id	sid	tid	token	lemma	pos
ejpam-5280	1	1	european	european	PROPN
ejpam-5280	1	2	journal	journal	PROPN
ejpam-5280	1	3	of	of	ADP
ejpam-5280	1	4	pure	pure	ADJ
ejpam-5280	1	5	and	and	CCONJ
ejpam-5280	1	6	applied	apply	VERB
ejpam-5280	1	7	mathematics	mathematic	NOUN
ejpam-5280	1	8	vol	vol	NOUN
ejpam-5280	1	9	.	.	PROPN
ejpam-5280	2	1	17	17	NUM
ejpam-5280	2	2	,	,	PUNCT
ejpam-5280	2	3	no	no	INTJ
ejpam-5280	2	4	.	.	NOUN
ejpam-5280	2	5	3	3	NUM
ejpam-5280	2	6	,	,	PUNCT
ejpam-5280	2	7	2024	2024	NUM
ejpam-5280	2	8	,	,	PUNCT
ejpam-5280	2	9	1429	1429	NUM
ejpam-5280	2	10	-	-	SYM
ejpam-5280	2	11	1448	1448	NUM
ejpam-5280	2	12	issn	issn	PROPN
ejpam-5280	2	13	1307	1307	NUM
ejpam-5280	2	14	-	-	SYM
ejpam-5280	2	15	5543	5543	NUM
ejpam-5280	2	16	–	–	PUNCT
ejpam-5280	3	1	ejpam.com	ejpam.com	X
ejpam-5280	3	2	published	publish	VERB
ejpam-5280	3	3	by	by	ADP
ejpam-5280	3	4	new	new	PROPN
ejpam-5280	3	5	york	york	PROPN
ejpam-5280	3	6	business	business	PROPN
ejpam-5280	3	7	global	global	PROPN
ejpam-5280	3	8	a	a	DET
ejpam-5280	3	9	numerical	numerical	ADJ
ejpam-5280	3	10	method	method	NOUN
ejpam-5280	3	11	for	for	ADP
ejpam-5280	3	12	investigating	investigate	VERB
ejpam-5280	3	13	fractional	fractional	ADJ
ejpam-5280	3	14	volterra	volterra	NOUN
ejpam-5280	3	15	-	-	PUNCT
ejpam-5280	3	16	fredholm	fredholm	NOUN
ejpam-5280	3	17	integro	integro	ADJ
ejpam-5280	3	18	-	-	PUNCT
ejpam-5280	3	19	differential	differential	NOUN
ejpam-5280	3	20	model	model	NOUN
ejpam-5280	3	21	muhammed	muhammed	PROPN
ejpam-5280	3	22	i.	i.	PROPN
ejpam-5280	3	23	syam1,∗	syam1,∗	PROPN
ejpam-5280	3	24	,	,	PUNCT
ejpam-5280	3	25	mwaffag	mwaffag	NOUN
ejpam-5280	3	26	sharadga2	sharadga2	NOUN
ejpam-5280	3	27	,	,	PUNCT
ejpam-5280	3	28	ishak	ishak	VERB
ejpam-5280	3	29	hashim2,3	hashim2,3	PROPN
ejpam-5280	3	30	1	1	NUM
ejpam-5280	3	31	department	department	NOUN
ejpam-5280	3	32	of	of	ADP
ejpam-5280	3	33	mathematical	mathematical	ADJ
ejpam-5280	3	34	sciences	sciences	PROPN
ejpam-5280	3	35	,	,	PUNCT
ejpam-5280	3	36	united	united	PROPN
ejpam-5280	3	37	arab	arab	PROPN
ejpam-5280	3	38	emirates	emirates	PROPN
ejpam-5280	3	39	university	university	PROPN
ejpam-5280	3	40	,	,	PUNCT
ejpam-5280	3	41	al	al	PROPN
ejpam-5280	3	42	-	-	PUNCT
ejpam-5280	3	43	ain	ain	PROPN
ejpam-5280	3	44	,	,	PUNCT
ejpam-5280	3	45	united	united	PROPN
ejpam-5280	3	46	arab	arab	PROPN
ejpam-5280	3	47	emirates	emirates	PROPN
ejpam-5280	3	48	2	2	NUM
ejpam-5280	3	49	department	department	NOUN
ejpam-5280	3	50	of	of	ADP
ejpam-5280	3	51	mathematical	mathematical	ADJ
ejpam-5280	3	52	sciences	science	NOUN
ejpam-5280	3	53	,	,	PUNCT
ejpam-5280	3	54	faculty	faculty	NOUN
ejpam-5280	3	55	of	of	ADP
ejpam-5280	3	56	science	science	NOUN
ejpam-5280	3	57	and	and	CCONJ
ejpam-5280	3	58	technology	technology	NOUN
ejpam-5280	3	59	,	,	PUNCT
ejpam-5280	3	60	universiti	universiti	PROPN
ejpam-5280	3	61	kebangsaan	kebangsaan	PROPN
ejpam-5280	3	62	malaysia	malaysia	PROPN
ejpam-5280	3	63	,	,	PUNCT
ejpam-5280	3	64	43600	43600	NUM
ejpam-5280	3	65	ukm	ukm	PROPN
ejpam-5280	3	66	bangi	bangi	PROPN
ejpam-5280	3	67	selangor	selangor	PROPN
ejpam-5280	3	68	,	,	PUNCT
ejpam-5280	3	69	malaysia	malaysia	PROPN
ejpam-5280	3	70	3	3	NUM
ejpam-5280	3	71	nonlinear	nonlinear	ADJ
ejpam-5280	3	72	dynamics	dynamic	NOUN
ejpam-5280	3	73	research	research	NOUN
ejpam-5280	3	74	center	center	NOUN
ejpam-5280	3	75	(	(	PUNCT
ejpam-5280	3	76	ndrc	ndrc	PROPN
ejpam-5280	3	77	)	)	PUNCT
ejpam-5280	3	78	,	,	PUNCT
ejpam-5280	3	79	ajman	ajman	PROPN
ejpam-5280	3	80	university	university	PROPN
ejpam-5280	3	81	,	,	PUNCT
ejpam-5280	3	82	ajman	ajman	PROPN
ejpam-5280	3	83	po	po	PROPN
ejpam-5280	3	84	box	box	PROPN
ejpam-5280	3	85	346	346	NUM
ejpam-5280	3	86	,	,	PUNCT
ejpam-5280	3	87	united	united	PROPN
ejpam-5280	3	88	arab	arab	PROPN
ejpam-5280	3	89	emirates	emirates	PROPN
ejpam-5280	3	90	abstract	abstract	ADJ
ejpam-5280	3	91	.	.	PUNCT
ejpam-5280	4	1	in	in	ADP
ejpam-5280	4	2	this	this	DET
ejpam-5280	4	3	article	article	NOUN
ejpam-5280	4	4	,	,	PUNCT
ejpam-5280	4	5	we	we	PRON
ejpam-5280	4	6	investigate	investigate	VERB
ejpam-5280	4	7	the	the	DET
ejpam-5280	4	8	fractional	fractional	PROPN
ejpam-5280	4	9	volterra	volterra	NOUN
ejpam-5280	4	10	-	-	PUNCT
ejpam-5280	4	11	fredholm	fredholm	NOUN
ejpam-5280	4	12	integro	integro	ADJ
ejpam-5280	4	13	-	-	PUNCT
ejpam-5280	4	14	differential	differential	NOUN
ejpam-5280	4	15	equations	equation	NOUN
ejpam-5280	4	16	.	.	PUNCT
ejpam-5280	5	1	these	these	DET
ejpam-5280	5	2	equations	equation	NOUN
ejpam-5280	5	3	appear	appear	VERB
ejpam-5280	5	4	in	in	ADP
ejpam-5280	5	5	several	several	ADJ
ejpam-5280	5	6	applications	application	NOUN
ejpam-5280	5	7	such	such	ADJ
ejpam-5280	5	8	as	as	ADP
ejpam-5280	5	9	control	control	NOUN
ejpam-5280	5	10	theory	theory	NOUN
ejpam-5280	5	11	,	,	PUNCT
ejpam-5280	5	12	biology	biology	NOUN
ejpam-5280	5	13	,	,	PUNCT
ejpam-5280	5	14	and	and	CCONJ
ejpam-5280	5	15	particle	particle	NOUN
ejpam-5280	5	16	dynamics	dynamic	NOUN
ejpam-5280	5	17	in	in	ADP
ejpam-5280	5	18	physics	physics	NOUN
ejpam-5280	5	19	.	.	PUNCT
ejpam-5280	6	1	we	we	PRON
ejpam-5280	6	2	derive	derive	VERB
ejpam-5280	6	3	a	a	DET
ejpam-5280	6	4	numerical	numerical	ADJ
ejpam-5280	6	5	method	method	NOUN
ejpam-5280	6	6	based	base	VERB
ejpam-5280	6	7	on	on	ADP
ejpam-5280	6	8	the	the	DET
ejpam-5280	6	9	operational	operational	ADJ
ejpam-5280	6	10	matrix	matrix	NOUN
ejpam-5280	6	11	method	method	NOUN
ejpam-5280	6	12	to	to	PART
ejpam-5280	6	13	solve	solve	VERB
ejpam-5280	6	14	this	this	DET
ejpam-5280	6	15	class	class	NOUN
ejpam-5280	6	16	of	of	ADP
ejpam-5280	6	17	integro	integro	ADJ
ejpam-5280	6	18	-	-	PUNCT
ejpam-5280	6	19	differential	differential	NOUN
ejpam-5280	6	20	equations	equation	NOUN
ejpam-5280	6	21	.	.	PUNCT
ejpam-5280	7	1	we	we	PRON
ejpam-5280	7	2	prove	prove	VERB
ejpam-5280	7	3	the	the	DET
ejpam-5280	7	4	existence	existence	NOUN
ejpam-5280	7	5	and	and	CCONJ
ejpam-5280	7	6	uniqueness	uniqueness	NOUN
ejpam-5280	7	7	of	of	ADP
ejpam-5280	7	8	the	the	DET
ejpam-5280	7	9	exact	exact	ADJ
ejpam-5280	7	10	solution	solution	NOUN
ejpam-5280	7	11	.	.	PUNCT
ejpam-5280	8	1	additionally	additionally	ADV
ejpam-5280	8	2	,	,	PUNCT
ejpam-5280	8	3	we	we	PRON
ejpam-5280	8	4	demonstrate	demonstrate	VERB
ejpam-5280	8	5	the	the	DET
ejpam-5280	8	6	uniform	uniform	ADJ
ejpam-5280	8	7	convergence	convergence	NOUN
ejpam-5280	8	8	of	of	ADP
ejpam-5280	8	9	the	the	DET
ejpam-5280	8	10	numerical	numerical	ADJ
ejpam-5280	8	11	solutions	solution	NOUN
ejpam-5280	8	12	to	to	ADP
ejpam-5280	8	13	the	the	DET
ejpam-5280	8	14	exact	exact	ADJ
ejpam-5280	8	15	solution	solution	NOUN
ejpam-5280	8	16	.	.	PUNCT
ejpam-5280	9	1	we	we	PRON
ejpam-5280	9	2	present	present	VERB
ejpam-5280	9	3	several	several	ADJ
ejpam-5280	9	4	numerical	numerical	ADJ
ejpam-5280	9	5	examples	example	NOUN
ejpam-5280	9	6	to	to	PART
ejpam-5280	9	7	show	show	VERB
ejpam-5280	9	8	the	the	DET
ejpam-5280	9	9	numerical	numerical	ADJ
ejpam-5280	9	10	efficiency	efficiency	NOUN
ejpam-5280	9	11	of	of	ADP
ejpam-5280	9	12	the	the	DET
ejpam-5280	9	13	proposed	propose	VERB
ejpam-5280	9	14	method	method	NOUN
ejpam-5280	9	15	.	.	PUNCT
ejpam-5280	10	1	in	in	ADP
ejpam-5280	10	2	the	the	DET
ejpam-5280	10	3	first	first	ADJ
ejpam-5280	10	4	example	example	NOUN
ejpam-5280	10	5	,	,	PUNCT
ejpam-5280	10	6	we	we	PRON
ejpam-5280	10	7	choose	choose	VERB
ejpam-5280	10	8	a	a	DET
ejpam-5280	10	9	linear	linear	ADJ
ejpam-5280	10	10	problem	problem	NOUN
ejpam-5280	10	11	and	and	CCONJ
ejpam-5280	10	12	find	find	VERB
ejpam-5280	10	13	that	that	SCONJ
ejpam-5280	10	14	the	the	DET
ejpam-5280	10	15	approximate	approximate	ADJ
ejpam-5280	10	16	solution	solution	NOUN
ejpam-5280	10	17	converges	converge	VERB
ejpam-5280	10	18	to	to	ADP
ejpam-5280	10	19	the	the	DET
ejpam-5280	10	20	exact	exact	ADJ
ejpam-5280	10	21	solution	solution	NOUN
ejpam-5280	10	22	when	when	SCONJ
ejpam-5280	10	23	the	the	DET
ejpam-5280	10	24	number	number	NOUN
ejpam-5280	10	25	of	of	ADP
ejpam-5280	10	26	block	block	NOUN
ejpam-5280	10	27	pulse	pulse	NOUN
ejpam-5280	10	28	functions	function	NOUN
ejpam-5280	10	29	is	be	AUX
ejpam-5280	10	30	very	very	ADV
ejpam-5280	10	31	large	large	ADJ
ejpam-5280	10	32	.	.	PUNCT
ejpam-5280	11	1	in	in	ADP
ejpam-5280	11	2	the	the	DET
ejpam-5280	11	3	next	next	ADJ
ejpam-5280	11	4	two	two	NUM
ejpam-5280	11	5	examples	example	NOUN
ejpam-5280	11	6	,	,	PUNCT
ejpam-5280	11	7	we	we	PRON
ejpam-5280	11	8	consider	consider	VERB
ejpam-5280	11	9	the	the	DET
ejpam-5280	11	10	nonlinear	nonlinear	ADJ
ejpam-5280	11	11	case	case	NOUN
ejpam-5280	11	12	and	and	CCONJ
ejpam-5280	11	13	compute	compute	VERB
ejpam-5280	11	14	the	the	DET
ejpam-5280	11	15	l2	l2	NOUN
ejpam-5280	11	16	-	-	PUNCT
ejpam-5280	11	17	local	local	ADJ
ejpam-5280	11	18	truncation	truncation	NOUN
ejpam-5280	11	19	error	error	NOUN
ejpam-5280	11	20	since	since	SCONJ
ejpam-5280	11	21	exact	exact	ADJ
ejpam-5280	11	22	solutions	solution	NOUN
ejpam-5280	11	23	are	be	AUX
ejpam-5280	11	24	not	not	PART
ejpam-5280	11	25	available	available	ADJ
ejpam-5280	11	26	.	.	PUNCT
ejpam-5280	12	1	the	the	DET
ejpam-5280	12	2	error	error	NOUN
ejpam-5280	12	3	was	be	AUX
ejpam-5280	12	4	of	of	ADP
ejpam-5280	12	5	order	order	NOUN
ejpam-5280	12	6	10−12	10−12	NOUN
ejpam-5280	12	7	.	.	PUNCT
ejpam-5280	13	1	furthermore	furthermore	ADV
ejpam-5280	13	2	,	,	PUNCT
ejpam-5280	13	3	we	we	PRON
ejpam-5280	13	4	sketch	sketch	VERB
ejpam-5280	13	5	the	the	DET
ejpam-5280	13	6	graph	graph	NOUN
ejpam-5280	13	7	of	of	ADP
ejpam-5280	13	8	the	the	DET
ejpam-5280	13	9	approximate	approximate	ADJ
ejpam-5280	13	10	solutions	solution	NOUN
ejpam-5280	13	11	for	for	ADP
ejpam-5280	13	12	different	different	ADJ
ejpam-5280	13	13	values	value	NOUN
ejpam-5280	13	14	of	of	ADP
ejpam-5280	13	15	the	the	DET
ejpam-5280	13	16	fractional	fractional	ADJ
ejpam-5280	13	17	derivative	derivative	NOUN
ejpam-5280	13	18	to	to	PART
ejpam-5280	13	19	observe	observe	VERB
ejpam-5280	13	20	the	the	DET
ejpam-5280	13	21	influence	influence	NOUN
ejpam-5280	13	22	of	of	ADP
ejpam-5280	13	23	the	the	DET
ejpam-5280	13	24	fractional	fractional	ADJ
ejpam-5280	13	25	derivative	derivative	NOUN
ejpam-5280	13	26	on	on	ADP
ejpam-5280	13	27	the	the	DET
ejpam-5280	13	28	profile	profile	NOUN
ejpam-5280	13	29	of	of	ADP
ejpam-5280	13	30	the	the	DET
ejpam-5280	13	31	solutions	solution	NOUN
ejpam-5280	13	32	.	.	PUNCT
ejpam-5280	14	1	theoretical	theoretical	ADJ
ejpam-5280	14	2	and	and	CCONJ
ejpam-5280	14	3	numerical	numerical	ADJ
ejpam-5280	14	4	results	result	NOUN
ejpam-5280	14	5	show	show	VERB
ejpam-5280	14	6	that	that	SCONJ
ejpam-5280	14	7	the	the	DET
ejpam-5280	14	8	proposed	propose	VERB
ejpam-5280	14	9	method	method	NOUN
ejpam-5280	14	10	is	be	AUX
ejpam-5280	14	11	accurate	accurate	ADJ
ejpam-5280	14	12	and	and	CCONJ
ejpam-5280	14	13	can	can	AUX
ejpam-5280	14	14	be	be	AUX
ejpam-5280	14	15	applied	apply	VERB
ejpam-5280	14	16	to	to	ADP
ejpam-5280	14	17	other	other	ADJ
ejpam-5280	14	18	nonlinear	nonlinear	ADJ
ejpam-5280	14	19	problems	problem	NOUN
ejpam-5280	14	20	in	in	ADP
ejpam-5280	14	21	science	science	NOUN
ejpam-5280	14	22	.	.	PUNCT
ejpam-5280	15	1	2020	2020	NUM
ejpam-5280	15	2	mathematics	mathematic	NOUN
ejpam-5280	15	3	subject	subject	NOUN
ejpam-5280	15	4	classifications	classification	NOUN
ejpam-5280	15	5	:	:	PUNCT
ejpam-5280	15	6	74s40	74s40	NUM
ejpam-5280	15	7	,	,	PUNCT
ejpam-5280	15	8	65d15	65d15	NUM
ejpam-5280	15	9	key	key	ADJ
ejpam-5280	15	10	words	word	NOUN
ejpam-5280	15	11	and	and	CCONJ
ejpam-5280	15	12	phrases	phrase	NOUN
ejpam-5280	15	13	:	:	PUNCT
ejpam-5280	15	14	block	block	NOUN
ejpam-5280	15	15	pulse	pulse	NOUN
ejpam-5280	15	16	function	function	NOUN
ejpam-5280	15	17	,	,	PUNCT
ejpam-5280	15	18	fractional	fractional	ADJ
ejpam-5280	15	19	derivative	derivative	ADJ
ejpam-5280	15	20	,	,	PUNCT
ejpam-5280	15	21	nonlinear	nonlinear	ADJ
ejpam-5280	15	22	dynamics	dynamic	NOUN
ejpam-5280	15	23	,	,	PUNCT
ejpam-5280	15	24	volterra	volterra	NOUN
ejpam-5280	15	25	-	-	PUNCT
ejpam-5280	15	26	fredholm	fredholm	NOUN
ejpam-5280	15	27	integro	integro	ADJ
ejpam-5280	15	28	-	-	PUNCT
ejpam-5280	15	29	differential	differential	ADJ
ejpam-5280	15	30	1	1	NUM
ejpam-5280	15	31	.	.	PUNCT
ejpam-5280	15	32	introduction	introduction	NOUN
ejpam-5280	15	33	fractional	fractional	ADJ
ejpam-5280	15	34	calculus	calculus	NOUN
ejpam-5280	15	35	,	,	PUNCT
ejpam-5280	15	36	a	a	DET
ejpam-5280	15	37	branch	branch	NOUN
ejpam-5280	15	38	of	of	ADP
ejpam-5280	15	39	mathematical	mathematical	ADJ
ejpam-5280	15	40	analysis	analysis	NOUN
ejpam-5280	15	41	,	,	PUNCT
ejpam-5280	15	42	extends	extend	VERB
ejpam-5280	15	43	the	the	DET
ejpam-5280	15	44	concepts	concept	NOUN
ejpam-5280	15	45	of	of	ADP
ejpam-5280	15	46	differentiation	differentiation	NOUN
ejpam-5280	15	47	and	and	CCONJ
ejpam-5280	15	48	integration	integration	NOUN
ejpam-5280	15	49	to	to	ADP
ejpam-5280	15	50	non	non	ADJ
ejpam-5280	15	51	-	-	ADJ
ejpam-5280	15	52	integer	integer	ADJ
ejpam-5280	15	53	orders	order	NOUN
ejpam-5280	15	54	.	.	PUNCT
ejpam-5280	16	1	the	the	DET
ejpam-5280	16	2	numerous	numerous	ADJ
ejpam-5280	16	3	applications	application	NOUN
ejpam-5280	16	4	it	it	PRON
ejpam-5280	16	5	has	have	AUX
ejpam-5280	16	6	found	find	VERB
ejpam-5280	16	7	in	in	ADP
ejpam-5280	16	8	physics	physics	NOUN
ejpam-5280	16	9	,	,	PUNCT
ejpam-5280	16	10	chemistry	chemistry	NOUN
ejpam-5280	16	11	,	,	PUNCT
ejpam-5280	16	12	biology	biology	NOUN
ejpam-5280	16	13	,	,	PUNCT
ejpam-5280	16	14	and	and	CCONJ
ejpam-5280	16	15	control	control	NOUN
ejpam-5280	16	16	theory	theory	NOUN
ejpam-5280	16	17	have	have	AUX
ejpam-5280	16	18	garnered	garner	VERB
ejpam-5280	16	19	considerable	considerable	ADJ
ejpam-5280	16	20	attention	attention	NOUN
ejpam-5280	16	21	.	.	PUNCT
ejpam-5280	17	1	∗corresponding	∗corresponde	VERB
ejpam-5280	17	2	author	author	NOUN
ejpam-5280	17	3	.	.	PUNCT
ejpam-5280	18	1	doi	doi	PROPN
ejpam-5280	18	2	:	:	PUNCT
ejpam-5280	18	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5280	https://doi.org/10.29020/nybg.ejpam.v17i3.5280	ADJ
ejpam-5280	18	4	email	email	NOUN
ejpam-5280	18	5	addresses	address	NOUN
ejpam-5280	18	6	:	:	PUNCT
ejpam-5280	18	7	m.syam@uaeu.ac.ae	m.syam@uaeu.ac.ae	NUM
ejpam-5280	18	8	(	(	PUNCT
ejpam-5280	18	9	m.	m.	NOUN
ejpam-5280	18	10	syam	syam	NOUN
ejpam-5280	18	11	)	)	PUNCT
ejpam-5280	18	12	,	,	PUNCT
ejpam-5280	18	13	p101953@siswa.ukm.edu.my	p101953@siswa.ukm.edu.my	NOUN
ejpam-5280	18	14	(	(	PUNCT
ejpam-5280	18	15	m.	m.	NOUN
ejpam-5280	18	16	sharadga	sharadga	NOUN
ejpam-5280	18	17	)	)	PUNCT
ejpam-5280	18	18	,	,	PUNCT
ejpam-5280	18	19	ishak	ishak	VERB
ejpam-5280	18	20	h@ukm.edu.my	h@ukm.edu.my	PROPN
ejpam-5280	18	21	(	(	PUNCT
ejpam-5280	18	22	i.	i.	PROPN
ejpam-5280	18	23	hashim	hashim	PROPN
ejpam-5280	18	24	)	)	PUNCT
ejpam-5280	18	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5280	18	26	1429	1429	NUM
ejpam-5280	19	1	©	©	PROPN
ejpam-5280	19	2	2024	2024	NUM
ejpam-5280	19	3	ejpam	ejpam	NOUN
ejpam-5280	19	4	all	all	DET
ejpam-5280	19	5	rights	right	NOUN
ejpam-5280	19	6	reserved	reserve	VERB
ejpam-5280	19	7	.	.	PUNCT
ejpam-5280	20	1	m.i	m.i	PROPN
ejpam-5280	20	2	.	.	PROPN
ejpam-5280	20	3	syam	syam	PROPN
ejpam-5280	20	4	,	,	PUNCT
ejpam-5280	20	5	m.	m.	NOUN
ejpam-5280	20	6	sharadga	sharadga	PROPN
ejpam-5280	20	7	,	,	PUNCT
ejpam-5280	20	8	i.	i.	PROPN
ejpam-5280	20	9	hashim	hashim	PROPN
ejpam-5280	20	10	/	/	SYM
ejpam-5280	20	11	eur	eur	PROPN
ejpam-5280	20	12	.	.	PUNCT
ejpam-5280	21	1	j.	j.	PROPN
ejpam-5280	21	2	pure	pure	PROPN
ejpam-5280	21	3	appl	appl	PROPN
ejpam-5280	21	4	.	.	PROPN
ejpam-5280	21	5	math	math	PROPN
ejpam-5280	21	6	,	,	PUNCT
ejpam-5280	21	7	17	17	NUM
ejpam-5280	21	8	(	(	PUNCT
ejpam-5280	21	9	3	3	NUM
ejpam-5280	21	10	)	)	PUNCT
ejpam-5280	21	11	(	(	PUNCT
ejpam-5280	21	12	2024	2024	NUM
ejpam-5280	21	13	)	)	PUNCT
ejpam-5280	21	14	,	,	PUNCT
ejpam-5280	21	15	1429	1429	NUM
ejpam-5280	21	16	-	-	SYM
ejpam-5280	21	17	1448	1448	NUM
ejpam-5280	21	18	1430	1430	NUM
ejpam-5280	21	19	for	for	ADP
ejpam-5280	21	20	example	example	NOUN
ejpam-5280	21	21	,	,	PUNCT
ejpam-5280	21	22	fractional	fractional	ADJ
ejpam-5280	21	23	calculus	calculus	NOUN
ejpam-5280	21	24	is	be	AUX
ejpam-5280	21	25	applied	apply	VERB
ejpam-5280	21	26	in	in	ADP
ejpam-5280	21	27	anomalous	anomalous	ADJ
ejpam-5280	21	28	diffusion	diffusion	NOUN
ejpam-5280	21	29	,	,	PUNCT
ejpam-5280	21	30	viscoelasticity	viscoelasticity	NOUN
ejpam-5280	21	31	,	,	PUNCT
ejpam-5280	21	32	and	and	CCONJ
ejpam-5280	21	33	electromagnetism	electromagnetism	NOUN
ejpam-5280	21	34	in	in	ADP
ejpam-5280	21	35	physics	physics	NOUN
ejpam-5280	21	36	,	,	PUNCT
ejpam-5280	21	37	as	as	ADV
ejpam-5280	21	38	well	well	ADV
ejpam-5280	21	39	as	as	ADP
ejpam-5280	21	40	control	control	NOUN
ejpam-5280	21	41	systems	system	NOUN
ejpam-5280	21	42	and	and	CCONJ
ejpam-5280	21	43	signal	signal	NOUN
ejpam-5280	21	44	processing	processing	NOUN
ejpam-5280	21	45	in	in	ADP
ejpam-5280	21	46	engineering	engineering	NOUN
ejpam-5280	21	47	.	.	PUNCT
ejpam-5280	22	1	for	for	ADP
ejpam-5280	22	2	more	more	ADJ
ejpam-5280	22	3	details	detail	NOUN
ejpam-5280	22	4	,	,	PUNCT
ejpam-5280	22	5	see	see	VERB
ejpam-5280	22	6	[	[	X
ejpam-5280	22	7	9	9	NUM
ejpam-5280	22	8	,	,	PUNCT
ejpam-5280	22	9	10	10	NUM
ejpam-5280	22	10	,	,	PUNCT
ejpam-5280	22	11	14	14	NUM
ejpam-5280	22	12	,	,	PUNCT
ejpam-5280	22	13	16	16	NUM
ejpam-5280	22	14	]	]	PUNCT
ejpam-5280	22	15	.	.	PUNCT
ejpam-5280	23	1	incorporating	incorporate	VERB
ejpam-5280	23	2	fractional	fractional	ADJ
ejpam-5280	23	3	derivatives	derivative	NOUN
ejpam-5280	23	4	and	and	CCONJ
ejpam-5280	23	5	integrals	integral	NOUN
ejpam-5280	23	6	is	be	AUX
ejpam-5280	23	7	one	one	NUM
ejpam-5280	23	8	of	of	ADP
ejpam-5280	23	9	the	the	DET
ejpam-5280	23	10	valuable	valuable	ADJ
ejpam-5280	23	11	tools	tool	NOUN
ejpam-5280	23	12	fc	fc	X
ejpam-5280	23	13	provides	provide	VERB
ejpam-5280	23	14	for	for	ADP
ejpam-5280	23	15	simulating	simulate	VERB
ejpam-5280	23	16	complex	complex	ADJ
ejpam-5280	23	17	systems	system	NOUN
ejpam-5280	23	18	with	with	ADP
ejpam-5280	23	19	memory	memory	NOUN
ejpam-5280	23	20	and	and	CCONJ
ejpam-5280	23	21	long	long	ADJ
ejpam-5280	23	22	-	-	PUNCT
ejpam-5280	23	23	term	term	NOUN
