id	sid	tid	token	lemma	pos
ejpam-3377	1	1	on	on	ADP
ejpam-3377	1	2	a	a	DET
ejpam-3377	1	3	computational	computational	ADJ
ejpam-3377	1	4	method	method	NOUN
ejpam-3377	1	5	for	for	ADP
ejpam-3377	1	6	non	non	ADJ
ejpam-3377	1	7	-	-	ADJ
ejpam-3377	1	8	integer	integer	ADJ
ejpam-3377	1	9	order	order	NOUN
ejpam-3377	1	10	partial	partial	ADJ
ejpam-3377	1	11	differential	differential	ADJ
ejpam-3377	1	12	equations	equation	NOUN
ejpam-3377	1	13	in	in	ADP
ejpam-3377	1	14	two	two	NUM
ejpam-3377	1	15	dimensions	dimension	NOUN
ejpam-3377	1	16	european	european	PROPN
ejpam-3377	1	17	journal	journal	PROPN
ejpam-3377	1	18	of	of	ADP
ejpam-3377	1	19	pure	pure	ADJ
ejpam-3377	1	20	and	and	CCONJ
ejpam-3377	1	21	applied	apply	VERB
ejpam-3377	1	22	mathematics	mathematic	NOUN
ejpam-3377	1	23	vol	vol	NOUN
ejpam-3377	1	24	.	.	PROPN
ejpam-3377	2	1	12	12	NUM
ejpam-3377	2	2	,	,	PUNCT
ejpam-3377	2	3	no	no	INTJ
ejpam-3377	2	4	.	.	NOUN
ejpam-3377	2	5	1	1	NUM
ejpam-3377	2	6	,	,	PUNCT
ejpam-3377	2	7	2019	2019	NUM
ejpam-3377	2	8	,	,	PUNCT
ejpam-3377	2	9	39	39	NUM
ejpam-3377	2	10	-	-	SYM
ejpam-3377	2	11	57	57	NUM
ejpam-3377	2	12	issn	issn	PROPN
ejpam-3377	2	13	1307	1307	NUM
ejpam-3377	2	14	-	-	SYM
ejpam-3377	2	15	5543	5543	NUM
ejpam-3377	2	16	–	–	PUNCT
ejpam-3377	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3377	2	18	published	publish	VERB
ejpam-3377	2	19	by	by	ADP
ejpam-3377	2	20	new	new	PROPN
ejpam-3377	2	21	york	york	PROPN
ejpam-3377	2	22	business	business	PROPN
ejpam-3377	2	23	global	global	PROPN
ejpam-3377	2	24	on	on	ADP
ejpam-3377	2	25	a	a	DET
ejpam-3377	2	26	computational	computational	ADJ
ejpam-3377	2	27	method	method	NOUN
ejpam-3377	2	28	for	for	ADP
ejpam-3377	2	29	non	non	ADJ
ejpam-3377	2	30	-	-	ADJ
ejpam-3377	2	31	integer	integer	ADJ
ejpam-3377	2	32	order	order	NOUN
ejpam-3377	2	33	partial	partial	ADJ
ejpam-3377	2	34	differential	differential	ADJ
ejpam-3377	2	35	equations	equation	NOUN
ejpam-3377	2	36	in	in	ADP
ejpam-3377	2	37	two	two	NUM
ejpam-3377	2	38	dimensions	dimension	NOUN
ejpam-3377	2	39	muhammad	muhammad	PROPN
ejpam-3377	2	40	ikhlaq	ikhlaq	PROPN
ejpam-3377	2	41	chohan1	chohan1	PROPN
ejpam-3377	2	42	,	,	PUNCT
ejpam-3377	2	43	kamal	kamal	PROPN
ejpam-3377	2	44	shah2,∗	shah2,∗	VERB
ejpam-3377	2	45	1	1	NUM
ejpam-3377	2	46	department	department	NOUN
ejpam-3377	2	47	of	of	ADP
ejpam-3377	2	48	business	business	PROPN
ejpam-3377	2	49	administration	administration	PROPN
ejpam-3377	2	50	and	and	CCONJ
ejpam-3377	2	51	accounting	accounting	PROPN
ejpam-3377	2	52	al	al	PROPN
ejpam-3377	2	53	buraimi	buraimi	PROPN
ejpam-3377	2	54	university	university	PROPN
ejpam-3377	2	55	college	college	PROPN
ejpam-3377	2	56	,	,	PUNCT
ejpam-3377	2	57	al	al	PROPN
ejpam-3377	2	58	-	-	PUNCT
ejpam-3377	2	59	buraimi	buraimi	PROPN
ejpam-3377	2	60	sultanate	sultanate	NOUN
ejpam-3377	2	61	of	of	ADP
ejpam-3377	2	62	oman	oman	PROPN
ejpam-3377	2	63	2	2	NUM
ejpam-3377	2	64	department	department	NOUN
ejpam-3377	2	65	of	of	ADP
ejpam-3377	2	66	mathematics	mathematic	NOUN
ejpam-3377	2	67	,	,	PUNCT
ejpam-3377	2	68	university	university	NOUN
ejpam-3377	2	69	of	of	ADP
ejpam-3377	2	70	malakand	malakand	PROPN
ejpam-3377	2	71	,	,	PUNCT
ejpam-3377	2	72	chakadara	chakadara	NOUN
ejpam-3377	2	73	dir(l	dir(l	PROPN
ejpam-3377	2	74	)	)	PUNCT
ejpam-3377	2	75	,	,	PUNCT
ejpam-3377	2	76	khyber	khyber	PROPN
ejpam-3377	2	77	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-3377	2	78	,	,	PUNCT
ejpam-3377	2	79	pakistan	pakistan	PROPN
ejpam-3377	2	80	abstract	abstract	NOUN
ejpam-3377	2	81	.	.	PUNCT
ejpam-3377	3	1	this	this	DET
ejpam-3377	3	2	manuscript	manuscript	NOUN
ejpam-3377	3	3	is	be	AUX
ejpam-3377	3	4	concerning	concern	VERB
ejpam-3377	3	5	to	to	PART
ejpam-3377	3	6	investigate	investigate	VERB
ejpam-3377	3	7	numerical	numerical	ADJ
ejpam-3377	3	8	solutions	solution	NOUN
ejpam-3377	3	9	for	for	ADP
ejpam-3377	3	10	different	different	ADJ
ejpam-3377	3	11	classes	class	NOUN
ejpam-3377	3	12	including	include	VERB
ejpam-3377	3	13	parabolic	parabolic	ADJ
ejpam-3377	3	14	,	,	PUNCT
ejpam-3377	3	15	elliptic	elliptic	ADJ
ejpam-3377	3	16	and	and	CCONJ
ejpam-3377	3	17	hyperbolic	hyperbolic	ADJ
ejpam-3377	3	18	partial	partial	ADJ
ejpam-3377	3	19	differential	differential	NOUN
ejpam-3377	3	20	equations	equation	NOUN
ejpam-3377	3	21	of	of	ADP
ejpam-3377	3	22	arbitrary	arbitrary	ADJ
ejpam-3377	3	23	order	order	NOUN
ejpam-3377	3	24	(	(	PUNCT
ejpam-3377	3	25	pdes	pde	NOUN
ejpam-3377	3	26	)	)	PUNCT
ejpam-3377	3	27	.	.	PUNCT
ejpam-3377	4	1	the	the	DET
ejpam-3377	4	2	proposed	propose	VERB
ejpam-3377	4	3	technique	technique	NOUN
ejpam-3377	4	4	depends	depend	VERB
ejpam-3377	4	5	on	on	ADP
ejpam-3377	4	6	some	some	DET
ejpam-3377	4	7	operational	operational	ADJ
ejpam-3377	4	8	matrices	matrix	NOUN
ejpam-3377	4	9	of	of	ADP
ejpam-3377	4	10	fractional	fractional	ADJ
ejpam-3377	4	11	order	order	NOUN
ejpam-3377	4	12	differentiation	differentiation	NOUN
ejpam-3377	4	13	and	and	CCONJ
ejpam-3377	4	14	integration	integration	NOUN
ejpam-3377	4	15	.	.	PUNCT
ejpam-3377	5	1	to	to	PART
ejpam-3377	5	2	compute	compute	VERB
ejpam-3377	5	3	the	the	DET
ejpam-3377	5	4	mentioned	mention	VERB
ejpam-3377	5	5	operational	operational	ADJ
ejpam-3377	5	6	matrices	matrix	NOUN
ejpam-3377	5	7	,	,	PUNCT
ejpam-3377	5	8	we	we	PRON
ejpam-3377	5	9	apply	apply	VERB
ejpam-3377	5	10	shifted	shift	VERB
ejpam-3377	5	11	jacobi	jacobi	PROPN
ejpam-3377	5	12	polynomials	polynomial	NOUN
ejpam-3377	5	13	in	in	ADP
ejpam-3377	5	14	two	two	NUM
ejpam-3377	5	15	dimension	dimension	NOUN
ejpam-3377	5	16	.	.	PUNCT
ejpam-3377	6	1	thank	thank	VERB
ejpam-3377	6	2	to	to	ADP
ejpam-3377	6	3	these	these	DET
ejpam-3377	6	4	matrices	matrix	NOUN
ejpam-3377	6	5	,	,	PUNCT
ejpam-3377	6	6	we	we	PRON
ejpam-3377	6	7	convert	convert	VERB
ejpam-3377	6	8	the	the	DET
ejpam-3377	6	9	pde	pde	NOUN
ejpam-3377	6	10	under	under	ADP
ejpam-3377	6	11	consideration	consideration	NOUN
ejpam-3377	6	12	to	to	ADP
ejpam-3377	6	13	an	an	DET
ejpam-3377	6	14	algebraic	algebraic	ADJ
ejpam-3377	6	15	equation	equation	NOUN
ejpam-3377	6	16	which	which	PRON
ejpam-3377	6	17	is	be	AUX
ejpam-3377	6	18	can	can	AUX
ejpam-3377	6	19	be	be	AUX
ejpam-3377	6	20	easily	easily	ADV
ejpam-3377	6	21	solved	solve	VERB
ejpam-3377	6	22	for	for	ADP
ejpam-3377	6	23	unknown	unknown	ADJ
ejpam-3377	6	24	coefficient	coefficient	NOUN
ejpam-3377	6	25	matrix	matrix	NOUN
ejpam-3377	6	26	required	require	VERB
ejpam-3377	6	27	for	for	ADP
ejpam-3377	6	28	the	the	DET
ejpam-3377	6	29	numerical	numerical	ADJ
ejpam-3377	6	30	solution	solution	NOUN
ejpam-3377	6	31	.	.	PUNCT
ejpam-3377	7	1	the	the	DET
ejpam-3377	7	2	proposed	propose	VERB
ejpam-3377	7	3	method	method	NOUN
ejpam-3377	7	4	is	be	AUX
ejpam-3377	7	5	very	very	ADV
ejpam-3377	7	6	efficient	efficient	ADJ
ejpam-3377	7	7	and	and	CCONJ
ejpam-3377	7	8	need	need	VERB
ejpam-3377	7	9	no	no	DET
ejpam-3377	7	10	discretization	discretization	NOUN
ejpam-3377	7	11	of	of	ADP
ejpam-3377	7	12	the	the	DET
ejpam-3377	7	13	data	datum	NOUN
ejpam-3377	7	14	for	for	ADP
ejpam-3377	7	15	the	the	DET
ejpam-3377	7	16	proposed	propose	VERB
ejpam-3377	7	17	pde	pde	NOUN
ejpam-3377	7	18	.	.	PUNCT
ejpam-3377	8	1	the	the	DET
ejpam-3377	8	2	approximate	approximate	ADJ
ejpam-3377	8	3	solution	solution	NOUN
ejpam-3377	8	4	obtain	obtain	VERB
ejpam-3377	8	5	via	via	ADP
ejpam-3377	8	6	this	this	DET
ejpam-3377	8	7	method	method	NOUN
ejpam-3377	8	8	is	be	AUX
ejpam-3377	8	9	highly	highly	ADV
ejpam-3377	8	10	accurate	accurate	ADJ
ejpam-3377	8	11	and	and	CCONJ
ejpam-3377	8	12	the	the	DET
ejpam-3377	8	13	computation	computation	NOUN
ejpam-3377	8	14	is	be	AUX
ejpam-3377	8	15	easy	easy	ADJ
ejpam-3377	8	16	.	.	PUNCT
ejpam-3377	9	1	the	the	DET
ejpam-3377	9	2	proposed	propose	VERB
ejpam-3377	9	3	method	method	NOUN
ejpam-3377	9	4	is	be	AUX
ejpam-3377	9	5	supported	support	VERB
ejpam-3377	9	6	by	by	ADP
ejpam-3377	9	7	solving	solve	VERB
ejpam-3377	9	8	various	various	ADJ
ejpam-3377	9	9	examples	example	NOUN
ejpam-3377	9	10	from	from	ADP
ejpam-3377	9	11	well	well	ADV
ejpam-3377	9	12	known	know	VERB
ejpam-3377	9	13	articles	article	NOUN
ejpam-3377	9	14	.	.	PUNCT
ejpam-3377	10	1	2010	2010	NUM
ejpam-3377	10	2	mathematics	mathematic	NOUN
ejpam-3377	10	3	subject	subject	NOUN
ejpam-3377	10	4	classifications	classification	NOUN
ejpam-3377	10	5	:	:	PUNCT
ejpam-3377	10	6	35r11	35r11	NUM
ejpam-3377	10	7	,	,	PUNCT
ejpam-3377	10	8	65m06	65m06	NUM
ejpam-3377	10	9	,	,	PUNCT
ejpam-3377	10	10	65n30	65n30	NUM
ejpam-3377	10	11	key	key	ADJ
ejpam-3377	10	12	words	word	NOUN
ejpam-3377	10	13	and	and	CCONJ
ejpam-3377	10	14	phrases	phrase	NOUN
ejpam-3377	10	15	:	:	PUNCT
ejpam-3377	10	16	jacobi	jacobi	PROPN
ejpam-3377	10	17	polynomials	polynomials	PROPN
ejpam-3377	10	18	,	,	PUNCT
ejpam-3377	10	19	different	different	ADJ
ejpam-3377	10	20	classes	class	NOUN
ejpam-3377	10	21	of	of	ADP
ejpam-3377	10	22	partial	partial	ADJ
ejpam-3377	10	23	differential	differential	NOUN
ejpam-3377	10	24	equations	equation	NOUN
ejpam-3377	10	25	,	,	PUNCT
ejpam-3377	10	26	operational	operational	ADJ
ejpam-3377	10	27	matrix	matrix	NOUN
ejpam-3377	10	28	,	,	PUNCT
ejpam-3377	10	29	algebraic	algebraic	ADJ
ejpam-3377	10	30	equation	equation	NOUN
ejpam-3377	10	31	,	,	PUNCT
ejpam-3377	10	32	numerical	numerical	ADJ
ejpam-3377	10	33	solution	solution	NOUN
ejpam-3377	10	34	.	.	PUNCT
ejpam-3377	11	1	1	1	X
ejpam-3377	11	2	.	.	X
ejpam-3377	11	3	introduction	introduction	NOUN
ejpam-3377	11	4	many	many	ADJ
ejpam-3377	11	5	phenomenons	phenomenon	NOUN
ejpam-3377	11	6	and	and	CCONJ
ejpam-3377	11	7	problems	problem	NOUN
ejpam-3377	11	8	in	in	ADP
ejpam-3377	11	9	biology	biology	NOUN
ejpam-3377	11	10	,	,	PUNCT
ejpam-3377	11	11	physics	physics	NOUN
ejpam-3377	11	12	,	,	PUNCT
ejpam-3377	11	13	chemistry	chemistry	NOUN
ejpam-3377	11	14	,	,	PUNCT
ejpam-3377	11	15	dynamics	dynamic	NOUN
ejpam-3377	11	16	,	,	PUNCT
ejpam-3377	11	17	fluid	fluid	ADJ
ejpam-3377	11	18	mechanics	mechanic	NOUN
ejpam-3377	11	19	,	,	PUNCT
ejpam-3377	11	20	optical	optical	ADJ
ejpam-3377	11	21	technology	technology	NOUN
ejpam-3377	11	22	,	,	PUNCT
ejpam-3377	11	23	etc	etc	X
ejpam-3377	11	24	and	and	CCONJ
ejpam-3377	11	25	in	in	ADP
ejpam-3377	11	26	engineering	engineering	NOUN
ejpam-3377	11	27	disciplines	discipline	NOUN
ejpam-3377	11	28	are	be	AUX
ejpam-3377	11	29	modeled	model	VERB
ejpam-3377	11	30	by	by	ADP
ejpam-3377	11	31	partial	partial	ADJ
ejpam-3377	11	32	differential	differential	ADJ
ejpam-3377	11	33	equations	equation	NOUN
ejpam-3377	11	34	.	.	PUNCT
ejpam-3377	12	1	the	the	DET
ejpam-3377	12	2	mentioned	mention	VERB
ejpam-3377	12	3	equations	equation	NOUN
ejpam-3377	12	4	arise	arise	VERB
ejpam-3377	12	5	in	in	ADP
ejpam-3377	12	6	numbers	number	NOUN
ejpam-3377	12	7	of	of	ADP
ejpam-3377	12	8	scientific	scientific	ADJ
ejpam-3377	12	9	models	model	NOUN
ejpam-3377	12	10	like	like	ADP
ejpam-3377	12	11	propagation	propagation	NOUN
ejpam-3377	12	12	of	of	ADP
ejpam-3377	12	13	water	water	NOUN
ejpam-3377	12	14	waves	wave	NOUN
ejpam-3377	12	15	,	,	PUNCT
ejpam-3377	12	16	long	long	ADJ
ejpam-3377	12	17	waves	wave	NOUN
ejpam-3377	12	18	and	and	CCONJ
ejpam-3377	12	19	chemical	chemical	NOUN
ejpam-3377	12	20	reaction	reaction	NOUN
ejpam-3377	12	21	diffusion	diffusion	NOUN
ejpam-3377	12	22	equations	equation	NOUN
ejpam-3377	12	23	,	,	PUNCT
ejpam-3377	12	24	for	for	ADP
ejpam-3377	12	25	detail	detail	NOUN
ejpam-3377	12	26	see	see	VERB
ejpam-3377	12	27	[	[	X
ejpam-3377	12	28	7	7	NUM
ejpam-3377	12	29	,	,	PUNCT
ejpam-3377	12	30	29	29	NUM
ejpam-3377	12	31	,	,	PUNCT
ejpam-3377	12	32	36	36	NUM
ejpam-3377	12	33	,	,	PUNCT
ejpam-3377	12	34	40	40	NUM
ejpam-3377	12	35	,	,	PUNCT
ejpam-3377	12	36	41	41	NUM
ejpam-3377	12	37	,	,	PUNCT
ejpam-3377	12	38	41	41	NUM
ejpam-3377	12	39	]	]	PUNCT
ejpam-3377	12	40	.	.	PUNCT
ejpam-3377	13	1	recently	recently	ADV
ejpam-3377	13	2	,	,	PUNCT
ejpam-3377	13	3	considerable	considerable	ADJ
ejpam-3377	13	4	attention	attention	NOUN
ejpam-3377	13	5	has	have	AUX
ejpam-3377	13	6	been	be	AUX
ejpam-3377	13	7	given	give	VERB
ejpam-3377	13	8	to	to	PART
ejpam-3377	13	9	study	study	VERB
ejpam-3377	13	10	partial	partial	ADJ
ejpam-3377	13	11	differential	differential	NOUN
ejpam-3377	13	12	equations	equation	NOUN
ejpam-3377	13	13	with	with	ADP
ejpam-3377	13	14	non	non	ADJ
ejpam-3377	13	15	-	-	ADJ
ejpam-3377	13	16	integer	integer	ADJ
ejpam-3377	13	17	order	order	NOUN
ejpam-3377	13	18	rather	rather	ADV
ejpam-3377	13	19	than	than	ADP
ejpam-3377	13	20	classical	classical	ADJ
ejpam-3377	13	21	order	order	NOUN
ejpam-3377	13	22	.	.	PUNCT
ejpam-3377	14	1	because	because	SCONJ
ejpam-3377	14	2	in	in	ADP
ejpam-3377	14	3	many	many	ADJ
ejpam-3377	14	4	situations	situation	NOUN
ejpam-3377	14	5	,	,	PUNCT
ejpam-3377	14	6	fractional	fractional	ADJ
ejpam-3377	14	7	order	order	NOUN
ejpam-3377	14	8	partial	partial	ADJ
ejpam-3377	14	9	differential	differential	ADJ
ejpam-3377	14	10	equations	equation	NOUN
ejpam-3377	14	11	(	(	PUNCT
ejpam-3377	14	12	fpdes	fpde	NOUN
ejpam-3377	14	13	)	)	PUNCT
ejpam-3377	14	14	modeled	model	VERB
ejpam-3377	14	15	real	real	ADJ
ejpam-3377	14	16	worlds	world	NOUN
ejpam-3377	14	17	phenomenons	phenomenon	NOUN
ejpam-3377	14	18	more	more	ADV
ejpam-3377	14	19	accurately	accurately	ADV
ejpam-3377	14	20	∗corresponding	∗corresponde	VERB
ejpam-3377	14	21	author	author	NOUN
ejpam-3377	14	22	.	.	PUNCT
ejpam-3377	15	1	doi	doi	NOUN
ejpam-3377	15	2	:	:	PUNCT
ejpam-3377	15	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3377	https://doi.org/10.29020/nybg.ejpam.v12i1.3377	NOUN
ejpam-3377	15	4	email	email	NOUN
ejpam-3377	15	5	addresses	address	NOUN
ejpam-3377	15	6	:	:	PUNCT
ejpam-3377	15	7	chohan@buc.edu.om	chohan@buc.edu.om	NOUN
ejpam-3377	15	8	(	(	PUNCT
ejpam-3377	15	9	m.i.chohan	m.i.chohan	PROPN
ejpam-3377	15	10	)	)	PUNCT
ejpam-3377	15	11	,	,	PUNCT
ejpam-3377	15	12	kamalshah408@gmail.com	kamalshah408@gmail.com	X
ejpam-3377	15	13	(	(	PUNCT
ejpam-3377	15	14	k.	k.	NOUN
ejpam-3377	15	15	shah	shah	PROPN
ejpam-3377	15	16	)	)	PUNCT
ejpam-3377	15	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3377	16	1	39	39	NUM
ejpam-3377	16	2	c	c	X
ejpam-3377	16	3	©	©	PROPN
ejpam-3377	16	4	2019	2019	NUM
ejpam-3377	16	5	ejpam	ejpam	NOUN
ejpam-3377	16	6	all	all	DET
ejpam-3377	16	7	rights	right	NOUN
ejpam-3377	16	8	reserved	reserve	VERB
ejpam-3377	16	9	.	.	PUNCT
ejpam-3377	17	1	m.i	m.i	PROPN
ejpam-3377	17	2	.	.	PROPN
ejpam-3377	17	3	chohan	chohan	PROPN
ejpam-3377	17	4	,	,	PUNCT
ejpam-3377	17	5	k.shah	k.shah	PROPN
ejpam-3377	17	6	/	/	SYM
ejpam-3377	17	7	eur	eur	PROPN
ejpam-3377	17	8	.	.	PUNCT
ejpam-3377	18	1	j.	j.	PROPN
ejpam-3377	18	2	pure	pure	PROPN
ejpam-3377	18	3	appl	appl	PROPN
ejpam-3377	18	4	.	.	PROPN
ejpam-3377	18	5	math	math	PROPN
ejpam-3377	18	6	,	,	PUNCT
ejpam-3377	18	7	12	12	NUM
ejpam-3377	18	8	(	(	PUNCT
ejpam-3377	18	9	1	1	NUM
ejpam-3377	18	10	)	)	PUNCT
ejpam-3377	18	11	(	(	PUNCT
ejpam-3377	18	12	2019	2019	NUM
ejpam-3377	18	13	)	)	PUNCT
ejpam-3377	18	14	,	,	PUNCT
ejpam-3377	18	15	39	39	NUM
ejpam-3377	18	16	-	-	SYM
ejpam-3377	18	17	57	57	NUM
ejpam-3377	18	18	40	40	NUM
ejpam-3377	18	19	as	as	SCONJ
ejpam-3377	18	20	compared	compare	VERB
ejpam-3377	18	21	to	to	ADP
ejpam-3377	18	22	classical	classical	ADJ
ejpam-3377	18	23	order	order	NOUN
ejpam-3377	18	24	partial	partial	ADJ
ejpam-3377	18	25	differential	differential	NOUN
ejpam-3377	18	26	equations	equation	NOUN
ejpam-3377	18	27	.	.	PUNCT
ejpam-3377	19	1	it	it	PRON
ejpam-3377	19	2	has	have	AUX
ejpam-3377	19	3	been	be	AUX
ejpam-3377	19	4	proved	prove	VERB
ejpam-3377	19	5	that	that	SCONJ
ejpam-3377	19	6	many	many	ADJ
ejpam-3377	19	7	interesting	interesting	ADJ
ejpam-3377	19	8	process	process	NOUN
ejpam-3377	19	9	of	of	ADP
ejpam-3377	19	10	electromagnetic	electromagnetic	ADJ
ejpam-3377	19	11	,	,	PUNCT
ejpam-3377	19	12	acoustics	acoustic	NOUN
ejpam-3377	19	13	,	,	PUNCT
ejpam-3377	19	14	viscoelasticity	viscoelasticity	NOUN
ejpam-3377	19	15	,	,	PUNCT
ejpam-3377	19	16	electrochemistry	electrochemistry	NOUN
ejpam-3377	19	17	and	and	CCONJ
ejpam-3377	19	18	material	material	NOUN
ejpam-3377	19	19	sciences	science	NOUN
ejpam-3377	19	20	are	be	AUX
ejpam-3377	19	21	well	well	ADV
ejpam-3377	19	22	described	describe	VERB
ejpam-3377	19	23	by	by	ADP
ejpam-3377	19	24	using	use	VERB
ejpam-3377	19	25	fractional	fractional	ADJ
ejpam-3377	19	26	order	order	NOUN
ejpam-3377	19	27	partial	partial	ADJ
ejpam-3377	19	28	differential	differential	NOUN
ejpam-3377	19	29	equations	equation	NOUN
ejpam-3377	19	30	,	,	PUNCT
ejpam-3377	19	31	see	see	VERB
ejpam-3377	19	32	[	[	X
ejpam-3377	19	33	6	6	NUM
ejpam-3377	19	34	,	,	PUNCT
ejpam-3377	19	35	14	14	NUM
ejpam-3377	19	36	,	,	PUNCT
ejpam-3377	19	37	17	17	NUM
ejpam-3377	19	38	,	,	PUNCT
ejpam-3377	19	39	35	35	NUM
ejpam-3377	19	40	]	]	PUNCT
ejpam-3377	19	41	.	.	PUNCT
ejpam-3377	20	1	the	the	DET
ejpam-3377	20	2	present	present	ADJ
ejpam-3377	20	3	work	work	NOUN
ejpam-3377	20	4	is	be	AUX
ejpam-3377	20	5	related	relate	VERB
ejpam-3377	20	6	to	to	PART
ejpam-3377	20	7	study	study	VERB
ejpam-3377	20	8	the	the	DET
ejpam-3377	20	9	following	following	ADJ
ejpam-3377	20	10	linear	linear	ADJ
ejpam-3377	20	11	fpde	fpde	NOUN
ejpam-3377	20	12	given	give	VERB
ejpam-3377	20	13	as	as	ADP
ejpam-3377	20	14			PROPN
ejpam-3377	20	15	a	a	DET
ejpam-3377	20	16	∂αw(x	∂αw(x	PROPN
ejpam-3377	20	17	,	,	PUNCT
ejpam-3377	20	18	y	y	NOUN
ejpam-3377	20	19	)	)	PUNCT
ejpam-3377	20	20	∂xα	∂xα	PROPN
ejpam-3377	20	21	+	+	PROPN
ejpam-3377	21	1	b	b	NOUN
ejpam-3377	21	2	∂αw(x	∂αw(x	ADJ
ejpam-3377	21	3	,	,	PUNCT
ejpam-3377	21	4	y	y	NOUN
ejpam-3377	21	5	)	)	PUNCT
ejpam-3377	21	6	∂x	∂x	NOUN
ejpam-3377	21	7	α	α	NOUN
ejpam-3377	21	8	2	2	NUM
ejpam-3377	21	9	y	y	PROPN
ejpam-3377	21	10	α	α	NOUN
ejpam-3377	21	11	2	2	NUM
ejpam-3377	22	1	+	+	CCONJ
ejpam-3377	22	2	c	c	NOUN
ejpam-3377	22	3	∂αw(x	∂αw(x	PROPN
ejpam-3377	22	4	,	,	PUNCT
ejpam-3377	22	5	y	y	NOUN
ejpam-3377	22	6	)	)	PUNCT
ejpam-3377	22	7	∂yα	∂yα	PROPN
ejpam-3377	22	8	+	+	PROPN
ejpam-3377	22	9	d	d	PROPN
ejpam-3377	22	10	∂βw(x	∂βw(x	PROPN
ejpam-3377	22	11	,	,	PUNCT
ejpam-3377	22	12	y	y	PROPN
ejpam-3377	22	13	)	)	PUNCT
ejpam-3377	23	1	∂xβ	∂xβ	PROPN
ejpam-3377	23	2	+	+	PROPN
ejpam-3377	23	3	e	e	PROPN
ejpam-3377	23	4	∂βw(x	∂βw(x	PROPN
ejpam-3377	23	5	,	,	PUNCT
ejpam-3377	23	6	y	y	NOUN
ejpam-3377	23	7	)	)	PUNCT
ejpam-3377	24	1	∂yβ	∂yβ	ADV
ejpam-3377	24	2	+	+	CCONJ
ejpam-3377	24	3	fw(x	fw(x	PROPN
ejpam-3377	24	4	,	,	PUNCT
ejpam-3377	24	5	y	y	NOUN
ejpam-3377	24	6	)	)	PUNCT
ejpam-3377	24	7	=	=	SYM
ejpam-3377	25	1	g(x	g(x	NOUN
ejpam-3377	25	2	,	,	PUNCT
ejpam-3377	25	3	y	y	PROPN
ejpam-3377	25	4	)	)	PUNCT
ejpam-3377	25	5	,	,	PUNCT
ejpam-3377	25	6	α	α	PROPN
ejpam-3377	25	7	∈	∈	PROPN
ejpam-3377	25	8	(	(	PUNCT
ejpam-3377	25	9	1	1	NUM
ejpam-3377	25	10	,	,	PUNCT
ejpam-3377	25	11	2	2	NUM
ejpam-3377	25	12	]	]	PUNCT
ejpam-3377	25	13	,	,	PUNCT
ejpam-3377	25	14	β	β	X
ejpam-3377	25	15	∈	∈	PROPN
ejpam-3377	25	16	(	(	PUNCT
ejpam-3377	25	17	0	0	NUM
ejpam-3377	25	18	,	,	PUNCT
ejpam-3377	25	19	1	1	NUM
ejpam-3377	25	20	]	]	PUNCT
ejpam-3377	25	21	,	,	PUNCT
ejpam-3377	25	22	corresponding	correspond	VERB
ejpam-3377	25	23	to	to	ADP
ejpam-3377	25	24	the	the	DET
ejpam-3377	25	25	initial	initial	ADJ
ejpam-3377	25	26	conditions	condition	NOUN
ejpam-3377	25	27	w(x	w(x	NOUN
ejpam-3377	25	28	,	,	PUNCT
ejpam-3377	25	29	y)|x=0	y)|x=0	PROPN
ejpam-3377	25	30	=	=	SYM
ejpam-3377	25	31	φ(y	φ(y	PROPN
ejpam-3377	25	32	)	)	PUNCT
ejpam-3377	25	33	,	,	PUNCT
ejpam-3377	25	34	wx(x	wx(x	X
ejpam-3377	25	35	,	,	PUNCT
ejpam-3377	25	36	y)|x=0	y)|x=0	PROPN
ejpam-3377	25	37	=	=	SYM
ejpam-3377	25	38	ψ(y	ψ(y	PROPN
ejpam-3377	25	39	)	)	PUNCT
ejpam-3377	25	40	.	.	PUNCT
ejpam-3377	26	1	(	(	PUNCT
ejpam-3377	26	2	1	1	X
ejpam-3377	26	3	)	)	PUNCT
ejpam-3377	26	4	where	where	SCONJ
ejpam-3377	26	5	a	a	DET
ejpam-3377	26	6	,	,	PUNCT
ejpam-3377	26	7	b	b	NOUN
ejpam-3377	26	8	,	,	PUNCT
ejpam-3377	26	9	c	c	NOUN
ejpam-3377	26	10	,	,	PUNCT
ejpam-3377	26	11	d	d	NOUN
ejpam-3377	26	12	,	,	PUNCT
ejpam-3377	26	13	e	e	NOUN
ejpam-3377	26	14	,	,	PUNCT
ejpam-3377	26	15	f	f	PROPN
ejpam-3377	26	16	are	be	AUX
ejpam-3377	26	17	real	real	ADJ
ejpam-3377	26	18	constants	constant	NOUN
ejpam-3377	26	19	and	and	CCONJ
ejpam-3377	26	20	w(x	w(x	NOUN
ejpam-3377	26	21	,	,	PUNCT
ejpam-3377	26	22	y	y	PROPN
ejpam-3377	26	23	)	)	PUNCT
ejpam-3377	26	24	is	be	AUX
ejpam-3377	26	25	the	the	DET
ejpam-3377	26	26	solution	solution	NOUN
ejpam-3377	26	27	of	of	ADP
ejpam-3377	26	28	the	the	DET
ejpam-3377	26	29	system	system	NOUN
ejpam-3377	26	30	to	to	PART
ejpam-3377	26	31	be	be	AUX
ejpam-3377	26	32	computed	compute	VERB
ejpam-3377	26	33	and	and	CCONJ
ejpam-3377	26	34	also	also	ADV
ejpam-3377	26	35	w(x	w(x	PROPN
ejpam-3377	26	36	,	,	PUNCT
ejpam-3377	26	37	y	y	NOUN
ejpam-3377	26	38	)	)	PUNCT
ejpam-3377	26	39	,	,	PUNCT
ejpam-3377	26	40	g(x	g(x	PROPN
ejpam-3377	26	41	,	,	PUNCT
ejpam-3377	26	42	y),∈	y),∈	PROPN
ejpam-3377	26	43	c([0	c([0	NOUN
ejpam-3377	26	44	,	,	PUNCT
ejpam-3377	26	45	δ	δ	PROPN
ejpam-3377	26	46	]	]	X
ejpam-3377	26	47	×	×	NOUN
ejpam-3377	27	1	[	[	X
ejpam-3377	27	2	0	0	NUM
ejpam-3377	27	3	,	,	PUNCT
ejpam-3377	27	4	δ	δ	PROPN
ejpam-3377	27	5	]	]	X
ejpam-3377	27	6	)	)	PUNCT
ejpam-3377	27	7	.	.	PUNCT
ejpam-3377	28	1	under	under	ADP
ejpam-3377	28	2	the	the	DET
ejpam-3377	28	3	classical	classical	ADJ
ejpam-3377	28	4	order	order	NOUN
ejpam-3377	28	5	α	α	NOUN
ejpam-3377	28	6	=	=	SYM
ejpam-3377	28	7	2	2	NUM
ejpam-3377	28	8	,	,	PUNCT
ejpam-3377	28	9	β	β	X
ejpam-3377	28	10	=	=	SYM
ejpam-3377	28	11	1	1	NUM
ejpam-3377	28	12	,	,	PUNCT
ejpam-3377	28	13	the	the	DET
ejpam-3377	28	14	class	class	NOUN
ejpam-3377	28	15	(	(	PUNCT
ejpam-3377	28	16	1	1	NUM
ejpam-3377	28	17	)	)	PUNCT
ejpam-3377	28	18	of	of	ADP
ejpam-3377	28	19	fpdes	fpde	NOUN
ejpam-3377	28	20	represents	represent	VERB
ejpam-3377	28	21	different	different	ADJ
ejpam-3377	28	22	classes	class	NOUN
ejpam-3377	28	23	of	of	ADP
ejpam-3377	28	24	integer	integer	PROPN
ejpam-3377	28	25	order	order	NOUN
ejpam-3377	28	26	pde	pde	NOUN
ejpam-3377	28	27	such	such	ADJ
ejpam-3377	28	28	as	as	ADP
ejpam-3377	28	29	parabolic	parabolic	ADJ
ejpam-3377	28	30	,	,	PUNCT
ejpam-3377	28	31	ecliptic	ecliptic	ADJ
ejpam-3377	28	32	and	and	CCONJ
ejpam-3377	28	33	hyperbolic	hyperbolic	ADJ
ejpam-3377	28	34	partial	partial	ADJ
ejpam-3377	28	35	differential	differential	NOUN
ejpam-3377	28	36	equations	equation	NOUN
ejpam-3377	28	37	.	.	PUNCT
ejpam-3377	29	1	the	the	DET
ejpam-3377	29	2	concerned	concerned	ADJ
ejpam-3377	29	3	pde	pde	NOUN
ejpam-3377	29	4	is	be	AUX
ejpam-3377	29	5	parabolic	parabolic	NOUN
ejpam-3377	29	6	corresponding	correspond	VERB
ejpam-3377	29	7	to	to	ADP
ejpam-3377	29	8	integer	integer	NOUN
ejpam-3377	29	9	order	order	NOUN
ejpam-3377	29	10	if	if	SCONJ
ejpam-3377	29	11	b2	b2	NOUN
ejpam-3377	29	12	−	−	NOUN
ejpam-3377	29	13	4ac	4ac	NOUN
ejpam-3377	30	1	=	=	SYM
ejpam-3377	31	1	0	0	NUM
ejpam-3377	31	2	,	,	PUNCT
ejpam-3377	31	3	ecliptic	ecliptic	ADJ
ejpam-3377	31	4	if	if	SCONJ
ejpam-3377	31	5	b2	b2	NOUN
ejpam-3377	31	6	−	−	PROPN
ejpam-3377	31	7	4ac	4ac	NOUN
ejpam-3377	31	8	<	<	X
ejpam-3377	31	9	0	0	PUNCT
ejpam-3377	31	10	and	and	CCONJ
ejpam-3377	31	11	hyperbolic	hyperbolic	ADJ
ejpam-3377	31	12	,	,	PUNCT
ejpam-3377	31	13	if	if	SCONJ
ejpam-3377	31	14	b2	b2	NOUN
ejpam-3377	31	15	−	−	PROPN
ejpam-3377	31	16	4ac	4ac	NOUN
ejpam-3377	31	17	>	>	X
ejpam-3377	31	18	0	0	PROPN
ejpam-3377	31	19	,	,	PUNCT
ejpam-3377	31	20	where	where	SCONJ
ejpam-3377	31	21	each	each	DET
ejpam-3377	31	22	category	category	NOUN
ejpam-3377	31	23	describes	describe	VERB
ejpam-3377	31	24	different	different	ADJ
ejpam-3377	31	25	phenomena	phenomenon	NOUN
ejpam-3377	31	26	in	in	ADP
ejpam-3377	31	27	various	various	ADJ
ejpam-3377	31	28	disciplines	discipline	NOUN
ejpam-3377	31	29	of	of	ADP
ejpam-3377	31	30	science	science	NOUN
ejpam-3377	31	31	and	and	CCONJ
ejpam-3377	31	32	engineering	engineering	NOUN
ejpam-3377	31	33	.	.	PUNCT
ejpam-3377	32	1	the	the	DET
ejpam-3377	32	2	aforesaid	aforesaid	ADJ
ejpam-3377	32	3	classes	class	NOUN
ejpam-3377	32	4	of	of	ADP
ejpam-3377	32	5	partial	partial	ADJ
ejpam-3377	32	6	differential	differential	NOUN
ejpam-3377	32	7	equations	equation	NOUN
ejpam-3377	32	8	have	have	VERB
ejpam-3377	32	9	many	many	ADJ
ejpam-3377	32	10	applications	application	NOUN
ejpam-3377	32	11	in	in	ADP
ejpam-3377	32	12	various	various	ADJ
ejpam-3377	32	13	field	field	NOUN
ejpam-3377	32	14	of	of	ADP
ejpam-3377	32	15	science	science	NOUN
ejpam-3377	32	16	and	and	CCONJ
ejpam-3377	32	17	technology	technology	NOUN
ejpam-3377	32	18	.	.	PUNCT
ejpam-3377	33	1	as	as	SCONJ
ejpam-3377	33	2	laplace	laplace	NOUN
ejpam-3377	33	3	and	and	CCONJ
ejpam-3377	33	4	poisson	poisson	PROPN
ejpam-3377	33	5	equations	equation	NOUN
ejpam-3377	33	6	are	be	AUX
ejpam-3377	33	7	ecliptic	ecliptic	ADJ
ejpam-3377	33	8	partial	partial	ADJ
ejpam-3377	33	9	differential	differential	NOUN
ejpam-3377	33	10	equations	equation	NOUN
ejpam-3377	33	11	which	which	PRON
ejpam-3377	33	12	have	have	VERB
ejpam-3377	33	13	many	many	ADJ
ejpam-3377	33	14	applications	application	NOUN
ejpam-3377	33	15	in	in	ADP
ejpam-3377	33	16	electromagnetic	electromagnetic	ADJ
ejpam-3377	33	17	theory	theory	NOUN
ejpam-3377	33	18	,	,	PUNCT
ejpam-3377	33	19	and	and	CCONJ
ejpam-3377	33	20	other	other	ADJ
ejpam-3377	33	21	branches	branch	NOUN
ejpam-3377	33	22	of	of	ADP
ejpam-3377	33	23	physics	physics	PROPN
ejpam-3377	33	24	,	,	PUNCT
ejpam-3377	33	25	mechanics	mechanic	NOUN
ejpam-3377	33	26	,	,	PUNCT
ejpam-3377	33	27	etc	etc	X
ejpam-3377	33	28	.	.	X
ejpam-3377	33	29	similarly	similarly	ADV
ejpam-3377	33	30	,	,	PUNCT
ejpam-3377	33	31	heat	heat	NOUN
ejpam-3377	33	32	equation	equation	NOUN
ejpam-3377	33	33	is	be	AUX
ejpam-3377	33	34	parabolic	parabolic	ADJ
ejpam-3377	33	35	and	and	CCONJ
ejpam-3377	33	36	wave	wave	NOUN
ejpam-3377	33	37	equation	equation	NOUN
ejpam-3377	33	38	is	be	AUX
ejpam-3377	33	39	hyperbolic	hyperbolic	ADJ
ejpam-3377	33	40	partial	partial	ADJ
ejpam-3377	33	41	differential	differential	NOUN
ejpam-3377	33	42	equations	equation	NOUN
ejpam-3377	33	43	.	.	PUNCT
ejpam-3377	34	1	for	for	ADP
ejpam-3377	34	2	the	the	DET
ejpam-3377	34	3	importance	importance	NOUN
ejpam-3377	34	4	and	and	CCONJ
ejpam-3377	34	5	uses	use	NOUN
ejpam-3377	34	6	of	of	ADP
ejpam-3377	34	7	these	these	DET
ejpam-3377	34	8	equations	equation	NOUN
ejpam-3377	34	9	,	,	PUNCT
ejpam-3377	34	10	we	we	PRON
ejpam-3377	34	11	refe[1	refe[1	PROPN
ejpam-3377	34	12	,	,	PUNCT
ejpam-3377	34	13	15	15	NUM
ejpam-3377	34	14	,	,	PUNCT
ejpam-3377	34	15	30	30	NUM
ejpam-3377	34	16	,	,	PUNCT
ejpam-3377	34	17	38	38	NUM
ejpam-3377	34	18	]	]	PUNCT
ejpam-3377	34	19	.	.	PUNCT
ejpam-3377	35	1	the	the	DET
ejpam-3377	35	2	area	area	NOUN
ejpam-3377	35	3	which	which	PRON
ejpam-3377	35	4	has	have	AUX
ejpam-3377	35	5	greatly	greatly	ADV
ejpam-3377	35	6	attracted	attract	VERB
ejpam-3377	35	7	the	the	DET
ejpam-3377	35	8	attention	attention	NOUN
ejpam-3377	35	9	of	of	ADP
ejpam-3377	35	10	researches	research	NOUN
ejpam-3377	35	11	is	be	AUX
ejpam-3377	35	12	devoted	devote	VERB
ejpam-3377	35	13	to	to	ADP
ejpam-3377	35	14	the	the	DET
ejpam-3377	35	15	existence	existence	NOUN
ejpam-3377	35	16	theory	theory	NOUN
ejpam-3377	35	17	and	and	CCONJ
ejpam-3377	35	18	numerical	numerical	ADJ
ejpam-3377	35	19	solution	solution	NOUN
ejpam-3377	35	20	of	of	ADP
ejpam-3377	35	21	fractional	fractional	ADJ
ejpam-3377	35	22	order	order	NOUN
ejpam-3377	35	23	partial	partial	ADJ
ejpam-3377	35	24	differential	differential	NOUN
ejpam-3377	35	25	equations	equation	NOUN
ejpam-3377	35	26	.	.	PUNCT
ejpam-3377	36	1	since	since	SCONJ
ejpam-3377	36	2	the	the	DET
ejpam-3377	36	3	differential	differential	ADJ
ejpam-3377	36	4	equations	equation	NOUN
ejpam-3377	36	5	involved	involve	VERB
ejpam-3377	36	6	fractional	fractional	ADJ
ejpam-3377	36	7	order	order	NOUN
ejpam-3377	36	8	are	be	AUX
ejpam-3377	36	9	not	not	PART
ejpam-3377	36	10	easy	easy	ADJ
ejpam-3377	36	11	to	to	PART
ejpam-3377	36	12	solve	solve	VERB
ejpam-3377	36	13	for	for	ADP
ejpam-3377	36	14	theirs	theirs	PRON
ejpam-3377	36	15	exact	exact	ADJ
ejpam-3377	36	16	solutions	solution	NOUN
ejpam-3377	36	17	in	in	ADP
ejpam-3377	36	18	many	many	ADJ
ejpam-3377	36	19	situations	situation	NOUN
ejpam-3377	36	20	,	,	PUNCT
ejpam-3377	36	21	therefore	therefore	ADV
ejpam-3377	36	22	a	a	DET
ejpam-3377	36	23	strong	strong	ADJ
ejpam-3377	36	24	motivation	motivation	NOUN
ejpam-3377	36	25	has	have	AUX
ejpam-3377	36	26	been	be	AUX
ejpam-3377	36	27	found	find	VERB
ejpam-3377	36	28	to	to	PART
ejpam-3377	36	29	find	find	VERB
ejpam-3377	36	30	the	the	DET
ejpam-3377	36	31	approximate	approximate	ADJ
ejpam-3377	36	32	solutions	solution	NOUN
ejpam-3377	36	33	.	.	PUNCT
ejpam-3377	37	1	in	in	ADP
ejpam-3377	37	2	general	general	ADJ
ejpam-3377	37	3	there	there	PRON
ejpam-3377	37	4	does	do	AUX
ejpam-3377	37	5	not	not	PART
ejpam-3377	37	6	exist	exist	VERB
ejpam-3377	37	7	a	a	DET
ejpam-3377	37	8	method	method	NOUN
ejpam-3377	37	9	which	which	PRON
ejpam-3377	37	10	produce	produce	VERB
ejpam-3377	37	11	exact	exact	ADJ
ejpam-3377	37	12	solutions	solution	NOUN
ejpam-3377	37	13	of	of	ADP
ejpam-3377	37	14	fpdes	fpde	NOUN
ejpam-3377	37	15	.	.	PUNCT
ejpam-3377	38	1	in	in	ADP
ejpam-3377	38	2	many	many	ADJ
ejpam-3377	38	3	situations	situation	NOUN
ejpam-3377	38	4	for	for	ADP
ejpam-3377	38	5	linear	linear	ADJ
ejpam-3377	38	6	partial	partial	ADJ
ejpam-3377	38	7	differential	differential	NOUN
ejpam-3377	38	8	equations	equation	NOUN
ejpam-3377	38	9	it	it	PRON
ejpam-3377	38	10	is	be	AUX
ejpam-3377	38	11	quite	quite	ADV
ejpam-3377	38	12	difficult	difficult	ADJ
ejpam-3377	38	13	task	task	NOUN
ejpam-3377	38	14	to	to	PART
ejpam-3377	38	15	find	find	VERB
ejpam-3377	38	16	exact	exact	ADJ
ejpam-3377	38	17	solutions	solution	NOUN
ejpam-3377	38	18	.	.	PUNCT
ejpam-3377	39	1	therefore	therefore	ADV
ejpam-3377	39	2	,	,	PUNCT
ejpam-3377	39	3	numerous	numerous	ADJ
ejpam-3377	39	4	techniques	technique	NOUN
ejpam-3377	39	5	were	be	AUX
ejpam-3377	39	6	developed	develop	VERB
ejpam-3377	39	7	to	to	PART
ejpam-3377	39	8	find	find	VERB
ejpam-3377	39	9	approximate	approximate	ADJ
ejpam-3377	39	10	solutions	solution	NOUN
ejpam-3377	39	11	to	to	ADP
ejpam-3377	39	12	the	the	DET
ejpam-3377	39	13	aforementioned	aforementioned	ADJ
ejpam-3377	39	14	equations	equation	NOUN
ejpam-3377	39	15	.	.	PUNCT
ejpam-3377	40	1	in	in	ADP
ejpam-3377	40	2	[	[	X
ejpam-3377	40	3	8	8	NUM
ejpam-3377	40	4	,	,	PUNCT
ejpam-3377	40	5	18	18	NUM
ejpam-3377	40	6	]	]	PUNCT
ejpam-3377	40	7	,	,	PUNCT
ejpam-3377	40	8	authors	author	NOUN
ejpam-3377	40	9	applied	apply	VERB
ejpam-3377	40	10	homotopy	homotopy	NOUN
ejpam-3377	40	11	analysis	analysis	NOUN
ejpam-3377	40	12	method(ham	method(ham	NOUN
ejpam-3377	40	13	)	)	PUNCT
ejpam-3377	40	14	and	and	CCONJ
ejpam-3377	40	15	he	he	PRON
ejpam-3377	40	16	’s	’	VERB
ejpam-3377	40	17	variation	variation	NOUN
ejpam-3377	40	18	iteration	iteration	NOUN
ejpam-3377	40	19	method(vim	method(vim	PROPN
ejpam-3377	40	20	)	)	PUNCT
ejpam-3377	40	21	to	to	PART
ejpam-3377	40	22	calculate	calculate	VERB
ejpam-3377	40	23	approximate	approximate	ADJ
ejpam-3377	40	24	solutions	solution	NOUN
ejpam-3377	40	25	of	of	ADP
ejpam-3377	40	26	nonlinear	nonlinear	ADJ
ejpam-3377	40	27	fpdes	fpde	NOUN
ejpam-3377	40	28	.	.	PUNCT
ejpam-3377	41	1	in	in	ADP
ejpam-3377	41	2	same	same	ADJ
ejpam-3377	41	3	line	line	NOUN
ejpam-3377	41	4	,	,	PUNCT
ejpam-3377	41	5	authors	author	NOUN
ejpam-3377	41	6	,	,	PUNCT
ejpam-3377	41	7	used	use	VERB
ejpam-3377	41	8	adomain	adomain	NOUN
ejpam-3377	41	9	decomposition	decomposition	NOUN
ejpam-3377	41	10	method(adm)[16	method(adm)[16	PROPN
ejpam-3377	41	11	]	]	PUNCT
ejpam-3377	41	12	,	,	PUNCT
ejpam-3377	41	13	homotopy	homotopy	VERB
ejpam-3377	41	14	perturbation	perturbation	NOUN
ejpam-3377	41	15	method(hpm)[21	method(hpm)[21	PROPN
ejpam-3377	41	16	]	]	PUNCT
ejpam-3377	41	17	,	,	PUNCT
ejpam-3377	41	18	fourier	fourier	NOUN
ejpam-3377	41	19	transform	transform	VERB
ejpam-3377	41	20	method(ftm)[49	method(ftm)[49	PROPN
ejpam-3377	41	21	]	]	PUNCT
ejpam-3377	41	22	,	,	PUNCT
ejpam-3377	41	23	laplace	laplace	NOUN
ejpam-3377	41	24	and	and	CCONJ
ejpam-3377	41	25	natural	natural	ADJ
ejpam-3377	41	26	transform	transform	NOUN
ejpam-3377	41	27	methods[42	methods[42	NOUN
ejpam-3377	41	28	,	,	PUNCT
ejpam-3377	41	29	43	43	NUM
ejpam-3377	41	30	]	]	PUNCT
ejpam-3377	41	31	to	to	PART
ejpam-3377	41	32	solve	solve	VERB
ejpam-3377	41	33	fractional	fractional	ADJ
ejpam-3377	41	34	order	order	NOUN
ejpam-3377	41	35	partial	partial	ADJ
ejpam-3377	41	36	differential	differential	NOUN
ejpam-3377	41	37	equation	equation	NOUN
ejpam-3377	41	38	.	.	PUNCT
ejpam-3377	42	1	also	also	ADV
ejpam-3377	42	2	,	,	PUNCT
ejpam-3377	42	3	some	some	DET
ejpam-3377	42	4	authors	author	NOUN
ejpam-3377	42	5	used	use	VERB
ejpam-3377	42	6	fractional	fractional	ADJ
ejpam-3377	42	7	differential	differential	NOUN
ejpam-3377	42	8	transform	transform	NOUN
ejpam-3377	42	9	(	(	PUNCT
ejpam-3377	42	10	fdtm)[2	fdtm)[2	NUM
ejpam-3377	42	11	,	,	PUNCT
ejpam-3377	42	12	3	3	NUM
ejpam-3377	42	13	,	,	PUNCT
ejpam-3377	42	14	37	37	NUM
ejpam-3377	42	15	]	]	PUNCT
ejpam-3377	42	16	,	,	PUNCT
ejpam-3377	42	17	to	to	PART
ejpam-3377	42	18	find	find	VERB
ejpam-3377	42	19	numerical	numerical	ADJ
ejpam-3377	42	20	solutions	solution	NOUN
ejpam-3377	42	21	of	of	ADP
ejpam-3377	42	22	fpdes	fpde	NOUN
ejpam-3377	42	23	.	.	PUNCT
ejpam-3377	43	1	but	but	CCONJ
ejpam-3377	43	2	all	all	DET
ejpam-3377	43	3	these	these	DET
ejpam-3377	43	4	method	method	NOUN
ejpam-3377	43	5	have	have	VERB
ejpam-3377	43	6	their	their	PRON
ejpam-3377	43	7	own	own	ADJ
ejpam-3377	43	8	advantages	advantage	NOUN
ejpam-3377	43	9	and	and	CCONJ
ejpam-3377	43	10	disadvantages	disadvantage	NOUN
ejpam-3377	43	11	in	in	ADP
ejpam-3377	43	12	application	application	NOUN
ejpam-3377	43	13	point	point	NOUN
ejpam-3377	43	14	of	of	ADP
ejpam-3377	43	15	view	view	NOUN
ejpam-3377	43	16	,	,	PUNCT
ejpam-3377	43	17	as	as	SCONJ
ejpam-3377	43	18	homotopy	homotopy	NOUN
ejpam-3377	43	19	methods	method	NOUN
ejpam-3377	43	20	depend	depend	VERB
ejpam-3377	43	21	on	on	ADP
ejpam-3377	43	22	small	small	ADJ
ejpam-3377	43	23	parameters	parameter	NOUN
ejpam-3377	43	24	which	which	PRON
ejpam-3377	43	25	restricted	restrict	VERB
ejpam-3377	43	26	these	these	DET
ejpam-3377	43	27	methods	method	NOUN
ejpam-3377	43	28	.	.	PUNCT
ejpam-3377	44	1	similarly	similarly	ADV
ejpam-3377	44	2	the	the	DET
ejpam-3377	44	3	methods	method	NOUN
ejpam-3377	44	4	that	that	PRON
ejpam-3377	44	5	are	be	AUX
ejpam-3377	44	6	involving	involve	VERB
ejpam-3377	44	7	integral	integral	ADJ
ejpam-3377	44	8	transform	transform	NOUN
ejpam-3377	44	9	are	be	AUX
ejpam-3377	44	10	also	also	ADV
ejpam-3377	44	11	limited	limit	VERB
ejpam-3377	44	12	in	in	ADP
ejpam-3377	44	13	applications	application	NOUN
ejpam-3377	44	14	.	.	PUNCT
ejpam-3377	45	1	in	in	ADP
ejpam-3377	45	2	last	last	ADJ
ejpam-3377	45	3	few	few	ADJ
ejpam-3377	45	4	decades	decade	NOUN
ejpam-3377	45	5	some	some	DET
ejpam-3377	45	6	interesting	interesting	ADJ
ejpam-3377	45	7	numerical	numerical	ADJ
ejpam-3377	45	8	schemes	scheme	NOUN
ejpam-3377	45	9	based	base	VERB
ejpam-3377	45	10	on	on	ADP
ejpam-3377	45	11	radial	radial	ADJ
ejpam-3377	45	12	basis	basis	NOUN
ejpam-3377	45	13	functions(rbfs	functions(rbfs	PROPN
ejpam-3377	45	14	)	)	PUNCT
ejpam-3377	45	15	and	and	CCONJ
ejpam-3377	45	16	meshless	meshless	ADJ
ejpam-3377	45	17	techniques	technique	NOUN
ejpam-3377	45	18	depend	depend	VERB
ejpam-3377	45	19	on	on	ADP
ejpam-3377	45	20	collocation	collocation	NOUN
ejpam-3377	45	21	and	and	CCONJ
ejpam-3377	45	22	(	(	PUNCT
ejpam-3377	45	23	rbfs	rbfs	NOUN
ejpam-3377	45	24	)	)	PUNCT
ejpam-3377	45	25	for	for	ADP
ejpam-3377	45	26	solving	solve	VERB
ejpam-3377	45	27	(	(	PUNCT
ejpam-3377	45	28	pdes	pde	NOUN
ejpam-3377	45	29	)	)	PUNCT
ejpam-3377	45	30	,	,	PUNCT
ejpam-3377	45	31	see[31	see[31	PROPN
ejpam-3377	45	32	,	,	PUNCT
ejpam-3377	45	33	47	47	NUM
ejpam-3377	45	34	]	]	PUNCT
ejpam-3377	45	35	.	.	PUNCT
ejpam-3377	46	1	m.i	m.i	PROPN
ejpam-3377	46	2	.	.	PROPN
ejpam-3377	46	3	chohan	chohan	PROPN
ejpam-3377	46	4	,	,	PUNCT
ejpam-3377	46	5	k.shah	k.shah	PROPN
ejpam-3377	46	6	/	/	SYM
ejpam-3377	46	7	eur	eur	PROPN
ejpam-3377	46	8	.	.	PUNCT
ejpam-3377	47	1	j.	j.	PROPN
