id	sid	tid	token	lemma	pos
ejpam-7095	1	1	european	european	PROPN
ejpam-7095	1	2	journal	journal	PROPN
ejpam-7095	1	3	of	of	ADP
ejpam-7095	1	4	pure	pure	ADJ
ejpam-7095	1	5	and	and	CCONJ
ejpam-7095	1	6	applied	applied	ADJ
ejpam-7095	1	7	mathematics	mathematic	NOUN
ejpam-7095	1	8	2025	2025	NUM
ejpam-7095	1	9	,	,	PUNCT
ejpam-7095	1	10	vol	vol	NOUN
ejpam-7095	1	11	.	.	PROPN
ejpam-7095	1	12	18	18	NUM
ejpam-7095	1	13	,	,	PUNCT
ejpam-7095	1	14	issue	issue	NOUN
ejpam-7095	1	15	4	4	NUM
ejpam-7095	1	16	,	,	PUNCT
ejpam-7095	1	17	article	article	NOUN
ejpam-7095	1	18	number	number	NOUN
ejpam-7095	1	19	7095	7095	NUM
ejpam-7095	1	20	issn	issn	PROPN
ejpam-7095	1	21	1307	1307	NUM
ejpam-7095	1	22	-	-	SYM
ejpam-7095	1	23	5543	5543	NUM
ejpam-7095	1	24	–	–	PUNCT
ejpam-7095	1	25	ejpam.com	ejpam.com	X
ejpam-7095	1	26	published	publish	VERB
ejpam-7095	1	27	by	by	ADP
ejpam-7095	1	28	new	new	PROPN
ejpam-7095	1	29	york	york	PROPN
ejpam-7095	1	30	business	business	PROPN
ejpam-7095	1	31	global	global	PROPN
ejpam-7095	1	32	a	a	DET
ejpam-7095	1	33	laplace	laplace	NOUN
ejpam-7095	1	34	-	-	PUNCT
ejpam-7095	1	35	chebyshev	chebyshev	NOUN
ejpam-7095	1	36	spectral	spectral	ADJ
ejpam-7095	1	37	method	method	NOUN
ejpam-7095	1	38	for	for	ADP
ejpam-7095	1	39	multi	multi	ADJ
ejpam-7095	1	40	-	-	ADJ
ejpam-7095	1	41	dimensional	dimensional	ADJ
ejpam-7095	1	42	anomalous	anomalous	ADJ
ejpam-7095	1	43	transport	transport	NOUN
ejpam-7095	1	44	kamran1,∗	kamran1,∗	NOUN
ejpam-7095	1	45	,	,	PUNCT
ejpam-7095	1	46	bibi	bibi	NOUN
ejpam-7095	1	47	zahra1	zahra1	PROPN
ejpam-7095	1	48	,	,	PUNCT
ejpam-7095	1	49	zeeshan	zeeshan	PROPN
ejpam-7095	1	50	ali2	ali2	PROPN
ejpam-7095	1	51	,	,	PUNCT
ejpam-7095	1	52	ahmad	ahmad	PROPN
ejpam-7095	1	53	aloqaily3	aloqaily3	PROPN
ejpam-7095	1	54	,	,	PUNCT
ejpam-7095	1	55	nabil	nabil	PROPN
ejpam-7095	1	56	mlaiki3	mlaiki3	PROPN
ejpam-7095	1	57	1	1	NUM
ejpam-7095	1	58	department	department	NOUN
ejpam-7095	1	59	of	of	ADP
ejpam-7095	1	60	mathematics	mathematics	PROPN
ejpam-7095	1	61	,	,	PUNCT
ejpam-7095	1	62	islamia	islamia	PROPN
ejpam-7095	1	63	college	college	PROPN
ejpam-7095	1	64	peshawar	peshawar	PROPN
ejpam-7095	1	65	,	,	PUNCT
ejpam-7095	1	66	peshawar	peshawar	PROPN
ejpam-7095	1	67	25120	25120	NUM
ejpam-7095	1	68	,	,	PUNCT
ejpam-7095	1	69	khyber	khyber	PROPN
ejpam-7095	1	70	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-7095	1	71	,	,	PUNCT
ejpam-7095	1	72	pakistan	pakistan	PROPN
ejpam-7095	1	73	2	2	NUM
ejpam-7095	1	74	department	department	NOUN
ejpam-7095	1	75	of	of	ADP
ejpam-7095	1	76	information	information	NOUN
ejpam-7095	1	77	management	management	NOUN
ejpam-7095	1	78	,	,	PUNCT
ejpam-7095	1	79	national	national	PROPN
ejpam-7095	1	80	yunlin	yunlin	PROPN
ejpam-7095	1	81	university	university	PROPN
ejpam-7095	1	82	of	of	ADP
ejpam-7095	1	83	science	science	NOUN
ejpam-7095	1	84	and	and	CCONJ
ejpam-7095	1	85	technology	technology	NOUN
ejpam-7095	1	86	,	,	PUNCT
ejpam-7095	1	87	douliu	douliu	NOUN
ejpam-7095	1	88	,	,	PUNCT
ejpam-7095	1	89	taiwan	taiwan	PROPN
ejpam-7095	1	90	,	,	PUNCT
ejpam-7095	1	91	republic	republic	NOUN
ejpam-7095	1	92	of	of	ADP
ejpam-7095	1	93	china	china	PROPN
ejpam-7095	1	94	3	3	PROPN
ejpam-7095	1	95	department	department	NOUN
ejpam-7095	1	96	of	of	ADP
ejpam-7095	1	97	mathematics	mathematic	NOUN
ejpam-7095	1	98	and	and	CCONJ
ejpam-7095	1	99	sciences	science	NOUN
ejpam-7095	1	100	,	,	PUNCT
ejpam-7095	1	101	prince	prince	PROPN
ejpam-7095	1	102	sultan	sultan	PROPN
ejpam-7095	1	103	university	university	PROPN
ejpam-7095	1	104	,	,	PUNCT
ejpam-7095	1	105	p.o	p.o	PROPN
ejpam-7095	1	106	.	.	PROPN
ejpam-7095	1	107	box	box	PROPN
ejpam-7095	1	108	66833	66833	NUM
ejpam-7095	1	109	,	,	PUNCT
ejpam-7095	1	110	riyadh	riyadh	PROPN
ejpam-7095	1	111	11586	11586	NUM
ejpam-7095	1	112	,	,	PUNCT
ejpam-7095	1	113	saudi	saudi	PROPN
ejpam-7095	1	114	arabia	arabia	PROPN
ejpam-7095	1	115	abstract	abstract	NOUN
ejpam-7095	1	116	.	.	PUNCT
ejpam-7095	2	1	anomalous	anomalous	ADJ
ejpam-7095	2	2	transport	transport	NOUN
ejpam-7095	2	3	processes	process	NOUN
ejpam-7095	2	4	,	,	PUNCT
ejpam-7095	2	5	such	such	ADJ
ejpam-7095	2	6	as	as	ADP
ejpam-7095	2	7	subsurface	subsurface	NOUN
ejpam-7095	2	8	contaminant	contaminant	NOUN
ejpam-7095	2	9	spread	spread	NOUN
ejpam-7095	2	10	or	or	CCONJ
ejpam-7095	2	11	wave	wave	NOUN
ejpam-7095	2	12	attenuation	attenuation	NOUN
ejpam-7095	2	13	in	in	ADP
ejpam-7095	2	14	viscoelastic	viscoelastic	ADJ
ejpam-7095	2	15	materials	material	NOUN
ejpam-7095	2	16	,	,	PUNCT
ejpam-7095	2	17	are	be	AUX
ejpam-7095	2	18	governed	govern	VERB
ejpam-7095	2	19	by	by	ADP
ejpam-7095	2	20	time	time	NOUN
ejpam-7095	2	21	-	-	PUNCT
ejpam-7095	2	22	fractional	fractional	ADJ
ejpam-7095	2	23	diffusion	diffusion	NOUN
ejpam-7095	2	24	-	-	PUNCT
ejpam-7095	2	25	wave	wave	NOUN
ejpam-7095	2	26	equations	equation	NOUN
ejpam-7095	2	27	.	.	PUNCT
ejpam-7095	3	1	the	the	DET
ejpam-7095	3	2	non	non	ADJ
ejpam-7095	3	3	-	-	ADJ
ejpam-7095	3	4	local	local	ADJ
ejpam-7095	3	5	nature	nature	NOUN
ejpam-7095	3	6	of	of	ADP
ejpam-7095	3	7	fractional	fractional	ADJ
ejpam-7095	3	8	operators	operator	NOUN
ejpam-7095	3	9	and	and	CCONJ
ejpam-7095	3	10	the	the	DET
ejpam-7095	3	11	high	high	ADJ
ejpam-7095	3	12	computational	computational	ADJ
ejpam-7095	3	13	cost	cost	NOUN
ejpam-7095	3	14	of	of	ADP
ejpam-7095	3	15	addressing	address	VERB
ejpam-7095	3	16	multidimensional	multidimensional	ADJ
ejpam-7095	3	17	spaces	space	NOUN
ejpam-7095	3	18	pose	pose	VERB
ejpam-7095	3	19	significant	significant	ADJ
ejpam-7095	3	20	challenges	challenge	NOUN
ejpam-7095	3	21	for	for	ADP
ejpam-7095	3	22	numerical	numerical	ADJ
ejpam-7095	3	23	simulations	simulation	NOUN
ejpam-7095	3	24	.	.	PUNCT
ejpam-7095	4	1	to	to	PART
ejpam-7095	4	2	overcome	overcome	VERB
ejpam-7095	4	3	this	this	PRON
ejpam-7095	4	4	,	,	PUNCT
ejpam-7095	4	5	we	we	PRON
ejpam-7095	4	6	develop	develop	VERB
ejpam-7095	4	7	a	a	DET
ejpam-7095	4	8	novel	novel	ADJ
ejpam-7095	4	9	hybrid	hybrid	ADJ
ejpam-7095	4	10	spectral	spectral	ADJ
ejpam-7095	4	11	method	method	NOUN
ejpam-7095	4	12	combining	combine	VERB
ejpam-7095	4	13	the	the	DET
ejpam-7095	4	14	laplace	laplace	NOUN
ejpam-7095	4	15	transform	transform	NOUN
ejpam-7095	4	16	(	(	PUNCT
ejpam-7095	4	17	lt	lt	NOUN
ejpam-7095	4	18	)	)	PUNCT
ejpam-7095	4	19	technique	technique	NOUN
ejpam-7095	4	20	with	with	ADP
ejpam-7095	4	21	the	the	DET
ejpam-7095	4	22	chebyshev	chebyshev	NOUN
ejpam-7095	4	23	spectral	spectral	ADJ
ejpam-7095	4	24	collocation	collocation	NOUN
ejpam-7095	4	25	method	method	NOUN
ejpam-7095	4	26	(	(	PUNCT
ejpam-7095	4	27	cscm	cscm	PROPN
ejpam-7095	4	28	)	)	PUNCT
ejpam-7095	4	29	for	for	ADP
ejpam-7095	4	30	solving	solve	VERB
ejpam-7095	4	31	tfdwes	tfdwe	NOUN
ejpam-7095	4	32	featuring	feature	VERB
ejpam-7095	4	33	the	the	DET
ejpam-7095	4	34	modified	modified	ADJ
ejpam-7095	4	35	atangana	atangana	PROPN
ejpam-7095	4	36	-	-	PUNCT
ejpam-7095	4	37	baleanu	baleanu	PROPN
ejpam-7095	4	38	-	-	PUNCT
ejpam-7095	4	39	caputo	caputo	PROPN
ejpam-7095	4	40	derivative	derivative	NOUN
ejpam-7095	4	41	,	,	PUNCT
ejpam-7095	4	42	chosen	choose	VERB
ejpam-7095	4	43	for	for	ADP
ejpam-7095	4	44	its	its	PRON
ejpam-7095	4	45	non	non	ADJ
ejpam-7095	4	46	-	-	ADJ
ejpam-7095	4	47	singular	singular	ADJ
ejpam-7095	4	48	kernel	kernel	NOUN
ejpam-7095	4	49	and	and	CCONJ
ejpam-7095	4	50	efficiency	efficiency	NOUN
ejpam-7095	4	51	in	in	ADP
ejpam-7095	4	52	modeling	model	VERB
ejpam-7095	4	53	complex	complex	ADJ
ejpam-7095	4	54	memory	memory	NOUN
ejpam-7095	4	55	effects	effect	NOUN
ejpam-7095	4	56	.	.	PUNCT
ejpam-7095	5	1	our	our	PRON
ejpam-7095	5	2	numerical	numerical	ADJ
ejpam-7095	5	3	scheme	scheme	NOUN
ejpam-7095	5	4	,	,	PUNCT
ejpam-7095	5	5	temporal	temporal	ADJ
ejpam-7095	5	6	and	and	CCONJ
ejpam-7095	5	7	spatial	spatial	ADJ
ejpam-7095	5	8	discretizations	discretization	NOUN
ejpam-7095	5	9	,	,	PUNCT
ejpam-7095	5	10	are	be	AUX
ejpam-7095	5	11	decoupled	decouple	VERB
ejpam-7095	5	12	.	.	PUNCT
ejpam-7095	6	1	the	the	DET
ejpam-7095	6	2	lt	lt	PROPN
ejpam-7095	6	3	handles	handle	VERB
ejpam-7095	6	4	the	the	DET
ejpam-7095	6	5	fractional	fractional	ADJ
ejpam-7095	6	6	time	time	NOUN
ejpam-7095	6	7	derivative	derivative	NOUN
ejpam-7095	6	8	exactly	exactly	ADV
ejpam-7095	6	9	in	in	ADP
ejpam-7095	6	10	the	the	DET
ejpam-7095	6	11	laplace	laplace	NOUN
ejpam-7095	6	12	domain	domain	NOUN
ejpam-7095	6	13	,	,	PUNCT
ejpam-7095	6	14	removing	remove	VERB
ejpam-7095	6	15	time	time	NOUN
ejpam-7095	6	16	-	-	PUNCT
ejpam-7095	6	17	stepping	step	VERB
ejpam-7095	6	18	restrictions	restriction	NOUN
ejpam-7095	6	19	and	and	CCONJ
ejpam-7095	6	20	convolution	convolution	NOUN
ejpam-7095	6	21	costs	cost	NOUN
ejpam-7095	6	22	,	,	PUNCT
ejpam-7095	6	23	while	while	SCONJ
ejpam-7095	6	24	the	the	DET
ejpam-7095	6	25	cscm	cscm	NOUN
ejpam-7095	6	26	ensures	ensure	VERB
ejpam-7095	6	27	the	the	DET
ejpam-7095	6	28	exponential	exponential	ADJ
ejpam-7095	6	29	convergence	convergence	NOUN
ejpam-7095	6	30	in	in	ADP
ejpam-7095	6	31	the	the	DET
ejpam-7095	6	32	spatial	spatial	ADJ
ejpam-7095	6	33	domain	domain	NOUN
ejpam-7095	6	34	.	.	PUNCT
ejpam-7095	7	1	the	the	DET
ejpam-7095	7	2	numerical	numerical	ADJ
ejpam-7095	7	3	inversion	inversion	NOUN
ejpam-7095	7	4	of	of	ADP
ejpam-7095	7	5	lt	lt	PRON
ejpam-7095	7	6	is	be	AUX
ejpam-7095	7	7	obtained	obtain	VERB
ejpam-7095	7	8	using	use	VERB
ejpam-7095	7	9	the	the	DET
ejpam-7095	7	10	improved	improved	ADJ
ejpam-7095	7	11	talbot	talbot	PROPN
ejpam-7095	7	12	method	method	NOUN
ejpam-7095	7	13	,	,	PUNCT
ejpam-7095	7	14	guaranteeing	guarantee	VERB
ejpam-7095	7	15	rapid	rapid	ADJ
ejpam-7095	7	16	o(e−cn	o(e−cn	ADJ
ejpam-7095	7	17	)	)	PUNCT
ejpam-7095	7	18	convergence	convergence	NOUN
ejpam-7095	7	19	.	.	PUNCT
ejpam-7095	8	1	this	this	DET
ejpam-7095	8	2	work	work	NOUN
ejpam-7095	8	3	provides	provide	VERB
ejpam-7095	8	4	not	not	PART
ejpam-7095	8	5	only	only	ADV
ejpam-7095	8	6	a	a	DET
ejpam-7095	8	7	robust	robust	ADJ
ejpam-7095	8	8	computational	computational	ADJ
ejpam-7095	8	9	technique	technique	NOUN
ejpam-7095	8	10	but	but	CCONJ
ejpam-7095	8	11	also	also	ADV
ejpam-7095	8	12	a	a	DET
ejpam-7095	8	13	rigorous	rigorous	ADJ
ejpam-7095	8	14	mathematical	mathematical	ADJ
ejpam-7095	8	15	analysis	analysis	NOUN
ejpam-7095	8	16	,	,	PUNCT
ejpam-7095	8	17	establishing	establish	VERB
ejpam-7095	8	18	clear	clear	ADJ
ejpam-7095	8	19	conditions	condition	NOUN
ejpam-7095	8	20	for	for	ADP
ejpam-7095	8	21	the	the	DET
ejpam-7095	8	22	existence	existence	NOUN
ejpam-7095	8	23	,	,	PUNCT
ejpam-7095	8	24	uniqueness	uniqueness	NOUN
ejpam-7095	8	25	,	,	PUNCT
ejpam-7095	8	26	and	and	CCONJ
ejpam-7095	8	27	ulam	ulam	NOUN
ejpam-7095	8	28	-	-	PUNCT
ejpam-7095	8	29	hyers	hyer	NOUN
ejpam-7095	8	30	stability	stability	NOUN
ejpam-7095	8	31	of	of	ADP
ejpam-7095	8	32	the	the	DET
ejpam-7095	8	33	solutions	solution	NOUN
ejpam-7095	8	34	.	.	PUNCT
ejpam-7095	9	1	the	the	DET
ejpam-7095	9	2	dimensional	dimensional	ADJ
ejpam-7095	9	3	flexibility	flexibility	NOUN
ejpam-7095	9	4	of	of	ADP
ejpam-7095	9	5	our	our	PRON
ejpam-7095	9	6	technique	technique	NOUN
ejpam-7095	9	7	is	be	AUX
ejpam-7095	9	8	demonstrated	demonstrate	VERB
ejpam-7095	9	9	through	through	ADP
ejpam-7095	9	10	1d	1d	NUM
ejpam-7095	9	11	,	,	PUNCT
ejpam-7095	9	12	2d	2d	NOUN
ejpam-7095	9	13	,	,	PUNCT
ejpam-7095	9	14	and	and	CCONJ
ejpam-7095	9	15	3d	3d	NUM
ejpam-7095	9	16	numerical	numerical	ADJ
ejpam-7095	9	17	examples	example	NOUN
ejpam-7095	9	18	,	,	PUNCT
ejpam-7095	9	19	which	which	PRON
ejpam-7095	9	20	confirm	confirm	VERB
ejpam-7095	9	21	its	its	PRON
ejpam-7095	9	22	computational	computational	ADJ
ejpam-7095	9	23	efficiency	efficiency	NOUN
ejpam-7095	9	24	and	and	CCONJ
ejpam-7095	9	25	high	high	ADJ
ejpam-7095	9	26	accuracy	accuracy	NOUN
ejpam-7095	9	27	.	.	PUNCT
ejpam-7095	10	1	this	this	DET
ejpam-7095	10	2	work	work	NOUN
ejpam-7095	10	3	provides	provide	VERB
ejpam-7095	10	4	a	a	DET
ejpam-7095	10	5	robust	robust	ADJ
ejpam-7095	10	6	and	and	CCONJ
ejpam-7095	10	7	stable	stable	ADJ
ejpam-7095	10	8	numerical	numerical	ADJ
ejpam-7095	10	9	approach	approach	NOUN
ejpam-7095	10	10	that	that	PRON
ejpam-7095	10	11	can	can	AUX
ejpam-7095	10	12	be	be	AUX
ejpam-7095	10	13	extended	extend	VERB
ejpam-7095	10	14	to	to	AUX
ejpam-7095	10	15	model	model	VERB
ejpam-7095	10	16	complex	complex	ADJ
ejpam-7095	10	17	multi	multi	ADJ
ejpam-7095	10	18	-	-	ADJ
ejpam-7095	10	19	scale	scale	ADJ
ejpam-7095	10	20	transport	transport	NOUN
ejpam-7095	10	21	problems	problem	NOUN
ejpam-7095	10	22	across	across	ADP
ejpam-7095	10	23	applied	applied	ADJ
ejpam-7095	10	24	mathematics	mathematic	NOUN
ejpam-7095	10	25	and	and	CCONJ
ejpam-7095	10	26	engineering	engineering	NOUN
ejpam-7095	10	27	.	.	PUNCT
ejpam-7095	11	1	2020	2020	NUM
ejpam-7095	11	2	mathematics	mathematic	NOUN
ejpam-7095	11	3	subject	subject	NOUN
ejpam-7095	11	4	classifications	classification	NOUN
ejpam-7095	11	5	:	:	PUNCT
ejpam-7095	11	6	44a10	44a10	NUM
ejpam-7095	11	7	,	,	PUNCT
ejpam-7095	11	8	65r10	65r10	NUM
ejpam-7095	11	9	,	,	PUNCT
ejpam-7095	11	10	35a22	35a22	NUM
ejpam-7095	11	11	key	key	ADJ
ejpam-7095	11	12	words	word	NOUN
ejpam-7095	11	13	and	and	CCONJ
ejpam-7095	11	14	phrases	phrase	NOUN
ejpam-7095	11	15	:	:	PUNCT
ejpam-7095	11	16	diffusion	diffusion	NOUN
ejpam-7095	11	17	-	-	PUNCT
ejpam-7095	11	18	wave	wave	NOUN
ejpam-7095	11	19	equation	equation	NOUN
ejpam-7095	11	20	,	,	PUNCT
ejpam-7095	11	21	modified	modify	VERB
ejpam-7095	11	22	atangana	atangana	PROPN
ejpam-7095	11	23	-	-	PUNCT
ejpam-7095	11	24	baleanu	baleanu	PROPN
ejpam-7095	11	25	derivative	derivative	NOUN
ejpam-7095	11	26	,	,	PUNCT
ejpam-7095	11	27	laplace	laplace	NOUN
ejpam-7095	11	28	transform	transform	NOUN
ejpam-7095	11	29	,	,	PUNCT
ejpam-7095	11	30	chebyshev	chebyshev	PROPN
ejpam-7095	11	31	spectral	spectral	ADJ
ejpam-7095	11	32	method	method	NOUN
ejpam-7095	11	33	,	,	PUNCT
ejpam-7095	11	34	talbot	talbot	PROPN
ejpam-7095	11	35	’s	’s	PART
ejpam-7095	11	36	method	method	NOUN
ejpam-7095	11	37	,	,	PUNCT
ejpam-7095	11	38	uniqueness	uniqueness	NOUN
ejpam-7095	11	39	and	and	CCONJ
ejpam-7095	11	40	existence	existence	NOUN
ejpam-7095	11	41	∗corresponding	∗corresponde	VERB
ejpam-7095	11	42	author	author	NOUN
ejpam-7095	11	43	.	.	PUNCT
ejpam-7095	12	1	doi	doi	NOUN
ejpam-7095	12	2	:	:	PUNCT
ejpam-7095	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7095	https://doi.org/10.29020/nybg.ejpam.v18i4.7095	NOUN
ejpam-7095	12	4	email	email	NOUN
ejpam-7095	12	5	addresses	address	NOUN
ejpam-7095	12	6	:	:	PUNCT
ejpam-7095	12	7	kamran.maths@icp.edu.pk	kamran.maths@icp.edu.pk	PROPN
ejpam-7095	12	8	(	(	PUNCT
ejpam-7095	12	9	kamran	kamran	PROPN
ejpam-7095	12	10	)	)	PUNCT
ejpam-7095	12	11	,	,	PUNCT
ejpam-7095	12	12	zeeshan@yuntech.edu.tw	zeeshan@yuntech.edu.tw	PROPN
ejpam-7095	12	13	(	(	PUNCT
ejpam-7095	12	14	z.	z.	PROPN
ejpam-7095	12	15	ali	ali	PROPN
ejpam-7095	12	16	)	)	PUNCT
ejpam-7095	12	17	,	,	PUNCT
ejpam-7095	12	18	maloqaily@psu.edu.sa	maloqaily@psu.edu.sa	PROPN
ejpam-7095	12	19	(	(	PUNCT
ejpam-7095	12	20	a.	a.	NOUN
ejpam-7095	12	21	aloqaily	aloqaily	ADV
ejpam-7095	12	22	)	)	PUNCT
ejpam-7095	12	23	,	,	PUNCT
ejpam-7095	12	24	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-7095	12	25	;	;	PUNCT
ejpam-7095	12	26	nmlaiki2012@gmail.com	nmlaiki2012@gmail.com	X
ejpam-7095	13	1	(	(	PUNCT
ejpam-7095	13	2	n.	n.	PROPN
ejpam-7095	13	3	mlaiki	mlaiki	PROPN
ejpam-7095	13	4	)	)	PUNCT
ejpam-7095	13	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-7095	14	1	1	1	NUM
ejpam-7095	14	2	copyright	copyright	NOUN
ejpam-7095	14	3	:	:	PUNCT
ejpam-7095	14	4	©	©	PROPN
ejpam-7095	14	5	2025	2025	NUM
ejpam-7095	14	6	the	the	DET
ejpam-7095	14	7	author(s	author(s	NOUN
ejpam-7095	14	8	)	)	PUNCT
ejpam-7095	14	9	.	.	PUNCT
ejpam-7095	15	1	(	(	PUNCT
ejpam-7095	15	2	cc	cc	NOUN
ejpam-7095	15	3	by	by	ADP
ejpam-7095	15	4	-	-	PUNCT
ejpam-7095	15	5	nc	nc	PROPN
ejpam-7095	15	6	4.0	4.0	NUM
ejpam-7095	15	7	)	)	PUNCT
ejpam-7095	15	8	kamran	kamran	PROPN
ejpam-7095	15	9	et	et	PROPN
ejpam-7095	15	10	al	al	PROPN
ejpam-7095	15	11	.	.	PUNCT
ejpam-7095	15	12	/	/	SYM
ejpam-7095	15	13	eur	eur	PROPN
ejpam-7095	15	14	.	.	PUNCT
ejpam-7095	16	1	j.	j.	PROPN
ejpam-7095	16	2	pure	pure	PROPN
ejpam-7095	16	3	appl	appl	PROPN
ejpam-7095	16	4	.	.	PROPN
ejpam-7095	16	5	math	math	PROPN
ejpam-7095	16	6	,	,	PUNCT
ejpam-7095	16	7	18	18	NUM
ejpam-7095	16	8	(	(	PUNCT
ejpam-7095	16	9	4	4	NUM
ejpam-7095	16	10	)	)	PUNCT
ejpam-7095	16	11	(	(	PUNCT
ejpam-7095	16	12	2025	2025	NUM
ejpam-7095	16	13	)	)	PUNCT
ejpam-7095	16	14	,	,	PUNCT
ejpam-7095	16	15	7095	7095	NUM
ejpam-7095	16	16	2	2	NUM
ejpam-7095	16	17	of	of	ADP
ejpam-7095	16	18	30	30	NUM
ejpam-7095	16	19	1	1	NUM
ejpam-7095	16	20	.	.	PUNCT
ejpam-7095	17	1	introduction	introduction	NOUN
ejpam-7095	17	2	anomalous	anomalous	ADJ
ejpam-7095	17	3	transport	transport	NOUN
ejpam-7095	17	4	processes	process	NOUN
ejpam-7095	17	5	,	,	PUNCT
ejpam-7095	17	6	such	such	ADJ
ejpam-7095	17	7	as	as	ADP
ejpam-7095	17	8	subsurface	subsurface	NOUN
ejpam-7095	17	9	pollutant	pollutant	ADJ
ejpam-7095	17	10	dispersion	dispersion	NOUN
ejpam-7095	17	11	or	or	CCONJ
ejpam-7095	17	12	wave	wave	NOUN
ejpam-7095	17	13	attenuation	attenuation	NOUN
ejpam-7095	17	14	in	in	ADP
ejpam-7095	17	15	viscoelastic	viscoelastic	ADJ
ejpam-7095	17	16	materials	material	NOUN
ejpam-7095	17	17	,	,	PUNCT
ejpam-7095	17	18	are	be	AUX
ejpam-7095	17	19	common	common	ADJ
ejpam-7095	17	20	throughout	throughout	ADP
ejpam-7095	17	21	scientific	scientific	ADJ
ejpam-7095	17	22	disciplines	discipline	NOUN
ejpam-7095	17	23	but	but	CCONJ
ejpam-7095	17	24	can	can	AUX
ejpam-7095	17	25	not	not	PART
ejpam-7095	17	26	be	be	AUX
ejpam-7095	17	27	described	describe	VERB
ejpam-7095	17	28	using	use	VERB
ejpam-7095	17	29	classical	classical	ADJ
ejpam-7095	17	30	integer	integer	NOUN
ejpam-7095	17	31	-	-	PUNCT
ejpam-7095	17	32	order	order	NOUN
ejpam-7095	17	33	models	model	NOUN
ejpam-7095	17	34	.	.	PUNCT
ejpam-7095	18	1	time	time	NOUN
ejpam-7095	18	2	-	-	PUNCT
ejpam-7095	18	3	fractional	fractional	ADJ
ejpam-7095	18	4	diffusion	diffusion	NOUN
ejpam-7095	18	5	-	-	PUNCT
ejpam-7095	18	6	wave	wave	NOUN
ejpam-7095	18	7	equations	equation	NOUN
ejpam-7095	18	8	(	(	PUNCT
ejpam-7095	18	9	tfdwes	tfdwe	NOUN
ejpam-7095	18	10	)	)	PUNCT
ejpam-7095	18	11	have	have	AUX
ejpam-7095	18	12	emerged	emerge	VERB
ejpam-7095	18	13	as	as	ADP
ejpam-7095	18	14	an	an	DET
ejpam-7095	18	15	effective	effective	ADJ
ejpam-7095	18	16	structure	structure	NOUN
ejpam-7095	18	17	for	for	ADP
ejpam-7095	18	18	describing	describe	VERB
ejpam-7095	18	19	these	these	DET
ejpam-7095	18	20	complicated	complicated	ADJ
ejpam-7095	18	21	phenomena	phenomenon	NOUN
ejpam-7095	18	22	,	,	PUNCT
ejpam-7095	18	23	effectively	effectively	ADV
ejpam-7095	18	24	integrating	integrate	VERB
ejpam-7095	18	25	memory	memory	NOUN
ejpam-7095	18	26	effects	effect	NOUN
ejpam-7095	18	27	and	and	CCONJ
ejpam-7095	18	28	power	power	NOUN
ejpam-7095	18	29	-	-	PUNCT
ejpam-7095	18	30	law	law	NOUN
ejpam-7095	18	31	dynamics	dynamic	NOUN
ejpam-7095	18	32	using	use	VERB
ejpam-7095	18	33	fractionalorder	fractionalorder	PROPN
ejpam-7095	18	34	operators	operator	NOUN
ejpam-7095	19	1	[	[	X
ejpam-7095	19	2	1–4	1–4	X
ejpam-7095	19	3	]	]	X
ejpam-7095	19	4	.	.	PUNCT
ejpam-7095	20	1	the	the	DET
ejpam-7095	20	2	growth	growth	NOUN
ejpam-7095	20	3	of	of	ADP
ejpam-7095	20	4	these	these	DET
ejpam-7095	20	5	operators	operator	NOUN
ejpam-7095	20	6	is	be	AUX
ejpam-7095	20	7	vital	vital	ADJ
ejpam-7095	20	8	:	:	PUNCT
ejpam-7095	20	9	from	from	ADP
ejpam-7095	20	10	the	the	DET
ejpam-7095	20	11	initial	initial	ADJ
ejpam-7095	20	12	work	work	NOUN
ejpam-7095	20	13	of	of	ADP
ejpam-7095	20	14	abel	abel	PROPN
ejpam-7095	20	15	,	,	PUNCT
ejpam-7095	20	16	riemann	riemann	PROPN
ejpam-7095	20	17	,	,	PUNCT
ejpam-7095	20	18	and	and	CCONJ
ejpam-7095	20	19	liouville	liouville	X
ejpam-7095	21	1	[	[	X
ejpam-7095	21	2	5	5	X
ejpam-7095	21	3	]	]	PUNCT
ejpam-7095	21	4	to	to	ADP
ejpam-7095	21	5	the	the	DET
ejpam-7095	21	6	broadly	broadly	ADV
ejpam-7095	21	7	recognized	recognize	VERB
ejpam-7095	21	8	caputo	caputo	PROPN
ejpam-7095	21	9	derivative	derivative	NOUN
ejpam-7095	22	1	[	[	X
ejpam-7095	22	2	6	6	NUM
ejpam-7095	22	3	]	]	PUNCT
ejpam-7095	22	4	,	,	PUNCT
ejpam-7095	22	5	which	which	PRON
ejpam-7095	22	6	added	add	VERB
ejpam-7095	22	7	historicity	historicity	NOUN
ejpam-7095	22	8	but	but	CCONJ
ejpam-7095	22	9	had	have	VERB
ejpam-7095	22	10	a	a	DET
ejpam-7095	22	11	singular	singular	ADJ
ejpam-7095	22	12	kernel	kernel	NOUN
ejpam-7095	22	13	.	.	PUNCT
ejpam-7095	23	1	this	this	DET
ejpam-7095	23	2	limitation	limitation	NOUN
ejpam-7095	23	3	motivated	motivate	VERB
ejpam-7095	23	4	the	the	DET
ejpam-7095	23	5	development	development	NOUN
ejpam-7095	23	6	of	of	ADP
ejpam-7095	23	7	non	non	ADJ
ejpam-7095	23	8	-	-	ADJ
ejpam-7095	23	9	singular	singular	ADJ
ejpam-7095	23	10	alternatives	alternative	NOUN
ejpam-7095	23	11	,	,	PUNCT
ejpam-7095	23	12	resulting	result	VERB
ejpam-7095	23	13	in	in	ADP
ejpam-7095	23	14	the	the	DET
ejpam-7095	23	15	modified	modified	ADJ
ejpam-7095	23	16	atangana	atangana	PROPN
ejpam-7095	23	17	-	-	PUNCT
ejpam-7095	23	18	baleanu	baleanu	PROPN
ejpam-7095	23	19	-	-	PUNCT
ejpam-7095	23	20	caputo	caputo	PROPN
ejpam-7095	23	21	(	(	PUNCT
ejpam-7095	23	22	mabc	mabc	PROPN
ejpam-7095	23	23	)	)	PUNCT
ejpam-7095	23	24	derivative	derivative	NOUN
ejpam-7095	24	1	[	[	X
ejpam-7095	24	2	7	7	NUM
ejpam-7095	24	3	]	]	PUNCT
ejpam-7095	24	4	.	.	PUNCT
ejpam-7095	25	1	the	the	DET
ejpam-7095	25	2	mabc	mabc	PROPN
ejpam-7095	25	3	derivative	derivative	NOUN
ejpam-7095	25	4	,	,	PUNCT
ejpam-7095	25	5	with	with	ADP
ejpam-7095	25	6	its	its	PRON
ejpam-7095	25	7	non	non	ADJ
ejpam-7095	25	8	-	-	ADJ
ejpam-7095	25	9	singular	singular	ADJ
ejpam-7095	25	10	mittag	mittag	ADJ
ejpam-7095	25	11	-	-	PUNCT
ejpam-7095	25	12	leffler	leffler	NOUN
ejpam-7095	25	13	kernel	kernel	NOUN
ejpam-7095	25	14	,	,	PUNCT
ejpam-7095	25	15	provides	provide	VERB
ejpam-7095	25	16	a	a	DET
ejpam-7095	25	17	more	more	ADV
ejpam-7095	25	18	reliable	reliable	ADJ
ejpam-7095	25	19	model	model	NOUN
ejpam-7095	25	20	for	for	ADP
ejpam-7095	25	21	systems	system	NOUN
ejpam-7095	25	22	with	with	ADP
ejpam-7095	25	23	complex	complex	ADJ
ejpam-7095	25	24	memory	memory	NOUN
ejpam-7095	25	25	and	and	CCONJ
ejpam-7095	25	26	hereditary	hereditary	ADJ
ejpam-7095	25	27	properties	property	NOUN
ejpam-7095	25	28	.	.	PUNCT
ejpam-7095	26	1	the	the	DET
ejpam-7095	26	2	modified	modify	VERB
ejpam-7095	26	3	atangana	atangana	PROPN
ejpam-7095	26	4	-	-	PUNCT
ejpam-7095	26	5	baleanu	baleanu	PROPN
ejpam-7095	26	6	(	(	PUNCT
ejpam-7095	26	7	mabc	mabc	PROPN
ejpam-7095	26	8	)	)	PUNCT
ejpam-7095	26	9	derivative	derivative	NOUN
ejpam-7095	26	10	extends	extend	VERB
ejpam-7095	26	11	the	the	DET
ejpam-7095	26	12	original	original	ADJ
ejpam-7095	26	13	abc	abc	NOUN
ejpam-7095	26	14	operator	operator	NOUN
ejpam-7095	26	15	to	to	ADP
ejpam-7095	26	16	a	a	DET
ejpam-7095	26	17	wider	wide	ADJ
ejpam-7095	26	18	function	function	NOUN
ejpam-7095	26	19	space	space	NOUN
ejpam-7095	26	20	.	.	PUNCT
ejpam-7095	27	1	crucially	crucially	ADV
ejpam-7095	27	2	,	,	PUNCT
ejpam-7095	27	3	as	as	SCONJ
ejpam-7095	27	4	demonstrated	demonstrate	VERB
ejpam-7095	27	5	in	in	ADP
ejpam-7095	27	6	[	[	X
ejpam-7095	27	7	7	7	NUM
ejpam-7095	27	8	]	]	PUNCT
ejpam-7095	27	9	,	,	PUNCT
ejpam-7095	27	10	the	the	DET
ejpam-7095	27	11	mabc	mabc	PROPN
ejpam-7095	27	12	derivative	derivative	NOUN
ejpam-7095	27	13	can	can	AUX
ejpam-7095	27	14	solve	solve	VERB
ejpam-7095	27	15	a	a	DET
ejpam-7095	27	16	class	class	NOUN
ejpam-7095	27	17	of	of	ADP
ejpam-7095	27	18	fractional	fractional	ADJ
ejpam-7095	27	19	differential	differential	ADJ
ejpam-7095	27	20	equations	equation	NOUN
ejpam-7095	27	21	intractable	intractable	ADJ
ejpam-7095	27	22	under	under	ADP
ejpam-7095	27	23	the	the	DET
ejpam-7095	27	24	standard	standard	ADJ
ejpam-7095	27	25	abc	abc	PROPN
ejpam-7095	27	26	definition	definition	NOUN
ejpam-7095	27	27	.	.	PUNCT
ejpam-7095	28	1	its	its	PRON
ejpam-7095	28	2	applications	application	NOUN
ejpam-7095	28	3	span	span	VERB
ejpam-7095	28	4	numerous	numerous	ADJ
ejpam-7095	28	5	scientific	scientific	ADJ
ejpam-7095	28	6	fields	field	NOUN
ejpam-7095	28	7	,	,	PUNCT
ejpam-7095	28	8	including	include	VERB
ejpam-7095	28	9	viscoelasticity	viscoelasticity	NOUN
ejpam-7095	28	10	[	[	X
ejpam-7095	28	11	8	8	NUM
ejpam-7095	28	12	,	,	PUNCT
ejpam-7095	28	13	9	9	NUM
ejpam-7095	28	14	]	]	PUNCT
ejpam-7095	28	15	,	,	PUNCT
ejpam-7095	28	16	control	control	NOUN
ejpam-7095	28	17	theory	theory	NOUN
ejpam-7095	28	18	[	[	X
ejpam-7095	28	19	?	?	PUNCT
ejpam-7095	28	20	]	]	X
ejpam-7095	28	21	,	,	PUNCT
ejpam-7095	28	22	and	and	CCONJ
ejpam-7095	28	23	biological	biological	ADJ
ejpam-7095	28	24	systems	system	NOUN
ejpam-7095	28	25	[	[	X
ejpam-7095	28	26	10–13	10–13	NUM
ejpam-7095	28	27	]	]	PUNCT
ejpam-7095	28	28	,	,	PUNCT
ejpam-7095	28	29	with	with	ADP
ejpam-7095	28	30	further	further	ADJ
ejpam-7095	28	31	examples	example	NOUN
ejpam-7095	28	32	available	available	ADJ
ejpam-7095	28	33	in	in	ADP
ejpam-7095	28	34	the	the	DET
ejpam-7095	28	35	cited	cite	VERB
ejpam-7095	28	36	literature	literature	NOUN
ejpam-7095	28	37	.	.	PUNCT
ejpam-7095	29	1	the	the	DET
ejpam-7095	29	2	numerical	numerical	ADJ
ejpam-7095	29	3	solution	solution	NOUN
ejpam-7095	29	4	of	of	ADP
ejpam-7095	29	5	tfdwes	tfdwe	NOUN
ejpam-7095	29	6	is	be	AUX
ejpam-7095	29	7	a	a	DET
ejpam-7095	29	8	dynamic	dynamic	ADJ
ejpam-7095	29	9	and	and	CCONJ
ejpam-7095	29	10	challenging	challenging	ADJ
ejpam-7095	29	11	area	area	NOUN
ejpam-7095	29	12	of	of	ADP
ejpam-7095	29	13	research	research	NOUN
ejpam-7095	29	14	.	.	PUNCT
ejpam-7095	30	1	a	a	DET
ejpam-7095	30	2	wide	wide	ADJ
ejpam-7095	30	3	range	range	NOUN
ejpam-7095	30	4	of	of	ADP
ejpam-7095	30	5	approaches	approach	NOUN
ejpam-7095	30	6	has	have	AUX
ejpam-7095	30	7	been	be	AUX
ejpam-7095	30	8	developed	develop	VERB
ejpam-7095	30	9	to	to	PART
ejpam-7095	30	10	address	address	VERB
ejpam-7095	30	11	these	these	DET
ejpam-7095	30	12	problems	problem	NOUN
ejpam-7095	30	13	,	,	PUNCT
ejpam-7095	30	14	each	each	PRON
ejpam-7095	30	15	with	with	ADP
ejpam-7095	30	16	its	its	PRON
ejpam-7095	30	17	own	own	ADJ
ejpam-7095	30	18	advantages	advantage	NOUN
ejpam-7095	30	19	.	.	PUNCT
ejpam-7095	31	1	analytical	analytical	ADJ
ejpam-7095	31	2	solutions	solution	NOUN
ejpam-7095	31	3	,	,	PUNCT
ejpam-7095	31	4	such	such	ADJ
ejpam-7095	31	5	as	as	ADP
ejpam-7095	31	6	those	those	PRON
ejpam-7095	31	7	by	by	ADP
ejpam-7095	31	8	mainardi	mainardi	PROPN
ejpam-7095	32	1	[	[	X
ejpam-7095	32	2	14	14	NUM
ejpam-7095	32	3	]	]	PUNCT
ejpam-7095	32	4	for	for	ADP
ejpam-7095	32	5	1d	1d	NUM
ejpam-7095	32	6	cases	case	NOUN
ejpam-7095	32	7	or	or	CCONJ
ejpam-7095	32	8	agrawal	agrawal	NOUN
ejpam-7095	32	9	[	[	X
ejpam-7095	32	10	15	15	NUM
ejpam-7095	32	11	]	]	PUNCT
ejpam-7095	32	12	for	for	ADP
ejpam-7095	32	13	bounded	bounded	ADJ
ejpam-7095	32	14	domains	domain	NOUN
ejpam-7095	32	15	,	,	PUNCT
ejpam-7095	32	16	provide	provide	VERB
ejpam-7095	32	17	foundational	foundational	ADJ
ejpam-7095	32	18	insights	insight	NOUN
ejpam-7095	32	19	but	but	CCONJ
ejpam-7095	32	20	are	be	AUX
ejpam-7095	32	21	impractical	impractical	ADJ
ejpam-7095	32	22	for	for	ADP
ejpam-7095	32	23	complex	complex	ADJ
ejpam-7095	32	24	,	,	PUNCT
ejpam-7095	32	25	multi	multi	ADJ
ejpam-7095	32	26	-	-	ADJ
ejpam-7095	32	27	dimensional	dimensional	ADJ
ejpam-7095	32	28	problems	problem	NOUN
ejpam-7095	32	29	.	.	PUNCT
ejpam-7095	33	1	therefore	therefore	ADV
ejpam-7095	33	2	,	,	PUNCT
ejpam-7095	33	3	numerical	numerical	ADJ
ejpam-7095	33	4	methods	method	NOUN
ejpam-7095	33	5	have	have	AUX
ejpam-7095	33	6	emerged	emerge	VERB
ejpam-7095	33	7	,	,	PUNCT
ejpam-7095	33	8	including	include	VERB
ejpam-7095	33	9	finite	finite	ADJ
ejpam-7095	33	10	difference	difference	NOUN
ejpam-7095	33	11	methods	method	NOUN
ejpam-7095	33	12	(	(	PUNCT
ejpam-7095	33	13	fdm	fdm	NOUN
ejpam-7095	33	14	)	)	PUNCT
ejpam-7095	33	15	with	with	ADP
ejpam-7095	33	16	compact	compact	ADJ
ejpam-7095	33	17	schemes	scheme	NOUN
ejpam-7095	33	18	[	[	X
ejpam-7095	33	19	16	16	NUM
ejpam-7095	33	20	]	]	PUNCT
ejpam-7095	33	21	,	,	PUNCT
ejpam-7095	33	22	solvers	solver	NOUN
ejpam-7095	33	23	for	for	ADP
ejpam-7095	33	24	multi	multi	ADJ
ejpam-7095	33	25	-	-	ADJ
ejpam-7095	33	26	term	term	ADJ
ejpam-7095	33	27	equations	equation	NOUN
ejpam-7095	33	28	[	[	X
ejpam-7095	33	29	17	17	NUM
ejpam-7095	33	30	]	]	PUNCT
ejpam-7095	33	31	,	,	PUNCT
ejpam-7095	33	32	and	and	CCONJ
ejpam-7095	33	33	the	the	DET
ejpam-7095	33	34	alternating	alternate	VERB
ejpam-7095	33	35	direction	direction	NOUN
ejpam-7095	33	36	implicit	implicit	ADJ
ejpam-7095	33	37	(	(	PUNCT
ejpam-7095	33	38	adi	adi	PROPN
ejpam-7095	33	39	)	)	PUNCT
ejpam-7095	33	40	method	method	NOUN
ejpam-7095	33	41	for	for	ADP
ejpam-7095	33	42	2d	2d	NOUN
ejpam-7095	33	43	problems	problem	NOUN
ejpam-7095	33	44	[	[	X
ejpam-7095	33	45	18	18	NUM
ejpam-7095	33	46	]	]	PUNCT
ejpam-7095	33	47	.	.	PUNCT
ejpam-7095	34	1	more	more	ADV
ejpam-7095	34	2	advanced	advanced	ADJ
ejpam-7095	34	3	techniques	technique	NOUN
ejpam-7095	34	4	,	,	PUNCT
ejpam-7095	34	5	such	such	ADJ
ejpam-7095	34	6	as	as	ADP
ejpam-7095	34	7	meshless	meshless	ADJ
ejpam-7095	34	8	techniques	technique	NOUN
ejpam-7095	34	9	[	[	X
ejpam-7095	34	10	19	19	NUM
ejpam-7095	34	11	]	]	PUNCT
ejpam-7095	34	12	,	,	PUNCT
ejpam-7095	34	13	spectral	spectral	ADJ
ejpam-7095	34	14	methods	method	NOUN
ejpam-7095	34	15	[	[	X
ejpam-7095	34	16	20	20	NUM
ejpam-7095	34	17	,	,	PUNCT
ejpam-7095	34	18	21	21	NUM
ejpam-7095	34	19	]	]	PUNCT
ejpam-7095	34	20	,	,	PUNCT
ejpam-7095	34	21	waveletbased	waveletbase	VERB
ejpam-7095	34	22	approaches	approach	NOUN
ejpam-7095	34	23	[	[	X
ejpam-7095	34	24	22	22	NUM
ejpam-7095	34	25	]	]	PUNCT
ejpam-7095	34	26	,	,	PUNCT
ejpam-7095	34	27	and	and	CCONJ
ejpam-7095	34	28	hybrid	hybrid	ADJ
ejpam-7095	34	29	laplace	laplace	NOUN
ejpam-7095	34	30	-	-	PUNCT
ejpam-7095	34	31	spectral	spectral	ADJ
ejpam-7095	34	32	methods	method	NOUN
ejpam-7095	34	33	[	[	X
ejpam-7095	34	34	23	23	NUM
ejpam-7095	34	35	]	]	PUNCT
ejpam-7095	34	36	,	,	PUNCT
ejpam-7095	34	37	have	have	AUX
ejpam-7095	34	38	further	far	ADV
ejpam-7095	34	39	improved	improve	VERB
ejpam-7095	34	40	spatial	spatial	ADJ
ejpam-7095	34	41	accuracy	accuracy	NOUN
ejpam-7095	34	42	and	and	CCONJ
ejpam-7095	34	43	computational	computational	ADJ
ejpam-7095	34	44	efficiency	efficiency	NOUN
ejpam-7095	34	45	.	.	PUNCT
ejpam-7095	35	1	these	these	DET
ejpam-7095	35	2	advancements	advancement	NOUN
ejpam-7095	35	3	are	be	AUX
ejpam-7095	35	4	further	far	ADV
ejpam-7095	35	5	exemplified	exemplify	VERB
ejpam-7095	35	6	by	by	ADP
ejpam-7095	35	7	recent	recent	ADJ
ejpam-7095	35	8	developments	development	NOUN
ejpam-7095	35	9	such	such	ADJ
ejpam-7095	35	10	as	as	ADP
ejpam-7095	35	11	the	the	DET
ejpam-7095	35	12	galerkin	galerkin	ADJ
ejpam-7095	35	13	spectral	spectral	ADJ
ejpam-7095	35	14	method	method	NOUN
ejpam-7095	35	15	with	with	ADP
ejpam-7095	35	16	high	high	ADJ
ejpam-7095	35	17	-	-	PUNCT
ejpam-7095	35	18	order	order	NOUN
ejpam-7095	35	19	differences	difference	NOUN
ejpam-7095	35	20	[	[	X
ejpam-7095	35	21	24	24	NUM
ejpam-7095	35	22	]	]	PUNCT
ejpam-7095	35	23	and	and	CCONJ
ejpam-7095	35	24	fractional	fractional	ADJ
ejpam-7095	35	25	multi	multi	ADJ
ejpam-7095	35	26	-	-	ADJ
ejpam-7095	35	27	step	step	ADJ
ejpam-7095	35	28	methods	method	NOUN
ejpam-7095	35	29	[	[	X
ejpam-7095	35	30	25	25	NUM
ejpam-7095	35	31	]	]	PUNCT
ejpam-7095	35	32	,	,	PUNCT
ejpam-7095	35	33	underscoring	underscore	VERB
ejpam-7095	35	34	the	the	DET
ejpam-7095	35	35	rapid	rapid	ADJ
ejpam-7095	35	36	progress	progress	NOUN
ejpam-7095	35	37	in	in	ADP
ejpam-7095	35	38	the	the	DET
ejpam-7095	35	39	field	field	NOUN
ejpam-7095	35	40	.	.	PUNCT
ejpam-7095	36	1	despite	despite	SCONJ
ejpam-7095	36	2	these	these	DET
ejpam-7095	36	3	advances	advance	NOUN
ejpam-7095	36	4	,	,	PUNCT
ejpam-7095	36	5	the	the	DET
ejpam-7095	36	6	non	non	ADJ
ejpam-7095	36	7	-	-	ADJ
ejpam-7095	36	8	local	local	ADJ
ejpam-7095	36	9	nature	nature	NOUN
ejpam-7095	36	10	of	of	ADP
ejpam-7095	36	11	fractional	fractional	ADJ
ejpam-7095	36	12	operators	operator	NOUN
ejpam-7095	36	13	like	like	ADP
ejpam-7095	36	14	the	the	DET
ejpam-7095	36	15	mabc	mabc	NOUN
ejpam-7095	36	16	poses	pose	VERB
ejpam-7095	36	17	a	a	DET
ejpam-7095	36	18	significant	significant	ADJ
ejpam-7095	36	19	computational	computational	ADJ
ejpam-7095	36	20	challenge	challenge	NOUN
ejpam-7095	36	21	.	.	PUNCT
ejpam-7095	37	1	time	time	NOUN
ejpam-7095	37	2	-	-	PUNCT
ejpam-7095	37	3	stepping	step	VERB
ejpam-7095	37	4	methods	method	NOUN
ejpam-7095	37	5	,	,	PUNCT
ejpam-7095	37	6	including	include	VERB
ejpam-7095	37	7	the	the	DET
ejpam-7095	37	8	fdm	fdm	NOUN
ejpam-7095	37	9	and	and	CCONJ
ejpam-7095	37	10	spectral	spectral	ADJ
ejpam-7095	37	11	methods	method	NOUN
ejpam-7095	37	12	,	,	PUNCT
ejpam-7095	37	13	suffer	suffer	VERB
ejpam-7095	37	14	significant	significant	ADJ
ejpam-7095	37	15	costs	cost	NOUN
ejpam-7095	37	16	in	in	ADP
ejpam-7095	37	17	long	long	ADJ
ejpam-7095	37	18	-	-	PUNCT
ejpam-7095	37	19	time	time	NOUN
ejpam-7095	37	20	or	or	CCONJ
ejpam-7095	37	21	high	high	ADJ
ejpam-7095	37	22	-	-	PUNCT
ejpam-7095	37	23	dimensional	dimensional	ADJ
ejpam-7095	37	24	simulations	simulation	NOUN
ejpam-7095	37	25	due	due	ADP
ejpam-7095	37	26	to	to	ADP
ejpam-7095	37	27	the	the	DET
ejpam-7095	37	28	need	need	NOUN
ejpam-7095	37	29	to	to	PART
ejpam-7095	37	30	store	store	VERB
ejpam-7095	37	31	and	and	CCONJ
ejpam-7095	37	32	process	process	VERB
ejpam-7095	37	33	the	the	DET
ejpam-7095	37	34	entire	entire	ADJ
ejpam-7095	37	35	solution	solution	NOUN
ejpam-7095	37	36	history	history	NOUN
ejpam-7095	37	37	at	at	ADP
ejpam-7095	37	38	each	each	DET
ejpam-7095	37	39	step	step	NOUN
ejpam-7095	37	40	.	.	PUNCT
ejpam-7095	38	1	this	this	DET
ejpam-7095	38	2	history	history	NOUN
ejpam-7095	38	3	dependence	dependence	NOUN
ejpam-7095	38	4	increases	increase	VERB
ejpam-7095	38	5	computational	computational	ADJ
ejpam-7095	38	6	cost	cost	NOUN
ejpam-7095	38	7	and	and	CCONJ
ejpam-7095	38	8	complexity	complexity	NOUN
ejpam-7095	38	9	,	,	PUNCT
ejpam-7095	38	10	making	make	VERB
ejpam-7095	38	11	accurate	accurate	ADJ
ejpam-7095	38	12	3d	3d	ADJ
ejpam-7095	38	13	simulations	simulation	NOUN
ejpam-7095	38	14	of	of	ADP
ejpam-7095	38	15	anomalous	anomalous	ADJ
ejpam-7095	38	16	transport	transport	NOUN
ejpam-7095	38	17	processes	process	VERB
ejpam-7095	38	18	a	a	DET
ejpam-7095	38	19	significant	significant	ADJ
ejpam-7095	38	20	challenge	challenge	NOUN
ejpam-7095	38	21	.	.	PUNCT
ejpam-7095	39	1	while	while	SCONJ
ejpam-7095	39	2	hybrid	hybrid	ADJ
ejpam-7095	39	3	methods	method	NOUN
ejpam-7095	39	4	,	,	PUNCT
ejpam-7095	39	5	such	such	ADJ
ejpam-7095	39	6	as	as	ADP
ejpam-7095	39	7	those	those	PRON
ejpam-7095	39	8	coupling	couple	VERB
ejpam-7095	39	9	the	the	DET
ejpam-7095	39	10	lt	lt	NOUN
ejpam-7095	39	11	with	with	ADP
ejpam-7095	39	12	a	a	DET
ejpam-7095	39	13	spectral	spectral	ADJ
ejpam-7095	39	14	collocation	collocation	NOUN
ejpam-7095	39	15	method	method	NOUN
ejpam-7095	39	16	[	[	X
ejpam-7095	39	17	23	23	NUM
ejpam-7095	39	18	]	]	PUNCT
ejpam-7095	39	19	,	,	PUNCT
ejpam-7095	39	20	minimize	minimize	VERB
ejpam-7095	39	21	temporal	temporal	ADJ
ejpam-7095	39	22	complexity	complexity	NOUN
ejpam-7095	39	23	,	,	PUNCT
ejpam-7095	39	24	a	a	DET
ejpam-7095	39	25	complete	complete	ADJ
ejpam-7095	39	26	framework	framework	NOUN
ejpam-7095	39	27	that	that	PRON
ejpam-7095	39	28	fully	fully	ADV
ejpam-7095	39	29	integrates	integrate	VERB
ejpam-7095	39	30	the	the	DET
ejpam-7095	39	31	time	time	NOUN
ejpam-7095	39	32	-	-	PUNCT
ejpam-7095	39	33	fractional	fractional	ADJ
ejpam-7095	39	34	derivative	derivative	NOUN
ejpam-7095	39	35	with	with	ADP
ejpam-7095	39	36	rigorous	rigorous	ADJ
ejpam-7095	39	37	mathematical	mathematical	ADJ
ejpam-7095	39	38	analysis	analysis	NOUN
ejpam-7095	39	39	and	and	CCONJ
ejpam-7095	39	40	demonstrates	demonstrate	VERB
ejpam-7095	39	41	high	high	ADJ
ejpam-7095	39	42	performance	performance	NOUN
ejpam-7095	39	43	in	in	ADP
ejpam-7095	39	44	a	a	DET
ejpam-7095	39	45	multi	multi	ADJ
ejpam-7095	39	46	-	-	ADJ
ejpam-7095	39	47	dimensional	dimensional	ADJ
ejpam-7095	39	48	setting	setting	NOUN
ejpam-7095	39	49	has	have	AUX
ejpam-7095	39	50	not	not	PART
ejpam-7095	39	51	yet	yet	ADV
ejpam-7095	39	52	been	be	AUX
ejpam-7095	39	53	developed	develop	VERB
ejpam-7095	39	54	.	.	PUNCT
ejpam-7095	40	1	this	this	DET
ejpam-7095	40	2	work	work	NOUN
ejpam-7095	40	3	addresses	address	NOUN
ejpam-7095	40	4	this	this	DET
ejpam-7095	40	5	gap	gap	NOUN
ejpam-7095	40	6	by	by	ADP
ejpam-7095	40	7	proposing	propose	VERB
ejpam-7095	40	8	a	a	DET
ejpam-7095	40	9	novel	novel	ADJ
ejpam-7095	40	10	hybrid	hybrid	ADJ
ejpam-7095	40	11	algorithm	algorithm	NOUN
ejpam-7095	40	12	that	that	PRON
ejpam-7095	40	13	combines	combine	VERB
ejpam-7095	40	14	the	the	DET
ejpam-7095	40	15	lt	lt	NOUN
ejpam-7095	40	16	with	with	ADP
ejpam-7095	40	17	the	the	DET
ejpam-7095	40	18	cscm	cscm	NOUN
ejpam-7095	40	19	.	.	PUNCT
ejpam-7095	41	1	our	our	PRON
ejpam-7095	41	2	approach	approach	NOUN
ejpam-7095	41	3	decouples	decouple	VERB
ejpam-7095	41	4	the	the	DET
ejpam-7095	41	5	temporal	temporal	ADJ
ejpam-7095	41	6	and	and	CCONJ
ejpam-7095	41	7	spatial	spatial	ADJ
ejpam-7095	41	8	challenges	challenge	NOUN
ejpam-7095	41	9	of	of	ADP
ejpam-7095	41	10	tfdwes	tfdwe	NOUN
ejpam-7095	41	11	:	:	PUNCT
ejpam-7095	41	12	the	the	DET
ejpam-7095	41	13	lt	lt	NOUN
ejpam-7095	41	14	transforms	transform	VERB
ejpam-7095	41	15	the	the	DET
ejpam-7095	41	16	mabc	mabc	ADJ
ejpam-7095	41	17	time	time	NOUN
ejpam-7095	41	18	-	-	PUNCT
ejpam-7095	41	19	fractional	fractional	ADJ
ejpam-7095	41	20	operator	operator	NOUN
ejpam-7095	41	21	exactly	exactly	ADV
ejpam-7095	41	22	into	into	ADP
ejpam-7095	41	23	the	the	DET
ejpam-7095	41	24	kamran	kamran	PROPN
ejpam-7095	41	25	et	et	PROPN
ejpam-7095	41	26	al	al	PROPN
ejpam-7095	41	27	.	.	PUNCT
ejpam-7095	41	28	/	/	SYM
ejpam-7095	41	29	eur	eur	PROPN
ejpam-7095	41	30	.	.	PUNCT
ejpam-7095	42	1	j.	j.	PROPN
ejpam-7095	42	2	pure	pure	PROPN
ejpam-7095	42	3	appl	appl	PROPN
ejpam-7095	42	4	.	.	PROPN
ejpam-7095	42	5	math	math	PROPN
ejpam-7095	42	6	,	,	PUNCT
ejpam-7095	42	7	18	18	NUM
ejpam-7095	42	8	(	(	PUNCT
ejpam-7095	42	9	4	4	NUM
ejpam-7095	42	10	)	)	PUNCT
ejpam-7095	42	11	(	(	PUNCT
ejpam-7095	42	12	2025	2025	NUM
ejpam-7095	42	13	)	)	PUNCT
ejpam-7095	42	14	,	,	PUNCT
ejpam-7095	42	15	7095	7095	NUM
ejpam-7095	42	16	3	3	NUM
ejpam-7095	42	17	of	of	ADP
ejpam-7095	42	18	30	30	NUM
ejpam-7095	42	19	laplace	laplace	NOUN
ejpam-7095	42	20	domain	domain	NOUN
ejpam-7095	42	21	,	,	PUNCT
ejpam-7095	42	22	eliminating	eliminate	VERB
ejpam-7095	42	23	the	the	DET
ejpam-7095	42	24	convolution	convolution	NOUN
ejpam-7095	42	25	burden	burden	NOUN
ejpam-7095	42	26	and	and	CCONJ
ejpam-7095	42	27	stability	stability	NOUN
ejpam-7095	42	28	constraints	constraint	NOUN
ejpam-7095	42	29	of	of	ADP
ejpam-7095	42	30	timestepping	timesteppe	VERB
ejpam-7095	42	31	methods	method	NOUN
ejpam-7095	42	32	.	.	PUNCT
ejpam-7095	43	1	the	the	DET
ejpam-7095	43	2	resulting	result	VERB
ejpam-7095	43	3	parameterized	parameterized	ADJ
ejpam-7095	43	4	helmholtz	helmholtz	NOUN
ejpam-7095	43	5	-	-	PUNCT
ejpam-7095	43	6	type	type	NOUN
ejpam-7095	43	7	problems	problem	NOUN
ejpam-7095	43	8	are	be	AUX
ejpam-7095	43	9	solved	solve	VERB
ejpam-7095	43	10	using	use	VERB
ejpam-7095	43	11	the	the	DET
ejpam-7095	43	12	cscm	cscm	NOUN
ejpam-7095	43	13	,	,	PUNCT
ejpam-7095	43	14	which	which	PRON
ejpam-7095	43	15	achieves	achieve	VERB
ejpam-7095	43	16	exponential	exponential	ADJ
ejpam-7095	43	17	convergence	convergence	NOUN
ejpam-7095	43	18	in	in	ADP
ejpam-7095	43	19	space	space	NOUN
ejpam-7095	43	20	for	for	ADP
ejpam-7095	43	21	smooth	smooth	ADJ
ejpam-7095	43	22	solutions	solution	NOUN
ejpam-7095	43	23	[	[	X
ejpam-7095	43	24	26–28	26–28	NUM
ejpam-7095	43	25	]	]	PUNCT
ejpam-7095	43	26	.	.	PUNCT
ejpam-7095	44	1	the	the	DET
ejpam-7095	44	2	time	time	NOUN
ejpam-7095	44	3	-	-	PUNCT
ejpam-7095	44	4	domain	domain	NOUN
ejpam-7095	44	5	solution	solution	NOUN
ejpam-7095	44	6	is	be	AUX
ejpam-7095	44	7	efficiently	efficiently	ADV
ejpam-7095	44	8	recovered	recover	VERB
ejpam-7095	44	9	using	use	VERB
ejpam-7095	44	10	the	the	DET
ejpam-7095	44	11	improved	improved	ADJ
ejpam-7095	44	12	talbot	talbot	PROPN
ejpam-7095	44	13	method	method	NOUN
ejpam-7095	44	14	for	for	ADP
ejpam-7095	44	15	numerical	numerical	ADJ
ejpam-7095	44	16	inversion	inversion	NOUN
ejpam-7095	44	17	[	[	X
ejpam-7095	44	18	29	29	NUM
ejpam-7095	44	19	]	]	PUNCT
ejpam-7095	44	20	.	.	PUNCT
ejpam-7095	45	1	this	this	DET
ejpam-7095	45	2	approach	approach	NOUN
ejpam-7095	45	3	not	not	PART
ejpam-7095	45	4	only	only	ADV
ejpam-7095	45	5	reduces	reduce	VERB
ejpam-7095	45	6	the	the	DET
ejpam-7095	45	7	computational	computational	ADJ
ejpam-7095	45	8	cost	cost	NOUN
ejpam-7095	45	9	but	but	CCONJ
ejpam-7095	45	10	also	also	ADV
ejpam-7095	45	11	offers	offer	VERB
ejpam-7095	45	12	a	a	DET
ejpam-7095	45	13	unified	unified	ADJ
ejpam-7095	45	14	framework	framework	NOUN
ejpam-7095	45	15	for	for	ADP
ejpam-7095	45	16	1d	1d	NUM
ejpam-7095	45	17	,	,	PUNCT
ejpam-7095	45	18	2d	2d	NOUN
ejpam-7095	45	19	,	,	PUNCT
ejpam-7095	45	20	and	and	CCONJ
ejpam-7095	45	21	3d	3d	NUM
ejpam-7095	45	22	problems	problem	NOUN
ejpam-7095	45	23	.	.	PUNCT
ejpam-7095	46	1	beyond	beyond	ADP
ejpam-7095	46	2	computational	computational	ADJ
ejpam-7095	46	3	efficiency	efficiency	NOUN
ejpam-7095	46	4	,	,	PUNCT
ejpam-7095	46	5	this	this	DET
ejpam-7095	46	6	work	work	NOUN
ejpam-7095	46	7	provides	provide	VERB
ejpam-7095	46	8	rigorous	rigorous	ADJ
ejpam-7095	46	9	mathematical	mathematical	ADJ
ejpam-7095	46	10	and	and	CCONJ
ejpam-7095	46	11	physical	physical	ADJ
ejpam-7095	46	12	insights	insight	NOUN
ejpam-7095	46	13	.	.	PUNCT
ejpam-7095	47	1	first	first	ADV
ejpam-7095	47	2	,	,	PUNCT
ejpam-7095	47	3	we	we	PRON
ejpam-7095	47	4	establish	establish	VERB
ejpam-7095	47	5	a	a	DET
ejpam-7095	47	6	solid	solid	ADJ
ejpam-7095	47	7	theoretical	theoretical	ADJ
ejpam-7095	47	8	foundation	foundation	NOUN
ejpam-7095	47	9	for	for	ADP
ejpam-7095	47	10	the	the	DET
ejpam-7095	47	11	mabc	mabc	NOUN
ejpam-7095	47	12	-	-	PUNCT
ejpam-7095	47	13	based	base	VERB
ejpam-7095	47	14	tfdwe	tfdwe	NOUN
ejpam-7095	47	15	by	by	ADP
ejpam-7095	47	16	proving	prove	VERB
ejpam-7095	47	17	the	the	DET
ejpam-7095	47	18	existence	existence	NOUN
ejpam-7095	47	19	,	,	PUNCT
ejpam-7095	47	20	uniqueness	uniqueness	NOUN
ejpam-7095	47	21	,	,	PUNCT
ejpam-7095	47	22	and	and	CCONJ
ejpam-7095	47	23	ulam	ulam	NOUN
ejpam-7095	47	24	-	-	PUNCT
ejpam-7095	47	25	hyers	hyer	NOUN
ejpam-7095	47	26	stability	stability	NOUN
ejpam-7095	47	27	of	of	ADP
ejpam-7095	47	28	its	its	PRON
ejpam-7095	47	29	solutions	solution	NOUN
ejpam-7095	47	30	,	,	PUNCT
ejpam-7095	47	31	thereby	thereby	ADV
ejpam-7095	47	32	ensuring	ensure	VERB
ejpam-7095	47	33	the	the	DET
ejpam-7095	47	34	model	model	NOUN
ejpam-7095	47	35	’s	’s	PART
ejpam-7095	47	36	well	well	ADV
ejpam-7095	47	37	-	-	PUNCT
ejpam-7095	47	38	posedness	posedness	NOUN
ejpam-7095	47	39	a	a	DET
ejpam-7095	47	40	critical	critical	ADJ
ejpam-7095	47	41	aspect	aspect	NOUN
ejpam-7095	47	42	often	often	ADV
ejpam-7095	47	43	overlooked	overlook	VERB
ejpam-7095	47	44	in	in	ADP
ejpam-7095	47	45	numerical	numerical	ADJ
ejpam-7095	47	46	studies	study	NOUN
ejpam-7095	47	47	.	.	PUNCT
ejpam-7095	48	1	furthermore	furthermore	ADV
ejpam-7095	48	2	,	,	PUNCT
ejpam-7095	48	3	by	by	ADP
ejpam-7095	48	4	eliminating	eliminate	VERB
ejpam-7095	48	5	time	time	NOUN
ejpam-7095	48	6	-	-	PUNCT
ejpam-7095	48	7	stepping	stepping	ADJ
ejpam-7095	48	8	,	,	PUNCT
ejpam-7095	48	9	our	our	PRON
ejpam-7095	48	10	method	method	NOUN
ejpam-7095	48	11	facilitates	facilitate	VERB
ejpam-7095	48	12	an	an	DET
ejpam-7095	48	13	efficient	efficient	ADJ
ejpam-7095	48	14	analysis	analysis	NOUN
ejpam-7095	48	15	of	of	ADP
ejpam-7095	48	16	how	how	SCONJ
ejpam-7095	48	17	the	the	DET
ejpam-7095	48	18	fractional	fractional	ADJ
ejpam-7095	48	19	order	order	NOUN
ejpam-7095	48	20	α	α	NOUN
ejpam-7095	48	21	influences	influence	NOUN
ejpam-7095	48	22	solution	solution	NOUN
ejpam-7095	48	23	behavior	behavior	NOUN
ejpam-7095	48	24	in	in	ADP
ejpam-7095	48	25	multi	multi	ADJ
ejpam-7095	48	26	-	-	ADJ
ejpam-7095	48	27	dimensional	dimensional	ADJ
ejpam-7095	48	28	settings	setting	NOUN
ejpam-7095	48	29	,	,	PUNCT
ejpam-7095	48	30	offering	offer	VERB
ejpam-7095	48	31	new	new	ADJ
ejpam-7095	48	32	insights	insight	NOUN
ejpam-7095	48	33	into	into	ADP
ejpam-7095	48	34	memory	memory	NOUN
ejpam-7095	48	35	effects	effect	NOUN
ejpam-7095	48	36	within	within	ADP
ejpam-7095	48	37	complex	complex	ADJ
ejpam-7095	48	38	systems	system	NOUN
ejpam-7095	48	39	.	.	PUNCT
ejpam-7095	49	1	the	the	DET
ejpam-7095	49	2	key	key	ADJ
ejpam-7095	49	3	advantages	advantage	NOUN
ejpam-7095	49	4	of	of	ADP
ejpam-7095	49	5	the	the	DET
ejpam-7095	49	6	proposed	propose	VERB
ejpam-7095	49	7	lt	lt	NOUN
ejpam-7095	49	8	-	-	PUNCT
ejpam-7095	49	9	based	base	VERB
ejpam-7095	49	10	cscm	cscm	NOUN
ejpam-7095	49	11	approach	approach	NOUN
ejpam-7095	49	12	are	be	AUX
ejpam-7095	49	13	threefold	threefold	ADJ
ejpam-7095	49	14	.	.	PUNCT
ejpam-7095	50	1	first	first	ADV
ejpam-7095	50	2	,	,	PUNCT
ejpam-7095	50	3	it	it	PRON
ejpam-7095	50	4	avoids	avoid	VERB
ejpam-7095	50	5	the	the	DET
ejpam-7095	50	6	time	time	NOUN
ejpam-7095	50	7	-	-	PUNCT
ejpam-7095	50	8	step	step	NOUN
ejpam-7095	50	9	restrictions	restriction	NOUN
ejpam-7095	50	10	and	and	CCONJ
ejpam-7095	50	11	temporal	temporal	ADJ
ejpam-7095	50	12	error	error	NOUN
ejpam-7095	50	13	accumulation	accumulation	NOUN
ejpam-7095	50	14	inherent	inherent	ADJ
ejpam-7095	50	15	in	in	ADP
ejpam-7095	50	16	step	step	NOUN
ejpam-7095	50	17	-	-	PUNCT
ejpam-7095	50	18	wise	wise	ADJ
ejpam-7095	50	19	methods	method	NOUN
ejpam-7095	50	20	.	.	PUNCT
ejpam-7095	51	1	second	second	ADJ
ejpam-7095	51	2	,	,	PUNCT
ejpam-7095	51	3	it	it	PRON
ejpam-7095	51	4	efficiently	efficiently	ADV
ejpam-7095	51	5	handles	handle	VERB
ejpam-7095	51	6	the	the	DET
ejpam-7095	51	7	memory	memory	NOUN
ejpam-7095	51	8	effects	effect	NOUN
ejpam-7095	51	9	of	of	ADP
ejpam-7095	51	10	the	the	DET
ejpam-7095	51	11	mabc	mabc	NOUN
ejpam-7095	51	12	derivative	derivative	NOUN
ejpam-7095	51	13	via	via	ADP
ejpam-7095	51	14	the	the	DET
ejpam-7095	51	15	laplace	laplace	NOUN
ejpam-7095	51	16	transform	transform	NOUN
ejpam-7095	51	17	while	while	SCONJ
ejpam-7095	51	18	leveraging	leverage	VERB
ejpam-7095	51	19	the	the	DET
ejpam-7095	51	20	cscm	cscm	NOUN
ejpam-7095	51	21	for	for	ADP
ejpam-7095	51	22	exponential	exponential	ADJ
ejpam-7095	51	23	convergence	convergence	NOUN
ejpam-7095	51	24	of	of	ADP
ejpam-7095	51	25	smooth	smooth	ADJ
ejpam-7095	51	26	spatial	spatial	ADJ
ejpam-7095	51	27	solutions	solution	NOUN
ejpam-7095	51	28	.	.	PUNCT
ejpam-7095	52	1	finally	finally	ADV
ejpam-7095	52	2	,	,	PUNCT
ejpam-7095	52	3	the	the	DET
ejpam-7095	52	4	method	method	NOUN
ejpam-7095	52	5	requires	require	VERB
ejpam-7095	52	6	fewer	few	ADJ
