpam-6763	445	3	,	,	PUNCT
ejpam-6763	445	4	b	b	NOUN
ejpam-6763	445	5	]	]	PUNCT
ejpam-6763	445	6	as	as	ADP
ejpam-6763	445	7	:	:	PUNCT
ejpam-6763	445	8	d.	d.	PROPN
ejpam-6763	445	9	kh	kh	PROPN
ejpam-6763	445	10	.	.	PUNCT
ejpam-6763	446	1	abdullah	abdullah	PROPN
ejpam-6763	446	2	,	,	PUNCT
ejpam-6763	446	3	sh	sh	PROPN
ejpam-6763	446	4	.	.	PROPN
ejpam-6763	446	5	sh	sh	PROPN
ejpam-6763	446	6	.	.	PROPN
ejpam-6763	446	7	ahmed	ahmed	PROPN
ejpam-6763	446	8	,	,	PUNCT
ejpam-6763	446	9	k.	k.	PROPN
ejpam-6763	446	10	h.	h.	PROPN
ejpam-6763	446	11	f.	f.	PROPN
ejpam-6763	446	12	jwamer	jwamer	PROPN
ejpam-6763	446	13	/	/	SYM
ejpam-6763	446	14	eur	eur	PROPN
ejpam-6763	446	15	.	.	PUNCT
ejpam-6763	447	1	j.	j.	PROPN
ejpam-6763	447	2	pure	pure	PROPN
ejpam-6763	447	3	appl	appl	PROPN
ejpam-6763	447	4	.	.	PROPN
ejpam-6763	447	5	math	math	PROPN
ejpam-6763	447	6	,	,	PUNCT
ejpam-6763	447	7	18	18	NUM
ejpam-6763	447	8	(	(	PUNCT
ejpam-6763	447	9	4	4	NUM
ejpam-6763	447	10	)	)	PUNCT
ejpam-6763	447	11	(	(	PUNCT
ejpam-6763	447	12	2025	2025	NUM
ejpam-6763	447	13	)	)	PUNCT
ejpam-6763	447	14	,	,	PUNCT
ejpam-6763	447	15	6763	6763	NUM
ejpam-6763	447	16	10	10	NUM
ejpam-6763	447	17	of	of	ADP
ejpam-6763	447	18	40	40	NUM
ejpam-6763	447	19	c	c	PROPN
ejpam-6763	447	20	adα	adα	PROPN
ejpam-6763	447	21	x?b{c,3}(x	x?b{c,3}(x	PROPN
ejpam-6763	447	22	?	?	PUNCT
ejpam-6763	447	23	)	)	PUNCT
ejpam-6763	448	1	=	=	SYM
ejpam-6763	448	2	ϑ0	ϑ0	NOUN
ejpam-6763	448	3	(	(	PUNCT
ejpam-6763	448	4	b−	b−	PROPN
ejpam-6763	448	5	a)3	a)3	ADV
ejpam-6763	448	6	[	[	PUNCT
ejpam-6763	448	7	−3(b−	−3(b−	PROPN
ejpam-6763	448	8	a	a	NOUN
ejpam-6763	448	9	)	)	PUNCT
ejpam-6763	448	10	γ(2−	γ(2−	PROPN
ejpam-6763	448	11	α	α	NOUN
ejpam-6763	448	12	)	)	PUNCT
ejpam-6763	448	13	(	(	PUNCT
ejpam-6763	448	14	x	x	X
ejpam-6763	448	15	?	?	PUNCT
ejpam-6763	449	1	−	−	PROPN
ejpam-6763	449	2	a)1−α	a)1−α	PROPN
ejpam-6763	449	3	+	+	CCONJ
ejpam-6763	449	4	6(b−	6(b−	NUM
ejpam-6763	449	5	a	a	X
ejpam-6763	449	6	)	)	PUNCT
ejpam-6763	449	7	γ(3−	γ(3−	ADP
ejpam-6763	449	8	α	α	NUM
ejpam-6763	449	9	)	)	PUNCT
ejpam-6763	449	10	(	(	PUNCT
ejpam-6763	449	11	x	x	X
ejpam-6763	449	12	?	?	PUNCT
ejpam-6763	449	13	−	−	PROPN
ejpam-6763	449	14	a)2−α	a)2−α	PROPN
ejpam-6763	449	15	−	−	PROPN
ejpam-6763	449	16	6	6	NUM
ejpam-6763	449	17	γ(4−	γ(4−	NOUN
ejpam-6763	449	18	α	α	NOUN
ejpam-6763	449	19	)	)	PUNCT
ejpam-6763	449	20	(	(	PUNCT
ejpam-6763	449	21	x	x	X
ejpam-6763	449	22	?	?	PUNCT
ejpam-6763	449	23	−	−	PROPN
ejpam-6763	449	24	a)3−α	a)3−α	PROPN
ejpam-6763	449	25	]	]	PUNCT
ejpam-6763	450	1	+	+	CCONJ
ejpam-6763	450	2	3ϑ1	3ϑ1	NUM
ejpam-6763	450	3	(	(	PUNCT
ejpam-6763	450	4	b−	b−	PROPN
ejpam-6763	450	5	a)3	a)3	ADV
ejpam-6763	450	6	[	[	PUNCT
ejpam-6763	450	7	(	(	PUNCT
ejpam-6763	450	8	b−	b−	PROPN
ejpam-6763	450	9	a)2	a)2	PROPN
ejpam-6763	450	10	γ(2−	γ(2−	PROPN
ejpam-6763	450	11	α	α	NOUN
ejpam-6763	450	12	)	)	PUNCT
ejpam-6763	450	13	(	(	PUNCT
ejpam-6763	450	14	x	x	X
ejpam-6763	450	15	?	?	PUNCT
ejpam-6763	450	16	−	−	PROPN
ejpam-6763	451	1	a)1−α	a)1−α	PROPN
ejpam-6763	451	2	−	−	PROPN
ejpam-6763	451	3	4(b−	4(b−	NUM
ejpam-6763	451	4	a	a	PRON
ejpam-6763	451	5	)	)	PUNCT
ejpam-6763	451	6	γ(3−	γ(3−	ADP
ejpam-6763	451	7	α	α	NUM
ejpam-6763	451	8	)	)	PUNCT
ejpam-6763	451	9	(	(	PUNCT
ejpam-6763	451	10	x	x	X
ejpam-6763	451	11	?	?	PUNCT
ejpam-6763	451	12	−	−	PROPN
ejpam-6763	451	13	a)2−α	a)2−α	PROPN
ejpam-6763	451	14	+	+	CCONJ
ejpam-6763	451	15	6	6	NUM
ejpam-6763	451	16	γ(4−	γ(4−	NOUN
ejpam-6763	451	17	α	α	NUM
ejpam-6763	451	18	)	)	PUNCT
ejpam-6763	451	19	(	(	PUNCT
ejpam-6763	451	20	x	x	X
ejpam-6763	451	21	?	?	PUNCT
ejpam-6763	451	22	−	−	PROPN
ejpam-6763	451	23	a)3−α	a)3−α	PROPN
ejpam-6763	451	24	]	]	PUNCT
ejpam-6763	452	1	+	+	CCONJ
ejpam-6763	452	2	3ϑ2	3ϑ2	NUM
ejpam-6763	452	3	(	(	PUNCT
ejpam-6763	452	4	b−	b−	PROPN
ejpam-6763	452	5	a)3	a)3	ADV
ejpam-6763	452	6	[	[	PUNCT
ejpam-6763	452	7	2(b−	2(b−	NUM
ejpam-6763	452	8	a	a	PRON
ejpam-6763	452	9	)	)	PUNCT
ejpam-6763	452	10	γ(3−	γ(3−	ADP
ejpam-6763	452	11	α	α	NUM
ejpam-6763	452	12	)	)	PUNCT
ejpam-6763	452	13	(	(	PUNCT
ejpam-6763	452	14	x	x	X
ejpam-6763	452	15	?	?	PUNCT
ejpam-6763	452	16	−	−	PROPN
ejpam-6763	452	17	a)2−α	a)2−α	PROPN
ejpam-6763	452	18	−	−	PROPN
ejpam-6763	452	19	6	6	NUM
ejpam-6763	452	20	γ(4−	γ(4−	NOUN
ejpam-6763	452	21	α	α	NOUN
ejpam-6763	452	22	)	)	PUNCT
ejpam-6763	452	23	(	(	PUNCT
ejpam-6763	452	24	x	x	X
ejpam-6763	452	25	?	?	PUNCT
ejpam-6763	452	26	−	−	PROPN
ejpam-6763	452	27	a)3−α	a)3−α	PROPN
ejpam-6763	452	28	]	]	PUNCT
ejpam-6763	452	29	+	+	CCONJ
ejpam-6763	452	30	6ϑ3	6ϑ3	NUM
ejpam-6763	452	31	(	(	PUNCT
ejpam-6763	452	32	b−	b−	PROPN
ejpam-6763	452	33	a)3γ(4−	a)3γ(4−	PROPN
ejpam-6763	452	34	α	α	NOUN
ejpam-6763	452	35	)	)	PUNCT
ejpam-6763	452	36	(	(	PUNCT
ejpam-6763	452	37	x	x	X
ejpam-6763	452	38	?	?	PUNCT
ejpam-6763	452	39	−	−	PROPN
ejpam-6763	452	40	a)3−α	a)3−α	PROPN
ejpam-6763	452	41	(	(	PUNCT
ejpam-6763	452	42	20	20	NUM
ejpam-6763	452	43	)	)	PUNCT
ejpam-6763	452	44	a	a	DET
ejpam-6763	452	45	cubic	cubic	ADJ
ejpam-6763	452	46	b	b	NOUN
ejpam-6763	452	47	-	-	PUNCT
ejpam-6763	452	48	spline	spline	NOUN
ejpam-6763	452	49	curve	curve	NOUN
ejpam-6763	452	50	defined	define	VERB
ejpam-6763	452	51	over	over	ADP
ejpam-6763	452	52	the	the	DET
ejpam-6763	452	53	closed	closed	ADJ
ejpam-6763	452	54	,	,	PUNCT
ejpam-6763	452	55	bounded	bound	VERB
ejpam-6763	452	56	interval	interval	NOUN
ejpam-6763	452	57	[	[	X
ejpam-6763	452	58	a	a	X
ejpam-6763	452	59	,	,	PUNCT
ejpam-6763	452	60	b	b	NOUN
ejpam-6763	452	61	]	]	X
ejpam-6763	452	62	with	with	ADP
ejpam-6763	452	63	control	control	NOUN
ejpam-6763	452	64	points	point	NOUN
ejpam-6763	452	65	ϑ0	ϑ0	PROPN
ejpam-6763	452	66	,	,	PUNCT
ejpam-6763	452	67	ϑ1	ϑ1	NOUN
ejpam-6763	452	68	,	,	PUNCT
ejpam-6763	452	69	ϑ2	ϑ2	NOUN
ejpam-6763	452	70	,	,	PUNCT
ejpam-6763	452	71	and	and	CCONJ
ejpam-6763	452	72	ϑ3	ϑ3	NOUN
ejpam-6763	452	73	where	where	SCONJ
ejpam-6763	452	74	h	h	NOUN
ejpam-6763	452	75	is	be	AUX
ejpam-6763	452	76	the	the	DET
ejpam-6763	452	77	step	step	NOUN
ejpam-6763	452	78	size	size	NOUN
ejpam-6763	452	79	and	and	CCONJ
ejpam-6763	452	80	n	n	NOUN
ejpam-6763	452	81	is	be	AUX
ejpam-6763	452	82	the	the	DET
ejpam-6763	452	83	number	number	NOUN
ejpam-6763	452	84	of	of	ADP
ejpam-6763	452	85	iterations	iteration	NOUN
ejpam-6763	452	86	therefore	therefore	ADV
ejpam-6763	452	87	,	,	PUNCT
ejpam-6763	452	88	(	(	PUNCT
ejpam-6763	452	89	17	17	NUM
ejpam-6763	452	90	)	)	PUNCT
ejpam-6763	452	91	yields	yield	VERB
ejpam-6763	452	92	the	the	DET
ejpam-6763	452	93	desired	desire	VERB
ejpam-6763	452	94	fractional	fractional	ADJ
ejpam-6763	452	95	derivative	derivative	ADJ
ejpam-6763	452	96	expression	expression	NOUN
ejpam-6763	452	97	.	.	PUNCT
ejpam-6763	453	1	4	4	X
ejpam-6763	453	2	.	.	X
ejpam-6763	453	3	derivation	derivation	NOUN
ejpam-6763	453	4	of	of	ADP
ejpam-6763	453	5	the	the	DET
ejpam-6763	453	6	method	method	NOUN
ejpam-6763	453	7	the	the	DET
ejpam-6763	453	8	main	main	ADJ
ejpam-6763	453	9	aim	aim	NOUN
ejpam-6763	453	10	of	of	ADP
ejpam-6763	453	11	this	this	DET
ejpam-6763	453	12	section	section	NOUN
ejpam-6763	453	13	is	be	AUX
ejpam-6763	453	14	to	to	PART
ejpam-6763	453	15	apply	apply	VERB
ejpam-6763	453	16	the	the	DET
ejpam-6763	453	17	cubic	cubic	ADJ
ejpam-6763	453	18	b	b	PROPN
ejpam-6763	453	19	-	-	PUNCT
ejpam-6763	453	20	spline	spline	NOUN
ejpam-6763	453	21	collocation	collocation	NOUN
ejpam-6763	453	22	method	method	NOUN
ejpam-6763	453	23	in	in	ADP
ejpam-6763	453	24	order	order	NOUN
ejpam-6763	453	25	to	to	PART
ejpam-6763	453	26	introduce	introduce	VERB
ejpam-6763	453	27	a	a	DET
ejpam-6763	453	28	numerical	numerical	ADJ
ejpam-6763	453	29	approximation	approximation	NOUN
ejpam-6763	453	30	technique	technique	NOUN
ejpam-6763	453	31	to	to	PART
ejpam-6763	453	32	solve	solve	VERB
ejpam-6763	453	33	the	the	DET
ejpam-6763	453	34	problem	problem	NOUN
ejpam-6763	453	35	(	(	PUNCT
ejpam-6763	453	36	1	1	NUM
ejpam-6763	453	37	)	)	PUNCT
ejpam-6763	453	38	,	,	PUNCT
ejpam-6763	453	39	under	under	ADP
ejpam-6763	453	40	the	the	DET
ejpam-6763	453	41	initial	initial	ADJ
ejpam-6763	453	42	condition	condition	NOUN
ejpam-6763	453	43	given	give	VERB
ejpam-6763	453	44	by	by	ADP
ejpam-6763	453	45	(	(	PUNCT
ejpam-6763	453	46	2	2	NUM
ejpam-6763	453	47	)	)	PUNCT
ejpam-6763	453	48	.	.	PUNCT
ejpam-6763	454	1	the	the	DET
ejpam-6763	454	2	method	method	NOUN
ejpam-6763	454	3	expresses	express	VERB
ejpam-6763	454	4	the	the	DET
ejpam-6763	454	5	solution	solution	NOUN
ejpam-6763	454	6	as	as	ADP
ejpam-6763	454	7	a	a	DET
ejpam-6763	454	8	cubic	cubic	ADJ
ejpam-6763	454	9	combination	combination	NOUN
ejpam-6763	454	10	of	of	ADP
ejpam-6763	454	11	b	b	NOUN
ejpam-6763	454	12	-	-	PUNCT
ejpam-6763	454	13	spline	spline	NOUN
ejpam-6763	454	14	basis	basis	NOUN
ejpam-6763	454	15	functions	function	NOUN
ejpam-6763	454	16	.	.	PUNCT
ejpam-6763	455	1	let	let	VERB
ejpam-6763	455	2	a	a	PRON
ejpam-6763	455	3	=	=	X
ejpam-6763	455	4	x?0	x?0	PUNCT
ejpam-6763	455	5	<	<	X
ejpam-6763	456	1	x?1	x?1	X
ejpam-6763	456	2	<	<	X
ejpam-6763	456	3	x?2	x?2	PROPN
ejpam-6763	456	4	<	<	X
ejpam-6763	456	5	·	·	PUNCT
ejpam-6763	456	6	·	·	PUNCT
ejpam-6763	456	7	·	·	PUNCT
ejpam-6763	456	8	<	<	X
ejpam-6763	456	9	x?n−1	x?n−1	X
ejpam-6763	456	10	<	<	X
ejpam-6763	456	11	x?n	x?n	PROPN
ejpam-6763	456	12	=	=	SYM
ejpam-6763	456	13	b	b	PROPN
ejpam-6763	456	14	,	,	PUNCT
ejpam-6763	456	15	be	be	AUX
ejpam-6763	456	16	a	a	DET
ejpam-6763	456	17	uniform	uniform	ADJ
ejpam-6763	456	18	mesh	mesh	NOUN
ejpam-6763	456	19	partition	partition	NOUN
ejpam-6763	456	20	of	of	ADP
ejpam-6763	456	21	the	the	DET
ejpam-6763	456	22	domain	domain	NOUN
ejpam-6763	456	23	[	[	X
ejpam-6763	456	24	a	a	X
ejpam-6763	456	25	,	,	PUNCT
ejpam-6763	456	26	b	b	NOUN
ejpam-6763	456	27	]	]	PUNCT
ejpam-6763	456	28	defined	define	VERB
ejpam-6763	456	29	by	by	ADP
ejpam-6763	456	30	the	the	DET
ejpam-6763	456	31	knots	knot	NOUN
ejpam-6763	456	32	x?r	x?r	PROPN
ejpam-6763	456	33	,	,	PUNCT
ejpam-6763	456	34	with	with	ADP
ejpam-6763	456	35	h	h	PROPN
ejpam-6763	456	36	=	=	PUNCT
ejpam-6763	456	37	x?r+1	x?r+1	PROPN
ejpam-6763	457	1	−	−	X
ejpam-6763	457	2	x?r	x?r	PROPN
ejpam-6763	458	1	n	n	PROPN
ejpam-6763	458	2	=	=	PROPN
ejpam-6763	458	3	b−	b−	PROPN
ejpam-6763	458	4	a	a	DET
ejpam-6763	458	5	n	n	NOUN
ejpam-6763	458	6	,	,	PUNCT
ejpam-6763	458	7	r	r	NOUN
ejpam-6763	458	8	=	=	SYM
ejpam-6763	458	9	0	0	NUM
ejpam-6763	458	10	,	,	PUNCT
ejpam-6763	458	11	1	1	NUM
ejpam-6763	458	12	,	,	PUNCT
ejpam-6763	458	13	.	.	PUNCT
ejpam-6763	458	14	.	.	PUNCT
ejpam-6763	459	1	.	.	PUNCT
ejpam-6763	460	1	,	,	PUNCT
ejpam-6763	461	1	n	n	CCONJ
ejpam-6763	461	2	−	−	PROPN
ejpam-6763	461	3	1	1	NUM
ejpam-6763	461	4	.	.	PUNCT
ejpam-6763	462	1	for	for	ADP
ejpam-6763	462	2	all	all	DET
ejpam-6763	462	3	x	x	NOUN
ejpam-6763	462	4	?	?	PUNCT
ejpam-6763	462	5	∈	∈	PROPN
ejpam-6763	463	1	[	[	X
ejpam-6763	463	2	a	a	X
ejpam-6763	463	3	,	,	PUNCT
ejpam-6763	463	4	b	b	NOUN
ejpam-6763	463	5	]	]	X
ejpam-6763	463	6	,	,	PUNCT
ejpam-6763	463	7	let	let	VERB
ejpam-6763	463	8	yi(x	yi(x	NOUN
ejpam-6763	463	9	)	)	PUNCT
ejpam-6763	464	1	≈	≈	PROPN
ejpam-6763	464	2	b{c,3	b{c,3	PROPN
ejpam-6763	464	3	}	}	PUNCT
ejpam-6763	464	4	i	i	PROPN
ejpam-6763	464	5	(	(	PUNCT
ejpam-6763	464	6	x	x	NOUN
ejpam-6763	464	7	?	?	PUNCT
ejpam-6763	464	8	)	)	PUNCT
ejpam-6763	464	9	for	for	ADP
ejpam-6763	464	10	each	each	DET
ejpam-6763	464	11	i	i	NOUN
ejpam-6763	464	12	=	=	NOUN
ejpam-6763	464	13	0	0	NUM
ejpam-6763	464	14	,	,	PUNCT
ejpam-6763	464	15	1	1	NUM
ejpam-6763	464	16	,	,	PUNCT
ejpam-6763	464	17	.	.	PUNCT
ejpam-6763	464	18	.	.	PUNCT
ejpam-6763	464	19	.	.	PUNCT
ejpam-6763	465	1	,	,	PUNCT
ejpam-6763	465	2	m	m	AUX
ejpam-6763	465	3	,	,	PUNCT
ejpam-6763	465	4	using	use	VERB
ejpam-6763	465	5	the	the	DET
ejpam-6763	465	6	collocation	collocation	NOUN
ejpam-6763	465	7	technique	technique	NOUN
ejpam-6763	465	8	with	with	ADP
ejpam-6763	465	9	cubic	cubic	ADJ
ejpam-6763	465	10	b	b	PROPN
ejpam-6763	465	11	-	-	PUNCT
ejpam-6763	465	12	spline	spline	NOUN
ejpam-6763	465	13	basis	basis	NOUN
ejpam-6763	465	14	functions	function	NOUN
ejpam-6763	465	15	to	to	PART
ejpam-6763	465	16	find	find	VERB
ejpam-6763	465	17	an	an	DET
ejpam-6763	465	18	approximate	approximate	ADJ
ejpam-6763	465	19	solution	solution	NOUN
ejpam-6763	465	20	b{c,3	b{c,3	NOUN
ejpam-6763	465	21	}	}	PUNCT
ejpam-6763	465	22	i	i	PROPN
ejpam-6763	465	23	(	(	PUNCT
ejpam-6763	465	24	x	x	NOUN
ejpam-6763	465	25	?	?	PUNCT
ejpam-6763	465	26	)	)	PUNCT
ejpam-6763	465	27	,	,	PUNCT
ejpam-6763	465	28	given	give	VERB
ejpam-6763	465	29	by	by	ADP
ejpam-6763	465	30	:	:	PUNCT
ejpam-6763	465	31	b{c,3	b{c,3	PROPN
ejpam-6763	465	32	}	}	PUNCT
ejpam-6763	465	33	i	i	PRON
ejpam-6763	465	34	(	(	PUNCT
ejpam-6763	465	35	x	x	NOUN
ejpam-6763	465	36	?	?	PUNCT
ejpam-6763	465	37	)	)	PUNCT
ejpam-6763	466	1	=	=	SYM
ejpam-6763	467	1	n∑	n∑	NOUN
ejpam-6763	467	2	z=0	z=0	NUM
ejpam-6763	467	3	ϑiz	ϑiz	ADV
ejpam-6763	467	4	bk	bk	ADP
ejpam-6763	467	5	iz(x	iz(x	NOUN
ejpam-6763	467	6	?	?	PUNCT
ejpam-6763	467	7	)	)	PUNCT
ejpam-6763	468	1	,	,	PUNCT
ejpam-6763	468	2	i	i	PRON
ejpam-6763	468	3	=	=	NOUN
ejpam-6763	468	4	0	0	NUM
ejpam-6763	468	5	,	,	PUNCT
ejpam-6763	468	6	1	1	NUM
ejpam-6763	468	7	,	,	PUNCT
ejpam-6763	468	8	.	.	PUNCT
ejpam-6763	468	9	.	.	PUNCT
ejpam-6763	468	10	.	.	PUNCT
ejpam-6763	469	1	,	,	PUNCT
ejpam-6763	469	2	m	m	PROPN
ejpam-6763	469	3	(	(	PUNCT
ejpam-6763	469	4	21	21	NUM
ejpam-6763	469	5	)	)	PUNCT
ejpam-6763	469	6	in	in	ADP
ejpam-6763	469	7	order	order	NOUN
ejpam-6763	469	8	to	to	PART
ejpam-6763	469	9	solve	solve	VERB
ejpam-6763	469	10	the	the	DET
ejpam-6763	469	11	approximate	approximate	ADJ
ejpam-6763	469	12	solution	solution	NOUN
ejpam-6763	469	13	of	of	ADP
ejpam-6763	469	14	(	(	PUNCT
ejpam-6763	469	15	21	21	NUM
ejpam-6763	469	16	)	)	PUNCT
ejpam-6763	469	17	,	,	PUNCT
ejpam-6763	469	18	we	we	PRON
ejpam-6763	469	19	determine	determine	VERB
ejpam-6763	469	20	the	the	DET
ejpam-6763	469	21	control	control	NOUN
ejpam-6763	469	22	points	point	VERB
ejpam-6763	469	23	ϑiz	ϑiz	ADV
ejpam-6763	469	24	for	for	ADP
ejpam-6763	469	25	all	all	DET
ejpam-6763	469	26	i	i	PRON
ejpam-6763	469	27	=	=	NOUN
ejpam-6763	469	28	0	0	NUM
ejpam-6763	469	29	,	,	PUNCT
ejpam-6763	469	30	1	1	NUM
ejpam-6763	469	31	,	,	PUNCT
ejpam-6763	469	32	.	.	PUNCT
ejpam-6763	469	33	.	.	PUNCT
ejpam-6763	470	1	.	.	PUNCT
ejpam-6763	471	1	,	,	PUNCT
ejpam-6763	471	2	m	m	VERB
ejpam-6763	471	3	and	and	CCONJ
ejpam-6763	471	4	z	z	NOUN
ejpam-6763	471	5	=	=	SYM
ejpam-6763	471	6	0	0	NUM
ejpam-6763	471	7	,	,	PUNCT
ejpam-6763	471	8	.	.	PUNCT
ejpam-6763	471	9	.	.	PUNCT
ejpam-6763	472	1	.	.	PUNCT
ejpam-6763	473	1	,	,	PUNCT
ejpam-6763	473	2	n.	n.	PROPN
ejpam-6763	473	3	d.	d.	PROPN
ejpam-6763	473	4	kh	kh	PROPN
ejpam-6763	473	5	.	.	PUNCT
ejpam-6763	474	1	abdullah	abdullah	PROPN
ejpam-6763	474	2	,	,	PUNCT
ejpam-6763	474	3	sh	sh	PROPN
ejpam-6763	474	4	.	.	PROPN
ejpam-6763	474	5	sh	sh	PROPN
ejpam-6763	474	6	.	.	PROPN
ejpam-6763	474	7	ahmed	ahmed	PROPN
ejpam-6763	474	8	,	,	PUNCT
ejpam-6763	474	9	k.	k.	PROPN
ejpam-6763	474	10	h.	h.	PROPN
ejpam-6763	474	11	f.	f.	PROPN
ejpam-6763	474	12	jwamer	jwamer	PROPN
ejpam-6763	474	13	/	/	SYM
ejpam-6763	474	14	eur	eur	PROPN
ejpam-6763	474	15	.	.	PUNCT
ejpam-6763	475	1	j.	j.	PROPN
ejpam-6763	475	2	pure	pure	PROPN
ejpam-6763	475	3	appl	appl	PROPN
ejpam-6763	475	4	.	.	PROPN
ejpam-6763	475	5	math	math	PROPN
ejpam-6763	475	6	,	,	PUNCT
ejpam-6763	475	7	18	18	NUM
ejpam-6763	475	8	(	(	PUNCT
ejpam-6763	475	9	4	4	NUM
ejpam-6763	475	10	)	)	PUNCT
ejpam-6763	475	11	(	(	PUNCT
ejpam-6763	475	12	2025	2025	NUM
ejpam-6763	475	13	)	)	PUNCT
ejpam-6763	475	14	,	,	PUNCT
ejpam-6763	475	15	6763	6763	NUM
ejpam-6763	475	16	11	11	NUM
ejpam-6763	475	17	of	of	ADP
ejpam-6763	475	18	40	40	NUM
ejpam-6763	475	19	•	•	NOUN
ejpam-6763	475	20	ϑi0	ϑi0	NOUN
ejpam-6763	475	21	is	be	AUX
ejpam-6763	475	22	determined	determine	VERB
ejpam-6763	475	23	by	by	ADP
ejpam-6763	475	24	the	the	DET
ejpam-6763	475	25	initial	initial	ADJ
ejpam-6763	475	26	condition	condition	NOUN
ejpam-6763	475	27	(	(	PUNCT
ejpam-6763	475	28	2	2	NUM
ejpam-6763	475	29	)	)	PUNCT
ejpam-6763	475	30	.	.	PUNCT
ejpam-6763	476	1	•	•	NUM
ejpam-6763	476	2	ϑi1	ϑi1	NOUN
ejpam-6763	476	3	is	be	AUX
ejpam-6763	476	4	determined	determine	VERB
ejpam-6763	476	5	from	from	ADP
ejpam-6763	476	6	ϑi1	ϑi1	NOUN
ejpam-6763	476	7	=	=	SYM
ejpam-6763	476	8	nh	nh	PROPN
ejpam-6763	476	9	3	3	NUM
ejpam-6763	476	10	db{c,3	db{c,3	PROPN
ejpam-6763	476	11	}	}	PUNCT
ejpam-6763	476	12	i1	i1	PROPN
ejpam-6763	476	13	(	(	PUNCT
ejpam-6763	476	14	x	x	NOUN
ejpam-6763	476	15	?	?	PUNCT
ejpam-6763	476	16	)	)	PUNCT
ejpam-6763	476	17	dx	dx	PROPN
ejpam-6763	476	18	?	?	PUNCT
ejpam-6763	477	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	477	2	x?=a	x?=a	PROPN
ejpam-6763	478	1	+	+	CCONJ
ejpam-6763	478	2	ϑi0	ϑi0	NOUN
ejpam-6763	478	3	,	,	PUNCT
ejpam-6763	478	4	where	where	SCONJ
ejpam-6763	478	5	db{c,3	db{c,3	PROPN
ejpam-6763	478	6	}	}	PUNCT
ejpam-6763	478	7	i1	i1	PROPN
ejpam-6763	478	8	(	(	PUNCT
ejpam-6763	478	9	x	x	NOUN
ejpam-6763	478	10	?	?	PUNCT
ejpam-6763	478	11	)	)	PUNCT
ejpam-6763	478	12	dx	dx	PROPN
ejpam-6763	478	13	?	?	PUNCT
ejpam-6763	479	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	479	2	x?=a	x?=a	PROPN
ejpam-6763	480	1	≈	≈	PROPN
ejpam-6763	480	2	y	y	PROPN
ejpam-6763	480	3	′	′	NOUN
ejpam-6763	480	4	i(x	i(x	NOUN
ejpam-6763	480	5	?	?	PUNCT
ejpam-6763	480	6	)	)	PUNCT
ejpam-6763	481	1	∣∣	∣∣	X
ejpam-6763	481	2	x?=a	x?=a	PUNCT
ejpam-6763	482	1	=	=	SYM
ejpam-6763	482	2	1	1	NUM
ejpam-6763	482	3	pi(x	pi(x	NOUN
ejpam-6763	482	4	?	?	PUNCT
ejpam-6763	482	5	)	)	PUNCT
ejpam-6763	483	1	[	[	PUNCT
ejpam-6763	483	2	fi(x	fi(x	NOUN
ejpam-6763	483	3	?	?	PUNCT
ejpam-6763	483	4	)	)	PUNCT
ejpam-6763	484	1	+	+	CCONJ
ejpam-6763	484	2	m∑	m∑	CCONJ
ejpam-6763	484	3	j=0	j=0	PROPN
ejpam-6763	484	4	ωij	ωij	PROPN
ejpam-6763	484	5	∫	∫	PROPN
ejpam-6763	484	6	x	x	X
ejpam-6763	484	7	?	?	PUNCT
ejpam-6763	485	1	a	a	DET
ejpam-6763	485	2	kij(x	kij(x	PROPN
ejpam-6763	485	3	?	?	PUNCT
ejpam-6763	485	4	,	,	PUNCT
ejpam-6763	485	5	s	s	X
ejpam-6763	485	6	)	)	PUNCT
ejpam-6763	485	7	ca	ca	NOUN
ejpam-6763	486	1	d	d	PROPN
ejpam-6763	486	2	βij	βij	PROPN
ejpam-6763	486	3	s	s	PART
ejpam-6763	486	4	yj(s	yj(s	NOUN
ejpam-6763	486	5	)	)	PUNCT
ejpam-6763	486	6	ds	ds	ADP
ejpam-6763	486	7	−	−	NOUN
ejpam-6763	486	8	ai0(x	ai0(x	PROPN
ejpam-6763	486	9	?	?	PUNCT
ejpam-6763	486	10	)	)	PUNCT
ejpam-6763	487	1	ca	can	AUX
ejpam-6763	487	2	d	d	NOUN
ejpam-6763	487	3	σi0	σi0	VERB
ejpam-6763	487	4	x	x	X
ejpam-6763	487	5	?	?	PUNCT
ejpam-6763	487	6	yi(x	yi(x	NUM
ejpam-6763	487	7	?	?	PUNCT
ejpam-6763	487	8	)	)	PUNCT
ejpam-6763	488	1	−	−	PROPN
ejpam-6763	488	2	ai1(x	ai1(x	NOUN
ejpam-6763	488	3	?	?	PUNCT
ejpam-6763	488	4	)	)	PUNCT
ejpam-6763	488	5	yi(x	yi(x	NUM
ejpam-6763	488	6	?	?	PUNCT
ejpam-6763	488	7	)	)	PUNCT
ejpam-6763	489	1	]	]	PUNCT
ejpam-6763	489	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	489	3	x?=a	x?=a	PROPN
ejpam-6763	489	4	•	•	DET
ejpam-6763	489	5	ϑi2	ϑi2	NOUN
ejpam-6763	489	6	is	be	AUX
ejpam-6763	489	7	determined	determine	VERB
ejpam-6763	489	8	from	from	ADP
ejpam-6763	489	9	ϑi2	ϑi2	NOUN
ejpam-6763	489	10	=	=	SYM
ejpam-6763	489	11	(	(	PUNCT
ejpam-6763	489	12	nh)2	nh)2	PROPN
ejpam-6763	489	13	6	6	NUM
ejpam-6763	489	14	d2b{c,3	d2b{c,3	PROPN
ejpam-6763	489	15	}	}	PUNCT
ejpam-6763	489	16	i1	i1	NOUN
ejpam-6763	489	17	(	(	PUNCT
ejpam-6763	490	1	x	x	NOUN
ejpam-6763	490	2	?	?	PUNCT
ejpam-6763	490	3	)	)	PUNCT
ejpam-6763	490	4	dx?2	dx?2	PROPN
ejpam-6763	491	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6763	491	2	x?=a	x?=a	PROPN
ejpam-6763	492	1	−	−	PROPN
ejpam-6763	492	2	ϑi0	ϑi0	NOUN
ejpam-6763	492	3	+	+	CCONJ
ejpam-6763	492	4	2ϑi1	2ϑi1	NUM
ejpam-6763	492	5	,	,	PUNCT
ejpam-6763	492	6	where	where	SCONJ
ejpam-6763	492	7	the	the	DET
ejpam-6763	492	8	second	second	ADJ
ejpam-6763	492	9	derivative	derivative	NOUN
ejpam-6763	492	10	is	be	AUX
ejpam-6763	492	11	approximated	approximate	VERB
ejpam-6763	492	12	using	use	VERB
ejpam-6763	492	13	a	a	DET
ejpam-6763	492	14	forward	forward	ADJ
ejpam-6763	492	15	difference	difference	NOUN
ejpam-6763	492	16	formula	formula	NOUN
ejpam-6763	492	17	:	:	PUNCT
ejpam-6763	492	18	d2b{c,3	d2b{c,3	PROPN
ejpam-6763	492	19	}	}	PUNCT
ejpam-6763	492	20	i1	i1	PROPN
ejpam-6763	492	21	(	(	PUNCT
ejpam-6763	492	22	x	x	NOUN
ejpam-6763	492	23	?	?	PUNCT
ejpam-6763	492	24	)	)	PUNCT
ejpam-6763	492	25	dx?2	dx?2	PROPN
ejpam-6763	493	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	493	2	x?=a	x?=a	PROPN
ejpam-6763	494	1	≈	≈	PROPN
ejpam-6763	494	2	y	y	PROPN
ejpam-6763	494	3	′′	′′	PROPN
ejpam-6763	494	4	i	i	PRON
ejpam-6763	494	5	(	(	PUNCT
ejpam-6763	494	6	x	x	X
ejpam-6763	494	7	?	?	PUNCT
ejpam-6763	494	8	r	r	X
ejpam-6763	494	9	)	)	PUNCT
ejpam-6763	494	10	≈	≈	PROPN
ejpam-6763	494	11	y(p	y(p	PROPN
ejpam-6763	494	12	)	)	PUNCT
ejpam-6763	494	13	i	i	PRON
ejpam-6763	494	14	(	(	PUNCT
ejpam-6763	494	15	x?r+2)−	x?r+2)−	PROPN
ejpam-6763	494	16	2y(p	2y(p	NUM
ejpam-6763	494	17	)	)	PUNCT
ejpam-6763	495	1	i	i	PRON
ejpam-6763	495	2	(	(	PUNCT
ejpam-6763	495	3	x?r+1	x?r+1	NOUN
ejpam-6763	495	4	)	)	PUNCT
ejpam-6763	496	1	+	+	NUM
ejpam-6763	496	2	yi(x	yi(x	NOUN
ejpam-6763	496	3	?	?	PUNCT
ejpam-6763	497	1	r	r	X
ejpam-6763	497	2	)	)	PUNCT
ejpam-6763	497	3	h2	h2	NOUN
ejpam-6763	497	4	in	in	ADP
ejpam-6763	497	5	this	this	DET
ejpam-6763	497	6	case	case	NOUN
ejpam-6763	497	7	,	,	PUNCT
ejpam-6763	497	8	yi(x	yi(x	NOUN
ejpam-6763	497	9	?	?	PUNCT
ejpam-6763	498	1	r	r	X
ejpam-6763	498	2	)	)	PUNCT
ejpam-6763	498	3	is	be	AUX
ejpam-6763	498	4	known	know	VERB
ejpam-6763	498	5	from	from	ADP
ejpam-6763	498	6	the	the	DET
ejpam-6763	498	7	initial	initial	ADJ
ejpam-6763	498	8	condition	condition	NOUN
ejpam-6763	498	9	(	(	PUNCT
ejpam-6763	498	10	2	2	NUM
ejpam-6763	498	11	)	)	PUNCT
ejpam-6763	498	12	,	,	PUNCT
ejpam-6763	498	13	and	and	CCONJ
ejpam-6763	498	14	y(p	y(p	NUM
ejpam-6763	498	15	)	)	PUNCT
ejpam-6763	498	16	i	i	PRON
ejpam-6763	498	17	(	(	PUNCT
ejpam-6763	498	18	x?r+2	x?r+2	NOUN
ejpam-6763	498	19	)	)	PUNCT
ejpam-6763	498	20	and	and	CCONJ
ejpam-6763	498	21	y(p	y(p	PROPN
ejpam-6763	498	22	)	)	PUNCT
ejpam-6763	499	1	i	i	PRON
ejpam-6763	499	2	(	(	PUNCT
ejpam-6763	499	3	x?r+1	x?r+1	NOUN
ejpam-6763	499	4	)	)	PUNCT
ejpam-6763	499	5	are	be	AUX
ejpam-6763	499	6	determined	determine	VERB
ejpam-6763	499	7	from	from	ADP
ejpam-6763	499	8	the	the	DET
ejpam-6763	499	9	first	first	ADJ
ejpam-6763	499	10	-	-	PUNCT
ejpam-6763	499	11	order	order	NOUN
ejpam-6763	499	12	b	b	X
ejpam-6763	499	13	-	-	NOUN
ejpam-6763	499	14	spline	spline	NOUN
ejpam-6763	500	1	[	[	X
ejpam-6763	500	2	31	31	NUM
ejpam-6763	500	3	]	]	PUNCT
ejpam-6763	500	4	.	.	PUNCT
ejpam-6763	501	1	•	•	NOUN
ejpam-6763	501	2	ϑi3	ϑi3	NOUN
ejpam-6763	501	3	is	be	AUX
ejpam-6763	501	4	determined	determine	VERB
ejpam-6763	501	5	from	from	ADP
ejpam-6763	501	6	the	the	DET
ejpam-6763	501	7	system	system	NOUN
ejpam-6763	501	8	of	of	ADP
ejpam-6763	501	9	(	(	PUNCT
ejpam-6763	501	10	vide’s	vide’s	NOUN
ejpam-6763	501	11	-	-	PUNCT
ejpam-6763	501	12	cf	cf	NOUN
ejpam-6763	501	13	)	)	PUNCT
ejpam-6763	501	14	in	in	ADP
ejpam-6763	501	15	(	(	PUNCT
ejpam-6763	501	16	1	1	NUM
ejpam-6763	501	17	)	)	PUNCT
ejpam-6763	501	18	.	.	PUNCT
ejpam-6763	502	1	let	let	VERB
ejpam-6763	502	2	the	the	DET
ejpam-6763	502	3	unknown	unknown	ADJ
ejpam-6763	502	4	function	function	NOUN
ejpam-6763	502	5	b{c,3	b{c,3	NOUN
ejpam-6763	502	6	}	}	PUNCT
ejpam-6763	502	7	i	i	PRON
ejpam-6763	502	8	(	(	PUNCT
ejpam-6763	502	9	x	x	NOUN
ejpam-6763	502	10	?	?	PUNCT
ejpam-6763	502	11	)	)	PUNCT
ejpam-6763	502	12	be	be	AUX
ejpam-6763	502	13	approximated	approximate	VERB
ejpam-6763	502	14	using	use	VERB
ejpam-6763	502	15	cubic	cubic	ADJ
ejpam-6763	502	16	b	b	PROPN
ejpam-6763	502	17	-	-	PUNCT
ejpam-6763	502	18	spline	spline	NOUN
ejpam-6763	502	19	interpolation	interpolation	NOUN
ejpam-6763	502	20	of	of	ADP
ejpam-6763	502	21	degree	degree	NOUN
ejpam-6763	502	22	3	3	NUM
ejpam-6763	502	23	,	,	PUNCT
ejpam-6763	502	24	as	as	SCONJ
ejpam-6763	502	25	given	give	VERB
ejpam-6763	502	26	in	in	ADP
ejpam-6763	502	27	(	(	PUNCT
ejpam-6763	502	28	21	21	NUM
ejpam-6763	502	29	)	)	PUNCT
ejpam-6763	502	30	.	.	PUNCT
ejpam-6763	503	1	substituting	substitute	VERB
ejpam-6763	503	2	this	this	DET
ejpam-6763	503	3	approximation	approximation	NOUN
ejpam-6763	503	4	into	into	ADP
ejpam-6763	503	5	(	(	PUNCT
ejpam-6763	503	6	1	1	NUM
ejpam-6763	503	7	)	)	PUNCT
ejpam-6763	503	8	,	,	PUNCT
ejpam-6763	503	9	we	we	PRON
ejpam-6763	503	10	obtain	obtain	VERB
ejpam-6763	503	11	:	:	PUNCT
ejpam-6763	503	12	pi(x	pi(x	NUM
ejpam-6763	503	13	?	?	PUNCT
ejpam-6763	503	14	)	)	PUNCT
ejpam-6763	504	1	d	d	X
ejpam-6763	504	2	dx	dx	PROPN
ejpam-6763	504	3	?	?	PUNCT
ejpam-6763	505	1	(	(	PUNCT
ejpam-6763	505	2	n∑	n∑	NOUN
ejpam-6763	505	3	z=0	z=0	PROPN
ejpam-6763	505	4	ϑiz	ϑiz	NOUN
ejpam-6763	505	5	bk	bk	ADP
ejpam-6763	505	6	iz(x	iz(x	NOUN
ejpam-6763	505	7	?	?	PUNCT
ejpam-6763	505	8	)	)	PUNCT
ejpam-6763	505	9	)	)	PUNCT
ejpam-6763	506	1	+	+	CCONJ
ejpam-6763	506	2	ai0(x	ai0(x	ADV
ejpam-6763	506	3	?	?	PUNCT
ejpam-6763	506	4	)	)	PUNCT
ejpam-6763	506	5	cad	cad	PROPN
ejpam-6763	506	6	σi0	σi0	NOUN
ejpam-6763	506	7	x	x	X
ejpam-6763	506	8	?	?	PUNCT
ejpam-6763	507	1	(	(	PUNCT
ejpam-6763	507	2	n∑	n∑	NOUN
ejpam-6763	507	3	z=0	z=0	PROPN
ejpam-6763	507	4	ϑiz	ϑiz	NOUN
ejpam-6763	507	5	bk	bk	ADP
ejpam-6763	507	6	iz(x	iz(x	NOUN
ejpam-6763	507	7	?	?	PUNCT
ejpam-6763	507	8	)	)	PUNCT
ejpam-6763	507	9	)	)	PUNCT
ejpam-6763	508	1	+	+	CCONJ
ejpam-6763	508	2	ai1(x	ai1(x	NOUN
ejpam-6763	508	3	?	?	PUNCT
ejpam-6763	508	4	)	)	PUNCT
ejpam-6763	509	1	n∑	n∑	NOUN
ejpam-6763	509	2	z=0	z=0	NUM
ejpam-6763	509	3	ϑiz	ϑiz	ADV
ejpam-6763	509	4	bk	bk	ADP
ejpam-6763	509	5	iz(x	iz(x	NOUN
ejpam-6763	509	6	?	?	PUNCT
ejpam-6763	509	7	)	)	PUNCT
ejpam-6763	510	1	=	=	SYM
ejpam-6763	510	2	fi(x	fi(x	NUM
ejpam-6763	510	3	?	?	PUNCT
ejpam-6763	510	4	)	)	PUNCT
ejpam-6763	511	1	+	+	CCONJ
ejpam-6763	511	2	m∑	m∑	CCONJ
ejpam-6763	511	3	j=0	j=0	PROPN
ejpam-6763	511	4	ωij	ωij	PROPN
ejpam-6763	511	5	∫	∫	PROPN
ejpam-6763	511	6	x	x	X
ejpam-6763	511	7	?	?	PUNCT
ejpam-6763	512	1	a	a	DET
ejpam-6763	512	2	kij(x	kij(x	PROPN
ejpam-6763	512	3	?	?	PUNCT
ejpam-6763	512	4	,	,	PUNCT
ejpam-6763	512	5	s	s	X
ejpam-6763	512	6	)	)	PUNCT
ejpam-6763	512	7	cad	cad	PROPN
ejpam-6763	512	8	βij	βij	PROPN
ejpam-6763	512	9	s	s	PART
ejpam-6763	512	10	(	(	PUNCT
ejpam-6763	512	11	n∑	n∑	ADJ
ejpam-6763	512	12	z=0	z=0	PROPN
ejpam-6763	512	13	ϑjz	ϑjz	NOUN
ejpam-6763	512	14	bk	bk	NOUN
ejpam-6763	512	15	jz(s	jz(s	PROPN
ejpam-6763	512	16	)	)	PUNCT
ejpam-6763	512	17	)	)	PUNCT
ejpam-6763	513	1	ds	ds	INTJ
ejpam-6763	513	2	(	(	PUNCT
ejpam-6763	513	3	22	22	NUM
ejpam-6763	513	4	)	)	PUNCT
ejpam-6763	513	5	d.	d.	PROPN
ejpam-6763	513	6	kh	kh	PROPN
ejpam-6763	513	7	.	.	PUNCT
ejpam-6763	514	1	abdullah	abdullah	PROPN
ejpam-6763	514	2	,	,	PUNCT
ejpam-6763	514	3	sh	sh	PROPN
ejpam-6763	514	4	.	.	PROPN
ejpam-6763	514	5	sh	sh	PROPN
ejpam-6763	514	6	.	.	PROPN
ejpam-6763	514	7	ahmed	ahmed	PROPN
ejpam-6763	514	8	,	,	PUNCT
ejpam-6763	514	9	k.	k.	PROPN
ejpam-6763	514	10	h.	h.	PROPN
ejpam-6763	514	11	f.	f.	PROPN
ejpam-6763	514	12	jwamer	jwamer	PROPN
ejpam-6763	514	13	/	/	SYM
ejpam-6763	514	14	eur	eur	PROPN
ejpam-6763	514	15	.	.	PUNCT
ejpam-6763	515	1	j.	j.	PROPN
ejpam-6763	515	2	pure	pure	PROPN
ejpam-6763	515	3	appl	appl	PROPN
ejpam-6763	515	4	.	.	PROPN
ejpam-6763	515	5	math	math	PROPN
ejpam-6763	515	6	,	,	PUNCT
ejpam-6763	515	7	18	18	NUM
ejpam-6763	515	8	(	(	PUNCT
ejpam-6763	515	9	4	4	NUM
ejpam-6763	515	10	)	)	PUNCT
ejpam-6763	515	11	(	(	PUNCT
ejpam-6763	515	12	2025	2025	NUM
ejpam-6763	515	13	)	)	PUNCT
ejpam-6763	515	14	,	,	PUNCT
ejpam-6763	515	15	6763	6763	NUM
ejpam-6763	515	16	12	12	NUM
ejpam-6763	515	17	of	of	ADP
ejpam-6763	515	18	40	40	NUM
ejpam-6763	515	19	consequently	consequently	ADV
ejpam-6763	515	20	,	,	PUNCT
ejpam-6763	515	21	applying	apply	VERB
ejpam-6763	515	22	the	the	DET
ejpam-6763	515	23	linearity	linearity	NOUN
ejpam-6763	515	24	property	property	NOUN
ejpam-6763	515	25	of	of	ADP
ejpam-6763	515	26	the	the	DET
ejpam-6763	515	27	caputo	caputo	PROPN
ejpam-6763	515	28	fractional	fractional	PROPN
ejpam-6763	515	29	derivative	derivative	NOUN
ejpam-6763	515	30	from	from	ADP
ejpam-6763	515	31	definition	definition	NOUN
ejpam-6763	515	32	2	2	NUM
ejpam-6763	515	33	,	,	PUNCT
ejpam-6763	515	34	along	along	ADP
ejpam-6763	515	35	with	with	ADP
ejpam-6763	515	36	the	the	DET
ejpam-6763	515	37	standard	standard	ADJ
ejpam-6763	515	38	derivative	derivative	NOUN
ejpam-6763	515	39	,	,	PUNCT
ejpam-6763	515	40	we	we	PRON
ejpam-6763	515	41	derive	derive	VERB
ejpam-6763	515	42	the	the	DET
ejpam-6763	515	43	following	follow	VERB
ejpam-6763	515	44	expression	expression	NOUN
ejpam-6763	515	45	:	:	PUNCT
ejpam-6763	515	46	pi(x	pi(x	NOUN
ejpam-6763	515	47	?	?	PUNCT
ejpam-6763	515	48	)	)	PUNCT
ejpam-6763	516	1	n∑	n∑	NOUN
ejpam-6763	516	2	z=0	z=0	PROPN
ejpam-6763	517	1	ϑiz	ϑiz	PROPN
ejpam-6763	517	2	d	d	NOUN
ejpam-6763	517	3	dx	dx	PROPN
ejpam-6763	517	4	?	?	PUNCT
ejpam-6763	518	1	[	[	PUNCT
ejpam-6763	518	2	bk	bk	NOUN
ejpam-6763	518	3	iz(x	iz(x	NOUN
ejpam-6763	518	4	?	?	PUNCT
ejpam-6763	518	5	)	)	PUNCT
ejpam-6763	518	6	]	]	PUNCT
ejpam-6763	519	1	+	+	CCONJ
ejpam-6763	519	2	ai0(x	ai0(x	NOUN
ejpam-6763	519	3	?	?	PUNCT
ejpam-6763	519	4	)	)	PUNCT
ejpam-6763	520	1	n∑	n∑	NOUN
ejpam-6763	520	2	z=0	z=0	PROPN
ejpam-6763	520	3	ϑiz	ϑiz	PROPN
ejpam-6763	520	4	c	c	PROPN
ejpam-6763	520	5	ad	ad	NOUN
ejpam-6763	520	6	σi0	σi0	NOUN
ejpam-6763	520	7	x	x	X
ejpam-6763	520	8	?	?	PUNCT
ejpam-6763	521	1	[	[	PUNCT
ejpam-6763	521	2	bk	bk	NOUN
ejpam-6763	521	3	iz(x	iz(x	NOUN
ejpam-6763	521	4	?	?	PUNCT
ejpam-6763	521	5	)	)	PUNCT
ejpam-6763	521	6	]	]	PUNCT
ejpam-6763	522	1	+	+	CCONJ
ejpam-6763	522	2	ai1(x	ai1(x	NOUN
ejpam-6763	522	3	?	?	PUNCT
ejpam-6763	522	4	)	)	PUNCT
ejpam-6763	523	1	n∑	n∑	NOUN
ejpam-6763	523	2	z=0	z=0	NUM
ejpam-6763	523	3	ϑiz	ϑiz	ADV
ejpam-6763	523	4	bk	bk	ADP
ejpam-6763	523	5	iz(x	iz(x	NOUN
ejpam-6763	523	6	?	?	PUNCT
ejpam-6763	523	7	)	)	PUNCT
ejpam-6763	524	1	=	=	SYM
ejpam-6763	524	2	fi(x	fi(x	NUM
ejpam-6763	524	3	?	?	PUNCT
ejpam-6763	524	4	)	)	PUNCT
ejpam-6763	525	1	+	+	CCONJ
ejpam-6763	525	2	m∑	m∑	CCONJ
ejpam-6763	525	3	j=0	j=0	PROPN
ejpam-6763	525	4	ωij	ωij	PROPN
ejpam-6763	525	5	∫	∫	PROPN
ejpam-6763	525	6	x	x	X
ejpam-6763	525	7	?	?	PUNCT
ejpam-6763	526	1	a	a	DET
ejpam-6763	526	2	kij(x	kij(x	PROPN
ejpam-6763	526	3	?	?	PUNCT
ejpam-6763	526	4	,	,	PUNCT
ejpam-6763	526	5	s	s	X
ejpam-6763	526	6	)	)	PUNCT
ejpam-6763	526	7	n∑	n∑	NOUN
ejpam-6763	526	8	z=0	z=0	PROPN
ejpam-6763	526	9	ϑjz	ϑjz	NOUN
ejpam-6763	526	10	c	c	PROPN
ejpam-6763	526	11	ad	ad	NOUN
ejpam-6763	526	12	βij	βij	NOUN
ejpam-6763	526	13	s	s	X
ejpam-6763	526	14	[	[	PUNCT
ejpam-6763	526	15	bk	bk	NOUN
ejpam-6763	526	16	jz(s	jz(s	PROPN
ejpam-6763	526	17	)	)	PUNCT
ejpam-6763	526	18	]	]	PUNCT
ejpam-6763	527	1	ds	ds	INTJ
ejpam-6763	527	2	(	(	PUNCT
ejpam-6763	527	3	23	23	NUM
ejpam-6763	527	4	)	)	PUNCT
ejpam-6763	527	5	by	by	ADP
ejpam-6763	527	6	defining	define	VERB
ejpam-6763	527	7	x	x	PRON
ejpam-6763	527	8	?	?	PUNCT
ejpam-6763	527	9	=	=	PUNCT
ejpam-6763	527	10	x?r+1	x?r+1	PROPN
ejpam-6763	527	11	and	and	CCONJ
ejpam-6763	527	12	analyzing	analyze	VERB
ejpam-6763	527	13	the	the	DET
ejpam-6763	527	14	collocation	collocation	NOUN
ejpam-6763	527	15	points	point	NOUN
ejpam-6763	527	16	,	,	PUNCT
ejpam-6763	527	17	we	we	PRON
ejpam-6763	527	18	employ	employ	VERB
ejpam-6763	527	19	a	a	DET
ejpam-6763	527	20	cubic	cubic	ADJ
ejpam-6763	527	21	b	b	NOUN
ejpam-6763	527	22	-	-	PUNCT
ejpam-6763	527	23	spline	spline	NOUN
ejpam-6763	527	24	function	function	NOUN
ejpam-6763	527	25	(	(	PUNCT
ejpam-6763	527	26	k	k	NOUN
ejpam-6763	527	27	=	=	SYM
ejpam-6763	527	28	3	3	NUM
ejpam-6763	527	29	,	,	PUNCT
ejpam-6763	527	30	n	n	NOUN
ejpam-6763	527	31	=	=	SYM
ejpam-6763	527	32	3	3	NUM
ejpam-6763	527	33	)	)	PUNCT
ejpam-6763	527	34	within	within	ADP
ejpam-6763	527	35	the	the	DET
ejpam-6763	527	36	interval	interval	NOUN
ejpam-6763	528	1	[	[	X
ejpam-6763	528	2	x?r	x?r	X
ejpam-6763	528	3	,	,	PUNCT
ejpam-6763	528	4	x	x	PUNCT
ejpam-6763	528	5	?	?	PUNCT
ejpam-6763	529	1	r+1	r+1	NOUN
ejpam-6763	529	2	]	]	X
ejpam-6763	529	3	.	.	PUNCT
ejpam-6763	530	1	we	we	PRON
ejpam-6763	530	2	then	then	ADV
ejpam-6763	530	3	apply	apply	VERB
ejpam-6763	530	4	the	the	DET
ejpam-6763	530	5	fractional	fractional	ADJ
ejpam-6763	530	6	derivative	derivative	NOUN
ejpam-6763	530	7	in	in	ADP
ejpam-6763	530	8	the	the	DET
ejpam-6763	530	9	caputo	caputo	PROPN
ejpam-6763	530	10	sense	sense	NOUN
ejpam-6763	530	11	.	.	PUNCT
ejpam-6763	531	1	from	from	ADP
ejpam-6763	531	2	(	(	PUNCT
ejpam-6763	531	3	16	16	NUM
ejpam-6763	531	4	)	)	PUNCT
ejpam-6763	531	5	,	,	PUNCT
ejpam-6763	531	6	the	the	DET
ejpam-6763	531	7	fractional	fractional	ADJ
ejpam-6763	531	8	orders	order	NOUN
ejpam-6763	531	9	σi0	σi0	NOUN
ejpam-6763	531	10	,	,	PUNCT
ejpam-6763	531	11	βij	βij	NOUN
ejpam-6763	531	12	∈	∈	PROPN
ejpam-6763	531	13	(	(	PUNCT
ejpam-6763	531	14	0	0	NUM
ejpam-6763	531	15	,	,	PUNCT
ejpam-6763	531	16	1	1	NUM
ejpam-6763	531	17	]	]	PUNCT
ejpam-6763	531	18	for	for	ADP
ejpam-6763	531	19	all	all	DET
ejpam-6763	531	20	i	i	PROPN
ejpam-6763	531	21	,	,	PUNCT
ejpam-6763	531	22	j	j	PROPN
ejpam-6763	531	23	=	=	SYM
ejpam-6763	531	24	0	0	NUM
ejpam-6763	531	25	,	,	PUNCT
ejpam-6763	531	26	1	1	NUM
ejpam-6763	531	27	,	,	PUNCT
ejpam-6763	531	28	.	.	PUNCT
ejpam-6763	531	29	.	.	PUNCT
ejpam-6763	531	30	.	.	PUNCT
ejpam-6763	532	1	,	,	PUNCT
ejpam-6763	532	2	m	m	AUX
ejpam-6763	532	3	,	,	PUNCT
ejpam-6763	532	4	yielding	yield	VERB
ejpam-6763	532	5	results	result	NOUN
ejpam-6763	532	6	for	for	ADP
ejpam-6763	532	7	each	each	DET
ejpam-6763	532	8	r	r	NOUN
ejpam-6763	532	9	=	=	SYM
ejpam-6763	532	10	0	0	NUM
ejpam-6763	532	11	,	,	PUNCT
ejpam-6763	532	12	1	1	NUM
ejpam-6763	532	13	,	,	PUNCT
ejpam-6763	532	14	.	.	PUNCT
ejpam-6763	532	15	.	.	PUNCT
ejpam-6763	533	1	.	.	PUNCT
ejpam-6763	534	1	,	,	PUNCT
ejpam-6763	535	1	n	n	CCONJ
ejpam-6763	535	2	−	−	PROPN
ejpam-6763	535	3	1	1	NUM
ejpam-6763	535	4	.	.	PUNCT
ejpam-6763	535	5	pi(x	pi(x	NOUN
ejpam-6763	535	6	?	?	PUNCT
ejpam-6763	536	1	r+1	r+1	NOUN
ejpam-6763	536	2	)	)	PUNCT
ejpam-6763	536	3	{	{	PUNCT
ejpam-6763	536	4	−3ϑi0(b−	−3ϑi0(b−	PROPN
ejpam-6763	536	5	x?r+1	x?r+1	NOUN
ejpam-6763	536	6	)	)	PUNCT
ejpam-6763	536	7	2	2	NUM
ejpam-6763	536	8	(	(	PUNCT
ejpam-6763	536	9	nh)3	nh)3	VERB
ejpam-6763	536	10	+	+	SYM
ejpam-6763	536	11	3ϑi1	3ϑi1	NUM
ejpam-6763	537	1	[	[	X
ejpam-6763	537	2	−2(x?r+1	−2(x?r+1	NOUN
ejpam-6763	537	3	−	−	PROPN
ejpam-6763	537	4	a)(b−	a)(b−	PROPN
ejpam-6763	537	5	x?r+1	x?r+1	PROPN
ejpam-6763	537	6	)	)	PUNCT
ejpam-6763	537	7	(	(	PUNCT
ejpam-6763	537	8	nh)3	nh)3	VERB
ejpam-6763	537	9	+	+	CCONJ
ejpam-6763	537	10	(	(	PUNCT
ejpam-6763	537	11	b−	b−	PROPN
ejpam-6763	537	12	x?r+1	x?r+1	PROPN
ejpam-6763	537	13	)	)	PUNCT
ejpam-6763	537	14	2	2	NUM
ejpam-6763	537	15	(	(	PUNCT
ejpam-6763	537	16	nh)3	nh)3	ADV
ejpam-6763	537	17	]	]	PUNCT
ejpam-6763	538	1	+3ϑi2	+3ϑi2	PUNCT
ejpam-6763	538	2	[	[	X
ejpam-6763	538	3	−(x?r+1	−(x?r+1	X
ejpam-6763	538	4	−	−	NOUN
ejpam-6763	538	5	a)2	a)2	PROPN
ejpam-6763	538	6	(	(	PUNCT
ejpam-6763	538	7	nh)3	nh)3	PROPN
ejpam-6763	538	8	+	+	CCONJ
ejpam-6763	538	9	2(b−	2(b−	NUM
ejpam-6763	538	10	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	538	11	?	?	PUNCT
ejpam-6763	539	1	r+1	r+1	PROPN
ejpam-6763	540	1	−	−	PROPN
ejpam-6763	540	2	a	a	NOUN
ejpam-6763	540	3	)	)	PUNCT
ejpam-6763	540	4	(	(	PUNCT
ejpam-6763	540	5	nh)3	nh)3	ADV
ejpam-6763	540	6	]	]	PUNCT
ejpam-6763	541	1	+	+	CCONJ
ejpam-6763	541	2	3ϑi3	3ϑi3	NUM
ejpam-6763	541	3	·	·	PUNCT
ejpam-6763	541	4	(	(	PUNCT
ejpam-6763	541	5	x?r+1	x?r+1	INTJ
ejpam-6763	541	6	−	−	PROPN
ejpam-6763	541	7	a)2	a)2	PROPN
ejpam-6763	541	8	(	(	PUNCT
ejpam-6763	541	9	nh)3	nh)3	PROPN
ejpam-6763	541	10	}	}	PUNCT
ejpam-6763	541	11	+	+	PROPN
ejpam-6763	541	12	ai0(x	ai0(x	PROPN
ejpam-6763	541	13	?	?	PUNCT
ejpam-6763	542	1	r+1	r+1	NOUN
ejpam-6763	542	2	)	)	PUNCT
ejpam-6763	542	3	·	·	PUNCT
ejpam-6763	543	1	(	(	PUNCT
ejpam-6763	543	2	x?r+1	x?r+1	INTJ
ejpam-6763	543	3	−	−	X
ejpam-6763	543	4	a)1−σi0	a)1−σi0	PROPN
ejpam-6763	543	5	(	(	PUNCT
ejpam-6763	543	6	nh)3	nh)3	PROPN
ejpam-6763	543	7	γ(4−	γ(4−	PROPN
ejpam-6763	543	8	σi0	σi0	PROPN
ejpam-6763	543	9	)	)	PUNCT
ejpam-6763	543	10	·	·	PUNCT
ejpam-6763	543	11	{	{	PUNCT
ejpam-6763	543	12	ϑi0	ϑi0	NOUN
ejpam-6763	543	13	[	[	PUNCT
ejpam-6763	543	14	−	−	PROPN
ejpam-6763	543	15	3(nh)2(2−	3(nh)2(2−	NUM
ejpam-6763	543	16	σi0)(3−	σi0)(3−	ADJ
ejpam-6763	543	17	σi0	σi0	NOUN
ejpam-6763	543	18	)	)	PUNCT
ejpam-6763	543	19	+6(nh)(3−	+6(nh)(3−	ADP
ejpam-6763	543	20	σi0)−	σi0)−	PROPN
ejpam-6763	543	21	6(x?r+1	6(x?r+1	PROPN
ejpam-6763	543	22	−	−	PROPN
ejpam-6763	543	23	a)2	a)2	PROPN
ejpam-6763	543	24	]	]	PUNCT
ejpam-6763	543	25	+	+	PUNCT
ejpam-6763	544	1	ϑi1	ϑi1	X
ejpam-6763	545	1	[	[	PUNCT
ejpam-6763	546	1	(	(	PUNCT
ejpam-6763	546	2	nh)2(2−	nh)2(2−	ADJ
ejpam-6763	546	3	σi0)(3−	σi0)(3−	ADJ
ejpam-6763	546	4	σi0	σi0	NOUN
ejpam-6763	546	5	)	)	PUNCT
ejpam-6763	547	1	−4(nh)(3−	−4(nh)(3−	PROPN
ejpam-6763	547	2	σi0)(x	σi0)(x	PROPN
ejpam-6763	547	3	?	?	PUNCT
ejpam-6763	548	1	r+1	r+1	PROPN
ejpam-6763	549	1	−	−	PROPN
ejpam-6763	549	2	a	a	X
ejpam-6763	549	3	)	)	PUNCT
ejpam-6763	550	1	+	+	NUM
ejpam-6763	550	2	6(x?r+1	6(x?r+1	NOUN
ejpam-6763	550	3	−	−	NOUN
ejpam-6763	550	4	a)2	a)2	NOUN
ejpam-6763	550	5	]	]	PUNCT
ejpam-6763	550	6	+3ϑi2	+3ϑi2	NOUN
ejpam-6763	550	7	[	[	PUNCT
ejpam-6763	550	8	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	550	9	σi0)(x	σi0)(x	PROPN
ejpam-6763	550	10	?	?	PUNCT
ejpam-6763	551	1	r+1	r+1	PROPN
ejpam-6763	552	1	−	−	PROPN
ejpam-6763	552	2	a)−	a)−	PROPN
ejpam-6763	552	3	6(x?r+1	6(x?r+1	PROPN
ejpam-6763	552	4	−	−	NOUN
ejpam-6763	552	5	a)2	a)2	NOUN
ejpam-6763	552	6	]	]	PUNCT
ejpam-6763	553	1	+	+	CCONJ
ejpam-6763	553	2	6ϑi3(x	6ϑi3(x	NUM
ejpam-6763	553	3	?	?	PUNCT
ejpam-6763	554	1	r+1	r+1	NOUN
ejpam-6763	554	2	−	−	PROPN
ejpam-6763	555	1	a)2	a)2	PROPN
ejpam-6763	555	2	}	}	PUNCT
ejpam-6763	555	3	+	+	PROPN
ejpam-6763	555	4	ai1(x	ai1(x	NOUN
ejpam-6763	555	5	?	?	PUNCT
ejpam-6763	556	1	r+1	r+1	NOUN
ejpam-6763	556	2	)	)	PUNCT
ejpam-6763	556	3	·	·	PUNCT
ejpam-6763	556	4	{	{	PUNCT
ejpam-6763	557	1	ϑi0	ϑi0	NOUN
ejpam-6763	557	2	(	(	PUNCT
ejpam-6763	557	3	b−	b−	PROPN
ejpam-6763	557	4	x?r+1	x?r+1	PROPN
ejpam-6763	557	5	nh	nh	PROPN
ejpam-6763	557	6	)	)	PUNCT
ejpam-6763	557	7	3	3	NUM
ejpam-6763	558	1	+	+	NUM
ejpam-6763	558	2	3ϑi1	3ϑi1	NUM
ejpam-6763	558	3	(	(	PUNCT
ejpam-6763	558	4	x?r+1	x?r+1	INTJ
ejpam-6763	558	5	−	−	PROPN
ejpam-6763	558	6	a	a	DET
ejpam-6763	558	7	nh	nh	NOUN
ejpam-6763	558	8	)	)	PUNCT
ejpam-6763	558	9	(	(	PUNCT
ejpam-6763	558	10	b−	b−	PROPN
ejpam-6763	558	11	x?r+1	x?r+1	PROPN
ejpam-6763	558	12	nh	nh	PROPN
ejpam-6763	558	13	)	)	PUNCT
ejpam-6763	558	14	2	2	NUM
ejpam-6763	558	15	+3ϑi2	+3ϑi2	NOUN
ejpam-6763	558	16	(	(	PUNCT
ejpam-6763	558	17	x?r+1	x?r+1	INTJ
ejpam-6763	558	18	−	−	PROPN
ejpam-6763	558	19	a	a	DET
ejpam-6763	558	20	nh	nh	PROPN
ejpam-6763	558	21	)	)	PUNCT
ejpam-6763	558	22	2(b−	2(b−	PROPN
ejpam-6763	558	23	x?r+1	x?r+1	PROPN
ejpam-6763	558	24	nh	nh	PROPN
ejpam-6763	558	25	)	)	PUNCT
ejpam-6763	559	1	+	+	CCONJ
ejpam-6763	559	2	ϑi3	ϑi3	PROPN
ejpam-6763	559	3	(	(	PUNCT
ejpam-6763	559	4	x?r+1	x?r+1	PROPN
ejpam-6763	559	5	−	−	PROPN
ejpam-6763	559	6	a	a	DET
ejpam-6763	559	7	nh	nh	PROPN
ejpam-6763	559	8	)	)	PUNCT
ejpam-6763	559	9	3	3	NUM
ejpam-6763	559	10	}	}	PUNCT
ejpam-6763	559	11	=	=	SYM
ejpam-6763	559	12	fi(x	fi(x	NOUN
ejpam-6763	559	13	?	?	PUNCT
ejpam-6763	560	1	r+1	r+1	NOUN
ejpam-6763	560	2	)	)	PUNCT
ejpam-6763	561	1	+	+	CCONJ
ejpam-6763	561	2	m∑	m∑	ADV
ejpam-6763	561	3	j=1	j=1	ADJ
ejpam-6763	561	4	ωij	ωij	PROPN
ejpam-6763	561	5	{	{	PUNCT
ejpam-6763	561	6	r−1∑	r−1∑	PROPN
ejpam-6763	561	7	q=0	q=0	PROPN
ejpam-6763	561	8	∫	∫	PROPN
ejpam-6763	561	9	x	x	X
ejpam-6763	561	10	?	?	PUNCT
ejpam-6763	562	1	q+1	q+1	NUM
ejpam-6763	563	1	x	x	X
ejpam-6763	563	2	?	?	PUNCT
ejpam-6763	563	3	q	q	PROPN
ejpam-6763	564	1	kij(x	kij(x	X
ejpam-6763	564	2	?	?	PUNCT
ejpam-6763	565	1	r+1	r+1	NOUN
ejpam-6763	565	2	,	,	PUNCT
ejpam-6763	565	3	s	s	NOUN
ejpam-6763	565	4	)	)	PUNCT
ejpam-6763	565	5	·	·	PUNCT
ejpam-6763	565	6	(	(	PUNCT
ejpam-6763	565	7	s−	s−	PROPN
ejpam-6763	565	8	a)1−βij	a)1−βij	PROPN
ejpam-6763	565	9	(	(	PUNCT
ejpam-6763	565	10	nh)3	nh)3	PROPN
ejpam-6763	565	11	γ(4−	γ(4−	PROPN
ejpam-6763	565	12	βij	βij	PROPN
ejpam-6763	565	13	)	)	PUNCT
ejpam-6763	565	14	·	·	PUNCT
ejpam-6763	566	1	[	[	PUNCT
ejpam-6763	566	2	ϑj0	ϑj0	NOUN
ejpam-6763	566	3	(	(	PUNCT
ejpam-6763	566	4	−3(nh)2(2−	−3(nh)2(2−	PROPN
ejpam-6763	566	5	βij)(3−	βij)(3−	NUM
ejpam-6763	566	6	βij	βij	NOUN
ejpam-6763	566	7	)	)	PUNCT
ejpam-6763	566	8	+	+	CCONJ
ejpam-6763	566	9	6(nh)(3−	6(nh)(3−	NUM
ejpam-6763	566	10	βij)−	βij)−	NOUN
ejpam-6763	566	11	6(s−	6(s−	NUM
ejpam-6763	566	12	a)2	a)2	NOUN
ejpam-6763	566	13	)	)	PUNCT
ejpam-6763	566	14	+3ϑj1	+3ϑj1	NOUN
ejpam-6763	566	15	(	(	PUNCT
ejpam-6763	566	16	(	(	PUNCT
ejpam-6763	566	17	nh)2(2−	nh)2(2−	NOUN
ejpam-6763	566	18	βij)(3−	βij)(3−	NUM
ejpam-6763	566	19	βij)−	βij)−	ADP
ejpam-6763	566	20	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	566	21	βij)(s−	βij)(s−	PROPN
ejpam-6763	566	22	a	a	X
ejpam-6763	566	23	)	)	PUNCT
ejpam-6763	566	24	+	+	CCONJ
ejpam-6763	566	25	6(s−	6(s−	NUM
ejpam-6763	566	26	a)2	a)2	NOUN
ejpam-6763	566	27	)	)	PUNCT
ejpam-6763	566	28	d.	d.	PROPN
ejpam-6763	566	29	kh	kh	PROPN
ejpam-6763	566	30	.	.	PUNCT
ejpam-6763	567	1	abdullah	abdullah	PROPN
ejpam-6763	567	2	,	,	PUNCT
ejpam-6763	567	3	sh	sh	PROPN
ejpam-6763	567	4	.	.	PROPN
ejpam-6763	567	5	sh	sh	PROPN
ejpam-6763	567	6	.	.	PROPN
ejpam-6763	567	7	ahmed	ahmed	PROPN
ejpam-6763	567	8	,	,	PUNCT
ejpam-6763	567	9	k.	k.	PROPN
ejpam-6763	567	10	h.	h.	PROPN
ejpam-6763	567	11	f.	f.	PROPN
ejpam-6763	567	12	jwamer	jwamer	PROPN
ejpam-6763	567	13	/	/	SYM
ejpam-6763	567	14	eur	eur	PROPN
ejpam-6763	567	15	.	.	PUNCT
ejpam-6763	568	1	j.	j.	PROPN
ejpam-6763	568	2	pure	pure	PROPN
ejpam-6763	568	3	appl	appl	PROPN
ejpam-6763	568	4	.	.	PROPN
ejpam-6763	568	5	math	math	PROPN
ejpam-6763	568	6	,	,	PUNCT
ejpam-6763	568	7	18	18	NUM
ejpam-6763	568	8	(	(	PUNCT
ejpam-6763	568	9	4	4	NUM
ejpam-6763	568	10	)	)	PUNCT
ejpam-6763	568	11	(	(	PUNCT
ejpam-6763	568	12	2025	2025	NUM
ejpam-6763	568	13	)	)	PUNCT
ejpam-6763	568	14	,	,	PUNCT
ejpam-6763	568	15	6763	6763	NUM
ejpam-6763	568	16	13	13	NUM
ejpam-6763	568	17	of	of	ADP
ejpam-6763	568	18	40	40	NUM
ejpam-6763	568	19	+3ϑj2	+3ϑj2	NOUN
ejpam-6763	568	20	(	(	PUNCT
ejpam-6763	568	21	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	568	22	βij)(s−	βij)(s−	X
ejpam-6763	568	23	a)−	a)−	ADV
ejpam-6763	568	24	6(s−	6(s−	NUM
ejpam-6763	568	25	a)2	a)2	NOUN
ejpam-6763	568	26	)	)	PUNCT
ejpam-6763	569	1	+	+	CCONJ
ejpam-6763	569	2	6ϑj3(s−	6ϑj3(s−	NUM
ejpam-6763	569	3	a)2	a)2	NOUN
ejpam-6763	569	4	]	]	PUNCT
ejpam-6763	569	5	ds	ds	PROPN
ejpam-6763	569	6	}	}	PUNCT
ejpam-6763	569	7	∫	∫	PROPN
ejpam-6763	569	8	x	x	X
ejpam-6763	569	9	?	?	PUNCT
ejpam-6763	570	1	r+1	r+1	PROPN
ejpam-6763	571	1	x	x	X
ejpam-6763	571	2	?	?	PUNCT
ejpam-6763	572	1	r	r	NOUN
ejpam-6763	572	2	kij(x	kij(x	PROPN
ejpam-6763	572	3	?	?	PUNCT
ejpam-6763	573	1	r+1	r+1	NOUN
ejpam-6763	573	2	,	,	PUNCT
ejpam-6763	573	3	s	s	NOUN
ejpam-6763	573	4	)	)	PUNCT
ejpam-6763	573	5	·	·	PUNCT
ejpam-6763	573	6	(	(	PUNCT
ejpam-6763	573	7	s−	s−	PROPN
ejpam-6763	573	8	a)1−βij	a)1−βij	PROPN
ejpam-6763	573	9	(	(	PUNCT
ejpam-6763	573	10	nh)3	nh)3	PROPN
ejpam-6763	573	11	γ(4−	γ(4−	PROPN
ejpam-6763	573	12	βij	βij	PROPN
ejpam-6763	573	13	)	)	PUNCT
ejpam-6763	573	14	·	·	PUNCT
ejpam-6763	574	1	[	[	PUNCT
ejpam-6763	574	2	ϑj0	ϑj0	NOUN
ejpam-6763	574	3	(	(	PUNCT
ejpam-6763	574	4	−3(nh)2(2−	−3(nh)2(2−	PROPN
ejpam-6763	574	5	βij)(3−	βij)(3−	NUM
ejpam-6763	574	6	βij	βij	NOUN
ejpam-6763	574	7	)	)	PUNCT
ejpam-6763	574	8	+	+	CCONJ
ejpam-6763	574	9	6(nh)(3−	6(nh)(3−	NUM
ejpam-6763	574	10	βij)−	βij)−	NOUN
ejpam-6763	574	11	6(s−	6(s−	NUM
ejpam-6763	574	12	a)2	a)2	NOUN
ejpam-6763	574	13	)	)	PUNCT
ejpam-6763	574	14	+3ϑj1	+3ϑj1	NOUN
ejpam-6763	574	15	(	(	PUNCT
ejpam-6763	574	16	(	(	PUNCT
ejpam-6763	574	17	nh)2(2−	nh)2(2−	NOUN
ejpam-6763	574	18	βij)(3−	βij)(3−	NUM
ejpam-6763	574	19	βij)−	βij)−	PROPN
ejpam-6763	574	20	2(s−	2(s−	NUM
ejpam-6763	574	21	a)−	a)−	PROPN
ejpam-6763	574	22	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	574	23	βij)(s−	βij)(s−	PROPN
ejpam-6763	574	24	a	a	PRON
ejpam-6763	574	25	)	)	PUNCT
ejpam-6763	574	26	)	)	PUNCT
ejpam-6763	574	27	+6(s−	+6(s−	NUM
ejpam-6763	574	28	a)2	a)2	PROPN
ejpam-6763	574	29	+	+	CCONJ
ejpam-6763	574	30	3ϑj2	3ϑj2	NUM
ejpam-6763	574	31	(	(	PUNCT
ejpam-6763	574	32	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	574	33	βij)(s−	βij)(s−	X
ejpam-6763	574	34	a)−	a)−	ADV
ejpam-6763	574	35	6(s−	6(s−	NUM
ejpam-6763	574	36	a)2	a)2	NOUN
ejpam-6763	574	37	)	)	PUNCT
ejpam-6763	574	38	+	+	CCONJ
ejpam-6763	574	39	6ϑj3(s−	6ϑj3(s−	NUM
ejpam-6763	574	40	a)2	a)2	NOUN
ejpam-6763	574	41	]	]	PUNCT
ejpam-6763	574	42	ds	ds	X
ejpam-6763	574	43	(	(	PUNCT
ejpam-6763	574	44	24	24	NUM
ejpam-6763	574	45	)	)	PUNCT
ejpam-6763	574	46	the	the	DET
ejpam-6763	574	47	cubic	cubic	ADJ
ejpam-6763	574	48	b	b	PROPN
ejpam-6763	574	49	-	-	PUNCT
ejpam-6763	574	50	spline	spline	NOUN
ejpam-6763	574	51	function	function	NOUN
ejpam-6763	574	52	over	over	ADP
ejpam-6763	574	53	the	the	DET
ejpam-6763	574	54	interval	interval	NOUN
ejpam-6763	574	55	[	[	X
ejpam-6763	574	56	x?r	x?r	X
ejpam-6763	574	57	,	,	PUNCT
ejpam-6763	574	58	x	x	PUNCT
ejpam-6763	574	59	?	?	PUNCT
ejpam-6763	575	1	r+1	r+1	NOUN
ejpam-6763	575	2	]	]	X
ejpam-6763	575	3	is	be	AUX
ejpam-6763	575	4	optimized	optimize	VERB
ejpam-6763	575	5	to	to	PART
ejpam-6763	575	6	simplify	simplify	VERB
ejpam-6763	575	7	its	its	PRON
ejpam-6763	575	8	representation	representation	NOUN
ejpam-6763	575	9	and	and	CCONJ
ejpam-6763	575	10	promote	promote	VERB
ejpam-6763	575	11	efficient	efficient	ADJ
ejpam-6763	575	12	solution	solution	NOUN
ejpam-6763	575	13	methods	method	NOUN
ejpam-6763	575	14	in	in	ADP
ejpam-6763	575	15	practice	practice	NOUN
ejpam-6763	575	16	,	,	PUNCT
ejpam-6763	575	17	these	these	DET
ejpam-6763	575	18	integrals	integral	NOUN
ejpam-6763	575	19	must	must	AUX
ejpam-6763	575	20	be	be	AUX
ejpam-6763	575	21	approximated	approximate	VERB
ejpam-6763	575	22	using	use	VERB
ejpam-6763	575	23	the	the	DET
ejpam-6763	575	24	clenshaw	clenshaw	ADJ
ejpam-6763	575	25	-	-	PUNCT
ejpam-6763	575	26	curtis	curtis	NOUN
ejpam-6763	575	27	quadrature	quadrature	NOUN
ejpam-6763	575	28	rule	rule	NOUN
ejpam-6763	575	29	[	[	X
ejpam-6763	575	30	12	12	NUM
ejpam-6763	575	31	,	,	PUNCT
ejpam-6763	575	32	25	25	NUM
ejpam-6763	575	33	,	,	PUNCT
ejpam-6763	575	34	26	26	NUM
ejpam-6763	575	35	]	]	PUNCT
ejpam-6763	575	36	,	,	PUNCT
ejpam-6763	575	37	hence	hence	ADV
ejpam-6763	575	38	,	,	PUNCT
ejpam-6763	575	39	(	(	PUNCT
ejpam-6763	575	40	25	25	NUM
ejpam-6763	575	41	)	)	PUNCT
ejpam-6763	575	42	is	be	AUX
ejpam-6763	575	43	applicable	applicable	ADJ
ejpam-6763	575	44	for	for	ADP
ejpam-6763	575	45	r	r	NOUN
ejpam-6763	575	46	=	=	SYM
ejpam-6763	575	47	0	0	NUM
ejpam-6763	575	48	,	,	PUNCT
ejpam-6763	575	49	1	1	NUM
ejpam-6763	575	50	,	,	PUNCT
ejpam-6763	575	51	.	.	PUNCT
ejpam-6763	575	52	.	.	PUNCT
ejpam-6763	576	1	.	.	PUNCT
ejpam-6763	577	1	,	,	PUNCT
ejpam-6763	577	2	n	n	CCONJ
ejpam-6763	577	3	−	−	PROPN
ejpam-6763	577	4	1	1	NUM
ejpam-6763	577	5	and	and	CCONJ
ejpam-6763	577	6	i	i	PRON
ejpam-6763	577	7	,	,	PUNCT
ejpam-6763	577	8	j	j	PROPN
ejpam-6763	577	9	=	=	SYM
ejpam-6763	577	10	0	0	NUM
ejpam-6763	577	11	,	,	PUNCT
ejpam-6763	577	12	1	1	NUM
ejpam-6763	577	13	,	,	PUNCT
ejpam-6763	577	14	.	.	PUNCT
ejpam-6763	577	15	.	.	PUNCT
ejpam-6763	578	1	.	.	PUNCT
ejpam-6763	579	1	,	,	PUNCT
ejpam-6763	579	2	m.	m.	NOUN
ejpam-6763	579	3	vσi0	vσi0	PROPN
ejpam-6763	579	4	i	i	PRON
ejpam-6763	579	5	,	,	PUNCT
ejpam-6763	579	6	x	x	X
ejpam-6763	579	7	?	?	PUNCT
ejpam-6763	580	1	r+1	r+1	PROPN
ejpam-6763	580	2	·	·	PUNCT
ejpam-6763	580	3	ϑi3	ϑi3	PROPN
ejpam-6763	581	1	+	+	PROPN
ejpam-6763	581	2	wσi0	wσi0	PROPN
ejpam-6763	581	3	i	i	PRON
ejpam-6763	581	4	,	,	PUNCT
ejpam-6763	581	5	x	x	X
ejpam-6763	581	6	?	?	PUNCT
ejpam-6763	582	1	r+1	r+1	PROPN
ejpam-6763	582	2	=	=	SYM
ejpam-6763	582	3	fi(x	fi(x	PROPN
ejpam-6763	582	4	?	?	PUNCT
ejpam-6763	583	1	r+1	r+1	NOUN
ejpam-6763	583	2	)	)	PUNCT
ejpam-6763	584	1	+	+	CCONJ
ejpam-6763	584	2	m∑	m∑	ADV
ejpam-6763	584	3	j=1	j=1	NOUN
ejpam-6763	584	4	ωij	ωij	VERB
ejpam-6763	584	5	{	{	PUNCT
ejpam-6763	584	6	er	er	INTJ
ejpam-6763	584	7	ij	ij	INTJ
ejpam-6763	584	8	}	}	PUNCT
ejpam-6763	584	9	+	+	CCONJ
ejpam-6763	584	10	m∑	m∑	ADV
ejpam-6763	584	11	j=1	j=1	ADJ
ejpam-6763	584	12	ωij	ωij	PROPN
ejpam-6763	584	13	{	{	PUNCT
ejpam-6763	584	14	ěr	ěr	NOUN
ejpam-6763	584	15	ij	ij	NOUN
ejpam-6763	584	16	}	}	PUNCT
ejpam-6763	584	17	·	·	PUNCT
ejpam-6763	584	18	ϑj3	ϑj3	NOUN
ejpam-6763	585	1	+	+	CCONJ
ejpam-6763	585	2	gr	gr	NUM
ejpam-6763	585	3	ij	ij	NOUN
ejpam-6763	586	1	+	+	CCONJ
ejpam-6763	587	1	ǧr	ǧr	VERB
ejpam-6763	587	2	i	i	PRON
ejpam-6763	587	3	·	·	PUNCT
ejpam-6763	587	4	ϑ03	ϑ03	PROPN
ejpam-6763	587	5	(	(	PUNCT
ejpam-6763	587	6	25	25	NUM
ejpam-6763	587	7	)	)	PUNCT