ejpam-3377	47	2	pure	pure	PROPN
ejpam-3377	47	3	appl	appl	PROPN
ejpam-3377	47	4	.	.	PROPN
ejpam-3377	47	5	math	math	PROPN
ejpam-3377	47	6	,	,	PUNCT
ejpam-3377	47	7	12	12	NUM
ejpam-3377	47	8	(	(	PUNCT
ejpam-3377	47	9	1	1	NUM
ejpam-3377	47	10	)	)	PUNCT
ejpam-3377	47	11	(	(	PUNCT
ejpam-3377	47	12	2019	2019	NUM
ejpam-3377	47	13	)	)	PUNCT
ejpam-3377	47	14	,	,	PUNCT
ejpam-3377	47	15	39	39	NUM
ejpam-3377	47	16	-	-	SYM
ejpam-3377	47	17	57	57	NUM
ejpam-3377	47	18	41	41	NUM
ejpam-3377	47	19	recently	recently	ADV
ejpam-3377	47	20	,	,	PUNCT
ejpam-3377	47	21	numerical	numerical	ADJ
ejpam-3377	47	22	schemes	scheme	NOUN
ejpam-3377	47	23	based	base	VERB
ejpam-3377	47	24	on	on	ADP
ejpam-3377	47	25	operational	operational	ADJ
ejpam-3377	47	26	matrices	matrix	NOUN
ejpam-3377	47	27	have	have	AUX
ejpam-3377	47	28	attracted	attract	VERB
ejpam-3377	47	29	the	the	DET
ejpam-3377	47	30	attention	attention	NOUN
ejpam-3377	47	31	of	of	ADP
ejpam-3377	47	32	many	many	ADJ
ejpam-3377	47	33	researches	research	NOUN
ejpam-3377	47	34	.	.	PUNCT
ejpam-3377	48	1	the	the	DET
ejpam-3377	48	2	mentioned	mention	VERB
ejpam-3377	48	3	techniques	technique	NOUN
ejpam-3377	48	4	provide	provide	VERB
ejpam-3377	48	5	highly	highly	ADV
ejpam-3377	48	6	accurate	accurate	ADJ
ejpam-3377	48	7	numerical	numerical	ADJ
ejpam-3377	48	8	solutions	solution	NOUN
ejpam-3377	48	9	to	to	ADP
ejpam-3377	48	10	both	both	CCONJ
ejpam-3377	48	11	linear	linear	ADJ
ejpam-3377	48	12	and	and	CCONJ
ejpam-3377	48	13	nonlinear	nonlinear	ADJ
ejpam-3377	48	14	ordinary	ordinary	ADJ
ejpam-3377	48	15	as	as	ADV
ejpam-3377	48	16	well	well	ADV
ejpam-3377	48	17	as	as	ADP
ejpam-3377	48	18	partial	partial	ADJ
ejpam-3377	48	19	differential	differential	ADJ
ejpam-3377	48	20	equations	equation	NOUN
ejpam-3377	48	21	of	of	ADP
ejpam-3377	48	22	classical	classical	ADJ
ejpam-3377	48	23	and	and	CCONJ
ejpam-3377	48	24	fractional	fractional	ADJ
ejpam-3377	48	25	order	order	NOUN
ejpam-3377	48	26	.	.	PUNCT
ejpam-3377	49	1	in	in	ADP
ejpam-3377	49	2	the	the	DET
ejpam-3377	49	3	concerned	concerned	ADJ
ejpam-3377	49	4	schemes	scheme	NOUN
ejpam-3377	49	5	some	some	DET
ejpam-3377	49	6	operational	operational	ADJ
ejpam-3377	49	7	matrices	matrix	NOUN
ejpam-3377	49	8	of	of	ADP
ejpam-3377	49	9	fractional	fractional	ADJ
ejpam-3377	49	10	order	order	NOUN
ejpam-3377	49	11	integration	integration	NOUN
ejpam-3377	49	12	and	and	CCONJ
ejpam-3377	49	13	differentiation	differentiation	NOUN
ejpam-3377	49	14	are	be	AUX
ejpam-3377	49	15	constructed	construct	VERB
ejpam-3377	49	16	which	which	PRON
ejpam-3377	49	17	play	play	VERB
ejpam-3377	49	18	central	central	ADJ
ejpam-3377	49	19	rules	rule	NOUN
ejpam-3377	49	20	in	in	ADP
ejpam-3377	49	21	approximation	approximation	NOUN
ejpam-3377	49	22	of	of	ADP
ejpam-3377	49	23	solutions	solution	NOUN
ejpam-3377	49	24	.	.	PUNCT
ejpam-3377	50	1	in	in	ADP
ejpam-3377	50	2	[	[	X
ejpam-3377	50	3	32	32	NUM
ejpam-3377	50	4	,	,	PUNCT
ejpam-3377	50	5	50	50	NUM
ejpam-3377	50	6	]	]	PUNCT
ejpam-3377	50	7	,	,	PUNCT
ejpam-3377	50	8	authors	author	NOUN
ejpam-3377	50	9	used	use	VERB
ejpam-3377	50	10	haar	haar	PROPN
ejpam-3377	50	11	wavelets	wavelet	NOUN
ejpam-3377	50	12	and	and	CCONJ
ejpam-3377	50	13	legendre	legendre	PROPN
ejpam-3377	50	14	wavelets	wavelet	NOUN
ejpam-3377	50	15	to	to	PART
ejpam-3377	50	16	solve	solve	VERB
ejpam-3377	50	17	linear	linear	ADJ
ejpam-3377	50	18	fpdes	fpde	NOUN
ejpam-3377	50	19	.	.	PUNCT
ejpam-3377	51	1	with	with	ADP
ejpam-3377	51	2	the	the	DET
ejpam-3377	51	3	same	same	ADJ
ejpam-3377	51	4	line	line	NOUN
ejpam-3377	51	5	some	some	DET
ejpam-3377	51	6	operational	operational	ADJ
ejpam-3377	51	7	matrices	matrix	NOUN
ejpam-3377	51	8	based	base	VERB
ejpam-3377	51	9	on	on	ADP
ejpam-3377	51	10	chebyshev	chebyshev	PROPN
ejpam-3377	51	11	wavelets	wavelet	NOUN
ejpam-3377	51	12	were	be	AUX
ejpam-3377	51	13	also	also	ADV
ejpam-3377	51	14	used	use	VERB
ejpam-3377	51	15	to	to	PART
ejpam-3377	51	16	find	find	VERB
ejpam-3377	51	17	numerical	numerical	ADJ
ejpam-3377	51	18	solutions	solution	NOUN
ejpam-3377	51	19	to	to	ADP
ejpam-3377	51	20	fpdes	fpde	NOUN
ejpam-3377	51	21	,	,	PUNCT
ejpam-3377	51	22	see	see	VERB
ejpam-3377	51	23	[	[	X
ejpam-3377	51	24	28	28	NUM
ejpam-3377	51	25	]	]	PUNCT
ejpam-3377	51	26	.	.	PUNCT
ejpam-3377	52	1	in	in	ADP
ejpam-3377	52	2	[	[	X
ejpam-3377	52	3	4	4	NUM
ejpam-3377	52	4	,	,	PUNCT
ejpam-3377	52	5	5	5	NUM
ejpam-3377	52	6	,	,	PUNCT
ejpam-3377	52	7	9	9	NUM
ejpam-3377	52	8	,	,	PUNCT
ejpam-3377	52	9	26	26	NUM
ejpam-3377	52	10	,	,	PUNCT
ejpam-3377	52	11	33	33	NUM
ejpam-3377	52	12	,	,	PUNCT
ejpam-3377	52	13	48	48	NUM
ejpam-3377	52	14	,	,	PUNCT
ejpam-3377	52	15	51	51	NUM
ejpam-3377	52	16	]	]	PUNCT
ejpam-3377	52	17	,	,	PUNCT
ejpam-3377	52	18	authors	author	NOUN
ejpam-3377	52	19	constructed	construct	VERB
ejpam-3377	52	20	operational	operational	ADJ
ejpam-3377	52	21	matrices	matrix	NOUN
ejpam-3377	52	22	based	base	VERB
ejpam-3377	52	23	on	on	ADP
ejpam-3377	52	24	lagendre	lagendre	PROPN
ejpam-3377	52	25	,	,	PUNCT
ejpam-3377	52	26	bernstein	bernstein	PROPN
ejpam-3377	52	27	and	and	CCONJ
ejpam-3377	52	28	jacobi	jacobi	PROPN
ejpam-3377	52	29	,	,	PUNCT
ejpam-3377	52	30	chebyshev	chebyshev	PROPN
ejpam-3377	52	31	polynomials	polynomial	NOUN
ejpam-3377	52	32	for	for	ADP
ejpam-3377	52	33	numerical	numerical	ADJ
ejpam-3377	52	34	solutions	solution	NOUN
ejpam-3377	52	35	of	of	ADP
ejpam-3377	52	36	fractional	fractional	ADJ
ejpam-3377	52	37	differential	differential	ADJ
ejpam-3377	52	38	equations	equation	NOUN
ejpam-3377	52	39	.	.	PUNCT
ejpam-3377	53	1	the	the	DET
ejpam-3377	53	2	concerned	concerned	ADJ
ejpam-3377	53	3	method	method	NOUN
ejpam-3377	53	4	used	use	VERB
ejpam-3377	53	5	tau	tau	NOUN
ejpam-3377	53	6	-	-	PUNCT
ejpam-3377	53	7	collocation	collocation	NOUN
ejpam-3377	53	8	method	method	NOUN
ejpam-3377	53	9	to	to	PART
ejpam-3377	53	10	form	form	VERB
ejpam-3377	53	11	the	the	DET
ejpam-3377	53	12	mentioned	mention	VERB
ejpam-3377	53	13	matrices	matrix	NOUN
ejpam-3377	53	14	.	.	PUNCT
ejpam-3377	54	1	as	as	ADP
ejpam-3377	54	2	in	in	ADP
ejpam-3377	54	3	these	these	DET
ejpam-3377	54	4	methods	method	NOUN
ejpam-3377	54	5	discretization	discretization	NOUN
ejpam-3377	54	6	of	of	ADP
ejpam-3377	54	7	date	date	NOUN
ejpam-3377	54	8	is	be	AUX
ejpam-3377	54	9	required	require	VERB
ejpam-3377	54	10	which	which	PRON
ejpam-3377	54	11	need	need	VERB
ejpam-3377	54	12	extra	extra	ADJ
ejpam-3377	54	13	memory	memory	NOUN
ejpam-3377	54	14	but	but	CCONJ
ejpam-3377	54	15	provided	provide	VERB
ejpam-3377	54	16	best	good	ADJ
ejpam-3377	54	17	approximate	approximate	ADJ
ejpam-3377	54	18	solutions	solution	NOUN
ejpam-3377	54	19	to	to	ADP
ejpam-3377	54	20	(	(	PUNCT
ejpam-3377	54	21	fpdes	fpde	NOUN
ejpam-3377	54	22	)	)	PUNCT
ejpam-3377	54	23	.	.	PUNCT
ejpam-3377	55	1	to	to	PART
ejpam-3377	55	2	overcome	overcome	VERB
ejpam-3377	55	3	this	this	DET
ejpam-3377	55	4	difficulty	difficulty	NOUN
ejpam-3377	55	5	,	,	PUNCT
ejpam-3377	55	6	in[22	in[22	PROPN
ejpam-3377	55	7	,	,	PUNCT
ejpam-3377	55	8	23	23	NUM
ejpam-3377	55	9	]	]	PUNCT
ejpam-3377	55	10	authors	author	NOUN
ejpam-3377	55	11	constructed	construct	VERB
ejpam-3377	55	12	the	the	DET
ejpam-3377	55	13	operational	operational	ADJ
ejpam-3377	55	14	matrices	matrix	NOUN
ejpam-3377	55	15	from	from	ADP
ejpam-3377	55	16	the	the	DET
ejpam-3377	55	17	afore	afore	NOUN
ejpam-3377	55	18	mentioned	mention	VERB
ejpam-3377	55	19	polynomial	polynomial	ADJ
ejpam-3377	55	20	directly	directly	ADV
ejpam-3377	55	21	without	without	ADP
ejpam-3377	55	22	discretizing	discretize	VERB
ejpam-3377	55	23	the	the	DET
ejpam-3377	55	24	polynomials	polynomial	NOUN
ejpam-3377	55	25	and	and	CCONJ
ejpam-3377	55	26	obtained	obtain	VERB
ejpam-3377	55	27	excellent	excellent	ADJ
ejpam-3377	55	28	solutions	solution	NOUN
ejpam-3377	55	29	to	to	ADP
ejpam-3377	55	30	(	(	PUNCT
ejpam-3377	55	31	fpdes	fpde	NOUN
ejpam-3377	55	32	)	)	PUNCT
ejpam-3377	55	33	.	.	PUNCT
ejpam-3377	56	1	the	the	DET
ejpam-3377	56	2	spectral	spectral	ADJ
ejpam-3377	56	3	methods	method	NOUN
ejpam-3377	56	4	based	base	VERB
ejpam-3377	56	5	on	on	ADP
ejpam-3377	56	6	operational	operational	ADJ
ejpam-3377	56	7	matrices	matrix	NOUN
ejpam-3377	56	8	are	be	AUX
ejpam-3377	56	9	the	the	DET
ejpam-3377	56	10	best	good	ADJ
ejpam-3377	56	11	tools	tool	NOUN
ejpam-3377	56	12	to	to	PART
ejpam-3377	56	13	find	find	VERB
ejpam-3377	56	14	approximate	approximate	ADJ
ejpam-3377	56	15	solutions	solution	NOUN
ejpam-3377	56	16	for	for	ADP
ejpam-3377	56	17	both	both	CCONJ
ejpam-3377	56	18	ordinary	ordinary	ADJ
ejpam-3377	56	19	and	and	CCONJ
ejpam-3377	56	20	partial	partial	ADJ
ejpam-3377	56	21	fractional	fractional	ADJ
ejpam-3377	56	22	differential	differential	NOUN
ejpam-3377	56	23	equations	equation	NOUN
ejpam-3377	56	24	,	,	PUNCT
ejpam-3377	56	25	for	for	ADP
ejpam-3377	56	26	detail	detail	NOUN
ejpam-3377	56	27	see[10	see[10	PROPN
ejpam-3377	56	28	,	,	PUNCT
ejpam-3377	56	29	12	12	NUM
ejpam-3377	56	30	,	,	PUNCT
ejpam-3377	56	31	20	20	NUM
ejpam-3377	56	32	,	,	PUNCT
ejpam-3377	56	33	25	25	NUM
ejpam-3377	56	34	,	,	PUNCT
ejpam-3377	56	35	27	27	NUM
ejpam-3377	56	36	,	,	PUNCT
ejpam-3377	56	37	45	45	NUM
ejpam-3377	56	38	,	,	PUNCT
ejpam-3377	56	39	46	46	NUM
ejpam-3377	56	40	]	]	PUNCT
ejpam-3377	56	41	.	.	PUNCT
ejpam-3377	57	1	motivated	motivate	VERB
ejpam-3377	57	2	by	by	ADP
ejpam-3377	57	3	the	the	DET
ejpam-3377	57	4	aforesaid	aforesaid	ADJ
ejpam-3377	57	5	work	work	NOUN
ejpam-3377	57	6	,	,	PUNCT
ejpam-3377	57	7	in	in	ADP
ejpam-3377	57	8	this	this	DET
ejpam-3377	57	9	paper	paper	NOUN
ejpam-3377	57	10	we	we	PRON
ejpam-3377	57	11	have	have	AUX
ejpam-3377	57	12	considered	consider	VERB
ejpam-3377	57	13	a	a	DET
ejpam-3377	57	14	general	general	ADJ
ejpam-3377	57	15	multi	multi	ADJ
ejpam-3377	57	16	-	-	ADJ
ejpam-3377	57	17	terms	term	NOUN
ejpam-3377	57	18	fractional	fractional	ADJ
ejpam-3377	57	19	order	order	NOUN
ejpam-3377	57	20	partial	partial	ADJ
ejpam-3377	57	21	differential	differential	NOUN
ejpam-3377	57	22	equations	equation	NOUN
ejpam-3377	57	23	which	which	PRON
ejpam-3377	57	24	represents	represent	VERB
ejpam-3377	57	25	different	different	ADJ
ejpam-3377	57	26	classes	class	NOUN
ejpam-3377	57	27	of	of	ADP
ejpam-3377	57	28	partial	partial	ADJ
ejpam-3377	57	29	differential	differential	NOUN
ejpam-3377	57	30	equations	equation	NOUN
ejpam-3377	57	31	by	by	ADP
ejpam-3377	57	32	assigning	assign	VERB
ejpam-3377	57	33	various	various	ADJ
ejpam-3377	57	34	values	value	NOUN
ejpam-3377	57	35	to	to	ADP
ejpam-3377	57	36	the	the	DET
ejpam-3377	57	37	constants	constant	NOUN
ejpam-3377	57	38	involved	involve	VERB
ejpam-3377	57	39	in	in	ADP
ejpam-3377	57	40	(	(	PUNCT
ejpam-3377	57	41	1	1	NUM
ejpam-3377	57	42	)	)	PUNCT
ejpam-3377	57	43	to	to	PART
ejpam-3377	57	44	satisfied	satisfied	VERB
ejpam-3377	57	45	the	the	DET
ejpam-3377	57	46	specific	specific	ADJ
ejpam-3377	57	47	conditions	condition	NOUN
ejpam-3377	57	48	.	.	PUNCT
ejpam-3377	58	1	the	the	DET
ejpam-3377	58	2	operational	operational	ADJ
ejpam-3377	58	3	matrices	matrix	NOUN
ejpam-3377	58	4	involved	involve	VERB
ejpam-3377	58	5	in	in	ADP
ejpam-3377	58	6	this	this	DET
ejpam-3377	58	7	paper	paper	NOUN
ejpam-3377	58	8	are	be	AUX
ejpam-3377	58	9	based	base	VERB
ejpam-3377	58	10	on	on	ADP
ejpam-3377	58	11	shifted	shift	VERB
ejpam-3377	58	12	jacobi	jacobi	PROPN
ejpam-3377	58	13	polynomials	polynomial	NOUN
ejpam-3377	58	14	.	.	PUNCT
ejpam-3377	59	1	with	with	ADP
ejpam-3377	59	2	the	the	DET
ejpam-3377	59	3	the	the	DET
ejpam-3377	59	4	help	help	NOUN
ejpam-3377	59	5	of	of	ADP
ejpam-3377	59	6	these	these	DET
ejpam-3377	59	7	matrices	matrix	NOUN
ejpam-3377	59	8	of	of	ADP
ejpam-3377	59	9	fractional	fractional	ADJ
ejpam-3377	59	10	order	order	NOUN
ejpam-3377	59	11	integration	integration	NOUN
ejpam-3377	59	12	and	and	CCONJ
ejpam-3377	59	13	differentiation	differentiation	NOUN
ejpam-3377	59	14	,	,	PUNCT
ejpam-3377	59	15	the	the	DET
ejpam-3377	59	16	considered	consider	VERB
ejpam-3377	59	17	equation	equation	NOUN
ejpam-3377	59	18	is	be	AUX
ejpam-3377	59	19	converted	convert	VERB
ejpam-3377	59	20	to	to	ADP
ejpam-3377	59	21	an	an	DET
ejpam-3377	59	22	algebraic	algebraic	ADJ
ejpam-3377	59	23	equation	equation	NOUN
ejpam-3377	59	24	which	which	PRON
ejpam-3377	59	25	is	be	AUX
ejpam-3377	59	26	easily	easily	ADV
ejpam-3377	59	27	soluble	soluble	ADJ
ejpam-3377	59	28	for	for	ADP
ejpam-3377	59	29	unknown	unknown	ADJ
ejpam-3377	59	30	coefficient	coefficient	NOUN
ejpam-3377	59	31	matrix	matrix	NOUN
ejpam-3377	59	32	needed	need	VERB
ejpam-3377	59	33	in	in	ADP
ejpam-3377	59	34	the	the	DET
ejpam-3377	59	35	approximate	approximate	ADJ
ejpam-3377	59	36	solution	solution	NOUN
ejpam-3377	59	37	.	.	PUNCT
ejpam-3377	60	1	all	all	DET
ejpam-3377	60	2	the	the	DET
ejpam-3377	60	3	computations	computation	NOUN
ejpam-3377	60	4	are	be	AUX
ejpam-3377	60	5	done	do	VERB
ejpam-3377	60	6	by	by	ADP
ejpam-3377	60	7	using	use	VERB
ejpam-3377	60	8	matlab	matlab	PROPN
ejpam-3377	60	9	.	.	PUNCT
ejpam-3377	61	1	for	for	ADP
ejpam-3377	61	2	the	the	DET
ejpam-3377	61	3	demonstration	demonstration	NOUN
ejpam-3377	61	4	,	,	PUNCT
ejpam-3377	61	5	we	we	PRON
ejpam-3377	61	6	solve	solve	VERB
ejpam-3377	61	7	different	different	ADJ
ejpam-3377	61	8	examples	example	NOUN
ejpam-3377	61	9	of	of	ADP
ejpam-3377	61	10	physical	physical	ADJ
ejpam-3377	61	11	interest	interest	NOUN
ejpam-3377	61	12	and	and	CCONJ
ejpam-3377	61	13	also	also	ADV
ejpam-3377	61	14	the	the	DET
ejpam-3377	61	15	comparison	comparison	NOUN
ejpam-3377	61	16	of	of	ADP
ejpam-3377	61	17	our	our	PRON
ejpam-3377	61	18	method	method	NOUN
ejpam-3377	61	19	with	with	ADP
ejpam-3377	61	20	other	other	ADJ
ejpam-3377	61	21	method	method	NOUN
ejpam-3377	61	22	is	be	AUX
ejpam-3377	61	23	provided	provide	VERB
ejpam-3377	61	24	.	.	PUNCT
ejpam-3377	62	1	2	2	X
ejpam-3377	62	2	.	.	NUM
ejpam-3377	62	3	preliminaries	preliminary	NOUN
ejpam-3377	62	4	some	some	DET
ejpam-3377	62	5	auxiliary	auxiliary	ADJ
ejpam-3377	62	6	results	result	NOUN
ejpam-3377	62	7	and	and	CCONJ
ejpam-3377	62	8	notions	notion	NOUN
ejpam-3377	62	9	needed	need	VERB
ejpam-3377	62	10	throughout	throughout	ADP
ejpam-3377	62	11	in	in	ADP
ejpam-3377	62	12	this	this	DET
ejpam-3377	62	13	paper	paper	NOUN
ejpam-3377	62	14	are	be	AUX
ejpam-3377	62	15	provided	provide	VERB
ejpam-3377	62	16	as	as	ADP
ejpam-3377	62	17	[	[	X
ejpam-3377	62	18	14	14	NUM
ejpam-3377	62	19	]	]	SYM
ejpam-3377	62	20	:	:	PUNCT
ejpam-3377	62	21	definition	definition	NOUN
ejpam-3377	62	22	2.1	2.1	NUM
ejpam-3377	62	23	.	.	PUNCT
ejpam-3377	63	1	the	the	DET
ejpam-3377	63	2	riemann	riemann	PROPN
ejpam-3377	63	3	-	-	PUNCT
ejpam-3377	63	4	liouville	liouville	NOUN
ejpam-3377	63	5	integral	integral	ADJ
ejpam-3377	63	6	of	of	ADP
ejpam-3377	63	7	arbitrary	arbitrary	ADJ
ejpam-3377	63	8	order	order	NOUN
ejpam-3377	63	9	α	α	X
ejpam-3377	63	10	∈	∈	PROPN
ejpam-3377	63	11	<	<	X
ejpam-3377	63	12	of	of	ADP
ejpam-3377	63	13	a	a	DET
ejpam-3377	63	14	function	function	NOUN
ejpam-3377	63	15	w(x	w(x	NOUN
ejpam-3377	63	16	)	)	PUNCT
ejpam-3377	63	17	is	be	AUX
ejpam-3377	63	18	defined	define	VERB
ejpam-3377	63	19	by	by	ADP
ejpam-3377	63	20	iαw(x	iαw(x	PROPN
ejpam-3377	63	21	)	)	PUNCT
ejpam-3377	63	22	=	=	SYM
ejpam-3377	63	23	1	1	NUM
ejpam-3377	63	24	γ(α	γ(α	NOUN
ejpam-3377	63	25	)	)	PUNCT
ejpam-3377	63	26	∫	∫	PROPN
ejpam-3377	64	1	x	x	X
ejpam-3377	64	2	0	0	PUNCT
ejpam-3377	64	3	(	(	PUNCT
ejpam-3377	64	4	x−	x−	PROPN
ejpam-3377	64	5	τ)α−1w(τ)dτ	τ)α−1w(τ)dτ	PROPN
ejpam-3377	64	6	,	,	PUNCT
ejpam-3377	64	7	such	such	ADJ
ejpam-3377	64	8	that	that	SCONJ
ejpam-3377	64	9	the	the	DET
ejpam-3377	64	10	integral	integral	ADJ
ejpam-3377	64	11	on	on	ADP
ejpam-3377	64	12	right	right	ADJ
ejpam-3377	64	13	hand	hand	NOUN
ejpam-3377	64	14	side	side	NOUN
ejpam-3377	64	15	converges	converge	VERB
ejpam-3377	64	16	pointwise	pointwise	VERB
ejpam-3377	64	17	on	on	ADP
ejpam-3377	64	18	[	[	X
ejpam-3377	64	19	0,∞	0,∞	NOUN
ejpam-3377	64	20	)	)	PUNCT
ejpam-3377	64	21	.	.	PUNCT
ejpam-3377	65	1	also	also	ADV
ejpam-3377	65	2	the	the	DET
ejpam-3377	65	3	aforesaid	aforesaid	ADJ
ejpam-3377	65	4	integral	integral	ADJ
ejpam-3377	65	5	satisfies	satisfie	NOUN
ejpam-3377	65	6	the	the	DET
ejpam-3377	65	7	following	follow	VERB
ejpam-3377	65	8	relations	relation	NOUN
ejpam-3377	65	9	(	(	PUNCT
ejpam-3377	65	10	1	1	NUM
ejpam-3377	65	11	)	)	PUNCT
ejpam-3377	65	12	iαiβw(x	iαiβw(x	NOUN
ejpam-3377	65	13	)	)	PUNCT
ejpam-3377	65	14	=	=	SYM
ejpam-3377	65	15	iβiαw(x	iβiαw(x	NOUN
ejpam-3377	65	16	)	)	PUNCT
ejpam-3377	65	17	;	;	PUNCT
ejpam-3377	65	18	(	(	PUNCT
ejpam-3377	65	19	2	2	X
ejpam-3377	65	20	)	)	PUNCT
ejpam-3377	65	21	iαiβw(x	iαiβw(x	NOUN
ejpam-3377	65	22	)	)	PUNCT
ejpam-3377	65	23	=	=	SYM
ejpam-3377	65	24	iα+βw(x	iα+βw(x	PROPN
ejpam-3377	65	25	)	)	PUNCT
ejpam-3377	65	26	;	;	PUNCT
ejpam-3377	65	27	m.i	m.i	PROPN
ejpam-3377	65	28	.	.	PROPN
ejpam-3377	65	29	chohan	chohan	PROPN
ejpam-3377	65	30	,	,	PUNCT
ejpam-3377	65	31	k.shah	k.shah	PROPN
ejpam-3377	65	32	/	/	SYM
ejpam-3377	65	33	eur	eur	PROPN
ejpam-3377	65	34	.	.	PUNCT
ejpam-3377	66	1	j.	j.	PROPN
ejpam-3377	66	2	pure	pure	PROPN
ejpam-3377	66	3	appl	appl	PROPN
ejpam-3377	66	4	.	.	PROPN
ejpam-3377	66	5	math	math	PROPN
ejpam-3377	66	6	,	,	PUNCT
ejpam-3377	66	7	12	12	NUM
ejpam-3377	66	8	(	(	PUNCT
ejpam-3377	66	9	1	1	NUM
ejpam-3377	66	10	)	)	PUNCT
ejpam-3377	66	11	(	(	PUNCT
ejpam-3377	66	12	2019	2019	NUM
ejpam-3377	66	13	)	)	PUNCT
ejpam-3377	66	14	,	,	PUNCT
ejpam-3377	66	15	39	39	NUM
ejpam-3377	66	16	-	-	SYM
ejpam-3377	66	17	57	57	NUM
ejpam-3377	66	18	42	42	NUM
ejpam-3377	66	19	(	(	PUNCT
ejpam-3377	66	20	3	3	NUM
ejpam-3377	66	21	)	)	PUNCT
ejpam-3377	66	22	iαxγ	iαxγ	NOUN
ejpam-3377	66	23	=	=	SYM
ejpam-3377	66	24	γ(γ+1	γ(γ+1	NUM
ejpam-3377	66	25	)	)	PUNCT
ejpam-3377	66	26	γ(α+γ+1)x	γ(α+γ+1)x	ADP
ejpam-3377	66	27	α+γ	α+γ	NUM
ejpam-3377	66	28	.	.	PUNCT
ejpam-3377	67	1	definition	definition	NOUN
ejpam-3377	67	2	2.2	2.2	NUM
ejpam-3377	67	3	.	.	PUNCT
ejpam-3377	68	1	let	let	VERB
ejpam-3377	68	2	w(x	w(x	PRON
ejpam-3377	68	3	)	)	PUNCT
ejpam-3377	68	4	∈	∈	PROPN
ejpam-3377	68	5	c2[0,∞	c2[0,∞	PROPN
ejpam-3377	68	6	)	)	PUNCT
ejpam-3377	68	7	,	,	PUNCT
ejpam-3377	68	8	the	the	DET
ejpam-3377	68	9	arbitrary	arbitrary	ADJ
ejpam-3377	68	10	order	order	NOUN
ejpam-3377	68	11	α	α	X
ejpam-3377	68	12	∈	∈	PROPN
ejpam-3377	68	13	(	(	PUNCT
ejpam-3377	68	14	0,∞	0,∞	NOUN
ejpam-3377	68	15	)	)	PUNCT
ejpam-3377	68	16	derivative	derivative	NOUN
ejpam-3377	68	17	is	be	AUX
ejpam-3377	68	18	recalled	recall	VERB
ejpam-3377	68	19	as	as	ADP
ejpam-3377	68	20	dαw(x	dαw(x	PROPN
ejpam-3377	68	21	)	)	PUNCT
ejpam-3377	68	22	=	=	SYM
ejpam-3377	69	1	∫	∫	PROPN
ejpam-3377	69	2	x	x	SYM
ejpam-3377	69	3	0	0	PUNCT
ejpam-3377	69	4	(	(	PUNCT
ejpam-3377	69	5	x−	x−	PROPN
ejpam-3377	69	6	τ)α+1−n	τ)α+1−n	PROPN
ejpam-3377	69	7	γ(n−	γ(n−	PROPN
ejpam-3377	69	8	α	α	PROPN
ejpam-3377	69	9	)	)	PUNCT
ejpam-3377	69	10	w(n)(x)dτ	w(n)(x)dτ	PROPN
ejpam-3377	69	11	,	,	PUNCT
ejpam-3377	69	12	α	α	PROPN
ejpam-3377	69	13	∈	∈	PROPN
ejpam-3377	69	14	(	(	PUNCT
ejpam-3377	69	15	n−	n−	NOUN
ejpam-3377	69	16	1	1	NUM
ejpam-3377	69	17	,	,	PUNCT
ejpam-3377	69	18	n	n	CCONJ
ejpam-3377	69	19	]	]	PUNCT
ejpam-3377	69	20	;	;	PUNCT
ejpam-3377	69	21	n	n	X
ejpam-3377	69	22	=	=	PUNCT
ejpam-3377	70	1	[	[	X
ejpam-3377	70	2	α	α	X
ejpam-3377	70	3	]	]	X
ejpam-3377	70	4	+	+	NOUN
ejpam-3377	70	5	1	1	NUM
ejpam-3377	70	6	,	,	PUNCT
ejpam-3377	70	7	where	where	SCONJ
ejpam-3377	70	8	the	the	DET
ejpam-3377	70	9	integral	integral	NOUN
ejpam-3377	70	10	on	on	ADP
ejpam-3377	70	11	the	the	DET
ejpam-3377	70	12	right	right	NOUN
ejpam-3377	70	13	is	be	AUX
ejpam-3377	70	14	converges	converge	NOUN
ejpam-3377	70	15	on	on	ADP
ejpam-3377	70	16	[	[	X
ejpam-3377	70	17	0,∞	0,∞	NOUN
ejpam-3377	70	18	)	)	PUNCT
ejpam-3377	70	19	.	.	PUNCT
ejpam-3377	71	1	further	far	ADV
ejpam-3377	71	2	,	,	PUNCT
ejpam-3377	71	3	the	the	DET
ejpam-3377	71	4	operator	operator	NOUN
ejpam-3377	71	5	d	d	NOUN
ejpam-3377	71	6	satisfies	satisfy	VERB
ejpam-3377	71	7	the	the	DET
ejpam-3377	71	8	following	follow	VERB
ejpam-3377	71	9	properties	property	NOUN
ejpam-3377	71	10	in	in	ADP
ejpam-3377	71	11	particular	particular	ADJ
ejpam-3377	71	12	for	for	ADP
ejpam-3377	71	13	any	any	DET
ejpam-3377	71	14	constant	constant	ADJ
ejpam-3377	71	15	c	c	NOUN
ejpam-3377	71	16	,	,	PUNCT
ejpam-3377	71	17	dαc	dαc	X
ejpam-3377	71	18	=	=	SYM
ejpam-3377	71	19	0	0	NUM
ejpam-3377	71	20	and	and	CCONJ
ejpam-3377	71	21	dαxi	dαxi	NOUN
ejpam-3377	71	22	=	=	PUNCT
ejpam-3377	71	23			PROPN
ejpam-3377	71	24	0	0	NUM
ejpam-3377	71	25	,	,	PUNCT
ejpam-3377	71	26	i	i	PRON
ejpam-3377	71	27	∈	∈	PROPN
ejpam-3377	71	28	n	n	CCONJ
ejpam-3377	71	29	,	,	PUNCT
ejpam-3377	72	1	i	i	PRON
ejpam-3377	72	2	<	<	X
ejpam-3377	73	1	[	[	X
ejpam-3377	73	2	α	α	X
ejpam-3377	73	3	]	]	X
ejpam-3377	73	4	,	,	PUNCT
ejpam-3377	74	1	γ(1	γ(1	PROPN
ejpam-3377	74	2	+	+	CCONJ
ejpam-3377	74	3	i	i	NOUN
ejpam-3377	74	4	)	)	PUNCT
ejpam-3377	75	1	γ(1	γ(1	PROPN
ejpam-3377	75	2	+	+	CCONJ
ejpam-3377	75	3	i−	i−	PROPN
ejpam-3377	75	4	α	α	NOUN
ejpam-3377	75	5	)	)	PUNCT
ejpam-3377	75	6	xi−α	xi−α	PROPN
ejpam-3377	75	7	.	.	PUNCT
ejpam-3377	76	1	the	the	DET
ejpam-3377	76	2	following	follow	VERB
ejpam-3377	76	3	relations	relation	NOUN
ejpam-3377	76	4	are	be	AUX
ejpam-3377	76	5	necessary	necessary	ADJ
ejpam-3377	76	6	throughout	throughout	ADP
ejpam-3377	76	7	this	this	DET
ejpam-3377	76	8	paper	paper	NOUN
ejpam-3377	76	9	.	.	PUNCT
ejpam-3377	77	1	theorem	theorem	VERB
ejpam-3377	77	2	2.3	2.3	NUM
ejpam-3377	77	3	.	.	PUNCT
ejpam-3377	78	1	for	for	ADP
ejpam-3377	78	2	any	any	DET
ejpam-3377	78	3	function	function	NOUN
ejpam-3377	78	4	w(x	w(x	PROPN
ejpam-3377	78	5	)	)	PUNCT
ejpam-3377	78	6	,	,	PUNCT
ejpam-3377	78	7	the	the	DET
ejpam-3377	78	8	following	follow	VERB
ejpam-3377	78	9	results	result	NOUN
ejpam-3377	78	10	hold	hold	VERB
ejpam-3377	78	11	.	.	PUNCT
ejpam-3377	79	1	(	(	PUNCT
ejpam-3377	79	2	a	a	X
ejpam-3377	79	3	)	)	PUNCT
ejpam-3377	79	4	dαiαw(x	dαiαw(x	NOUN
ejpam-3377	79	5	)	)	PUNCT
ejpam-3377	79	6	=	=	SYM
ejpam-3377	80	1	w(x	w(x	NOUN
ejpam-3377	80	2	)	)	PUNCT
ejpam-3377	80	3	;	;	PUNCT
ejpam-3377	80	4	(	(	PUNCT
ejpam-3377	80	5	b	b	X
ejpam-3377	80	6	)	)	PUNCT
ejpam-3377	80	7	iαdαw(x	iαdαw(x	NOUN
ejpam-3377	80	8	)	)	PUNCT
ejpam-3377	80	9	=	=	SYM
ejpam-3377	80	10	w(x)−	w(x)−	NOUN
ejpam-3377	80	11	∑n−1	∑n−1	ADP
ejpam-3377	81	1	i=0	i=0	PROPN
ejpam-3377	81	2	w	w	PROPN
ejpam-3377	81	3	(	(	PUNCT
ejpam-3377	81	4	i	i	NOUN
ejpam-3377	81	5	)	)	PUNCT
ejpam-3377	81	6	xi	xi	ADP
ejpam-3377	81	7	γ(i+1	γ(i+1	PROPN
ejpam-3377	81	8	)	)	PUNCT
ejpam-3377	81	9	;	;	PUNCT
ejpam-3377	81	10	(	(	PUNCT
ejpam-3377	81	11	c	c	X
ejpam-3377	81	12	)	)	PUNCT
ejpam-3377	81	13	dα(λu(x	dα(λu(x	PROPN
ejpam-3377	81	14	)	)	PUNCT
ejpam-3377	82	1	+	+	CCONJ
ejpam-3377	82	2	µv(x	µv(x	NUM
ejpam-3377	82	3	)	)	PUNCT
ejpam-3377	82	4	)	)	PUNCT
ejpam-3377	83	1	=	=	PUNCT
ejpam-3377	83	2	λdαu(x	λdαu(x	X
ejpam-3377	83	3	)	)	PUNCT
ejpam-3377	83	4	+	+	CCONJ
ejpam-3377	83	5	µdαv(x	µdαv(x	NOUN
ejpam-3377	83	6	)	)	PUNCT
ejpam-3377	83	7	.	.	PUNCT
ejpam-3377	84	1	2.1	2.1	NUM
ejpam-3377	84	2	.	.	PUNCT
ejpam-3377	85	1	the	the	DET
ejpam-3377	85	2	shifted	shift	VERB
ejpam-3377	85	3	jacobi	jacobi	NOUN
ejpam-3377	85	4	polynomials	polynomial	VERB
ejpam-3377	85	5	the	the	DET
ejpam-3377	85	6	famous	famous	ADJ
ejpam-3377	85	7	jacobi	jacobi	NOUN
ejpam-3377	85	8	polynomials	polynomial	NOUN
ejpam-3377	85	9	with	with	ADP
ejpam-3377	85	10	two	two	NUM
ejpam-3377	85	11	parameters	parameter	NOUN
ejpam-3377	85	12	say	say	VERB
ejpam-3377	85	13	p	p	X
ejpam-3377	85	14	,	,	PUNCT
ejpam-3377	85	15	q	q	X
ejpam-3377	85	16	are	be	AUX
ejpam-3377	85	17	defined	define	VERB
ejpam-3377	85	18	on	on	ADP
ejpam-3377	85	19	[	[	X
ejpam-3377	85	20	0	0	NUM
ejpam-3377	85	21	,	,	PUNCT
ejpam-3377	85	22	δ	δ	PROPN
ejpam-3377	85	23	]	]	PUNCT
ejpam-3377	85	24	as	as	ADP
ejpam-3377	85	25	z(p	z(p	ADJ
ejpam-3377	85	26	,	,	PUNCT
ejpam-3377	85	27	q	q	ADJ
ejpam-3377	85	28	)	)	PUNCT
ejpam-3377	85	29	δ	δ	PROPN
ejpam-3377	85	30	,	,	PUNCT
ejpam-3377	85	31	k	k	PROPN
ejpam-3377	85	32	(	(	PUNCT
ejpam-3377	85	33	x	x	X
ejpam-3377	85	34	)	)	PUNCT
ejpam-3377	86	1	=	=	SYM
ejpam-3377	86	2	i∑	i∑	NOUN
ejpam-3377	86	3	k=0	k=0	PROPN
ejpam-3377	86	4	(	(	PUNCT
ejpam-3377	86	5	−1)i−kγ(k	−1)i−kγ(k	NOUN
ejpam-3377	86	6	+	+	CCONJ
ejpam-3377	86	7	q	q	NOUN
ejpam-3377	87	1	+	+	PROPN
ejpam-3377	87	2	1)γ(i+	1)γ(i+	NUM
ejpam-3377	87	3	k	k	X
ejpam-3377	88	1	+	+	PROPN
ejpam-3377	88	2	p+	p+	NOUN
ejpam-3377	88	3	q	q	X
ejpam-3377	88	4	+	+	PROPN
ejpam-3377	88	5	1	1	NUM
ejpam-3377	88	6	)	)	PUNCT
ejpam-3377	88	7	γ(i+	γ(i+	VERB
ejpam-3377	88	8	q	q	PROPN
ejpam-3377	89	1	+	+	NUM
ejpam-3377	89	2	1)γ(k	1)γ(k	NUM
ejpam-3377	89	3	+	+	NUM
ejpam-3377	89	4	p+	p+	NOUN
ejpam-3377	89	5	q	q	NOUN
ejpam-3377	89	6	+	+	NUM
ejpam-3377	89	7	1)γ(i−	1)γ(i−	NUM
ejpam-3377	90	1	k	k	NOUN
ejpam-3377	91	1	+	+	CCONJ
ejpam-3377	91	2	1)γ(k	1)γ(k	NUM
ejpam-3377	91	3	+	+	NUM
ejpam-3377	91	4	1)δk	1)δk	NUM
ejpam-3377	91	5	xk	xk	X
ejpam-3377	91	6	,	,	PUNCT
ejpam-3377	91	7	i	i	NOUN
ejpam-3377	91	8	=	=	NOUN
ejpam-3377	91	9	0	0	NUM
ejpam-3377	91	10	,	,	PUNCT
ejpam-3377	91	11	1	1	NUM
ejpam-3377	91	12	,	,	PUNCT
ejpam-3377	91	13	2	2	NUM
ejpam-3377	91	14	,	,	PUNCT
ejpam-3377	91	15	3	3	NUM
ejpam-3377	91	16	.	.	PUNCT
ejpam-3377	91	17	.	.	PUNCT
ejpam-3377	91	18	.	.	PUNCT
ejpam-3377	92	1	.	.	PUNCT
ejpam-3377	93	1	(	(	PUNCT
ejpam-3377	93	2	2	2	X
ejpam-3377	93	3	)	)	PUNCT
ejpam-3377	93	4	the	the	DET
ejpam-3377	93	5	orthogonality	orthogonality	NOUN
ejpam-3377	93	6	condition	condition	NOUN
ejpam-3377	93	7	is∫	is∫	NOUN
ejpam-3377	93	8	1	1	NUM
ejpam-3377	93	9	0	0	NUM
ejpam-3377	93	10	z(p	z(p	NUM
ejpam-3377	93	11	,	,	PUNCT
ejpam-3377	93	12	q	q	NOUN
ejpam-3377	93	13	)	)	PUNCT
ejpam-3377	93	14	δ	δ	PROPN
ejpam-3377	93	15	,	,	PUNCT
ejpam-3377	93	16	i	i	PRON
ejpam-3377	93	17	(	(	PUNCT
ejpam-3377	93	18	x)z(p	x)z(p	PROPN
ejpam-3377	93	19	,	,	PUNCT
ejpam-3377	93	20	q	q	ADJ
ejpam-3377	93	21	)	)	PUNCT
ejpam-3377	93	22	δ	δ	PROPN
ejpam-3377	93	23	,	,	PUNCT
ejpam-3377	93	24	i	i	PRON
ejpam-3377	93	25	(	(	PUNCT
ejpam-3377	93	26	x)w(p	x)w(p	ADJ
ejpam-3377	93	27	,	,	PUNCT
ejpam-3377	93	28	q	q	NOUN
ejpam-3377	93	29	)	)	PUNCT
ejpam-3377	93	30	δ	δ	NOUN
ejpam-3377	94	1	(	(	PUNCT
ejpam-3377	94	2	x)dx	x)dx	PROPN
ejpam-3377	94	3	=	=	SYM
ejpam-3377	94	4	r	r	NOUN
ejpam-3377	94	5	(	(	PUNCT
ejpam-3377	94	6	p	p	X
ejpam-3377	94	7	,	,	PUNCT
ejpam-3377	94	8	q	q	NOUN
ejpam-3377	94	9	)	)	PUNCT
ejpam-3377	94	10	δ	δ	PROPN
ejpam-3377	94	11	,	,	PUNCT
ejpam-3377	94	12	k	k	PROPN
ejpam-3377	94	13	∆k	∆k	PROPN
ejpam-3377	94	14	,	,	PUNCT
ejpam-3377	94	15	i	i	PRON
ejpam-3377	94	16	(	(	PUNCT
ejpam-3377	94	17	3	3	NUM
ejpam-3377	94	18	)	)	PUNCT
ejpam-3377	94	19	where	where	SCONJ
ejpam-3377	94	20	w(p	w(p	NOUN
ejpam-3377	94	21	,	,	PUNCT
ejpam-3377	94	22	q	q	NOUN
ejpam-3377	94	23	)	)	PUNCT
ejpam-3377	94	24	δ	δ	PROPN
ejpam-3377	94	25	(	(	PUNCT
ejpam-3377	94	26	x	x	NOUN
ejpam-3377	94	27	)	)	PUNCT
ejpam-3377	94	28	=	=	SYM
ejpam-3377	94	29	(	(	PUNCT
ejpam-3377	94	30	δ	δ	PROPN
ejpam-3377	94	31	−	−	PROPN
ejpam-3377	94	32	x)pxq	x)pxq	PROPN
ejpam-3377	94	33	(	(	PUNCT
ejpam-3377	94	34	4	4	NUM
ejpam-3377	94	35	)	)	PUNCT
ejpam-3377	94	36	is	be	AUX
ejpam-3377	94	37	the	the	DET
ejpam-3377	94	38	weight	weight	NOUN
ejpam-3377	94	39	function	function	NOUN
ejpam-3377	94	40	,	,	PUNCT
ejpam-3377	94	41	r	r	NOUN
ejpam-3377	94	42	(	(	PUNCT
ejpam-3377	94	43	p	p	X
ejpam-3377	94	44	,	,	PUNCT
ejpam-3377	94	45	q	q	NOUN
ejpam-3377	94	46	)	)	PUNCT
ejpam-3377	94	47	δ	δ	PROPN
ejpam-3377	94	48	,	,	PUNCT
ejpam-3377	94	49	k	k	PROPN
ejpam-3377	94	50	∆k	∆k	PROPN
ejpam-3377	94	51	,	,	PUNCT
ejpam-3377	94	52	i	i	PRON
ejpam-3377	94	53	=	=	PUNCT
ejpam-3377	94	54	zp+q+1γ(i+	zp+q+1γ(i+	X
ejpam-3377	94	55	p+	p+	VERB
ejpam-3377	94	56	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	94	57	q	q	NOUN
ejpam-3377	95	1	+	+	NUM
ejpam-3377	95	2	1	1	NUM
ejpam-3377	95	3	)	)	PUNCT
ejpam-3377	95	4	(	(	PUNCT
ejpam-3377	95	5	2i+	2i+	NUM
ejpam-3377	95	6	p+	p+	NOUN
ejpam-3377	95	7	q	q	NOUN
ejpam-3377	96	1	+	+	PROPN
ejpam-3377	96	2	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	96	3	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	96	4	p+	p+	NOUN
ejpam-3377	96	5	q	q	NOUN
ejpam-3377	96	6	+	+	PROPN
ejpam-3377	96	7	1	1	NUM
ejpam-3377	96	8	)	)	PUNCT
ejpam-3377	96	9	.	.	PUNCT
ejpam-3377	97	1	(	(	PUNCT
ejpam-3377	97	2	5	5	NUM
ejpam-3377	97	3	)	)	PUNCT
ejpam-3377	97	4	thus	thus	ADV
ejpam-3377	97	5	any	any	DET
ejpam-3377	97	6	any	any	DET
ejpam-3377	97	7	function	function	NOUN
ejpam-3377	97	8	w(x	w(x	NOUN
ejpam-3377	97	9	)	)	PUNCT
ejpam-3377	97	10	which	which	PRON
ejpam-3377	97	11	is	be	AUX
ejpam-3377	97	12	square	square	ADJ
ejpam-3377	97	13	integrable	integrable	ADJ
ejpam-3377	97	14	in	in	ADP
ejpam-3377	97	15	[	[	X
ejpam-3377	97	16	0	0	NUM
ejpam-3377	97	17	,	,	PUNCT
ejpam-3377	97	18	δ	δ	PROPN
ejpam-3377	97	19	]	]	X
ejpam-3377	97	20	may	may	AUX
ejpam-3377	97	21	be	be	AUX
ejpam-3377	97	22	approximated	approximate	VERB
ejpam-3377	97	23	interm	interm	NOUN
ejpam-3377	97	24	of	of	ADP
ejpam-3377	97	25	shifted	shift	VERB
ejpam-3377	97	26	jacobi	jacobi	PROPN
ejpam-3377	97	27	polynomials	polynomial	NOUN
ejpam-3377	97	28	as	as	ADP
ejpam-3377	97	29	w(x	w(x	NOUN
ejpam-3377	97	30	)	)	PUNCT
ejpam-3377	98	1	≈	≈	PROPN
ejpam-3377	98	2	n∑	n∑	PROPN
ejpam-3377	99	1	l=0	l=0	PROPN
ejpam-3377	99	2	dlz	dlz	PROPN
ejpam-3377	99	3	(	(	PUNCT
ejpam-3377	99	4	p	p	X
ejpam-3377	99	5	,	,	PUNCT
ejpam-3377	99	6	q	q	NOUN
ejpam-3377	99	7	)	)	PUNCT
ejpam-3377	99	8	δ	δ	PROPN
ejpam-3377	99	9	,	,	PUNCT
ejpam-3377	99	10	k	k	PROPN
ejpam-3377	99	11	(	(	PUNCT
ejpam-3377	99	12	x	x	NOUN
ejpam-3377	99	13	)	)	PUNCT
ejpam-3377	99	14	,	,	PUNCT
ejpam-3377	99	15	(	(	PUNCT
ejpam-3377	99	16	6	6	X
ejpam-3377	99	17	)	)	PUNCT
ejpam-3377	99	18	m.i	m.i	PROPN
ejpam-3377	99	19	.	.	PROPN
ejpam-3377	99	20	chohan	chohan	PROPN
ejpam-3377	99	21	,	,	PUNCT
ejpam-3377	99	22	k.shah	k.shah	PROPN
ejpam-3377	99	23	/	/	SYM
ejpam-3377	99	24	eur	eur	PROPN
ejpam-3377	99	25	.	.	PUNCT
ejpam-3377	100	1	j.	j.	PROPN
ejpam-3377	100	2	pure	pure	PROPN
ejpam-3377	100	3	appl	appl	PROPN
ejpam-3377	100	4	.	.	PROPN
ejpam-3377	100	5	math	math	PROPN
ejpam-3377	100	6	,	,	PUNCT
ejpam-3377	100	7	12	12	NUM
ejpam-3377	100	8	(	(	PUNCT
ejpam-3377	100	9	1	1	NUM
ejpam-3377	100	10	)	)	PUNCT
ejpam-3377	100	11	(	(	PUNCT
ejpam-3377	100	12	2019	2019	NUM
ejpam-3377	100	13	)	)	PUNCT
ejpam-3377	100	14	,	,	PUNCT
ejpam-3377	100	15	39	39	NUM
ejpam-3377	100	16	-	-	SYM
ejpam-3377	100	17	57	57	NUM
ejpam-3377	100	18	43	43	NUM
ejpam-3377	100	19	as	as	ADP
ejpam-3377	100	20	n	n	PROPN
ejpam-3377	100	21	→	→	SYM
ejpam-3377	100	22	∞	∞	NOUN
ejpam-3377	100	23	the	the	DET
ejpam-3377	100	24	approximation	approximation	NOUN
ejpam-3377	100	25	is	be	AUX
ejpam-3377	100	26	converging	converge	VERB
ejpam-3377	100	27	to	to	ADP
ejpam-3377	100	28	the	the	DET
ejpam-3377	100	29	exact	exact	ADJ
ejpam-3377	100	30	function	function	NOUN
ejpam-3377	100	31	.	.	PUNCT
ejpam-3377	101	1	inview	inview	NOUN
ejpam-3377	101	2	of	of	ADP
ejpam-3377	101	3	(	(	PUNCT
ejpam-3377	101	4	3	3	NUM
ejpam-3377	101	5	)	)	PUNCT
ejpam-3377	101	6	(	(	PUNCT
ejpam-3377	101	7	4),(5	4),(5	NOUN
ejpam-3377	101	8	)	)	PUNCT
ejpam-3377	101	9	,	,	PUNCT
ejpam-3377	101	10	we	we	PRON
ejpam-3377	101	11	can	can	AUX
ejpam-3377	101	12	easily	easily	ADV
ejpam-3377	101	13	find	find	VERB
ejpam-3377	101	14	the	the	DET
ejpam-3377	101	15	constant	constant	ADJ
ejpam-3377	101	16	dl	dl	PROPN
ejpam-3377	101	17	.	.	PUNCT
ejpam-3377	101	18	writing(6	writing(6	PUNCT
ejpam-3377	101	19	)	)	PUNCT
ejpam-3377	101	20	in	in	ADP
ejpam-3377	101	21	matrix	matrix	NOUN
ejpam-3377	101	22	form	form	NOUN
ejpam-3377	101	23	as	as	ADP
ejpam-3377	101	24	w(x	w(x	NOUN
ejpam-3377	101	25	)	)	PUNCT
ejpam-3377	102	1	≈	≈	PROPN
ejpam-3377	102	2	ht	ht	PROPN
ejpam-3377	102	3	n	n	PROPN
ejpam-3377	102	4	φ̂n	φ̂n	NUM
ejpam-3377	102	5	(	(	PUNCT
ejpam-3377	102	6	x	x	X
ejpam-3377	102	7	)	)	PUNCT
ejpam-3377	102	8	,	,	PUNCT
ejpam-3377	102	9	(	(	PUNCT
ejpam-3377	102	10	7	7	X
ejpam-3377	102	11	)	)	PUNCT
ejpam-3377	102	12	such	such	ADJ
ejpam-3377	102	13	that	that	SCONJ
ejpam-3377	102	14	n	n	NOUN
ejpam-3377	102	15	=	=	SYM
ejpam-3377	102	16	n+1	n+1	PROPN
ejpam-3377	102	17	,	,	PUNCT
ejpam-3377	102	18	kn	kn	PROPN
ejpam-3377	102	19	is	be	AUX
ejpam-3377	102	20	the	the	DET
ejpam-3377	102	21	coefficient	coefficient	NOUN
ejpam-3377	102	22	matrix	matrix	NOUN
ejpam-3377	102	23	and	and	CCONJ
ejpam-3377	102	24	φ̂n	φ̂n	NUM
ejpam-3377	102	25	(	(	PUNCT
ejpam-3377	102	26	x	x	X
ejpam-3377	102	27	)	)	PUNCT
ejpam-3377	102	28	is	be	AUX
ejpam-3377	102	29	matrix	matrix	NOUN
ejpam-3377	102	30	of	of	ADP
ejpam-3377	102	31	vectors	vector	NOUN
ejpam-3377	102	32	function	function	VERB
ejpam-3377	102	33	.	.	PUNCT
ejpam-3377	103	1	extending	extend	VERB
ejpam-3377	103	2	the	the	DET
ejpam-3377	103	3	notation	notation	NOUN
ejpam-3377	103	4	from	from	ADP
ejpam-3377	103	5	uni	uni	ADJ
ejpam-3377	103	6	-	-	NOUN
ejpam-3377	103	7	dimension	dimension	NOUN
ejpam-3377	103	8	to	to	ADP
ejpam-3377	103	9	two	two	NUM
ejpam-3377	103	10	dimension	dimension	NOUN
ejpam-3377	103	11	space	space	NOUN
ejpam-3377	103	12	in	in	ADP
ejpam-3377	103	13	order	order	NOUN
ejpam-3377	103	14	to	to	PART
ejpam-3377	103	15	define	define	VERB
ejpam-3377	103	16	two	two	NUM
ejpam-3377	103	17	dimensional	dimensional	ADJ
ejpam-3377	103	18	shifted	shift	VERB
ejpam-3377	103	19	jacobi	jacobi	NOUN
ejpam-3377	103	20	polynomials	polynomial	NOUN
ejpam-3377	103	21	of	of	ADP
ejpam-3377	103	22	order	order	NOUN
ejpam-3377	103	23	n	n	CCONJ
ejpam-3377	103	24	over	over	ADP
ejpam-3377	103	25	the	the	DET
ejpam-3377	103	26	region	region	NOUN
ejpam-3377	103	27	[	[	X
ejpam-3377	103	28	0	0	NUM
ejpam-3377	103	29	,	,	PUNCT
ejpam-3377	103	30	δ]×	δ]×	VERB
ejpam-3377	103	31	[	[	X
ejpam-3377	103	32	0	0	NUM
ejpam-3377	103	33	,	,	PUNCT
ejpam-3377	103	34	δ	δ	PROPN
ejpam-3377	103	35	]	]	PUNCT
ejpam-3377	103	36	as	as	ADP
ejpam-3377	103	37	z(p	z(p	ADJ
ejpam-3377	103	38	,	,	PUNCT
ejpam-3377	103	39	q	q	ADJ
ejpam-3377	103	40	)	)	PUNCT
ejpam-3377	103	41	δ	δ	PROPN
ejpam-3377	103	42	,	,	PUNCT
ejpam-3377	103	43	n	n	PROPN
ejpam-3377	103	44	(	(	PUNCT
ejpam-3377	103	45	x	x	NOUN
ejpam-3377	103	46	,	,	PUNCT
ejpam-3377	103	47	y	y	NOUN
ejpam-3377	103	48	)	)	PUNCT
ejpam-3377	103	49	=	=	PUNCT
ejpam-3377	104	1	(	(	PUNCT
ejpam-3377	104	2	z(p	z(p	X
ejpam-3377	104	3	,	,	PUNCT
ejpam-3377	104	4	q	q	NOUN
ejpam-3377	104	5	)	)	PUNCT
ejpam-3377	104	6	δ	δ	PROPN
ejpam-3377	104	7	,	,	PUNCT
ejpam-3377	104	8	k	k	PROPN
ejpam-3377	104	9	(	(	PUNCT
ejpam-3377	104	10	x))(z(p	x))(z(p	PROPN
ejpam-3377	104	11	,	,	PUNCT
ejpam-3377	104	12	q	q	NOUN
ejpam-3377	104	13	)	)	PUNCT
ejpam-3377	104	14	δ	δ	PROPN
ejpam-3377	104	15	,	,	PUNCT
ejpam-3377	104	16	i	i	PRON
ejpam-3377	104	17	(	(	PUNCT
ejpam-3377	104	18	y	y	NOUN
ejpam-3377	104	19	)	)	PUNCT
ejpam-3377	104	20	)	)	PUNCT
ejpam-3377	104	21	,	,	PUNCT
ejpam-3377	104	22	n	n	NOUN
ejpam-3377	104	23	=	=	SYM
ejpam-3377	104	24	nk	nk	PROPN
ejpam-3377	105	1	+	+	CCONJ
ejpam-3377	105	2	i+	i+	NUM
ejpam-3377	105	3	1	1	NUM
ejpam-3377	105	4	,	,	PUNCT
ejpam-3377	105	5	k	k	NOUN
ejpam-3377	105	6	,	,	PUNCT
ejpam-3377	105	7	i	i	NOUN
ejpam-3377	105	8	=	=	NOUN
ejpam-3377	105	9	0	0	NUM
ejpam-3377	105	10	,	,	PUNCT
ejpam-3377	105	11	1	1	NUM
ejpam-3377	105	12	,	,	PUNCT
ejpam-3377	105	13	2	2	NUM
ejpam-3377	105	14	,	,	PUNCT
ejpam-3377	105	15	.	.	PUNCT
ejpam-3377	105	16	.	.	PUNCT
ejpam-3377	106	1	.	.	PUNCT
ejpam-3377	107	1	,	,	PUNCT
ejpam-3377	107	2	n.	n.	NOUN
ejpam-3377	107	3	(	(	PUNCT
ejpam-3377	107	4	8)	8)	NUM
ejpam-3377	107	5	the	the	DET
ejpam-3377	107	6	orthogonality	orthogonality	NOUN
ejpam-3377	107	7	condition	condition	NOUN
ejpam-3377	107	8	for	for	ADP
ejpam-3377	107	9	z(p	z(p	ADJ
ejpam-3377	107	10	,	,	PUNCT
ejpam-3377	107	11	q	q	NOUN
ejpam-3377	107	12	)	)	PUNCT
ejpam-3377	107	13	δ	δ	PROPN
ejpam-3377	107	14	,	,	PUNCT
ejpam-3377	107	15	n	n	PROPN
ejpam-3377	107	16	(	(	PUNCT
ejpam-3377	107	17	x	x	NOUN
ejpam-3377	107	18	,	,	PUNCT
ejpam-3377	107	19	y	y	NOUN
ejpam-3377	107	20	)	)	PUNCT
ejpam-3377	107	21	can	can	AUX
ejpam-3377	107	22	be	be	AUX
ejpam-3377	107	23	computed	compute	VERB
ejpam-3377	107	24	as∫	as∫	PROPN
ejpam-3377	107	25	δ	δ	PROPN
ejpam-3377	107	26	0	0	NUM