ejpam-7095	52	7	discretization	discretization	NOUN
ejpam-7095	52	8	nodes	node	NOUN
ejpam-7095	52	9	for	for	ADP
ejpam-7095	52	10	high	high	ADJ
ejpam-7095	52	11	accuracy	accuracy	NOUN
ejpam-7095	52	12	compared	compare	VERB
ejpam-7095	52	13	to	to	ADP
ejpam-7095	52	14	other	other	ADJ
ejpam-7095	52	15	methods	method	NOUN
ejpam-7095	52	16	,	,	PUNCT
ejpam-7095	52	17	which	which	PRON
ejpam-7095	52	18	significantly	significantly	ADV
ejpam-7095	52	19	reduces	reduce	VERB
ejpam-7095	52	20	computational	computational	ADJ
ejpam-7095	52	21	and	and	CCONJ
ejpam-7095	52	22	storage	storage	NOUN
ejpam-7095	52	23	costs	cost	NOUN
ejpam-7095	52	24	and	and	CCONJ
ejpam-7095	52	25	provides	provide	VERB
ejpam-7095	52	26	a	a	DET
ejpam-7095	52	27	unified	unified	ADJ
ejpam-7095	52	28	framework	framework	NOUN
ejpam-7095	52	29	for	for	ADP
ejpam-7095	52	30	solving	solve	VERB
ejpam-7095	52	31	1d	1d	NUM
ejpam-7095	52	32	,	,	PUNCT
ejpam-7095	52	33	2d	2d	NOUN
ejpam-7095	52	34	,	,	PUNCT
ejpam-7095	52	35	and	and	CCONJ
ejpam-7095	52	36	3d	3d	NUM
ejpam-7095	52	37	problems	problem	NOUN
ejpam-7095	52	38	.	.	PUNCT
ejpam-7095	53	1	the	the	DET
ejpam-7095	53	2	rest	rest	NOUN
ejpam-7095	53	3	of	of	ADP
ejpam-7095	53	4	this	this	DET
ejpam-7095	53	5	paper	paper	NOUN
ejpam-7095	53	6	is	be	AUX
ejpam-7095	53	7	organized	organize	VERB
ejpam-7095	53	8	as	as	SCONJ
ejpam-7095	53	9	follows	follow	VERB
ejpam-7095	53	10	.	.	PUNCT
ejpam-7095	54	1	section	section	NOUN
ejpam-7095	54	2	2	2	NUM
ejpam-7095	54	3	introduces	introduce	NOUN
ejpam-7095	54	4	the	the	DET
ejpam-7095	54	5	necessary	necessary	ADJ
ejpam-7095	54	6	preliminary	preliminary	ADJ
ejpam-7095	54	7	definitions	definition	NOUN
ejpam-7095	54	8	.	.	PUNCT
ejpam-7095	55	1	the	the	DET
ejpam-7095	55	2	analysis	analysis	NOUN
ejpam-7095	55	3	of	of	ADP
ejpam-7095	55	4	existence	existence	NOUN
ejpam-7095	55	5	,	,	PUNCT
ejpam-7095	55	6	uniqueness	uniqueness	NOUN
ejpam-7095	55	7	,	,	PUNCT
ejpam-7095	55	8	and	and	CCONJ
ejpam-7095	55	9	stability	stability	NOUN
ejpam-7095	55	10	is	be	AUX
ejpam-7095	55	11	presented	present	VERB
ejpam-7095	55	12	in	in	ADP
ejpam-7095	55	13	section	section	NOUN
ejpam-7095	55	14	3	3	NUM
ejpam-7095	55	15	.	.	PUNCT
ejpam-7095	55	16	section	section	NOUN
ejpam-7095	55	17	4	4	NUM
ejpam-7095	55	18	provides	provide	VERB
ejpam-7095	55	19	a	a	DET
ejpam-7095	55	20	detailed	detailed	ADJ
ejpam-7095	55	21	description	description	NOUN
ejpam-7095	55	22	of	of	ADP
ejpam-7095	55	23	the	the	DET
ejpam-7095	55	24	proposed	propose	VERB
ejpam-7095	55	25	numerical	numerical	ADJ
ejpam-7095	55	26	method	method	PROPN
ejpam-7095	55	27	.	.	PUNCT
ejpam-7095	56	1	numerical	numerical	ADJ
ejpam-7095	56	2	results	result	NOUN
ejpam-7095	56	3	for	for	ADP
ejpam-7095	56	4	1d	1d	NUM
ejpam-7095	56	5	,	,	PUNCT
ejpam-7095	56	6	2d	2d	NOUN
ejpam-7095	56	7	,	,	PUNCT
ejpam-7095	56	8	and	and	CCONJ
ejpam-7095	56	9	3d	3d	NUM
ejpam-7095	56	10	examples	example	NOUN
ejpam-7095	56	11	are	be	AUX
ejpam-7095	56	12	discussed	discuss	VERB
ejpam-7095	56	13	in	in	ADP
ejpam-7095	56	14	section	section	NOUN
ejpam-7095	56	15	5	5	NUM
ejpam-7095	56	16	,	,	PUNCT
ejpam-7095	56	17	and	and	CCONJ
ejpam-7095	56	18	finally	finally	ADV
ejpam-7095	56	19	,	,	PUNCT
ejpam-7095	56	20	conclusions	conclusion	NOUN
ejpam-7095	56	21	are	be	AUX
ejpam-7095	56	22	drawn	draw	VERB
ejpam-7095	56	23	in	in	ADP
ejpam-7095	56	24	section	section	NOUN
ejpam-7095	56	25	6	6	NUM
ejpam-7095	56	26	.	.	NOUN
ejpam-7095	57	1	2	2	NUM
ejpam-7095	57	2	.	.	X
ejpam-7095	57	3	preliminaries	preliminary	NOUN
ejpam-7095	57	4	this	this	DET
ejpam-7095	57	5	section	section	NOUN
ejpam-7095	57	6	presents	present	VERB
ejpam-7095	57	7	the	the	DET
ejpam-7095	57	8	fundamental	fundamental	ADJ
ejpam-7095	57	9	definitions	definition	NOUN
ejpam-7095	57	10	and	and	CCONJ
ejpam-7095	57	11	mathematical	mathematical	ADJ
ejpam-7095	57	12	prerequisites	prerequisite	NOUN
ejpam-7095	57	13	for	for	ADP
ejpam-7095	57	14	the	the	DET
ejpam-7095	57	15	current	current	ADJ
ejpam-7095	57	16	study	study	NOUN
ejpam-7095	57	17	.	.	PUNCT
ejpam-7095	58	1	definition	definition	NOUN
ejpam-7095	58	2	1	1	NUM
ejpam-7095	58	3	.	.	PUNCT
ejpam-7095	59	1	the	the	DET
ejpam-7095	59	2	laplace	laplace	NOUN
ejpam-7095	59	3	transform	transform	NOUN
ejpam-7095	59	4	(	(	PUNCT
ejpam-7095	59	5	lt	lt	NOUN
ejpam-7095	59	6	)	)	PUNCT
ejpam-7095	59	7	of	of	ADP
ejpam-7095	59	8	a	a	DET
ejpam-7095	59	9	function	function	NOUN
ejpam-7095	59	10	u(x̄	u(x̄	NUM
ejpam-7095	59	11	,	,	PUNCT
ejpam-7095	59	12	t	t	PROPN
ejpam-7095	59	13	)	)	PUNCT
ejpam-7095	59	14	is	be	AUX
ejpam-7095	59	15	defined	define	VERB
ejpam-7095	59	16	as	as	ADP
ejpam-7095	59	17	:	:	PUNCT
ejpam-7095	59	18	l	l	NOUN
ejpam-7095	59	19	{	{	PUNCT
ejpam-7095	59	20	u(x̄	u(x̄	PROPN
ejpam-7095	59	21	,	,	PUNCT
ejpam-7095	59	22	τ	τ	PROPN
ejpam-7095	59	23	)	)	PUNCT
ejpam-7095	59	24	}	}	PUNCT
ejpam-7095	60	1	=	=	SYM
ejpam-7095	60	2	û(x̄	û(x̄	X
ejpam-7095	60	3	,	,	PUNCT
ejpam-7095	60	4	s	s	X
ejpam-7095	60	5	)	)	PUNCT
ejpam-7095	60	6	=	=	SYM
ejpam-7095	61	1	∫	∫	PROPN
ejpam-7095	61	2	∞	∞	NOUN
ejpam-7095	61	3	0	0	NUM
ejpam-7095	62	1	esτu(x̄	esτu(x̄	ADJ
ejpam-7095	62	2	,	,	PUNCT
ejpam-7095	62	3	τ)dτ	τ)dτ	ADJ
ejpam-7095	62	4	definition	definition	NOUN
ejpam-7095	62	5	2	2	NUM
ejpam-7095	62	6	.	.	PUNCT
ejpam-7095	63	1	the	the	DET
ejpam-7095	63	2	mabc	mabc	PROPN
ejpam-7095	63	3	derivative	derivative	NOUN
ejpam-7095	63	4	of	of	ADP
ejpam-7095	63	5	order	order	NOUN
ejpam-7095	63	6	0	0	PUNCT
ejpam-7095	63	7	<	<	X
ejpam-7095	63	8	α	α	X
ejpam-7095	63	9	<	<	X
ejpam-7095	63	10	1	1	NUM
ejpam-7095	63	11	of	of	ADP
ejpam-7095	63	12	a	a	DET
ejpam-7095	63	13	function	function	NOUN
ejpam-7095	63	14	u(x̄	u(x̄	NUM
ejpam-7095	63	15	,	,	PUNCT
ejpam-7095	63	16	τ	τ	NOUN
ejpam-7095	63	17	)	)	PUNCT
ejpam-7095	63	18	∈	∈	PROPN
ejpam-7095	63	19	l1(0	l1(0	PROPN
ejpam-7095	63	20	,	,	PUNCT
ejpam-7095	63	21	t	t	PROPN
ejpam-7095	63	22	)	)	PUNCT
ejpam-7095	63	23	in	in	ADP
ejpam-7095	63	24	caputo	caputo	PROPN
ejpam-7095	63	25	sense	sense	NOUN
ejpam-7095	63	26	is	be	AUX
ejpam-7095	63	27	defined	define	VERB
ejpam-7095	63	28	by	by	ADP
ejpam-7095	63	29	[	[	X
ejpam-7095	63	30	30	30	NUM
ejpam-7095	63	31	]	]	SYM
ejpam-7095	63	32	:	:	PUNCT
ejpam-7095	63	33	mabc	mabc	NOUN
ejpam-7095	63	34	0	0	PUNCT
ejpam-7095	64	1	dα	dα	PROPN
ejpam-7095	64	2	τ	τ	PROPN
ejpam-7095	64	3	u(x̄	u(x̄	PROPN
ejpam-7095	64	4	,	,	PUNCT
ejpam-7095	64	5	τ	τ	X
ejpam-7095	64	6	)	)	PUNCT
ejpam-7095	64	7	=	=	SYM
ejpam-7095	64	8	β(α	β(α	ADJ
ejpam-7095	64	9	)	)	PUNCT
ejpam-7095	64	10	1−	1−	NUM
ejpam-7095	64	11	α	α	NOUN
ejpam-7095	64	12	[	[	PUNCT
ejpam-7095	64	13	u(x̄	u(x̄	PROPN
ejpam-7095	64	14	,	,	PUNCT
ejpam-7095	64	15	τ)−	τ)−	PROPN
ejpam-7095	64	16	eα	eα	X
ejpam-7095	64	17	(	(	PUNCT
ejpam-7095	64	18	−ηατ	−ηατ	NOUN
ejpam-7095	64	19	α	α	NOUN
ejpam-7095	64	20	)	)	PUNCT
ejpam-7095	64	21	u(x̄	u(x̄	NOUN
ejpam-7095	64	22	,	,	PUNCT
ejpam-7095	64	23	0	0	NUM
ejpam-7095	64	24	)	)	PUNCT
ejpam-7095	64	25	−	−	NOUN
ejpam-7095	65	1	ηα	ηα	PROPN
ejpam-7095	65	2	∫	∫	PROPN
ejpam-7095	65	3	τ	τ	X
ejpam-7095	65	4	0	0	NUM
ejpam-7095	65	5	(	(	PUNCT
ejpam-7095	65	6	τ	τ	X
ejpam-7095	65	7	−	−	PROPN
ejpam-7095	65	8	ϑ)α−1eα	ϑ)α−1eα	NOUN
ejpam-7095	65	9	,	,	PUNCT
ejpam-7095	65	10	α	α	PROPN
ejpam-7095	65	11	(	(	PUNCT
ejpam-7095	65	12	−ηα(τ	−ηα(τ	ADV
ejpam-7095	65	13	−	−	ADP
ejpam-7095	65	14	ϑ)α	ϑ)α	ADJ
ejpam-7095	65	15	)	)	PUNCT
ejpam-7095	65	16	u(x̄	u(x̄	NOUN
ejpam-7095	65	17	,	,	PUNCT
ejpam-7095	65	18	ϑ)dϑ	ϑ)dϑ	PROPN
ejpam-7095	65	19	]	]	PUNCT
ejpam-7095	65	20	,	,	PUNCT
ejpam-7095	65	21	kamran	kamran	PROPN
ejpam-7095	65	22	et	et	PROPN
ejpam-7095	65	23	al	al	PROPN
ejpam-7095	65	24	.	.	PUNCT
ejpam-7095	65	25	/	/	SYM
ejpam-7095	65	26	eur	eur	PROPN
ejpam-7095	65	27	.	.	PUNCT
ejpam-7095	66	1	j.	j.	PROPN
ejpam-7095	66	2	pure	pure	PROPN
ejpam-7095	66	3	appl	appl	PROPN
ejpam-7095	66	4	.	.	PROPN
ejpam-7095	66	5	math	math	PROPN
ejpam-7095	66	6	,	,	PUNCT
ejpam-7095	66	7	18	18	NUM
ejpam-7095	66	8	(	(	PUNCT
ejpam-7095	66	9	4	4	NUM
ejpam-7095	66	10	)	)	PUNCT
ejpam-7095	66	11	(	(	PUNCT
ejpam-7095	66	12	2025	2025	NUM
ejpam-7095	66	13	)	)	PUNCT
ejpam-7095	66	14	,	,	PUNCT
ejpam-7095	66	15	7095	7095	NUM
ejpam-7095	66	16	4	4	NUM
ejpam-7095	66	17	of	of	ADP
ejpam-7095	66	18	30	30	NUM
ejpam-7095	66	19	definition	definition	NOUN
ejpam-7095	66	20	3	3	NUM
ejpam-7095	66	21	.	.	PUNCT
ejpam-7095	67	1	let	let	VERB
ejpam-7095	67	2	u(n−1)(x̄	u(n−1)(x̄	PRON
ejpam-7095	67	3	,	,	PUNCT
ejpam-7095	67	4	τ	τ	PROPN
ejpam-7095	67	5	)	)	PUNCT
ejpam-7095	67	6	∈	∈	PROPN
ejpam-7095	67	7	l1(0	l1(0	PROPN
ejpam-7095	67	8	,	,	PUNCT
ejpam-7095	67	9	t	t	PROPN
ejpam-7095	67	10	)	)	PUNCT
ejpam-7095	67	11	,	,	PUNCT
ejpam-7095	67	12	then	then	ADV
ejpam-7095	67	13	the	the	DET
ejpam-7095	67	14	mabc	mabc	PROPN
ejpam-7095	67	15	derivative	derivative	NOUN
ejpam-7095	67	16	of	of	ADP
ejpam-7095	67	17	order	order	NOUN
ejpam-7095	67	18	n	n	CCONJ
ejpam-7095	67	19	−	−	PROPN
ejpam-7095	67	20	1	1	NUM
ejpam-7095	67	21	<	<	X
ejpam-7095	67	22	α1	α1	PROPN
ejpam-7095	67	23	<	<	X
ejpam-7095	67	24	n	n	X
ejpam-7095	67	25	of	of	ADP
ejpam-7095	67	26	a	a	DET
ejpam-7095	67	27	function	function	NOUN
ejpam-7095	67	28	in	in	ADP
ejpam-7095	67	29	caputo	caputo	PROPN
ejpam-7095	67	30	sense	sense	NOUN
ejpam-7095	67	31	is	be	AUX
ejpam-7095	67	32	defined	define	VERB
ejpam-7095	67	33	by	by	ADP
ejpam-7095	67	34	[	[	X
ejpam-7095	67	35	30	30	NUM
ejpam-7095	67	36	]	]	SYM
ejpam-7095	67	37	:	:	PUNCT
ejpam-7095	67	38	mabc	mabc	NOUN
ejpam-7095	67	39	0	0	NUM
ejpam-7095	67	40	dα1	dα1	PROPN
ejpam-7095	67	41	τ	τ	PROPN
ejpam-7095	67	42	u(x̄	u(x̄	NUM
ejpam-7095	67	43	,	,	PUNCT
ejpam-7095	67	44	τ	τ	X
ejpam-7095	67	45	)	)	PUNCT
ejpam-7095	68	1	=	=	SYM
ejpam-7095	68	2	β(α	β(α	ADJ
ejpam-7095	68	3	)	)	PUNCT
ejpam-7095	68	4	1−	1−	NUM
ejpam-7095	68	5	α	α	PROPN
ejpam-7095	68	6	[	[	PUNCT
ejpam-7095	68	7	u(n−1)(x̄	u(n−1)(x̄	PROPN
ejpam-7095	68	8	,	,	PUNCT
ejpam-7095	68	9	τ)−	τ)−	PROPN
ejpam-7095	68	10	eα	eα	X
ejpam-7095	68	11	(	(	PUNCT
ejpam-7095	68	12	−ηατ	−ηατ	NOUN
ejpam-7095	68	13	α	α	X
ejpam-7095	68	14	)	)	PUNCT
ejpam-7095	68	15	u(n−1)(x̄	u(n−1)(x̄	PROPN
ejpam-7095	68	16	,	,	PUNCT
ejpam-7095	68	17	0	0	NUM
ejpam-7095	68	18	)	)	PUNCT
ejpam-7095	68	19	−	−	NOUN
ejpam-7095	69	1	ηα	ηα	PROPN
ejpam-7095	69	2	∫	∫	PROPN
ejpam-7095	69	3	τ	τ	X
ejpam-7095	69	4	0	0	NUM
ejpam-7095	69	5	(	(	PUNCT
ejpam-7095	69	6	τ	τ	X
ejpam-7095	69	7	−	−	PROPN
ejpam-7095	69	8	ϑ)α−1eα	ϑ)α−1eα	NOUN
ejpam-7095	69	9	,	,	PUNCT
ejpam-7095	69	10	α	α	PROPN
ejpam-7095	69	11	(	(	PUNCT
ejpam-7095	69	12	−ηα(τ	−ηα(τ	ADV
ejpam-7095	69	13	−	−	ADP
ejpam-7095	69	14	ϑ)α	ϑ)α	ADJ
ejpam-7095	69	15	)	)	PUNCT
ejpam-7095	69	16	u(n−1)(x̄	u(n−1)(x̄	PRON
ejpam-7095	69	17	,	,	PUNCT
ejpam-7095	69	18	ϑ)dϑ	ϑ)dϑ	PROPN
ejpam-7095	69	19	]	]	PUNCT
ejpam-7095	69	20	,	,	PUNCT
ejpam-7095	69	21	where	where	SCONJ
ejpam-7095	69	22	α1	α1	PROPN
ejpam-7095	69	23	=	=	PUNCT
ejpam-7095	69	24	α	α	PROPN
ejpam-7095	69	25	+	+	CCONJ
ejpam-7095	69	26	n	n	CCONJ
ejpam-7095	69	27	−	−	PROPN
ejpam-7095	69	28	1	1	NUM
ejpam-7095	69	29	,	,	PUNCT
ejpam-7095	69	30	ηα	ηα	PROPN
ejpam-7095	69	31	=	=	PUNCT
ejpam-7095	69	32	α	α	PROPN
ejpam-7095	69	33	1−α	1−α	NUM
ejpam-7095	69	34	,	,	PUNCT
ejpam-7095	69	35	β(α	β(α	PROPN
ejpam-7095	69	36	)	)	PUNCT
ejpam-7095	69	37	is	be	AUX
ejpam-7095	69	38	a	a	DET
ejpam-7095	69	39	normalized	normalize	VERB
ejpam-7095	69	40	function	function	NOUN
ejpam-7095	69	41	having	have	VERB
ejpam-7095	69	42	the	the	DET
ejpam-7095	69	43	property	property	NOUN
ejpam-7095	69	44	β(0	β(0	PROPN
ejpam-7095	69	45	)	)	PUNCT
ejpam-7095	69	46	=	=	SYM
ejpam-7095	70	1	β(1	β(1	PROPN
ejpam-7095	70	2	)	)	PUNCT
ejpam-7095	70	3	=	=	SYM
ejpam-7095	70	4	1	1	NUM
ejpam-7095	70	5	,	,	PUNCT
ejpam-7095	70	6	and	and	CCONJ
ejpam-7095	70	7	eα	eα	PRON
ejpam-7095	70	8	(	(	PUNCT
ejpam-7095	70	9	·	·	PUNCT
ejpam-7095	70	10	)	)	PUNCT
ejpam-7095	70	11	is	be	AUX
ejpam-7095	70	12	a	a	DET
ejpam-7095	70	13	mittag	mittag	ADJ
ejpam-7095	70	14	-	-	PUNCT
ejpam-7095	70	15	leffler	leffler	NOUN
ejpam-7095	70	16	function	function	NOUN
ejpam-7095	70	17	defined	define	VERB
ejpam-7095	70	18	as	as	ADP
ejpam-7095	70	19	eα(τ	eα(τ	ADJ
ejpam-7095	70	20	)	)	PUNCT
ejpam-7095	71	1	=	=	NOUN
ejpam-7095	72	1	∞∑	∞∑	NUM
ejpam-7095	72	2	ℓ=0	ℓ=0	NUM
ejpam-7095	72	3	τ	τ	PROPN
ejpam-7095	72	4	ℓ	ℓ	NOUN
ejpam-7095	72	5	γ(αℓ+	γ(αℓ+	X
ejpam-7095	72	6	1	1	NUM
ejpam-7095	72	7	)	)	PUNCT
ejpam-7095	72	8	.	.	PUNCT
ejpam-7095	73	1	definition	definition	NOUN
ejpam-7095	73	2	4	4	NUM
ejpam-7095	73	3	.	.	PUNCT
ejpam-7095	74	1	for	for	ADP
ejpam-7095	74	2	u(x̄	u(x̄	NUM
ejpam-7095	74	3	,	,	PUNCT
ejpam-7095	74	4	τ	τ	PROPN
ejpam-7095	74	5	)	)	PUNCT
ejpam-7095	74	6	∈	∈	PROPN
ejpam-7095	74	7	l1(0	l1(0	PROPN
ejpam-7095	74	8	,	,	PUNCT
ejpam-7095	74	9	t	t	PROPN
ejpam-7095	74	10	)	)	PUNCT
ejpam-7095	74	11	,	,	PUNCT
ejpam-7095	74	12	the	the	DET
ejpam-7095	74	13	mabc	mabc	ADJ
ejpam-7095	74	14	fractional	fractional	ADJ
ejpam-7095	74	15	integral	integral	ADJ
ejpam-7095	74	16	operator	operator	NOUN
ejpam-7095	74	17	is	be	AUX
ejpam-7095	74	18	defined	define	VERB
ejpam-7095	74	19	by	by	ADP
ejpam-7095	74	20	[	[	X
ejpam-7095	74	21	30	30	NUM
ejpam-7095	74	22	]	]	PUNCT
ejpam-7095	74	23	:	:	PUNCT
ejpam-7095	74	24	mabct	mabct	NOUN
ejpam-7095	74	25	α	α	PROPN
ejpam-7095	74	26	0u(x̄	0u(x̄	PROPN
ejpam-7095	74	27	,	,	PUNCT
ejpam-7095	74	28	τ	τ	X
ejpam-7095	74	29	)	)	PUNCT
ejpam-7095	74	30	=	=	SYM
ejpam-7095	74	31	1−	1−	NUM
ejpam-7095	74	32	α	α	DET
ejpam-7095	74	33	β(α	β(α	PROPN
ejpam-7095	74	34	)	)	PUNCT
ejpam-7095	74	35	u(x̄	u(x̄	NOUN
ejpam-7095	74	36	,	,	PUNCT
ejpam-7095	74	37	τ	τ	X
ejpam-7095	74	38	)	)	PUNCT
ejpam-7095	75	1	+	+	CCONJ
ejpam-7095	75	2	α	α	PROPN
ejpam-7095	75	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	75	4	)	)	PUNCT
ejpam-7095	75	5	∫	∫	PROPN
ejpam-7095	76	1	τ	τ	PROPN
ejpam-7095	76	2	0	0	NUM
ejpam-7095	76	3	(	(	PUNCT
ejpam-7095	76	4	τ	τ	PROPN
ejpam-7095	76	5	−	−	PROPN
ejpam-7095	76	6	ϑ)αu(x̄	ϑ)αu(x̄	PROPN
ejpam-7095	76	7	,	,	PUNCT
ejpam-7095	76	8	τ)dτ	τ)dτ	PROPN
ejpam-7095	76	9	,	,	PUNCT
ejpam-7095	76	10	τ	τ	X
ejpam-7095	76	11	≥	≥	NOUN
ejpam-7095	76	12	0	0	NUM
ejpam-7095	76	13	.	.	PUNCT
ejpam-7095	77	1	definition	definition	NOUN
ejpam-7095	77	2	5	5	NUM
ejpam-7095	77	3	.	.	PUNCT
ejpam-7095	78	1	the	the	DET
ejpam-7095	78	2	lt	lt	NOUN
ejpam-7095	78	3	of	of	ADP
ejpam-7095	78	4	mabc	mabc	PROPN
ejpam-7095	78	5	derivative	derivative	NOUN
ejpam-7095	78	6	of	of	ADP
ejpam-7095	78	7	a	a	DET
ejpam-7095	78	8	function	function	NOUN
ejpam-7095	78	9	u(x̄	u(x̄	NUM
ejpam-7095	78	10	,	,	PUNCT
ejpam-7095	78	11	τ	τ	X
ejpam-7095	78	12	)	)	PUNCT
ejpam-7095	78	13	is	be	AUX
ejpam-7095	78	14	defined	define	VERB
ejpam-7095	78	15	by	by	ADP
ejpam-7095	78	16	[	[	X
ejpam-7095	78	17	30	30	NUM
ejpam-7095	78	18	]	]	SYM
ejpam-7095	78	19	:	:	PUNCT
ejpam-7095	78	20	l	l	NOUN
ejpam-7095	78	21	{	{	PUNCT
ejpam-7095	78	22	mabc	mabc	PROPN
ejpam-7095	78	23	0	0	NUM
ejpam-7095	78	24	dα	dα	PROPN
ejpam-7095	78	25	τ	τ	PROPN
ejpam-7095	78	26	u(x̄	u(x̄	PROPN
ejpam-7095	78	27	,	,	PUNCT
ejpam-7095	78	28	τ	τ	PROPN
ejpam-7095	78	29	)	)	PUNCT
ejpam-7095	78	30	}	}	PUNCT
ejpam-7095	79	1	=	=	SYM
ejpam-7095	79	2	sαû(x̄	sαû(x̄	PROPN
ejpam-7095	79	3	,	,	PUNCT
ejpam-7095	79	4	s)−	s)−	PROPN
ejpam-7095	79	5	sα−1û(x̄	sα−1û(x̄	NOUN
ejpam-7095	79	6	,	,	PUNCT
ejpam-7095	79	7	0	0	NUM
ejpam-7095	79	8	)	)	PUNCT
ejpam-7095	79	9	sα(1−	sα(1−	PROPN
ejpam-7095	79	10	α	α	NUM
ejpam-7095	79	11	)	)	PUNCT
ejpam-7095	79	12	+	+	CCONJ
ejpam-7095	79	13	α	α	NOUN
ejpam-7095	79	14	.	.	PUNCT
ejpam-7095	80	1	3	3	X
ejpam-7095	80	2	.	.	X
ejpam-7095	80	3	existence	existence	NOUN
ejpam-7095	80	4	and	and	CCONJ
ejpam-7095	80	5	uniqueness	uniqueness	NOUN
ejpam-7095	80	6	results	result	NOUN
ejpam-7095	80	7	we	we	PRON
ejpam-7095	80	8	establish	establish	VERB
ejpam-7095	80	9	the	the	DET
ejpam-7095	80	10	existence	existence	NOUN
ejpam-7095	80	11	and	and	CCONJ
ejpam-7095	80	12	uniqueness	uniqueness	NOUN
ejpam-7095	80	13	of	of	ADP
ejpam-7095	80	14	the	the	DET
ejpam-7095	80	15	solution	solution	NOUN
ejpam-7095	80	16	to	to	ADP
ejpam-7095	80	17	the	the	DET
ejpam-7095	80	18	given	give	VERB
ejpam-7095	80	19	problem	problem	NOUN
ejpam-7095	80	20	in	in	ADP
ejpam-7095	80	21	this	this	DET
ejpam-7095	80	22	section	section	NOUN
ejpam-7095	80	23	.	.	PUNCT
ejpam-7095	81	1	we	we	PRON
ejpam-7095	81	2	begin	begin	VERB
ejpam-7095	81	3	by	by	ADP
ejpam-7095	81	4	defining	define	VERB
ejpam-7095	81	5	an	an	DET
ejpam-7095	81	6	appropriate	appropriate	ADJ
ejpam-7095	81	7	functional	functional	ADJ
ejpam-7095	81	8	framework	framework	NOUN
ejpam-7095	81	9	:	:	PUNCT
ejpam-7095	81	10	let	let	VERB
ejpam-7095	81	11	b(ω	b(ω	ADV
ejpam-7095	81	12	,	,	PUNCT
ejpam-7095	81	13	r	r	NOUN
ejpam-7095	81	14	)	)	PUNCT
ejpam-7095	81	15	represent	represent	VERB
ejpam-7095	81	16	the	the	DET
ejpam-7095	81	17	banach	banach	NOUN
ejpam-7095	81	18	space	space	NOUN
ejpam-7095	81	19	comprising	comprise	VERB
ejpam-7095	81	20	all	all	DET
ejpam-7095	81	21	continuous	continuous	ADJ
ejpam-7095	81	22	real	real	ADV
ejpam-7095	81	23	-	-	PUNCT
ejpam-7095	81	24	valued	value	VERB
ejpam-7095	81	25	functions	function	NOUN
ejpam-7095	81	26	defined	define	VERB
ejpam-7095	81	27	on	on	ADP
ejpam-7095	81	28	the	the	DET
ejpam-7095	81	29	compact	compact	ADJ
ejpam-7095	81	30	domain	domain	NOUN
ejpam-7095	81	31	ω	ω	NOUN
ejpam-7095	81	32	=	=	SYM
ejpam-7095	81	33	θ×	θ×	PROPN
ejpam-7095	82	1	[	[	X
ejpam-7095	82	2	0	0	NUM
ejpam-7095	82	3	,	,	PUNCT
ejpam-7095	82	4	1	1	NUM
ejpam-7095	82	5	]	]	PUNCT
ejpam-7095	82	6	where	where	SCONJ
ejpam-7095	82	7	θ	θ	PROPN
ejpam-7095	82	8	⊂	⊂	PROPN
ejpam-7095	82	9	r3	r3	PROPN
ejpam-7095	82	10	.	.	PUNCT
ejpam-7095	83	1	the	the	DET
ejpam-7095	83	2	compactness	compactness	NOUN
ejpam-7095	83	3	of	of	ADP
ejpam-7095	83	4	ω	ω	PROPN
ejpam-7095	83	5	ensures	ensure	VERB
ejpam-7095	83	6	that	that	SCONJ
ejpam-7095	83	7	b(ω	b(ω	ADV
ejpam-7095	83	8	,	,	PUNCT
ejpam-7095	83	9	r	r	NOUN
ejpam-7095	83	10	)	)	PUNCT
ejpam-7095	83	11	is	be	AUX
ejpam-7095	83	12	well	well	ADV
ejpam-7095	83	13	suited	suited	ADJ
ejpam-7095	83	14	for	for	ADP
ejpam-7095	83	15	studying	study	VERB
ejpam-7095	83	16	the	the	DET
ejpam-7095	83	17	continuity	continuity	NOUN
ejpam-7095	83	18	and	and	CCONJ
ejpam-7095	83	19	boundedness	boundedness	NOUN
ejpam-7095	83	20	properties	property	NOUN
ejpam-7095	83	21	of	of	ADP
ejpam-7095	83	22	sections	section	NOUN
ejpam-7095	83	23	.	.	PUNCT
ejpam-7095	84	1	the	the	DET
ejpam-7095	84	2	norm	norm	NOUN
ejpam-7095	84	3	on	on	ADP
ejpam-7095	84	4	b(ω	b(ω	ADV
ejpam-7095	84	5	,	,	PUNCT
ejpam-7095	84	6	r	r	NOUN
ejpam-7095	84	7	)	)	PUNCT
ejpam-7095	84	8	is	be	AUX
ejpam-7095	84	9	a	a	DET
ejpam-7095	84	10	supremum	supremum	ADJ
ejpam-7095	84	11	norm	norm	NOUN
ejpam-7095	84	12	given	give	VERB
ejpam-7095	84	13	by	by	ADP
ejpam-7095	84	14	:	:	PUNCT
ejpam-7095	84	15	∥u∥∞	∥u∥∞	X
ejpam-7095	84	16	=	=	SYM
ejpam-7095	85	1	sup{|u(x̄	sup{|u(x̄	X
ejpam-7095	85	2	,	,	PUNCT
ejpam-7095	85	3	τ)|	τ)|	PRON
ejpam-7095	85	4	:	:	PUNCT
ejpam-7095	85	5	(	(	PUNCT
ejpam-7095	85	6	x̄	x̄	PROPN
ejpam-7095	85	7	,	,	PUNCT
ejpam-7095	85	8	τ	τ	PROPN
ejpam-7095	85	9	)	)	PUNCT
ejpam-7095	85	10	∈	∈	PROPN
ejpam-7095	85	11	ω	ω	PROPN
ejpam-7095	85	12	}	}	PUNCT
ejpam-7095	85	13	,	,	PUNCT
ejpam-7095	85	14	where	where	SCONJ
ejpam-7095	85	15	x̄	x̄	PRON
ejpam-7095	85	16	∈	∈	PROPN
ejpam-7095	85	17	θ	θ	PROPN
ejpam-7095	85	18	represents	represent	VERB
ejpam-7095	85	19	the	the	DET
ejpam-7095	85	20	spatial	spatial	ADJ
ejpam-7095	85	21	co	co	NOUN
ejpam-7095	85	22	ordinates	ordinate	NOUN
ejpam-7095	85	23	and	and	CCONJ
ejpam-7095	85	24	τ	τ	PRON
ejpam-7095	85	25	∈	∈	PROPN
ejpam-7095	86	1	[	[	X
ejpam-7095	86	2	0	0	NUM
ejpam-7095	86	3	,	,	PUNCT
ejpam-7095	86	4	1	1	NUM
ejpam-7095	86	5	]	]	PUNCT
ejpam-7095	86	6	denotes	denote	VERB
ejpam-7095	86	7	the	the	DET
ejpam-7095	86	8	temporal	temporal	ADJ
ejpam-7095	86	9	variable	variable	NOUN
ejpam-7095	86	10	.	.	PUNCT
ejpam-7095	87	1	we	we	PRON
ejpam-7095	87	2	study	study	VERB
ejpam-7095	87	3	the	the	DET
ejpam-7095	87	4	fractional	fractional	ADJ
ejpam-7095	87	5	diffusion	diffusion	NOUN
ejpam-7095	87	6	-	-	PUNCT
ejpam-7095	87	7	wave	wave	NOUN
ejpam-7095	87	8	equation	equation	NOUN
ejpam-7095	87	9	of	of	ADP
ejpam-7095	87	10	the	the	DET
ejpam-7095	87	11	form	form	NOUN
ejpam-7095	87	12	[	[	X
ejpam-7095	87	13	31	31	NUM
ejpam-7095	87	14	]	]	SYM
ejpam-7095	87	15	:	:	PUNCT
ejpam-7095	87	16	mabc	mabc	NOUN
ejpam-7095	87	17	0	0	PUNCT
ejpam-7095	88	1	dα	dα	PROPN
ejpam-7095	88	2	τ	τ	PROPN
ejpam-7095	88	3	u(x̄	u(x̄	PROPN
ejpam-7095	88	4	,	,	PUNCT
ejpam-7095	88	5	τ	τ	X
ejpam-7095	88	6	)	)	PUNCT
ejpam-7095	88	7	=	=	SYM
ejpam-7095	89	1	λ1∇2u(x̄	λ1∇2u(x̄	NOUN
ejpam-7095	89	2	,	,	PUNCT
ejpam-7095	89	3	τ)−	τ)−	PROPN
ejpam-7095	89	4	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	89	5	,	,	PUNCT
ejpam-7095	89	6	τ	τ	X
ejpam-7095	89	7	)	)	PUNCT
ejpam-7095	89	8	+	+	CCONJ
ejpam-7095	89	9	f(x̄	f(x̄	NOUN
ejpam-7095	89	10	,	,	PUNCT
ejpam-7095	89	11	τ	τ	PROPN
ejpam-7095	89	12	)	)	PUNCT
ejpam-7095	89	13	,	,	PUNCT
ejpam-7095	89	14	1	1	NUM
ejpam-7095	89	15	<	<	X
ejpam-7095	89	16	α	α	PROPN
ejpam-7095	89	17	≤	≤	NUM
ejpam-7095	89	18	2	2	NUM
ejpam-7095	89	19	,	,	PUNCT
ejpam-7095	89	20	x̄	x̄	NOUN
ejpam-7095	89	21	∈	∈	PROPN
ejpam-7095	89	22	θ	θ	PROPN
ejpam-7095	89	23	,	,	PUNCT
ejpam-7095	89	24	(	(	PUNCT
ejpam-7095	89	25	1	1	NUM
ejpam-7095	89	26	)	)	PUNCT
ejpam-7095	89	27	with	with	ADP
ejpam-7095	89	28	boundary	boundary	ADJ
ejpam-7095	89	29	conditions	condition	NOUN
ejpam-7095	89	30	bu(x̄	bu(x̄	VERB
ejpam-7095	89	31	,	,	PUNCT
ejpam-7095	89	32	τ	τ	X
ejpam-7095	89	33	)	)	PUNCT
ejpam-7095	89	34	=	=	SYM
ejpam-7095	89	35	g1(x̄	g1(x̄	PROPN
ejpam-7095	89	36	,	,	PUNCT
ejpam-7095	89	37	τ	τ	PROPN
ejpam-7095	89	38	)	)	PUNCT
ejpam-7095	89	39	,	,	PUNCT
ejpam-7095	90	1	x̄	x̄	NOUN
ejpam-7095	90	2	∈	∈	PROPN
ejpam-7095	90	3	∂θ	∂θ	PROPN
ejpam-7095	90	4	,	,	PUNCT
ejpam-7095	90	5	(	(	PUNCT
ejpam-7095	90	6	2	2	NUM
ejpam-7095	90	7	)	)	PUNCT
ejpam-7095	90	8	and	and	CCONJ
ejpam-7095	90	9	initial	initial	ADJ
ejpam-7095	90	10	conditions	condition	NOUN
ejpam-7095	90	11	u(x̄	u(x̄	NUM
ejpam-7095	90	12	,	,	PUNCT
ejpam-7095	90	13	0	0	NUM
ejpam-7095	90	14	)	)	PUNCT
ejpam-7095	90	15	=	=	SYM
ejpam-7095	90	16	g2(x̄	g2(x̄	PROPN
ejpam-7095	90	17	)	)	PUNCT
ejpam-7095	90	18	,	,	PUNCT
ejpam-7095	90	19	uτ	uτ	PROPN
ejpam-7095	90	20	(	(	PUNCT
ejpam-7095	90	21	x̄	x̄	PROPN
ejpam-7095	90	22	,	,	PUNCT
ejpam-7095	90	23	0	0	NUM
ejpam-7095	90	24	)	)	PUNCT
ejpam-7095	90	25	=	=	SYM
ejpam-7095	90	26	g3(x̄	g3(x̄	NOUN
ejpam-7095	90	27	)	)	PUNCT
ejpam-7095	90	28	,	,	PUNCT
ejpam-7095	90	29	(	(	PUNCT
ejpam-7095	90	30	3	3	X
ejpam-7095	90	31	)	)	PUNCT
ejpam-7095	90	32	kamran	kamran	PROPN
ejpam-7095	90	33	et	et	PROPN
ejpam-7095	90	34	al	al	PROPN
ejpam-7095	90	35	.	.	PUNCT
ejpam-7095	90	36	/	/	SYM
ejpam-7095	90	37	eur	eur	PROPN
ejpam-7095	90	38	.	.	PUNCT
ejpam-7095	91	1	j.	j.	PROPN
ejpam-7095	91	2	pure	pure	PROPN
ejpam-7095	91	3	appl	appl	PROPN
ejpam-7095	91	4	.	.	PROPN
ejpam-7095	91	5	math	math	PROPN
ejpam-7095	91	6	,	,	PUNCT
ejpam-7095	91	7	18	18	NUM
ejpam-7095	91	8	(	(	PUNCT
ejpam-7095	91	9	4	4	NUM
ejpam-7095	91	10	)	)	PUNCT
ejpam-7095	91	11	(	(	PUNCT
ejpam-7095	91	12	2025	2025	NUM
ejpam-7095	91	13	)	)	PUNCT
ejpam-7095	91	14	,	,	PUNCT
ejpam-7095	91	15	7095	7095	NUM
ejpam-7095	91	16	5	5	NUM
ejpam-7095	91	17	of	of	ADP
ejpam-7095	91	18	30	30	NUM
ejpam-7095	91	19	where	where	SCONJ
ejpam-7095	91	20	∇2	∇2	PROPN
ejpam-7095	91	21	is	be	AUX
ejpam-7095	91	22	the	the	DET
ejpam-7095	91	23	laplacian	laplacian	ADJ
ejpam-7095	91	24	operator	operator	NOUN
ejpam-7095	91	25	,	,	PUNCT
ejpam-7095	91	26	defined	define	VERB
ejpam-7095	91	27	as	as	ADP
ejpam-7095	91	28	:	:	PUNCT
ejpam-7095	91	29	for	for	ADP
ejpam-7095	91	30	1d	1d	NUM
ejpam-7095	91	31	problem	problem	NOUN
ejpam-7095	91	32	,	,	PUNCT
ejpam-7095	91	33	x̄	x̄	PUNCT
ejpam-7095	91	34	=	=	PUNCT
ejpam-7095	91	35	x	x	PUNCT
ejpam-7095	91	36	and	and	CCONJ
ejpam-7095	91	37	∇2	∇2	PROPN
ejpam-7095	91	38	=	=	SYM
ejpam-7095	91	39	∂2	∂2	PROPN
ejpam-7095	91	40	∂x2	∂x2	NOUN
ejpam-7095	91	41	;	;	PUNCT
ejpam-7095	91	42	for	for	ADP
ejpam-7095	91	43	a	a	DET
ejpam-7095	91	44	2d	2d	NUM
ejpam-7095	91	45	problem	problem	NOUN
ejpam-7095	91	46	,	,	PUNCT
ejpam-7095	91	47	x̄	x̄	PUNCT
ejpam-7095	91	48	=	=	PUNCT
ejpam-7095	91	49	(	(	PUNCT
ejpam-7095	91	50	x	x	X
ejpam-7095	91	51	,	,	PUNCT
ejpam-7095	91	52	y	y	PROPN
ejpam-7095	91	53	)	)	PUNCT
ejpam-7095	91	54	and	and	CCONJ
ejpam-7095	91	55	∇2	∇2	PROPN
ejpam-7095	91	56	=	=	SYM
ejpam-7095	91	57	∂2	∂2	PROPN
ejpam-7095	91	58	∂x2	∂x2	NOUN
ejpam-7095	91	59	+	+	CCONJ
ejpam-7095	91	60	∂2	∂2	PROPN
ejpam-7095	91	61	∂y2	∂y2	NOUN
ejpam-7095	91	62	;	;	PUNCT
ejpam-7095	91	63	and	and	CCONJ
ejpam-7095	91	64	for	for	ADP
ejpam-7095	91	65	a	a	DET
ejpam-7095	91	66	3d	3d	PROPN
ejpam-7095	91	67	problem	problem	NOUN
ejpam-7095	91	68	,	,	PUNCT
ejpam-7095	91	69	x̄	x̄	PUNCT
ejpam-7095	91	70	=	=	PUNCT
ejpam-7095	91	71	(	(	PUNCT
ejpam-7095	91	72	x	x	X
ejpam-7095	91	73	,	,	PUNCT
ejpam-7095	91	74	y	y	PROPN
ejpam-7095	91	75	,	,	PUNCT
ejpam-7095	91	76	z	z	NOUN
ejpam-7095	91	77	)	)	PUNCT
ejpam-7095	91	78	and	and	CCONJ
ejpam-7095	91	79	∇2	∇2	PROPN
ejpam-7095	91	80	=	=	SYM
ejpam-7095	91	81	∂2	∂2	PROPN
ejpam-7095	91	82	∂x2	∂x2	NOUN
ejpam-7095	91	83	+	+	CCONJ
ejpam-7095	91	84	∂2	∂2	NOUN
ejpam-7095	91	85	∂y2	∂y2	ADJ
ejpam-7095	91	86	+	+	CCONJ
ejpam-7095	91	87	∂2	∂2	PROPN
ejpam-7095	91	88	∂z2	∂z2	NOUN
ejpam-7095	91	89	.	.	PUNCT
ejpam-7095	92	1	here	here	ADV
ejpam-7095	92	2	θ	θ	PROPN
ejpam-7095	92	3	is	be	AUX
ejpam-7095	92	4	the	the	DET
ejpam-7095	92	5	domain	domain	NOUN
ejpam-7095	92	6	and	and	CCONJ
ejpam-7095	92	7	∂θ	∂θ	PROPN
ejpam-7095	92	8	is	be	AUX
ejpam-7095	92	9	its	its	PRON
ejpam-7095	92	10	boundary	boundary	NOUN
ejpam-7095	92	11	.	.	PUNCT
ejpam-7095	93	1	the	the	DET
ejpam-7095	93	2	constants	constant	NOUN
ejpam-7095	93	3	λ1	λ1	ADJ
ejpam-7095	93	4	and	and	CCONJ
ejpam-7095	93	5	λ2	λ2	NOUN
ejpam-7095	93	6	are	be	AUX
ejpam-7095	93	7	arbitrary	arbitrary	ADJ
ejpam-7095	93	8	,	,	PUNCT
ejpam-7095	93	9	and	and	CCONJ
ejpam-7095	93	10	the	the	DET
ejpam-7095	93	11	forcing	force	VERB
ejpam-7095	93	12	term	term	NOUN
ejpam-7095	93	13	f(x̄	f(x̄	PROPN
ejpam-7095	93	14	,	,	PUNCT
ejpam-7095	93	15	τ	τ	X
ejpam-7095	93	16	)	)	PUNCT
ejpam-7095	93	17	is	be	AUX
ejpam-7095	93	18	sufficiently	sufficiently	ADV
ejpam-7095	93	19	smooth	smooth	ADJ
ejpam-7095	93	20	.	.	PUNCT
ejpam-7095	94	1	the	the	DET
ejpam-7095	94	2	functions	function	NOUN
ejpam-7095	94	3	g1(x̄	g1(x̄	PROPN
ejpam-7095	94	4	,	,	PUNCT
ejpam-7095	94	5	τ	τ	PROPN
ejpam-7095	94	6	)	)	PUNCT
ejpam-7095	94	7	,	,	PUNCT
ejpam-7095	94	8	g2(x̄	g2(x̄	PROPN
ejpam-7095	94	9	)	)	PUNCT
ejpam-7095	94	10	,	,	PUNCT
ejpam-7095	94	11	and	and	CCONJ
ejpam-7095	94	12	g3(x̄	g3(x̄	NUM
ejpam-7095	94	13	)	)	PUNCT
ejpam-7095	94	14	are	be	AUX
ejpam-7095	94	15	given	give	VERB
ejpam-7095	94	16	continuous	continuous	ADJ
ejpam-7095	94	17	functions	function	NOUN
ejpam-7095	94	18	.	.	PUNCT
ejpam-7095	95	1	b	b	NOUN
ejpam-7095	95	2	is	be	AUX
ejpam-7095	95	3	the	the	DET
ejpam-7095	95	4	boundary	boundary	ADJ
ejpam-7095	95	5	differential	differential	NOUN
ejpam-7095	95	6	operator	operator	NOUN
ejpam-7095	95	7	,	,	PUNCT
ejpam-7095	95	8	and	and	CCONJ
ejpam-7095	95	9	mabc	mabc	NOUN
ejpam-7095	95	10	0	0	PROPN
ejpam-7095	96	1	dα	dα	ADP
ejpam-7095	96	2	τ	τ	PROPN
ejpam-7095	96	3	u(x̄	u(x̄	PROPN
ejpam-7095	96	4	,	,	PUNCT
ejpam-7095	96	5	τ	τ	PROPN
ejpam-7095	96	6	)	)	PUNCT
ejpam-7095	97	1	,	,	PUNCT
ejpam-7095	97	2	denotes	denote	VERB
ejpam-7095	97	3	the	the	DET
ejpam-7095	97	4	mabc	mabc	PROPN
ejpam-7095	97	5	derivative	derivative	NOUN
ejpam-7095	97	6	of	of	ADP
ejpam-7095	97	7	order	order	NOUN
ejpam-7095	97	8	1	1	NUM
ejpam-7095	97	9	<	<	X
ejpam-7095	97	10	α	α	X
ejpam-7095	97	11	<	<	X
ejpam-7095	97	12	2	2	NUM
ejpam-7095	97	13	.	.	PUNCT
ejpam-7095	97	14	applying	apply	VERB
ejpam-7095	97	15	the	the	DET
ejpam-7095	97	16	mabc	mabc	ADJ
ejpam-7095	97	17	fractional	fractional	ADJ
ejpam-7095	97	18	integral	integral	ADJ
ejpam-7095	97	19	operator	operator	NOUN
ejpam-7095	97	20	to	to	ADP
ejpam-7095	97	21	eq	eq	NOUN
ejpam-7095	97	22	(	(	PUNCT
ejpam-7095	97	23	1	1	NUM
ejpam-7095	97	24	)	)	PUNCT
ejpam-7095	97	25	,	,	PUNCT
ejpam-7095	97	26	yields	yield	NOUN
ejpam-7095	97	27	:	:	PUNCT
ejpam-7095	97	28	u(x̄	u(x̄	NUM
ejpam-7095	97	29	,	,	PUNCT
ejpam-7095	97	30	τ	τ	X
ejpam-7095	97	31	)	)	PUNCT
ejpam-7095	97	32	=	=	SYM
ejpam-7095	97	33	g2(x̄	g2(x̄	PROPN
ejpam-7095	97	34	)	)	PUNCT
ejpam-7095	98	1	+	+	NUM
ejpam-7095	98	2	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	98	3	(	(	PUNCT
ejpam-7095	98	4	1−	1−	NUM
ejpam-7095	98	5	α	α	NOUN
ejpam-7095	98	6	)	)	PUNCT
ejpam-7095	98	7	β(α	β(α	PROPN
ejpam-7095	98	8	)	)	PUNCT
ejpam-7095	98	9	(	(	PUNCT
ejpam-7095	98	10	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	98	11	,	,	PUNCT
ejpam-7095	98	12	τ)−	τ)−	PROPN
ejpam-7095	98	13	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	98	14	,	,	PUNCT
ejpam-7095	98	15	τ	τ	X
ejpam-7095	98	16	)	)	PUNCT
ejpam-7095	98	17	+	+	CCONJ
ejpam-7095	98	18	f(x̄	f(x̄	PROPN
ejpam-7095	98	19	,	,	PUNCT
ejpam-7095	98	20	τ	τ	X
ejpam-7095	98	21	)	)	PUNCT
ejpam-7095	98	22	)	)	PUNCT
ejpam-7095	99	1	+	+	CCONJ
ejpam-7095	99	2	α	α	PROPN
ejpam-7095	99	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	99	4	)	)	PUNCT
ejpam-7095	99	5	(	(	PUNCT
ejpam-7095	99	6	∫	∫	PROPN
ejpam-7095	99	7	τ	τ	X
ejpam-7095	99	8	0	0	NUM
ejpam-7095	99	9	(	(	PUNCT
ejpam-7095	99	10	τ	τ	PROPN
ejpam-7095	99	11	−	−	PROPN
ejpam-7095	99	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	99	13	(	(	PUNCT
ejpam-7095	99	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	99	15	,	,	PUNCT
ejpam-7095	99	16	ϑ)−	ϑ)−	PROPN
ejpam-7095	99	17	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	99	18	,	,	PUNCT
ejpam-7095	99	19	ϑ	ϑ	NOUN
ejpam-7095	99	20	)	)	PUNCT
ejpam-7095	99	21	+	+	CCONJ
ejpam-7095	99	22	f(x̄	f(x̄	NOUN
ejpam-7095	99	23	,	,	PUNCT
ejpam-7095	99	24	ϑ	ϑ	NOUN
ejpam-7095	99	25	)	)	PUNCT
ejpam-7095	99	26	)	)	PUNCT
ejpam-7095	99	27	dϑ	dϑ	NOUN
ejpam-7095	99	28	)	)	PUNCT
ejpam-7095	99	29	.	.	PUNCT
ejpam-7095	100	1	(	(	PUNCT
ejpam-7095	100	2	4	4	X
ejpam-7095	100	3	)	)	PUNCT
ejpam-7095	100	4	next	next	ADV
ejpam-7095	100	5	,	,	PUNCT
ejpam-7095	100	6	we	we	PRON
ejpam-7095	100	7	define	define	VERB
ejpam-7095	100	8	the	the	DET
ejpam-7095	100	9	operator	operator	NOUN
ejpam-7095	100	10	j	j	NOUN
ejpam-7095	100	11	:	:	PUNCT
ejpam-7095	101	1	b(ω	b(ω	ADV
ejpam-7095	101	2	,	,	PUNCT
ejpam-7095	101	3	r	r	NOUN
ejpam-7095	101	4	)	)	PUNCT
ejpam-7095	101	5	→	→	SYM
ejpam-7095	101	6	b(ω	b(ω	ADV
ejpam-7095	101	7	,	,	PUNCT
ejpam-7095	101	8	r	r	NOUN
ejpam-7095	101	9	)	)	PUNCT
ejpam-7095	101	10	,	,	PUNCT
ejpam-7095	101	11	transforming	transform	VERB
ejpam-7095	101	12	the	the	DET
ejpam-7095	101	13	problem	problem	NOUN
ejpam-7095	101	14	into	into	ADP
ejpam-7095	101	15	a	a	DET
ejpam-7095	101	16	fixed	fix	VERB
ejpam-7095	101	17	-	-	PUNCT
ejpam-7095	101	18	point	point	NOUN
ejpam-7095	101	19	formulation	formulation	NOUN
ejpam-7095	101	20	:	:	PUNCT
ejpam-7095	102	1	j	j	PROPN
ejpam-7095	102	2	u(x̄	u(x̄	NUM
ejpam-7095	102	3	,	,	PUNCT
ejpam-7095	102	4	τ	τ	X
ejpam-7095	102	5	)	)	PUNCT
ejpam-7095	102	6	=	=	SYM
ejpam-7095	102	7	g2(x̄	g2(x̄	PROPN
ejpam-7095	102	8	)	)	PUNCT
ejpam-7095	102	9	+	+	NUM
ejpam-7095	102	10	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	102	11	(	(	PUNCT
ejpam-7095	102	12	1−	1−	NUM
ejpam-7095	102	13	α	α	NOUN
ejpam-7095	102	14	)	)	PUNCT
ejpam-7095	102	15	β(α	β(α	PROPN
ejpam-7095	102	16	)	)	PUNCT
ejpam-7095	102	17	(	(	PUNCT
ejpam-7095	102	18	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	102	19	,	,	PUNCT
ejpam-7095	102	20	τ)−	τ)−	PROPN
ejpam-7095	102	21	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	102	22	,	,	PUNCT
ejpam-7095	102	23	τ	τ	X
ejpam-7095	102	24	)	)	PUNCT
ejpam-7095	102	25	+	+	CCONJ
ejpam-7095	102	26	f(x̄	f(x̄	PROPN
ejpam-7095	102	27	,	,	PUNCT
ejpam-7095	102	28	τ	τ	X
ejpam-7095	102	29	)	)	PUNCT
ejpam-7095	102	30	)	)	PUNCT
ejpam-7095	103	1	+	+	CCONJ
ejpam-7095	103	2	α	α	PROPN
ejpam-7095	103	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	103	4	)	)	PUNCT
ejpam-7095	103	5	(	(	PUNCT
ejpam-7095	103	6	∫	∫	PROPN
ejpam-7095	103	7	τ	τ	X
ejpam-7095	103	8	0	0	NUM
ejpam-7095	103	9	(	(	PUNCT
ejpam-7095	103	10	τ	τ	PROPN
ejpam-7095	103	11	−	−	PROPN
ejpam-7095	103	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	103	13	(	(	PUNCT
ejpam-7095	103	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	103	15	,	,	PUNCT
ejpam-7095	103	16	ϑ)−	ϑ)−	PROPN
ejpam-7095	103	17	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	103	18	,	,	PUNCT
ejpam-7095	103	19	ϑ	ϑ	NOUN
ejpam-7095	103	20	)	)	PUNCT
ejpam-7095	103	21	+	+	CCONJ
ejpam-7095	103	22	f(x̄	f(x̄	NOUN
ejpam-7095	103	23	,	,	PUNCT
ejpam-7095	103	24	ϑ	ϑ	NOUN
ejpam-7095	103	25	)	)	PUNCT
ejpam-7095	103	26	)	)	PUNCT
ejpam-7095	103	27	dϑ	dϑ	NOUN
ejpam-7095	103	28	)	)	PUNCT
ejpam-7095	103	29	.	.	PUNCT
ejpam-7095	104	1	(	(	PUNCT
ejpam-7095	104	2	5	5	X
ejpam-7095	104	3	)	)	PUNCT
ejpam-7095	104	4	the	the	DET
ejpam-7095	104	5	fixed	fix	VERB
ejpam-7095	104	6	point	point	NOUN
ejpam-7095	104	7	of	of	ADP
ejpam-7095	104	8	the	the	DET
ejpam-7095	104	9	operator	operator	NOUN
ejpam-7095	104	10	corresponds	correspond	VERB
ejpam-7095	104	11	to	to	ADP
ejpam-7095	104	12	the	the	DET
ejpam-7095	104	13	solution	solution	NOUN
ejpam-7095	104	14	to	to	ADP
ejpam-7095	104	15	eqs	eqs	PROPN
ejpam-7095	104	16	.	.	PUNCT
ejpam-7095	105	1	(	(	PUNCT
ejpam-7095	105	2	1)–(3	1)–(3	NUM
ejpam-7095	105	3	)	)	PUNCT
ejpam-7095	105	4	.	.	PUNCT
ejpam-7095	106	1	we	we	PRON
ejpam-7095	106	2	introduce	introduce	VERB
ejpam-7095	106	3	the	the	DET
ejpam-7095	106	4	following	follow	VERB
ejpam-7095	106	5	hypotheses	hypothesis	NOUN
ejpam-7095	106	6	for	for	ADP
ejpam-7095	106	7	any	any	DET
ejpam-7095	106	8	(	(	PUNCT
ejpam-7095	106	9	ϑ	ϑ	X
ejpam-7095	106	10	,	,	PUNCT
ejpam-7095	106	11	τ	τ	NOUN
ejpam-7095	106	12	)	)	PUNCT
ejpam-7095	106	13	∈	∈	PROPN
ejpam-7095	106	14	(	(	PUNCT
ejpam-7095	106	15	ω	ω	NOUN
ejpam-7095	106	16	):	):	PUNCT
ejpam-7095	106	17	(	(	PUNCT
ejpam-7095	106	18	h1	h1	PROPN
ejpam-7095	106	19	)	)	PUNCT
ejpam-7095	106	20	|∇2u(x̄	|∇2u(x̄	PROPN
ejpam-7095	106	21	,	,	PUNCT
ejpam-7095	106	22	τ)|	τ)|	ADJ
ejpam-7095	106	23	≤	≤	PUNCT
ejpam-7095	106	24	ϵ1|u(x̄	ϵ1|u(x̄	PROPN
ejpam-7095	106	25	,	,	PUNCT
ejpam-7095	106	26	τ)|	τ)|	PROPN
ejpam-7095	106	27	,	,	PUNCT
ejpam-7095	106	28	(	(	PUNCT
ejpam-7095	106	29	h2	h2	NOUN
ejpam-7095	106	30	)	)	PUNCT
ejpam-7095	106	31	|g2|	|g2|	VERB
ejpam-7095	106	32	≤	≤	PROPN
ejpam-7095	106	33	ϵ2	ϵ2	NOUN
ejpam-7095	106	34	,	,	PUNCT
ejpam-7095	106	35	(	(	PUNCT
ejpam-7095	106	36	h3	h3	NOUN
ejpam-7095	106	37	)	)	PUNCT
ejpam-7095	106	38	|g3|	|g3|	PROPN
ejpam-7095	106	39	≤	≤	NOUN
ejpam-7095	106	40	ϵ3	ϵ3	PROPN
ejpam-7095	106	41	,	,	PUNCT
ejpam-7095	106	42	(	(	PUNCT
ejpam-7095	106	43	h4	h4	PROPN
ejpam-7095	106	44	)	)	PUNCT
ejpam-7095	106	45	|f(x̄	|f(x̄	NOUN
ejpam-7095	106	46	,	,	PUNCT
ejpam-7095	106	47	τ)|	τ)|	PROPN
ejpam-7095	106	48	≤	≤	NUM
ejpam-7095	106	49	ϵ4	ϵ4	NOUN
ejpam-7095	106	50	,	,	PUNCT
ejpam-7095	106	51	(	(	PUNCT
ejpam-7095	106	52	h5	h5	PROPN
ejpam-7095	106	53	)	)	PUNCT
ejpam-7095	106	54	|∇2u1(x̄	|∇2u1(x̄	PROPN
ejpam-7095	106	55	,	,	PUNCT
ejpam-7095	106	56	τ)−∇2u2(x̄	τ)−∇2u2(x̄	PROPN
ejpam-7095	106	57	,	,	PUNCT
ejpam-7095	106	58	τ)|	τ)|	ADJ
ejpam-7095	106	59	≤	≤	PROPN
ejpam-7095	106	60	ϵ5|u1(x̄	ϵ5|u1(x̄	NOUN
ejpam-7095	106	61	,	,	PUNCT
ejpam-7095	106	62	τ)−	τ)−	PROPN
ejpam-7095	106	63	u2(x̄	u2(x̄	PROPN
ejpam-7095	106	64	,	,	PUNCT
ejpam-7095	106	65	τ)|	τ)|	PROPN
ejpam-7095	106	66	,	,	PUNCT
ejpam-7095	106	67	(	(	PUNCT
ejpam-7095	106	68	h6	h6	PROPN
ejpam-7095	106	69	)	)	PUNCT
ejpam-7095	106	70	|∇2u1(x̄1	|∇2u1(x̄1	PROPN
ejpam-7095	106	71	,	,	PUNCT
ejpam-7095	106	72	τ1)−∇2u2(x̄2	τ1)−∇2u2(x̄2	NOUN
ejpam-7095	106	73	,	,	PUNCT
ejpam-7095	106	74	τ2)|	τ2)|	NOUN
ejpam-7095	106	75	≤	≤	ADV
ejpam-7095	106	76	lf1	lf1	PROPN
ejpam-7095	106	77	(	(	PUNCT
ejpam-7095	106	78	|x̄1	|x̄1	NOUN
ejpam-7095	106	79	−	−	PROPN
ejpam-7095	106	80	x̄2|+	x̄2|+	PROPN
ejpam-7095	106	81	|τ1	|τ1	ADJ
ejpam-7095	106	82	−	−	PROPN
ejpam-7095	106	83	τ2||	τ2||	PROPN
ejpam-7095	106	84	)	)	PUNCT
ejpam-7095	106	85	,	,	PUNCT
ejpam-7095	106	86	(	(	PUNCT
ejpam-7095	106	87	h7	h7	NOUN
ejpam-7095	106	88	)	)	PUNCT
ejpam-7095	106	89	|u1(x̄1	|u1(x̄1	NOUN
ejpam-7095	106	90	,	,	PUNCT
ejpam-7095	106	91	τ1)−	τ1)−	NOUN
ejpam-7095	106	92	u2(x̄2	u2(x̄2	NOUN
ejpam-7095	106	93	,	,	PUNCT
ejpam-7095	106	94	τ2)|	τ2)|	PROPN
ejpam-7095	106	95	≤	≤	NUM
ejpam-7095	106	96	lf2	lf2	PROPN
ejpam-7095	106	97	(	(	PUNCT
ejpam-7095	106	98	|x̄1	|x̄1	NOUN
ejpam-7095	106	99	−	−	PROPN
ejpam-7095	106	100	x̄2|+	x̄2|+	PROPN
ejpam-7095	106	101	|τ1	|τ1	ADJ
ejpam-7095	106	102	−	−	PROPN
ejpam-7095	106	103	τ2||	τ2||	PROPN
ejpam-7095	106	104	)	)	PUNCT
ejpam-7095	106	105	,	,	PUNCT
ejpam-7095	106	106	(	(	PUNCT
ejpam-7095	106	107	h8	h8	PROPN
ejpam-7095	106	108	)	)	PUNCT
ejpam-7095	106	109	|f(x̄1	|f(x̄1	PROPN
ejpam-7095	106	110	,	,	PUNCT
ejpam-7095	106	111	τ1)−	τ1)−	NOUN
ejpam-7095	106	112	f(x̄2	f(x̄2	NOUN
ejpam-7095	106	113	,	,	PUNCT
ejpam-7095	106	114	τ2)|	τ2)|	NOUN
ejpam-7095	106	115	≤	≤	NUM
ejpam-7095	106	116	lf3	lf3	NOUN
ejpam-7095	106	117	(	(	PUNCT
ejpam-7095	106	118	|x̄1	|x̄1	NOUN
ejpam-7095	106	119	−	−	PROPN
ejpam-7095	106	120	x̄2|+	x̄2|+	PROPN
ejpam-7095	106	121	|τ1	|τ1	ADJ
ejpam-7095	106	122	−	−	PROPN
ejpam-7095	106	123	τ2||	τ2||	PROPN
ejpam-7095	106	124	)	)	PUNCT
ejpam-7095	106	125	,	,	PUNCT
ejpam-7095	106	126	(	(	PUNCT
ejpam-7095	106	127	h9	h9	NOUN
ejpam-7095	106	128	)	)	PUNCT
ejpam-7095	106	129	|g2(x̄1)−	|g2(x̄1)−	PART
ejpam-7095	106	130	g2(x̄2)|	g2(x̄2)|	NOUN
ejpam-7095	106	131	≤	≤	NUM
ejpam-7095	107	1	lg2	lg2	X
ejpam-7095	107	2	|x̄1	|x̄1	NOUN
ejpam-7095	107	3	−	−	PROPN
ejpam-7095	107	4	x̄2|	x̄2|	PROPN
ejpam-7095	107	5	≤	≤	PROPN
ejpam-7095	107	6	lg2δ1	lg2δ1	PROPN
ejpam-7095	107	7	,	,	PUNCT
ejpam-7095	107	8	(	(	PUNCT
ejpam-7095	107	9	h10	h10	NOUN
ejpam-7095	107	10	)	)	PUNCT
ejpam-7095	107	11	|g3(x̄1)−	|g3(x̄1)−	VERB
ejpam-7095	107	12	g3(x̄2)|	g3(x̄2)|	ADJ
ejpam-7095	107	13	≤	≤	NUM
ejpam-7095	107	14	lg3	lg3	NOUN
ejpam-7095	107	15	|x̄1	|x̄1	NOUN
ejpam-7095	107	16	−	−	PROPN
ejpam-7095	107	17	x̄2|	x̄2|	PROPN
ejpam-7095	107	18	≤	≤	PROPN
ejpam-7095	107	19	lg3δ1	lg3δ1	PROPN
ejpam-7095	107	20	,	,	PUNCT
ejpam-7095	107	21	where	where	SCONJ
ejpam-7095	107	22	ϵ1	ϵ1	ADJ
ejpam-7095	107	23	,	,	PUNCT
ejpam-7095	107	24	ϵ2	ϵ2	ADJ
ejpam-7095	107	25	,	,	PUNCT
ejpam-7095	107	26	ϵ3	ϵ3	PROPN
ejpam-7095	107	27	,	,	PUNCT
ejpam-7095	107	28	ϵ4	ϵ4	PROPN
ejpam-7095	107	29	,	,	PUNCT
ejpam-7095	107	30	ϵ5,lf1	ϵ5,lf1	PROPN
ejpam-7095	107	31	,	,	PUNCT
ejpam-7095	107	32	lf2	lf2	PROPN
ejpam-7095	107	33	,	,	PUNCT
ejpam-7095	107	34	lf3	lf3	NOUN
ejpam-7095	107	35	,	,	PUNCT
ejpam-7095	107	36	lg2	lg2	INTJ
ejpam-7095	107	37	,	,	PUNCT
ejpam-7095	107	38	lg3	lg3	VERB
ejpam-7095	107	39	>	>	X
ejpam-7095	107	40	0	0	NUM
ejpam-7095	107	41	are	be	AUX
ejpam-7095	107	42	constants	constant	NOUN
ejpam-7095	107	43	.	.	PUNCT
ejpam-7095	108	1	the	the	DET
ejpam-7095	108	2	problem	problem	NOUN
ejpam-7095	108	3	defined	define	VERB
ejpam-7095	108	4	by	by	ADP
ejpam-7095	108	5	eqs	eqs	PROPN
ejpam-7095	108	6	.	.	PUNCT
ejpam-7095	108	7	(	(	PUNCT
ejpam-7095	108	8	1)–(3	1)–(3	X
ejpam-7095	108	9	)	)	PUNCT
ejpam-7095	108	10	has	have	VERB
ejpam-7095	108	11	at	at	ADV
ejpam-7095	108	12	least	least	ADJ
ejpam-7095	108	13	one	one	NUM
ejpam-7095	108	14	solution	solution	NOUN
ejpam-7095	108	15	.	.	PUNCT
ejpam-7095	109	1	proof	proof	NOUN
ejpam-7095	109	2	.	.	PUNCT
ejpam-7095	110	1	the	the	DET
ejpam-7095	110	2	proof	proof	NOUN
ejpam-7095	110	3	proceeds	proceed	VERB
ejpam-7095	110	4	in	in	ADP
ejpam-7095	110	5	several	several	ADJ
ejpam-7095	110	6	steps	step	NOUN
ejpam-7095	110	7	.	.	PUNCT
ejpam-7095	111	1	we	we	PRON
ejpam-7095	111	2	apply	apply	VERB
ejpam-7095	111	3	the	the	DET
ejpam-7095	111	4	schaefer	schaefer	NOUN
ejpam-7095	111	5	fixed	fix	VERB
ejpam-7095	111	6	-	-	PUNCT
ejpam-7095	111	7	point	point	NOUN
ejpam-7095	111	8	theorem	theorem	NOUN
ejpam-7095	111	9	to	to	PART
ejpam-7095	111	10	establish	establish	VERB
ejpam-7095	111	11	the	the	DET
ejpam-7095	111	12	existence	existence	NOUN
ejpam-7095	111	13	of	of	ADP
ejpam-7095	111	14	a	a	DET
ejpam-7095	111	15	solution	solution	NOUN
ejpam-7095	111	16	.	.	PUNCT
ejpam-7095	112	1	step	step	NOUN
ejpam-7095	112	2	1	1	NUM
ejpam-7095	112	3	:	:	PUNCT
ejpam-7095	112	4	in	in	ADP
ejpam-7095	112	5	the	the	DET
ejpam-7095	112	6	first	first	ADJ
ejpam-7095	112	7	we	we	PRON
ejpam-7095	112	8	show	show	VERB
ejpam-7095	112	9	that	that	SCONJ
ejpam-7095	112	10	the	the	DET
ejpam-7095	112	11	operator	operator	NOUN
ejpam-7095	112	12	j	j	PROPN
ejpam-7095	112	13	is	be	AUX
ejpam-7095	112	14	continuous	continuous	ADJ
ejpam-7095	112	15	.	.	PUNCT
ejpam-7095	113	1	consider	consider	VERB
ejpam-7095	113	2	a	a	DET
ejpam-7095	113	3	sequence	sequence	NOUN
ejpam-7095	113	4	kamran	kamran	PROPN
ejpam-7095	113	5	et	et	PROPN
ejpam-7095	113	6	al	al	PROPN
ejpam-7095	113	7	.	.	PUNCT
ejpam-7095	113	8	/	/	SYM
ejpam-7095	113	9	eur	eur	PROPN
ejpam-7095	113	10	.	.	PUNCT
ejpam-7095	114	1	j.	j.	PROPN
ejpam-7095	114	2	pure	pure	PROPN
ejpam-7095	114	3	appl	appl	PROPN
ejpam-7095	114	4	.	.	PROPN
ejpam-7095	114	5	math	math	PROPN
ejpam-7095	114	6	,	,	PUNCT
ejpam-7095	114	7	18	18	NUM
ejpam-7095	114	8	(	(	PUNCT
ejpam-7095	114	9	4	4	NUM
ejpam-7095	114	10	)	)	PUNCT
ejpam-7095	114	11	(	(	PUNCT
ejpam-7095	114	12	2025	2025	NUM
ejpam-7095	114	13	)	)	PUNCT
ejpam-7095	114	14	,	,	PUNCT
ejpam-7095	114	15	7095	7095	NUM
ejpam-7095	114	16	6	6	NUM
ejpam-7095	114	17	of	of	ADP
ejpam-7095	114	18	30	30	NUM
ejpam-7095	114	19	um	um	INTJ
ejpam-7095	114	20	→	→	SYM
ejpam-7095	114	21	u	u	NOUN
ejpam-7095	114	22	in	in	ADP
ejpam-7095	114	23	b(ω	b(ω	ADV
ejpam-7095	114	24	,	,	PUNCT
ejpam-7095	114	25	r	r	NOUN
ejpam-7095	114	26	)	)	PUNCT
ejpam-7095	114	27	.	.	PUNCT
ejpam-7095	115	1	for	for	ADP
ejpam-7095	115	2	(	(	PUNCT
ejpam-7095	115	3	x̄	x̄	PROPN
ejpam-7095	115	4	,	,	PUNCT
ejpam-7095	115	5	τ	τ	PROPN
ejpam-7095	115	6	)	)	PUNCT
ejpam-7095	115	7	∈	∈	PROPN
ejpam-7095	115	8	ω	ω	PROPN
ejpam-7095	115	9	,	,	PUNCT
ejpam-7095	115	10	we	we	PRON
ejpam-7095	115	11	compute	compute	VERB
ejpam-7095	115	12	:	:	PUNCT
ejpam-7095	115	13	∥j	∥j	PROPN
ejpam-7095	115	14	um(x̄	um(x̄	PROPN
ejpam-7095	115	15	,	,	PUNCT
ejpam-7095	115	16	τ)−	τ)−	PROPN
ejpam-7095	115	17	j	j	PROPN
ejpam-7095	115	18	u(x̄	u(x̄	PROPN
ejpam-7095	115	19	,	,	PUNCT
ejpam-7095	115	20	τ)∥∞	τ)∥∞	NOUN
ejpam-7095	115	21	=	=	SYM
ejpam-7095	115	22	sup	sup	NOUN
ejpam-7095	115	23	(	(	PUNCT
ejpam-7095	115	24	x̄,τ)∈ω	x̄,τ)∈ω	PROPN
ejpam-7095	115	25	{	{	PUNCT
ejpam-7095	115	26	|j	|j	NOUN
ejpam-7095	115	27	um(x̄	um(x̄	PROPN
ejpam-7095	115	28	,	,	PUNCT
ejpam-7095	115	29	τ)−	τ)−	PROPN
ejpam-7095	115	30	j	j	PROPN
ejpam-7095	115	31	u(x̄	u(x̄	PROPN
ejpam-7095	115	32	,	,	PUNCT
ejpam-7095	115	33	τ)|	τ)|	ADV
ejpam-7095	115	34	}	}	PUNCT
ejpam-7095	115	35	=	=	PUNCT
ejpam-7095	115	36	sup	sup	NOUN
ejpam-7095	115	37	(	(	PUNCT
ejpam-7095	115	38	x̄,τ)∈ω	x̄,τ)∈ω	NUM
ejpam-7095	115	39	{	{	PUNCT
ejpam-7095	115	40	∣∣∣∣1−	∣∣∣∣1−	PROPN
ejpam-7095	115	41	α	α	PRON
ejpam-7095	115	42	β(α	β(α	PROPN
ejpam-7095	115	43	)	)	PUNCT
ejpam-7095	115	44	(	(	PUNCT
ejpam-7095	115	45	λ1∇2um(x̄	λ1∇2um(x̄	X
ejpam-7095	115	46	,	,	PUNCT
ejpam-7095	115	47	τ)−	τ)−	PROPN
ejpam-7095	115	48	λ2um(x̄	λ2um(x̄	PROPN
ejpam-7095	115	49	,	,	PUNCT
ejpam-7095	115	50	τ	τ	PROPN
ejpam-7095	115	51	)	)	PUNCT
ejpam-7095	115	52	)	)	PUNCT
ejpam-7095	116	1	+	+	CCONJ
ejpam-7095	116	2	α	α	PROPN
ejpam-7095	116	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	116	4	)	)	PUNCT
ejpam-7095	116	5	∫	∫	PROPN
ejpam-7095	117	1	τ	τ	PROPN
ejpam-7095	117	2	0	0	NUM
ejpam-7095	117	3	(	(	PUNCT
ejpam-7095	117	4	τ	τ	PROPN
ejpam-7095	117	5	−	−	PROPN
ejpam-7095	117	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	117	7	(	(	PUNCT
ejpam-7095	117	8	λ1∇2um(x̄	λ1∇2um(x̄	X
ejpam-7095	117	9	,	,	PUNCT
ejpam-7095	117	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	117	11	λ2um(x̄	λ2um(x̄	PROPN
ejpam-7095	117	12	,	,	PUNCT
ejpam-7095	117	13	ϑ	ϑ	NOUN
ejpam-7095	117	14	)	)	PUNCT
ejpam-7095	117	15	)	)	PUNCT
ejpam-7095	117	16	dϑ	dϑ	NOUN
ejpam-7095	117	17	−	−	PROPN
ejpam-7095	117	18	1−	1−	NUM
ejpam-7095	117	19	α	α	DET
ejpam-7095	117	20	β(α	β(α	PROPN
ejpam-7095	117	21	)	)	PUNCT
ejpam-7095	117	22	(	(	PUNCT
ejpam-7095	117	23	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	117	24	,	,	PUNCT
ejpam-7095	117	25	τ)−	τ)−	PROPN
ejpam-7095	117	26	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	117	27	,	,	PUNCT
ejpam-7095	117	28	τ	τ	X
ejpam-7095	117	29	)	)	PUNCT
ejpam-7095	117	30	)	)	PUNCT
ejpam-7095	118	1	−	−	PROPN
ejpam-7095	118	2	α	α	X
ejpam-7095	118	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	118	4	)	)	PUNCT
ejpam-7095	118	5	∫	∫	PROPN
ejpam-7095	119	1	τ	τ	PROPN
ejpam-7095	119	2	0	0	NUM
ejpam-7095	119	3	(	(	PUNCT
ejpam-7095	119	4	τ	τ	PROPN
ejpam-7095	119	5	−	−	PROPN
ejpam-7095	119	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	119	7	(	(	PUNCT
ejpam-7095	119	8	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	119	9	,	,	PUNCT
ejpam-7095	119	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	119	11	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	119	12	,	,	PUNCT
ejpam-7095	119	13	ϑ	ϑ	NOUN
ejpam-7095	119	14	)	)	PUNCT
ejpam-7095	119	15	)	)	PUNCT
ejpam-7095	119	16	dϑ	dϑ	ADP
ejpam-7095	119	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	119	18	}	}	PUNCT
ejpam-7095	119	19	≤	≤	NUM
ejpam-7095	119	20	sup	sup	NOUN
ejpam-7095	119	21	(	(	PUNCT
ejpam-7095	119	22	x̄,τ)∈ω	x̄,τ)∈ω	PROPN
ejpam-7095	119	23	{	{	PUNCT
ejpam-7095	119	24	1−	1−	NUM
ejpam-7095	119	25	α	α	PRON
ejpam-7095	119	26	β(α	β(α	PROPN
ejpam-7095	119	27	)	)	PUNCT
ejpam-7095	119	28	(	(	PUNCT
ejpam-7095	119	29	|λ1||∇2um(x̄	|λ1||∇2um(x̄	PROPN
ejpam-7095	119	30	,	,	PUNCT
ejpam-7095	119	31	τ)−∇2u(x̄	τ)−∇2u(x̄	ADV
ejpam-7095	119	32	,	,	PUNCT
ejpam-7095	119	33	τ)|+	τ)|+	NOUN
ejpam-7095	119	34	|λ2||um(x̄	|λ2||um(x̄	NUM
ejpam-7095	119	35	,	,	PUNCT
ejpam-7095	119	36	τ)−	τ)−	PROPN
ejpam-7095	119	37	u(x̄	u(x̄	NUM
ejpam-7095	119	38	,	,	PUNCT
ejpam-7095	119	39	τ)|	τ)|	PROPN
ejpam-7095	119	40	)	)	PUNCT
ejpam-7095	119	41	−	−	PROPN
ejpam-7095	120	1	α	α	X
ejpam-7095	120	2	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	120	3	)	)	PUNCT
ejpam-7095	120	4	∫	∫	PROPN
ejpam-7095	121	1	τ	τ	PROPN
ejpam-7095	121	2	0	0	NUM
ejpam-7095	121	3	(	(	PUNCT
ejpam-7095	121	4	τ	τ	PROPN
ejpam-7095	121	5	−	−	PROPN
ejpam-7095	121	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	121	7	(	(	PUNCT
ejpam-7095	121	8	|λ1||∇2um(x̄	|λ1||∇2um(x̄	X
ejpam-7095	121	9	,	,	PUNCT
ejpam-7095	121	10	ϑ)−∇2u(x̄	ϑ)−∇2u(x̄	ADJ
ejpam-7095	121	11	,	,	PUNCT
ejpam-7095	121	12	ϑ)|+	ϑ)|+	NOUN
ejpam-7095	121	13	|λ2||um(x̄	|λ2||um(x̄	NUM
ejpam-7095	121	14	,	,	PUNCT
ejpam-7095	121	15	ϑ)−	ϑ)−	PROPN
ejpam-7095	121	16	u(x̄	u(x̄	SYM
ejpam-7095	121	17	,	,	PUNCT
ejpam-7095	121	18	ϑ)|	ϑ)|	NOUN
ejpam-7095	121	19	)	)	PUNCT
ejpam-7095	121	20	dϑ.	dϑ.	NOUN
ejpam-7095	121	21	}	}	PUNCT
ejpam-7095	121	22	using	use	VERB
ejpam-7095	121	23	hypotheses	hypothesis	NOUN
ejpam-7095	121	24	h5	h5	NOUN
