id	sid	tid	token	lemma	pos
ejpam-6838	1	1	european	european	PROPN
ejpam-6838	1	2	journal	journal	PROPN
ejpam-6838	1	3	of	of	ADP
ejpam-6838	1	4	pure	pure	ADJ
ejpam-6838	1	5	and	and	CCONJ
ejpam-6838	1	6	applied	applied	ADJ
ejpam-6838	1	7	mathematics	mathematic	NOUN
ejpam-6838	1	8	2025	2025	NUM
ejpam-6838	1	9	,	,	PUNCT
ejpam-6838	1	10	vol	vol	NOUN
ejpam-6838	1	11	.	.	PROPN
ejpam-6838	1	12	18	18	NUM
ejpam-6838	1	13	,	,	PUNCT
ejpam-6838	1	14	issue	issue	NOUN
ejpam-6838	1	15	4	4	NUM
ejpam-6838	1	16	,	,	PUNCT
ejpam-6838	1	17	article	article	NOUN
ejpam-6838	1	18	number	number	NOUN
ejpam-6838	1	19	6838	6838	NUM
ejpam-6838	1	20	issn	issn	VERB
ejpam-6838	1	21	1307	1307	NUM
ejpam-6838	1	22	-	-	SYM
ejpam-6838	1	23	5543	5543	NUM
ejpam-6838	1	24	–	–	PUNCT
ejpam-6838	1	25	ejpam.com	ejpam.com	X
ejpam-6838	1	26	published	publish	VERB
ejpam-6838	1	27	by	by	ADP
ejpam-6838	1	28	new	new	PROPN
ejpam-6838	1	29	york	york	PROPN
ejpam-6838	1	30	business	business	PROPN
ejpam-6838	1	31	global	global	PROPN
ejpam-6838	1	32	tau	tau	PROPN
ejpam-6838	1	33	approach	approach	NOUN
ejpam-6838	1	34	for	for	ADP
ejpam-6838	1	35	the	the	DET
ejpam-6838	1	36	time	time	NOUN
ejpam-6838	1	37	-	-	PUNCT
ejpam-6838	1	38	fractional	fractional	ADJ
ejpam-6838	1	39	diffusion	diffusion	NOUN
ejpam-6838	1	40	equation	equation	NOUN
ejpam-6838	1	41	using	use	VERB
ejpam-6838	1	42	certain	certain	ADJ
ejpam-6838	1	43	chebyshev	chebyshev	NOUN
ejpam-6838	1	44	polynomials	polynomial	NOUN
ejpam-6838	1	45	w.	w.	PROPN
ejpam-6838	1	46	m.	m.	PROPN
ejpam-6838	1	47	abd	abd	PROPN
ejpam-6838	1	48	-	-	PUNCT
ejpam-6838	1	49	elhameed1,2	elhameed1,2	PROPN
ejpam-6838	1	50	,	,	PUNCT
ejpam-6838	1	51	h.	h.	PROPN
ejpam-6838	1	52	m.	m.	PROPN
ejpam-6838	1	53	alshehri2	alshehri2	PROPN
ejpam-6838	1	54	,	,	PUNCT
ejpam-6838	1	55	m.	m.	PROPN
ejpam-6838	1	56	h.	h.	PROPN
ejpam-6838	1	57	alharbi2	alharbi2	PROPN
ejpam-6838	1	58	,	,	PUNCT
ejpam-6838	1	59	m.	m.	NOUN
ejpam-6838	1	60	adel3,∗	adel3,∗	NOUN
ejpam-6838	1	61	,	,	PUNCT
ejpam-6838	1	62	a.	a.	NOUN
ejpam-6838	1	63	g.	g.	PROPN
ejpam-6838	1	64	atta4	atta4	PROPN
ejpam-6838	1	65	1	1	NUM
ejpam-6838	1	66	department	department	NOUN
ejpam-6838	1	67	of	of	ADP
ejpam-6838	1	68	mathematics	mathematic	NOUN
ejpam-6838	1	69	,	,	PUNCT
ejpam-6838	1	70	faculty	faculty	NOUN
ejpam-6838	1	71	of	of	ADP
ejpam-6838	1	72	science	science	NOUN
ejpam-6838	1	73	,	,	PUNCT
ejpam-6838	1	74	cairo	cairo	PROPN
ejpam-6838	1	75	university	university	PROPN
ejpam-6838	1	76	,	,	PUNCT
ejpam-6838	1	77	giza	giza	PROPN
ejpam-6838	1	78	12613	12613	NUM
ejpam-6838	1	79	,	,	PUNCT
ejpam-6838	1	80	egypt	egypt	PROPN
ejpam-6838	1	81	2	2	NUM
ejpam-6838	1	82	department	department	NOUN
ejpam-6838	1	83	of	of	ADP
ejpam-6838	1	84	mathematics	mathematic	NOUN
ejpam-6838	1	85	and	and	CCONJ
ejpam-6838	1	86	statistics	statistic	NOUN
ejpam-6838	1	87	,	,	PUNCT
ejpam-6838	1	88	college	college	NOUN
ejpam-6838	1	89	of	of	ADP
ejpam-6838	1	90	science	science	NOUN
ejpam-6838	1	91	,	,	PUNCT
ejpam-6838	1	92	university	university	NOUN
ejpam-6838	1	93	of	of	ADP
ejpam-6838	1	94	jeddah	jeddah	PROPN
ejpam-6838	1	95	,	,	PUNCT
ejpam-6838	1	96	jeddah	jeddah	PROPN
ejpam-6838	1	97	21589	21589	NUM
ejpam-6838	1	98	,	,	PUNCT
ejpam-6838	1	99	saudi	saudi	PROPN
ejpam-6838	1	100	arabia	arabia	PROPN
ejpam-6838	1	101	3	3	NUM
ejpam-6838	1	102	department	department	NOUN
ejpam-6838	1	103	of	of	ADP
ejpam-6838	1	104	mathematics	mathematic	NOUN
ejpam-6838	1	105	,	,	PUNCT
ejpam-6838	1	106	faculty	faculty	NOUN
ejpam-6838	1	107	of	of	ADP
ejpam-6838	1	108	science	science	NOUN
ejpam-6838	1	109	,	,	PUNCT
ejpam-6838	1	110	islamic	islamic	PROPN
ejpam-6838	1	111	university	university	PROPN
ejpam-6838	1	112	of	of	ADP
ejpam-6838	1	113	madinah	madinah	PROPN
ejpam-6838	1	114	,	,	PUNCT
ejpam-6838	1	115	madinah	madinah	PROPN
ejpam-6838	1	116	,	,	PUNCT
ejpam-6838	1	117	42351	42351	NUM
ejpam-6838	1	118	,	,	PUNCT
ejpam-6838	1	119	saudi	saudi	PROPN
ejpam-6838	1	120	arabia	arabia	PROPN
ejpam-6838	1	121	4	4	NUM
ejpam-6838	1	122	department	department	NOUN
ejpam-6838	1	123	of	of	ADP
ejpam-6838	1	124	mathematics	mathematic	NOUN
ejpam-6838	1	125	,	,	PUNCT
ejpam-6838	1	126	faculty	faculty	NOUN
ejpam-6838	1	127	of	of	ADP
ejpam-6838	1	128	education	education	NOUN
ejpam-6838	1	129	,	,	PUNCT
ejpam-6838	1	130	ain	ain	PROPN
ejpam-6838	1	131	shams	shams	PROPN
ejpam-6838	1	132	university	university	PROPN
ejpam-6838	1	133	,	,	PUNCT
ejpam-6838	1	134	cairo	cairo	PROPN
ejpam-6838	1	135	11877	11877	NUM
ejpam-6838	1	136	,	,	PUNCT
ejpam-6838	1	137	egypt	egypt	PROPN
ejpam-6838	1	138	abstract	abstract	PROPN
ejpam-6838	1	139	.	.	PUNCT
ejpam-6838	2	1	this	this	DET
ejpam-6838	2	2	research	research	NOUN
ejpam-6838	2	3	article	article	NOUN
ejpam-6838	2	4	presents	present	VERB
ejpam-6838	2	5	a	a	DET
ejpam-6838	2	6	numerical	numerical	ADJ
ejpam-6838	2	7	technique	technique	NOUN
ejpam-6838	2	8	for	for	ADP
ejpam-6838	2	9	solving	solve	VERB
ejpam-6838	2	10	the	the	DET
ejpam-6838	2	11	time	time	NOUN
ejpam-6838	2	12	-	-	PUNCT
ejpam-6838	2	13	fractional	fractional	ADJ
ejpam-6838	2	14	diffusion	diffusion	NOUN
ejpam-6838	2	15	equation	equation	NOUN
ejpam-6838	2	16	(	(	PUNCT
ejpam-6838	2	17	tfde	tfde	NOUN
ejpam-6838	2	18	)	)	PUNCT
ejpam-6838	2	19	.	.	PUNCT
ejpam-6838	3	1	the	the	DET
ejpam-6838	3	2	approach	approach	NOUN
ejpam-6838	3	3	uses	use	VERB
ejpam-6838	3	4	certain	certain	ADJ
ejpam-6838	3	5	chebyshev	chebyshev	NOUN
ejpam-6838	3	6	polynomials	polynomial	NOUN
ejpam-6838	3	7	as	as	ADP
ejpam-6838	3	8	basis	basis	NOUN
ejpam-6838	3	9	functions	function	NOUN
ejpam-6838	3	10	.	.	PUNCT
ejpam-6838	4	1	these	these	DET
ejpam-6838	4	2	polynomials	polynomial	NOUN
ejpam-6838	4	3	are	be	AUX
ejpam-6838	4	4	particular	particular	ADJ
ejpam-6838	4	5	cases	case	NOUN
ejpam-6838	4	6	of	of	ADP
ejpam-6838	4	7	the	the	DET
ejpam-6838	4	8	generalized	generalized	ADJ
ejpam-6838	4	9	gegenbauer	gegenbauer	NOUN
ejpam-6838	4	10	polynomials	polynomial	NOUN
ejpam-6838	4	11	.	.	PUNCT
ejpam-6838	5	1	the	the	DET
ejpam-6838	5	2	operational	operational	ADJ
ejpam-6838	5	3	matrices	matrix	NOUN
ejpam-6838	5	4	of	of	ADP
ejpam-6838	5	5	integer	integer	NOUN
ejpam-6838	5	6	and	and	CCONJ
ejpam-6838	5	7	fractional	fractional	ADJ
ejpam-6838	5	8	derivatives	derivative	NOUN
ejpam-6838	5	9	are	be	AUX
ejpam-6838	5	10	used	use	VERB
ejpam-6838	5	11	,	,	PUNCT
ejpam-6838	5	12	along	along	ADP
ejpam-6838	5	13	with	with	ADP
ejpam-6838	5	14	the	the	DET
ejpam-6838	5	15	tau	tau	PROPN
ejpam-6838	5	16	method	method	NOUN
ejpam-6838	5	17	,	,	PUNCT
ejpam-6838	5	18	for	for	ADP
ejpam-6838	5	19	the	the	DET
ejpam-6838	5	20	spatial	spatial	ADJ
ejpam-6838	5	21	and	and	CCONJ
ejpam-6838	5	22	temporal	temporal	ADJ
ejpam-6838	5	23	discretization	discretization	NOUN
ejpam-6838	5	24	.	.	PUNCT
ejpam-6838	6	1	hence	hence	ADV
ejpam-6838	6	2	,	,	PUNCT
ejpam-6838	6	3	the	the	DET
ejpam-6838	6	4	problem	problem	NOUN
ejpam-6838	6	5	with	with	ADP
ejpam-6838	6	6	its	its	PRON
ejpam-6838	6	7	underlying	underlie	VERB
ejpam-6838	6	8	conditions	condition	NOUN
ejpam-6838	6	9	is	be	AUX
ejpam-6838	6	10	converted	convert	VERB
ejpam-6838	6	11	into	into	ADP
ejpam-6838	6	12	a	a	DET
ejpam-6838	6	13	system	system	NOUN
ejpam-6838	6	14	of	of	ADP
ejpam-6838	6	15	equations	equation	NOUN
ejpam-6838	6	16	that	that	PRON
ejpam-6838	6	17	can	can	AUX
ejpam-6838	6	18	be	be	AUX
ejpam-6838	6	19	handled	handle	VERB
ejpam-6838	6	20	.	.	PUNCT
ejpam-6838	7	1	we	we	PRON
ejpam-6838	7	2	investigate	investigate	VERB
ejpam-6838	7	3	the	the	DET
ejpam-6838	7	4	convergence	convergence	NOUN
ejpam-6838	7	5	of	of	ADP
ejpam-6838	7	6	the	the	DET
ejpam-6838	7	7	double	double	ADJ
ejpam-6838	7	8	chebyshev	chebyshev	NOUN
ejpam-6838	7	9	expansion	expansion	NOUN
ejpam-6838	7	10	and	and	CCONJ
ejpam-6838	7	11	derive	derive	VERB
ejpam-6838	7	12	rigorous	rigorous	ADJ
ejpam-6838	7	13	error	error	NOUN
ejpam-6838	7	14	bounds	bound	NOUN
ejpam-6838	7	15	.	.	PUNCT
ejpam-6838	8	1	numerical	numerical	ADJ
ejpam-6838	8	2	examples	example	NOUN
ejpam-6838	8	3	show	show	VERB
ejpam-6838	8	4	the	the	DET
ejpam-6838	8	5	method	method	NOUN
ejpam-6838	8	6	’s	’s	PART
ejpam-6838	8	7	superior	superior	ADJ
ejpam-6838	8	8	accuracy	accuracy	NOUN
ejpam-6838	8	9	and	and	CCONJ
ejpam-6838	8	10	efficiency	efficiency	NOUN
ejpam-6838	8	11	over	over	ADP
ejpam-6838	8	12	some	some	DET
ejpam-6838	8	13	existing	exist	VERB
ejpam-6838	8	14	methods	method	NOUN
ejpam-6838	8	15	in	in	ADP
ejpam-6838	8	16	the	the	DET
ejpam-6838	8	17	literature	literature	NOUN
ejpam-6838	8	18	.	.	PUNCT
ejpam-6838	9	1	2020	2020	NUM
ejpam-6838	9	2	mathematics	mathematics	PROPN
ejpam-6838	9	3	subject	subject	NOUN
ejpam-6838	9	4	classifications	classification	NOUN
ejpam-6838	9	5	:	:	PUNCT
ejpam-6838	9	6	35r11	35r11	NUM
ejpam-6838	9	7	,	,	PUNCT
ejpam-6838	9	8	65n35	65n35	NUM
ejpam-6838	9	9	,	,	PUNCT
ejpam-6838	9	10	40a05	40a05	NUM
ejpam-6838	9	11	key	key	ADJ
ejpam-6838	9	12	words	word	NOUN
ejpam-6838	9	13	and	and	CCONJ
ejpam-6838	9	14	phrases	phrase	NOUN
ejpam-6838	9	15	:	:	PUNCT
ejpam-6838	9	16	time	time	NOUN
ejpam-6838	9	17	-	-	PUNCT
ejpam-6838	9	18	fractional	fractional	ADJ
ejpam-6838	9	19	diffusion	diffusion	NOUN
ejpam-6838	9	20	equation	equation	NOUN
ejpam-6838	9	21	,	,	PUNCT
ejpam-6838	9	22	chebyshev	chebyshev	PROPN
ejpam-6838	9	23	polynomials	polynomial	NOUN
ejpam-6838	9	24	,	,	PUNCT
ejpam-6838	9	25	tau	tau	PROPN
ejpam-6838	9	26	method	method	NOUN
ejpam-6838	9	27	,	,	PUNCT
ejpam-6838	9	28	convergence	convergence	NOUN
ejpam-6838	9	29	analysis	analysis	NOUN
ejpam-6838	9	30	1	1	NUM
ejpam-6838	9	31	.	.	PUNCT
ejpam-6838	9	32	introduction	introduction	NOUN
ejpam-6838	9	33	the	the	DET
ejpam-6838	9	34	fractional	fractional	ADJ
ejpam-6838	9	35	differentiation	differentiation	NOUN
ejpam-6838	9	36	extends	extend	VERB
ejpam-6838	9	37	the	the	DET
ejpam-6838	9	38	standard	standard	ADJ
ejpam-6838	9	39	ordinary	ordinary	ADJ
ejpam-6838	9	40	differentiation	differentiation	NOUN
ejpam-6838	9	41	.	.	PUNCT
ejpam-6838	10	1	fractional	fractional	ADJ
ejpam-6838	10	2	differential	differential	ADJ
ejpam-6838	10	3	equations	equation	NOUN
ejpam-6838	10	4	(	(	PUNCT
ejpam-6838	10	5	fdes	fde	NOUN
ejpam-6838	10	6	)	)	PUNCT
ejpam-6838	10	7	,	,	PUNCT
ejpam-6838	10	8	in	in	ADP
ejpam-6838	10	9	contrast	contrast	NOUN
ejpam-6838	10	10	to	to	ADP
ejpam-6838	10	11	ordinary	ordinary	ADJ
ejpam-6838	10	12	differential	differential	ADJ
ejpam-6838	10	13	equations	equation	NOUN
ejpam-6838	10	14	(	(	PUNCT
ejpam-6838	10	15	des	des	PROPN
ejpam-6838	10	16	)	)	PUNCT
ejpam-6838	10	17	,	,	PUNCT
ejpam-6838	10	18	are	be	AUX
ejpam-6838	10	19	systems	system	NOUN
ejpam-6838	10	20	that	that	PRON
ejpam-6838	10	21	include	include	VERB
ejpam-6838	10	22	memory	memory	NOUN
ejpam-6838	10	23	effects	effect	NOUN
ejpam-6838	10	24	and	and	CCONJ
ejpam-6838	10	25	long	long	ADJ
ejpam-6838	10	26	-	-	PUNCT
ejpam-6838	10	27	range	range	NOUN
ejpam-6838	10	28	temporal	temporal	ADJ
ejpam-6838	10	29	dependencies	dependency	NOUN
ejpam-6838	10	30	that	that	PRON
ejpam-6838	10	31	are	be	AUX
ejpam-6838	10	32	wellrepresented	wellrepresente	VERB
ejpam-6838	10	33	by	by	ADP
ejpam-6838	10	34	fdes	fde	NOUN
ejpam-6838	10	35	.	.	PUNCT
ejpam-6838	11	1	this	this	PRON
ejpam-6838	11	2	is	be	AUX
ejpam-6838	11	3	particularly	particularly	ADV
ejpam-6838	11	4	useful	useful	ADJ
ejpam-6838	11	5	when	when	SCONJ
ejpam-6838	11	6	they	they	PRON
ejpam-6838	11	7	have	have	VERB
ejpam-6838	11	8	to	to	PART
ejpam-6838	11	9	explain	explain	VERB
ejpam-6838	11	10	complex	complex	ADJ
ejpam-6838	11	11	real	real	ADJ
ejpam-6838	11	12	-	-	PUNCT
ejpam-6838	11	13	life	life	NOUN
ejpam-6838	11	14	occurrences	occurrence	NOUN
ejpam-6838	11	15	.	.	PUNCT
ejpam-6838	12	1	for	for	ADP
ejpam-6838	12	2	instance	instance	NOUN
ejpam-6838	12	3	,	,	PUNCT
ejpam-6838	12	4	they	they	PRON
ejpam-6838	12	5	model	model	VERB
ejpam-6838	12	6	anomalous	anomalous	ADJ
ejpam-6838	12	7	diffusion	diffusion	NOUN
ejpam-6838	12	8	and	and	CCONJ
ejpam-6838	12	9	stress	stress	NOUN
ejpam-6838	12	10	-	-	PUNCT
ejpam-6838	12	11	strain	strain	NOUN
ejpam-6838	12	12	correlations	correlation	NOUN
ejpam-6838	12	13	in	in	ADP
ejpam-6838	12	14	viscoelastic	viscoelastic	ADJ
ejpam-6838	12	15	materials	material	NOUN
ejpam-6838	12	16	in	in	ADP
ejpam-6838	12	17	the	the	DET
ejpam-6838	12	18	physical	physical	ADJ
ejpam-6838	12	19	sciences	science	NOUN
ejpam-6838	12	20	.	.	PUNCT
ejpam-6838	13	1	using	use	VERB
ejpam-6838	13	2	fdes	fde	NOUN
ejpam-6838	13	3	,	,	PUNCT
ejpam-6838	13	4	we	we	PRON
ejpam-6838	13	5	can	can	AUX
ejpam-6838	13	6	better	well	ADV
ejpam-6838	13	7	∗corresponding	∗corresponde	VERB
ejpam-6838	13	8	author	author	NOUN
ejpam-6838	13	9	.	.	PUNCT
ejpam-6838	14	1	doi	doi	NOUN
ejpam-6838	14	2	:	:	PUNCT
ejpam-6838	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6838	https://doi.org/10.29020/nybg.ejpam.v18i4.6838	NOUN
ejpam-6838	14	4	email	email	NOUN
ejpam-6838	14	5	addresses	address	NOUN
ejpam-6838	14	6	:	:	PUNCT
ejpam-6838	14	7	waleed@cu.edu.eg	waleed@cu.edu.eg	PROPN
ejpam-6838	14	8	(	(	PUNCT
ejpam-6838	14	9	w.	w.	PROPN
ejpam-6838	14	10	m.	m.	PROPN
ejpam-6838	14	11	abd	abd	PROPN
ejpam-6838	14	12	-	-	PUNCT
ejpam-6838	14	13	elhameed	elhameed	NOUN
ejpam-6838	14	14	)	)	PUNCT
ejpam-6838	14	15	,	,	PUNCT
ejpam-6838	14	16	halshehri0271.stu@uj.edu.sa	halshehri0271.stu@uj.edu.sa	PROPN
ejpam-6838	14	17	(	(	PUNCT
ejpam-6838	14	18	h.	h.	PROPN
ejpam-6838	14	19	m.	m.	PROPN
ejpam-6838	14	20	alshehri	alshehri	PROPN
ejpam-6838	14	21	)	)	PUNCT
ejpam-6838	14	22	,	,	PUNCT
ejpam-6838	14	23	mhhalharbi1@uj.edu.sa	mhhalharbi1@uj.edu.sa	PROPN
ejpam-6838	14	24	(	(	PUNCT
ejpam-6838	14	25	m.	m.	NOUN
ejpam-6838	14	26	h.	h.	PROPN
ejpam-6838	14	27	alharbi	alharbi	PROPN
ejpam-6838	14	28	)	)	PUNCT
ejpam-6838	14	29	,	,	PUNCT
ejpam-6838	14	30	adel@sci.cu.edu.eg	adel@sci.cu.edu.eg	PROPN
ejpam-6838	14	31	(	(	PUNCT
ejpam-6838	14	32	m.	m.	NOUN
ejpam-6838	14	33	adel	adel	PROPN
ejpam-6838	14	34	)	)	PUNCT
ejpam-6838	14	35	,	,	PUNCT
ejpam-6838	14	36	ahmed	ahmed	PROPN
ejpam-6838	14	37	gamal@edu.asu.edu.eg	gamal@edu.asu.edu.eg	PROPN
ejpam-6838	14	38	(	(	PUNCT
ejpam-6838	14	39	a.	a.	NOUN
ejpam-6838	14	40	g.	g.	PROPN
ejpam-6838	14	41	atta	atta	PROPN
ejpam-6838	14	42	)	)	PUNCT
ejpam-6838	14	43	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6838	14	44	1	1	NUM
ejpam-6838	14	45	copyright	copyright	NOUN
ejpam-6838	14	46	:	:	PUNCT
ejpam-6838	15	1	©	©	PROPN
ejpam-6838	15	2	2025	2025	NUM
ejpam-6838	15	3	the	the	DET
ejpam-6838	15	4	author(s	author(s	NOUN
ejpam-6838	15	5	)	)	PUNCT
ejpam-6838	15	6	.	.	PUNCT
ejpam-6838	16	1	(	(	PUNCT
ejpam-6838	16	2	cc	cc	NOUN
ejpam-6838	16	3	by	by	ADP
ejpam-6838	16	4	-	-	PUNCT
ejpam-6838	16	5	nc	nc	PROPN
ejpam-6838	16	6	4.0	4.0	NUM
ejpam-6838	16	7	)	)	PUNCT
ejpam-6838	16	8	w.	w.	PROPN
ejpam-6838	16	9	m.	m.	PROPN
ejpam-6838	16	10	abd	abd	PROPN
ejpam-6838	16	11	-	-	PUNCT
ejpam-6838	16	12	elhameed	elhameed	PROPN
ejpam-6838	16	13	et	et	PROPN
ejpam-6838	16	14	al	al	PROPN
ejpam-6838	16	15	.	.	PUNCT
ejpam-6838	16	16	/	/	SYM
ejpam-6838	16	17	eur	eur	PROPN
ejpam-6838	16	18	.	.	PUNCT
ejpam-6838	17	1	j.	j.	PROPN
ejpam-6838	17	2	pure	pure	PROPN
ejpam-6838	17	3	appl	appl	PROPN
ejpam-6838	17	4	.	.	PROPN
ejpam-6838	17	5	math	math	PROPN
ejpam-6838	17	6	,	,	PUNCT
ejpam-6838	17	7	18	18	NUM
ejpam-6838	17	8	(	(	PUNCT
ejpam-6838	17	9	4	4	NUM
ejpam-6838	17	10	)	)	PUNCT
ejpam-6838	17	11	(	(	PUNCT
ejpam-6838	17	12	2025	2025	NUM
ejpam-6838	17	13	)	)	PUNCT
ejpam-6838	17	14	,	,	PUNCT
ejpam-6838	17	15	6838	6838	NUM
ejpam-6838	17	16	2	2	NUM
ejpam-6838	17	17	of	of	ADP
ejpam-6838	17	18	25	25	NUM
ejpam-6838	17	19	understand	understand	VERB
ejpam-6838	17	20	how	how	SCONJ
ejpam-6838	17	21	past	past	ADJ
ejpam-6838	17	22	conditions	condition	NOUN
ejpam-6838	17	23	impact	impact	VERB
ejpam-6838	17	24	current	current	ADJ
ejpam-6838	17	25	processes	process	NOUN
ejpam-6838	17	26	in	in	ADP
ejpam-6838	17	27	biological	biological	ADJ
ejpam-6838	17	28	systems	system	NOUN
ejpam-6838	17	29	,	,	PUNCT
ejpam-6838	17	30	such	such	ADJ
ejpam-6838	17	31	as	as	ADP
ejpam-6838	17	32	the	the	DET
ejpam-6838	17	33	spread	spread	NOUN
ejpam-6838	17	34	of	of	ADP
ejpam-6838	17	35	illness	illness	NOUN
ejpam-6838	17	36	or	or	CCONJ
ejpam-6838	17	37	changes	change	NOUN
ejpam-6838	17	38	in	in	ADP
ejpam-6838	17	39	population	population	NOUN
ejpam-6838	17	40	size	size	NOUN
ejpam-6838	17	41	.	.	PUNCT
ejpam-6838	18	1	control	control	PROPN
ejpam-6838	18	2	theory	theory	NOUN
ejpam-6838	18	3	,	,	PUNCT
ejpam-6838	18	4	signal	signal	VERB
ejpam-6838	18	5	analysis	analysis	NOUN
ejpam-6838	18	6	,	,	PUNCT
ejpam-6838	18	7	and	and	CCONJ
ejpam-6838	18	8	electrical	electrical	ADJ
ejpam-6838	18	9	circuit	circuit	NOUN
ejpam-6838	18	10	modeling	modeling	NOUN
ejpam-6838	18	11	with	with	ADP
ejpam-6838	18	12	memory	memory	NOUN
ejpam-6838	18	13	components	component	NOUN
ejpam-6838	18	14	are	be	AUX
ejpam-6838	18	15	other	other	ADJ
ejpam-6838	18	16	engineering	engineering	NOUN
ejpam-6838	18	17	fields	field	NOUN
ejpam-6838	18	18	that	that	PRON
ejpam-6838	18	19	benefit	benefit	VERB
ejpam-6838	18	20	from	from	ADP
ejpam-6838	18	21	fdes	fde	NOUN
ejpam-6838	18	22	.	.	PUNCT
ejpam-6838	19	1	they	they	PRON
ejpam-6838	19	2	are	be	AUX
ejpam-6838	19	3	also	also	ADV
ejpam-6838	19	4	employed	employ	VERB
ejpam-6838	19	5	in	in	ADP
ejpam-6838	19	6	environmental	environmental	ADJ
ejpam-6838	19	7	studies	study	NOUN
ejpam-6838	19	8	to	to	PART
ejpam-6838	19	9	represent	represent	VERB
ejpam-6838	19	10	the	the	DET
ejpam-6838	19	11	flow	flow	NOUN
ejpam-6838	19	12	in	in	ADP
ejpam-6838	19	13	a	a	DET
ejpam-6838	19	14	porous	porous	ADJ
ejpam-6838	19	15	or	or	CCONJ
ejpam-6838	19	16	fractured	fractured	ADJ
ejpam-6838	19	17	material	material	NOUN
ejpam-6838	19	18	and	and	CCONJ
ejpam-6838	19	19	in	in	ADP
ejpam-6838	19	20	finance	finance	NOUN
ejpam-6838	19	21	to	to	PART
ejpam-6838	19	22	illustrate	illustrate	VERB
ejpam-6838	19	23	market	market	NOUN
ejpam-6838	19	24	linkages	linkage	NOUN
ejpam-6838	19	25	spanning	span	VERB
ejpam-6838	19	26	several	several	ADJ
ejpam-6838	19	27	years	year	NOUN
ejpam-6838	19	28	.	.	PUNCT
ejpam-6838	20	1	due	due	ADP
ejpam-6838	20	2	to	to	ADP
ejpam-6838	20	3	their	their	PRON
ejpam-6838	20	4	increased	increase	VERB
ejpam-6838	20	5	modeling	modeling	NOUN
ejpam-6838	20	6	capabilities	capability	NOUN
ejpam-6838	20	7	and	and	CCONJ
ejpam-6838	20	8	broad	broad	ADJ
ejpam-6838	20	9	applicability	applicability	NOUN
ejpam-6838	20	10	,	,	PUNCT
ejpam-6838	20	11	fdes	fde	NOUN
ejpam-6838	20	12	have	have	AUX
ejpam-6838	20	13	been	be	AUX
ejpam-6838	20	14	a	a	DET
ejpam-6838	20	15	hot	hot	ADJ
ejpam-6838	20	16	topic	topic	NOUN
ejpam-6838	20	17	in	in	ADP
ejpam-6838	20	18	scientific	scientific	ADJ
ejpam-6838	20	19	computing	computing	NOUN
ejpam-6838	20	20	and	and	CCONJ
ejpam-6838	20	21	applied	apply	VERB
ejpam-6838	20	22	mathematics	mathematic	NOUN
ejpam-6838	20	23	.	.	PUNCT
ejpam-6838	21	1	some	some	DET
ejpam-6838	21	2	applications	application	NOUN
ejpam-6838	21	3	of	of	ADP
ejpam-6838	21	4	fdes	fde	NOUN
ejpam-6838	21	5	can	can	AUX
ejpam-6838	21	6	be	be	AUX
ejpam-6838	21	7	found	find	VERB
ejpam-6838	21	8	in	in	ADP
ejpam-6838	21	9	[	[	X
ejpam-6838	21	10	1–4	1–4	NOUN
ejpam-6838	21	11	]	]	X
ejpam-6838	21	12	.	.	PUNCT
ejpam-6838	22	1	due	due	ADP
ejpam-6838	22	2	to	to	ADP
ejpam-6838	22	3	the	the	DET
ejpam-6838	22	4	non	non	NOUN
ejpam-6838	22	5	-	-	NOUN
ejpam-6838	22	6	availability	availability	NOUN
ejpam-6838	22	7	of	of	ADP
ejpam-6838	22	8	analytic	analytic	ADJ
ejpam-6838	22	9	solutions	solution	NOUN
ejpam-6838	22	10	for	for	ADP
ejpam-6838	22	11	most	most	ADJ
ejpam-6838	22	12	fdes	fde	NOUN
ejpam-6838	22	13	,	,	PUNCT
ejpam-6838	22	14	it	it	PRON
ejpam-6838	22	15	is	be	AUX
ejpam-6838	22	16	necessary	necessary	ADJ
ejpam-6838	22	17	to	to	PART
ejpam-6838	22	18	design	design	VERB
ejpam-6838	22	19	effective	effective	ADJ
ejpam-6838	22	20	numerical	numerical	ADJ
ejpam-6838	22	21	solutions	solution	NOUN
ejpam-6838	22	22	for	for	ADP
ejpam-6838	22	23	these	these	DET
ejpam-6838	22	24	equations	equation	NOUN
ejpam-6838	22	25	.	.	PUNCT
ejpam-6838	23	1	there	there	PRON
ejpam-6838	23	2	are	be	VERB
ejpam-6838	23	3	several	several	ADJ
ejpam-6838	23	4	numerical	numerical	ADJ
ejpam-6838	23	5	approaches	approach	NOUN
ejpam-6838	23	6	for	for	ADP
ejpam-6838	23	7	solving	solve	VERB
ejpam-6838	23	8	fdes	fde	NOUN
ejpam-6838	23	9	.	.	PUNCT
ejpam-6838	24	1	the	the	DET
ejpam-6838	24	2	authors	author	NOUN
ejpam-6838	24	3	in	in	ADP
ejpam-6838	24	4	[	[	X
ejpam-6838	24	5	5	5	NUM
ejpam-6838	24	6	]	]	PUNCT
ejpam-6838	24	7	analyzed	analyze	VERB
ejpam-6838	24	8	a	a	DET
ejpam-6838	24	9	numerical	numerical	ADJ
ejpam-6838	24	10	algorithm	algorithm	NOUN
ejpam-6838	24	11	to	to	PART
ejpam-6838	24	12	treat	treat	VERB
ejpam-6838	24	13	the	the	DET
ejpam-6838	24	14	fractional	fractional	ADJ
ejpam-6838	24	15	lane	lane	NOUN
ejpam-6838	24	16	-	-	PUNCT
ejpam-6838	24	17	emden	emden	NOUN
ejpam-6838	24	18	equations	equation	NOUN
ejpam-6838	24	19	based	base	VERB
ejpam-6838	24	20	on	on	ADP
ejpam-6838	24	21	using	use	VERB
ejpam-6838	24	22	the	the	DET
ejpam-6838	24	23	laplace	laplace	NOUN
ejpam-6838	24	24	transform	transform	NOUN
ejpam-6838	24	25	.	.	PUNCT
ejpam-6838	25	1	the	the	DET
ejpam-6838	25	2	authors	author	NOUN
ejpam-6838	25	3	in	in	ADP
ejpam-6838	25	4	[	[	X
ejpam-6838	25	5	6	6	NUM
ejpam-6838	25	6	]	]	PUNCT
ejpam-6838	25	7	treated	treat	VERB
ejpam-6838	25	8	a	a	DET
ejpam-6838	25	9	nonlinear	nonlinear	ADJ
ejpam-6838	25	10	system	system	NOUN
ejpam-6838	25	11	of	of	ADP
ejpam-6838	25	12	fdes	fde	NOUN
ejpam-6838	25	13	utilizing	utilize	VERB
ejpam-6838	25	14	the	the	DET
ejpam-6838	25	15	adomian	adomian	NOUN
ejpam-6838	25	16	decomposition	decomposition	NOUN
ejpam-6838	25	17	method	method	NOUN
ejpam-6838	25	18	.	.	PUNCT
ejpam-6838	26	1	the	the	DET
ejpam-6838	26	2	authors	author	NOUN
ejpam-6838	26	3	in	in	ADP
ejpam-6838	26	4	[	[	X
ejpam-6838	26	5	7	7	NUM
ejpam-6838	26	6	]	]	PUNCT
ejpam-6838	26	7	used	use	VERB
ejpam-6838	26	8	the	the	DET
ejpam-6838	26	9	differential	differential	ADJ
ejpam-6838	26	10	transform	transform	NOUN
ejpam-6838	26	11	method	method	NOUN
ejpam-6838	26	12	for	for	ADP
ejpam-6838	26	13	analyzing	analyze	VERB
ejpam-6838	26	14	fractional	fractional	ADJ
ejpam-6838	26	15	dynamical	dynamical	ADJ
ejpam-6838	26	16	systems	system	NOUN
ejpam-6838	26	17	.	.	PUNCT
ejpam-6838	27	1	in	in	ADP
ejpam-6838	27	2	[	[	X
ejpam-6838	27	3	8	8	NUM
ejpam-6838	27	4	]	]	PUNCT
ejpam-6838	27	5	,	,	PUNCT
ejpam-6838	27	6	the	the	DET
ejpam-6838	27	7	authors	author	NOUN
ejpam-6838	27	8	designed	design	VERB
ejpam-6838	27	9	a	a	DET
ejpam-6838	27	10	numerical	numerical	ADJ
ejpam-6838	27	11	scheme	scheme	NOUN
ejpam-6838	27	12	to	to	PART
ejpam-6838	27	13	treat	treat	VERB
ejpam-6838	27	14	the	the	DET
ejpam-6838	27	15	fractional	fractional	ADJ
ejpam-6838	27	16	burgers	burger	NOUN
ejpam-6838	27	17	’	'	PUNCT
ejpam-6838	27	18	equation	equation	NOUN
ejpam-6838	27	19	,	,	PUNCT
ejpam-6838	27	20	which	which	PRON
ejpam-6838	27	21	used	use	VERB
ejpam-6838	27	22	the	the	DET
ejpam-6838	27	23	convolved	convolve	VERB
ejpam-6838	27	24	fermat	fermat	PROPN
ejpam-6838	27	25	polynomials	polynomial	NOUN
ejpam-6838	27	26	as	as	ADP
ejpam-6838	27	27	basis	basis	NOUN
ejpam-6838	27	28	functions	function	NOUN
ejpam-6838	27	29	,	,	PUNCT
ejpam-6838	27	30	enabling	enable	VERB
ejpam-6838	27	31	precise	precise	ADJ
ejpam-6838	27	32	and	and	CCONJ
ejpam-6838	27	33	computationally	computationally	ADV
ejpam-6838	27	34	efficient	efficient	ADJ
ejpam-6838	27	35	solutions	solution	NOUN
ejpam-6838	27	36	.	.	PUNCT
ejpam-6838	28	1	the	the	DET
ejpam-6838	28	2	authors	author	NOUN
ejpam-6838	28	3	in	in	ADP
ejpam-6838	28	4	[	[	X
ejpam-6838	28	5	9	9	NUM
ejpam-6838	28	6	]	]	PUNCT
ejpam-6838	28	7	implemented	implement	VERB
ejpam-6838	28	8	a	a	DET
ejpam-6838	28	9	numerical	numerical	ADJ
ejpam-6838	28	10	approach	approach	NOUN
ejpam-6838	28	11	for	for	ADP
ejpam-6838	28	12	the	the	DET
ejpam-6838	28	13	time	time	NOUN
ejpam-6838	28	14	-	-	PUNCT
ejpam-6838	28	15	fractional	fractional	ADJ
ejpam-6838	28	16	generalized	generalized	ADJ
ejpam-6838	28	17	kawahara	kawahara	NOUN
ejpam-6838	28	18	equation	equation	NOUN
ejpam-6838	28	19	using	use	VERB
ejpam-6838	28	20	the	the	DET
ejpam-6838	28	21	eighth	eighth	ADJ
ejpam-6838	28	22	-	-	PUNCT
ejpam-6838	28	23	kind	kind	NOUN
ejpam-6838	28	24	cps	cp	NOUN
ejpam-6838	28	25	.	.	PUNCT
ejpam-6838	29	1	in	in	ADP
ejpam-6838	29	2	[	[	X
ejpam-6838	29	3	10	10	NUM
ejpam-6838	29	4	]	]	PUNCT
ejpam-6838	29	5	,	,	PUNCT
ejpam-6838	29	6	a	a	DET
ejpam-6838	29	7	shifted	shift	VERB
ejpam-6838	29	8	jacobi	jacobi	NOUN
ejpam-6838	29	9	collocation	collocation	NOUN
ejpam-6838	29	10	scheme	scheme	NOUN
ejpam-6838	29	11	was	be	AUX
ejpam-6838	29	12	developed	develop	VERB
ejpam-6838	29	13	to	to	PART
ejpam-6838	29	14	solve	solve	VERB
ejpam-6838	29	15	multidimensional	multidimensional	ADJ
ejpam-6838	29	16	time	time	NOUN
ejpam-6838	29	17	-	-	PUNCT
ejpam-6838	29	18	fractional	fractional	ADJ
ejpam-6838	29	19	telegraph	telegraph	NOUN
ejpam-6838	29	20	equations	equation	NOUN
ejpam-6838	29	21	.	.	PUNCT
ejpam-6838	30	1	in	in	ADP
ejpam-6838	30	2	[	[	X
ejpam-6838	30	3	11	11	NUM
ejpam-6838	30	4	]	]	PUNCT
ejpam-6838	30	5	,	,	PUNCT
ejpam-6838	30	6	the	the	DET
ejpam-6838	30	7	authors	author	NOUN
ejpam-6838	30	8	investigated	investigate	VERB
ejpam-6838	30	9	a	a	DET
ejpam-6838	30	10	(	(	PUNCT
ejpam-6838	30	11	3	3	NUM
ejpam-6838	30	12	+	+	NOUN
ejpam-6838	30	13	1)-dimensional	1)-dimensional	ADJ
ejpam-6838	30	14	fractional	fractional	ADJ
ejpam-6838	30	15	coupled	couple	VERB
ejpam-6838	30	16	burgers	burger	NOUN
ejpam-6838	30	17	’	'	PUNCT
ejpam-6838	30	18	equation	equation	NOUN
ejpam-6838	30	19	using	use	VERB
ejpam-6838	30	20	a	a	DET
ejpam-6838	30	21	four	four	NUM
ejpam-6838	30	22	-	-	PUNCT
ejpam-6838	30	23	dimensional	dimensional	ADJ
ejpam-6838	30	24	natural	natural	ADJ
ejpam-6838	30	25	transform	transform	NOUN
ejpam-6838	30	26	combined	combine	VERB
ejpam-6838	30	27	with	with	ADP
ejpam-6838	30	28	the	the	DET
ejpam-6838	30	29	adomian	adomian	NOUN
ejpam-6838	30	30	decomposition	decomposition	NOUN
ejpam-6838	30	31	method	method	NOUN
ejpam-6838	30	32	.	.	PUNCT
ejpam-6838	31	1	in	in	ADP
ejpam-6838	31	2	addition	addition	NOUN
ejpam-6838	31	3	,	,	PUNCT
ejpam-6838	31	4	in	in	ADP
ejpam-6838	31	5	[	[	X
ejpam-6838	31	6	12	12	NUM
ejpam-6838	31	7	]	]	PUNCT
ejpam-6838	31	8	,	,	PUNCT
ejpam-6838	31	9	the	the	DET
ejpam-6838	31	10	authors	author	NOUN
ejpam-6838	31	11	presented	present	VERB
ejpam-6838	31	12	a	a	DET
ejpam-6838	31	13	numerical	numerical	ADJ
ejpam-6838	31	14	scheme	scheme	NOUN
ejpam-6838	31	15	with	with	ADP
ejpam-6838	31	16	adaptive	adaptive	ADJ
ejpam-6838	31	17	step	step	NOUN
ejpam-6838	31	18	sizing	sizing	NOUN
ejpam-6838	31	19	to	to	PART
ejpam-6838	31	20	solve	solve	VERB
ejpam-6838	31	21	general	general	ADJ
ejpam-6838	31	22	fdes	fde	NOUN
ejpam-6838	31	23	.	.	PUNCT
ejpam-6838	32	1	in	in	ADP
ejpam-6838	32	2	[	[	X
ejpam-6838	32	3	13	13	NUM
ejpam-6838	32	4	]	]	PUNCT
ejpam-6838	32	5	,	,	PUNCT
ejpam-6838	32	6	some	some	DET
ejpam-6838	32	7	analytical	analytical	ADJ
ejpam-6838	32	8	solutions	solution	NOUN
ejpam-6838	32	9	of	of	ADP
ejpam-6838	32	10	certain	certain	ADJ
ejpam-6838	32	11	time	time	NOUN
ejpam-6838	32	12	-	-	PUNCT
ejpam-6838	32	13	fractional	fractional	ADJ
ejpam-6838	32	14	heat	heat	NOUN
ejpam-6838	32	15	order	order	NOUN
ejpam-6838	32	16	was	be	AUX
ejpam-6838	32	17	treated	treat	VERB
ejpam-6838	32	18	.	.	PUNCT
ejpam-6838	33	1	modeling	model	VERB
ejpam-6838	33	2	several	several	ADJ
ejpam-6838	33	3	physical	physical	ADJ
ejpam-6838	33	4	phenomena	phenomenon	NOUN
ejpam-6838	33	5	across	across	ADP
ejpam-6838	33	6	several	several	ADJ
ejpam-6838	33	7	fields	field	NOUN
ejpam-6838	33	8	still	still	ADV
ejpam-6838	33	9	depends	depend	VERB
ejpam-6838	33	10	much	much	ADV
ejpam-6838	33	11	on	on	ADP
ejpam-6838	33	12	the	the	DET
ejpam-6838	33	13	time	time	NOUN
ejpam-6838	33	14	diffusion	diffusion	NOUN
ejpam-6838	33	15	equation	equation	NOUN
ejpam-6838	33	16	.	.	PUNCT
ejpam-6838	34	1	recent	recent	ADJ
ejpam-6838	34	2	studies	study	NOUN
ejpam-6838	34	3	have	have	AUX
ejpam-6838	34	4	used	use	VERB
ejpam-6838	34	5	sophisticated	sophisticated	ADJ
ejpam-6838	34	6	computational	computational	ADJ
ejpam-6838	34	7	methods	method	NOUN
ejpam-6838	34	8	and	and	CCONJ
ejpam-6838	34	9	investigated	investigate	VERB
ejpam-6838	34	10	new	new	ADJ
ejpam-6838	34	11	areas	area	NOUN
ejpam-6838	34	12	,	,	PUNCT
ejpam-6838	34	13	therefore	therefore	ADV
ejpam-6838	34	14	broadening	broaden	VERB
ejpam-6838	34	15	their	their	PRON
ejpam-6838	34	16	relevance	relevance	NOUN
ejpam-6838	34	17	.	.	PUNCT
ejpam-6838	35	1	in	in	ADP
ejpam-6838	35	2	computational	computational	ADJ
ejpam-6838	35	3	mathematics	mathematic	NOUN
ejpam-6838	35	4	,	,	PUNCT
ejpam-6838	35	5	several	several	ADJ
ejpam-6838	35	6	numerical	numerical	ADJ
ejpam-6838	35	7	approaches	approach	NOUN
ejpam-6838	35	8	have	have	AUX
ejpam-6838	35	9	been	be	AUX
ejpam-6838	35	10	developed	develop	VERB
ejpam-6838	35	11	to	to	PART
ejpam-6838	35	12	solve	solve	VERB
ejpam-6838	35	13	the	the	DET
ejpam-6838	35	14	various	various	ADJ
ejpam-6838	35	15	forms	form	NOUN
ejpam-6838	35	16	of	of	ADP
ejpam-6838	35	17	the	the	DET
ejpam-6838	35	18	diffusion	diffusion	NOUN
ejpam-6838	35	19	equations	equation	NOUN
ejpam-6838	35	20	more	more	ADV
ejpam-6838	35	21	effectively	effectively	ADV
ejpam-6838	35	22	.	.	PUNCT
ejpam-6838	36	1	the	the	DET
ejpam-6838	36	2	authors	author	NOUN
ejpam-6838	36	3	in	in	ADP
ejpam-6838	36	4	[	[	X
ejpam-6838	36	5	14	14	NUM
ejpam-6838	36	6	]	]	PUNCT
ejpam-6838	36	7	proposed	propose	VERB
ejpam-6838	36	8	a	a	DET
ejpam-6838	36	9	kernel	kernel	NOUN
ejpam-6838	36	10	-	-	PUNCT
ejpam-6838	36	11	based	base	VERB
ejpam-6838	36	12	approach	approach	NOUN
ejpam-6838	36	13	to	to	PART
ejpam-6838	36	14	treat	treat	VERB
ejpam-6838	36	15	the	the	DET
ejpam-6838	36	16	tfde	tfde	NOUN
ejpam-6838	36	17	.	.	PUNCT
ejpam-6838	37	1	in	in	ADP
ejpam-6838	37	2	[	[	X
ejpam-6838	37	3	15	15	NUM
ejpam-6838	37	4	]	]	X
ejpam-6838	37	5	,	,	PUNCT
ejpam-6838	37	6	a	a	DET
ejpam-6838	37	7	finite	finite	ADJ
ejpam-6838	37	8	difference	difference	NOUN
ejpam-6838	37	9	–	–	PUNCT
ejpam-6838	37	10	collocation	collocation	NOUN
ejpam-6838	37	11	scheme	scheme	NOUN
ejpam-6838	37	12	was	be	AUX
ejpam-6838	37	13	designed	design	VERB
ejpam-6838	37	14	for	for	ADP
ejpam-6838	37	15	the	the	DET
ejpam-6838	37	16	tfde	tfde	NOUN
ejpam-6838	37	17	,	,	PUNCT
ejpam-6838	37	18	which	which	PRON
ejpam-6838	37	19	combines	combine	VERB
ejpam-6838	37	20	the	the	DET
ejpam-6838	37	21	robustness	robustness	NOUN
ejpam-6838	37	22	of	of	ADP
ejpam-6838	37	23	finite	finite	ADJ
ejpam-6838	37	24	difference	difference	NOUN
ejpam-6838	37	25	schemes	scheme	NOUN
ejpam-6838	37	26	with	with	ADP
ejpam-6838	37	27	the	the	DET
ejpam-6838	37	28	advantages	advantage	NOUN
ejpam-6838	37	29	of	of	ADP
ejpam-6838	37	30	using	use	VERB
ejpam-6838	37	31	the	the	DET
ejpam-6838	37	32	collocation	collocation	NOUN
ejpam-6838	37	33	method	method	NOUN
ejpam-6838	37	34	.	.	PUNCT
ejpam-6838	38	1	the	the	DET
ejpam-6838	38	2	authors	author	NOUN
ejpam-6838	38	3	in	in	ADP
ejpam-6838	38	4	[	[	X
ejpam-6838	38	5	16	16	NUM
ejpam-6838	38	6	]	]	PUNCT
ejpam-6838	38	7	used	use	VERB
ejpam-6838	38	8	iterative	iterative	NOUN
ejpam-6838	38	9	methods	method	NOUN
ejpam-6838	38	10	for	for	ADP
ejpam-6838	38	11	the	the	DET
ejpam-6838	38	12	tfde	tfde	NOUN
ejpam-6838	38	13	.	.	PUNCT
ejpam-6838	39	1	the	the	DET
ejpam-6838	39	2	authors	author	NOUN
ejpam-6838	39	3	in	in	ADP
ejpam-6838	39	4	[	[	X
ejpam-6838	39	5	17	17	NUM
ejpam-6838	39	6	]	]	PUNCT
ejpam-6838	39	7	offered	offer	VERB
ejpam-6838	39	8	a	a	DET
ejpam-6838	39	9	difference	difference	NOUN
ejpam-6838	39	10	scheme	scheme	NOUN
ejpam-6838	39	11	for	for	ADP
ejpam-6838	39	12	solving	solve	VERB
ejpam-6838	39	13	the	the	DET
ejpam-6838	39	14	tfde	tfde	NOUN
ejpam-6838	39	15	.	.	PUNCT
ejpam-6838	40	1	in	in	ADP
ejpam-6838	40	2	[	[	X
ejpam-6838	40	3	18	18	NUM
ejpam-6838	40	4	]	]	PUNCT
ejpam-6838	40	5	,	,	PUNCT
ejpam-6838	40	6	the	the	DET
ejpam-6838	40	7	authors	author	NOUN
ejpam-6838	40	8	analyzed	analyze	VERB
ejpam-6838	40	9	a	a	DET
ejpam-6838	40	10	numerical	numerical	ADJ
ejpam-6838	40	11	approach	approach	NOUN
ejpam-6838	40	12	to	to	ADP
ejpam-6838	40	13	the	the	DET
ejpam-6838	40	14	tfde	tfde	NOUN
ejpam-6838	40	15	.	.	PUNCT
ejpam-6838	41	1	hosoya	hosoya	PROPN
ejpam-6838	41	2	polynomial	polynomial	PROPN
ejpam-6838	41	3	was	be	AUX
ejpam-6838	41	4	utilized	utilize	VERB
ejpam-6838	41	5	in	in	ADP
ejpam-6838	41	6	[	[	X
ejpam-6838	41	7	19	19	NUM
ejpam-6838	41	8	]	]	PUNCT
ejpam-6838	41	9	to	to	PART
ejpam-6838	41	10	handle	handle	VERB
ejpam-6838	41	11	a	a	DET
ejpam-6838	41	12	class	class	NOUN
ejpam-6838	41	13	of	of	ADP
ejpam-6838	41	14	tfde	tfde	NOUN
ejpam-6838	41	15	,	,	PUNCT
ejpam-6838	41	16	contributing	contribute	VERB
ejpam-6838	41	17	an	an	DET
ejpam-6838	41	18	algebraic	algebraic	ADJ
ejpam-6838	41	19	perspective	perspective	NOUN
ejpam-6838	41	20	to	to	ADP
ejpam-6838	41	21	the	the	DET
ejpam-6838	41	22	numerical	numerical	ADJ
ejpam-6838	41	23	analysis	analysis	NOUN
ejpam-6838	41	24	.	.	PUNCT
ejpam-6838	42	1	a	a	DET
ejpam-6838	42	2	numerical	numerical	ADJ
ejpam-6838	42	3	scheme	scheme	NOUN
ejpam-6838	42	4	based	base	VERB
ejpam-6838	42	5	on	on	ADP
ejpam-6838	42	6	b	b	X
ejpam-6838	42	7	-	-	PUNCT
ejpam-6838	42	8	splines	spline	NOUN
ejpam-6838	42	9	was	be	AUX
ejpam-6838	42	10	presented	present	VERB
ejpam-6838	42	11	in	in	ADP
ejpam-6838	42	12	[	[	X
ejpam-6838	42	13	20	20	NUM
ejpam-6838	42	14	]	]	PUNCT
ejpam-6838	42	15	for	for	ADP
ejpam-6838	42	16	addressing	address	VERB
ejpam-6838	42	17	the	the	DET
ejpam-6838	42	18	tfde	tfde	NOUN
ejpam-6838	42	19	.	.	PUNCT
ejpam-6838	43	1	the	the	DET
ejpam-6838	43	2	authors	author	NOUN
ejpam-6838	43	3	in	in	ADP
ejpam-6838	43	4	[	[	X
ejpam-6838	43	5	21	21	NUM
ejpam-6838	43	6	]	]	PUNCT
ejpam-6838	43	7	used	use	VERB
ejpam-6838	43	8	an	an	DET
ejpam-6838	43	9	efficient	efficient	ADJ
ejpam-6838	43	10	method	method	NOUN
ejpam-6838	43	11	for	for	ADP
ejpam-6838	43	12	distributed	distribute	VERB
ejpam-6838	43	13	-	-	PUNCT
ejpam-6838	43	14	order	order	NOUN
ejpam-6838	43	15	tfde	tfde	NOUN
ejpam-6838	43	16	.	.	PUNCT
ejpam-6838	44	1	in	in	ADP
ejpam-6838	44	2	[	[	X
ejpam-6838	44	3	22	22	NUM
ejpam-6838	44	4	]	]	PUNCT
ejpam-6838	44	5	,	,	PUNCT
ejpam-6838	44	6	an	an	DET
ejpam-6838	44	7	exponential	exponential	ADJ
ejpam-6838	44	8	-	-	PUNCT
ejpam-6838	44	9	sum	sum	NOUN
ejpam-6838	44	10	-	-	PUNCT
ejpam-6838	44	11	approximation	approximation	NOUN
ejpam-6838	44	12	technique	technique	NOUN
ejpam-6838	44	13	was	be	AUX
ejpam-6838	44	14	followed	follow	VERB
ejpam-6838	44	15	to	to	PART
ejpam-6838	44	16	tackle	tackle	VERB
ejpam-6838	44	17	variable	variable	ADJ
ejpam-6838	44	18	-	-	PUNCT
ejpam-6838	44	19	order	order	NOUN
ejpam-6838	44	20	tfde	tfde	NOUN
ejpam-6838	44	21	.	.	PUNCT
ejpam-6838	45	1	the	the	DET
ejpam-6838	45	2	authors	author	NOUN
ejpam-6838	45	3	in	in	ADP
ejpam-6838	45	4	[	[	X
ejpam-6838	45	5	23	23	NUM
ejpam-6838	45	6	]	]	PUNCT
ejpam-6838	45	7	proposed	propose	VERB
ejpam-6838	45	8	analytical	analytical	ADJ
ejpam-6838	45	9	solutions	solution	NOUN
ejpam-6838	45	10	for	for	ADP
ejpam-6838	45	11	both	both	DET
ejpam-6838	45	12	time	time	NOUN
ejpam-6838	45	13	-	-	PUNCT
ejpam-6838	45	14	fractional	fractional	ADJ
ejpam-6838	45	15	diffusion	diffusion	NOUN
ejpam-6838	45	16	and	and	CCONJ
ejpam-6838	45	17	convection	convection	NOUN
ejpam-6838	45	18	–	–	PUNCT
ejpam-6838	45	19	diffusion	diffusion	NOUN
ejpam-6838	45	20	equations	equation	NOUN
ejpam-6838	45	21	.	.	PUNCT
ejpam-6838	46	1	other	other	ADJ
ejpam-6838	46	2	contributions	contribution	NOUN
ejpam-6838	46	3	regarding	regard	VERB
ejpam-6838	46	4	some	some	DET
ejpam-6838	46	5	types	type	NOUN
ejpam-6838	46	6	of	of	ADP
ejpam-6838	46	7	the	the	DET
ejpam-6838	46	8	tfde	tfde	NOUN
ejpam-6838	46	9	can	can	AUX
ejpam-6838	46	10	be	be	AUX
ejpam-6838	46	11	found	find	VERB
ejpam-6838	46	12	in	in	ADP
ejpam-6838	46	13	[	[	X
ejpam-6838	46	14	24–27	24–27	NUM
ejpam-6838	46	15	]	]	PUNCT
ejpam-6838	46	16	.	.	PUNCT
ejpam-6838	47	1	chebyshev	chebyshev	PROPN
ejpam-6838	47	2	polynomials	polynomial	NOUN
ejpam-6838	47	3	(	(	PUNCT
ejpam-6838	47	4	cps	cp	NOUN
ejpam-6838	47	5	)	)	PUNCT
ejpam-6838	47	6	have	have	VERB
ejpam-6838	47	7	vital	vital	ADJ
ejpam-6838	47	8	roles	role	NOUN
ejpam-6838	47	9	in	in	ADP
ejpam-6838	47	10	several	several	ADJ
ejpam-6838	47	11	branches	branch	NOUN
ejpam-6838	47	12	of	of	ADP
ejpam-6838	47	13	the	the	DET
ejpam-6838	47	14	applied	apply	VERB
ejpam-6838	47	15	sciences	science	NOUN
ejpam-6838	47	16	.	.	PUNCT
ejpam-6838	48	1	in	in	ADP
ejpam-6838	48	2	particular	particular	ADJ
ejpam-6838	48	3	,	,	PUNCT
ejpam-6838	48	4	they	they	PRON
ejpam-6838	48	5	are	be	AUX
ejpam-6838	48	6	extremely	extremely	ADV
ejpam-6838	48	7	significant	significant	ADJ
ejpam-6838	48	8	in	in	ADP
ejpam-6838	48	9	areas	area	NOUN
ejpam-6838	48	10	like	like	ADP
ejpam-6838	48	11	approximation	approximation	NOUN
ejpam-6838	48	12	theory	theory	NOUN
ejpam-6838	48	13	,	,	PUNCT
ejpam-6838	49	1	w.	w.	PROPN
ejpam-6838	49	2	m.	m.	PROPN
ejpam-6838	49	3	abd	abd	PROPN
ejpam-6838	49	4	-	-	PUNCT
ejpam-6838	49	5	elhameed	elhameed	PROPN
ejpam-6838	49	6	et	et	PROPN
ejpam-6838	49	7	al	al	PROPN
ejpam-6838	49	8	.	.	PUNCT
ejpam-6838	49	9	/	/	SYM
ejpam-6838	49	10	eur	eur	PROPN
ejpam-6838	49	11	.	.	PUNCT
ejpam-6838	50	1	j.	j.	PROPN
ejpam-6838	50	2	pure	pure	PROPN
ejpam-6838	50	3	appl	appl	PROPN
ejpam-6838	50	4	.	.	PROPN
ejpam-6838	50	5	math	math	PROPN
ejpam-6838	50	6	,	,	PUNCT
ejpam-6838	50	7	18	18	NUM
ejpam-6838	50	8	(	(	PUNCT
ejpam-6838	50	9	4	4	NUM
ejpam-6838	50	10	)	)	PUNCT
ejpam-6838	50	11	(	(	PUNCT
ejpam-6838	50	12	2025	2025	NUM
ejpam-6838	50	13	)	)	PUNCT
ejpam-6838	50	14	,	,	PUNCT
ejpam-6838	50	15	6838	6838	NUM
ejpam-6838	50	16	3	3	NUM
ejpam-6838	50	17	of	of	ADP
ejpam-6838	50	18	25	25	NUM
ejpam-6838	50	19	numerical	numerical	ADJ
ejpam-6838	50	20	analysis	analysis	NOUN
ejpam-6838	50	21	,	,	PUNCT
ejpam-6838	50	22	and	and	CCONJ
ejpam-6838	50	23	applied	apply	VERB
ejpam-6838	50	24	mathematics	mathematic	NOUN
ejpam-6838	50	25	.	.	PUNCT
ejpam-6838	51	1	this	this	DET
ejpam-6838	51	2	versatility	versatility	NOUN
ejpam-6838	51	3	is	be	AUX
ejpam-6838	51	4	due	due	ADJ
ejpam-6838	51	5	to	to	ADP
ejpam-6838	51	6	their	their	PRON
ejpam-6838	51	7	exceptional	exceptional	ADJ
ejpam-6838	51	8	approximation	approximation	NOUN
ejpam-6838	51	9	properties	property	NOUN
ejpam-6838	51	10	;	;	PUNCT
ejpam-6838	51	11	see	see	VERB
ejpam-6838	51	12	,	,	PUNCT
ejpam-6838	51	13	for	for	ADP
ejpam-6838	51	14	example	example	NOUN
ejpam-6838	51	15	,	,	PUNCT
ejpam-6838	51	16	[	[	X
ejpam-6838	51	17	28	28	NUM
ejpam-6838	51	18	,	,	PUNCT
ejpam-6838	51	19	29	29	NUM
ejpam-6838	51	20	]	]	PUNCT
ejpam-6838	51	21	.	.	PUNCT
ejpam-6838	52	1	these	these	DET
ejpam-6838	52	2	polynomials	polynomial	NOUN
ejpam-6838	52	3	are	be	AUX
ejpam-6838	52	4	widely	widely	ADV
ejpam-6838	52	5	used	use	VERB
ejpam-6838	52	6	in	in	ADP
ejpam-6838	52	7	spectral	spectral	ADJ
ejpam-6838	52	8	and	and	CCONJ
ejpam-6838	52	9	pseudospectral	pseudospectral	ADJ
ejpam-6838	52	10	methods	method	NOUN
ejpam-6838	52	11	to	to	PART
ejpam-6838	52	12	solve	solve	VERB
ejpam-6838	52	13	various	various	ADJ
ejpam-6838	52	14	differential	differential	NOUN
ejpam-6838	52	15	and	and	CCONJ
ejpam-6838	52	16	integral	integral	ADJ
ejpam-6838	52	17	equations	equation	NOUN
ejpam-6838	52	18	.	.	PUNCT
ejpam-6838	53	1	the	the	DET
ejpam-6838	53	2	most	most	ADV
ejpam-6838	53	3	used	used	ADJ
ejpam-6838	53	4	kinds	kind	NOUN
ejpam-6838	53	5	of	of	ADP
ejpam-6838	53	6	cps	cp	NOUN
ejpam-6838	53	7	are	be	AUX
ejpam-6838	53	8	the	the	DET
ejpam-6838	53	9	first	first	ADJ
ejpam-6838	53	10	and	and	CCONJ
ejpam-6838	53	11	second	second	ADJ
ejpam-6838	53	12	kinds	kind	NOUN
ejpam-6838	53	13	;	;	PUNCT
ejpam-6838	53	14	see	see	VERB
ejpam-6838	53	15	,	,	PUNCT
ejpam-6838	53	16	for	for	ADP
ejpam-6838	53	17	example	example	NOUN
ejpam-6838	53	18	,	,	PUNCT
ejpam-6838	53	19	[	[	X
ejpam-6838	53	20	30–33	30–33	NUM
ejpam-6838	53	21	]	]	PUNCT
ejpam-6838	53	22	.	.	PUNCT
ejpam-6838	54	1	other	other	ADJ
ejpam-6838	54	2	publications	publication	NOUN
ejpam-6838	54	3	were	be	AUX
ejpam-6838	54	4	devoted	devote	VERB
ejpam-6838	54	5	to	to	ADP
ejpam-6838	54	6	the	the	DET
ejpam-6838	54	7	use	use	NOUN
ejpam-6838	54	8	of	of	ADP
ejpam-6838	54	9	the	the	DET
ejpam-6838	54	10	third	third	ADJ
ejpam-6838	54	11	and	and	CCONJ
ejpam-6838	54	12	fourth	fourth	ADJ
ejpam-6838	54	13	kinds	kind	NOUN
ejpam-6838	54	14	.	.	PUNCT
ejpam-6838	55	1	these	these	DET
ejpam-6838	55	2	four	four	NUM
ejpam-6838	55	3	kinds	kind	NOUN
ejpam-6838	55	4	are	be	AUX
ejpam-6838	55	5	all	all	PRON
ejpam-6838	55	6	particular	particular	ADJ
ejpam-6838	55	7	ones	one	NOUN
ejpam-6838	55	8	of	of	ADP
ejpam-6838	55	9	the	the	DET
ejpam-6838	55	10	classical	classical	ADJ
ejpam-6838	55	11	jacobi	jacobi	NOUN
ejpam-6838	55	12	polynomials	polynomial	NOUN
ejpam-6838	55	13	[	[	X
ejpam-6838	55	14	34	34	NUM
ejpam-6838	55	15	]	]	PUNCT
ejpam-6838	55	16	.	.	PUNCT
ejpam-6838	56	1	in	in	ADP
ejpam-6838	56	2	addition	addition	NOUN
ejpam-6838	56	3	to	to	ADP
ejpam-6838	56	4	the	the	DET
ejpam-6838	56	5	classical	classical	ADJ
ejpam-6838	56	6	jacobi	jacobi	NOUN
ejpam-6838	56	7	polynomials	polynomial	NOUN
ejpam-6838	56	8	,	,	PUNCT
ejpam-6838	56	9	there	there	PRON
ejpam-6838	56	10	are	be	VERB
ejpam-6838	56	11	other	other	ADJ
ejpam-6838	56	12	types	type	NOUN
ejpam-6838	56	13	of	of	ADP
ejpam-6838	56	14	cps	cps	PROPN
ejpam-6838	56	15	.	.	PUNCT
ejpam-6838	56	16	masjed	masjed	PROPN
ejpam-6838	56	17	-	-	PUNCT
ejpam-6838	56	18	jamei	jamei	PROPN
ejpam-6838	56	19	,	,	PUNCT
ejpam-6838	56	20	in	in	ADP
ejpam-6838	56	21	his	his	PRON
ejpam-6838	56	22	ph.d	ph.d	NOUN
ejpam-6838	56	23	.	.	PUNCT
ejpam-6838	57	1	thesis	thesis	NOUN
ejpam-6838	58	1	[	[	X
ejpam-6838	58	2	35	35	NUM
ejpam-6838	58	3	]	]	PUNCT
ejpam-6838	58	4	,	,	PUNCT
ejpam-6838	58	5	introduced	introduce	VERB
ejpam-6838	58	6	two	two	NUM
ejpam-6838	58	7	other	other	ADJ
ejpam-6838	58	8	trigonometric	trigonometric	ADJ
ejpam-6838	58	9	polynomials	polynomial	NOUN
ejpam-6838	58	10	;	;	PUNCT
ejpam-6838	58	11	he	he	PRON
ejpam-6838	58	12	called	call	VERB
ejpam-6838	58	13	them	they	PRON
ejpam-6838	58	14	cps	cp	NOUN
ejpam-6838	58	15	of	of	ADP
ejpam-6838	58	16	the	the	DET
ejpam-6838	58	17	fifth	fifth	ADJ
ejpam-6838	58	18	and	and	CCONJ
ejpam-6838	58	19	sixth	sixth	ADJ
ejpam-6838	58	20	kinds	kind	NOUN
ejpam-6838	58	21	.	.	PUNCT
ejpam-6838	59	1	various	various	ADJ
ejpam-6838	59	2	papers	paper	NOUN
ejpam-6838	59	3	employed	employ	VERB
ejpam-6838	59	4	these	these	DET
ejpam-6838	59	5	polynomials	polynomial	NOUN
ejpam-6838	59	6	;	;	PUNCT
ejpam-6838	59	7	see	see	VERB
ejpam-6838	59	8	,	,	PUNCT
ejpam-6838	59	9	for	for	ADP
ejpam-6838	59	10	example	example	NOUN
ejpam-6838	59	11	,	,	PUNCT
ejpam-6838	59	12	[	[	X
ejpam-6838	59	13	36	36	NUM
ejpam-6838	59	14	,	,	PUNCT
ejpam-6838	59	15	37	37	NUM
ejpam-6838	59	16	]	]	PUNCT
ejpam-6838	59	17	.	.	PUNCT
ejpam-6838	60	1	in	in	ADP
ejpam-6838	60	2	addition	addition	NOUN
ejpam-6838	60	3	,	,	PUNCT
ejpam-6838	60	4	there	there	PRON
ejpam-6838	60	5	are	be	VERB
ejpam-6838	60	6	two	two	NUM
ejpam-6838	60	7	other	other	ADJ
ejpam-6838	60	8	types	type	NOUN
ejpam-6838	60	9	of	of	ADP
ejpam-6838	60	10	cps	cp	NOUN
ejpam-6838	60	11	,	,	PUNCT
ejpam-6838	60	12	namely	namely	ADV
ejpam-6838	60	13	,	,	PUNCT
ejpam-6838	60	14	cps	cp	NOUN
ejpam-6838	60	15	of	of	ADP
ejpam-6838	60	16	the	the	DET
ejpam-6838	60	17	seventh	seventh	ADJ
ejpam-6838	60	18	and	and	CCONJ
ejpam-6838	60	19	eighth	eighth	ADJ
ejpam-6838	60	20	kinds	kind	NOUN
ejpam-6838	60	21	.	.	PUNCT
ejpam-6838	61	1	they	they	PRON
ejpam-6838	61	2	are	be	AUX
ejpam-6838	61	3	specific	specific	ADJ
ejpam-6838	61	4	polynomials	polynomial	NOUN
ejpam-6838	61	5	of	of	ADP
ejpam-6838	61	6	the	the	DET
ejpam-6838	61	7	generalized	generalized	ADJ
ejpam-6838	61	8	gegenbauer	gegenbauer	NOUN
ejpam-6838	61	9	polynomials	polynomial	NOUN
ejpam-6838	61	10	.	.	PUNCT
ejpam-6838	62	1	in	in	ADP
ejpam-6838	62	2	[	[	X
ejpam-6838	62	3	38	38	NUM
ejpam-6838	62	4	]	]	PUNCT
ejpam-6838	62	5	,	,	PUNCT
ejpam-6838	62	6	the	the	DET
ejpam-6838	62	7	seventh	seventh	ADJ
ejpam-6838	62	8	kind	kind	NOUN
ejpam-6838	62	9	of	of	ADP
ejpam-6838	62	10	cps	cp	NOUN
ejpam-6838	62	11	was	be	AUX
ejpam-6838	62	12	used	use	VERB
ejpam-6838	62	13	to	to	PART
ejpam-6838	62	14	solve	solve	VERB
ejpam-6838	62	15	the	the	DET
ejpam-6838	62	16	fractional	fractional	ADJ
ejpam-6838	62	17	diffusion	diffusion	NOUN
ejpam-6838	62	18	equation	equation	NOUN
ejpam-6838	62	19	,	,	PUNCT
ejpam-6838	62	20	while	while	SCONJ
ejpam-6838	62	21	the	the	DET
ejpam-6838	62	22	authors	author	NOUN
ejpam-6838	62	23	of	of	ADP
ejpam-6838	62	24	[	[	X
ejpam-6838	62	25	39	39	NUM
ejpam-6838	62	26	]	]	PUNCT
ejpam-6838	62	27	used	use	VERB
ejpam-6838	62	28	the	the	DET
ejpam-6838	62	29	eighth	eighth	ADJ
ejpam-6838	62	30	kind	kind	NOUN
ejpam-6838	62	31	of	of	ADP
ejpam-6838	62	32	cps	cp	NOUN
ejpam-6838	62	33	to	to	PART
ejpam-6838	62	34	solve	solve	VERB
ejpam-6838	62	35	the	the	DET
ejpam-6838	62	36	nonlinear	nonlinear	ADJ
ejpam-6838	62	37	time	time	NOUN
ejpam-6838	62	38	-	-	PUNCT
ejpam-6838	62	39	fractional	fractional	ADJ
ejpam-6838	62	40	generalized	generalized	ADJ
ejpam-6838	62	41	kawahara	kawahara	NOUN
ejpam-6838	62	42	equation	equation	NOUN
ejpam-6838	62	43	.	.	PUNCT
ejpam-6838	63	1	other	other	ADJ