ejpam-5280	23	24	interactions	interaction	NOUN
ejpam-5280	23	25	.	.	PUNCT
ejpam-5280	24	1	this	this	DET
ejpam-5280	24	2	theory	theory	NOUN
ejpam-5280	24	3	has	have	AUX
ejpam-5280	24	4	revolutionized	revolutionize	VERB
ejpam-5280	24	5	the	the	DET
ejpam-5280	24	6	approach	approach	NOUN
ejpam-5280	24	7	to	to	ADP
ejpam-5280	24	8	many	many	ADJ
ejpam-5280	24	9	previously	previously	ADV
ejpam-5280	24	10	challenging	challenging	ADJ
ejpam-5280	24	11	problems	problem	NOUN
ejpam-5280	24	12	and	and	CCONJ
ejpam-5280	24	13	has	have	AUX
ejpam-5280	24	14	found	find	VERB
ejpam-5280	24	15	applications	application	NOUN
ejpam-5280	24	16	in	in	ADP
ejpam-5280	24	17	modeling	model	VERB
ejpam-5280	24	18	anomalous	anomalous	ADJ
ejpam-5280	24	19	diffusion	diffusion	NOUN
ejpam-5280	24	20	,	,	PUNCT
ejpam-5280	24	21	viscoelasticity	viscoelasticity	NOUN
ejpam-5280	24	22	,	,	PUNCT
ejpam-5280	24	23	fractional	fractional	ADJ
ejpam-5280	24	24	control	control	NOUN
ejpam-5280	24	25	systems	system	NOUN
ejpam-5280	24	26	,	,	PUNCT
ejpam-5280	24	27	and	and	CCONJ
ejpam-5280	24	28	more	more	ADJ
ejpam-5280	24	29	.	.	PUNCT
ejpam-5280	25	1	the	the	DET
ejpam-5280	25	2	caputo	caputo	PROPN
ejpam-5280	25	3	derivative	derivative	NOUN
ejpam-5280	25	4	,	,	PUNCT
ejpam-5280	25	5	introduced	introduce	VERB
ejpam-5280	25	6	by	by	ADP
ejpam-5280	25	7	michele	michele	PROPN
ejpam-5280	25	8	caputo	caputo	PROPN
ejpam-5280	25	9	in	in	ADP
ejpam-5280	25	10	1967	1967	NUM
ejpam-5280	25	11	,	,	PUNCT
ejpam-5280	25	12	stands	stand	VERB
ejpam-5280	25	13	out	out	ADP
ejpam-5280	25	14	for	for	ADP
ejpam-5280	25	15	its	its	PRON
ejpam-5280	25	16	practicality	practicality	NOUN
ejpam-5280	25	17	.	.	PUNCT
ejpam-5280	26	1	the	the	DET
ejpam-5280	26	2	caputo	caputo	PROPN
ejpam-5280	26	3	derivative	derivative	NOUN
ejpam-5280	26	4	is	be	AUX
ejpam-5280	26	5	more	more	ADV
ejpam-5280	26	6	suitable	suitable	ADJ
ejpam-5280	26	7	for	for	ADP
ejpam-5280	26	8	real	real	ADJ
ejpam-5280	26	9	-	-	PUNCT
ejpam-5280	26	10	world	world	NOUN
ejpam-5280	26	11	simulations	simulation	NOUN
ejpam-5280	26	12	because	because	SCONJ
ejpam-5280	26	13	it	it	PRON
ejpam-5280	26	14	does	do	AUX
ejpam-5280	26	15	n’t	not	PART
ejpam-5280	26	16	require	require	VERB
ejpam-5280	26	17	the	the	DET
ejpam-5280	26	18	function	function	NOUN
ejpam-5280	26	19	to	to	PART
ejpam-5280	26	20	be	be	AUX
ejpam-5280	26	21	different	different	ADJ
ejpam-5280	26	22	throughout	throughout	ADP
ejpam-5280	26	23	the	the	DET
ejpam-5280	26	24	domain	domain	NOUN
ejpam-5280	26	25	,	,	PUNCT
ejpam-5280	26	26	unlike	unlike	ADP
ejpam-5280	26	27	the	the	DET
ejpam-5280	26	28	riemannliouville	riemannliouville	NOUN
ejpam-5280	26	29	fractional	fractional	ADJ
ejpam-5280	26	30	derivative	derivative	NOUN
ejpam-5280	26	31	.	.	PUNCT
ejpam-5280	27	1	phenomena	phenomenon	NOUN
ejpam-5280	27	2	like	like	ADP
ejpam-5280	27	3	fractional	fractional	ADJ
ejpam-5280	27	4	control	control	NOUN
ejpam-5280	27	5	systems	system	NOUN
ejpam-5280	27	6	,	,	PUNCT
ejpam-5280	27	7	viscoelasticity	viscoelasticity	NOUN
ejpam-5280	27	8	,	,	PUNCT
ejpam-5280	27	9	and	and	CCONJ
ejpam-5280	27	10	atypical	atypical	ADJ
ejpam-5280	27	11	diffusion	diffusion	NOUN
ejpam-5280	27	12	are	be	AUX
ejpam-5280	27	13	all	all	PRON
ejpam-5280	27	14	modeled	model	VERB
ejpam-5280	27	15	using	use	VERB
ejpam-5280	27	16	the	the	DET
ejpam-5280	27	17	caputo	caputo	PROPN
ejpam-5280	27	18	derivative	derivative	NOUN
ejpam-5280	27	19	in	in	ADP
ejpam-5280	27	20	engineering	engineering	NOUN
ejpam-5280	27	21	and	and	CCONJ
ejpam-5280	27	22	research	research	NOUN
ejpam-5280	27	23	.	.	PUNCT
ejpam-5280	28	1	it	it	PRON
ejpam-5280	28	2	is	be	AUX
ejpam-5280	28	3	used	use	VERB
ejpam-5280	28	4	for	for	ADP
ejpam-5280	28	5	mathematical	mathematical	ADJ
ejpam-5280	28	6	modeling	modeling	NOUN
ejpam-5280	28	7	of	of	ADP
ejpam-5280	28	8	physical	physical	ADJ
ejpam-5280	28	9	and	and	CCONJ
ejpam-5280	28	10	biological	biological	ADJ
ejpam-5280	28	11	systems	system	NOUN
ejpam-5280	28	12	such	such	ADJ
ejpam-5280	28	13	as	as	ADP
ejpam-5280	28	14	heat	heat	NOUN
ejpam-5280	28	15	transfer	transfer	NOUN
ejpam-5280	28	16	and	and	CCONJ
ejpam-5280	28	17	groundwater	groundwater	NOUN
ejpam-5280	28	18	flow	flow	NOUN
ejpam-5280	28	19	.	.	PUNCT
ejpam-5280	29	1	the	the	DET
ejpam-5280	29	2	following	follow	VERB
ejpam-5280	29	3	references	reference	NOUN
ejpam-5280	29	4	are	be	AUX
ejpam-5280	29	5	recommended	recommend	VERB
ejpam-5280	29	6	for	for	ADP
ejpam-5280	29	7	further	further	ADJ
ejpam-5280	29	8	reading	reading	NOUN
ejpam-5280	29	9	[	[	X
ejpam-5280	29	10	6	6	NUM
ejpam-5280	29	11	,	,	PUNCT
ejpam-5280	29	12	11	11	NUM
ejpam-5280	29	13	,	,	PUNCT
ejpam-5280	29	14	12	12	NUM
ejpam-5280	29	15	]	]	PUNCT
ejpam-5280	29	16	.	.	PUNCT
ejpam-5280	30	1	a	a	DET
ejpam-5280	30	2	powerful	powerful	ADJ
ejpam-5280	30	3	technique	technique	NOUN
ejpam-5280	30	4	for	for	ADP
ejpam-5280	30	5	solving	solve	VERB
ejpam-5280	30	6	fractional	fractional	ADJ
ejpam-5280	30	7	differential	differential	ADJ
ejpam-5280	30	8	equations	equation	NOUN
ejpam-5280	30	9	is	be	AUX
ejpam-5280	30	10	the	the	DET
ejpam-5280	30	11	operational	operational	ADJ
ejpam-5280	30	12	matrix	matrix	NOUN
ejpam-5280	30	13	method	method	NOUN
ejpam-5280	30	14	.	.	PUNCT
ejpam-5280	31	1	a	a	DET
ejpam-5280	31	2	linear	linear	ADJ
ejpam-5280	31	3	combination	combination	NOUN
ejpam-5280	31	4	of	of	ADP
ejpam-5280	31	5	basis	basis	NOUN
ejpam-5280	31	6	functions	function	NOUN
ejpam-5280	31	7	,	,	PUNCT
ejpam-5280	31	8	usually	usually	ADV
ejpam-5280	31	9	starting	start	VERB
ejpam-5280	31	10	with	with	ADP
ejpam-5280	31	11	block	block	NOUN
ejpam-5280	31	12	pulse	pulse	NOUN
ejpam-5280	31	13	functions	function	NOUN
ejpam-5280	31	14	,	,	PUNCT
ejpam-5280	31	15	is	be	AUX
ejpam-5280	31	16	used	use	VERB
ejpam-5280	31	17	to	to	PART
ejpam-5280	31	18	approximate	approximate	VERB
ejpam-5280	31	19	the	the	DET
ejpam-5280	31	20	solution	solution	NOUN
ejpam-5280	31	21	.	.	PUNCT
ejpam-5280	32	1	these	these	DET
ejpam-5280	32	2	functions	function	NOUN
ejpam-5280	32	3	are	be	AUX
ejpam-5280	32	4	constructed	construct	VERB
ejpam-5280	32	5	using	use	VERB
ejpam-5280	32	6	operational	operational	ADJ
ejpam-5280	32	7	matrixes	matrix	NOUN
ejpam-5280	32	8	,	,	PUNCT
ejpam-5280	32	9	which	which	PRON
ejpam-5280	32	10	represent	represent	VERB
ejpam-5280	32	11	differentiation	differentiation	NOUN
ejpam-5280	32	12	and	and	CCONJ
ejpam-5280	32	13	integration	integration	NOUN
ejpam-5280	32	14	operations	operation	NOUN
ejpam-5280	32	15	,	,	PUNCT
ejpam-5280	32	16	and	and	CCONJ
ejpam-5280	32	17	the	the	DET
ejpam-5280	32	18	coefficients	coefficient	NOUN
ejpam-5280	32	19	of	of	ADP
ejpam-5280	32	20	the	the	DET
ejpam-5280	32	21	linear	linear	ADJ
ejpam-5280	32	22	combination	combination	NOUN
ejpam-5280	32	23	are	be	AUX
ejpam-5280	32	24	determined	determine	VERB
ejpam-5280	32	25	by	by	ADP
ejpam-5280	32	26	resolving	resolve	VERB
ejpam-5280	32	27	algebraic	algebraic	ADJ
ejpam-5280	32	28	equations	equation	NOUN
ejpam-5280	32	29	.	.	PUNCT
ejpam-5280	33	1	the	the	DET
ejpam-5280	33	2	omm	omm	PROPN
ejpam-5280	33	3	has	have	AUX
ejpam-5280	33	4	been	be	AUX
ejpam-5280	33	5	successfully	successfully	ADV
ejpam-5280	33	6	applied	apply	VERB
ejpam-5280	33	7	to	to	ADP
ejpam-5280	33	8	various	various	ADJ
ejpam-5280	33	9	issues	issue	NOUN
ejpam-5280	33	10	,	,	PUNCT
ejpam-5280	33	11	including	include	VERB
ejpam-5280	33	12	fractional	fractional	ADJ
ejpam-5280	33	13	delay	delay	NOUN
ejpam-5280	33	14	equations	equation	NOUN
ejpam-5280	33	15	[	[	X
ejpam-5280	33	16	15	15	NUM
ejpam-5280	33	17	]	]	PUNCT
ejpam-5280	33	18	,	,	PUNCT
ejpam-5280	33	19	ricatti	ricatti	ADJ
ejpam-5280	33	20	equations	equation	NOUN
ejpam-5280	34	1	[	[	X
ejpam-5280	34	2	5	5	NUM
ejpam-5280	34	3	]	]	PUNCT
ejpam-5280	34	4	,	,	PUNCT
ejpam-5280	34	5	systems	system	NOUN
ejpam-5280	34	6	of	of	ADP
ejpam-5280	34	7	differential	differential	ADJ
ejpam-5280	34	8	equations	equation	NOUN
ejpam-5280	35	1	[	[	X
ejpam-5280	35	2	8	8	NUM
ejpam-5280	35	3	]	]	PUNCT
ejpam-5280	35	4	,	,	PUNCT
ejpam-5280	35	5	and	and	CCONJ
ejpam-5280	35	6	nonlinear	nonlinear	ADJ
ejpam-5280	35	7	differential	differential	ADJ
ejpam-5280	35	8	equations	equation	NOUN
ejpam-5280	36	1	[	[	X
ejpam-5280	36	2	1	1	NUM
ejpam-5280	36	3	]	]	PUNCT
ejpam-5280	36	4	.	.	PUNCT
ejpam-5280	37	1	researchers	researcher	NOUN
ejpam-5280	37	2	investigated	investigate	VERB
ejpam-5280	37	3	alternative	alternative	ADJ
ejpam-5280	37	4	basis	basis	NOUN
ejpam-5280	37	5	functions	function	NOUN
ejpam-5280	37	6	to	to	PART
ejpam-5280	37	7	enhance	enhance	VERB
ejpam-5280	37	8	computational	computational	ADJ
ejpam-5280	37	9	effectiveness	effectiveness	NOUN
ejpam-5280	37	10	and	and	CCONJ
ejpam-5280	37	11	precision	precision	NOUN
ejpam-5280	37	12	[	[	X
ejpam-5280	37	13	2–4	2–4	NUM
ejpam-5280	37	14	,	,	PUNCT
ejpam-5280	37	15	7	7	NUM
ejpam-5280	37	16	]	]	PUNCT
ejpam-5280	37	17	.	.	PUNCT
ejpam-5280	38	1	in	in	ADP
ejpam-5280	38	2	this	this	DET
ejpam-5280	38	3	article	article	NOUN
ejpam-5280	38	4	,	,	PUNCT
ejpam-5280	38	5	we	we	PRON
ejpam-5280	38	6	will	will	AUX
ejpam-5280	38	7	study	study	VERB
ejpam-5280	38	8	the	the	DET
ejpam-5280	38	9	following	follow	VERB
ejpam-5280	38	10	class	class	NOUN
ejpam-5280	38	11	of	of	ADP
ejpam-5280	38	12	integro	integro	ADJ
ejpam-5280	38	13	-	-	PUNCT
ejpam-5280	38	14	differential	differential	NOUN
ejpam-5280	38	15	equations	equation	NOUN
ejpam-5280	38	16	:	:	PUNCT
ejpam-5280	38	17	dµω(t	dµω(t	NOUN
ejpam-5280	38	18	)	)	PUNCT
ejpam-5280	38	19	=	=	SYM
ejpam-5280	38	20	g1(t	g1(t	PROPN
ejpam-5280	38	21	,	,	PUNCT
ejpam-5280	38	22	ω(t	ω(t	NOUN
ejpam-5280	38	23	)	)	PUNCT
ejpam-5280	38	24	)	)	PUNCT
ejpam-5280	39	1	+	+	PUNCT
ejpam-5280	39	2	g2(t	g2(t	NOUN
ejpam-5280	39	3	)	)	PUNCT
ejpam-5280	39	4	+	+	NUM
ejpam-5280	39	5	∫	∫	PROPN
ejpam-5280	39	6	t	t	PROPN
ejpam-5280	39	7	0	0	NUM
ejpam-5280	39	8	π1(t	π1(t	PROPN
ejpam-5280	39	9	,	,	PUNCT
ejpam-5280	39	10	s)g3(ω(s))ds+	s)g3(ω(s))ds+	X
ejpam-5280	39	11	∫	∫	PROPN
ejpam-5280	39	12	1	1	NUM
ejpam-5280	39	13	0	0	X
ejpam-5280	39	14	π2(t	π2(t	PROPN
ejpam-5280	39	15	,	,	PUNCT
ejpam-5280	39	16	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	39	17	,	,	PUNCT
ejpam-5280	39	18	(	(	PUNCT
ejpam-5280	39	19	1	1	NUM
ejpam-5280	39	20	)	)	PUNCT
ejpam-5280	39	21	ω(0	ω(0	PROPN
ejpam-5280	39	22	)	)	PUNCT
ejpam-5280	39	23	=	=	PUNCT
ejpam-5280	39	24	ω0	ω0	NOUN
ejpam-5280	39	25	,	,	PUNCT
ejpam-5280	39	26	(	(	PUNCT
ejpam-5280	39	27	2	2	X
ejpam-5280	39	28	)	)	PUNCT
ejpam-5280	39	29	where	where	SCONJ
ejpam-5280	39	30	t	t	PROPN
ejpam-5280	39	31	∈	∈	PROPN
ejpam-5280	40	1	[	[	X
ejpam-5280	40	2	0	0	NUM
ejpam-5280	40	3	,	,	PUNCT
ejpam-5280	40	4	1	1	NUM
ejpam-5280	40	5	]	]	PUNCT
ejpam-5280	40	6	,	,	PUNCT
ejpam-5280	40	7	π1,π2	π1,π2	PROPN
ejpam-5280	40	8	∈	∈	PROPN
ejpam-5280	40	9	c([0	c([0	NOUN
ejpam-5280	40	10	,	,	PUNCT
ejpam-5280	40	11	1]×[0	1]×[0	NUM
ejpam-5280	40	12	,	,	PUNCT
ejpam-5280	40	13	1]),g1	1]),g1	PROPN
ejpam-5280	40	14	∈	∈	PROPN
ejpam-5280	40	15	c([0	c([0	NOUN
ejpam-5280	40	16	,	,	PUNCT
ejpam-5280	40	17	1]×ℜ	1]×ℜ	NUM
ejpam-5280	40	18	)	)	PUNCT
ejpam-5280	40	19	,	,	PUNCT
ejpam-5280	40	20	g3	g3	NOUN
ejpam-5280	40	21	,	,	PUNCT
ejpam-5280	40	22	g4	g4	NOUN
ejpam-5280	40	23	∈	∈	PROPN
ejpam-5280	40	24	c(ℜ	c(ℜ	NOUN
ejpam-5280	40	25	)	)	PUNCT
ejpam-5280	40	26	,	,	PUNCT
ejpam-5280	40	27	g2	g2	PROPN
ejpam-5280	40	28	∈	∈	PROPN
ejpam-5280	40	29	c([0	c([0	PROPN
ejpam-5280	40	30	,	,	PUNCT
ejpam-5280	40	31	1	1	NUM
ejpam-5280	40	32	]	]	NUM
ejpam-5280	40	33	)	)	PUNCT
ejpam-5280	40	34	,	,	PUNCT
ejpam-5280	40	35	and	and	CCONJ
ejpam-5280	40	36	0	0	NUM
ejpam-5280	40	37	<	<	X
ejpam-5280	40	38	µ	µ	X
ejpam-5280	40	39	≤	≤	NUM
ejpam-5280	40	40	1	1	NUM
ejpam-5280	40	41	.	.	PUNCT
ejpam-5280	41	1	the	the	DET
ejpam-5280	41	2	derivative	derivative	NOUN
ejpam-5280	41	3	her	she	PRON
ejpam-5280	41	4	is	be	AUX
ejpam-5280	41	5	in	in	ADP
ejpam-5280	41	6	the	the	DET
ejpam-5280	41	7	caputo	caputo	PROPN
ejpam-5280	41	8	sense	sense	NOUN
ejpam-5280	41	9	.	.	PUNCT
ejpam-5280	42	1	the	the	DET
ejpam-5280	42	2	fractional	fractional	PROPN
ejpam-5280	42	3	volterra	volterra	PROPN
ejpam-5280	42	4	-	-	PUNCT
ejpam-5280	42	5	fredholm	fredholm	NOUN
ejpam-5280	42	6	integro	integro	ADJ
ejpam-5280	42	7	-	-	PUNCT
ejpam-5280	42	8	differential	differential	NOUN
ejpam-5280	42	9	model	model	NOUN
ejpam-5280	42	10	(	(	PUNCT
ejpam-5280	42	11	fvfidm	fvfidm	NOUN
ejpam-5280	42	12	)	)	PUNCT
ejpam-5280	42	13	represents	represent	VERB
ejpam-5280	42	14	a	a	DET
ejpam-5280	42	15	significant	significant	ADJ
ejpam-5280	42	16	extension	extension	NOUN
ejpam-5280	42	17	of	of	ADP
ejpam-5280	42	18	classical	classical	ADJ
ejpam-5280	42	19	volterra	volterra	NOUN
ejpam-5280	42	20	and	and	CCONJ
ejpam-5280	42	21	fredholm	fredholm	VERB
ejpam-5280	42	22	integral	integral	ADJ
ejpam-5280	42	23	equations	equation	NOUN
ejpam-5280	42	24	by	by	ADP
ejpam-5280	42	25	incorporating	incorporate	VERB
ejpam-5280	42	26	fractional	fractional	ADJ
ejpam-5280	42	27	calculus	calculus	NOUN
ejpam-5280	42	28	concepts	concept	NOUN
ejpam-5280	42	29	.	.	PUNCT
ejpam-5280	43	1	this	this	DET
ejpam-5280	43	2	model	model	NOUN
ejpam-5280	43	3	plays	play	VERB
ejpam-5280	43	4	a	a	DET
ejpam-5280	43	5	crucial	crucial	ADJ
ejpam-5280	43	6	role	role	NOUN
ejpam-5280	43	7	in	in	ADP
ejpam-5280	43	8	various	various	ADJ
ejpam-5280	43	9	fields	field	NOUN
ejpam-5280	43	10	such	such	ADJ
ejpam-5280	43	11	as	as	ADP
ejpam-5280	43	12	physics	physics	NOUN
ejpam-5280	43	13	,	,	PUNCT
ejpam-5280	43	14	engineering	engineering	NOUN
ejpam-5280	43	15	,	,	PUNCT
ejpam-5280	43	16	biology	biology	NOUN
ejpam-5280	43	17	,	,	PUNCT
ejpam-5280	43	18	and	and	CCONJ
ejpam-5280	43	19	finance	finance	NOUN
ejpam-5280	43	20	,	,	PUNCT
ejpam-5280	43	21	where	where	SCONJ
ejpam-5280	43	22	systems	system	NOUN
ejpam-5280	43	23	exhibit	exhibit	VERB
ejpam-5280	43	24	memory	memory	NOUN
ejpam-5280	43	25	effects	effect	NOUN
ejpam-5280	43	26	,	,	PUNCT
ejpam-5280	43	27	longrange	longrange	ADJ
ejpam-5280	43	28	interactions	interaction	NOUN
ejpam-5280	43	29	,	,	PUNCT
ejpam-5280	43	30	and	and	CCONJ
ejpam-5280	43	31	complex	complex	ADJ
ejpam-5280	43	32	dynamics	dynamic	NOUN
ejpam-5280	43	33	.	.	PUNCT
ejpam-5280	44	1	volterra	volterra	NOUN
ejpam-5280	44	2	and	and	CCONJ
ejpam-5280	44	3	fredholm	fredholm	VERB
ejpam-5280	44	4	integrodifferential	integrodifferential	ADJ
ejpam-5280	44	5	equations	equation	NOUN
ejpam-5280	44	6	are	be	AUX
ejpam-5280	44	7	two	two	NUM
ejpam-5280	44	8	types	type	NOUN
ejpam-5280	44	9	of	of	ADP
ejpam-5280	44	10	integral	integral	ADJ
ejpam-5280	44	11	equations	equation	NOUN
ejpam-5280	44	12	with	with	ADP
ejpam-5280	44	13	important	important	ADJ
ejpam-5280	44	14	applications	application	NOUN
ejpam-5280	44	15	in	in	ADP
ejpam-5280	44	16	various	various	ADJ
ejpam-5280	44	17	fields	field	NOUN
ejpam-5280	44	18	such	such	ADJ
ejpam-5280	44	19	as	as	ADP
ejpam-5280	44	20	physics	physics	NOUN
ejpam-5280	44	21	,	,	PUNCT
ejpam-5280	44	22	engineering	engineering	NOUN
ejpam-5280	44	23	,	,	PUNCT
ejpam-5280	44	24	and	and	CCONJ
ejpam-5280	44	25	applied	apply	VERB
ejpam-5280	44	26	mathematics	mathematic	NOUN
ejpam-5280	44	27	.	.	PUNCT
ejpam-5280	45	1	although	although	SCONJ
ejpam-5280	45	2	they	they	PRON
ejpam-5280	45	3	are	be	AUX
ejpam-5280	45	4	related	relate	VERB
ejpam-5280	45	5	,	,	PUNCT
ejpam-5280	45	6	they	they	PRON
ejpam-5280	45	7	differ	differ	VERB
ejpam-5280	45	8	in	in	ADP
ejpam-5280	45	9	their	their	PRON
ejpam-5280	45	10	formulation	formulation	NOUN
ejpam-5280	45	11	and	and	CCONJ
ejpam-5280	45	12	properties	property	NOUN
ejpam-5280	45	13	.	.	PUNCT
ejpam-5280	46	1	volterra	volterra	PROPN
ejpam-5280	46	2	integrodifferential	integrodifferential	PROPN
ejpam-5280	46	3	equations	equation	NOUN
ejpam-5280	46	4	involve	involve	VERB
ejpam-5280	46	5	an	an	DET
ejpam-5280	46	6	integral	integral	NOUN
ejpam-5280	46	7	that	that	PRON
ejpam-5280	46	8	extends	extend	VERB
ejpam-5280	46	9	over	over	ADP
ejpam-5280	46	10	a	a	DET
ejpam-5280	46	11	variable	variable	ADJ
ejpam-5280	46	12	limit	limit	NOUN
ejpam-5280	46	13	of	of	ADP
ejpam-5280	46	14	integration	integration	NOUN
ejpam-5280	46	15	,	,	PUNCT
ejpam-5280	46	16	typically	typically	ADV
ejpam-5280	46	17	from	from	ADP
ejpam-5280	46	18	a	a	DET
ejpam-5280	46	19	fixed	fix	VERB
ejpam-5280	46	20	starting	starting	NOUN
ejpam-5280	46	21	point	point	NOUN
ejpam-5280	46	22	to	to	ADP
ejpam-5280	46	23	the	the	DET
ejpam-5280	46	24	independent	independent	ADJ
ejpam-5280	46	25	variable	variable	NOUN
ejpam-5280	46	26	,	,	PUNCT
ejpam-5280	46	27	while	while	SCONJ
ejpam-5280	46	28	fredholm	fredholm	ADJ
ejpam-5280	46	29	integrodifferential	integrodifferential	ADJ
ejpam-5280	46	30	equations	equation	NOUN
ejpam-5280	46	31	involve	involve	VERB
ejpam-5280	46	32	an	an	DET
ejpam-5280	46	33	integral	integral	ADJ
ejpam-5280	46	34	with	with	ADP
ejpam-5280	46	35	fixed	fix	VERB
ejpam-5280	46	36	limits	limit	NOUN
ejpam-5280	46	37	of	of	ADP
ejpam-5280	46	38	integration	integration	NOUN
ejpam-5280	46	39	that	that	PRON
ejpam-5280	46	40	do	do	AUX
ejpam-5280	46	41	not	not	PART
ejpam-5280	46	42	depend	depend	VERB
ejpam-5280	46	43	on	on	ADP
ejpam-5280	46	44	the	the	DET
ejpam-5280	46	45	independent	independent	ADJ
ejpam-5280	46	46	variable	variable	NOUN
ejpam-5280	46	47	.	.	PUNCT
ejpam-5280	47	1	m.i	m.i	PROPN
ejpam-5280	47	2	.	.	PROPN
ejpam-5280	47	3	syam	syam	PROPN
ejpam-5280	47	4	,	,	PUNCT
ejpam-5280	47	5	m.	m.	NOUN
ejpam-5280	47	6	sharadga	sharadga	PROPN
ejpam-5280	47	7	,	,	PUNCT
ejpam-5280	47	8	i.	i.	PROPN
ejpam-5280	47	9	hashim	hashim	PROPN
ejpam-5280	47	10	/	/	SYM
ejpam-5280	47	11	eur	eur	PROPN
ejpam-5280	47	12	.	.	PUNCT
ejpam-5280	48	1	j.	j.	PROPN
ejpam-5280	48	2	pure	pure	PROPN
ejpam-5280	48	3	appl	appl	PROPN
ejpam-5280	48	4	.	.	PROPN
ejpam-5280	48	5	math	math	PROPN
ejpam-5280	48	6	,	,	PUNCT
ejpam-5280	48	7	17	17	NUM
ejpam-5280	48	8	(	(	PUNCT
ejpam-5280	48	9	3	3	NUM
ejpam-5280	48	10	)	)	PUNCT
ejpam-5280	48	11	(	(	PUNCT
ejpam-5280	48	12	2024	2024	NUM
ejpam-5280	48	13	)	)	PUNCT
ejpam-5280	48	14	,	,	PUNCT
ejpam-5280	48	15	1429	1429	NUM
ejpam-5280	48	16	-	-	SYM
ejpam-5280	48	17	1448	1448	NUM
ejpam-5280	48	18	1431	1431	NUM
ejpam-5280	48	19	applications	application	NOUN
ejpam-5280	48	20	of	of	ADP