ejpam-7095	121	25	,	,	PUNCT
ejpam-7095	121	26	we	we	PRON
ejpam-7095	121	27	have	have	VERB
ejpam-7095	121	28	∥j	∥j	PROPN
ejpam-7095	121	29	um(x̄	um(x̄	PROPN
ejpam-7095	121	30	,	,	PUNCT
ejpam-7095	121	31	τ)−	τ)−	PROPN
ejpam-7095	121	32	j	j	PROPN
ejpam-7095	121	33	u(x̄	u(x̄	PROPN
ejpam-7095	121	34	,	,	PUNCT
ejpam-7095	121	35	τ)∥∞	τ)∥∞	ADJ
ejpam-7095	121	36	≤	≤	NUM
ejpam-7095	121	37	sup	sup	NOUN
ejpam-7095	121	38	(	(	PUNCT
ejpam-7095	121	39	x̄,τ)∈ω	x̄,τ)∈ω	PROPN
ejpam-7095	121	40	{	{	PUNCT
ejpam-7095	121	41	1−	1−	NUM
ejpam-7095	121	42	α	α	PRON
ejpam-7095	121	43	β(α	β(α	PROPN
ejpam-7095	121	44	)	)	PUNCT
ejpam-7095	121	45	(	(	PUNCT
ejpam-7095	121	46	|λ1|ϵ5|um(x̄	|λ1|ϵ5|um(x̄	PROPN
ejpam-7095	121	47	,	,	PUNCT
ejpam-7095	121	48	τ)−	τ)−	PROPN
ejpam-7095	121	49	u(x̄	u(x̄	NUM
ejpam-7095	121	50	,	,	PUNCT
ejpam-7095	121	51	τ)|+	τ)|+	NOUN
ejpam-7095	121	52	|λ2||um(x̄	|λ2||um(x̄	NUM
ejpam-7095	121	53	,	,	PUNCT
ejpam-7095	121	54	τ)−	τ)−	PROPN
ejpam-7095	121	55	u(x̄	u(x̄	NUM
ejpam-7095	121	56	,	,	PUNCT
ejpam-7095	121	57	τ)|	τ)|	PROPN
ejpam-7095	121	58	)	)	PUNCT
ejpam-7095	122	1	+	+	CCONJ
ejpam-7095	122	2	α	α	PROPN
ejpam-7095	122	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	122	4	)	)	PUNCT
ejpam-7095	122	5	∫	∫	PROPN
ejpam-7095	123	1	τ	τ	PROPN
ejpam-7095	123	2	0	0	NUM
ejpam-7095	123	3	(	(	PUNCT
ejpam-7095	123	4	τ	τ	PROPN
ejpam-7095	123	5	−	−	PROPN
ejpam-7095	123	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	123	7	(	(	PUNCT
ejpam-7095	123	8	ϵ5|λ1||um(x̄	ϵ5|λ1||um(x̄	PROPN
ejpam-7095	123	9	,	,	PUNCT
ejpam-7095	123	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	123	11	u(x̄	u(x̄	NOUN
ejpam-7095	123	12	,	,	PUNCT
ejpam-7095	123	13	ϑ)|+	ϑ)|+	ADV
ejpam-7095	123	14	|λ2||um(x̄	|λ2||um(x̄	NUM
ejpam-7095	123	15	,	,	PUNCT
ejpam-7095	123	16	ϑ)−	ϑ)−	PROPN
ejpam-7095	123	17	u(x̄	u(x̄	SYM
ejpam-7095	123	18	,	,	PUNCT
ejpam-7095	123	19	ϑ)|	ϑ)|	ADJ
ejpam-7095	123	20	)	)	PUNCT
ejpam-7095	123	21	dϑ	dϑ	NOUN
ejpam-7095	123	22	}	}	PUNCT
ejpam-7095	123	23	≤1−	≤1−	ADP
ejpam-7095	123	24	α	α	DET
ejpam-7095	123	25	β(α	β(α	PROPN
ejpam-7095	123	26	)	)	PUNCT
ejpam-7095	123	27	(	(	PUNCT
ejpam-7095	123	28	(	(	PUNCT
ejpam-7095	123	29	|λ1|ϵ5	|λ1|ϵ5	NOUN
ejpam-7095	123	30	+	+	X
ejpam-7095	123	31	|λ2|)∥um	|λ2|)∥um	PROPN
ejpam-7095	123	32	−	−	NUM
ejpam-7095	123	33	u∥∞	u∥∞	PROPN
ejpam-7095	123	34	)	)	PUNCT
ejpam-7095	124	1	+	+	CCONJ
ejpam-7095	124	2	α	α	PROPN
ejpam-7095	124	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	124	4	)	)	PUNCT
ejpam-7095	124	5	∫	∫	PROPN
ejpam-7095	125	1	τ	τ	PROPN
ejpam-7095	125	2	0	0	NUM
ejpam-7095	125	3	(	(	PUNCT
ejpam-7095	125	4	τ	τ	PROPN
ejpam-7095	125	5	−	−	PROPN
ejpam-7095	125	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	125	7	(	(	PUNCT
ejpam-7095	125	8	(	(	PUNCT
ejpam-7095	125	9	ϵ5|λ1|+	ϵ5|λ1|+	INTJ
ejpam-7095	125	10	|λ2|)∥um	|λ2|)∥um	PROPN
ejpam-7095	125	11	−	−	PROPN
ejpam-7095	125	12	u∥∞	u∥∞	PROPN
ejpam-7095	125	13	)	)	PUNCT
ejpam-7095	125	14	dϑ	dϑ	NOUN
ejpam-7095	125	15	=	=	SYM
ejpam-7095	125	16	1−	1−	NUM
ejpam-7095	125	17	α	α	DET
ejpam-7095	125	18	β(α	β(α	PROPN
ejpam-7095	125	19	)	)	PUNCT
ejpam-7095	125	20	(	(	PUNCT
ejpam-7095	125	21	(	(	PUNCT
ejpam-7095	125	22	|λ1|ϵ5	|λ1|ϵ5	NOUN
ejpam-7095	125	23	+	+	X
ejpam-7095	126	1	|λ2|)∥um	|λ2|)∥um	PROPN
ejpam-7095	126	2	−	−	NUM
ejpam-7095	126	3	u∥∞	u∥∞	PROPN
ejpam-7095	126	4	)	)	PUNCT
ejpam-7095	127	1	+	+	CCONJ
ejpam-7095	127	2	τα	τα	NOUN
ejpam-7095	127	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	127	4	)	)	PUNCT
ejpam-7095	127	5	(	(	PUNCT
ejpam-7095	127	6	(	(	PUNCT
ejpam-7095	127	7	ϵ5|λ1|+	ϵ5|λ1|+	INTJ
ejpam-7095	127	8	|λ2|)∥um	|λ2|)∥um	PROPN
ejpam-7095	127	9	−	−	NOUN
ejpam-7095	128	1	u∥∞	u∥∞	PROPN
ejpam-7095	128	2	)	)	PUNCT
ejpam-7095	129	1	=	=	SYM
ejpam-7095	129	2	(	(	PUNCT
ejpam-7095	129	3	1−	1−	NUM
ejpam-7095	129	4	α)γ(α	α)γ(α	NOUN
ejpam-7095	129	5	)	)	PUNCT
ejpam-7095	130	1	+	+	NUM
ejpam-7095	130	2	τα	τα	NOUN
ejpam-7095	130	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	130	4	)	)	PUNCT
ejpam-7095	130	5	(	(	PUNCT
ejpam-7095	130	6	(	(	PUNCT
ejpam-7095	130	7	|λ1|ϵ5	|λ1|ϵ5	NOUN
ejpam-7095	130	8	+	+	X
ejpam-7095	130	9	|λ2|)∥um	|λ2|)∥um	PROPN
ejpam-7095	130	10	−	−	NUM
ejpam-7095	130	11	u∥∞	u∥∞	PROPN
ejpam-7095	130	12	)	)	PUNCT
ejpam-7095	130	13	since	since	SCONJ
ejpam-7095	130	14	um	um	INTJ
ejpam-7095	130	15	→	→	SYM
ejpam-7095	130	16	u	u	NOUN
ejpam-7095	130	17	in	in	ADP
ejpam-7095	130	18	b(ω	b(ω	ADV
ejpam-7095	130	19	,	,	PUNCT
ejpam-7095	130	20	r	r	NOUN
ejpam-7095	130	21	)	)	PUNCT
ejpam-7095	130	22	,	,	PUNCT
ejpam-7095	130	23	we	we	PRON
ejpam-7095	130	24	have∥um	have∥um	PROPN
ejpam-7095	130	25	−	−	PROPN
ejpam-7095	130	26	u∥∞	u∥∞	PROPN
ejpam-7095	130	27	→	→	SYM
ejpam-7095	130	28	0	0	NUM
ejpam-7095	130	29	,	,	PUNCT
ejpam-7095	130	30	as	as	ADP
ejpam-7095	130	31	m	m	PROPN
ejpam-7095	130	32	→	→	SYM
ejpam-7095	130	33	∞.	∞.	PROPN
ejpam-7095	130	34	hence	hence	ADV
ejpam-7095	130	35	,	,	PUNCT
ejpam-7095	130	36	∥j	∥j	PROPN
ejpam-7095	130	37	um	um	INTJ
ejpam-7095	130	38	−	−	PROPN
ejpam-7095	131	1	j	j	PROPN
ejpam-7095	131	2	u∥∞	u∥∞	PROPN
ejpam-7095	131	3	→	→	SYM
ejpam-7095	131	4	0	0	NUM
ejpam-7095	131	5	,	,	PUNCT
ejpam-7095	131	6	proving	prove	VERB
ejpam-7095	131	7	that	that	SCONJ
ejpam-7095	131	8	j	j	PROPN
ejpam-7095	131	9	is	be	AUX
ejpam-7095	131	10	continuous	continuous	ADJ
ejpam-7095	131	11	.	.	PUNCT
ejpam-7095	132	1	step	step	NOUN
ejpam-7095	132	2	2	2	NUM
ejpam-7095	132	3	:	:	PUNCT
ejpam-7095	132	4	boundedness	boundedness	NOUN
ejpam-7095	132	5	of	of	ADP
ejpam-7095	132	6	j	j	PROPN
ejpam-7095	132	7	.	.	PUNCT
ejpam-7095	133	1	let	let	VERB
ejpam-7095	133	2	rγ	rγ	VERB
ejpam-7095	133	3	=	=	PUNCT
ejpam-7095	133	4	{	{	PUNCT
ejpam-7095	133	5	u	u	NOUN
ejpam-7095	133	6	∈	∈	PROPN
ejpam-7095	133	7	c(λ	c(λ	PROPN
ejpam-7095	133	8	,	,	PUNCT
ejpam-7095	133	9	r	r	NOUN
ejpam-7095	133	10	)	)	PUNCT
ejpam-7095	133	11	:	:	PUNCT
ejpam-7095	133	12	∥u∥∞	∥u∥∞	X
ejpam-7095	133	13	≤	≤	X
ejpam-7095	133	14	γ	γ	X
ejpam-7095	133	15	}	}	PUNCT
ejpam-7095	133	16	for	for	ADP
ejpam-7095	133	17	some	some	DET
ejpam-7095	133	18	γ	γ	X
ejpam-7095	133	19	>	>	X
ejpam-7095	133	20	0	0	NUM
ejpam-7095	133	21	.	.	PUNCT
ejpam-7095	134	1	for	for	ADP
ejpam-7095	134	2	u	u	PROPN
ejpam-7095	134	3	∈	∈	PROPN
ejpam-7095	134	4	rγ	rγ	NOUN
ejpam-7095	134	5	,	,	PUNCT
ejpam-7095	134	6	we	we	PRON
ejpam-7095	134	7	estimate	estimate	VERB
ejpam-7095	134	8	:	:	PUNCT
ejpam-7095	134	9	|j	|j	NOUN
ejpam-7095	134	10	u(x̄	u(x̄	VERB
ejpam-7095	134	11	,	,	PUNCT
ejpam-7095	134	12	τ)|	τ)|	PROPN
ejpam-7095	134	13	=	=	PUNCT
ejpam-7095	134	14	∣∣∣∣g2(x̄	∣∣∣∣g2(x̄	X
ejpam-7095	134	15	)	)	PUNCT
ejpam-7095	135	1	+	+	CCONJ
ejpam-7095	135	2	g3(x̄)τ	g3(x̄)τ	NOUN
ejpam-7095	135	3	+	+	CCONJ
ejpam-7095	135	4	1−	1−	NUM
ejpam-7095	135	5	α	α	DET
ejpam-7095	135	6	β(α	β(α	PROPN
ejpam-7095	135	7	)	)	PUNCT
ejpam-7095	135	8	(	(	PUNCT
ejpam-7095	135	9	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	135	10	,	,	PUNCT
ejpam-7095	135	11	τ)−	τ)−	PROPN
ejpam-7095	135	12	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	135	13	,	,	PUNCT
ejpam-7095	135	14	τ	τ	X
ejpam-7095	135	15	)	)	PUNCT
ejpam-7095	135	16	+	+	CCONJ
ejpam-7095	135	17	f(x̄	f(x̄	PROPN
ejpam-7095	135	18	,	,	PUNCT
ejpam-7095	135	19	τ	τ	X
ejpam-7095	135	20	)	)	PUNCT
ejpam-7095	135	21	)	)	PUNCT
ejpam-7095	136	1	+	+	CCONJ
ejpam-7095	136	2	α	α	PROPN
ejpam-7095	136	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	136	4	)	)	PUNCT
ejpam-7095	136	5	∫	∫	PROPN
ejpam-7095	137	1	τ	τ	PROPN
ejpam-7095	137	2	0	0	NUM
ejpam-7095	137	3	(	(	PUNCT
ejpam-7095	137	4	τ	τ	PROPN
ejpam-7095	137	5	−	−	PROPN
ejpam-7095	137	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	137	7	(	(	PUNCT
ejpam-7095	137	8	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	137	9	,	,	PUNCT
ejpam-7095	137	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	137	11	λ2u(x̄	λ2u(x̄	PROPN
ejpam-7095	137	12	,	,	PUNCT
ejpam-7095	137	13	ϑ	ϑ	NOUN
ejpam-7095	137	14	)	)	PUNCT
ejpam-7095	137	15	+	+	CCONJ
ejpam-7095	137	16	f(x̄	f(x̄	NOUN
ejpam-7095	137	17	,	,	PUNCT
ejpam-7095	137	18	ϑ	ϑ	NOUN
ejpam-7095	137	19	)	)	PUNCT
ejpam-7095	137	20	)	)	PUNCT
ejpam-7095	137	21	dϑ	dϑ	NOUN
ejpam-7095	137	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7095	137	23	≤|g2(x̄)|+	≤|g2(x̄)|+	VERB
ejpam-7095	137	24	|g3(x̄)|τ	|g3(x̄)|τ	PUNCT
ejpam-7095	138	1	+	+	CCONJ
ejpam-7095	138	2	1−	1−	NUM
ejpam-7095	138	3	α	α	DET
ejpam-7095	138	4	β(α	β(α	PROPN
ejpam-7095	138	5	)	)	PUNCT
ejpam-7095	138	6	(	(	PUNCT
ejpam-7095	138	7	|λ1||∇2u(x̄	|λ1||∇2u(x̄	X
ejpam-7095	138	8	,	,	PUNCT
ejpam-7095	138	9	τ)|+	τ)|+	NOUN
ejpam-7095	139	1	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	139	2	,	,	PUNCT
ejpam-7095	139	3	τ)|+	τ)|+	VERB
ejpam-7095	139	4	|f(x̄	|f(x̄	PRON
ejpam-7095	139	5	,	,	PUNCT
ejpam-7095	139	6	τ)|	τ)|	PROPN
ejpam-7095	139	7	)	)	PUNCT
ejpam-7095	140	1	+	+	CCONJ
ejpam-7095	140	2	α	α	PROPN
ejpam-7095	140	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	140	4	)	)	PUNCT
ejpam-7095	140	5	∫	∫	PROPN
ejpam-7095	141	1	τ	τ	PROPN
ejpam-7095	141	2	0	0	NUM
ejpam-7095	141	3	(	(	PUNCT
ejpam-7095	141	4	τ	τ	PROPN
ejpam-7095	141	5	−	−	PROPN
ejpam-7095	141	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	141	7	(	(	PUNCT
ejpam-7095	141	8	|λ1||∇2u(x̄	|λ1||∇2u(x̄	X
ejpam-7095	141	9	,	,	PUNCT
ejpam-7095	141	10	ϑ)|+	ϑ)|+	ADJ
ejpam-7095	141	11	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	141	12	,	,	PUNCT
ejpam-7095	141	13	ϑ)|+	ϑ)|+	ADV
ejpam-7095	141	14	|f(x̄	|f(x̄	PRON
ejpam-7095	141	15	,	,	PUNCT
ejpam-7095	141	16	ϑ)|	ϑ)|	ADJ
ejpam-7095	141	17	)	)	PUNCT
ejpam-7095	141	18	dϑ	dϑ	ADP
ejpam-7095	141	19	∣∣∣∣.	∣∣∣∣.	PROPN
ejpam-7095	141	20	using	use	VERB
ejpam-7095	141	21	h1	h1	PROPN
ejpam-7095	141	22	−h4	−h4	PROPN
ejpam-7095	141	23	,	,	PUNCT
ejpam-7095	141	24	we	we	PRON
ejpam-7095	141	25	have	have	VERB
ejpam-7095	141	26	kamran	kamran	PROPN
ejpam-7095	141	27	et	et	PROPN
ejpam-7095	141	28	al	al	PROPN
ejpam-7095	141	29	.	.	PUNCT
ejpam-7095	141	30	/	/	SYM
ejpam-7095	141	31	eur	eur	PROPN
ejpam-7095	141	32	.	.	PUNCT
ejpam-7095	142	1	j.	j.	PROPN
ejpam-7095	142	2	pure	pure	PROPN
ejpam-7095	142	3	appl	appl	PROPN
ejpam-7095	142	4	.	.	PROPN
ejpam-7095	142	5	math	math	PROPN
ejpam-7095	142	6	,	,	PUNCT
ejpam-7095	142	7	18	18	NUM
ejpam-7095	142	8	(	(	PUNCT
ejpam-7095	142	9	4	4	NUM
ejpam-7095	142	10	)	)	PUNCT
ejpam-7095	142	11	(	(	PUNCT
ejpam-7095	142	12	2025	2025	NUM
ejpam-7095	142	13	)	)	PUNCT
ejpam-7095	142	14	,	,	PUNCT
ejpam-7095	142	15	7095	7095	NUM
ejpam-7095	142	16	7	7	NUM
ejpam-7095	142	17	of	of	ADP
ejpam-7095	142	18	30	30	NUM
ejpam-7095	142	19	|j	|j	NOUN
ejpam-7095	142	20	u(x̄	u(x̄	NUM
ejpam-7095	142	21	,	,	PUNCT
ejpam-7095	142	22	τ)|	τ)|	PROPN
ejpam-7095	142	23	≤	≤	PUNCT
ejpam-7095	142	24	ϵ2	ϵ2	VERB
ejpam-7095	142	25	+	+	CCONJ
ejpam-7095	142	26	τϵ3	τϵ3	NOUN
ejpam-7095	143	1	+	+	SYM
ejpam-7095	143	2	1−	1−	NUM
ejpam-7095	143	3	α	α	DET
ejpam-7095	143	4	β(α	β(α	PROPN
ejpam-7095	143	5	)	)	PUNCT
ejpam-7095	143	6	(	(	PUNCT
ejpam-7095	143	7	|λ1|ϵ1|u(x̄	|λ1|ϵ1|u(x̄	X
ejpam-7095	143	8	,	,	PUNCT
ejpam-7095	143	9	τ)|+	τ)|+	NOUN
ejpam-7095	143	10	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	143	11	,	,	PUNCT
ejpam-7095	143	12	τ)|+	τ)|+	NOUN
ejpam-7095	143	13	ϵ4	ϵ4	NOUN
ejpam-7095	143	14	)	)	PUNCT
ejpam-7095	144	1	+	+	CCONJ
ejpam-7095	144	2	α	α	PROPN
ejpam-7095	144	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	144	4	)	)	PUNCT
ejpam-7095	144	5	∫	∫	PROPN
ejpam-7095	145	1	τ	τ	PROPN
ejpam-7095	145	2	0	0	NUM
ejpam-7095	145	3	(	(	PUNCT
ejpam-7095	145	4	τ	τ	PROPN
ejpam-7095	145	5	−	−	PROPN
ejpam-7095	145	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	145	7	(	(	PUNCT
ejpam-7095	145	8	|λ1|ϵ1|u(x̄	|λ1|ϵ1|u(x̄	X
ejpam-7095	145	9	,	,	PUNCT
ejpam-7095	145	10	ϑ)|+	ϑ)|+	PROPN
ejpam-7095	145	11	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	145	12	,	,	PUNCT
ejpam-7095	145	13	ϑ)|+	ϑ)|+	ADJ
ejpam-7095	145	14	ϵ4	ϵ4	PROPN
ejpam-7095	145	15	)	)	PUNCT
ejpam-7095	145	16	dϑ	dϑ	NOUN
ejpam-7095	145	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	145	18	or	or	CCONJ
ejpam-7095	145	19	∥j	∥j	ADJ
ejpam-7095	145	20	u∥∞	u∥∞	NUM
ejpam-7095	145	21	≤ϵ2	≤ϵ2	ADJ
ejpam-7095	145	22	+	+	NOUN
ejpam-7095	145	23	τϵ3	τϵ3	PROPN
ejpam-7095	146	1	+	+	CCONJ
ejpam-7095	146	2	1−	1−	NUM
ejpam-7095	146	3	α	α	DET
ejpam-7095	146	4	β(α	β(α	PROPN
ejpam-7095	146	5	)	)	PUNCT
ejpam-7095	146	6	(	(	PUNCT
ejpam-7095	146	7	|λ1|ϵ1∥u∥∞	|λ1|ϵ1∥u∥∞	X
ejpam-7095	146	8	+	+	CCONJ
ejpam-7095	146	9	|λ2|∥u∥∞	|λ2|∥u∥∞	PROPN
ejpam-7095	146	10	+	+	CCONJ
ejpam-7095	146	11	ϵ4	ϵ4	PROPN
ejpam-7095	146	12	)	)	PUNCT
ejpam-7095	147	1	+	+	CCONJ
ejpam-7095	147	2	α	α	PROPN
ejpam-7095	147	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	147	4	)	)	PUNCT
ejpam-7095	147	5	∫	∫	PROPN
ejpam-7095	148	1	τ	τ	PROPN
ejpam-7095	148	2	0	0	NUM
ejpam-7095	148	3	(	(	PUNCT
ejpam-7095	148	4	τ	τ	PROPN
ejpam-7095	148	5	−	−	PROPN
ejpam-7095	148	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	148	7	(	(	PUNCT
ejpam-7095	148	8	|λ1|ϵ1∥u∥∞	|λ1|ϵ1∥u∥∞	X
ejpam-7095	148	9	+	+	NUM
ejpam-7095	148	10	|λ2|∥u∥∞	|λ2|∥u∥∞	PROPN
ejpam-7095	148	11	+	+	CCONJ
ejpam-7095	148	12	ϵ4	ϵ4	PROPN
ejpam-7095	148	13	)	)	PUNCT
ejpam-7095	148	14	dϑ	dϑ	NOUN
ejpam-7095	148	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	148	16	=	=	PUNCT
ejpam-7095	148	17	ϵ2	ϵ2	PROPN
ejpam-7095	149	1	+	+	CCONJ
ejpam-7095	149	2	τϵ3	τϵ3	NOUN
ejpam-7095	150	1	+	+	CCONJ
ejpam-7095	150	2	γ(α)(1−	γ(α)(1−	NUM
ejpam-7095	150	3	α	α	X
ejpam-7095	150	4	)	)	PUNCT
ejpam-7095	150	5	+	+	NUM
ejpam-7095	150	6	τα	τα	NOUN
ejpam-7095	150	7	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	150	8	)	)	PUNCT
ejpam-7095	150	9	(	(	PUNCT
ejpam-7095	150	10	|λ1|ϵ1∥u∥∞	|λ1|ϵ1∥u∥∞	X
ejpam-7095	150	11	+	+	CCONJ
ejpam-7095	150	12	|λ2|∥u∥∞	|λ2|∥u∥∞	PROPN
ejpam-7095	150	13	+	+	CCONJ
ejpam-7095	150	14	ϵ4	ϵ4	PROPN
ejpam-7095	150	15	)	)	PUNCT
ejpam-7095	150	16	≤	≤	PUNCT
ejpam-7095	151	1	ϵ2	ϵ2	VERB
ejpam-7095	152	1	+	+	CCONJ
ejpam-7095	152	2	τϵ3	τϵ3	NOUN
ejpam-7095	153	1	+	+	CCONJ
ejpam-7095	153	2	γ(α)(1−	γ(α)(1−	NUM
ejpam-7095	153	3	α	α	X
ejpam-7095	153	4	)	)	PUNCT
ejpam-7095	153	5	+	+	NUM
ejpam-7095	153	6	τα	τα	NOUN
ejpam-7095	153	7	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	153	8	)	)	PUNCT
ejpam-7095	153	9	(	(	PUNCT
ejpam-7095	153	10	|λ1|ϵ1γ	|λ1|ϵ1γ	NOUN
ejpam-7095	153	11	+	+	NUM
ejpam-7095	153	12	|λ2|γ	|λ2|γ	NOUN
ejpam-7095	153	13	+	+	X
ejpam-7095	153	14	ϵ4	ϵ4	NOUN
ejpam-7095	153	15	)	)	PUNCT
ejpam-7095	153	16	,	,	PUNCT
ejpam-7095	153	17	since	since	SCONJ
ejpam-7095	153	18	τ	τ	PROPN
ejpam-7095	153	19	∈	∈	PROPN
ejpam-7095	154	1	[	[	X
ejpam-7095	154	2	0	0	NUM
ejpam-7095	154	3	,	,	PUNCT
ejpam-7095	154	4	1	1	NUM
ejpam-7095	154	5	]	]	PUNCT
ejpam-7095	154	6	,	,	PUNCT
ejpam-7095	154	7	we	we	PRON
ejpam-7095	154	8	have	have	VERB
ejpam-7095	154	9	∥j	∥j	PROPN
ejpam-7095	154	10	≤	≤	NUM
ejpam-7095	154	11	u∥∞	u∥∞	PROPN
ejpam-7095	154	12	≤	≤	PROPN
ejpam-7095	154	13	ϵ2	ϵ2	PROPN
ejpam-7095	154	14	+	+	CCONJ
ejpam-7095	154	15	ϵ3	ϵ3	NUM
ejpam-7095	154	16	+	+	CCONJ
ejpam-7095	154	17	γ(α)(1−	γ(α)(1−	NUM
ejpam-7095	154	18	α	α	X
ejpam-7095	154	19	)	)	PUNCT
ejpam-7095	154	20	+	+	CCONJ
ejpam-7095	154	21	1	1	NUM
ejpam-7095	154	22	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	154	23	)	)	PUNCT
ejpam-7095	154	24	(	(	PUNCT
ejpam-7095	154	25	|λ1|ϵ1γ	|λ1|ϵ1γ	NOUN
ejpam-7095	154	26	+	+	NUM
ejpam-7095	154	27	|λ2|γ	|λ2|γ	NOUN
ejpam-7095	154	28	+	+	X
ejpam-7095	154	29	ϵ4	ϵ4	NOUN
ejpam-7095	154	30	)	)	PUNCT
ejpam-7095	155	1	=	=	NOUN
ejpam-7095	155	2	:	:	PUNCT
ejpam-7095	155	3	ρab	ρab	NOUN
ejpam-7095	155	4	,	,	PUNCT
ejpam-7095	155	5	where	where	SCONJ
ejpam-7095	155	6	ρab	ρab	NOUN
ejpam-7095	155	7	is	be	AUX
ejpam-7095	155	8	a	a	DET
ejpam-7095	155	9	constant	constant	ADJ
ejpam-7095	155	10	independent	independent	NOUN
ejpam-7095	155	11	of	of	ADP
ejpam-7095	155	12	u.	u.	PROPN
ejpam-7095	155	13	thus	thus	ADV
ejpam-7095	155	14	,	,	PUNCT
ejpam-7095	155	15	j	j	PROPN
ejpam-7095	155	16	is	be	AUX
ejpam-7095	155	17	bounded	bound	VERB
ejpam-7095	155	18	.	.	PUNCT
ejpam-7095	156	1	step	step	NOUN
ejpam-7095	156	2	3	3	NUM
ejpam-7095	156	3	:	:	PUNCT
ejpam-7095	156	4	equicontinuity	equicontinuity	NOUN
ejpam-7095	156	5	of	of	ADP
ejpam-7095	156	6	j	j	PROPN
ejpam-7095	156	7	.	.	PUNCT
ejpam-7095	157	1	let	let	VERB
ejpam-7095	157	2	u	u	PRON
ejpam-7095	157	3	∈	∈	PROPN
ejpam-7095	157	4	rγ	rγ	PROPN
ejpam-7095	157	5	and	and	CCONJ
ejpam-7095	157	6	(	(	PUNCT
ejpam-7095	157	7	x̄1	x̄1	NOUN
ejpam-7095	157	8	,	,	PUNCT
ejpam-7095	157	9	τ1	τ1	NOUN
ejpam-7095	157	10	)	)	PUNCT
ejpam-7095	157	11	,	,	PUNCT
ejpam-7095	157	12	(	(	PUNCT
ejpam-7095	157	13	x̄2	x̄2	X
ejpam-7095	157	14	,	,	PUNCT
ejpam-7095	157	15	τ2	τ2	ADJ
ejpam-7095	157	16	)	)	PUNCT
ejpam-7095	157	17	∈	∈	PROPN
ejpam-7095	157	18	ω	ω	PROPN
ejpam-7095	157	19	with	with	ADP
ejpam-7095	157	20	∥x̄1−x̄2∥	∥x̄1−x̄2∥	ADP
ejpam-7095	157	21	<	<	X
ejpam-7095	157	22	δ1	δ1	NOUN
ejpam-7095	157	23	and	and	CCONJ
ejpam-7095	157	24	|τ1	|τ1	ADJ
ejpam-7095	157	25	−	−	PROPN
ejpam-7095	158	1	τ2|	τ2|	PUNCT
ejpam-7095	159	1	<	<	X
ejpam-7095	159	2	δ2	δ2	X
ejpam-7095	159	3	.	.	PUNCT
ejpam-7095	160	1	we	we	PRON
ejpam-7095	160	2	analyze	analyze	VERB
ejpam-7095	160	3	:	:	PUNCT
ejpam-7095	160	4	|j	|j	NOUN
ejpam-7095	160	5	u(x̄1	u(x̄1	NOUN
ejpam-7095	160	6	,	,	PUNCT
ejpam-7095	160	7	τ1)−	τ1)−	PROPN
ejpam-7095	160	8	j	j	PROPN
ejpam-7095	160	9	u(x̄2	u(x̄2	NOUN
ejpam-7095	160	10	,	,	PUNCT
ejpam-7095	160	11	τ2)|	τ2)|	PROPN
ejpam-7095	160	12	≤	≤	PROPN
ejpam-7095	160	13	|g2(x̄1)−	|g2(x̄1)−	PROPN
ejpam-7095	160	14	g2(x̄2)|+	g2(x̄2)|+	PROPN
ejpam-7095	160	15	|g3(x̄1)−	|g3(x̄1)−	VERB
ejpam-7095	160	16	g3(x̄2)|τ1	g3(x̄2)|τ1	VERB
ejpam-7095	160	17	+	+	CCONJ
ejpam-7095	160	18	|g3(x̄2)||τ1	|g3(x̄2)||τ1	NOUN
ejpam-7095	160	19	−	−	NOUN
ejpam-7095	160	20	τ2|	τ2|	PUNCT
ejpam-7095	161	1	+	+	NUM
ejpam-7095	161	2	1−	1−	NUM
ejpam-7095	161	3	α	α	DET
ejpam-7095	161	4	β(α	β(α	PROPN
ejpam-7095	161	5	)	)	PUNCT
ejpam-7095	161	6	∣∣∣∣λ1∇2u(x̄1	∣∣∣∣λ1∇2u(x̄1	NOUN
ejpam-7095	161	7	,	,	PUNCT
ejpam-7095	161	8	τ1)−	τ1)−	NOUN
ejpam-7095	161	9	λ1∇2u(x̄2	λ1∇2u(x̄2	PROPN
ejpam-7095	161	10	,	,	PUNCT
ejpam-7095	161	11	τ2	τ2	NOUN
ejpam-7095	161	12	)	)	PUNCT
ejpam-7095	162	1	+	+	CCONJ
ejpam-7095	162	2	λ2u(x̄2	λ2u(x̄2	PROPN
ejpam-7095	162	3	,	,	PUNCT
ejpam-7095	162	4	τ2)−	τ2)−	X
ejpam-7095	162	5	λ2u(x̄1	λ2u(x̄1	PROPN
ejpam-7095	162	6	,	,	PUNCT
ejpam-7095	162	7	τ1	τ1	NOUN
ejpam-7095	162	8	)	)	PUNCT
ejpam-7095	162	9	+	+	NUM
ejpam-7095	162	10	f(x̄1	f(x̄1	NOUN
ejpam-7095	162	11	,	,	PUNCT
ejpam-7095	162	12	τ1)−	τ1)−	NOUN
ejpam-7095	162	13	f(x̄2	f(x̄2	NOUN
ejpam-7095	162	14	,	,	PUNCT
ejpam-7095	162	15	τ2	τ2	NOUN
ejpam-7095	162	16	)	)	PUNCT
ejpam-7095	162	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	162	18	+	+	NUM
ejpam-7095	162	19	α	α	PROPN
ejpam-7095	162	20	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	162	21	)	)	PUNCT
ejpam-7095	162	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	162	23	∫	∫	PROPN
ejpam-7095	162	24	τ1	τ1	PROPN
ejpam-7095	162	25	0	0	NUM
ejpam-7095	162	26	(	(	PUNCT
ejpam-7095	162	27	τ1	τ1	NOUN
ejpam-7095	162	28	−	−	NOUN
ejpam-7095	162	29	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	162	30	(	(	PUNCT
ejpam-7095	162	31	λ1∇2u(x̄1	λ1∇2u(x̄1	NOUN
ejpam-7095	162	32	,	,	PUNCT
ejpam-7095	162	33	ϑ)−	ϑ)−	PROPN
ejpam-7095	162	34	λ2u(x̄1	λ2u(x̄1	PROPN
ejpam-7095	162	35	,	,	PUNCT
ejpam-7095	162	36	ϑ	ϑ	NOUN
ejpam-7095	162	37	)	)	PUNCT
ejpam-7095	162	38	+	+	NUM
ejpam-7095	162	39	f(x̄1	f(x̄1	NOUN
ejpam-7095	162	40	,	,	PUNCT
ejpam-7095	162	41	ϑ	ϑ	NOUN
ejpam-7095	162	42	)	)	PUNCT
ejpam-7095	162	43	)	)	PUNCT
ejpam-7095	162	44	dϑ	dϑ	NOUN
ejpam-7095	162	45	−	−	PROPN
ejpam-7095	162	46	∫	∫	PROPN
ejpam-7095	163	1	τ2	τ2	NOUN
ejpam-7095	163	2	0	0	NUM
ejpam-7095	163	3	(	(	PUNCT
ejpam-7095	163	4	τ2	τ2	NOUN
ejpam-7095	163	5	−	−	NOUN
ejpam-7095	163	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	163	7	(	(	PUNCT
ejpam-7095	163	8	λ1∇2u(x̄2	λ1∇2u(x̄2	PROPN
ejpam-7095	163	9	,	,	PUNCT
ejpam-7095	163	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	163	11	λ2u(x̄2	λ2u(x̄2	PROPN
ejpam-7095	163	12	,	,	PUNCT
ejpam-7095	163	13	ϑ	ϑ	NOUN
ejpam-7095	163	14	)	)	PUNCT
ejpam-7095	163	15	+	+	NUM
ejpam-7095	163	16	f(x̄2	f(x̄2	NOUN
ejpam-7095	163	17	,	,	PUNCT
ejpam-7095	163	18	ϑ	ϑ	NOUN
ejpam-7095	163	19	)	)	PUNCT
ejpam-7095	163	20	)	)	PUNCT
ejpam-7095	163	21	dϑ	dϑ	NOUN
ejpam-7095	163	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	163	23	using	use	VERB
ejpam-7095	163	24	h3	h3	NOUN
ejpam-7095	163	25	and	and	CCONJ
ejpam-7095	163	26	h6	h6	PROPN
ejpam-7095	163	27	−h10	−h10	NUM
ejpam-7095	163	28	,	,	PUNCT
ejpam-7095	163	29	we	we	PRON
ejpam-7095	163	30	have	have	VERB
ejpam-7095	163	31	|j	|j	ADJ
ejpam-7095	163	32	u(x̄1	u(x̄1	NOUN
ejpam-7095	163	33	,	,	PUNCT
ejpam-7095	163	34	τ1)−	τ1)−	PROPN
ejpam-7095	163	35	j	j	PROPN
ejpam-7095	163	36	u(x̄2	u(x̄2	NOUN
ejpam-7095	163	37	,	,	PUNCT
ejpam-7095	163	38	τ2)|	τ2)|	PROPN
ejpam-7095	163	39	≤	≤	PUNCT
ejpam-7095	164	1	lg2δ1	lg2δ1	PUNCT
ejpam-7095	164	2	+	+	PUNCT
ejpam-7095	164	3	lg3δ1	lg3δ1	PROPN
ejpam-7095	164	4	+	+	SYM
ejpam-7095	164	5	ϵ3δ2	ϵ3δ2	NUM
ejpam-7095	164	6	+	+	NUM
ejpam-7095	164	7	1−	1−	NUM
ejpam-7095	164	8	α	α	PRON
ejpam-7095	164	9	β(α	β(α	PROPN
ejpam-7095	164	10	)	)	PUNCT
ejpam-7095	164	11	(	(	PUNCT
ejpam-7095	164	12	|λ1|lf1	|λ1|lf1	PROPN
ejpam-7095	164	13	(	(	PUNCT
ejpam-7095	164	14	|x̄1	|x̄1	NOUN
ejpam-7095	164	15	−	−	PROPN
ejpam-7095	164	16	x̄2|+	x̄2|+	PROPN
ejpam-7095	164	17	|τ1	|τ1	ADJ
ejpam-7095	164	18	−	−	PROPN
ejpam-7095	164	19	τ2||	τ2||	PROPN
ejpam-7095	164	20	)	)	PUNCT
ejpam-7095	165	1	+	+	CCONJ
ejpam-7095	165	2	|λ2|lf2	|λ2|lf2	PROPN
ejpam-7095	165	3	(	(	PUNCT
ejpam-7095	165	4	|x̄1	|x̄1	NOUN
ejpam-7095	165	5	−	−	PROPN
ejpam-7095	165	6	x̄2|	x̄2|	PROPN
ejpam-7095	166	1	+	+	PROPN
ejpam-7095	166	2	|τ1	|τ1	ADJ
ejpam-7095	166	3	−	−	ADP
ejpam-7095	166	4	τ2||	τ2||	NOUN
ejpam-7095	166	5	)	)	PUNCT
ejpam-7095	167	1	+	+	CCONJ
ejpam-7095	167	2	lf3	lf3	NOUN
ejpam-7095	167	3	(	(	PUNCT
ejpam-7095	167	4	|x̄1	|x̄1	NOUN
ejpam-7095	167	5	−	−	PROPN
ejpam-7095	167	6	x̄2|+	x̄2|+	PROPN
ejpam-7095	167	7	|τ1	|τ1	ADJ
ejpam-7095	167	8	−	−	PROPN
ejpam-7095	167	9	τ2||	τ2||	NOUN
ejpam-7095	167	10	)	)	PUNCT
ejpam-7095	167	11	)	)	PUNCT
ejpam-7095	168	1	+	+	CCONJ
ejpam-7095	168	2	α	α	PROPN
ejpam-7095	168	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	168	4	)	)	PUNCT
ejpam-7095	168	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	168	6	∫	∫	PROPN
ejpam-7095	168	7	τ1	τ1	PROPN
ejpam-7095	168	8	0	0	NUM
ejpam-7095	168	9	(	(	PUNCT
ejpam-7095	168	10	τ1	τ1	NOUN
ejpam-7095	168	11	−	−	NOUN
ejpam-7095	168	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	168	13	(	(	PUNCT
ejpam-7095	168	14	λ1∇2u(x̄1	λ1∇2u(x̄1	NOUN
ejpam-7095	168	15	,	,	PUNCT
ejpam-7095	168	16	ϑ)−	ϑ)−	PROPN
ejpam-7095	168	17	λ2u(x̄1	λ2u(x̄1	PROPN
ejpam-7095	168	18	,	,	PUNCT
ejpam-7095	168	19	ϑ	ϑ	NOUN
ejpam-7095	168	20	)	)	PUNCT
ejpam-7095	168	21	+	+	NUM
ejpam-7095	168	22	f(x̄1	f(x̄1	NOUN
ejpam-7095	168	23	,	,	PUNCT
ejpam-7095	168	24	ϑ	ϑ	NOUN
ejpam-7095	168	25	)	)	PUNCT
ejpam-7095	168	26	)	)	PUNCT
ejpam-7095	168	27	dϑ	dϑ	NOUN
ejpam-7095	168	28	−	−	PROPN
ejpam-7095	168	29	∫	∫	PROPN
ejpam-7095	169	1	τ2	τ2	NOUN
ejpam-7095	169	2	0	0	NUM
ejpam-7095	169	3	(	(	PUNCT
ejpam-7095	169	4	τ2	τ2	NOUN
ejpam-7095	169	5	−	−	NOUN
ejpam-7095	169	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	169	7	(	(	PUNCT
ejpam-7095	169	8	λ1∇2u(x̄2	λ1∇2u(x̄2	PROPN
ejpam-7095	169	9	,	,	PUNCT
ejpam-7095	169	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	169	11	λ2u(x̄2	λ2u(x̄2	PROPN
ejpam-7095	169	12	,	,	PUNCT
ejpam-7095	169	13	ϑ	ϑ	NOUN
ejpam-7095	169	14	)	)	PUNCT
ejpam-7095	169	15	+	+	NUM
ejpam-7095	169	16	f(x̄2	f(x̄2	NOUN
ejpam-7095	169	17	,	,	PUNCT
ejpam-7095	169	18	ϑ	ϑ	NOUN
ejpam-7095	169	19	)	)	PUNCT
ejpam-7095	169	20	)	)	PUNCT
ejpam-7095	169	21	dϑ	dϑ	PROPN
ejpam-7095	169	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7095	169	23	,	,	PUNCT
ejpam-7095	169	24	kamran	kamran	PROPN
ejpam-7095	169	25	et	et	PROPN
ejpam-7095	169	26	al	al	PROPN
ejpam-7095	169	27	.	.	PUNCT
ejpam-7095	169	28	/	/	SYM
ejpam-7095	169	29	eur	eur	PROPN
ejpam-7095	169	30	.	.	PUNCT
ejpam-7095	170	1	j.	j.	PROPN
ejpam-7095	170	2	pure	pure	PROPN
ejpam-7095	170	3	appl	appl	PROPN
ejpam-7095	170	4	.	.	PROPN
ejpam-7095	170	5	math	math	PROPN
ejpam-7095	170	6	,	,	PUNCT
ejpam-7095	170	7	18	18	NUM
ejpam-7095	170	8	(	(	PUNCT
ejpam-7095	170	9	4	4	NUM
ejpam-7095	170	10	)	)	PUNCT
ejpam-7095	170	11	(	(	PUNCT
ejpam-7095	170	12	2025	2025	NUM
ejpam-7095	170	13	)	)	PUNCT
ejpam-7095	170	14	,	,	PUNCT
ejpam-7095	170	15	7095	7095	NUM
ejpam-7095	170	16	8	8	NUM
ejpam-7095	170	17	of	of	ADP
ejpam-7095	170	18	30	30	NUM
ejpam-7095	170	19	next	next	ADV
ejpam-7095	171	1	,	,	PUNCT
ejpam-7095	171	2	we	we	PRON
ejpam-7095	171	3	split	split	VERB
ejpam-7095	171	4	the	the	DET
ejpam-7095	171	5	difference	difference	NOUN
ejpam-7095	171	6	of	of	ADP
ejpam-7095	171	7	integrals	integral	NOUN
ejpam-7095	171	8	into	into	ADP
ejpam-7095	171	9	three	three	NUM
ejpam-7095	171	10	parts	part	NOUN
ejpam-7095	171	11	as	as	ADP
ejpam-7095	171	12	follows:∣∣∣∣	follows:∣∣∣∣	PROPN
ejpam-7095	171	13	∫	∫	PROPN
ejpam-7095	171	14	τ1	τ1	PROPN
ejpam-7095	171	15	0	0	NUM
ejpam-7095	172	1	(	(	PUNCT
ejpam-7095	172	2	τ1	τ1	NOUN
ejpam-7095	172	3	−	−	NOUN
ejpam-7095	172	4	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	172	5	(	(	PUNCT
ejpam-7095	172	6	λ1∇2u(x̄1	λ1∇2u(x̄1	NOUN
ejpam-7095	172	7	,	,	PUNCT
ejpam-7095	172	8	ϑ)−	ϑ)−	PROPN
ejpam-7095	172	9	λ2u(x̄1	λ2u(x̄1	PROPN
ejpam-7095	172	10	,	,	PUNCT
ejpam-7095	172	11	ϑ	ϑ	NOUN
ejpam-7095	172	12	)	)	PUNCT
ejpam-7095	173	1	+	+	NUM
ejpam-7095	173	2	f(x̄1	f(x̄1	NOUN
ejpam-7095	173	3	,	,	PUNCT
ejpam-7095	173	4	ϑ	ϑ	NOUN
ejpam-7095	173	5	)	)	PUNCT
ejpam-7095	173	6	)	)	PUNCT
ejpam-7095	173	7	dϑ	dϑ	NOUN
ejpam-7095	173	8	−	−	PROPN
ejpam-7095	173	9	∫	∫	PROPN
ejpam-7095	174	1	τ2	τ2	NOUN
ejpam-7095	174	2	0	0	NUM
ejpam-7095	174	3	(	(	PUNCT
ejpam-7095	174	4	τ2	τ2	NOUN
ejpam-7095	174	5	−	−	NOUN
ejpam-7095	174	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	174	7	(	(	PUNCT
ejpam-7095	174	8	λ1∇2u(x̄2	λ1∇2u(x̄2	PROPN
ejpam-7095	174	9	,	,	PUNCT
ejpam-7095	174	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	174	11	λ2u(x̄2	λ2u(x̄2	PROPN
ejpam-7095	174	12	,	,	PUNCT
ejpam-7095	174	13	ϑ	ϑ	NOUN
ejpam-7095	174	14	)	)	PUNCT
ejpam-7095	174	15	+	+	NUM
ejpam-7095	174	16	f(x̄2	f(x̄2	NOUN
ejpam-7095	174	17	,	,	PUNCT
ejpam-7095	174	18	ϑ	ϑ	NOUN
ejpam-7095	174	19	)	)	PUNCT
ejpam-7095	174	20	)	)	PUNCT
ejpam-7095	174	21	dϑ	dϑ	NOUN
ejpam-7095	174	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	175	1	=	=	PUNCT
ejpam-7095	175	2	[	[	PUNCT
ejpam-7095	175	3	∫	∫	PROPN
ejpam-7095	175	4	τ1	τ1	NOUN
ejpam-7095	175	5	0	0	NUM
ejpam-7095	175	6	[	[	PUNCT
ejpam-7095	175	7	(	(	PUNCT
ejpam-7095	175	8	τ1	τ1	NOUN
ejpam-7095	175	9	−	−	NOUN
ejpam-7095	175	10	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	175	11	−	−	PROPN
ejpam-7095	175	12	(	(	PUNCT
ejpam-7095	175	13	τ2	τ2	NOUN
ejpam-7095	175	14	−	−	NOUN
ejpam-7095	175	15	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	175	16	]	]	PUNCT
ejpam-7095	175	17	(	(	PUNCT
ejpam-7095	175	18	λ1∇2u(x̄1	λ1∇2u(x̄1	NOUN
ejpam-7095	175	19	,	,	PUNCT
ejpam-7095	175	20	ϑ)−	ϑ)−	PROPN
ejpam-7095	175	21	λ2u(x̄1	λ2u(x̄1	PROPN
ejpam-7095	175	22	,	,	PUNCT
ejpam-7095	175	23	ϑ	ϑ	NOUN
ejpam-7095	175	24	)	)	PUNCT
ejpam-7095	175	25	+	+	NUM
ejpam-7095	175	26	f(x̄1	f(x̄1	NOUN
ejpam-7095	175	27	,	,	PUNCT
ejpam-7095	175	28	ϑ	ϑ	NOUN
ejpam-7095	175	29	)	)	PUNCT
ejpam-7095	175	30	)	)	PUNCT
ejpam-7095	176	1	dϑ︸	dϑ︸	PROPN
ejpam-7095	176	2	︷︷	︷︷	PROPN
ejpam-7095	176	3	︸	︸	X
ejpam-7095	176	4	(	(	PUNCT
ejpam-7095	176	5	i	i	NOUN
ejpam-7095	176	6	)	)	PUNCT
ejpam-7095	177	1	+	+	CCONJ
ejpam-7095	177	2	∫	∫	PROPN
ejpam-7095	177	3	τ1	τ1	NOUN
ejpam-7095	177	4	0	0	NUM
ejpam-7095	177	5	(	(	PUNCT
ejpam-7095	177	6	τ2	τ2	NOUN
ejpam-7095	177	7	−	−	NOUN
ejpam-7095	177	8	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	177	9	(	(	PUNCT
ejpam-7095	177	10	λ1[∇2u(x̄1	λ1[∇2u(x̄1	NOUN
ejpam-7095	177	11	,	,	PUNCT
ejpam-7095	177	12	ϑ)−∇2u(x̄2	ϑ)−∇2u(x̄2	PROPN
ejpam-7095	177	13	,	,	PUNCT
ejpam-7095	177	14	ϑ)]−	ϑ)]−	CCONJ
ejpam-7095	177	15	λ2[u(x̄1	λ2[u(x̄1	NOUN
ejpam-7095	177	16	,	,	PUNCT
ejpam-7095	177	17	ϑ)−	ϑ)−	PROPN
ejpam-7095	177	18	u(x̄2	u(x̄2	NOUN
ejpam-7095	177	19	,	,	PUNCT
ejpam-7095	177	20	ϑ	ϑ	NOUN
ejpam-7095	177	21	)	)	PUNCT
ejpam-7095	177	22	]	]	PUNCT
ejpam-7095	178	1	+	+	CCONJ
ejpam-7095	178	2	[	[	X
ejpam-7095	178	3	f(x̄1	f(x̄1	X
ejpam-7095	178	4	,	,	PUNCT
ejpam-7095	178	5	ϑ)−	ϑ)−	PROPN
ejpam-7095	178	6	f(x̄2	f(x̄2	NOUN
ejpam-7095	178	7	,	,	PUNCT
ejpam-7095	178	8	ϑ	ϑ	NOUN
ejpam-7095	178	9	)	)	PUNCT
ejpam-7095	178	10	]	]	PUNCT
ejpam-7095	178	11	)	)	PUNCT
ejpam-7095	178	12	dϑ︸	dϑ︸	PROPN
ejpam-7095	178	13	︷︷	︷︷	PROPN
ejpam-7095	178	14	︸	︸	X
ejpam-7095	178	15	(	(	PUNCT
ejpam-7095	178	16	ii	ii	NOUN
ejpam-7095	178	17	)	)	PUNCT
ejpam-7095	179	1	+	+	NUM
ejpam-7095	179	2	∫	∫	PROPN
ejpam-7095	179	3	τ2	τ2	PROPN
ejpam-7095	179	4	τ1	τ1	PROPN
ejpam-7095	179	5	(	(	PUNCT
ejpam-7095	179	6	τ2	τ2	NOUN
ejpam-7095	179	7	−	−	NOUN
ejpam-7095	179	8	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	179	9	(	(	PUNCT
ejpam-7095	179	10	λ1∇2u(x̄2	λ1∇2u(x̄2	PROPN
ejpam-7095	179	11	,	,	PUNCT
ejpam-7095	179	12	ϑ)−	ϑ)−	PROPN
ejpam-7095	179	13	λ2u(x̄2	λ2u(x̄2	PROPN
ejpam-7095	179	14	,	,	PUNCT
ejpam-7095	179	15	ϑ	ϑ	NOUN
ejpam-7095	179	16	)	)	PUNCT
ejpam-7095	179	17	+	+	NUM
ejpam-7095	179	18	f(x̄2	f(x̄2	NOUN
ejpam-7095	179	19	,	,	PUNCT
ejpam-7095	179	20	ϑ	ϑ	NOUN
ejpam-7095	179	21	)	)	PUNCT
ejpam-7095	179	22	)	)	PUNCT
ejpam-7095	180	1	dϑ︸	dϑ︸	PROPN
ejpam-7095	180	2	︷︷	︷︷	PROPN
ejpam-7095	180	3	︸	︸	X
ejpam-7095	180	4	(	(	PUNCT
ejpam-7095	180	5	iii	iii	NOUN
ejpam-7095	180	6	)	)	PUNCT
ejpam-7095	180	7	]	]	PUNCT
ejpam-7095	180	8	for	for	ADP
ejpam-7095	180	9	the	the	DET
ejpam-7095	180	10	integral	integral	ADJ
ejpam-7095	180	11	(	(	PUNCT
ejpam-7095	180	12	i	i	NOUN
ejpam-7095	180	13	)	)	PUNCT
ejpam-7095	180	14	,	,	PUNCT
ejpam-7095	180	15	using	use	VERB
ejpam-7095	180	16	the	the	DET
ejpam-7095	180	17	mean	mean	ADJ
ejpam-7095	180	18	value	value	NOUN
ejpam-7095	180	19	theorem	theorem	VERB
ejpam-7095	180	20	,	,	PUNCT
ejpam-7095	180	21	we	we	PRON
ejpam-7095	180	22	have	have	AUX
ejpam-7095	180	23	|(τ1	|(τ1	NOUN
ejpam-7095	180	24	−	−	PROPN
ejpam-7095	180	25	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	180	26	−	−	PROPN
ejpam-7095	181	1	(	(	PUNCT
ejpam-7095	181	2	τ2	τ2	NOUN
ejpam-7095	181	3	−	−	PROPN
ejpam-7095	181	4	ϑ)α−1|	ϑ)α−1|	NOUN
ejpam-7095	181	5	≤	≤	NOUN
ejpam-7095	181	6	(	(	PUNCT
ejpam-7095	181	7	α−	α−	ADP
ejpam-7095	181	8	1)(τ2	1)(τ2	NUM
ejpam-7095	181	9	−	−	NOUN
ejpam-7095	181	10	τ1)(τ1	τ1)(τ1	NOUN
ejpam-7095	181	11	−	−	PROPN
ejpam-7095	181	12	ϑ)α−2	ϑ)α−2	NOUN
ejpam-7095	181	13	therefore	therefore	ADV
ejpam-7095	181	14	:	:	PUNCT
ejpam-7095	181	15	(	(	PUNCT
ejpam-7095	181	16	i	i	NOUN
ejpam-7095	181	17	)	)	PUNCT
ejpam-7095	181	18	≤	≤	NOUN
ejpam-7095	181	19	(	(	PUNCT
ejpam-7095	181	20	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	181	21	+	+	CCONJ
ejpam-7095	182	1	λ2∥u∥∞	λ2∥u∥∞	PROPN
ejpam-7095	183	1	+	+	PUNCT
ejpam-7095	184	1	∥f∥∞)(α−	∥f∥∞)(α−	PRON
ejpam-7095	184	2	1)δ2	1)δ2	NUM
ejpam-7095	184	3	∫	∫	NOUN
ejpam-7095	184	4	τ1	τ1	NOUN
ejpam-7095	184	5	0	0	NUM
ejpam-7095	184	6	(	(	PUNCT
ejpam-7095	184	7	τ1	τ1	NOUN
ejpam-7095	184	8	−	−	PROPN
ejpam-7095	184	9	ϑ)α−2dϑ	ϑ)α−2dϑ	PROPN
ejpam-7095	184	10	=	=	SYM
ejpam-7095	184	11	(	(	PUNCT
ejpam-7095	184	12	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	184	13	+	+	CCONJ
ejpam-7095	185	1	λ2∥u∥∞	λ2∥u∥∞	ADJ
ejpam-7095	185	2	+	+	CCONJ
ejpam-7095	185	3	∥f∥∞)δ2τ	∥f∥∞)δ2τ	PROPN
ejpam-7095	185	4	α−1	α−1	PROPN
ejpam-7095	185	5	1	1	NUM
ejpam-7095	185	6	.	.	PUNCT
ejpam-7095	186	1	similarly	similarly	ADV
ejpam-7095	186	2	,	,	PUNCT
ejpam-7095	186	3	using	use	VERB
ejpam-7095	186	4	lipschitz	lipschitz	NOUN
ejpam-7095	186	5	conditions	condition	NOUN
ejpam-7095	186	6	for	for	ADP
ejpam-7095	186	7	integral	integral	ADJ
ejpam-7095	186	8	(	(	PUNCT
ejpam-7095	186	9	ii	ii	NOUN
ejpam-7095	186	10	)	)	PUNCT
ejpam-7095	186	11	,	,	PUNCT
ejpam-7095	186	12	we	we	PRON
ejpam-7095	186	13	have	have	VERB
ejpam-7095	186	14	:	:	PUNCT
ejpam-7095	186	15	(	(	PUNCT
ejpam-7095	186	16	ii	ii	NOUN
ejpam-7095	186	17	)	)	PUNCT
ejpam-7095	186	18	≤	≤	NOUN
ejpam-7095	186	19	(	(	PUNCT
ejpam-7095	186	20	λ1lf1	λ1lf1	NOUN
ejpam-7095	186	21	+	+	CCONJ
ejpam-7095	186	22	λ2lf2	λ2lf2	NOUN
ejpam-7095	186	23	+	+	CCONJ
ejpam-7095	186	24	lf3)δ1	lf3)δ1	NUM
ejpam-7095	186	25	∫	∫	PROPN
ejpam-7095	186	26	τ1	τ1	PROPN
ejpam-7095	186	27	0	0	NUM
ejpam-7095	187	1	(	(	PUNCT
ejpam-7095	187	2	τ2	τ2	NOUN
ejpam-7095	187	3	−	−	NOUN
ejpam-7095	187	4	ϑ)α−1dϑ	ϑ)α−1dϑ	NOUN
ejpam-7095	187	5	=	=	SYM
ejpam-7095	187	6	(	(	PUNCT
ejpam-7095	187	7	λ1lf1	λ1lf1	NOUN
ejpam-7095	187	8	+	+	CCONJ
ejpam-7095	187	9	λ2lf2	λ2lf2	NOUN
ejpam-7095	187	10	+	+	X
ejpam-7095	187	11	lf3)δ1	lf3)δ1	NOUN
ejpam-7095	187	12	(	(	PUNCT
ejpam-7095	187	13	τα2	τα2	NOUN
ejpam-7095	187	14	α	α	X
ejpam-7095	187	15	−	−	PROPN
ejpam-7095	187	16	δ2	δ2	VERB
ejpam-7095	187	17	α	α	NOUN
ejpam-7095	187	18	)	)	PUNCT
ejpam-7095	187	19	.	.	PUNCT
ejpam-7095	188	1	and	and	CCONJ
ejpam-7095	188	2	using	use	VERB
ejpam-7095	188	3	direct	direct	ADJ
ejpam-7095	188	4	estimation	estimation	NOUN
ejpam-7095	188	5	,	,	PUNCT
ejpam-7095	188	6	we	we	PRON
ejpam-7095	188	7	have	have	VERB
ejpam-7095	188	8	:	:	PUNCT
ejpam-7095	188	9	(	(	PUNCT
ejpam-7095	188	10	iii	iii	X
ejpam-7095	188	11	)	)	PUNCT
ejpam-7095	188	12	≤	≤	NOUN
ejpam-7095	188	13	(	(	PUNCT
ejpam-7095	188	14	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	188	15	+	+	CCONJ
ejpam-7095	188	16	λ2∥u∥∞	λ2∥u∥∞	ADJ
ejpam-7095	188	17	+	+	NUM
ejpam-7095	188	18	∥f∥∞	∥f∥∞	NUM
ejpam-7095	188	19	)	)	PUNCT
ejpam-7095	188	20	∫	∫	PROPN
ejpam-7095	189	1	τ2	τ2	PROPN
ejpam-7095	189	2	τ1	τ1	PROPN
ejpam-7095	189	3	(	(	PUNCT
ejpam-7095	189	4	τ2	τ2	NOUN
ejpam-7095	189	5	−	−	NOUN
ejpam-7095	189	6	ϑ)α−1dϑ	ϑ)α−1dϑ	NOUN
ejpam-7095	189	7	=	=	PUNCT
ejpam-7095	189	8	(	(	PUNCT
ejpam-7095	189	9	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	189	10	+	+	CCONJ
ejpam-7095	189	11	λ2∥u∥∞	λ2∥u∥∞	ADJ
ejpam-7095	189	12	+	+	NUM
ejpam-7095	189	13	∥f∥∞	∥f∥∞	X
ejpam-7095	189	14	)	)	PUNCT
ejpam-7095	189	15	δ2	δ2	VERB
ejpam-7095	189	16	α	α	NOUN
ejpam-7095	189	17	.	.	PUNCT
ejpam-7095	190	1	combining	combine	VERB
ejpam-7095	190	2	all	all	DET
ejpam-7095	190	3	the	the	DET
ejpam-7095	190	4	results	result	NOUN
ejpam-7095	190	5	,	,	PUNCT
ejpam-7095	190	6	we	we	PRON
ejpam-7095	190	7	obtain	obtain	VERB
ejpam-7095	190	8	:	:	PUNCT
ejpam-7095	191	1	kamran	kamran	PROPN
ejpam-7095	191	2	et	et	PROPN
ejpam-7095	191	3	al	al	PROPN
ejpam-7095	191	4	.	.	PUNCT
ejpam-7095	191	5	/	/	SYM
ejpam-7095	191	6	eur	eur	PROPN
ejpam-7095	191	7	.	.	PUNCT
ejpam-7095	192	1	j.	j.	PROPN
ejpam-7095	192	2	pure	pure	PROPN
ejpam-7095	192	3	appl	appl	PROPN
ejpam-7095	192	4	.	.	PROPN
ejpam-7095	192	5	math	math	PROPN
ejpam-7095	192	6	,	,	PUNCT
ejpam-7095	192	7	18	18	NUM
ejpam-7095	192	8	(	(	PUNCT
ejpam-7095	192	9	4	4	NUM
ejpam-7095	192	10	)	)	PUNCT
ejpam-7095	192	11	(	(	PUNCT
ejpam-7095	192	12	2025	2025	NUM
ejpam-7095	192	13	)	)	PUNCT
ejpam-7095	192	14	,	,	PUNCT
ejpam-7095	192	15	7095	7095	NUM
ejpam-7095	192	16	9	9	NUM
ejpam-7095	192	17	of	of	ADP
ejpam-7095	192	18	30	30	NUM
ejpam-7095	192	19	∥j	∥j	ADJ
ejpam-7095	192	20	u(x̄1	u(x̄1	NOUN
ejpam-7095	192	21	,	,	PUNCT
ejpam-7095	192	22	τ1)−	τ1)−	PROPN
ejpam-7095	192	23	j	j	PROPN
ejpam-7095	192	24	u(x̄2	u(x̄2	NOUN
ejpam-7095	192	25	,	,	PUNCT
ejpam-7095	192	26	τ2)∥∞	τ2)∥∞	ADP
ejpam-7095	192	27	≤	≤	ADJ
ejpam-7095	192	28	lg2δ1	lg2δ1	NOUN
ejpam-7095	192	29	+	+	PUNCT
ejpam-7095	192	30	lg3δ1	lg3δ1	PROPN
ejpam-7095	192	31	+	+	SYM
ejpam-7095	192	32	ϵ3δ2	ϵ3δ2	NUM
ejpam-7095	192	33	+	+	NUM
ejpam-7095	192	34	1−	1−	NUM
ejpam-7095	192	35	α	α	DET
ejpam-7095	192	36	β(α	β(α	PROPN
ejpam-7095	192	37	)	)	PUNCT
ejpam-7095	192	38	(	(	PUNCT
ejpam-7095	192	39	|λ1|lf1(δ1	|λ1|lf1(δ1	VERB
ejpam-7095	192	40	+	+	CCONJ
ejpam-7095	192	41	δ2	δ2	ADJ
ejpam-7095	192	42	)	)	PUNCT
ejpam-7095	192	43	+	+	NUM
ejpam-7095	192	44	|λ2|lf2(δ1	|λ2|lf2(δ1	NOUN
ejpam-7095	192	45	+	+	X
ejpam-7095	192	46	δ2	δ2	VERB
ejpam-7095	192	47	)	)	PUNCT
ejpam-7095	192	48	+	+	NUM
ejpam-7095	192	49	lf3(δ1	lf3(δ1	NOUN
ejpam-7095	192	50	+	+	CCONJ
ejpam-7095	192	51	δ2	δ2	VERB
ejpam-7095	192	52	)	)	PUNCT
ejpam-7095	192	53	)	)	PUNCT
ejpam-7095	193	1	+	+	CCONJ
ejpam-7095	193	2	α	α	PROPN
ejpam-7095	193	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	193	4	)	)	PUNCT
ejpam-7095	193	5	(	(	PUNCT
ejpam-7095	193	6	(	(	PUNCT
ejpam-7095	193	7	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	193	8	+	+	CCONJ
ejpam-7095	193	9	λ2∥u∥∞	λ2∥u∥∞	ADJ
ejpam-7095	193	10	+	+	CCONJ
ejpam-7095	193	11	∥f∥∞)δ2τ	∥f∥∞)δ2τ	PROPN
ejpam-7095	193	12	α−1	α−1	PROPN
ejpam-7095	193	13	1	1	NUM
ejpam-7095	193	14	+	+	CCONJ
ejpam-7095	193	15	(	(	PUNCT
ejpam-7095	193	16	λ1lf1	λ1lf1	ADJ
ejpam-7095	193	17	+	+	CCONJ
ejpam-7095	193	18	λ2lf2	λ2lf2	NOUN
ejpam-7095	193	19	+	+	X
ejpam-7095	193	20	lf3)δ1	lf3)δ1	NOUN
ejpam-7095	193	21	(	(	PUNCT
ejpam-7095	193	22	τα2	τα2	NOUN
ejpam-7095	193	23	α	α	X
ejpam-7095	193	24	−	−	PROPN
ejpam-7095	193	25	δ2	δ2	VERB
ejpam-7095	193	26	α	α	NOUN
ejpam-7095	193	27	)	)	PUNCT
ejpam-7095	194	1	+	+	CCONJ
ejpam-7095	194	2	(	(	PUNCT
ejpam-7095	194	3	λ1∥∇2u∥∞	λ1∥∇2u∥∞	NUM
ejpam-7095	194	4	+	+	CCONJ
ejpam-7095	194	5	λ2∥u∥∞	λ2∥u∥∞	ADJ
ejpam-7095	194	6	+	+	NUM
ejpam-7095	194	7	∥f∥∞	∥f∥∞	X
ejpam-7095	194	8	)	)	PUNCT
ejpam-7095	194	9	δ2	δ2	VERB
ejpam-7095	194	10	α	α	NOUN
ejpam-7095	194	11	)	)	PUNCT
ejpam-7095	194	12	.	.	PUNCT
ejpam-7095	195	1	hence	hence	ADV
ejpam-7095	195	2	∥j	∥j	ADV
ejpam-7095	195	3	u(x̄1	u(x̄1	NOUN
ejpam-7095	195	4	,	,	PUNCT
ejpam-7095	195	5	τ1)−	τ1)−	PROPN
ejpam-7095	195	6	j	j	PROPN
ejpam-7095	195	7	u(x̄2	u(x̄2	NOUN
ejpam-7095	195	8	,	,	PUNCT
ejpam-7095	195	9	τ2)∥∞	τ2)∥∞	PUNCT
ejpam-7095	195	10	→	→	SYM
ejpam-7095	195	11	0	0	NUM
ejpam-7095	195	12	as	as	ADP
ejpam-7095	195	13	δ1	δ1	NOUN
ejpam-7095	195	14	,	,	PUNCT
ejpam-7095	195	15	δ2	δ2	VERB
ejpam-7095	195	16	→	→	SYM
ejpam-7095	195	17	0	0	NUM
ejpam-7095	195	18	,	,	PUNCT
ejpam-7095	195	19	proving	prove	VERB
ejpam-7095	195	20	equicontinuity	equicontinuity	NOUN
ejpam-7095	195	21	.	.	PUNCT
ejpam-7095	196	1	step	step	NOUN
ejpam-7095	196	2	4	4	NUM
ejpam-7095	196	3	:	:	PUNCT
ejpam-7095	196	4	a	a	PRON
ejpam-7095	196	5	priori	priori	ADV
ejpam-7095	196	6	bound	bind	VERB
ejpam-7095	196	7	.	.	PUNCT
ejpam-7095	197	1	define	define	VERB
ejpam-7095	197	2	ℵ	ℵ	NOUN
ejpam-7095	197	3	=	=	SYM
ejpam-7095	197	4	{	{	PUNCT
ejpam-7095	197	5	u	u	NOUN
ejpam-7095	197	6	∈	∈	PROPN
ejpam-7095	197	7	b(ω	b(ω	ADV
ejpam-7095	197	8	,	,	PUNCT
ejpam-7095	197	9	r	r	NOUN
ejpam-7095	197	10	)	)	PUNCT
ejpam-7095	197	11	:	:	PUNCT
ejpam-7095	197	12	u	u	NOUN
ejpam-7095	197	13	=	=	PUNCT
ejpam-7095	197	14	εj	εj	PROPN
ejpam-7095	197	15	u	u	PROPN
ejpam-7095	197	16	,	,	PUNCT
ejpam-7095	197	17	ε	ε	PROPN
ejpam-7095	197	18	∈	∈	PROPN
ejpam-7095	197	19	(	(	PUNCT
ejpam-7095	197	20	0	0	NUM
ejpam-7095	197	21	,	,	PUNCT
ejpam-7095	197	22	1	1	NUM
ejpam-7095	197	23	)	)	PUNCT
ejpam-7095	197	24	}	}	PUNCT
ejpam-7095	197	25	.	.	PUNCT
ejpam-7095	198	1	for	for	ADP
ejpam-7095	198	2	u	u	PROPN
ejpam-7095	198	3	∈	∈	PROPN
ejpam-7095	198	4	ℵ	ℵ	NOUN
ejpam-7095	198	5	,	,	PUNCT
ejpam-7095	198	6	we	we	PRON
ejpam-7095	198	7	have	have	VERB
ejpam-7095	198	8	|u|	|u|	NOUN
ejpam-7095	198	9	=	=	SYM
ejpam-7095	198	10	|εj	|εj	X
ejpam-7095	198	11	u|	u|	ADV
ejpam-7095	198	12	=	=	PUNCT
ejpam-7095	198	13	ε|j	ε|j	X
ejpam-7095	198	14	u|	u|	ADJ
ejpam-7095	198	15	≤	≤	ADJ
ejpam-7095	198	16	ερab	ερab	NOUN
ejpam-7095	198	17	,	,	PUNCT
ejpam-7095	198	18	where	where	SCONJ
ejpam-7095	198	19	ρab	ρab	NOUN
ejpam-7095	198	20	is	be	AUX
ejpam-7095	198	21	defined	define	VERB
ejpam-7095	198	22	as	as	ADP
ejpam-7095	198	23	in	in	ADP
ejpam-7095	198	24	step	step	NOUN
ejpam-7095	198	25	2	2	NUM
ejpam-7095	198	26	.	.	PUNCT
ejpam-7095	199	1	the	the	DET
ejpam-7095	199	2	inequality	inequality	NOUN
ejpam-7095	199	3	∥u∥∞	∥u∥∞	PUNCT
ejpam-7095	199	4	≤	≤	X
ejpam-7095	199	5	ρab	ρab	NOUN
ejpam-7095	199	6	implies	imply	VERB
ejpam-7095	199	7	the	the	DET
ejpam-7095	199	8	operator	operator	NOUN
ejpam-7095	199	9	ℵ	ℵ	NOUN
ejpam-7095	199	10	is	be	AUX
ejpam-7095	199	11	bounded	bound	VERB
ejpam-7095	199	12	.	.	PUNCT
ejpam-7095	200	1	therefore	therefore	ADV
ejpam-7095	200	2	,	,	PUNCT
ejpam-7095	200	3	by	by	ADP
ejpam-7095	200	4	the	the	DET
ejpam-7095	200	5	schaefer	schaefer	NOUN
ejpam-7095	200	6	fixed	fix	VERB
ejpam-7095	200	7	-	-	PUNCT
ejpam-7095	200	8	point	point	NOUN
ejpam-7095	200	9	theorem	theorem	NOUN
ejpam-7095	200	10	[	[	X
ejpam-7095	200	11	32	32	NUM
ejpam-7095	200	12	]	]	PUNCT
ejpam-7095	200	13	,	,	PUNCT
ejpam-7095	200	14	j	j	PROPN
ejpam-7095	200	15	has	have	VERB
ejpam-7095	200	16	at	at	ADV
ejpam-7095	200	17	least	least	ADV
ejpam-7095	200	18	one	one	NUM
ejpam-7095	200	19	fixed	fix	VERB
ejpam-7095	200	20	point	point	NOUN
ejpam-7095	200	21	,	,	PUNCT
ejpam-7095	200	22	ensuring	ensure	VERB
ejpam-7095	200	23	the	the	DET
ejpam-7095	200	24	existence	existence	NOUN
ejpam-7095	200	25	of	of	ADP
ejpam-7095	200	26	a	a	DET
ejpam-7095	200	27	solution	solution	NOUN
ejpam-7095	200	28	to	to	ADP
ejpam-7095	200	29	the	the	DET
ejpam-7095	200	30	problem	problem	NOUN
ejpam-7095	200	31	.	.	PUNCT
ejpam-7095	201	1	the	the	DET
ejpam-7095	201	2	problem	problem	NOUN
ejpam-7095	201	3	defined	define	VERB
ejpam-7095	201	4	in	in	ADP
ejpam-7095	201	5	eq	eq	ADP
ejpam-7095	201	6	.	.	PUNCT
ejpam-7095	202	1	(	(	PUNCT
ejpam-7095	202	2	1	1	X
ejpam-7095	202	3	)	)	PUNCT
ejpam-7095	202	4	has	have	VERB
ejpam-7095	202	5	a	a	DET
ejpam-7095	202	6	unique	unique	ADJ
ejpam-7095	202	7	solution	solution	NOUN
ejpam-7095	202	8	if	if	SCONJ
ejpam-7095	202	9	the	the	DET
ejpam-7095	202	10	following	follow	VERB
ejpam-7095	202	11	condition	condition	NOUN
ejpam-7095	202	12	is	be	AUX
ejpam-7095	202	13	satisfied	satisfied	ADJ
ejpam-7095	202	14	:	:	PUNCT
ejpam-7095	202	15	(	(	PUNCT
ejpam-7095	202	16	1−	1−	NUM
ejpam-7095	202	17	α)γ(α	α)γ(α	NOUN
ejpam-7095	202	18	)	)	PUNCT
ejpam-7095	203	1	+	+	NUM
ejpam-7095	203	2	τα	τα	NOUN
ejpam-7095	203	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	203	4	)	)	PUNCT
ejpam-7095	203	5	(	(	PUNCT
ejpam-7095	203	6	(	(	PUNCT
ejpam-7095	203	7	ϵ5|λ1|+	ϵ5|λ1|+	X
ejpam-7095	203	8	|λ2|	|λ2|	NOUN
ejpam-7095	203	9	)	)	PUNCT
ejpam-7095	203	10	∥u1	∥u1	PROPN
ejpam-7095	203	11	−	−	PUNCT
ejpam-7095	203	12	u2∥∞	u2∥∞	PUNCT
ejpam-7095	203	13	)	)	PUNCT
ejpam-7095	204	1	<	<	X
ejpam-7095	204	2	1	1	X
ejpam-7095	204	3	.	.	PUNCT
ejpam-7095	204	4	(	(	PUNCT
ejpam-7095	204	5	6	6	X
ejpam-7095	204	6	)	)	PUNCT
ejpam-7095	204	7	kamran	kamran	PROPN
ejpam-7095	204	8	et	et	PROPN
ejpam-7095	204	9	al	al	PROPN
ejpam-7095	204	10	.	.	PUNCT
ejpam-7095	204	11	/	/	SYM
ejpam-7095	204	12	eur	eur	PROPN
ejpam-7095	204	13	.	.	PUNCT
ejpam-7095	205	1	j.	j.	PROPN
ejpam-7095	205	2	pure	pure	PROPN
ejpam-7095	205	3	appl	appl	PROPN
ejpam-7095	205	4	.	.	PROPN
ejpam-7095	205	5	math	math	PROPN
ejpam-7095	205	6	,	,	PUNCT
ejpam-7095	205	7	18	18	NUM
ejpam-7095	205	8	(	(	PUNCT
ejpam-7095	205	9	4	4	NUM
ejpam-7095	205	10	)	)	PUNCT
ejpam-7095	205	11	(	(	PUNCT
ejpam-7095	205	12	2025	2025	NUM
ejpam-7095	205	13	)	)	PUNCT
ejpam-7095	205	14	,	,	PUNCT
ejpam-7095	205	15	7095	7095	NUM
ejpam-7095	205	16	10	10	NUM
ejpam-7095	205	17	of	of	ADP
ejpam-7095	205	18	30	30	NUM
ejpam-7095	205	19	proof	proof	NOUN
ejpam-7095	205	20	.	.	PUNCT
ejpam-7095	206	1	∥j	∥j	ADV
ejpam-7095	206	2	u1(x̄	u1(x̄	SYM
ejpam-7095	206	3	,	,	PUNCT
ejpam-7095	206	4	τ)−	τ)−	PROPN
ejpam-7095	206	5	j	j	PROPN
ejpam-7095	206	6	u2(x̄	u2(x̄	PROPN
ejpam-7095	206	7	,	,	PUNCT
ejpam-7095	206	8	τ)∥∞	τ)∥∞	NOUN
ejpam-7095	206	9	=	=	SYM
ejpam-7095	206	10	sup	sup	NOUN
ejpam-7095	206	11	{	{	PUNCT
ejpam-7095	206	12	|j	|j	NOUN
ejpam-7095	206	13	u1(x̄	u1(x̄	ADP
ejpam-7095	206	14	,	,	PUNCT
ejpam-7095	206	15	τ)−	τ)−	PROPN
ejpam-7095	206	16	j	j	PROPN
ejpam-7095	206	17	u2(x̄	u2(x̄	PROPN
ejpam-7095	206	18	,	,	PUNCT
ejpam-7095	206	19	τ)|	τ)|	PROPN
ejpam-7095	206	20	}	}	PUNCT
ejpam-7095	206	21	=	=	PUNCT
ejpam-7095	206	22	sup	sup	NUM
ejpam-7095	206	23	{	{	PUNCT
ejpam-7095	206	24	∣∣∣∣1−	∣∣∣∣1−	PROPN
ejpam-7095	206	25	σ	σ	X
ejpam-7095	206	26	β(α	β(α	PROPN
ejpam-7095	206	27	)	)	PUNCT
ejpam-7095	206	28	(	(	PUNCT
ejpam-7095	206	29	λ1∇2u1(x̄	λ1∇2u1(x̄	PROPN
ejpam-7095	206	30	,	,	PUNCT
ejpam-7095	206	31	τ)−	τ)−	PROPN
ejpam-7095	206	32	λ2u1(x̄	λ2u1(x̄	PROPN
ejpam-7095	206	33	,	,	PUNCT
ejpam-7095	206	34	τ	τ	PROPN
ejpam-7095	206	35	)	)	PUNCT
ejpam-7095	206	36	)	)	PUNCT
ejpam-7095	207	1	+	+	CCONJ
ejpam-7095	207	2	σ	σ	NOUN
ejpam-7095	207	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	207	4	)	)	PUNCT
ejpam-7095	207	5	∫	∫	PROPN
ejpam-7095	208	1	τ	τ	PROPN
ejpam-7095	208	2	0	0	NUM
ejpam-7095	208	3	(	(	PUNCT
ejpam-7095	208	4	τ	τ	PROPN
ejpam-7095	208	5	−	−	PROPN
ejpam-7095	208	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	208	7	(	(	PUNCT
ejpam-7095	208	8	λ1∇2u1(x̄	λ1∇2u1(x̄	PROPN
ejpam-7095	208	9	,	,	PUNCT
ejpam-7095	208	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	208	11	λ2u1(x̄	λ2u1(x̄	PROPN
ejpam-7095	208	12	,	,	PUNCT
ejpam-7095	208	13	ϑ	ϑ	NOUN
ejpam-7095	208	14	)	)	PUNCT
ejpam-7095	208	15	)	)	PUNCT
ejpam-7095	208	16	dϑ	dϑ	NOUN
ejpam-7095	208	17	−	−	PROPN
ejpam-7095	208	18	1−	1−	NUM
ejpam-7095	208	19	α	α	DET
ejpam-7095	208	20	β(α	β(α	PROPN
ejpam-7095	208	21	)	)	PUNCT
ejpam-7095	208	22	(	(	PUNCT
ejpam-7095	208	23	λ1∇2u2(x̄	λ1∇2u2(x̄	PROPN
ejpam-7095	208	24	,	,	PUNCT
ejpam-7095	208	25	ϑ)−	ϑ)−	PROPN
ejpam-7095	208	26	λ2u2(x̄	λ2u2(x̄	PROPN
ejpam-7095	208	27	,	,	PUNCT
ejpam-7095	208	28	ϑ	ϑ	NOUN
ejpam-7095	208	29	)	)	PUNCT
ejpam-7095	208	30	)	)	PUNCT
ejpam-7095	209	1	−	−	PROPN
ejpam-7095	210	1	α	α	X
ejpam-7095	210	2	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	210	3	)	)	PUNCT
ejpam-7095	210	4	∫	∫	PROPN
ejpam-7095	211	1	τ	τ	PROPN
ejpam-7095	211	2	0	0	NUM
ejpam-7095	211	3	(	(	PUNCT
ejpam-7095	211	4	τ	τ	PROPN
ejpam-7095	211	5	−	−	PROPN
ejpam-7095	211	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	211	7	(	(	PUNCT
ejpam-7095	211	8	λ1∇2u2(x̄	λ1∇2u2(x̄	PROPN
ejpam-7095	211	9	,	,	PUNCT
ejpam-7095	211	10	ϑ)−	ϑ)−	PROPN
ejpam-7095	211	11	λ2u2(x̄	λ2u2(x̄	PROPN
ejpam-7095	211	12	,	,	PUNCT
ejpam-7095	211	13	ϑ	ϑ	NOUN
ejpam-7095	211	14	)	)	PUNCT
ejpam-7095	211	15	)	)	PUNCT
ejpam-7095	211	16	dϑ	dϑ	ADP
ejpam-7095	211	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	211	18	}	}	PUNCT
ejpam-7095	211	19	≤	≤	NUM
ejpam-7095	211	20	sup	sup	NOUN
ejpam-7095	211	21	{	{	PUNCT
ejpam-7095	211	22	1−	1−	NUM
ejpam-7095	211	23	α	α	DET
ejpam-7095	211	24	β(α	β(α	PROPN
ejpam-7095	211	25	)	)	PUNCT
ejpam-7095	211	26	(	(	PUNCT
ejpam-7095	211	27	|λ1||∇2u1(x̄	|λ1||∇2u1(x̄	PROPN
ejpam-7095	211	28	,	,	PUNCT
ejpam-7095	211	29	τ)−∇2u2(x̄	τ)−∇2u2(x̄	PROPN
ejpam-7095	211	30	,	,	PUNCT
ejpam-7095	211	31	τ)|+	τ)|+	NOUN
ejpam-7095	211	32	|λ2||u1(x̄	|λ2||u1(x̄	PROPN
ejpam-7095	211	33	,	,	PUNCT
ejpam-7095	211	34	τ)−	τ)−	PROPN
ejpam-7095	211	35	u2(x̄	u2(x̄	PART
ejpam-7095	211	36	,	,	PUNCT