ejpam-6838	63	2	cps	cps	PROPN
ejpam-6838	63	3	were	be	AUX
ejpam-6838	63	4	proposed	propose	VERB
ejpam-6838	63	5	and	and	CCONJ
ejpam-6838	63	6	used	use	VERB
ejpam-6838	63	7	to	to	PART
ejpam-6838	63	8	handle	handle	VERB
ejpam-6838	63	9	the	the	DET
ejpam-6838	63	10	fitzhugh	fitzhugh	PROPN
ejpam-6838	63	11	-	-	PUNCT
ejpam-6838	63	12	nagumo	nagumo	ADJ
ejpam-6838	63	13	equation	equation	NOUN
ejpam-6838	63	14	in	in	ADP
ejpam-6838	63	15	[	[	X
ejpam-6838	63	16	40	40	NUM
ejpam-6838	63	17	]	]	PUNCT
ejpam-6838	63	18	.	.	PUNCT
ejpam-6838	64	1	spectral	spectral	ADJ
ejpam-6838	64	2	methods	method	NOUN
ejpam-6838	64	3	are	be	AUX
ejpam-6838	64	4	numerical	numerical	ADJ
ejpam-6838	64	5	techniques	technique	NOUN
ejpam-6838	64	6	employed	employ	VERB
ejpam-6838	64	7	to	to	PART
ejpam-6838	64	8	solve	solve	VERB
ejpam-6838	64	9	different	different	ADJ
ejpam-6838	64	10	types	type	NOUN
ejpam-6838	64	11	of	of	ADP
ejpam-6838	64	12	differential	differential	ADJ
ejpam-6838	64	13	equations	equation	NOUN
ejpam-6838	64	14	(	(	PUNCT
ejpam-6838	64	15	des	des	PROPN
ejpam-6838	64	16	)	)	PUNCT
ejpam-6838	64	17	.	.	PUNCT
ejpam-6838	65	1	the	the	DET
ejpam-6838	65	2	philosophy	philosophy	NOUN
ejpam-6838	65	3	of	of	ADP
ejpam-6838	65	4	applying	apply	VERB
ejpam-6838	65	5	this	this	DET
ejpam-6838	65	6	method	method	NOUN
ejpam-6838	65	7	is	be	AUX
ejpam-6838	65	8	based	base	VERB
ejpam-6838	65	9	on	on	ADP
ejpam-6838	65	10	expanding	expand	VERB
ejpam-6838	65	11	the	the	DET
ejpam-6838	65	12	solution	solution	NOUN
ejpam-6838	65	13	in	in	ADP
ejpam-6838	65	14	terms	term	NOUN
ejpam-6838	65	15	of	of	ADP
ejpam-6838	65	16	global	global	ADJ
ejpam-6838	65	17	basis	basis	NOUN
ejpam-6838	65	18	functions	function	NOUN
ejpam-6838	65	19	such	such	ADJ
ejpam-6838	65	20	as	as	ADP
ejpam-6838	65	21	trigonometric	trigonometric	ADJ
ejpam-6838	65	22	functions	function	NOUN
ejpam-6838	65	23	(	(	PUNCT
ejpam-6838	65	24	fourier	fourier	NOUN
ejpam-6838	65	25	series	series	NOUN
ejpam-6838	65	26	)	)	PUNCT
ejpam-6838	65	27	,	,	PUNCT
ejpam-6838	65	28	orthogonal	orthogonal	ADJ
ejpam-6838	65	29	polynomials	polynomial	NOUN
ejpam-6838	65	30	,	,	PUNCT
ejpam-6838	65	31	or	or	CCONJ
ejpam-6838	65	32	any	any	DET
ejpam-6838	65	33	other	other	ADJ
ejpam-6838	65	34	complete	complete	ADJ
ejpam-6838	65	35	function	function	NOUN
ejpam-6838	65	36	systems	system	NOUN
ejpam-6838	65	37	.	.	PUNCT
ejpam-6838	66	1	spectral	spectral	ADJ
ejpam-6838	66	2	methods	method	NOUN
ejpam-6838	66	3	are	be	AUX
ejpam-6838	66	4	able	able	ADJ
ejpam-6838	66	5	to	to	PART
ejpam-6838	66	6	attain	attain	VERB
ejpam-6838	66	7	exponential	exponential	NOUN
ejpam-6838	66	8	or	or	CCONJ
ejpam-6838	66	9	“	"	PUNCT
ejpam-6838	66	10	spectral	spectral	ADJ
ejpam-6838	66	11	”	"	PUNCT
ejpam-6838	66	12	convergence	convergence	NOUN
ejpam-6838	66	13	rates	rate	NOUN
ejpam-6838	66	14	,	,	PUNCT
ejpam-6838	66	15	in	in	ADP
ejpam-6838	66	16	contrast	contrast	NOUN
ejpam-6838	66	17	to	to	ADP
ejpam-6838	66	18	the	the	DET
ejpam-6838	66	19	algebraic	algebraic	ADJ
ejpam-6838	66	20	convergence	convergence	NOUN
ejpam-6838	66	21	that	that	PRON
ejpam-6838	66	22	is	be	AUX
ejpam-6838	66	23	produced	produce	VERB
ejpam-6838	66	24	by	by	ADP
ejpam-6838	66	25	classic	classic	ADJ
ejpam-6838	66	26	finite	finite	ADJ
ejpam-6838	66	27	difference	difference	NOUN
ejpam-6838	66	28	or	or	CCONJ
ejpam-6838	66	29	finite	finite	ADJ
ejpam-6838	66	30	element	element	NOUN
ejpam-6838	66	31	approaches	approach	NOUN
ejpam-6838	66	32	that	that	PRON
ejpam-6838	66	33	rely	rely	VERB
ejpam-6838	66	34	on	on	ADP
ejpam-6838	66	35	local	local	ADJ
ejpam-6838	66	36	approximations	approximation	NOUN
ejpam-6838	66	37	.	.	PUNCT
ejpam-6838	67	1	because	because	SCONJ
ejpam-6838	67	2	of	of	ADP
ejpam-6838	67	3	this	this	PRON
ejpam-6838	67	4	,	,	PUNCT
ejpam-6838	67	5	they	they	PRON
ejpam-6838	67	6	arise	arise	VERB
ejpam-6838	67	7	in	in	ADP
ejpam-6838	67	8	fields	field	NOUN
ejpam-6838	67	9	like	like	ADP
ejpam-6838	67	10	quantum	quantum	NOUN
ejpam-6838	67	11	physics	physics	NOUN
ejpam-6838	67	12	,	,	PUNCT
ejpam-6838	67	13	fluid	fluid	ADJ
ejpam-6838	67	14	dynamics	dynamic	NOUN
ejpam-6838	67	15	,	,	PUNCT
ejpam-6838	67	16	and	and	CCONJ
ejpam-6838	67	17	wave	wave	NOUN
ejpam-6838	67	18	propagation	propagation	NOUN
ejpam-6838	67	19	.	.	PUNCT
ejpam-6838	68	1	for	for	ADP
ejpam-6838	68	2	some	some	DET
ejpam-6838	68	3	applications	application	NOUN
ejpam-6838	68	4	of	of	ADP
ejpam-6838	68	5	spectral	spectral	ADJ
ejpam-6838	68	6	methods	method	NOUN
ejpam-6838	68	7	,	,	PUNCT
ejpam-6838	68	8	one	one	PRON
ejpam-6838	68	9	can	can	AUX
ejpam-6838	68	10	refer	refer	VERB
ejpam-6838	68	11	to	to	ADP
ejpam-6838	68	12	[	[	X
ejpam-6838	68	13	41–44	41–44	NUM
ejpam-6838	68	14	]	]	PUNCT
ejpam-6838	68	15	.	.	PUNCT
ejpam-6838	69	1	galerkin	galerkin	ADJ
ejpam-6838	69	2	,	,	PUNCT
ejpam-6838	69	3	collocation	collocation	NOUN
ejpam-6838	69	4	(	(	PUNCT
ejpam-6838	69	5	or	or	CCONJ
ejpam-6838	69	6	pseudospectral	pseudospectral	ADJ
ejpam-6838	69	7	)	)	PUNCT
ejpam-6838	69	8	,	,	PUNCT
ejpam-6838	69	9	and	and	CCONJ
ejpam-6838	69	10	tau	tau	PROPN
ejpam-6838	69	11	are	be	AUX
ejpam-6838	69	12	the	the	DET
ejpam-6838	69	13	main	main	ADJ
ejpam-6838	69	14	spectral	spectral	ADJ
ejpam-6838	69	15	methods	method	NOUN
ejpam-6838	69	16	.	.	PUNCT
ejpam-6838	70	1	the	the	DET
ejpam-6838	70	2	collocation	collocation	NOUN
ejpam-6838	70	3	approach	approach	NOUN
ejpam-6838	70	4	,	,	PUNCT
ejpam-6838	70	5	on	on	ADP
ejpam-6838	70	6	the	the	DET
ejpam-6838	70	7	other	other	ADJ
ejpam-6838	70	8	hand	hand	NOUN
ejpam-6838	70	9	,	,	PUNCT
ejpam-6838	70	10	uses	use	VERB
ejpam-6838	70	11	discrete	discrete	ADJ
ejpam-6838	70	12	places	place	NOUN
ejpam-6838	70	13	—	—	PUNCT
ejpam-6838	70	14	the	the	DET
ejpam-6838	70	15	collocation	collocation	NOUN
ejpam-6838	70	16	points	point	NOUN
ejpam-6838	70	17	—	—	PUNCT
ejpam-6838	70	18	to	to	PART
ejpam-6838	70	19	ensure	ensure	VERB
ejpam-6838	70	20	that	that	SCONJ
ejpam-6838	70	21	the	the	DET
ejpam-6838	70	22	differential	differential	ADJ
ejpam-6838	70	23	equation	equation	NOUN
ejpam-6838	70	24	is	be	AUX
ejpam-6838	70	25	fulfilled	fulfil	VERB
ejpam-6838	70	26	.	.	PUNCT
ejpam-6838	71	1	these	these	DET
ejpam-6838	71	2	collocation	collocation	NOUN
ejpam-6838	71	3	points	point	NOUN
ejpam-6838	71	4	are	be	AUX
ejpam-6838	71	5	often	often	ADV
ejpam-6838	71	6	chosen	choose	VERB
ejpam-6838	71	7	to	to	PART
ejpam-6838	71	8	represent	represent	VERB
ejpam-6838	71	9	the	the	DET
ejpam-6838	71	10	roots	root	NOUN
ejpam-6838	71	11	of	of	ADP
ejpam-6838	71	12	orthogonal	orthogonal	ADJ
ejpam-6838	71	13	polynomials	polynomial	NOUN
ejpam-6838	71	14	;	;	PUNCT
ejpam-6838	71	15	see	see	VERB
ejpam-6838	71	16	[	[	X
ejpam-6838	71	17	45–49	45–49	X
ejpam-6838	71	18	]	]	X
ejpam-6838	71	19	.	.	PUNCT
ejpam-6838	72	1	in	in	ADP
ejpam-6838	72	2	the	the	DET
ejpam-6838	72	3	galerkin	galerkin	ADJ
ejpam-6838	72	4	method	method	NOUN
ejpam-6838	72	5	,	,	PUNCT
ejpam-6838	72	6	we	we	PRON
ejpam-6838	72	7	use	use	VERB
ejpam-6838	72	8	basis	basis	NOUN
ejpam-6838	72	9	functions	function	NOUN
ejpam-6838	72	10	and	and	CCONJ
ejpam-6838	72	11	enforce	enforce	VERB
ejpam-6838	72	12	the	the	DET
ejpam-6838	72	13	residual	residual	NOUN
ejpam-6838	72	14	of	of	ADP
ejpam-6838	72	15	the	the	DET
ejpam-6838	72	16	equation	equation	NOUN
ejpam-6838	72	17	to	to	PART
ejpam-6838	72	18	be	be	AUX
ejpam-6838	72	19	orthogonal	orthogonal	ADJ
ejpam-6838	72	20	to	to	ADP
ejpam-6838	72	21	them	they	PRON
ejpam-6838	72	22	;	;	PUNCT
ejpam-6838	72	23	see	see	VERB
ejpam-6838	72	24	,	,	PUNCT
ejpam-6838	72	25	for	for	ADP
ejpam-6838	72	26	example	example	NOUN
ejpam-6838	72	27	[	[	X
ejpam-6838	72	28	50–54	50–54	NUM
ejpam-6838	72	29	]	]	X
ejpam-6838	72	30	,	,	PUNCT
ejpam-6838	72	31	the	the	DET
ejpam-6838	72	32	tau	tau	PROPN
ejpam-6838	72	33	approach	approach	NOUN
ejpam-6838	72	34	is	be	AUX
ejpam-6838	72	35	more	more	ADV
ejpam-6838	72	36	flexible	flexible	ADJ
ejpam-6838	72	37	than	than	ADP
ejpam-6838	72	38	the	the	DET
ejpam-6838	72	39	galerkin	galerkin	ADJ
ejpam-6838	72	40	approach	approach	NOUN
ejpam-6838	72	41	in	in	ADP
ejpam-6838	72	42	choosing	choose	VERB
ejpam-6838	72	43	the	the	DET
ejpam-6838	72	44	basis	basis	NOUN
ejpam-6838	72	45	functions	function	NOUN
ejpam-6838	72	46	,	,	PUNCT
ejpam-6838	72	47	since	since	SCONJ
ejpam-6838	72	48	there	there	PRON
ejpam-6838	72	49	are	be	VERB
ejpam-6838	72	50	no	no	DET
ejpam-6838	72	51	restrictions	restriction	NOUN
ejpam-6838	72	52	for	for	ADP
ejpam-6838	72	53	the	the	DET
ejpam-6838	72	54	choice	choice	NOUN
ejpam-6838	72	55	of	of	ADP
ejpam-6838	72	56	them	they	PRON
ejpam-6838	72	57	,	,	PUNCT
ejpam-6838	72	58	and	and	CCONJ
ejpam-6838	72	59	the	the	DET
ejpam-6838	72	60	underlying	underlie	VERB
ejpam-6838	72	61	conditions	condition	NOUN
ejpam-6838	72	62	are	be	AUX
ejpam-6838	72	63	assumed	assume	VERB
ejpam-6838	72	64	to	to	PART
ejpam-6838	72	65	be	be	AUX
ejpam-6838	72	66	as	as	ADP
ejpam-6838	72	67	constraints	constraint	NOUN
ejpam-6838	72	68	;	;	PUNCT
ejpam-6838	72	69	see	see	VERB
ejpam-6838	72	70	,	,	PUNCT
ejpam-6838	72	71	for	for	ADP
ejpam-6838	72	72	example	example	NOUN
ejpam-6838	72	73	,	,	PUNCT
ejpam-6838	73	1	[	[	X
ejpam-6838	73	2	55–58	55–58	NUM
ejpam-6838	73	3	]	]	PUNCT
ejpam-6838	73	4	.	.	PUNCT
ejpam-6838	74	1	the	the	DET
ejpam-6838	74	2	main	main	ADJ
ejpam-6838	74	3	objective	objective	NOUN
ejpam-6838	74	4	of	of	ADP
ejpam-6838	74	5	this	this	DET
ejpam-6838	74	6	article	article	NOUN
ejpam-6838	74	7	is	be	AUX
ejpam-6838	74	8	to	to	PART
ejpam-6838	74	9	use	use	VERB
ejpam-6838	74	10	certain	certain	ADJ
ejpam-6838	74	11	cps	cp	NOUN
ejpam-6838	74	12	,	,	PUNCT
ejpam-6838	74	13	which	which	PRON
ejpam-6838	74	14	are	be	AUX
ejpam-6838	74	15	particular	particular	ADJ
ejpam-6838	74	16	polynomials	polynomial	NOUN
ejpam-6838	74	17	of	of	ADP
ejpam-6838	74	18	the	the	DET
ejpam-6838	74	19	generalized	generalized	ADJ
ejpam-6838	74	20	gegenbauer	gegenbauer	NOUN
ejpam-6838	74	21	polynomials	polynomial	NOUN
ejpam-6838	74	22	,	,	PUNCT
ejpam-6838	74	23	to	to	PART
ejpam-6838	74	24	solve	solve	VERB
ejpam-6838	74	25	the	the	DET
ejpam-6838	74	26	tfde	tfde	NOUN
ejpam-6838	74	27	by	by	ADP
ejpam-6838	74	28	applying	apply	VERB
ejpam-6838	74	29	the	the	DET
ejpam-6838	74	30	tau	tau	PROPN
ejpam-6838	74	31	method	method	NOUN
ejpam-6838	74	32	.	.	PUNCT
ejpam-6838	75	1	theoretical	theoretical	ADJ
ejpam-6838	75	2	and	and	CCONJ
ejpam-6838	75	3	numerical	numerical	ADJ
ejpam-6838	75	4	studies	study	NOUN
ejpam-6838	75	5	of	of	ADP
ejpam-6838	75	6	the	the	DET
ejpam-6838	75	7	errors	error	NOUN
ejpam-6838	75	8	obtained	obtain	VERB
ejpam-6838	75	9	are	be	AUX
ejpam-6838	75	10	given	give	VERB
ejpam-6838	75	11	.	.	PUNCT
ejpam-6838	76	1	the	the	DET
ejpam-6838	76	2	main	main	ADJ
ejpam-6838	76	3	contribution	contribution	NOUN
ejpam-6838	76	4	of	of	ADP
ejpam-6838	76	5	the	the	DET
ejpam-6838	76	6	paper	paper	NOUN
ejpam-6838	76	7	can	can	AUX
ejpam-6838	76	8	be	be	AUX
ejpam-6838	76	9	summarized	summarize	VERB
ejpam-6838	76	10	in	in	ADP
ejpam-6838	76	11	the	the	DET
ejpam-6838	76	12	following	following	ADJ
ejpam-6838	76	13	points	point	NOUN
ejpam-6838	76	14	:	:	PUNCT
ejpam-6838	76	15	•	•	ADP
ejpam-6838	76	16	constructing	construct	VERB
ejpam-6838	76	17	the	the	DET
ejpam-6838	76	18	integer	integer	NOUN
ejpam-6838	76	19	and	and	CCONJ
ejpam-6838	76	20	fractional	fractional	ADJ
ejpam-6838	76	21	derivatives	derivative	NOUN
ejpam-6838	76	22	of	of	ADP
ejpam-6838	76	23	the	the	DET
ejpam-6838	76	24	chebyshev	chebyshev	NOUN
ejpam-6838	76	25	polynomials	polynomial	NOUN
ejpam-6838	76	26	.	.	PUNCT
ejpam-6838	77	1	•	•	NUM
ejpam-6838	77	2	applying	apply	VERB
ejpam-6838	77	3	the	the	DET
ejpam-6838	77	4	spectral	spectral	ADJ
ejpam-6838	77	5	tau	tau	PROPN
ejpam-6838	77	6	method	method	NOUN
ejpam-6838	77	7	for	for	ADP
ejpam-6838	77	8	spatial	spatial	ADJ
ejpam-6838	77	9	and	and	CCONJ
ejpam-6838	77	10	temporal	temporal	ADJ
ejpam-6838	77	11	discretization	discretization	NOUN
ejpam-6838	77	12	.	.	PUNCT
ejpam-6838	78	1	•	•	ADP
ejpam-6838	78	2	investigating	investigate	VERB
ejpam-6838	78	3	the	the	DET
ejpam-6838	78	4	convergence	convergence	NOUN
ejpam-6838	78	5	and	and	CCONJ
ejpam-6838	78	6	error	error	NOUN
ejpam-6838	78	7	analysis	analysis	NOUN
ejpam-6838	78	8	of	of	ADP
ejpam-6838	78	9	the	the	DET
ejpam-6838	78	10	proposed	propose	VERB
ejpam-6838	78	11	expansion	expansion	NOUN
ejpam-6838	78	12	.	.	PUNCT
ejpam-6838	79	1	•	•	NUM
ejpam-6838	79	2	testing	test	VERB
ejpam-6838	79	3	the	the	DET
ejpam-6838	79	4	numerical	numerical	ADJ
ejpam-6838	79	5	algorithm	algorithm	NOUN
ejpam-6838	79	6	by	by	ADP
ejpam-6838	79	7	presenting	present	VERB
ejpam-6838	79	8	some	some	DET
ejpam-6838	79	9	numerical	numerical	ADJ
ejpam-6838	79	10	results	result	NOUN
ejpam-6838	79	11	supported	support	VERB
ejpam-6838	79	12	by	by	ADP
ejpam-6838	79	13	some	some	DET
ejpam-6838	79	14	comparisons	comparison	NOUN
ejpam-6838	79	15	.	.	PUNCT
ejpam-6838	80	1	w.	w.	PROPN
ejpam-6838	80	2	m.	m.	PROPN
ejpam-6838	80	3	abd	abd	PROPN
ejpam-6838	80	4	-	-	PUNCT
ejpam-6838	80	5	elhameed	elhameed	PROPN
ejpam-6838	80	6	et	et	PROPN
ejpam-6838	80	7	al	al	PROPN
ejpam-6838	80	8	.	.	PUNCT
ejpam-6838	80	9	/	/	SYM
ejpam-6838	80	10	eur	eur	PROPN
ejpam-6838	80	11	.	.	PUNCT
ejpam-6838	81	1	j.	j.	PROPN
ejpam-6838	81	2	pure	pure	PROPN
ejpam-6838	81	3	appl	appl	PROPN
ejpam-6838	81	4	.	.	PROPN
ejpam-6838	81	5	math	math	PROPN
ejpam-6838	81	6	,	,	PUNCT
ejpam-6838	81	7	18	18	NUM
ejpam-6838	81	8	(	(	PUNCT
ejpam-6838	81	9	4	4	NUM
ejpam-6838	81	10	)	)	PUNCT
ejpam-6838	81	11	(	(	PUNCT
ejpam-6838	81	12	2025	2025	NUM
ejpam-6838	81	13	)	)	PUNCT
ejpam-6838	81	14	,	,	PUNCT
ejpam-6838	81	15	6838	6838	NUM
ejpam-6838	81	16	4	4	NUM
ejpam-6838	81	17	of	of	ADP
ejpam-6838	81	18	25	25	NUM
ejpam-6838	81	19	the	the	DET
ejpam-6838	81	20	advantages	advantage	NOUN
ejpam-6838	81	21	of	of	ADP
ejpam-6838	81	22	the	the	DET
ejpam-6838	81	23	proposed	propose	VERB
ejpam-6838	81	24	algorithm	algorithm	NOUN
ejpam-6838	81	25	can	can	AUX
ejpam-6838	81	26	be	be	AUX
ejpam-6838	81	27	listed	list	VERB
ejpam-6838	81	28	as	as	SCONJ
ejpam-6838	81	29	follows	follow	VERB
ejpam-6838	81	30	:	:	PUNCT
ejpam-6838	81	31	•	•	ADV
ejpam-6838	81	32	obtaining	obtain	VERB
ejpam-6838	81	33	highly	highly	ADV
ejpam-6838	81	34	accurate	accurate	ADJ
ejpam-6838	81	35	approximations	approximation	NOUN
ejpam-6838	81	36	using	use	VERB
ejpam-6838	81	37	a	a	DET
ejpam-6838	81	38	few	few	ADJ
ejpam-6838	81	39	terms	term	NOUN
ejpam-6838	81	40	of	of	ADP
ejpam-6838	81	41	the	the	DET
ejpam-6838	81	42	basis	basis	NOUN
ejpam-6838	81	43	functions	function	NOUN
ejpam-6838	81	44	.	.	PUNCT
ejpam-6838	82	1	•	•	NUM
ejpam-6838	83	1	reducing	reduce	VERB
ejpam-6838	83	2	the	the	DET
ejpam-6838	83	3	equation	equation	NOUN
ejpam-6838	83	4	governed	govern	VERB
ejpam-6838	83	5	by	by	ADP
ejpam-6838	83	6	its	its	PRON
ejpam-6838	83	7	conditions	condition	NOUN
ejpam-6838	83	8	into	into	ADP
ejpam-6838	83	9	a	a	DET
ejpam-6838	83	10	system	system	NOUN
ejpam-6838	83	11	of	of	ADP
ejpam-6838	83	12	equations	equation	NOUN
ejpam-6838	83	13	that	that	PRON
ejpam-6838	83	14	can	can	AUX
ejpam-6838	83	15	be	be	AUX
ejpam-6838	83	16	efficiently	efficiently	ADV
ejpam-6838	83	17	handled	handle	VERB
ejpam-6838	83	18	.	.	PUNCT
ejpam-6838	84	1	•	•	NUM
ejpam-6838	84	2	the	the	DET
ejpam-6838	84	3	capability	capability	NOUN
ejpam-6838	84	4	of	of	ADP
ejpam-6838	84	5	extending	extend	VERB
ejpam-6838	84	6	the	the	DET
ejpam-6838	84	7	tau	tau	PROPN
ejpam-6838	84	8	approach	approach	NOUN
ejpam-6838	84	9	for	for	ADP
ejpam-6838	84	10	treating	treat	VERB
ejpam-6838	84	11	other	other	ADJ
ejpam-6838	84	12	types	type	NOUN
ejpam-6838	84	13	of	of	ADP
ejpam-6838	84	14	fdes	fde	NOUN
ejpam-6838	84	15	.	.	PUNCT
ejpam-6838	85	1	the	the	DET
ejpam-6838	85	2	paper	paper	NOUN
ejpam-6838	85	3	follows	follow	VERB
ejpam-6838	85	4	the	the	DET
ejpam-6838	85	5	following	follow	VERB
ejpam-6838	85	6	structure	structure	NOUN
ejpam-6838	85	7	:	:	PUNCT
ejpam-6838	85	8	in	in	ADP
ejpam-6838	85	9	the	the	DET
ejpam-6838	85	10	next	next	ADJ
ejpam-6838	85	11	section	section	NOUN
ejpam-6838	85	12	,	,	PUNCT
ejpam-6838	85	13	we	we	PRON
ejpam-6838	85	14	present	present	VERB
ejpam-6838	85	15	the	the	DET
ejpam-6838	85	16	necessary	necessary	ADJ
ejpam-6838	85	17	mathematical	mathematical	ADJ
ejpam-6838	85	18	preliminaries	preliminary	NOUN
ejpam-6838	85	19	,	,	PUNCT
ejpam-6838	85	20	including	include	VERB
ejpam-6838	85	21	some	some	DET
ejpam-6838	85	22	properties	property	NOUN
ejpam-6838	85	23	of	of	ADP
ejpam-6838	85	24	caputo	caputo	PROPN
ejpam-6838	85	25	’s	’s	PART
ejpam-6838	85	26	fractional	fractional	ADJ
ejpam-6838	85	27	derivative	derivative	NOUN
ejpam-6838	85	28	,	,	PUNCT
ejpam-6838	85	29	and	and	CCONJ
ejpam-6838	85	30	also	also	ADV
ejpam-6838	85	31	some	some	DET
ejpam-6838	85	32	formulas	formula	NOUN
ejpam-6838	85	33	concerned	concern	VERB
ejpam-6838	85	34	with	with	ADP
ejpam-6838	85	35	the	the	DET
ejpam-6838	85	36	specific	specific	ADJ
ejpam-6838	85	37	cps	cp	NOUN
ejpam-6838	85	38	that	that	PRON
ejpam-6838	85	39	we	we	PRON
ejpam-6838	85	40	will	will	AUX
ejpam-6838	85	41	employ	employ	VERB
ejpam-6838	85	42	.	.	PUNCT
ejpam-6838	86	1	section	section	NOUN
ejpam-6838	86	2	3	3	NUM
ejpam-6838	86	3	is	be	AUX
ejpam-6838	86	4	interested	interested	ADJ
ejpam-6838	86	5	in	in	ADP
ejpam-6838	86	6	analyzing	analyze	VERB
ejpam-6838	86	7	in	in	ADP
ejpam-6838	86	8	detail	detail	NOUN
ejpam-6838	86	9	the	the	DET
ejpam-6838	86	10	spectral	spectral	ADJ
ejpam-6838	86	11	tau	tau	PROPN
ejpam-6838	86	12	method	method	NOUN
ejpam-6838	86	13	for	for	ADP
ejpam-6838	86	14	the	the	DET
ejpam-6838	86	15	tfde	tfde	NOUN
ejpam-6838	86	16	using	use	VERB
ejpam-6838	86	17	the	the	DET
ejpam-6838	86	18	proposed	propose	VERB
ejpam-6838	86	19	cps	cp	NOUN
ejpam-6838	86	20	.	.	PUNCT
ejpam-6838	87	1	in	in	ADP
ejpam-6838	87	2	section	section	NOUN
ejpam-6838	87	3	4	4	NUM
ejpam-6838	87	4	,	,	PUNCT
ejpam-6838	87	5	a	a	DET
ejpam-6838	87	6	thorough	thorough	ADJ
ejpam-6838	87	7	error	error	NOUN
ejpam-6838	87	8	analysis	analysis	NOUN
ejpam-6838	87	9	of	of	ADP
ejpam-6838	87	10	the	the	DET
ejpam-6838	87	11	proposed	propose	VERB
ejpam-6838	87	12	chebyshev	chebyshev	NOUN
ejpam-6838	87	13	expansion	expansion	NOUN
ejpam-6838	87	14	is	be	AUX
ejpam-6838	87	15	conducted	conduct	VERB
ejpam-6838	87	16	.	.	PUNCT
ejpam-6838	88	1	furthermore	furthermore	ADV
ejpam-6838	88	2	,	,	PUNCT
ejpam-6838	88	3	we	we	PRON
ejpam-6838	88	4	derive	derive	VERB
ejpam-6838	88	5	theoretical	theoretical	ADJ
ejpam-6838	88	6	bounds	bound	NOUN
ejpam-6838	88	7	for	for	ADP
ejpam-6838	88	8	the	the	DET
ejpam-6838	88	9	double	double	ADJ
ejpam-6838	88	10	expansion	expansion	NOUN
ejpam-6838	88	11	.	.	PUNCT
ejpam-6838	89	1	section	section	NOUN
ejpam-6838	89	2	5	5	NUM
ejpam-6838	89	3	ensures	ensure	VERB
ejpam-6838	89	4	the	the	DET
ejpam-6838	89	5	applicability	applicability	NOUN
ejpam-6838	89	6	and	and	CCONJ
ejpam-6838	89	7	accuracy	accuracy	NOUN
ejpam-6838	89	8	of	of	ADP
ejpam-6838	89	9	the	the	DET
ejpam-6838	89	10	presented	present	VERB
ejpam-6838	89	11	algorithm	algorithm	NOUN
ejpam-6838	89	12	through	through	ADP
ejpam-6838	89	13	displaying	display	VERB
ejpam-6838	89	14	several	several	ADJ
ejpam-6838	89	15	numerical	numerical	ADJ
ejpam-6838	89	16	experiments	experiment	NOUN
ejpam-6838	89	17	supported	support	VERB
ejpam-6838	89	18	by	by	ADP
ejpam-6838	89	19	some	some	DET
ejpam-6838	89	20	comparisons	comparison	NOUN
ejpam-6838	89	21	.	.	PUNCT
ejpam-6838	90	1	finally	finally	ADV
ejpam-6838	90	2	,	,	PUNCT
ejpam-6838	90	3	concluding	conclude	VERB
ejpam-6838	90	4	remarks	remark	NOUN
ejpam-6838	90	5	are	be	AUX
ejpam-6838	90	6	reported	report	VERB
ejpam-6838	90	7	in	in	ADP
ejpam-6838	90	8	section	section	NOUN
ejpam-6838	90	9	6	6	NUM
ejpam-6838	90	10	.	.	NOUN
ejpam-6838	91	1	2	2	NUM
ejpam-6838	91	2	.	.	X
ejpam-6838	92	1	some	some	DET
ejpam-6838	92	2	fundamentals	fundamental	NOUN
ejpam-6838	92	3	and	and	CCONJ
ejpam-6838	92	4	formulas	formula	NOUN
ejpam-6838	92	5	this	this	DET
ejpam-6838	92	6	section	section	NOUN
ejpam-6838	92	7	is	be	AUX
ejpam-6838	92	8	confined	confine	VERB
ejpam-6838	92	9	to	to	ADP
ejpam-6838	92	10	displaying	display	VERB
ejpam-6838	92	11	an	an	DET
ejpam-6838	92	12	overview	overview	NOUN
ejpam-6838	92	13	of	of	ADP
ejpam-6838	92	14	the	the	DET
ejpam-6838	92	15	fractional	fractional	ADJ
ejpam-6838	92	16	calculus	calculus	NOUN
ejpam-6838	92	17	.	.	PUNCT
ejpam-6838	93	1	furthermore	furthermore	ADV
ejpam-6838	93	2	,	,	PUNCT
ejpam-6838	93	3	an	an	DET
ejpam-6838	93	4	account	account	NOUN
ejpam-6838	93	5	of	of	ADP
ejpam-6838	93	6	the	the	DET
ejpam-6838	93	7	generalized	generalized	ADJ
ejpam-6838	93	8	gegenbauer	gegenbauer	NOUN
ejpam-6838	93	9	polynomials	polynomial	NOUN
ejpam-6838	93	10	is	be	AUX
ejpam-6838	93	11	given	give	VERB
ejpam-6838	93	12	.	.	PUNCT
ejpam-6838	94	1	particular	particular	ADJ
ejpam-6838	94	2	cps	cp	NOUN
ejpam-6838	94	3	that	that	PRON
ejpam-6838	94	4	will	will	AUX
ejpam-6838	94	5	be	be	AUX
ejpam-6838	94	6	used	use	VERB
ejpam-6838	94	7	as	as	SCONJ
ejpam-6838	94	8	basis	basis	NOUN
ejpam-6838	94	9	functions	function	NOUN
ejpam-6838	94	10	are	be	AUX
ejpam-6838	94	11	introduced	introduce	VERB
ejpam-6838	94	12	.	.	PUNCT
ejpam-6838	95	1	some	some	PRON
ejpam-6838	95	2	of	of	ADP
ejpam-6838	95	3	their	their	PRON
ejpam-6838	95	4	formulas	formula	NOUN
ejpam-6838	95	5	that	that	PRON
ejpam-6838	95	6	are	be	AUX
ejpam-6838	95	7	pivotal	pivotal	ADJ
ejpam-6838	95	8	to	to	ADP
ejpam-6838	95	9	deriving	derive	VERB
ejpam-6838	95	10	our	our	PRON
ejpam-6838	95	11	proposed	propose	VERB
ejpam-6838	95	12	numerical	numerical	ADJ
ejpam-6838	95	13	algorithm	algorithm	PROPN
ejpam-6838	95	14	are	be	AUX
ejpam-6838	95	15	also	also	ADV
ejpam-6838	95	16	provided	provide	VERB
ejpam-6838	95	17	.	.	PUNCT
ejpam-6838	96	1	2.1	2.1	NUM
ejpam-6838	96	2	.	.	PUNCT
ejpam-6838	97	1	caputo	caputo	PROPN
ejpam-6838	97	2	’s	’s	PART
ejpam-6838	97	3	fractional	fractional	ADJ
ejpam-6838	97	4	derivative	derivative	ADJ
ejpam-6838	97	5	definition	definition	NOUN
ejpam-6838	97	6	1	1	NUM
ejpam-6838	97	7	.	.	PUNCT
ejpam-6838	98	1	[	[	X
ejpam-6838	98	2	1	1	NUM
ejpam-6838	98	3	]	]	PUNCT
ejpam-6838	98	4	,	,	PUNCT
ejpam-6838	98	5	a	a	DET
ejpam-6838	98	6	fractional	fractional	ADJ
ejpam-6838	98	7	-	-	PUNCT
ejpam-6838	98	8	order	order	NOUN
ejpam-6838	98	9	derivative	derivative	NOUN
ejpam-6838	98	10	,	,	PUNCT
ejpam-6838	98	11	according	accord	VERB
ejpam-6838	98	12	to	to	ADP
ejpam-6838	98	13	caputo	caputo	PROPN
ejpam-6838	98	14	,	,	PUNCT
ejpam-6838	98	15	is	be	AUX
ejpam-6838	98	16	defined	define	VERB
ejpam-6838	98	17	as	as	ADP
ejpam-6838	98	18	dν	dν	PROPN
ejpam-6838	98	19	t	t	PROPN
ejpam-6838	98	20	ψ(s	ψ(s	PROPN
ejpam-6838	98	21	)	)	PUNCT
ejpam-6838	99	1	=	=	SYM
ejpam-6838	99	2	1	1	NUM
ejpam-6838	99	3	γ(k	γ(k	NOUN
ejpam-6838	99	4	−	−	NOUN
ejpam-6838	99	5	ν	ν	PROPN
ejpam-6838	99	6	)	)	PUNCT
ejpam-6838	99	7	∫	∫	PROPN
ejpam-6838	99	8	s	s	PART
ejpam-6838	99	9	0	0	NUM
ejpam-6838	99	10	(	(	PUNCT
ejpam-6838	99	11	s−	s−	PROPN
ejpam-6838	99	12	t)k−ν−1ψ(k)(t)dt	t)k−ν−1ψ(k)(t)dt	PROPN
ejpam-6838	99	13	,	,	PUNCT
ejpam-6838	99	14	ν	ν	X
ejpam-6838	99	15	>	>	X
ejpam-6838	99	16	0	0	NUM
ejpam-6838	99	17	,	,	PUNCT
ejpam-6838	99	18	s	s	VERB
ejpam-6838	99	19	>	>	X
ejpam-6838	99	20	0	0	PROPN
ejpam-6838	99	21	,	,	PUNCT
ejpam-6838	99	22	k	k	PROPN
ejpam-6838	99	23	−	−	PROPN
ejpam-6838	100	1	1	1	NUM
ejpam-6838	100	2	<	<	X
ejpam-6838	100	3	ν	ν	X
ejpam-6838	100	4	≤	≤	PROPN
ejpam-6838	100	5	k	k	PROPN
ejpam-6838	100	6	,	,	PUNCT
ejpam-6838	100	7	k	k	PROPN
ejpam-6838	100	8	∈	∈	PROPN
ejpam-6838	100	9	n.	n.	NOUN
ejpam-6838	100	10	(	(	PUNCT
ejpam-6838	100	11	1	1	NUM
ejpam-6838	100	12	)	)	PUNCT
ejpam-6838	100	13	for	for	ADP
ejpam-6838	100	14	dν	dν	PROPN
ejpam-6838	100	15	t	t	PROPN
ejpam-6838	100	16	with	with	ADP
ejpam-6838	100	17	k	k	PROPN
ejpam-6838	100	18	−	−	PROPN
ejpam-6838	101	1	1	1	NUM
ejpam-6838	101	2	<	<	X
ejpam-6838	101	3	ν	ν	X
ejpam-6838	101	4	≤	≤	PROPN
ejpam-6838	101	5	k	k	PROPN
ejpam-6838	101	6	,	,	PUNCT
ejpam-6838	101	7	k	k	PROPN
ejpam-6838	101	8	∈	∈	PROPN
ejpam-6838	101	9	n	n	CCONJ
ejpam-6838	101	10	,	,	PUNCT
ejpam-6838	101	11	the	the	DET
ejpam-6838	101	12	following	follow	VERB
ejpam-6838	101	13	identities	identity	NOUN
ejpam-6838	101	14	hold	hold	VERB
ejpam-6838	101	15	:	:	PUNCT
ejpam-6838	101	16	dν	dν	PROPN
ejpam-6838	101	17	t	t	PROPN
ejpam-6838	101	18	c	c	NOUN
ejpam-6838	101	19	=	=	PROPN
ejpam-6838	101	20	0	0	PROPN
ejpam-6838	101	21	,	,	PUNCT
ejpam-6838	101	22	c	c	PROPN
ejpam-6838	101	23	is	be	AUX
ejpam-6838	101	24	a	a	DET
ejpam-6838	101	25	constant	constant	ADJ
ejpam-6838	101	26	,	,	PUNCT
ejpam-6838	101	27	(	(	PUNCT
ejpam-6838	101	28	2	2	X
ejpam-6838	101	29	)	)	PUNCT
ejpam-6838	101	30	dν	dν	VERB
ejpam-6838	101	31	t	t	PROPN
ejpam-6838	101	32	s	s	PART
ejpam-6838	101	33	k	k	X
ejpam-6838	101	34	=	=	X
ejpam-6838	101	35	{	{	PUNCT
ejpam-6838	101	36	0	0	NUM
ejpam-6838	101	37	,	,	PUNCT
ejpam-6838	102	1	if	if	SCONJ
ejpam-6838	102	2	k	k	PROPN
ejpam-6838	102	3	∈	∈	PROPN
ejpam-6838	102	4	n0	n0	PROPN
ejpam-6838	102	5	and	and	CCONJ
ejpam-6838	102	6	k	k	X
ejpam-6838	102	7	<	<	X
ejpam-6838	102	8	⌈ν⌉	⌈ν⌉	X
ejpam-6838	102	9	,	,	PUNCT
ejpam-6838	102	10	(	(	PUNCT
ejpam-6838	102	11	k	k	NOUN
ejpam-6838	102	12	)	)	PUNCT
ejpam-6838	103	1	!	!	PUNCT
ejpam-6838	104	1	γ(k−ν+1	γ(k−ν+1	NOUN
ejpam-6838	104	2	)	)	PUNCT
ejpam-6838	104	3	s	s	PART
ejpam-6838	104	4	k−ν	k−ν	PROPN
ejpam-6838	104	5	,	,	PUNCT
ejpam-6838	104	6	if	if	SCONJ
ejpam-6838	104	7	k	k	PROPN
ejpam-6838	104	8	∈	∈	PROPN
ejpam-6838	104	9	n0	n0	PROPN
ejpam-6838	104	10	and	and	CCONJ
ejpam-6838	104	11	k	k	PROPN
ejpam-6838	104	12	≥	≥	NUM
ejpam-6838	104	13	⌈ν⌉	⌈ν⌉	ADV
ejpam-6838	104	14	,	,	PUNCT
ejpam-6838	104	15	(	(	PUNCT
ejpam-6838	104	16	3	3	NUM
ejpam-6838	104	17	)	)	PUNCT
ejpam-6838	104	18	where	where	SCONJ
ejpam-6838	104	19	n	n	ADV
ejpam-6838	104	20	=	=	SYM
ejpam-6838	104	21	{	{	PUNCT
ejpam-6838	104	22	1	1	NUM
ejpam-6838	104	23	,	,	PUNCT
ejpam-6838	104	24	2	2	NUM
ejpam-6838	104	25	,	,	PUNCT
ejpam-6838	104	26	...	...	PUNCT
ejpam-6838	104	27	}	}	PUNCT
ejpam-6838	104	28	and	and	CCONJ
ejpam-6838	104	29	n0	n0	NUM
ejpam-6838	104	30	=	=	SYM
ejpam-6838	104	31	{	{	PUNCT
ejpam-6838	104	32	0	0	NUM
ejpam-6838	104	33	,	,	PUNCT
ejpam-6838	104	34	1	1	NUM
ejpam-6838	104	35	,	,	PUNCT
ejpam-6838	104	36	2	2	NUM
ejpam-6838	104	37	,	,	PUNCT
ejpam-6838	104	38	.	.	PUNCT
ejpam-6838	104	39	.	.	PUNCT
ejpam-6838	104	40	.	.	PUNCT
ejpam-6838	104	41	}	}	PUNCT
ejpam-6838	104	42	,	,	PUNCT
ejpam-6838	104	43	and	and	CCONJ
ejpam-6838	104	44	⌈ν⌉	⌈ν⌉	X
ejpam-6838	104	45	is	be	AUX
ejpam-6838	104	46	the	the	DET
ejpam-6838	104	47	ceiling	ceiling	NOUN
ejpam-6838	104	48	function	function	NOUN
ejpam-6838	104	49	.	.	PUNCT
ejpam-6838	105	1	w.	w.	PROPN
ejpam-6838	105	2	m.	m.	PROPN
ejpam-6838	105	3	abd	abd	PROPN
ejpam-6838	105	4	-	-	PUNCT
ejpam-6838	105	5	elhameed	elhameed	PROPN
ejpam-6838	105	6	et	et	PROPN
ejpam-6838	105	7	al	al	PROPN
ejpam-6838	105	8	.	.	PUNCT
ejpam-6838	105	9	/	/	SYM
ejpam-6838	105	10	eur	eur	PROPN
ejpam-6838	105	11	.	.	PUNCT
ejpam-6838	106	1	j.	j.	PROPN
ejpam-6838	106	2	pure	pure	PROPN
ejpam-6838	106	3	appl	appl	PROPN
ejpam-6838	106	4	.	.	PROPN
ejpam-6838	106	5	math	math	PROPN
ejpam-6838	106	6	,	,	PUNCT
ejpam-6838	106	7	18	18	NUM
ejpam-6838	106	8	(	(	PUNCT
ejpam-6838	106	9	4	4	NUM
ejpam-6838	106	10	)	)	PUNCT
ejpam-6838	106	11	(	(	PUNCT
ejpam-6838	106	12	2025	2025	NUM
ejpam-6838	106	13	)	)	PUNCT
ejpam-6838	106	14	,	,	PUNCT
ejpam-6838	106	15	6838	6838	NUM
ejpam-6838	106	16	5	5	NUM
ejpam-6838	106	17	of	of	ADP
ejpam-6838	106	18	25	25	NUM
ejpam-6838	106	19	2.2	2.2	NUM
ejpam-6838	106	20	.	.	PUNCT
ejpam-6838	107	1	an	an	DET
ejpam-6838	107	2	account	account	NOUN
ejpam-6838	107	3	on	on	ADP
ejpam-6838	107	4	generalized	generalized	ADJ
ejpam-6838	107	5	gegenbauer	gegenbauer	NOUN
ejpam-6838	107	6	polynomials	polynomial	NOUN
ejpam-6838	107	7	we	we	PRON
ejpam-6838	107	8	give	give	VERB
ejpam-6838	107	9	an	an	DET
ejpam-6838	107	10	account	account	NOUN
ejpam-6838	107	11	of	of	ADP
ejpam-6838	107	12	the	the	DET
ejpam-6838	107	13	generalized	generalized	ADJ
ejpam-6838	107	14	gegenbauer	gegenbauer	NOUN
ejpam-6838	107	15	polynomials	polynomial	VERB
ejpam-6838	107	16	g	g	PROPN
ejpam-6838	107	17	(	(	PUNCT
ejpam-6838	107	18	µ,β	µ,β	PROPN
ejpam-6838	107	19	)	)	PUNCT
ejpam-6838	107	20	k	k	PROPN
ejpam-6838	107	21	(	(	PUNCT
ejpam-6838	107	22	x	x	NOUN
ejpam-6838	107	23	)	)	PUNCT
ejpam-6838	107	24	.	.	PUNCT
ejpam-6838	108	1	they	they	PRON
ejpam-6838	108	2	are	be	AUX
ejpam-6838	108	3	orthogonal	orthogonal	ADJ
ejpam-6838	108	4	on	on	ADP
ejpam-6838	108	5	[	[	X
ejpam-6838	108	6	−1	−1	NOUN
ejpam-6838	108	7	,	,	PUNCT
ejpam-6838	108	8	1	1	NUM
ejpam-6838	108	9	]	]	PUNCT
ejpam-6838	108	10	regarding	regard	VERB
ejpam-6838	108	11	w(x	w(x	NOUN
ejpam-6838	108	12	)	)	PUNCT
ejpam-6838	108	13	=	=	PUNCT
ejpam-6838	109	1	(	(	PUNCT
ejpam-6838	109	2	1	1	NUM
ejpam-6838	109	3	−	−	NOUN
ejpam-6838	109	4	x2)µ−	x2)µ−	SYM
ejpam-6838	109	5	1	1	NUM
ejpam-6838	109	6	2	2	NUM
ejpam-6838	109	7	|x|2β	|x|2β	NOUN
ejpam-6838	109	8	.	.	PUNCT
ejpam-6838	110	1	they	they	PRON
ejpam-6838	110	2	can	can	AUX
ejpam-6838	110	3	be	be	AUX
ejpam-6838	110	4	represented	represent	VERB
ejpam-6838	110	5	as	as	ADP
ejpam-6838	110	6	[	[	X
ejpam-6838	110	7	59	59	NUM
ejpam-6838	110	8	,	,	PUNCT
ejpam-6838	110	9	60	60	NUM
ejpam-6838	110	10	]	]	X
ejpam-6838	110	11	g	g	PROPN
ejpam-6838	110	12	(	(	PUNCT
ejpam-6838	110	13	µ,β	µ,β	PROPN
ejpam-6838	110	14	)	)	PUNCT
ejpam-6838	110	15	k	k	NOUN
ejpam-6838	110	16	(	(	PUNCT
ejpam-6838	110	17	x	x	X
ejpam-6838	110	18	)	)	PUNCT
ejpam-6838	110	19	=	=	PUNCT
ejpam-6838	110	20			X
ejpam-6838	110	21	(	(	PUNCT
ejpam-6838	110	22	µ+	µ+	X
ejpam-6838	110	23	β	β	X
ejpam-6838	110	24	)	)	PUNCT
ejpam-6838	110	25	k	k	PROPN
ejpam-6838	110	26	2	2	X
ejpam-6838	110	27	(	(	PUNCT
ejpam-6838	110	28	β	β	X
ejpam-6838	110	29	+	+	NOUN
ejpam-6838	110	30	1	1	NUM
ejpam-6838	110	31	2	2	NUM
ejpam-6838	110	32	)	)	PUNCT
ejpam-6838	110	33	k	k	NOUN
ejpam-6838	110	34	2	2	NUM
ejpam-6838	110	35	p	p	NOUN
ejpam-6838	110	36	(	(	PUNCT
ejpam-6838	110	37	µ−	µ−	PROPN
ejpam-6838	110	38	1	1	NUM
ejpam-6838	110	39	2	2	NUM
ejpam-6838	110	40	,	,	PUNCT
ejpam-6838	110	41	β−	β−	PROPN
ejpam-6838	110	42	1	1	NUM
ejpam-6838	110	43	2	2	NUM
ejpam-6838	110	44	)	)	PUNCT
ejpam-6838	110	45	k	k	NOUN
ejpam-6838	110	46	2	2	NUM
ejpam-6838	110	47	(	(	PUNCT
ejpam-6838	110	48	2x2	2x2	NUM
ejpam-6838	110	49	−	−	NUM
ejpam-6838	110	50	1	1	NUM
ejpam-6838	110	51	)	)	PUNCT
ejpam-6838	110	52	,	,	PUNCT
ejpam-6838	110	53	if	if	SCONJ
ejpam-6838	110	54	k	k	PROPN
ejpam-6838	110	55	is	be	AUX
ejpam-6838	110	56	even	even	ADV
ejpam-6838	110	57	,	,	PUNCT
ejpam-6838	110	58	(	(	PUNCT
ejpam-6838	110	59	µ+	µ+	X
ejpam-6838	110	60	β	β	NOUN
ejpam-6838	110	61	)	)	PUNCT
ejpam-6838	110	62	k+1	k+1	PRON
ejpam-6838	110	63	2	2	NUM
ejpam-6838	110	64	(	(	PUNCT
ejpam-6838	110	65	β	β	X
ejpam-6838	110	66	+	+	NOUN
ejpam-6838	110	67	1	1	NUM
ejpam-6838	110	68	2	2	NUM
ejpam-6838	110	69	)	)	PUNCT
ejpam-6838	111	1	k+1	k+1	NOUN
ejpam-6838	111	2	2	2	NUM
ejpam-6838	111	3	xp	xp	NOUN
ejpam-6838	111	4	(	(	PUNCT
ejpam-6838	111	5	µ−	µ−	PROPN
ejpam-6838	111	6	1	1	NUM
ejpam-6838	111	7	2	2	NUM
ejpam-6838	111	8	,	,	PUNCT
ejpam-6838	111	9	β+	β+	PUNCT
ejpam-6838	111	10	1	1	NUM
ejpam-6838	111	11	2	2	NUM
ejpam-6838	111	12	)	)	PUNCT
ejpam-6838	111	13	k−1	k−1	PROPN
ejpam-6838	111	14	2	2	NUM
ejpam-6838	111	15	(	(	PUNCT
ejpam-6838	111	16	2x2	2x2	NUM
ejpam-6838	111	17	−	−	NUM
ejpam-6838	111	18	1	1	NUM
ejpam-6838	111	19	)	)	PUNCT
ejpam-6838	111	20	,	,	PUNCT
ejpam-6838	111	21	if	if	SCONJ
ejpam-6838	111	22	k	k	PROPN
ejpam-6838	111	23	is	be	AUX
ejpam-6838	111	24	odd	odd	ADJ
ejpam-6838	111	25	,	,	PUNCT
ejpam-6838	111	26	(	(	PUNCT
ejpam-6838	111	27	4	4	NUM
ejpam-6838	111	28	)	)	PUNCT
ejpam-6838	111	29	where	where	SCONJ
ejpam-6838	111	30	(	(	PUNCT
ejpam-6838	111	31	z)k	z)k	NOUN
ejpam-6838	111	32	=	=	SYM
ejpam-6838	111	33	γ(z+k	γ(z+k	SYM
ejpam-6838	111	34	)	)	PUNCT
ejpam-6838	111	35	γ(z	γ(z	ADJ
ejpam-6838	111	36	)	)	PUNCT
ejpam-6838	111	37	denotes	denote	VERB
ejpam-6838	111	38	the	the	DET
ejpam-6838	111	39	pochhammer	pochhammer	NOUN
ejpam-6838	111	40	symbol	symbol	NOUN
ejpam-6838	111	41	and	and	CCONJ
ejpam-6838	111	42	p	p	X
ejpam-6838	111	43	(	(	PUNCT
ejpam-6838	111	44	µ,β	µ,β	PROPN
ejpam-6838	111	45	)	)	PUNCT
ejpam-6838	111	46	k	k	NOUN
ejpam-6838	111	47	(	(	PUNCT
ejpam-6838	111	48	x	x	X
ejpam-6838	111	49	)	)	PUNCT
ejpam-6838	111	50	are	be	AUX
ejpam-6838	111	51	the	the	DET
ejpam-6838	111	52	standard	standard	ADJ
ejpam-6838	111	53	jacobi	jacobi	NOUN
ejpam-6838	111	54	polynomials	polynomial	NOUN
ejpam-6838	111	55	.	.	PUNCT
ejpam-6838	112	1	the	the	DET
ejpam-6838	112	2	orthogonality	orthogonality	NOUN
ejpam-6838	112	3	relation	relation	NOUN
ejpam-6838	112	4	for	for	ADP
ejpam-6838	112	5	g	g	PROPN
ejpam-6838	112	6	(	(	PUNCT
ejpam-6838	112	7	µ,β	µ,β	PROPN
ejpam-6838	112	8	)	)	PUNCT
ejpam-6838	112	9	k	k	NOUN
ejpam-6838	112	10	(	(	PUNCT
ejpam-6838	112	11	x	x	X
ejpam-6838	112	12	)	)	PUNCT
ejpam-6838	112	13	is	be	AUX
ejpam-6838	112	14	1∫	1∫	NUM
ejpam-6838	112	15	−1	−1	NOUN
ejpam-6838	112	16	w(x)g	w(x)g	X
ejpam-6838	112	17	(	(	PUNCT
ejpam-6838	112	18	µ,β	µ,β	PROPN
ejpam-6838	112	19	)	)	PUNCT
ejpam-6838	112	20	k	k	PROPN
ejpam-6838	112	21	(	(	PUNCT
ejpam-6838	112	22	x)g(µ,β	x)g(µ,β	PROPN
ejpam-6838	112	23	)	)	PUNCT
ejpam-6838	112	24	m	m	VERB
ejpam-6838	112	25	(	(	PUNCT
ejpam-6838	112	26	x	x	X
ejpam-6838	112	27	)	)	PUNCT
ejpam-6838	112	28	dx	dx	PROPN
ejpam-6838	113	1	=	=	PRON
ejpam-6838	113	2	{	{	PUNCT
ejpam-6838	113	3	hµ,βk	hµ,βk	NOUN
ejpam-6838	113	4	,	,	PUNCT
ejpam-6838	113	5	k	k	PROPN
ejpam-6838	113	6	=	=	PUNCT
ejpam-6838	113	7	m	m	PROPN
ejpam-6838	113	8	,	,	PUNCT
ejpam-6838	113	9	0	0	NUM
ejpam-6838	113	10	,	,	PUNCT
ejpam-6838	113	11	k	k	PROPN
ejpam-6838	113	12	̸=	̸=	PROPN
ejpam-6838	113	13	m	m	PROPN
ejpam-6838	113	14	,	,	PUNCT
ejpam-6838	113	15	(	(	PUNCT
ejpam-6838	113	16	5	5	NUM
ejpam-6838	113	17	)	)	PUNCT
ejpam-6838	113	18	where	where	SCONJ
ejpam-6838	113	19	hµ,βk	hµ,βk	NOUN
ejpam-6838	113	20	is	be	AUX
ejpam-6838	113	21	given	give	VERB
ejpam-6838	113	22	by	by	ADP
ejpam-6838	113	23	hµ,βk	hµ,βk	NOUN
ejpam-6838	113	24	=	=	SYM
ejpam-6838	113	25	(	(	PUNCT
ejpam-6838	113	26	γ	γ	X
ejpam-6838	113	27	(	(	PUNCT
ejpam-6838	113	28	β	β	X
ejpam-6838	113	29	+	+	NOUN
ejpam-6838	113	30	1	1	NUM
ejpam-6838	113	31	2	2	NUM
ejpam-6838	113	32	)	)	PUNCT
ejpam-6838	113	33	)	)	PUNCT
ejpam-6838	113	34	2	2	NUM
ejpam-6838	113	35	(	(	PUNCT
ejpam-6838	113	36	k	k	NOUN
ejpam-6838	113	37	+	+	X
ejpam-6838	113	38	µ+	µ+	X
ejpam-6838	113	39	β	β	X
ejpam-6838	113	40	)	)	PUNCT
ejpam-6838	113	41	(	(	PUNCT
ejpam-6838	113	42	γ(µ+	γ(µ+	X
ejpam-6838	113	43	β))2	β))2	X
ejpam-6838	113	44			PROPN
ejpam-6838	113	45	γ	γ	X
ejpam-6838	113	46	(	(	PUNCT
ejpam-6838	113	47	µ+	µ+	X
ejpam-6838	113	48	k+1	k+1	X
ejpam-6838	113	49	2	2	X
ejpam-6838	113	50	)	)	PUNCT
ejpam-6838	113	51	γ	γ	PROPN
ejpam-6838	113	52	(	(	PUNCT
ejpam-6838	113	53	k	k	PROPN
ejpam-6838	113	54	2	2	NUM
ejpam-6838	113	55	+	+	CCONJ
ejpam-6838	113	56	µ+	µ+	X
ejpam-6838	113	57	β	β	NOUN
ejpam-6838	113	58	)	)	PUNCT
ejpam-6838	113	59	(	(	PUNCT
ejpam-6838	113	60	k	k	NOUN
ejpam-6838	113	61	2	2	NUM
ejpam-6838	113	62	)	)	PUNCT
ejpam-6838	113	63	!	!	PUNCT
ejpam-6838	114	1	γ	γ	X
ejpam-6838	114	2	(	(	PUNCT
ejpam-6838	114	3	1+k	1+k	NUM
ejpam-6838	114	4	2	2	NUM
ejpam-6838	114	5	+	+	CCONJ
ejpam-6838	114	6	β	β	X
ejpam-6838	114	7	)	)	PUNCT
ejpam-6838	114	8	,	,	PUNCT
ejpam-6838	114	9	k	k	PROPN
ejpam-6838	114	10	even	even	ADV
ejpam-6838	114	11	,	,	PUNCT
ejpam-6838	114	12	γ	γ	X
ejpam-6838	114	13	(	(	PUNCT
ejpam-6838	114	14	k	k	PROPN
ejpam-6838	114	15	2	2	NUM
ejpam-6838	114	16	+	+	SYM
ejpam-6838	114	17	µ	µ	X
ejpam-6838	114	18	)	)	PUNCT
ejpam-6838	114	19	γ	γ	PROPN
ejpam-6838	114	20	(	(	PUNCT
ejpam-6838	114	21	k	k	PROPN
ejpam-6838	114	22	2	2	NUM
ejpam-6838	114	23	+	+	CCONJ
ejpam-6838	114	24	µ+	µ+	X
ejpam-6838	114	25	β	β	X
ejpam-6838	114	26	+	+	NOUN
ejpam-6838	114	27	1	1	NUM
ejpam-6838	114	28	2	2	NUM
ejpam-6838	114	29	)	)	PUNCT
ejpam-6838	114	30	(	(	PUNCT
ejpam-6838	114	31	k−1	k−1	PROPN
ejpam-6838	114	32	2	2	NUM
ejpam-6838	114	33	)	)	PUNCT
ejpam-6838	114	34	!	!	PUNCT
ejpam-6838	115	1	γ	γ	X
ejpam-6838	115	2	(	(	PUNCT
ejpam-6838	115	3	k	k	PROPN
ejpam-6838	115	4	2	2	NUM
ejpam-6838	115	5	+	+	CCONJ
ejpam-6838	115	6	β	β	X
ejpam-6838	115	7	+	+	ADP
ejpam-6838	115	8	1	1	NUM
ejpam-6838	115	9	)	)	PUNCT
ejpam-6838	115	10	,	,	PUNCT
ejpam-6838	115	11	k	k	PROPN
ejpam-6838	115	12	odd	odd	ADJ
ejpam-6838	115	13	.	.	PUNCT
ejpam-6838	116	1	(	(	PUNCT
ejpam-6838	116	2	6	6	NUM
ejpam-6838	116	3	)	)	PUNCT
ejpam-6838	116	4	remark	remark	NOUN
ejpam-6838	116	5	1	1	NUM
ejpam-6838	116	6	.	.	PUNCT
ejpam-6838	116	7	several	several	ADJ
ejpam-6838	116	8	particular	particular	ADJ
ejpam-6838	116	9	polynomials	polynomial	NOUN
ejpam-6838	116	10	,	,	PUNCT
ejpam-6838	116	11	including	include	VERB
ejpam-6838	116	12	cps	cp	NOUN
ejpam-6838	116	13	,	,	PUNCT
ejpam-6838	116	14	are	be	AUX
ejpam-6838	116	15	particular	particular	ADJ
ejpam-6838	116	16	ones	one	NOUN
ejpam-6838	116	17	of	of	ADP
ejpam-6838	116	18	the	the	DET
ejpam-6838	116	19	generalized	generalize	VERB
ejpam-6838	116	20	polynomials	polynomial	NOUN
ejpam-6838	116	21	g	g	PROPN
ejpam-6838	116	22	(	(	PUNCT
ejpam-6838	116	23	µ,β	µ,β	PROPN
ejpam-6838	116	24	)	)	PUNCT
ejpam-6838	116	25	k	k	NOUN
ejpam-6838	116	26	(	(	PUNCT
ejpam-6838	116	27	x	x	NOUN
ejpam-6838	116	28	)	)	PUNCT
ejpam-6838	116	29	,	,	PUNCT
ejpam-6838	116	30	see	see	VERB
ejpam-6838	116	31	[	[	X
ejpam-6838	116	32	40	40	NUM
ejpam-6838	116	33	]	]	PUNCT
ejpam-6838	116	34	.	.	PUNCT
ejpam-6838	117	1	the	the	DET
ejpam-6838	117	2	authors	author	NOUN
ejpam-6838	117	3	in	in	ADP
ejpam-6838	117	4	the	the	DET
ejpam-6838	117	5	same	same	ADJ
ejpam-6838	117	6	paper	paper	NOUN
ejpam-6838	117	7	introduced	introduce	VERB
ejpam-6838	117	8	certain	certain	ADJ
ejpam-6838	117	9	cps	cp	NOUN
ejpam-6838	117	10	as	as	ADP
ejpam-6838	117	11	particular	particular	ADJ
ejpam-6838	117	12	ones	one	NOUN
ejpam-6838	117	13	of	of	ADP
ejpam-6838	117	14	g	g	PROPN
ejpam-6838	117	15	(	(	PUNCT
ejpam-6838	117	16	µ,β	µ,β	PROPN
ejpam-6838	117	17	)	)	PUNCT
ejpam-6838	117	18	k	k	NOUN
ejpam-6838	117	19	(	(	PUNCT
ejpam-6838	117	20	x	x	NOUN
ejpam-6838	117	21	)	)	PUNCT
ejpam-6838	117	22	,	,	PUNCT
ejpam-6838	117	23	and	and	CCONJ
ejpam-6838	117	24	derived	derive	VERB
ejpam-6838	117	25	some	some	DET
ejpam-6838	117	26	formulas	formula	NOUN
ejpam-6838	117	27	regarding	regard	VERB
ejpam-6838	117	28	them	they	PRON
ejpam-6838	117	29	.	.	PUNCT
ejpam-6838	118	1	2.3	2.3	NUM
ejpam-6838	118	2	.	.	PUNCT
ejpam-6838	119	1	some	some	DET
ejpam-6838	119	2	properties	property	NOUN
ejpam-6838	119	3	and	and	CCONJ
ejpam-6838	119	4	formulas	formula	NOUN
ejpam-6838	119	5	of	of	ADP
ejpam-6838	119	6	a	a	DET
ejpam-6838	119	7	certain	certain	ADJ
ejpam-6838	119	8	kind	kind	NOUN
ejpam-6838	119	9	of	of	ADP
ejpam-6838	119	10	cps	cp	NOUN
ejpam-6838	119	11	the	the	DET
ejpam-6838	119	12	authors	author	NOUN
ejpam-6838	119	13	in	in	ADP
ejpam-6838	119	14	[	[	X
ejpam-6838	119	15	40	40	NUM
ejpam-6838	119	16	]	]	PUNCT
ejpam-6838	119	17	proposed	propose	VERB
ejpam-6838	119	18	the	the	DET
ejpam-6838	119	19	polynomials	polynomial	NOUN
ejpam-6838	119	20	nk(x	nk(x	PUNCT
ejpam-6838	119	21	)	)	PUNCT
ejpam-6838	120	1	=	=	SYM
ejpam-6838	120	2	g2,1	g2,1	PROPN
ejpam-6838	120	3	k	k	X
ejpam-6838	120	4	(	(	PUNCT
ejpam-6838	120	5	x	x	NOUN
ejpam-6838	120	6	)	)	PUNCT
ejpam-6838	120	7	.	.	PUNCT
ejpam-6838	121	1	they	they	PRON
ejpam-6838	121	2	are	be	AUX
ejpam-6838	121	3	defined	define	VERB
ejpam-6838	121	4	as	as	ADP
ejpam-6838	121	5	nk(x	nk(x	NOUN
ejpam-6838	121	6	)	)	PUNCT
ejpam-6838	122	1	=	=	SYM
ejpam-6838	123	1			PROPN
ejpam-6838	123	2	(	(	PUNCT
ejpam-6838	123	3	3	3	NUM
ejpam-6838	123	4	)	)	PUNCT
ejpam-6838	123	5	k	k	NOUN
ejpam-6838	123	6	2	2	NUM
ejpam-6838	123	7	(	(	PUNCT
ejpam-6838	123	8	3	3	NUM
ejpam-6838	123	9	2	2	NUM
ejpam-6838	123	10	)	)	PUNCT
ejpam-6838	123	11	k	k	NOUN
ejpam-6838	123	12	2	2	NUM
ejpam-6838	123	13	p	p	NOUN
ejpam-6838	123	14	(	(	PUNCT
ejpam-6838	123	15	3	3	NUM
ejpam-6838	123	16	2	2	NUM
ejpam-6838	123	17	,	,	PUNCT
ejpam-6838	123	18	1	1	NUM
ejpam-6838	123	19	2	2	NUM
ejpam-6838	123	20	)	)	PUNCT
ejpam-6838	123	21	k	k	NOUN
ejpam-6838	123	22	2	2	NUM
ejpam-6838	123	23	(	(	PUNCT
ejpam-6838	123	24	2x2	2x2	NUM
ejpam-6838	123	25	−	−	NUM
ejpam-6838	123	26	1	1	NUM
ejpam-6838	123	27	)	)	PUNCT
ejpam-6838	123	28	,	,	PUNCT
ejpam-6838	124	1	if	if	SCONJ
ejpam-6838	124	2	k	k	PROPN
ejpam-6838	124	3	even	even	ADV
ejpam-6838	124	4	,	,	PUNCT
ejpam-6838	124	5	x(3	x(3	PROPN
ejpam-6838	124	6	)	)	PUNCT
ejpam-6838	124	7	k+1	k+1	PART
ejpam-6838	124	8	2	2	NUM
ejpam-6838	124	9	(	(	PUNCT
ejpam-6838	124	10	3	3	NUM
ejpam-6838	124	11	2	2	NUM
ejpam-6838	124	12	)	)	PUNCT
ejpam-6838	124	13	k+1	k+1	NOUN
ejpam-6838	124	14	2	2	NUM
ejpam-6838	124	15	p	p	NOUN
ejpam-6838	124	16	(	(	PUNCT
ejpam-6838	124	17	3	3	NUM
ejpam-6838	124	18	2	2	NUM
ejpam-6838	124	19	,	,	PUNCT
ejpam-6838	124	20	3	3	NUM
ejpam-6838	124	21	2	2	NUM
ejpam-6838	124	22	)	)	PUNCT
ejpam-6838	124	23	k−1	k−1	PROPN
ejpam-6838	124	24	2	2	NUM
ejpam-6838	124	25	(	(	PUNCT
ejpam-6838	124	26	2x2	2x2	NUM
ejpam-6838	124	27	−	−	NUM
ejpam-6838	124	28	1	1	NUM
ejpam-6838	124	29	)	)	PUNCT
ejpam-6838	124	30	,	,	PUNCT
ejpam-6838	124	31	if	if	SCONJ
ejpam-6838	124	32	k	k	PROPN
ejpam-6838	124	33	odd	odd	ADJ
ejpam-6838	124	34	.	.	PUNCT
ejpam-6838	125	1	(	(	PUNCT
ejpam-6838	125	2	7	7	X
ejpam-6838	125	3	)	)	PUNCT
ejpam-6838	125	4	{	{	PUNCT
ejpam-6838	125	5	nk(x)}k≥0	nk(x)}k≥0	PROPN
ejpam-6838	125	6	are	be	AUX
ejpam-6838	125	7	orthogonal	orthogonal	ADJ
ejpam-6838	125	8	on	on	ADP
ejpam-6838	125	9	[	[	X
ejpam-6838	125	10	−1	−1	NOUN
ejpam-6838	125	11	,	,	PUNCT
ejpam-6838	125	12	1	1	NUM
ejpam-6838	125	13	]	]	PUNCT
ejpam-6838	125	14	in	in	ADP
ejpam-6838	125	15	the	the	DET
ejpam-6838	125	16	sense	sense	NOUN
ejpam-6838	125	17	that∫	that∫	NOUN
ejpam-6838	126	1	1	1	NUM
ejpam-6838	126	2	−1	−1	NOUN
ejpam-6838	126	3	x2	x2	NOUN
ejpam-6838	126	4	(	(	PUNCT
ejpam-6838	126	5	1−	1−	NUM
ejpam-6838	126	6	x2	x2	NOUN
ejpam-6838	126	7	)	)	PUNCT
ejpam-6838	126	8	3/2	3/2	NUM
ejpam-6838	126	9	nk(x	nk(x	NOUN
ejpam-6838	126	10	)	)	PUNCT
ejpam-6838	126	11	nj(x	nj(x	PUNCT
ejpam-6838	126	12	)	)	PUNCT
ejpam-6838	126	13	dx	dx	PROPN
ejpam-6838	127	1	=	=	SYM
ejpam-6838	127	2	hk	hk	PROPN
ejpam-6838	127	3	,	,	PUNCT
ejpam-6838	127	4	(	(	PUNCT
ejpam-6838	127	5	8)	8)	NUM
ejpam-6838	127	6	w.	w.	PROPN
ejpam-6838	127	7	m.	m.	PROPN
ejpam-6838	127	8	abd	abd	PROPN
ejpam-6838	127	9	-	-	PUNCT
ejpam-6838	127	10	elhameed	elhameed	PROPN
ejpam-6838	127	11	et	et	PROPN
ejpam-6838	127	12	al	al	PROPN
ejpam-6838	127	13	.	.	PUNCT
ejpam-6838	127	14	/	/	SYM
ejpam-6838	127	15	eur	eur	PROPN
ejpam-6838	127	16	.	.	PUNCT
ejpam-6838	128	1	j.	j.	PROPN
ejpam-6838	128	2	pure	pure	PROPN
ejpam-6838	128	3	appl	appl	PROPN
ejpam-6838	128	4	.	.	PROPN
ejpam-6838	128	5	math	math	PROPN
ejpam-6838	128	6	,	,	PUNCT
ejpam-6838	128	7	18	18	NUM
ejpam-6838	128	8	(	(	PUNCT
ejpam-6838	128	9	4	4	NUM
ejpam-6838	128	10	)	)	PUNCT
ejpam-6838	128	11	(	(	PUNCT
ejpam-6838	128	12	2025	2025	NUM
ejpam-6838	128	13	)	)	PUNCT
ejpam-6838	128	14	,	,	PUNCT
ejpam-6838	128	15	6838	6838	NUM
ejpam-6838	128	16	6	6	NUM
ejpam-6838	128	17	of	of	ADP
ejpam-6838	128	18	25	25	NUM
ejpam-6838	129	1	where	where	SCONJ
ejpam-6838	129	2	hn	hn	PROPN
ejpam-6838	129	3	=	=	PUNCT
ejpam-6838	129	4	π	π	PROPN
ejpam-6838	129	5	128	128	NUM
ejpam-6838	129	6			PROPN
ejpam-6838	129	7	(	(	PUNCT
ejpam-6838	129	8	k	k	PROPN
ejpam-6838	129	9	+	+	PROPN
ejpam-6838	129	10	2	2	NUM
ejpam-6838	129	11	)	)	PUNCT
ejpam-6838	129	12	(	(	PUNCT
ejpam-6838	129	13	k	k	NOUN
ejpam-6838	129	14	+	+	PROPN
ejpam-6838	129	15	4	4	NUM
ejpam-6838	129	16	)	)	PUNCT
ejpam-6838	129	17	,	,	PUNCT
ejpam-6838	129	18	if	if	SCONJ
ejpam-6838	129	19	k	k	PROPN
ejpam-6838	129	20	=	=	SYM
ejpam-6838	129	21	j	j	PROPN
ejpam-6838	129	22	,	,	PUNCT
ejpam-6838	129	23	k	k	PROPN
ejpam-6838	129	24	even	even	ADV
ejpam-6838	129	25	,	,	PUNCT
ejpam-6838	129	26	(	(	PUNCT
ejpam-6838	129	27	k	k	X
ejpam-6838	129	28	+	+	PROPN
ejpam-6838	129	29	1	1	X
ejpam-6838	129	30	)	)	PUNCT
ejpam-6838	129	31	(	(	PUNCT
ejpam-6838	129	32	k	k	X
ejpam-6838	129	33	+	+	PROPN
ejpam-6838	129	34	5	5	NUM
ejpam-6838	129	35	)	)	PUNCT
ejpam-6838	129	36	,	,	PUNCT
ejpam-6838	129	37	if	if	SCONJ
ejpam-6838	129	38	k	k	PROPN
ejpam-6838	129	39	=	=	SYM
ejpam-6838	129	40	j	j	PROPN
ejpam-6838	129	41	,	,	PUNCT
ejpam-6838	129	42	k	k	PROPN
ejpam-6838	129	43	odd	odd	ADJ
ejpam-6838	129	44	,	,	PUNCT
ejpam-6838	129	45	0	0	NUM
ejpam-6838	129	46	,	,	PUNCT
ejpam-6838	129	47	if	if	SCONJ
ejpam-6838	129	48	k	k	PROPN
ejpam-6838	129	49	̸=	̸=	PROPN
ejpam-6838	129	50	j.	j.	PROPN
ejpam-6838	129	51	(	(	PUNCT
ejpam-6838	129	52	9	9	NUM
ejpam-6838	129	53	)	)	PUNCT
ejpam-6838	129	54	the	the	DET
ejpam-6838	129	55	following	follow	VERB
ejpam-6838	129	56	two	two	NUM
ejpam-6838	129	57	lemmas	lemma	NOUN
ejpam-6838	129	58	give	give	VERB
ejpam-6838	129	59	the	the	DET
ejpam-6838	129	60	explicit	explicit	ADJ
ejpam-6838	129	61	analytic	analytic	ADJ
ejpam-6838	129	62	form	form	NOUN
ejpam-6838	129	63	ofnk(x	ofnk(x	ADP
ejpam-6838	129	64	)	)	PUNCT
ejpam-6838	129	65	and	and	CCONJ
ejpam-6838	129	66	its	its	PRON
ejpam-6838	129	67	inversion	inversion	NOUN
ejpam-6838	129	68	formula	formula	NOUN
ejpam-6838	129	69	.	.	PUNCT
ejpam-6838	130	1	lemma	lemma	PROPN