ejpam-6763	587	8	to	to	PART
ejpam-6763	587	9	obtain	obtain	VERB
ejpam-6763	587	10	the	the	DET
ejpam-6763	587	11	unique	unique	ADJ
ejpam-6763	587	12	solution	solution	NOUN
ejpam-6763	587	13	of	of	ADP
ejpam-6763	587	14	the	the	DET
ejpam-6763	587	15	system	system	NOUN
ejpam-6763	587	16	described	describe	VERB
ejpam-6763	587	17	in	in	ADP
ejpam-6763	587	18	(	(	PUNCT
ejpam-6763	587	19	26	26	NUM
ejpam-6763	587	20	)	)	PUNCT
ejpam-6763	587	21	,	,	PUNCT
ejpam-6763	587	22	we	we	PRON
ejpam-6763	587	23	require	require	VERB
ejpam-6763	587	24	three	three	NUM
ejpam-6763	587	25	additional	additional	ADJ
ejpam-6763	587	26	equations	equation	NOUN
ejpam-6763	587	27	.	.	PUNCT
ejpam-6763	588	1	these	these	PRON
ejpam-6763	588	2	are	be	AUX
ejpam-6763	588	3	obtained	obtain	VERB
ejpam-6763	588	4	by	by	ADP
ejpam-6763	588	5	computing	compute	VERB
ejpam-6763	588	6	the	the	DET
ejpam-6763	588	7	coefficients	coefficient	NOUN
ejpam-6763	588	8	ϑi0	ϑi0	PROPN
ejpam-6763	588	9	,	,	PUNCT
ejpam-6763	588	10	ϑi1	ϑi1	NOUN
ejpam-6763	588	11	,	,	PUNCT
ejpam-6763	588	12	and	and	CCONJ
ejpam-6763	588	13	ϑi2	ϑi2	NOUN
ejpam-6763	588	14	.	.	PUNCT
ejpam-6763	589	1	once	once	SCONJ
ejpam-6763	589	2	these	these	PRON
ejpam-6763	589	3	are	be	AUX
ejpam-6763	589	4	determined	determine	VERB
ejpam-6763	589	5	,	,	PUNCT
ejpam-6763	589	6	the	the	DET
ejpam-6763	589	7	remaining	remain	VERB
ejpam-6763	589	8	coefficient	coefficient	NOUN
ejpam-6763	589	9	ϑi3	ϑi3	PROPN
ejpam-6763	589	10	can	can	AUX
ejpam-6763	589	11	be	be	AUX
ejpam-6763	589	12	calculated	calculate	VERB
ejpam-6763	589	13	by	by	ADP
ejpam-6763	589	14	solving	solve	VERB
ejpam-6763	589	15	the	the	DET
ejpam-6763	589	16	following	follow	VERB
ejpam-6763	589	17	linear	linear	ADJ
ejpam-6763	589	18	system	system	NOUN
ejpam-6763	589	19	of	of	ADP
ejpam-6763	589	20	algebraic	algebraic	ADJ
ejpam-6763	589	21	equations	equation	NOUN
ejpam-6763	589	22	of	of	ADP
ejpam-6763	589	23	size	size	NOUN
ejpam-6763	589	24	(	(	PUNCT
ejpam-6763	589	25	m+	m+	NOUN
ejpam-6763	589	26	1)×	1)×	NUM
ejpam-6763	589	27	(	(	PUNCT
ejpam-6763	589	28	m+	m+	NOUN
ejpam-6763	589	29	1	1	NUM
ejpam-6763	589	30	):	):	PUNCT
ejpam-6763	590	1	a	a	DET
ejpam-6763	590	2	·	·	SYM
ejpam-6763	590	3	b	b	X
ejpam-6763	590	4	=	=	SYM
ejpam-6763	590	5	c	c	PROPN
ejpam-6763	590	6	(	(	PUNCT
ejpam-6763	590	7	26	26	NUM
ejpam-6763	590	8	)	)	PUNCT
ejpam-6763	590	9	a	a	DET
ejpam-6763	590	10	=	=	NOUN
ejpam-6763	590	11			NOUN
ejpam-6763	590	12	vσ00	vσ00	PROPN
ejpam-6763	590	13	0,x	0,x	PROPN
ejpam-6763	590	14	?	?	PUNCT
ejpam-6763	591	1	r+1	r+1	PROPN
ejpam-6763	592	1	−	−	PROPN
ejpam-6763	592	2	ǧr	ǧr	NOUN
ejpam-6763	592	3	0	0	NUM
ejpam-6763	592	4	−ω01ěr	−ω01ěr	NUM
ejpam-6763	592	5	01	01	NUM
ejpam-6763	592	6	−ω02ěr	−ω02ěr	PROPN
ejpam-6763	592	7	02	02	NUM
ejpam-6763	592	8	·	·	PUNCT
ejpam-6763	592	9	·	·	PUNCT
ejpam-6763	592	10	·	·	PUNCT
ejpam-6763	593	1	−ω0měr	−ω0měr	VERB
ejpam-6763	593	2	0	0	NUM
ejpam-6763	593	3	m	m	NUM
ejpam-6763	593	4	−ǧr	−ǧr	NUM
ejpam-6763	593	5	1	1	NUM
ejpam-6763	593	6	vσ10	vσ10	PROPN
ejpam-6763	593	7	1,x	1,x	NUM
ejpam-6763	593	8	?	?	PUNCT
ejpam-6763	594	1	r+1	r+1	X
ejpam-6763	594	2	−	−	NOUN
ejpam-6763	594	3	ω11ěr	ω11ěr	NUM
ejpam-6763	594	4	11	11	NUM
ejpam-6763	594	5	−ω12ěr	−ω12ěr	NOUN
ejpam-6763	594	6	12	12	NUM
ejpam-6763	594	7	·	·	PUNCT
ejpam-6763	594	8	·	·	PUNCT
ejpam-6763	594	9	·	·	PUNCT
ejpam-6763	595	1	−ω1měr	−ω1měr	VERB
ejpam-6763	595	2	1	1	NUM
ejpam-6763	595	3	m	m	NOUN
ejpam-6763	595	4	−ǧr	−ǧr	NUM
ejpam-6763	595	5	2	2	NUM
ejpam-6763	595	6	−ω21ěr	−ω21ěr	NOUN
ejpam-6763	595	7	21	21	NUM
ejpam-6763	595	8	vσ20	vσ20	PROPN
ejpam-6763	595	9	2,x	2,x	PROPN
ejpam-6763	595	10	?	?	PUNCT
ejpam-6763	596	1	r+1	r+1	NOUN
ejpam-6763	597	1	−	−	PROPN
ejpam-6763	597	2	ω22ěr	ω22ěr	SYM
ejpam-6763	597	3	22	22	NUM
ejpam-6763	597	4	·	·	PUNCT
ejpam-6763	597	5	·	·	PUNCT
ejpam-6763	597	6	·	·	PUNCT
ejpam-6763	597	7	−ω2měr	−ω2měr	NOUN
ejpam-6763	597	8	2	2	NUM
ejpam-6763	597	9	m	m	VERB
ejpam-6763	597	10	...	...	PUNCT
ejpam-6763	597	11	...	...	PUNCT
ejpam-6763	597	12	...	...	PUNCT
ejpam-6763	597	13	.	.	PUNCT
ejpam-6763	597	14	.	.	PUNCT
ejpam-6763	597	15	.	.	PUNCT
ejpam-6763	598	1	...	...	PUNCT
ejpam-6763	599	1	−ǧr	−ǧr	NUM
ejpam-6763	599	2	m	m	NOUN
ejpam-6763	599	3	−ωm1ěr	−ωm1ěr	PROPN
ejpam-6763	599	4	m1	m1	PROPN
ejpam-6763	599	5	−ωm2ěr	−ωm2ěr	PROPN
ejpam-6763	599	6	m2	m2	PROPN
ejpam-6763	599	7	·	·	PUNCT
ejpam-6763	599	8	·	·	PUNCT
ejpam-6763	599	9	·	·	PUNCT
ejpam-6763	599	10	vσm0	vσm0	NOUN
ejpam-6763	599	11	m	m	PRON
ejpam-6763	599	12	,	,	PUNCT
ejpam-6763	599	13	x	x	PRON
ejpam-6763	599	14	?	?	PUNCT
ejpam-6763	600	1	r+1	r+1	NOUN
ejpam-6763	600	2	−	−	NUM
ejpam-6763	601	1	ωmměr	ωmměr	DET
ejpam-6763	601	2	mm	mm	PROPN
ejpam-6763	601	3			NOUN
ejpam-6763	601	4	(	(	PUNCT
ejpam-6763	601	5	27	27	NUM
ejpam-6763	601	6	)	)	PUNCT
ejpam-6763	601	7	b	b	NOUN
ejpam-6763	601	8	=	=	PROPN
ejpam-6763	601	9			PROPN
ejpam-6763	601	10	ϑ03	ϑ03	PROPN
ejpam-6763	601	11	ϑ13	ϑ13	VERB
ejpam-6763	601	12	ϑ23	ϑ23	NOUN
ejpam-6763	601	13	...	...	PUNCT
ejpam-6763	601	14	ϑm3	ϑm3	NOUN
ejpam-6763	601	15			PUNCT
ejpam-6763	601	16	(	(	PUNCT
ejpam-6763	601	17	28	28	NUM
ejpam-6763	601	18	)	)	PUNCT
ejpam-6763	601	19	c	c	NOUN
ejpam-6763	601	20	=	=	SYM
ejpam-6763	601	21			NOUN
ejpam-6763	601	22	l0	l0	PROPN
ejpam-6763	601	23	r	r	NOUN
ejpam-6763	601	24	l1	l1	PROPN
ejpam-6763	601	25	r	r	NOUN
ejpam-6763	601	26	l2	l2	NOUN
ejpam-6763	601	27	r	r	NOUN
ejpam-6763	601	28	...	...	PUNCT
ejpam-6763	601	29	lm	lm	INTJ
ejpam-6763	602	1	r	r	NOUN
ejpam-6763	602	2			PUNCT
ejpam-6763	602	3	(	(	PUNCT
ejpam-6763	602	4	29	29	NUM
ejpam-6763	602	5	)	)	PUNCT
ejpam-6763	602	6	d.	d.	PROPN
ejpam-6763	602	7	kh	kh	PROPN
ejpam-6763	602	8	.	.	PUNCT
ejpam-6763	603	1	abdullah	abdullah	PROPN
ejpam-6763	603	2	,	,	PUNCT
ejpam-6763	603	3	sh	sh	PROPN
ejpam-6763	603	4	.	.	PROPN
ejpam-6763	603	5	sh	sh	PROPN
ejpam-6763	603	6	.	.	PROPN
ejpam-6763	603	7	ahmed	ahmed	PROPN
ejpam-6763	603	8	,	,	PUNCT
ejpam-6763	603	9	k.	k.	PROPN
ejpam-6763	603	10	h.	h.	PROPN
ejpam-6763	603	11	f.	f.	PROPN
ejpam-6763	603	12	jwamer	jwamer	PROPN
ejpam-6763	603	13	/	/	SYM
ejpam-6763	603	14	eur	eur	PROPN
ejpam-6763	603	15	.	.	PUNCT
ejpam-6763	604	1	j.	j.	PROPN
ejpam-6763	604	2	pure	pure	PROPN
ejpam-6763	604	3	appl	appl	PROPN
ejpam-6763	604	4	.	.	PROPN
ejpam-6763	604	5	math	math	PROPN
ejpam-6763	604	6	,	,	PUNCT
ejpam-6763	604	7	18	18	NUM
ejpam-6763	604	8	(	(	PUNCT
ejpam-6763	604	9	4	4	NUM
ejpam-6763	604	10	)	)	PUNCT
ejpam-6763	604	11	(	(	PUNCT
ejpam-6763	604	12	2025	2025	NUM
ejpam-6763	604	13	)	)	PUNCT
ejpam-6763	604	14	,	,	PUNCT
ejpam-6763	604	15	6763	6763	NUM
ejpam-6763	604	16	14	14	NUM
ejpam-6763	604	17	of	of	ADP
ejpam-6763	604	18	40	40	NUM
ejpam-6763	604	19	where	where	SCONJ
ejpam-6763	604	20	,	,	PUNCT
ejpam-6763	604	21	•	•	NUM
ejpam-6763	604	22	vσi0	vσi0	NOUN
ejpam-6763	604	23	i	i	PRON
ejpam-6763	604	24	,	,	PUNCT
ejpam-6763	604	25	x	x	X
ejpam-6763	604	26	?	?	PUNCT
ejpam-6763	605	1	r+1	r+1	PROPN
ejpam-6763	605	2	=	=	PUNCT
ejpam-6763	605	3	3pi(x	3pi(x	NUM
ejpam-6763	605	4	?	?	PUNCT
ejpam-6763	606	1	r+1)(x	r+1)(x	NOUN
ejpam-6763	606	2	?	?	PUNCT
ejpam-6763	607	1	r+1	r+1	PROPN
ejpam-6763	607	2	−	−	PROPN
ejpam-6763	608	1	a)2	a)2	PROPN
ejpam-6763	608	2	(	(	PUNCT
ejpam-6763	608	3	nh)3	nh)3	VERB
ejpam-6763	608	4	+	+	CCONJ
ejpam-6763	608	5	6	6	NUM
ejpam-6763	608	6	ai0(x	ai0(x	ADV
ejpam-6763	608	7	?	?	PUNCT
ejpam-6763	609	1	r+1)(x	r+1)(x	NOUN
ejpam-6763	609	2	?	?	PUNCT
ejpam-6763	610	1	r+1	r+1	PROPN
ejpam-6763	610	2	−	−	PROPN
ejpam-6763	610	3	a)3−σi0	a)3−σi0	PROPN
ejpam-6763	610	4	(	(	PUNCT
ejpam-6763	610	5	nh)3γ(4−	nh)3γ(4−	PROPN
ejpam-6763	610	6	σi0	σi0	PROPN
ejpam-6763	610	7	)	)	PUNCT
ejpam-6763	610	8	+	+	CCONJ
ejpam-6763	610	9	ai1(x	ai1(x	NOUN
ejpam-6763	610	10	?	?	PUNCT
ejpam-6763	611	1	r+1	r+1	NOUN
ejpam-6763	611	2	)	)	PUNCT
ejpam-6763	611	3	·	·	PUNCT
ejpam-6763	612	1	(	(	PUNCT
ejpam-6763	612	2	x?r+1	x?r+1	INTJ
ejpam-6763	612	3	−	−	PROPN
ejpam-6763	612	4	a	a	DET
ejpam-6763	612	5	nh	nh	PROPN
ejpam-6763	612	6	)	)	PUNCT
ejpam-6763	612	7	3	3	NUM
ejpam-6763	612	8	.	.	PUNCT
ejpam-6763	612	9	•	•	NUM
ejpam-6763	612	10	wσi0	wσi0	PROPN
ejpam-6763	613	1	i	i	PRON
ejpam-6763	613	2	,	,	PUNCT
ejpam-6763	613	3	x	x	X
ejpam-6763	613	4	?	?	PUNCT
ejpam-6763	614	1	r+1	r+1	PROPN
ejpam-6763	614	2	=	=	SYM
ejpam-6763	614	3	pi(x	pi(x	NOUN
ejpam-6763	614	4	?	?	PUNCT
ejpam-6763	615	1	r+1	r+1	NOUN
ejpam-6763	615	2	)	)	PUNCT
ejpam-6763	615	3	{	{	PUNCT
ejpam-6763	615	4	−3ϑi0(b−	−3ϑi0(b−	PROPN
ejpam-6763	615	5	x?r+1	x?r+1	NOUN
ejpam-6763	615	6	)	)	PUNCT
ejpam-6763	615	7	(	(	PUNCT
ejpam-6763	615	8	nh)3	nh)3	VERB
ejpam-6763	615	9	+	+	SYM
ejpam-6763	615	10	3ϑi1	3ϑi1	NUM
ejpam-6763	615	11	[	[	X
ejpam-6763	615	12	−2(x?r+1	−2(x?r+1	NOUN
ejpam-6763	615	13	−	−	PROPN
ejpam-6763	615	14	a)(b−	a)(b−	PROPN
ejpam-6763	615	15	x?r+1	x?r+1	PROPN
ejpam-6763	615	16	)	)	PUNCT
ejpam-6763	615	17	(	(	PUNCT
ejpam-6763	615	18	nh)3	nh)3	VERB
ejpam-6763	615	19	+	+	CCONJ
ejpam-6763	615	20	(	(	PUNCT
ejpam-6763	615	21	b−	b−	PROPN
ejpam-6763	615	22	x?r+1	x?r+1	PROPN
ejpam-6763	615	23	)	)	PUNCT
ejpam-6763	615	24	2	2	NUM
ejpam-6763	615	25	(	(	PUNCT
ejpam-6763	615	26	nh)3	nh)3	ADV
ejpam-6763	615	27	]	]	PUNCT
ejpam-6763	616	1	+3ϑi2	+3ϑi2	PUNCT
ejpam-6763	617	1	[	[	X
ejpam-6763	617	2	−(x?r+1	−(x?r+1	X
ejpam-6763	617	3	−	−	NOUN
ejpam-6763	617	4	a)2	a)2	PROPN
ejpam-6763	617	5	(	(	PUNCT
ejpam-6763	617	6	nh)3	nh)3	PROPN
ejpam-6763	617	7	+	+	CCONJ
ejpam-6763	617	8	2(b−	2(b−	NUM
ejpam-6763	617	9	x?r+1)(x	x?r+1)(x	NOUN
ejpam-6763	617	10	?	?	PUNCT
ejpam-6763	618	1	r+1	r+1	PROPN
ejpam-6763	619	1	−	−	PROPN
ejpam-6763	619	2	a	a	NOUN
ejpam-6763	619	3	)	)	PUNCT
ejpam-6763	619	4	(	(	PUNCT
ejpam-6763	619	5	nh)3	nh)3	ADV
ejpam-6763	619	6	]	]	PUNCT
ejpam-6763	619	7	}	}	PUNCT
ejpam-6763	620	1	+	+	ADJ
ejpam-6763	620	2	ai0(x	ai0(x	PROPN
ejpam-6763	620	3	?	?	PUNCT
ejpam-6763	621	1	r+1	r+1	NOUN
ejpam-6763	621	2	)	)	PUNCT
ejpam-6763	621	3	·	·	PUNCT
ejpam-6763	622	1	(	(	PUNCT
ejpam-6763	622	2	x?r+1	x?r+1	INTJ
ejpam-6763	622	3	−	−	PROPN
ejpam-6763	622	4	a)1−σi0	a)1−σi0	PROPN
ejpam-6763	622	5	(	(	PUNCT
ejpam-6763	622	6	nh)3γ(4−	nh)3γ(4−	PROPN
ejpam-6763	622	7	σi0	σi0	PROPN
ejpam-6763	622	8	)	)	PUNCT
ejpam-6763	622	9	·	·	PUNCT
ejpam-6763	623	1	[	[	PUNCT
ejpam-6763	623	2	ϑi0	ϑi0	NOUN
ejpam-6763	623	3	(	(	PUNCT
ejpam-6763	623	4	−3(nh)2(2−	−3(nh)2(2−	NOUN
ejpam-6763	623	5	σi0	σi0	NOUN
ejpam-6763	623	6	)	)	PUNCT
ejpam-6763	623	7	)	)	PUNCT
ejpam-6763	624	1	(	(	PUNCT
ejpam-6763	624	2	3−	3−	NUM
ejpam-6763	624	3	σi0	σi0	NOUN
ejpam-6763	624	4	)	)	PUNCT
ejpam-6763	625	1	+	+	CCONJ
ejpam-6763	625	2	6(nh)(3−	6(nh)(3−	NUM
ejpam-6763	625	3	σi0)−	σi0)−	PROPN
ejpam-6763	625	4	6(x?r+1	6(x?r+1	PROPN
ejpam-6763	625	5	−	−	PROPN
ejpam-6763	625	6	a)2	a)2	NOUN
ejpam-6763	625	7	+	+	CCONJ
ejpam-6763	625	8	ϑi1	ϑi1	X
ejpam-6763	625	9	(	(	PUNCT
ejpam-6763	625	10	(	(	PUNCT
ejpam-6763	625	11	nh)2	nh)2	NOUN
ejpam-6763	625	12	)	)	PUNCT
ejpam-6763	625	13	(	(	PUNCT
ejpam-6763	625	14	2−	2−	NUM
ejpam-6763	625	15	σi0)(3−	σi0)(3−	ADP
ejpam-6763	625	16	σi0)−	σi0)−	NOUN
ejpam-6763	625	17	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	625	18	σi0)(x	σi0)(x	PROPN
ejpam-6763	625	19	?	?	PUNCT
ejpam-6763	626	1	r+1	r+1	PROPN
ejpam-6763	627	1	−	−	PROPN
ejpam-6763	627	2	a	a	X
ejpam-6763	627	3	)	)	PUNCT
ejpam-6763	628	1	+	+	NUM
ejpam-6763	628	2	6(x?r+1	6(x?r+1	NOUN
ejpam-6763	628	3	−	−	NOUN
ejpam-6763	628	4	a)2	a)2	NOUN
ejpam-6763	628	5	+3ϑi2	+3ϑi2	NOUN
ejpam-6763	628	6	(	(	PUNCT
ejpam-6763	628	7	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	628	8	σi0)(x	σi0)(x	PROPN
ejpam-6763	628	9	?	?	PUNCT
ejpam-6763	629	1	r+1	r+1	PROPN
ejpam-6763	630	1	−	−	PROPN
ejpam-6763	630	2	a)−	a)−	PROPN
ejpam-6763	630	3	6(x?r+1	6(x?r+1	PROPN
ejpam-6763	630	4	−	−	NOUN
ejpam-6763	630	5	a)2	a)2	PROPN
ejpam-6763	630	6	)	)	PUNCT
ejpam-6763	630	7	]	]	PUNCT
ejpam-6763	631	1	+	+	PUNCT
ejpam-6763	631	2	ai1(x	ai1(x	NOUN
ejpam-6763	631	3	?	?	PUNCT
ejpam-6763	632	1	r+1	r+1	NOUN
ejpam-6763	632	2	)	)	PUNCT
ejpam-6763	632	3	·	·	PUNCT
ejpam-6763	633	1	[	[	PUNCT
ejpam-6763	633	2	ϑi0	ϑi0	NOUN
ejpam-6763	633	3	(	(	PUNCT
ejpam-6763	633	4	b−	b−	PROPN
ejpam-6763	633	5	x?r+1	x?r+1	PROPN
ejpam-6763	633	6	nh	nh	PROPN
ejpam-6763	633	7	)	)	PUNCT
ejpam-6763	633	8	3	3	NUM
ejpam-6763	634	1	+	+	NUM
ejpam-6763	634	2	3ϑi1	3ϑi1	NUM
ejpam-6763	634	3	(	(	PUNCT
ejpam-6763	634	4	x?r+1	x?r+1	INTJ
ejpam-6763	634	5	−	−	PROPN
ejpam-6763	634	6	a	a	DET
ejpam-6763	634	7	nh	nh	NOUN
ejpam-6763	634	8	)	)	PUNCT
ejpam-6763	634	9	(	(	PUNCT
ejpam-6763	634	10	b−	b−	PROPN
ejpam-6763	634	11	x?r+1	x?r+1	PROPN
ejpam-6763	634	12	nh	nh	PROPN
ejpam-6763	634	13	)	)	PUNCT
ejpam-6763	634	14	2	2	NUM
ejpam-6763	634	15	+3ϑi2	+3ϑi2	NOUN
ejpam-6763	634	16	(	(	PUNCT
ejpam-6763	634	17	x?r+1	x?r+1	INTJ
ejpam-6763	634	18	−	−	PROPN
ejpam-6763	634	19	a	a	DET
ejpam-6763	634	20	nh	nh	PROPN
ejpam-6763	634	21	)	)	PUNCT
ejpam-6763	634	22	2(b−	2(b−	PROPN
ejpam-6763	634	23	x?r+1	x?r+1	PROPN
ejpam-6763	634	24	nh	nh	PROPN
ejpam-6763	634	25	)	)	PUNCT
ejpam-6763	634	26	]	]	PUNCT
ejpam-6763	634	27	.	.	PUNCT
ejpam-6763	635	1	•	•	NUM
ejpam-6763	635	2	er	er	INTJ
ejpam-6763	635	3	ij	ij	INTJ
ejpam-6763	635	4	=	=	PUNCT
ejpam-6763	635	5	r−1∑	r−1∑	PROPN
ejpam-6763	635	6	q=0	q=0	PROPN
ejpam-6763	635	7	n∑	n∑	PROPN
ejpam-6763	635	8	ξ=0	ξ=0	PROPN
ejpam-6763	636	1	λξ	λξ	ADP
ejpam-6763	636	2	kij(x	kij(x	PROPN
ejpam-6763	636	3	?	?	PUNCT
ejpam-6763	637	1	r+1	r+1	NOUN
ejpam-6763	637	2	,	,	PUNCT
ejpam-6763	637	3	sξ	sξ	PROPN
ejpam-6763	637	4	)	)	PUNCT
ejpam-6763	637	5	·	·	PUNCT
ejpam-6763	638	1	(	(	PUNCT
ejpam-6763	638	2	x?q+1	x?q+1	PROPN
ejpam-6763	638	3	−	−	PROPN
ejpam-6763	638	4	x?q)(sξ	x?q)(sξ	VERB
ejpam-6763	638	5	−	−	PROPN
ejpam-6763	639	1	a)1−βij	a)1−βij	PROPN
ejpam-6763	639	2	2(nh)3γ(4−	2(nh)3γ(4−	NUM
ejpam-6763	639	3	βij	βij	NOUN
ejpam-6763	639	4	)	)	PUNCT
ejpam-6763	639	5	·	·	PUNCT
ejpam-6763	640	1			PRON
ejpam-6763	640	2	ϑj0	ϑj0	VERB
ejpam-6763	640	3	[	[	PUNCT
ejpam-6763	640	4	−3(nh)2(2−	−3(nh)2(2−	PROPN
ejpam-6763	640	5	βij)(3−	βij)(3−	NUM
ejpam-6763	640	6	βij	βij	NOUN
ejpam-6763	640	7	)	)	PUNCT
ejpam-6763	641	1	+	+	CCONJ
ejpam-6763	641	2	6(nh)(3−	6(nh)(3−	NUM
ejpam-6763	641	3	βij)−	βij)−	NOUN
ejpam-6763	641	4	6(sξ	6(sξ	NOUN
ejpam-6763	641	5	−	−	NOUN
ejpam-6763	641	6	a)2	a)2	NOUN
ejpam-6763	641	7	]	]	PUNCT
ejpam-6763	642	1	+	+	NUM
ejpam-6763	642	2	3ϑj1	3ϑj1	NUM
ejpam-6763	642	3	[	[	PUNCT
ejpam-6763	642	4	(	(	PUNCT
ejpam-6763	642	5	nh)2(2−	nh)2(2−	NOUN
ejpam-6763	642	6	βij)(3−	βij)(3−	NUM
ejpam-6763	642	7	βij)−	βij)−	SYM
ejpam-6763	642	8	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	642	9	βij)(sξ	βij)(sξ	NOUN
ejpam-6763	642	10	−	−	PROPN
ejpam-6763	642	11	a)−	a)−	ADJ
ejpam-6763	642	12	2(sξ	2(sξ	NUM
ejpam-6763	642	13	−	−	PROPN
ejpam-6763	642	14	a	a	NOUN
ejpam-6763	642	15	)	)	PUNCT
ejpam-6763	643	1	+	+	NOUN
ejpam-6763	643	2	6(sξ	6(sξ	NUM
ejpam-6763	643	3	−	−	NOUN
ejpam-6763	643	4	a)2	a)2	NOUN
ejpam-6763	643	5	]	]	PUNCT
ejpam-6763	644	1	+	+	CCONJ
ejpam-6763	644	2	3ϑj2	3ϑj2	NUM
ejpam-6763	644	3	[	[	PUNCT
ejpam-6763	644	4	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	644	5	βij)(sξ	βij)(sξ	NOUN
ejpam-6763	644	6	−	−	PROPN
ejpam-6763	644	7	a)−	a)−	ADJ
ejpam-6763	644	8	6(sξ	6(sξ	NOUN
ejpam-6763	644	9	−	−	NOUN
ejpam-6763	644	10	a)2	a)2	NOUN
ejpam-6763	644	11	]	]	PUNCT
ejpam-6763	644	12			PROPN
ejpam-6763	645	1	+	+	CCONJ
ejpam-6763	645	2	n∑	n∑	PROPN
ejpam-6763	645	3	ξ=0	ξ=0	PROPN
ejpam-6763	645	4	λξ	λξ	ADP
ejpam-6763	645	5	kij(x	kij(x	PROPN
ejpam-6763	645	6	?	?	PUNCT
ejpam-6763	646	1	r+1	r+1	NOUN
ejpam-6763	646	2	,	,	PUNCT
ejpam-6763	646	3	sξ	sξ	PROPN
ejpam-6763	646	4	)	)	PUNCT
ejpam-6763	646	5	·	·	PUNCT
ejpam-6763	647	1	(	(	PUNCT
ejpam-6763	647	2	x?r+1	x?r+1	INTJ
ejpam-6763	647	3	−	−	PROPN
ejpam-6763	647	4	x?r)(sξ	x?r)(sξ	INTJ
ejpam-6763	648	1	−	−	PROPN
ejpam-6763	649	1	a)1−βij	a)1−βij	PROPN
ejpam-6763	649	2	2(nh)3γ(4−	2(nh)3γ(4−	NUM
ejpam-6763	649	3	βij	βij	NOUN
ejpam-6763	649	4	)	)	PUNCT
ejpam-6763	649	5	·	·	PUNCT
ejpam-6763	650	1			PRON
ejpam-6763	650	2	ϑj0	ϑj0	VERB
ejpam-6763	650	3	[	[	PUNCT
ejpam-6763	650	4	−3(nh)2(2−	−3(nh)2(2−	PROPN
ejpam-6763	650	5	βij)(3−	βij)(3−	NUM
ejpam-6763	650	6	βij	βij	NOUN
ejpam-6763	650	7	)	)	PUNCT
ejpam-6763	651	1	+	+	CCONJ
ejpam-6763	651	2	6(nh)(3−	6(nh)(3−	NUM
ejpam-6763	651	3	βij)−	βij)−	NOUN
ejpam-6763	651	4	6(sξ	6(sξ	NOUN
ejpam-6763	651	5	−	−	NOUN
ejpam-6763	651	6	a)2	a)2	NOUN
ejpam-6763	651	7	]	]	PUNCT
ejpam-6763	652	1	+	+	NUM
ejpam-6763	652	2	3ϑj1	3ϑj1	NUM
ejpam-6763	652	3	[	[	PUNCT
ejpam-6763	652	4	(	(	PUNCT
ejpam-6763	652	5	nh)2(2−	nh)2(2−	NOUN
ejpam-6763	652	6	βij)(3−	βij)(3−	NUM
ejpam-6763	652	7	βij)−	βij)−	SYM
ejpam-6763	652	8	4(nh)(3−	4(nh)(3−	NUM
ejpam-6763	652	9	βij)(sξ	βij)(sξ	NOUN
ejpam-6763	652	10	−	−	PROPN
ejpam-6763	652	11	a)−	a)−	ADJ
ejpam-6763	652	12	2(sξ	2(sξ	NUM
ejpam-6763	652	13	−	−	PROPN
ejpam-6763	652	14	a	a	NOUN
ejpam-6763	652	15	)	)	PUNCT
ejpam-6763	653	1	+	+	NOUN
ejpam-6763	653	2	6(sξ	6(sξ	NUM
ejpam-6763	653	3	−	−	NOUN
ejpam-6763	653	4	a)2	a)2	NOUN
ejpam-6763	653	5	]	]	PUNCT
ejpam-6763	654	1	+	+	CCONJ
ejpam-6763	654	2	3ϑj2	3ϑj2	NUM
ejpam-6763	654	3	[	[	PUNCT
ejpam-6763	654	4	2(nh)(3−	2(nh)(3−	NUM
ejpam-6763	654	5	βij)(sξ	βij)(sξ	NOUN
ejpam-6763	654	6	−	−	PROPN
ejpam-6763	654	7	a)−	a)−	ADJ
ejpam-6763	654	8	6(sξ	6(sξ	NOUN
ejpam-6763	654	9	−	−	NOUN
ejpam-6763	654	10	a)2	a)2	PROPN
ejpam-6763	654	11	]	]	PUNCT
ejpam-6763	654	12			PROPN
ejpam-6763	654	13	.	.	PUNCT
ejpam-6763	655	1	d.	d.	PROPN
ejpam-6763	655	2	kh	kh	PROPN
ejpam-6763	655	3	.	.	PUNCT
ejpam-6763	656	1	abdullah	abdullah	PROPN
ejpam-6763	656	2	,	,	PUNCT
ejpam-6763	656	3	sh	sh	PROPN
ejpam-6763	656	4	.	.	PROPN
ejpam-6763	656	5	sh	sh	PROPN
ejpam-6763	656	6	.	.	PROPN
ejpam-6763	656	7	ahmed	ahmed	PROPN
ejpam-6763	656	8	,	,	PUNCT
ejpam-6763	656	9	k.	k.	PROPN
ejpam-6763	656	10	h.	h.	PROPN
ejpam-6763	656	11	f.	f.	PROPN
ejpam-6763	656	12	jwamer	jwamer	PROPN
ejpam-6763	656	13	/	/	SYM
ejpam-6763	656	14	eur	eur	PROPN
ejpam-6763	656	15	.	.	PUNCT
ejpam-6763	657	1	j.	j.	PROPN
ejpam-6763	657	2	pure	pure	PROPN
ejpam-6763	657	3	appl	appl	PROPN
ejpam-6763	657	4	.	.	PROPN
ejpam-6763	657	5	math	math	PROPN
ejpam-6763	657	6	,	,	PUNCT
ejpam-6763	657	7	18	18	NUM
ejpam-6763	657	8	(	(	PUNCT
ejpam-6763	657	9	4	4	NUM
ejpam-6763	657	10	)	)	PUNCT
ejpam-6763	657	11	(	(	PUNCT
ejpam-6763	657	12	2025	2025	NUM
ejpam-6763	657	13	)	)	PUNCT
ejpam-6763	657	14	,	,	PUNCT
ejpam-6763	657	15	6763	6763	NUM
ejpam-6763	657	16	15	15	NUM
ejpam-6763	657	17	of	of	ADP
ejpam-6763	657	18	40	40	NUM
ejpam-6763	657	19	•	•	NOUN
ejpam-6763	657	20	ěr	ěr	PROPN
ejpam-6763	657	21	ij	ij	NOUN
ejpam-6763	657	22	=	=	PUNCT
ejpam-6763	657	23	r−1∑	r−1∑	PROPN
ejpam-6763	658	1	q=0	q=0	PROPN
ejpam-6763	658	2	n∑	n∑	PROPN
ejpam-6763	658	3	ξ=0	ξ=0	PROPN
ejpam-6763	658	4	3λξ	3λξ	ADJ
ejpam-6763	658	5	kij(x	kij(x	X
ejpam-6763	658	6	?	?	PUNCT
ejpam-6763	659	1	r+1	r+1	NOUN
ejpam-6763	659	2	,	,	PUNCT
ejpam-6763	659	3	sξ	sξ	PROPN
ejpam-6763	659	4	)	)	PUNCT
ejpam-6763	659	5	(	(	PUNCT
ejpam-6763	659	6	x	x	X
ejpam-6763	659	7	?	?	PUNCT
ejpam-6763	660	1	q+1	q+1	NUM
ejpam-6763	661	1	−	−	NOUN
ejpam-6763	661	2	x?q	x?q	PROPN
ejpam-6763	661	3	)	)	PUNCT
ejpam-6763	661	4	(	(	PUNCT
ejpam-6763	661	5	sξ	sξ	PROPN
ejpam-6763	661	6	−	−	PROPN
ejpam-6763	661	7	a)3−βij	a)3−βij	PROPN
ejpam-6763	661	8	(	(	PUNCT
ejpam-6763	661	9	nh)3	nh)3	PROPN
ejpam-6763	661	10	γ(4−	γ(4−	PROPN
ejpam-6763	661	11	βij	βij	PROPN
ejpam-6763	661	12	)	)	PUNCT
ejpam-6763	662	1	+	+	CCONJ
ejpam-6763	662	2	n∑	n∑	ADJ
ejpam-6763	662	3	ξ=0	ξ=0	PROPN
ejpam-6763	662	4	3λξ	3λξ	ADJ
ejpam-6763	662	5	kij(x	kij(x	X
ejpam-6763	662	6	?	?	PUNCT
ejpam-6763	663	1	r+1	r+1	NOUN
ejpam-6763	663	2	,	,	PUNCT
ejpam-6763	663	3	sξ	sξ	PROPN
ejpam-6763	663	4	)	)	PUNCT
ejpam-6763	663	5	(	(	PUNCT
ejpam-6763	663	6	x	x	X
ejpam-6763	663	7	?	?	PUNCT
ejpam-6763	664	1	r+1	r+1	PROPN
ejpam-6763	664	2	−	−	PROPN
ejpam-6763	664	3	x?r	x?r	PROPN
ejpam-6763	664	4	)	)	PUNCT
ejpam-6763	664	5	(	(	PUNCT
ejpam-6763	664	6	sξ	sξ	PROPN
ejpam-6763	664	7	−	−	PROPN
ejpam-6763	664	8	a)3−βij	a)3−βij	PROPN
ejpam-6763	664	9	(	(	PUNCT
ejpam-6763	664	10	nh)3	nh)3	PROPN
ejpam-6763	664	11	γ(4−	γ(4−	PROPN
ejpam-6763	664	12	βij	βij	PROPN
ejpam-6763	664	13	)	)	PUNCT
ejpam-6763	664	14	•	•	NOUN
ejpam-6763	665	1	gr	gr	INTJ
ejpam-6763	666	1	i	i	NOUN
ejpam-6763	666	2	=	=	PUNCT
ejpam-6763	666	3	r−1∑	r−1∑	PROPN
ejpam-6763	667	1	q=0	q=0	PROPN
ejpam-6763	667	2	n∑	n∑	PROPN
ejpam-6763	667	3	ξ=0	ξ=0	PROPN
ejpam-6763	668	1	λξ	λξ	ADP
ejpam-6763	668	2	ki0(x	ki0(x	NOUN
ejpam-6763	668	3	?	?	PUNCT
ejpam-6763	669	1	r+1	r+1	NOUN
ejpam-6763	669	2	,	,	PUNCT
ejpam-6763	669	3	sξ	sξ	PROPN
ejpam-6763	669	4	)	)	PUNCT
ejpam-6763	669	5	·	·	PUNCT
ejpam-6763	670	1	(	(	PUNCT
ejpam-6763	670	2	x?q+1	x?q+1	PROPN
ejpam-6763	670	3	−	−	PROPN
ejpam-6763	670	4	x?q	x?q	PROPN
ejpam-6763	670	5	)	)	PUNCT
ejpam-6763	670	6	2	2	NUM
ejpam-6763	670	7	·	·	PUNCT
ejpam-6763	670	8	[	[	PUNCT
ejpam-6763	670	9	ϑ00	ϑ00	X
ejpam-6763	670	10	(	(	PUNCT
ejpam-6763	670	11	b−	b−	PROPN
ejpam-6763	670	12	sξ	sξ	PROPN
ejpam-6763	670	13	nh	nh	PROPN
ejpam-6763	670	14	)	)	PUNCT
ejpam-6763	670	15	3	3	PROPN
ejpam-6763	670	16	+3ϑ01	+3ϑ01	NUM
ejpam-6763	670	17	(	(	PUNCT
ejpam-6763	670	18	sξ	sξ	INTJ
ejpam-6763	670	19	−	−	PROPN
ejpam-6763	670	20	a	a	DET
ejpam-6763	670	21	nh	nh	NOUN
ejpam-6763	670	22	)	)	PUNCT
ejpam-6763	670	23	(	(	PUNCT
ejpam-6763	670	24	b−	b−	PROPN
ejpam-6763	670	25	sξ	sξ	PROPN
ejpam-6763	670	26	nh	nh	PROPN
ejpam-6763	670	27	)	)	PUNCT
ejpam-6763	670	28	2	2	NUM
ejpam-6763	670	29	+	+	NUM
ejpam-6763	670	30	3ϑ02	3ϑ02	NUM
ejpam-6763	670	31	(	(	PUNCT
ejpam-6763	670	32	sξ	sξ	INTJ
ejpam-6763	670	33	−	−	PROPN
ejpam-6763	670	34	a	a	DET
ejpam-6763	670	35	nh	nh	PROPN
ejpam-6763	670	36	)	)	PUNCT
ejpam-6763	670	37	2(b−	2(b−	PROPN
ejpam-6763	670	38	sξ	sξ	PROPN
ejpam-6763	670	39	nh	nh	PROPN
ejpam-6763	670	40	)	)	PUNCT
ejpam-6763	670	41	]	]	PUNCT
ejpam-6763	671	1	+	+	CCONJ
ejpam-6763	671	2	n∑	n∑	ADJ
ejpam-6763	671	3	ξ=0	ξ=0	PROPN
ejpam-6763	671	4	λξ	λξ	ADP
ejpam-6763	671	5	ki0(x	ki0(x	NOUN
ejpam-6763	671	6	?	?	PUNCT
ejpam-6763	672	1	r+1	r+1	NOUN
ejpam-6763	672	2	,	,	PUNCT
ejpam-6763	672	3	sξ	sξ	PROPN
ejpam-6763	672	4	)	)	PUNCT
ejpam-6763	672	5	·	·	PUNCT
ejpam-6763	673	1	(	(	PUNCT
ejpam-6763	673	2	x?r+1	x?r+1	INTJ
ejpam-6763	673	3	−	−	PROPN
ejpam-6763	673	4	x?r	x?r	NOUN
ejpam-6763	673	5	)	)	PUNCT
ejpam-6763	673	6	2	2	NUM
ejpam-6763	673	7	·	·	PUNCT
ejpam-6763	673	8	[	[	PUNCT
ejpam-6763	673	9	ϑ00	ϑ00	X
ejpam-6763	673	10	(	(	PUNCT
ejpam-6763	673	11	b−	b−	PROPN
ejpam-6763	673	12	sξ	sξ	PROPN
ejpam-6763	673	13	nh	nh	PROPN
ejpam-6763	673	14	)	)	PUNCT
ejpam-6763	673	15	3	3	NUM
ejpam-6763	674	1	+	+	NUM
ejpam-6763	674	2	3ϑ01	3ϑ01	NUM
ejpam-6763	674	3	(	(	PUNCT
ejpam-6763	674	4	sξ	sξ	INTJ
ejpam-6763	674	5	−	−	PROPN
ejpam-6763	674	6	a	a	DET
ejpam-6763	674	7	nh	nh	NOUN
ejpam-6763	674	8	)	)	PUNCT
ejpam-6763	674	9	(	(	PUNCT
ejpam-6763	674	10	b−	b−	PROPN
ejpam-6763	674	11	sξ	sξ	PROPN
ejpam-6763	674	12	nh	nh	PROPN
ejpam-6763	674	13	)	)	PUNCT
ejpam-6763	674	14	2	2	NUM
ejpam-6763	674	15	+	+	NUM
ejpam-6763	674	16	3ϑ02	3ϑ02	NUM
ejpam-6763	674	17	(	(	PUNCT
ejpam-6763	674	18	sξ	sξ	INTJ
ejpam-6763	674	19	−	−	PROPN
ejpam-6763	674	20	a	a	DET
ejpam-6763	674	21	nh	nh	PROPN
ejpam-6763	674	22	)	)	PUNCT
ejpam-6763	674	23	2(b−	2(b−	PROPN
ejpam-6763	674	24	sξ	sξ	PROPN
ejpam-6763	674	25	nh	nh	PROPN
ejpam-6763	674	26	)	)	PUNCT
ejpam-6763	674	27	]	]	PUNCT
ejpam-6763	675	1	•	•	X
ejpam-6763	676	1	ǧr	ǧr	VERB
ejpam-6763	677	1	i	i	NOUN
ejpam-6763	677	2	=	=	PUNCT
ejpam-6763	677	3	r−1∑	r−1∑	PROPN
ejpam-6763	677	4	q=0	q=0	PROPN
ejpam-6763	677	5	n∑	n∑	PROPN
ejpam-6763	678	1	ξ=0	ξ=0	PROPN
ejpam-6763	679	1	λξ	λξ	ADP
ejpam-6763	679	2	ki0(x	ki0(x	NOUN
ejpam-6763	679	3	?	?	PUNCT
ejpam-6763	680	1	r+1	r+1	NOUN
ejpam-6763	680	2	,	,	PUNCT
ejpam-6763	680	3	sξ	sξ	PROPN
ejpam-6763	680	4	)	)	PUNCT
ejpam-6763	680	5	·	·	PUNCT
ejpam-6763	681	1	(	(	PUNCT
ejpam-6763	681	2	x?q+1	x?q+1	PROPN
ejpam-6763	681	3	−	−	PROPN
ejpam-6763	681	4	x?q	x?q	PROPN
ejpam-6763	681	5	)	)	PUNCT
ejpam-6763	681	6	2	2	NUM
ejpam-6763	681	7	(	(	PUNCT
ejpam-6763	681	8	sξ	sξ	INTJ
ejpam-6763	681	9	−	−	PROPN
ejpam-6763	681	10	a	a	DET
ejpam-6763	681	11	nh	nh	NOUN
ejpam-6763	681	12	)	)	PUNCT
ejpam-6763	681	13	3	3	NUM
ejpam-6763	682	1	+	+	CCONJ
ejpam-6763	682	2	n∑	n∑	PROPN
ejpam-6763	682	3	ξ=0	ξ=0	PROPN
ejpam-6763	682	4	λξ	λξ	ADP
ejpam-6763	682	5	ki0(x	ki0(x	NOUN
ejpam-6763	682	6	?	?	PUNCT
ejpam-6763	683	1	r+1	r+1	NOUN
ejpam-6763	683	2	,	,	PUNCT
ejpam-6763	683	3	sξ	sξ	PROPN
ejpam-6763	683	4	)	)	PUNCT
ejpam-6763	683	5	·	·	PUNCT
ejpam-6763	684	1	(	(	PUNCT
ejpam-6763	684	2	x?r+1	x?r+1	INTJ
ejpam-6763	684	3	−	−	PROPN
ejpam-6763	684	4	x?r	x?r	NOUN
ejpam-6763	684	5	)	)	PUNCT
ejpam-6763	684	6	2	2	NUM
ejpam-6763	684	7	(	(	PUNCT
ejpam-6763	684	8	sξ	sξ	INTJ
ejpam-6763	684	9	−	−	PROPN
ejpam-6763	684	10	a	a	DET
ejpam-6763	684	11	nh	nh	PROPN
ejpam-6763	684	12	)	)	PUNCT
ejpam-6763	684	13	3	3	NUM
ejpam-6763	684	14	li	li	NOUN
ejpam-6763	684	15	r	r	NOUN
ejpam-6763	684	16	=	=	SYM
ejpam-6763	684	17	fi(x	fi(x	NOUN
ejpam-6763	684	18	?	?	PUNCT
ejpam-6763	684	19	r+1	r+1	NOUN
ejpam-6763	684	20	)	)	PUNCT
ejpam-6763	685	1	+	+	CCONJ
ejpam-6763	685	2	m∑	m∑	ADV
ejpam-6763	685	3	j=1	j=1	NOUN
ejpam-6763	685	4	ωij	ωij	VERB
ejpam-6763	685	5	er	er	INTJ
ejpam-6763	686	1	ij	ij	INTJ
ejpam-6763	686	2	−wσi0	−wσi0	PROPN
ejpam-6763	687	1	i	i	PRON
ejpam-6763	687	2	,	,	PUNCT
ejpam-6763	687	3	x	x	X
ejpam-6763	687	4	?	?	PUNCT
ejpam-6763	688	1	r+1	r+1	PROPN
ejpam-6763	689	1	+	+	CCONJ
ejpam-6763	689	2	gr	gr	NUM
ejpam-6763	689	3	ij	ij	X
ejpam-6763	689	4	(	(	PUNCT
ejpam-6763	689	5	30	30	NUM
ejpam-6763	689	6	)	)	PUNCT
ejpam-6763	689	7	where	where	SCONJ
ejpam-6763	689	8	,	,	PUNCT
ejpam-6763	689	9	t?ξ	t?ξ	NOUN
ejpam-6763	689	10	=	=	SYM
ejpam-6763	689	11	n	n	PRON
ejpam-6763	689	12	′′∑	′′∑	VERB
ejpam-6763	689	13	ξ=0	ξ=0	PROPN
ejpam-6763	689	14	cos	cos	PROPN
ejpam-6763	689	15	(	(	PUNCT
ejpam-6763	689	16	ξπ	ξπ	ADP
ejpam-6763	689	17	n	n	NOUN
ejpam-6763	689	18	)	)	PUNCT
ejpam-6763	689	19	(	(	PUNCT
ejpam-6763	689	20	31	31	NUM
ejpam-6763	689	21	)	)	PUNCT
ejpam-6763	689	22	are	be	AUX
ejpam-6763	689	23	the	the	DET
ejpam-6763	689	24	nodes	node	NOUN
ejpam-6763	689	25	evaluated	evaluate	VERB
ejpam-6763	689	26	to	to	PART
ejpam-6763	689	27	correspond	correspond	VERB
ejpam-6763	689	28	to	to	ADP
ejpam-6763	689	29	the	the	DET
ejpam-6763	689	30	extrema	extrema	NOUN
ejpam-6763	689	31	of	of	ADP
ejpam-6763	689	32	the	the	DET
ejpam-6763	689	33	chebyshev	chebyshev	NOUN
ejpam-6763	689	34	polynomials	polynomial	NOUN
ejpam-6763	689	35	on	on	ADP
ejpam-6763	689	36	the	the	DET
ejpam-6763	689	37	interval	interval	NOUN
ejpam-6763	689	38	[	[	X
ejpam-6763	689	39	−1	−1	NOUN
ejpam-6763	689	40	,	,	PUNCT
ejpam-6763	689	41	1	1	NUM
ejpam-6763	689	42	]	]	PUNCT
ejpam-6763	689	43	.	.	PUNCT
ejpam-6763	690	1	the	the	DET
ejpam-6763	690	2	mapped	map	VERB
ejpam-6763	690	3	node	node	NOUN
ejpam-6763	690	4	sξ	sξ	PROPN
ejpam-6763	690	5	is	be	AUX
ejpam-6763	690	6	calculated	calculate	VERB
ejpam-6763	690	7	by	by	ADP
ejpam-6763	690	8	:	:	PUNCT
ejpam-6763	690	9	sξ	sξ	PROPN
ejpam-6763	690	10	=	=	PUNCT
ejpam-6763	690	11	x?q+1	x?q+1	PROPN
ejpam-6763	690	12	−	−	PROPN
ejpam-6763	690	13	x?q	x?q	ADP
ejpam-6763	690	14	2	2	NUM
ejpam-6763	690	15	t?ξ	t?ξ	NOUN
ejpam-6763	691	1	+	+	CCONJ
ejpam-6763	691	2	x?q+1	x?q+1	PROPN
ejpam-6763	692	1	+	+	CCONJ
ejpam-6763	692	2	x?q	x?q	PROPN
ejpam-6763	692	3	2	2	NUM
ejpam-6763	692	4	(	(	PUNCT
ejpam-6763	692	5	32	32	NUM
ejpam-6763	692	6	)	)	PUNCT
ejpam-6763	692	7	the	the	DET
ejpam-6763	692	8	weights	weight	NOUN
ejpam-6763	692	9	λξ	λξ	X
ejpam-6763	692	10	are	be	AUX
ejpam-6763	692	11	coefficients	coefficient	NOUN
ejpam-6763	692	12	that	that	PRON
ejpam-6763	692	13	multiply	multiply	VERB
ejpam-6763	692	14	the	the	DET
ejpam-6763	692	15	function	function	NOUN
ejpam-6763	692	16	values	value	NOUN
ejpam-6763	692	17	at	at	ADP
ejpam-6763	692	18	the	the	DET
ejpam-6763	692	19	nodes	node	NOUN
ejpam-6763	692	20	to	to	PART
ejpam-6763	692	21	approximate	approximate	VERB
ejpam-6763	692	22	the	the	DET
ejpam-6763	692	23	integral	integral	ADJ
ejpam-6763	692	24	,	,	PUNCT
ejpam-6763	692	25	given	give	VERB
ejpam-6763	692	26	by	by	ADP
ejpam-6763	692	27	:	:	PUNCT
ejpam-6763	692	28	λξ	λξ	PROPN
ejpam-6763	692	29	=	=	SYM
ejpam-6763	692	30	2	2	NUM
ejpam-6763	692	31	n	n	NOUN
ejpam-6763	692	32	n	n	PRON
ejpam-6763	692	33	′′∑	′′∑	NOUN
ejpam-6763	692	34	r=0	r=0	PROPN
ejpam-6763	693	1	even	even	ADV
ejpam-6763	693	2	cos	cos	PROPN
ejpam-6763	693	3	(	(	PUNCT
ejpam-6763	693	4	rξπ	rξπ	PROPN
ejpam-6763	693	5	n	n	PROPN
ejpam-6763	693	6	)	)	PUNCT
ejpam-6763	693	7	(	(	PUNCT
ejpam-6763	693	8	33	33	NUM
ejpam-6763	693	9	)	)	PUNCT
ejpam-6763	693	10	d.	d.	PROPN
ejpam-6763	693	11	kh	kh	PROPN
ejpam-6763	693	12	.	.	PUNCT
ejpam-6763	694	1	abdullah	abdullah	PROPN
ejpam-6763	694	2	,	,	PUNCT
ejpam-6763	694	3	sh	sh	PROPN
ejpam-6763	694	4	.	.	PROPN
ejpam-6763	694	5	sh	sh	PROPN
ejpam-6763	694	6	.	.	PROPN
ejpam-6763	694	7	ahmed	ahmed	PROPN
ejpam-6763	694	8	,	,	PUNCT
ejpam-6763	694	9	k.	k.	PROPN
ejpam-6763	694	10	h.	h.	PROPN
ejpam-6763	694	11	f.	f.	PROPN
ejpam-6763	694	12	jwamer	jwamer	PROPN
ejpam-6763	694	13	/	/	SYM
ejpam-6763	694	14	eur	eur	PROPN
ejpam-6763	694	15	.	.	PUNCT
ejpam-6763	695	1	j.	j.	PROPN
ejpam-6763	695	2	pure	pure	PROPN
ejpam-6763	695	3	appl	appl	PROPN
ejpam-6763	695	4	.	.	PROPN
ejpam-6763	695	5	math	math	PROPN
ejpam-6763	695	6	,	,	PUNCT
ejpam-6763	695	7	18	18	NUM
ejpam-6763	695	8	(	(	PUNCT
ejpam-6763	695	9	4	4	NUM
ejpam-6763	695	10	)	)	PUNCT
ejpam-6763	695	11	(	(	PUNCT
ejpam-6763	695	12	2025	2025	NUM
ejpam-6763	695	13	)	)	PUNCT
ejpam-6763	695	14	,	,	PUNCT
ejpam-6763	695	15	6763	6763	NUM
ejpam-6763	695	16	16	16	NUM
ejpam-6763	695	17	of	of	ADP
ejpam-6763	695	18	40	40	NUM
ejpam-6763	695	19	5	5	NUM
ejpam-6763	695	20	.	.	PUNCT
ejpam-6763	696	1	algorithms	algorithm	NOUN
ejpam-6763	696	2	in	in	ADP
ejpam-6763	696	3	this	this	DET
ejpam-6763	696	4	section	section	NOUN
ejpam-6763	696	5	,	,	PUNCT
ejpam-6763	696	6	we	we	PRON
ejpam-6763	696	7	present	present	VERB
ejpam-6763	696	8	a	a	DET
ejpam-6763	696	9	step	step	NOUN
ejpam-6763	696	10	-	-	PUNCT
ejpam-6763	696	11	by	by	ADP
ejpam-6763	696	12	-	-	PUNCT
ejpam-6763	696	13	step	step	NOUN
ejpam-6763	696	14	algorithmic	algorithmic	ADJ
ejpam-6763	696	15	description	description	NOUN
ejpam-6763	696	16	of	of	ADP
ejpam-6763	696	17	the	the	DET
ejpam-6763	696	18	proposed	propose	VERB
ejpam-6763	696	19	approach	approach	NOUN
ejpam-6763	696	20	.	.	PUNCT
ejpam-6763	697	1	to	to	PART
ejpam-6763	697	2	facilitate	facilitate	VERB
ejpam-6763	697	3	practical	practical	ADJ
ejpam-6763	697	4	implementation	implementation	NOUN
ejpam-6763	697	5	,	,	PUNCT
ejpam-6763	697	6	an	an	DET
ejpam-6763	697	7	itemized	itemize	VERB
ejpam-6763	697	8	version	version	NOUN
ejpam-6763	697	9	of	of	ADP
ejpam-6763	697	10	the	the	DET
ejpam-6763	697	11	algorithm	algorithm	NOUN
ejpam-6763	697	12	is	be	AUX
ejpam-6763	697	13	provided	provide	VERB
ejpam-6763	697	14	below	below	ADP
ejpam-6763	697	15	.	.	PUNCT
ejpam-6763	698	1	main	main	ADJ
ejpam-6763	698	2	algorithm	algorithm	NOUN
ejpam-6763	698	3	:	:	PUNCT
ejpam-6763	698	4	lsvifde	lsvifde	PROPN
ejpam-6763	698	5	’s	’s	PART
ejpam-6763	698	6	(	(	PUNCT
ejpam-6763	698	7	using	use	VERB
ejpam-6763	698	8	cubic	cubic	ADJ
ejpam-6763	698	9	b	b	PROPN
ejpam-6763	698	10	-	-	PUNCT
ejpam-6763	698	11	spline	spline	NOUN
ejpam-6763	698	12	)	)	PUNCT
ejpam-6763	698	13	input	input	NOUN
ejpam-6763	698	14	data	datum	NOUN
ejpam-6763	698	15	:	:	PUNCT
ejpam-6763	698	16	•	•	NUM
ejpam-6763	698	17	domain	domain	NOUN
ejpam-6763	698	18	bounds	bound	VERB
ejpam-6763	698	19	a	a	DET
ejpam-6763	698	20	,	,	PUNCT
ejpam-6763	698	21	b	b	NOUN
ejpam-6763	698	22	,	,	PUNCT
ejpam-6763	698	23	and	and	CCONJ
ejpam-6763	698	24	total	total	ADJ
ejpam-6763	698	25	number	number	NOUN
ejpam-6763	698	26	of	of	ADP
ejpam-6763	698	27	steps	step	NOUN
ejpam-6763	698	28	n	n	X
ejpam-6763	698	29	.	.	PUNCT
ejpam-6763	699	1	•	•	NUM
ejpam-6763	699	2	number	number	NOUN
ejpam-6763	699	3	of	of	ADP
ejpam-6763	699	4	equations	equation	NOUN
ejpam-6763	699	5	:	:	PUNCT
ejpam-6763	699	6	m+	m+	NUM
ejpam-6763	699	7	1	1	NUM
ejpam-6763	699	8	.	.	NOUN
ejpam-6763	699	9	•	•	NUM
ejpam-6763	699	10	functions	function	NOUN
ejpam-6763	699	11	:	:	PUNCT
ejpam-6763	699	12	pi(x	pi(x	NOUN
ejpam-6763	699	13	?	?	PUNCT
ejpam-6763	699	14	)	)	PUNCT
ejpam-6763	699	15	,	,	PUNCT
ejpam-6763	699	16	ai0(x	ai0(x	PROPN
ejpam-6763	699	17	?	?	PUNCT
ejpam-6763	699	18	)	)	PUNCT
ejpam-6763	699	19	,	,	PUNCT
ejpam-6763	699	20	ai1(x	ai1(x	NOUN
ejpam-6763	699	21	?	?	PUNCT
ejpam-6763	699	22	)	)	PUNCT
ejpam-6763	699	23	,	,	PUNCT
ejpam-6763	699	24	fi(x	fi(x	NUM
ejpam-6763	699	25	?	?	PUNCT
ejpam-6763	699	26	)	)	PUNCT
ejpam-6763	699	27	.	.	PUNCT
ejpam-6763	700	1	•	•	NUM
ejpam-6763	700	2	parameters	parameter	NOUN
ejpam-6763	700	3	:	:	PUNCT
ejpam-6763	700	4	ωij	ωij	VERB
ejpam-6763	700	5	,	,	PUNCT
ejpam-6763	700	6	kij(x	kij(x	X
ejpam-6763	700	7	?	?	PUNCT
ejpam-6763	700	8	,	,	PUNCT
ejpam-6763	700	9	s	s	X
ejpam-6763	700	10	)	)	PUNCT
ejpam-6763	700	11	,	,	PUNCT
ejpam-6763	700	12	σi0	σi0	NOUN
ejpam-6763	700	13	,	,	PUNCT
ejpam-6763	700	14	βij	βij	NOUN
ejpam-6763	700	15	,	,	PUNCT
ejpam-6763	700	16	for	for	ADP
ejpam-6763	700	17	all	all	DET
ejpam-6763	700	18	i	i	PROPN
ejpam-6763	700	19	,	,	PUNCT
ejpam-6763	700	20	j	j	PROPN
ejpam-6763	700	21	=	=	SYM
ejpam-6763	700	22	0	0	NUM
ejpam-6763	700	23	,	,	PUNCT
ejpam-6763	700	24	1	1	NUM
ejpam-6763	700	25	,	,	PUNCT
ejpam-6763	700	26	.	.	PUNCT
ejpam-6763	700	27	.	.	PUNCT
ejpam-6763	700	28	.	.	PUNCT
ejpam-6763	701	1	,	,	PUNCT
ejpam-6763	701	2	m.	m.	NOUN
ejpam-6763	701	3	output	output	NOUN
ejpam-6763	701	4	:	:	PUNCT
ejpam-6763	701	5	vector	vector	PROPN
ejpam-6763	701	6	b	b	PROPN
ejpam-6763	701	7	from	from	ADP
ejpam-6763	701	8	(	(	PUNCT
ejpam-6763	701	9	28	28	NUM
ejpam-6763	701	10	)	)	PUNCT
ejpam-6763	701	11	,	,	PUNCT
ejpam-6763	701	12	containing	contain	VERB
ejpam-6763	701	13	control	control	NOUN
ejpam-6763	701	14	points	point	NOUN
ejpam-6763	701	15	ϑi3	ϑi3	PROPN
ejpam-6763	701	16	,	,	PUNCT
ejpam-6763	701	17	i	i	PRON
ejpam-6763	701	18	=	=	NOUN
ejpam-6763	701	19	0	0	NUM
ejpam-6763	701	20	,	,	PUNCT
ejpam-6763	701	21	1	1	NUM
ejpam-6763	701	22	,	,	PUNCT
ejpam-6763	701	23	.	.	PUNCT
ejpam-6763	701	24	.	.	PUNCT
ejpam-6763	701	25	.	.	PUNCT
ejpam-6763	702	1	,	,	PUNCT
ejpam-6763	702	2	m.	m.	NOUN
ejpam-6763	702	3	steps	step	NOUN
ejpam-6763	702	4	:	:	PUNCT
ejpam-6763	702	5	(	(	PUNCT
ejpam-6763	702	6	i	i	NOUN
ejpam-6763	702	7	)	)	PUNCT
ejpam-6763	702	8	construct	construct	VERB
ejpam-6763	702	9	vectors	vector	NOUN
ejpam-6763	702	10	b	b	PROPN
ejpam-6763	702	11	and	and	CCONJ
ejpam-6763	702	12	c	c	PROPN
ejpam-6763	702	13	of	of	ADP
ejpam-6763	702	14	size	size	NOUN
ejpam-6763	702	15	m+	m+	NUM
ejpam-6763	702	16	1	1	NUM
ejpam-6763	702	17	,	,	PUNCT
ejpam-6763	702	18	and	and	CCONJ
ejpam-6763	702	19	matrix	matrix	VERB
ejpam-6763	702	20	a	a	PRON
ejpam-6763	702	21	of	of	ADP
ejpam-6763	702	22	size	size	NOUN
ejpam-6763	702	23	(	(	PUNCT
ejpam-6763	702	24	m+	m+	NOUN
ejpam-6763	702	25	1)×	1)×	NUM
ejpam-6763	702	26	(	(	PUNCT
ejpam-6763	702	27	m+	m+	NOUN
ejpam-6763	702	28	1	1	NUM
ejpam-6763	702	29	)	)	PUNCT
ejpam-6763	702	30	.	.	PUNCT
ejpam-6763	703	1	(	(	PUNCT
ejpam-6763	703	2	ii	ii	X
ejpam-6763	703	3	)	)	PUNCT
ejpam-6763	703	4	compute	compute	VERB
ejpam-6763	703	5	the	the	DET
ejpam-6763	703	6	step	step	NOUN
ejpam-6763	703	7	size	size	NOUN
ejpam-6763	703	8	:	:	PUNCT
ejpam-6763	704	1	h	h	NOUN
ejpam-6763	704	2	=	=	PUNCT
ejpam-6763	704	3	b−	b−	PROPN
ejpam-6763	704	4	a	a	PRON
ejpam-6763	704	5	n	n	NOUN
ejpam-6763	704	6	,	,	PUNCT
ejpam-6763	704	7	with	with	ADP
ejpam-6763	704	8	n	n	PRON
ejpam-6763	704	9	∈	∈	PROPN
ejpam-6763	704	10	n	n	NOUN
ejpam-6763	704	11	and	and	CCONJ
ejpam-6763	704	12	define	define	VERB
ejpam-6763	704	13	the	the	DET
ejpam-6763	704	14	partition	partition	NOUN
ejpam-6763	704	15	points	point	NOUN
ejpam-6763	704	16	:	:	PUNCT
ejpam-6763	704	17	x?r+1	x?r+1	PROPN
ejpam-6763	704	18	=	=	X
ejpam-6763	704	19	a+	a+	PUNCT
ejpam-6763	704	20	(	(	PUNCT
ejpam-6763	704	21	r	r	NOUN
ejpam-6763	704	22	+	+	PROPN
ejpam-6763	704	23	1)h	1)h	NUM
ejpam-6763	704	24	,	,	PUNCT
ejpam-6763	704	25	for	for	ADP
ejpam-6763	704	26	r	r	NOUN
ejpam-6763	704	27	=	=	SYM
ejpam-6763	704	28	0	0	NUM
ejpam-6763	704	29	,	,	PUNCT
ejpam-6763	704	30	1	1	NUM
ejpam-6763	704	31	,	,	PUNCT
ejpam-6763	704	32	.	.	PUNCT
ejpam-6763	704	33	.	.	PUNCT
ejpam-6763	705	1	.	.	PUNCT
ejpam-6763	706	1	,	,	PUNCT
ejpam-6763	706	2	n	n	CCONJ
ejpam-6763	706	3	−	−	PROPN
ejpam-6763	706	4	1	1	NUM
ejpam-6763	706	5	(	(	PUNCT
ejpam-6763	706	6	iii	iii	NOUN
ejpam-6763	706	7	)	)	PUNCT
ejpam-6763	706	8	approximate	approximate	ADJ
ejpam-6763	706	9	:	:	PUNCT
ejpam-6763	707	1	db{c,3	db{c,3	PROPN
ejpam-6763	707	2	}	}	PUNCT
ejpam-6763	707	3	i	i	PRON
ejpam-6763	707	4	(	(	PUNCT
ejpam-6763	707	5	x	x	NOUN
ejpam-6763	707	6	?	?	PUNCT
ejpam-6763	707	7	)	)	PUNCT
ejpam-6763	707	8	dx	dx	PROPN
ejpam-6763	707	9	?	?	PUNCT
ejpam-6763	708	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	708	2	x?=a	x?=a	PROPN
ejpam-6763	709	1	≈	≈	PROPN
ejpam-6763	709	2	y	y	PROPN
ejpam-6763	709	3	′	′	NUM
ejpam-6763	709	4	i(a	i(a	PROPN
ejpam-6763	709	5	)	)	PUNCT
ejpam-6763	709	6	using	use	VERB
ejpam-6763	709	7	the	the	DET
ejpam-6763	709	8	expression	expression	NOUN
ejpam-6763	709	9	:	:	PUNCT
ejpam-6763	709	10	1	1	NUM
ejpam-6763	709	11	pi(a	pi(a	NUM
ejpam-6763	709	12	)	)	PUNCT
ejpam-6763	709	13	fi(a	fi(a	PROPN
ejpam-6763	709	14	)	)	PUNCT
ejpam-6763	710	1	+	+	CCONJ
ejpam-6763	710	2	m∑	m∑	ADV
ejpam-6763	710	3	j=0	j=0	PROPN
ejpam-6763	710	4	ωij	ωij	PROPN
ejpam-6763	710	5	∫	∫	PROPN
ejpam-6763	710	6	a	a	DET
ejpam-6763	710	7	a	a	DET
ejpam-6763	710	8	kij(a	kij(a	PROPN
ejpam-6763	710	9	,	,	PUNCT
ejpam-6763	710	10	s	s	PART
ejpam-6763	710	11	)	)	PUNCT
ejpam-6763	710	12	c	c	NOUN
ejpam-6763	710	13	ad	ad	NOUN
ejpam-6763	710	14	βij	βij	NOUN
ejpam-6763	710	15	s	s	PART
ejpam-6763	710	16	yj(s	yj(s	NOUN
ejpam-6763	710	17	)	)	PUNCT
ejpam-6763	710	18	ds−	ds−	PROPN
ejpam-6763	710	19	ai0(a	ai0(a	PROPN
ejpam-6763	710	20	)	)	PUNCT
ejpam-6763	710	21	c	c	NOUN
ejpam-6763	710	22	ad	ad	NOUN
ejpam-6763	710	23	σi0	σi0	VERB
ejpam-6763	710	24	a	a	DET
ejpam-6763	710	25	yi(a)−	yi(a)−	NOUN
ejpam-6763	710	26	ai1(a)yi(a	ai1(a)yi(a	NOUN
ejpam-6763	710	27	)	)	PUNCT
ejpam-6763	710	28			NOUN
ejpam-6763	710	29	(	(	PUNCT
ejpam-6763	710	30	iv	iv	X
ejpam-6763	710	31	)	)	PUNCT
ejpam-6763	710	32	compute	compute	NOUN
ejpam-6763	710	33	:	:	PUNCT
ejpam-6763	710	34	ϑi0	ϑi0	NOUN
ejpam-6763	710	35	=	=	PUNCT
ejpam-6763	710	36	from	from	ADP
ejpam-6763	710	37	given	give	VERB
ejpam-6763	710	38	initial	initial	ADJ
ejpam-6763	710	39	condition	condition	NOUN
ejpam-6763	710	40	(	(	PUNCT
ejpam-6763	710	41	2	2	X
ejpam-6763	710	42	)	)	PUNCT
ejpam-6763	710	43	d.	d.	PROPN
ejpam-6763	710	44	kh	kh	PROPN
ejpam-6763	710	45	.	.	PUNCT
ejpam-6763	711	1	abdullah	abdullah	PROPN
ejpam-6763	711	2	,	,	PUNCT
ejpam-6763	711	3	sh	sh	PROPN
ejpam-6763	711	4	.	.	PROPN
ejpam-6763	711	5	sh	sh	PROPN
ejpam-6763	711	6	.	.	PROPN
ejpam-6763	711	7	ahmed	ahmed	PROPN
ejpam-6763	711	8	,	,	PUNCT
ejpam-6763	711	9	k.	k.	PROPN
ejpam-6763	711	10	h.	h.	PROPN
ejpam-6763	711	11	f.	f.	PROPN
ejpam-6763	711	12	jwamer	jwamer	PROPN
ejpam-6763	711	13	/	/	SYM
ejpam-6763	711	14	eur	eur	PROPN
ejpam-6763	711	15	.	.	PUNCT
ejpam-6763	712	1	j.	j.	PROPN
ejpam-6763	712	2	pure	pure	PROPN
ejpam-6763	712	3	appl	appl	PROPN
ejpam-6763	712	4	.	.	PROPN
ejpam-6763	712	5	math	math	PROPN
ejpam-6763	712	6	,	,	PUNCT
ejpam-6763	712	7	18	18	NUM
ejpam-6763	712	8	(	(	PUNCT
ejpam-6763	712	9	4	4	NUM
ejpam-6763	712	10	)	)	PUNCT
ejpam-6763	712	11	(	(	PUNCT
ejpam-6763	712	12	2025	2025	NUM
ejpam-6763	712	13	)	)	PUNCT
ejpam-6763	712	14	,	,	PUNCT
ejpam-6763	712	15	6763	6763	NUM
ejpam-6763	712	16	17	17	NUM
ejpam-6763	712	17	of	of	ADP
ejpam-6763	712	18	40	40	NUM
ejpam-6763	712	19	ϑi1	ϑi1	NOUN
ejpam-6763	712	20	=	=	SYM
ejpam-6763	712	21	nh	nh	PROPN
ejpam-6763	712	22	3	3	NUM
ejpam-6763	712	23	·	·	PUNCT
ejpam-6763	712	24	db{c,3	db{c,3	PROPN
ejpam-6763	712	25	}	}	PUNCT
ejpam-6763	712	26	i	i	PRON
ejpam-6763	712	27	(	(	PUNCT
ejpam-6763	712	28	x	x	NOUN
ejpam-6763	712	29	?	?	PUNCT
ejpam-6763	712	30	)	)	PUNCT
ejpam-6763	712	31	dx	dx	PROPN
ejpam-6763	712	32	?	?	PUNCT
ejpam-6763	712	33	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6763	713	1	x?=a	x?=a	PROPN
ejpam-6763	714	1	+	+	NUM
ejpam-6763	714	2	ϑi0	ϑi0	NOUN
ejpam-6763	714	3	ϑi2	ϑi2	NOUN
ejpam-6763	714	4	=	=	SYM
ejpam-6763	714	5	(	(	PUNCT
ejpam-6763	714	6	nh)2	nh)2	PROPN
ejpam-6763	714	7	6	6	NUM
ejpam-6763	714	8	·	·	PUNCT
ejpam-6763	714	9	d2b{c,3	d2b{c,3	ADP
ejpam-6763	714	10	}	}	PUNCT
ejpam-6763	714	11	i	i	PRON
ejpam-6763	714	12	(	(	PUNCT
ejpam-6763	714	13	x	x	NOUN
ejpam-6763	714	14	?	?	PUNCT
ejpam-6763	714	15	)	)	PUNCT
ejpam-6763	714	16	d(x?)2	d(x?)2	NUM
ejpam-6763	715	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-6763	715	2	x?=a	x?=a	PROPN
ejpam-6763	716	1	−	−	PROPN
ejpam-6763	716	2	ϑi0	ϑi0	NOUN
ejpam-6763	716	3	+	+	CCONJ
ejpam-6763	716	4	2ϑi1	2ϑi1	NUM
ejpam-6763	716	5	(	(	PUNCT
ejpam-6763	716	6	v	v	NOUN
ejpam-6763	716	7	)	)	PUNCT
ejpam-6763	716	8	use	use	VERB
ejpam-6763	716	9	forward	forward	ADJ
ejpam-6763	716	10	difference	difference	NOUN
ejpam-6763	716	11	to	to	PART
ejpam-6763	716	12	approximate	approximate	VERB
ejpam-6763	716	13	:	:	PUNCT
ejpam-6763	716	14	d2b{c,3	d2b{c,3	VERB
ejpam-6763	716	15	}	}	PUNCT
ejpam-6763	716	16	i	i	PRON
ejpam-6763	716	17	(	(	PUNCT
ejpam-6763	716	18	x	x	NOUN
ejpam-6763	716	19	?	?	PUNCT
ejpam-6763	716	20	)	)	PUNCT
ejpam-6763	716	21	d(x?)2	d(x?)2	NUM
ejpam-6763	717	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-6763	717	2	x?=a	x?=a	PROPN
ejpam-6763	718	1	≈	≈	PROPN
ejpam-6763	718	2	y(p	y(p	PROPN
ejpam-6763	718	3	)	)	PUNCT
ejpam-6763	719	1	i	i	PRON
ejpam-6763	719	2	(	(	PUNCT
ejpam-6763	719	3	x?r+2)−	x?r+2)−	PROPN
ejpam-6763	719	4	2y(p	2y(p	NUM
ejpam-6763	719	5	)	)	PUNCT
ejpam-6763	720	1	i	i	PRON
ejpam-6763	720	2	(	(	PUNCT
ejpam-6763	720	3	x?r+1	x?r+1	NOUN
ejpam-6763	720	4	)	)	PUNCT
ejpam-6763	721	1	+	+	NUM
ejpam-6763	721	2	yi(x	yi(x	NOUN
ejpam-6763	721	3	?	?	PUNCT
ejpam-6763	722	1	r	r	X
ejpam-6763	722	2	)	)	PUNCT
ejpam-6763	722	3	h2	h2	NOUN
ejpam-6763	722	4	(	(	PUNCT
ejpam-6763	722	5	vi	vi	NOUN
ejpam-6763	722	6	)	)	PUNCT
ejpam-6763	722	7	evaluate	evaluate	VERB
ejpam-6763	722	8	yi(x	yi(x	NOUN
ejpam-6763	722	9	?	?	PUNCT
ejpam-6763	723	1	r	r	X
ejpam-6763	723	2	)	)	PUNCT
ejpam-6763	723	3	from	from	ADP
ejpam-6763	723	4	(	(	PUNCT
ejpam-6763	723	5	2	2	NUM
ejpam-6763	723	6	)	)	PUNCT
ejpam-6763	723	7	,	,	PUNCT
ejpam-6763	723	8	and	and	CCONJ
ejpam-6763	723	9	y(p	y(p	NUM
ejpam-6763	723	10	)	)	PUNCT
ejpam-6763	723	11	i	i	PRON
ejpam-6763	723	12	(	(	PUNCT
ejpam-6763	723	13	x?r+1	x?r+1	PROPN
ejpam-6763	723	14	)	)	PUNCT
ejpam-6763	723	15	,	,	PUNCT
ejpam-6763	723	16	y	y	PROPN
ejpam-6763	723	17	(	(	PUNCT
ejpam-6763	723	18	p	p	NOUN
ejpam-6763	723	19	)	)	PUNCT
ejpam-6763	723	20	i	i	PROPN
ejpam-6763	723	21	(	(	PUNCT
ejpam-6763	723	22	x?r+2	x?r+2	NOUN
ejpam-6763	723	23	)	)	PUNCT
ejpam-6763	723	24	using	use	VERB
ejpam-6763	723	25	first	first	ADJ
ejpam-6763	723	26	-	-	PUNCT
ejpam-6763	723	27	order	order	NOUN
ejpam-6763	723	28	b	b	NOUN
ejpam-6763	723	29	-	-	NOUN
ejpam-6763	723	30	spline	spline	NOUN
ejpam-6763	723	31	.	.	PUNCT
ejpam-6763	724	1	(	(	PUNCT
ejpam-6763	724	2	vii	vii	PROPN
ejpam-6763	724	3	)	)	PUNCT
ejpam-6763	724	4	compute	compute	NOUN
ejpam-6763	724	5	entries	entry	NOUN
ejpam-6763	724	6	of	of	ADP
ejpam-6763	724	7	c	c	NOUN
ejpam-6763	724	8	using	use	VERB
ejpam-6763	724	9	(	(	PUNCT
ejpam-6763	724	10	29	29	NUM
ejpam-6763	724	11	):	):	PUNCT
ejpam-6763	724	12	c	c	NOUN
ejpam-6763	724	13	=	=	SYM
ejpam-6763	724	14			PROPN
ejpam-6763	724	15	l0	l0	PROPN
ejpam-6763	724	16	r	r	PROPN
ejpam-6763	724	17	l1	l1	PROPN
ejpam-6763	724	18	r	r	NOUN
ejpam-6763	724	19	...	...	PUNCT
ejpam-6763	725	1	lm	lm	INTJ
ejpam-6763	725	2	r	r	NOUN
ejpam-6763	725	3			X
ejpam-6763	725	4	(	(	PUNCT
ejpam-6763	725	5	viii	viii	NOUN
ejpam-6763	725	6	)	)	PUNCT
ejpam-6763	725	7	construct	construct	VERB
ejpam-6763	725	8	the	the	DET
ejpam-6763	725	9	matrix	matrix	NOUN
ejpam-6763	725	10	a	a	PRON
ejpam-6763	725	11	and	and	CCONJ
ejpam-6763	725	12	modify	modify	VERB
ejpam-6763	725	13	its	its	PRON
ejpam-6763	725	14	entries	entry	NOUN
ejpam-6763	725	15	using	use	VERB
ejpam-6763	725	16	the	the	DET
ejpam-6763	725	17	computed	computed	ADJ
ejpam-6763	725	18	ϑi0	ϑi0	NOUN
ejpam-6763	725	19	,	,	PUNCT
ejpam-6763	725	20	ϑi1	ϑi1	NOUN
ejpam-6763	725	21	,	,	PUNCT
ejpam-6763	725	22	and	and	CCONJ
ejpam-6763	725	23	ϑi2	ϑi2	NOUN
ejpam-6763	725	24	.	.	PUNCT
ejpam-6763	726	1	(	(	PUNCT
ejpam-6763	726	2	ix	ix	CCONJ
ejpam-6763	726	3	)	)	PUNCT
ejpam-6763	726	4	solve	solve	VERB
ejpam-6763	726	5	the	the	DET
ejpam-6763	726	6	system	system	NOUN
ejpam-6763	726	7	a	a	DET
ejpam-6763	726	8	·	·	SYM
ejpam-6763	726	9	b	b	NOUN
ejpam-6763	726	10	=	=	SYM
ejpam-6763	726	11	c	c	NOUN
ejpam-6763	726	12	,	,	PUNCT
ejpam-6763	726	13	using	use	VERB
ejpam-6763	726	14	clenshaw	clenshaw	ADJ
ejpam-6763	726	15	-	-	PUNCT
ejpam-6763	726	16	curtis	curtis	NOUN
ejpam-6763	726	17	quadrature	quadrature	NOUN
ejpam-6763	726	18	for	for	ADP
ejpam-6763	726	19	numerical	numerical	ADJ
ejpam-6763	726	20	integration	integration	NOUN
ejpam-6763	726	21	.	.	PUNCT
ejpam-6763	727	1	output	output	NOUN
ejpam-6763	727	2	:	:	PUNCT
ejpam-6763	728	1	b	b	X
ejpam-6763	728	2	=	=	SYM
ejpam-6763	728	3	[	[	PUNCT
ejpam-6763	728	4	ϑ03	ϑ03	NOUN
ejpam-6763	728	5	ϑ13	ϑ13	VERB
ejpam-6763	728	6	ϑ23	ϑ23	NOUN
ejpam-6763	728	7	.	.	PUNCT
ejpam-6763	728	8	.	.	PUNCT
ejpam-6763	728	9	.	.	PUNCT
ejpam-6763	729	1	ϑm3	ϑm3	NOUN
ejpam-6763	729	2	]	]	X
ejpam-6763	729	3	t	t	X
ejpam-6763	729	4	first	first	ADJ
ejpam-6763	729	5	procedure	procedure	NOUN
ejpam-6763	729	6	:	:	PUNCT
ejpam-6763	729	7	normalize	normalize	VERB
ejpam-6763	729	8	finding	find	VERB
ejpam-6763	729	9	cubic	cubic	ADJ
ejpam-6763	729	10	b	b	NOUN
ejpam-6763	729	11	-	-	NOUN
ejpam-6763	729	12	spline	spline	NOUN
ejpam-6763	729	13	for	for	ADP
ejpam-6763	729	14	each	each	DET
ejpam-6763	729	15	interval	interval	NOUN
ejpam-6763	729	16	(	(	PUNCT
ejpam-6763	729	17	nfcbi	nfcbi	PROPN
ejpam-6763	729	18	)	)	PUNCT
ejpam-6763	729	19	we	we	PRON
ejpam-6763	729	20	first	first	ADV
ejpam-6763	729	21	perform	perform	VERB
ejpam-6763	729	22	all	all	DET
ejpam-6763	729	23	steps	step	NOUN
ejpam-6763	729	24	outlined	outline	VERB
ejpam-6763	729	25	in	in	ADP
ejpam-6763	729	26	the	the	DET
ejpam-6763	729	27	main	main	ADJ
ejpam-6763	729	28	algorithm	algorithm	NOUN
ejpam-6763	729	29	(	(	PUNCT
ejpam-6763	729	30	lsvifde	lsvifde	PROPN
ejpam-6763	729	31	’s	’s	PART
ejpam-6763	729	32	)	)	PUNCT
ejpam-6763	729	33	,	,	PUNCT
ejpam-6763	729	34	and	and	CCONJ
ejpam-6763	729	35	then	then	ADV
ejpam-6763	729	36	proceed	proceed	VERB
ejpam-6763	729	37	with	with	ADP
ejpam-6763	729	38	the	the	DET
ejpam-6763	729	39	following	follow	VERB
ejpam-6763	729	40	additional	additional	ADJ
ejpam-6763	729	41	steps	step	NOUN
ejpam-6763	729	42	:	:	PUNCT
ejpam-6763	729	43	(	(	PUNCT
ejpam-6763	729	44	i	i	NOUN
ejpam-6763	729	45	)	)	PUNCT
ejpam-6763	729	46	for	for	ADP
ejpam-6763	729	47	r	r	NOUN
ejpam-6763	729	48	=	=	SYM
ejpam-6763	729	49	0	0	NUM
ejpam-6763	729	50	,	,	PUNCT
ejpam-6763	729	51	1	1	NUM
ejpam-6763	729	52	,	,	PUNCT
ejpam-6763	729	53	.	.	PUNCT
ejpam-6763	729	54	.	.	PUNCT
ejpam-6763	729	55	.	.	PUNCT
ejpam-6763	730	1	,	,	PUNCT
ejpam-6763	731	1	n	n	CCONJ
ejpam-6763	731	2	−	−	PROPN
ejpam-6763	731	3	1	1	NUM
ejpam-6763	731	4	,	,	PUNCT
ejpam-6763	731	5	set	set	VERB
ejpam-6763	731	6	:	:	PUNCT
ejpam-6763	731	7	x	x	X
ejpam-6763	731	8	?	?	PUNCT
ejpam-6763	732	1	=	=	PUNCT
ejpam-6763	732	2	x?r+1	x?r+1	PROPN
ejpam-6763	733	1	=	=	PUNCT
ejpam-6763	733	2	a+	a+	PUNCT
ejpam-6763	733	3	(	(	PUNCT
ejpam-6763	733	4	r	r	NOUN
ejpam-6763	733	5	+	+	PROPN
ejpam-6763	733	6	1)h	1)h	NUM
ejpam-6763	733	7	,	,	PUNCT
ejpam-6763	733	8	n	n	NOUN
ejpam-6763	733	9	=	=	SYM
ejpam-6763	733	10	3	3	NUM
ejpam-6763	733	11	,	,	PUNCT
ejpam-6763	733	12	k	k	PROPN
ejpam-6763	733	13	=	=	SYM
ejpam-6763	733	14	3	3	NUM
ejpam-6763	733	15	(	(	PUNCT
ejpam-6763	733	16	ii	ii	NOUN
ejpam-6763	733	17	)	)	PUNCT
ejpam-6763	733	18	for	for	ADP
ejpam-6763	733	19	each	each	DET
ejpam-6763	733	20	i	i	NOUN
ejpam-6763	733	21	=	=	NOUN
ejpam-6763	733	22	0	0	NUM
ejpam-6763	733	23	,	,	PUNCT
ejpam-6763	733	24	1	1	NUM
ejpam-6763	733	25	,	,	PUNCT
ejpam-6763	733	26	.	.	PUNCT
ejpam-6763	733	27	.	.	PUNCT
ejpam-6763	733	28	.	.	PUNCT
ejpam-6763	734	1	,	,	PUNCT
ejpam-6763	734	2	m	m	VERB
ejpam-6763	734	3	,	,	PUNCT
ejpam-6763	734	4	evaluate	evaluate	VERB
ejpam-6763	734	5	the	the	DET
ejpam-6763	734	6	approximate	approximate	ADJ
ejpam-6763	734	7	cubic	cubic	ADJ
ejpam-6763	734	8	b	b	PROPN
ejpam-6763	734	9	-	-	PUNCT
ejpam-6763	734	10	spline	spline	NOUN
ejpam-6763	734	11	solution	solution	NOUN
ejpam-6763	734	12	as	as	ADP
ejpam-6763	734	13	:	:	PUNCT
ejpam-6763	734	14	b{c,3	b{c,3	NOUN
ejpam-6763	734	15	}	}	PUNCT
ejpam-6763	734	16	i	i	PROPN
ejpam-6763	734	17	(	(	PUNCT
ejpam-6763	734	18	x?r+1	x?r+1	NOUN
ejpam-6763	734	19	)	)	PUNCT
ejpam-6763	735	1	≈	≈	PROPN
ejpam-6763	735	2	n∑	n∑	PROPN