ejpam-7095	211	37	τ)|	τ)|	PROPN
ejpam-7095	211	38	)	)	PUNCT
ejpam-7095	211	39	−	−	PROPN
ejpam-7095	212	1	α	α	X
ejpam-7095	212	2	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	212	3	)	)	PUNCT
ejpam-7095	212	4	∫	∫	PROPN
ejpam-7095	213	1	τ	τ	PROPN
ejpam-7095	213	2	0	0	NUM
ejpam-7095	213	3	(	(	PUNCT
ejpam-7095	213	4	τ	τ	PROPN
ejpam-7095	213	5	−	−	PROPN
ejpam-7095	213	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	213	7	(	(	PUNCT
ejpam-7095	213	8	|λ1||∇2u1(x̄	|λ1||∇2u1(x̄	PROPN
ejpam-7095	213	9	,	,	PUNCT
ejpam-7095	213	10	ϑ)−∇2u2(x̄	ϑ)−∇2u2(x̄	NOUN
ejpam-7095	213	11	,	,	PUNCT
ejpam-7095	213	12	ϑ)|+	ϑ)|+	ADJ
ejpam-7095	213	13	|λ2||u1(x̄	|λ2||u1(x̄	PROPN
ejpam-7095	213	14	,	,	PUNCT
ejpam-7095	213	15	ϑ)−	ϑ)−	PROPN
ejpam-7095	213	16	u2(x̄	u2(x̄	PART
ejpam-7095	213	17	,	,	PUNCT
ejpam-7095	213	18	ϑ)|	ϑ)|	ADJ
ejpam-7095	213	19	)	)	PUNCT
ejpam-7095	213	20	dϑ	dϑ	NOUN
ejpam-7095	213	21	}	}	PUNCT
ejpam-7095	213	22	≤	≤	NUM
ejpam-7095	213	23	sup	sup	NOUN
ejpam-7095	213	24	{	{	PUNCT
ejpam-7095	213	25	1−	1−	NUM
ejpam-7095	213	26	α	α	DET
ejpam-7095	213	27	β(α	β(α	PROPN
ejpam-7095	213	28	)	)	PUNCT
ejpam-7095	213	29	(	(	PUNCT
ejpam-7095	213	30	ϵ5|λ1||u1(x̄	ϵ5|λ1||u1(x̄	X
ejpam-7095	213	31	,	,	PUNCT
ejpam-7095	213	32	τ)−	τ)−	PROPN
ejpam-7095	213	33	u2(x̄	u2(x̄	PROPN
ejpam-7095	213	34	,	,	PUNCT
ejpam-7095	213	35	τ)|+	τ)|+	NOUN
ejpam-7095	213	36	|λ2||u1(x̄	|λ2||u1(x̄	PROPN
ejpam-7095	213	37	,	,	PUNCT
ejpam-7095	213	38	τ)−	τ)−	PROPN
ejpam-7095	213	39	u2(x̄	u2(x̄	PART
ejpam-7095	213	40	,	,	PUNCT
ejpam-7095	213	41	τ)|	τ)|	PROPN
ejpam-7095	213	42	)	)	PUNCT
ejpam-7095	214	1	+	+	CCONJ
ejpam-7095	214	2	α	α	PROPN
ejpam-7095	214	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	214	4	)	)	PUNCT
ejpam-7095	214	5	∫	∫	PROPN
ejpam-7095	215	1	τ	τ	PROPN
ejpam-7095	215	2	0	0	NUM
ejpam-7095	215	3	(	(	PUNCT
ejpam-7095	215	4	τ	τ	PROPN
ejpam-7095	215	5	−	−	PROPN
ejpam-7095	215	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	215	7	(	(	PUNCT
ejpam-7095	215	8	ϵ5|λ1||u1(x̄	ϵ5|λ1||u1(x̄	X
ejpam-7095	215	9	,	,	PUNCT
ejpam-7095	215	10	τ)−	τ)−	PROPN
ejpam-7095	215	11	u2(x̄	u2(x̄	PROPN
ejpam-7095	215	12	,	,	PUNCT
ejpam-7095	215	13	τ)|+	τ)|+	NOUN
ejpam-7095	215	14	|λ2||u1(x̄	|λ2||u1(x̄	PROPN
ejpam-7095	215	15	,	,	PUNCT
ejpam-7095	215	16	τ)−	τ)−	PROPN
ejpam-7095	215	17	u2(x̄	u2(x̄	PART
ejpam-7095	215	18	,	,	PUNCT
ejpam-7095	215	19	τ)|	τ)|	NOUN
ejpam-7095	215	20	)	)	PUNCT
ejpam-7095	215	21	dϑ	dϑ	NOUN
ejpam-7095	215	22	}	}	PUNCT
ejpam-7095	215	23	=	=	SYM
ejpam-7095	215	24	1−	1−	NUM
ejpam-7095	215	25	α	α	PRON
ejpam-7095	215	26	β(α	β(α	PROPN
ejpam-7095	215	27	)	)	PUNCT
ejpam-7095	215	28	(	(	PUNCT
ejpam-7095	215	29	(	(	PUNCT
ejpam-7095	215	30	ϵ5|λ1|+	ϵ5|λ1|+	X
ejpam-7095	215	31	|λ2|	|λ2|	NOUN
ejpam-7095	215	32	)	)	PUNCT
ejpam-7095	215	33	∥u1	∥u1	PROPN
ejpam-7095	215	34	−	−	PUNCT
ejpam-7095	215	35	u2∥∞	u2∥∞	PUNCT
ejpam-7095	215	36	)	)	PUNCT
ejpam-7095	216	1	+	+	CCONJ
ejpam-7095	216	2	α	α	PROPN
ejpam-7095	216	3	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	216	4	)	)	PUNCT
ejpam-7095	216	5	∫	∫	PROPN
ejpam-7095	217	1	τ	τ	PROPN
ejpam-7095	217	2	0	0	NUM
ejpam-7095	217	3	(	(	PUNCT
ejpam-7095	217	4	τ	τ	PROPN
ejpam-7095	217	5	−	−	PROPN
ejpam-7095	217	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	217	7	(	(	PUNCT
ejpam-7095	217	8	(	(	PUNCT
ejpam-7095	217	9	ϵ5|λ1|+	ϵ5|λ1|+	X
ejpam-7095	217	10	|λ2|	|λ2|	NOUN
ejpam-7095	217	11	)	)	PUNCT
ejpam-7095	217	12	∥u1	∥u1	PROPN
ejpam-7095	217	13	−	−	PUNCT
ejpam-7095	217	14	u2∥∞	u2∥∞	PUNCT
ejpam-7095	217	15	)	)	PUNCT
ejpam-7095	217	16	dϑ	dϑ	NOUN
ejpam-7095	218	1	=	=	SYM
ejpam-7095	218	2	(	(	PUNCT
ejpam-7095	218	3	1−	1−	NUM
ejpam-7095	218	4	α)γ(α	α)γ(α	NOUN
ejpam-7095	218	5	)	)	PUNCT
ejpam-7095	218	6	+	+	NUM
ejpam-7095	218	7	τα	τα	NOUN
ejpam-7095	218	8	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	218	9	)	)	PUNCT
ejpam-7095	218	10	(	(	PUNCT
ejpam-7095	218	11	(	(	PUNCT
ejpam-7095	218	12	ϵ5|λ1|+	ϵ5|λ1|+	X
ejpam-7095	218	13	|λ2|	|λ2|	NOUN
ejpam-7095	218	14	)	)	PUNCT
ejpam-7095	218	15	∥u1	∥u1	PROPN
ejpam-7095	218	16	−	−	PUNCT
ejpam-7095	218	17	u2∥∞	u2∥∞	PUNCT
ejpam-7095	218	18	)	)	PUNCT
ejpam-7095	218	19	.	.	PUNCT
ejpam-7095	219	1	if	if	SCONJ
ejpam-7095	219	2	condition	condition	NOUN
ejpam-7095	219	3	(	(	PUNCT
ejpam-7095	219	4	6	6	NUM
ejpam-7095	219	5	)	)	PUNCT
ejpam-7095	219	6	holds	hold	VERB
ejpam-7095	219	7	,	,	PUNCT
ejpam-7095	219	8	then	then	ADV
ejpam-7095	219	9	the	the	DET
ejpam-7095	219	10	operator	operator	NOUN
ejpam-7095	219	11	j	j	PROPN
ejpam-7095	219	12	is	be	AUX
ejpam-7095	219	13	a	a	DET
ejpam-7095	219	14	contraction	contraction	NOUN
ejpam-7095	219	15	.	.	PUNCT
ejpam-7095	220	1	by	by	ADP
ejpam-7095	220	2	the	the	DET
ejpam-7095	220	3	banach	banach	ADV
ejpam-7095	220	4	fixed	fix	VERB
ejpam-7095	220	5	-	-	PUNCT
ejpam-7095	220	6	point	point	NOUN
ejpam-7095	220	7	theorem	theorem	NOUN
ejpam-7095	220	8	[	[	X
ejpam-7095	220	9	32	32	NUM
ejpam-7095	220	10	]	]	PUNCT
ejpam-7095	220	11	,	,	PUNCT
ejpam-7095	220	12	this	this	PRON
ejpam-7095	220	13	implies	imply	VERB
ejpam-7095	220	14	that	that	SCONJ
ejpam-7095	220	15	j	j	PROPN
ejpam-7095	220	16	admits	admit	VERB
ejpam-7095	220	17	a	a	DET
ejpam-7095	220	18	unique	unique	ADJ
ejpam-7095	220	19	fixed	fix	VERB
ejpam-7095	220	20	point	point	NOUN
ejpam-7095	220	21	,	,	PUNCT
ejpam-7095	220	22	which	which	PRON
ejpam-7095	220	23	in	in	ADP
ejpam-7095	220	24	turn	turn	NOUN
ejpam-7095	220	25	implies	imply	VERB
ejpam-7095	220	26	that	that	PRON
ejpam-7095	220	27	problem	problem	NOUN
ejpam-7095	220	28	(	(	PUNCT
ejpam-7095	220	29	1	1	X
ejpam-7095	220	30	)	)	PUNCT
ejpam-7095	220	31	has	have	VERB
ejpam-7095	220	32	a	a	DET
ejpam-7095	220	33	unique	unique	ADJ
ejpam-7095	220	34	solution	solution	NOUN
ejpam-7095	220	35	.	.	PUNCT
ejpam-7095	221	1	4	4	X
ejpam-7095	221	2	.	.	X
ejpam-7095	221	3	ulam	ulam	NOUN
ejpam-7095	221	4	-	-	PUNCT
ejpam-7095	221	5	hyers	hyer	NOUN
ejpam-7095	221	6	stability	stability	VERB
ejpam-7095	221	7	the	the	DET
ejpam-7095	221	8	solution	solution	NOUN
ejpam-7095	221	9	of	of	ADP
ejpam-7095	221	10	problem	problem	NOUN
ejpam-7095	221	11	(	(	PUNCT
ejpam-7095	221	12	1)–(3	1)–(3	NUM
ejpam-7095	221	13	)	)	PUNCT
ejpam-7095	221	14	is	be	AUX
ejpam-7095	221	15	ulam	ulam	NOUN
ejpam-7095	221	16	-	-	PUNCT
ejpam-7095	221	17	hyers	hyer	NOUN
ejpam-7095	221	18	stable	stable	ADJ
ejpam-7095	221	19	under	under	ADP
ejpam-7095	221	20	hypotheses	hypothesis	NOUN
ejpam-7095	221	21	h5	h5	NOUN
ejpam-7095	221	22	.	.	PUNCT
ejpam-7095	222	1	proof	proof	NOUN
ejpam-7095	222	2	.	.	PUNCT
ejpam-7095	223	1	let	let	VERB
ejpam-7095	223	2	the	the	DET
ejpam-7095	223	3	exact	exact	ADJ
ejpam-7095	223	4	solution	solution	NOUN
ejpam-7095	223	5	of	of	ADP
ejpam-7095	223	6	the	the	DET
ejpam-7095	223	7	problem	problem	NOUN
ejpam-7095	223	8	is	be	AUX
ejpam-7095	223	9	given	give	VERB
ejpam-7095	223	10	by	by	ADP
ejpam-7095	223	11	:	:	PUNCT
ejpam-7095	223	12	u(x̄	u(x̄	NUM
ejpam-7095	223	13	,	,	PUNCT
ejpam-7095	223	14	τ	τ	X
ejpam-7095	223	15	)	)	PUNCT
ejpam-7095	223	16	=	=	SYM
ejpam-7095	223	17	g2(x̄	g2(x̄	PROPN
ejpam-7095	223	18	)	)	PUNCT
ejpam-7095	224	1	+	+	NUM
ejpam-7095	224	2	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	224	3	(	(	PUNCT
ejpam-7095	224	4	1−	1−	NUM
ejpam-7095	224	5	α	α	NOUN
ejpam-7095	224	6	)	)	PUNCT
ejpam-7095	224	7	β(α	β(α	PROPN
ejpam-7095	224	8	)	)	PUNCT
ejpam-7095	224	9	(	(	PUNCT
ejpam-7095	224	10	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	224	11	,	,	PUNCT
ejpam-7095	224	12	τ	τ	X
ejpam-7095	224	13	)	)	PUNCT
ejpam-7095	224	14	+	+	CCONJ
ejpam-7095	224	15	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	224	16	,	,	PUNCT
ejpam-7095	224	17	τ	τ	X
ejpam-7095	224	18	)	)	PUNCT
ejpam-7095	224	19	+	+	CCONJ
ejpam-7095	224	20	f(x̄	f(x̄	PROPN
ejpam-7095	224	21	,	,	PUNCT
ejpam-7095	224	22	τ	τ	X
ejpam-7095	224	23	)	)	PUNCT
ejpam-7095	224	24	)	)	PUNCT
ejpam-7095	225	1	+	+	CCONJ
ejpam-7095	225	2	α	α	PROPN
ejpam-7095	225	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	225	4	)	)	PUNCT
ejpam-7095	225	5	(	(	PUNCT
ejpam-7095	225	6	∫	∫	PROPN
ejpam-7095	225	7	τ	τ	X
ejpam-7095	225	8	0	0	NUM
ejpam-7095	225	9	(	(	PUNCT
ejpam-7095	225	10	τ	τ	PROPN
ejpam-7095	225	11	−	−	PROPN
ejpam-7095	225	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	225	13	(	(	PUNCT
ejpam-7095	225	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	225	15	,	,	PUNCT
ejpam-7095	225	16	ϑ	ϑ	NOUN
ejpam-7095	225	17	)	)	PUNCT
ejpam-7095	225	18	+	+	CCONJ
ejpam-7095	225	19	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	225	20	,	,	PUNCT
ejpam-7095	225	21	ϑ	ϑ	NOUN
ejpam-7095	225	22	)	)	PUNCT
ejpam-7095	225	23	+	+	CCONJ
ejpam-7095	225	24	f(x̄	f(x̄	NOUN
ejpam-7095	225	25	,	,	PUNCT
ejpam-7095	225	26	ϑ	ϑ	NOUN
ejpam-7095	225	27	)	)	PUNCT
ejpam-7095	225	28	)	)	PUNCT
ejpam-7095	225	29	dϑ	dϑ	NOUN
ejpam-7095	225	30	)	)	PUNCT
ejpam-7095	225	31	,	,	PUNCT
ejpam-7095	225	32	(	(	PUNCT
ejpam-7095	225	33	7	7	X
ejpam-7095	225	34	)	)	PUNCT
ejpam-7095	225	35	and	and	CCONJ
ejpam-7095	225	36	let	let	VERB
ejpam-7095	225	37	u(x̄	u(x̄	NOUN
ejpam-7095	225	38	,	,	PUNCT
ejpam-7095	225	39	τ	τ	X
ejpam-7095	225	40	)	)	PUNCT
ejpam-7095	225	41	be	be	VERB
ejpam-7095	225	42	the	the	DET
ejpam-7095	225	43	approximate	approximate	ADJ
ejpam-7095	225	44	solution	solution	NOUN
ejpam-7095	225	45	defined	define	VERB
ejpam-7095	225	46	as	as	ADP
ejpam-7095	225	47	:	:	PUNCT
ejpam-7095	225	48	u(x̄	u(x̄	NUM
ejpam-7095	225	49	,	,	PUNCT
ejpam-7095	225	50	τ	τ	X
ejpam-7095	225	51	)	)	PUNCT
ejpam-7095	225	52	=	=	SYM
ejpam-7095	225	53	g2(x̄	g2(x̄	PROPN
ejpam-7095	225	54	)	)	PUNCT
ejpam-7095	225	55	+	+	NUM
ejpam-7095	225	56	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	225	57	(	(	PUNCT
ejpam-7095	225	58	1−	1−	NUM
ejpam-7095	225	59	α	α	NOUN
ejpam-7095	225	60	)	)	PUNCT
ejpam-7095	225	61	β(α	β(α	PROPN
ejpam-7095	225	62	)	)	PUNCT
ejpam-7095	225	63	(	(	PUNCT
ejpam-7095	225	64	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	225	65	,	,	PUNCT
ejpam-7095	225	66	τ	τ	X
ejpam-7095	225	67	)	)	PUNCT
ejpam-7095	225	68	+	+	CCONJ
ejpam-7095	225	69	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	225	70	,	,	PUNCT
ejpam-7095	225	71	τ	τ	X
ejpam-7095	225	72	)	)	PUNCT
ejpam-7095	225	73	+	+	CCONJ
ejpam-7095	225	74	f(x̄	f(x̄	PROPN
ejpam-7095	225	75	,	,	PUNCT
ejpam-7095	225	76	τ	τ	X
ejpam-7095	225	77	)	)	PUNCT
ejpam-7095	225	78	)	)	PUNCT
ejpam-7095	226	1	+	+	CCONJ
ejpam-7095	226	2	α	α	PROPN
ejpam-7095	226	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	226	4	)	)	PUNCT
ejpam-7095	226	5	(	(	PUNCT
ejpam-7095	226	6	∫	∫	PROPN
ejpam-7095	226	7	τ	τ	X
ejpam-7095	226	8	0	0	NUM
ejpam-7095	226	9	(	(	PUNCT
ejpam-7095	226	10	τ	τ	PROPN
ejpam-7095	226	11	−	−	PROPN
ejpam-7095	226	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	226	13	(	(	PUNCT
ejpam-7095	226	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	226	15	,	,	PUNCT
ejpam-7095	226	16	ϑ	ϑ	NOUN
ejpam-7095	226	17	)	)	PUNCT
ejpam-7095	226	18	+	+	CCONJ
ejpam-7095	226	19	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	226	20	,	,	PUNCT
ejpam-7095	226	21	ϑ	ϑ	NOUN
ejpam-7095	226	22	)	)	PUNCT
ejpam-7095	226	23	+	+	CCONJ
ejpam-7095	226	24	f(x̄	f(x̄	NOUN
ejpam-7095	226	25	,	,	PUNCT
ejpam-7095	226	26	ϑ	ϑ	NOUN
ejpam-7095	226	27	)	)	PUNCT
ejpam-7095	226	28	+	+	CCONJ
ejpam-7095	226	29	f(x̄	f(x̄	NOUN
ejpam-7095	226	30	,	,	PUNCT
ejpam-7095	226	31	ϑ	ϑ	NOUN
ejpam-7095	226	32	)	)	PUNCT
ejpam-7095	226	33	)	)	PUNCT
ejpam-7095	226	34	dϑ	dϑ	NOUN
ejpam-7095	226	35	)	)	PUNCT
ejpam-7095	226	36	,	,	PUNCT
ejpam-7095	226	37	(	(	PUNCT
ejpam-7095	226	38	8)	8)	NUM
ejpam-7095	226	39	kamran	kamran	PROPN
ejpam-7095	226	40	et	et	PROPN
ejpam-7095	226	41	al	al	PROPN
ejpam-7095	226	42	.	.	PUNCT
ejpam-7095	226	43	/	/	SYM
ejpam-7095	226	44	eur	eur	PROPN
ejpam-7095	226	45	.	.	PUNCT
ejpam-7095	227	1	j.	j.	PROPN
ejpam-7095	227	2	pure	pure	PROPN
ejpam-7095	227	3	appl	appl	PROPN
ejpam-7095	227	4	.	.	PROPN
ejpam-7095	227	5	math	math	PROPN
ejpam-7095	227	6	,	,	PUNCT
ejpam-7095	227	7	18	18	NUM
ejpam-7095	227	8	(	(	PUNCT
ejpam-7095	227	9	4	4	NUM
ejpam-7095	227	10	)	)	PUNCT
ejpam-7095	227	11	(	(	PUNCT
ejpam-7095	227	12	2025	2025	NUM
ejpam-7095	227	13	)	)	PUNCT
ejpam-7095	227	14	,	,	PUNCT
ejpam-7095	227	15	7095	7095	NUM
ejpam-7095	227	16	11	11	NUM
ejpam-7095	227	17	of	of	ADP
ejpam-7095	227	18	30	30	NUM
ejpam-7095	227	19	where	where	SCONJ
ejpam-7095	227	20	f(x̄	f(x̄	NOUN
ejpam-7095	227	21	,	,	PUNCT
ejpam-7095	227	22	ϑ	ϑ	NOUN
ejpam-7095	227	23	)	)	PUNCT
ejpam-7095	227	24	is	be	AUX
ejpam-7095	227	25	a	a	DET
ejpam-7095	227	26	perturbation	perturbation	NOUN
ejpam-7095	227	27	term	term	NOUN
ejpam-7095	227	28	with	with	ADP
ejpam-7095	227	29	|f(x̄	|f(x̄	PRON
ejpam-7095	227	30	,	,	PUNCT
ejpam-7095	227	31	ϑ)|	ϑ)|	VERB
ejpam-7095	227	32	≤	≤	ADJ
ejpam-7095	227	33	ϵ7	ϵ7	NOUN
ejpam-7095	227	34	for	for	ADP
ejpam-7095	227	35	some	some	DET
ejpam-7095	227	36	constant	constant	ADJ
ejpam-7095	227	37	ϵ7	ϵ7	NOUN
ejpam-7095	227	38	>	>	X
ejpam-7095	227	39	0	0	X
ejpam-7095	227	40	.	.	PUNCT
ejpam-7095	228	1	subtracting	subtract	VERB
ejpam-7095	228	2	(	(	PUNCT
ejpam-7095	228	3	8)	8)	NUM
ejpam-7095	228	4	from	from	ADP
ejpam-7095	228	5	(	(	PUNCT
ejpam-7095	228	6	7	7	NUM
ejpam-7095	228	7	)	)	PUNCT
ejpam-7095	228	8	,	,	PUNCT
ejpam-7095	228	9	we	we	PRON
ejpam-7095	228	10	get	get	VERB
ejpam-7095	228	11	:	:	PUNCT
ejpam-7095	228	12	|u(x̄	|u(x̄	X
ejpam-7095	228	13	,	,	PUNCT
ejpam-7095	228	14	τ)−	τ)−	PROPN
ejpam-7095	228	15	u(x̄	u(x̄	NUM
ejpam-7095	228	16	,	,	PUNCT
ejpam-7095	228	17	τ)|	τ)|	PROPN
ejpam-7095	228	18	=	=	PUNCT
ejpam-7095	228	19	∣∣∣∣(g2(x̄	∣∣∣∣(g2(x̄	X
ejpam-7095	228	20	)	)	PUNCT
ejpam-7095	228	21	+	+	NUM
ejpam-7095	228	22	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	228	23	(	(	PUNCT
ejpam-7095	228	24	1−	1−	NUM
ejpam-7095	228	25	α	α	NOUN
ejpam-7095	228	26	)	)	PUNCT
ejpam-7095	228	27	β(α	β(α	PROPN
ejpam-7095	228	28	)	)	PUNCT
ejpam-7095	228	29	(	(	PUNCT
ejpam-7095	228	30	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	228	31	,	,	PUNCT
ejpam-7095	228	32	τ	τ	X
ejpam-7095	228	33	)	)	PUNCT
ejpam-7095	228	34	+	+	CCONJ
ejpam-7095	228	35	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	228	36	,	,	PUNCT
ejpam-7095	228	37	τ	τ	X
ejpam-7095	228	38	)	)	PUNCT
ejpam-7095	228	39	+	+	CCONJ
ejpam-7095	228	40	f(x̄	f(x̄	PROPN
ejpam-7095	228	41	,	,	PUNCT
ejpam-7095	228	42	τ	τ	X
ejpam-7095	228	43	)	)	PUNCT
ejpam-7095	228	44	)	)	PUNCT
ejpam-7095	229	1	+	+	CCONJ
ejpam-7095	229	2	α	α	PROPN
ejpam-7095	229	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	229	4	)	)	PUNCT
ejpam-7095	229	5	(	(	PUNCT
ejpam-7095	229	6	∫	∫	PROPN
ejpam-7095	229	7	τ	τ	X
ejpam-7095	229	8	0	0	NUM
ejpam-7095	229	9	(	(	PUNCT
ejpam-7095	229	10	τ	τ	PROPN
ejpam-7095	229	11	−	−	PROPN
ejpam-7095	229	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	229	13	(	(	PUNCT
ejpam-7095	229	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	229	15	,	,	PUNCT
ejpam-7095	229	16	ϑ	ϑ	NOUN
ejpam-7095	229	17	)	)	PUNCT
ejpam-7095	229	18	+	+	CCONJ
ejpam-7095	229	19	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	229	20	,	,	PUNCT
ejpam-7095	229	21	ϑ	ϑ	NOUN
ejpam-7095	229	22	)	)	PUNCT
ejpam-7095	229	23	+	+	CCONJ
ejpam-7095	229	24	f(x̄	f(x̄	NOUN
ejpam-7095	229	25	,	,	PUNCT
ejpam-7095	229	26	ϑ	ϑ	NOUN
ejpam-7095	229	27	)	)	PUNCT
ejpam-7095	229	28	)	)	PUNCT
ejpam-7095	229	29	dϑ	dϑ	NOUN
ejpam-7095	229	30	)	)	PUNCT
ejpam-7095	229	31	)	)	PUNCT
ejpam-7095	230	1	−	−	PROPN
ejpam-7095	230	2	(	(	PUNCT
ejpam-7095	230	3	g2(x̄	g2(x̄	PROPN
ejpam-7095	230	4	)	)	PUNCT
ejpam-7095	230	5	+	+	NUM
ejpam-7095	230	6	g3(x̄)t+	g3(x̄)t+	NOUN
ejpam-7095	230	7	(	(	PUNCT
ejpam-7095	230	8	1−	1−	NUM
ejpam-7095	230	9	α	α	NOUN
ejpam-7095	230	10	)	)	PUNCT
ejpam-7095	230	11	β(α	β(α	PROPN
ejpam-7095	230	12	)	)	PUNCT
ejpam-7095	230	13	(	(	PUNCT
ejpam-7095	230	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	230	15	,	,	PUNCT
ejpam-7095	230	16	τ	τ	X
ejpam-7095	230	17	)	)	PUNCT
ejpam-7095	231	1	+	+	CCONJ
ejpam-7095	231	2	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	231	3	,	,	PUNCT
ejpam-7095	231	4	τ	τ	X
ejpam-7095	231	5	)	)	PUNCT
ejpam-7095	231	6	+	+	CCONJ
ejpam-7095	231	7	f(x̄	f(x̄	PROPN
ejpam-7095	231	8	,	,	PUNCT
ejpam-7095	231	9	τ	τ	X
ejpam-7095	231	10	)	)	PUNCT
ejpam-7095	231	11	)	)	PUNCT
ejpam-7095	232	1	+	+	CCONJ
ejpam-7095	232	2	α	α	PROPN
ejpam-7095	232	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	232	4	)	)	PUNCT
ejpam-7095	232	5	(	(	PUNCT
ejpam-7095	232	6	∫	∫	PROPN
ejpam-7095	232	7	τ	τ	X
ejpam-7095	232	8	0	0	NUM
ejpam-7095	232	9	(	(	PUNCT
ejpam-7095	232	10	τ	τ	PROPN
ejpam-7095	232	11	−	−	PROPN
ejpam-7095	232	12	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	232	13	(	(	PUNCT
ejpam-7095	232	14	λ1∇2u(x̄	λ1∇2u(x̄	X
ejpam-7095	232	15	,	,	PUNCT
ejpam-7095	232	16	ϑ	ϑ	NOUN
ejpam-7095	232	17	)	)	PUNCT
ejpam-7095	232	18	+	+	CCONJ
ejpam-7095	232	19	λ2u(x̄	λ2u(x̄	NOUN
ejpam-7095	232	20	,	,	PUNCT
ejpam-7095	232	21	ϑ	ϑ	NOUN
ejpam-7095	232	22	)	)	PUNCT
ejpam-7095	232	23	+	+	CCONJ
ejpam-7095	232	24	f(x̄	f(x̄	NOUN
ejpam-7095	232	25	,	,	PUNCT
ejpam-7095	232	26	ϑ	ϑ	NOUN
ejpam-7095	232	27	)	)	PUNCT
ejpam-7095	232	28	+	+	CCONJ
ejpam-7095	232	29	f(x̄	f(x̄	NOUN
ejpam-7095	232	30	,	,	PUNCT
ejpam-7095	232	31	ϑ	ϑ	NOUN
ejpam-7095	232	32	)	)	PUNCT
ejpam-7095	232	33	)	)	PUNCT
ejpam-7095	232	34	dϑ	dϑ	NOUN
ejpam-7095	232	35	)	)	PUNCT
ejpam-7095	232	36	)	)	PUNCT
ejpam-7095	232	37	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7095	232	38	≤	≤	NOUN
ejpam-7095	232	39	(	(	PUNCT
ejpam-7095	232	40	1−	1−	NUM
ejpam-7095	232	41	α	α	NOUN
ejpam-7095	232	42	)	)	PUNCT
ejpam-7095	232	43	β(α	β(α	PROPN
ejpam-7095	232	44	)	)	PUNCT
ejpam-7095	232	45	(	(	PUNCT
ejpam-7095	232	46	|λ1||∇2u(x̄	|λ1||∇2u(x̄	X
ejpam-7095	232	47	,	,	PUNCT
ejpam-7095	232	48	τ)−∇2u(x̄	τ)−∇2u(x̄	ADV
ejpam-7095	232	49	,	,	PUNCT
ejpam-7095	232	50	τ)|+	τ)|+	NOUN
ejpam-7095	232	51	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	232	52	,	,	PUNCT
ejpam-7095	232	53	τ)−	τ)−	PROPN
ejpam-7095	232	54	u(x̄	u(x̄	NUM
ejpam-7095	232	55	,	,	PUNCT
ejpam-7095	232	56	τ)|	τ)|	PROPN
ejpam-7095	232	57	)	)	PUNCT
ejpam-7095	233	1	+	+	CCONJ
ejpam-7095	233	2	α	α	PROPN
ejpam-7095	233	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	233	4	)	)	PUNCT
ejpam-7095	233	5	∫	∫	PROPN
ejpam-7095	234	1	τ	τ	PROPN
ejpam-7095	234	2	0	0	PROPN
ejpam-7095	234	3	(	(	PUNCT
ejpam-7095	234	4	τ	τ	PROPN
ejpam-7095	234	5	−	−	PROPN
ejpam-7095	234	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	234	7	(	(	PUNCT
ejpam-7095	234	8	|λ1||∇2u(x̄	|λ1||∇2u(x̄	NOUN
ejpam-7095	234	9	,	,	PUNCT
ejpam-7095	234	10	τ)−∇2u(x̄	τ)−∇2u(x̄	PROPN
ejpam-7095	234	11	,	,	PUNCT
ejpam-7095	234	12	τ)|+	τ)|+	NOUN
ejpam-7095	234	13	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	234	14	,	,	PUNCT
ejpam-7095	234	15	τ)−	τ)−	PROPN
ejpam-7095	234	16	u(x̄	u(x̄	NUM
ejpam-7095	234	17	,	,	PUNCT
ejpam-7095	234	18	τ)|	τ)|	PROPN
ejpam-7095	234	19	+	+	PROPN
ejpam-7095	234	20	|f(x̄	|f(x̄	NOUN
ejpam-7095	234	21	,	,	PUNCT
ejpam-7095	234	22	τ)|	τ)|	PROPN
ejpam-7095	234	23	)	)	PUNCT
ejpam-7095	234	24	dϑ	dϑ	NOUN
ejpam-7095	234	25	≤	≤	NUM
ejpam-7095	234	26	(	(	PUNCT
ejpam-7095	234	27	1−	1−	NUM
ejpam-7095	234	28	α	α	NOUN
ejpam-7095	234	29	)	)	PUNCT
ejpam-7095	234	30	β(α	β(α	PROPN
ejpam-7095	234	31	)	)	PUNCT
ejpam-7095	234	32	(	(	PUNCT
ejpam-7095	234	33	|λ1|ϵ5|u(x̄	|λ1|ϵ5|u(x̄	X
ejpam-7095	234	34	,	,	PUNCT
ejpam-7095	234	35	τ)−	τ)−	PROPN
ejpam-7095	234	36	u(x̄	u(x̄	NUM
ejpam-7095	234	37	,	,	PUNCT
ejpam-7095	234	38	τ)|+	τ)|+	VERB
ejpam-7095	234	39	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	234	40	,	,	PUNCT
ejpam-7095	234	41	τ)−	τ)−	PROPN
ejpam-7095	234	42	u(x̄	u(x̄	NUM
ejpam-7095	234	43	,	,	PUNCT
ejpam-7095	234	44	τ)|	τ)|	PROPN
ejpam-7095	234	45	)	)	PUNCT
ejpam-7095	235	1	+	+	CCONJ
ejpam-7095	235	2	α	α	PROPN
ejpam-7095	235	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	235	4	)	)	PUNCT
ejpam-7095	235	5	∫	∫	PROPN
ejpam-7095	236	1	τ	τ	PROPN
ejpam-7095	236	2	0	0	PROPN
ejpam-7095	236	3	(	(	PUNCT
ejpam-7095	236	4	τ	τ	PROPN
ejpam-7095	236	5	−	−	PROPN
ejpam-7095	236	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	236	7	(	(	PUNCT
ejpam-7095	236	8	|λ1|ϵ5|u(x̄	|λ1|ϵ5|u(x̄	X
ejpam-7095	236	9	,	,	PUNCT
ejpam-7095	236	10	τ)−	τ)−	PROPN
ejpam-7095	236	11	u(x̄	u(x̄	NUM
ejpam-7095	236	12	,	,	PUNCT
ejpam-7095	236	13	τ)|+	τ)|+	VERB
ejpam-7095	236	14	|λ2||u(x̄	|λ2||u(x̄	PROPN
ejpam-7095	236	15	,	,	PUNCT
ejpam-7095	236	16	τ)−	τ)−	PROPN
ejpam-7095	236	17	u(x̄	u(x̄	NUM
ejpam-7095	236	18	,	,	PUNCT
ejpam-7095	236	19	τ)|+	τ)|+	NOUN
ejpam-7095	236	20	ϵ7	ϵ7	NOUN
ejpam-7095	236	21	)	)	PUNCT
ejpam-7095	236	22	dϑ	dϑ	NOUN
ejpam-7095	236	23	taking	take	VERB
ejpam-7095	236	24	the	the	DET
ejpam-7095	236	25	supremum	supremum	ADJ
ejpam-7095	236	26	norm	norm	NOUN
ejpam-7095	236	27	:	:	PUNCT
ejpam-7095	236	28	∥u−	∥u−	PROPN
ejpam-7095	236	29	u∥∞	u∥∞	PROPN
ejpam-7095	236	30	≤	≤	NOUN
ejpam-7095	236	31	(	(	PUNCT
ejpam-7095	236	32	1−	1−	NUM
ejpam-7095	236	33	α	α	NOUN
ejpam-7095	236	34	)	)	PUNCT
ejpam-7095	236	35	β(α	β(α	PROPN
ejpam-7095	236	36	)	)	PUNCT
ejpam-7095	236	37	(	(	PUNCT
ejpam-7095	236	38	|λ1|ϵ5∥u−	|λ1|ϵ5∥u−	PROPN
ejpam-7095	236	39	u∥∞	u∥∞	PROPN
ejpam-7095	236	40	+	+	PROPN
ejpam-7095	236	41	|λ2|∥u−	|λ2|∥u−	NUM
ejpam-7095	236	42	u∥∞	u∥∞	PROPN
ejpam-7095	236	43	)	)	PUNCT
ejpam-7095	237	1	+	+	CCONJ
ejpam-7095	237	2	α	α	PROPN
ejpam-7095	237	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	237	4	)	)	PUNCT
ejpam-7095	237	5	∫	∫	PROPN
ejpam-7095	238	1	τ	τ	PROPN
ejpam-7095	238	2	0	0	PROPN
ejpam-7095	238	3	(	(	PUNCT
ejpam-7095	238	4	τ	τ	PROPN
ejpam-7095	238	5	−	−	PROPN
ejpam-7095	238	6	ϑ)α−1	ϑ)α−1	NOUN
ejpam-7095	238	7	(	(	PUNCT
ejpam-7095	238	8	|λ1|ϵ5∥u−	|λ1|ϵ5∥u−	PROPN
ejpam-7095	238	9	u∥∞	u∥∞	PROPN
ejpam-7095	238	10	+	+	PROPN
ejpam-7095	238	11	|λ2|∥u−	|λ2|∥u−	ADJ
ejpam-7095	238	12	u∥∞	u∥∞	NOUN
ejpam-7095	238	13	+	+	CCONJ
ejpam-7095	238	14	ϵ7	ϵ7	ADJ
ejpam-7095	238	15	)	)	PUNCT
ejpam-7095	238	16	dϑ	dϑ	NOUN
ejpam-7095	238	17	≤	≤	NUM
ejpam-7095	238	18	(	(	PUNCT
ejpam-7095	238	19	(	(	PUNCT
ejpam-7095	238	20	1−	1−	NUM
ejpam-7095	238	21	α	α	NOUN
ejpam-7095	238	22	)	)	PUNCT
ejpam-7095	238	23	β(α	β(α	ADJ
ejpam-7095	238	24	)	)	PUNCT
ejpam-7095	239	1	+	+	NUM
ejpam-7095	239	2	τα	τα	NOUN
ejpam-7095	239	3	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	239	4	)	)	PUNCT
ejpam-7095	239	5	)	)	PUNCT
ejpam-7095	240	1	(	(	PUNCT
ejpam-7095	240	2	|λ1|ϵ5∥u−	|λ1|ϵ5∥u−	PROPN
ejpam-7095	240	3	u∥∞	u∥∞	PROPN
ejpam-7095	240	4	+	+	PROPN
ejpam-7095	240	5	|λ2|∥u−	|λ2|∥u−	NUM
ejpam-7095	240	6	u∥∞	u∥∞	PROPN
ejpam-7095	240	7	)	)	PUNCT
ejpam-7095	241	1	+	+	CCONJ
ejpam-7095	241	2	ϵ7τ	ϵ7τ	PROPN
ejpam-7095	241	3	α	α	NOUN
ejpam-7095	241	4	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	241	5	)	)	PUNCT
ejpam-7095	241	6	)	)	PUNCT
ejpam-7095	242	1	=	=	PUNCT
ejpam-7095	242	2	(	(	PUNCT
ejpam-7095	242	3	(	(	PUNCT
ejpam-7095	242	4	(	(	PUNCT
ejpam-7095	242	5	1−	1−	NUM
ejpam-7095	242	6	α)γ(α	α)γ(α	NOUN
ejpam-7095	242	7	)	)	PUNCT
ejpam-7095	243	1	+	+	CCONJ
ejpam-7095	243	2	τα)(|λ1|ϵ5	τα)(|λ1|ϵ5	X
ejpam-7095	243	3	+	+	CCONJ
ejpam-7095	243	4	|λ2|	|λ2|	NOUN
ejpam-7095	243	5	)	)	PUNCT
ejpam-7095	243	6	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	243	7	)	)	PUNCT
ejpam-7095	243	8	)	)	PUNCT
ejpam-7095	244	1	∥u−	∥u−	PROPN
ejpam-7095	244	2	u∥∞	u∥∞	PROPN
ejpam-7095	245	1	+	+	PROPN
ejpam-7095	245	2	ϵ7τ	ϵ7τ	PROPN
ejpam-7095	245	3	α	α	PROPN
ejpam-7095	245	4	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	245	5	)	)	PUNCT
ejpam-7095	245	6	.	.	PUNCT
ejpam-7095	246	1	rearranging	rearrange	VERB
ejpam-7095	246	2	,	,	PUNCT
ejpam-7095	246	3	we	we	PRON
ejpam-7095	246	4	get	get	VERB
ejpam-7095	246	5	:	:	PUNCT
ejpam-7095	246	6	[	[	PUNCT
ejpam-7095	246	7	1−	1−	NUM
ejpam-7095	246	8	(	(	PUNCT
ejpam-7095	246	9	(	(	PUNCT
ejpam-7095	246	10	(	(	PUNCT
ejpam-7095	246	11	1−	1−	NUM
ejpam-7095	246	12	α)γ(α	α)γ(α	NOUN
ejpam-7095	246	13	)	)	PUNCT
ejpam-7095	247	1	+	+	CCONJ
ejpam-7095	247	2	τα)(|λ1|ϵ5	τα)(|λ1|ϵ5	X
ejpam-7095	247	3	+	+	CCONJ
ejpam-7095	247	4	|λ2|	|λ2|	NOUN
ejpam-7095	247	5	)	)	PUNCT
ejpam-7095	247	6	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	247	7	)	)	PUNCT
ejpam-7095	247	8	)	)	PUNCT
ejpam-7095	247	9	]	]	PUNCT
ejpam-7095	248	1	∥u−	∥u−	PROPN
ejpam-7095	248	2	u∥∞	u∥∞	PROPN
ejpam-7095	248	3	≤	≤	PROPN
ejpam-7095	248	4	ϵ7τ	ϵ7τ	PROPN
ejpam-7095	248	5	α	α	PROPN
ejpam-7095	248	6	β(α)γ(α	β(α)γ(α	NOUN
ejpam-7095	248	7	)	)	PUNCT
ejpam-7095	248	8	.	.	PUNCT
ejpam-7095	249	1	since	since	SCONJ
ejpam-7095	249	2	eq.(6	eq.(6	ADJ
ejpam-7095	249	3	)	)	PUNCT
ejpam-7095	249	4	ensures	ensure	VERB
ejpam-7095	249	5	that	that	SCONJ
ejpam-7095	249	6	(	(	PUNCT
ejpam-7095	249	7	1−α)γ(α)+τα	1−α)γ(α)+τα	NUM
ejpam-7095	249	8	γ(α)β(α	γ(α)β(α	NOUN
ejpam-7095	249	9	)	)	PUNCT
ejpam-7095	249	10	(	(	PUNCT
ejpam-7095	249	11	(	(	PUNCT
ejpam-7095	249	12	ϵ5|λ1|+	ϵ5|λ1|+	X
ejpam-7095	249	13	|λ2|	|λ2|	NOUN
ejpam-7095	249	14	)	)	PUNCT
ejpam-7095	249	15	∥u1	∥u1	PROPN
ejpam-7095	249	16	−	−	PUNCT
ejpam-7095	249	17	u2∥∞	u2∥∞	PUNCT
ejpam-7095	249	18	)	)	PUNCT
ejpam-7095	250	1	<	<	X
ejpam-7095	251	1	1	1	NUM
ejpam-7095	251	2	,	,	PUNCT
ejpam-7095	251	3	we	we	PRON
ejpam-7095	251	4	have	have	AUX
ejpam-7095	251	5	∥u−	∥u−	VERB
ejpam-7095	251	6	u∥∞	u∥∞	PROPN
ejpam-7095	251	7	≤	≤	PROPN
ejpam-7095	251	8	gϵ.	gϵ.	PROPN
ejpam-7095	251	9	kamran	kamran	PROPN
ejpam-7095	251	10	et	et	PROPN
ejpam-7095	251	11	al	al	PROPN
ejpam-7095	251	12	.	.	PUNCT
ejpam-7095	251	13	/	/	SYM
ejpam-7095	251	14	eur	eur	PROPN
ejpam-7095	251	15	.	.	PUNCT
ejpam-7095	252	1	j.	j.	PROPN
ejpam-7095	252	2	pure	pure	PROPN
ejpam-7095	252	3	appl	appl	PROPN
ejpam-7095	252	4	.	.	PROPN
ejpam-7095	252	5	math	math	PROPN
ejpam-7095	252	6	,	,	PUNCT
ejpam-7095	252	7	18	18	NUM
ejpam-7095	252	8	(	(	PUNCT
ejpam-7095	252	9	4	4	NUM
ejpam-7095	252	10	)	)	PUNCT
ejpam-7095	252	11	(	(	PUNCT
ejpam-7095	252	12	2025	2025	NUM
ejpam-7095	252	13	)	)	PUNCT
ejpam-7095	252	14	,	,	PUNCT
ejpam-7095	252	15	7095	7095	NUM
ejpam-7095	252	16	12	12	NUM
ejpam-7095	252	17	of	of	ADP
ejpam-7095	252	18	30	30	NUM
ejpam-7095	253	1	where	where	SCONJ
ejpam-7095	253	2	g	g	NOUN
ejpam-7095	253	3	=	=	SYM
ejpam-7095	253	4	τα	τα	PROPN
ejpam-7095	253	5	{	{	PUNCT
ejpam-7095	253	6	β(α)γ(α)−	β(α)γ(α)−	NOUN
ejpam-7095	254	1	[	[	X
ejpam-7095	254	2	(	(	PUNCT
ejpam-7095	254	3	(	(	PUNCT
ejpam-7095	254	4	1−	1−	NUM
ejpam-7095	254	5	α)γ(α	α)γ(α	NOUN
ejpam-7095	254	6	)	)	PUNCT
ejpam-7095	255	1	+	+	CCONJ
ejpam-7095	255	2	τα)(|λ1|ϵ5	τα)(|λ1|ϵ5	X
ejpam-7095	255	3	+	+	CCONJ
ejpam-7095	255	4	|λ2|	|λ2|	NOUN
ejpam-7095	255	5	)	)	PUNCT
ejpam-7095	255	6	]	]	PUNCT
ejpam-7095	255	7	}	}	PUNCT
ejpam-7095	255	8	.	.	PUNCT
ejpam-7095	256	1	since	since	SCONJ
ejpam-7095	256	2	g	g	PROPN
ejpam-7095	256	3	>	>	X
ejpam-7095	256	4	0	0	NUM
ejpam-7095	256	5	,	,	PUNCT
ejpam-7095	256	6	the	the	DET
ejpam-7095	256	7	solution	solution	NOUN
ejpam-7095	256	8	is	be	AUX
ejpam-7095	256	9	ulam	ulam	NOUN
ejpam-7095	256	10	-	-	PUNCT
ejpam-7095	256	11	hyers	hyer	NOUN
ejpam-7095	256	12	stable	stable	ADJ
ejpam-7095	256	13	.	.	PUNCT
ejpam-7095	257	1	5	5	X
ejpam-7095	257	2	.	.	NUM
ejpam-7095	257	3	proposed	propose	VERB
ejpam-7095	257	4	numerical	numerical	PROPN
ejpam-7095	257	5	method	method	PROPN
ejpam-7095	257	6	the	the	DET
ejpam-7095	257	7	proposed	propose	VERB
ejpam-7095	257	8	numerical	numerical	ADJ
ejpam-7095	257	9	method	method	NOUN
ejpam-7095	257	10	for	for	ADP
ejpam-7095	257	11	solving	solve	VERB
ejpam-7095	257	12	the	the	DET
ejpam-7095	257	13	tfdwe	tfdwe	NOUN
ejpam-7095	257	14	with	with	ADP
ejpam-7095	257	15	the	the	DET
ejpam-7095	257	16	mabc	mabc	ADJ
ejpam-7095	257	17	derivative	derivative	ADJ
ejpam-7095	257	18	consists	consist	NOUN
ejpam-7095	257	19	of	of	ADP
ejpam-7095	257	20	three	three	NUM
ejpam-7095	257	21	main	main	ADJ
ejpam-7095	257	22	steps	step	NOUN
ejpam-7095	257	23	:	:	PUNCT
ejpam-7095	257	24	(	(	PUNCT
ejpam-7095	257	25	a	a	X
ejpam-7095	257	26	)	)	PUNCT
ejpam-7095	257	27	discretization	discretization	NOUN
ejpam-7095	257	28	of	of	ADP
ejpam-7095	257	29	the	the	DET
ejpam-7095	257	30	time	time	NOUN
ejpam-7095	257	31	variable	variable	NOUN
ejpam-7095	257	32	via	via	ADP
ejpam-7095	257	33	the	the	DET
ejpam-7095	257	34	laplace	laplace	NOUN
ejpam-7095	257	35	transform	transform	NOUN
ejpam-7095	257	36	,	,	PUNCT
ejpam-7095	257	37	which	which	PRON
ejpam-7095	257	38	converts	convert	VERB
ejpam-7095	257	39	the	the	DET
ejpam-7095	257	40	problem	problem	NOUN
ejpam-7095	257	41	to	to	ADP
ejpam-7095	257	42	the	the	DET
ejpam-7095	257	43	laplace	laplace	NOUN
ejpam-7095	257	44	domain	domain	NOUN
ejpam-7095	257	45	;	;	PUNCT
ejpam-7095	257	46	(	(	PUNCT
ejpam-7095	257	47	b	b	X
ejpam-7095	257	48	)	)	PUNCT
ejpam-7095	257	49	solution	solution	NOUN
ejpam-7095	257	50	of	of	ADP
ejpam-7095	257	51	the	the	DET
ejpam-7095	257	52	resulting	result	VERB
ejpam-7095	257	53	boundary	boundary	ADJ
ejpam-7095	257	54	value	value	NOUN
ejpam-7095	257	55	problem	problem	NOUN
ejpam-7095	257	56	in	in	ADP
ejpam-7095	257	57	the	the	DET
ejpam-7095	257	58	laplace	laplace	NOUN
ejpam-7095	257	59	domain	domain	NOUN
ejpam-7095	257	60	using	use	VERB
ejpam-7095	257	61	the	the	DET
ejpam-7095	257	62	cscm	cscm	NOUN
ejpam-7095	257	63	;	;	PUNCT
ejpam-7095	257	64	and	and	CCONJ
ejpam-7095	257	65	(	(	PUNCT
ejpam-7095	257	66	c	c	NOUN
ejpam-7095	257	67	)	)	PUNCT
ejpam-7095	257	68	recovery	recovery	NOUN
ejpam-7095	257	69	of	of	ADP
ejpam-7095	257	70	the	the	DET
ejpam-7095	257	71	time	time	NOUN
ejpam-7095	257	72	-	-	PUNCT
ejpam-7095	257	73	domain	domain	NOUN
ejpam-7095	257	74	solution	solution	NOUN
ejpam-7095	257	75	by	by	ADP
ejpam-7095	257	76	applying	apply	VERB
ejpam-7095	257	77	a	a	DET
ejpam-7095	257	78	numerical	numerical	ADJ
ejpam-7095	257	79	inverse	inverse	NOUN
ejpam-7095	257	80	laplace	laplace	NOUN
ejpam-7095	257	81	transform	transform	NOUN
ejpam-7095	257	82	based	base	VERB
ejpam-7095	257	83	on	on	ADP
ejpam-7095	257	84	a	a	DET
ejpam-7095	257	85	modified	modify	VERB
ejpam-7095	257	86	talbot	talbot	PROPN
ejpam-7095	257	87	contour	contour	NOUN
ejpam-7095	257	88	and	and	CCONJ
ejpam-7095	257	89	the	the	DET
ejpam-7095	257	90	midpoint	midpoint	NOUN
ejpam-7095	257	91	rule	rule	NOUN
ejpam-7095	257	92	.	.	PUNCT
ejpam-7095	258	1	5.1	5.1	NUM
ejpam-7095	258	2	.	.	PUNCT
ejpam-7095	259	1	laplace	laplace	PROPN
ejpam-7095	259	2	transform	transform	VERB
ejpam-7095	259	3	the	the	DET
ejpam-7095	259	4	lt	lt	NOUN
ejpam-7095	259	5	is	be	AUX
ejpam-7095	259	6	applied	apply	VERB
ejpam-7095	259	7	to	to	ADP
ejpam-7095	259	8	tfdwe	tfdwe	PROPN
ejpam-7095	259	9	(	(	PUNCT
ejpam-7095	259	10	1)–(3	1)–(3	NUM
ejpam-7095	259	11	)	)	PUNCT
ejpam-7095	259	12	to	to	PART
ejpam-7095	259	13	discretize	discretize	VERB
ejpam-7095	259	14	the	the	DET
ejpam-7095	259	15	time	time	NOUN
ejpam-7095	259	16	variable	variable	NOUN
ejpam-7095	259	17	.	.	PUNCT
ejpam-7095	260	1	applying	apply	VERB
ejpam-7095	260	2	the	the	DET
ejpam-7095	260	3	lt	lt	NOUN
ejpam-7095	260	4	to	to	ADP
ejpam-7095	260	5	the	the	DET
ejpam-7095	260	6	model	model	NOUN
ejpam-7095	260	7	,	,	PUNCT
ejpam-7095	260	8	we	we	PRON
ejpam-7095	260	9	have	have	AUX
ejpam-7095	260	10	:	:	PUNCT
ejpam-7095	260	11	β(α	β(α	ADJ
ejpam-7095	260	12	)	)	PUNCT
ejpam-7095	260	13	(	(	PUNCT
ejpam-7095	260	14	sαû(x̄	sαû(x̄	PROPN
ejpam-7095	260	15	,	,	PUNCT
ejpam-7095	260	16	s)−	s)−	PROPN
ejpam-7095	260	17	sα−1u(x̄	sα−1u(x̄	NOUN
ejpam-7095	260	18	,	,	PUNCT
ejpam-7095	260	19	0)−	0)−	PUNCT
ejpam-7095	261	1	sα−2ut(x̄	sα−2ut(x̄	ADJ
ejpam-7095	261	2	,	,	PUNCT
ejpam-7095	261	3	0	0	NUM
ejpam-7095	261	4	)	)	PUNCT
ejpam-7095	261	5	)	)	PUNCT
ejpam-7095	262	1	sα(1−	sα(1−	PROPN
ejpam-7095	262	2	α	α	X
ejpam-7095	262	3	)	)	PUNCT
ejpam-7095	262	4	+	+	CCONJ
ejpam-7095	262	5	α	α	NOUN
ejpam-7095	262	6	−	−	VERB
ejpam-7095	262	7	λ1∇2û(x̄	λ1∇2û(x̄	NOUN
ejpam-7095	262	8	,	,	PUNCT
ejpam-7095	262	9	s)−	s)−	PROPN
ejpam-7095	262	10	λ2û(x̄	λ2û(x̄	PROPN
ejpam-7095	262	11	,	,	PUNCT
ejpam-7095	262	12	s	s	X
ejpam-7095	262	13	)	)	PUNCT
ejpam-7095	262	14	=	=	PUNCT
ejpam-7095	263	1	f̂(x̄	f̂(x̄	X
ejpam-7095	263	2	,	,	PUNCT
ejpam-7095	263	3	s	s	NOUN
ejpam-7095	263	4	)	)	PUNCT
ejpam-7095	263	5	,	,	PUNCT
ejpam-7095	263	6	x̄	x̄	NOUN
ejpam-7095	263	7	∈	∈	PROPN
ejpam-7095	263	8	θ	θ	PROPN
ejpam-7095	263	9	for	for	ADP
ejpam-7095	263	10	x̄	x̄	NOUN
ejpam-7095	263	11	∈	∈	PROPN
ejpam-7095	263	12	θ	θ	PROPN
ejpam-7095	263	13	with	with	ADP
ejpam-7095	263	14	boundary	boundary	ADJ
ejpam-7095	263	15	condtions	condtion	NOUN
ejpam-7095	263	16	:	:	PUNCT
ejpam-7095	263	17	bû(x̄	bû(x̄	NUM
ejpam-7095	263	18	,	,	PUNCT
ejpam-7095	263	19	s	s	NOUN
ejpam-7095	263	20	)	)	PUNCT
ejpam-7095	263	21	=	=	SYM
ejpam-7095	263	22	ĝ1(x̄	ĝ1(x̄	X
ejpam-7095	263	23	,	,	PUNCT
ejpam-7095	263	24	s	s	PART
ejpam-7095	263	25	)	)	PUNCT
ejpam-7095	263	26	,	,	PUNCT
ejpam-7095	263	27	x̄	x̄	NOUN
ejpam-7095	263	28	∈	∈	PROPN
ejpam-7095	263	29	∂θ	∂θ	PROPN
ejpam-7095	263	30	,	,	PUNCT
ejpam-7095	263	31	the	the	DET
ejpam-7095	263	32	above	above	ADJ
ejpam-7095	263	33	expression	expression	NOUN
ejpam-7095	263	34	can	can	AUX
ejpam-7095	263	35	be	be	AUX
ejpam-7095	263	36	written	write	VERB
ejpam-7095	263	37	in	in	ADP
ejpam-7095	263	38	operator	operator	NOUN
ejpam-7095	263	39	form	form	NOUN
ejpam-7095	263	40	as	as	ADP
ejpam-7095	263	41	:	:	PUNCT
ejpam-7095	263	42	{	{	PUNCT
ejpam-7095	263	43	(	(	PUNCT
ejpam-7095	263	44	β(α)sα	β(α)sα	ADV
ejpam-7095	263	45	sα(1−	sα(1−	PROPN
ejpam-7095	263	46	α	α	NOUN
ejpam-7095	263	47	)	)	PUNCT
ejpam-7095	263	48	+	+	CCONJ
ejpam-7095	263	49	α	α	NOUN
ejpam-7095	263	50	)	)	PUNCT
ejpam-7095	264	1	i	i	PRON
ejpam-7095	264	2	−	−	VERB
ejpam-7095	265	1	λ1£−	λ1£−	X
ejpam-7095	265	2	λ2i	λ2i	X
ejpam-7095	265	3	}	}	PUNCT
ejpam-7095	265	4	û(x̄	û(x̄	PROPN
ejpam-7095	265	5	,	,	PUNCT
ejpam-7095	265	6	s	s	X
ejpam-7095	265	7	)	)	PUNCT
ejpam-7095	265	8	=	=	SYM
ejpam-7095	266	1	ĥ(x̄	ĥ(x̄	PROPN
ejpam-7095	266	2	,	,	PUNCT
ejpam-7095	266	3	s	s	PART
ejpam-7095	266	4	)	)	PUNCT
ejpam-7095	266	5	,	,	PUNCT
ejpam-7095	266	6	(	(	PUNCT
ejpam-7095	266	7	9	9	X
ejpam-7095	266	8	)	)	PUNCT
ejpam-7095	266	9	where	where	SCONJ
ejpam-7095	266	10	:	:	PUNCT
ejpam-7095	266	11	ĥ(x̄	ĥ(x̄	PROPN
ejpam-7095	266	12	,	,	PUNCT
ejpam-7095	266	13	s	s	PART
ejpam-7095	266	14	)	)	PUNCT
ejpam-7095	266	15	=	=	SYM
ejpam-7095	266	16	β(α)sα−1g2(x̄	β(α)sα−1g2(x̄	X
ejpam-7095	266	17	)	)	PUNCT
ejpam-7095	266	18	sα(1−	sα(1−	PROPN
ejpam-7095	266	19	α	α	NUM
ejpam-7095	266	20	)	)	PUNCT
ejpam-7095	266	21	+	+	CCONJ
ejpam-7095	266	22	α	α	PROPN
ejpam-7095	266	23	+	+	NOUN
ejpam-7095	266	24	β(α)sα−2g3(x̄	β(α)sα−2g3(x̄	NOUN
ejpam-7095	266	25	)	)	PUNCT
ejpam-7095	266	26	sα(1−	sα(1−	PROPN
ejpam-7095	266	27	α	α	NUM
ejpam-7095	266	28	)	)	PUNCT
ejpam-7095	266	29	+	+	CCONJ
ejpam-7095	266	30	α	α	NOUN
ejpam-7095	266	31	+	+	X
ejpam-7095	266	32	f̂(x̄	f̂(x̄	PROPN
ejpam-7095	266	33	,	,	PUNCT
ejpam-7095	266	34	s	s	X
ejpam-7095	266	35	)	)	PUNCT
ejpam-7095	266	36	and	and	CCONJ
ejpam-7095	266	37	the	the	DET
ejpam-7095	266	38	boundary	boundary	ADJ
ejpam-7095	266	39	conditions	condition	NOUN
ejpam-7095	266	40	remain	remain	VERB
ejpam-7095	266	41	bû(x̄	bû(x̄	NOUN
ejpam-7095	266	42	,	,	PUNCT
ejpam-7095	266	43	s	s	PART
ejpam-7095	266	44	)	)	PUNCT
ejpam-7095	266	45	=	=	SYM
ejpam-7095	266	46	ĝ1(x̄	ĝ1(x̄	X
ejpam-7095	266	47	,	,	PUNCT
ejpam-7095	266	48	s	s	PART
ejpam-7095	266	49	)	)	PUNCT
ejpam-7095	266	50	,	,	PUNCT
ejpam-7095	266	51	x̄	x̄	NOUN
ejpam-7095	266	52	∈	∈	PROPN
ejpam-7095	266	53	∂θ	∂θ	PROPN
ejpam-7095	266	54	.	.	PUNCT
ejpam-7095	267	1	(	(	PUNCT
ejpam-7095	267	2	10	10	NUM
ejpam-7095	267	3	)	)	PUNCT
ejpam-7095	267	4	here	here	ADV
ejpam-7095	267	5	,	,	PUNCT
ejpam-7095	267	6	l	l	NOUN
ejpam-7095	267	7	=	=	SYM
ejpam-7095	267	8	∇2	∇2	PROPN
ejpam-7095	267	9	denotes	denote	VERB
ejpam-7095	267	10	the	the	DET
ejpam-7095	267	11	laplacian	laplacian	ADJ
ejpam-7095	267	12	operator	operator	NOUN
ejpam-7095	267	13	.	.	PUNCT
ejpam-7095	268	1	the	the	DET
ejpam-7095	268	2	spatial	spatial	ADJ
ejpam-7095	268	3	operators	operator	NOUN
ejpam-7095	268	4	in	in	ADP
ejpam-7095	268	5	eqs	eqs	PROPN
ejpam-7095	268	6	.	.	PUNCT
ejpam-7095	269	1	(	(	PUNCT
ejpam-7095	269	2	9	9	NUM
ejpam-7095	269	3	)	)	PUNCT
ejpam-7095	269	4	–	–	PUNCT
ejpam-7095	269	5	(	(	PUNCT
ejpam-7095	269	6	10	10	NUM
ejpam-7095	269	7	)	)	PUNCT
ejpam-7095	269	8	are	be	AUX
ejpam-7095	269	9	then	then	ADV
ejpam-7095	269	10	discretized	discretize	VERB
ejpam-7095	269	11	using	use	VERB
ejpam-7095	269	12	the	the	DET
ejpam-7095	269	13	cscm	cscm	NOUN
ejpam-7095	269	14	,	,	PUNCT
ejpam-7095	269	15	which	which	PRON
ejpam-7095	269	16	transforms	transform	VERB
ejpam-7095	269	17	the	the	DET
ejpam-7095	269	18	problem	problem	NOUN
ejpam-7095	269	19	into	into	ADP
ejpam-7095	269	20	a	a	DET
ejpam-7095	269	21	system	system	NOUN
ejpam-7095	269	22	of	of	ADP
ejpam-7095	269	23	linear	linear	ADJ
ejpam-7095	269	24	equations	equation	NOUN
ejpam-7095	269	25	in	in	ADP
ejpam-7095	269	26	the	the	DET
ejpam-7095	269	27	laplace	laplace	NOUN
ejpam-7095	269	28	domain	domain	NOUN
ejpam-7095	269	29	.	.	PUNCT
ejpam-7095	270	1	this	this	DET
ejpam-7095	270	2	system	system	NOUN
ejpam-7095	270	3	is	be	AUX
ejpam-7095	270	4	solved	solve	VERB
ejpam-7095	270	5	for	for	ADP
ejpam-7095	270	6	each	each	DET
ejpam-7095	270	7	value	value	NOUN
ejpam-7095	270	8	of	of	ADP
ejpam-7095	270	9	the	the	DET
ejpam-7095	270	10	laplace	laplace	NOUN
ejpam-7095	270	11	parameter	parameter	NOUN
ejpam-7095	270	12	s.	s.	PROPN
ejpam-7095	270	13	finally	finally	ADV
ejpam-7095	270	14	,	,	PUNCT
ejpam-7095	270	15	the	the	DET
ejpam-7095	270	16	solution	solution	NOUN
ejpam-7095	270	17	in	in	ADP
ejpam-7095	270	18	the	the	DET
ejpam-7095	270	19	time	time	NOUN
ejpam-7095	270	20	domain	domain	NOUN
ejpam-7095	270	21	,	,	PUNCT
ejpam-7095	270	22	u(x̄	u(x̄	NUM
ejpam-7095	270	23	,	,	PUNCT
ejpam-7095	270	24	t	t	PROPN
ejpam-7095	270	25	)	)	PUNCT
ejpam-7095	270	26	,	,	PUNCT
ejpam-7095	270	27	is	be	AUX
ejpam-7095	270	28	recovered	recover	VERB
ejpam-7095	270	29	by	by	ADP
ejpam-7095	270	30	applying	apply	VERB
ejpam-7095	270	31	a	a	DET
ejpam-7095	270	32	numerical	numerical	ADJ
ejpam-7095	270	33	inverse	inverse	NOUN
ejpam-7095	270	34	laplace	laplace	NOUN
ejpam-7095	270	35	transform	transform	NOUN
ejpam-7095	270	36	.	.	PUNCT
ejpam-7095	271	1	kamran	kamran	PROPN
ejpam-7095	271	2	et	et	PROPN
ejpam-7095	271	3	al	al	PROPN
ejpam-7095	271	4	.	.	PUNCT
ejpam-7095	271	5	/	/	SYM
ejpam-7095	271	6	eur	eur	PROPN
ejpam-7095	271	7	.	.	PUNCT
ejpam-7095	272	1	j.	j.	PROPN
ejpam-7095	272	2	pure	pure	PROPN
ejpam-7095	272	3	appl	appl	PROPN
ejpam-7095	272	4	.	.	PROPN
ejpam-7095	272	5	math	math	PROPN
ejpam-7095	272	6	,	,	PUNCT
ejpam-7095	272	7	18	18	NUM
ejpam-7095	272	8	(	(	PUNCT
ejpam-7095	272	9	4	4	NUM
ejpam-7095	272	10	)	)	PUNCT
ejpam-7095	272	11	(	(	PUNCT
ejpam-7095	272	12	2025	2025	NUM
ejpam-7095	272	13	)	)	PUNCT
ejpam-7095	272	14	,	,	PUNCT
ejpam-7095	272	15	7095	7095	NUM
ejpam-7095	272	16	13	13	NUM
ejpam-7095	272	17	of	of	ADP
ejpam-7095	272	18	30	30	NUM
ejpam-7095	272	19	5.2	5.2	NUM
ejpam-7095	272	20	.	.	PUNCT
ejpam-7095	273	1	spectral	spectral	ADJ
ejpam-7095	273	2	method	method	NOUN
ejpam-7095	273	3	the	the	DET
ejpam-7095	273	4	cscm	cscm	NOUN
ejpam-7095	273	5	is	be	AUX
ejpam-7095	273	6	employed	employ	VERB
ejpam-7095	273	7	in	in	ADP
ejpam-7095	273	8	this	this	DET
ejpam-7095	273	9	section	section	NOUN
ejpam-7095	273	10	to	to	PART
ejpam-7095	273	11	discretize	discretize	VERB
ejpam-7095	273	12	the	the	DET
ejpam-7095	273	13	spatial	spatial	ADJ
ejpam-7095	273	14	operators	operator	NOUN
ejpam-7095	273	15	in	in	ADP
ejpam-7095	273	16	the	the	DET
ejpam-7095	273	17	transformed	transform	VERB
ejpam-7095	273	18	system	system	NOUN
ejpam-7095	273	19	given	give	VERB
ejpam-7095	273	20	in	in	ADP
ejpam-7095	273	21	eqs	eqs	PROPN
ejpam-7095	273	22	.	.	PUNCT
ejpam-7095	274	1	(	(	PUNCT
ejpam-7095	274	2	9)–(10	9)–(10	NUM
ejpam-7095	274	3	)	)	PUNCT
ejpam-7095	274	4	.	.	PUNCT
ejpam-7095	275	1	this	this	DET
ejpam-7095	275	2	method	method	NOUN
ejpam-7095	275	3	uses	use	VERB
ejpam-7095	275	4	lagrange	lagrange	NOUN
ejpam-7095	275	5	interpolation	interpolation	NOUN
ejpam-7095	275	6	polynomials	polynomial	NOUN
ejpam-7095	275	7	(	(	PUNCT
ejpam-7095	275	8	lips	lip	NOUN
ejpam-7095	275	9	)	)	PUNCT
ejpam-7095	275	10	based	base	VERB
ejpam-7095	275	11	on	on	ADP
ejpam-7095	275	12	chebyshev	chebyshev	NOUN
ejpam-7095	275	13	nodes	node	NOUN
ejpam-7095	275	14	to	to	PART
ejpam-7095	275	15	approximate	approximate	VERB
ejpam-7095	275	16	the	the	DET
ejpam-7095	275	17	solution	solution	NOUN
ejpam-7095	275	18	over	over	ADP
ejpam-7095	275	19	the	the	DET
ejpam-7095	275	20	domain	domain	NOUN
ejpam-7095	275	21	θ	θ	NOUN
ejpam-7095	275	22	,	,	PUNCT
ejpam-7095	275	23	which	which	PRON
ejpam-7095	275	24	is	be	AUX
ejpam-7095	275	25	[	[	X
ejpam-7095	275	26	−1	−1	NOUN
ejpam-7095	275	27	,	,	PUNCT
ejpam-7095	275	28	1	1	NUM
ejpam-7095	275	29	]	]	PUNCT
ejpam-7095	275	30	in	in	ADP
ejpam-7095	275	31	1d	1d	NUM
ejpam-7095	275	32	,	,	PUNCT
ejpam-7095	275	33	[	[	X
ejpam-7095	275	34	−1	−1	NOUN
ejpam-7095	275	35	,	,	PUNCT
ejpam-7095	275	36	1]2	1]2	NUM
ejpam-7095	275	37	in	in	ADP
ejpam-7095	275	38	2d	2d	NUM
ejpam-7095	275	39	,	,	PUNCT
ejpam-7095	275	40	and	and	CCONJ
ejpam-7095	275	41	[	[	X
ejpam-7095	275	42	−1	−1	NOUN
ejpam-7095	275	43	,	,	PUNCT
ejpam-7095	275	44	1]3	1]3	NUM
ejpam-7095	275	45	in	in	ADP
ejpam-7095	275	46	3d	3d	NUM
ejpam-7095	275	47	,	,	PUNCT
ejpam-7095	275	48	with	with	ADP
ejpam-7095	275	49	x̄	x̄	PUNCT
ejpam-7095	275	50	=	=	PUNCT
ejpam-7095	275	51	x	x	X
ejpam-7095	275	52	,	,	PUNCT
ejpam-7095	275	53	(	(	PUNCT
ejpam-7095	275	54	x	x	NOUN
ejpam-7095	275	55	,	,	PUNCT
ejpam-7095	275	56	y	y	PROPN
ejpam-7095	275	57	)	)	PUNCT
ejpam-7095	275	58	,	,	PUNCT
ejpam-7095	275	59	or	or	CCONJ
ejpam-7095	275	60	(	(	PUNCT
ejpam-7095	275	61	x	x	X
ejpam-7095	275	62	,	,	PUNCT
ejpam-7095	275	63	y	y	PROPN
ejpam-7095	275	64	,	,	PUNCT
ejpam-7095	275	65	z	z	NOUN
ejpam-7095	275	66	)	)	PUNCT
ejpam-7095	275	67	respectively	respectively	ADV
ejpam-7095	275	68	.	.	PUNCT
ejpam-7095	276	1	for	for	ADP
ejpam-7095	276	2	the	the	DET
ejpam-7095	276	3	1d	1d	NUM
ejpam-7095	276	4	case	case	NOUN
ejpam-7095	276	5	the	the	DET
ejpam-7095	276	6	solution	solution	NOUN
ejpam-7095	276	7	û(x	û(x	ADP
ejpam-7095	276	8	,	,	PUNCT
ejpam-7095	276	9	s	s	PART
ejpam-7095	276	10	)	)	PUNCT
ejpam-7095	276	11	is	be	AUX
ejpam-7095	276	12	approximated	approximate	VERB
ejpam-7095	276	13	as	as	ADP
ejpam-7095	276	14	[	[	X
ejpam-7095	276	15	33	33	NUM
ejpam-7095	276	16	,	,	PUNCT
ejpam-7095	276	17	34	34	NUM
ejpam-7095	276	18	]	]	X
ejpam-7095	276	19	:	:	PUNCT
ejpam-7095	276	20	in(x	in(x	X
ejpam-7095	276	21	)	)	PUNCT
ejpam-7095	277	1	=	=	SYM
ejpam-7095	277	2	n∑	n∑	PUNCT
ejpam-7095	278	1	=	=	NOUN
ejpam-7095	278	2	0	0	NUM
ejpam-7095	278	3	ℓ(x)û(x	ℓ(x)û(x	NOUN
ejpam-7095	278	4	,	,	PUNCT
ejpam-7095	278	5	s	s	PART
ejpam-7095	278	6	)	)	PUNCT
ejpam-7095	278	7	,	,	PUNCT
ejpam-7095	278	8	where	where	SCONJ
ejpam-7095	278	9	ℓ(x	ℓ(x	PROPN
ejpam-7095	278	10	)	)	PUNCT
ejpam-7095	278	11	are	be	AUX
ejpam-7095	278	12	lips	lip	NOUN
ejpam-7095	278	13	defined	define	VERB
ejpam-7095	278	14	as	as	ADP
ejpam-7095	278	15	chebyshev	chebyshev	NOUN
ejpam-7095	278	16	nodes	node	NOUN
ejpam-7095	278	17	x	x	X
ejpam-7095	278	18	,	,	PUNCT
ejpam-7095	278	19	which	which	PRON
ejpam-7095	278	20	are	be	AUX
ejpam-7095	278	21	given	give	VERB
ejpam-7095	278	22	by	by	ADP
ejpam-7095	278	23	:	:	PUNCT
ejpam-7095	278	24	x	x	SYM
ejpam-7095	278	25	=	=	PRON
ejpam-7095	278	26	{	{	PUNCT
ejpam-7095	278	27	cos	cos	X
ejpam-7095	278	28	(	(	PUNCT
ejpam-7095	278	29	π	π	PROPN
ejpam-7095	278	30	n	n	CCONJ
ejpam-7095	278	31	)	)	PUNCT
ejpam-7095	278	32	}	}	PUNCT
ejpam-7095	278	33	n	n	PRON
ejpam-7095	278	34	=	=	NOUN
ejpam-7095	278	35	0	0	NUM
ejpam-7095	278	36	.	.	PUNCT
ejpam-7095	279	1	(	(	PUNCT
ejpam-7095	279	2	11	11	NUM
ejpam-7095	279	3	)	)	PUNCT
ejpam-7095	279	4	and	and	CCONJ
ejpam-7095	279	5	ℓ(x	ℓ(x	PROPN
ejpam-7095	279	6	)	)	PUNCT
ejpam-7095	279	7	=	=	PUNCT
ejpam-7095	279	8	n∏	n∏	NOUN
ejpam-7095	279	9	j=0,j	j=0,j	NOUN
ejpam-7095	279	10	̸=	̸=	PROPN
ejpam-7095	279	11	x−	x−	PROPN
ejpam-7095	279	12	xj	xj	PROPN
ejpam-7095	279	13	x	x	PROPN
ejpam-7095	280	1	−	−	PROPN
ejpam-7095	280	2	xj	xj	PROPN
ejpam-7095	280	3	,	,	PUNCT
ejpam-7095	280	4	(	(	PUNCT
ejpam-7095	280	5	12	12	NUM
ejpam-7095	280	6	)	)	PUNCT
ejpam-7095	280	7	the	the	DET
ejpam-7095	280	8	derivative	derivative	ADJ
ejpam-7095	280	9	∂û(x	∂û(x	NOUN
ejpam-7095	280	10	)	)	PUNCT
ejpam-7095	280	11	∂x	∂x	PROPN
ejpam-7095	280	12	is	be	AUX
ejpam-7095	280	13	approximated	approximate	VERB
ejpam-7095	280	14	using	use	VERB
ejpam-7095	280	15	the	the	DET
ejpam-7095	280	16	differentiation	differentiation	NOUN
ejpam-7095	280	17	matrix	matrix	NOUN
ejpam-7095	280	18	n	n	CCONJ
ejpam-7095	280	19	,	,	PUNCT
ejpam-7095	280	20	with	with	ADP
ejpam-7095	280	21	elements	element	NOUN
ejpam-7095	280	22	:	:	PUNCT
ejpam-7095	280	23	{	{	PUNCT
ejpam-7095	280	24	n}k	n}k	NOUN
ejpam-7095	280	25	,	,	PUNCT
ejpam-7095	280	26	=	=	SYM
ejpam-7095	280	27	ℓ′(xk	ℓ′(xk	PROPN
ejpam-7095	280	28	)	)	PUNCT
ejpam-7095	280	29	,	,	PUNCT
ejpam-7095	280	30	k	k	NOUN
ejpam-7095	280	31	,	,	PUNCT
ejpam-7095	280	32	=	=	NOUN
ejpam-7095	280	33	0	0	NUM
ejpam-7095	280	34	,	,	PUNCT
ejpam-7095	280	35	1	1	NUM
ejpam-7095	280	36	,	,	PUNCT
ejpam-7095	280	37	2	2	NUM
ejpam-7095	280	38	,	,	PUNCT
ejpam-7095	280	39	...	...	PUNCT
ejpam-7095	280	40	,	,	PUNCT
ejpam-7095	280	41	n	n	CCONJ
ejpam-7095	280	42	,	,	PUNCT
ejpam-7095	280	43	where	where	SCONJ
ejpam-7095	280	44	the	the	DET
ejpam-7095	280	45	off	off	ADP
ejpam-7095	280	46	-	-	PUNCT
ejpam-7095	280	47	diagonal	diagonal	ADJ
ejpam-7095	280	48	entries	entry	NOUN
ejpam-7095	280	49	are	be	AUX
ejpam-7095	280	50	:	:	PUNCT
ejpam-7095	280	51	{	{	PUNCT
ejpam-7095	280	52	n}k	n}k	NOUN
ejpam-7095	280	53	,	,	PUNCT
ejpam-7095	280	54	=	=	PUNCT
ejpam-7095	280	55	υ	υ	NOUN
ejpam-7095	280	56	υk(xk	υk(xk	X
ejpam-7095	280	57	−	−	PROPN
ejpam-7095	280	58	x	x	NOUN
ejpam-7095	280	59	)	)	PUNCT
ejpam-7095	280	60	,	,	PUNCT
ejpam-7095	280	61	k	k	PROPN
ejpam-7095	280	62	̸=	̸=	PROPN
ejpam-7095	280	63	,	,	PUNCT
ejpam-7095	280	64	with	with	ADP
ejpam-7095	280	65	υ−1	υ−1	PROPN
ejpam-7095	280	66	=	=	PROPN
ejpam-7095	280	67	∏n	∏n	PROPN
ejpam-7095	280	68	k=0,k	k=0,k	PROPN
ejpam-7095	280	69	̸=(xk	̸=(xk	ADJ
ejpam-7095	280	70	−	−	PROPN
ejpam-7095	280	71	x	x	NOUN
ejpam-7095	280	72	)	)	PUNCT
ejpam-7095	280	73	,	,	PUNCT
ejpam-7095	280	74	and	and	CCONJ
ejpam-7095	280	75	the	the	DET
ejpam-7095	280	76	diagonal	diagonal	ADJ
ejpam-7095	280	77	entries	entry	NOUN
ejpam-7095	280	78	:	:	PUNCT
ejpam-7095	280	79	{	{	PUNCT
ejpam-7095	280	80	n}k	n}k	NOUN
ejpam-7095	280	81	,	,	PUNCT
ejpam-7095	280	82	=	=	PUNCT
ejpam-7095	280	83	−	−	PROPN
ejpam-7095	280	84	n∑	n∑	NOUN
ejpam-7095	280	85	=	=	NOUN
ejpam-7095	280	86	0	0	PROPN
ejpam-7095	280	87	,	,	PUNCT
ejpam-7095	280	88	̸=k	̸=k	PROPN
ejpam-7095	280	89	{	{	PUNCT
ejpam-7095	280	90	n}k	n}k	PROPN
ejpam-7095	280	91	,	,	PUNCT
ejpam-7095	280	92	,	,	PUNCT
ejpam-7095	280	93	k	k	PROPN
ejpam-7095	280	94	=	=	SYM
ejpam-7095	280	95	0	0	NUM
ejpam-7095	280	96	,	,	PUNCT
ejpam-7095	280	97	1	1	NUM
ejpam-7095	280	98	,	,	PUNCT
ejpam-7095	280	99	2	2	NUM
ejpam-7095	280	100	,	,	PUNCT
ejpam-7095	280	101	..	..	PUNCT