ejpam-6838	130	2	1	1	NUM
ejpam-6838	130	3	.	.	PUNCT
ejpam-6838	131	1	[	[	X
ejpam-6838	131	2	40	40	NUM
ejpam-6838	131	3	]	]	PUNCT
ejpam-6838	131	4	for	for	ADP
ejpam-6838	131	5	every	every	DET
ejpam-6838	131	6	positive	positive	ADJ
ejpam-6838	131	7	integer	integer	NOUN
ejpam-6838	131	8	s	s	PROPN
ejpam-6838	131	9	,	,	PUNCT
ejpam-6838	131	10	the	the	DET
ejpam-6838	131	11	polynomials	polynomial	NOUN
ejpam-6838	131	12	ns(x	ns(x	PUNCT
ejpam-6838	131	13	)	)	PUNCT
ejpam-6838	131	14	have	have	VERB
ejpam-6838	131	15	the	the	DET
ejpam-6838	131	16	following	follow	VERB
ejpam-6838	131	17	expression	expression	NOUN
ejpam-6838	131	18	:	:	PUNCT
ejpam-6838	131	19	ns(x	ns(x	PUNCT
ejpam-6838	131	20	)	)	PUNCT
ejpam-6838	132	1	=	=	PUNCT
ejpam-6838	132	2	⌊	⌊	PROPN
ejpam-6838	132	3	s	s	PART
ejpam-6838	132	4	2⌋∑	2⌋∑	PROPN
ejpam-6838	132	5	m=0	m=0	PROPN
ejpam-6838	132	6	(	(	PUNCT
ejpam-6838	132	7	−1)m	−1)m	PROPN
ejpam-6838	132	8	(	(	PUNCT
ejpam-6838	132	9	3)s−m	3)s−m	NUM
ejpam-6838	132	10	m	m	NOUN
ejpam-6838	132	11	!	!	PUNCT
ejpam-6838	133	1	(	(	PUNCT
ejpam-6838	133	2	⌊	⌊	PROPN
ejpam-6838	133	3	s	s	NOUN
ejpam-6838	133	4	2	2	NUM
ejpam-6838	133	5	⌋	⌋	NOUN
ejpam-6838	133	6	−m	−m	NOUN
ejpam-6838	133	7	)	)	PUNCT
ejpam-6838	133	8	!	!	PUNCT
ejpam-6838	134	1	(	(	PUNCT
ejpam-6838	134	2	3	3	NUM
ejpam-6838	134	3	2	2	NUM
ejpam-6838	134	4	)	)	PUNCT
ejpam-6838	134	5	−m+⌊	−m+⌊	NOUN
ejpam-6838	134	6	1+s	1+s	NUM
ejpam-6838	134	7	2	2	NUM
ejpam-6838	134	8	⌋	⌋	NOUN
ejpam-6838	134	9	xs−2	xs−2	PROPN
ejpam-6838	134	10	m.	m.	NOUN
ejpam-6838	134	11	(	(	PUNCT
ejpam-6838	134	12	10	10	NUM
ejpam-6838	134	13	)	)	PUNCT
ejpam-6838	134	14	lemma	lemma	PROPN
ejpam-6838	134	15	2	2	NUM
ejpam-6838	134	16	.	.	PUNCT
ejpam-6838	135	1	[	[	X
ejpam-6838	135	2	40	40	NUM
ejpam-6838	135	3	]	]	PUNCT
ejpam-6838	135	4	for	for	ADP
ejpam-6838	135	5	every	every	DET
ejpam-6838	135	6	positive	positive	ADJ
ejpam-6838	135	7	integer	integer	NOUN
ejpam-6838	135	8	s	s	PROPN
ejpam-6838	135	9	,	,	PUNCT
ejpam-6838	135	10	xs	xs	PROPN
ejpam-6838	135	11	can	can	AUX
ejpam-6838	135	12	be	be	AUX
ejpam-6838	135	13	expanded	expand	VERB
ejpam-6838	135	14	as	as	ADP
ejpam-6838	135	15	xs	xs	NOUN
ejpam-6838	135	16	=	=	PUNCT
ejpam-6838	136	1	⌊	⌊	PROPN
ejpam-6838	136	2	s	s	PART
ejpam-6838	136	3	2⌋∑	2⌋∑	PROPN
ejpam-6838	136	4	m=0	m=0	PROPN
ejpam-6838	136	5	(	(	PUNCT
ejpam-6838	136	6	s−	s−	PROPN
ejpam-6838	136	7	2m+	2m+	NUM
ejpam-6838	136	8	3	3	NUM
ejpam-6838	136	9	)	)	PUNCT
ejpam-6838	136	10	⌊	⌊	ADP
ejpam-6838	136	11	s	s	NOUN
ejpam-6838	136	12	2	2	NUM
ejpam-6838	136	13	⌋	⌋	NOUN
ejpam-6838	136	14	!	!	PUNCT
ejpam-6838	137	1	(	(	PUNCT
ejpam-6838	137	2	3	3	NUM
ejpam-6838	137	3	2	2	NUM
ejpam-6838	137	4	)	)	PUNCT
ejpam-6838	137	5	⌊	⌊	VERB
ejpam-6838	137	6	s+1	s+1	NOUN
ejpam-6838	137	7	2	2	NUM
ejpam-6838	137	8	⌋	⌋	NUM
ejpam-6838	137	9	m	m	NOUN
ejpam-6838	137	10	!	!	PUNCT
ejpam-6838	138	1	(	(	PUNCT
ejpam-6838	138	2	3)s−m+1	3)s−m+1	NUM
ejpam-6838	138	3	ns−2m(x	ns−2m(x	NOUN
ejpam-6838	138	4	)	)	PUNCT
ejpam-6838	138	5	.	.	PUNCT
ejpam-6838	139	1	(	(	PUNCT
ejpam-6838	139	2	11	11	NUM
ejpam-6838	139	3	)	)	PUNCT
ejpam-6838	139	4	now	now	ADV
ejpam-6838	139	5	,	,	PUNCT
ejpam-6838	139	6	we	we	PRON
ejpam-6838	139	7	give	give	VERB
ejpam-6838	139	8	the	the	DET
ejpam-6838	139	9	high	high	ADJ
ejpam-6838	139	10	-	-	PUNCT
ejpam-6838	139	11	order	order	NOUN
ejpam-6838	139	12	derivatives	derivative	NOUN
ejpam-6838	139	13	expression	expression	NOUN
ejpam-6838	139	14	for	for	ADP
ejpam-6838	139	15	the	the	DET
ejpam-6838	139	16	polynomials	polynomial	NOUN
ejpam-6838	139	17	g	g	PROPN
ejpam-6838	139	18	(	(	PUNCT
ejpam-6838	139	19	µ,β	µ,β	PROPN
ejpam-6838	139	20	)	)	PUNCT
ejpam-6838	139	21	k	k	PROPN
ejpam-6838	139	22	(	(	PUNCT
ejpam-6838	139	23	x	x	X
ejpam-6838	139	24	)	)	PUNCT
ejpam-6838	139	25	in	in	ADP
ejpam-6838	139	26	terms	term	NOUN
ejpam-6838	139	27	of	of	ADP
ejpam-6838	139	28	their	their	PRON
ejpam-6838	139	29	original	original	ADJ
ejpam-6838	139	30	polynomials	polynomial	NOUN
ejpam-6838	139	31	.	.	PUNCT
ejpam-6838	140	1	theorem	theorem	NOUN
ejpam-6838	140	2	1	1	NUM
ejpam-6838	140	3	.	.	PUNCT
ejpam-6838	141	1	[	[	X
ejpam-6838	141	2	40	40	NUM
ejpam-6838	141	3	]	]	PUNCT
ejpam-6838	141	4	the	the	DET
ejpam-6838	141	5	m	m	PROPN
ejpam-6838	141	6	-	-	PUNCT
ejpam-6838	141	7	th	th	VERB
ejpam-6838	141	8	derivative	derivative	NOUN
ejpam-6838	141	9	:	:	PUNCT
ejpam-6838	141	10	dk	dk	PROPN
ejpam-6838	141	11	ns(x	ns(x	PUNCT
ejpam-6838	141	12	)	)	PUNCT
ejpam-6838	142	1	d	d	X
ejpam-6838	142	2	xk	xk	PROPN
ejpam-6838	142	3	can	can	AUX
ejpam-6838	142	4	be	be	AUX
ejpam-6838	142	5	represented	represent	VERB
ejpam-6838	142	6	as	as	ADP
ejpam-6838	142	7	dmns(x	dmns(x	PROPN
ejpam-6838	142	8	)	)	PUNCT
ejpam-6838	143	1	d	d	NOUN
ejpam-6838	143	2	xm	xm	NOUN
ejpam-6838	143	3	=	=	PUNCT
ejpam-6838	143	4	⌊	⌊	VERB
ejpam-6838	143	5	s−m	s−m	NOUN
ejpam-6838	143	6	2	2	NUM
ejpam-6838	143	7	⌋∑	⌋∑	NOUN
ejpam-6838	144	1	r=0	r=0	PROPN
ejpam-6838	144	2	gm	gm	PROPN
ejpam-6838	144	3	r	r	NOUN
ejpam-6838	144	4	,	,	PUNCT
ejpam-6838	144	5	sns−m−2r(x	sns−m−2r(x	PROPN
ejpam-6838	144	6	)	)	PUNCT
ejpam-6838	144	7	,	,	PUNCT
ejpam-6838	144	8	s	s	VERB
ejpam-6838	144	9	≥	≥	NOUN
ejpam-6838	144	10	m	m	PROPN
ejpam-6838	144	11	,	,	PUNCT
ejpam-6838	144	12	(	(	PUNCT
ejpam-6838	144	13	12	12	NUM
ejpam-6838	144	14	)	)	PUNCT
ejpam-6838	144	15	w.	w.	PROPN
ejpam-6838	144	16	m.	m.	PROPN
ejpam-6838	144	17	abd	abd	PROPN
ejpam-6838	144	18	-	-	PUNCT
ejpam-6838	144	19	elhameed	elhameed	PROPN
ejpam-6838	144	20	et	et	PROPN
ejpam-6838	144	21	al	al	PROPN
ejpam-6838	144	22	.	.	PUNCT
ejpam-6838	144	23	/	/	SYM
ejpam-6838	144	24	eur	eur	PROPN
ejpam-6838	144	25	.	.	PUNCT
ejpam-6838	145	1	j.	j.	PROPN
ejpam-6838	145	2	pure	pure	PROPN
ejpam-6838	145	3	appl	appl	PROPN
ejpam-6838	145	4	.	.	PROPN
ejpam-6838	145	5	math	math	PROPN
ejpam-6838	145	6	,	,	PUNCT
ejpam-6838	145	7	18	18	NUM
ejpam-6838	145	8	(	(	PUNCT
ejpam-6838	145	9	4	4	NUM
ejpam-6838	145	10	)	)	PUNCT
ejpam-6838	145	11	(	(	PUNCT
ejpam-6838	145	12	2025	2025	NUM
ejpam-6838	145	13	)	)	PUNCT
ejpam-6838	145	14	,	,	PUNCT
ejpam-6838	145	15	6838	6838	NUM
ejpam-6838	145	16	7	7	NUM
ejpam-6838	145	17	of	of	ADP
ejpam-6838	145	18	25	25	NUM
ejpam-6838	146	1	where	where	SCONJ
ejpam-6838	146	2	gm	gm	PROPN
ejpam-6838	146	3	r	r	NOUN
ejpam-6838	146	4	,	,	PUNCT
ejpam-6838	146	5	s	s	PART
ejpam-6838	146	6	=	=	SYM
ejpam-6838	146	7	2	2	NUM
ejpam-6838	146	8	m	m	NOUN
ejpam-6838	146	9			PROPN
ejpam-6838	146	10	(	(	PUNCT
ejpam-6838	146	11	1	1	NUM
ejpam-6838	146	12	+	+	CCONJ
ejpam-6838	146	13	s−m)(3	s−m)(3	NOUN
ejpam-6838	146	14	+	+	CCONJ
ejpam-6838	146	15	s−	s−	PROPN
ejpam-6838	146	16	2r	2r	NUM
ejpam-6838	146	17	−m)(s+	−m)(s+	NUM
ejpam-6838	146	18	2	2	NUM
ejpam-6838	146	19	)	)	PUNCT
ejpam-6838	146	20	!	!	PUNCT
ejpam-6838	147	1	(	(	PUNCT
ejpam-6838	147	2	s+	s+	NUM
ejpam-6838	147	3	1)!r!(s−	1)!r!(s−	NUM
ejpam-6838	147	4	r	r	NOUN
ejpam-6838	147	5	−m+	−m+	NOUN
ejpam-6838	147	6	3	3	NUM
ejpam-6838	147	7	)	)	PUNCT
ejpam-6838	147	8	!	!	PUNCT
ejpam-6838	148	1	×	×	NOUN
ejpam-6838	148	2	4f3	4f3	NUM
ejpam-6838	149	1	(	(	PUNCT
ejpam-6838	149	2	−r,−1	−r,−1	ADV
ejpam-6838	149	3	2	2	NUM
ejpam-6838	149	4	−	−	NOUN
ejpam-6838	149	5	s	s	NOUN
ejpam-6838	149	6	2	2	NUM
ejpam-6838	149	7	,	,	PUNCT
ejpam-6838	149	8	1	1	NUM
ejpam-6838	149	9	2	2	NUM
ejpam-6838	149	10	−	−	NOUN
ejpam-6838	149	11	s	s	PART
ejpam-6838	149	12	2	2	NUM
ejpam-6838	149	13	+	+	CCONJ
ejpam-6838	149	14	m	m	PROPN
ejpam-6838	149	15	2	2	NUM
ejpam-6838	149	16	,	,	PUNCT
ejpam-6838	149	17	−3−	−3−	PROPN
ejpam-6838	149	18	s+	s+	ADP
ejpam-6838	149	19	r	r	PROPN
ejpam-6838	149	20	+	+	NOUN
ejpam-6838	149	21	m	m	VERB
ejpam-6838	149	22	−2−	−2−	PROPN
ejpam-6838	149	23	s	s	NOUN
ejpam-6838	149	24	,	,	PUNCT
ejpam-6838	149	25	12	12	NUM
ejpam-6838	149	26	−	−	PROPN
ejpam-6838	149	27	s	s	NOUN
ejpam-6838	149	28	2	2	NUM
ejpam-6838	149	29	,	,	PUNCT
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ejpam-6838	149	31	1	1	NUM
ejpam-6838	149	32	2	2	NUM
ejpam-6838	149	33	−	−	NOUN
ejpam-6838	149	34	s	s	PART
ejpam-6838	149	35	2	2	NUM
ejpam-6838	149	36	+	+	NUM
ejpam-6838	149	37	m	m	PROPN
ejpam-6838	149	38	2	2	NUM
ejpam-6838	149	39	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6838	149	40	1	1	NUM
ejpam-6838	149	41	)	)	PUNCT
ejpam-6838	149	42	,	,	PUNCT
ejpam-6838	149	43	s	s	VERB
ejpam-6838	149	44	even	even	ADV
ejpam-6838	149	45	,	,	PUNCT
ejpam-6838	149	46	m	m	VERB
ejpam-6838	149	47	even	even	ADV
ejpam-6838	149	48	,	,	PUNCT
ejpam-6838	149	49	(	(	PUNCT
ejpam-6838	149	50	−1−	−1−	NOUN
ejpam-6838	149	51	s+m)(−3−	s+m)(−3−	PUNCT
ejpam-6838	149	52	s+	s+	NUM
ejpam-6838	149	53	2r	2r	NUM
ejpam-6838	150	1	+	+	NOUN
ejpam-6838	150	2	m)(s+	m)(s+	NOUN
ejpam-6838	150	3	1	1	NUM
ejpam-6838	150	4	)	)	PUNCT
ejpam-6838	150	5	!	!	PUNCT
ejpam-6838	151	1	r	r	X
ejpam-6838	151	2	!	!	PUNCT
ejpam-6838	152	1	(	(	PUNCT
ejpam-6838	152	2	s−	s−	PROPN
ejpam-6838	152	3	r	r	PROPN
ejpam-6838	152	4	−m+	−m+	NOUN
ejpam-6838	152	5	3	3	NUM
ejpam-6838	152	6	)	)	PUNCT
ejpam-6838	152	7	!	!	PUNCT
ejpam-6838	153	1	×	×	NOUN
ejpam-6838	153	2	4f3	4f3	NUM
ejpam-6838	153	3	(	(	PUNCT
ejpam-6838	153	4	−r,−1−	−r,−1−	X
ejpam-6838	153	5	s	s	NOUN
ejpam-6838	153	6	2	2	NUM
ejpam-6838	153	7	,	,	PUNCT
ejpam-6838	153	8	1	1	NUM
ejpam-6838	153	9	2	2	NUM
ejpam-6838	153	10	−	−	NOUN
ejpam-6838	153	11	s	s	PART
ejpam-6838	153	12	2	2	NUM
ejpam-6838	153	13	+	+	CCONJ
ejpam-6838	153	14	m	m	PROPN
ejpam-6838	153	15	2	2	NUM
ejpam-6838	153	16	,	,	PUNCT
ejpam-6838	153	17	−3−	−3−	PROPN
ejpam-6838	153	18	s+	s+	ADP
ejpam-6838	153	19	r	r	PROPN
ejpam-6838	153	20	+	+	NOUN
ejpam-6838	153	21	m	m	VERB
ejpam-6838	153	22	−2−	−2−	NUM
ejpam-6838	153	23	s,−	s,−	PROPN
ejpam-6838	153	24	s	s	NOUN
ejpam-6838	153	25	2	2	NUM
ejpam-6838	153	26	,	,	PUNCT
ejpam-6838	153	27	−	−	PROPN
ejpam-6838	153	28	1	1	NUM
ejpam-6838	153	29	2	2	NUM
ejpam-6838	153	30	−	−	NOUN
ejpam-6838	153	31	s	s	PART
ejpam-6838	153	32	2	2	NUM
ejpam-6838	153	33	+	+	NUM
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ejpam-6838	153	35	2	2	NUM
ejpam-6838	153	36	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6838	153	37	1	1	NUM
ejpam-6838	153	38	)	)	PUNCT
ejpam-6838	153	39	,	,	PUNCT
ejpam-6838	153	40	s	s	VERB
ejpam-6838	153	41	odd	odd	ADJ
ejpam-6838	153	42	,	,	PUNCT
ejpam-6838	153	43	m	m	VERB
ejpam-6838	153	44	odd	odd	ADJ
ejpam-6838	153	45	,	,	PUNCT
ejpam-6838	153	46	(	(	PUNCT
ejpam-6838	153	47	−2−	−2−	PROPN
ejpam-6838	153	48	s+m)(−3−	s+m)(−3−	PROPN
ejpam-6838	153	49	s+	s+	NUM
ejpam-6838	153	50	2r	2r	NUM
ejpam-6838	154	1	+	+	NOUN
ejpam-6838	154	2	m)(s+	m)(s+	NOUN
ejpam-6838	154	3	1	1	NUM
ejpam-6838	154	4	)	)	PUNCT
ejpam-6838	154	5	!	!	PUNCT
ejpam-6838	155	1	r	r	X
ejpam-6838	155	2	!	!	PUNCT
ejpam-6838	156	1	(	(	PUNCT
ejpam-6838	156	2	s−	s−	PROPN
ejpam-6838	156	3	r	r	PROPN
ejpam-6838	156	4	−m+	−m+	NOUN
ejpam-6838	156	5	3	3	NUM
ejpam-6838	156	6	)	)	PUNCT
ejpam-6838	156	7	!	!	PUNCT
ejpam-6838	157	1	×	×	NOUN
ejpam-6838	157	2	4f3	4f3	NUM
ejpam-6838	157	3	(	(	PUNCT
ejpam-6838	157	4	−r,−1−	−r,−1−	X
ejpam-6838	157	5	s	s	NOUN
ejpam-6838	157	6	2	2	NUM
ejpam-6838	157	7	,	,	PUNCT
ejpam-6838	157	8	−	−	PROPN
ejpam-6838	157	9	s	s	PART
ejpam-6838	157	10	2	2	NUM
ejpam-6838	157	11	+	+	CCONJ
ejpam-6838	157	12	m	m	PROPN
ejpam-6838	157	13	2	2	NUM
ejpam-6838	157	14	,	,	PUNCT
ejpam-6838	157	15	−3−	−3−	PROPN
ejpam-6838	157	16	s+	s+	ADP
ejpam-6838	157	17	r	r	PROPN
ejpam-6838	157	18	+	+	NOUN
ejpam-6838	157	19	m	m	VERB
ejpam-6838	157	20	−2−	−2−	NUM
ejpam-6838	157	21	s,−	s,−	PROPN
ejpam-6838	157	22	s	s	NOUN
ejpam-6838	157	23	2	2	NUM
ejpam-6838	157	24	,	,	PUNCT
ejpam-6838	157	25	−1−	−1−	PROPN
ejpam-6838	157	26	s	s	PART
ejpam-6838	157	27	2	2	NUM
ejpam-6838	157	28	+	+	CCONJ
ejpam-6838	157	29	m	m	PROPN
ejpam-6838	157	30	2	2	NUM
ejpam-6838	157	31	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6838	157	32	1	1	NUM
ejpam-6838	157	33	)	)	PUNCT
ejpam-6838	157	34	,	,	PUNCT
ejpam-6838	157	35	s	s	VERB
ejpam-6838	157	36	odd	odd	ADJ
ejpam-6838	157	37	,	,	PUNCT
ejpam-6838	157	38	m	m	VERB
ejpam-6838	157	39	even	even	ADV
ejpam-6838	157	40	,	,	PUNCT
ejpam-6838	157	41	(	(	PUNCT
ejpam-6838	157	42	2	2	NUM
ejpam-6838	157	43	+	+	NOUN
ejpam-6838	157	44	s−m)(3	s−m)(3	NOUN
ejpam-6838	157	45	+	+	CCONJ
ejpam-6838	157	46	s−	s−	PROPN
ejpam-6838	157	47	2r	2r	NUM
ejpam-6838	157	48	−m)(s+	−m)(s+	NUM
ejpam-6838	157	49	2	2	NUM
ejpam-6838	157	50	)	)	PUNCT
ejpam-6838	157	51	!	!	PUNCT
ejpam-6838	158	1	(	(	PUNCT
ejpam-6838	158	2	1	1	NUM
ejpam-6838	158	3	+	+	NUM
ejpam-6838	158	4	s	s	X
ejpam-6838	158	5	)	)	PUNCT
ejpam-6838	158	6	r	r	NOUN
ejpam-6838	158	7	!	!	PUNCT
ejpam-6838	159	1	(	(	PUNCT
ejpam-6838	159	2	s−	s−	PROPN
ejpam-6838	159	3	r	r	PROPN
ejpam-6838	159	4	−m+	−m+	NOUN
ejpam-6838	159	5	3	3	NUM
ejpam-6838	159	6	)	)	PUNCT
ejpam-6838	159	7	!	!	PUNCT
ejpam-6838	160	1	×	×	NOUN
ejpam-6838	160	2	4f3	4f3	NUM
ejpam-6838	161	1	(	(	PUNCT
ejpam-6838	161	2	−r,−1	−r,−1	ADV
ejpam-6838	161	3	2	2	NUM
ejpam-6838	161	4	−	−	NOUN
ejpam-6838	161	5	s	s	NOUN
ejpam-6838	161	6	2	2	NUM
ejpam-6838	161	7	,	,	PUNCT
ejpam-6838	161	8	−	−	PROPN
ejpam-6838	161	9	s	s	PART
ejpam-6838	161	10	2	2	NUM
ejpam-6838	161	11	+	+	CCONJ
ejpam-6838	161	12	m	m	PROPN
ejpam-6838	161	13	2	2	NUM
ejpam-6838	161	14	,	,	PUNCT
ejpam-6838	161	15	−3−	−3−	PROPN
ejpam-6838	161	16	s+	s+	ADP
ejpam-6838	161	17	r	r	PROPN
ejpam-6838	161	18	+	+	NOUN
ejpam-6838	161	19	m	m	VERB
ejpam-6838	161	20	−2−	−2−	PROPN
ejpam-6838	161	21	s	s	NOUN
ejpam-6838	161	22	,	,	PUNCT
ejpam-6838	161	23	12	12	NUM
ejpam-6838	161	24	−	−	PROPN
ejpam-6838	161	25	s	s	NOUN
ejpam-6838	161	26	2	2	NUM
ejpam-6838	161	27	,	,	PUNCT
ejpam-6838	161	28	−1−	−1−	PROPN
ejpam-6838	161	29	s	s	PART
ejpam-6838	161	30	2	2	NUM
ejpam-6838	161	31	+	+	CCONJ
ejpam-6838	161	32	m	m	PROPN
ejpam-6838	161	33	2	2	NUM
ejpam-6838	161	34	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6838	161	35	1	1	NUM
ejpam-6838	161	36	)	)	PUNCT
ejpam-6838	161	37	,	,	PUNCT
ejpam-6838	161	38	s	s	VERB
ejpam-6838	161	39	even	even	ADV
ejpam-6838	161	40	,	,	PUNCT
ejpam-6838	161	41	m	m	VERB
ejpam-6838	161	42	odd	odd	ADJ
ejpam-6838	161	43	.	.	PUNCT
ejpam-6838	162	1	(	(	PUNCT
ejpam-6838	162	2	13	13	NUM
ejpam-6838	162	3	)	)	PUNCT
ejpam-6838	162	4	2.4	2.4	NUM
ejpam-6838	162	5	.	.	PUNCT
ejpam-6838	163	1	the	the	DET
ejpam-6838	163	2	shifted	shift	VERB
ejpam-6838	163	3	cps	cp	NOUN
ejpam-6838	163	4	now	now	ADV
ejpam-6838	163	5	,	,	PUNCT
ejpam-6838	163	6	we	we	PRON
ejpam-6838	163	7	introduce	introduce	VERB
ejpam-6838	163	8	the	the	DET
ejpam-6838	163	9	corresponding	corresponding	ADJ
ejpam-6838	163	10	shifted	shift	VERB
ejpam-6838	163	11	polynomials	polynomial	NOUN
ejpam-6838	163	12	on	on	ADP
ejpam-6838	163	13	[	[	X
ejpam-6838	163	14	0	0	NUM
ejpam-6838	163	15	,	,	PUNCT
ejpam-6838	163	16	1	1	NUM
ejpam-6838	163	17	]	]	PUNCT
ejpam-6838	163	18	to	to	ADP
ejpam-6838	163	19	the	the	DET
ejpam-6838	163	20	polynomials	polynomial	NOUN
ejpam-6838	163	21	nk(x	nk(x	PUNCT
ejpam-6838	163	22	)	)	PUNCT
ejpam-6838	163	23	.	.	PUNCT
ejpam-6838	164	1	we	we	PRON
ejpam-6838	164	2	denote	denote	VERB
ejpam-6838	164	3	them	they	PRON
ejpam-6838	164	4	by	by	ADP
ejpam-6838	164	5	h∗	h∗	PROPN
ejpam-6838	164	6	k(x	k(x	PROPN
ejpam-6838	164	7	)	)	PUNCT
ejpam-6838	164	8	and	and	CCONJ
ejpam-6838	164	9	define	define	VERB
ejpam-6838	164	10	them	they	PRON
ejpam-6838	164	11	as	as	ADP
ejpam-6838	164	12	h∗	h∗	PROPN
ejpam-6838	164	13	k(x	k(x	PROPN
ejpam-6838	164	14	)	)	PUNCT
ejpam-6838	165	1	=	=	PUNCT
ejpam-6838	165	2	nk(2x−	nk(2x−	NOUN
ejpam-6838	165	3	1	1	NUM
ejpam-6838	165	4	)	)	PUNCT
ejpam-6838	165	5	.	.	PUNCT
ejpam-6838	166	1	(	(	PUNCT
ejpam-6838	166	2	14	14	NUM
ejpam-6838	166	3	)	)	PUNCT
ejpam-6838	166	4	all	all	DET
ejpam-6838	166	5	the	the	DET
ejpam-6838	166	6	formulas	formula	NOUN
ejpam-6838	166	7	of	of	ADP
ejpam-6838	166	8	the	the	DET
ejpam-6838	166	9	polynomials	polynomial	NOUN
ejpam-6838	166	10	nk(x	nk(x	PUNCT
ejpam-6838	166	11	)	)	PUNCT
ejpam-6838	166	12	can	can	AUX
ejpam-6838	166	13	be	be	AUX
ejpam-6838	166	14	transformed	transform	VERB
ejpam-6838	166	15	to	to	PART
ejpam-6838	166	16	give	give	VERB
ejpam-6838	166	17	their	their	PRON
ejpam-6838	166	18	counterparts	counterpart	NOUN
ejpam-6838	166	19	on	on	ADP
ejpam-6838	166	20	[	[	X
ejpam-6838	166	21	0	0	NUM
ejpam-6838	166	22	,	,	PUNCT
ejpam-6838	166	23	1	1	NUM
ejpam-6838	166	24	]	]	PUNCT
ejpam-6838	166	25	.	.	PUNCT
ejpam-6838	167	1	from	from	ADP
ejpam-6838	167	2	(	(	PUNCT
ejpam-6838	167	3	8)	8)	NUM
ejpam-6838	167	4	,	,	PUNCT
ejpam-6838	167	5	the	the	DET
ejpam-6838	167	6	set	set	NOUN
ejpam-6838	167	7	{	{	PUNCT
ejpam-6838	167	8	h∗	h∗	PROPN
ejpam-6838	167	9	k(x)}k≥0	k(x)}k≥0	PROPN
ejpam-6838	167	10	is	be	AUX
ejpam-6838	167	11	an	an	DET
ejpam-6838	167	12	orthogonal	orthogonal	ADJ
ejpam-6838	167	13	set	set	NOUN
ejpam-6838	167	14	on	on	ADP
ejpam-6838	167	15	[	[	X
ejpam-6838	167	16	0	0	NUM
ejpam-6838	167	17	,	,	PUNCT
ejpam-6838	167	18	1	1	NUM
ejpam-6838	167	19	]	]	PUNCT
ejpam-6838	167	20	with∫	with∫	NOUN
ejpam-6838	167	21	1	1	NUM
ejpam-6838	167	22	0	0	NUM
ejpam-6838	167	23	h∗	h∗	NOUN
ejpam-6838	167	24	n(x)h∗	n(x)h∗	PROPN
ejpam-6838	167	25	m(x)w∗(x	m(x)w∗(x	PROPN
ejpam-6838	167	26	)	)	PUNCT
ejpam-6838	167	27	dx	dx	PROPN
ejpam-6838	168	1	=	=	SYM
ejpam-6838	168	2	1	1	NUM
ejpam-6838	168	3	16	16	NUM
ejpam-6838	168	4	hn	hn	PROPN
ejpam-6838	168	5	,	,	PUNCT
ejpam-6838	168	6	(	(	PUNCT
ejpam-6838	168	7	15	15	NUM
ejpam-6838	168	8	)	)	PUNCT
ejpam-6838	168	9	with	with	ADP
ejpam-6838	168	10	w∗(x	w∗(x	NOUN
ejpam-6838	168	11	)	)	PUNCT
ejpam-6838	168	12	=	=	SYM
ejpam-6838	168	13	(	(	PUNCT
ejpam-6838	168	14	1−	1−	NUM
ejpam-6838	168	15	2x)2(x(1−	2x)2(x(1−	NUM
ejpam-6838	168	16	x))3/2	x))3/2	PROPN
ejpam-6838	168	17	,	,	PUNCT
ejpam-6838	168	18	and	and	CCONJ
ejpam-6838	168	19	hn	hn	PROPN
ejpam-6838	168	20	is	be	AUX
ejpam-6838	168	21	defined	define	VERB
ejpam-6838	168	22	in	in	ADP
ejpam-6838	168	23	(	(	PUNCT
ejpam-6838	168	24	9	9	NUM
ejpam-6838	168	25	)	)	PUNCT
ejpam-6838	168	26	.	.	PUNCT
ejpam-6838	169	1	theorem	theorem	NOUN
ejpam-6838	169	2	2	2	NUM
ejpam-6838	169	3	.	.	PUNCT
ejpam-6838	170	1	the	the	DET
ejpam-6838	170	2	mth	mth	NOUN
ejpam-6838	170	3	-	-	PUNCT
ejpam-6838	170	4	derivative	derivative	NOUN
ejpam-6838	170	5	of	of	ADP
ejpam-6838	170	6	h∗	h∗	PROPN
ejpam-6838	170	7	j	j	PROPN
ejpam-6838	170	8	(	(	PUNCT
ejpam-6838	170	9	x	x	X
ejpam-6838	170	10	)	)	PUNCT
ejpam-6838	170	11	can	can	AUX
ejpam-6838	170	12	be	be	AUX
ejpam-6838	170	13	expressed	express	VERB
ejpam-6838	170	14	as	as	ADP
ejpam-6838	170	15	dmh∗	dmh∗	ADJ
ejpam-6838	170	16	s(x	s(x	NOUN
ejpam-6838	170	17	)	)	PUNCT
ejpam-6838	171	1	d	d	X
ejpam-6838	171	2	xm	xm	NOUN
ejpam-6838	172	1	=	=	PUNCT
ejpam-6838	173	1	⌊	⌊	VERB
ejpam-6838	173	2	s−m	s−m	NOUN
ejpam-6838	173	3	2	2	NUM
ejpam-6838	173	4	⌋∑	⌋∑	NOUN
ejpam-6838	173	5	r=0	r=0	ADP
ejpam-6838	173	6	b̃m	b̃m	ADV
ejpam-6838	173	7	r	r	NOUN
ejpam-6838	173	8	,	,	PUNCT
ejpam-6838	173	9	sh∗	sh∗	NOUN
ejpam-6838	173	10	s−m−2r(x	s−m−2r(x	PROPN
ejpam-6838	173	11	)	)	PUNCT
ejpam-6838	173	12	,	,	PUNCT
ejpam-6838	173	13	s	s	VERB
ejpam-6838	173	14	≥	≥	NOUN
ejpam-6838	173	15	m	m	PROPN
ejpam-6838	173	16	,	,	PUNCT
ejpam-6838	173	17	(	(	PUNCT
ejpam-6838	173	18	16	16	X
ejpam-6838	173	19	)	)	PUNCT
ejpam-6838	173	20	w.	w.	PROPN
ejpam-6838	173	21	m.	m.	PROPN
ejpam-6838	173	22	abd	abd	PROPN
ejpam-6838	173	23	-	-	PUNCT
ejpam-6838	173	24	elhameed	elhameed	PROPN
ejpam-6838	173	25	et	et	PROPN
ejpam-6838	173	26	al	al	PROPN
ejpam-6838	173	27	.	.	PUNCT
ejpam-6838	173	28	/	/	SYM
ejpam-6838	173	29	eur	eur	PROPN
ejpam-6838	173	30	.	.	PUNCT
ejpam-6838	174	1	j.	j.	PROPN
ejpam-6838	174	2	pure	pure	PROPN
ejpam-6838	174	3	appl	appl	PROPN
ejpam-6838	174	4	.	.	PROPN
ejpam-6838	174	5	math	math	PROPN
ejpam-6838	174	6	,	,	PUNCT
ejpam-6838	174	7	18	18	NUM
ejpam-6838	174	8	(	(	PUNCT
ejpam-6838	174	9	4	4	NUM
ejpam-6838	174	10	)	)	PUNCT
ejpam-6838	174	11	(	(	PUNCT
ejpam-6838	174	12	2025	2025	NUM
ejpam-6838	174	13	)	)	PUNCT
ejpam-6838	174	14	,	,	PUNCT
ejpam-6838	174	15	6838	6838	NUM
ejpam-6838	174	16	8	8	NUM
ejpam-6838	174	17	of	of	ADP
ejpam-6838	174	18	25	25	NUM
ejpam-6838	174	19	with	with	ADP
ejpam-6838	174	20	b̃k	b̃k	PROPN
ejpam-6838	174	21	r	r	PROPN
ejpam-6838	174	22	,	,	PUNCT
ejpam-6838	174	23	j	j	NOUN
ejpam-6838	174	24	=	=	SYM
ejpam-6838	174	25	2k	2k	PROPN
ejpam-6838	174	26	gk	gk	PROPN
ejpam-6838	174	27	r	r	PROPN
ejpam-6838	174	28	,	,	PUNCT
ejpam-6838	174	29	j	j	PROPN
ejpam-6838	174	30	,	,	PUNCT
ejpam-6838	174	31	where	where	SCONJ
ejpam-6838	174	32	gk	gk	PROPN
ejpam-6838	174	33	r	r	PROPN
ejpam-6838	174	34	,	,	PUNCT
ejpam-6838	174	35	j	j	PROPN
ejpam-6838	174	36	is	be	AUX
ejpam-6838	174	37	given	give	VERB
ejpam-6838	174	38	in	in	ADP
ejpam-6838	174	39	(	(	PUNCT
ejpam-6838	174	40	13	13	NUM
ejpam-6838	174	41	)	)	PUNCT
ejpam-6838	174	42	.	.	PUNCT
ejpam-6838	175	1	proof	proof	NOUN
ejpam-6838	175	2	.	.	PUNCT
ejpam-6838	176	1	replacing	replace	VERB
ejpam-6838	176	2	x	x	SYM
ejpam-6838	176	3	by	by	ADP
ejpam-6838	176	4	(	(	PUNCT
ejpam-6838	176	5	2x−	2x−	PROPN
ejpam-6838	176	6	1	1	NUM
ejpam-6838	176	7	)	)	PUNCT
ejpam-6838	176	8	in	in	ADP
ejpam-6838	176	9	theorem	theorem	NOUN
ejpam-6838	176	10	1	1	NUM
ejpam-6838	176	11	,	,	PUNCT
ejpam-6838	176	12	we	we	PRON
ejpam-6838	176	13	get	get	VERB
ejpam-6838	176	14	the	the	DET
ejpam-6838	176	15	result	result	NOUN
ejpam-6838	176	16	in	in	ADP
ejpam-6838	176	17	(	(	PUNCT
ejpam-6838	176	18	16	16	NUM
ejpam-6838	176	19	)	)	PUNCT
ejpam-6838	176	20	.	.	PUNCT
ejpam-6838	177	1	3	3	X
ejpam-6838	177	2	.	.	X
ejpam-6838	177	3	tau	tau	PROPN
ejpam-6838	177	4	procedure	procedure	NOUN
ejpam-6838	177	5	for	for	ADP
ejpam-6838	177	6	the	the	DET
ejpam-6838	177	7	tfde	tfde	NOUN
ejpam-6838	177	8	consider	consider	VERB
ejpam-6838	177	9	the	the	DET
ejpam-6838	177	10	following	follow	VERB
ejpam-6838	177	11	tfde	tfde	NOUN
ejpam-6838	177	12	[	[	X
ejpam-6838	177	13	20	20	NUM
ejpam-6838	177	14	,	,	PUNCT
ejpam-6838	177	15	61	61	NUM
ejpam-6838	177	16	]	]	PUNCT
ejpam-6838	177	17	:	:	PUNCT
ejpam-6838	177	18	dζ	dζ	PROPN
ejpam-6838	177	19	t	t	PROPN
ejpam-6838	177	20	λ(x	λ(x	PROPN
ejpam-6838	177	21	,	,	PUNCT
ejpam-6838	177	22	t)−	t)−	PROPN
ejpam-6838	177	23	β	β	X
ejpam-6838	177	24	λxx(x	λxx(x	PROPN
ejpam-6838	177	25	,	,	PUNCT
ejpam-6838	177	26	t	t	PROPN
ejpam-6838	177	27	)	)	PUNCT
ejpam-6838	177	28	=	=	SYM
ejpam-6838	178	1	g(x	g(x	PROPN
ejpam-6838	178	2	,	,	PUNCT
ejpam-6838	178	3	t	t	PROPN
ejpam-6838	178	4	)	)	PUNCT
ejpam-6838	178	5	,	,	PUNCT
ejpam-6838	178	6	0	0	PUNCT
ejpam-6838	178	7	<	<	X
ejpam-6838	178	8	ζ	ζ	X
ejpam-6838	178	9	≤	≤	NUM
ejpam-6838	178	10	1	1	NUM
ejpam-6838	178	11	,	,	PUNCT
ejpam-6838	178	12	(	(	PUNCT
ejpam-6838	178	13	17	17	NUM
ejpam-6838	178	14	)	)	PUNCT
ejpam-6838	178	15	governed	govern	VERB
ejpam-6838	178	16	by	by	ADP
ejpam-6838	178	17	the	the	DET
ejpam-6838	178	18	following	following	ADJ
ejpam-6838	178	19	conditions	condition	NOUN
ejpam-6838	178	20	:	:	PUNCT
ejpam-6838	178	21	λ(x	λ(x	ADJ
ejpam-6838	178	22	,	,	PUNCT
ejpam-6838	178	23	0	0	NUM
ejpam-6838	178	24	)	)	PUNCT
ejpam-6838	178	25	=	=	SYM
ejpam-6838	178	26	ρ1(x	ρ1(x	NUM
ejpam-6838	178	27	)	)	PUNCT
ejpam-6838	178	28	,	,	PUNCT
ejpam-6838	178	29	0	0	PUNCT
ejpam-6838	178	30	<	<	X
ejpam-6838	178	31	x	x	X
ejpam-6838	178	32	<	<	X
ejpam-6838	178	33	1	1	NUM
ejpam-6838	178	34	,	,	PUNCT
ejpam-6838	178	35	(	(	PUNCT
ejpam-6838	178	36	18	18	NUM
ejpam-6838	178	37	)	)	PUNCT
ejpam-6838	178	38	λ(0	λ(0	PROPN
ejpam-6838	178	39	,	,	PUNCT
ejpam-6838	178	40	t	t	PROPN
ejpam-6838	178	41	)	)	PUNCT
ejpam-6838	178	42	=	=	SYM
ejpam-6838	178	43	ρ2(t	ρ2(t	NUM
ejpam-6838	178	44	)	)	PUNCT
ejpam-6838	178	45	,	,	PUNCT
ejpam-6838	178	46	λ(1	λ(1	PROPN
ejpam-6838	178	47	,	,	PUNCT
ejpam-6838	178	48	t	t	PROPN
ejpam-6838	178	49	)	)	PUNCT
ejpam-6838	178	50	=	=	SYM
ejpam-6838	178	51	ρ3(t	ρ3(t	NOUN
ejpam-6838	178	52	)	)	PUNCT
ejpam-6838	178	53	,	,	PUNCT
ejpam-6838	178	54	0	0	NUM
ejpam-6838	178	55	<	<	X
ejpam-6838	178	56	t	t	X
ejpam-6838	178	57	<	<	X
ejpam-6838	178	58	τ	τ	X
ejpam-6838	178	59	,	,	PUNCT
ejpam-6838	178	60	(	(	PUNCT
ejpam-6838	178	61	19	19	NUM
ejpam-6838	178	62	)	)	PUNCT
ejpam-6838	178	63	where	where	SCONJ
ejpam-6838	178	64	β	β	PROPN
ejpam-6838	178	65	is	be	AUX
ejpam-6838	178	66	a	a	DET
ejpam-6838	178	67	positive	positive	ADJ
ejpam-6838	178	68	constant	constant	ADJ
ejpam-6838	178	69	,	,	PUNCT
ejpam-6838	178	70	ρ1(x	ρ1(x	NUM
ejpam-6838	178	71	)	)	PUNCT
ejpam-6838	178	72	,	,	PUNCT
ejpam-6838	178	73	ρ2(t	ρ2(t	NUM
ejpam-6838	178	74	)	)	PUNCT
ejpam-6838	178	75	,	,	PUNCT
ejpam-6838	178	76	and	and	CCONJ
ejpam-6838	178	77	ρ3(t	ρ3(t	X
ejpam-6838	178	78	)	)	PUNCT
ejpam-6838	178	79	are	be	AUX
ejpam-6838	178	80	known	know	VERB
ejpam-6838	178	81	continuous	continuous	ADJ
ejpam-6838	178	82	functions	function	NOUN
ejpam-6838	178	83	,	,	PUNCT
ejpam-6838	178	84	and	and	CCONJ
ejpam-6838	178	85	g(x	g(x	NOUN
ejpam-6838	178	86	,	,	PUNCT
ejpam-6838	178	87	t	t	PROPN
ejpam-6838	178	88	)	)	PUNCT
ejpam-6838	178	89	is	be	AUX
ejpam-6838	178	90	the	the	DET
ejpam-6838	178	91	source	source	NOUN
ejpam-6838	178	92	term	term	NOUN
ejpam-6838	178	93	.	.	PUNCT
ejpam-6838	179	1	if	if	SCONJ
ejpam-6838	179	2	we	we	PRON
ejpam-6838	179	3	let	let	VERB
ejpam-6838	179	4	pm	pm	VERB
ejpam-6838	179	5	=	=	PUNCT
ejpam-6838	179	6	span{h∗	span{h∗	PUNCT
ejpam-6838	179	7	i	i	PRON
ejpam-6838	179	8	(	(	PUNCT
ejpam-6838	179	9	x)h∗	x)h∗	PROPN
ejpam-6838	179	10	j	j	PROPN
ejpam-6838	179	11	(	(	PUNCT
ejpam-6838	179	12	t	t	PROPN
ejpam-6838	179	13	)	)	PUNCT
ejpam-6838	179	14	:	:	PUNCT
ejpam-6838	180	1	0	0	NUM
ejpam-6838	180	2	≤	≤	X
ejpam-6838	180	3	i	i	PRON
ejpam-6838	180	4	,	,	PUNCT
ejpam-6838	180	5	j	j	PROPN
ejpam-6838	180	6	≤	≤	PROPN
ejpam-6838	180	7	m	m	ADP
ejpam-6838	180	8	}	}	PUNCT
ejpam-6838	180	9	,	,	PUNCT
ejpam-6838	180	10	then	then	ADV
ejpam-6838	180	11	;	;	PUNCT
ejpam-6838	180	12	any	any	DET
ejpam-6838	180	13	function	function	NOUN
ejpam-6838	180	14	λm(x	λm(x	SYM
ejpam-6838	180	15	,	,	PUNCT
ejpam-6838	180	16	t	t	PROPN
ejpam-6838	180	17	)	)	PUNCT
ejpam-6838	180	18	∈	∈	PROPN
ejpam-6838	180	19	pm	pm	NOUN
ejpam-6838	180	20	can	can	AUX
ejpam-6838	180	21	be	be	AUX
ejpam-6838	180	22	represented	represent	VERB
ejpam-6838	180	23	as	as	ADP
ejpam-6838	180	24	λm(x	λm(x	X
ejpam-6838	180	25	,	,	PUNCT
ejpam-6838	180	26	t	t	PROPN
ejpam-6838	180	27	)	)	PUNCT
ejpam-6838	180	28	=	=	PUNCT
ejpam-6838	181	1	m∑	m∑	CCONJ
ejpam-6838	181	2	i=0	i=0	PROPN
ejpam-6838	181	3	m∑	m∑	CCONJ
ejpam-6838	181	4	j=0	j=0	PROPN
ejpam-6838	181	5	cij	cij	PROPN
ejpam-6838	181	6	h∗	h∗	PROPN
ejpam-6838	181	7	i	i	PRON
ejpam-6838	181	8	(	(	PUNCT
ejpam-6838	181	9	x)h∗	x)h∗	PROPN
ejpam-6838	181	10	j	j	PROPN
ejpam-6838	181	11	(	(	PUNCT
ejpam-6838	181	12	t	t	PROPN
ejpam-6838	181	13	)	)	PUNCT
ejpam-6838	181	14	=	=	NOUN
ejpam-6838	181	15	h∗(x)ch∗(t)t	h∗(x)ch∗(t)t	NOUN
ejpam-6838	181	16	,	,	PUNCT
ejpam-6838	181	17	(	(	PUNCT
ejpam-6838	181	18	20	20	NUM
ejpam-6838	181	19	)	)	PUNCT
ejpam-6838	181	20	where	where	SCONJ
ejpam-6838	181	21	h∗(t)t	h∗(t)t	NOUN
ejpam-6838	181	22	=	=	PUNCT
ejpam-6838	182	1	[	[	X
ejpam-6838	182	2	h∗	h∗	NOUN
ejpam-6838	182	3	0(t),h∗	0(t),h∗	NUM
ejpam-6838	182	4	1(t	1(t	NUM
ejpam-6838	182	5	)	)	PUNCT
ejpam-6838	182	6	,	,	PUNCT
ejpam-6838	182	7	.	.	PUNCT
ejpam-6838	182	8	.	.	PUNCT
ejpam-6838	182	9	.	.	PUNCT
ejpam-6838	183	1	,	,	PUNCT
ejpam-6838	183	2	h∗	h∗	PROPN
ejpam-6838	183	3	m(t)]t	m(t)]t	X
ejpam-6838	183	4	,	,	PUNCT
ejpam-6838	183	5	and	and	CCONJ
ejpam-6838	183	6	c	c	X
ejpam-6838	183	7	=	=	SYM
ejpam-6838	183	8	(	(	PUNCT
ejpam-6838	183	9	cij)0≤i	cij)0≤i	PROPN
ejpam-6838	183	10	,	,	PUNCT
ejpam-6838	183	11	j≤m	j≤m	PROPN
ejpam-6838	183	12	is	be	AUX
ejpam-6838	183	13	the	the	DET
ejpam-6838	183	14	(	(	PUNCT
ejpam-6838	183	15	m	m	PROPN
ejpam-6838	183	16	+	+	PROPN
ejpam-6838	183	17	1)2dimensional	1)2dimensional	ADJ
ejpam-6838	183	18	matrix	matrix	NOUN
ejpam-6838	183	19	of	of	ADP
ejpam-6838	183	20	unknowns	unknown	NOUN
ejpam-6838	183	21	.	.	PUNCT
ejpam-6838	184	1	the	the	DET
ejpam-6838	184	2	residual	residual	ADJ
ejpam-6838	184	3	rm(x	rm(x	NOUN
ejpam-6838	184	4	,	,	PUNCT
ejpam-6838	184	5	t	t	PROPN
ejpam-6838	184	6	)	)	PUNCT
ejpam-6838	184	7	of	of	ADP
ejpam-6838	184	8	eq	eq	NOUN
ejpam-6838	184	9	(	(	PUNCT
ejpam-6838	184	10	17	17	NUM
ejpam-6838	184	11	)	)	PUNCT
ejpam-6838	184	12	is	be	AUX
ejpam-6838	184	13	given	give	VERB
ejpam-6838	184	14	by	by	ADP
ejpam-6838	184	15	rm(x	rm(x	NOUN
ejpam-6838	184	16	,	,	PUNCT
ejpam-6838	184	17	t	t	PROPN
ejpam-6838	184	18	)	)	PUNCT
ejpam-6838	184	19	=	=	PUNCT
ejpam-6838	184	20	dζ	dζ	PROPN
ejpam-6838	184	21	t	t	PROPN
ejpam-6838	184	22	λ	λ	PROPN
ejpam-6838	184	23	m(x	m(x	PROPN
ejpam-6838	184	24	,	,	PUNCT
ejpam-6838	184	25	t)−	t)−	PROPN
ejpam-6838	184	26	β	β	NOUN
ejpam-6838	184	27	λmxx(x	λmxx(x	PROPN
ejpam-6838	184	28	,	,	PUNCT
ejpam-6838	184	29	t)−	t)−	PROPN
ejpam-6838	184	30	g(x	g(x	PROPN
ejpam-6838	184	31	,	,	PUNCT
ejpam-6838	184	32	t	t	PROPN
ejpam-6838	184	33	)	)	PUNCT
ejpam-6838	184	34	.	.	PUNCT
ejpam-6838	185	1	(	(	PUNCT
ejpam-6838	185	2	21	21	NUM
ejpam-6838	185	3	)	)	PUNCT
ejpam-6838	185	4	if	if	SCONJ
ejpam-6838	185	5	we	we	PRON
ejpam-6838	185	6	apply	apply	VERB
ejpam-6838	185	7	the	the	DET
ejpam-6838	185	8	tau	tau	PROPN
ejpam-6838	185	9	method	method	NOUN
ejpam-6838	185	10	,	,	PUNCT
ejpam-6838	185	11	then	then	ADV
ejpam-6838	185	12	we	we	PRON
ejpam-6838	185	13	get∫	get∫	VERB
ejpam-6838	185	14	1	1	NUM
ejpam-6838	185	15	0	0	NUM
ejpam-6838	185	16	∫	∫	PROPN
ejpam-6838	185	17	1	1	NUM
ejpam-6838	185	18	0	0	NUM
ejpam-6838	185	19	rm(x	rm(x	NOUN
ejpam-6838	185	20	,	,	PUNCT
ejpam-6838	185	21	t)h∗	t)h∗	INTJ
ejpam-6838	185	22	r(x)h∗	r(x)h∗	PROPN
ejpam-6838	185	23	s(t))w	s(t))w	VERB
ejpam-6838	185	24	∗(x)w∗(t	∗(x)w∗(t	NOUN
ejpam-6838	185	25	)	)	PUNCT
ejpam-6838	186	1	dx	dx	PROPN
ejpam-6838	186	2	dt	dt	NOUN
ejpam-6838	187	1	=	=	SYM
ejpam-6838	187	2	0	0	NUM
ejpam-6838	187	3	,	,	PUNCT
ejpam-6838	187	4	1	1	NUM
ejpam-6838	187	5	≤	≤	NOUN
ejpam-6838	187	6	r	r	NOUN
ejpam-6838	187	7	≤	≤	NUM
ejpam-6838	187	8	m−	m−	PROPN
ejpam-6838	187	9	1	1	NUM
ejpam-6838	187	10	,	,	PUNCT
ejpam-6838	187	11	1	1	NUM
ejpam-6838	187	12	≤	≤	NOUN
ejpam-6838	187	13	s	s	PART
ejpam-6838	187	14	≤	≤	NOUN
ejpam-6838	187	15	m.	m.	NOUN
ejpam-6838	187	16	(	(	PUNCT
ejpam-6838	187	17	22	22	NUM
ejpam-6838	187	18	)	)	PUNCT
ejpam-6838	187	19	now	now	ADV
ejpam-6838	187	20	,	,	PUNCT
ejpam-6838	187	21	consider	consider	VERB
ejpam-6838	187	22	the	the	DET
ejpam-6838	187	23	following	follow	VERB
ejpam-6838	187	24	matrices	matrix	NOUN
ejpam-6838	187	25	:	:	PUNCT
ejpam-6838	187	26	g	g	NOUN
ejpam-6838	187	27	=	=	SYM
ejpam-6838	187	28	(	(	PUNCT
ejpam-6838	187	29	gr	gr	PROPN
ejpam-6838	187	30	,	,	PUNCT
ejpam-6838	187	31	s)(m−1)×m	s)(m−1)×m	PROPN
ejpam-6838	187	32	,	,	PUNCT
ejpam-6838	187	33	gr	gr	PROPN
ejpam-6838	187	34	,	,	PUNCT
ejpam-6838	187	35	s	s	PART
ejpam-6838	187	36	=	=	NOUN
ejpam-6838	187	37	∫	∫	PROPN
ejpam-6838	187	38	1	1	NUM
ejpam-6838	187	39	0	0	NUM
ejpam-6838	187	40	∫	∫	PROPN
ejpam-6838	187	41	1	1	NUM
ejpam-6838	187	42	0	0	NUM
ejpam-6838	187	43	g(x	g(x	NOUN
ejpam-6838	187	44	,	,	PUNCT
ejpam-6838	187	45	t)h∗	t)h∗	INTJ
ejpam-6838	187	46	r(x)h∗	r(x)h∗	PROPN
ejpam-6838	187	47	s(t)w	s(t)w	NOUN
ejpam-6838	187	48	∗(x)w∗(t	∗(x)w∗(t	NOUN
ejpam-6838	187	49	)	)	PUNCT
ejpam-6838	187	50	dx	dx	PROPN
ejpam-6838	188	1	dt	dt	PROPN
ejpam-6838	188	2	,	,	PUNCT
ejpam-6838	188	3	(	(	PUNCT
ejpam-6838	188	4	23	23	NUM
ejpam-6838	188	5	)	)	PUNCT
ejpam-6838	188	6	z	z	NOUN
ejpam-6838	189	1	=	=	SYM
ejpam-6838	189	2	(	(	PUNCT
ejpam-6838	189	3	zi	zi	NOUN
ejpam-6838	189	4	,	,	PUNCT
ejpam-6838	189	5	r)(m+1)×(m−1	r)(m+1)×(m−1	PROPN
ejpam-6838	189	6	)	)	PUNCT
ejpam-6838	189	7	,	,	PUNCT
ejpam-6838	189	8	zi	zi	NOUN
ejpam-6838	189	9	,	,	PUNCT
ejpam-6838	189	10	r	r	NOUN
ejpam-6838	189	11	=	=	SYM
ejpam-6838	189	12	∫	∫	PROPN
ejpam-6838	189	13	1	1	NUM
ejpam-6838	189	14	0	0	NUM
ejpam-6838	189	15	h∗	h∗	PROPN
ejpam-6838	189	16	i	i	PRON
ejpam-6838	189	17	(	(	PUNCT
ejpam-6838	189	18	x)h∗	x)h∗	PROPN
ejpam-6838	189	19	r(x)w	r(x)w	PROPN
ejpam-6838	189	20	∗(x	∗(x	PROPN
ejpam-6838	189	21	)	)	PUNCT
ejpam-6838	189	22	dx	dx	PROPN
ejpam-6838	189	23	,	,	PUNCT
ejpam-6838	189	24	(	(	PUNCT
ejpam-6838	189	25	24	24	NUM
ejpam-6838	189	26	)	)	PUNCT
ejpam-6838	189	27	w.	w.	PROPN
ejpam-6838	189	28	m.	m.	PROPN
ejpam-6838	190	1	abd	abd	PROPN
ejpam-6838	190	2	-	-	PUNCT
ejpam-6838	190	3	elhameed	elhameed	PROPN
ejpam-6838	190	4	et	et	PROPN
ejpam-6838	190	5	al	al	PROPN
ejpam-6838	190	6	.	.	PUNCT
ejpam-6838	190	7	/	/	SYM
ejpam-6838	190	8	eur	eur	PROPN
ejpam-6838	190	9	.	.	PUNCT
ejpam-6838	191	1	j.	j.	PROPN
ejpam-6838	191	2	pure	pure	PROPN
ejpam-6838	191	3	appl	appl	PROPN
ejpam-6838	191	4	.	.	PROPN
ejpam-6838	191	5	math	math	PROPN
ejpam-6838	191	6	,	,	PUNCT
ejpam-6838	191	7	18	18	NUM
ejpam-6838	191	8	(	(	PUNCT
ejpam-6838	191	9	4	4	NUM
ejpam-6838	191	10	)	)	PUNCT
ejpam-6838	191	11	(	(	PUNCT
ejpam-6838	191	12	2025	2025	NUM
ejpam-6838	191	13	)	)	PUNCT
ejpam-6838	191	14	,	,	PUNCT
ejpam-6838	191	15	6838	6838	NUM
ejpam-6838	191	16	9	9	NUM
ejpam-6838	191	17	of	of	ADP
ejpam-6838	191	18	25	25	NUM
ejpam-6838	191	19	b	b	NOUN
ejpam-6838	191	20	=	=	PUNCT
ejpam-6838	191	21	(	(	PUNCT
ejpam-6838	191	22	bj	bj	NOUN
ejpam-6838	191	23	,	,	PUNCT
ejpam-6838	191	24	s)(m+1)×m	s)(m+1)×m	ADJ
ejpam-6838	191	25	,	,	PUNCT
ejpam-6838	191	26	bj	bj	VERB
ejpam-6838	191	27	,	,	PUNCT
ejpam-6838	191	28	s	s	PART
ejpam-6838	191	29	=	=	NOUN
ejpam-6838	191	30	∫	∫	PROPN
ejpam-6838	191	31	1	1	NUM
ejpam-6838	191	32	0	0	NUM
ejpam-6838	191	33	h∗	h∗	PROPN
ejpam-6838	191	34	j	j	PROPN
ejpam-6838	191	35	(	(	PUNCT
ejpam-6838	191	36	t)h∗	t)h∗	NOUN
ejpam-6838	191	37	s(t)w	s(t)w	NOUN
ejpam-6838	191	38	∗(t	∗(t	NOUN
ejpam-6838	191	39	)	)	PUNCT
ejpam-6838	191	40	dt	dt	PROPN
ejpam-6838	191	41	,	,	PUNCT
ejpam-6838	191	42	(	(	PUNCT
ejpam-6838	191	43	25	25	NUM
ejpam-6838	191	44	)	)	PUNCT
ejpam-6838	191	45	y	y	NOUN
ejpam-6838	191	46	=	=	SYM
ejpam-6838	191	47	(	(	PUNCT
ejpam-6838	191	48	yi	yi	PROPN
ejpam-6838	191	49	,	,	PUNCT
ejpam-6838	191	50	r)(m+1)×(m−1	r)(m+1)×(m−1	PROPN
ejpam-6838	191	51	)	)	PUNCT
ejpam-6838	191	52	,	,	PUNCT
ejpam-6838	191	53	yi	yi	PROPN
ejpam-6838	191	54	,	,	PUNCT
ejpam-6838	191	55	r	r	NOUN
ejpam-6838	191	56	=	=	SYM
ejpam-6838	191	57	∫	∫	PROPN
ejpam-6838	191	58	1	1	NUM
ejpam-6838	191	59	0	0	NUM
ejpam-6838	191	60	d2h∗	d2h∗	PROPN
ejpam-6838	192	1	i	i	INTJ
ejpam-6838	192	2	(	(	PUNCT
ejpam-6838	192	3	x	x	X
ejpam-6838	192	4	)	)	PUNCT
ejpam-6838	193	1	d	d	X
ejpam-6838	193	2	x2	x2	PROPN
ejpam-6838	193	3	h∗	h∗	PROPN
ejpam-6838	193	4	r(x)w	r(x)w	PROPN
ejpam-6838	193	5	∗(x	∗(x	VERB
ejpam-6838	193	6	)	)	PUNCT
ejpam-6838	193	7	dx	dx	PROPN
ejpam-6838	193	8	,	,	PUNCT
ejpam-6838	193	9	(	(	PUNCT
ejpam-6838	193	10	26	26	NUM
ejpam-6838	193	11	)	)	PUNCT
ejpam-6838	193	12	k	k	NOUN
ejpam-6838	194	1	=	=	SYM
ejpam-6838	194	2	(	(	PUNCT
ejpam-6838	194	3	kj	kj	PROPN
ejpam-6838	194	4	,	,	PUNCT
ejpam-6838	194	5	s)(m+1)×m	s)(m+1)×m	ADJ
ejpam-6838	194	6	,	,	PUNCT
ejpam-6838	194	7	kj	kj	PROPN
ejpam-6838	194	8	,	,	PUNCT
ejpam-6838	194	9	s	s	PART
ejpam-6838	194	10	=	=	NOUN
ejpam-6838	194	11	∫	∫	PROPN
ejpam-6838	194	12	1	1	NUM
ejpam-6838	194	13	0	0	NUM
ejpam-6838	194	14	dζ	dζ	PROPN
ejpam-6838	194	15	th∗	th∗	ADJ
ejpam-6838	194	16	j	j	PROPN
ejpam-6838	194	17	(	(	PUNCT
ejpam-6838	194	18	t)h∗	t)h∗	NOUN
ejpam-6838	194	19	s(t)w	s(t)w	NOUN
ejpam-6838	194	20	∗(t	∗(t	NOUN
ejpam-6838	194	21	)	)	PUNCT
ejpam-6838	194	22	dt	dt	PROPN
ejpam-6838	194	23	.	.	PUNCT
ejpam-6838	195	1	(	(	PUNCT
ejpam-6838	195	2	27	27	NUM
ejpam-6838	195	3	)	)	PUNCT
ejpam-6838	195	4	therefore	therefore	ADV
ejpam-6838	195	5	,	,	PUNCT
ejpam-6838	195	6	eq	eq	ADJ
ejpam-6838	195	7	.	.	PUNCT
ejpam-6838	196	1	(	(	PUNCT
ejpam-6838	196	2	22	22	NUM
ejpam-6838	196	3	)	)	PUNCT
ejpam-6838	196	4	can	can	AUX
ejpam-6838	196	5	be	be	AUX
ejpam-6838	196	6	rewritten	rewrite	VERB
ejpam-6838	196	7	as	as	ADP
ejpam-6838	196	8	m∑	m∑	INTJ
ejpam-6838	196	9	i=0	i=0	PROPN
ejpam-6838	196	10	m∑	m∑	CCONJ
ejpam-6838	196	11	j=0	j=0	PROPN
ejpam-6838	196	12	cij	cij	PROPN
ejpam-6838	196	13	zi	zi	PROPN
ejpam-6838	196	14	,	,	PUNCT
ejpam-6838	196	15	r	r	PROPN
ejpam-6838	196	16	kj	kj	PROPN
ejpam-6838	196	17	,	,	PUNCT
ejpam-6838	196	18	s	s	PART
ejpam-6838	196	19	−	−	PROPN
ejpam-6838	196	20	β	β	NOUN
ejpam-6838	196	21	m∑	m∑	VERB
ejpam-6838	196	22	i=0	i=0	PROPN
ejpam-6838	196	23	m∑	m∑	CCONJ
ejpam-6838	196	24	j=0	j=0	PROPN
ejpam-6838	196	25	cij	cij	PROPN
ejpam-6838	196	26	yi	yi	PROPN
ejpam-6838	196	27	,	,	PUNCT
ejpam-6838	196	28	r	r	NOUN
ejpam-6838	196	29	bj	bj	NOUN
ejpam-6838	196	30	,	,	PUNCT
ejpam-6838	196	31	s	s	PART
ejpam-6838	196	32	=	=	ADJ
ejpam-6838	196	33	fr	fr	PROPN
ejpam-6838	196	34	,	,	PUNCT
ejpam-6838	196	35	s	s	PROPN
ejpam-6838	196	36	,	,	PUNCT
ejpam-6838	196	37	0	0	NUM
ejpam-6838	196	38	≤	≤	NUM
ejpam-6838	196	39	r	r	NOUN
ejpam-6838	196	40	≤	≤	NUM
ejpam-6838	196	41	m−	m−	PROPN
ejpam-6838	196	42	2	2	NUM
ejpam-6838	196	43	,	,	PUNCT
ejpam-6838	196	44	0	0	NUM
ejpam-6838	196	45	≤	≤	NUM
ejpam-6838	196	46	s	s	PART
ejpam-6838	196	47	≤	≤	NUM
ejpam-6838	196	48	m−	m−	PROPN
ejpam-6838	196	49	1	1	NUM
ejpam-6838	196	50	,	,	PUNCT
ejpam-6838	196	51	(	(	PUNCT
ejpam-6838	196	52	28	28	NUM
ejpam-6838	196	53	)	)	PUNCT
ejpam-6838	196	54	or	or	CCONJ
ejpam-6838	196	55	in	in	ADP
ejpam-6838	196	56	the	the	DET
ejpam-6838	196	57	following	follow	VERB
ejpam-6838	196	58	matrix	matrix	NOUN
ejpam-6838	196	59	form	form	NOUN
ejpam-6838	196	60	:	:	PUNCT
ejpam-6838	196	61	zt	zt	PROPN
ejpam-6838	196	62	ck−	ck−	PROPN
ejpam-6838	196	63	βytc	βytc	PROPN
ejpam-6838	196	64	b	b	PROPN
ejpam-6838	196	65	=	=	PUNCT
ejpam-6838	196	66	g.	g.	PROPN
ejpam-6838	196	67	in	in	ADP
ejpam-6838	196	68	addition	addition	NOUN
ejpam-6838	196	69	,	,	PUNCT
ejpam-6838	196	70	the	the	DET
ejpam-6838	196	71	conditions	condition	NOUN
ejpam-6838	196	72	in	in	ADP
ejpam-6838	196	73	(	(	PUNCT
ejpam-6838	196	74	18	18	NUM
ejpam-6838	196	75	)	)	PUNCT
ejpam-6838	196	76	and	and	CCONJ
ejpam-6838	196	77	(	(	PUNCT
ejpam-6838	196	78	19	19	NUM
ejpam-6838	196	79	)	)	PUNCT
ejpam-6838	196	80	lead	lead	NOUN
ejpam-6838	196	81	to	to	ADP
ejpam-6838	196	82	the	the	DET
ejpam-6838	196	83	following	follow	VERB
ejpam-6838	196	84	equations	equation	NOUN
ejpam-6838	196	85	:	:	PUNCT
ejpam-6838	196	86	m∑	m∑	CCONJ
ejpam-6838	196	87	i=0	i=0	PROPN
ejpam-6838	196	88	m∑	m∑	CCONJ
ejpam-6838	196	89	j=0	j=0	PROPN
ejpam-6838	196	90	cij	cij	PROPN
ejpam-6838	196	91	ai	ai	VERB
ejpam-6838	196	92	,	,	PUNCT
ejpam-6838	196	93	r	r	PROPN
ejpam-6838	196	94	h∗	h∗	PROPN
ejpam-6838	196	95	j	j	PROPN
ejpam-6838	196	96	(	(	PUNCT
ejpam-6838	196	97	0	0	NUM
ejpam-6838	196	98	)	)	PUNCT
ejpam-6838	196	99	=	=	SYM
ejpam-6838	197	1	∫	∫	PROPN
ejpam-6838	197	2	1	1	NUM
ejpam-6838	197	3	0	0	NUM
ejpam-6838	197	4	ρ1(x)h∗	ρ1(x)h∗	NOUN
ejpam-6838	197	5	r(x)w	r(x)w	PROPN
ejpam-6838	197	6	∗(x	∗(x	VERB
ejpam-6838	197	7	)	)	PUNCT
ejpam-6838	197	8	dx	dx	PROPN
ejpam-6838	197	9	,	,	PUNCT
ejpam-6838	197	10	0	0	NUM
ejpam-6838	197	11	≤	≤	NUM
ejpam-6838	197	12	r	r	NOUN
ejpam-6838	197	13	≤	≤	NUM
ejpam-6838	197	14	m	m	ADP
ejpam-6838	197	15	,	,	PUNCT
ejpam-6838	197	16	(	(	PUNCT
ejpam-6838	197	17	29	29	NUM
ejpam-6838	197	18	)	)	PUNCT
ejpam-6838	197	19	m∑	m∑	CCONJ
ejpam-6838	197	20	i=0	i=0	PROPN
ejpam-6838	197	21	m∑	m∑	CCONJ
ejpam-6838	197	22	j=0	j=0	PROPN
ejpam-6838	197	23	cij	cij	PROPN
ejpam-6838	197	24	aj	aj	PROPN
ejpam-6838	197	25	,	,	PUNCT
ejpam-6838	197	26	sh∗	sh∗	VERB
ejpam-6838	197	27	i	i	PRON
ejpam-6838	197	28	(	(	PUNCT
ejpam-6838	197	29	0	0	NUM
ejpam-6838	197	30	)	)	PUNCT
ejpam-6838	197	31	=	=	SYM
ejpam-6838	198	1	∫	∫	PROPN
ejpam-6838	198	2	1	1	NUM
ejpam-6838	198	3	0	0	NUM
ejpam-6838	198	4	ρ2(t)h∗	ρ2(t)h∗	NOUN
ejpam-6838	198	5	s(t)w	s(t)w	NOUN
ejpam-6838	198	6	∗(t	∗(t	NOUN
ejpam-6838	198	7	)	)	PUNCT
ejpam-6838	198	8	dt	dt	PROPN
ejpam-6838	198	9	,	,	PUNCT
ejpam-6838	198	10	0	0	NUM
ejpam-6838	198	11	≤	≤	NUM
ejpam-6838	198	12	s	s	PART
ejpam-6838	198	13	≤	≤	NUM
ejpam-6838	198	14	m−	m−	PROPN
ejpam-6838	198	15	1	1	NUM
ejpam-6838	198	16	,	,	PUNCT
ejpam-6838	198	17	(	(	PUNCT
ejpam-6838	198	18	30	30	NUM
ejpam-6838	198	19	)	)	PUNCT
ejpam-6838	198	20	m∑	m∑	CCONJ
ejpam-6838	199	1	i=0	i=0	PROPN
ejpam-6838	199	2	m∑	m∑	CCONJ
ejpam-6838	199	3	j=0	j=0	PROPN
ejpam-6838	199	4	cij	cij	PROPN
ejpam-6838	199	5	aj	aj	PROPN
ejpam-6838	199	6	,	,	PUNCT
ejpam-6838	199	7	sh∗	sh∗	VERB
ejpam-6838	199	8	i	i	PRON
ejpam-6838	199	9	(	(	PUNCT
ejpam-6838	199	10	1	1	X
ejpam-6838	199	11	)	)	PUNCT
ejpam-6838	199	12	=	=	SYM
ejpam-6838	200	1	∫	∫	PROPN
ejpam-6838	200	2	1	1	NUM
ejpam-6838	200	3	0	0	NUM
ejpam-6838	200	4	ρ3(t)h∗	ρ3(t)h∗	PROPN
ejpam-6838	200	5	s(t)w	s(t)w	NOUN
ejpam-6838	200	6	∗(t	∗(t	NOUN
ejpam-6838	200	7	)	)	PUNCT
ejpam-6838	200	8	dt	dt	PROPN
ejpam-6838	200	9	,	,	PUNCT
ejpam-6838	200	10	0	0	NUM
ejpam-6838	200	11	≤	≤	NUM
ejpam-6838	200	12	s	s	PART
ejpam-6838	200	13	≤	≤	NUM
ejpam-6838	200	14	m−	m−	PROPN
ejpam-6838	200	15	1	1	NUM
ejpam-6838	200	16	.	.	PUNCT
ejpam-6838	201	1	(	(	PUNCT
ejpam-6838	201	2	31	31	NUM
ejpam-6838	201	3	)	)	PUNCT
ejpam-6838	201	4	the	the	DET
ejpam-6838	201	5	resultant	resultant	NOUN
ejpam-6838	201	6	algebraic	algebraic	ADJ
ejpam-6838	201	7	system	system	NOUN
ejpam-6838	201	8	of	of	ADP
ejpam-6838	201	9	equations	equation	NOUN
ejpam-6838	201	10	,	,	PUNCT
ejpam-6838	201	11	consisting	consist	VERB
ejpam-6838	201	12	of	of	ADP
ejpam-6838	201	13	eqs	eqs	PROPN
ejpam-6838	201	14	.	.	PUNCT
ejpam-6838	201	15	(	(	PUNCT
ejpam-6838	201	16	28)-(31	28)-(31	NUM
ejpam-6838	201	17	)	)	PUNCT
ejpam-6838	201	18	,	,	PUNCT
ejpam-6838	201	19	has	have	VERB
ejpam-6838	201	20	an	an	DET
ejpam-6838	201	21	order	order	NOUN
ejpam-6838	201	22	of	of	ADP
ejpam-6838	201	23	(	(	PUNCT
ejpam-6838	201	24	m+	m+	NOUN
ejpam-6838	201	25	1)2	1)2	NUM
ejpam-6838	201	26	and	and	CCONJ
ejpam-6838	201	27	may	may	AUX
ejpam-6838	201	28	be	be	AUX
ejpam-6838	201	29	solved	solve	VERB
ejpam-6838	201	30	using	use	VERB
ejpam-6838	201	31	an	an	DET
ejpam-6838	201	32	appropriate	appropriate	ADJ
ejpam-6838	201	33	method	method	NOUN
ejpam-6838	201	34	.	.	PUNCT
ejpam-6838	202	1	now	now	ADV
ejpam-6838	202	2	,	,	PUNCT
ejpam-6838	202	3	we	we	PRON
ejpam-6838	202	4	give	give	VERB
ejpam-6838	202	5	an	an	DET
ejpam-6838	202	6	explicit	explicit	ADJ
ejpam-6838	202	7	form	form	NOUN
ejpam-6838	202	8	for	for	ADP
ejpam-6838	202	9	the	the	DET
ejpam-6838	202	10	elements	element	NOUN
ejpam-6838	202	11	of	of	ADP
ejpam-6838	202	12	the	the	DET
ejpam-6838	202	13	matrices	matrix	NOUN
ejpam-6838	202	14	z	z	NOUN
ejpam-6838	202	15	,	,	PUNCT
ejpam-6838	202	16	k	k	PROPN
ejpam-6838	202	17	,	,	PUNCT
ejpam-6838	202	18	y	y	PROPN
ejpam-6838	202	19	.	.	PUNCT
ejpam-6838	203	1	theorem	theorem	VERB
ejpam-6838	203	2	3	3	NUM
ejpam-6838	203	3	.	.	PUNCT
ejpam-6838	204	1	the	the	DET
ejpam-6838	204	2	elements	element	NOUN
ejpam-6838	204	3	zi	zi	PROPN
ejpam-6838	204	4	,	,	PUNCT
ejpam-6838	204	5	r	r	NOUN
ejpam-6838	204	6	,	,	PUNCT
ejpam-6838	204	7	bj	bj	NOUN
ejpam-6838	204	8	,	,	PUNCT
ejpam-6838	204	9	s	s	PART
ejpam-6838	204	10	,	,	PUNCT
ejpam-6838	204	11	yi	yi	PROPN
ejpam-6838	204	12	,	,	PUNCT
ejpam-6838	204	13	r	r	NOUN
ejpam-6838	204	14	,	,	PUNCT
ejpam-6838	204	15	and	and	CCONJ
ejpam-6838	204	16	kj	kj	PROPN
ejpam-6838	204	17	,	,	PUNCT
ejpam-6838	204	18	s	s	PART
ejpam-6838	204	19	have	have	VERB
ejpam-6838	204	20	the	the	DET
ejpam-6838	204	21	following	follow	VERB
ejpam-6838	204	22	forms	form	NOUN
ejpam-6838	204	23	:	:	PUNCT
ejpam-6838	204	24	zi	zi	NOUN
ejpam-6838	204	25	,	,	PUNCT
ejpam-6838	204	26	r	r	NOUN
ejpam-6838	204	27	=	=	SYM
ejpam-6838	204	28	∫	∫	PROPN
ejpam-6838	204	29	1	1	NUM
ejpam-6838	204	30	0	0	NUM
ejpam-6838	204	31	h∗	h∗	PROPN
ejpam-6838	204	32	i	i	PRON
ejpam-6838	204	33	(	(	PUNCT
ejpam-6838	204	34	x)h∗	x)h∗	PROPN
ejpam-6838	204	35	r(x)w	r(x)w	PROPN
ejpam-6838	204	36	∗(x	∗(x	VERB
ejpam-6838	204	37	)	)	PUNCT
ejpam-6838	204	38	dx	dx	PROPN
ejpam-6838	205	1	=	=	NOUN
ejpam-6838	205	2	1	1	NUM
ejpam-6838	205	3	16	16	NUM
ejpam-6838	205	4	hi	hi	INTJ
ejpam-6838	205	5	,	,	PUNCT
ejpam-6838	205	6	(	(	PUNCT
ejpam-6838	205	7	32	32	NUM
ejpam-6838	205	8	)	)	PUNCT
ejpam-6838	205	9	bj	bj	NOUN
ejpam-6838	205	10	,	,	PUNCT
ejpam-6838	205	11	s	s	PART
ejpam-6838	205	12	=	=	NOUN
ejpam-6838	205	13	∫	∫	PROPN
ejpam-6838	205	14	1	1	NUM
ejpam-6838	205	15	0	0	NUM
ejpam-6838	205	16	h∗	h∗	PROPN
ejpam-6838	205	17	j	j	PROPN
ejpam-6838	205	18	(	(	PUNCT
ejpam-6838	205	19	t)h∗	t)h∗	NOUN
ejpam-6838	205	20	s(t)w	s(t)w	NOUN
ejpam-6838	205	21	∗(t	∗(t	NOUN
ejpam-6838	205	22	)	)	PUNCT
ejpam-6838	205	23	dt	dt	NOUN
ejpam-6838	206	1	=	=	NOUN
ejpam-6838	206	2	1	1	NUM
ejpam-6838	206	3	16	16	NUM
ejpam-6838	206	4	hj	hj	NOUN
ejpam-6838	206	5	,	,	PUNCT
ejpam-6838	206	6	(	(	PUNCT
ejpam-6838	206	7	33	33	NUM
ejpam-6838	206	8	)	)	PUNCT
ejpam-6838	206	9	yi	yi	PROPN
ejpam-6838	206	10	,	,	PUNCT
ejpam-6838	206	11	j	j	PROPN
ejpam-6838	206	12	=	=	SYM
ejpam-6838	206	13	∫	∫	PROPN
ejpam-6838	206	14	1	1	NUM
ejpam-6838	206	15	0	0	NUM
ejpam-6838	206	16	d2h∗	d2h∗	PROPN
ejpam-6838	207	1	i	i	INTJ
ejpam-6838	207	2	(	(	PUNCT
ejpam-6838	207	3	x	x	X
ejpam-6838	207	4	)	)	PUNCT
ejpam-6838	207	5	dθ2	dθ2	NOUN
ejpam-6838	208	1	h∗	h∗	PROPN
ejpam-6838	208	2	j	j	PROPN
ejpam-6838	208	3	(	(	PUNCT
ejpam-6838	208	4	x)w	x)w	PUNCT
ejpam-6838	208	5	∗(x	∗(x	PROPN
ejpam-6838	208	6	)	)	PUNCT
ejpam-6838	208	7	dx	dx	PROPN
ejpam-6838	208	8	=	=	NOUN
ejpam-6838	209	1	1	1	NUM
ejpam-6838	209	2	16	16	NUM
ejpam-6838	209	3	⌊	⌊	PROPN
ejpam-6838	209	4	i−2	i−2	VERB
ejpam-6838	209	5	2	2	NUM
ejpam-6838	209	6	⌋∑	⌋∑	NOUN
ejpam-6838	210	1	r=0	r=0	NUM
ejpam-6838	210	2	b̃2	b̃2	NOUN
ejpam-6838	210	3	r	r	NOUN
ejpam-6838	210	4	,	,	PUNCT