ejpam-6763	735	3	z=0	z=0	PROPN
ejpam-6763	735	4	ϑiz	ϑiz	ADV
ejpam-6763	735	5	bk	bk	ADP
ejpam-6763	735	6	iz(x	iz(x	NOUN
ejpam-6763	735	7	?	?	PUNCT
ejpam-6763	736	1	r+1	r+1	X
ejpam-6763	736	2	)	)	PUNCT
ejpam-6763	736	3	d.	d.	PROPN
ejpam-6763	736	4	kh	kh	PROPN
ejpam-6763	736	5	.	.	PUNCT
ejpam-6763	737	1	abdullah	abdullah	PROPN
ejpam-6763	737	2	,	,	PUNCT
ejpam-6763	737	3	sh	sh	PROPN
ejpam-6763	737	4	.	.	PROPN
ejpam-6763	737	5	sh	sh	PROPN
ejpam-6763	737	6	.	.	PROPN
ejpam-6763	737	7	ahmed	ahmed	PROPN
ejpam-6763	737	8	,	,	PUNCT
ejpam-6763	737	9	k.	k.	PROPN
ejpam-6763	737	10	h.	h.	PROPN
ejpam-6763	737	11	f.	f.	PROPN
ejpam-6763	737	12	jwamer	jwamer	PROPN
ejpam-6763	737	13	/	/	SYM
ejpam-6763	737	14	eur	eur	PROPN
ejpam-6763	737	15	.	.	PUNCT
ejpam-6763	738	1	j.	j.	PROPN
ejpam-6763	738	2	pure	pure	PROPN
ejpam-6763	738	3	appl	appl	PROPN
ejpam-6763	738	4	.	.	PROPN
ejpam-6763	738	5	math	math	PROPN
ejpam-6763	738	6	,	,	PUNCT
ejpam-6763	738	7	18	18	NUM
ejpam-6763	738	8	(	(	PUNCT
ejpam-6763	738	9	4	4	NUM
ejpam-6763	738	10	)	)	PUNCT
ejpam-6763	738	11	(	(	PUNCT
ejpam-6763	738	12	2025	2025	NUM
ejpam-6763	738	13	)	)	PUNCT
ejpam-6763	738	14	,	,	PUNCT
ejpam-6763	738	15	6763	6763	NUM
ejpam-6763	738	16	18	18	NUM
ejpam-6763	738	17	of	of	ADP
ejpam-6763	738	18	40	40	NUM
ejpam-6763	738	19	output	output	NOUN
ejpam-6763	738	20	:	:	PUNCT
ejpam-6763	738	21	the	the	DET
ejpam-6763	738	22	set	set	NOUN
ejpam-6763	738	23	of	of	ADP
ejpam-6763	738	24	approximate	approximate	ADJ
ejpam-6763	738	25	solutions	solution	NOUN
ejpam-6763	738	26	for	for	ADP
ejpam-6763	738	27	each	each	DET
ejpam-6763	738	28	function	function	NOUN
ejpam-6763	738	29	:	:	PUNCT
ejpam-6763	738	30	b{c,3	b{c,3	NOUN
ejpam-6763	738	31	}	}	PUNCT
ejpam-6763	738	32	0	0	NUM
ejpam-6763	739	1	(	(	PUNCT
ejpam-6763	739	2	x?r+1	x?r+1	NOUN
ejpam-6763	739	3	)	)	PUNCT
ejpam-6763	739	4	,	,	PUNCT
ejpam-6763	739	5	b{c,3	b{c,3	NOUN
ejpam-6763	739	6	}	}	PUNCT
ejpam-6763	739	7	1	1	NUM
ejpam-6763	739	8	(	(	PUNCT
ejpam-6763	739	9	x?r+1	x?r+1	NOUN
ejpam-6763	739	10	)	)	PUNCT
ejpam-6763	739	11	,	,	PUNCT
ejpam-6763	739	12	.	.	PUNCT
ejpam-6763	739	13	.	.	PUNCT
ejpam-6763	740	1	.	.	PUNCT
ejpam-6763	741	1	,	,	PUNCT
ejpam-6763	741	2	b{c,3	b{c,3	VERB
ejpam-6763	741	3	}	}	PUNCT
ejpam-6763	741	4	m	m	PROPN
ejpam-6763	741	5	(	(	PUNCT
ejpam-6763	741	6	x?r+1	x?r+1	NOUN
ejpam-6763	741	7	)	)	PUNCT
ejpam-6763	741	8	represent	represent	VERB
ejpam-6763	741	9	the	the	DET
ejpam-6763	741	10	cubic	cubic	ADJ
ejpam-6763	741	11	b	b	PROPN
ejpam-6763	741	12	-	-	PUNCT
ejpam-6763	741	13	spline	spline	NOUN
ejpam-6763	741	14	approximation	approximation	NOUN
ejpam-6763	741	15	to	to	ADP
ejpam-6763	741	16	each	each	DET
ejpam-6763	741	17	yi(x	yi(x	NOUN
ejpam-6763	741	18	)	)	PUNCT
ejpam-6763	741	19	over	over	ADP
ejpam-6763	741	20	the	the	DET
ejpam-6763	741	21	interval	interval	NOUN
ejpam-6763	742	1	[	[	X
ejpam-6763	742	2	x?r	x?r	PROPN
ejpam-6763	742	3	,	,	PUNCT
ejpam-6763	742	4	x?r+1	x?r+1	X
ejpam-6763	742	5	]	]	X
ejpam-6763	742	6	.	.	PUNCT
ejpam-6763	743	1	ii	ii	PROPN
ejpam-6763	743	2	.	.	PUNCT
ejpam-6763	743	3	second	second	ADJ
ejpam-6763	743	4	procedure	procedure	NOUN
ejpam-6763	743	5	:	:	PUNCT
ejpam-6763	743	6	first	first	ADJ
ejpam-6763	743	7	control	control	NOUN
ejpam-6763	743	8	point	point	VERB
ejpam-6763	743	9	cubic	cubic	ADJ
ejpam-6763	743	10	b	b	PROPN
ejpam-6763	743	11	-	-	NOUN
ejpam-6763	743	12	spline	spline	NOUN
ejpam-6763	743	13	(	(	PUNCT
ejpam-6763	743	14	fcpcbs	fcpcbs	PROPN
ejpam-6763	743	15	)	)	PUNCT
ejpam-6763	743	16	we	we	PRON
ejpam-6763	743	17	begin	begin	VERB
ejpam-6763	743	18	by	by	ADP
ejpam-6763	743	19	performing	perform	VERB
ejpam-6763	743	20	all	all	DET
ejpam-6763	743	21	steps	step	NOUN
ejpam-6763	743	22	from	from	ADP
ejpam-6763	743	23	the	the	DET
ejpam-6763	743	24	main	main	ADJ
ejpam-6763	743	25	algorithm	algorithm	NOUN
ejpam-6763	743	26	(	(	PUNCT
ejpam-6763	743	27	lsvifde	lsvifde	PROPN
ejpam-6763	743	28	’s	’s	PART
ejpam-6763	743	29	)	)	PUNCT
ejpam-6763	743	30	,	,	PUNCT
ejpam-6763	743	31	and	and	CCONJ
ejpam-6763	743	32	then	then	ADV
ejpam-6763	743	33	follow	follow	VERB
ejpam-6763	743	34	the	the	DET
ejpam-6763	743	35	additional	additional	ADJ
ejpam-6763	743	36	steps	step	NOUN
ejpam-6763	743	37	below	below	ADV
ejpam-6763	743	38	:	:	PUNCT
ejpam-6763	743	39	(	(	PUNCT
ejpam-6763	743	40	i	i	NOUN
ejpam-6763	743	41	)	)	PUNCT
ejpam-6763	743	42	use	use	NOUN
ejpam-6763	743	43	:	:	PUNCT
ejpam-6763	743	44	ϑi3	ϑi3	X
ejpam-6763	743	45	=	=	PUNCT
ejpam-6763	743	46	ϑi3(x	ϑi3(x	PROPN
ejpam-6763	743	47	?	?	PUNCT
ejpam-6763	744	1	1	1	NUM
ejpam-6763	744	2	)	)	PUNCT
ejpam-6763	744	3	,	,	PUNCT
ejpam-6763	744	4	i	i	PRON
ejpam-6763	744	5	=	=	NOUN
ejpam-6763	744	6	0	0	NUM
ejpam-6763	744	7	,	,	PUNCT
ejpam-6763	744	8	1	1	NUM
ejpam-6763	744	9	,	,	PUNCT
ejpam-6763	744	10	.	.	PUNCT
ejpam-6763	744	11	.	.	PUNCT
ejpam-6763	745	1	.	.	PUNCT
ejpam-6763	746	1	,	,	PUNCT
ejpam-6763	746	2	m	m	PROPN
ejpam-6763	746	3	(	(	PUNCT
ejpam-6763	746	4	ii	ii	NOUN
ejpam-6763	746	5	)	)	PUNCT
ejpam-6763	746	6	for	for	ADP
ejpam-6763	746	7	r	r	NOUN
ejpam-6763	746	8	=	=	SYM
ejpam-6763	746	9	0	0	NUM
ejpam-6763	746	10	,	,	PUNCT
ejpam-6763	746	11	1	1	NUM
ejpam-6763	746	12	,	,	PUNCT
ejpam-6763	746	13	.	.	PUNCT
ejpam-6763	746	14	.	.	PUNCT
ejpam-6763	747	1	.	.	PUNCT
ejpam-6763	748	1	,	,	PUNCT
ejpam-6763	749	1	n	n	CCONJ
ejpam-6763	749	2	−	−	PROPN
ejpam-6763	749	3	1	1	NUM
ejpam-6763	749	4	,	,	PUNCT
ejpam-6763	749	5	set	set	VERB
ejpam-6763	749	6	:	:	PUNCT
ejpam-6763	749	7	x	x	X
ejpam-6763	749	8	?	?	PUNCT
ejpam-6763	750	1	=	=	PUNCT
ejpam-6763	750	2	x?r+1	x?r+1	PROPN
ejpam-6763	751	1	=	=	PUNCT
ejpam-6763	751	2	a+	a+	PUNCT
ejpam-6763	751	3	(	(	PUNCT
ejpam-6763	751	4	r	r	NOUN
ejpam-6763	751	5	+	+	PROPN
ejpam-6763	751	6	1)h	1)h	NUM
ejpam-6763	751	7	,	,	PUNCT
ejpam-6763	751	8	n	n	NOUN
ejpam-6763	751	9	=	=	SYM
ejpam-6763	751	10	3	3	NUM
ejpam-6763	751	11	,	,	PUNCT
ejpam-6763	751	12	k	k	PROPN
ejpam-6763	751	13	=	=	SYM
ejpam-6763	751	14	3	3	NUM
ejpam-6763	751	15	(	(	PUNCT
ejpam-6763	751	16	iii	iii	NOUN
ejpam-6763	751	17	)	)	PUNCT
ejpam-6763	751	18	for	for	ADP
ejpam-6763	751	19	each	each	DET
ejpam-6763	751	20	i	i	NOUN
ejpam-6763	751	21	=	=	NOUN
ejpam-6763	751	22	0	0	NUM
ejpam-6763	751	23	,	,	PUNCT
ejpam-6763	751	24	1	1	NUM
ejpam-6763	751	25	,	,	PUNCT
ejpam-6763	751	26	.	.	PUNCT
ejpam-6763	751	27	.	.	PUNCT
ejpam-6763	751	28	.	.	PUNCT
ejpam-6763	752	1	,	,	PUNCT
ejpam-6763	752	2	m	m	PROPN
ejpam-6763	752	3	,	,	PUNCT
ejpam-6763	752	4	evaluate	evaluate	VERB
ejpam-6763	752	5	:	:	PUNCT
ejpam-6763	752	6	b{c,3	b{c,3	PROPN
ejpam-6763	752	7	}	}	PUNCT
ejpam-6763	752	8	i	i	PROPN
ejpam-6763	752	9	(	(	PUNCT
ejpam-6763	752	10	x?r+1	x?r+1	NOUN
ejpam-6763	752	11	)	)	PUNCT
ejpam-6763	753	1	≈	≈	PROPN
ejpam-6763	753	2	n∑	n∑	PROPN
ejpam-6763	753	3	z=0	z=0	PROPN
ejpam-6763	753	4	ϑiz	ϑiz	ADV
ejpam-6763	753	5	bk	bk	ADP
ejpam-6763	753	6	iz(x	iz(x	NOUN
ejpam-6763	753	7	?	?	PUNCT
ejpam-6763	754	1	r+1	r+1	NOUN
ejpam-6763	754	2	)	)	PUNCT
ejpam-6763	754	3	output	output	NOUN
ejpam-6763	754	4	:	:	PUNCT
ejpam-6763	754	5	the	the	DET
ejpam-6763	754	6	approximate	approximate	ADJ
ejpam-6763	754	7	solutions	solution	NOUN
ejpam-6763	754	8	for	for	ADP
ejpam-6763	754	9	each	each	DET
ejpam-6763	754	10	function	function	NOUN
ejpam-6763	754	11	:	:	PUNCT
ejpam-6763	754	12	b{c,3	b{c,3	NOUN
ejpam-6763	754	13	}	}	PUNCT
ejpam-6763	754	14	0	0	NUM
ejpam-6763	755	1	(	(	PUNCT
ejpam-6763	755	2	x?r+1	x?r+1	NOUN
ejpam-6763	755	3	)	)	PUNCT
ejpam-6763	755	4	,	,	PUNCT
ejpam-6763	755	5	b{c,3	b{c,3	NOUN
ejpam-6763	755	6	}	}	PUNCT
ejpam-6763	755	7	1	1	NUM
ejpam-6763	755	8	(	(	PUNCT
ejpam-6763	755	9	x?r+1	x?r+1	NOUN
ejpam-6763	755	10	)	)	PUNCT
ejpam-6763	755	11	,	,	PUNCT
ejpam-6763	755	12	.	.	PUNCT
ejpam-6763	755	13	.	.	PUNCT
ejpam-6763	756	1	.	.	PUNCT
ejpam-6763	757	1	,	,	PUNCT
ejpam-6763	757	2	b{c,3	b{c,3	VERB
ejpam-6763	757	3	}	}	PUNCT
ejpam-6763	757	4	m	m	PROPN
ejpam-6763	757	5	(	(	PUNCT
ejpam-6763	757	6	x?r+1	x?r+1	PROPN
ejpam-6763	757	7	)	)	PUNCT
ejpam-6763	757	8	iii	iii	PROPN
ejpam-6763	757	9	.	.	PUNCT
ejpam-6763	757	10	third	third	ADJ
ejpam-6763	757	11	procedure	procedure	NOUN
ejpam-6763	757	12	:	:	PUNCT
ejpam-6763	757	13	average	average	ADJ
ejpam-6763	757	14	first	first	ADJ
ejpam-6763	757	15	and	and	CCONJ
ejpam-6763	757	16	final	final	ADJ
ejpam-6763	757	17	control	control	NOUN
ejpam-6763	757	18	point	point	NOUN
ejpam-6763	757	19	cubic	cubic	ADJ
ejpam-6763	757	20	bspline	bspline	NOUN
ejpam-6763	757	21	(	(	PUNCT
ejpam-6763	757	22	ffcpcbs	ffcpcbs	X
ejpam-6763	757	23	)	)	PUNCT
ejpam-6763	757	24	after	after	ADP
ejpam-6763	757	25	completing	complete	VERB
ejpam-6763	757	26	the	the	DET
ejpam-6763	757	27	main	main	ADJ
ejpam-6763	757	28	algorithm	algorithm	NOUN
ejpam-6763	757	29	,	,	PUNCT
ejpam-6763	757	30	proceed	proceed	VERB
ejpam-6763	757	31	with	with	ADP
ejpam-6763	757	32	the	the	DET
ejpam-6763	757	33	following	follow	VERB
ejpam-6763	757	34	steps	step	NOUN
ejpam-6763	757	35	:	:	PUNCT
ejpam-6763	757	36	(	(	PUNCT
ejpam-6763	757	37	i	i	NOUN
ejpam-6763	757	38	)	)	PUNCT
ejpam-6763	757	39	use	use	NOUN
ejpam-6763	757	40	:	:	PUNCT
ejpam-6763	757	41	ϑi3	ϑi3	X
ejpam-6763	757	42	=	=	SYM
ejpam-6763	757	43	1	1	NUM
ejpam-6763	757	44	2	2	NUM
ejpam-6763	757	45	(	(	PUNCT
ejpam-6763	757	46	ϑi3(x	ϑi3(x	PROPN
ejpam-6763	757	47	?	?	PUNCT
ejpam-6763	757	48	1	1	X
ejpam-6763	757	49	)	)	PUNCT
ejpam-6763	758	1	+	+	CCONJ
ejpam-6763	759	1	ϑi3(x	ϑi3(x	PROPN
ejpam-6763	759	2	?	?	PUNCT
ejpam-6763	760	1	n−1	n−1	PROPN
ejpam-6763	760	2	)	)	PUNCT
ejpam-6763	760	3	)	)	PUNCT
ejpam-6763	761	1	,	,	PUNCT
ejpam-6763	761	2	i	i	PRON
ejpam-6763	761	3	=	=	NOUN
ejpam-6763	761	4	0	0	NUM
ejpam-6763	761	5	,	,	PUNCT
ejpam-6763	761	6	1	1	NUM
ejpam-6763	761	7	,	,	PUNCT
ejpam-6763	761	8	.	.	PUNCT
ejpam-6763	761	9	.	.	PUNCT
ejpam-6763	762	1	.	.	PUNCT
ejpam-6763	763	1	,	,	PUNCT
ejpam-6763	763	2	m	m	PROPN
ejpam-6763	763	3	(	(	PUNCT
ejpam-6763	763	4	ii	ii	NOUN
ejpam-6763	763	5	)	)	PUNCT
ejpam-6763	763	6	for	for	ADP
ejpam-6763	763	7	r	r	NOUN
ejpam-6763	763	8	=	=	SYM
ejpam-6763	763	9	0	0	NUM
ejpam-6763	763	10	,	,	PUNCT
ejpam-6763	763	11	1	1	NUM
ejpam-6763	763	12	,	,	PUNCT
ejpam-6763	763	13	.	.	PUNCT
ejpam-6763	763	14	.	.	PUNCT
ejpam-6763	764	1	.	.	PUNCT
ejpam-6763	765	1	,	,	PUNCT
ejpam-6763	766	1	n	n	CCONJ
ejpam-6763	766	2	−	−	PROPN
ejpam-6763	766	3	1	1	NUM
ejpam-6763	766	4	,	,	PUNCT
ejpam-6763	766	5	set	set	VERB
ejpam-6763	766	6	:	:	PUNCT
ejpam-6763	766	7	x	x	X
ejpam-6763	766	8	?	?	PUNCT
ejpam-6763	767	1	=	=	PUNCT
ejpam-6763	767	2	x?r+1	x?r+1	PROPN
ejpam-6763	768	1	=	=	PUNCT
ejpam-6763	768	2	a+	a+	PUNCT
ejpam-6763	768	3	(	(	PUNCT
ejpam-6763	768	4	r	r	NOUN
ejpam-6763	768	5	+	+	PROPN
ejpam-6763	768	6	1)h	1)h	NUM
ejpam-6763	768	7	,	,	PUNCT
ejpam-6763	768	8	n	n	NOUN
ejpam-6763	768	9	=	=	SYM
ejpam-6763	768	10	3	3	NUM
ejpam-6763	768	11	,	,	PUNCT
ejpam-6763	768	12	k	k	PROPN
ejpam-6763	768	13	=	=	SYM
ejpam-6763	768	14	3	3	NUM
ejpam-6763	768	15	(	(	PUNCT
ejpam-6763	768	16	iii	iii	NOUN
ejpam-6763	768	17	)	)	PUNCT
ejpam-6763	768	18	for	for	ADP
ejpam-6763	768	19	each	each	DET
ejpam-6763	768	20	i	i	NOUN
ejpam-6763	768	21	=	=	NOUN
ejpam-6763	768	22	0	0	NUM
ejpam-6763	768	23	,	,	PUNCT
ejpam-6763	768	24	1	1	NUM
ejpam-6763	768	25	,	,	PUNCT
ejpam-6763	768	26	.	.	PUNCT
ejpam-6763	768	27	.	.	PUNCT
ejpam-6763	768	28	.	.	PUNCT
ejpam-6763	769	1	,	,	PUNCT
ejpam-6763	769	2	m	m	PROPN
ejpam-6763	769	3	,	,	PUNCT
ejpam-6763	769	4	compute	compute	NOUN
ejpam-6763	769	5	:	:	PUNCT
ejpam-6763	769	6	b{c,3	b{c,3	PROPN
ejpam-6763	769	7	}	}	PUNCT
ejpam-6763	769	8	i	i	PROPN
ejpam-6763	769	9	(	(	PUNCT
ejpam-6763	769	10	x?r+1	x?r+1	NOUN
ejpam-6763	769	11	)	)	PUNCT
ejpam-6763	770	1	≈	≈	PROPN
ejpam-6763	770	2	n∑	n∑	PROPN
ejpam-6763	770	3	z=0	z=0	PROPN
ejpam-6763	770	4	ϑiz	ϑiz	ADV
ejpam-6763	770	5	bk	bk	ADP
ejpam-6763	770	6	iz(x	iz(x	NOUN
ejpam-6763	770	7	?	?	PUNCT
ejpam-6763	771	1	r+1	r+1	NOUN
ejpam-6763	771	2	)	)	PUNCT
ejpam-6763	771	3	output	output	NOUN
ejpam-6763	771	4	:	:	PUNCT
ejpam-6763	771	5	the	the	DET
ejpam-6763	771	6	resulting	result	VERB
ejpam-6763	771	7	approximations	approximation	NOUN
ejpam-6763	771	8	:	:	PUNCT
ejpam-6763	771	9	b{c,3	b{c,3	NOUN
ejpam-6763	771	10	}	}	PUNCT
ejpam-6763	771	11	0	0	NUM
ejpam-6763	772	1	(	(	PUNCT
ejpam-6763	772	2	x?r+1	x?r+1	NOUN
ejpam-6763	772	3	)	)	PUNCT
ejpam-6763	772	4	,	,	PUNCT
ejpam-6763	772	5	b{c,3	b{c,3	NOUN
ejpam-6763	772	6	}	}	PUNCT
ejpam-6763	772	7	1	1	NUM
ejpam-6763	772	8	(	(	PUNCT
ejpam-6763	772	9	x?r+1	x?r+1	NOUN
ejpam-6763	772	10	)	)	PUNCT
ejpam-6763	772	11	,	,	PUNCT
ejpam-6763	772	12	.	.	PUNCT
ejpam-6763	772	13	.	.	PUNCT
ejpam-6763	773	1	.	.	PUNCT
ejpam-6763	774	1	,	,	PUNCT
ejpam-6763	774	2	b{c,3	b{c,3	VERB
ejpam-6763	774	3	}	}	PUNCT
ejpam-6763	774	4	m	m	PROPN
ejpam-6763	774	5	(	(	PUNCT
ejpam-6763	774	6	x?r+1	x?r+1	PROPN
ejpam-6763	774	7	)	)	PUNCT
ejpam-6763	774	8	d.	d.	PROPN
ejpam-6763	774	9	kh	kh	PROPN
ejpam-6763	774	10	.	.	PUNCT
ejpam-6763	775	1	abdullah	abdullah	PROPN
ejpam-6763	775	2	,	,	PUNCT
ejpam-6763	775	3	sh	sh	PROPN
ejpam-6763	775	4	.	.	PROPN
ejpam-6763	775	5	sh	sh	PROPN
ejpam-6763	775	6	.	.	PROPN
ejpam-6763	775	7	ahmed	ahmed	PROPN
ejpam-6763	775	8	,	,	PUNCT
ejpam-6763	775	9	k.	k.	PROPN
ejpam-6763	775	10	h.	h.	PROPN
ejpam-6763	775	11	f.	f.	PROPN
ejpam-6763	775	12	jwamer	jwamer	PROPN
ejpam-6763	775	13	/	/	SYM
ejpam-6763	775	14	eur	eur	PROPN
ejpam-6763	775	15	.	.	PUNCT
ejpam-6763	776	1	j.	j.	PROPN
ejpam-6763	776	2	pure	pure	PROPN
ejpam-6763	776	3	appl	appl	PROPN
ejpam-6763	776	4	.	.	PROPN
ejpam-6763	776	5	math	math	PROPN
ejpam-6763	776	6	,	,	PUNCT
ejpam-6763	776	7	18	18	NUM
ejpam-6763	776	8	(	(	PUNCT
ejpam-6763	776	9	4	4	NUM
ejpam-6763	776	10	)	)	PUNCT
ejpam-6763	776	11	(	(	PUNCT
ejpam-6763	776	12	2025	2025	NUM
ejpam-6763	776	13	)	)	PUNCT
ejpam-6763	776	14	,	,	PUNCT
ejpam-6763	776	15	6763	6763	NUM
ejpam-6763	776	16	19	19	NUM
ejpam-6763	776	17	of	of	ADP
ejpam-6763	776	18	40	40	NUM
ejpam-6763	776	19	6	6	NUM
ejpam-6763	776	20	.	.	PUNCT
ejpam-6763	776	21	numerical	numerical	ADJ
ejpam-6763	776	22	results	result	NOUN
ejpam-6763	776	23	in	in	ADP
ejpam-6763	776	24	this	this	DET
ejpam-6763	776	25	section	section	NOUN
ejpam-6763	776	26	,	,	PUNCT
ejpam-6763	776	27	we	we	PRON
ejpam-6763	776	28	present	present	VERB
ejpam-6763	776	29	some	some	DET
ejpam-6763	776	30	numerical	numerical	ADJ
ejpam-6763	776	31	examples	example	NOUN
ejpam-6763	776	32	to	to	PART
ejpam-6763	776	33	demonstrate	demonstrate	VERB
ejpam-6763	776	34	the	the	DET
ejpam-6763	776	35	accuracy	accuracy	NOUN
ejpam-6763	776	36	and	and	CCONJ
ejpam-6763	776	37	efficiency	efficiency	NOUN
ejpam-6763	776	38	of	of	ADP
ejpam-6763	776	39	the	the	DET
ejpam-6763	776	40	proposed	propose	VERB
ejpam-6763	776	41	method	method	NOUN
ejpam-6763	776	42	.	.	PUNCT
ejpam-6763	777	1	we	we	PRON
ejpam-6763	777	2	examine	examine	VERB
ejpam-6763	777	3	a	a	DET
ejpam-6763	777	4	set	set	NOUN
ejpam-6763	777	5	of	of	ADP
ejpam-6763	777	6	test	test	NOUN
ejpam-6763	777	7	cases	case	NOUN
ejpam-6763	777	8	to	to	PART
ejpam-6763	777	9	evaluate	evaluate	VERB
ejpam-6763	777	10	the	the	DET
ejpam-6763	777	11	performance	performance	NOUN
ejpam-6763	777	12	of	of	ADP
ejpam-6763	777	13	the	the	DET
ejpam-6763	777	14	developed	develop	VERB
ejpam-6763	777	15	algorithm	algorithm	NOUN
ejpam-6763	777	16	in	in	ADP
ejpam-6763	777	17	solving	solve	VERB
ejpam-6763	777	18	a	a	DET
ejpam-6763	777	19	system	system	NOUN
ejpam-6763	777	20	of	of	ADP
ejpam-6763	777	21	volterra	volterra	PROPN
ejpam-6763	777	22	integro	integro	PROPN
ejpam-6763	777	23	-	-	PUNCT
ejpam-6763	777	24	differential	differential	NOUN
ejpam-6763	777	25	equations	equation	NOUN
ejpam-6763	777	26	with	with	ADP
ejpam-6763	777	27	classical	classical	ADJ
ejpam-6763	777	28	and	and	CCONJ
ejpam-6763	777	29	fractional	fractional	ADJ
ejpam-6763	777	30	orders	order	NOUN
ejpam-6763	777	31	.	.	PUNCT
ejpam-6763	778	1	the	the	DET
ejpam-6763	778	2	obtained	obtain	VERB
ejpam-6763	778	3	results	result	NOUN
ejpam-6763	778	4	are	be	AUX
ejpam-6763	778	5	compared	compare	VERB
ejpam-6763	778	6	with	with	ADP
ejpam-6763	778	7	the	the	DET
ejpam-6763	778	8	exact	exact	ADJ
ejpam-6763	778	9	solution	solution	NOUN
ejpam-6763	778	10	;	;	PUNCT
ejpam-6763	778	11	this	this	DET
ejpam-6763	778	12	method	method	NOUN
ejpam-6763	778	13	’s	’s	PART
ejpam-6763	778	14	implementation	implementation	NOUN
ejpam-6763	778	15	is	be	AUX
ejpam-6763	778	16	supported	support	VERB
ejpam-6763	778	17	by	by	ADP
ejpam-6763	778	18	a	a	DET
ejpam-6763	778	19	python	python	NOUN
ejpam-6763	778	20	program	program	NOUN
ejpam-6763	778	21	.	.	PUNCT
ejpam-6763	779	1	all	all	DET
ejpam-6763	779	2	the	the	DET
ejpam-6763	779	3	calculations	calculation	NOUN
ejpam-6763	779	4	are	be	AUX
ejpam-6763	779	5	executed	execute	VERB
ejpam-6763	779	6	in	in	ADP
ejpam-6763	779	7	least	least	ADJ
ejpam-6763	779	8	square	square	ADJ
ejpam-6763	779	9	error	error	NOUN
ejpam-6763	779	10	.	.	PUNCT
ejpam-6763	780	1	example	example	NOUN
ejpam-6763	780	2	1	1	NUM
ejpam-6763	780	3	.	.	X
ejpam-6763	781	1	consider	consider	VERB
ejpam-6763	781	2	the	the	DET
ejpam-6763	781	3	following	follow	VERB
ejpam-6763	781	4	classical	classical	ADJ
ejpam-6763	781	5	and	and	CCONJ
ejpam-6763	781	6	fractional	fractional	ADJ
ejpam-6763	781	7	order	order	NOUN
ejpam-6763	781	8	system	system	NOUN
ejpam-6763	781	9	of	of	ADP
ejpam-6763	781	10	volterra	volterra	PROPN
ejpam-6763	781	11	integro	integro	PROPN
ejpam-6763	781	12	-	-	PUNCT
ejpam-6763	781	13	differential	differential	NOUN
ejpam-6763	781	14	equations	equation	NOUN
ejpam-6763	781	15	(	(	PUNCT
ejpam-6763	781	16	cfvides	cfvide	NOUN
ejpam-6763	781	17	):	):	PUNCT
ejpam-6763	781	18	ex	ex	X
ejpam-6763	781	19	y	y	PROPN
ejpam-6763	781	20	′	′	NUM
ejpam-6763	781	21	0(x	0(x	NOUN
ejpam-6763	781	22	)	)	PUNCT
ejpam-6763	782	1	+	+	CCONJ
ejpam-6763	782	2	x2	x2	PROPN
ejpam-6763	782	3	c	c	PROPN
ejpam-6763	782	4	adσ00	adσ00	PROPN
ejpam-6763	782	5	x	x	SYM
ejpam-6763	782	6	y0(x	y0(x	PROPN
ejpam-6763	782	7	)	)	PUNCT
ejpam-6763	783	1	+	+	X
ejpam-6763	783	2	cos(x)y0(x	cos(x)y0(x	NOUN
ejpam-6763	783	3	)	)	PUNCT
ejpam-6763	783	4	=	=	PUNCT
ejpam-6763	783	5	f0(x	f0(x	NOUN
ejpam-6763	783	6	)	)	PUNCT
ejpam-6763	784	1	+	+	CCONJ
ejpam-6763	784	2	ω00	ω00	ADJ
ejpam-6763	784	3	∫	∫	PROPN
ejpam-6763	784	4	x	x	SYM
ejpam-6763	784	5	0	0	NUM
ejpam-6763	784	6	exsy0(s	exsy0(s	NUM
ejpam-6763	784	7	)	)	PUNCT
ejpam-6763	784	8	ds	ds	NOUN
ejpam-6763	784	9	+	+	NUM
ejpam-6763	784	10	ω01	ω01	NUM
ejpam-6763	784	11	∫	∫	NOUN
ejpam-6763	784	12	x	x	X
ejpam-6763	784	13	0	0	PUNCT
ejpam-6763	784	14	(	(	PUNCT
ejpam-6763	784	15	sx2	sx2	NOUN
ejpam-6763	784	16	−	−	PROPN
ejpam-6763	784	17	1	1	NUM
ejpam-6763	784	18	)	)	PUNCT
ejpam-6763	784	19	cadβ01	cadβ01	NOUN
ejpam-6763	784	20	s	s	X
ejpam-6763	784	21	y1(s	y1(s	NOUN
ejpam-6763	784	22	)	)	PUNCT
ejpam-6763	784	23	ds	ds	NOUN
ejpam-6763	784	24	+	+	CCONJ
ejpam-6763	784	25	ω02	ω02	NOUN
ejpam-6763	784	26	∫	∫	PROPN
ejpam-6763	784	27	x	x	SYM
ejpam-6763	784	28	0	0	NUM
ejpam-6763	784	29	s2	s2	PROPN
ejpam-6763	784	30	sin(x	sin(x	PROPN
ejpam-6763	784	31	)	)	PUNCT
ejpam-6763	784	32	cadβ02	cadβ02	NOUN
ejpam-6763	784	33	s	s	PART
ejpam-6763	784	34	y2(s	y2(s	NOUN
ejpam-6763	784	35	)	)	PUNCT
ejpam-6763	784	36	ds	ds	ADJ
ejpam-6763	784	37	,	,	PUNCT
ejpam-6763	784	38	cos(x)y	cos(x)y	ADJ
ejpam-6763	784	39	′	′	NOUN
ejpam-6763	784	40	1(x	1(x	NUM
ejpam-6763	784	41	)	)	PUNCT
ejpam-6763	785	1	+	+	CCONJ
ejpam-6763	786	1	x3	x3	ADJ
ejpam-6763	786	2	c	c	NOUN
ejpam-6763	786	3	0d0.6	0d0.6	NOUN
ejpam-6763	786	4	x	x	SYM
ejpam-6763	786	5	y1(x	y1(x	NOUN
ejpam-6763	786	6	)	)	PUNCT
ejpam-6763	787	1	+	+	CCONJ
ejpam-6763	787	2	ex	ex	ADJ
ejpam-6763	787	3	y1(x	y1(x	NOUN
ejpam-6763	787	4	)	)	PUNCT
ejpam-6763	787	5	=	=	SYM
ejpam-6763	787	6	f1(x	f1(x	X
ejpam-6763	787	7	)	)	PUNCT
ejpam-6763	787	8	+	+	CCONJ
ejpam-6763	787	9	ω10	ω10	NUM
ejpam-6763	787	10	∫	∫	PROPN
ejpam-6763	787	11	x	x	X
ejpam-6763	787	12	0	0	PUNCT
ejpam-6763	787	13	(	(	PUNCT
ejpam-6763	787	14	x2s+	x2s+	PROPN
ejpam-6763	787	15	1)y0(s	1)y0(s	NUM
ejpam-6763	787	16	)	)	PUNCT
ejpam-6763	788	1	ds	ds	PROPN
ejpam-6763	788	2	+	+	CCONJ
ejpam-6763	788	3	ω11	ω11	ADJ
ejpam-6763	788	4	∫	∫	PROPN
ejpam-6763	788	5	x	x	X
ejpam-6763	788	6	0	0	PROPN
ejpam-6763	788	7	s	s	PART
ejpam-6763	788	8	sin(x	sin(x	PROPN
ejpam-6763	788	9	)	)	PUNCT
ejpam-6763	788	10	c0dβ11	c0dβ11	PROPN
ejpam-6763	788	11	s	s	PART
ejpam-6763	788	12	y1(s	y1(s	NOUN
ejpam-6763	788	13	)	)	PUNCT
ejpam-6763	788	14	ds	ds	NOUN
ejpam-6763	788	15	+	+	NUM
ejpam-6763	788	16	ω12	ω12	NUM
ejpam-6763	788	17	∫	∫	PROPN
ejpam-6763	788	18	x	x	SYM
ejpam-6763	788	19	0	0	NUM
ejpam-6763	788	20	x2(s−	x2(s−	PROPN
ejpam-6763	788	21	1	1	NUM
ejpam-6763	788	22	)	)	PUNCT
ejpam-6763	788	23	c0dβ12	c0dβ12	X
ejpam-6763	789	1	s	s	PROPN
ejpam-6763	789	2	y2(s	y2(s	NOUN
ejpam-6763	789	3	)	)	PUNCT
ejpam-6763	789	4	ds	ds	ADJ
ejpam-6763	789	5	,	,	PUNCT
ejpam-6763	789	6	2y	2y	NUM
ejpam-6763	789	7	′	′	NUM
ejpam-6763	789	8	2(x	2(x	NUM
ejpam-6763	789	9	)	)	PUNCT
ejpam-6763	790	1	+	+	CCONJ
ejpam-6763	790	2	ex	ex	PRON
ejpam-6763	790	3	c	c	NOUN
ejpam-6763	790	4	0d0.5	0d0.5	NUM
ejpam-6763	790	5	x	x	SYM
ejpam-6763	790	6	y2(x	y2(x	PROPN
ejpam-6763	790	7	)	)	PUNCT
ejpam-6763	790	8	+	+	CCONJ
ejpam-6763	790	9	sin(x)y2(x	sin(x)y2(x	PROPN
ejpam-6763	790	10	)	)	PUNCT
ejpam-6763	790	11	=	=	SYM
ejpam-6763	790	12	f2(x	f2(x	PROPN
ejpam-6763	790	13	)	)	PUNCT
ejpam-6763	790	14	+	+	NUM
ejpam-6763	790	15	ω20	ω20	NUM
ejpam-6763	790	16	∫	∫	PROPN
ejpam-6763	790	17	x	x	X
ejpam-6763	790	18	0	0	PUNCT
ejpam-6763	790	19	(	(	PUNCT
ejpam-6763	790	20	x3s2	x3s2	NOUN
ejpam-6763	790	21	−	−	NOUN
ejpam-6763	790	22	1)y0(s	1)y0(s	NUM
ejpam-6763	790	23	)	)	PUNCT
ejpam-6763	790	24	ds	ds	PROPN
ejpam-6763	790	25	+	+	CCONJ
ejpam-6763	790	26	ω21	ω21	VERB
ejpam-6763	790	27	∫	∫	PROPN
ejpam-6763	790	28	x	x	SYM
ejpam-6763	790	29	0	0	NUM
ejpam-6763	790	30	sex	sex	NOUN
ejpam-6763	790	31	c	c	X
ejpam-6763	790	32	0dβ21	0dβ21	PROPN
ejpam-6763	790	33	s	s	PROPN
ejpam-6763	790	34	y1(s	y1(s	NOUN
ejpam-6763	790	35	)	)	PUNCT
ejpam-6763	790	36	ds	ds	NOUN
ejpam-6763	791	1	+	+	CCONJ
ejpam-6763	791	2	ω22	ω22	ADP
ejpam-6763	791	3	∫	∫	PROPN
ejpam-6763	791	4	x	x	X
ejpam-6763	791	5	0	0	PUNCT
ejpam-6763	791	6	(	(	PUNCT
ejpam-6763	791	7	s2	s2	NOUN
ejpam-6763	791	8	+	+	CCONJ
ejpam-6763	791	9	1	1	X
ejpam-6763	791	10	)	)	PUNCT
ejpam-6763	791	11	c0dβ22	c0dβ22	PROPN
ejpam-6763	791	12	s	s	NOUN
ejpam-6763	791	13	y2(s	y2(s	NOUN
ejpam-6763	791	14	)	)	PUNCT
ejpam-6763	791	15	ds	ds	NOUN
ejpam-6763	791	16	.	.	PUNCT
ejpam-6763	792	1	the	the	DET
ejpam-6763	792	2	given	give	VERB
ejpam-6763	792	3	functions	function	NOUN
ejpam-6763	792	4	f0(x	f0(x	NOUN
ejpam-6763	792	5	)	)	PUNCT
ejpam-6763	792	6	,	,	PUNCT
ejpam-6763	792	7	f1(x	f1(x	PROPN
ejpam-6763	792	8	)	)	PUNCT
ejpam-6763	792	9	,	,	PUNCT
ejpam-6763	792	10	and	and	CCONJ
ejpam-6763	792	11	f2(x	f2(x	NUM
ejpam-6763	792	12	)	)	PUNCT
ejpam-6763	792	13	are	be	AUX
ejpam-6763	792	14	defined	define	VERB
ejpam-6763	792	15	as	as	SCONJ
ejpam-6763	792	16	follows	follow	VERB
ejpam-6763	792	17	:	:	PUNCT
ejpam-6763	792	18	f0(x	f0(x	NOUN
ejpam-6763	792	19	)	)	PUNCT
ejpam-6763	792	20	=	=	SYM
ejpam-6763	793	1	ex	ex	X
ejpam-6763	794	1	+	+	SYM
ejpam-6763	794	2	x2.3	x2.3	PROPN
ejpam-6763	794	3	γ(1.3	γ(1.3	PROPN
ejpam-6763	794	4	)	)	PUNCT
ejpam-6763	795	1	+	+	CCONJ
ejpam-6763	795	2	(	(	PUNCT
ejpam-6763	795	3	x+	x+	ADJ
ejpam-6763	795	4	1	1	X
ejpam-6763	795	5	)	)	PUNCT
ejpam-6763	795	6	cos(x	cos(x	PROPN
ejpam-6763	795	7	)	)	PUNCT
ejpam-6763	796	1	−	−	PROPN
ejpam-6763	796	2	ω00	ω00	NOUN
ejpam-6763	796	3	(	(	PUNCT
ejpam-6763	796	4	exx3	exx3	NOUN
ejpam-6763	796	5	3	3	NUM
ejpam-6763	796	6	+	+	CCONJ
ejpam-6763	796	7	exx2	exx2	PROPN
ejpam-6763	796	8	2	2	NUM
ejpam-6763	796	9	)	)	PUNCT
ejpam-6763	796	10	+	+	CCONJ
ejpam-6763	796	11	2ω01	2ω01	NUM
ejpam-6763	796	12	γ(1.2	γ(1.2	NOUN
ejpam-6763	796	13	)	)	PUNCT
ejpam-6763	796	14	(	(	PUNCT
ejpam-6763	796	15	x4.2	x4.2	X
ejpam-6763	796	16	2.2	2.2	NUM
ejpam-6763	796	17	−	−	NOUN
ejpam-6763	796	18	x1.2	x1.2	PROPN
ejpam-6763	796	19	1.2	1.2	NUM
ejpam-6763	796	20	)	)	PUNCT
ejpam-6763	796	21	−	−	NUM
ejpam-6763	796	22	3ω02	3ω02	NUM
ejpam-6763	796	23	γ(1.5	γ(1.5	PROPN
ejpam-6763	796	24	)	)	PUNCT
ejpam-6763	796	25	·	·	PUNCT
ejpam-6763	796	26	x	x	SYM
ejpam-6763	796	27	3.5	3.5	NUM
ejpam-6763	796	28	3.5	3.5	NUM
ejpam-6763	796	29	sin(x	sin(x	PROPN
ejpam-6763	796	30	)	)	PUNCT
ejpam-6763	796	31	,	,	PUNCT
ejpam-6763	796	32	f1(x	f1(x	NOUN
ejpam-6763	796	33	)	)	PUNCT
ejpam-6763	796	34	=	=	SYM
ejpam-6763	797	1	−2	−2	NOUN
ejpam-6763	797	2	cos(x)−	cos(x)−	NOUN
ejpam-6763	797	3	2x3.4	2x3.4	NUM
ejpam-6763	797	4	γ(1.4	γ(1.4	PROPN
ejpam-6763	797	5	)	)	PUNCT
ejpam-6763	798	1	+	+	CCONJ
ejpam-6763	798	2	(	(	PUNCT
ejpam-6763	798	3	1−	1−	NUM
ejpam-6763	798	4	2x)ex	2x)ex	NUM
ejpam-6763	798	5	−	−	NOUN
ejpam-6763	799	1	ω10	ω10	PROPN
ejpam-6763	799	2	(	(	PUNCT
ejpam-6763	799	3	x5	x5	NOUN
ejpam-6763	799	4	3	3	NUM
ejpam-6763	799	5	+	+	CCONJ
ejpam-6763	799	6	x4	x4	PROPN
ejpam-6763	799	7	2	2	NUM
ejpam-6763	800	1	+	+	CCONJ
ejpam-6763	800	2	x2	x2	PROPN
ejpam-6763	800	3	2	2	NUM
ejpam-6763	800	4	+	+	NOUN
ejpam-6763	800	5	x	x	X
ejpam-6763	800	6	)	)	PUNCT
ejpam-6763	801	1	+	+	CCONJ
ejpam-6763	801	2	2ω11	2ω11	ADJ
ejpam-6763	801	3	γ(1.3	γ(1.3	PROPN
ejpam-6763	801	4	)	)	PUNCT
ejpam-6763	801	5	·	·	PUNCT
ejpam-6763	802	1	x	x	SYM
ejpam-6763	803	1	2.3	2.3	NUM
ejpam-6763	803	2	2.3	2.3	NUM
ejpam-6763	803	3	sin(x)−	sin(x)−	PROPN
ejpam-6763	803	4	3ω12	3ω12	NUM
ejpam-6763	803	5	γ(1.6	γ(1.6	NOUN
ejpam-6763	803	6	)	)	PUNCT
ejpam-6763	803	7	(	(	PUNCT
ejpam-6763	803	8	x4.6	x4.6	PROPN
ejpam-6763	803	9	2.6	2.6	NUM
ejpam-6763	803	10	−	−	NOUN
ejpam-6763	803	11	x3.6	x3.6	PROPN
ejpam-6763	803	12	1.6	1.6	NUM
ejpam-6763	803	13	)	)	PUNCT
ejpam-6763	803	14	,	,	PUNCT
ejpam-6763	803	15	d.	d.	PROPN
ejpam-6763	803	16	kh	kh	PROPN
ejpam-6763	803	17	.	.	PUNCT
ejpam-6763	804	1	abdullah	abdullah	PROPN
ejpam-6763	804	2	,	,	PUNCT
ejpam-6763	804	3	sh	sh	PROPN
ejpam-6763	804	4	.	.	PROPN
ejpam-6763	804	5	sh	sh	PROPN
ejpam-6763	804	6	.	.	PROPN
ejpam-6763	804	7	ahmed	ahmed	PROPN
ejpam-6763	804	8	,	,	PUNCT
ejpam-6763	804	9	k.	k.	PROPN
ejpam-6763	804	10	h.	h.	PROPN
ejpam-6763	804	11	f.	f.	PROPN
ejpam-6763	804	12	jwamer	jwamer	PROPN
ejpam-6763	804	13	/	/	SYM
ejpam-6763	804	14	eur	eur	PROPN
ejpam-6763	804	15	.	.	PUNCT
ejpam-6763	805	1	j.	j.	PROPN
ejpam-6763	805	2	pure	pure	PROPN
ejpam-6763	805	3	appl	appl	PROPN
ejpam-6763	805	4	.	.	PROPN
ejpam-6763	805	5	math	math	PROPN
ejpam-6763	805	6	,	,	PUNCT
ejpam-6763	805	7	18	18	NUM
ejpam-6763	805	8	(	(	PUNCT
ejpam-6763	805	9	4	4	NUM
ejpam-6763	805	10	)	)	PUNCT
ejpam-6763	805	11	(	(	PUNCT
ejpam-6763	805	12	2025	2025	NUM
ejpam-6763	805	13	)	)	PUNCT
ejpam-6763	805	14	,	,	PUNCT
ejpam-6763	805	15	6763	6763	NUM
ejpam-6763	805	16	20	20	NUM
ejpam-6763	805	17	of	of	ADP
ejpam-6763	805	18	40	40	NUM
ejpam-6763	805	19	f2(x	f2(x	NUM
ejpam-6763	805	20	)	)	PUNCT
ejpam-6763	805	21	=	=	NOUN
ejpam-6763	805	22	6	6	NUM
ejpam-6763	805	23	+	+	NUM
ejpam-6763	805	24	3exx0.5	3exx0.5	NUM
ejpam-6763	805	25	γ(1.5	γ(1.5	NOUN
ejpam-6763	805	26	)	)	PUNCT
ejpam-6763	806	1	+	+	CCONJ
ejpam-6763	806	2	(	(	PUNCT
ejpam-6763	806	3	3x−	3x−	PROPN
ejpam-6763	806	4	1	1	NUM
ejpam-6763	806	5	)	)	PUNCT
ejpam-6763	806	6	sin(x	sin(x	PROPN
ejpam-6763	806	7	)	)	PUNCT
ejpam-6763	806	8	−	−	NOUN
ejpam-6763	806	9	ω20	ω20	NOUN
ejpam-6763	806	10	(	(	PUNCT
ejpam-6763	806	11	x7	x7	NOUN
ejpam-6763	806	12	4	4	NUM
ejpam-6763	806	13	+	+	NUM
ejpam-6763	806	14	x6	x6	PROPN
ejpam-6763	806	15	3	3	NUM
ejpam-6763	806	16	−	−	NOUN
ejpam-6763	806	17	x2	x2	INTJ
ejpam-6763	806	18	2	2	NUM
ejpam-6763	806	19	−	−	NOUN
ejpam-6763	806	20	x	x	SYM
ejpam-6763	806	21	)	)	PUNCT
ejpam-6763	807	1	+	+	NUM
ejpam-6763	807	2	2ω21	2ω21	NUM
ejpam-6763	807	3	γ(1.1	γ(1.1	NOUN
ejpam-6763	807	4	)	)	PUNCT
ejpam-6763	807	5	·	·	PUNCT
ejpam-6763	808	1	e	e	X
ejpam-6763	808	2	xx2.1	xx2.1	X
ejpam-6763	808	3	2.1	2.1	NUM
ejpam-6763	808	4	−	−	NOUN
ejpam-6763	808	5	3ω22	3ω22	NUM
ejpam-6763	808	6	γ(1.7	γ(1.7	PROPN
ejpam-6763	808	7	)	)	PUNCT
ejpam-6763	808	8	(	(	PUNCT
ejpam-6763	808	9	x3.7	x3.7	NOUN
ejpam-6763	808	10	3.7	3.7	NUM
ejpam-6763	808	11	+	+	CCONJ
ejpam-6763	808	12	x1.7	x1.7	PROPN
ejpam-6763	808	13	1.7	1.7	NUM
ejpam-6763	808	14	)	)	PUNCT
ejpam-6763	808	15	.	.	PUNCT
ejpam-6763	809	1	initial	initial	ADJ
ejpam-6763	809	2	conditions	condition	NOUN
ejpam-6763	809	3	:	:	PUNCT
ejpam-6763	809	4	y0(0	y0(0	PROPN
ejpam-6763	809	5	)	)	PUNCT
ejpam-6763	810	1	=	=	SYM
ejpam-6763	810	2	1	1	NUM
ejpam-6763	810	3	,	,	PUNCT
ejpam-6763	810	4	y1(0	y1(0	PROPN
ejpam-6763	810	5	)	)	PUNCT
ejpam-6763	810	6	=	=	SYM
ejpam-6763	810	7	1	1	NUM
ejpam-6763	810	8	,	,	PUNCT
ejpam-6763	810	9	y2(0	y2(0	PROPN
ejpam-6763	810	10	)	)	PUNCT
ejpam-6763	810	11	=	=	SYM
ejpam-6763	810	12	−1	−1	NOUN
ejpam-6763	810	13	exact	exact	ADJ
ejpam-6763	810	14	solutions	solution	NOUN
ejpam-6763	810	15	:	:	PUNCT
ejpam-6763	810	16	y0(x	y0(x	X
ejpam-6763	810	17	)	)	PUNCT
ejpam-6763	810	18	=	=	SYM
ejpam-6763	811	1	x+	x+	PROPN
ejpam-6763	811	2	1	1	NUM
ejpam-6763	811	3	,	,	PUNCT
ejpam-6763	811	4	y1(x	y1(x	NOUN
ejpam-6763	811	5	)	)	PUNCT
ejpam-6763	811	6	=	=	SYM
ejpam-6763	811	7	1−	1−	NUM
ejpam-6763	811	8	2x	2x	NUM
ejpam-6763	811	9	,	,	PUNCT
ejpam-6763	811	10	y2(x	y2(x	NOUN
ejpam-6763	811	11	)	)	PUNCT
ejpam-6763	811	12	=	=	SYM
ejpam-6763	811	13	3x−	3x−	PROPN
ejpam-6763	811	14	1	1	NUM
ejpam-6763	811	15	parameters	parameter	NOUN
ejpam-6763	811	16	:	:	PUNCT
ejpam-6763	811	17	σ00	σ00	NOUN
ejpam-6763	811	18	=	=	SYM
ejpam-6763	811	19	0.7	0.7	NUM
ejpam-6763	811	20	,	,	PUNCT
ejpam-6763	811	21	σ10	σ10	ADJ
ejpam-6763	811	22	=	=	SYM
ejpam-6763	811	23	0.6	0.6	NUM
ejpam-6763	811	24	,	,	PUNCT
ejpam-6763	811	25	σ20	σ20	NOUN
ejpam-6763	811	26	=	=	SYM
ejpam-6763	811	27	0.5	0.5	NUM
ejpam-6763	811	28	,	,	PUNCT
ejpam-6763	811	29	β01	β01	NOUN
ejpam-6763	811	30	=	=	NUM
ejpam-6763	811	31	0.8	0.8	NUM
ejpam-6763	811	32	,	,	PUNCT
ejpam-6763	811	33	β02	β02	PROPN
ejpam-6763	811	34	=	=	SYM
ejpam-6763	811	35	0.5	0.5	NUM
ejpam-6763	811	36	,	,	PUNCT
ejpam-6763	811	37	β11	β11	NOUN
ejpam-6763	811	38	=	=	SYM
ejpam-6763	811	39	0.7	0.7	NUM
ejpam-6763	811	40	,	,	PUNCT
ejpam-6763	811	41	β12	β12	NOUN
ejpam-6763	811	42	=	=	NOUN
ejpam-6763	811	43	0.4	0.4	NUM
ejpam-6763	811	44	,	,	PUNCT
ejpam-6763	811	45	β21	β21	NOUN
ejpam-6763	811	46	=	=	SYM
ejpam-6763	811	47	0.9	0.9	NUM
ejpam-6763	811	48	,	,	PUNCT
ejpam-6763	811	49	β22	β22	X
ejpam-6763	811	50	=	=	NOUN
ejpam-6763	811	51	0.3	0.3	NUM
ejpam-6763	811	52	,	,	PUNCT
ejpam-6763	811	53	ω00	ω00	NOUN
ejpam-6763	811	54	=	=	SYM
ejpam-6763	811	55	sin(0.3	sin(0.3	PROPN
ejpam-6763	811	56	)	)	PUNCT
ejpam-6763	811	57	γ(13	γ(13	NOUN
ejpam-6763	811	58	)	)	PUNCT
ejpam-6763	811	59	,	,	PUNCT
ejpam-6763	811	60	ω01	ω01	NOUN
ejpam-6763	811	61	=	=	SYM
ejpam-6763	811	62	sinh(0.7	sinh(0.7	NOUN
ejpam-6763	811	63	)	)	PUNCT
ejpam-6763	811	64	γ4(16	γ4(16	NOUN
ejpam-6763	811	65	)	)	PUNCT
ejpam-6763	811	66	,	,	PUNCT
ejpam-6763	811	67	ω02	ω02	NOUN
ejpam-6763	811	68	=	=	SYM
ejpam-6763	811	69	cosh(30	cosh(30	NOUN
ejpam-6763	811	70	)	)	PUNCT
ejpam-6763	811	71	γ5(14	γ5(14	NOUN
ejpam-6763	811	72	)	)	PUNCT
ejpam-6763	811	73	,	,	PUNCT
ejpam-6763	811	74	ω10	ω10	NUM
ejpam-6763	811	75	=	=	PUNCT
ejpam-6763	811	76	cos(89	cos(89	PROPN
ejpam-6763	811	77	)	)	PUNCT
ejpam-6763	811	78	γ(12	γ(12	PROPN
ejpam-6763	811	79	)	)	PUNCT
ejpam-6763	811	80	,	,	PUNCT
ejpam-6763	811	81	ω11	ω11	NOUN
ejpam-6763	811	82	=	=	SYM
ejpam-6763	811	83	ln(5	ln(5	NOUN
ejpam-6763	811	84	)	)	PUNCT
ejpam-6763	811	85	γ(12	γ(12	PROPN
ejpam-6763	811	86	)	)	PUNCT
ejpam-6763	811	87	,	,	PUNCT
ejpam-6763	811	88	ω12	ω12	NUM
ejpam-6763	811	89	=	=	SYM
ejpam-6763	811	90	sinh(0.3	sinh(0.3	ADJ
ejpam-6763	811	91	)	)	PUNCT
ejpam-6763	811	92	γ(11	γ(11	NUM
ejpam-6763	811	93	)	)	PUNCT
ejpam-6763	811	94	,	,	PUNCT
ejpam-6763	811	95	ω20	ω20	NOUN
ejpam-6763	811	96	=	=	SYM
ejpam-6763	811	97	cos(89	cos(89	PROPN
ejpam-6763	811	98	)	)	PUNCT
ejpam-6763	811	99	γ2(9	γ2(9	PROPN
ejpam-6763	811	100	)	)	PUNCT
ejpam-6763	811	101	,	,	PUNCT
ejpam-6763	811	102	ω21	ω21	VERB
ejpam-6763	811	103	=	=	SYM
ejpam-6763	811	104	sin(179	sin(179	PROPN
ejpam-6763	811	105	)	)	PUNCT
ejpam-6763	811	106	γ(11	γ(11	NUM
ejpam-6763	811	107	)	)	PUNCT
ejpam-6763	811	108	,	,	PUNCT
ejpam-6763	811	109	ω22	ω22	ADV
ejpam-6763	811	110	=	=	SYM
ejpam-6763	811	111	sin(30	sin(30	PROPN
ejpam-6763	811	112	)	)	PUNCT
ejpam-6763	811	113	γ(12	γ(12	PROPN
ejpam-6763	811	114	)	)	PUNCT
ejpam-6763	811	115	,	,	PUNCT
ejpam-6763	811	116	n	n	NOUN
ejpam-6763	811	117	=	=	SYM
ejpam-6763	811	118	10	10	NUM
ejpam-6763	811	119	,	,	PUNCT
ejpam-6763	811	120	h	h	NOUN
ejpam-6763	811	121	=	=	NOUN
ejpam-6763	811	122	0.1	0.1	NUM
ejpam-6763	811	123	,	,	PUNCT
ejpam-6763	811	124	x?r	x?r	X
ejpam-6763	811	125	=	=	SYM
ejpam-6763	811	126	a+	a+	PUNCT
ejpam-6763	811	127	rh	rh	PROPN
ejpam-6763	811	128	,	,	PUNCT
ejpam-6763	811	129	r	r	NOUN
ejpam-6763	811	130	=	=	SYM
ejpam-6763	811	131	0	0	NUM
ejpam-6763	811	132	,	,	PUNCT
ejpam-6763	811	133	1	1	NUM
ejpam-6763	811	134	,	,	PUNCT
ejpam-6763	811	135	.	.	PUNCT
ejpam-6763	811	136	.	.	PUNCT
ejpam-6763	811	137	.	.	PUNCT
ejpam-6763	812	1	,	,	PUNCT
ejpam-6763	813	1	n	n	CCONJ
ejpam-6763	813	2	−	−	PROPN
ejpam-6763	814	1	1	1	X
ejpam-6763	814	2	.	.	PUNCT
ejpam-6763	815	1	we	we	PRON
ejpam-6763	815	2	aim	aim	VERB
ejpam-6763	815	3	to	to	PART
ejpam-6763	815	4	approximate	approximate	VERB
ejpam-6763	815	5	the	the	DET
ejpam-6763	815	6	solutions	solution	NOUN
ejpam-6763	815	7	b{c,3	b{c,3	NOUN
ejpam-6763	815	8	}	}	PUNCT
ejpam-6763	815	9	i	i	PROPN
ejpam-6763	815	10	(	(	PUNCT
ejpam-6763	815	11	x?r+1	x?r+1	PROPN
ejpam-6763	815	12	)	)	PUNCT
ejpam-6763	815	13	,	,	PUNCT
ejpam-6763	815	14	i	i	PRON
ejpam-6763	815	15	=	=	NOUN
ejpam-6763	815	16	0	0	NUM
ejpam-6763	815	17	,	,	PUNCT
ejpam-6763	815	18	1	1	NUM
ejpam-6763	815	19	,	,	PUNCT
ejpam-6763	815	20	2	2	NUM
ejpam-6763	815	21	as	as	SCONJ
ejpam-6763	815	22	defined	define	VERB
ejpam-6763	815	23	in	in	ADP
ejpam-6763	815	24	(	(	PUNCT
ejpam-6763	815	25	21	21	NUM
ejpam-6763	815	26	)	)	PUNCT
ejpam-6763	815	27	.	.	PUNCT
ejpam-6763	816	1	we	we	PRON
ejpam-6763	816	2	execute	execute	VERB
ejpam-6763	816	3	the	the	DET
ejpam-6763	816	4	programs	program	NOUN
ejpam-6763	816	5	nfcbi	nfcbi	VERB
ejpam-6763	816	6	,	,	PUNCT
ejpam-6763	816	7	fcpcbs	fcpcbs	PROPN
ejpam-6763	816	8	,	,	PUNCT
ejpam-6763	816	9	and	and	CCONJ
ejpam-6763	816	10	ffcpcbs	ffcpcbs	PRON
ejpam-6763	816	11	to	to	PART
ejpam-6763	816	12	compute	compute	VERB
ejpam-6763	816	13	the	the	DET
ejpam-6763	816	14	unknown	unknown	ADJ
ejpam-6763	816	15	control	control	NOUN
ejpam-6763	816	16	points	point	VERB
ejpam-6763	816	17	ϑi0	ϑi0	NOUN
ejpam-6763	816	18	,	,	PUNCT
ejpam-6763	816	19	ϑi1	ϑi1	NOUN
ejpam-6763	816	20	,	,	PUNCT
ejpam-6763	816	21	ϑi2	ϑi2	PROPN
ejpam-6763	816	22	,	,	PUNCT
ejpam-6763	816	23	ϑi3	ϑi3	NOUN
ejpam-6763	816	24	for	for	ADP
ejpam-6763	816	25	i	i	PROPN
ejpam-6763	816	26	=	=	SYM
ejpam-6763	816	27	0	0	NUM
ejpam-6763	816	28	,	,	PUNCT
ejpam-6763	816	29	1	1	NUM
ejpam-6763	816	30	,	,	PUNCT
ejpam-6763	816	31	2	2	NUM
ejpam-6763	816	32	.	.	X
ejpam-6763	817	1	these	these	DET
ejpam-6763	817	2	control	control	NOUN
ejpam-6763	817	3	points	point	NOUN
ejpam-6763	817	4	are	be	AUX
ejpam-6763	817	5	used	use	VERB
ejpam-6763	817	6	to	to	PART
ejpam-6763	817	7	construct	construct	VERB
ejpam-6763	817	8	the	the	DET
ejpam-6763	817	9	approximate	approximate	ADJ
ejpam-6763	817	10	solutions	solution	NOUN
ejpam-6763	817	11	for	for	ADP
ejpam-6763	817	12	the	the	DET
ejpam-6763	817	13	given	give	VERB
ejpam-6763	817	14	system	system	NOUN
ejpam-6763	817	15	.	.	PUNCT
ejpam-6763	818	1	the	the	DET
ejpam-6763	818	2	first	first	ADJ
ejpam-6763	818	3	table	table	NOUN
ejpam-6763	818	4	demonstrates	demonstrate	VERB
ejpam-6763	818	5	values	value	NOUN
ejpam-6763	818	6	of	of	ADP
ejpam-6763	818	7	all	all	DET
ejpam-6763	818	8	control	control	NOUN
ejpam-6763	818	9	points	point	NOUN
ejpam-6763	818	10	for	for	ADP
ejpam-6763	818	11	b{c,3	b{c,3	NOUN
ejpam-6763	818	12	}	}	PUNCT
ejpam-6763	818	13	0	0	NUM
ejpam-6763	819	1	(	(	PUNCT
ejpam-6763	819	2	x?r+1	x?r+1	NOUN
ejpam-6763	819	3	)	)	PUNCT
ejpam-6763	819	4	,	,	PUNCT
ejpam-6763	819	5	b	b	X
ejpam-6763	819	6	{	{	PUNCT
ejpam-6763	819	7	c,3	c,3	NOUN
ejpam-6763	819	8	}	}	PUNCT
ejpam-6763	819	9	1	1	NUM
ejpam-6763	819	10	(	(	PUNCT
ejpam-6763	819	11	x?r+1	x?r+1	NOUN
ejpam-6763	819	12	)	)	PUNCT
ejpam-6763	819	13	,	,	PUNCT
ejpam-6763	819	14	and	and	CCONJ
ejpam-6763	819	15	b{c,3	b{c,3	NOUN
ejpam-6763	819	16	}	}	PUNCT
ejpam-6763	819	17	2	2	NUM
ejpam-6763	819	18	(	(	PUNCT
ejpam-6763	819	19	x?r+1	x?r+1	NOUN
ejpam-6763	819	20	)	)	PUNCT
ejpam-6763	819	21	according	accord	VERB
ejpam-6763	819	22	to	to	ADP
ejpam-6763	819	23	the	the	DET
ejpam-6763	819	24	three	three	NUM
ejpam-6763	819	25	algorithms	algorithm	NOUN
ejpam-6763	819	26	nfcbi	nfcbi	VERB
ejpam-6763	819	27	,	,	PUNCT
ejpam-6763	819	28	fcpcbs	fcpcbs	PROPN
ejpam-6763	819	29	,	,	PUNCT
ejpam-6763	819	30	and	and	CCONJ
ejpam-6763	819	31	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	819	32	,	,	PUNCT
ejpam-6763	819	33	respectively	respectively	ADV
ejpam-6763	819	34	.	.	PUNCT
ejpam-6763	819	35	example	example	NOUN
ejpam-6763	820	1	2	2	NUM
ejpam-6763	820	2	.	.	X
ejpam-6763	820	3	consider	consider	VERB
ejpam-6763	820	4	the	the	DET
ejpam-6763	820	5	following	follow	VERB
ejpam-6763	820	6	classical	classical	ADJ
ejpam-6763	820	7	and	and	CCONJ
ejpam-6763	820	8	fractional	fractional	ADJ
ejpam-6763	820	9	order	order	NOUN
ejpam-6763	820	10	system	system	NOUN
ejpam-6763	820	11	of	of	ADP
ejpam-6763	820	12	volterra	volterra	PROPN
ejpam-6763	820	13	integro	integro	PROPN
ejpam-6763	820	14	-	-	PUNCT
ejpam-6763	820	15	differential	differential	NOUN
ejpam-6763	820	16	equations	equation	NOUN
ejpam-6763	820	17	(	(	PUNCT
ejpam-6763	820	18	cfvides	cfvide	NOUN
ejpam-6763	820	19	):	):	PUNCT
ejpam-6763	820	20	ex	ex	X
ejpam-6763	820	21	y	y	PROPN
ejpam-6763	820	22	′	′	NUM
ejpam-6763	820	23	0(x	0(x	NOUN
ejpam-6763	820	24	)	)	PUNCT
ejpam-6763	821	1	+	+	CCONJ
ejpam-6763	822	1	x4	x4	PROPN
ejpam-6763	822	2	c	c	NOUN
ejpam-6763	822	3	0dσ00	0dσ00	NUM
ejpam-6763	822	4	x	x	SYM
ejpam-6763	822	5	y0(x	y0(x	NOUN
ejpam-6763	822	6	)	)	PUNCT
ejpam-6763	822	7	+	+	X
ejpam-6763	822	8	cos(x)y0(x	cos(x)y0(x	NOUN
ejpam-6763	822	9	)	)	PUNCT
ejpam-6763	822	10	=	=	PUNCT
ejpam-6763	822	11	f0(x	f0(x	NOUN
ejpam-6763	822	12	)	)	PUNCT
ejpam-6763	823	1	+	+	CCONJ
ejpam-6763	823	2	ω00	ω00	ADJ
ejpam-6763	823	3	∫	∫	PROPN
ejpam-6763	823	4	x	x	SYM
ejpam-6763	823	5	0	0	PROPN
ejpam-6763	823	6	(	(	PUNCT
ejpam-6763	823	7	cos(x)−	cos(x)−	NOUN
ejpam-6763	823	8	s2)y0(s	s2)y0(s	NOUN
ejpam-6763	823	9	)	)	PUNCT
ejpam-6763	824	1	ds	ds	NOUN
ejpam-6763	824	2	+	+	NUM
ejpam-6763	824	3	ω01	ω01	NUM
ejpam-6763	824	4	∫	∫	NOUN
ejpam-6763	824	5	x	x	SYM
ejpam-6763	824	6	0	0	PUNCT
ejpam-6763	824	7	(	(	PUNCT
ejpam-6763	824	8	3x−	3x−	PROPN
ejpam-6763	824	9	s2	s2	PROPN
ejpam-6763	824	10	)	)	PUNCT
ejpam-6763	824	11	c0dβ01	c0dβ01	PROPN
ejpam-6763	824	12	s	s	NOUN
ejpam-6763	824	13	y1(s	y1(s	NOUN
ejpam-6763	824	14	)	)	PUNCT
ejpam-6763	824	15	ds	ds	ADJ
ejpam-6763	824	16	,	,	PUNCT
ejpam-6763	824	17	cos(x)y	cos(x)y	ADJ
ejpam-6763	824	18	′	′	NOUN
ejpam-6763	824	19	1(x	1(x	NUM
ejpam-6763	824	20	)	)	PUNCT
ejpam-6763	825	1	+	+	CCONJ
ejpam-6763	825	2	x	x	SYM
ejpam-6763	825	3	c	c	X
ejpam-6763	825	4	0dσ10	0dσ10	NUM
ejpam-6763	825	5	x	x	NOUN
ejpam-6763	825	6	y1(x	y1(x	NOUN
ejpam-6763	825	7	)	)	PUNCT
ejpam-6763	825	8	+	+	CCONJ
ejpam-6763	825	9	ex	ex	ADJ
ejpam-6763	825	10	y1(x	y1(x	NOUN
ejpam-6763	825	11	)	)	PUNCT
ejpam-6763	825	12	=	=	SYM
ejpam-6763	825	13	f1(x	f1(x	X
ejpam-6763	825	14	)	)	PUNCT
ejpam-6763	825	15	+	+	CCONJ
ejpam-6763	825	16	ω10	ω10	NUM
ejpam-6763	825	17	∫	∫	PROPN
ejpam-6763	825	18	x	x	X
ejpam-6763	825	19	0	0	PUNCT
ejpam-6763	825	20	(	(	PUNCT
ejpam-6763	825	21	x3	x3	ADJ
ejpam-6763	825	22	−	−	PROPN
ejpam-6763	825	23	s4	s4	PROPN
ejpam-6763	825	24	+	+	CCONJ
ejpam-6763	825	25	4)y0(s	4)y0(s	NOUN
ejpam-6763	825	26	)	)	PUNCT
ejpam-6763	825	27	ds	ds	PROPN
ejpam-6763	825	28	d.	d.	PROPN
ejpam-6763	825	29	kh	kh	PROPN
ejpam-6763	825	30	.	.	PUNCT
ejpam-6763	826	1	abdullah	abdullah	PROPN
ejpam-6763	826	2	,	,	PUNCT
ejpam-6763	826	3	sh	sh	PROPN
ejpam-6763	826	4	.	.	PROPN
ejpam-6763	826	5	sh	sh	PROPN
ejpam-6763	826	6	.	.	PROPN
ejpam-6763	826	7	ahmed	ahmed	PROPN
ejpam-6763	826	8	,	,	PUNCT
ejpam-6763	826	9	k.	k.	PROPN
ejpam-6763	826	10	h.	h.	PROPN
ejpam-6763	826	11	f.	f.	PROPN
ejpam-6763	826	12	jwamer	jwamer	PROPN
ejpam-6763	826	13	/	/	SYM
ejpam-6763	826	14	eur	eur	PROPN
ejpam-6763	826	15	.	.	PUNCT
ejpam-6763	827	1	j.	j.	PROPN
ejpam-6763	827	2	pure	pure	PROPN
ejpam-6763	827	3	appl	appl	PROPN
ejpam-6763	827	4	.	.	PROPN
ejpam-6763	827	5	math	math	PROPN
ejpam-6763	827	6	,	,	PUNCT
ejpam-6763	827	7	18	18	NUM
ejpam-6763	827	8	(	(	PUNCT
ejpam-6763	827	9	4	4	NUM
ejpam-6763	827	10	)	)	PUNCT
ejpam-6763	827	11	(	(	PUNCT
ejpam-6763	827	12	2025	2025	NUM
ejpam-6763	827	13	)	)	PUNCT
ejpam-6763	827	14	,	,	PUNCT
ejpam-6763	827	15	6763	6763	NUM
ejpam-6763	827	16	21	21	NUM
ejpam-6763	827	17	of	of	ADP
ejpam-6763	827	18	40	40	NUM
ejpam-6763	827	19	+	+	CCONJ
ejpam-6763	827	20	ω11	ω11	ADP
ejpam-6763	827	21	∫	∫	PROPN
ejpam-6763	827	22	x	x	X
ejpam-6763	827	23	0	0	NUM
ejpam-6763	827	24	(	(	PUNCT
ejpam-6763	827	25	sin(x	sin(x	PROPN
ejpam-6763	827	26	)	)	PUNCT
ejpam-6763	828	1	+	+	NOUN
ejpam-6763	828	2	1	1	X
ejpam-6763	828	3	)	)	PUNCT
ejpam-6763	828	4	c0dβ11	c0dβ11	PROPN
ejpam-6763	828	5	s	s	PART
ejpam-6763	828	6	y1(s	y1(s	NOUN
ejpam-6763	828	7	)	)	PUNCT
ejpam-6763	828	8	ds	ds	NOUN
ejpam-6763	828	9	.	.	PUNCT
ejpam-6763	829	1	the	the	DET
ejpam-6763	829	2	given	give	VERB
ejpam-6763	829	3	functions	function	NOUN
ejpam-6763	829	4	f0(x	f0(x	NOUN
ejpam-6763	829	5	)	)	PUNCT
ejpam-6763	829	6	,	,	PUNCT
ejpam-6763	829	7	and	and	CCONJ
ejpam-6763	829	8	f1(x	f1(x	NUM
ejpam-6763	829	9	)	)	PUNCT
ejpam-6763	829	10	are	be	AUX
ejpam-6763	829	11	defined	define	VERB
ejpam-6763	829	12	as	as	SCONJ
ejpam-6763	829	13	follows	follow	VERB
ejpam-6763	829	14	:	:	PUNCT
ejpam-6763	829	15	f0(x	f0(x	NOUN
ejpam-6763	829	16	)	)	PUNCT
ejpam-6763	829	17	=	=	SYM
ejpam-6763	829	18	2xex	2xex	NUM
ejpam-6763	829	19	+	+	CCONJ
ejpam-6763	829	20	2	2	NUM
ejpam-6763	829	21	γ(2.3	γ(2.3	NOUN
ejpam-6763	829	22	)	)	PUNCT
ejpam-6763	829	23	x5.3	x5.3	PROPN
ejpam-6763	830	1	+	+	CCONJ
ejpam-6763	830	2	(	(	PUNCT
ejpam-6763	830	3	x2	x2	INTJ
ejpam-6763	830	4	−	−	PROPN
ejpam-6763	830	5	1	1	X
ejpam-6763	830	6	)	)	PUNCT
ejpam-6763	830	7	cos(x	cos(x	PROPN
ejpam-6763	830	8	)	)	PUNCT
ejpam-6763	831	1	−	−	PROPN
ejpam-6763	831	2	ω00	ω00	NOUN
ejpam-6763	831	3	(	(	PUNCT
ejpam-6763	831	4	x3	x3	NOUN
ejpam-6763	831	5	3	3	NUM
ejpam-6763	831	6	cos(x)−	cos(x)−	NOUN
ejpam-6763	831	7	x	x	PUNCT
ejpam-6763	831	8	cos(x)−	cos(x)−	NOUN
ejpam-6763	831	9	x5	x5	NOUN
ejpam-6763	831	10	5	5	NUM
ejpam-6763	831	11	−	−	NOUN
ejpam-6763	831	12	x3	x3	ADJ
ejpam-6763	831	13	3	3	NUM
ejpam-6763	831	14	)	)	PUNCT
ejpam-6763	831	15	+	+	CCONJ
ejpam-6763	831	16	2ω01	2ω01	NUM
ejpam-6763	831	17	γ(2.4	γ(2.4	NOUN
ejpam-6763	831	18	)	)	PUNCT
ejpam-6763	831	19	(	(	PUNCT
ejpam-6763	831	20	3x3.4	3x3.4	NUM
ejpam-6763	831	21	2.4	2.4	NUM
ejpam-6763	831	22	−	−	NOUN
ejpam-6763	831	23	x4.4	x4.4	PROPN
ejpam-6763	831	24	4.4	4.4	NUM
ejpam-6763	831	25	)	)	PUNCT
ejpam-6763	831	26	,	,	PUNCT
ejpam-6763	831	27	f1(x	f1(x	NOUN
ejpam-6763	831	28	)	)	PUNCT
ejpam-6763	831	29	=	=	PUNCT
ejpam-6763	832	1	−2x	−2x	PROPN
ejpam-6763	832	2	cos(x)−	cos(x)−	NOUN
ejpam-6763	832	3	2	2	NUM
ejpam-6763	832	4	γ(2.6	γ(2.6	PROPN
ejpam-6763	832	5	)	)	PUNCT
ejpam-6763	832	6	x2.6	x2.6	PUNCT
ejpam-6763	833	1	+	+	CCONJ
ejpam-6763	833	2	(	(	PUNCT
ejpam-6763	833	3	−x2	−x2	PROPN
ejpam-6763	833	4	+	+	NOUN
ejpam-6763	833	5	1)ex	1)ex	PROPN
ejpam-6763	833	6	−	−	NOUN
ejpam-6763	834	1	ω10	ω10	NUM
ejpam-6763	834	2	(	(	PUNCT
ejpam-6763	834	3	x6	x6	PROPN
ejpam-6763	834	4	3	3	NUM
ejpam-6763	834	5	−	−	NOUN
ejpam-6763	834	6	x7	x7	NOUN
ejpam-6763	834	7	7	7	NUM
ejpam-6763	834	8	−	−	NUM
ejpam-6763	834	9	4x3	4x3	NUM
ejpam-6763	834	10	3	3	NUM
ejpam-6763	834	11	−	−	PROPN
ejpam-6763	835	1	x4	x4	PROPN
ejpam-6763	836	1	+	+	NUM
ejpam-6763	836	2	x5	x5	NOUN
ejpam-6763	836	3	5	5	NUM
ejpam-6763	836	4	−	−	NOUN
ejpam-6763	836	5	4x	4x	NUM
ejpam-6763	836	6	)	)	PUNCT
ejpam-6763	836	7	−	−	PROPN
ejpam-6763	836	8	2ω11	2ω11	ADJ
ejpam-6763	836	9	γ(2.2	γ(2.2	NOUN
ejpam-6763	836	10	)	)	PUNCT
ejpam-6763	837	1	(	(	PUNCT
ejpam-6763	837	2	x2.2	x2.2	PROPN
ejpam-6763	837	3	2.4	2.4	NUM
ejpam-6763	837	4	sin(x	sin(x	PROPN
ejpam-6763	837	5	)	)	PUNCT
ejpam-6763	838	1	+	+	CCONJ
ejpam-6763	838	2	x2.2	x2.2	PROPN
ejpam-6763	838	3	2.2	2.2	NUM
ejpam-6763	838	4	)	)	PUNCT
ejpam-6763	838	5	.	.	PUNCT
ejpam-6763	839	1	initial	initial	ADJ
ejpam-6763	839	2	conditions	condition	NOUN
ejpam-6763	839	3	:	:	PUNCT
ejpam-6763	839	4	y0(0	y0(0	PROPN
ejpam-6763	839	5	)	)	PUNCT
ejpam-6763	840	1	=	=	SYM
ejpam-6763	840	2	−1	−1	NOUN
ejpam-6763	840	3	,	,	PUNCT
ejpam-6763	840	4	y1(0	y1(0	PROPN
ejpam-6763	840	5	)	)	PUNCT
ejpam-6763	840	6	=	=	SYM
ejpam-6763	840	7	1	1	NUM
ejpam-6763	840	8	exact	exact	ADJ
ejpam-6763	840	9	solutions	solution	NOUN
ejpam-6763	840	10	:	:	PUNCT
ejpam-6763	840	11	y0(x	y0(x	X
ejpam-6763	840	12	)	)	PUNCT
ejpam-6763	840	13	=	=	SYM
ejpam-6763	841	1	x2	x2	PROPN
ejpam-6763	841	2	−	−	NOUN
ejpam-6763	841	3	1	1	NUM
ejpam-6763	841	4	,	,	PUNCT
ejpam-6763	841	5	y1(x	y1(x	NOUN
ejpam-6763	841	6	)	)	PUNCT
ejpam-6763	841	7	=	=	PUNCT
ejpam-6763	842	1	−x2	−x2	NOUN
ejpam-6763	842	2	+	+	NOUN
ejpam-6763	842	3	1	1	NUM
ejpam-6763	842	4	parameters	parameter	NOUN
ejpam-6763	842	5	:	:	PUNCT
ejpam-6763	842	6	σ00	σ00	NOUN
ejpam-6763	842	7	=	=	SYM
ejpam-6763	842	8	0.7	0.7	NUM
ejpam-6763	842	9	,	,	PUNCT
ejpam-6763	842	10	σ10	σ10	ADJ
ejpam-6763	842	11	=	=	SYM
ejpam-6763	842	12	0.4	0.4	NUM
ejpam-6763	842	13	,	,	PUNCT
ejpam-6763	842	14	β01	β01	NOUN
ejpam-6763	842	15	=	=	SYM
ejpam-6763	842	16	0.6	0.6	NUM
ejpam-6763	842	17	,	,	PUNCT
ejpam-6763	842	18	β11	β11	NOUN
ejpam-6763	842	19	=	=	NUM
ejpam-6763	842	20	0.8	0.8	NUM
ejpam-6763	842	21	,	,	PUNCT
ejpam-6763	842	22	ω00	ω00	NOUN
ejpam-6763	842	23	=	=	SYM
ejpam-6763	842	24	sin(0.3	sin(0.3	PROPN
ejpam-6763	842	25	)	)	PUNCT
ejpam-6763	842	26	γ(13	γ(13	NOUN
ejpam-6763	842	27	)	)	PUNCT
ejpam-6763	842	28	,	,	PUNCT
ejpam-6763	842	29	ω01	ω01	NOUN
ejpam-6763	842	30	=	=	SYM
ejpam-6763	842	31	sinh(0.7	sinh(0.7	NOUN
ejpam-6763	842	32	)	)	PUNCT
ejpam-6763	842	33	γ4(16	γ4(16	NOUN
ejpam-6763	842	34	)	)	PUNCT
ejpam-6763	842	35	,	,	PUNCT
ejpam-6763	842	36	ω10	ω10	NUM
ejpam-6763	842	37	=	=	SYM
ejpam-6763	842	38	cos(89	cos(89	PROPN
ejpam-6763	842	39	)	)	PUNCT
ejpam-6763	842	40	γ(15	γ(15	PROPN
ejpam-6763	842	41	)	)	PUNCT
ejpam-6763	842	42	,	,	PUNCT
ejpam-6763	842	43	ω11	ω11	NOUN
ejpam-6763	842	44	=	=	SYM
ejpam-6763	842	45	ln(2	ln(2	ADJ
ejpam-6763	842	46	)	)	PUNCT
ejpam-6763	842	47	γ(14	γ(14	NOUN
ejpam-6763	842	48	)	)	PUNCT
ejpam-6763	842	49	,	,	PUNCT
ejpam-6763	842	50	n	n	NOUN
ejpam-6763	842	51	=	=	SYM
ejpam-6763	842	52	10	10	NUM
ejpam-6763	842	53	,	,	PUNCT
ejpam-6763	842	54	h	h	NOUN
ejpam-6763	842	55	=	=	NOUN
ejpam-6763	842	56	0.1	0.1	NUM
ejpam-6763	842	57	,	,	PUNCT
ejpam-6763	842	58	x?r	x?r	X
ejpam-6763	842	59	=	=	SYM
ejpam-6763	842	60	a+	a+	PUNCT
ejpam-6763	842	61	rh	rh	PROPN
ejpam-6763	842	62	,	,	PUNCT
ejpam-6763	842	63	r	r	NOUN
ejpam-6763	842	64	=	=	SYM
ejpam-6763	842	65	0	0	NUM
ejpam-6763	842	66	,	,	PUNCT
ejpam-6763	842	67	1	1	NUM
ejpam-6763	842	68	,	,	PUNCT
ejpam-6763	842	69	.	.	PUNCT
ejpam-6763	842	70	.	.	PUNCT
ejpam-6763	842	71	.	.	PUNCT
ejpam-6763	843	1	,	,	PUNCT
ejpam-6763	844	1	n	n	CCONJ
ejpam-6763	844	2	−	−	PROPN
ejpam-6763	845	1	1	1	X
ejpam-6763	845	2	.	.	PUNCT
ejpam-6763	846	1	we	we	PRON
ejpam-6763	846	2	aim	aim	VERB
ejpam-6763	846	3	to	to	PART
ejpam-6763	846	4	approximate	approximate	VERB
ejpam-6763	846	5	the	the	DET
ejpam-6763	846	6	solutions	solution	NOUN
ejpam-6763	846	7	b{c,3	b{c,3	NOUN
ejpam-6763	846	8	}	}	PUNCT
ejpam-6763	846	9	i	i	PROPN
ejpam-6763	846	10	(	(	PUNCT
ejpam-6763	846	11	x?r+1	x?r+1	PROPN
ejpam-6763	846	12	)	)	PUNCT
ejpam-6763	846	13	,	,	PUNCT
ejpam-6763	846	14	i	i	PRON
ejpam-6763	846	15	=	=	NOUN
ejpam-6763	846	16	0	0	NUM
ejpam-6763	846	17	,	,	PUNCT
ejpam-6763	846	18	1	1	NUM
ejpam-6763	846	19	as	as	SCONJ
ejpam-6763	846	20	defined	define	VERB
ejpam-6763	846	21	in	in	ADP
ejpam-6763	846	22	(	(	PUNCT
ejpam-6763	846	23	21	21	NUM
ejpam-6763	846	24	)	)	PUNCT
ejpam-6763	846	25	.	.	PUNCT
ejpam-6763	847	1	we	we	PRON
ejpam-6763	847	2	execute	execute	VERB
ejpam-6763	847	3	the	the	DET
ejpam-6763	847	4	programs	program	NOUN
ejpam-6763	847	5	nfcbi	nfcbi	VERB
ejpam-6763	847	6	,	,	PUNCT
ejpam-6763	847	7	fcpcbs	fcpcbs	PROPN
ejpam-6763	847	8	,	,	PUNCT
ejpam-6763	847	9	and	and	CCONJ
ejpam-6763	847	10	ffcpcbs	ffcpcbs	PRON
ejpam-6763	847	11	to	to	PART
ejpam-6763	847	12	compute	compute	VERB
ejpam-6763	847	13	the	the	DET
ejpam-6763	847	14	unknown	unknown	ADJ
ejpam-6763	847	15	control	control	NOUN
ejpam-6763	847	16	points	point	VERB
ejpam-6763	847	17	ϑi0	ϑi0	NOUN
ejpam-6763	847	18	,	,	PUNCT
ejpam-6763	847	19	ϑi1	ϑi1	NOUN
ejpam-6763	847	20	,	,	PUNCT
ejpam-6763	847	21	ϑi2	ϑi2	PROPN
ejpam-6763	847	22	,	,	PUNCT
ejpam-6763	847	23	ϑi3	ϑi3	NOUN