ejpam-7095	280	102	,	,	PUNCT
ejpam-7095	280	103	n.	n.	NOUN
ejpam-7095	280	104	higher	high	ADJ
ejpam-7095	280	105	derivatives	derivative	NOUN
ejpam-7095	280	106	are	be	AUX
ejpam-7095	280	107	obtained	obtain	VERB
ejpam-7095	280	108	as	as	ADP
ejpam-7095	280	109	:	:	PUNCT
ejpam-7095	280	110	{	{	PUNCT
ejpam-7095	280	111	(	(	PUNCT
ejpam-7095	280	112	m	m	NOUN
ejpam-7095	280	113	)	)	PUNCT
ejpam-7095	280	114	n	n	CCONJ
ejpam-7095	280	115	}	}	PUNCT
ejpam-7095	280	116	k	k	PROPN
ejpam-7095	280	117	,	,	PUNCT
ejpam-7095	280	118	=	=	PUNCT
ejpam-7095	280	119	ℓ(m)(xk	ℓ(m)(xk	NUM
ejpam-7095	280	120	)	)	PUNCT
ejpam-7095	280	121	.	.	PUNCT
ejpam-7095	281	1	for	for	ADP
ejpam-7095	281	2	1d	1d	NUM
ejpam-7095	281	3	,	,	PUNCT
ejpam-7095	281	4	£	£	NOUN
ejpam-7095	281	5	disc	disc	NOUN
ejpam-7095	281	6	=	=	SYM
ejpam-7095	281	7	∂2	∂2	NOUN
ejpam-7095	281	8	∂x2	∂x2	NOUN
ejpam-7095	281	9	,	,	PUNCT
ejpam-7095	281	10	approximated	approximate	VERB
ejpam-7095	281	11	by	by	ADP
ejpam-7095	281	12	2	2	NUM
ejpam-7095	281	13	n.	n.	NOUN
ejpam-7095	281	14	the	the	DET
ejpam-7095	281	15	authors	author	NOUN
ejpam-7095	281	16	of	of	ADP
ejpam-7095	281	17	[	[	X
ejpam-7095	281	18	35	35	NUM
ejpam-7095	281	19	,	,	PUNCT
ejpam-7095	281	20	36	36	NUM
ejpam-7095	281	21	]	]	PUNCT
ejpam-7095	281	22	developed	develop	VERB
ejpam-7095	281	23	an	an	DET
ejpam-7095	281	24	effective	effective	ADJ
ejpam-7095	281	25	and	and	CCONJ
ejpam-7095	281	26	precise	precise	ADJ
ejpam-7095	281	27	formulation	formulation	NOUN
ejpam-7095	281	28	for	for	ADP
ejpam-7095	281	29	constructing	construct	VERB
ejpam-7095	281	30	differentiation	differentiation	NOUN
ejpam-7095	281	31	matrices	matrix	NOUN
ejpam-7095	281	32	.	.	PUNCT
ejpam-7095	282	1	specifically	specifically	ADV
ejpam-7095	282	2	,	,	PUNCT
ejpam-7095	282	3	[	[	X
ejpam-7095	282	4	35	35	NUM
ejpam-7095	282	5	]	]	PUNCT
ejpam-7095	282	6	provides	provide	VERB
ejpam-7095	282	7	a	a	DET
ejpam-7095	282	8	practical	practical	ADJ
ejpam-7095	282	9	method	method	NOUN
ejpam-7095	282	10	for	for	ADP
ejpam-7095	282	11	deriving	derive	VERB
ejpam-7095	282	12	the	the	DET
ejpam-7095	282	13	matrix	matrix	NOUN
ejpam-7095	282	14	m	m	VERB
ejpam-7095	282	15	n	n	PRON
ejpam-7095	282	16	,	,	PUNCT
ejpam-7095	282	17	presented	present	VERB
ejpam-7095	282	18	as	as	SCONJ
ejpam-7095	282	19	follows	follow	VERB
ejpam-7095	282	20	:	:	PUNCT
ejpam-7095	282	21	{	{	PUNCT
ejpam-7095	282	22	(	(	PUNCT
ejpam-7095	282	23	m	m	NOUN
ejpam-7095	282	24	)	)	PUNCT
ejpam-7095	283	1	n	n	CCONJ
ejpam-7095	283	2	}	}	PUNCT
ejpam-7095	283	3	k	k	X
ejpam-7095	284	1	=	=	PUNCT
ejpam-7095	284	2	m	m	VERB
ejpam-7095	284	3	xk	xk	NOUN
ejpam-7095	284	4	−	−	PROPN
ejpam-7095	284	5	x	x	INTJ
ejpam-7095	284	6	(	(	PUNCT
ejpam-7095	284	7	υ	υ	NOUN
ejpam-7095	284	8	υk	υk	VERB
ejpam-7095	284	9	{	{	PUNCT
ejpam-7095	284	10	(	(	PUNCT
ejpam-7095	284	11	m−1	m−1	PROPN
ejpam-7095	284	12	)	)	PUNCT
ejpam-7095	284	13	n	n	CCONJ
ejpam-7095	284	14	}	}	PUNCT
ejpam-7095	284	15	kk	kk	PROPN
ejpam-7095	284	16	−	−	PROPN
ejpam-7095	284	17	{	{	PUNCT
ejpam-7095	284	18	(	(	PUNCT
ejpam-7095	284	19	m−1	m−1	PROPN
ejpam-7095	284	20	)	)	PUNCT
ejpam-7095	284	21	n	n	CCONJ
ejpam-7095	284	22	}	}	PUNCT
ejpam-7095	284	23	k	k	PROPN
ejpam-7095	284	24	)	)	PUNCT
ejpam-7095	284	25	,	,	PUNCT
ejpam-7095	284	26	k	k	PROPN
ejpam-7095	284	27	̸=	̸=	PROPN
ejpam-7095	284	28	.	.	PUNCT
ejpam-7095	285	1	kamran	kamran	PROPN
ejpam-7095	285	2	et	et	PROPN
ejpam-7095	285	3	al	al	PROPN
ejpam-7095	285	4	.	.	PUNCT
ejpam-7095	285	5	/	/	SYM
ejpam-7095	285	6	eur	eur	PROPN
ejpam-7095	285	7	.	.	PUNCT
ejpam-7095	286	1	j.	j.	PROPN
ejpam-7095	286	2	pure	pure	PROPN
ejpam-7095	286	3	appl	appl	PROPN
ejpam-7095	286	4	.	.	PROPN
ejpam-7095	286	5	math	math	PROPN
ejpam-7095	286	6	,	,	PUNCT
ejpam-7095	286	7	18	18	NUM
ejpam-7095	286	8	(	(	PUNCT
ejpam-7095	286	9	4	4	NUM
ejpam-7095	286	10	)	)	PUNCT
ejpam-7095	286	11	(	(	PUNCT
ejpam-7095	286	12	2025	2025	NUM
ejpam-7095	286	13	)	)	PUNCT
ejpam-7095	286	14	,	,	PUNCT
ejpam-7095	286	15	7095	7095	NUM
ejpam-7095	286	16	14	14	NUM
ejpam-7095	286	17	of	of	ADP
ejpam-7095	286	18	30	30	NUM
ejpam-7095	286	19	for	for	ADP
ejpam-7095	286	20	γ	γ	X
ejpam-7095	286	21	=	=	SYM
ejpam-7095	287	1	[	[	X
ejpam-7095	287	2	−1	−1	NOUN
ejpam-7095	287	3	,	,	PUNCT
ejpam-7095	287	4	1]2	1]2	NUM
ejpam-7095	287	5	,	,	PUNCT
ejpam-7095	287	6	the	the	DET
ejpam-7095	287	7	points	point	NOUN
ejpam-7095	287	8	x̄k	x̄k	PROPN
ejpam-7095	287	9	are	be	AUX
ejpam-7095	287	10	presented	present	VERB
ejpam-7095	287	11	as	as	SCONJ
ejpam-7095	287	12	follows	follow	VERB
ejpam-7095	287	13	:	:	PUNCT
ejpam-7095	288	1	x̄k	x̄k	X
ejpam-7095	288	2	=	=	PUNCT
ejpam-7095	288	3	(	(	PUNCT
ejpam-7095	288	4	cos	cos	X
ejpam-7095	288	5	(	(	PUNCT
ejpam-7095	288	6	π	π	PROPN
ejpam-7095	288	7	n	n	PROPN
ejpam-7095	288	8	)	)	PUNCT
ejpam-7095	288	9	,	,	PUNCT
ejpam-7095	288	10	cos	cos	PROPN
ejpam-7095	288	11	(	(	PUNCT
ejpam-7095	288	12	πk	πk	ADP
ejpam-7095	288	13	n	n	PROPN
ejpam-7095	288	14	)	)	PUNCT
ejpam-7095	288	15	)	)	PUNCT
ejpam-7095	288	16	,	,	PUNCT
ejpam-7095	288	17	,	,	PUNCT
ejpam-7095	288	18	k	k	PROPN
ejpam-7095	288	19	=	=	SYM
ejpam-7095	288	20	0	0	NUM
ejpam-7095	288	21	,	,	PUNCT
ejpam-7095	288	22	1	1	NUM
ejpam-7095	288	23	,	,	PUNCT
ejpam-7095	288	24	2	2	NUM
ejpam-7095	288	25	,	,	PUNCT
ejpam-7095	288	26	...	...	PUNCT
ejpam-7095	288	27	,	,	PUNCT
ejpam-7095	288	28	n.	n.	NOUN
ejpam-7095	288	29	the	the	DET
ejpam-7095	288	30	lips	lip	NOUN
ejpam-7095	288	31	are	be	AUX
ejpam-7095	288	32	:	:	PUNCT
ejpam-7095	288	33	ℓk(x̄	ℓk(x̄	X
ejpam-7095	288	34	)	)	PUNCT
ejpam-7095	288	35	=	=	SYM
ejpam-7095	288	36	ℓ(x)ℓk(y	ℓ(x)ℓk(y	NOUN
ejpam-7095	288	37	)	)	PUNCT
ejpam-7095	288	38	,	,	PUNCT
ejpam-7095	288	39	,	,	PUNCT
ejpam-7095	288	40	k	k	PROPN
ejpam-7095	288	41	=	=	SYM
ejpam-7095	288	42	0	0	NUM
ejpam-7095	288	43	,	,	PUNCT
ejpam-7095	288	44	1	1	NUM
ejpam-7095	288	45	,	,	PUNCT
ejpam-7095	288	46	2	2	NUM
ejpam-7095	288	47	,	,	PUNCT
ejpam-7095	288	48	...	...	PUNCT
ejpam-7095	288	49	,	,	PUNCT
ejpam-7095	288	50	n.	n.	NOUN
ejpam-7095	288	51	(	(	PUNCT
ejpam-7095	288	52	13	13	NUM
ejpam-7095	288	53	)	)	PUNCT
ejpam-7095	288	54	where	where	SCONJ
ejpam-7095	288	55	ℓk(x̄k	ℓk(x̄k	NOUN
ejpam-7095	288	56	)	)	PUNCT
ejpam-7095	288	57	=	=	SYM
ejpam-7095	288	58	σk	σk	PROPN
ejpam-7095	288	59	.	.	PUNCT
ejpam-7095	289	1	the	the	DET
ejpam-7095	289	2	2nd	2nd	ADJ
ejpam-7095	289	3	-	-	PUNCT
ejpam-7095	289	4	order	order	NOUN
ejpam-7095	289	5	derivatives	derivative	NOUN
ejpam-7095	289	6	of	of	ADP
ejpam-7095	289	7	the	the	DET
ejpam-7095	289	8	lips	lip	NOUN
ejpam-7095	289	9	(	(	PUNCT
ejpam-7095	289	10	13	13	NUM
ejpam-7095	289	11	)	)	PUNCT
ejpam-7095	289	12	are	be	AUX
ejpam-7095	289	13	given	give	VERB
ejpam-7095	289	14	as	as	ADP
ejpam-7095	289	15	:	:	PUNCT
ejpam-7095	289	16	∂2ℓk(x̄rp	∂2ℓk(x̄rp	NOUN
ejpam-7095	289	17	)	)	PUNCT
ejpam-7095	289	18	∂x2	∂x2	NOUN
ejpam-7095	289	19	=	=	SYM
ejpam-7095	289	20	ℓ′′(xr)ℓk(yp	ℓ′′(xr)ℓk(yp	PROPN
ejpam-7095	289	21	)	)	PUNCT
ejpam-7095	289	22	=	=	SYM
ejpam-7095	289	23	{	{	PUNCT
ejpam-7095	289	24	2n}rσkp	2n}rσkp	NOUN
ejpam-7095	289	25	,	,	PUNCT
ejpam-7095	289	26	∂2ℓk(x̄rp	∂2ℓk(x̄rp	NOUN
ejpam-7095	289	27	)	)	PUNCT
ejpam-7095	289	28	∂y2	∂y2	ADJ
ejpam-7095	289	29	=	=	SYM
ejpam-7095	289	30	ℓ(xr)ℓ	ℓ(xr)ℓ	PROPN
ejpam-7095	289	31	′′	′′	PROPN
ejpam-7095	289	32	k(yp	k(yp	NOUN
ejpam-7095	289	33	)	)	PUNCT
ejpam-7095	289	34	=	=	PUNCT
ejpam-7095	290	1	σr{2n}pk	σr{2n}pk	NOUN
ejpam-7095	290	2	,	,	PUNCT
ejpam-7095	290	3	where	where	SCONJ
ejpam-7095	290	4	2	2	NUM
ejpam-7095	290	5	n	n	NOUN
ejpam-7095	290	6	is	be	AUX
ejpam-7095	290	7	the	the	DET
ejpam-7095	290	8	2nd	2nd	ADJ
ejpam-7095	290	9	order	order	NOUN
ejpam-7095	290	10	differentiation	differentiation	NOUN
ejpam-7095	290	11	matrix	matrix	NOUN
ejpam-7095	290	12	.	.	PUNCT
ejpam-7095	291	1	employing	employ	VERB
ejpam-7095	291	2	£	£	NOUN
ejpam-7095	291	3	on	on	ADP
ejpam-7095	291	4	ℓk(x̄rp	ℓk(x̄rp	NOUN
ejpam-7095	291	5	)	)	PUNCT
ejpam-7095	291	6	at	at	ADP
ejpam-7095	291	7	x̄rp	x̄rp	NOUN
ejpam-7095	291	8	gives	give	VERB
ejpam-7095	291	9	£	£	SYM
ejpam-7095	291	10	(	(	PUNCT
ejpam-7095	291	11	ℓk(x̄rp	ℓk(x̄rp	NOUN
ejpam-7095	291	12	)	)	PUNCT
ejpam-7095	291	13	)	)	PUNCT
ejpam-7095	292	1	=	=	PUNCT
ejpam-7095	292	2	(	(	PUNCT
ejpam-7095	292	3	{	{	PUNCT
ejpam-7095	292	4	2n}rσkp	2n}rσkp	NOUN
ejpam-7095	292	5	+	+	CCONJ
ejpam-7095	292	6	σr{2n}pk	σr{2n}pk	NOUN
ejpam-7095	292	7	)	)	PUNCT
ejpam-7095	292	8	(	(	PUNCT
ejpam-7095	292	9	14	14	NUM
ejpam-7095	292	10	)	)	PUNCT
ejpam-7095	292	11	thus	thus	ADV
ejpam-7095	292	12	,	,	PUNCT
ejpam-7095	292	13	the	the	DET
ejpam-7095	292	14	discretized	discretized	ADJ
ejpam-7095	292	15	representation	representation	NOUN
ejpam-7095	292	16	of	of	ADP
ejpam-7095	292	17	the	the	DET
ejpam-7095	292	18	linear	linear	ADJ
ejpam-7095	292	19	differential	differential	NOUN
ejpam-7095	292	20	operator	operator	NOUN
ejpam-7095	292	21	£	£	SYM
ejpam-7095	292	22	,	,	PUNCT
ejpam-7095	292	23	derived	derive	VERB
ejpam-7095	292	24	using	use	VERB
ejpam-7095	292	25	the	the	DET
ejpam-7095	292	26	cscm	cscm	NOUN
ejpam-7095	292	27	,	,	PUNCT
ejpam-7095	292	28	is	be	AUX
ejpam-7095	292	29	given	give	VERB
ejpam-7095	292	30	as	as	ADP
ejpam-7095	292	31	:	:	PUNCT
ejpam-7095	292	32	£	£	NOUN
ejpam-7095	292	33	disc	disc	NOUN
ejpam-7095	292	34	=	=	VERB
ejpam-7095	292	35	in	in	ADP
ejpam-7095	292	36	⊗	⊗	PROPN
ejpam-7095	292	37	2	2	NUM
ejpam-7095	292	38	n	n	NOUN
ejpam-7095	292	39	+	+	NUM
ejpam-7095	292	40	2	2	NUM
ejpam-7095	292	41	n	n	NOUN
ejpam-7095	292	42	⊗	⊗	ADJ
ejpam-7095	292	43	in	in	ADP
ejpam-7095	292	44	,	,	PUNCT
ejpam-7095	292	45	(	(	PUNCT
ejpam-7095	292	46	2d	2d	NOUN
ejpam-7095	292	47	)	)	PUNCT
ejpam-7095	292	48	(	(	PUNCT
ejpam-7095	292	49	15	15	NUM
ejpam-7095	292	50	)	)	PUNCT
ejpam-7095	292	51	where	where	SCONJ
ejpam-7095	292	52	⊗	⊗	PROPN
ejpam-7095	292	53	represent	represent	VERB
ejpam-7095	292	54	the	the	DET
ejpam-7095	292	55	kronecker	kronecker	NOUN
ejpam-7095	292	56	product	product	NOUN
ejpam-7095	292	57	.	.	PUNCT
ejpam-7095	293	1	in	in	ADP
ejpam-7095	293	2	3d	3d	NUM
ejpam-7095	293	3	,	,	PUNCT
ejpam-7095	293	4	the	the	DET
ejpam-7095	293	5	domain	domain	NOUN
ejpam-7095	293	6	is	be	AUX
ejpam-7095	293	7	γ	γ	X
ejpam-7095	293	8	=	=	X
ejpam-7095	294	1	[	[	X
ejpam-7095	294	2	−1	−1	NOUN
ejpam-7095	294	3	,	,	PUNCT
ejpam-7095	294	4	1]3	1]3	NUM
ejpam-7095	294	5	,	,	PUNCT
ejpam-7095	294	6	and	and	CCONJ
ejpam-7095	294	7	the	the	DET
ejpam-7095	294	8	chebyshev	chebyshev	NOUN
ejpam-7095	294	9	nodes	node	NOUN
ejpam-7095	294	10	are	be	AUX
ejpam-7095	294	11	:	:	PUNCT
ejpam-7095	295	1	x̄ℓkm	x̄ℓkm	PROPN
ejpam-7095	295	2	=	=	SYM
ejpam-7095	295	3	(	(	PUNCT
ejpam-7095	295	4	cos	cos	X
ejpam-7095	295	5	(	(	PUNCT
ejpam-7095	295	6	πℓ	πℓ	INTJ
ejpam-7095	295	7	n	n	PROPN
ejpam-7095	295	8	)	)	PUNCT
ejpam-7095	295	9	,	,	PUNCT
ejpam-7095	295	10	cos	cos	PROPN
ejpam-7095	295	11	(	(	PUNCT
ejpam-7095	295	12	πk	πk	PROPN
ejpam-7095	295	13	n	n	PROPN
ejpam-7095	295	14	)	)	PUNCT
ejpam-7095	295	15	,	,	PUNCT
ejpam-7095	295	16	cos	cos	PROPN
ejpam-7095	295	17	(	(	PUNCT
ejpam-7095	295	18	πm	πm	ADP
ejpam-7095	295	19	n	n	PROPN
ejpam-7095	295	20	)	)	PUNCT
ejpam-7095	295	21	)	)	PUNCT
ejpam-7095	295	22	,	,	PUNCT
ejpam-7095	295	23	ℓ	ℓ	X
ejpam-7095	295	24	,	,	PUNCT
ejpam-7095	295	25	k	k	NOUN
ejpam-7095	295	26	,	,	PUNCT
ejpam-7095	295	27	m	m	VERB
ejpam-7095	295	28	=	=	NOUN
ejpam-7095	295	29	0	0	NUM
ejpam-7095	295	30	,	,	PUNCT
ejpam-7095	295	31	1	1	NUM
ejpam-7095	295	32	,	,	PUNCT
ejpam-7095	295	33	.	.	PUNCT
ejpam-7095	295	34	.	.	PUNCT
ejpam-7095	295	35	.	.	PUNCT
ejpam-7095	296	1	,	,	PUNCT
ejpam-7095	296	2	n.	n.	VERB
ejpam-7095	296	3	the	the	DET
ejpam-7095	296	4	associated	associated	ADJ
ejpam-7095	296	5	lips	lip	NOUN
ejpam-7095	296	6	in	in	ADP
ejpam-7095	296	7	3d	3d	NUM
ejpam-7095	296	8	are	be	AUX
ejpam-7095	296	9	:	:	PUNCT
ejpam-7095	296	10	ℓkm(x̄	ℓkm(x̄	NOUN
ejpam-7095	296	11	)	)	PUNCT
ejpam-7095	296	12	=	=	SYM
ejpam-7095	296	13	ℓ(x)ℓk(y)ℓm(z	ℓ(x)ℓk(y)ℓm(z	NOUN
ejpam-7095	296	14	)	)	PUNCT
ejpam-7095	296	15	,	,	PUNCT
ejpam-7095	296	16	,	,	PUNCT
ejpam-7095	296	17	k	k	X
ejpam-7095	296	18	,	,	PUNCT
ejpam-7095	296	19	m	m	VERB
ejpam-7095	296	20	=	=	NOUN
ejpam-7095	296	21	0	0	NUM
ejpam-7095	296	22	,	,	PUNCT
ejpam-7095	296	23	1	1	NUM
ejpam-7095	296	24	,	,	PUNCT
ejpam-7095	296	25	.	.	PUNCT
ejpam-7095	296	26	.	.	PUNCT
ejpam-7095	297	1	.	.	PUNCT
ejpam-7095	298	1	,	,	PUNCT
ejpam-7095	298	2	n	n	CCONJ
ejpam-7095	298	3	,	,	PUNCT
ejpam-7095	298	4	(	(	PUNCT
ejpam-7095	298	5	16	16	NUM
ejpam-7095	298	6	)	)	PUNCT
ejpam-7095	298	7	where	where	SCONJ
ejpam-7095	298	8	ℓkm(x̄km	ℓkm(x̄km	PROPN
ejpam-7095	298	9	)	)	PUNCT
ejpam-7095	298	10	=	=	SYM
ejpam-7095	298	11	σkm	σkm	PROPN
ejpam-7095	298	12	,	,	PUNCT
ejpam-7095	298	13	and	and	CCONJ
ejpam-7095	298	14	the	the	DET
ejpam-7095	298	15	second	second	ADJ
ejpam-7095	298	16	-	-	PUNCT
ejpam-7095	298	17	order	order	NOUN
ejpam-7095	298	18	derivatives	derivative	NOUN
ejpam-7095	298	19	are	be	AUX
ejpam-7095	298	20	obtained	obtain	VERB
ejpam-7095	298	21	as	as	ADP
ejpam-7095	298	22	:	:	PUNCT
ejpam-7095	298	23	∂2ℓkm(x̄rpτ	∂2ℓkm(x̄rpτ	ADJ
ejpam-7095	298	24	)	)	PUNCT
ejpam-7095	298	25	∂x2	∂x2	NOUN
ejpam-7095	298	26	=	=	SYM
ejpam-7095	298	27	ℓ′′(xr)ℓk(yp)ℓm(zτ	ℓ′′(xr)ℓk(yp)ℓm(zτ	NOUN
ejpam-7095	298	28	)	)	PUNCT
ejpam-7095	299	1	=	=	PRON
ejpam-7095	299	2	{	{	PUNCT
ejpam-7095	299	3	2n}rσkpσmt	2n}rσkpσmt	NOUN
ejpam-7095	299	4	,	,	PUNCT
ejpam-7095	299	5	∂2ℓkm(x̄rpτ	∂2ℓkm(x̄rpτ	ADJ
ejpam-7095	299	6	)	)	PUNCT
ejpam-7095	300	1	∂y2	∂y2	ADJ
ejpam-7095	300	2	=	=	SYM
ejpam-7095	300	3	ℓ(xr)ℓ	ℓ(xr)ℓ	PROPN
ejpam-7095	300	4	′′	′′	PROPN
ejpam-7095	300	5	k(yp)ℓm(zτ	k(yp)ℓm(zτ	PROPN
ejpam-7095	300	6	)	)	PUNCT
ejpam-7095	301	1	=	=	PUNCT
ejpam-7095	301	2	σr{2n}pkσmt	σr{2n}pkσmt	ADJ
ejpam-7095	301	3	,	,	PUNCT
ejpam-7095	301	4	∂2ℓkm(x̄rpτ	∂2ℓkm(x̄rpτ	ADJ
ejpam-7095	301	5	)	)	PUNCT
ejpam-7095	301	6	∂z2	∂z2	NOUN
ejpam-7095	301	7	=	=	SYM
ejpam-7095	301	8	ℓ(xr)ℓk(yp)ℓ	ℓ(xr)ℓk(yp)ℓ	NUM
ejpam-7095	301	9	′′	′′	PROPN
ejpam-7095	301	10	m(zτ	m(zτ	NUM
ejpam-7095	301	11	)	)	PUNCT
ejpam-7095	302	1	=	=	SYM
ejpam-7095	302	2	σrσkp{2n}tm	σrσkp{2n}tm	NOUN
ejpam-7095	302	3	,	,	PUNCT
ejpam-7095	302	4	where	where	SCONJ
ejpam-7095	302	5	x̄rpτ	x̄rpτ	PROPN
ejpam-7095	302	6	=	=	SYM
ejpam-7095	302	7	(	(	PUNCT
ejpam-7095	302	8	xr	xr	PROPN
ejpam-7095	302	9	,	,	PUNCT
ejpam-7095	302	10	yp	yp	PROPN
ejpam-7095	302	11	,	,	PUNCT
ejpam-7095	302	12	zτ	zτ	PROPN
ejpam-7095	302	13	)	)	PUNCT
ejpam-7095	302	14	.	.	PUNCT
ejpam-7095	303	1	applying	apply	VERB
ejpam-7095	303	2	£	£	SYM
ejpam-7095	303	3	to	to	ADP
ejpam-7095	303	4	ℓkm(x̄rpτ	ℓkm(x̄rpτ	PUNCT
ejpam-7095	303	5	)	)	PUNCT
ejpam-7095	304	1	at	at	ADP
ejpam-7095	304	2	x̄rpτ	x̄rpτ	PROPN
ejpam-7095	304	3	gives	give	VERB
ejpam-7095	304	4	:	:	PUNCT
ejpam-7095	304	5	£	£	PROPN
ejpam-7095	304	6	(	(	PUNCT
ejpam-7095	304	7	ℓkm(x̄rpτ	ℓkm(x̄rpτ	NUM
ejpam-7095	304	8	)	)	PUNCT
ejpam-7095	304	9	)	)	PUNCT
ejpam-7095	305	1	=	=	PRON
ejpam-7095	305	2	(	(	PUNCT
ejpam-7095	305	3	{	{	PUNCT
ejpam-7095	305	4	2n}rσkpσmτ	2n}rσkpσmτ	NOUN
ejpam-7095	305	5	+	+	CCONJ
ejpam-7095	305	6	σr{2n}pkσmτ	σr{2n}pkσmτ	NOUN
ejpam-7095	305	7	+	+	CCONJ
ejpam-7095	305	8	σrσkp{2n}τm	σrσkp{2n}τm	ADJ
ejpam-7095	305	9	)	)	PUNCT
ejpam-7095	305	10	,	,	PUNCT
ejpam-7095	305	11	(	(	PUNCT
ejpam-7095	305	12	17	17	NUM
ejpam-7095	305	13	)	)	PUNCT
ejpam-7095	305	14	kamran	kamran	PROPN
ejpam-7095	305	15	et	et	PROPN
ejpam-7095	305	16	al	al	PROPN
ejpam-7095	305	17	.	.	PUNCT
ejpam-7095	305	18	/	/	SYM
ejpam-7095	305	19	eur	eur	PROPN
ejpam-7095	305	20	.	.	PUNCT
ejpam-7095	306	1	j.	j.	PROPN
ejpam-7095	306	2	pure	pure	PROPN
ejpam-7095	306	3	appl	appl	PROPN
ejpam-7095	306	4	.	.	PROPN
ejpam-7095	306	5	math	math	PROPN
ejpam-7095	306	6	,	,	PUNCT
ejpam-7095	306	7	18	18	NUM
ejpam-7095	306	8	(	(	PUNCT
ejpam-7095	306	9	4	4	NUM
ejpam-7095	306	10	)	)	PUNCT
ejpam-7095	306	11	(	(	PUNCT
ejpam-7095	306	12	2025	2025	NUM
ejpam-7095	306	13	)	)	PUNCT
ejpam-7095	306	14	,	,	PUNCT
ejpam-7095	306	15	7095	7095	NUM
ejpam-7095	306	16	15	15	NUM
ejpam-7095	306	17	of	of	ADP
ejpam-7095	306	18	30	30	NUM
ejpam-7095	306	19	the	the	DET
ejpam-7095	306	20	discrete	discrete	ADJ
ejpam-7095	306	21	3d	3d	PROPN
ejpam-7095	306	22	laplacian	laplacian	NOUN
ejpam-7095	306	23	is	be	AUX
ejpam-7095	306	24	£	£	SYM
ejpam-7095	306	25	disc	disc	NOUN
ejpam-7095	306	26	=	=	PUNCT
ejpam-7095	306	27	in	in	ADP
ejpam-7095	306	28	⊗	⊗	PROPN
ejpam-7095	306	29	in	in	ADP
ejpam-7095	306	30	⊗	⊗	PROPN
ejpam-7095	306	31	2	2	NUM
ejpam-7095	306	32	n	n	NOUN
ejpam-7095	306	33	+	+	X
ejpam-7095	306	34	in	in	ADP
ejpam-7095	306	35	⊗	⊗	PROPN
ejpam-7095	306	36	2	2	NUM
ejpam-7095	306	37	n	n	ADV
ejpam-7095	306	38	⊗	⊗	NOUN
ejpam-7095	306	39	in	in	ADP
ejpam-7095	306	40	+	+	CCONJ
ejpam-7095	306	41	2	2	NUM
ejpam-7095	306	42	n	n	NOUN
ejpam-7095	306	43	⊗	⊗	NUM
ejpam-7095	306	44	in	in	ADP
ejpam-7095	306	45	⊗	⊗	PROPN
ejpam-7095	306	46	in	in	ADP
ejpam-7095	306	47	,	,	PUNCT
ejpam-7095	306	48	(	(	PUNCT
ejpam-7095	306	49	3d	3d	NOUN
ejpam-7095	306	50	)	)	PUNCT
ejpam-7095	306	51	,	,	PUNCT
ejpam-7095	306	52	(	(	PUNCT
ejpam-7095	306	53	18	18	NUM
ejpam-7095	306	54	)	)	PUNCT
ejpam-7095	306	55	using	use	VERB
ejpam-7095	306	56	matrix	matrix	NOUN
ejpam-7095	306	57	£	£	NOUN
ejpam-7095	306	58	disc	disc	NOUN
ejpam-7095	306	59	in	in	ADP
ejpam-7095	306	60	eq	eq	ADP
ejpam-7095	306	61	.	.	PUNCT
ejpam-7095	307	1	(	(	PUNCT
ejpam-7095	307	2	9	9	NUM
ejpam-7095	307	3	)	)	PUNCT
ejpam-7095	307	4	,	,	PUNCT
ejpam-7095	307	5	we	we	PRON
ejpam-7095	307	6	obtain	obtain	VERB
ejpam-7095	307	7	the	the	DET
ejpam-7095	307	8	discretized	discretized	ADJ
ejpam-7095	307	9	system	system	NOUN
ejpam-7095	307	10	as	as	ADP
ejpam-7095	307	11	:	:	PUNCT
ejpam-7095	307	12	{	{	PUNCT
ejpam-7095	307	13	(	(	PUNCT
ejpam-7095	307	14	β(α)sα	β(α)sα	ADV
ejpam-7095	307	15	sα(1−	sα(1−	PROPN
ejpam-7095	307	16	α	α	NOUN
ejpam-7095	307	17	)	)	PUNCT
ejpam-7095	307	18	+	+	CCONJ
ejpam-7095	307	19	α	α	NOUN
ejpam-7095	307	20	)	)	PUNCT
ejpam-7095	308	1	i	i	PRON
ejpam-7095	308	2	−	−	VERB
ejpam-7095	309	1	λ1£disc	λ1£disc	ADJ
ejpam-7095	309	2	−	−	NOUN
ejpam-7095	309	3	λ2i	λ2i	X
ejpam-7095	309	4	}	}	PUNCT
ejpam-7095	309	5	û(x̄	û(x̄	PROPN
ejpam-7095	309	6	,	,	PUNCT
ejpam-7095	309	7	s	s	X
ejpam-7095	309	8	)	)	PUNCT
ejpam-7095	309	9	=	=	SYM
ejpam-7095	310	1	ĥ(x̄	ĥ(x̄	PROPN
ejpam-7095	310	2	,	,	PUNCT
ejpam-7095	310	3	s	s	PART
ejpam-7095	310	4	)	)	PUNCT
ejpam-7095	310	5	,	,	PUNCT
ejpam-7095	310	6	(	(	PUNCT
ejpam-7095	310	7	19	19	NUM
ejpam-7095	310	8	)	)	PUNCT
ejpam-7095	310	9	the	the	DET
ejpam-7095	310	10	conditions	condition	NOUN
ejpam-7095	310	11	in	in	ADP
ejpam-7095	310	12	eq	eq	NOUN
ejpam-7095	310	13	(	(	PUNCT
ejpam-7095	310	14	10	10	NUM
ejpam-7095	310	15	)	)	PUNCT
ejpam-7095	310	16	are	be	AUX
ejpam-7095	310	17	incorporating	incorporate	VERB
ejpam-7095	310	18	by	by	ADP
ejpam-7095	310	19	considering	consider	VERB
ejpam-7095	310	20	the	the	DET
ejpam-7095	310	21	interpolation	interpolation	NOUN
ejpam-7095	310	22	matrix	matrix	NOUN
ejpam-7095	310	23	£	£	NOUN
ejpam-7095	310	24	disc	disc	NOUN
ejpam-7095	310	25	and	and	CCONJ
ejpam-7095	310	26	considering	consider	VERB
ejpam-7095	310	27	all	all	DET
ejpam-7095	310	28	points	point	NOUN
ejpam-7095	310	29	x̄.	x̄.	PUNCT
ejpam-7095	310	30	furthermore	furthermore	ADV
ejpam-7095	310	31	,	,	PUNCT
ejpam-7095	310	32	the	the	DET
ejpam-7095	310	33	rows	row	NOUN
ejpam-7095	310	34	of	of	ADP
ejpam-7095	310	35	£	£	SYM
ejpam-7095	310	36	disc	disc	NOUN
ejpam-7095	310	37	in	in	ADP
ejpam-7095	310	38	correspondence	correspondence	NOUN
ejpam-7095	310	39	with	with	ADP
ejpam-7095	310	40	boundary	boundary	ADJ
ejpam-7095	310	41	nodes	node	NOUN
ejpam-7095	310	42	are	be	AUX
ejpam-7095	310	43	replaced	replace	VERB
ejpam-7095	310	44	with	with	ADP
ejpam-7095	310	45	unit	unit	NOUN
ejpam-7095	310	46	vectors	vector	NOUN
ejpam-7095	310	47	that	that	PRON
ejpam-7095	310	48	have	have	VERB
ejpam-7095	310	49	a	a	DET
ejpam-7095	310	50	one	one	NOUN
ejpam-7095	310	51	in	in	ADP
ejpam-7095	310	52	accordance	accordance	NOUN
ejpam-7095	310	53	with	with	ADP
ejpam-7095	310	54	the	the	DET
ejpam-7095	310	55	diagonal	diagonal	ADJ
ejpam-7095	310	56	elements	element	NOUN
ejpam-7095	310	57	of	of	ADP
ejpam-7095	310	58	£	£	SYM
ejpam-7095	310	59	disc	disc	NOUN
ejpam-7095	310	60	.	.	PUNCT
ejpam-7095	311	1	hence	hence	ADV
ejpam-7095	311	2	,	,	PUNCT
ejpam-7095	311	3	the	the	DET
ejpam-7095	311	4	boundary	boundary	ADJ
ejpam-7095	311	5	conditions	condition	NOUN
ejpam-7095	311	6	bû(x̄	bû(x̄	NOUN
ejpam-7095	311	7	,	,	PUNCT
ejpam-7095	311	8	s	s	NOUN
ejpam-7095	311	9	)	)	PUNCT
ejpam-7095	311	10	=	=	SYM
ejpam-7095	311	11	ĝ1(x̄	ĝ1(x̄	X
ejpam-7095	311	12	,	,	PUNCT
ejpam-7095	311	13	s	s	PART
ejpam-7095	311	14	)	)	PUNCT
ejpam-7095	311	15	in	in	ADP
ejpam-7095	311	16	eq	eq	NOUN
ejpam-7095	311	17	(	(	PUNCT
ejpam-7095	311	18	10	10	NUM
ejpam-7095	311	19	)	)	PUNCT
ejpam-7095	311	20	will	will	AUX
ejpam-7095	311	21	be	be	AUX
ejpam-7095	311	22	implemented	implement	VERB
ejpam-7095	311	23	directly	directly	ADV
ejpam-7095	311	24	[	[	X
ejpam-7095	311	25	33	33	NUM
ejpam-7095	311	26	]	]	PUNCT
ejpam-7095	311	27	.	.	PUNCT
ejpam-7095	312	1	rearranging	rearrange	VERB
ejpam-7095	312	2	the	the	DET
ejpam-7095	312	3	columns	column	NOUN
ejpam-7095	312	4	and	and	CCONJ
ejpam-7095	312	5	rows	row	NOUN
ejpam-7095	312	6	of	of	ADP
ejpam-7095	312	7	the	the	DET
ejpam-7095	312	8	matrix	matrix	NOUN
ejpam-7095	312	9	£	£	SYM
ejpam-7095	312	10	disc	disc	NOUN
ejpam-7095	312	11	,	,	PUNCT
ejpam-7095	312	12	the	the	DET
ejpam-7095	312	13	following	follow	VERB
ejpam-7095	312	14	block	block	NOUN
ejpam-7095	312	15	matrix	matrix	NOUN
ejpam-7095	312	16	is	be	AUX
ejpam-7095	312	17	obtained	obtain	VERB
ejpam-7095	312	18	.	.	PUNCT
ejpam-7095	313	1	£	£	SYM
ejpam-7095	313	2	γ	γ	X
ejpam-7095	313	3	=	=	X
ejpam-7095	313	4	[	[	PUNCT
ejpam-7095	313	5	w	w	NOUN
ejpam-7095	313	6	f	f	PROPN
ejpam-7095	313	7	0	0	PUNCT
ejpam-7095	314	1	i	i	NOUN
ejpam-7095	314	2	]	]	PUNCT
ejpam-7095	314	3	,	,	PUNCT
ejpam-7095	314	4	where	where	SCONJ
ejpam-7095	314	5	the	the	DET
ejpam-7095	314	6	non	non	ADJ
ejpam-7095	314	7	-	-	ADJ
ejpam-7095	314	8	zero	zero	NUM
ejpam-7095	314	9	block	block	NOUN
ejpam-7095	314	10	w	w	NOUN
ejpam-7095	314	11	and	and	CCONJ
ejpam-7095	314	12	i	i	PRON
ejpam-7095	314	13	is	be	AUX
ejpam-7095	314	14	of	of	ADP
ejpam-7095	314	15	size	size	NOUN
ejpam-7095	314	16	having	have	VERB
ejpam-7095	314	17	order	order	NOUN
ejpam-7095	314	18	(	(	PUNCT
ejpam-7095	314	19	n−nb)×(n−nb	n−nb)×(n−nb	VERB
ejpam-7095	314	20	)	)	PUNCT
ejpam-7095	314	21	and	and	CCONJ
ejpam-7095	314	22	nb×nb	nb×nb	PROPN
ejpam-7095	314	23	.	.	PUNCT
ejpam-7095	315	1	here	here	ADV
ejpam-7095	315	2	nb	nb	INTJ
ejpam-7095	315	3	denotes	denote	VERB
ejpam-7095	315	4	the	the	DET
ejpam-7095	315	5	boundary	boundary	ADJ
ejpam-7095	315	6	nodes	node	NOUN
ejpam-7095	315	7	.	.	PUNCT
ejpam-7095	316	1	thus	thus	ADV
ejpam-7095	316	2	,	,	PUNCT
ejpam-7095	316	3	the	the	DET
ejpam-7095	316	4	system	system	NOUN
ejpam-7095	316	5	(	(	PUNCT
ejpam-7095	316	6	9)-(10	9)-(10	NOUN
ejpam-7095	316	7	)	)	PUNCT
ejpam-7095	316	8	has	have	VERB
ejpam-7095	316	9	the	the	DET
ejpam-7095	316	10	following	follow	VERB
ejpam-7095	316	11	form	form	NOUN
ejpam-7095	316	12	:	:	PUNCT
ejpam-7095	316	13	£	£	SYM
ejpam-7095	316	14	γû(x̄	γû(x̄	NUM
ejpam-7095	316	15	,	,	PUNCT
ejpam-7095	316	16	s	s	PART
ejpam-7095	316	17	)	)	PUNCT
ejpam-7095	316	18	=	=	NOUN
ejpam-7095	316	19	[	[	PUNCT
ejpam-7095	316	20	ĥ(x̄	ĥ(x̄	PROPN
ejpam-7095	316	21	,	,	PUNCT
ejpam-7095	316	22	s	s	PART
ejpam-7095	316	23	)	)	PUNCT
ejpam-7095	316	24	f̂(x̄	f̂(x̄	PROPN
ejpam-7095	316	25	,	,	PUNCT
ejpam-7095	316	26	s	s	NOUN
ejpam-7095	316	27	)	)	PUNCT
ejpam-7095	316	28	]	]	PUNCT
ejpam-7095	316	29	.	.	PUNCT
ejpam-7095	317	1	(	(	PUNCT
ejpam-7095	317	2	20	20	NUM
ejpam-7095	317	3	)	)	PUNCT
ejpam-7095	317	4	the	the	DET
ejpam-7095	317	5	solution	solution	NOUN
ejpam-7095	317	6	û(x̄	û(x̄	NUM
ejpam-7095	317	7	,	,	PUNCT
ejpam-7095	317	8	s	s	X
ejpam-7095	317	9	)	)	PUNCT
ejpam-7095	317	10	in	in	ADP
ejpam-7095	317	11	the	the	DET
ejpam-7095	317	12	laplace	laplace	NOUN
ejpam-7095	317	13	domain	domain	NOUN
ejpam-7095	317	14	is	be	AUX
ejpam-7095	317	15	determined	determine	VERB
ejpam-7095	317	16	by	by	ADP
ejpam-7095	317	17	solving	solve	VERB
ejpam-7095	317	18	(	(	PUNCT
ejpam-7095	317	19	20	20	NUM
ejpam-7095	317	20	)	)	PUNCT
ejpam-7095	317	21	.	.	PUNCT
ejpam-7095	318	1	the	the	DET
ejpam-7095	318	2	solution	solution	NOUN
ejpam-7095	318	3	u(x̄	u(x̄	NUM
ejpam-7095	318	4	,	,	PUNCT
ejpam-7095	318	5	t	t	PROPN
ejpam-7095	318	6	)	)	PUNCT
ejpam-7095	318	7	of	of	ADP
ejpam-7095	318	8	the	the	DET
ejpam-7095	318	9	original	original	ADJ
ejpam-7095	318	10	problem	problem	NOUN
ejpam-7095	318	11	(	(	PUNCT
ejpam-7095	318	12	1)–(3	1)–(3	NUM
ejpam-7095	318	13	)	)	PUNCT
ejpam-7095	318	14	is	be	AUX
ejpam-7095	318	15	then	then	ADV
ejpam-7095	318	16	recovered	recover	VERB
ejpam-7095	318	17	by	by	ADP
ejpam-7095	318	18	applying	apply	VERB
ejpam-7095	318	19	the	the	DET
ejpam-7095	318	20	inverse	inverse	NOUN
ejpam-7095	318	21	laplace	laplace	NOUN
ejpam-7095	318	22	transform	transform	VERB
ejpam-7095	318	23	to	to	ADP
ejpam-7095	318	24	û(x̄	û(x̄	PRON
ejpam-7095	318	25	,	,	PUNCT
ejpam-7095	318	26	s	s	AUX
ejpam-7095	318	27	)	)	PUNCT
ejpam-7095	318	28	as	as	SCONJ
ejpam-7095	318	29	follows	follow	VERB
ejpam-7095	318	30	:	:	PUNCT
ejpam-7095	318	31	u(x̄	u(x̄	NUM
ejpam-7095	318	32	,	,	PUNCT
ejpam-7095	318	33	τ	τ	X
ejpam-7095	318	34	)	)	PUNCT
ejpam-7095	318	35	=	=	SYM
ejpam-7095	318	36	1	1	NUM
ejpam-7095	318	37	2πi	2πi	ADJ
ejpam-7095	318	38	∫	∫	PROPN
ejpam-7095	318	39	µ+i∞	µ+i∞	NOUN
ejpam-7095	318	40	µ−i∞	µ−i∞	PRON
ejpam-7095	318	41	esτ	esτ	VERB
ejpam-7095	318	42	û(x̄	û(x̄	PROPN
ejpam-7095	318	43	,	,	PUNCT
ejpam-7095	318	44	s)ds	s)ds	PROPN
ejpam-7095	318	45	=	=	SYM
ejpam-7095	318	46	1	1	NUM
ejpam-7095	318	47	2πi	2πi	NOUN
ejpam-7095	318	48	∫	∫	PROPN
ejpam-7095	318	49	γc	γc	PROPN
ejpam-7095	318	50	esτ	esτ	PROPN
ejpam-7095	318	51	û(x̄	û(x̄	PROPN
ejpam-7095	318	52	,	,	PUNCT
ejpam-7095	318	53	s)ds	s)ds	PROPN
ejpam-7095	318	54	,	,	PUNCT
ejpam-7095	318	55	re(s	re(s	ADJ
ejpam-7095	318	56	)	)	PUNCT
ejpam-7095	318	57	>	>	X
ejpam-7095	318	58	0	0	NUM
ejpam-7095	318	59	,	,	PUNCT
ejpam-7095	318	60	(	(	PUNCT
ejpam-7095	318	61	21	21	NUM
ejpam-7095	318	62	)	)	PUNCT
ejpam-7095	318	63	5.3	5.3	NUM
ejpam-7095	318	64	.	.	PUNCT
ejpam-7095	318	65	contour	contour	NOUN
ejpam-7095	318	66	selection	selection	NOUN
ejpam-7095	318	67	and	and	CCONJ
ejpam-7095	318	68	quadrature	quadrature	NOUN
ejpam-7095	318	69	one	one	NUM
ejpam-7095	318	70	of	of	ADP
ejpam-7095	318	71	the	the	DET
ejpam-7095	318	72	most	most	ADV
ejpam-7095	318	73	effective	effective	ADJ
ejpam-7095	318	74	approaches	approach	NOUN
ejpam-7095	318	75	for	for	ADP
ejpam-7095	318	76	computing	compute	VERB
ejpam-7095	318	77	eq	eq	X
ejpam-7095	318	78	.	.	PUNCT
ejpam-7095	319	1	(	(	PUNCT
ejpam-7095	319	2	21	21	NUM
ejpam-7095	319	3	)	)	PUNCT
ejpam-7095	319	4	is	be	AUX
ejpam-7095	319	5	to	to	PART
ejpam-7095	319	6	deform	deform	VERB
ejpam-7095	319	7	the	the	DET
ejpam-7095	319	8	integration	integration	NOUN
ejpam-7095	319	9	contour	contour	NOUN
ejpam-7095	319	10	γc	γc	NOUN
ejpam-7095	319	11	into	into	ADP
ejpam-7095	319	12	the	the	DET
ejpam-7095	319	13	left	left	ADJ
ejpam-7095	319	14	half	half	ADJ
ejpam-7095	319	15	plane	plane	NOUN
ejpam-7095	319	16	to	to	PART
ejpam-7095	319	17	ensure	ensure	VERB
ejpam-7095	319	18	the	the	DET
ejpam-7095	319	19	integrand	integrand	NOUN
ejpam-7095	319	20	decays	decay	NOUN
ejpam-7095	319	21	,	,	PUNCT
ejpam-7095	319	22	followed	follow	VERB
ejpam-7095	319	23	by	by	ADP
ejpam-7095	319	24	applying	apply	VERB
ejpam-7095	319	25	the	the	DET
ejpam-7095	319	26	quadrature	quadrature	NOUN
ejpam-7095	319	27	methods	method	NOUN
ejpam-7095	319	28	.	.	PUNCT
ejpam-7095	320	1	this	this	DET
ejpam-7095	320	2	idea	idea	NOUN
ejpam-7095	320	3	traces	trace	VERB
ejpam-7095	320	4	back	back	ADV
ejpam-7095	320	5	to	to	ADP
ejpam-7095	320	6	1950	1950	NUM
ejpam-7095	320	7	,	,	PUNCT
ejpam-7095	320	8	originating	originate	VERB
ejpam-7095	320	9	in	in	ADP
ejpam-7095	320	10	the	the	DET
ejpam-7095	320	11	work	work	NOUN
ejpam-7095	320	12	of	of	ADP
ejpam-7095	320	13	talbot	talbot	PROPN
ejpam-7095	320	14	’s	’s	PART
ejpam-7095	320	15	doctoral	doctoral	ADJ
ejpam-7095	320	16	student	student	NOUN
ejpam-7095	320	17	green	green	NOUN
ejpam-7095	321	1	[	[	X
ejpam-7095	321	2	37	37	NUM
ejpam-7095	321	3	]	]	PUNCT
ejpam-7095	321	4	.	.	PUNCT
ejpam-7095	322	1	talbot	talbot	PROPN
ejpam-7095	322	2	later	later	ADV
ejpam-7095	322	3	published	publish	VERB
ejpam-7095	322	4	a	a	DET
ejpam-7095	322	5	paper	paper	NOUN
ejpam-7095	322	6	[	[	X
ejpam-7095	322	7	38	38	NUM
ejpam-7095	322	8	]	]	PUNCT
ejpam-7095	322	9	in	in	ADP
ejpam-7095	322	10	which	which	PRON
ejpam-7095	322	11	he	he	PRON
ejpam-7095	322	12	generalized	generalize	VERB
ejpam-7095	322	13	and	and	CCONJ
ejpam-7095	322	14	improved	improve	VERB
ejpam-7095	322	15	the	the	DET
ejpam-7095	322	16	work	work	NOUN
ejpam-7095	322	17	of	of	ADP
ejpam-7095	322	18	green	green	NOUN
ejpam-7095	322	19	.	.	PUNCT
ejpam-7095	323	1	talbot	talbot	PROPN
ejpam-7095	323	2	suggested	suggest	VERB
ejpam-7095	323	3	to	to	PART
ejpam-7095	323	4	deform	deform	VERB
ejpam-7095	323	5	the	the	DET
ejpam-7095	323	6	integration	integration	NOUN
ejpam-7095	323	7	contour	contour	NOUN
ejpam-7095	323	8	into	into	ADP
ejpam-7095	323	9	a	a	DET
ejpam-7095	323	10	contour	contour	NOUN
ejpam-7095	323	11	γc	γc	NOUN
ejpam-7095	323	12	that	that	PRON
ejpam-7095	323	13	begins	begin	VERB
ejpam-7095	323	14	and	and	CCONJ
ejpam-7095	323	15	ends	end	VERB
ejpam-7095	323	16	in	in	ADP
ejpam-7095	323	17	the	the	DET
ejpam-7095	323	18	left	left	ADJ
ejpam-7095	323	19	plane	plane	NOUN
ejpam-7095	323	20	,	,	PUNCT
ejpam-7095	324	1	such	such	ADJ
ejpam-7095	324	2	that	that	SCONJ
ejpam-7095	324	3	re(s	re(s	ADJ
ejpam-7095	324	4	)	)	PUNCT
ejpam-7095	324	5	−→	−→	NOUN
ejpam-7095	324	6	−∞	−∞	X
ejpam-7095	324	7	as	as	ADP
ejpam-7095	324	8	|s|	|s|	NOUN
ejpam-7095	324	9	→	→	SYM
ejpam-7095	324	10	∞.	∞.	PROPN
ejpam-7095	324	11	in	in	ADP
ejpam-7095	324	12	literature	literature	NOUN
ejpam-7095	324	13	,	,	PUNCT
ejpam-7095	324	14	many	many	ADJ
ejpam-7095	324	15	popular	popular	ADJ
ejpam-7095	324	16	contours	contours	NOUN
ejpam-7095	324	17	have	have	AUX
ejpam-7095	324	18	been	be	AUX
ejpam-7095	324	19	proposed	propose	VERB
ejpam-7095	324	20	,	,	PUNCT
ejpam-7095	324	21	such	such	ADJ
ejpam-7095	324	22	as	as	ADP
ejpam-7095	324	23	talbot	talbot	PROPN
ejpam-7095	324	24	’s	’s	PART
ejpam-7095	324	25	contour	contour	NOUN
ejpam-7095	325	1	[	[	X
ejpam-7095	325	2	29	29	NUM
ejpam-7095	325	3	,	,	PUNCT
ejpam-7095	325	4	38	38	NUM
ejpam-7095	325	5	]	]	PUNCT
ejpam-7095	325	6	,	,	PUNCT
ejpam-7095	325	7	the	the	DET
ejpam-7095	325	8	parabolic	parabolic	ADJ
ejpam-7095	325	9	and	and	CCONJ
ejpam-7095	325	10	hyperbolic	hyperbolic	ADJ
ejpam-7095	325	11	contours	contours	NOUN
ejpam-7095	326	1	[	[	X
ejpam-7095	326	2	39	39	NUM
ejpam-7095	326	3	]	]	PUNCT
ejpam-7095	326	4	.	.	PUNCT
ejpam-7095	327	1	the	the	DET
ejpam-7095	327	2	work	work	NOUN
ejpam-7095	327	3	utilizes	utilize	VERB
ejpam-7095	327	4	the	the	DET
ejpam-7095	327	5	modified	modified	PROPN
ejpam-7095	327	6	talbot	talbot	PROPN
ejpam-7095	327	7	’s	’s	PART
ejpam-7095	327	8	contour	contour	NOUN
ejpam-7095	327	9	proposed	propose	VERB
ejpam-7095	327	10	in	in	ADP
ejpam-7095	327	11	[	[	X
ejpam-7095	327	12	29	29	NUM
ejpam-7095	327	13	]	]	PUNCT
ejpam-7095	327	14	as	as	ADP
ejpam-7095	327	15	:	:	PUNCT
ejpam-7095	327	16	γc	γc	X
ejpam-7095	327	17	:	:	PUNCT
ejpam-7095	327	18	s	s	X
ejpam-7095	327	19	=	=	SYM
ejpam-7095	327	20	s(ξ	s(ξ	PROPN
ejpam-7095	327	21	)	)	PUNCT
ejpam-7095	327	22	,	,	PUNCT
ejpam-7095	327	23	ξ	ξ	PROPN
ejpam-7095	327	24	∈	∈	PROPN
ejpam-7095	327	25	[	[	X
ejpam-7095	327	26	−π	−π	PROPN
ejpam-7095	327	27	,	,	PUNCT
ejpam-7095	327	28	π	π	PROPN
ejpam-7095	327	29	]	]	X
ejpam-7095	327	30	,	,	PUNCT
ejpam-7095	327	31	re	re	X
ejpam-7095	327	32	(	(	PUNCT
ejpam-7095	327	33	s(±π	s(±π	PROPN
ejpam-7095	327	34	)	)	PUNCT
ejpam-7095	327	35	)	)	PUNCT
ejpam-7095	328	1	=	=	PUNCT
ejpam-7095	328	2	−∞	−∞	NOUN
ejpam-7095	328	3	,	,	PUNCT
ejpam-7095	328	4	(	(	PUNCT
ejpam-7095	328	5	22	22	NUM
ejpam-7095	328	6	)	)	PUNCT
ejpam-7095	328	7	kamran	kamran	PROPN
ejpam-7095	328	8	et	et	PROPN
ejpam-7095	328	9	al	al	PROPN
ejpam-7095	328	10	.	.	PUNCT
ejpam-7095	328	11	/	/	SYM
ejpam-7095	328	12	eur	eur	PROPN
ejpam-7095	328	13	.	.	PUNCT
ejpam-7095	329	1	j.	j.	PROPN
ejpam-7095	329	2	pure	pure	PROPN
ejpam-7095	329	3	appl	appl	PROPN
ejpam-7095	329	4	.	.	PROPN
ejpam-7095	329	5	math	math	PROPN
ejpam-7095	329	6	,	,	PUNCT
ejpam-7095	329	7	18	18	NUM
ejpam-7095	329	8	(	(	PUNCT
ejpam-7095	329	9	4	4	NUM
ejpam-7095	329	10	)	)	PUNCT
ejpam-7095	329	11	(	(	PUNCT
ejpam-7095	329	12	2025	2025	NUM
ejpam-7095	329	13	)	)	PUNCT
ejpam-7095	329	14	,	,	PUNCT
ejpam-7095	329	15	7095	7095	NUM
ejpam-7095	329	16	16	16	NUM
ejpam-7095	329	17	of	of	ADP
ejpam-7095	329	18	30	30	NUM
ejpam-7095	329	19	we	we	PRON
ejpam-7095	329	20	have	have	VERB
ejpam-7095	329	21	s(ξ	s(ξ	NUM
ejpam-7095	329	22	)	)	PUNCT
ejpam-7095	329	23	=	=	SYM
ejpam-7095	329	24	mt	mt	PROPN
ejpam-7095	329	25	τ	τ	PROPN
ejpam-7095	329	26	ε(ξ	ε(ξ	PROPN
ejpam-7095	329	27	)	)	PUNCT
ejpam-7095	329	28	,	,	PUNCT
ejpam-7095	329	29	ε(ξ	ε(ξ	PROPN
ejpam-7095	329	30	)	)	PUNCT
ejpam-7095	329	31	=	=	SYM
ejpam-7095	330	1	−θ1	−θ1	PROPN
ejpam-7095	330	2	+	+	PUNCT
ejpam-7095	330	3	θ2ξ	θ2ξ	NOUN
ejpam-7095	330	4	cot(θ3ξ	cot(θ3ξ	PROPN
ejpam-7095	330	5	)	)	PUNCT
ejpam-7095	331	1	+	+	CCONJ
ejpam-7095	331	2	θ4iξ	θ4iξ	NUM
ejpam-7095	331	3	,	,	PUNCT
ejpam-7095	331	4	(	(	PUNCT
ejpam-7095	331	5	23	23	NUM
ejpam-7095	331	6	)	)	PUNCT
ejpam-7095	331	7	where	where	SCONJ
ejpam-7095	331	8	the	the	DET
ejpam-7095	331	9	user	user	NOUN
ejpam-7095	331	10	will	will	AUX
ejpam-7095	331	11	select	select	VERB
ejpam-7095	331	12	the	the	DET
ejpam-7095	331	13	parameters	parameter	NOUN
ejpam-7095	331	14	θ1	θ1	PROPN
ejpam-7095	331	15	,	,	PUNCT
ejpam-7095	331	16	θ2	θ2	PROPN
ejpam-7095	331	17	,	,	PUNCT
ejpam-7095	331	18	θ3	θ3	PROPN
ejpam-7095	331	19	,	,	PUNCT
ejpam-7095	331	20	and	and	CCONJ
ejpam-7095	331	21	θ4	θ4	NOUN
ejpam-7095	331	22	.	.	PUNCT
ejpam-7095	332	1	from	from	ADP
ejpam-7095	332	2	(	(	PUNCT
ejpam-7095	332	3	23	23	NUM
ejpam-7095	332	4	)	)	PUNCT
ejpam-7095	332	5	and	and	CCONJ
ejpam-7095	332	6	(	(	PUNCT
ejpam-7095	332	7	21	21	NUM
ejpam-7095	332	8	)	)	PUNCT
ejpam-7095	332	9	,	,	PUNCT
ejpam-7095	332	10	we	we	PRON
ejpam-7095	332	11	have	have	VERB
ejpam-7095	332	12	u(x̄	u(x̄	NUM
ejpam-7095	332	13	,	,	PUNCT
ejpam-7095	332	14	τ	τ	X
ejpam-7095	332	15	)	)	PUNCT
ejpam-7095	332	16	=	=	SYM
ejpam-7095	332	17	1	1	NUM
ejpam-7095	332	18	2πi	2πi	NOUN
ejpam-7095	332	19	∫	∫	PROPN
ejpam-7095	333	1	π	π	NOUN
ejpam-7095	333	2	−π	−π	PROPN
ejpam-7095	333	3	es(ξ)τ	es(ξ)τ	ADP
ejpam-7095	333	4	û(x̄	û(x̄	PROPN
ejpam-7095	333	5	,	,	PUNCT
ejpam-7095	333	6	s(ξ))s′(ξ)dξ	s(ξ))s′(ξ)dξ	PROPN
ejpam-7095	333	7	.	.	PUNCT
ejpam-7095	334	1	(	(	PUNCT
ejpam-7095	334	2	24	24	NUM
ejpam-7095	334	3	)	)	PUNCT
ejpam-7095	334	4	fast	fast	ADJ
ejpam-7095	334	5	and	and	CCONJ
ejpam-7095	334	6	accurate	accurate	ADJ
ejpam-7095	334	7	approximation	approximation	NOUN
ejpam-7095	334	8	of	of	ADP
ejpam-7095	334	9	(	(	PUNCT
ejpam-7095	334	10	24	24	NUM
ejpam-7095	334	11	)	)	PUNCT
ejpam-7095	334	12	can	can	AUX
ejpam-7095	334	13	be	be	AUX
ejpam-7095	334	14	achieved	achieve	VERB
ejpam-7095	334	15	using	use	VERB
ejpam-7095	334	16	trapezoidal	trapezoidal	ADJ
ejpam-7095	334	17	or	or	CCONJ
ejpam-7095	334	18	midpoint	midpoint	NOUN
ejpam-7095	334	19	rule	rule	NOUN
ejpam-7095	334	20	[	[	X
ejpam-7095	334	21	29	29	NUM
ejpam-7095	334	22	]	]	PUNCT
ejpam-7095	334	23	.	.	PUNCT
ejpam-7095	335	1	this	this	DET
ejpam-7095	335	2	work	work	NOUN
ejpam-7095	335	3	focuses	focus	VERB
ejpam-7095	335	4	on	on	ADP
ejpam-7095	335	5	the	the	DET
ejpam-7095	335	6	midpoint	midpoint	NOUN
ejpam-7095	335	7	rule	rule	NOUN
ejpam-7095	335	8	with	with	ADP
ejpam-7095	335	9	a	a	DET
ejpam-7095	335	10	step	step	NOUN
ejpam-7095	335	11	ℏ	ℏ	NOUN
ejpam-7095	335	12	=	=	SYM
ejpam-7095	335	13	2π	2π	PROPN
ejpam-7095	335	14	mt	mt	NOUN
ejpam-7095	335	15	given	give	VERB
ejpam-7095	335	16	by	by	ADP
ejpam-7095	335	17	:	:	PUNCT
ejpam-7095	335	18	uapp(x̄	uapp(x̄	PROPN
ejpam-7095	335	19	,	,	PUNCT
ejpam-7095	335	20	τ	τ	X
ejpam-7095	335	21	)	)	PUNCT
ejpam-7095	335	22	≈	≈	PROPN
ejpam-7095	335	23	1	1	NUM
ejpam-7095	335	24	mti	mti	NOUN
ejpam-7095	335	25	mt∑	mt∑	PROPN
ejpam-7095	335	26	k=1	k=1	X
ejpam-7095	335	27	es(ξk)τ	es(ξk)τ	PROPN
ejpam-7095	335	28	û(x̄	û(x̄	PROPN
ejpam-7095	335	29	,	,	PUNCT
ejpam-7095	335	30	s(ξk))s	s(ξk))	NOUN
ejpam-7095	335	31	′(ξk	′(ξk	PROPN
ejpam-7095	335	32	)	)	PUNCT
ejpam-7095	335	33	,	,	PUNCT
ejpam-7095	335	34	ξk	ξk	ADP
ejpam-7095	335	35	=	=	PUNCT
ejpam-7095	336	1	−π	−π	PROPN
ejpam-7095	337	1	+	+	CCONJ
ejpam-7095	337	2	(	(	PUNCT
ejpam-7095	337	3	2k	2k	NUM
ejpam-7095	337	4	−	−	NUM
ejpam-7095	337	5	1	1	NUM
ejpam-7095	337	6	2	2	NUM
ejpam-7095	337	7	)	)	PUNCT
ejpam-7095	337	8	ℏ.	ℏ.	NOUN
ejpam-7095	337	9	(	(	PUNCT
ejpam-7095	337	10	25	25	NUM
ejpam-7095	337	11	)	)	PUNCT
ejpam-7095	337	12	5.3.1	5.3.1	NUM
ejpam-7095	337	13	.	.	NOUN
ejpam-7095	337	14	error	error	NOUN
ejpam-7095	337	15	analysis	analysis	NOUN
ejpam-7095	337	16	the	the	DET
ejpam-7095	337	17	error	error	NOUN
ejpam-7095	337	18	analysis	analysis	NOUN
ejpam-7095	337	19	is	be	AUX
ejpam-7095	337	20	performed	perform	VERB
ejpam-7095	337	21	in	in	ADP
ejpam-7095	337	22	three	three	NUM
ejpam-7095	337	23	stages	stage	NOUN
ejpam-7095	337	24	:	:	PUNCT
ejpam-7095	337	25	step	step	NOUN
ejpam-7095	337	26	1	1	NUM
ejpam-7095	337	27	:	:	PUNCT
ejpam-7095	337	28	in	in	ADP
ejpam-7095	337	29	the	the	DET
ejpam-7095	337	30	first	first	ADJ
ejpam-7095	337	31	step	step	NOUN
ejpam-7095	337	32	,	,	PUNCT
ejpam-7095	337	33	the	the	DET
ejpam-7095	337	34	lt	lt	NOUN
ejpam-7095	337	35	is	be	AUX
ejpam-7095	337	36	employed	employ	VERB
ejpam-7095	337	37	,	,	PUNCT
ejpam-7095	337	38	which	which	PRON
ejpam-7095	337	39	transforms	transform	VERB
ejpam-7095	337	40	the	the	DET
ejpam-7095	337	41	given	give	VERB
ejpam-7095	337	42	problem	problem	NOUN
ejpam-7095	337	43	into	into	ADP
ejpam-7095	337	44	a	a	DET
ejpam-7095	337	45	time	time	NOUN
ejpam-7095	337	46	-	-	PUNCT
ejpam-7095	337	47	independent	independent	ADJ
ejpam-7095	337	48	problem	problem	NOUN
ejpam-7095	337	49	,	,	PUNCT
ejpam-7095	337	50	since	since	SCONJ
ejpam-7095	337	51	this	this	DET
ejpam-7095	337	52	transformation	transformation	NOUN
ejpam-7095	337	53	is	be	AUX
ejpam-7095	337	54	exact	exact	ADJ
ejpam-7095	337	55	,	,	PUNCT
ejpam-7095	337	56	no	no	DET
ejpam-7095	337	57	error	error	NOUN
ejpam-7095	337	58	is	be	AUX
ejpam-7095	337	59	introduced	introduce	VERB
ejpam-7095	337	60	in	in	ADP
ejpam-7095	337	61	this	this	DET
ejpam-7095	337	62	step	step	NOUN
ejpam-7095	337	63	.	.	PUNCT
ejpam-7095	338	1	step	step	NOUN
ejpam-7095	338	2	2	2	NUM
ejpam-7095	338	3	:	:	PUNCT
ejpam-7095	338	4	in	in	ADP
ejpam-7095	338	5	step	step	NOUN
ejpam-7095	338	6	2	2	NUM
ejpam-7095	338	7	,	,	PUNCT
ejpam-7095	338	8	we	we	PRON
ejpam-7095	338	9	employ	employ	VERB
ejpam-7095	338	10	the	the	DET
ejpam-7095	338	11	cscm	cscm	NOUN
ejpam-7095	338	12	discretization	discretization	NOUN
ejpam-7095	338	13	technique	technique	NOUN
ejpam-7095	338	14	to	to	PART
ejpam-7095	338	15	solve	solve	VERB
ejpam-7095	338	16	the	the	DET
ejpam-7095	338	17	transformed	transform	VERB
ejpam-7095	338	18	problem	problem	NOUN
ejpam-7095	338	19	,	,	PUNCT
ejpam-7095	338	20	with	with	ADP
ejpam-7095	338	21	the	the	DET
ejpam-7095	338	22	corresponding	correspond	VERB
ejpam-7095	338	23	error	error	NOUN
ejpam-7095	338	24	estimate	estimate	NOUN
ejpam-7095	338	25	developed	develop	VERB
ejpam-7095	338	26	below	below	ADV
ejpam-7095	338	27	:	:	PUNCT
ejpam-7095	338	28	utilizing	utilize	VERB
ejpam-7095	338	29	the	the	DET
ejpam-7095	338	30	points	point	NOUN
ejpam-7095	338	31	in	in	ADP
ejpam-7095	338	32	eq	eq	ADP
ejpam-7095	338	33	.	.	PUNCT
ejpam-7095	339	1	(	(	PUNCT
ejpam-7095	339	2	11	11	NUM
ejpam-7095	339	3	)	)	PUNCT
ejpam-7095	339	4	and	and	CCONJ
ejpam-7095	339	5	the	the	DET
ejpam-7095	339	6	lps	lps	PROPN
ejpam-7095	339	7	in	in	ADP
ejpam-7095	339	8	eq	eq	ADP
ejpam-7095	339	9	.	.	PUNCT
ejpam-7095	340	1	(	(	PUNCT
ejpam-7095	340	2	12	12	NUM
ejpam-7095	340	3	)	)	PUNCT
ejpam-7095	340	4	,	,	PUNCT
ejpam-7095	340	5	the	the	DET
ejpam-7095	340	6	interpolation	interpolation	NOUN
ejpam-7095	340	7	operator	operator	NOUN
ejpam-7095	340	8	presented	present	VERB
ejpam-7095	340	9	in	in	ADP
ejpam-7095	340	10	[	[	X
ejpam-7095	340	11	34	34	NUM
ejpam-7095	340	12	]	]	PUNCT
ejpam-7095	340	13	is	be	AUX
ejpam-7095	340	14	expressed	express	VERB
ejpam-7095	340	15	as	as	ADP
ejpam-7095	340	16	:	:	PUNCT
ejpam-7095	340	17	in	in	ADP
ejpam-7095	340	18	:	:	PUNCT
ejpam-7095	340	19	c(θ	c(θ	PROPN
ejpam-7095	340	20	)	)	PUNCT
ejpam-7095	341	1	→	→	SYM
ejpam-7095	341	2	pn	pn	PROPN
ejpam-7095	341	3	,	,	PUNCT
ejpam-7095	341	4	in(û	in(û	NOUN
ejpam-7095	341	5	)	)	PUNCT
ejpam-7095	341	6	=	=	SYM
ejpam-7095	341	7	n∑	n∑	PUNCT
ejpam-7095	341	8	=	=	NOUN
ejpam-7095	341	9	0	0	NUM
ejpam-7095	341	10	û(x	û(x	NOUN
ejpam-7095	341	11	,	,	PUNCT
ejpam-7095	341	12	s)ℓ(x	s)ℓ(x	NOUN
ejpam-7095	341	13	)	)	PUNCT
ejpam-7095	341	14	.	.	PUNCT
ejpam-7095	342	1	(	(	PUNCT
ejpam-7095	342	2	26	26	NUM
ejpam-7095	342	3	)	)	PUNCT
ejpam-7095	342	4	following	follow	VERB
ejpam-7095	342	5	the	the	DET
ejpam-7095	342	6	technique	technique	NOUN
ejpam-7095	342	7	in	in	ADP
ejpam-7095	342	8	[	[	X
ejpam-7095	342	9	40	40	NUM
ejpam-7095	342	10	]	]	PUNCT
ejpam-7095	342	11	,	,	PUNCT
ejpam-7095	342	12	we	we	PRON
ejpam-7095	342	13	establish	establish	VERB
ejpam-7095	342	14	the	the	DET
ejpam-7095	342	15	error	error	NOUN
ejpam-7095	342	16	bound	bind	VERB
ejpam-7095	342	17	.	.	PUNCT
ejpam-7095	343	1	let	let	VERB
ejpam-7095	343	2	qn	qn	NOUN
ejpam-7095	343	3	be	be	AUX
ejpam-7095	343	4	a	a	DET
ejpam-7095	343	5	constant	constant	ADJ
ejpam-7095	343	6	;	;	PUNCT
ejpam-7095	343	7	then	then	ADV
ejpam-7095	343	8	,	,	PUNCT
ejpam-7095	343	9	the	the	DET
ejpam-7095	343	10	stability	stability	NOUN
ejpam-7095	343	11	estimate	estimate	NOUN
ejpam-7095	343	12	is	be	AUX
ejpam-7095	343	13	expressed	express	VERB
ejpam-7095	343	14	as	as	ADP
ejpam-7095	343	15	:	:	PUNCT
ejpam-7095	343	16	∥in(û)∥∞	∥in(û)∥∞	NOUN
ejpam-7095	343	17	≤	≤	ADJ
ejpam-7095	343	18	qn∥û∥∞	qn∥û∥∞	NOUN
ejpam-7095	343	19	,	,	PUNCT
ejpam-7095	343	20	∀	∀	X
ejpam-7095	343	21	û	û	DET
ejpam-7095	343	22	∈	∈	PROPN
ejpam-7095	343	23	c[−1	c[−1	NOUN
ejpam-7095	343	24	,	,	PUNCT
ejpam-7095	343	25	1	1	NUM
ejpam-7095	343	26	]	]	PUNCT
ejpam-7095	343	27	.	.	PUNCT
ejpam-7095	344	1	(	(	PUNCT
ejpam-7095	344	2	27	27	NUM
ejpam-7095	344	3	)	)	PUNCT
ejpam-7095	344	4	additionally	additionally	ADV
ejpam-7095	344	5	,	,	PUNCT
ejpam-7095	344	6	in(û	in(û	PRON
ejpam-7095	344	7	)	)	PUNCT
ejpam-7095	344	8	=	=	SYM
ejpam-7095	345	1	û	û	PROPN
ejpam-7095	345	2	,	,	PUNCT
ejpam-7095	345	3	for	for	ADP
ejpam-7095	345	4	all	all	DET
ejpam-7095	345	5	û	û	NUM
ejpam-7095	345	6	∈	∈	PROPN
ejpam-7095	345	7	pn	pn	NOUN
ejpam-7095	345	8	.	.	PUNCT
ejpam-7095	345	9	(	(	PUNCT
ejpam-7095	345	10	28	28	NUM
ejpam-7095	345	11	)	)	PUNCT
ejpam-7095	345	12	for	for	ADP
ejpam-7095	345	13	chebyshev	chebyshev	NOUN
ejpam-7095	345	14	interpolation	interpolation	NOUN
ejpam-7095	345	15	,	,	PUNCT
ejpam-7095	345	16	the	the	DET
ejpam-7095	345	17	stability	stability	NOUN
ejpam-7095	345	18	constant	constant	ADJ
ejpam-7095	345	19	grows	grow	VERB
ejpam-7095	345	20	logarithmically	logarithmically	ADV
ejpam-7095	345	21	with	with	ADP
ejpam-7095	345	22	n	n	CCONJ
ejpam-7095	345	23	:	:	PUNCT
ejpam-7095	345	24	qn	qn	NOUN
ejpam-7095	345	25	=	=	NOUN
ejpam-7095	345	26	1	1	NUM
ejpam-7095	345	27	+	+	CCONJ
ejpam-7095	345	28	(	(	PUNCT
ejpam-7095	345	29	ln(1	ln(1	PROPN
ejpam-7095	345	30	+	+	NUM
ejpam-7095	345	31	n)π	n)π	ADJ
ejpam-7095	345	32	2	2	NUM
ejpam-7095	345	33	)	)	PUNCT
ejpam-7095	345	34	≤	≤	NOUN
ejpam-7095	345	35	(	(	PUNCT
ejpam-7095	345	36	n	n	NOUN
ejpam-7095	345	37	+	+	NOUN
ejpam-7095	345	38	1	1	NUM
ejpam-7095	345	39	)	)	PUNCT
ejpam-7095	345	40	.	.	PUNCT
ejpam-7095	346	1	(	(	PUNCT
ejpam-7095	346	2	29	29	NUM
ejpam-7095	346	3	)	)	PUNCT
ejpam-7095	346	4	for	for	ADP
ejpam-7095	346	5	any	any	DET
ejpam-7095	346	6	û	û	NUM
ejpam-7095	346	7	∈	∈	PROPN
ejpam-7095	346	8	cn+1[−1	cn+1[−1	NOUN
ejpam-7095	346	9	,	,	PUNCT
ejpam-7095	346	10	1	1	NUM
ejpam-7095	346	11	]	]	PUNCT
ejpam-7095	346	12	,	,	PUNCT
ejpam-7095	346	13	the	the	DET
ejpam-7095	346	14	interpolation	interpolation	NOUN
ejpam-7095	346	15	error	error	NOUN
ejpam-7095	346	16	bound	bind	VERB
ejpam-7095	346	17	is	be	AUX
ejpam-7095	346	18	expressed	express	VERB
ejpam-7095	346	19	as	as	ADP
ejpam-7095	346	20	[	[	NOUN
ejpam-7095	346	21	?	?	PUNCT
ejpam-7095	347	1	]	]	X
ejpam-7095	347	2	:	:	PUNCT
ejpam-7095	348	1	∥û−	∥û−	PROPN
ejpam-7095	348	2	in(û)∥∞	in(û)∥∞	PROPN
ejpam-7095	348	3	≤	≤	PROPN
ejpam-7095	348	4	2−n	2−n	NUM
ejpam-7095	348	5	γ(n	γ(n	X
ejpam-7095	348	6	+	+	CCONJ
ejpam-7095	348	7	2	2	X
ejpam-7095	348	8	)	)	PUNCT
ejpam-7095	348	9	∥ûn+1∥∞.	∥ûn+1∥∞.	NOUN
ejpam-7095	349	1	(	(	PUNCT
ejpam-7095	349	2	30	30	NUM
ejpam-7095	349	3	)	)	PUNCT
ejpam-7095	349	4	kamran	kamran	PROPN
ejpam-7095	349	5	et	et	PROPN
ejpam-7095	349	6	al	al	PROPN
ejpam-7095	349	7	.	.	PUNCT
ejpam-7095	349	8	/	/	SYM
ejpam-7095	349	9	eur	eur	PROPN
ejpam-7095	349	10	.	.	PUNCT
ejpam-7095	350	1	j.	j.	PROPN
ejpam-7095	350	2	pure	pure	PROPN
ejpam-7095	350	3	appl	appl	PROPN
ejpam-7095	350	4	.	.	PROPN
ejpam-7095	350	5	math	math	PROPN
ejpam-7095	350	6	,	,	PUNCT
ejpam-7095	350	7	18	18	NUM
ejpam-7095	350	8	(	(	PUNCT
ejpam-7095	350	9	4	4	NUM
ejpam-7095	350	10	)	)	PUNCT
ejpam-7095	350	11	(	(	PUNCT
ejpam-7095	350	12	2025	2025	NUM
ejpam-7095	350	13	)	)	PUNCT
ejpam-7095	350	14	,	,	PUNCT
ejpam-7095	350	15	7095	7095	NUM
ejpam-7095	350	16	17	17	NUM
ejpam-7095	350	17	of	of	ADP
ejpam-7095	350	18	30	30	NUM
ejpam-7095	350	19	theorem	theorem	NOUN
ejpam-7095	350	20	1	1	NUM
ejpam-7095	350	21	.	.	PUNCT
ejpam-7095	351	1	[	[	X
ejpam-7095	351	2	40	40	NUM
ejpam-7095	351	3	]	]	PUNCT
ejpam-7095	351	4	if	if	SCONJ
ejpam-7095	351	5	û	û	NUM
ejpam-7095	351	6	∈	∈	PROPN
ejpam-7095	351	7	c(n+1)[−1	c(n+1)[−1	NOUN
ejpam-7095	351	8	,	,	PUNCT
ejpam-7095	351	9	1	1	NUM
ejpam-7095	351	10	]	]	PUNCT
ejpam-7095	351	11	,	,	PUNCT
ejpam-7095	351	12	then	then	ADV
ejpam-7095	351	13	for	for	ADP
ejpam-7095	351	14	q	q	PROPN
ejpam-7095	351	15	=	=	SYM
ejpam-7095	351	16	0	0	NUM
ejpam-7095	351	17	,	,	PUNCT
ejpam-7095	351	18	1	1	NUM
ejpam-7095	351	19	,	,	PUNCT
ejpam-7095	351	20	...	...	PUNCT
ejpam-7095	351	21	,	,	PUNCT
ejpam-7095	351	22	n	n	PROPN
ejpam-7095	351	23	∥û(q	∥û(q	PROPN
ejpam-7095	351	24	)	)	PUNCT
ejpam-7095	351	25	−	−	NOUN
ejpam-7095	351	26	in(û	in(û	PART
ejpam-7095	351	27	)	)	PUNCT
ejpam-7095	351	28	(	(	PUNCT
ejpam-7095	351	29	q)∥∞	q)∥∞	X
ejpam-7095	351	30	≤	≤	NUM
ejpam-7095	351	31	2(q	2(q	NUM
ejpam-7095	351	32	(	(	PUNCT
ejpam-7095	351	33	q	q	NOUN
ejpam-7095	351	34	)	)	PUNCT
ejpam-7095	351	35	n	n	NOUN
ejpam-7095	351	36	+	+	NOUN
ejpam-7095	351	37	1	1	X
ejpam-7095	351	38	)	)	PUNCT
ejpam-7095	351	39	γ(n−	γ(n−	PROPN
ejpam-7095	351	40	q	q	PROPN