ejpam-3377	107	27	∫	∫	PROPN
ejpam-3377	107	28	δ	δ	PROPN
ejpam-3377	107	29	0	0	NUM
ejpam-3377	108	1	(	(	PUNCT
ejpam-3377	108	2	z(p	z(p	ADJ
ejpam-3377	108	3	,	,	PUNCT
ejpam-3377	108	4	q	q	NOUN
ejpam-3377	108	5	)	)	PUNCT
ejpam-3377	108	6	δ	δ	PROPN
ejpam-3377	108	7	,	,	PUNCT
ejpam-3377	108	8	l	l	PROPN
ejpam-3377	108	9	(	(	PUNCT
ejpam-3377	108	10	x))(z(p	x))(z(p	PROPN
ejpam-3377	108	11	,	,	PUNCT
ejpam-3377	108	12	q	q	NOUN
ejpam-3377	108	13	)	)	PUNCT
ejpam-3377	108	14	δ	δ	PROPN
ejpam-3377	108	15	,	,	PUNCT
ejpam-3377	108	16	m	m	PROPN
ejpam-3377	108	17	(	(	PUNCT
ejpam-3377	108	18	y))(z(p	y))(z(p	PROPN
ejpam-3377	108	19	,	,	PUNCT
ejpam-3377	108	20	q	q	ADJ
ejpam-3377	108	21	)	)	PUNCT
ejpam-3377	108	22	δ	δ	PROPN
ejpam-3377	108	23	,	,	PUNCT
ejpam-3377	108	24	r	r	NOUN
ejpam-3377	108	25	(	(	PUNCT
ejpam-3377	108	26	x))(z(p	x))(z(p	PROPN
ejpam-3377	108	27	,	,	PUNCT
ejpam-3377	108	28	q	q	NOUN
ejpam-3377	108	29	)	)	PUNCT
ejpam-3377	108	30	δ	δ	PROPN
ejpam-3377	108	31	,	,	PUNCT
ejpam-3377	108	32	s	s	PART
ejpam-3377	108	33	(	(	PUNCT
ejpam-3377	108	34	x))w(p	x))w(p	PROPN
ejpam-3377	108	35	,	,	PUNCT
ejpam-3377	108	36	q	q	NOUN
ejpam-3377	108	37	)	)	PUNCT
ejpam-3377	108	38	δ	δ	PROPN
ejpam-3377	108	39	(	(	PUNCT
ejpam-3377	108	40	x)w(p	x)w(p	ADJ
ejpam-3377	108	41	,	,	PUNCT
ejpam-3377	108	42	q	q	NOUN
ejpam-3377	108	43	)	)	PUNCT
ejpam-3377	108	44	δ	δ	PROPN
ejpam-3377	108	45	(	(	PUNCT
ejpam-3377	108	46	y)dxdy	y)dxdy	NOUN
ejpam-3377	109	1	=	=	SYM
ejpam-3377	109	2	r	r	NOUN
ejpam-3377	109	3	(	(	PUNCT
ejpam-3377	109	4	p	p	X
ejpam-3377	109	5	,	,	PUNCT
ejpam-3377	109	6	q	q	NOUN
ejpam-3377	109	7	)	)	PUNCT
ejpam-3377	109	8	δ	δ	PROPN
ejpam-3377	109	9	,	,	PUNCT
ejpam-3377	109	10	r	r	PROPN
ejpam-3377	109	11	∆l	∆l	PROPN
ejpam-3377	109	12	,	,	PUNCT
ejpam-3377	109	13	rr	rr	X
ejpam-3377	109	14	(	(	PUNCT
ejpam-3377	109	15	p	p	X
ejpam-3377	109	16	,	,	PUNCT
ejpam-3377	109	17	q	q	NOUN
ejpam-3377	109	18	)	)	PUNCT
ejpam-3377	109	19	δ	δ	PROPN
ejpam-3377	109	20	,	,	PUNCT
ejpam-3377	109	21	s	s	PART
ejpam-3377	109	22	∆m	∆m	PROPN
ejpam-3377	109	23	,	,	PUNCT
ejpam-3377	109	24	s.	s.	PROPN
ejpam-3377	109	25	(	(	PUNCT
ejpam-3377	109	26	9	9	X
ejpam-3377	109	27	)	)	PUNCT
ejpam-3377	109	28	an	an	DET
ejpam-3377	109	29	integrable	integrable	ADJ
ejpam-3377	109	30	function	function	NOUN
ejpam-3377	109	31	over	over	ADP
ejpam-3377	109	32	the	the	DET
ejpam-3377	109	33	region	region	NOUN
ejpam-3377	109	34	[	[	X
ejpam-3377	109	35	0	0	NUM
ejpam-3377	109	36	,	,	PUNCT
ejpam-3377	109	37	δ	δ	PROPN
ejpam-3377	109	38	]	]	X
ejpam-3377	109	39	×	×	NOUN
ejpam-3377	110	1	[	[	X
ejpam-3377	110	2	0	0	NUM
ejpam-3377	110	3	,	,	PUNCT
ejpam-3377	110	4	δ	δ	PROPN
ejpam-3377	110	5	]	]	PUNCT
ejpam-3377	110	6	is	be	AUX
ejpam-3377	110	7	approximated	approximate	VERB
ejpam-3377	110	8	interms	interm	NOUN
ejpam-3377	110	9	of	of	ADP
ejpam-3377	110	10	the	the	DET
ejpam-3377	110	11	twodimensional	twodimensional	ADJ
ejpam-3377	110	12	shifted	shift	VERB
ejpam-3377	110	13	jacobi	jacobi	PROPN
ejpam-3377	110	14	polynomials	polynomial	VERB
ejpam-3377	110	15	z(p	z(p	ADV
ejpam-3377	110	16	,	,	PUNCT
ejpam-3377	110	17	q	q	ADJ
ejpam-3377	110	18	)	)	PUNCT
ejpam-3377	110	19	δ	δ	PROPN
ejpam-3377	110	20	,	,	PUNCT
ejpam-3377	110	21	n	n	PROPN
ejpam-3377	110	22	(	(	PUNCT
ejpam-3377	110	23	x	x	NOUN
ejpam-3377	110	24	,	,	PUNCT
ejpam-3377	110	25	y	y	PROPN
ejpam-3377	110	26	)	)	PUNCT
ejpam-3377	110	27	as	as	ADP
ejpam-3377	110	28	f(x	f(x	PROPN
ejpam-3377	110	29	,	,	PUNCT
ejpam-3377	110	30	y	y	PROPN
ejpam-3377	110	31	)	)	PUNCT
ejpam-3377	111	1	≈	≈	PROPN
ejpam-3377	111	2	n∑	n∑	PROPN
ejpam-3377	111	3	l=0	l=0	PROPN
ejpam-3377	111	4	n∑	n∑	PROPN
ejpam-3377	111	5	m=0	m=0	PROPN
ejpam-3377	111	6	dlm(z(p	dlm(z(p	PROPN
ejpam-3377	111	7	,	,	PUNCT
ejpam-3377	111	8	q	q	NOUN
ejpam-3377	111	9	)	)	PUNCT
ejpam-3377	111	10	δ	δ	PROPN
ejpam-3377	111	11	,	,	PUNCT
ejpam-3377	111	12	l	l	PROPN
ejpam-3377	111	13	(	(	PUNCT
ejpam-3377	111	14	x))(z(p	x))(z(p	PROPN
ejpam-3377	111	15	,	,	PUNCT
ejpam-3377	111	16	q	q	NOUN
ejpam-3377	111	17	)	)	PUNCT
ejpam-3377	111	18	δ	δ	PROPN
ejpam-3377	111	19	,	,	PUNCT
ejpam-3377	111	20	m	m	PROPN
ejpam-3377	111	21	(	(	PUNCT
ejpam-3377	111	22	y	y	NOUN
ejpam-3377	111	23	)	)	PUNCT
ejpam-3377	111	24	)	)	PUNCT
ejpam-3377	111	25	,	,	PUNCT
ejpam-3377	111	26	(	(	PUNCT
ejpam-3377	111	27	10	10	NUM
ejpam-3377	111	28	)	)	PUNCT
ejpam-3377	111	29	where	where	SCONJ
ejpam-3377	111	30	dlm	dlm	PROPN
ejpam-3377	111	31	can	can	AUX
ejpam-3377	111	32	be	be	AUX
ejpam-3377	111	33	computed	compute	VERB
ejpam-3377	111	34	as	as	ADP
ejpam-3377	111	35	dlm	dlm	PROPN
ejpam-3377	111	36	=	=	SYM
ejpam-3377	111	37	1	1	NUM
ejpam-3377	111	38	r	r	NOUN
ejpam-3377	111	39	(	(	PUNCT
ejpam-3377	111	40	p	p	X
ejpam-3377	111	41	,	,	PUNCT
ejpam-3377	111	42	q	q	NOUN
ejpam-3377	111	43	)	)	PUNCT
ejpam-3377	111	44	δ	δ	PROPN
ejpam-3377	111	45	,	,	PUNCT
ejpam-3377	111	46	l	l	NOUN
ejpam-3377	111	47	r	r	NOUN
ejpam-3377	111	48	(	(	PUNCT
ejpam-3377	111	49	p	p	X
ejpam-3377	111	50	,	,	PUNCT
ejpam-3377	111	51	q	q	NOUN
ejpam-3377	111	52	)	)	PUNCT
ejpam-3377	111	53	δ	δ	PROPN
ejpam-3377	111	54	,	,	PUNCT
ejpam-3377	111	55	m	m	VERB
ejpam-3377	111	56	∫	∫	PROPN
ejpam-3377	111	57	δ	δ	PROPN
ejpam-3377	111	58	0	0	NUM
ejpam-3377	112	1	∫	∫	PROPN
ejpam-3377	112	2	δ	δ	PROPN
ejpam-3377	112	3	0	0	NUM
ejpam-3377	112	4	f(x	f(x	PROPN
ejpam-3377	112	5	,	,	PUNCT
ejpam-3377	112	6	y)(z(p	y)(z(p	NOUN
ejpam-3377	112	7	,	,	PUNCT
ejpam-3377	112	8	q	q	NOUN
ejpam-3377	112	9	)	)	PUNCT
ejpam-3377	112	10	δ	δ	PROPN
ejpam-3377	112	11	,	,	PUNCT
ejpam-3377	112	12	l	l	PROPN
ejpam-3377	112	13	(	(	PUNCT
ejpam-3377	112	14	x))(z(p	x))(z(p	PROPN
ejpam-3377	112	15	,	,	PUNCT
ejpam-3377	112	16	q	q	NOUN
ejpam-3377	112	17	)	)	PUNCT
ejpam-3377	112	18	δ	δ	PROPN
ejpam-3377	112	19	,	,	PUNCT
ejpam-3377	112	20	m	m	PROPN
ejpam-3377	112	21	(	(	PUNCT
ejpam-3377	112	22	y))w(p	y))w(p	NOUN
ejpam-3377	112	23	,	,	PUNCT
ejpam-3377	112	24	q	q	NOUN
ejpam-3377	112	25	)	)	PUNCT
ejpam-3377	112	26	δ	δ	PROPN
ejpam-3377	112	27	(	(	PUNCT
ejpam-3377	112	28	x	x	PROPN
ejpam-3377	112	29	,	,	PUNCT
ejpam-3377	112	30	y)dxdy	y)dxdy	PROPN
ejpam-3377	112	31	,	,	PUNCT
ejpam-3377	112	32	(	(	PUNCT
ejpam-3377	112	33	11	11	NUM
ejpam-3377	112	34	)	)	PUNCT
ejpam-3377	112	35	while	while	SCONJ
ejpam-3377	112	36	w(p	w(p	NOUN
ejpam-3377	112	37	,	,	PUNCT
ejpam-3377	112	38	q	q	NOUN
ejpam-3377	112	39	)	)	PUNCT
ejpam-3377	112	40	δ	δ	NOUN
ejpam-3377	112	41	(	(	PUNCT
ejpam-3377	112	42	x	x	PROPN
ejpam-3377	112	43	,	,	PUNCT
ejpam-3377	112	44	y	y	NOUN
ejpam-3377	112	45	)	)	PUNCT
ejpam-3377	112	46	=	=	SYM
ejpam-3377	112	47	w(p	w(p	ADJ
ejpam-3377	112	48	,	,	PUNCT
ejpam-3377	112	49	q	q	NOUN
ejpam-3377	112	50	)	)	PUNCT
ejpam-3377	112	51	δ	δ	PROPN
ejpam-3377	112	52	(	(	PUNCT
ejpam-3377	112	53	x)w(p	x)w(p	ADJ
ejpam-3377	112	54	,	,	PUNCT
ejpam-3377	112	55	q	q	NOUN
ejpam-3377	112	56	)	)	PUNCT
ejpam-3377	112	57	δ	δ	PROPN
ejpam-3377	112	58	(	(	PUNCT
ejpam-3377	112	59	y	y	PROPN
ejpam-3377	112	60	)	)	PUNCT
ejpam-3377	112	61	.	.	PUNCT
ejpam-3377	113	1	(	(	PUNCT
ejpam-3377	113	2	12	12	X
ejpam-3377	113	3	)	)	PUNCT
ejpam-3377	113	4	writing	write	VERB
ejpam-3377	113	5	the	the	DET
ejpam-3377	113	6	notation	notation	NOUN
ejpam-3377	113	7	dn	dn	NOUN
ejpam-3377	113	8	=	=	SYM
ejpam-3377	113	9	dab	dab	PROPN
ejpam-3377	113	10	,	,	PUNCT
ejpam-3377	113	11	then	then	ADV
ejpam-3377	113	12	(	(	PUNCT
ejpam-3377	113	13	10	10	NUM
ejpam-3377	113	14	)	)	PUNCT
ejpam-3377	113	15	implies	imply	VERB
ejpam-3377	113	16	f(x	f(x	PROPN
ejpam-3377	113	17	,	,	PUNCT
ejpam-3377	113	18	y	y	PROPN
ejpam-3377	113	19	)	)	PUNCT
ejpam-3377	114	1	≈	≈	PROPN
ejpam-3377	114	2	n2∑	n2∑	PROPN
ejpam-3377	114	3	n=1	n=1	PROPN
ejpam-3377	114	4	dnz	dnz	NOUN
ejpam-3377	114	5	(	(	PUNCT
ejpam-3377	114	6	p	p	NOUN
ejpam-3377	114	7	,	,	PUNCT
ejpam-3377	114	8	q	q	NOUN
ejpam-3377	114	9	)	)	PUNCT
ejpam-3377	114	10	δ	δ	PROPN
ejpam-3377	114	11	,	,	PUNCT
ejpam-3377	114	12	n	n	PROPN
ejpam-3377	114	13	(	(	PUNCT
ejpam-3377	114	14	x	x	NOUN
ejpam-3377	114	15	,	,	PUNCT
ejpam-3377	114	16	y	y	NOUN
ejpam-3377	114	17	)	)	PUNCT
ejpam-3377	114	18	=	=	PUNCT
ejpam-3377	115	1	ktn2φn2(x	ktn2φn2(x	PROPN
ejpam-3377	115	2	,	,	PUNCT
ejpam-3377	115	3	y	y	PROPN
ejpam-3377	115	4	)	)	PUNCT
ejpam-3377	115	5	,	,	PUNCT
ejpam-3377	115	6	(	(	PUNCT
ejpam-3377	115	7	13	13	NUM
ejpam-3377	115	8	)	)	PUNCT
ejpam-3377	115	9	where	where	SCONJ
ejpam-3377	115	10	hn2	hn2	PROPN
ejpam-3377	115	11	is	be	AUX
ejpam-3377	115	12	n2×1	n2×1	ADJ
ejpam-3377	115	13	coefficient	coefficient	NOUN
ejpam-3377	115	14	matrix	matrix	NOUN
ejpam-3377	115	15	and	and	CCONJ
ejpam-3377	115	16	φn2(x	φn2(x	PROPN
ejpam-3377	115	17	,	,	PUNCT
ejpam-3377	115	18	y	y	NOUN
ejpam-3377	115	19	)	)	PUNCT
ejpam-3377	115	20	is	be	AUX
ejpam-3377	115	21	n2×1	n2×1	ADJ
ejpam-3377	115	22	column	column	NOUN
ejpam-3377	115	23	matrix	matrix	NOUN
ejpam-3377	115	24	of	of	ADP
ejpam-3377	115	25	functions	function	NOUN
ejpam-3377	115	26	given	give	VERB
ejpam-3377	115	27	by	by	ADP
ejpam-3377	115	28	φn2(x	φn2(x	PROPN
ejpam-3377	115	29	,	,	PUNCT
ejpam-3377	115	30	y	y	NOUN
ejpam-3377	115	31	)	)	PUNCT
ejpam-3377	115	32	=	=	PUNCT
ejpam-3377	116	1	(	(	PUNCT
ejpam-3377	116	2	φ11(x	φ11(x	NOUN
ejpam-3377	116	3	,	,	PUNCT
ejpam-3377	116	4	y	y	PROPN
ejpam-3377	116	5	)	)	PUNCT
ejpam-3377	116	6	·	·	PUNCT
ejpam-3377	116	7	·	·	PUNCT
ejpam-3377	116	8	·	·	PUNCT
ejpam-3377	117	1	φ1n	φ1n	PUNCT
ejpam-3377	117	2	(	(	PUNCT
ejpam-3377	117	3	x	x	NOUN
ejpam-3377	117	4	,	,	PUNCT
ejpam-3377	117	5	y	y	NOUN
ejpam-3377	117	6	)	)	PUNCT
ejpam-3377	117	7	φ21(x	φ21(x	NOUN
ejpam-3377	117	8	,	,	PUNCT
ejpam-3377	117	9	y	y	NOUN
ejpam-3377	117	10	)	)	PUNCT
ejpam-3377	117	11	·	·	PUNCT
ejpam-3377	117	12	·	·	PUNCT
ejpam-3377	117	13	·	·	PUNCT
ejpam-3377	118	1	φ2n	φ2n	INTJ
ejpam-3377	118	2	(	(	PUNCT
ejpam-3377	118	3	x	x	X
ejpam-3377	118	4	,	,	PUNCT
ejpam-3377	118	5	y	y	PROPN
ejpam-3377	118	6	)	)	PUNCT
ejpam-3377	118	7	·	·	PUNCT
ejpam-3377	118	8	·	·	PUNCT
ejpam-3377	118	9	·	·	PUNCT
ejpam-3377	119	1	φnn	φnn	NOUN
ejpam-3377	119	2	(	(	PUNCT
ejpam-3377	119	3	x	x	NOUN
ejpam-3377	119	4	,	,	PUNCT
ejpam-3377	119	5	y	y	PROPN
ejpam-3377	119	6	)	)	PUNCT
ejpam-3377	119	7	)	)	PUNCT
ejpam-3377	120	1	t	t	NOUN
ejpam-3377	120	2	,	,	PUNCT
ejpam-3377	120	3	(	(	PUNCT
ejpam-3377	120	4	14	14	NUM
ejpam-3377	120	5	)	)	PUNCT
ejpam-3377	121	1	where	where	SCONJ
ejpam-3377	121	2	φk+1,i+1(x	φk+1,i+1(x	NOUN
ejpam-3377	121	3	,	,	PUNCT
ejpam-3377	121	4	y	y	NOUN
ejpam-3377	121	5	)	)	PUNCT
ejpam-3377	121	6	=	=	PUNCT
ejpam-3377	121	7	(	(	PUNCT
ejpam-3377	121	8	z(p	z(p	X
ejpam-3377	121	9	,	,	PUNCT
ejpam-3377	121	10	q	q	NOUN
ejpam-3377	121	11	)	)	PUNCT
ejpam-3377	121	12	δ	δ	PROPN
ejpam-3377	121	13	,	,	PUNCT
ejpam-3377	121	14	k	k	PROPN
ejpam-3377	121	15	(	(	PUNCT
ejpam-3377	121	16	x))(z(p	x))(z(p	PROPN
ejpam-3377	121	17	,	,	PUNCT
ejpam-3377	121	18	q	q	NOUN
ejpam-3377	121	19	)	)	PUNCT
ejpam-3377	121	20	δ	δ	PROPN
ejpam-3377	121	21	,	,	PUNCT
ejpam-3377	121	22	i	i	PRON
ejpam-3377	121	23	(	(	PUNCT
ejpam-3377	121	24	y	y	NOUN
ejpam-3377	121	25	)	)	PUNCT
ejpam-3377	121	26	)	)	PUNCT
ejpam-3377	121	27	,	,	PUNCT
ejpam-3377	121	28	i	i	PRON
ejpam-3377	121	29	,	,	PUNCT
ejpam-3377	121	30	k	k	PROPN
ejpam-3377	121	31	=	=	SYM
ejpam-3377	121	32	0	0	NUM
ejpam-3377	121	33	,	,	PUNCT
ejpam-3377	121	34	1	1	NUM
ejpam-3377	121	35	,	,	PUNCT
ejpam-3377	121	36	2	2	NUM
ejpam-3377	121	37	,	,	PUNCT
ejpam-3377	121	38	.	.	PUNCT
ejpam-3377	121	39	.	.	PUNCT
ejpam-3377	121	40	.	.	PUNCT
ejpam-3377	122	1	,	,	PUNCT
ejpam-3377	122	2	n.	n.	PROPN
ejpam-3377	122	3	theorem	theorem	VERB
ejpam-3377	122	4	2.4	2.4	NUM
ejpam-3377	122	5	.	.	PUNCT
ejpam-3377	123	1	[	[	X
ejpam-3377	123	2	10	10	NUM
ejpam-3377	123	3	,	,	PUNCT
ejpam-3377	123	4	12	12	NUM
ejpam-3377	123	5	,	,	PUNCT
ejpam-3377	123	6	51	51	NUM
ejpam-3377	123	7	]	]	PUNCT
ejpam-3377	123	8	if	if	SCONJ
ejpam-3377	123	9	a	a	DET
ejpam-3377	123	10	continuous	continuous	ADJ
ejpam-3377	123	11	function	function	NOUN
ejpam-3377	123	12	w(x	w(x	PROPN
ejpam-3377	123	13	,	,	PUNCT
ejpam-3377	123	14	y	y	NOUN
ejpam-3377	123	15	)	)	PUNCT
ejpam-3377	123	16	defined	define	VERB
ejpam-3377	123	17	over	over	ADP
ejpam-3377	123	18	a	a	DET
ejpam-3377	123	19	region	region	NOUN
ejpam-3377	124	1	[	[	X
ejpam-3377	124	2	0	0	NUM
ejpam-3377	124	3	,	,	PUNCT
ejpam-3377	124	4	δ]×	δ]×	VERB
ejpam-3377	125	1	[	[	X
ejpam-3377	125	2	0	0	NUM
ejpam-3377	125	3	,	,	PUNCT
ejpam-3377	125	4	δ	δ	PROPN
ejpam-3377	125	5	]	]	PUNCT
ejpam-3377	125	6	has	have	AUX
ejpam-3377	125	7	bounded	bound	VERB
ejpam-3377	125	8	mixed	mixed	ADJ
ejpam-3377	125	9	fourth	fourth	ADJ
ejpam-3377	125	10	order	order	NOUN
ejpam-3377	125	11	partial	partial	ADJ
ejpam-3377	125	12	derivative	derivative	ADJ
ejpam-3377	125	13	∂4w(x	∂4w(x	NOUN
ejpam-3377	125	14	,	,	PUNCT
ejpam-3377	125	15	y	y	NOUN
ejpam-3377	125	16	)	)	PUNCT
ejpam-3377	125	17	∂2x∂2y	∂2x∂2y	PROPN
ejpam-3377	125	18	,	,	PUNCT
ejpam-3377	125	19	then	then	ADV
ejpam-3377	125	20	the	the	DET
ejpam-3377	125	21	jacobi	jacobi	PROPN
ejpam-3377	125	22	expansion	expansion	PROPN
ejpam-3377	125	23	m.i	m.i	PROPN
ejpam-3377	125	24	.	.	PROPN
ejpam-3377	125	25	chohan	chohan	PROPN
ejpam-3377	125	26	,	,	PUNCT
ejpam-3377	125	27	k.shah	k.shah	PROPN
ejpam-3377	125	28	/	/	SYM
ejpam-3377	125	29	eur	eur	PROPN
ejpam-3377	125	30	.	.	PUNCT
ejpam-3377	126	1	j.	j.	PROPN
ejpam-3377	126	2	pure	pure	PROPN
ejpam-3377	126	3	appl	appl	PROPN
ejpam-3377	126	4	.	.	PROPN
ejpam-3377	126	5	math	math	PROPN
ejpam-3377	126	6	,	,	PUNCT
ejpam-3377	126	7	12	12	NUM
ejpam-3377	126	8	(	(	PUNCT
ejpam-3377	126	9	1	1	NUM
ejpam-3377	126	10	)	)	PUNCT
ejpam-3377	126	11	(	(	PUNCT
ejpam-3377	126	12	2019	2019	NUM
ejpam-3377	126	13	)	)	PUNCT
ejpam-3377	126	14	,	,	PUNCT
ejpam-3377	126	15	39	39	NUM
ejpam-3377	126	16	-	-	SYM
ejpam-3377	126	17	57	57	NUM
ejpam-3377	126	18	44	44	NUM
ejpam-3377	126	19	of	of	ADP
ejpam-3377	126	20	the	the	DET
ejpam-3377	126	21	function	function	NOUN
ejpam-3377	126	22	converges	converge	VERB
ejpam-3377	126	23	uniformly	uniformly	ADV
ejpam-3377	126	24	to	to	ADP
ejpam-3377	126	25	the	the	DET
ejpam-3377	126	26	function	function	NOUN
ejpam-3377	126	27	.	.	PUNCT
ejpam-3377	127	1	moreover	moreover	ADV
ejpam-3377	127	2	the	the	DET
ejpam-3377	127	3	error	error	NOUN
ejpam-3377	127	4	of	of	ADP
ejpam-3377	127	5	the	the	DET
ejpam-3377	127	6	approximation	approximation	NOUN
ejpam-3377	127	7	for	for	ADP
ejpam-3377	127	8	sufficiently	sufficiently	ADV
ejpam-3377	127	9	smooth	smooth	ADJ
ejpam-3377	127	10	function	function	NOUN
ejpam-3377	127	11	w(x	w(x	PROPN
ejpam-3377	127	12	,	,	PUNCT
ejpam-3377	127	13	y	y	NOUN
ejpam-3377	127	14	)	)	PUNCT
ejpam-3377	127	15	over	over	ADP
ejpam-3377	127	16	the	the	DET
ejpam-3377	127	17	region	region	NOUN
ejpam-3377	127	18	[	[	X
ejpam-3377	127	19	0	0	NUM
ejpam-3377	127	20	,	,	PUNCT
ejpam-3377	127	21	δ]×	δ]×	VERB
ejpam-3377	127	22	[	[	X
ejpam-3377	127	23	0	0	NUM
ejpam-3377	127	24	,	,	PUNCT
ejpam-3377	127	25	δ	δ	PROPN
ejpam-3377	127	26	]	]	PUNCT
ejpam-3377	127	27	is	be	AUX
ejpam-3377	127	28	given	give	VERB
ejpam-3377	127	29	by	by	ADP
ejpam-3377	127	30	‖w(x	‖w(x	NUM
ejpam-3377	127	31	,	,	PUNCT
ejpam-3377	127	32	y)−z(n	y)−z(n	NOUN
ejpam-3377	127	33	,	,	PUNCT
ejpam-3377	127	34	n)(x	n)(x	PROPN
ejpam-3377	127	35	,	,	PUNCT
ejpam-3377	127	36	y)‖2	y)‖2	PROPN
ejpam-3377	127	37	≤	≤	NUM
ejpam-3377	127	38	1	1	NUM
ejpam-3377	127	39	16	16	NUM
ejpam-3377	127	40	sup	sup	NOUN
ejpam-3377	127	41	(	(	PUNCT
ejpam-3377	127	42	x	x	NOUN
ejpam-3377	127	43	,	,	PUNCT
ejpam-3377	127	44	y)∈[0,1]×[0,1	y)∈[0,1]×[0,1	PROPN
ejpam-3377	127	45	]	]	X
ejpam-3377	127	46	[	[	PUNCT
ejpam-3377	127	47	4	4	NUM
ejpam-3377	127	48	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3377	127	49	∂n+1	∂n+1	PROPN
ejpam-3377	127	50	∂xn+1	∂xn+1	PROPN
ejpam-3377	127	51	w(x	w(x	PROPN
ejpam-3377	127	52	,	,	PUNCT
ejpam-3377	127	53	y	y	PROPN
ejpam-3377	127	54	)	)	PUNCT
ejpam-3377	127	55	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3377	127	56	4	4	NUM
ejpam-3377	127	57	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3377	127	58	∂n+1	∂n+1	PROPN
ejpam-3377	127	59	∂yn+1	∂yn+1	PROPN
ejpam-3377	127	60	w(x	w(x	PROPN
ejpam-3377	127	61	,	,	PUNCT
ejpam-3377	127	62	y	y	NOUN
ejpam-3377	127	63	)	)	PUNCT
ejpam-3377	127	64	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3377	127	65	+	+	CCONJ
ejpam-3377	127	66	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3377	127	67	∂2n+2	∂2n+2	PROPN
ejpam-3377	127	68	∂xn+1∂yn+1	∂xn+1∂yn+1	PROPN
ejpam-3377	127	69	w(x	w(x	PROPN
ejpam-3377	127	70	,	,	PUNCT
ejpam-3377	127	71	y	y	NOUN
ejpam-3377	127	72	)	)	PUNCT
ejpam-3377	127	73	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3377	127	74	1	1	NUM
ejpam-3377	127	75	nn+1	nn+1	NOUN
ejpam-3377	127	76	]	]	PUNCT
ejpam-3377	127	77	1	1	NUM
ejpam-3377	127	78	nn+1	nn+1	NOUN
ejpam-3377	127	79	.	.	PUNCT
ejpam-3377	128	1	(	(	PUNCT
ejpam-3377	128	2	15	15	NUM
ejpam-3377	128	3	)	)	SYM
ejpam-3377	128	4	3	3	NUM
ejpam-3377	128	5	.	.	PUNCT
ejpam-3377	128	6	operational	operational	ADJ
ejpam-3377	128	7	matrices	matrix	NOUN
ejpam-3377	128	8	of	of	ADP
ejpam-3377	128	9	integrations	integration	NOUN
ejpam-3377	128	10	and	and	CCONJ
ejpam-3377	128	11	differentiations	differentiation	NOUN
ejpam-3377	128	12	this	this	DET
ejpam-3377	128	13	section	section	NOUN
ejpam-3377	128	14	is	be	AUX
ejpam-3377	128	15	devoted	devote	VERB
ejpam-3377	128	16	to	to	PART
ejpam-3377	128	17	construct	construct	VERB
ejpam-3377	128	18	and	and	CCONJ
ejpam-3377	128	19	recall	recall	VERB
ejpam-3377	128	20	some	some	DET
ejpam-3377	128	21	operational	operational	ADJ
ejpam-3377	128	22	matrices	matrix	NOUN
ejpam-3377	128	23	based	base	VERB
ejpam-3377	128	24	on	on	ADP
ejpam-3377	128	25	shifted	shift	VERB
ejpam-3377	128	26	jacobi	jacobi	PROPN
ejpam-3377	128	27	polynomials	polynomial	NOUN
ejpam-3377	128	28	,	,	PUNCT
ejpam-3377	128	29	which	which	PRON
ejpam-3377	128	30	are	be	AUX
ejpam-3377	128	31	needed	need	VERB
ejpam-3377	128	32	throughout	throughout	ADP
ejpam-3377	128	33	in	in	ADP
ejpam-3377	128	34	this	this	DET
ejpam-3377	128	35	paper	paper	NOUN
ejpam-3377	128	36	.	.	PUNCT
ejpam-3377	129	1	for	for	ADP
ejpam-3377	129	2	the	the	DET
ejpam-3377	129	3	proof	proof	NOUN
ejpam-3377	129	4	of	of	ADP
ejpam-3377	129	5	the	the	DET
ejpam-3377	129	6	required	require	VERB
ejpam-3377	129	7	operational	operational	ADJ
ejpam-3377	129	8	matrices	matrix	NOUN
ejpam-3377	129	9	,	,	PUNCT
ejpam-3377	129	10	see	see	VERB
ejpam-3377	129	11	[	[	X
ejpam-3377	129	12	24	24	NUM
ejpam-3377	129	13	]	]	PUNCT
ejpam-3377	129	14	.	.	PUNCT
ejpam-3377	130	1	theorem	theorem	NOUN
ejpam-3377	130	2	3.1	3.1	NUM
ejpam-3377	130	3	.	.	PUNCT
ejpam-3377	131	1	consider	consider	VERB
ejpam-3377	131	2	φn2(x	φn2(x	PROPN
ejpam-3377	131	3	,	,	PUNCT
ejpam-3377	131	4	y	y	NOUN
ejpam-3377	131	5	)	)	PUNCT
ejpam-3377	131	6	as	as	ADP
ejpam-3377	131	7	in	in	ADP
ejpam-3377	131	8	given	give	VERB
ejpam-3377	131	9	(	(	PUNCT
ejpam-3377	131	10	14	14	NUM
ejpam-3377	131	11	)	)	PUNCT
ejpam-3377	131	12	,	,	PUNCT
ejpam-3377	131	13	then	then	ADV
ejpam-3377	131	14	the	the	DET
ejpam-3377	131	15	α	α	NOUN
ejpam-3377	131	16	-	-	PUNCT
ejpam-3377	131	17	the	the	DET
ejpam-3377	131	18	order	order	NOUN
ejpam-3377	131	19	integration	integration	NOUN
ejpam-3377	131	20	of	of	ADP
ejpam-3377	131	21	φn2(x	φn2(x	PROPN
ejpam-3377	131	22	,	,	PUNCT
ejpam-3377	131	23	y	y	NOUN
ejpam-3377	131	24	)	)	PUNCT
ejpam-3377	131	25	corresponding	correspond	VERB
ejpam-3377	131	26	to	to	ADP
ejpam-3377	131	27	‘	'	PUNCT
ejpam-3377	131	28	x′	x′	PROPN
ejpam-3377	131	29	is	be	AUX
ejpam-3377	131	30	provided	provide	VERB
ejpam-3377	131	31	by	by	ADP
ejpam-3377	131	32	iαx	iαx	PROPN
ejpam-3377	131	33	(	(	PUNCT
ejpam-3377	131	34	φn2(x	φn2(x	PROPN
ejpam-3377	131	35	,	,	PUNCT
ejpam-3377	131	36	y	y	NOUN
ejpam-3377	131	37	)	)	PUNCT
ejpam-3377	131	38	)	)	PUNCT
ejpam-3377	131	39	'	'	PUNCT
ejpam-3377	132	1	s	s	X
ejpam-3377	132	2	(	(	PUNCT
ejpam-3377	132	3	α	α	NOUN
ejpam-3377	132	4	,	,	PUNCT
ejpam-3377	132	5	x	x	NOUN
ejpam-3377	132	6	)	)	PUNCT
ejpam-3377	132	7	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	132	8	,	,	PUNCT
ejpam-3377	132	9	y	y	NOUN
ejpam-3377	132	10	)	)	PUNCT
ejpam-3377	132	11	(	(	PUNCT
ejpam-3377	132	12	16	16	NUM
ejpam-3377	132	13	)	)	PUNCT
ejpam-3377	132	14	with	with	ADP
ejpam-3377	132	15	s	s	PROPN
ejpam-3377	132	16	(	(	PUNCT
ejpam-3377	132	17	α	α	NOUN
ejpam-3377	132	18	,	,	PUNCT
ejpam-3377	132	19	x	x	NOUN
ejpam-3377	132	20	)	)	PUNCT
ejpam-3377	132	21	n2×n2	n2×n2	NOUN
ejpam-3377	132	22	is	be	AUX
ejpam-3377	132	23	the	the	DET
ejpam-3377	132	24	operational	operational	ADJ
ejpam-3377	132	25	matrix	matrix	NOUN
ejpam-3377	132	26	given	give	VERB
ejpam-3377	132	27	by	by	ADP
ejpam-3377	132	28	s	s	PRON
ejpam-3377	132	29	(	(	PUNCT
ejpam-3377	132	30	α	α	NOUN
ejpam-3377	132	31	,	,	PUNCT
ejpam-3377	132	32	x	x	NOUN
ejpam-3377	132	33	)	)	PUNCT
ejpam-3377	132	34	n2×n2	n2×n2	NOUN
ejpam-3377	132	35	=	=	SYM
ejpam-3377	132	36			NOUN
ejpam-3377	132	37	ℵ1,1,k	ℵ1,1,k	PROPN
ejpam-3377	132	38	ℵ1,2,k	ℵ1,2,k	NOUN
ejpam-3377	132	39	·	·	PUNCT
ejpam-3377	132	40	·	·	PUNCT
ejpam-3377	132	41	·	·	PUNCT
ejpam-3377	133	1	ℵ1,r	ℵ1,r	PROPN
ejpam-3377	133	2	,	,	PUNCT
ejpam-3377	133	3	k	k	PROPN
ejpam-3377	133	4	·	·	PUNCT
ejpam-3377	133	5	·	·	PUNCT
ejpam-3377	133	6	·	·	PUNCT
ejpam-3377	134	1	ℵ1,n2,k	ℵ1,n2,k	NOUN
ejpam-3377	134	2	ℵ2,1,k	ℵ2,1,k	PROPN
ejpam-3377	134	3	ℵ2,2,k	ℵ2,2,k	PROPN
ejpam-3377	134	4	·	·	PUNCT
ejpam-3377	134	5	·	·	PUNCT
ejpam-3377	134	6	·	·	PUNCT
ejpam-3377	135	1	ℵ2,r	ℵ2,r	PROPN
ejpam-3377	135	2	,	,	PUNCT
ejpam-3377	135	3	k	k	PROPN
ejpam-3377	135	4	·	·	PUNCT
ejpam-3377	135	5	·	·	PUNCT
ejpam-3377	135	6	·	·	PUNCT
ejpam-3377	136	1	ℵ2,n2,k	ℵ2,n2,k	ADV
ejpam-3377	136	2	...	...	PUNCT
ejpam-3377	136	3	...	...	PUNCT
ejpam-3377	136	4	...	...	PUNCT
ejpam-3377	136	5	...	...	PUNCT
ejpam-3377	136	6	...	...	PUNCT
ejpam-3377	136	7	...	...	PUNCT
ejpam-3377	137	1	ℵv,1,k	ℵv,1,k	PROPN
ejpam-3377	137	2	ℵv,2,k	ℵv,2,k	PROPN
ejpam-3377	137	3	·	·	PUNCT
ejpam-3377	137	4	·	·	PUNCT
ejpam-3377	137	5	·	·	PUNCT
ejpam-3377	137	6	ℵv	ℵv	X
ejpam-3377	137	7	,	,	PUNCT
ejpam-3377	137	8	r	r	NOUN
ejpam-3377	137	9	,	,	PUNCT
ejpam-3377	137	10	k	k	PROPN
ejpam-3377	137	11	·	·	PUNCT
ejpam-3377	137	12	·	·	PUNCT
ejpam-3377	137	13	·	·	PUNCT
ejpam-3377	137	14	ℵv	ℵv	X
ejpam-3377	137	15	,	,	PUNCT
ejpam-3377	137	16	n2,k	n2,k	PROPN
ejpam-3377	137	17	...	...	PUNCT
ejpam-3377	137	18	...	...	PUNCT
ejpam-3377	137	19	...	...	PUNCT
ejpam-3377	137	20	...	...	PUNCT
ejpam-3377	137	21	...	...	PUNCT
ejpam-3377	137	22	...	...	PUNCT
ejpam-3377	138	1	ℵn2,1,k	ℵn2,1,k	NOUN
ejpam-3377	138	2	ℵn2,2,k	ℵn2,2,k	X
ejpam-3377	138	3	·	·	PUNCT
ejpam-3377	139	1	·	·	PUNCT
ejpam-3377	139	2	·	·	PUNCT
ejpam-3377	139	3	ℵn2,r	ℵn2,r	NOUN
ejpam-3377	139	4	,	,	PUNCT
ejpam-3377	139	5	k	k	X
ejpam-3377	139	6	·	·	PUNCT
ejpam-3377	139	7	·	·	PUNCT
ejpam-3377	139	8	·	·	PUNCT
ejpam-3377	139	9	ℵn2,n2,k	ℵn2,n2,k	PROPN
ejpam-3377	139	10			NUM
ejpam-3377	139	11	,	,	PUNCT
ejpam-3377	139	12	and	and	CCONJ
ejpam-3377	139	13	r	r	NOUN
ejpam-3377	139	14	=	=	PUNCT
ejpam-3377	139	15	ni+	ni+	NOUN
ejpam-3377	139	16	j	j	PROPN
ejpam-3377	139	17	+	+	PROPN
ejpam-3377	139	18	1	1	NUM
ejpam-3377	139	19	,	,	PUNCT
ejpam-3377	139	20	v	v	NOUN
ejpam-3377	139	21	=	=	SYM
ejpam-3377	139	22	na+	na+	NOUN
ejpam-3377	139	23	b+	b+	PUNCT
ejpam-3377	139	24	1	1	NUM
ejpam-3377	139	25	,	,	PUNCT
ejpam-3377	139	26	ℵq	ℵq	NOUN
ejpam-3377	139	27	,	,	PUNCT
ejpam-3377	139	28	r	r	NOUN
ejpam-3377	139	29	,	,	PUNCT
ejpam-3377	139	30	k	k	NOUN
ejpam-3377	139	31	=	=	SYM
ejpam-3377	139	32	ωi	ωi	PROPN
ejpam-3377	139	33	,	,	PUNCT
ejpam-3377	139	34	j	j	PROPN
ejpam-3377	139	35	,	,	PUNCT
ejpam-3377	139	36	a	a	DET
ejpam-3377	139	37	,	,	PUNCT
ejpam-3377	139	38	b	b	NOUN
ejpam-3377	139	39	,	,	PUNCT
ejpam-3377	139	40	k	k	PROPN
ejpam-3377	139	41	for	for	ADP
ejpam-3377	139	42	i	i	PROPN
ejpam-3377	139	43	,	,	PUNCT
ejpam-3377	139	44	j	j	PROPN
ejpam-3377	139	45	,	,	PUNCT
ejpam-3377	139	46	a	a	PRON
ejpam-3377	139	47	,	,	PUNCT
ejpam-3377	139	48	b	b	NOUN
ejpam-3377	139	49	=	=	SYM
ejpam-3377	139	50	0	0	NUM
ejpam-3377	139	51	,	,	PUNCT
ejpam-3377	139	52	1	1	NUM
ejpam-3377	139	53	,	,	PUNCT
ejpam-3377	139	54	2	2	NUM
ejpam-3377	139	55	,	,	PUNCT
ejpam-3377	139	56	.	.	PUNCT
ejpam-3377	139	57	.	.	PUNCT
ejpam-3377	139	58	.	.	PUNCT
ejpam-3377	140	1	,	,	PUNCT
ejpam-3377	140	2	m	m	PROPN
ejpam-3377	140	3	,	,	PUNCT
ejpam-3377	140	4	ωi	ωi	PROPN
ejpam-3377	140	5	,	,	PUNCT
ejpam-3377	140	6	j	j	PROPN
ejpam-3377	140	7	,	,	PUNCT
ejpam-3377	140	8	a	a	DET
ejpam-3377	140	9	,	,	PUNCT
ejpam-3377	140	10	b	b	NOUN
ejpam-3377	140	11	,	,	PUNCT
ejpam-3377	140	12	k	k	PROPN
ejpam-3377	140	13	=	=	SYM
ejpam-3377	140	14	a∑	a∑	PROPN
ejpam-3377	140	15	k=0	k=0	PROPN
ejpam-3377	140	16	∆a	∆a	PROPN
ejpam-3377	140	17	,	,	PUNCT
ejpam-3377	140	18	k	k	NOUN
ejpam-3377	140	19	,	,	PUNCT
ejpam-3377	140	20	αgi	αgi	ADJ
ejpam-3377	140	21	,	,	PUNCT
ejpam-3377	140	22	j	j	PROPN
ejpam-3377	140	23	,	,	PUNCT
ejpam-3377	140	24	b	b	PROPN
ejpam-3377	141	1	gijb	gijb	NOUN
ejpam-3377	142	1	=	=	PUNCT
ejpam-3377	143	1	δj	δj	PROPN
ejpam-3377	143	2	,	,	PUNCT
ejpam-3377	143	3	b	b	NOUN
ejpam-3377	143	4	i∑	i∑	PROPN
ejpam-3377	143	5	l=0	l=0	PROPN
ejpam-3377	143	6	(	(	PUNCT
ejpam-3377	143	7	−1)i−l(2i+	−1)i−l(2i+	PROPN
ejpam-3377	143	8	p+	p+	NOUN
ejpam-3377	143	9	q	q	NOUN
ejpam-3377	143	10	+	+	PROPN
ejpam-3377	143	11	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	143	12	1)γ(i+	1)γ(i+	NUM
ejpam-3377	143	13	l	l	NOUN
ejpam-3377	143	14	+	+	X
ejpam-3377	143	15	p+	p+	NOUN
ejpam-3377	143	16	q	q	X
ejpam-3377	143	17	+	+	NUM
ejpam-3377	143	18	1)γ(k	1)γ(k	NUM
ejpam-3377	143	19	+	+	CCONJ
ejpam-3377	143	20	α+	α+	PUNCT
ejpam-3377	143	21	l	l	NOUN
ejpam-3377	143	22	+	+	X
ejpam-3377	143	23	p+	p+	PROPN
ejpam-3377	143	24	1)γ(p+	1)γ(p+	PROPN
ejpam-3377	143	25	1)δα	1)δα	PROPN
ejpam-3377	143	26	γ(i+	γ(i+	NUM
ejpam-3377	143	27	p+	p+	PROPN
ejpam-3377	143	28	1)γ(l	1)γ(l	NUM
ejpam-3377	143	29	+	+	CCONJ
ejpam-3377	143	30	q	q	PUNCT
ejpam-3377	143	31	+	+	NUM
ejpam-3377	143	32	1)γ(i−	1)γ(i−	NUM
ejpam-3377	143	33	l+)γ(l	l+)γ(l	NOUN
ejpam-3377	144	1	+	+	CCONJ
ejpam-3377	144	2	1)γ(k	1)γ(k	NUM
ejpam-3377	144	3	+	+	CCONJ
ejpam-3377	144	4	α+	α+	PUNCT
ejpam-3377	144	5	l	l	NOUN
ejpam-3377	144	6	+	+	X
ejpam-3377	144	7	p+	p+	NOUN
ejpam-3377	144	8	q	q	X
ejpam-3377	144	9	+	+	PROPN
ejpam-3377	144	10	2	2	NUM
ejpam-3377	144	11	)	)	PUNCT
ejpam-3377	144	12	.	.	PUNCT
ejpam-3377	145	1	where	where	SCONJ
ejpam-3377	145	2	∆a	∆a	NOUN
ejpam-3377	145	3	,	,	PUNCT
ejpam-3377	145	4	k	k	PROPN
ejpam-3377	145	5	,	,	PUNCT
ejpam-3377	145	6	α	α	NOUN
ejpam-3377	145	7	=	=	PUNCT
ejpam-3377	145	8	(	(	PUNCT
ejpam-3377	145	9	−1)a−kγ(a+	−1)a−kγ(a+	NOUN
ejpam-3377	145	10	q	q	NOUN
ejpam-3377	146	1	+	+	NUM
ejpam-3377	147	1	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	147	2	k	k	PROPN
ejpam-3377	147	3	+	+	PROPN
ejpam-3377	147	4	p+	p+	NOUN
ejpam-3377	147	5	q	q	NOUN
ejpam-3377	147	6	+	+	NUM
ejpam-3377	147	7	1)γ(1	1)γ(1	NOUN
ejpam-3377	147	8	+	+	CCONJ
ejpam-3377	147	9	k	k	X
ejpam-3377	147	10	)	)	PUNCT
ejpam-3377	147	11	γ(k	γ(k	NOUN
ejpam-3377	147	12	+	+	CCONJ
ejpam-3377	147	13	q	q	PROPN
ejpam-3377	148	1	+	+	NUM
ejpam-3377	148	2	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	148	3	p+	p+	NOUN
ejpam-3377	148	4	q	q	NOUN
ejpam-3377	149	1	+	+	NUM
ejpam-3377	149	2	1)γ(a−	1)γ(a−	PROPN
ejpam-3377	149	3	k	k	PROPN
ejpam-3377	150	1	+	+	CCONJ
ejpam-3377	150	2	1)γ(k	1)γ(k	NUM
ejpam-3377	150	3	+	+	NUM
ejpam-3377	150	4	1)γ(1	1)γ(1	NOUN
ejpam-3377	151	1	+	+	CCONJ
ejpam-3377	151	2	k	k	PROPN
ejpam-3377	152	1	+	+	X
ejpam-3377	152	2	α)δk	α)δk	PROPN
ejpam-3377	152	3	.	.	PUNCT
ejpam-3377	153	1	(	(	PUNCT
ejpam-3377	153	2	17	17	NUM
ejpam-3377	153	3	)	)	PUNCT
ejpam-3377	153	4	m.i	m.i	PROPN
ejpam-3377	153	5	.	.	PROPN
ejpam-3377	153	6	chohan	chohan	PROPN
ejpam-3377	153	7	,	,	PUNCT
ejpam-3377	153	8	k.shah	k.shah	PROPN
ejpam-3377	153	9	/	/	SYM
ejpam-3377	153	10	eur	eur	PROPN
ejpam-3377	153	11	.	.	PUNCT
ejpam-3377	154	1	j.	j.	PROPN
ejpam-3377	154	2	pure	pure	PROPN
ejpam-3377	154	3	appl	appl	PROPN
ejpam-3377	154	4	.	.	PROPN
ejpam-3377	154	5	math	math	PROPN
ejpam-3377	154	6	,	,	PUNCT
ejpam-3377	154	7	12	12	NUM
ejpam-3377	154	8	(	(	PUNCT
ejpam-3377	154	9	1	1	NUM
ejpam-3377	154	10	)	)	PUNCT
ejpam-3377	154	11	(	(	PUNCT
ejpam-3377	154	12	2019	2019	NUM
ejpam-3377	154	13	)	)	PUNCT
ejpam-3377	154	14	,	,	PUNCT
ejpam-3377	154	15	39	39	NUM
ejpam-3377	154	16	-	-	SYM
ejpam-3377	154	17	57	57	NUM
ejpam-3377	154	18	45	45	NUM
ejpam-3377	154	19	theorem	theorem	NOUN
ejpam-3377	154	20	3.2	3.2	NUM
ejpam-3377	154	21	.	.	PUNCT
ejpam-3377	155	1	the	the	DET
ejpam-3377	155	2	fractional	fractional	ADJ
ejpam-3377	155	3	order	order	NOUN
ejpam-3377	155	4	differentiation	differentiation	NOUN
ejpam-3377	155	5	of	of	ADP
ejpam-3377	155	6	φn2(x	φn2(x	PROPN
ejpam-3377	155	7	,	,	PUNCT
ejpam-3377	155	8	y	y	NOUN
ejpam-3377	155	9	)	)	PUNCT
ejpam-3377	155	10	as	as	SCONJ
ejpam-3377	155	11	defined	define	VERB
ejpam-3377	155	12	in	in	ADP
ejpam-3377	155	13	(	(	PUNCT
ejpam-3377	155	14	14	14	NUM
ejpam-3377	155	15	)	)	PUNCT
ejpam-3377	155	16	corresponding	correspond	VERB
ejpam-3377	155	17	to	to	ADP
ejpam-3377	155	18	‘	'	PUNCT
ejpam-3377	155	19	y′	y′	PROPN
ejpam-3377	155	20	as	as	ADP
ejpam-3377	155	21	dαy	dαy	PROPN
ejpam-3377	155	22	(	(	PUNCT
ejpam-3377	155	23	φn2(x	φn2(x	PROPN
ejpam-3377	155	24	,	,	PUNCT
ejpam-3377	155	25	y	y	NOUN
ejpam-3377	155	26	)	)	PUNCT
ejpam-3377	155	27	)	)	PUNCT
ejpam-3377	155	28	'	'	PUNCT
ejpam-3377	155	29	h	h	NOUN
ejpam-3377	155	30	(	(	PUNCT
ejpam-3377	155	31	α	α	NOUN
ejpam-3377	155	32	,	,	PUNCT
ejpam-3377	155	33	y	y	NOUN
ejpam-3377	155	34	)	)	PUNCT
ejpam-3377	155	35	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	155	36	,	,	PUNCT
ejpam-3377	155	37	y	y	NOUN
ejpam-3377	155	38	)	)	PUNCT
ejpam-3377	155	39	(	(	PUNCT
ejpam-3377	155	40	18	18	NUM
ejpam-3377	155	41	)	)	PUNCT
ejpam-3377	155	42	where	where	SCONJ
ejpam-3377	155	43	h	h	PROPN
ejpam-3377	155	44	(	(	PUNCT
ejpam-3377	155	45	α	α	NOUN
ejpam-3377	155	46	,	,	PUNCT
ejpam-3377	155	47	y	y	NOUN
ejpam-3377	155	48	)	)	PUNCT
ejpam-3377	155	49	n2×n2	n2×n2	NOUN
ejpam-3377	155	50	is	be	AUX
ejpam-3377	155	51	the	the	DET
ejpam-3377	155	52	operational	operational	ADJ
ejpam-3377	155	53	matrix	matrix	NOUN
ejpam-3377	155	54	given	give	VERB
ejpam-3377	155	55	as	as	ADP
ejpam-3377	155	56	h	h	PROPN
ejpam-3377	155	57	(	(	PUNCT
ejpam-3377	155	58	α	α	NOUN
ejpam-3377	155	59	,	,	PUNCT
ejpam-3377	155	60	y	y	NOUN
ejpam-3377	155	61	)	)	PUNCT
ejpam-3377	155	62	n2×n2	n2×n2	NOUN
ejpam-3377	155	63	=	=	SYM
ejpam-3377	155	64			NOUN
ejpam-3377	155	65	ℵ1,1,k	ℵ1,1,k	PROPN
ejpam-3377	155	66	ℵ1,2,k	ℵ1,2,k	NOUN
ejpam-3377	155	67	·	·	PUNCT
ejpam-3377	155	68	·	·	PUNCT
ejpam-3377	155	69	·	·	PUNCT
ejpam-3377	156	1	ℵ1,r	ℵ1,r	PROPN
ejpam-3377	156	2	,	,	PUNCT
ejpam-3377	156	3	k	k	PROPN
ejpam-3377	156	4	·	·	PUNCT
ejpam-3377	156	5	·	·	PUNCT
ejpam-3377	156	6	·	·	PUNCT
ejpam-3377	157	1	ℵ1,n2,k	ℵ1,n2,k	NOUN
ejpam-3377	157	2	ℵ2,1,k	ℵ2,1,k	PROPN
ejpam-3377	157	3	ℵ2,2,k	ℵ2,2,k	PROPN
ejpam-3377	157	4	·	·	PUNCT
ejpam-3377	157	5	·	·	PUNCT
ejpam-3377	157	6	·	·	PUNCT
ejpam-3377	158	1	ℵ2,r	ℵ2,r	PROPN
ejpam-3377	158	2	,	,	PUNCT
ejpam-3377	158	3	k	k	PROPN
ejpam-3377	158	4	·	·	PUNCT
ejpam-3377	158	5	·	·	PUNCT
ejpam-3377	158	6	·	·	PUNCT
ejpam-3377	159	1	ℵ2,n2,k	ℵ2,n2,k	ADV
ejpam-3377	159	2	...	...	PUNCT
ejpam-3377	159	3	...	...	PUNCT
ejpam-3377	159	4	...	...	PUNCT
ejpam-3377	159	5	...	...	PUNCT
ejpam-3377	159	6	...	...	PUNCT
ejpam-3377	159	7	...	...	PUNCT
ejpam-3377	160	1	ℵv,1,k	ℵv,1,k	PROPN
ejpam-3377	160	2	ℵv,2,k	ℵv,2,k	PROPN
ejpam-3377	160	3	·	·	PUNCT
ejpam-3377	160	4	·	·	PUNCT
ejpam-3377	160	5	·	·	PUNCT
ejpam-3377	160	6	ℵv	ℵv	X
ejpam-3377	160	7	,	,	PUNCT
ejpam-3377	160	8	r	r	NOUN
ejpam-3377	160	9	,	,	PUNCT
ejpam-3377	160	10	k	k	PROPN
ejpam-3377	160	11	·	·	PUNCT
ejpam-3377	160	12	·	·	PUNCT
ejpam-3377	160	13	·	·	PUNCT
ejpam-3377	160	14	ℵv	ℵv	X
ejpam-3377	160	15	,	,	PUNCT
ejpam-3377	160	16	n2,k	n2,k	PROPN
ejpam-3377	160	17	...	...	PUNCT
ejpam-3377	160	18	...	...	PUNCT
ejpam-3377	160	19	...	...	PUNCT
ejpam-3377	160	20	...	...	PUNCT
ejpam-3377	160	21	...	...	PUNCT
ejpam-3377	160	22	...	...	PUNCT
ejpam-3377	161	1	ℵn2,1,k	ℵn2,1,k	NOUN
ejpam-3377	161	2	ℵn2,2,k	ℵn2,2,k	X
ejpam-3377	161	3	·	·	PUNCT
ejpam-3377	162	1	·	·	PUNCT
ejpam-3377	162	2	·	·	PUNCT
ejpam-3377	162	3	ℵn2,r	ℵn2,r	NOUN
ejpam-3377	162	4	,	,	PUNCT
ejpam-3377	162	5	k	k	X
ejpam-3377	162	6	·	·	PUNCT
ejpam-3377	162	7	·	·	PUNCT
ejpam-3377	162	8	·	·	PUNCT
ejpam-3377	162	9	ℵn2,n2,k	ℵn2,n2,k	PROPN
ejpam-3377	162	10			NUM
ejpam-3377	162	11	,	,	PUNCT
ejpam-3377	162	12	(	(	PUNCT
ejpam-3377	162	13	19	19	NUM
ejpam-3377	162	14	)	)	PUNCT
ejpam-3377	162	15	and	and	CCONJ
ejpam-3377	162	16	v	v	X
ejpam-3377	162	17	=	=	PUNCT
ejpam-3377	162	18	ni+	ni+	NOUN
ejpam-3377	162	19	j	j	PROPN
ejpam-3377	162	20	+	+	PROPN
ejpam-3377	162	21	1	1	NUM
ejpam-3377	162	22	,	,	PUNCT
ejpam-3377	162	23	r	r	NOUN
ejpam-3377	162	24	=	=	SYM
ejpam-3377	162	25	na+	na+	NOUN
ejpam-3377	162	26	b+	b+	PUNCT
ejpam-3377	162	27	1	1	NUM
ejpam-3377	162	28	,	,	PUNCT
ejpam-3377	162	29	ℵv	ℵv	VERB
ejpam-3377	162	30	,	,	PUNCT
ejpam-3377	162	31	r	r	NOUN
ejpam-3377	162	32	,	,	PUNCT
ejpam-3377	162	33	k	k	NOUN
ejpam-3377	162	34	=	=	SYM
ejpam-3377	162	35	ωi	ωi	PROPN
ejpam-3377	162	36	,	,	PUNCT
ejpam-3377	162	37	j	j	PROPN
ejpam-3377	162	38	,	,	PUNCT
ejpam-3377	162	39	a	a	DET
ejpam-3377	162	40	,	,	PUNCT
ejpam-3377	162	41	b	b	NOUN
ejpam-3377	162	42	,	,	PUNCT
ejpam-3377	162	43	k	k	PROPN
ejpam-3377	162	44	for	for	ADP
ejpam-3377	162	45	i	i	PROPN
ejpam-3377	162	46	,	,	PUNCT
ejpam-3377	162	47	j	j	PROPN
ejpam-3377	162	48	,	,	PUNCT
ejpam-3377	162	49	a	a	PRON
ejpam-3377	162	50	,	,	PUNCT
ejpam-3377	162	51	b	b	NOUN
ejpam-3377	162	52	=	=	SYM
ejpam-3377	162	53	0	0	NUM
ejpam-3377	162	54	,	,	PUNCT
ejpam-3377	162	55	1	1	NUM
ejpam-3377	162	56	,	,	PUNCT
ejpam-3377	162	57	2	2	NUM
ejpam-3377	162	58	,	,	PUNCT
ejpam-3377	162	59	.	.	PUNCT
ejpam-3377	162	60	.	.	PUNCT
ejpam-3377	162	61	.	.	PUNCT
ejpam-3377	162	62	,	,	PUNCT
ejpam-3377	162	63	n	n	CCONJ
ejpam-3377	162	64	,	,	PUNCT
ejpam-3377	162	65	ωi	ωi	PROPN
ejpam-3377	162	66	,	,	PUNCT
ejpam-3377	162	67	j	j	PROPN
ejpam-3377	162	68	,	,	PUNCT
ejpam-3377	162	69	a	a	DET
ejpam-3377	162	70	,	,	PUNCT
ejpam-3377	162	71	b	b	NOUN
ejpam-3377	162	72	,	,	PUNCT
ejpam-3377	162	73	k	k	PROPN
ejpam-3377	162	74	=	=	PUNCT
ejpam-3377	162	75	a∑	a∑	PROPN
ejpam-3377	162	76	k=0	k=0	PROPN
ejpam-3377	162	77	λa	λa	PROPN
ejpam-3377	162	78	,	,	PUNCT
ejpam-3377	162	79	k	k	PROPN
ejpam-3377	162	80	,	,	PUNCT
ejpam-3377	162	81	σ∆i	σ∆i	VERB
ejpam-3377	162	82	,	,	PUNCT
ejpam-3377	162	83	j	j	PROPN
ejpam-3377	162	84	,	,	PUNCT
ejpam-3377	162	85	b	b	PROPN
ejpam-3377	162	86	,	,	PUNCT
ejpam-3377	162	87	(	(	PUNCT
ejpam-3377	162	88	20	20	NUM
ejpam-3377	162	89	)	)	PUNCT
ejpam-3377	162	90	gijb	gijb	NOUN
ejpam-3377	162	91	=	=	PUNCT
ejpam-3377	162	92	δj	δj	PROPN
ejpam-3377	162	93	,	,	PUNCT
ejpam-3377	162	94	b	b	NOUN
ejpam-3377	162	95	i∑	i∑	PROPN
ejpam-3377	162	96	l=0	l=0	PROPN
ejpam-3377	162	97	(	(	PUNCT
ejpam-3377	162	98	−1)i−l(2i+	−1)i−l(2i+	PROPN
ejpam-3377	162	99	p+	p+	NOUN
ejpam-3377	162	100	q	q	NOUN
ejpam-3377	162	101	+	+	PROPN
ejpam-3377	162	102	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	162	103	1)γ(i+	1)γ(i+	NUM
ejpam-3377	162	104	l	l	NOUN
ejpam-3377	162	105	+	+	X
ejpam-3377	162	106	p+	p+	NOUN
ejpam-3377	162	107	q	q	X
ejpam-3377	162	108	+	+	NUM
ejpam-3377	162	109	1)γ(k	1)γ(k	NUM
ejpam-3377	162	110	−	−	PROPN
ejpam-3377	162	111	σ	σ	NOUN
ejpam-3377	162	112	+	+	NOUN
ejpam-3377	162	113	l	l	NOUN
ejpam-3377	163	1	+	+	CCONJ
ejpam-3377	163	2	q	q	PUNCT
ejpam-3377	164	1	+	+	CCONJ
ejpam-3377	164	2	1)γ(p+	1)γ(p+	PROPN
ejpam-3377	164	3	1)δα	1)δα	PROPN
ejpam-3377	164	4	γ(i+	γ(i+	NUM
ejpam-3377	164	5	p+	p+	PROPN
ejpam-3377	164	6	1)γ(l	1)γ(l	NUM
ejpam-3377	164	7	+	+	CCONJ
ejpam-3377	164	8	q	q	PUNCT
ejpam-3377	164	9	+	+	NUM
ejpam-3377	164	10	1)γ(i−	1)γ(i−	NUM
ejpam-3377	164	11	l	l	NOUN
ejpam-3377	164	12	+	+	CCONJ
ejpam-3377	164	13	1)γ(l	1)γ(l	NUM
ejpam-3377	164	14	+	+	NUM
ejpam-3377	164	15	1)γ(k	1)γ(k	NUM
ejpam-3377	164	16	−	−	NOUN
ejpam-3377	164	17	α+	α+	PUNCT
ejpam-3377	164	18	l	l	NOUN
ejpam-3377	165	1	+	+	X
ejpam-3377	165	2	p+	p+	NOUN
ejpam-3377	165	3	q	q	X
ejpam-3377	165	4	+	+	PROPN
ejpam-3377	165	5	2	2	NUM
ejpam-3377	165	6	)	)	PUNCT