ejpam-6763	847	24	for	for	ADP
ejpam-6763	847	25	i	i	PROPN
ejpam-6763	847	26	=	=	SYM
ejpam-6763	847	27	0	0	NUM
ejpam-6763	847	28	,	,	PUNCT
ejpam-6763	847	29	1	1	NUM
ejpam-6763	847	30	.	.	PUNCT
ejpam-6763	848	1	these	these	DET
ejpam-6763	848	2	control	control	NOUN
ejpam-6763	848	3	points	point	NOUN
ejpam-6763	848	4	are	be	AUX
ejpam-6763	848	5	used	use	VERB
ejpam-6763	848	6	to	to	PART
ejpam-6763	848	7	construct	construct	VERB
ejpam-6763	848	8	the	the	DET
ejpam-6763	848	9	approximate	approximate	ADJ
ejpam-6763	848	10	solutions	solution	NOUN
ejpam-6763	848	11	for	for	ADP
ejpam-6763	848	12	the	the	DET
ejpam-6763	848	13	given	give	VERB
ejpam-6763	848	14	system	system	NOUN
ejpam-6763	848	15	.	.	PUNCT
ejpam-6763	849	1	the	the	DET
ejpam-6763	849	2	sixth	sixth	ADJ
ejpam-6763	849	3	table	table	NOUN
ejpam-6763	849	4	demonstrates	demonstrate	VERB
ejpam-6763	849	5	values	value	NOUN
ejpam-6763	849	6	of	of	ADP
ejpam-6763	849	7	all	all	DET
ejpam-6763	849	8	control	control	NOUN
ejpam-6763	849	9	points	point	NOUN
ejpam-6763	849	10	for	for	ADP
ejpam-6763	849	11	b{c,3	b{c,3	NOUN
ejpam-6763	849	12	}	}	PUNCT
ejpam-6763	849	13	0	0	NUM
ejpam-6763	850	1	(	(	PUNCT
ejpam-6763	850	2	x?r+1	x?r+1	NOUN
ejpam-6763	850	3	)	)	PUNCT
ejpam-6763	850	4	and	and	CCONJ
ejpam-6763	850	5	b{c,3	b{c,3	NOUN
ejpam-6763	850	6	}	}	PUNCT
ejpam-6763	850	7	1	1	NUM
ejpam-6763	850	8	(	(	PUNCT
ejpam-6763	850	9	x?r+1	x?r+1	NOUN
ejpam-6763	850	10	)	)	PUNCT
ejpam-6763	850	11	according	accord	VERB
ejpam-6763	850	12	to	to	ADP
ejpam-6763	850	13	the	the	DET
ejpam-6763	850	14	three	three	NUM
ejpam-6763	850	15	algorithms	algorithm	NOUN
ejpam-6763	850	16	nfcbi	nfcbi	VERB
ejpam-6763	850	17	,	,	PUNCT
ejpam-6763	850	18	fcpcbs	fcpcbs	PROPN
ejpam-6763	850	19	,	,	PUNCT
ejpam-6763	850	20	and	and	CCONJ
ejpam-6763	850	21	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	850	22	,	,	PUNCT
ejpam-6763	850	23	respectively	respectively	ADV
ejpam-6763	850	24	.	.	PUNCT
ejpam-6763	850	25	example	example	NOUN
ejpam-6763	851	1	3	3	X
ejpam-6763	851	2	.	.	X
ejpam-6763	851	3	consider	consider	VERB
ejpam-6763	851	4	the	the	DET
ejpam-6763	851	5	following	follow	VERB
ejpam-6763	851	6	classical	classical	ADJ
ejpam-6763	851	7	and	and	CCONJ
ejpam-6763	851	8	fractional	fractional	ADJ
ejpam-6763	851	9	order	order	NOUN
ejpam-6763	851	10	system	system	NOUN
ejpam-6763	851	11	of	of	ADP
ejpam-6763	851	12	volterra	volterra	PROPN
ejpam-6763	851	13	integro	integro	PROPN
ejpam-6763	851	14	-	-	PUNCT
ejpam-6763	851	15	differential	differential	NOUN
ejpam-6763	851	16	equations	equation	NOUN
ejpam-6763	851	17	(	(	PUNCT
ejpam-6763	851	18	cfvides	cfvide	NOUN
ejpam-6763	851	19	):	):	PUNCT
ejpam-6763	851	20	y	y	PROPN
ejpam-6763	851	21	′	′	NUM
ejpam-6763	851	22	0(x	0(x	NOUN
ejpam-6763	851	23	)	)	PUNCT
ejpam-6763	852	1	+	+	CCONJ
ejpam-6763	852	2	x	x	AUX
ejpam-6763	852	3	c	c	NOUN
ejpam-6763	852	4	0d0.4	0d0.4	NUM
ejpam-6763	852	5	x	x	SYM
ejpam-6763	852	6	y0(x	y0(x	X
ejpam-6763	852	7	)	)	PUNCT
ejpam-6763	852	8	+	+	SYM
ejpam-6763	852	9	sin(x)y0(x	sin(x)y0(x	NOUN
ejpam-6763	852	10	)	)	PUNCT
ejpam-6763	852	11	=	=	SYM
ejpam-6763	852	12	f0(x	f0(x	NOUN
ejpam-6763	852	13	)	)	PUNCT
ejpam-6763	852	14	+	+	CCONJ
ejpam-6763	852	15	ω00	ω00	ADJ
ejpam-6763	852	16	∫	∫	PROPN
ejpam-6763	852	17	x	x	SYM
ejpam-6763	852	18	0	0	NUM
ejpam-6763	852	19	xsy0(s	xsy0(s	NUM
ejpam-6763	852	20	)	)	PUNCT
ejpam-6763	852	21	ds	ds	NOUN
ejpam-6763	852	22	+	+	NUM
ejpam-6763	852	23	ω01	ω01	NUM
ejpam-6763	852	24	∫	∫	NOUN
ejpam-6763	852	25	x	x	SYM
ejpam-6763	852	26	0	0	PUNCT
ejpam-6763	853	1	ex	ex	PRON
ejpam-6763	853	2	c	c	NOUN
ejpam-6763	853	3	0d0.9	0d0.9	PRON
ejpam-6763	853	4	s	s	VERB
ejpam-6763	853	5	y1(s	y1(s	PRON
ejpam-6763	853	6	)	)	PUNCT
ejpam-6763	853	7	ds	ds	PROPN
ejpam-6763	853	8	,	,	PUNCT
ejpam-6763	853	9	y	y	PROPN
ejpam-6763	853	10	′	′	NOUN
ejpam-6763	853	11	1(x	1(x	NUM
ejpam-6763	853	12	)	)	PUNCT
ejpam-6763	854	1	+	+	CCONJ
ejpam-6763	854	2	x2	x2	PROPN
ejpam-6763	854	3	c	c	NOUN
ejpam-6763	854	4	0d0.5	0d0.5	NUM
ejpam-6763	854	5	x	x	SYM
ejpam-6763	854	6	y1(x	y1(x	NOUN
ejpam-6763	854	7	)	)	PUNCT
ejpam-6763	854	8	+	+	CCONJ
ejpam-6763	854	9	ex	ex	ADJ
ejpam-6763	854	10	y1(x	y1(x	NOUN
ejpam-6763	854	11	)	)	PUNCT
ejpam-6763	854	12	=	=	SYM
ejpam-6763	854	13	f1(x	f1(x	X
ejpam-6763	854	14	)	)	PUNCT
ejpam-6763	854	15	+	+	CCONJ
ejpam-6763	854	16	ω10	ω10	NUM
ejpam-6763	854	17	∫	∫	PROPN
ejpam-6763	854	18	x	x	SYM
ejpam-6763	854	19	0	0	PUNCT
ejpam-6763	854	20	(	(	PUNCT
ejpam-6763	854	21	1	1	NUM
ejpam-6763	854	22	+	+	SYM
ejpam-6763	854	23	3x)y0(s	3x)y0(s	X
ejpam-6763	854	24	)	)	PUNCT
ejpam-6763	854	25	ds	ds	PROPN
ejpam-6763	854	26	d.	d.	PROPN
ejpam-6763	854	27	kh	kh	PROPN
ejpam-6763	854	28	.	.	PUNCT
ejpam-6763	855	1	abdullah	abdullah	PROPN
ejpam-6763	855	2	,	,	PUNCT
ejpam-6763	855	3	sh	sh	PROPN
ejpam-6763	855	4	.	.	PROPN
ejpam-6763	855	5	sh	sh	PROPN
ejpam-6763	855	6	.	.	PROPN
ejpam-6763	855	7	ahmed	ahmed	PROPN
ejpam-6763	855	8	,	,	PUNCT
ejpam-6763	855	9	k.	k.	PROPN
ejpam-6763	855	10	h.	h.	PROPN
ejpam-6763	855	11	f.	f.	PROPN
ejpam-6763	855	12	jwamer	jwamer	PROPN
ejpam-6763	855	13	/	/	SYM
ejpam-6763	855	14	eur	eur	PROPN
ejpam-6763	855	15	.	.	PUNCT
ejpam-6763	856	1	j.	j.	PROPN
ejpam-6763	856	2	pure	pure	PROPN
ejpam-6763	856	3	appl	appl	PROPN
ejpam-6763	856	4	.	.	PROPN
ejpam-6763	856	5	math	math	PROPN
ejpam-6763	856	6	,	,	PUNCT
ejpam-6763	856	7	18	18	NUM
ejpam-6763	856	8	(	(	PUNCT
ejpam-6763	856	9	4	4	NUM
ejpam-6763	856	10	)	)	PUNCT
ejpam-6763	856	11	(	(	PUNCT
ejpam-6763	856	12	2025	2025	NUM
ejpam-6763	856	13	)	)	PUNCT
ejpam-6763	856	14	,	,	PUNCT
ejpam-6763	856	15	6763	6763	NUM
ejpam-6763	856	16	22	22	NUM
ejpam-6763	856	17	of	of	ADP
ejpam-6763	856	18	40	40	NUM
ejpam-6763	856	19	+	+	CCONJ
ejpam-6763	856	20	ω11	ω11	ADP
ejpam-6763	856	21	∫	∫	PROPN
ejpam-6763	856	22	x	x	SYM
ejpam-6763	856	23	0	0	NUM
ejpam-6763	856	24	cos(x	cos(x	PROPN
ejpam-6763	856	25	)	)	PUNCT
ejpam-6763	856	26	c0d0.7	c0d0.7	VERB
ejpam-6763	857	1	s	s	PART
ejpam-6763	857	2	y1(s	y1(s	NOUN
ejpam-6763	857	3	)	)	PUNCT
ejpam-6763	857	4	ds	ds	NOUN
ejpam-6763	857	5	.	.	PUNCT
ejpam-6763	858	1	the	the	DET
ejpam-6763	858	2	given	give	VERB
ejpam-6763	858	3	functions	function	NOUN
ejpam-6763	858	4	f0(x	f0(x	NOUN
ejpam-6763	858	5	)	)	PUNCT
ejpam-6763	858	6	and	and	CCONJ
ejpam-6763	858	7	f1(x	f1(x	NUM
ejpam-6763	858	8	)	)	PUNCT
ejpam-6763	858	9	are	be	AUX
ejpam-6763	858	10	defined	define	VERB
ejpam-6763	858	11	as	as	SCONJ
ejpam-6763	858	12	follows	follow	VERB
ejpam-6763	858	13	:	:	PUNCT
ejpam-6763	858	14	f0(x	f0(x	NOUN
ejpam-6763	858	15	)	)	PUNCT
ejpam-6763	858	16	=	=	SYM
ejpam-6763	858	17	3x2	3x2	NUM
ejpam-6763	858	18	+	+	CCONJ
ejpam-6763	858	19	6	6	NUM
ejpam-6763	858	20	γ(3.6	γ(3.6	NUM
ejpam-6763	858	21	)	)	PUNCT
ejpam-6763	858	22	x3.6	x3.6	PROPN
ejpam-6763	859	1	+	+	CCONJ
ejpam-6763	859	2	(	(	PUNCT
ejpam-6763	859	3	x3	x3	ADJ
ejpam-6763	859	4	+	+	CCONJ
ejpam-6763	859	5	1	1	X
ejpam-6763	859	6	)	)	PUNCT
ejpam-6763	859	7	sin(x)−	sin(x)−	PROPN
ejpam-6763	859	8	ω00	ω00	NOUN
ejpam-6763	859	9	(	(	PUNCT
ejpam-6763	859	10	x6	x6	PROPN
ejpam-6763	859	11	5	5	NUM
ejpam-6763	859	12	+	+	CCONJ
ejpam-6763	859	13	x3	x3	ADJ
ejpam-6763	859	14	2	2	NUM
ejpam-6763	859	15	)	)	PUNCT
ejpam-6763	859	16	−	−	PROPN
ejpam-6763	859	17	2ω01e	2ω01e	NUM
ejpam-6763	859	18	x	x	SYM
ejpam-6763	859	19	1.1γ(1.1	1.1γ(1.1	NUM
ejpam-6763	859	20	)	)	PUNCT
ejpam-6763	859	21	x1.1	x1.1	PROPN
ejpam-6763	859	22	f1(x	f1(x	CCONJ
ejpam-6763	859	23	)	)	PUNCT
ejpam-6763	859	24	=	=	SYM
ejpam-6763	859	25	2	2	NUM
ejpam-6763	859	26	+	+	SYM
ejpam-6763	859	27	2	2	NUM
ejpam-6763	859	28	γ(1.5	γ(1.5	NOUN
ejpam-6763	859	29	)	)	PUNCT
ejpam-6763	859	30	x2.5	x2.5	PROPN
ejpam-6763	860	1	+	+	CCONJ
ejpam-6763	861	1	ex(1	ex(1	PROPN
ejpam-6763	861	2	+	+	PROPN
ejpam-6763	861	3	2x)−	2x)−	NUM
ejpam-6763	861	4	ω10	ω10	NUM
ejpam-6763	861	5	(	(	PUNCT
ejpam-6763	861	6	x4	x4	ADV
ejpam-6763	861	7	4	4	NUM
ejpam-6763	861	8	+	+	CCONJ
ejpam-6763	861	9	x+	x+	SYM
ejpam-6763	861	10	3x5	3x5	NUM
ejpam-6763	861	11	4	4	NUM
ejpam-6763	861	12	+	+	SYM
ejpam-6763	861	13	3x2	3x2	NUM
ejpam-6763	861	14	)	)	PUNCT
ejpam-6763	861	15	−	−	PROPN
ejpam-6763	861	16	2ω11	2ω11	ADJ
ejpam-6763	861	17	cos(x	cos(x	PROPN
ejpam-6763	861	18	)	)	PUNCT
ejpam-6763	861	19	1.3γ(1.3	1.3γ(1.3	NUM
ejpam-6763	861	20	)	)	PUNCT
ejpam-6763	861	21	x1.3	x1.3	PROPN
ejpam-6763	861	22	initial	initial	ADJ
ejpam-6763	861	23	conditions	condition	NOUN
ejpam-6763	861	24	:	:	PUNCT
ejpam-6763	861	25	y0(0	y0(0	PROPN
ejpam-6763	861	26	)	)	PUNCT
ejpam-6763	862	1	=	=	SYM
ejpam-6763	862	2	1	1	NUM
ejpam-6763	862	3	,	,	PUNCT
ejpam-6763	862	4	y1(0	y1(0	PROPN
ejpam-6763	862	5	)	)	PUNCT
ejpam-6763	862	6	=	=	SYM
ejpam-6763	862	7	1	1	NUM
ejpam-6763	862	8	exact	exact	ADJ
ejpam-6763	862	9	solutions	solution	NOUN
ejpam-6763	862	10	:	:	PUNCT
ejpam-6763	862	11	y0(x	y0(x	X
ejpam-6763	862	12	)	)	PUNCT
ejpam-6763	862	13	=	=	SYM
ejpam-6763	863	1	x3	x3	ADJ
ejpam-6763	863	2	+	+	CCONJ
ejpam-6763	863	3	1	1	NUM
ejpam-6763	863	4	,	,	PUNCT
ejpam-6763	863	5	y1(x	y1(x	NOUN
ejpam-6763	863	6	)	)	PUNCT
ejpam-6763	863	7	=	=	SYM
ejpam-6763	864	1	1	1	NUM
ejpam-6763	864	2	+	+	NUM
ejpam-6763	864	3	2x	2x	NUM
ejpam-6763	864	4	parameters	parameter	NOUN
ejpam-6763	864	5	:	:	PUNCT
ejpam-6763	864	6	σ00	σ00	NOUN
ejpam-6763	864	7	=	=	NUM
ejpam-6763	864	8	0.4	0.4	NUM
ejpam-6763	864	9	,	,	PUNCT
ejpam-6763	864	10	σ10	σ10	ADJ
ejpam-6763	864	11	=	=	SYM
ejpam-6763	864	12	0.5	0.5	NUM
ejpam-6763	864	13	,	,	PUNCT
ejpam-6763	864	14	β01	β01	NOUN
ejpam-6763	864	15	=	=	SYM
ejpam-6763	864	16	0.9	0.9	NUM
ejpam-6763	864	17	,	,	PUNCT
ejpam-6763	864	18	β11	β11	NOUN
ejpam-6763	864	19	=	=	SYM
ejpam-6763	864	20	0.7	0.7	NUM
ejpam-6763	864	21	,	,	PUNCT
ejpam-6763	864	22	ω00	ω00	NOUN
ejpam-6763	864	23	=	=	SYM
ejpam-6763	864	24	sin(0.3	sin(0.3	PROPN
ejpam-6763	864	25	)	)	PUNCT
ejpam-6763	864	26	γ2(10	γ2(10	ADJ
ejpam-6763	864	27	)	)	PUNCT
ejpam-6763	864	28	,	,	PUNCT
ejpam-6763	864	29	ω01	ω01	NOUN
ejpam-6763	864	30	=	=	SYM
ejpam-6763	864	31	−	−	PROPN
ejpam-6763	864	32	ln(0.4×	ln(0.4×	PROPN
ejpam-6763	864	33	0.7	0.7	NUM
ejpam-6763	864	34	)	)	PUNCT
ejpam-6763	864	35	γ(20	γ(20	NUM
ejpam-6763	864	36	)	)	PUNCT
ejpam-6763	864	37	,	,	PUNCT
ejpam-6763	864	38	ω10	ω10	NUM
ejpam-6763	864	39	=	=	PUNCT
ejpam-6763	864	40	cos(89	cos(89	PROPN
ejpam-6763	864	41	)	)	PUNCT
ejpam-6763	864	42	γ2(10	γ2(10	ADJ
ejpam-6763	864	43	)	)	PUNCT
ejpam-6763	864	44	,	,	PUNCT
ejpam-6763	864	45	ω11	ω11	NOUN
ejpam-6763	864	46	=	=	SYM
ejpam-6763	864	47	log(0.99999	log(0.99999	PROPN
ejpam-6763	864	48	)	)	PUNCT
ejpam-6763	864	49	γ(1.5	γ(1.5	PROPN
ejpam-6763	864	50	)	)	PUNCT
ejpam-6763	864	51	,	,	PUNCT
ejpam-6763	864	52	n	n	NOUN
ejpam-6763	864	53	=	=	SYM
ejpam-6763	864	54	10	10	NUM
ejpam-6763	864	55	,	,	PUNCT
ejpam-6763	864	56	h	h	NOUN
ejpam-6763	864	57	=	=	NOUN
ejpam-6763	864	58	0.1	0.1	NUM
ejpam-6763	864	59	,	,	PUNCT
ejpam-6763	864	60	x?r	x?r	X
ejpam-6763	864	61	=	=	SYM
ejpam-6763	864	62	a+	a+	PUNCT
ejpam-6763	864	63	rh	rh	PROPN
ejpam-6763	864	64	,	,	PUNCT
ejpam-6763	864	65	r	r	NOUN
ejpam-6763	864	66	=	=	SYM
ejpam-6763	864	67	0	0	NUM
ejpam-6763	864	68	,	,	PUNCT
ejpam-6763	864	69	1	1	NUM
ejpam-6763	864	70	,	,	PUNCT
ejpam-6763	864	71	.	.	PUNCT
ejpam-6763	864	72	.	.	PUNCT
ejpam-6763	864	73	.	.	PUNCT
ejpam-6763	865	1	,	,	PUNCT
ejpam-6763	865	2	n	n	CCONJ
ejpam-6763	865	3	−	−	PROPN
ejpam-6763	865	4	1	1	NUM
ejpam-6763	865	5	we	we	PRON
ejpam-6763	865	6	aim	aim	VERB
ejpam-6763	865	7	to	to	PART
ejpam-6763	865	8	approximate	approximate	VERB
ejpam-6763	865	9	the	the	DET
ejpam-6763	865	10	solutions	solution	NOUN
ejpam-6763	865	11	b{c,3	b{c,3	NOUN
ejpam-6763	865	12	}	}	PUNCT
ejpam-6763	865	13	i	i	PROPN
ejpam-6763	865	14	(	(	PUNCT
ejpam-6763	865	15	x?r+1	x?r+1	PROPN
ejpam-6763	865	16	)	)	PUNCT
ejpam-6763	865	17	,	,	PUNCT
ejpam-6763	865	18	for	for	ADP
ejpam-6763	865	19	i	i	PROPN
ejpam-6763	865	20	=	=	SYM
ejpam-6763	865	21	0	0	NUM
ejpam-6763	865	22	,	,	PUNCT
ejpam-6763	865	23	1	1	NUM
ejpam-6763	865	24	,	,	PUNCT
ejpam-6763	865	25	as	as	SCONJ
ejpam-6763	865	26	defined	define	VERB
ejpam-6763	865	27	in	in	ADP
ejpam-6763	865	28	equation	equation	NOUN
ejpam-6763	865	29	(	(	PUNCT
ejpam-6763	865	30	21	21	NUM
ejpam-6763	865	31	)	)	PUNCT
ejpam-6763	865	32	.	.	PUNCT
ejpam-6763	866	1	we	we	PRON
ejpam-6763	866	2	execute	execute	VERB
ejpam-6763	866	3	the	the	DET
ejpam-6763	866	4	programs	program	NOUN
ejpam-6763	866	5	nfcbi	nfcbi	VERB
ejpam-6763	866	6	,	,	PUNCT
ejpam-6763	866	7	fcpcbs	fcpcbs	PROPN
ejpam-6763	866	8	,	,	PUNCT
ejpam-6763	866	9	and	and	CCONJ
ejpam-6763	866	10	ffcpcbs	ffcpcbs	PRON
ejpam-6763	866	11	to	to	PART
ejpam-6763	866	12	compute	compute	VERB
ejpam-6763	866	13	the	the	DET
ejpam-6763	866	14	unknown	unknown	ADJ
ejpam-6763	866	15	control	control	NOUN
ejpam-6763	866	16	points	point	VERB
ejpam-6763	866	17	ϑi0	ϑi0	NOUN
ejpam-6763	866	18	,	,	PUNCT
ejpam-6763	866	19	ϑi1	ϑi1	NOUN
ejpam-6763	866	20	,	,	PUNCT
ejpam-6763	866	21	ϑi2	ϑi2	PROPN
ejpam-6763	866	22	,	,	PUNCT
ejpam-6763	866	23	ϑi3	ϑi3	NOUN
ejpam-6763	866	24	for	for	ADP
ejpam-6763	866	25	i	i	PROPN
ejpam-6763	866	26	=	=	SYM
ejpam-6763	866	27	0	0	NUM
ejpam-6763	866	28	,	,	PUNCT
ejpam-6763	866	29	1	1	NUM
ejpam-6763	866	30	.	.	PUNCT
ejpam-6763	867	1	these	these	DET
ejpam-6763	867	2	control	control	NOUN
ejpam-6763	867	3	points	point	NOUN
ejpam-6763	867	4	are	be	AUX
ejpam-6763	867	5	used	use	VERB
ejpam-6763	867	6	to	to	PART
ejpam-6763	867	7	construct	construct	VERB
ejpam-6763	867	8	the	the	DET
ejpam-6763	867	9	approximate	approximate	ADJ
ejpam-6763	867	10	solutions	solution	NOUN
ejpam-6763	867	11	for	for	ADP
ejpam-6763	867	12	the	the	DET
ejpam-6763	867	13	given	give	VERB
ejpam-6763	867	14	system	system	NOUN
ejpam-6763	867	15	.	.	PUNCT
ejpam-6763	868	1	the	the	DET
ejpam-6763	868	2	10th	10th	ADJ
ejpam-6763	868	3	table	table	NOUN
ejpam-6763	868	4	demonstrates	demonstrate	VERB
ejpam-6763	868	5	values	value	NOUN
ejpam-6763	868	6	of	of	ADP
ejpam-6763	868	7	all	all	DET
ejpam-6763	868	8	control	control	NOUN
ejpam-6763	868	9	points	point	NOUN
ejpam-6763	868	10	for	for	ADP
ejpam-6763	868	11	b{c,3	b{c,3	NOUN
ejpam-6763	868	12	}	}	PUNCT
ejpam-6763	868	13	0	0	NUM
ejpam-6763	869	1	(	(	PUNCT
ejpam-6763	869	2	x?r+1	x?r+1	NOUN
ejpam-6763	869	3	)	)	PUNCT
ejpam-6763	869	4	and	and	CCONJ
ejpam-6763	869	5	b{c,3	b{c,3	NOUN
ejpam-6763	869	6	}	}	PUNCT
ejpam-6763	869	7	1	1	NUM
ejpam-6763	869	8	(	(	PUNCT
ejpam-6763	869	9	x?r+1	x?r+1	NOUN
ejpam-6763	869	10	)	)	PUNCT
ejpam-6763	869	11	,	,	PUNCT
ejpam-6763	869	12	according	accord	VERB
ejpam-6763	869	13	to	to	ADP
ejpam-6763	869	14	the	the	DET
ejpam-6763	869	15	three	three	NUM
ejpam-6763	869	16	algorithms	algorithm	NOUN
ejpam-6763	869	17	:	:	PUNCT
ejpam-6763	869	18	nfcbi	nfcbi	VERB
ejpam-6763	869	19	,	,	PUNCT
ejpam-6763	869	20	fcpcbs	fcpcbs	PROPN
ejpam-6763	869	21	,	,	PUNCT
ejpam-6763	869	22	and	and	CCONJ
ejpam-6763	869	23	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	869	24	,	,	PUNCT
ejpam-6763	869	25	respectively	respectively	ADV
ejpam-6763	869	26	.	.	PUNCT
ejpam-6763	869	27	table	table	NOUN
ejpam-6763	869	28	1	1	NUM
ejpam-6763	869	29	:	:	PUNCT
ejpam-6763	869	30	the	the	DET
ejpam-6763	869	31	values	value	NOUN
ejpam-6763	869	32	of	of	ADP
ejpam-6763	869	33	control	control	NOUN
ejpam-6763	869	34	points	point	NOUN
ejpam-6763	869	35	of	of	ADP
ejpam-6763	869	36	b{c,3	b{c,3	NOUN
ejpam-6763	869	37	}	}	PUNCT
ejpam-6763	869	38	0	0	NUM
ejpam-6763	870	1	(	(	PUNCT
ejpam-6763	870	2	x	x	X
ejpam-6763	870	3	?	?	PUNCT
ejpam-6763	870	4	r+1	r+1	NOUN
ejpam-6763	870	5	)	)	PUNCT
ejpam-6763	870	6	,	,	PUNCT
ejpam-6763	870	7	b	b	X
ejpam-6763	870	8	{	{	PUNCT
ejpam-6763	870	9	c,3	c,3	NOUN
ejpam-6763	870	10	}	}	PUNCT
ejpam-6763	870	11	1	1	NUM
ejpam-6763	870	12	(	(	PUNCT
ejpam-6763	870	13	x	x	NOUN
ejpam-6763	870	14	?	?	PUNCT
ejpam-6763	870	15	r+1	r+1	NOUN
ejpam-6763	870	16	)	)	PUNCT
ejpam-6763	870	17	,	,	PUNCT
ejpam-6763	870	18	and	and	CCONJ
ejpam-6763	870	19	b{c,3	b{c,3	NOUN
ejpam-6763	870	20	}	}	PUNCT
ejpam-6763	870	21	2	2	NUM
ejpam-6763	870	22	(	(	PUNCT
ejpam-6763	870	23	x	x	NOUN
ejpam-6763	870	24	?	?	PUNCT
ejpam-6763	871	1	r+1	r+1	NOUN
ejpam-6763	871	2	)	)	PUNCT
ejpam-6763	871	3	for	for	ADP
ejpam-6763	871	4	three	three	NUM
ejpam-6763	871	5	methods	method	NOUN
ejpam-6763	871	6	nfcbi	nfcbi	VERB
ejpam-6763	871	7	,	,	PUNCT
ejpam-6763	871	8	fcpcbs	fcpcbs	PROPN
ejpam-6763	871	9	and	and	CCONJ
ejpam-6763	871	10	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	871	11	,	,	PUNCT
ejpam-6763	871	12	respectively	respectively	ADV
ejpam-6763	871	13	,	,	PUNCT
ejpam-6763	871	14	for	for	ADP
ejpam-6763	871	15	example	example	NOUN
ejpam-6763	871	16	1	1	NUM
ejpam-6763	871	17	.	.	PUNCT
ejpam-6763	871	18	method	method	NOUN
ejpam-6763	871	19	interval	interval	NOUN
ejpam-6763	871	20	cp	cp	NUM
ejpam-6763	871	21	of	of	ADP
ejpam-6763	871	22	the	the	DET
ejpam-6763	871	23	b{c,3	b{c,3	NOUN
ejpam-6763	871	24	}	}	PUNCT
ejpam-6763	871	25	0	0	NUM
ejpam-6763	872	1	(	(	PUNCT
ejpam-6763	872	2	x	x	X
ejpam-6763	872	3	?	?	PUNCT
ejpam-6763	872	4	r+1	r+1	NOUN
ejpam-6763	872	5	)	)	PUNCT
ejpam-6763	872	6	cp	cp	NUM
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ejpam-6763	872	13	x	x	X
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ejpam-6763	873	1	r+1	r+1	NOUN
ejpam-6763	873	2	)	)	PUNCT
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ejpam-6763	873	6	b{c,3	b{c,3	NOUN
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ejpam-6763	873	10	x	x	NOUN
ejpam-6763	873	11	?	?	PUNCT
ejpam-6763	874	1	r+1	r+1	NOUN
ejpam-6763	874	2	)	)	PUNCT
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ejpam-6763	874	4	=	=	SYM
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ejpam-6763	874	7	=	=	SYM
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ejpam-6763	874	18	=	=	SYM
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ejpam-6763	874	21	=	=	NOUN
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ejpam-6763	874	24	=	=	SYM
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ejpam-6763	874	27	=	=	SYM
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ejpam-6763	874	30	=	=	SYM
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ejpam-6763	874	33	=	=	SYM
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ejpam-6763	874	36	=	=	SYM
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ejpam-6763	874	39	=	=	PUNCT
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ejpam-6763	874	42	=	=	NOUN
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ejpam-6763	874	45	=	=	SYM
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ejpam-6763	874	48	=	=	SYM
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ejpam-6763	874	59	=	=	SYM
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ejpam-6763	874	62	=	=	NOUN
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ejpam-6763	874	65	=	=	SYM
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ejpam-6763	874	71	d.	d.	PROPN
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ejpam-6763	875	5	sh	sh	PROPN
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ejpam-6763	875	8	,	,	PUNCT
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ejpam-6763	876	9	4	4	NUM
ejpam-6763	876	10	)	)	PUNCT
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ejpam-6763	876	12	2025	2025	NUM
ejpam-6763	876	13	)	)	PUNCT
ejpam-6763	876	14	,	,	PUNCT
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ejpam-6763	877	2	x	x	X
ejpam-6763	877	3	?	?	PUNCT
ejpam-6763	877	4	r+1	r+1	NOUN
ejpam-6763	877	5	)	)	PUNCT
ejpam-6763	877	6	cp	cp	NUM
ejpam-6763	877	7	of	of	ADP
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ejpam-6763	877	9	b{c,3	b{c,3	NOUN
ejpam-6763	877	10	}	}	PUNCT
ejpam-6763	877	11	1	1	NUM
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ejpam-6763	877	13	x	x	X
ejpam-6763	877	14	?	?	PUNCT
ejpam-6763	878	1	r+1	r+1	NOUN
ejpam-6763	878	2	)	)	PUNCT
ejpam-6763	878	3	cp	cp	NUM
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ejpam-6763	878	6	b{c,3	b{c,3	NOUN
ejpam-6763	878	7	}	}	PUNCT
ejpam-6763	878	8	2	2	NUM
ejpam-6763	878	9	(	(	PUNCT
ejpam-6763	878	10	x	x	NOUN
ejpam-6763	878	11	?	?	PUNCT
ejpam-6763	879	1	r+1	r+1	NOUN
ejpam-6763	879	2	)	)	PUNCT
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ejpam-6763	879	4	=	=	PUNCT
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ejpam-6763	879	7	=	=	SYM
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ejpam-6763	879	10	=	=	SYM
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ejpam-6763	879	13	=	=	SYM
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ejpam-6763	879	16	=	=	SYM
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ejpam-6763	879	19	=	=	NOUN
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ejpam-6763	879	22	=	=	SYM
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ejpam-6763	879	25	=	=	SYM
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ejpam-6763	879	28	=	=	SYM
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ejpam-6763	879	36	=	=	SYM
ejpam-6763	879	37	1.3333333333	1.3333333333	NUM
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ejpam-6763	879	39	=	=	NOUN
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ejpam-6763	879	42	=	=	SYM
ejpam-6763	879	43	0.0000000000	0.0000000000	NUM
ejpam-6763	879	44	ϑ02	ϑ02	NOUN
ejpam-6763	879	45	=	=	SYM
ejpam-6763	879	46	1.6666733490	1.6666733490	NUM
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ejpam-6763	879	48	=	=	SYM
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ejpam-6763	879	51	=	=	SYM
ejpam-6763	879	52	0.9999999996	0.9999999996	NUM
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ejpam-6763	879	54	=	=	SYM
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ejpam-6763	879	60	=	=	SYM
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ejpam-6763	879	63	=	=	SYM
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ejpam-6763	879	66	=	=	SYM
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ejpam-6763	879	69	=	=	SYM
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ejpam-6763	879	77	=	=	SYM
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ejpam-6763	879	83	=	=	SYM
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ejpam-6763	879	86	=	=	SYM
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ejpam-6763	879	89	=	=	SYM
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ejpam-6763	879	181	=	=	PUNCT
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ejpam-6763	879	184	=	=	VERB
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ejpam-6763	879	207	=	=	SYM
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ejpam-6763	879	210	=	=	SYM
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ejpam-6763	879	213	=	=	SYM
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ejpam-6763	879	218	ϑ03	ϑ03	NOUN
ejpam-6763	879	219	=	=	SYM
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ejpam-6763	879	221	ϑ13	ϑ13	NOUN
ejpam-6763	879	222	=	=	SYM
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ejpam-6763	879	224	ϑ23	ϑ23	NOUN
ejpam-6763	879	225	=	=	NOUN
ejpam-6763	879	226	2.0000000013	2.0000000013	NUM
ejpam-6763	879	227	ϑ00	ϑ00	ADJ
ejpam-6763	879	228	=	=	SYM
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ejpam-6763	879	230	ϑ10	ϑ10	NOUN
ejpam-6763	879	231	=	=	SYM
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ejpam-6763	879	233	ϑ20	ϑ20	NOUN
ejpam-6763	879	234	=	=	SYM
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ejpam-6763	879	236	]	]	PUNCT
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ejpam-6763	879	242	=	=	SYM
ejpam-6763	879	243	1.3333333333	1.3333333333	NUM
ejpam-6763	879	244	ϑ11	ϑ11	NOUN
ejpam-6763	879	245	=	=	NOUN
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ejpam-6763	879	248	=	=	SYM
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ejpam-6763	879	251	=	=	SYM
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ejpam-6763	879	254	=	=	SYM
ejpam-6763	879	255	−0.333333327	−0.333333327	NOUN
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ejpam-6763	879	257	=	=	SYM
ejpam-6763	879	258	0.9999999996	0.9999999996	NUM
ejpam-6763	879	259	ϑ03	ϑ03	NOUN
ejpam-6763	879	260	=	=	SYM
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ejpam-6763	879	262	ϑ13	ϑ13	NOUN
ejpam-6763	879	263	=	=	SYM
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ejpam-6763	879	266	=	=	SYM
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ejpam-6763	879	268	ϑ00	ϑ00	ADJ
ejpam-6763	879	269	=	=	SYM
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ejpam-6763	879	271	ϑ10	ϑ10	NOUN
ejpam-6763	879	272	=	=	SYM
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ejpam-6763	879	274	ϑ20	ϑ20	NOUN
ejpam-6763	879	275	=	=	SYM
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ejpam-6763	879	277	]	]	PUNCT
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ejpam-6763	879	279	,	,	PUNCT
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ejpam-6763	879	281	]	]	PUNCT
ejpam-6763	879	282	ϑ01	ϑ01	NOUN
ejpam-6763	879	283	=	=	SYM
ejpam-6763	879	284	1.3333333333	1.3333333333	NUM
ejpam-6763	879	285	ϑ11	ϑ11	NOUN
ejpam-6763	879	286	=	=	NOUN
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ejpam-6763	879	288	ϑ21	ϑ21	NOUN
ejpam-6763	879	289	=	=	SYM
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ejpam-6763	879	291	ϑ02	ϑ02	NOUN
ejpam-6763	879	292	=	=	SYM
ejpam-6763	879	293	1.6666733490	1.6666733490	NUM
ejpam-6763	879	294	ϑ12	ϑ12	NOUN
ejpam-6763	879	295	=	=	SYM
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ejpam-6763	879	298	=	=	SYM
ejpam-6763	879	299	0.9999999996	0.9999999996	NUM
ejpam-6763	879	300	ϑ03	ϑ03	NOUN
ejpam-6763	879	301	=	=	SYM
ejpam-6763	879	302	2.0000041419	2.0000041419	NUM
ejpam-6763	879	303	ϑ13	ϑ13	NOUN
ejpam-6763	879	304	=	=	SYM
ejpam-6763	879	305	−0.999999995	−0.999999995	PROPN
ejpam-6763	879	306	ϑ23	ϑ23	NOUN
ejpam-6763	879	307	=	=	SYM
ejpam-6763	879	308	2.0000000023	2.0000000023	NUM
ejpam-6763	879	309	ϑ00	ϑ00	NOUN
ejpam-6763	879	310	=	=	SYM
ejpam-6763	879	311	1.0000000000	1.0000000000	NUM
ejpam-6763	879	312	ϑ10	ϑ10	NOUN
ejpam-6763	879	313	=	=	SYM
ejpam-6763	879	314	1.0000000000	1.0000000000	NUM
ejpam-6763	879	315	ϑ20	ϑ20	NOUN
ejpam-6763	879	316	=	=	SYM
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ejpam-6763	879	318	]	]	PUNCT
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ejpam-6763	879	324	=	=	SYM
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ejpam-6763	879	326	ϑ11	ϑ11	NOUN
ejpam-6763	879	327	=	=	NOUN
ejpam-6763	879	328	0.3333333333	0.3333333333	NUM
ejpam-6763	879	329	ϑ21	ϑ21	NOUN
ejpam-6763	879	330	=	=	SYM
ejpam-6763	879	331	0.0000000000	0.0000000000	NUM
ejpam-6763	879	332	ϑ02	ϑ02	NOUN
ejpam-6763	879	333	=	=	SYM
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ejpam-6763	879	336	=	=	SYM
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ejpam-6763	879	339	=	=	PUNCT
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ejpam-6763	879	343	next	next	ADJ
ejpam-6763	879	344	page	page	NOUN
ejpam-6763	879	345	d.	d.	PROPN
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ejpam-6763	880	2	,	,	PUNCT
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ejpam-6763	880	4	.	.	PROPN
ejpam-6763	880	5	sh	sh	PROPN
ejpam-6763	880	6	.	.	PROPN
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ejpam-6763	880	8	,	,	PUNCT
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ejpam-6763	880	15	.	.	PUNCT
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ejpam-6763	881	2	pure	pure	PROPN
ejpam-6763	881	3	appl	appl	PROPN
ejpam-6763	881	4	.	.	PROPN
ejpam-6763	881	5	math	math	PROPN
ejpam-6763	881	6	,	,	PUNCT
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ejpam-6763	881	8	(	(	PUNCT
ejpam-6763	881	9	4	4	NUM
ejpam-6763	881	10	)	)	PUNCT
ejpam-6763	881	11	(	(	PUNCT
ejpam-6763	881	12	2025	2025	NUM
ejpam-6763	881	13	)	)	PUNCT
ejpam-6763	881	14	,	,	PUNCT
ejpam-6763	881	15	6763	6763	NUM
ejpam-6763	881	16	24	24	NUM
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ejpam-6763	881	18	40	40	NUM
ejpam-6763	881	19	method	method	NOUN
ejpam-6763	881	20	interval	interval	NOUN
ejpam-6763	881	21	cp	cp	NUM
ejpam-6763	881	22	of	of	ADP
ejpam-6763	881	23	the	the	DET
ejpam-6763	881	24	b{c,3	b{c,3	NOUN
ejpam-6763	881	25	}	}	PUNCT
ejpam-6763	881	26	0	0	NUM
ejpam-6763	882	1	(	(	PUNCT
ejpam-6763	882	2	x	x	X
ejpam-6763	882	3	?	?	PUNCT
ejpam-6763	882	4	r+1	r+1	NOUN
ejpam-6763	882	5	)	)	PUNCT
ejpam-6763	882	6	cp	cp	NUM
ejpam-6763	882	7	of	of	ADP
ejpam-6763	882	8	the	the	DET
ejpam-6763	882	9	b{c,3	b{c,3	NOUN
ejpam-6763	882	10	}	}	PUNCT
ejpam-6763	882	11	1	1	NUM
ejpam-6763	882	12	(	(	PUNCT
ejpam-6763	882	13	x	x	X
ejpam-6763	882	14	?	?	PUNCT
ejpam-6763	883	1	r+1	r+1	NOUN
ejpam-6763	883	2	)	)	PUNCT
ejpam-6763	883	3	cp	cp	NUM
ejpam-6763	883	4	of	of	ADP
ejpam-6763	883	5	the	the	DET
ejpam-6763	883	6	b{c,3	b{c,3	NOUN
ejpam-6763	883	7	}	}	PUNCT
ejpam-6763	883	8	2	2	NUM
ejpam-6763	883	9	(	(	PUNCT
ejpam-6763	883	10	x	x	NOUN
ejpam-6763	883	11	?	?	PUNCT
ejpam-6763	884	1	r+1	r+1	NOUN
ejpam-6763	884	2	)	)	PUNCT
ejpam-6763	884	3	ϑ03	ϑ03	NOUN
ejpam-6763	884	4	=	=	NOUN
ejpam-6763	885	1	2.000005702	2.000005702	NUM
ejpam-6763	885	2	ϑ13	ϑ13	NOUN
ejpam-6763	885	3	=	=	SYM
ejpam-6763	885	4	−0.999999994	−0.999999994	NUM
ejpam-6763	885	5	ϑ23	ϑ23	NOUN
ejpam-6763	885	6	=	=	PUNCT
ejpam-6763	885	7	2.0000000029	2.0000000029	NUM
ejpam-6763	885	8	fcpcbs	fcpcbs	NOUN
ejpam-6763	885	9	ϑ00	ϑ00	ADJ
ejpam-6763	885	10	=	=	SYM
ejpam-6763	885	11	1.0000000000	1.0000000000	NUM
ejpam-6763	885	12	ϑ10	ϑ10	NOUN
ejpam-6763	885	13	=	=	SYM
ejpam-6763	885	14	1.0000000000	1.0000000000	NUM
ejpam-6763	885	15	ϑ20	ϑ20	NOUN
ejpam-6763	885	16	=	=	SYM
ejpam-6763	885	17	−1.0000000000	−1.0000000000	NUM
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ejpam-6763	885	20	,	,	PUNCT
ejpam-6763	885	21	1.0	1.0	NUM
ejpam-6763	885	22	]	]	PUNCT
ejpam-6763	885	23	ϑ01	ϑ01	NOUN
ejpam-6763	885	24	=	=	SYM
ejpam-6763	885	25	1.3333333333	1.3333333333	NUM
ejpam-6763	885	26	ϑ11	ϑ11	NOUN
ejpam-6763	885	27	=	=	NOUN
ejpam-6763	885	28	0.3333333333	0.3333333333	NUM
ejpam-6763	885	29	ϑ21	ϑ21	NOUN
ejpam-6763	885	30	=	=	SYM
ejpam-6763	885	31	0.0000000000	0.0000000000	NUM
ejpam-6763	885	32	ϑ02	ϑ02	NOUN
ejpam-6763	885	33	=	=	SYM
ejpam-6763	885	34	1.66667334902	1.66667334902	NUM
ejpam-6763	885	35	ϑ12	ϑ12	NOUN
ejpam-6763	885	36	=	=	SYM
ejpam-6763	885	37	−0.333333327	−0.333333327	NOUN
ejpam-6763	885	38	ϑ22	ϑ22	NOUN
ejpam-6763	885	39	=	=	SYM
ejpam-6763	885	40	0.9999999996	0.9999999996	NUM
ejpam-6763	885	41	ϑ03	ϑ03	NOUN
ejpam-6763	885	42	=	=	SYM
ejpam-6763	885	43	1.9998843842	1.9998843842	NUM
ejpam-6763	885	44	ϑ13	ϑ13	NOUN
ejpam-6763	885	45	=	=	PUNCT
ejpam-6763	885	46	−1.000000104	−1.000000104	NOUN
ejpam-6763	885	47	ϑ23	ϑ23	NOUN
ejpam-6763	885	48	=	=	NOUN
ejpam-6763	885	49	2.0000000055	2.0000000055	NUM
ejpam-6763	885	50	ffcpcbs	ffcpcbs	ADJ
ejpam-6763	885	51	ϑ00	ϑ00	ADJ
ejpam-6763	885	52	=	=	SYM
ejpam-6763	885	53	1.0000000000	1.0000000000	NUM
ejpam-6763	885	54	ϑ10	ϑ10	NOUN
ejpam-6763	885	55	=	=	SYM
ejpam-6763	885	56	1.0000000000	1.0000000000	NUM
ejpam-6763	885	57	ϑ20	ϑ20	NOUN
ejpam-6763	885	58	=	=	SYM
ejpam-6763	885	59	−1.000000000	−1.000000000	NUM
ejpam-6763	885	60	]	]	PUNCT
ejpam-6763	885	61	0.0	0.0	NUM
ejpam-6763	885	62	,	,	PUNCT
ejpam-6763	885	63	1.0	1.0	NUM
ejpam-6763	885	64	]	]	PUNCT
ejpam-6763	885	65	ϑ01	ϑ01	NOUN
ejpam-6763	885	66	=	=	SYM
ejpam-6763	885	67	1.3333333333	1.3333333333	NUM
ejpam-6763	885	68	ϑ11	ϑ11	NOUN
ejpam-6763	885	69	=	=	NOUN
ejpam-6763	885	70	0.3333333333	0.3333333333	NUM
ejpam-6763	885	71	ϑ21	ϑ21	NOUN
ejpam-6763	885	72	=	=	SYM
ejpam-6763	885	73	0.0000000000	0.0000000000	NUM
ejpam-6763	885	74	ϑ02	ϑ02	NOUN
ejpam-6763	885	75	=	=	SYM
ejpam-6763	885	76	1.6666733490	1.6666733490	NUM
ejpam-6763	885	77	ϑ12	ϑ12	NOUN
ejpam-6763	885	78	=	=	SYM
ejpam-6763	885	79	−0.333333327	−0.333333327	NOUN
ejpam-6763	885	80	ϑ22	ϑ22	NOUN
ejpam-6763	885	81	=	=	SYM
ejpam-6763	885	82	0.9999999996	0.9999999996	NUM
ejpam-6763	885	83	ϑ03	ϑ03	NOUN
ejpam-6763	885	84	=	=	SYM
ejpam-6763	885	85	1.9999450432	1.9999450432	NUM
ejpam-6763	885	86	ϑ13	ϑ13	NOUN
ejpam-6763	885	87	=	=	PUNCT
ejpam-6763	885	88	−1.000000049	−1.000000049	NOUN
ejpam-6763	885	89	ϑ23	ϑ23	NOUN
ejpam-6763	885	90	=	=	NOUN
ejpam-6763	885	91	2.0000000042	2.0000000042	NUM
ejpam-6763	885	92	from	from	ADP
ejpam-6763	885	93	(	(	PUNCT
ejpam-6763	885	94	21	21	NUM
ejpam-6763	885	95	)	)	PUNCT
ejpam-6763	885	96	,	,	PUNCT
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ejpam-6763	885	98	obtain	obtain	VERB
ejpam-6763	885	99	the	the	DET
ejpam-6763	885	100	approximate	approximate	ADJ
ejpam-6763	885	101	solution	solution	NOUN
ejpam-6763	885	102	for	for	ADP
ejpam-6763	885	103	the	the	DET
ejpam-6763	885	104	classical	classical	ADJ
ejpam-6763	885	105	and	and	CCONJ
ejpam-6763	885	106	fractional	fractional	ADJ
ejpam-6763	885	107	order	order	NOUN
ejpam-6763	885	108	linear	linear	NOUN
ejpam-6763	885	109	system	system	NOUN
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ejpam-6763	885	112	integro	integro	PROPN
ejpam-6763	885	113	-	-	PUNCT
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ejpam-6763	885	115	equations	equation	NOUN
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ejpam-6763	885	117	svides	svide	NOUN
ejpam-6763	885	118	-	-	PUNCT
ejpam-6763	885	119	cf	cf	NOUN
ejpam-6763	885	120	)	)	PUNCT
ejpam-6763	885	121	with	with	ADP
ejpam-6763	885	122	variable	variable	ADJ
ejpam-6763	885	123	coefficients	coefficient	NOUN
ejpam-6763	885	124	,	,	PUNCT
ejpam-6763	885	125	for	for	ADP
ejpam-6763	885	126	example	example	NOUN
ejpam-6763	885	127	1	1	NUM
ejpam-6763	885	128	as	as	SCONJ
ejpam-6763	885	129	shown	show	VERB
ejpam-6763	885	130	below	below	ADP
ejpam-6763	885	131	:	:	PUNCT
ejpam-6763	885	132	b{c,3	b{c,3	NOUN
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ejpam-6763	885	134	0	0	NUM
ejpam-6763	886	1	(	(	PUNCT
ejpam-6763	886	2	x	x	NOUN
ejpam-6763	886	3	?	?	PUNCT
ejpam-6763	886	4	)	)	PUNCT
ejpam-6763	886	5	(	(	PUNCT
ejpam-6763	886	6	nfcbi	nfcbi	NOUN
ejpam-6763	886	7	)	)	PUNCT
ejpam-6763	886	8	=	=	SYM
ejpam-6763	886	9			X
ejpam-6763	887	1	−0.00013566283x?3	−0.00013566283x?3	PROPN
ejpam-6763	887	2	+	+	CCONJ
ejpam-6763	887	3	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	887	4	+	+	CCONJ
ejpam-6763	887	5	x	x	X
ejpam-6763	887	6	?	?	PUNCT
ejpam-6763	888	1	+	+	CCONJ
ejpam-6763	888	2	1	1	NUM
ejpam-6763	888	3	if	if	SCONJ
ejpam-6763	888	4	0	0	NUM
ejpam-6763	888	5	<	<	X
ejpam-6763	888	6	x	x	X
ejpam-6763	888	7	?	?	PUNCT
ejpam-6763	888	8	≤	≤	NUM
ejpam-6763	888	9	1	1	NUM
ejpam-6763	888	10	10	10	NUM
ejpam-6763	888	11	−0.0000486226x?3	−0.0000486226x?3	NOUN
ejpam-6763	889	1	+	+	PUNCT
ejpam-6763	889	2	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	889	3	+	+	NOUN
ejpam-6763	889	4	x	x	X
ejpam-6763	889	5	?	?	PUNCT
ejpam-6763	890	1	+	+	CCONJ
ejpam-6763	890	2	1	1	NUM
ejpam-6763	890	3	if	if	SCONJ
ejpam-6763	890	4	1	1	NUM
ejpam-6763	890	5	10	10	NUM
ejpam-6763	890	6	<	<	X
ejpam-6763	890	7	x	x	X
ejpam-6763	890	8	?	?	PUNCT
ejpam-6763	890	9	≤	≤	NUM
ejpam-6763	890	10	1	1	NUM
ejpam-6763	890	11	5	5	NUM
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ejpam-6763	890	13	+	+	CCONJ
ejpam-6763	890	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	891	1	+	+	NOUN
ejpam-6763	891	2	x	x	X
ejpam-6763	891	3	?	?	PUNCT
ejpam-6763	892	1	+	+	CCONJ
ejpam-6763	892	2	1	1	NUM
ejpam-6763	892	3	if	if	SCONJ
ejpam-6763	892	4	1	1	NUM
ejpam-6763	892	5	5	5	NUM
ejpam-6763	892	6	<	<	X
ejpam-6763	892	7	x	x	X
ejpam-6763	892	8	?	?	PUNCT
ejpam-6763	892	9	≤	≤	NUM
ejpam-6763	892	10	3	3	NUM
ejpam-6763	892	11	10	10	NUM
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ejpam-6763	892	13	+	+	CCONJ
ejpam-6763	892	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	892	15	+	+	NOUN
ejpam-6763	892	16	x	x	X
ejpam-6763	892	17	?	?	PUNCT
ejpam-6763	893	1	+	+	CCONJ
ejpam-6763	893	2	1	1	NUM
ejpam-6763	893	3	if	if	SCONJ
ejpam-6763	893	4	3	3	NUM
ejpam-6763	893	5	10	10	NUM
ejpam-6763	893	6	<	<	X
ejpam-6763	893	7	x	x	X
ejpam-6763	893	8	?	?	PUNCT
ejpam-6763	893	9	≤	≤	NUM
ejpam-6763	893	10	2	2	NUM
ejpam-6763	893	11	5	5	NUM
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ejpam-6763	893	13	+	+	CCONJ
ejpam-6763	893	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	893	15	+	+	NOUN
ejpam-6763	893	16	x	x	X
ejpam-6763	893	17	?	?	PUNCT
ejpam-6763	894	1	+	+	CCONJ
ejpam-6763	894	2	1	1	NUM
ejpam-6763	894	3	if	if	SCONJ
ejpam-6763	894	4	2	2	NUM
ejpam-6763	894	5	5	5	NUM
ejpam-6763	894	6	<	<	X
ejpam-6763	894	7	x	x	X
ejpam-6763	894	8	?	?	PUNCT
ejpam-6763	894	9	≤	≤	NUM
ejpam-6763	894	10	1	1	NUM
ejpam-6763	894	11	2	2	NUM
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ejpam-6763	894	13	+	+	CCONJ
ejpam-6763	894	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	895	1	+	+	NOUN
ejpam-6763	895	2	x	x	X
ejpam-6763	895	3	?	?	PUNCT
ejpam-6763	896	1	+	+	CCONJ
ejpam-6763	896	2	1	1	NUM
ejpam-6763	896	3	if	if	SCONJ
ejpam-6763	896	4	1	1	NUM
ejpam-6763	896	5	2	2	NUM
ejpam-6763	896	6	<	<	X
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ejpam-6763	896	8	?	?	PUNCT
ejpam-6763	896	9	≤	≤	NUM
ejpam-6763	896	10	3	3	NUM
ejpam-6763	896	11	5	5	NUM
ejpam-6763	896	12	−0.0000002752x?3	−0.0000002752x?3	NOUN
ejpam-6763	896	13	+	+	CCONJ
ejpam-6763	896	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	896	15	+	+	NOUN
ejpam-6763	896	16	x	x	X
ejpam-6763	896	17	?	?	PUNCT
ejpam-6763	897	1	+	+	CCONJ
ejpam-6763	897	2	1	1	NUM
ejpam-6763	897	3	if	if	SCONJ
ejpam-6763	897	4	3	3	NUM
ejpam-6763	897	5	5	5	NUM
ejpam-6763	897	6	<	<	X
ejpam-6763	897	7	x	x	X
ejpam-6763	897	8	?	?	PUNCT
ejpam-6763	897	9	≤	≤	NUM
ejpam-6763	897	10	7	7	NUM
ejpam-6763	897	11	10	10	NUM
ejpam-6763	897	12	0.00000220271x?3	0.00000220271x?3	NOUN
ejpam-6763	898	1	+	+	CCONJ
ejpam-6763	898	2	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	899	1	+	+	NOUN
ejpam-6763	899	2	x	x	X
ejpam-6763	899	3	?	?	PUNCT
ejpam-6763	900	1	+	+	CCONJ
ejpam-6763	900	2	1	1	NUM
ejpam-6763	900	3	if	if	SCONJ
ejpam-6763	900	4	7	7	NUM
ejpam-6763	900	5	10	10	NUM
ejpam-6763	900	6	<	<	X
ejpam-6763	900	7	x	x	X
ejpam-6763	900	8	?	?	PUNCT
ejpam-6763	900	9	≤	≤	NUM
ejpam-6763	901	1	4	4	NUM
ejpam-6763	901	2	5	5	NUM
ejpam-6763	901	3	0.00000414190x?3	0.00000414190x?3	NOUN
ejpam-6763	901	4	+	+	CCONJ
ejpam-6763	901	5	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	901	6	+	+	CCONJ
ejpam-6763	901	7	x	x	X
ejpam-6763	901	8	?	?	PUNCT
ejpam-6763	902	1	+	+	CCONJ
ejpam-6763	902	2	1	1	NUM
ejpam-6763	902	3	if	if	SCONJ
ejpam-6763	902	4	4	4	NUM
ejpam-6763	902	5	5	5	NUM
ejpam-6763	902	6	<	<	X
ejpam-6763	902	7	x	x	X
ejpam-6763	902	8	?	?	PUNCT
ejpam-6763	902	9	≤	≤	NUM
ejpam-6763	902	10	9	9	NUM
ejpam-6763	902	11	10	10	NUM
ejpam-6763	902	12	0.00000570220x?3	0.00000570220x?3	NUM
ejpam-6763	903	1	+	+	PUNCT
ejpam-6763	903	2	0.0000000181x?2	0.0000000181x?2	NUM
ejpam-6763	903	3	+	+	CCONJ
ejpam-6763	903	4	x	x	X
ejpam-6763	903	5	?	?	PUNCT
ejpam-6763	904	1	+	+	CCONJ
ejpam-6763	904	2	1	1	NUM
ejpam-6763	904	3	if	if	SCONJ
ejpam-6763	904	4	9	9	NUM
ejpam-6763	904	5	10	10	NUM
ejpam-6763	904	6	<	<	X
ejpam-6763	904	7	x	x	X
ejpam-6763	904	8	?	?	SYM
ejpam-6763	904	9	≤	≤	NUM
ejpam-6763	904	10	1	1	NUM
ejpam-6763	904	11	b{c,3	b{c,3	NOUN
ejpam-6763	904	12	}	}	PUNCT
ejpam-6763	904	13	1	1	NUM
ejpam-6763	904	14	(	(	PUNCT
ejpam-6763	904	15	x	x	NOUN
ejpam-6763	904	16	?	?	PUNCT
ejpam-6763	904	17	)	)	PUNCT
ejpam-6763	904	18	(	(	PUNCT
ejpam-6763	904	19	nfcbi	nfcbi	NOUN
ejpam-6763	904	20	)	)	PUNCT
ejpam-6763	904	21	=	=	SYM
ejpam-6763	904	22			X
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ejpam-6763	905	1	+	+	CCONJ
ejpam-6763	905	2	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	905	3	−	−	NOUN
ejpam-6763	905	4	2x	2x	NUM
ejpam-6763	905	5	?	?	PUNCT
ejpam-6763	906	1	+	+	CCONJ
ejpam-6763	906	2	1	1	NUM
ejpam-6763	906	3	if	if	SCONJ
ejpam-6763	906	4	0	0	NUM
ejpam-6763	906	5	<	<	X
ejpam-6763	906	6	x	x	X
ejpam-6763	906	7	?	?	PUNCT
ejpam-6763	906	8	≤	≤	NUM
ejpam-6763	906	9	1	1	NUM
ejpam-6763	906	10	10	10	NUM
ejpam-6763	906	11	−0.0000000442x?3	−0.0000000442x?3	NOUN
ejpam-6763	907	1	+	+	CCONJ
ejpam-6763	907	2	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	907	3	−	−	NOUN
ejpam-6763	907	4	2x	2x	NUM
ejpam-6763	907	5	?	?	PUNCT
ejpam-6763	908	1	+	+	CCONJ
ejpam-6763	908	2	1	1	NUM
ejpam-6763	908	3	if	if	SCONJ
ejpam-6763	908	4	1	1	NUM
ejpam-6763	908	5	10	10	NUM
ejpam-6763	908	6	<	<	X
ejpam-6763	908	7	x	x	X
ejpam-6763	908	8	?	?	PUNCT
ejpam-6763	908	9	≤	≤	NUM
ejpam-6763	908	10	1	1	NUM
ejpam-6763	908	11	5	5	NUM
ejpam-6763	908	12	−0.0000000242x?3	−0.0000000242x?3	NOUN
ejpam-6763	908	13	+	+	CCONJ
ejpam-6763	908	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	908	15	−	−	NOUN
ejpam-6763	908	16	2x	2x	NUM
ejpam-6763	908	17	?	?	PUNCT
ejpam-6763	909	1	+	+	CCONJ
ejpam-6763	909	2	1	1	NUM
ejpam-6763	909	3	if	if	SCONJ
ejpam-6763	909	4	1	1	NUM
ejpam-6763	909	5	5	5	NUM
ejpam-6763	909	6	<	<	X
ejpam-6763	909	7	x	x	X
ejpam-6763	909	8	?	?	PUNCT
ejpam-6763	909	9	≤	≤	NUM
ejpam-6763	909	10	3	3	NUM
ejpam-6763	909	11	10	10	NUM
ejpam-6763	909	12	−0.0000000140x?3	−0.0000000140x?3	NOUN
ejpam-6763	909	13	+	+	CCONJ
ejpam-6763	909	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	909	15	−	−	NOUN
ejpam-6763	909	16	2x	2x	NUM
ejpam-6763	909	17	?	?	PUNCT
ejpam-6763	910	1	+	+	CCONJ
ejpam-6763	910	2	1	1	NUM
ejpam-6763	910	3	if	if	SCONJ
ejpam-6763	910	4	3	3	NUM
ejpam-6763	910	5	10	10	NUM
ejpam-6763	910	6	<	<	X
ejpam-6763	910	7	x	x	X
ejpam-6763	910	8	?	?	PUNCT
ejpam-6763	910	9	≤	≤	NUM
ejpam-6763	910	10	2	2	NUM
ejpam-6763	910	11	5	5	NUM
ejpam-6763	910	12	−0.0000000077x?3	−0.0000000077x?3	NOUN
ejpam-6763	910	13	+	+	PUNCT
ejpam-6763	910	14	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	910	15	−	−	NOUN
ejpam-6763	910	16	2x	2x	NUM
ejpam-6763	910	17	?	?	PUNCT
ejpam-6763	911	1	+	+	CCONJ
ejpam-6763	911	2	1	1	NUM
ejpam-6763	911	3	if	if	SCONJ
ejpam-6763	911	4	2	2	NUM
ejpam-6763	911	5	5	5	NUM
ejpam-6763	911	6	<	<	X
ejpam-6763	911	7	x	x	X
ejpam-6763	911	8	?	?	PUNCT
ejpam-6763	911	9	≤	≤	NUM
ejpam-6763	911	10	1	1	NUM
ejpam-6763	911	11	2	2	NUM
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ejpam-6763	911	13	+	+	CCONJ
ejpam-6763	911	14	0.00002004706x?2	0.00002004706x?2	PROPN
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ejpam-6763	911	16	2x	2x	NUM
ejpam-6763	911	17	?	?	PUNCT
ejpam-6763	912	1	+	+	CCONJ
ejpam-6763	912	2	1	1	NUM
ejpam-6763	912	3	if	if	SCONJ
ejpam-6763	912	4	1	1	NUM
ejpam-6763	912	5	2	2	NUM
ejpam-6763	912	6	<	<	X
ejpam-6763	912	7	x	x	X
ejpam-6763	912	8	?	?	PUNCT
ejpam-6763	912	9	≤	≤	NUM
ejpam-6763	912	10	3	3	NUM
ejpam-6763	912	11	5	5	NUM
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ejpam-6763	912	13	+	+	CCONJ
ejpam-6763	912	14	0.00002004706x?2	0.00002004706x?2	PROPN
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ejpam-6763	912	16	2x	2x	NUM
ejpam-6763	912	17	?	?	PUNCT
ejpam-6763	913	1	+	+	CCONJ
ejpam-6763	913	2	1	1	NUM
ejpam-6763	913	3	if	if	SCONJ
ejpam-6763	913	4	3	3	NUM
ejpam-6763	913	5	5	5	NUM
ejpam-6763	913	6	<	<	X
ejpam-6763	913	7	x	x	X
ejpam-6763	913	8	?	?	PUNCT
ejpam-6763	913	9	≤	≤	NUM
ejpam-6763	913	10	7	7	NUM
ejpam-6763	913	11	10	10	NUM
ejpam-6763	913	12	0.0000000024x?3	0.0000000024x?3	PROPN
ejpam-6763	914	1	+	+	CCONJ
ejpam-6763	914	2	0.00002004706x?2	0.00002004706x?2	NUM
ejpam-6763	914	3	−	−	NOUN
ejpam-6763	914	4	2x	2x	NUM
ejpam-6763	914	5	?	?	PUNCT
ejpam-6763	915	1	+	+	CCONJ
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ejpam-6763	915	3	if	if	SCONJ
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ejpam-6763	915	5	10	10	NUM
ejpam-6763	915	6	<	<	X
ejpam-6763	915	7	x	x	X
ejpam-6763	915	8	?	?	PUNCT
ejpam-6763	915	9	≤	≤	NUM
ejpam-6763	915	10	4	4	NUM
ejpam-6763	915	11	5	5	NUM
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ejpam-6763	915	13	+	+	PUNCT
ejpam-6763	915	14	0.00002004706x?2	0.00002004706x?2	NUM
ejpam-6763	915	15	−	−	NOUN
ejpam-6763	915	16	2x	2x	NUM
ejpam-6763	915	17	?	?	PUNCT
ejpam-6763	916	1	+	+	CCONJ
ejpam-6763	916	2	1	1	NUM
ejpam-6763	916	3	if	if	SCONJ
ejpam-6763	916	4	4	4	NUM
ejpam-6763	916	5	5	5	NUM
ejpam-6763	916	6	<	<	X
ejpam-6763	916	7	x	x	X
ejpam-6763	916	8	?	?	PUNCT
ejpam-6763	916	9	≤	≤	NUM
ejpam-6763	916	10	9	9	NUM
ejpam-6763	916	11	10	10	NUM
ejpam-6763	916	12	0.0000000054x?3	0.0000000054x?3	NOUN
ejpam-6763	917	1	+	+	CCONJ
ejpam-6763	917	2	0.00002004706x?2	0.00002004706x?2	NUM
ejpam-6763	917	3	−	−	NOUN
ejpam-6763	917	4	2x	2x	NUM
ejpam-6763	917	5	?	?	PUNCT
ejpam-6763	918	1	+	+	CCONJ
ejpam-6763	918	2	1	1	NUM
ejpam-6763	918	3	if	if	SCONJ
ejpam-6763	918	4	9	9	NUM
ejpam-6763	918	5	10	10	NUM
ejpam-6763	918	6	<	<	X
ejpam-6763	918	7	x	x	X
ejpam-6763	918	8	?	?	PUNCT
ejpam-6763	918	9	≤	≤	NUM
ejpam-6763	918	10	1	1	NUM
ejpam-6763	918	11	d.	d.	PROPN
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ejpam-6763	918	13	.	.	PUNCT
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ejpam-6763	919	2	,	,	PUNCT
ejpam-6763	919	3	sh	sh	PROPN
ejpam-6763	919	4	.	.	PROPN
ejpam-6763	919	5	sh	sh	PROPN
ejpam-6763	919	6	.	.	PROPN
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ejpam-6763	919	8	,	,	PUNCT
ejpam-6763	919	9	k.	k.	PROPN
ejpam-6763	919	10	h.	h.	PROPN
ejpam-6763	919	11	f.	f.	PROPN
ejpam-6763	919	12	jwamer	jwamer	PROPN
ejpam-6763	919	13	/	/	SYM
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ejpam-6763	919	15	.	.	PUNCT
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ejpam-6763	920	3	appl	appl	PROPN
ejpam-6763	920	4	.	.	PROPN
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ejpam-6763	920	6	,	,	PUNCT
ejpam-6763	920	7	18	18	NUM
ejpam-6763	920	8	(	(	PUNCT
ejpam-6763	920	9	4	4	NUM
ejpam-6763	920	10	)	)	PUNCT
ejpam-6763	920	11	(	(	PUNCT
ejpam-6763	920	12	2025	2025	NUM
ejpam-6763	920	13	)	)	PUNCT
ejpam-6763	920	14	,	,	PUNCT
ejpam-6763	920	15	6763	6763	NUM
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ejpam-6763	920	18	40	40	NUM
ejpam-6763	920	19	b{c,3	b{c,3	NOUN
ejpam-6763	920	20	}	}	PUNCT
ejpam-6763	920	21	2	2	NUM
ejpam-6763	920	22	(	(	PUNCT
ejpam-6763	920	23	x	x	NOUN
ejpam-6763	920	24	?	?	PUNCT
ejpam-6763	920	25	)	)	PUNCT
ejpam-6763	920	26	(	(	PUNCT
ejpam-6763	920	27	nfcbi	nfcbi	NOUN
ejpam-6763	920	28	)	)	PUNCT
ejpam-6763	920	29	=	=	PUNCT
ejpam-6763	920	30			X
ejpam-6763	921	1	0.00000000652x?3	0.00000000652x?3	NUM
ejpam-6763	922	1	−	−	NOUN
ejpam-6763	923	1	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	924	1	+	+	CCONJ
ejpam-6763	924	2	3x	3x	NUM
ejpam-6763	924	3	?	?	PUNCT
ejpam-6763	925	1	−	−	NOUN
ejpam-6763	925	2	1	1	NUM
ejpam-6763	926	1	if	if	SCONJ
ejpam-6763	926	2	0	0	NUM
ejpam-6763	926	3	<	<	X
ejpam-6763	926	4	x	x	X
ejpam-6763	926	5	?	?	PUNCT
ejpam-6763	926	6	≤	≤	NUM
ejpam-6763	926	7	1	1	NUM
ejpam-6763	926	8	10	10	NUM
ejpam-6763	926	9	0.00000000241x?3	0.00000000241x?3	NUM
ejpam-6763	927	1	−	−	NOUN
ejpam-6763	928	1	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	929	1	+	+	CCONJ
ejpam-6763	929	2	3x	3x	NUM
ejpam-6763	929	3	?	?	PUNCT
ejpam-6763	930	1	−	−	NOUN
ejpam-6763	930	2	1	1	NUM
ejpam-6763	931	1	if	if	SCONJ
ejpam-6763	931	2	1	1	NUM
ejpam-6763	931	3	10	10	NUM
ejpam-6763	931	4	<	<	X
ejpam-6763	931	5	x	x	X
ejpam-6763	931	6	?	?	PUNCT
ejpam-6763	931	7	≤	≤	NUM
ejpam-6763	931	8	1	1	NUM
ejpam-6763	931	9	5	5	NUM
ejpam-6763	931	10	0.00000000145x?3	0.00000000145x?3	NUM
ejpam-6763	931	11	−	−	NOUN
ejpam-6763	932	1	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	932	2	+	+	CCONJ
ejpam-6763	932	3	3x	3x	NUM
ejpam-6763	932	4	?	?	PUNCT
ejpam-6763	933	1	−	−	NOUN
ejpam-6763	933	2	1	1	NUM
ejpam-6763	933	3	if	if	SCONJ
ejpam-6763	933	4	1	1	NUM
ejpam-6763	933	5	5	5	NUM
ejpam-6763	933	6	<	<	X
ejpam-6763	933	7	x	x	X
ejpam-6763	933	8	?	?	PUNCT
ejpam-6763	933	9	≤	≤	NUM
ejpam-6763	934	1	3	3	NUM
ejpam-6763	934	2	10	10	NUM
ejpam-6763	934	3	0.00000000108x?3	0.00000000108x?3	NUM
ejpam-6763	934	4	−	−	NOUN
ejpam-6763	934	5	0.00000000096x?2	0.00000000096x?2	NUM
ejpam-6763	934	6	+	+	CCONJ
ejpam-6763	934	7	3x	3x	NUM
ejpam-6763	934	8	?	?	PUNCT
ejpam-6763	935	1	−	−	NOUN
ejpam-6763	935	2	1	1	NUM
ejpam-6763	935	3	if	if	SCONJ
ejpam-6763	935	4	3	3	NUM
ejpam-6763	935	5	10	10	NUM
ejpam-6763	935	6	<	<	X
ejpam-6763	935	7	x	x	X
ejpam-6763	935	8	?	?	PUNCT
ejpam-6763	935	9	≤	≤	NUM
ejpam-6763	935	10	2	2	NUM
ejpam-6763	935	11	5	5	NUM
ejpam-6763	935	12	0.00000000101x?3	0.00000000101x?3	NUM
ejpam-6763	935	13	−	−	NOUN
ejpam-6763	936	1	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	936	2	+	+	CCONJ
ejpam-6763	936	3	3x	3x	NUM
ejpam-6763	936	4	?	?	PUNCT
ejpam-6763	937	1	−	−	NOUN
ejpam-6763	937	2	1	1	NUM
ejpam-6763	937	3	if	if	SCONJ
ejpam-6763	937	4	2	2	NUM
ejpam-6763	937	5	5	5	NUM
ejpam-6763	937	6	<	<	X
ejpam-6763	937	7	x	x	X
ejpam-6763	937	8	?	?	PUNCT
ejpam-6763	937	9	≤	≤	NUM
ejpam-6763	937	10	1	1	NUM
ejpam-6763	937	11	2	2	NUM
ejpam-6763	937	12	0.00000000113x?3	0.00000000113x?3	NUM
ejpam-6763	937	13	−	−	NOUN
ejpam-6763	937	14	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	938	1	+	+	CCONJ
ejpam-6763	938	2	3x	3x	NUM
ejpam-6763	938	3	?	?	PUNCT
ejpam-6763	939	1	−	−	NOUN
ejpam-6763	939	2	1	1	NUM
ejpam-6763	939	3	if	if	SCONJ
ejpam-6763	939	4	1	1	NUM
ejpam-6763	939	5	2	2	NUM
ejpam-6763	939	6	<	<	X
ejpam-6763	939	7	x	x	X
ejpam-6763	939	8	?	?	PUNCT
ejpam-6763	939	9	≤	≤	NUM
ejpam-6763	940	1	3	3	NUM