ejpam-7095	352	1	+	+	NUM
ejpam-7095	352	2	2	2	NUM
ejpam-7095	352	3	)	)	PUNCT
ejpam-7095	352	4	(	(	PUNCT
ejpam-7095	352	5	1	1	NUM
ejpam-7095	352	6	2	2	NUM
ejpam-7095	352	7	)	)	PUNCT
ejpam-7095	352	8	(	(	PUNCT
ejpam-7095	352	9	n−q+1	n−q+1	PROPN
ejpam-7095	352	10	)	)	PUNCT
ejpam-7095	352	11	∥û(n+1)∥∞	∥û(n+1)∥∞	NOUN
ejpam-7095	352	12	,	,	PUNCT
ejpam-7095	352	13	(	(	PUNCT
ejpam-7095	352	14	31	31	NUM
ejpam-7095	352	15	)	)	PUNCT
ejpam-7095	352	16	where	where	SCONJ
ejpam-7095	352	17	q	q	X
ejpam-7095	352	18	(	(	PUNCT
ejpam-7095	352	19	q	q	NOUN
ejpam-7095	352	20	)	)	PUNCT
ejpam-7095	352	21	n	n	NOUN
ejpam-7095	352	22	=	=	SYM
ejpam-7095	352	23	qn	qn	PROPN
ejpam-7095	352	24	γ(q	γ(q	PROPN
ejpam-7095	352	25	+	+	CCONJ
ejpam-7095	352	26	1	1	NUM
ejpam-7095	352	27	)	)	PUNCT
ejpam-7095	352	28	(	(	PUNCT
ejpam-7095	352	29	γ(n	γ(n	X
ejpam-7095	352	30	+	+	CCONJ
ejpam-7095	352	31	1	1	X
ejpam-7095	352	32	)	)	PUNCT
ejpam-7095	352	33	γ(n−	γ(n−	PROPN
ejpam-7095	352	34	q	q	PROPN
ejpam-7095	353	1	+	+	NUM
ejpam-7095	353	2	1	1	NUM
ejpam-7095	353	3	)	)	PUNCT
ejpam-7095	353	4	)	)	PUNCT
ejpam-7095	353	5	.	.	PUNCT
ejpam-7095	354	1	application	application	NOUN
ejpam-7095	354	2	to	to	ADP
ejpam-7095	354	3	1d	1d	NUM
ejpam-7095	354	4	case	case	NOUN
ejpam-7095	354	5	:	:	PUNCT
ejpam-7095	354	6	for	for	ADP
ejpam-7095	354	7	1d	1d	NUM
ejpam-7095	354	8	operator	operator	NOUN
ejpam-7095	354	9	£	£	SYM
ejpam-7095	354	10	û	û	NUM
ejpam-7095	354	11	=	=	SYM
ejpam-7095	354	12	∂2û(x̄,t	∂2û(x̄,t	PROPN
ejpam-7095	354	13	)	)	PUNCT
ejpam-7095	354	14	∂x2	∂x2	NOUN
ejpam-7095	354	15	,	,	PUNCT
ejpam-7095	354	16	the	the	DET
ejpam-7095	354	17	error	error	NOUN
ejpam-7095	354	18	bound	bind	VERB
ejpam-7095	354	19	is	be	AUX
ejpam-7095	354	20	expressed	express	VERB
ejpam-7095	354	21	as	as	ADP
ejpam-7095	354	22	:	:	PUNCT
ejpam-7095	354	23	e	e	X
ejpam-7095	354	24	=	=	SYM
ejpam-7095	354	25	∥∥∥∥	∥∥∥∥	PROPN
ejpam-7095	354	26	{	{	PUNCT
ejpam-7095	354	27	(	(	PUNCT
ejpam-7095	354	28	β(α)sα	β(α)sα	ADV
ejpam-7095	354	29	sα(1−	sα(1−	PROPN
ejpam-7095	354	30	α	α	NOUN
ejpam-7095	354	31	)	)	PUNCT
ejpam-7095	355	1	+	+	CCONJ
ejpam-7095	355	2	α	α	NOUN
ejpam-7095	355	3	)	)	PUNCT
ejpam-7095	356	1	i	i	PRON
ejpam-7095	356	2	−	−	VERB
ejpam-7095	357	1	λ1£−	λ1£−	X
ejpam-7095	357	2	λ2i	λ2i	X
ejpam-7095	357	3	}	}	PUNCT
ejpam-7095	357	4	û−	û−	PROPN
ejpam-7095	357	5	{	{	PUNCT
ejpam-7095	357	6	(	(	PUNCT
ejpam-7095	357	7	β(α)sα	β(α)sα	ADV
ejpam-7095	357	8	sα(1−	sα(1−	PROPN
ejpam-7095	357	9	α	α	NOUN
ejpam-7095	357	10	)	)	PUNCT
ejpam-7095	357	11	+	+	CCONJ
ejpam-7095	357	12	α	α	NOUN
ejpam-7095	357	13	)	)	PUNCT
ejpam-7095	358	1	i	i	PRON
ejpam-7095	358	2	−	−	VERB
ejpam-7095	359	1	λ1£−	λ1£−	X
ejpam-7095	359	2	λ2i	λ2i	X
ejpam-7095	359	3	}	}	PUNCT
ejpam-7095	359	4	inû	inû	PROPN
ejpam-7095	359	5	∥∥∥∥	∥∥∥∥	NUM
ejpam-7095	359	6	∞	∞	NUM
ejpam-7095	359	7	=	=	SYM
ejpam-7095	359	8	∥∥∥∥	∥∥∥∥	PROPN
ejpam-7095	359	9	(	(	PUNCT
ejpam-7095	359	10	β(α)sα	β(α)sα	ADV
ejpam-7095	359	11	sα(1−	sα(1−	PROPN
ejpam-7095	359	12	α	α	NOUN
ejpam-7095	359	13	)	)	PUNCT
ejpam-7095	360	1	+	+	CCONJ
ejpam-7095	360	2	α	α	NOUN
ejpam-7095	360	3	)	)	PUNCT
ejpam-7095	360	4	(	(	PUNCT
ejpam-7095	360	5	û−	û−	PROPN
ejpam-7095	360	6	inû)−	inû)−	PROPN
ejpam-7095	360	7	λ1£(û−	λ1£(û−	PRON
ejpam-7095	360	8	inû)−	inû)−	PROPN
ejpam-7095	360	9	λ2(û−	λ2(û−	PROPN
ejpam-7095	360	10	inû	inû	PROPN
ejpam-7095	360	11	)	)	PUNCT
ejpam-7095	360	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-7095	361	1	∞	∞	PROPN
ejpam-7095	361	2	≤	≤	NOUN
ejpam-7095	361	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7095	361	4	(	(	PUNCT
ejpam-7095	361	5	β(α)sα	β(α)sα	ADV
ejpam-7095	361	6	sα(1−	sα(1−	PROPN
ejpam-7095	361	7	α	α	NOUN
ejpam-7095	361	8	)	)	PUNCT
ejpam-7095	361	9	+	+	CCONJ
ejpam-7095	361	10	α	α	NOUN
ejpam-7095	361	11	)	)	PUNCT
ejpam-7095	361	12	∣∣∣∣∥û−	∣∣∣∣∥û−	ADJ
ejpam-7095	361	13	inû∥∞	inû∥∞	NOUN
ejpam-7095	361	14	+	+	CCONJ
ejpam-7095	361	15	|λ1|∥£(û−	|λ1|∥£(û−	X
ejpam-7095	361	16	inû)∥∞	inû)∥∞	PROPN
ejpam-7095	361	17	+	+	CCONJ
ejpam-7095	361	18	|λ2|∥û−	|λ2|∥û−	ADJ
ejpam-7095	361	19	inû∥∞	inû∥∞	NOUN
ejpam-7095	361	20	,	,	PUNCT
ejpam-7095	361	21	since	since	SCONJ
ejpam-7095	361	22	sα	sα	ADV
ejpam-7095	361	23	,	,	PUNCT
ejpam-7095	361	24	and	and	CCONJ
ejpam-7095	361	25	β(α	β(α	PROPN
ejpam-7095	361	26	)	)	PUNCT
ejpam-7095	361	27	are	be	AUX
ejpam-7095	361	28	constants	constant	NOUN
ejpam-7095	361	29	,	,	PUNCT
ejpam-7095	361	30	so	so	SCONJ
ejpam-7095	361	31	we	we	PRON
ejpam-7095	361	32	have	have	VERB
ejpam-7095	361	33	e	e	NOUN
ejpam-7095	361	34	≤	≤	X
ejpam-7095	361	35	(	(	PUNCT
ejpam-7095	361	36	(	(	PUNCT
ejpam-7095	361	37	β(α)sα	β(α)sα	ADV
ejpam-7095	361	38	sα(1−	sα(1−	PROPN
ejpam-7095	361	39	α	α	NOUN
ejpam-7095	361	40	)	)	PUNCT
ejpam-7095	362	1	+	+	CCONJ
ejpam-7095	362	2	α	α	NOUN
ejpam-7095	362	3	)	)	PUNCT
ejpam-7095	363	1	+	+	CCONJ
ejpam-7095	363	2	λ2	λ2	NOUN
ejpam-7095	363	3	)	)	PUNCT
ejpam-7095	363	4	2−n	2−n	NUM
ejpam-7095	364	1	γ(n	γ(n	X
ejpam-7095	365	1	+	+	CCONJ
ejpam-7095	365	2	2	2	X
ejpam-7095	365	3	)	)	PUNCT
ejpam-7095	365	4	∥ûn+1∥∞	∥ûn+1∥∞	PUNCT
ejpam-7095	366	1	+	+	CCONJ
ejpam-7095	366	2	|λ1|	|λ1|	NOUN
ejpam-7095	366	3	2(q	2(q	NUM
ejpam-7095	366	4	(	(	PUNCT
ejpam-7095	366	5	2	2	NUM
ejpam-7095	366	6	)	)	PUNCT
ejpam-7095	366	7	n	n	NOUN
ejpam-7095	366	8	+	+	CCONJ
ejpam-7095	366	9	1	1	NUM
ejpam-7095	366	10	)	)	PUNCT
ejpam-7095	366	11	γ(n	γ(n	X
ejpam-7095	366	12	)	)	PUNCT
ejpam-7095	366	13	(	(	PUNCT
ejpam-7095	366	14	1	1	NUM
ejpam-7095	366	15	2	2	NUM
ejpam-7095	366	16	)	)	PUNCT
ejpam-7095	366	17	(	(	PUNCT
ejpam-7095	366	18	n−1	n−1	PROPN
ejpam-7095	366	19	)	)	PUNCT
ejpam-7095	366	20	∥û(n+1)∥∞.	∥û(n+1)∥∞.	NOUN
ejpam-7095	366	21	hence	hence	ADV
ejpam-7095	366	22	,	,	PUNCT
ejpam-7095	366	23	we	we	PRON
ejpam-7095	366	24	obtain	obtain	VERB
ejpam-7095	366	25	e	e	NOUN
ejpam-7095	366	26	≤	≤	PROPN
ejpam-7095	366	27	k∥û(n+1)∥∞	k∥û(n+1)∥∞	PROPN
ejpam-7095	366	28	,	,	PUNCT
ejpam-7095	366	29	where	where	SCONJ
ejpam-7095	366	30	k	k	PROPN
ejpam-7095	366	31	is	be	AUX
ejpam-7095	366	32	a	a	DET
ejpam-7095	366	33	constant	constant	ADJ
ejpam-7095	366	34	combining	combine	VERB
ejpam-7095	366	35	all	all	DET
ejpam-7095	366	36	coefficients	coefficient	NOUN
ejpam-7095	366	37	of	of	ADP
ejpam-7095	366	38	∥û(n+1)∥∞.	∥û(n+1)∥∞.	PROPN
ejpam-7095	366	39	for	for	ADP
ejpam-7095	366	40	higher	high	ADJ
ejpam-7095	366	41	dimensions	dimension	NOUN
ejpam-7095	366	42	see	see	VERB
ejpam-7095	366	43	[	[	X
ejpam-7095	366	44	40	40	NUM
ejpam-7095	366	45	]	]	PUNCT
ejpam-7095	366	46	.	.	PUNCT
ejpam-7095	367	1	step	step	NOUN
ejpam-7095	367	2	3	3	NUM
ejpam-7095	367	3	:	:	PUNCT
ejpam-7095	367	4	the	the	DET
ejpam-7095	367	5	final	final	ADJ
ejpam-7095	367	6	step	step	NOUN
ejpam-7095	367	7	is	be	AUX
ejpam-7095	367	8	the	the	DET
ejpam-7095	367	9	numerical	numerical	ADJ
ejpam-7095	367	10	approximation	approximation	NOUN
ejpam-7095	367	11	of	of	ADP
ejpam-7095	367	12	the	the	DET
ejpam-7095	367	13	integral	integral	ADJ
ejpam-7095	367	14	in	in	ADP
ejpam-7095	367	15	eq.(24	eq.(24	NOUN
ejpam-7095	367	16	)	)	PUNCT
ejpam-7095	367	17	via	via	ADP
ejpam-7095	367	18	talbot	talbot	PROPN
ejpam-7095	367	19	’s	’s	PART
ejpam-7095	367	20	method	method	NOUN
ejpam-7095	367	21	,	,	PUNCT
ejpam-7095	367	22	implemented	implement	VERB
ejpam-7095	367	23	with	with	ADP
ejpam-7095	367	24	the	the	DET
ejpam-7095	367	25	midpoint	midpoint	NOUN
ejpam-7095	367	26	rule	rule	NOUN
ejpam-7095	367	27	,	,	PUNCT
ejpam-7095	367	28	whose	whose	DET
ejpam-7095	367	29	convergence	convergence	NOUN
ejpam-7095	367	30	rate	rate	NOUN
ejpam-7095	367	31	depends	depend	VERB
ejpam-7095	367	32	on	on	ADP
ejpam-7095	367	33	the	the	DET
ejpam-7095	367	34	following	follow	VERB
ejpam-7095	367	35	factors	factor	NOUN
ejpam-7095	367	36	:	:	PUNCT
ejpam-7095	367	37	•	•	ADP
ejpam-7095	367	38	the	the	DET
ejpam-7095	367	39	contour	contour	NOUN
ejpam-7095	367	40	selection	selection	NOUN
ejpam-7095	367	41	,	,	PUNCT
ejpam-7095	367	42	•	•	ADP
ejpam-7095	367	43	the	the	DET
ejpam-7095	367	44	step	step	NOUN
ejpam-7095	367	45	size	size	NOUN
ejpam-7095	367	46	.	.	PUNCT
ejpam-7095	368	1	parameters	parameter	NOUN
ejpam-7095	368	2	for	for	ADP
ejpam-7095	368	3	optimal	optimal	ADJ
ejpam-7095	368	4	accuracy	accuracy	NOUN
ejpam-7095	368	5	as	as	SCONJ
ejpam-7095	368	6	determined	determined	ADJ
ejpam-7095	368	7	in	in	ADP
ejpam-7095	368	8	[	[	X
ejpam-7095	368	9	29	29	NUM
ejpam-7095	368	10	]	]	PUNCT
ejpam-7095	368	11	are	be	AUX
ejpam-7095	368	12	:	:	PUNCT
ejpam-7095	368	13	θ1	θ1	NOUN
ejpam-7095	368	14	=	=	SYM
ejpam-7095	368	15	0.61220	0.61220	NUM
ejpam-7095	368	16	,	,	PUNCT
ejpam-7095	368	17	θ2	θ2	PROPN
ejpam-7095	368	18	=	=	SYM
ejpam-7095	368	19	0.50170	0.50170	NUM
ejpam-7095	368	20	,	,	PUNCT
ejpam-7095	368	21	θ3	θ3	NOUN
ejpam-7095	368	22	=	=	PROPN
ejpam-7095	368	23	0.640700	0.640700	NUM
ejpam-7095	368	24	,	,	PUNCT
ejpam-7095	368	25	and	and	CCONJ
ejpam-7095	368	26	θ4	θ4	NOUN
ejpam-7095	368	27	=	=	SYM
ejpam-7095	368	28	0.26450s	0.26450	NOUN
ejpam-7095	368	29	,	,	PUNCT
ejpam-7095	368	30	and	and	CCONJ
ejpam-7095	368	31	corresponding	correspond	VERB
ejpam-7095	368	32	error	error	NOUN
ejpam-7095	368	33	estimate	estimate	NOUN
ejpam-7095	368	34	:	:	PUNCT
ejpam-7095	368	35	eest	e	ADJ
ejpam-7095	368	36	=	=	SYM
ejpam-7095	368	37	|uapp(x̄	|uapp(x̄	PROPN
ejpam-7095	368	38	,	,	PUNCT
ejpam-7095	368	39	τ)−	τ)−	PROPN
ejpam-7095	368	40	u(x̄	u(x̄	NUM
ejpam-7095	368	41	,	,	PUNCT
ejpam-7095	368	42	τ)|	τ)|	PROPN
ejpam-7095	368	43	=	=	PUNCT
ejpam-7095	368	44	o(exp((−1.35800)mt	o(exp((−1.35800)mt	ADJ
ejpam-7095	368	45	)	)	PUNCT
ejpam-7095	368	46	)	)	PUNCT
ejpam-7095	368	47	.	.	PUNCT
ejpam-7095	369	1	kamran	kamran	PROPN
ejpam-7095	369	2	et	et	PROPN
ejpam-7095	369	3	al	al	PROPN
ejpam-7095	369	4	.	.	PUNCT
ejpam-7095	369	5	/	/	SYM
ejpam-7095	369	6	eur	eur	PROPN
ejpam-7095	369	7	.	.	PUNCT
ejpam-7095	370	1	j.	j.	PROPN
ejpam-7095	370	2	pure	pure	PROPN
ejpam-7095	370	3	appl	appl	PROPN
ejpam-7095	370	4	.	.	PROPN
ejpam-7095	370	5	math	math	PROPN
ejpam-7095	370	6	,	,	PUNCT
ejpam-7095	370	7	18	18	NUM
ejpam-7095	370	8	(	(	PUNCT
ejpam-7095	370	9	4	4	NUM
ejpam-7095	370	10	)	)	PUNCT
ejpam-7095	370	11	(	(	PUNCT
ejpam-7095	370	12	2025	2025	NUM
ejpam-7095	370	13	)	)	PUNCT
ejpam-7095	370	14	,	,	PUNCT
ejpam-7095	370	15	7095	7095	NUM
ejpam-7095	370	16	18	18	NUM
ejpam-7095	370	17	of	of	ADP
ejpam-7095	370	18	30	30	NUM
ejpam-7095	370	19	6	6	NUM
ejpam-7095	370	20	.	.	PUNCT
ejpam-7095	371	1	numerical	numerical	ADJ
ejpam-7095	371	2	experiments	experiment	NOUN
ejpam-7095	371	3	the	the	DET
ejpam-7095	371	4	performance	performance	NOUN
ejpam-7095	371	5	of	of	ADP
ejpam-7095	371	6	the	the	DET
ejpam-7095	371	7	proposed	propose	VERB
ejpam-7095	371	8	method	method	NOUN
ejpam-7095	371	9	is	be	AUX
ejpam-7095	371	10	evaluated	evaluate	VERB
ejpam-7095	371	11	using	use	VERB
ejpam-7095	371	12	three	three	NUM
ejpam-7095	371	13	numerical	numerical	ADJ
ejpam-7095	371	14	examples	example	NOUN
ejpam-7095	371	15	.	.	PUNCT
ejpam-7095	372	1	accuracy	accuracy	NOUN
ejpam-7095	372	2	is	be	AUX
ejpam-7095	372	3	measured	measure	VERB
ejpam-7095	372	4	with	with	ADP
ejpam-7095	372	5	two	two	NUM
ejpam-7095	372	6	error	error	NOUN
ejpam-7095	372	7	metrics	metric	NOUN
ejpam-7095	372	8	:	:	PUNCT
ejpam-7095	372	9	the	the	DET
ejpam-7095	372	10	absolute	absolute	ADJ
ejpam-7095	372	11	error	error	NOUN
ejpam-7095	372	12	(	(	PUNCT
ejpam-7095	372	13	labs	lab	NOUN
ejpam-7095	372	14	)	)	PUNCT
ejpam-7095	372	15	and	and	CCONJ
ejpam-7095	372	16	the	the	DET
ejpam-7095	372	17	maximum	maximum	ADJ
ejpam-7095	372	18	absolute	absolute	ADJ
ejpam-7095	372	19	error	error	NOUN
ejpam-7095	372	20	(	(	PUNCT
ejpam-7095	372	21	l∞	l∞	NOUN
ejpam-7095	372	22	)	)	PUNCT
ejpam-7095	372	23	,	,	PUNCT
ejpam-7095	372	24	defined	define	VERB
ejpam-7095	372	25	as	as	ADP
ejpam-7095	372	26	:	:	PUNCT
ejpam-7095	372	27	labs	labs	PROPN
ejpam-7095	372	28	=	=	SYM
ejpam-7095	372	29	∣∣∣∣u(x̄k	∣∣∣∣u(x̄k	PROPN
ejpam-7095	372	30	,	,	PUNCT
ejpam-7095	372	31	τ)−	τ)−	PROPN
ejpam-7095	372	32	uapp(x̄k	uapp(x̄k	PROPN
ejpam-7095	372	33	,	,	PUNCT
ejpam-7095	372	34	τ	τ	NOUN
ejpam-7095	372	35	)	)	PUNCT
ejpam-7095	372	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7095	372	37	,	,	PUNCT
ejpam-7095	372	38	l∞	l∞	NOUN
ejpam-7095	372	39	=	=	SYM
ejpam-7095	372	40	max	max	PROPN
ejpam-7095	372	41	1≤k≤n	1≤k≤n	PROPN
ejpam-7095	372	42	∣∣∣∣u(x̄k	∣∣∣∣u(x̄k	PROPN
ejpam-7095	372	43	,	,	PUNCT
ejpam-7095	372	44	τ)−	τ)−	PROPN
ejpam-7095	372	45	uapp(x̄k	uapp(x̄k	PROPN
ejpam-7095	372	46	,	,	PUNCT
ejpam-7095	372	47	τ	τ	NOUN
ejpam-7095	372	48	)	)	PUNCT
ejpam-7095	372	49	∣∣∣∣	∣∣∣∣	PROPN
ejpam-7095	372	50	,	,	PUNCT
ejpam-7095	372	51	where	where	SCONJ
ejpam-7095	372	52	u(x̄	u(x̄	NUM
ejpam-7095	372	53	,	,	PUNCT
ejpam-7095	372	54	τ	τ	X
ejpam-7095	372	55	)	)	PUNCT
ejpam-7095	372	56	and	and	CCONJ
ejpam-7095	372	57	uapp(x̄	uapp(x̄	PROPN
ejpam-7095	372	58	,	,	PUNCT
ejpam-7095	372	59	τ	τ	X
ejpam-7095	372	60	)	)	PUNCT
ejpam-7095	372	61	denote	denote	VERB
ejpam-7095	372	62	the	the	DET
ejpam-7095	372	63	exact	exact	ADJ
ejpam-7095	372	64	and	and	CCONJ
ejpam-7095	372	65	approximate	approximate	ADJ
ejpam-7095	372	66	solutions	solution	NOUN
ejpam-7095	372	67	,	,	PUNCT
ejpam-7095	372	68	respectively	respectively	ADV
ejpam-7095	372	69	.	.	PUNCT
ejpam-7095	373	1	here	here	ADV
ejpam-7095	373	2	,	,	PUNCT
ejpam-7095	373	3	n	n	PROPN
ejpam-7095	373	4	and	and	CCONJ
ejpam-7095	373	5	mq	mq	PROPN
ejpam-7095	373	6	denote	denote	VERB
ejpam-7095	373	7	the	the	DET
ejpam-7095	373	8	number	number	NOUN
ejpam-7095	373	9	of	of	ADP
ejpam-7095	373	10	chebyshev	chebyshev	NOUN
ejpam-7095	373	11	nodes	node	NOUN
ejpam-7095	373	12	and	and	CCONJ
ejpam-7095	373	13	quadrature	quadrature	NOUN
ejpam-7095	373	14	nodes	node	NOUN
ejpam-7095	373	15	,	,	PUNCT
ejpam-7095	373	16	respectively	respectively	ADV
ejpam-7095	373	17	.	.	PUNCT
ejpam-7095	374	1	all	all	DET
ejpam-7095	374	2	simulations	simulation	NOUN
ejpam-7095	374	3	employ	employ	VERB
ejpam-7095	374	4	fixed	fix	VERB
ejpam-7095	374	5	parameters	parameter	NOUN
ejpam-7095	375	1	λ1	λ1	ADJ
ejpam-7095	375	2	=	=	SYM
ejpam-7095	375	3	1	1	NUM
ejpam-7095	375	4	and	and	CCONJ
ejpam-7095	375	5	λ2	λ2	NOUN
ejpam-7095	375	6	=	=	SYM
ejpam-7095	375	7	0	0	NUM
ejpam-7095	375	8	.	.	PUNCT
ejpam-7095	376	1	for	for	ADP
ejpam-7095	376	2	each	each	DET
ejpam-7095	376	3	example	example	NOUN
ejpam-7095	376	4	,	,	PUNCT
ejpam-7095	376	5	the	the	DET
ejpam-7095	376	6	source	source	NOUN
ejpam-7095	376	7	term	term	NOUN
ejpam-7095	376	8	,	,	PUNCT
ejpam-7095	376	9	initial	initial	ADJ
ejpam-7095	376	10	conditions	condition	NOUN
ejpam-7095	376	11	,	,	PUNCT
ejpam-7095	376	12	and	and	CCONJ
ejpam-7095	376	13	boundary	boundary	ADJ
ejpam-7095	376	14	conditions	condition	NOUN
ejpam-7095	376	15	are	be	AUX
ejpam-7095	376	16	derived	derive	VERB
ejpam-7095	376	17	from	from	ADP
ejpam-7095	376	18	the	the	DET
ejpam-7095	376	19	exact	exact	ADJ
ejpam-7095	376	20	solution	solution	NOUN
ejpam-7095	376	21	.	.	PUNCT
ejpam-7095	377	1	example	example	NOUN
ejpam-7095	377	2	1	1	NUM
ejpam-7095	377	3	in	in	ADP
ejpam-7095	377	4	the	the	DET
ejpam-7095	377	5	first	first	ADJ
ejpam-7095	377	6	example	example	NOUN
ejpam-7095	377	7	,	,	PUNCT
ejpam-7095	377	8	we	we	PRON
ejpam-7095	377	9	consider	consider	VERB
ejpam-7095	377	10	the	the	DET
ejpam-7095	377	11	1d	1d	NUM
ejpam-7095	377	12	version	version	NOUN
ejpam-7095	377	13	of	of	ADP
ejpam-7095	377	14	(	(	PUNCT
ejpam-7095	377	15	1)–(3	1)–(3	NUM
ejpam-7095	377	16	)	)	PUNCT
ejpam-7095	377	17	with	with	ADP
ejpam-7095	377	18	λ1	λ1	PROPN
ejpam-7095	377	19	=	=	SYM
ejpam-7095	377	20	1	1	NUM
ejpam-7095	377	21	,	,	PUNCT
ejpam-7095	377	22	λ2	λ2	NOUN
ejpam-7095	377	23	=	=	SYM
ejpam-7095	377	24	0	0	NUM
ejpam-7095	377	25	,	,	PUNCT
ejpam-7095	377	26	and	and	CCONJ
ejpam-7095	377	27	exact	exact	ADJ
ejpam-7095	377	28	solution	solution	NOUN
ejpam-7095	377	29	u(x	u(x	NOUN
ejpam-7095	377	30	,	,	PUNCT
ejpam-7095	377	31	τ	τ	X
ejpam-7095	377	32	)	)	PUNCT
ejpam-7095	377	33	=	=	SYM
ejpam-7095	377	34	sin(πx)τ2	sin(πx)τ2	PROPN
ejpam-7095	377	35	.	.	PUNCT
ejpam-7095	378	1	the	the	DET
ejpam-7095	378	2	performance	performance	NOUN
ejpam-7095	378	3	of	of	ADP
ejpam-7095	378	4	the	the	DET
ejpam-7095	378	5	proposed	propose	VERB
ejpam-7095	378	6	numerical	numerical	ADJ
ejpam-7095	378	7	method	method	NOUN
ejpam-7095	378	8	is	be	AUX
ejpam-7095	378	9	evaluated	evaluate	VERB
ejpam-7095	378	10	through	through	ADP
ejpam-7095	378	11	comprehensive	comprehensive	ADJ
ejpam-7095	378	12	error	error	NOUN
ejpam-7095	378	13	analysis	analysis	NOUN
ejpam-7095	378	14	and	and	CCONJ
ejpam-7095	378	15	computational	computational	ADJ
ejpam-7095	378	16	benchmarks	benchmark	NOUN
ejpam-7095	378	17	.	.	PUNCT
ejpam-7095	379	1	table	table	NOUN
ejpam-7095	379	2	1	1	NUM
ejpam-7095	379	3	shows	show	VERB
ejpam-7095	379	4	the	the	DET
ejpam-7095	379	5	l∞	l∞	NOUN
ejpam-7095	379	6	error	error	NOUN
ejpam-7095	379	7	norms	norm	NOUN
ejpam-7095	379	8	for	for	ADP
ejpam-7095	379	9	varying	vary	VERB
ejpam-7095	379	10	chebyshev	chebyshev	NOUN
ejpam-7095	379	11	nodes	node	NOUN
ejpam-7095	379	12	n	n	PRON
ejpam-7095	379	13	and	and	CCONJ
ejpam-7095	379	14	quadrature	quadrature	NOUN
ejpam-7095	379	15	points	point	NOUN
ejpam-7095	379	16	(	(	PUNCT
ejpam-7095	379	17	mq	mq	NOUN
ejpam-7095	379	18	)	)	PUNCT
ejpam-7095	379	19	,	,	PUNCT
ejpam-7095	379	20	demonstrating	demonstrate	VERB
ejpam-7095	379	21	both	both	DET
ejpam-7095	379	22	computational	computational	ADJ
ejpam-7095	379	23	efficiency	efficiency	NOUN
ejpam-7095	379	24	and	and	CCONJ
ejpam-7095	379	25	high	high	ADJ
ejpam-7095	379	26	accuracy	accuracy	NOUN
ejpam-7095	379	27	.	.	PUNCT
ejpam-7095	380	1	the	the	DET
ejpam-7095	380	2	solution	solution	NOUN
ejpam-7095	380	3	accuracy	accuracy	NOUN
ejpam-7095	380	4	is	be	AUX
ejpam-7095	380	5	verified	verify	VERB
ejpam-7095	380	6	in	in	ADP
ejpam-7095	380	7	figure	figure	NOUN
ejpam-7095	380	8	1a	1a	NOUN
ejpam-7095	380	9	,	,	PUNCT
ejpam-7095	380	10	where	where	SCONJ
ejpam-7095	380	11	the	the	DET
ejpam-7095	380	12	upper	upper	ADJ
ejpam-7095	380	13	panel	panel	NOUN
ejpam-7095	380	14	shows	show	VERB
ejpam-7095	380	15	excellent	excellent	ADJ
ejpam-7095	380	16	agreement	agreement	NOUN
ejpam-7095	380	17	between	between	ADP
ejpam-7095	380	18	exact	exact	ADJ
ejpam-7095	380	19	and	and	CCONJ
ejpam-7095	380	20	approximate	approximate	ADJ
ejpam-7095	380	21	solutions	solution	NOUN
ejpam-7095	380	22	,	,	PUNCT
ejpam-7095	380	23	while	while	SCONJ
ejpam-7095	380	24	the	the	DET
ejpam-7095	380	25	lower	low	ADJ
ejpam-7095	380	26	panel	panel	NOUN
ejpam-7095	380	27	depicts	depict	VERB
ejpam-7095	380	28	the	the	DET
ejpam-7095	380	29	corresponding	correspond	VERB
ejpam-7095	380	30	pointwise	pointwise	ADJ
ejpam-7095	380	31	absolute	absolute	ADJ
ejpam-7095	380	32	error	error	NOUN
ejpam-7095	380	33	distribution	distribution	NOUN
ejpam-7095	380	34	,	,	PUNCT
ejpam-7095	380	35	confirming	confirm	VERB
ejpam-7095	380	36	the	the	DET
ejpam-7095	380	37	method	method	NOUN
ejpam-7095	380	38	’s	’s	PART
ejpam-7095	380	39	high	high	ADJ
ejpam-7095	380	40	accuracy	accuracy	NOUN
ejpam-7095	380	41	.	.	PUNCT
ejpam-7095	381	1	further	far	ADV
ejpam-7095	381	2	,	,	PUNCT
ejpam-7095	381	3	figure	figure	VERB
ejpam-7095	381	4	1b	1b	NUM
ejpam-7095	381	5	further	further	ADJ
ejpam-7095	381	6	examines	examine	VERB
ejpam-7095	381	7	solution	solution	NOUN
ejpam-7095	381	8	accuracy	accuracy	NOUN
ejpam-7095	381	9	for	for	ADP
ejpam-7095	381	10	different	different	ADJ
ejpam-7095	381	11	values	value	NOUN
ejpam-7095	381	12	of	of	ADP
ejpam-7095	381	13	α	α	NOUN
ejpam-7095	381	14	,	,	PUNCT
ejpam-7095	381	15	showing	show	VERB
ejpam-7095	381	16	consistent	consistent	ADJ
ejpam-7095	381	17	and	and	CCONJ
ejpam-7095	381	18	stable	stable	ADJ
ejpam-7095	381	19	numerical	numerical	ADJ
ejpam-7095	381	20	behavior	behavior	NOUN
ejpam-7095	381	21	.	.	PUNCT
ejpam-7095	382	1	two	two	NUM
ejpam-7095	382	2	major	major	ADJ
ejpam-7095	382	3	features	feature	NOUN
ejpam-7095	382	4	are	be	AUX
ejpam-7095	382	5	shown	show	VERB
ejpam-7095	382	6	by	by	ADP
ejpam-7095	382	7	convergence	convergence	NOUN
ejpam-7095	382	8	analysis	analysis	NOUN
ejpam-7095	382	9	:	:	PUNCT
ejpam-7095	382	10	up	up	ADP
ejpam-7095	382	11	to	to	ADP
ejpam-7095	382	12	mq	mq	NOUN
ejpam-7095	382	13	=	=	SYM
ejpam-7095	382	14	36	36	NUM
ejpam-7095	382	15	,	,	PUNCT
ejpam-7095	382	16	figure	figure	NOUN
ejpam-7095	382	17	2a	2a	NUM
ejpam-7095	382	18	demonstrates	demonstrate	VERB
ejpam-7095	382	19	ideal	ideal	ADJ
ejpam-7095	382	20	quadrature	quadrature	NOUN
ejpam-7095	382	21	convergence	convergence	NOUN
ejpam-7095	382	22	,	,	PUNCT
ejpam-7095	382	23	after	after	ADP
ejpam-7095	382	24	that	that	PRON
ejpam-7095	382	25	,	,	PUNCT
ejpam-7095	382	26	there	there	PRON
ejpam-7095	382	27	is	be	VERB
ejpam-7095	382	28	a	a	DET
ejpam-7095	382	29	slight	slight	ADJ
ejpam-7095	382	30	increase	increase	NOUN
ejpam-7095	382	31	in	in	ADP
ejpam-7095	382	32	the	the	DET
ejpam-7095	382	33	error	error	NOUN
ejpam-7095	382	34	,	,	PUNCT
ejpam-7095	382	35	most	most	ADV
ejpam-7095	382	36	likely	likely	ADJ
ejpam-7095	382	37	as	as	ADP
ejpam-7095	382	38	a	a	DET
ejpam-7095	382	39	result	result	NOUN
ejpam-7095	382	40	of	of	ADP
ejpam-7095	382	41	numerical	numerical	ADJ
ejpam-7095	382	42	conditioning	conditioning	NOUN
ejpam-7095	382	43	effects	effect	NOUN
ejpam-7095	382	44	.	.	PUNCT
ejpam-7095	383	1	similarly	similarly	ADV
ejpam-7095	383	2	,	,	PUNCT
ejpam-7095	383	3	spectral	spectral	ADJ
ejpam-7095	383	4	convergence	convergence	NOUN
ejpam-7095	383	5	with	with	ADP
ejpam-7095	383	6	respect	respect	NOUN
ejpam-7095	383	7	to	to	ADP
ejpam-7095	383	8	spatial	spatial	ADJ
ejpam-7095	383	9	discretization	discretization	NOUN
ejpam-7095	383	10	is	be	AUX
ejpam-7095	383	11	shown	show	VERB
ejpam-7095	383	12	in	in	ADP
ejpam-7095	383	13	figure	figure	NOUN
ejpam-7095	383	14	2b	2b	NOUN
ejpam-7095	383	15	,	,	PUNCT
ejpam-7095	383	16	with	with	ADP
ejpam-7095	383	17	slight	slight	ADJ
ejpam-7095	383	18	error	error	NOUN
ejpam-7095	383	19	variation	variation	NOUN
ejpam-7095	383	20	at	at	ADP
ejpam-7095	383	21	higher	high	ADJ
ejpam-7095	383	22	n	n	PRON
ejpam-7095	383	23	values	value	NOUN
ejpam-7095	383	24	caused	cause	VERB
ejpam-7095	383	25	by	by	ADP
ejpam-7095	383	26	the	the	DET
ejpam-7095	383	27	round	round	NOUN
ejpam-7095	383	28	-	-	PUNCT
ejpam-7095	383	29	off	off	ADP
ejpam-7095	383	30	errors	error	NOUN
ejpam-7095	383	31	in	in	ADP
ejpam-7095	383	32	the	the	DET
ejpam-7095	383	33	chebyshev	chebyshev	NOUN
ejpam-7095	383	34	differentiation	differentiation	NOUN
ejpam-7095	383	35	matrices	matrix	NOUN
ejpam-7095	383	36	.	.	PUNCT
ejpam-7095	384	1	figures	figure	NOUN
ejpam-7095	384	2	3a	3a	NUM
ejpam-7095	384	3	and	and	CCONJ
ejpam-7095	384	4	3b	3b	NUM
ejpam-7095	384	5	quantify	quantify	VERB
ejpam-7095	384	6	parametric	parametric	ADJ
ejpam-7095	384	7	sensitivity	sensitivity	NOUN
ejpam-7095	384	8	by	by	ADP
ejpam-7095	384	9	plotting	plot	VERB
ejpam-7095	384	10	the	the	DET
ejpam-7095	384	11	l∞	l∞	NOUN
ejpam-7095	384	12	error	error	NOUN
ejpam-7095	384	13	dependence	dependence	NOUN
ejpam-7095	384	14	on	on	ADP
ejpam-7095	384	15	t	t	PROPN
ejpam-7095	384	16	and	and	CCONJ
ejpam-7095	384	17	α	α	PRON
ejpam-7095	384	18	,	,	PUNCT
ejpam-7095	384	19	respectively	respectively	ADV
ejpam-7095	384	20	,	,	PUNCT
ejpam-7095	384	21	both	both	PRON
ejpam-7095	384	22	showing	show	VERB
ejpam-7095	384	23	accurate	accurate	ADJ
ejpam-7095	384	24	results	result	NOUN
ejpam-7095	384	25	.	.	PUNCT
ejpam-7095	385	1	the	the	DET
ejpam-7095	385	2	surface	surface	NOUN
ejpam-7095	385	3	and	and	CCONJ
ejpam-7095	385	4	contour	contour	NOUN
ejpam-7095	385	5	plots	plot	NOUN
ejpam-7095	385	6	(	(	PUNCT
ejpam-7095	385	7	figures	figure	NOUN
ejpam-7095	385	8	4a	4a	NOUN
ejpam-7095	385	9	and	and	CCONJ
ejpam-7095	385	10	4b	4b	NUM
ejpam-7095	385	11	)	)	PUNCT
ejpam-7095	385	12	in	in	ADP
ejpam-7095	385	13	the	the	DET
ejpam-7095	385	14	α−τ	α−τ	PROPN
ejpam-7095	385	15	plane	plane	NOUN
ejpam-7095	385	16	show	show	VERB
ejpam-7095	385	17	the	the	DET
ejpam-7095	385	18	whole	whole	ADJ
ejpam-7095	385	19	error	error	NOUN
ejpam-7095	385	20	nature	nature	NOUN
ejpam-7095	385	21	and	and	CCONJ
ejpam-7095	385	22	provide	provide	VERB
ejpam-7095	385	23	a	a	DET
ejpam-7095	385	24	thorough	thorough	ADJ
ejpam-7095	385	25	proof	proof	NOUN
ejpam-7095	385	26	of	of	ADP
ejpam-7095	385	27	the	the	DET
ejpam-7095	385	28	method	method	NOUN
ejpam-7095	385	29	’s	’s	PART
ejpam-7095	385	30	stability	stability	NOUN
ejpam-7095	385	31	over	over	ADP
ejpam-7095	385	32	the	the	DET
ejpam-7095	385	33	whole	whole	ADJ
ejpam-7095	385	34	domain	domain	NOUN
ejpam-7095	385	35	.	.	PUNCT
ejpam-7095	386	1	overall	overall	ADV
ejpam-7095	386	2	,	,	PUNCT
ejpam-7095	386	3	these	these	DET
ejpam-7095	386	4	findings	finding	NOUN
ejpam-7095	386	5	demonstrate	demonstrate	VERB
ejpam-7095	386	6	that	that	SCONJ
ejpam-7095	386	7	the	the	DET
ejpam-7095	386	8	proposed	propose	VERB
ejpam-7095	386	9	scheme	scheme	NOUN
ejpam-7095	386	10	achieves	achieve	VERB
ejpam-7095	386	11	the	the	DET
ejpam-7095	386	12	following	following	NOUN
ejpam-7095	386	13	:	:	PUNCT
ejpam-7095	386	14	(	(	PUNCT
ejpam-7095	386	15	i	i	NOUN
ejpam-7095	386	16	)	)	PUNCT
ejpam-7095	386	17	uniform	uniform	ADJ
ejpam-7095	386	18	stability	stability	NOUN
ejpam-7095	386	19	for	for	ADP
ejpam-7095	386	20	various	various	ADJ
ejpam-7095	386	21	values	value	NOUN
ejpam-7095	386	22	of	of	ADP
ejpam-7095	386	23	α	α	NOUN
ejpam-7095	386	24	;	;	PUNCT
ejpam-7095	386	25	(	(	PUNCT
ejpam-7095	386	26	ii	ii	NOUN
ejpam-7095	386	27	)	)	PUNCT
ejpam-7095	386	28	exponential	exponential	ADJ
ejpam-7095	386	29	convergence	convergence	NOUN
ejpam-7095	386	30	in	in	ADP
ejpam-7095	386	31	quadrature	quadrature	NOUN
ejpam-7095	386	32	approximation	approximation	NOUN
ejpam-7095	386	33	;	;	PUNCT
ejpam-7095	386	34	and	and	CCONJ
ejpam-7095	386	35	(	(	PUNCT
ejpam-7095	386	36	iii	iii	X
ejpam-7095	386	37	)	)	PUNCT
ejpam-7095	386	38	spectral	spectral	ADJ
ejpam-7095	386	39	accuracy	accuracy	NOUN
ejpam-7095	386	40	in	in	ADP
ejpam-7095	386	41	spatial	spatial	ADJ
ejpam-7095	386	42	discretization	discretization	NOUN
ejpam-7095	386	43	.	.	PUNCT
ejpam-7095	387	1	thus	thus	ADV
ejpam-7095	387	2	,	,	PUNCT
ejpam-7095	387	3	the	the	DET
ejpam-7095	387	4	method	method	NOUN
ejpam-7095	387	5	represents	represent	VERB
ejpam-7095	387	6	an	an	DET
ejpam-7095	387	7	effective	effective	ADJ
ejpam-7095	387	8	technique	technique	NOUN
ejpam-7095	387	9	for	for	ADP
ejpam-7095	387	10	solving	solve	VERB
ejpam-7095	387	11	fractional	fractional	ADJ
ejpam-7095	387	12	-	-	PUNCT
ejpam-7095	387	13	order	order	NOUN
ejpam-7095	387	14	pde	pde	NOUN
ejpam-7095	387	15	problems	problem	NOUN
ejpam-7095	387	16	.	.	PUNCT
ejpam-7095	388	1	kamran	kamran	PROPN
ejpam-7095	388	2	et	et	PROPN
ejpam-7095	388	3	al	al	PROPN
ejpam-7095	388	4	.	.	PUNCT
ejpam-7095	388	5	/	/	SYM
ejpam-7095	388	6	eur	eur	PROPN
ejpam-7095	388	7	.	.	PUNCT
ejpam-7095	389	1	j.	j.	PROPN
ejpam-7095	389	2	pure	pure	PROPN
ejpam-7095	389	3	appl	appl	PROPN
ejpam-7095	389	4	.	.	PROPN
ejpam-7095	389	5	math	math	PROPN
ejpam-7095	389	6	,	,	PUNCT
ejpam-7095	389	7	18	18	NUM
ejpam-7095	389	8	(	(	PUNCT
ejpam-7095	389	9	4	4	NUM
ejpam-7095	389	10	)	)	PUNCT
ejpam-7095	389	11	(	(	PUNCT
ejpam-7095	389	12	2025	2025	NUM
ejpam-7095	389	13	)	)	PUNCT
ejpam-7095	389	14	,	,	PUNCT
ejpam-7095	389	15	7095	7095	NUM
ejpam-7095	389	16	19	19	NUM
ejpam-7095	389	17	of	of	ADP
ejpam-7095	389	18	30	30	NUM
ejpam-7095	389	19	table	table	NOUN
ejpam-7095	389	20	1	1	NUM
ejpam-7095	389	21	:	:	PUNCT
ejpam-7095	389	22	errors	error	NOUN
ejpam-7095	389	23	norms	norm	VERB
ejpam-7095	389	24	for	for	ADP
ejpam-7095	389	25	example	example	NOUN
ejpam-7095	389	26	1	1	NUM
ejpam-7095	389	27	with	with	ADP
ejpam-7095	389	28	varying	vary	VERB
ejpam-7095	389	29	mq	mq	PROPN
ejpam-7095	389	30	,	,	PUNCT
ejpam-7095	389	31	α	α	NOUN
ejpam-7095	389	32	,	,	PUNCT
ejpam-7095	389	33	and	and	CCONJ
ejpam-7095	389	34	n.	n.	PROPN
ejpam-7095	389	35	mq	mq	PROPN
ejpam-7095	389	36	n	n	PROPN
ejpam-7095	389	37	α	α	NOUN
ejpam-7095	389	38	=	=	SYM
ejpam-7095	389	39	1.5	1.5	NUM
ejpam-7095	389	40	α	α	NOUN
ejpam-7095	389	41	=	=	SYM
ejpam-7095	389	42	1.75	1.75	NUM
ejpam-7095	389	43	l∞	l∞	NOUN
ejpam-7095	389	44	c.time(s	c.time(s	PROPN
ejpam-7095	389	45	)	)	PUNCT
ejpam-7095	389	46	l∞	l∞	NOUN
ejpam-7095	389	47	c.time(s	c.time(s	PROPN
ejpam-7095	389	48	)	)	PUNCT
ejpam-7095	389	49	36	36	NUM
ejpam-7095	389	50	400	400	NUM
ejpam-7095	389	51	1.1419×10−12	1.1419×10−12	NUM
ejpam-7095	389	52	0.270315	0.270315	NUM
ejpam-7095	390	1	2.2197×10−12	2.2197×10−12	NUM
ejpam-7095	390	2	0.434348	0.434348	NUM
ejpam-7095	390	3	500	500	NUM
ejpam-7095	390	4	6.2560×10−12	6.2560×10−12	NUM
ejpam-7095	390	5	1.212901	1.212901	NUM
ejpam-7095	390	6	5.1609×10−12	5.1609×10−12	NUM
ejpam-7095	390	7	1.193002	1.193002	NUM
ejpam-7095	390	8	600	600	NUM
ejpam-7095	390	9	1.1793×10−12	1.1793×10−12	NUM
ejpam-7095	390	10	1.119774	1.119774	NUM
ejpam-7095	390	11	2.7161×10−12	2.7161×10−12	NUM
ejpam-7095	390	12	0.904267	0.904267	NUM
ejpam-7095	390	13	700	700	NUM
ejpam-7095	390	14	7.3037×10−12	7.3037×10−12	NUM
ejpam-7095	390	15	1.541679	1.541679	NUM
ejpam-7095	390	16	3.0467×10−12	3.0467×10−12	NUM
ejpam-7095	390	17	1.403863	1.403863	NUM
ejpam-7095	390	18	26	26	NUM
ejpam-7095	390	19	850	850	NUM
ejpam-7095	390	20	1.6612×10−11	1.6612×10−11	NUM
ejpam-7095	390	21	1.114587	1.114587	NUM
ejpam-7095	390	22	1.1432×10−11	1.1432×10−11	NUM
ejpam-7095	390	23	1.473688	1.473688	NUM
ejpam-7095	390	24	28	28	NUM
ejpam-7095	390	25	3.2163×10−12	3.2163×10−12	NUM
ejpam-7095	390	26	1.106680	1.106680	NUM
ejpam-7095	390	27	1.2373×10−11	1.2373×10−11	NUM
ejpam-7095	390	28	1.363364	1.363364	NUM
ejpam-7095	390	29	30	30	NUM
ejpam-7095	390	30	4.2749×10−12	4.2749×10−12	NUM
ejpam-7095	390	31	1.425263	1.425263	NUM
ejpam-7095	390	32	1.2061×10−11	1.2061×10−11	NUM
ejpam-7095	390	33	1.471200	1.471200	NUM
ejpam-7095	390	34	32	32	NUM
ejpam-7095	390	35	7.5047×10−12	7.5047×10−12	NUM
ejpam-7095	390	36	2.004526	2.004526	NUM
ejpam-7095	390	37	6.4597×10−12	6.4597×10−12	NUM
ejpam-7095	390	38	1.563570	1.563570	NUM
ejpam-7095	390	39	34	34	NUM
ejpam-7095	390	40	5.1494×10−12	5.1494×10−12	NUM
ejpam-7095	390	41	1.505562	1.505562	NUM
ejpam-7095	390	42	6.6363×10−12	6.6363×10−12	NUM
ejpam-7095	390	43	1.666364	1.666364	NUM
ejpam-7095	390	44	0	0	NUM
ejpam-7095	390	45	0.1	0.1	NUM
ejpam-7095	390	46	0.2	0.2	NUM
ejpam-7095	390	47	0.3	0.3	NUM
ejpam-7095	390	48	0.4	0.4	NUM
ejpam-7095	390	49	0.5	0.5	NUM
ejpam-7095	390	50	0.6	0.6	NUM
ejpam-7095	390	51	0.7	0.7	NUM
ejpam-7095	390	52	0.8	0.8	NUM
ejpam-7095	390	53	0.9	0.9	NUM
ejpam-7095	390	54	1	1	NUM
ejpam-7095	390	55	0	0	NUM
ejpam-7095	390	56	0.5	0.5	NUM
ejpam-7095	390	57	1	1	NUM
ejpam-7095	390	58	0	0	NUM
ejpam-7095	390	59	0.1	0.1	NUM
ejpam-7095	390	60	0.2	0.2	NUM
ejpam-7095	390	61	0.3	0.3	NUM
ejpam-7095	390	62	0.4	0.4	NUM
ejpam-7095	390	63	0.5	0.5	NUM
ejpam-7095	390	64	0.6	0.6	NUM
ejpam-7095	390	65	0.7	0.7	NUM
ejpam-7095	390	66	0.8	0.8	NUM
ejpam-7095	390	67	0.9	0.9	NUM
ejpam-7095	390	68	1	1	NUM
ejpam-7095	390	69	0	0	NUM
ejpam-7095	390	70	0.5	0.5	NUM
ejpam-7095	390	71	1	1	NUM
ejpam-7095	390	72	10	10	NUM
ejpam-7095	390	73	-12	-12	NOUN
ejpam-7095	390	74	(	(	PUNCT
ejpam-7095	390	75	a	a	X
ejpam-7095	390	76	)	)	PUNCT
ejpam-7095	390	77	0	0	NUM
ejpam-7095	390	78	0.2	0.2	NUM
ejpam-7095	390	79	0.4	0.4	NUM
ejpam-7095	390	80	0.6	0.6	NUM
ejpam-7095	390	81	0.8	0.8	NUM
ejpam-7095	390	82	1	1	NUM
ejpam-7095	390	83	10	10	NUM
ejpam-7095	390	84	-18	-18	SYM
ejpam-7095	390	85	10	10	NUM
ejpam-7095	390	86	-16	-16	NUM
ejpam-7095	390	87	10	10	NUM
ejpam-7095	390	88	-14	-14	SYM
ejpam-7095	390	89	10	10	NUM
ejpam-7095	390	90	-12	-12	NUM
ejpam-7095	390	91	10	10	NUM
ejpam-7095	390	92	-10	-10	PUNCT
ejpam-7095	390	93	(	(	PUNCT
ejpam-7095	390	94	b	b	NOUN
ejpam-7095	390	95	)	)	PUNCT
ejpam-7095	390	96	figure	figure	NOUN
ejpam-7095	390	97	1	1	NUM
ejpam-7095	390	98	:	:	PUNCT
ejpam-7095	390	99	(	(	PUNCT
ejpam-7095	390	100	a	a	X
ejpam-7095	390	101	)	)	PUNCT
ejpam-7095	390	102	comparison	comparison	NOUN
ejpam-7095	390	103	of	of	ADP
ejpam-7095	390	104	approximate	approximate	ADJ
ejpam-7095	390	105	and	and	CCONJ
ejpam-7095	390	106	exact	exact	ADJ
ejpam-7095	390	107	solutions	solution	NOUN
ejpam-7095	390	108	in	in	ADP
ejpam-7095	390	109	the	the	DET
ejpam-7095	390	110	subplot	subplot	NOUN
ejpam-7095	390	111	1	1	NUM
ejpam-7095	390	112	and	and	CCONJ
ejpam-7095	390	113	the	the	DET
ejpam-7095	390	114	labs	lab	NOUN
ejpam-7095	390	115	in	in	ADP
ejpam-7095	390	116	the	the	DET
ejpam-7095	390	117	subplot	subplot	NOUN
ejpam-7095	390	118	2	2	NUM
ejpam-7095	390	119	n	n	NOUN
ejpam-7095	390	120	=	=	SYM
ejpam-7095	390	121	700	700	NUM
ejpam-7095	390	122	,	,	PUNCT
ejpam-7095	390	123	mq	mq	PROPN
ejpam-7095	390	124	=	=	SYM
ejpam-7095	390	125	36	36	NUM
ejpam-7095	390	126	(	(	PUNCT
ejpam-7095	390	127	example	example	NOUN
ejpam-7095	390	128	1	1	NUM
ejpam-7095	390	129	)	)	PUNCT
ejpam-7095	390	130	.	.	PUNCT
ejpam-7095	391	1	(	(	PUNCT
ejpam-7095	391	2	b	b	X
ejpam-7095	391	3	)	)	PUNCT
ejpam-7095	391	4	comparison	comparison	NOUN
ejpam-7095	391	5	of	of	ADP
ejpam-7095	391	6	labs	lab	NOUN
ejpam-7095	391	7	for	for	ADP
ejpam-7095	391	8	different	different	ADJ
ejpam-7095	391	9	α	α	NOUN
ejpam-7095	391	10	with	with	ADP
ejpam-7095	391	11	n	n	NOUN
ejpam-7095	391	12	=	=	SYM
ejpam-7095	391	13	1000	1000	NUM
ejpam-7095	391	14	,	,	PUNCT
ejpam-7095	391	15	mq	mq	PROPN
ejpam-7095	391	16	=	=	SYM
ejpam-7095	391	17	34	34	NUM
ejpam-7095	391	18	(	(	PUNCT
ejpam-7095	391	19	example	example	NOUN
ejpam-7095	391	20	1	1	NUM
ejpam-7095	391	21	)	)	PUNCT
ejpam-7095	391	22	.	.	PUNCT
ejpam-7095	392	1	kamran	kamran	PROPN
ejpam-7095	392	2	et	et	PROPN
ejpam-7095	392	3	al	al	PROPN
ejpam-7095	392	4	.	.	PUNCT
ejpam-7095	392	5	/	/	SYM
ejpam-7095	392	6	eur	eur	PROPN
ejpam-7095	392	7	.	.	PUNCT
ejpam-7095	393	1	j.	j.	PROPN
ejpam-7095	393	2	pure	pure	PROPN
ejpam-7095	393	3	appl	appl	PROPN
ejpam-7095	393	4	.	.	PROPN
ejpam-7095	393	5	math	math	PROPN
ejpam-7095	393	6	,	,	PUNCT
ejpam-7095	393	7	18	18	NUM
ejpam-7095	393	8	(	(	PUNCT
ejpam-7095	393	9	4	4	NUM
ejpam-7095	393	10	)	)	PUNCT
ejpam-7095	393	11	(	(	PUNCT
ejpam-7095	393	12	2025	2025	NUM
ejpam-7095	393	13	)	)	PUNCT
ejpam-7095	393	14	,	,	PUNCT
ejpam-7095	393	15	7095	7095	NUM
ejpam-7095	393	16	20	20	NUM
ejpam-7095	393	17	of	of	ADP
ejpam-7095	393	18	30	30	NUM
ejpam-7095	393	19	(	(	PUNCT
ejpam-7095	393	20	a	a	NOUN
ejpam-7095	393	21	)	)	PUNCT
ejpam-7095	393	22	(	(	PUNCT
ejpam-7095	393	23	b	b	X
ejpam-7095	393	24	)	)	PUNCT
ejpam-7095	393	25	figure	figure	NOUN
ejpam-7095	393	26	2	2	NUM
ejpam-7095	393	27	:	:	PUNCT
ejpam-7095	393	28	(	(	PUNCT
ejpam-7095	393	29	a	a	X
ejpam-7095	393	30	)	)	PUNCT
ejpam-7095	393	31	graph	graph	NOUN
ejpam-7095	393	32	of	of	ADP
ejpam-7095	393	33	l∞	l∞	NOUN
ejpam-7095	393	34	vs	vs	ADP
ejpam-7095	393	35	quadrature	quadrature	NOUN
ejpam-7095	393	36	nodes	node	NOUN
ejpam-7095	393	37	mq	mq	VERB
ejpam-7095	393	38	with	with	ADP
ejpam-7095	393	39	n	n	NOUN
ejpam-7095	393	40	=	=	SYM
ejpam-7095	393	41	700	700	NUM
ejpam-7095	393	42	(	(	PUNCT
ejpam-7095	393	43	example	example	NOUN
ejpam-7095	393	44	1	1	NUM
ejpam-7095	393	45	)	)	PUNCT
ejpam-7095	393	46	.	.	PUNCT
ejpam-7095	394	1	(	(	PUNCT
ejpam-7095	394	2	b	b	X
ejpam-7095	394	3	)	)	PUNCT
ejpam-7095	394	4	graph	graph	NOUN
ejpam-7095	394	5	of	of	ADP
ejpam-7095	394	6	l∞	l∞	NOUN
ejpam-7095	394	7	vs	vs	ADP
ejpam-7095	394	8	quadrature	quadrature	NOUN
ejpam-7095	394	9	nodes	node	NOUN
ejpam-7095	394	10	n	n	X
ejpam-7095	394	11	with	with	ADP
ejpam-7095	394	12	mq	mq	PROPN
ejpam-7095	394	13	=	=	SYM
ejpam-7095	394	14	36	36	NUM
ejpam-7095	394	15	(	(	PUNCT
ejpam-7095	394	16	example	example	NOUN
ejpam-7095	394	17	1	1	NUM
ejpam-7095	394	18	)	)	PUNCT
ejpam-7095	394	19	.	.	PUNCT
ejpam-7095	395	1	0.1	0.1	NUM
ejpam-7095	395	2	0.2	0.2	NUM
ejpam-7095	395	3	0.3	0.3	NUM
ejpam-7095	395	4	0.4	0.4	NUM
ejpam-7095	395	5	0.5	0.5	NUM
ejpam-7095	395	6	0.6	0.6	NUM
ejpam-7095	395	7	0.7	0.7	NUM
ejpam-7095	395	8	0.8	0.8	NUM
ejpam-7095	395	9	0.9	0.9	NUM
ejpam-7095	395	10	1	1	NUM
ejpam-7095	395	11	10	10	NUM
ejpam-7095	395	12	-13	-13	SYM
ejpam-7095	395	13	10	10	NUM
ejpam-7095	395	14	-12	-12	SYM
ejpam-7095	395	15	10	10	NUM
ejpam-7095	395	16	-11	-11	PUNCT
ejpam-7095	395	17	(	(	PUNCT
ejpam-7095	395	18	a	a	X
ejpam-7095	395	19	)	)	PUNCT
ejpam-7095	395	20	1.1	1.1	NUM
ejpam-7095	395	21	1.2	1.2	NUM
ejpam-7095	395	22	1.3	1.3	NUM
ejpam-7095	395	23	1.4	1.4	NUM
ejpam-7095	395	24	1.5	1.5	NUM
ejpam-7095	395	25	1.6	1.6	NUM
ejpam-7095	395	26	1.7	1.7	NUM
ejpam-7095	395	27	1.8	1.8	NUM
ejpam-7095	395	28	1.9	1.9	NUM
ejpam-7095	395	29	2	2	NUM
ejpam-7095	395	30	0.5	0.5	NUM
ejpam-7095	395	31	1	1	NUM
ejpam-7095	395	32	1.5	1.5	NUM
ejpam-7095	395	33	2	2	NUM
ejpam-7095	395	34	2.5	2.5	NUM
ejpam-7095	395	35	3	3	NUM
ejpam-7095	395	36	3.5	3.5	NUM
ejpam-7095	395	37	4	4	NUM
ejpam-7095	395	38	4.5	4.5	NUM
ejpam-7095	395	39	10	10	NUM
ejpam-7095	395	40	-12	-12	NOUN
ejpam-7095	395	41	(	(	PUNCT
ejpam-7095	395	42	b	b	NOUN
ejpam-7095	395	43	)	)	PUNCT
ejpam-7095	395	44	figure	figure	NOUN
ejpam-7095	395	45	3	3	NUM
ejpam-7095	395	46	:	:	PUNCT
ejpam-7095	395	47	(	(	PUNCT
ejpam-7095	395	48	a	a	X
ejpam-7095	395	49	)	)	PUNCT
ejpam-7095	395	50	graph	graph	NOUN
ejpam-7095	395	51	of	of	ADP
ejpam-7095	395	52	l∞	l∞	NOUN
ejpam-7095	395	53	vs	vs	ADP
ejpam-7095	395	54	τ	τ	PROPN
ejpam-7095	395	55	with	with	ADP
ejpam-7095	395	56	mq	mq	PROPN
ejpam-7095	395	57	=	=	SYM
ejpam-7095	395	58	36	36	NUM
ejpam-7095	395	59	and	and	CCONJ
ejpam-7095	395	60	n	n	CCONJ
ejpam-7095	395	61	=	=	SYM
ejpam-7095	395	62	700	700	NUM
ejpam-7095	395	63	(	(	PUNCT
ejpam-7095	395	64	example	example	NOUN
ejpam-7095	395	65	1	1	NUM
ejpam-7095	395	66	)	)	PUNCT
ejpam-7095	395	67	.	.	PUNCT
ejpam-7095	396	1	(	(	PUNCT
ejpam-7095	396	2	b	b	X
ejpam-7095	396	3	)	)	PUNCT
ejpam-7095	396	4	graph	graph	NOUN
ejpam-7095	396	5	of	of	ADP
ejpam-7095	396	6	l∞	l∞	NOUN
ejpam-7095	396	7	vs	vs	ADP
ejpam-7095	396	8	fractional	fractional	ADJ
ejpam-7095	396	9	order	order	NOUN
ejpam-7095	396	10	α	α	NOUN
ejpam-7095	396	11	with	with	ADP
ejpam-7095	396	12	n	n	NOUN
ejpam-7095	396	13	=	=	SYM
ejpam-7095	396	14	700	700	NUM
ejpam-7095	396	15	and	and	CCONJ
ejpam-7095	396	16	mq	mq	NUM
ejpam-7095	396	17	=	=	SYM
ejpam-7095	396	18	36	36	NUM
ejpam-7095	396	19	(	(	PUNCT
ejpam-7095	396	20	example	example	NOUN
ejpam-7095	396	21	1	1	NUM
ejpam-7095	396	22	)	)	PUNCT
ejpam-7095	396	23	.	.	PUNCT
ejpam-7095	397	1	kamran	kamran	PROPN
ejpam-7095	397	2	et	et	PROPN
ejpam-7095	397	3	al	al	PROPN
ejpam-7095	397	4	.	.	PUNCT
ejpam-7095	397	5	/	/	SYM
ejpam-7095	397	6	eur	eur	PROPN
ejpam-7095	397	7	.	.	PUNCT
ejpam-7095	398	1	j.	j.	PROPN
ejpam-7095	398	2	pure	pure	PROPN
ejpam-7095	398	3	appl	appl	PROPN
ejpam-7095	398	4	.	.	PROPN
ejpam-7095	398	5	math	math	PROPN
ejpam-7095	398	6	,	,	PUNCT
ejpam-7095	398	7	18	18	NUM
ejpam-7095	398	8	(	(	PUNCT
ejpam-7095	398	9	4	4	NUM
ejpam-7095	398	10	)	)	PUNCT
ejpam-7095	398	11	(	(	PUNCT
ejpam-7095	398	12	2025	2025	NUM
ejpam-7095	398	13	)	)	PUNCT
ejpam-7095	398	14	,	,	PUNCT
ejpam-7095	398	15	7095	7095	NUM
ejpam-7095	398	16	21	21	NUM
ejpam-7095	398	17	of	of	ADP
ejpam-7095	398	18	30	30	NUM
ejpam-7095	398	19	(	(	PUNCT
ejpam-7095	398	20	a	a	NOUN
ejpam-7095	398	21	)	)	PUNCT
ejpam-7095	398	22	error	error	NOUN
ejpam-7095	398	23	contour	contour	NOUN
ejpam-7095	398	24	plot	plot	NOUN
ejpam-7095	399	1	0.1	0.1	NUM
ejpam-7095	399	2	0.2	0.2	NUM
ejpam-7095	399	3	0.3	0.3	NUM
ejpam-7095	399	4	0.4	0.4	NUM
ejpam-7095	399	5	0.5	0.5	NUM
ejpam-7095	399	6	0.6	0.6	NUM
ejpam-7095	399	7	0.7	0.7	NUM
ejpam-7095	399	8	0.8	0.8	NUM
ejpam-7095	399	9	0.9	0.9	NUM
ejpam-7095	399	10	1	1	NUM
ejpam-7095	399	11	1.1	1.1	NUM
ejpam-7095	399	12	1.2	1.2	NUM
ejpam-7095	399	13	1.3	1.3	NUM
ejpam-7095	399	14	1.4	1.4	NUM
ejpam-7095	399	15	1.5	1.5	NUM
ejpam-7095	399	16	1.6	1.6	NUM
ejpam-7095	399	17	1.7	1.7	NUM
ejpam-7095	399	18	1.8	1.8	NUM
ejpam-7095	399	19	1.9	1.9	NUM
ejpam-7095	399	20	2	2	NUM
ejpam-7095	399	21	-13.5	-13.5	NUM
ejpam-7095	399	22	-13	-13	NUM
ejpam-7095	399	23	-12.5	-12.5	NUM
ejpam-7095	399	24	-12	-12	PRON
ejpam-7095	399	25	-11.5	-11.5	PROPN
ejpam-7095	399	26	-11	-11	PUNCT
ejpam-7095	399	27	(	(	PUNCT
ejpam-7095	399	28	b	b	NOUN
ejpam-7095	399	29	)	)	PUNCT
ejpam-7095	399	30	figure	figure	NOUN
ejpam-7095	399	31	4	4	NUM
ejpam-7095	399	32	:	:	PUNCT
ejpam-7095	399	33	(	(	PUNCT
ejpam-7095	399	34	a	a	X
ejpam-7095	399	35	)	)	PUNCT
ejpam-7095	399	36	the	the	DET
ejpam-7095	399	37	graph	graph	NOUN
ejpam-7095	399	38	shows	show	VERB
ejpam-7095	399	39	l∞	l∞	NOUN
ejpam-7095	399	40	error	error	NOUN
ejpam-7095	399	41	in	in	ADP
ejpam-7095	399	42	τα	τα	NOUN
ejpam-7095	399	43	plane	plane	NOUN
ejpam-7095	399	44	with	with	ADP
ejpam-7095	399	45	mq	mq	PROPN
ejpam-7095	399	46	=	=	SYM
ejpam-7095	399	47	36	36	NUM
ejpam-7095	399	48	and	and	CCONJ
ejpam-7095	399	49	n	n	CCONJ
ejpam-7095	399	50	=	=	SYM
ejpam-7095	399	51	700	700	NUM
ejpam-7095	399	52	(	(	PUNCT
ejpam-7095	399	53	example	example	NOUN
ejpam-7095	399	54	1	1	NUM
ejpam-7095	399	55	)	)	PUNCT
ejpam-7095	399	56	.	.	PUNCT
ejpam-7095	400	1	(	(	PUNCT
ejpam-7095	400	2	b	b	X
ejpam-7095	400	3	)	)	PUNCT
ejpam-7095	400	4	contour	contour	NOUN
ejpam-7095	400	5	plot	plot	NOUN
ejpam-7095	400	6	of	of	ADP
ejpam-7095	400	7	l∞	l∞	NOUN
ejpam-7095	400	8	in	in	ADP
ejpam-7095	400	9	τα	τα	NOUN
ejpam-7095	400	10	plane	plane	NOUN
ejpam-7095	400	11	with	with	ADP
ejpam-7095	400	12	mq	mq	PROPN
ejpam-7095	400	13	=	=	SYM
ejpam-7095	400	14	36	36	NUM
ejpam-7095	400	15	and	and	CCONJ
ejpam-7095	400	16	n	n	CCONJ
ejpam-7095	400	17	=	=	SYM
ejpam-7095	400	18	700	700	NUM
ejpam-7095	400	19	(	(	PUNCT
ejpam-7095	400	20	example	example	NOUN
ejpam-7095	400	21	1	1	NUM
ejpam-7095	400	22	)	)	PUNCT
ejpam-7095	400	23	.	.	PUNCT
ejpam-7095	401	1	example	example	NOUN
ejpam-7095	401	2	2	2	NUM
ejpam-7095	401	3	in	in	ADP
ejpam-7095	401	4	the	the	DET
ejpam-7095	401	5	second	second	ADJ
ejpam-7095	401	6	example	example	NOUN
ejpam-7095	401	7	,	,	PUNCT
ejpam-7095	401	8	we	we	PRON
ejpam-7095	401	9	consider	consider	VERB
ejpam-7095	401	10	the	the	DET
ejpam-7095	401	11	2d	2d	NUM
ejpam-7095	401	12	version	version	NOUN
ejpam-7095	401	13	of	of	ADP
ejpam-7095	401	14	(	(	PUNCT
ejpam-7095	401	15	1)–(3	1)–(3	NUM
ejpam-7095	401	16	)	)	PUNCT
ejpam-7095	401	17	with	with	ADP
ejpam-7095	401	18	λ1	λ1	PROPN
ejpam-7095	401	19	=	=	SYM
ejpam-7095	401	20	1	1	NUM
ejpam-7095	401	21	,	,	PUNCT
ejpam-7095	401	22	λ2	λ2	NOUN
ejpam-7095	401	23	=	=	SYM
ejpam-7095	401	24	0	0	NUM
ejpam-7095	401	25	,	,	PUNCT
ejpam-7095	401	26	and	and	CCONJ
ejpam-7095	401	27	exact	exact	ADJ
ejpam-7095	401	28	solution	solution	NOUN
ejpam-7095	401	29	u(x	u(x	NOUN
ejpam-7095	401	30	,	,	PUNCT
ejpam-7095	401	31	τ	τ	X
ejpam-7095	401	32	)	)	PUNCT
ejpam-7095	401	33	=	=	SYM
ejpam-7095	402	1	(	(	PUNCT
ejpam-7095	402	2	1−	1−	NUM
ejpam-7095	402	3	x2	x2	NOUN
ejpam-7095	403	1	−	−	PROPN
ejpam-7095	403	2	y2)τ.3	y2)τ.3	PROPN
ejpam-7095	403	3	.	.	PUNCT
ejpam-7095	404	1	the	the	DET
ejpam-7095	404	2	performance	performance	NOUN
ejpam-7095	404	3	of	of	ADP
ejpam-7095	404	4	the	the	DET
ejpam-7095	404	5	proposed	propose	VERB
ejpam-7095	404	6	numerical	numerical	ADJ
ejpam-7095	404	7	method	method	NOUN
ejpam-7095	404	8	is	be	AUX
ejpam-7095	404	9	validated	validate	VERB
ejpam-7095	404	10	through	through	ADP
ejpam-7095	404	11	detailed	detailed	ADJ
ejpam-7095	404	12	error	error	NOUN
ejpam-7095	404	13	analysis	analysis	NOUN
ejpam-7095	404	14	and	and	CCONJ
ejpam-7095	404	15	computational	computational	ADJ
ejpam-7095	404	16	tests	test	NOUN
ejpam-7095	404	17	.	.	PUNCT
ejpam-7095	405	1	the	the	DET
ejpam-7095	405	2	l∞	l∞	NOUN
ejpam-7095	405	3	error	error	NOUN
ejpam-7095	405	4	for	for	ADP
ejpam-7095	405	5	various	various	ADJ
ejpam-7095	405	6	values	value	NOUN
ejpam-7095	405	7	of	of	ADP
ejpam-7095	405	8	n	n	PRON
ejpam-7095	405	9	and	and	CCONJ
ejpam-7095	405	10	quadrature	quadrature	NOUN
ejpam-7095	405	11	points	point	NOUN
ejpam-7095	405	12	mq	mq	NOUN
ejpam-7095	405	13	is	be	AUX
ejpam-7095	405	14	shown	show	VERB
ejpam-7095	405	15	in	in	ADP
ejpam-7095	405	16	table	table	NOUN
ejpam-7095	405	17	2	2	NUM
ejpam-7095	405	18	,	,	PUNCT
ejpam-7095	405	19	showing	show	VERB
ejpam-7095	405	20	both	both	PRON
ejpam-7095	405	21	high	high	ADJ
ejpam-7095	405	22	accuracy	accuracy	NOUN
ejpam-7095	405	23	and	and	CCONJ
ejpam-7095	405	24	computational	computational	ADJ
ejpam-7095	405	25	efficiency	efficiency	NOUN
ejpam-7095	405	26	.	.	PUNCT
ejpam-7095	406	1	the	the	DET
ejpam-7095	406	2	numerical	numerical	ADJ
ejpam-7095	406	3	solution	solution	NOUN
ejpam-7095	406	4	of	of	ADP
ejpam-7095	406	5	example	example	NOUN
ejpam-7095	406	6	2	2	NUM
ejpam-7095	406	7	is	be	AUX
ejpam-7095	406	8	shown	show	VERB
ejpam-7095	406	9	in	in	ADP
ejpam-7095	406	10	figure	figure	NOUN
ejpam-7095	406	11	5a	5a	NUM
ejpam-7095	406	12	,	,	PUNCT
ejpam-7095	406	13	and	and	CCONJ
ejpam-7095	406	14	the	the	DET
ejpam-7095	406	15	surface	surface	NOUN
ejpam-7095	406	16	plot	plot	NOUN
ejpam-7095	406	17	presented	present	VERB
ejpam-7095	406	18	in	in	ADP
ejpam-7095	406	19	figure	figure	NOUN
ejpam-7095	406	20	5b	5b	PROPN
ejpam-7095	406	21	shows	show	VERB
ejpam-7095	406	22	the	the	DET
ejpam-7095	406	23	absolute	absolute	ADJ
ejpam-7095	406	24	error	error	NOUN
ejpam-7095	406	25	distribution	distribution	NOUN
ejpam-7095	406	26	demonstrating	demonstrate	VERB
ejpam-7095	406	27	stable	stable	ADJ
ejpam-7095	406	28	numerical	numerical	ADJ
ejpam-7095	406	29	performance	performance	NOUN
ejpam-7095	406	30	.	.	PUNCT
ejpam-7095	407	1	figure	figure	NOUN
ejpam-7095	407	2	6a	6a	NOUN
ejpam-7095	407	3	demonstrates	demonstrate	VERB
ejpam-7095	407	4	perfect	perfect	ADJ
ejpam-7095	407	5	quadrature	quadrature	NOUN
ejpam-7095	407	6	convergence	convergence	NOUN
ejpam-7095	407	7	up	up	ADP
ejpam-7095	407	8	to	to	ADP
ejpam-7095	407	9	mq	mq	NOUN
ejpam-7095	407	10	=	=	SYM
ejpam-7095	407	11	36	36	NUM
ejpam-7095	407	12	,	,	PUNCT
ejpam-7095	407	13	after	after	ADP
ejpam-7095	407	14	which	which	PRON
ejpam-7095	407	15	the	the	DET
ejpam-7095	407	16	error	error	NOUN
ejpam-7095	407	17	experiences	experience	VERB
ejpam-7095	407	18	a	a	DET
ejpam-7095	407	19	small	small	ADJ
ejpam-7095	407	20	rise	rise	NOUN
ejpam-7095	407	21	.	.	PUNCT
ejpam-7095	408	1	spectral	spectral	ADJ
ejpam-7095	408	2	convergence	convergence	NOUN
ejpam-7095	408	3	with	with	ADP
ejpam-7095	408	4	respect	respect	NOUN
ejpam-7095	408	5	to	to	ADP
ejpam-7095	408	6	spatial	spatial	ADJ
ejpam-7095	408	7	discretization	discretization	NOUN
ejpam-7095	408	8	is	be	AUX
ejpam-7095	408	9	evident	evident	ADJ
ejpam-7095	408	10	in	in	ADP
ejpam-7095	408	11	figure	figure	NOUN
ejpam-7095	408	12	6b	6b	NOUN
ejpam-7095	408	13	,	,	PUNCT
ejpam-7095	408	14	where	where	SCONJ
ejpam-7095	408	15	minor	minor	ADJ
ejpam-7095	408	16	error	error	NOUN
ejpam-7095	408	17	oscillations	oscillation	NOUN
ejpam-7095	408	18	appear	appear	VERB
ejpam-7095	408	19	at	at	ADP
ejpam-7095	408	20	higher	high	ADJ
ejpam-7095	408	21	orders	order	NOUN
ejpam-7095	408	22	because	because	SCONJ
ejpam-7095	408	23	of	of	ADP
ejpam-7095	408	24	round	round	VERB
ejpam-7095	408	25	-	-	PUNCT
ejpam-7095	408	26	off	off	ADP
ejpam-7095	408	27	errors	error	NOUN