ejpam-6838	210	5	i	i	PRON
ejpam-6838	210	6	hi−k−2r	hi−k−2r	VERB
ejpam-6838	210	7	,	,	PUNCT
ejpam-6838	210	8	(	(	PUNCT
ejpam-6838	210	9	34	34	X
ejpam-6838	210	10	)	)	PUNCT
ejpam-6838	210	11	w.	w.	PROPN
ejpam-6838	210	12	m.	m.	PROPN
ejpam-6838	210	13	abd	abd	PROPN
ejpam-6838	210	14	-	-	PUNCT
ejpam-6838	210	15	elhameed	elhameed	PROPN
ejpam-6838	210	16	et	et	PROPN
ejpam-6838	210	17	al	al	PROPN
ejpam-6838	210	18	.	.	PUNCT
ejpam-6838	210	19	/	/	SYM
ejpam-6838	210	20	eur	eur	PROPN
ejpam-6838	210	21	.	.	PUNCT
ejpam-6838	211	1	j.	j.	PROPN
ejpam-6838	211	2	pure	pure	PROPN
ejpam-6838	211	3	appl	appl	PROPN
ejpam-6838	211	4	.	.	PROPN
ejpam-6838	211	5	math	math	PROPN
ejpam-6838	211	6	,	,	PUNCT
ejpam-6838	211	7	18	18	NUM
ejpam-6838	211	8	(	(	PUNCT
ejpam-6838	211	9	4	4	NUM
ejpam-6838	211	10	)	)	PUNCT
ejpam-6838	211	11	(	(	PUNCT
ejpam-6838	211	12	2025	2025	NUM
ejpam-6838	211	13	)	)	PUNCT
ejpam-6838	211	14	,	,	PUNCT
ejpam-6838	211	15	6838	6838	NUM
ejpam-6838	211	16	10	10	NUM
ejpam-6838	211	17	of	of	ADP
ejpam-6838	211	18	25	25	NUM
ejpam-6838	211	19	and	and	CCONJ
ejpam-6838	211	20	kj	kj	PROPN
ejpam-6838	211	21	,	,	PUNCT
ejpam-6838	211	22	s	s	PART
ejpam-6838	211	23	=	=	NOUN
ejpam-6838	211	24	∫	∫	PROPN
ejpam-6838	211	25	1	1	NUM
ejpam-6838	211	26	0	0	NUM
ejpam-6838	211	27	dζ	dζ	PROPN
ejpam-6838	211	28	th∗	th∗	ADJ
ejpam-6838	211	29	j	j	PROPN
ejpam-6838	211	30	(	(	PUNCT
ejpam-6838	211	31	t)h∗	t)h∗	NOUN
ejpam-6838	211	32	s(t)w	s(t)w	NOUN
ejpam-6838	211	33	∗(t	∗(t	NOUN
ejpam-6838	211	34	)	)	PUNCT
ejpam-6838	211	35	dt	dt	NOUN
ejpam-6838	212	1	=	=	SYM
ejpam-6838	212	2	j∑	j∑	PROPN
ejpam-6838	212	3	r=1	r=1	PROPN
ejpam-6838	212	4	j∑	j∑	PROPN
ejpam-6838	212	5	m=0	m=0	PROPN
ejpam-6838	212	6	s∑	s∑	PROPN
ejpam-6838	213	1	p=0	p=0	PROPN
ejpam-6838	213	2	s∑	s∑	PROPN
ejpam-6838	213	3	n=0	n=0	NUM
ejpam-6838	213	4	2rr!(−1	2rr!(−1	NUM
ejpam-6838	213	5	)	)	PUNCT
ejpam-6838	213	6	)	)	PUNCT
ejpam-6838	214	1	j−m	j−m	ADJ
ejpam-6838	214	2	2	2	NUM
ejpam-6838	214	3	(	(	PUNCT
ejpam-6838	214	4	−1)m−ra(j	−1)m−ra(j	PROPN
ejpam-6838	214	5	+	+	PROPN
ejpam-6838	214	6	m	m	X
ejpam-6838	214	7	)	)	PUNCT
ejpam-6838	214	8	(	(	PUNCT
ejpam-6838	214	9	m	m	NOUN
ejpam-6838	214	10	r	r	NOUN
ejpam-6838	214	11	)	)	PUNCT
ejpam-6838	214	12	(	(	PUNCT
ejpam-6838	214	13	3	3	X
ejpam-6838	214	14	)	)	PUNCT
ejpam-6838	214	15	j+m	j+m	NOUN
ejpam-6838	214	16	2	2	NUM
ejpam-6838	214	17	(	(	PUNCT
ejpam-6838	214	18	j−m	j−m	NOUN
ejpam-6838	214	19	2	2	NUM
ejpam-6838	214	20	)	)	PUNCT
ejpam-6838	214	21	!	!	PUNCT
ejpam-6838	215	1	γ(r	γ(r	PROPN
ejpam-6838	216	1	−	−	NOUN
ejpam-6838	216	2	α+	α+	NOUN
ejpam-6838	216	3	1	1	NUM
ejpam-6838	216	4	)	)	PUNCT
ejpam-6838	216	5	(	(	PUNCT
ejpam-6838	216	6	3	3	NUM
ejpam-6838	216	7	2	2	NUM
ejpam-6838	216	8	)	)	PUNCT
ejpam-6838	216	9	m−j	m−j	NOUN
ejpam-6838	216	10	2	2	NUM
ejpam-6838	217	1	+	+	NOUN
ejpam-6838	217	2	⌊	⌊	PROPN
ejpam-6838	217	3	j+1	j+1	ADJ
ejpam-6838	217	4	2	2	NUM
ejpam-6838	217	5	⌋	⌋	NOUN
ejpam-6838	217	6	γ	γ	X
ejpam-6838	217	7	(	(	PUNCT
ejpam-6838	217	8	1	1	NUM
ejpam-6838	217	9	2(−j	2(−j	NUM
ejpam-6838	217	10	+	+	NOUN
ejpam-6838	217	11	m+	m+	NUM
ejpam-6838	217	12	2	2	NUM
ejpam-6838	217	13	)	)	PUNCT
ejpam-6838	218	1	+	+	CCONJ
ejpam-6838	218	2	⌊	⌊	PROPN
ejpam-6838	218	3	j	j	PROPN
ejpam-6838	218	4	2	2	NUM
ejpam-6838	218	5	⌋)×	⌋)×	PROPN
ejpam-6838	218	6	3	3	NUM
ejpam-6838	218	7	√	√	NUM
ejpam-6838	218	8	π2p−2(−1)n−p(−1	π2p−2(−1)n−p(−1	NUM
ejpam-6838	218	9	)	)	PUNCT
ejpam-6838	218	10	s−n	s−n	PROPN
ejpam-6838	218	11	2	2	NUM
ejpam-6838	218	12	a(n+	a(n+	NOUN
ejpam-6838	218	13	s	s	PART
ejpam-6838	218	14	)	)	PUNCT
ejpam-6838	218	15	(	(	PUNCT
ejpam-6838	218	16	n	n	PRON
ejpam-6838	218	17	p	p	NOUN
ejpam-6838	218	18	)	)	PUNCT
ejpam-6838	218	19	(	(	PUNCT
ejpam-6838	218	20	3)n+s	3)n+s	NUM
ejpam-6838	218	21	2	2	NUM
ejpam-6838	218	22	(	(	PUNCT
ejpam-6838	218	23	α2	α2	ADV
ejpam-6838	218	24	−	−	PROPN
ejpam-6838	218	25	α(2p+	α(2p+	NOUN
ejpam-6838	218	26	2r	2r	NUM
ejpam-6838	219	1	+	+	CCONJ
ejpam-6838	219	2	1	1	X
ejpam-6838	219	3	)	)	PUNCT
ejpam-6838	219	4	+	+	CCONJ
ejpam-6838	219	5	(	(	PUNCT
ejpam-6838	219	6	p+	p+	NOUN
ejpam-6838	219	7	r)2	r)2	NOUN
ejpam-6838	219	8	+	+	SYM
ejpam-6838	219	9	p+	p+	NOUN
ejpam-6838	219	10	r	r	NOUN
ejpam-6838	219	11	+	+	CCONJ
ejpam-6838	219	12	5	5	NUM
ejpam-6838	219	13	)	)	PUNCT
ejpam-6838	219	14	s−n	s−n	PROPN
ejpam-6838	219	15	2	2	NUM
ejpam-6838	219	16	!	!	PUNCT
ejpam-6838	220	1	(	(	PUNCT
ejpam-6838	220	2	3	3	NUM
ejpam-6838	220	3	2	2	NUM
ejpam-6838	220	4	)	)	PUNCT
ejpam-6838	220	5	n−s	n−s	ADV
ejpam-6838	220	6	2	2	NUM
ejpam-6838	221	1	+	+	ADP
ejpam-6838	221	2	⌊	⌊	VERB
ejpam-6838	221	3	s+1	s+1	NUM
ejpam-6838	221	4	2	2	NUM
ejpam-6838	221	5	⌋	⌋	NOUN
ejpam-6838	221	6	γ	γ	X
ejpam-6838	221	7	(	(	PUNCT
ejpam-6838	221	8	1	1	NUM
ejpam-6838	221	9	2(n−	2(n−	NUM
ejpam-6838	221	10	s+	s+	PUNCT
ejpam-6838	221	11	2	2	NUM
ejpam-6838	221	12	)	)	PUNCT
ejpam-6838	221	13	+	+	CCONJ
ejpam-6838	221	14	⌊	⌊	PROPN
ejpam-6838	221	15	s	s	PART
ejpam-6838	221	16	2	2	NUM
ejpam-6838	221	17	⌋	⌋	NOUN
ejpam-6838	221	18	)	)	PUNCT
ejpam-6838	221	19	×	×	NOUN
ejpam-6838	221	20	γ	γ	X
ejpam-6838	221	21	(	(	PUNCT
ejpam-6838	221	22	p+	p+	NOUN
ejpam-6838	221	23	r	r	NOUN
ejpam-6838	221	24	−	−	PROPN
ejpam-6838	221	25	α+	α+	NOUN
ejpam-6838	221	26	5	5	NUM
ejpam-6838	221	27	2	2	NUM
ejpam-6838	221	28	)	)	PUNCT
ejpam-6838	221	29	γ(p+	γ(p+	PROPN
ejpam-6838	222	1	r	r	NOUN
ejpam-6838	222	2	−	−	PROPN
ejpam-6838	222	3	α+	α+	NOUN
ejpam-6838	222	4	7	7	NUM
ejpam-6838	222	5	)	)	PUNCT
ejpam-6838	222	6	.	.	PUNCT
ejpam-6838	223	1	(	(	PUNCT
ejpam-6838	223	2	35	35	NUM
ejpam-6838	223	3	)	)	PUNCT
ejpam-6838	223	4	proof	proof	NOUN
ejpam-6838	223	5	.	.	PUNCT
ejpam-6838	224	1	with	with	ADP
ejpam-6838	224	2	the	the	DET
ejpam-6838	224	3	direct	direct	ADJ
ejpam-6838	224	4	application	application	NOUN
ejpam-6838	224	5	of	of	ADP
ejpam-6838	224	6	the	the	DET
ejpam-6838	224	7	orthogonality	orthogonality	NOUN
ejpam-6838	224	8	relation	relation	NOUN
ejpam-6838	224	9	(	(	PUNCT
ejpam-6838	224	10	15	15	NUM
ejpam-6838	224	11	)	)	PUNCT
ejpam-6838	224	12	,	,	PUNCT
ejpam-6838	224	13	we	we	PRON
ejpam-6838	224	14	can	can	AUX
ejpam-6838	224	15	easily	easily	ADV
ejpam-6838	224	16	acquire	acquire	VERB
ejpam-6838	224	17	the	the	DET
ejpam-6838	224	18	elements	element	NOUN
ejpam-6838	224	19	zi	zi	NOUN
ejpam-6838	224	20	,	,	PUNCT
ejpam-6838	224	21	r	r	NOUN
ejpam-6838	224	22	and	and	CCONJ
ejpam-6838	224	23	bj	bj	VERB
ejpam-6838	224	24	,	,	PUNCT
ejpam-6838	224	25	s.	s.	PROPN
ejpam-6838	224	26	with	with	ADP
ejpam-6838	224	27	the	the	DET
ejpam-6838	224	28	direct	direct	ADJ
ejpam-6838	224	29	application	application	NOUN
ejpam-6838	224	30	of	of	ADP
ejpam-6838	224	31	(	(	PUNCT
ejpam-6838	224	32	15	15	NUM
ejpam-6838	224	33	)	)	PUNCT
ejpam-6838	224	34	with	with	ADP
ejpam-6838	224	35	(	(	PUNCT
ejpam-6838	224	36	16	16	NUM
ejpam-6838	224	37	)	)	PUNCT
ejpam-6838	224	38	,	,	PUNCT
ejpam-6838	224	39	we	we	PRON
ejpam-6838	224	40	can	can	AUX
ejpam-6838	224	41	easily	easily	ADV
ejpam-6838	224	42	obtain	obtain	VERB
ejpam-6838	224	43	the	the	DET
ejpam-6838	224	44	elements	element	NOUN
ejpam-6838	224	45	yi	yi	PROPN
ejpam-6838	224	46	,	,	PUNCT
ejpam-6838	224	47	j	j	PROPN
ejpam-6838	224	48	.	.	PUNCT
ejpam-6838	225	1	now	now	ADV
ejpam-6838	225	2	,	,	PUNCT
ejpam-6838	225	3	we	we	PRON
ejpam-6838	225	4	will	will	AUX
ejpam-6838	225	5	compute	compute	VERB
ejpam-6838	225	6	kj	kj	PROPN
ejpam-6838	225	7	,	,	PUNCT
ejpam-6838	225	8	s	s	PROPN
ejpam-6838	225	9	,	,	PUNCT
ejpam-6838	225	10	based	base	VERB
ejpam-6838	225	11	on	on	ADP
ejpam-6838	225	12	eq	eq	ADP
ejpam-6838	225	13	.	.	PUNCT
ejpam-6838	226	1	(	(	PUNCT
ejpam-6838	226	2	10	10	NUM
ejpam-6838	226	3	)	)	PUNCT
ejpam-6838	226	4	,	,	PUNCT
ejpam-6838	226	5	the	the	DET
ejpam-6838	226	6	power	power	NOUN
ejpam-6838	226	7	form	form	NOUN
ejpam-6838	226	8	representation	representation	NOUN
ejpam-6838	226	9	of	of	ADP
ejpam-6838	226	10	nj(t	nj(t	PROPN
ejpam-6838	226	11	)	)	PUNCT
ejpam-6838	226	12	as	as	SCONJ
ejpam-6838	226	13	can	can	AUX
ejpam-6838	226	14	be	be	AUX
ejpam-6838	226	15	rewritten	rewrite	VERB
ejpam-6838	226	16	as	as	ADP
ejpam-6838	226	17	nj(t	nj(t	NUM
ejpam-6838	226	18	)	)	PUNCT
ejpam-6838	227	1	=	=	PUNCT
ejpam-6838	228	1	j∑	j∑	PROPN
ejpam-6838	228	2	r=0	r=0	X
ejpam-6838	228	3	(	(	PUNCT
ejpam-6838	228	4	−1	−1	NOUN
ejpam-6838	228	5	)	)	PUNCT
ejpam-6838	228	6	j−r	j−r	NOUN
ejpam-6838	228	7	2	2	NUM
ejpam-6838	228	8	aj+r	aj+r	X
ejpam-6838	228	9	(	(	PUNCT
ejpam-6838	228	10	3)j−	3)j−	NUM
ejpam-6838	228	11	j−r	j−r	NOUN
ejpam-6838	228	12	2	2	NUM
ejpam-6838	228	13	(	(	PUNCT
ejpam-6838	228	14	j−r	j−r	PROPN
ejpam-6838	228	15	2	2	NUM
ejpam-6838	228	16	)	)	PUNCT
ejpam-6838	228	17	!	!	PUNCT
ejpam-6838	229	1	(	(	PUNCT
ejpam-6838	229	2	3	3	NUM
ejpam-6838	229	3	2	2	NUM
ejpam-6838	229	4	)	)	PUNCT
ejpam-6838	229	5	⌊	⌊	VERB
ejpam-6838	229	6	j+1	j+1	ADV
ejpam-6838	229	7	2	2	NUM
ejpam-6838	229	8	⌋−	⌋−	PUNCT
ejpam-6838	229	9	j−r	j−r	PROPN
ejpam-6838	229	10	2	2	NUM
ejpam-6838	229	11	γ	γ	X
ejpam-6838	229	12	(	(	PUNCT
ejpam-6838	229	13	−1	−1	NOUN
ejpam-6838	229	14	2(j	2(j	NUM
ejpam-6838	229	15	−	−	NOUN
ejpam-6838	229	16	r	r	NOUN
ejpam-6838	229	17	)	)	PUNCT
ejpam-6838	230	1	+	+	CCONJ
ejpam-6838	230	2	⌊	⌊	X
ejpam-6838	230	3	j	j	PROPN
ejpam-6838	230	4	2	2	NUM
ejpam-6838	230	5	⌋	⌋	NOUN
ejpam-6838	230	6	+	+	CCONJ
ejpam-6838	230	7	1	1	NUM
ejpam-6838	230	8	)	)	PUNCT
ejpam-6838	230	9	tr	tr	VERB
ejpam-6838	230	10	,	,	PUNCT
ejpam-6838	230	11	(	(	PUNCT
ejpam-6838	230	12	36	36	NUM
ejpam-6838	230	13	)	)	PUNCT
ejpam-6838	230	14	where	where	SCONJ
ejpam-6838	230	15	ar	ar	NOUN
ejpam-6838	230	16	=	=	SYM
ejpam-6838	230	17	{	{	PUNCT
ejpam-6838	230	18	1	1	NUM
ejpam-6838	230	19	,	,	PUNCT
ejpam-6838	230	20	if	if	SCONJ
ejpam-6838	230	21	r	r	NOUN
ejpam-6838	230	22	even	even	ADV
ejpam-6838	230	23	,	,	PUNCT
ejpam-6838	230	24	0	0	NUM
ejpam-6838	230	25	,	,	PUNCT
ejpam-6838	230	26	otherwise	otherwise	ADV
ejpam-6838	230	27	.	.	PUNCT
ejpam-6838	231	1	(	(	PUNCT
ejpam-6838	231	2	37	37	NUM
ejpam-6838	231	3	)	)	PUNCT
ejpam-6838	231	4	and	and	CCONJ
ejpam-6838	231	5	hence	hence	ADV
ejpam-6838	231	6	,	,	PUNCT
ejpam-6838	231	7	h∗	h∗	PROPN
ejpam-6838	231	8	j	j	PROPN
ejpam-6838	231	9	(	(	PUNCT
ejpam-6838	231	10	t	t	PROPN
ejpam-6838	231	11	)	)	PUNCT
ejpam-6838	231	12	given	give	VERB
ejpam-6838	231	13	in	in	ADP
ejpam-6838	231	14	(	(	PUNCT
ejpam-6838	231	15	14	14	NUM
ejpam-6838	231	16	)	)	PUNCT
ejpam-6838	231	17	may	may	AUX
ejpam-6838	231	18	be	be	AUX
ejpam-6838	231	19	represented	represent	VERB
ejpam-6838	231	20	as	as	ADP
ejpam-6838	231	21	h∗	h∗	PROPN
ejpam-6838	231	22	j	j	PROPN
ejpam-6838	231	23	(	(	PUNCT
ejpam-6838	231	24	t	t	PROPN
ejpam-6838	231	25	)	)	PUNCT
ejpam-6838	231	26	=	=	VERB
ejpam-6838	232	1	j∑	j∑	PROPN
ejpam-6838	233	1	r=0	r=0	X
ejpam-6838	233	2	(	(	PUNCT
ejpam-6838	233	3	−1	−1	NOUN
ejpam-6838	233	4	)	)	PUNCT
ejpam-6838	233	5	j−r	j−r	NOUN
ejpam-6838	233	6	2	2	NUM
ejpam-6838	233	7	aj+r	aj+r	X
ejpam-6838	233	8	(	(	PUNCT
ejpam-6838	233	9	3)j−	3)j−	NUM
ejpam-6838	233	10	j−r	j−r	NOUN
ejpam-6838	233	11	2	2	NUM
ejpam-6838	233	12	(	(	PUNCT
ejpam-6838	233	13	j−r	j−r	PROPN
ejpam-6838	233	14	2	2	NUM
ejpam-6838	233	15	)	)	PUNCT
ejpam-6838	233	16	!	!	PUNCT
ejpam-6838	234	1	(	(	PUNCT
ejpam-6838	234	2	3	3	NUM
ejpam-6838	234	3	2	2	NUM
ejpam-6838	234	4	)	)	PUNCT
ejpam-6838	234	5	⌊	⌊	VERB
ejpam-6838	234	6	j+1	j+1	ADV
ejpam-6838	234	7	2	2	NUM
ejpam-6838	234	8	⌋−	⌋−	PUNCT
ejpam-6838	234	9	j−r	j−r	PROPN
ejpam-6838	234	10	2	2	NUM
ejpam-6838	234	11	γ	γ	X
ejpam-6838	234	12	(	(	PUNCT
ejpam-6838	234	13	−1	−1	NOUN
ejpam-6838	234	14	2(j	2(j	NUM
ejpam-6838	234	15	−	−	NOUN
ejpam-6838	234	16	r	r	NOUN
ejpam-6838	234	17	)	)	PUNCT
ejpam-6838	235	1	+	+	CCONJ
ejpam-6838	235	2	⌊	⌊	X
ejpam-6838	235	3	j	j	PROPN
ejpam-6838	235	4	2	2	NUM
ejpam-6838	235	5	⌋	⌋	NOUN
ejpam-6838	235	6	+	+	CCONJ
ejpam-6838	235	7	1	1	X
ejpam-6838	235	8	)	)	PUNCT
ejpam-6838	235	9	(	(	PUNCT
ejpam-6838	235	10	2	2	NUM
ejpam-6838	235	11	t−	t−	PROPN
ejpam-6838	235	12	1)r	1)r	NUM
ejpam-6838	235	13	,	,	PUNCT
ejpam-6838	235	14	(	(	PUNCT
ejpam-6838	235	15	38	38	NUM
ejpam-6838	235	16	)	)	PUNCT
ejpam-6838	235	17	the	the	DET
ejpam-6838	235	18	last	last	ADJ
ejpam-6838	235	19	equation	equation	NOUN
ejpam-6838	235	20	can	can	AUX
ejpam-6838	235	21	be	be	AUX
ejpam-6838	235	22	rewritten	rewrite	VERB
ejpam-6838	235	23	after	after	ADP
ejpam-6838	235	24	using	use	VERB
ejpam-6838	235	25	the	the	DET
ejpam-6838	235	26	relation	relation	NOUN
ejpam-6838	235	27	(	(	PUNCT
ejpam-6838	235	28	2	2	NUM
ejpam-6838	235	29	t−1)2	t−1)2	NOUN
ejpam-6838	235	30	=	=	SYM
ejpam-6838	235	31	r∑	r∑	NOUN
ejpam-6838	235	32	n=0	n=0	NUM
ejpam-6838	235	33	(	(	PUNCT
ejpam-6838	235	34	2	2	NUM
ejpam-6838	235	35	t)n(−1)r−n	t)n(−1)r−n	NOUN
ejpam-6838	235	36	(	(	PUNCT
ejpam-6838	235	37	r	r	NOUN
ejpam-6838	235	38	n	n	PROPN
ejpam-6838	235	39	)	)	PUNCT
ejpam-6838	235	40	,	,	PUNCT
ejpam-6838	235	41	expanding	expand	VERB
ejpam-6838	235	42	,	,	PUNCT
ejpam-6838	235	43	rearranging	rearrange	VERB
ejpam-6838	235	44	and	and	CCONJ
ejpam-6838	235	45	collecting	collect	VERB
ejpam-6838	235	46	similar	similar	ADJ
ejpam-6838	235	47	terms	term	NOUN
ejpam-6838	235	48	as	as	ADP
ejpam-6838	235	49	h∗	h∗	PROPN
ejpam-6838	235	50	j	j	PROPN
ejpam-6838	235	51	(	(	PUNCT
ejpam-6838	235	52	t	t	PROPN
ejpam-6838	235	53	)	)	PUNCT
ejpam-6838	235	54	=	=	PUNCT
ejpam-6838	236	1	j∑	j∑	PROPN
ejpam-6838	237	1	r=0	r=0	PROPN
ejpam-6838	237	2	j∑	j∑	PROPN
ejpam-6838	237	3	m=0	m=0	PROPN
ejpam-6838	237	4	2r	2r	NUM
ejpam-6838	237	5	(	(	PUNCT
ejpam-6838	237	6	−1	−1	NOUN
ejpam-6838	237	7	)	)	PUNCT
ejpam-6838	237	8	j−m	j−m	ADJ
ejpam-6838	237	9	2	2	NUM
ejpam-6838	237	10	(	(	PUNCT
ejpam-6838	237	11	−1)m−r	−1)m−r	NOUN
ejpam-6838	237	12	aj+m	aj+m	PROPN
ejpam-6838	237	13	(	(	PUNCT
ejpam-6838	237	14	m	m	NOUN
ejpam-6838	237	15	r	r	NOUN
ejpam-6838	237	16	)	)	PUNCT
ejpam-6838	237	17	(	(	PUNCT
ejpam-6838	237	18	3	3	X
ejpam-6838	237	19	)	)	PUNCT
ejpam-6838	237	20	j+m	j+m	NOUN
ejpam-6838	237	21	2	2	NUM
ejpam-6838	237	22	(	(	PUNCT
ejpam-6838	237	23	j−m	j−m	NOUN
ejpam-6838	237	24	2	2	NUM
ejpam-6838	237	25	)	)	PUNCT
ejpam-6838	237	26	!	!	PUNCT
ejpam-6838	238	1	(	(	PUNCT
ejpam-6838	238	2	3	3	NUM
ejpam-6838	238	3	2	2	NUM
ejpam-6838	238	4	)	)	PUNCT
ejpam-6838	238	5	m−j	m−j	NOUN
ejpam-6838	238	6	2	2	NUM
ejpam-6838	239	1	+	+	NOUN
ejpam-6838	239	2	⌊	⌊	PROPN
ejpam-6838	239	3	j+1	j+1	ADJ
ejpam-6838	239	4	2	2	NUM
ejpam-6838	239	5	⌋	⌋	NOUN
ejpam-6838	239	6	γ	γ	X
ejpam-6838	239	7	(	(	PUNCT
ejpam-6838	239	8	1	1	NUM
ejpam-6838	239	9	2(−j	2(−j	NUM
ejpam-6838	239	10	+	+	NOUN
ejpam-6838	239	11	m+	m+	NUM
ejpam-6838	239	12	2	2	NUM
ejpam-6838	239	13	)	)	PUNCT
ejpam-6838	240	1	+	+	CCONJ
ejpam-6838	240	2	⌊	⌊	PROPN
ejpam-6838	240	3	j	j	PROPN
ejpam-6838	240	4	2	2	NUM
ejpam-6838	240	5	⌋	⌋	NOUN
ejpam-6838	240	6	)	)	PUNCT
ejpam-6838	240	7	tr	tr	VERB
ejpam-6838	240	8	.	.	PUNCT
ejpam-6838	240	9	(	(	PUNCT
ejpam-6838	240	10	39	39	NUM
ejpam-6838	240	11	)	)	PUNCT
ejpam-6838	240	12	therefore	therefore	ADV
ejpam-6838	240	13	,	,	PUNCT
ejpam-6838	240	14	the	the	DET
ejpam-6838	240	15	identity	identity	NOUN
ejpam-6838	240	16	of	of	ADP
ejpam-6838	240	17	fractional	fractional	PROPN
ejpam-6838	240	18	caputo	caputo	PROPN
ejpam-6838	240	19	derivative	derivative	NOUN
ejpam-6838	240	20	(	(	PUNCT
ejpam-6838	240	21	3	3	NUM
ejpam-6838	240	22	)	)	PUNCT
ejpam-6838	240	23	along	along	ADP
ejpam-6838	240	24	with	with	ADP
ejpam-6838	240	25	eq	eq	NOUN
ejpam-6838	240	26	.	.	PUNCT
ejpam-6838	241	1	(	(	PUNCT
ejpam-6838	241	2	39	39	NUM
ejpam-6838	241	3	)	)	PUNCT
ejpam-6838	241	4	enables	enable	VERB
ejpam-6838	241	5	us	we	PRON
ejpam-6838	241	6	w.	w.	PROPN
ejpam-6838	241	7	m.	m.	PROPN
ejpam-6838	241	8	abd	abd	PROPN
ejpam-6838	241	9	-	-	PUNCT
ejpam-6838	241	10	elhameed	elhameed	PROPN
ejpam-6838	241	11	et	et	PROPN
ejpam-6838	241	12	al	al	PROPN
ejpam-6838	241	13	.	.	PUNCT
ejpam-6838	241	14	/	/	SYM
ejpam-6838	241	15	eur	eur	PROPN
ejpam-6838	241	16	.	.	PUNCT
ejpam-6838	242	1	j.	j.	PROPN
ejpam-6838	242	2	pure	pure	PROPN
ejpam-6838	242	3	appl	appl	PROPN
ejpam-6838	242	4	.	.	PROPN
ejpam-6838	242	5	math	math	PROPN
ejpam-6838	242	6	,	,	PUNCT
ejpam-6838	242	7	18	18	NUM
ejpam-6838	242	8	(	(	PUNCT
ejpam-6838	242	9	4	4	NUM
ejpam-6838	242	10	)	)	PUNCT
ejpam-6838	242	11	(	(	PUNCT
ejpam-6838	242	12	2025	2025	NUM
ejpam-6838	242	13	)	)	PUNCT
ejpam-6838	242	14	,	,	PUNCT
ejpam-6838	242	15	6838	6838	NUM
ejpam-6838	242	16	11	11	NUM
ejpam-6838	242	17	of	of	ADP
ejpam-6838	242	18	25	25	NUM
ejpam-6838	242	19	to	to	PART
ejpam-6838	242	20	write	write	VERB
ejpam-6838	242	21	dζ	dζ	PROPN
ejpam-6838	242	22	th∗	th∗	ADJ
ejpam-6838	242	23	j	j	PROPN
ejpam-6838	242	24	(	(	PUNCT
ejpam-6838	242	25	t	t	PROPN
ejpam-6838	242	26	)	)	PUNCT
ejpam-6838	242	27	=	=	SYM
ejpam-6838	242	28	j∑	j∑	PROPN
ejpam-6838	243	1	r=1	r=1	NOUN
ejpam-6838	243	2	j∑	j∑	PROPN
ejpam-6838	243	3	m=0	m=0	PROPN
ejpam-6838	243	4	2rr!(−1	2rr!(−1	NUM
ejpam-6838	243	5	)	)	PUNCT
ejpam-6838	243	6	j−m	j−m	ADJ
ejpam-6838	243	7	2	2	NUM
ejpam-6838	243	8	(	(	PUNCT
ejpam-6838	243	9	−1)m−r	−1)m−r	NOUN
ejpam-6838	243	10	aj+m	aj+m	PROPN
ejpam-6838	243	11	(	(	PUNCT
ejpam-6838	243	12	m	m	NOUN
ejpam-6838	243	13	r	r	NOUN
ejpam-6838	243	14	)	)	PUNCT
ejpam-6838	243	15	(	(	PUNCT
ejpam-6838	243	16	3	3	X
ejpam-6838	243	17	)	)	PUNCT
ejpam-6838	243	18	j+m	j+m	NOUN
ejpam-6838	243	19	2	2	NUM
ejpam-6838	243	20	(	(	PUNCT
ejpam-6838	243	21	j−m	j−m	NOUN
ejpam-6838	243	22	2	2	NUM
ejpam-6838	243	23	)	)	PUNCT
ejpam-6838	243	24	!	!	PUNCT
ejpam-6838	244	1	γ(r	γ(r	PROPN
ejpam-6838	245	1	−	−	NOUN
ejpam-6838	245	2	α+	α+	NOUN
ejpam-6838	245	3	1	1	NUM
ejpam-6838	245	4	)	)	PUNCT
ejpam-6838	245	5	(	(	PUNCT
ejpam-6838	245	6	3	3	NUM
ejpam-6838	245	7	2	2	NUM
ejpam-6838	245	8	)	)	PUNCT
ejpam-6838	245	9	m−j	m−j	NOUN
ejpam-6838	245	10	2	2	NUM
ejpam-6838	246	1	+	+	NOUN
ejpam-6838	246	2	⌊	⌊	PROPN
ejpam-6838	246	3	j+1	j+1	ADJ
ejpam-6838	246	4	2	2	NUM
ejpam-6838	246	5	⌋	⌋	NOUN
ejpam-6838	246	6	γ	γ	X
ejpam-6838	246	7	(	(	PUNCT
ejpam-6838	246	8	1	1	NUM
ejpam-6838	246	9	2(−j	2(−j	NUM
ejpam-6838	246	10	+	+	NOUN
ejpam-6838	246	11	m+	m+	NUM
ejpam-6838	246	12	2	2	NUM
ejpam-6838	246	13	)	)	PUNCT
ejpam-6838	247	1	+	+	CCONJ
ejpam-6838	247	2	⌊	⌊	PROPN
ejpam-6838	247	3	j	j	PROPN
ejpam-6838	247	4	2	2	NUM
ejpam-6838	247	5	⌋	⌋	NOUN
ejpam-6838	247	6	)	)	PUNCT
ejpam-6838	247	7	tr−ζ	tr−ζ	VERB
ejpam-6838	247	8	.	.	PUNCT
ejpam-6838	248	1	(	(	PUNCT
ejpam-6838	248	2	40	40	NUM
ejpam-6838	248	3	)	)	PUNCT
ejpam-6838	248	4	now	now	ADV
ejpam-6838	248	5	,	,	PUNCT
ejpam-6838	248	6	kj	kj	PROPN
ejpam-6838	248	7	,	,	PUNCT
ejpam-6838	248	8	s	s	AUX
ejpam-6838	248	9	is	be	AUX
ejpam-6838	248	10	given	give	VERB
ejpam-6838	248	11	by	by	ADP
ejpam-6838	248	12	kj	kj	PROPN
ejpam-6838	248	13	,	,	PUNCT
ejpam-6838	248	14	s	s	PART
ejpam-6838	248	15	=	=	NOUN
ejpam-6838	248	16	∫	∫	PROPN
ejpam-6838	248	17	1	1	NUM
ejpam-6838	248	18	0	0	NUM
ejpam-6838	248	19	dζ	dζ	PROPN
ejpam-6838	248	20	th∗	th∗	ADJ
ejpam-6838	248	21	j	j	PROPN
ejpam-6838	248	22	(	(	PUNCT
ejpam-6838	248	23	t)h∗	t)h∗	NOUN
ejpam-6838	248	24	s(t)w	s(t)w	NOUN
ejpam-6838	248	25	∗(t	∗(t	NOUN
ejpam-6838	248	26	)	)	PUNCT
ejpam-6838	248	27	dt	dt	NOUN
ejpam-6838	249	1	=	=	SYM
ejpam-6838	249	2	j∑	j∑	PROPN
ejpam-6838	249	3	r=1	r=1	PROPN
ejpam-6838	249	4	j∑	j∑	PROPN
ejpam-6838	249	5	m=0	m=0	PROPN
ejpam-6838	249	6	2rr!(−1	2rr!(−1	NUM
ejpam-6838	249	7	)	)	PUNCT
ejpam-6838	249	8	j−m	j−m	ADJ
ejpam-6838	249	9	2	2	NUM
ejpam-6838	249	10	(	(	PUNCT
ejpam-6838	249	11	−1)m−r	−1)m−r	NOUN
ejpam-6838	249	12	aj+m	aj+m	PROPN
ejpam-6838	249	13	(	(	PUNCT
ejpam-6838	249	14	m	m	NOUN
ejpam-6838	249	15	r	r	NOUN
ejpam-6838	249	16	)	)	PUNCT
ejpam-6838	249	17	(	(	PUNCT
ejpam-6838	249	18	3	3	X
ejpam-6838	249	19	)	)	PUNCT
ejpam-6838	249	20	j+m	j+m	NOUN
ejpam-6838	249	21	2	2	NUM
ejpam-6838	249	22	(	(	PUNCT
ejpam-6838	249	23	j−m	j−m	NOUN
ejpam-6838	249	24	2	2	NUM
ejpam-6838	249	25	)	)	PUNCT
ejpam-6838	249	26	!	!	PUNCT
ejpam-6838	250	1	γ(r	γ(r	PROPN
ejpam-6838	251	1	−	−	NOUN
ejpam-6838	251	2	α+	α+	NOUN
ejpam-6838	251	3	1	1	NUM
ejpam-6838	251	4	)	)	PUNCT
ejpam-6838	251	5	(	(	PUNCT
ejpam-6838	251	6	3	3	NUM
ejpam-6838	251	7	2	2	NUM
ejpam-6838	251	8	)	)	PUNCT
ejpam-6838	251	9	m−j	m−j	NOUN
ejpam-6838	251	10	2	2	NUM
ejpam-6838	252	1	+	+	NOUN
ejpam-6838	252	2	⌊	⌊	PROPN
ejpam-6838	252	3	j+1	j+1	ADJ
ejpam-6838	252	4	2	2	NUM
ejpam-6838	252	5	⌋	⌋	NOUN
ejpam-6838	252	6	γ	γ	X
ejpam-6838	252	7	(	(	PUNCT
ejpam-6838	252	8	1	1	NUM
ejpam-6838	252	9	2(−j	2(−j	NUM
ejpam-6838	252	10	+	+	NOUN
ejpam-6838	252	11	m+	m+	NUM
ejpam-6838	252	12	2	2	NUM
ejpam-6838	252	13	)	)	PUNCT
ejpam-6838	253	1	+	+	CCONJ
ejpam-6838	253	2	⌊	⌊	PROPN
ejpam-6838	253	3	j	j	PROPN
ejpam-6838	253	4	2	2	NUM
ejpam-6838	253	5	⌋)×	⌋)×	PROPN
ejpam-6838	253	6	∫	∫	NOUN
ejpam-6838	253	7	1	1	NUM
ejpam-6838	253	8	0	0	NUM
ejpam-6838	253	9	tr−ζh∗	tr−ζh∗	NOUN
ejpam-6838	253	10	s(t)w	s(t)w	NOUN
ejpam-6838	253	11	∗(t	∗(t	NOUN
ejpam-6838	253	12	)	)	PUNCT
ejpam-6838	254	1	dt	dt	NOUN
ejpam-6838	255	1	=	=	SYM
ejpam-6838	255	2	j∑	j∑	PROPN
ejpam-6838	255	3	r=1	r=1	PROPN
ejpam-6838	255	4	j∑	j∑	PROPN
ejpam-6838	255	5	m=0	m=0	PROPN
ejpam-6838	255	6	2rr!(−1	2rr!(−1	NUM
ejpam-6838	255	7	)	)	PUNCT
ejpam-6838	255	8	j−m	j−m	ADJ
ejpam-6838	255	9	2	2	NUM
ejpam-6838	255	10	(	(	PUNCT
ejpam-6838	255	11	−1)m−r	−1)m−r	NOUN
ejpam-6838	255	12	aj+m	aj+m	PROPN
ejpam-6838	255	13	(	(	PUNCT
ejpam-6838	255	14	m	m	NOUN
ejpam-6838	255	15	r	r	NOUN
ejpam-6838	255	16	)	)	PUNCT
ejpam-6838	255	17	(	(	PUNCT
ejpam-6838	255	18	3	3	X
ejpam-6838	255	19	)	)	PUNCT
ejpam-6838	255	20	j+m	j+m	NOUN
ejpam-6838	255	21	2	2	NUM
ejpam-6838	255	22	(	(	PUNCT
ejpam-6838	255	23	j−m	j−m	NOUN
ejpam-6838	255	24	2	2	NUM
ejpam-6838	255	25	)	)	PUNCT
ejpam-6838	255	26	!	!	PUNCT
ejpam-6838	256	1	γ(r	γ(r	PROPN
ejpam-6838	257	1	−	−	NOUN
ejpam-6838	257	2	α+	α+	NOUN
ejpam-6838	257	3	1	1	NUM
ejpam-6838	257	4	)	)	PUNCT
ejpam-6838	257	5	(	(	PUNCT
ejpam-6838	257	6	3	3	NUM
ejpam-6838	257	7	2	2	NUM
ejpam-6838	257	8	)	)	PUNCT
ejpam-6838	257	9	m−j	m−j	NOUN
ejpam-6838	257	10	2	2	NUM
ejpam-6838	258	1	+	+	NOUN
ejpam-6838	258	2	⌊	⌊	PROPN
ejpam-6838	258	3	j+1	j+1	ADJ
ejpam-6838	258	4	2	2	NUM
ejpam-6838	258	5	⌋	⌋	NOUN
ejpam-6838	258	6	γ	γ	X
ejpam-6838	258	7	(	(	PUNCT
ejpam-6838	258	8	1	1	NUM
ejpam-6838	258	9	2(−j	2(−j	NUM
ejpam-6838	258	10	+	+	NOUN
ejpam-6838	258	11	m+	m+	NUM
ejpam-6838	258	12	2	2	NUM
ejpam-6838	258	13	)	)	PUNCT
ejpam-6838	259	1	+	+	CCONJ
ejpam-6838	259	2	⌊	⌊	PROPN
ejpam-6838	259	3	j	j	PROPN
ejpam-6838	259	4	2	2	NUM
ejpam-6838	259	5	⌋	⌋	NOUN
ejpam-6838	259	6	)	)	PUNCT
ejpam-6838	259	7	×	×	NOUN
ejpam-6838	259	8	s∑	s∑	PROPN
ejpam-6838	259	9	p=0	p=0	PROPN
ejpam-6838	260	1	s∑	s∑	PROPN
ejpam-6838	260	2	n=0	n=0	NUM
ejpam-6838	261	1	2p(−1)n−pis−na(n+	2p(−1)n−pis−na(n+	NUM
ejpam-6838	261	2	s	s	X
ejpam-6838	261	3	)	)	PUNCT
ejpam-6838	261	4	(	(	PUNCT
ejpam-6838	261	5	n	n	PRON
ejpam-6838	261	6	p	p	NOUN
ejpam-6838	261	7	)	)	PUNCT
ejpam-6838	261	8	(	(	PUNCT
ejpam-6838	261	9	3)n+s	3)n+s	NUM
ejpam-6838	261	10	2	2	NUM
ejpam-6838	261	11	s−n	s−n	NOUN
ejpam-6838	261	12	2	2	NUM
ejpam-6838	261	13	!	!	PUNCT
ejpam-6838	262	1	(	(	PUNCT
ejpam-6838	262	2	3	3	NUM
ejpam-6838	262	3	2	2	NUM
ejpam-6838	262	4	)	)	PUNCT
ejpam-6838	262	5	n−s	n−s	ADV
ejpam-6838	262	6	2	2	NUM
ejpam-6838	263	1	+	+	ADP
ejpam-6838	263	2	⌊	⌊	VERB
ejpam-6838	263	3	s+1	s+1	NUM
ejpam-6838	263	4	2	2	NUM
ejpam-6838	263	5	⌋	⌋	NOUN
ejpam-6838	263	6	γ	γ	X
ejpam-6838	263	7	(	(	PUNCT
ejpam-6838	263	8	1	1	NUM
ejpam-6838	263	9	2(n−	2(n−	NUM
ejpam-6838	263	10	s+	s+	PUNCT
ejpam-6838	263	11	2	2	NUM
ejpam-6838	263	12	)	)	PUNCT
ejpam-6838	263	13	+	+	CCONJ
ejpam-6838	263	14	⌊	⌊	PROPN
ejpam-6838	263	15	s	s	PART
ejpam-6838	263	16	2	2	NUM
ejpam-6838	263	17	⌋	⌋	NOUN
ejpam-6838	263	18	)	)	PUNCT
ejpam-6838	263	19	∫	∫	PROPN
ejpam-6838	264	1	1	1	NUM
ejpam-6838	264	2	0	0	NUM
ejpam-6838	264	3	(	(	PUNCT
ejpam-6838	264	4	1−	1−	NUM
ejpam-6838	264	5	2	2	NUM
ejpam-6838	264	6	t)2(t	t)2(t	PROPN
ejpam-6838	264	7	(	(	PUNCT
ejpam-6838	264	8	1−	1−	NUM
ejpam-6838	264	9	t))3/2t−α+p+r	t))3/2t−α+p+r	PROPN
ejpam-6838	264	10	dt	dt	PROPN
ejpam-6838	264	11	.	.	PUNCT
ejpam-6838	265	1	(	(	PUNCT
ejpam-6838	265	2	41	41	NUM
ejpam-6838	265	3	)	)	PUNCT
ejpam-6838	265	4	finally	finally	ADV
ejpam-6838	265	5	,	,	PUNCT
ejpam-6838	265	6	after	after	ADP
ejpam-6838	265	7	evaluating	evaluate	VERB
ejpam-6838	265	8	the	the	DET
ejpam-6838	265	9	integral	integral	NOUN
ejpam-6838	265	10	on	on	ADP
ejpam-6838	265	11	the	the	DET
ejpam-6838	265	12	right	right	ADJ
ejpam-6838	265	13	-	-	PUNCT
ejpam-6838	265	14	hand	hand	NOUN
ejpam-6838	265	15	side	side	NOUN
ejpam-6838	265	16	of	of	ADP
ejpam-6838	265	17	the	the	DET
ejpam-6838	265	18	previous	previous	ADJ
ejpam-6838	265	19	equation	equation	NOUN
ejpam-6838	265	20	,	,	PUNCT
ejpam-6838	265	21	we	we	PRON
ejpam-6838	265	22	get	get	VERB
ejpam-6838	265	23	the	the	DET
ejpam-6838	265	24	desired	desire	VERB
ejpam-6838	265	25	result	result	NOUN
ejpam-6838	265	26	(	(	PUNCT
ejpam-6838	265	27	35	35	NUM
ejpam-6838	265	28	)	)	PUNCT
ejpam-6838	265	29	.	.	PUNCT
ejpam-6838	266	1	4	4	X
ejpam-6838	266	2	.	.	X
ejpam-6838	266	3	error	error	NOUN
ejpam-6838	266	4	bound	bind	VERB
ejpam-6838	266	5	in	in	ADP
ejpam-6838	266	6	this	this	DET
ejpam-6838	266	7	part	part	NOUN
ejpam-6838	266	8	,	,	PUNCT
ejpam-6838	266	9	we	we	PRON
ejpam-6838	266	10	analyze	analyze	VERB
ejpam-6838	266	11	the	the	DET
ejpam-6838	266	12	errors	error	NOUN
ejpam-6838	266	13	in	in	ADP
ejpam-6838	266	14	the	the	DET
ejpam-6838	266	15	proposed	propose	VERB
ejpam-6838	266	16	polynomial	polynomial	ADJ
ejpam-6838	266	17	expansion	expansion	NOUN
ejpam-6838	266	18	in	in	ADP
ejpam-6838	266	19	detail	detail	NOUN
ejpam-6838	266	20	.	.	PUNCT
ejpam-6838	267	1	it	it	PRON
ejpam-6838	267	2	is	be	AUX
ejpam-6838	267	3	planned	plan	VERB
ejpam-6838	267	4	to	to	PART
ejpam-6838	267	5	prove	prove	VERB
ejpam-6838	267	6	four	four	NUM
ejpam-6838	267	7	theorems	theorem	NOUN
ejpam-6838	267	8	.	.	PUNCT
ejpam-6838	268	1	•	•	NUM
ejpam-6838	268	2	the	the	DET
ejpam-6838	268	3	first	first	ADJ
ejpam-6838	268	4	theorem	theorem	NOUN
ejpam-6838	268	5	provides	provide	VERB
ejpam-6838	268	6	an	an	DET
ejpam-6838	268	7	upper	upper	ADJ
ejpam-6838	268	8	bound	bind	VERB
ejpam-6838	268	9	for	for	ADP
ejpam-6838	268	10	the	the	DET
ejpam-6838	268	11	truncation	truncation	NOUN
ejpam-6838	268	12	error	error	NOUN
ejpam-6838	268	13	.	.	PUNCT
ejpam-6838	269	1	•	•	NUM
ejpam-6838	269	2	the	the	DET
ejpam-6838	269	3	second	second	ADJ
ejpam-6838	269	4	theorem	theorem	NOUN
ejpam-6838	269	5	,	,	PUNCT
ejpam-6838	269	6	provides	provide	VERB
ejpam-6838	269	7	a	a	DET
ejpam-6838	269	8	maximum	maximum	ADJ
ejpam-6838	269	9	estimate	estimate	NOUN
ejpam-6838	269	10	for	for	ADP
ejpam-6838	269	11	the	the	DET
ejpam-6838	269	12	m	m	PROPN
ejpam-6838	269	13	-	-	PUNCT
ejpam-6838	269	14	th	th	VERB
ejpam-6838	269	15	derivative	derivative	NOUN
ejpam-6838	269	16	of	of	ADP
ejpam-6838	269	17	truncation	truncation	NOUN
ejpam-6838	269	18	error	error	NOUN
ejpam-6838	269	19	with	with	ADP
ejpam-6838	269	20	respect	respect	NOUN
ejpam-6838	269	21	to	to	ADP
ejpam-6838	269	22	the	the	DET
ejpam-6838	269	23	variable	variable	ADJ
ejpam-6838	269	24	x.	x.	NOUN
ejpam-6838	269	25	•	•	ADP
ejpam-6838	269	26	the	the	DET
ejpam-6838	269	27	third	third	ADJ
ejpam-6838	269	28	theorem	theorem	NOUN
ejpam-6838	269	29	provides	provide	VERB
ejpam-6838	269	30	a	a	DET
ejpam-6838	269	31	maximum	maximum	ADJ
ejpam-6838	269	32	estimate	estimate	NOUN
ejpam-6838	269	33	for	for	ADP
ejpam-6838	269	34	the	the	DET
ejpam-6838	269	35	fractional	fractional	ADJ
ejpam-6838	269	36	derivative	derivative	NOUN
ejpam-6838	269	37	of	of	ADP
ejpam-6838	269	38	the	the	DET
ejpam-6838	269	39	truncation	truncation	NOUN
ejpam-6838	269	40	error	error	NOUN
ejpam-6838	269	41	with	with	ADP
ejpam-6838	269	42	respect	respect	NOUN
ejpam-6838	269	43	to	to	ADP
ejpam-6838	269	44	the	the	DET
ejpam-6838	269	45	variable	variable	ADJ
ejpam-6838	269	46	t	t	PROPN
ejpam-6838	269	47	•	•	NOUN
ejpam-6838	269	48	the	the	DET
ejpam-6838	269	49	last	last	ADJ
ejpam-6838	269	50	theorem	theorem	NOUN
ejpam-6838	269	51	shows	show	NOUN
ejpam-6838	269	52	∥rm(x	∥rm(x	PROPN
ejpam-6838	269	53	,	,	PUNCT
ejpam-6838	269	54	t)∥l2	t)∥l2	ADJ
ejpam-6838	269	55	ω(ω	ω(ω	NOUN
ejpam-6838	269	56	)	)	PUNCT
ejpam-6838	269	57	for	for	ADP
ejpam-6838	269	58	sufficiently	sufficiently	ADV
ejpam-6838	269	59	high	high	ADJ
ejpam-6838	269	60	m	m	NOUN
ejpam-6838	269	61	,	,	PUNCT
ejpam-6838	269	62	will	will	AUX
ejpam-6838	269	63	be	be	AUX
ejpam-6838	269	64	small	small	ADJ
ejpam-6838	269	65	enough	enough	ADV
ejpam-6838	269	66	,	,	PUNCT
ejpam-6838	269	67	where	where	SCONJ
ejpam-6838	269	68	ω	ω	NOUN
ejpam-6838	269	69	=	=	SYM
ejpam-6838	269	70	w∗(x)w∗(t	w∗(x)w∗(t	NUM
ejpam-6838	269	71	)	)	PUNCT
ejpam-6838	269	72	.	.	PUNCT
ejpam-6838	270	1	lemma	lemma	PROPN
ejpam-6838	270	2	3	3	X
ejpam-6838	270	3	.	.	PUNCT
ejpam-6838	271	1	[	[	X
ejpam-6838	271	2	62	62	NUM
ejpam-6838	271	3	]	]	PUNCT
ejpam-6838	271	4	given	give	VERB
ejpam-6838	271	5	that	that	SCONJ
ejpam-6838	271	6	m	m	PROPN
ejpam-6838	271	7	≥	≥	NOUN
ejpam-6838	271	8	1	1	NUM
ejpam-6838	271	9	and	and	CCONJ
ejpam-6838	271	10	that	that	SCONJ
ejpam-6838	271	11	m+c	m+c	AUX
ejpam-6838	271	12	>	>	X
ejpam-6838	271	13	1	1	NUM
ejpam-6838	271	14	and	and	CCONJ
ejpam-6838	271	15	m+d	m+d	NUM
ejpam-6838	271	16	>	>	SYM
ejpam-6838	271	17	1	1	NUM
ejpam-6838	271	18	,	,	PUNCT
ejpam-6838	271	19	respectively	respectively	ADV
ejpam-6838	271	20	,	,	PUNCT
ejpam-6838	271	21	for	for	ADP
ejpam-6838	271	22	all	all	DET
ejpam-6838	271	23	constants	constant	NOUN
ejpam-6838	271	24	c	c	NOUN
ejpam-6838	271	25	,	,	PUNCT
ejpam-6838	271	26	d	d	PROPN
ejpam-6838	271	27	,	,	PUNCT
ejpam-6838	271	28	one	one	NUM
ejpam-6838	271	29	has	have	VERB
ejpam-6838	271	30	γ(m	γ(m	PROPN
ejpam-6838	271	31	+	+	CCONJ
ejpam-6838	271	32	c	c	X
ejpam-6838	271	33	)	)	PUNCT
ejpam-6838	271	34	γ(m	γ(m	PROPN
ejpam-6838	271	35	+	+	CCONJ
ejpam-6838	271	36	d	d	X
ejpam-6838	271	37	)	)	PUNCT
ejpam-6838	271	38	≤	≤	NUM
ejpam-6838	271	39	oc	oc	NOUN
ejpam-6838	271	40	,	,	PUNCT
ejpam-6838	271	41	dm	dm	PROPN
ejpam-6838	271	42	mc−d	mc−d	PROPN
ejpam-6838	271	43	,	,	PUNCT
ejpam-6838	271	44	(	(	PUNCT
ejpam-6838	271	45	42	42	X
ejpam-6838	271	46	)	)	PUNCT
ejpam-6838	271	47	w.	w.	PROPN
ejpam-6838	271	48	m.	m.	PROPN
ejpam-6838	271	49	abd	abd	PROPN
ejpam-6838	271	50	-	-	PUNCT
ejpam-6838	271	51	elhameed	elhameed	PROPN
ejpam-6838	271	52	et	et	PROPN
ejpam-6838	271	53	al	al	PROPN
ejpam-6838	271	54	.	.	PUNCT
ejpam-6838	271	55	/	/	SYM
ejpam-6838	271	56	eur	eur	PROPN
ejpam-6838	271	57	.	.	PUNCT
ejpam-6838	272	1	j.	j.	PROPN
ejpam-6838	272	2	pure	pure	PROPN
ejpam-6838	272	3	appl	appl	PROPN
ejpam-6838	272	4	.	.	PROPN
ejpam-6838	272	5	math	math	PROPN
ejpam-6838	272	6	,	,	PUNCT
ejpam-6838	272	7	18	18	NUM
ejpam-6838	272	8	(	(	PUNCT
ejpam-6838	272	9	4	4	NUM
ejpam-6838	272	10	)	)	PUNCT
ejpam-6838	272	11	(	(	PUNCT
ejpam-6838	272	12	2025	2025	NUM
ejpam-6838	272	13	)	)	PUNCT
ejpam-6838	272	14	,	,	PUNCT
ejpam-6838	272	15	6838	6838	NUM
ejpam-6838	272	16	12	12	NUM
ejpam-6838	272	17	of	of	ADP
ejpam-6838	272	18	25	25	NUM
ejpam-6838	272	19	where	where	SCONJ
ejpam-6838	272	20	oc	oc	NOUN
ejpam-6838	272	21	,	,	PUNCT
ejpam-6838	272	22	dm	dm	PROPN
ejpam-6838	272	23	=	=	PUNCT
ejpam-6838	272	24	exp	exp	NOUN
ejpam-6838	272	25	(	(	PUNCT
ejpam-6838	272	26	c−	c−	PROPN
ejpam-6838	272	27	d	d	NOUN
ejpam-6838	272	28	2	2	NUM
ejpam-6838	272	29	(	(	PUNCT
ejpam-6838	272	30	m	m	PROPN
ejpam-6838	272	31	+	+	CCONJ
ejpam-6838	272	32	d−	d−	PROPN
ejpam-6838	272	33	1	1	NUM
ejpam-6838	272	34	)	)	PUNCT
ejpam-6838	272	35	+	+	CCONJ
ejpam-6838	272	36	1	1	NUM
ejpam-6838	272	37	12	12	NUM
ejpam-6838	272	38	(	(	PUNCT
ejpam-6838	272	39	m	m	VERB
ejpam-6838	272	40	+	+	X
ejpam-6838	272	41	c−	c−	NOUN
ejpam-6838	272	42	1	1	NUM
ejpam-6838	272	43	)	)	PUNCT
ejpam-6838	272	44	+	+	CCONJ
ejpam-6838	272	45	(	(	PUNCT
ejpam-6838	272	46	c−	c−	ADJ
ejpam-6838	272	47	d)2	d)2	PROPN
ejpam-6838	272	48	m	m	NOUN
ejpam-6838	272	49	)	)	PUNCT
ejpam-6838	272	50	.	.	PUNCT
ejpam-6838	273	1	(	(	PUNCT
ejpam-6838	273	2	43	43	NUM
ejpam-6838	273	3	)	)	PUNCT
ejpam-6838	273	4	remark	remark	NOUN
ejpam-6838	273	5	2	2	NUM
ejpam-6838	273	6	.	.	PUNCT
ejpam-6838	273	7	for	for	ADP
ejpam-6838	273	8	fixed	fix	VERB
ejpam-6838	273	9	c	c	PROPN
ejpam-6838	273	10	,	,	PUNCT
ejpam-6838	273	11	d.	d.	PROPN
ejpam-6838	273	12	oc	oc	PROPN
ejpam-6838	273	13	,	,	PUNCT
ejpam-6838	273	14	dm	dm	PROPN
ejpam-6838	273	15	can	can	AUX
ejpam-6838	273	16	be	be	AUX
ejpam-6838	273	17	written	write	VERB
ejpam-6838	273	18	as	as	ADP
ejpam-6838	273	19	:	:	PUNCT
ejpam-6838	273	20	oc	oc	PART
ejpam-6838	273	21	,	,	PUNCT
ejpam-6838	273	22	dm	dm	NOUN
ejpam-6838	273	23	=	=	SYM
ejpam-6838	273	24	1	1	NUM
ejpam-6838	273	25	+	+	NOUN
ejpam-6838	273	26	o(m−1	o(m−1	NUM
ejpam-6838	273	27	)	)	PUNCT
ejpam-6838	273	28	.	.	PUNCT
ejpam-6838	274	1	theorem	theorem	ADJ
ejpam-6838	274	2	4	4	NUM
ejpam-6838	274	3	.	.	PUNCT
ejpam-6838	274	4	assume	assume	VERB
ejpam-6838	274	5	that	that	SCONJ
ejpam-6838	274	6	∂i+j	∂i+j	PROPN
ejpam-6838	274	7	λ(x	λ(x	PROPN
ejpam-6838	274	8	,	,	PUNCT
ejpam-6838	274	9	t	t	PROPN
ejpam-6838	274	10	)	)	PUNCT
ejpam-6838	274	11	∂	∂	NOUN
ejpam-6838	274	12	xi	xi	ADP
ejpam-6838	274	13	∂	∂	PROPN
ejpam-6838	274	14	tj	tj	PROPN
ejpam-6838	274	15	∈	∈	PROPN
ejpam-6838	274	16	c(ω	c(ω	PROPN
ejpam-6838	274	17	)	)	PUNCT
ejpam-6838	274	18	,	,	PUNCT
ejpam-6838	275	1	i	i	PRON
ejpam-6838	275	2	,	,	PUNCT
ejpam-6838	275	3	j	j	PROPN
ejpam-6838	275	4	=	=	SYM
ejpam-6838	275	5	0	0	NUM
ejpam-6838	275	6	,	,	PUNCT
ejpam-6838	275	7	1	1	NUM
ejpam-6838	275	8	,	,	PUNCT
ejpam-6838	275	9	2	2	NUM
ejpam-6838	275	10	,	,	PUNCT
ejpam-6838	275	11	.	.	PUNCT
ejpam-6838	275	12	.	.	PUNCT
ejpam-6838	275	13	.	.	PUNCT
ejpam-6838	276	1	,	,	PUNCT
ejpam-6838	276	2	m+	m+	NOUN
ejpam-6838	276	3	1	1	NUM
ejpam-6838	276	4	and	and	CCONJ
ejpam-6838	276	5	λm(x	λm(x	NUM
ejpam-6838	276	6	,	,	PUNCT
ejpam-6838	276	7	t	t	PROPN
ejpam-6838	276	8	)	)	PUNCT
ejpam-6838	276	9	is	be	AUX
ejpam-6838	276	10	the	the	DET
ejpam-6838	276	11	suggested	suggest	VERB
ejpam-6838	276	12	approximate	approximate	ADJ
ejpam-6838	276	13	solution	solution	NOUN
ejpam-6838	276	14	belonging	belong	VERB
ejpam-6838	276	15	to	to	ADP
ejpam-6838	276	16	pm	pm	NOUN
ejpam-6838	276	17	and	and	CCONJ
ejpam-6838	276	18	ℓm	ℓm	ADV
ejpam-6838	276	19	=	=	NOUN
ejpam-6838	276	20	sup	sup	NOUN
ejpam-6838	276	21	(	(	PUNCT
ejpam-6838	276	22	x	x	NOUN
ejpam-6838	276	23	,	,	PUNCT
ejpam-6838	276	24	t)∈ω	t)∈ω	X
ejpam-6838	276	25	∣∣∣∣∣∂2	∣∣∣∣∣∂2	X
ejpam-6838	276	26	(	(	PUNCT
ejpam-6838	276	27	m+1	m+1	NUM
ejpam-6838	276	28	)	)	PUNCT
ejpam-6838	276	29	λ(x	λ(x	PROPN
ejpam-6838	276	30	,	,	PUNCT
ejpam-6838	276	31	t	t	PROPN
ejpam-6838	276	32	)	)	PUNCT
ejpam-6838	276	33	∂	∂	NUM
ejpam-6838	276	34	xm+1	xm+1	PROPN
ejpam-6838	276	35	∂	∂	NUM
ejpam-6838	276	36	tm+1	tm+1	PRON
ejpam-6838	276	37	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6838	276	38	.	.	PUNCT
ejpam-6838	277	1	(	(	PUNCT
ejpam-6838	277	2	44	44	NUM
ejpam-6838	277	3	)	)	PUNCT
ejpam-6838	277	4	consequently	consequently	ADV
ejpam-6838	277	5	,	,	PUNCT
ejpam-6838	277	6	this	this	DET
ejpam-6838	277	7	estimate	estimate	NOUN
ejpam-6838	277	8	is	be	AUX
ejpam-6838	277	9	valid	valid	ADJ
ejpam-6838	277	10	:	:	PUNCT
ejpam-6838	277	11	∥λ(x	∥λ(x	ADJ
ejpam-6838	277	12	,	,	PUNCT
ejpam-6838	277	13	t)−	t)−	PROPN
ejpam-6838	277	14	λm(x	λm(x	ADJ
ejpam-6838	277	15	,	,	PUNCT
ejpam-6838	277	16	t)∥l2	t)∥l2	ADJ
ejpam-6838	277	17	ω(ω	ω(ω	NOUN
ejpam-6838	277	18	)	)	PUNCT
ejpam-6838	277	19	≲	≲	PROPN
ejpam-6838	277	20	ℓm	ℓm	ADP
ejpam-6838	277	21	m	m	PROPN
ejpam-6838	277	22	1	1	NUM
ejpam-6838	277	23	2	2	NUM
ejpam-6838	277	24	(	(	PUNCT
ejpam-6838	277	25	(	(	PUNCT
ejpam-6838	277	26	m+	m+	NOUN
ejpam-6838	277	27	1)!)2	1)!)2	NUM
ejpam-6838	277	28	,	,	PUNCT
ejpam-6838	277	29	(	(	PUNCT
ejpam-6838	277	30	45	45	NUM
ejpam-6838	277	31	)	)	PUNCT
ejpam-6838	277	32	where	where	SCONJ
ejpam-6838	277	33	q1	q1	NOUN
ejpam-6838	277	34	≲	≲	PROPN
ejpam-6838	277	35	q2	q2	NOUN
ejpam-6838	277	36	implies	imply	VERB
ejpam-6838	277	37	the	the	DET
ejpam-6838	277	38	existence	existence	NOUN
ejpam-6838	277	39	of	of	ADP
ejpam-6838	277	40	a	a	DET
ejpam-6838	277	41	constant	constant	ADJ
ejpam-6838	277	42	n	n	NOUN
ejpam-6838	277	43	satisfies	satisfie	NOUN
ejpam-6838	277	44	q1	q1	VERB
ejpam-6838	277	45	≤	≤	NOUN
ejpam-6838	277	46	n	n	PRON
ejpam-6838	277	47	q2	q2	NOUN
ejpam-6838	277	48	.	.	PUNCT
ejpam-6838	278	1	proof	proof	NOUN
ejpam-6838	278	2	.	.	PUNCT
ejpam-6838	279	1	consider	consider	VERB
ejpam-6838	279	2	the	the	DET
ejpam-6838	279	3	following	follow	VERB
ejpam-6838	279	4	taylor	taylor	PROPN
ejpam-6838	279	5	expansion	expansion	NOUN
ejpam-6838	279	6	of	of	ADP
ejpam-6838	279	7	λ(x	λ(x	PROPN
ejpam-6838	279	8	,	,	PUNCT
ejpam-6838	279	9	t	t	PROPN
ejpam-6838	279	10	):	):	PUNCT
ejpam-6838	279	11	χm(x	χm(x	PROPN
ejpam-6838	279	12	,	,	PUNCT
ejpam-6838	279	13	t	t	PROPN
ejpam-6838	279	14	)	)	PUNCT
ejpam-6838	279	15	=	=	PUNCT
ejpam-6838	280	1	m∑	m∑	CCONJ
ejpam-6838	280	2	i=0	i=0	PROPN
ejpam-6838	280	3	m−i∑	m−i∑	ADJ
ejpam-6838	280	4	j=0	j=0	PROPN
ejpam-6838	280	5	(	(	PUNCT
ejpam-6838	280	6	∂i+j	∂i+j	PROPN
ejpam-6838	280	7	λ(x	λ(x	PROPN
ejpam-6838	280	8	,	,	PUNCT
ejpam-6838	280	9	t	t	PROPN
ejpam-6838	280	10	)	)	PUNCT
ejpam-6838	280	11	∂	∂	NOUN
ejpam-6838	280	12	xi	xi	ADP
ejpam-6838	280	13	∂	∂	NOUN
ejpam-6838	280	14	tj	tj	NOUN
ejpam-6838	280	15	)	)	PUNCT
ejpam-6838	280	16	(	(	PUNCT
ejpam-6838	280	17	0,0	0,0	NOUN
ejpam-6838	280	18	)	)	PUNCT
ejpam-6838	280	19	xi	xi	X
ejpam-6838	280	20	tj	tj	PROPN
ejpam-6838	280	21	i	i	PROPN
ejpam-6838	280	22	!	!	PUNCT
ejpam-6838	281	1	j	j	PROPN
ejpam-6838	281	2	!	!	PROPN
ejpam-6838	281	3	,	,	PUNCT
ejpam-6838	281	4	(	(	PUNCT
ejpam-6838	281	5	46	46	X
ejpam-6838	281	6	)	)	PUNCT
ejpam-6838	281	7	λ(x	λ(x	PROPN
ejpam-6838	281	8	,	,	PUNCT
ejpam-6838	281	9	t)−	t)−	PROPN
ejpam-6838	281	10	χm(x	χm(x	NUM
ejpam-6838	281	11	,	,	PUNCT
ejpam-6838	281	12	t	t	PROPN
ejpam-6838	281	13	)	)	PUNCT
ejpam-6838	281	14	=	=	SYM
ejpam-6838	281	15	xm+1	xm+1	PROPN
ejpam-6838	281	16	tm+1	tm+1	NUM
ejpam-6838	281	17	∂2	∂2	NOUN
ejpam-6838	281	18	(	(	PUNCT
ejpam-6838	281	19	m+1	m+1	NUM
ejpam-6838	281	20	)	)	PUNCT
ejpam-6838	281	21	λ(n1	λ(n1	NOUN
ejpam-6838	281	22	,	,	PUNCT
ejpam-6838	281	23	n2	n2	NOUN
ejpam-6838	281	24	)	)	PUNCT
ejpam-6838	281	25	(	(	PUNCT
ejpam-6838	281	26	(	(	PUNCT
ejpam-6838	281	27	m+	m+	NOUN
ejpam-6838	281	28	1)!)2	1)!)2	NUM
ejpam-6838	281	29	∂	∂	NUM
ejpam-6838	281	30	xm+1	xm+1	NUM
ejpam-6838	281	31	∂	∂	NUM
ejpam-6838	281	32	tm+1	tm+1	PROPN
ejpam-6838	281	33	,	,	PUNCT
ejpam-6838	281	34	(	(	PUNCT
ejpam-6838	281	35	n1	n1	NOUN
ejpam-6838	281	36	,	,	PUNCT
ejpam-6838	281	37	n2	n2	ADJ
ejpam-6838	281	38	)	)	PUNCT
ejpam-6838	281	39	∈	∈	PROPN
ejpam-6838	281	40	ω	ω	PROPN
ejpam-6838	281	41	.	.	PUNCT
ejpam-6838	282	1	(	(	PUNCT
ejpam-6838	282	2	47	47	NUM
ejpam-6838	282	3	)	)	PUNCT
ejpam-6838	282	4	since	since	SCONJ
ejpam-6838	282	5	zm(x	zm(x	NUM
ejpam-6838	282	6	,	,	PUNCT
ejpam-6838	282	7	t	t	PROPN
ejpam-6838	282	8	)	)	PUNCT
ejpam-6838	282	9	is	be	AUX
ejpam-6838	282	10	the	the	DET
ejpam-6838	282	11	best	good	ADJ
ejpam-6838	282	12	approximate	approximate	ADJ
ejpam-6838	282	13	solution	solution	NOUN
ejpam-6838	282	14	of	of	ADP
ejpam-6838	282	15	z(x	z(x	PROPN
ejpam-6838	282	16	,	,	PUNCT
ejpam-6838	282	17	t	t	PROPN
ejpam-6838	282	18	)	)	PUNCT
ejpam-6838	282	19	,	,	PUNCT
ejpam-6838	282	20	we	we	PRON
ejpam-6838	282	21	get	get	VERB
ejpam-6838	282	22	,	,	PUNCT
ejpam-6838	282	23	in	in	ADP
ejpam-6838	282	24	accordance	accordance	NOUN
ejpam-6838	282	25	with	with	ADP
ejpam-6838	282	26	the	the	DET
ejpam-6838	282	27	best	good	ADJ
ejpam-6838	282	28	approximation	approximation	NOUN
ejpam-6838	282	29	concept	concept	NOUN
ejpam-6838	282	30	:	:	PUNCT
ejpam-6838	282	31	∥λ(x	∥λ(x	PROPN
ejpam-6838	282	32	,	,	PUNCT
ejpam-6838	282	33	t)−	t)−	PROPN
ejpam-6838	282	34	λm(x	λm(x	NUM
ejpam-6838	282	35	,	,	PUNCT
ejpam-6838	282	36	t)∥2l2	t)∥2l2	VERB
ejpam-6838	282	37	ω(ω	ω(ω	PROPN
ejpam-6838	282	38	)	)	PUNCT
ejpam-6838	282	39	≤	≤	NUM
ejpam-6838	282	40	∥λ(x	∥λ(x	PROPN
ejpam-6838	282	41	,	,	PUNCT
ejpam-6838	282	42	t)−	t)−	PROPN
ejpam-6838	282	43	χm(x	χm(x	NUM
ejpam-6838	282	44	,	,	PUNCT
ejpam-6838	282	45	t)∥2l2	t)∥2l2	VERB
ejpam-6838	282	46	ω(ω	ω(ω	PROPN
ejpam-6838	282	47	)	)	PUNCT
ejpam-6838	282	48	=	=	SYM
ejpam-6838	283	1	∫	∫	PROPN
ejpam-6838	283	2	1	1	NUM
ejpam-6838	283	3	0	0	NUM
ejpam-6838	283	4	∫	∫	PROPN
ejpam-6838	283	5	1	1	NUM
ejpam-6838	283	6	0	0	NUM
ejpam-6838	283	7	ℓm	ℓm	ADP
ejpam-6838	283	8	2	2	NUM
ejpam-6838	283	9	x2	x2	NOUN
ejpam-6838	283	10	(	(	PUNCT
ejpam-6838	283	11	m+1	m+1	NUM
ejpam-6838	283	12	)	)	PUNCT
ejpam-6838	283	13	t2	t2	NOUN
ejpam-6838	283	14	(	(	PUNCT
ejpam-6838	283	15	m+1	m+1	NUM
ejpam-6838	283	16	)	)	PUNCT
ejpam-6838	283	17	(	(	PUNCT
ejpam-6838	283	18	(	(	PUNCT
ejpam-6838	283	19	m+	m+	NUM
ejpam-6838	283	20	1)!)4	1)!)4	NUM
ejpam-6838	283	21	ω	ω	NOUN
ejpam-6838	283	22	dx	dx	PROPN
ejpam-6838	283	23	d	d	X
ejpam-6838	283	24	t	t	PROPN
ejpam-6838	283	25	=	=	SYM
ejpam-6838	283	26	ℓm	ℓm	ADP
ejpam-6838	283	27	2	2	NUM
ejpam-6838	283	28	π	π	NOUN
ejpam-6838	283	29	(	(	PUNCT
ejpam-6838	283	30	(	(	PUNCT
ejpam-6838	283	31	m+	m+	NUM
ejpam-6838	283	32	1)!)4	1)!)4	NUM
ejpam-6838	283	33	(	(	PUNCT
ejpam-6838	283	34	γ	γ	X
ejpam-6838	283	35	(	(	PUNCT
ejpam-6838	283	36	2m+	2m+	NUM
ejpam-6838	283	37	9	9	NUM
ejpam-6838	283	38	2	2	NUM
ejpam-6838	283	39	)	)	PUNCT
ejpam-6838	283	40	γ(2m+	γ(2m+	NOUN
ejpam-6838	283	41	5	5	NUM
ejpam-6838	283	42	)	)	PUNCT
ejpam-6838	283	43	−	−	PROPN
ejpam-6838	283	44	5	5	NUM
ejpam-6838	283	45	γ	γ	X
ejpam-6838	283	46	(	(	PUNCT
ejpam-6838	283	47	2m+	2m+	NUM
ejpam-6838	283	48	11	11	NUM
ejpam-6838	283	49	2	2	NUM
ejpam-6838	283	50	)	)	PUNCT
ejpam-6838	283	51	γ(2m+	γ(2m+	NOUN
ejpam-6838	283	52	6	6	NUM
ejpam-6838	283	53	)	)	PUNCT
ejpam-6838	283	54	+	+	CCONJ
ejpam-6838	283	55	8	8	NUM
ejpam-6838	283	56	γ	γ	X
ejpam-6838	283	57	(	(	PUNCT
ejpam-6838	283	58	2m+	2m+	NUM
ejpam-6838	283	59	13	13	NUM
ejpam-6838	283	60	2	2	NUM
ejpam-6838	283	61	)	)	PUNCT
ejpam-6838	283	62	γ(2m+	γ(2m+	NOUN
ejpam-6838	283	63	7	7	NUM
ejpam-6838	283	64	)	)	PUNCT
ejpam-6838	283	65	−4	−4	X
ejpam-6838	284	1	γ	γ	X
ejpam-6838	284	2	(	(	PUNCT
ejpam-6838	284	3	2m+	2m+	NUM
ejpam-6838	284	4	15	15	NUM
ejpam-6838	284	5	2	2	NUM
ejpam-6838	284	6	)	)	PUNCT
ejpam-6838	284	7	γ(2m+	γ(2m+	NOUN
ejpam-6838	284	8	8)	8)	NUM
ejpam-6838	284	9	)	)	PUNCT
ejpam-6838	284	10	2	2	NUM
ejpam-6838	284	11	.	.	PUNCT
ejpam-6838	285	1	(	(	PUNCT
ejpam-6838	285	2	48	48	NUM
ejpam-6838	285	3	)	)	PUNCT
ejpam-6838	285	4	the	the	DET
ejpam-6838	285	5	following	follow	VERB
ejpam-6838	285	6	estimate	estimate	NOUN
ejpam-6838	285	7	may	may	AUX
ejpam-6838	285	8	be	be	AUX
ejpam-6838	285	9	written	write	VERB
ejpam-6838	285	10	using	use	VERB
ejpam-6838	285	11	lemma	lemma	PROPN
ejpam-6838	285	12	3	3	NUM
ejpam-6838	285	13	.	.	PUNCT
ejpam-6838	285	14	∥λ(x	∥λ(x	PROPN
ejpam-6838	285	15	,	,	PUNCT
ejpam-6838	285	16	t)−	t)−	PROPN
ejpam-6838	285	17	λm(x	λm(x	ADJ
ejpam-6838	285	18	,	,	PUNCT
ejpam-6838	285	19	t)∥l2	t)∥l2	ADJ
ejpam-6838	285	20	ω(ω	ω(ω	NOUN
ejpam-6838	285	21	)	)	PUNCT
ejpam-6838	285	22	≲	≲	PROPN
ejpam-6838	285	23	ℓm	ℓm	ADP
ejpam-6838	285	24	m	m	PROPN
ejpam-6838	285	25	1	1	NUM
ejpam-6838	285	26	2	2	NUM
ejpam-6838	285	27	(	(	PUNCT
ejpam-6838	285	28	(	(	PUNCT
ejpam-6838	285	29	m+	m+	NOUN
ejpam-6838	285	30	1)!)2	1)!)2	NUM
ejpam-6838	285	31	.	.	PUNCT
ejpam-6838	286	1	(	(	PUNCT
ejpam-6838	286	2	49	49	X
ejpam-6838	286	3	)	)	PUNCT
ejpam-6838	286	4	w.	w.	PROPN
ejpam-6838	286	5	m.	m.	PROPN
ejpam-6838	286	6	abd	abd	PROPN
ejpam-6838	286	7	-	-	PUNCT
ejpam-6838	286	8	elhameed	elhameed	PROPN
ejpam-6838	286	9	et	et	PROPN
ejpam-6838	286	10	al	al	PROPN
ejpam-6838	286	11	.	.	PUNCT
ejpam-6838	286	12	/	/	SYM
ejpam-6838	286	13	eur	eur	PROPN
ejpam-6838	286	14	.	.	PUNCT
ejpam-6838	287	1	j.	j.	PROPN
ejpam-6838	287	2	pure	pure	PROPN
ejpam-6838	287	3	appl	appl	PROPN
ejpam-6838	287	4	.	.	PROPN
ejpam-6838	287	5	math	math	PROPN
ejpam-6838	287	6	,	,	PUNCT
ejpam-6838	287	7	18	18	NUM
ejpam-6838	287	8	(	(	PUNCT
ejpam-6838	287	9	4	4	NUM
ejpam-6838	287	10	)	)	PUNCT
ejpam-6838	287	11	(	(	PUNCT
ejpam-6838	287	12	2025	2025	NUM
ejpam-6838	287	13	)	)	PUNCT
ejpam-6838	287	14	,	,	PUNCT
ejpam-6838	287	15	6838	6838	NUM
ejpam-6838	287	16	13	13	NUM
ejpam-6838	287	17	of	of	ADP
ejpam-6838	287	18	25	25	NUM
ejpam-6838	287	19	theorem	theorem	NOUN
ejpam-6838	287	20	5	5	NUM
ejpam-6838	287	21	.	.	PUNCT
ejpam-6838	287	22	suppose	suppose	VERB
ejpam-6838	287	23	that	that	SCONJ
ejpam-6838	287	24	λ(x	λ(x	PROPN
ejpam-6838	287	25	,	,	PUNCT
ejpam-6838	287	26	t	t	PROPN
ejpam-6838	287	27	)	)	PUNCT
ejpam-6838	287	28	,	,	PUNCT
ejpam-6838	287	29	λm(x	λm(x	X
ejpam-6838	287	30	,	,	PUNCT
ejpam-6838	287	31	t	t	PROPN
ejpam-6838	287	32	)	)	PUNCT
ejpam-6838	287	33	and	and	CCONJ
ejpam-6838	287	34	∂i+j	∂i+j	VERB
ejpam-6838	287	35	λ(x	λ(x	PROPN
ejpam-6838	287	36	,	,	PUNCT
ejpam-6838	287	37	t	t	PROPN
ejpam-6838	287	38	)	)	PUNCT
ejpam-6838	287	39	∂	∂	NOUN
ejpam-6838	287	40	xi	xi	ADP
ejpam-6838	287	41	∂	∂	PROPN
ejpam-6838	287	42	tj	tj	NOUN
ejpam-6838	287	43	meet	meet	VERB
ejpam-6838	287	44	the	the	DET
ejpam-6838	287	45	assumption	assumption	NOUN
ejpam-6838	287	46	of	of	ADP
ejpam-6838	287	47	theorem	theorem	ADJ
ejpam-6838	287	48	4	4	NUM
ejpam-6838	287	49	and	and	CCONJ
ejpam-6838	287	50	τm	τm	NOUN
ejpam-6838	287	51	,	,	PUNCT
ejpam-6838	287	52	m	m	VERB
ejpam-6838	287	53	=	=	ADJ
ejpam-6838	287	54	sup	sup	NOUN
ejpam-6838	287	55	(	(	PUNCT