ejpam-6763	940	2	5	5	NUM
ejpam-6763	940	3	0.00000000139x?3	0.00000000139x?3	NUM
ejpam-6763	940	4	−	−	NOUN
ejpam-6763	940	5	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	941	1	+	+	CCONJ
ejpam-6763	941	2	3x	3x	NUM
ejpam-6763	941	3	?	?	PUNCT
ejpam-6763	942	1	−	−	NOUN
ejpam-6763	942	2	1	1	NUM
ejpam-6763	942	3	if	if	SCONJ
ejpam-6763	942	4	3	3	NUM
ejpam-6763	942	5	5	5	NUM
ejpam-6763	942	6	<	<	X
ejpam-6763	942	7	x	x	X
ejpam-6763	942	8	?	?	PUNCT
ejpam-6763	942	9	≤	≤	NUM
ejpam-6763	942	10	7	7	NUM
ejpam-6763	942	11	10	10	NUM
ejpam-6763	942	12	0.00000000179x?3	0.00000000179x?3	PROPN
ejpam-6763	942	13	−	−	NOUN
ejpam-6763	943	1	0.00000000096x?2	0.00000000096x?2	NUM
ejpam-6763	943	2	+	+	CCONJ
ejpam-6763	943	3	3x	3x	NUM
ejpam-6763	943	4	?	?	PUNCT
ejpam-6763	944	1	−	−	NOUN
ejpam-6763	944	2	1	1	NUM
ejpam-6763	944	3	if	if	SCONJ
ejpam-6763	944	4	7	7	NUM
ejpam-6763	944	5	10	10	NUM
ejpam-6763	944	6	<	<	X
ejpam-6763	944	7	x	x	X
ejpam-6763	944	8	?	?	PUNCT
ejpam-6763	944	9	≤	≤	NUM
ejpam-6763	945	1	4	4	NUM
ejpam-6763	945	2	5	5	NUM
ejpam-6763	945	3	0.00000000232x?3	0.00000000232x?3	NUM
ejpam-6763	945	4	−	−	NOUN
ejpam-6763	945	5	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	945	6	+	+	CCONJ
ejpam-6763	945	7	3x	3x	NUM
ejpam-6763	945	8	?	?	PUNCT
ejpam-6763	946	1	−	−	NOUN
ejpam-6763	946	2	1	1	NUM
ejpam-6763	947	1	if	if	SCONJ
ejpam-6763	947	2	4	4	NUM
ejpam-6763	947	3	5	5	NUM
ejpam-6763	947	4	<	<	X
ejpam-6763	947	5	x	x	X
ejpam-6763	947	6	?	?	PUNCT
ejpam-6763	947	7	≤	≤	NUM
ejpam-6763	947	8	9	9	NUM
ejpam-6763	947	9	10	10	NUM
ejpam-6763	947	10	0.00000000298x?3	0.00000000298x?3	NOUN
ejpam-6763	947	11	−	−	PROPN
ejpam-6763	948	1	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	948	2	+	+	CCONJ
ejpam-6763	948	3	3x	3x	NUM
ejpam-6763	948	4	?	?	PUNCT
ejpam-6763	949	1	−	−	NOUN
ejpam-6763	949	2	1	1	NUM
ejpam-6763	950	1	if	if	SCONJ
ejpam-6763	950	2	9	9	NUM
ejpam-6763	950	3	10	10	NUM
ejpam-6763	950	4	<	<	X
ejpam-6763	950	5	x	x	X
ejpam-6763	950	6	?	?	PUNCT
ejpam-6763	950	7	≤	≤	NUM
ejpam-6763	950	8	1	1	NUM
ejpam-6763	950	9	fcpcbs	fcpcbs	NOUN
ejpam-6763	950	10	=	=	NOUN
ejpam-6763	951	1			PROPN
ejpam-6763	951	2	b{c,3	b{c,3	VERB
ejpam-6763	951	3	}	}	PUNCT
ejpam-6763	951	4	0	0	NUM
ejpam-6763	952	1	(	(	PUNCT
ejpam-6763	952	2	x	x	NOUN
ejpam-6763	952	3	?	?	PUNCT
ejpam-6763	952	4	)	)	PUNCT
ejpam-6763	952	5	=	=	PUNCT
ejpam-6763	953	1	−0.00013566283x?3	−0.00013566283x?3	PROPN
ejpam-6763	953	2	+	+	CCONJ
ejpam-6763	953	3	0.00002004706x?2	0.00002004706x?2	PROPN
ejpam-6763	953	4	+	+	CCONJ
ejpam-6763	953	5	x	x	X
ejpam-6763	953	6	?	?	PUNCT
ejpam-6763	954	1	+	+	CCONJ
ejpam-6763	954	2	1	1	NUM
ejpam-6763	954	3	if	if	SCONJ
ejpam-6763	954	4	0	0	NUM
ejpam-6763	954	5	<	<	X
ejpam-6763	954	6	x	x	X
ejpam-6763	954	7	?	?	PUNCT
ejpam-6763	954	8	≤	≤	NUM
ejpam-6763	954	9	1.0	1.0	NUM
ejpam-6763	954	10	b{c,3	b{c,3	NOUN
ejpam-6763	954	11	}	}	PUNCT
ejpam-6763	954	12	1	1	NUM
ejpam-6763	954	13	(	(	PUNCT
ejpam-6763	954	14	x	x	NOUN
ejpam-6763	954	15	?	?	PUNCT
ejpam-6763	954	16	)	)	PUNCT
ejpam-6763	954	17	=	=	PUNCT
ejpam-6763	955	1	−0.0000001223x?3	−0.0000001223x?3	NOUN
ejpam-6763	956	1	+	+	CCONJ
ejpam-6763	956	2	0.00002004706x?2	0.00002004706x?2	NUM
ejpam-6763	956	3	−	−	NOUN
ejpam-6763	956	4	2x	2x	NUM
ejpam-6763	956	5	?	?	PUNCT
ejpam-6763	957	1	+	+	CCONJ
ejpam-6763	957	2	1	1	NUM
ejpam-6763	957	3	if	if	SCONJ
ejpam-6763	957	4	0	0	NUM
ejpam-6763	957	5	<	<	X
ejpam-6763	957	6	x	x	X
ejpam-6763	957	7	?	?	PUNCT
ejpam-6763	957	8	≤	≤	NUM
ejpam-6763	957	9	1.0	1.0	NUM
ejpam-6763	957	10	b{c,3	b{c,3	NOUN
ejpam-6763	957	11	}	}	PUNCT
ejpam-6763	957	12	2	2	NUM
ejpam-6763	957	13	(	(	PUNCT
ejpam-6763	957	14	x	x	NOUN
ejpam-6763	957	15	?	?	PUNCT
ejpam-6763	957	16	)	)	PUNCT
ejpam-6763	957	17	=	=	PUNCT
ejpam-6763	958	1	0.00000000652x?3	0.00000000652x?3	NUM
ejpam-6763	959	1	−	−	NOUN
ejpam-6763	959	2	0.00000000096x?2	0.00000000096x?2	PROPN
ejpam-6763	960	1	+	+	CCONJ
ejpam-6763	960	2	3x	3x	NUM
ejpam-6763	960	3	?	?	PUNCT
ejpam-6763	961	1	−	−	NOUN
ejpam-6763	961	2	1	1	NUM
ejpam-6763	962	1	if	if	SCONJ
ejpam-6763	962	2	0	0	NUM
ejpam-6763	962	3	<	<	X
ejpam-6763	962	4	x	x	X
ejpam-6763	962	5	?	?	PUNCT
ejpam-6763	962	6	≤	≤	NUM
ejpam-6763	962	7	1.0	1.0	NUM
ejpam-6763	962	8	ffcpcbs	ffcpcb	NOUN
ejpam-6763	962	9	=	=	PUNCT
ejpam-6763	962	10			PRON
ejpam-6763	962	11	b{c,3	b{c,3	VERB
ejpam-6763	962	12	}	}	PUNCT
ejpam-6763	962	13	0	0	NUM
ejpam-6763	963	1	(	(	PUNCT
ejpam-6763	963	2	x	x	NOUN
ejpam-6763	963	3	?	?	PUNCT
ejpam-6763	963	4	)	)	PUNCT
ejpam-6763	964	1	=	=	SYM
ejpam-6763	964	2	1	1	NUM
ejpam-6763	964	3	+	+	NOUN
ejpam-6763	964	4	x	x	X
ejpam-6763	964	5	?	?	PUNCT
ejpam-6763	965	1	+	+	CCONJ
ejpam-6763	965	2	0.00002004706x?2	0.00002004706x?2	NUM
ejpam-6763	965	3	−	−	NOUN
ejpam-6763	965	4	0.00005495675x?3	0.00005495675x?3	NUM
ejpam-6763	965	5	if	if	SCONJ
ejpam-6763	965	6	0	0	NUM
ejpam-6763	965	7	<	<	X
ejpam-6763	965	8	x	x	X
ejpam-6763	965	9	?	?	PUNCT
ejpam-6763	965	10	≤	≤	NUM
ejpam-6763	965	11	1.0	1.0	NUM
ejpam-6763	965	12	b{c,3	b{c,3	NOUN
ejpam-6763	965	13	}	}	PUNCT
ejpam-6763	965	14	1	1	NUM
ejpam-6763	965	15	(	(	PUNCT
ejpam-6763	965	16	x	x	NOUN
ejpam-6763	965	17	?	?	PUNCT
ejpam-6763	965	18	)	)	PUNCT
ejpam-6763	965	19	=	=	SYM
ejpam-6763	965	20	1−	1−	NUM
ejpam-6763	965	21	2x	2x	NUM
ejpam-6763	965	22	?	?	PUNCT
ejpam-6763	966	1	+	+	CCONJ
ejpam-6763	966	2	0.0000000181x?2	0.0000000181x?2	NUM
ejpam-6763	966	3	−	−	NOUN
ejpam-6763	966	4	0.0000000494x?3	0.0000000494x?3	PUNCT
ejpam-6763	967	1	if	if	SCONJ
ejpam-6763	967	2	0	0	NUM
ejpam-6763	967	3	<	<	X
ejpam-6763	967	4	x	x	X
ejpam-6763	967	5	?	?	PUNCT
ejpam-6763	967	6	≤	≤	NUM
ejpam-6763	967	7	1.0	1.0	NUM
ejpam-6763	967	8	b{c,3	b{c,3	NOUN
ejpam-6763	967	9	}	}	PUNCT
ejpam-6763	967	10	2	2	NUM
ejpam-6763	967	11	(	(	PUNCT
ejpam-6763	967	12	x	x	NOUN
ejpam-6763	967	13	?	?	PUNCT
ejpam-6763	967	14	)	)	PUNCT
ejpam-6763	967	15	=	=	PUNCT
ejpam-6763	968	1	−1	−1	NOUN
ejpam-6763	969	1	+	+	NOUN
ejpam-6763	969	2	3x	3x	NUM
ejpam-6763	969	3	?	?	PUNCT
ejpam-6763	970	1	−	−	PUNCT
ejpam-6763	971	1	0.00000000096x?2	0.00000000096x?2	PRON
ejpam-6763	971	2	+	+	CCONJ
ejpam-6763	971	3	0.00000000427x?3	0.00000000427x?3	PROPN
ejpam-6763	972	1	if	if	SCONJ
ejpam-6763	972	2	0	0	NUM
ejpam-6763	972	3	<	<	X
ejpam-6763	972	4	x	x	X
ejpam-6763	972	5	?	?	PUNCT
ejpam-6763	972	6	≤	≤	NUM
ejpam-6763	972	7	1.0	1.0	NUM
ejpam-6763	972	8	tables	table	NOUN
ejpam-6763	972	9	2–4	2–4	NUM
ejpam-6763	972	10	present	present	ADJ
ejpam-6763	972	11	a	a	DET
ejpam-6763	972	12	comparison	comparison	NOUN
ejpam-6763	972	13	between	between	ADP
ejpam-6763	972	14	the	the	DET
ejpam-6763	972	15	approximate	approximate	ADJ
ejpam-6763	972	16	and	and	CCONJ
ejpam-6763	972	17	exact	exact	ADJ
ejpam-6763	972	18	solutions	solution	NOUN
ejpam-6763	972	19	of	of	ADP
ejpam-6763	972	20	the	the	DET
ejpam-6763	972	21	functions	function	NOUN
ejpam-6763	972	22	y0(x	y0(x	NUM
ejpam-6763	972	23	)	)	PUNCT
ejpam-6763	972	24	,	,	PUNCT
ejpam-6763	972	25	y1(x	y1(x	NOUN
ejpam-6763	972	26	)	)	PUNCT
ejpam-6763	972	27	,	,	PUNCT
ejpam-6763	972	28	and	and	CCONJ
ejpam-6763	972	29	y2(x	y2(x	NOUN
ejpam-6763	972	30	)	)	PUNCT
ejpam-6763	972	31	.	.	PUNCT
ejpam-6763	973	1	the	the	DET
ejpam-6763	973	2	computations	computation	NOUN
ejpam-6763	973	3	are	be	AUX
ejpam-6763	973	4	carried	carry	VERB
ejpam-6763	973	5	out	out	ADP
ejpam-6763	973	6	using	use	VERB
ejpam-6763	973	7	n	n	NOUN
ejpam-6763	973	8	=	=	SYM
ejpam-6763	973	9	10	10	NUM
ejpam-6763	973	10	,	,	PUNCT
ejpam-6763	973	11	step	step	NOUN
ejpam-6763	973	12	size	size	NOUN
ejpam-6763	973	13	h	h	NOUN
ejpam-6763	973	14	=	=	NOUN
ejpam-6763	973	15	0.1	0.1	NUM
ejpam-6763	973	16	,	,	PUNCT
ejpam-6763	973	17	and	and	CCONJ
ejpam-6763	973	18	sampling	sample	VERB
ejpam-6763	973	19	points	point	NOUN
ejpam-6763	973	20	defined	define	VERB
ejpam-6763	973	21	by	by	ADP
ejpam-6763	973	22	x?r	x?r	PROPN
ejpam-6763	973	23	=	=	PUNCT
ejpam-6763	973	24	a	a	DET
ejpam-6763	973	25	+	+	NUM
ejpam-6763	973	26	rh	rh	PROPN
ejpam-6763	973	27	,	,	PUNCT
ejpam-6763	973	28	for	for	ADP
ejpam-6763	973	29	r	r	NOUN
ejpam-6763	973	30	=	=	SYM
ejpam-6763	973	31	0	0	NUM
ejpam-6763	973	32	,	,	PUNCT
ejpam-6763	973	33	1	1	NUM
ejpam-6763	973	34	,	,	PUNCT
ejpam-6763	973	35	.	.	PUNCT
ejpam-6763	973	36	.	.	PUNCT
ejpam-6763	974	1	.	.	PUNCT
ejpam-6763	975	1	,	,	PUNCT
ejpam-6763	976	1	n	n	CCONJ
ejpam-6763	976	2	−	−	PROPN
ejpam-6763	976	3	1	1	NUM
ejpam-6763	976	4	.	.	PUNCT
ejpam-6763	976	5	three	three	NUM
ejpam-6763	976	6	cubic	cubic	ADJ
ejpam-6763	976	7	b	b	NOUN
ejpam-6763	976	8	-	-	PUNCT
ejpam-6763	976	9	spline	spline	NOUN
ejpam-6763	976	10	methods	method	NOUN
ejpam-6763	976	11	are	be	AUX
ejpam-6763	976	12	considered	consider	VERB
ejpam-6763	976	13	:	:	PUNCT
ejpam-6763	976	14	nfcbi	nfcbi	VERB
ejpam-6763	976	15	,	,	PUNCT
ejpam-6763	976	16	fcpcbs	fcpcbs	PROPN
ejpam-6763	976	17	,	,	PUNCT
ejpam-6763	976	18	and	and	CCONJ
ejpam-6763	976	19	ffcpcbs	ffcpcbs	X
ejpam-6763	976	20	,	,	PUNCT
ejpam-6763	976	21	for	for	ADP
ejpam-6763	976	22	example	example	NOUN
ejpam-6763	976	23	1	1	NUM
ejpam-6763	976	24	respectively	respectively	ADV
ejpam-6763	976	25	.	.	PUNCT
ejpam-6763	977	1	table	table	NOUN
ejpam-6763	977	2	2	2	NUM
ejpam-6763	977	3	:	:	PUNCT
ejpam-6763	977	4	compares	compare	VERB
ejpam-6763	977	5	the	the	DET
ejpam-6763	977	6	exact	exact	ADJ
ejpam-6763	977	7	and	and	CCONJ
ejpam-6763	977	8	approximate	approximate	ADJ
ejpam-6763	977	9	based	base	VERB
ejpam-6763	977	10	on	on	ADP
ejpam-6763	977	11	a	a	DET
ejpam-6763	977	12	least	least	ADJ
ejpam-6763	977	13	square	square	ADJ
ejpam-6763	977	14	error	error	NOUN
ejpam-6763	977	15	of	of	ADP
ejpam-6763	977	16	y0(x	y0(x	NUM
ejpam-6763	977	17	)	)	PUNCT
ejpam-6763	977	18	for	for	ADP
ejpam-6763	977	19	example	example	NOUN
ejpam-6763	977	20	1	1	NUM
ejpam-6763	977	21	x	x	NOUN
ejpam-6763	977	22	?	?	PUNCT
ejpam-6763	978	1	r	r	NOUN
ejpam-6763	978	2	exact	exact	ADJ
ejpam-6763	978	3	b{c,3	b{c,3	NOUN
ejpam-6763	978	4	}	}	PUNCT
ejpam-6763	978	5	0	0	NUM
ejpam-6763	979	1	(	(	PUNCT
ejpam-6763	979	2	x	x	NOUN
ejpam-6763	979	3	?	?	SYM
ejpam-6763	979	4	r	r	X
ejpam-6763	979	5	)	)	PUNCT
ejpam-6763	979	6	(	(	PUNCT
ejpam-6763	979	7	nfcbi	nfcbi	NOUN
ejpam-6763	979	8	)	)	PUNCT
ejpam-6763	979	9	b{c,3	b{c,3	NOUN
ejpam-6763	979	10	}	}	PUNCT
ejpam-6763	979	11	0	0	NUM
ejpam-6763	980	1	(	(	PUNCT
ejpam-6763	980	2	x	x	NOUN
ejpam-6763	980	3	?	?	SYM
ejpam-6763	980	4	r	r	X
ejpam-6763	980	5	)	)	PUNCT
ejpam-6763	980	6	(	(	PUNCT
ejpam-6763	980	7	fcpcbs	fcpcbs	NOUN
ejpam-6763	980	8	)	)	PUNCT
ejpam-6763	980	9	b{c,3	b{c,3	NOUN
ejpam-6763	980	10	}	}	PUNCT
ejpam-6763	980	11	0	0	NUM
ejpam-6763	981	1	(	(	PUNCT
ejpam-6763	981	2	x	x	NOUN
ejpam-6763	981	3	?	?	SYM
ejpam-6763	981	4	r	r	X
ejpam-6763	981	5	)	)	PUNCT
ejpam-6763	981	6	(	(	PUNCT
ejpam-6763	981	7	ffcpcbs	ffcpcbs	X
ejpam-6763	981	8	)	)	PUNCT
ejpam-6763	981	9	0	0	NUM
ejpam-6763	981	10	1.0	1.0	NUM
ejpam-6763	981	11	1.0000000000	1.0000000000	NUM
ejpam-6763	981	12	1.0000000000	1.0000000000	NUM
ejpam-6763	981	13	1.0000000000	1.0000000000	NUM
ejpam-6763	981	14	1/10	1/10	NUM
ejpam-6763	981	15	1.1	1.1	NUM
ejpam-6763	981	16	1.1000000648	1.1000000648	NUM
ejpam-6763	981	17	1.1000001689	1.1000001689	NUM
ejpam-6763	981	18	1.1000001255	1.1000001255	NUM
ejpam-6763	981	19	1/5	1/5	NUM
ejpam-6763	981	20	1.2	1.2	NUM
ejpam-6763	981	21	1.2000002525	1.2000002525	NUM
ejpam-6763	981	22	1.2000005490	1.2000005490	NUM
ejpam-6763	981	23	1.2000002019	1.2000002019	NUM
ejpam-6763	981	24	3/10	3/10	NUM
ejpam-6763	981	25	1.3	1.3	NUM
ejpam-6763	981	26	1.3000005556	1.3000005556	NUM
ejpam-6763	981	27	1.3000009508	1.3000009508	NUM
ejpam-6763	981	28	1.2999997791	1.2999997791	NUM
ejpam-6763	981	29	2/5	2/5	NUM
ejpam-6763	981	30	1.4	1.4	NUM
ejpam-6763	981	31	1.4000009692	1.4000009692	NUM
ejpam-6763	981	32	1.4000011846	1.4000011846	NUM
ejpam-6763	981	33	1.3999984073	1.3999984073	NUM
ejpam-6763	981	34	1/2	1/2	NUM
ejpam-6763	981	35	1.5	1.5	NUM
ejpam-6763	981	36	1.5000014905	1.5000014905	NUM
ejpam-6763	981	37	1.5000010607	1.5000010607	NUM
ejpam-6763	981	38	1.4999956363	1.4999956363	NUM
ejpam-6763	981	39	3/5	3/5	NUM
ejpam-6763	981	40	1.6	1.6	NUM
ejpam-6763	981	41	1.6000021183	1.6000021183	NUM
ejpam-6763	981	42	1.6000003895	1.6000003895	NUM
ejpam-6763	981	43	1.5999910161	1.5999910161	NUM
ejpam-6763	981	44	7/10	7/10	NUM
ejpam-6763	981	45	1.7	1.7	NUM
ejpam-6763	981	46	1.7000028525	1.7000028525	NUM
ejpam-6763	981	47	1.6999989813	1.6999989813	NUM
ejpam-6763	981	48	1.6999840968	1.6999840968	NUM
ejpam-6763	981	49	4/5	4/5	NUM
ejpam-6763	981	50	1.8	1.8	NUM
ejpam-6763	981	51	1.8000036938	1.8000036938	NUM
ejpam-6763	981	52	1.7999966465	1.7999966465	NUM
ejpam-6763	981	53	1.7999744282	1.7999744282	NUM
ejpam-6763	981	54	9/10	9/10	NUM
ejpam-6763	981	55	1.9	1.9	NUM
ejpam-6763	981	56	1.9000046433	1.9000046433	NUM
ejpam-6763	981	57	1.8999931954	1.8999931954	NUM
ejpam-6763	981	58	1.8999615604	1.8999615604	NUM
ejpam-6763	981	59	1.0	1.0	NUM
ejpam-6763	981	60	2.0	2.0	NUM
ejpam-6763	981	61	2.0000057023	2.0000057023	NUM
ejpam-6763	981	62	1.9999884384	1.9999884384	NUM
ejpam-6763	981	63	1.9999450433	1.9999450433	NUM
ejpam-6763	981	64	l.s.e	l.s.e	NOUN
ejpam-6763	981	65	8.3881×	8.3881×	NUM
ejpam-6763	981	66	10−11	10−11	NUM
ejpam-6763	981	67	1.9617×	1.9617×	NUM
ejpam-6763	981	68	10−10	10−10	NUM
ejpam-6763	981	69	5.5071×	5.5071×	NUM
ejpam-6763	981	70	10−9	10−9	NUM
ejpam-6763	981	71	runtime	runtime	NOUN
ejpam-6763	981	72	(	(	PUNCT
ejpam-6763	981	73	sec	sec	PROPN
ejpam-6763	981	74	)	)	PUNCT
ejpam-6763	981	75	2.7607	2.7607	NUM
ejpam-6763	981	76	2.3051	2.3051	NUM
ejpam-6763	981	77	2.2901	2.2901	NUM
ejpam-6763	981	78	d.	d.	PROPN
ejpam-6763	981	79	kh	kh	PROPN
ejpam-6763	981	80	.	.	PUNCT
ejpam-6763	982	1	abdullah	abdullah	PROPN
ejpam-6763	982	2	,	,	PUNCT
ejpam-6763	982	3	sh	sh	PROPN
ejpam-6763	982	4	.	.	PROPN
ejpam-6763	982	5	sh	sh	PROPN
ejpam-6763	982	6	.	.	PROPN
ejpam-6763	982	7	ahmed	ahmed	PROPN
ejpam-6763	982	8	,	,	PUNCT
ejpam-6763	982	9	k.	k.	PROPN
ejpam-6763	982	10	h.	h.	PROPN
ejpam-6763	982	11	f.	f.	PROPN
ejpam-6763	982	12	jwamer	jwamer	PROPN
ejpam-6763	982	13	/	/	SYM
ejpam-6763	982	14	eur	eur	PROPN
ejpam-6763	982	15	.	.	PUNCT
ejpam-6763	983	1	j.	j.	PROPN
ejpam-6763	983	2	pure	pure	PROPN
ejpam-6763	983	3	appl	appl	PROPN
ejpam-6763	983	4	.	.	PROPN
ejpam-6763	983	5	math	math	PROPN
ejpam-6763	983	6	,	,	PUNCT
ejpam-6763	983	7	18	18	NUM
ejpam-6763	983	8	(	(	PUNCT
ejpam-6763	983	9	4	4	NUM
ejpam-6763	983	10	)	)	PUNCT
ejpam-6763	983	11	(	(	PUNCT
ejpam-6763	983	12	2025	2025	NUM
ejpam-6763	983	13	)	)	PUNCT
ejpam-6763	983	14	,	,	PUNCT
ejpam-6763	983	15	6763	6763	NUM
ejpam-6763	983	16	26	26	NUM
ejpam-6763	983	17	of	of	ADP
ejpam-6763	983	18	40	40	NUM
ejpam-6763	983	19	table	table	NOUN
ejpam-6763	983	20	3	3	NUM
ejpam-6763	983	21	:	:	PUNCT
ejpam-6763	983	22	compares	compare	VERB
ejpam-6763	983	23	the	the	DET
ejpam-6763	983	24	exact	exact	ADJ
ejpam-6763	983	25	and	and	CCONJ
ejpam-6763	983	26	approximate	approximate	ADJ
ejpam-6763	983	27	based	base	VERB
ejpam-6763	983	28	on	on	ADP
ejpam-6763	983	29	a	a	DET
ejpam-6763	983	30	least	least	ADJ
ejpam-6763	983	31	square	square	ADJ
ejpam-6763	983	32	error	error	NOUN
ejpam-6763	983	33	of	of	ADP
ejpam-6763	983	34	y1(x	y1(x	NOUN
ejpam-6763	983	35	)	)	PUNCT
ejpam-6763	983	36	for	for	ADP
ejpam-6763	983	37	example	example	NOUN
ejpam-6763	983	38	1	1	NUM
ejpam-6763	983	39	x	x	NOUN
ejpam-6763	983	40	?	?	PUNCT
ejpam-6763	984	1	r	r	NOUN
ejpam-6763	984	2	exact	exact	ADJ
ejpam-6763	984	3	b{c,3	b{c,3	NOUN
ejpam-6763	984	4	}	}	PUNCT
ejpam-6763	984	5	1	1	NUM
ejpam-6763	984	6	(	(	PUNCT
ejpam-6763	984	7	x	x	NOUN
ejpam-6763	984	8	?	?	SYM
ejpam-6763	985	1	r	r	X
ejpam-6763	985	2	)	)	PUNCT
ejpam-6763	985	3	(	(	PUNCT
ejpam-6763	985	4	nfcbi	nfcbi	NOUN
ejpam-6763	985	5	)	)	PUNCT
ejpam-6763	985	6	b{c,3	b{c,3	NOUN
ejpam-6763	985	7	}	}	PUNCT
ejpam-6763	985	8	1	1	NUM
ejpam-6763	985	9	(	(	PUNCT
ejpam-6763	985	10	x	x	NOUN
ejpam-6763	985	11	?	?	SYM
ejpam-6763	986	1	r	r	X
ejpam-6763	986	2	)	)	PUNCT
ejpam-6763	986	3	(	(	PUNCT
ejpam-6763	986	4	fcpcbs	fcpcbs	NOUN
ejpam-6763	986	5	)	)	PUNCT
ejpam-6763	986	6	b{c,3	b{c,3	NOUN
ejpam-6763	986	7	}	}	PUNCT
ejpam-6763	986	8	1	1	NUM
ejpam-6763	986	9	(	(	PUNCT
ejpam-6763	986	10	x	x	NOUN
ejpam-6763	986	11	?	?	SYM
ejpam-6763	987	1	r	r	X
ejpam-6763	987	2	)	)	PUNCT
ejpam-6763	987	3	(	(	PUNCT
ejpam-6763	987	4	ffcpcbs	ffcpcbs	X
ejpam-6763	987	5	)	)	PUNCT
ejpam-6763	987	6	0	0	NUM
ejpam-6763	987	7	1.0	1.0	NUM
ejpam-6763	987	8	1.000000000000	1.000000000000	NUM
ejpam-6763	987	9	1.000000000000	1.000000000000	NUM
ejpam-6763	987	10	1.000000000000	1.000000000000	NUM
ejpam-6763	987	11	1/10	1/10	NUM
ejpam-6763	987	12	0.8	0.8	NUM
ejpam-6763	987	13	0.800000000058	0.800000000058	NUM
ejpam-6763	987	14	0.800000000058	0.800000000058	NUM
ejpam-6763	987	15	0.800000000113	0.800000000113	NUM
ejpam-6763	987	16	1/5	1/5	NUM
ejpam-6763	987	17	0.6	0.6	NUM
ejpam-6763	987	18	0.600000000222	0.600000000222	NUM
ejpam-6763	987	19	0.599999999743	0.599999999743	NUM
ejpam-6763	987	20	0.600000000181	0.600000000181	NUM
ejpam-6763	987	21	3/10	3/10	NUM
ejpam-6763	987	22	0.4	0.4	NUM
ejpam-6763	987	23	0.400000000475	0.400000000475	NUM
ejpam-6763	987	24	0.399999998322	0.399999998322	NUM
ejpam-6763	987	25	0.399999999888	0.399999999888	NUM
ejpam-6763	987	26	2/5	2/5	NUM
ejpam-6763	987	27	0.2	0.2	NUM
ejpam-6763	987	28	0.200000000796	0.200000000796	NUM
ejpam-6763	987	29	0.199999995056	0.199999995056	NUM
ejpam-6763	987	30	0.199999998564	0.199999998564	NUM
ejpam-6763	987	31	1/2	1/2	NUM
ejpam-6763	987	32	0.0	0.0	NUM
ejpam-6763	987	33	1.16518×	1.16518×	NUM
ejpam-6763	987	34	10−9	10−9	NUM
ejpam-6763	987	35	−1.0782×	−1.0782×	NOUN
ejpam-6763	987	36	10−8	10−8	NUM
ejpam-6763	987	37	−3.931×	−3.931×	NUM
ejpam-6763	987	38	10−9	10−9	NUM
ejpam-6763	987	39	3/5	3/5	NUM
ejpam-6763	987	40	-0.2	-0.2	PROPN
ejpam-6763	987	41	-0.199999998438	-0.199999998438	NOUN
ejpam-6763	987	42	-0.200000019929	-0.200000019929	NOUN
ejpam-6763	987	43	-0.200000008090	-0.200000008090	VERB
ejpam-6763	987	44	7/10	7/10	NUM
ejpam-6763	987	45	-0.4	-0.4	NUM
ejpam-6763	987	46	-0.399999998025	-0.399999998025	NOUN
ejpam-6763	987	47	-0.400000033119	-0.400000033119	NOUN
ejpam-6763	987	48	-0.400000014319	-0.400000014319	PUNCT
ejpam-6763	988	1	4/5	4/5	NUM
ejpam-6763	988	2	-0.6	-0.6	X
ejpam-6763	988	3	-0.599999997604	-0.599999997604	NOUN
ejpam-6763	988	4	-0.600000051085	-0.600000051085	NOUN
ejpam-6763	988	5	-0.600000023023	-0.600000023023	PROPN
ejpam-6763	989	1	9/10	9/10	NUM
ejpam-6763	989	2	-0.8	-0.8	PROPN
ejpam-6763	989	3	-0.799999997174	-0.799999997174	NOUN
ejpam-6763	989	4	-0.800000074561	-0.800000074561	NOUN
ejpam-6763	989	5	-0.800000034606	-0.800000034606	VERB
ejpam-6763	989	6	1.0	1.0	NUM
ejpam-6763	989	7	-1.0	-1.0	PROPN
ejpam-6763	989	8	-0.999999996730	-0.999999996730	NOUN
ejpam-6763	989	9	-1.000000104288	-1.000000104288	PUNCT
ejpam-6763	989	10	-1.000000049477	-1.000000049477	PUNCT
ejpam-6763	990	1	l.s.e	l.s.e	NOUN
ejpam-6763	990	2	3.3029×	3.3029×	NUM
ejpam-6763	990	3	10−17	10−17	NUM
ejpam-6763	990	4	2.0681×	2.0681×	NUM
ejpam-6763	990	5	10−14	10−14	NUM
ejpam-6763	990	6	4.4633×	4.4633×	NUM
ejpam-6763	990	7	10−15	10−15	PROPN
ejpam-6763	990	8	runtime	runtime	NOUN
ejpam-6763	990	9	(	(	PUNCT
ejpam-6763	990	10	sec	sec	PROPN
ejpam-6763	990	11	)	)	PUNCT
ejpam-6763	990	12	2.7607	2.7607	NUM
ejpam-6763	990	13	2.3051	2.3051	NUM
ejpam-6763	990	14	2.2901	2.2901	NUM
ejpam-6763	990	15	table	table	NOUN
ejpam-6763	990	16	4	4	NUM
ejpam-6763	990	17	:	:	PUNCT
ejpam-6763	990	18	compares	compare	VERB
ejpam-6763	990	19	the	the	DET
ejpam-6763	990	20	exact	exact	ADJ
ejpam-6763	990	21	and	and	CCONJ
ejpam-6763	990	22	approximate	approximate	ADJ
ejpam-6763	990	23	based	base	VERB
ejpam-6763	990	24	on	on	ADP
ejpam-6763	990	25	a	a	DET
ejpam-6763	990	26	least	least	ADJ
ejpam-6763	990	27	square	square	ADJ
ejpam-6763	990	28	error	error	NOUN
ejpam-6763	990	29	of	of	ADP
ejpam-6763	990	30	y2(x	y2(x	PROPN
ejpam-6763	990	31	)	)	PUNCT
ejpam-6763	990	32	for	for	ADP
ejpam-6763	990	33	example	example	NOUN
ejpam-6763	990	34	1	1	NUM
ejpam-6763	990	35	x	x	NOUN
ejpam-6763	990	36	?	?	PUNCT
ejpam-6763	991	1	r	r	NOUN
ejpam-6763	991	2	exact	exact	ADJ
ejpam-6763	991	3	b{c,3	b{c,3	NOUN
ejpam-6763	991	4	}	}	PUNCT
ejpam-6763	991	5	2	2	NUM
ejpam-6763	991	6	(	(	PUNCT
ejpam-6763	991	7	x	x	NOUN
ejpam-6763	991	8	?	?	SYM
ejpam-6763	992	1	r	r	X
ejpam-6763	992	2	)	)	PUNCT
ejpam-6763	992	3	(	(	PUNCT
ejpam-6763	992	4	nfcbi	nfcbi	NOUN
ejpam-6763	992	5	)	)	PUNCT
ejpam-6763	992	6	b{c,3	b{c,3	NOUN
ejpam-6763	992	7	}	}	PUNCT
ejpam-6763	992	8	2	2	NUM
ejpam-6763	992	9	(	(	PUNCT
ejpam-6763	992	10	x	x	NOUN
ejpam-6763	992	11	?	?	SYM
ejpam-6763	993	1	r	r	X
ejpam-6763	993	2	)	)	PUNCT
ejpam-6763	993	3	(	(	PUNCT
ejpam-6763	993	4	fcpcbs	fcpcbs	NOUN
ejpam-6763	993	5	)	)	PUNCT
ejpam-6763	993	6	b{c,3	b{c,3	NOUN
ejpam-6763	993	7	}	}	PUNCT
ejpam-6763	993	8	2	2	NUM
ejpam-6763	993	9	(	(	PUNCT
ejpam-6763	993	10	x	x	NOUN
ejpam-6763	993	11	?	?	SYM
ejpam-6763	994	1	r	r	X
ejpam-6763	994	2	)	)	PUNCT
ejpam-6763	994	3	(	(	PUNCT
ejpam-6763	994	4	ffcpcbs	ffcpcbs	X
ejpam-6763	994	5	)	)	PUNCT
ejpam-6763	994	6	0	0	PUNCT
ejpam-6763	995	1	-1.0	-1.0	PROPN
ejpam-6763	995	2	-1.000000000000	-1.000000000000	PROPN
ejpam-6763	995	3	-1.000000000000	-1.000000000000	PUNCT
ejpam-6763	996	1	-1.000000000000	-1.000000000000	PUNCT
ejpam-6763	997	1	1/10	1/10	NUM
ejpam-6763	997	2	-0.7	-0.7	PROPN
ejpam-6763	997	3	-0.700000000003	-0.700000000003	NOUN
ejpam-6763	997	4	-0.700000000003	-0.700000000003	NOUN
ejpam-6763	997	5	-0.700000000004	-0.700000000004	VERB
ejpam-6763	997	6	1/5	1/5	NUM
ejpam-6763	997	7	-0.4	-0.4	NUM
ejpam-6763	997	8	-0.400000000012	-0.400000000012	NOUN
ejpam-6763	997	9	-0.399999999986	-0.399999999986	PROPN
ejpam-6763	997	10	-0.399999999996	-0.399999999996	PUNCT
ejpam-6763	997	11	3/10	3/10	NUM
ejpam-6763	997	12	-0.1	-0.1	PROPN
ejpam-6763	997	13	-0.100000000026	-0.100000000026	NOUN
ejpam-6763	997	14	-0.099999999911	-0.099999999911	NOUN
ejpam-6763	997	15	-0.099999999945	-0.099999999945	NOUN
ejpam-6763	998	1	2/5	2/5	NUM
ejpam-6763	998	2	0.2	0.2	NUM
ejpam-6763	998	3	0.199999999956	0.199999999956	NUM
ejpam-6763	998	4	0.200000000265	0.200000000265	NUM
ejpam-6763	998	5	0.200000000182	0.200000000182	NUM
ejpam-6763	998	6	1/2	1/2	NUM
ejpam-6763	998	7	0.5	0.5	NUM
ejpam-6763	998	8	0.499999999931	0.499999999931	NUM
ejpam-6763	998	9	0.500000000576	0.500000000576	NUM
ejpam-6763	998	10	0.500000000415	0.500000000415	NUM
ejpam-6763	998	11	3/5	3/5	NUM
ejpam-6763	998	12	0.8	0.8	NUM
ejpam-6763	998	13	0.799999999903	0.799999999903	NUM
ejpam-6763	998	14	0.800000001064	0.800000001064	NUM
ejpam-6763	998	15	0.800000000786	0.800000000786	NUM
ejpam-6763	998	16	7/10	7/10	NUM
ejpam-6763	998	17	1.1	1.1	NUM
ejpam-6763	998	18	1.099999999878	1.099999999878	NUM
ejpam-6763	998	19	1.100000001777	1.100000001777	NUM
ejpam-6763	998	20	1.100000001333	1.100000001333	NUM
ejpam-6763	998	21	4/5	4/5	NUM
ejpam-6763	998	22	1.4	1.4	NUM
ejpam-6763	998	23	1.399999999844	1.399999999844	NUM
ejpam-6763	998	24	1.400000002733	1.400000002733	NUM
ejpam-6763	998	25	1.400000002077	1.400000002077	NUM
ejpam-6763	998	26	9/10	9/10	NUM
ejpam-6763	998	27	1.7	1.7	NUM
ejpam-6763	998	28	1.699999999889	1.699999999889	NUM
ejpam-6763	998	29	1.700000003988	1.700000003988	NUM
ejpam-6763	998	30	1.700000003044	1.700000003044	NUM
ejpam-6763	998	31	1.0	1.0	NUM
ejpam-6763	998	32	2.0	2.0	NUM
ejpam-6763	998	33	1.999999999756	1.999999999756	NUM
ejpam-6763	998	34	2.000000005566	2.000000005566	NUM
ejpam-6763	998	35	2.000000004277	2.000000004277	NUM
ejpam-6763	998	36	l.s.e	l.s.e	NOUN
ejpam-6763	998	37	1.6268×	1.6268×	NUM
ejpam-6763	998	38	10−19	10−19	NUM
ejpam-6763	998	39	5.8856×	5.8856×	NUM
ejpam-6763	998	40	10−17	10−17	NUM
ejpam-6763	998	41	3.4339×	3.4339×	NUM
ejpam-6763	998	42	10−17	10−17	NUM
ejpam-6763	998	43	runtime	runtime	NOUN
ejpam-6763	998	44	(	(	PUNCT
ejpam-6763	998	45	sec	sec	PROPN
ejpam-6763	998	46	)	)	PUNCT
ejpam-6763	998	47	2.7607	2.7607	NUM
ejpam-6763	998	48	2.3051	2.3051	NUM
ejpam-6763	998	49	2.2901	2.2901	NUM
ejpam-6763	998	50	table	table	NOUN
ejpam-6763	998	51	5	5	NUM
ejpam-6763	998	52	:	:	PUNCT
ejpam-6763	998	53	least	least	ADJ
ejpam-6763	998	54	square	square	ADJ
ejpam-6763	998	55	error	error	NOUN
ejpam-6763	998	56	for	for	ADP
ejpam-6763	998	57	b{c,3	b{c,3	NOUN
ejpam-6763	998	58	}	}	PUNCT
ejpam-6763	998	59	0	0	NUM
ejpam-6763	998	60	(	(	PUNCT
ejpam-6763	998	61	x	x	NOUN
ejpam-6763	998	62	?	?	NUM
ejpam-6763	998	63	)	)	PUNCT
ejpam-6763	998	64	,	,	PUNCT
ejpam-6763	998	65	b{c,3	b{c,3	NOUN
ejpam-6763	998	66	}	}	PUNCT
ejpam-6763	998	67	1	1	NUM
ejpam-6763	998	68	(	(	PUNCT
ejpam-6763	998	69	x	x	NOUN
ejpam-6763	998	70	?	?	PUNCT
ejpam-6763	998	71	)	)	PUNCT
ejpam-6763	998	72	,	,	PUNCT
ejpam-6763	998	73	and	and	CCONJ
ejpam-6763	998	74	b{c,3	b{c,3	NOUN
ejpam-6763	998	75	}	}	PUNCT
ejpam-6763	998	76	2	2	NUM
ejpam-6763	998	77	(	(	PUNCT
ejpam-6763	998	78	x	x	NOUN
ejpam-6763	998	79	?	?	PUNCT
ejpam-6763	998	80	)	)	PUNCT
ejpam-6763	998	81	in	in	ADP
ejpam-6763	998	82	example	example	NOUN
ejpam-6763	998	83	1	1	NUM
ejpam-6763	998	84	using	use	VERB
ejpam-6763	998	85	different	different	ADJ
ejpam-6763	998	86	step	step	NOUN
ejpam-6763	998	87	sizes	size	NOUN
ejpam-6763	998	88	.	.	PUNCT
ejpam-6763	999	1	method	method	NOUN
ejpam-6763	999	2	step	step	NOUN
ejpam-6763	999	3	size	size	NOUN
ejpam-6763	999	4	h	h	NOUN
ejpam-6763	999	5	l.s.e	l.s.e	NOUN
ejpam-6763	999	6	.	.	PUNCT
ejpam-6763	1000	1	b{c,3	b{c,3	NOUN
ejpam-6763	1000	2	}	}	PUNCT
ejpam-6763	1000	3	0	0	NUM
ejpam-6763	1001	1	(	(	PUNCT
ejpam-6763	1001	2	x	x	NOUN
ejpam-6763	1001	3	?	?	PUNCT
ejpam-6763	1001	4	)	)	PUNCT
ejpam-6763	1001	5	l.s.e	l.s.e	NOUN
ejpam-6763	1001	6	.	.	PUNCT
ejpam-6763	1002	1	b{c,3	b{c,3	NOUN
ejpam-6763	1002	2	}	}	PUNCT
ejpam-6763	1002	3	1	1	NUM
ejpam-6763	1002	4	(	(	PUNCT
ejpam-6763	1002	5	x	x	NOUN
ejpam-6763	1002	6	?	?	PUNCT
ejpam-6763	1002	7	)	)	PUNCT
ejpam-6763	1002	8	l.s.e	l.s.e	NOUN
ejpam-6763	1002	9	.	.	PUNCT
ejpam-6763	1003	1	b{c,3	b{c,3	NOUN
ejpam-6763	1003	2	}	}	PUNCT
ejpam-6763	1003	3	2	2	NUM
ejpam-6763	1003	4	(	(	PUNCT
ejpam-6763	1003	5	x	x	NOUN
ejpam-6763	1003	6	?	?	PUNCT
ejpam-6763	1003	7	)	)	PUNCT
ejpam-6763	1003	8	nfcbi	nfcbi	VERB
ejpam-6763	1003	9	1/20	1/20	NUM
ejpam-6763	1003	10	8.3882×	8.3882×	NOUN
ejpam-6763	1003	11	10−13	10−13	NUM
ejpam-6763	1003	12	3.3029×	3.3029×	NUM
ejpam-6763	1003	13	10−19	10−19	ADJ
ejpam-6763	1003	14	1.6271×	1.6271×	NUM
ejpam-6763	1003	15	10−21	10−21	NUM
ejpam-6763	1003	16	1/50	1/50	NUM
ejpam-6763	1003	17	8.3882×	8.3882×	NOUN
ejpam-6763	1003	18	10−15	10−15	NUM
ejpam-6763	1003	19	3.3028×	3.3028×	NUM
ejpam-6763	1003	20	10−21	10−21	NUM
ejpam-6763	1003	21	1.6305×	1.6305×	NUM
ejpam-6763	1003	22	10−23	10−23	NUM
ejpam-6763	1003	23	continued	continue	VERB
ejpam-6763	1003	24	on	on	ADP
ejpam-6763	1003	25	next	next	ADJ
ejpam-6763	1003	26	page	page	NOUN
ejpam-6763	1003	27	d.	d.	PROPN
ejpam-6763	1003	28	kh	kh	PROPN
ejpam-6763	1003	29	.	.	PUNCT
ejpam-6763	1004	1	abdullah	abdullah	PROPN
ejpam-6763	1004	2	,	,	PUNCT
ejpam-6763	1004	3	sh	sh	PROPN
ejpam-6763	1004	4	.	.	PROPN
ejpam-6763	1004	5	sh	sh	PROPN
ejpam-6763	1004	6	.	.	PROPN
ejpam-6763	1004	7	ahmed	ahmed	PROPN
ejpam-6763	1004	8	,	,	PUNCT
ejpam-6763	1004	9	k.	k.	PROPN
ejpam-6763	1004	10	h.	h.	PROPN
ejpam-6763	1004	11	f.	f.	PROPN
ejpam-6763	1004	12	jwamer	jwamer	PROPN
ejpam-6763	1004	13	/	/	SYM
ejpam-6763	1004	14	eur	eur	PROPN
ejpam-6763	1004	15	.	.	PUNCT
ejpam-6763	1005	1	j.	j.	PROPN
ejpam-6763	1005	2	pure	pure	PROPN
ejpam-6763	1005	3	appl	appl	PROPN
ejpam-6763	1005	4	.	.	PROPN
ejpam-6763	1005	5	math	math	PROPN
ejpam-6763	1005	6	,	,	PUNCT
ejpam-6763	1005	7	18	18	NUM
ejpam-6763	1005	8	(	(	PUNCT
ejpam-6763	1005	9	4	4	NUM
ejpam-6763	1005	10	)	)	PUNCT
ejpam-6763	1005	11	(	(	PUNCT
ejpam-6763	1005	12	2025	2025	NUM
ejpam-6763	1005	13	)	)	PUNCT
ejpam-6763	1005	14	,	,	PUNCT
ejpam-6763	1005	15	6763	6763	NUM
ejpam-6763	1005	16	27	27	NUM
ejpam-6763	1005	17	of	of	ADP
ejpam-6763	1005	18	40	40	NUM
ejpam-6763	1005	19	method	method	NOUN
ejpam-6763	1005	20	step	step	NOUN
ejpam-6763	1005	21	size	size	NOUN
ejpam-6763	1005	22	h	h	NOUN
ejpam-6763	1005	23	l.s.e	l.s.e	NOUN
ejpam-6763	1005	24	.	.	PUNCT
ejpam-6763	1006	1	b{c,3	b{c,3	NOUN
ejpam-6763	1006	2	}	}	PUNCT
ejpam-6763	1006	3	0	0	NUM
ejpam-6763	1007	1	(	(	PUNCT
ejpam-6763	1007	2	x	x	NOUN
ejpam-6763	1007	3	?	?	PUNCT
ejpam-6763	1007	4	)	)	PUNCT
ejpam-6763	1007	5	l.s.e	l.s.e	NOUN
ejpam-6763	1007	6	.	.	PUNCT
ejpam-6763	1008	1	b{c,3	b{c,3	NOUN
ejpam-6763	1008	2	}	}	PUNCT
ejpam-6763	1008	3	1	1	NUM
ejpam-6763	1008	4	(	(	PUNCT
ejpam-6763	1008	5	x	x	NOUN
ejpam-6763	1008	6	?	?	PUNCT
ejpam-6763	1008	7	)	)	PUNCT
ejpam-6763	1008	8	l.s.e	l.s.e	NOUN
ejpam-6763	1008	9	.	.	PUNCT
ejpam-6763	1009	1	b{c,3	b{c,3	NOUN
ejpam-6763	1009	2	}	}	PUNCT
ejpam-6763	1009	3	2	2	NUM
ejpam-6763	1009	4	(	(	PUNCT
ejpam-6763	1009	5	x	x	NOUN
ejpam-6763	1009	6	?	?	PUNCT
ejpam-6763	1009	7	)	)	PUNCT
ejpam-6763	1010	1	1/100	1/100	NUM
ejpam-6763	1010	2	2.0676×	2.0676×	NUM
ejpam-6763	1010	3	10−15	10−15	NUM
ejpam-6763	1010	4	3.3021×	3.3021×	NUM
ejpam-6763	1010	5	10−22	10−22	NOUN
ejpam-6763	1010	6	1.6875×	1.6875×	NOUN
ejpam-6763	1010	7	10−25	10−25	NOUN
ejpam-6763	1010	8	1/1000	1/1000	NUM
ejpam-6763	1010	9	2.0677×	2.0677×	NOUN
ejpam-6763	1010	10	10−19	10−19	NOUN
ejpam-6763	1010	11	3.2342×	3.2342×	NUM
ejpam-6763	1010	12	10−27	10−27	NUM
ejpam-6763	1010	13	1.4463×	1.4463×	NUM
ejpam-6763	1010	14	10−28	10−28	NUM
ejpam-6763	1010	15	fcpcbs	fcpcbs	NOUN
ejpam-6763	1010	16	1/20	1/20	NUM
ejpam-6763	1010	17	1.0386×	1.0386×	NUM
ejpam-6763	1010	18	10−9	10−9	NUM
ejpam-6763	1010	19	8.4106×	8.4106×	NOUN
ejpam-6763	1010	20	10−16	10−16	PROPN
ejpam-6763	1010	21	2.4058×	2.4058×	NUM
ejpam-6763	1010	22	10−18	10−18	NUM
ejpam-6763	1010	23	1/50	1/50	NUM
ejpam-6763	1010	24	6.2009×	6.2009×	NUM
ejpam-6763	1010	25	10−11	10−11	NUM
ejpam-6763	1010	26	5.0151×	5.0151×	NUM
ejpam-6763	1010	27	10−17	10−17	NUM
ejpam-6763	1010	28	1.4232×	1.4232×	NUM
ejpam-6763	1010	29	10−19	10−19	NUM
ejpam-6763	1010	30	1/100	1/100	NUM
ejpam-6763	1010	31	1.8338×	1.8338×	NUM
ejpam-6763	1010	32	10−11	10−11	NUM
ejpam-6763	1010	33	2.3886×	2.3886×	NUM
ejpam-6763	1010	34	10−17	10−17	NUM
ejpam-6763	1010	35	6.6535×	6.6535×	NOUN
ejpam-6763	1010	36	10−20	10−20	PROPN
ejpam-6763	1010	37	1/1000	1/1000	NUM
ejpam-6763	1010	38	4.5237×	4.5237×	NOUN
ejpam-6763	1010	39	10−11	10−11	NUM
ejpam-6763	1010	40	3.0396×	3.0396×	NUM
ejpam-6763	1010	41	10−17	10−17	NUM
ejpam-6763	1010	42	1.0171×	1.0171×	NUM
ejpam-6763	1010	43	10−20	10−20	NOUN
ejpam-6763	1010	44	ffcpcbs	ffcpcbs	NOUN
ejpam-6763	1010	45	1/20	1/20	NUM
ejpam-6763	1010	46	2.1963×	2.1963×	NUM
ejpam-6763	1010	47	10−10	10−10	NUM
ejpam-6763	1010	48	1.4663×	1.4663×	NUM
ejpam-6763	1011	1	10−16	10−16	PROPN
ejpam-6763	1011	2	8.7157×	8.7157×	NUM
ejpam-6763	1011	3	10−18	10−18	NUM
ejpam-6763	1011	4	1/50	1/50	NUM
ejpam-6763	1011	5	3.3795×	3.3795×	NUM
ejpam-6763	1011	6	10−11	10−11	NUM
ejpam-6763	1011	7	3.5882×	3.5882×	NUM
ejpam-6763	1011	8	10−17	10−17	NUM
ejpam-6763	1011	9	4.7505×	4.7505×	NUM
ejpam-6763	1011	10	10−18	10−18	NUM
ejpam-6763	1011	11	1/100	1/100	NUM
ejpam-6763	1011	12	4.0923×	4.0923×	NUM
ejpam-6763	1011	13	10−11	10−11	NOUN
ejpam-6763	1011	14	4.1016×	4.1016×	NUM
ejpam-6763	1012	1	10−17	10−17	NUM
ejpam-6763	1012	2	4.6055×	4.6055×	NUM
ejpam-6763	1012	3	10−18	10−18	NOUN
ejpam-6763	1012	4	1/1000	1/1000	NUM
ejpam-6763	1012	5	3.8287×	3.8287×	NUM
ejpam-6763	1012	6	10−11	10−11	NOUN
ejpam-6763	1012	7	4.1630×	4.1630×	NUM
ejpam-6763	1013	1	10−17	10−17	NUM
ejpam-6763	1013	2	4.5875×	4.5875×	NUM
ejpam-6763	1013	3	10−18	10−18	NOUN
ejpam-6763	1013	4	the	the	DET
ejpam-6763	1013	5	plots	plot	NOUN
ejpam-6763	1013	6	of	of	ADP
ejpam-6763	1013	7	the	the	DET
ejpam-6763	1013	8	approximate	approximate	ADJ
ejpam-6763	1013	9	solutions	solution	NOUN
ejpam-6763	1013	10	obtained	obtain	VERB
ejpam-6763	1013	11	by	by	ADP
ejpam-6763	1013	12	the	the	DET
ejpam-6763	1013	13	nfcbi	nfcbi	NOUN
ejpam-6763	1013	14	,	,	PUNCT
ejpam-6763	1013	15	fcpcbs	fcpcbs	PROPN
ejpam-6763	1013	16	,	,	PUNCT
ejpam-6763	1013	17	and	and	CCONJ
ejpam-6763	1013	18	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1013	19	methods	method	NOUN
ejpam-6763	1013	20	for	for	ADP
ejpam-6763	1013	21	y0(x	y0(x	NOUN
ejpam-6763	1013	22	)	)	PUNCT
ejpam-6763	1013	23	,	,	PUNCT
ejpam-6763	1013	24	y1(x	y1(x	NOUN
ejpam-6763	1013	25	)	)	PUNCT
ejpam-6763	1013	26	,	,	PUNCT
ejpam-6763	1013	27	and	and	CCONJ
ejpam-6763	1013	28	y2(x	y2(x	NOUN
ejpam-6763	1013	29	)	)	PUNCT
ejpam-6763	1013	30	are	be	AUX
ejpam-6763	1013	31	illustrated	illustrate	VERB
ejpam-6763	1013	32	in	in	ADP
ejpam-6763	1013	33	figures	figure	NOUN
ejpam-6763	1013	34	1	1	NUM
ejpam-6763	1013	35	,	,	PUNCT
ejpam-6763	1013	36	3	3	NUM
ejpam-6763	1013	37	,	,	PUNCT
ejpam-6763	1013	38	and	and	CCONJ
ejpam-6763	1013	39	5	5	NUM
ejpam-6763	1013	40	,	,	PUNCT
ejpam-6763	1013	41	respectively	respectively	ADV
ejpam-6763	1013	42	,	,	PUNCT
ejpam-6763	1013	43	along	along	ADP
ejpam-6763	1013	44	with	with	ADP
ejpam-6763	1013	45	the	the	DET
ejpam-6763	1013	46	corresponding	corresponding	ADJ
ejpam-6763	1013	47	exact	exact	ADJ
ejpam-6763	1013	48	solutions	solution	NOUN
ejpam-6763	1013	49	.	.	PUNCT
ejpam-6763	1014	1	the	the	DET
ejpam-6763	1014	2	least	least	ADJ
ejpam-6763	1014	3	square	square	ADJ
ejpam-6763	1014	4	errors	error	NOUN
ejpam-6763	1014	5	for	for	ADP
ejpam-6763	1014	6	each	each	DET
ejpam-6763	1014	7	iteration	iteration	NOUN
ejpam-6763	1014	8	are	be	AUX
ejpam-6763	1014	9	presented	present	VERB
ejpam-6763	1014	10	in	in	ADP
ejpam-6763	1014	11	figures	figure	NOUN
ejpam-6763	1014	12	2	2	NUM
ejpam-6763	1014	13	,	,	PUNCT
ejpam-6763	1014	14	4	4	NUM
ejpam-6763	1014	15	,	,	PUNCT
ejpam-6763	1014	16	and	and	CCONJ
ejpam-6763	1014	17	6	6	NUM
ejpam-6763	1014	18	.	.	PUNCT
ejpam-6763	1015	1	these	these	DET
ejpam-6763	1015	2	results	result	NOUN
ejpam-6763	1015	3	are	be	AUX
ejpam-6763	1015	4	based	base	VERB
ejpam-6763	1015	5	on	on	ADP
ejpam-6763	1015	6	example	example	NOUN
ejpam-6763	1015	7	1	1	NUM
ejpam-6763	1015	8	using	use	VERB
ejpam-6763	1015	9	n	n	NOUN
ejpam-6763	1015	10	=	=	SYM
ejpam-6763	1015	11	10	10	NUM
ejpam-6763	1015	12	and	and	CCONJ
ejpam-6763	1015	13	h	h	NOUN
ejpam-6763	1015	14	=	=	NOUN
ejpam-6763	1015	15	0.1	0.1	NUM
ejpam-6763	1015	16	.	.	PUNCT
ejpam-6763	1016	1	figure	figure	NOUN
ejpam-6763	1016	2	1	1	NUM
ejpam-6763	1016	3	:	:	PUNCT
ejpam-6763	1016	4	approximate	approximate	ADJ
ejpam-6763	1016	5	solution	solution	NOUN
ejpam-6763	1016	6	using	use	VERB
ejpam-6763	1016	7	nfcbi	nfcbi	NOUN
ejpam-6763	1016	8	for	for	ADP
ejpam-6763	1016	9	example	example	NOUN
ejpam-6763	1016	10	1	1	NUM
ejpam-6763	1016	11	.	.	PUNCT
ejpam-6763	1016	12	figure	figure	NOUN
ejpam-6763	1016	13	2	2	NUM
ejpam-6763	1016	14	:	:	PUNCT
ejpam-6763	1016	15	least	least	ADJ
ejpam-6763	1016	16	square	square	ADJ
ejpam-6763	1016	17	error	error	NOUN
ejpam-6763	1016	18	plot	plot	NOUN
ejpam-6763	1016	19	using	use	VERB
ejpam-6763	1016	20	nfcbi	nfcbi	NOUN
ejpam-6763	1016	21	for	for	ADP
ejpam-6763	1016	22	example	example	NOUN
ejpam-6763	1017	1	1	1	NUM
ejpam-6763	1017	2	.	.	X
ejpam-6763	1017	3	figure	figure	VERB
ejpam-6763	1017	4	3	3	NUM
ejpam-6763	1017	5	:	:	PUNCT
ejpam-6763	1017	6	approximate	approximate	ADJ
ejpam-6763	1017	7	solution	solution	NOUN
ejpam-6763	1017	8	using	use	VERB
ejpam-6763	1017	9	fcpcbs	fcpcbs	PROPN
ejpam-6763	1017	10	for	for	ADP
ejpam-6763	1017	11	example	example	NOUN
ejpam-6763	1017	12	1	1	NUM
ejpam-6763	1017	13	.	.	X
ejpam-6763	1017	14	figure	figure	VERB
ejpam-6763	1017	15	4	4	NUM
ejpam-6763	1017	16	:	:	PUNCT
ejpam-6763	1017	17	least	least	ADJ
ejpam-6763	1017	18	square	square	ADJ
ejpam-6763	1017	19	error	error	NOUN
ejpam-6763	1017	20	plot	plot	NOUN
ejpam-6763	1017	21	using	use	VERB
ejpam-6763	1017	22	fcpcbs	fcpcb	NOUN
ejpam-6763	1017	23	for	for	ADP
ejpam-6763	1017	24	example	example	NOUN
ejpam-6763	1018	1	1	1	X
ejpam-6763	1018	2	.	.	PUNCT
ejpam-6763	1018	3	d.	d.	PROPN
ejpam-6763	1018	4	kh	kh	PROPN
ejpam-6763	1018	5	.	.	PUNCT
ejpam-6763	1019	1	abdullah	abdullah	PROPN
ejpam-6763	1019	2	,	,	PUNCT
ejpam-6763	1019	3	sh	sh	PROPN
ejpam-6763	1019	4	.	.	PROPN
ejpam-6763	1019	5	sh	sh	PROPN
ejpam-6763	1019	6	.	.	PROPN
ejpam-6763	1019	7	ahmed	ahmed	PROPN
ejpam-6763	1019	8	,	,	PUNCT
ejpam-6763	1019	9	k.	k.	PROPN
ejpam-6763	1019	10	h.	h.	PROPN
ejpam-6763	1019	11	f.	f.	PROPN
ejpam-6763	1019	12	jwamer	jwamer	PROPN
ejpam-6763	1019	13	/	/	SYM
ejpam-6763	1019	14	eur	eur	PROPN
ejpam-6763	1019	15	.	.	PUNCT
ejpam-6763	1020	1	j.	j.	PROPN
ejpam-6763	1020	2	pure	pure	PROPN
ejpam-6763	1020	3	appl	appl	PROPN
ejpam-6763	1020	4	.	.	PROPN
ejpam-6763	1020	5	math	math	PROPN
ejpam-6763	1020	6	,	,	PUNCT
ejpam-6763	1020	7	18	18	NUM
ejpam-6763	1020	8	(	(	PUNCT
ejpam-6763	1020	9	4	4	NUM
ejpam-6763	1020	10	)	)	PUNCT
ejpam-6763	1020	11	(	(	PUNCT
ejpam-6763	1020	12	2025	2025	NUM
ejpam-6763	1020	13	)	)	PUNCT
ejpam-6763	1020	14	,	,	PUNCT
ejpam-6763	1020	15	6763	6763	NUM
ejpam-6763	1020	16	28	28	NUM
ejpam-6763	1020	17	of	of	ADP
ejpam-6763	1020	18	40	40	NUM
ejpam-6763	1020	19	figure	figure	NOUN
ejpam-6763	1020	20	5	5	NUM
ejpam-6763	1020	21	:	:	PUNCT
ejpam-6763	1020	22	approximate	approximate	ADJ
ejpam-6763	1020	23	solution	solution	NOUN
ejpam-6763	1020	24	using	use	VERB
ejpam-6763	1020	25	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1020	26	for	for	ADP
ejpam-6763	1020	27	example	example	NOUN
ejpam-6763	1020	28	1	1	NUM
ejpam-6763	1020	29	.	.	X
ejpam-6763	1020	30	figure	figure	VERB
ejpam-6763	1020	31	6	6	NUM
ejpam-6763	1020	32	:	:	PUNCT
ejpam-6763	1020	33	least	least	ADJ
ejpam-6763	1020	34	square	square	ADJ
ejpam-6763	1020	35	error	error	NOUN
ejpam-6763	1020	36	plot	plot	NOUN
ejpam-6763	1020	37	using	use	VERB
ejpam-6763	1020	38	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1020	39	for	for	ADP
ejpam-6763	1020	40	example	example	NOUN
ejpam-6763	1020	41	1	1	NUM
ejpam-6763	1020	42	.	.	PUNCT
ejpam-6763	1020	43	table	table	NOUN
ejpam-6763	1020	44	6	6	NUM
ejpam-6763	1020	45	:	:	PUNCT
ejpam-6763	1020	46	the	the	DET
ejpam-6763	1020	47	values	value	NOUN
ejpam-6763	1020	48	of	of	ADP
ejpam-6763	1020	49	control	control	NOUN
ejpam-6763	1020	50	points	point	NOUN
ejpam-6763	1020	51	of	of	ADP
ejpam-6763	1020	52	b{c,3	b{c,3	NOUN
ejpam-6763	1020	53	}	}	PUNCT
ejpam-6763	1020	54	0	0	NUM
ejpam-6763	1021	1	(	(	PUNCT
ejpam-6763	1021	2	x	x	X
ejpam-6763	1021	3	?	?	PUNCT
ejpam-6763	1021	4	r+1	r+1	NOUN
ejpam-6763	1021	5	)	)	PUNCT
ejpam-6763	1021	6	and	and	CCONJ
ejpam-6763	1021	7	b{c,3	b{c,3	NOUN
ejpam-6763	1021	8	}	}	PUNCT
ejpam-6763	1021	9	1	1	NUM
ejpam-6763	1021	10	(	(	PUNCT
ejpam-6763	1021	11	x	x	NOUN
ejpam-6763	1021	12	?	?	PUNCT
ejpam-6763	1022	1	r+1	r+1	NOUN
ejpam-6763	1022	2	)	)	PUNCT
ejpam-6763	1022	3	for	for	ADP
ejpam-6763	1022	4	three	three	NUM
ejpam-6763	1022	5	methods	method	NOUN
ejpam-6763	1022	6	nfcbi	nfcbi	VERB
ejpam-6763	1022	7	,	,	PUNCT
ejpam-6763	1022	8	fcpcbs	fcpcbs	PROPN
ejpam-6763	1022	9	,	,	PUNCT
ejpam-6763	1022	10	and	and	CCONJ
ejpam-6763	1022	11	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	1022	12	,	,	PUNCT
ejpam-6763	1022	13	respectively	respectively	ADV
ejpam-6763	1022	14	,	,	PUNCT
ejpam-6763	1022	15	for	for	ADP
ejpam-6763	1022	16	example	example	NOUN
ejpam-6763	1022	17	2	2	NUM
ejpam-6763	1022	18	method	method	NOUN
ejpam-6763	1022	19	interval	interval	NOUN
ejpam-6763	1022	20	cp	cp	NUM
ejpam-6763	1022	21	of	of	ADP
ejpam-6763	1022	22	b{c,3	b{c,3	PROPN
ejpam-6763	1022	23	}	}	PUNCT
ejpam-6763	1022	24	0	0	NUM
ejpam-6763	1023	1	(	(	PUNCT
ejpam-6763	1023	2	x	x	X
ejpam-6763	1023	3	?	?	PUNCT
ejpam-6763	1023	4	r+1	r+1	NOUN
ejpam-6763	1023	5	)	)	PUNCT
ejpam-6763	1023	6	cp	cp	PROPN
ejpam-6763	1023	7	of	of	ADP
ejpam-6763	1023	8	b{c,3	b{c,3	PROPN
ejpam-6763	1023	9	}	}	PUNCT
ejpam-6763	1023	10	1	1	NUM
ejpam-6763	1023	11	(	(	PUNCT
ejpam-6763	1023	12	x	x	NOUN
ejpam-6763	1023	13	?	?	PUNCT
ejpam-6763	1024	1	r+1	r+1	NOUN
ejpam-6763	1024	2	)	)	PUNCT
ejpam-6763	1025	1	]	]	X
ejpam-6763	1025	2	0.0	0.0	NUM
ejpam-6763	1025	3	,	,	PUNCT
ejpam-6763	1025	4	0.1	0.1	NUM
ejpam-6763	1025	5	]	]	PUNCT
ejpam-6763	1025	6	ϑ00	ϑ00	ADJ
ejpam-6763	1025	7	=	=	SYM
ejpam-6763	1025	8	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1025	9	ϑ01	ϑ01	NOUN
ejpam-6763	1025	10	=	=	NOUN
ejpam-6763	1025	11	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1025	12	ϑ02	ϑ02	NOUN
ejpam-6763	1025	13	=	=	SYM
ejpam-6763	1025	14	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1025	15	ϑ03	ϑ03	PROPN
ejpam-6763	1025	16	=	=	SYM
ejpam-6763	1025	17	1.20000000000011×	1.20000000000011×	NUM
ejpam-6763	1025	18	10−11	10−11	NUM
ejpam-6763	1025	19	ϑ20	ϑ20	NOUN
ejpam-6763	1026	1	=	=	SYM
ejpam-6763	1026	2	1.0000000000000000000	1.0000000000000000000	NUM
ejpam-6763	1026	3	ϑ21	ϑ21	NOUN
ejpam-6763	1026	4	=	=	SYM
ejpam-6763	1026	5	1.0000000000000000000	1.0000000000000000000	NUM
ejpam-6763	1026	6	ϑ22	ϑ22	NOUN
ejpam-6763	1026	7	=	=	SYM
ejpam-6763	1026	8	0.6666666666608888882	0.6666666666608888882	NUM
ejpam-6763	1026	9	ϑ23	ϑ23	NOUN
ejpam-6763	1026	10	=	=	SYM
ejpam-6763	1026	11	1.55986334959834×	1.55986334959834×	NUM
ejpam-6763	1026	12	10−10	10−10	NUM
ejpam-6763	1026	13	]	]	SYM
ejpam-6763	1026	14	0.1	0.1	NUM
ejpam-6763	1026	15	,	,	PUNCT
ejpam-6763	1026	16	0.2	0.2	NUM
ejpam-6763	1026	17	]	]	PUNCT
ejpam-6763	1026	18	ϑ00	ϑ00	ADJ
ejpam-6763	1026	19	=	=	SYM
ejpam-6763	1026	20	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1026	21	ϑ01	ϑ01	NOUN
ejpam-6763	1026	22	=	=	NOUN
ejpam-6763	1026	23	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1026	24	ϑ02	ϑ02	NOUN
ejpam-6763	1026	25	=	=	SYM
ejpam-6763	1026	26	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1026	27	ϑ03	ϑ03	X
ejpam-6763	1026	28	=	=	SYM
ejpam-6763	1026	29	2.12500000000011×	2.12500000000011×	NUM
ejpam-6763	1026	30	10−11	10−11	NUM
ejpam-6763	1026	31	ϑ20	ϑ20	NOUN
ejpam-6763	1026	32	=	=	SYM
ejpam-6763	1026	33	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	34	ϑ21	ϑ21	NOUN
ejpam-6763	1026	35	=	=	SYM
ejpam-6763	1026	36	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1026	37	ϑ22	ϑ22	NOUN
ejpam-6763	1026	38	=	=	NOUN
ejpam-6763	1026	39	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1026	40	ϑ23	ϑ23	NOUN
ejpam-6763	1026	41	=	=	SYM
ejpam-6763	1026	42	−5.5622173533720×	−5.5622173533720×	NUM
ejpam-6763	1026	43	10−11	10−11	NOUN
ejpam-6763	1026	44	]	]	PUNCT
ejpam-6763	1026	45	0.2	0.2	NUM
ejpam-6763	1026	46	,	,	PUNCT
ejpam-6763	1026	47	0.3	0.3	NUM
ejpam-6763	1026	48	]	]	PUNCT
ejpam-6763	1026	49	ϑ00	ϑ00	ADJ
ejpam-6763	1026	50	=	=	SYM
ejpam-6763	1026	51	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1026	52	ϑ01	ϑ01	NOUN
ejpam-6763	1026	53	=	=	NOUN
ejpam-6763	1026	54	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1026	55	ϑ02	ϑ02	NOUN
ejpam-6763	1026	56	=	=	SYM
ejpam-6763	1026	57	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1026	58	ϑ03	ϑ03	PROPN
ejpam-6763	1026	59	=	=	SYM
ejpam-6763	1026	60	2.5185185185185765×	2.5185185185185765×	NUM
ejpam-6763	1026	61	10−11	10−11	NUM
ejpam-6763	1026	62	ϑ20	ϑ20	NOUN
ejpam-6763	1026	63	=	=	SYM
ejpam-6763	1026	64	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	65	ϑ21	ϑ21	NOUN
ejpam-6763	1026	66	=	=	SYM
ejpam-6763	1026	67	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	68	ϑ22	ϑ22	NOUN
ejpam-6763	1026	69	=	=	NOUN
ejpam-6763	1026	70	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1026	71	ϑ23	ϑ23	NOUN
ejpam-6763	1026	72	=	=	PUNCT
ejpam-6763	1026	73	−3.35780785892×	−3.35780785892×	X
ejpam-6763	1026	74	10−11	10−11	PROPN
ejpam-6763	1026	75	]	]	PUNCT
ejpam-6763	1026	76	0.3	0.3	NUM
ejpam-6763	1026	77	,	,	PUNCT
ejpam-6763	1026	78	0.4	0.4	NUM
ejpam-6763	1026	79	]	]	PUNCT
ejpam-6763	1026	80	ϑ00	ϑ00	ADJ
ejpam-6763	1026	81	=	=	SYM
ejpam-6763	1026	82	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1026	83	ϑ01	ϑ01	NOUN
ejpam-6763	1026	84	=	=	NOUN
ejpam-6763	1026	85	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1026	86	ϑ02	ϑ02	NOUN
ejpam-6763	1026	87	=	=	SYM
ejpam-6763	1026	88	−0.6666666666666666666	−0.6666666666666666666	NOUN
ejpam-6763	1026	89	ϑ03	ϑ03	NOUN
ejpam-6763	1026	90	=	=	SYM
ejpam-6763	1026	91	2.18749999999993×	2.18749999999993×	NUM
ejpam-6763	1026	92	10−11	10−11	NUM
ejpam-6763	1026	93	ϑ20	ϑ20	NOUN
ejpam-6763	1026	94	=	=	SYM
ejpam-6763	1026	95	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	96	ϑ21	ϑ21	NOUN
ejpam-6763	1026	97	=	=	SYM
ejpam-6763	1026	98	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	99	ϑ22	ϑ22	NOUN
ejpam-6763	1026	100	=	=	NOUN
ejpam-6763	1026	101	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1026	102	ϑ23	ϑ23	NOUN
ejpam-6763	1026	103	=	=	PUNCT
ejpam-6763	1026	104	−2.08461720108132×	−2.08461720108132×	PUNCT
ejpam-6763	1026	105	10−11	10−11	PROPN
ejpam-6763	1026	106	nfcbi	nfcbi	VERB
ejpam-6763	1026	107	]	]	X
ejpam-6763	1026	108	0.4	0.4	NUM
ejpam-6763	1026	109	,	,	PUNCT
ejpam-6763	1026	110	0.5	0.5	NUM
ejpam-6763	1026	111	]	]	PUNCT
ejpam-6763	1026	112	ϑ00	ϑ00	ADJ
ejpam-6763	1026	113	=	=	SYM
ejpam-6763	1026	114	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1026	115	ϑ01	ϑ01	NOUN
ejpam-6763	1026	116	=	=	NOUN
ejpam-6763	1026	117	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1026	118	ϑ02	ϑ02	NOUN
ejpam-6763	1026	119	=	=	SYM
ejpam-6763	1026	120	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1026	121	ϑ03	ϑ03	NOUN
ejpam-6763	1026	122	=	=	SYM
ejpam-6763	1026	123	1.15000000000002×	1.15000000000002×	NUM
ejpam-6763	1026	124	10−11	10−11	NUM
ejpam-6763	1026	125	ϑ20	ϑ20	NOUN
ejpam-6763	1026	126	=	=	SYM
ejpam-6763	1026	127	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	128	ϑ21	ϑ21	NOUN
ejpam-6763	1026	129	=	=	SYM
ejpam-6763	1026	130	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	131	ϑ22	ϑ22	NOUN
ejpam-6763	1026	132	=	=	NOUN
ejpam-6763	1026	133	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1026	134	ϑ23	ϑ23	NOUN
ejpam-6763	1026	135	=	=	PUNCT
ejpam-6763	1026	136	−3.06465963717528×	−3.06465963717528×	NUM
ejpam-6763	1026	137	10−11	10−11	NUM
ejpam-6763	1026	138	]	]	PUNCT
ejpam-6763	1026	139	0.5	0.5	NUM
ejpam-6763	1026	140	,	,	PUNCT
ejpam-6763	1026	141	0.6	0.6	NUM
ejpam-6763	1026	142	]	]	PUNCT
ejpam-6763	1026	143	ϑ00	ϑ00	ADJ
ejpam-6763	1026	144	=	=	SYM
ejpam-6763	1026	145	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1026	146	ϑ01	ϑ01	NOUN
ejpam-6763	1026	147	=	=	NOUN
ejpam-6763	1026	148	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1026	149	ϑ02	ϑ02	NOUN
ejpam-6763	1026	150	=	=	SYM
ejpam-6763	1026	151	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1026	152	ϑ03	ϑ03	PROPN
ejpam-6763	1026	153	=	=	SYM
ejpam-6763	1026	154	−3.20000000000103×	−3.20000000000103×	NUM
ejpam-6763	1026	155	10−12	10−12	NOUN
ejpam-6763	1026	156	ϑ20	ϑ20	NOUN
ejpam-6763	1026	157	=	=	SYM
ejpam-6763	1026	158	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	159	ϑ21	ϑ21	NOUN
ejpam-6763	1026	160	=	=	SYM
ejpam-6763	1026	161	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1026	162	ϑ22	ϑ22	NOUN
ejpam-6763	1026	163	=	=	NOUN
ejpam-6763	1026	164	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1026	165	ϑ23	ϑ23	NOUN
ejpam-6763	1026	166	=	=	PRON
ejpam-6763	1026	167	−3.00983517944444×	−3.00983517944444×	PUNCT
ejpam-6763	1026	168	10−11	10−11	PRON
ejpam-6763	1026	169	continued	continue	VERB
ejpam-6763	1026	170	on	on	ADP
ejpam-6763	1026	171	next	next	ADJ
ejpam-6763	1026	172	page	page	NOUN
ejpam-6763	1026	173	d.	d.	PROPN
ejpam-6763	1026	174	kh	kh	PROPN
ejpam-6763	1026	175	.	.	PUNCT
ejpam-6763	1027	1	abdullah	abdullah	PROPN
ejpam-6763	1027	2	,	,	PUNCT
ejpam-6763	1027	3	sh	sh	PROPN
ejpam-6763	1027	4	.	.	PROPN
ejpam-6763	1027	5	sh	sh	PROPN
ejpam-6763	1027	6	.	.	PROPN
ejpam-6763	1027	7	ahmed	ahmed	PROPN
ejpam-6763	1027	8	,	,	PUNCT
ejpam-6763	1027	9	k.	k.	PROPN
ejpam-6763	1027	10	h.	h.	PROPN
ejpam-6763	1027	11	f.	f.	PROPN
ejpam-6763	1027	12	jwamer	jwamer	PROPN
ejpam-6763	1027	13	/	/	SYM
ejpam-6763	1027	14	eur	eur	PROPN
ejpam-6763	1027	15	.	.	PUNCT
ejpam-6763	1028	1	j.	j.	PROPN
ejpam-6763	1028	2	pure	pure	PROPN
ejpam-6763	1028	3	appl	appl	PROPN
ejpam-6763	1028	4	.	.	PROPN
ejpam-6763	1028	5	math	math	PROPN
ejpam-6763	1028	6	,	,	PUNCT
ejpam-6763	1028	7	18	18	NUM
ejpam-6763	1028	8	(	(	PUNCT
ejpam-6763	1028	9	4	4	NUM
ejpam-6763	1028	10	)	)	PUNCT
ejpam-6763	1028	11	(	(	PUNCT
ejpam-6763	1028	12	2025	2025	NUM
ejpam-6763	1028	13	)	)	PUNCT
ejpam-6763	1028	14	,	,	PUNCT
ejpam-6763	1028	15	6763	6763	NUM
ejpam-6763	1028	16	29	29	NUM
ejpam-6763	1028	17	of	of	ADP
ejpam-6763	1028	18	40	40	NUM
ejpam-6763	1028	19	method	method	NOUN
ejpam-6763	1028	20	interval	interval	NOUN
ejpam-6763	1028	21	cp	cp	NUM
ejpam-6763	1028	22	of	of	ADP
ejpam-6763	1028	23	b{c,3	b{c,3	PROPN
ejpam-6763	1028	24	}	}	PUNCT
ejpam-6763	1028	25	0	0	NUM
ejpam-6763	1029	1	(	(	PUNCT
ejpam-6763	1029	2	x	x	X
ejpam-6763	1029	3	?	?	PUNCT
ejpam-6763	1029	4	r+1	r+1	NOUN
ejpam-6763	1029	5	)	)	PUNCT
ejpam-6763	1029	6	cp	cp	PROPN
ejpam-6763	1029	7	of	of	ADP
ejpam-6763	1029	8	b{c,3	b{c,3	PROPN
ejpam-6763	1029	9	}	}	PUNCT
ejpam-6763	1029	10	1	1	NUM
ejpam-6763	1029	11	(	(	PUNCT
ejpam-6763	1029	12	x	x	NOUN
ejpam-6763	1029	13	?	?	PUNCT
ejpam-6763	1029	14	r+1	r+1	NOUN
ejpam-6763	1029	15	)	)	PUNCT
ejpam-6763	1030	1	]	]	PUNCT