ejpam-5280	48	21	fvfidms	fvfidms	NOUN
ejpam-5280	48	22	are	be	AUX
ejpam-5280	48	23	widespread	widespread	ADJ
ejpam-5280	48	24	,	,	PUNCT
ejpam-5280	48	25	ranging	range	VERB
ejpam-5280	48	26	from	from	ADP
ejpam-5280	48	27	modeling	model	VERB
ejpam-5280	48	28	viscoelastic	viscoelastic	ADJ
ejpam-5280	48	29	materials	material	NOUN
ejpam-5280	48	30	and	and	CCONJ
ejpam-5280	48	31	anomalous	anomalous	ADJ
ejpam-5280	48	32	diffusion	diffusion	NOUN
ejpam-5280	48	33	processes	process	NOUN
ejpam-5280	48	34	to	to	ADP
ejpam-5280	48	35	analyzing	analyze	VERB
ejpam-5280	48	36	population	population	NOUN
ejpam-5280	48	37	dynamics	dynamic	NOUN
ejpam-5280	48	38	in	in	ADP
ejpam-5280	48	39	ecology	ecology	NOUN
ejpam-5280	48	40	and	and	CCONJ
ejpam-5280	48	41	pricing	price	VERB
ejpam-5280	48	42	financial	financial	ADJ
ejpam-5280	48	43	derivatives	derivative	NOUN
ejpam-5280	48	44	.	.	PUNCT
ejpam-5280	49	1	understanding	understand	VERB
ejpam-5280	49	2	the	the	DET
ejpam-5280	49	3	behavior	behavior	NOUN
ejpam-5280	49	4	of	of	ADP
ejpam-5280	49	5	fvfidms	fvfidms	PROPN
ejpam-5280	49	6	is	be	AUX
ejpam-5280	49	7	essential	essential	ADJ
ejpam-5280	49	8	for	for	ADP
ejpam-5280	49	9	predicting	predict	VERB
ejpam-5280	49	10	and	and	CCONJ
ejpam-5280	49	11	controlling	control	VERB
ejpam-5280	49	12	complex	complex	ADJ
ejpam-5280	49	13	systems	system	NOUN
ejpam-5280	49	14	in	in	ADP
ejpam-5280	49	15	various	various	ADJ
ejpam-5280	49	16	scientific	scientific	ADJ
ejpam-5280	49	17	and	and	CCONJ
ejpam-5280	49	18	engineering	engineering	NOUN
ejpam-5280	49	19	domains	domain	NOUN
ejpam-5280	49	20	.	.	PUNCT
ejpam-5280	50	1	fore	fore	NOUN
ejpam-5280	50	2	more	more	ADJ
ejpam-5280	50	3	details	detail	NOUN
ejpam-5280	50	4	,	,	PUNCT
ejpam-5280	50	5	see	see	VERB
ejpam-5280	50	6	[	[	X
ejpam-5280	50	7	6	6	NUM
ejpam-5280	50	8	,	,	PUNCT
ejpam-5280	50	9	11	11	NUM
ejpam-5280	50	10	,	,	PUNCT
ejpam-5280	50	11	12	12	NUM
ejpam-5280	50	12	]	]	PUNCT
ejpam-5280	50	13	.	.	PUNCT
ejpam-5280	51	1	the	the	DET
ejpam-5280	51	2	structure	structure	NOUN
ejpam-5280	51	3	of	of	ADP
ejpam-5280	51	4	our	our	PRON
ejpam-5280	51	5	paper	paper	NOUN
ejpam-5280	51	6	is	be	AUX
ejpam-5280	51	7	listed	list	VERB
ejpam-5280	51	8	below	below	ADV
ejpam-5280	51	9	.	.	PUNCT
ejpam-5280	52	1	several	several	ADJ
ejpam-5280	52	2	definitions	definition	NOUN
ejpam-5280	52	3	and	and	CCONJ
ejpam-5280	52	4	lemmas	lemma	NOUN
ejpam-5280	52	5	will	will	AUX
ejpam-5280	52	6	be	be	AUX
ejpam-5280	52	7	introduced	introduce	VERB
ejpam-5280	52	8	in	in	ADP
ejpam-5280	52	9	the	the	DET
ejpam-5280	52	10	next	next	ADJ
ejpam-5280	52	11	section	section	NOUN
ejpam-5280	52	12	.	.	PUNCT
ejpam-5280	53	1	section	section	NOUN
ejpam-5280	53	2	three	three	NUM
ejpam-5280	53	3	will	will	AUX
ejpam-5280	53	4	develop	develop	VERB
ejpam-5280	53	5	a	a	DET
ejpam-5280	53	6	version	version	NOUN
ejpam-5280	53	7	of	of	ADP
ejpam-5280	53	8	the	the	DET
ejpam-5280	53	9	omm	omm	NOUN
ejpam-5280	53	10	to	to	PART
ejpam-5280	53	11	solve	solve	VERB
ejpam-5280	53	12	the	the	DET
ejpam-5280	53	13	proposed	propose	VERB
ejpam-5280	53	14	problem	problem	NOUN
ejpam-5280	53	15	.	.	PUNCT
ejpam-5280	54	1	some	some	DET
ejpam-5280	54	2	theoretical	theoretical	ADJ
ejpam-5280	54	3	outcomes	outcome	NOUN
ejpam-5280	54	4	,	,	PUNCT
ejpam-5280	54	5	such	such	ADJ
ejpam-5280	54	6	as	as	ADP
ejpam-5280	54	7	existence	existence	NOUN
ejpam-5280	54	8	and	and	CCONJ
ejpam-5280	54	9	uniqueness	uniqueness	NOUN
ejpam-5280	54	10	,	,	PUNCT
ejpam-5280	54	11	estimations	estimation	NOUN
ejpam-5280	54	12	of	of	ADP
ejpam-5280	54	13	errors	error	NOUN
ejpam-5280	54	14	,	,	PUNCT
ejpam-5280	54	15	and	and	CCONJ
ejpam-5280	54	16	convergence	convergence	NOUN
ejpam-5280	54	17	of	of	ADP
ejpam-5280	54	18	the	the	DET
ejpam-5280	54	19	solution	solution	NOUN
ejpam-5280	54	20	,	,	PUNCT
ejpam-5280	54	21	will	will	AUX
ejpam-5280	54	22	be	be	AUX
ejpam-5280	54	23	demonstrated	demonstrate	VERB
ejpam-5280	54	24	in	in	ADP
ejpam-5280	54	25	section	section	NOUN
ejpam-5280	54	26	4	4	NUM
ejpam-5280	54	27	.	.	PUNCT
ejpam-5280	55	1	three	three	NUM
ejpam-5280	55	2	illustrative	illustrative	ADJ
ejpam-5280	55	3	examples	example	NOUN
ejpam-5280	55	4	will	will	AUX
ejpam-5280	55	5	be	be	AUX
ejpam-5280	55	6	presented	present	VERB
ejpam-5280	55	7	in	in	ADP
ejpam-5280	55	8	section	section	NOUN
ejpam-5280	55	9	5	5	NUM
ejpam-5280	55	10	.	.	PUNCT
ejpam-5280	55	11	numerical	numerical	ADJ
ejpam-5280	55	12	validation	validation	NOUN
ejpam-5280	55	13	of	of	ADP
ejpam-5280	55	14	the	the	DET
ejpam-5280	55	15	proposed	propose	VERB
ejpam-5280	55	16	method	method	NOUN
ejpam-5280	55	17	’s	’s	PART
ejpam-5280	55	18	convergence	convergence	NOUN
ejpam-5280	55	19	to	to	ADP
ejpam-5280	55	20	the	the	DET
ejpam-5280	55	21	unique	unique	ADJ
ejpam-5280	55	22	solution	solution	NOUN
ejpam-5280	55	23	of	of	ADP
ejpam-5280	55	24	our	our	PRON
ejpam-5280	55	25	problems	problem	NOUN
ejpam-5280	55	26	provided	provide	VERB
ejpam-5280	55	27	by	by	ADP
ejpam-5280	55	28	these	these	DET
ejpam-5280	55	29	examples	example	NOUN
ejpam-5280	55	30	.	.	PUNCT
ejpam-5280	56	1	finally	finally	ADV
ejpam-5280	56	2	,	,	PUNCT
ejpam-5280	56	3	we	we	PRON
ejpam-5280	56	4	will	will	AUX
ejpam-5280	56	5	draw	draw	VERB
ejpam-5280	56	6	conclusions	conclusion	NOUN
ejpam-5280	56	7	and	and	CCONJ
ejpam-5280	56	8	provide	provide	VERB
ejpam-5280	56	9	closing	closing	NOUN
ejpam-5280	56	10	remarks	remark	NOUN
ejpam-5280	56	11	in	in	ADP
ejpam-5280	56	12	the	the	DET
ejpam-5280	56	13	final	final	ADJ
ejpam-5280	56	14	section	section	NOUN
ejpam-5280	56	15	.	.	PUNCT
ejpam-5280	57	1	2	2	X
ejpam-5280	57	2	.	.	X
ejpam-5280	57	3	foundational	foundational	ADJ
ejpam-5280	57	4	concepts	concept	NOUN
ejpam-5280	57	5	this	this	DET
ejpam-5280	57	6	section	section	NOUN
ejpam-5280	57	7	presents	present	VERB
ejpam-5280	57	8	various	various	ADJ
ejpam-5280	57	9	fundamental	fundamental	ADJ
ejpam-5280	57	10	concepts	concept	NOUN
ejpam-5280	57	11	and	and	CCONJ
ejpam-5280	57	12	results	result	NOUN
ejpam-5280	57	13	employed	employ	VERB
ejpam-5280	57	14	within	within	ADP
ejpam-5280	57	15	this	this	DET
ejpam-5280	57	16	paper	paper	NOUN
ejpam-5280	57	17	.	.	PUNCT
ejpam-5280	58	1	definition	definition	NOUN
ejpam-5280	58	2	1	1	NUM
ejpam-5280	58	3	.	.	PUNCT
ejpam-5280	59	1	[	[	X
ejpam-5280	59	2	6	6	NUM
ejpam-5280	59	3	,	,	PUNCT
ejpam-5280	59	4	11	11	NUM
ejpam-5280	59	5	,	,	PUNCT
ejpam-5280	59	6	12	12	NUM
ejpam-5280	59	7	]	]	PUNCT
ejpam-5280	59	8	for	for	ADP
ejpam-5280	59	9	µ	µ	DET
ejpam-5280	59	10	∈	∈	NOUN
ejpam-5280	59	11	(	(	PUNCT
ejpam-5280	59	12	0	0	NUM
ejpam-5280	59	13	,	,	PUNCT
ejpam-5280	59	14	1	1	NUM
ejpam-5280	59	15	)	)	PUNCT
ejpam-5280	59	16	and	and	CCONJ
ejpam-5280	59	17	t	t	X
ejpam-5280	59	18	>	>	X
ejpam-5280	59	19	0	0	PROPN
ejpam-5280	59	20	,	,	PUNCT
ejpam-5280	59	21	the	the	DET
ejpam-5280	59	22	caputo	caputo	PROPN
ejpam-5280	59	23	derivative	derivative	NOUN
ejpam-5280	59	24	of	of	ADP
ejpam-5280	59	25	ω(t	ω(t	NOUN
ejpam-5280	59	26	)	)	PUNCT
ejpam-5280	59	27	is	be	AUX
ejpam-5280	59	28	defined	define	VERB
ejpam-5280	59	29	as	as	SCONJ
ejpam-5280	59	30	follows	follow	VERB
ejpam-5280	59	31	dµω(t	dµω(t	NOUN
ejpam-5280	59	32	)	)	PUNCT
ejpam-5280	59	33	=	=	SYM
ejpam-5280	59	34	1	1	NUM
ejpam-5280	59	35	γ(1−	γ(1−	NOUN
ejpam-5280	59	36	µ	µ	NUM
ejpam-5280	59	37	)	)	PUNCT
ejpam-5280	59	38	∫	∫	PROPN
ejpam-5280	59	39	t	t	PROPN
ejpam-5280	59	40	0	0	NUM
ejpam-5280	60	1	(	(	PUNCT
ejpam-5280	60	2	t−	t−	PROPN
ejpam-5280	60	3	τ)−µω′(τ)dτ	τ)−µω′(τ)dτ	NOUN
ejpam-5280	60	4	,	,	PUNCT
ejpam-5280	60	5	(	(	PUNCT
ejpam-5280	60	6	3	3	X
ejpam-5280	60	7	)	)	PUNCT
ejpam-5280	60	8	and	and	CCONJ
ejpam-5280	60	9	the	the	DET
ejpam-5280	60	10	fractional	fractional	ADJ
ejpam-5280	60	11	integral	integral	ADJ
ejpam-5280	60	12	operator	operator	NOUN
ejpam-5280	60	13	is	be	AUX
ejpam-5280	60	14	given	give	VERB
ejpam-5280	60	15	by	by	ADP
ejpam-5280	60	16	iµω(t	iµω(t	NOUN
ejpam-5280	60	17	)	)	PUNCT
ejpam-5280	60	18	=	=	NOUN
ejpam-5280	60	19	1	1	NUM
ejpam-5280	60	20	γ(µ	γ(µ	PROPN
ejpam-5280	60	21	)	)	PUNCT
ejpam-5280	60	22	∫	∫	PROPN
ejpam-5280	60	23	t	t	PROPN
ejpam-5280	60	24	0	0	NUM
ejpam-5280	61	1	(	(	PUNCT
ejpam-5280	61	2	t−	t−	PROPN
ejpam-5280	61	3	τ)µ−1ω(τ)dτ	τ)µ−1ω(τ)dτ	NOUN
ejpam-5280	61	4	.	.	PUNCT
ejpam-5280	62	1	(	(	PUNCT
ejpam-5280	62	2	4	4	X
ejpam-5280	62	3	)	)	PUNCT
ejpam-5280	62	4	the	the	DET
ejpam-5280	62	5	fractional	fractional	ADJ
ejpam-5280	62	6	fundamental	fundamental	ADJ
ejpam-5280	62	7	theorem	theorem	NOUN
ejpam-5280	62	8	of	of	ADP
ejpam-5280	62	9	calculus	calculus	NOUN
ejpam-5280	62	10	is	be	AUX
ejpam-5280	62	11	given	give	VERB
ejpam-5280	62	12	as	as	ADP
ejpam-5280	62	13	lemma	lemma	PROPN
ejpam-5280	62	14	1	1	NUM
ejpam-5280	62	15	.	.	PUNCT
ejpam-5280	63	1	[	[	X
ejpam-5280	63	2	13	13	NUM
ejpam-5280	63	3	,	,	PUNCT
ejpam-5280	63	4	20	20	NUM
ejpam-5280	63	5	]	]	PUNCT
ejpam-5280	63	6	for	for	ADP
ejpam-5280	63	7	µ	µ	NOUN
ejpam-5280	63	8	>	>	SYM
ejpam-5280	63	9	0	0	NUM
ejpam-5280	63	10	∈	∈	NOUN
ejpam-5280	63	11	(	(	PUNCT
ejpam-5280	63	12	0	0	NUM
ejpam-5280	63	13	,	,	PUNCT
ejpam-5280	63	14	1	1	NUM
ejpam-5280	63	15	)	)	PUNCT
ejpam-5280	63	16	,	,	PUNCT
ejpam-5280	63	17	and	and	CCONJ
ejpam-5280	63	18	ω(t	ω(t	NOUN
ejpam-5280	63	19	)	)	PUNCT
ejpam-5280	63	20	∈	∈	PROPN
ejpam-5280	63	21	c[0	c[0	PROPN
ejpam-5280	63	22	,	,	PUNCT
ejpam-5280	63	23	1	1	NUM
ejpam-5280	63	24	]	]	PUNCT
ejpam-5280	63	25	,	,	PUNCT
ejpam-5280	63	26	the	the	DET
ejpam-5280	63	27	following	follow	VERB
ejpam-5280	63	28	equations	equation	NOUN
ejpam-5280	63	29	hold	hold	VERB
ejpam-5280	63	30	iµdµω(t	iµdµω(t	NOUN
ejpam-5280	63	31	)	)	PUNCT
ejpam-5280	63	32	=	=	SYM
ejpam-5280	63	33	ω(t)−	ω(t)−	PROPN
ejpam-5280	63	34	ω(0	ω(0	PROPN
ejpam-5280	63	35	)	)	PUNCT
ejpam-5280	63	36	,	,	PUNCT
ejpam-5280	63	37	(	(	PUNCT
ejpam-5280	63	38	5	5	X
ejpam-5280	63	39	)	)	PUNCT
ejpam-5280	63	40	dµiµω(t	dµiµω(t	PROPN
ejpam-5280	63	41	)	)	PUNCT
ejpam-5280	63	42	=	=	SYM
ejpam-5280	63	43	ω(t	ω(t	NOUN
ejpam-5280	63	44	)	)	PUNCT
ejpam-5280	63	45	.	.	PUNCT
ejpam-5280	64	1	(	(	PUNCT
ejpam-5280	64	2	6	6	NUM
ejpam-5280	64	3	)	)	PUNCT
ejpam-5280	64	4	another	another	DET
ejpam-5280	64	5	important	important	ADJ
ejpam-5280	64	6	concept	concept	NOUN
ejpam-5280	64	7	in	in	ADP
ejpam-5280	64	8	this	this	DET
ejpam-5280	64	9	paper	paper	NOUN
ejpam-5280	64	10	is	be	AUX
ejpam-5280	64	11	the	the	DET
ejpam-5280	64	12	block	block	NOUN
ejpam-5280	64	13	pulse	pulse	NOUN
ejpam-5280	64	14	function	function	NOUN
ejpam-5280	64	15	(	(	PUNCT
ejpam-5280	64	16	bpf	bpf	NOUN
ejpam-5280	64	17	)	)	PUNCT
ejpam-5280	64	18	which	which	PRON
ejpam-5280	64	19	is	be	AUX
ejpam-5280	64	20	defined	define	VERB
ejpam-5280	64	21	as	as	ADP
ejpam-5280	64	22	follows	follow	VERB
ejpam-5280	64	23	.	.	PUNCT
ejpam-5280	65	1	definition	definition	NOUN
ejpam-5280	65	2	2	2	NUM
ejpam-5280	65	3	.	.	PUNCT
ejpam-5280	66	1	[	[	X
ejpam-5280	66	2	15	15	NUM
ejpam-5280	66	3	,	,	PUNCT
ejpam-5280	66	4	18	18	NUM
ejpam-5280	66	5	,	,	PUNCT
ejpam-5280	66	6	19	19	NUM
ejpam-5280	66	7	]	]	PUNCT
ejpam-5280	66	8	let	let	AUX
ejpam-5280	66	9	m	m	PRON
ejpam-5280	66	10	be	be	AUX
ejpam-5280	66	11	a	a	DET
ejpam-5280	66	12	postive	postive	ADJ
ejpam-5280	66	13	integer	integer	NOUN
ejpam-5280	66	14	.	.	PUNCT
ejpam-5280	67	1	tr	tr	VERB
ejpam-5280	67	2	=	=	PROPN
ejpam-5280	67	3	jr	jr	PROPN
ejpam-5280	67	4	,	,	PUNCT
ejpam-5280	67	5	j	j	PROPN
ejpam-5280	67	6	∈	∈	PROPN
ejpam-5280	67	7	0	0	NUM
ejpam-5280	67	8	,	,	PUNCT
ejpam-5280	67	9	1	1	NUM
ejpam-5280	67	10	,	,	PUNCT
ejpam-5280	67	11	2	2	NUM
ejpam-5280	67	12	,	,	PUNCT
ejpam-5280	67	13	...	...	PUNCT
ejpam-5280	67	14	,	,	PUNCT
ejpam-5280	67	15	m	m	VERB
ejpam-5280	67	16	−	−	NOUN
ejpam-5280	67	17	1	1	NUM
ejpam-5280	67	18	,	,	PUNCT
ejpam-5280	67	19	r	r	NOUN
ejpam-5280	67	20	=	=	SYM
ejpam-5280	67	21	1	1	NUM
ejpam-5280	67	22	m	m	NOUN
ejpam-5280	67	23	.	.	PUNCT
ejpam-5280	68	1	then	then	ADV
ejpam-5280	68	2	,	,	PUNCT
ejpam-5280	68	3	the	the	DET
ejpam-5280	68	4	j	j	PROPN
ejpam-5280	68	5	-	-	PUNCT
ejpam-5280	68	6	block	block	NOUN
ejpam-5280	68	7	pulse	pulse	NOUN
ejpam-5280	68	8	function	function	NOUN
ejpam-5280	68	9	is	be	AUX
ejpam-5280	68	10	give	give	VERB
ejpam-5280	68	11	by	by	ADP
ejpam-5280	68	12	γj(t	γj(t	PUNCT
ejpam-5280	68	13	)	)	PUNCT
ejpam-5280	68	14	=	=	PRON
ejpam-5280	68	15	{	{	PUNCT
ejpam-5280	68	16	1	1	NUM
ejpam-5280	68	17	,	,	PUNCT
ejpam-5280	69	1	t	t	PROPN
ejpam-5280	69	2	∈	∈	PROPN
ejpam-5280	70	1	[	[	X
ejpam-5280	70	2	tj	tj	X
ejpam-5280	70	3	,	,	PUNCT
ejpam-5280	70	4	tj+1	tj+1	PROPN
ejpam-5280	70	5	)	)	PUNCT
ejpam-5280	70	6	0	0	NUM
ejpam-5280	70	7	,	,	PUNCT
ejpam-5280	70	8	[	[	X
ejpam-5280	70	9	0	0	NUM
ejpam-5280	70	10	,	,	PUNCT
ejpam-5280	70	11	1]−	1]−	NUM
ejpam-5280	70	12	[	[	X
ejpam-5280	70	13	tj	tj	X
ejpam-5280	70	14	,	,	PUNCT
ejpam-5280	70	15	tj+1	tj+1	PROPN
ejpam-5280	70	16	)	)	PUNCT
ejpam-5280	70	17	,	,	PUNCT
ejpam-5280	70	18	0	0	NUM
ejpam-5280	70	19	≤	≤	NOUN
ejpam-5280	70	20	s	s	PART
ejpam-5280	70	21	<	<	X
ejpam-5280	70	22	m.	m.	NOUN
ejpam-5280	70	23	(	(	PUNCT
ejpam-5280	70	24	7	7	NUM
ejpam-5280	70	25	)	)	PUNCT
ejpam-5280	70	26	in	in	ADP
ejpam-5280	70	27	the	the	DET
ejpam-5280	70	28	next	next	ADJ
ejpam-5280	70	29	theorem	theorem	NOUN
ejpam-5280	70	30	,	,	PUNCT
ejpam-5280	70	31	we	we	PRON
ejpam-5280	70	32	present	present	VERB
ejpam-5280	70	33	two	two	NUM
ejpam-5280	70	34	properties	property	NOUN
ejpam-5280	70	35	of	of	ADP
ejpam-5280	70	36	the	the	DET
ejpam-5280	70	37	bpfs	bpf	NOUN
ejpam-5280	70	38	which	which	PRON
ejpam-5280	70	39	are	be	AUX
ejpam-5280	70	40	the	the	DET
ejpam-5280	70	41	disjoint	disjoint	ADJ
ejpam-5280	70	42	and	and	CCONJ
ejpam-5280	70	43	orthogonal	orthogonal	ADJ
ejpam-5280	70	44	properties	property	NOUN
ejpam-5280	70	45	.	.	PUNCT
ejpam-5280	71	1	m.i	m.i	PROPN
ejpam-5280	71	2	.	.	PROPN
ejpam-5280	71	3	syam	syam	PROPN
ejpam-5280	71	4	,	,	PUNCT
ejpam-5280	71	5	m.	m.	NOUN
ejpam-5280	71	6	sharadga	sharadga	PROPN
ejpam-5280	71	7	,	,	PUNCT
ejpam-5280	71	8	i.	i.	PROPN
ejpam-5280	71	9	hashim	hashim	PROPN
ejpam-5280	71	10	/	/	SYM
ejpam-5280	71	11	eur	eur	PROPN
ejpam-5280	71	12	.	.	PUNCT
ejpam-5280	72	1	j.	j.	PROPN
ejpam-5280	72	2	pure	pure	PROPN
ejpam-5280	72	3	appl	appl	PROPN
ejpam-5280	72	4	.	.	PROPN
ejpam-5280	72	5	math	math	PROPN
ejpam-5280	72	6	,	,	PUNCT
ejpam-5280	72	7	17	17	NUM
ejpam-5280	72	8	(	(	PUNCT
ejpam-5280	72	9	3	3	NUM
ejpam-5280	72	10	)	)	PUNCT
ejpam-5280	72	11	(	(	PUNCT
ejpam-5280	72	12	2024	2024	NUM
ejpam-5280	72	13	)	)	PUNCT
ejpam-5280	72	14	,	,	PUNCT
ejpam-5280	72	15	1429	1429	NUM
ejpam-5280	72	16	-	-	SYM
ejpam-5280	72	17	1448	1448	NUM
ejpam-5280	72	18	1432	1432	NUM
ejpam-5280	72	19	theorem	theorem	NOUN
ejpam-5280	72	20	1	1	NUM
ejpam-5280	72	21	.	.	PUNCT
ejpam-5280	73	1	[	[	X
ejpam-5280	73	2	5	5	NUM
ejpam-5280	73	3	,	,	PUNCT
ejpam-5280	73	4	17	17	NUM
ejpam-5280	73	5	,	,	PUNCT
ejpam-5280	73	6	21	21	NUM
ejpam-5280	73	7	]	]	PUNCT
ejpam-5280	73	8	then	then	ADV
ejpam-5280	73	9	,	,	PUNCT
ejpam-5280	73	10	for	for	ADP
ejpam-5280	73	11	any	any	DET
ejpam-5280	73	12	i	i	PROPN
ejpam-5280	73	13	,	,	PUNCT
ejpam-5280	73	14	j	j	PROPN
ejpam-5280	73	15	∈	∈	PROPN
ejpam-5280	73	16	{	{	PUNCT
ejpam-5280	73	17	0	0	NUM
ejpam-5280	73	18	,	,	PUNCT
ejpam-5280	73	19	1	1	NUM
ejpam-5280	73	20	,	,	PUNCT
ejpam-5280	73	21	.	.	PUNCT
ejpam-5280	73	22	.	.	PUNCT
ejpam-5280	73	23	.	.	PUNCT
ejpam-5280	74	1	,	,	PUNCT
ejpam-5280	74	2	m	m	VERB
ejpam-5280	74	3	−	−	NOUN
ejpam-5280	74	4	1	1	NUM
ejpam-5280	74	5	}	}	PUNCT
ejpam-5280	74	6	,	,	PUNCT
ejpam-5280	74	7	we	we	PRON
ejpam-5280	74	8	have	have	VERB
ejpam-5280	74	9	γi(t)γj(t	γi(t)γj(t	PROPN
ejpam-5280	74	10	)	)	PUNCT
ejpam-5280	74	11	=	=	NOUN
ejpam-5280	74	12	{	{	PUNCT
ejpam-5280	74	13	γi(t	γi(t	NOUN
ejpam-5280	74	14	)	)	PUNCT
ejpam-5280	74	15	,	,	PUNCT
ejpam-5280	74	16	if	if	SCONJ
ejpam-5280	74	17	i	i	PRON
ejpam-5280	74	18	=	=	SYM
ejpam-5280	74	19	j	j	PROPN
ejpam-5280	74	20	0	0	NUM
ejpam-5280	74	21	,	,	PUNCT
ejpam-5280	74	22	if	if	SCONJ
ejpam-5280	74	23	i	i	PRON
ejpam-5280	74	24	̸=	̸=	PROPN
ejpam-5280	74	25	j	j	PROPN
ejpam-5280	74	26	,	,	PUNCT
ejpam-5280	74	27	(	(	PUNCT
ejpam-5280	74	28	8)	8)	NUM
ejpam-5280	74	29	and	and	CCONJ
ejpam-5280	74	30	∫	∫	PROPN
ejpam-5280	74	31	1	1	NUM
ejpam-5280	74	32	0	0	X
ejpam-5280	74	33	γi(t)γj(t)dt	γi(t)γj(t)dt	PROPN
ejpam-5280	74	34	=	=	SYM
ejpam-5280	74	35	{	{	PUNCT
ejpam-5280	74	36	r	r	NOUN
ejpam-5280	74	37	,	,	PUNCT
ejpam-5280	74	38	if	if	SCONJ
ejpam-5280	74	39	i	i	PRON
ejpam-5280	74	40	=	=	SYM
ejpam-5280	74	41	j	j	PROPN
ejpam-5280	74	42	0	0	NUM
ejpam-5280	74	43	,	,	PUNCT
ejpam-5280	74	44	if	if	SCONJ
ejpam-5280	74	45	i	i	PRON
ejpam-5280	74	46	̸=	̸=	PROPN
ejpam-5280	74	47	j	j	PROPN
ejpam-5280	74	48	.	.	PUNCT
ejpam-5280	75	1	(	(	PUNCT
ejpam-5280	75	2	9	9	NUM
ejpam-5280	75	3	)	)	PUNCT
ejpam-5280	75	4	for	for	ADP
ejpam-5280	75	5	numerical	numerical	ADJ
ejpam-5280	75	6	purposes	purpose	NOUN
ejpam-5280	75	7	,	,	PUNCT
ejpam-5280	75	8	we	we	PRON
ejpam-5280	75	9	present	present	VERB
ejpam-5280	75	10	the	the	DET
ejpam-5280	75	11	following	follow	VERB
ejpam-5280	75	12	important	important	ADJ
ejpam-5280	75	13	lemma	lemma	PROPN
ejpam-5280	75	14	.	.	PUNCT
ejpam-5280	76	1	lemma	lemma	PROPN
ejpam-5280	76	2	2	2	NUM
ejpam-5280	76	3	.	.	PUNCT
ejpam-5280	77	1	[	[	X
ejpam-5280	77	2	5	5	NUM
ejpam-5280	77	3	,	,	PUNCT
ejpam-5280	77	4	17	17	NUM
ejpam-5280	77	5	,	,	PUNCT
ejpam-5280	77	6	21	21	NUM
ejpam-5280	77	7	]	]	PUNCT
ejpam-5280	77	8	if	if	SCONJ
ejpam-5280	77	9	ω	ω	PROPN
ejpam-5280	77	10	∈	∈	PROPN
ejpam-5280	77	11	l2[0	l2[0	PROPN
ejpam-5280	77	12	,	,	PUNCT
ejpam-5280	77	13	1	1	NUM
ejpam-5280	77	14	]	]	PUNCT
ejpam-5280	77	15	,	,	PUNCT
ejpam-5280	77	16	then	then	ADV
ejpam-5280	77	17	ω(t	ω(t	NOUN
ejpam-5280	77	18	)	)	PUNCT
ejpam-5280	77	19	=	=	SYM
ejpam-5280	77	20	lim	lim	PROPN
ejpam-5280	77	21	m→∞	m→∞	NOUN
ejpam-5280	77	22	m−1∑	m−1∑	PROPN
ejpam-5280	77	23	j=0	j=0	PROPN
ejpam-5280	77	24	ωjγj(t	ωjγj(t	PROPN
ejpam-5280	77	25	)	)	PUNCT
ejpam-5280	77	26	,	,	PUNCT
ejpam-5280	77	27	(	(	PUNCT
ejpam-5280	77	28	10	10	NUM
ejpam-5280	77	29	)	)	PUNCT
ejpam-5280	77	30	where	where	SCONJ
ejpam-5280	77	31	ωj	ωj	ADV
ejpam-5280	77	32	=	=	SYM
ejpam-5280	77	33	1	1	NUM
ejpam-5280	77	34	r	r	NOUN
ejpam-5280	77	35	∫	∫	PROPN