ejpam-6838	287	56	x	x	NOUN
ejpam-6838	287	57	,	,	PUNCT
ejpam-6838	287	58	t)∈ω	t)∈ω	X
ejpam-6838	287	59	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6838	287	60	∂2m−m+2	∂2m−m+2	ADJ
ejpam-6838	287	61	λ(x	λ(x	PROPN
ejpam-6838	287	62	,	,	PUNCT
ejpam-6838	287	63	t	t	PROPN
ejpam-6838	287	64	)	)	PUNCT
ejpam-6838	287	65	∂	∂	NUM
ejpam-6838	288	1	xm−m+1	xm−m+1	PROPN
ejpam-6838	288	2	∂	∂	NUM
ejpam-6838	288	3	tm+1	tm+1	PROPN
ejpam-6838	288	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6838	288	5	,	,	PUNCT
ejpam-6838	288	6	m	m	VERB
ejpam-6838	288	7	∈	∈	PROPN
ejpam-6838	288	8	n	n	CCONJ
ejpam-6838	288	9	,	,	PUNCT
ejpam-6838	288	10	(	(	PUNCT
ejpam-6838	288	11	50	50	NUM
ejpam-6838	288	12	)	)	PUNCT
ejpam-6838	288	13	where	where	SCONJ
ejpam-6838	288	14	n	n	ADV
ejpam-6838	288	15	=	=	SYM
ejpam-6838	288	16	{	{	PUNCT
ejpam-6838	288	17	1	1	NUM
ejpam-6838	288	18	,	,	PUNCT
ejpam-6838	288	19	2	2	NUM
ejpam-6838	288	20	,	,	PUNCT
ejpam-6838	288	21	.	.	PUNCT
ejpam-6838	288	22	.	.	PUNCT
ejpam-6838	288	23	.	.	PUNCT
ejpam-6838	288	24	}	}	PUNCT
ejpam-6838	288	25	.	.	PUNCT
ejpam-6838	289	1	then	then	ADV
ejpam-6838	289	2	,	,	PUNCT
ejpam-6838	289	3	we	we	PRON
ejpam-6838	289	4	can	can	AUX
ejpam-6838	289	5	write∥∥∥∥	write∥∥∥∥	PROPN
ejpam-6838	289	6	∂m	∂m	PROPN
ejpam-6838	289	7	∂	∂	NOUN
ejpam-6838	289	8	xm	xm	NOUN
ejpam-6838	290	1	(	(	PUNCT
ejpam-6838	290	2	λ(x	λ(x	PROPN
ejpam-6838	290	3	,	,	PUNCT
ejpam-6838	290	4	t)−	t)−	PROPN
ejpam-6838	290	5	λm(x	λm(x	NUM
ejpam-6838	290	6	,	,	PUNCT
ejpam-6838	290	7	t	t	PROPN
ejpam-6838	290	8	)	)	PUNCT
ejpam-6838	290	9	)	)	PUNCT
ejpam-6838	290	10	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6838	290	11	l2	l2	NOUN
ejpam-6838	290	12	ω(ω	ω(ω	NOUN
ejpam-6838	290	13	)	)	PUNCT
ejpam-6838	290	14	≲	≲	PROPN
ejpam-6838	290	15	τm	τm	PROPN
ejpam-6838	290	16	,	,	PUNCT
ejpam-6838	290	17	m	m	PROPN
ejpam-6838	290	18	(	(	PUNCT
ejpam-6838	290	19	m	m	PROPN
ejpam-6838	290	20	(	(	PUNCT
ejpam-6838	290	21	m−m	m−m	PROPN
ejpam-6838	290	22	)	)	PUNCT
ejpam-6838	290	23	)	)	PUNCT
ejpam-6838	290	24	1	1	NUM
ejpam-6838	290	25	4	4	NUM
ejpam-6838	290	26	(	(	PUNCT
ejpam-6838	290	27	m+	m+	NOUN
ejpam-6838	290	28	1	1	NUM
ejpam-6838	290	29	)	)	PUNCT
ejpam-6838	290	30	!	!	PUNCT
ejpam-6838	291	1	(	(	PUNCT
ejpam-6838	291	2	m−m+	m−m+	PROPN
ejpam-6838	291	3	1	1	NUM
ejpam-6838	291	4	)	)	PUNCT
ejpam-6838	291	5	!	!	PUNCT
ejpam-6838	291	6	.	.	PUNCT
ejpam-6838	292	1	(	(	PUNCT
ejpam-6838	292	2	51	51	NUM
ejpam-6838	292	3	)	)	PUNCT
ejpam-6838	292	4	proof	proof	NOUN
ejpam-6838	292	5	.	.	PUNCT
ejpam-6838	293	1	assume	assume	VERB
ejpam-6838	293	2	that	that	SCONJ
ejpam-6838	293	3	∂m	∂m	PROPN
ejpam-6838	293	4	χm(x	χm(x	ADP
ejpam-6838	293	5	,	,	PUNCT
ejpam-6838	293	6	t	t	PROPN
ejpam-6838	293	7	)	)	PUNCT
ejpam-6838	293	8	∂	∂	NOUN
ejpam-6838	293	9	xm	xm	PROPN
ejpam-6838	293	10	is	be	AUX
ejpam-6838	293	11	the	the	DET
ejpam-6838	293	12	taylor	taylor	PROPN
ejpam-6838	293	13	expansion	expansion	NOUN
ejpam-6838	293	14	of	of	ADP
ejpam-6838	293	15	∂m	∂m	PROPN
ejpam-6838	293	16	λ(x	λ(x	PROPN
ejpam-6838	293	17	,	,	PUNCT
ejpam-6838	293	18	t	t	PROPN
ejpam-6838	293	19	)	)	PUNCT
ejpam-6838	293	20	∂	∂	NOUN
ejpam-6838	293	21	xm	xm	NOUN
ejpam-6838	293	22	about	about	ADP
ejpam-6838	293	23	the	the	DET
ejpam-6838	293	24	point	point	NOUN
ejpam-6838	293	25	(	(	PUNCT
ejpam-6838	293	26	0	0	NUM
ejpam-6838	293	27	,	,	PUNCT
ejpam-6838	293	28	0	0	NUM
ejpam-6838	293	29	)	)	PUNCT
ejpam-6838	293	30	,	,	PUNCT
ejpam-6838	293	31	then	then	ADV
ejpam-6838	293	32	the	the	DET
ejpam-6838	293	33	residual	residual	ADJ
ejpam-6838	293	34	between	between	ADP
ejpam-6838	293	35	∂m	∂m	PROPN
ejpam-6838	293	36	λ(x	λ(x	PROPN
ejpam-6838	293	37	,	,	PUNCT
ejpam-6838	293	38	t	t	PROPN
ejpam-6838	293	39	)	)	PUNCT
ejpam-6838	293	40	∂	∂	NOUN
ejpam-6838	293	41	xm	xm	PROPN
ejpam-6838	293	42	and	and	CCONJ
ejpam-6838	293	43	∂m	∂m	PROPN
ejpam-6838	293	44	χm(x	χm(x	PROPN
ejpam-6838	293	45	,	,	PUNCT
ejpam-6838	293	46	t	t	PROPN
ejpam-6838	293	47	)	)	PUNCT
ejpam-6838	293	48	∂	∂	NOUN
ejpam-6838	293	49	xm	xm	PROPN
ejpam-6838	293	50	can	can	AUX
ejpam-6838	293	51	be	be	AUX
ejpam-6838	293	52	written	write	VERB
ejpam-6838	293	53	as	as	ADP
ejpam-6838	293	54	[	[	X
ejpam-6838	293	55	63	63	NUM
ejpam-6838	293	56	]	]	PUNCT
ejpam-6838	293	57	∂m	∂m	PROPN
ejpam-6838	293	58	∂	∂	ADV
ejpam-6838	293	59	xm	xm	NOUN
ejpam-6838	293	60	(	(	PUNCT
ejpam-6838	293	61	λ(x	λ(x	PROPN
ejpam-6838	293	62	,	,	PUNCT
ejpam-6838	293	63	t)−	t)−	PROPN
ejpam-6838	293	64	χm(x	χm(x	NUM
ejpam-6838	293	65	,	,	PUNCT
ejpam-6838	293	66	t	t	PROPN
ejpam-6838	293	67	)	)	PUNCT
ejpam-6838	293	68	)	)	PUNCT
ejpam-6838	294	1	=	=	PUNCT
ejpam-6838	294	2	xm−m+1	xm−m+1	PROPN
ejpam-6838	294	3	tm+1	tm+1	PROPN
ejpam-6838	294	4	∂2m−m+2	∂2m−m+2	ADJ
ejpam-6838	294	5	λ(n̄1	λ(n̄1	NOUN
ejpam-6838	294	6	,	,	PUNCT
ejpam-6838	294	7	n̄2	n̄2	NUM
ejpam-6838	294	8	)	)	PUNCT
ejpam-6838	294	9	(	(	PUNCT
ejpam-6838	294	10	m+	m+	NOUN
ejpam-6838	294	11	1	1	NUM
ejpam-6838	294	12	)	)	PUNCT
ejpam-6838	294	13	!	!	PUNCT
ejpam-6838	295	1	(	(	PUNCT
ejpam-6838	295	2	m−m+	m−m+	PROPN
ejpam-6838	295	3	1	1	NUM
ejpam-6838	295	4	)	)	PUNCT
ejpam-6838	295	5	!	!	PUNCT
ejpam-6838	295	6	∂	∂	NUM
ejpam-6838	296	1	xm−m+1	xm−m+1	PROPN
ejpam-6838	296	2	∂	∂	NUM
ejpam-6838	296	3	tm+1	tm+1	PROPN
ejpam-6838	296	4	,	,	PUNCT
ejpam-6838	296	5	(	(	PUNCT
ejpam-6838	296	6	n̄1	n̄1	ADV
ejpam-6838	296	7	,	,	PUNCT
ejpam-6838	296	8	n̄2	n̄2	NOUN
ejpam-6838	296	9	)	)	PUNCT
ejpam-6838	296	10	∈	∈	PROPN
ejpam-6838	296	11	ω	ω	PROPN
ejpam-6838	296	12	.	.	PUNCT
ejpam-6838	296	13	(	(	PUNCT
ejpam-6838	296	14	52	52	NUM
ejpam-6838	296	15	)	)	PUNCT
ejpam-6838	296	16	since	since	SCONJ
ejpam-6838	296	17	∂m	∂m	PROPN
ejpam-6838	296	18	λm(x	λm(x	NUM
ejpam-6838	296	19	,	,	PUNCT
ejpam-6838	296	20	t	t	PROPN
ejpam-6838	296	21	)	)	PUNCT
ejpam-6838	296	22	∂	∂	NOUN
ejpam-6838	297	1	xm	xm	PROPN
ejpam-6838	297	2	is	be	AUX
ejpam-6838	297	3	the	the	DET
ejpam-6838	297	4	best	good	ADJ
ejpam-6838	297	5	approximate	approximate	ADJ
ejpam-6838	297	6	solution	solution	NOUN
ejpam-6838	297	7	of	of	ADP
ejpam-6838	297	8	∂m	∂m	PROPN
ejpam-6838	297	9	λ(x	λ(x	PROPN
ejpam-6838	297	10	,	,	PUNCT
ejpam-6838	297	11	t	t	PROPN
ejpam-6838	297	12	)	)	PUNCT
ejpam-6838	297	13	∂	∂	NOUN
ejpam-6838	297	14	xm	xm	PROPN
ejpam-6838	297	15	,	,	PUNCT
ejpam-6838	297	16	then	then	ADV
ejpam-6838	297	17	according	accord	VERB
ejpam-6838	297	18	to	to	ADP
ejpam-6838	297	19	the	the	DET
ejpam-6838	297	20	definition	definition	NOUN
ejpam-6838	297	21	of	of	ADP
ejpam-6838	297	22	the	the	DET
ejpam-6838	297	23	best	good	ADJ
ejpam-6838	297	24	approximation	approximation	NOUN
ejpam-6838	297	25	,	,	PUNCT
ejpam-6838	297	26	we	we	PRON
ejpam-6838	297	27	get∥∥∥∥	get∥∥∥∥	VERB
ejpam-6838	297	28	∂m	∂m	PROPN
ejpam-6838	297	29	∂	∂	NOUN
ejpam-6838	297	30	xm	xm	NOUN
ejpam-6838	298	1	(	(	PUNCT
ejpam-6838	298	2	λ(x	λ(x	PROPN
ejpam-6838	298	3	,	,	PUNCT
ejpam-6838	298	4	t)−	t)−	PROPN
ejpam-6838	298	5	λm(x	λm(x	NUM
ejpam-6838	298	6	,	,	PUNCT
ejpam-6838	298	7	t	t	PROPN
ejpam-6838	298	8	)	)	PUNCT
ejpam-6838	298	9	)	)	PUNCT
ejpam-6838	298	10	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6838	298	11	l2	l2	NOUN
ejpam-6838	298	12	ω(ω	ω(ω	NOUN
ejpam-6838	298	13	)	)	PUNCT
ejpam-6838	298	14	≤	≤	NOUN
ejpam-6838	298	15	∥∥∥∥	∥∥∥∥	NUM
ejpam-6838	299	1	∂m	∂m	PROPN
ejpam-6838	299	2	∂	∂	NUM
ejpam-6838	299	3	xm	xm	NOUN
ejpam-6838	299	4	(	(	PUNCT
ejpam-6838	299	5	λ(x	λ(x	PROPN
ejpam-6838	299	6	,	,	PUNCT
ejpam-6838	299	7	t)−	t)−	PROPN
ejpam-6838	299	8	χm(x	χm(x	NUM
ejpam-6838	299	9	,	,	PUNCT
ejpam-6838	299	10	t	t	PROPN
ejpam-6838	299	11	)	)	PUNCT
ejpam-6838	299	12	)	)	PUNCT
ejpam-6838	299	13	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6838	299	14	l2	l2	NOUN
ejpam-6838	299	15	ω(ω	ω(ω	NUM
ejpam-6838	299	16	)	)	PUNCT
ejpam-6838	299	17	.	.	PUNCT
ejpam-6838	300	1	(	(	PUNCT
ejpam-6838	300	2	53	53	NUM
ejpam-6838	300	3	)	)	PUNCT
ejpam-6838	300	4	we	we	PRON
ejpam-6838	300	5	get	get	VERB
ejpam-6838	300	6	the	the	DET
ejpam-6838	300	7	desired	desire	VERB
ejpam-6838	300	8	result	result	NOUN
ejpam-6838	300	9	by	by	ADP
ejpam-6838	300	10	following	follow	VERB
ejpam-6838	300	11	similar	similar	ADJ
ejpam-6838	300	12	steps	step	NOUN
ejpam-6838	300	13	to	to	ADP
ejpam-6838	300	14	those	those	PRON
ejpam-6838	300	15	followed	follow	VERB
ejpam-6838	300	16	in	in	ADP
ejpam-6838	300	17	theorem	theorem	ADJ
ejpam-6838	300	18	4	4	NUM
ejpam-6838	300	19	.	.	PUNCT
ejpam-6838	300	20	theorem	theorem	NOUN
ejpam-6838	300	21	6	6	NUM
ejpam-6838	300	22	.	.	PUNCT
ejpam-6838	300	23	suppose	suppose	VERB
ejpam-6838	300	24	that	that	SCONJ
ejpam-6838	300	25	dζ	dζ	PROPN
ejpam-6838	300	26	t	t	PROPN
ejpam-6838	300	27	λ(x	λ(x	PROPN
ejpam-6838	300	28	,	,	PUNCT
ejpam-6838	300	29	t	t	PROPN
ejpam-6838	300	30	)	)	PUNCT
ejpam-6838	300	31	∈	∈	PROPN
ejpam-6838	300	32	c(ω	c(ω	PROPN
ejpam-6838	300	33	)	)	PUNCT
ejpam-6838	300	34	satisfies	satisfy	VERB
ejpam-6838	300	35	the	the	DET
ejpam-6838	300	36	conditions	condition	NOUN
ejpam-6838	300	37	of	of	ADP
ejpam-6838	300	38	theorem	theorem	NOUN
ejpam-6838	300	39	4	4	NUM
ejpam-6838	300	40	,	,	PUNCT
ejpam-6838	300	41	then	then	ADV
ejpam-6838	300	42	the	the	DET
ejpam-6838	300	43	following	follow	VERB
ejpam-6838	300	44	estimation	estimation	NOUN
ejpam-6838	300	45	holds∥∥∥dζ	holds∥∥∥dζ	VERB
ejpam-6838	300	46	t	t	NOUN
ejpam-6838	300	47	(	(	PUNCT
ejpam-6838	300	48	λ(x	λ(x	PROPN
ejpam-6838	300	49	,	,	PUNCT
ejpam-6838	300	50	t)−	t)−	PROPN
ejpam-6838	300	51	λm(x	λm(x	NUM
ejpam-6838	300	52	,	,	PUNCT
ejpam-6838	300	53	t	t	PROPN
ejpam-6838	300	54	)	)	PUNCT
ejpam-6838	300	55	)	)	PUNCT
ejpam-6838	300	56	∥∥∥	∥∥∥	PROPN
ejpam-6838	300	57	l2	l2	NOUN
ejpam-6838	300	58	ω(ω	ω(ω	NOUN
ejpam-6838	300	59	)	)	PUNCT
ejpam-6838	300	60	≲	≲	PROPN
ejpam-6838	300	61	ℓm	ℓm	ADP
ejpam-6838	300	62	m	m	PROPN
ejpam-6838	300	63	1	1	NUM
ejpam-6838	300	64	4	4	NUM
ejpam-6838	300	65	(	(	PUNCT
ejpam-6838	300	66	m−	m−	PROPN
ejpam-6838	300	67	ζ	ζ	NOUN
ejpam-6838	300	68	)	)	PUNCT
ejpam-6838	300	69	1	1	NUM
ejpam-6838	300	70	4	4	NUM
ejpam-6838	300	71	(	(	PUNCT
ejpam-6838	300	72	m+	m+	NOUN
ejpam-6838	300	73	1	1	NUM
ejpam-6838	300	74	)	)	PUNCT
ejpam-6838	300	75	!	!	PUNCT
ejpam-6838	301	1	γ(m+	γ(m+	PUNCT
ejpam-6838	302	1	2−	2−	NUM
ejpam-6838	302	2	ζ	ζ	NOUN
ejpam-6838	302	3	)	)	PUNCT
ejpam-6838	302	4	.	.	PUNCT
ejpam-6838	303	1	(	(	PUNCT
ejpam-6838	303	2	54	54	NUM
ejpam-6838	303	3	)	)	PUNCT
ejpam-6838	303	4	proof	proof	NOUN
ejpam-6838	303	5	.	.	PUNCT
ejpam-6838	304	1	according	accord	VERB
ejpam-6838	304	2	to	to	ADP
ejpam-6838	304	3	eq	eq	PROPN
ejpam-6838	304	4	.	.	PUNCT
ejpam-6838	305	1	(	(	PUNCT
ejpam-6838	305	2	47	47	NUM
ejpam-6838	305	3	)	)	PUNCT
ejpam-6838	305	4	and	and	CCONJ
ejpam-6838	305	5	properties	property	NOUN
ejpam-6838	305	6	of	of	ADP
ejpam-6838	305	7	the	the	DET
ejpam-6838	305	8	caputo	caputo	PROPN
ejpam-6838	305	9	operator	operator	NOUN
ejpam-6838	305	10	in	in	ADP
ejpam-6838	305	11	(	(	PUNCT
ejpam-6838	305	12	3	3	NUM
ejpam-6838	305	13	)	)	PUNCT
ejpam-6838	305	14	,	,	PUNCT
ejpam-6838	305	15	one	one	NUM
ejpam-6838	305	16	gets∣∣∣dζ	gets∣∣∣dζ	NOUN
ejpam-6838	305	17	t	t	PROPN
ejpam-6838	305	18	(	(	PUNCT
ejpam-6838	305	19	λ(x	λ(x	PROPN
ejpam-6838	305	20	,	,	PUNCT
ejpam-6838	305	21	t)−	t)−	PROPN
ejpam-6838	305	22	χm(x	χm(x	NUM
ejpam-6838	305	23	,	,	PUNCT
ejpam-6838	305	24	t	t	PROPN
ejpam-6838	305	25	)	)	PUNCT
ejpam-6838	305	26	)	)	PUNCT
ejpam-6838	306	1	∣∣∣	∣∣∣	ADP
ejpam-6838	306	2	≤	≤	NUM
ejpam-6838	306	3	xm+1	xm+1	NUM
ejpam-6838	306	4	tm+1−ζ	tm+1−ζ	NOUN
ejpam-6838	306	5	ℓm	ℓm	ADP
ejpam-6838	306	6	γ(m+	γ(m+	NUM
ejpam-6838	306	7	2−	2−	NUM
ejpam-6838	306	8	ζ	ζ	NOUN
ejpam-6838	306	9	)	)	PUNCT
ejpam-6838	306	10	(	(	PUNCT
ejpam-6838	306	11	m+	m+	NOUN
ejpam-6838	306	12	1	1	NUM
ejpam-6838	306	13	)	)	PUNCT
ejpam-6838	306	14	!	!	PUNCT
ejpam-6838	307	1	,	,	PUNCT
ejpam-6838	307	2	(	(	PUNCT
ejpam-6838	307	3	n1	n1	NOUN
ejpam-6838	307	4	,	,	PUNCT
ejpam-6838	307	5	n2	n2	ADJ
ejpam-6838	307	6	)	)	PUNCT
ejpam-6838	307	7	∈	∈	PROPN
ejpam-6838	307	8	ω	ω	PROPN
ejpam-6838	307	9	.	.	PUNCT
ejpam-6838	307	10	(	(	PUNCT
ejpam-6838	307	11	55	55	NUM
ejpam-6838	307	12	)	)	PUNCT
ejpam-6838	307	13	taking	take	VERB
ejpam-6838	307	14	∥.∥l2	∥.∥l2	PROPN
ejpam-6838	307	15	ω(ω	ω(ω	NOUN
ejpam-6838	307	16	)	)	PUNCT
ejpam-6838	307	17	yields∥∥∥dζ	yields∥∥∥dζ	ADP
ejpam-6838	307	18	t	t	PROPN
ejpam-6838	307	19	(	(	PUNCT
ejpam-6838	307	20	λ(x	λ(x	PROPN
ejpam-6838	307	21	,	,	PUNCT
ejpam-6838	307	22	t)−	t)−	PROPN
ejpam-6838	307	23	λm(x	λm(x	NUM
ejpam-6838	307	24	,	,	PUNCT
ejpam-6838	307	25	t	t	PROPN
ejpam-6838	307	26	)	)	PUNCT
ejpam-6838	307	27	)	)	PUNCT
ejpam-6838	308	1	∥∥∥	∥∥∥	PROPN
ejpam-6838	308	2	l2	l2	NOUN
ejpam-6838	308	3	ω(ω	ω(ω	NOUN
ejpam-6838	308	4	)	)	PUNCT
ejpam-6838	308	5	≤	≤	NUM
ejpam-6838	308	6	∫	∫	PROPN
ejpam-6838	308	7	1	1	NUM
ejpam-6838	308	8	0	0	NUM
ejpam-6838	308	9	∫	∫	PROPN
ejpam-6838	308	10	1	1	NUM
ejpam-6838	308	11	0	0	NUM
ejpam-6838	308	12	ℓm	ℓm	ADP
ejpam-6838	308	13	2	2	NUM
ejpam-6838	308	14	x2	x2	NOUN
ejpam-6838	308	15	(	(	PUNCT
ejpam-6838	308	16	m+1	m+1	NUM
ejpam-6838	308	17	)	)	PUNCT
ejpam-6838	308	18	t2	t2	NOUN
ejpam-6838	308	19	(	(	PUNCT
ejpam-6838	308	20	m+1−ζ	m+1−ζ	NOUN
ejpam-6838	308	21	)	)	PUNCT
ejpam-6838	308	22	(	(	PUNCT
ejpam-6838	308	23	γ(m+	γ(m+	NUM
ejpam-6838	308	24	2−	2−	NUM
ejpam-6838	308	25	ζ))2((m+	ζ))2((m+	NOUN
ejpam-6838	308	26	1)!)2	1)!)2	NUM
ejpam-6838	308	27	ω	ω	NUM
ejpam-6838	308	28	dx	dx	PROPN
ejpam-6838	308	29	d	d	X
ejpam-6838	308	30	t.	t.	PROPN
ejpam-6838	308	31	(	(	PUNCT
ejpam-6838	308	32	56	56	NUM
ejpam-6838	308	33	)	)	PUNCT
ejpam-6838	308	34	now	now	ADV
ejpam-6838	308	35	,	,	PUNCT
ejpam-6838	308	36	imitating	imitate	VERB
ejpam-6838	308	37	similar	similar	ADJ
ejpam-6838	308	38	steps	step	NOUN
ejpam-6838	308	39	as	as	ADP
ejpam-6838	308	40	in	in	ADP
ejpam-6838	308	41	theorem	theorem	NOUN
ejpam-6838	308	42	4	4	NUM
ejpam-6838	308	43	,	,	PUNCT
ejpam-6838	308	44	we	we	PRON
ejpam-6838	308	45	get∥∥∥dζ	get∥∥∥dζ	VERB
ejpam-6838	308	46	t	t	PROPN
ejpam-6838	308	47	(	(	PUNCT
ejpam-6838	308	48	λ(x	λ(x	PROPN
ejpam-6838	308	49	,	,	PUNCT
ejpam-6838	308	50	t)−	t)−	PROPN
ejpam-6838	308	51	λm(x	λm(x	NUM
ejpam-6838	308	52	,	,	PUNCT
ejpam-6838	308	53	t	t	PROPN
ejpam-6838	308	54	)	)	PUNCT
ejpam-6838	308	55	)	)	PUNCT
ejpam-6838	308	56	∥∥∥	∥∥∥	PROPN
ejpam-6838	308	57	l2	l2	NOUN
ejpam-6838	308	58	ω(ω	ω(ω	NOUN
ejpam-6838	308	59	)	)	PUNCT
ejpam-6838	308	60	≲	≲	PROPN
ejpam-6838	308	61	ℓm	ℓm	ADP
ejpam-6838	308	62	m	m	PROPN
ejpam-6838	308	63	1	1	NUM
ejpam-6838	308	64	4	4	NUM
ejpam-6838	308	65	(	(	PUNCT
ejpam-6838	308	66	m−	m−	PROPN
ejpam-6838	308	67	ζ	ζ	NOUN
ejpam-6838	308	68	)	)	PUNCT
ejpam-6838	308	69	1	1	NUM
ejpam-6838	308	70	4	4	NUM
ejpam-6838	308	71	(	(	PUNCT
ejpam-6838	308	72	m+	m+	NOUN
ejpam-6838	308	73	1	1	NUM
ejpam-6838	308	74	)	)	PUNCT
ejpam-6838	308	75	!	!	PUNCT
ejpam-6838	309	1	γ(m+	γ(m+	PUNCT
ejpam-6838	310	1	2−	2−	NUM
ejpam-6838	310	2	ζ	ζ	NOUN
ejpam-6838	310	3	)	)	PUNCT
ejpam-6838	310	4	.	.	PUNCT
ejpam-6838	311	1	(	(	PUNCT
ejpam-6838	311	2	57	57	NUM
ejpam-6838	311	3	)	)	PUNCT
ejpam-6838	311	4	w.	w.	PROPN
ejpam-6838	311	5	m.	m.	PROPN
ejpam-6838	311	6	abd	abd	PROPN
ejpam-6838	311	7	-	-	PUNCT
ejpam-6838	311	8	elhameed	elhameed	PROPN
ejpam-6838	311	9	et	et	PROPN
ejpam-6838	311	10	al	al	PROPN
ejpam-6838	311	11	.	.	PUNCT
ejpam-6838	311	12	/	/	SYM
ejpam-6838	311	13	eur	eur	PROPN
ejpam-6838	311	14	.	.	PUNCT
ejpam-6838	312	1	j.	j.	PROPN
ejpam-6838	312	2	pure	pure	PROPN
ejpam-6838	312	3	appl	appl	PROPN
ejpam-6838	312	4	.	.	PROPN
ejpam-6838	312	5	math	math	PROPN
ejpam-6838	312	6	,	,	PUNCT
ejpam-6838	312	7	18	18	NUM
ejpam-6838	312	8	(	(	PUNCT
ejpam-6838	312	9	4	4	NUM
ejpam-6838	312	10	)	)	PUNCT
ejpam-6838	312	11	(	(	PUNCT
ejpam-6838	312	12	2025	2025	NUM
ejpam-6838	312	13	)	)	PUNCT
ejpam-6838	312	14	,	,	PUNCT
ejpam-6838	312	15	6838	6838	NUM
ejpam-6838	312	16	14	14	NUM
ejpam-6838	312	17	of	of	ADP
ejpam-6838	312	18	25	25	NUM
ejpam-6838	312	19	theorem	theorem	NOUN
ejpam-6838	312	20	7	7	NUM
ejpam-6838	312	21	.	.	PUNCT
ejpam-6838	312	22	assume	assume	VERB
ejpam-6838	312	23	that	that	SCONJ
ejpam-6838	312	24	rm(x	rm(x	NOUN
ejpam-6838	312	25	,	,	PUNCT
ejpam-6838	312	26	t	t	PROPN
ejpam-6838	312	27	)	)	PUNCT
ejpam-6838	312	28	be	be	AUX
ejpam-6838	312	29	the	the	DET
ejpam-6838	312	30	residual	residual	NOUN
ejpam-6838	312	31	of	of	ADP
ejpam-6838	312	32	eq	eq	PROPN
ejpam-6838	312	33	.	.	PUNCT
ejpam-6838	313	1	(	(	PUNCT
ejpam-6838	313	2	17	17	NUM
ejpam-6838	313	3	)	)	PUNCT
ejpam-6838	313	4	,	,	PUNCT
ejpam-6838	313	5	then	then	ADV
ejpam-6838	313	6	∥rm(x	∥rm(x	PROPN
ejpam-6838	313	7	,	,	PUNCT
ejpam-6838	313	8	t)∥l2	t)∥l2	ADJ
ejpam-6838	313	9	ω(ω	ω(ω	NOUN
ejpam-6838	313	10	)	)	PUNCT
ejpam-6838	313	11	will	will	AUX
ejpam-6838	313	12	be	be	AUX
ejpam-6838	313	13	sufficiently	sufficiently	ADV
ejpam-6838	313	14	small	small	ADJ
ejpam-6838	313	15	for	for	ADP
ejpam-6838	313	16	the	the	DET
ejpam-6838	313	17	sufficiently	sufficiently	ADV
ejpam-6838	313	18	large	large	ADJ
ejpam-6838	313	19	values	value	NOUN
ejpam-6838	313	20	of	of	ADP
ejpam-6838	313	21	m.	m.	NOUN
ejpam-6838	313	22	proof	proof	NOUN
ejpam-6838	313	23	.	.	PUNCT
ejpam-6838	314	1	eqs	eqs	PROPN
ejpam-6838	314	2	.	.	PUNCT
ejpam-6838	315	1	(	(	PUNCT
ejpam-6838	315	2	21	21	NUM
ejpam-6838	315	3	)	)	PUNCT
ejpam-6838	315	4	and	and	CCONJ
ejpam-6838	315	5	(	(	PUNCT
ejpam-6838	315	6	17	17	NUM
ejpam-6838	315	7	)	)	PUNCT
ejpam-6838	315	8	enables	enable	VERB
ejpam-6838	315	9	us	we	PRON
ejpam-6838	315	10	too	too	ADV
ejpam-6838	315	11	write	write	VERB
ejpam-6838	315	12	rm(x	rm(x	NOUN
ejpam-6838	315	13	,	,	PUNCT
ejpam-6838	315	14	t	t	PROPN
ejpam-6838	315	15	)	)	PUNCT
ejpam-6838	315	16	as	as	ADP
ejpam-6838	315	17	rm(x	rm(x	NOUN
ejpam-6838	315	18	,	,	PUNCT
ejpam-6838	315	19	t	t	PROPN
ejpam-6838	315	20	)	)	PUNCT
ejpam-6838	315	21	=	=	PUNCT
ejpam-6838	315	22	dζ	dζ	PROPN
ejpam-6838	315	23	t	t	PROPN
ejpam-6838	315	24	(	(	PUNCT
ejpam-6838	315	25	λm(x	λm(x	X
ejpam-6838	315	26	,	,	PUNCT
ejpam-6838	315	27	t)−	t)−	PROPN
ejpam-6838	315	28	λ(x	λ(x	PROPN
ejpam-6838	315	29	,	,	PUNCT
ejpam-6838	315	30	t	t	PROPN
ejpam-6838	315	31	)	)	PUNCT
ejpam-6838	315	32	)	)	PUNCT
ejpam-6838	316	1	−	−	PROPN
ejpam-6838	316	2	β	β	X
ejpam-6838	316	3	∂2	∂2	PROPN
ejpam-6838	316	4	∂	∂	NOUN
ejpam-6838	316	5	x2	x2	NOUN
ejpam-6838	316	6	(	(	PUNCT
ejpam-6838	316	7	λm(x	λm(x	X
ejpam-6838	316	8	,	,	PUNCT
ejpam-6838	316	9	t)−	t)−	PROPN
ejpam-6838	316	10	λ(x	λ(x	PROPN
ejpam-6838	316	11	,	,	PUNCT
ejpam-6838	316	12	t	t	PROPN
ejpam-6838	316	13	)	)	PUNCT
ejpam-6838	316	14	)	)	PUNCT
ejpam-6838	316	15	.	.	PUNCT
ejpam-6838	317	1	(	(	PUNCT
ejpam-6838	317	2	58	58	NUM
ejpam-6838	317	3	)	)	PUNCT
ejpam-6838	317	4	if	if	SCONJ
ejpam-6838	317	5	we	we	PRON
ejpam-6838	317	6	consider	consider	VERB
ejpam-6838	317	7	l2	l2	NOUN
ejpam-6838	317	8	-	-	PUNCT
ejpam-6838	317	9	norm	norm	NOUN
ejpam-6838	317	10	,	,	PUNCT
ejpam-6838	317	11	then	then	ADV
ejpam-6838	317	12	using	use	VERB
ejpam-6838	317	13	theorems	theorem	NOUN
ejpam-6838	317	14	4,5	4,5	NUM
ejpam-6838	317	15	and	and	CCONJ
ejpam-6838	317	16	6	6	NUM
ejpam-6838	317	17	,	,	PUNCT
ejpam-6838	317	18	we	we	PRON
ejpam-6838	317	19	get	get	VERB
ejpam-6838	317	20	∥rm(x	∥rm(x	VERB
ejpam-6838	317	21	,	,	PUNCT
ejpam-6838	317	22	t)∥l2	t)∥l2	ADJ
ejpam-6838	317	23	ω(ω	ω(ω	NOUN
ejpam-6838	317	24	)	)	PUNCT
ejpam-6838	317	25	≲	≲	PROPN
ejpam-6838	317	26	ℓm	ℓm	ADP
ejpam-6838	317	27	m	m	PROPN
ejpam-6838	317	28	1	1	NUM
ejpam-6838	317	29	4	4	NUM
ejpam-6838	317	30	(	(	PUNCT
ejpam-6838	317	31	m−	m−	PROPN
ejpam-6838	317	32	ζ	ζ	NOUN
ejpam-6838	317	33	)	)	PUNCT
ejpam-6838	317	34	1	1	NUM
ejpam-6838	317	35	4	4	NUM
ejpam-6838	317	36	(	(	PUNCT
ejpam-6838	317	37	m+	m+	NOUN
ejpam-6838	317	38	1	1	NUM
ejpam-6838	317	39	)	)	PUNCT
ejpam-6838	317	40	!	!	PUNCT
ejpam-6838	318	1	γ(m+	γ(m+	PUNCT
ejpam-6838	319	1	2−	2−	NUM
ejpam-6838	319	2	ζ	ζ	NOUN
ejpam-6838	319	3	)	)	PUNCT
ejpam-6838	319	4	−	−	NOUN
ejpam-6838	319	5	β	β	X
ejpam-6838	319	6	τm,2	τm,2	PROPN
ejpam-6838	319	7	(	(	PUNCT
ejpam-6838	319	8	m	m	PROPN
ejpam-6838	319	9	(	(	PUNCT
ejpam-6838	319	10	m−	m−	PROPN
ejpam-6838	319	11	2	2	NUM
ejpam-6838	319	12	)	)	PUNCT
ejpam-6838	319	13	)	)	PUNCT
ejpam-6838	319	14	1	1	NUM
ejpam-6838	319	15	4	4	NUM
ejpam-6838	319	16	(	(	PUNCT
ejpam-6838	319	17	m+	m+	NOUN
ejpam-6838	319	18	1	1	NUM
ejpam-6838	319	19	)	)	PUNCT
ejpam-6838	319	20	!	!	PUNCT
ejpam-6838	320	1	(	(	PUNCT
ejpam-6838	320	2	m−	m−	PROPN
ejpam-6838	320	3	2	2	NUM
ejpam-6838	320	4	+	+	CCONJ
ejpam-6838	320	5	1	1	NUM
ejpam-6838	320	6	)	)	PUNCT
ejpam-6838	320	7	!	!	PUNCT
ejpam-6838	320	8	.	.	PUNCT
ejpam-6838	321	1	(	(	PUNCT
ejpam-6838	321	2	59	59	NUM
ejpam-6838	321	3	)	)	PUNCT
ejpam-6838	321	4	for	for	ADP
ejpam-6838	321	5	large	large	ADJ
ejpam-6838	321	6	enough	enough	ADJ
ejpam-6838	321	7	values	value	NOUN
ejpam-6838	321	8	of	of	ADP
ejpam-6838	321	9	m	m	PRON
ejpam-6838	321	10	,	,	PUNCT
ejpam-6838	321	11	it	it	PRON
ejpam-6838	321	12	is	be	AUX
ejpam-6838	321	13	evident	evident	ADJ
ejpam-6838	321	14	from	from	ADP
ejpam-6838	321	15	eq	eq	ADP
ejpam-6838	321	16	.	.	PUNCT
ejpam-6838	322	1	(	(	PUNCT
ejpam-6838	322	2	59	59	NUM
ejpam-6838	322	3	)	)	PUNCT
ejpam-6838	322	4	that	that	PRON
ejpam-6838	322	5	∥rm(x	∥rm(x	VERB
ejpam-6838	322	6	,	,	PUNCT
ejpam-6838	322	7	t)∥l2	t)∥l2	ADJ
ejpam-6838	322	8	ω(ω	ω(ω	NOUN
ejpam-6838	322	9	)	)	PUNCT
ejpam-6838	322	10	will	will	AUX
ejpam-6838	322	11	be	be	AUX
ejpam-6838	322	12	small	small	ADJ
ejpam-6838	322	13	enough	enough	ADV
ejpam-6838	322	14	.	.	PUNCT
ejpam-6838	323	1	this	this	PRON
ejpam-6838	323	2	concludes	conclude	VERB
ejpam-6838	323	3	the	the	DET
ejpam-6838	323	4	proof	proof	NOUN
ejpam-6838	323	5	of	of	ADP
ejpam-6838	323	6	the	the	DET
ejpam-6838	323	7	theorem	theorem	NOUN
ejpam-6838	323	8	.	.	PROPN
ejpam-6838	323	9	5	5	NUM
ejpam-6838	323	10	.	.	X
ejpam-6838	324	1	some	some	DET
ejpam-6838	324	2	numerical	numerical	ADJ
ejpam-6838	324	3	tests	test	NOUN
ejpam-6838	324	4	in	in	ADP
ejpam-6838	324	5	this	this	DET
ejpam-6838	324	6	section	section	NOUN
ejpam-6838	324	7	,	,	PUNCT
ejpam-6838	324	8	we	we	PRON
ejpam-6838	324	9	present	present	VERB
ejpam-6838	324	10	some	some	DET
ejpam-6838	324	11	numerical	numerical	ADJ
ejpam-6838	324	12	examples	example	NOUN
ejpam-6838	324	13	to	to	PART
ejpam-6838	324	14	demonstrate	demonstrate	VERB
ejpam-6838	324	15	the	the	DET
ejpam-6838	324	16	accuracy	accuracy	NOUN
ejpam-6838	324	17	and	and	CCONJ
ejpam-6838	324	18	efficiency	efficiency	NOUN
ejpam-6838	324	19	of	of	ADP
ejpam-6838	324	20	the	the	DET
ejpam-6838	324	21	suggested	suggest	VERB
ejpam-6838	324	22	numerical	numerical	ADJ
ejpam-6838	324	23	algorithm	algorithm	NOUN
ejpam-6838	324	24	by	by	ADP
ejpam-6838	324	25	using	use	VERB
ejpam-6838	324	26	the	the	DET
ejpam-6838	324	27	absolute	absolute	ADJ
ejpam-6838	324	28	error	error	NOUN
ejpam-6838	324	29	(	(	PUNCT
ejpam-6838	324	30	ae	ae	PROPN
ejpam-6838	324	31	)	)	PUNCT
ejpam-6838	324	32	,	,	PUNCT
ejpam-6838	324	33	maximum	maximum	ADJ
ejpam-6838	324	34	absolute	absolute	ADJ
ejpam-6838	324	35	error	error	NOUN
ejpam-6838	324	36	(	(	PUNCT
ejpam-6838	324	37	mae	mae	PROPN
ejpam-6838	324	38	)	)	PUNCT
ejpam-6838	324	39	and	and	CCONJ
ejpam-6838	324	40	l∞	l∞	NOUN
ejpam-6838	324	41	error	error	NOUN
ejpam-6838	324	42	ae	ae	PROPN
ejpam-6838	324	43	=	=	SYM
ejpam-6838	324	44	∣∣λ(x	∣∣λ(x	PROPN
ejpam-6838	324	45	,	,	PUNCT
ejpam-6838	324	46	t)−	t)−	PROPN
ejpam-6838	324	47	λm(x	λm(x	NUM
ejpam-6838	324	48	,	,	PUNCT
ejpam-6838	324	49	t	t	PROPN
ejpam-6838	324	50	)	)	PUNCT
ejpam-6838	324	51	∣∣	∣∣	NUM
ejpam-6838	324	52	,	,	PUNCT
ejpam-6838	324	53	(	(	PUNCT
ejpam-6838	324	54	60	60	NUM
ejpam-6838	324	55	)	)	PUNCT
ejpam-6838	324	56	mae	mae	PROPN
ejpam-6838	324	57	=	=	PROPN
ejpam-6838	324	58	max	max	PROPN
ejpam-6838	324	59	xi	xi	X
ejpam-6838	324	60	∣∣λ(xi	∣∣λ(xi	PROPN
ejpam-6838	324	61	,	,	PUNCT
ejpam-6838	324	62	xj)−	xj)−	PUNCT
ejpam-6838	325	1	λm(xi	λm(xi	PROPN
ejpam-6838	325	2	,	,	PUNCT
ejpam-6838	325	3	xj	xj	PROPN
ejpam-6838	325	4	)	)	PUNCT
ejpam-6838	325	5	∣∣	∣∣	NUM
ejpam-6838	325	6	,	,	PUNCT
ejpam-6838	325	7	xi	xi	PROPN
ejpam-6838	325	8	∈	∈	PROPN
ejpam-6838	325	9	{	{	PUNCT
ejpam-6838	325	10	1	1	NUM
ejpam-6838	325	11	10	10	NUM
ejpam-6838	325	12	,	,	PUNCT
ejpam-6838	325	13	2	2	NUM
ejpam-6838	325	14	10	10	NUM
ejpam-6838	325	15	,	,	PUNCT
ejpam-6838	325	16	3	3	NUM
ejpam-6838	325	17	10	10	NUM
ejpam-6838	325	18	,	,	PUNCT
ejpam-6838	325	19	.	.	PUNCT
ejpam-6838	325	20	.	.	PUNCT
ejpam-6838	325	21	.	.	PUNCT
ejpam-6838	326	1	,	,	PUNCT
ejpam-6838	326	2	1	1	X
ejpam-6838	326	3	}	}	PUNCT
ejpam-6838	326	4	,	,	PUNCT
ejpam-6838	326	5	(	(	PUNCT
ejpam-6838	326	6	61	61	NUM
ejpam-6838	326	7	)	)	PUNCT
ejpam-6838	326	8	l∞	l∞	NOUN
ejpam-6838	326	9	=	=	SYM
ejpam-6838	326	10	max	max	PROPN
ejpam-6838	326	11	(	(	PUNCT
ejpam-6838	326	12	x	x	X
ejpam-6838	326	13	,	,	PUNCT
ejpam-6838	326	14	t)∈ω	t)∈ω	CCONJ
ejpam-6838	326	15	∣∣λ(x	∣∣λ(x	PROPN
ejpam-6838	326	16	,	,	PUNCT
ejpam-6838	326	17	t)−	t)−	PROPN
ejpam-6838	326	18	λm(x	λm(x	NUM
ejpam-6838	326	19	,	,	PUNCT
ejpam-6838	326	20	t	t	PROPN
ejpam-6838	326	21	)	)	PUNCT
ejpam-6838	326	22	∣∣	∣∣	X
ejpam-6838	326	23	.	.	PUNCT
ejpam-6838	327	1	(	(	PUNCT
ejpam-6838	327	2	62	62	NUM
ejpam-6838	327	3	)	)	PUNCT
ejpam-6838	327	4	in	in	ADP
ejpam-6838	327	5	addition	addition	NOUN
ejpam-6838	327	6	,	,	PUNCT
ejpam-6838	327	7	comparisons	comparison	NOUN
ejpam-6838	327	8	with	with	ADP
ejpam-6838	327	9	some	some	DET
ejpam-6838	327	10	methods	method	NOUN
ejpam-6838	327	11	are	be	AUX
ejpam-6838	327	12	given	give	VERB
ejpam-6838	327	13	.	.	PUNCT
ejpam-6838	327	14	example	example	NOUN
ejpam-6838	328	1	1	1	NUM
ejpam-6838	328	2	.	.	PUNCT
ejpam-6838	329	1	[	[	X
ejpam-6838	329	2	64	64	NUM
ejpam-6838	329	3	]	]	PUNCT
ejpam-6838	329	4	consider	consider	VERB
ejpam-6838	329	5	the	the	DET
ejpam-6838	329	6	following	follow	VERB
ejpam-6838	329	7	equation	equation	NOUN
ejpam-6838	329	8	:	:	PUNCT
ejpam-6838	329	9	dζ	dζ	PROPN
ejpam-6838	329	10	t	t	PROPN
ejpam-6838	329	11	λ(x	λ(x	PROPN
ejpam-6838	329	12	,	,	PUNCT
ejpam-6838	329	13	t)−	t)−	PROPN
ejpam-6838	329	14	λxx(x	λxx(x	PROPN
ejpam-6838	329	15	,	,	PUNCT
ejpam-6838	329	16	t	t	PROPN
ejpam-6838	329	17	)	)	PUNCT
ejpam-6838	329	18	=	=	SYM
ejpam-6838	329	19	1	1	NUM
ejpam-6838	329	20	γ(2−	γ(2−	NOUN
ejpam-6838	329	21	α	α	NOUN
ejpam-6838	329	22	)	)	PUNCT
ejpam-6838	329	23	t1−α	t1−α	PROPN
ejpam-6838	329	24	x2	x2	NOUN
ejpam-6838	329	25	(	(	PUNCT
ejpam-6838	329	26	1−	1−	NUM
ejpam-6838	329	27	x	x	NOUN
ejpam-6838	329	28	)	)	PUNCT
ejpam-6838	329	29	+	+	CCONJ
ejpam-6838	329	30	2	2	NUM
ejpam-6838	329	31	t	t	NOUN
ejpam-6838	329	32	(	(	PUNCT
ejpam-6838	329	33	3x−	3x−	PROPN
ejpam-6838	329	34	1	1	NUM
ejpam-6838	329	35	)	)	PUNCT
ejpam-6838	329	36	,	,	PUNCT
ejpam-6838	329	37	0	0	NUM
ejpam-6838	329	38	<	<	X
ejpam-6838	329	39	α	α	PROPN
ejpam-6838	329	40	≤	≤	NUM
ejpam-6838	329	41	1	1	NUM
ejpam-6838	329	42	,	,	PUNCT
ejpam-6838	329	43	(	(	PUNCT
ejpam-6838	329	44	63	63	NUM
ejpam-6838	329	45	)	)	PUNCT
ejpam-6838	329	46	subject	subject	NOUN
ejpam-6838	329	47	to	to	ADP
ejpam-6838	329	48	the	the	DET
ejpam-6838	329	49	initial	initial	ADJ
ejpam-6838	329	50	condition	condition	NOUN
ejpam-6838	329	51	(	(	PUNCT
ejpam-6838	329	52	ic	ic	X
ejpam-6838	329	53	)	)	PUNCT
ejpam-6838	329	54	λ(x	λ(x	PROPN
ejpam-6838	329	55	,	,	PUNCT
ejpam-6838	329	56	0	0	NUM
ejpam-6838	329	57	)	)	PUNCT
ejpam-6838	329	58	=	=	SYM
ejpam-6838	329	59	0	0	NUM
ejpam-6838	329	60	,	,	PUNCT
ejpam-6838	329	61	0	0	NUM
ejpam-6838	329	62	<	<	X
ejpam-6838	329	63	x	x	SYM
ejpam-6838	329	64	≤	≤	NUM
ejpam-6838	329	65	1	1	NUM
ejpam-6838	329	66	,	,	PUNCT
ejpam-6838	329	67	(	(	PUNCT
ejpam-6838	329	68	64	64	NUM
ejpam-6838	329	69	)	)	PUNCT
ejpam-6838	329	70	and	and	CCONJ
ejpam-6838	329	71	the	the	DET
ejpam-6838	329	72	homogeneous	homogeneous	ADJ
ejpam-6838	329	73	boundary	boundary	ADJ
ejpam-6838	329	74	conditions	condition	NOUN
ejpam-6838	329	75	(	(	PUNCT
ejpam-6838	329	76	hbcs	hbc	NOUN
ejpam-6838	329	77	)	)	PUNCT
ejpam-6838	329	78	λ(0	λ(0	PROPN
ejpam-6838	329	79	,	,	PUNCT
ejpam-6838	329	80	t	t	PROPN
ejpam-6838	329	81	)	)	PUNCT
ejpam-6838	329	82	=	=	SYM
ejpam-6838	330	1	λ(1	λ(1	PROPN
ejpam-6838	330	2	,	,	PUNCT
ejpam-6838	330	3	t	t	PROPN
ejpam-6838	330	4	)	)	PUNCT
ejpam-6838	330	5	=	=	SYM
ejpam-6838	330	6	0	0	NUM
ejpam-6838	330	7	,	,	PUNCT
ejpam-6838	330	8	0	0	NUM
ejpam-6838	330	9	<	<	X
ejpam-6838	330	10	t	t	X
ejpam-6838	330	11	≤	≤	NUM
ejpam-6838	330	12	1	1	NUM
ejpam-6838	330	13	,	,	PUNCT
ejpam-6838	330	14	(	(	PUNCT
ejpam-6838	330	15	65	65	NUM
ejpam-6838	330	16	)	)	PUNCT
ejpam-6838	331	1	where	where	SCONJ
ejpam-6838	331	2	λ(x	λ(x	PROPN
ejpam-6838	331	3	,	,	PUNCT
ejpam-6838	331	4	t	t	PROPN
ejpam-6838	331	5	)	)	PUNCT
ejpam-6838	331	6	=	=	SYM
ejpam-6838	331	7	t	t	NOUN
ejpam-6838	331	8	x2	x2	SYM
ejpam-6838	331	9	(	(	PUNCT
ejpam-6838	331	10	1−	1−	NUM
ejpam-6838	331	11	x	x	X
ejpam-6838	331	12	)	)	PUNCT
ejpam-6838	331	13	is	be	AUX
ejpam-6838	331	14	the	the	DET
ejpam-6838	331	15	exact	exact	ADJ
ejpam-6838	331	16	solution	solution	NOUN
ejpam-6838	331	17	of	of	ADP
ejpam-6838	331	18	this	this	DET
ejpam-6838	331	19	problem	problem	NOUN
ejpam-6838	331	20	.	.	PUNCT
ejpam-6838	332	1	table	table	NOUN
ejpam-6838	332	2	1	1	NUM
ejpam-6838	332	3	shows	show	VERB
ejpam-6838	332	4	the	the	DET
ejpam-6838	332	5	ae	ae	PROPN
ejpam-6838	332	6	at	at	ADP
ejpam-6838	332	7	various	various	ADJ
ejpam-6838	332	8	values	value	NOUN
ejpam-6838	332	9	of	of	ADP
ejpam-6838	332	10	ζ	ζ	NOUN
ejpam-6838	332	11	when	when	SCONJ
ejpam-6838	332	12	m	m	VERB
ejpam-6838	332	13	=	=	SYM
ejpam-6838	332	14	3	3	X
ejpam-6838	332	15	.	.	X
ejpam-6838	332	16	figure	figure	NOUN
ejpam-6838	332	17	1	1	NUM
ejpam-6838	332	18	illustrates	illustrate	VERB
ejpam-6838	332	19	the	the	DET
ejpam-6838	332	20	ae	ae	PROPN
ejpam-6838	332	21	w.	w.	PROPN
ejpam-6838	332	22	m.	m.	PROPN
ejpam-6838	332	23	abd	abd	PROPN
ejpam-6838	332	24	-	-	PUNCT
ejpam-6838	332	25	elhameed	elhameed	PROPN
ejpam-6838	333	1	et	et	PROPN
ejpam-6838	333	2	al	al	PROPN
ejpam-6838	333	3	.	.	PUNCT
ejpam-6838	333	4	/	/	SYM
ejpam-6838	333	5	eur	eur	PROPN
ejpam-6838	333	6	.	.	PUNCT
ejpam-6838	334	1	j.	j.	PROPN
ejpam-6838	334	2	pure	pure	PROPN
ejpam-6838	334	3	appl	appl	PROPN
ejpam-6838	334	4	.	.	PROPN
ejpam-6838	334	5	math	math	PROPN
ejpam-6838	334	6	,	,	PUNCT
ejpam-6838	334	7	18	18	NUM
ejpam-6838	334	8	(	(	PUNCT
ejpam-6838	334	9	4	4	NUM
ejpam-6838	334	10	)	)	PUNCT
ejpam-6838	334	11	(	(	PUNCT
ejpam-6838	334	12	2025	2025	NUM
ejpam-6838	334	13	)	)	PUNCT
ejpam-6838	334	14	,	,	PUNCT
ejpam-6838	334	15	6838	6838	NUM
ejpam-6838	334	16	15	15	NUM
ejpam-6838	334	17	of	of	ADP
ejpam-6838	334	18	25	25	NUM
ejpam-6838	334	19	table	table	NOUN
ejpam-6838	334	20	1	1	NUM
ejpam-6838	334	21	:	:	PUNCT
ejpam-6838	334	22	the	the	DET
ejpam-6838	334	23	ae	ae	PROPN
ejpam-6838	334	24	of	of	ADP
ejpam-6838	334	25	example	example	NOUN
ejpam-6838	334	26	1	1	NUM
ejpam-6838	334	27	at	at	ADP
ejpam-6838	334	28	m	m	PROPN
ejpam-6838	334	29	=	=	NOUN
ejpam-6838	334	30	3	3	X
ejpam-6838	334	31	.	.	PUNCT
ejpam-6838	334	32	(	(	PUNCT
ejpam-6838	334	33	x	x	NOUN
ejpam-6838	334	34	,	,	PUNCT
ejpam-6838	334	35	t	t	NOUN
ejpam-6838	334	36	)	)	PUNCT
ejpam-6838	334	37	ζ	ζ	NOUN
ejpam-6838	334	38	=	=	SYM
ejpam-6838	334	39	0.2	0.2	NUM
ejpam-6838	334	40	cpu	cpu	NOUN
ejpam-6838	334	41	time	time	NOUN
ejpam-6838	334	42	ζ	ζ	NOUN
ejpam-6838	334	43	=	=	SYM
ejpam-6838	334	44	0.4	0.4	NUM
ejpam-6838	334	45	cpu	cpu	NOUN
ejpam-6838	334	46	time	time	NOUN
ejpam-6838	334	47	ζ	ζ	NOUN
ejpam-6838	334	48	=	=	SYM
ejpam-6838	334	49	0.6	0.6	NUM
ejpam-6838	334	50	cpu	cpu	NOUN
ejpam-6838	334	51	time	time	NOUN
ejpam-6838	334	52	ζ	ζ	NOUN
ejpam-6838	334	53	=	=	SYM
ejpam-6838	334	54	0.8	0.8	NUM
ejpam-6838	334	55	cpu	cpu	NOUN
ejpam-6838	334	56	time	time	NOUN
ejpam-6838	334	57	(	(	PUNCT
ejpam-6838	334	58	0.1,0.1	0.1,0.1	PROPN
ejpam-6838	334	59	)	)	PUNCT
ejpam-6838	334	60	3.74914×	3.74914×	NUM
ejpam-6838	335	1	10−14	10−14	NUM
ejpam-6838	335	2	8.69194×	8.69194×	NUM
ejpam-6838	335	3	10−15	10−15	NUM
ejpam-6838	335	4	8.28406×	8.28406×	NOUN
ejpam-6838	335	5	10−15	10−15	PROPN
ejpam-6838	335	6	1.75789×	1.75789×	NUM
ejpam-6838	335	7	10−14	10−14	NOUN
ejpam-6838	335	8	(	(	PUNCT
ejpam-6838	335	9	0.2,0.2	0.2,0.2	PROPN
ejpam-6838	335	10	)	)	PUNCT
ejpam-6838	335	11	5.27894×	5.27894×	NOUN
ejpam-6838	335	12	10−14	10−14	NUM
ejpam-6838	335	13	1.66768×	1.66768×	NUM
ejpam-6838	335	14	10−14	10−14	NUM
ejpam-6838	335	15	1.26583×	1.26583×	NUM
ejpam-6838	335	16	10−14	10−14	NUM
ejpam-6838	335	17	2.83619×	2.83619×	NUM
ejpam-6838	335	18	10−14	10−14	NUM
ejpam-6838	335	19	(	(	PUNCT
ejpam-6838	335	20	0.3,0.3	0.3,0.3	PROPN
ejpam-6838	335	21	)	)	PUNCT
ejpam-6838	335	22	6.04031×	6.04031×	NUM
ejpam-6838	335	23	10−15	10−15	NUM
ejpam-6838	335	24	9.24955×	9.24955×	NUM
ejpam-6838	335	25	10−15	10−15	PROPN
ejpam-6838	335	26	7.10196×	7.10196×	NUM
ejpam-6838	335	27	10−15	10−15	PROPN
ejpam-6838	335	28	1.20529×	1.20529×	NUM
ejpam-6838	335	29	10−14	10−14	PROPN
ejpam-6838	335	30	(	(	PUNCT
ejpam-6838	335	31	0.4,0.4	0.4,0.4	PROPN
ejpam-6838	335	32	)	)	PUNCT
ejpam-6838	335	33	6.2942×	6.2942×	NUM
ejpam-6838	335	34	10−14	10−14	NUM
ejpam-6838	335	35	1.40582×	1.40582×	NUM
ejpam-6838	335	36	10−14	10−14	NUM
ejpam-6838	335	37	6.8695×	6.8695×	NUM
ejpam-6838	335	38	10−16	10−16	NUM
ejpam-6838	335	39	1.98938×	1.98938×	NUM
ejpam-6838	335	40	10−14	10−14	PROPN
ejpam-6838	335	41	(	(	PUNCT
ejpam-6838	335	42	0.5,0.5	0.5,0.5	PROPN
ejpam-6838	335	43	)	)	PUNCT
ejpam-6838	335	44	1.13222×	1.13222×	NUM
ejpam-6838	335	45	10−13	10−13	PROPN
ejpam-6838	335	46	2.469	2.469	NUM
ejpam-6838	335	47	4.27158×	4.27158×	NOUN
ejpam-6838	335	48	10−14	10−14	NUM
ejpam-6838	335	49	2.656	2.656	NUM
ejpam-6838	335	50	1.77636×	1.77636×	NOUN
ejpam-6838	335	51	10−15	10−15	NUM
ejpam-6838	335	52	2.999	2.999	NUM
ejpam-6838	335	53	4.69347×	4.69347×	NUM
ejpam-6838	335	54	10−14	10−14	NUM
ejpam-6838	335	55	2.578	2.578	NUM
ejpam-6838	335	56	(	(	PUNCT
ejpam-6838	335	57	0.6,0.6	0.6,0.6	PROPN
ejpam-6838	335	58	)	)	PUNCT
ejpam-6838	335	59	1.07289×	1.07289×	NUM
ejpam-6838	336	1	10−13	10−13	NUM
ejpam-6838	337	1	6.05765×	6.05765×	NUM
ejpam-6838	338	1	10−14	10−14	NUM
ejpam-6838	339	1	9.96425×	9.96425×	NUM
ejpam-6838	339	2	10−15	10−15	NUM
ejpam-6838	339	3	5.43871×	5.43871×	NUM
ejpam-6838	339	4	10−14	10−14	NOUN
ejpam-6838	339	5	(	(	PUNCT
ejpam-6838	339	6	0.7,0.7	0.7,0.7	PROPN
ejpam-6838	339	7	)	)	PUNCT
ejpam-6838	339	8	5.93969×	5.93969×	NUM
ejpam-6838	339	9	10−14	10−14	NUM
ejpam-6838	339	10	5.37348×	5.37348×	NUM
ejpam-6838	339	11	10−14	10−14	NUM
ejpam-6838	339	12	1.57374×	1.57374×	NUM
ejpam-6838	340	1	10−14	10−14	NUM
ejpam-6838	340	2	4.09117×	4.09117×	NUM
ejpam-6838	340	3	10−14	10−14	PROPN
ejpam-6838	340	4	(	(	PUNCT
ejpam-6838	340	5	0.8,0.8	0.8,0.8	NUM
ejpam-6838	340	6	)	)	PUNCT
ejpam-6838	340	7	9.90874×	9.90874×	NUM
ejpam-6838	340	8	10−15	10−15	NUM
ejpam-6838	340	9	2.01922×	2.01922×	NUM
ejpam-6838	340	10	10−14	10−14	NUM
ejpam-6838	340	11	8.20177×	8.20177×	NUM
ejpam-6838	340	12	10−15	10−15	PROPN
ejpam-6838	340	13	1.8055×	1.8055×	NOUN
ejpam-6838	340	14	10−14	10−14	PROPN
ejpam-6838	340	15	(	(	PUNCT
ejpam-6838	340	16	0.9,0.9	0.9,0.9	PROPN
ejpam-6838	340	17	)	)	PUNCT
ejpam-6838	340	18	3.08087×	3.08087×	NUM
ejpam-6838	340	19	10−15	10−15	NUM
ejpam-6838	340	20	1.78052×	1.78052×	NUM
ejpam-6838	340	21	10−14	10−14	NUM
ejpam-6838	340	22	1.01724×	1.01724×	NUM
ejpam-6838	340	23	10−14	10−14	NUM
ejpam-6838	340	24	2.45637×	2.45637×	NUM
ejpam-6838	340	25	10−15	10−15	NOUN
ejpam-6838	340	26	at	at	ADP
ejpam-6838	340	27	ζ	ζ	NOUN
ejpam-6838	340	28	=	=	SYM
ejpam-6838	340	29	0.5	0.5	NUM
ejpam-6838	340	30	and	and	CCONJ
ejpam-6838	340	31	ζ	ζ	NOUN
ejpam-6838	340	32	=	=	SYM
ejpam-6838	340	33	0.9	0.9	NUM
ejpam-6838	340	34	when	when	SCONJ
ejpam-6838	340	35	m	m	VERB
ejpam-6838	340	36	=	=	SYM
ejpam-6838	340	37	3	3	X
ejpam-6838	340	38	.	.	PUNCT
ejpam-6838	340	39	also	also	ADV
ejpam-6838	340	40	,	,	PUNCT
ejpam-6838	340	41	the	the	DET
ejpam-6838	340	42	cpu	cpu	ADJ
ejpam-6838	340	43	time	time	NOUN
ejpam-6838	340	44	(	(	PUNCT
ejpam-6838	340	45	in	in	ADP
ejpam-6838	340	46	seconds	second	NOUN
ejpam-6838	340	47	)	)	PUNCT
ejpam-6838	340	48	for	for	ADP
ejpam-6838	340	49	the	the	DET
ejpam-6838	340	50	method	method	NOUN
ejpam-6838	340	51	is	be	AUX
ejpam-6838	340	52	computed	compute	VERB
ejpam-6838	340	53	in	in	ADP
ejpam-6838	340	54	this	this	DET
ejpam-6838	340	55	table	table	NOUN
ejpam-6838	340	56	.	.	PUNCT
ejpam-6838	341	1	table	table	NOUN
ejpam-6838	341	2	2	2	NUM
ejpam-6838	341	3	gives	give	VERB
ejpam-6838	341	4	a	a	DET
ejpam-6838	341	5	comparison	comparison	NOUN
ejpam-6838	341	6	of	of	ADP
ejpam-6838	341	7	l2	l2	NOUN
ejpam-6838	341	8	and	and	CCONJ
ejpam-6838	341	9	l∞	l∞	NOUN
ejpam-6838	341	10	errors	error	NOUN
ejpam-6838	341	11	between	between	ADP
ejpam-6838	341	12	our	our	PRON
ejpam-6838	341	13	method	method	NOUN
ejpam-6838	341	14	at	at	ADP
ejpam-6838	341	15	m	m	PROPN
ejpam-6838	341	16	=	=	SYM
ejpam-6838	341	17	3	3	NUM
ejpam-6838	341	18	and	and	CCONJ
ejpam-6838	341	19	the	the	DET
ejpam-6838	341	20	method	method	NOUN
ejpam-6838	341	21	in	in	ADP
ejpam-6838	341	22	[	[	X
ejpam-6838	341	23	64	64	NUM
ejpam-6838	341	24	]	]	PUNCT
ejpam-6838	341	25	at	at	ADP
ejpam-6838	341	26	∆t	∆t	PROPN
ejpam-6838	341	27	=	=	SYM
ejpam-6838	341	28	0.001	0.001	NUM
ejpam-6838	341	29	and	and	CCONJ
ejpam-6838	341	30	∆x	∆x	PROPN
ejpam-6838	341	31	=	=	SYM
ejpam-6838	341	32	0.015625	0.015625	PROPN
ejpam-6838	341	33	.	.	PUNCT
ejpam-6838	342	1	figure	figure	NOUN
ejpam-6838	342	2	1	1	NUM
ejpam-6838	342	3	:	:	PUNCT
ejpam-6838	342	4	the	the	DET
ejpam-6838	342	5	ae	ae	PROPN
ejpam-6838	342	6	for	for	ADP
ejpam-6838	342	7	example	example	NOUN
ejpam-6838	342	8	1	1	NUM
ejpam-6838	342	9	at	at	ADP
ejpam-6838	342	10	ζ	ζ	NOUN
ejpam-6838	342	11	=	=	SYM
ejpam-6838	342	12	0.5	0.5	NUM
ejpam-6838	342	13	and	and	CCONJ
ejpam-6838	342	14	ζ	ζ	NOUN
ejpam-6838	342	15	=	=	SYM
ejpam-6838	342	16	0.9	0.9	NUM
ejpam-6838	342	17	when	when	SCONJ
ejpam-6838	342	18	m	m	VERB
ejpam-6838	342	19	=	=	SYM
ejpam-6838	342	20	3	3	X
ejpam-6838	342	21	.	.	NOUN
ejpam-6838	342	22	table	table	NOUN
ejpam-6838	342	23	2	2	NUM
ejpam-6838	342	24	:	:	PUNCT
ejpam-6838	342	25	comparison	comparison	NOUN
ejpam-6838	342	26	of	of	ADP
ejpam-6838	342	27	errors	error	NOUN
ejpam-6838	342	28	for	for	ADP
ejpam-6838	342	29	problem	problem	NOUN
ejpam-6838	342	30	1	1	NUM
ejpam-6838	342	31	.	.	PUNCT
ejpam-6838	342	32	method	method	NOUN
ejpam-6838	342	33	in	in	ADP
ejpam-6838	342	34	[	[	X
ejpam-6838	342	35	64	64	NUM
ejpam-6838	342	36	]	]	PUNCT
ejpam-6838	342	37	at	at	ADP
ejpam-6838	342	38	∆t	∆t	PROPN
ejpam-6838	342	39	=	=	SYM
ejpam-6838	342	40	0.001	0.001	NUM
ejpam-6838	342	41	and	and	CCONJ
ejpam-6838	342	42	∆x	∆x	PROPN
ejpam-6838	342	43	=	=	SYM
ejpam-6838	342	44	0.015625	0.015625	NUM
ejpam-6838	342	45	our	our	PRON
ejpam-6838	342	46	method	method	NOUN
ejpam-6838	342	47	at	at	ADP
ejpam-6838	342	48	m	m	PROPN
ejpam-6838	342	49	=	=	SYM
ejpam-6838	342	50	3	3	NUM
ejpam-6838	342	51	l2	l2	NOUN
ejpam-6838	342	52	error	error	NOUN
ejpam-6838	342	53	l∞	l∞	NOUN
ejpam-6838	342	54	error	error	NOUN
ejpam-6838	342	55	l2	l2	NOUN
ejpam-6838	342	56	error	error	NOUN
ejpam-6838	342	57	l∞	l∞	NOUN
ejpam-6838	342	58	error	error	NOUN
ejpam-6838	342	59	1.6868×	1.6868×	NUM
ejpam-6838	342	60	10−12	10−12	NOUN
ejpam-6838	342	61	2.3978×	2.3978×	NUM
ejpam-6838	342	62	10−12	10−12	NOUN
ejpam-6838	342	63	6.37117×	6.37117×	NUM
ejpam-6838	342	64	10−16	10−16	PROPN
ejpam-6838	342	65	1.44382×	1.44382×	NUM
ejpam-6838	342	66	10−13	10−13	NUM
ejpam-6838	342	67	example	example	NOUN
ejpam-6838	342	68	2	2	NUM
ejpam-6838	342	69	.	.	PUNCT
ejpam-6838	343	1	[	[	X
ejpam-6838	343	2	20	20	NUM
ejpam-6838	343	3	]	]	PUNCT
ejpam-6838	343	4	consider	consider	VERB
ejpam-6838	343	5	the	the	DET
ejpam-6838	343	6	following	follow	VERB
ejpam-6838	343	7	equation	equation	NOUN
ejpam-6838	343	8	:	:	PUNCT
ejpam-6838	343	9	dζ	dζ	PROPN
ejpam-6838	343	10	t	t	PROPN
ejpam-6838	343	11	λ(x	λ(x	PROPN
ejpam-6838	343	12	,	,	PUNCT
ejpam-6838	343	13	t)−	t)−	PROPN
ejpam-6838	343	14	λxx(x	λxx(x	PROPN
ejpam-6838	343	15	,	,	PUNCT
ejpam-6838	343	16	t	t	PROPN
ejpam-6838	343	17	)	)	PUNCT
ejpam-6838	343	18	=	=	SYM
ejpam-6838	344	1	g(x	g(x	PROPN
ejpam-6838	344	2	,	,	PUNCT
ejpam-6838	344	3	t	t	PROPN
ejpam-6838	344	4	)	)	PUNCT
ejpam-6838	344	5	,	,	PUNCT
ejpam-6838	344	6	0	0	PUNCT
ejpam-6838	344	7	<	<	X
ejpam-6838	344	8	ζ	ζ	X
ejpam-6838	344	9	≤	≤	NUM
ejpam-6838	344	10	1	1	NUM
ejpam-6838	344	11	,	,	PUNCT
ejpam-6838	344	12	(	(	PUNCT
ejpam-6838	344	13	66	66	NUM
ejpam-6838	344	14	)	)	PUNCT
ejpam-6838	344	15	controlled	control	VERB
ejpam-6838	344	16	by	by	ADP
ejpam-6838	344	17	λ(x	λ(x	PROPN
ejpam-6838	344	18	,	,	PUNCT
ejpam-6838	344	19	0	0	NUM
ejpam-6838	344	20	)	)	PUNCT
ejpam-6838	344	21	=	=	SYM
ejpam-6838	344	22	0	0	NUM
ejpam-6838	344	23	,	,	PUNCT
ejpam-6838	344	24	0	0	PUNCT
ejpam-6838	344	25	<	<	X
ejpam-6838	344	26	x	x	X
ejpam-6838	344	27	<	<	X
ejpam-6838	344	28	1	1	NUM
ejpam-6838	344	29	,	,	PUNCT
ejpam-6838	344	30	λ(0	λ(0	PROPN
ejpam-6838	344	31	,	,	PUNCT
ejpam-6838	344	32	t	t	PROPN
ejpam-6838	344	33	)	)	PUNCT
ejpam-6838	344	34	=	=	SYM
ejpam-6838	345	1	λ(1	λ(1	PROPN
ejpam-6838	345	2	,	,	PUNCT
ejpam-6838	345	3	t	t	PROPN
ejpam-6838	345	4	)	)	PUNCT
ejpam-6838	345	5	=	=	SYM
ejpam-6838	345	6	0	0	NUM
ejpam-6838	345	7	,	,	PUNCT
ejpam-6838	345	8	0	0	NUM
ejpam-6838	345	9	<	<	X
ejpam-6838	345	10	t	t	X
ejpam-6838	345	11	<	<	X
ejpam-6838	345	12	1	1	NUM
ejpam-6838	345	13	,	,	PUNCT
ejpam-6838	345	14	(	(	PUNCT
ejpam-6838	345	15	67	67	NUM
ejpam-6838	345	16	)	)	PUNCT
ejpam-6838	345	17	where	where	SCONJ
ejpam-6838	345	18	g(x	g(x	NOUN
ejpam-6838	345	19	,	,	PUNCT
ejpam-6838	345	20	t	t	PROPN
ejpam-6838	345	21	)	)	PUNCT
ejpam-6838	345	22	is	be	AUX
ejpam-6838	345	23	chosen	choose	VERB
ejpam-6838	345	24	to	to	PART
ejpam-6838	345	25	meet	meet	VERB
ejpam-6838	345	26	the	the	DET
ejpam-6838	345	27	exact	exact	ADJ
ejpam-6838	345	28	solution	solution	NOUN
ejpam-6838	345	29	given	give	VERB
ejpam-6838	345	30	by	by	ADP
ejpam-6838	345	31	λ(x	λ(x	PROPN
ejpam-6838	345	32	,	,	PUNCT
ejpam-6838	345	33	t	t	PROPN
ejpam-6838	345	34	)	)	PUNCT
ejpam-6838	345	35	=	=	PUNCT
ejpam-6838	346	1	sin(π	sin(π	PROPN
ejpam-6838	346	2	t	t	PROPN
ejpam-6838	346	3	)	)	PUNCT
ejpam-6838	346	4	sin(π	sin(π	PROPN
ejpam-6838	346	5	x	x	SYM
ejpam-6838	346	6	)	)	PUNCT
ejpam-6838	346	7	.	.	PUNCT
ejpam-6838	347	1	table	table	NOUN
ejpam-6838	347	2	3	3	NUM
ejpam-6838	347	3	gives	give	VERB
ejpam-6838	347	4	a	a	DET
ejpam-6838	347	5	comparison	comparison	NOUN
ejpam-6838	347	6	of	of	ADP
ejpam-6838	347	7	mae	mae	PROPN
ejpam-6838	347	8	between	between	ADP
ejpam-6838	347	9	our	our	PRON
ejpam-6838	347	10	method	method	NOUN
ejpam-6838	347	11	at	at	ADP
ejpam-6838	347	12	m	m	PROPN
ejpam-6838	347	13	=	=	NOUN
ejpam-6838	347	14	8	8	NUM
ejpam-6838	347	15	and	and	CCONJ
ejpam-6838	347	16	the	the	DET
ejpam-6838	347	17	method	method	NOUN
ejpam-6838	347	18	in	in	ADP
ejpam-6838	347	19	[	[	X
ejpam-6838	347	20	20	20	NUM
ejpam-6838	347	21	]	]	PUNCT
ejpam-6838	347	22	w.	w.	PROPN
ejpam-6838	347	23	m.	m.	PROPN
ejpam-6838	347	24	abd	abd	PROPN
ejpam-6838	347	25	-	-	PUNCT
ejpam-6838	347	26	elhameed	elhameed	PROPN
ejpam-6838	347	27	et	et	PROPN
ejpam-6838	347	28	al	al	PROPN
ejpam-6838	347	29	.	.	PUNCT
ejpam-6838	347	30	/	/	SYM
ejpam-6838	347	31	eur	eur	PROPN
ejpam-6838	347	32	.	.	PUNCT
ejpam-6838	348	1	j.	j.	PROPN
ejpam-6838	348	2	pure	pure	PROPN
ejpam-6838	348	3	appl	appl	PROPN
ejpam-6838	348	4	.	.	PROPN
ejpam-6838	348	5	math	math	PROPN
ejpam-6838	348	6	,	,	PUNCT
ejpam-6838	348	7	18	18	NUM
ejpam-6838	348	8	(	(	PUNCT
ejpam-6838	348	9	4	4	NUM
ejpam-6838	348	10	)	)	PUNCT
ejpam-6838	348	11	(	(	PUNCT
ejpam-6838	348	12	2025	2025	NUM
ejpam-6838	348	13	)	)	PUNCT
ejpam-6838	348	14	,	,	PUNCT
ejpam-6838	348	15	6838	6838	NUM
ejpam-6838	348	16	16	16	NUM
ejpam-6838	348	17	of	of	ADP
ejpam-6838	348	18	25	25	NUM
ejpam-6838	348	19	at	at	ADP
ejpam-6838	348	20	m	m	PROPN
ejpam-6838	348	21	=	=	NOUN
ejpam-6838	348	22	32	32	NUM
ejpam-6838	348	23	and	and	CCONJ
ejpam-6838	348	24	∆x	∆x	PROPN
ejpam-6838	348	25	=	=	SYM
ejpam-6838	348	26	0.001	0.001	NUM
ejpam-6838	348	27	.	.	PUNCT
ejpam-6838	348	28	figures	figure	NOUN
ejpam-6838	348	29	2	2	NUM
ejpam-6838	348	30	and	and	CCONJ
ejpam-6838	348	31	3	3	NUM
ejpam-6838	348	32	illustrate	illustrate	VERB
ejpam-6838	348	33	the	the	DET
ejpam-6838	348	34	mae	mae	PROPN
ejpam-6838	348	35	and	and	CCONJ
ejpam-6838	348	36	l∞-error	l∞-error	NOUN
ejpam-6838	348	37	at	at	ADP
ejpam-6838	348	38	various	various	ADJ
ejpam-6838	348	39	values	value	NOUN
ejpam-6838	348	40	of	of	ADP
ejpam-6838	348	41	m	m	PRON
ejpam-6838	348	42	when	when	SCONJ
ejpam-6838	348	43	ζ	ζ	X
ejpam-6838	348	44	=	=	SYM
ejpam-6838	348	45	0.5	0.5	NUM
ejpam-6838	348	46	.	.	PUNCT
ejpam-6838	348	47	table	table	NOUN
ejpam-6838	348	48	4	4	NUM
ejpam-6838	348	49	shows	show	VERB
ejpam-6838	348	50	the	the	DET
ejpam-6838	348	51	ae	ae	PROPN
ejpam-6838	348	52	at	at	ADP
ejpam-6838	348	53	various	various	ADJ
ejpam-6838	348	54	values	value	NOUN
ejpam-6838	348	55	of	of	ADP
ejpam-6838	348	56	t	t	NOUN
ejpam-6838	348	57	when	when	SCONJ
ejpam-6838	348	58	ζ	ζ	NOUN
ejpam-6838	348	59	=	=	SYM
ejpam-6838	348	60	0.7	0.7	NUM
ejpam-6838	348	61	and	and	CCONJ
ejpam-6838	348	62	m	m	VERB
ejpam-6838	348	63	=	=	ADJ
ejpam-6838	348	64	8	8	NUM
ejpam-6838	348	65	.	.	PUNCT
ejpam-6838	348	66	table	table	NOUN
ejpam-6838	348	67	5	5	NUM
ejpam-6838	348	68	shows	show	VERB
ejpam-6838	348	69	the	the	DET
ejpam-6838	348	70	mae	mae	PROPN
ejpam-6838	348	71	and	and	CCONJ