ejpam-6763	1030	2	0.6	0.6	NUM
ejpam-6763	1030	3	,	,	PUNCT
ejpam-6763	1030	4	0.7	0.7	NUM
ejpam-6763	1030	5	]	]	PUNCT
ejpam-6763	1030	6	ϑ00	ϑ00	ADJ
ejpam-6763	1030	7	=	=	SYM
ejpam-6763	1030	8	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1030	9	ϑ01	ϑ01	NOUN
ejpam-6763	1030	10	=	=	NOUN
ejpam-6763	1030	11	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1030	12	ϑ02	ϑ02	NOUN
ejpam-6763	1030	13	=	=	SYM
ejpam-6763	1030	14	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1030	15	ϑ03	ϑ03	PROPN
ejpam-6763	1030	16	=	=	SYM
ejpam-6763	1030	17	−2.28435374149652×	−2.28435374149652×	CCONJ
ejpam-6763	1030	18	10−11	10−11	NUM
ejpam-6763	1031	1	ϑ20	ϑ20	NOUN
ejpam-6763	1031	2	=	=	SYM
ejpam-6763	1031	3	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1031	4	ϑ21	ϑ21	NOUN
ejpam-6763	1031	5	=	=	SYM
ejpam-6763	1031	6	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1031	7	ϑ22	ϑ22	NOUN
ejpam-6763	1031	8	=	=	NOUN
ejpam-6763	1031	9	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1031	10	ϑ23	ϑ23	NOUN
ejpam-6763	1031	11	=	=	SYM
ejpam-6763	1031	12	−3.046413137949×	−3.046413137949×	PUNCT
ejpam-6763	1031	13	10−11	10−11	X
ejpam-6763	1031	14	]	]	X
ejpam-6763	1031	15	0.7	0.7	NUM
ejpam-6763	1031	16	,	,	PUNCT
ejpam-6763	1031	17	0.8	0.8	NUM
ejpam-6763	1031	18	]	]	PUNCT
ejpam-6763	1031	19	ϑ00	ϑ00	ADJ
ejpam-6763	1031	20	=	=	SYM
ejpam-6763	1031	21	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1031	22	ϑ01	ϑ01	NOUN
ejpam-6763	1031	23	=	=	NOUN
ejpam-6763	1032	1	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1032	2	ϑ02	ϑ02	NOUN
ejpam-6763	1032	3	=	=	SYM
ejpam-6763	1032	4	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1032	5	ϑ03	ϑ03	NOUN
ejpam-6763	1032	6	=	=	SYM
ejpam-6763	1032	7	−4.572916666667×	−4.572916666667×	NOUN
ejpam-6763	1032	8	10−11	10−11	NUM
ejpam-6763	1032	9	ϑ20	ϑ20	NOUN
ejpam-6763	1032	10	=	=	SYM
ejpam-6763	1032	11	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	12	ϑ21	ϑ21	NOUN
ejpam-6763	1032	13	=	=	SYM
ejpam-6763	1032	14	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	15	ϑ22	ϑ22	NOUN
ejpam-6763	1032	16	=	=	NOUN
ejpam-6763	1032	17	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1032	18	ϑ23	ϑ23	NOUN
ejpam-6763	1032	19	=	=	SYM
ejpam-6763	1032	20	−3.08179046518142×	−3.08179046518142×	NOUN
ejpam-6763	1032	21	10−11	10−11	NUM
ejpam-6763	1032	22	]	]	PUNCT
ejpam-6763	1032	23	0.8	0.8	NUM
ejpam-6763	1032	24	,	,	PUNCT
ejpam-6763	1032	25	0.9	0.9	NUM
ejpam-6763	1032	26	]	]	PUNCT
ejpam-6763	1032	27	ϑ00	ϑ00	ADJ
ejpam-6763	1032	28	=	=	SYM
ejpam-6763	1032	29	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1032	30	ϑ01	ϑ01	NOUN
ejpam-6763	1032	31	=	=	NOUN
ejpam-6763	1032	32	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1032	33	ϑ02	ϑ02	NOUN
ejpam-6763	1032	34	=	=	SYM
ejpam-6763	1032	35	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1032	36	ϑ03	ϑ03	PROPN
ejpam-6763	1032	37	=	=	SYM
ejpam-6763	1032	38	−8.17622410546180×	−8.17622410546180×	NOUN
ejpam-6763	1032	39	10−11	10−11	NUM
ejpam-6763	1032	40	ϑ20	ϑ20	NOUN
ejpam-6763	1032	41	=	=	SYM
ejpam-6763	1032	42	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	43	ϑ21	ϑ21	NOUN
ejpam-6763	1032	44	=	=	SYM
ejpam-6763	1032	45	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	46	ϑ22	ϑ22	NOUN
ejpam-6763	1032	47	=	=	NOUN
ejpam-6763	1032	48	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1032	49	ϑ23	ϑ23	NOUN
ejpam-6763	1032	50	=	=	PUNCT
ejpam-6763	1032	51	−2.96219001164554×	−2.96219001164554×	PUNCT
ejpam-6763	1032	52	10−11	10−11	X
ejpam-6763	1032	53	]	]	PUNCT
ejpam-6763	1032	54	0.9	0.9	NUM
ejpam-6763	1032	55	,	,	PUNCT
ejpam-6763	1032	56	1.0	1.0	NUM
ejpam-6763	1032	57	]	]	PUNCT
ejpam-6763	1032	58	ϑ00	ϑ00	ADJ
ejpam-6763	1032	59	=	=	SYM
ejpam-6763	1032	60	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1032	61	ϑ01	ϑ01	NOUN
ejpam-6763	1032	62	=	=	NOUN
ejpam-6763	1032	63	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1032	64	ϑ02	ϑ02	NOUN
ejpam-6763	1032	65	=	=	SYM
ejpam-6763	1032	66	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1032	67	ϑ03	ϑ03	NOUN
ejpam-6763	1032	68	=	=	PUNCT
ejpam-6763	1032	69	−1.389125188695603×	−1.389125188695603×	PUNCT
ejpam-6763	1032	70	10−10	10−10	NUM
ejpam-6763	1032	71	ϑ20	ϑ20	NOUN
ejpam-6763	1032	72	=	=	SYM
ejpam-6763	1032	73	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	74	ϑ21	ϑ21	NOUN
ejpam-6763	1032	75	=	=	SYM
ejpam-6763	1032	76	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	77	ϑ22	ϑ22	NOUN
ejpam-6763	1032	78	=	=	NOUN
ejpam-6763	1032	79	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1032	80	ϑ23	ϑ23	NOUN
ejpam-6763	1032	81	=	=	SYM
ejpam-6763	1032	82	−5.600000000000×	−5.600000000000×	CCONJ
ejpam-6763	1032	83	10−11	10−11	NUM
ejpam-6763	1032	84	fcpcbs	fcpcbs	PROPN
ejpam-6763	1032	85	]	]	X
ejpam-6763	1032	86	0.0	0.0	NUM
ejpam-6763	1032	87	,	,	PUNCT
ejpam-6763	1032	88	1.0	1.0	NUM
ejpam-6763	1032	89	]	]	PUNCT
ejpam-6763	1032	90	ϑ00	ϑ00	ADJ
ejpam-6763	1032	91	=	=	SYM
ejpam-6763	1032	92	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1032	93	ϑ01	ϑ01	NOUN
ejpam-6763	1032	94	=	=	NOUN
ejpam-6763	1032	95	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1032	96	ϑ02	ϑ02	NOUN
ejpam-6763	1032	97	=	=	SYM
ejpam-6763	1032	98	−0.6666666666666666667	−0.6666666666666666667	ADJ
ejpam-6763	1032	99	b03	b03	X
ejpam-6763	1032	100	=	=	SYM
ejpam-6763	1032	101	1.20000000000011×	1.20000000000011×	NUM
ejpam-6763	1032	102	10−11	10−11	NUM
ejpam-6763	1032	103	ϑ20	ϑ20	NOUN
ejpam-6763	1032	104	=	=	SYM
ejpam-6763	1032	105	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	106	b21	b21	NOUN
ejpam-6763	1032	107	=	=	SYM
ejpam-6763	1032	108	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	109	ϑ22	ϑ22	NOUN
ejpam-6763	1032	110	=	=	NOUN
ejpam-6763	1032	111	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1032	112	ϑ23	ϑ23	NOUN
ejpam-6763	1032	113	=	=	NOUN
ejpam-6763	1032	114	1.559863349598×	1.559863349598×	NUM
ejpam-6763	1032	115	10−10	10−10	NUM
ejpam-6763	1032	116	ffcpcbs	ffcpcbs	ADJ
ejpam-6763	1032	117	]	]	X
ejpam-6763	1032	118	0.0	0.0	NUM
ejpam-6763	1032	119	,	,	PUNCT
ejpam-6763	1032	120	1.0	1.0	NUM
ejpam-6763	1032	121	]	]	PUNCT
ejpam-6763	1032	122	ϑ00	ϑ00	ADJ
ejpam-6763	1032	123	=	=	SYM
ejpam-6763	1032	124	−1.0000000000000000000	−1.0000000000000000000	NOUN
ejpam-6763	1032	125	ϑ01	ϑ01	NOUN
ejpam-6763	1032	126	=	=	NOUN
ejpam-6763	1032	127	−1.0000000000000000000	−1.0000000000000000000	NUM
ejpam-6763	1032	128	ϑ02	ϑ02	NOUN
ejpam-6763	1032	129	=	=	SYM
ejpam-6763	1032	130	−0.6666666666666666667	−0.6666666666666666667	NOUN
ejpam-6763	1032	131	ϑ03	ϑ03	PROPN
ejpam-6763	1032	132	=	=	SYM
ejpam-6763	1032	133	−6.345625943477962×	−6.345625943477962×	SYM
ejpam-6763	1032	134	10−11	10−11	NUM
ejpam-6763	1032	135	ϑ20	ϑ20	NOUN
ejpam-6763	1032	136	=	=	SYM
ejpam-6763	1032	137	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	138	ϑ21	ϑ21	NOUN
ejpam-6763	1032	139	=	=	SYM
ejpam-6763	1032	140	1.00000000000000000000	1.00000000000000000000	NUM
ejpam-6763	1032	141	ϑ22	ϑ22	NOUN
ejpam-6763	1032	142	=	=	NOUN
ejpam-6763	1032	143	0.66666666666088888882	0.66666666666088888882	NUM
ejpam-6763	1032	144	ϑ23	ϑ23	NOUN
ejpam-6763	1032	145	=	=	SYM
ejpam-6763	1032	146	4.999316747991×	4.999316747991×	NUM
ejpam-6763	1032	147	10−11	10−11	NUM
ejpam-6763	1032	148	from	from	ADP
ejpam-6763	1032	149	(	(	PUNCT
ejpam-6763	1032	150	21	21	NUM
ejpam-6763	1032	151	)	)	PUNCT
ejpam-6763	1032	152	,	,	PUNCT
ejpam-6763	1032	153	we	we	PRON
ejpam-6763	1032	154	obtain	obtain	VERB
ejpam-6763	1032	155	the	the	DET
ejpam-6763	1032	156	approximate	approximate	ADJ
ejpam-6763	1032	157	solution	solution	NOUN
ejpam-6763	1032	158	for	for	ADP
ejpam-6763	1032	159	the	the	DET
ejpam-6763	1032	160	classical	classical	ADJ
ejpam-6763	1032	161	and	and	CCONJ
ejpam-6763	1032	162	fractional	fractional	ADJ
ejpam-6763	1032	163	order	order	NOUN
ejpam-6763	1032	164	linear	linear	NOUN
ejpam-6763	1032	165	system	system	NOUN
ejpam-6763	1032	166	of	of	ADP
ejpam-6763	1032	167	volterra	volterra	PROPN
ejpam-6763	1032	168	integro	integro	PROPN
ejpam-6763	1032	169	-	-	PUNCT
ejpam-6763	1032	170	differential	differential	NOUN
ejpam-6763	1032	171	equations	equation	NOUN
ejpam-6763	1032	172	(	(	PUNCT
ejpam-6763	1032	173	svides	svide	NOUN
ejpam-6763	1032	174	-	-	PUNCT
ejpam-6763	1032	175	cf	cf	NOUN
ejpam-6763	1032	176	)	)	PUNCT
ejpam-6763	1032	177	with	with	ADP
ejpam-6763	1032	178	variable	variable	ADJ
ejpam-6763	1032	179	coefficients	coefficient	NOUN
ejpam-6763	1032	180	,	,	PUNCT
ejpam-6763	1032	181	for	for	ADP
ejpam-6763	1032	182	example	example	NOUN
ejpam-6763	1032	183	2	2	NUM
ejpam-6763	1032	184	,	,	PUNCT
ejpam-6763	1032	185	as	as	SCONJ
ejpam-6763	1032	186	shown	show	VERB
ejpam-6763	1032	187	below	below	ADP
ejpam-6763	1032	188	:	:	PUNCT
ejpam-6763	1032	189	b{c,3	b{c,3	NOUN
ejpam-6763	1032	190	}	}	PUNCT
ejpam-6763	1032	191	0	0	NUM
ejpam-6763	1033	1	(	(	PUNCT
ejpam-6763	1033	2	x	x	NOUN
ejpam-6763	1033	3	?	?	PUNCT
ejpam-6763	1033	4	)	)	PUNCT
ejpam-6763	1033	5	(	(	PUNCT
ejpam-6763	1033	6	nfcbi	nfcbi	NOUN
ejpam-6763	1033	7	)	)	PUNCT
ejpam-6763	1033	8	=	=	PUNCT
ejpam-6763	1034	1			X
ejpam-6763	1034	2	1.55986334959834×	1.55986334959834×	NUM
ejpam-6763	1034	3	10−10x?3	10−10x?3	NUM
ejpam-6763	1034	4	+	+	CCONJ
ejpam-6763	1034	5	0.666666666660882x?2	0.666666666660882x?2	PROPN
ejpam-6763	1034	6	+	+	CCONJ
ejpam-6763	1034	7	1	1	NUM
ejpam-6763	1034	8	,	,	PUNCT
ejpam-6763	1034	9	0	0	PUNCT
ejpam-6763	1034	10	<	<	X
ejpam-6763	1034	11	x	x	X
ejpam-6763	1034	12	?	?	PUNCT
ejpam-6763	1034	13	≤	≤	NUM
ejpam-6763	1034	14	1	1	NUM
ejpam-6763	1034	15	10	10	NUM
ejpam-6763	1034	16	−5.56221735337203×	−5.56221735337203×	NOUN
ejpam-6763	1034	17	10−11x?3	10−11x?3	PROPN
ejpam-6763	1035	1	+	+	CCONJ
ejpam-6763	1035	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1036	1	+	+	CCONJ
ejpam-6763	1036	2	1	1	NUM
ejpam-6763	1036	3	,	,	PUNCT
ejpam-6763	1036	4	1	1	NUM
ejpam-6763	1036	5	10	10	NUM
ejpam-6763	1036	6	<	<	X
ejpam-6763	1036	7	x	x	X
ejpam-6763	1036	8	?	?	PUNCT
ejpam-6763	1036	9	≤	≤	NUM
ejpam-6763	1036	10	1	1	NUM
ejpam-6763	1036	11	5	5	NUM
ejpam-6763	1036	12	−3.35780785892186×	−3.35780785892186×	NUM
ejpam-6763	1036	13	10−11x?3	10−11x?3	PROPN
ejpam-6763	1037	1	+	+	CCONJ
ejpam-6763	1037	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1038	1	+	+	CCONJ
ejpam-6763	1038	2	1	1	NUM
ejpam-6763	1038	3	,	,	PUNCT
ejpam-6763	1038	4	1	1	NUM
ejpam-6763	1038	5	5	5	NUM
ejpam-6763	1038	6	<	<	X
ejpam-6763	1038	7	x	x	X
ejpam-6763	1038	8	?	?	PUNCT
ejpam-6763	1039	1	≤	≤	NUM
ejpam-6763	1039	2	3	3	NUM
ejpam-6763	1039	3	10	10	NUM
ejpam-6763	1039	4	−2.08461720108132×	−2.08461720108132×	NUM
ejpam-6763	1039	5	10−11x?3	10−11x?3	PROPN
ejpam-6763	1040	1	+	+	CCONJ
ejpam-6763	1040	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1041	1	+	+	CCONJ
ejpam-6763	1041	2	1	1	NUM
ejpam-6763	1041	3	,	,	PUNCT
ejpam-6763	1041	4	3	3	NUM
ejpam-6763	1041	5	10	10	NUM
ejpam-6763	1041	6	<	<	X
ejpam-6763	1041	7	x	x	X
ejpam-6763	1041	8	?	?	PUNCT
ejpam-6763	1041	9	≤	≤	NUM
ejpam-6763	1041	10	2	2	NUM
ejpam-6763	1041	11	5	5	NUM
ejpam-6763	1041	12	−3.06465963717528×	−3.06465963717528×	NUM
ejpam-6763	1041	13	10−11x?3	10−11x?3	PROPN
ejpam-6763	1042	1	+	+	CCONJ
ejpam-6763	1042	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1043	1	+	+	CCONJ
ejpam-6763	1043	2	1	1	NUM
ejpam-6763	1043	3	,	,	PUNCT
ejpam-6763	1043	4	2	2	NUM
ejpam-6763	1043	5	5	5	NUM
ejpam-6763	1043	6	<	<	X
ejpam-6763	1043	7	x	x	X
ejpam-6763	1043	8	?	?	PUNCT
ejpam-6763	1043	9	≤	≤	NUM
ejpam-6763	1043	10	1	1	NUM
ejpam-6763	1043	11	2	2	NUM
ejpam-6763	1043	12	−3.00983517944444×	−3.00983517944444×	NOUN
ejpam-6763	1043	13	10−11x?3	10−11x?3	PROPN
ejpam-6763	1044	1	+	+	CCONJ
ejpam-6763	1044	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1044	3	+	+	CCONJ
ejpam-6763	1044	4	1	1	NUM
ejpam-6763	1044	5	,	,	PUNCT
ejpam-6763	1044	6	1	1	NUM
ejpam-6763	1044	7	2	2	NUM
ejpam-6763	1044	8	<	<	X
ejpam-6763	1044	9	x	x	X
ejpam-6763	1044	10	?	?	PUNCT
ejpam-6763	1044	11	≤	≤	NUM
ejpam-6763	1044	12	3	3	NUM
ejpam-6763	1044	13	5	5	NUM
ejpam-6763	1044	14	−3.04641313794957×	−3.04641313794957×	NUM
ejpam-6763	1044	15	10−11x?3	10−11x?3	PROPN
ejpam-6763	1045	1	+	+	CCONJ
ejpam-6763	1045	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1045	3	+	+	CCONJ
ejpam-6763	1045	4	1	1	NUM
ejpam-6763	1045	5	,	,	PUNCT
ejpam-6763	1045	6	3	3	NUM
ejpam-6763	1045	7	5	5	NUM
ejpam-6763	1045	8	<	<	X
ejpam-6763	1045	9	x	x	X
ejpam-6763	1045	10	?	?	PUNCT
ejpam-6763	1045	11	≤	≤	NUM
ejpam-6763	1045	12	7	7	NUM
ejpam-6763	1045	13	10	10	NUM
ejpam-6763	1045	14	−3.08179046518142×	−3.08179046518142×	NOUN
ejpam-6763	1045	15	10−11x?3	10−11x?3	PROPN
ejpam-6763	1045	16	+	+	CCONJ
ejpam-6763	1045	17	0.666666666660882x?2	0.666666666660882x?2	PROPN
ejpam-6763	1045	18	+	+	CCONJ
ejpam-6763	1045	19	1	1	NUM
ejpam-6763	1045	20	,	,	PUNCT
ejpam-6763	1045	21	7	7	NUM
ejpam-6763	1045	22	10	10	NUM
ejpam-6763	1045	23	<	<	X
ejpam-6763	1045	24	x	x	X
ejpam-6763	1045	25	?	?	PUNCT
ejpam-6763	1045	26	≤	≤	NUM
ejpam-6763	1045	27	4	4	NUM
ejpam-6763	1045	28	5	5	NUM
ejpam-6763	1045	29	−2.96219001164554×	−2.96219001164554×	NUM
ejpam-6763	1045	30	10−11x?3	10−11x?3	PROPN
ejpam-6763	1046	1	+	+	CCONJ
ejpam-6763	1046	2	0.666666666660882x?2	0.666666666660882x?2	PRON
ejpam-6763	1047	1	+	+	CCONJ
ejpam-6763	1047	2	1	1	NUM
ejpam-6763	1047	3	,	,	PUNCT
ejpam-6763	1047	4	4	4	NUM
ejpam-6763	1047	5	5	5	NUM
ejpam-6763	1047	6	<	<	X
ejpam-6763	1047	7	x	x	X
ejpam-6763	1047	8	?	?	PUNCT
ejpam-6763	1047	9	≤	≤	NUM
ejpam-6763	1047	10	9	9	NUM
ejpam-6763	1047	11	10	10	NUM
ejpam-6763	1047	12	−5.60000000000000×	−5.60000000000000×	NUM
ejpam-6763	1047	13	10−11x?3	10−11x?3	NUM
ejpam-6763	1048	1	+	+	CCONJ
ejpam-6763	1048	2	0.666666666660882x?2	0.666666666660882x?2	PROPN
ejpam-6763	1049	1	+	+	CCONJ
ejpam-6763	1049	2	1	1	NUM
ejpam-6763	1049	3	,	,	PUNCT
ejpam-6763	1049	4	9	9	NUM
ejpam-6763	1049	5	10	10	NUM
ejpam-6763	1049	6	<	<	X
ejpam-6763	1049	7	x	x	X
ejpam-6763	1049	8	?	?	PUNCT
ejpam-6763	1049	9	≤	≤	NUM
ejpam-6763	1049	10	1	1	NUM
ejpam-6763	1049	11	d.	d.	PROPN
ejpam-6763	1049	12	kh	kh	PROPN
ejpam-6763	1049	13	.	.	PUNCT
ejpam-6763	1050	1	abdullah	abdullah	PROPN
ejpam-6763	1050	2	,	,	PUNCT
ejpam-6763	1050	3	sh	sh	PROPN
ejpam-6763	1050	4	.	.	PROPN
ejpam-6763	1050	5	sh	sh	PROPN
ejpam-6763	1050	6	.	.	PROPN
ejpam-6763	1050	7	ahmed	ahmed	PROPN
ejpam-6763	1050	8	,	,	PUNCT
ejpam-6763	1050	9	k.	k.	PROPN
ejpam-6763	1050	10	h.	h.	PROPN
ejpam-6763	1050	11	f.	f.	PROPN
ejpam-6763	1050	12	jwamer	jwamer	PROPN
ejpam-6763	1050	13	/	/	SYM
ejpam-6763	1050	14	eur	eur	PROPN
ejpam-6763	1050	15	.	.	PUNCT
ejpam-6763	1051	1	j.	j.	PROPN
ejpam-6763	1051	2	pure	pure	PROPN
ejpam-6763	1051	3	appl	appl	PROPN
ejpam-6763	1051	4	.	.	PROPN
ejpam-6763	1051	5	math	math	PROPN
ejpam-6763	1051	6	,	,	PUNCT
ejpam-6763	1051	7	18	18	NUM
ejpam-6763	1051	8	(	(	PUNCT
ejpam-6763	1051	9	4	4	NUM
ejpam-6763	1051	10	)	)	PUNCT
ejpam-6763	1051	11	(	(	PUNCT
ejpam-6763	1051	12	2025	2025	NUM
ejpam-6763	1051	13	)	)	PUNCT
ejpam-6763	1051	14	,	,	PUNCT
ejpam-6763	1051	15	6763	6763	NUM
ejpam-6763	1051	16	30	30	NUM
ejpam-6763	1051	17	of	of	ADP
ejpam-6763	1051	18	40	40	NUM
ejpam-6763	1051	19	b{c,3	b{c,3	NOUN
ejpam-6763	1051	20	}	}	PUNCT
ejpam-6763	1051	21	1	1	NUM
ejpam-6763	1051	22	(	(	PUNCT
ejpam-6763	1051	23	x	x	NOUN
ejpam-6763	1051	24	?	?	PUNCT
ejpam-6763	1051	25	)	)	PUNCT
ejpam-6763	1051	26	(	(	PUNCT
ejpam-6763	1051	27	nfcbi	nfcbi	NOUN
ejpam-6763	1051	28	)	)	PUNCT
ejpam-6763	1051	29	=	=	SYM
ejpam-6763	1051	30			X
ejpam-6763	1051	31	1.73339564923936×	1.73339564923936×	NUM
ejpam-6763	1051	32	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	33	−	−	PROPN
ejpam-6763	1051	34	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	35	+	+	NUM
ejpam-6763	1051	36	1	1	NUM
ejpam-6763	1051	37	,	,	PUNCT
ejpam-6763	1051	38	0	0	PUNCT
ejpam-6763	1051	39	<	<	X
ejpam-6763	1051	40	x	x	X
ejpam-6763	1051	41	?	?	PUNCT
ejpam-6763	1051	42	≤	≤	NUM
ejpam-6763	1051	43	1	1	NUM
ejpam-6763	1051	44	10	10	NUM
ejpam-6763	1051	45	−3.82689435696193×	−3.82689435696193×	NUM
ejpam-6763	1051	46	10−11x?3	10−11x?3	NUM
ejpam-6763	1051	47	−	−	NOUN
ejpam-6763	1051	48	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	49	+	+	NUM
ejpam-6763	1051	50	1	1	NUM
ejpam-6763	1051	51	,	,	PUNCT
ejpam-6763	1051	52	1	1	NUM
ejpam-6763	1051	53	10	10	NUM
ejpam-6763	1051	54	<	<	X
ejpam-6763	1051	55	x	x	X
ejpam-6763	1051	56	?	?	PUNCT
ejpam-6763	1051	57	≤	≤	NUM
ejpam-6763	1051	58	1	1	NUM
ejpam-6763	1051	59	5	5	NUM
ejpam-6763	1051	60	−1.6224799281872×	−1.6224799281872×	NUM
ejpam-6763	1051	61	10−12x?3	10−12x?3	NUM
ejpam-6763	1051	62	−	−	NOUN
ejpam-6763	1051	63	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	64	+	+	NUM
ejpam-6763	1051	65	1	1	NUM
ejpam-6763	1051	66	,	,	PUNCT
ejpam-6763	1051	67	1	1	NUM
ejpam-6763	1051	68	5	5	NUM
ejpam-6763	1051	69	<	<	X
ejpam-6763	1051	70	x	x	X
ejpam-6763	1051	71	?	?	PUNCT
ejpam-6763	1051	72	≤	≤	NUM
ejpam-6763	1051	73	3	3	NUM
ejpam-6763	1051	74	10	10	NUM
ejpam-6763	1051	75	−3.49298368007567×	−3.49298368007567×	NUM
ejpam-6763	1051	76	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	77	−	−	PROPN
ejpam-6763	1051	78	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	79	+	+	NUM
ejpam-6763	1051	80	1	1	NUM
ejpam-6763	1051	81	,	,	PUNCT
ejpam-6763	1051	82	3	3	NUM
ejpam-6763	1051	83	10	10	NUM
ejpam-6763	1051	84	<	<	X
ejpam-6763	1051	85	x	x	X
ejpam-6763	1051	86	?	?	PUNCT
ejpam-6763	1051	87	≤	≤	NUM
ejpam-6763	1051	88	2	2	NUM
ejpam-6763	1051	89	5	5	NUM
ejpam-6763	1051	90	−1.32933664076518×	−1.32933664076518×	NUM
ejpam-6763	1051	91	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	92	−	−	PROPN
ejpam-6763	1051	93	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	94	+	+	NUM
ejpam-6763	1051	95	1	1	NUM
ejpam-6763	1051	96	,	,	PUNCT
ejpam-6763	1051	97	2	2	NUM
ejpam-6763	1051	98	5	5	NUM
ejpam-6763	1051	99	<	<	X
ejpam-6763	1051	100	x	x	X
ejpam-6763	1051	101	?	?	PUNCT
ejpam-6763	1051	102	≤	≤	NUM
ejpam-6763	1051	103	1	1	NUM
ejpam-6763	1051	104	2	2	NUM
ejpam-6763	1051	105	−1.27451382780919×	−1.27451382780919×	NOUN
ejpam-6763	1051	106	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	107	−	−	PROPN
ejpam-6763	1051	108	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	109	+	+	NUM
ejpam-6763	1051	110	1	1	NUM
ejpam-6763	1051	111	,	,	PUNCT
ejpam-6763	1051	112	1	1	NUM
ejpam-6763	1051	113	2	2	NUM
ejpam-6763	1051	114	<	<	X
ejpam-6763	1051	115	x	x	X
ejpam-6763	1051	116	?	?	PUNCT
ejpam-6763	1051	117	≤	≤	NUM
ejpam-6763	1051	118	3	3	NUM
ejpam-6763	1051	119	5	5	NUM
ejpam-6763	1051	120	−1.31108457424034×	−1.31108457424034×	NUM
ejpam-6763	1051	121	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	122	−	−	PROPN
ejpam-6763	1051	123	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	124	+	+	NUM
ejpam-6763	1051	125	1	1	NUM
ejpam-6763	1051	126	,	,	PUNCT
ejpam-6763	1051	127	3	3	NUM
ejpam-6763	1051	128	5	5	NUM
ejpam-6763	1051	129	<	<	X
ejpam-6763	1051	130	x	x	X
ejpam-6763	1051	131	?	?	PUNCT
ejpam-6763	1051	132	≤	≤	NUM
ejpam-6763	1051	133	7	7	NUM
ejpam-6763	1051	134	10	10	NUM
ejpam-6763	1051	135	−1.34647848426539×	−1.34647848426539×	NUM
ejpam-6763	1051	136	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	137	−	−	NOUN
ejpam-6763	1051	138	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	139	+	+	NUM
ejpam-6763	1051	140	1	1	NUM
ejpam-6763	1051	141	,	,	PUNCT
ejpam-6763	1051	142	7	7	NUM
ejpam-6763	1051	143	10	10	NUM
ejpam-6763	1051	144	<	<	X
ejpam-6763	1051	145	x	x	X
ejpam-6763	1051	146	?	?	PUNCT
ejpam-6763	1051	147	≤	≤	NUM
ejpam-6763	1051	148	4	4	NUM
ejpam-6763	1051	149	5	5	NUM
ejpam-6763	1051	150	−1.22686305559228×	−1.22686305559228×	NUM
ejpam-6763	1051	151	10−10x?3	10−10x?3	NOUN
ejpam-6763	1051	152	−	−	PROPN
ejpam-6763	1051	153	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	154	+	+	NUM
ejpam-6763	1051	155	1	1	NUM
ejpam-6763	1051	156	,	,	PUNCT
ejpam-6763	1051	157	4	4	NUM
ejpam-6763	1051	158	5	5	NUM
ejpam-6763	1051	159	<	<	X
ejpam-6763	1051	160	x	x	X
ejpam-6763	1051	161	?	?	PUNCT
ejpam-6763	1051	162	≤	≤	NUM
ejpam-6763	1051	163	9	9	NUM
ejpam-6763	1051	164	10	10	NUM
ejpam-6763	1051	165	−3.86468634872017×	−3.86468634872017×	NOUN
ejpam-6763	1051	166	10−10x?3	10−10x?3	NUM
ejpam-6763	1051	167	−	−	NOUN
ejpam-6763	1051	168	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1051	169	+	+	NUM
ejpam-6763	1051	170	1	1	NUM
ejpam-6763	1051	171	,	,	PUNCT
ejpam-6763	1051	172	9	9	NUM
ejpam-6763	1051	173	10	10	NUM
ejpam-6763	1051	174	<	<	X
ejpam-6763	1051	175	x	x	X
ejpam-6763	1051	176	?	?	SYM
ejpam-6763	1051	177	≤	≤	NUM
ejpam-6763	1051	178	1	1	NUM
ejpam-6763	1051	179	b{c,3	b{c,3	NOUN
ejpam-6763	1051	180	}	}	PUNCT
ejpam-6763	1051	181	0	0	NUM
ejpam-6763	1051	182	(	(	PUNCT
ejpam-6763	1051	183	x	x	NOUN
ejpam-6763	1051	184	?	?	PUNCT
ejpam-6763	1051	185	)	)	PUNCT
ejpam-6763	1051	186	(	(	PUNCT
ejpam-6763	1051	187	fcpcbs	fcpcbs	PROPN
ejpam-6763	1051	188	)	)	PUNCT
ejpam-6763	1051	189	=	=	PUNCT
ejpam-6763	1052	1	1.199929045014870×	1.199929045014870×	NUM
ejpam-6763	1052	2	10−11x?3	10−11x?3	NUM
ejpam-6763	1053	1	+	+	CCONJ
ejpam-6763	1053	2	1.000000x?2	1.000000x?2	NUM
ejpam-6763	1053	3	−	−	PROPN
ejpam-6763	1053	4	1	1	NUM
ejpam-6763	1053	5	,	,	PUNCT
ejpam-6763	1053	6	0	0	PUNCT
ejpam-6763	1053	7	<	<	X
ejpam-6763	1053	8	x	x	X
ejpam-6763	1053	9	?	?	SYM
ejpam-6763	1053	10	≤	≤	NUM
ejpam-6763	1053	11	1	1	NUM
ejpam-6763	1053	12	b{c,3	b{c,3	NOUN
ejpam-6763	1053	13	}	}	PUNCT
ejpam-6763	1053	14	1	1	NUM
ejpam-6763	1053	15	(	(	PUNCT
ejpam-6763	1053	16	x	x	NOUN
ejpam-6763	1053	17	?	?	PUNCT
ejpam-6763	1053	18	)	)	PUNCT
ejpam-6763	1053	19	(	(	PUNCT
ejpam-6763	1053	20	fcpcbs	fcpcbs	PROPN
ejpam-6763	1053	21	)	)	PUNCT
ejpam-6763	1053	22	=	=	PUNCT
ejpam-6763	1054	1	1.73339564923936×	1.73339564923936×	NUM
ejpam-6763	1054	2	10−10x?3	10−10x?3	NUM
ejpam-6763	1054	3	−	−	PROPN
ejpam-6763	1054	4	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1054	5	+	+	NUM
ejpam-6763	1054	6	1	1	NUM
ejpam-6763	1054	7	,	,	PUNCT
ejpam-6763	1054	8	0	0	PUNCT
ejpam-6763	1054	9	<	<	X
ejpam-6763	1054	10	x	x	X
ejpam-6763	1054	11	?	?	SYM
ejpam-6763	1054	12	≤	≤	NUM
ejpam-6763	1054	13	1	1	NUM
ejpam-6763	1054	14	b{c,3	b{c,3	NOUN
ejpam-6763	1054	15	}	}	PUNCT
ejpam-6763	1054	16	0	0	NUM
ejpam-6763	1055	1	(	(	PUNCT
ejpam-6763	1055	2	x	x	NOUN
ejpam-6763	1055	3	?	?	PUNCT
ejpam-6763	1055	4	)	)	PUNCT
ejpam-6763	1055	5	(	(	PUNCT
ejpam-6763	1055	6	ffcpcbs	ffcpcbs	X
ejpam-6763	1055	7	)	)	PUNCT
ejpam-6763	1055	8	=	=	PUNCT
ejpam-6763	1055	9	−6.34567953738951×	−6.34567953738951×	NUM
ejpam-6763	1055	10	10−11x?3	10−11x?3	PROPN
ejpam-6763	1056	1	+	+	CCONJ
ejpam-6763	1056	2	1.000000x?2	1.000000x?2	NUM
ejpam-6763	1056	3	−	−	PROPN
ejpam-6763	1056	4	1	1	NUM
ejpam-6763	1056	5	,	,	PUNCT
ejpam-6763	1056	6	0	0	PUNCT
ejpam-6763	1056	7	<	<	X
ejpam-6763	1056	8	x	x	X
ejpam-6763	1056	9	?	?	SYM
ejpam-6763	1056	10	≤	≤	NUM
ejpam-6763	1056	11	1	1	NUM
ejpam-6763	1056	12	b{c,3	b{c,3	NOUN
ejpam-6763	1056	13	}	}	PUNCT
ejpam-6763	1056	14	1	1	NUM
ejpam-6763	1056	15	(	(	PUNCT
ejpam-6763	1056	16	x	x	NOUN
ejpam-6763	1056	17	?	?	PUNCT
ejpam-6763	1056	18	)	)	PUNCT
ejpam-6763	1056	19	(	(	PUNCT
ejpam-6763	1056	20	ffcpcbs	ffcpcbs	X
ejpam-6763	1056	21	)	)	PUNCT
ejpam-6763	1056	22	=	=	PUNCT
ejpam-6763	1057	1	6.7346128673762×	6.7346128673762×	NUM
ejpam-6763	1058	1	10−11x?3	10−11x?3	NUM
ejpam-6763	1058	2	−	−	NUM
ejpam-6763	1058	3	1.00000000001735x?2	1.00000000001735x?2	NUM
ejpam-6763	1058	4	+	+	NUM
ejpam-6763	1058	5	1	1	NUM
ejpam-6763	1058	6	,	,	PUNCT
ejpam-6763	1058	7	0	0	PUNCT
ejpam-6763	1058	8	<	<	X
ejpam-6763	1058	9	x	x	X
ejpam-6763	1058	10	?	?	SYM
ejpam-6763	1058	11	≤	≤	NUM
ejpam-6763	1058	12	1	1	NUM
ejpam-6763	1058	13	table	table	NOUN
ejpam-6763	1058	14	7	7	NUM
ejpam-6763	1058	15	:	:	PUNCT
ejpam-6763	1058	16	compares	compare	VERB
ejpam-6763	1058	17	the	the	DET
ejpam-6763	1058	18	exact	exact	ADJ
ejpam-6763	1058	19	and	and	CCONJ
ejpam-6763	1058	20	approximate	approximate	ADJ
ejpam-6763	1058	21	based	base	VERB
ejpam-6763	1058	22	on	on	ADP
ejpam-6763	1058	23	a	a	DET
ejpam-6763	1058	24	least	least	ADJ
ejpam-6763	1058	25	square	square	ADJ
ejpam-6763	1058	26	error	error	NOUN
ejpam-6763	1058	27	of	of	ADP
ejpam-6763	1058	28	y0(x	y0(x	NUM
ejpam-6763	1058	29	)	)	PUNCT
ejpam-6763	1058	30	for	for	ADP
ejpam-6763	1058	31	example	example	NOUN
ejpam-6763	1058	32	2	2	NUM
ejpam-6763	1058	33	.	.	NUM
ejpam-6763	1059	1	x	x	X
ejpam-6763	1059	2	?	?	PUNCT
ejpam-6763	1060	1	r	r	NOUN
ejpam-6763	1060	2	exact	exact	ADJ
ejpam-6763	1060	3	b{c,3	b{c,3	NOUN
ejpam-6763	1060	4	}	}	PUNCT
ejpam-6763	1060	5	0	0	NUM
ejpam-6763	1060	6	(	(	PUNCT
ejpam-6763	1060	7	x	x	NOUN
ejpam-6763	1060	8	?	?	SYM
ejpam-6763	1061	1	r	r	X
ejpam-6763	1061	2	)	)	PUNCT
ejpam-6763	1061	3	(	(	PUNCT
ejpam-6763	1061	4	nfcbi	nfcbi	NOUN
ejpam-6763	1061	5	)	)	PUNCT
ejpam-6763	1061	6	b{c,3	b{c,3	NOUN
ejpam-6763	1061	7	}	}	PUNCT
ejpam-6763	1061	8	0	0	NUM
ejpam-6763	1062	1	(	(	PUNCT
ejpam-6763	1062	2	x	x	NOUN
ejpam-6763	1062	3	?	?	SYM
ejpam-6763	1062	4	r	r	X
ejpam-6763	1062	5	)	)	PUNCT
ejpam-6763	1062	6	(	(	PUNCT
ejpam-6763	1062	7	fcpcbs	fcpcbs	NOUN
ejpam-6763	1062	8	)	)	PUNCT
ejpam-6763	1062	9	b{c,3	b{c,3	NOUN
ejpam-6763	1062	10	}	}	PUNCT
ejpam-6763	1062	11	0	0	NUM
ejpam-6763	1063	1	(	(	PUNCT
ejpam-6763	1063	2	x	x	NOUN
ejpam-6763	1063	3	?	?	SYM
ejpam-6763	1063	4	r	r	X
ejpam-6763	1063	5	)	)	PUNCT
ejpam-6763	1063	6	(	(	PUNCT
ejpam-6763	1063	7	ffcpcbs	ffcpcbs	X
ejpam-6763	1063	8	)	)	PUNCT
ejpam-6763	1063	9	0	0	NUM
ejpam-6763	1063	10	-1.00	-1.00	NUM
ejpam-6763	1063	11	-1.00	-1.00	PROPN
ejpam-6763	1063	12	-1.00	-1.00	NUM
ejpam-6763	1063	13	-1.00	-1.00	NUM
ejpam-6763	1063	14	1/10	1/10	NUM
ejpam-6763	1063	15	-0.99	-0.99	NUM
ejpam-6763	1063	16	-0.99	-0.99	NOUN
ejpam-6763	1063	17	-0.99	-0.99	INTJ
ejpam-6763	1063	18	-0.99	-0.99	NOUN
ejpam-6763	1063	19	1/5	1/5	NUM
ejpam-6763	1063	20	-0.96	-0.96	NUM
ejpam-6763	1063	21	-0.96	-0.96	NUM
ejpam-6763	1063	22	-0.96	-0.96	NUM
ejpam-6763	1063	23	-0.960000000001	-0.960000000001	NOUN
ejpam-6763	1063	24	3/10	3/10	NUM
ejpam-6763	1063	25	-0.91	-0.91	NOUN
ejpam-6763	1063	26	-0.909999999999	-0.909999999999	NOUN
ejpam-6763	1063	27	-0.910000000000	-0.910000000000	PROPN
ejpam-6763	1063	28	-0.910000000002	-0.910000000002	NOUN
ejpam-6763	1064	1	2/5	2/5	NUM
ejpam-6763	1064	2	-0.84	-0.84	NOUN
ejpam-6763	1064	3	-0.839999999998	-0.839999999998	ADJ
ejpam-6763	1064	4	-0.839999999999	-0.839999999999	NOUN
ejpam-6763	1064	5	-0.840000000004	-0.840000000004	VERB
ejpam-6763	1064	6	1/2	1/2	NUM
ejpam-6763	1064	7	-0.75	-0.75	NUM
ejpam-6763	1064	8	-0.749999999995	-0.749999999995	NOUN
ejpam-6763	1064	9	-0.749999999998	-0.749999999998	PROPN
ejpam-6763	1064	10	-0.750000000008	-0.750000000008	PROPN
ejpam-6763	1065	1	3/5	3/5	NUM
ejpam-6763	1065	2	-0.64	-0.64	NUM
ejpam-6763	1065	3	-0.639999999992	-0.639999999992	ADV
ejpam-6763	1065	4	-0.639999999997	-0.639999999997	PROPN
ejpam-6763	1065	5	-0.640000000014	-0.640000000014	PROPN
ejpam-6763	1066	1	7/10	7/10	NUM
ejpam-6763	1066	2	-0.51	-0.51	NOUN
ejpam-6763	1066	3	-0.509999999986	-0.509999999986	NOUN
ejpam-6763	1066	4	-0.509999999996	-0.509999999996	PROPN
ejpam-6763	1066	5	-0.510000000022	-0.510000000022	PROPN
ejpam-6763	1066	6	4/5	4/5	NUM
ejpam-6763	1066	7	-0.36	-0.36	NUM
ejpam-6763	1066	8	-0.359999999980	-0.359999999980	NOUN
ejpam-6763	1066	9	-0.359999999994	-0.359999999994	PUNCT
ejpam-6763	1066	10	-0.360000000032	-0.360000000032	PROPN
ejpam-6763	1067	1	9/10	9/10	NUM
ejpam-6763	1067	2	-0.19	-0.19	NUM
ejpam-6763	1067	3	-0.189999999972	-0.189999999972	PROPN
ejpam-6763	1067	4	-0.189999999991	-0.189999999991	PROPN
ejpam-6763	1067	5	-0.190000000046	-0.190000000046	PROPN
ejpam-6763	1068	1	1.0	1.0	NUM
ejpam-6763	1068	2	0.00	0.00	NUM
ejpam-6763	1068	3	3.61087481×10−11	3.61087481×10−11	NUM
ejpam-6763	1068	4	1.2000000×10−11	1.2000000×10−11	NUM
ejpam-6763	1068	5	-6.3000000×10−11	-6.3000000×10−11	X
ejpam-6763	1068	6	l.s.e	l.s.e	NOUN
ejpam-6763	1068	7	8.3881×	8.3881×	NUM
ejpam-6763	1068	8	10−11	10−11	NUM
ejpam-6763	1068	9	2.7712×	2.7712×	NUM
ejpam-6763	1068	10	10−21	10−21	NUM
ejpam-6763	1068	11	2.8489×	2.8489×	NOUN
ejpam-6763	1068	12	10−22	10−22	NOUN
ejpam-6763	1068	13	run	run	NOUN
ejpam-6763	1068	14	time	time	NOUN
ejpam-6763	1068	15	(	(	PUNCT
ejpam-6763	1068	16	s	s	NOUN
ejpam-6763	1068	17	)	)	PUNCT
ejpam-6763	1068	18	2.7607	2.7607	NUM
ejpam-6763	1068	19	0.9465	0.9465	NUM
ejpam-6763	1068	20	1.1776	1.1776	NUM
ejpam-6763	1068	21	d.	d.	PROPN
ejpam-6763	1068	22	kh	kh	PROPN
ejpam-6763	1068	23	.	.	PUNCT
ejpam-6763	1069	1	abdullah	abdullah	PROPN
ejpam-6763	1069	2	,	,	PUNCT
ejpam-6763	1069	3	sh	sh	PROPN
ejpam-6763	1069	4	.	.	PROPN
ejpam-6763	1069	5	sh	sh	PROPN
ejpam-6763	1069	6	.	.	PROPN
ejpam-6763	1069	7	ahmed	ahmed	PROPN
ejpam-6763	1069	8	,	,	PUNCT
ejpam-6763	1069	9	k.	k.	PROPN
ejpam-6763	1069	10	h.	h.	PROPN
ejpam-6763	1069	11	f.	f.	PROPN
ejpam-6763	1069	12	jwamer	jwamer	PROPN
ejpam-6763	1069	13	/	/	SYM
ejpam-6763	1069	14	eur	eur	PROPN
ejpam-6763	1069	15	.	.	PUNCT
ejpam-6763	1070	1	j.	j.	PROPN
ejpam-6763	1070	2	pure	pure	PROPN
ejpam-6763	1070	3	appl	appl	PROPN
ejpam-6763	1070	4	.	.	PROPN
ejpam-6763	1070	5	math	math	PROPN
ejpam-6763	1070	6	,	,	PUNCT
ejpam-6763	1070	7	18	18	NUM
ejpam-6763	1070	8	(	(	PUNCT
ejpam-6763	1070	9	4	4	NUM
ejpam-6763	1070	10	)	)	PUNCT
ejpam-6763	1070	11	(	(	PUNCT
ejpam-6763	1070	12	2025	2025	NUM
ejpam-6763	1070	13	)	)	PUNCT
ejpam-6763	1070	14	,	,	PUNCT
ejpam-6763	1070	15	6763	6763	NUM
ejpam-6763	1070	16	31	31	NUM
ejpam-6763	1070	17	of	of	ADP
ejpam-6763	1070	18	40	40	NUM
ejpam-6763	1070	19	table	table	NOUN
ejpam-6763	1070	20	8	8	NUM
ejpam-6763	1070	21	:	:	PUNCT
ejpam-6763	1070	22	compares	compare	VERB
ejpam-6763	1070	23	the	the	DET
ejpam-6763	1070	24	exact	exact	ADJ
ejpam-6763	1070	25	and	and	CCONJ
ejpam-6763	1070	26	approximate	approximate	ADJ
ejpam-6763	1070	27	based	base	VERB
ejpam-6763	1070	28	on	on	ADP
ejpam-6763	1070	29	a	a	DET
ejpam-6763	1070	30	least	least	ADJ
ejpam-6763	1070	31	square	square	ADJ
ejpam-6763	1070	32	error	error	NOUN
ejpam-6763	1070	33	of	of	ADP
ejpam-6763	1070	34	y1(x	y1(x	NOUN
ejpam-6763	1070	35	)	)	PUNCT
ejpam-6763	1070	36	for	for	ADP
ejpam-6763	1070	37	example	example	NOUN
ejpam-6763	1070	38	2	2	NUM
ejpam-6763	1070	39	.	.	NUM
ejpam-6763	1071	1	x	x	X
ejpam-6763	1071	2	?	?	PUNCT
ejpam-6763	1072	1	r	r	NOUN
ejpam-6763	1072	2	exact	exact	ADJ
ejpam-6763	1072	3	b{c,3	b{c,3	NOUN
ejpam-6763	1072	4	}	}	PUNCT
ejpam-6763	1072	5	1	1	NUM
ejpam-6763	1072	6	(	(	PUNCT
ejpam-6763	1072	7	x	x	NOUN
ejpam-6763	1072	8	?	?	SYM
ejpam-6763	1073	1	r	r	X
ejpam-6763	1073	2	)	)	PUNCT
ejpam-6763	1073	3	(	(	PUNCT
ejpam-6763	1073	4	nfcbi	nfcbi	NOUN
ejpam-6763	1073	5	)	)	PUNCT
ejpam-6763	1073	6	b{c,3	b{c,3	NOUN
ejpam-6763	1073	7	}	}	PUNCT
ejpam-6763	1073	8	1	1	NUM
ejpam-6763	1073	9	(	(	PUNCT
ejpam-6763	1073	10	x	x	NOUN
ejpam-6763	1073	11	?	?	SYM
ejpam-6763	1074	1	r	r	X
ejpam-6763	1074	2	)	)	PUNCT
ejpam-6763	1074	3	(	(	PUNCT
ejpam-6763	1074	4	fcpcbs	fcpcbs	NOUN
ejpam-6763	1074	5	)	)	PUNCT
ejpam-6763	1074	6	b{c,3	b{c,3	NOUN
ejpam-6763	1074	7	}	}	PUNCT
ejpam-6763	1074	8	1	1	NUM
ejpam-6763	1074	9	(	(	PUNCT
ejpam-6763	1074	10	x	x	NOUN
ejpam-6763	1074	11	?	?	SYM
ejpam-6763	1075	1	r	r	X
ejpam-6763	1075	2	)	)	PUNCT
ejpam-6763	1075	3	(	(	PUNCT
ejpam-6763	1075	4	ffcpcbs	ffcpcbs	X
ejpam-6763	1075	5	)	)	PUNCT
ejpam-6763	1075	6	0	0	NUM
ejpam-6763	1076	1	1.00	1.00	NUM
ejpam-6763	1076	2	1.00	1.00	NUM
ejpam-6763	1076	3	1.00	1.00	NUM
ejpam-6763	1076	4	1.00	1.00	NUM
ejpam-6763	1076	5	1/10	1/10	NUM
ejpam-6763	1076	6	0.99	0.99	NUM
ejpam-6763	1076	7	0.99	0.99	NUM
ejpam-6763	1076	8	0.99	0.99	NUM
ejpam-6763	1076	9	0.99	0.99	NUM
ejpam-6763	1076	10	1/5	1/5	NUM
ejpam-6763	1076	11	0.96	0.96	NUM
ejpam-6763	1076	12	0.959999999999	0.959999999999	NUM
ejpam-6763	1076	13	0.960000000001	0.960000000001	NUM
ejpam-6763	1076	14	0.96	0.96	NUM
ejpam-6763	1076	15	3/10	3/10	NUM
ejpam-6763	1076	16	0.91	0.91	NUM
ejpam-6763	1076	17	0.909999999998	0.909999999998	NUM
ejpam-6763	1076	18	0.910000000003	0.910000000003	NUM
ejpam-6763	1076	19	0.91	0.91	NUM
ejpam-6763	1076	20	2/5	2/5	NUM
ejpam-6763	1076	21	0.84	0.84	NUM
ejpam-6763	1076	22	0.839999999997	0.839999999997	NUM
ejpam-6763	1076	23	0.840000000008	0.840000000008	NUM
ejpam-6763	1076	24	0.840000000002	0.840000000002	NUM
ejpam-6763	1076	25	1/2	1/2	NUM
ejpam-6763	1076	26	0.75	0.75	NUM
ejpam-6763	1076	27	0.749999999994	0.749999999994	NUM
ejpam-6763	1076	28	0.750000000017	0.750000000017	NUM
ejpam-6763	1076	29	0.750000000004	0.750000000004	NUM
ejpam-6763	1076	30	3/5	3/5	NUM
ejpam-6763	1076	31	0.64	0.64	NUM
ejpam-6763	1076	32	0.639999999991	0.639999999991	NUM
ejpam-6763	1076	33	0.640000000031	0.640000000031	NUM
ejpam-6763	1076	34	0.640000000008	0.640000000008	NUM
ejpam-6763	1076	35	7/10	7/10	NUM
ejpam-6763	1076	36	0.51	0.51	NUM
ejpam-6763	1076	37	0.509999999987	0.509999999987	NUM
ejpam-6763	1076	38	0.510000000051	0.510000000051	NUM
ejpam-6763	1076	39	0.510000000015	0.510000000015	NUM
ejpam-6763	1076	40	4/5	4/5	NUM
ejpam-6763	1076	41	0.36	0.36	NUM
ejpam-6763	1076	42	0.359999999982	0.359999999982	NUM
ejpam-6763	1076	43	0.360000000078	0.360000000078	NUM
ejpam-6763	1076	44	0.360000000023	0.360000000023	NUM
ejpam-6763	1076	45	9/10	9/10	NUM
ejpam-6763	1076	46	0.19	0.19	NUM
ejpam-6763	1076	47	0.189999999977	0.189999999977	NUM
ejpam-6763	1076	48	0.190000000112	0.190000000112	NUM
ejpam-6763	1076	49	0.190000000035	0.190000000035	NUM
ejpam-6763	1076	50	1.0	1.0	NUM
ejpam-6763	1076	51	0.00	0.00	NUM
ejpam-6763	1076	52	-2.8274724×10−11	-2.8274724×10−11	PUNCT
ejpam-6763	1076	53	1.560000×10−10	1.560000×10−10	NUM
ejpam-6763	1076	54	5.000000×10−11	5.000000×10−11	NUM
ejpam-6763	1076	55	l.s.e	l.s.e	NOUN
ejpam-6763	1076	56	2.7712×	2.7712×	NUM
ejpam-6763	1076	57	10−21	10−21	NUM
ejpam-6763	1076	58	1.9151×	1.9151×	NUM
ejpam-6763	1076	59	10−21	10−21	NUM
ejpam-6763	1076	60	4.6922×	4.6922×	NUM
ejpam-6763	1076	61	10−21	10−21	NOUN
ejpam-6763	1076	62	run	run	NOUN
ejpam-6763	1076	63	time	time	NOUN
ejpam-6763	1076	64	(	(	PUNCT
ejpam-6763	1076	65	s	s	NOUN
ejpam-6763	1076	66	)	)	PUNCT
ejpam-6763	1076	67	0.9465	0.9465	NUM
ejpam-6763	1076	68	0.9465	0.9465	NUM
ejpam-6763	1076	69	1.1776	1.1776	NUM
ejpam-6763	1076	70	table	table	NOUN
ejpam-6763	1076	71	9	9	NUM
ejpam-6763	1076	72	:	:	PUNCT
ejpam-6763	1076	73	least	least	ADJ
ejpam-6763	1076	74	square	square	ADJ
ejpam-6763	1076	75	error	error	NOUN
ejpam-6763	1076	76	for	for	ADP
ejpam-6763	1076	77	y0(x	y0(x	NOUN
ejpam-6763	1076	78	)	)	PUNCT
ejpam-6763	1076	79	,	,	PUNCT
ejpam-6763	1076	80	and	and	CCONJ
ejpam-6763	1076	81	y1(x	y1(x	NOUN
ejpam-6763	1076	82	)	)	PUNCT
ejpam-6763	1076	83	,	,	PUNCT
ejpam-6763	1076	84	in	in	ADP
ejpam-6763	1076	85	example	example	NOUN
ejpam-6763	1076	86	2	2	NUM
ejpam-6763	1076	87	using	use	VERB
ejpam-6763	1076	88	different	different	ADJ
ejpam-6763	1076	89	step	step	NOUN
ejpam-6763	1076	90	sizes	size	NOUN
ejpam-6763	1076	91	.	.	PUNCT
ejpam-6763	1077	1	method	method	NOUN
ejpam-6763	1077	2	step	step	NOUN
ejpam-6763	1077	3	size	size	NOUN
ejpam-6763	1077	4	h	h	PROPN
ejpam-6763	1077	5	lse	lse	PROPN
ejpam-6763	1077	6	of	of	ADP
ejpam-6763	1077	7	b{c,3	b{c,3	PROPN
ejpam-6763	1077	8	}	}	PUNCT
ejpam-6763	1077	9	0	0	NUM
ejpam-6763	1078	1	(	(	PUNCT
ejpam-6763	1078	2	x	x	NOUN
ejpam-6763	1078	3	?	?	PUNCT
ejpam-6763	1078	4	)	)	PUNCT
ejpam-6763	1078	5	lse	lse	NOUN
ejpam-6763	1078	6	of	of	ADP
ejpam-6763	1078	7	b{c,3	b{c,3	PROPN
ejpam-6763	1078	8	}	}	PUNCT
ejpam-6763	1078	9	1	1	NUM
ejpam-6763	1078	10	(	(	PUNCT
ejpam-6763	1078	11	x	x	NOUN
ejpam-6763	1078	12	?	?	PUNCT
ejpam-6763	1078	13	)	)	PUNCT
ejpam-6763	1078	14	nfcbi	nfcbi	VERB
ejpam-6763	1078	15	1/10	1/10	NUM
ejpam-6763	1078	16	2.7712×	2.7712×	NUM
ejpam-6763	1078	17	10−21	10−21	NUM
ejpam-6763	1078	18	1.9151×	1.9151×	NUM
ejpam-6763	1078	19	10−21	10−21	NUM
ejpam-6763	1078	20	1/40	1/40	NUM
ejpam-6763	1078	21	2.1379×	2.1379×	NUM
ejpam-6763	1078	22	10−23	10−23	NUM
ejpam-6763	1078	23	2.1333×	2.1333×	NUM
ejpam-6763	1078	24	10−23	10−23	NOUN
ejpam-6763	1078	25	1/80	1/80	NUM
ejpam-6763	1078	26	5.8327×	5.8327×	NUM
ejpam-6763	1078	27	10−25	10−25	NOUN
ejpam-6763	1078	28	1.1559×	1.1559×	NUM
ejpam-6763	1078	29	10−24	10−24	NOUN
ejpam-6763	1078	30	1/100	1/100	NUM
ejpam-6763	1078	31	1.4706×	1.4706×	NUM
ejpam-6763	1078	32	10−25	10−25	NOUN
ejpam-6763	1078	33	1.0112×	1.0112×	NUM
ejpam-6763	1078	34	10−24	10−24	NOUN
ejpam-6763	1078	35	fcpcbs	fcpcbs	ADV
ejpam-6763	1078	36	1/10	1/10	NUM
ejpam-6763	1078	37	2.8489×	2.8489×	NOUN
ejpam-6763	1078	38	10−22	10−22	NUM
ejpam-6763	1078	39	4.6922×	4.6922×	NUM
ejpam-6763	1078	40	10−21	10−21	NUM
ejpam-6763	1078	41	1/40	1/40	NUM
ejpam-6763	1078	42	2.8487×	2.8487×	NUM
ejpam-6763	1078	43	10−24	10−24	NUM
ejpam-6763	1078	44	4.8138×	4.8138×	NOUN
ejpam-6763	1078	45	10−22	10−22	NOUN
ejpam-6763	1078	46	1/80	1/80	NUM
ejpam-6763	1078	47	2.8303×	2.8303×	NUM
ejpam-6763	1078	48	10−28	10−28	NUM
ejpam-6763	1078	49	4.8167×	4.8167×	NUM
ejpam-6763	1079	1	10−26	10−26	NUM
ejpam-6763	1079	2	1/100	1/100	NUM
ejpam-6763	1079	3	2.8490×	2.8490×	NUM
ejpam-6763	1079	4	10−30	10−30	NUM
ejpam-6763	1079	5	2.2284×	2.2284×	NUM
ejpam-6763	1079	6	10−28	10−28	NOUN
ejpam-6763	1079	7	ffcpcbs	ffcpcbs	ADJ
ejpam-6763	1079	8	1/10	1/10	NUM
ejpam-6763	1079	9	7.9664×	7.9664×	NUM
ejpam-6763	1079	10	10−21	10−21	NUM
ejpam-6763	1079	11	4.5745×	4.5745×	NUM
ejpam-6763	1079	12	10−21	10−21	NUM
ejpam-6763	1079	13	1/40	1/40	NUM
ejpam-6763	1079	14	3.7361×	3.7361×	NUM
ejpam-6763	1079	15	10−21	10−21	NUM
ejpam-6763	1079	16	1.7798×	1.7798×	NUM
ejpam-6763	1079	17	10−21	10−21	NUM
ejpam-6763	1079	18	1/80	1/80	NUM
ejpam-6763	1079	19	5.6535×	5.6535×	NUM
ejpam-6763	1079	20	10−23	10−23	NUM
ejpam-6763	1079	21	3.1644×	3.1644×	NUM
ejpam-6763	1079	22	10−23	10−23	NUM
ejpam-6763	1079	23	1/100	1/100	NUM
ejpam-6763	1079	24	3.5825×	3.5825×	NUM
ejpam-6763	1079	25	10−24	10−24	NUM
ejpam-6763	1079	26	7.9086×	7.9086×	NUM
ejpam-6763	1079	27	10−24	10−24	NOUN
ejpam-6763	1079	28	the	the	DET
ejpam-6763	1079	29	plots	plot	NOUN
ejpam-6763	1079	30	of	of	ADP
ejpam-6763	1079	31	the	the	DET
ejpam-6763	1079	32	approximate	approximate	ADJ
ejpam-6763	1079	33	solutions	solution	NOUN
ejpam-6763	1079	34	obtained	obtain	VERB
ejpam-6763	1079	35	by	by	ADP
ejpam-6763	1079	36	nfcbi	nfcbi	NOUN
ejpam-6763	1079	37	,	,	PUNCT
ejpam-6763	1079	38	fcpcbs	fcpcbs	PROPN
ejpam-6763	1079	39	,	,	PUNCT
ejpam-6763	1079	40	and	and	CCONJ
ejpam-6763	1079	41	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	1079	42	for	for	ADP
ejpam-6763	1079	43	y0(x	y0(x	NOUN
ejpam-6763	1079	44	)	)	PUNCT
ejpam-6763	1079	45	and	and	CCONJ
ejpam-6763	1079	46	y1(x	y1(x	NOUN
ejpam-6763	1079	47	)	)	PUNCT
ejpam-6763	1079	48	are	be	AUX
ejpam-6763	1079	49	shown	show	VERB
ejpam-6763	1079	50	in	in	ADP
ejpam-6763	1079	51	figures	figure	NOUN
ejpam-6763	1079	52	7	7	NUM
ejpam-6763	1079	53	,	,	PUNCT
ejpam-6763	1079	54	9	9	NUM
ejpam-6763	1079	55	,	,	PUNCT
ejpam-6763	1079	56	and	and	CCONJ
ejpam-6763	1079	57	11	11	NUM
ejpam-6763	1079	58	,	,	PUNCT
ejpam-6763	1079	59	respectively	respectively	ADV
ejpam-6763	1079	60	,	,	PUNCT
ejpam-6763	1079	61	along	along	ADP
ejpam-6763	1079	62	with	with	ADP
ejpam-6763	1079	63	the	the	DET
ejpam-6763	1079	64	exact	exact	ADJ
ejpam-6763	1079	65	solution	solution	NOUN
ejpam-6763	1079	66	plots	plot	NOUN
ejpam-6763	1079	67	.	.	PUNCT
ejpam-6763	1080	1	the	the	DET
ejpam-6763	1080	2	corresponding	corresponding	ADJ
ejpam-6763	1080	3	least	least	ADJ
ejpam-6763	1080	4	square	square	ADJ
ejpam-6763	1080	5	errors	error	NOUN
ejpam-6763	1080	6	for	for	ADP
ejpam-6763	1080	7	each	each	DET
ejpam-6763	1080	8	iteration	iteration	NOUN
ejpam-6763	1080	9	are	be	AUX
ejpam-6763	1080	10	illustrated	illustrate	VERB
ejpam-6763	1080	11	in	in	ADP
ejpam-6763	1080	12	figures	figure	NOUN
ejpam-6763	1080	13	8	8	NUM
ejpam-6763	1080	14	,	,	PUNCT
ejpam-6763	1080	15	10	10	NUM
ejpam-6763	1080	16	,	,	PUNCT
ejpam-6763	1080	17	and	and	CCONJ
ejpam-6763	1080	18	12	12	NUM
ejpam-6763	1080	19	,	,	PUNCT
ejpam-6763	1080	20	respectively	respectively	ADV
ejpam-6763	1080	21	,	,	PUNCT
ejpam-6763	1080	22	for	for	ADP
ejpam-6763	1080	23	example	example	NOUN
ejpam-6763	1080	24	2	2	X
ejpam-6763	1080	25	.	.	X
ejpam-6763	1080	26	d.	d.	PROPN
ejpam-6763	1080	27	kh	kh	PROPN
ejpam-6763	1080	28	.	.	PUNCT
ejpam-6763	1081	1	abdullah	abdullah	PROPN
ejpam-6763	1081	2	,	,	PUNCT
ejpam-6763	1081	3	sh	sh	PROPN
ejpam-6763	1081	4	.	.	PROPN
ejpam-6763	1081	5	sh	sh	PROPN
ejpam-6763	1081	6	.	.	PROPN
ejpam-6763	1081	7	ahmed	ahmed	PROPN
ejpam-6763	1081	8	,	,	PUNCT
ejpam-6763	1081	9	k.	k.	PROPN
ejpam-6763	1081	10	h.	h.	PROPN
ejpam-6763	1081	11	f.	f.	PROPN
ejpam-6763	1081	12	jwamer	jwamer	PROPN
ejpam-6763	1081	13	/	/	SYM
ejpam-6763	1081	14	eur	eur	PROPN
ejpam-6763	1081	15	.	.	PUNCT
ejpam-6763	1082	1	j.	j.	PROPN
ejpam-6763	1082	2	pure	pure	PROPN
ejpam-6763	1082	3	appl	appl	PROPN
ejpam-6763	1082	4	.	.	PROPN
ejpam-6763	1082	5	math	math	PROPN
ejpam-6763	1082	6	,	,	PUNCT
ejpam-6763	1082	7	18	18	NUM
ejpam-6763	1082	8	(	(	PUNCT
ejpam-6763	1082	9	4	4	NUM
ejpam-6763	1082	10	)	)	PUNCT
ejpam-6763	1082	11	(	(	PUNCT
ejpam-6763	1082	12	2025	2025	NUM
ejpam-6763	1082	13	)	)	PUNCT
ejpam-6763	1082	14	,	,	PUNCT
ejpam-6763	1082	15	6763	6763	NUM
ejpam-6763	1082	16	32	32	NUM
ejpam-6763	1082	17	of	of	ADP
ejpam-6763	1082	18	40	40	NUM
ejpam-6763	1082	19	figure	figure	NOUN
ejpam-6763	1082	20	7	7	NUM
ejpam-6763	1082	21	:	:	PUNCT
ejpam-6763	1082	22	approximation	approximation	NOUN
ejpam-6763	1082	23	solution	solution	NOUN
ejpam-6763	1082	24	of	of	ADP
ejpam-6763	1082	25	y0(x	y0(x	NUM
ejpam-6763	1082	26	)	)	PUNCT
ejpam-6763	1082	27	and	and	CCONJ
ejpam-6763	1082	28	y1(x	y1(x	NOUN
ejpam-6763	1082	29	)	)	PUNCT
ejpam-6763	1082	30	method	method	NOUN
ejpam-6763	1082	31	nfcbi	nfcbi	VERB
ejpam-6763	1082	32	for	for	ADP
ejpam-6763	1082	33	example	example	NOUN
ejpam-6763	1082	34	2	2	NUM
ejpam-6763	1082	35	.	.	X
ejpam-6763	1082	36	figure	figure	VERB
ejpam-6763	1082	37	8	8	NUM
ejpam-6763	1082	38	:	:	PUNCT
ejpam-6763	1082	39	least	least	ADJ
ejpam-6763	1082	40	square	square	ADJ
ejpam-6763	1082	41	error	error	NOUN
ejpam-6763	1082	42	plot	plot	NOUN
ejpam-6763	1082	43	of	of	ADP
ejpam-6763	1082	44	y0(x	y0(x	NOUN
ejpam-6763	1082	45	)	)	PUNCT
ejpam-6763	1082	46	and	and	CCONJ
ejpam-6763	1082	47	y1(x	y1(x	NOUN
ejpam-6763	1082	48	)	)	PUNCT
ejpam-6763	1082	49	method	method	NOUN
ejpam-6763	1082	50	nfcbi	nfcbi	VERB
ejpam-6763	1082	51	for	for	ADP
ejpam-6763	1082	52	example	example	NOUN
ejpam-6763	1082	53	2	2	NUM
ejpam-6763	1082	54	.	.	X
ejpam-6763	1082	55	figure	figure	VERB
ejpam-6763	1082	56	9	9	NUM
ejpam-6763	1082	57	:	:	PUNCT
ejpam-6763	1082	58	approximation	approximation	NOUN
ejpam-6763	1082	59	solution	solution	NOUN
ejpam-6763	1082	60	of	of	ADP
ejpam-6763	1082	61	y0(x	y0(x	NUM
ejpam-6763	1082	62	)	)	PUNCT
ejpam-6763	1082	63	and	and	CCONJ
ejpam-6763	1082	64	y1(x	y1(x	NOUN
ejpam-6763	1082	65	)	)	PUNCT
ejpam-6763	1082	66	method	method	NOUN
ejpam-6763	1082	67	fcpcbs	fcpcbs	NOUN
ejpam-6763	1082	68	for	for	ADP
ejpam-6763	1082	69	example	example	NOUN
ejpam-6763	1082	70	2	2	NUM
ejpam-6763	1082	71	.	.	X
ejpam-6763	1082	72	figure	figure	NOUN
ejpam-6763	1082	73	10	10	NUM
ejpam-6763	1082	74	:	:	PUNCT
ejpam-6763	1082	75	least	least	ADJ
ejpam-6763	1082	76	square	square	ADJ
ejpam-6763	1082	77	error	error	NOUN
ejpam-6763	1082	78	plot	plot	NOUN
ejpam-6763	1082	79	of	of	ADP
ejpam-6763	1082	80	y0(x	y0(x	NOUN
ejpam-6763	1082	81	)	)	PUNCT
ejpam-6763	1082	82	and	and	CCONJ
ejpam-6763	1082	83	y1(x	y1(x	NOUN
ejpam-6763	1082	84	)	)	PUNCT
ejpam-6763	1082	85	method	method	NOUN
ejpam-6763	1082	86	fcpcbsfor	fcpcbsfor	ADP
ejpam-6763	1082	87	example	example	NOUN
ejpam-6763	1082	88	6.2	6.2	NUM
ejpam-6763	1082	89	.	.	PUNCT
ejpam-6763	1083	1	figure	figure	VERB
ejpam-6763	1083	2	11	11	NUM
ejpam-6763	1083	3	:	:	PUNCT
ejpam-6763	1083	4	approximation	approximation	NOUN
ejpam-6763	1083	5	solution	solution	NOUN
ejpam-6763	1083	6	of	of	ADP
ejpam-6763	1083	7	y0(x	y0(x	NUM
ejpam-6763	1083	8	)	)	PUNCT
ejpam-6763	1083	9	and	and	CCONJ
ejpam-6763	1083	10	y1(x	y1(x	NOUN
ejpam-6763	1083	11	)	)	PUNCT
ejpam-6763	1083	12	method	method	NOUN
ejpam-6763	1083	13	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1083	14	for	for	ADP
ejpam-6763	1083	15	example	example	NOUN
ejpam-6763	1083	16	2	2	NUM
ejpam-6763	1083	17	.	.	X
ejpam-6763	1083	18	figure	figure	NOUN
ejpam-6763	1083	19	12	12	NUM
ejpam-6763	1083	20	:	:	PUNCT
ejpam-6763	1083	21	least	least	ADJ
ejpam-6763	1083	22	square	square	ADJ
ejpam-6763	1083	23	error	error	NOUN
ejpam-6763	1083	24	plot	plot	NOUN
ejpam-6763	1083	25	of	of	ADP
ejpam-6763	1083	26	y0(x	y0(x	NOUN
ejpam-6763	1083	27	)	)	PUNCT
ejpam-6763	1083	28	and	and	CCONJ
ejpam-6763	1083	29	y1(x	y1(x	NOUN
ejpam-6763	1083	30	)	)	PUNCT
ejpam-6763	1083	31	method	method	NOUN
ejpam-6763	1083	32	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1083	33	for	for	ADP
ejpam-6763	1083	34	example	example	NOUN
ejpam-6763	1084	1	2	2	X
ejpam-6763	1084	2	.	.	X
ejpam-6763	1084	3	d.	d.	PROPN
ejpam-6763	1084	4	kh	kh	PROPN
ejpam-6763	1084	5	.	.	PUNCT
ejpam-6763	1085	1	abdullah	abdullah	PROPN
ejpam-6763	1085	2	,	,	PUNCT
ejpam-6763	1085	3	sh	sh	PROPN
ejpam-6763	1085	4	.	.	PROPN
ejpam-6763	1085	5	sh	sh	PROPN
ejpam-6763	1085	6	.	.	PROPN
ejpam-6763	1085	7	ahmed	ahmed	PROPN
ejpam-6763	1085	8	,	,	PUNCT
ejpam-6763	1085	9	k.	k.	PROPN
ejpam-6763	1085	10	h.	h.	PROPN
ejpam-6763	1085	11	f.	f.	PROPN
ejpam-6763	1085	12	jwamer	jwamer	PROPN
ejpam-6763	1085	13	/	/	SYM
ejpam-6763	1085	14	eur	eur	PROPN
ejpam-6763	1085	15	.	.	PUNCT
ejpam-6763	1086	1	j.	j.	PROPN
ejpam-6763	1086	2	pure	pure	PROPN
ejpam-6763	1086	3	appl	appl	PROPN
ejpam-6763	1086	4	.	.	PROPN
ejpam-6763	1086	5	math	math	PROPN
ejpam-6763	1086	6	,	,	PUNCT
ejpam-6763	1086	7	18	18	NUM
ejpam-6763	1086	8	(	(	PUNCT
ejpam-6763	1086	9	4	4	NUM
ejpam-6763	1086	10	)	)	PUNCT
ejpam-6763	1086	11	(	(	PUNCT
ejpam-6763	1086	12	2025	2025	NUM
ejpam-6763	1086	13	)	)	PUNCT
ejpam-6763	1086	14	,	,	PUNCT
ejpam-6763	1086	15	6763	6763	NUM
ejpam-6763	1086	16	33	33	NUM
ejpam-6763	1086	17	of	of	ADP
ejpam-6763	1086	18	40	40	NUM
ejpam-6763	1086	19	table	table	NOUN
ejpam-6763	1086	20	10	10	NUM
ejpam-6763	1086	21	:	:	PUNCT
ejpam-6763	1086	22	the	the	DET
ejpam-6763	1086	23	values	value	NOUN
ejpam-6763	1086	24	of	of	ADP
ejpam-6763	1086	25	control	control	NOUN
ejpam-6763	1086	26	points	point	NOUN
ejpam-6763	1086	27	of	of	ADP
ejpam-6763	1086	28	b{c,3	b{c,3	NOUN
ejpam-6763	1086	29	}	}	PUNCT
ejpam-6763	1086	30	0	0	NUM
ejpam-6763	1087	1	(	(	PUNCT
ejpam-6763	1087	2	x	x	X
ejpam-6763	1087	3	?	?	PUNCT
ejpam-6763	1087	4	r+1	r+1	NOUN
ejpam-6763	1087	5	)	)	PUNCT
ejpam-6763	1087	6	and	and	CCONJ
ejpam-6763	1087	7	b{c,3	b{c,3	NOUN
ejpam-6763	1087	8	}	}	PUNCT
ejpam-6763	1087	9	1	1	NUM
ejpam-6763	1087	10	(	(	PUNCT
ejpam-6763	1087	11	x	x	NOUN
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ejpam-6763	1089	4	r+1	r+1	NOUN
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ejpam-6763	1089	11	(	(	PUNCT
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ejpam-6763	1089	13	?	?	PUNCT
ejpam-6763	1090	1	r+1	r+1	NOUN
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ejpam-6763	1090	9	=	=	SYM
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ejpam-6763	1095	12	2.000000000271051181	2.000000000271051181	NUM
ejpam-6763	1095	13	ϑ20	ϑ20	NOUN
ejpam-6763	1095	14	=	=	SYM
ejpam-6763	1095	15	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	16	ϑ21	ϑ21	NOUN
ejpam-6763	1095	17	=	=	SYM
ejpam-6763	1095	18	1.666666666666666666	1.666666666666666666	NUM
ejpam-6763	1095	19	ϑ22	ϑ22	NOUN
ejpam-6763	1095	20	=	=	SYM
ejpam-6763	1095	21	2.333333333333333335	2.333333333333333335	NUM
ejpam-6763	1095	22	ϑ23	ϑ23	NOUN
ejpam-6763	1095	23	=	=	SYM
ejpam-6763	1095	24	2.999999999999969358	2.999999999999969358	NUM
ejpam-6763	1095	25	]	]	SYM
ejpam-6763	1095	26	0.9	0.9	NUM
ejpam-6763	1095	27	,	,	PUNCT
ejpam-6763	1095	28	1.0	1.0	NUM
ejpam-6763	1095	29	]	]	PUNCT
ejpam-6763	1095	30	ϑ00	ϑ00	PROPN
ejpam-6763	1095	31	=	=	SYM
ejpam-6763	1095	32	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	33	ϑ01	ϑ01	NOUN
ejpam-6763	1095	34	=	=	SYM
ejpam-6763	1095	35	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	36	ϑ02	ϑ02	NOUN
ejpam-6763	1095	37	=	=	SYM
ejpam-6763	1095	38	1.000000000478453520	1.000000000478453520	NUM
ejpam-6763	1095	39	ϑ03	ϑ03	NOUN
ejpam-6763	1095	40	=	=	SYM
ejpam-6763	1095	41	2.000000000376601861	2.000000000376601861	NUM
ejpam-6763	1095	42	ϑ20	ϑ20	NOUN
ejpam-6763	1095	43	=	=	SYM
ejpam-6763	1095	44	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	45	ϑ21	ϑ21	NOUN
ejpam-6763	1095	46	=	=	SYM
ejpam-6763	1095	47	1.666666666666666666	1.666666666666666666	NUM
ejpam-6763	1095	48	ϑ22	ϑ22	NOUN
ejpam-6763	1095	49	=	=	SYM
ejpam-6763	1095	50	2.333333333333333335	2.333333333333333335	NUM
ejpam-6763	1095	51	ϑ23	ϑ23	NOUN
ejpam-6763	1095	52	=	=	PROPN
ejpam-6763	1095	53	2.999999999999964917	2.999999999999964917	NUM
ejpam-6763	1095	54	fcpcbs	fcpcbs	NOUN
ejpam-6763	1095	55	]	]	X
ejpam-6763	1095	56	0.0	0.0	NUM
ejpam-6763	1095	57	,	,	PUNCT
ejpam-6763	1095	58	1.0	1.0	NUM
ejpam-6763	1095	59	]	]	PUNCT
ejpam-6763	1095	60	ϑ00	ϑ00	PROPN
ejpam-6763	1095	61	=	=	SYM
ejpam-6763	1095	62	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	63	ϑ01	ϑ01	NOUN