ejpam-5280	77	36	(	(	PUNCT
ejpam-5280	77	37	j+1)r	j+1)r	PROPN
ejpam-5280	77	38	jr	jr	PROPN
ejpam-5280	77	39	ω(t)dt	ω(t)dt	PROPN
ejpam-5280	77	40	.	.	PUNCT
ejpam-5280	78	1	(	(	PUNCT
ejpam-5280	78	2	11	11	NUM
ejpam-5280	78	3	)	)	PUNCT
ejpam-5280	78	4	for	for	ADP
ejpam-5280	78	5	the	the	DET
ejpam-5280	78	6	approximation	approximation	NOUN
ejpam-5280	78	7	purposes	purpose	NOUN
ejpam-5280	78	8	,	,	PUNCT
ejpam-5280	78	9	we	we	PRON
ejpam-5280	78	10	choose	choose	VERB
ejpam-5280	78	11	m	m	PRON
ejpam-5280	78	12	large	large	ADJ
ejpam-5280	78	13	enough	enough	ADV
ejpam-5280	78	14	.	.	PUNCT
ejpam-5280	79	1	for	for	ADP
ejpam-5280	79	2	such	such	ADJ
ejpam-5280	79	3	m	m	NOUN
ejpam-5280	79	4	,	,	PUNCT
ejpam-5280	79	5	we	we	PRON
ejpam-5280	79	6	can	can	AUX
ejpam-5280	79	7	rewrite	rewrite	VERB
ejpam-5280	79	8	ω	ω	PROPN
ejpam-5280	79	9	in	in	ADP
ejpam-5280	79	10	the	the	DET
ejpam-5280	79	11	matrix	matrix	NOUN
ejpam-5280	79	12	form	form	NOUN
ejpam-5280	79	13	as	as	ADP
ejpam-5280	79	14	ω(t	ω(t	NOUN
ejpam-5280	79	15	)	)	PUNCT
ejpam-5280	80	1	≈	≈	PROPN
ejpam-5280	80	2	ω	ω	NUM
ejpam-5280	80	3	t	t	PROPN
ejpam-5280	80	4	γ(t	γ(t	NOUN
ejpam-5280	80	5	)	)	PUNCT
ejpam-5280	80	6	(	(	PUNCT
ejpam-5280	80	7	12	12	NUM
ejpam-5280	80	8	)	)	PUNCT
ejpam-5280	80	9	where	where	SCONJ
ejpam-5280	80	10	ω	ω	NOUN
ejpam-5280	80	11	=	=	SYM
ejpam-5280	80	12			PROPN
ejpam-5280	80	13	ω0	ω0	PROPN
ejpam-5280	80	14	ω1	ω1	PROPN
ejpam-5280	80	15	...	...	PUNCT
ejpam-5280	80	16	ωm−1	ωm−1	NOUN
ejpam-5280	80	17			NUM
ejpam-5280	80	18	,	,	PUNCT
ejpam-5280	80	19	γ(t	γ(t	PROPN
ejpam-5280	80	20	)	)	PUNCT
ejpam-5280	80	21			PROPN
ejpam-5280	81	1	γ0(t	γ0(t	PROPN
ejpam-5280	81	2	)	)	PUNCT
ejpam-5280	81	3	γ1(t	γ1(t	PROPN
ejpam-5280	81	4	)	)	PUNCT
ejpam-5280	81	5	...	...	PUNCT
ejpam-5280	82	1	γm−1(t	γm−1(t	X
ejpam-5280	82	2	)	)	PUNCT
ejpam-5280	83	1			X
ejpam-5280	83	2	.	.	PUNCT
ejpam-5280	84	1	(	(	PUNCT
ejpam-5280	84	2	13	13	NUM
ejpam-5280	84	3	)	)	SYM
ejpam-5280	84	4	3	3	NUM
ejpam-5280	84	5	.	.	NOUN
ejpam-5280	84	6	method	method	NOUN
ejpam-5280	84	7	of	of	ADP
ejpam-5280	84	8	solution	solution	NOUN
ejpam-5280	84	9	in	in	ADP
ejpam-5280	84	10	this	this	DET
ejpam-5280	84	11	section	section	NOUN
ejpam-5280	85	1	,	,	PUNCT
ejpam-5280	85	2	we	we	PRON
ejpam-5280	85	3	present	present	VERB
ejpam-5280	85	4	the	the	DET
ejpam-5280	85	5	method	method	NOUN
ejpam-5280	85	6	of	of	ADP
ejpam-5280	85	7	solution	solution	NOUN
ejpam-5280	85	8	for	for	ADP
ejpam-5280	85	9	problem	problem	NOUN
ejpam-5280	85	10	(	(	PUNCT
ejpam-5280	85	11	1)-(2	1)-(2	NUM
ejpam-5280	85	12	)	)	PUNCT
ejpam-5280	85	13	.	.	PUNCT
ejpam-5280	86	1	let	let	VERB
ejpam-5280	86	2	us	we	PRON
ejpam-5280	86	3	assume	assume	VERB
ejpam-5280	86	4	that	that	SCONJ
ejpam-5280	86	5	i1(t	i1(t	ADV
ejpam-5280	86	6	)	)	PUNCT
ejpam-5280	86	7	=	=	SYM
ejpam-5280	87	1	∫	∫	PROPN
ejpam-5280	87	2	t	t	PROPN
ejpam-5280	87	3	0	0	NUM
ejpam-5280	88	1	π1(t	π1(t	PROPN
ejpam-5280	88	2	,	,	PUNCT
ejpam-5280	88	3	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	88	4	(	(	PUNCT
ejpam-5280	88	5	14	14	NUM
ejpam-5280	88	6	)	)	PUNCT
ejpam-5280	88	7	and	and	CCONJ
ejpam-5280	88	8	i2(t	i2(t	NOUN
ejpam-5280	88	9	)	)	PUNCT
ejpam-5280	88	10	=	=	SYM
ejpam-5280	89	1	∫	∫	PROPN
ejpam-5280	89	2	1	1	NUM
ejpam-5280	89	3	0	0	X
ejpam-5280	89	4	π2(t	π2(t	PROPN
ejpam-5280	89	5	,	,	PUNCT
ejpam-5280	89	6	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	89	7	.	.	PUNCT
ejpam-5280	89	8	(	(	PUNCT
ejpam-5280	89	9	15	15	NUM
ejpam-5280	89	10	)	)	PUNCT
ejpam-5280	89	11	let	let	VERB
ejpam-5280	89	12	us	we	PRON
ejpam-5280	89	13	approximate	approximate	VERB
ejpam-5280	89	14	ω(t	ω(t	NOUN
ejpam-5280	89	15	)	)	PUNCT
ejpam-5280	89	16	by	by	ADP
ejpam-5280	89	17	ω(t	ω(t	NOUN
ejpam-5280	89	18	)	)	PUNCT
ejpam-5280	90	1	≈	≈	PROPN
ejpam-5280	90	2	m−1∑	m−1∑	NUM
ejpam-5280	90	3	i=0	i=0	PROPN
ejpam-5280	90	4	ωiγi(t	ωiγi(t	NOUN
ejpam-5280	90	5	)	)	PUNCT
ejpam-5280	90	6	.	.	PUNCT
ejpam-5280	91	1	(	(	PUNCT
ejpam-5280	91	2	16	16	X
ejpam-5280	91	3	)	)	PUNCT
ejpam-5280	91	4	m.i	m.i	PROPN
ejpam-5280	91	5	.	.	PROPN
ejpam-5280	91	6	syam	syam	PROPN
ejpam-5280	91	7	,	,	PUNCT
ejpam-5280	91	8	m.	m.	NOUN
ejpam-5280	91	9	sharadga	sharadga	PROPN
ejpam-5280	91	10	,	,	PUNCT
ejpam-5280	91	11	i.	i.	PROPN
ejpam-5280	91	12	hashim	hashim	PROPN
ejpam-5280	91	13	/	/	SYM
ejpam-5280	91	14	eur	eur	PROPN
ejpam-5280	91	15	.	.	PUNCT
ejpam-5280	92	1	j.	j.	PROPN
ejpam-5280	92	2	pure	pure	PROPN
ejpam-5280	92	3	appl	appl	PROPN
ejpam-5280	92	4	.	.	PROPN
ejpam-5280	92	5	math	math	PROPN
ejpam-5280	92	6	,	,	PUNCT
ejpam-5280	92	7	17	17	NUM
ejpam-5280	92	8	(	(	PUNCT
ejpam-5280	92	9	3	3	NUM
ejpam-5280	92	10	)	)	PUNCT
ejpam-5280	92	11	(	(	PUNCT
ejpam-5280	92	12	2024	2024	NUM
ejpam-5280	92	13	)	)	PUNCT
ejpam-5280	92	14	,	,	PUNCT
ejpam-5280	92	15	1429	1429	NUM
ejpam-5280	92	16	-	-	SYM
ejpam-5280	92	17	1448	1448	NUM
ejpam-5280	92	18	1433	1433	NUM
ejpam-5280	92	19	let	let	VERB
ejpam-5280	92	20	g3(ω(t	g3(ω(t	NOUN
ejpam-5280	92	21	)	)	PUNCT
ejpam-5280	92	22	)	)	PUNCT
ejpam-5280	93	1	=	=	SYM
ejpam-5280	93	2	n3∑	n3∑	PROPN
ejpam-5280	93	3	i=0	i=0	PROPN
ejpam-5280	93	4	a3,iω	a3,iω	PRON
ejpam-5280	93	5	i(t	i(t	PROPN
ejpam-5280	93	6	)	)	PUNCT
ejpam-5280	93	7	,	,	PUNCT
ejpam-5280	93	8	g4(ω(t	g4(ω(t	NOUN
ejpam-5280	93	9	)	)	PUNCT
ejpam-5280	93	10	)	)	PUNCT
ejpam-5280	94	1	=	=	SYM
ejpam-5280	95	1	n4∑	n4∑	PROPN
ejpam-5280	95	2	i=0	i=0	PROPN
ejpam-5280	95	3	a4,iω	a4,iω	PUNCT
ejpam-5280	95	4	i(t	i(t	PROPN
ejpam-5280	95	5	)	)	PUNCT
ejpam-5280	95	6	,	,	PUNCT
ejpam-5280	95	7	(	(	PUNCT
ejpam-5280	95	8	17	17	NUM
ejpam-5280	95	9	)	)	PUNCT
ejpam-5280	95	10	π1(t	π1(t	PROPN
ejpam-5280	95	11	,	,	PUNCT
ejpam-5280	95	12	s	s	X
ejpam-5280	95	13	)	)	PUNCT
ejpam-5280	95	14	=	=	SYM
ejpam-5280	96	1	m−1∑	m−1∑	PROPN
ejpam-5280	96	2	i=0	i=0	PROPN
ejpam-5280	96	3	m−1∑	m−1∑	NUM
ejpam-5280	96	4	j=0	j=0	PROPN
ejpam-5280	96	5	b1,i	b1,i	PROPN
ejpam-5280	96	6	,	,	PUNCT
ejpam-5280	96	7	jγi(t)γj(s	jγi(t)γj(s	NOUN
ejpam-5280	96	8	)	)	PUNCT
ejpam-5280	96	9	,	,	PUNCT
ejpam-5280	96	10	π2(t	π2(t	PROPN
ejpam-5280	96	11	,	,	PUNCT
ejpam-5280	96	12	s	s	PART
ejpam-5280	96	13	)	)	PUNCT
ejpam-5280	96	14	=	=	SYM
ejpam-5280	96	15	m−1∑	m−1∑	PROPN
ejpam-5280	96	16	i=0	i=0	PROPN
ejpam-5280	96	17	m−1∑	m−1∑	NUM
ejpam-5280	96	18	j=0	j=0	PROPN
ejpam-5280	96	19	b2,i	b2,i	PROPN
ejpam-5280	96	20	,	,	PUNCT
ejpam-5280	96	21	jγi(t)γj(s	jγi(t)γj(s	NOUN
ejpam-5280	96	22	)	)	PUNCT
ejpam-5280	96	23	.	.	PUNCT
ejpam-5280	97	1	(	(	PUNCT
ejpam-5280	97	2	18	18	NUM
ejpam-5280	97	3	)	)	PUNCT
ejpam-5280	97	4	using	use	VERB
ejpam-5280	97	5	equation	equation	NOUN
ejpam-5280	97	6	(	(	PUNCT
ejpam-5280	97	7	8)	8)	NUM
ejpam-5280	97	8	and	and	CCONJ
ejpam-5280	97	9	by	by	ADP
ejpam-5280	97	10	substituting	substitute	VERB
ejpam-5280	97	11	equation	equation	NOUN
ejpam-5280	97	12	(	(	PUNCT
ejpam-5280	97	13	16	16	NUM
ejpam-5280	97	14	)	)	PUNCT
ejpam-5280	97	15	into	into	ADP
ejpam-5280	97	16	equation	equation	NOUN
ejpam-5280	97	17	(	(	PUNCT
ejpam-5280	97	18	17	17	NUM
ejpam-5280	97	19	)	)	PUNCT
ejpam-5280	97	20	,	,	PUNCT
ejpam-5280	97	21	we	we	PRON
ejpam-5280	97	22	get	get	VERB
ejpam-5280	97	23	g3(ω(t	g3(ω(t	NOUN
ejpam-5280	97	24	)	)	PUNCT
ejpam-5280	97	25	)	)	PUNCT
ejpam-5280	98	1	=	=	SYM
ejpam-5280	98	2	n3∑	n3∑	PROPN
ejpam-5280	98	3	i=0	i=0	PROPN
ejpam-5280	98	4	a3,iω	a3,iω	NOUN
ejpam-5280	98	5	i(t	i(t	PROPN
ejpam-5280	98	6	)	)	PUNCT
ejpam-5280	98	7	=	=	SYM
ejpam-5280	98	8	n3∑	n3∑	PROPN
ejpam-5280	98	9	i=0	i=0	PROPN
ejpam-5280	98	10	a3,i	a3,i	PROPN
ejpam-5280	98	11	m−1∑	m−1∑	PROPN
ejpam-5280	98	12	j=0	j=0	PROPN
ejpam-5280	98	13	ωjγj(t	ωjγj(t	PROPN
ejpam-5280	98	14	)	)	PUNCT
ejpam-5280	98	15	i	i	PROPN
ejpam-5280	98	16	=	=	SYM
ejpam-5280	98	17	n3∑	n3∑	PROPN
ejpam-5280	98	18	i=0	i=0	PROPN
ejpam-5280	98	19	a3,i	a3,i	PROPN
ejpam-5280	98	20	m−1∑	m−1∑	PROPN
ejpam-5280	98	21	j=0	j=0	PROPN
ejpam-5280	98	22	ωi	ωi	PROPN
ejpam-5280	98	23	jγj(t	jγj(t	PROPN
ejpam-5280	98	24	)	)	PUNCT
ejpam-5280	98	25			PROPN
ejpam-5280	98	26	=	=	SYM
ejpam-5280	98	27	n3∑	n3∑	PROPN
ejpam-5280	98	28	i=0	i=0	PROPN
ejpam-5280	98	29	m−1∑	m−1∑	PROPN
ejpam-5280	98	30	j=0	j=0	PROPN
ejpam-5280	98	31	a3,iω	a3,iω	NOUN
ejpam-5280	98	32	i	i	PRON
ejpam-5280	98	33	jγj(t	jγj(t	PROPN
ejpam-5280	98	34	)	)	PUNCT
ejpam-5280	98	35	(	(	PUNCT
ejpam-5280	98	36	19	19	NUM
ejpam-5280	98	37	)	)	PUNCT
ejpam-5280	98	38	and	and	CCONJ
ejpam-5280	98	39	g4(ω(t	g4(ω(t	NOUN
ejpam-5280	98	40	)	)	PUNCT
ejpam-5280	98	41	)	)	PUNCT
ejpam-5280	99	1	=	=	SYM
ejpam-5280	100	1	n4∑	n4∑	PROPN
ejpam-5280	100	2	i=0	i=0	PROPN
ejpam-5280	100	3	a4,iω	a4,iω	PUNCT
ejpam-5280	100	4	i(t	i(t	PROPN
ejpam-5280	100	5	)	)	PUNCT
ejpam-5280	101	1	=	=	PUNCT
ejpam-5280	102	1	n4∑	n4∑	PROPN
ejpam-5280	102	2	i=0	i=0	PROPN
ejpam-5280	102	3	a4,i	a4,i	PROPN
ejpam-5280	102	4	m−1∑	m−1∑	ADP
ejpam-5280	102	5	j=0	j=0	PROPN
ejpam-5280	102	6	ωjγj(t	ωjγj(t	PROPN
ejpam-5280	102	7	)	)	PUNCT
ejpam-5280	102	8	i	i	NOUN
ejpam-5280	102	9	=	=	PUNCT
ejpam-5280	103	1	n4∑	n4∑	PROPN
ejpam-5280	103	2	i=0	i=0	PROPN
ejpam-5280	103	3	a4,i	a4,i	PROPN
ejpam-5280	103	4	m−1∑	m−1∑	ADP
ejpam-5280	103	5	j=0	j=0	PROPN
ejpam-5280	103	6	ωi	ωi	PROPN
ejpam-5280	103	7	jγj(t	jγj(t	PROPN
ejpam-5280	103	8	)	)	PUNCT
ejpam-5280	103	9			PROPN
ejpam-5280	103	10	=	=	SYM
ejpam-5280	103	11	n4∑	n4∑	PROPN
ejpam-5280	103	12	i=0	i=0	PROPN
ejpam-5280	103	13	m−1∑	m−1∑	NUM
ejpam-5280	103	14	j=0	j=0	PROPN
ejpam-5280	103	15	a4,iω	a4,iω	PROPN
ejpam-5280	103	16	i	i	PROPN
ejpam-5280	103	17	jγj(t	jγj(t	PROPN
ejpam-5280	103	18	)	)	PUNCT
ejpam-5280	103	19	.	.	PUNCT
ejpam-5280	104	1	(	(	PUNCT
ejpam-5280	104	2	20	20	NUM
ejpam-5280	104	3	)	)	PUNCT
ejpam-5280	104	4	substitute	substitute	NOUN
ejpam-5280	104	5	equation	equation	NOUN
ejpam-5280	104	6	(	(	PUNCT
ejpam-5280	104	7	19	19	NUM
ejpam-5280	104	8	)	)	PUNCT
ejpam-5280	104	9	and	and	CCONJ
ejpam-5280	104	10	(	(	PUNCT
ejpam-5280	104	11	18	18	NUM
ejpam-5280	104	12	)	)	PUNCT
ejpam-5280	104	13	into	into	ADP
ejpam-5280	104	14	equation	equation	NOUN
ejpam-5280	104	15	(	(	PUNCT
ejpam-5280	104	16	14	14	NUM
ejpam-5280	104	17	)	)	PUNCT
ejpam-5280	104	18	and	and	CCONJ
ejpam-5280	104	19	using	use	VERB
ejpam-5280	104	20	equation	equation	NOUN
ejpam-5280	104	21	(	(	PUNCT
ejpam-5280	104	22	8)	8)	NUM
ejpam-5280	104	23	to	to	PART
ejpam-5280	104	24	get	get	VERB
ejpam-5280	104	25	i1(t	i1(t	PROPN
ejpam-5280	104	26	)	)	PUNCT
ejpam-5280	104	27	=	=	SYM
ejpam-5280	105	1	∫	∫	PROPN
ejpam-5280	105	2	t	t	PROPN
ejpam-5280	105	3	0	0	NUM
ejpam-5280	106	1	π1(t	π1(t	PROPN
ejpam-5280	106	2	,	,	PUNCT
ejpam-5280	106	3	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	106	4	=	=	SYM
ejpam-5280	106	5	∫	∫	PROPN
ejpam-5280	106	6	t	t	NOUN
ejpam-5280	106	7	0	0	NUM
ejpam-5280	106	8	m−1∑	m−1∑	PROPN
ejpam-5280	106	9	i=0	i=0	PROPN
ejpam-5280	106	10	m−1∑	m−1∑	X
ejpam-5280	106	11	j=0	j=0	PROPN
ejpam-5280	106	12	b1,i	b1,i	PROPN
ejpam-5280	106	13	,	,	PUNCT
ejpam-5280	106	14	jγi(t)γj(s)ds	jγi(t)γj(s)ds	NOUN
ejpam-5280	106	15			PUNCT
ejpam-5280	107	1	n3∑	n3∑	PROPN
ejpam-5280	107	2	i=0	i=0	PROPN
ejpam-5280	107	3	m−1∑	m−1∑	NUM
ejpam-5280	107	4	j=0	j=0	PROPN
ejpam-5280	107	5	a3,iω	a3,iω	NOUN
ejpam-5280	107	6	i	i	PRON
ejpam-5280	107	7	jγj(s	jγj(s	PROPN
ejpam-5280	107	8	)	)	PUNCT
ejpam-5280	107	9			PROPN
ejpam-5280	107	10	m.i	m.i	PROPN
ejpam-5280	107	11	.	.	PROPN
ejpam-5280	107	12	syam	syam	PROPN
ejpam-5280	107	13	,	,	PUNCT
ejpam-5280	107	14	m.	m.	NOUN
ejpam-5280	107	15	sharadga	sharadga	PROPN
ejpam-5280	107	16	,	,	PUNCT
ejpam-5280	107	17	i.	i.	PROPN
ejpam-5280	107	18	hashim	hashim	PROPN
ejpam-5280	107	19	/	/	SYM
ejpam-5280	107	20	eur	eur	PROPN
ejpam-5280	107	21	.	.	PUNCT
ejpam-5280	108	1	j.	j.	PROPN
ejpam-5280	108	2	pure	pure	PROPN
ejpam-5280	108	3	appl	appl	PROPN
ejpam-5280	108	4	.	.	PROPN
ejpam-5280	108	5	math	math	PROPN
ejpam-5280	108	6	,	,	PUNCT
ejpam-5280	108	7	17	17	NUM
ejpam-5280	108	8	(	(	PUNCT
ejpam-5280	108	9	3	3	NUM
ejpam-5280	108	10	)	)	PUNCT
ejpam-5280	108	11	(	(	PUNCT
ejpam-5280	108	12	2024	2024	NUM
ejpam-5280	108	13	)	)	PUNCT
ejpam-5280	108	14	,	,	PUNCT
ejpam-5280	108	15	1429	1429	NUM
ejpam-5280	108	16	-	-	SYM
ejpam-5280	108	17	1448	1448	NUM
ejpam-5280	108	18	1434	1434	NUM
ejpam-5280	108	19	=	=	SYM
ejpam-5280	108	20	m−1∑	m−1∑	PROPN
ejpam-5280	108	21	i=0	i=0	PROPN
ejpam-5280	108	22	m−1∑	m−1∑	NUM
ejpam-5280	108	23	j=0	j=0	PROPN
ejpam-5280	108	24	n3∑	n3∑	PROPN
ejpam-5280	108	25	l=0	l=0	PROPN
ejpam-5280	108	26	m−1∑	m−1∑	NUM
ejpam-5280	108	27	k=0	k=0	PROPN
ejpam-5280	108	28	b1,i	b1,i	PROPN
ejpam-5280	108	29	,	,	PUNCT
ejpam-5280	108	30	ja3,lω	ja3,lω	PROPN
ejpam-5280	108	31	l	l	PROPN
ejpam-5280	108	32	kγj(t	kγj(t	PROPN
ejpam-5280	108	33	)	)	PUNCT
ejpam-5280	109	1	∫	∫	PROPN
ejpam-5280	110	1	t	t	PROPN
ejpam-5280	110	2	0	0	NUM
ejpam-5280	110	3	γj(s)γk(s)ds	γj(s)γk(s)ds	PROPN
ejpam-5280	110	4	=	=	SYM
ejpam-5280	110	5	m−1∑	m−1∑	PROPN
ejpam-5280	110	6	i=0	i=0	PROPN
ejpam-5280	110	7	m−1∑	m−1∑	NUM
ejpam-5280	110	8	j=0	j=0	PROPN
ejpam-5280	110	9	n3∑	n3∑	PROPN
ejpam-5280	110	10	l=0	l=0	PROPN
ejpam-5280	110	11	b1,i	b1,i	PROPN
ejpam-5280	110	12	,	,	PUNCT
ejpam-5280	110	13	ja3,lω	ja3,lω	PROPN
ejpam-5280	110	14	l	l	PROPN
ejpam-5280	110	15	jγj(t	jγj(t	PROPN
ejpam-5280	110	16	)	)	PUNCT
ejpam-5280	110	17	∫	∫	PROPN
ejpam-5280	111	1	t	t	PROPN
ejpam-5280	111	2	0	0	NUM
ejpam-5280	111	3	γj(s)ds	γj(s)ds	PROPN
ejpam-5280	111	4	.	.	PUNCT
ejpam-5280	112	1	(	(	PUNCT
ejpam-5280	112	2	21	21	NUM
ejpam-5280	112	3	)	)	PUNCT
ejpam-5280	112	4	using	use	VERB
ejpam-5280	112	5	the	the	DET
ejpam-5280	112	6	definition	definition	NOUN
ejpam-5280	112	7	of	of	ADP
ejpam-5280	112	8	the	the	DET
ejpam-5280	112	9	bpfs	bpf	NOUN
ejpam-5280	112	10	,	,	PUNCT
ejpam-5280	112	11	we	we	PRON
ejpam-5280	112	12	can	can	AUX
ejpam-5280	112	13	see	see	VERB
ejpam-5280	112	14	that	that	DET
ejpam-5280	112	15	∫	∫	PROPN
ejpam-5280	112	16	t	t	NOUN
ejpam-5280	112	17	0	0	NUM
ejpam-5280	112	18	γj(s)ds	γj(s)ds	PROPN
ejpam-5280	113	1	=	=	PUNCT
ejpam-5280	114	1			PRON
ejpam-5280	114	2	∫	∫	PROPN
ejpam-5280	114	3	t	t	PROPN
ejpam-5280	114	4	0	0	NUM
ejpam-5280	114	5	0ds	0ds	NOUN
ejpam-5280	114	6	,	,	PUNCT
ejpam-5280	114	7	t	t	X
ejpam-5280	114	8	<	<	X
ejpam-5280	114	9	jr∫	jr∫	PROPN
ejpam-5280	114	10	t	t	PROPN
ejpam-5280	114	11	jr	jr	PROPN
ejpam-5280	114	12	1ds	1ds	NOUN
ejpam-5280	114	13	,	,	PUNCT
ejpam-5280	114	14	r	r	NOUN
ejpam-5280	114	15	<	<	X
ejpam-5280	114	16	t	t	X
ejpam-5280	114	17	<	<	X
ejpam-5280	114	18	(	(	PUNCT
ejpam-5280	114	19	j	j	PROPN
ejpam-5280	114	20	+	+	PROPN
ejpam-5280	114	21	1)r∫	1)r∫	NUM
ejpam-5280	114	22	(	(	PUNCT
ejpam-5280	114	23	j+1)r	j+1)r	PROPN
ejpam-5280	114	24	jr	jr	PROPN
ejpam-5280	114	25	1ds	1ds	PROPN
ejpam-5280	114	26	,	,	PUNCT
ejpam-5280	114	27	t	t	PROPN
ejpam-5280	114	28	≥	≥	NUM
ejpam-5280	114	29	(	(	PUNCT
ejpam-5280	114	30	j	j	PROPN
ejpam-5280	114	31	+	+	X
ejpam-5280	114	32	1)r	1)r	NUM
ejpam-5280	114	33	=	=	PUNCT
ejpam-5280	115	1			NOUN
ejpam-5280	115	2	0	0	NUM
ejpam-5280	115	3	,	,	PUNCT
ejpam-5280	115	4	t	t	X
ejpam-5280	115	5	<	<	X
ejpam-5280	115	6	jr	jr	PROPN
ejpam-5280	115	7	(	(	PUNCT
ejpam-5280	115	8	t−	t−	PROPN
ejpam-5280	115	9	jr	jr	PROPN
ejpam-5280	115	10	)	)	PUNCT
ejpam-5280	115	11	,	,	PUNCT
ejpam-5280	115	12	jr	jr	PROPN
ejpam-5280	115	13	<	<	X
ejpam-5280	115	14	t	t	X
ejpam-5280	115	15	<	<	X
ejpam-5280	115	16	(	(	PUNCT
ejpam-5280	115	17	j	j	PROPN
ejpam-5280	115	18	+	+	CCONJ
ejpam-5280	115	19	1)r	1)r	NUM
ejpam-5280	115	20	1	1	NUM
ejpam-5280	115	21	,	,	PUNCT
ejpam-5280	115	22	t	t	PROPN
ejpam-5280	115	23	≥	≥	NUM
ejpam-5280	115	24	(	(	PUNCT
ejpam-5280	115	25	j	j	PROPN
ejpam-5280	115	26	+	+	X
ejpam-5280	115	27	1)r	1)r	NUM
ejpam-5280	115	28	.	.	PUNCT
ejpam-5280	116	1	(	(	PUNCT
ejpam-5280	116	2	22	22	NUM
ejpam-5280	116	3	)	)	PUNCT
ejpam-5280	116	4	using	use	VERB
ejpam-5280	116	5	lemma	lemma	PROPN
ejpam-5280	116	6	(	(	PUNCT
ejpam-5280	116	7	2	2	NUM
ejpam-5280	116	8	)	)	PUNCT
ejpam-5280	116	9	,	,	PUNCT
ejpam-5280	116	10	we	we	PRON
ejpam-5280	116	11	have	have	VERB
ejpam-5280	116	12	∫	∫	PROPN
ejpam-5280	116	13	t	t	PROPN
ejpam-5280	116	14	0	0	NUM
ejpam-5280	116	15	γj(s)ds	γj(s)d	NOUN
ejpam-5280	117	1	=	=	PUNCT
ejpam-5280	117	2	m−1∑	m−1∑	PROPN
ejpam-5280	117	3	k=0	k=0	PROPN
ejpam-5280	117	4	θkγk(t	θkγk(t	PROPN
ejpam-5280	117	5	)	)	PUNCT
ejpam-5280	117	6	(	(	PUNCT
ejpam-5280	117	7	23	23	NUM
ejpam-5280	117	8	)	)	PUNCT
ejpam-5280	117	9	where	where	SCONJ
ejpam-5280	117	10	θk	θk	NOUN
ejpam-5280	117	11	=	=	SYM
ejpam-5280	117	12			NOUN
ejpam-5280	117	13	0	0	NUM
ejpam-5280	117	14	,	,	PUNCT
ejpam-5280	117	15	k	k	X
ejpam-5280	117	16	<	<	X
ejpam-5280	117	17	j	j	PROPN
ejpam-5280	117	18	r	r	NOUN
ejpam-5280	117	19	2	2	NUM
ejpam-5280	117	20	,	,	PUNCT
ejpam-5280	117	21	k	k	PROPN
ejpam-5280	117	22	=	=	PUNCT
ejpam-5280	117	23	j	j	PROPN
ejpam-5280	117	24	r	r	PROPN
ejpam-5280	117	25	,	,	PUNCT
ejpam-5280	117	26	j	j	PROPN
ejpam-5280	117	27	<	<	X
ejpam-5280	117	28	k	k	X
ejpam-5280	117	29	<	<	X
ejpam-5280	117	30	m	m	X
ejpam-5280	117	31	.	.	PUNCT
ejpam-5280	118	1	(	(	PUNCT
ejpam-5280	118	2	24	24	NUM
ejpam-5280	118	3	)	)	PUNCT
ejpam-5280	118	4	thus	thus	ADV
ejpam-5280	118	5	,	,	PUNCT
ejpam-5280	118	6	equation	equation	NOUN
ejpam-5280	118	7	(	(	PUNCT
ejpam-5280	118	8	21	21	NUM
ejpam-5280	118	9	)	)	PUNCT
ejpam-5280	118	10	becomes	become	VERB
ejpam-5280	118	11	i1(t	i1(t	PROPN
ejpam-5280	118	12	)	)	PUNCT
ejpam-5280	118	13	=	=	PUNCT
ejpam-5280	118	14	m−1∑	m−1∑	PROPN
ejpam-5280	118	15	i=0	i=0	PROPN
ejpam-5280	118	16	m−1∑	m−1∑	NUM
ejpam-5280	118	17	j=0	j=0	PROPN
ejpam-5280	118	18	n3∑	n3∑	PROPN
ejpam-5280	118	19	l=0	l=0	PROPN
ejpam-5280	118	20	b1,i	b1,i	PROPN
ejpam-5280	118	21	,	,	PUNCT
ejpam-5280	118	22	ja3,lω	ja3,lω	PROPN
ejpam-5280	118	23	l	l	PROPN
ejpam-5280	118	24	jγj(t	jγj(t	PROPN
ejpam-5280	118	25	)	)	PUNCT
ejpam-5280	118	26	(	(	PUNCT
ejpam-5280	118	27	m−1∑	m−1∑	PROPN
ejpam-5280	118	28	k=0	k=0	PROPN
ejpam-5280	118	29	θkγk(t	θkγk(t	PROPN
ejpam-5280	118	30	)	)	PUNCT
ejpam-5280	118	31	)	)	PUNCT
ejpam-5280	119	1	=	=	PUNCT
ejpam-5280	119	2	m−1∑	m−1∑	PROPN
ejpam-5280	119	3	i=0	i=0	PROPN
ejpam-5280	119	4	m−1∑	m−1∑	NUM
ejpam-5280	119	5	j=0	j=0	PROPN
ejpam-5280	119	6	n3∑	n3∑	PROPN
ejpam-5280	119	7	l=0	l=0	PROPN
ejpam-5280	119	8	b1,i	b1,i	PROPN
ejpam-5280	119	9	,	,	PUNCT
ejpam-5280	119	10	ja3,lω	ja3,lω	PROPN