ejpam-3377	165	7	(	(	PUNCT
ejpam-3377	165	8	21	21	NUM
ejpam-3377	165	9	)	)	PUNCT
ejpam-3377	165	10	and	and	CCONJ
ejpam-3377	165	11	∆a	∆a	VERB
ejpam-3377	165	12	,	,	PUNCT
ejpam-3377	165	13	k	k	PROPN
ejpam-3377	165	14	,	,	PUNCT
ejpam-3377	165	15	α	α	NOUN
ejpam-3377	165	16	=	=	PUNCT
ejpam-3377	165	17	(	(	PUNCT
ejpam-3377	165	18	−1)a−kγ(a+	−1)a−kγ(a+	NOUN
ejpam-3377	165	19	q	q	NOUN
ejpam-3377	166	1	+	+	NUM
ejpam-3377	167	1	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	167	2	k	k	PROPN
ejpam-3377	167	3	+	+	PROPN
ejpam-3377	167	4	p+	p+	NOUN
ejpam-3377	167	5	q	q	NOUN
ejpam-3377	167	6	+	+	NUM
ejpam-3377	167	7	1)γ(1	1)γ(1	NOUN
ejpam-3377	167	8	+	+	CCONJ
ejpam-3377	167	9	k	k	X
ejpam-3377	167	10	)	)	PUNCT
ejpam-3377	167	11	γ(k	γ(k	NOUN
ejpam-3377	167	12	+	+	CCONJ
ejpam-3377	167	13	q	q	PROPN
ejpam-3377	168	1	+	+	NUM
ejpam-3377	168	2	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	168	3	p+	p+	NOUN
ejpam-3377	168	4	q	q	NOUN
ejpam-3377	168	5	+	+	CCONJ
ejpam-3377	168	6	1)(a−	1)(a−	NUM
ejpam-3377	168	7	k)!k!γ(1	k)!k!γ(1	NOUN
ejpam-3377	169	1	+	+	CCONJ
ejpam-3377	170	1	k	k	PROPN
ejpam-3377	170	2	−	−	PROPN
ejpam-3377	170	3	α)δk	α)δk	PROPN
ejpam-3377	170	4	.	.	PUNCT
ejpam-3377	171	1	(	(	PUNCT
ejpam-3377	171	2	22	22	NUM
ejpam-3377	171	3	)	)	PUNCT
ejpam-3377	171	4	in	in	ADP
ejpam-3377	171	5	the	the	DET
ejpam-3377	171	6	same	same	ADJ
ejpam-3377	171	7	line	line	NOUN
ejpam-3377	171	8	,	,	PUNCT
ejpam-3377	171	9	the	the	DET
ejpam-3377	171	10	fractional	fractional	ADJ
ejpam-3377	171	11	order	order	NOUN
ejpam-3377	171	12	differentiation	differentiation	NOUN
ejpam-3377	171	13	of	of	ADP
ejpam-3377	171	14	φn2(x	φn2(x	PROPN
ejpam-3377	171	15	,	,	PUNCT
ejpam-3377	171	16	y	y	NOUN
ejpam-3377	171	17	)	)	PUNCT
ejpam-3377	171	18	corresponding	correspond	VERB
ejpam-3377	171	19	to	to	ADP
ejpam-3377	171	20	‘	'	PUNCT
ejpam-3377	171	21	x′	x′	PROPN
ejpam-3377	171	22	as	as	SCONJ
ejpam-3377	171	23	provided	provide	VERB
ejpam-3377	171	24	as	as	ADP
ejpam-3377	171	25	dαx	dαx	NOUN
ejpam-3377	171	26	(	(	PUNCT
ejpam-3377	171	27	φn2(x	φn2(x	PROPN
ejpam-3377	171	28	,	,	PUNCT
ejpam-3377	171	29	y	y	NOUN
ejpam-3377	171	30	)	)	PUNCT
ejpam-3377	171	31	)	)	PUNCT
ejpam-3377	171	32	'	'	PUNCT
ejpam-3377	172	1	h	h	NOUN
ejpam-3377	172	2	(	(	PUNCT
ejpam-3377	172	3	α	α	NOUN
ejpam-3377	172	4	,	,	PUNCT
ejpam-3377	172	5	x	x	NOUN
ejpam-3377	172	6	)	)	PUNCT
ejpam-3377	172	7	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	172	8	,	,	PUNCT
ejpam-3377	172	9	y	y	PROPN
ejpam-3377	172	10	)	)	PUNCT
ejpam-3377	172	11	,	,	PUNCT
ejpam-3377	172	12	(	(	PUNCT
ejpam-3377	172	13	23	23	NUM
ejpam-3377	172	14	)	)	PUNCT
ejpam-3377	172	15	where	where	SCONJ
ejpam-3377	172	16	h	h	PROPN
ejpam-3377	172	17	(	(	PUNCT
ejpam-3377	172	18	α	α	NOUN
ejpam-3377	172	19	,	,	PUNCT
ejpam-3377	172	20	x	x	NOUN
ejpam-3377	172	21	)	)	PUNCT
ejpam-3377	172	22	n2×n2	n2×n2	NOUN
ejpam-3377	172	23	is	be	AUX
ejpam-3377	172	24	the	the	DET
ejpam-3377	172	25	operational	operational	ADJ
ejpam-3377	172	26	matrix	matrix	NOUN
ejpam-3377	172	27	defined	define	VERB
ejpam-3377	172	28	as	as	ADP
ejpam-3377	172	29	h	h	NOUN
ejpam-3377	172	30	(	(	PUNCT
ejpam-3377	172	31	α	α	NOUN
ejpam-3377	172	32	,	,	PUNCT
ejpam-3377	172	33	x	x	NOUN
ejpam-3377	172	34	)	)	PUNCT
ejpam-3377	172	35	n2×n2	n2×n2	NOUN
ejpam-3377	172	36	=	=	SYM
ejpam-3377	172	37			NOUN
ejpam-3377	172	38	ℵ1,1,k	ℵ1,1,k	PROPN
ejpam-3377	172	39	ℵ1,2,k	ℵ1,2,k	NOUN
ejpam-3377	172	40	·	·	PUNCT
ejpam-3377	172	41	·	·	PUNCT
ejpam-3377	172	42	·	·	PUNCT
ejpam-3377	173	1	ℵ1,r	ℵ1,r	PROPN
ejpam-3377	173	2	,	,	PUNCT
ejpam-3377	173	3	k	k	PROPN
ejpam-3377	173	4	·	·	PUNCT
ejpam-3377	173	5	·	·	PUNCT
ejpam-3377	173	6	·	·	PUNCT
ejpam-3377	174	1	ℵ1,n2,k	ℵ1,n2,k	NOUN
ejpam-3377	174	2	ℵ2,1,k	ℵ2,1,k	PROPN
ejpam-3377	174	3	ℵ2,2,k	ℵ2,2,k	PROPN
ejpam-3377	174	4	·	·	PUNCT
ejpam-3377	174	5	·	·	PUNCT
ejpam-3377	174	6	·	·	PUNCT
ejpam-3377	175	1	ℵ2,r	ℵ2,r	PROPN
ejpam-3377	175	2	,	,	PUNCT
ejpam-3377	175	3	k	k	PROPN
ejpam-3377	175	4	·	·	PUNCT
ejpam-3377	175	5	·	·	PUNCT
ejpam-3377	175	6	·	·	PUNCT
ejpam-3377	176	1	ℵ2,n2,k	ℵ2,n2,k	ADV
ejpam-3377	176	2	...	...	PUNCT
ejpam-3377	176	3	...	...	PUNCT
ejpam-3377	176	4	...	...	PUNCT
ejpam-3377	176	5	...	...	PUNCT
ejpam-3377	176	6	...	...	PUNCT
ejpam-3377	176	7	...	...	PUNCT
ejpam-3377	177	1	ℵv,1,k	ℵv,1,k	PROPN
ejpam-3377	177	2	ℵv,2,k	ℵv,2,k	PROPN
ejpam-3377	177	3	·	·	PUNCT
ejpam-3377	177	4	·	·	PUNCT
ejpam-3377	177	5	·	·	PUNCT
ejpam-3377	177	6	ℵv	ℵv	X
ejpam-3377	177	7	,	,	PUNCT
ejpam-3377	177	8	r	r	NOUN
ejpam-3377	177	9	,	,	PUNCT
ejpam-3377	177	10	k	k	PROPN
ejpam-3377	177	11	·	·	PUNCT
ejpam-3377	177	12	·	·	PUNCT
ejpam-3377	177	13	·	·	PUNCT
ejpam-3377	177	14	ℵv	ℵv	X
ejpam-3377	177	15	,	,	PUNCT
ejpam-3377	177	16	n2,k	n2,k	PROPN
ejpam-3377	177	17	...	...	PUNCT
ejpam-3377	177	18	...	...	PUNCT
ejpam-3377	177	19	...	...	PUNCT
ejpam-3377	177	20	...	...	PUNCT
ejpam-3377	177	21	...	...	PUNCT
ejpam-3377	177	22	...	...	PUNCT
ejpam-3377	178	1	ℵn2,1,k	ℵn2,1,k	NOUN
ejpam-3377	178	2	ℵn2,2,k	ℵn2,2,k	X
ejpam-3377	178	3	·	·	PUNCT
ejpam-3377	179	1	·	·	PUNCT
ejpam-3377	179	2	·	·	PUNCT
ejpam-3377	179	3	ℵn2,r	ℵn2,r	NOUN
ejpam-3377	179	4	,	,	PUNCT
ejpam-3377	179	5	k	k	X
ejpam-3377	179	6	·	·	PUNCT
ejpam-3377	179	7	·	·	PUNCT
ejpam-3377	179	8	·	·	PUNCT
ejpam-3377	179	9	ℵn2,n2,k	ℵn2,n2,k	PROPN
ejpam-3377	179	10			NUM
ejpam-3377	179	11	.	.	PUNCT
ejpam-3377	180	1	(	(	PUNCT
ejpam-3377	180	2	24	24	NUM
ejpam-3377	180	3	)	)	PUNCT
ejpam-3377	180	4	theorem	theorem	VERB
ejpam-3377	180	5	3.3	3.3	NUM
ejpam-3377	180	6	.	.	PUNCT
ejpam-3377	181	1	the	the	DET
ejpam-3377	181	2	fractional	fractional	ADJ
ejpam-3377	181	3	order	order	NOUN
ejpam-3377	181	4	derivative	derivative	NOUN
ejpam-3377	181	5	of	of	ADP
ejpam-3377	181	6	φn2(x	φn2(x	PROPN
ejpam-3377	181	7	,	,	PUNCT
ejpam-3377	181	8	y	y	NOUN
ejpam-3377	181	9	)	)	PUNCT
ejpam-3377	181	10	is	be	AUX
ejpam-3377	181	11	constructed	construct	VERB
ejpam-3377	181	12	in	in	ADP
ejpam-3377	181	13	(	(	PUNCT
ejpam-3377	181	14	14	14	NUM
ejpam-3377	181	15	)	)	PUNCT
ejpam-3377	181	16	corresponding	correspond	VERB
ejpam-3377	181	17	to	to	ADP
ejpam-3377	181	18	′x′	′x′	PROPN
ejpam-3377	181	19	and	and	CCONJ
ejpam-3377	181	20	′y′	′y′	PROPN
ejpam-3377	181	21	as	as	ADP
ejpam-3377	181	22	∂α	∂α	PROPN
ejpam-3377	181	23	∂x(α/2)∂y(α/2	∂x(α/2)∂y(α/2	NOUN
ejpam-3377	181	24	)	)	PUNCT
ejpam-3377	181	25	(	(	PUNCT
ejpam-3377	181	26	φn2(x	φn2(x	PROPN
ejpam-3377	181	27	,	,	PUNCT
ejpam-3377	181	28	y	y	NOUN
ejpam-3377	181	29	)	)	PUNCT
ejpam-3377	181	30	)	)	PUNCT
ejpam-3377	181	31	'	'	PUNCT
ejpam-3377	182	1	h	h	NOUN
ejpam-3377	182	2	(	(	PUNCT
ejpam-3377	182	3	α	α	NOUN
ejpam-3377	182	4	,	,	PUNCT
ejpam-3377	182	5	x	x	NOUN
ejpam-3377	182	6	,	,	PUNCT
ejpam-3377	182	7	y	y	NOUN
ejpam-3377	182	8	)	)	PUNCT
ejpam-3377	182	9	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	182	10	,	,	PUNCT
ejpam-3377	182	11	y	y	PROPN
ejpam-3377	182	12	)	)	PUNCT
ejpam-3377	182	13	,	,	PUNCT
ejpam-3377	182	14	(	(	PUNCT
ejpam-3377	182	15	25	25	NUM
ejpam-3377	182	16	)	)	PUNCT
ejpam-3377	182	17	m.i	m.i	PROPN
ejpam-3377	182	18	.	.	PROPN
ejpam-3377	182	19	chohan	chohan	PROPN
ejpam-3377	182	20	,	,	PUNCT
ejpam-3377	182	21	k.shah	k.shah	PROPN
ejpam-3377	182	22	/	/	SYM
ejpam-3377	182	23	eur	eur	PROPN
ejpam-3377	182	24	.	.	PUNCT
ejpam-3377	183	1	j.	j.	PROPN
ejpam-3377	183	2	pure	pure	PROPN
ejpam-3377	183	3	appl	appl	PROPN
ejpam-3377	183	4	.	.	PROPN
ejpam-3377	183	5	math	math	PROPN
ejpam-3377	183	6	,	,	PUNCT
ejpam-3377	183	7	12	12	NUM
ejpam-3377	183	8	(	(	PUNCT
ejpam-3377	183	9	1	1	NUM
ejpam-3377	183	10	)	)	PUNCT
ejpam-3377	183	11	(	(	PUNCT
ejpam-3377	183	12	2019	2019	NUM
ejpam-3377	183	13	)	)	PUNCT
ejpam-3377	183	14	,	,	PUNCT
ejpam-3377	183	15	39	39	NUM
ejpam-3377	183	16	-	-	SYM
ejpam-3377	183	17	57	57	NUM
ejpam-3377	183	18	46	46	NUM
ejpam-3377	183	19	where	where	SCONJ
ejpam-3377	183	20	h	h	PROPN
ejpam-3377	183	21	(	(	PUNCT
ejpam-3377	183	22	α	α	NOUN
ejpam-3377	183	23	,	,	PUNCT
ejpam-3377	183	24	x	x	NOUN
ejpam-3377	183	25	,	,	PUNCT
ejpam-3377	183	26	y	y	NOUN
ejpam-3377	183	27	)	)	PUNCT
ejpam-3377	183	28	n2×n2	n2×n2	NOUN
ejpam-3377	183	29	is	be	AUX
ejpam-3377	183	30	the	the	DET
ejpam-3377	183	31	operational	operational	ADJ
ejpam-3377	183	32	matrix	matrix	NOUN
ejpam-3377	183	33	of	of	ADP
ejpam-3377	183	34	given	give	VERB
ejpam-3377	183	35	as	as	ADP
ejpam-3377	183	36	h	h	NOUN
ejpam-3377	183	37	(	(	PUNCT
ejpam-3377	183	38	α	α	NOUN
ejpam-3377	183	39	,	,	PUNCT
ejpam-3377	183	40	x	x	NOUN
ejpam-3377	183	41	,	,	PUNCT
ejpam-3377	183	42	y	y	NOUN
ejpam-3377	183	43	)	)	PUNCT
ejpam-3377	183	44	n2×n2	n2×n2	NOUN
ejpam-3377	183	45	=	=	SYM
ejpam-3377	183	46			NOUN
ejpam-3377	183	47	ℵ1,1,k	ℵ1,1,k	PROPN
ejpam-3377	183	48	ℵ1,2,k	ℵ1,2,k	NOUN
ejpam-3377	183	49	·	·	PUNCT
ejpam-3377	183	50	·	·	PUNCT
ejpam-3377	184	1	·	·	PUNCT
ejpam-3377	184	2	ℵ1,r	ℵ1,r	PROPN
ejpam-3377	184	3	,	,	PUNCT
ejpam-3377	184	4	k	k	PROPN
ejpam-3377	184	5	·	·	PUNCT
ejpam-3377	184	6	·	·	PUNCT
ejpam-3377	184	7	·	·	PUNCT
ejpam-3377	185	1	ℵ1,n2,k	ℵ1,n2,k	NOUN
ejpam-3377	185	2	ℵ2,1,k	ℵ2,1,k	PROPN
ejpam-3377	185	3	ℵ2,2,k	ℵ2,2,k	PROPN
ejpam-3377	185	4	·	·	PUNCT
ejpam-3377	185	5	·	·	PUNCT
ejpam-3377	185	6	·	·	PUNCT
ejpam-3377	186	1	ℵ2,r	ℵ2,r	PROPN
ejpam-3377	186	2	,	,	PUNCT
ejpam-3377	186	3	k	k	PROPN
ejpam-3377	186	4	·	·	PUNCT
ejpam-3377	186	5	·	·	PUNCT
ejpam-3377	186	6	·	·	PUNCT
ejpam-3377	187	1	ℵ2,n2,k	ℵ2,n2,k	ADV
ejpam-3377	187	2	...	...	PUNCT
ejpam-3377	187	3	...	...	PUNCT
ejpam-3377	187	4	...	...	PUNCT
ejpam-3377	187	5	...	...	PUNCT
ejpam-3377	187	6	...	...	PUNCT
ejpam-3377	187	7	...	...	PUNCT
ejpam-3377	188	1	ℵv,1,k	ℵv,1,k	PROPN
ejpam-3377	188	2	ℵv,2,k	ℵv,2,k	PROPN
ejpam-3377	188	3	·	·	PUNCT
ejpam-3377	188	4	·	·	PUNCT
ejpam-3377	188	5	·	·	PUNCT
ejpam-3377	188	6	ℵv	ℵv	X
ejpam-3377	188	7	,	,	PUNCT
ejpam-3377	188	8	r	r	NOUN
ejpam-3377	188	9	,	,	PUNCT
ejpam-3377	188	10	k	k	PROPN
ejpam-3377	188	11	·	·	PUNCT
ejpam-3377	188	12	·	·	PUNCT
ejpam-3377	188	13	·	·	PUNCT
ejpam-3377	188	14	ℵv	ℵv	X
ejpam-3377	188	15	,	,	PUNCT
ejpam-3377	188	16	n2,k	n2,k	PROPN
ejpam-3377	188	17	...	...	PUNCT
ejpam-3377	188	18	...	...	PUNCT
ejpam-3377	188	19	...	...	PUNCT
ejpam-3377	188	20	...	...	PUNCT
ejpam-3377	188	21	...	...	PUNCT
ejpam-3377	188	22	...	...	PUNCT
ejpam-3377	189	1	ℵn2,1,k	ℵn2,1,k	NOUN
ejpam-3377	189	2	ℵn2,2,k	ℵn2,2,k	X
ejpam-3377	189	3	·	·	PUNCT
ejpam-3377	190	1	·	·	PUNCT
ejpam-3377	190	2	·	·	PUNCT
ejpam-3377	190	3	ℵn2,r	ℵn2,r	NOUN
ejpam-3377	190	4	,	,	PUNCT
ejpam-3377	190	5	k	k	X
ejpam-3377	190	6	·	·	PUNCT
ejpam-3377	190	7	·	·	PUNCT
ejpam-3377	190	8	·	·	PUNCT
ejpam-3377	190	9	ℵn2,n2,k	ℵn2,n2,k	PROPN
ejpam-3377	190	10			NUM
ejpam-3377	190	11	,	,	PUNCT
ejpam-3377	190	12	(	(	PUNCT
ejpam-3377	190	13	26	26	NUM
ejpam-3377	190	14	)	)	PUNCT
ejpam-3377	190	15	and	and	CCONJ
ejpam-3377	190	16	r	r	NOUN
ejpam-3377	190	17	=	=	PUNCT
ejpam-3377	190	18	ni+	ni+	NOUN
ejpam-3377	190	19	j	j	PROPN
ejpam-3377	190	20	+	+	PROPN
ejpam-3377	190	21	1	1	NUM
ejpam-3377	190	22	,	,	PUNCT
ejpam-3377	190	23	v	v	NOUN
ejpam-3377	190	24	=	=	SYM
ejpam-3377	190	25	na+	na+	NOUN
ejpam-3377	190	26	b+	b+	PUNCT
ejpam-3377	190	27	1	1	NUM
ejpam-3377	190	28	,	,	PUNCT
ejpam-3377	190	29	ℵv	ℵv	VERB
ejpam-3377	190	30	,	,	PUNCT
ejpam-3377	190	31	r	r	NOUN
ejpam-3377	190	32	,	,	PUNCT
ejpam-3377	190	33	k	k	NOUN
ejpam-3377	190	34	=	=	SYM
ejpam-3377	190	35	ωi	ωi	PROPN
ejpam-3377	190	36	,	,	PUNCT
ejpam-3377	190	37	j	j	PROPN
ejpam-3377	190	38	,	,	PUNCT
ejpam-3377	190	39	a	a	DET
ejpam-3377	190	40	,	,	PUNCT
ejpam-3377	190	41	b	b	NOUN
ejpam-3377	190	42	,	,	PUNCT
ejpam-3377	190	43	k	k	PROPN
ejpam-3377	190	44	for	for	ADP
ejpam-3377	190	45	i	i	PROPN
ejpam-3377	190	46	,	,	PUNCT
ejpam-3377	190	47	j	j	PROPN
ejpam-3377	190	48	,	,	PUNCT
ejpam-3377	190	49	a	a	PRON
ejpam-3377	190	50	,	,	PUNCT
ejpam-3377	190	51	b	b	NOUN
ejpam-3377	190	52	=	=	SYM
ejpam-3377	190	53	0	0	NUM
ejpam-3377	190	54	,	,	PUNCT
ejpam-3377	190	55	1	1	NUM
ejpam-3377	190	56	,	,	PUNCT
ejpam-3377	190	57	2	2	NUM
ejpam-3377	190	58	,	,	PUNCT
ejpam-3377	190	59	.	.	PUNCT
ejpam-3377	190	60	.	.	PUNCT
ejpam-3377	191	1	.	.	PUNCT
ejpam-3377	192	1	,	,	PUNCT
ejpam-3377	192	2	n	n	CCONJ
ejpam-3377	192	3	,	,	PUNCT
ejpam-3377	192	4	ωi	ωi	PROPN
ejpam-3377	192	5	,	,	PUNCT
ejpam-3377	192	6	j	j	PROPN
ejpam-3377	192	7	,	,	PUNCT
ejpam-3377	192	8	a	a	DET
ejpam-3377	192	9	,	,	PUNCT
ejpam-3377	192	10	b	b	NOUN
ejpam-3377	192	11	,	,	PUNCT
ejpam-3377	192	12	k	k	PROPN
ejpam-3377	192	13	=	=	SYM
ejpam-3377	192	14	a∑	a∑	PROPN
ejpam-3377	192	15	k=0	k=0	PROPN
ejpam-3377	192	16	∆a	∆a	PROPN
ejpam-3377	192	17	,	,	PUNCT
ejpam-3377	192	18	k	k	NOUN
ejpam-3377	192	19	,	,	PUNCT
ejpam-3377	192	20	αθi	αθi	NOUN
ejpam-3377	192	21	,	,	PUNCT
ejpam-3377	192	22	j	j	PROPN
ejpam-3377	192	23	,	,	PUNCT
ejpam-3377	192	24	b	b	PROPN
ejpam-3377	192	25	(	(	PUNCT
ejpam-3377	192	26	27	27	NUM
ejpam-3377	192	27	)	)	PUNCT
ejpam-3377	192	28	θijb	θijb	NOUN
ejpam-3377	192	29	=	=	PUNCT
ejpam-3377	193	1	δj	δj	PROPN
ejpam-3377	193	2	,	,	PUNCT
ejpam-3377	193	3	b	b	NOUN
ejpam-3377	193	4	i∑	i∑	PROPN
ejpam-3377	193	5	l=0	l=0	PROPN
ejpam-3377	193	6	(	(	PUNCT
ejpam-3377	193	7	−1)i−l(2i+	−1)i−l(2i+	PROPN
ejpam-3377	193	8	p+	p+	NOUN
ejpam-3377	193	9	q	q	NOUN
ejpam-3377	194	1	+	+	PROPN
ejpam-3377	194	2	1)γ(i+	1)γ(i+	PROPN
ejpam-3377	194	3	1)γ(i+	1)γ(i+	NUM
ejpam-3377	194	4	l	l	NOUN
ejpam-3377	194	5	+	+	X
ejpam-3377	194	6	p+	p+	NOUN
ejpam-3377	194	7	q	q	X
ejpam-3377	195	1	+	+	NUM
ejpam-3377	195	2	1)γ(k	1)γ(k	NUM
ejpam-3377	195	3	−	−	NOUN
ejpam-3377	195	4	α+	α+	NOUN
ejpam-3377	195	5	l	l	NOUN
ejpam-3377	196	1	+	+	CCONJ
ejpam-3377	196	2	q	q	PUNCT
ejpam-3377	196	3	+	+	CCONJ
ejpam-3377	196	4	1)γ(p+	1)γ(p+	PROPN
ejpam-3377	196	5	1)δα	1)δα	PROPN
ejpam-3377	196	6	γ(i+	γ(i+	NUM
ejpam-3377	196	7	p+	p+	PROPN
ejpam-3377	196	8	1)γ(l	1)γ(l	NUM
ejpam-3377	196	9	+	+	CCONJ
ejpam-3377	196	10	q	q	PUNCT
ejpam-3377	196	11	+	+	NUM
ejpam-3377	197	1	1)γ(i−	1)γ(i−	NUM
ejpam-3377	197	2	l	l	NOUN
ejpam-3377	198	1	+	+	CCONJ
ejpam-3377	198	2	1)γ(l	1)γ(l	NUM
ejpam-3377	198	3	+	+	NUM
ejpam-3377	198	4	1)γ(k	1)γ(k	NUM
ejpam-3377	198	5	−	−	NOUN
ejpam-3377	198	6	α+	α+	PUNCT
ejpam-3377	198	7	l	l	NOUN
ejpam-3377	198	8	+	+	X
ejpam-3377	198	9	p+	p+	NOUN
ejpam-3377	198	10	q	q	X
ejpam-3377	198	11	+	+	PROPN
ejpam-3377	198	12	2	2	NUM
ejpam-3377	198	13	)	)	PUNCT
ejpam-3377	198	14	(	(	PUNCT
ejpam-3377	198	15	28	28	NUM
ejpam-3377	198	16	)	)	PUNCT
ejpam-3377	198	17	and	and	CCONJ
ejpam-3377	198	18	∆a	∆a	VERB
ejpam-3377	198	19	,	,	PUNCT
ejpam-3377	198	20	k	k	PROPN
ejpam-3377	198	21	,	,	PUNCT
ejpam-3377	198	22	α	α	NOUN
ejpam-3377	198	23	=	=	PUNCT
ejpam-3377	198	24	(	(	PUNCT
ejpam-3377	198	25	−1)a−kγ(a+	−1)a−kγ(a+	NOUN
ejpam-3377	198	26	q	q	NOUN
ejpam-3377	199	1	+	+	NUM
ejpam-3377	200	1	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	200	2	k	k	PROPN
ejpam-3377	200	3	+	+	PROPN
ejpam-3377	200	4	p+	p+	NOUN
ejpam-3377	200	5	q	q	NOUN
ejpam-3377	200	6	+	+	NUM
ejpam-3377	200	7	1)γ(1	1)γ(1	NOUN
ejpam-3377	200	8	+	+	CCONJ
ejpam-3377	200	9	k	k	X
ejpam-3377	200	10	)	)	PUNCT
ejpam-3377	200	11	γ(k	γ(k	NOUN
ejpam-3377	200	12	+	+	CCONJ
ejpam-3377	200	13	q	q	PROPN
ejpam-3377	201	1	+	+	NUM
ejpam-3377	201	2	1)γ(a+	1)γ(a+	PROPN
ejpam-3377	201	3	p+	p+	NOUN
ejpam-3377	201	4	q	q	NOUN
ejpam-3377	202	1	+	+	NUM
ejpam-3377	202	2	1)γ(a−	1)γ(a−	PROPN
ejpam-3377	202	3	k	k	PROPN
ejpam-3377	203	1	+	+	CCONJ
ejpam-3377	203	2	1)γ(k	1)γ(k	NUM
ejpam-3377	203	3	+	+	NUM
ejpam-3377	203	4	1)γ(1	1)γ(1	NOUN
ejpam-3377	204	1	+	+	CCONJ
ejpam-3377	205	1	k	k	PROPN
ejpam-3377	205	2	−	−	PROPN
ejpam-3377	205	3	α)δk	α)δk	PROPN
ejpam-3377	205	4	.	.	PUNCT
ejpam-3377	206	1	(	(	PUNCT
ejpam-3377	206	2	29	29	NUM
ejpam-3377	206	3	)	)	PUNCT
ejpam-3377	206	4	proof	proof	NOUN
ejpam-3377	206	5	.	.	PUNCT
ejpam-3377	207	1	the	the	DET
ejpam-3377	207	2	operational	operational	ADJ
ejpam-3377	207	3	matrix	matrix	NOUN
ejpam-3377	207	4	h	h	NOUN
ejpam-3377	207	5	(	(	PUNCT
ejpam-3377	207	6	α	α	NOUN
ejpam-3377	207	7	,	,	PUNCT
ejpam-3377	207	8	x	x	NOUN
ejpam-3377	207	9	,	,	PUNCT
ejpam-3377	207	10	y	y	NOUN
ejpam-3377	207	11	)	)	PUNCT
ejpam-3377	207	12	n2×n2	n2×n2	NOUN
ejpam-3377	207	13	can	can	AUX
ejpam-3377	207	14	be	be	AUX
ejpam-3377	207	15	easily	easily	ADV
ejpam-3377	207	16	obtain	obtain	VERB
ejpam-3377	207	17	by	by	ADP
ejpam-3377	207	18	using	use	VERB
ejpam-3377	207	19	the	the	DET
ejpam-3377	207	20	product	product	NOUN
ejpam-3377	207	21	of	of	ADP
ejpam-3377	207	22	two	two	NUM
ejpam-3377	207	23	operational	operational	ADJ
ejpam-3377	207	24	matrices	matrix	NOUN
ejpam-3377	207	25	,	,	PUNCT
ejpam-3377	207	26	h	h	PROPN
ejpam-3377	207	27	(	(	PUNCT
ejpam-3377	207	28	α	α	NOUN
ejpam-3377	207	29	,	,	PUNCT
ejpam-3377	207	30	y	y	NOUN
ejpam-3377	207	31	)	)	PUNCT
ejpam-3377	207	32	n2×n2	n2×n2	NOUN
ejpam-3377	207	33	and	and	CCONJ
ejpam-3377	207	34	h	h	NOUN
ejpam-3377	207	35	(	(	PUNCT
ejpam-3377	207	36	α	α	NOUN
ejpam-3377	207	37	,	,	PUNCT
ejpam-3377	207	38	x	x	NOUN
ejpam-3377	207	39	)	)	PUNCT
ejpam-3377	207	40	n2×n2	n2×n2	NOUN
ejpam-3377	207	41	given	give	VERB
ejpam-3377	207	42	in	in	ADP
ejpam-3377	207	43	theorem	theorem	ADJ
ejpam-3377	207	44	3.2	3.2	NUM
ejpam-3377	207	45	.	.	PUNCT
ejpam-3377	208	1	4	4	NUM
ejpam-3377	208	2	.	.	X
ejpam-3377	208	3	numerical	numerical	ADJ
ejpam-3377	208	4	procedure	procedure	NOUN
ejpam-3377	208	5	based	base	VERB
ejpam-3377	208	6	on	on	ADP
ejpam-3377	208	7	the	the	DET
ejpam-3377	208	8	operational	operational	ADJ
ejpam-3377	208	9	matrices	matrix	NOUN
ejpam-3377	208	10	for	for	ADP
ejpam-3377	208	11	fpde	fpde	NOUN
ejpam-3377	208	12	(	(	PUNCT
ejpam-3377	208	13	1	1	NUM
ejpam-3377	208	14	)	)	PUNCT
ejpam-3377	208	15	with	with	ADP
ejpam-3377	208	16	the	the	DET
ejpam-3377	208	17	help	help	NOUN
ejpam-3377	208	18	of	of	ADP
ejpam-3377	208	19	operational	operational	ADJ
ejpam-3377	208	20	matrices	matrix	NOUN
ejpam-3377	208	21	constructed	construct	VERB
ejpam-3377	208	22	in	in	ADP
ejpam-3377	208	23	section	section	NOUN
ejpam-3377	208	24	3	3	NUM
ejpam-3377	208	25	,	,	PUNCT
ejpam-3377	208	26	the	the	DET
ejpam-3377	208	27	considered	considered	ADJ
ejpam-3377	208	28	class	class	NOUN
ejpam-3377	208	29	of	of	ADP
ejpam-3377	208	30	fpdes	fpde	NOUN
ejpam-3377	208	31	(	(	PUNCT
ejpam-3377	208	32	1	1	X
ejpam-3377	208	33	)	)	PUNCT
ejpam-3377	208	34	is	be	AUX
ejpam-3377	208	35	converted	convert	VERB
ejpam-3377	208	36	to	to	ADP
ejpam-3377	208	37	simple	simple	ADJ
ejpam-3377	208	38	algebraic	algebraic	ADJ
ejpam-3377	208	39	equations	equation	NOUN
ejpam-3377	208	40	which	which	PRON
ejpam-3377	208	41	is	be	AUX
ejpam-3377	208	42	easily	easily	ADV
ejpam-3377	208	43	soluble	soluble	ADJ
ejpam-3377	208	44	.	.	PUNCT
ejpam-3377	209	1	assume	assume	VERB
ejpam-3377	209	2	that	that	SCONJ
ejpam-3377	209	3	the	the	DET
ejpam-3377	209	4	following	follow	VERB
ejpam-3377	209	5	hold	hold	VERB
ejpam-3377	209	6	∂αw(x	∂αw(x	PROPN
ejpam-3377	209	7	,	,	PUNCT
ejpam-3377	209	8	y	y	NOUN
ejpam-3377	209	9	)	)	PUNCT
ejpam-3377	209	10	∂xα	∂xα	PROPN
ejpam-3377	209	11	=	=	SYM
ejpam-3377	209	12	kn2φn2(x	kn2φn2(x	PROPN
ejpam-3377	209	13	,	,	PUNCT
ejpam-3377	209	14	y	y	NOUN
ejpam-3377	209	15	)	)	PUNCT
ejpam-3377	209	16	.	.	PUNCT
ejpam-3377	210	1	(	(	PUNCT
ejpam-3377	210	2	30	30	NUM
ejpam-3377	210	3	)	)	PUNCT
ejpam-3377	210	4	then	then	ADV
ejpam-3377	210	5	inview	inview	NOUN
ejpam-3377	210	6	of	of	ADP
ejpam-3377	210	7	definition	definition	NOUN
ejpam-3377	210	8	2.1	2.1	NUM
ejpam-3377	210	9	,	,	PUNCT
ejpam-3377	210	10	we	we	PRON
ejpam-3377	210	11	have	have	VERB
ejpam-3377	210	12	w(x	w(x	NOUN
ejpam-3377	210	13	,	,	PUNCT
ejpam-3377	210	14	y)−	y)−	PROPN
ejpam-3377	210	15	c1	c1	NOUN
ejpam-3377	210	16	−	−	PROPN
ejpam-3377	210	17	c2y	c2y	PROPN
ejpam-3377	210	18	=	=	SYM
ejpam-3377	210	19	kn2sα	kn2sα	PROPN
ejpam-3377	210	20	,	,	PUNCT
ejpam-3377	210	21	x	x	SYM
ejpam-3377	210	22	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	210	23	,	,	PUNCT
ejpam-3377	210	24	y	y	PROPN
ejpam-3377	210	25	)	)	PUNCT
ejpam-3377	210	26	(	(	PUNCT
ejpam-3377	210	27	31	31	NUM
ejpam-3377	210	28	)	)	PUNCT
ejpam-3377	211	1	which	which	PRON
ejpam-3377	211	2	on	on	ADP
ejpam-3377	211	3	using	use	VERB
ejpam-3377	211	4	initial	initial	ADJ
ejpam-3377	211	5	conditions	condition	NOUN
ejpam-3377	211	6	of	of	ADP
ejpam-3377	211	7	(	(	PUNCT
ejpam-3377	211	8	1	1	X
ejpam-3377	211	9	)	)	PUNCT
ejpam-3377	211	10	yields	yield	NOUN
ejpam-3377	211	11	that	that	PRON
ejpam-3377	211	12	w(x	w(x	PROPN
ejpam-3377	211	13	,	,	PUNCT
ejpam-3377	211	14	y	y	NOUN
ejpam-3377	211	15	)	)	PUNCT
ejpam-3377	211	16	=	=	SYM
ejpam-3377	211	17	kn2sα	kn2sα	PROPN
ejpam-3377	211	18	,	,	PUNCT
ejpam-3377	211	19	x	x	SYM
ejpam-3377	211	20	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	211	21	,	,	PUNCT
ejpam-3377	211	22	y	y	NOUN
ejpam-3377	211	23	)	)	PUNCT
ejpam-3377	211	24	+	+	CCONJ
ejpam-3377	211	25	φ(y	φ(y	ADJ
ejpam-3377	211	26	)	)	PUNCT
ejpam-3377	211	27	+	+	NUM
ejpam-3377	211	28	yψ(y	yψ(y	NOUN
ejpam-3377	211	29	)	)	PUNCT
ejpam-3377	211	30	=	=	SYM
ejpam-3377	211	31	kn2sα	kn2sα	PROPN
ejpam-3377	211	32	,	,	PUNCT
ejpam-3377	211	33	x	x	SYM
ejpam-3377	211	34	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	211	35	,	,	PUNCT
ejpam-3377	211	36	y	y	PROPN
ejpam-3377	211	37	)	)	PUNCT
ejpam-3377	211	38	+	+	CCONJ
ejpam-3377	211	39	ln2φn2(x	ln2φn2(x	PROPN
ejpam-3377	211	40	,	,	PUNCT
ejpam-3377	211	41	y	y	PROPN
ejpam-3377	211	42	)	)	PUNCT
ejpam-3377	211	43	,	,	PUNCT
ejpam-3377	211	44	where	where	SCONJ
ejpam-3377	211	45	φ(y	φ(y	NOUN
ejpam-3377	211	46	)	)	PUNCT
ejpam-3377	211	47	+	+	NUM
ejpam-3377	211	48	yψ(y	yψ(y	NOUN
ejpam-3377	211	49	)	)	PUNCT
ejpam-3377	212	1	=	=	SYM
ejpam-3377	212	2	ln2φn2(x	ln2φn2(x	PROPN
ejpam-3377	212	3	,	,	PUNCT
ejpam-3377	212	4	y	y	PROPN
ejpam-3377	212	5	)	)	PUNCT
ejpam-3377	212	6	=	=	PUNCT
ejpam-3377	213	1	[	[	X
ejpam-3377	213	2	kn2s	kn2s	X
ejpam-3377	213	3	(	(	PUNCT
ejpam-3377	213	4	α	α	NOUN
ejpam-3377	213	5	,	,	PUNCT
ejpam-3377	213	6	x	x	NOUN
ejpam-3377	213	7	)	)	PUNCT
ejpam-3377	213	8	n2×n2	n2×n2	NOUN
ejpam-3377	213	9	+	+	CCONJ
ejpam-3377	213	10	ln2	ln2	ADJ
ejpam-3377	213	11	]	]	X
ejpam-3377	213	12	φn2(x	φn2(x	PROPN
ejpam-3377	213	13	,	,	PUNCT
ejpam-3377	213	14	y	y	NOUN
ejpam-3377	213	15	)	)	PUNCT
ejpam-3377	213	16	.	.	PUNCT
ejpam-3377	214	1	(	(	PUNCT
ejpam-3377	214	2	32	32	NUM
ejpam-3377	214	3	)	)	PUNCT
ejpam-3377	214	4	m.i	m.i	PROPN
ejpam-3377	214	5	.	.	PROPN
ejpam-3377	214	6	chohan	chohan	PROPN
ejpam-3377	214	7	,	,	PUNCT
ejpam-3377	214	8	k.shah	k.shah	PROPN
ejpam-3377	214	9	/	/	SYM
ejpam-3377	214	10	eur	eur	PROPN
ejpam-3377	214	11	.	.	PUNCT
ejpam-3377	215	1	j.	j.	PROPN
ejpam-3377	215	2	pure	pure	PROPN
ejpam-3377	215	3	appl	appl	PROPN
ejpam-3377	215	4	.	.	PROPN
ejpam-3377	215	5	math	math	PROPN
ejpam-3377	215	6	,	,	PUNCT
ejpam-3377	215	7	12	12	NUM
ejpam-3377	215	8	(	(	PUNCT
ejpam-3377	215	9	1	1	NUM
ejpam-3377	215	10	)	)	PUNCT
ejpam-3377	215	11	(	(	PUNCT
ejpam-3377	215	12	2019	2019	NUM
ejpam-3377	215	13	)	)	PUNCT
ejpam-3377	215	14	,	,	PUNCT
ejpam-3377	215	15	39	39	NUM
ejpam-3377	215	16	-	-	SYM
ejpam-3377	215	17	57	57	NUM
ejpam-3377	215	18	47	47	NUM
ejpam-3377	215	19	now	now	ADV
ejpam-3377	215	20	inview	inview	NOUN
ejpam-3377	215	21	of	of	ADP
ejpam-3377	215	22	the	the	DET
ejpam-3377	215	23	relation	relation	NOUN
ejpam-3377	215	24	obtained	obtain	VERB
ejpam-3377	215	25	in	in	ADP
ejpam-3377	215	26	(	(	PUNCT
ejpam-3377	215	27	32	32	NUM
ejpam-3377	215	28	)	)	PUNCT
ejpam-3377	215	29	,	,	PUNCT
ejpam-3377	215	30	we	we	PRON
ejpam-3377	215	31	have	have	VERB
ejpam-3377	215	32	∂αw(x	∂αw(x	PROPN
ejpam-3377	215	33	,	,	PUNCT
ejpam-3377	215	34	y	y	NOUN
ejpam-3377	215	35	)	)	PUNCT
ejpam-3377	215	36	∂yα	∂yα	NOUN
ejpam-3377	215	37	=	=	PUNCT
ejpam-3377	216	1	[	[	X
ejpam-3377	216	2	kn2s	kn2s	PROPN
ejpam-3377	216	3	(	(	PUNCT
ejpam-3377	216	4	α	α	NOUN
ejpam-3377	216	5	,	,	PUNCT
ejpam-3377	216	6	x	x	NOUN
ejpam-3377	216	7	)	)	PUNCT
ejpam-3377	216	8	n2×n2	n2×n2	NOUN
ejpam-3377	216	9	+	+	CCONJ
ejpam-3377	216	10	ln2	ln2	ADJ
ejpam-3377	216	11	]	]	X
ejpam-3377	216	12	h	h	NOUN
ejpam-3377	216	13	(	(	PUNCT
ejpam-3377	216	14	α	α	NOUN
ejpam-3377	216	15	,	,	PUNCT
ejpam-3377	216	16	y	y	NOUN
ejpam-3377	216	17	)	)	PUNCT
ejpam-3377	216	18	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	216	19	,	,	PUNCT
ejpam-3377	216	20	y	y	NOUN
ejpam-3377	216	21	)	)	PUNCT
ejpam-3377	216	22	,	,	PUNCT
ejpam-3377	216	23	∂βw(x	∂βw(x	PROPN
ejpam-3377	216	24	,	,	PUNCT
ejpam-3377	216	25	y	y	NOUN
ejpam-3377	216	26	)	)	PUNCT
ejpam-3377	216	27	∂xβ	∂xβ	NOUN
ejpam-3377	216	28	=	=	PUNCT
ejpam-3377	217	1	[	[	X
ejpam-3377	217	2	kn2s	kn2s	PROPN
ejpam-3377	217	3	(	(	PUNCT
ejpam-3377	217	4	α	α	NOUN
ejpam-3377	217	5	,	,	PUNCT
ejpam-3377	217	6	x	x	NOUN
ejpam-3377	217	7	)	)	PUNCT
ejpam-3377	217	8	n2×n2	n2×n2	NOUN
ejpam-3377	217	9	+	+	CCONJ
ejpam-3377	218	1	ln2	ln2	ADJ
ejpam-3377	218	2	]	]	X
ejpam-3377	218	3	h	h	NOUN
ejpam-3377	218	4	(	(	PUNCT
ejpam-3377	218	5	β	β	X
ejpam-3377	218	6	,	,	PUNCT
ejpam-3377	218	7	x	x	NOUN
ejpam-3377	218	8	)	)	PUNCT
ejpam-3377	218	9	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	218	10	,	,	PUNCT
ejpam-3377	218	11	y	y	NOUN
ejpam-3377	218	12	)	)	PUNCT
ejpam-3377	218	13	,	,	PUNCT
ejpam-3377	218	14	∂βw(x	∂βw(x	PROPN
ejpam-3377	218	15	,	,	PUNCT
ejpam-3377	218	16	y	y	NOUN
ejpam-3377	218	17	)	)	PUNCT
ejpam-3377	218	18	∂yβ	∂yβ	NOUN
ejpam-3377	218	19	=	=	PUNCT
ejpam-3377	219	1	[	[	X
ejpam-3377	219	2	kn2s	kn2s	X
ejpam-3377	219	3	(	(	PUNCT
ejpam-3377	219	4	α	α	NOUN
ejpam-3377	219	5	,	,	PUNCT
ejpam-3377	219	6	x	x	NOUN
ejpam-3377	219	7	)	)	PUNCT
ejpam-3377	219	8	n2×n2	n2×n2	NOUN
ejpam-3377	219	9	+	+	CCONJ
ejpam-3377	220	1	ln2	ln2	ADJ
ejpam-3377	220	2	]	]	X
ejpam-3377	220	3	h	h	NOUN
ejpam-3377	220	4	(	(	PUNCT
ejpam-3377	220	5	β	β	X
ejpam-3377	220	6	,	,	PUNCT
ejpam-3377	220	7	y	y	NOUN
ejpam-3377	220	8	)	)	PUNCT
ejpam-3377	220	9	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	220	10	,	,	PUNCT
ejpam-3377	220	11	y	y	NOUN
ejpam-3377	220	12	)	)	PUNCT
ejpam-3377	220	13	,	,	PUNCT
ejpam-3377	220	14	∂αw(x	∂αw(x	PROPN
ejpam-3377	220	15	,	,	PUNCT
ejpam-3377	220	16	y	y	NOUN
ejpam-3377	220	17	)	)	PUNCT
ejpam-3377	220	18	∂x	∂x	NOUN
ejpam-3377	220	19	α	α	NOUN
ejpam-3377	220	20	2	2	NUM
ejpam-3377	220	21	∂y	∂y	SYM
ejpam-3377	220	22	α	α	NOUN
ejpam-3377	220	23	2	2	NUM
ejpam-3377	221	1	=	=	SYM
ejpam-3377	222	1	[	[	X
ejpam-3377	222	2	kn2s	kn2s	PROPN
ejpam-3377	222	3	(	(	PUNCT
ejpam-3377	222	4	α	α	NOUN
ejpam-3377	222	5	,	,	PUNCT
ejpam-3377	222	6	x	x	NOUN
ejpam-3377	222	7	)	)	PUNCT
ejpam-3377	222	8	n2×n2	n2×n2	NOUN
ejpam-3377	222	9	+	+	CCONJ
ejpam-3377	222	10	ln2	ln2	ADJ
ejpam-3377	222	11	]	]	X
ejpam-3377	222	12	h	h	NOUN
ejpam-3377	222	13	(	(	PUNCT
ejpam-3377	222	14	α	α	NOUN
ejpam-3377	222	15	,	,	PUNCT
ejpam-3377	222	16	x	x	NOUN
ejpam-3377	222	17	,	,	PUNCT
ejpam-3377	222	18	y	y	NOUN
ejpam-3377	222	19	)	)	PUNCT
ejpam-3377	222	20	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	222	21	,	,	PUNCT
ejpam-3377	222	22	y	y	NOUN
ejpam-3377	222	23	)	)	PUNCT
ejpam-3377	222	24	,	,	PUNCT
ejpam-3377	222	25	g(x	g(x	PROPN
ejpam-3377	222	26	,	,	PUNCT
ejpam-3377	222	27	y	y	NOUN
ejpam-3377	222	28	)	)	PUNCT
ejpam-3377	222	29	=	=	SYM
ejpam-3377	223	1	mn2φn2(x	mn2φn2(x	PROPN
ejpam-3377	223	2	,	,	PUNCT
ejpam-3377	223	3	y	y	PROPN
ejpam-3377	223	4	)	)	PUNCT
ejpam-3377	223	5	.	.	PUNCT
ejpam-3377	224	1	(	(	PUNCT
ejpam-3377	224	2	33	33	NUM
ejpam-3377	224	3	)	)	PUNCT
ejpam-3377	224	4	therefore	therefore	ADV
ejpam-3377	224	5	,	,	PUNCT
ejpam-3377	224	6	with	with	ADP
ejpam-3377	224	7	the	the	DET
ejpam-3377	224	8	help	help	NOUN
ejpam-3377	224	9	of	of	ADP
ejpam-3377	224	10	(	(	PUNCT
ejpam-3377	224	11	30	30	NUM
ejpam-3377	224	12	)	)	PUNCT
ejpam-3377	224	13	,	,	PUNCT
ejpam-3377	224	14	(	(	PUNCT
ejpam-3377	224	15	31),(32	31),(32	NOUN
ejpam-3377	224	16	)	)	PUNCT
ejpam-3377	224	17	and	and	CCONJ
ejpam-3377	224	18	(	(	PUNCT
ejpam-3377	224	19	33	33	NUM
ejpam-3377	224	20	)	)	PUNCT
ejpam-3377	224	21	,	,	PUNCT
ejpam-3377	224	22	our	our	PRON
ejpam-3377	224	23	considered	consider	VERB
ejpam-3377	224	24	class	class	NOUN
ejpam-3377	224	25	of	of	ADP
ejpam-3377	224	26	fpdes	fpde	NOUN
ejpam-3377	224	27	(	(	PUNCT
ejpam-3377	224	28	1	1	X
ejpam-3377	224	29	)	)	PUNCT
ejpam-3377	224	30	becomes	become	VERB
ejpam-3377	224	31	akn2φn2(x	akn2φn2(x	NOUN
ejpam-3377	224	32	,	,	PUNCT
ejpam-3377	224	33	y	y	PROPN
ejpam-3377	224	34	)	)	PUNCT
ejpam-3377	225	1	+	+	NOUN
ejpam-3377	225	2	b[kn2s	b[kn2s	PROPN
ejpam-3377	225	3	(	(	PUNCT
ejpam-3377	225	4	α	α	NOUN
ejpam-3377	225	5	,	,	PUNCT
ejpam-3377	225	6	x	x	NOUN
ejpam-3377	225	7	)	)	PUNCT
ejpam-3377	225	8	n2×n2	n2×n2	NOUN
ejpam-3377	225	9	+	+	CCONJ
ejpam-3377	225	10	ln2	ln2	ADJ
ejpam-3377	225	11	]	]	X
ejpam-3377	225	12	h	h	NOUN
ejpam-3377	225	13	(	(	PUNCT
ejpam-3377	225	14	α	α	NOUN
ejpam-3377	225	15	,	,	PUNCT
ejpam-3377	225	16	x	x	NOUN
ejpam-3377	225	17	,	,	PUNCT
ejpam-3377	225	18	y	y	NOUN
ejpam-3377	225	19	)	)	PUNCT
ejpam-3377	225	20	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	225	21	,	,	PUNCT
ejpam-3377	225	22	y	y	NOUN
ejpam-3377	225	23	)	)	PUNCT
ejpam-3377	226	1	+	+	CCONJ
ejpam-3377	226	2	c[kn2s	c[kn2s	PROPN
ejpam-3377	226	3	(	(	PUNCT
ejpam-3377	226	4	α	α	NOUN
ejpam-3377	226	5	,	,	PUNCT
ejpam-3377	226	6	x	x	NOUN
ejpam-3377	226	7	)	)	PUNCT
ejpam-3377	226	8	n2×n2	n2×n2	NOUN
ejpam-3377	226	9	+	+	CCONJ
ejpam-3377	226	10	ln2	ln2	ADJ
ejpam-3377	226	11	]	]	X
ejpam-3377	226	12	h	h	NOUN
ejpam-3377	226	13	(	(	PUNCT
ejpam-3377	226	14	α	α	NOUN
ejpam-3377	226	15	,	,	PUNCT
ejpam-3377	226	16	y	y	NOUN
ejpam-3377	226	17	)	)	PUNCT
ejpam-3377	226	18	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	226	19	,	,	PUNCT
ejpam-3377	226	20	y	y	NOUN
ejpam-3377	226	21	)	)	PUNCT
ejpam-3377	227	1	+	+	ADP
ejpam-3377	227	2	d[kn2s	d[kn2s	PROPN
ejpam-3377	227	3	(	(	PUNCT
ejpam-3377	227	4	α	α	X
ejpam-3377	227	5	,	,	PUNCT
ejpam-3377	227	6	x	x	NOUN
ejpam-3377	227	7	)	)	PUNCT
ejpam-3377	227	8	n2×n2	n2×n2	NOUN
ejpam-3377	227	9	+	+	CCONJ
ejpam-3377	227	10	ln2	ln2	ADJ
ejpam-3377	227	11	]	]	X
ejpam-3377	227	12	h	h	NOUN
ejpam-3377	227	13	(	(	PUNCT
ejpam-3377	227	14	β	β	X
ejpam-3377	227	15	,	,	PUNCT
ejpam-3377	227	16	x	x	NOUN
ejpam-3377	227	17	)	)	PUNCT
ejpam-3377	227	18	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	227	19	,	,	PUNCT
ejpam-3377	227	20	y	y	NOUN
ejpam-3377	227	21	)	)	PUNCT
ejpam-3377	227	22	+	+	CCONJ
ejpam-3377	227	23	e[kn2s	e[kn2s	PROPN
ejpam-3377	227	24	(	(	PUNCT
ejpam-3377	227	25	α	α	X
ejpam-3377	227	26	,	,	PUNCT
ejpam-3377	227	27	x	x	NOUN
ejpam-3377	227	28	)	)	PUNCT
ejpam-3377	227	29	n2×n2	n2×n2	NOUN
ejpam-3377	227	30	+	+	CCONJ
ejpam-3377	227	31	ln2	ln2	ADJ
ejpam-3377	227	32	]	]	X
ejpam-3377	227	33	h	h	NOUN
ejpam-3377	227	34	(	(	PUNCT
ejpam-3377	227	35	β	β	X
ejpam-3377	227	36	,	,	PUNCT
ejpam-3377	227	37	y	y	NOUN
ejpam-3377	227	38	)	)	PUNCT
ejpam-3377	227	39	n2×n2φn2(x	n2×n2φn2(x	PROPN
ejpam-3377	227	40	,	,	PUNCT
ejpam-3377	227	41	y	y	NOUN
ejpam-3377	227	42	)	)	PUNCT
ejpam-3377	228	1	+	+	NUM
ejpam-3377	228	2	f	f	X
ejpam-3377	229	1	[	[	X
ejpam-3377	229	2	kn2s	kn2s	X
ejpam-3377	229	3	(	(	PUNCT
ejpam-3377	229	4	α	α	NOUN
ejpam-3377	229	5	,	,	PUNCT
ejpam-3377	229	6	x	x	NOUN
ejpam-3377	229	7	)	)	PUNCT
ejpam-3377	229	8	n2×n2	n2×n2	NOUN
ejpam-3377	229	9	+	+	CCONJ
ejpam-3377	229	10	ln2	ln2	ADJ
ejpam-3377	229	11	]	]	X
ejpam-3377	229	12	φn2(x	φn2(x	PROPN
ejpam-3377	229	13	,	,	PUNCT
ejpam-3377	229	14	y	y	NOUN
ejpam-3377	229	15	)	)	PUNCT
ejpam-3377	229	16	=	=	SYM
ejpam-3377	230	1	mn2φn2(x	mn2φn2(x	PROPN
ejpam-3377	230	2	,	,	PUNCT
ejpam-3377	230	3	y	y	PROPN
ejpam-3377	230	4	)	)	PUNCT
ejpam-3377	230	5	,	,	PUNCT
ejpam-3377	230	6	(	(	PUNCT
ejpam-3377	230	7	34	34	NUM
ejpam-3377	230	8	)	)	PUNCT
ejpam-3377	230	9	which	which	PRON
ejpam-3377	230	10	on	on	ADP
ejpam-3377	230	11	simplification	simplification	NOUN
ejpam-3377	230	12	yields	yield	NOUN
ejpam-3377	230	13	akn2	akn2	PROPN
ejpam-3377	231	1	+	+	CCONJ
ejpam-3377	231	2	kn2s	kn2s	PROPN
ejpam-3377	231	3	(	(	PUNCT
ejpam-3377	231	4	α	α	NOUN
ejpam-3377	231	5	,	,	PUNCT
ejpam-3377	231	6	x	x	NOUN
ejpam-3377	231	7	)	)	PUNCT
ejpam-3377	231	8	n2×n2	n2×n2	NOUN
ejpam-3377	232	1	[	[	X
ejpam-3377	232	2	bh	bh	X
ejpam-3377	232	3	(	(	PUNCT
ejpam-3377	232	4	α	α	NOUN
ejpam-3377	232	5	,	,	PUNCT
ejpam-3377	232	6	x	x	NOUN
ejpam-3377	232	7	,	,	PUNCT
ejpam-3377	232	8	y	y	NOUN
ejpam-3377	232	9	)	)	PUNCT
ejpam-3377	232	10	n2×n2	n2×n2	NOUN
ejpam-3377	232	11	+	+	CCONJ
ejpam-3377	232	12	ch	ch	NOUN
ejpam-3377	232	13	(	(	PUNCT
ejpam-3377	232	14	α	α	NOUN
ejpam-3377	232	15	,	,	PUNCT
ejpam-3377	232	16	y	y	NOUN
ejpam-3377	232	17	)	)	PUNCT
ejpam-3377	232	18	n2×n2	n2×n2	NOUN
ejpam-3377	233	1	+	+	PROPN
ejpam-3377	233	2	dh	dh	PROPN
ejpam-3377	233	3	(	(	PUNCT
ejpam-3377	233	4	β	β	X
ejpam-3377	233	5	,	,	PUNCT
ejpam-3377	233	6	x	x	NOUN
ejpam-3377	233	7	)	)	PUNCT
ejpam-3377	233	8	n2×n2	n2×n2	NOUN
ejpam-3377	233	9	+	+	X
ejpam-3377	233	10	eh	eh	INTJ
ejpam-3377	233	11	(	(	PUNCT
ejpam-3377	233	12	β	β	X
ejpam-3377	233	13	,	,	PUNCT
ejpam-3377	233	14	y	y	NOUN
ejpam-3377	233	15	)	)	PUNCT
ejpam-3377	233	16	n2×n2	n2×n2	NOUN
ejpam-3377	233	17	+	+	CCONJ
ejpam-3377	233	18	f	f	PROPN
ejpam-3377	233	19	in2×n2	in2×n2	NOUN
ejpam-3377	233	20	]	]	PUNCT
ejpam-3377	234	1	+	+	CCONJ
ejpam-3377	234	2	ln2	ln2	ADJ
ejpam-3377	234	3	[	[	X
ejpam-3377	234	4	bh	bh	NOUN
ejpam-3377	234	5	(	(	PUNCT
ejpam-3377	234	6	α	α	NOUN
ejpam-3377	234	7	,	,	PUNCT
ejpam-3377	234	8	x	x	NOUN
ejpam-3377	234	9	,	,	PUNCT
ejpam-3377	234	10	y	y	NOUN
ejpam-3377	234	11	)	)	PUNCT
ejpam-3377	234	12	n2×n2	n2×n2	NOUN
ejpam-3377	234	13	+	+	CCONJ
ejpam-3377	234	14	ch	ch	NOUN
ejpam-3377	234	15	(	(	PUNCT
ejpam-3377	234	16	α	α	NOUN
ejpam-3377	234	17	,	,	PUNCT
ejpam-3377	234	18	y	y	NOUN
ejpam-3377	234	19	)	)	PUNCT
ejpam-3377	234	20	n2×n2	n2×n2	NOUN
ejpam-3377	235	1	+	+	PROPN
ejpam-3377	235	2	dh	dh	PROPN
ejpam-3377	235	3	(	(	PUNCT
ejpam-3377	235	4	β	β	X
ejpam-3377	235	5	,	,	PUNCT
ejpam-3377	235	6	x	x	NOUN
ejpam-3377	235	7	)	)	PUNCT
ejpam-3377	235	8	n2×n2	n2×n2	NOUN
ejpam-3377	235	9	+	+	X
ejpam-3377	235	10	eh	eh	INTJ
ejpam-3377	235	11	(	(	PUNCT
ejpam-3377	235	12	β	β	X
ejpam-3377	235	13	,	,	PUNCT
ejpam-3377	235	14	y	y	NOUN
ejpam-3377	235	15	)	)	PUNCT
ejpam-3377	235	16	n2×n2	n2×n2	NOUN
ejpam-3377	235	17	+	+	CCONJ
ejpam-3377	235	18	f	f	PROPN
ejpam-3377	235	19	in2×n2	in2×n2	NOUN
ejpam-3377	235	20	]	]	PUNCT
ejpam-3377	235	21	−mn2	−mn2	PROPN
ejpam-3377	235	22	=	=	ADJ
ejpam-3377	235	23	on2	on2	PROPN
ejpam-3377	235	24	.	.	PUNCT
ejpam-3377	236	1	(	(	PUNCT
ejpam-3377	236	2	35	35	NUM
ejpam-3377	236	3	)	)	PUNCT
ejpam-3377	236	4	on	on	ADP
ejpam-3377	236	5	writing	write	VERB
ejpam-3377	236	6	q	q	PROPN
ejpam-3377	236	7	=	=	SYM
ejpam-3377	236	8	s	s	X
ejpam-3377	236	9	(	(	PUNCT
ejpam-3377	236	10	α	α	NOUN
ejpam-3377	236	11	,	,	PUNCT
ejpam-3377	236	12	x	x	NOUN
ejpam-3377	236	13	)	)	PUNCT
ejpam-3377	236	14	n2×n2	n2×n2	NOUN
ejpam-3377	237	1	[	[	X
ejpam-3377	237	2	bh	bh	X
ejpam-3377	237	3	(	(	PUNCT
ejpam-3377	237	4	α	α	NOUN
ejpam-3377	237	5	,	,	PUNCT
ejpam-3377	237	6	x	x	NOUN
ejpam-3377	237	7	,	,	PUNCT
ejpam-3377	237	8	y	y	NOUN
ejpam-3377	237	9	)	)	PUNCT
ejpam-3377	237	10	n2×n2	n2×n2	NOUN
ejpam-3377	237	11	+	+	CCONJ
ejpam-3377	237	12	ch	ch	NOUN
ejpam-3377	237	13	(	(	PUNCT
ejpam-3377	237	14	α	α	NOUN
ejpam-3377	237	15	,	,	PUNCT
ejpam-3377	237	16	y	y	NOUN
ejpam-3377	237	17	)	)	PUNCT
ejpam-3377	237	18	n2×n2	n2×n2	NOUN
ejpam-3377	238	1	+	+	PROPN
ejpam-3377	238	2	dh	dh	PROPN
ejpam-3377	238	3	(	(	PUNCT
ejpam-3377	238	4	β	β	X
ejpam-3377	238	5	,	,	PUNCT
ejpam-3377	238	6	x	x	NOUN
ejpam-3377	238	7	)	)	PUNCT
ejpam-3377	238	8	n2×n2	n2×n2	NOUN
ejpam-3377	238	9	+	+	X
ejpam-3377	238	10	eh	eh	INTJ
ejpam-3377	238	11	(	(	PUNCT
ejpam-3377	238	12	β	β	X
ejpam-3377	238	13	,	,	PUNCT
ejpam-3377	238	14	y	y	NOUN
ejpam-3377	238	15	)	)	PUNCT
ejpam-3377	238	16	n2×n2	n2×n2	NOUN
ejpam-3377	238	17	+	+	CCONJ
ejpam-3377	238	18	f	f	PROPN
ejpam-3377	238	19	in2×n2	in2×n2	NOUN
ejpam-3377	238	20	]	]	PUNCT
ejpam-3377	238	21	,	,	PUNCT
ejpam-3377	238	22	p	p	X
ejpam-3377	238	23	=	=	PUNCT
ejpam-3377	238	24	ln2q−mn2	ln2q−mn2	VERB
ejpam-3377	238	25	,	,	PUNCT
ejpam-3377	238	26	we	we	PRON
ejpam-3377	238	27	,	,	PUNCT
ejpam-3377	238	28	have	have	VERB
ejpam-3377	238	29	from	from	ADP
ejpam-3377	238	30	(	(	PUNCT
ejpam-3377	238	31	35	35	NUM
ejpam-3377	238	32	)	)	PUNCT
ejpam-3377	238	33	akn2	akn2	PROPN
ejpam-3377	239	1	+	+	CCONJ