ejpam-6763	1095	64	=	=	SYM
ejpam-6763	1095	65	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	66	ϑ02	ϑ02	NOUN
ejpam-6763	1095	67	=	=	SYM
ejpam-6763	1095	68	1.000000000478453520	1.000000000478453520	NUM
ejpam-6763	1095	69	ϑ03	ϑ03	NOUN
ejpam-6763	1095	70	=	=	SYM
ejpam-6763	1095	71	1.999999991827737578	1.999999991827737578	NUM
ejpam-6763	1095	72	ϑ20	ϑ20	NOUN
ejpam-6763	1095	73	=	=	SYM
ejpam-6763	1095	74	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	75	ϑ21	ϑ21	NOUN
ejpam-6763	1095	76	=	=	SYM
ejpam-6763	1095	77	1.666666666666666666	1.666666666666666666	NUM
ejpam-6763	1095	78	ϑ22	ϑ22	NOUN
ejpam-6763	1095	79	=	=	SYM
ejpam-6763	1095	80	2.333333333333333335	2.333333333333333335	NUM
ejpam-6763	1095	81	ϑ23	ϑ23	NOUN
ejpam-6763	1095	82	=	=	NUM
ejpam-6763	1095	83	2.999999999999988454	2.999999999999988454	NUM
ejpam-6763	1095	84	ffcpcbs	ffcpcbs	X
ejpam-6763	1095	85	]	]	X
ejpam-6763	1095	86	0.0	0.0	NUM
ejpam-6763	1095	87	,	,	PUNCT
ejpam-6763	1095	88	1.0	1.0	NUM
ejpam-6763	1095	89	]	]	PUNCT
ejpam-6763	1095	90	ϑ00	ϑ00	PROPN
ejpam-6763	1095	91	=	=	SYM
ejpam-6763	1095	92	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	93	ϑ01	ϑ01	NOUN
ejpam-6763	1095	94	=	=	SYM
ejpam-6763	1095	95	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	96	ϑ02	ϑ02	NOUN
ejpam-6763	1095	97	=	=	SYM
ejpam-6763	1095	98	1.000000000478453520	1.000000000478453520	NUM
ejpam-6763	1095	99	ϑ03	ϑ03	NOUN
ejpam-6763	1095	100	=	=	NOUN
ejpam-6763	1095	101	1.999999996102169719	1.999999996102169719	NUM
ejpam-6763	1095	102	ϑ20	ϑ20	NOUN
ejpam-6763	1095	103	=	=	SYM
ejpam-6763	1095	104	1.000000000000000000	1.000000000000000000	NUM
ejpam-6763	1095	105	ϑ21	ϑ21	NOUN
ejpam-6763	1095	106	=	=	SYM
ejpam-6763	1095	107	1.666666666666666666	1.666666666666666666	NUM
ejpam-6763	1095	108	ϑ22	ϑ22	NOUN
ejpam-6763	1095	109	=	=	SYM
ejpam-6763	1095	110	2.333333333333333335	2.333333333333333335	NUM
ejpam-6763	1095	111	ϑ23	ϑ23	NOUN
ejpam-6763	1095	112	=	=	NUM
ejpam-6763	1095	113	2.999999999999976907	2.999999999999976907	NUM
ejpam-6763	1095	114	from	from	ADP
ejpam-6763	1095	115	(	(	PUNCT
ejpam-6763	1095	116	21	21	NUM
ejpam-6763	1095	117	)	)	PUNCT
ejpam-6763	1095	118	,	,	PUNCT
ejpam-6763	1095	119	we	we	PRON
ejpam-6763	1095	120	obtain	obtain	VERB
ejpam-6763	1095	121	the	the	DET
ejpam-6763	1095	122	approximate	approximate	ADJ
ejpam-6763	1095	123	solution	solution	NOUN
ejpam-6763	1095	124	for	for	ADP
ejpam-6763	1095	125	the	the	DET
ejpam-6763	1095	126	classical	classical	ADJ
ejpam-6763	1095	127	and	and	CCONJ
ejpam-6763	1095	128	fractional	fractional	ADJ
ejpam-6763	1095	129	order	order	NOUN
ejpam-6763	1095	130	linear	linear	NOUN
ejpam-6763	1095	131	system	system	NOUN
ejpam-6763	1095	132	of	of	ADP
ejpam-6763	1095	133	volterra	volterra	PROPN
ejpam-6763	1095	134	integro	integro	PROPN
ejpam-6763	1095	135	-	-	PUNCT
ejpam-6763	1095	136	differential	differential	NOUN
ejpam-6763	1095	137	equations	equation	NOUN
ejpam-6763	1095	138	(	(	PUNCT
ejpam-6763	1095	139	svides	svide	NOUN
ejpam-6763	1095	140	-	-	PUNCT
ejpam-6763	1095	141	cf	cf	NOUN
ejpam-6763	1095	142	)	)	PUNCT
ejpam-6763	1095	143	with	with	ADP
ejpam-6763	1095	144	variable	variable	ADJ
ejpam-6763	1095	145	coefficients	coefficient	NOUN
ejpam-6763	1095	146	,	,	PUNCT
ejpam-6763	1095	147	for	for	ADP
ejpam-6763	1095	148	example	example	NOUN
ejpam-6763	1095	149	3	3	NUM
ejpam-6763	1095	150	,	,	PUNCT
ejpam-6763	1095	151	as	as	SCONJ
ejpam-6763	1095	152	shown	show	VERB
ejpam-6763	1095	153	below	below	ADP
ejpam-6763	1095	154	:	:	PUNCT
ejpam-6763	1095	155	b{c,3	b{c,3	NOUN
ejpam-6763	1095	156	}	}	PUNCT
ejpam-6763	1095	157	0	0	NUM
ejpam-6763	1096	1	(	(	PUNCT
ejpam-6763	1096	2	x	x	NOUN
ejpam-6763	1096	3	?	?	PUNCT
ejpam-6763	1096	4	)	)	PUNCT
ejpam-6763	1096	5	(	(	PUNCT
ejpam-6763	1096	6	nfcbi	nfcbi	NOUN
ejpam-6763	1096	7	)	)	PUNCT
ejpam-6763	1096	8	=	=	PUNCT
ejpam-6763	1096	9			X
ejpam-6763	1096	10	0.999999990392377x?3	0.999999990392377x?3	PUNCT
ejpam-6763	1097	1	+	+	CCONJ
ejpam-6763	1097	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1097	3	10−9	10−9	NUM
ejpam-6763	1097	4	x?2	x?2	PROPN
ejpam-6763	1098	1	+	+	CCONJ
ejpam-6763	1098	2	1	1	NUM
ejpam-6763	1098	3	,	,	PUNCT
ejpam-6763	1098	4	0	0	PUNCT
ejpam-6763	1098	5	<	<	X
ejpam-6763	1098	6	x	x	X
ejpam-6763	1098	7	?	?	PUNCT
ejpam-6763	1098	8	≤	≤	NUM
ejpam-6763	1098	9	1	1	NUM
ejpam-6763	1098	10	10	10	NUM
ejpam-6763	1098	11	0.999999995158451x?3	0.999999995158451x?3	NUM
ejpam-6763	1099	1	+	+	CCONJ
ejpam-6763	1099	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1099	3	10−9	10−9	NUM
ejpam-6763	1099	4	x?2	x?2	PROPN
ejpam-6763	1099	5	+	+	CCONJ
ejpam-6763	1099	6	1	1	NUM
ejpam-6763	1099	7	,	,	PUNCT
ejpam-6763	1099	8	1	1	NUM
ejpam-6763	1099	9	10	10	NUM
ejpam-6763	1099	10	<	<	X
ejpam-6763	1099	11	x	x	X
ejpam-6763	1099	12	?	?	PUNCT
ejpam-6763	1099	13	≤	≤	NUM
ejpam-6763	1099	14	1	1	NUM
ejpam-6763	1099	15	5	5	NUM
ejpam-6763	1099	16	0.999999996740016x?3	0.999999996740016x?3	NOUN
ejpam-6763	1099	17	+	+	CCONJ
ejpam-6763	1099	18	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1099	19	10−9	10−9	NUM
ejpam-6763	1099	20	x?2	x?2	PROPN
ejpam-6763	1100	1	+	+	CCONJ
ejpam-6763	1100	2	1	1	NUM
ejpam-6763	1100	3	,	,	PUNCT
ejpam-6763	1100	4	1	1	NUM
ejpam-6763	1100	5	5	5	NUM
ejpam-6763	1100	6	<	<	X
ejpam-6763	1100	7	x	x	X
ejpam-6763	1100	8	?	?	PUNCT
ejpam-6763	1100	9	≤	≤	NUM
ejpam-6763	1100	10	3	3	NUM
ejpam-6763	1100	11	10	10	NUM
ejpam-6763	1100	12	0.999999997527520x?3	0.999999997527520x?3	NOUN
ejpam-6763	1100	13	+	+	CCONJ
ejpam-6763	1100	14	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1100	15	10−9	10−9	NUM
ejpam-6763	1100	16	x?2	x?2	PROPN
ejpam-6763	1100	17	+	+	CCONJ
ejpam-6763	1100	18	1	1	NUM
ejpam-6763	1100	19	,	,	PUNCT
ejpam-6763	1100	20	3	3	NUM
ejpam-6763	1100	21	10	10	NUM
ejpam-6763	1100	22	<	<	X
ejpam-6763	1100	23	x	x	X
ejpam-6763	1100	24	?	?	PUNCT
ejpam-6763	1100	25	≤	≤	NUM
ejpam-6763	1101	1	2	2	NUM
ejpam-6763	1101	2	5	5	NUM
ejpam-6763	1101	3	0.999999997998566x?3	0.999999997998566x?3	NUM
ejpam-6763	1101	4	+	+	NUM
ejpam-6763	1101	5	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1101	6	10−9	10−9	NUM
ejpam-6763	1101	7	x?2	x?2	PROPN
ejpam-6763	1101	8	+	+	CCONJ
ejpam-6763	1101	9	1	1	NUM
ejpam-6763	1101	10	,	,	PUNCT
ejpam-6763	1101	11	2	2	NUM
ejpam-6763	1101	12	5	5	NUM
ejpam-6763	1101	13	<	<	X
ejpam-6763	1101	14	x	x	X
ejpam-6763	1101	15	?	?	PUNCT
ejpam-6763	1101	16	≤	≤	NUM
ejpam-6763	1102	1	1	1	NUM
ejpam-6763	1102	2	2	2	NUM
ejpam-6763	1102	3	0.999999998312103x?3	0.999999998312103x?3	NUM
ejpam-6763	1102	4	+	+	CCONJ
ejpam-6763	1102	5	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1102	6	10−9	10−9	NUM
ejpam-6763	1102	7	x?2	x?2	PROPN
ejpam-6763	1103	1	+	+	CCONJ
ejpam-6763	1104	1	1	1	NUM
ejpam-6763	1104	2	,	,	PUNCT
ejpam-6763	1104	3	1	1	NUM
ejpam-6763	1104	4	2	2	NUM
ejpam-6763	1104	5	<	<	X
ejpam-6763	1104	6	x	x	X
ejpam-6763	1104	7	?	?	PUNCT
ejpam-6763	1104	8	≤	≤	NUM
ejpam-6763	1105	1	3	3	NUM
ejpam-6763	1105	2	5	5	NUM
ejpam-6763	1105	3	0.999999998536081x?3	0.999999998536081x?3	NOUN
ejpam-6763	1105	4	+	+	CCONJ
ejpam-6763	1105	5	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1105	6	10−9	10−9	NUM
ejpam-6763	1105	7	x?2	x?2	PROPN
ejpam-6763	1106	1	+	+	CCONJ
ejpam-6763	1106	2	1	1	NUM
ejpam-6763	1106	3	,	,	PUNCT
ejpam-6763	1106	4	3	3	NUM
ejpam-6763	1106	5	5	5	NUM
ejpam-6763	1106	6	<	<	X
ejpam-6763	1106	7	x	x	X
ejpam-6763	1106	8	?	?	PUNCT
ejpam-6763	1106	9	≤	≤	NUM
ejpam-6763	1106	10	7	7	NUM
ejpam-6763	1106	11	10	10	NUM
ejpam-6763	1106	12	0.999999998704366x?3	0.999999998704366x?3	NOUN
ejpam-6763	1106	13	+	+	CCONJ
ejpam-6763	1106	14	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1106	15	10−9	10−9	NUM
ejpam-6763	1106	16	x?2	x?2	PROPN
ejpam-6763	1107	1	+	+	CCONJ
ejpam-6763	1107	2	1	1	NUM
ejpam-6763	1107	3	,	,	PUNCT
ejpam-6763	1107	4	7	7	NUM
ejpam-6763	1107	5	10	10	NUM
ejpam-6763	1107	6	<	<	X
ejpam-6763	1107	7	x	x	X
ejpam-6763	1107	8	?	?	PUNCT
ejpam-6763	1107	9	≤	≤	NUM
ejpam-6763	1107	10	4	4	NUM
ejpam-6763	1107	11	5	5	NUM
ejpam-6763	1107	12	0.999999998835690x?3	0.999999998835690x?3	NOUN
ejpam-6763	1108	1	+	+	CCONJ
ejpam-6763	1108	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1108	3	10−9	10−9	NUM
ejpam-6763	1108	4	x?2	x?2	PROPN
ejpam-6763	1108	5	+	+	CCONJ
ejpam-6763	1108	6	1	1	NUM
ejpam-6763	1108	7	,	,	PUNCT
ejpam-6763	1108	8	4	4	NUM
ejpam-6763	1108	9	5	5	NUM
ejpam-6763	1108	10	<	<	X
ejpam-6763	1108	11	x	x	X
ejpam-6763	1108	12	?	?	PUNCT
ejpam-6763	1108	13	≤	≤	NUM
ejpam-6763	1108	14	9	9	NUM
ejpam-6763	1108	15	10	10	NUM
ejpam-6763	1108	16	0.999999998941242x?3	0.999999998941242x?3	NOUN
ejpam-6763	1109	1	+	+	CCONJ
ejpam-6763	1109	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1109	3	10−9	10−9	NUM
ejpam-6763	1109	4	x?2	x?2	PROPN
ejpam-6763	1109	5	+	+	CCONJ
ejpam-6763	1109	6	1	1	NUM
ejpam-6763	1109	7	,	,	PUNCT
ejpam-6763	1109	8	9	9	NUM
ejpam-6763	1109	9	10	10	NUM
ejpam-6763	1109	10	<	<	X
ejpam-6763	1109	11	x	x	X
ejpam-6763	1109	12	?	?	PUNCT
ejpam-6763	1109	13	≤	≤	NUM
ejpam-6763	1109	14	1	1	NUM
ejpam-6763	1109	15	d.	d.	PROPN
ejpam-6763	1109	16	kh	kh	PROPN
ejpam-6763	1109	17	.	.	PUNCT
ejpam-6763	1110	1	abdullah	abdullah	PROPN
ejpam-6763	1110	2	,	,	PUNCT
ejpam-6763	1110	3	sh	sh	PROPN
ejpam-6763	1110	4	.	.	PROPN
ejpam-6763	1110	5	sh	sh	PROPN
ejpam-6763	1110	6	.	.	PROPN
ejpam-6763	1110	7	ahmed	ahmed	PROPN
ejpam-6763	1110	8	,	,	PUNCT
ejpam-6763	1110	9	k.	k.	PROPN
ejpam-6763	1110	10	h.	h.	PROPN
ejpam-6763	1110	11	f.	f.	PROPN
ejpam-6763	1110	12	jwamer	jwamer	PROPN
ejpam-6763	1110	13	/	/	SYM
ejpam-6763	1110	14	eur	eur	PROPN
ejpam-6763	1110	15	.	.	PUNCT
ejpam-6763	1111	1	j.	j.	PROPN
ejpam-6763	1111	2	pure	pure	PROPN
ejpam-6763	1111	3	appl	appl	PROPN
ejpam-6763	1111	4	.	.	PROPN
ejpam-6763	1111	5	math	math	PROPN
ejpam-6763	1111	6	,	,	PUNCT
ejpam-6763	1111	7	18	18	NUM
ejpam-6763	1111	8	(	(	PUNCT
ejpam-6763	1111	9	4	4	NUM
ejpam-6763	1111	10	)	)	PUNCT
ejpam-6763	1111	11	(	(	PUNCT
ejpam-6763	1111	12	2025	2025	NUM
ejpam-6763	1111	13	)	)	PUNCT
ejpam-6763	1111	14	,	,	PUNCT
ejpam-6763	1111	15	6763	6763	NUM
ejpam-6763	1111	16	35	35	NUM
ejpam-6763	1111	17	of	of	ADP
ejpam-6763	1111	18	40	40	NUM
ejpam-6763	1111	19	b{c,3	b{c,3	NOUN
ejpam-6763	1111	20	}	}	PUNCT
ejpam-6763	1111	21	1	1	NUM
ejpam-6763	1111	22	(	(	PUNCT
ejpam-6763	1111	23	x	x	NOUN
ejpam-6763	1111	24	?	?	PUNCT
ejpam-6763	1111	25	)	)	PUNCT
ejpam-6763	1111	26	(	(	PUNCT
ejpam-6763	1111	27	nfcbi	nfcbi	NOUN
ejpam-6763	1111	28	)	)	PUNCT
ejpam-6763	1111	29	=	=	SYM
ejpam-6763	1111	30			X
ejpam-6763	1111	31	−1.15463194561016×	−1.15463194561016×	X
ejpam-6763	1111	32	10−14	10−14	NUM
ejpam-6763	1111	33	x?3	x?3	NOUN
ejpam-6763	1111	34	+	+	PUNCT
ejpam-6763	1111	35	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1111	36	?	?	PUNCT
ejpam-6763	1112	1	+	+	CCONJ
ejpam-6763	1112	2	1	1	NUM
ejpam-6763	1112	3	,	,	PUNCT
ejpam-6763	1112	4	0	0	PUNCT
ejpam-6763	1112	5	<	<	X
ejpam-6763	1112	6	x	x	X
ejpam-6763	1112	7	?	?	PUNCT
ejpam-6763	1112	8	≤	≤	NUM
ejpam-6763	1112	9	1	1	NUM
ejpam-6763	1112	10	10	10	NUM
ejpam-6763	1112	11	−7.99360577730113×	−7.99360577730113×	NUM
ejpam-6763	1112	12	10−15	10−15	PROPN
ejpam-6763	1112	13	x?3	x?3	NOUN
ejpam-6763	1112	14	+	+	PUNCT
ejpam-6763	1112	15	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1112	16	?	?	PUNCT
ejpam-6763	1113	1	+	+	CCONJ
ejpam-6763	1113	2	1	1	NUM
ejpam-6763	1113	3	,	,	PUNCT
ejpam-6763	1113	4	1	1	NUM
ejpam-6763	1113	5	10	10	NUM
ejpam-6763	1113	6	<	<	X
ejpam-6763	1113	7	x	x	X
ejpam-6763	1113	8	?	?	PUNCT
ejpam-6763	1113	9	≤	≤	NUM
ejpam-6763	1113	10	1	1	NUM
ejpam-6763	1113	11	5	5	NUM
ejpam-6763	1113	12	−5.32907051820075×	−5.32907051820075×	NUM
ejpam-6763	1113	13	10−15	10−15	NUM
ejpam-6763	1113	14	x?3	x?3	NOUN
ejpam-6763	1113	15	+	+	PUNCT
ejpam-6763	1113	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1113	17	?	?	PUNCT
ejpam-6763	1114	1	+	+	CCONJ
ejpam-6763	1115	1	1	1	NUM
ejpam-6763	1115	2	,	,	PUNCT
ejpam-6763	1115	3	1	1	NUM
ejpam-6763	1115	4	5	5	NUM
ejpam-6763	1115	5	<	<	X
ejpam-6763	1115	6	x	x	X
ejpam-6763	1115	7	?	?	PUNCT
ejpam-6763	1115	8	≤	≤	NUM
ejpam-6763	1115	9	3	3	NUM
ejpam-6763	1115	10	10	10	NUM
ejpam-6763	1115	11	−5.32907051820075×	−5.32907051820075×	NOUN
ejpam-6763	1115	12	10−15	10−15	NUM
ejpam-6763	1115	13	x?3	x?3	NOUN
ejpam-6763	1115	14	+	+	PUNCT
ejpam-6763	1115	15	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1115	16	?	?	PUNCT
ejpam-6763	1116	1	+	+	CCONJ
ejpam-6763	1116	2	1	1	NUM
ejpam-6763	1116	3	,	,	PUNCT
ejpam-6763	1116	4	3	3	NUM
ejpam-6763	1116	5	10	10	NUM
ejpam-6763	1116	6	<	<	X
ejpam-6763	1116	7	x	x	X
ejpam-6763	1116	8	?	?	PUNCT
ejpam-6763	1116	9	≤	≤	NUM
ejpam-6763	1116	10	2	2	NUM
ejpam-6763	1116	11	5	5	NUM
ejpam-6763	1116	12	−1.06581410364015×	−1.06581410364015×	NOUN
ejpam-6763	1116	13	10−14	10−14	NUM
ejpam-6763	1116	14	x?3	x?3	NOUN
ejpam-6763	1116	15	+	+	PUNCT
ejpam-6763	1116	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1116	17	?	?	PUNCT
ejpam-6763	1117	1	+	+	CCONJ
ejpam-6763	1117	2	1	1	NUM
ejpam-6763	1117	3	,	,	PUNCT
ejpam-6763	1117	4	2	2	NUM
ejpam-6763	1117	5	5	5	NUM
ejpam-6763	1117	6	<	<	X
ejpam-6763	1117	7	x	x	X
ejpam-6763	1117	8	?	?	PUNCT
ejpam-6763	1117	9	≤	≤	NUM
ejpam-6763	1117	10	1	1	NUM
ejpam-6763	1117	11	2	2	NUM
ejpam-6763	1117	12	−1.42108547152020×	−1.42108547152020×	NUM
ejpam-6763	1117	13	10−14	10−14	NUM
ejpam-6763	1117	14	x?3	x?3	NOUN
ejpam-6763	1117	15	+	+	PUNCT
ejpam-6763	1117	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1117	17	?	?	PUNCT
ejpam-6763	1118	1	+	+	CCONJ
ejpam-6763	1119	1	1	1	NUM
ejpam-6763	1119	2	,	,	PUNCT
ejpam-6763	1119	3	1	1	NUM
ejpam-6763	1119	4	2	2	NUM
ejpam-6763	1119	5	<	<	X
ejpam-6763	1119	6	x	x	X
ejpam-6763	1119	7	?	?	PUNCT
ejpam-6763	1119	8	≤	≤	NUM
ejpam-6763	1120	1	3	3	NUM
ejpam-6763	1120	2	5	5	NUM
ejpam-6763	1120	3	−1.86517468137026×	−1.86517468137026×	NUM
ejpam-6763	1120	4	10−14	10−14	NUM
ejpam-6763	1120	5	x?3	x?3	NOUN
ejpam-6763	1120	6	+	+	PUNCT
ejpam-6763	1120	7	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1120	8	?	?	PUNCT
ejpam-6763	1121	1	+	+	CCONJ
ejpam-6763	1121	2	1	1	NUM
ejpam-6763	1121	3	,	,	PUNCT
ejpam-6763	1121	4	3	3	NUM
ejpam-6763	1121	5	5	5	NUM
ejpam-6763	1121	6	<	<	X
ejpam-6763	1121	7	x	x	X
ejpam-6763	1121	8	?	?	PUNCT
ejpam-6763	1121	9	≤	≤	NUM
ejpam-6763	1121	10	7	7	NUM
ejpam-6763	1121	11	10	10	NUM
ejpam-6763	1121	12	−2.48689957516035×	−2.48689957516035×	NOUN
ejpam-6763	1121	13	10−14	10−14	NUM
ejpam-6763	1121	14	x?3	x?3	NOUN
ejpam-6763	1121	15	+	+	PUNCT
ejpam-6763	1121	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1121	17	?	?	PUNCT
ejpam-6763	1122	1	+	+	CCONJ
ejpam-6763	1122	2	1	1	NUM
ejpam-6763	1122	3	,	,	PUNCT
ejpam-6763	1122	4	7	7	NUM
ejpam-6763	1122	5	10	10	NUM
ejpam-6763	1122	6	<	<	X
ejpam-6763	1122	7	x	x	X
ejpam-6763	1122	8	?	?	PUNCT
ejpam-6763	1122	9	≤	≤	NUM
ejpam-6763	1122	10	4	4	NUM
ejpam-6763	1122	11	5	5	NUM
ejpam-6763	1122	12	−3.01980662698043×	−3.01980662698043×	NOUN
ejpam-6763	1122	13	10−14	10−14	NUM
ejpam-6763	1122	14	x?3	x?3	NOUN
ejpam-6763	1122	15	+	+	PUNCT
ejpam-6763	1122	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1122	17	?	?	PUNCT
ejpam-6763	1123	1	+	+	CCONJ
ejpam-6763	1123	2	1	1	NUM
ejpam-6763	1123	3	,	,	PUNCT
ejpam-6763	1123	4	4	4	NUM
ejpam-6763	1123	5	5	5	NUM
ejpam-6763	1123	6	<	<	X
ejpam-6763	1123	7	x	x	X
ejpam-6763	1123	8	?	?	PUNCT
ejpam-6763	1123	9	≤	≤	NUM
ejpam-6763	1123	10	9	9	NUM
ejpam-6763	1123	11	10	10	NUM
ejpam-6763	1123	12	−3.55271367880050×	−3.55271367880050×	NUM
ejpam-6763	1123	13	10−14	10−14	NUM
ejpam-6763	1123	14	x?3	x?3	NOUN
ejpam-6763	1123	15	+	+	PUNCT
ejpam-6763	1123	16	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1123	17	?	?	PUNCT
ejpam-6763	1124	1	+	+	CCONJ
ejpam-6763	1124	2	1	1	NUM
ejpam-6763	1124	3	,	,	PUNCT
ejpam-6763	1124	4	9	9	NUM
ejpam-6763	1124	5	10	10	NUM
ejpam-6763	1124	6	<	<	X
ejpam-6763	1124	7	x	x	X
ejpam-6763	1124	8	?	?	SYM
ejpam-6763	1124	9	≤	≤	NUM
ejpam-6763	1124	10	1	1	NUM
ejpam-6763	1124	11	b{c,3	b{c,3	NOUN
ejpam-6763	1124	12	}	}	PUNCT
ejpam-6763	1124	13	0	0	NUM
ejpam-6763	1125	1	(	(	PUNCT
ejpam-6763	1125	2	x	x	NOUN
ejpam-6763	1125	3	?	?	PUNCT
ejpam-6763	1125	4	)	)	PUNCT
ejpam-6763	1125	5	(	(	PUNCT
ejpam-6763	1125	6	fcpcbs	fcpcbs	PROPN
ejpam-6763	1125	7	)	)	PUNCT
ejpam-6763	1125	8	=	=	PUNCT
ejpam-6763	1126	1	0.999999990392377x?3	0.999999990392377x?3	NOUN
ejpam-6763	1127	1	+	+	NUM
ejpam-6763	1127	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1127	3	10−9	10−9	NUM
ejpam-6763	1127	4	x?2	x?2	PROPN
ejpam-6763	1127	5	+	+	CCONJ
ejpam-6763	1127	6	1	1	NUM
ejpam-6763	1127	7	,	,	PUNCT
ejpam-6763	1127	8	0	0	PUNCT
ejpam-6763	1127	9	<	<	X
ejpam-6763	1127	10	x	x	X
ejpam-6763	1127	11	?	?	PUNCT
ejpam-6763	1127	12	≤	≤	NUM
ejpam-6763	1127	13	1.0	1.0	NUM
ejpam-6763	1127	14	b{c,3	b{c,3	NOUN
ejpam-6763	1127	15	}	}	PUNCT
ejpam-6763	1127	16	1	1	NUM
ejpam-6763	1127	17	(	(	PUNCT
ejpam-6763	1127	18	x	x	NOUN
ejpam-6763	1127	19	?	?	PUNCT
ejpam-6763	1127	20	)	)	PUNCT
ejpam-6763	1127	21	(	(	PUNCT
ejpam-6763	1127	22	fcpcbs	fcpcbs	PROPN
ejpam-6763	1127	23	)	)	PUNCT
ejpam-6763	1127	24	=	=	PUNCT
ejpam-6763	1128	1	−1.15463194561016×	−1.15463194561016×	NUM
ejpam-6763	1128	2	10−14	10−14	NUM
ejpam-6763	1128	3	x?3	x?3	NOUN
ejpam-6763	1128	4	+	+	PUNCT
ejpam-6763	1128	5	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1128	6	?	?	PUNCT
ejpam-6763	1129	1	+	+	CCONJ
ejpam-6763	1129	2	1	1	NUM
ejpam-6763	1129	3	,	,	PUNCT
ejpam-6763	1129	4	0	0	PUNCT
ejpam-6763	1129	5	<	<	X
ejpam-6763	1129	6	x	x	X
ejpam-6763	1129	7	?	?	PUNCT
ejpam-6763	1129	8	≤	≤	NUM
ejpam-6763	1129	9	1.0	1.0	NUM
ejpam-6763	1129	10	b{c,3	b{c,3	NOUN
ejpam-6763	1129	11	}	}	PUNCT
ejpam-6763	1129	12	0	0	NUM
ejpam-6763	1129	13	(	(	PUNCT
ejpam-6763	1129	14	x	x	NOUN
ejpam-6763	1129	15	?	?	PUNCT
ejpam-6763	1129	16	)	)	PUNCT
ejpam-6763	1129	17	(	(	PUNCT
ejpam-6763	1129	18	ffcpcbs	ffcpcbs	X
ejpam-6763	1129	19	)	)	PUNCT
ejpam-6763	1129	20	=	=	PUNCT
ejpam-6763	1130	1	0.999999994666809x?3	0.999999994666809x?3	NUM
ejpam-6763	1131	1	+	+	CCONJ
ejpam-6763	1131	2	1.43536027508162×	1.43536027508162×	NUM
ejpam-6763	1131	3	10−9	10−9	NUM
ejpam-6763	1131	4	x?2	x?2	PROPN
ejpam-6763	1131	5	+	+	CCONJ
ejpam-6763	1131	6	1	1	NUM
ejpam-6763	1131	7	,	,	PUNCT
ejpam-6763	1131	8	0	0	PUNCT
ejpam-6763	1131	9	<	<	X
ejpam-6763	1131	10	x	x	X
ejpam-6763	1131	11	?	?	PUNCT
ejpam-6763	1131	12	≤	≤	NUM
ejpam-6763	1131	13	1.0	1.0	NUM
ejpam-6763	1131	14	b{c,3	b{c,3	NOUN
ejpam-6763	1131	15	}	}	PUNCT
ejpam-6763	1131	16	1	1	NUM
ejpam-6763	1131	17	(	(	PUNCT
ejpam-6763	1131	18	x	x	NOUN
ejpam-6763	1131	19	?	?	PUNCT
ejpam-6763	1131	20	)	)	PUNCT
ejpam-6763	1131	21	(	(	PUNCT
ejpam-6763	1131	22	ffcpcbs	ffcpcbs	X
ejpam-6763	1131	23	)	)	PUNCT
ejpam-6763	1131	24	=	=	SYM
ejpam-6763	1132	1	−2.30926389122033×	−2.30926389122033×	NUM
ejpam-6763	1132	2	10−14	10−14	NUM
ejpam-6763	1132	3	x?3	x?3	NOUN
ejpam-6763	1132	4	+	+	PUNCT
ejpam-6763	1132	5	2.00000000000000x	2.00000000000000x	NUM
ejpam-6763	1132	6	?	?	PUNCT
ejpam-6763	1133	1	+	+	CCONJ
ejpam-6763	1133	2	1	1	NUM
ejpam-6763	1133	3	,	,	PUNCT
ejpam-6763	1133	4	0	0	PUNCT
ejpam-6763	1133	5	<	<	X
ejpam-6763	1133	6	x	x	X
ejpam-6763	1133	7	?	?	PUNCT
ejpam-6763	1133	8	≤	≤	NUM
ejpam-6763	1133	9	1.0	1.0	NUM
ejpam-6763	1133	10	tables	table	NOUN
ejpam-6763	1133	11	11	11	NUM
ejpam-6763	1133	12	and	and	CCONJ
ejpam-6763	1133	13	12	12	NUM
ejpam-6763	1133	14	demonstrate	demonstrate	VERB
ejpam-6763	1133	15	a	a	DET
ejpam-6763	1133	16	comparison	comparison	NOUN
ejpam-6763	1133	17	between	between	ADP
ejpam-6763	1133	18	the	the	DET
ejpam-6763	1133	19	approximate	approximate	ADJ
ejpam-6763	1133	20	and	and	CCONJ
ejpam-6763	1133	21	exact	exact	ADJ
ejpam-6763	1133	22	solutions	solution	NOUN
ejpam-6763	1133	23	of	of	ADP
ejpam-6763	1133	24	y0(x	y0(x	NOUN
ejpam-6763	1133	25	)	)	PUNCT
ejpam-6763	1133	26	and	and	CCONJ
ejpam-6763	1133	27	y1(x	y1(x	NOUN
ejpam-6763	1133	28	)	)	PUNCT
ejpam-6763	1133	29	,	,	PUNCT
ejpam-6763	1133	30	respectively	respectively	ADV
ejpam-6763	1133	31	.	.	PUNCT
ejpam-6763	1134	1	the	the	DET
ejpam-6763	1134	2	computations	computation	NOUN
ejpam-6763	1134	3	are	be	AUX
ejpam-6763	1134	4	carried	carry	VERB
ejpam-6763	1134	5	out	out	ADP
ejpam-6763	1134	6	by	by	ADP
ejpam-6763	1134	7	setting	set	VERB
ejpam-6763	1134	8	n	n	X
ejpam-6763	1134	9	=	=	SYM
ejpam-6763	1134	10	10	10	NUM
ejpam-6763	1134	11	,	,	PUNCT
ejpam-6763	1134	12	h	h	NOUN
ejpam-6763	1134	13	=	=	NOUN
ejpam-6763	1134	14	0.1	0.1	NUM
ejpam-6763	1134	15	,	,	PUNCT
ejpam-6763	1134	16	and	and	CCONJ
ejpam-6763	1134	17	x	x	X
ejpam-6763	1134	18	?	?	PUNCT
ejpam-6763	1135	1	r	r	X
ejpam-6763	1135	2	=	=	PUNCT
ejpam-6763	1135	3	a	a	PRON
ejpam-6763	1135	4	+	+	X
ejpam-6763	1135	5	rh	rh	NOUN
ejpam-6763	1135	6	for	for	ADP
ejpam-6763	1135	7	r	r	NOUN
ejpam-6763	1135	8	=	=	SYM
ejpam-6763	1135	9	0	0	NUM
ejpam-6763	1135	10	,	,	PUNCT
ejpam-6763	1135	11	1	1	NUM
ejpam-6763	1135	12	,	,	PUNCT
ejpam-6763	1135	13	.	.	PUNCT
ejpam-6763	1135	14	.	.	PUNCT
ejpam-6763	1135	15	.	.	PUNCT
ejpam-6763	1136	1	,	,	PUNCT
ejpam-6763	1136	2	n	n	CCONJ
ejpam-6763	1136	3	−	−	PROPN
ejpam-6763	1136	4	1	1	NUM
ejpam-6763	1136	5	,	,	PUNCT
ejpam-6763	1136	6	using	use	VERB
ejpam-6763	1136	7	three	three	NUM
ejpam-6763	1136	8	cubic	cubic	ADJ
ejpam-6763	1136	9	b	b	NOUN
ejpam-6763	1136	10	-	-	PUNCT
ejpam-6763	1136	11	spline	spline	NOUN
ejpam-6763	1136	12	methods	method	NOUN
ejpam-6763	1136	13	:	:	PUNCT
ejpam-6763	1136	14	nfcbi	nfcbi	NOUN
ejpam-6763	1136	15	,	,	PUNCT
ejpam-6763	1136	16	fcpcbs	fcpcbs	PROPN
ejpam-6763	1136	17	,	,	PUNCT
ejpam-6763	1136	18	and	and	CCONJ
ejpam-6763	1136	19	ffcpcbs	ffcpcbs	X
ejpam-6763	1136	20	.	.	PUNCT
ejpam-6763	1137	1	table	table	NOUN
ejpam-6763	1137	2	11	11	NUM
ejpam-6763	1137	3	:	:	PUNCT
ejpam-6763	1137	4	comparison	comparison	NOUN
ejpam-6763	1137	5	of	of	ADP
ejpam-6763	1137	6	the	the	DET
ejpam-6763	1137	7	exact	exact	ADJ
ejpam-6763	1137	8	and	and	CCONJ
ejpam-6763	1137	9	approximate	approximate	ADJ
ejpam-6763	1137	10	solutions	solution	NOUN
ejpam-6763	1137	11	based	base	VERB
ejpam-6763	1137	12	on	on	ADP
ejpam-6763	1137	13	least	least	ADJ
ejpam-6763	1137	14	square	square	ADJ
ejpam-6763	1137	15	error	error	NOUN
ejpam-6763	1137	16	for	for	ADP
ejpam-6763	1137	17	y0(x	y0(x	NOUN
ejpam-6763	1137	18	)	)	PUNCT
ejpam-6763	1137	19	for	for	ADP
ejpam-6763	1137	20	example	example	NOUN
ejpam-6763	1137	21	3	3	NUM
ejpam-6763	1137	22	.	.	PUNCT
ejpam-6763	1138	1	x	x	X
ejpam-6763	1138	2	?	?	PUNCT
ejpam-6763	1138	3	r	r	NOUN
ejpam-6763	1138	4	exact	exact	ADJ
ejpam-6763	1138	5	b{c,3	b{c,3	NOUN
ejpam-6763	1138	6	}	}	PUNCT
ejpam-6763	1138	7	0	0	NUM
ejpam-6763	1139	1	(	(	PUNCT
ejpam-6763	1139	2	x	x	NOUN
ejpam-6763	1139	3	?	?	SYM
ejpam-6763	1139	4	r	r	X
ejpam-6763	1139	5	)	)	PUNCT
ejpam-6763	1139	6	(	(	PUNCT
ejpam-6763	1139	7	nfcbi	nfcbi	NOUN
ejpam-6763	1139	8	)	)	PUNCT
ejpam-6763	1139	9	b{c,3	b{c,3	NOUN
ejpam-6763	1139	10	}	}	PUNCT
ejpam-6763	1139	11	0	0	NUM
ejpam-6763	1140	1	(	(	PUNCT
ejpam-6763	1140	2	x	x	NOUN
ejpam-6763	1140	3	?	?	SYM
ejpam-6763	1140	4	r	r	X
ejpam-6763	1140	5	)	)	PUNCT
ejpam-6763	1140	6	(	(	PUNCT
ejpam-6763	1140	7	fcpcbs	fcpcbs	NOUN
ejpam-6763	1140	8	)	)	PUNCT
ejpam-6763	1140	9	b{c,3	b{c,3	NOUN
ejpam-6763	1140	10	}	}	PUNCT
ejpam-6763	1140	11	0	0	NUM
ejpam-6763	1141	1	(	(	PUNCT
ejpam-6763	1141	2	x	x	NOUN
ejpam-6763	1141	3	?	?	SYM
ejpam-6763	1141	4	r	r	X
ejpam-6763	1141	5	)	)	PUNCT
ejpam-6763	1141	6	(	(	PUNCT
ejpam-6763	1141	7	ffcpcbs	ffcpcbs	X
ejpam-6763	1141	8	)	)	PUNCT
ejpam-6763	1141	9	0	0	NUM
ejpam-6763	1141	10	1.000	1.000	NUM
ejpam-6763	1141	11	1.000	1.000	NUM
ejpam-6763	1141	12	1.000	1.000	NUM
ejpam-6763	1141	13	1.000	1.000	NUM
ejpam-6763	1141	14	1/10	1/10	NUM
ejpam-6763	1141	15	1.001	1.001	NUM
ejpam-6763	1141	16	1.00100000000475	1.00100000000475	NUM
ejpam-6763	1141	17	1.001000000005	1.001000000005	NUM
ejpam-6763	1141	18	1.001000000009	1.001000000009	NUM
ejpam-6763	1141	19	1/5	1/5	NUM
ejpam-6763	1141	20	1.008	1.008	NUM
ejpam-6763	1141	21	1.00800000001868	1.00800000001868	NUM
ejpam-6763	1141	22	1.007999999981	1.007999999981	NUM
ejpam-6763	1141	23	1.008000000015	1.008000000015	NUM
ejpam-6763	1141	24	3/10	3/10	NUM
ejpam-6763	1141	25	1.027	1.027	NUM
ejpam-6763	1141	26	1.02700000004116	1.02700000004116	NUM
ejpam-6763	1141	27	1.026999999870	1.026999999870	NUM
ejpam-6763	1141	28	1.026999999985	1.026999999985	NUM
ejpam-6763	1141	29	2/5	2/5	NUM
ejpam-6763	1141	30	1.064	1.064	NUM
ejpam-6763	1141	31	1.06400000007142	1.06400000007142	NUM
ejpam-6763	1141	32	1.063999999615	1.063999999615	NUM
ejpam-6763	1141	33	1.063999999888	1.063999999888	NUM
ejpam-6763	1141	34	1/2	1/2	NUM
ejpam-6763	1141	35	1.125	1.125	NUM
ejpam-6763	1141	36	1.12500000010866	1.12500000010866	NUM
ejpam-6763	1141	37	1.124999999158	1.124999999158	NUM
ejpam-6763	1141	38	1.124999999692	1.124999999692	NUM
ejpam-6763	1141	39	3/5	3/5	NUM
ejpam-6763	1141	40	1.216	1.216	NUM
ejpam-6763	1141	41	1.21600000015215	1.21600000015215	NUM
ejpam-6763	1141	42	1.215999998441	1.215999998441	NUM
ejpam-6763	1141	43	1.215999999365	1.215999999365	NUM
ejpam-6763	1141	44	7/10	7/10	NUM
ejpam-6763	1141	45	1.343	1.343	NUM
ejpam-6763	1141	46	1.34300000020120	1.34300000020120	NUM
ejpam-6763	1141	47	1.342999997408	1.342999997408	NUM
ejpam-6763	1141	48	1.342999998874	1.342999998874	NUM
ejpam-6763	1141	49	4/5	4/5	NUM
ejpam-6763	1141	50	1.512	1.512	NUM
ejpam-6763	1141	51	1.51200000025526	1.51200000025526	NUM
ejpam-6763	1141	52	1.511999996000	1.511999996000	NUM
ejpam-6763	1141	53	1.511999998188	1.511999998188	NUM
ejpam-6763	1141	54	9/10	9/10	NUM
ejpam-6763	1141	55	1.729	1.729	NUM
ejpam-6763	1141	56	1.72900000031386	1.72900000031386	NUM
ejpam-6763	1141	57	1.728999994159	1.728999994159	NUM
ejpam-6763	1141	58	1.728999997275	1.728999997275	NUM
ejpam-6763	1141	59	1.0	1.0	NUM
ejpam-6763	1141	60	2.000	2.000	NUM
ejpam-6763	1141	61	2.00000000037660	2.00000000037660	NUM
ejpam-6763	1141	62	1.999999991828	1.999999991828	NUM
ejpam-6763	1141	63	1.999999996102	1.999999996102	NUM
ejpam-6763	1141	64	l.s.e	l.s.e	NOUN
ejpam-6763	1141	65	3.881×	3.881×	NUM
ejpam-6763	1141	66	10−19	10−19	NOUN
ejpam-6763	1141	67	1.269×	1.269×	NUM
ejpam-6763	1141	68	10−16	10−16	PROPN
ejpam-6763	1141	69	2.768×	2.768×	NUM
ejpam-6763	1141	70	10−17	10−17	NUM
ejpam-6763	1141	71	runtime	runtime	NOUN
ejpam-6763	1141	72	(	(	PUNCT
ejpam-6763	1141	73	s	s	X
ejpam-6763	1141	74	)	)	PUNCT
ejpam-6763	1141	75	1.2066	1.2066	NUM
ejpam-6763	1141	76	1.2065	1.2065	NUM
ejpam-6763	1141	77	1.2085	1.2085	NUM
ejpam-6763	1141	78	d.	d.	PROPN
ejpam-6763	1141	79	kh	kh	PROPN
ejpam-6763	1141	80	.	.	PUNCT
ejpam-6763	1142	1	abdullah	abdullah	PROPN
ejpam-6763	1142	2	,	,	PUNCT
ejpam-6763	1142	3	sh	sh	PROPN
ejpam-6763	1142	4	.	.	PROPN
ejpam-6763	1142	5	sh	sh	PROPN
ejpam-6763	1142	6	.	.	PROPN
ejpam-6763	1142	7	ahmed	ahmed	PROPN
ejpam-6763	1142	8	,	,	PUNCT
ejpam-6763	1142	9	k.	k.	PROPN
ejpam-6763	1142	10	h.	h.	PROPN
ejpam-6763	1142	11	f.	f.	PROPN
ejpam-6763	1142	12	jwamer	jwamer	PROPN
ejpam-6763	1142	13	/	/	SYM
ejpam-6763	1142	14	eur	eur	PROPN
ejpam-6763	1142	15	.	.	PUNCT
ejpam-6763	1143	1	j.	j.	PROPN
ejpam-6763	1143	2	pure	pure	PROPN
ejpam-6763	1143	3	appl	appl	PROPN
ejpam-6763	1143	4	.	.	PROPN
ejpam-6763	1143	5	math	math	PROPN
ejpam-6763	1143	6	,	,	PUNCT
ejpam-6763	1143	7	18	18	NUM
ejpam-6763	1143	8	(	(	PUNCT
ejpam-6763	1143	9	4	4	NUM
ejpam-6763	1143	10	)	)	PUNCT
ejpam-6763	1143	11	(	(	PUNCT
ejpam-6763	1143	12	2025	2025	NUM
ejpam-6763	1143	13	)	)	PUNCT
ejpam-6763	1143	14	,	,	PUNCT
ejpam-6763	1143	15	6763	6763	NUM
ejpam-6763	1143	16	36	36	NUM
ejpam-6763	1143	17	of	of	ADP
ejpam-6763	1143	18	40	40	NUM
ejpam-6763	1143	19	table	table	NOUN
ejpam-6763	1143	20	12	12	NUM
ejpam-6763	1143	21	:	:	PUNCT
ejpam-6763	1143	22	comparison	comparison	NOUN
ejpam-6763	1143	23	of	of	ADP
ejpam-6763	1143	24	the	the	DET
ejpam-6763	1143	25	exact	exact	ADJ
ejpam-6763	1143	26	and	and	CCONJ
ejpam-6763	1143	27	approximate	approximate	ADJ
ejpam-6763	1143	28	solutions	solution	NOUN
ejpam-6763	1143	29	based	base	VERB
ejpam-6763	1143	30	on	on	ADP
ejpam-6763	1143	31	least	least	ADJ
ejpam-6763	1143	32	square	square	ADJ
ejpam-6763	1143	33	error	error	NOUN
ejpam-6763	1143	34	for	for	ADP
ejpam-6763	1143	35	y1(x	y1(x	NOUN
ejpam-6763	1143	36	)	)	PUNCT
ejpam-6763	1143	37	for	for	ADP
ejpam-6763	1143	38	example	example	NOUN
ejpam-6763	1143	39	3	3	NUM
ejpam-6763	1143	40	.	.	PUNCT
ejpam-6763	1143	41	x	x	X
ejpam-6763	1143	42	?	?	PUNCT
ejpam-6763	1144	1	r	r	NOUN
ejpam-6763	1144	2	exact	exact	ADJ
ejpam-6763	1144	3	b{c,3	b{c,3	NOUN
ejpam-6763	1144	4	}	}	PUNCT
ejpam-6763	1144	5	1	1	NUM
ejpam-6763	1144	6	(	(	PUNCT
ejpam-6763	1144	7	x	x	NOUN
ejpam-6763	1144	8	?	?	SYM
ejpam-6763	1145	1	r	r	X
ejpam-6763	1145	2	)	)	PUNCT
ejpam-6763	1145	3	(	(	PUNCT
ejpam-6763	1145	4	nfcbi	nfcbi	NOUN
ejpam-6763	1145	5	)	)	PUNCT
ejpam-6763	1145	6	b{c,3	b{c,3	NOUN
ejpam-6763	1145	7	}	}	PUNCT
ejpam-6763	1145	8	1	1	NUM
ejpam-6763	1145	9	(	(	PUNCT
ejpam-6763	1145	10	x	x	NOUN
ejpam-6763	1145	11	?	?	SYM
ejpam-6763	1146	1	r	r	X
ejpam-6763	1146	2	)	)	PUNCT
ejpam-6763	1146	3	(	(	PUNCT
ejpam-6763	1146	4	fcpcbs	fcpcbs	NOUN
ejpam-6763	1146	5	)	)	PUNCT
ejpam-6763	1146	6	b{c,3	b{c,3	NOUN
ejpam-6763	1146	7	}	}	PUNCT
ejpam-6763	1146	8	1	1	NUM
ejpam-6763	1146	9	(	(	PUNCT
ejpam-6763	1146	10	x	x	NOUN
ejpam-6763	1146	11	?	?	SYM
ejpam-6763	1147	1	r	r	X
ejpam-6763	1147	2	)	)	PUNCT
ejpam-6763	1147	3	(	(	PUNCT
ejpam-6763	1147	4	ffcpcbs	ffcpcbs	X
ejpam-6763	1147	5	)	)	PUNCT
ejpam-6763	1147	6	0	0	NUM
ejpam-6763	1147	7	1.0	1.0	NUM
ejpam-6763	1147	8	1.0	1.0	NUM
ejpam-6763	1147	9	1.0	1.0	NUM
ejpam-6763	1147	10	1.0	1.0	NUM
ejpam-6763	1147	11	1/10	1/10	NUM
ejpam-6763	1147	12	1.2	1.2	NUM
ejpam-6763	1147	13	1.2	1.2	NUM
ejpam-6763	1147	14	1.2	1.2	NUM
ejpam-6763	1147	15	1.2	1.2	NUM
ejpam-6763	1147	16	1/5	1/5	NUM
ejpam-6763	1147	17	1.4	1.4	NUM
ejpam-6763	1147	18	1.4	1.4	NUM
ejpam-6763	1147	19	1.4	1.4	NUM
ejpam-6763	1147	20	1.4	1.4	NUM
ejpam-6763	1147	21	3/10	3/10	NUM
ejpam-6763	1147	22	1.6	1.6	NUM
ejpam-6763	1147	23	1.6	1.6	NUM
ejpam-6763	1147	24	1.6	1.6	NUM
ejpam-6763	1147	25	1.6	1.6	NUM
ejpam-6763	1147	26	2/5	2/5	NUM
ejpam-6763	1147	27	1.8	1.8	NUM
ejpam-6763	1147	28	1.8	1.8	NUM
ejpam-6763	1147	29	1.8	1.8	NUM
ejpam-6763	1147	30	1.80000000000009	1.80000000000009	NUM
ejpam-6763	1147	31	1/2	1/2	NUM
ejpam-6763	1147	32	2.0	2.0	NUM
ejpam-6763	1147	33	2.0	2.0	NUM
ejpam-6763	1147	34	2.0000000000008	2.0000000000008	NUM
ejpam-6763	1147	35	2.0000000000007	2.0000000000007	NUM
ejpam-6763	1147	36	3/5	3/5	NUM
ejpam-6763	1147	37	2.2	2.2	NUM
ejpam-6763	1147	38	2.2	2.2	NUM
ejpam-6763	1147	39	2.2000000000007	2.2000000000007	NUM
ejpam-6763	1147	40	2.2000000000017	2.2000000000017	NUM
ejpam-6763	1147	41	7/10	7/10	NUM
ejpam-6763	1147	42	2.4	2.4	NUM
ejpam-6763	1147	43	2.4	2.4	NUM
ejpam-6763	1147	44	2.4000000000099	2.4000000000099	NUM
ejpam-6763	1147	45	2.4000000000058	2.4000000000058	NUM
ejpam-6763	1147	46	4/5	4/5	NUM
ejpam-6763	1147	47	2.6	2.6	NUM
ejpam-6763	1147	48	2.6	2.6	NUM
ejpam-6763	1147	49	2.6000000000023	2.6000000000023	NUM
ejpam-6763	1147	50	2.6000000000014	2.6000000000014	NUM
ejpam-6763	1147	51	9/10	9/10	NUM
ejpam-6763	1147	52	2.8	2.8	NUM
ejpam-6763	1147	53	2.79999999999999	2.79999999999999	NUM
ejpam-6763	1147	54	2.7999999999998	2.7999999999998	NUM
ejpam-6763	1147	55	2.7000000000238	2.7000000000238	NUM
ejpam-6763	1147	56	1.0	1.0	NUM
ejpam-6763	1147	57	3.0	3.0	NUM
ejpam-6763	1147	58	3.00000000000001	3.00000000000001	NUM
ejpam-6763	1147	59	3.00000000000013	3.00000000000013	NUM
ejpam-6763	1147	60	3.00000000000013	3.00000000000013	NUM
ejpam-6763	1147	61	l.s.e	l.s.e	NOUN
ejpam-6763	1147	62	8.239×	8.239×	NUM
ejpam-6763	1147	63	10−29	10−29	NOUN
ejpam-6763	1147	64	2.598×	2.598×	NUM
ejpam-6763	1147	65	10−28	10−28	NUM
ejpam-6763	1147	66	1.060×	1.060×	NUM
ejpam-6763	1147	67	10−27	10−27	NUM
ejpam-6763	1147	68	runtime	runtime	NOUN
ejpam-6763	1147	69	(	(	PUNCT
ejpam-6763	1147	70	s	s	X
ejpam-6763	1147	71	)	)	PUNCT
ejpam-6763	1147	72	1.2066	1.2066	NUM
ejpam-6763	1147	73	1.2065	1.2065	NUM
ejpam-6763	1147	74	1.2085	1.2085	NUM
ejpam-6763	1147	75	table	table	NOUN
ejpam-6763	1147	76	13	13	NUM
ejpam-6763	1147	77	:	:	PUNCT
ejpam-6763	1147	78	least	least	ADJ
ejpam-6763	1147	79	square	square	ADJ
ejpam-6763	1147	80	error	error	NOUN
ejpam-6763	1147	81	for	for	ADP
ejpam-6763	1147	82	y0(x	y0(x	NOUN
ejpam-6763	1147	83	)	)	PUNCT
ejpam-6763	1147	84	,	,	PUNCT
ejpam-6763	1147	85	and	and	CCONJ
ejpam-6763	1147	86	y1(x	y1(x	NOUN
ejpam-6763	1147	87	)	)	PUNCT
ejpam-6763	1147	88	,	,	PUNCT
ejpam-6763	1147	89	in	in	ADP
ejpam-6763	1147	90	example	example	NOUN
ejpam-6763	1147	91	3	3	NUM
ejpam-6763	1147	92	using	use	VERB
ejpam-6763	1147	93	different	different	ADJ
ejpam-6763	1147	94	step	step	NOUN
ejpam-6763	1147	95	sizes	size	NOUN
ejpam-6763	1147	96	.	.	PUNCT
ejpam-6763	1148	1	method	method	NOUN
ejpam-6763	1148	2	step	step	NOUN
ejpam-6763	1148	3	size	size	NOUN
ejpam-6763	1148	4	h	h	PROPN
ejpam-6763	1148	5	lse	lse	PROPN
ejpam-6763	1148	6	of	of	ADP
ejpam-6763	1148	7	b{c,3	b{c,3	PROPN
ejpam-6763	1148	8	}	}	PUNCT
ejpam-6763	1148	9	0	0	NUM
ejpam-6763	1149	1	(	(	PUNCT
ejpam-6763	1149	2	x	x	NOUN
ejpam-6763	1149	3	?	?	PUNCT
ejpam-6763	1149	4	)	)	PUNCT
ejpam-6763	1149	5	lse	lse	NOUN
ejpam-6763	1149	6	of	of	ADP
ejpam-6763	1149	7	b{c,3	b{c,3	PROPN
ejpam-6763	1149	8	}	}	PUNCT
ejpam-6763	1149	9	1	1	NUM
ejpam-6763	1149	10	(	(	PUNCT
ejpam-6763	1149	11	x	x	NOUN
ejpam-6763	1149	12	?	?	PUNCT
ejpam-6763	1149	13	)	)	PUNCT
ejpam-6763	1149	14	nfcbi	nfcbi	VERB
ejpam-6763	1149	15	1/10	1/10	NUM
ejpam-6763	1149	16	3.88101892329981×	3.88101892329981×	NUM
ejpam-6763	1149	17	10−19	10−19	NUM
ejpam-6763	1149	18	8.23866607890194×	8.23866607890194×	NUM
ejpam-6763	1149	19	10−29	10−29	PROPN
ejpam-6763	1149	20	1/50	1/50	NUM
ejpam-6763	1149	21	2.43602430852715×	2.43602430852715×	NUM
ejpam-6763	1149	22	10−22	10−22	NOUN
ejpam-6763	1149	23	7.13328499648335×	7.13328499648335×	NUM
ejpam-6763	1149	24	10−29	10−29	NOUN
ejpam-6763	1149	25	1/1000	1/1000	NUM
ejpam-6763	1149	26	1.38050658413677×	1.38050658413677×	NUM
ejpam-6763	1149	27	10−29	10−29	PROPN
ejpam-6763	1149	28	2.23866607890190×	2.23866607890190×	NUM
ejpam-6763	1149	29	10−29	10−29	NOUN
ejpam-6763	1149	30	fcpcbs	fcpcbs	NOUN
ejpam-6763	1149	31	1/10	1/10	NUM
ejpam-6763	1149	32	1.2693341933429862×	1.2693341933429862×	NUM
ejpam-6763	1150	1	10−16	10−16	PROPN
ejpam-6763	1150	2	2.5983106065717076×	2.5983106065717076×	NUM
ejpam-6763	1150	3	10−28	10−28	NUM
ejpam-6763	1150	4	1/50	1/50	NUM
ejpam-6763	1150	5	7.966390404945247×	7.966390404945247×	NUM
ejpam-6763	1150	6	10−20	10−20	NUM
ejpam-6763	1150	7	1.2232274411583314×	1.2232274411583314×	NUM
ejpam-6763	1150	8	10−28	10−28	PROPN
ejpam-6763	1150	9	1/1000	1/1000	NUM
ejpam-6763	1150	10	3.944304526105059×	3.944304526105059×	NUM
ejpam-6763	1150	11	10−31	10−31	NUM
ejpam-6763	1150	12	3.4512664603419266×	3.4512664603419266×	NUM
ejpam-6763	1150	13	10−31	10−31	NUM
ejpam-6763	1150	14	ffcpcbs	ffcpcbs	ADJ
ejpam-6763	1151	1	1/10	1/10	NUM
ejpam-6763	1151	2	2.768234509326171×	2.768234509326171×	NUM
ejpam-6763	1151	3	10−17	10−17	NUM
ejpam-6763	1151	4	1.0601304490038872×	1.0601304490038872×	NUM
ejpam-6763	1151	5	10−27	10−27	NUM
ejpam-6763	1151	6	1/50	1/50	NUM
ejpam-6763	1151	7	6.488786754097752×	6.488786754097752×	NUM
ejpam-6763	1151	8	10−19	10−19	NUM
ejpam-6763	1151	9	1.0597574191466658×	1.0597574191466658×	NUM
ejpam-6763	1151	10	10−27	10−27	NUM
ejpam-6763	1151	11	1/1000	1/1000	NUM
ejpam-6763	1151	12	1.7749370367472766×	1.7749370367472766×	NUM
ejpam-6763	1151	13	10−29	10−29	NUM
ejpam-6763	1151	14	1.0601304490038872×	1.0601304490038872×	NUM
ejpam-6763	1151	15	10−28	10−28	NOUN
ejpam-6763	1151	16	the	the	DET
ejpam-6763	1151	17	plot	plot	NOUN
ejpam-6763	1151	18	of	of	ADP
ejpam-6763	1151	19	these	these	DET
ejpam-6763	1151	20	approximate	approximate	ADJ
ejpam-6763	1151	21	solutions	solution	NOUN
ejpam-6763	1151	22	obtained	obtain	VERB
ejpam-6763	1151	23	by	by	ADP
ejpam-6763	1151	24	nfcbi	nfcbi	NOUN
ejpam-6763	1151	25	,	,	PUNCT
ejpam-6763	1151	26	fcpcbs	fcpcbs	PROPN
ejpam-6763	1151	27	and	and	CCONJ
ejpam-6763	1151	28	ffcpcbs	ffcpcbs	PROPN
ejpam-6763	1151	29	for	for	ADP
ejpam-6763	1151	30	y0(x	y0(x	NOUN
ejpam-6763	1151	31	)	)	PUNCT
ejpam-6763	1151	32	,	,	PUNCT
ejpam-6763	1151	33	and	and	CCONJ
ejpam-6763	1151	34	y1(x	y1(x	NOUN
ejpam-6763	1151	35	)	)	PUNCT
ejpam-6763	1151	36	are	be	AUX
ejpam-6763	1151	37	demonstrate	demonstrate	VERB
ejpam-6763	1151	38	in	in	ADP
ejpam-6763	1151	39	figures	figure	NOUN
ejpam-6763	1151	40	13,15	13,15	NUM
ejpam-6763	1151	41	and	and	CCONJ
ejpam-6763	1151	42	17	17	NUM
ejpam-6763	1151	43	with	with	ADP
ejpam-6763	1151	44	the	the	DET
ejpam-6763	1151	45	exact	exact	ADJ
ejpam-6763	1151	46	solution	solution	NOUN
ejpam-6763	1151	47	plots	plot	NOUN
ejpam-6763	1151	48	,	,	PUNCT
ejpam-6763	1151	49	respectively	respectively	ADV
ejpam-6763	1151	50	.	.	PUNCT
ejpam-6763	1152	1	the	the	DET
ejpam-6763	1152	2	least	least	ADJ
ejpam-6763	1152	3	square	square	ADJ
ejpam-6763	1152	4	error	error	NOUN
ejpam-6763	1152	5	of	of	ADP
ejpam-6763	1152	6	each	each	DET
ejpam-6763	1152	7	iteration	iteration	NOUN
ejpam-6763	1152	8	are	be	AUX
ejpam-6763	1152	9	shows	show	NOUN
ejpam-6763	1152	10	in	in	ADP
ejpam-6763	1152	11	figures	figure	NOUN
ejpam-6763	1152	12	14	14	NUM
ejpam-6763	1152	13	,	,	PUNCT
ejpam-6763	1152	14	16	16	NUM
ejpam-6763	1152	15	and	and	CCONJ
ejpam-6763	1152	16	18	18	NUM
ejpam-6763	1152	17	for	for	ADP
ejpam-6763	1152	18	example	example	NOUN
ejpam-6763	1152	19	3	3	X
ejpam-6763	1152	20	.	.	PUNCT
ejpam-6763	1152	21	d.	d.	PROPN
ejpam-6763	1152	22	kh	kh	PROPN
ejpam-6763	1152	23	.	.	PUNCT
ejpam-6763	1153	1	abdullah	abdullah	PROPN
ejpam-6763	1153	2	,	,	PUNCT
ejpam-6763	1153	3	sh	sh	PROPN
ejpam-6763	1153	4	.	.	PROPN
ejpam-6763	1153	5	sh	sh	PROPN
ejpam-6763	1153	6	.	.	PROPN
ejpam-6763	1153	7	ahmed	ahmed	PROPN
ejpam-6763	1153	8	,	,	PUNCT
ejpam-6763	1153	9	k.	k.	PROPN
ejpam-6763	1153	10	h.	h.	PROPN
ejpam-6763	1153	11	f.	f.	PROPN
ejpam-6763	1153	12	jwamer	jwamer	PROPN
ejpam-6763	1153	13	/	/	SYM
ejpam-6763	1153	14	eur	eur	PROPN
ejpam-6763	1153	15	.	.	PUNCT
ejpam-6763	1154	1	j.	j.	PROPN
ejpam-6763	1154	2	pure	pure	PROPN
ejpam-6763	1154	3	appl	appl	PROPN
ejpam-6763	1154	4	.	.	PROPN
ejpam-6763	1154	5	math	math	PROPN
ejpam-6763	1154	6	,	,	PUNCT
ejpam-6763	1154	7	18	18	NUM
ejpam-6763	1154	8	(	(	PUNCT
ejpam-6763	1154	9	4	4	NUM
ejpam-6763	1154	10	)	)	PUNCT
ejpam-6763	1154	11	(	(	PUNCT
ejpam-6763	1154	12	2025	2025	NUM
ejpam-6763	1154	13	)	)	PUNCT
ejpam-6763	1154	14	,	,	PUNCT
ejpam-6763	1154	15	6763	6763	NUM
ejpam-6763	1154	16	37	37	NUM
ejpam-6763	1154	17	of	of	ADP
ejpam-6763	1154	18	40	40	NUM
ejpam-6763	1154	19	figure	figure	NOUN
ejpam-6763	1154	20	13	13	NUM
ejpam-6763	1154	21	:	:	PUNCT
ejpam-6763	1154	22	approximation	approximation	NOUN
ejpam-6763	1154	23	solution	solution	NOUN
ejpam-6763	1154	24	of	of	ADP
ejpam-6763	1154	25	y0(x	y0(x	NUM
ejpam-6763	1154	26	)	)	PUNCT
ejpam-6763	1154	27	and	and	CCONJ
ejpam-6763	1154	28	y1(x	y1(x	NOUN
ejpam-6763	1154	29	)	)	PUNCT
ejpam-6763	1154	30	method	method	NOUN
ejpam-6763	1154	31	nfcbi	nfcbi	VERB
ejpam-6763	1154	32	for	for	ADP
ejpam-6763	1154	33	example	example	NOUN
ejpam-6763	1154	34	3	3	NUM
ejpam-6763	1154	35	.	.	X
ejpam-6763	1154	36	figure	figure	NOUN
ejpam-6763	1154	37	14	14	NUM
ejpam-6763	1154	38	:	:	PUNCT
ejpam-6763	1154	39	least	least	ADJ
ejpam-6763	1154	40	square	square	ADJ
ejpam-6763	1154	41	error	error	NOUN
ejpam-6763	1154	42	plot	plot	NOUN
ejpam-6763	1154	43	of	of	ADP
ejpam-6763	1154	44	y0(x	y0(x	NOUN
ejpam-6763	1154	45	)	)	PUNCT
ejpam-6763	1154	46	and	and	CCONJ
ejpam-6763	1154	47	y1(x	y1(x	NOUN
ejpam-6763	1154	48	)	)	PUNCT
ejpam-6763	1154	49	method	method	NOUN
ejpam-6763	1154	50	nfcbi	nfcbi	VERB
ejpam-6763	1154	51	for	for	ADP
ejpam-6763	1154	52	example	example	NOUN
ejpam-6763	1154	53	5.3	5.3	NUM
ejpam-6763	1154	54	.	.	PUNCT
ejpam-6763	1155	1	figure	figure	VERB
ejpam-6763	1155	2	15	15	NUM
ejpam-6763	1155	3	:	:	PUNCT
ejpam-6763	1155	4	approximation	approximation	NOUN
ejpam-6763	1155	5	solution	solution	NOUN
ejpam-6763	1155	6	of	of	ADP
ejpam-6763	1155	7	y0(x	y0(x	NUM
ejpam-6763	1155	8	)	)	PUNCT
ejpam-6763	1155	9	and	and	CCONJ
ejpam-6763	1155	10	y1(x	y1(x	NOUN
ejpam-6763	1155	11	)	)	PUNCT
ejpam-6763	1155	12	method	method	NOUN
ejpam-6763	1155	13	fcpcbs	fcpcbs	NOUN
ejpam-6763	1155	14	for	for	ADP
ejpam-6763	1155	15	example	example	NOUN
ejpam-6763	1155	16	3	3	NUM
ejpam-6763	1155	17	.	.	X
ejpam-6763	1155	18	figure	figure	VERB
ejpam-6763	1155	19	16	16	NUM
ejpam-6763	1155	20	:	:	PUNCT
ejpam-6763	1155	21	least	least	ADJ
ejpam-6763	1155	22	square	square	ADJ
ejpam-6763	1155	23	error	error	NOUN
ejpam-6763	1155	24	plot	plot	NOUN
ejpam-6763	1155	25	of	of	ADP
ejpam-6763	1155	26	y0(x	y0(x	NOUN
ejpam-6763	1155	27	)	)	PUNCT
ejpam-6763	1155	28	and	and	CCONJ
ejpam-6763	1155	29	y1(x	y1(x	NOUN
ejpam-6763	1155	30	)	)	PUNCT
ejpam-6763	1155	31	method	method	NOUN
ejpam-6763	1155	32	fcpcbsfor	fcpcbsfor	ADP
ejpam-6763	1155	33	example	example	NOUN
ejpam-6763	1155	34	3	3	NUM
ejpam-6763	1155	35	.	.	X
ejpam-6763	1155	36	figure	figure	NOUN
ejpam-6763	1155	37	17	17	NUM
ejpam-6763	1155	38	:	:	PUNCT
ejpam-6763	1155	39	approximation	approximation	NOUN
ejpam-6763	1155	40	solution	solution	NOUN
ejpam-6763	1155	41	of	of	ADP
ejpam-6763	1155	42	y0(x)and	y0(x)and	NUM
ejpam-6763	1155	43	y1(x	y1(x	NOUN
ejpam-6763	1155	44	)	)	PUNCT
ejpam-6763	1155	45	method	method	NOUN
ejpam-6763	1155	46	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1155	47	for	for	ADP
ejpam-6763	1155	48	example	example	NOUN
ejpam-6763	1155	49	3	3	NUM
ejpam-6763	1155	50	.	.	X
ejpam-6763	1155	51	figure	figure	NOUN
ejpam-6763	1155	52	18	18	NUM
ejpam-6763	1155	53	:	:	PUNCT
ejpam-6763	1155	54	least	least	ADJ
ejpam-6763	1155	55	square	square	ADJ
ejpam-6763	1155	56	error	error	NOUN
ejpam-6763	1155	57	plot	plot	NOUN
ejpam-6763	1155	58	of	of	ADP
ejpam-6763	1155	59	y0(x	y0(x	NOUN
ejpam-6763	1155	60	)	)	PUNCT
ejpam-6763	1155	61	and	and	CCONJ
ejpam-6763	1155	62	y1(x	y1(x	NOUN
ejpam-6763	1155	63	)	)	PUNCT
ejpam-6763	1155	64	method	method	NOUN
ejpam-6763	1155	65	ffcpcbs	ffcpcbs	PRON
ejpam-6763	1155	66	for	for	ADP
ejpam-6763	1155	67	example	example	NOUN
ejpam-6763	1155	68	3	3	NUM
ejpam-6763	1155	69	.	.	NOUN
ejpam-6763	1155	70	7	7	NUM
ejpam-6763	1155	71	.	.	X
ejpam-6763	1155	72	conclusion	conclusion	NOUN
ejpam-6763	1155	73	in	in	ADP
ejpam-6763	1155	74	this	this	DET
ejpam-6763	1155	75	work	work	NOUN
ejpam-6763	1155	76	,	,	PUNCT
ejpam-6763	1155	77	a	a	DET
ejpam-6763	1155	78	high	high	ADJ
ejpam-6763	1155	79	-	-	PUNCT
ejpam-6763	1155	80	accuracy	accuracy	NOUN
ejpam-6763	1155	81	cubic	cubic	ADJ
ejpam-6763	1155	82	b	b	NOUN
ejpam-6763	1155	83	-	-	PUNCT
ejpam-6763	1155	84	spline	spline	NOUN
ejpam-6763	1155	85	collocation	collocation	NOUN
ejpam-6763	1155	86	method	method	NOUN
ejpam-6763	1155	87	is	be	AUX
ejpam-6763	1155	88	presented	present	VERB
ejpam-6763	1155	89	for	for	ADP
ejpam-6763	1155	90	solving	solve	VERB
ejpam-6763	1155	91	a	a	DET
ejpam-6763	1155	92	system	system	NOUN
ejpam-6763	1155	93	of	of	ADP
ejpam-6763	1155	94	volterra	volterra	PROPN
ejpam-6763	1155	95	integro	integro	PROPN
ejpam-6763	1155	96	-	-	PUNCT
ejpam-6763	1155	97	differential	differential	NOUN
ejpam-6763	1155	98	equations	equation	NOUN
ejpam-6763	1155	99	with	with	ADP
ejpam-6763	1155	100	classical	classical	ADJ
ejpam-6763	1155	101	and	and	CCONJ
ejpam-6763	1155	102	fractional	fractional	ADJ
ejpam-6763	1155	103	caputo	caputo	PROPN
ejpam-6763	1155	104	derivatives	derivative	NOUN
ejpam-6763	1155	105	(	(	PUNCT
ejpam-6763	1155	106	svide’s	svide’s	NOUN
ejpam-6763	1155	107	-	-	PUNCT
ejpam-6763	1155	108	cf	cf	NOUN
ejpam-6763	1155	109	)	)	PUNCT
ejpam-6763	1155	110	.	.	PUNCT
ejpam-6763	1156	1	unlike	unlike	ADP
ejpam-6763	1156	2	previous	previous	ADJ
ejpam-6763	1156	3	studies	study	NOUN
ejpam-6763	1156	4	that	that	PRON
ejpam-6763	1156	5	primarily	primarily	ADV
ejpam-6763	1156	6	focus	focus	VERB
ejpam-6763	1156	7	on	on	ADP
ejpam-6763	1156	8	single	single	ADJ
ejpam-6763	1156	9	equations	equation	NOUN
ejpam-6763	1156	10	[	[	X
ejpam-6763	1156	11	29	29	NUM
ejpam-6763	1156	12	,	,	PUNCT
ejpam-6763	1156	13	32–34	32–34	NUM
ejpam-6763	1156	14	]	]	PUNCT
ejpam-6763	1156	15	,	,	PUNCT
ejpam-6763	1156	16	the	the	DET
ejpam-6763	1156	17	d.	d.	PROPN
ejpam-6763	1156	18	kh	kh	PROPN
ejpam-6763	1156	19	.	.	PUNCT
ejpam-6763	1157	1	abdullah	abdullah	PROPN
ejpam-6763	1157	2	,	,	PUNCT
ejpam-6763	1157	3	sh	sh	PROPN
ejpam-6763	1157	4	.	.	PROPN
ejpam-6763	1157	5	sh	sh	PROPN
ejpam-6763	1157	6	.	.	PROPN
ejpam-6763	1157	7	ahmed	ahmed	PROPN
ejpam-6763	1157	8	,	,	PUNCT
ejpam-6763	1157	9	k.	k.	PROPN
ejpam-6763	1157	10	h.	h.	PROPN
ejpam-6763	1157	11	f.	f.	PROPN
ejpam-6763	1157	12	jwamer	jwamer	PROPN
ejpam-6763	1157	13	/	/	SYM
ejpam-6763	1157	14	eur	eur	PROPN
ejpam-6763	1157	15	.	.	PUNCT
ejpam-6763	1158	1	j.	j.	PROPN
ejpam-6763	1158	2	pure	pure	PROPN
ejpam-6763	1158	3	appl	appl	PROPN
ejpam-6763	1158	4	.	.	PROPN
ejpam-6763	1158	5	math	math	PROPN
ejpam-6763	1158	6	,	,	PUNCT
ejpam-6763	1158	7	18	18	NUM
ejpam-6763	1158	8	(	(	PUNCT
ejpam-6763	1158	9	4	4	NUM
ejpam-6763	1158	10	)	)	PUNCT
ejpam-6763	1158	11	(	(	PUNCT
ejpam-6763	1158	12	2025	2025	NUM
ejpam-6763	1158	13	)	)	PUNCT
ejpam-6763	1158	14	,	,	PUNCT
ejpam-6763	1158	15	6763	6763	NUM
ejpam-6763	1158	16	38	38	NUM
ejpam-6763	1158	17	of	of	ADP
ejpam-6763	1158	18	40	40	NUM
ejpam-6763	1158	19	proposed	propose	VERB
ejpam-6763	1158	20	approach	approach	NOUN
ejpam-6763	1158	21	efficiently	efficiently	ADV
ejpam-6763	1158	22	handles	handle	VERB
ejpam-6763	1158	23	systems	system	NOUN
ejpam-6763	1158	24	of	of	ADP
ejpam-6763	1158	25	equations	equation	NOUN
ejpam-6763	1158	26	.	.	PUNCT
ejpam-6763	1159	1	the	the	DET
ejpam-6763	1159	2	method	method	NOUN
ejpam-6763	1159	3	was	be	AUX
ejpam-6763	1159	4	implemented	implement	VERB
ejpam-6763	1159	5	in	in	ADP
ejpam-6763	1159	6	python	python	NOUN
ejpam-6763	1159	7	and	and	CCONJ
ejpam-6763	1159	8	validated	validate	VERB
ejpam-6763	1159	9	through	through	ADP
ejpam-6763	1159	10	several	several	ADJ
ejpam-6763	1159	11	benchmark	benchmark	ADJ
ejpam-6763	1159	12	examples	example	NOUN
ejpam-6763	1159	13	(	(	PUNCT
ejpam-6763	1159	14	tables	table	NOUN
ejpam-6763	1159	15	5	5	NUM
ejpam-6763	1159	16	,	,	PUNCT
ejpam-6763	1159	17	9	9	NUM
ejpam-6763	1159	18	,	,	PUNCT
ejpam-6763	1159	19	and	and	CCONJ
ejpam-6763	1159	20	13	13	NUM
ejpam-6763	1159	21	)	)	PUNCT
ejpam-6763	1159	22	.	.	PUNCT
ejpam-6763	1160	1	the	the	DET
ejpam-6763	1160	2	resulting	result	VERB
ejpam-6763	1160	3	least	least	ADJ
ejpam-6763	1160	4	-	-	PUNCT
ejpam-6763	1160	5	squares	square	NOUN
ejpam-6763	1160	6	errors	error	NOUN
ejpam-6763	1160	7	demonstrate	demonstrate	VERB
ejpam-6763	1160	8	improvements	improvement	NOUN
ejpam-6763	1160	9	by	by	ADP
ejpam-6763	1160	10	several	several	ADJ
ejpam-6763	1160	11	orders	order	NOUN
ejpam-6763	1160	12	of	of	ADP
ejpam-6763	1160	13	magnitude	magnitude	NOUN
ejpam-6763	1160	14	,	,	PUNCT
ejpam-6763	1160	15	highlighting	highlight	VERB
ejpam-6763	1160	16	the	the	DET
ejpam-6763	1160	17	method	method	NOUN
ejpam-6763	1160	18	’s	’s	PART
ejpam-6763	1160	19	superior	superior	ADJ
ejpam-6763	1160	20	numerical	numerical	ADJ
ejpam-6763	1160	21	accuracy	accuracy	NOUN
ejpam-6763	1160	22	and	and	CCONJ
ejpam-6763	1160	23	stable	stable	ADJ
ejpam-6763	1160	24	convergence	convergence	NOUN
ejpam-6763	1160	25	properties	property	NOUN
ejpam-6763	1160	26	across	across	ADP
ejpam-6763	1160	27	a	a	DET
ejpam-6763	1160	28	variety	variety	NOUN
ejpam-6763	1160	29	of	of	ADP
ejpam-6763	1160	30	test	test	NOUN
ejpam-6763	1160	31	problems	problem	NOUN
ejpam-6763	1160	32	.	.	PUNCT
ejpam-6763	1161	1	to	to	PART
ejpam-6763	1161	2	further	far	ADV
ejpam-6763	1161	3	develop	develop	VERB
ejpam-6763	1161	4	the	the	DET
ejpam-6763	1161	5	method	method	NOUN
ejpam-6763	1161	6	,	,	PUNCT
ejpam-6763	1161	7	future	future	ADJ
ejpam-6763	1161	8	research	research	NOUN
ejpam-6763	1161	9	can	can	AUX
ejpam-6763	1161	10	explore	explore	VERB
ejpam-6763	1161	11	its	its	PRON
ejpam-6763	1161	12	generalization	generalization	NOUN
ejpam-6763	1161	13	to	to	ADP
ejpam-6763	1161	14	nonlinear	nonlinear	ADJ
ejpam-6763	1161	15	systems	system	NOUN
ejpam-6763	1161	16	,	,	PUNCT
ejpam-6763	1161	17	time	time	NOUN
ejpam-6763	1161	18	-	-	PUNCT
ejpam-6763	1161	19	dependent	dependent	ADJ
ejpam-6763	1161	20	parameters	parameter	NOUN
ejpam-6763	1161	21	,	,	PUNCT
ejpam-6763	1161	22	and	and	CCONJ
ejpam-6763	1161	23	non	non	ADJ
ejpam-6763	1161	24	-	-	ADJ
ejpam-6763	1161	25	local	local	ADJ
ejpam-6763	1161	26	operators	operator	NOUN
ejpam-6763	1161	27	.	.	PUNCT
ejpam-6763	1162	1	additionally	additionally	ADV
ejpam-6763	1162	2	,	,	PUNCT
ejpam-6763	1162	3	incorporating	incorporate	VERB
ejpam-6763	1162	4	adaptive	adaptive	ADJ
ejpam-6763	1162	5	mesh	mesh	NOUN
ejpam-6763	1162	6	generation	generation	NOUN
ejpam-6763	1162	7	and	and	CCONJ
ejpam-6763	1162	8	refinement	refinement	NOUN
ejpam-6763	1162	9	algorithms	algorithm	NOUN
ejpam-6763	1162	10	can	can	AUX
ejpam-6763	1162	11	render	render	VERB
ejpam-6763	1162	12	it	it	PRON
ejpam-6763	1162	13	more	more	ADV
ejpam-6763	1162	14	versatile	versatile	ADJ
ejpam-6763	1162	15	and	and	CCONJ