ejpam-6838	348	72	l∞-error	l∞-error	NOUN
ejpam-6838	348	73	at	at	ADP
ejpam-6838	348	74	various	various	ADJ
ejpam-6838	348	75	values	value	NOUN
ejpam-6838	348	76	of	of	ADP
ejpam-6838	348	77	m	m	PRON
ejpam-6838	348	78	when	when	SCONJ
ejpam-6838	348	79	ζ	ζ	NOUN
ejpam-6838	348	80	=	=	SYM
ejpam-6838	348	81	0.9	0.9	NUM
ejpam-6838	348	82	.	.	PUNCT
ejpam-6838	349	1	also	also	ADV
ejpam-6838	349	2	,	,	PUNCT
ejpam-6838	349	3	table	table	NOUN
ejpam-6838	349	4	6	6	NUM
ejpam-6838	349	5	shows	show	VERB
ejpam-6838	349	6	the	the	DET
ejpam-6838	349	7	mae	mae	PROPN
ejpam-6838	349	8	and	and	CCONJ
ejpam-6838	349	9	l∞-error	l∞-error	NOUN
ejpam-6838	349	10	at	at	ADP
ejpam-6838	349	11	various	various	ADJ
ejpam-6838	349	12	values	value	NOUN
ejpam-6838	349	13	of	of	ADP
ejpam-6838	349	14	m	m	PRON
ejpam-6838	349	15	when	when	SCONJ
ejpam-6838	349	16	ζ	ζ	X
ejpam-6838	349	17	=	=	SYM
ejpam-6838	349	18	0.3	0.3	NUM
ejpam-6838	349	19	.	.	PUNCT
ejpam-6838	349	20	table	table	NOUN
ejpam-6838	349	21	3	3	NUM
ejpam-6838	349	22	:	:	PUNCT
ejpam-6838	349	23	comparison	comparison	NOUN
ejpam-6838	349	24	of	of	ADP
ejpam-6838	349	25	the	the	DET
ejpam-6838	349	26	mae	mae	PROPN
ejpam-6838	349	27	for	for	ADP
ejpam-6838	349	28	example	example	NOUN
ejpam-6838	349	29	2	2	NUM
ejpam-6838	349	30	.	.	X
ejpam-6838	349	31	ζ	ζ	NOUN
ejpam-6838	349	32	method	method	NOUN
ejpam-6838	349	33	in	in	ADP
ejpam-6838	349	34	[	[	X
ejpam-6838	349	35	20	20	NUM
ejpam-6838	349	36	]	]	PUNCT
ejpam-6838	349	37	(	(	PUNCT
ejpam-6838	349	38	m	m	NOUN
ejpam-6838	349	39	=	=	SYM
ejpam-6838	349	40	32	32	NUM
ejpam-6838	349	41	and	and	CCONJ
ejpam-6838	349	42	∆x	∆x	PROPN
ejpam-6838	349	43	=	=	SYM
ejpam-6838	349	44	0.001	0.001	NUM
ejpam-6838	349	45	)	)	PUNCT
ejpam-6838	349	46	our	our	PRON
ejpam-6838	349	47	method	method	NOUN
ejpam-6838	349	48	(	(	PUNCT
ejpam-6838	349	49	m	m	PROPN
ejpam-6838	349	50	=	=	SYM
ejpam-6838	349	51	8)	8)	NUM
ejpam-6838	349	52	0.5	0.5	NUM
ejpam-6838	349	53	1.10×	1.10×	NUM
ejpam-6838	349	54	10−3	10−3	NUM
ejpam-6838	349	55	3.30215×	3.30215×	NUM
ejpam-6838	349	56	10−6	10−6	NUM
ejpam-6838	349	57	0.7	0.7	NUM
ejpam-6838	349	58	3.21×	3.21×	NUM
ejpam-6838	349	59	10−3	10−3	NUM
ejpam-6838	349	60	3.30734×	3.30734×	NUM
ejpam-6838	349	61	10−6	10−6	NUM
ejpam-6838	349	62	◆	◆	NOUN
ejpam-6838	349	63	◆	◆	PUNCT
ejpam-6838	349	64	◆	◆	NOUN
ejpam-6838	349	65	◆	◆	NOUN
ejpam-6838	349	66	◆	◆	X
ejpam-6838	349	67	◆	◆	SYM
ejpam-6838	349	68	◆	◆	SYM
ejpam-6838	349	69	2	2	NUM
ejpam-6838	349	70	3	3	NUM
ejpam-6838	349	71	4	4	NUM
ejpam-6838	349	72	5	5	NUM
ejpam-6838	349	73	6	6	NUM
ejpam-6838	349	74	7	7	NUM
ejpam-6838	349	75	8	8	NUM
ejpam-6838	349	76	10	10	NUM
ejpam-6838	349	77	5	5	NUM
ejpam-6838	349	78	10	10	NUM
ejpam-6838	349	79	4	4	NUM
ejpam-6838	349	80	0.001	0.001	NUM
ejpam-6838	349	81	0.010	0.010	NUM
ejpam-6838	349	82	0.100	0.100	NUM
ejpam-6838	349	83	ℳ	ℳ	PROPN
ejpam-6838	349	84	e	e	NOUN
ejpam-6838	349	85	rr	rr	NOUN
ejpam-6838	349	86	o	o	PROPN
ejpam-6838	349	87	rs	rs	PROPN
ejpam-6838	349	88	◆	◆	PROPN
ejpam-6838	349	89	maes	maes	PROPN
ejpam-6838	349	90	figure	figure	NOUN
ejpam-6838	349	91	2	2	NUM
ejpam-6838	349	92	:	:	PUNCT
ejpam-6838	349	93	the	the	DET
ejpam-6838	349	94	mae	mae	PROPN
ejpam-6838	349	95	of	of	ADP
ejpam-6838	349	96	example	example	NOUN
ejpam-6838	349	97	2	2	NUM
ejpam-6838	349	98	at	at	ADP
ejpam-6838	349	99	various	various	ADJ
ejpam-6838	349	100	values	value	NOUN
ejpam-6838	349	101	of	of	ADP
ejpam-6838	349	102	m	m	PRON
ejpam-6838	349	103	when	when	SCONJ
ejpam-6838	349	104	ζ	ζ	X
ejpam-6838	349	105	=	=	SYM
ejpam-6838	349	106	0.5	0.5	NUM
ejpam-6838	349	107	.	.	PUNCT
ejpam-6838	349	108	table	table	NOUN
ejpam-6838	349	109	4	4	NUM
ejpam-6838	349	110	:	:	PUNCT
ejpam-6838	349	111	the	the	DET
ejpam-6838	349	112	ae	ae	PROPN
ejpam-6838	349	113	of	of	ADP
ejpam-6838	349	114	example	example	NOUN
ejpam-6838	349	115	2	2	NUM
ejpam-6838	349	116	at	at	ADP
ejpam-6838	349	117	ζ	ζ	NOUN
ejpam-6838	349	118	=	=	SYM
ejpam-6838	349	119	0.7	0.7	NUM
ejpam-6838	349	120	,	,	PUNCT
ejpam-6838	349	121	m	m	VERB
ejpam-6838	349	122	=	=	NOUN
ejpam-6838	349	123	8	8	NUM
ejpam-6838	349	124	.	.	PUNCT
ejpam-6838	350	1	x	x	X
ejpam-6838	350	2	t	t	NOUN
ejpam-6838	350	3	=	=	NUM
ejpam-6838	350	4	0.2	0.2	NUM
ejpam-6838	350	5	t	t	NOUN
ejpam-6838	350	6	=	=	NUM
ejpam-6838	350	7	0.4	0.4	NUM
ejpam-6838	350	8	t	t	NOUN
ejpam-6838	350	9	=	=	SYM
ejpam-6838	350	10	0.6	0.6	NUM
ejpam-6838	350	11	t	t	NOUN
ejpam-6838	350	12	=	=	NOUN
ejpam-6838	350	13	0.8	0.8	NUM
ejpam-6838	350	14	0.1	0.1	NUM
ejpam-6838	350	15	2.98478×	2.98478×	NUM
ejpam-6838	350	16	10−7	10−7	NUM
ejpam-6838	350	17	5.82311×	5.82311×	NOUN
ejpam-6838	350	18	10−7	10−7	NUM
ejpam-6838	350	19	6.6952×	6.6952×	PRON
ejpam-6838	350	20	10−7	10−7	NUM
ejpam-6838	350	21	4.94957×	4.94957×	NOUN
ejpam-6838	350	22	10−7	10−7	NUM
ejpam-6838	350	23	0.2	0.2	NUM
ejpam-6838	350	24	6.22613×	6.22613×	NUM
ejpam-6838	350	25	10−7	10−7	NUM
ejpam-6838	350	26	1.19821×	1.19821×	NUM
ejpam-6838	350	27	10−6	10−6	NUM
ejpam-6838	350	28	1.36547×	1.36547×	NUM
ejpam-6838	350	29	10−6	10−6	NUM
ejpam-6838	350	30	9.99651×	9.99651×	NUM
ejpam-6838	350	31	10−7	10−7	NUM
ejpam-6838	350	32	0.3	0.3	NUM
ejpam-6838	350	33	9.18475×	9.18475×	NOUN
ejpam-6838	350	34	10−7	10−7	NUM
ejpam-6838	350	35	1.75345×	1.75345×	NUM
ejpam-6838	350	36	10−6	10−6	NUM
ejpam-6838	350	37	1.98639×	1.98639×	NUM
ejpam-6838	350	38	10−6	10−6	NUM
ejpam-6838	350	39	1.44529×	1.44529×	NUM
ejpam-6838	350	40	10−6	10−6	NUM
ejpam-6838	350	41	0.4	0.4	NUM
ejpam-6838	350	42	1.33961×	1.33961×	NUM
ejpam-6838	350	43	10−6	10−6	NUM
ejpam-6838	350	44	2.48775×	2.48775×	NOUN
ejpam-6838	350	45	10−6	10−6	NUM
ejpam-6838	350	46	2.76405×	2.76405×	NUM
ejpam-6838	350	47	10−6	10−6	NUM
ejpam-6838	350	48	1.96795×	1.96795×	NUM
ejpam-6838	350	49	10−6	10−6	NUM
ejpam-6838	350	50	0.5	0.5	NUM
ejpam-6838	350	51	1.57757×	1.57757×	NUM
ejpam-6838	350	52	10−6	10−6	NUM
ejpam-6838	350	53	2.89203×	2.89203×	NUM
ejpam-6838	350	54	10−6	10−6	NUM
ejpam-6838	350	55	3.18343×	3.18343×	NUM
ejpam-6838	350	56	10−6	10−6	NUM
ejpam-6838	350	57	2.24218×	2.24218×	NUM
ejpam-6838	350	58	10−6	10−6	NUM
ejpam-6838	350	59	0.6	0.6	NUM
ejpam-6838	350	60	1.33959×	1.33959×	NUM
ejpam-6838	350	61	10−6	10−6	NUM
ejpam-6838	350	62	2.488×	2.488×	NUM
ejpam-6838	350	63	10−6	10−6	NUM
ejpam-6838	350	64	2.76412×	2.76412×	NUM
ejpam-6838	350	65	10−6	10−6	NUM
ejpam-6838	350	66	1.96804×	1.96804×	NUM
ejpam-6838	350	67	10−6	10−6	NUM
ejpam-6838	350	68	0.7	0.7	NUM
ejpam-6838	350	69	9.18451×	9.18451×	NUM
ejpam-6838	350	70	10−7	10−7	NUM
ejpam-6838	350	71	1.75373×	1.75373×	NUM
ejpam-6838	350	72	10−6	10−6	NUM
ejpam-6838	350	73	1.98646×	1.98646×	NUM
ejpam-6838	350	74	10−6	10−6	NUM
ejpam-6838	350	75	1.44539×	1.44539×	NUM
ejpam-6838	350	76	10−6	10−6	NUM
ejpam-6838	350	77	0.8	0.8	NUM
ejpam-6838	350	78	6.22605×	6.22605×	NUM
ejpam-6838	350	79	10−7	10−7	NUM
ejpam-6838	350	80	1.19833×	1.19833×	NUM
ejpam-6838	350	81	10−6	10−6	NUM
ejpam-6838	350	82	1.36551×	1.36551×	NUM
ejpam-6838	350	83	10−6	10−6	NUM
ejpam-6838	350	84	9.99693×	9.99693×	NUM
ejpam-6838	350	85	10−7	10−7	NUM
ejpam-6838	350	86	0.9	0.9	NUM
ejpam-6838	350	87	2.98475×	2.98475×	NOUN
ejpam-6838	350	88	10−7	10−7	NUM
ejpam-6838	350	89	5.82369×	5.82369×	NUM
ejpam-6838	350	90	10−7	10−7	NUM
ejpam-6838	350	91	6.69545×	6.69545×	NUM
ejpam-6838	350	92	10−7	10−7	NUM
ejpam-6838	350	93	4.94976×	4.94976×	NUM
ejpam-6838	350	94	10−7	10−7	NUM
ejpam-6838	350	95	w.	w.	PROPN
ejpam-6838	350	96	m.	m.	PROPN
ejpam-6838	350	97	abd	abd	PROPN
ejpam-6838	350	98	-	-	PUNCT
ejpam-6838	350	99	elhameed	elhameed	PROPN
ejpam-6838	350	100	et	et	PROPN
ejpam-6838	350	101	al	al	PROPN
ejpam-6838	350	102	.	.	PUNCT
ejpam-6838	350	103	/	/	SYM
ejpam-6838	350	104	eur	eur	PROPN
ejpam-6838	350	105	.	.	PUNCT
ejpam-6838	351	1	j.	j.	PROPN
ejpam-6838	351	2	pure	pure	PROPN
ejpam-6838	351	3	appl	appl	PROPN
ejpam-6838	351	4	.	.	PROPN
ejpam-6838	351	5	math	math	PROPN
ejpam-6838	351	6	,	,	PUNCT
ejpam-6838	351	7	18	18	NUM
ejpam-6838	351	8	(	(	PUNCT
ejpam-6838	351	9	4	4	NUM
ejpam-6838	351	10	)	)	PUNCT
ejpam-6838	351	11	(	(	PUNCT
ejpam-6838	351	12	2025	2025	NUM
ejpam-6838	351	13	)	)	PUNCT
ejpam-6838	351	14	,	,	PUNCT
ejpam-6838	351	15	6838	6838	NUM
ejpam-6838	351	16	17	17	NUM
ejpam-6838	351	17	of	of	ADP
ejpam-6838	351	18	25	25	NUM
ejpam-6838	351	19	2	2	NUM
ejpam-6838	351	20	3	3	NUM
ejpam-6838	351	21	4	4	NUM
ejpam-6838	351	22	5	5	NUM
ejpam-6838	351	23	6	6	NUM
ejpam-6838	351	24	7	7	NUM
ejpam-6838	351	25	8	8	NUM
ejpam-6838	351	26	10	10	NUM
ejpam-6838	351	27	-5	-5	NUM
ejpam-6838	351	28	10	10	NUM
ejpam-6838	351	29	-4	-4	SYM
ejpam-6838	351	30	0.001	0.001	NUM
ejpam-6838	351	31	0.010	0.010	NUM
ejpam-6838	351	32	0.100	0.100	NUM
ejpam-6838	351	33	ℳ	ℳ	PROPN
ejpam-6838	351	34	e	e	NOUN
ejpam-6838	351	35	rr	rr	NOUN
ejpam-6838	351	36	o	o	PROPN
ejpam-6838	351	37	rs	rs	PROPN
ejpam-6838	351	38	l∞-error	l∞-error	PROPN
ejpam-6838	351	39	figure	figure	NOUN
ejpam-6838	351	40	3	3	NUM
ejpam-6838	351	41	:	:	PUNCT
ejpam-6838	351	42	the	the	DET
ejpam-6838	351	43	l∞-error	l∞-error	NOUN
ejpam-6838	351	44	of	of	ADP
ejpam-6838	351	45	example	example	NOUN
ejpam-6838	351	46	2	2	NUM
ejpam-6838	351	47	at	at	ADP
ejpam-6838	351	48	various	various	ADJ
ejpam-6838	351	49	values	value	NOUN
ejpam-6838	351	50	of	of	ADP
ejpam-6838	351	51	m	m	PRON
ejpam-6838	351	52	when	when	SCONJ
ejpam-6838	351	53	ζ	ζ	X
ejpam-6838	351	54	=	=	SYM
ejpam-6838	351	55	0.5	0.5	NUM
ejpam-6838	351	56	.	.	PUNCT
ejpam-6838	351	57	table	table	NOUN
ejpam-6838	351	58	5	5	NUM
ejpam-6838	351	59	:	:	PUNCT
ejpam-6838	351	60	the	the	DET
ejpam-6838	351	61	errors	error	NOUN
ejpam-6838	351	62	of	of	ADP
ejpam-6838	351	63	example	example	NOUN
ejpam-6838	351	64	2	2	NUM
ejpam-6838	351	65	at	at	ADP
ejpam-6838	351	66	various	various	ADJ
ejpam-6838	351	67	values	value	NOUN
ejpam-6838	351	68	of	of	ADP
ejpam-6838	351	69	m	m	PRON
ejpam-6838	351	70	when	when	SCONJ
ejpam-6838	351	71	ζ	ζ	NOUN
ejpam-6838	351	72	=	=	SYM
ejpam-6838	351	73	0.9	0.9	NUM
ejpam-6838	351	74	.	.	PUNCT
ejpam-6838	352	1	m	m	VERB
ejpam-6838	352	2	2	2	NUM
ejpam-6838	352	3	4	4	NUM
ejpam-6838	352	4	6	6	NUM
ejpam-6838	352	5	8	8	NUM
ejpam-6838	352	6	mae	mae	PROPN
ejpam-6838	352	7	2.90874×10−1	2.90874×10−1	NUM
ejpam-6838	352	8	1.55707×10−2	1.55707×10−2	NUM
ejpam-6838	352	9	2.98468×10−4	2.98468×10−4	NUM
ejpam-6838	352	10	3.31145×10−6	3.31145×10−6	NUM
ejpam-6838	352	11	l∞-error	l∞-error	NOUN
ejpam-6838	352	12	2.91952×10−1	2.91952×10−1	NUM
ejpam-6838	352	13	1.57822×10−2	1.57822×10−2	NUM
ejpam-6838	352	14	3.02187×10−4	3.02187×10−4	NUM
ejpam-6838	352	15	3.35344×10−6	3.35344×10−6	NUM
ejpam-6838	352	16	table	table	NOUN
ejpam-6838	352	17	6	6	NUM
ejpam-6838	352	18	:	:	PUNCT
ejpam-6838	352	19	the	the	DET
ejpam-6838	352	20	errors	error	NOUN
ejpam-6838	352	21	of	of	ADP
ejpam-6838	352	22	example	example	NOUN
ejpam-6838	352	23	2	2	NUM
ejpam-6838	352	24	at	at	ADP
ejpam-6838	352	25	various	various	ADJ
ejpam-6838	352	26	values	value	NOUN
ejpam-6838	352	27	of	of	ADP
ejpam-6838	352	28	m	m	PRON
ejpam-6838	352	29	when	when	SCONJ
ejpam-6838	352	30	ζ	ζ	NOUN
ejpam-6838	352	31	=	=	SYM
ejpam-6838	352	32	0.3	0.3	NUM
ejpam-6838	352	33	.	.	PUNCT
ejpam-6838	353	1	m	m	VERB
ejpam-6838	353	2	2	2	NUM
ejpam-6838	353	3	3	3	NUM
ejpam-6838	353	4	4	4	NUM
ejpam-6838	353	5	5	5	NUM
ejpam-6838	353	6	6	6	NUM
ejpam-6838	353	7	7	7	NUM
ejpam-6838	353	8	8	8	NUM
ejpam-6838	353	9	mae	mae	PROPN
ejpam-6838	353	10	3.0980×10−1	3.0980×10−1	NUM
ejpam-6838	353	11	2.854×10−1	2.854×10−1	NUM
ejpam-6838	353	12	2.8600×10−2	2.8600×10−2	NUM
ejpam-6838	353	13	1.4596×10−2	1.4596×10−2	NUM
ejpam-6838	353	14	3.0076×10−4	3.0076×10−4	NUM
ejpam-6838	353	15	2.8939×10−4	2.8939×10−4	NUM
ejpam-6838	353	16	3.3021×10−6	3.3021×10−6	NOUN
ejpam-6838	353	17	l∞-error	l∞-error	NOUN
ejpam-6838	353	18	3.0986×10−1	3.0986×10−1	NUM
ejpam-6838	353	19	2.8600×10−1	2.8600×10−1	NUM
ejpam-6838	353	20	1.5560×10−2	1.5560×10−2	NUM
ejpam-6838	353	21	1.4612×10−2	1.4612×10−2	NUM
ejpam-6838	353	22	3.0092×10−4	3.0092×10−4	NUM
ejpam-6838	353	23	2.8949×10−4	2.8949×10−4	NUM
ejpam-6838	353	24	3.3090×10−6	3.3090×10−6	NUM
ejpam-6838	353	25	example	example	NOUN
ejpam-6838	353	26	3	3	NUM
ejpam-6838	353	27	.	.	X
ejpam-6838	353	28	consider	consider	VERB
ejpam-6838	353	29	the	the	DET
ejpam-6838	353	30	following	follow	VERB
ejpam-6838	353	31	equation	equation	NOUN
ejpam-6838	353	32	:	:	PUNCT
ejpam-6838	353	33	dζ	dζ	PROPN
ejpam-6838	353	34	t	t	PROPN
ejpam-6838	353	35	λ(x	λ(x	PROPN
ejpam-6838	353	36	,	,	PUNCT
ejpam-6838	353	37	t)−	t)−	PROPN
ejpam-6838	353	38	λxx(x	λxx(x	PROPN
ejpam-6838	353	39	,	,	PUNCT
ejpam-6838	353	40	t	t	PROPN
ejpam-6838	353	41	)	)	PUNCT
ejpam-6838	353	42	=	=	SYM
ejpam-6838	353	43	(	(	PUNCT
ejpam-6838	353	44	π2	π2	X
ejpam-6838	353	45	t2	t2	NOUN
ejpam-6838	353	46	+	+	CCONJ
ejpam-6838	353	47	2	2	NUM
ejpam-6838	353	48	t2−α	t2−α	PROPN
ejpam-6838	353	49	γ(3−	γ(3−	ADP
ejpam-6838	353	50	α	α	NUM
ejpam-6838	353	51	)	)	PUNCT
ejpam-6838	353	52	)	)	PUNCT
ejpam-6838	354	1	sin(π	sin(π	PROPN
ejpam-6838	354	2	x	x	SYM
ejpam-6838	354	3	)	)	PUNCT
ejpam-6838	354	4	,	,	PUNCT
ejpam-6838	354	5	0	0	NUM
ejpam-6838	354	6	<	<	X
ejpam-6838	354	7	α	α	PROPN
ejpam-6838	354	8	≤	≤	NUM
ejpam-6838	354	9	1	1	NUM
ejpam-6838	354	10	,	,	PUNCT
ejpam-6838	354	11	(	(	PUNCT
ejpam-6838	354	12	68	68	NUM
ejpam-6838	354	13	)	)	PUNCT
ejpam-6838	354	14	subject	subject	NOUN
ejpam-6838	354	15	to	to	ADP
ejpam-6838	354	16	the	the	DET
ejpam-6838	354	17	ic	ic	PROPN
ejpam-6838	354	18	λ(x	λ(x	PROPN
ejpam-6838	354	19	,	,	PUNCT
ejpam-6838	354	20	0	0	NUM
ejpam-6838	354	21	)	)	PUNCT
ejpam-6838	354	22	=	=	SYM
ejpam-6838	354	23	0	0	NUM
ejpam-6838	354	24	,	,	PUNCT
ejpam-6838	354	25	0	0	NUM
ejpam-6838	354	26	<	<	X
ejpam-6838	354	27	x	x	SYM
ejpam-6838	354	28	≤	≤	NUM
ejpam-6838	354	29	1	1	NUM
ejpam-6838	354	30	,	,	PUNCT
ejpam-6838	354	31	(	(	PUNCT
ejpam-6838	354	32	69	69	NUM
ejpam-6838	354	33	)	)	PUNCT
ejpam-6838	354	34	and	and	CCONJ
ejpam-6838	354	35	the	the	DET
ejpam-6838	354	36	hbcs	hbc	NOUN
ejpam-6838	354	37	λ(0	λ(0	PROPN
ejpam-6838	354	38	,	,	PUNCT
ejpam-6838	354	39	t	t	PROPN
ejpam-6838	354	40	)	)	PUNCT
ejpam-6838	354	41	=	=	SYM
ejpam-6838	355	1	λ(1	λ(1	PROPN
ejpam-6838	355	2	,	,	PUNCT
ejpam-6838	355	3	t	t	PROPN
ejpam-6838	355	4	)	)	PUNCT
ejpam-6838	355	5	=	=	SYM
ejpam-6838	355	6	0	0	NUM
ejpam-6838	355	7	,	,	PUNCT
ejpam-6838	355	8	0	0	NUM
ejpam-6838	355	9	<	<	X
ejpam-6838	355	10	t	t	X
ejpam-6838	355	11	≤	≤	NUM
ejpam-6838	355	12	1	1	NUM
ejpam-6838	355	13	,	,	PUNCT
ejpam-6838	355	14	(	(	PUNCT
ejpam-6838	355	15	70	70	NUM
ejpam-6838	355	16	)	)	PUNCT
ejpam-6838	356	1	where	where	SCONJ
ejpam-6838	356	2	λ(x	λ(x	PROPN
ejpam-6838	356	3	,	,	PUNCT
ejpam-6838	356	4	t	t	PROPN
ejpam-6838	356	5	)	)	PUNCT
ejpam-6838	356	6	=	=	SYM
ejpam-6838	356	7	t2	t2	NOUN
ejpam-6838	356	8	sin(π	sin(π	PROPN
ejpam-6838	356	9	x	x	SYM
ejpam-6838	356	10	)	)	PUNCT
ejpam-6838	356	11	is	be	AUX
ejpam-6838	356	12	the	the	DET
ejpam-6838	356	13	exact	exact	ADJ
ejpam-6838	356	14	solution	solution	NOUN
ejpam-6838	356	15	of	of	ADP
ejpam-6838	356	16	this	this	DET
ejpam-6838	356	17	problem	problem	NOUN
ejpam-6838	356	18	.	.	PUNCT
ejpam-6838	357	1	figure	figure	NOUN
ejpam-6838	357	2	4	4	NUM
ejpam-6838	357	3	illustrates	illustrate	VERB
ejpam-6838	357	4	the	the	DET
ejpam-6838	357	5	mae	mae	PROPN
ejpam-6838	357	6	and	and	CCONJ
ejpam-6838	357	7	l∞-error	l∞-error	NOUN
ejpam-6838	357	8	at	at	ADP
ejpam-6838	357	9	various	various	ADJ
ejpam-6838	357	10	values	value	NOUN
ejpam-6838	357	11	of	of	ADP
ejpam-6838	357	12	m	m	PRON
ejpam-6838	357	13	when	when	SCONJ
ejpam-6838	357	14	ζ	ζ	X
ejpam-6838	357	15	=	=	SYM
ejpam-6838	357	16	0.5	0.5	NUM
ejpam-6838	357	17	.	.	PUNCT
ejpam-6838	357	18	table	table	NOUN
ejpam-6838	357	19	7	7	NUM
ejpam-6838	357	20	shows	show	VERB
ejpam-6838	357	21	the	the	DET
ejpam-6838	357	22	ae	ae	PROPN
ejpam-6838	357	23	at	at	ADP
ejpam-6838	357	24	various	various	ADJ
ejpam-6838	357	25	values	value	NOUN
ejpam-6838	357	26	of	of	ADP
ejpam-6838	357	27	t	t	NOUN
ejpam-6838	357	28	when	when	SCONJ
ejpam-6838	357	29	ζ	ζ	NOUN
ejpam-6838	357	30	=	=	SYM
ejpam-6838	357	31	0.9	0.9	NUM
ejpam-6838	357	32	and	and	CCONJ
ejpam-6838	357	33	m	m	PROPN
ejpam-6838	357	34	=	=	ADJ
ejpam-6838	357	35	8	8	NUM
ejpam-6838	357	36	.	.	PUNCT
ejpam-6838	357	37	table	table	NOUN
ejpam-6838	357	38	8	8	NUM
ejpam-6838	357	39	shows	show	VERB
ejpam-6838	357	40	the	the	DET
ejpam-6838	357	41	mae	mae	PROPN
ejpam-6838	357	42	and	and	CCONJ
ejpam-6838	357	43	l∞-error	l∞-error	NOUN
ejpam-6838	357	44	at	at	ADP
ejpam-6838	357	45	various	various	ADJ
ejpam-6838	357	46	values	value	NOUN
ejpam-6838	357	47	of	of	ADP
ejpam-6838	357	48	m	m	PRON
ejpam-6838	357	49	when	when	SCONJ
ejpam-6838	357	50	ζ	ζ	X
ejpam-6838	357	51	=	=	SYM
ejpam-6838	357	52	0.9	0.9	NUM
ejpam-6838	357	53	.	.	PUNCT
ejpam-6838	358	1	figure	figure	NOUN
ejpam-6838	358	2	5	5	NUM
ejpam-6838	358	3	illustrates	illustrate	VERB
ejpam-6838	358	4	the	the	DET
ejpam-6838	358	5	ae	ae	PROPN
ejpam-6838	358	6	at	at	ADP
ejpam-6838	358	7	various	various	ADJ
ejpam-6838	358	8	values	value	NOUN
ejpam-6838	358	9	of	of	ADP
ejpam-6838	358	10	m	m	PRON
ejpam-6838	358	11	when	when	SCONJ
ejpam-6838	358	12	ζ	ζ	NOUN
ejpam-6838	358	13	=	=	SYM
ejpam-6838	358	14	0.3	0.3	NUM
ejpam-6838	358	15	.	.	PUNCT
ejpam-6838	359	1	w.	w.	PROPN
ejpam-6838	359	2	m.	m.	PROPN
ejpam-6838	359	3	abd	abd	PROPN
ejpam-6838	359	4	-	-	PUNCT
ejpam-6838	359	5	elhameed	elhameed	PROPN
ejpam-6838	359	6	et	et	PROPN
ejpam-6838	359	7	al	al	PROPN
ejpam-6838	359	8	.	.	PUNCT
ejpam-6838	359	9	/	/	SYM
ejpam-6838	359	10	eur	eur	PROPN
ejpam-6838	359	11	.	.	PUNCT
ejpam-6838	360	1	j.	j.	PROPN
ejpam-6838	360	2	pure	pure	PROPN
ejpam-6838	360	3	appl	appl	PROPN
ejpam-6838	360	4	.	.	PROPN
ejpam-6838	360	5	math	math	PROPN
ejpam-6838	360	6	,	,	PUNCT
ejpam-6838	360	7	18	18	NUM
ejpam-6838	360	8	(	(	PUNCT
ejpam-6838	360	9	4	4	NUM
ejpam-6838	360	10	)	)	PUNCT
ejpam-6838	360	11	(	(	PUNCT
ejpam-6838	360	12	2025	2025	NUM
ejpam-6838	360	13	)	)	PUNCT
ejpam-6838	360	14	,	,	PUNCT
ejpam-6838	360	15	6838	6838	NUM
ejpam-6838	360	16	18	18	NUM
ejpam-6838	360	17	of	of	ADP
ejpam-6838	360	18	25	25	NUM
ejpam-6838	360	19	◆	◆	NOUN
ejpam-6838	360	20	◆	◆	PUNCT
ejpam-6838	360	21	◆	◆	NOUN
ejpam-6838	360	22	◆	◆	NOUN
ejpam-6838	360	23	◆	◆	X
ejpam-6838	360	24	◆	◆	SYM
ejpam-6838	360	25	◆	◆	SYM
ejpam-6838	360	26	2	2	NUM
ejpam-6838	360	27	3	3	NUM
ejpam-6838	360	28	4	4	NUM
ejpam-6838	360	29	5	5	NUM
ejpam-6838	360	30	6	6	NUM
ejpam-6838	360	31	7	7	NUM
ejpam-6838	360	32	8	8	NUM
ejpam-6838	360	33	10	10	NUM
ejpam-6838	360	34	6	6	NUM
ejpam-6838	360	35	10	10	NUM
ejpam-6838	360	36	5	5	NUM
ejpam-6838	360	37	10	10	NUM
ejpam-6838	360	38	4	4	NUM
ejpam-6838	360	39	0.001	0.001	NUM
ejpam-6838	360	40	0.010	0.010	NUM
ejpam-6838	360	41	0.100	0.100	NUM
ejpam-6838	360	42	ℳ	ℳ	PROPN
ejpam-6838	360	43	e	e	NOUN
ejpam-6838	360	44	rr	rr	NOUN
ejpam-6838	360	45	o	o	PROPN
ejpam-6838	360	46	rs	rs	PROPN
ejpam-6838	360	47	◆	◆	PROPN
ejpam-6838	360	48	maes	maes	PROPN
ejpam-6838	360	49	l∞-error	l∞-error	PROPN
ejpam-6838	360	50	figure	figure	NOUN
ejpam-6838	360	51	4	4	NUM
ejpam-6838	360	52	:	:	PUNCT
ejpam-6838	360	53	the	the	DET
ejpam-6838	360	54	errors	error	NOUN
ejpam-6838	360	55	of	of	ADP
ejpam-6838	360	56	example	example	NOUN
ejpam-6838	360	57	3	3	NUM
ejpam-6838	360	58	at	at	ADP
ejpam-6838	360	59	various	various	ADJ
ejpam-6838	360	60	values	value	NOUN
ejpam-6838	360	61	of	of	ADP
ejpam-6838	360	62	m	m	PRON
ejpam-6838	360	63	when	when	SCONJ
ejpam-6838	360	64	ζ	ζ	X
ejpam-6838	360	65	=	=	SYM
ejpam-6838	360	66	0.5	0.5	NUM
ejpam-6838	360	67	.	.	PUNCT
ejpam-6838	360	68	table	table	NOUN
ejpam-6838	360	69	7	7	NUM
ejpam-6838	360	70	:	:	PUNCT
ejpam-6838	360	71	the	the	DET
ejpam-6838	360	72	ae	ae	PROPN
ejpam-6838	360	73	of	of	ADP
ejpam-6838	360	74	example	example	NOUN
ejpam-6838	360	75	3	3	NUM
ejpam-6838	360	76	at	at	ADP
ejpam-6838	360	77	ζ	ζ	NOUN
ejpam-6838	360	78	=	=	SYM
ejpam-6838	360	79	0.9	0.9	NUM
ejpam-6838	360	80	,	,	PUNCT
ejpam-6838	360	81	m	m	VERB
ejpam-6838	360	82	=	=	NOUN
ejpam-6838	360	83	8	8	NUM
ejpam-6838	360	84	.	.	PUNCT
ejpam-6838	361	1	x	x	X
ejpam-6838	361	2	t	t	NOUN
ejpam-6838	361	3	=	=	NUM
ejpam-6838	361	4	0.2	0.2	NUM
ejpam-6838	361	5	t	t	NOUN
ejpam-6838	361	6	=	=	NUM
ejpam-6838	361	7	0.4	0.4	NUM
ejpam-6838	361	8	t	t	NOUN
ejpam-6838	361	9	=	=	SYM
ejpam-6838	361	10	0.6	0.6	NUM
ejpam-6838	361	11	t	t	NOUN
ejpam-6838	361	12	=	=	NOUN
ejpam-6838	361	13	0.8	0.8	NUM
ejpam-6838	361	14	0.1	0.1	NUM
ejpam-6838	361	15	1.1953×	1.1953×	NUM
ejpam-6838	361	16	10−8	10−8	NUM
ejpam-6838	361	17	6.96178×	6.96178×	NOUN
ejpam-6838	362	1	10−8	10−8	NUM
ejpam-6838	362	2	1.83032×	1.83032×	NUM
ejpam-6838	362	3	10−7	10−7	NUM
ejpam-6838	362	4	3.5209×	3.5209×	NUM
ejpam-6838	362	5	10−7	10−7	NUM
ejpam-6838	362	6	0.2	0.2	NUM
ejpam-6838	362	7	2.62526×	2.62526×	NUM
ejpam-6838	362	8	10−8	10−8	NUM
ejpam-6838	362	9	1.47194×	1.47194×	NUM
ejpam-6838	362	10	10−7	10−7	NUM
ejpam-6838	362	11	3.81809×	3.81809×	NUM
ejpam-6838	362	12	10−7	10−7	NUM
ejpam-6838	362	13	7.30076×	7.30076×	NUM
ejpam-6838	362	14	10−7	10−7	NUM
ejpam-6838	362	15	0.3	0.3	NUM
ejpam-6838	362	16	3.98826×	3.98826×	NUM
ejpam-6838	362	17	10−8	10−8	NUM
ejpam-6838	362	18	2.18594×	2.18594×	NUM
ejpam-6838	362	19	10−7	10−7	NUM
ejpam-6838	362	20	5.63519×	5.63519×	NUM
ejpam-6838	362	21	10−7	10−7	NUM
ejpam-6838	362	22	1.44529×	1.44529×	NUM
ejpam-6838	362	23	10−6	10−6	NUM
ejpam-6838	362	24	0.4	0.4	NUM
ejpam-6838	362	25	6.41293×	6.41293×	NUM
ejpam-6838	362	26	10−8	10−8	NUM
ejpam-6838	362	27	3.26744×	3.26744×	NUM
ejpam-6838	362	28	10−7	10−7	NUM
ejpam-6838	362	29	8.22244×	8.22244×	NOUN
ejpam-6838	362	30	10−7	10−7	NUM
ejpam-6838	362	31	1.07306×	1.07306×	NUM
ejpam-6838	362	32	10−6	10−6	NUM
ejpam-6838	362	33	0.5	0.5	NUM
ejpam-6838	362	34	7.8752×	7.8752×	NUM
ejpam-6838	362	35	10−8	10−8	NUM
ejpam-6838	362	36	3.89168×	3.89168×	NUM
ejpam-6838	362	37	10−7	10−7	NUM
ejpam-6838	362	38	9.68425×	9.68425×	NUM
ejpam-6838	362	39	10−7	10−7	NUM
ejpam-6838	362	40	1.54566×	1.54566×	NOUN
ejpam-6838	362	41	10−6	10−6	NUM
ejpam-6838	362	42	0.6	0.6	NUM
ejpam-6838	362	43	6.41292×	6.41292×	NOUN
ejpam-6838	362	44	10−8	10−8	NUM
ejpam-6838	362	45	3.26811×	3.26811×	NUM
ejpam-6838	362	46	10−7	10−7	NUM
ejpam-6838	362	47	8.22324×	8.22324×	NUM
ejpam-6838	362	48	10−7	10−7	NUM
ejpam-6838	362	49	1.80976×	1.80976×	NUM
ejpam-6838	362	50	10−6	10−6	NUM
ejpam-6838	362	51	0.7	0.7	NUM
ejpam-6838	362	52	3.98859×	3.98859×	NUM
ejpam-6838	362	53	10−8	10−8	NUM
ejpam-6838	362	54	2.1865×	2.1865×	NUM
ejpam-6838	362	55	10−7	10−7	NUM
ejpam-6838	362	56	5.63611×	5.63611×	NUM
ejpam-6838	362	57	10−7	10−7	NUM
ejpam-6838	362	58	1.54565×	1.54565×	NUM
ejpam-6838	362	59	10−6	10−6	NUM
ejpam-6838	362	60	0.8	0.8	NUM
ejpam-6838	362	61	2.62589×	2.62589×	NOUN
ejpam-6838	362	62	10−8	10−8	NUM
ejpam-6838	362	63	1.47195×	1.47195×	NUM
ejpam-6838	362	64	10−7	10−7	NUM
ejpam-6838	362	65	3.81857×	3.81857×	NUM
ejpam-6838	362	66	10−7	10−7	NUM
ejpam-6838	362	67	7.3006×	7.3006×	NUM
ejpam-6838	362	68	10−7	10−7	NUM
ejpam-6838	362	69	0.9	0.9	NUM
ejpam-6838	362	70	1.19538×	1.19538×	NUM
ejpam-6838	362	71	10−8	10−8	NUM
ejpam-6838	362	72	6.96403×	6.96403×	NOUN
ejpam-6838	362	73	10−8	10−8	NUM
ejpam-6838	362	74	1.83059×	1.83059×	NUM
ejpam-6838	362	75	10−7	10−7	NUM
ejpam-6838	362	76	3.52091×	3.52091×	NUM
ejpam-6838	362	77	10−7	10−7	NUM
ejpam-6838	362	78	table	table	NOUN
ejpam-6838	362	79	8	8	NUM
ejpam-6838	362	80	:	:	PUNCT
ejpam-6838	362	81	the	the	DET
ejpam-6838	362	82	errors	error	NOUN
ejpam-6838	362	83	of	of	ADP
ejpam-6838	362	84	example	example	NOUN
ejpam-6838	362	85	3	3	NUM
ejpam-6838	362	86	at	at	ADP
ejpam-6838	362	87	various	various	ADJ
ejpam-6838	362	88	values	value	NOUN
ejpam-6838	362	89	of	of	ADP
ejpam-6838	362	90	m	m	PRON
ejpam-6838	362	91	when	when	SCONJ
ejpam-6838	362	92	ζ	ζ	NOUN
ejpam-6838	362	93	=	=	SYM
ejpam-6838	362	94	0.7	0.7	NUM
ejpam-6838	362	95	.	.	PUNCT
ejpam-6838	363	1	m	m	VERB
ejpam-6838	363	2	2	2	NUM
ejpam-6838	363	3	4	4	NUM
ejpam-6838	363	4	6	6	NUM
ejpam-6838	363	5	8	8	NUM
ejpam-6838	363	6	mae	mae	PROPN
ejpam-6838	363	7	8.7641×10−2	8.7641×10−2	NUM
ejpam-6838	363	8	4.11803×10−3	4.11803×10−3	NOUN
ejpam-6838	363	9	7.9429×10−5	7.9429×10−5	NUM
ejpam-6838	363	10	8.71518×10−7	8.71518×10−7	NUM
ejpam-6838	363	11	l∞-error	l∞-error	NOUN
ejpam-6838	363	12	2.54328×10−1	2.54328×10−1	NUM
ejpam-6838	363	13	1.32×10−2	1.32×10−2	NUM
ejpam-6838	364	1	2.66423×10−4	2.66423×10−4	NUM
ejpam-6838	364	2	2.94457×10−6	2.94457×10−6	NUM
ejpam-6838	364	3	example	example	NOUN
ejpam-6838	364	4	4	4	NUM
ejpam-6838	364	5	.	.	PUNCT
ejpam-6838	365	1	[	[	X
ejpam-6838	365	2	64	64	NUM
ejpam-6838	365	3	]	]	PUNCT
ejpam-6838	365	4	consider	consider	VERB
ejpam-6838	365	5	the	the	DET
ejpam-6838	365	6	following	follow	VERB
ejpam-6838	365	7	equation	equation	NOUN
ejpam-6838	365	8	dζ	dζ	PROPN
ejpam-6838	365	9	t	t	PROPN
ejpam-6838	365	10	λ(x	λ(x	PROPN
ejpam-6838	365	11	,	,	PUNCT
ejpam-6838	365	12	t)−	t)−	PROPN
ejpam-6838	365	13	λxx(x	λxx(x	PROPN
ejpam-6838	365	14	,	,	PUNCT
ejpam-6838	365	15	t	t	PROPN
ejpam-6838	365	16	)	)	PUNCT
ejpam-6838	365	17	=	=	SYM
ejpam-6838	366	1	(	(	PUNCT
ejpam-6838	366	2	4π2	4π2	NUM
ejpam-6838	366	3	t2	t2	NOUN
ejpam-6838	366	4	+	+	CCONJ
ejpam-6838	366	5	2	2	NUM
ejpam-6838	366	6	t2−α	t2−α	PROPN
ejpam-6838	366	7	γ(3−	γ(3−	ADP
ejpam-6838	366	8	α	α	NUM
ejpam-6838	366	9	)	)	PUNCT
ejpam-6838	366	10	)	)	PUNCT
ejpam-6838	366	11	sin(2π	sin(2π	NOUN
ejpam-6838	366	12	x	x	X
ejpam-6838	366	13	)	)	PUNCT
ejpam-6838	366	14	,	,	PUNCT
ejpam-6838	366	15	0	0	NUM
ejpam-6838	366	16	<	<	X
ejpam-6838	366	17	α	α	PROPN
ejpam-6838	366	18	≤	≤	NUM
ejpam-6838	366	19	1	1	NUM
ejpam-6838	366	20	,	,	PUNCT
ejpam-6838	366	21	(	(	PUNCT
ejpam-6838	366	22	71	71	NUM
ejpam-6838	366	23	)	)	PUNCT
ejpam-6838	366	24	subject	subject	NOUN
ejpam-6838	366	25	to	to	ADP
ejpam-6838	366	26	the	the	DET
ejpam-6838	366	27	initial	initial	ADJ
ejpam-6838	366	28	condition	condition	NOUN
ejpam-6838	366	29	(	(	PUNCT
ejpam-6838	366	30	ic	ic	NUM
ejpam-6838	366	31	):	):	PUNCT
ejpam-6838	366	32	λ(x	λ(x	PROPN
ejpam-6838	366	33	,	,	PUNCT
ejpam-6838	366	34	0	0	NUM
ejpam-6838	366	35	)	)	PUNCT
ejpam-6838	366	36	=	=	SYM
ejpam-6838	366	37	0	0	NUM
ejpam-6838	366	38	,	,	PUNCT
ejpam-6838	366	39	0	0	NUM
ejpam-6838	366	40	<	<	X
ejpam-6838	366	41	x	x	SYM
ejpam-6838	366	42	≤	≤	NUM
ejpam-6838	366	43	1	1	NUM
ejpam-6838	366	44	,	,	PUNCT
ejpam-6838	366	45	(	(	PUNCT
ejpam-6838	366	46	72	72	X
ejpam-6838	366	47	)	)	PUNCT
ejpam-6838	366	48	w.	w.	PROPN
ejpam-6838	366	49	m.	m.	PROPN
ejpam-6838	366	50	abd	abd	PROPN
ejpam-6838	366	51	-	-	PUNCT
ejpam-6838	366	52	elhameed	elhameed	PROPN
ejpam-6838	366	53	et	et	PROPN
ejpam-6838	366	54	al	al	PROPN
ejpam-6838	366	55	.	.	PUNCT
ejpam-6838	366	56	/	/	SYM
ejpam-6838	366	57	eur	eur	PROPN
ejpam-6838	366	58	.	.	PUNCT
ejpam-6838	367	1	j.	j.	PROPN
ejpam-6838	367	2	pure	pure	PROPN
ejpam-6838	367	3	appl	appl	PROPN
ejpam-6838	367	4	.	.	PROPN
ejpam-6838	367	5	math	math	PROPN
ejpam-6838	367	6	,	,	PUNCT
ejpam-6838	367	7	18	18	NUM
ejpam-6838	367	8	(	(	PUNCT
ejpam-6838	367	9	4	4	NUM
ejpam-6838	367	10	)	)	PUNCT
ejpam-6838	367	11	(	(	PUNCT
ejpam-6838	367	12	2025	2025	NUM
ejpam-6838	367	13	)	)	PUNCT
ejpam-6838	367	14	,	,	PUNCT
ejpam-6838	367	15	6838	6838	NUM
ejpam-6838	367	16	19	19	NUM
ejpam-6838	367	17	of	of	ADP
ejpam-6838	367	18	25	25	NUM
ejpam-6838	367	19	figure	figure	NOUN
ejpam-6838	367	20	5	5	NUM
ejpam-6838	367	21	:	:	PUNCT
ejpam-6838	367	22	the	the	DET
ejpam-6838	367	23	ae	ae	PROPN
ejpam-6838	367	24	of	of	ADP
ejpam-6838	367	25	example	example	NOUN
ejpam-6838	367	26	3	3	NUM
ejpam-6838	367	27	at	at	ADP
ejpam-6838	367	28	various	various	ADJ
ejpam-6838	367	29	values	value	NOUN
ejpam-6838	367	30	of	of	ADP
ejpam-6838	367	31	m	m	PRON
ejpam-6838	367	32	when	when	SCONJ
ejpam-6838	367	33	ζ	ζ	NOUN
ejpam-6838	367	34	=	=	SYM
ejpam-6838	367	35	0.3	0.3	NUM
ejpam-6838	367	36	.	.	PUNCT
ejpam-6838	368	1	and	and	CCONJ
ejpam-6838	368	2	the	the	DET
ejpam-6838	368	3	hbcs	hbc	NOUN
ejpam-6838	368	4	λ(0	λ(0	PROPN
ejpam-6838	368	5	,	,	PUNCT
ejpam-6838	368	6	t	t	PROPN
ejpam-6838	368	7	)	)	PUNCT
ejpam-6838	368	8	=	=	SYM
ejpam-6838	369	1	λ(1	λ(1	PROPN
ejpam-6838	369	2	,	,	PUNCT
ejpam-6838	369	3	t	t	PROPN
ejpam-6838	369	4	)	)	PUNCT
ejpam-6838	369	5	=	=	SYM
ejpam-6838	369	6	0	0	NUM
ejpam-6838	369	7	,	,	PUNCT
ejpam-6838	369	8	0	0	NUM
ejpam-6838	369	9	<	<	X
ejpam-6838	369	10	t	t	X
ejpam-6838	369	11	≤	≤	NUM
ejpam-6838	369	12	1	1	NUM
ejpam-6838	369	13	,	,	PUNCT
ejpam-6838	369	14	(	(	PUNCT
ejpam-6838	369	15	73	73	NUM
ejpam-6838	369	16	)	)	PUNCT
ejpam-6838	370	1	where	where	SCONJ
ejpam-6838	370	2	λ(x	λ(x	PROPN
ejpam-6838	370	3	,	,	PUNCT
ejpam-6838	370	4	t	t	PROPN
ejpam-6838	370	5	)	)	PUNCT
ejpam-6838	370	6	=	=	SYM
ejpam-6838	370	7	t2	t2	PROPN
ejpam-6838	370	8	sin(2π	sin(2π	NOUN
ejpam-6838	370	9	x	x	X
ejpam-6838	370	10	)	)	PUNCT
ejpam-6838	370	11	is	be	AUX
ejpam-6838	370	12	the	the	DET
ejpam-6838	370	13	exact	exact	ADJ
ejpam-6838	370	14	solution	solution	NOUN
ejpam-6838	370	15	of	of	ADP
ejpam-6838	370	16	this	this	DET
ejpam-6838	370	17	problem	problem	NOUN
ejpam-6838	370	18	.	.	PUNCT
ejpam-6838	371	1	table	table	NOUN
ejpam-6838	371	2	9	9	NUM
ejpam-6838	371	3	gives	give	VERB
ejpam-6838	371	4	a	a	DET
ejpam-6838	371	5	comparison	comparison	NOUN
ejpam-6838	371	6	of	of	ADP
ejpam-6838	371	7	mae	mae	PROPN
ejpam-6838	371	8	between	between	ADP
ejpam-6838	371	9	our	our	PRON
ejpam-6838	371	10	method	method	NOUN
ejpam-6838	371	11	at	at	ADP
ejpam-6838	371	12	m	m	PROPN
ejpam-6838	371	13	=	=	SYM
ejpam-6838	371	14	9	9	NUM
ejpam-6838	371	15	and	and	CCONJ
ejpam-6838	371	16	method	method	NOUN
ejpam-6838	371	17	in	in	ADP
ejpam-6838	371	18	[	[	X
ejpam-6838	371	19	64	64	NUM
ejpam-6838	371	20	]	]	PUNCT
ejpam-6838	371	21	at	at	ADP
ejpam-6838	371	22	∆t	∆t	PROPN
ejpam-6838	371	23	=	=	SYM
ejpam-6838	371	24	0.001	0.001	NUM
ejpam-6838	371	25	and	and	CCONJ
ejpam-6838	371	26	m	m	PROPN
ejpam-6838	371	27	=	=	ADJ
ejpam-6838	371	28	64	64	NUM
ejpam-6838	371	29	.	.	PUNCT
ejpam-6838	371	30	table	table	NOUN
ejpam-6838	371	31	10	10	NUM
ejpam-6838	371	32	displays	display	VERB
ejpam-6838	371	33	the	the	DET
ejpam-6838	371	34	ae	ae	PROPN
ejpam-6838	371	35	at	at	ADP
ejpam-6838	371	36	m	m	PROPN
ejpam-6838	371	37	=	=	NOUN
ejpam-6838	371	38	9	9	NUM
ejpam-6838	371	39	and	and	CCONJ
ejpam-6838	371	40	ζ	ζ	NOUN
ejpam-6838	371	41	=	=	SYM
ejpam-6838	371	42	0.5	0.5	NUM
ejpam-6838	371	43	.	.	PUNCT
ejpam-6838	371	44	table	table	NOUN
ejpam-6838	371	45	11	11	NUM
ejpam-6838	371	46	reports	report	NOUN
ejpam-6838	371	47	the	the	DET
ejpam-6838	371	48	mae	mae	PROPN
ejpam-6838	371	49	and	and	CCONJ
ejpam-6838	371	50	l∞-error	l∞-error	NOUN
ejpam-6838	371	51	at	at	ADP
ejpam-6838	371	52	various	various	ADJ
ejpam-6838	371	53	values	value	NOUN
ejpam-6838	371	54	of	of	ADP
ejpam-6838	371	55	m	m	PRON
ejpam-6838	371	56	when	when	SCONJ
ejpam-6838	371	57	ζ	ζ	NOUN
ejpam-6838	371	58	=	=	SYM
ejpam-6838	371	59	0.8	0.8	NUM
ejpam-6838	371	60	figure	figure	NOUN
ejpam-6838	371	61	6	6	NUM
ejpam-6838	371	62	illustrates	illustrate	VERB
ejpam-6838	371	63	the	the	DET
ejpam-6838	371	64	ae	ae	PROPN
ejpam-6838	371	65	at	at	ADP
ejpam-6838	371	66	various	various	ADJ
ejpam-6838	371	67	values	value	NOUN
ejpam-6838	371	68	of	of	ADP
ejpam-6838	371	69	t	t	NOUN
ejpam-6838	371	70	when	when	SCONJ
ejpam-6838	371	71	m	m	VERB
ejpam-6838	371	72	=	=	SYM
ejpam-6838	371	73	9	9	NUM
ejpam-6838	371	74	and	and	CCONJ
ejpam-6838	371	75	ζ	ζ	NOUN
ejpam-6838	371	76	=	=	SYM
ejpam-6838	371	77	0.3	0.3	NUM
ejpam-6838	371	78	.	.	PUNCT
ejpam-6838	371	79	table	table	NOUN
ejpam-6838	371	80	9	9	NUM
ejpam-6838	371	81	:	:	PUNCT
ejpam-6838	371	82	comparison	comparison	NOUN
ejpam-6838	371	83	of	of	ADP
ejpam-6838	371	84	the	the	DET
ejpam-6838	371	85	mae	mae	PROPN
ejpam-6838	371	86	for	for	ADP
ejpam-6838	371	87	example	example	NOUN
ejpam-6838	371	88	4	4	NUM
ejpam-6838	371	89	.	.	X
ejpam-6838	371	90	method	method	NOUN
ejpam-6838	371	91	in	in	ADP
ejpam-6838	371	92	[	[	X
ejpam-6838	371	93	64	64	NUM
ejpam-6838	371	94	]	]	PUNCT
ejpam-6838	371	95	at	at	ADP
ejpam-6838	371	96	∆t	∆t	PROPN
ejpam-6838	371	97	=	=	SYM
ejpam-6838	371	98	0.001	0.001	NUM
ejpam-6838	371	99	and	and	CCONJ
ejpam-6838	371	100	m	m	PROPN
ejpam-6838	371	101	=	=	ADJ
ejpam-6838	371	102	64	64	NUM
ejpam-6838	371	103	our	our	PRON
ejpam-6838	371	104	method	method	NOUN
ejpam-6838	371	105	at	at	ADP
ejpam-6838	371	106	m	m	NOUN
ejpam-6838	371	107	=	=	SYM
ejpam-6838	371	108	9	9	NUM
ejpam-6838	371	109	7.70×	7.70×	NUM
ejpam-6838	371	110	10−4	10−4	NUM
ejpam-6838	371	111	1.66×	1.66×	NUM
ejpam-6838	371	112	10−5	10−5	NUM
ejpam-6838	371	113	table	table	NOUN
ejpam-6838	371	114	11	11	NUM
ejpam-6838	371	115	:	:	PUNCT
ejpam-6838	371	116	the	the	DET
ejpam-6838	371	117	errors	error	NOUN
ejpam-6838	371	118	of	of	ADP
ejpam-6838	371	119	example	example	NOUN
ejpam-6838	371	120	4	4	NUM
ejpam-6838	371	121	at	at	ADP
ejpam-6838	371	122	various	various	ADJ
ejpam-6838	371	123	values	value	NOUN
ejpam-6838	371	124	of	of	ADP
ejpam-6838	371	125	m	m	PRON
ejpam-6838	371	126	when	when	SCONJ
ejpam-6838	371	127	ζ	ζ	NOUN
ejpam-6838	371	128	=	=	NOUN
ejpam-6838	371	129	0.8	0.8	NUM
ejpam-6838	371	130	.	.	PUNCT
ejpam-6838	372	1	m	m	VERB
ejpam-6838	372	2	3	3	NUM
ejpam-6838	372	3	6	6	NUM
ejpam-6838	372	4	9	9	NUM
ejpam-6838	372	5	maes	maes	PROPN
ejpam-6838	372	6	1.37846×10−1	1.37846×10−1	PROPN
ejpam-6838	372	7	1.42851×10−2	1.42851×10−2	NUM
ejpam-6838	372	8	1.5862×10−5	1.5862×10−5	NUM
ejpam-6838	372	9	l∞-error	l∞-error	NOUN
ejpam-6838	372	10	2.83552×10−1	2.83552×10−1	NUM
ejpam-6838	372	11	3.13749×10−2	3.13749×10−2	NUM
ejpam-6838	372	12	4.61017×10−5	4.61017×10−5	PROPN
ejpam-6838	372	13	w.	w.	PROPN
ejpam-6838	372	14	m.	m.	PROPN
ejpam-6838	372	15	abd	abd	PROPN
ejpam-6838	372	16	-	-	PUNCT
ejpam-6838	372	17	elhameed	elhameed	PROPN
ejpam-6838	372	18	et	et	PROPN
ejpam-6838	372	19	al	al	PROPN
ejpam-6838	372	20	.	.	PUNCT
ejpam-6838	372	21	/	/	SYM
ejpam-6838	372	22	eur	eur	PROPN
ejpam-6838	372	23	.	.	PUNCT
ejpam-6838	373	1	j.	j.	PROPN
ejpam-6838	373	2	pure	pure	PROPN
ejpam-6838	373	3	appl	appl	PROPN
ejpam-6838	373	4	.	.	PROPN
ejpam-6838	373	5	math	math	PROPN
ejpam-6838	373	6	,	,	PUNCT
ejpam-6838	373	7	18	18	NUM
ejpam-6838	373	8	(	(	PUNCT
ejpam-6838	373	9	4	4	NUM
ejpam-6838	373	10	)	)	PUNCT
ejpam-6838	373	11	(	(	PUNCT
ejpam-6838	373	12	2025	2025	NUM
ejpam-6838	373	13	)	)	PUNCT
ejpam-6838	373	14	,	,	PUNCT
ejpam-6838	373	15	6838	6838	NUM
ejpam-6838	373	16	20	20	NUM
ejpam-6838	373	17	of	of	ADP
ejpam-6838	373	18	25	25	NUM
ejpam-6838	373	19	table	table	NOUN
ejpam-6838	373	20	10	10	NUM
ejpam-6838	373	21	:	:	PUNCT
ejpam-6838	373	22	the	the	DET
ejpam-6838	373	23	ae	ae	PROPN
ejpam-6838	373	24	of	of	ADP
ejpam-6838	373	25	example	example	NOUN
ejpam-6838	373	26	4	4	NUM
ejpam-6838	373	27	at	at	ADP
ejpam-6838	373	28	m	m	PROPN
ejpam-6838	373	29	=	=	SYM
ejpam-6838	373	30	9	9	NUM
ejpam-6838	373	31	and	and	CCONJ
ejpam-6838	373	32	ζ	ζ	NOUN
ejpam-6838	373	33	=	=	SYM
ejpam-6838	373	34	0.5	0.5	NUM
ejpam-6838	373	35	.	.	PUNCT
ejpam-6838	374	1	x	x	PROPN
ejpam-6838	374	2	t	t	NOUN
ejpam-6838	374	3	=	=	NUM
ejpam-6838	374	4	0.2	0.2	NUM
ejpam-6838	374	5	t	t	NOUN
ejpam-6838	374	6	=	=	NUM
ejpam-6838	374	7	0.4	0.4	NUM
ejpam-6838	374	8	t	t	NOUN
ejpam-6838	374	9	=	=	SYM
ejpam-6838	374	10	0.6	0.6	NUM
ejpam-6838	374	11	t	t	NOUN
ejpam-6838	374	12	=	=	NOUN
ejpam-6838	374	13	0.8	0.8	NUM
ejpam-6838	374	14	0.1	0.1	NUM
ejpam-6838	374	15	4.33573×	4.33573×	NUM
ejpam-6838	374	16	10−7	10−7	NUM
ejpam-6838	374	17	1.71139×	1.71139×	NUM
ejpam-6838	374	18	10−6	10−6	NUM
ejpam-6838	374	19	4.02304×	4.02304×	NUM
ejpam-6838	375	1	10−6	10−6	NUM
ejpam-6838	375	2	7.16437×	7.16437×	NUM
ejpam-6838	375	3	10−6	10−6	NUM
ejpam-6838	375	4	0.2	0.2	NUM
ejpam-6838	375	5	7.58102×	7.58102×	NUM
ejpam-6838	375	6	10−7	10−7	NUM
ejpam-6838	375	7	3.01934×	3.01934×	NUM
ejpam-6838	375	8	10−6	10−6	NUM
ejpam-6838	375	9	7.05377×	7.05377×	NUM
ejpam-6838	375	10	10−6	10−6	NUM
ejpam-6838	375	11	1.25795×	1.25795×	NUM
ejpam-6838	375	12	10−5	10−5	NUM
ejpam-6838	375	13	0.3	0.3	NUM
ejpam-6838	375	14	1.16957×	1.16957×	NUM
ejpam-6838	375	15	10−6	10−6	NUM
ejpam-6838	375	16	4.53537×	4.53537×	NUM
ejpam-6838	375	17	10−6	10−6	NUM
ejpam-6838	375	18	1.06733×	1.06733×	NUM
ejpam-6838	375	19	10−5	10−5	NUM
ejpam-6838	375	20	1.89359×	1.89359×	NUM
ejpam-6838	375	21	10−5	10−5	NUM
ejpam-6838	375	22	0.4	0.4	NUM
ejpam-6838	375	23	1.86083×	1.86083×	NOUN
ejpam-6838	375	24	10−6	10−6	NUM
ejpam-6838	375	25	7.1667×	7.1667×	NUM
ejpam-6838	375	26	10−6	10−6	NUM
ejpam-6838	375	27	1.66918×	1.66918×	NUM
ejpam-6838	375	28	10−5	10−5	NUM
ejpam-6838	375	29	2.95361×	2.95361×	NUM
ejpam-6838	375	30	10−5	10−5	NUM
ejpam-6838	375	31	0.5	0.5	NUM
ejpam-6838	375	32	2.46676×	2.46676×	NUM
ejpam-6838	375	33	10−8	10−8	NUM
ejpam-6838	375	34	9.86345×	9.86345×	NOUN
ejpam-6838	375	35	10−8	10−8	NUM
ejpam-6838	375	36	5.44645×	5.44645×	NUM
ejpam-6838	375	37	10−8	10−8	NUM
ejpam-6838	375	38	1.4437×	1.4437×	NUM
ejpam-6838	375	39	10−8	10−8	NUM
ejpam-6838	375	40	0.6	0.6	NUM
ejpam-6838	375	41	1.81921×	1.81921×	NUM
ejpam-6838	375	42	10−6	10−6	NUM
ejpam-6838	375	43	7.3363×	7.3363×	NUM
ejpam-6838	375	44	10−6	10−6	NUM
ejpam-6838	375	45	1.66×	1.66×	NUM
ejpam-6838	375	46	10−5	10−5	NUM
ejpam-6838	375	47	2.95617×	2.95617×	NUM
ejpam-6838	375	48	10−5	10−5	NUM
ejpam-6838	375	49	0.7	0.7	NUM
ejpam-6838	375	50	1.1434×	1.1434×	NUM
ejpam-6838	375	51	10−6	10−6	NUM
ejpam-6838	375	52	4.64781×	4.64781×	NUM
ejpam-6838	375	53	10−6	10−6	NUM
ejpam-6838	375	54	1.06156×	1.06156×	NUM
ejpam-6838	375	55	10−5	10−5	NUM
ejpam-6838	375	56	1.89542×	1.89542×	NUM
ejpam-6838	375	57	10−5	10−5	NUM
ejpam-6838	375	58	0.8	0.8	NUM
ejpam-6838	375	59	7.42571×	7.42571×	NUM
ejpam-6838	375	60	10−7	10−7	NUM
ejpam-6838	375	61	3.08815×	3.08815×	NUM
ejpam-6838	375	62	10−6	10−6	NUM
ejpam-6838	375	63	7.01915×	7.01915×	NOUN
ejpam-6838	375	64	10−6	10−6	NUM
ejpam-6838	375	65	1.25912×	1.25912×	NUM
ejpam-6838	375	66	10−5	10−5	NUM
ejpam-6838	375	67	0.9	0.9	NUM
ejpam-6838	375	68	4.25343×	4.25343×	NOUN
ejpam-6838	375	69	10−7	10−7	NUM
ejpam-6838	375	70	1.74765×	1.74765×	NUM
ejpam-6838	375	71	10−6	10−6	NUM
ejpam-6838	375	72	4.00476×	4.00476×	NOUN
ejpam-6838	376	1	10−6	10−6	NUM
ejpam-6838	376	2	7.17045×	7.17045×	NUM
ejpam-6838	376	3	10−6	10−6	NUM
ejpam-6838	376	4	0.0	0.0	NUM
ejpam-6838	376	5	0.2	0.2	NUM
ejpam-6838	376	6	0.4	0.4	NUM
ejpam-6838	376	7	0.6	0.6	NUM
ejpam-6838	376	8	0.8	0.8	NUM
ejpam-6838	376	9	1.0	1.0	NUM
ejpam-6838	376	10	0.00000	0.00000	NUM
ejpam-6838	376	11	0.00001	0.00001	NUM
ejpam-6838	376	12	0.00002	0.00002	NUM
ejpam-6838	376	13	0.00003	0.00003	NUM
ejpam-6838	376	14	0.00004	0.00004	NUM
ejpam-6838	376	15	x	x	PUNCT
ejpam-6838	376	16	e	e	NOUN
ejpam-6838	376	17	rr	rr	NOUN
ejpam-6838	376	18	o	o	NOUN
ejpam-6838	376	19	rs	rs	NOUN
ejpam-6838	376	20	t=0.1	t=0.1	X
ejpam-6838	377	1	t=0.3	t=0.3	X
ejpam-6838	377	2	t=0.5	t=0.5	NOUN
ejpam-6838	377	3	t=0.7	t=0.7	NOUN
ejpam-6838	377	4	figure	figure	VERB
ejpam-6838	377	5	6	6	NUM
ejpam-6838	377	6	:	:	PUNCT
ejpam-6838	377	7	the	the	DET
ejpam-6838	377	8	ae	ae	PROPN
ejpam-6838	377	9	of	of	ADP
ejpam-6838	377	10	example	example	NOUN
ejpam-6838	377	11	4	4	NUM
ejpam-6838	377	12	at	at	ADP
ejpam-6838	377	13	m	m	PROPN
ejpam-6838	377	14	=	=	SYM
ejpam-6838	377	15	9	9	NUM
ejpam-6838	377	16	and	and	CCONJ
ejpam-6838	377	17	ζ	ζ	NOUN
ejpam-6838	377	18	=	=	SYM
ejpam-6838	377	19	0.3	0.3	NUM
ejpam-6838	377	20	.	.	NOUN
ejpam-6838	378	1	6	6	NUM
ejpam-6838	378	2	.	.	X
ejpam-6838	378	3	concluding	conclude	VERB
ejpam-6838	378	4	remarks	remark	NOUN
ejpam-6838	378	5	this	this	DET
ejpam-6838	378	6	article	article	NOUN
ejpam-6838	378	7	presented	present	VERB
ejpam-6838	378	8	an	an	DET
ejpam-6838	378	9	effective	effective	ADJ
ejpam-6838	378	10	tau	tau	NOUN
ejpam-6838	378	11	-	-	PUNCT
ejpam-6838	378	12	based	base	VERB
ejpam-6838	378	13	numerical	numerical	ADJ
ejpam-6838	378	14	scheme	scheme	NOUN
ejpam-6838	378	15	for	for	ADP
ejpam-6838	378	16	solving	solve	VERB
ejpam-6838	378	17	the	the	DET
ejpam-6838	378	18	tfde	tfde	NOUN
ejpam-6838	378	19	based	base	VERB
ejpam-6838	378	20	on	on	ADP
ejpam-6838	378	21	employing	employ	VERB
ejpam-6838	378	22	certain	certain	ADJ
ejpam-6838	378	23	cps	cp	NOUN
ejpam-6838	378	24	,	,	PUNCT
ejpam-6838	378	25	which	which	PRON
ejpam-6838	378	26	are	be	AUX
ejpam-6838	378	27	particular	particular	ADJ
ejpam-6838	378	28	polynomials	polynomial	NOUN
ejpam-6838	378	29	of	of	ADP
ejpam-6838	378	30	the	the	DET
ejpam-6838	378	31	generalized	generalized	ADJ
ejpam-6838	378	32	gegenbauer	gegenbauer	NOUN
ejpam-6838	378	33	polynomials	polynomial	NOUN
ejpam-6838	378	34	.	.	PUNCT
ejpam-6838	379	1	our	our	PRON
ejpam-6838	379	2	tau	tau	PROPN
ejpam-6838	379	3	algorithm	algorithm	NOUN
ejpam-6838	379	4	transforms	transform	VERB
ejpam-6838	379	5	the	the	DET
ejpam-6838	379	6	equation	equation	NOUN
ejpam-6838	379	7	with	with	ADP
ejpam-6838	379	8	its	its	PRON
ejpam-6838	379	9	initialboundary	initialboundary	ADJ
ejpam-6838	379	10	equations	equation	NOUN
ejpam-6838	379	11	into	into	ADP
ejpam-6838	379	12	an	an	DET
ejpam-6838	379	13	algebraic	algebraic	ADJ
ejpam-6838	379	14	system	system	NOUN
ejpam-6838	379	15	of	of	ADP
ejpam-6838	379	16	equations	equation	NOUN
ejpam-6838	379	17	that	that	PRON
ejpam-6838	379	18	can	can	AUX
ejpam-6838	379	19	be	be	AUX
ejpam-6838	379	20	numerically	numerically	ADV
ejpam-6838	379	21	solved	solve	VERB
ejpam-6838	379	22	.	.	PUNCT
ejpam-6838	380	1	the	the	DET
ejpam-6838	380	2	method	method	NOUN
ejpam-6838	380	3	exhibits	exhibit	VERB
ejpam-6838	380	4	excellent	excellent	ADJ
ejpam-6838	380	5	approximation	approximation	NOUN
ejpam-6838	380	6	capabilities	capability	NOUN
ejpam-6838	380	7	,	,	PUNCT
ejpam-6838	380	8	as	as	SCONJ
ejpam-6838	380	9	evidenced	evidence	VERB
ejpam-6838	380	10	by	by	ADP
ejpam-6838	380	11	the	the	DET
ejpam-6838	380	12	low	low	ADJ
ejpam-6838	380	13	errors	error	NOUN
ejpam-6838	380	14	in	in	ADP
ejpam-6838	380	15	various	various	ADJ
ejpam-6838	380	16	test	test	NOUN
ejpam-6838	380	17	problems	problem	NOUN
ejpam-6838	380	18	.	.	PUNCT
ejpam-6838	381	1	the	the	DET
ejpam-6838	381	2	approach	approach	NOUN
ejpam-6838	381	3	used	use	VERB
ejpam-6838	381	4	in	in	ADP
ejpam-6838	381	5	this	this	DET
ejpam-6838	381	6	paper	paper	NOUN
ejpam-6838	381	7	may	may	AUX
ejpam-6838	381	8	be	be	AUX
ejpam-6838	381	9	a	a	DET
ejpam-6838	381	10	powerful	powerful	ADJ
ejpam-6838	381	11	tool	tool	NOUN
ejpam-6838	381	12	for	for	ADP
ejpam-6838	381	13	handling	handle	VERB
ejpam-6838	381	14	other	other	ADJ
ejpam-6838	381	15	fractional	fractional	ADJ
ejpam-6838	381	16	pdes	pde	NOUN
ejpam-6838	381	17	in	in	ADP
ejpam-6838	381	18	future	future	ADJ
ejpam-6838	381	19	research	research	NOUN
ejpam-6838	381	20	.	.	PUNCT
ejpam-6838	382	1	in	in	ADP
ejpam-6838	382	2	addition	addition	NOUN
ejpam-6838	382	3	,	,	PUNCT
ejpam-6838	382	4	we	we	PRON
ejpam-6838	382	5	anticipate	anticipate	VERB
ejpam-6838	382	6	that	that	SCONJ
ejpam-6838	382	7	other	other	ADJ
ejpam-6838	382	8	generalized	generalized	ADJ
ejpam-6838	382	9	cps	cp	NOUN
ejpam-6838	382	10	as	as	ADP
ejpam-6838	382	11	special	special	ADJ
ejpam-6838	382	12	cases	case	NOUN
ejpam-6838	382	13	of	of	ADP
ejpam-6838	382	14	the	the	DET
ejpam-6838	382	15	generalized	generalized	ADJ
ejpam-6838	382	16	gegenbauer	gegenbauer	NOUN
ejpam-6838	382	17	polynomials	polynomial	NOUN
ejpam-6838	382	18	may	may	AUX
ejpam-6838	382	19	be	be	AUX
ejpam-6838	382	20	introduced	introduce	VERB
ejpam-6838	382	21	and	and	CCONJ
ejpam-6838	382	22	used	use	VERB
ejpam-6838	382	23	along	along	ADP
ejpam-6838	382	24	with	with	ADP
ejpam-6838	382	25	suitable	suitable	ADJ
ejpam-6838	382	26	spectral	spectral	ADJ
ejpam-6838	382	27	methods	method	NOUN
ejpam-6838	382	28	to	to	PART
ejpam-6838	382	29	treat	treat	VERB
ejpam-6838	382	30	different	different	ADJ
ejpam-6838	382	31	types	type	NOUN
ejpam-6838	382	32	of	of	ADP
ejpam-6838	382	33	differential	differential	ADJ
ejpam-6838	382	34	equations	equation	NOUN
ejpam-6838	382	35	.	.	PUNCT
ejpam-6838	383	1	acknowledgements	acknowledgement	NOUN
ejpam-6838	383	2	the	the	DET
ejpam-6838	383	3	researchers	researcher	NOUN
ejpam-6838	383	4	wish	wish	VERB
ejpam-6838	383	5	to	to	PART
ejpam-6838	383	6	extend	extend	VERB
ejpam-6838	383	7	their	their	PRON
ejpam-6838	383	8	sincere	sincere	ADJ
ejpam-6838	383	9	gratitude	gratitude	NOUN
ejpam-6838	383	10	to	to	ADP
ejpam-6838	383	11	the	the	DET
ejpam-6838	383	12	deanship	deanship	NOUN
ejpam-6838	383	13	of	of	ADP
ejpam-6838	383	14	scientific	scientific	ADJ
ejpam-6838	383	15	research	research	NOUN
ejpam-6838	383	16	at	at	ADP
ejpam-6838	383	17	the	the	DET
ejpam-6838	383	18	islamic	islamic	PROPN
ejpam-6838	383	19	university	university	PROPN
ejpam-6838	383	20	of	of	ADP
ejpam-6838	383	21	madinah	madinah	PROPN
ejpam-6838	383	22	for	for	ADP
ejpam-6838	383	23	the	the	DET
ejpam-6838	383	24	support	support	NOUN
ejpam-6838	383	25	provided	provide	VERB
ejpam-6838	383	26	to	to	ADP
ejpam-6838	383	27	the	the	DET
ejpam-6838	383	28	postpublishing	postpublishe	VERB
ejpam-6838	383	29	program	program	NOUN
ejpam-6838	383	30	.	.	PUNCT
ejpam-6838	384	1	w.	w.	PROPN
ejpam-6838	384	2	m.	m.	PROPN
ejpam-6838	384	3	abd	abd	PROPN
ejpam-6838	384	4	-	-	PUNCT
ejpam-6838	384	5	elhameed	elhameed	PROPN
ejpam-6838	384	6	et	et	PROPN
ejpam-6838	384	7	al	al	PROPN
ejpam-6838	384	8	.	.	PUNCT
ejpam-6838	384	9	/	/	SYM
ejpam-6838	384	10	eur	eur	PROPN
ejpam-6838	384	11	.	.	PUNCT
ejpam-6838	385	1	j.	j.	PROPN
ejpam-6838	385	2	pure	pure	PROPN
ejpam-6838	385	3	appl	appl	PROPN
ejpam-6838	385	4	.	.	PROPN
ejpam-6838	385	5	math	math	PROPN