ejpam-3377	239	2	kn2q	kn2q	X
ejpam-3377	239	3	+	+	CCONJ
ejpam-3377	239	4	p	p	X
ejpam-3377	239	5	=	=	PUNCT
ejpam-3377	239	6	on2	on2	PROPN
ejpam-3377	239	7	(	(	PUNCT
ejpam-3377	239	8	36	36	NUM
ejpam-3377	239	9	)	)	PUNCT
ejpam-3377	239	10	it	it	PRON
ejpam-3377	239	11	is	be	AUX
ejpam-3377	239	12	obvious	obvious	ADJ
ejpam-3377	239	13	that	that	SCONJ
ejpam-3377	239	14	(	(	PUNCT
ejpam-3377	239	15	36	36	NUM
ejpam-3377	239	16	)	)	PUNCT
ejpam-3377	239	17	is	be	AUX
ejpam-3377	239	18	an	an	DET
ejpam-3377	239	19	algebraic	algebraic	ADJ
ejpam-3377	239	20	equation	equation	NOUN
ejpam-3377	239	21	of	of	ADP
ejpam-3377	239	22	matrices	matrix	NOUN
ejpam-3377	239	23	.	.	PUNCT
ejpam-3377	240	1	solving	solve	VERB
ejpam-3377	240	2	the	the	DET
ejpam-3377	240	3	(	(	PUNCT
ejpam-3377	240	4	36	36	NUM
ejpam-3377	240	5	)	)	PUNCT
ejpam-3377	240	6	,	,	PUNCT
ejpam-3377	240	7	for	for	ADP
ejpam-3377	240	8	kn2	kn2	NOUN
ejpam-3377	240	9	,	,	PUNCT
ejpam-3377	240	10	plugging	plug	VERB
ejpam-3377	240	11	its	its	PRON
ejpam-3377	240	12	value	value	NOUN
ejpam-3377	240	13	in	in	ADP
ejpam-3377	240	14	(	(	PUNCT
ejpam-3377	240	15	32	32	NUM
ejpam-3377	240	16	)	)	PUNCT
ejpam-3377	240	17	,	,	PUNCT
ejpam-3377	240	18	we	we	PRON
ejpam-3377	240	19	can	can	AUX
ejpam-3377	240	20	get	get	VERB
ejpam-3377	240	21	the	the	DET
ejpam-3377	240	22	numerical	numerical	ADJ
ejpam-3377	240	23	solution	solution	NOUN
ejpam-3377	240	24	of	of	ADP
ejpam-3377	240	25	the	the	DET
ejpam-3377	240	26	problem	problem	NOUN
ejpam-3377	240	27	under	under	ADP
ejpam-3377	240	28	consideration	consideration	NOUN
ejpam-3377	240	29	.	.	PUNCT
ejpam-3377	241	1	5	5	X
ejpam-3377	241	2	.	.	X
ejpam-3377	241	3	numerical	numerical	ADJ
ejpam-3377	241	4	examples	example	NOUN
ejpam-3377	241	5	this	this	DET
ejpam-3377	241	6	section	section	NOUN
ejpam-3377	241	7	is	be	AUX
ejpam-3377	241	8	concerning	concern	VERB
ejpam-3377	241	9	to	to	PART
ejpam-3377	241	10	test	test	VERB
ejpam-3377	241	11	the	the	DET
ejpam-3377	241	12	above	above	ADP
ejpam-3377	241	13	techniques	technique	NOUN
ejpam-3377	241	14	by	by	ADP
ejpam-3377	241	15	some	some	DET
ejpam-3377	241	16	well	well	ADV
ejpam-3377	241	17	known	know	VERB
ejpam-3377	241	18	problems	problem	NOUN
ejpam-3377	241	19	of	of	ADP
ejpam-3377	241	20	physical	physical	ADJ
ejpam-3377	241	21	interest	interest	NOUN
ejpam-3377	241	22	given	give	VERB
ejpam-3377	241	23	bellow	bellow	PROPN
ejpam-3377	241	24	.	.	PUNCT
ejpam-3377	242	1	m.i	m.i	PROPN
ejpam-3377	242	2	.	.	PROPN
ejpam-3377	242	3	chohan	chohan	PROPN
ejpam-3377	242	4	,	,	PUNCT
ejpam-3377	242	5	k.shah	k.shah	PROPN
ejpam-3377	242	6	/	/	SYM
ejpam-3377	242	7	eur	eur	PROPN
ejpam-3377	242	8	.	.	PUNCT
ejpam-3377	243	1	j.	j.	PROPN
ejpam-3377	243	2	pure	pure	PROPN
ejpam-3377	243	3	appl	appl	PROPN
ejpam-3377	243	4	.	.	PROPN
ejpam-3377	243	5	math	math	PROPN
ejpam-3377	243	6	,	,	PUNCT
ejpam-3377	243	7	12	12	NUM
ejpam-3377	243	8	(	(	PUNCT
ejpam-3377	243	9	1	1	NUM
ejpam-3377	243	10	)	)	PUNCT
ejpam-3377	243	11	(	(	PUNCT
ejpam-3377	243	12	2019	2019	NUM
ejpam-3377	243	13	)	)	PUNCT
ejpam-3377	243	14	,	,	PUNCT
ejpam-3377	243	15	39	39	NUM
ejpam-3377	243	16	-	-	SYM
ejpam-3377	243	17	57	57	NUM
ejpam-3377	243	18	48	48	NUM
ejpam-3377	243	19	α	α	NOUN
ejpam-3377	243	20	l∞	l∞	NOUN
ejpam-3377	243	21	at	at	ADP
ejpam-3377	243	22	n	n	NOUN
ejpam-3377	243	23	=	=	NUM
ejpam-3377	243	24	6	6	NUM
ejpam-3377	243	25	l∞	l∞	NOUN
ejpam-3377	243	26	at	at	ADP
ejpam-3377	243	27	n	n	NOUN
ejpam-3377	243	28	=	=	SYM
ejpam-3377	243	29	8	8	NUM
ejpam-3377	243	30	l∞	l∞	NOUN
ejpam-3377	243	31	at	at	ADP
ejpam-3377	243	32	n	n	NOUN
ejpam-3377	243	33	=	=	SYM
ejpam-3377	243	34	10	10	NUM
ejpam-3377	243	35	l∞	l∞	NOUN
ejpam-3377	243	36	at	at	ADP
ejpam-3377	243	37	n	n	NOUN
ejpam-3377	243	38	=	=	NUM
ejpam-3377	243	39	12	12	NUM
ejpam-3377	243	40	1.5	1.5	NUM
ejpam-3377	243	41	5.707(−5	5.707(−5	NUM
ejpam-3377	243	42	)	)	PUNCT
ejpam-3377	243	43	5.3325(−6	5.3325(−6	NUM
ejpam-3377	243	44	)	)	PUNCT
ejpam-3377	243	45	1.6826(−7	1.6826(−7	NUM
ejpam-3377	243	46	)	)	PUNCT
ejpam-3377	243	47	1.6009(−8	1.6009(−8	NUM
ejpam-3377	243	48	)	)	PUNCT
ejpam-3377	243	49	1.6	1.6	NUM
ejpam-3377	243	50	5.956(−5	5.956(−5	NUM
ejpam-3377	243	51	)	)	PUNCT
ejpam-3377	243	52	4.0196(−6	4.0196(−6	NOUN
ejpam-3377	243	53	)	)	PUNCT
ejpam-3377	243	54	7.0638(−8	7.0638(−8	NOUN
ejpam-3377	243	55	)	)	PUNCT
ejpam-3377	243	56	7.5009(−9	7.5009(−9	NUM
ejpam-3377	243	57	)	)	PUNCT
ejpam-3377	243	58	1.7	1.7	NUM
ejpam-3377	243	59	7.236(−6	7.236(−6	NUM
ejpam-3377	243	60	)	)	PUNCT
ejpam-3377	243	61	7.1703(−8	7.1703(−8	NUM
ejpam-3377	243	62	)	)	PUNCT
ejpam-3377	243	63	8.9126(−9	8.9126(−9	NUM
ejpam-3377	243	64	)	)	PUNCT
ejpam-3377	243	65	9.9998(−12	9.9998(−12	NOUN
ejpam-3377	243	66	)	)	PUNCT
ejpam-3377	243	67	1.8	1.8	NUM
ejpam-3377	243	68	2.0873(−7	2.0873(−7	NUM
ejpam-3377	243	69	)	)	PUNCT
ejpam-3377	243	70	6.0386(−8	6.0386(−8	NOUN
ejpam-3377	243	71	)	)	PUNCT
ejpam-3377	244	1	5.9451(−10	5.9451(−10	NUM
ejpam-3377	244	2	)	)	PUNCT
ejpam-3377	244	3	2.7945(−12	2.7945(−12	NUM
ejpam-3377	244	4	)	)	PUNCT
ejpam-3377	244	5	1.9	1.9	NUM
ejpam-3377	244	6	9.0002(−8	9.0002(−8	NUM
ejpam-3377	244	7	)	)	PUNCT
ejpam-3377	244	8	1.0158(−9	1.0158(−9	NUM
ejpam-3377	244	9	)	)	PUNCT
ejpam-3377	244	10	3.0781(−11	3.0781(−11	NUM
ejpam-3377	244	11	)	)	PUNCT
ejpam-3377	244	12	1.0520(−14	1.0520(−14	NOUN
ejpam-3377	244	13	)	)	PUNCT
ejpam-3377	244	14	2.0	2.0	NUM
ejpam-3377	244	15	2.5000(−11	2.5000(−11	SYM
ejpam-3377	244	16	)	)	PUNCT
ejpam-3377	244	17	1.0019(−13	1.0019(−13	NUM
ejpam-3377	244	18	)	)	PUNCT
ejpam-3377	244	19	1.0933(−15	1.0933(−15	NUM
ejpam-3377	244	20	)	)	PUNCT
ejpam-3377	244	21	2.0251(−16	2.0251(−16	NUM
ejpam-3377	244	22	)	)	PUNCT
ejpam-3377	244	23	table	table	NOUN
ejpam-3377	244	24	1	1	NUM
ejpam-3377	244	25	:	:	PUNCT
ejpam-3377	244	26	absolute	absolute	ADJ
ejpam-3377	244	27	error	error	NOUN
ejpam-3377	244	28	in	in	ADP
ejpam-3377	244	29	w(x	w(x	PROPN
ejpam-3377	244	30	,	,	PUNCT
ejpam-3377	244	31	y	y	NOUN
ejpam-3377	244	32	)	)	PUNCT
ejpam-3377	244	33	of	of	ADP
ejpam-3377	244	34	example	example	NOUN
ejpam-3377	244	35	1	1	NUM
ejpam-3377	244	36	for	for	ADP
ejpam-3377	244	37	(	(	PUNCT
ejpam-3377	244	38	p	p	X
ejpam-3377	244	39	,	,	PUNCT
ejpam-3377	244	40	q	q	NOUN
ejpam-3377	244	41	)	)	PUNCT
ejpam-3377	244	42	=	=	SYM
ejpam-3377	244	43	(	(	PUNCT
ejpam-3377	244	44	0	0	NUM
ejpam-3377	244	45	,	,	PUNCT
ejpam-3377	244	46	0	0	NUM
ejpam-3377	244	47	)	)	PUNCT
ejpam-3377	244	48	and	and	CCONJ
ejpam-3377	244	49	at	at	ADP
ejpam-3377	244	50	various	various	ADJ
ejpam-3377	244	51	values	value	NOUN
ejpam-3377	244	52	of	of	ADP
ejpam-3377	244	53	n	n	PROPN
ejpam-3377	244	54	and	and	CCONJ
ejpam-3377	244	55	α	α	PROPN
ejpam-3377	244	56	.	.	PUNCT
ejpam-3377	244	57	example	example	NOUN
ejpam-3377	245	1	1	1	NUM
ejpam-3377	245	2	.	.	X
ejpam-3377	245	3	consider	consider	VERB
ejpam-3377	245	4	the	the	DET
ejpam-3377	245	5	helmholtz	helmholtz	NOUN
ejpam-3377	245	6	equation	equation	NOUN
ejpam-3377	245	7	[	[	X
ejpam-3377	246	1	34	34	NUM
ejpam-3377	246	2	]	]	X
ejpam-3377	246	3	∂αw(x	∂αw(x	PROPN
ejpam-3377	246	4	,	,	PUNCT
ejpam-3377	246	5	y	y	NOUN
ejpam-3377	246	6	)	)	PUNCT
ejpam-3377	246	7	∂xα	∂xα	PROPN
ejpam-3377	246	8	+	+	CCONJ
ejpam-3377	246	9	∂αw(x	∂αw(x	PROPN
ejpam-3377	246	10	,	,	PUNCT
ejpam-3377	246	11	y	y	NOUN
ejpam-3377	246	12	)	)	PUNCT
ejpam-3377	246	13	∂yα	∂yα	PROPN
ejpam-3377	246	14	+	+	CCONJ
ejpam-3377	246	15	8w(x	8w(x	NUM
ejpam-3377	246	16	,	,	PUNCT
ejpam-3377	246	17	y	y	PROPN
ejpam-3377	246	18	)	)	PUNCT
ejpam-3377	246	19	=	=	SYM
ejpam-3377	246	20	0	0	NUM
ejpam-3377	246	21	,	,	PUNCT
ejpam-3377	246	22	1	1	NUM
ejpam-3377	246	23	<	<	X
ejpam-3377	246	24	α	α	PROPN
ejpam-3377	246	25	≤	≤	NUM
ejpam-3377	246	26	2	2	NUM
ejpam-3377	246	27	,	,	PUNCT
ejpam-3377	246	28	w(0	w(0	PROPN
ejpam-3377	246	29	,	,	PUNCT
ejpam-3377	246	30	y	y	PROPN
ejpam-3377	246	31	)	)	PUNCT
ejpam-3377	246	32	=	=	SYM
ejpam-3377	246	33	sin(2y	sin(2y	NOUN
ejpam-3377	246	34	)	)	PUNCT
ejpam-3377	246	35	,	,	PUNCT
ejpam-3377	246	36	wx(0	wx(0	PROPN
ejpam-3377	246	37	,	,	PUNCT
ejpam-3377	246	38	y	y	PROPN
ejpam-3377	246	39	)	)	PUNCT
ejpam-3377	246	40	=	=	SYM
ejpam-3377	247	1	0	0	X
ejpam-3377	247	2	.	.	PUNCT
ejpam-3377	248	1	(	(	PUNCT
ejpam-3377	248	2	37	37	NUM
ejpam-3377	248	3	)	)	PUNCT
ejpam-3377	248	4	at	at	ADP
ejpam-3377	248	5	α	α	NOUN
ejpam-3377	248	6	=	=	SYM
ejpam-3377	248	7	2	2	NUM
ejpam-3377	248	8	the	the	DET
ejpam-3377	248	9	exact	exact	ADJ
ejpam-3377	248	10	solution	solution	NOUN
ejpam-3377	248	11	of	of	ADP
ejpam-3377	248	12	(	(	PUNCT
ejpam-3377	248	13	37	37	NUM
ejpam-3377	248	14	)	)	PUNCT
ejpam-3377	248	15	is	be	AUX
ejpam-3377	248	16	w(x	w(x	PROPN
ejpam-3377	248	17	,	,	PUNCT
ejpam-3377	248	18	y	y	NOUN
ejpam-3377	248	19	)	)	PUNCT
ejpam-3377	248	20	=	=	PRON
ejpam-3377	248	21	cos(2x	cos(2x	VERB
ejpam-3377	248	22	)	)	PUNCT
ejpam-3377	248	23	sin(2y	sin(2y	PROPN
ejpam-3377	248	24	)	)	PUNCT
ejpam-3377	248	25	.	.	PUNCT
ejpam-3377	249	1	here	here	ADV
ejpam-3377	249	2	a	a	DET
ejpam-3377	249	3	=	=	SYM
ejpam-3377	249	4	1	1	NUM
ejpam-3377	249	5	,	,	PUNCT
ejpam-3377	249	6	b	b	NOUN
ejpam-3377	249	7	=	=	SYM
ejpam-3377	249	8	0	0	NUM
ejpam-3377	249	9	,	,	PUNCT
ejpam-3377	249	10	c	c	NOUN
ejpam-3377	249	11	=	=	SYM
ejpam-3377	249	12	1	1	NUM
ejpam-3377	249	13	,	,	PUNCT
ejpam-3377	249	14	d	d	NOUN
ejpam-3377	249	15	=	=	SYM
ejpam-3377	249	16	e	e	NOUN
ejpam-3377	249	17	=	=	SYM
ejpam-3377	249	18	0	0	PROPN
ejpam-3377	249	19	,	,	PUNCT
ejpam-3377	249	20	f	f	PROPN
ejpam-3377	249	21	=	=	SYM
ejpam-3377	249	22	8	8	NUM
ejpam-3377	249	23	,	,	PUNCT
ejpam-3377	249	24	clearly	clearly	ADV
ejpam-3377	249	25	b2	b2	VERB
ejpam-3377	249	26	−	−	PROPN
ejpam-3377	249	27	4ac	4ac	NOUN
ejpam-3377	249	28	<	<	X
ejpam-3377	249	29	0	0	PROPN
ejpam-3377	249	30	,	,	PUNCT
ejpam-3377	249	31	the	the	DET
ejpam-3377	249	32	given	give	VERB
ejpam-3377	249	33	fpde	fpde	NOUN
ejpam-3377	249	34	is	be	AUX
ejpam-3377	249	35	ecliptic	ecliptic	ADJ
ejpam-3377	249	36	.	.	PUNCT
ejpam-3377	250	1	we	we	PRON
ejpam-3377	250	2	plot	plot	VERB
ejpam-3377	250	3	the	the	DET
ejpam-3377	250	4	approximate	approximate	ADJ
ejpam-3377	250	5	solution	solution	NOUN
ejpam-3377	250	6	corresponding	correspond	VERB
ejpam-3377	250	7	to	to	ADP
ejpam-3377	250	8	the	the	DET
ejpam-3377	250	9	exact	exact	ADJ
ejpam-3377	250	10	solution	solution	NOUN
ejpam-3377	250	11	at	at	ADP
ejpam-3377	250	12	α	α	NOUN
ejpam-3377	250	13	=	=	SYM
ejpam-3377	250	14	2	2	X
ejpam-3377	250	15	.	.	X
ejpam-3377	251	1	we	we	PRON
ejpam-3377	251	2	see	see	VERB
ejpam-3377	251	3	from	from	ADP
ejpam-3377	251	4	the	the	DET
ejpam-3377	251	5	figure	figure	NOUN
ejpam-3377	251	6	1	1	NUM
ejpam-3377	251	7	,	,	PUNCT
ejpam-3377	251	8	that	that	SCONJ
ejpam-3377	251	9	the	the	DET
ejpam-3377	251	10	proposed	propose	VERB
ejpam-3377	251	11	scheme	scheme	NOUN
ejpam-3377	251	12	provides	provide	VERB
ejpam-3377	251	13	close	close	ADJ
ejpam-3377	251	14	agreement	agreement	NOUN
ejpam-3377	251	15	to	to	ADP
ejpam-3377	251	16	that	that	PRON
ejpam-3377	251	17	of	of	ADP
ejpam-3377	251	18	exact	exact	ADJ
ejpam-3377	251	19	solution	solution	NOUN
ejpam-3377	251	20	at	at	ADP
ejpam-3377	251	21	very	very	ADV
ejpam-3377	251	22	small	small	ADJ
ejpam-3377	251	23	scale	scale	NOUN
ejpam-3377	251	24	level	level	NOUN
ejpam-3377	251	25	.	.	PUNCT
ejpam-3377	252	1	further	far	ADV
ejpam-3377	252	2	,	,	PUNCT
ejpam-3377	252	3	we	we	PRON
ejpam-3377	252	4	compared	compare	VERB
ejpam-3377	252	5	the	the	DET
ejpam-3377	252	6	absolute	absolute	ADJ
ejpam-3377	252	7	error	error	NOUN
ejpam-3377	252	8	l∞	l∞	NOUN
ejpam-3377	252	9	=	=	SYM
ejpam-3377	252	10	‖w−wn‖∞	‖w−wn‖∞	PROPN
ejpam-3377	252	11	at	at	ADP
ejpam-3377	252	12	various	various	ADJ
ejpam-3377	252	13	fractional	fractional	ADJ
ejpam-3377	252	14	order	order	NOUN
ejpam-3377	252	15	corresponding	correspond	VERB
ejpam-3377	252	16	to	to	ADP
ejpam-3377	252	17	different	different	ADJ
ejpam-3377	252	18	scale	scale	NOUN
ejpam-3377	252	19	level	level	NOUN
ejpam-3377	252	20	n	n	CCONJ
ejpam-3377	252	21	in	in	ADP
ejpam-3377	252	22	the	the	DET
ejpam-3377	252	23	following	follow	VERB
ejpam-3377	252	24	table	table	NOUN
ejpam-3377	252	25	1	1	NUM
ejpam-3377	252	26	.	.	PUNCT
ejpam-3377	252	27	x	x	SYM
ejpam-3377	253	1	y	y	NOUN
ejpam-3377	253	2	1	1	NUM
ejpam-3377	253	3	0.8	0.8	NUM
ejpam-3377	253	4	-0.4	-0.4	NUM
ejpam-3377	253	5	0.61	0.61	NUM
ejpam-3377	253	6	0.8	0.8	NUM
ejpam-3377	253	7	0.4	0.4	NUM
ejpam-3377	253	8	0.6	0.6	NUM
ejpam-3377	253	9	0.4	0.4	NUM
ejpam-3377	253	10	0.2	0.2	NUM
ejpam-3377	253	11	-0.2	-0.2	NUM
ejpam-3377	253	12	0.2	0.2	NUM
ejpam-3377	253	13	00	00	NUM
ejpam-3377	253	14	0	0	NUM
ejpam-3377	253	15	0.2	0.2	NUM
ejpam-3377	253	16	(	(	PUNCT
ejpam-3377	253	17	a	a	NOUN
ejpam-3377	253	18	)	)	PUNCT
ejpam-3377	253	19	w	w	NOUN
ejpam-3377	253	20	(	(	PUNCT
ejpam-3377	253	21	x	x	INTJ
ejpam-3377	253	22	,	,	PUNCT
ejpam-3377	253	23	y	y	PROPN
ejpam-3377	253	24	)	)	PUNCT
ejpam-3377	253	25	0.4	0.4	NUM
ejpam-3377	253	26	0.6	0.6	NUM
ejpam-3377	253	27	0.8	0.8	NUM
ejpam-3377	253	28	approximate	approximate	ADJ
ejpam-3377	253	29	solution	solution	NOUN
ejpam-3377	253	30	at	at	ADP
ejpam-3377	253	31	n=6	n=6	NOUN
ejpam-3377	253	32	exact	exact	ADJ
ejpam-3377	253	33	solution	solution	NOUN
ejpam-3377	253	34	y	y	PROPN
ejpam-3377	253	35	x	x	SYM
ejpam-3377	253	36	-2	-2	NOUN
ejpam-3377	253	37	1	1	NUM
ejpam-3377	253	38	-1	-1	SYM
ejpam-3377	253	39	1	1	NUM
ejpam-3377	253	40	0	0	NUM
ejpam-3377	253	41	‖w	‖w	NOUN
ejpam-3377	253	42	a	a	DET
ejpam-3377	253	43	p	p	X
ejpam-3377	253	44	p	p	NOUN
ejpam-3377	253	45	−	−	PROPN
ejpam-3377	253	46	w	w	NOUN
ejpam-3377	253	47	e	e	NOUN
ejpam-3377	253	48	x	x	SYM
ejpam-3377	253	49	‖	‖	PROPN
ejpam-3377	253	50	∞	∞	PROPN
ejpam-3377	253	51	×10	×10	PROPN
ejpam-3377	253	52	-	-	SYM
ejpam-3377	253	53	16	16	NUM
ejpam-3377	253	54	0.8	0.8	NUM
ejpam-3377	253	55	1	1	NUM
ejpam-3377	253	56	(	(	PUNCT
ejpam-3377	253	57	b	b	NOUN
ejpam-3377	253	58	)	)	PUNCT
ejpam-3377	253	59	0.5	0.5	NUM
ejpam-3377	253	60	0.6	0.6	NUM
ejpam-3377	253	61	2	2	NUM
ejpam-3377	253	62	0.4	0.4	NUM
ejpam-3377	253	63	0.2	0.2	NUM
ejpam-3377	253	64	0	0	NUM
ejpam-3377	253	65	0	0	NUM
ejpam-3377	253	66	absolute	absolute	ADJ
ejpam-3377	253	67	error	error	NOUN
ejpam-3377	253	68	at	at	ADP
ejpam-3377	253	69	n=6	n=6	NOUN
ejpam-3377	253	70	figure	figure	NOUN
ejpam-3377	253	71	1	1	NUM
ejpam-3377	253	72	.	.	PUNCT
ejpam-3377	254	1	(	(	PUNCT
ejpam-3377	254	2	a	a	X
ejpam-3377	254	3	)	)	PUNCT
ejpam-3377	254	4	comparison	comparison	NOUN
ejpam-3377	254	5	between	between	ADP
ejpam-3377	254	6	exact	exact	ADJ
ejpam-3377	254	7	and	and	CCONJ
ejpam-3377	254	8	approximate	approximate	ADJ
ejpam-3377	254	9	solutions	solution	NOUN
ejpam-3377	254	10	at	at	ADP
ejpam-3377	254	11	n	n	NOUN
ejpam-3377	254	12	=	=	NUM
ejpam-3377	254	13	6	6	NUM
ejpam-3377	254	14	,	,	PUNCT
ejpam-3377	254	15	p	p	NOUN
ejpam-3377	254	16	=	=	X
ejpam-3377	254	17	q	q	NOUN
ejpam-3377	255	1	=	=	SYM
ejpam-3377	255	2	0	0	NUM
ejpam-3377	255	3	,	,	PUNCT
ejpam-3377	255	4	α	α	NOUN
ejpam-3377	255	5	=	=	SYM
ejpam-3377	255	6	2	2	NUM
ejpam-3377	255	7	for	for	ADP
ejpam-3377	255	8	example	example	NOUN
ejpam-3377	255	9	1	1	NUM
ejpam-3377	255	10	.	.	PUNCT
ejpam-3377	256	1	(	(	PUNCT
ejpam-3377	256	2	b	b	X
ejpam-3377	256	3	)	)	PUNCT
ejpam-3377	256	4	absolute	absolute	ADJ
ejpam-3377	256	5	error	error	NOUN
ejpam-3377	256	6	at	at	ADP
ejpam-3377	256	7	n	n	NOUN
ejpam-3377	256	8	=	=	SYM
ejpam-3377	256	9	6	6	NUM
ejpam-3377	256	10	,	,	PUNCT
ejpam-3377	256	11	p	p	NOUN
ejpam-3377	256	12	=	=	X
ejpam-3377	256	13	q	q	NOUN
ejpam-3377	256	14	=	=	SYM
ejpam-3377	256	15	0	0	NUM
ejpam-3377	256	16	,	,	PUNCT
ejpam-3377	256	17	α	α	NOUN
ejpam-3377	256	18	=	=	SYM
ejpam-3377	256	19	2	2	NUM
ejpam-3377	256	20	for	for	ADP
ejpam-3377	256	21	example	example	NOUN
ejpam-3377	256	22	1	1	NUM
ejpam-3377	256	23	.	.	X
ejpam-3377	257	1	from	from	ADP
ejpam-3377	257	2	the	the	DET
ejpam-3377	257	3	table	table	NOUN
ejpam-3377	257	4	1	1	NUM
ejpam-3377	257	5	,	,	PUNCT
ejpam-3377	257	6	we	we	PRON
ejpam-3377	257	7	see	see	VERB
ejpam-3377	257	8	that	that	SCONJ
ejpam-3377	257	9	as	as	SCONJ
ejpam-3377	257	10	the	the	DET
ejpam-3377	257	11	fractional	fractional	ADJ
ejpam-3377	257	12	order	order	NOUN
ejpam-3377	257	13	approaches	approach	NOUN
ejpam-3377	257	14	to	to	ADP
ejpam-3377	257	15	its	its	PRON
ejpam-3377	257	16	integer	integer	NOUN
ejpam-3377	257	17	values	value	NOUN
ejpam-3377	257	18	the	the	DET
ejpam-3377	257	19	absolute	absolute	ADJ
ejpam-3377	257	20	error	error	NOUN
ejpam-3377	257	21	decreasing	decreasing	NOUN
ejpam-3377	257	22	and	and	CCONJ
ejpam-3377	257	23	vice	vice	NOUN
ejpam-3377	257	24	versa	versa	ADV
ejpam-3377	257	25	and	and	CCONJ
ejpam-3377	257	26	on	on	ADP
ejpam-3377	257	27	the	the	DET
ejpam-3377	257	28	other	other	ADJ
ejpam-3377	257	29	hand	hand	NOUN
ejpam-3377	257	30	enlarging	enlarge	VERB
ejpam-3377	257	31	the	the	DET
ejpam-3377	257	32	scale	scale	NOUN
ejpam-3377	257	33	level	level	NOUN
ejpam-3377	257	34	,	,	PUNCT
ejpam-3377	257	35	the	the	DET
ejpam-3377	257	36	accuracy	accuracy	NOUN
ejpam-3377	257	37	also	also	ADV
ejpam-3377	257	38	increases	increase	VERB
ejpam-3377	257	39	even	even	ADV
ejpam-3377	257	40	for	for	ADP
ejpam-3377	257	41	fractional	fractional	ADJ
ejpam-3377	257	42	order	order	NOUN
ejpam-3377	257	43	.	.	PUNCT
ejpam-3377	258	1	example	example	NOUN
ejpam-3377	258	2	2	2	NUM
ejpam-3377	258	3	.	.	X
ejpam-3377	258	4	taking	take	VERB
ejpam-3377	258	5	fpde	fpde	NOUN
ejpam-3377	258	6	consider	consider	VERB
ejpam-3377	258	7	in	in	ADP
ejpam-3377	258	8	[	[	X
ejpam-3377	258	9	19	19	NUM
ejpam-3377	258	10	]	]	X
ejpam-3377	258	11	∂αw(x	∂αw(x	PROPN
ejpam-3377	258	12	,	,	PUNCT
ejpam-3377	258	13	y	y	NOUN
ejpam-3377	258	14	)	)	PUNCT
ejpam-3377	258	15	∂xα	∂xα	PROPN
ejpam-3377	258	16	+	+	CCONJ
ejpam-3377	258	17	∂αw(x	∂αw(x	PROPN
ejpam-3377	258	18	,	,	PUNCT
ejpam-3377	258	19	y	y	NOUN
ejpam-3377	258	20	)	)	PUNCT
ejpam-3377	258	21	∂x	∂x	NOUN
ejpam-3377	258	22	α	α	NOUN
ejpam-3377	258	23	2	2	NUM
ejpam-3377	258	24	∂y	∂y	SYM
ejpam-3377	258	25	α	α	NOUN
ejpam-3377	258	26	2	2	NUM
ejpam-3377	258	27	+	+	CCONJ
ejpam-3377	258	28	∂αw(x	∂αw(x	ADJ
ejpam-3377	258	29	,	,	PUNCT
ejpam-3377	258	30	y	y	NOUN
ejpam-3377	258	31	)	)	PUNCT
ejpam-3377	258	32	∂yα	∂yα	PROPN
ejpam-3377	258	33	=	=	SYM
ejpam-3377	258	34	g(x	g(x	PROPN
ejpam-3377	258	35	,	,	PUNCT
ejpam-3377	258	36	y	y	PROPN
ejpam-3377	258	37	)	)	PUNCT
ejpam-3377	258	38	,	,	PUNCT
ejpam-3377	259	1	1	1	NUM
ejpam-3377	259	2	<	<	X
ejpam-3377	259	3	α	α	PROPN
ejpam-3377	259	4	≤	≤	NUM
ejpam-3377	259	5	2	2	NUM
ejpam-3377	259	6	,	,	PUNCT
ejpam-3377	259	7	w(0	w(0	PROPN
ejpam-3377	259	8	,	,	PUNCT
ejpam-3377	259	9	y	y	PROPN
ejpam-3377	259	10	)	)	PUNCT
ejpam-3377	259	11	=	=	SYM
ejpam-3377	259	12	2y	2y	NUM
ejpam-3377	259	13	,	,	PUNCT
ejpam-3377	259	14	wx(0	wx(0	PROPN
ejpam-3377	259	15	,	,	PUNCT
ejpam-3377	259	16	y	y	NOUN
ejpam-3377	259	17	)	)	PUNCT
ejpam-3377	259	18	=	=	SYM
ejpam-3377	259	19	y2	y2	PROPN
ejpam-3377	259	20	.	.	PUNCT
ejpam-3377	260	1	(	(	PUNCT
ejpam-3377	260	2	38	38	NUM
ejpam-3377	260	3	)	)	PUNCT
ejpam-3377	260	4	m.i	m.i	PROPN
ejpam-3377	260	5	.	.	PROPN
ejpam-3377	260	6	chohan	chohan	PROPN
ejpam-3377	260	7	,	,	PUNCT
ejpam-3377	260	8	k.shah	k.shah	PROPN
ejpam-3377	260	9	/	/	SYM
ejpam-3377	260	10	eur	eur	PROPN
ejpam-3377	260	11	.	.	PUNCT
ejpam-3377	261	1	j.	j.	PROPN
ejpam-3377	261	2	pure	pure	PROPN
ejpam-3377	261	3	appl	appl	PROPN
ejpam-3377	261	4	.	.	PROPN
ejpam-3377	261	5	math	math	PROPN
ejpam-3377	261	6	,	,	PUNCT
ejpam-3377	261	7	12	12	NUM
ejpam-3377	261	8	(	(	PUNCT
ejpam-3377	261	9	1	1	NUM
ejpam-3377	261	10	)	)	PUNCT
ejpam-3377	261	11	(	(	PUNCT
ejpam-3377	261	12	2019	2019	NUM
ejpam-3377	261	13	)	)	PUNCT
ejpam-3377	261	14	,	,	PUNCT
ejpam-3377	261	15	39	39	NUM
ejpam-3377	261	16	-	-	SYM
ejpam-3377	261	17	57	57	NUM
ejpam-3377	261	18	49	49	NUM
ejpam-3377	261	19	α	α	NOUN
ejpam-3377	261	20	l∞	l∞	NOUN
ejpam-3377	261	21	at	at	ADP
ejpam-3377	261	22	n	n	NOUN
ejpam-3377	261	23	=	=	NUM
ejpam-3377	261	24	6	6	NUM
ejpam-3377	261	25	l∞	l∞	NOUN
ejpam-3377	261	26	at	at	ADP
ejpam-3377	261	27	n	n	NOUN
ejpam-3377	261	28	=	=	SYM
ejpam-3377	261	29	8	8	NUM
ejpam-3377	261	30	l∞	l∞	NOUN
ejpam-3377	261	31	at	at	ADP
ejpam-3377	261	32	n	n	NOUN
ejpam-3377	261	33	=	=	SYM
ejpam-3377	261	34	10	10	NUM
ejpam-3377	261	35	l∞	l∞	NOUN
ejpam-3377	261	36	at	at	ADP
ejpam-3377	261	37	n	n	NOUN
ejpam-3377	261	38	=	=	NUM
ejpam-3377	261	39	12	12	NUM
ejpam-3377	261	40	1.5	1.5	NUM
ejpam-3377	261	41	1.0707(−6	1.0707(−6	NUM
ejpam-3377	261	42	)	)	PUNCT
ejpam-3377	261	43	5.3325(−8	5.3325(−8	NOUN
ejpam-3377	261	44	)	)	PUNCT
ejpam-3377	262	1	6.0826(−10	6.0826(−10	NUM
ejpam-3377	262	2	)	)	PUNCT
ejpam-3377	262	3	1.6009(−12	1.6009(−12	NUM
ejpam-3377	262	4	)	)	PUNCT
ejpam-3377	262	5	1.6	1.6	NUM
ejpam-3377	262	6	9.9056(−7	9.9056(−7	NUM
ejpam-3377	262	7	)	)	PUNCT
ejpam-3377	262	8	9.0196(−9	9.0196(−9	NUM
ejpam-3377	262	9	)	)	PUNCT
ejpam-3377	262	10	7.0638(−11	7.0638(−11	NOUN
ejpam-3377	262	11	)	)	PUNCT
ejpam-3377	262	12	9.5009(−13	9.5009(−13	NOUN
ejpam-3377	262	13	)	)	PUNCT
ejpam-3377	262	14	1.7	1.7	NUM
ejpam-3377	262	15	6.2036(−7	6.2036(−7	NUM
ejpam-3377	262	16	)	)	PUNCT
ejpam-3377	262	17	7.1703(−9	7.1703(−9	NUM
ejpam-3377	262	18	)	)	PUNCT
ejpam-3377	262	19	8.9126(−12	8.9126(−12	NOUN
ejpam-3377	262	20	)	)	PUNCT
ejpam-3377	262	21	1.0998(−13	1.0998(−13	PROPN
ejpam-3377	262	22	)	)	PUNCT
ejpam-3377	262	23	1.8	1.8	NUM
ejpam-3377	262	24	9.0073(−9	9.0073(−9	NUM
ejpam-3377	262	25	)	)	PUNCT
ejpam-3377	262	26	1.0386(−10	1.0386(−10	NUM
ejpam-3377	262	27	)	)	PUNCT
ejpam-3377	262	28	3.0457(−12	3.0457(−12	NOUN
ejpam-3377	262	29	)	)	PUNCT
ejpam-3377	262	30	1.0945(−14	1.0945(−14	NUM
ejpam-3377	262	31	)	)	PUNCT
ejpam-3377	262	32	1.9	1.9	NUM
ejpam-3377	262	33	2.0002(−10	2.0002(−10	NUM
ejpam-3377	262	34	)	)	PUNCT
ejpam-3377	262	35	2.0158(−11	2.0158(−11	NUM
ejpam-3377	262	36	)	)	PUNCT
ejpam-3377	262	37	5.0081(−12	5.0081(−12	NOUN
ejpam-3377	262	38	)	)	PUNCT
ejpam-3377	262	39	6.4520(−15	6.4520(−15	NOUN
ejpam-3377	262	40	)	)	PUNCT
ejpam-3377	262	41	2.0	2.0	NUM
ejpam-3377	262	42	1.0000(−11	1.0000(−11	NUM
ejpam-3377	262	43	)	)	PUNCT
ejpam-3377	262	44	1.0019(−12	1.0019(−12	NOUN
ejpam-3377	262	45	)	)	PUNCT
ejpam-3377	262	46	3.7935(−15	3.7935(−15	ADJ
ejpam-3377	262	47	)	)	PUNCT
ejpam-3377	262	48	1.0001(−16	1.0001(−16	NOUN
ejpam-3377	262	49	)	)	PUNCT
ejpam-3377	262	50	table	table	NOUN
ejpam-3377	262	51	2	2	NUM
ejpam-3377	262	52	:	:	PUNCT
ejpam-3377	262	53	absolute	absolute	ADJ
ejpam-3377	262	54	error	error	NOUN
ejpam-3377	262	55	in	in	ADP
ejpam-3377	262	56	w(x	w(x	PROPN
ejpam-3377	262	57	,	,	PUNCT
ejpam-3377	262	58	y	y	NOUN
ejpam-3377	262	59	)	)	PUNCT
ejpam-3377	262	60	of	of	ADP
ejpam-3377	262	61	example	example	NOUN
ejpam-3377	262	62	2	2	NUM
ejpam-3377	262	63	for	for	ADP
ejpam-3377	262	64	(	(	PUNCT
ejpam-3377	262	65	p	p	X
ejpam-3377	262	66	,	,	PUNCT
ejpam-3377	262	67	q	q	NOUN
ejpam-3377	262	68	)	)	PUNCT
ejpam-3377	262	69	=	=	SYM
ejpam-3377	262	70	(	(	PUNCT
ejpam-3377	262	71	0	0	NUM
ejpam-3377	262	72	,	,	PUNCT
ejpam-3377	262	73	0	0	NUM
ejpam-3377	262	74	)	)	PUNCT
ejpam-3377	262	75	and	and	CCONJ
ejpam-3377	262	76	at	at	ADP
ejpam-3377	262	77	various	various	ADJ
ejpam-3377	262	78	values	value	NOUN
ejpam-3377	262	79	of	of	ADP
ejpam-3377	262	80	n	n	PROPN
ejpam-3377	262	81	and	and	CCONJ
ejpam-3377	262	82	α	α	X
ejpam-3377	262	83	.	.	PUNCT
ejpam-3377	263	1	at	at	ADP
ejpam-3377	263	2	α	α	NOUN
ejpam-3377	263	3	=	=	SYM
ejpam-3377	263	4	2	2	NUM
ejpam-3377	263	5	the	the	DET
ejpam-3377	263	6	exact	exact	ADJ
ejpam-3377	263	7	solution	solution	NOUN
ejpam-3377	263	8	of	of	ADP
ejpam-3377	263	9	(	(	PUNCT
ejpam-3377	263	10	39	39	NUM
ejpam-3377	263	11	)	)	PUNCT
ejpam-3377	263	12	is	be	AUX
ejpam-3377	263	13	w(x	w(x	PROPN
ejpam-3377	263	14	,	,	PUNCT
ejpam-3377	263	15	y	y	NOUN
ejpam-3377	263	16	)	)	PUNCT
ejpam-3377	263	17	=	=	SYM
ejpam-3377	264	1	2y+	2y+	NUM
ejpam-3377	264	2	xy2	xy2	PROPN
ejpam-3377	264	3	.	.	PUNCT
ejpam-3377	265	1	here	here	ADV
ejpam-3377	265	2	a	a	DET
ejpam-3377	265	3	=	=	SYM
ejpam-3377	265	4	1	1	NUM
ejpam-3377	265	5	,	,	PUNCT
ejpam-3377	265	6	b	b	NOUN
ejpam-3377	265	7	=	=	SYM
ejpam-3377	265	8	1	1	NUM
ejpam-3377	265	9	,	,	PUNCT
ejpam-3377	265	10	c	c	NOUN
ejpam-3377	265	11	=	=	SYM
ejpam-3377	265	12	1	1	NUM
ejpam-3377	265	13	,	,	PUNCT
ejpam-3377	265	14	d	d	NOUN
ejpam-3377	265	15	=	=	SYM
ejpam-3377	265	16	e	e	X
ejpam-3377	265	17	=	=	PUNCT
ejpam-3377	265	18	f	f	PROPN
ejpam-3377	265	19	=	=	SYM
ejpam-3377	265	20	0	0	NUM
ejpam-3377	265	21	,	,	PUNCT
ejpam-3377	265	22	clearly	clearly	ADV
ejpam-3377	265	23	b2	b2	VERB
ejpam-3377	265	24	−	−	NOUN
ejpam-3377	265	25	4ac	4ac	NOUN
ejpam-3377	265	26	=	=	SYM
ejpam-3377	265	27	0	0	NUM
ejpam-3377	265	28	,	,	PUNCT
ejpam-3377	265	29	the	the	DET
ejpam-3377	265	30	given	give	VERB
ejpam-3377	265	31	fpde	fpde	NOUN
ejpam-3377	265	32	is	be	AUX
ejpam-3377	265	33	parabolic	parabolic	ADJ
ejpam-3377	265	34	.	.	PUNCT
ejpam-3377	266	1	also	also	ADV
ejpam-3377	266	2	g(x	g(x	PROPN
ejpam-3377	266	3	,	,	PUNCT
ejpam-3377	266	4	y	y	NOUN
ejpam-3377	266	5	)	)	PUNCT
ejpam-3377	266	6	=	=	PUNCT
ejpam-3377	267	1	2(x+	2(x+	NUM
ejpam-3377	267	2	y	y	NOUN
ejpam-3377	267	3	)	)	PUNCT
ejpam-3377	267	4	.	.	PUNCT
ejpam-3377	268	1	we	we	PRON
ejpam-3377	268	2	plot	plot	VERB
ejpam-3377	268	3	the	the	DET
ejpam-3377	268	4	approximate	approximate	ADJ
ejpam-3377	268	5	solution	solution	NOUN
ejpam-3377	268	6	corresponding	correspond	VERB
ejpam-3377	268	7	to	to	ADP
ejpam-3377	268	8	the	the	DET
ejpam-3377	268	9	exact	exact	ADJ
ejpam-3377	268	10	solution	solution	NOUN
ejpam-3377	268	11	at	at	ADP
ejpam-3377	268	12	α	α	NOUN
ejpam-3377	268	13	=	=	SYM
ejpam-3377	268	14	2	2	X
ejpam-3377	268	15	.	.	X
ejpam-3377	269	1	we	we	PRON
ejpam-3377	269	2	see	see	VERB
ejpam-3377	269	3	from	from	ADP
ejpam-3377	269	4	the	the	DET
ejpam-3377	269	5	figure	figure	NOUN
ejpam-3377	269	6	2	2	NUM
ejpam-3377	269	7	,	,	PUNCT
ejpam-3377	269	8	that	that	SCONJ
ejpam-3377	269	9	the	the	DET
ejpam-3377	269	10	approximate	approximate	ADJ
ejpam-3377	269	11	solution	solution	NOUN
ejpam-3377	269	12	obtained	obtain	VERB
ejpam-3377	269	13	via	via	ADP
ejpam-3377	269	14	adapting	adapt	VERB
ejpam-3377	269	15	procedure	procedure	NOUN
ejpam-3377	269	16	gives	give	VERB
ejpam-3377	269	17	close	close	ADJ
ejpam-3377	269	18	agreement	agreement	NOUN
ejpam-3377	269	19	to	to	ADP
ejpam-3377	269	20	that	that	PRON
ejpam-3377	269	21	of	of	ADP
ejpam-3377	269	22	exact	exact	ADJ
ejpam-3377	269	23	solution	solution	NOUN
ejpam-3377	269	24	at	at	ADP
ejpam-3377	269	25	very	very	ADV
ejpam-3377	269	26	small	small	ADJ
ejpam-3377	269	27	scale	scale	NOUN
ejpam-3377	269	28	level	level	NOUN
ejpam-3377	269	29	.	.	PUNCT
ejpam-3377	270	1	we	we	PRON
ejpam-3377	270	2	also	also	ADV
ejpam-3377	270	3	compute	compute	VERB
ejpam-3377	270	4	the	the	DET
ejpam-3377	270	5	absolute	absolute	ADJ
ejpam-3377	270	6	error	error	NOUN
ejpam-3377	270	7	l∞	l∞	NOUN
ejpam-3377	270	8	=	=	SYM
ejpam-3377	270	9	‖w	‖w	PROPN
ejpam-3377	270	10	−	−	PROPN
ejpam-3377	270	11	wn‖∞	wn‖∞	NOUN
ejpam-3377	270	12	for	for	ADP
ejpam-3377	270	13	different	different	ADJ
ejpam-3377	270	14	fractional	fractional	ADJ
ejpam-3377	270	15	order	order	NOUN
ejpam-3377	270	16	using	use	VERB
ejpam-3377	270	17	various	various	ADJ
ejpam-3377	270	18	values	value	NOUN
ejpam-3377	270	19	of	of	ADP
ejpam-3377	270	20	n	n	NOUN
ejpam-3377	270	21	in	in	ADP
ejpam-3377	270	22	the	the	DET
ejpam-3377	270	23	given	give	VERB
ejpam-3377	270	24	table	table	NOUN
ejpam-3377	270	25	2	2	NUM
ejpam-3377	270	26	.	.	PUNCT
ejpam-3377	271	1	we	we	PRON
ejpam-3377	271	2	observe	observe	VERB
ejpam-3377	271	3	from	from	ADP
ejpam-3377	271	4	the	the	DET
ejpam-3377	271	5	table	table	NOUN
ejpam-3377	271	6	2	2	NUM
ejpam-3377	271	7	that	that	SCONJ
ejpam-3377	271	8	as	as	SCONJ
ejpam-3377	271	9	α	α	PROPN
ejpam-3377	271	10	approaches	approach	NOUN
ejpam-3377	271	11	to	to	ADP
ejpam-3377	271	12	its	its	PRON
ejpam-3377	271	13	integer	integer	NOUN
ejpam-3377	271	14	value	value	NOUN
ejpam-3377	271	15	,	,	PUNCT
ejpam-3377	271	16	the	the	DET
ejpam-3377	271	17	absolute	absolute	ADJ
ejpam-3377	271	18	error	error	NOUN
ejpam-3377	271	19	decreasing	decreasing	NOUN
ejpam-3377	271	20	.	.	PUNCT
ejpam-3377	272	1	similarly	similarly	ADV
ejpam-3377	272	2	,	,	PUNCT
ejpam-3377	272	3	on	on	ADP
ejpam-3377	272	4	the	the	DET
ejpam-3377	272	5	other	other	ADJ
ejpam-3377	272	6	hand	hand	NOUN
ejpam-3377	272	7	increasing	increase	VERB
ejpam-3377	272	8	the	the	DET
ejpam-3377	272	9	scale	scale	NOUN
ejpam-3377	272	10	level	level	NOUN
ejpam-3377	272	11	,	,	PUNCT
ejpam-3377	272	12	the	the	DET
ejpam-3377	272	13	accuracy	accuracy	NOUN
ejpam-3377	272	14	also	also	ADV
ejpam-3377	272	15	increases	increase	VERB
ejpam-3377	272	16	for	for	ADP
ejpam-3377	272	17	using	use	VERB
ejpam-3377	272	18	different	different	ADJ
ejpam-3377	272	19	fractional	fractional	ADJ
ejpam-3377	272	20	order	order	NOUN
ejpam-3377	272	21	α	α	NOUN
ejpam-3377	272	22	.	.	PUNCT
ejpam-3377	273	1	y	y	NOUN
ejpam-3377	273	2	x	x	SYM
ejpam-3377	273	3	0	0	NUM
ejpam-3377	273	4	1	1	NUM
ejpam-3377	273	5	0.2	0.2	NUM
ejpam-3377	273	6	0.4	0.4	NUM
ejpam-3377	273	7	1	1	NUM
ejpam-3377	273	8	×10	×10	NOUN
ejpam-3377	273	9	-	-	SYM
ejpam-3377	273	10	8	8	NUM
ejpam-3377	273	11	‖w	‖w	NOUN
ejpam-3377	273	12	e	e	NOUN
ejpam-3377	273	13	x	x	X
ejpam-3377	273	14	−	−	PROPN
ejpam-3377	273	15	w	w	NOUN
ejpam-3377	273	16	a	a	DET
ejpam-3377	273	17	p	p	X
ejpam-3377	273	18	p	p	NOUN
ejpam-3377	273	19	‖	‖	PROPN
ejpam-3377	273	20	∞	∞	PROPN
ejpam-3377	273	21	0.6	0.6	NUM
ejpam-3377	273	22	0.8	0.8	NUM
ejpam-3377	273	23	(	(	PUNCT
ejpam-3377	273	24	b	b	NOUN
ejpam-3377	273	25	)	)	PUNCT
ejpam-3377	273	26	0.8	0.8	NUM
ejpam-3377	273	27	0.5	0.5	NUM
ejpam-3377	273	28	0.6	0.6	NUM
ejpam-3377	273	29	1	1	NUM
ejpam-3377	273	30	0.4	0.4	NUM
ejpam-3377	273	31	0.2	0.2	NUM
ejpam-3377	273	32	0	0	NUM
ejpam-3377	273	33	0	0	NUM
ejpam-3377	273	34	absolute	absolute	ADJ
ejpam-3377	273	35	error	error	NOUN
ejpam-3377	273	36	at	at	ADP
ejpam-3377	273	37	n=5	n=5	PROPN
ejpam-3377	273	38	y	y	PROPN
ejpam-3377	273	39	x	x	SYM
ejpam-3377	273	40	0	0	NUM
ejpam-3377	273	41	1	1	NUM
ejpam-3377	273	42	0.5	0.5	NUM
ejpam-3377	273	43	1	1	NUM
ejpam-3377	273	44	0.8	0.8	NUM
ejpam-3377	273	45	1	1	NUM
ejpam-3377	273	46	1.5	1.5	NUM
ejpam-3377	273	47	w	w	NOUN
ejpam-3377	273	48	(	(	PUNCT
ejpam-3377	273	49	x	x	INTJ
ejpam-3377	273	50	,	,	PUNCT
ejpam-3377	273	51	y	y	PROPN
ejpam-3377	273	52	)	)	PUNCT
ejpam-3377	273	53	2	2	NUM
ejpam-3377	273	54	0.6	0.6	NUM
ejpam-3377	273	55	0.8	0.8	NUM
ejpam-3377	273	56	(	(	PUNCT
ejpam-3377	273	57	a	a	X
ejpam-3377	273	58	)	)	PUNCT
ejpam-3377	273	59	2.5	2.5	NUM
ejpam-3377	273	60	0.60.4	0.60.4	NUM
ejpam-3377	273	61	0.4	0.4	NUM
ejpam-3377	273	62	0.2	0.2	NUM
ejpam-3377	273	63	0.2	0.2	NUM
ejpam-3377	273	64	0	0	NUM
ejpam-3377	273	65	0	0	NUM
ejpam-3377	273	66	approximate	approximate	ADJ
ejpam-3377	273	67	solution	solution	NOUN
ejpam-3377	273	68	at	at	ADP
ejpam-3377	273	69	n=5	n=5	ADJ
ejpam-3377	273	70	exact	exact	ADJ
ejpam-3377	273	71	solution	solution	NOUN
ejpam-3377	273	72	figure	figure	NOUN
ejpam-3377	273	73	2	2	NUM
ejpam-3377	273	74	.	.	PUNCT
ejpam-3377	273	75	(	(	PUNCT
ejpam-3377	273	76	a	a	X
ejpam-3377	273	77	)	)	PUNCT
ejpam-3377	273	78	comparison	comparison	NOUN
ejpam-3377	273	79	between	between	ADP
ejpam-3377	273	80	exact	exact	ADJ
ejpam-3377	273	81	and	and	CCONJ
ejpam-3377	273	82	approximate	approximate	ADJ
ejpam-3377	273	83	solutions	solution	NOUN
ejpam-3377	273	84	at	at	ADP
ejpam-3377	273	85	n	n	NOUN
ejpam-3377	273	86	=	=	SYM
ejpam-3377	273	87	5	5	NUM
ejpam-3377	273	88	,	,	PUNCT
ejpam-3377	273	89	p	p	NOUN
ejpam-3377	273	90	=	=	X
ejpam-3377	273	91	q	q	NOUN
ejpam-3377	273	92	=	=	SYM
ejpam-3377	273	93	0	0	NUM
ejpam-3377	273	94	,	,	PUNCT
ejpam-3377	273	95	α	α	NOUN
ejpam-3377	273	96	=	=	SYM
ejpam-3377	273	97	2	2	NUM
ejpam-3377	273	98	for	for	ADP
ejpam-3377	273	99	example	example	NOUN
ejpam-3377	273	100	2	2	NUM
ejpam-3377	273	101	.	.	PUNCT
ejpam-3377	273	102	(	(	PUNCT
ejpam-3377	273	103	b	b	X
ejpam-3377	273	104	)	)	PUNCT
ejpam-3377	273	105	absolute	absolute	ADJ
ejpam-3377	273	106	error	error	NOUN
ejpam-3377	273	107	at	at	ADP
ejpam-3377	273	108	n	n	NOUN
ejpam-3377	273	109	=	=	SYM
ejpam-3377	273	110	5	5	NUM
ejpam-3377	273	111	,	,	PUNCT
ejpam-3377	273	112	p	p	NOUN
ejpam-3377	273	113	=	=	X
ejpam-3377	273	114	q	q	NOUN
ejpam-3377	274	1	=	=	SYM
ejpam-3377	274	2	0	0	NUM
ejpam-3377	274	3	,	,	PUNCT
ejpam-3377	274	4	α	α	NOUN
ejpam-3377	274	5	=	=	SYM
ejpam-3377	274	6	2	2	NUM
ejpam-3377	274	7	for	for	ADP
ejpam-3377	274	8	example	example	NOUN
ejpam-3377	274	9	2	2	NUM
ejpam-3377	274	10	.	.	NOUN
ejpam-3377	274	11	example	example	NOUN
ejpam-3377	275	1	3	3	X
ejpam-3377	275	2	.	.	PUNCT
ejpam-3377	275	3	consider	consider	VERB
ejpam-3377	275	4	the	the	DET
ejpam-3377	275	5	following	follow	VERB
ejpam-3377	275	6	fractional	fractional	ADJ
ejpam-3377	275	7	partial	partial	ADJ
ejpam-3377	275	8	differential	differential	NOUN
ejpam-3377	275	9	equation	equation	NOUN
ejpam-3377	275	10	5	5	NUM
ejpam-3377	275	11	∂αw(x	∂αw(x	PROPN
ejpam-3377	275	12	,	,	PUNCT
ejpam-3377	275	13	y	y	NOUN
ejpam-3377	275	14	)	)	PUNCT
ejpam-3377	275	15	∂xα	∂xα	NOUN
ejpam-3377	275	16	+	+	CCONJ
ejpam-3377	275	17	6	6	NUM
ejpam-3377	275	18	∂αw(x	∂αw(x	ADJ
ejpam-3377	275	19	,	,	PUNCT
ejpam-3377	275	20	y	y	NOUN
ejpam-3377	275	21	)	)	PUNCT
ejpam-3377	275	22	∂x	∂x	NOUN
ejpam-3377	276	1	α	α	NOUN
ejpam-3377	276	2	2	2	NUM
ejpam-3377	276	3	∂y	∂y	SYM
ejpam-3377	276	4	α	α	NOUN
ejpam-3377	276	5	2	2	NUM
ejpam-3377	276	6	−	−	NOUN
ejpam-3377	276	7	4	4	NUM
ejpam-3377	276	8	∂αw(x	∂αw(x	ADJ
ejpam-3377	276	9	,	,	PUNCT
ejpam-3377	276	10	y	y	NOUN
ejpam-3377	276	11	)	)	PUNCT
ejpam-3377	276	12	∂yα	∂yα	PROPN
ejpam-3377	276	13	+	+	CCONJ
ejpam-3377	276	14	7	7	NUM
ejpam-3377	276	15	∂βw(x	∂βw(x	ADJ
ejpam-3377	276	16	,	,	PUNCT
ejpam-3377	276	17	y	y	NOUN
ejpam-3377	276	18	)	)	PUNCT
ejpam-3377	276	19	∂xβ	∂xβ	NOUN
ejpam-3377	276	20	+	+	CCONJ
ejpam-3377	276	21	8	8	NUM
ejpam-3377	276	22	∂βw(x	∂βw(x	PROPN
ejpam-3377	276	23	,	,	PUNCT
ejpam-3377	276	24	y	y	NOUN
ejpam-3377	276	25	)	)	PUNCT
ejpam-3377	277	1	∂yβ	∂yβ	ADV
ejpam-3377	277	2	+	+	CCONJ
ejpam-3377	277	3	9w(x	9w(x	NUM
ejpam-3377	277	4	,	,	PUNCT
ejpam-3377	277	5	y	y	NOUN
ejpam-3377	277	6	)	)	PUNCT
ejpam-3377	277	7	=	=	SYM
ejpam-3377	278	1	g(x	g(x	NOUN
ejpam-3377	278	2	,	,	PUNCT
ejpam-3377	278	3	y	y	NOUN
ejpam-3377	278	4	)	)	PUNCT
ejpam-3377	278	5	,	,	PUNCT
ejpam-3377	278	6	w(0	w(0	PROPN
ejpam-3377	278	7	,	,	PUNCT
ejpam-3377	278	8	y	y	PROPN
ejpam-3377	278	9	)	)	PUNCT
ejpam-3377	278	10	=	=	SYM
ejpam-3377	278	11	0	0	NUM
ejpam-3377	278	12	,	,	PUNCT
ejpam-3377	278	13	wx(0	wx(0	PROPN
ejpam-3377	278	14	,	,	PUNCT
ejpam-3377	278	15	y	y	PROPN
ejpam-3377	278	16	)	)	PUNCT
ejpam-3377	278	17	=	=	SYM
ejpam-3377	278	18	0	0	X
ejpam-3377	278	19	.	.	PUNCT
ejpam-3377	279	1	(	(	PUNCT
ejpam-3377	279	2	39	39	NUM
ejpam-3377	279	3	)	)	PUNCT
ejpam-3377	279	4	m.i	m.i	PROPN
ejpam-3377	279	5	.	.	PROPN
ejpam-3377	279	6	chohan	chohan	PROPN
ejpam-3377	279	7	,	,	PUNCT
ejpam-3377	279	8	k.shah	k.shah	PROPN
ejpam-3377	279	9	/	/	SYM
ejpam-3377	279	10	eur	eur	PROPN
ejpam-3377	279	11	.	.	PUNCT
ejpam-3377	280	1	j.	j.	PROPN
ejpam-3377	280	2	pure	pure	PROPN
ejpam-3377	280	3	appl	appl	PROPN
ejpam-3377	280	4	.	.	PROPN
ejpam-3377	280	5	math	math	PROPN
ejpam-3377	280	6	,	,	PUNCT
ejpam-3377	280	7	12	12	NUM
ejpam-3377	280	8	(	(	PUNCT
ejpam-3377	280	9	1	1	NUM
ejpam-3377	280	10	)	)	PUNCT
ejpam-3377	280	11	(	(	PUNCT
ejpam-3377	280	12	2019	2019	NUM
ejpam-3377	280	13	)	)	PUNCT
ejpam-3377	280	14	,	,	PUNCT
ejpam-3377	280	15	39	39	NUM
ejpam-3377	280	16	-	-	SYM
ejpam-3377	280	17	57	57	NUM
ejpam-3377	280	18	50	50	NUM
ejpam-3377	280	19	α	α	NOUN
ejpam-3377	280	20	l∞	l∞	NOUN
ejpam-3377	280	21	at	at	ADP
ejpam-3377	280	22	n	n	NOUN
ejpam-3377	280	23	=	=	NUM
ejpam-3377	280	24	6	6	NUM
ejpam-3377	280	25	l∞	l∞	NOUN
ejpam-3377	280	26	at	at	ADP
ejpam-3377	280	27	n	n	NOUN
ejpam-3377	280	28	=	=	SYM
ejpam-3377	280	29	8	8	NUM
ejpam-3377	280	30	l∞	l∞	NOUN
ejpam-3377	280	31	at	at	ADP
ejpam-3377	280	32	n	n	NOUN
ejpam-3377	280	33	=	=	SYM
ejpam-3377	280	34	10	10	NUM
ejpam-3377	280	35	l∞	l∞	NOUN
ejpam-3377	280	36	at	at	ADP
ejpam-3377	280	37	n	n	NOUN
ejpam-3377	280	38	=	=	NUM
ejpam-3377	280	39	12	12	NUM
ejpam-3377	280	40	1.5	1.5	NUM
ejpam-3377	280	41	8.0707(−7	8.0707(−7	NUM