ejpam-6763	1162	16	efficient	efficient	ADJ
ejpam-6763	1162	17	.	.	PUNCT
ejpam-6763	1163	1	indeed	indeed	ADV
ejpam-6763	1163	2	,	,	PUNCT
ejpam-6763	1163	3	this	this	DET
ejpam-6763	1163	4	method	method	NOUN
ejpam-6763	1163	5	is	be	AUX
ejpam-6763	1163	6	a	a	DET
ejpam-6763	1163	7	powerful	powerful	ADJ
ejpam-6763	1163	8	computational	computational	ADJ
ejpam-6763	1163	9	technique	technique	NOUN
ejpam-6763	1163	10	with	with	ADP
ejpam-6763	1163	11	applications	application	NOUN
ejpam-6763	1163	12	across	across	ADP
ejpam-6763	1163	13	many	many	ADJ
ejpam-6763	1163	14	disciplines	discipline	NOUN
ejpam-6763	1163	15	of	of	ADP
ejpam-6763	1163	16	applied	applied	ADJ
ejpam-6763	1163	17	mathematics	mathematic	NOUN
ejpam-6763	1163	18	,	,	PUNCT
ejpam-6763	1163	19	physics	physics	NOUN
ejpam-6763	1163	20	,	,	PUNCT
ejpam-6763	1163	21	and	and	CCONJ
ejpam-6763	1163	22	engineering	engineering	NOUN
ejpam-6763	1163	23	.	.	PUNCT
ejpam-6763	1164	1	acknowledgements	acknowledgement	NOUN
ejpam-6763	1164	2	this	this	DET
ejpam-6763	1164	3	work	work	NOUN
ejpam-6763	1164	4	is	be	AUX
ejpam-6763	1164	5	part	part	NOUN
ejpam-6763	1164	6	of	of	ADP
ejpam-6763	1164	7	the	the	DET
ejpam-6763	1164	8	phd	phd	NOUN
ejpam-6763	1164	9	research	research	NOUN
ejpam-6763	1164	10	conducted	conduct	VERB
ejpam-6763	1164	11	by	by	ADP
ejpam-6763	1164	12	the	the	DET
ejpam-6763	1164	13	student	student	NOUN
ejpam-6763	1164	14	diar	diar	PROPN
ejpam-6763	1164	15	khalid	khalid	PROPN
ejpam-6763	1164	16	abdullah	abdullah	PROPN
ejpam-6763	1164	17	in	in	ADP
ejpam-6763	1164	18	the	the	DET
ejpam-6763	1164	19	department	department	NOUN
ejpam-6763	1164	20	of	of	ADP
ejpam-6763	1164	21	mathematics	mathematics	PROPN
ejpam-6763	1164	22	,	,	PUNCT
ejpam-6763	1164	23	college	college	NOUN
ejpam-6763	1164	24	of	of	ADP
ejpam-6763	1164	25	science	science	NOUN
ejpam-6763	1164	26	,	,	PUNCT
ejpam-6763	1164	27	university	university	NOUN
ejpam-6763	1164	28	of	of	ADP
ejpam-6763	1164	29	sulaimani	sulaimani	PROPN
ejpam-6763	1164	30	,	,	PUNCT
ejpam-6763	1164	31	iraq	iraq	PROPN
ejpam-6763	1164	32	.	.	PUNCT
ejpam-6763	1165	1	conflict	conflict	NOUN
ejpam-6763	1165	2	of	of	ADP
ejpam-6763	1165	3	interest	interest	NOUN
ejpam-6763	1165	4	the	the	DET
ejpam-6763	1165	5	authors	author	NOUN
ejpam-6763	1165	6	declare	declare	VERB
ejpam-6763	1165	7	no	no	DET
ejpam-6763	1165	8	conflict	conflict	NOUN
ejpam-6763	1165	9	of	of	ADP
ejpam-6763	1165	10	interest	interest	NOUN
ejpam-6763	1165	11	.	.	PUNCT
ejpam-6763	1166	1	availability	availability	NOUN
ejpam-6763	1166	2	of	of	ADP
ejpam-6763	1166	3	data	datum	NOUN
ejpam-6763	1166	4	material	material	NOUN
ejpam-6763	1166	5	all	all	DET
ejpam-6763	1166	6	the	the	DET
ejpam-6763	1166	7	data	datum	NOUN
ejpam-6763	1166	8	of	of	ADP
ejpam-6763	1166	9	the	the	DET
ejpam-6763	1166	10	study	study	NOUN
ejpam-6763	1166	11	are	be	AUX
ejpam-6763	1166	12	included	include	VERB
ejpam-6763	1166	13	.	.	PUNCT
ejpam-6763	1167	1	authors	author	NOUN
ejpam-6763	1167	2	’	’	PART
ejpam-6763	1167	3	contributions	contribution	NOUN
ejpam-6763	1167	4	d.kh.a	d.kh.a	PROPN
ejpam-6763	1167	5	.	.	PUNCT
ejpam-6763	1167	6	,	,	PUNCT
ejpam-6763	1167	7	sh.sh.a	sh.sh.a	PROPN
ejpam-6763	1167	8	.	.	PUNCT
ejpam-6763	1168	1	and	and	CCONJ
ejpam-6763	1168	2	k.	k.	PROPN
ejpam-6763	1168	3	h.f	h.f	PROPN
ejpam-6763	1168	4	.	.	PROPN
ejpam-6763	1168	5	wrote	write	VERB
ejpam-6763	1168	6	the	the	DET
ejpam-6763	1168	7	main	main	ADJ
ejpam-6763	1168	8	manuscript	manuscript	NOUN
ejpam-6763	1168	9	.	.	PUNCT
ejpam-6763	1169	1	all	all	DET
ejpam-6763	1169	2	authors	author	NOUN
ejpam-6763	1169	3	reviewed	review	VERB
ejpam-6763	1169	4	the	the	DET
ejpam-6763	1169	5	manuscript	manuscript	NOUN
ejpam-6763	1169	6	.	.	PUNCT
ejpam-6763	1170	1	references	reference	NOUN
ejpam-6763	1170	2	[	[	X
ejpam-6763	1170	3	1	1	NUM
ejpam-6763	1170	4	]	]	PUNCT
ejpam-6763	1170	5	a.	a.	NOUN
ejpam-6763	1170	6	domoshnitsky	domoshnitsky	PROPN
ejpam-6763	1170	7	,	,	PUNCT
ejpam-6763	1170	8	a.	a.	NOUN
ejpam-6763	1170	9	sitkin	sitkin	PROPN
ejpam-6763	1170	10	,	,	PUNCT
ejpam-6763	1170	11	and	and	CCONJ
ejpam-6763	1170	12	l.	l.	PROPN
ejpam-6763	1170	13	zuckerman	zuckerman	PROPN
ejpam-6763	1170	14	.	.	PUNCT
ejpam-6763	1171	1	mathematical	mathematical	ADJ
ejpam-6763	1171	2	modeling	modeling	NOUN
ejpam-6763	1171	3	of	of	ADP
ejpam-6763	1171	4	covid-19	covid-19	PROPN
ejpam-6763	1171	5	transmission	transmission	NOUN
ejpam-6763	1171	6	in	in	ADP
ejpam-6763	1171	7	the	the	DET
ejpam-6763	1171	8	form	form	NOUN
ejpam-6763	1171	9	of	of	ADP
ejpam-6763	1171	10	system	system	NOUN
ejpam-6763	1171	11	of	of	ADP
ejpam-6763	1171	12	integro	integro	ADJ
ejpam-6763	1171	13	-	-	PUNCT
ejpam-6763	1171	14	differential	differential	NOUN
ejpam-6763	1171	15	equations	equation	NOUN
ejpam-6763	1171	16	.	.	PUNCT
ejpam-6763	1172	1	mathematics	mathematic	NOUN
ejpam-6763	1172	2	,	,	PUNCT
ejpam-6763	1172	3	10(23):4500	10(23):4500	NUM
ejpam-6763	1172	4	,	,	PUNCT
ejpam-6763	1172	5	2022	2022	NUM
ejpam-6763	1172	6	.	.	PUNCT
ejpam-6763	1173	1	[	[	X
ejpam-6763	1173	2	2	2	NUM
ejpam-6763	1173	3	]	]	PUNCT
ejpam-6763	1173	4	a.	a.	NOUN
ejpam-6763	1173	5	turab	turab	NOUN
ejpam-6763	1173	6	,	,	PUNCT
ejpam-6763	1173	7	a.	a.	NOUN
ejpam-6763	1173	8	montoyo	montoyo	NOUN
ejpam-6763	1173	9	,	,	PUNCT
ejpam-6763	1173	10	and	and	CCONJ
ejpam-6763	1173	11	j.	j.	PROPN
ejpam-6763	1173	12	a.	a.	PROPN
ejpam-6763	1173	13	nescolarde	nescolarde	PROPN
ejpam-6763	1173	14	-	-	PUNCT
ejpam-6763	1173	15	selva	selva	PROPN
ejpam-6763	1173	16	.	.	PUNCT
ejpam-6763	1174	1	computational	computational	ADJ
ejpam-6763	1174	2	and	and	CCONJ
ejpam-6763	1174	3	analytical	analytical	ADJ
ejpam-6763	1174	4	analysis	analysis	NOUN
ejpam-6763	1174	5	of	of	ADP
ejpam-6763	1174	6	integral	integral	ADJ
ejpam-6763	1174	7	-	-	PUNCT
ejpam-6763	1174	8	differential	differential	NOUN
ejpam-6763	1174	9	equations	equation	NOUN
ejpam-6763	1174	10	for	for	ADP
ejpam-6763	1174	11	modeling	model	VERB
ejpam-6763	1174	12	avoidance	avoidance	NOUN
ejpam-6763	1174	13	learning	learn	VERB
ejpam-6763	1174	14	behavior	behavior	NOUN
ejpam-6763	1174	15	.	.	PUNCT
ejpam-6763	1175	1	journal	journal	PROPN
ejpam-6763	1175	2	of	of	ADP
ejpam-6763	1175	3	applied	apply	VERB
ejpam-6763	1175	4	mathematics	mathematic	NOUN
ejpam-6763	1175	5	and	and	CCONJ
ejpam-6763	1175	6	computing	computing	NOUN
ejpam-6763	1175	7	,	,	PUNCT
ejpam-6763	1175	8	70(5):4423–4439	70(5):4423–4439	NUM
ejpam-6763	1175	9	,	,	PUNCT
ejpam-6763	1175	10	2024	2024	NUM
ejpam-6763	1175	11	.	.	PUNCT
ejpam-6763	1176	1	[	[	X
ejpam-6763	1176	2	3	3	NUM
ejpam-6763	1176	3	]	]	X
ejpam-6763	1176	4	i.	i.	NOUN
ejpam-6763	1176	5	podlubny	podlubny	PROPN
ejpam-6763	1176	6	.	.	PUNCT
ejpam-6763	1177	1	fractional	fractional	ADJ
ejpam-6763	1177	2	differential	differential	ADJ
ejpam-6763	1177	3	equations	equation	NOUN
ejpam-6763	1177	4	,	,	PUNCT
ejpam-6763	1177	5	volume	volume	NOUN
ejpam-6763	1177	6	198	198	NUM
ejpam-6763	1177	7	of	of	ADP
ejpam-6763	1177	8	mathematics	mathematic	NOUN
ejpam-6763	1177	9	in	in	ADP
ejpam-6763	1177	10	science	science	NOUN
ejpam-6763	1177	11	and	and	CCONJ
ejpam-6763	1177	12	engineering	engineering	NOUN
ejpam-6763	1177	13	.	.	PUNCT
ejpam-6763	1178	1	academic	academic	ADJ
ejpam-6763	1178	2	press	press	PROPN
ejpam-6763	1178	3	,	,	PUNCT
ejpam-6763	1178	4	usa	usa	PROPN
ejpam-6763	1178	5	,	,	PUNCT
ejpam-6763	1178	6	1999	1999	NUM
ejpam-6763	1178	7	.	.	PUNCT
ejpam-6763	1179	1	[	[	X
ejpam-6763	1179	2	4	4	X
ejpam-6763	1179	3	]	]	X
ejpam-6763	1179	4	h.	h.	NOUN
ejpam-6763	1179	5	mohammadi	mohammadi	PROPN
ejpam-6763	1179	6	,	,	PUNCT
ejpam-6763	1179	7	s.	s.	PROPN
ejpam-6763	1179	8	kumar	kumar	PROPN
ejpam-6763	1179	9	,	,	PUNCT
ejpam-6763	1179	10	sh	sh	PROPN
ejpam-6763	1179	11	.	.	PROPN
ejpam-6763	1179	12	rezapour	rezapour	PROPN
ejpam-6763	1179	13	,	,	PUNCT
ejpam-6763	1179	14	and	and	CCONJ
ejpam-6763	1179	15	s.	s.	PROPN
ejpam-6763	1179	16	etemad	etemad	PROPN
ejpam-6763	1179	17	.	.	PUNCT
ejpam-6763	1180	1	a	a	DET
ejpam-6763	1180	2	theoretical	theoretical	ADJ
ejpam-6763	1180	3	study	study	NOUN
ejpam-6763	1180	4	of	of	ADP
ejpam-6763	1180	5	the	the	DET
ejpam-6763	1180	6	caputofabrizio	caputofabrizio	NOUN
ejpam-6763	1180	7	fractional	fractional	ADJ
ejpam-6763	1180	8	modeling	modeling	NOUN
ejpam-6763	1180	9	for	for	ADP
ejpam-6763	1180	10	hearing	hear	VERB
ejpam-6763	1180	11	loss	loss	NOUN
ejpam-6763	1180	12	due	due	ADP
ejpam-6763	1180	13	to	to	ADP
ejpam-6763	1180	14	mumps	mump	NOUN
ejpam-6763	1180	15	virus	virus	NOUN
ejpam-6763	1180	16	with	with	ADP
ejpam-6763	1180	17	optimal	optimal	ADJ
ejpam-6763	1180	18	control	control	NOUN
ejpam-6763	1180	19	.	.	PUNCT
ejpam-6763	1181	1	chaos	chaos	NOUN
ejpam-6763	1181	2	,	,	PUNCT
ejpam-6763	1181	3	solitons	soliton	NOUN
ejpam-6763	1181	4	&	&	CCONJ
ejpam-6763	1181	5	fractals	fractal	NOUN
ejpam-6763	1181	6	,	,	PUNCT
ejpam-6763	1181	7	144:110668	144:110668	NUM
ejpam-6763	1181	8	,	,	PUNCT
ejpam-6763	1181	9	2021	2021	NUM
ejpam-6763	1181	10	.	.	PUNCT
ejpam-6763	1182	1	[	[	X
ejpam-6763	1182	2	5	5	NUM
ejpam-6763	1182	3	]	]	PUNCT
ejpam-6763	1182	4	s.	s.	PROPN
ejpam-6763	1182	5	alshammari	alshammari	PROPN
ejpam-6763	1182	6	,	,	PUNCT
ejpam-6763	1182	7	m.	m.	NOUN
ejpam-6763	1182	8	alshammari	alshammari	PROPN
ejpam-6763	1182	9	,	,	PUNCT
ejpam-6763	1182	10	m.	m.	NOUN
ejpam-6763	1182	11	alabedalhadi	alabedalhadi	NOUN
ejpam-6763	1182	12	,	,	PUNCT
ejpam-6763	1182	13	m.	m.	NOUN
ejpam-6763	1182	14	m.	m.	PROPN
ejpam-6763	1182	15	al	al	PROPN
ejpam-6763	1182	16	-	-	PUNCT
ejpam-6763	1182	17	sawalha	sawalha	NOUN
ejpam-6763	1182	18	,	,	PUNCT
ejpam-6763	1182	19	and	and	CCONJ
ejpam-6763	1182	20	m.	m.	PROPN
ejpam-6763	1182	21	al	al	PROPN
ejpam-6763	1182	22	-	-	PUNCT
ejpam-6763	1182	23	smadi	smadi	NOUN
ejpam-6763	1182	24	.	.	PUNCT
ejpam-6763	1183	1	numerical	numerical	ADJ
ejpam-6763	1183	2	investigation	investigation	NOUN
ejpam-6763	1183	3	of	of	ADP
ejpam-6763	1183	4	a	a	DET
ejpam-6763	1183	5	fractional	fractional	ADJ
ejpam-6763	1183	6	model	model	NOUN
ejpam-6763	1183	7	of	of	ADP
ejpam-6763	1183	8	a	a	DET
ejpam-6763	1183	9	tumor	tumor	NOUN
ejpam-6763	1183	10	-	-	PUNCT
ejpam-6763	1183	11	immune	immune	ADJ
ejpam-6763	1183	12	surveillance	surveillance	NOUN
ejpam-6763	1183	13	via	via	ADP
ejpam-6763	1183	14	caputo	caputo	PROPN
ejpam-6763	1183	15	operator	operator	PROPN
ejpam-6763	1183	16	.	.	PUNCT
ejpam-6763	1184	1	alexandria	alexandria	PROPN
ejpam-6763	1184	2	engineering	engineering	PROPN
ejpam-6763	1184	3	journal	journal	PROPN
ejpam-6763	1184	4	,	,	PUNCT
ejpam-6763	1184	5	86:525–536	86:525–536	PROPN
ejpam-6763	1184	6	,	,	PUNCT
ejpam-6763	1184	7	2024	2024	NUM
ejpam-6763	1184	8	.	.	PUNCT
ejpam-6763	1185	1	[	[	X
ejpam-6763	1185	2	6	6	NUM
ejpam-6763	1185	3	]	]	X
ejpam-6763	1185	4	i.	i.	PROPN
ejpam-6763	1185	5	ali	ali	PROPN
ejpam-6763	1185	6	,	,	PUNCT
ejpam-6763	1185	7	m.	m.	NOUN
ejpam-6763	1185	8	yaseen	yaseen	PROPN
ejpam-6763	1185	9	,	,	PUNCT
ejpam-6763	1185	10	and	and	CCONJ
ejpam-6763	1185	11	i.	i.	PROPN
ejpam-6763	1185	12	akram	akram	PROPN
ejpam-6763	1185	13	.	.	PUNCT
ejpam-6763	1186	1	utilizing	utilize	VERB
ejpam-6763	1186	2	cubic	cubic	ADJ
ejpam-6763	1186	3	b	b	NOUN
ejpam-6763	1186	4	-	-	PUNCT
ejpam-6763	1186	5	spline	spline	NOUN
ejpam-6763	1186	6	collocation	collocation	NOUN
ejpam-6763	1186	7	technique	technique	NOUN
ejpam-6763	1186	8	for	for	ADP
ejpam-6763	1186	9	solving	solve	VERB
ejpam-6763	1186	10	linear	linear	NOUN
ejpam-6763	1186	11	and	and	CCONJ
ejpam-6763	1186	12	nonlinear	nonlinear	ADJ
ejpam-6763	1186	13	fractional	fractional	ADJ
ejpam-6763	1186	14	integro	integro	ADJ
ejpam-6763	1186	15	-	-	PUNCT
ejpam-6763	1186	16	differential	differential	NOUN
ejpam-6763	1186	17	equations	equation	NOUN
ejpam-6763	1186	18	of	of	ADP
ejpam-6763	1186	19	volterra	volterra	NOUN
ejpam-6763	1186	20	and	and	CCONJ
ejpam-6763	1186	21	fredholm	fredholm	NOUN
ejpam-6763	1186	22	types	type	NOUN
ejpam-6763	1186	23	.	.	PUNCT
ejpam-6763	1187	1	fractal	fractal	ADJ
ejpam-6763	1187	2	and	and	CCONJ
ejpam-6763	1187	3	fractional	fractional	ADJ
ejpam-6763	1187	4	,	,	PUNCT
ejpam-6763	1187	5	8(5):268	8(5):268	NUM
ejpam-6763	1187	6	,	,	PUNCT
ejpam-6763	1187	7	2024	2024	NUM
ejpam-6763	1187	8	.	.	PUNCT
ejpam-6763	1188	1	d.	d.	PROPN
ejpam-6763	1188	2	kh	kh	PROPN
ejpam-6763	1188	3	.	.	PUNCT
ejpam-6763	1189	1	abdullah	abdullah	PROPN
ejpam-6763	1189	2	,	,	PUNCT
ejpam-6763	1189	3	sh	sh	PROPN
ejpam-6763	1189	4	.	.	PROPN
ejpam-6763	1189	5	sh	sh	PROPN
ejpam-6763	1189	6	.	.	PROPN
ejpam-6763	1189	7	ahmed	ahmed	PROPN
ejpam-6763	1189	8	,	,	PUNCT
ejpam-6763	1189	9	k.	k.	PROPN
ejpam-6763	1189	10	h.	h.	PROPN
ejpam-6763	1189	11	f.	f.	PROPN
ejpam-6763	1189	12	jwamer	jwamer	PROPN
ejpam-6763	1189	13	/	/	SYM
ejpam-6763	1189	14	eur	eur	PROPN
ejpam-6763	1189	15	.	.	PUNCT
ejpam-6763	1190	1	j.	j.	PROPN
ejpam-6763	1190	2	pure	pure	PROPN
ejpam-6763	1190	3	appl	appl	PROPN
ejpam-6763	1190	4	.	.	PROPN
ejpam-6763	1190	5	math	math	PROPN
ejpam-6763	1190	6	,	,	PUNCT
ejpam-6763	1190	7	18	18	NUM
ejpam-6763	1190	8	(	(	PUNCT
ejpam-6763	1190	9	4	4	NUM
ejpam-6763	1190	10	)	)	PUNCT
ejpam-6763	1190	11	(	(	PUNCT
ejpam-6763	1190	12	2025	2025	NUM
ejpam-6763	1190	13	)	)	PUNCT
ejpam-6763	1190	14	,	,	PUNCT
ejpam-6763	1190	15	6763	6763	NUM
ejpam-6763	1190	16	39	39	NUM
ejpam-6763	1190	17	of	of	ADP
ejpam-6763	1190	18	40	40	NUM
ejpam-6763	1190	19	[	[	X
ejpam-6763	1190	20	7	7	NUM
ejpam-6763	1190	21	]	]	PUNCT
ejpam-6763	1190	22	k.	k.	PROPN
ejpam-6763	1190	23	hama	hama	PROPN
ejpam-6763	1190	24	faraj	faraj	PROPN
ejpam-6763	1190	25	,	,	PUNCT
ejpam-6763	1190	26	sh	sh	PROPN
ejpam-6763	1190	27	.	.	PROPN
ejpam-6763	1190	28	shawki	shawki	PROPN
ejpam-6763	1190	29	,	,	PUNCT
ejpam-6763	1190	30	and	and	CCONJ
ejpam-6763	1190	31	d.	d.	PROPN
ejpam-6763	1190	32	khalid	khalid	PROPN
ejpam-6763	1190	33	.	.	PUNCT
ejpam-6763	1191	1	numerical	numerical	PROPN
ejpam-6763	1191	2	treatment	treatment	NOUN
ejpam-6763	1191	3	solution	solution	NOUN
ejpam-6763	1191	4	of	of	ADP
ejpam-6763	1191	5	volterra	volterra	PROPN
ejpam-6763	1191	6	integrofractional	integrofractional	ADJ
ejpam-6763	1191	7	differential	differential	NOUN
ejpam-6763	1191	8	equation	equation	NOUN
ejpam-6763	1191	9	by	by	ADP
ejpam-6763	1191	10	using	use	VERB
ejpam-6763	1191	11	linear	linear	PROPN
ejpam-6763	1191	12	spline	spline	NOUN
ejpam-6763	1191	13	function	function	NOUN
ejpam-6763	1191	14	.	.	PUNCT
ejpam-6763	1192	1	journal	journal	PROPN
ejpam-6763	1192	2	of	of	ADP
ejpam-6763	1192	3	zankoy	zankoy	PROPN
ejpam-6763	1192	4	sulaimani	sulaimani	PROPN
ejpam-6763	1192	5	part	part	NOUN
ejpam-6763	1192	6	a	a	PRON
ejpam-6763	1192	7	,	,	PUNCT
ejpam-6763	1192	8	22(2	22(2	NUM
ejpam-6763	1192	9	)	)	PUNCT
ejpam-6763	1192	10	,	,	PUNCT
ejpam-6763	1192	11	2020	2020	NUM
ejpam-6763	1192	12	.	.	PUNCT
ejpam-6763	1193	1	[	[	X
ejpam-6763	1193	2	8	8	X
ejpam-6763	1193	3	]	]	PUNCT
ejpam-6763	1193	4	j.	j.	PROPN
ejpam-6763	1193	5	chang	chang	PROPN
ejpam-6763	1193	6	,	,	PUNCT
ejpam-6763	1193	7	q.	q.	PROPN
ejpam-6763	1193	8	yang	yang	PROPN
ejpam-6763	1193	9	,	,	PUNCT
ejpam-6763	1193	10	and	and	CCONJ
ejpam-6763	1193	11	c.	c.	PROPN
ejpam-6763	1193	12	liu	liu	PROPN
ejpam-6763	1193	13	.	.	PUNCT
ejpam-6763	1194	1	b	b	X
ejpam-6763	1194	2	-	-	PUNCT
ejpam-6763	1194	3	spline	spline	NOUN
ejpam-6763	1194	4	method	method	NOUN
ejpam-6763	1194	5	for	for	ADP
ejpam-6763	1194	6	solving	solve	VERB
ejpam-6763	1194	7	boundary	boundary	ADJ
ejpam-6763	1194	8	value	value	NOUN
ejpam-6763	1194	9	problems	problem	NOUN
ejpam-6763	1194	10	of	of	ADP
ejpam-6763	1194	11	linear	linear	ADJ
ejpam-6763	1194	12	ordinary	ordinary	ADJ
ejpam-6763	1194	13	differential	differential	ADJ
ejpam-6763	1194	14	equations	equation	NOUN
ejpam-6763	1194	15	.	.	PUNCT
ejpam-6763	1195	1	in	in	ADP
ejpam-6763	1195	2	advances	advance	NOUN
ejpam-6763	1195	3	in	in	ADP
ejpam-6763	1195	4	computer	computer	NOUN
ejpam-6763	1195	5	science	science	NOUN
ejpam-6763	1195	6	and	and	CCONJ
ejpam-6763	1195	7	information	information	NOUN
ejpam-6763	1195	8	engineering	engineering	NOUN
ejpam-6763	1195	9	,	,	PUNCT
ejpam-6763	1195	10	pages	page	NOUN
ejpam-6763	1195	11	326–333	326–333	NUM
ejpam-6763	1195	12	.	.	PUNCT
ejpam-6763	1195	13	springer	springer	NOUN
ejpam-6763	1195	14	,	,	PUNCT
ejpam-6763	1195	15	2010	2010	NUM
ejpam-6763	1195	16	.	.	PUNCT
ejpam-6763	1196	1	[	[	X
ejpam-6763	1196	2	9	9	NUM
ejpam-6763	1196	3	]	]	PUNCT
ejpam-6763	1196	4	m.	m.	NOUN
ejpam-6763	1196	5	yi	yi	PROPN
ejpam-6763	1196	6	and	and	CCONJ
ejpam-6763	1196	7	j.	j.	PROPN
ejpam-6763	1196	8	huang	huang	PROPN
ejpam-6763	1196	9	.	.	PROPN
ejpam-6763	1196	10	cas	cas	PROPN
ejpam-6763	1196	11	wavelet	wavelet	PROPN
ejpam-6763	1196	12	method	method	NOUN
ejpam-6763	1196	13	for	for	ADP
ejpam-6763	1196	14	solving	solve	VERB
ejpam-6763	1196	15	the	the	DET
ejpam-6763	1196	16	fractional	fractional	ADJ
ejpam-6763	1196	17	integro	integro	ADJ
ejpam-6763	1196	18	-	-	PUNCT
ejpam-6763	1196	19	differential	differential	NOUN
ejpam-6763	1196	20	equation	equation	NOUN
ejpam-6763	1196	21	with	with	ADP
ejpam-6763	1196	22	a	a	DET
ejpam-6763	1196	23	weakly	weakly	ADJ
ejpam-6763	1196	24	singular	singular	ADJ
ejpam-6763	1196	25	kernel	kernel	NOUN
ejpam-6763	1196	26	.	.	PUNCT
ejpam-6763	1197	1	international	international	ADJ
ejpam-6763	1197	2	journal	journal	PROPN
ejpam-6763	1197	3	of	of	ADP
ejpam-6763	1197	4	computer	computer	NOUN
ejpam-6763	1197	5	mathematics	mathematic	NOUN
ejpam-6763	1197	6	,	,	PUNCT
ejpam-6763	1197	7	92(8):1715–1728	92(8):1715–1728	NOUN
ejpam-6763	1197	8	,	,	PUNCT
ejpam-6763	1197	9	2015	2015	NUM
ejpam-6763	1197	10	.	.	PUNCT
ejpam-6763	1198	1	[	[	X
ejpam-6763	1198	2	10	10	NUM
ejpam-6763	1198	3	]	]	PUNCT
ejpam-6763	1198	4	k.	k.	PROPN
ejpam-6763	1198	5	r.	r.	PROPN
ejpam-6763	1198	6	raslan	raslan	PROPN
ejpam-6763	1198	7	and	and	CCONJ
ejpam-6763	1198	8	t.	t.	PROPN
ejpam-6763	1198	9	s.	s.	PROPN
ejpam-6763	1198	10	el	el	PROPN
ejpam-6763	1198	11	-	-	PROPN
ejpam-6763	1198	12	danaf	danaf	PROPN
ejpam-6763	1198	13	.	.	PUNCT
ejpam-6763	1199	1	solitary	solitary	ADJ
ejpam-6763	1199	2	waves	wave	NOUN
ejpam-6763	1199	3	solutions	solution	NOUN
ejpam-6763	1199	4	of	of	ADP
ejpam-6763	1199	5	the	the	DET
ejpam-6763	1199	6	mrlw	mrlw	NOUN
ejpam-6763	1199	7	equation	equation	NOUN
ejpam-6763	1199	8	using	use	VERB
ejpam-6763	1199	9	quintic	quintic	ADJ
ejpam-6763	1199	10	b	b	NOUN
ejpam-6763	1199	11	-	-	PUNCT
ejpam-6763	1199	12	splines	spline	NOUN
ejpam-6763	1199	13	.	.	PUNCT
ejpam-6763	1200	1	journal	journal	NOUN
ejpam-6763	1200	2	of	of	ADP
ejpam-6763	1200	3	king	king	PROPN
ejpam-6763	1200	4	saud	saud	PROPN
ejpam-6763	1200	5	university	university	PROPN
ejpam-6763	1200	6	science	science	NOUN
ejpam-6763	1200	7	,	,	PUNCT
ejpam-6763	1200	8	22(3):161–166	22(3):161–166	PROPN
ejpam-6763	1200	9	,	,	PUNCT
ejpam-6763	1200	10	2010	2010	NUM
ejpam-6763	1200	11	.	.	PUNCT
ejpam-6763	1201	1	[	[	X
ejpam-6763	1201	2	11	11	NUM
ejpam-6763	1201	3	]	]	X
ejpam-6763	1201	4	f.	f.	PROPN
ejpam-6763	1201	5	haq	haq	PROPN
ejpam-6763	1201	6	,	,	PUNCT
ejpam-6763	1201	7	s.	s.	PROPN
ejpam-6763	1201	8	islam	islam	PROPN
ejpam-6763	1201	9	,	,	PUNCT
ejpam-6763	1201	10	and	and	CCONJ
ejpam-6763	1201	11	i.	i.	PROPN
ejpam-6763	1201	12	tirmizi	tirmizi	PROPN
ejpam-6763	1201	13	.	.	PUNCT
ejpam-6763	1202	1	a	a	DET
ejpam-6763	1202	2	numerical	numerical	ADJ
ejpam-6763	1202	3	technique	technique	NOUN
ejpam-6763	1202	4	for	for	ADP
ejpam-6763	1202	5	solution	solution	NOUN
ejpam-6763	1202	6	of	of	ADP
ejpam-6763	1202	7	the	the	DET
ejpam-6763	1202	8	mrlw	mrlw	NOUN
ejpam-6763	1202	9	equation	equation	NOUN
ejpam-6763	1202	10	using	use	VERB
ejpam-6763	1202	11	quartic	quartic	ADJ
ejpam-6763	1202	12	b	b	NOUN
ejpam-6763	1202	13	-	-	PUNCT
ejpam-6763	1202	14	splines	spline	NOUN
ejpam-6763	1202	15	.	.	PUNCT
ejpam-6763	1203	1	applied	apply	VERB
ejpam-6763	1203	2	mathematical	mathematical	ADJ
ejpam-6763	1203	3	modelling	modelling	NOUN
ejpam-6763	1203	4	,	,	PUNCT
ejpam-6763	1203	5	34(12):4151–4160	34(12):4151–4160	NUM
ejpam-6763	1203	6	,	,	PUNCT
ejpam-6763	1203	7	2010	2010	NUM
ejpam-6763	1203	8	.	.	PUNCT
ejpam-6763	1204	1	[	[	X
ejpam-6763	1204	2	12	12	NUM
ejpam-6763	1204	3	]	]	PUNCT
ejpam-6763	1204	4	k.	k.	PROPN
ejpam-6763	1204	5	hama	hama	PROPN
ejpam-6763	1204	6	faraj	faraj	PROPN
ejpam-6763	1204	7	,	,	PUNCT
ejpam-6763	1204	8	sh	sh	PROPN
ejpam-6763	1204	9	.	.	PROPN
ejpam-6763	1204	10	shawki	shawki	PROPN
ejpam-6763	1204	11	,	,	PUNCT
ejpam-6763	1204	12	and	and	CCONJ
ejpam-6763	1204	13	d.	d.	PROPN
ejpam-6763	1204	14	khalid	khalid	PROPN
ejpam-6763	1204	15	.	.	PROPN
ejpam-6763	1205	1	approximate	approximate	ADJ
ejpam-6763	1205	2	solution	solution	NOUN
ejpam-6763	1205	3	of	of	ADP
ejpam-6763	1205	4	volterra	volterra	PROPN
ejpam-6763	1205	5	integro	integro	PROPN
ejpam-6763	1205	6	-	-	PUNCT
ejpam-6763	1205	7	fractional	fractional	ADJ
ejpam-6763	1205	8	differential	differential	ADJ
ejpam-6763	1205	9	equations	equation	NOUN
ejpam-6763	1205	10	using	use	VERB
ejpam-6763	1205	11	quadratic	quadratic	ADJ
ejpam-6763	1205	12	spline	spline	NOUN
ejpam-6763	1205	13	function	function	NOUN
ejpam-6763	1205	14	.	.	PUNCT
ejpam-6763	1206	1	bulletin	bulletin	NOUN
ejpam-6763	1206	2	of	of	ADP
ejpam-6763	1206	3	karaganda	karaganda	PROPN
ejpam-6763	1206	4	university	university	PROPN
ejpam-6763	1206	5	.	.	PUNCT
ejpam-6763	1207	1	mathematics	mathematic	NOUN
ejpam-6763	1207	2	series	series	PROPN
ejpam-6763	1207	3	,	,	PUNCT
ejpam-6763	1207	4	101(1):50–64	101(1):50–64	PROPN
ejpam-6763	1207	5	,	,	PUNCT
ejpam-6763	1207	6	2021	2021	NUM
ejpam-6763	1207	7	.	.	PUNCT
ejpam-6763	1208	1	[	[	X
ejpam-6763	1208	2	13	13	NUM
ejpam-6763	1208	3	]	]	PUNCT
ejpam-6763	1208	4	m.	m.	NOUN
ejpam-6763	1208	5	ebrahimi	ebrahimi	PROPN
ejpam-6763	1208	6	and	and	CCONJ
ejpam-6763	1208	7	s.	s.	PROPN
ejpam-6763	1208	8	rouhani	rouhani	PROPN
ejpam-6763	1208	9	rankoohi	rankoohi	PROPN
ejpam-6763	1208	10	.	.	PUNCT
ejpam-6763	1209	1	spline	spline	NOUN
ejpam-6763	1209	2	collocation	collocation	NOUN
ejpam-6763	1209	3	for	for	ADP
ejpam-6763	1209	4	system	system	NOUN
ejpam-6763	1209	5	of	of	ADP
ejpam-6763	1209	6	fredholm	fredholm	NOUN
ejpam-6763	1209	7	and	and	CCONJ
ejpam-6763	1209	8	volterra	volterra	NOUN
ejpam-6763	1209	9	integro	integro	PROPN
ejpam-6763	1209	10	-	-	PUNCT
ejpam-6763	1209	11	differential	differential	NOUN
ejpam-6763	1209	12	equations	equation	NOUN
ejpam-6763	1209	13	.	.	PUNCT
ejpam-6763	1210	1	knowledge	knowledge	NOUN
ejpam-6763	1210	2	and	and	CCONJ
ejpam-6763	1210	3	information	information	NOUN
ejpam-6763	1210	4	systems	system	NOUN
ejpam-6763	1210	5	,	,	PUNCT
ejpam-6763	1210	6	43(1):219–247	43(1):219–247	PROPN
ejpam-6763	1210	7	,	,	PUNCT
ejpam-6763	1210	8	2015	2015	NUM
ejpam-6763	1210	9	.	.	PUNCT
ejpam-6763	1211	1	[	[	X
ejpam-6763	1211	2	14	14	NUM
ejpam-6763	1211	3	]	]	PUNCT
ejpam-6763	1211	4	m.	m.	NOUN
ejpam-6763	1211	5	abbas	abbas	PROPN
ejpam-6763	1211	6	,	,	PUNCT
ejpam-6763	1211	7	s.	s.	PROPN
ejpam-6763	1211	8	aslam	aslam	PROPN
ejpam-6763	1211	9	,	,	PUNCT
ejpam-6763	1211	10	f.	f.	PROPN
ejpam-6763	1211	11	a.	a.	PROPN
ejpam-6763	1211	12	abdullah	abdullah	PROPN
ejpam-6763	1211	13	,	,	PUNCT
ejpam-6763	1211	14	m.	m.	PROPN
ejpam-6763	1211	15	b.	b.	PROPN
ejpam-6763	1211	16	riaz	riaz	PROPN
ejpam-6763	1211	17	,	,	PUNCT
ejpam-6763	1211	18	and	and	CCONJ
ejpam-6763	1211	19	k.	k.	PROPN
ejpam-6763	1211	20	a.	a.	PROPN
ejpam-6763	1211	21	gepreel	gepreel	PROPN
ejpam-6763	1211	22	.	.	PUNCT
ejpam-6763	1212	1	an	an	DET
ejpam-6763	1212	2	efficient	efficient	ADJ
ejpam-6763	1212	3	spline	spline	NOUN
ejpam-6763	1212	4	technique	technique	NOUN
ejpam-6763	1212	5	for	for	ADP
ejpam-6763	1212	6	solving	solve	VERB
ejpam-6763	1212	7	time	time	NOUN
ejpam-6763	1212	8	-	-	PUNCT
ejpam-6763	1212	9	fractional	fractional	ADJ
ejpam-6763	1212	10	integro	integro	ADJ
ejpam-6763	1212	11	-	-	PUNCT
ejpam-6763	1212	12	differential	differential	NOUN
ejpam-6763	1212	13	equations	equation	NOUN
ejpam-6763	1212	14	.	.	PUNCT
ejpam-6763	1213	1	heliyon	heliyon	NOUN
ejpam-6763	1213	2	,	,	PUNCT
ejpam-6763	1213	3	9(9	9(9	NUM
ejpam-6763	1213	4	)	)	PUNCT
ejpam-6763	1213	5	,	,	PUNCT
ejpam-6763	1213	6	2023	2023	NUM
ejpam-6763	1213	7	.	.	PUNCT
ejpam-6763	1214	1	[	[	X
ejpam-6763	1214	2	15	15	NUM
ejpam-6763	1214	3	]	]	X
ejpam-6763	1214	4	b.	b.	PROPN
ejpam-6763	1214	5	ghosh	ghosh	PROPN
ejpam-6763	1214	6	and	and	CCONJ
ejpam-6763	1214	7	j.	j.	PROPN
ejpam-6763	1214	8	mohapatra	mohapatra	PROPN
ejpam-6763	1214	9	.	.	PUNCT
ejpam-6763	1215	1	an	an	DET
ejpam-6763	1215	2	iterative	iterative	ADJ
ejpam-6763	1215	3	difference	difference	NOUN
ejpam-6763	1215	4	scheme	scheme	NOUN
ejpam-6763	1215	5	for	for	ADP
ejpam-6763	1215	6	solving	solve	VERB
ejpam-6763	1215	7	arbitrary	arbitrary	ADJ
ejpam-6763	1215	8	order	order	NOUN
ejpam-6763	1215	9	nonlinear	nonlinear	PROPN
ejpam-6763	1215	10	volterra	volterra	PROPN
ejpam-6763	1215	11	integro	integro	PROPN
ejpam-6763	1215	12	-	-	PUNCT
ejpam-6763	1215	13	differential	differential	ADJ
ejpam-6763	1215	14	population	population	NOUN
ejpam-6763	1215	15	growth	growth	NOUN
ejpam-6763	1215	16	model	model	NOUN
ejpam-6763	1215	17	.	.	PUNCT
ejpam-6763	1216	1	journal	journal	NOUN
ejpam-6763	1216	2	of	of	ADP
ejpam-6763	1216	3	analysis	analysis	NOUN
ejpam-6763	1216	4	,	,	PUNCT
ejpam-6763	1216	5	2023	2023	NUM
ejpam-6763	1216	6	.	.	PUNCT
ejpam-6763	1217	1	[	[	X
ejpam-6763	1217	2	16	16	NUM
ejpam-6763	1217	3	]	]	X
ejpam-6763	1217	4	i.	i.	PROPN
ejpam-6763	1217	5	masti	masti	PROPN
ejpam-6763	1217	6	and	and	CCONJ
ejpam-6763	1217	7	k.	k.	PROPN
ejpam-6763	1217	8	sayevand	sayevand	PROPN
ejpam-6763	1217	9	.	.	PUNCT
ejpam-6763	1218	1	on	on	ADP
ejpam-6763	1218	2	collocation	collocation	NOUN
ejpam-6763	1218	3	-	-	PUNCT
ejpam-6763	1218	4	galerkin	galerkin	NOUN
ejpam-6763	1218	5	method	method	NOUN
ejpam-6763	1218	6	and	and	CCONJ
ejpam-6763	1218	7	fractional	fractional	ADJ
ejpam-6763	1218	8	b	b	X
ejpam-6763	1218	9	-	-	PUNCT
ejpam-6763	1218	10	spline	spline	NOUN
ejpam-6763	1218	11	functions	function	NOUN
ejpam-6763	1218	12	for	for	ADP
ejpam-6763	1218	13	a	a	DET
ejpam-6763	1218	14	class	class	NOUN
ejpam-6763	1218	15	of	of	ADP
ejpam-6763	1218	16	stochastic	stochastic	ADJ
ejpam-6763	1218	17	fractional	fractional	ADJ
ejpam-6763	1218	18	integro	integro	ADJ
ejpam-6763	1218	19	-	-	PUNCT
ejpam-6763	1218	20	differential	differential	NOUN
ejpam-6763	1218	21	equations	equation	NOUN
ejpam-6763	1218	22	.	.	PUNCT
ejpam-6763	1219	1	mathematics	mathematic	NOUN
ejpam-6763	1219	2	and	and	CCONJ
ejpam-6763	1219	3	computers	computer	NOUN
ejpam-6763	1219	4	in	in	ADP
ejpam-6763	1219	5	simulation	simulation	NOUN
ejpam-6763	1219	6	,	,	PUNCT
ejpam-6763	1219	7	216:263–287	216:263–287	NUM
ejpam-6763	1219	8	,	,	PUNCT
ejpam-6763	1219	9	2024	2024	NUM
ejpam-6763	1219	10	.	.	PUNCT
ejpam-6763	1220	1	[	[	X
ejpam-6763	1220	2	17	17	NUM
ejpam-6763	1220	3	]	]	X
ejpam-6763	1220	4	q.	q.	PROPN
ejpam-6763	1220	5	khan	khan	PROPN
ejpam-6763	1220	6	,	,	PUNCT
ejpam-6763	1220	7	h.	h.	PROPN
ejpam-6763	1220	8	khan	khan	PROPN
ejpam-6763	1220	9	,	,	PUNCT
ejpam-6763	1220	10	p.	p.	PROPN
ejpam-6763	1220	11	kumam	kumam	PROPN
ejpam-6763	1220	12	,	,	PUNCT
ejpam-6763	1220	13	f.	f.	PROPN
ejpam-6763	1220	14	tchier	tchier	PROPN
ejpam-6763	1220	15	,	,	PUNCT
ejpam-6763	1220	16	and	and	CCONJ
ejpam-6763	1220	17	g.	g.	PROPN
ejpam-6763	1220	18	singh	singh	PROPN
ejpam-6763	1220	19	.	.	PUNCT
ejpam-6763	1221	1	ladm	ladm	ADJ
ejpam-6763	1221	2	procedure	procedure	NOUN
ejpam-6763	1221	3	to	to	PART
ejpam-6763	1221	4	find	find	VERB
ejpam-6763	1221	5	the	the	DET
ejpam-6763	1221	6	analytical	analytical	ADJ
ejpam-6763	1221	7	solutions	solution	NOUN
ejpam-6763	1221	8	of	of	ADP
ejpam-6763	1221	9	the	the	DET
ejpam-6763	1221	10	nonlinear	nonlinear	ADJ
ejpam-6763	1221	11	fractional	fractional	ADJ
ejpam-6763	1221	12	dynamics	dynamic	NOUN
ejpam-6763	1221	13	of	of	ADP
ejpam-6763	1221	14	partial	partial	ADJ
ejpam-6763	1221	15	integro	integro	ADJ
ejpam-6763	1221	16	-	-	PUNCT
ejpam-6763	1221	17	differential	differential	NOUN
ejpam-6763	1221	18	equations	equation	NOUN
ejpam-6763	1221	19	.	.	PUNCT
ejpam-6763	1222	1	demonstratio	demonstratio	PROPN
ejpam-6763	1222	2	mathematica	mathematica	PROPN
ejpam-6763	1222	3	,	,	PUNCT
ejpam-6763	1222	4	57(1	57(1	PROPN
ejpam-6763	1222	5	)	)	PUNCT
ejpam-6763	1222	6	,	,	PUNCT
ejpam-6763	1222	7	2024	2024	NUM
ejpam-6763	1222	8	.	.	PUNCT
ejpam-6763	1223	1	[	[	X
ejpam-6763	1223	2	18	18	NUM
ejpam-6763	1223	3	]	]	PUNCT
ejpam-6763	1223	4	m.	m.	NOUN
ejpam-6763	1223	5	khader	khader	PROPN
ejpam-6763	1223	6	and	and	CCONJ
ejpam-6763	1223	7	n.	n.	PROPN
ejpam-6763	1223	8	sweilam	sweilam	PROPN
ejpam-6763	1223	9	.	.	PUNCT
ejpam-6763	1224	1	on	on	ADP
ejpam-6763	1224	2	the	the	DET
ejpam-6763	1224	3	approximate	approximate	ADJ
ejpam-6763	1224	4	solutions	solution	NOUN
ejpam-6763	1224	5	for	for	ADP
ejpam-6763	1224	6	system	system	NOUN
ejpam-6763	1224	7	of	of	ADP
ejpam-6763	1224	8	fractional	fractional	ADJ
ejpam-6763	1224	9	integrodifferential	integrodifferential	ADJ
ejpam-6763	1224	10	equations	equation	NOUN
ejpam-6763	1224	11	using	use	VERB
ejpam-6763	1224	12	chebyshev	chebyshev	NOUN
ejpam-6763	1224	13	pseudo	pseudo	NOUN
ejpam-6763	1224	14	-	-	ADJ
ejpam-6763	1224	15	spectral	spectral	ADJ
ejpam-6763	1224	16	method	method	NOUN
ejpam-6763	1224	17	.	.	PUNCT
ejpam-6763	1225	1	applied	apply	VERB
ejpam-6763	1225	2	mathematical	mathematical	ADJ
ejpam-6763	1225	3	modelling	modelling	NOUN
ejpam-6763	1225	4	,	,	PUNCT
ejpam-6763	1225	5	37(24):9819–9828	37(24):9819–9828	NUM
ejpam-6763	1225	6	,	,	PUNCT
ejpam-6763	1225	7	2013	2013	NUM
ejpam-6763	1225	8	.	.	PUNCT
ejpam-6763	1226	1	[	[	X
ejpam-6763	1226	2	19	19	NUM
ejpam-6763	1226	3	]	]	PUNCT
ejpam-6763	1226	4	l.	l.	PROPN
ejpam-6763	1226	5	huang	huang	PROPN
ejpam-6763	1226	6	,	,	PUNCT
ejpam-6763	1226	7	x.	x.	PROPN
ejpam-6763	1226	8	li	li	PROPN
ejpam-6763	1226	9	,	,	PUNCT
ejpam-6763	1226	10	y.	y.	PROPN
ejpam-6763	1226	11	zhao	zhao	PROPN
ejpam-6763	1226	12	,	,	PUNCT
ejpam-6763	1226	13	and	and	CCONJ
ejpam-6763	1226	14	x.	x.	PROPN
ejpam-6763	1226	15	duan	duan	PROPN
ejpam-6763	1226	16	.	.	PROPN
ejpam-6763	1226	17	approximate	approximate	ADJ
ejpam-6763	1226	18	solution	solution	NOUN
ejpam-6763	1226	19	of	of	ADP
ejpam-6763	1226	20	fractional	fractional	ADJ
ejpam-6763	1226	21	integrodifferential	integrodifferential	ADJ
ejpam-6763	1226	22	equations	equation	NOUN
ejpam-6763	1226	23	by	by	ADP
ejpam-6763	1226	24	taylor	taylor	PROPN
ejpam-6763	1226	25	expansion	expansion	NOUN
ejpam-6763	1226	26	method	method	NOUN
ejpam-6763	1226	27	.	.	PUNCT
ejpam-6763	1227	1	computers	computer	NOUN
ejpam-6763	1227	2	&	&	CCONJ
ejpam-6763	1227	3	mathematics	mathematics	PROPN
ejpam-6763	1227	4	with	with	ADP
ejpam-6763	1227	5	applications	application	NOUN
ejpam-6763	1227	6	,	,	PUNCT
ejpam-6763	1227	7	62(3):1127–1134	62(3):1127–1134	NUM
ejpam-6763	1227	8	,	,	PUNCT
ejpam-6763	1227	9	2011	2011	NUM
ejpam-6763	1227	10	.	.	PUNCT
ejpam-6763	1228	1	[	[	X
ejpam-6763	1228	2	20	20	NUM
ejpam-6763	1228	3	]	]	X
ejpam-6763	1228	4	h.	h.	PROPN
ejpam-6763	1228	5	yu	yu	PROPN
ejpam-6763	1228	6	and	and	CCONJ
ejpam-6763	1228	7	w.	w.	PROPN
ejpam-6763	1228	8	zhang	zhang	PROPN
ejpam-6763	1228	9	.	.	PUNCT
ejpam-6763	1229	1	solving	solve	VERB
ejpam-6763	1229	2	fractional	fractional	ADJ
ejpam-6763	1229	3	integro	integro	ADJ
ejpam-6763	1229	4	-	-	PUNCT
ejpam-6763	1229	5	differential	differential	NOUN
ejpam-6763	1229	6	equations	equation	NOUN
ejpam-6763	1229	7	with	with	ADP
ejpam-6763	1229	8	singular	singular	ADJ
ejpam-6763	1229	9	kernels	kernel	NOUN
ejpam-6763	1229	10	using	use	VERB
ejpam-6763	1229	11	the	the	DET
ejpam-6763	1229	12	fractional	fractional	PROPN
ejpam-6763	1229	13	taylor	taylor	PROPN
ejpam-6763	1229	14	series	series	PROPN
ejpam-6763	1229	15	method	method	PROPN
ejpam-6763	1229	16	.	.	PUNCT
ejpam-6763	1230	1	journal	journal	NOUN
ejpam-6763	1230	2	of	of	ADP
ejpam-6763	1230	3	computational	computational	ADJ
ejpam-6763	1230	4	and	and	CCONJ
ejpam-6763	1230	5	applied	applied	ADJ
ejpam-6763	1230	6	mathematics	mathematic	NOUN
ejpam-6763	1230	7	,	,	PUNCT
ejpam-6763	1230	8	421	421	NUM
ejpam-6763	1230	9	,	,	PUNCT
ejpam-6763	1230	10	2023	2023	NUM
ejpam-6763	1230	11	.	.	PUNCT
ejpam-6763	1231	1	[	[	X
ejpam-6763	1231	2	21	21	NUM
ejpam-6763	1231	3	]	]	X
ejpam-6763	1231	4	a.	a.	NOUN
ejpam-6763	1231	5	singh	singh	PROPN
ejpam-6763	1231	6	,	,	PUNCT
ejpam-6763	1231	7	r.	r.	PROPN
ejpam-6763	1231	8	gupta	gupta	PROPN
ejpam-6763	1231	9	,	,	PUNCT
ejpam-6763	1231	10	and	and	CCONJ
ejpam-6763	1231	11	t.	t.	PROPN
ejpam-6763	1231	12	patel	patel	PROPN
ejpam-6763	1231	13	.	.	PUNCT
ejpam-6763	1232	1	an	an	DET
ejpam-6763	1232	2	adaptive	adaptive	ADJ
ejpam-6763	1232	3	mesh	mesh	NOUN
ejpam-6763	1232	4	method	method	NOUN
ejpam-6763	1232	5	for	for	ADP
ejpam-6763	1232	6	fractional	fractional	ADJ
ejpam-6763	1232	7	integro	integro	ADJ
ejpam-6763	1232	8	-	-	PUNCT
ejpam-6763	1232	9	differential	differential	NOUN
ejpam-6763	1232	10	equations	equation	NOUN
ejpam-6763	1232	11	.	.	PUNCT
ejpam-6763	1233	1	numerical	numerical	PROPN
ejpam-6763	1233	2	mathematics	mathematics	PROPN
ejpam-6763	1233	3	methods	method	NOUN
ejpam-6763	1233	4	and	and	CCONJ
ejpam-6763	1233	5	applications	application	NOUN
ejpam-6763	1233	6	,	,	PUNCT
ejpam-6763	1233	7	17(1):55–78	17(1):55–78	NUM
ejpam-6763	1233	8	,	,	PUNCT
ejpam-6763	1233	9	2024	2024	NUM
ejpam-6763	1233	10	.	.	PUNCT
ejpam-6763	1234	1	[	[	X
ejpam-6763	1234	2	22	22	NUM
ejpam-6763	1234	3	]	]	PUNCT
ejpam-6763	1234	4	l.	l.	PROPN
ejpam-6763	1234	5	li	li	PROPN
ejpam-6763	1234	6	and	and	CCONJ
ejpam-6763	1234	7	y.	y.	PROPN
ejpam-6763	1234	8	liu	liu	PROPN
ejpam-6763	1234	9	.	.	PUNCT
ejpam-6763	1235	1	fractional	fractional	ADJ
ejpam-6763	1235	2	integro	integro	ADJ
ejpam-6763	1235	3	-	-	PUNCT
ejpam-6763	1235	4	differential	differential	NOUN
ejpam-6763	1235	5	equations	equation	NOUN
ejpam-6763	1235	6	:	:	PUNCT
ejpam-6763	1235	7	numerical	numerical	ADJ
ejpam-6763	1235	8	solutions	solution	NOUN
ejpam-6763	1235	9	using	use	VERB
ejpam-6763	1235	10	deep	deep	ADJ
ejpam-6763	1235	11	learning	learning	NOUN
ejpam-6763	1235	12	techniques	technique	NOUN
ejpam-6763	1235	13	.	.	PUNCT
ejpam-6763	1236	1	journal	journal	PROPN
ejpam-6763	1236	2	of	of	ADP
ejpam-6763	1236	3	computational	computational	ADJ
ejpam-6763	1236	4	physics	physics	NOUN
ejpam-6763	1236	5	,	,	PUNCT
ejpam-6763	1236	6	2024	2024	NUM
ejpam-6763	1236	7	.	.	PUNCT
ejpam-6763	1237	1	[	[	X
ejpam-6763	1237	2	23	23	NUM
ejpam-6763	1237	3	]	]	X
ejpam-6763	1237	4	sh	sh	PROPN
ejpam-6763	1237	5	.	.	PROPN
ejpam-6763	1237	6	shawki	shawki	PROPN
ejpam-6763	1237	7	.	.	PUNCT
ejpam-6763	1238	1	on	on	ADP
ejpam-6763	1238	2	system	system	NOUN
ejpam-6763	1238	3	of	of	ADP
ejpam-6763	1238	4	linear	linear	PROPN
ejpam-6763	1238	5	volterra	volterra	PROPN
ejpam-6763	1238	6	integro	integro	PROPN
ejpam-6763	1238	7	-	-	PUNCT
ejpam-6763	1238	8	fractional	fractional	ADJ
ejpam-6763	1238	9	differential	differential	ADJ
ejpam-6763	1238	10	equations	equation	NOUN
ejpam-6763	1238	11	.	.	PUNCT
ejpam-6763	1239	1	sulaimani	sulaimani	PROPN
ejpam-6763	1239	2	university	university	PROPN
ejpam-6763	1239	3	,	,	PUNCT
ejpam-6763	1239	4	sulaimani	sulaimani	NOUN
ejpam-6763	1239	5	,	,	PUNCT
ejpam-6763	1239	6	2006	2006	NUM
ejpam-6763	1239	7	.	.	PUNCT
ejpam-6763	1240	1	[	[	X
ejpam-6763	1240	2	24	24	NUM
ejpam-6763	1240	3	]	]	PUNCT
ejpam-6763	1240	4	k.	k.	PROPN
ejpam-6763	1240	5	mariya	mariya	PROPN
ejpam-6763	1240	6	.	.	PUNCT
ejpam-6763	1241	1	properties	property	NOUN
ejpam-6763	1241	2	and	and	CCONJ
ejpam-6763	1241	3	applications	application	NOUN
ejpam-6763	1241	4	of	of	ADP
ejpam-6763	1241	5	the	the	DET
ejpam-6763	1241	6	caputo	caputo	PROPN
ejpam-6763	1241	7	fractional	fractional	PROPN
ejpam-6763	1241	8	operator	operator	NOUN
ejpam-6763	1241	9	.	.	PUNCT
ejpam-6763	1242	1	karlsruhe	karlsruhe	PROPN
ejpam-6763	1242	2	,	,	PUNCT
ejpam-6763	1242	3	bulgaria	bulgaria	PROPN
ejpam-6763	1242	4	,	,	PUNCT
ejpam-6763	1242	5	2005	2005	NUM
ejpam-6763	1242	6	.	.	PUNCT
ejpam-6763	1243	1	[	[	X
ejpam-6763	1243	2	25	25	NUM
ejpam-6763	1243	3	]	]	PUNCT
ejpam-6763	1243	4	b.	b.	PROPN
ejpam-6763	1243	5	rajani	rajani	PROPN
ejpam-6763	1243	6	and	and	CCONJ
ejpam-6763	1243	7	d.	d.	PROPN
ejpam-6763	1243	8	debasish	debasish	PROPN
ejpam-6763	1243	9	.	.	PUNCT
ejpam-6763	1244	1	a	a	DET
ejpam-6763	1244	2	mixed	mixed	ADJ
ejpam-6763	1244	3	quadrature	quadrature	NOUN
ejpam-6763	1244	4	rule	rule	NOUN
ejpam-6763	1244	5	by	by	ADP
ejpam-6763	1244	6	blending	blend	VERB
ejpam-6763	1244	7	clenshaw	clenshaw	ADJ
ejpam-6763	1244	8	-	-	PUNCT
ejpam-6763	1244	9	curtis	curtis	ADJ
ejpam-6763	1244	10	and	and	CCONJ
ejpam-6763	1244	11	gausslegendre	gausslegendre	NOUN
ejpam-6763	1244	12	quadrature	quadrature	NOUN
ejpam-6763	1244	13	rules	rule	NOUN
ejpam-6763	1244	14	for	for	ADP
ejpam-6763	1244	15	approximation	approximation	NOUN
ejpam-6763	1244	16	of	of	ADP
ejpam-6763	1244	17	real	real	ADJ
ejpam-6763	1244	18	definite	definite	ADJ
ejpam-6763	1244	19	integrals	integral	NOUN
ejpam-6763	1244	20	in	in	ADP
ejpam-6763	1244	21	adaptive	adaptive	ADJ
ejpam-6763	1244	22	environment	environment	NOUN
ejpam-6763	1244	23	.	.	PUNCT
ejpam-6763	1245	1	international	international	ADJ
ejpam-6763	1245	2	association	association	PROPN
ejpam-6763	1245	3	of	of	ADP
ejpam-6763	1245	4	engineers	engineer	NOUN
ejpam-6763	1245	5	,	,	PUNCT
ejpam-6763	1245	6	1	1	NUM
ejpam-6763	1245	7	,	,	PUNCT
ejpam-6763	1245	8	2011	2011	NUM
ejpam-6763	1245	9	.	.	PUNCT
ejpam-6763	1246	1	d.	d.	PROPN
ejpam-6763	1246	2	kh	kh	PROPN
ejpam-6763	1246	3	.	.	PUNCT
ejpam-6763	1247	1	abdullah	abdullah	PROPN
ejpam-6763	1247	2	,	,	PUNCT
ejpam-6763	1247	3	sh	sh	PROPN
ejpam-6763	1247	4	.	.	PROPN
ejpam-6763	1247	5	sh	sh	PROPN
ejpam-6763	1247	6	.	.	PROPN
ejpam-6763	1247	7	ahmed	ahmed	PROPN
ejpam-6763	1247	8	,	,	PUNCT
ejpam-6763	1247	9	k.	k.	PROPN
ejpam-6763	1247	10	h.	h.	PROPN
ejpam-6763	1247	11	f.	f.	PROPN
ejpam-6763	1247	12	jwamer	jwamer	PROPN
ejpam-6763	1247	13	/	/	SYM
ejpam-6763	1247	14	eur	eur	PROPN
ejpam-6763	1247	15	.	.	PUNCT
ejpam-6763	1248	1	j.	j.	PROPN
ejpam-6763	1248	2	pure	pure	PROPN
ejpam-6763	1248	3	appl	appl	PROPN
ejpam-6763	1248	4	.	.	PROPN
ejpam-6763	1248	5	math	math	PROPN
ejpam-6763	1248	6	,	,	PUNCT
ejpam-6763	1248	7	18	18	NUM
ejpam-6763	1248	8	(	(	PUNCT
ejpam-6763	1248	9	4	4	NUM
ejpam-6763	1248	10	)	)	PUNCT
ejpam-6763	1248	11	(	(	PUNCT
ejpam-6763	1248	12	2025	2025	NUM
ejpam-6763	1248	13	)	)	PUNCT
ejpam-6763	1248	14	,	,	PUNCT
ejpam-6763	1248	15	6763	6763	NUM
ejpam-6763	1248	16	40	40	NUM
ejpam-6763	1248	17	of	of	ADP
ejpam-6763	1248	18	40	40	NUM
ejpam-6763	1248	19	[	[	SYM
ejpam-6763	1248	20	26	26	NUM
ejpam-6763	1248	21	]	]	PUNCT
ejpam-6763	1248	22	m.	m.	NOUN
ejpam-6763	1248	23	sun	sun	NOUN
ejpam-6763	1248	24	and	and	CCONJ
ejpam-6763	1248	25	q.	q.	PROPN
ejpam-6763	1248	26	wu	wu	PROPN
ejpam-6763	1248	27	.	.	PUNCT
ejpam-6763	1249	1	on	on	ADP
ejpam-6763	1249	2	the	the	DET
ejpam-6763	1249	3	chebyshev	chebyshev	PROPN
ejpam-6763	1249	4	spectral	spectral	ADJ
ejpam-6763	1249	5	collocation	collocation	NOUN
ejpam-6763	1249	6	method	method	NOUN
ejpam-6763	1249	7	for	for	ADP
ejpam-6763	1249	8	the	the	DET
ejpam-6763	1249	9	solution	solution	NOUN
ejpam-6763	1249	10	of	of	ADP
ejpam-6763	1249	11	highly	highly	ADV
ejpam-6763	1249	12	oscillatory	oscillatory	ADJ
ejpam-6763	1249	13	volterra	volterra	NOUN
ejpam-6763	1249	14	integral	integral	ADJ
ejpam-6763	1249	15	equations	equation	NOUN
ejpam-6763	1249	16	of	of	ADP
ejpam-6763	1249	17	the	the	DET
ejpam-6763	1249	18	second	second	ADJ
ejpam-6763	1249	19	kind	kind	NOUN
ejpam-6763	1249	20	.	.	PUNCT
ejpam-6763	1250	1	applied	apply	VERB
ejpam-6763	1250	2	mathematics	mathematic	NOUN
ejpam-6763	1250	3	and	and	CCONJ
ejpam-6763	1250	4	nonlinear	nonlinear	ADJ
ejpam-6763	1250	5	sciences	science	NOUN
ejpam-6763	1250	6	,	,	PUNCT
ejpam-6763	1250	7	9(1	9(1	NUM
ejpam-6763	1250	8	)	)	PUNCT
ejpam-6763	1250	9	,	,	PUNCT
ejpam-6763	1250	10	2024	2024	NUM
ejpam-6763	1250	11	.	.	PUNCT
ejpam-6763	1251	1	[	[	X
ejpam-6763	1251	2	27	27	NUM
ejpam-6763	1251	3	]	]	X
ejpam-6763	1251	4	n.	n.	PROPN
ejpam-6763	1251	5	ronald	ronald	PROPN
ejpam-6763	1251	6	and	and	CCONJ
ejpam-6763	1251	7	l.	l.	PROPN
ejpam-6763	1251	8	tom	tom	PROPN
ejpam-6763	1251	9	.	.	PROPN
ejpam-6763	1251	10	knot	knot	PROPN
ejpam-6763	1251	11	insertion	insertion	NOUN
ejpam-6763	1251	12	and	and	CCONJ
ejpam-6763	1251	13	deletion	deletion	NOUN
ejpam-6763	1251	14	algorithms	algorithm	NOUN
ejpam-6763	1251	15	for	for	ADP
ejpam-6763	1251	16	b	b	NOUN
ejpam-6763	1251	17	-	-	PUNCT
ejpam-6763	1251	18	spline	spline	NOUN
ejpam-6763	1251	19	curves	curve	NOUN
ejpam-6763	1251	20	and	and	CCONJ
ejpam-6763	1251	21	surfaces	surface	NOUN
ejpam-6763	1251	22	.	.	PUNCT
ejpam-6763	1252	1	library	library	NOUN
ejpam-6763	1252	2	of	of	ADP
ejpam-6763	1252	3	congress	congress	PROPN
ejpam-6763	1252	4	cataloging	catalog	VERB
ejpam-6763	1252	5	in	in	ADP
ejpam-6763	1252	6	publication	publication	NOUN
ejpam-6763	1252	7	,	,	PUNCT
ejpam-6763	1252	8	1993	1993	NUM
ejpam-6763	1252	9	.	.	PUNCT
ejpam-6763	1253	1	[	[	X
ejpam-6763	1253	2	28	28	NUM
ejpam-6763	1253	3	]	]	X
ejpam-6763	1253	4	z.	z.	PROPN
ejpam-6763	1253	5	mahmoodi	mahmoodi	PROPN
ejpam-6763	1253	6	,	,	PUNCT
ejpam-6763	1253	7	j.	j.	PROPN
ejpam-6763	1253	8	rashidinia	rashidinia	PROPN
ejpam-6763	1253	9	,	,	PUNCT
ejpam-6763	1253	10	and	and	CCONJ
ejpam-6763	1253	11	e.	e.	PROPN
ejpam-6763	1253	12	babolian	babolian	PROPN
ejpam-6763	1253	13	.	.	PUNCT
ejpam-6763	1254	1	b	b	X
ejpam-6763	1254	2	-	-	PUNCT
ejpam-6763	1254	3	spline	spline	NOUN
ejpam-6763	1254	4	collocation	collocation	NOUN
ejpam-6763	1254	5	method	method	NOUN
ejpam-6763	1254	6	for	for	ADP
ejpam-6763	1254	7	linear	linear	ADJ
ejpam-6763	1254	8	and	and	CCONJ
ejpam-6763	1254	9	nonlinear	nonlinear	ADJ
ejpam-6763	1254	10	fredholm	fredholm	NOUN
ejpam-6763	1254	11	and	and	CCONJ
ejpam-6763	1254	12	volterra	volterra	NOUN
ejpam-6763	1254	13	integro	integro	PROPN
ejpam-6763	1254	14	-	-	PUNCT
ejpam-6763	1254	15	differential	differential	NOUN
ejpam-6763	1254	16	equations	equation	NOUN
ejpam-6763	1254	17	.	.	PUNCT
ejpam-6763	1255	1	applied	apply	VERB
ejpam-6763	1255	2	analysis	analysis	NOUN
ejpam-6763	1255	3	,	,	PUNCT
ejpam-6763	1255	4	92(9):1787–1802	92(9):1787–1802	PRON
ejpam-6763	1255	5	,	,	PUNCT
ejpam-6763	1255	6	2013	2013	NUM
ejpam-6763	1255	7	.	.	PUNCT
ejpam-6763	1256	1	[	[	X
ejpam-6763	1256	2	29	29	NUM
ejpam-6763	1256	3	]	]	PUNCT
ejpam-6763	1256	4	m.	m.	NOUN
ejpam-6763	1256	5	gholamian	gholamian	PROPN
ejpam-6763	1256	6	and	and	CCONJ
ejpam-6763	1256	7	j.	j.	PROPN
ejpam-6763	1256	8	saberi	saberi	PROPN
ejpam-6763	1256	9	-	-	PUNCT
ejpam-6763	1256	10	nadjafi	nadjafi	PROPN
ejpam-6763	1256	11	.	.	PUNCT
ejpam-6763	1257	1	cubic	cubic	PROPN
ejpam-6763	1257	2	b	b	X
ejpam-6763	1257	3	-	-	PUNCT
ejpam-6763	1257	4	splines	spline	NOUN
ejpam-6763	1257	5	collocation	collocation	NOUN
ejpam-6763	1257	6	method	method	NOUN
ejpam-6763	1257	7	for	for	ADP
ejpam-6763	1257	8	a	a	DET
ejpam-6763	1257	9	class	class	NOUN
ejpam-6763	1257	10	of	of	ADP
ejpam-6763	1257	11	partial	partial	ADJ
ejpam-6763	1257	12	integro	integro	ADJ
ejpam-6763	1257	13	-	-	PUNCT
ejpam-6763	1257	14	differential	differential	NOUN
ejpam-6763	1257	15	equation	equation	NOUN
ejpam-6763	1257	16	.	.	PUNCT
ejpam-6763	1258	1	alexandria	alexandria	PROPN
ejpam-6763	1258	2	engineering	engineering	PROPN
ejpam-6763	1258	3	journal	journal	PROPN
ejpam-6763	1258	4	,	,	PUNCT
ejpam-6763	1258	5	57(3):2157–2165	57(3):2157–2165	NUM
ejpam-6763	1258	6	,	,	PUNCT
ejpam-6763	1258	7	2018	2018	NUM
ejpam-6763	1258	8	.	.	PUNCT
ejpam-6763	1259	1	[	[	X
ejpam-6763	1259	2	30	30	NUM
ejpam-6763	1259	3	]	]	X
ejpam-6763	1259	4	b.	b.	PROPN
ejpam-6763	1259	5	sambhunath	sambhunath	PROPN
ejpam-6763	1259	6	and	and	CCONJ
ejpam-6763	1259	7	c.	c.	PROPN
ejpam-6763	1259	8	brain	brain	PROPN
ejpam-6763	1259	9	.	.	PUNCT
ejpam-6763	1260	1	bézier	bézier	NOUN
ejpam-6763	1260	2	and	and	CCONJ
ejpam-6763	1260	3	splines	spline	NOUN
ejpam-6763	1260	4	in	in	ADP
ejpam-6763	1260	5	image	image	NOUN
ejpam-6763	1260	6	processing	processing	NOUN
ejpam-6763	1260	7	and	and	CCONJ
ejpam-6763	1260	8	machine	machine	NOUN
ejpam-6763	1260	9	vision	vision	NOUN
ejpam-6763	1260	10	.	.	PUNCT
ejpam-6763	1261	1	springer	springer	PROPN
ejpam-6763	1261	2	,	,	PUNCT
ejpam-6763	1261	3	london	london	PROPN
ejpam-6763	1261	4	,	,	PUNCT
ejpam-6763	1261	5	2008	2008	NUM
ejpam-6763	1261	6	.	.	PUNCT
ejpam-6763	1262	1	[	[	X
ejpam-6763	1262	2	31	31	NUM
ejpam-6763	1262	3	]	]	X
ejpam-6763	1262	4	d.	d.	PROPN
ejpam-6763	1262	5	khalid	khalid	PROPN
ejpam-6763	1262	6	,	,	PUNCT
ejpam-6763	1262	7	sh	sh	PROPN
ejpam-6763	1262	8	.	.	PROPN
ejpam-6763	1262	9	shawki	shawki	PROPN
ejpam-6763	1262	10	,	,	PUNCT
ejpam-6763	1262	11	and	and	CCONJ
ejpam-6763	1262	12	k.	k.	PROPN
ejpam-6763	1262	13	hama	hama	PROPN
ejpam-6763	1262	14	faraj	faraj	PROPN
ejpam-6763	1262	15	.	.	PUNCT
ejpam-6763	1263	1	numerical	numerical	ADJ
ejpam-6763	1263	2	approximation	approximation	NOUN
ejpam-6763	1263	3	of	of	ADP
ejpam-6763	1263	4	solving	solve	VERB
ejpam-6763	1263	5	volterra	volterra	NOUN
ejpam-6763	1263	6	integro	integro	PROPN
ejpam-6763	1263	7	-	-	PUNCT
ejpam-6763	1263	8	fractional	fractional	ADJ
ejpam-6763	1263	9	differential	differential	ADJ
ejpam-6763	1263	10	equations	equation	NOUN
ejpam-6763	1263	11	using	use	VERB
ejpam-6763	1263	12	b	b	NOUN
ejpam-6763	1263	13	-	-	PUNCT
ejpam-6763	1263	14	spline	spline	NOUN
ejpam-6763	1263	15	functions	function	NOUN
ejpam-6763	1263	16	.	.	PUNCT
ejpam-6763	1264	1	journal	journal	NOUN
ejpam-6763	1264	2	of	of	ADP
ejpam-6763	1264	3	southwest	southwest	PROPN
ejpam-6763	1264	4	jiaotong	jiaotong	PROPN
ejpam-6763	1264	5	university	university	PROPN
ejpam-6763	1264	6	,	,	PUNCT
ejpam-6763	1264	7	59(4	59(4	NUM
ejpam-6763	1264	8	)	)	PUNCT
ejpam-6763	1264	9	,	,	PUNCT
ejpam-6763	1264	10	2024	2024	NUM
ejpam-6763	1264	11	.	.	PUNCT
ejpam-6763	1265	1	[	[	X
ejpam-6763	1265	2	32	32	NUM
ejpam-6763	1265	3	]	]	PUNCT
ejpam-6763	1265	4	s.	s.	PROPN
ejpam-6763	1265	5	khan	khan	PROPN
ejpam-6763	1265	6	and	and	CCONJ
ejpam-6763	1265	7	m.	m.	NOUN
ejpam-6763	1265	8	misro	misro	PROPN
ejpam-6763	1265	9	.	.	PUNCT
ejpam-6763	1266	1	numerical	numerical	ADJ
ejpam-6763	1266	2	applications	application	NOUN
ejpam-6763	1266	3	of	of	ADP
ejpam-6763	1266	4	cubic	cubic	ADJ
ejpam-6763	1266	5	b	b	PROPN
ejpam-6763	1266	6	-	-	PUNCT
ejpam-6763	1266	7	spline	spline	NOUN
ejpam-6763	1266	8	collocation	collocation	NOUN
ejpam-6763	1266	9	methods	method	NOUN
ejpam-6763	1266	10	:	:	PUNCT
ejpam-6763	1266	11	a	a	DET
ejpam-6763	1266	12	systematic	systematic	ADJ
ejpam-6763	1266	13	review	review	NOUN
ejpam-6763	1266	14	.	.	PUNCT
ejpam-6763	1267	1	page	page	NOUN
ejpam-6763	1267	2	030019	030019	NUM
ejpam-6763	1267	3	,	,	PUNCT
ejpam-6763	1267	4	2024	2024	NUM
ejpam-6763	1267	5	.	.	PUNCT
ejpam-6763	1268	1	[	[	X
ejpam-6763	1268	2	33	33	NUM
ejpam-6763	1268	3	]	]	PUNCT
ejpam-6763	1268	4	m.	m.	NOUN
ejpam-6763	1268	5	farshid	farshid	NOUN
ejpam-6763	1268	6	and	and	CCONJ
ejpam-6763	1268	7	a.	a.	NOUN
ejpam-6763	1268	8	sahar	sahar	PROPN
ejpam-6763	1268	9	.	.	PUNCT
ejpam-6763	1269	1	cubic	cubic	PROPN
ejpam-6763	1269	2	b	b	PROPN
ejpam-6763	1269	3	-	-	PUNCT
ejpam-6763	1269	4	spline	spline	NOUN
ejpam-6763	1269	5	approximation	approximation	NOUN
ejpam-6763	1269	6	for	for	ADP
ejpam-6763	1269	7	linear	linear	ADJ
ejpam-6763	1269	8	stochastic	stochastic	ADJ
ejpam-6763	1269	9	integrodifferential	integrodifferential	ADJ
ejpam-6763	1269	10	equation	equation	NOUN
ejpam-6763	1269	11	of	of	ADP
ejpam-6763	1269	12	fractional	fractional	ADJ
ejpam-6763	1269	13	order	order	NOUN
ejpam-6763	1269	14	.	.	PUNCT
ejpam-6763	1270	1	journal	journal	NOUN
ejpam-6763	1270	2	of	of	ADP
ejpam-6763	1270	3	computational	computational	ADJ
ejpam-6763	1270	4	and	and	CCONJ
ejpam-6763	1270	5	applied	applied	ADJ
ejpam-6763	1270	6	mathematics	mathematic	NOUN
ejpam-6763	1270	7	,	,	PUNCT
ejpam-6763	1270	8	366	366	NUM
ejpam-6763	1270	9	,	,	PUNCT
ejpam-6763	1270	10	2020	2020	NUM
ejpam-6763	1270	11	.	.	PUNCT
ejpam-6763	1271	1	[	[	X
ejpam-6763	1271	2	34	34	NUM
ejpam-6763	1271	3	]	]	X
ejpam-6763	1271	4	f.	f.	PROPN
ejpam-6763	1271	5	mirzaee	mirzaee	PROPN
ejpam-6763	1271	6	and	and	CCONJ
ejpam-6763	1271	7	s.	s.	PROPN
ejpam-6763	1271	8	alipour	alipour	PROPN
ejpam-6763	1271	9	.	.	PUNCT
ejpam-6763	1271	10	cubic	cubic	PROPN
ejpam-6763	1271	11	b	b	PROPN
ejpam-6763	1271	12	-	-	PUNCT
ejpam-6763	1271	13	spline	spline	NOUN
ejpam-6763	1271	14	approximation	approximation	NOUN
ejpam-6763	1271	15	for	for	ADP
ejpam-6763	1271	16	linear	linear	ADJ
ejpam-6763	1271	17	stochastic	stochastic	ADJ
ejpam-6763	1271	18	integrodifferential	integrodifferential	ADJ
ejpam-6763	1271	19	equation	equation	NOUN
ejpam-6763	1271	20	of	of	ADP
ejpam-6763	1271	21	fractional	fractional	ADJ
ejpam-6763	1271	22	order	order	NOUN
ejpam-6763	1271	23	.	.	PUNCT
ejpam-6763	1272	1	journal	journal	NOUN
ejpam-6763	1272	2	of	of	ADP
ejpam-6763	1272	3	computational	computational	ADJ
ejpam-6763	1272	4	and	and	CCONJ
ejpam-6763	1272	5	applied	applied	ADJ
ejpam-6763	1272	6	mathematics	mathematic	NOUN
ejpam-6763	1272	7	,	,	PUNCT
ejpam-6763	1272	8	336:112440	336:112440	NUM
ejpam-6763	1272	9	,	,	PUNCT
ejpam-6763	1272	10	2020	2020	NUM
ejpam-6763	1272	11	.	.	PUNCT