ejpam-5280	119	11	l	l	PROPN
ejpam-5280	119	12	jθjγj(t	jθjγj(t	PROPN
ejpam-5280	119	13	)	)	PUNCT
ejpam-5280	119	14	=	=	SYM
ejpam-5280	119	15	p1(ω	p1(ω	PROPN
ejpam-5280	119	16	)	)	PUNCT
ejpam-5280	119	17	tγ(t	tγ(t	NOUN
ejpam-5280	119	18	)	)	PUNCT
ejpam-5280	119	19	(	(	PUNCT
ejpam-5280	119	20	25	25	NUM
ejpam-5280	119	21	)	)	PUNCT
ejpam-5280	119	22	where	where	SCONJ
ejpam-5280	119	23	(	(	PUNCT
ejpam-5280	119	24	p1(ω))j	p1(ω))j	NOUN
ejpam-5280	119	25	=	=	SYM
ejpam-5280	119	26	m−1∑	m−1∑	NUM
ejpam-5280	119	27	i=0	i=0	PROPN
ejpam-5280	119	28	m−1∑	m−1∑	NUM
ejpam-5280	119	29	j=0	j=0	PROPN
ejpam-5280	119	30	n3∑	n3∑	PROPN
ejpam-5280	119	31	l=0	l=0	PROPN
ejpam-5280	119	32	b1,i	b1,i	PROPN
ejpam-5280	119	33	,	,	PUNCT
ejpam-5280	119	34	ja3,lω	ja3,lω	PROPN
ejpam-5280	119	35	l	l	PROPN
ejpam-5280	119	36	jθj	jθj	NOUN
ejpam-5280	119	37	.	.	PUNCT
ejpam-5280	120	1	(	(	PUNCT
ejpam-5280	120	2	26	26	NUM
ejpam-5280	120	3	)	)	PUNCT
ejpam-5280	120	4	similarly	similarly	ADV
ejpam-5280	120	5	,	,	PUNCT
ejpam-5280	120	6	substitute	substitute	ADJ
ejpam-5280	120	7	equation	equation	NOUN
ejpam-5280	120	8	(	(	PUNCT
ejpam-5280	120	9	19	19	NUM
ejpam-5280	120	10	)	)	PUNCT
ejpam-5280	120	11	and	and	CCONJ
ejpam-5280	120	12	(	(	PUNCT
ejpam-5280	120	13	20	20	NUM
ejpam-5280	120	14	)	)	PUNCT
ejpam-5280	120	15	into	into	ADP
ejpam-5280	120	16	equation	equation	NOUN
ejpam-5280	120	17	(	(	PUNCT
ejpam-5280	120	18	15	15	NUM
ejpam-5280	120	19	)	)	PUNCT
ejpam-5280	120	20	and	and	CCONJ
ejpam-5280	120	21	using	use	VERB
ejpam-5280	120	22	equation	equation	NOUN
ejpam-5280	120	23	(	(	PUNCT
ejpam-5280	120	24	8)	8)	NUM
ejpam-5280	120	25	to	to	PART
ejpam-5280	120	26	get	get	VERB
ejpam-5280	120	27	i2(t	i2(t	PRON
ejpam-5280	120	28	)	)	PUNCT
ejpam-5280	120	29	=	=	SYM
ejpam-5280	121	1	∫	∫	PROPN
ejpam-5280	121	2	1	1	NUM
ejpam-5280	121	3	0	0	X
ejpam-5280	121	4	π2(t	π2(t	PROPN
ejpam-5280	121	5	,	,	PUNCT
ejpam-5280	121	6	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	121	7	m.i	m.i	PROPN
ejpam-5280	121	8	.	.	PROPN
ejpam-5280	121	9	syam	syam	PROPN
ejpam-5280	121	10	,	,	PUNCT
ejpam-5280	121	11	m.	m.	NOUN
ejpam-5280	121	12	sharadga	sharadga	PROPN
ejpam-5280	121	13	,	,	PUNCT
ejpam-5280	121	14	i.	i.	PROPN
ejpam-5280	121	15	hashim	hashim	PROPN
ejpam-5280	121	16	/	/	SYM
ejpam-5280	121	17	eur	eur	PROPN
ejpam-5280	121	18	.	.	PUNCT
ejpam-5280	122	1	j.	j.	PROPN
ejpam-5280	122	2	pure	pure	PROPN
ejpam-5280	122	3	appl	appl	PROPN
ejpam-5280	122	4	.	.	PROPN
ejpam-5280	122	5	math	math	PROPN
ejpam-5280	122	6	,	,	PUNCT
ejpam-5280	122	7	17	17	NUM
ejpam-5280	122	8	(	(	PUNCT
ejpam-5280	122	9	3	3	NUM
ejpam-5280	122	10	)	)	PUNCT
ejpam-5280	122	11	(	(	PUNCT
ejpam-5280	122	12	2024	2024	NUM
ejpam-5280	122	13	)	)	PUNCT
ejpam-5280	122	14	,	,	PUNCT
ejpam-5280	122	15	1429	1429	NUM
ejpam-5280	122	16	-	-	SYM
ejpam-5280	122	17	1448	1448	NUM
ejpam-5280	122	18	1435	1435	NUM
ejpam-5280	122	19	=	=	SYM
ejpam-5280	122	20	∫	∫	PROPN
ejpam-5280	122	21	1	1	NUM
ejpam-5280	122	22	0	0	NUM
ejpam-5280	122	23	m−1∑	m−1∑	PROPN
ejpam-5280	122	24	i=0	i=0	PROPN
ejpam-5280	122	25	m−1∑	m−1∑	PROPN
ejpam-5280	122	26	j=0	j=0	PROPN
ejpam-5280	122	27	b2,i	b2,i	PROPN
ejpam-5280	122	28	,	,	PUNCT
ejpam-5280	122	29	jγi(t)γj(s)ds	jγi(t)γj(s)d	NOUN
ejpam-5280	122	30			PUNCT
ejpam-5280	123	1	n4∑	n4∑	PROPN
ejpam-5280	123	2	i=0	i=0	PROPN
ejpam-5280	123	3	m−1∑	m−1∑	NUM
ejpam-5280	123	4	j=0	j=0	PROPN
ejpam-5280	123	5	a4,iω	a4,iω	PROPN
ejpam-5280	123	6	i	i	PROPN
ejpam-5280	123	7	jγj(s	jγj(s	PROPN
ejpam-5280	123	8	)	)	PUNCT
ejpam-5280	123	9			PROPN
ejpam-5280	124	1	=	=	SYM
ejpam-5280	124	2	m−1∑	m−1∑	PROPN
ejpam-5280	124	3	i=0	i=0	PROPN
ejpam-5280	124	4	m−1∑	m−1∑	NUM
ejpam-5280	124	5	j=0	j=0	PROPN
ejpam-5280	124	6	n4∑	n4∑	PROPN
ejpam-5280	124	7	l=0	l=0	PROPN
ejpam-5280	124	8	m−1∑	m−1∑	NUM
ejpam-5280	124	9	k=0	k=0	PROPN
ejpam-5280	124	10	b2,i	b2,i	PROPN
ejpam-5280	124	11	,	,	PUNCT
ejpam-5280	124	12	ja4,lω	ja4,lω	PROPN
ejpam-5280	124	13	l	l	NOUN
ejpam-5280	124	14	kγj(t	kγj(t	PROPN
ejpam-5280	124	15	)	)	PUNCT
ejpam-5280	124	16	∫	∫	PROPN
ejpam-5280	124	17	1	1	NUM
ejpam-5280	124	18	0	0	NUM
ejpam-5280	124	19	γj(s)γk(s)ds	γj(s)γk(s)ds	PROPN
ejpam-5280	124	20	=	=	SYM
ejpam-5280	124	21	m−1∑	m−1∑	PROPN
ejpam-5280	124	22	i=0	i=0	PROPN
ejpam-5280	124	23	m−1∑	m−1∑	NUM
ejpam-5280	124	24	j=0	j=0	PROPN
ejpam-5280	124	25	n4∑	n4∑	PROPN
ejpam-5280	124	26	l=0	l=0	PROPN
ejpam-5280	124	27	b2,i	b2,i	PROPN
ejpam-5280	124	28	,	,	PUNCT
ejpam-5280	124	29	ja4,lω	ja4,lω	PROPN
ejpam-5280	124	30	l	l	NOUN
ejpam-5280	124	31	jγj(t	jγj(t	PROPN
ejpam-5280	124	32	)	)	PUNCT
ejpam-5280	124	33	∫	∫	PROPN
ejpam-5280	124	34	1	1	NUM
ejpam-5280	124	35	0	0	NUM
ejpam-5280	124	36	γj(s)ds	γj(s)ds	PROPN
ejpam-5280	124	37	.	.	PUNCT
ejpam-5280	125	1	(	(	PUNCT
ejpam-5280	125	2	27	27	NUM
ejpam-5280	125	3	)	)	PUNCT
ejpam-5280	125	4	using	use	VERB
ejpam-5280	125	5	the	the	DET
ejpam-5280	125	6	definition	definition	NOUN
ejpam-5280	125	7	of	of	ADP
ejpam-5280	125	8	the	the	DET
ejpam-5280	125	9	bpfs	bpf	NOUN
ejpam-5280	125	10	,	,	PUNCT
ejpam-5280	125	11	we	we	PRON
ejpam-5280	125	12	can	can	AUX
ejpam-5280	125	13	see	see	VERB
ejpam-5280	125	14	that∫	that∫	NOUN
ejpam-5280	125	15	1	1	NUM
ejpam-5280	125	16	0	0	NUM
ejpam-5280	125	17	γj(s)ds	γj(s)ds	PROPN
ejpam-5280	125	18	=	=	SYM
ejpam-5280	125	19	r.	r.	PROPN
ejpam-5280	125	20	(	(	PUNCT
ejpam-5280	125	21	28	28	NUM
ejpam-5280	125	22	)	)	PUNCT
ejpam-5280	125	23	using	use	VERB
ejpam-5280	125	24	lemma	lemma	PROPN
ejpam-5280	125	25	(	(	PUNCT
ejpam-5280	125	26	2	2	NUM
ejpam-5280	125	27	)	)	PUNCT
ejpam-5280	125	28	,	,	PUNCT
ejpam-5280	125	29	we	we	PRON
ejpam-5280	125	30	have	have	VERB
ejpam-5280	125	31	∫	∫	PROPN
ejpam-5280	125	32	1	1	NUM
ejpam-5280	125	33	0	0	NUM
ejpam-5280	125	34	γj(s)ds	γj(s)d	NOUN
ejpam-5280	125	35	=	=	PUNCT
ejpam-5280	125	36	m−1∑	m−1∑	PROPN
ejpam-5280	125	37	k=0	k=0	PROPN
ejpam-5280	125	38	rγk(t	rγk(t	PROPN
ejpam-5280	125	39	)	)	PUNCT
ejpam-5280	125	40	.	.	PUNCT
ejpam-5280	126	1	(	(	PUNCT
ejpam-5280	126	2	29	29	NUM
ejpam-5280	126	3	)	)	PUNCT
ejpam-5280	126	4	thus	thus	ADV
ejpam-5280	126	5	,	,	PUNCT
ejpam-5280	126	6	equation	equation	NOUN
ejpam-5280	126	7	(	(	PUNCT
ejpam-5280	126	8	27	27	NUM
ejpam-5280	126	9	)	)	PUNCT
ejpam-5280	126	10	becomes	become	VERB
ejpam-5280	126	11	i2(t	i2(t	PROPN
ejpam-5280	126	12	)	)	PUNCT
ejpam-5280	127	1	=	=	PUNCT
ejpam-5280	127	2	m−1∑	m−1∑	PROPN
ejpam-5280	127	3	i=0	i=0	PROPN
ejpam-5280	127	4	m−1∑	m−1∑	NUM
ejpam-5280	127	5	j=0	j=0	PROPN
ejpam-5280	127	6	n3∑	n3∑	PROPN
ejpam-5280	127	7	l=0	l=0	PROPN
ejpam-5280	127	8	b1,i	b1,i	PROPN
ejpam-5280	127	9	,	,	PUNCT
ejpam-5280	127	10	ja3,lω	ja3,lω	PROPN
ejpam-5280	127	11	l	l	PROPN
ejpam-5280	127	12	jγj(t	jγj(t	PROPN
ejpam-5280	127	13	)	)	PUNCT
ejpam-5280	127	14	(	(	PUNCT
ejpam-5280	127	15	m−1∑	m−1∑	PROPN
ejpam-5280	127	16	k=0	k=0	PROPN
ejpam-5280	127	17	rγk(t	rγk(t	PROPN
ejpam-5280	127	18	)	)	PUNCT
ejpam-5280	127	19	)	)	PUNCT
ejpam-5280	128	1	=	=	PUNCT
ejpam-5280	128	2	m−1∑	m−1∑	PROPN
ejpam-5280	128	3	i=0	i=0	PROPN
ejpam-5280	128	4	m−1∑	m−1∑	NUM
ejpam-5280	128	5	j=0	j=0	PROPN
ejpam-5280	128	6	n3∑	n3∑	PROPN
ejpam-5280	128	7	l=0	l=0	PROPN
ejpam-5280	128	8	b1,i	b1,i	PROPN
ejpam-5280	128	9	,	,	PUNCT
ejpam-5280	128	10	ja3,lω	ja3,lω	PROPN
ejpam-5280	128	11	l	l	NOUN
ejpam-5280	128	12	jrγj(t	jrγj(t	NOUN
ejpam-5280	128	13	)	)	PUNCT
ejpam-5280	128	14	=	=	PUNCT
ejpam-5280	128	15	p2(ω	p2(ω	NOUN
ejpam-5280	128	16	)	)	PUNCT
ejpam-5280	128	17	tγ(t	tγ(t	NOUN
ejpam-5280	128	18	)	)	PUNCT
ejpam-5280	128	19	(	(	PUNCT
ejpam-5280	128	20	30	30	NUM
ejpam-5280	128	21	)	)	PUNCT
ejpam-5280	128	22	where	where	SCONJ
ejpam-5280	128	23	(	(	PUNCT
ejpam-5280	128	24	p2(ω))j	p2(ω))j	NOUN
ejpam-5280	128	25	=	=	SYM
ejpam-5280	128	26	m−1∑	m−1∑	PROPN
ejpam-5280	128	27	i=0	i=0	PROPN
ejpam-5280	128	28	m−1∑	m−1∑	NUM
ejpam-5280	128	29	j=0	j=0	PROPN
ejpam-5280	128	30	n3∑	n3∑	PROPN
ejpam-5280	128	31	l=0	l=0	PROPN
ejpam-5280	128	32	b1,i	b1,i	PROPN
ejpam-5280	128	33	,	,	PUNCT
ejpam-5280	128	34	ja3,lω	ja3,lω	PROPN
ejpam-5280	128	35	l	l	PROPN
ejpam-5280	128	36	jr	jr	PROPN
ejpam-5280	128	37	.	.	PROPN
ejpam-5280	129	1	(	(	PUNCT
ejpam-5280	129	2	31	31	NUM
ejpam-5280	129	3	)	)	PUNCT
ejpam-5280	129	4	let	let	VERB
ejpam-5280	129	5	g1(t	g1(t	NOUN
ejpam-5280	129	6	,	,	PUNCT
ejpam-5280	129	7	ω(t	ω(t	NOUN
ejpam-5280	129	8	)	)	PUNCT
ejpam-5280	129	9	)	)	PUNCT
ejpam-5280	130	1	=	=	SYM
ejpam-5280	131	1	n1∑	n1∑	PROPN
ejpam-5280	131	2	i=0	i=0	PROPN
ejpam-5280	131	3	b1,i(t)ω	b1,i(t)ω	PROPN
ejpam-5280	131	4	i(t	i(t	PROPN
ejpam-5280	131	5	)	)	PUNCT
ejpam-5280	131	6	=	=	SYM
ejpam-5280	132	1	n1∑	n1∑	PROPN
ejpam-5280	132	2	i=0	i=0	PROPN
ejpam-5280	132	3	m−1∑	m−1∑	PROPN
ejpam-5280	132	4	j=0	j=0	PROPN
ejpam-5280	132	5	a1,i	a1,i	PROPN
ejpam-5280	132	6	,	,	PUNCT
ejpam-5280	132	7	jγj(t	jγj(t	PROPN
ejpam-5280	132	8	)	)	PUNCT
ejpam-5280	132	9	m−1∑	m−1∑	NOUN
ejpam-5280	132	10	j=0	j=0	PROPN
ejpam-5280	132	11	ωjγj(t	ωjγj(t	PROPN
ejpam-5280	132	12	)	)	PUNCT
ejpam-5280	132	13	i	i	PROPN
ejpam-5280	132	14	=	=	PUNCT
ejpam-5280	133	1	n1∑	n1∑	PROPN
ejpam-5280	133	2	i=0	i=0	PROPN
ejpam-5280	133	3	m−1∑	m−1∑	PROPN
ejpam-5280	133	4	j=0	j=0	PROPN
ejpam-5280	133	5	a1,i	a1,i	PROPN
ejpam-5280	133	6	,	,	PUNCT
ejpam-5280	133	7	jγj(t	jγj(t	PROPN
ejpam-5280	133	8	)	)	PUNCT
ejpam-5280	133	9	m−1∑	m−1∑	NOUN
ejpam-5280	134	1	j=0	j=0	PROPN
ejpam-5280	134	2	ωi	ωi	PROPN
ejpam-5280	134	3	jγj(t	jγj(t	PROPN
ejpam-5280	134	4	)	)	PUNCT
ejpam-5280	134	5			PROPN
ejpam-5280	134	6	=	=	SYM
ejpam-5280	134	7	n1∑	n1∑	PROPN
ejpam-5280	134	8	i=0	i=0	PROPN
ejpam-5280	134	9	m−1∑	m−1∑	NUM
ejpam-5280	134	10	j=0	j=0	PROPN
ejpam-5280	134	11	a1,i	a1,i	PROPN
ejpam-5280	134	12	,	,	PUNCT
ejpam-5280	134	13	jω	jω	INTJ
ejpam-5280	134	14	i	i	PRON
ejpam-5280	134	15	jγj(t	jγj(t	PROPN
ejpam-5280	134	16	)	)	PUNCT
ejpam-5280	134	17	m.i	m.i	PROPN
ejpam-5280	134	18	.	.	PROPN
ejpam-5280	134	19	syam	syam	PROPN
ejpam-5280	134	20	,	,	PUNCT
ejpam-5280	134	21	m.	m.	NOUN
ejpam-5280	134	22	sharadga	sharadga	PROPN
ejpam-5280	134	23	,	,	PUNCT
ejpam-5280	134	24	i.	i.	PROPN
ejpam-5280	134	25	hashim	hashim	PROPN
ejpam-5280	134	26	/	/	SYM
ejpam-5280	134	27	eur	eur	PROPN
ejpam-5280	134	28	.	.	PUNCT
ejpam-5280	135	1	j.	j.	PROPN
ejpam-5280	135	2	pure	pure	PROPN
ejpam-5280	135	3	appl	appl	PROPN
ejpam-5280	135	4	.	.	PROPN
ejpam-5280	135	5	math	math	PROPN
ejpam-5280	135	6	,	,	PUNCT
ejpam-5280	135	7	17	17	NUM
ejpam-5280	135	8	(	(	PUNCT
ejpam-5280	135	9	3	3	NUM
ejpam-5280	135	10	)	)	PUNCT
ejpam-5280	135	11	(	(	PUNCT
ejpam-5280	135	12	2024	2024	NUM
ejpam-5280	135	13	)	)	PUNCT
ejpam-5280	135	14	,	,	PUNCT
ejpam-5280	135	15	1429	1429	NUM
ejpam-5280	135	16	-	-	SYM
ejpam-5280	135	17	1448	1448	NUM
ejpam-5280	135	18	1436	1436	NUM
ejpam-5280	135	19	=	=	SYM
ejpam-5280	135	20	p3(ω	p3(ω	NOUN
ejpam-5280	135	21	)	)	PUNCT
ejpam-5280	135	22	tγ(t	tγ(t	NOUN
ejpam-5280	135	23	)	)	PUNCT
ejpam-5280	135	24	(	(	PUNCT
ejpam-5280	135	25	32	32	NUM
ejpam-5280	135	26	)	)	PUNCT
ejpam-5280	135	27	where	where	SCONJ
ejpam-5280	135	28	(	(	PUNCT
ejpam-5280	135	29	p3(ω))j	p3(ω))j	PROPN
ejpam-5280	135	30	=	=	SYM
ejpam-5280	135	31	n1∑	n1∑	PROPN
ejpam-5280	135	32	i=0	i=0	PROPN
ejpam-5280	135	33	a1,i	a1,i	PROPN
ejpam-5280	135	34	,	,	PUNCT
ejpam-5280	135	35	jω	jω	INTJ
ejpam-5280	136	1	i	i	PRON
ejpam-5280	136	2	j	j	PROPN
ejpam-5280	136	3	.	.	PUNCT
ejpam-5280	137	1	(	(	PUNCT
ejpam-5280	137	2	33	33	NUM
ejpam-5280	137	3	)	)	PUNCT
ejpam-5280	137	4	finally	finally	ADV
ejpam-5280	137	5	,	,	PUNCT
ejpam-5280	137	6	we	we	PRON
ejpam-5280	137	7	write	write	VERB
ejpam-5280	137	8	g2(t	g2(t	NOUN
ejpam-5280	137	9	)	)	PUNCT
ejpam-5280	137	10	as	as	ADP
ejpam-5280	137	11	g2(t	g2(t	NOUN
ejpam-5280	137	12	)	)	PUNCT
ejpam-5280	137	13	=	=	PUNCT
ejpam-5280	138	1	m−1∑	m−1∑	PROPN
ejpam-5280	138	2	i=0	i=0	PROPN
ejpam-5280	138	3	a2,iγi(t	a2,iγi(t	PROPN
ejpam-5280	138	4	)	)	PUNCT
ejpam-5280	138	5	,	,	PUNCT
ejpam-5280	138	6	=	=	PUNCT
ejpam-5280	139	1	p	p	X
ejpam-5280	139	2	t	t	PROPN
ejpam-5280	139	3	4	4	NUM
ejpam-5280	139	4	γ(t	γ(t	NOUN
ejpam-5280	139	5	)	)	PUNCT
ejpam-5280	139	6	(	(	PUNCT
ejpam-5280	139	7	34	34	NUM
ejpam-5280	139	8	)	)	PUNCT
ejpam-5280	139	9	where	where	SCONJ
ejpam-5280	139	10	(	(	PUNCT
ejpam-5280	139	11	p4)i	p4)i	NOUN
ejpam-5280	139	12	=	=	SYM
ejpam-5280	139	13	a2,i	a2,i	PROPN
ejpam-5280	139	14	.	.	PUNCT
ejpam-5280	140	1	(	(	PUNCT
ejpam-5280	140	2	35	35	NUM
ejpam-5280	140	3	)	)	PUNCT
ejpam-5280	140	4	now	now	ADV
ejpam-5280	140	5	,	,	PUNCT
ejpam-5280	140	6	we	we	PRON
ejpam-5280	140	7	will	will	AUX
ejpam-5280	140	8	derive	derive	VERB
ejpam-5280	140	9	the	the	DET
ejpam-5280	140	10	the	the	DET
ejpam-5280	140	11	riemann	riemann	PROPN
ejpam-5280	140	12	-	-	PUNCT
ejpam-5280	140	13	liouville	liouville	VERB
ejpam-5280	140	14	fractional	fractional	ADJ
ejpam-5280	140	15	integral	integral	ADJ
ejpam-5280	140	16	operator	operator	NOUN
ejpam-5280	140	17	which	which	PRON
ejpam-5280	140	18	plays	play	VERB
ejpam-5280	140	19	an	an	DET
ejpam-5280	140	20	important	important	ADJ
ejpam-5280	140	21	role	role	NOUN
ejpam-5280	140	22	in	in	ADP
ejpam-5280	140	23	our	our	PRON
ejpam-5280	140	24	derivation	derivation	NOUN
ejpam-5280	140	25	.	.	PUNCT
ejpam-5280	141	1	theorem	theorem	NOUN
ejpam-5280	141	2	2	2	NUM
ejpam-5280	141	3	.	.	PUNCT
ejpam-5280	142	1	the	the	DET
ejpam-5280	142	2	operational	operational	ADJ
ejpam-5280	142	3	matrix	matrix	NOUN
ejpam-5280	142	4	of	of	ADP
ejpam-5280	142	5	iµ	iµ	PROPN
ejpam-5280	142	6	is	be	AUX
ejpam-5280	142	7	given	give	VERB
ejpam-5280	142	8	by	by	ADP
ejpam-5280	142	9	oµ	oµ	NOUN
ejpam-5280	142	10	=	=	NOUN
ejpam-5280	142	11	rµ	rµ	INTJ
ejpam-5280	142	12	γ(µ+	γ(µ+	NOUN
ejpam-5280	142	13	2	2	X
ejpam-5280	142	14	)	)	PUNCT
ejpam-5280	142	15			ADJ
ejpam-5280	142	16	1	1	NUM
ejpam-5280	142	17	σ1	σ1	PROPN
ejpam-5280	142	18	σ2	σ2	PROPN
ejpam-5280	142	19	.	.	PUNCT
ejpam-5280	142	20	.	.	PUNCT
ejpam-5280	142	21	.	.	PUNCT
ejpam-5280	143	1	σm−2	σm−2	ADV
ejpam-5280	143	2	σm−1	σm−1	PROPN
ejpam-5280	143	3	0	0	NUM
ejpam-5280	143	4	1	1	NUM
ejpam-5280	143	5	σ1	σ1	NOUN
ejpam-5280	143	6	.	.	PUNCT
ejpam-5280	143	7	.	.	PUNCT
ejpam-5280	143	8	.	.	PUNCT
ejpam-5280	144	1	σm−3	σm−3	VERB
ejpam-5280	144	2	σm−2	σm−2	PROPN
ejpam-5280	144	3	0	0	NUM
ejpam-5280	144	4	0	0	NUM
ejpam-5280	144	5	1	1	NUM
ejpam-5280	144	6	.	.	PUNCT
ejpam-5280	144	7	.	.	PUNCT
ejpam-5280	144	8	.	.	PUNCT
ejpam-5280	145	1	σm−4	σm−4	ADJ
ejpam-5280	145	2	σm−3	σm−3	PROPN
ejpam-5280	145	3	...	...	PUNCT
ejpam-5280	145	4	...	...	PUNCT
ejpam-5280	145	5	...	...	PUNCT
ejpam-5280	145	6	.	.	PUNCT
ejpam-5280	145	7	.	.	PUNCT
ejpam-5280	145	8	.	.	PUNCT
ejpam-5280	145	9	.	.	PUNCT
ejpam-5280	145	10	.	.	PUNCT
ejpam-5280	145	11	.	.	PUNCT
ejpam-5280	146	1	...	...	PUNCT
ejpam-5280	147	1	0	0	NUM
ejpam-5280	147	2	0	0	NUM
ejpam-5280	147	3	0	0	NUM
ejpam-5280	147	4	.	.	PUNCT
ejpam-5280	147	5	.	.	PUNCT
ejpam-5280	147	6	.	.	PUNCT
ejpam-5280	148	1	1	1	NUM
ejpam-5280	148	2	σ1	σ1	NOUN
ejpam-5280	148	3	0	0	NUM
ejpam-5280	148	4	0	0	NUM
ejpam-5280	148	5	0	0	NUM
ejpam-5280	148	6	.	.	PUNCT
ejpam-5280	148	7	.	.	PUNCT
ejpam-5280	148	8	.	.	PUNCT
ejpam-5280	149	1	0	0	NUM
ejpam-5280	149	2	1	1	NUM
ejpam-5280	149	3			NOUN
ejpam-5280	149	4	(	(	PUNCT
ejpam-5280	149	5	36	36	NUM
ejpam-5280	149	6	)	)	PUNCT
ejpam-5280	149	7	where	where	SCONJ
ejpam-5280	149	8	σς	σς	ADP
ejpam-5280	149	9	=	=	SYM
ejpam-5280	149	10	(	(	PUNCT
ejpam-5280	149	11	ς	ς	PROPN
ejpam-5280	149	12	+	+	NOUN
ejpam-5280	149	13	1)µ+1	1)µ+1	NUM
ejpam-5280	149	14	−	−	NOUN
ejpam-5280	149	15	2ςµ+1	2ςµ+1	NUM
ejpam-5280	149	16	+	+	CCONJ
ejpam-5280	149	17	(	(	PUNCT
ejpam-5280	149	18	ς	ς	PROPN
ejpam-5280	149	19	−	−	PROPN
ejpam-5280	149	20	1)µ+1	1)µ+1	NUM
ejpam-5280	149	21	,	,	PUNCT
ejpam-5280	149	22	ς	ς	PROPN
ejpam-5280	149	23	=	=	SYM
ejpam-5280	149	24	1	1	NUM
ejpam-5280	149	25	,	,	PUNCT
ejpam-5280	149	26	2	2	NUM
ejpam-5280	149	27	,	,	PUNCT
ejpam-5280	149	28	.	.	PUNCT
ejpam-5280	149	29	.	.	PUNCT
ejpam-5280	149	30	.	.	PUNCT
ejpam-5280	150	1	,	,	PUNCT
ejpam-5280	150	2	m	m	VERB
ejpam-5280	150	3	−	−	NOUN
ejpam-5280	150	4	1	1	NUM
ejpam-5280	150	5	.	.	PUNCT
ejpam-5280	151	1	proof	proof	NOUN
ejpam-5280	151	2	.	.	PUNCT
ejpam-5280	152	1	let	let	VERB
ejpam-5280	152	2	l	l	NOUN
ejpam-5280	152	3	∈	∈	PROPN
ejpam-5280	152	4	{	{	PUNCT
ejpam-5280	152	5	0	0	NUM
ejpam-5280	152	6	,	,	PUNCT
ejpam-5280	152	7	1	1	NUM
ejpam-5280	152	8	,	,	PUNCT
ejpam-5280	152	9	.	.	PUNCT
ejpam-5280	152	10	.	.	PUNCT
ejpam-5280	152	11	.	.	PUNCT
ejpam-5280	153	1	,	,	PUNCT
ejpam-5280	153	2	m	m	VERB
ejpam-5280	153	3	−	−	NOUN
ejpam-5280	153	4	1	1	NUM
ejpam-5280	153	5	}	}	PUNCT
ejpam-5280	153	6	.	.	PUNCT
ejpam-5280	154	1	then	then	ADV
ejpam-5280	154	2	,	,	PUNCT
ejpam-5280	154	3	iµγl(t	iµγl(t	INTJ
ejpam-5280	154	4	)	)	PUNCT
ejpam-5280	154	5	=	=	SYM
ejpam-5280	154	6	1	1	NUM
ejpam-5280	154	7	γ(µ	γ(µ	PROPN
ejpam-5280	154	8	)	)	PUNCT
ejpam-5280	154	9	∫	∫	PROPN
ejpam-5280	155	1	t	t	PROPN
ejpam-5280	155	2	0	0	NUM
ejpam-5280	156	1	(	(	PUNCT
ejpam-5280	156	2	t−	t−	PROPN
ejpam-5280	156	3	s)µ−1γl(s)ds	s)µ−1γl(s)ds	NOUN
ejpam-5280	156	4	=	=	SYM
ejpam-5280	156	5			X
ejpam-5280	156	6	0	0	NUM
ejpam-5280	156	7	,	,	PUNCT
ejpam-5280	156	8	t	t	X
ejpam-5280	156	9	<	<	X
ejpam-5280	156	10	lr	lr	X
ejpam-5280	156	11	(	(	PUNCT
ejpam-5280	156	12	t−lr)µ	t−lr)µ	PROPN
ejpam-5280	156	13	γ(µ+1	γ(µ+1	NUM
ejpam-5280	156	14	)	)	PUNCT
ejpam-5280	156	15	,	,	PUNCT
ejpam-5280	156	16	lr	lr	VERB
ejpam-5280	156	17	≤	≤	PROPN
ejpam-5280	156	18	t	t	NOUN
ejpam-5280	156	19	<	<	X
ejpam-5280	156	20	(	(	PUNCT
ejpam-5280	156	21	l	l	NOUN
ejpam-5280	156	22	+	+	X
ejpam-5280	156	23	1)r	1)r	NUM
ejpam-5280	156	24	(	(	PUNCT
ejpam-5280	156	25	t−lr)µ−(t−lr−r)µ	t−lr)µ−(t−lr−r)µ	PROPN
ejpam-5280	156	26	γ(µ+1	γ(µ+1	PRON
ejpam-5280	156	27	)	)	PUNCT
ejpam-5280	156	28	,	,	PUNCT
ejpam-5280	156	29	(	(	PUNCT
ejpam-5280	156	30	l	l	NOUN
ejpam-5280	156	31	+	+	SYM
ejpam-5280	156	32	1)r	1)r	ADJ
ejpam-5280	156	33	≤	≤	PUNCT
ejpam-5280	156	34	t	t	X
ejpam-5280	156	35	<	<	X
ejpam-5280	156	36	1	1	NUM
ejpam-5280	156	37	.	.	PUNCT
ejpam-5280	157	1	(	(	PUNCT
ejpam-5280	157	2	37	37	NUM
ejpam-5280	157	3	)	)	PUNCT
ejpam-5280	157	4	let	let	VERB
ejpam-5280	157	5	iµγl(t	iµγl(t	PRON
ejpam-5280	157	6	)	)	PUNCT
ejpam-5280	158	1	=	=	PUNCT
ejpam-5280	158	2	m−1∑	m−1∑	PROPN
ejpam-5280	158	3	i=0	i=0	PROPN