ejpam-3377	280	42	)	)	PUNCT
ejpam-3377	280	43	6.7325(−9	6.7325(−9	NUM
ejpam-3377	280	44	)	)	PUNCT
ejpam-3377	280	45	8.7826(−10	8.7826(−10	NOUN
ejpam-3377	280	46	)	)	PUNCT
ejpam-3377	280	47	8.3459(−11	8.3459(−11	PROPN
ejpam-3377	280	48	)	)	PUNCT
ejpam-3377	280	49	1.6	1.6	NUM
ejpam-3377	280	50	8.6056(−8	8.6056(−8	NUM
ejpam-3377	280	51	)	)	PUNCT
ejpam-3377	281	1	9.0196(−10	9.0196(−10	PROPN
ejpam-3377	281	2	)	)	PUNCT
ejpam-3377	281	3	7.0638(−11	7.0638(−11	NOUN
ejpam-3377	281	4	)	)	PUNCT
ejpam-3377	281	5	8.5009(−12	8.5009(−12	NOUN
ejpam-3377	281	6	)	)	PUNCT
ejpam-3377	281	7	1.7	1.7	NUM
ejpam-3377	281	8	9.2036(−9	9.2036(−9	NUM
ejpam-3377	281	9	)	)	PUNCT
ejpam-3377	281	10	9.1703(−10	9.1703(−10	PROPN
ejpam-3377	281	11	)	)	PUNCT
ejpam-3377	281	12	8.9126(−12	8.9126(−12	NOUN
ejpam-3377	281	13	)	)	PUNCT
ejpam-3377	281	14	1.0998(−13	1.0998(−13	PROPN
ejpam-3377	281	15	)	)	PUNCT
ejpam-3377	281	16	1.8	1.8	NUM
ejpam-3377	281	17	7.3073(−10	7.3073(−10	NOUN
ejpam-3377	281	18	)	)	PUNCT
ejpam-3377	281	19	1.0386(−11	1.0386(−11	ADJ
ejpam-3377	281	20	)	)	PUNCT
ejpam-3377	281	21	5.0457(−13	5.0457(−13	NOUN
ejpam-3377	281	22	)	)	PUNCT
ejpam-3377	281	23	9.0945(−14	9.0945(−14	NOUN
ejpam-3377	281	24	)	)	PUNCT
ejpam-3377	281	25	1.9	1.9	NUM
ejpam-3377	281	26	5.9002(−10	5.9002(−10	NUM
ejpam-3377	281	27	)	)	PUNCT
ejpam-3377	281	28	2.0145(−11	2.0145(−11	NUM
ejpam-3377	281	29	)	)	PUNCT
ejpam-3377	281	30	8.1081(−12	8.1081(−12	ADJ
ejpam-3377	281	31	)	)	PUNCT
ejpam-3377	281	32	9.4520(−15	9.4520(−15	NOUN
ejpam-3377	281	33	)	)	PUNCT
ejpam-3377	281	34	2.0	2.0	NUM
ejpam-3377	281	35	3.0000(−11	3.0000(−11	NUM
ejpam-3377	281	36	)	)	PUNCT
ejpam-3377	281	37	1.9019(−12	1.9019(−12	NOUN
ejpam-3377	281	38	)	)	PUNCT
ejpam-3377	281	39	1.7035(−15	1.7035(−15	PROPN
ejpam-3377	281	40	)	)	PUNCT
ejpam-3377	281	41	9.0001(−16	9.0001(−16	NOUN
ejpam-3377	281	42	)	)	PUNCT
ejpam-3377	281	43	table	table	NOUN
ejpam-3377	281	44	3	3	NUM
ejpam-3377	281	45	:	:	PUNCT
ejpam-3377	281	46	absolute	absolute	ADJ
ejpam-3377	281	47	error	error	NOUN
ejpam-3377	281	48	in	in	ADP
ejpam-3377	281	49	w(x	w(x	PROPN
ejpam-3377	281	50	,	,	PUNCT
ejpam-3377	281	51	y	y	NOUN
ejpam-3377	281	52	)	)	PUNCT
ejpam-3377	281	53	of	of	ADP
ejpam-3377	281	54	example	example	NOUN
ejpam-3377	281	55	3	3	NUM
ejpam-3377	281	56	for	for	ADP
ejpam-3377	281	57	(	(	PUNCT
ejpam-3377	281	58	p	p	X
ejpam-3377	281	59	,	,	PUNCT
ejpam-3377	281	60	q	q	NOUN
ejpam-3377	281	61	)	)	PUNCT
ejpam-3377	281	62	=	=	SYM
ejpam-3377	281	63	(	(	PUNCT
ejpam-3377	281	64	0	0	NUM
ejpam-3377	281	65	,	,	PUNCT
ejpam-3377	281	66	0	0	NUM
ejpam-3377	281	67	)	)	PUNCT
ejpam-3377	281	68	and	and	CCONJ
ejpam-3377	281	69	at	at	ADP
ejpam-3377	281	70	various	various	ADJ
ejpam-3377	281	71	values	value	NOUN
ejpam-3377	281	72	of	of	ADP
ejpam-3377	281	73	n	n	PROPN
ejpam-3377	281	74	and	and	CCONJ
ejpam-3377	281	75	α	α	X
ejpam-3377	281	76	.	.	PUNCT
ejpam-3377	282	1	at	at	ADP
ejpam-3377	282	2	α	α	NOUN
ejpam-3377	282	3	=	=	SYM
ejpam-3377	282	4	2	2	NUM
ejpam-3377	282	5	,	,	PUNCT
ejpam-3377	282	6	β	β	X
ejpam-3377	282	7	=	=	SYM
ejpam-3377	282	8	1	1	NUM
ejpam-3377	282	9	the	the	DET
ejpam-3377	282	10	exact	exact	ADJ
ejpam-3377	282	11	solution	solution	NOUN
ejpam-3377	282	12	of	of	ADP
ejpam-3377	282	13	(	(	PUNCT
ejpam-3377	282	14	39	39	NUM
ejpam-3377	282	15	)	)	PUNCT
ejpam-3377	282	16	is	be	AUX
ejpam-3377	282	17	w(x	w(x	PROPN
ejpam-3377	282	18	,	,	PUNCT
ejpam-3377	282	19	y	y	NOUN
ejpam-3377	282	20	)	)	PUNCT
ejpam-3377	282	21	=	=	PRON
ejpam-3377	283	1	(	(	PUNCT
ejpam-3377	283	2	xy)4	xy)4	PROPN
ejpam-3377	283	3	−	−	PROPN
ejpam-3377	283	4	(	(	PUNCT
ejpam-3377	283	5	xy)3	xy)3	PROPN
ejpam-3377	283	6	.	.	PUNCT
ejpam-3377	284	1	here	here	ADV
ejpam-3377	284	2	a	a	DET
ejpam-3377	284	3	=	=	SYM
ejpam-3377	284	4	5	5	NUM
ejpam-3377	284	5	,	,	PUNCT
ejpam-3377	284	6	b	b	NOUN
ejpam-3377	284	7	=	=	SYM
ejpam-3377	284	8	6	6	NUM
ejpam-3377	284	9	,	,	PUNCT
ejpam-3377	284	10	c	c	NOUN
ejpam-3377	284	11	=	=	SYM
ejpam-3377	284	12	−4	−4	PROPN
ejpam-3377	284	13	,	,	PUNCT
ejpam-3377	284	14	d	d	X
ejpam-3377	284	15	=	=	SYM
ejpam-3377	284	16	7	7	NUM
ejpam-3377	284	17	,	,	PUNCT
ejpam-3377	284	18	e	e	NOUN
ejpam-3377	284	19	=	=	SYM
ejpam-3377	284	20	8	8	NUM
ejpam-3377	284	21	,	,	PUNCT
ejpam-3377	284	22	f	f	NOUN
ejpam-3377	284	23	=	=	SYM
ejpam-3377	284	24	9	9	NUM
ejpam-3377	284	25	.	.	PUNCT
ejpam-3377	285	1	as	as	ADP
ejpam-3377	285	2	b2	b2	NOUN
ejpam-3377	285	3	−	−	PROPN
ejpam-3377	285	4	4ac	4ac	NOUN
ejpam-3377	285	5	>	>	X
ejpam-3377	285	6	0	0	PROPN
ejpam-3377	285	7	,	,	PUNCT
ejpam-3377	285	8	the	the	DET
ejpam-3377	285	9	given	give	VERB
ejpam-3377	285	10	fpde	fpde	NOUN
ejpam-3377	285	11	is	be	AUX
ejpam-3377	285	12	hyperbolic	hyperbolic	ADJ
ejpam-3377	285	13	.	.	PUNCT
ejpam-3377	286	1	in	in	ADP
ejpam-3377	286	2	the	the	DET
ejpam-3377	286	3	figure	figure	NOUN
ejpam-3377	286	4	?	?	PUNCT
ejpam-3377	286	5	?	?	PUNCT
ejpam-3377	286	6	,	,	PUNCT
ejpam-3377	286	7	we	we	PRON
ejpam-3377	286	8	have	have	AUX
ejpam-3377	286	9	plotted	plot	VERB
ejpam-3377	286	10	the	the	DET
ejpam-3377	286	11	approximate	approximate	ADJ
ejpam-3377	286	12	solution	solution	NOUN
ejpam-3377	286	13	corresponding	correspond	VERB
ejpam-3377	286	14	to	to	ADP
ejpam-3377	286	15	the	the	DET
ejpam-3377	286	16	exact	exact	ADJ
ejpam-3377	286	17	solution	solution	NOUN
ejpam-3377	286	18	at	at	ADP
ejpam-3377	286	19	α	α	NOUN
ejpam-3377	286	20	=	=	SYM
ejpam-3377	286	21	2	2	X
ejpam-3377	286	22	.	.	X
ejpam-3377	287	1	we	we	PRON
ejpam-3377	287	2	see	see	VERB
ejpam-3377	287	3	that	that	SCONJ
ejpam-3377	287	4	the	the	DET
ejpam-3377	287	5	approximate	approximate	ADJ
ejpam-3377	287	6	solution	solution	NOUN
ejpam-3377	287	7	obtained	obtain	VERB
ejpam-3377	287	8	via	via	ADP
ejpam-3377	287	9	proposed	propose	VERB
ejpam-3377	287	10	method	method	NOUN
ejpam-3377	287	11	has	have	VERB
ejpam-3377	287	12	the	the	DET
ejpam-3377	287	13	close	close	ADJ
ejpam-3377	287	14	agreement	agreement	NOUN
ejpam-3377	287	15	to	to	ADP
ejpam-3377	287	16	that	that	PRON
ejpam-3377	287	17	of	of	ADP
ejpam-3377	287	18	exact	exact	ADJ
ejpam-3377	287	19	solution	solution	NOUN
ejpam-3377	287	20	at	at	ADP
ejpam-3377	287	21	sufficiently	sufficiently	ADV
ejpam-3377	287	22	small	small	ADJ
ejpam-3377	287	23	scale	scale	NOUN
ejpam-3377	287	24	level	level	NOUN
ejpam-3377	287	25	.	.	PUNCT
ejpam-3377	288	1	further	far	ADV
ejpam-3377	288	2	,	,	PUNCT
ejpam-3377	288	3	we	we	PRON
ejpam-3377	288	4	compute	compute	VERB
ejpam-3377	288	5	the	the	DET
ejpam-3377	288	6	absolute	absolute	ADJ
ejpam-3377	288	7	error	error	NOUN
ejpam-3377	288	8	l∞	l∞	NOUN
ejpam-3377	288	9	=	=	SYM
ejpam-3377	288	10	‖w	‖w	PROPN
ejpam-3377	288	11	−	−	PROPN
ejpam-3377	288	12	wn‖∞	wn‖∞	NOUN
ejpam-3377	288	13	for	for	ADP
ejpam-3377	288	14	different	different	ADJ
ejpam-3377	288	15	fractional	fractional	ADJ
ejpam-3377	288	16	order	order	NOUN
ejpam-3377	288	17	and	and	CCONJ
ejpam-3377	288	18	using	use	VERB
ejpam-3377	288	19	various	various	ADJ
ejpam-3377	288	20	values	value	NOUN
ejpam-3377	288	21	of	of	ADP
ejpam-3377	288	22	n	n	NOUN
ejpam-3377	288	23	in	in	ADP
ejpam-3377	288	24	the	the	DET
ejpam-3377	288	25	given	give	VERB
ejpam-3377	288	26	table	table	NOUN
ejpam-3377	288	27	3	3	X
ejpam-3377	288	28	.	.	PUNCT
ejpam-3377	289	1	we	we	PRON
ejpam-3377	289	2	observe	observe	VERB
ejpam-3377	289	3	from	from	ADP
ejpam-3377	289	4	the	the	DET
ejpam-3377	289	5	table	table	NOUN
ejpam-3377	289	6	3	3	NUM
ejpam-3377	289	7	that	that	DET
ejpam-3377	289	8	as	as	SCONJ
ejpam-3377	289	9	α	α	PROPN
ejpam-3377	289	10	approaches	approach	NOUN
ejpam-3377	289	11	to	to	ADP
ejpam-3377	289	12	its	its	PRON
ejpam-3377	289	13	integer	integer	NOUN
ejpam-3377	289	14	value	value	NOUN
ejpam-3377	289	15	,	,	PUNCT
ejpam-3377	289	16	the	the	DET
ejpam-3377	289	17	absolute	absolute	ADJ
ejpam-3377	289	18	error	error	NOUN
ejpam-3377	289	19	decreasing	decreasing	NOUN
ejpam-3377	289	20	.	.	PUNCT
ejpam-3377	290	1	similarly	similarly	ADV
ejpam-3377	290	2	,	,	PUNCT
ejpam-3377	290	3	by	by	ADP
ejpam-3377	290	4	increasing	increase	VERB
ejpam-3377	290	5	the	the	DET
ejpam-3377	290	6	scale	scale	NOUN
ejpam-3377	290	7	level	level	NOUN
ejpam-3377	290	8	,	,	PUNCT
ejpam-3377	290	9	the	the	DET
ejpam-3377	290	10	accuracy	accuracy	NOUN
ejpam-3377	290	11	also	also	ADV
ejpam-3377	290	12	increases	increase	VERB
ejpam-3377	290	13	for	for	ADP
ejpam-3377	290	14	taking	take	VERB
ejpam-3377	290	15	different	different	ADJ
ejpam-3377	290	16	fractional	fractional	ADJ
ejpam-3377	290	17	order	order	NOUN
ejpam-3377	290	18	.	.	PUNCT
ejpam-3377	291	1	x	x	PUNCT
ejpam-3377	291	2	y	y	NOUN
ejpam-3377	291	3	0	0	NUM
ejpam-3377	291	4	1	1	NUM
ejpam-3377	291	5	1	1	NUM
ejpam-3377	291	6	1	1	NUM
ejpam-3377	291	7	2	2	NUM
ejpam-3377	291	8	‖w	‖w	NOUN
ejpam-3377	291	9	a	a	DET
ejpam-3377	291	10	p	p	X
ejpam-3377	291	11	p	p	NOUN
ejpam-3377	291	12	−	−	PROPN
ejpam-3377	291	13	w	w	NOUN
ejpam-3377	291	14	e	e	NOUN
ejpam-3377	291	15	x	x	SYM
ejpam-3377	291	16	‖	‖	PROPN
ejpam-3377	291	17	∞	∞	PROPN
ejpam-3377	291	18	×10	×10	NOUN
ejpam-3377	291	19	-	-	SYM
ejpam-3377	291	20	11	11	NUM
ejpam-3377	291	21	0.8	0.8	NUM
ejpam-3377	291	22	(	(	PUNCT
ejpam-3377	291	23	a	a	X
ejpam-3377	291	24	)	)	PUNCT
ejpam-3377	291	25	3	3	NUM
ejpam-3377	291	26	0.5	0.5	NUM
ejpam-3377	291	27	0.6	0.6	NUM
ejpam-3377	291	28	4	4	NUM
ejpam-3377	291	29	0.4	0.4	NUM
ejpam-3377	291	30	0.2	0.2	NUM
ejpam-3377	291	31	0	0	NUM
ejpam-3377	291	32	0	0	NUM
ejpam-3377	291	33	absolute	absolute	ADJ
ejpam-3377	291	34	error	error	NOUN
ejpam-3377	291	35	at	at	ADP
ejpam-3377	291	36	n=6	n=6	NOUN
ejpam-3377	291	37	x	x	SYM
ejpam-3377	291	38	w	w	X
ejpam-3377	291	39	(	(	PUNCT
ejpam-3377	291	40	x	x	INTJ
ejpam-3377	291	41	,	,	PUNCT
ejpam-3377	291	42	y	y	PROPN
ejpam-3377	291	43	)	)	PUNCT
ejpam-3377	292	1	y	y	PROPN
ejpam-3377	292	2	1	1	NUM
ejpam-3377	292	3	-0.1	-0.1	NOUN
ejpam-3377	292	4	10.8	10.8	NUM
ejpam-3377	292	5	0.8	0.8	NUM
ejpam-3377	292	6	0.6	0.6	NUM
ejpam-3377	292	7	0.6	0.6	NUM
ejpam-3377	292	8	0.4	0.4	NUM
ejpam-3377	292	9	0.4	0.4	NUM
ejpam-3377	292	10	0.2	0.2	NUM
ejpam-3377	292	11	0.2	0.2	NUM
ejpam-3377	292	12	0	0	NUM
ejpam-3377	292	13	0	0	NUM
ejpam-3377	292	14	-0.05	-0.05	NUM
ejpam-3377	292	15	(	(	PUNCT
ejpam-3377	292	16	b	b	NOUN
ejpam-3377	292	17	)	)	PUNCT
ejpam-3377	292	18	0	0	NUM
ejpam-3377	292	19	approximate	approximate	ADJ
ejpam-3377	292	20	solution	solution	NOUN
ejpam-3377	292	21	at	at	ADP
ejpam-3377	292	22	n=6	n=6	NOUN
ejpam-3377	292	23	exact	exact	ADJ
ejpam-3377	292	24	solution	solution	NOUN
ejpam-3377	292	25	figure	figure	NOUN
ejpam-3377	292	26	3	3	NUM
ejpam-3377	292	27	.	.	PUNCT
ejpam-3377	293	1	(	(	PUNCT
ejpam-3377	293	2	a)absolute	a)absolute	ADP
ejpam-3377	293	3	error	error	NOUN
ejpam-3377	293	4	at	at	ADP
ejpam-3377	293	5	n	n	NOUN
ejpam-3377	293	6	=	=	SYM
ejpam-3377	293	7	6	6	NUM
ejpam-3377	293	8	,	,	PUNCT
ejpam-3377	293	9	p	p	NOUN
ejpam-3377	293	10	=	=	X
ejpam-3377	293	11	q	q	NOUN
ejpam-3377	293	12	=	=	SYM
ejpam-3377	293	13	0	0	NUM
ejpam-3377	293	14	,	,	PUNCT
ejpam-3377	293	15	α	α	NOUN
ejpam-3377	293	16	=	=	SYM
ejpam-3377	293	17	2	2	NUM
ejpam-3377	293	18	,	,	PUNCT
ejpam-3377	293	19	β	β	X
ejpam-3377	293	20	=	=	SYM
ejpam-3377	293	21	1	1	NUM
ejpam-3377	293	22	for	for	ADP
ejpam-3377	293	23	example	example	NOUN
ejpam-3377	293	24	3	3	NUM
ejpam-3377	293	25	.	.	PUNCT
ejpam-3377	293	26	(	(	PUNCT
ejpam-3377	293	27	b	b	X
ejpam-3377	293	28	)	)	PUNCT
ejpam-3377	293	29	comparison	comparison	NOUN
ejpam-3377	293	30	between	between	ADP
ejpam-3377	293	31	exact	exact	ADJ
ejpam-3377	293	32	and	and	CCONJ
ejpam-3377	293	33	approximate	approximate	ADJ
ejpam-3377	293	34	solutions	solution	NOUN
ejpam-3377	293	35	at	at	ADP
ejpam-3377	293	36	n	n	NOUN
ejpam-3377	293	37	=	=	NUM
ejpam-3377	293	38	6	6	NUM
ejpam-3377	293	39	,	,	PUNCT
ejpam-3377	293	40	p	p	NOUN
ejpam-3377	293	41	=	=	X
ejpam-3377	293	42	q	q	NOUN
ejpam-3377	293	43	=	=	SYM
ejpam-3377	293	44	0	0	NUM
ejpam-3377	293	45	,	,	PUNCT
ejpam-3377	293	46	α	α	NOUN
ejpam-3377	293	47	=	=	SYM
ejpam-3377	293	48	2	2	NUM
ejpam-3377	293	49	,	,	PUNCT
ejpam-3377	293	50	β	β	X
ejpam-3377	293	51	=	=	SYM
ejpam-3377	293	52	1	1	NUM
ejpam-3377	293	53	for	for	ADP
ejpam-3377	293	54	example	example	NOUN
ejpam-3377	293	55	3	3	NUM
ejpam-3377	293	56	.	.	NOUN
ejpam-3377	293	57	remark	remark	PROPN
ejpam-3377	293	58	1	1	NUM
ejpam-3377	293	59	.	.	PUNCT
ejpam-3377	294	1	the	the	DET
ejpam-3377	294	2	numerical	numerical	ADJ
ejpam-3377	294	3	solutions	solution	NOUN
ejpam-3377	294	4	of	of	ADP
ejpam-3377	294	5	fpdes	fpde	NOUN
ejpam-3377	294	6	by	by	ADP
ejpam-3377	294	7	using	use	VERB
ejpam-3377	294	8	shifted	shift	VERB
ejpam-3377	294	9	jacobi	jacobi	PROPN
ejpam-3377	294	10	polynomials	polynomial	NOUN
ejpam-3377	294	11	are	be	AUX
ejpam-3377	294	12	also	also	ADV
ejpam-3377	294	13	depending	depend	VERB
ejpam-3377	294	14	on	on	ADP
ejpam-3377	294	15	the	the	DET
ejpam-3377	294	16	values	value	NOUN
ejpam-3377	294	17	of	of	ADP
ejpam-3377	294	18	the	the	DET
ejpam-3377	294	19	parameters	parameter	NOUN
ejpam-3377	294	20	of	of	ADP
ejpam-3377	294	21	the	the	DET
ejpam-3377	294	22	considered	consider	VERB
ejpam-3377	294	23	polynomials	polynomial	NOUN
ejpam-3377	294	24	.	.	PUNCT
ejpam-3377	295	1	therefore	therefore	ADV
ejpam-3377	295	2	the	the	DET
ejpam-3377	295	3	absolute	absolute	ADJ
ejpam-3377	295	4	error	error	NOUN
ejpam-3377	295	5	also	also	ADV
ejpam-3377	295	6	depends	depend	VERB
ejpam-3377	295	7	upon	upon	SCONJ
ejpam-3377	295	8	on	on	ADP
ejpam-3377	295	9	the	the	DET
ejpam-3377	295	10	values	value	NOUN
ejpam-3377	295	11	of	of	ADP
ejpam-3377	295	12	the	the	DET
ejpam-3377	295	13	jacobi	jacobi	PROPN
ejpam-3377	295	14	polynomials	polynomial	VERB
ejpam-3377	295	15	parameters	parameter	NOUN
ejpam-3377	295	16	.	.	PUNCT
ejpam-3377	296	1	we	we	PRON
ejpam-3377	296	2	give	give	VERB
ejpam-3377	296	3	the	the	DET
ejpam-3377	296	4	following	follow	VERB
ejpam-3377	296	5	table	table	NOUN
ejpam-3377	296	6	4	4	NUM
ejpam-3377	296	7	,	,	PUNCT
ejpam-3377	296	8	for	for	ADP
ejpam-3377	296	9	all	all	DET
ejpam-3377	296	10	three	three	NUM
ejpam-3377	296	11	examples	example	NOUN
ejpam-3377	296	12	and	and	CCONJ
ejpam-3377	296	13	the	the	DET
ejpam-3377	296	14	absolute	absolute	ADJ
ejpam-3377	296	15	error	error	NOUN
ejpam-3377	296	16	at	at	ADP
ejpam-3377	296	17	scale	scale	NOUN
ejpam-3377	296	18	level	level	NOUN
ejpam-3377	296	19	n	n	NOUN
ejpam-3377	296	20	=	=	SYM
ejpam-3377	296	21	6	6	NUM
ejpam-3377	296	22	and	and	CCONJ
ejpam-3377	296	23	taking	take	VERB
ejpam-3377	296	24	fractional	fractional	ADJ
ejpam-3377	296	25	order	order	NOUN
ejpam-3377	296	26	α	α	NOUN
ejpam-3377	296	27	=	=	SYM
ejpam-3377	296	28	1.8	1.8	NUM
ejpam-3377	296	29	.	.	PUNCT
ejpam-3377	297	1	we	we	PRON
ejpam-3377	297	2	see	see	VERB
ejpam-3377	297	3	that	that	SCONJ
ejpam-3377	297	4	as	as	SCONJ
ejpam-3377	297	5	the	the	DET
ejpam-3377	297	6	values	value	NOUN
ejpam-3377	297	7	of	of	ADP
ejpam-3377	297	8	parameters	parameter	NOUN
ejpam-3377	297	9	(	(	PUNCT
ejpam-3377	297	10	p	p	X
ejpam-3377	297	11	,	,	PUNCT
ejpam-3377	297	12	q	q	NOUN
ejpam-3377	297	13	)	)	PUNCT
ejpam-3377	297	14	tends	tend	VERB
ejpam-3377	297	15	to	to	ADP
ejpam-3377	297	16	its	its	PRON
ejpam-3377	297	17	integer	integer	NOUN
ejpam-3377	297	18	values	value	NOUN
ejpam-3377	297	19	the	the	DET
ejpam-3377	297	20	absolute	absolute	ADJ
ejpam-3377	297	21	error	error	NOUN
ejpam-3377	297	22	decreases	decrease	NOUN
ejpam-3377	297	23	and	and	CCONJ
ejpam-3377	297	24	vice	vice	NOUN
ejpam-3377	297	25	versa	versa	ADV
ejpam-3377	297	26	.	.	PUNCT
ejpam-3377	298	1	m.i	m.i	PROPN
ejpam-3377	298	2	.	.	PROPN
ejpam-3377	298	3	chohan	chohan	PROPN
ejpam-3377	298	4	,	,	PUNCT
ejpam-3377	298	5	k.shah	k.shah	PROPN
ejpam-3377	298	6	/	/	SYM
ejpam-3377	298	7	eur	eur	PROPN
ejpam-3377	298	8	.	.	PUNCT
ejpam-3377	299	1	j.	j.	PROPN
ejpam-3377	299	2	pure	pure	PROPN
ejpam-3377	299	3	appl	appl	PROPN
ejpam-3377	299	4	.	.	PROPN
ejpam-3377	299	5	math	math	PROPN
ejpam-3377	299	6	,	,	PUNCT
ejpam-3377	299	7	12	12	NUM
ejpam-3377	299	8	(	(	PUNCT
ejpam-3377	299	9	1	1	NUM
ejpam-3377	299	10	)	)	PUNCT
ejpam-3377	299	11	(	(	PUNCT
ejpam-3377	299	12	2019	2019	NUM
ejpam-3377	299	13	)	)	PUNCT
ejpam-3377	299	14	,	,	PUNCT
ejpam-3377	299	15	39	39	NUM
ejpam-3377	299	16	-	-	SYM
ejpam-3377	299	17	57	57	NUM
ejpam-3377	299	18	51	51	NUM
ejpam-3377	299	19	(	(	PUNCT
ejpam-3377	299	20	p	p	X
ejpam-3377	299	21	,	,	PUNCT
ejpam-3377	299	22	q	q	NOUN
ejpam-3377	299	23	)	)	PUNCT
ejpam-3377	299	24	l∞	l∞	NOUN
ejpam-3377	299	25	of	of	ADP
ejpam-3377	299	26	example	example	NOUN
ejpam-3377	299	27	1	1	NUM
ejpam-3377	299	28	l∞	l∞	NOUN
ejpam-3377	299	29	of	of	ADP
ejpam-3377	299	30	example	example	NOUN
ejpam-3377	299	31	2	2	NUM
ejpam-3377	299	32	l∞	l∞	NOUN
ejpam-3377	299	33	of	of	ADP
ejpam-3377	299	34	example	example	NOUN
ejpam-3377	299	35	3	3	NUM
ejpam-3377	299	36	(	(	PUNCT
ejpam-3377	299	37	0	0	NUM
ejpam-3377	299	38	,	,	PUNCT
ejpam-3377	299	39	0	0	NUM
ejpam-3377	299	40	)	)	PUNCT
ejpam-3377	299	41	2.0025(−11	2.0025(−11	PROPN
ejpam-3377	299	42	)	)	PUNCT
ejpam-3377	299	43	1.0000(−10	1.0000(−10	NUM
ejpam-3377	299	44	)	)	PUNCT
ejpam-3377	299	45	3.000(−11	3.000(−11	NUM
ejpam-3377	299	46	)	)	PUNCT
ejpam-3377	299	47	(	(	PUNCT
ejpam-3377	299	48	0.5	0.5	NUM
ejpam-3377	299	49	,	,	PUNCT
ejpam-3377	299	50	0.5	0.5	NUM
ejpam-3377	299	51	)	)	PUNCT
ejpam-3377	299	52	9.2455(−7	9.2455(−7	PROPN
ejpam-3377	299	53	)	)	PUNCT
ejpam-3377	299	54	9.0638(−6	9.0638(−6	NUM
ejpam-3377	299	55	)	)	PUNCT
ejpam-3377	299	56	1.8999(−8	1.8999(−8	NUM
ejpam-3377	299	57	)	)	PUNCT
ejpam-3377	299	58	(	(	PUNCT
ejpam-3377	299	59	1	1	NUM
ejpam-3377	299	60	,	,	PUNCT
ejpam-3377	299	61	1	1	NUM
ejpam-3377	299	62	)	)	PUNCT
ejpam-3377	299	63	1.9703(−10	1.9703(−10	NUM
ejpam-3377	299	64	)	)	PUNCT
ejpam-3377	299	65	7.0126(−9	7.0126(−9	NUM
ejpam-3377	299	66	)	)	PUNCT
ejpam-3377	299	67	9.0998(−10	9.0998(−10	NOUN
ejpam-3377	299	68	)	)	PUNCT
ejpam-3377	299	69	(	(	PUNCT
ejpam-3377	299	70	1	1	NUM
ejpam-3377	299	71	,	,	PUNCT
ejpam-3377	299	72	0.5	0.5	NUM
ejpam-3377	299	73	)	)	PUNCT
ejpam-3377	299	74	1.0386(−8	1.0386(−8	NUM
ejpam-3377	299	75	)	)	PUNCT
ejpam-3377	299	76	8.0457(−8	8.0457(−8	NUM
ejpam-3377	299	77	)	)	PUNCT
ejpam-3377	299	78	8.9945(−9	8.9945(−9	NUM
ejpam-3377	299	79	)	)	PUNCT
ejpam-3377	299	80	(	(	PUNCT
ejpam-3377	299	81	1.5	1.5	NUM
ejpam-3377	299	82	,	,	PUNCT
ejpam-3377	299	83	1.5	1.5	NUM
ejpam-3377	299	84	)	)	PUNCT
ejpam-3377	299	85	9.0145(−7	9.0145(−7	NUM
ejpam-3377	299	86	)	)	PUNCT
ejpam-3377	299	87	9.1081(−7	9.1081(−7	NUM
ejpam-3377	299	88	)	)	PUNCT
ejpam-3377	299	89	7.9520(−8	7.9520(−8	NOUN
ejpam-3377	299	90	)	)	PUNCT
ejpam-3377	299	91	(	(	PUNCT
ejpam-3377	299	92	2	2	NUM
ejpam-3377	299	93	,	,	PUNCT
ejpam-3377	299	94	2	2	NUM
ejpam-3377	299	95	)	)	PUNCT
ejpam-3377	299	96	9.9019(−10	9.9019(−10	NUM
ejpam-3377	299	97	)	)	PUNCT
ejpam-3377	299	98	9.7035(−9	9.7035(−9	NUM
ejpam-3377	299	99	)	)	PUNCT
ejpam-3377	299	100	1.9901(−10	1.9901(−10	NUM
ejpam-3377	299	101	)	)	PUNCT
ejpam-3377	299	102	table	table	NOUN
ejpam-3377	299	103	4	4	NUM
ejpam-3377	299	104	:	:	PUNCT
ejpam-3377	299	105	absolute	absolute	ADJ
ejpam-3377	299	106	error	error	NOUN
ejpam-3377	299	107	in	in	ADP
ejpam-3377	299	108	w(x	w(x	PROPN
ejpam-3377	299	109	,	,	PUNCT
ejpam-3377	299	110	y	y	NOUN
ejpam-3377	299	111	)	)	PUNCT
ejpam-3377	299	112	of	of	ADP
ejpam-3377	299	113	example	example	NOUN
ejpam-3377	299	114	3	3	NUM
ejpam-3377	299	115	at	at	ADP
ejpam-3377	299	116	various	various	ADJ
ejpam-3377	299	117	values	value	NOUN
ejpam-3377	299	118	of	of	ADP
ejpam-3377	299	119	n	n	PROPN
ejpam-3377	299	120	and	and	CCONJ
ejpam-3377	299	121	α	α	NOUN
ejpam-3377	299	122	.	.	PROPN
ejpam-3377	300	1	6	6	NUM
ejpam-3377	300	2	.	.	X
ejpam-3377	300	3	comparison	comparison	NOUN
ejpam-3377	300	4	of	of	ADP
ejpam-3377	300	5	the	the	DET
ejpam-3377	300	6	proposed	propose	VERB
ejpam-3377	300	7	method	method	NOUN
ejpam-3377	300	8	with	with	ADP
ejpam-3377	300	9	some	some	DET
ejpam-3377	300	10	already	already	ADV
ejpam-3377	300	11	existing	exist	VERB
ejpam-3377	300	12	haar	haar	PROPN
ejpam-3377	300	13	wavelet	wavelet	NOUN
ejpam-3377	300	14	method	method	NOUN
ejpam-3377	300	15	the	the	DET
ejpam-3377	300	16	shifted	shift	VERB
ejpam-3377	300	17	legendre	legendre	PROPN
ejpam-3377	300	18	polynomials	polynomial	NOUN
ejpam-3377	300	19	are	be	AUX
ejpam-3377	300	20	the	the	DET
ejpam-3377	300	21	special	special	ADJ
ejpam-3377	300	22	case	case	NOUN
ejpam-3377	300	23	of	of	ADP
ejpam-3377	300	24	shifted	shift	VERB
ejpam-3377	300	25	jacobi	jacobi	PROPN
ejpam-3377	300	26	polynomials	polynomial	NOUN
ejpam-3377	300	27	and	and	CCONJ
ejpam-3377	300	28	they	they	PRON
ejpam-3377	300	29	can	can	AUX
ejpam-3377	300	30	be	be	AUX
ejpam-3377	300	31	obtained	obtain	VERB
ejpam-3377	300	32	by	by	ADP
ejpam-3377	300	33	p	p	NOUN
ejpam-3377	300	34	=	=	NOUN
ejpam-3377	300	35	q	q	NOUN
ejpam-3377	300	36	=	=	SYM
ejpam-3377	300	37	0	0	NUM
ejpam-3377	300	38	,	,	PUNCT
ejpam-3377	300	39	δ	δ	X
ejpam-3377	300	40	=	=	NOUN
ejpam-3377	300	41	1	1	NUM
ejpam-3377	300	42	in	in	ADP
ejpam-3377	300	43	the	the	DET
ejpam-3377	300	44	relation	relation	NOUN
ejpam-3377	300	45	(	(	PUNCT
ejpam-3377	300	46	2	2	NUM
ejpam-3377	300	47	)	)	PUNCT
ejpam-3377	300	48	.	.	PUNCT
ejpam-3377	301	1	we	we	PRON
ejpam-3377	301	2	compared	compare	VERB
ejpam-3377	301	3	our	our	PRON
ejpam-3377	301	4	technique	technique	NOUN
ejpam-3377	301	5	with	with	ADP
ejpam-3377	301	6	the	the	DET
ejpam-3377	301	7	existing	exist	VERB
ejpam-3377	301	8	methods	method	NOUN
ejpam-3377	301	9	available	available	ADJ
ejpam-3377	301	10	in	in	ADP
ejpam-3377	301	11	[	[	X
ejpam-3377	301	12	39	39	NUM
ejpam-3377	301	13	]	]	PUNCT
ejpam-3377	301	14	,	,	PUNCT
ejpam-3377	301	15	where	where	SCONJ
ejpam-3377	301	16	the	the	DET
ejpam-3377	301	17	authors	author	NOUN
ejpam-3377	301	18	constructed	construct	VERB
ejpam-3377	301	19	the	the	DET
ejpam-3377	301	20	procedure	procedure	NOUN
ejpam-3377	301	21	by	by	ADP
ejpam-3377	301	22	discretizing	discretize	VERB
ejpam-3377	301	23	the	the	DET
ejpam-3377	301	24	data	datum	NOUN
ejpam-3377	301	25	and	and	CCONJ
ejpam-3377	301	26	using	use	VERB
ejpam-3377	301	27	the	the	DET
ejpam-3377	301	28	haar	haar	PROPN
ejpam-3377	301	29	wavelet	wavelet	NOUN
ejpam-3377	301	30	method	method	NOUN
ejpam-3377	301	31	,	,	PUNCT
ejpam-3377	301	32	which	which	PRON
ejpam-3377	301	33	need	need	VERB
ejpam-3377	301	34	extra	extra	ADJ
ejpam-3377	301	35	memory	memory	NOUN
ejpam-3377	301	36	to	to	PART
ejpam-3377	301	37	obtained	obtain	VERB
ejpam-3377	301	38	the	the	DET
ejpam-3377	301	39	operational	operational	ADJ
ejpam-3377	301	40	matrices	matrix	NOUN
ejpam-3377	301	41	of	of	ADP
ejpam-3377	301	42	fractional	fractional	ADJ
ejpam-3377	301	43	derivative	derivative	NOUN
ejpam-3377	301	44	and	and	CCONJ
ejpam-3377	301	45	integration	integration	NOUN
ejpam-3377	301	46	because	because	SCONJ
ejpam-3377	301	47	data	datum	NOUN
ejpam-3377	301	48	need	need	VERB
ejpam-3377	301	49	discretization	discretization	NOUN
ejpam-3377	301	50	and	and	CCONJ
ejpam-3377	301	51	collocation	collocation	NOUN
ejpam-3377	301	52	.	.	PUNCT
ejpam-3377	302	1	while	while	SCONJ
ejpam-3377	302	2	in	in	ADP
ejpam-3377	302	3	our	our	PRON
ejpam-3377	302	4	prosed	prosed	ADJ
ejpam-3377	302	5	method	method	NOUN
ejpam-3377	302	6	,	,	PUNCT
ejpam-3377	302	7	we	we	PRON
ejpam-3377	302	8	have	have	AUX
ejpam-3377	302	9	obtained	obtain	VERB
ejpam-3377	302	10	the	the	DET
ejpam-3377	302	11	operational	operational	ADJ
ejpam-3377	302	12	matrices	matrix	NOUN
ejpam-3377	302	13	without	without	ADP
ejpam-3377	302	14	discretization	discretization	NOUN
ejpam-3377	302	15	of	of	ADP
ejpam-3377	302	16	data	datum	NOUN
ejpam-3377	302	17	and	and	CCONJ
ejpam-3377	302	18	using	use	VERB
ejpam-3377	302	19	any	any	DET
ejpam-3377	302	20	collocation	collocation	NOUN
ejpam-3377	302	21	method	method	NOUN
ejpam-3377	302	22	.	.	PUNCT
ejpam-3377	303	1	in	in	ADP
ejpam-3377	303	2	the	the	DET
ejpam-3377	303	3	following	follow	VERB
ejpam-3377	303	4	examples	example	NOUN
ejpam-3377	303	5	we	we	PRON
ejpam-3377	303	6	provide	provide	VERB
ejpam-3377	303	7	the	the	DET
ejpam-3377	303	8	comparison	comparison	NOUN
ejpam-3377	303	9	of	of	ADP
ejpam-3377	303	10	the	the	DET
ejpam-3377	303	11	proposed	propose	VERB
ejpam-3377	303	12	method	method	NOUN
ejpam-3377	303	13	with	with	ADP
ejpam-3377	303	14	the	the	DET
ejpam-3377	303	15	existing	exist	VERB
ejpam-3377	303	16	some	some	DET
ejpam-3377	303	17	methods	method	NOUN
ejpam-3377	303	18	.	.	PUNCT
ejpam-3377	303	19	example	example	NOUN
ejpam-3377	303	20	4	4	NUM
ejpam-3377	303	21	.	.	PUNCT
ejpam-3377	303	22	consider	consider	VERB
ejpam-3377	303	23	the	the	DET
ejpam-3377	303	24	given	give	VERB
ejpam-3377	303	25	equation	equation	NOUN
ejpam-3377	303	26	as	as	ADP
ejpam-3377	303	27	∂αw(x	∂αw(x	PROPN
ejpam-3377	303	28	,	,	PUNCT
ejpam-3377	303	29	y	y	NOUN
ejpam-3377	303	30	)	)	PUNCT
ejpam-3377	303	31	∂xα	∂xα	PROPN
ejpam-3377	303	32	+	+	CCONJ
ejpam-3377	303	33	∂α−1w(x	∂α−1w(x	PROPN
ejpam-3377	303	34	,	,	PUNCT
ejpam-3377	303	35	y	y	NOUN
ejpam-3377	303	36	)	)	PUNCT
ejpam-3377	303	37	∂xα−1	∂xα−1	PROPN
ejpam-3377	304	1	+	+	CCONJ
ejpam-3377	304	2	w(x	w(x	PROPN
ejpam-3377	304	3	,	,	PUNCT
ejpam-3377	304	4	y	y	NOUN
ejpam-3377	304	5	)	)	PUNCT
ejpam-3377	304	6	=	=	PUNCT
ejpam-3377	305	1	∂2w(x	∂2w(x	NUM
ejpam-3377	305	2	,	,	PUNCT
ejpam-3377	305	3	y	y	PROPN
ejpam-3377	305	4	)	)	PUNCT
ejpam-3377	305	5	∂y2	∂y2	ADJ
ejpam-3377	306	1	+	+	CCONJ
ejpam-3377	306	2	[	[	PUNCT
ejpam-3377	306	3	γ(2α+	γ(2α+	NOUN
ejpam-3377	306	4	1	1	NUM
ejpam-3377	306	5	)	)	PUNCT
ejpam-3377	306	6	γ(α+	γ(α+	DET
ejpam-3377	306	7	1	1	NUM
ejpam-3377	306	8	)	)	PUNCT
ejpam-3377	306	9	(	(	PUNCT
ejpam-3377	306	10	1	1	NUM
ejpam-3377	306	11	+	+	CCONJ
ejpam-3377	306	12	x	x	SYM
ejpam-3377	306	13	α+	α+	X
ejpam-3377	306	14	x	x	SYM
ejpam-3377	306	15	)	)	PUNCT
ejpam-3377	306	16	−	−	PROPN
ejpam-3377	306	17	xα	xα	CCONJ
ejpam-3377	306	18	]	]	PUNCT
ejpam-3377	307	1	x2α	x2α	PROPN
ejpam-3377	307	2	cos(7y	cos(7y	PROPN
ejpam-3377	307	3	)	)	PUNCT
ejpam-3377	307	4	,	,	PUNCT
ejpam-3377	307	5	1	1	NUM
ejpam-3377	307	6	<	<	X
ejpam-3377	307	7	α	α	PROPN
ejpam-3377	307	8	≤	≤	NUM
ejpam-3377	307	9	2	2	NUM
ejpam-3377	307	10	,	,	PUNCT
ejpam-3377	307	11	w(0	w(0	PROPN
ejpam-3377	307	12	,	,	PUNCT
ejpam-3377	307	13	y	y	PROPN
ejpam-3377	307	14	)	)	PUNCT
ejpam-3377	307	15	=	=	SYM
ejpam-3377	307	16	0	0	NUM
ejpam-3377	307	17	,	,	PUNCT
ejpam-3377	307	18	wx(0	wx(0	PROPN
ejpam-3377	307	19	,	,	PUNCT
ejpam-3377	307	20	y	y	PROPN
ejpam-3377	307	21	)	)	PUNCT
ejpam-3377	307	22	=	=	SYM
ejpam-3377	307	23	0	0	NUM
ejpam-3377	307	24	,	,	PUNCT
ejpam-3377	307	25	w(0	w(0	PROPN
ejpam-3377	307	26	,	,	PUNCT
ejpam-3377	307	27	x	x	NOUN
ejpam-3377	307	28	)	)	PUNCT
ejpam-3377	307	29	=	=	SYM
ejpam-3377	307	30	x2α	x2α	PROPN
ejpam-3377	307	31	,	,	PUNCT
ejpam-3377	307	32	w(1	w(1	X
ejpam-3377	307	33	,	,	PUNCT
ejpam-3377	307	34	x	x	NOUN
ejpam-3377	307	35	)	)	PUNCT
ejpam-3377	307	36	=	=	SYM
ejpam-3377	307	37	0.7539022x2α	0.7539022x2α	NUM
ejpam-3377	307	38	.	.	PUNCT
ejpam-3377	308	1	(	(	PUNCT
ejpam-3377	308	2	40	40	NUM
ejpam-3377	308	3	)	)	PUNCT
ejpam-3377	308	4	the	the	DET
ejpam-3377	308	5	exact	exact	ADJ
ejpam-3377	308	6	solution	solution	NOUN
ejpam-3377	308	7	of	of	ADP
ejpam-3377	308	8	the	the	DET
ejpam-3377	308	9	problem	problem	NOUN
ejpam-3377	308	10	(	(	PUNCT
ejpam-3377	308	11	40	40	NUM
ejpam-3377	308	12	)	)	PUNCT
ejpam-3377	308	13	is	be	AUX
ejpam-3377	308	14	w(x	w(x	PROPN
ejpam-3377	308	15	,	,	PUNCT
ejpam-3377	308	16	y	y	NOUN
ejpam-3377	308	17	)	)	PUNCT
ejpam-3377	308	18	=	=	SYM
ejpam-3377	308	19	x2α	x2α	PROPN
ejpam-3377	308	20	cos(7y	cos(7y	PROPN
ejpam-3377	308	21	)	)	PUNCT
ejpam-3377	308	22	.	.	PUNCT
ejpam-3377	309	1	m.i	m.i	PROPN
ejpam-3377	309	2	.	.	PROPN
ejpam-3377	309	3	chohan	chohan	PROPN
ejpam-3377	309	4	,	,	PUNCT
ejpam-3377	309	5	k.shah	k.shah	PROPN
ejpam-3377	309	6	/	/	SYM
ejpam-3377	309	7	eur	eur	PROPN
ejpam-3377	309	8	.	.	PUNCT
ejpam-3377	310	1	j.	j.	PROPN
ejpam-3377	310	2	pure	pure	PROPN
ejpam-3377	310	3	appl	appl	PROPN
ejpam-3377	310	4	.	.	PROPN
ejpam-3377	310	5	math	math	PROPN
ejpam-3377	310	6	,	,	PUNCT
ejpam-3377	310	7	12	12	NUM
ejpam-3377	310	8	(	(	PUNCT
ejpam-3377	310	9	1	1	NUM
ejpam-3377	310	10	)	)	PUNCT
ejpam-3377	310	11	(	(	PUNCT
ejpam-3377	310	12	2019	2019	NUM
ejpam-3377	310	13	)	)	PUNCT
ejpam-3377	310	14	,	,	PUNCT
ejpam-3377	310	15	39	39	NUM
ejpam-3377	310	16	-	-	SYM
ejpam-3377	310	17	57	57	NUM
ejpam-3377	310	18	52	52	NUM
ejpam-3377	310	19	comparison	comparison	NOUN
ejpam-3377	310	20	between	between	ADP
ejpam-3377	310	21	our	our	PRON
ejpam-3377	310	22	proposed	propose	VERB
ejpam-3377	310	23	method	method	NOUN
ejpam-3377	310	24	and	and	CCONJ
ejpam-3377	310	25	that	that	SCONJ
ejpam-3377	310	26	given	give	VERB
ejpam-3377	310	27	in	in	ADP
ejpam-3377	310	28	[	[	X
ejpam-3377	310	29	39	39	NUM
ejpam-3377	310	30	]	]	PUNCT
ejpam-3377	310	31	(	(	PUNCT
ejpam-3377	310	32	x	x	X
ejpam-3377	310	33	,	,	PUNCT
ejpam-3377	310	34	y	y	PROPN
ejpam-3377	310	35	)	)	PUNCT
ejpam-3377	310	36	α	α	PRON
ejpam-3377	310	37	l∞	l∞	NOUN
ejpam-3377	310	38	of	of	ADP
ejpam-3377	310	39	proposed	propose	VERB
ejpam-3377	310	40	method	method	NOUN
ejpam-3377	310	41	l∞	l∞	PROPN
ejpam-3377	310	42	of	of	ADP
ejpam-3377	310	43	haar	haar	PROPN
ejpam-3377	310	44	wavelet	wavelet	NOUN
ejpam-3377	310	45	method	method	NOUN
ejpam-3377	310	46	(	(	PUNCT
ejpam-3377	310	47	0.5	0.5	NUM
ejpam-3377	310	48	,	,	PUNCT
ejpam-3377	310	49	0.5	0.5	NUM
ejpam-3377	310	50	)	)	PUNCT
ejpam-3377	310	51	1.30	1.30	NUM
ejpam-3377	310	52	2.0025(−04	2.0025(−04	NOUN
ejpam-3377	310	53	)	)	PUNCT
ejpam-3377	310	54	1.8000(−03	1.8000(−03	PROPN
ejpam-3377	310	55	)	)	PUNCT
ejpam-3377	310	56	1.50	1.50	NUM
ejpam-3377	310	57	8.2455(−05	8.2455(−05	NOUN
ejpam-3377	310	58	)	)	PUNCT
ejpam-3377	310	59	7.0638(−04	7.0638(−04	NOUN
ejpam-3377	310	60	)	)	PUNCT
ejpam-3377	310	61	1.75	1.75	NUM
ejpam-3377	310	62	7.0003(−06	7.0003(−06	NOUN
ejpam-3377	310	63	)	)	PUNCT
ejpam-3377	310	64	8.8126(−05	8.8126(−05	NOUN
ejpam-3377	310	65	)	)	PUNCT
ejpam-3377	310	66	1.85	1.85	NUM
ejpam-3377	310	67	1.1936(−06	1.1936(−06	NUM
ejpam-3377	310	68	)	)	PUNCT
ejpam-3377	310	69	9.1234(−06	9.1234(−06	NOUN
ejpam-3377	310	70	)	)	PUNCT
ejpam-3377	310	71	1.95	1.95	NUM
ejpam-3377	310	72	3.9141(−07	3.9141(−07	NUM
ejpam-3377	310	73	)	)	PUNCT
ejpam-3377	310	74	9.2087(−07	9.2087(−07	NUM
ejpam-3377	310	75	)	)	PUNCT
ejpam-3377	310	76	2.00	2.00	NUM
ejpam-3377	310	77	1.0001(−12	1.0001(−12	NUM
ejpam-3377	310	78	)	)	PUNCT
ejpam-3377	310	79	2.0012(−10	2.0012(−10	NUM
ejpam-3377	310	80	)	)	PUNCT
ejpam-3377	310	81	table	table	NOUN
ejpam-3377	310	82	5	5	NUM
ejpam-3377	310	83	:	:	PUNCT
ejpam-3377	310	84	comparison	comparison	NOUN
ejpam-3377	310	85	of	of	ADP
ejpam-3377	310	86	the	the	DET
ejpam-3377	310	87	absolute	absolute	ADJ
ejpam-3377	310	88	errors	error	NOUN
ejpam-3377	310	89	for	for	ADP
ejpam-3377	310	90	the	the	DET
ejpam-3377	310	91	solution	solution	NOUN
ejpam-3377	310	92	w(x	w(x	PROPN
ejpam-3377	310	93	,	,	PUNCT
ejpam-3377	310	94	y	y	NOUN
ejpam-3377	310	95	)	)	PUNCT
ejpam-3377	310	96	of	of	ADP
ejpam-3377	310	97	example	example	NOUN
ejpam-3377	310	98	4	4	NUM
ejpam-3377	310	99	at	at	ADP
ejpam-3377	310	100	various	various	ADJ
ejpam-3377	310	101	values	value	NOUN
ejpam-3377	310	102	of	of	ADP
ejpam-3377	310	103	α	α	PROPN
ejpam-3377	310	104	and	and	CCONJ
ejpam-3377	310	105	n	n	CCONJ
ejpam-3377	310	106	=	=	NOUN
ejpam-3377	310	107	10	10	NUM
ejpam-3377	310	108	.	.	PUNCT
ejpam-3377	311	1	y	y	NOUN
ejpam-3377	311	2	x	x	SYM
ejpam-3377	311	3	1	1	NUM
ejpam-3377	311	4	0.8	0.8	NUM
ejpam-3377	311	5	10.6	10.6	NUM
ejpam-3377	311	6	0.8	0.8	NUM
ejpam-3377	311	7	0.4	0.4	NUM
ejpam-3377	311	8	0.6	0.6	NUM
ejpam-3377	311	9	-0.5	-0.5	NOUN
ejpam-3377	311	10	0.40.2	0.40.2	NUM
ejpam-3377	311	11	0.2	0.2	NUM
ejpam-3377	311	12	0	0	NUM
ejpam-3377	311	13	0	0	NUM
ejpam-3377	311	14	0	0	NUM
ejpam-3377	312	1	w	w	NOUN
ejpam-3377	312	2	(	(	PUNCT
ejpam-3377	312	3	x	x	INTJ
ejpam-3377	312	4	,	,	PUNCT
ejpam-3377	312	5	y	y	PROPN
ejpam-3377	312	6	)	)	PUNCT
ejpam-3377	312	7	(	(	PUNCT
ejpam-3377	312	8	a	a	X
ejpam-3377	312	9	)	)	PUNCT
ejpam-3377	312	10	0.5	0.5	NUM
ejpam-3377	312	11	1	1	NUM
ejpam-3377	312	12	approximate	approximate	ADJ
ejpam-3377	312	13	solution	solution	NOUN
ejpam-3377	312	14	at	at	ADP
ejpam-3377	312	15	n=6	n=6	NOUN
ejpam-3377	312	16	exact	exact	ADJ
ejpam-3377	312	17	solution	solution	NOUN
ejpam-3377	312	18	‖w	‖w	VERB
ejpam-3377	312	19	a	a	DET
ejpam-3377	312	20	p	p	X
ejpam-3377	312	21	p	p	NOUN
ejpam-3377	312	22	−	−	PROPN
ejpam-3377	312	23	w	w	NOUN
ejpam-3377	312	24	e	e	NOUN
ejpam-3377	312	25	x	x	PUNCT
ejpam-3377	312	26	‖	‖	PROPN
ejpam-3377	312	27	∞	∞	PROPN
ejpam-3377	312	28	x	x	SYM
ejpam-3377	312	29	y	y	PROPN
ejpam-3377	312	30	1	1	NUM
ejpam-3377	312	31	-1	-1	SYM
ejpam-3377	312	32	1	1	NUM
ejpam-3377	312	33	0	0	NUM
ejpam-3377	312	34	×10	×10	NOUN
ejpam-3377	312	35	-	-	SYM
ejpam-3377	312	36	8	8	NUM
ejpam-3377	312	37	0.8	0.8	NUM
ejpam-3377	312	38	(	(	PUNCT
ejpam-3377	312	39	b	b	NOUN
ejpam-3377	312	40	)	)	PUNCT
ejpam-3377	312	41	1	1	NUM
ejpam-3377	312	42	0.5	0.5	NUM
ejpam-3377	312	43	0.6	0.6	NUM
ejpam-3377	312	44	0.4	0.4	NUM
ejpam-3377	312	45	0.2	0.2	NUM
ejpam-3377	312	46	0	0	NUM
ejpam-3377	312	47	0	0	NUM
ejpam-3377	312	48	absolute	absolute	ADJ
ejpam-3377	312	49	error	error	NOUN
ejpam-3377	312	50	at	at	ADP
ejpam-3377	312	51	n=6	n=6	NOUN
ejpam-3377	312	52	figure	figure	NOUN
ejpam-3377	312	53	3	3	NUM
ejpam-3377	312	54	.	.	PUNCT
ejpam-3377	313	1	(	(	PUNCT
ejpam-3377	313	2	a	a	X
ejpam-3377	313	3	)	)	PUNCT
ejpam-3377	313	4	comparison	comparison	NOUN
ejpam-3377	313	5	between	between	ADP
ejpam-3377	313	6	exact	exact	ADJ
ejpam-3377	313	7	and	and	CCONJ
ejpam-3377	313	8	approximate	approximate	ADJ
ejpam-3377	313	9	solutions	solution	NOUN
ejpam-3377	313	10	at	at	ADP
ejpam-3377	313	11	n	n	NOUN
ejpam-3377	313	12	=	=	NUM
ejpam-3377	313	13	6	6	NUM
ejpam-3377	313	14	,	,	PUNCT
ejpam-3377	313	15	p	p	NOUN
ejpam-3377	313	16	=	=	X
ejpam-3377	313	17	q	q	NOUN
ejpam-3377	314	1	=	=	SYM
ejpam-3377	314	2	0	0	NUM
ejpam-3377	314	3	,	,	PUNCT
ejpam-3377	314	4	α	α	NOUN
ejpam-3377	314	5	=	=	SYM
ejpam-3377	314	6	1.9	1.9	NUM
ejpam-3377	314	7	,	,	PUNCT
ejpam-3377	314	8	for	for	ADP
ejpam-3377	314	9	example	example	NOUN
ejpam-3377	314	10	4	4	NUM
ejpam-3377	314	11	.	.	PUNCT
ejpam-3377	314	12	(	(	PUNCT
ejpam-3377	314	13	b	b	X
ejpam-3377	314	14	)	)	PUNCT
ejpam-3377	314	15	absolute	absolute	ADJ
ejpam-3377	314	16	error	error	NOUN
ejpam-3377	314	17	at	at	ADP
ejpam-3377	314	18	n	n	NOUN
ejpam-3377	314	19	=	=	SYM
ejpam-3377	314	20	6	6	NUM
ejpam-3377	314	21	,	,	PUNCT
ejpam-3377	314	22	p	p	NOUN
ejpam-3377	314	23	=	=	X
ejpam-3377	314	24	q	q	NOUN
ejpam-3377	314	25	=	=	SYM
ejpam-3377	314	26	0	0	NUM
ejpam-3377	314	27	,	,	PUNCT
ejpam-3377	314	28	α	α	NOUN
ejpam-3377	314	29	=	=	SYM
ejpam-3377	314	30	1.9	1.9	NUM
ejpam-3377	314	31	,	,	PUNCT
ejpam-3377	314	32	for	for	ADP
ejpam-3377	314	33	example	example	NOUN
ejpam-3377	314	34	4	4	NUM
ejpam-3377	314	35	similarly	similarly	ADV
ejpam-3377	314	36	,	,	PUNCT
ejpam-3377	314	37	we	we	PRON
ejpam-3377	314	38	can	can	AUX
ejpam-3377	314	39	also	also	ADV
ejpam-3377	314	40	bring	bring	VERB
ejpam-3377	314	41	out	out	ADP
ejpam-3377	314	42	comparison	comparison	NOUN
ejpam-3377	314	43	for	for	ADP
ejpam-3377	314	44	other	other	ADJ
ejpam-3377	314	45	problems	problem	NOUN
ejpam-3377	314	46	of	of	ADP
ejpam-3377	314	47	fdes	fde	NOUN
ejpam-3377	314	48	and	and	CCONJ
ejpam-3377	314	49	fpdes	fpde	NOUN
ejpam-3377	314	50	.	.	PUNCT
ejpam-3377	315	1	from	from	ADP
ejpam-3377	315	2	the	the	DET
ejpam-3377	315	3	table	table	NOUN
ejpam-3377	315	4	5	5	NUM
ejpam-3377	315	5	,	,	PUNCT
ejpam-3377	315	6	it	it	PRON
ejpam-3377	315	7	is	be	AUX
ejpam-3377	315	8	clear	clear	ADJ
ejpam-3377	315	9	that	that	SCONJ
ejpam-3377	315	10	the	the	DET
ejpam-3377	315	11	proposed	propose	VERB
ejpam-3377	315	12	method	method	NOUN
ejpam-3377	315	13	provides	provide	VERB
ejpam-3377	315	14	powerful	powerful	ADJ
ejpam-3377	315	15	tools	tool	NOUN
ejpam-3377	315	16	to	to	PART
ejpam-3377	315	17	obtain	obtain	VERB
ejpam-3377	315	18	approximate	approximate	ADJ
ejpam-3377	315	19	solutions	solution	NOUN
ejpam-3377	315	20	which	which	PRON
ejpam-3377	315	21	is	be	AUX
ejpam-3377	315	22	closely	closely	ADV
ejpam-3377	315	23	related	relate	VERB