ejpam-6838	385	6	,	,	PUNCT
ejpam-6838	385	7	18	18	NUM
ejpam-6838	385	8	(	(	PUNCT
ejpam-6838	385	9	4	4	NUM
ejpam-6838	385	10	)	)	PUNCT
ejpam-6838	385	11	(	(	PUNCT
ejpam-6838	385	12	2025	2025	NUM
ejpam-6838	385	13	)	)	PUNCT
ejpam-6838	385	14	,	,	PUNCT
ejpam-6838	385	15	6838	6838	NUM
ejpam-6838	385	16	21	21	NUM
ejpam-6838	385	17	of	of	ADP
ejpam-6838	385	18	25	25	NUM
ejpam-6838	385	19	declarations	declaration	NOUN
ejpam-6838	385	20	•	•	ADP
ejpam-6838	385	21	conflicts	conflict	NOUN
ejpam-6838	385	22	of	of	ADP
ejpam-6838	385	23	interest	interest	NOUN
ejpam-6838	385	24	:	:	PUNCT
ejpam-6838	385	25	the	the	DET
ejpam-6838	385	26	authors	author	NOUN
ejpam-6838	385	27	declare	declare	VERB
ejpam-6838	385	28	that	that	SCONJ
ejpam-6838	385	29	they	they	PRON
ejpam-6838	385	30	have	have	VERB
ejpam-6838	385	31	no	no	DET
ejpam-6838	385	32	conflicts	conflict	NOUN
ejpam-6838	385	33	of	of	ADP
ejpam-6838	385	34	interest	interest	NOUN
ejpam-6838	385	35	.	.	PUNCT
ejpam-6838	386	1	references	reference	NOUN
ejpam-6838	386	2	[	[	X
ejpam-6838	386	3	1	1	NUM
ejpam-6838	386	4	]	]	PUNCT
ejpam-6838	386	5	i.	i.	NOUN
ejpam-6838	386	6	podlubny	podlubny	PROPN
ejpam-6838	386	7	.	.	PUNCT
ejpam-6838	387	1	fractional	fractional	ADJ
ejpam-6838	387	2	differential	differential	ADJ
ejpam-6838	387	3	equations	equation	NOUN
ejpam-6838	387	4	:	:	PUNCT
ejpam-6838	387	5	an	an	DET
ejpam-6838	387	6	introduction	introduction	NOUN
ejpam-6838	387	7	to	to	ADP
ejpam-6838	387	8	fractional	fractional	ADJ
ejpam-6838	387	9	derivatives	derivative	NOUN
ejpam-6838	387	10	,	,	PUNCT
ejpam-6838	387	11	fractional	fractional	ADJ
ejpam-6838	387	12	differential	differential	ADJ
ejpam-6838	387	13	equations	equation	NOUN
ejpam-6838	387	14	,	,	PUNCT
ejpam-6838	387	15	to	to	ADP
ejpam-6838	387	16	methods	method	NOUN
ejpam-6838	387	17	of	of	ADP
ejpam-6838	387	18	their	their	PRON
ejpam-6838	387	19	solution	solution	NOUN
ejpam-6838	387	20	and	and	CCONJ
ejpam-6838	387	21	some	some	PRON
ejpam-6838	387	22	of	of	ADP
ejpam-6838	387	23	their	their	PRON
ejpam-6838	387	24	applications	application	NOUN
ejpam-6838	387	25	.	.	PUNCT
ejpam-6838	388	1	elsevier	elsevier	NOUN
ejpam-6838	388	2	,	,	PUNCT
ejpam-6838	388	3	1998	1998	NUM
ejpam-6838	388	4	.	.	PUNCT
ejpam-6838	389	1	[	[	X
ejpam-6838	389	2	2	2	NUM
ejpam-6838	389	3	]	]	PUNCT
ejpam-6838	389	4	r.	r.	NOUN
ejpam-6838	389	5	hilfer	hilfer	PROPN
ejpam-6838	389	6	.	.	PUNCT
ejpam-6838	390	1	applications	application	NOUN
ejpam-6838	390	2	of	of	ADP
ejpam-6838	390	3	fractional	fractional	ADJ
ejpam-6838	390	4	calculus	calculus	NOUN
ejpam-6838	390	5	in	in	ADP
ejpam-6838	390	6	physics	physics	PROPN
ejpam-6838	390	7	.	.	PUNCT
ejpam-6838	391	1	world	world	PROPN
ejpam-6838	391	2	scientific	scientific	PROPN
ejpam-6838	391	3	,	,	PUNCT
ejpam-6838	391	4	singapore	singapore	PROPN
ejpam-6838	391	5	,	,	PUNCT
ejpam-6838	391	6	2000	2000	NUM
ejpam-6838	391	7	.	.	PUNCT
ejpam-6838	392	1	[	[	X
ejpam-6838	392	2	3	3	X
ejpam-6838	392	3	]	]	X
ejpam-6838	392	4	m.d	m.d	PROPN
ejpam-6838	392	5	.	.	PROPN
ejpam-6838	392	6	ortigueira	ortigueira	PROPN
ejpam-6838	392	7	.	.	PUNCT
ejpam-6838	393	1	fractional	fractional	ADJ
ejpam-6838	393	2	calculus	calculus	NOUN
ejpam-6838	393	3	in	in	ADP
ejpam-6838	393	4	applied	apply	VERB
ejpam-6838	393	5	sciences	science	NOUN
ejpam-6838	393	6	and	and	CCONJ
ejpam-6838	393	7	engineering	engineering	NOUN
ejpam-6838	393	8	.	.	PUNCT
ejpam-6838	394	1	springer	springer	PROPN
ejpam-6838	394	2	,	,	PUNCT
ejpam-6838	394	3	cham	cham	PROPN
ejpam-6838	394	4	,	,	PUNCT
ejpam-6838	394	5	2015	2015	NUM
ejpam-6838	394	6	.	.	PUNCT
ejpam-6838	395	1	[	[	X
ejpam-6838	395	2	4	4	X
ejpam-6838	395	3	]	]	X
ejpam-6838	395	4	v.e	v.e	PROPN
ejpam-6838	395	5	.	.	PROPN
ejpam-6838	395	6	tarasov	tarasov	PROPN
ejpam-6838	395	7	.	.	PUNCT
ejpam-6838	396	1	fractional	fractional	ADJ
ejpam-6838	396	2	dynamics	dynamic	NOUN
ejpam-6838	396	3	:	:	PUNCT
ejpam-6838	396	4	applications	application	NOUN
ejpam-6838	396	5	of	of	ADP
ejpam-6838	396	6	fractional	fractional	ADJ
ejpam-6838	396	7	calculus	calculus	NOUN
ejpam-6838	396	8	to	to	ADP
ejpam-6838	396	9	dynamics	dynamic	NOUN
ejpam-6838	396	10	of	of	ADP
ejpam-6838	396	11	particles	particle	NOUN
ejpam-6838	396	12	,	,	PUNCT
ejpam-6838	396	13	fields	field	NOUN
ejpam-6838	396	14	,	,	PUNCT
ejpam-6838	396	15	and	and	CCONJ
ejpam-6838	396	16	media	medium	NOUN
ejpam-6838	396	17	.	.	PUNCT
ejpam-6838	397	1	springer	springer	PROPN
ejpam-6838	397	2	,	,	PUNCT
ejpam-6838	397	3	berlin	berlin	PROPN
ejpam-6838	397	4	,	,	PUNCT
ejpam-6838	397	5	2011	2011	NUM
ejpam-6838	397	6	.	.	PUNCT
ejpam-6838	398	1	[	[	X
ejpam-6838	398	2	5	5	NUM
ejpam-6838	398	3	]	]	X
ejpam-6838	398	4	r.	r.	PROPN
ejpam-6838	398	5	saadeh	saadeh	PROPN
ejpam-6838	398	6	,	,	PUNCT
ejpam-6838	398	7	a.	a.	NOUN
ejpam-6838	398	8	burqan	burqan	PROPN
ejpam-6838	398	9	,	,	PUNCT
ejpam-6838	398	10	and	and	CCONJ
ejpam-6838	398	11	a.	a.	PROPN
ejpam-6838	398	12	el	el	PROPN
ejpam-6838	398	13	-	-	PUNCT
ejpam-6838	398	14	ajou	ajou	ADJ
ejpam-6838	398	15	.	.	PUNCT
ejpam-6838	399	1	reliable	reliable	ADJ
ejpam-6838	399	2	solutions	solution	NOUN
ejpam-6838	399	3	to	to	ADP
ejpam-6838	399	4	fractional	fractional	ADJ
ejpam-6838	399	5	laneemden	laneemden	ADJ
ejpam-6838	399	6	equations	equation	NOUN
ejpam-6838	399	7	via	via	ADP
ejpam-6838	399	8	laplace	laplace	NOUN
ejpam-6838	399	9	transform	transform	NOUN
ejpam-6838	399	10	and	and	CCONJ
ejpam-6838	399	11	residual	residual	ADJ
ejpam-6838	399	12	error	error	NOUN
ejpam-6838	399	13	function	function	NOUN
ejpam-6838	399	14	.	.	PUNCT
ejpam-6838	400	1	alex	alex	PROPN
ejpam-6838	400	2	.	.	PUNCT
ejpam-6838	401	1	eng	eng	PROPN
ejpam-6838	401	2	.	.	PUNCT
ejpam-6838	402	1	j.	j.	PROPN
ejpam-6838	402	2	,	,	PUNCT
ejpam-6838	402	3	61(12):10551–10562	61(12):10551–10562	NUM
ejpam-6838	402	4	,	,	PUNCT
ejpam-6838	402	5	2022	2022	NUM
ejpam-6838	402	6	.	.	PUNCT
ejpam-6838	403	1	[	[	X
ejpam-6838	403	2	6	6	NUM
ejpam-6838	403	3	]	]	PUNCT
ejpam-6838	403	4	a.	a.	NOUN
ejpam-6838	403	5	afreen	afreen	PROPN
ejpam-6838	403	6	and	and	CCONJ
ejpam-6838	403	7	a.	a.	NOUN
ejpam-6838	403	8	raheem	raheem	PROPN
ejpam-6838	403	9	.	.	PUNCT
ejpam-6838	404	1	study	study	NOUN
ejpam-6838	404	2	of	of	ADP
ejpam-6838	404	3	a	a	DET
ejpam-6838	404	4	nonlinear	nonlinear	ADJ
ejpam-6838	404	5	system	system	NOUN
ejpam-6838	404	6	of	of	ADP
ejpam-6838	404	7	fractional	fractional	ADJ
ejpam-6838	404	8	differential	differential	ADJ
ejpam-6838	404	9	equations	equation	NOUN
ejpam-6838	404	10	with	with	ADP
ejpam-6838	404	11	deviated	deviate	VERB
ejpam-6838	404	12	arguments	argument	NOUN
ejpam-6838	404	13	via	via	ADP
ejpam-6838	404	14	adomian	adomian	ADJ
ejpam-6838	404	15	decomposition	decomposition	NOUN
ejpam-6838	404	16	method	method	NOUN
ejpam-6838	404	17	.	.	PUNCT
ejpam-6838	405	1	int	int	NOUN
ejpam-6838	405	2	.	.	PUNCT
ejpam-6838	406	1	j.	j.	PROPN
ejpam-6838	406	2	appl	appl	PROPN
ejpam-6838	406	3	.	.	PUNCT
ejpam-6838	407	1	comput	comput	PROPN
ejpam-6838	407	2	.	.	PUNCT
ejpam-6838	408	1	math	math	NOUN
ejpam-6838	408	2	.	.	PUNCT
ejpam-6838	408	3	,	,	PUNCT
ejpam-6838	408	4	8(5):269	8(5):269	NUM
ejpam-6838	408	5	,	,	PUNCT
ejpam-6838	408	6	2022	2022	NUM
ejpam-6838	408	7	.	.	PUNCT
ejpam-6838	409	1	[	[	X
ejpam-6838	409	2	7	7	NUM
ejpam-6838	409	3	]	]	PUNCT
ejpam-6838	409	4	a.	a.	NOUN
ejpam-6838	409	5	rysak	rysak	NOUN
ejpam-6838	409	6	and	and	CCONJ
ejpam-6838	409	7	m.	m.	NOUN
ejpam-6838	409	8	gregorczyk	gregorczyk	PROPN
ejpam-6838	409	9	.	.	PUNCT
ejpam-6838	410	1	differential	differential	ADJ
ejpam-6838	410	2	transform	transform	NOUN
ejpam-6838	410	3	method	method	NOUN
ejpam-6838	410	4	as	as	ADP
ejpam-6838	410	5	an	an	DET
ejpam-6838	410	6	effective	effective	ADJ
ejpam-6838	410	7	tool	tool	NOUN
ejpam-6838	410	8	for	for	ADP
ejpam-6838	410	9	investigating	investigate	VERB
ejpam-6838	410	10	fractional	fractional	ADJ
ejpam-6838	410	11	dynamical	dynamical	ADJ
ejpam-6838	410	12	systems	system	NOUN
ejpam-6838	410	13	.	.	PUNCT
ejpam-6838	411	1	appl	appl	PROPN
ejpam-6838	411	2	.	.	PUNCT
ejpam-6838	412	1	sci	sci	PROPN
ejpam-6838	412	2	.	.	PROPN
ejpam-6838	412	3	,	,	PUNCT
ejpam-6838	412	4	11(15):6955	11(15):6955	NUM
ejpam-6838	412	5	,	,	PUNCT
ejpam-6838	412	6	2021	2021	NUM
ejpam-6838	412	7	.	.	PUNCT
ejpam-6838	413	1	[	[	X
ejpam-6838	413	2	8	8	NUM
ejpam-6838	413	3	]	]	X
ejpam-6838	413	4	w.m	w.m	PROPN
ejpam-6838	413	5	.	.	PROPN
ejpam-6838	413	6	abd	abd	PROPN
ejpam-6838	413	7	-	-	PUNCT
ejpam-6838	413	8	elhameed	elhameed	PROPN
ejpam-6838	413	9	,	,	PUNCT
ejpam-6838	413	10	o.m	o.m	PROPN
ejpam-6838	413	11	.	.	PROPN
ejpam-6838	413	12	alqubori	alqubori	PROPN
ejpam-6838	413	13	,	,	PUNCT
ejpam-6838	413	14	n.m.a	n.m.a	NOUN
ejpam-6838	413	15	.	.	PUNCT
ejpam-6838	413	16	alsafri	alsafri	PROPN
ejpam-6838	413	17	,	,	PUNCT
ejpam-6838	413	18	a.k	a.k	PROPN
ejpam-6838	413	19	.	.	PROPN
ejpam-6838	413	20	amin	amin	PROPN
ejpam-6838	413	21	,	,	PUNCT
ejpam-6838	413	22	and	and	CCONJ
ejpam-6838	413	23	a.g	a.g	PROPN
ejpam-6838	413	24	.	.	PROPN
ejpam-6838	413	25	atta	atta	PROPN
ejpam-6838	413	26	.	.	PUNCT
ejpam-6838	414	1	a	a	DET
ejpam-6838	414	2	matrix	matrix	NOUN
ejpam-6838	414	3	approach	approach	NOUN
ejpam-6838	414	4	by	by	ADP
ejpam-6838	414	5	convolved	convolve	VERB
ejpam-6838	414	6	fermat	fermat	PROPN
ejpam-6838	414	7	polynomials	polynomial	NOUN
ejpam-6838	414	8	for	for	ADP
ejpam-6838	414	9	solving	solve	VERB
ejpam-6838	414	10	the	the	DET
ejpam-6838	414	11	fractional	fractional	ADJ
ejpam-6838	414	12	burgers	burger	NOUN
ejpam-6838	414	13	’	'	PUNCT
ejpam-6838	414	14	equation	equation	NOUN
ejpam-6838	414	15	.	.	PUNCT
ejpam-6838	415	1	mathematics	mathematic	NOUN
ejpam-6838	415	2	,	,	PUNCT
ejpam-6838	415	3	13(7):1135	13(7):1135	NUM
ejpam-6838	415	4	,	,	PUNCT
ejpam-6838	415	5	2025	2025	NUM
ejpam-6838	415	6	.	.	PUNCT
ejpam-6838	416	1	[	[	X
ejpam-6838	416	2	9	9	NUM
ejpam-6838	416	3	]	]	X
ejpam-6838	416	4	h.m	h.m	PROPN
ejpam-6838	416	5	.	.	PROPN
ejpam-6838	416	6	ahmed	ahmed	PROPN
ejpam-6838	416	7	,	,	PUNCT
ejpam-6838	416	8	r.m	r.m	PROPN
ejpam-6838	416	9	.	.	PROPN
ejpam-6838	416	10	hafez	hafez	PROPN
ejpam-6838	416	11	,	,	PUNCT
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ejpam-6838	416	13	w.m	w.m	PROPN
ejpam-6838	416	14	.	.	PROPN
ejpam-6838	416	15	abd	abd	PROPN
ejpam-6838	416	16	-	-	PUNCT
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ejpam-6838	416	18	.	.	PUNCT
ejpam-6838	417	1	a	a	DET
ejpam-6838	417	2	computational	computational	ADJ
ejpam-6838	417	3	strategy	strategy	NOUN
ejpam-6838	417	4	for	for	ADP
ejpam-6838	417	5	nonlinear	nonlinear	ADJ
ejpam-6838	417	6	time	time	NOUN
ejpam-6838	417	7	-	-	PUNCT
ejpam-6838	417	8	fractional	fractional	ADJ
ejpam-6838	417	9	generalized	generalized	ADJ
ejpam-6838	417	10	kawahara	kawahara	NOUN
ejpam-6838	417	11	equation	equation	NOUN
ejpam-6838	417	12	using	use	VERB
ejpam-6838	417	13	new	new	ADJ
ejpam-6838	417	14	eighth	eighth	ADJ
ejpam-6838	417	15	-	-	PUNCT
ejpam-6838	417	16	kind	kind	NOUN
ejpam-6838	417	17	chebyshev	chebyshev	NOUN
ejpam-6838	417	18	operational	operational	ADJ
ejpam-6838	417	19	matrices	matrix	NOUN
ejpam-6838	417	20	.	.	PUNCT
ejpam-6838	418	1	phys	phy	NOUN
ejpam-6838	418	2	.	.	PUNCT
ejpam-6838	419	1	scr	scr	PROPN
ejpam-6838	419	2	.	.	PROPN
ejpam-6838	419	3	,	,	PUNCT
ejpam-6838	419	4	99(4):045250	99(4):045250	NUM
ejpam-6838	419	5	,	,	PUNCT
ejpam-6838	419	6	2024	2024	NUM
ejpam-6838	419	7	.	.	PUNCT
ejpam-6838	420	1	[	[	X
ejpam-6838	420	2	10	10	NUM
ejpam-6838	420	3	]	]	X
ejpam-6838	420	4	r.m	r.m	PROPN
ejpam-6838	420	5	.	.	PROPN
ejpam-6838	420	6	hafez	hafez	PROPN
ejpam-6838	420	7	and	and	CCONJ
ejpam-6838	420	8	y.h	y.h	PROPN
ejpam-6838	420	9	.	.	PROPN
ejpam-6838	420	10	youssri	youssri	PROPN
ejpam-6838	420	11	.	.	PUNCT
ejpam-6838	421	1	shifted	shift	VERB
ejpam-6838	421	2	jacobi	jacobi	PROPN
ejpam-6838	421	3	collocation	collocation	NOUN
ejpam-6838	421	4	scheme	scheme	NOUN
ejpam-6838	421	5	for	for	ADP
ejpam-6838	421	6	multidimensional	multidimensional	ADJ
ejpam-6838	421	7	time	time	NOUN
ejpam-6838	421	8	-	-	PUNCT
ejpam-6838	421	9	fractional	fractional	ADJ
ejpam-6838	421	10	order	order	NOUN
ejpam-6838	421	11	telegraph	telegraph	NOUN
ejpam-6838	421	12	equation	equation	NOUN
ejpam-6838	421	13	.	.	PUNCT
ejpam-6838	422	1	iran	iran	PROPN
ejpam-6838	422	2	.	.	PUNCT
ejpam-6838	423	1	j.	j.	PROPN
ejpam-6838	423	2	numer	numer	PROPN
ejpam-6838	423	3	.	.	PUNCT
ejpam-6838	424	1	anal	anal	PROPN
ejpam-6838	424	2	.	.	PUNCT
ejpam-6838	425	1	optim	optim	PROPN
ejpam-6838	425	2	.	.	PROPN
ejpam-6838	425	3	,	,	PUNCT
ejpam-6838	425	4	10(1):195	10(1):195	NUM
ejpam-6838	425	5	–	–	PUNCT
ejpam-6838	425	6	223	223	NUM
ejpam-6838	425	7	,	,	PUNCT
ejpam-6838	425	8	2020	2020	NUM
ejpam-6838	425	9	.	.	PUNCT
ejpam-6838	426	1	[	[	X
ejpam-6838	426	2	11	11	NUM
ejpam-6838	426	3	]	]	X
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ejpam-6838	426	6	and	and	CCONJ
ejpam-6838	426	7	h.	h.	PROPN
ejpam-6838	426	8	eltayeb	eltayeb	PROPN
ejpam-6838	426	9	.	.	PUNCT
ejpam-6838	427	1	the	the	DET
ejpam-6838	427	2	four	four	NUM
ejpam-6838	427	3	-	-	PUNCT
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ejpam-6838	427	5	natural	natural	ADJ
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ejpam-6838	427	7	adomian	adomian	NOUN
ejpam-6838	427	8	decomposition	decomposition	NOUN
ejpam-6838	427	9	method	method	NOUN
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ejpam-6838	427	11	(	(	PUNCT
ejpam-6838	427	12	3	3	NUM
ejpam-6838	427	13	+	+	NOUN
ejpam-6838	427	14	1)-dimensional	1)-dimensional	ADJ
ejpam-6838	427	15	fractional	fractional	ADJ
ejpam-6838	427	16	coupled	couple	VERB
ejpam-6838	427	17	burgers	burger	NOUN
ejpam-6838	427	18	’	'	PUNCT
ejpam-6838	427	19	equation	equation	NOUN
ejpam-6838	427	20	.	.	PUNCT
ejpam-6838	428	1	fractals	fractal	NOUN
ejpam-6838	428	2	,	,	PUNCT
ejpam-6838	428	3	8(4):227	8(4):227	NUM
ejpam-6838	428	4	,	,	PUNCT
ejpam-6838	428	5	2024	2024	NUM
ejpam-6838	428	6	.	.	PUNCT
ejpam-6838	429	1	[	[	X
ejpam-6838	429	2	12	12	NUM
ejpam-6838	429	3	]	]	PUNCT
ejpam-6838	429	4	m.	m.	NOUN
ejpam-6838	429	5	shams	sham	NOUN
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ejpam-6838	429	7	a.	a.	NOUN
ejpam-6838	429	8	alalyani	alalyani	PROPN
ejpam-6838	429	9	.	.	PUNCT
ejpam-6838	430	1	high	high	ADJ
ejpam-6838	430	2	performance	performance	NOUN
ejpam-6838	430	3	adaptive	adaptive	ADJ
ejpam-6838	430	4	step	step	NOUN
ejpam-6838	430	5	size	size	NOUN
ejpam-6838	430	6	fractional	fractional	ADJ
ejpam-6838	430	7	numerical	numerical	ADJ
ejpam-6838	430	8	scheme	scheme	NOUN
ejpam-6838	430	9	for	for	ADP
ejpam-6838	430	10	solving	solve	VERB
ejpam-6838	430	11	fractional	fractional	ADJ
ejpam-6838	430	12	differential	differential	ADJ
ejpam-6838	430	13	equations	equation	NOUN
ejpam-6838	430	14	.	.	PUNCT
ejpam-6838	431	1	sci	sci	PROPN
ejpam-6838	431	2	.	.	PROPN
ejpam-6838	431	3	rep	rep	PROPN
ejpam-6838	431	4	.	.	PROPN
ejpam-6838	431	5	,	,	PUNCT
ejpam-6838	431	6	15(1):13006	15(1):13006	NUM
ejpam-6838	431	7	,	,	PUNCT
ejpam-6838	431	8	2025	2025	NUM
ejpam-6838	431	9	.	.	PUNCT
ejpam-6838	432	1	[	[	X
ejpam-6838	432	2	13	13	NUM
ejpam-6838	432	3	]	]	X
ejpam-6838	432	4	a.m.s	a.m.s	PROPN
ejpam-6838	432	5	.	.	PUNCT
ejpam-6838	432	6	mahdy	mahdy	PROPN
ejpam-6838	432	7	,	,	PUNCT
ejpam-6838	432	8	kh	kh	PROPN
ejpam-6838	432	9	.	.	PROPN
ejpam-6838	432	10	lotfy	lotfy	PROPN
ejpam-6838	432	11	,	,	PUNCT
ejpam-6838	432	12	e.a	e.a	PROPN
ejpam-6838	432	13	.	.	PROPN
ejpam-6838	432	14	ismail	ismail	PROPN
ejpam-6838	432	15	,	,	PUNCT
ejpam-6838	432	16	a.	a.	PROPN
ejpam-6838	432	17	el	el	PROPN
ejpam-6838	432	18	-	-	PUNCT
ejpam-6838	432	19	bary	bary	PROPN
ejpam-6838	432	20	,	,	PUNCT
ejpam-6838	432	21	m.	m.	NOUN
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ejpam-6838	432	23	,	,	PUNCT
ejpam-6838	432	24	and	and	CCONJ
ejpam-6838	432	25	a.a	a.a	PROPN
ejpam-6838	432	26	.	.	PROPN
ejpam-6838	432	27	el	el	PROPN
ejpam-6838	432	28	-	-	PUNCT
ejpam-6838	432	29	dahdouh	dahdouh	NOUN
ejpam-6838	432	30	.	.	PUNCT
ejpam-6838	433	1	analytical	analytical	ADJ
ejpam-6838	433	2	solutions	solution	NOUN
ejpam-6838	433	3	of	of	ADP
ejpam-6838	433	4	time	time	NOUN
ejpam-6838	433	5	-	-	PUNCT
ejpam-6838	433	6	fractional	fractional	ADJ
ejpam-6838	433	7	heat	heat	NOUN
ejpam-6838	433	8	order	order	NOUN
ejpam-6838	433	9	for	for	ADP
ejpam-6838	433	10	a	a	DET
ejpam-6838	433	11	magneto	magneto	ADJ
ejpam-6838	433	12	-	-	PUNCT
ejpam-6838	433	13	photothermal	photothermal	ADJ
ejpam-6838	433	14	semiconductor	semiconductor	NOUN
ejpam-6838	433	15	medium	medium	NOUN
ejpam-6838	433	16	with	with	ADP
ejpam-6838	433	17	thomson	thomson	NOUN
ejpam-6838	433	18	effects	effect	NOUN
ejpam-6838	433	19	and	and	CCONJ
ejpam-6838	433	20	initial	initial	ADJ
ejpam-6838	433	21	stress	stress	NOUN
ejpam-6838	433	22	.	.	PUNCT
ejpam-6838	434	1	results	result	VERB
ejpam-6838	434	2	phys	phy	NOUN
ejpam-6838	434	3	.	.	PUNCT
ejpam-6838	434	4	,	,	PUNCT
ejpam-6838	434	5	18:103174	18:103174	NUM
ejpam-6838	434	6	,	,	PUNCT
ejpam-6838	434	7	2020	2020	NUM
ejpam-6838	434	8	.	.	PUNCT
ejpam-6838	435	1	[	[	X
ejpam-6838	435	2	14	14	NUM
ejpam-6838	435	3	]	]	PUNCT
ejpam-6838	435	4	m.	m.	NOUN
ejpam-6838	435	5	fardi	fardi	PROPN
ejpam-6838	435	6	.	.	PUNCT
ejpam-6838	436	1	a	a	DET
ejpam-6838	436	2	kernel	kernel	NOUN
ejpam-6838	436	3	-	-	PUNCT
ejpam-6838	436	4	based	base	VERB
ejpam-6838	436	5	method	method	NOUN
ejpam-6838	436	6	for	for	ADP
ejpam-6838	436	7	solving	solve	VERB
ejpam-6838	436	8	the	the	DET
ejpam-6838	436	9	time	time	NOUN
ejpam-6838	436	10	-	-	PUNCT
ejpam-6838	436	11	fractional	fractional	ADJ
ejpam-6838	436	12	diffusion	diffusion	NOUN
ejpam-6838	436	13	equation	equation	NOUN
ejpam-6838	436	14	.	.	PUNCT
ejpam-6838	437	1	numer	numer	PROPN
ejpam-6838	437	2	.	.	PUNCT
ejpam-6838	438	1	methods	method	NOUN
ejpam-6838	438	2	partial	partial	ADJ
ejpam-6838	438	3	differ	differ	VERB
ejpam-6838	438	4	.	.	PUNCT
ejpam-6838	439	1	equations	equation	NOUN
ejpam-6838	439	2	,	,	PUNCT
ejpam-6838	439	3	39(3):2719–2733	39(3):2719–2733	NUM
ejpam-6838	439	4	,	,	PUNCT
ejpam-6838	439	5	2023	2023	NUM
ejpam-6838	439	6	.	.	PUNCT
ejpam-6838	440	1	w.	w.	PROPN
ejpam-6838	440	2	m.	m.	PROPN
ejpam-6838	440	3	abd	abd	PROPN
ejpam-6838	440	4	-	-	PUNCT
ejpam-6838	440	5	elhameed	elhameed	PROPN
ejpam-6838	440	6	et	et	PROPN
ejpam-6838	440	7	al	al	PROPN
ejpam-6838	440	8	.	.	PUNCT
ejpam-6838	440	9	/	/	SYM
ejpam-6838	440	10	eur	eur	PROPN
ejpam-6838	440	11	.	.	PUNCT
ejpam-6838	441	1	j.	j.	PROPN
ejpam-6838	441	2	pure	pure	PROPN
ejpam-6838	441	3	appl	appl	PROPN
ejpam-6838	441	4	.	.	PROPN
ejpam-6838	441	5	math	math	PROPN
ejpam-6838	441	6	,	,	PUNCT
ejpam-6838	441	7	18	18	NUM
ejpam-6838	441	8	(	(	PUNCT
ejpam-6838	441	9	4	4	NUM
ejpam-6838	441	10	)	)	PUNCT
ejpam-6838	441	11	(	(	PUNCT
ejpam-6838	441	12	2025	2025	NUM
ejpam-6838	441	13	)	)	PUNCT
ejpam-6838	441	14	,	,	PUNCT
ejpam-6838	441	15	6838	6838	NUM
ejpam-6838	441	16	22	22	NUM
ejpam-6838	441	17	of	of	ADP
ejpam-6838	441	18	25	25	NUM
ejpam-6838	441	19	[	[	SYM
ejpam-6838	441	20	15	15	NUM
ejpam-6838	441	21	]	]	X
ejpam-6838	441	22	s.	s.	PROPN
ejpam-6838	441	23	kumar	kumar	PROPN
ejpam-6838	441	24	,	,	PUNCT
ejpam-6838	441	25	r.k	r.k	PROPN
ejpam-6838	441	26	.	.	PROPN
ejpam-6838	441	27	pandey	pandey	PROPN
ejpam-6838	441	28	,	,	PUNCT
ejpam-6838	441	29	k.	k.	PROPN
ejpam-6838	441	30	kumar	kumar	PROPN
ejpam-6838	441	31	,	,	PUNCT
ejpam-6838	441	32	s.	s.	PROPN
ejpam-6838	441	33	kamal	kamal	PROPN
ejpam-6838	441	34	,	,	PUNCT
ejpam-6838	441	35	and	and	CCONJ
ejpam-6838	441	36	t.n	t.n	PROPN
ejpam-6838	441	37	.	.	PROPN
ejpam-6838	441	38	dinh	dinh	PROPN
ejpam-6838	441	39	.	.	PUNCT
ejpam-6838	442	1	finite	finite	ADJ
ejpam-6838	442	2	difference	difference	NOUN
ejpam-6838	442	3	–	–	PUNCT
ejpam-6838	442	4	collocation	collocation	NOUN
ejpam-6838	442	5	method	method	NOUN
ejpam-6838	442	6	for	for	ADP
ejpam-6838	442	7	the	the	DET
ejpam-6838	442	8	generalized	generalize	VERB
ejpam-6838	442	9	fractional	fractional	ADJ
ejpam-6838	442	10	diffusion	diffusion	NOUN
ejpam-6838	442	11	equation	equation	NOUN
ejpam-6838	442	12	.	.	PUNCT
ejpam-6838	443	1	fractal	fractal	ADJ
ejpam-6838	443	2	fract	fract	PROPN
ejpam-6838	443	3	.	.	PUNCT
ejpam-6838	443	4	,	,	PUNCT
ejpam-6838	443	5	6(7):387	6(7):387	NUM
ejpam-6838	443	6	,	,	PUNCT
ejpam-6838	443	7	2022	2022	NUM
ejpam-6838	443	8	.	.	PUNCT
ejpam-6838	444	1	[	[	X
ejpam-6838	444	2	16	16	NUM
ejpam-6838	444	3	]	]	X
ejpam-6838	444	4	m.a	m.a	PROPN
ejpam-6838	444	5	.	.	PROPN
ejpam-6838	444	6	sultanov	sultanov	PROPN
ejpam-6838	444	7	,	,	PUNCT
ejpam-6838	444	8	e.n	e.n	PROPN
ejpam-6838	444	9	.	.	PROPN
ejpam-6838	444	10	akimova	akimova	PROPN
ejpam-6838	444	11	,	,	PUNCT
ejpam-6838	444	12	v.e	v.e	PROPN
ejpam-6838	444	13	.	.	PROPN
ejpam-6838	444	14	misilov	misilov	PROPN
ejpam-6838	444	15	,	,	PUNCT
ejpam-6838	444	16	and	and	CCONJ
ejpam-6838	444	17	y.	y.	PROPN
ejpam-6838	444	18	nurlanuly	nurlanuly	ADV
ejpam-6838	444	19	.	.	PUNCT
ejpam-6838	445	1	parallel	parallel	ADJ
ejpam-6838	445	2	direct	direct	ADJ
ejpam-6838	445	3	and	and	CCONJ
ejpam-6838	445	4	iterative	iterative	NOUN
ejpam-6838	445	5	methods	method	NOUN
ejpam-6838	445	6	for	for	ADP
ejpam-6838	445	7	solving	solve	VERB
ejpam-6838	445	8	the	the	DET
ejpam-6838	445	9	time	time	NOUN
ejpam-6838	445	10	-	-	PUNCT
ejpam-6838	445	11	fractional	fractional	ADJ
ejpam-6838	445	12	diffusion	diffusion	NOUN
ejpam-6838	445	13	equation	equation	NOUN
ejpam-6838	445	14	on	on	ADP
ejpam-6838	445	15	multicore	multicore	ADJ
ejpam-6838	445	16	processors	processor	NOUN
ejpam-6838	445	17	.	.	PUNCT
ejpam-6838	446	1	mathematics	mathematic	NOUN
ejpam-6838	446	2	,	,	PUNCT
ejpam-6838	446	3	10(3):323	10(3):323	NUM
ejpam-6838	446	4	,	,	PUNCT
ejpam-6838	446	5	2022	2022	NUM
ejpam-6838	446	6	.	.	PUNCT
ejpam-6838	447	1	[	[	X
ejpam-6838	447	2	17	17	NUM
ejpam-6838	447	3	]	]	PUNCT
ejpam-6838	447	4	s.	s.	PROPN
ejpam-6838	447	5	kumari	kumari	PROPN
ejpam-6838	447	6	and	and	CCONJ
ejpam-6838	447	7	m.	m.	PROPN
ejpam-6838	447	8	mehra	mehra	PROPN
ejpam-6838	447	9	.	.	PUNCT
ejpam-6838	448	1	numerical	numerical	ADJ
ejpam-6838	448	2	solution	solution	NOUN
ejpam-6838	448	3	to	to	ADP
ejpam-6838	448	4	loaded	load	VERB
ejpam-6838	448	5	difference	difference	NOUN
ejpam-6838	448	6	scheme	scheme	NOUN
ejpam-6838	448	7	for	for	ADP
ejpam-6838	448	8	timefractional	timefractional	ADJ
ejpam-6838	448	9	diffusion	diffusion	NOUN
ejpam-6838	448	10	equation	equation	NOUN
ejpam-6838	448	11	with	with	ADP
ejpam-6838	448	12	temporal	temporal	ADJ
ejpam-6838	448	13	loads	load	NOUN
ejpam-6838	448	14	.	.	PUNCT
ejpam-6838	449	1	j.	j.	PROPN
ejpam-6838	449	2	math	math	PROPN
ejpam-6838	449	3	.	.	PUNCT
ejpam-6838	450	1	chem	chem	PROPN
ejpam-6838	450	2	.	.	PUNCT
ejpam-6838	450	3	,	,	PUNCT
ejpam-6838	451	1	63(1):105–131	63(1):105–131	NOUN
ejpam-6838	451	2	,	,	PUNCT
ejpam-6838	451	3	2025	2025	NUM
ejpam-6838	451	4	.	.	PUNCT
ejpam-6838	452	1	[	[	X
ejpam-6838	452	2	18	18	NUM
ejpam-6838	452	3	]	]	X
ejpam-6838	452	4	j.	j.	PROPN
ejpam-6838	452	5	singh	singh	PROPN
ejpam-6838	452	6	,	,	PUNCT
ejpam-6838	452	7	a.m.	a.m.	PROPN
ejpam-6838	452	8	alshehri	alshehri	PROPN
ejpam-6838	452	9	,	,	PUNCT
ejpam-6838	452	10	s.	s.	PROPN
ejpam-6838	452	11	momani	momani	PROPN
ejpam-6838	452	12	,	,	PUNCT
ejpam-6838	452	13	s.	s.	PROPN
ejpam-6838	452	14	hadid	hadid	PROPN
ejpam-6838	452	15	,	,	PUNCT
ejpam-6838	452	16	and	and	CCONJ
ejpam-6838	452	17	d.	d.	PROPN
ejpam-6838	452	18	kumar	kumar	PROPN
ejpam-6838	452	19	.	.	PUNCT
ejpam-6838	453	1	computational	computational	ADJ
ejpam-6838	453	2	analysis	analysis	NOUN
ejpam-6838	453	3	of	of	ADP
ejpam-6838	453	4	fractional	fractional	ADJ
ejpam-6838	453	5	diffusion	diffusion	NOUN
ejpam-6838	453	6	equations	equation	NOUN
ejpam-6838	453	7	occurring	occur	VERB
ejpam-6838	453	8	in	in	ADP
ejpam-6838	453	9	oil	oil	NOUN
ejpam-6838	453	10	pollution	pollution	NOUN
ejpam-6838	453	11	.	.	PUNCT
ejpam-6838	454	1	mathematics	mathematic	NOUN
ejpam-6838	454	2	,	,	PUNCT
ejpam-6838	454	3	10(20):3827	10(20):3827	NUM
ejpam-6838	454	4	,	,	PUNCT
ejpam-6838	454	5	2022	2022	NUM
ejpam-6838	454	6	.	.	PUNCT
ejpam-6838	455	1	[	[	X
ejpam-6838	455	2	19	19	NUM
ejpam-6838	455	3	]	]	X
ejpam-6838	455	4	h.	h.	PROPN
ejpam-6838	455	5	jafari	jafari	PROPN
ejpam-6838	455	6	,	,	PUNCT
ejpam-6838	455	7	r.m	r.m	PROPN
ejpam-6838	455	8	.	.	PROPN
ejpam-6838	455	9	ganji	ganji	PROPN
ejpam-6838	455	10	,	,	PUNCT
ejpam-6838	455	11	s.m	s.m	PROPN
ejpam-6838	455	12	.	.	PROPN
ejpam-6838	455	13	narsale	narsale	PROPN
ejpam-6838	455	14	,	,	PUNCT
ejpam-6838	455	15	m.	m.	NOUN
ejpam-6838	455	16	kgarose	kgarose	PROPN
ejpam-6838	455	17	,	,	PUNCT
ejpam-6838	455	18	and	and	CCONJ
ejpam-6838	455	19	v.t	v.t	PROPN
ejpam-6838	455	20	.	.	PROPN
ejpam-6838	455	21	nguyen	nguyen	PROPN
ejpam-6838	455	22	.	.	PUNCT
ejpam-6838	456	1	application	application	NOUN
ejpam-6838	456	2	of	of	ADP
ejpam-6838	456	3	hosoya	hosoya	PROPN
ejpam-6838	456	4	polynomial	polynomial	ADJ
ejpam-6838	456	5	to	to	PART
ejpam-6838	456	6	solve	solve	VERB
ejpam-6838	456	7	a	a	DET
ejpam-6838	456	8	class	class	NOUN
ejpam-6838	456	9	of	of	ADP
ejpam-6838	456	10	time	time	NOUN
ejpam-6838	456	11	-	-	PUNCT
ejpam-6838	456	12	fractional	fractional	ADJ
ejpam-6838	456	13	diffusion	diffusion	NOUN
ejpam-6838	456	14	equations	equation	NOUN
ejpam-6838	456	15	.	.	PUNCT
ejpam-6838	457	1	fractals	fractal	NOUN
ejpam-6838	457	2	,	,	PUNCT
ejpam-6838	457	3	31(04):2340059	31(04):2340059	NUM
ejpam-6838	457	4	,	,	PUNCT
ejpam-6838	457	5	2023	2023	NUM
ejpam-6838	457	6	.	.	PUNCT
ejpam-6838	458	1	[	[	X
ejpam-6838	458	2	20	20	NUM
ejpam-6838	458	3	]	]	PUNCT
ejpam-6838	458	4	p.	p.	PROPN
ejpam-6838	458	5	roul	roul	PROPN
ejpam-6838	458	6	,	,	PUNCT
ejpam-6838	458	7	v.m.k.p	v.m.k.p	PROPN
ejpam-6838	458	8	.	.	PROPN
ejpam-6838	458	9	goura	goura	NOUN
ejpam-6838	458	10	,	,	PUNCT
ejpam-6838	458	11	and	and	CCONJ
ejpam-6838	458	12	r.	r.	PROPN
ejpam-6838	458	13	cavoretto	cavoretto	PROPN
ejpam-6838	458	14	.	.	PUNCT
ejpam-6838	459	1	a	a	DET
ejpam-6838	459	2	numerical	numerical	ADJ
ejpam-6838	459	3	technique	technique	NOUN
ejpam-6838	459	4	based	base	VERB
ejpam-6838	459	5	on	on	ADP
ejpam-6838	459	6	bspline	bspline	NOUN
ejpam-6838	459	7	for	for	ADP
ejpam-6838	459	8	a	a	DET
ejpam-6838	459	9	class	class	NOUN
ejpam-6838	459	10	of	of	ADP
ejpam-6838	459	11	time	time	NOUN
ejpam-6838	459	12	-	-	PUNCT
ejpam-6838	459	13	fractional	fractional	ADJ
ejpam-6838	459	14	diffusion	diffusion	NOUN
ejpam-6838	459	15	equation	equation	NOUN
ejpam-6838	459	16	.	.	PUNCT
ejpam-6838	460	1	numer	numer	PROPN
ejpam-6838	460	2	.	.	PUNCT
ejpam-6838	461	1	methods	method	NOUN
ejpam-6838	461	2	partial	partial	ADJ
ejpam-6838	461	3	differ	differ	VERB
ejpam-6838	461	4	.	.	PUNCT
ejpam-6838	462	1	equations	equation	NOUN
ejpam-6838	462	2	,	,	PUNCT
ejpam-6838	462	3	39(1):45–64	39(1):45–64	NUM
ejpam-6838	462	4	,	,	PUNCT
ejpam-6838	462	5	2023	2023	NUM
ejpam-6838	462	6	.	.	PUNCT
ejpam-6838	463	1	[	[	X
ejpam-6838	463	2	21	21	NUM
ejpam-6838	463	3	]	]	X
ejpam-6838	463	4	s.	s.	PROPN
ejpam-6838	463	5	irandoust	irandoust	PROPN
ejpam-6838	463	6	-	-	PUNCT
ejpam-6838	463	7	pakchin	pakchin	ADJ
ejpam-6838	463	8	,	,	PUNCT
ejpam-6838	463	9	m.	m.	PROPN
ejpam-6838	463	10	hossein	hossein	PROPN
ejpam-6838	463	11	derakhshan	derakhshan	PROPN
ejpam-6838	463	12	,	,	PUNCT
ejpam-6838	463	13	s.	s.	PROPN
ejpam-6838	463	14	rezapour	rezapour	PROPN
ejpam-6838	463	15	,	,	PUNCT
ejpam-6838	463	16	and	and	CCONJ
ejpam-6838	463	17	m.	m.	PROPN
ejpam-6838	463	18	adel	adel	PROPN
ejpam-6838	463	19	.	.	PUNCT
ejpam-6838	464	1	an	an	DET
ejpam-6838	464	2	efficient	efficient	ADJ
ejpam-6838	464	3	numerical	numerical	ADJ
ejpam-6838	464	4	method	method	NOUN
ejpam-6838	464	5	for	for	ADP
ejpam-6838	464	6	the	the	DET
ejpam-6838	464	7	distributed	distribute	VERB
ejpam-6838	464	8	-	-	PUNCT
ejpam-6838	464	9	order	order	NOUN
ejpam-6838	464	10	time	time	NOUN
ejpam-6838	464	11	-	-	PUNCT
ejpam-6838	464	12	fractional	fractional	ADJ
ejpam-6838	464	13	diffusion	diffusion	NOUN
ejpam-6838	464	14	equation	equation	NOUN
ejpam-6838	464	15	with	with	ADP
ejpam-6838	464	16	the	the	DET
ejpam-6838	464	17	error	error	NOUN
ejpam-6838	464	18	analysis	analysis	NOUN
ejpam-6838	464	19	and	and	CCONJ
ejpam-6838	464	20	stability	stability	NOUN
ejpam-6838	464	21	properties	property	NOUN
ejpam-6838	464	22	.	.	PUNCT
ejpam-6838	465	1	math	math	NOUN
ejpam-6838	465	2	.	.	PUNCT
ejpam-6838	466	1	methods	method	NOUN
ejpam-6838	466	2	appl	appl	PROPN
ejpam-6838	466	3	.	.	PUNCT
ejpam-6838	467	1	sci	sci	PROPN
ejpam-6838	467	2	.	.	PROPN
ejpam-6838	467	3	,	,	PUNCT
ejpam-6838	467	4	48(3):2743–2765	48(3):2743–2765	NUM
ejpam-6838	467	5	,	,	PUNCT
ejpam-6838	467	6	2025	2025	NUM
ejpam-6838	467	7	.	.	PUNCT
ejpam-6838	468	1	[	[	X
ejpam-6838	468	2	22	22	NUM
ejpam-6838	468	3	]	]	PUNCT
ejpam-6838	468	4	j.-l	j.-l	PROPN
ejpam-6838	468	5	.	.	PUNCT
ejpam-6838	469	1	zhang	zhang	PROPN
ejpam-6838	469	2	,	,	PUNCT
ejpam-6838	469	3	z.-w	z.-w	PROPN
ejpam-6838	469	4	.	.	PUNCT
ejpam-6838	469	5	fang	fang	PROPN
ejpam-6838	469	6	,	,	PUNCT
ejpam-6838	469	7	and	and	CCONJ
ejpam-6838	469	8	h.-w	h.-w	PROPN
ejpam-6838	469	9	.	.	PUNCT
ejpam-6838	470	1	sun	sun	PROPN
ejpam-6838	470	2	.	.	PUNCT
ejpam-6838	471	1	exponential	exponential	ADJ
ejpam-6838	471	2	-	-	PUNCT
ejpam-6838	471	3	sum	sum	NOUN
ejpam-6838	471	4	-	-	PUNCT
ejpam-6838	471	5	approximation	approximation	NOUN
ejpam-6838	471	6	technique	technique	NOUN
ejpam-6838	471	7	for	for	ADP
ejpam-6838	471	8	variable	variable	ADJ
ejpam-6838	471	9	-	-	PUNCT
ejpam-6838	471	10	order	order	NOUN
ejpam-6838	471	11	time	time	NOUN
ejpam-6838	471	12	-	-	PUNCT
ejpam-6838	471	13	fractional	fractional	ADJ
ejpam-6838	471	14	diffusion	diffusion	NOUN
ejpam-6838	471	15	equations	equation	NOUN
ejpam-6838	471	16	.	.	PUNCT
ejpam-6838	472	1	j.	j.	PROPN
ejpam-6838	472	2	appl	appl	PROPN
ejpam-6838	472	3	.	.	PROPN
ejpam-6838	472	4	math	math	PROPN
ejpam-6838	472	5	.	.	PUNCT
ejpam-6838	473	1	comput	comput	NOUN
ejpam-6838	473	2	.	.	PUNCT
ejpam-6838	473	3	,	,	PUNCT
ejpam-6838	473	4	48(3):323–347	48(3):323–347	PROPN
ejpam-6838	473	5	,	,	PUNCT
ejpam-6838	473	6	2022	2022	NUM
ejpam-6838	473	7	.	.	PUNCT
ejpam-6838	474	1	[	[	X
ejpam-6838	474	2	23	23	NUM
ejpam-6838	474	3	]	]	X
ejpam-6838	474	4	v.f	v.f	PROPN
ejpam-6838	474	5	.	.	PROPN
ejpam-6838	474	6	morales	morales	PROPN
ejpam-6838	474	7	-	-	PUNCT
ejpam-6838	474	8	delgado	delgado	PROPN
ejpam-6838	474	9	,	,	PUNCT
ejpam-6838	474	10	j.f	j.f	PROPN
ejpam-6838	474	11	.	.	PROPN
ejpam-6838	474	12	gómez	gómez	NOUN
ejpam-6838	474	13	-	-	PUNCT
ejpam-6838	474	14	aguilar	aguilar	ADJ
ejpam-6838	474	15	,	,	PUNCT
ejpam-6838	474	16	and	and	CCONJ
ejpam-6838	474	17	m.a	m.a	PROPN
ejpam-6838	474	18	.	.	PROPN
ejpam-6838	474	19	taneco	taneco	PROPN
ejpam-6838	474	20	-	-	PUNCT
ejpam-6838	474	21	hernandez	hernandez	PROPN
ejpam-6838	474	22	.	.	PUNCT
ejpam-6838	475	1	analytical	analytical	ADJ
ejpam-6838	475	2	solution	solution	NOUN
ejpam-6838	475	3	of	of	ADP
ejpam-6838	475	4	the	the	DET
ejpam-6838	475	5	time	time	NOUN
ejpam-6838	475	6	fractional	fractional	ADJ
ejpam-6838	475	7	diffusion	diffusion	NOUN
ejpam-6838	475	8	equation	equation	NOUN
ejpam-6838	475	9	and	and	CCONJ
ejpam-6838	475	10	fractional	fractional	ADJ
ejpam-6838	475	11	convection	convection	NOUN
ejpam-6838	475	12	-	-	PUNCT
ejpam-6838	475	13	diffusion	diffusion	NOUN
ejpam-6838	475	14	equation	equation	NOUN
ejpam-6838	475	15	.	.	PUNCT
ejpam-6838	476	1	rev	rev	PROPN
ejpam-6838	476	2	.	.	PROPN
ejpam-6838	477	1	mex	mex	PROPN
ejpam-6838	477	2	.	.	PUNCT
ejpam-6838	477	3	fis	fis	PROPN
ejpam-6838	477	4	.	.	PROPN
ejpam-6838	477	5	,	,	PUNCT
ejpam-6838	477	6	65(1):82–88	65(1):82–88	NUM
ejpam-6838	477	7	,	,	PUNCT
ejpam-6838	477	8	2019	2019	NUM
ejpam-6838	477	9	.	.	PUNCT
ejpam-6838	478	1	[	[	X
ejpam-6838	478	2	24	24	NUM
ejpam-6838	478	3	]	]	X
ejpam-6838	478	4	h.	h.	PROPN
ejpam-6838	478	5	zhu	zhu	PROPN
ejpam-6838	478	6	and	and	CCONJ
ejpam-6838	478	7	c.	c.	PROPN
ejpam-6838	478	8	xu	xu	PROPN
ejpam-6838	478	9	.	.	PUNCT
ejpam-6838	479	1	a	a	DET
ejpam-6838	479	2	highly	highly	ADV
ejpam-6838	479	3	efficient	efficient	ADJ
ejpam-6838	479	4	numerical	numerical	ADJ
ejpam-6838	479	5	method	method	NOUN
ejpam-6838	479	6	for	for	ADP
ejpam-6838	479	7	the	the	DET
ejpam-6838	479	8	time	time	NOUN
ejpam-6838	479	9	-	-	PUNCT
ejpam-6838	479	10	fractional	fractional	ADJ
ejpam-6838	479	11	diffusion	diffusion	NOUN
ejpam-6838	479	12	equation	equation	NOUN
ejpam-6838	479	13	on	on	ADP
ejpam-6838	479	14	unbounded	unbounded	ADJ
ejpam-6838	479	15	domains	domain	NOUN
ejpam-6838	479	16	.	.	PUNCT
ejpam-6838	480	1	j.	j.	PROPN
ejpam-6838	480	2	sci	sci	PROPN
ejpam-6838	480	3	.	.	PUNCT
ejpam-6838	481	1	comput	comput	PROPN
ejpam-6838	481	2	.	.	PUNCT
ejpam-6838	481	3	,	,	PUNCT
ejpam-6838	481	4	99(2):47	99(2):47	PROPN
ejpam-6838	481	5	,	,	PUNCT
ejpam-6838	481	6	2024	2024	NUM
ejpam-6838	481	7	.	.	PUNCT
ejpam-6838	482	1	[	[	X
ejpam-6838	482	2	25	25	NUM
ejpam-6838	482	3	]	]	X
ejpam-6838	482	4	o.	o.	PROPN
ejpam-6838	482	5	imanuvilov	imanuvilov	PROPN
ejpam-6838	482	6	,	,	PUNCT
ejpam-6838	482	7	k.	k.	PROPN
ejpam-6838	482	8	ito	ito	PROPN
ejpam-6838	482	9	,	,	PUNCT
ejpam-6838	482	10	and	and	CCONJ
ejpam-6838	482	11	m.	m.	PROPN
ejpam-6838	482	12	yamamoto	yamamoto	PROPN
ejpam-6838	482	13	.	.	PUNCT
ejpam-6838	483	1	inverse	inverse	PROPN
ejpam-6838	483	2	coefficient	coefficient	NOUN
ejpam-6838	483	3	problems	problem	NOUN
ejpam-6838	483	4	for	for	ADP
ejpam-6838	483	5	onedimensional	onedimensional	ADJ
ejpam-6838	483	6	time	time	NOUN
ejpam-6838	483	7	-	-	PUNCT
ejpam-6838	483	8	fractional	fractional	ADJ
ejpam-6838	483	9	diffusion	diffusion	NOUN
ejpam-6838	483	10	equations	equation	NOUN
ejpam-6838	483	11	.	.	PUNCT
ejpam-6838	484	1	appl	appl	PROPN
ejpam-6838	484	2	.	.	PROPN
ejpam-6838	484	3	math	math	PROPN
ejpam-6838	484	4	.	.	PUNCT
ejpam-6838	485	1	lett	lett	PROPN
ejpam-6838	485	2	.	.	PROPN
ejpam-6838	485	3	,	,	PUNCT
ejpam-6838	485	4	160:109351	160:109351	NUM
ejpam-6838	485	5	,	,	PUNCT
ejpam-6838	485	6	2025	2025	NUM
ejpam-6838	485	7	.	.	PUNCT
ejpam-6838	486	1	[	[	X
ejpam-6838	486	2	26	26	NUM
ejpam-6838	486	3	]	]	PUNCT
ejpam-6838	486	4	x.	x.	PROPN
ejpam-6838	486	5	liu	liu	PROPN
ejpam-6838	486	6	.	.	PUNCT
ejpam-6838	487	1	error	error	NOUN
ejpam-6838	487	2	analysis	analysis	NOUN
ejpam-6838	487	3	of	of	ADP
ejpam-6838	487	4	a	a	DET
ejpam-6838	487	5	fully	fully	ADV
ejpam-6838	487	6	discrete	discrete	ADJ
ejpam-6838	487	7	method	method	NOUN
ejpam-6838	487	8	for	for	ADP
ejpam-6838	487	9	time	time	NOUN
ejpam-6838	487	10	-	-	PUNCT
ejpam-6838	487	11	fractional	fractional	ADJ
ejpam-6838	487	12	diffusion	diffusion	NOUN
ejpam-6838	487	13	equations	equation	NOUN
ejpam-6838	487	14	with	with	ADP
ejpam-6838	487	15	a	a	DET
ejpam-6838	487	16	tempered	temper	VERB
ejpam-6838	487	17	fractional	fractional	ADJ
ejpam-6838	487	18	gaussian	gaussian	NOUN
ejpam-6838	487	19	noise	noise	NOUN
ejpam-6838	487	20	.	.	PUNCT
ejpam-6838	488	1	j.	j.	PROPN
ejpam-6838	488	2	comput	comput	PROPN
ejpam-6838	488	3	.	.	PUNCT
ejpam-6838	489	1	appl	appl	PROPN
ejpam-6838	489	2	.	.	PROPN
ejpam-6838	489	3	math	math	PROPN
ejpam-6838	489	4	.	.	PUNCT
ejpam-6838	489	5	,	,	PUNCT
ejpam-6838	489	6	449:115953	449:115953	NOUN
ejpam-6838	489	7	,	,	PUNCT
ejpam-6838	489	8	2024	2024	NUM
ejpam-6838	489	9	.	.	PUNCT
ejpam-6838	490	1	[	[	X
ejpam-6838	490	2	27	27	NUM
ejpam-6838	490	3	]	]	X
ejpam-6838	490	4	n.	n.	PROPN
ejpam-6838	490	5	kedia	kedia	PROPN
ejpam-6838	490	6	,	,	PUNCT
ejpam-6838	490	7	a.a	a.a	PROPN
ejpam-6838	490	8	.	.	PROPN
ejpam-6838	490	9	alikhanov	alikhanov	PROPN
ejpam-6838	490	10	,	,	PUNCT
ejpam-6838	490	11	and	and	CCONJ
ejpam-6838	490	12	v.k	v.k	PROPN
ejpam-6838	490	13	.	.	PROPN
ejpam-6838	490	14	singh	singh	PROPN
ejpam-6838	490	15	.	.	PUNCT
ejpam-6838	491	1	robust	robust	ADJ
ejpam-6838	491	2	finite	finite	ADJ
ejpam-6838	491	3	difference	difference	NOUN
ejpam-6838	491	4	scheme	scheme	NOUN
ejpam-6838	491	5	for	for	ADP
ejpam-6838	491	6	the	the	DET
ejpam-6838	491	7	non	non	ADJ
ejpam-6838	491	8	-	-	ADJ
ejpam-6838	491	9	linear	linear	ADJ
ejpam-6838	491	10	generalized	generalized	ADJ
ejpam-6838	491	11	time	time	NOUN
ejpam-6838	491	12	-	-	PUNCT
ejpam-6838	491	13	fractional	fractional	ADJ
ejpam-6838	491	14	diffusion	diffusion	NOUN
ejpam-6838	491	15	equation	equation	NOUN
ejpam-6838	491	16	with	with	ADP
ejpam-6838	491	17	non	non	ADJ
ejpam-6838	491	18	-	-	ADJ
ejpam-6838	491	19	smooth	smooth	ADJ
ejpam-6838	491	20	solution	solution	NOUN
ejpam-6838	491	21	.	.	PUNCT
ejpam-6838	492	1	math	math	NOUN
ejpam-6838	492	2	.	.	PUNCT
ejpam-6838	493	1	comput	comput	NOUN
ejpam-6838	493	2	.	.	PUNCT
ejpam-6838	494	1	simul	simul	PROPN
ejpam-6838	494	2	.	.	PROPN
ejpam-6838	494	3	,	,	PUNCT
ejpam-6838	494	4	219:337–354	219:337–354	NUM
ejpam-6838	494	5	,	,	PUNCT
ejpam-6838	494	6	2024	2024	NUM
ejpam-6838	494	7	.	.	PUNCT
ejpam-6838	495	1	[	[	X
ejpam-6838	495	2	28	28	NUM
ejpam-6838	495	3	]	]	X
ejpam-6838	495	4	j.p	j.p	PROPN
ejpam-6838	495	5	.	.	PROPN
ejpam-6838	495	6	boyd	boyd	PROPN
ejpam-6838	495	7	.	.	PUNCT
ejpam-6838	496	1	chebyshev	chebyshev	PROPN
ejpam-6838	496	2	and	and	CCONJ
ejpam-6838	496	3	fourier	fourier	ADJ
ejpam-6838	496	4	spectral	spectral	ADJ
ejpam-6838	496	5	methods	method	NOUN
ejpam-6838	496	6	.	.	PUNCT
ejpam-6838	497	1	dover	dover	PROPN
ejpam-6838	497	2	publications	publications	PROPN
ejpam-6838	497	3	,	,	PUNCT
ejpam-6838	497	4	mineola	mineola	PROPN
ejpam-6838	497	5	,	,	PUNCT
ejpam-6838	497	6	ny	ny	PROPN
ejpam-6838	497	7	,	,	PUNCT
ejpam-6838	497	8	2nd	2nd	PROPN
ejpam-6838	497	9	edition	edition	NOUN
ejpam-6838	497	10	,	,	PUNCT
ejpam-6838	497	11	2001	2001	NUM
ejpam-6838	497	12	.	.	PUNCT
ejpam-6838	498	1	[	[	X
ejpam-6838	498	2	29	29	NUM
ejpam-6838	498	3	]	]	X
ejpam-6838	498	4	l.n	l.n	PROPN
ejpam-6838	498	5	.	.	PROPN
ejpam-6838	498	6	trefethen	trefethen	NOUN
ejpam-6838	498	7	.	.	PUNCT
ejpam-6838	499	1	spectral	spectral	ADJ
ejpam-6838	499	2	methods	method	NOUN
ejpam-6838	499	3	in	in	ADP
ejpam-6838	499	4	matlab	matlab	PROPN
ejpam-6838	499	5	.	.	PUNCT
ejpam-6838	500	1	siam	siam	PROPN
ejpam-6838	500	2	,	,	PUNCT
ejpam-6838	500	3	philadelphia	philadelphia	PROPN
ejpam-6838	500	4	,	,	PUNCT
ejpam-6838	500	5	2000	2000	NUM
ejpam-6838	500	6	.	.	PUNCT
ejpam-6838	501	1	[	[	X
ejpam-6838	501	2	30	30	NUM
ejpam-6838	501	3	]	]	X
ejpam-6838	501	4	h.m	h.m	PROPN
ejpam-6838	501	5	.	.	PROPN
ejpam-6838	501	6	ahmed	ahmed	PROPN
ejpam-6838	501	7	.	.	PUNCT
ejpam-6838	502	1	numerical	numerical	ADJ
ejpam-6838	502	2	solutions	solution	NOUN
ejpam-6838	502	3	for	for	ADP
ejpam-6838	502	4	singular	singular	ADJ
ejpam-6838	502	5	lane	lane	NOUN
ejpam-6838	502	6	-	-	PUNCT
ejpam-6838	502	7	emden	emden	NOUN
ejpam-6838	502	8	equations	equation	NOUN
ejpam-6838	502	9	using	use	VERB
ejpam-6838	502	10	shifted	shift	VERB
ejpam-6838	502	11	chebyshev	chebyshev	NOUN
ejpam-6838	502	12	polynomials	polynomial	NOUN
ejpam-6838	502	13	of	of	ADP
ejpam-6838	502	14	the	the	DET
ejpam-6838	502	15	first	first	ADJ
ejpam-6838	502	16	kind	kind	NOUN
ejpam-6838	502	17	.	.	PUNCT
ejpam-6838	503	1	contemp	contemp	NOUN
ejpam-6838	503	2	.	.	PUNCT
ejpam-6838	504	1	math	math	NOUN
ejpam-6838	504	2	.	.	PUNCT
ejpam-6838	504	3	,	,	PUNCT
ejpam-6838	504	4	4:132–149	4:132–149	PROPN
ejpam-6838	504	5	,	,	PUNCT
ejpam-6838	504	6	2023	2023	NUM
ejpam-6838	504	7	.	.	PUNCT
ejpam-6838	505	1	[	[	X
ejpam-6838	505	2	31	31	NUM
ejpam-6838	505	3	]	]	PUNCT
ejpam-6838	505	4	m.	m.	NOUN
ejpam-6838	505	5	abdelhakem	abdelhakem	PROPN
ejpam-6838	505	6	,	,	PUNCT
ejpam-6838	505	7	t.	t.	PROPN
ejpam-6838	505	8	alaa	alaa	PROPN
ejpam-6838	505	9	-	-	PUNCT
ejpam-6838	505	10	eldeen	eldeen	PROPN
ejpam-6838	505	11	,	,	PUNCT
ejpam-6838	505	12	d.	d.	PROPN
ejpam-6838	505	13	baleanu	baleanu	PROPN
ejpam-6838	505	14	,	,	PUNCT
ejpam-6838	505	15	m.g	m.g	PROPN
ejpam-6838	505	16	.	.	PROPN
ejpam-6838	505	17	alshehri	alshehri	PROPN
ejpam-6838	505	18	,	,	PUNCT
ejpam-6838	505	19	and	and	CCONJ
ejpam-6838	505	20	m.	m.	PROPN
ejpam-6838	505	21	el	el	PROPN
ejpam-6838	505	22	-	-	PUNCT
ejpam-6838	505	23	kady	kady	PROPN
ejpam-6838	505	24	.	.	PUNCT
ejpam-6838	506	1	w.	w.	PROPN
ejpam-6838	506	2	m.	m.	PROPN
ejpam-6838	506	3	abd	abd	PROPN
ejpam-6838	506	4	-	-	PUNCT
ejpam-6838	506	5	elhameed	elhameed	PROPN
ejpam-6838	506	6	et	et	PROPN
ejpam-6838	506	7	al	al	PROPN
ejpam-6838	506	8	.	.	PUNCT
ejpam-6838	506	9	/	/	SYM
ejpam-6838	506	10	eur	eur	PROPN
ejpam-6838	506	11	.	.	PUNCT
ejpam-6838	507	1	j.	j.	PROPN
ejpam-6838	507	2	pure	pure	PROPN
ejpam-6838	507	3	appl	appl	PROPN
ejpam-6838	507	4	.	.	PROPN
ejpam-6838	507	5	math	math	PROPN
ejpam-6838	507	6	,	,	PUNCT
ejpam-6838	507	7	18	18	NUM
ejpam-6838	507	8	(	(	PUNCT
ejpam-6838	507	9	4	4	NUM
ejpam-6838	507	10	)	)	PUNCT
ejpam-6838	507	11	(	(	PUNCT
ejpam-6838	507	12	2025	2025	NUM
ejpam-6838	507	13	)	)	PUNCT
ejpam-6838	507	14	,	,	PUNCT
ejpam-6838	507	15	6838	6838	NUM
ejpam-6838	507	16	23	23	NUM
ejpam-6838	507	17	of	of	ADP
ejpam-6838	507	18	25	25	NUM
ejpam-6838	507	19	approximating	approximate	VERB
ejpam-6838	507	20	real	real	ADJ
ejpam-6838	507	21	-	-	PUNCT
ejpam-6838	507	22	life	life	NOUN
ejpam-6838	507	23	bvps	bvps	NOUN
ejpam-6838	507	24	via	via	ADP
ejpam-6838	507	25	chebyshev	chebyshev	PROPN
ejpam-6838	507	26	polynomials	polynomial	NOUN
ejpam-6838	507	27	’	'	PUNCT
ejpam-6838	507	28	first	first	ADJ
ejpam-6838	507	29	derivative	derivative	ADJ
ejpam-6838	507	30	pseudogalerkin	pseudogalerkin	ADJ
ejpam-6838	507	31	method	method	NOUN
ejpam-6838	507	32	.	.	PUNCT
ejpam-6838	508	1	fractal	fractal	ADJ
ejpam-6838	508	2	fract	fract	PROPN
ejpam-6838	508	3	.	.	PUNCT
ejpam-6838	508	4	,	,	PUNCT
ejpam-6838	508	5	5(4):165	5(4):165	NUM
ejpam-6838	508	6	,	,	PUNCT
ejpam-6838	508	7	2021	2021	NUM
ejpam-6838	508	8	.	.	PUNCT
ejpam-6838	509	1	[	[	X
ejpam-6838	509	2	32	32	NUM
ejpam-6838	509	3	]	]	X
ejpam-6838	509	4	y.h	y.h	PROPN
ejpam-6838	509	5	.	.	PROPN
ejpam-6838	509	6	youssri	youssri	PROPN
ejpam-6838	509	7	,	,	PUNCT
ejpam-6838	509	8	w.m	w.m	PROPN
ejpam-6838	509	9	.	.	PROPN
ejpam-6838	509	10	abd	abd	PROPN
ejpam-6838	509	11	-	-	PUNCT
ejpam-6838	509	12	elhameed	elhameed	PROPN
ejpam-6838	509	13	,	,	PUNCT
ejpam-6838	509	14	a.a	a.a	PROPN
ejpam-6838	509	15	.	.	PROPN
ejpam-6838	509	16	elmasry	elmasry	PROPN
ejpam-6838	509	17	,	,	PUNCT
ejpam-6838	509	18	and	and	CCONJ
ejpam-6838	509	19	a.g	a.g	PROPN
ejpam-6838	509	20	.	.	PROPN
ejpam-6838	509	21	atta	atta	PROPN
ejpam-6838	509	22	.	.	PUNCT
ejpam-6838	510	1	an	an	DET
ejpam-6838	510	2	efficient	efficient	ADJ
ejpam-6838	510	3	petrov	petrov	PROPN
ejpam-6838	510	4	–	–	PUNCT
ejpam-6838	510	5	galerkin	galerkin	ADJ
ejpam-6838	510	6	scheme	scheme	NOUN
ejpam-6838	510	7	for	for	ADP
ejpam-6838	510	8	the	the	DET
ejpam-6838	510	9	euler	euler	PROPN
ejpam-6838	510	10	–	–	PUNCT
ejpam-6838	510	11	bernoulli	bernoulli	PROPN
ejpam-6838	510	12	beam	beam	NOUN
ejpam-6838	510	13	equation	equation	NOUN
ejpam-6838	510	14	via	via	ADP
ejpam-6838	510	15	second	second	ADJ
ejpam-6838	510	16	-	-	PUNCT
ejpam-6838	510	17	kind	kind	NOUN
ejpam-6838	510	18	chebyshev	chebyshev	NOUN
ejpam-6838	510	19	polynomials	polynomial	NOUN
ejpam-6838	510	20	.	.	PUNCT
ejpam-6838	511	1	fractal	fractal	ADJ
ejpam-6838	511	2	fract	fract	PROPN
ejpam-6838	511	3	.	.	PUNCT
ejpam-6838	511	4	,	,	PUNCT
ejpam-6838	512	1	9(2):78	9(2):78	NUM
ejpam-6838	512	2	,	,	PUNCT
ejpam-6838	512	3	2025	2025	NUM
ejpam-6838	512	4	.	.	PUNCT
ejpam-6838	513	1	[	[	X
ejpam-6838	513	2	33	33	NUM
ejpam-6838	513	3	]	]	X
ejpam-6838	513	4	y.h	y.h	PROPN
ejpam-6838	513	5	.	.	PROPN
ejpam-6838	513	6	youssri	youssri	PROPN
ejpam-6838	513	7	,	,	PUNCT
ejpam-6838	513	8	w.m	w.m	PROPN
ejpam-6838	513	9	.	.	PROPN
ejpam-6838	513	10	abd	abd	PROPN
ejpam-6838	513	11	-	-	PUNCT
ejpam-6838	513	12	elhameed	elhameed	PROPN
ejpam-6838	513	13	,	,	PUNCT
ejpam-6838	513	14	and	and	CCONJ
ejpam-6838	513	15	m.	m.	NOUN
ejpam-6838	513	16	abdelhakem	abdelhakem	PROPN
ejpam-6838	513	17	.	.	PUNCT
ejpam-6838	514	1	a	a	DET
ejpam-6838	514	2	robust	robust	ADJ
ejpam-6838	514	3	spectral	spectral	ADJ
ejpam-6838	514	4	treatment	treatment	NOUN
ejpam-6838	514	5	of	of	ADP
ejpam-6838	514	6	a	a	DET
ejpam-6838	514	7	class	class	NOUN
ejpam-6838	514	8	of	of	ADP
ejpam-6838	514	9	initial	initial	ADJ
ejpam-6838	514	10	value	value	NOUN
ejpam-6838	514	11	problems	problem	NOUN
ejpam-6838	514	12	using	use	VERB
ejpam-6838	514	13	modified	modified	ADJ
ejpam-6838	514	14	chebyshev	chebyshev	NOUN
ejpam-6838	514	15	polynomials	polynomial	NOUN
ejpam-6838	514	16	.	.	PUNCT
ejpam-6838	515	1	math	math	NOUN
ejpam-6838	515	2	.	.	PUNCT
ejpam-6838	516	1	methods	method	NOUN
ejpam-6838	516	2	appl	appl	PROPN
ejpam-6838	516	3	.	.	PUNCT
ejpam-6838	517	1	sci	sci	PROPN
ejpam-6838	517	2	.	.	PROPN
ejpam-6838	517	3	,	,	PUNCT
ejpam-6838	517	4	44(11):9224–9236	44(11):9224–9236	NUM
ejpam-6838	517	5	,	,	PUNCT
ejpam-6838	517	6	2021	2021	NUM
ejpam-6838	517	7	.	.	PUNCT
ejpam-6838	518	1	[	[	X
ejpam-6838	518	2	34	34	NUM
ejpam-6838	518	3	]	]	X
ejpam-6838	518	4	j.c	j.c	PROPN
ejpam-6838	518	5	.	.	PROPN
ejpam-6838	518	6	mason	mason	PROPN
ejpam-6838	518	7	and	and	CCONJ
ejpam-6838	518	8	d.c	d.c	PROPN
ejpam-6838	518	9	.	.	PUNCT
ejpam-6838	518	10	handscomb	handscomb	PROPN
ejpam-6838	518	11	.	.	PUNCT
ejpam-6838	519	1	chebyshev	chebyshev	PROPN
ejpam-6838	519	2	polynomials	polynomial	NOUN
ejpam-6838	519	3	.	.	PUNCT
ejpam-6838	520	1	chapman	chapman	PROPN
ejpam-6838	520	2	and	and	CCONJ
ejpam-6838	520	3	hall	hall	PROPN
ejpam-6838	520	4	,	,	PUNCT
ejpam-6838	520	5	new	new	PROPN
ejpam-6838	520	6	york	york	PROPN
ejpam-6838	520	7	,	,	PUNCT
ejpam-6838	520	8	ny	ny	PROPN
ejpam-6838	520	9	,	,	PUNCT
ejpam-6838	520	10	crc	crc	PROPN