ejpam-5280	158	4	ci	ci	PROPN
ejpam-5280	158	5	,	,	PUNCT
ejpam-5280	158	6	lγi(t	lγi(t	PROPN
ejpam-5280	158	7	)	)	PUNCT
ejpam-5280	158	8	.	.	PUNCT
ejpam-5280	159	1	(	(	PUNCT
ejpam-5280	159	2	38	38	NUM
ejpam-5280	159	3	)	)	PUNCT
ejpam-5280	159	4	then	then	ADV
ejpam-5280	159	5	,	,	PUNCT
ejpam-5280	159	6	ci	ci	NOUN
ejpam-5280	159	7	,	,	PUNCT
ejpam-5280	159	8	l	l	NOUN
ejpam-5280	159	9	=	=	SYM
ejpam-5280	159	10	1	1	NUM
ejpam-5280	159	11	r	r	NOUN
ejpam-5280	159	12	∫	∫	PROPN
ejpam-5280	159	13	1	1	NUM
ejpam-5280	159	14	0	0	NUM
ejpam-5280	159	15	(	(	PUNCT
ejpam-5280	159	16	iµγl(t	iµγl(t	NOUN
ejpam-5280	159	17	)	)	PUNCT
ejpam-5280	159	18	)	)	PUNCT
ejpam-5280	159	19	γi(t)dt	γi(t)dt	PROPN
ejpam-5280	159	20	m.i	m.i	PROPN
ejpam-5280	159	21	.	.	PROPN
ejpam-5280	159	22	syam	syam	PROPN
ejpam-5280	159	23	,	,	PUNCT
ejpam-5280	159	24	m.	m.	NOUN
ejpam-5280	159	25	sharadga	sharadga	PROPN
ejpam-5280	159	26	,	,	PUNCT
ejpam-5280	159	27	i.	i.	PROPN
ejpam-5280	159	28	hashim	hashim	PROPN
ejpam-5280	159	29	/	/	SYM
ejpam-5280	159	30	eur	eur	PROPN
ejpam-5280	159	31	.	.	PUNCT
ejpam-5280	160	1	j.	j.	PROPN
ejpam-5280	160	2	pure	pure	PROPN
ejpam-5280	160	3	appl	appl	PROPN
ejpam-5280	160	4	.	.	PROPN
ejpam-5280	160	5	math	math	PROPN
ejpam-5280	160	6	,	,	PUNCT
ejpam-5280	160	7	17	17	NUM
ejpam-5280	160	8	(	(	PUNCT
ejpam-5280	160	9	3	3	NUM
ejpam-5280	160	10	)	)	PUNCT
ejpam-5280	160	11	(	(	PUNCT
ejpam-5280	160	12	2024	2024	NUM
ejpam-5280	160	13	)	)	PUNCT
ejpam-5280	160	14	,	,	PUNCT
ejpam-5280	160	15	1429	1429	NUM
ejpam-5280	160	16	-	-	SYM
ejpam-5280	160	17	1448	1448	NUM
ejpam-5280	160	18	1437	1437	NUM
ejpam-5280	160	19	=	=	SYM
ejpam-5280	160	20	1	1	NUM
ejpam-5280	160	21	r	r	NOUN
ejpam-5280	160	22	∫	∫	NOUN
ejpam-5280	160	23	(	(	PUNCT
ejpam-5280	160	24	i+1)r	i+1)r	PROPN
ejpam-5280	160	25	ir	ir	PROPN
ejpam-5280	160	26	(	(	PUNCT
ejpam-5280	160	27	iµγl(t	iµγl(t	NOUN
ejpam-5280	160	28	)	)	PUNCT
ejpam-5280	160	29	)	)	PUNCT
ejpam-5280	160	30	dt	dt	PUNCT
ejpam-5280	161	1	=	=	SYM
ejpam-5280	161	2			PROPN
ejpam-5280	161	3	rµ	rµ	VERB
ejpam-5280	161	4	γ(µ+2	γ(µ+2	PROPN
ejpam-5280	161	5	)	)	PUNCT
ejpam-5280	161	6	,	,	PUNCT
ejpam-5280	161	7	0	0	NUM
ejpam-5280	161	8	≤	≤	X
ejpam-5280	162	1	i	i	PRON
ejpam-5280	162	2	=	=	PUNCT
ejpam-5280	162	3	l	l	NOUN
ejpam-5280	163	1	≤	≤	NUM
ejpam-5280	163	2	m	m	VERB
ejpam-5280	163	3	−	−	NUM
ejpam-5280	163	4	1	1	NUM
ejpam-5280	163	5	rµ((l−i+1)µ+1−2(l−i)µ+1+(l−i−1)µ+1	rµ((l−i+1)µ+1−2(l−i)µ+1+(l−i−1)µ+1	NOUN
ejpam-5280	163	6	)	)	PUNCT
ejpam-5280	163	7	γ(µ+2	γ(µ+2	PROPN
ejpam-5280	163	8	)	)	PUNCT
ejpam-5280	163	9	,	,	PUNCT
ejpam-5280	163	10	0	0	NUM
ejpam-5280	163	11	≤	≤	PUNCT
ejpam-5280	164	1	i	i	PRON
ejpam-5280	164	2	<	<	X
ejpam-5280	164	3	l	l	X
ejpam-5280	164	4	≤	≤	NUM
ejpam-5280	164	5	m	m	VERB
ejpam-5280	164	6	−	−	NUM
ejpam-5280	164	7	1	1	NUM
ejpam-5280	164	8	0	0	NUM
ejpam-5280	164	9	,	,	PUNCT
ejpam-5280	164	10	0	0	NUM
ejpam-5280	164	11	≤	≤	NUM
ejpam-5280	165	1	l	l	NOUN
ejpam-5280	165	2	<	<	X
ejpam-5280	166	1	i	i	X
ejpam-5280	166	2	≤	≤	PUNCT
ejpam-5280	166	3	m	m	VERB
ejpam-5280	166	4	−	−	PROPN
ejpam-5280	166	5	1	1	NUM
ejpam-5280	166	6	.	.	PUNCT
ejpam-5280	167	1	(	(	PUNCT
ejpam-5280	167	2	39	39	NUM
ejpam-5280	167	3	)	)	PUNCT
ejpam-5280	167	4	let	let	VERB
ejpam-5280	168	1	ς	ς	PROPN
ejpam-5280	168	2	=	=	SYM
ejpam-5280	168	3	j	j	PROPN
ejpam-5280	168	4	−	−	PROPN
ejpam-5280	169	1	i	i	PRON
ejpam-5280	169	2	and	and	CCONJ
ejpam-5280	169	3	σς	σς	NOUN
ejpam-5280	169	4	=	=	SYM
ejpam-5280	169	5	(	(	PUNCT
ejpam-5280	169	6	ς	ς	PROPN
ejpam-5280	169	7	+	+	NOUN
ejpam-5280	169	8	1)µ+1	1)µ+1	NUM
ejpam-5280	169	9	−	−	NOUN
ejpam-5280	169	10	2ςµ+1	2ςµ+1	NUM
ejpam-5280	169	11	+	+	CCONJ
ejpam-5280	169	12	(	(	PUNCT
ejpam-5280	169	13	ς	ς	PROPN
ejpam-5280	169	14	−	−	PROPN
ejpam-5280	169	15	1)µ+1	1)µ+1	NUM
ejpam-5280	169	16	.	.	PUNCT
ejpam-5280	170	1	then	then	ADV
ejpam-5280	170	2	,	,	PUNCT
ejpam-5280	170	3	the	the	DET
ejpam-5280	170	4	operational	operational	ADJ
ejpam-5280	170	5	matrix	matrix	NOUN
ejpam-5280	170	6	of	of	ADP
ejpam-5280	170	7	iµ	iµ	PROPN
ejpam-5280	170	8	is	be	AUX
ejpam-5280	170	9	oµ	oµ	ADP
ejpam-5280	170	10	=	=	PRON
ejpam-5280	170	11	rµ	rµ	INTJ
ejpam-5280	170	12	γ(µ+	γ(µ+	NOUN
ejpam-5280	170	13	2	2	X
ejpam-5280	170	14	)	)	PUNCT
ejpam-5280	170	15			ADJ
ejpam-5280	170	16	1	1	NUM
ejpam-5280	170	17	σ1	σ1	PROPN
ejpam-5280	170	18	σ2	σ2	PROPN
ejpam-5280	170	19	.	.	PUNCT
ejpam-5280	170	20	.	.	PUNCT
ejpam-5280	170	21	.	.	PUNCT
ejpam-5280	171	1	σm−2	σm−2	ADV
ejpam-5280	171	2	σm−1	σm−1	PROPN
ejpam-5280	171	3	0	0	NUM
ejpam-5280	171	4	1	1	NUM
ejpam-5280	171	5	σ1	σ1	NOUN
ejpam-5280	171	6	.	.	PUNCT
ejpam-5280	171	7	.	.	PUNCT
ejpam-5280	171	8	.	.	PUNCT
ejpam-5280	172	1	σm−3	σm−3	VERB
ejpam-5280	172	2	σm−2	σm−2	PROPN
ejpam-5280	172	3	0	0	NUM
ejpam-5280	172	4	0	0	NUM
ejpam-5280	172	5	1	1	NUM
ejpam-5280	172	6	.	.	PUNCT
ejpam-5280	172	7	.	.	PUNCT
ejpam-5280	172	8	.	.	PUNCT
ejpam-5280	173	1	σm−4	σm−4	ADJ
ejpam-5280	173	2	σm−3	σm−3	PROPN
ejpam-5280	173	3	...	...	PUNCT
ejpam-5280	173	4	...	...	PUNCT
ejpam-5280	173	5	...	...	PUNCT
ejpam-5280	173	6	.	.	PUNCT
ejpam-5280	173	7	.	.	PUNCT
ejpam-5280	173	8	.	.	PUNCT
ejpam-5280	173	9	.	.	PUNCT
ejpam-5280	173	10	.	.	PUNCT
ejpam-5280	173	11	.	.	PUNCT
ejpam-5280	174	1	...	...	PUNCT
ejpam-5280	175	1	0	0	NUM
ejpam-5280	175	2	0	0	NUM
ejpam-5280	175	3	0	0	NUM
ejpam-5280	175	4	.	.	PUNCT
ejpam-5280	175	5	.	.	PUNCT
ejpam-5280	175	6	.	.	PUNCT
ejpam-5280	176	1	1	1	NUM
ejpam-5280	176	2	σ1	σ1	NOUN
ejpam-5280	176	3	0	0	NUM
ejpam-5280	176	4	0	0	NUM
ejpam-5280	176	5	0	0	NUM
ejpam-5280	176	6	.	.	PUNCT
ejpam-5280	176	7	.	.	PUNCT
ejpam-5280	176	8	.	.	PUNCT
ejpam-5280	177	1	0	0	NUM
ejpam-5280	177	2	1	1	NUM
ejpam-5280	177	3			NOUN
ejpam-5280	177	4	.	.	PUNCT
ejpam-5280	178	1	(	(	PUNCT
ejpam-5280	178	2	40	40	NUM
ejpam-5280	178	3	)	)	PUNCT
ejpam-5280	178	4	now	now	ADV
ejpam-5280	178	5	,	,	PUNCT
ejpam-5280	178	6	we	we	PRON
ejpam-5280	178	7	can	can	AUX
ejpam-5280	178	8	rewrite	rewrite	VERB
ejpam-5280	178	9	equation	equation	NOUN
ejpam-5280	178	10	(	(	PUNCT
ejpam-5280	178	11	1	1	NUM
ejpam-5280	178	12	)	)	PUNCT
ejpam-5280	178	13	as	as	ADP
ejpam-5280	178	14	dµω(t	dµω(t	NOUN
ejpam-5280	178	15	)	)	PUNCT
ejpam-5280	178	16	=	=	SYM
ejpam-5280	178	17	(	(	PUNCT
ejpam-5280	178	18	p3(ω	p3(ω	X
ejpam-5280	178	19	)	)	PUNCT
ejpam-5280	178	20	+	+	CCONJ
ejpam-5280	178	21	p4	p4	ADJ
ejpam-5280	178	22	+	+	CCONJ
ejpam-5280	178	23	p1(ω	p1(ω	PROPN
ejpam-5280	178	24	)	)	PUNCT
ejpam-5280	178	25	+	+	NUM
ejpam-5280	178	26	p2(ω	p2(ω	NUM
ejpam-5280	178	27	)	)	PUNCT
ejpam-5280	178	28	)	)	PUNCT
ejpam-5280	178	29	t	t	PROPN
ejpam-5280	178	30	γ(t	γ(t	NOUN
ejpam-5280	178	31	)	)	PUNCT
ejpam-5280	178	32	.	.	PUNCT
ejpam-5280	179	1	(	(	PUNCT
ejpam-5280	179	2	41	41	NUM
ejpam-5280	179	3	)	)	PUNCT
ejpam-5280	179	4	using	use	VERB
ejpam-5280	179	5	lemma	lemma	PROPN
ejpam-5280	179	6	(	(	PUNCT
ejpam-5280	179	7	1	1	NUM
ejpam-5280	179	8	)	)	PUNCT
ejpam-5280	179	9	,	,	PUNCT
ejpam-5280	179	10	we	we	PRON
ejpam-5280	179	11	have	have	VERB
ejpam-5280	179	12	ω(t	ω(t	NOUN
ejpam-5280	179	13	)	)	PUNCT
ejpam-5280	179	14	=	=	SYM
ejpam-5280	179	15	ω(0	ω(0	PROPN
ejpam-5280	179	16	)	)	PUNCT
ejpam-5280	179	17	+	+	CCONJ
ejpam-5280	179	18	(	(	PUNCT
ejpam-5280	179	19	p3(ω	p3(ω	X
ejpam-5280	179	20	)	)	PUNCT
ejpam-5280	179	21	+	+	CCONJ
ejpam-5280	179	22	p4	p4	ADJ
ejpam-5280	179	23	+	+	CCONJ
ejpam-5280	179	24	p1(ω	p1(ω	PROPN
ejpam-5280	179	25	)	)	PUNCT
ejpam-5280	179	26	+	+	NUM
ejpam-5280	179	27	p2(ω	p2(ω	NUM
ejpam-5280	179	28	)	)	PUNCT
ejpam-5280	179	29	)	)	PUNCT
ejpam-5280	180	1	t	t	PROPN
ejpam-5280	180	2	iµγ(t	iµγ(t	PROPN
ejpam-5280	180	3	)	)	PUNCT
ejpam-5280	180	4	=	=	PUNCT
ejpam-5280	180	5	ω0	ω0	ADV
ejpam-5280	180	6	+	+	CCONJ
ejpam-5280	180	7	(	(	PUNCT
ejpam-5280	180	8	p3(ω	p3(ω	X
ejpam-5280	180	9	)	)	PUNCT
ejpam-5280	180	10	+	+	CCONJ
ejpam-5280	180	11	p4	p4	ADJ
ejpam-5280	180	12	+	+	CCONJ
ejpam-5280	180	13	p1(ω	p1(ω	PROPN
ejpam-5280	180	14	)	)	PUNCT
ejpam-5280	180	15	+	+	NUM
ejpam-5280	180	16	p2(ω	p2(ω	NUM
ejpam-5280	180	17	)	)	PUNCT
ejpam-5280	180	18	)	)	PUNCT
ejpam-5280	181	1	t	t	PROPN
ejpam-5280	181	2	iµγ(t	iµγ(t	PROPN
ejpam-5280	181	3	)	)	PUNCT
ejpam-5280	181	4	=	=	SYM
ejpam-5280	181	5	(	(	PUNCT
ejpam-5280	181	6	ω0p5	ω0p5	PUNCT
ejpam-5280	181	7	+	+	CCONJ
ejpam-5280	181	8	(	(	PUNCT
ejpam-5280	181	9	p3(ω	p3(ω	X
ejpam-5280	181	10	)	)	PUNCT
ejpam-5280	181	11	+	+	CCONJ
ejpam-5280	181	12	p4	p4	ADJ
ejpam-5280	181	13	+	+	CCONJ
ejpam-5280	181	14	p1(ω	p1(ω	PROPN
ejpam-5280	181	15	)	)	PUNCT
ejpam-5280	181	16	+	+	NUM
ejpam-5280	181	17	p2(ω	p2(ω	NUM
ejpam-5280	181	18	)	)	PUNCT
ejpam-5280	181	19	)	)	PUNCT
ejpam-5280	182	1	t	t	PROPN
ejpam-5280	182	2	oµ	oµ	NOUN
ejpam-5280	182	3	)	)	PUNCT
ejpam-5280	182	4	γ(t	γ(t	NOUN
ejpam-5280	182	5	)	)	PUNCT
ejpam-5280	182	6	(	(	PUNCT
ejpam-5280	182	7	42	42	NUM
ejpam-5280	182	8	)	)	PUNCT
ejpam-5280	182	9	where	where	SCONJ
ejpam-5280	182	10	(	(	PUNCT
ejpam-5280	182	11	p5)i	p5)i	NOUN
ejpam-5280	182	12	=	=	SYM
ejpam-5280	182	13	1	1	NUM
ejpam-5280	182	14	.	.	PUNCT
ejpam-5280	183	1	(	(	PUNCT
ejpam-5280	183	2	43	43	NUM
ejpam-5280	183	3	)	)	PUNCT
ejpam-5280	183	4	hence	hence	ADV
ejpam-5280	183	5	,	,	PUNCT
ejpam-5280	183	6	ω	ω	PROPN
ejpam-5280	183	7	t	t	NOUN
ejpam-5280	183	8	γ(t	γ(t	PROPN
ejpam-5280	183	9	)	)	PUNCT
ejpam-5280	184	1	=	=	SYM
ejpam-5280	184	2	(	(	PUNCT
ejpam-5280	184	3	ω0p5	ω0p5	PUNCT
ejpam-5280	184	4	+	+	CCONJ
ejpam-5280	184	5	(	(	PUNCT
ejpam-5280	184	6	p3(ω	p3(ω	X
ejpam-5280	184	7	)	)	PUNCT
ejpam-5280	184	8	+	+	CCONJ
ejpam-5280	184	9	p4	p4	ADJ
ejpam-5280	184	10	+	+	CCONJ
ejpam-5280	184	11	p1(ω	p1(ω	PROPN
ejpam-5280	184	12	)	)	PUNCT
ejpam-5280	184	13	+	+	NUM
ejpam-5280	184	14	p2(ω	p2(ω	NUM
ejpam-5280	184	15	)	)	PUNCT
ejpam-5280	184	16	)	)	PUNCT
ejpam-5280	184	17	t	t	PROPN
ejpam-5280	184	18	oµ	oµ	NOUN
ejpam-5280	184	19	)	)	PUNCT
ejpam-5280	184	20	γ(t	γ(t	NOUN
ejpam-5280	184	21	)	)	PUNCT
ejpam-5280	184	22	.	.	PUNCT
ejpam-5280	185	1	(	(	PUNCT
ejpam-5280	185	2	44	44	NUM
ejpam-5280	185	3	)	)	PUNCT
ejpam-5280	185	4	using	use	VERB
ejpam-5280	185	5	the	the	DET
ejpam-5280	185	6	orthogonality	orthogonality	NOUN
ejpam-5280	185	7	property	property	NOUN
ejpam-5280	185	8	of	of	ADP
ejpam-5280	185	9	the	the	DET
ejpam-5280	185	10	bpfs	bpf	NOUN
ejpam-5280	185	11	,	,	PUNCT
ejpam-5280	185	12	equation	equation	NOUN
ejpam-5280	185	13	(	(	PUNCT
ejpam-5280	185	14	44	44	NUM
ejpam-5280	185	15	)	)	PUNCT
ejpam-5280	185	16	becomes	become	VERB
ejpam-5280	185	17	ω0p5	ω0p5	PUNCT
ejpam-5280	185	18	+	+	CCONJ
ejpam-5280	185	19	(	(	PUNCT
ejpam-5280	185	20	p3(ω	p3(ω	X
ejpam-5280	185	21	)	)	PUNCT
ejpam-5280	185	22	+	+	CCONJ
ejpam-5280	185	23	p4	p4	ADJ
ejpam-5280	185	24	+	+	CCONJ
ejpam-5280	185	25	p1(ω	p1(ω	PROPN
ejpam-5280	185	26	)	)	PUNCT
ejpam-5280	185	27	+	+	NUM
ejpam-5280	186	1	p2(ω	p2(ω	NUM
ejpam-5280	186	2	)	)	PUNCT
ejpam-5280	186	3	)	)	PUNCT
ejpam-5280	187	1	t	t	NOUN
ejpam-5280	187	2	oµ	oµ	ADV
ejpam-5280	187	3	−	−	PROPN
ejpam-5280	187	4	ω	ω	X
ejpam-5280	187	5	=	=	SYM
ejpam-5280	187	6	0	0	PROPN
ejpam-5280	187	7	.	.	PUNCT
ejpam-5280	188	1	(	(	PUNCT
ejpam-5280	188	2	45	45	NUM
ejpam-5280	188	3	)	)	PUNCT
ejpam-5280	188	4	then	then	ADV
ejpam-5280	188	5	,	,	PUNCT
ejpam-5280	188	6	we	we	PRON
ejpam-5280	188	7	solve	solve	VERB
ejpam-5280	188	8	the	the	DET
ejpam-5280	188	9	algebraic	algebraic	ADJ
ejpam-5280	188	10	system	system	NOUN
ejpam-5280	188	11	(	(	PUNCT
ejpam-5280	188	12	45	45	NUM
ejpam-5280	188	13	)	)	PUNCT
ejpam-5280	188	14	to	to	PART
ejpam-5280	188	15	find	find	VERB
ejpam-5280	188	16	the	the	DET
ejpam-5280	188	17	coefficients	coefficient	NOUN
ejpam-5280	188	18	ω	ω	NOUN
ejpam-5280	188	19	of	of	ADP
ejpam-5280	188	20	the	the	DET
ejpam-5280	188	21	approximate	approximate	ADJ
ejpam-5280	188	22	solution	solution	NOUN
ejpam-5280	188	23	.	.	PUNCT
ejpam-5280	189	1	we	we	PRON
ejpam-5280	189	2	can	can	AUX
ejpam-5280	189	3	summarize	summarize	VERB
ejpam-5280	189	4	(	(	PUNCT
ejpam-5280	189	5	omm	omm	NOUN
ejpam-5280	189	6	)	)	PUNCT
ejpam-5280	189	7	as	as	SCONJ
ejpam-5280	189	8	follows	follow	VERB
ejpam-5280	189	9	:	:	PUNCT
ejpam-5280	189	10	algorithm	algorithm	NOUN
ejpam-5280	189	11	1	1	NUM
ejpam-5280	189	12	(	(	PUNCT
ejpam-5280	189	13	i	i	NOUN
ejpam-5280	189	14	)	)	PUNCT
ejpam-5280	189	15	find	find	VERB
ejpam-5280	189	16	the	the	DET
ejpam-5280	189	17	operational	operational	ADJ
ejpam-5280	189	18	matrices	matrix	NOUN
ejpam-5280	189	19	for	for	ADP
ejpam-5280	189	20	integral	integral	ADJ
ejpam-5280	189	21	operators	operator	NOUN
ejpam-5280	189	22	.	.	PUNCT
ejpam-5280	190	1	m.i	m.i	PROPN
ejpam-5280	190	2	.	.	PROPN
ejpam-5280	190	3	syam	syam	PROPN
ejpam-5280	190	4	,	,	PUNCT
ejpam-5280	190	5	m.	m.	NOUN
ejpam-5280	190	6	sharadga	sharadga	PROPN
ejpam-5280	190	7	,	,	PUNCT
ejpam-5280	190	8	i.	i.	PROPN
ejpam-5280	190	9	hashim	hashim	PROPN
ejpam-5280	190	10	/	/	SYM
ejpam-5280	190	11	eur	eur	PROPN
ejpam-5280	190	12	.	.	PUNCT
ejpam-5280	191	1	j.	j.	PROPN
ejpam-5280	191	2	pure	pure	PROPN
ejpam-5280	191	3	appl	appl	PROPN
ejpam-5280	191	4	.	.	PROPN
ejpam-5280	191	5	math	math	PROPN
ejpam-5280	191	6	,	,	PUNCT
ejpam-5280	191	7	17	17	NUM
ejpam-5280	191	8	(	(	PUNCT
ejpam-5280	191	9	3	3	NUM
ejpam-5280	191	10	)	)	PUNCT
ejpam-5280	191	11	(	(	PUNCT
ejpam-5280	191	12	2024	2024	NUM
ejpam-5280	191	13	)	)	PUNCT
ejpam-5280	191	14	,	,	PUNCT
ejpam-5280	191	15	1429	1429	NUM
ejpam-5280	191	16	-	-	SYM
ejpam-5280	191	17	1448	1448	NUM
ejpam-5280	191	18	1438	1438	NUM
ejpam-5280	191	19	(	(	PUNCT
ejpam-5280	191	20	ii	ii	NOUN
ejpam-5280	191	21	)	)	PUNCT
ejpam-5280	191	22	approximate	approximate	VERB
ejpam-5280	191	23	the	the	DET
ejpam-5280	191	24	solution	solution	NOUN
ejpam-5280	191	25	in	in	ADP
ejpam-5280	191	26	terms	term	NOUN
ejpam-5280	191	27	of	of	ADP
ejpam-5280	191	28	the	the	DET
ejpam-5280	191	29	block	block	NOUN
ejpam-5280	191	30	pulse	pulse	NOUN
ejpam-5280	191	31	functions	function	NOUN
ejpam-5280	191	32	(	(	PUNCT
ejpam-5280	191	33	bpf	bpf	NOUN
ejpam-5280	191	34	)	)	PUNCT
ejpam-5280	191	35	.	.	PUNCT
ejpam-5280	192	1	(	(	PUNCT
ejpam-5280	192	2	iii	iii	X
ejpam-5280	192	3	)	)	PUNCT
ejpam-5280	192	4	take	take	VERB
ejpam-5280	192	5	the	the	DET
ejpam-5280	192	6	integral	integral	NOUN
ejpam-5280	192	7	of	of	ADP
ejpam-5280	192	8	both	both	DET
ejpam-5280	192	9	sides	side	NOUN
ejpam-5280	192	10	of	of	ADP
ejpam-5280	192	11	the	the	DET
ejpam-5280	192	12	proposed	propose	VERB
ejpam-5280	192	13	problem	problem	NOUN
ejpam-5280	192	14	.	.	PUNCT
ejpam-5280	193	1	(	(	PUNCT
ejpam-5280	193	2	iv	iv	X
ejpam-5280	193	3	)	)	PUNCT
ejpam-5280	193	4	substitute	substitute	NOUN
ejpam-5280	193	5	the	the	DET
ejpam-5280	193	6	operational	operational	ADJ
ejpam-5280	193	7	matrices	matrix	NOUN
ejpam-5280	193	8	to	to	PART
ejpam-5280	193	9	generate	generate	VERB
ejpam-5280	193	10	an	an	DET
ejpam-5280	193	11	algebraic	algebraic	ADJ
ejpam-5280	193	12	system	system	NOUN
ejpam-5280	193	13	.	.	PUNCT
ejpam-5280	194	1	(	(	PUNCT
ejpam-5280	194	2	v	v	NOUN
ejpam-5280	194	3	)	)	PUNCT
ejpam-5280	194	4	solve	solve	VERB
ejpam-5280	194	5	the	the	DET
ejpam-5280	194	6	algebraic	algebraic	ADJ
ejpam-5280	194	7	system	system	NOUN
ejpam-5280	194	8	to	to	PART
ejpam-5280	194	9	obtain	obtain	VERB
ejpam-5280	194	10	the	the	DET
ejpam-5280	194	11	coefficients	coefficient	NOUN
ejpam-5280	194	12	of	of	ADP
ejpam-5280	194	13	the	the	DET
ejpam-5280	194	14	solution	solution	NOUN
ejpam-5280	194	15	.	.	PUNCT
ejpam-5280	195	1	4	4	X
ejpam-5280	195	2	.	.	X
ejpam-5280	195	3	theoretical	theoretical	ADJ
ejpam-5280	195	4	results	result	NOUN
ejpam-5280	195	5	in	in	ADP
ejpam-5280	195	6	the	the	DET
ejpam-5280	195	7	first	first	ADJ
ejpam-5280	195	8	theorem	theorem	NOUN
ejpam-5280	195	9	,	,	PUNCT
ejpam-5280	195	10	we	we	PRON
ejpam-5280	195	11	want	want	VERB
ejpam-5280	195	12	to	to	PART
ejpam-5280	195	13	prove	prove	VERB
ejpam-5280	195	14	that	that	DET
ejpam-5280	195	15	problem	problem	NOUN
ejpam-5280	195	16	(	(	PUNCT
ejpam-5280	195	17	1)-(2	1)-(2	NUM
ejpam-5280	195	18	)	)	PUNCT
ejpam-5280	195	19	has	have	VERB
ejpam-5280	195	20	a	a	DET
ejpam-5280	195	21	unique	unique	ADJ
ejpam-5280	195	22	solution	solution	NOUN
ejpam-5280	195	23	.	.	PUNCT
ejpam-5280	196	1	theorem	theorem	NOUN
ejpam-5280	196	2	3	3	X
ejpam-5280	196	3	.	.	PUNCT
ejpam-5280	197	1	let	let	VERB
ejpam-5280	197	2	π1,π2	π1,π2	PRON
ejpam-5280	197	3	:	:	PUNCT
ejpam-5280	198	1	[	[	X
ejpam-5280	198	2	0	0	NUM
ejpam-5280	198	3	,	,	PUNCT
ejpam-5280	198	4	1	1	NUM
ejpam-5280	198	5	]	]	SYM
ejpam-5280	198	6	×	×	NOUN
ejpam-5280	199	1	[	[	X
ejpam-5280	199	2	0	0	NUM
ejpam-5280	199	3	,	,	PUNCT
ejpam-5280	199	4	1	1	NUM
ejpam-5280	199	5	]	]	PUNCT
ejpam-5280	199	6	→	→	SYM
ejpam-5280	199	7	ℜ	ℜ	PROPN
ejpam-5280	199	8	and	and	CCONJ
ejpam-5280	199	9	g2	g2	PROPN
ejpam-5280	199	10	:	:	PUNCT
ejpam-5280	200	1	[	[	X
ejpam-5280	200	2	0	0	NUM
ejpam-5280	200	3	,	,	PUNCT
ejpam-5280	200	4	1	1	NUM
ejpam-5280	200	5	]	]	PUNCT
ejpam-5280	200	6	→	→	PUNCT
ejpam-5280	200	7	ℜ	ℜ	PROPN
ejpam-5280	200	8	be	be	AUX
ejpam-5280	200	9	continuous	continuous	ADJ
ejpam-5280	200	10	functions	function	NOUN
ejpam-5280	200	11	which	which	PRON
ejpam-5280	200	12	are	be	AUX
ejpam-5280	200	13	bounded	bound	VERB
ejpam-5280	200	14	by	by	ADP
ejpam-5280	200	15	q1	q1	PROPN
ejpam-5280	200	16	and	and	CCONJ
ejpam-5280	200	17	q2	q2	NOUN
ejpam-5280	200	18	,	,	PUNCT
ejpam-5280	200	19	respectively	respectively	ADV
ejpam-5280	200	20	,	,	PUNCT
ejpam-5280	200	21	g3	g3	NOUN
ejpam-5280	200	22	,	,	PUNCT
ejpam-5280	200	23	g4	g4	NOUN
ejpam-5280	200	24	:	:	PUNCT
ejpam-5280	200	25	ℜ	ℜ	ADJ
ejpam-5280	200	26	→	→	SYM
ejpam-5280	200	27	ℜ	ℜ	PROPN
ejpam-5280	200	28	be	be	AUX
ejpam-5280	200	29	continuous	continuous	ADJ
ejpam-5280	200	30	lipschitz	lipschitz	NOUN
ejpam-5280	200	31	functions	function	NOUN
ejpam-5280	200	32	with	with	ADP
ejpam-5280	200	33	lipschitz	lipschitz	NOUN
ejpam-5280	200	34	constants	constant	NOUN
ejpam-5280	200	35	l3	l3	PROPN
ejpam-5280	200	36	and	and	CCONJ
ejpam-5280	200	37	l4	l4	PROPN
ejpam-5280	200	38	,	,	PUNCT
ejpam-5280	200	39	respectively	respectively	ADV
ejpam-5280	200	40	,	,	PUNCT
ejpam-5280	200	41	and	and	CCONJ
ejpam-5280	200	42	g1	g1	VERB
ejpam-5280	200	43	:	:	PUNCT
ejpam-5280	201	1	[	[	X
ejpam-5280	201	2	0	0	NUM
ejpam-5280	201	3	,	,	PUNCT
ejpam-5280	201	4	1	1	NUM