ejpam-3377	315	24	with	with	ADP
ejpam-3377	315	25	the	the	DET
ejpam-3377	315	26	exact	exact	ADJ
ejpam-3377	315	27	solution	solution	NOUN
ejpam-3377	315	28	of	of	ADP
ejpam-3377	315	29	the	the	DET
ejpam-3377	315	30	problem	problem	NOUN
ejpam-3377	315	31	.	.	PUNCT
ejpam-3377	316	1	conclusion	conclusion	NOUN
ejpam-3377	316	2	in	in	ADP
ejpam-3377	316	3	this	this	DET
ejpam-3377	316	4	study	study	NOUN
ejpam-3377	316	5	,	,	PUNCT
ejpam-3377	316	6	we	we	PRON
ejpam-3377	316	7	have	have	AUX
ejpam-3377	316	8	successfully	successfully	ADV
ejpam-3377	316	9	applied	apply	VERB
ejpam-3377	316	10	the	the	DET
ejpam-3377	316	11	operational	operational	ADJ
ejpam-3377	316	12	matrices	matrix	NOUN
ejpam-3377	316	13	methods	method	NOUN
ejpam-3377	316	14	of	of	ADP
ejpam-3377	316	15	shifted	shift	VERB
ejpam-3377	316	16	jacobi	jacobi	PROPN
ejpam-3377	316	17	polynomials	polynomial	NOUN
ejpam-3377	316	18	to	to	ADP
ejpam-3377	316	19	various	various	ADJ
ejpam-3377	316	20	classes	class	NOUN
ejpam-3377	316	21	of	of	ADP
ejpam-3377	316	22	fpdes	fpde	NOUN
ejpam-3377	316	23	in	in	ADP
ejpam-3377	316	24	two	two	NUM
ejpam-3377	316	25	dimensions	dimension	NOUN
ejpam-3377	316	26	.	.	PUNCT
ejpam-3377	317	1	thank	thank	VERB
ejpam-3377	317	2	to	to	ADP
ejpam-3377	317	3	these	these	DET
ejpam-3377	317	4	matrices	matrix	NOUN
ejpam-3377	317	5	,	,	PUNCT
ejpam-3377	317	6	the	the	DET
ejpam-3377	317	7	concerned	concerned	ADJ
ejpam-3377	317	8	fpde	fpde	NOUN
ejpam-3377	317	9	is	be	AUX
ejpam-3377	317	10	converted	convert	VERB
ejpam-3377	317	11	to	to	ADP
ejpam-3377	317	12	a	a	DET
ejpam-3377	317	13	simple	simple	ADJ
ejpam-3377	317	14	algebraic	algebraic	ADJ
ejpam-3377	317	15	equations	equation	NOUN
ejpam-3377	317	16	which	which	PRON
ejpam-3377	317	17	is	be	AUX
ejpam-3377	317	18	further	far	ADV
ejpam-3377	317	19	solved	solve	VERB
ejpam-3377	317	20	for	for	ADP
ejpam-3377	317	21	coefficient	coefficient	NOUN
ejpam-3377	317	22	matrix	matrix	NOUN
ejpam-3377	317	23	needed	need	VERB
ejpam-3377	317	24	in	in	ADP
ejpam-3377	317	25	the	the	DET
ejpam-3377	317	26	approximate	approximate	ADJ
ejpam-3377	317	27	solutions	solution	NOUN
ejpam-3377	317	28	of	of	ADP
ejpam-3377	317	29	the	the	DET
ejpam-3377	317	30	considered	consider	VERB
ejpam-3377	317	31	equation	equation	NOUN
ejpam-3377	317	32	.	.	PUNCT
ejpam-3377	318	1	the	the	DET
ejpam-3377	318	2	method	method	NOUN
ejpam-3377	318	3	provides	provide	VERB
ejpam-3377	318	4	an	an	DET
ejpam-3377	318	5	excellent	excellent	ADJ
ejpam-3377	318	6	agreement	agreement	NOUN
ejpam-3377	318	7	to	to	ADP
ejpam-3377	318	8	the	the	DET
ejpam-3377	318	9	exact	exact	ADJ
ejpam-3377	318	10	solutions	solution	NOUN
ejpam-3377	318	11	a	a	DET
ejpam-3377	318	12	very	very	ADV
ejpam-3377	318	13	small	small	ADJ
ejpam-3377	318	14	scale	scale	NOUN
ejpam-3377	318	15	level	level	NOUN
ejpam-3377	318	16	.	.	PUNCT
ejpam-3377	319	1	the	the	DET
ejpam-3377	319	2	important	important	ADJ
ejpam-3377	319	3	point	point	NOUN
ejpam-3377	319	4	in	in	ADP
ejpam-3377	319	5	the	the	DET
ejpam-3377	319	6	method	method	NOUN
ejpam-3377	319	7	proposed	propose	VERB
ejpam-3377	319	8	in	in	ADP
ejpam-3377	319	9	this	this	DET
ejpam-3377	319	10	study	study	NOUN
ejpam-3377	319	11	need	need	VERB
ejpam-3377	319	12	no	no	DET
ejpam-3377	319	13	extra	extra	ADJ
ejpam-3377	319	14	parameter	parameter	NOUN
ejpam-3377	319	15	like	like	ADP
ejpam-3377	319	16	perturbation	perturbation	NOUN
ejpam-3377	319	17	method	method	NOUN
ejpam-3377	319	18	neither	neither	CCONJ
ejpam-3377	319	19	required	required	ADJ
ejpam-3377	319	20	discretization	discretization	NOUN
ejpam-3377	319	21	of	of	ADP
ejpam-3377	319	22	the	the	DET
ejpam-3377	319	23	data	datum	NOUN
ejpam-3377	319	24	which	which	PRON
ejpam-3377	319	25	need	need	VERB
ejpam-3377	319	26	extra	extra	ADJ
ejpam-3377	319	27	references	reference	NOUN
ejpam-3377	319	28	53	53	NUM
ejpam-3377	319	29	memory	memory	NOUN
ejpam-3377	319	30	and	and	CCONJ
ejpam-3377	319	31	waste	waste	NOUN
ejpam-3377	319	32	of	of	ADP
ejpam-3377	319	33	time	time	NOUN
ejpam-3377	319	34	and	and	CCONJ
ejpam-3377	319	35	suffers	suffer	VERB
ejpam-3377	319	36	from	from	ADP
ejpam-3377	319	37	computational	computational	ADJ
ejpam-3377	319	38	complexity	complexity	NOUN
ejpam-3377	319	39	some	some	DET
ejpam-3377	319	40	times	time	NOUN
ejpam-3377	319	41	.	.	PUNCT
ejpam-3377	320	1	all	all	DET
ejpam-3377	320	2	these	these	PRON
ejpam-3377	320	3	mentioned	mention	VERB
ejpam-3377	320	4	things	thing	NOUN
ejpam-3377	320	5	are	be	AUX
ejpam-3377	320	6	avoided	avoid	VERB
ejpam-3377	320	7	in	in	ADP
ejpam-3377	320	8	this	this	DET
ejpam-3377	320	9	method	method	NOUN
ejpam-3377	320	10	and	and	CCONJ
ejpam-3377	320	11	a	a	DET
ejpam-3377	320	12	direct	direct	ADJ
ejpam-3377	320	13	computational	computational	ADJ
ejpam-3377	320	14	procedure	procedure	NOUN
ejpam-3377	320	15	has	have	AUX
ejpam-3377	320	16	been	be	AUX
ejpam-3377	320	17	adopted	adopt	VERB
ejpam-3377	320	18	.	.	PUNCT
ejpam-3377	321	1	in	in	ADP
ejpam-3377	321	2	future	future	ADJ
ejpam-3377	321	3	this	this	DET
ejpam-3377	321	4	method	method	NOUN
ejpam-3377	321	5	,	,	PUNCT
ejpam-3377	321	6	we	we	PRON
ejpam-3377	321	7	can	can	AUX
ejpam-3377	321	8	easily	easily	ADV
ejpam-3377	321	9	extended	extend	VERB
ejpam-3377	321	10	to	to	ADP
ejpam-3377	321	11	nonlinear	nonlinear	ADJ
ejpam-3377	321	12	fpdes	fpde	NOUN
ejpam-3377	321	13	.	.	PUNCT
ejpam-3377	322	1	acknowledgements	acknowledgement	NOUN
ejpam-3377	322	2	we	we	PRON
ejpam-3377	322	3	are	be	AUX
ejpam-3377	322	4	very	very	ADV
ejpam-3377	322	5	thankful	thankful	ADJ
ejpam-3377	322	6	to	to	ADP
ejpam-3377	322	7	the	the	DET
ejpam-3377	322	8	reviewers	reviewer	NOUN
ejpam-3377	322	9	for	for	ADP
ejpam-3377	322	10	their	their	PRON
ejpam-3377	322	11	useful	useful	ADJ
ejpam-3377	322	12	suggestions	suggestion	NOUN
ejpam-3377	322	13	/	/	SYM
ejpam-3377	322	14	corrections	correction	NOUN
ejpam-3377	322	15	which	which	PRON
ejpam-3377	322	16	improved	improve	VERB
ejpam-3377	322	17	this	this	DET
ejpam-3377	322	18	manuscript	manuscript	NOUN
ejpam-3377	322	19	very	very	ADV
ejpam-3377	322	20	well	well	ADV
ejpam-3377	322	21	.	.	PUNCT
ejpam-3377	323	1	references	reference	NOUN
ejpam-3377	323	2	[	[	X
ejpam-3377	323	3	1	1	X
ejpam-3377	323	4	]	]	PUNCT
ejpam-3377	323	5	i	i	PRON
ejpam-3377	323	6	aksikas	aksikas	PROPN
ejpam-3377	323	7	,	,	PUNCT
ejpam-3377	323	8	a	a	DET
ejpam-3377	323	9	fuxman	fuxman	NOUN
ejpam-3377	323	10	,	,	PUNCT
ejpam-3377	323	11	j	j	PROPN
ejpam-3377	323	12	f	f	PROPN
ejpam-3377	323	13	forbes	forbes	PROPN
ejpam-3377	323	14	,	,	PUNCT
ejpam-3377	323	15	j	j	PROPN
ejpam-3377	323	16	winkin	winkin	PROPN
ejpam-3377	323	17	.	.	PUNCT
ejpam-3377	324	1	lq	lq	NOUN
ejpam-3377	324	2	control	control	NOUN
ejpam-3377	324	3	design	design	NOUN
ejpam-3377	324	4	of	of	ADP
ejpam-3377	324	5	a	a	DET
ejpam-3377	324	6	class	class	NOUN
ejpam-3377	324	7	of	of	ADP
ejpam-3377	324	8	hyperbolic	hyperbolic	ADJ
ejpam-3377	324	9	pde	pde	NOUN
ejpam-3377	324	10	systems	system	NOUN
ejpam-3377	324	11	:	:	PUNCT
ejpam-3377	324	12	application	application	NOUN
ejpam-3377	324	13	to	to	ADP
ejpam-3377	324	14	fixed	fix	VERB
ejpam-3377	324	15	-	-	PUNCT
ejpam-3377	324	16	bed	bed	NOUN
ejpam-3377	324	17	reactor	reactor	NOUN
ejpam-3377	324	18	.	.	PUNCT
ejpam-3377	325	1	automatica	automatica	PROPN
ejpam-3377	325	2	,	,	PUNCT
ejpam-3377	325	3	45	45	NUM
ejpam-3377	325	4	:	:	SYM
ejpam-3377	325	5	1542–1548	1542–1548	NUM
ejpam-3377	325	6	,	,	PUNCT
ejpam-3377	325	7	2012	2012	NUM
ejpam-3377	325	8	.	.	PUNCT
ejpam-3377	326	1	[	[	X
ejpam-3377	326	2	2	2	NUM
ejpam-3377	326	3	]	]	X
ejpam-3377	326	4	e	e	X
ejpam-3377	326	5	abuteen	abuteen	ADV
ejpam-3377	326	6	,	,	PUNCT
ejpam-3377	326	7	a	a	DET
ejpam-3377	326	8	freihat	freihat	NOUN
ejpam-3377	326	9	,	,	PUNCT
ejpam-3377	326	10	m	m	PROPN
ejpam-3377	326	11	al	al	PROPN
ejpam-3377	326	12	-	-	PUNCT
ejpam-3377	326	13	smadi	smadi	NOUN
ejpam-3377	326	14	,	,	PUNCT
ejpam-3377	326	15	h	h	PROPN
ejpam-3377	326	16	khalil	khalil	PROPN
ejpam-3377	326	17	,	,	PUNCT
ejpam-3377	326	18	r	r	PROPN
ejpam-3377	326	19	a	a	DET
ejpam-3377	326	20	khan	khan	PROPN
ejpam-3377	326	21	:	:	PUNCT
ejpam-3377	326	22	approximate	approximate	ADJ
ejpam-3377	326	23	series	series	NOUN
ejpam-3377	326	24	solution	solution	NOUN
ejpam-3377	326	25	of	of	ADP
ejpam-3377	326	26	nonlinear	nonlinear	ADJ
ejpam-3377	326	27	,	,	PUNCT
ejpam-3377	326	28	fractional	fractional	PROPN
ejpam-3377	326	29	klein	klein	PROPN
ejpam-3377	326	30	-	-	PUNCT
ejpam-3377	326	31	gordon	gordon	PROPN
ejpam-3377	326	32	equations	equation	NOUN
ejpam-3377	326	33	using	use	VERB
ejpam-3377	326	34	fractional	fractional	ADJ
ejpam-3377	326	35	reduced	reduce	VERB
ejpam-3377	326	36	differential	differential	ADJ
ejpam-3377	326	37	transform	transform	NOUN
ejpam-3377	326	38	method	method	NOUN
ejpam-3377	326	39	.	.	PUNCT
ejpam-3377	327	1	journal	journal	NOUN
ejpam-3377	327	2	of	of	ADP
ejpam-3377	327	3	mathematics	mathematic	NOUN
ejpam-3377	327	4	and	and	CCONJ
ejpam-3377	327	5	statistics	statistic	NOUN
ejpam-3377	327	6	,	,	PUNCT
ejpam-3377	327	7	12(1	12(1	NUM
ejpam-3377	327	8	):	):	PUNCT
ejpam-3377	327	9	23–33	23–33	NUM
ejpam-3377	327	10	,	,	PUNCT
ejpam-3377	327	11	2016	2016	NUM
ejpam-3377	327	12	.	.	PUNCT
ejpam-3377	328	1	[	[	X
ejpam-3377	328	2	3	3	X
ejpam-3377	328	3	]	]	X
ejpam-3377	328	4	m	m	VERB
ejpam-3377	328	5	al	al	PROPN
ejpam-3377	328	6	-	-	PUNCT
ejpam-3377	328	7	smadi	smadi	NOUN
ejpam-3377	328	8	,	,	PUNCT
ejpam-3377	328	9	a	a	DET
ejpam-3377	328	10	freihat	freihat	NOUN
ejpam-3377	328	11	,	,	PUNCT
ejpam-3377	328	12	h	h	PROPN
ejpam-3377	328	13	khalil	khalil	PROPN
ejpam-3377	328	14	,	,	PUNCT
ejpam-3377	328	15	s	s	VERB
ejpam-3377	328	16	momani	momani	NOUN
ejpam-3377	328	17	,	,	PUNCT
ejpam-3377	328	18	r	r	PROPN
ejpam-3377	328	19	a	a	DET
ejpam-3377	328	20	khan	khan	PROPN
ejpam-3377	328	21	.	.	PUNCT
ejpam-3377	329	1	numerical	numerical	PROPN
ejpam-3377	329	2	multistep	multistep	PROPN
ejpam-3377	329	3	approach	approach	NOUN
ejpam-3377	329	4	for	for	ADP
ejpam-3377	329	5	solving	solve	VERB
ejpam-3377	329	6	fractional	fractional	ADJ
ejpam-3377	329	7	partial	partial	ADJ
ejpam-3377	329	8	differential	differential	NOUN
ejpam-3377	329	9	equations	equation	NOUN
ejpam-3377	329	10	.	.	PUNCT
ejpam-3377	330	1	international	international	ADJ
ejpam-3377	330	2	journal	journal	NOUN
ejpam-3377	330	3	of	of	ADP
ejpam-3377	330	4	computational	computational	ADJ
ejpam-3377	330	5	methods	method	NOUN
ejpam-3377	330	6	,	,	PUNCT
ejpam-3377	330	7	14	14	NUM
ejpam-3377	330	8	:	:	SYM
ejpam-3377	330	9	1	1	NUM
ejpam-3377	330	10	-	-	SYM
ejpam-3377	330	11	15	15	NUM
ejpam-3377	330	12	,	,	PUNCT
ejpam-3377	330	13	2017	2017	NUM
ejpam-3377	330	14	.	.	PUNCT
ejpam-3377	331	1	[	[	X
ejpam-3377	331	2	4	4	X
ejpam-3377	331	3	]	]	X
ejpam-3377	331	4	m	m	VERB
ejpam-3377	331	5	al	al	PROPN
ejpam-3377	331	6	-	-	PUNCT
ejpam-3377	331	7	smadi	smadi	NOUN
ejpam-3377	331	8	and	and	CCONJ
ejpam-3377	331	9	o	o	X
ejpam-3377	331	10	a	a	DET
ejpam-3377	331	11	arqub	arqub	NOUN
ejpam-3377	331	12	.	.	PUNCT
ejpam-3377	332	1	computational	computational	ADJ
ejpam-3377	332	2	algorithm	algorithm	NOUN
ejpam-3377	332	3	for	for	ADP
ejpam-3377	332	4	solving	solve	VERB
ejpam-3377	332	5	fredholm	fredholm	NOUN
ejpam-3377	332	6	timefractional	timefractional	ADJ
ejpam-3377	332	7	partial	partial	ADJ
ejpam-3377	332	8	integrodifferential	integrodifferential	ADJ
ejpam-3377	332	9	equations	equation	NOUN
ejpam-3377	332	10	of	of	ADP
ejpam-3377	332	11	dirichlet	dirichlet	PROPN
ejpam-3377	332	12	functions	function	NOUN
ejpam-3377	332	13	type	type	VERB
ejpam-3377	332	14	with	with	ADP
ejpam-3377	332	15	error	error	NOUN
ejpam-3377	332	16	estimates	estimate	NOUN
ejpam-3377	332	17	.	.	PUNCT
ejpam-3377	333	1	applied	apply	VERB
ejpam-3377	333	2	mathematics	mathematic	NOUN
ejpam-3377	333	3	and	and	CCONJ
ejpam-3377	333	4	computation	computation	NOUN
ejpam-3377	333	5	,	,	PUNCT
ejpam-3377	333	6	342	342	NUM
ejpam-3377	333	7	:	:	PUNCT
ejpam-3377	333	8	280–294	280–294	NUM
ejpam-3377	333	9	,	,	PUNCT
ejpam-3377	333	10	2019	2019	NUM
ejpam-3377	333	11	.	.	PUNCT
ejpam-3377	334	1	[	[	X
ejpam-3377	334	2	5	5	X
ejpam-3377	334	3	]	]	X
ejpam-3377	334	4	o	o	NOUN
ejpam-3377	334	5	a	a	DET
ejpam-3377	334	6	arqub	arqub	NOUN
ejpam-3377	334	7	and	and	CCONJ
ejpam-3377	334	8	m	m	PROPN
ejpam-3377	334	9	al	al	PROPN
ejpam-3377	334	10	-	-	PUNCT
ejpam-3377	334	11	smadi	smadi	NOUN
ejpam-3377	334	12	.	.	PUNCT
ejpam-3377	335	1	numerical	numerical	ADJ
ejpam-3377	335	2	algorithm	algorithm	NOUN
ejpam-3377	335	3	for	for	ADP
ejpam-3377	335	4	solving	solve	VERB
ejpam-3377	335	5	time	time	NOUN
ejpam-3377	335	6	-	-	PUNCT
ejpam-3377	335	7	fractional	fractional	ADJ
ejpam-3377	335	8	partial	partial	ADJ
ejpam-3377	335	9	integrodifferential	integrodifferential	ADJ
ejpam-3377	335	10	equations	equation	NOUN
ejpam-3377	335	11	subject	subject	ADJ
ejpam-3377	335	12	to	to	ADP
ejpam-3377	335	13	initial	initial	ADJ
ejpam-3377	335	14	and	and	CCONJ
ejpam-3377	335	15	dirichlet	dirichlet	PROPN
ejpam-3377	335	16	boundary	boundary	ADJ
ejpam-3377	335	17	conditions	condition	NOUN
ejpam-3377	335	18	.	.	PUNCT
ejpam-3377	336	1	num	num	ADJ
ejpam-3377	336	2	.	.	PUNCT
ejpam-3377	336	3	meth	meth	NOUN
ejpam-3377	336	4	.	.	PUNCT
ejpam-3377	337	1	partial	partial	ADJ
ejpam-3377	337	2	differential	differential	NOUN
ejpam-3377	337	3	equations	equation	NOUN
ejpam-3377	337	4	,	,	PUNCT
ejpam-3377	337	5	34(5	34(5	NUM
ejpam-3377	337	6	):	):	PUNCT
ejpam-3377	337	7	1577–1597	1577–1597	NUM
ejpam-3377	337	8	,	,	PUNCT
ejpam-3377	337	9	2018	2018	NUM
ejpam-3377	337	10	.	.	PUNCT
ejpam-3377	338	1	[	[	X
ejpam-3377	338	2	6	6	NUM
ejpam-3377	338	3	]	]	X
ejpam-3377	338	4	k	k	PROPN
ejpam-3377	338	5	b	b	PROPN
ejpam-3377	338	6	oldham	oldham	PROPN
ejpam-3377	338	7	.	.	PUNCT
ejpam-3377	339	1	fractional	fractional	ADJ
ejpam-3377	339	2	differential	differential	ADJ
ejpam-3377	339	3	equations	equation	NOUN
ejpam-3377	339	4	in	in	ADP
ejpam-3377	339	5	electrochemistry	electrochemistry	NOUN
ejpam-3377	339	6	.	.	PUNCT
ejpam-3377	340	1	adv	adv	PROPN
ejpam-3377	340	2	.	.	PUNCT
ejpam-3377	341	1	eng	eng	PROPN
ejpam-3377	341	2	.	.	PROPN
ejpam-3377	341	3	soft	soft	ADJ
ejpam-3377	341	4	,	,	PUNCT
ejpam-3377	341	5	41	41	NUM
ejpam-3377	341	6	:	:	PUNCT
ejpam-3377	341	7	9–12	9–12	NOUN
ejpam-3377	341	8	,	,	PUNCT
ejpam-3377	341	9	2010	2010	NUM
ejpam-3377	341	10	.	.	PUNCT
ejpam-3377	342	1	[	[	X
ejpam-3377	342	2	7	7	X
ejpam-3377	342	3	]	]	X
ejpam-3377	342	4	p	p	X
ejpam-3377	342	5	j	j	PROPN
ejpam-3377	342	6	caudrey	caudrey	PROPN
ejpam-3377	342	7	,	,	PUNCT
ejpam-3377	342	8	i	i	PRON
ejpam-3377	342	9	c	c	PROPN
ejpam-3377	342	10	eilbeck	eilbeck	NOUN
ejpam-3377	342	11	,	,	PUNCT
ejpam-3377	342	12	j	j	PROPN
ejpam-3377	342	13	d	d	PROPN
ejpam-3377	342	14	gibbon	gibbon	PROPN
ejpam-3377	342	15	,	,	PUNCT
ejpam-3377	342	16	the	the	DET
ejpam-3377	342	17	sine	sine	NOUN
ejpam-3377	342	18	-	-	PUNCT
ejpam-3377	342	19	gordon	gordon	PROPN
ejpam-3377	342	20	equation	equation	NOUN
ejpam-3377	342	21	as	as	ADP
ejpam-3377	342	22	a	a	DET
ejpam-3377	342	23	model	model	ADJ
ejpam-3377	342	24	classical	classical	ADJ
ejpam-3377	342	25	field	field	NOUN
ejpam-3377	342	26	theory	theory	NOUN
ejpam-3377	342	27	.	.	PUNCT
ejpam-3377	343	1	nuovo	nuovo	PROPN
ejpam-3377	343	2	cimento	cimento	PROPN
ejpam-3377	343	3	,	,	PUNCT
ejpam-3377	343	4	25:497–511	25:497–511	PROPN
ejpam-3377	343	5	,	,	PUNCT
ejpam-3377	343	6	1975	1975	NUM
ejpam-3377	343	7	.	.	PUNCT
ejpam-3377	344	1	[	[	X
ejpam-3377	344	2	8	8	NUM
ejpam-3377	344	3	]	]	SYM
ejpam-3377	344	4	m	m	VERB
ejpam-3377	344	5	deghan	deghan	ADJ
ejpam-3377	344	6	,	,	PUNCT
ejpam-3377	344	7	y	y	PROPN
ejpam-3377	344	8	a	a	DET
ejpam-3377	344	9	yousefi	yousefi	PROPN
ejpam-3377	344	10	,	,	PUNCT
ejpam-3377	344	11	a	a	DET
ejpam-3377	344	12	lotfi	lotfi	NOUN
ejpam-3377	344	13	.	.	PUNCT
ejpam-3377	345	1	the	the	DET
ejpam-3377	345	2	use	use	NOUN
ejpam-3377	345	3	of	of	ADP
ejpam-3377	345	4	he	he	PRON
ejpam-3377	345	5	’s	’	VERB
ejpam-3377	345	6	variational	variational	ADJ
ejpam-3377	345	7	iteration	iteration	NOUN
ejpam-3377	345	8	method	method	NOUN
ejpam-3377	345	9	for	for	ADP
ejpam-3377	345	10	solving	solve	VERB
ejpam-3377	345	11	the	the	DET
ejpam-3377	345	12	telegraph	telegraph	NOUN
ejpam-3377	345	13	and	and	CCONJ
ejpam-3377	345	14	fractional	fractional	ADJ
ejpam-3377	345	15	telegraph	telegraph	NOUN
ejpam-3377	345	16	equations	equation	NOUN
ejpam-3377	345	17	.	.	PUNCT
ejpam-3377	346	1	comm	comm	NOUN
ejpam-3377	346	2	.	.	PUNCT
ejpam-3377	347	1	numer	numer	PROPN
ejpam-3377	347	2	.	.	PROPN
ejpam-3377	347	3	method	method	PROPN
ejpam-3377	347	4	.	.	PUNCT
ejpam-3377	348	1	engrg	engrg	PROPN
ejpam-3377	348	2	.	.	PROPN
ejpam-3377	348	3	,	,	PUNCT
ejpam-3377	348	4	27	27	NUM
ejpam-3377	348	5	:	:	PUNCT
ejpam-3377	349	1	219–231	219–231	NUM
ejpam-3377	349	2	,	,	PUNCT
ejpam-3377	349	3	2011	2011	NUM
ejpam-3377	349	4	.	.	PUNCT
ejpam-3377	350	1	[	[	X
ejpam-3377	350	2	9	9	NUM
ejpam-3377	350	3	]	]	PUNCT
ejpam-3377	350	4	e	e	X
ejpam-3377	350	5	h	h	PROPN
ejpam-3377	350	6	doha	doha	PROPN
ejpam-3377	350	7	,	,	PUNCT
ejpam-3377	350	8	a	a	DET
ejpam-3377	350	9	h	h	NOUN
ejpam-3377	350	10	bhrawy	bhrawy	NOUN
ejpam-3377	350	11	,	,	PUNCT
ejpam-3377	350	12	d	d	NOUN
ejpam-3377	350	13	baleanu	baleanu	NOUN
ejpam-3377	350	14	and	and	CCONJ
ejpam-3377	350	15	s	s	NOUN
ejpam-3377	350	16	s	s	NOUN
ejpam-3377	350	17	ezz	ezz	NOUN
ejpam-3377	350	18	-	-	PUNCT
ejpam-3377	350	19	eldien	eldien	NOUN
ejpam-3377	350	20	.	.	PUNCT
ejpam-3377	351	1	the	the	DET
ejpam-3377	351	2	operational	operational	ADJ
ejpam-3377	351	3	matrix	matrix	NOUN
ejpam-3377	351	4	formulation	formulation	NOUN
ejpam-3377	351	5	of	of	ADP
ejpam-3377	351	6	the	the	DET
ejpam-3377	351	7	jacobi	jacobi	PROPN
ejpam-3377	351	8	tau	tau	PROPN
ejpam-3377	351	9	approximation	approximation	NOUN
ejpam-3377	351	10	for	for	ADP
ejpam-3377	351	11	space	space	NOUN
ejpam-3377	351	12	fractional	fractional	ADJ
ejpam-3377	351	13	diffusion	diffusion	NOUN
ejpam-3377	351	14	equation	equation	NOUN
ejpam-3377	351	15	.	.	PUNCT
ejpam-3377	352	1	adv	adv	PROPN
ejpam-3377	352	2	.	.	PROPN
ejpam-3377	352	3	differ	differ	VERB
ejpam-3377	352	4	.	.	PUNCT
ejpam-3377	353	1	equns	equn	NOUN
ejpam-3377	353	2	.	.	PUNCT
ejpam-3377	354	1	,	,	PUNCT
ejpam-3377	354	2	231	231	NUM
ejpam-3377	354	3	:	:	SYM
ejpam-3377	354	4	1687–1847	1687–1847	NUM
ejpam-3377	354	5	,	,	PUNCT
ejpam-3377	354	6	2014	2014	NUM
ejpam-3377	354	7	.	.	PUNCT
ejpam-3377	355	1	[	[	X
ejpam-3377	355	2	10	10	NUM
ejpam-3377	355	3	]	]	X
ejpam-3377	355	4	e	e	PROPN
ejpam-3377	355	5	h	h	PROPN
ejpam-3377	355	6	doha	doha	PROPN
ejpam-3377	355	7	,	,	PUNCT
ejpam-3377	355	8	a	a	DET
ejpam-3377	355	9	h	h	NOUN
ejpam-3377	355	10	bhrawy	bhrawy	NOUN
ejpam-3377	355	11	,	,	PUNCT
ejpam-3377	355	12	r	r	NOUN
ejpam-3377	355	13	m	m	PROPN
ejpam-3377	355	14	hafez	hafez	NOUN
ejpam-3377	355	15	.	.	PUNCT
ejpam-3377	356	1	on	on	ADP
ejpam-3377	356	2	shifted	shift	VERB
ejpam-3377	356	3	jacobi	jacobi	PROPN
ejpam-3377	356	4	spectral	spectral	PROPN
ejpam-3377	356	5	method	method	NOUN
ejpam-3377	356	6	for	for	ADP
ejpam-3377	356	7	highorder	highorder	NOUN
ejpam-3377	356	8	multi	multi	ADJ
ejpam-3377	356	9	-	-	ADJ
ejpam-3377	356	10	point	point	ADJ
ejpam-3377	356	11	boundary	boundary	ADJ
ejpam-3377	356	12	value	value	NOUN
ejpam-3377	356	13	problems	problem	NOUN
ejpam-3377	356	14	.	.	PUNCT
ejpam-3377	357	1	commun	commun	PROPN
ejpam-3377	357	2	.	.	PUNCT
ejpam-3377	358	1	nonl	nonl	PROPN
ejpam-3377	358	2	.	.	PUNCT
ejpam-3377	359	1	sci.num	sci.num	NUM
ejpam-3377	359	2	.	.	PUNCT
ejpam-3377	360	1	simul	simul	PROPN
ejpam-3377	360	2	.	.	PROPN
ejpam-3377	360	3	,	,	PUNCT
ejpam-3377	360	4	17(10	17(10	NUM
ejpam-3377	360	5	):	):	PUNCT
ejpam-3377	360	6	3802–3810	3802–3810	NUM
ejpam-3377	360	7	,	,	PUNCT
ejpam-3377	360	8	2012	2012	NUM
ejpam-3377	360	9	.	.	PUNCT
ejpam-3377	361	1	references	reference	NOUN
ejpam-3377	361	2	54	54	NUM
ejpam-3377	362	1	[	[	X
ejpam-3377	362	2	11	11	NUM
ejpam-3377	362	3	]	]	PUNCT
ejpam-3377	362	4	a	a	DET
ejpam-3377	362	5	freihat	freihat	NOUN
ejpam-3377	362	6	,	,	PUNCT
ejpam-3377	362	7	r	r	NOUN
ejpam-3377	362	8	abu	abu	PROPN
ejpam-3377	362	9	-	-	PUNCT
ejpam-3377	362	10	gdairi	gdairi	PROPN
ejpam-3377	362	11	,	,	PUNCT
ejpam-3377	362	12	h	h	PROPN
ejpam-3377	362	13	khalil	khalil	PROPN
ejpam-3377	362	14	,	,	PUNCT
ejpam-3377	362	15	e	e	X
ejpam-3377	362	16	abuteen	abuteen	ADV
ejpam-3377	362	17	,	,	PUNCT
ejpam-3377	362	18	m	m	PROPN
ejpam-3377	362	19	al	al	PROPN
ejpam-3377	362	20	-	-	PUNCT
ejpam-3377	362	21	smadi	smadi	NOUN
ejpam-3377	362	22	,	,	PUNCT
ejpam-3377	362	23	r	r	NOUN
ejpam-3377	362	24	a	a	DET
ejpam-3377	362	25	khan	khan	PROPN
ejpam-3377	362	26	.	.	PUNCT
ejpam-3377	363	1	fitted	fit	VERB
ejpam-3377	363	2	reproducing	reproduce	VERB
ejpam-3377	363	3	kernel	kernel	NOUN
ejpam-3377	363	4	method	method	NOUN
ejpam-3377	363	5	for	for	ADP
ejpam-3377	363	6	solving	solve	VERB
ejpam-3377	363	7	a	a	DET
ejpam-3377	363	8	class	class	NOUN
ejpam-3377	363	9	of	of	ADP
ejpam-3377	363	10	third	third	ADJ
ejpam-3377	363	11	-	-	PUNCT
ejpam-3377	363	12	order	order	NOUN
ejpam-3377	363	13	periodic	periodic	ADJ
ejpam-3377	363	14	boundary	boundary	ADJ
ejpam-3377	363	15	value	value	NOUN
ejpam-3377	363	16	problems	problem	NOUN
ejpam-3377	363	17	.	.	PUNCT
ejpam-3377	364	1	american	american	PROPN
ejpam-3377	364	2	journal	journal	PROPN
ejpam-3377	364	3	of	of	ADP
ejpam-3377	364	4	applied	apply	VERB
ejpam-3377	364	5	sciences	science	NOUN
ejpam-3377	364	6	,	,	PUNCT
ejpam-3377	364	7	13	13	NUM
ejpam-3377	364	8	(	(	PUNCT
ejpam-3377	364	9	5	5	NUM
ejpam-3377	364	10	):	):	PUNCT
ejpam-3377	364	11	501–510	501–510	NUM
ejpam-3377	364	12	,	,	PUNCT
ejpam-3377	364	13	2016	2016	NUM
ejpam-3377	364	14	.	.	PUNCT
ejpam-3377	365	1	[	[	X
ejpam-3377	365	2	12	12	NUM
ejpam-3377	365	3	]	]	X
ejpam-3377	365	4	m	m	VERB
ejpam-3377	365	5	gasea	gasea	NOUN
ejpam-3377	365	6	,	,	PUNCT
ejpam-3377	365	7	t	t	PROPN
ejpam-3377	365	8	sauer	sauer	NOUN
ejpam-3377	365	9	.	.	PUNCT
ejpam-3377	366	1	on	on	ADP
ejpam-3377	366	2	the	the	DET
ejpam-3377	366	3	history	history	NOUN
ejpam-3377	366	4	of	of	ADP
ejpam-3377	366	5	multivariate	multivariate	NOUN
ejpam-3377	366	6	polynomial	polynomial	ADJ
ejpam-3377	366	7	interpolation	interpolation	NOUN
ejpam-3377	366	8	.	.	PUNCT
ejpam-3377	367	1	j.	j.	PROPN
ejpam-3377	367	2	comp	comp	PROPN
ejpam-3377	367	3	.	.	PROPN
ejpam-3377	368	1	app.math	app.math	PROPN
ejpam-3377	368	2	,	,	PUNCT
ejpam-3377	368	3	122	122	NUM
ejpam-3377	368	4	:	:	SYM
ejpam-3377	368	5	23–35	23–35	NUM
ejpam-3377	368	6	,	,	PUNCT
ejpam-3377	368	7	2000	2000	NUM
ejpam-3377	368	8	.	.	PUNCT
ejpam-3377	369	1	[	[	X
ejpam-3377	369	2	13	13	NUM
ejpam-3377	369	3	]	]	PUNCT
ejpam-3377	369	4	t	t	PROPN
ejpam-3377	369	5	hayat	hayat	PROPN
ejpam-3377	369	6	,	,	PUNCT
ejpam-3377	369	7	f	f	PROPN
ejpam-3377	369	8	shahzad	shahzad	PROPN
ejpam-3377	369	9	,	,	PUNCT
ejpam-3377	369	10	m	m	PROPN
ejpam-3377	369	11	ayub	ayub	NOUN
ejpam-3377	369	12	.	.	PUNCT
ejpam-3377	370	1	analytical	analytical	ADJ
ejpam-3377	370	2	solution	solution	NOUN
ejpam-3377	370	3	for	for	ADP
ejpam-3377	370	4	the	the	DET
ejpam-3377	370	5	steady	steady	ADJ
ejpam-3377	370	6	flow	flow	NOUN
ejpam-3377	370	7	of	of	ADP
ejpam-3377	370	8	the	the	DET
ejpam-3377	370	9	third	third	ADJ
ejpam-3377	370	10	grad	grad	ADJ
ejpam-3377	370	11	fluid	fluid	NOUN
ejpam-3377	370	12	in	in	ADP
ejpam-3377	370	13	a	a	DET
ejpam-3377	370	14	porous	porous	ADJ
ejpam-3377	370	15	half	half	NOUN
ejpam-3377	370	16	space	space	NOUN
ejpam-3377	370	17	.	.	PUNCT
ejpam-3377	371	1	appl	appl	PROPN
ejpam-3377	371	2	.	.	PROPN
ejpam-3377	371	3	math	math	PROPN
ejpam-3377	371	4	.	.	PUNCT
ejpam-3377	372	1	model	model	PROPN
ejpam-3377	372	2	.	.	PROPN
ejpam-3377	372	3	,	,	PUNCT
ejpam-3377	372	4	31	31	NUM
ejpam-3377	372	5	:	:	PUNCT
ejpam-3377	373	1	243–250	243–250	NUM
ejpam-3377	373	2	,	,	PUNCT
ejpam-3377	373	3	2007	2007	NUM
ejpam-3377	373	4	.	.	PUNCT
ejpam-3377	374	1	[	[	X
ejpam-3377	374	2	14	14	NUM
ejpam-3377	374	3	]	]	X
ejpam-3377	374	4	r	r	NOUN
ejpam-3377	374	5	hilfer	hilfer	NOUN
ejpam-3377	374	6	.	.	PUNCT
ejpam-3377	375	1	applications	application	NOUN
ejpam-3377	375	2	of	of	ADP
ejpam-3377	375	3	fractional	fractional	ADJ
ejpam-3377	375	4	calculus	calculus	NOUN
ejpam-3377	375	5	in	in	ADP
ejpam-3377	375	6	physics	physics	PROPN
ejpam-3377	375	7	.	.	PUNCT
ejpam-3377	376	1	world	world	NOUN
ejpam-3377	376	2	scientifc	scientifc	PROPN
ejpam-3377	376	3	publishing	publish	VERB
ejpam-3377	376	4	company	company	NOUN
ejpam-3377	376	5	,	,	PUNCT
ejpam-3377	376	6	singapore	singapore	PROPN
ejpam-3377	376	7	,	,	PUNCT
ejpam-3377	376	8	2000	2000	NUM
ejpam-3377	376	9	.	.	PUNCT
ejpam-3377	377	1	[	[	X
ejpam-3377	377	2	15	15	NUM
ejpam-3377	377	3	]	]	X
ejpam-3377	377	4	w	w	PROPN
ejpam-3377	377	5	hackbusch	hackbusch	PROPN
ejpam-3377	377	6	.	.	PUNCT
ejpam-3377	378	1	elliptic	elliptic	ADJ
ejpam-3377	378	2	differential	differential	ADJ
ejpam-3377	378	3	equations	equation	NOUN
ejpam-3377	378	4	:	:	PUNCT
ejpam-3377	378	5	theory	theory	NOUN
ejpam-3377	378	6	and	and	CCONJ
ejpam-3377	378	7	numerical	numerical	ADJ
ejpam-3377	378	8	treatment	treatment	NOUN
ejpam-3377	378	9	.	.	PUNCT
ejpam-3377	379	1	volume	volume	NOUN
ejpam-3377	379	2	18	18	NUM
ejpam-3377	379	3	of	of	ADP
ejpam-3377	379	4	springer	springer	NOUN
ejpam-3377	379	5	series	series	NOUN
ejpam-3377	379	6	in	in	ADP
ejpam-3377	379	7	computational	computational	ADJ
ejpam-3377	379	8	mathematics	mathematic	NOUN
ejpam-3377	379	9	,	,	PUNCT
ejpam-3377	379	10	springer	springer	NOUN
ejpam-3377	379	11	,	,	PUNCT
ejpam-3377	379	12	berlin	berlin	PROPN
ejpam-3377	379	13	,	,	PUNCT
ejpam-3377	379	14	1992	1992	NUM
ejpam-3377	379	15	.	.	PUNCT
ejpam-3377	380	1	[	[	X
ejpam-3377	380	2	16	16	NUM
ejpam-3377	380	3	]	]	X
ejpam-3377	380	4	y	y	PROPN
ejpam-3377	380	5	hu	hu	PROPN
ejpam-3377	380	6	,	,	PUNCT
ejpam-3377	380	7	y	y	PROPN
ejpam-3377	380	8	luo	luo	PROPN
ejpam-3377	380	9	and	and	CCONJ
ejpam-3377	380	10	z	z	PROPN
ejpam-3377	380	11	lu	lu	PROPN
ejpam-3377	380	12	.	.	PUNCT
ejpam-3377	381	1	analytical	analytical	ADJ
ejpam-3377	381	2	solution	solution	NOUN
ejpam-3377	381	3	of	of	ADP
ejpam-3377	381	4	the	the	DET
ejpam-3377	381	5	linear	linear	ADJ
ejpam-3377	381	6	fractional	fractional	ADJ
ejpam-3377	381	7	differential	differential	NOUN
ejpam-3377	381	8	equation	equation	NOUN
ejpam-3377	381	9	by	by	ADP
ejpam-3377	381	10	adomian	adomian	NOUN
ejpam-3377	381	11	decomposition	decomposition	NOUN
ejpam-3377	381	12	method	method	NOUN
ejpam-3377	381	13	.	.	PUNCT
ejpam-3377	382	1	j.comput	j.comput	NOUN
ejpam-3377	382	2	.	.	PUNCT
ejpam-3377	383	1	appl	appl	PROPN
ejpam-3377	383	2	.	.	PROPN
ejpam-3377	383	3	math	math	PROPN
ejpam-3377	383	4	.	.	PUNCT
ejpam-3377	383	5	,	,	PUNCT
ejpam-3377	383	6	215	215	NUM
ejpam-3377	383	7	:	:	SYM
ejpam-3377	383	8	220	220	NUM
ejpam-3377	383	9	–	–	SYM
ejpam-3377	383	10	229	229	NUM
ejpam-3377	383	11	,	,	PUNCT
ejpam-3377	383	12	2008	2008	NUM
ejpam-3377	383	13	.	.	PUNCT
ejpam-3377	384	1	[	[	X
ejpam-3377	384	2	17	17	NUM
ejpam-3377	384	3	]	]	X
ejpam-3377	384	4	h	h	NOUN
ejpam-3377	384	5	jafari	jafari	X
ejpam-3377	384	6	,	,	PUNCT
ejpam-3377	384	7	s	s	PART
ejpam-3377	384	8	seifi	seifi	NOUN
ejpam-3377	384	9	.	.	PUNCT
ejpam-3377	385	1	homotopy	homotopy	VERB
ejpam-3377	385	2	analysis	analysis	NOUN
ejpam-3377	385	3	method	method	NOUN
ejpam-3377	385	4	for	for	ADP
ejpam-3377	385	5	solving	solve	VERB
ejpam-3377	385	6	linear	linear	NOUN
ejpam-3377	385	7	and	and	CCONJ
ejpam-3377	385	8	nonlinear	nonlinear	ADJ
ejpam-3377	385	9	fractional	fractional	ADJ
ejpam-3377	385	10	diffusion	diffusion	NOUN
ejpam-3377	385	11	-	-	PUNCT
ejpam-3377	385	12	wave	wave	NOUN
ejpam-3377	385	13	equation	equation	NOUN
ejpam-3377	385	14	.	.	PUNCT
ejpam-3377	386	1	common	common	ADJ
ejpam-3377	386	2	.	.	PUNCT
ejpam-3377	386	3	nonl	nonl	PROPN
ejpam-3377	386	4	.	.	PUNCT
ejpam-3377	387	1	sci	sci	PROPN
ejpam-3377	387	2	.	.	PUNCT
ejpam-3377	387	3	numer	numer	PROPN
ejpam-3377	387	4	.	.	PUNCT
ejpam-3377	388	1	simul	simul	PROPN
ejpam-3377	388	2	.	.	PROPN
ejpam-3377	388	3	,	,	PUNCT
ejpam-3377	388	4	14	14	NUM
ejpam-3377	388	5	(	(	PUNCT
ejpam-3377	388	6	5	5	NUM
ejpam-3377	388	7	)	)	PUNCT
ejpam-3377	388	8	:	:	PUNCT
ejpam-3377	388	9	2006–2012	2006–2012	NUM
ejpam-3377	388	10	,	,	PUNCT
ejpam-3377	388	11	2009	2009	NUM
ejpam-3377	388	12	.	.	PUNCT
ejpam-3377	389	1	[	[	X
ejpam-3377	389	2	18	18	NUM
ejpam-3377	389	3	]	]	X
ejpam-3377	389	4	h	h	NOUN
ejpam-3377	389	5	jafari	jafari	PROPN
ejpam-3377	389	6	and	and	CCONJ
ejpam-3377	389	7	s	s	X
ejpam-3377	389	8	seifi	seifi	NOUN
ejpam-3377	389	9	.	.	PUNCT
ejpam-3377	390	1	solving	solve	VERB
ejpam-3377	390	2	a	a	DET
ejpam-3377	390	3	system	system	NOUN
ejpam-3377	390	4	of	of	ADP
ejpam-3377	390	5	nonlinear	nonlinear	ADJ
ejpam-3377	390	6	fractional	fractional	ADJ
ejpam-3377	390	7	partial	partial	ADJ
ejpam-3377	390	8	differential	differential	NOUN
ejpam-3377	390	9	equations	equation	NOUN
ejpam-3377	390	10	using	use	VERB
ejpam-3377	390	11	homotopy	homotopy	NOUN
ejpam-3377	390	12	analysis	analysis	NOUN
ejpam-3377	390	13	method	method	NOUN
ejpam-3377	390	14	.	.	PUNCT
ejpam-3377	391	1	commun	commun	PROPN
ejpam-3377	391	2	.	.	PUNCT
ejpam-3377	392	1	nonl	nonl	PROPN
ejpam-3377	392	2	.	.	PUNCT
ejpam-3377	393	1	sci	sci	PROPN
ejpam-3377	393	2	.	.	PUNCT
ejpam-3377	394	1	num	num	PROPN
ejpam-3377	394	2	.	.	PROPN
ejpam-3377	394	3	simun	simun	PROPN
ejpam-3377	394	4	.	.	PUNCT
ejpam-3377	394	5	,	,	PUNCT
ejpam-3377	394	6	14:1962	14:1962	NUM
ejpam-3377	394	7	–	–	PUNCT
ejpam-3377	394	8	1969	1969	NUM
ejpam-3377	394	9	,	,	PUNCT
ejpam-3377	394	10	2009	2009	NUM
ejpam-3377	394	11	.	.	PUNCT
ejpam-3377	395	1	[	[	X
ejpam-3377	395	2	19	19	NUM
ejpam-3377	395	3	]	]	X
ejpam-3377	395	4	m	m	VERB
ejpam-3377	395	5	a	a	DET
ejpam-3377	395	6	jafari	jafari	ADJ
ejpam-3377	395	7	and	and	CCONJ
ejpam-3377	395	8	a	a	DET
ejpam-3377	395	9	aminataei	aminataei	NOUN
ejpam-3377	395	10	.	.	PUNCT
ejpam-3377	395	11	improved	improve	VERB
ejpam-3377	395	12	homotopy	homotopy	PROPN
ejpam-3377	395	13	purturbation	purturbation	PROPN
ejpam-3377	395	14	method.int	method.int	PROPN
ejpam-3377	395	15	.	.	PUNCT
ejpam-3377	395	16	math	math	PROPN
ejpam-3377	395	17	.	.	PUNCT
ejpam-3377	396	1	forum	forum	PROPN
ejpam-3377	396	2	,	,	PUNCT
ejpam-3377	396	3	32(5	32(5	NOUN
ejpam-3377	396	4	):	):	PUNCT
ejpam-3377	396	5	1567–1579	1567–1579	NUM
ejpam-3377	396	6	,	,	PUNCT
ejpam-3377	396	7	2010	2010	NUM
ejpam-3377	396	8	.	.	PUNCT
ejpam-3377	397	1	[	[	X
ejpam-3377	397	2	20	20	NUM
ejpam-3377	397	3	]	]	SYM
ejpam-3377	397	4	s	s	PART
ejpam-3377	397	5	kazem	kazem	PROPN
ejpam-3377	397	6	,	,	PUNCT
ejpam-3377	397	7	s	s	PART
ejpam-3377	397	8	abbasbandy	abbasbandy	NOUN
ejpam-3377	397	9	,	,	PUNCT
ejpam-3377	397	10	s	s	PROPN
ejpam-3377	397	11	kumar	kumar	PROPN
ejpam-3377	397	12	.	.	PUNCT
ejpam-3377	397	13	fractional	fractional	ADJ
ejpam-3377	397	14	-	-	PUNCT
ejpam-3377	397	15	order	order	NOUN
ejpam-3377	397	16	legendre	legendre	NOUN
ejpam-3377	397	17	functions	function	NOUN
ejpam-3377	397	18	for	for	ADP
ejpam-3377	397	19	solving	solve	VERB
ejpam-3377	397	20	fractional	fractional	ADJ
ejpam-3377	397	21	-	-	PUNCT
ejpam-3377	397	22	order	order	NOUN
ejpam-3377	397	23	differential	differential	ADJ
ejpam-3377	397	24	equations	equation	NOUN
ejpam-3377	397	25	.	.	PUNCT
ejpam-3377	398	1	applied	apply	VERB
ejpam-3377	398	2	mathematical	mathematical	ADJ
ejpam-3377	398	3	modelling	modelling	NOUN
ejpam-3377	398	4	,	,	PUNCT
ejpam-3377	398	5	37	37	NUM
ejpam-3377	398	6	:	:	SYM
ejpam-3377	398	7	5498	5498	NUM
ejpam-3377	398	8	–	–	PUNCT
ejpam-3377	398	9	5510	5510	NUM
ejpam-3377	398	10	,	,	PUNCT
ejpam-3377	398	11	2013	2013	NUM
ejpam-3377	398	12	.	.	PUNCT
ejpam-3377	399	1	[	[	X
ejpam-3377	399	2	21	21	NUM
ejpam-3377	399	3	]	]	X
ejpam-3377	399	4	d	d	X
ejpam-3377	399	5	kumar	kumar	PROPN
ejpam-3377	399	6	,	,	PUNCT
ejpam-3377	399	7	j	j	PROPN
ejpam-3377	399	8	singh	singh	PROPN
ejpam-3377	399	9	and	and	CCONJ
ejpam-3377	399	10	s	s	PROPN
ejpam-3377	399	11	kumar	kumar	PROPN
ejpam-3377	399	12	.	.	PROPN
ejpam-3377	399	13	numerical	numerical	PROPN
ejpam-3377	399	14	computation	computation	NOUN
ejpam-3377	399	15	of	of	ADP
ejpam-3377	399	16	fractional	fractional	ADJ
ejpam-3377	399	17	multidimensional	multidimensional	ADJ
ejpam-3377	399	18	diffusion	diffusion	NOUN
ejpam-3377	399	19	equations	equation	NOUN
ejpam-3377	399	20	by	by	ADP
ejpam-3377	399	21	using	use	VERB
ejpam-3377	399	22	a	a	DET
ejpam-3377	399	23	modified	modify	VERB
ejpam-3377	399	24	homotopy	homotopy	NOUN
ejpam-3377	399	25	perturbation	perturbation	NOUN
ejpam-3377	399	26	method	method	NOUN
ejpam-3377	399	27	.	.	PUNCT
ejpam-3377	400	1	j.	j.	PROPN
ejpam-3377	400	2	association	association	PROPN
ejpam-3377	400	3	of	of	ADP
ejpam-3377	400	4	arab	arab	ADJ
ejpam-3377	400	5	universities	university	NOUN
ejpam-3377	400	6	for	for	ADP
ejpam-3377	400	7	basic	basic	ADJ
ejpam-3377	400	8	and	and	CCONJ
ejpam-3377	400	9	applied	applied	ADJ
ejpam-3377	400	10	sciences	science	NOUN
ejpam-3377	400	11	,	,	PUNCT
ejpam-3377	400	12	17:20–26	17:20–26	NUM
ejpam-3377	400	13	,	,	PUNCT
ejpam-3377	400	14	2015	2015	NUM
ejpam-3377	400	15	.	.	PUNCT
ejpam-3377	401	1	[	[	X
ejpam-3377	401	2	22	22	NUM
ejpam-3377	401	3	]	]	X
ejpam-3377	401	4	h	h	NOUN
ejpam-3377	401	5	khalil	khalil	PROPN
ejpam-3377	401	6	,	,	PUNCT
ejpam-3377	401	7	r	r	PROPN
ejpam-3377	401	8	a	a	DET
ejpam-3377	401	9	khan	khan	PROPN
ejpam-3377	401	10	.	.	PUNCT
ejpam-3377	402	1	a	a	DET
ejpam-3377	402	2	new	new	ADJ
ejpam-3377	402	3	method	method	NOUN
ejpam-3377	402	4	based	base	VERB
ejpam-3377	402	5	on	on	ADP
ejpam-3377	402	6	legendre	legendre	PROPN
ejpam-3377	402	7	polynomials	polynomial	NOUN
ejpam-3377	402	8	for	for	ADP
ejpam-3377	402	9	solutions	solution	NOUN
ejpam-3377	402	10	of	of	ADP
ejpam-3377	402	11	the	the	DET
ejpam-3377	402	12	fractional	fractional	ADJ
ejpam-3377	402	13	twodimensional	twodimensional	ADJ
ejpam-3377	402	14	heat	heat	NOUN
ejpam-3377	402	15	conduction	conduction	NOUN
ejpam-3377	402	16	equation	equation	NOUN
ejpam-3377	402	17	.	.	PUNCT
ejpam-3377	403	1	comput.math	comput.math	NOUN
ejpam-3377	403	2	.	.	PUNCT
ejpam-3377	404	1	appl	appl	PROPN
ejpam-3377	404	2	.	.	PROPN
ejpam-3377	404	3	,	,	PUNCT
ejpam-3377	404	4	67:1938	67:1938	NUM
ejpam-3377	404	5	–	–	PUNCT
ejpam-3377	404	6	1953	1953	NUM
ejpam-3377	404	7	,	,	PUNCT
ejpam-3377	404	8	2014	2014	NUM
ejpam-3377	404	9	.	.	PUNCT
ejpam-3377	405	1	[	[	X
ejpam-3377	405	2	23	23	NUM
ejpam-3377	405	3	]	]	X
ejpam-3377	405	4	h	h	PROPN
ejpam-3377	405	5	khalil	khalil	PROPN
ejpam-3377	405	6	and	and	CCONJ
ejpam-3377	405	7	r	r	PROPN
ejpam-3377	405	8	a	a	DET
ejpam-3377	405	9	khan	khan	PROPN
ejpam-3377	405	10	.	.	PUNCT
ejpam-3377	406	1	a	a	DET
ejpam-3377	406	2	new	new	ADJ
ejpam-3377	406	3	method	method	NOUN
ejpam-3377	406	4	based	base	VERB
ejpam-3377	406	5	on	on	ADP
ejpam-3377	406	6	legendre	legendre	PROPN
ejpam-3377	406	7	polynomials	polynomial	NOUN
ejpam-3377	406	8	for	for	ADP
ejpam-3377	406	9	solution	solution	NOUN
ejpam-3377	406	10	of	of	ADP
ejpam-3377	406	11	system	system	NOUN
ejpam-3377	406	12	of	of	ADP
ejpam-3377	406	13	fractional	fractional	ADJ
ejpam-3377	406	14	order	order	NOUN
ejpam-3377	406	15	partial	partial	ADJ
ejpam-3377	406	16	differential	differential	NOUN
ejpam-3377	406	17	equations	equation	NOUN
ejpam-3377	406	18	.	.	PUNCT
ejpam-3377	407	1	int.j.comput.math	int.j.comput.math	PROPN
ejpam-3377	407	2	.	.	PROPN
ejpam-3377	407	3	,	,	PUNCT
ejpam-3377	407	4	91(12	91(12	NUM
ejpam-3377	407	5	):	):	PUNCT
ejpam-3377	407	6	2554–2567	2554–2567	NUM
ejpam-3377	407	7	,	,	PUNCT
ejpam-3377	407	8	2014	2014	NUM
ejpam-3377	407	9	.	.	PUNCT
ejpam-3377	408	1	references	reference	NOUN
ejpam-3377	408	2	55	55	NUM
ejpam-3377	409	1	[	[	X
ejpam-3377	409	2	24	24	NUM
ejpam-3377	409	3	]	]	X
ejpam-3377	409	4	h	h	NOUN
ejpam-3377	409	5	khalil	khalil	PROPN
ejpam-3377	409	6	,	,	PUNCT
ejpam-3377	409	7	r	r	PROPN
ejpam-3377	409	8	a	a	DET
ejpam-3377	409	9	khan	khan	PROPN
ejpam-3377	409	10	,	,	PUNCT
ejpam-3377	409	11	m	m	PROPN
ejpam-3377	409	12	al	al	PROPN
ejpam-3377	409	13	-	-	PUNCT
ejpam-3377	409	14	smadi	smadi	NOUN
ejpam-3377	409	15	,	,	PUNCT
ejpam-3377	409	16	a	a	DET
ejpam-3377	409	17	freihat	freihat	NOUN
ejpam-3377	409	18	.	.	PUNCT
ejpam-3377	410	1	approximation	approximation	NOUN
ejpam-3377	410	2	of	of	ADP