ejpam-6838	520	11	,	,	PUNCT
ejpam-6838	520	12	boca	boca	PROPN
ejpam-6838	520	13	raton	raton	PROPN
ejpam-6838	520	14	,	,	PUNCT
ejpam-6838	520	15	2003	2003	NUM
ejpam-6838	520	16	.	.	PUNCT
ejpam-6838	521	1	[	[	X
ejpam-6838	521	2	35	35	NUM
ejpam-6838	521	3	]	]	PUNCT
ejpam-6838	521	4	m.	m.	NOUN
ejpam-6838	521	5	masjed	masjed	NOUN
ejpam-6838	521	6	-	-	PUNCT
ejpam-6838	521	7	jamei	jamei	PROPN
ejpam-6838	521	8	.	.	PUNCT
ejpam-6838	522	1	some	some	DET
ejpam-6838	522	2	new	new	ADJ
ejpam-6838	522	3	classes	class	NOUN
ejpam-6838	522	4	of	of	ADP
ejpam-6838	522	5	orthogonal	orthogonal	ADJ
ejpam-6838	522	6	polynomials	polynomial	NOUN
ejpam-6838	522	7	and	and	CCONJ
ejpam-6838	522	8	special	special	ADJ
ejpam-6838	522	9	functions	function	NOUN
ejpam-6838	522	10	:	:	PUNCT
ejpam-6838	522	11	a	a	DET
ejpam-6838	522	12	symmetric	symmetric	ADJ
ejpam-6838	522	13	generalization	generalization	NOUN
ejpam-6838	522	14	of	of	ADP
ejpam-6838	522	15	sturm	sturm	PROPN
ejpam-6838	522	16	-	-	PUNCT
ejpam-6838	522	17	liouville	liouville	NOUN
ejpam-6838	522	18	problems	problem	NOUN
ejpam-6838	522	19	and	and	CCONJ
ejpam-6838	522	20	its	its	PRON
ejpam-6838	522	21	consequences	consequence	NOUN
ejpam-6838	522	22	.	.	PUNCT
ejpam-6838	523	1	phd	phd	NOUN
ejpam-6838	523	2	thesis	thesis	PROPN
ejpam-6838	523	3	,	,	PUNCT
ejpam-6838	523	4	university	university	PROPN
ejpam-6838	523	5	of	of	ADP
ejpam-6838	523	6	kassel	kassel	PROPN
ejpam-6838	523	7	,	,	PUNCT
ejpam-6838	523	8	kassel	kassel	PROPN
ejpam-6838	523	9	,	,	PUNCT
ejpam-6838	523	10	germany	germany	PROPN
ejpam-6838	523	11	,	,	PUNCT
ejpam-6838	523	12	2006	2006	NUM
ejpam-6838	523	13	.	.	PUNCT
ejpam-6838	524	1	[	[	X
ejpam-6838	524	2	36	36	NUM
ejpam-6838	524	3	]	]	X
ejpam-6838	524	4	m.m	m.m	PROPN
ejpam-6838	524	5	.	.	PROPN
ejpam-6838	524	6	khader	khader	PROPN
ejpam-6838	524	7	and	and	CCONJ
ejpam-6838	524	8	m.m	m.m	PROPN
ejpam-6838	524	9	.	.	PROPN
ejpam-6838	524	10	babatin	babatin	PROPN
ejpam-6838	524	11	.	.	PUNCT
ejpam-6838	525	1	evaluating	evaluate	VERB
ejpam-6838	525	2	the	the	DET
ejpam-6838	525	3	impacts	impact	NOUN
ejpam-6838	525	4	of	of	ADP
ejpam-6838	525	5	thermal	thermal	ADJ
ejpam-6838	525	6	conductivity	conductivity	NOUN
ejpam-6838	525	7	on	on	ADP
ejpam-6838	525	8	casson	casson	PROPN
ejpam-6838	525	9	fluid	fluid	NOUN
ejpam-6838	525	10	flow	flow	NOUN
ejpam-6838	525	11	near	near	ADP
ejpam-6838	525	12	a	a	DET
ejpam-6838	525	13	slippery	slippery	ADJ
ejpam-6838	525	14	sheet	sheet	NOUN
ejpam-6838	525	15	:	:	PUNCT
ejpam-6838	525	16	numerical	numerical	PROPN
ejpam-6838	525	17	simulation	simulation	PROPN
ejpam-6838	525	18	using	use	VERB
ejpam-6838	525	19	sixth	sixth	ADJ
ejpam-6838	525	20	-	-	PUNCT
ejpam-6838	525	21	kind	kind	NOUN
ejpam-6838	525	22	chebyshev	chebyshev	NOUN
ejpam-6838	525	23	polynomials	polynomial	NOUN
ejpam-6838	525	24	.	.	PUNCT
ejpam-6838	526	1	j.	j.	PROPN
ejpam-6838	526	2	nonlinear	nonlinear	PROPN
ejpam-6838	526	3	math	math	PROPN
ejpam-6838	526	4	.	.	PUNCT
ejpam-6838	527	1	phys	phy	NOUN
ejpam-6838	527	2	.	.	PUNCT
ejpam-6838	527	3	,	,	PUNCT
ejpam-6838	527	4	30(4):1834–1853	30(4):1834–1853	NUM
ejpam-6838	527	5	,	,	PUNCT
ejpam-6838	527	6	2023	2023	NUM
ejpam-6838	527	7	.	.	PUNCT
ejpam-6838	528	1	[	[	X
ejpam-6838	528	2	37	37	NUM
ejpam-6838	528	3	]	]	X
ejpam-6838	528	4	k.	k.	PROPN
ejpam-6838	528	5	sadri	sadri	PROPN
ejpam-6838	528	6	and	and	CCONJ
ejpam-6838	528	7	h.	h.	PROPN
ejpam-6838	528	8	aminikhah	aminikhah	PROPN
ejpam-6838	528	9	.	.	PUNCT
ejpam-6838	529	1	a	a	DET
ejpam-6838	529	2	new	new	ADJ
ejpam-6838	529	3	efficient	efficient	ADJ
ejpam-6838	529	4	algorithm	algorithm	NOUN
ejpam-6838	529	5	based	base	VERB
ejpam-6838	529	6	on	on	ADP
ejpam-6838	529	7	fifth	fifth	ADJ
ejpam-6838	529	8	-	-	PUNCT
ejpam-6838	529	9	kind	kind	NOUN
ejpam-6838	529	10	chebyshev	chebyshev	NOUN
ejpam-6838	529	11	polynomials	polynomial	NOUN
ejpam-6838	529	12	for	for	ADP
ejpam-6838	529	13	solving	solve	VERB
ejpam-6838	529	14	multi	multi	ADJ
ejpam-6838	529	15	-	-	ADJ
ejpam-6838	529	16	term	term	ADJ
ejpam-6838	529	17	variable	variable	ADJ
ejpam-6838	529	18	-	-	PUNCT
ejpam-6838	529	19	order	order	NOUN
ejpam-6838	529	20	time	time	NOUN
ejpam-6838	529	21	-	-	PUNCT
ejpam-6838	529	22	fractional	fractional	ADJ
ejpam-6838	529	23	diffusion	diffusion	NOUN
ejpam-6838	529	24	-	-	PUNCT
ejpam-6838	529	25	wave	wave	NOUN
ejpam-6838	529	26	equation	equation	NOUN
ejpam-6838	529	27	.	.	PUNCT
ejpam-6838	530	1	int	int	NOUN
ejpam-6838	530	2	.	.	PUNCT
ejpam-6838	531	1	j.	j.	PROPN
ejpam-6838	531	2	comput	comput	PROPN
ejpam-6838	531	3	.	.	PUNCT
ejpam-6838	532	1	math	math	NOUN
ejpam-6838	532	2	.	.	PUNCT
ejpam-6838	532	3	,	,	PUNCT
ejpam-6838	532	4	99(5):966–992	99(5):966–992	NUM
ejpam-6838	532	5	,	,	PUNCT
ejpam-6838	532	6	2022	2022	NUM
ejpam-6838	532	7	.	.	PUNCT
ejpam-6838	533	1	[	[	X
ejpam-6838	533	2	38	38	NUM
ejpam-6838	533	3	]	]	X
ejpam-6838	533	4	w.m	w.m	PROPN
ejpam-6838	533	5	.	.	PROPN
ejpam-6838	533	6	abd	abd	PROPN
ejpam-6838	533	7	-	-	PUNCT
ejpam-6838	533	8	elhameed	elhameed	PROPN
ejpam-6838	533	9	,	,	PUNCT
ejpam-6838	533	10	y.h	y.h	PROPN
ejpam-6838	533	11	.	.	PROPN
ejpam-6838	533	12	youssri	youssri	PROPN
ejpam-6838	533	13	,	,	PUNCT
ejpam-6838	533	14	and	and	CCONJ
ejpam-6838	533	15	a.g	a.g	PROPN
ejpam-6838	533	16	.	.	PROPN
ejpam-6838	533	17	atta	atta	PROPN
ejpam-6838	533	18	.	.	PUNCT
ejpam-6838	534	1	adopted	adopt	VERB
ejpam-6838	534	2	spectral	spectral	ADJ
ejpam-6838	534	3	tau	tau	PROPN
ejpam-6838	534	4	approach	approach	NOUN
ejpam-6838	534	5	for	for	ADP
ejpam-6838	534	6	the	the	DET
ejpam-6838	534	7	time	time	NOUN
ejpam-6838	534	8	-	-	PUNCT
ejpam-6838	534	9	fractional	fractional	ADJ
ejpam-6838	534	10	diffusion	diffusion	NOUN
ejpam-6838	534	11	equation	equation	NOUN
ejpam-6838	534	12	via	via	ADP
ejpam-6838	534	13	seventh	seventh	ADJ
ejpam-6838	534	14	-	-	PUNCT
ejpam-6838	534	15	kind	kind	NOUN
ejpam-6838	534	16	chebyshev	chebyshev	NOUN
ejpam-6838	534	17	polynomials	polynomial	NOUN
ejpam-6838	534	18	.	.	PUNCT
ejpam-6838	535	1	bound	bind	VERB
ejpam-6838	535	2	.	.	PUNCT
ejpam-6838	536	1	value	value	PROPN
ejpam-6838	536	2	probl	probl	PROPN
ejpam-6838	536	3	.	.	PUNCT
ejpam-6838	536	4	,	,	PUNCT
ejpam-6838	536	5	2024(1):102	2024(1):102	NUM
ejpam-6838	536	6	,	,	PUNCT
ejpam-6838	536	7	2024	2024	NUM
ejpam-6838	536	8	.	.	PUNCT
ejpam-6838	537	1	[	[	X
ejpam-6838	537	2	39	39	NUM
ejpam-6838	537	3	]	]	X
ejpam-6838	537	4	w.m	w.m	PROPN
ejpam-6838	537	5	.	.	PROPN
ejpam-6838	537	6	abd	abd	PROPN
ejpam-6838	537	7	-	-	PUNCT
ejpam-6838	537	8	elhameed	elhameed	PROPN
ejpam-6838	537	9	,	,	PUNCT
ejpam-6838	537	10	y.h	y.h	PROPN
ejpam-6838	537	11	.	.	PROPN
ejpam-6838	537	12	youssri	youssri	PROPN
ejpam-6838	537	13	,	,	PUNCT
ejpam-6838	537	14	a.k	a.k	PROPN
ejpam-6838	537	15	.	.	PROPN
ejpam-6838	537	16	amin	amin	PROPN
ejpam-6838	537	17	,	,	PUNCT
ejpam-6838	537	18	and	and	CCONJ
ejpam-6838	537	19	a.g	a.g	PROPN
ejpam-6838	537	20	.	.	PROPN
ejpam-6838	537	21	atta	atta	PROPN
ejpam-6838	537	22	.	.	PUNCT
ejpam-6838	538	1	eighth	eighth	ADJ
ejpam-6838	538	2	-	-	PUNCT
ejpam-6838	538	3	kind	kind	NOUN
ejpam-6838	538	4	chebyshev	chebyshev	NOUN
ejpam-6838	538	5	polynomials	polynomial	NOUN
ejpam-6838	538	6	collocation	collocation	NOUN
ejpam-6838	538	7	algorithm	algorithm	NOUN
ejpam-6838	538	8	for	for	ADP
ejpam-6838	538	9	the	the	DET
ejpam-6838	538	10	nonlinear	nonlinear	ADJ
ejpam-6838	538	11	time	time	NOUN
ejpam-6838	538	12	-	-	PUNCT
ejpam-6838	538	13	fractional	fractional	ADJ
ejpam-6838	538	14	generalized	generalized	ADJ
ejpam-6838	538	15	kawahara	kawahara	NOUN
ejpam-6838	538	16	equation	equation	NOUN
ejpam-6838	538	17	.	.	PUNCT
ejpam-6838	539	1	fractal	fractal	ADJ
ejpam-6838	539	2	fract	fract	PROPN
ejpam-6838	539	3	.	.	PUNCT
ejpam-6838	539	4	,	,	PUNCT
ejpam-6838	539	5	7(9):652	7(9):652	NUM
ejpam-6838	539	6	,	,	PUNCT
ejpam-6838	539	7	2023	2023	NUM
ejpam-6838	539	8	.	.	PUNCT
ejpam-6838	540	1	[	[	X
ejpam-6838	540	2	40	40	NUM
ejpam-6838	540	3	]	]	X
ejpam-6838	540	4	w.m	w.m	PROPN
ejpam-6838	540	5	.	.	PROPN
ejpam-6838	540	6	abd	abd	PROPN
ejpam-6838	540	7	-	-	PUNCT
ejpam-6838	540	8	elhameed	elhameed	PROPN
ejpam-6838	540	9	,	,	PUNCT
ejpam-6838	540	10	o.m	o.m	PROPN
ejpam-6838	540	11	.	.	PROPN
ejpam-6838	540	12	alqubori	alqubori	PROPN
ejpam-6838	540	13	,	,	PUNCT
ejpam-6838	540	14	and	and	CCONJ
ejpam-6838	540	15	a.g	a.g	PROPN
ejpam-6838	540	16	.	.	PROPN
ejpam-6838	540	17	atta	atta	PROPN
ejpam-6838	540	18	.	.	PUNCT
ejpam-6838	541	1	a	a	DET
ejpam-6838	541	2	collocation	collocation	NOUN
ejpam-6838	541	3	procedure	procedure	NOUN
ejpam-6838	541	4	for	for	ADP
ejpam-6838	541	5	the	the	DET
ejpam-6838	541	6	numerical	numerical	ADJ
ejpam-6838	541	7	treatment	treatment	NOUN
ejpam-6838	541	8	of	of	ADP
ejpam-6838	541	9	fitzhugh	fitzhugh	PROPN
ejpam-6838	541	10	–	–	PUNCT
ejpam-6838	541	11	nagumo	nagumo	ADJ
ejpam-6838	541	12	equation	equation	NOUN
ejpam-6838	541	13	using	use	VERB
ejpam-6838	541	14	a	a	DET
ejpam-6838	541	15	kind	kind	NOUN
ejpam-6838	541	16	of	of	ADP
ejpam-6838	541	17	chebyshev	chebyshev	NOUN
ejpam-6838	541	18	polynomials	polynomial	NOUN
ejpam-6838	541	19	.	.	PUNCT
ejpam-6838	542	1	aims	aim	VERB
ejpam-6838	542	2	math	math	NOUN
ejpam-6838	542	3	.	.	PUNCT
ejpam-6838	542	4	,	,	PUNCT
ejpam-6838	542	5	10(1):1201–1223	10(1):1201–1223	NUM
ejpam-6838	542	6	,	,	PUNCT
ejpam-6838	542	7	2025	2025	NUM
ejpam-6838	542	8	.	.	PUNCT
ejpam-6838	543	1	[	[	X
ejpam-6838	543	2	41	41	NUM
ejpam-6838	543	3	]	]	PUNCT
ejpam-6838	543	4	j.	j.	PROPN
ejpam-6838	543	5	shen	shen	PROPN
ejpam-6838	543	6	,	,	PUNCT
ejpam-6838	543	7	t.	t.	PROPN
ejpam-6838	543	8	tang	tang	PROPN
ejpam-6838	543	9	,	,	PUNCT
ejpam-6838	543	10	and	and	CCONJ
ejpam-6838	543	11	l.-l	l.-l	PROPN
ejpam-6838	543	12	.	.	PUNCT
ejpam-6838	544	1	wang	wang	PROPN
ejpam-6838	544	2	.	.	PUNCT
ejpam-6838	545	1	spectral	spectral	ADJ
ejpam-6838	545	2	methods	method	NOUN
ejpam-6838	545	3	:	:	PUNCT
ejpam-6838	545	4	algorithms	algorithm	NOUN
ejpam-6838	545	5	,	,	PUNCT
ejpam-6838	545	6	analysis	analysis	NOUN
ejpam-6838	545	7	and	and	CCONJ
ejpam-6838	545	8	applications	application	NOUN
ejpam-6838	545	9	,	,	PUNCT
ejpam-6838	545	10	volume	volume	NOUN
ejpam-6838	545	11	41	41	NUM
ejpam-6838	545	12	of	of	ADP
ejpam-6838	545	13	springer	springer	NOUN
ejpam-6838	545	14	series	series	NOUN
ejpam-6838	545	15	in	in	ADP
ejpam-6838	545	16	computational	computational	ADJ
ejpam-6838	545	17	mathematics	mathematic	NOUN
ejpam-6838	545	18	.	.	PUNCT
ejpam-6838	546	1	springer	springer	PROPN
ejpam-6838	546	2	,	,	PUNCT
ejpam-6838	546	3	berlin	berlin	PROPN
ejpam-6838	546	4	,	,	PUNCT
ejpam-6838	546	5	heidelberg	heidelberg	PROPN
ejpam-6838	546	6	,	,	PUNCT
ejpam-6838	546	7	2011	2011	NUM
ejpam-6838	546	8	.	.	PUNCT
ejpam-6838	547	1	[	[	X
ejpam-6838	547	2	42	42	NUM
ejpam-6838	547	3	]	]	X
ejpam-6838	547	4	c.	c.	PROPN
ejpam-6838	547	5	canuto	canuto	PROPN
ejpam-6838	547	6	,	,	PUNCT
ejpam-6838	547	7	m.y	m.y	PROPN
ejpam-6838	547	8	.	.	PROPN
ejpam-6838	547	9	hussaini	hussaini	PROPN
ejpam-6838	547	10	,	,	PUNCT
ejpam-6838	547	11	a.	a.	NOUN
ejpam-6838	547	12	quarteroni	quarteroni	NOUN
ejpam-6838	547	13	,	,	PUNCT
ejpam-6838	547	14	and	and	CCONJ
ejpam-6838	547	15	t.a	t.a	PROPN
ejpam-6838	547	16	.	.	PROPN
ejpam-6838	547	17	zang	zang	PROPN
ejpam-6838	547	18	.	.	PUNCT
ejpam-6838	547	19	spectral	spectral	ADJ
ejpam-6838	547	20	methods	method	NOUN
ejpam-6838	547	21	:	:	PUNCT
ejpam-6838	547	22	evolution	evolution	NOUN
ejpam-6838	547	23	to	to	ADP
ejpam-6838	547	24	complex	complex	ADJ
ejpam-6838	547	25	geometries	geometry	NOUN
ejpam-6838	547	26	and	and	CCONJ
ejpam-6838	547	27	applications	application	NOUN
ejpam-6838	547	28	to	to	ADP
ejpam-6838	547	29	fluid	fluid	ADJ
ejpam-6838	547	30	dynamics	dynamic	NOUN
ejpam-6838	547	31	.	.	PUNCT
ejpam-6838	548	1	scientific	scientific	ADJ
ejpam-6838	548	2	computation	computation	NOUN
ejpam-6838	548	3	.	.	PUNCT
ejpam-6838	549	1	springer	springer	NOUN
ejpam-6838	549	2	,	,	PUNCT
ejpam-6838	549	3	berlin	berlin	PROPN
ejpam-6838	549	4	,	,	PUNCT
ejpam-6838	549	5	heidelberg	heidelberg	PROPN
ejpam-6838	549	6	,	,	PUNCT
ejpam-6838	549	7	2007	2007	NUM
ejpam-6838	549	8	.	.	PUNCT
ejpam-6838	550	1	[	[	X
ejpam-6838	550	2	43	43	NUM
ejpam-6838	550	3	]	]	X
ejpam-6838	550	4	j.s	j.s	PROPN
ejpam-6838	550	5	.	.	PROPN
ejpam-6838	550	6	hesthaven	hesthaven	PROPN
ejpam-6838	550	7	,	,	PUNCT
ejpam-6838	550	8	s.	s.	PROPN
ejpam-6838	550	9	gottlieb	gottlieb	PROPN
ejpam-6838	550	10	,	,	PUNCT
ejpam-6838	550	11	and	and	CCONJ
ejpam-6838	550	12	d.	d.	PROPN
ejpam-6838	550	13	gottlieb	gottlieb	PROPN
ejpam-6838	550	14	.	.	PUNCT
ejpam-6838	551	1	spectral	spectral	ADJ
ejpam-6838	551	2	methods	method	NOUN
ejpam-6838	551	3	for	for	ADP
ejpam-6838	551	4	time	time	NOUN
ejpam-6838	551	5	-	-	PUNCT
ejpam-6838	551	6	dependent	dependent	ADJ
ejpam-6838	551	7	problems	problem	NOUN
ejpam-6838	551	8	,	,	PUNCT
ejpam-6838	551	9	volume	volume	NOUN
ejpam-6838	551	10	21	21	NUM
ejpam-6838	551	11	of	of	ADP
ejpam-6838	551	12	cambridge	cambridge	PROPN
ejpam-6838	551	13	monographs	monograph	NOUN
ejpam-6838	551	14	on	on	ADP
ejpam-6838	551	15	applied	applied	ADJ
ejpam-6838	551	16	and	and	CCONJ
ejpam-6838	551	17	computational	computational	ADJ
ejpam-6838	551	18	mathematics	mathematic	NOUN
ejpam-6838	551	19	.	.	PUNCT
ejpam-6838	552	1	cambridge	cambridge	PROPN
ejpam-6838	552	2	university	university	PROPN
ejpam-6838	552	3	press	press	PROPN
ejpam-6838	552	4	,	,	PUNCT
ejpam-6838	552	5	cambridge	cambridge	PROPN
ejpam-6838	552	6	,	,	PUNCT
ejpam-6838	552	7	2007	2007	NUM
ejpam-6838	552	8	.	.	PUNCT
ejpam-6838	553	1	[	[	X
ejpam-6838	553	2	44	44	NUM
ejpam-6838	553	3	]	]	PUNCT
ejpam-6838	553	4	c.	c.	PROPN
ejpam-6838	553	5	canuto	canuto	PROPN
ejpam-6838	553	6	,	,	PUNCT
ejpam-6838	553	7	m.y	m.y	PROPN
ejpam-6838	553	8	.	.	PROPN
ejpam-6838	553	9	hussaini	hussaini	PROPN
ejpam-6838	553	10	,	,	PUNCT
ejpam-6838	553	11	a.	a.	NOUN
ejpam-6838	553	12	quarteroni	quarteroni	NOUN
ejpam-6838	553	13	,	,	PUNCT
ejpam-6838	553	14	and	and	CCONJ
ejpam-6838	553	15	t.a	t.a	PROPN
ejpam-6838	553	16	.	.	PROPN
ejpam-6838	553	17	zang	zang	PROPN
ejpam-6838	553	18	.	.	PUNCT
ejpam-6838	553	19	spectral	spectral	ADJ
ejpam-6838	553	20	methods	method	NOUN
ejpam-6838	553	21	in	in	ADP
ejpam-6838	553	22	fluid	fluid	ADJ
ejpam-6838	553	23	dynamics	dynamic	NOUN
ejpam-6838	553	24	.	.	PUNCT
ejpam-6838	554	1	springer	springer	NOUN
ejpam-6838	554	2	series	series	PROPN
ejpam-6838	554	3	in	in	ADP
ejpam-6838	554	4	computational	computational	ADJ
ejpam-6838	554	5	physics	physic	NOUN
ejpam-6838	554	6	.	.	PUNCT
ejpam-6838	555	1	springer	springer	NOUN
ejpam-6838	555	2	-	-	PUNCT
ejpam-6838	555	3	verlag	verlag	PROPN
ejpam-6838	555	4	,	,	PUNCT
ejpam-6838	555	5	berlin	berlin	PROPN
ejpam-6838	555	6	,	,	PUNCT
ejpam-6838	555	7	heidelberg	heidelberg	PROPN
ejpam-6838	555	8	,	,	PUNCT
ejpam-6838	555	9	1988	1988	NUM
ejpam-6838	555	10	.	.	PUNCT
ejpam-6838	556	1	[	[	X
ejpam-6838	556	2	45	45	NUM
ejpam-6838	556	3	]	]	PUNCT
ejpam-6838	556	4	s.	s.	PROPN
ejpam-6838	556	5	kumar	kumar	PROPN
ejpam-6838	556	6	,	,	PUNCT
ejpam-6838	556	7	v.	v.	PROPN
ejpam-6838	556	8	gupta	gupta	PROPN
ejpam-6838	556	9	,	,	PUNCT
ejpam-6838	556	10	and	and	CCONJ
ejpam-6838	556	11	d.	d.	PROPN
ejpam-6838	556	12	zeidan	zeidan	PROPN
ejpam-6838	556	13	.	.	PUNCT
ejpam-6838	557	1	an	an	DET
ejpam-6838	557	2	efficient	efficient	ADJ
ejpam-6838	557	3	collocation	collocation	NOUN
ejpam-6838	557	4	technique	technique	NOUN
ejpam-6838	557	5	based	base	VERB
ejpam-6838	557	6	on	on	ADP
ejpam-6838	557	7	operational	operational	ADJ
ejpam-6838	557	8	matrix	matrix	NOUN
ejpam-6838	557	9	of	of	ADP
ejpam-6838	557	10	fractional	fractional	ADJ
ejpam-6838	557	11	-	-	PUNCT
ejpam-6838	557	12	order	order	NOUN
ejpam-6838	557	13	lagrange	lagrange	NOUN
ejpam-6838	557	14	polynomials	polynomial	NOUN
ejpam-6838	557	15	for	for	ADP
ejpam-6838	557	16	solving	solve	VERB
ejpam-6838	557	17	the	the	DET
ejpam-6838	557	18	spacetime	spacetime	ADJ
ejpam-6838	557	19	fractional	fractional	ADJ
ejpam-6838	557	20	-	-	PUNCT
ejpam-6838	557	21	order	order	NOUN
ejpam-6838	557	22	partial	partial	ADJ
ejpam-6838	557	23	differential	differential	NOUN
ejpam-6838	557	24	equations	equation	NOUN
ejpam-6838	557	25	.	.	PUNCT
ejpam-6838	558	1	appl	appl	PROPN
ejpam-6838	558	2	.	.	PUNCT
ejpam-6838	559	1	numer	numer	PROPN
ejpam-6838	559	2	.	.	PUNCT
ejpam-6838	559	3	math	math	PROPN
ejpam-6838	559	4	.	.	PUNCT
ejpam-6838	559	5	,	,	PUNCT
ejpam-6838	559	6	204:249–264	204:249–264	NUM
ejpam-6838	559	7	,	,	PUNCT
ejpam-6838	559	8	w.	w.	PROPN
ejpam-6838	559	9	m.	m.	PROPN
ejpam-6838	559	10	abd	abd	PROPN
ejpam-6838	559	11	-	-	PUNCT
ejpam-6838	559	12	elhameed	elhameed	PROPN
ejpam-6838	559	13	et	et	PROPN
ejpam-6838	559	14	al	al	PROPN
ejpam-6838	559	15	.	.	PUNCT
ejpam-6838	559	16	/	/	SYM
ejpam-6838	559	17	eur	eur	PROPN
ejpam-6838	559	18	.	.	PUNCT
ejpam-6838	560	1	j.	j.	PROPN
ejpam-6838	560	2	pure	pure	PROPN
ejpam-6838	560	3	appl	appl	PROPN
ejpam-6838	560	4	.	.	PROPN
ejpam-6838	560	5	math	math	PROPN
ejpam-6838	560	6	,	,	PUNCT
ejpam-6838	560	7	18	18	NUM
ejpam-6838	560	8	(	(	PUNCT
ejpam-6838	560	9	4	4	NUM
ejpam-6838	560	10	)	)	PUNCT
ejpam-6838	560	11	(	(	PUNCT
ejpam-6838	560	12	2025	2025	NUM
ejpam-6838	560	13	)	)	PUNCT
ejpam-6838	560	14	,	,	PUNCT
ejpam-6838	560	15	6838	6838	NUM
ejpam-6838	560	16	24	24	NUM
ejpam-6838	560	17	of	of	ADP
ejpam-6838	560	18	25	25	NUM
ejpam-6838	560	19	2024	2024	NUM
ejpam-6838	560	20	.	.	PUNCT
ejpam-6838	561	1	[	[	X
ejpam-6838	561	2	46	46	NUM
ejpam-6838	561	3	]	]	X
ejpam-6838	561	4	g.	g.	PROPN
ejpam-6838	561	5	manohara	manohara	PROPN
ejpam-6838	561	6	and	and	CCONJ
ejpam-6838	561	7	s.	s.	PROPN
ejpam-6838	561	8	kumbinarasaiah	kumbinarasaiah	PROPN
ejpam-6838	561	9	.	.	PUNCT
ejpam-6838	562	1	an	an	DET
ejpam-6838	562	2	innovative	innovative	ADJ
ejpam-6838	562	3	fibonacci	fibonacci	NOUN
ejpam-6838	562	4	wavelet	wavelet	NOUN
ejpam-6838	562	5	collocation	collocation	NOUN
ejpam-6838	562	6	method	method	NOUN
ejpam-6838	562	7	for	for	ADP
ejpam-6838	562	8	the	the	DET
ejpam-6838	562	9	numerical	numerical	ADJ
ejpam-6838	562	10	approximation	approximation	NOUN
ejpam-6838	562	11	of	of	ADP
ejpam-6838	562	12	emden	emden	ADJ
ejpam-6838	562	13	-	-	PUNCT
ejpam-6838	562	14	fowler	fowler	PROPN
ejpam-6838	562	15	equations	equation	NOUN
ejpam-6838	562	16	.	.	PUNCT
ejpam-6838	563	1	appl	appl	PROPN
ejpam-6838	563	2	.	.	PUNCT
ejpam-6838	564	1	numer	numer	PROPN
ejpam-6838	564	2	.	.	PUNCT
ejpam-6838	564	3	math	math	PROPN
ejpam-6838	564	4	.	.	PUNCT
ejpam-6838	564	5	,	,	PUNCT
ejpam-6838	564	6	201:347–369	201:347–369	NUM
ejpam-6838	564	7	,	,	PUNCT
ejpam-6838	564	8	2024	2024	NUM
ejpam-6838	564	9	.	.	PUNCT
ejpam-6838	565	1	[	[	X
ejpam-6838	565	2	47	47	NUM
ejpam-6838	565	3	]	]	X
ejpam-6838	565	4	m.a	m.a	PROPN
ejpam-6838	565	5	.	.	PROPN
ejpam-6838	565	6	taema	taema	PROPN
ejpam-6838	565	7	,	,	PUNCT
ejpam-6838	565	8	m.a	m.a	PROPN
ejpam-6838	565	9	.	.	PROPN
ejpam-6838	565	10	dagher	dagher	PROPN
ejpam-6838	565	11	,	,	PUNCT
ejpam-6838	565	12	and	and	CCONJ
ejpam-6838	565	13	y.h	y.h	PROPN
ejpam-6838	565	14	.	.	PROPN
ejpam-6838	565	15	youssri	youssri	PROPN
ejpam-6838	565	16	.	.	PUNCT
ejpam-6838	566	1	spectral	spectral	ADJ
ejpam-6838	566	2	collocation	collocation	NOUN
ejpam-6838	566	3	method	method	NOUN
ejpam-6838	566	4	via	via	ADP
ejpam-6838	566	5	fermat	fermat	PROPN
ejpam-6838	566	6	polynomials	polynomial	NOUN
ejpam-6838	566	7	for	for	ADP
ejpam-6838	566	8	fredholm	fredholm	NOUN
ejpam-6838	566	9	–	–	PUNCT
ejpam-6838	566	10	volterra	volterra	NOUN
ejpam-6838	566	11	integral	integral	ADJ
ejpam-6838	566	12	equations	equation	NOUN
ejpam-6838	566	13	with	with	ADP
ejpam-6838	566	14	singular	singular	ADJ
ejpam-6838	566	15	kernels	kernel	NOUN
ejpam-6838	566	16	and	and	CCONJ
ejpam-6838	566	17	fractional	fractional	ADJ
ejpam-6838	566	18	differential	differential	ADJ
ejpam-6838	566	19	equations	equation	NOUN
ejpam-6838	566	20	.	.	PUNCT
ejpam-6838	567	1	palestine	palestine	PROPN
ejpam-6838	567	2	j.	j.	PROPN
ejpam-6838	567	3	math	math	PROPN
ejpam-6838	567	4	.	.	PUNCT
ejpam-6838	567	5	,	,	PUNCT
ejpam-6838	567	6	14(2):481–492	14(2):481–492	PROPN
ejpam-6838	567	7	,	,	PUNCT
ejpam-6838	567	8	2025	2025	NUM
ejpam-6838	567	9	.	.	PUNCT
ejpam-6838	568	1	[	[	X
ejpam-6838	568	2	48	48	NUM
ejpam-6838	568	3	]	]	X
ejpam-6838	568	4	m.a	m.a	PROPN
ejpam-6838	568	5	.	.	PROPN
ejpam-6838	568	6	taema	taema	NOUN
ejpam-6838	568	7	and	and	CCONJ
ejpam-6838	568	8	y.h	y.h	PROPN
ejpam-6838	568	9	.	.	PROPN
ejpam-6838	568	10	youssri	youssri	PROPN
ejpam-6838	568	11	.	.	PUNCT
ejpam-6838	569	1	third	third	ADJ
ejpam-6838	569	2	-	-	PUNCT
ejpam-6838	569	3	kind	kind	NOUN
ejpam-6838	569	4	chebyshev	chebyshev	NOUN
ejpam-6838	569	5	spectral	spectral	ADJ
ejpam-6838	569	6	collocation	collocation	NOUN
ejpam-6838	569	7	method	method	NOUN
ejpam-6838	569	8	for	for	ADP
ejpam-6838	569	9	solving	solve	VERB
ejpam-6838	569	10	models	model	NOUN
ejpam-6838	569	11	of	of	ADP
ejpam-6838	569	12	two	two	NUM
ejpam-6838	569	13	interacting	interact	VERB
ejpam-6838	569	14	biological	biological	ADJ
ejpam-6838	569	15	species	specie	NOUN
ejpam-6838	569	16	.	.	PUNCT
ejpam-6838	570	1	contemp	contemp	NOUN
ejpam-6838	570	2	.	.	PUNCT
ejpam-6838	571	1	math	math	NOUN
ejpam-6838	571	2	.	.	PUNCT
ejpam-6838	571	3	,	,	PUNCT
ejpam-6838	571	4	5:6189–6207	5:6189–6207	NUM
ejpam-6838	571	5	,	,	PUNCT
ejpam-6838	571	6	2024	2024	NUM
ejpam-6838	571	7	.	.	PUNCT
ejpam-6838	572	1	[	[	X
ejpam-6838	572	2	49	49	NUM
ejpam-6838	572	3	]	]	X
ejpam-6838	572	4	a.h	a.h	PROPN
ejpam-6838	572	5	.	.	PROPN
ejpam-6838	572	6	bhrawy	bhrawy	PROPN
ejpam-6838	572	7	and	and	CCONJ
ejpam-6838	572	8	w.m	w.m	PROPN
ejpam-6838	572	9	.	.	PROPN
ejpam-6838	572	10	abd	abd	PROPN
ejpam-6838	572	11	-	-	PUNCT
ejpam-6838	572	12	elhameed	elhameed	NOUN
ejpam-6838	572	13	.	.	PUNCT
ejpam-6838	573	1	new	new	ADJ
ejpam-6838	573	2	algorithm	algorithm	NOUN
ejpam-6838	573	3	for	for	ADP
ejpam-6838	573	4	the	the	DET
ejpam-6838	573	5	numerical	numerical	ADJ
ejpam-6838	573	6	solutions	solution	NOUN
ejpam-6838	573	7	of	of	ADP
ejpam-6838	573	8	nonlinear	nonlinear	ADJ
ejpam-6838	573	9	third	third	ADJ
ejpam-6838	573	10	-	-	PUNCT
ejpam-6838	573	11	order	order	NOUN
ejpam-6838	573	12	differential	differential	ADJ
ejpam-6838	573	13	equations	equation	NOUN
ejpam-6838	573	14	using	use	VERB
ejpam-6838	573	15	jacobi	jacobi	PROPN
ejpam-6838	573	16	–	–	PUNCT
ejpam-6838	573	17	gauss	gauss	ADJ
ejpam-6838	573	18	collocation	collocation	NOUN
ejpam-6838	573	19	method	method	NOUN
ejpam-6838	573	20	.	.	PUNCT
ejpam-6838	574	1	math	math	NOUN
ejpam-6838	574	2	.	.	PUNCT
ejpam-6838	575	1	probl	probl	PROPN
ejpam-6838	575	2	.	.	PUNCT
ejpam-6838	576	1	eng	eng	PROPN
ejpam-6838	576	2	.	.	PROPN
ejpam-6838	576	3	,	,	PUNCT
ejpam-6838	576	4	2011:837218	2011:837218	NOUN
ejpam-6838	576	5	,	,	PUNCT
ejpam-6838	576	6	2011	2011	NUM
ejpam-6838	576	7	.	.	PUNCT
ejpam-6838	577	1	[	[	X
ejpam-6838	577	2	50	50	NUM
ejpam-6838	577	3	]	]	X
ejpam-6838	577	4	w.m	w.m	PROPN
ejpam-6838	577	5	.	.	PROPN
ejpam-6838	577	6	abd	abd	PROPN
ejpam-6838	577	7	-	-	PUNCT
ejpam-6838	577	8	elhameed	elhameed	PROPN
ejpam-6838	577	9	,	,	PUNCT
ejpam-6838	577	10	a.m.	a.m.	PROPN
ejpam-6838	577	11	al	al	PROPN
ejpam-6838	577	12	-	-	PUNCT
ejpam-6838	577	13	sady	sady	PROPN
ejpam-6838	577	14	,	,	PUNCT
ejpam-6838	577	15	o.m	o.m	PROPN
ejpam-6838	577	16	.	.	PROPN
ejpam-6838	577	17	alqubori	alqubori	PROPN
ejpam-6838	577	18	,	,	PUNCT
ejpam-6838	577	19	and	and	CCONJ
ejpam-6838	577	20	a.g	a.g	PROPN
ejpam-6838	577	21	.	.	PROPN
ejpam-6838	577	22	atta	atta	PROPN
ejpam-6838	577	23	.	.	PUNCT
ejpam-6838	578	1	numerical	numerical	ADJ
ejpam-6838	578	2	treatment	treatment	NOUN
ejpam-6838	578	3	of	of	ADP
ejpam-6838	578	4	the	the	DET
ejpam-6838	578	5	fractional	fractional	ADJ
ejpam-6838	578	6	rayleigh	rayleigh	PROPN
ejpam-6838	578	7	-	-	PUNCT
ejpam-6838	578	8	stokes	stoke	NOUN
ejpam-6838	578	9	problem	problem	NOUN
ejpam-6838	578	10	using	use	VERB
ejpam-6838	578	11	some	some	DET
ejpam-6838	578	12	orthogonal	orthogonal	ADJ
ejpam-6838	578	13	combinations	combination	NOUN
ejpam-6838	578	14	of	of	ADP
ejpam-6838	578	15	chebyshev	chebyshev	NOUN
ejpam-6838	578	16	polynomials	polynomial	NOUN
ejpam-6838	578	17	.	.	PUNCT
ejpam-6838	579	1	aims	aim	VERB
ejpam-6838	579	2	math	math	NOUN
ejpam-6838	579	3	.	.	PUNCT
ejpam-6838	580	1	,	,	PUNCT
ejpam-6838	580	2	9(09):25457–25481	9(09):25457–25481	NUM
ejpam-6838	580	3	,	,	PUNCT
ejpam-6838	580	4	2024	2024	NUM
ejpam-6838	580	5	.	.	PUNCT
ejpam-6838	581	1	[	[	X
ejpam-6838	581	2	51	51	NUM
ejpam-6838	581	3	]	]	X
ejpam-6838	581	4	m.a	m.a	PROPN
ejpam-6838	581	5	.	.	PROPN
ejpam-6838	581	6	abbas	abbas	PROPN
ejpam-6838	581	7	,	,	PUNCT
ejpam-6838	581	8	y.h	y.h	PROPN
ejpam-6838	581	9	.	.	PROPN
ejpam-6838	581	10	youssri	youssri	PROPN
ejpam-6838	581	11	,	,	PUNCT
ejpam-6838	581	12	m.	m.	PROPN
ejpam-6838	581	13	el	el	PROPN
ejpam-6838	581	14	-	-	PUNCT
ejpam-6838	581	15	kady	kady	PROPN
ejpam-6838	581	16	,	,	PUNCT
ejpam-6838	581	17	and	and	CCONJ
ejpam-6838	581	18	m.	m.	NOUN
ejpam-6838	581	19	abdelhakem	abdelhakem	PROPN
ejpam-6838	581	20	.	.	PUNCT
ejpam-6838	582	1	high	high	ADJ
ejpam-6838	582	2	-	-	PUNCT
ejpam-6838	582	3	accuracy	accuracy	NOUN
ejpam-6838	582	4	modified	modify	VERB
ejpam-6838	582	5	spectral	spectral	ADJ
ejpam-6838	582	6	techniques	technique	NOUN
ejpam-6838	582	7	for	for	ADP
ejpam-6838	582	8	two	two	NUM
ejpam-6838	582	9	-	-	PUNCT
ejpam-6838	582	10	dimensional	dimensional	ADJ
ejpam-6838	582	11	integral	integral	ADJ
ejpam-6838	582	12	equations	equation	NOUN
ejpam-6838	582	13	.	.	PUNCT
ejpam-6838	583	1	j.	j.	PROPN
ejpam-6838	583	2	comput	comput	PROPN
ejpam-6838	583	3	.	.	PUNCT
ejpam-6838	584	1	appl	appl	PROPN
ejpam-6838	584	2	.	.	PROPN
ejpam-6838	584	3	mech	mech	PROPN
ejpam-6838	584	4	.	.	PROPN
ejpam-6838	584	5	,	,	PUNCT
ejpam-6838	584	6	56(2):364–379	56(2):364–379	PROPN
ejpam-6838	584	7	,	,	PUNCT
ejpam-6838	584	8	2025	2025	NUM
ejpam-6838	584	9	.	.	PUNCT
ejpam-6838	585	1	[	[	X
ejpam-6838	585	2	52	52	NUM
ejpam-6838	585	3	]	]	SYM
ejpam-6838	585	4	s.m	s.m	PROPN
ejpam-6838	585	5	.	.	PROPN
ejpam-6838	585	6	sayed	sayed	PROPN
ejpam-6838	585	7	,	,	PUNCT
ejpam-6838	585	8	a.s	a.s	PROPN
ejpam-6838	585	9	.	.	PROPN
ejpam-6838	585	10	mohamed	mohamed	PROPN
ejpam-6838	585	11	,	,	PUNCT
ejpam-6838	585	12	e.m	e.m	PROPN
ejpam-6838	585	13	.	.	PROPN
ejpam-6838	585	14	abo	abo	NOUN
ejpam-6838	585	15	-	-	PUNCT
ejpam-6838	585	16	eldahab	eldahab	NOUN
ejpam-6838	585	17	,	,	PUNCT
ejpam-6838	585	18	and	and	CCONJ
ejpam-6838	585	19	y.h	y.h	PROPN
ejpam-6838	585	20	.	.	PROPN
ejpam-6838	585	21	youssri	youssri	PROPN
ejpam-6838	585	22	.	.	PUNCT
ejpam-6838	586	1	spectral	spectral	ADJ
ejpam-6838	586	2	framework	framework	NOUN
ejpam-6838	586	3	using	use	VERB
ejpam-6838	586	4	modified	modify	VERB
ejpam-6838	586	5	shifted	shift	VERB
ejpam-6838	586	6	chebyshev	chebyshev	NOUN
ejpam-6838	586	7	polynomials	polynomial	NOUN
ejpam-6838	586	8	of	of	ADP
ejpam-6838	586	9	the	the	DET
ejpam-6838	586	10	third	third	ADJ
ejpam-6838	586	11	kind	kind	NOUN
ejpam-6838	586	12	for	for	ADP
ejpam-6838	586	13	numerical	numerical	ADJ
ejpam-6838	586	14	solutions	solution	NOUN
ejpam-6838	586	15	of	of	ADP
ejpam-6838	586	16	oneand	oneand	ADJ
ejpam-6838	586	17	two	two	NUM
ejpam-6838	586	18	-	-	PUNCT
ejpam-6838	586	19	dimensional	dimensional	ADJ
ejpam-6838	586	20	hyperbolic	hyperbolic	ADJ
ejpam-6838	586	21	telegraph	telegraph	NOUN
ejpam-6838	586	22	equations	equation	NOUN
ejpam-6838	586	23	.	.	PUNCT
ejpam-6838	587	1	bound	bind	VERB
ejpam-6838	587	2	.	.	PUNCT
ejpam-6838	588	1	value	value	PROPN
ejpam-6838	588	2	probl	probl	PROPN
ejpam-6838	588	3	.	.	PUNCT
ejpam-6838	588	4	,	,	PUNCT
ejpam-6838	588	5	2025(1):7	2025(1):7	NUM
ejpam-6838	588	6	,	,	PUNCT
ejpam-6838	588	7	2025	2025	NUM
ejpam-6838	588	8	.	.	PUNCT
ejpam-6838	589	1	[	[	X
ejpam-6838	589	2	53	53	NUM
ejpam-6838	589	3	]	]	X
ejpam-6838	589	4	r.m	r.m	PROPN
ejpam-6838	589	5	.	.	PROPN
ejpam-6838	589	6	hafez	hafez	PROPN
ejpam-6838	589	7	,	,	PUNCT
ejpam-6838	589	8	h.m	h.m	PROPN
ejpam-6838	589	9	.	.	PROPN
ejpam-6838	589	10	ahmed	ahmed	PROPN
ejpam-6838	589	11	,	,	PUNCT
ejpam-6838	589	12	o.m	o.m	PROPN
ejpam-6838	589	13	.	.	PROPN
ejpam-6838	589	14	alqubori	alqubori	PROPN
ejpam-6838	589	15	,	,	PUNCT
ejpam-6838	589	16	a.k	a.k	PROPN
ejpam-6838	589	17	.	.	PROPN
ejpam-6838	589	18	amin	amin	PROPN
ejpam-6838	589	19	,	,	PUNCT
ejpam-6838	589	20	and	and	CCONJ
ejpam-6838	589	21	w.m	w.m	PROPN
ejpam-6838	589	22	.	.	PROPN
ejpam-6838	589	23	abd	abd	PROPN
ejpam-6838	589	24	-	-	PUNCT
ejpam-6838	589	25	elhameed	elhameed	PROPN
ejpam-6838	589	26	.	.	PUNCT
ejpam-6838	590	1	efficient	efficient	ADJ
ejpam-6838	590	2	spectral	spectral	ADJ
ejpam-6838	590	3	galerkin	galerkin	ADJ
ejpam-6838	590	4	and	and	CCONJ
ejpam-6838	590	5	collocation	collocation	NOUN
ejpam-6838	590	6	approaches	approach	NOUN
ejpam-6838	590	7	using	use	VERB
ejpam-6838	590	8	telephone	telephone	NOUN
ejpam-6838	590	9	polynomials	polynomial	NOUN
ejpam-6838	590	10	for	for	ADP
ejpam-6838	590	11	solving	solve	VERB
ejpam-6838	590	12	some	some	DET
ejpam-6838	590	13	models	model	NOUN
ejpam-6838	590	14	of	of	ADP
ejpam-6838	590	15	differential	differential	ADJ
ejpam-6838	590	16	equations	equation	NOUN
ejpam-6838	590	17	with	with	ADP
ejpam-6838	590	18	convergence	convergence	NOUN
ejpam-6838	590	19	analysis	analysis	NOUN
ejpam-6838	590	20	.	.	PUNCT
ejpam-6838	591	1	mathematics	mathematic	NOUN
ejpam-6838	591	2	,	,	PUNCT
ejpam-6838	591	3	13(6):918	13(6):918	NOUN
ejpam-6838	591	4	,	,	PUNCT
ejpam-6838	591	5	2025	2025	NUM
ejpam-6838	591	6	.	.	PUNCT
ejpam-6838	592	1	[	[	X
ejpam-6838	592	2	54	54	NUM
ejpam-6838	592	3	]	]	X
ejpam-6838	592	4	y.	y.	PROPN
ejpam-6838	592	5	h.	h.	PROPN
ejpam-6838	592	6	youssri	youssri	PROPN
ejpam-6838	592	7	,	,	PUNCT
ejpam-6838	592	8	r.	r.	PROPN
ejpam-6838	592	9	m.	m.	PROPN
ejpam-6838	592	10	hafez	hafez	PROPN
ejpam-6838	592	11	,	,	PUNCT
ejpam-6838	592	12	and	and	CCONJ
ejpam-6838	592	13	a.	a.	NOUN
ejpam-6838	592	14	g.	g.	PROPN
ejpam-6838	592	15	atta	atta	PROPN
ejpam-6838	592	16	.	.	PUNCT
ejpam-6838	593	1	an	an	DET
ejpam-6838	593	2	innovative	innovative	ADJ
ejpam-6838	593	3	pseudo	pseudo	NOUN
ejpam-6838	593	4	-	-	ADJ
ejpam-6838	593	5	spectral	spectral	ADJ
ejpam-6838	593	6	galerkin	galerkin	ADJ
ejpam-6838	593	7	algorithm	algorithm	NOUN
ejpam-6838	593	8	for	for	ADP
ejpam-6838	593	9	the	the	DET
ejpam-6838	593	10	time	time	NOUN
ejpam-6838	593	11	-	-	PUNCT
ejpam-6838	593	12	fractional	fractional	ADJ
ejpam-6838	593	13	tricomi	tricomi	NOUN
ejpam-6838	593	14	-	-	PUNCT
ejpam-6838	593	15	type	type	NOUN
ejpam-6838	593	16	equation	equation	NOUN
ejpam-6838	593	17	.	.	PUNCT
ejpam-6838	594	1	phys	phy	NOUN
ejpam-6838	594	2	.	.	PUNCT
ejpam-6838	595	1	scr	scr	PROPN
ejpam-6838	595	2	.	.	PROPN
ejpam-6838	595	3	,	,	PUNCT
ejpam-6838	595	4	99(10):105238	99(10):105238	NUM
ejpam-6838	595	5	,	,	PUNCT
ejpam-6838	595	6	2024	2024	NUM
ejpam-6838	595	7	.	.	PUNCT
ejpam-6838	596	1	[	[	X
ejpam-6838	596	2	55	55	NUM
ejpam-6838	596	3	]	]	SYM
ejpam-6838	596	4	a.a	a.a	PROPN
ejpam-6838	596	5	.	.	PROPN
ejpam-6838	596	6	el	el	PROPN
ejpam-6838	596	7	-	-	PUNCT
ejpam-6838	596	8	sayed	sayed	PROPN
ejpam-6838	596	9	,	,	PUNCT
ejpam-6838	596	10	s.	s.	PROPN
ejpam-6838	596	11	boulaaras	boulaaras	PROPN
ejpam-6838	596	12	,	,	PUNCT
ejpam-6838	596	13	and	and	CCONJ
ejpam-6838	596	14	n.h	n.h	PROPN
ejpam-6838	596	15	.	.	PROPN
ejpam-6838	597	1	sweilam	sweilam	PROPN
ejpam-6838	597	2	.	.	PUNCT
ejpam-6838	598	1	numerical	numerical	ADJ
ejpam-6838	598	2	solution	solution	NOUN
ejpam-6838	598	3	of	of	ADP
ejpam-6838	598	4	the	the	DET
ejpam-6838	598	5	fractionalorder	fractionalorder	ADJ
ejpam-6838	598	6	logistic	logistic	ADJ
ejpam-6838	598	7	equation	equation	NOUN
ejpam-6838	598	8	via	via	ADP
ejpam-6838	598	9	the	the	DET
ejpam-6838	598	10	first	first	ADJ
ejpam-6838	598	11	-	-	PUNCT
ejpam-6838	598	12	kind	kind	NOUN
ejpam-6838	598	13	dickson	dickson	PROPN
ejpam-6838	598	14	polynomials	polynomial	NOUN
ejpam-6838	598	15	and	and	CCONJ
ejpam-6838	598	16	spectral	spectral	ADJ
ejpam-6838	598	17	tau	tau	PROPN
ejpam-6838	598	18	method	method	NOUN
ejpam-6838	598	19	.	.	PUNCT
ejpam-6838	599	1	math	math	NOUN
ejpam-6838	599	2	.	.	PUNCT
ejpam-6838	600	1	methods	method	NOUN
ejpam-6838	600	2	appl	appl	PROPN
ejpam-6838	600	3	.	.	PUNCT
ejpam-6838	601	1	sci	sci	PROPN
ejpam-6838	601	2	.	.	PROPN
ejpam-6838	601	3	,	,	PUNCT
ejpam-6838	601	4	46(7):8004–8017	46(7):8004–8017	NUM
ejpam-6838	601	5	,	,	PUNCT
ejpam-6838	601	6	2023	2023	NUM
ejpam-6838	601	7	.	.	PUNCT
ejpam-6838	602	1	[	[	X
ejpam-6838	602	2	56	56	NUM
ejpam-6838	602	3	]	]	X
ejpam-6838	602	4	w.m	w.m	PROPN
ejpam-6838	602	5	.	.	PROPN
ejpam-6838	602	6	abd	abd	PROPN
ejpam-6838	602	7	-	-	PUNCT
ejpam-6838	602	8	elhameed	elhameed	PROPN
ejpam-6838	602	9	,	,	PUNCT
ejpam-6838	602	10	j.a.t	j.a.t	NOUN
ejpam-6838	602	11	.	.	PUNCT
ejpam-6838	602	12	machado	machado	PROPN
ejpam-6838	602	13	,	,	PUNCT
ejpam-6838	602	14	and	and	CCONJ
ejpam-6838	602	15	y.h	y.h	PROPN
ejpam-6838	602	16	.	.	PROPN
ejpam-6838	602	17	youssri	youssri	PROPN
ejpam-6838	602	18	.	.	PUNCT
ejpam-6838	603	1	hypergeometric	hypergeometric	ADJ
ejpam-6838	603	2	fractional	fractional	ADJ
ejpam-6838	603	3	derivatives	derivative	NOUN
ejpam-6838	603	4	formula	formula	NOUN
ejpam-6838	603	5	of	of	ADP
ejpam-6838	603	6	shifted	shift	VERB
ejpam-6838	603	7	chebyshev	chebyshev	NOUN
ejpam-6838	603	8	polynomials	polynomial	NOUN
ejpam-6838	603	9	:	:	PUNCT
ejpam-6838	603	10	tau	tau	PROPN
ejpam-6838	603	11	algorithm	algorithm	NOUN
ejpam-6838	603	12	for	for	ADP
ejpam-6838	603	13	a	a	DET
ejpam-6838	603	14	type	type	NOUN
ejpam-6838	603	15	of	of	ADP
ejpam-6838	603	16	fractional	fractional	ADJ
ejpam-6838	603	17	delay	delay	NOUN
ejpam-6838	603	18	differential	differential	NOUN
ejpam-6838	603	19	equations	equation	NOUN
ejpam-6838	603	20	.	.	PUNCT
ejpam-6838	604	1	int	int	NOUN
ejpam-6838	604	2	.	.	PUNCT
ejpam-6838	605	1	j.	j.	PROPN
ejpam-6838	605	2	nonlinear	nonlinear	PROPN
ejpam-6838	605	3	sci	sci	PROPN
ejpam-6838	605	4	.	.	PUNCT
ejpam-6838	605	5	numer	numer	PROPN
ejpam-6838	605	6	.	.	PUNCT
ejpam-6838	606	1	simul	simul	PROPN
ejpam-6838	606	2	.	.	PROPN
ejpam-6838	606	3	,	,	PUNCT
ejpam-6838	606	4	23(78):1253–1268	23(78):1253–1268	NUM
ejpam-6838	606	5	,	,	PUNCT
ejpam-6838	606	6	2022	2022	NUM
ejpam-6838	606	7	.	.	PUNCT
ejpam-6838	607	1	[	[	X
ejpam-6838	607	2	57	57	NUM
ejpam-6838	607	3	]	]	X
ejpam-6838	607	4	w.m	w.m	PROPN
ejpam-6838	607	5	.	.	PROPN
ejpam-6838	607	6	abd	abd	PROPN
ejpam-6838	607	7	-	-	PUNCT
ejpam-6838	607	8	elhameed	elhameed	PROPN
ejpam-6838	607	9	,	,	PUNCT
ejpam-6838	607	10	o.m	o.m	PROPN
ejpam-6838	607	11	.	.	PROPN
ejpam-6838	607	12	alqubori	alqubori	PROPN
ejpam-6838	607	13	,	,	PUNCT
ejpam-6838	607	14	a.k	a.k	PROPN
ejpam-6838	607	15	.	.	PROPN
ejpam-6838	607	16	al	al	PROPN
ejpam-6838	607	17	-	-	PUNCT
ejpam-6838	607	18	harbi	harbi	PROPN
ejpam-6838	607	19	,	,	PUNCT
ejpam-6838	607	20	m.h	m.h	PROPN
ejpam-6838	607	21	.	.	PROPN
ejpam-6838	607	22	alharbi	alharbi	PROPN
ejpam-6838	607	23	,	,	PUNCT
ejpam-6838	607	24	and	and	CCONJ
ejpam-6838	607	25	a.g	a.g	PROPN
ejpam-6838	607	26	.	.	PROPN
ejpam-6838	607	27	atta	atta	PROPN
ejpam-6838	607	28	.	.	PUNCT
ejpam-6838	608	1	generalized	generalized	ADJ
ejpam-6838	608	2	third	third	ADJ
ejpam-6838	608	3	-	-	PUNCT
ejpam-6838	608	4	kind	kind	NOUN
ejpam-6838	608	5	chebyshev	chebyshev	NOUN
ejpam-6838	608	6	tau	tau	PROPN
ejpam-6838	608	7	approach	approach	NOUN
ejpam-6838	608	8	for	for	ADP
ejpam-6838	608	9	treating	treat	VERB
ejpam-6838	608	10	the	the	DET
ejpam-6838	608	11	time	time	NOUN
ejpam-6838	608	12	fractional	fractional	ADJ
ejpam-6838	608	13	cable	cable	NOUN
ejpam-6838	608	14	problem	problem	NOUN
ejpam-6838	608	15	.	.	PUNCT
ejpam-6838	609	1	electron	electron	NOUN
ejpam-6838	609	2	.	.	PUNCT
ejpam-6838	610	1	res	re	NOUN
ejpam-6838	610	2	.	.	PROPN
ejpam-6838	610	3	archive	archive	PROPN
ejpam-6838	610	4	,	,	PUNCT
ejpam-6838	610	5	32(11	32(11	NUM
ejpam-6838	610	6	)	)	PUNCT
ejpam-6838	610	7	,	,	PUNCT
ejpam-6838	610	8	2024	2024	NUM
ejpam-6838	610	9	.	.	PUNCT
ejpam-6838	611	1	[	[	X
ejpam-6838	611	2	58	58	NUM
ejpam-6838	611	3	]	]	X
ejpam-6838	611	4	w.m	w.m	PROPN
ejpam-6838	611	5	.	.	PROPN
ejpam-6838	611	6	abd	abd	PROPN
ejpam-6838	611	7	-	-	PUNCT
ejpam-6838	611	8	elhameed	elhameed	PROPN
ejpam-6838	611	9	,	,	PUNCT
ejpam-6838	611	10	m.a	m.a	PROPN
ejpam-6838	611	11	.	.	PROPN
ejpam-6838	611	12	abdelkawy	abdelkawy	PROPN
ejpam-6838	611	13	,	,	PUNCT
ejpam-6838	611	14	o.m	o.m	PROPN
ejpam-6838	611	15	.	.	PROPN
ejpam-6838	611	16	alqubori	alqubori	PROPN
ejpam-6838	611	17	,	,	PUNCT
ejpam-6838	611	18	and	and	CCONJ
ejpam-6838	611	19	a.g	a.g	PROPN
ejpam-6838	611	20	.	.	PROPN
ejpam-6838	611	21	atta	atta	PROPN
ejpam-6838	611	22	.	.	PUNCT
ejpam-6838	612	1	an	an	DET
ejpam-6838	612	2	accurate	accurate	ADJ
ejpam-6838	612	3	tau	tau	NOUN
ejpam-6838	612	4	-	-	PUNCT
ejpam-6838	612	5	based	base	VERB
ejpam-6838	612	6	spectral	spectral	ADJ
ejpam-6838	612	7	algorithm	algorithm	NOUN
ejpam-6838	612	8	for	for	ADP
ejpam-6838	612	9	the	the	DET
ejpam-6838	612	10	time	time	NOUN
ejpam-6838	612	11	fractional	fractional	ADJ
ejpam-6838	612	12	bioheat	bioheat	NOUN
ejpam-6838	612	13	transfer	transfer	NOUN
ejpam-6838	612	14	model	model	NOUN
ejpam-6838	612	15	.	.	PUNCT
ejpam-6838	613	1	bound	bind	VERB
ejpam-6838	613	2	.	.	PUNCT
ejpam-6838	614	1	value	value	PROPN
ejpam-6838	614	2	probl	probl	NOUN
ejpam-6838	614	3	.	.	PUNCT
ejpam-6838	614	4	,	,	PUNCT
ejpam-6838	614	5	2025:124	2025:124	NUM
ejpam-6838	614	6	,	,	PUNCT
ejpam-6838	614	7	2025	2025	NUM
ejpam-6838	614	8	.	.	PUNCT
ejpam-6838	615	1	w.	w.	PROPN
ejpam-6838	615	2	m.	m.	PROPN
ejpam-6838	615	3	abd	abd	PROPN
ejpam-6838	615	4	-	-	PUNCT
ejpam-6838	615	5	elhameed	elhameed	PROPN
ejpam-6838	615	6	et	et	PROPN
ejpam-6838	615	7	al	al	PROPN
ejpam-6838	615	8	.	.	PUNCT
ejpam-6838	615	9	/	/	SYM
ejpam-6838	615	10	eur	eur	PROPN
ejpam-6838	615	11	.	.	PUNCT
ejpam-6838	616	1	j.	j.	PROPN
ejpam-6838	616	2	pure	pure	PROPN
ejpam-6838	616	3	appl	appl	PROPN
ejpam-6838	616	4	.	.	PROPN
ejpam-6838	616	5	math	math	PROPN
ejpam-6838	616	6	,	,	PUNCT
ejpam-6838	616	7	18	18	NUM
ejpam-6838	616	8	(	(	PUNCT
ejpam-6838	616	9	4	4	NUM
ejpam-6838	616	10	)	)	PUNCT
ejpam-6838	616	11	(	(	PUNCT
ejpam-6838	616	12	2025	2025	NUM
ejpam-6838	616	13	)	)	PUNCT
ejpam-6838	616	14	,	,	PUNCT
ejpam-6838	616	15	6838	6838	NUM
ejpam-6838	616	16	25	25	NUM
ejpam-6838	616	17	of	of	ADP
ejpam-6838	616	18	25	25	NUM
ejpam-6838	616	19	[	[	SYM
ejpam-6838	616	20	59	59	NUM
ejpam-6838	616	21	]	]	X
ejpam-6838	616	22	y.	y.	PROPN
ejpam-6838	616	23	xu	xu	PROPN
ejpam-6838	616	24	.	.	PUNCT
ejpam-6838	617	1	an	an	DET
ejpam-6838	617	2	integral	integral	ADJ
ejpam-6838	617	3	formula	formula	NOUN
ejpam-6838	617	4	for	for	ADP
ejpam-6838	617	5	generalized	generalized	ADJ
ejpam-6838	617	6	gegenbauer	gegenbauer	NOUN
ejpam-6838	617	7	polynomials	polynomial	NOUN
ejpam-6838	617	8	and	and	CCONJ
ejpam-6838	617	9	jacobi	jacobi	PROPN
ejpam-6838	617	10	polynomials	polynomial	NOUN
ejpam-6838	617	11	.	.	PUNCT
ejpam-6838	618	1	adv	adv	PROPN
ejpam-6838	618	2	.	.	PUNCT
ejpam-6838	618	3	appl	appl	PROPN
ejpam-6838	618	4	.	.	PROPN
ejpam-6838	618	5	math	math	PROPN
ejpam-6838	618	6	.	.	PUNCT
ejpam-6838	618	7	,	,	PUNCT
ejpam-6838	619	1	29(2):328–343	29(2):328–343	PROPN
ejpam-6838	619	2	,	,	PUNCT
ejpam-6838	619	3	2002	2002	NUM
ejpam-6838	619	4	.	.	PUNCT
ejpam-6838	620	1	[	[	X
ejpam-6838	620	2	60	60	NUM
ejpam-6838	620	3	]	]	PUNCT
ejpam-6838	620	4	a.	a.	NOUN
ejpam-6838	620	5	draux	draux	PROPN
ejpam-6838	620	6	,	,	PUNCT
ejpam-6838	620	7	m.	m.	NOUN
ejpam-6838	620	8	sadik	sadik	PROPN
ejpam-6838	620	9	,	,	PUNCT
ejpam-6838	620	10	and	and	CCONJ
ejpam-6838	620	11	b.	b.	PROPN
ejpam-6838	620	12	moalla	moalla	PROPN
ejpam-6838	620	13	.	.	PUNCT
ejpam-6838	621	1	markov	markov	PROPN
ejpam-6838	621	2	–	–	PUNCT
ejpam-6838	621	3	bernstein	bernstein	PROPN
ejpam-6838	621	4	inequalities	inequality	NOUN
ejpam-6838	621	5	for	for	ADP
ejpam-6838	621	6	generalized	generalized	ADJ
ejpam-6838	621	7	gegenbauer	gegenbauer	NOUN
ejpam-6838	621	8	weight	weight	PROPN
ejpam-6838	621	9	.	.	PUNCT
ejpam-6838	622	1	appl	appl	PROPN
ejpam-6838	622	2	.	.	PUNCT
ejpam-6838	623	1	numer	numer	PROPN
ejpam-6838	623	2	.	.	PUNCT
ejpam-6838	623	3	math	math	PROPN
ejpam-6838	623	4	.	.	PUNCT
ejpam-6838	623	5	,	,	PUNCT
ejpam-6838	623	6	61(12):1301–1321	61(12):1301–1321	ADP
ejpam-6838	623	7	,	,	PUNCT
ejpam-6838	623	8	2011	2011	NUM
ejpam-6838	623	9	.	.	PUNCT
ejpam-6838	624	1	[	[	X
ejpam-6838	624	2	61	61	NUM
ejpam-6838	624	3	]	]	X
ejpam-6838	624	4	y.h	y.h	PROPN
ejpam-6838	624	5	.	.	PROPN
ejpam-6838	624	6	youssri	youssri	PROPN
ejpam-6838	624	7	and	and	CCONJ
ejpam-6838	624	8	a.g	a.g	PROPN
ejpam-6838	624	9	.	.	PROPN
ejpam-6838	624	10	atta	atta	PROPN
ejpam-6838	624	11	.	.	PUNCT
ejpam-6838	625	1	petrov	petrov	PROPN
ejpam-6838	625	2	-	-	PUNCT
ejpam-6838	625	3	galerkin	galerkin	PROPN
ejpam-6838	625	4	lucas	lucas	PROPN
ejpam-6838	625	5	polynomials	polynomial	NOUN
ejpam-6838	625	6	procedure	procedure	NOUN
ejpam-6838	625	7	for	for	ADP
ejpam-6838	625	8	the	the	DET
ejpam-6838	625	9	time	time	NOUN
ejpam-6838	625	10	-	-	PUNCT
ejpam-6838	625	11	fractional	fractional	ADJ
ejpam-6838	625	12	diffusion	diffusion	NOUN
ejpam-6838	625	13	equation	equation	NOUN
ejpam-6838	625	14	.	.	PUNCT
ejpam-6838	626	1	contemp	contemp	NOUN
ejpam-6838	626	2	.	.	PUNCT
ejpam-6838	627	1	math	math	NOUN
ejpam-6838	627	2	.	.	PUNCT
ejpam-6838	627	3	,	,	PUNCT
ejpam-6838	627	4	4:230–248	4:230–248	PROPN
ejpam-6838	627	5	,	,	PUNCT
ejpam-6838	627	6	2023	2023	NUM
ejpam-6838	627	7	.	.	PUNCT
ejpam-6838	628	1	[	[	X
ejpam-6838	628	2	62	62	NUM
ejpam-6838	628	3	]	]	PUNCT
ejpam-6838	628	4	x.	x.	NOUN
ejpam-6838	628	5	zhao	zhao	PROPN
ejpam-6838	628	6	,	,	PUNCT
ejpam-6838	628	7	l.l	l.l	PROPN
ejpam-6838	628	8	.	.	PROPN
ejpam-6838	628	9	wang	wang	PROPN
ejpam-6838	628	10	,	,	PUNCT
ejpam-6838	628	11	and	and	CCONJ
ejpam-6838	628	12	z.	z.	PROPN
ejpam-6838	628	13	xie	xie	PROPN
ejpam-6838	628	14	.	.	PUNCT
ejpam-6838	629	1	sharp	sharp	ADJ
ejpam-6838	629	2	error	error	NOUN
ejpam-6838	629	3	bounds	bound	NOUN
ejpam-6838	629	4	for	for	ADP
ejpam-6838	629	5	jacobi	jacobi	PROPN
ejpam-6838	629	6	expansions	expansion	NOUN
ejpam-6838	629	7	and	and	CCONJ
ejpam-6838	629	8	gegenbauer	gegenbauer	PROPN
ejpam-6838	629	9	–	–	PUNCT
ejpam-6838	629	10	gauss	gauss	ADJ
ejpam-6838	629	11	quadrature	quadrature	NOUN
ejpam-6838	629	12	of	of	ADP
ejpam-6838	629	13	analytic	analytic	ADJ
ejpam-6838	629	14	functions	function	NOUN
ejpam-6838	629	15	.	.	PUNCT
ejpam-6838	630	1	siam	siam	PROPN
ejpam-6838	630	2	j.	j.	PROPN
ejpam-6838	630	3	numer	numer	PROPN
ejpam-6838	630	4	.	.	PUNCT
ejpam-6838	631	1	anal	anal	PROPN
ejpam-6838	631	2	.	.	PUNCT
ejpam-6838	631	3	,	,	PUNCT
ejpam-6838	631	4	51(3):1443–1469	51(3):1443–1469	NUM
ejpam-6838	631	5	,	,	PUNCT
ejpam-6838	631	6	2013	2013	NUM
ejpam-6838	631	7	.	.	PUNCT
ejpam-6838	632	1	[	[	X
ejpam-6838	632	2	63	63	NUM
ejpam-6838	632	3	]	]	PUNCT
ejpam-6838	632	4	k.	k.	PROPN
ejpam-6838	632	5	sadri	sadri	PROPN
ejpam-6838	632	6	and	and	CCONJ
ejpam-6838	632	7	h.	h.	PROPN
ejpam-6838	632	8	aminikhah	aminikhah	PROPN
ejpam-6838	632	9	.	.	PUNCT
ejpam-6838	633	1	chebyshev	chebyshev	PROPN
ejpam-6838	633	2	polynomials	polynomial	NOUN
ejpam-6838	633	3	of	of	ADP
ejpam-6838	633	4	sixth	sixth	ADJ
ejpam-6838	633	5	kind	kind	NOUN
ejpam-6838	633	6	for	for	ADP
ejpam-6838	633	7	solving	solve	VERB
ejpam-6838	633	8	nonlinear	nonlinear	ADJ
ejpam-6838	633	9	fractional	fractional	ADJ
ejpam-6838	633	10	pdes	pde	NOUN
ejpam-6838	633	11	with	with	ADP
ejpam-6838	633	12	proportional	proportional	ADJ
ejpam-6838	633	13	delay	delay	NOUN
ejpam-6838	633	14	and	and	CCONJ
ejpam-6838	633	15	its	its	PRON
ejpam-6838	633	16	convergence	convergence	NOUN
ejpam-6838	633	17	analysis	analysis	NOUN
ejpam-6838	633	18	.	.	PUNCT
ejpam-6838	634	1	j.	j.	PROPN
ejpam-6838	634	2	funct	funct	PROPN
ejpam-6838	634	3	.	.	PUNCT
ejpam-6838	635	1	spaces	space	NOUN
ejpam-6838	635	2	,	,	PUNCT
ejpam-6838	635	3	2022(1):9512048	2022(1):9512048	NUM
ejpam-6838	635	4	,	,	PUNCT
ejpam-6838	635	5	2022	2022	NUM
ejpam-6838	635	6	.	.	PUNCT
ejpam-6838	636	1	[	[	X
ejpam-6838	636	2	64	64	NUM
ejpam-6838	636	3	]	]	PUNCT
ejpam-6838	636	4	k.	k.	PROPN
ejpam-6838	636	5	sayevand	sayevand	PROPN
ejpam-6838	636	6	,	,	PUNCT
ejpam-6838	636	7	a.	a.	PROPN
ejpam-6838	636	8	yazdani	yazdani	PROPN
ejpam-6838	636	9	,	,	PUNCT
ejpam-6838	636	10	and	and	CCONJ
ejpam-6838	636	11	f.	f.	PROPN
ejpam-6838	636	12	arjang	arjang	PROPN
ejpam-6838	636	13	.	.	PUNCT
ejpam-6838	637	1	cubic	cubic	PROPN
ejpam-6838	637	2	b	b	PROPN
ejpam-6838	637	3	-	-	PUNCT
ejpam-6838	637	4	spline	spline	NOUN
ejpam-6838	637	5	collocation	collocation	NOUN
ejpam-6838	637	6	method	method	NOUN
ejpam-6838	637	7	and	and	CCONJ
ejpam-6838	637	8	its	its	PRON
ejpam-6838	637	9	application	application	NOUN
ejpam-6838	637	10	for	for	ADP
ejpam-6838	637	11	anomalous	anomalous	ADJ
ejpam-6838	637	12	fractional	fractional	ADJ
ejpam-6838	637	13	diffusion	diffusion	NOUN
ejpam-6838	637	14	equations	equation	NOUN
ejpam-6838	637	15	in	in	ADP
ejpam-6838	637	16	transport	transport	NOUN
ejpam-6838	637	17	dynamic	dynamic	ADJ
ejpam-6838	637	18	systems	system	NOUN
ejpam-6838	637	19	.	.	PUNCT
ejpam-6838	638	1	j.	j.	PROPN
ejpam-6838	638	2	vib	vib	PROPN
ejpam-6838	638	3	.	.	PUNCT
ejpam-6838	638	4	control	control	PROPN
ejpam-6838	638	5	,	,	PUNCT
ejpam-6838	638	6	22(9):2173–2186	22(9):2173–2186	PROPN
ejpam-6838	638	7	,	,	PUNCT
ejpam-6838	638	8	2016	2016	NUM
ejpam-6838	638	9	.	.	PUNCT