ejpam-5280	201	5	]	]	PUNCT
ejpam-5280	201	6	×	×	PROPN
ejpam-5280	201	7	ℜ	ℜ	PROPN
ejpam-5280	201	8	→	→	SYM
ejpam-5280	201	9	ℜ	ℜ	PROPN
ejpam-5280	201	10	be	be	AUX
ejpam-5280	201	11	continuous	continuous	ADJ
ejpam-5280	201	12	lipschitz	lipschitz	NOUN
ejpam-5280	201	13	function	function	NOUN
ejpam-5280	201	14	with	with	ADP
ejpam-5280	201	15	respect	respect	NOUN
ejpam-5280	201	16	to	to	ADP
ejpam-5280	201	17	the	the	DET
ejpam-5280	201	18	second	second	ADJ
ejpam-5280	201	19	component	component	NOUN
ejpam-5280	201	20	with	with	ADP
ejpam-5280	201	21	lipschitz	lipschitz	NOUN
ejpam-5280	201	22	constant	constant	ADJ
ejpam-5280	201	23	l1	l1	PROPN
ejpam-5280	201	24	.	.	PUNCT
ejpam-5280	202	1	then	then	ADV
ejpam-5280	202	2	,	,	PUNCT
ejpam-5280	202	3	the	the	DET
ejpam-5280	202	4	the	the	DET
ejpam-5280	202	5	following	following	ADJ
ejpam-5280	202	6	problem	problem	NOUN
ejpam-5280	202	7	dµω(t	dµω(t	NOUN
ejpam-5280	202	8	)	)	PUNCT
ejpam-5280	202	9	=	=	SYM
ejpam-5280	202	10	g1(t	g1(t	PROPN
ejpam-5280	202	11	,	,	PUNCT
ejpam-5280	202	12	ω(t	ω(t	NOUN
ejpam-5280	202	13	)	)	PUNCT
ejpam-5280	202	14	)	)	PUNCT
ejpam-5280	203	1	+	+	PUNCT
ejpam-5280	203	2	g2(t	g2(t	NOUN
ejpam-5280	203	3	)	)	PUNCT
ejpam-5280	203	4	+	+	NUM
ejpam-5280	203	5	∫	∫	PROPN
ejpam-5280	203	6	t	t	PROPN
ejpam-5280	203	7	0	0	NUM
ejpam-5280	203	8	π1(t	π1(t	PROPN
ejpam-5280	203	9	,	,	PUNCT
ejpam-5280	203	10	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	203	11	+	+	NUM
ejpam-5280	203	12	∫	∫	PROPN
ejpam-5280	203	13	1	1	NUM
ejpam-5280	203	14	0	0	PUNCT
ejpam-5280	203	15	π2(t	π2(t	PROPN
ejpam-5280	203	16	,	,	PUNCT
ejpam-5280	203	17	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	203	18	,	,	PUNCT
ejpam-5280	203	19	(	(	PUNCT
ejpam-5280	203	20	46	46	NUM
ejpam-5280	203	21	)	)	PUNCT
ejpam-5280	203	22	ω(0	ω(0	PROPN
ejpam-5280	203	23	)	)	PUNCT
ejpam-5280	203	24	=	=	PUNCT
ejpam-5280	203	25	ω0	ω0	NOUN
ejpam-5280	203	26	,	,	PUNCT
ejpam-5280	203	27	(	(	PUNCT
ejpam-5280	203	28	47	47	NUM
ejpam-5280	203	29	)	)	PUNCT
ejpam-5280	203	30	has	have	VERB
ejpam-5280	203	31	a	a	DET
ejpam-5280	203	32	unique	unique	ADJ
ejpam-5280	203	33	solution	solution	NOUN
ejpam-5280	203	34	if	if	SCONJ
ejpam-5280	203	35	l1(µ+	l1(µ+	PROPN
ejpam-5280	203	36	1	1	NUM
ejpam-5280	203	37	)	)	PUNCT
ejpam-5280	203	38	+	+	CCONJ
ejpam-5280	203	39	(	(	PUNCT
ejpam-5280	203	40	l3q1	l3q1	X
ejpam-5280	203	41	+	+	CCONJ
ejpam-5280	203	42	l4q2	l4q2	NOUN
ejpam-5280	203	43	)	)	PUNCT
ejpam-5280	203	44	γ(µ+	γ(µ+	X
ejpam-5280	204	1	2	2	X
ejpam-5280	204	2	)	)	PUNCT
ejpam-5280	204	3	<	<	X
ejpam-5280	204	4	1	1	X
ejpam-5280	204	5	.	.	PUNCT
ejpam-5280	204	6	(	(	PUNCT
ejpam-5280	204	7	48	48	NUM
ejpam-5280	204	8	)	)	PUNCT
ejpam-5280	204	9	proof	proof	NOUN
ejpam-5280	204	10	.	.	PUNCT
ejpam-5280	205	1	take	take	VERB
ejpam-5280	205	2	the	the	DET
ejpam-5280	205	3	fractional	fractional	ADJ
ejpam-5280	205	4	integral	integral	ADJ
ejpam-5280	205	5	operator	operator	NOUN
ejpam-5280	205	6	for	for	ADP
ejpam-5280	205	7	both	both	DET
ejpam-5280	205	8	sides	side	NOUN
ejpam-5280	205	9	of	of	ADP
ejpam-5280	205	10	equation	equation	NOUN
ejpam-5280	205	11	(	(	PUNCT
ejpam-5280	205	12	46	46	NUM
ejpam-5280	205	13	)	)	PUNCT
ejpam-5280	205	14	to	to	PART
ejpam-5280	205	15	get	get	VERB
ejpam-5280	205	16	ω(t)−	ω(t)−	PROPN
ejpam-5280	205	17	ω0	ω0	NOUN
ejpam-5280	205	18	=	=	SYM
ejpam-5280	205	19	1	1	NUM
ejpam-5280	205	20	γ(µ	γ(µ	PROPN
ejpam-5280	205	21	)	)	PUNCT
ejpam-5280	205	22	∫	∫	PROPN
ejpam-5280	205	23	t	t	PROPN
ejpam-5280	205	24	0	0	NUM
ejpam-5280	206	1	(	(	PUNCT
ejpam-5280	206	2	g1(z	g1(z	PROPN
ejpam-5280	206	3	,	,	PUNCT
ejpam-5280	206	4	ω(z	ω(z	NUM
ejpam-5280	206	5	)	)	PUNCT
ejpam-5280	206	6	)	)	PUNCT
ejpam-5280	207	1	+	+	PUNCT
ejpam-5280	207	2	g2(z	g2(z	X
ejpam-5280	207	3	)	)	PUNCT
ejpam-5280	207	4	+	+	NUM
ejpam-5280	207	5	∫	∫	PROPN
ejpam-5280	207	6	z	z	NOUN
ejpam-5280	207	7	0	0	NUM
ejpam-5280	207	8	π1(z	π1(z	PROPN
ejpam-5280	207	9	,	,	PUNCT
ejpam-5280	207	10	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	207	11	)	)	PUNCT
ejpam-5280	207	12	(	(	PUNCT
ejpam-5280	207	13	t−	t−	PROPN
ejpam-5280	207	14	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	207	15	+	+	CCONJ
ejpam-5280	207	16	1	1	NUM
ejpam-5280	207	17	γ(µ	γ(µ	PROPN
ejpam-5280	207	18	)	)	PUNCT
ejpam-5280	207	19	∫	∫	PROPN
ejpam-5280	207	20	t	t	PROPN
ejpam-5280	207	21	0	0	NUM
ejpam-5280	207	22	(	(	PUNCT
ejpam-5280	207	23	∫	∫	PROPN
ejpam-5280	207	24	1	1	NUM
ejpam-5280	207	25	0	0	NUM
ejpam-5280	207	26	π2(z	π2(z	NOUN
ejpam-5280	207	27	,	,	PUNCT
ejpam-5280	207	28	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	207	29	)	)	PUNCT
ejpam-5280	207	30	(	(	PUNCT
ejpam-5280	207	31	t−	t−	PROPN
ejpam-5280	207	32	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	207	33	.	.	PUNCT
ejpam-5280	208	1	(	(	PUNCT
ejpam-5280	208	2	49	49	NUM
ejpam-5280	208	3	)	)	PUNCT
ejpam-5280	208	4	let	let	VERB
ejpam-5280	208	5	℘(ω	℘(ω	PRON
ejpam-5280	208	6	)	)	PUNCT
ejpam-5280	208	7	=	=	PUNCT
ejpam-5280	209	1	ω0	ω0	ADV
ejpam-5280	209	2	+	+	NOUN
ejpam-5280	209	3	1	1	NUM
ejpam-5280	209	4	γ(µ	γ(µ	PROPN
ejpam-5280	209	5	)	)	PUNCT
ejpam-5280	209	6	∫	∫	PROPN
ejpam-5280	210	1	t	t	PROPN
ejpam-5280	210	2	0	0	NUM
ejpam-5280	210	3	(	(	PUNCT
ejpam-5280	210	4	g1(z	g1(z	PROPN
ejpam-5280	210	5	,	,	PUNCT
ejpam-5280	210	6	ω(z	ω(z	NUM
ejpam-5280	210	7	)	)	PUNCT
ejpam-5280	210	8	)	)	PUNCT
ejpam-5280	211	1	+	+	PUNCT
ejpam-5280	211	2	g2(z	g2(z	X
ejpam-5280	211	3	)	)	PUNCT
ejpam-5280	211	4	+	+	NUM
ejpam-5280	211	5	∫	∫	PROPN
ejpam-5280	211	6	z	z	NOUN
ejpam-5280	211	7	0	0	NUM
ejpam-5280	211	8	π1(z	π1(z	PROPN
ejpam-5280	211	9	,	,	PUNCT
ejpam-5280	211	10	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	211	11	)	)	PUNCT
ejpam-5280	211	12	(	(	PUNCT
ejpam-5280	211	13	t−	t−	PROPN
ejpam-5280	211	14	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	211	15	+	+	CCONJ
ejpam-5280	211	16	1	1	NUM
ejpam-5280	211	17	γ(µ	γ(µ	PROPN
ejpam-5280	211	18	)	)	PUNCT
ejpam-5280	211	19	∫	∫	PROPN
ejpam-5280	211	20	t	t	PROPN
ejpam-5280	211	21	0	0	NUM
ejpam-5280	211	22	(	(	PUNCT
ejpam-5280	211	23	∫	∫	PROPN
ejpam-5280	211	24	1	1	NUM
ejpam-5280	211	25	0	0	NUM
ejpam-5280	211	26	π2(z	π2(z	NOUN
ejpam-5280	211	27	,	,	PUNCT
ejpam-5280	211	28	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	211	29	)	)	PUNCT
ejpam-5280	211	30	(	(	PUNCT
ejpam-5280	211	31	t−	t−	PROPN
ejpam-5280	211	32	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	211	33	.	.	PUNCT
ejpam-5280	212	1	(	(	PUNCT
ejpam-5280	212	2	50	50	NUM
ejpam-5280	212	3	)	)	PUNCT
ejpam-5280	212	4	therefor	therefor	ADV
ejpam-5280	212	5	,	,	PUNCT
ejpam-5280	212	6	|℘(ω1)−	|℘(ω1)−	NOUN
ejpam-5280	212	7	℘(ω2)|	℘(ω2)|	PROPN
ejpam-5280	212	8	≤	≤	NOUN
ejpam-5280	212	9	1	1	NUM
ejpam-5280	212	10	γ(µ	γ(µ	PROPN
ejpam-5280	212	11	)	)	PUNCT
ejpam-5280	213	1	|	|	ADV
ejpam-5280	213	2	∫	∫	PROPN
ejpam-5280	213	3	t	t	PROPN
ejpam-5280	213	4	0	0	NUM
ejpam-5280	214	1	(	(	PUNCT
ejpam-5280	214	2	g1(z	g1(z	PROPN
ejpam-5280	214	3	,	,	PUNCT
ejpam-5280	214	4	ω1(z))−g1(z	ω1(z))−g1(z	NOUN
ejpam-5280	214	5	,	,	PUNCT
ejpam-5280	214	6	ω2(z	ω2(z	NUM
ejpam-5280	214	7	)	)	PUNCT
ejpam-5280	214	8	)	)	PUNCT
ejpam-5280	214	9	)	)	PUNCT
ejpam-5280	215	1	(	(	PUNCT
ejpam-5280	215	2	t−	t−	PROPN
ejpam-5280	215	3	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	215	4	|	|	ADV
ejpam-5280	215	5	m.i	m.i	PROPN
ejpam-5280	215	6	.	.	PROPN
ejpam-5280	215	7	syam	syam	PROPN
ejpam-5280	215	8	,	,	PUNCT
ejpam-5280	215	9	m.	m.	NOUN
ejpam-5280	215	10	sharadga	sharadga	PROPN
ejpam-5280	215	11	,	,	PUNCT
ejpam-5280	215	12	i.	i.	PROPN
ejpam-5280	215	13	hashim	hashim	PROPN
ejpam-5280	215	14	/	/	SYM
ejpam-5280	215	15	eur	eur	PROPN
ejpam-5280	215	16	.	.	PUNCT
ejpam-5280	216	1	j.	j.	PROPN
ejpam-5280	216	2	pure	pure	PROPN
ejpam-5280	216	3	appl	appl	PROPN
ejpam-5280	216	4	.	.	PROPN
ejpam-5280	216	5	math	math	PROPN
ejpam-5280	216	6	,	,	PUNCT
ejpam-5280	216	7	17	17	NUM
ejpam-5280	216	8	(	(	PUNCT
ejpam-5280	216	9	3	3	NUM
ejpam-5280	216	10	)	)	PUNCT
ejpam-5280	216	11	(	(	PUNCT
ejpam-5280	216	12	2024	2024	NUM
ejpam-5280	216	13	)	)	PUNCT
ejpam-5280	216	14	,	,	PUNCT
ejpam-5280	216	15	1429	1429	NUM
ejpam-5280	216	16	-	-	SYM
ejpam-5280	216	17	1448	1448	NUM
ejpam-5280	216	18	1439	1439	NUM
ejpam-5280	216	19	+	+	CCONJ
ejpam-5280	216	20	1	1	NUM
ejpam-5280	216	21	γ(µ	γ(µ	PROPN
ejpam-5280	216	22	)	)	PUNCT
ejpam-5280	217	1	|	|	ADV
ejpam-5280	217	2	∫	∫	PROPN
ejpam-5280	217	3	t	t	PROPN
ejpam-5280	217	4	0	0	NUM
ejpam-5280	218	1	∫	∫	PROPN
ejpam-5280	218	2	z	z	PROPN
ejpam-5280	218	3	0	0	NUM
ejpam-5280	218	4	π1(z	π1(z	PROPN
ejpam-5280	218	5	,	,	PUNCT
ejpam-5280	218	6	s	s	NOUN
ejpam-5280	218	7	)	)	PUNCT
ejpam-5280	218	8	(	(	PUNCT
ejpam-5280	218	9	g3(ω1(s))−g3(ω2(s	g3(ω1(s))−g3(ω2(s	PROPN
ejpam-5280	218	10	)	)	PUNCT
ejpam-5280	218	11	)	)	PUNCT
ejpam-5280	218	12	)	)	PUNCT
ejpam-5280	219	1	ds(t−	ds(t−	PROPN
ejpam-5280	219	2	z)µ−1dz	z)µ−1dz	NOUN
ejpam-5280	220	1	|	|	ADV
ejpam-5280	221	1	+	+	CCONJ
ejpam-5280	221	2	1	1	NUM
ejpam-5280	221	3	γ(µ	γ(µ	PROPN
ejpam-5280	221	4	)	)	PUNCT
ejpam-5280	222	1	|	|	ADV
ejpam-5280	222	2	∫	∫	PROPN
ejpam-5280	222	3	t	t	PROPN
ejpam-5280	222	4	0	0	NUM
ejpam-5280	223	1	∫	∫	PROPN
ejpam-5280	223	2	1	1	NUM
ejpam-5280	223	3	0	0	NUM
ejpam-5280	223	4	π2(z	π2(z	NOUN
ejpam-5280	223	5	,	,	PUNCT
ejpam-5280	223	6	s	s	PART
ejpam-5280	223	7	)	)	PUNCT
ejpam-5280	223	8	(	(	PUNCT
ejpam-5280	223	9	g4(ω1(s))−g4(ω2(s	g4(ω1(s))−g4(ω2(s	NOUN
ejpam-5280	223	10	)	)	PUNCT
ejpam-5280	223	11	)	)	PUNCT
ejpam-5280	223	12	)	)	PUNCT
ejpam-5280	224	1	ds(t−	ds(t−	PROPN
ejpam-5280	224	2	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	225	1	|	|	INTJ
ejpam-5280	225	2	.	.	PUNCT
ejpam-5280	226	1	since	since	SCONJ
ejpam-5280	226	2	g1	g1	PROPN
ejpam-5280	226	3	,	,	PUNCT
ejpam-5280	226	4	g3	g3	NOUN
ejpam-5280	226	5	,	,	PUNCT
ejpam-5280	226	6	g4	g4	NOUN
ejpam-5280	226	7	are	be	AUX
ejpam-5280	226	8	lipschitz	lipschitz	NOUN
ejpam-5280	226	9	functions	function	NOUN
ejpam-5280	226	10	,	,	PUNCT
ejpam-5280	226	11	then	then	ADV
ejpam-5280	226	12	|℘(ω1)−	|℘(ω1)−	PROPN
ejpam-5280	226	13	℘(ω2)|	℘(ω2)|	PROPN
ejpam-5280	226	14	≤	≤	PROPN
ejpam-5280	226	15	l1	l1	PROPN
ejpam-5280	226	16	∥	∥	PROPN
ejpam-5280	226	17	ω1	ω1	PROPN
ejpam-5280	226	18	−	−	PROPN
ejpam-5280	227	1	ω2	ω2	ADJ
ejpam-5280	227	2	∥	∥	PUNCT
ejpam-5280	227	3	γ(µ	γ(µ	PROPN
ejpam-5280	227	4	)	)	PUNCT
ejpam-5280	228	1	|	|	ADV
ejpam-5280	228	2	∫	∫	PROPN
ejpam-5280	228	3	t	t	PROPN
ejpam-5280	228	4	0	0	NUM
ejpam-5280	228	5	(	(	PUNCT
ejpam-5280	228	6	t−	t−	PROPN
ejpam-5280	228	7	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	229	1	|	|	ADV
ejpam-5280	230	1	+	+	CCONJ
ejpam-5280	230	2	l3	l3	PROPN
ejpam-5280	230	3	∥	∥	PUNCT
ejpam-5280	230	4	ω1	ω1	PROPN
ejpam-5280	230	5	−	−	PROPN
ejpam-5280	230	6	ω2	ω2	ADJ
ejpam-5280	230	7	∥	∥	PUNCT
ejpam-5280	230	8	γ(µ	γ(µ	PROPN
ejpam-5280	230	9	)	)	PUNCT
ejpam-5280	231	1	|	|	ADV
ejpam-5280	231	2	∫	∫	PROPN
ejpam-5280	231	3	t	t	PROPN
ejpam-5280	231	4	0	0	NUM
ejpam-5280	232	1	∫	∫	PROPN
ejpam-5280	232	2	z	z	PROPN
ejpam-5280	232	3	0	0	NUM
ejpam-5280	232	4	π1(z	π1(z	PROPN
ejpam-5280	232	5	,	,	PUNCT
ejpam-5280	232	6	s)ds(t−	s)ds(t−	X
ejpam-5280	232	7	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	233	1	|	|	ADV
ejpam-5280	233	2	+	+	CCONJ
ejpam-5280	233	3	l4	l4	PROPN
ejpam-5280	233	4	∥	∥	PROPN
ejpam-5280	233	5	ω1	ω1	PROPN
ejpam-5280	233	6	−	−	PROPN
ejpam-5280	233	7	ω2	ω2	ADJ
ejpam-5280	233	8	∥	∥	PUNCT
ejpam-5280	233	9	γ(µ	γ(µ	PROPN
ejpam-5280	233	10	)	)	PUNCT
ejpam-5280	234	1	|	|	ADV
ejpam-5280	234	2	∫	∫	PROPN
ejpam-5280	234	3	t	t	PROPN
ejpam-5280	234	4	0	0	NUM
ejpam-5280	235	1	∫	∫	PROPN
ejpam-5280	235	2	1	1	NUM
ejpam-5280	235	3	0	0	NUM
ejpam-5280	235	4	π2(z	π2(z	NOUN
ejpam-5280	235	5	,	,	PUNCT
ejpam-5280	235	6	s)ds(t−	s)ds(t−	X
ejpam-5280	235	7	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	236	1	|	|	INTJ
ejpam-5280	236	2	.	.	PUNCT
ejpam-5280	237	1	(	(	PUNCT
ejpam-5280	237	2	51	51	NUM
ejpam-5280	237	3	)	)	PUNCT
ejpam-5280	237	4	since	since	SCONJ
ejpam-5280	237	5	π1	π1	NOUN
ejpam-5280	237	6	and	and	CCONJ
ejpam-5280	237	7	π2	π2	NOUN
ejpam-5280	237	8	are	be	AUX
ejpam-5280	237	9	continuous	continuous	ADJ
ejpam-5280	237	10	on	on	ADP
ejpam-5280	237	11	a	a	DET
ejpam-5280	237	12	compact	compact	ADJ
ejpam-5280	237	13	set	set	NOUN
ejpam-5280	237	14	[	[	X
ejpam-5280	237	15	0	0	NUM
ejpam-5280	237	16	,	,	PUNCT
ejpam-5280	237	17	1]×	1]×	NUM
ejpam-5280	238	1	[	[	X
ejpam-5280	238	2	0	0	NUM
ejpam-5280	238	3	,	,	PUNCT
ejpam-5280	238	4	1	1	NUM
ejpam-5280	238	5	]	]	PUNCT
ejpam-5280	238	6	,	,	PUNCT
ejpam-5280	238	7	then	then	ADV
ejpam-5280	238	8	they	they	PRON
ejpam-5280	238	9	are	be	AUX
ejpam-5280	238	10	bounded	bound	VERB
ejpam-5280	238	11	by	by	ADP
ejpam-5280	238	12	q1	q1	PROPN
ejpam-5280	238	13	and	and	CCONJ
ejpam-5280	238	14	q2	q2	NOUN
ejpam-5280	238	15	,	,	PUNCT
ejpam-5280	238	16	respectively	respectively	ADV
ejpam-5280	238	17	.	.	PUNCT
ejpam-5280	239	1	thus	thus	ADV
ejpam-5280	239	2	,	,	PUNCT
ejpam-5280	239	3	|℘(ω1)−	|℘(ω1)−	PROPN
ejpam-5280	239	4	℘(ω2)|	℘(ω2)|	PROPN
ejpam-5280	239	5	≤	≤	PROPN
ejpam-5280	239	6	l1	l1	PROPN
ejpam-5280	239	7	∥	∥	PROPN
ejpam-5280	239	8	ω1	ω1	PROPN
ejpam-5280	239	9	−	−	PROPN
ejpam-5280	239	10	ω2	ω2	ADJ
ejpam-5280	239	11	∥	∥	PUNCT
ejpam-5280	239	12	γ(µ	γ(µ	PROPN
ejpam-5280	239	13	)	)	PUNCT
ejpam-5280	240	1	|	|	ADV
ejpam-5280	240	2	∫	∫	PROPN
ejpam-5280	240	3	t	t	PROPN
ejpam-5280	240	4	0	0	NUM
ejpam-5280	240	5	(	(	PUNCT
ejpam-5280	240	6	t−	t−	PROPN
ejpam-5280	240	7	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	241	1	|	|	ADV
ejpam-5280	241	2	+	+	CCONJ
ejpam-5280	241	3	l3q1	l3q1	NOUN
ejpam-5280	241	4	∥	∥	X
ejpam-5280	241	5	ω1	ω1	PROPN
ejpam-5280	241	6	−	−	PROPN
ejpam-5280	241	7	ω2	ω2	ADJ
ejpam-5280	241	8	∥	∥	PUNCT
ejpam-5280	241	9	γ(µ	γ(µ	PROPN
ejpam-5280	241	10	)	)	PUNCT
ejpam-5280	242	1	|	|	ADV
ejpam-5280	242	2	∫	∫	PROPN
ejpam-5280	242	3	t	t	PROPN
ejpam-5280	242	4	0	0	NUM
ejpam-5280	243	1	∫	∫	PROPN
ejpam-5280	243	2	z	z	PROPN
ejpam-5280	243	3	0	0	NUM
ejpam-5280	244	1	ds(t−	ds(t−	NOUN
ejpam-5280	244	2	z)µ−1dz	z)µ−1dz	NOUN
ejpam-5280	245	1	|	|	ADV
ejpam-5280	246	1	+	+	CCONJ
ejpam-5280	246	2	l4q2	l4q2	X
ejpam-5280	246	3	∥	∥	PUNCT
ejpam-5280	246	4	ω1	ω1	PROPN
ejpam-5280	246	5	−	−	PROPN
ejpam-5280	246	6	ω2	ω2	ADJ
ejpam-5280	246	7	∥	∥	PUNCT
ejpam-5280	246	8	γ(µ	γ(µ	PROPN
ejpam-5280	246	9	)	)	PUNCT
ejpam-5280	247	1	|	|	ADV
ejpam-5280	247	2	∫	∫	PROPN
ejpam-5280	247	3	t	t	PROPN
ejpam-5280	247	4	0	0	NUM
ejpam-5280	248	1	∫	∫	PROPN
ejpam-5280	248	2	1	1	NUM
ejpam-5280	248	3	0	0	NUM
ejpam-5280	249	1	ds(t−	ds(t−	NOUN
ejpam-5280	249	2	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	249	3	|	|	ADV
ejpam-5280	249	4	≤	≤	PROPN
ejpam-5280	249	5	(	(	PUNCT
ejpam-5280	249	6	l1	l1	PROPN
ejpam-5280	249	7	t	t	PROPN
ejpam-5280	249	8	µ	µ	X
ejpam-5280	249	9	γ(µ+	γ(µ+	X
ejpam-5280	249	10	1	1	NUM
ejpam-5280	249	11	)	)	PUNCT
ejpam-5280	249	12	+	+	CCONJ
ejpam-5280	249	13	(	(	PUNCT
ejpam-5280	249	14	l3q1	l3q1	X
ejpam-5280	250	1	+	+	CCONJ
ejpam-5280	250	2	l4q2)t	l4q2)t	NOUN
ejpam-5280	250	3	µ+1	µ+1	X
ejpam-5280	250	4	γ(µ+	γ(µ+	X
ejpam-5280	250	5	2	2	NUM
ejpam-5280	250	6	)	)	PUNCT
ejpam-5280	250	7	)	)	PUNCT
ejpam-5280	250	8	∥	∥	PUNCT
ejpam-5280	250	9	ω1	ω1	PROPN
ejpam-5280	250	10	−	−	PROPN
ejpam-5280	250	11	ω2	ω2	ADJ
ejpam-5280	250	12	∥	∥	PUNCT
ejpam-5280	250	13	≤	≤	NOUN
ejpam-5280	250	14	(	(	PUNCT
ejpam-5280	250	15	l1(µ+	l1(µ+	PROPN
ejpam-5280	250	16	1	1	NUM
ejpam-5280	250	17	)	)	PUNCT
ejpam-5280	250	18	+	+	CCONJ
ejpam-5280	250	19	(	(	PUNCT
ejpam-5280	250	20	l3q1	l3q1	X
ejpam-5280	250	21	+	+	CCONJ
ejpam-5280	250	22	l4q2	l4q2	NOUN
ejpam-5280	250	23	)	)	PUNCT
ejpam-5280	250	24	γ(µ+	γ(µ+	X
ejpam-5280	250	25	2	2	NUM
ejpam-5280	250	26	)	)	PUNCT
ejpam-5280	250	27	)	)	PUNCT
ejpam-5280	250	28	∥	∥	PUNCT
ejpam-5280	250	29	ω1	ω1	PROPN
ejpam-5280	250	30	−	−	PROPN
ejpam-5280	250	31	ω2	ω2	ADJ
ejpam-5280	250	32	∥	∥	PROPN
ejpam-5280	250	33	.	.	PUNCT
ejpam-5280	251	1	(	(	PUNCT
ejpam-5280	251	2	52	52	NUM
ejpam-5280	251	3	)	)	PUNCT
ejpam-5280	251	4	since	since	SCONJ
ejpam-5280	251	5	l1(µ+1)+(l3q1+l4q2	l1(µ+1)+(l3q1+l4q2	NUM
ejpam-5280	251	6	)	)	PUNCT
ejpam-5280	251	7	γ(µ+2	γ(µ+2	PROPN
ejpam-5280	251	8	)	)	PUNCT
ejpam-5280	251	9	<	<	X
ejpam-5280	251	10	1	1	NUM
ejpam-5280	251	11	,	,	PUNCT
ejpam-5280	251	12	then	then	ADV
ejpam-5280	251	13	℘	℘	PROPN
ejpam-5280	251	14	is	be	AUX
ejpam-5280	251	15	contraction	contraction	NOUN
ejpam-5280	251	16	on	on	ADP
ejpam-5280	251	17	ω	ω	PROPN
ejpam-5280	251	18	.	.	PUNCT
ejpam-5280	252	1	by	by	ADP
ejpam-5280	252	2	banach	banach	ADV
ejpam-5280	252	3	fixed	fix	VERB
ejpam-5280	252	4	point	point	NOUN
ejpam-5280	252	5	theorem	theorem	ADJ
ejpam-5280	252	6	,	,	PUNCT
ejpam-5280	252	7	problem	problem	NOUN
ejpam-5280	252	8	(	(	PUNCT
ejpam-5280	252	9	46)-(47	46)-(47	NOUN
ejpam-5280	252	10	)	)	PUNCT
ejpam-5280	252	11	has	have	VERB
ejpam-5280	252	12	unique	unique	ADJ
ejpam-5280	252	13	solution	solution	NOUN
ejpam-5280	252	14	.	.	PUNCT
ejpam-5280	253	1	next	next	ADV
ejpam-5280	253	2	,	,	PUNCT
ejpam-5280	253	3	our	our	PRON
ejpam-5280	253	4	target	target	NOUN
ejpam-5280	253	5	is	be	AUX
ejpam-5280	253	6	to	to	PART
ejpam-5280	253	7	prove	prove	VERB
ejpam-5280	253	8	that	that	SCONJ
ejpam-5280	253	9	the	the	DET
ejpam-5280	253	10	sequence	sequence	NOUN
ejpam-5280	253	11	{	{	PUNCT
ejpam-5280	253	12	∑m−1	∑m−1	ADJ
ejpam-5280	253	13	i=0	i=0	PUNCT
ejpam-5280	253	14	ωiγi(t	ωiγi(t	NOUN
ejpam-5280	253	15	)	)	PUNCT
ejpam-5280	253	16	}	}	PUNCT
ejpam-5280	253	17	∞	∞	PROPN
ejpam-5280	253	18	m=1	m=1	PROPN
ejpam-5280	253	19	is	be	AUX
ejpam-5280	253	20	uniformly	uniformly	ADV
ejpam-5280	253	21	convergent	convergent	ADJ
ejpam-5280	253	22	to	to	ADP
ejpam-5280	253	23	the	the	DET
ejpam-5280	253	24	unique	unique	ADJ
ejpam-5280	253	25	solution	solution	NOUN
ejpam-5280	253	26	of	of	ADP
ejpam-5280	253	27	problem	problem	NOUN
ejpam-5280	253	28	(	(	PUNCT
ejpam-5280	253	29	1)-(2	1)-(2	NUM
ejpam-5280	253	30	)	)	PUNCT
ejpam-5280	253	31	on	on	ADP
ejpam-5280	253	32	[	[	X
ejpam-5280	253	33	0	0	NUM
ejpam-5280	253	34	,	,	PUNCT
ejpam-5280	253	35	1	1	NUM
ejpam-5280	253	36	]	]	PUNCT
ejpam-5280	253	37	.	.	PUNCT
ejpam-5280	254	1	theorem	theorem	ADJ
ejpam-5280	254	2	4	4	NUM
ejpam-5280	254	3	.	.	PUNCT