ejpam-7095	408	28	in	in	ADP
ejpam-7095	408	29	chebyshev	chebyshev	NOUN
ejpam-7095	408	30	differentiation	differentiation	NOUN
ejpam-7095	408	31	matrices	matrix	NOUN
ejpam-7095	408	32	.	.	PUNCT
ejpam-7095	409	1	figure	figure	NOUN
ejpam-7095	409	2	7a	7a	NOUN
ejpam-7095	409	3	shows	show	VERB
ejpam-7095	409	4	the	the	DET
ejpam-7095	409	5	dependence	dependence	NOUN
ejpam-7095	409	6	of	of	ADP
ejpam-7095	409	7	l∞	l∞	NOUN
ejpam-7095	409	8	on	on	ADP
ejpam-7095	409	9	τ	τ	PROPN
ejpam-7095	409	10	for	for	ADP
ejpam-7095	409	11	1.1	1.1	NUM
ejpam-7095	409	12	≤	≤	NUM
ejpam-7095	409	13	α	α	PRON
ejpam-7095	409	14	≤	≤	NUM
ejpam-7095	409	15	1.9	1.9	NUM
ejpam-7095	409	16	,	,	PUNCT
ejpam-7095	409	17	while	while	SCONJ
ejpam-7095	409	18	figure	figure	NOUN
ejpam-7095	409	19	7b	7b	PROPN
ejpam-7095	409	20	shows	show	VERB
ejpam-7095	409	21	its	its	PRON
ejpam-7095	409	22	dependence	dependence	NOUN
ejpam-7095	409	23	on	on	ADP
ejpam-7095	409	24	α	α	NOUN
ejpam-7095	409	25	for	for	ADP
ejpam-7095	409	26	τ	τ	X
ejpam-7095	409	27	=	=	PUNCT
ejpam-7095	409	28	{	{	PUNCT
ejpam-7095	409	29	0.1	0.1	NUM
ejpam-7095	409	30	,	,	PUNCT
ejpam-7095	409	31	0.4	0.4	NUM
ejpam-7095	409	32	,	,	PUNCT
ejpam-7095	409	33	0.7	0.7	NUM
ejpam-7095	409	34	,	,	PUNCT
ejpam-7095	409	35	1	1	NUM
ejpam-7095	409	36	}	}	PUNCT
ejpam-7095	409	37	,	,	PUNCT
ejpam-7095	409	38	both	both	PRON
ejpam-7095	409	39	demonstrating	demonstrate	VERB
ejpam-7095	409	40	consistently	consistently	ADV
ejpam-7095	409	41	high	high	ADJ
ejpam-7095	409	42	accuracy	accuracy	NOUN
ejpam-7095	409	43	.	.	PUNCT
ejpam-7095	410	1	figures	figure	NOUN
ejpam-7095	410	2	8a	8a	NUM
ejpam-7095	410	3	and	and	CCONJ
ejpam-7095	410	4	8b	8b	NUM
ejpam-7095	410	5	present	present	ADJ
ejpam-7095	410	6	comprehensive	comprehensive	ADJ
ejpam-7095	410	7	error	error	NOUN
ejpam-7095	410	8	visualization	visualization	NOUN
ejpam-7095	410	9	using	use	VERB
ejpam-7095	410	10	surface	surface	NOUN
ejpam-7095	410	11	and	and	CCONJ
ejpam-7095	410	12	contour	contour	NOUN
ejpam-7095	410	13	plots	plot	NOUN
ejpam-7095	410	14	in	in	ADP
ejpam-7095	410	15	the	the	DET
ejpam-7095	410	16	ατ	ατ	NOUN
ejpam-7095	410	17	plane	plane	NOUN
ejpam-7095	410	18	,	,	PUNCT
ejpam-7095	410	19	demonstrating	demonstrate	VERB
ejpam-7095	410	20	the	the	DET
ejpam-7095	410	21	method	method	NOUN
ejpam-7095	410	22	’s	’s	PART
ejpam-7095	410	23	robust	robust	ADJ
ejpam-7095	410	24	stability	stability	NOUN
ejpam-7095	410	25	across	across	ADP
ejpam-7095	410	26	the	the	DET
ejpam-7095	410	27	entire	entire	ADJ
ejpam-7095	410	28	parameter	parameter	NOUN
ejpam-7095	410	29	domain	domain	NOUN
ejpam-7095	410	30	.	.	PUNCT
ejpam-7095	411	1	kamran	kamran	PROPN
ejpam-7095	411	2	et	et	PROPN
ejpam-7095	411	3	al	al	PROPN
ejpam-7095	411	4	.	.	PUNCT
ejpam-7095	411	5	/	/	SYM
ejpam-7095	411	6	eur	eur	PROPN
ejpam-7095	411	7	.	.	PUNCT
ejpam-7095	412	1	j.	j.	PROPN
ejpam-7095	412	2	pure	pure	PROPN
ejpam-7095	412	3	appl	appl	PROPN
ejpam-7095	412	4	.	.	PROPN
ejpam-7095	412	5	math	math	PROPN
ejpam-7095	412	6	,	,	PUNCT
ejpam-7095	412	7	18	18	NUM
ejpam-7095	412	8	(	(	PUNCT
ejpam-7095	412	9	4	4	NUM
ejpam-7095	412	10	)	)	PUNCT
ejpam-7095	412	11	(	(	PUNCT
ejpam-7095	412	12	2025	2025	NUM
ejpam-7095	412	13	)	)	PUNCT
ejpam-7095	412	14	,	,	PUNCT
ejpam-7095	412	15	7095	7095	NUM
ejpam-7095	412	16	22	22	NUM
ejpam-7095	412	17	of	of	ADP
ejpam-7095	412	18	30	30	NUM
ejpam-7095	412	19	table	table	NOUN
ejpam-7095	412	20	2	2	NUM
ejpam-7095	412	21	:	:	PUNCT
ejpam-7095	412	22	errors	error	NOUN
ejpam-7095	412	23	norms	norm	VERB
ejpam-7095	412	24	for	for	ADP
ejpam-7095	412	25	example	example	NOUN
ejpam-7095	412	26	2	2	NUM
ejpam-7095	412	27	with	with	ADP
ejpam-7095	412	28	varying	vary	VERB
ejpam-7095	412	29	mq	mq	PROPN
ejpam-7095	412	30	,	,	PUNCT
ejpam-7095	412	31	α	α	NOUN
ejpam-7095	412	32	,	,	PUNCT
ejpam-7095	412	33	and	and	CCONJ
ejpam-7095	412	34	n.	n.	PROPN
ejpam-7095	412	35	mq	mq	PROPN
ejpam-7095	412	36	n	n	PROPN
ejpam-7095	412	37	α	α	NOUN
ejpam-7095	412	38	=	=	SYM
ejpam-7095	412	39	1.5	1.5	NUM
ejpam-7095	412	40	α	α	NOUN
ejpam-7095	412	41	=	=	SYM
ejpam-7095	412	42	1.75	1.75	NUM
ejpam-7095	412	43	l∞	l∞	NOUN
ejpam-7095	412	44	c.time(s	c.time(s	PROPN
ejpam-7095	412	45	)	)	PUNCT
ejpam-7095	412	46	l∞	l∞	NOUN
ejpam-7095	412	47	c.time(s	c.time(s	PROPN
ejpam-7095	412	48	)	)	PUNCT
ejpam-7095	412	49	24	24	NUM
ejpam-7095	412	50	441	441	NUM
ejpam-7095	412	51	3.3135×10−9	3.3135×10−9	NUM
ejpam-7095	412	52	0.525874	0.525874	NUM
ejpam-7095	412	53	3.3135×10−9	3.3135×10−9	NOUN
ejpam-7095	412	54	0.430171	0.430171	NUM
ejpam-7095	412	55	784	784	NUM
ejpam-7095	412	56	3.3137×10−9	3.3137×10−9	NUM
ejpam-7095	412	57	1.371348	1.371348	NUM
ejpam-7095	412	58	3.3135×10−9	3.3135×10−9	NOUN
ejpam-7095	412	59	1.370788	1.370788	NUM
ejpam-7095	412	60	900	900	NUM
ejpam-7095	412	61	3.3135×10−9	3.3135×10−9	NUM
ejpam-7095	412	62	1.790163	1.790163	NUM
ejpam-7095	412	63	3.3138×10−9	3.3138×10−9	NUM
ejpam-7095	412	64	2.238885	2.238885	NUM
ejpam-7095	412	65	1089	1089	NUM
ejpam-7095	412	66	3.3135×10−9	3.3135×10−9	NUM
ejpam-7095	412	67	3.175910	3.175910	NUM
ejpam-7095	412	68	3.3135×10−9	3.3135×10−9	NOUN
ejpam-7095	412	69	3.317322	3.317322	NUM
ejpam-7095	412	70	26	26	NUM
ejpam-7095	412	71	1681	1681	NUM
ejpam-7095	412	72	5.4329×10−10	5.4329×10−10	NUM
ejpam-7095	412	73	9.138562	9.138562	NUM
ejpam-7095	412	74	4.3794×10−10	4.3794×10−10	NUM
ejpam-7095	412	75	9.125002	9.125002	NUM
ejpam-7095	412	76	28	28	NUM
ejpam-7095	412	77	7.1942×10−10	7.1942×10−10	NUM
ejpam-7095	412	78	9.830315	9.830315	NUM
ejpam-7095	412	79	2.2237×10−10	2.2237×10−10	NUM
ejpam-7095	412	80	9.696946	9.696946	NUM
ejpam-7095	412	81	30	30	NUM
ejpam-7095	412	82	3.7555×10−10	3.7555×10−10	NUM
ejpam-7095	412	83	10.442032	10.442032	NUM
ejpam-7095	412	84	4.5945×10−10	4.5945×10−10	NUM
ejpam-7095	412	85	10.396021	10.396021	NUM
ejpam-7095	412	86	32	32	NUM
ejpam-7095	412	87	7.4227×10−10	7.4227×10−10	NUM
ejpam-7095	412	88	11.273246	11.273246	NUM
ejpam-7095	412	89	7.7937×10−10	7.7937×10−10	NUM
ejpam-7095	412	90	11.177015	11.177015	NUM
ejpam-7095	412	91	34	34	NUM
ejpam-7095	412	92	3.1544×10−10	3.1544×10−10	NUM
ejpam-7095	412	93	13.683367	13.683367	NUM
ejpam-7095	412	94	5.2071×10−10	5.2071×10−10	NUM
ejpam-7095	412	95	12.233212	12.233212	NUM
ejpam-7095	412	96	(	(	PUNCT
ejpam-7095	412	97	a	a	NOUN
ejpam-7095	412	98	)	)	PUNCT
ejpam-7095	412	99	(	(	PUNCT
ejpam-7095	412	100	b	b	X
ejpam-7095	412	101	)	)	PUNCT
ejpam-7095	412	102	figure	figure	NOUN
ejpam-7095	412	103	5	5	NUM
ejpam-7095	412	104	:	:	PUNCT
ejpam-7095	412	105	(	(	PUNCT
ejpam-7095	412	106	a	a	X
ejpam-7095	412	107	)	)	PUNCT
ejpam-7095	412	108	comparison	comparison	NOUN
ejpam-7095	412	109	of	of	ADP
ejpam-7095	412	110	approximate	approximate	ADJ
ejpam-7095	412	111	and	and	CCONJ
ejpam-7095	412	112	exact	exact	ADJ
ejpam-7095	412	113	solutions	solution	NOUN
ejpam-7095	412	114	in	in	ADP
ejpam-7095	412	115	the	the	DET
ejpam-7095	412	116	subplot	subplot	NOUN
ejpam-7095	412	117	1	1	NUM
ejpam-7095	412	118	and	and	CCONJ
ejpam-7095	412	119	the	the	DET
ejpam-7095	412	120	labs	lab	NOUN
ejpam-7095	412	121	in	in	ADP
ejpam-7095	412	122	the	the	DET
ejpam-7095	412	123	subplot	subplot	NOUN
ejpam-7095	412	124	2	2	NUM
ejpam-7095	412	125	n	n	NOUN
ejpam-7095	412	126	=	=	SYM
ejpam-7095	412	127	1681	1681	NUM
ejpam-7095	412	128	,	,	PUNCT
ejpam-7095	412	129	mq	mq	PROPN
ejpam-7095	412	130	=	=	SYM
ejpam-7095	412	131	36	36	NUM
ejpam-7095	412	132	(	(	PUNCT
ejpam-7095	412	133	example	example	NOUN
ejpam-7095	412	134	2	2	NUM
ejpam-7095	412	135	)	)	PUNCT
ejpam-7095	412	136	.	.	PUNCT
ejpam-7095	413	1	(	(	PUNCT
ejpam-7095	413	2	b	b	X
ejpam-7095	413	3	)	)	PUNCT
ejpam-7095	413	4	plot	plot	NOUN
ejpam-7095	413	5	of	of	ADP
ejpam-7095	413	6	labs	lab	NOUN
ejpam-7095	413	7	of	of	ADP
ejpam-7095	413	8	the	the	DET
ejpam-7095	413	9	method	method	NOUN
ejpam-7095	413	10	n	n	PROPN
ejpam-7095	413	11	=	=	SYM
ejpam-7095	413	12	1681	1681	NUM
ejpam-7095	413	13	,	,	PUNCT
ejpam-7095	413	14	mq	mq	PROPN
ejpam-7095	413	15	=	=	SYM
ejpam-7095	413	16	36	36	NUM
ejpam-7095	413	17	(	(	PUNCT
ejpam-7095	413	18	example	example	NOUN
ejpam-7095	413	19	2	2	NUM
ejpam-7095	413	20	)	)	PUNCT
ejpam-7095	413	21	.	.	PUNCT
ejpam-7095	414	1	kamran	kamran	PROPN
ejpam-7095	414	2	et	et	PROPN
ejpam-7095	414	3	al	al	PROPN
ejpam-7095	414	4	.	.	PUNCT
ejpam-7095	414	5	/	/	SYM
ejpam-7095	414	6	eur	eur	PROPN
ejpam-7095	414	7	.	.	PUNCT
ejpam-7095	415	1	j.	j.	PROPN
ejpam-7095	415	2	pure	pure	PROPN
ejpam-7095	415	3	appl	appl	PROPN
ejpam-7095	415	4	.	.	PROPN
ejpam-7095	415	5	math	math	PROPN
ejpam-7095	415	6	,	,	PUNCT
ejpam-7095	415	7	18	18	NUM
ejpam-7095	415	8	(	(	PUNCT
ejpam-7095	415	9	4	4	NUM
ejpam-7095	415	10	)	)	PUNCT
ejpam-7095	415	11	(	(	PUNCT
ejpam-7095	415	12	2025	2025	NUM
ejpam-7095	415	13	)	)	PUNCT
ejpam-7095	415	14	,	,	PUNCT
ejpam-7095	415	15	7095	7095	NUM
ejpam-7095	415	16	23	23	NUM
ejpam-7095	415	17	of	of	ADP
ejpam-7095	415	18	30	30	NUM
ejpam-7095	415	19	(	(	PUNCT
ejpam-7095	415	20	a	a	NOUN
ejpam-7095	415	21	)	)	PUNCT
ejpam-7095	415	22	(	(	PUNCT
ejpam-7095	415	23	b	b	X
ejpam-7095	415	24	)	)	PUNCT
ejpam-7095	415	25	figure	figure	NOUN
ejpam-7095	415	26	6	6	NUM
ejpam-7095	415	27	:	:	PUNCT
ejpam-7095	415	28	(	(	PUNCT
ejpam-7095	415	29	a	a	X
ejpam-7095	415	30	)	)	PUNCT
ejpam-7095	415	31	graph	graph	NOUN
ejpam-7095	415	32	of	of	ADP
ejpam-7095	415	33	l∞	l∞	NOUN
ejpam-7095	415	34	vs	vs	ADP
ejpam-7095	415	35	quadrature	quadrature	NOUN
ejpam-7095	415	36	nodes	node	NOUN
ejpam-7095	415	37	mq	mq	VERB
ejpam-7095	415	38	with	with	ADP
ejpam-7095	415	39	n	n	NOUN
ejpam-7095	415	40	=	=	SYM
ejpam-7095	415	41	1681	1681	NUM
ejpam-7095	415	42	(	(	PUNCT
ejpam-7095	415	43	example	example	NOUN
ejpam-7095	415	44	2	2	NUM
ejpam-7095	415	45	)	)	PUNCT
ejpam-7095	415	46	.	.	PUNCT
ejpam-7095	416	1	(	(	PUNCT
ejpam-7095	416	2	b	b	X
ejpam-7095	416	3	)	)	PUNCT
ejpam-7095	416	4	graph	graph	NOUN
ejpam-7095	416	5	of	of	ADP
ejpam-7095	416	6	l∞	l∞	NOUN
ejpam-7095	416	7	vs	vs	ADP
ejpam-7095	416	8	quadrature	quadrature	NOUN
ejpam-7095	416	9	nodes	node	NOUN
ejpam-7095	416	10	n	n	X
ejpam-7095	416	11	with	with	ADP
ejpam-7095	416	12	mq	mq	PROPN
ejpam-7095	416	13	=	=	SYM
ejpam-7095	416	14	36	36	NUM
ejpam-7095	416	15	(	(	PUNCT
ejpam-7095	416	16	example	example	NOUN
ejpam-7095	416	17	2	2	NUM
ejpam-7095	416	18	)	)	PUNCT
ejpam-7095	416	19	.	.	PUNCT
ejpam-7095	417	1	(	(	PUNCT
ejpam-7095	417	2	a	a	X
ejpam-7095	417	3	)	)	PUNCT
ejpam-7095	417	4	(	(	PUNCT
ejpam-7095	417	5	b	b	X
ejpam-7095	417	6	)	)	PUNCT
ejpam-7095	417	7	figure	figure	NOUN
ejpam-7095	417	8	7	7	NUM
ejpam-7095	417	9	:	:	PUNCT
ejpam-7095	417	10	(	(	PUNCT
ejpam-7095	417	11	a	a	X
ejpam-7095	417	12	)	)	PUNCT
ejpam-7095	417	13	graph	graph	NOUN
ejpam-7095	417	14	of	of	ADP
ejpam-7095	417	15	l∞	l∞	NOUN
ejpam-7095	417	16	vs	vs	ADP
ejpam-7095	417	17	τ	τ	PROPN
ejpam-7095	417	18	with	with	ADP
ejpam-7095	417	19	mq	mq	PROPN
ejpam-7095	417	20	=	=	SYM
ejpam-7095	417	21	36	36	NUM
ejpam-7095	417	22	and	and	CCONJ
ejpam-7095	417	23	n	n	CCONJ
ejpam-7095	417	24	=	=	SYM
ejpam-7095	417	25	1681	1681	NUM
ejpam-7095	417	26	(	(	PUNCT
ejpam-7095	417	27	example	example	NOUN
ejpam-7095	417	28	2	2	NUM
ejpam-7095	417	29	)	)	PUNCT
ejpam-7095	417	30	.	.	PUNCT
ejpam-7095	418	1	(	(	PUNCT
ejpam-7095	418	2	b	b	X
ejpam-7095	418	3	)	)	PUNCT
ejpam-7095	418	4	graph	graph	NOUN
ejpam-7095	418	5	of	of	ADP
ejpam-7095	418	6	l∞	l∞	NOUN
ejpam-7095	418	7	vs	vs	ADP
ejpam-7095	418	8	fractional	fractional	ADJ
ejpam-7095	418	9	order	order	NOUN
ejpam-7095	418	10	α	α	NOUN
ejpam-7095	418	11	with	with	ADP
ejpam-7095	418	12	n	n	NOUN
ejpam-7095	418	13	=	=	SYM
ejpam-7095	418	14	1681	1681	NUM
ejpam-7095	418	15	and	and	CCONJ
ejpam-7095	418	16	mq	mq	PROPN
ejpam-7095	418	17	=	=	SYM
ejpam-7095	418	18	36	36	NUM
ejpam-7095	418	19	(	(	PUNCT
ejpam-7095	418	20	example	example	NOUN
ejpam-7095	418	21	2	2	NUM
ejpam-7095	418	22	)	)	PUNCT
ejpam-7095	418	23	.	.	PUNCT
ejpam-7095	419	1	kamran	kamran	PROPN
ejpam-7095	419	2	et	et	PROPN
ejpam-7095	419	3	al	al	PROPN
ejpam-7095	419	4	.	.	PUNCT
ejpam-7095	419	5	/	/	SYM
ejpam-7095	419	6	eur	eur	PROPN
ejpam-7095	419	7	.	.	PUNCT
ejpam-7095	420	1	j.	j.	PROPN
ejpam-7095	420	2	pure	pure	PROPN
ejpam-7095	420	3	appl	appl	PROPN
ejpam-7095	420	4	.	.	PROPN
ejpam-7095	420	5	math	math	PROPN
ejpam-7095	420	6	,	,	PUNCT
ejpam-7095	420	7	18	18	NUM
ejpam-7095	420	8	(	(	PUNCT
ejpam-7095	420	9	4	4	NUM
ejpam-7095	420	10	)	)	PUNCT
ejpam-7095	420	11	(	(	PUNCT
ejpam-7095	420	12	2025	2025	NUM
ejpam-7095	420	13	)	)	PUNCT
ejpam-7095	420	14	,	,	PUNCT
ejpam-7095	420	15	7095	7095	NUM
ejpam-7095	420	16	24	24	NUM
ejpam-7095	420	17	of	of	ADP
ejpam-7095	420	18	30	30	NUM
ejpam-7095	420	19	(	(	PUNCT
ejpam-7095	420	20	a	a	NOUN
ejpam-7095	420	21	)	)	PUNCT
ejpam-7095	420	22	-12	-12	PROPN
ejpam-7095	421	1	-11.5	-11.5	PROPN
ejpam-7095	421	2	-11	-11	PUNCT
ejpam-7095	421	3	-10.5	-10.5	NUM
ejpam-7095	421	4	-10	-10	NUM
ejpam-7095	421	5	-9.5	-9.5	NOUN
ejpam-7095	421	6	(	(	PUNCT
ejpam-7095	421	7	b	b	X
ejpam-7095	421	8	)	)	PUNCT
ejpam-7095	421	9	figure	figure	NOUN
ejpam-7095	421	10	8	8	NUM
ejpam-7095	421	11	:	:	PUNCT
ejpam-7095	421	12	(	(	PUNCT
ejpam-7095	421	13	a	a	X
ejpam-7095	421	14	)	)	PUNCT
ejpam-7095	421	15	the	the	DET
ejpam-7095	421	16	graph	graph	NOUN
ejpam-7095	421	17	shows	show	VERB
ejpam-7095	421	18	the	the	DET
ejpam-7095	421	19	l∞	l∞	NOUN
ejpam-7095	421	20	error	error	NOUN
ejpam-7095	421	21	in	in	ADP
ejpam-7095	421	22	τα	τα	NOUN
ejpam-7095	421	23	plane	plane	NOUN
ejpam-7095	421	24	with	with	ADP
ejpam-7095	421	25	mq	mq	PROPN
ejpam-7095	421	26	=	=	SYM
ejpam-7095	421	27	36	36	NUM
ejpam-7095	421	28	and	and	CCONJ
ejpam-7095	421	29	n	n	CCONJ
ejpam-7095	421	30	=	=	SYM
ejpam-7095	421	31	1681	1681	NUM
ejpam-7095	421	32	(	(	PUNCT
ejpam-7095	421	33	example	example	NOUN
ejpam-7095	421	34	2	2	NUM
ejpam-7095	421	35	)	)	PUNCT
ejpam-7095	421	36	.	.	PUNCT
ejpam-7095	422	1	(	(	PUNCT
ejpam-7095	422	2	b	b	X
ejpam-7095	422	3	)	)	PUNCT
ejpam-7095	422	4	contour	contour	NOUN
ejpam-7095	422	5	plot	plot	NOUN
ejpam-7095	422	6	of	of	ADP
ejpam-7095	422	7	l∞	l∞	NOUN
ejpam-7095	422	8	in	in	ADP
ejpam-7095	422	9	τα	τα	NOUN
ejpam-7095	422	10	plane	plane	NOUN
ejpam-7095	422	11	with	with	ADP
ejpam-7095	422	12	mq	mq	PROPN
ejpam-7095	422	13	=	=	SYM
ejpam-7095	422	14	36	36	NUM
ejpam-7095	422	15	and	and	CCONJ
ejpam-7095	422	16	n	n	CCONJ
ejpam-7095	422	17	=	=	SYM
ejpam-7095	422	18	1681	1681	NUM
ejpam-7095	422	19	(	(	PUNCT
ejpam-7095	422	20	example	example	NOUN
ejpam-7095	422	21	2	2	NUM
ejpam-7095	422	22	)	)	PUNCT
ejpam-7095	422	23	.	.	PUNCT
ejpam-7095	423	1	example	example	NOUN
ejpam-7095	423	2	3	3	NUM
ejpam-7095	423	3	in	in	ADP
ejpam-7095	423	4	the	the	DET
ejpam-7095	423	5	third	third	ADJ
ejpam-7095	423	6	example	example	NOUN
ejpam-7095	423	7	,	,	PUNCT
ejpam-7095	423	8	we	we	PRON
ejpam-7095	423	9	consider	consider	VERB
ejpam-7095	423	10	the	the	DET
ejpam-7095	423	11	3d	3d	NUM
ejpam-7095	423	12	version	version	NOUN
ejpam-7095	423	13	of	of	ADP
ejpam-7095	423	14	(	(	PUNCT
ejpam-7095	423	15	1)–(3	1)–(3	NUM
ejpam-7095	423	16	)	)	PUNCT
ejpam-7095	423	17	with	with	ADP
ejpam-7095	423	18	λ1	λ1	PROPN
ejpam-7095	423	19	=	=	SYM
ejpam-7095	423	20	1	1	NUM
ejpam-7095	423	21	,	,	PUNCT
ejpam-7095	423	22	λ2	λ2	NOUN
ejpam-7095	423	23	=	=	SYM
ejpam-7095	423	24	0	0	NUM
ejpam-7095	423	25	,	,	PUNCT
ejpam-7095	423	26	and	and	CCONJ
ejpam-7095	423	27	exact	exact	ADJ
ejpam-7095	423	28	solution	solution	NOUN
ejpam-7095	423	29	u(x	u(x	NOUN
ejpam-7095	423	30	,	,	PUNCT
ejpam-7095	423	31	τ	τ	X
ejpam-7095	423	32	)	)	PUNCT
ejpam-7095	423	33	=	=	SYM
ejpam-7095	424	1	exp(x	exp(x	PROPN
ejpam-7095	424	2	+	+	NUM
ejpam-7095	424	3	y	y	PROPN
ejpam-7095	424	4	+	+	CCONJ
ejpam-7095	424	5	z)τ3	z)τ3	PROPN
ejpam-7095	424	6	.	.	PUNCT
ejpam-7095	425	1	the	the	DET
ejpam-7095	425	2	l∞	l∞	NOUN
ejpam-7095	425	3	error	error	NOUN
ejpam-7095	425	4	for	for	ADP
ejpam-7095	425	5	various	various	ADJ
ejpam-7095	425	6	values	value	NOUN
ejpam-7095	425	7	of	of	ADP
ejpam-7095	425	8	n	n	PRON
ejpam-7095	425	9	and	and	CCONJ
ejpam-7095	425	10	quadrature	quadrature	NOUN
ejpam-7095	425	11	points	point	NOUN
ejpam-7095	425	12	mq	mq	NOUN
ejpam-7095	425	13	is	be	AUX
ejpam-7095	425	14	shown	show	VERB
ejpam-7095	425	15	in	in	ADP
ejpam-7095	425	16	table	table	NOUN
ejpam-7095	425	17	3	3	NUM
ejpam-7095	425	18	,	,	PUNCT
ejpam-7095	425	19	showing	show	VERB
ejpam-7095	425	20	both	both	PRON
ejpam-7095	425	21	high	high	ADJ
ejpam-7095	425	22	accuracy	accuracy	NOUN
ejpam-7095	425	23	and	and	CCONJ
ejpam-7095	425	24	computational	computational	ADJ
ejpam-7095	425	25	efficiency	efficiency	NOUN
ejpam-7095	425	26	.	.	PUNCT
ejpam-7095	426	1	the	the	DET
ejpam-7095	426	2	slice	slice	NOUN
ejpam-7095	426	3	plots	plot	NOUN
ejpam-7095	426	4	of	of	ADP
ejpam-7095	426	5	numerical	numerical	ADJ
ejpam-7095	426	6	solution	solution	NOUN
ejpam-7095	426	7	and	and	CCONJ
ejpam-7095	426	8	absolute	absolute	ADJ
ejpam-7095	426	9	error	error	NOUN
ejpam-7095	426	10	computed	compute	VERB
ejpam-7095	426	11	usingn	usingn	NOUN
ejpam-7095	426	12	=	=	SYM
ejpam-7095	426	13	1331	1331	NUM
ejpam-7095	426	14	,	,	PUNCT
ejpam-7095	426	15	mq	mq	PROPN
ejpam-7095	426	16	=	=	SYM
ejpam-7095	426	17	36	36	NUM
ejpam-7095	426	18	,	,	PUNCT
ejpam-7095	426	19	τ	τ	PROPN
ejpam-7095	426	20	=	=	SYM
ejpam-7095	426	21	1	1	NUM
ejpam-7095	426	22	,	,	PUNCT
ejpam-7095	426	23	and	and	CCONJ
ejpam-7095	426	24	α	α	X
ejpam-7095	426	25	=	=	SYM
ejpam-7095	426	26	1.5	1.5	NUM
ejpam-7095	426	27	are	be	AUX
ejpam-7095	426	28	presented	present	VERB
ejpam-7095	426	29	in	in	ADP
ejpam-7095	426	30	figures	figure	NOUN
ejpam-7095	426	31	9a	9a	NOUN
ejpam-7095	426	32	and	and	CCONJ
ejpam-7095	426	33	9b	9b	NOUN
ejpam-7095	426	34	respectively	respectively	ADV
ejpam-7095	426	35	.	.	PUNCT
ejpam-7095	427	1	a	a	DET
ejpam-7095	427	2	highly	highly	ADV
ejpam-7095	427	3	efficient	efficient	ADJ
ejpam-7095	427	4	performance	performance	NOUN
ejpam-7095	427	5	is	be	AUX
ejpam-7095	427	6	evident	evident	ADJ
ejpam-7095	427	7	.	.	PUNCT
ejpam-7095	428	1	the	the	DET
ejpam-7095	428	2	variation	variation	NOUN
ejpam-7095	428	3	of	of	ADP
ejpam-7095	428	4	l∞	l∞	NOUN
ejpam-7095	428	5	vs	vs	ADP
ejpam-7095	428	6	mq	mq	PROPN
ejpam-7095	428	7	is	be	AUX
ejpam-7095	428	8	presented	present	VERB
ejpam-7095	428	9	in	in	ADP
ejpam-7095	428	10	figure	figure	NOUN
ejpam-7095	428	11	10a	10a	PROPN
ejpam-7095	428	12	computed	compute	VERB
ejpam-7095	428	13	with	with	ADP
ejpam-7095	428	14	n	n	NOUN
ejpam-7095	428	15	=	=	SYM
ejpam-7095	428	16	1728	1728	NUM
ejpam-7095	428	17	,	,	PUNCT
ejpam-7095	428	18	α	α	X
ejpam-7095	428	19	=	=	SYM
ejpam-7095	428	20	1.5	1.5	NUM
ejpam-7095	428	21	,	,	PUNCT
ejpam-7095	428	22	and	and	CCONJ
ejpam-7095	428	23	τ	τ	PROPN
ejpam-7095	428	24	=	=	SYM
ejpam-7095	428	25	1	1	X
ejpam-7095	428	26	.	.	PUNCT
ejpam-7095	428	27	similarly	similarly	ADV
ejpam-7095	428	28	,	,	PUNCT
ejpam-7095	428	29	the	the	DET
ejpam-7095	428	30	variation	variation	NOUN
ejpam-7095	428	31	of	of	ADP
ejpam-7095	428	32	l∞	l∞	NOUN
ejpam-7095	428	33	vs	vs	ADP
ejpam-7095	428	34	n	n	PROPN
ejpam-7095	428	35	is	be	AUX
ejpam-7095	428	36	shown	show	VERB
ejpam-7095	428	37	in	in	ADP
ejpam-7095	428	38	figure	figure	NOUN
ejpam-7095	428	39	10b	10b	NOUN
ejpam-7095	428	40	computed	compute	VERB
ejpam-7095	428	41	with	with	ADP
ejpam-7095	428	42	mq	mq	PROPN
ejpam-7095	428	43	=	=	SYM
ejpam-7095	428	44	30	30	NUM
ejpam-7095	428	45	,	,	PUNCT
ejpam-7095	428	46	α	α	NOUN
ejpam-7095	428	47	=	=	SYM
ejpam-7095	428	48	1.5	1.5	NUM
ejpam-7095	428	49	,	,	PUNCT
ejpam-7095	428	50	and	and	CCONJ
ejpam-7095	428	51	τ	τ	PROPN
ejpam-7095	428	52	=	=	SYM
ejpam-7095	428	53	1	1	X
ejpam-7095	428	54	.	.	NUM
ejpam-7095	428	55	figures	figure	NOUN
ejpam-7095	428	56	11a	11a	NOUN
ejpam-7095	428	57	and	and	CCONJ
ejpam-7095	428	58	11b	11b	NOUN
ejpam-7095	428	59	presents	present	VERB
ejpam-7095	428	60	the	the	DET
ejpam-7095	428	61	dependence	dependence	NOUN
ejpam-7095	428	62	of	of	ADP
ejpam-7095	428	63	l∞	l∞	NOUN
ejpam-7095	428	64	on	on	ADP
ejpam-7095	428	65	τ	τ	PROPN
ejpam-7095	428	66	and	and	CCONJ
ejpam-7095	428	67	α	α	NOUN
ejpam-7095	428	68	respectively	respectively	ADV
ejpam-7095	428	69	,	,	PUNCT
ejpam-7095	428	70	both	both	PRON
ejpam-7095	428	71	demonstrate	demonstrate	VERB
ejpam-7095	428	72	high	high	ADJ
ejpam-7095	428	73	accuracy	accuracy	NOUN
ejpam-7095	428	74	.	.	PUNCT
ejpam-7095	429	1	further	far	ADV
ejpam-7095	429	2	,	,	PUNCT
ejpam-7095	429	3	figures	figure	NOUN
ejpam-7095	429	4	12a	12a	NOUN
ejpam-7095	429	5	show	show	VERB
ejpam-7095	429	6	the	the	DET
ejpam-7095	429	7	error	error	NOUN
ejpam-7095	429	8	distribution	distribution	NOUN
ejpam-7095	429	9	in	in	ADP
ejpam-7095	429	10	the	the	DET
ejpam-7095	429	11	αt	αt	NOUN
ejpam-7095	429	12	plane	plane	NOUN
ejpam-7095	429	13	.	.	PUNCT
ejpam-7095	430	1	the	the	DET
ejpam-7095	430	2	contour	contour	NOUN
ejpam-7095	430	3	slice	slice	NOUN
ejpam-7095	430	4	plot	plot	NOUN
ejpam-7095	430	5	of	of	ADP
ejpam-7095	430	6	absolute	absolute	ADJ
ejpam-7095	430	7	error	error	NOUN
ejpam-7095	430	8	is	be	AUX
ejpam-7095	430	9	presented	present	VERB
ejpam-7095	430	10	in	in	ADP
ejpam-7095	430	11	figure	figure	NOUN
ejpam-7095	430	12	12b	12b	NOUN
ejpam-7095	430	13	.	.	PUNCT
ejpam-7095	431	1	overall	overall	ADV
ejpam-7095	431	2	,	,	PUNCT
ejpam-7095	431	3	it	it	PRON
ejpam-7095	431	4	is	be	AUX
ejpam-7095	431	5	evident	evident	ADJ
ejpam-7095	431	6	that	that	SCONJ
ejpam-7095	431	7	the	the	DET
ejpam-7095	431	8	method	method	NOUN
ejpam-7095	431	9	has	have	VERB
ejpam-7095	431	10	the	the	DET
ejpam-7095	431	11	capability	capability	NOUN
ejpam-7095	431	12	of	of	ADP
ejpam-7095	431	13	solving	solve	VERB
ejpam-7095	431	14	fractional	fractional	ADJ
ejpam-7095	431	15	-	-	PUNCT
ejpam-7095	431	16	order	order	NOUN
ejpam-7095	431	17	three	three	NUM
ejpam-7095	431	18	-	-	PUNCT
ejpam-7095	431	19	dimensional	dimensional	ADJ
ejpam-7095	431	20	problems	problem	NOUN
ejpam-7095	431	21	with	with	ADP
ejpam-7095	431	22	high	high	ADJ
ejpam-7095	431	23	accuracy	accuracy	NOUN
ejpam-7095	431	24	without	without	ADP
ejpam-7095	431	25	facing	face	VERB
ejpam-7095	431	26	any	any	DET
ejpam-7095	431	27	time	time	NOUN
ejpam-7095	431	28	instability	instability	NOUN
ejpam-7095	431	29	issues	issue	NOUN
ejpam-7095	431	30	.	.	PUNCT
ejpam-7095	432	1	kamran	kamran	PROPN
ejpam-7095	432	2	et	et	PROPN
ejpam-7095	432	3	al	al	PROPN
ejpam-7095	432	4	.	.	PUNCT
ejpam-7095	432	5	/	/	SYM
ejpam-7095	432	6	eur	eur	PROPN
ejpam-7095	432	7	.	.	PUNCT
ejpam-7095	433	1	j.	j.	PROPN
ejpam-7095	433	2	pure	pure	PROPN
ejpam-7095	433	3	appl	appl	PROPN
ejpam-7095	433	4	.	.	PROPN
ejpam-7095	433	5	math	math	PROPN
ejpam-7095	433	6	,	,	PUNCT
ejpam-7095	433	7	18	18	NUM
ejpam-7095	433	8	(	(	PUNCT
ejpam-7095	433	9	4	4	NUM
ejpam-7095	433	10	)	)	PUNCT
ejpam-7095	433	11	(	(	PUNCT
ejpam-7095	433	12	2025	2025	NUM
ejpam-7095	433	13	)	)	PUNCT
ejpam-7095	433	14	,	,	PUNCT
ejpam-7095	433	15	7095	7095	NUM
ejpam-7095	433	16	25	25	NUM
ejpam-7095	433	17	of	of	ADP
ejpam-7095	433	18	30	30	NUM
ejpam-7095	433	19	table	table	NOUN
ejpam-7095	433	20	3	3	NUM
ejpam-7095	433	21	:	:	PUNCT
ejpam-7095	433	22	errors	error	NOUN
ejpam-7095	433	23	norms	norm	VERB
ejpam-7095	433	24	for	for	ADP
ejpam-7095	433	25	example	example	NOUN
ejpam-7095	433	26	2	2	NUM
ejpam-7095	433	27	with	with	ADP
ejpam-7095	433	28	varying	vary	VERB
ejpam-7095	433	29	mq	mq	PROPN
ejpam-7095	433	30	,	,	PUNCT
ejpam-7095	433	31	α	α	NOUN
ejpam-7095	433	32	,	,	PUNCT
ejpam-7095	433	33	and	and	CCONJ
ejpam-7095	433	34	n.	n.	PROPN
ejpam-7095	433	35	mq	mq	PROPN
ejpam-7095	433	36	n	n	PROPN
ejpam-7095	433	37	α	α	NOUN
ejpam-7095	433	38	=	=	SYM
ejpam-7095	433	39	1.5	1.5	NUM
ejpam-7095	433	40	α	α	NOUN
ejpam-7095	433	41	=	=	SYM
ejpam-7095	433	42	1.75	1.75	NUM
ejpam-7095	433	43	l∞	l∞	NOUN
ejpam-7095	433	44	c.time(s	c.time(s	PROPN
ejpam-7095	433	45	)	)	PUNCT
ejpam-7095	433	46	l∞	l∞	NOUN
ejpam-7095	433	47	c.time(s	c.time(s	PROPN
ejpam-7095	433	48	)	)	PUNCT
ejpam-7095	433	49	24	24	NUM
ejpam-7095	433	50	729	729	NUM
ejpam-7095	433	51	2.2140×10−9	2.2140×10−9	NUM
ejpam-7095	433	52	1.265030	1.265030	NUM
ejpam-7095	433	53	2.2140×10−9	2.2140×10−9	NOUN
ejpam-7095	433	54	1.013569	1.013569	NUM
ejpam-7095	433	55	1331	1331	NUM
ejpam-7095	433	56	2.2140×10−9	2.2140×10−9	NUM
ejpam-7095	433	57	5.213977	5.213977	NUM
ejpam-7095	433	58	2.2140×10−9	2.2140×10−9	NOUN
ejpam-7095	433	59	4.466417	4.466417	NUM
ejpam-7095	433	60	2197	2197	NUM
ejpam-7095	433	61	2.2140×10−9	2.2140×10−9	NUM
ejpam-7095	433	62	17.880434	17.880434	NUM
ejpam-7095	433	63	2.2140×10−9	2.2140×10−9	NOUN
ejpam-7095	433	64	15.620776	15.620776	NUM
ejpam-7095	433	65	3375	3375	NUM
ejpam-7095	433	66	2.2140×10−9	2.2140×10−9	NOUN
ejpam-7095	433	67	58.898524	58.898524	NUM
ejpam-7095	433	68	2.2140×10−9	2.2140×10−9	NOUN
ejpam-7095	433	69	52.157271	52.157271	NUM
ejpam-7095	433	70	26	26	NUM
ejpam-7095	433	71	1331	1331	NUM
ejpam-7095	433	72	1.7283×10−10	1.7283×10−10	NUM
ejpam-7095	433	73	5.531386	5.531386	NUM
ejpam-7095	433	74	1.7283×10−10	1.7283×10−10	NUM
ejpam-7095	433	75	4.843518	4.843518	NUM
ejpam-7095	433	76	28	28	NUM
ejpam-7095	433	77	3.9919×10−11	3.9919×10−11	NUM
ejpam-7095	433	78	6.134771	6.134771	NUM
ejpam-7095	433	79	3.1216×10−11	3.1216×10−11	NUM
ejpam-7095	433	80	5.339569	5.339569	NUM
ejpam-7095	433	81	30	30	NUM
ejpam-7095	433	82	2.4134×10−11	2.4134×10−11	X
ejpam-7095	433	83	6.425285	6.425285	NUM
ejpam-7095	433	84	1.8025×10−11	1.8025×10−11	NUM
ejpam-7095	433	85	5.591827	5.591827	NUM
ejpam-7095	433	86	32	32	NUM
ejpam-7095	433	87	2.6654×10−11	2.6654×10−11	NUM
ejpam-7095	433	88	5.969752	5.969752	NUM
ejpam-7095	433	89	4.6171×10−11	4.6171×10−11	NUM
ejpam-7095	433	90	6.005012	6.005012	NUM
ejpam-7095	433	91	34	34	NUM
ejpam-7095	433	92	3.5469×10−11	3.5469×10−11	NUM
ejpam-7095	433	93	6.343325	6.343325	NUM
ejpam-7095	433	94	3.9908×10−11	3.9908×10−11	NUM
ejpam-7095	433	95	6.308768	6.308768	NUM
ejpam-7095	433	96	(	(	PUNCT
ejpam-7095	433	97	a	a	NOUN
ejpam-7095	433	98	)	)	PUNCT
ejpam-7095	433	99	(	(	PUNCT
ejpam-7095	433	100	b	b	X
ejpam-7095	433	101	)	)	PUNCT
ejpam-7095	433	102	figure	figure	NOUN
ejpam-7095	433	103	9	9	NUM
ejpam-7095	433	104	:	:	PUNCT
ejpam-7095	433	105	(	(	PUNCT
ejpam-7095	433	106	a	a	X
ejpam-7095	433	107	)	)	PUNCT
ejpam-7095	433	108	the	the	DET
ejpam-7095	433	109	slice	slice	NOUN
ejpam-7095	433	110	plot	plot	NOUN
ejpam-7095	433	111	of	of	ADP
ejpam-7095	433	112	numerical	numerical	ADJ
ejpam-7095	433	113	solution	solution	NOUN
ejpam-7095	433	114	with	with	ADP
ejpam-7095	433	115	n	n	NOUN
ejpam-7095	433	116	=	=	SYM
ejpam-7095	433	117	1331	1331	NUM
ejpam-7095	433	118	,	,	PUNCT
ejpam-7095	433	119	mq	mq	PROPN
ejpam-7095	433	120	=	=	SYM
ejpam-7095	433	121	36	36	NUM
ejpam-7095	433	122	,	,	PUNCT
ejpam-7095	433	123	τ	τ	PROPN
ejpam-7095	433	124	=	=	SYM
ejpam-7095	433	125	1	1	NUM
ejpam-7095	433	126	,	,	PUNCT
ejpam-7095	433	127	and	and	CCONJ
ejpam-7095	433	128	α	α	X
ejpam-7095	433	129	=	=	SYM
ejpam-7095	433	130	1.5	1.5	NUM
ejpam-7095	433	131	(	(	PUNCT
ejpam-7095	433	132	example	example	NOUN
ejpam-7095	433	133	3	3	NUM
ejpam-7095	433	134	)	)	PUNCT
ejpam-7095	433	135	.	.	PUNCT
ejpam-7095	434	1	(	(	PUNCT
ejpam-7095	434	2	b	b	X
ejpam-7095	434	3	)	)	PUNCT
ejpam-7095	434	4	the	the	DET
ejpam-7095	434	5	slice	slice	NOUN
ejpam-7095	434	6	plot	plot	NOUN
ejpam-7095	434	7	of	of	ADP
ejpam-7095	434	8	labs	lab	NOUN
ejpam-7095	434	9	with	with	ADP
ejpam-7095	434	10	n	n	NOUN
ejpam-7095	434	11	=	=	SYM
ejpam-7095	434	12	1331	1331	NUM
ejpam-7095	434	13	,	,	PUNCT
ejpam-7095	434	14	mq	mq	PROPN
ejpam-7095	434	15	=	=	SYM
ejpam-7095	434	16	36	36	NUM
ejpam-7095	434	17	,	,	PUNCT
ejpam-7095	434	18	τ	τ	PROPN
ejpam-7095	434	19	=	=	SYM
ejpam-7095	434	20	1	1	NUM
ejpam-7095	434	21	,	,	PUNCT
ejpam-7095	434	22	and	and	CCONJ
ejpam-7095	434	23	α	α	X
ejpam-7095	434	24	=	=	SYM
ejpam-7095	434	25	1.5	1.5	NUM
ejpam-7095	434	26	(	(	PUNCT
ejpam-7095	434	27	example	example	NOUN
ejpam-7095	434	28	3	3	NUM
ejpam-7095	434	29	)	)	PUNCT
ejpam-7095	434	30	.	.	PUNCT
ejpam-7095	435	1	kamran	kamran	PROPN
ejpam-7095	435	2	et	et	PROPN
ejpam-7095	435	3	al	al	PROPN
ejpam-7095	435	4	.	.	PUNCT
ejpam-7095	435	5	/	/	SYM
ejpam-7095	435	6	eur	eur	PROPN
ejpam-7095	435	7	.	.	PUNCT
ejpam-7095	436	1	j.	j.	PROPN
ejpam-7095	436	2	pure	pure	PROPN
ejpam-7095	436	3	appl	appl	PROPN
ejpam-7095	436	4	.	.	PROPN
ejpam-7095	436	5	math	math	PROPN
ejpam-7095	436	6	,	,	PUNCT
ejpam-7095	436	7	18	18	NUM
ejpam-7095	436	8	(	(	PUNCT
ejpam-7095	436	9	4	4	NUM
ejpam-7095	436	10	)	)	PUNCT
ejpam-7095	436	11	(	(	PUNCT
ejpam-7095	436	12	2025	2025	NUM
ejpam-7095	436	13	)	)	PUNCT
ejpam-7095	436	14	,	,	PUNCT
ejpam-7095	436	15	7095	7095	NUM
ejpam-7095	436	16	26	26	NUM
ejpam-7095	436	17	of	of	ADP
ejpam-7095	436	18	30	30	NUM
ejpam-7095	436	19	(	(	PUNCT
ejpam-7095	436	20	a	a	NOUN
ejpam-7095	436	21	)	)	PUNCT
ejpam-7095	436	22	(	(	PUNCT
ejpam-7095	436	23	b	b	X
ejpam-7095	436	24	)	)	PUNCT
ejpam-7095	436	25	figure	figure	NOUN
ejpam-7095	436	26	10	10	NUM
ejpam-7095	436	27	:	:	PUNCT
ejpam-7095	436	28	(	(	PUNCT
ejpam-7095	436	29	a	a	X
ejpam-7095	436	30	)	)	PUNCT
ejpam-7095	436	31	graph	graph	NOUN
ejpam-7095	436	32	of	of	ADP
ejpam-7095	436	33	l∞	l∞	NOUN
ejpam-7095	436	34	vs	vs	ADP
ejpam-7095	436	35	quadrature	quadrature	NOUN
ejpam-7095	436	36	nodes	node	NOUN
ejpam-7095	436	37	mq	mq	VERB
ejpam-7095	436	38	with	with	ADP
ejpam-7095	436	39	n	n	PROPN
ejpam-7095	436	40	=	=	SYM
ejpam-7095	436	41	1728	1728	NUM
ejpam-7095	436	42	(	(	PUNCT
ejpam-7095	436	43	example	example	NOUN
ejpam-7095	436	44	3	3	NUM
ejpam-7095	436	45	)	)	PUNCT
ejpam-7095	436	46	.	.	PUNCT
ejpam-7095	437	1	(	(	PUNCT
ejpam-7095	437	2	b	b	X
ejpam-7095	437	3	)	)	PUNCT
ejpam-7095	437	4	graph	graph	NOUN
ejpam-7095	437	5	of	of	ADP
ejpam-7095	437	6	l∞	l∞	NOUN
ejpam-7095	437	7	vs	vs	ADP
ejpam-7095	437	8	quadrature	quadrature	NOUN
ejpam-7095	437	9	nodes	node	NOUN
ejpam-7095	437	10	n	n	X
ejpam-7095	437	11	with	with	ADP
ejpam-7095	437	12	mq	mq	PROPN
ejpam-7095	437	13	=	=	SYM
ejpam-7095	437	14	30	30	NUM
ejpam-7095	437	15	(	(	PUNCT
ejpam-7095	437	16	example	example	NOUN
ejpam-7095	437	17	3	3	NUM
ejpam-7095	437	18	)	)	PUNCT
ejpam-7095	437	19	.	.	PUNCT
ejpam-7095	438	1	(	(	PUNCT
ejpam-7095	438	2	a	a	X
ejpam-7095	438	3	)	)	PUNCT
ejpam-7095	438	4	(	(	PUNCT
ejpam-7095	438	5	b	b	X
ejpam-7095	438	6	)	)	PUNCT
ejpam-7095	438	7	figure	figure	NOUN
ejpam-7095	438	8	11	11	NUM
ejpam-7095	438	9	:	:	PUNCT
ejpam-7095	438	10	(	(	PUNCT
ejpam-7095	438	11	a	a	X
ejpam-7095	438	12	)	)	PUNCT
ejpam-7095	438	13	graph	graph	NOUN
ejpam-7095	438	14	of	of	ADP
ejpam-7095	438	15	l∞	l∞	NOUN
ejpam-7095	438	16	vs	vs	ADP
ejpam-7095	438	17	τ	τ	PROPN
ejpam-7095	438	18	with	with	ADP
ejpam-7095	438	19	mq	mq	PROPN
ejpam-7095	438	20	=	=	SYM
ejpam-7095	438	21	36	36	NUM
ejpam-7095	438	22	and	and	CCONJ
ejpam-7095	438	23	n	n	CCONJ
ejpam-7095	438	24	=	=	SYM
ejpam-7095	438	25	1728	1728	NUM
ejpam-7095	438	26	(	(	PUNCT
ejpam-7095	438	27	example	example	NOUN
ejpam-7095	438	28	3	3	NUM
ejpam-7095	438	29	)	)	PUNCT
ejpam-7095	438	30	.	.	PUNCT
ejpam-7095	439	1	(	(	PUNCT
ejpam-7095	439	2	b	b	X
ejpam-7095	439	3	)	)	PUNCT
ejpam-7095	439	4	graph	graph	NOUN
ejpam-7095	439	5	of	of	ADP
ejpam-7095	439	6	l∞	l∞	NOUN
ejpam-7095	439	7	vs	vs	ADP
ejpam-7095	439	8	fractional	fractional	ADJ
ejpam-7095	439	9	order	order	NOUN
ejpam-7095	439	10	α	α	NOUN
ejpam-7095	439	11	with	with	ADP
ejpam-7095	439	12	n	n	NOUN
ejpam-7095	439	13	=	=	SYM
ejpam-7095	439	14	1728	1728	NUM
ejpam-7095	439	15	and	and	CCONJ
ejpam-7095	439	16	mq	mq	PROPN
ejpam-7095	439	17	=	=	SYM
ejpam-7095	439	18	36	36	NUM
ejpam-7095	439	19	(	(	PUNCT
ejpam-7095	439	20	example	example	NOUN
ejpam-7095	439	21	3	3	NUM
ejpam-7095	439	22	)	)	PUNCT
ejpam-7095	439	23	.	.	PUNCT
ejpam-7095	440	1	kamran	kamran	PROPN
ejpam-7095	440	2	et	et	PROPN
ejpam-7095	440	3	al	al	PROPN
ejpam-7095	440	4	.	.	PUNCT
ejpam-7095	440	5	/	/	SYM
ejpam-7095	440	6	eur	eur	PROPN
ejpam-7095	440	7	.	.	PUNCT
ejpam-7095	441	1	j.	j.	PROPN
ejpam-7095	441	2	pure	pure	PROPN
ejpam-7095	441	3	appl	appl	PROPN
ejpam-7095	441	4	.	.	PROPN
ejpam-7095	441	5	math	math	PROPN
ejpam-7095	441	6	,	,	PUNCT
ejpam-7095	441	7	18	18	NUM
ejpam-7095	441	8	(	(	PUNCT
ejpam-7095	441	9	4	4	NUM
ejpam-7095	441	10	)	)	PUNCT
ejpam-7095	441	11	(	(	PUNCT
ejpam-7095	441	12	2025	2025	NUM
ejpam-7095	441	13	)	)	PUNCT
ejpam-7095	441	14	,	,	PUNCT
ejpam-7095	441	15	7095	7095	NUM
ejpam-7095	441	16	27	27	NUM
ejpam-7095	441	17	of	of	ADP
ejpam-7095	441	18	30	30	NUM
ejpam-7095	441	19	(	(	PUNCT
ejpam-7095	441	20	a	a	NOUN
ejpam-7095	441	21	)	)	PUNCT
ejpam-7095	441	22	(	(	PUNCT
ejpam-7095	441	23	b	b	X
ejpam-7095	441	24	)	)	PUNCT
ejpam-7095	441	25	figure	figure	NOUN
ejpam-7095	441	26	12	12	NUM
ejpam-7095	441	27	:	:	PUNCT
ejpam-7095	441	28	(	(	PUNCT
ejpam-7095	441	29	a	a	X
ejpam-7095	441	30	)	)	PUNCT
ejpam-7095	441	31	the	the	DET
ejpam-7095	441	32	graph	graph	NOUN
ejpam-7095	441	33	shows	show	VERB
ejpam-7095	441	34	the	the	DET
ejpam-7095	441	35	l∞	l∞	NOUN
ejpam-7095	441	36	error	error	NOUN
ejpam-7095	441	37	in	in	ADP
ejpam-7095	441	38	τα	τα	NOUN
ejpam-7095	441	39	plane	plane	NOUN
ejpam-7095	441	40	with	with	ADP
ejpam-7095	441	41	mq	mq	PROPN
ejpam-7095	441	42	=	=	SYM
ejpam-7095	441	43	30	30	NUM
ejpam-7095	441	44	and	and	CCONJ
ejpam-7095	441	45	n	n	CCONJ
ejpam-7095	441	46	=	=	SYM
ejpam-7095	441	47	1728	1728	NUM
ejpam-7095	441	48	(	(	PUNCT
ejpam-7095	441	49	example	example	NOUN
ejpam-7095	441	50	3	3	NUM
ejpam-7095	441	51	)	)	PUNCT
ejpam-7095	441	52	.	.	PUNCT
ejpam-7095	442	1	(	(	PUNCT
ejpam-7095	442	2	b	b	X
ejpam-7095	442	3	)	)	PUNCT
ejpam-7095	442	4	contour	contour	NOUN
ejpam-7095	442	5	plot	plot	NOUN
ejpam-7095	442	6	of	of	ADP
ejpam-7095	442	7	l∞	l∞	NOUN
ejpam-7095	442	8	in	in	ADP
ejpam-7095	442	9	τα	τα	NOUN
ejpam-7095	442	10	plane	plane	NOUN
ejpam-7095	442	11	with	with	ADP
ejpam-7095	442	12	mq	mq	PROPN
ejpam-7095	442	13	=	=	SYM
ejpam-7095	442	14	30	30	NUM
ejpam-7095	442	15	and	and	CCONJ
ejpam-7095	442	16	n	n	CCONJ
ejpam-7095	442	17	=	=	SYM
ejpam-7095	442	18	1728	1728	NUM
ejpam-7095	442	19	(	(	PUNCT
ejpam-7095	442	20	example	example	NOUN
ejpam-7095	442	21	3	3	NUM
ejpam-7095	442	22	)	)	PUNCT
ejpam-7095	442	23	.	.	PUNCT
ejpam-7095	443	1	7	7	X
ejpam-7095	443	2	.	.	X
ejpam-7095	443	3	conclusion	conclusion	NOUN
ejpam-7095	443	4	the	the	DET
ejpam-7095	443	5	paper	paper	NOUN
ejpam-7095	443	6	develops	develop	VERB
ejpam-7095	443	7	the	the	PRON
ejpam-7095	443	8	lt	lt	NOUN
ejpam-7095	443	9	based	base	VERB
ejpam-7095	443	10	cscm	cscm	NOUN
ejpam-7095	443	11	method	method	NOUN
ejpam-7095	443	12	for	for	ADP
ejpam-7095	443	13	numerical	numerical	ADJ
ejpam-7095	443	14	modelling	modelling	NOUN
ejpam-7095	443	15	of	of	ADP
ejpam-7095	443	16	timefractional	timefractional	ADJ
ejpam-7095	443	17	wave	wave	NOUN
ejpam-7095	443	18	-	-	PUNCT
ejpam-7095	443	19	diffusion	diffusion	NOUN
ejpam-7095	443	20	equations	equation	NOUN
ejpam-7095	443	21	including	include	VERB
ejpam-7095	443	22	the	the	DET
ejpam-7095	443	23	mabc	mabc	PROPN
ejpam-7095	443	24	derivative	derivative	NOUN
ejpam-7095	443	25	.	.	PUNCT
ejpam-7095	444	1	unlike	unlike	ADP
ejpam-7095	444	2	standard	standard	ADJ
ejpam-7095	444	3	finite	finite	ADJ
ejpam-7095	444	4	difference	difference	NOUN
ejpam-7095	444	5	methods	method	NOUN
ejpam-7095	444	6	,	,	PUNCT
ejpam-7095	444	7	the	the	DET
ejpam-7095	444	8	proposed	propose	VERB
ejpam-7095	444	9	numerical	numerical	PROPN
ejpam-7095	444	10	method	method	PROPN
ejpam-7095	444	11	implements	implement	VERB
ejpam-7095	444	12	the	the	DET
ejpam-7095	444	13	lt	lt	PROPN
ejpam-7095	444	14	and	and	CCONJ
ejpam-7095	444	15	the	the	DET
ejpam-7095	444	16	numerical	numerical	ADJ
ejpam-7095	444	17	inverse	inverse	NOUN
ejpam-7095	444	18	lt	lt	PART
ejpam-7095	444	19	to	to	PART
ejpam-7095	444	20	efficiently	efficiently	ADV
ejpam-7095	444	21	handle	handle	VERB
ejpam-7095	444	22	the	the	DET
ejpam-7095	444	23	time	time	NOUN
ejpam-7095	444	24	-	-	PUNCT
ejpam-7095	444	25	fractional	fractional	ADJ
ejpam-7095	444	26	derivative	derivative	NOUN
ejpam-7095	444	27	.	.	PUNCT
ejpam-7095	445	1	it	it	PRON
ejpam-7095	445	2	first	first	ADV
ejpam-7095	445	3	utilizes	utilize	VERB
ejpam-7095	445	4	the	the	DET
ejpam-7095	445	5	lt	lt	NOUN
ejpam-7095	445	6	to	to	PART
ejpam-7095	445	7	transform	transform	VERB
ejpam-7095	445	8	the	the	DET
ejpam-7095	445	9	considered	consider	VERB
ejpam-7095	445	10	problem	problem	NOUN
ejpam-7095	445	11	into	into	ADP
ejpam-7095	445	12	a	a	DET
ejpam-7095	445	13	time	time	NOUN
ejpam-7095	445	14	-	-	PUNCT
ejpam-7095	445	15	independent	independent	ADJ
ejpam-7095	445	16	inhomogeneous	inhomogeneous	ADJ
ejpam-7095	445	17	problem	problem	NOUN
ejpam-7095	445	18	in	in	ADP
ejpam-7095	445	19	laplace	laplace	NOUN
ejpam-7095	445	20	space	space	NOUN
ejpam-7095	445	21	.	.	PUNCT
ejpam-7095	446	1	then	then	ADV
ejpam-7095	446	2	it	it	PRON
ejpam-7095	446	3	employs	employ	VERB
ejpam-7095	446	4	the	the	DET
ejpam-7095	446	5	cscm	cscm	NOUN
ejpam-7095	446	6	to	to	PART
ejpam-7095	446	7	discretize	discretize	VERB
ejpam-7095	446	8	the	the	DET
ejpam-7095	446	9	spatial	spatial	ADJ
ejpam-7095	446	10	derivatives	derivative	NOUN
ejpam-7095	446	11	of	of	ADP
ejpam-7095	446	12	the	the	DET
ejpam-7095	446	13	transformed	transform	VERB
ejpam-7095	446	14	problem	problem	NOUN
ejpam-7095	446	15	.	.	PUNCT
ejpam-7095	447	1	finally	finally	ADV
ejpam-7095	447	2	,	,	PUNCT
ejpam-7095	447	3	it	it	PRON
ejpam-7095	447	4	uses	use	VERB
ejpam-7095	447	5	the	the	DET
ejpam-7095	447	6	improved	improve	VERB
ejpam-7095	447	7	talbot	talbot	PROPN
ejpam-7095	447	8	method	method	NOUN
ejpam-7095	447	9	to	to	PART
ejpam-7095	447	10	recover	recover	VERB
ejpam-7095	447	11	the	the	DET
ejpam-7095	447	12	timedomain	timedomain	ADJ
ejpam-7095	447	13	solution	solution	NOUN
ejpam-7095	447	14	.	.	PUNCT
ejpam-7095	448	1	compared	compare	VERB
ejpam-7095	448	2	to	to	ADP
ejpam-7095	448	3	conventional	conventional	ADJ
ejpam-7095	448	4	finite	finite	ADJ
ejpam-7095	448	5	difference	difference	NOUN
ejpam-7095	448	6	methods	method	NOUN
ejpam-7095	448	7	,	,	PUNCT
ejpam-7095	448	8	the	the	DET
ejpam-7095	448	9	proposed	propose	VERB
ejpam-7095	448	10	lt	lt	ADJ
ejpam-7095	448	11	-	-	PUNCT
ejpam-7095	448	12	cscm	cscm	ADJ
ejpam-7095	448	13	method	method	NOUN
ejpam-7095	448	14	provides	provide	VERB
ejpam-7095	448	15	two	two	NUM
ejpam-7095	448	16	key	key	ADJ
ejpam-7095	448	17	features	feature	NOUN
ejpam-7095	448	18	:	:	PUNCT
ejpam-7095	448	19	(	(	PUNCT
ejpam-7095	448	20	i	i	NOUN
ejpam-7095	448	21	)	)	PUNCT
ejpam-7095	448	22	elimination	elimination	NOUN
ejpam-7095	448	23	of	of	ADP
ejpam-7095	448	24	computationally	computationally	ADV
ejpam-7095	448	25	expensive	expensive	ADJ
ejpam-7095	448	26	convolution	convolution	NOUN
ejpam-7095	448	27	integrals	integral	NOUN
ejpam-7095	448	28	of	of	ADP
ejpam-7095	448	29	fractional	fractional	ADJ
ejpam-7095	448	30	derivatives	derivative	NOUN
ejpam-7095	448	31	through	through	ADP
ejpam-7095	448	32	lt	lt	PROPN
ejpam-7095	448	33	;	;	PUNCT
ejpam-7095	448	34	and	and	CCONJ
ejpam-7095	448	35	(	(	PUNCT
ejpam-7095	448	36	ii	ii	NOUN
ejpam-7095	448	37	)	)	PUNCT
ejpam-7095	448	38	unconditional	unconditional	ADJ
ejpam-7095	448	39	stability	stability	NOUN
ejpam-7095	448	40	independent	independent	ADJ
ejpam-7095	448	41	of	of	ADP
ejpam-7095	448	42	time	time	NOUN
ejpam-7095	448	43	-	-	PUNCT
ejpam-7095	448	44	stepping	step	VERB
ejpam-7095	448	45	constraints	constraint	NOUN
ejpam-7095	448	46	.	.	PUNCT
ejpam-7095	449	1	the	the	DET
ejpam-7095	449	2	features	feature	NOUN
ejpam-7095	449	3	enable	enable	VERB
ejpam-7095	449	4	efficient	efficient	ADJ
ejpam-7095	449	5	and	and	CCONJ
ejpam-7095	449	6	accurate	accurate	ADJ
ejpam-7095	449	7	long	long	ADJ
ejpam-7095	449	8	-	-	PUNCT
ejpam-7095	449	9	time	time	NOUN
ejpam-7095	449	10	simulation	simulation	NOUN
ejpam-7095	449	11	of	of	ADP
ejpam-7095	449	12	diffusion	diffusion	NOUN
ejpam-7095	449	13	-	-	PUNCT
ejpam-7095	449	14	wave	wave	NOUN
ejpam-7095	449	15	systems	system	NOUN
ejpam-7095	449	16	.	.	PUNCT
ejpam-7095	450	1	the	the	DET
ejpam-7095	450	2	cscm	cscm	NOUN
ejpam-7095	450	3	further	far	ADV
ejpam-7095	450	4	improves	improve	VERB
ejpam-7095	450	5	the	the	DET
ejpam-7095	450	6	method	method	NOUN
ejpam-7095	450	7	’s	’s	PART
ejpam-7095	450	8	efficiency	efficiency	NOUN
ejpam-7095	450	9	for	for	ADP
ejpam-7095	450	10	highdimensional	highdimensional	ADJ
ejpam-7095	450	11	problems	problem	NOUN
ejpam-7095	450	12	,	,	PUNCT
ejpam-7095	450	13	requiring	require	VERB
ejpam-7095	450	14	fewer	few	ADJ
ejpam-7095	450	15	nodes	node	NOUN
ejpam-7095	450	16	while	while	SCONJ
ejpam-7095	450	17	maintaining	maintain	VERB
ejpam-7095	450	18	exponential	exponential	ADJ
ejpam-7095	450	19	convergence	convergence	NOUN
ejpam-7095	450	20	.	.	PUNCT
ejpam-7095	451	1	numerical	numerical	ADJ
ejpam-7095	451	2	experiments	experiment	NOUN
ejpam-7095	451	3	confirm	confirm	VERB
ejpam-7095	451	4	the	the	DET
ejpam-7095	451	5	lt	lt	NOUN
ejpam-7095	451	6	based	base	VERB
ejpam-7095	451	7	cscm	cscm	NOUN
ejpam-7095	451	8	’s	’s	PART
ejpam-7095	451	9	ability	ability	NOUN
ejpam-7095	451	10	to	to	PART
ejpam-7095	451	11	handle	handle	VERB
ejpam-7095	451	12	multi	multi	ADJ
ejpam-7095	451	13	-	-	ADJ
ejpam-7095	451	14	dimensional	dimensional	ADJ
ejpam-7095	451	15	diffusion	diffusion	NOUN
ejpam-7095	451	16	-	-	PUNCT
ejpam-7095	451	17	wave	wave	NOUN
ejpam-7095	451	18	problems	problem	NOUN
ejpam-7095	451	19	.	.	PUNCT
ejpam-7095	452	1	looking	look	VERB
ejpam-7095	452	2	forward	forward	ADV
ejpam-7095	452	3	,	,	PUNCT
ejpam-7095	452	4	the	the	DET
ejpam-7095	452	5	robustness	robustness	NOUN
ejpam-7095	452	6	and	and	CCONJ
ejpam-7095	452	7	efficiency	efficiency	NOUN
ejpam-7095	452	8	of	of	ADP
ejpam-7095	452	9	the	the	DET
ejpam-7095	452	10	lt	lt	NOUN
ejpam-7095	452	11	based	base	VERB
ejpam-7095	452	12	cscm	cscm	NOUN
ejpam-7095	452	13	scheme	scheme	NOUN
ejpam-7095	452	14	make	make	VERB
ejpam-7095	452	15	it	it	PRON
ejpam-7095	452	16	a	a	DET
ejpam-7095	452	17	strong	strong	ADJ
ejpam-7095	452	18	candidate	candidate	NOUN
ejpam-7095	452	19	for	for	ADP
ejpam-7095	452	20	simulating	simulate	VERB
ejpam-7095	452	21	more	more	ADV
ejpam-7095	452	22	complex	complex	ADJ
ejpam-7095	452	23	fractional	fractional	ADJ
ejpam-7095	452	24	dynamical	dynamical	ADJ
ejpam-7095	452	25	systems	system	NOUN
ejpam-7095	452	26	in	in	ADP
ejpam-7095	452	27	applied	apply	VERB
ejpam-7095	452	28	mathematics	mathematic	NOUN
ejpam-7095	452	29	and	and	CCONJ
ejpam-7095	452	30	engineering	engineering	NOUN
ejpam-7095	452	31	.	.	PUNCT
ejpam-7095	453	1	future	future	ADJ
ejpam-7095	453	2	work	work	NOUN
ejpam-7095	453	3	will	will	AUX
ejpam-7095	453	4	focus	focus	VERB
ejpam-7095	453	5	on	on	ADP
ejpam-7095	453	6	adapting	adapt	VERB
ejpam-7095	453	7	this	this	DET
ejpam-7095	453	8	methodology	methodology	NOUN
ejpam-7095	453	9	to	to	PART
ejpam-7095	453	10	solve	solve	VERB
ejpam-7095	453	11	fractional	fractional	ADJ
ejpam-7095	453	12	delay	delay	NOUN
ejpam-7095	453	13	partial	partial	ADJ
ejpam-7095	453	14	differential	differential	NOUN
ejpam-7095	453	15	equations	equation	NOUN
ejpam-7095	453	16	and	and	CCONJ
ejpam-7095	453	17	coupled	couple	VERB
ejpam-7095	453	18	systems	system	NOUN
ejpam-7095	453	19	.	.	PUNCT
ejpam-7095	454	1	kamran	kamran	PROPN
ejpam-7095	454	2	et	et	PROPN
ejpam-7095	454	3	al	al	PROPN
ejpam-7095	454	4	.	.	PUNCT
ejpam-7095	454	5	/	/	SYM
ejpam-7095	454	6	eur	eur	PROPN
ejpam-7095	454	7	.	.	PUNCT
ejpam-7095	455	1	j.	j.	PROPN
ejpam-7095	455	2	pure	pure	PROPN
ejpam-7095	455	3	appl	appl	PROPN
ejpam-7095	455	4	.	.	PROPN
ejpam-7095	455	5	math	math	PROPN
ejpam-7095	455	6	,	,	PUNCT
ejpam-7095	455	7	18	18	NUM
ejpam-7095	455	8	(	(	PUNCT
ejpam-7095	455	9	4	4	NUM
ejpam-7095	455	10	)	)	PUNCT
ejpam-7095	455	11	(	(	PUNCT
ejpam-7095	455	12	2025	2025	NUM
ejpam-7095	455	13	)	)	PUNCT
ejpam-7095	455	14	,	,	PUNCT
ejpam-7095	455	15	7095	7095	NUM
ejpam-7095	455	16	28	28	NUM
ejpam-7095	455	17	of	of	ADP
ejpam-7095	455	18	30	30	NUM
ejpam-7095	455	19	acknowledgements	acknowledgement	NOUN
ejpam-7095	455	20	the	the	DET
ejpam-7095	455	21	authors	author	NOUN
ejpam-7095	455	22	a.	a.	PROPN
ejpam-7095	455	23	aloqaily	aloqaily	ADV
ejpam-7095	455	24	and	and	CCONJ
ejpam-7095	455	25	n.	n.	PROPN
ejpam-7095	455	26	mlaiki	mlaiki	PROPN
ejpam-7095	455	27	would	would	AUX
ejpam-7095	455	28	like	like	VERB
ejpam-7095	455	29	to	to	PART
ejpam-7095	455	30	thank	thank	VERB
ejpam-7095	455	31	prince	prince	PROPN
ejpam-7095	455	32	sultan	sultan	PROPN
ejpam-7095	455	33	university	university	PROPN
ejpam-7095	455	34	for	for	ADP
ejpam-7095	455	35	paying	pay	VERB
ejpam-7095	455	36	the	the	DET
ejpam-7095	455	37	publication	publication	NOUN
ejpam-7095	455	38	fees	fee	NOUN
ejpam-7095	455	39	for	for	ADP
ejpam-7095	455	40	this	this	DET
ejpam-7095	455	41	work	work	NOUN
ejpam-7095	455	42	through	through	ADP
ejpam-7095	455	43	tas	ta	NOUN
ejpam-7095	455	44	lab	lab	NOUN
ejpam-7095	455	45	.	.	PUNCT
ejpam-7095	456	1	competing	compete	VERB
ejpam-7095	456	2	interests	interest	NOUN
ejpam-7095	456	3	there	there	PRON
ejpam-7095	456	4	are	be	VERB
ejpam-7095	456	5	no	no	DET
ejpam-7095	456	6	conflicting	conflict	VERB
ejpam-7095	456	7	interests	interest	NOUN
ejpam-7095	456	8	,	,	PUNCT
ejpam-7095	456	9	according	accord	VERB
ejpam-7095	456	10	to	to	ADP
ejpam-7095	456	11	the	the	DET
ejpam-7095	456	12	authors	author	NOUN
ejpam-7095	456	13	.	.	PUNCT
ejpam-7095	457	1	author	author	NOUN
ejpam-7095	457	2	’s	’s	PART
ejpam-7095	457	3	contributions	contribution	NOUN
ejpam-7095	457	4	each	each	DET
ejpam-7095	457	5	author	author	NOUN
ejpam-7095	457	6	contributed	contribute	VERB
ejpam-7095	457	7	equally	equally	ADV
ejpam-7095	457	8	to	to	ADP
ejpam-7095	457	9	the	the	DET
ejpam-7095	457	10	writing	writing	NOUN
ejpam-7095	457	11	of	of	ADP
ejpam-7095	457	12	this	this	DET
ejpam-7095	457	13	work	work	NOUN
ejpam-7095	457	14	,	,	PUNCT
ejpam-7095	457	15	and	and	CCONJ
ejpam-7095	457	16	they	they	PRON
ejpam-7095	457	17	have	have	AUX
ejpam-7095	457	18	all	all	ADV
ejpam-7095	457	19	read	read	VERB
ejpam-7095	457	20	and	and	CCONJ
ejpam-7095	457	21	approved	approve	VERB
ejpam-7095	457	22	the	the	DET
ejpam-7095	457	23	finished	finished	ADJ
ejpam-7095	457	24	work	work	NOUN
ejpam-7095	457	25	.	.	PUNCT
ejpam-7095	458	1	declarations	declaration	NOUN
ejpam-7095	458	2	ethical	ethical	ADJ
ejpam-7095	458	3	approval	approval	NOUN
ejpam-7095	458	4	not	not	PART
ejpam-7095	458	5	applicable	applicable	ADJ
ejpam-7095	458	6	.	.	PUNCT
ejpam-7095	459	1	funding	fund	VERB
ejpam-7095	459	2	this	this	DET
ejpam-7095	459	3	work	work	NOUN
ejpam-7095	459	4	did	do	AUX
ejpam-7095	459	5	not	not	PART
ejpam-7095	459	6	receive	receive	VERB
ejpam-7095	459	7	any	any	DET
ejpam-7095	459	8	external	external	ADJ
ejpam-7095	459	9	funding	funding	NOUN
ejpam-7095	459	10	.	.	PUNCT
ejpam-7095	460	1	references	reference	NOUN
ejpam-7095	460	2	[	[	X
ejpam-7095	460	3	1	1	NUM
ejpam-7095	460	4	]	]	PUNCT
ejpam-7095	460	5	f.	f.	PROPN
ejpam-7095	460	6	mainardi	mainardi	PROPN
ejpam-7095	460	7	.	.	PUNCT
ejpam-7095	461	1	fractional	fractional	ADJ
ejpam-7095	461	2	calculus	calculus	NOUN
ejpam-7095	461	3	:	:	PUNCT
ejpam-7095	461	4	theory	theory	NOUN
ejpam-7095	461	5	and	and	CCONJ
ejpam-7095	461	6	applications	application	NOUN