ejpam-3377	410	3	solution	solution	NOUN
ejpam-3377	410	4	of	of	ADP
ejpam-3377	410	5	time	time	NOUN
ejpam-3377	410	6	fractional	fractional	ADJ
ejpam-3377	410	7	order	order	NOUN
ejpam-3377	410	8	three	three	NUM
ejpam-3377	410	9	-	-	PUNCT
ejpam-3377	410	10	dimensional	dimensional	ADJ
ejpam-3377	410	11	heat	heat	NOUN
ejpam-3377	410	12	conduction	conduction	NOUN
ejpam-3377	410	13	problems	problem	NOUN
ejpam-3377	410	14	with	with	ADP
ejpam-3377	410	15	jacobi	jacobi	PROPN
ejpam-3377	410	16	polynomials	polynomials	PROPN
ejpam-3377	410	17	.	.	PUNCT
ejpam-3377	411	1	punjab	punjab	PROPN
ejpam-3377	411	2	university	university	PROPN
ejpam-3377	411	3	journal	journal	NOUN
ejpam-3377	411	4	of	of	ADP
ejpam-3377	411	5	mathematics	mathematic	NOUN
ejpam-3377	411	6	,	,	PUNCT
ejpam-3377	411	7	47	47	NUM
ejpam-3377	411	8	:	:	PUNCT
ejpam-3377	411	9	35–56	35–56	NUM
ejpam-3377	411	10	,	,	PUNCT
ejpam-3377	411	11	2015	2015	NUM
ejpam-3377	411	12	.	.	PUNCT
ejpam-3377	412	1	[	[	X
ejpam-3377	412	2	25	25	NUM
ejpam-3377	412	3	]	]	X
ejpam-3377	412	4	h	h	NOUN
ejpam-3377	412	5	khalil	khalil	PROPN
ejpam-3377	412	6	,	,	PUNCT
ejpam-3377	412	7	r	r	PROPN
ejpam-3377	412	8	a	a	DET
ejpam-3377	412	9	khan	khan	PROPN
ejpam-3377	412	10	,	,	PUNCT
ejpam-3377	412	11	m	m	PROPN
ejpam-3377	412	12	al	al	PROPN
ejpam-3377	412	13	-	-	PUNCT
ejpam-3377	412	14	smadi	smadi	NOUN
ejpam-3377	412	15	,	,	PUNCT
ejpam-3377	412	16	a	a	DET
ejpam-3377	412	17	freihat	freihat	NOUN
ejpam-3377	412	18	,	,	PUNCT
ejpam-3377	412	19	n	n	X
ejpam-3377	412	20	shawagfeh	shawagfeh	NOUN
ejpam-3377	412	21	.	.	PUNCT
ejpam-3377	413	1	new	new	ADJ
ejpam-3377	413	2	operational	operational	ADJ
ejpam-3377	413	3	matrix	matrix	NOUN
ejpam-3377	413	4	for	for	ADP
ejpam-3377	413	5	shifted	shift	VERB
ejpam-3377	413	6	legendre	legendre	PROPN
ejpam-3377	413	7	polynomials	polynomial	NOUN
ejpam-3377	413	8	and	and	CCONJ
ejpam-3377	413	9	fractional	fractional	ADJ
ejpam-3377	413	10	differential	differential	ADJ
ejpam-3377	413	11	equations	equation	NOUN
ejpam-3377	413	12	with	with	ADP
ejpam-3377	413	13	variable	variable	ADJ
ejpam-3377	413	14	coefficients	coefficient	NOUN
ejpam-3377	413	15	.	.	PUNCT
ejpam-3377	414	1	punjab	punjab	PROPN
ejpam-3377	414	2	university	university	PROPN
ejpam-3377	414	3	journal	journal	NOUN
ejpam-3377	414	4	of	of	ADP
ejpam-3377	414	5	mathematics	mathematic	NOUN
ejpam-3377	414	6	,	,	PUNCT
ejpam-3377	414	7	47	47	NUM
ejpam-3377	414	8	:	:	PUNCT
ejpam-3377	414	9	81–103	81–103	NUM
ejpam-3377	414	10	,	,	PUNCT
ejpam-3377	414	11	2015	2015	NUM
ejpam-3377	414	12	.	.	PUNCT
ejpam-3377	415	1	[	[	X
ejpam-3377	415	2	26	26	NUM
ejpam-3377	415	3	]	]	X
ejpam-3377	415	4	h	h	PROPN
ejpam-3377	415	5	khan	khan	PROPN
ejpam-3377	415	6	,	,	PUNCT
ejpam-3377	415	7	m	m	VERB
ejpam-3377	415	8	alipour	alipour	ADJ
ejpam-3377	415	9	,	,	PUNCT
ejpam-3377	415	10	r	r	PROPN
ejpam-3377	415	11	a	a	DET
ejpam-3377	415	12	khan	khan	PROPN
ejpam-3377	415	13	,	,	PUNCT
ejpam-3377	415	14	h	h	NOUN
ejpam-3377	415	15	tajadodi	tajadodi	PROPN
ejpam-3377	415	16	and	and	CCONJ
ejpam-3377	415	17	a	a	DET
ejpam-3377	415	18	khan	khan	PROPN
ejpam-3377	415	19	.	.	PUNCT
ejpam-3377	416	1	on	on	ADP
ejpam-3377	416	2	approximate	approximate	ADJ
ejpam-3377	416	3	solution	solution	NOUN
ejpam-3377	416	4	of	of	ADP
ejpam-3377	416	5	fractional	fractional	ADJ
ejpam-3377	416	6	order	order	NOUN
ejpam-3377	416	7	logistic	logistic	ADJ
ejpam-3377	416	8	equations	equation	NOUN
ejpam-3377	416	9	by	by	ADP
ejpam-3377	416	10	operational	operational	ADJ
ejpam-3377	416	11	matrices	matrix	NOUN
ejpam-3377	416	12	of	of	ADP
ejpam-3377	416	13	bernstein	bernstein	PROPN
ejpam-3377	416	14	polynomials	polynomials	PROPN
ejpam-3377	416	15	.	.	PUNCT
ejpam-3377	417	1	j.	j.	PROPN
ejpam-3377	417	2	math	math	PROPN
ejpam-3377	417	3	.	.	PUNCT
ejpam-3377	418	1	computer	computer	NOUN
ejpam-3377	418	2	science	science	NOUN
ejpam-3377	418	3	,	,	PUNCT
ejpam-3377	418	4	14	14	NUM
ejpam-3377	418	5	:	:	PUNCT
ejpam-3377	418	6	222–232	222–232	NUM
ejpam-3377	418	7	,	,	PUNCT
ejpam-3377	418	8	2015	2015	NUM
ejpam-3377	418	9	.	.	PUNCT
ejpam-3377	419	1	[	[	X
ejpam-3377	419	2	27	27	NUM
ejpam-3377	419	3	]	]	X
ejpam-3377	419	4	m	m	VERB
ejpam-3377	419	5	m	m	VERB
ejpam-3377	419	6	khader	khader	NOUN
ejpam-3377	419	7	,	,	PUNCT
ejpam-3377	419	8	a	a	DET
ejpam-3377	419	9	s	s	NOUN
ejpam-3377	419	10	hendy	hendy	NOUN
ejpam-3377	419	11	.	.	PUNCT
ejpam-3377	420	1	the	the	DET
ejpam-3377	420	2	approximate	approximate	ADJ
ejpam-3377	420	3	and	and	CCONJ
ejpam-3377	420	4	exact	exact	ADJ
ejpam-3377	420	5	solutions	solution	NOUN
ejpam-3377	420	6	of	of	ADP
ejpam-3377	420	7	the	the	DET
ejpam-3377	420	8	fractional	fractional	ADJ
ejpam-3377	420	9	-	-	PUNCT
ejpam-3377	420	10	order	order	NOUN
ejpam-3377	420	11	delay	delay	NOUN
ejpam-3377	420	12	differential	differential	ADJ
ejpam-3377	420	13	equations	equation	NOUN
ejpam-3377	420	14	using	use	VERB
ejpam-3377	420	15	legendre	legendre	PROPN
ejpam-3377	420	16	seudospectral	seudospectral	ADJ
ejpam-3377	420	17	method	method	PROPN
ejpam-3377	420	18	the	the	DET
ejpam-3377	420	19	approximate	approximate	ADJ
ejpam-3377	420	20	and	and	CCONJ
ejpam-3377	420	21	exact	exact	ADJ
ejpam-3377	420	22	solutions	solution	NOUN
ejpam-3377	420	23	of	of	ADP
ejpam-3377	420	24	the	the	DET
ejpam-3377	420	25	fractional	fractional	ADJ
ejpam-3377	420	26	-	-	PUNCT
ejpam-3377	420	27	order	order	NOUN
ejpam-3377	420	28	delay	delay	NOUN
ejpam-3377	420	29	differential	differential	ADJ
ejpam-3377	420	30	equations	equation	NOUN
ejpam-3377	420	31	using	use	VERB
ejpam-3377	420	32	legendre	legendre	PROPN
ejpam-3377	420	33	seudospectral	seudospectral	ADJ
ejpam-3377	420	34	method	method	NOUN
ejpam-3377	420	35	.	.	PUNCT
ejpam-3377	421	1	int	int	NOUN
ejpam-3377	421	2	.	.	PUNCT
ejpam-3377	422	1	j.	j.	PROPN
ejpam-3377	422	2	pure	pure	PROPN
ejpam-3377	422	3	and	and	CCONJ
ejpam-3377	422	4	appl	appl	PROPN
ejpam-3377	422	5	.	.	PROPN
ejpam-3377	422	6	math	math	PROPN
ejpam-3377	422	7	.	.	PUNCT
ejpam-3377	423	1	,	,	PUNCT
ejpam-3377	423	2	74	74	NUM
ejpam-3377	423	3	(	(	PUNCT
ejpam-3377	423	4	3	3	NUM
ejpam-3377	423	5	):	):	PUNCT
ejpam-3377	423	6	287–297	287–297	NUM
ejpam-3377	423	7	,	,	PUNCT
ejpam-3377	423	8	2012	2012	NUM
ejpam-3377	423	9	.	.	PUNCT
ejpam-3377	424	1	[	[	X
ejpam-3377	424	2	28	28	NUM
ejpam-3377	424	3	]	]	X
ejpam-3377	424	4	y	y	PROPN
ejpam-3377	424	5	li	li	PROPN
ejpam-3377	424	6	.	.	PUNCT
ejpam-3377	425	1	solving	solve	VERB
ejpam-3377	425	2	a	a	DET
ejpam-3377	425	3	nonlinear	nonlinear	ADJ
ejpam-3377	425	4	fractional	fractional	ADJ
ejpam-3377	425	5	differential	differential	NOUN
ejpam-3377	425	6	equation	equation	NOUN
ejpam-3377	425	7	using	use	VERB
ejpam-3377	425	8	chebyshev	chebyshev	NOUN
ejpam-3377	425	9	wavelets	wavelet	NOUN
ejpam-3377	425	10	.	.	PUNCT
ejpam-3377	426	1	nonlinear	nonlinear	PROPN
ejpam-3377	426	2	sci	sci	PROPN
ejpam-3377	426	3	.	.	PUNCT
ejpam-3377	426	4	numer	numer	PROPN
ejpam-3377	426	5	.	.	PUNCT
ejpam-3377	427	1	simul	simul	PROPN
ejpam-3377	427	2	.	.	PROPN
ejpam-3377	427	3	,	,	PUNCT
ejpam-3377	427	4	15:2284–2292	15:2284–2292	NUM
ejpam-3377	427	5	,	,	PUNCT
ejpam-3377	427	6	2010	2010	NUM
ejpam-3377	427	7	.	.	PUNCT
ejpam-3377	428	1	[	[	X
ejpam-3377	428	2	29	29	NUM
ejpam-3377	428	3	]	]	X
ejpam-3377	428	4	s	s	PROPN
ejpam-3377	428	5	linge	linge	PROPN
ejpam-3377	428	6	,	,	PUNCT
ejpam-3377	428	7	j	j	PROPN
ejpam-3377	428	8	sundnem	sundnem	PROPN
ejpam-3377	428	9	,	,	PUNCT
ejpam-3377	428	10	m	m	PROPN
ejpam-3377	428	11	hanslien	hanslien	NOUN
ejpam-3377	428	12	,	,	PUNCT
ejpam-3377	428	13	gt	gt	PROPN
ejpam-3377	428	14	lines	line	NOUN
ejpam-3377	428	15	,	,	PUNCT
ejpam-3377	428	16	a	a	DET
ejpam-3377	428	17	tveito	tveito	NOUN
ejpam-3377	428	18	.	.	PUNCT
ejpam-3377	428	19	numerical	numerical	ADJ
ejpam-3377	428	20	solution	solution	NOUN
ejpam-3377	428	21	of	of	ADP
ejpam-3377	428	22	the	the	DET
ejpam-3377	428	23	bidomain	bidomain	NOUN
ejpam-3377	428	24	equations	equation	NOUN
ejpam-3377	428	25	.	.	PUNCT
ejpam-3377	429	1	philosophical	philosophical	ADJ
ejpam-3377	429	2	transactions	transaction	NOUN
ejpam-3377	429	3	,	,	PUNCT
ejpam-3377	429	4	series	series	NOUN
ejpam-3377	429	5	a	a	PRON
ejpam-3377	429	6	:	:	PUNCT
ejpam-3377	429	7	mathematical	mathematical	ADJ
ejpam-3377	429	8	,	,	PUNCT
ejpam-3377	429	9	physical	physical	ADJ
ejpam-3377	429	10	and	and	CCONJ
ejpam-3377	429	11	engineering	engineering	NOUN
ejpam-3377	429	12	sciences	science	NOUN
ejpam-3377	429	13	,	,	PUNCT
ejpam-3377	429	14	367	367	NUM
ejpam-3377	429	15	:	:	PUNCT
ejpam-3377	429	16	1931–1950	1931–1950	NUM
ejpam-3377	429	17	,	,	PUNCT
ejpam-3377	429	18	2009	2009	NUM
ejpam-3377	429	19	.	.	PUNCT
ejpam-3377	430	1	[	[	X
ejpam-3377	430	2	30	30	NUM
ejpam-3377	430	3	]	]	X
ejpam-3377	430	4	a	a	DET
ejpam-3377	430	5	a	a	DET
ejpam-3377	430	6	moghadam	moghadam	NOUN
ejpam-3377	430	7	,	,	PUNCT
ejpam-3377	430	8	i	i	PRON
ejpam-3377	430	9	aksikas	aksikas	PROPN
ejpam-3377	430	10	,	,	PUNCT
ejpam-3377	430	11	s	s	VERB
ejpam-3377	430	12	dubljevic	dubljevic	ADJ
ejpam-3377	430	13	,	,	PUNCT
ejpam-3377	430	14	j	j	PROPN
ejpam-3377	430	15	f	f	PROPN
ejpam-3377	430	16	forbes	forbes	PROPN
ejpam-3377	430	17	.	.	PUNCT
ejpam-3377	431	1	lq	lq	NOUN
ejpam-3377	431	2	control	control	NOUN
ejpam-3377	431	3	of	of	ADP
ejpam-3377	431	4	coupled	couple	VERB
ejpam-3377	431	5	hyperbolic	hyperbolic	ADJ
ejpam-3377	431	6	pdes	pde	NOUN
ejpam-3377	431	7	and	and	CCONJ
ejpam-3377	431	8	odes	ode	NOUN
ejpam-3377	431	9	:	:	PUNCT
ejpam-3377	431	10	application	application	NOUN
ejpam-3377	431	11	to	to	ADP
ejpam-3377	431	12	a	a	DET
ejpam-3377	431	13	cstr	cstr	NOUN
ejpam-3377	431	14	-	-	PUNCT
ejpam-3377	431	15	pfr	pfr	NOUN
ejpam-3377	431	16	system	system	NOUN
ejpam-3377	431	17	.	.	PUNCT
ejpam-3377	432	1	proceedings	proceeding	NOUN
ejpam-3377	432	2	of	of	ADP
ejpam-3377	432	3	the	the	DET
ejpam-3377	432	4	9th	9th	ADJ
ejpam-3377	432	5	international	international	ADJ
ejpam-3377	432	6	symposium	symposium	NOUN
ejpam-3377	432	7	on	on	ADP
ejpam-3377	432	8	dynamics	dynamic	NOUN
ejpam-3377	432	9	and	and	CCONJ
ejpam-3377	432	10	control	control	NOUN
ejpam-3377	432	11	of	of	ADP
ejpam-3377	432	12	process	process	NOUN
ejpam-3377	432	13	systems	system	NOUN
ejpam-3377	432	14	(	(	PUNCT
ejpam-3377	432	15	dycops	dycop	NOUN
ejpam-3377	432	16	2010	2010	NUM
ejpam-3377	432	17	)	)	PUNCT
ejpam-3377	432	18	,	,	PUNCT
ejpam-3377	432	19	leuven	leuven	PROPN
ejpam-3377	432	20	,	,	PUNCT
ejpam-3377	432	21	belgium	belgium	PROPN
ejpam-3377	432	22	,	,	PUNCT
ejpam-3377	432	23	july	july	PROPN
ejpam-3377	432	24	5	5	NUM
ejpam-3377	432	25	-	-	SYM
ejpam-3377	432	26	7	7	NUM
ejpam-3377	432	27	,	,	PUNCT
ejpam-3377	432	28	2010	2010	NUM
ejpam-3377	432	29	.	.	PUNCT
ejpam-3377	433	1	[	[	X
ejpam-3377	433	2	31	31	NUM
ejpam-3377	433	3	]	]	PUNCT
ejpam-3377	433	4	a	a	DET
ejpam-3377	433	5	mohebbi	mohebbi	NOUN
ejpam-3377	433	6	,	,	PUNCT
ejpam-3377	433	7	m	m	NOUN
ejpam-3377	433	8	abbaszadeh	abbaszadeh	NOUN
ejpam-3377	433	9	and	and	CCONJ
ejpam-3377	433	10	m	m	PROPN
ejpam-3377	433	11	dehghan	dehghan	ADJ
ejpam-3377	433	12	.	.	PUNCT
ejpam-3377	434	1	the	the	DET
ejpam-3377	434	2	use	use	NOUN
ejpam-3377	434	3	of	of	ADP
ejpam-3377	434	4	a	a	DET
ejpam-3377	434	5	meshless	meshless	ADJ
ejpam-3377	434	6	technique	technique	NOUN
ejpam-3377	434	7	based	base	VERB
ejpam-3377	434	8	on	on	ADP
ejpam-3377	434	9	collocation	collocation	NOUN
ejpam-3377	434	10	and	and	CCONJ
ejpam-3377	434	11	radial	radial	ADJ
ejpam-3377	434	12	basis	basis	NOUN
ejpam-3377	434	13	functions	function	NOUN
ejpam-3377	434	14	for	for	ADP
ejpam-3377	434	15	solving	solve	VERB
ejpam-3377	434	16	the	the	DET
ejpam-3377	434	17	fractional	fractional	ADJ
ejpam-3377	434	18	nonlinear	nonlinear	ADJ
ejpam-3377	434	19	schrodinger	schrodinger	PROPN
ejpam-3377	434	20	equation	equation	NOUN
ejpam-3377	434	21	arising	arise	VERB
ejpam-3377	434	22	in	in	ADP
ejpam-3377	434	23	quantum	quantum	ADJ
ejpam-3377	434	24	mechnics	mechnic	NOUN
ejpam-3377	434	25	.	.	PUNCT
ejpam-3377	435	1	eng	eng	PROPN
ejpam-3377	435	2	.	.	PROPN
ejpam-3377	436	1	anal	anal	PROPN
ejpam-3377	436	2	.	.	PUNCT
ejpam-3377	437	1	bound	bind	VERB
ejpam-3377	437	2	.	.	PUNCT
ejpam-3377	437	3	elem	elem	NOUN
ejpam-3377	437	4	.	.	PUNCT
ejpam-3377	438	1	,	,	PUNCT
ejpam-3377	439	1	37	37	NUM
ejpam-3377	439	2	:	:	PUNCT
ejpam-3377	439	3	475–485	475–485	NUM
ejpam-3377	439	4	,	,	PUNCT
ejpam-3377	439	5	2013	2013	NUM
ejpam-3377	439	6	.	.	PUNCT
ejpam-3377	440	1	[	[	X
ejpam-3377	440	2	32	32	NUM
ejpam-3377	440	3	]	]	X
ejpam-3377	440	4	m	m	VERB
ejpam-3377	440	5	a	a	DET
ejpam-3377	440	6	mohamed	mohamed	ADJ
ejpam-3377	440	7	and	and	CCONJ
ejpam-3377	440	8	m	m	PROPN
ejpam-3377	440	9	s	s	PART
ejpam-3377	440	10	torky	torky	NOUN
ejpam-3377	440	11	.	.	PUNCT
ejpam-3377	441	1	solution	solution	NOUN
ejpam-3377	441	2	of	of	ADP
ejpam-3377	441	3	linear	linear	ADJ
ejpam-3377	441	4	system	system	NOUN
ejpam-3377	441	5	of	of	ADP
ejpam-3377	441	6	partial	partial	ADJ
ejpam-3377	441	7	differential	differential	ADJ
ejpam-3377	441	8	equations	equation	NOUN
ejpam-3377	441	9	by	by	ADP
ejpam-3377	441	10	legendre	legendre	PROPN
ejpam-3377	441	11	multiwavelet	multiwavelet	PROPN
ejpam-3377	441	12	and	and	CCONJ
ejpam-3377	441	13	chebyshev	chebyshev	PROPN
ejpam-3377	441	14	multiwavelet	multiwavelet	NOUN
ejpam-3377	441	15	.	.	PUNCT
ejpam-3377	442	1	int.j	int.j	PROPN
ejpam-3377	442	2	.	.	PROPN
ejpam-3377	442	3	sci.inno	sci.inno	PROPN
ejpam-3377	442	4	.	.	PUNCT
ejpam-3377	442	5	math	math	PROPN
ejpam-3377	442	6	.	.	PUNCT
ejpam-3377	443	1	research	research	NOUN
ejpam-3377	443	2	,	,	PUNCT
ejpam-3377	443	3	2(12	2(12	NUM
ejpam-3377	443	4	):	):	PUNCT
ejpam-3377	443	5	966–976	966–976	NUM
ejpam-3377	443	6	,	,	PUNCT
ejpam-3377	443	7	2014	2014	NUM
ejpam-3377	443	8	.	.	PUNCT
ejpam-3377	444	1	[	[	X
ejpam-3377	444	2	33	33	NUM
ejpam-3377	444	3	]	]	SYM
ejpam-3377	444	4	s	s	X
ejpam-3377	444	5	momani	momani	NOUN
ejpam-3377	444	6	,	,	PUNCT
ejpam-3377	444	7	o	o	X
ejpam-3377	444	8	a	a	DET
ejpam-3377	444	9	arqub	arqub	NOUN
ejpam-3377	444	10	,	,	PUNCT
ejpam-3377	444	11	t	t	PROPN
ejpam-3377	444	12	hayat	hayat	PROPN
ejpam-3377	444	13	,	,	PUNCT
ejpam-3377	444	14	h	h	PROPN
ejpam-3377	444	15	al	al	PROPN
ejpam-3377	444	16	-	-	PUNCT
ejpam-3377	444	17	sulami	sulami	PROPN
ejpam-3377	444	18	.	.	PUNCT
ejpam-3377	445	1	a	a	DET
ejpam-3377	445	2	computational	computational	ADJ
ejpam-3377	445	3	method	method	NOUN
ejpam-3377	445	4	for	for	ADP
ejpam-3377	445	5	solving	solve	VERB
ejpam-3377	445	6	periodic	periodic	ADJ
ejpam-3377	445	7	boundary	boundary	ADJ
ejpam-3377	445	8	value	value	NOUN
ejpam-3377	445	9	problems	problem	NOUN
ejpam-3377	445	10	for	for	ADP
ejpam-3377	445	11	integro	integro	ADJ
ejpam-3377	445	12	-	-	PUNCT
ejpam-3377	445	13	differential	differential	NOUN
ejpam-3377	445	14	equations	equation	NOUN
ejpam-3377	445	15	of	of	ADP
ejpam-3377	445	16	fredholmvolterra	fredholmvolterra	NOUN
ejpam-3377	445	17	type	type	NOUN
ejpam-3377	445	18	.	.	PUNCT
ejpam-3377	446	1	applied	apply	VERB
ejpam-3377	446	2	mathematics	mathematic	NOUN
ejpam-3377	446	3	and	and	CCONJ
ejpam-3377	446	4	computation	computation	NOUN
ejpam-3377	446	5	,	,	PUNCT
ejpam-3377	446	6	240(1	240(1	NUM
ejpam-3377	446	7	):	):	PUNCT
ejpam-3377	446	8	229–39	229–39	NOUN
ejpam-3377	446	9	,	,	PUNCT
ejpam-3377	446	10	2014	2014	NUM
ejpam-3377	446	11	.	.	PUNCT
ejpam-3377	447	1	[	[	X
ejpam-3377	447	2	34	34	NUM
ejpam-3377	447	3	]	]	SYM
ejpam-3377	447	4	s	s	PART
ejpam-3377	447	5	t	t	PROPN
ejpam-3377	447	6	mohyud	mohyud	NOUN
ejpam-3377	447	7	-	-	PUNCT
ejpam-3377	447	8	din	din	NOUN
ejpam-3377	447	9	and	and	CCONJ
ejpam-3377	447	10	ma	ma	PROPN
ejpam-3377	447	11	noor	noor	PROPN
ejpam-3377	447	12	.	.	PUNCT
ejpam-3377	448	1	homotopy	homotopy	PROPN
ejpam-3377	448	2	purturbation	purturbation	NOUN
ejpam-3377	448	3	method	method	NOUN
ejpam-3377	448	4	for	for	ADP
ejpam-3377	448	5	solving	solve	VERB
ejpam-3377	448	6	partial	partial	ADJ
ejpam-3377	448	7	differential	differential	NOUN
ejpam-3377	448	8	equations	equation	NOUN
ejpam-3377	448	9	.	.	PUNCT
ejpam-3377	449	1	z.naturforsch	z.naturforsch	NOUN
ejpam-3377	449	2	,	,	PUNCT
ejpam-3377	449	3	64a	64a	NOUN
ejpam-3377	449	4	:	:	PUNCT
ejpam-3377	449	5	157–170	157–170	NUM
ejpam-3377	449	6	,	,	PUNCT
ejpam-3377	449	7	2009	2009	NUM
ejpam-3377	449	8	.	.	PUNCT
ejpam-3377	450	1	[	[	X
ejpam-3377	450	2	35	35	NUM
ejpam-3377	450	3	]	]	X
ejpam-3377	450	4	k	k	PROPN
ejpam-3377	450	5	b	b	PROPN
ejpam-3377	450	6	oldham	oldham	PROPN
ejpam-3377	450	7	,	,	PUNCT
ejpam-3377	450	8	j	j	PROPN
ejpam-3377	450	9	spanier	spanier	NOUN
ejpam-3377	450	10	.	.	PUNCT
ejpam-3377	451	1	the	the	DET
ejpam-3377	451	2	fractional	fractional	ADJ
ejpam-3377	451	3	calculus	calculus	NOUN
ejpam-3377	451	4	.	.	PUNCT
ejpam-3377	452	1	academic	academic	ADJ
ejpam-3377	452	2	press	press	NOUN
ejpam-3377	452	3	,	,	PUNCT
ejpam-3377	452	4	new	new	PROPN
ejpam-3377	452	5	york	york	PROPN
ejpam-3377	452	6	,	,	PUNCT
ejpam-3377	452	7	1974	1974	NUM
ejpam-3377	452	8	.	.	PUNCT
ejpam-3377	453	1	references	reference	NOUN
ejpam-3377	453	2	56	56	NUM
ejpam-3377	454	1	[	[	X
ejpam-3377	454	2	36	36	NUM
ejpam-3377	454	3	]	]	PUNCT
ejpam-3377	454	4	s	s	PART
ejpam-3377	454	5	wensheng	wensheng	NOUN
ejpam-3377	454	6	.	.	PUNCT
ejpam-3377	455	1	computer	computer	NOUN
ejpam-3377	455	2	simulation	simulation	NOUN
ejpam-3377	455	3	and	and	CCONJ
ejpam-3377	455	4	modeling	modeling	NOUN
ejpam-3377	455	5	of	of	ADP
ejpam-3377	455	6	physical	physical	ADJ
ejpam-3377	455	7	and	and	CCONJ
ejpam-3377	455	8	biological	biological	ADJ
ejpam-3377	455	9	processes	process	NOUN
ejpam-3377	455	10	using	use	VERB
ejpam-3377	455	11	partial	partial	ADJ
ejpam-3377	455	12	differential	differential	ADJ
ejpam-3377	455	13	equations	equation	NOUN
ejpam-3377	455	14	,	,	PUNCT
ejpam-3377	455	15	university	university	PROPN
ejpam-3377	455	16	of	of	ADP
ejpam-3377	455	17	kentucky	kentucky	PROPN
ejpam-3377	455	18	doctoral	doctoral	ADJ
ejpam-3377	455	19	dissertations	dissertation	NOUN
ejpam-3377	455	20	,	,	PUNCT
ejpam-3377	455	21	2007	2007	NUM
ejpam-3377	455	22	.	.	PUNCT
ejpam-3377	456	1	[	[	X
ejpam-3377	456	2	37	37	NUM
ejpam-3377	456	3	]	]	X
ejpam-3377	456	4	z	z	NOUN
ejpam-3377	456	5	odibat	odibat	NOUN
ejpam-3377	456	6	and	and	CCONJ
ejpam-3377	456	7	s	s	NOUN
ejpam-3377	456	8	momani	momani	NOUN
ejpam-3377	456	9	.	.	PUNCT
ejpam-3377	457	1	a	a	DET
ejpam-3377	457	2	generalized	generalize	VERB
ejpam-3377	457	3	differential	differential	NOUN
ejpam-3377	457	4	transform	transform	NOUN
ejpam-3377	457	5	method	method	NOUN
ejpam-3377	457	6	for	for	ADP
ejpam-3377	457	7	linear	linear	ADJ
ejpam-3377	457	8	partial	partial	ADJ
ejpam-3377	457	9	differential	differential	ADJ
ejpam-3377	457	10	equations	equation	NOUN
ejpam-3377	457	11	of	of	ADP
ejpam-3377	457	12	fractional	fractional	ADJ
ejpam-3377	457	13	order	order	NOUN
ejpam-3377	457	14	,	,	PUNCT
ejpam-3377	457	15	appl	appl	PROPN
ejpam-3377	457	16	.	.	PROPN
ejpam-3377	457	17	math	math	PROPN
ejpam-3377	457	18	.	.	PUNCT
ejpam-3377	458	1	lett	lett	PROPN
ejpam-3377	458	2	.	.	PROPN
ejpam-3377	458	3	,	,	PUNCT
ejpam-3377	458	4	21(2):194–199	21(2):194–199	PROPN
ejpam-3377	458	5	,	,	PUNCT
ejpam-3377	458	6	2008	2008	NUM
ejpam-3377	458	7	.	.	PUNCT
ejpam-3377	459	1	[	[	X
ejpam-3377	459	2	38	38	NUM
ejpam-3377	459	3	]	]	SYM
ejpam-3377	459	4	v	v	NOUN
ejpam-3377	459	5	parthiban	parthiban	NOUN
ejpam-3377	459	6	and	and	CCONJ
ejpam-3377	459	7	k	k	PROPN
ejpam-3377	459	8	balachandran	balachandran	PROPN
ejpam-3377	459	9	.	.	PUNCT
ejpam-3377	460	1	solutions	solution	NOUN
ejpam-3377	460	2	of	of	ADP
ejpam-3377	460	3	system	system	NOUN
ejpam-3377	460	4	of	of	ADP
ejpam-3377	460	5	fractional	fractional	ADJ
ejpam-3377	460	6	partial	partial	ADJ
ejpam-3377	460	7	differential	differential	NOUN
ejpam-3377	460	8	equations	equation	NOUN
ejpam-3377	460	9	.	.	PUNCT
ejpam-3377	461	1	appl.applied	appl.applie	VERB
ejpam-3377	461	2	mathematics	mathematic	NOUN
ejpam-3377	461	3	,	,	PUNCT
ejpam-3377	461	4	8(1	8(1	NOUN
ejpam-3377	461	5	):	):	PUNCT
ejpam-3377	461	6	289	289	NUM
ejpam-3377	461	7	–	–	PUNCT
ejpam-3377	461	8	304	304	NUM
ejpam-3377	461	9	,	,	PUNCT
ejpam-3377	461	10	2013	2013	NUM
ejpam-3377	461	11	.	.	PUNCT
ejpam-3377	462	1	[	[	X
ejpam-3377	462	2	39	39	NUM
ejpam-3377	462	3	]	]	PUNCT
ejpam-3377	462	4	m	m	VERB
ejpam-3377	462	5	rahman	rahman	PROPN
ejpam-3377	462	6	.	.	PUNCT
ejpam-3377	463	1	boundary	boundary	ADJ
ejpam-3377	463	2	value	value	NOUN
ejpam-3377	463	3	problems	problem	NOUN
ejpam-3377	463	4	for	for	ADP
ejpam-3377	463	5	fractional	fractional	ADJ
ejpam-3377	463	6	differential	differential	ADJ
ejpam-3377	463	7	equations	equation	NOUN
ejpam-3377	463	8	:	:	PUNCT
ejpam-3377	463	9	existence	existence	NOUN
ejpam-3377	463	10	theory	theory	NOUN
ejpam-3377	463	11	and	and	CCONJ
ejpam-3377	463	12	numerical	numerical	ADJ
ejpam-3377	463	13	solutions	solution	NOUN
ejpam-3377	463	14	.	.	PUNCT
ejpam-3377	464	1	phd	phd	NOUN
ejpam-3377	464	2	thesis	thesis	PROPN
ejpam-3377	464	3	,	,	PUNCT
ejpam-3377	464	4	nust	nust	PROPN
ejpam-3377	464	5	university	university	PROPN
ejpam-3377	464	6	,	,	PUNCT
ejpam-3377	464	7	pakistan	pakistan	PROPN
ejpam-3377	464	8	,	,	PUNCT
ejpam-3377	464	9	2011	2011	NUM
ejpam-3377	464	10	.	.	PUNCT
ejpam-3377	465	1	[	[	X
ejpam-3377	465	2	40	40	NUM
ejpam-3377	465	3	]	]	X
ejpam-3377	465	4	j	j	PROPN
ejpam-3377	465	5	sundnes	sundne	NOUN
ejpam-3377	465	6	,	,	PUNCT
ejpam-3377	465	7	gt	gt	PROPN
ejpam-3377	465	8	lines	line	NOUN
ejpam-3377	465	9	,	,	PUNCT
ejpam-3377	465	10	ka	ka	PROPN
ejpam-3377	465	11	mardal	mardal	PROPN
ejpam-3377	465	12	,	,	PUNCT
ejpam-3377	465	13	a	a	DET
ejpam-3377	465	14	tveito	tveito	NOUN
ejpam-3377	465	15	,	,	PUNCT
ejpam-3377	465	16	multigrid	multigrid	ADJ
ejpam-3377	465	17	block	block	NOUN
ejpam-3377	465	18	preconditioning	precondition	VERB
ejpam-3377	465	19	for	for	ADP
ejpam-3377	465	20	a	a	DET
ejpam-3377	465	21	coupled	couple	VERB
ejpam-3377	465	22	system	system	NOUN
ejpam-3377	465	23	of	of	ADP
ejpam-3377	465	24	partial	partial	ADJ
ejpam-3377	465	25	differential	differential	ADJ
ejpam-3377	465	26	equations	equation	NOUN
ejpam-3377	465	27	modeling	model	VERB
ejpam-3377	465	28	the	the	DET
ejpam-3377	465	29	electrical	electrical	ADJ
ejpam-3377	465	30	activity	activity	NOUN
ejpam-3377	465	31	in	in	ADP
ejpam-3377	465	32	the	the	DET
ejpam-3377	465	33	heart	heart	NOUN
ejpam-3377	465	34	.	.	PUNCT
ejpam-3377	466	1	comput	comput	NOUN
ejpam-3377	466	2	.	.	PUNCT
ejpam-3377	467	1	method.biomech	method.biomech	NOUN
ejpam-3377	467	2	.	.	PROPN
ejpam-3377	467	3	biomed	biome	VERB
ejpam-3377	467	4	.	.	PUNCT
ejpam-3377	468	1	eng	eng	PROPN
ejpam-3377	468	2	.	.	PROPN
ejpam-3377	468	3	,	,	PUNCT
ejpam-3377	468	4	5(6	5(6	NUM
ejpam-3377	468	5	):	):	PUNCT
ejpam-3377	468	6	397–409	397–409	NUM
ejpam-3377	468	7	,	,	PUNCT
ejpam-3377	468	8	2002	2002	NUM
ejpam-3377	468	9	.	.	PUNCT
ejpam-3377	469	1	[	[	X
ejpam-3377	469	2	41	41	NUM
ejpam-3377	469	3	]	]	X
ejpam-3377	469	4	j	j	PROPN
ejpam-3377	469	5	sundnes	sundnes	PROPN
ejpam-3377	469	6	,	,	PUNCT
ejpam-3377	469	7	gt	gt	PROPN
ejpam-3377	469	8	lines	line	NOUN
ejpam-3377	469	9	,	,	PUNCT
ejpam-3377	469	10	a	a	DET
ejpam-3377	469	11	tveito	tveito	NOUN
ejpam-3377	469	12	.	.	PUNCT
ejpam-3377	470	1	an	an	DET
ejpam-3377	470	2	operator	operator	NOUN
ejpam-3377	470	3	splitting	splitting	NOUN
ejpam-3377	470	4	method	method	NOUN
ejpam-3377	470	5	for	for	ADP
ejpam-3377	470	6	solving	solve	VERB
ejpam-3377	470	7	the	the	DET
ejpam-3377	470	8	bidomain	bidomain	NOUN
ejpam-3377	470	9	equations	equation	NOUN
ejpam-3377	470	10	coupled	couple	VERB
ejpam-3377	470	11	to	to	ADP
ejpam-3377	470	12	a	a	DET
ejpam-3377	470	13	volume	volume	NOUN
ejpam-3377	470	14	conductor	conductor	NOUN
ejpam-3377	470	15	model	model	NOUN
ejpam-3377	470	16	for	for	ADP
ejpam-3377	470	17	the	the	DET
ejpam-3377	470	18	torso	torso	PROPN
ejpam-3377	470	19	.	.	PUNCT
ejpam-3377	471	1	mathematical	mathematical	ADJ
ejpam-3377	471	2	biosciences	bioscience	NOUN
ejpam-3377	471	3	,	,	PUNCT
ejpam-3377	471	4	194(2):233–248	194(2):233–248	NUM
ejpam-3377	471	5	,	,	PUNCT
ejpam-3377	471	6	2005	2005	NUM
ejpam-3377	471	7	.	.	PUNCT
ejpam-3377	472	1	[	[	X
ejpam-3377	472	2	42	42	NUM
ejpam-3377	472	3	]	]	X
ejpam-3377	472	4	j	j	PROPN
ejpam-3377	472	5	singh	singh	PROPN
ejpam-3377	472	6	,	,	PUNCT
ejpam-3377	472	7	d	d	PROPN
ejpam-3377	472	8	kumar	kumar	PROPN
ejpam-3377	472	9	,	,	PUNCT
ejpam-3377	472	10	s	s	PROPN
ejpam-3377	472	11	kumar	kumar	PROPN
ejpam-3377	472	12	.	.	PUNCT
ejpam-3377	473	1	new	new	ADJ
ejpam-3377	473	2	treatment	treatment	NOUN
ejpam-3377	473	3	of	of	ADP
ejpam-3377	473	4	fractional	fractional	ADJ
ejpam-3377	473	5	fornberg	fornberg	PROPN
ejpam-3377	473	6	-	-	PUNCT
ejpam-3377	473	7	whitham	whitham	NOUN
ejpam-3377	473	8	equation	equation	NOUN
ejpam-3377	473	9	via	via	ADP
ejpam-3377	473	10	laplace	laplace	NOUN
ejpam-3377	473	11	transform	transform	NOUN
ejpam-3377	473	12	.	.	PUNCT
ejpam-3377	474	1	ain	ain	PROPN
ejpam-3377	474	2	sham	sham	PROPN
ejpam-3377	474	3	eng	eng	PROPN
ejpam-3377	474	4	.	.	PUNCT
ejpam-3377	475	1	j.	j.	PROPN
ejpam-3377	475	2	,	,	PUNCT
ejpam-3377	475	3	4	4	NUM
ejpam-3377	475	4	:	:	PUNCT
ejpam-3377	475	5	557–562	557–562	NUM
ejpam-3377	475	6	,	,	PUNCT
ejpam-3377	475	7	2013	2013	NUM
ejpam-3377	475	8	.	.	PUNCT
ejpam-3377	476	1	[	[	X
ejpam-3377	476	2	43	43	NUM
ejpam-3377	476	3	]	]	X
ejpam-3377	476	4	k	k	PROPN
ejpam-3377	476	5	shah	shah	PROPN
ejpam-3377	476	6	,	,	PUNCT
ejpam-3377	476	7	h	h	PROPN
ejpam-3377	476	8	khalil	khalil	PROPN
ejpam-3377	476	9	and	and	CCONJ
ejpam-3377	476	10	ra	ra	PROPN
ejpam-3377	476	11	khan	khan	PROPN
ejpam-3377	476	12	.	.	PUNCT
ejpam-3377	477	1	analytical	analytical	ADJ
ejpam-3377	477	2	solutions	solution	NOUN
ejpam-3377	477	3	of	of	ADP
ejpam-3377	477	4	fractional	fractional	ADJ
ejpam-3377	477	5	order	order	NOUN
ejpam-3377	477	6	diffusion	diffusion	NOUN
ejpam-3377	477	7	equations	equation	NOUN
ejpam-3377	477	8	by	by	ADP
ejpam-3377	477	9	natural	natural	ADJ
ejpam-3377	477	10	transform	transform	NOUN
ejpam-3377	477	11	method	method	NOUN
ejpam-3377	477	12	.	.	PUNCT
ejpam-3377	478	1	iran	iran	PROPN
ejpam-3377	478	2	.	.	PUNCT
ejpam-3377	479	1	j.	j.	PROPN
ejpam-3377	479	2	sci	sci	PROPN
ejpam-3377	479	3	.	.	PROPN
ejpam-3377	479	4	technol	technol	PROPN
ejpam-3377	479	5	:	:	PUNCT
ejpam-3377	479	6	trans	trans	PROPN
ejpam-3377	479	7	sci	sci	PROPN
ejpam-3377	479	8	a	a	PRON
ejpam-3377	479	9	,	,	PUNCT
ejpam-3377	479	10	2016	2016	NUM
ejpam-3377	479	11	:	:	PUNCT
ejpam-3377	479	12	12	12	NUM
ejpam-3377	479	13	pages	page	NOUN
ejpam-3377	479	14	,	,	PUNCT
ejpam-3377	479	15	2016	2016	NUM
ejpam-3377	479	16	.	.	PUNCT
ejpam-3377	480	1	[	[	X
ejpam-3377	480	2	44	44	NUM
ejpam-3377	480	3	]	]	X
ejpam-3377	480	4	r	r	NOUN
ejpam-3377	480	5	saadeh	saadeh	PROPN
ejpam-3377	480	6	,	,	PUNCT
ejpam-3377	480	7	m	m	PROPN
ejpam-3377	480	8	al	al	PROPN
ejpam-3377	480	9	-	-	PUNCT
ejpam-3377	480	10	smadi	smadi	NOUN
ejpam-3377	480	11	,	,	PUNCT
ejpam-3377	480	12	g	g	PROPN
ejpam-3377	480	13	gumah	gumah	PROPN
ejpam-3377	480	14	,	,	PUNCT
ejpam-3377	480	15	h	h	PROPN
ejpam-3377	480	16	khalil	khalil	PROPN
ejpam-3377	480	17	,	,	PUNCT
ejpam-3377	480	18	r	r	PROPN
ejpam-3377	480	19	a	a	DET
ejpam-3377	480	20	khan	khan	PROPN
ejpam-3377	480	21	.	.	PUNCT
ejpam-3377	481	1	numerical	numerical	PROPN
ejpam-3377	481	2	investigation	investigation	NOUN
ejpam-3377	481	3	for	for	ADP
ejpam-3377	481	4	solving	solve	VERB
ejpam-3377	481	5	two	two	NUM
ejpam-3377	481	6	-	-	PUNCT
ejpam-3377	481	7	point	point	NOUN
ejpam-3377	481	8	fuzzy	fuzzy	ADJ
ejpam-3377	481	9	boundary	boundary	ADJ
ejpam-3377	481	10	value	value	NOUN
ejpam-3377	481	11	problems	problem	NOUN
ejpam-3377	481	12	by	by	ADP
ejpam-3377	481	13	reproducing	reproduce	VERB
ejpam-3377	481	14	kernel	kernel	PROPN
ejpam-3377	481	15	approach	approach	NOUN
ejpam-3377	481	16	.	.	PUNCT
ejpam-3377	482	1	applied	apply	VERB
ejpam-3377	482	2	mathematics	mathematics	PROPN
ejpam-3377	482	3	&	&	CCONJ
ejpam-3377	482	4	information	information	NOUN
ejpam-3377	482	5	sciences	sciences	PROPN
ejpam-3377	482	6	,	,	PUNCT
ejpam-3377	482	7	10(6	10(6	ADV
ejpam-3377	482	8	):	):	PUNCT
ejpam-3377	482	9	1–13	1–13	NUM
ejpam-3377	482	10	,	,	PUNCT
ejpam-3377	482	11	2016	2016	NUM
ejpam-3377	482	12	.	.	PUNCT
ejpam-3377	483	1	[	[	X
ejpam-3377	483	2	45	45	NUM
ejpam-3377	483	3	]	]	X
ejpam-3377	483	4	k	k	PROPN
ejpam-3377	483	5	shah	shah	PROPN
ejpam-3377	483	6	,	,	PUNCT
ejpam-3377	483	7	a	a	DET
ejpam-3377	483	8	ali	ali	PROPN
ejpam-3377	483	9	and	and	CCONJ
ejpam-3377	483	10	r	r	PROPN
ejpam-3377	483	11	a	a	DET
ejpam-3377	483	12	khan	khan	PROPN
ejpam-3377	483	13	.	.	PUNCT
ejpam-3377	484	1	numerical	numerical	ADJ
ejpam-3377	484	2	solutions	solution	NOUN
ejpam-3377	484	3	of	of	ADP
ejpam-3377	484	4	fractional	fractional	ADJ
ejpam-3377	484	5	order	order	NOUN
ejpam-3377	484	6	system	system	NOUN
ejpam-3377	484	7	of	of	ADP
ejpam-3377	484	8	bagley	bagley	NOUN
ejpam-3377	484	9	-	-	PUNCT
ejpam-3377	484	10	torvik	torvik	NOUN
ejpam-3377	484	11	equation	equation	NOUN
ejpam-3377	484	12	using	use	VERB
ejpam-3377	484	13	operational	operational	ADJ
ejpam-3377	484	14	matrices	matrix	NOUN
ejpam-3377	484	15	.	.	PUNCT
ejpam-3377	485	1	sindh	sindh	PROPN
ejpam-3377	485	2	univ	univ	PROPN
ejpam-3377	485	3	.	.	PUNCT
ejpam-3377	486	1	res	re	NOUN
ejpam-3377	486	2	.	.	PUNCT
ejpam-3377	487	1	j.	j.	PROPN
ejpam-3377	487	2	,	,	PUNCT
ejpam-3377	487	3	47(4	47(4	PROPN
ejpam-3377	487	4	)	)	PUNCT
ejpam-3377	487	5	:	:	PUNCT
ejpam-3377	488	1	757–762	757–762	NUM
ejpam-3377	488	2	,	,	PUNCT
ejpam-3377	488	3	2015	2015	NUM
ejpam-3377	488	4	.	.	PUNCT
ejpam-3377	489	1	[	[	X
ejpam-3377	489	2	46	46	NUM
ejpam-3377	489	3	]	]	PUNCT
ejpam-3377	489	4	a	a	DET
ejpam-3377	489	5	saadatmandi	saadatmandi	NOUN
ejpam-3377	489	6	and	and	CCONJ
ejpam-3377	489	7	m	m	VERB
ejpam-3377	489	8	deghan	deghan	ADJ
ejpam-3377	489	9	.	.	PUNCT
ejpam-3377	490	1	a	a	DET
ejpam-3377	490	2	new	new	ADJ
ejpam-3377	490	3	operational	operational	ADJ
ejpam-3377	490	4	matrix	matrix	NOUN
ejpam-3377	490	5	for	for	ADP
ejpam-3377	490	6	solving	solve	VERB
ejpam-3377	490	7	fractional	fractional	ADJ
ejpam-3377	490	8	-	-	PUNCT
ejpam-3377	490	9	order	order	NOUN
ejpam-3377	490	10	differential	differential	ADJ
ejpam-3377	490	11	equation	equation	NOUN
ejpam-3377	490	12	.	.	PUNCT
ejpam-3377	491	1	comp	comp	PROPN
ejpam-3377	491	2	.	.	PUNCT
ejpam-3377	492	1	math	math	PROPN
ejpam-3377	492	2	.	.	PUNCT
ejpam-3377	493	1	appl	appl	PROPN
ejpam-3377	493	2	.	.	PROPN
ejpam-3377	493	3	,	,	PUNCT
ejpam-3377	493	4	59:1326–1336	59:1326–1336	NOUN
ejpam-3377	493	5	,	,	PUNCT
ejpam-3377	493	6	2010	2010	NUM
ejpam-3377	493	7	.	.	PUNCT
ejpam-3377	494	1	[	[	X
ejpam-3377	494	2	47	47	NUM
ejpam-3377	494	3	]	]	X
ejpam-3377	494	4	m	m	AUX
ejpam-3377	494	5	uddin	uddin	ADJ
ejpam-3377	494	6	and	and	CCONJ
ejpam-3377	494	7	s	s	VERB
ejpam-3377	494	8	haq	haq	PROPN
ejpam-3377	494	9	.	.	PUNCT
ejpam-3377	495	1	rbfs	rbfs	NOUN
ejpam-3377	495	2	approximation	approximation	NOUN
ejpam-3377	495	3	method	method	NOUN
ejpam-3377	495	4	for	for	ADP
ejpam-3377	495	5	time	time	NOUN
ejpam-3377	495	6	fractional	fractional	ADJ
ejpam-3377	495	7	partial	partial	ADJ
ejpam-3377	495	8	differential	differential	NOUN
ejpam-3377	495	9	equations	equation	NOUN
ejpam-3377	495	10	.	.	PUNCT
ejpam-3377	496	1	commun	commun	PROPN
ejpam-3377	496	2	.	.	PUNCT
ejpam-3377	497	1	nonlinear	nonlinear	PROPN
ejpam-3377	497	2	sci.numer.simul	sci.numer.simul	PROPN
ejpam-3377	497	3	,	,	PUNCT
ejpam-3377	497	4	16	16	NUM
ejpam-3377	497	5	:	:	SYM
ejpam-3377	497	6	4208–4214	4208–4214	NUM
ejpam-3377	497	7	,	,	PUNCT
ejpam-3377	497	8	2011	2011	NUM
ejpam-3377	497	9	.	.	PUNCT
ejpam-3377	498	1	[	[	X
ejpam-3377	498	2	48	48	NUM
ejpam-3377	498	3	]	]	X
ejpam-3377	498	4	y	y	PROPN
ejpam-3377	498	5	wang	wang	PROPN
ejpam-3377	498	6	and	and	CCONJ
ejpam-3377	498	7	q	q	PROPN
ejpam-3377	498	8	fan	fan	PROPN
ejpam-3377	498	9	.	.	PUNCT
ejpam-3377	499	1	the	the	DET
ejpam-3377	499	2	second	second	ADJ
ejpam-3377	499	3	kind	kind	NOUN
ejpam-3377	499	4	chebyshev	chebyshev	PROPN
ejpam-3377	499	5	wavelet	wavelet	NOUN
ejpam-3377	499	6	method	method	NOUN
ejpam-3377	499	7	for	for	ADP
ejpam-3377	499	8	solving	solve	VERB
ejpam-3377	499	9	fractional	fractional	ADJ
ejpam-3377	499	10	differential	differential	ADJ
ejpam-3377	499	11	equation	equation	NOUN
ejpam-3377	499	12	.	.	PUNCT
ejpam-3377	500	1	appl	appl	PROPN
ejpam-3377	500	2	.	.	PROPN
ejpam-3377	500	3	math	math	PROPN
ejpam-3377	500	4	.	.	PUNCT
ejpam-3377	501	1	comput	comput	NOUN
ejpam-3377	501	2	.	.	PUNCT
ejpam-3377	501	3	,	,	PUNCT
ejpam-3377	501	4	218	218	NUM
ejpam-3377	501	5	:	:	PUNCT
ejpam-3377	501	6	85–92	85–92	NUM
ejpam-3377	501	7	,	,	PUNCT
ejpam-3377	501	8	2012	2012	NUM
ejpam-3377	501	9	.	.	PUNCT
ejpam-3377	502	1	[	[	X
ejpam-3377	502	2	49	49	NUM
ejpam-3377	502	3	]	]	PUNCT
ejpam-3377	502	4	a	a	DET
ejpam-3377	502	5	m	m	PROPN
ejpam-3377	502	6	yang	yang	PROPN
ejpam-3377	502	7	,	,	PUNCT
ejpam-3377	502	8	y	y	PROPN
ejpam-3377	502	9	z	z	PROPN
ejpam-3377	502	10	zhang	zhang	PROPN
ejpam-3377	502	11	and	and	CCONJ
ejpam-3377	502	12	y	y	PROPN
ejpam-3377	502	13	long	long	ADV
ejpam-3377	502	14	.	.	PUNCT
ejpam-3377	503	1	fourier	fourier	PROPN
ejpam-3377	503	2	transforms	transform	VERB
ejpam-3377	503	3	to	to	ADP
ejpam-3377	503	4	heat	heat	NOUN
ejpam-3377	503	5	-	-	PUNCT
ejpam-3377	503	6	conduction	conduction	NOUN
ejpam-3377	503	7	in	in	ADP
ejpam-3377	503	8	a	a	DET
ejpam-3377	503	9	semi	semi	ADJ
ejpam-3377	503	10	-	-	ADJ
ejpam-3377	503	11	infnite	infnite	ADJ
ejpam-3377	503	12	fractal	fractal	ADJ
ejpam-3377	503	13	bar	bar	NOUN
ejpam-3377	503	14	.	.	PUNCT
ejpam-3377	504	1	thermal	thermal	ADJ
ejpam-3377	504	2	science	science	NOUN
ejpam-3377	504	3	,	,	PUNCT
ejpam-3377	504	4	17(3):707–713	17(3):707–713	PROPN
ejpam-3377	504	5	,	,	PUNCT
ejpam-3377	504	6	2013	2013	NUM
ejpam-3377	504	7	.	.	PUNCT
ejpam-3377	505	1	references	reference	NOUN
ejpam-3377	505	2	57	57	NUM
ejpam-3377	506	1	[	[	X
ejpam-3377	506	2	50	50	NUM
ejpam-3377	506	3	]	]	PUNCT
ejpam-3377	506	4	m	m	VERB
ejpam-3377	506	5	yi	yi	NOUN
ejpam-3377	506	6	and	and	CCONJ
ejpam-3377	506	7	y	y	PROPN
ejpam-3377	506	8	chen	chen	PROPN
ejpam-3377	506	9	.	.	PUNCT
ejpam-3377	507	1	haar	haar	PROPN
ejpam-3377	507	2	wavelet	wavelet	PROPN
ejpam-3377	507	3	operational	operational	ADJ
ejpam-3377	507	4	matrix	matrix	NOUN
ejpam-3377	507	5	method	method	NOUN
ejpam-3377	507	6	for	for	ADP
ejpam-3377	507	7	solving	solve	VERB
ejpam-3377	507	8	fractional	fractional	ADJ
ejpam-3377	507	9	partial	partial	ADJ
ejpam-3377	507	10	differential	differential	NOUN
ejpam-3377	507	11	equations	equation	NOUN
ejpam-3377	507	12	.	.	PUNCT
ejpam-3377	508	1	appl	appl	PROPN
ejpam-3377	508	2	.	.	PUNCT
ejpam-3377	509	1	math.comput	math.comput	PROPN
ejpam-3377	509	2	.	.	PUNCT
ejpam-3377	509	3	,	,	PUNCT
ejpam-3377	509	4	282(17	282(17	NUM
ejpam-3377	509	5	)	)	PUNCT
ejpam-3377	509	6	:	:	PUNCT
ejpam-3377	510	1	229–242	229–242	NUM
ejpam-3377	510	2	,	,	PUNCT
ejpam-3377	510	3	2012	2012	NUM
ejpam-3377	510	4	.	.	PUNCT
ejpam-3377	511	1	[	[	X
ejpam-3377	511	2	51	51	NUM
ejpam-3377	511	3	]	]	X
ejpam-3377	511	4	y	y	PROPN
ejpam-3377	511	5	yang	yang	PROPN
ejpam-3377	511	6	,	,	PUNCT
ejpam-3377	511	7	y	y	PROPN
ejpam-3377	511	8	ma	ma	PROPN
ejpam-3377	511	9	and	and	CCONJ
ejpam-3377	511	10	l	l	PROPN
ejpam-3377	511	11	wang	wang	PROPN
ejpam-3377	511	12	.	.	PUNCT
ejpam-3377	512	1	legendre	legendre	PROPN
ejpam-3377	512	2	polynomials	polynomial	VERB
ejpam-3377	512	3	operational	operational	ADJ
ejpam-3377	512	4	matrix	matrix	NOUN
ejpam-3377	512	5	method	method	NOUN
ejpam-3377	512	6	for	for	ADP
ejpam-3377	512	7	solving	solve	VERB
ejpam-3377	512	8	fractional	fractional	ADJ
ejpam-3377	512	9	partial	partial	ADJ
ejpam-3377	512	10	differential	differential	NOUN
ejpam-3377	512	11	equations	equation	NOUN
ejpam-3377	512	12	with	with	ADP
ejpam-3377	512	13	variable	variable	ADJ
ejpam-3377	512	14	coefficients	coefficient	NOUN
ejpam-3377	512	15	.	.	PUNCT
ejpam-3377	513	1	math.prob	math.prob	VERB
ejpam-3377	513	2	.	.	PUNCT
ejpam-3377	514	1	eng	eng	PROPN
ejpam-3377	514	2	.	.	PROPN
ejpam-3377	514	3	,	,	PUNCT
ejpam-3377	514	4	2015	2015	NUM
ejpam-3377	514	5	:	:	SYM
ejpam-3377	514	6	9	9	NUM
ejpam-3377	514	7	pages	page	NOUN
ejpam-3377	514	8	,	,	PUNCT
ejpam-3377	514	9	2015	2015	NUM
ejpam-3377	514	10	.	.	PUNCT