ejpam-7095	461	7	.	.	PUNCT
ejpam-7095	462	1	mathematics	mathematic	NOUN
ejpam-7095	462	2	,	,	PUNCT
ejpam-7095	462	3	6(9):145	6(9):145	NUM
ejpam-7095	462	4	,	,	PUNCT
ejpam-7095	462	5	2018	2018	NUM
ejpam-7095	462	6	.	.	PUNCT
ejpam-7095	463	1	[	[	X
ejpam-7095	463	2	2	2	NUM
ejpam-7095	463	3	]	]	PUNCT
ejpam-7095	463	4	i.	i.	NOUN
ejpam-7095	463	5	podlubny	podlubny	PROPN
ejpam-7095	463	6	.	.	PUNCT
ejpam-7095	464	1	fractional	fractional	ADJ
ejpam-7095	464	2	differential	differential	ADJ
ejpam-7095	464	3	equations	equation	NOUN
ejpam-7095	464	4	:	:	PUNCT
ejpam-7095	464	5	an	an	DET
ejpam-7095	464	6	introduction	introduction	NOUN
ejpam-7095	464	7	to	to	ADP
ejpam-7095	464	8	fractional	fractional	ADJ
ejpam-7095	464	9	derivatives	derivative	NOUN
ejpam-7095	464	10	,	,	PUNCT
ejpam-7095	464	11	fractional	fractional	ADJ
ejpam-7095	464	12	differential	differential	ADJ
ejpam-7095	464	13	equations	equation	NOUN
ejpam-7095	464	14	,	,	PUNCT
ejpam-7095	464	15	to	to	ADP
ejpam-7095	464	16	methods	method	NOUN
ejpam-7095	464	17	of	of	ADP
ejpam-7095	464	18	their	their	PRON
ejpam-7095	464	19	solution	solution	NOUN
ejpam-7095	464	20	and	and	CCONJ
ejpam-7095	464	21	some	some	PRON
ejpam-7095	464	22	of	of	ADP
ejpam-7095	464	23	their	their	PRON
ejpam-7095	464	24	applications	application	NOUN
ejpam-7095	464	25	,	,	PUNCT
ejpam-7095	464	26	volume	volume	NOUN
ejpam-7095	464	27	198	198	NUM
ejpam-7095	464	28	.	.	PUNCT
ejpam-7095	465	1	elsevier	elsevier	NOUN
ejpam-7095	465	2	,	,	PUNCT
ejpam-7095	465	3	1998	1998	NUM
ejpam-7095	465	4	.	.	PUNCT
ejpam-7095	466	1	[	[	X
ejpam-7095	466	2	3	3	X
ejpam-7095	466	3	]	]	PUNCT
ejpam-7095	466	4	emad	emad	NOUN
ejpam-7095	466	5	a	a	DET
ejpam-7095	466	6	az	az	PROPN
ejpam-7095	466	7	-	-	PUNCT
ejpam-7095	466	8	zo’bi	zo’bi	PROPN
ejpam-7095	466	9	,	,	PUNCT
ejpam-7095	466	10	qais	qais	NOUN
ejpam-7095	466	11	mm	mm	PROPN
ejpam-7095	466	12	alomari	alomari	PROPN
ejpam-7095	466	13	,	,	PUNCT
ejpam-7095	466	14	kallekh	kallekh	ADJ
ejpam-7095	466	15	afef	afef	NOUN
ejpam-7095	466	16	,	,	PUNCT
ejpam-7095	466	17	and	and	CCONJ
ejpam-7095	466	18	mustafa	mustafa	PROPN
ejpam-7095	466	19	inc	inc	PROPN
ejpam-7095	466	20	.	.	PROPN
ejpam-7095	466	21	dynamics	dynamic	NOUN
ejpam-7095	466	22	of	of	ADP
ejpam-7095	466	23	generalized	generalized	ADJ
ejpam-7095	466	24	time	time	NOUN
ejpam-7095	466	25	-	-	PUNCT
ejpam-7095	466	26	fractional	fractional	ADJ
ejpam-7095	466	27	viscous	viscous	ADJ
ejpam-7095	466	28	-	-	PUNCT
ejpam-7095	466	29	capillarity	capillarity	NOUN
ejpam-7095	466	30	compressible	compressible	ADJ
ejpam-7095	466	31	fluid	fluid	ADJ
ejpam-7095	466	32	model	model	NOUN
ejpam-7095	466	33	.	.	PUNCT
ejpam-7095	467	1	optical	optical	ADJ
ejpam-7095	467	2	and	and	CCONJ
ejpam-7095	467	3	quantum	quantum	ADJ
ejpam-7095	467	4	electronics	electronic	NOUN
ejpam-7095	467	5	,	,	PUNCT
ejpam-7095	467	6	56(4):629	56(4):629	NUM
ejpam-7095	467	7	,	,	PUNCT
ejpam-7095	467	8	2024	2024	NUM
ejpam-7095	467	9	.	.	PUNCT
ejpam-7095	468	1	[	[	X
ejpam-7095	468	2	4	4	NUM
ejpam-7095	468	3	]	]	X
ejpam-7095	468	4	mohammad	mohammad	PROPN
ejpam-7095	468	5	a	a	DET
ejpam-7095	468	6	al	al	PROPN
ejpam-7095	468	7	zubi	zubi	PROPN
ejpam-7095	468	8	,	,	PUNCT
ejpam-7095	468	9	kallekh	kallekh	ADJ
ejpam-7095	468	10	afef	afef	NOUN
ejpam-7095	468	11	,	,	PUNCT
ejpam-7095	468	12	and	and	CCONJ
ejpam-7095	468	13	emad	emad	NOUN
ejpam-7095	468	14	a	a	DET
ejpam-7095	468	15	az	az	PROPN
ejpam-7095	468	16	-	-	PUNCT
ejpam-7095	468	17	zo’bi	zo’bi	PROPN
ejpam-7095	468	18	.	.	PUNCT
ejpam-7095	469	1	assorted	assort	VERB
ejpam-7095	469	2	spatial	spatial	ADJ
ejpam-7095	469	3	optical	optical	ADJ
ejpam-7095	469	4	dynamics	dynamic	NOUN
ejpam-7095	469	5	of	of	ADP
ejpam-7095	469	6	a	a	DET
ejpam-7095	469	7	generalized	generalize	VERB
ejpam-7095	469	8	fractional	fractional	ADJ
ejpam-7095	469	9	quadruple	quadruple	NOUN
ejpam-7095	469	10	nematic	nematic	ADJ
ejpam-7095	469	11	liquid	liquid	NOUN
ejpam-7095	469	12	crystal	crystal	NOUN
ejpam-7095	469	13	system	system	NOUN
ejpam-7095	469	14	in	in	ADP
ejpam-7095	469	15	nonlocal	nonlocal	ADJ
ejpam-7095	469	16	media	medium	NOUN
ejpam-7095	469	17	.	.	PUNCT
ejpam-7095	470	1	symmetry	symmetry	NOUN
ejpam-7095	470	2	,	,	PUNCT
ejpam-7095	470	3	16(6):778	16(6):778	PROPN
ejpam-7095	470	4	,	,	PUNCT
ejpam-7095	470	5	2024	2024	NUM
ejpam-7095	470	6	.	.	PUNCT
ejpam-7095	471	1	[	[	X
ejpam-7095	471	2	5	5	X
ejpam-7095	471	3	]	]	PUNCT
ejpam-7095	471	4	s.	s.	PROPN
ejpam-7095	471	5	g.	g.	PROPN
ejpam-7095	471	6	samko	samko	PROPN
ejpam-7095	471	7	,	,	PUNCT
ejpam-7095	471	8	a.	a.	NOUN
ejpam-7095	471	9	a.	a.	NOUN
ejpam-7095	471	10	kilbas	kilbas	PROPN
ejpam-7095	471	11	,	,	PUNCT
ejpam-7095	471	12	and	and	CCONJ
ejpam-7095	471	13	o.	o.	PROPN
ejpam-7095	471	14	i.	i.	PROPN
ejpam-7095	471	15	marichev	marichev	PROPN
ejpam-7095	471	16	.	.	PUNCT
ejpam-7095	472	1	fractional	fractional	ADJ
ejpam-7095	472	2	integrals	integral	NOUN
ejpam-7095	472	3	and	and	CCONJ
ejpam-7095	472	4	derivatives	derivative	NOUN
ejpam-7095	472	5	:	:	PUNCT
ejpam-7095	472	6	theory	theory	NOUN
ejpam-7095	472	7	and	and	CCONJ
ejpam-7095	472	8	applications	application	NOUN
ejpam-7095	472	9	.	.	PUNCT
ejpam-7095	473	1	gordon	gordon	PROPN
ejpam-7095	473	2	and	and	CCONJ
ejpam-7095	473	3	breach	breach	VERB
ejpam-7095	473	4	science	science	NOUN
ejpam-7095	473	5	publishers	publisher	NOUN
ejpam-7095	473	6	,	,	PUNCT
ejpam-7095	473	7	1993	1993	NUM
ejpam-7095	473	8	.	.	PUNCT
ejpam-7095	474	1	[	[	X
ejpam-7095	474	2	6	6	NUM
ejpam-7095	474	3	]	]	PUNCT
ejpam-7095	474	4	f.	f.	PROPN
ejpam-7095	474	5	mainardi	mainardi	PROPN
ejpam-7095	474	6	.	.	PUNCT
ejpam-7095	475	1	fractional	fractional	ADJ
ejpam-7095	475	2	calculus	calculus	NOUN
ejpam-7095	475	3	and	and	CCONJ
ejpam-7095	475	4	waves	wave	NOUN
ejpam-7095	475	5	in	in	ADP
ejpam-7095	475	6	linear	linear	PROPN
ejpam-7095	475	7	viscoelasticity	viscoelasticity	NOUN
ejpam-7095	475	8	.	.	PUNCT
ejpam-7095	476	1	world	world	PROPN
ejpam-7095	476	2	scientific	scientific	PROPN
ejpam-7095	476	3	,	,	PUNCT
ejpam-7095	476	4	2010	2010	NUM
ejpam-7095	476	5	.	.	PUNCT
ejpam-7095	477	1	[	[	X
ejpam-7095	477	2	7	7	X
ejpam-7095	477	3	]	]	PUNCT
ejpam-7095	477	4	m.	m.	NOUN
ejpam-7095	477	5	al	al	PROPN
ejpam-7095	477	6	-	-	PUNCT
ejpam-7095	477	7	refai	refai	PROPN
ejpam-7095	477	8	and	and	CCONJ
ejpam-7095	477	9	d.	d.	PROPN
ejpam-7095	477	10	baleanu	baleanu	PROPN
ejpam-7095	477	11	.	.	PUNCT
ejpam-7095	478	1	on	on	ADP
ejpam-7095	478	2	an	an	DET
ejpam-7095	478	3	extension	extension	NOUN
ejpam-7095	478	4	of	of	ADP
ejpam-7095	478	5	the	the	DET
ejpam-7095	478	6	operator	operator	NOUN
ejpam-7095	478	7	with	with	ADP
ejpam-7095	478	8	mittag	mittag	ADJ
ejpam-7095	478	9	-	-	PUNCT
ejpam-7095	478	10	leffler	leffler	NOUN
ejpam-7095	478	11	kernel	kernel	NOUN
ejpam-7095	478	12	.	.	PUNCT
ejpam-7095	478	13	fractals	fractal	NOUN
ejpam-7095	478	14	,	,	PUNCT
ejpam-7095	478	15	30(05):2240129	30(05):2240129	NUM
ejpam-7095	478	16	,	,	PUNCT
ejpam-7095	478	17	2022	2022	NUM
ejpam-7095	478	18	.	.	PUNCT
ejpam-7095	479	1	[	[	X
ejpam-7095	479	2	8	8	NUM
ejpam-7095	479	3	]	]	X
ejpam-7095	479	4	n.	n.	PROPN
ejpam-7095	479	5	shimizu	shimizu	PROPN
ejpam-7095	479	6	and	and	CCONJ
ejpam-7095	479	7	w.	w.	PROPN
ejpam-7095	479	8	zhang	zhang	PROPN
ejpam-7095	479	9	.	.	PUNCT
ejpam-7095	480	1	fractional	fractional	PROPN
ejpam-7095	480	2	calculus	calculus	NOUN
ejpam-7095	480	3	approach	approach	NOUN
ejpam-7095	480	4	to	to	ADP
ejpam-7095	480	5	dynamic	dynamic	ADJ
ejpam-7095	480	6	problems	problem	NOUN
ejpam-7095	480	7	of	of	ADP
ejpam-7095	480	8	viscoelastic	viscoelastic	ADJ
ejpam-7095	480	9	materials	material	NOUN
ejpam-7095	480	10	.	.	PUNCT
ejpam-7095	481	1	jsme	jsme	PROPN
ejpam-7095	481	2	international	international	PROPN
ejpam-7095	481	3	journal	journal	PROPN
ejpam-7095	481	4	series	series	PROPN
ejpam-7095	481	5	c	c	PROPN
ejpam-7095	481	6	mechanical	mechanical	PROPN
ejpam-7095	481	7	systems	system	NOUN
ejpam-7095	481	8	,	,	PUNCT
ejpam-7095	481	9	machine	machine	NOUN
ejpam-7095	481	10	elements	element	NOUN
ejpam-7095	481	11	and	and	CCONJ
ejpam-7095	481	12	manufacturing	manufacturing	NOUN
ejpam-7095	481	13	,	,	PUNCT
ejpam-7095	481	14	42(4):825–837	42(4):825–837	PROPN
ejpam-7095	481	15	,	,	PUNCT
ejpam-7095	481	16	1999	1999	NUM
ejpam-7095	481	17	.	.	PUNCT
ejpam-7095	482	1	kamran	kamran	PROPN
ejpam-7095	482	2	et	et	PROPN
ejpam-7095	482	3	al	al	PROPN
ejpam-7095	482	4	.	.	PUNCT
ejpam-7095	482	5	/	/	SYM
ejpam-7095	482	6	eur	eur	PROPN
ejpam-7095	482	7	.	.	PUNCT
ejpam-7095	483	1	j.	j.	PROPN
ejpam-7095	483	2	pure	pure	PROPN
ejpam-7095	483	3	appl	appl	PROPN
ejpam-7095	483	4	.	.	PROPN
ejpam-7095	483	5	math	math	PROPN
ejpam-7095	483	6	,	,	PUNCT
ejpam-7095	483	7	18	18	NUM
ejpam-7095	483	8	(	(	PUNCT
ejpam-7095	483	9	4	4	NUM
ejpam-7095	483	10	)	)	PUNCT
ejpam-7095	483	11	(	(	PUNCT
ejpam-7095	483	12	2025	2025	NUM
ejpam-7095	483	13	)	)	PUNCT
ejpam-7095	483	14	,	,	PUNCT
ejpam-7095	483	15	7095	7095	NUM
ejpam-7095	483	16	29	29	NUM
ejpam-7095	483	17	of	of	ADP
ejpam-7095	483	18	30	30	NUM
ejpam-7095	483	19	[	[	SYM
ejpam-7095	483	20	9	9	NUM
ejpam-7095	483	21	]	]	PUNCT
ejpam-7095	483	22	k.	k.	PROPN
ejpam-7095	483	23	shah	shah	PROPN
ejpam-7095	483	24	,	,	PUNCT
ejpam-7095	483	25	h.	h.	PROPN
ejpam-7095	483	26	khalil	khalil	PROPN
ejpam-7095	483	27	,	,	PUNCT
ejpam-7095	483	28	and	and	CCONJ
ejpam-7095	483	29	r.	r.	PROPN
ejpam-7095	483	30	a.	a.	PROPN
ejpam-7095	483	31	khan	khan	PROPN
ejpam-7095	483	32	.	.	PUNCT
ejpam-7095	484	1	analytical	analytical	ADJ
ejpam-7095	484	2	solutions	solution	NOUN
ejpam-7095	484	3	of	of	ADP
ejpam-7095	484	4	fractional	fractional	ADJ
ejpam-7095	484	5	order	order	NOUN
ejpam-7095	484	6	diffusion	diffusion	NOUN
ejpam-7095	484	7	equations	equation	NOUN
ejpam-7095	484	8	by	by	ADP
ejpam-7095	484	9	natural	natural	ADJ
ejpam-7095	484	10	transform	transform	NOUN
ejpam-7095	484	11	method	method	NOUN
ejpam-7095	484	12	.	.	PUNCT
ejpam-7095	485	1	iranian	iranian	ADJ
ejpam-7095	485	2	journal	journal	PROPN
ejpam-7095	485	3	of	of	ADP
ejpam-7095	485	4	science	science	NOUN
ejpam-7095	485	5	and	and	CCONJ
ejpam-7095	485	6	technology	technology	NOUN
ejpam-7095	485	7	,	,	PUNCT
ejpam-7095	485	8	transactions	transaction	VERB
ejpam-7095	485	9	a	a	DET
ejpam-7095	485	10	:	:	PUNCT
ejpam-7095	485	11	science	science	NOUN
ejpam-7095	485	12	,	,	PUNCT
ejpam-7095	485	13	42(3):1479–1490	42(3):1479–1490	NUM
ejpam-7095	485	14	,	,	PUNCT
ejpam-7095	485	15	2018	2018	NUM
ejpam-7095	485	16	.	.	PUNCT
ejpam-7095	486	1	[	[	X
ejpam-7095	486	2	10	10	NUM
ejpam-7095	486	3	]	]	X
ejpam-7095	486	4	m.	m.	PROPN
ejpam-7095	486	5	caputo	caputo	PROPN
ejpam-7095	486	6	.	.	PUNCT
ejpam-7095	486	7	linear	linear	PROPN
ejpam-7095	486	8	models	model	NOUN
ejpam-7095	486	9	of	of	ADP
ejpam-7095	486	10	dissipation	dissipation	NOUN
ejpam-7095	486	11	whose	whose	DET
ejpam-7095	486	12	q	q	NOUN
ejpam-7095	486	13	is	be	AUX
ejpam-7095	486	14	almost	almost	ADV
ejpam-7095	486	15	frequency	frequency	ADJ
ejpam-7095	486	16	independent	independent	ADJ
ejpam-7095	486	17	.	.	PUNCT
ejpam-7095	486	18	annals	annal	NOUN
ejpam-7095	486	19	of	of	ADP
ejpam-7095	486	20	geophysics	geophysic	NOUN
ejpam-7095	486	21	,	,	PUNCT
ejpam-7095	486	22	19(4):383–393	19(4):383–393	PROPN
ejpam-7095	486	23	,	,	PUNCT
ejpam-7095	486	24	1966	1966	NUM
ejpam-7095	486	25	.	.	PUNCT
ejpam-7095	487	1	[	[	X
ejpam-7095	487	2	11	11	NUM
ejpam-7095	487	3	]	]	PUNCT
ejpam-7095	487	4	m.	m.	NOUN
ejpam-7095	487	5	a.	a.	PROPN
ejpam-7095	487	6	khan	khan	PROPN
ejpam-7095	487	7	and	and	CCONJ
ejpam-7095	487	8	a.	a.	PROPN
ejpam-7095	487	9	atangana	atangana	PROPN
ejpam-7095	487	10	.	.	PUNCT
ejpam-7095	488	1	modeling	model	VERB
ejpam-7095	488	2	the	the	DET
ejpam-7095	488	3	dynamics	dynamic	NOUN
ejpam-7095	488	4	of	of	ADP
ejpam-7095	488	5	hepatitis	hepatitis	PROPN
ejpam-7095	488	6	e	e	NOUN
ejpam-7095	488	7	via	via	ADP
ejpam-7095	488	8	the	the	DET
ejpam-7095	488	9	mab	mab	PROPN
ejpam-7095	488	10	derivative	derivative	NOUN
ejpam-7095	488	11	.	.	PUNCT
ejpam-7095	489	1	journal	journal	PROPN
ejpam-7095	489	2	of	of	ADP
ejpam-7095	489	3	applied	apply	VERB
ejpam-7095	489	4	mathematics	mathematic	NOUN
ejpam-7095	489	5	and	and	CCONJ
ejpam-7095	489	6	computing	computing	NOUN
ejpam-7095	489	7	,	,	PUNCT
ejpam-7095	489	8	55(1	55(1	NOUN
ejpam-7095	489	9	-	-	SYM
ejpam-7095	489	10	2):345–358	2):345–358	NOUN
ejpam-7095	489	11	,	,	PUNCT
ejpam-7095	489	12	2017	2017	NUM
ejpam-7095	489	13	.	.	PUNCT
ejpam-7095	490	1	[	[	X
ejpam-7095	490	2	12	12	NUM
ejpam-7095	490	3	]	]	X
ejpam-7095	490	4	f.	f.	PROPN
ejpam-7095	490	5	haq	haq	PROPN
ejpam-7095	490	6	,	,	PUNCT
ejpam-7095	490	7	k.	k.	PROPN
ejpam-7095	490	8	shah	shah	PROPN
ejpam-7095	490	9	,	,	PUNCT
ejpam-7095	490	10	g.	g.	PROPN
ejpam-7095	490	11	ur	ur	PROPN
ejpam-7095	490	12	rahman	rahman	PROPN
ejpam-7095	490	13	,	,	PUNCT
ejpam-7095	490	14	and	and	CCONJ
ejpam-7095	490	15	m.	m.	PROPN
ejpam-7095	490	16	shahzad	shahzad	PROPN
ejpam-7095	490	17	.	.	PUNCT
ejpam-7095	491	1	numerical	numerical	ADJ
ejpam-7095	491	2	solution	solution	NOUN
ejpam-7095	491	3	of	of	ADP
ejpam-7095	491	4	fractional	fractional	ADJ
ejpam-7095	491	5	order	order	NOUN
ejpam-7095	491	6	smoking	smoking	NOUN
ejpam-7095	491	7	model	model	NOUN
ejpam-7095	491	8	via	via	ADP
ejpam-7095	491	9	laplace	laplace	NOUN
ejpam-7095	491	10	adomian	adomian	NOUN
ejpam-7095	491	11	decomposition	decomposition	NOUN
ejpam-7095	491	12	method	method	NOUN
ejpam-7095	491	13	.	.	PUNCT
ejpam-7095	492	1	alexandria	alexandria	PROPN
ejpam-7095	492	2	engineering	engineering	PROPN
ejpam-7095	492	3	journal	journal	PROPN
ejpam-7095	492	4	,	,	PUNCT
ejpam-7095	492	5	57(2):1061–1069	57(2):1061–1069	NUM
ejpam-7095	492	6	,	,	PUNCT
ejpam-7095	492	7	2018	2018	NUM
ejpam-7095	492	8	.	.	PUNCT
ejpam-7095	493	1	[	[	X
ejpam-7095	493	2	13	13	NUM
ejpam-7095	493	3	]	]	PUNCT
ejpam-7095	493	4	k.	k.	PROPN
ejpam-7095	493	5	shah	shah	PROPN
ejpam-7095	493	6	,	,	PUNCT
ejpam-7095	493	7	m.	m.	NOUN
ejpam-7095	493	8	a.	a.	NOUN
ejpam-7095	493	9	alqudah	alqudah	PROPN
ejpam-7095	493	10	,	,	PUNCT
ejpam-7095	493	11	f.	f.	PROPN
ejpam-7095	493	12	jarad	jarad	PROPN
ejpam-7095	493	13	,	,	PUNCT
ejpam-7095	493	14	and	and	CCONJ
ejpam-7095	493	15	t.	t.	PROPN
ejpam-7095	493	16	abdeljawad	abdeljawad	NOUN
ejpam-7095	493	17	.	.	PUNCT
ejpam-7095	494	1	semi	semi	ADJ
ejpam-7095	494	2	-	-	ADJ
ejpam-7095	494	3	analytical	analytical	ADJ
ejpam-7095	494	4	study	study	NOUN
ejpam-7095	494	5	of	of	ADP
ejpam-7095	494	6	pine	pine	ADJ
ejpam-7095	494	7	wilt	wilt	ADJ
ejpam-7095	494	8	disease	disease	NOUN
ejpam-7095	494	9	model	model	NOUN
ejpam-7095	494	10	with	with	ADP
ejpam-7095	494	11	convex	convex	ADJ
ejpam-7095	494	12	rate	rate	NOUN
ejpam-7095	494	13	under	under	ADP
ejpam-7095	494	14	caputo	caputo	PROPN
ejpam-7095	494	15	-	-	PUNCT
ejpam-7095	494	16	febrizio	febrizio	NOUN
ejpam-7095	494	17	fractional	fractional	ADJ
ejpam-7095	494	18	order	order	NOUN
ejpam-7095	494	19	derivative	derivative	NOUN
ejpam-7095	494	20	.	.	PUNCT
ejpam-7095	495	1	chaos	chaos	NOUN
ejpam-7095	495	2	,	,	PUNCT
ejpam-7095	495	3	solitons	soliton	NOUN
ejpam-7095	495	4	&	&	CCONJ
ejpam-7095	495	5	fractals	fractal	NOUN
ejpam-7095	495	6	,	,	PUNCT
ejpam-7095	495	7	135:109754	135:109754	NUM
ejpam-7095	495	8	,	,	PUNCT
ejpam-7095	495	9	2020	2020	NUM
ejpam-7095	495	10	.	.	PUNCT
ejpam-7095	496	1	[	[	X
ejpam-7095	496	2	14	14	NUM
ejpam-7095	496	3	]	]	X
ejpam-7095	496	4	f.	f.	PROPN
ejpam-7095	496	5	mainardi	mainardi	PROPN
ejpam-7095	496	6	.	.	PUNCT
ejpam-7095	497	1	the	the	DET
ejpam-7095	497	2	fundamental	fundamental	ADJ
ejpam-7095	497	3	solutions	solution	NOUN
ejpam-7095	497	4	for	for	ADP
ejpam-7095	497	5	the	the	DET
ejpam-7095	497	6	fractional	fractional	ADJ
ejpam-7095	497	7	diffusion	diffusion	NOUN
ejpam-7095	497	8	-	-	PUNCT
ejpam-7095	497	9	wave	wave	NOUN
ejpam-7095	497	10	equation	equation	NOUN
ejpam-7095	497	11	.	.	PUNCT
ejpam-7095	498	1	applied	apply	VERB
ejpam-7095	498	2	mathematics	mathematics	NOUN
ejpam-7095	498	3	letters	letter	NOUN
ejpam-7095	498	4	,	,	PUNCT
ejpam-7095	498	5	9(6):23–28	9(6):23–28	NUM
ejpam-7095	498	6	,	,	PUNCT
ejpam-7095	498	7	1996	1996	NUM
ejpam-7095	498	8	.	.	PUNCT
ejpam-7095	499	1	[	[	X
ejpam-7095	499	2	15	15	NUM
ejpam-7095	499	3	]	]	X
ejpam-7095	499	4	o.	o.	PROPN
ejpam-7095	499	5	p.	p.	PROPN
ejpam-7095	499	6	agrawal	agrawal	PROPN
ejpam-7095	499	7	.	.	PUNCT
ejpam-7095	500	1	solution	solution	NOUN
ejpam-7095	500	2	for	for	ADP
ejpam-7095	500	3	a	a	DET
ejpam-7095	500	4	fractional	fractional	ADJ
ejpam-7095	500	5	diffusion	diffusion	NOUN
ejpam-7095	500	6	-	-	PUNCT
ejpam-7095	500	7	wave	wave	NOUN
ejpam-7095	500	8	equation	equation	NOUN
ejpam-7095	500	9	defined	define	VERB
ejpam-7095	500	10	in	in	ADP
ejpam-7095	500	11	a	a	DET
ejpam-7095	500	12	bounded	bounded	ADJ
ejpam-7095	500	13	domain	domain	NOUN
ejpam-7095	500	14	.	.	PUNCT
ejpam-7095	501	1	nonlinear	nonlinear	ADJ
ejpam-7095	501	2	dynamics	dynamic	NOUN
ejpam-7095	501	3	,	,	PUNCT
ejpam-7095	501	4	29:145–155	29:145–155	PROPN
ejpam-7095	501	5	,	,	PUNCT
ejpam-7095	501	6	2002	2002	NUM
ejpam-7095	501	7	.	.	PUNCT
ejpam-7095	502	1	[	[	X
ejpam-7095	502	2	16	16	NUM
ejpam-7095	502	3	]	]	X
ejpam-7095	502	4	j.	j.	PROPN
ejpam-7095	502	5	ren	ren	PROPN
ejpam-7095	502	6	and	and	CCONJ
ejpam-7095	502	7	z.	z.	PROPN
ejpam-7095	502	8	z.	z.	PROPN
ejpam-7095	502	9	sun	sun	PROPN
ejpam-7095	502	10	.	.	PUNCT
ejpam-7095	503	1	efficient	efficient	PROPN
ejpam-7095	503	2	numerical	numerical	ADJ
ejpam-7095	503	3	solution	solution	NOUN
ejpam-7095	503	4	of	of	ADP
ejpam-7095	503	5	the	the	DET
ejpam-7095	503	6	multi	multi	ADJ
ejpam-7095	503	7	-	-	ADJ
ejpam-7095	503	8	term	term	ADJ
ejpam-7095	503	9	time	time	NOUN
ejpam-7095	503	10	fractional	fractional	ADJ
ejpam-7095	503	11	diffusion	diffusion	NOUN
ejpam-7095	503	12	wave	wave	NOUN
ejpam-7095	503	13	equation	equation	NOUN
ejpam-7095	503	14	.	.	PUNCT
ejpam-7095	504	1	east	east	ADJ
ejpam-7095	504	2	asian	asian	PROPN
ejpam-7095	504	3	journal	journal	PROPN
ejpam-7095	504	4	on	on	ADP
ejpam-7095	504	5	applied	applied	ADJ
ejpam-7095	504	6	mathematics	mathematic	NOUN
ejpam-7095	504	7	,	,	PUNCT
ejpam-7095	504	8	5(1):1–28	5(1):1–28	PROPN
ejpam-7095	504	9	,	,	PUNCT
ejpam-7095	504	10	2015	2015	NUM
ejpam-7095	504	11	.	.	PUNCT
ejpam-7095	505	1	[	[	X
ejpam-7095	505	2	17	17	NUM
ejpam-7095	505	3	]	]	X
ejpam-7095	505	4	f.	f.	PROPN
ejpam-7095	505	5	liu	liu	PROPN
ejpam-7095	505	6	,	,	PUNCT
ejpam-7095	505	7	m.	m.	NOUN
ejpam-7095	505	8	meerschaert	meerschaert	PROPN
ejpam-7095	505	9	,	,	PUNCT
ejpam-7095	505	10	r.	r.	PROPN
ejpam-7095	505	11	mcgough	mcgough	PROPN
ejpam-7095	505	12	,	,	PUNCT
ejpam-7095	505	13	p.	p.	PROPN
ejpam-7095	505	14	zhuang	zhuang	PROPN
ejpam-7095	505	15	,	,	PUNCT
ejpam-7095	505	16	and	and	CCONJ
ejpam-7095	505	17	q.	q.	PROPN
ejpam-7095	505	18	liu	liu	PROPN
ejpam-7095	505	19	.	.	PROPN
ejpam-7095	506	1	numerical	numerical	ADJ
ejpam-7095	506	2	methods	method	NOUN
ejpam-7095	506	3	for	for	ADP
ejpam-7095	506	4	solving	solve	VERB
ejpam-7095	506	5	the	the	DET
ejpam-7095	506	6	multi	multi	ADJ
ejpam-7095	506	7	-	-	ADJ
ejpam-7095	506	8	term	term	ADJ
ejpam-7095	506	9	time	time	NOUN
ejpam-7095	506	10	-	-	PUNCT
ejpam-7095	506	11	fractional	fractional	ADJ
ejpam-7095	506	12	wave	wave	NOUN
ejpam-7095	506	13	-	-	PUNCT
ejpam-7095	506	14	diffusion	diffusion	NOUN
ejpam-7095	506	15	equation	equation	NOUN
ejpam-7095	506	16	.	.	PUNCT
ejpam-7095	507	1	fractional	fractional	ADJ
ejpam-7095	507	2	calculus	calculus	NOUN
ejpam-7095	507	3	and	and	CCONJ
ejpam-7095	507	4	applied	apply	VERB
ejpam-7095	507	5	analysis	analysis	NOUN
ejpam-7095	507	6	,	,	PUNCT
ejpam-7095	507	7	16(1):9–25	16(1):9–25	NUM
ejpam-7095	507	8	,	,	PUNCT
ejpam-7095	507	9	2013	2013	NUM
ejpam-7095	507	10	.	.	PUNCT
ejpam-7095	508	1	[	[	X
ejpam-7095	508	2	18	18	NUM
ejpam-7095	508	3	]	]	X
ejpam-7095	508	4	y.	y.	PROPN
ejpam-7095	508	5	n.	n.	PROPN
ejpam-7095	508	6	zhang	zhang	PROPN
ejpam-7095	508	7	,	,	PUNCT
ejpam-7095	508	8	z.	z.	PROPN
ejpam-7095	508	9	z.	z.	PROPN
ejpam-7095	508	10	sun	sun	PROPN
ejpam-7095	508	11	,	,	PUNCT
ejpam-7095	508	12	and	and	CCONJ
ejpam-7095	508	13	x.	x.	PROPN
ejpam-7095	508	14	zhao	zhao	PROPN
ejpam-7095	508	15	.	.	PUNCT
ejpam-7095	509	1	compact	compact	ADJ
ejpam-7095	509	2	alternating	alternating	NOUN
ejpam-7095	509	3	direction	direction	NOUN
ejpam-7095	509	4	implicit	implicit	ADJ
ejpam-7095	509	5	scheme	scheme	NOUN
ejpam-7095	509	6	for	for	ADP
ejpam-7095	509	7	the	the	DET
ejpam-7095	509	8	two	two	NUM
ejpam-7095	509	9	-	-	PUNCT
ejpam-7095	509	10	dimensional	dimensional	ADJ
ejpam-7095	509	11	fractional	fractional	ADJ
ejpam-7095	509	12	diffusion	diffusion	NOUN
ejpam-7095	509	13	-	-	PUNCT
ejpam-7095	509	14	wave	wave	NOUN
ejpam-7095	509	15	equation	equation	NOUN
ejpam-7095	509	16	.	.	PUNCT
ejpam-7095	510	1	siam	siam	PROPN
ejpam-7095	510	2	journal	journal	PROPN
ejpam-7095	510	3	on	on	ADP
ejpam-7095	510	4	numerical	numerical	ADJ
ejpam-7095	510	5	analysis	analysis	NOUN
ejpam-7095	510	6	,	,	PUNCT
ejpam-7095	510	7	50(3):1535–1555	50(3):1535–1555	NUM
ejpam-7095	510	8	,	,	PUNCT
ejpam-7095	510	9	2012	2012	NUM
ejpam-7095	510	10	.	.	PUNCT
ejpam-7095	511	1	[	[	X
ejpam-7095	511	2	19	19	NUM
ejpam-7095	511	3	]	]	X
ejpam-7095	511	4	r.	r.	PROPN
ejpam-7095	511	5	salehi	salehi	PROPN
ejpam-7095	511	6	.	.	PUNCT
ejpam-7095	512	1	a	a	DET
ejpam-7095	512	2	meshless	meshless	ADJ
ejpam-7095	512	3	point	point	NOUN
ejpam-7095	512	4	collocation	collocation	NOUN
ejpam-7095	512	5	method	method	NOUN
ejpam-7095	512	6	for	for	ADP
ejpam-7095	512	7	2	2	NUM
ejpam-7095	512	8	-	-	PUNCT
ejpam-7095	512	9	d	d	NOUN
ejpam-7095	512	10	multi	multi	ADJ
ejpam-7095	512	11	-	-	ADJ
ejpam-7095	512	12	term	term	ADJ
ejpam-7095	512	13	time	time	NOUN
ejpam-7095	512	14	fractional	fractional	ADJ
ejpam-7095	512	15	diffusion	diffusion	NOUN
ejpam-7095	512	16	-	-	PUNCT
ejpam-7095	512	17	wave	wave	NOUN
ejpam-7095	512	18	equation	equation	NOUN
ejpam-7095	512	19	.	.	PUNCT
ejpam-7095	513	1	numerical	numerical	ADJ
ejpam-7095	513	2	algorithms	algorithms	PROPN
ejpam-7095	513	3	,	,	PUNCT
ejpam-7095	513	4	74:1145–1168	74:1145–1168	PROPN
ejpam-7095	513	5	,	,	PUNCT
ejpam-7095	513	6	2017	2017	NUM
ejpam-7095	513	7	.	.	PUNCT
ejpam-7095	514	1	[	[	X
ejpam-7095	514	2	20	20	NUM
ejpam-7095	514	3	]	]	PUNCT
ejpam-7095	514	4	a.	a.	NOUN
ejpam-7095	514	5	h.	h.	PROPN
ejpam-7095	514	6	bhrawy	bhrawy	PROPN
ejpam-7095	514	7	,	,	PUNCT
ejpam-7095	514	8	e.	e.	PROPN
ejpam-7095	514	9	h.	h.	PROPN
ejpam-7095	514	10	doha	doha	PROPN
ejpam-7095	514	11	,	,	PUNCT
ejpam-7095	514	12	d.	d.	PROPN
ejpam-7095	514	13	baleanu	baleanu	PROPN
ejpam-7095	514	14	,	,	PUNCT
ejpam-7095	514	15	and	and	CCONJ
ejpam-7095	514	16	s.	s.	PROPN
ejpam-7095	514	17	s.	s.	PROPN
ejpam-7095	514	18	ezz	ezz	PROPN
ejpam-7095	514	19	-	-	PUNCT
ejpam-7095	514	20	eldien	eldien	NOUN
ejpam-7095	514	21	.	.	PUNCT
ejpam-7095	515	1	a	a	DET
ejpam-7095	515	2	spectral	spectral	ADJ
ejpam-7095	515	3	tau	tau	PROPN
ejpam-7095	515	4	algorithm	algorithm	NOUN
ejpam-7095	515	5	based	base	VERB
ejpam-7095	515	6	on	on	ADP
ejpam-7095	515	7	jacobi	jacobi	PROPN
ejpam-7095	515	8	operational	operational	ADJ
ejpam-7095	515	9	matrix	matrix	NOUN
ejpam-7095	515	10	for	for	ADP
ejpam-7095	515	11	numerical	numerical	ADJ
ejpam-7095	515	12	solution	solution	NOUN
ejpam-7095	515	13	of	of	ADP
ejpam-7095	515	14	time	time	NOUN
ejpam-7095	515	15	fractional	fractional	ADJ
ejpam-7095	515	16	diffusionwave	diffusionwave	NOUN
ejpam-7095	515	17	equations	equation	NOUN
ejpam-7095	515	18	.	.	PUNCT
ejpam-7095	516	1	journal	journal	NOUN
ejpam-7095	516	2	of	of	ADP
ejpam-7095	516	3	computational	computational	ADJ
ejpam-7095	516	4	physics	physics	NOUN
ejpam-7095	516	5	,	,	PUNCT
ejpam-7095	516	6	293:142–156	293:142–156	NUM
ejpam-7095	516	7	,	,	PUNCT
ejpam-7095	516	8	2015	2015	NUM
ejpam-7095	516	9	.	.	PUNCT
ejpam-7095	517	1	[	[	X
ejpam-7095	517	2	21	21	NUM
ejpam-7095	517	3	]	]	X
ejpam-7095	517	4	y.	y.	PROPN
ejpam-7095	517	5	yang	yang	PROPN
ejpam-7095	517	6	,	,	PUNCT
ejpam-7095	517	7	y.	y.	PROPN
ejpam-7095	517	8	chen	chen	PROPN
ejpam-7095	517	9	,	,	PUNCT
ejpam-7095	517	10	y.	y.	PROPN
ejpam-7095	517	11	huang	huang	PROPN
ejpam-7095	517	12	,	,	PUNCT
ejpam-7095	517	13	and	and	CCONJ
ejpam-7095	517	14	h.	h.	PROPN
ejpam-7095	517	15	wei	wei	PROPN
ejpam-7095	517	16	.	.	PUNCT
ejpam-7095	517	17	spectral	spectral	ADJ
ejpam-7095	517	18	collocation	collocation	NOUN
ejpam-7095	517	19	method	method	NOUN
ejpam-7095	517	20	for	for	ADP
ejpam-7095	517	21	the	the	DET
ejpam-7095	517	22	timefractional	timefractional	ADJ
ejpam-7095	517	23	diffusion	diffusion	NOUN
ejpam-7095	517	24	-	-	PUNCT
ejpam-7095	517	25	wave	wave	NOUN
ejpam-7095	517	26	equation	equation	NOUN
ejpam-7095	517	27	and	and	CCONJ
ejpam-7095	517	28	convergence	convergence	NOUN
ejpam-7095	517	29	analysis	analysis	NOUN
ejpam-7095	517	30	.	.	PUNCT
ejpam-7095	518	1	computers	computer	NOUN
ejpam-7095	518	2	&	&	CCONJ
ejpam-7095	518	3	mathematics	mathematics	PROPN
ejpam-7095	518	4	with	with	ADP
ejpam-7095	518	5	applications	application	NOUN
ejpam-7095	518	6	,	,	PUNCT
ejpam-7095	518	7	73(6):1218–1232	73(6):1218–1232	NOUN
ejpam-7095	518	8	,	,	PUNCT
ejpam-7095	518	9	2017	2017	NUM
ejpam-7095	518	10	.	.	PUNCT
ejpam-7095	519	1	[	[	X
ejpam-7095	519	2	22	22	NUM
ejpam-7095	519	3	]	]	PUNCT
ejpam-7095	519	4	m.	m.	NOUN
ejpam-7095	519	5	h.	h.	PROPN
ejpam-7095	519	6	heydari	heydari	PROPN
ejpam-7095	519	7	,	,	PUNCT
ejpam-7095	519	8	m.	m.	PROPN
ejpam-7095	519	9	r.	r.	PROPN
ejpam-7095	519	10	hooshmandasl	hooshmandasl	PROPN
ejpam-7095	519	11	,	,	PUNCT
ejpam-7095	519	12	f.	f.	PROPN
ejpam-7095	519	13	m.	m.	PROPN
ejpam-7095	519	14	ghaini	ghaini	PROPN
ejpam-7095	519	15	,	,	PUNCT
ejpam-7095	519	16	and	and	CCONJ
ejpam-7095	519	17	c.	c.	PROPN
ejpam-7095	519	18	cattani	cattani	PROPN
ejpam-7095	519	19	.	.	PUNCT
ejpam-7095	520	1	wavelets	wavelet	NOUN
ejpam-7095	520	2	method	method	VERB
ejpam-7095	520	3	for	for	ADP
ejpam-7095	520	4	the	the	DET
ejpam-7095	520	5	time	time	NOUN
ejpam-7095	520	6	fractional	fractional	ADJ
ejpam-7095	520	7	diffusion	diffusion	NOUN
ejpam-7095	520	8	-	-	PUNCT
ejpam-7095	520	9	wave	wave	NOUN
ejpam-7095	520	10	equation	equation	NOUN
ejpam-7095	520	11	.	.	PUNCT
ejpam-7095	521	1	physics	physics	NOUN
ejpam-7095	521	2	letters	letter	NOUN
ejpam-7095	521	3	a	a	PRON
ejpam-7095	521	4	,	,	PUNCT
ejpam-7095	521	5	379(3):71–76	379(3):71–76	NUM
ejpam-7095	521	6	,	,	PUNCT
ejpam-7095	521	7	2015	2015	NUM
ejpam-7095	521	8	.	.	PUNCT
ejpam-7095	522	1	[	[	X
ejpam-7095	522	2	23	23	NUM
ejpam-7095	522	3	]	]	X
ejpam-7095	522	4	f.	f.	PROPN
ejpam-7095	522	5	a.	a.	PROPN
ejpam-7095	522	6	shah	shah	PROPN
ejpam-7095	522	7	,	,	PUNCT
ejpam-7095	522	8	kamran	kamran	PROPN
ejpam-7095	522	9	,	,	PUNCT
ejpam-7095	522	10	z.	z.	PROPN
ejpam-7095	522	11	a.	a.	PROPN
ejpam-7095	522	12	khan	khan	PROPN
ejpam-7095	522	13	,	,	PUNCT
ejpam-7095	522	14	f.	f.	PROPN
ejpam-7095	522	15	azmi	azmi	PROPN
ejpam-7095	522	16	,	,	PUNCT
ejpam-7095	522	17	and	and	CCONJ
ejpam-7095	522	18	n.	n.	PROPN
ejpam-7095	522	19	mlaiki	mlaiki	PROPN
ejpam-7095	522	20	.	.	PUNCT
ejpam-7095	523	1	a	a	DET
ejpam-7095	523	2	hybrid	hybrid	ADJ
ejpam-7095	523	3	collocation	collocation	NOUN
ejpam-7095	523	4	method	method	NOUN
ejpam-7095	523	5	for	for	ADP
ejpam-7095	523	6	the	the	DET
ejpam-7095	523	7	approximation	approximation	NOUN
ejpam-7095	523	8	of	of	ADP
ejpam-7095	523	9	2d	2d	NUM
ejpam-7095	523	10	time	time	NOUN
ejpam-7095	523	11	fractional	fractional	ADJ
ejpam-7095	523	12	diffusion	diffusion	NOUN
ejpam-7095	523	13	-	-	PUNCT
ejpam-7095	523	14	wave	wave	NOUN
ejpam-7095	523	15	equation	equation	NOUN
ejpam-7095	523	16	.	.	PUNCT
ejpam-7095	524	1	aims	aim	VERB
ejpam-7095	524	2	mathematics	mathematic	NOUN
ejpam-7095	524	3	,	,	PUNCT
ejpam-7095	524	4	9(10):27122–27149	9(10):27122–27149	NUM
ejpam-7095	524	5	,	,	PUNCT
ejpam-7095	524	6	2024	2024	NUM
ejpam-7095	524	7	.	.	PUNCT
ejpam-7095	525	1	[	[	X
ejpam-7095	525	2	24	24	NUM
ejpam-7095	525	3	]	]	PUNCT
ejpam-7095	525	4	m.	m.	NOUN
ejpam-7095	525	5	dehghan	dehghan	PROPN
ejpam-7095	525	6	,	,	PUNCT
ejpam-7095	525	7	m.	m.	NOUN
ejpam-7095	525	8	safarpoor	safarpoor	PROPN
ejpam-7095	525	9	,	,	PUNCT
ejpam-7095	525	10	and	and	CCONJ
ejpam-7095	525	11	m.	m.	NOUN
ejpam-7095	525	12	abbaszadeh	abbaszadeh	PROPN
ejpam-7095	525	13	.	.	PUNCT
ejpam-7095	526	1	two	two	NUM
ejpam-7095	526	2	high	high	ADJ
ejpam-7095	526	3	-	-	PUNCT
ejpam-7095	526	4	order	order	NOUN
ejpam-7095	526	5	numerical	numerical	ADJ
ejpam-7095	526	6	algorithms	algorithm	NOUN
ejpam-7095	526	7	for	for	ADP
ejpam-7095	526	8	solving	solve	VERB
ejpam-7095	526	9	the	the	DET
ejpam-7095	526	10	multi	multi	ADJ
ejpam-7095	526	11	-	-	ADJ
ejpam-7095	526	12	term	term	ADJ
ejpam-7095	526	13	time	time	NOUN
ejpam-7095	526	14	fractional	fractional	ADJ
ejpam-7095	526	15	diffusion	diffusion	NOUN
ejpam-7095	526	16	-	-	PUNCT
ejpam-7095	526	17	wave	wave	NOUN
ejpam-7095	526	18	equations	equation	NOUN
ejpam-7095	526	19	.	.	PUNCT
ejpam-7095	527	1	journal	journal	NOUN
ejpam-7095	527	2	of	of	ADP
ejpam-7095	527	3	computational	computational	ADJ
ejpam-7095	527	4	and	and	CCONJ
ejpam-7095	527	5	applied	applied	ADJ
ejpam-7095	527	6	mathematics	mathematic	NOUN
ejpam-7095	527	7	,	,	PUNCT
ejpam-7095	527	8	290:174–195	290:174–195	NUM
ejpam-7095	527	9	,	,	PUNCT
ejpam-7095	527	10	2015	2015	NUM
ejpam-7095	527	11	.	.	PUNCT
ejpam-7095	528	1	[	[	X
ejpam-7095	528	2	25	25	NUM
ejpam-7095	528	3	]	]	PUNCT
ejpam-7095	528	4	j.	j.	PROPN
ejpam-7095	528	5	y.	y.	PROPN
ejpam-7095	528	6	yang	yang	PROPN
ejpam-7095	528	7	,	,	PUNCT
ejpam-7095	528	8	j.	j.	PROPN
ejpam-7095	528	9	f.	f.	PROPN
ejpam-7095	528	10	huang	huang	PROPN
ejpam-7095	528	11	,	,	PUNCT
ejpam-7095	528	12	d.	d.	PROPN
ejpam-7095	528	13	m.	m.	PROPN
ejpam-7095	528	14	liang	liang	PROPN
ejpam-7095	528	15	,	,	PUNCT
ejpam-7095	528	16	and	and	CCONJ
ejpam-7095	528	17	y.	y.	PROPN
ejpam-7095	528	18	f.	f.	PROPN
ejpam-7095	528	19	tang	tang	PROPN
ejpam-7095	528	20	.	.	PUNCT
ejpam-7095	529	1	numerical	numerical	ADJ
ejpam-7095	529	2	solution	solution	NOUN
ejpam-7095	529	3	of	of	ADP
ejpam-7095	529	4	fractional	fractional	ADJ
ejpam-7095	529	5	diffusion	diffusion	NOUN
ejpam-7095	529	6	-	-	PUNCT
ejpam-7095	529	7	wave	wave	NOUN
ejpam-7095	529	8	equation	equation	NOUN
ejpam-7095	529	9	based	base	VERB
ejpam-7095	529	10	on	on	ADP
ejpam-7095	529	11	fractional	fractional	ADJ
ejpam-7095	529	12	multistep	multistep	ADJ
ejpam-7095	529	13	method	method	NOUN
ejpam-7095	529	14	.	.	PUNCT
ejpam-7095	530	1	applied	apply	VERB
ejpam-7095	530	2	mathematical	mathematical	ADJ
ejpam-7095	530	3	kamran	kamran	PROPN
ejpam-7095	530	4	et	et	PROPN
ejpam-7095	530	5	al	al	PROPN
ejpam-7095	530	6	.	.	PUNCT
ejpam-7095	530	7	/	/	SYM
ejpam-7095	530	8	eur	eur	PROPN
ejpam-7095	530	9	.	.	PUNCT
ejpam-7095	531	1	j.	j.	PROPN
ejpam-7095	531	2	pure	pure	PROPN
ejpam-7095	531	3	appl	appl	PROPN
ejpam-7095	531	4	.	.	PROPN
ejpam-7095	531	5	math	math	PROPN
ejpam-7095	531	6	,	,	PUNCT
ejpam-7095	531	7	18	18	NUM
ejpam-7095	531	8	(	(	PUNCT
ejpam-7095	531	9	4	4	NUM
ejpam-7095	531	10	)	)	PUNCT
ejpam-7095	531	11	(	(	PUNCT
ejpam-7095	531	12	2025	2025	NUM
ejpam-7095	531	13	)	)	PUNCT
ejpam-7095	531	14	,	,	PUNCT
ejpam-7095	531	15	7095	7095	NUM
ejpam-7095	531	16	30	30	NUM
ejpam-7095	531	17	of	of	ADP
ejpam-7095	531	18	30	30	NUM
ejpam-7095	531	19	modelling	modelling	NOUN
ejpam-7095	531	20	,	,	PUNCT
ejpam-7095	531	21	38(14):3652–3661	38(14):3652–3661	NUM
ejpam-7095	531	22	,	,	PUNCT
ejpam-7095	531	23	2014	2014	NUM
ejpam-7095	531	24	.	.	PUNCT
ejpam-7095	532	1	[	[	X
ejpam-7095	532	2	26	26	NUM
ejpam-7095	532	3	]	]	X
ejpam-7095	532	4	b.	b.	PROPN
ejpam-7095	532	5	l.	l.	PROPN
ejpam-7095	532	6	buzbee	buzbee	PROPN
ejpam-7095	532	7	,	,	PUNCT
ejpam-7095	532	8	g.	g.	PROPN
ejpam-7095	532	9	h.	h.	PROPN
ejpam-7095	532	10	golub	golub	PROPN
ejpam-7095	532	11	,	,	PUNCT
ejpam-7095	532	12	and	and	CCONJ
ejpam-7095	532	13	c.	c.	PROPN
ejpam-7095	532	14	w.	w.	PROPN
ejpam-7095	532	15	nielson	nielson	PROPN
ejpam-7095	532	16	.	.	PUNCT
ejpam-7095	533	1	on	on	ADP
ejpam-7095	533	2	direct	direct	ADJ
ejpam-7095	533	3	methods	method	NOUN
ejpam-7095	533	4	for	for	ADP
ejpam-7095	533	5	solving	solve	VERB
ejpam-7095	533	6	poisson	poisson	NOUN
ejpam-7095	533	7	’s	’s	PART
ejpam-7095	533	8	equations	equation	NOUN
ejpam-7095	533	9	.	.	PUNCT
ejpam-7095	534	1	siam	siam	PROPN
ejpam-7095	534	2	journal	journal	PROPN
ejpam-7095	534	3	on	on	ADP
ejpam-7095	534	4	numerical	numerical	ADJ
ejpam-7095	534	5	analysis	analysis	NOUN
ejpam-7095	534	6	,	,	PUNCT
ejpam-7095	534	7	7(4):627–656	7(4):627–656	NOUN
ejpam-7095	534	8	,	,	PUNCT
ejpam-7095	534	9	1970	1970	NUM
ejpam-7095	534	10	.	.	PUNCT
ejpam-7095	535	1	[	[	X
ejpam-7095	535	2	27	27	NUM
ejpam-7095	535	3	]	]	PUNCT
ejpam-7095	535	4	j.	j.	PROPN
ejpam-7095	535	5	p.	p.	PROPN
ejpam-7095	535	6	boyd	boyd	PROPN
ejpam-7095	535	7	.	.	PUNCT
ejpam-7095	536	1	chebyshev	chebyshev	PROPN
ejpam-7095	536	2	and	and	CCONJ
ejpam-7095	536	3	fourier	fourier	ADJ
ejpam-7095	536	4	spectral	spectral	ADJ
ejpam-7095	536	5	methods	method	NOUN
ejpam-7095	536	6	.	.	PUNCT
ejpam-7095	537	1	dover	dover	PROPN
ejpam-7095	537	2	publications	publications	PROPN
ejpam-7095	537	3	,	,	PUNCT
ejpam-7095	537	4	2001	2001	NUM
ejpam-7095	537	5	.	.	PUNCT
ejpam-7095	538	1	[	[	X
ejpam-7095	538	2	28	28	NUM
ejpam-7095	538	3	]	]	X
ejpam-7095	538	4	c.	c.	PROPN
ejpam-7095	538	5	canuto	canuto	PROPN
ejpam-7095	538	6	,	,	PUNCT
ejpam-7095	538	7	m.	m.	PROPN
ejpam-7095	538	8	y.	y.	PROPN
ejpam-7095	538	9	hussaini	hussaini	PROPN
ejpam-7095	538	10	,	,	PUNCT
ejpam-7095	538	11	a.	a.	NOUN
ejpam-7095	538	12	quarteroni	quarteroni	NOUN
ejpam-7095	538	13	,	,	PUNCT
ejpam-7095	538	14	and	and	CCONJ
ejpam-7095	538	15	t.	t.	PROPN
ejpam-7095	538	16	a.	a.	PROPN
ejpam-7095	538	17	zang	zang	PROPN
ejpam-7095	538	18	.	.	PUNCT
ejpam-7095	539	1	spectral	spectral	ADJ
ejpam-7095	539	2	methods	method	NOUN
ejpam-7095	539	3	:	:	PUNCT
ejpam-7095	539	4	fundamentals	fundamental	NOUN
ejpam-7095	539	5	in	in	ADP
ejpam-7095	539	6	single	single	ADJ
ejpam-7095	539	7	domains	domain	NOUN
ejpam-7095	539	8	.	.	PUNCT
ejpam-7095	540	1	springer	springer	NOUN
ejpam-7095	540	2	science	science	PROPN
ejpam-7095	540	3	&	&	CCONJ
ejpam-7095	540	4	business	business	NOUN
ejpam-7095	540	5	media	medium	NOUN
ejpam-7095	540	6	,	,	PUNCT
ejpam-7095	540	7	2006	2006	NUM
ejpam-7095	540	8	.	.	PUNCT
ejpam-7095	541	1	[	[	X
ejpam-7095	541	2	29	29	NUM
ejpam-7095	541	3	]	]	X
ejpam-7095	541	4	b.	b.	NOUN
ejpam-7095	541	5	dingfelder	dingfelder	NOUN
ejpam-7095	541	6	and	and	CCONJ
ejpam-7095	541	7	j.	j.	PROPN
ejpam-7095	541	8	a.	a.	PROPN
ejpam-7095	541	9	c.	c.	PROPN
ejpam-7095	541	10	weideman	weideman	NOUN
ejpam-7095	541	11	.	.	PUNCT
ejpam-7095	542	1	an	an	DET
ejpam-7095	542	2	improved	improved	ADJ
ejpam-7095	542	3	talbot	talbot	PROPN
ejpam-7095	542	4	method	method	NOUN
ejpam-7095	542	5	for	for	ADP
ejpam-7095	542	6	numerical	numerical	ADJ
ejpam-7095	542	7	laplace	laplace	NOUN
ejpam-7095	542	8	transform	transform	NOUN
ejpam-7095	542	9	inversion	inversion	NOUN
ejpam-7095	542	10	.	.	PUNCT
ejpam-7095	543	1	numerical	numerical	ADJ
ejpam-7095	543	2	algorithms	algorithms	PROPN
ejpam-7095	543	3	,	,	PUNCT
ejpam-7095	543	4	68(1):167–183	68(1):167–183	NOUN
ejpam-7095	543	5	,	,	PUNCT
ejpam-7095	543	6	2015	2015	NUM
ejpam-7095	543	7	.	.	PUNCT
ejpam-7095	544	1	[	[	X
ejpam-7095	544	2	30	30	NUM
ejpam-7095	544	3	]	]	X
ejpam-7095	544	4	w.	w.	PROPN
ejpam-7095	544	5	h.	h.	PROPN
ejpam-7095	544	6	huang	huang	PROPN
ejpam-7095	544	7	,	,	PUNCT
ejpam-7095	544	8	m.	m.	PROPN
ejpam-7095	544	9	samraiz	samraiz	PROPN
ejpam-7095	544	10	,	,	PUNCT
ejpam-7095	544	11	a.	a.	PROPN
ejpam-7095	544	12	mehmood	mehmood	PROPN
ejpam-7095	544	13	,	,	PUNCT
ejpam-7095	544	14	d.	d.	PROPN
ejpam-7095	544	15	baleanu	baleanu	PROPN
ejpam-7095	544	16	,	,	PUNCT
ejpam-7095	544	17	g.	g.	PROPN
ejpam-7095	544	18	rahman	rahman	PROPN
ejpam-7095	544	19	,	,	PUNCT
ejpam-7095	544	20	and	and	CCONJ
ejpam-7095	544	21	s.	s.	PROPN
ejpam-7095	544	22	naheed	naheed	PROPN
ejpam-7095	544	23	.	.	PUNCT
ejpam-7095	545	1	modified	modify	VERB
ejpam-7095	545	2	atangana	atangana	PROPN
ejpam-7095	545	3	-	-	PUNCT
ejpam-7095	545	4	baleanu	baleanu	ADJ
ejpam-7095	545	5	fractional	fractional	ADJ
ejpam-7095	545	6	operators	operator	NOUN
ejpam-7095	545	7	involving	involve	VERB
ejpam-7095	545	8	generalized	generalize	VERB
ejpam-7095	545	9	mittag	mittag	ADJ
ejpam-7095	545	10	-	-	PUNCT
ejpam-7095	545	11	leffler	leffler	NOUN
ejpam-7095	545	12	function	function	NOUN
ejpam-7095	545	13	.	.	PUNCT
ejpam-7095	546	1	alexandria	alexandria	PROPN
ejpam-7095	546	2	engineering	engineering	PROPN
ejpam-7095	546	3	journal	journal	PROPN
ejpam-7095	546	4	,	,	PUNCT
ejpam-7095	546	5	75:639–648	75:639–648	PROPN
ejpam-7095	546	6	,	,	PUNCT
ejpam-7095	546	7	2023	2023	NUM
ejpam-7095	546	8	.	.	PUNCT
ejpam-7095	547	1	[	[	X
ejpam-7095	547	2	31	31	NUM
ejpam-7095	547	3	]	]	X
ejpam-7095	547	4	r.	r.	PROPN
ejpam-7095	547	5	chawla	chawla	PROPN
ejpam-7095	547	6	,	,	PUNCT
ejpam-7095	547	7	k.	k.	PROPN
ejpam-7095	547	8	deswal	deswal	PROPN
ejpam-7095	547	9	,	,	PUNCT
ejpam-7095	547	10	d.	d.	PROPN
ejpam-7095	547	11	kumar	kumar	PROPN
ejpam-7095	547	12	,	,	PUNCT
ejpam-7095	547	13	and	and	CCONJ
ejpam-7095	547	14	d.	d.	PROPN
ejpam-7095	547	15	baleanu	baleanu	PROPN
ejpam-7095	547	16	.	.	PUNCT
ejpam-7095	548	1	a	a	DET
ejpam-7095	548	2	novel	novel	ADJ
ejpam-7095	548	3	finite	finite	ADJ
ejpam-7095	548	4	difference	difference	NOUN
ejpam-7095	548	5	based	base	VERB
ejpam-7095	548	6	numerical	numerical	ADJ
ejpam-7095	548	7	approach	approach	NOUN
ejpam-7095	548	8	for	for	ADP
ejpam-7095	548	9	modified	modify	VERB
ejpam-7095	548	10	atangana	atangana	PROPN
ejpam-7095	548	11	-	-	PUNCT
ejpam-7095	548	12	baleanu	baleanu	PROPN
ejpam-7095	548	13	caputo	caputo	PROPN
ejpam-7095	548	14	derivative	derivative	PROPN
ejpam-7095	548	15	.	.	PUNCT
ejpam-7095	549	1	aims	aim	VERB
ejpam-7095	549	2	mathematics	mathematic	NOUN
ejpam-7095	549	3	,	,	PUNCT
ejpam-7095	549	4	7(9):17252–17268	7(9):17252–17268	PROPN
ejpam-7095	549	5	,	,	PUNCT
ejpam-7095	549	6	2022	2022	NUM
ejpam-7095	549	7	.	.	PUNCT
ejpam-7095	550	1	[	[	X
ejpam-7095	550	2	32	32	NUM
ejpam-7095	550	3	]	]	PUNCT
ejpam-7095	550	4	p.	p.	PROPN
ejpam-7095	550	5	verma	verma	PROPN
ejpam-7095	550	6	and	and	CCONJ
ejpam-7095	550	7	m.	m.	PROPN
ejpam-7095	550	8	kumar	kumar	PROPN
ejpam-7095	550	9	.	.	PUNCT
ejpam-7095	551	1	new	new	ADJ
ejpam-7095	551	2	existence	existence	NOUN
ejpam-7095	551	3	,	,	PUNCT
ejpam-7095	551	4	uniqueness	uniqueness	NOUN
ejpam-7095	551	5	results	result	NOUN
ejpam-7095	551	6	for	for	ADP
ejpam-7095	551	7	multi	multi	ADJ
ejpam-7095	551	8	-	-	ADJ
ejpam-7095	551	9	dimensional	dimensional	ADJ
ejpam-7095	551	10	multi	multi	ADJ
ejpam-7095	551	11	-	-	ADJ
ejpam-7095	551	12	term	term	ADJ
ejpam-7095	551	13	caputo	caputo	PROPN
ejpam-7095	551	14	time	time	NOUN
ejpam-7095	551	15	-	-	PUNCT
ejpam-7095	551	16	fractional	fractional	ADJ
ejpam-7095	551	17	mixed	mixed	ADJ
ejpam-7095	551	18	sub	sub	NOUN
ejpam-7095	551	19	-	-	NOUN
ejpam-7095	551	20	diffusion	diffusion	NOUN
ejpam-7095	551	21	and	and	CCONJ
ejpam-7095	551	22	diffusion	diffusion	NOUN
ejpam-7095	551	23	-	-	PUNCT
ejpam-7095	551	24	wave	wave	NOUN
ejpam-7095	551	25	equation	equation	NOUN
ejpam-7095	551	26	on	on	ADP
ejpam-7095	551	27	convex	convex	NOUN
ejpam-7095	551	28	domains	domain	NOUN
ejpam-7095	551	29	.	.	PUNCT
ejpam-7095	552	1	journal	journal	NOUN
ejpam-7095	552	2	of	of	ADP
ejpam-7095	552	3	applied	apply	VERB
ejpam-7095	552	4	analysis	analysis	NOUN
ejpam-7095	552	5	and	and	CCONJ
ejpam-7095	552	6	computation	computation	NOUN
ejpam-7095	552	7	,	,	PUNCT
ejpam-7095	552	8	11:1455–1480	11:1455–1480	NUM
ejpam-7095	552	9	,	,	PUNCT
ejpam-7095	552	10	2021	2021	NUM
ejpam-7095	552	11	.	.	PUNCT
ejpam-7095	553	1	[	[	X
ejpam-7095	553	2	33	33	NUM
ejpam-7095	553	3	]	]	PUNCT
ejpam-7095	553	4	l.	l.	PROPN
ejpam-7095	553	5	n.	n.	PROPN
ejpam-7095	553	6	trefethen	trefethen	PROPN
ejpam-7095	553	7	.	.	PUNCT
ejpam-7095	554	1	spectral	spectral	ADJ
ejpam-7095	554	2	methods	method	NOUN
ejpam-7095	554	3	in	in	ADP
ejpam-7095	554	4	matlab	matlab	PROPN
ejpam-7095	554	5	.	.	PUNCT
ejpam-7095	555	1	siam	siam	PROPN
ejpam-7095	555	2	,	,	PUNCT
ejpam-7095	555	3	philadelphia	philadelphia	PROPN
ejpam-7095	555	4	,	,	PUNCT
ejpam-7095	555	5	2000	2000	NUM
ejpam-7095	555	6	.	.	PUNCT
ejpam-7095	556	1	[	[	X
ejpam-7095	556	2	34	34	NUM
ejpam-7095	556	3	]	]	SYM
ejpam-7095	556	4	a.	a.	NOUN
ejpam-7095	556	5	shokri	shokri	PROPN
ejpam-7095	556	6	and	and	CCONJ
ejpam-7095	556	7	s.	s.	PROPN
ejpam-7095	556	8	mirzaei	mirzaei	PROPN
ejpam-7095	556	9	.	.	PUNCT
ejpam-7095	557	1	a	a	DET
ejpam-7095	557	2	pseudo	pseudo	NOUN
ejpam-7095	557	3	-	-	ADJ
ejpam-7095	557	4	spectral	spectral	ADJ
ejpam-7095	557	5	based	base	VERB
ejpam-7095	557	6	method	method	NOUN
ejpam-7095	557	7	for	for	ADP
ejpam-7095	557	8	time	time	NOUN
ejpam-7095	557	9	-	-	PUNCT
ejpam-7095	557	10	fractional	fractional	ADJ
ejpam-7095	557	11	advection	advection	NOUN
ejpam-7095	557	12	-	-	PUNCT
ejpam-7095	557	13	diffusion	diffusion	NOUN
ejpam-7095	557	14	equation	equation	NOUN
ejpam-7095	557	15	.	.	PUNCT
ejpam-7095	558	1	computational	computational	ADJ
ejpam-7095	558	2	methods	method	NOUN
ejpam-7095	558	3	in	in	ADP
ejpam-7095	558	4	differential	differential	ADJ
ejpam-7095	558	5	equations	equation	NOUN
ejpam-7095	558	6	,	,	PUNCT
ejpam-7095	558	7	8(3):454–467	8(3):454–467	NUM
ejpam-7095	558	8	,	,	PUNCT
ejpam-7095	558	9	2020	2020	NUM
ejpam-7095	558	10	.	.	PUNCT
ejpam-7095	559	1	[	[	X
ejpam-7095	559	2	35	35	NUM
ejpam-7095	559	3	]	]	X
ejpam-7095	559	4	b.	b.	PROPN
ejpam-7095	559	5	d.	d.	PROPN
ejpam-7095	559	6	welfert	welfert	PROPN
ejpam-7095	559	7	.	.	PUNCT
ejpam-7095	560	1	generation	generation	NOUN
ejpam-7095	560	2	of	of	ADP
ejpam-7095	560	3	pseudospectral	pseudospectral	ADJ
ejpam-7095	560	4	differentiation	differentiation	NOUN
ejpam-7095	560	5	matrices	matrix	NOUN
ejpam-7095	560	6	i.	i.	PROPN
ejpam-7095	560	7	siam	siam	PROPN
ejpam-7095	560	8	journal	journal	PROPN
ejpam-7095	560	9	on	on	ADP
ejpam-7095	560	10	numerical	numerical	ADJ
ejpam-7095	560	11	analysis	analysis	NOUN
ejpam-7095	560	12	,	,	PUNCT
ejpam-7095	560	13	34(4):1640–1657	34(4):1640–1657	NUM
ejpam-7095	560	14	,	,	PUNCT
ejpam-7095	560	15	1997	1997	NUM
ejpam-7095	560	16	.	.	PUNCT
ejpam-7095	561	1	[	[	X
ejpam-7095	561	2	36	36	NUM
ejpam-7095	561	3	]	]	X
ejpam-7095	561	4	r.	r.	NOUN
ejpam-7095	561	5	baltensperger	baltensperger	PROPN
ejpam-7095	561	6	and	and	CCONJ
ejpam-7095	561	7	m.	m.	PROPN
ejpam-7095	561	8	r.	r.	PROPN
ejpam-7095	561	9	trummer	trummer	PROPN
ejpam-7095	561	10	.	.	PUNCT
ejpam-7095	562	1	spectral	spectral	ADJ
ejpam-7095	562	2	differencing	differencing	NOUN
ejpam-7095	562	3	with	with	ADP
ejpam-7095	562	4	a	a	DET
ejpam-7095	562	5	twist	twist	NOUN
ejpam-7095	562	6	.	.	PUNCT
ejpam-7095	563	1	siam	siam	PROPN
ejpam-7095	563	2	journal	journal	PROPN
ejpam-7095	563	3	on	on	ADP
ejpam-7095	563	4	scientific	scientific	ADJ
ejpam-7095	563	5	computing	computing	NOUN
ejpam-7095	563	6	,	,	PUNCT
ejpam-7095	563	7	24(5):1465–1487	24(5):1465–1487	NUM
ejpam-7095	563	8	,	,	PUNCT
ejpam-7095	563	9	2003	2003	NUM
ejpam-7095	563	10	.	.	PUNCT
ejpam-7095	564	1	[	[	X
ejpam-7095	564	2	37	37	NUM
ejpam-7095	564	3	]	]	PUNCT
ejpam-7095	564	4	j.	j.	PROPN
ejpam-7095	564	5	s.	s.	PROPN
ejpam-7095	564	6	green	green	PROPN
ejpam-7095	564	7	.	.	PUNCT
ejpam-7095	565	1	the	the	DET
ejpam-7095	565	2	calculation	calculation	NOUN
ejpam-7095	565	3	of	of	ADP
ejpam-7095	565	4	the	the	DET
ejpam-7095	565	5	time	time	NOUN
ejpam-7095	565	6	-	-	PUNCT
ejpam-7095	565	7	responses	response	NOUN
ejpam-7095	565	8	of	of	ADP
ejpam-7095	565	9	linear	linear	PROPN
ejpam-7095	565	10	systems	system	NOUN
ejpam-7095	565	11	.	.	PUNCT
ejpam-7095	566	1	phd	phd	NOUN
ejpam-7095	566	2	thesis	thesis	PROPN
ejpam-7095	566	3	,	,	PUNCT
ejpam-7095	566	4	department	department	NOUN
ejpam-7095	566	5	of	of	ADP
ejpam-7095	566	6	applied	apply	VERB
ejpam-7095	566	7	mathematics	mathematic	NOUN
ejpam-7095	566	8	,	,	PUNCT
ejpam-7095	566	9	imperial	imperial	ADJ
ejpam-7095	566	10	college	college	NOUN
ejpam-7095	566	11	,	,	PUNCT
ejpam-7095	566	12	london	london	PROPN
ejpam-7095	566	13	,	,	PUNCT
ejpam-7095	566	14	1955	1955	NUM
ejpam-7095	566	15	.	.	PUNCT
ejpam-7095	567	1	[	[	X
ejpam-7095	567	2	38	38	NUM
ejpam-7095	567	3	]	]	PUNCT
ejpam-7095	567	4	a.	a.	PROPN
ejpam-7095	567	5	talbot	talbot	PROPN
ejpam-7095	567	6	.	.	PUNCT
ejpam-7095	568	1	the	the	DET
ejpam-7095	568	2	accurate	accurate	ADJ
ejpam-7095	568	3	numerical	numerical	ADJ
ejpam-7095	568	4	inversion	inversion	NOUN
ejpam-7095	568	5	of	of	ADP
ejpam-7095	568	6	laplace	laplace	NOUN
ejpam-7095	568	7	transforms	transform	VERB
ejpam-7095	568	8	.	.	PUNCT
ejpam-7095	569	1	i	i	PRON
ejpam-7095	569	2	m	m	VERB
ejpam-7095	569	3	a	a	DET
ejpam-7095	569	4	journal	journal	NOUN
ejpam-7095	569	5	of	of	ADP
ejpam-7095	569	6	applied	apply	VERB
ejpam-7095	569	7	mathematics	mathematic	NOUN
ejpam-7095	569	8	,	,	PUNCT
ejpam-7095	569	9	23(1):97–120	23(1):97–120	NUM
ejpam-7095	569	10	,	,	PUNCT
ejpam-7095	569	11	1979	1979	NUM
ejpam-7095	569	12	.	.	PUNCT
ejpam-7095	570	1	[	[	X
ejpam-7095	570	2	39	39	NUM
ejpam-7095	570	3	]	]	PUNCT
ejpam-7095	570	4	j.	j.	PROPN
ejpam-7095	570	5	weideman	weideman	PROPN
ejpam-7095	570	6	and	and	CCONJ
ejpam-7095	570	7	l.	l.	PROPN
ejpam-7095	570	8	n.	n.	PROPN
ejpam-7095	570	9	trefethen	trefethen	PROPN
ejpam-7095	570	10	.	.	PUNCT
ejpam-7095	571	1	parabolic	parabolic	ADJ
ejpam-7095	571	2	and	and	CCONJ
ejpam-7095	571	3	hyperbolic	hyperbolic	ADJ
ejpam-7095	571	4	contours	contours	NOUN
ejpam-7095	571	5	for	for	ADP
ejpam-7095	571	6	computing	compute	VERB
ejpam-7095	571	7	the	the	DET
ejpam-7095	571	8	bromwich	bromwich	NOUN
ejpam-7095	571	9	integral	integral	ADJ
ejpam-7095	571	10	.	.	PUNCT
ejpam-7095	572	1	mathematics	mathematic	NOUN
ejpam-7095	572	2	of	of	ADP
ejpam-7095	572	3	computation	computation	NOUN
ejpam-7095	572	4	,	,	PUNCT
ejpam-7095	572	5	76(259):1341–1356	76(259):1341–1356	NOUN
ejpam-7095	572	6	,	,	PUNCT
ejpam-7095	572	7	2007	2007	NUM
ejpam-7095	572	8	.	.	PUNCT
ejpam-7095	573	1	[	[	X
ejpam-7095	573	2	40	40	NUM
ejpam-7095	573	3	]	]	PUNCT
ejpam-7095	573	4	steffen	steffen	PROPN
ejpam-7095	573	5	börm	börm	PROPN
ejpam-7095	573	6	,	,	PUNCT
ejpam-7095	573	7	lars	lars	PROPN
ejpam-7095	573	8	grasedyck	grasedyck	PROPN
ejpam-7095	573	9	,	,	PUNCT
ejpam-7095	573	10	and	and	CCONJ
ejpam-7095	573	11	wolfgang	wolfgang	PROPN
ejpam-7095	573	12	hackbusch	hackbusch	PROPN
ejpam-7095	573	13	.	.	PUNCT
ejpam-7095	574	1	introduction	introduction	NOUN
ejpam-7095	574	2	to	to	ADP
ejpam-7095	574	3	hierarchical	hierarchical	ADJ
ejpam-7095	574	4	matrices	matrix	NOUN
ejpam-7095	574	5	with	with	ADP
ejpam-7095	574	6	applications	application	NOUN
ejpam-7095	574	7	.	.	PUNCT
ejpam-7095	575	1	engineering	engineer	VERB
ejpam-7095	575	2	analysis	analysis	NOUN
ejpam-7095	575	3	with	with	ADP
ejpam-7095	575	4	boundary	boundary	ADJ
ejpam-7095	575	5	elements	element	NOUN
ejpam-7095	575	6	,	,	PUNCT
ejpam-7095	575	7	27(5):405	27(5):405	PROPN
ejpam-7095	575	8	–	–	PUNCT
ejpam-7095	575	9	422	422	NUM
ejpam-7095	575	10	,	,	PUNCT
ejpam-7095	575	11	2003	2003	NUM
ejpam-7095	575	12	.	.	PUNCT