ejpam-5280	255	1	let	let	VERB
ejpam-5280	255	2	π1,π2	π1,π2	PRON
ejpam-5280	255	3	:	:	PUNCT
ejpam-5280	256	1	[	[	X
ejpam-5280	256	2	0	0	NUM
ejpam-5280	256	3	,	,	PUNCT
ejpam-5280	256	4	1	1	NUM
ejpam-5280	256	5	]	]	SYM
ejpam-5280	256	6	×	×	NOUN
ejpam-5280	257	1	[	[	X
ejpam-5280	257	2	0	0	NUM
ejpam-5280	257	3	,	,	PUNCT
ejpam-5280	257	4	1	1	NUM
ejpam-5280	257	5	]	]	PUNCT
ejpam-5280	257	6	→	→	SYM
ejpam-5280	257	7	ℜ	ℜ	PROPN
ejpam-5280	257	8	and	and	CCONJ
ejpam-5280	257	9	g2	g2	PROPN
ejpam-5280	257	10	:	:	PUNCT
ejpam-5280	258	1	[	[	X
ejpam-5280	258	2	0	0	NUM
ejpam-5280	258	3	,	,	PUNCT
ejpam-5280	258	4	1	1	NUM
ejpam-5280	258	5	]	]	PUNCT
ejpam-5280	258	6	→	→	PUNCT
ejpam-5280	258	7	ℜ	ℜ	PROPN
ejpam-5280	258	8	be	be	AUX
ejpam-5280	258	9	continuous	continuous	ADJ
ejpam-5280	258	10	functions	function	NOUN
ejpam-5280	258	11	which	which	PRON
ejpam-5280	258	12	are	be	AUX
ejpam-5280	258	13	bounded	bound	VERB
ejpam-5280	258	14	by	by	ADP
ejpam-5280	258	15	q1	q1	PROPN
ejpam-5280	258	16	and	and	CCONJ
ejpam-5280	258	17	q2	q2	NOUN
ejpam-5280	258	18	,	,	PUNCT
ejpam-5280	258	19	respectively	respectively	ADV
ejpam-5280	258	20	,	,	PUNCT
ejpam-5280	258	21	g3	g3	NOUN
ejpam-5280	258	22	,	,	PUNCT
ejpam-5280	258	23	g4	g4	NOUN
ejpam-5280	258	24	:	:	PUNCT
ejpam-5280	258	25	ℜ	ℜ	ADJ
ejpam-5280	258	26	→	→	SYM
ejpam-5280	258	27	ℜ	ℜ	PROPN
ejpam-5280	258	28	be	be	AUX
ejpam-5280	258	29	continuous	continuous	ADJ
ejpam-5280	258	30	lipschitz	lipschitz	NOUN
ejpam-5280	258	31	functions	function	NOUN
ejpam-5280	258	32	with	with	ADP
ejpam-5280	258	33	lipschitz	lipschitz	NOUN
ejpam-5280	258	34	constants	constant	NOUN
ejpam-5280	258	35	l3	l3	PROPN
ejpam-5280	258	36	and	and	CCONJ
ejpam-5280	258	37	l4	l4	PROPN
ejpam-5280	258	38	,	,	PUNCT
ejpam-5280	258	39	respectively	respectively	ADV
ejpam-5280	258	40	,	,	PUNCT
ejpam-5280	258	41	and	and	CCONJ
ejpam-5280	258	42	g1	g1	VERB
ejpam-5280	258	43	:	:	PUNCT
ejpam-5280	259	1	[	[	X
ejpam-5280	259	2	0	0	NUM
ejpam-5280	259	3	,	,	PUNCT
ejpam-5280	259	4	1	1	NUM
ejpam-5280	259	5	]	]	PUNCT
ejpam-5280	259	6	×	×	PROPN
ejpam-5280	259	7	ℜ	ℜ	PROPN
ejpam-5280	259	8	→	→	SYM
ejpam-5280	259	9	ℜ	ℜ	PROPN
ejpam-5280	259	10	be	be	AUX
ejpam-5280	259	11	continuous	continuous	ADJ
ejpam-5280	259	12	lipschitz	lipschitz	NOUN
ejpam-5280	259	13	function	function	NOUN
ejpam-5280	259	14	with	with	ADP
ejpam-5280	259	15	respect	respect	NOUN
ejpam-5280	259	16	to	to	ADP
ejpam-5280	259	17	the	the	DET
ejpam-5280	259	18	second	second	ADJ
ejpam-5280	259	19	component	component	NOUN
ejpam-5280	259	20	with	with	ADP
ejpam-5280	259	21	lipschitz	lipschitz	NOUN
ejpam-5280	259	22	constant	constant	ADJ
ejpam-5280	259	23	l1	l1	PROPN
ejpam-5280	259	24	,	,	PUNCT
ejpam-5280	259	25	then	then	ADV
ejpam-5280	259	26	the	the	DET
ejpam-5280	259	27	sequence	sequence	NOUN
ejpam-5280	259	28	{	{	PUNCT
ejpam-5280	259	29	m−1∑	m−1∑	PROPN
ejpam-5280	259	30	i=0	i=0	ADJ
ejpam-5280	259	31	ωiγi(t	ωiγi(t	NOUN
ejpam-5280	259	32	)	)	PUNCT
ejpam-5280	259	33	}	}	PUNCT
ejpam-5280	259	34	∞	∞	PROPN
ejpam-5280	259	35	m=0	m=0	PROPN
ejpam-5280	259	36	(	(	PUNCT
ejpam-5280	259	37	53	53	NUM
ejpam-5280	259	38	)	)	PUNCT
ejpam-5280	259	39	converges	converge	VERB
ejpam-5280	259	40	to	to	ADP
ejpam-5280	259	41	the	the	DET
ejpam-5280	259	42	unique	unique	ADJ
ejpam-5280	259	43	solution	solution	NOUN
ejpam-5280	259	44	of	of	ADP
ejpam-5280	259	45	problem	problem	NOUN
ejpam-5280	259	46	(	(	PUNCT
ejpam-5280	259	47	1)-(2	1)-(2	NUM
ejpam-5280	259	48	)	)	PUNCT
ejpam-5280	259	49	if	if	SCONJ
ejpam-5280	259	50	l1(µ+	l1(µ+	PROPN
ejpam-5280	259	51	1	1	NUM
ejpam-5280	259	52	)	)	PUNCT
ejpam-5280	259	53	+	+	CCONJ
ejpam-5280	259	54	(	(	PUNCT
ejpam-5280	259	55	l3q1	l3q1	X
ejpam-5280	259	56	+	+	CCONJ
ejpam-5280	259	57	l4q2	l4q2	NOUN
ejpam-5280	259	58	)	)	PUNCT
ejpam-5280	259	59	γ(µ+	γ(µ+	X
ejpam-5280	259	60	2	2	X
ejpam-5280	259	61	)	)	PUNCT
ejpam-5280	259	62	<	<	X
ejpam-5280	259	63	1	1	X
ejpam-5280	259	64	.	.	PUNCT
ejpam-5280	259	65	(	(	PUNCT
ejpam-5280	259	66	54	54	NUM
ejpam-5280	259	67	)	)	PUNCT
ejpam-5280	259	68	m.i	m.i	PROPN
ejpam-5280	259	69	.	.	PROPN
ejpam-5280	259	70	syam	syam	PROPN
ejpam-5280	259	71	,	,	PUNCT
ejpam-5280	259	72	m.	m.	NOUN
ejpam-5280	259	73	sharadga	sharadga	PROPN
ejpam-5280	259	74	,	,	PUNCT
ejpam-5280	259	75	i.	i.	PROPN
ejpam-5280	259	76	hashim	hashim	PROPN
ejpam-5280	259	77	/	/	SYM
ejpam-5280	259	78	eur	eur	PROPN
ejpam-5280	259	79	.	.	PUNCT
ejpam-5280	260	1	j.	j.	PROPN
ejpam-5280	260	2	pure	pure	PROPN
ejpam-5280	260	3	appl	appl	PROPN
ejpam-5280	260	4	.	.	PROPN
ejpam-5280	260	5	math	math	PROPN
ejpam-5280	260	6	,	,	PUNCT
ejpam-5280	260	7	17	17	NUM
ejpam-5280	260	8	(	(	PUNCT
ejpam-5280	260	9	3	3	NUM
ejpam-5280	260	10	)	)	PUNCT
ejpam-5280	260	11	(	(	PUNCT
ejpam-5280	260	12	2024	2024	NUM
ejpam-5280	260	13	)	)	PUNCT
ejpam-5280	260	14	,	,	PUNCT
ejpam-5280	260	15	1429	1429	NUM
ejpam-5280	260	16	-	-	SYM
ejpam-5280	260	17	1448	1448	NUM
ejpam-5280	260	18	1440	1440	NUM
ejpam-5280	260	19	proof	proof	NOUN
ejpam-5280	260	20	.	.	PUNCT
ejpam-5280	261	1	let	let	VERB
ejpam-5280	261	2	ω(t	ω(t	NOUN
ejpam-5280	261	3	)	)	PUNCT
ejpam-5280	261	4	be	be	AUX
ejpam-5280	261	5	the	the	DET
ejpam-5280	261	6	exact	exact	ADJ
ejpam-5280	261	7	solution	solution	NOUN
ejpam-5280	261	8	of	of	ADP
ejpam-5280	261	9	problem	problem	NOUN
ejpam-5280	261	10	(	(	PUNCT
ejpam-5280	261	11	1)-(2	1)-(2	NUM
ejpam-5280	261	12	)	)	PUNCT
ejpam-5280	261	13	.	.	PUNCT
ejpam-5280	262	1	using	use	VERB
ejpam-5280	262	2	lemma	lemma	PROPN
ejpam-5280	262	3	(	(	PUNCT
ejpam-5280	262	4	2	2	NUM
ejpam-5280	262	5	)	)	PUNCT
ejpam-5280	262	6	,	,	PUNCT
ejpam-5280	262	7	ω	ω	PROPN
ejpam-5280	262	8	can	can	AUX
ejpam-5280	262	9	be	be	AUX
ejpam-5280	262	10	written	write	VERB
ejpam-5280	262	11	as	as	ADP
ejpam-5280	262	12	ω(t	ω(t	NOUN
ejpam-5280	262	13	)	)	PUNCT
ejpam-5280	262	14	=	=	PUNCT
ejpam-5280	263	1	∞∑	∞∑	NUM
ejpam-5280	263	2	i=0	i=0	ADJ
ejpam-5280	263	3	ωiγi(t	ωiγi(t	NOUN
ejpam-5280	263	4	)	)	PUNCT
ejpam-5280	263	5	.	.	PUNCT
ejpam-5280	264	1	(	(	PUNCT
ejpam-5280	264	2	55	55	NUM
ejpam-5280	264	3	)	)	PUNCT
ejpam-5280	264	4	for	for	ADP
ejpam-5280	264	5	any	any	DET
ejpam-5280	264	6	0	0	NUM
ejpam-5280	264	7	≤	≤	NOUN
ejpam-5280	264	8	i	i	PRON
ejpam-5280	264	9	,	,	PUNCT
ejpam-5280	264	10	j	j	PROPN
ejpam-5280	264	11	≤	≤	PROPN
ejpam-5280	264	12	m	m	VERB
ejpam-5280	264	13	−	−	PROPN
ejpam-5280	264	14	1	1	NUM
ejpam-5280	264	15	,	,	PUNCT
ejpam-5280	264	16	we	we	PRON
ejpam-5280	264	17	have	have	VERB
ejpam-5280	264	18	γi(tj	γi(tj	NUM
ejpam-5280	264	19	)	)	PUNCT
ejpam-5280	265	1	=	=	PRON
ejpam-5280	265	2	{	{	PUNCT
ejpam-5280	265	3	1	1	NUM
ejpam-5280	265	4	,	,	PUNCT
ejpam-5280	265	5	i	i	PRON
ejpam-5280	265	6	=	=	PUNCT
ejpam-5280	265	7	j	j	PROPN
ejpam-5280	265	8	0	0	NUM
ejpam-5280	265	9	,	,	PUNCT
ejpam-5280	265	10	i	i	PRON
ejpam-5280	265	11	̸=	̸=	PROPN
ejpam-5280	265	12	j	j	PROPN
ejpam-5280	265	13	.	.	PUNCT
ejpam-5280	266	1	(	(	PUNCT
ejpam-5280	266	2	56	56	NUM
ejpam-5280	266	3	)	)	PUNCT
ejpam-5280	266	4	then	then	ADV
ejpam-5280	266	5	,	,	PUNCT
ejpam-5280	266	6	ω(tj	ω(tj	PROPN
ejpam-5280	266	7	)	)	PUNCT
ejpam-5280	266	8	=	=	PUNCT
ejpam-5280	267	1	∞∑	∞∑	NUM
ejpam-5280	267	2	i=0	i=0	PROPN
ejpam-5280	267	3	ωiγi(tj	ωiγi(tj	NOUN
ejpam-5280	267	4	)	)	PUNCT
ejpam-5280	267	5	=	=	SYM
ejpam-5280	267	6	ωj	ωj	PROPN
ejpam-5280	267	7	.	.	PUNCT
ejpam-5280	268	1	(	(	PUNCT
ejpam-5280	268	2	57	57	NUM
ejpam-5280	268	3	)	)	PUNCT
ejpam-5280	268	4	using	use	VERB
ejpam-5280	268	5	equation	equation	NOUN
ejpam-5280	268	6	(	(	PUNCT
ejpam-5280	268	7	49	49	NUM
ejpam-5280	268	8	)	)	PUNCT
ejpam-5280	268	9	and	and	CCONJ
ejpam-5280	268	10	(	(	PUNCT
ejpam-5280	268	11	57	57	NUM
ejpam-5280	268	12	)	)	PUNCT
ejpam-5280	268	13	,	,	PUNCT
ejpam-5280	268	14	we	we	PRON
ejpam-5280	268	15	have	have	VERB
ejpam-5280	268	16	ωj	ωj	ADP
ejpam-5280	268	17	=	=	VERB
ejpam-5280	268	18	ω0	ω0	ADV
ejpam-5280	268	19	+	+	NOUN
ejpam-5280	268	20	1	1	NUM
ejpam-5280	268	21	γ(µ	γ(µ	PROPN
ejpam-5280	268	22	)	)	PUNCT
ejpam-5280	268	23	∫	∫	PROPN
ejpam-5280	269	1	tj	tj	NOUN
ejpam-5280	269	2	0	0	NUM
ejpam-5280	269	3	(	(	PUNCT
ejpam-5280	269	4	g1(z	g1(z	PROPN
ejpam-5280	269	5	,	,	PUNCT
ejpam-5280	269	6	ω(z	ω(z	NUM
ejpam-5280	269	7	)	)	PUNCT
ejpam-5280	269	8	)	)	PUNCT
ejpam-5280	270	1	+	+	PUNCT
ejpam-5280	270	2	g2(z	g2(z	X
ejpam-5280	270	3	)	)	PUNCT
ejpam-5280	270	4	+	+	NUM
ejpam-5280	270	5	∫	∫	PROPN
ejpam-5280	270	6	z	z	NOUN
ejpam-5280	270	7	0	0	NUM
ejpam-5280	270	8	π1(z	π1(z	PROPN
ejpam-5280	270	9	,	,	PUNCT
ejpam-5280	270	10	s)g3(ω(s))ds	s)g3(ω(s))ds	PROPN
ejpam-5280	270	11	)	)	PUNCT
ejpam-5280	270	12	(	(	PUNCT
ejpam-5280	270	13	t−	t−	PROPN
ejpam-5280	270	14	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	270	15	+	+	CCONJ
ejpam-5280	270	16	1	1	NUM
ejpam-5280	270	17	γ(µ	γ(µ	PROPN
ejpam-5280	270	18	)	)	PUNCT
ejpam-5280	270	19	∫	∫	PROPN
ejpam-5280	271	1	tj	tj	PROPN
ejpam-5280	271	2	0	0	PROPN
ejpam-5280	271	3	(	(	PUNCT
ejpam-5280	271	4	∫	∫	PROPN
ejpam-5280	271	5	1	1	NUM
ejpam-5280	271	6	0	0	NUM
ejpam-5280	271	7	π2(z	π2(z	NOUN
ejpam-5280	271	8	,	,	PUNCT
ejpam-5280	271	9	s)g4(ω(s))ds	s)g4(ω(s))ds	PROPN
ejpam-5280	271	10	)	)	PUNCT
ejpam-5280	271	11	(	(	PUNCT
ejpam-5280	271	12	t−	t−	PROPN
ejpam-5280	271	13	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	271	14	.	.	PUNCT
ejpam-5280	272	1	(	(	PUNCT
ejpam-5280	272	2	58	58	X
ejpam-5280	272	3	)	)	PUNCT
ejpam-5280	272	4	let	let	VERB
ejpam-5280	272	5	ωm	ωm	X
ejpam-5280	272	6	(	(	PUNCT
ejpam-5280	272	7	t	t	NOUN
ejpam-5280	272	8	)	)	PUNCT
ejpam-5280	272	9	be	be	VERB
ejpam-5280	272	10	the	the	DET
ejpam-5280	272	11	approximate	approximate	ADJ
ejpam-5280	272	12	solution	solution	NOUN
ejpam-5280	272	13	of	of	ADP
ejpam-5280	272	14	problem	problem	NOUN
ejpam-5280	272	15	(	(	PUNCT
ejpam-5280	272	16	1)-(2	1)-(2	NUM
ejpam-5280	272	17	)	)	PUNCT
ejpam-5280	272	18	.	.	PUNCT
ejpam-5280	273	1	then	then	ADV
ejpam-5280	273	2	,	,	PUNCT
ejpam-5280	273	3	ωm	ωm	X
ejpam-5280	273	4	(	(	PUNCT
ejpam-5280	273	5	t	t	NOUN
ejpam-5280	273	6	)	)	PUNCT
ejpam-5280	273	7	=	=	PUNCT
ejpam-5280	273	8	m−1∑	m−1∑	NUM
ejpam-5280	273	9	i=0	i=0	PROPN
ejpam-5280	273	10	ωiγi(t	ωiγi(t	NOUN
ejpam-5280	273	11	)	)	PUNCT
ejpam-5280	273	12	.	.	PUNCT
ejpam-5280	274	1	(	(	PUNCT
ejpam-5280	274	2	59	59	NUM
ejpam-5280	274	3	)	)	PUNCT
ejpam-5280	274	4	using	use	VERB
ejpam-5280	274	5	previous	previous	ADJ
ejpam-5280	274	6	argument	argument	NOUN
ejpam-5280	274	7	,	,	PUNCT
ejpam-5280	274	8	we	we	PRON
ejpam-5280	274	9	have	have	VERB
ejpam-5280	274	10	ωj	ωj	ADP
ejpam-5280	274	11	=	=	VERB
ejpam-5280	274	12	ω0	ω0	ADV
ejpam-5280	274	13	+	+	NOUN
ejpam-5280	274	14	1	1	NUM
ejpam-5280	274	15	γ(µ	γ(µ	PROPN
ejpam-5280	274	16	)	)	PUNCT
ejpam-5280	274	17	∫	∫	PROPN
ejpam-5280	275	1	tj	tj	NOUN
ejpam-5280	275	2	0	0	NUM
ejpam-5280	275	3	(	(	PUNCT
ejpam-5280	275	4	g1(z	g1(z	PROPN
ejpam-5280	275	5	,	,	PUNCT
ejpam-5280	275	6	ωm	ωm	X
ejpam-5280	275	7	(	(	PUNCT
ejpam-5280	275	8	z	z	NOUN
ejpam-5280	275	9	)	)	PUNCT
ejpam-5280	275	10	)	)	PUNCT
ejpam-5280	276	1	+	+	PUNCT
ejpam-5280	276	2	g2(z	g2(z	X
ejpam-5280	276	3	)	)	PUNCT
ejpam-5280	276	4	+	+	NUM
ejpam-5280	276	5	∫	∫	PROPN
ejpam-5280	276	6	z	z	NOUN
ejpam-5280	276	7	0	0	NUM
ejpam-5280	276	8	π1(z	π1(z	PROPN
ejpam-5280	276	9	,	,	PUNCT
ejpam-5280	276	10	s)g3(ωm	s)g3(ωm	PROPN
ejpam-5280	276	11	(	(	PUNCT
ejpam-5280	276	12	s))ds	s))ds	NOUN
ejpam-5280	276	13	)	)	PUNCT
ejpam-5280	276	14	(	(	PUNCT
ejpam-5280	276	15	t−	t−	PROPN
ejpam-5280	276	16	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	276	17	+	+	CCONJ
ejpam-5280	276	18	1	1	NUM
ejpam-5280	276	19	γ(µ	γ(µ	PROPN
ejpam-5280	276	20	)	)	PUNCT
ejpam-5280	276	21	∫	∫	PROPN
ejpam-5280	277	1	tj	tj	PROPN
ejpam-5280	277	2	0	0	PROPN
ejpam-5280	277	3	(	(	PUNCT
ejpam-5280	277	4	∫	∫	PROPN
ejpam-5280	277	5	1	1	NUM
ejpam-5280	277	6	0	0	NUM
ejpam-5280	277	7	π2(z	π2(z	NOUN
ejpam-5280	277	8	,	,	PUNCT
ejpam-5280	277	9	s)g4(ωm	s)g4(ωm	PROPN
ejpam-5280	277	10	(	(	PUNCT
ejpam-5280	277	11	s))ds	s))ds	NOUN
ejpam-5280	277	12	)	)	PUNCT
ejpam-5280	277	13	(	(	PUNCT
ejpam-5280	277	14	t−	t−	PROPN
ejpam-5280	277	15	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	277	16	.	.	PUNCT
ejpam-5280	278	1	(	(	PUNCT
ejpam-5280	278	2	60	60	NUM
ejpam-5280	278	3	)	)	PUNCT
ejpam-5280	278	4	from	from	ADP
ejpam-5280	278	5	equations	equation	NOUN
ejpam-5280	278	6	(	(	PUNCT
ejpam-5280	278	7	58	58	NUM
ejpam-5280	278	8	)	)	PUNCT
ejpam-5280	278	9	and	and	CCONJ
ejpam-5280	278	10	(	(	PUNCT
ejpam-5280	278	11	60	60	NUM
ejpam-5280	278	12	)	)	PUNCT
ejpam-5280	278	13	,	,	PUNCT
ejpam-5280	278	14	we	we	PRON
ejpam-5280	278	15	have	have	VERB
ejpam-5280	278	16	|	|	ADV
ejpam-5280	278	17	ωj	ωj	ADP
ejpam-5280	278	18	−	−	PROPN
ejpam-5280	278	19	ωj	ωj	ADP
ejpam-5280	278	20	|	|	ADV
ejpam-5280	278	21	≤	≤	ADJ
ejpam-5280	278	22	1	1	NUM
ejpam-5280	278	23	γ(µ	γ(µ	PROPN
ejpam-5280	278	24	)	)	PUNCT
ejpam-5280	279	1	|	|	ADV
ejpam-5280	279	2	∫	∫	PROPN
ejpam-5280	280	1	tj	tj	PROPN
ejpam-5280	280	2	0	0	NUM
ejpam-5280	280	3	(	(	PUNCT
ejpam-5280	280	4	g1(z	g1(z	PROPN
ejpam-5280	280	5	,	,	PUNCT
ejpam-5280	280	6	ω(z))−g1(z	ω(z))−g1(z	NOUN
ejpam-5280	280	7	,	,	PUNCT
ejpam-5280	280	8	ωm	ωm	X
ejpam-5280	280	9	(	(	PUNCT
ejpam-5280	280	10	z	z	NOUN
ejpam-5280	280	11	)	)	PUNCT
ejpam-5280	280	12	)	)	PUNCT
ejpam-5280	280	13	)	)	PUNCT
ejpam-5280	281	1	(	(	PUNCT
ejpam-5280	281	2	t−	t−	PROPN
ejpam-5280	281	3	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	281	4	|	|	ADV
ejpam-5280	281	5	+	+	CCONJ
ejpam-5280	281	6	1	1	NUM
ejpam-5280	281	7	γ(µ	γ(µ	PROPN
ejpam-5280	281	8	)	)	PUNCT
ejpam-5280	282	1	|	|	ADV
ejpam-5280	282	2	∫	∫	PROPN
ejpam-5280	283	1	tj	tj	PROPN
ejpam-5280	283	2	0	0	PROPN
ejpam-5280	283	3	∫	∫	PROPN
ejpam-5280	283	4	z	z	PROPN
ejpam-5280	283	5	0	0	NUM
ejpam-5280	283	6	π1(z	π1(z	PROPN
ejpam-5280	283	7	,	,	PUNCT
ejpam-5280	283	8	s	s	NOUN
ejpam-5280	283	9	)	)	PUNCT
ejpam-5280	283	10	(	(	PUNCT
ejpam-5280	283	11	g3(ω(s))−g3(ωm	g3(ω(s))−g3(ωm	X
ejpam-5280	283	12	(	(	PUNCT
ejpam-5280	283	13	s	s	NOUN
ejpam-5280	283	14	)	)	PUNCT
ejpam-5280	283	15	)	)	PUNCT
ejpam-5280	283	16	)	)	PUNCT
ejpam-5280	284	1	ds(t−	ds(t−	PROPN
ejpam-5280	284	2	z)µ−1dz	z)µ−1dz	NOUN
ejpam-5280	285	1	|	|	ADV
ejpam-5280	285	2	+	+	CCONJ
ejpam-5280	285	3	1	1	NUM
ejpam-5280	285	4	γ(µ	γ(µ	PROPN
ejpam-5280	285	5	)	)	PUNCT
ejpam-5280	286	1	|	|	ADV
ejpam-5280	287	1	∫	∫	PROPN
ejpam-5280	287	2	tj	tj	PROPN
ejpam-5280	287	3	0	0	PROPN
ejpam-5280	287	4	∫	∫	PROPN
ejpam-5280	287	5	1	1	NUM
ejpam-5280	287	6	0	0	NUM
ejpam-5280	287	7	π2(z	π2(z	NOUN
ejpam-5280	287	8	,	,	PUNCT
ejpam-5280	287	9	s	s	PART
ejpam-5280	287	10	)	)	PUNCT
ejpam-5280	287	11	(	(	PUNCT
ejpam-5280	287	12	g4(ω(s))−g4(ωm	g4(ω(s))−g4(ωm	PROPN
ejpam-5280	287	13	(	(	PUNCT
ejpam-5280	287	14	s	s	NOUN
ejpam-5280	287	15	)	)	PUNCT
ejpam-5280	287	16	)	)	PUNCT
ejpam-5280	287	17	)	)	PUNCT
ejpam-5280	288	1	ds(t−	ds(t−	PROPN
ejpam-5280	288	2	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	289	1	|	|	INTJ
ejpam-5280	289	2	.	.	PUNCT
ejpam-5280	290	1	thus	thus	ADV
ejpam-5280	290	2	,	,	PUNCT
ejpam-5280	290	3	|	|	ADV
ejpam-5280	290	4	ωj	ωj	ADP
ejpam-5280	290	5	−	−	PROPN
ejpam-5280	290	6	ωj	ωj	ADP
ejpam-5280	290	7	|	|	ADV
ejpam-5280	290	8	≤	≤	NUM
ejpam-5280	290	9	l1	l1	PROPN
ejpam-5280	290	10	∥	∥	PUNCT
ejpam-5280	290	11	ω−	ω−	PROPN
ejpam-5280	290	12	ωm	ωm	X
ejpam-5280	290	13	∥	∥	X
ejpam-5280	290	14	γ(µ	γ(µ	PROPN
ejpam-5280	290	15	)	)	PUNCT
ejpam-5280	291	1	|	|	ADV
ejpam-5280	291	2	∫	∫	PROPN
ejpam-5280	291	3	tj	tj	PROPN
ejpam-5280	291	4	0	0	NUM
ejpam-5280	292	1	(	(	PUNCT
ejpam-5280	292	2	tj	tj	NOUN
ejpam-5280	292	3	−	−	PROPN
ejpam-5280	292	4	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	292	5	|	|	ADV
ejpam-5280	292	6	m.i	m.i	PROPN
ejpam-5280	292	7	.	.	PROPN
ejpam-5280	292	8	syam	syam	PROPN
ejpam-5280	292	9	,	,	PUNCT
ejpam-5280	292	10	m.	m.	NOUN
ejpam-5280	292	11	sharadga	sharadga	PROPN
ejpam-5280	292	12	,	,	PUNCT
ejpam-5280	292	13	i.	i.	PROPN
ejpam-5280	292	14	hashim	hashim	PROPN
ejpam-5280	292	15	/	/	SYM
ejpam-5280	292	16	eur	eur	PROPN
ejpam-5280	292	17	.	.	PUNCT
ejpam-5280	293	1	j.	j.	PROPN
ejpam-5280	293	2	pure	pure	PROPN
ejpam-5280	293	3	appl	appl	PROPN
ejpam-5280	293	4	.	.	PROPN
ejpam-5280	293	5	math	math	PROPN
ejpam-5280	293	6	,	,	PUNCT
ejpam-5280	293	7	17	17	NUM
ejpam-5280	293	8	(	(	PUNCT
ejpam-5280	293	9	3	3	NUM
ejpam-5280	293	10	)	)	PUNCT
ejpam-5280	293	11	(	(	PUNCT
ejpam-5280	293	12	2024	2024	NUM
ejpam-5280	293	13	)	)	PUNCT
ejpam-5280	293	14	,	,	PUNCT
ejpam-5280	293	15	1429	1429	NUM
ejpam-5280	293	16	-	-	SYM
ejpam-5280	293	17	1448	1448	NUM
ejpam-5280	293	18	1441	1441	NUM
ejpam-5280	293	19	+	+	CCONJ
ejpam-5280	293	20	l3	l3	PROPN
ejpam-5280	293	21	∥	∥	NUM
ejpam-5280	293	22	ω−	ω−	PROPN
ejpam-5280	293	23	ωm	ωm	X
ejpam-5280	293	24	∥	∥	X
ejpam-5280	293	25	γ(µ	γ(µ	PROPN
ejpam-5280	293	26	)	)	PUNCT
ejpam-5280	294	1	|	|	ADV
ejpam-5280	294	2	∫	∫	PROPN
ejpam-5280	294	3	tj	tj	PROPN
ejpam-5280	294	4	0	0	PROPN
ejpam-5280	295	1	∫	∫	PROPN
ejpam-5280	295	2	z	z	PROPN
ejpam-5280	295	3	0	0	NUM
ejpam-5280	295	4	π1(z	π1(z	PROPN
ejpam-5280	295	5	,	,	PUNCT
ejpam-5280	295	6	s)ds(tj	s)ds(tj	ADJ
ejpam-5280	295	7	−	−	PROPN
ejpam-5280	295	8	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	296	1	|	|	ADV
ejpam-5280	296	2	+	+	CCONJ
ejpam-5280	296	3	l4	l4	PROPN
ejpam-5280	296	4	∥	∥	PUNCT
ejpam-5280	296	5	ω−	ω−	PROPN
ejpam-5280	296	6	ωm	ωm	PUNCT
ejpam-5280	296	7	∥	∥	X
ejpam-5280	296	8	γ(µ	γ(µ	PROPN
ejpam-5280	296	9	)	)	PUNCT
ejpam-5280	297	1	|	|	ADV
ejpam-5280	297	2	∫	∫	PROPN
ejpam-5280	297	3	tj	tj	PROPN
ejpam-5280	297	4	0	0	PROPN
ejpam-5280	297	5	∫	∫	PROPN
ejpam-5280	297	6	1	1	NUM
ejpam-5280	297	7	0	0	NUM
ejpam-5280	297	8	π2(z	π2(z	NOUN
ejpam-5280	297	9	,	,	PUNCT
ejpam-5280	297	10	s)ds(tj	s)ds(tj	ADJ
ejpam-5280	297	11	−	−	PROPN
ejpam-5280	297	12	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	297	13	|	|	ADV
ejpam-5280	297	14	.	.	PUNCT
ejpam-5280	298	1	(	(	PUNCT
ejpam-5280	298	2	61	61	NUM
ejpam-5280	298	3	)	)	PUNCT
ejpam-5280	298	4	since	since	SCONJ
ejpam-5280	298	5	π1	π1	NOUN
ejpam-5280	298	6	and	and	CCONJ
ejpam-5280	298	7	π2	π2	NOUN
ejpam-5280	298	8	are	be	AUX
ejpam-5280	298	9	continuous	continuous	ADJ
ejpam-5280	298	10	on	on	ADP
ejpam-5280	298	11	a	a	DET
ejpam-5280	298	12	compact	compact	ADJ
ejpam-5280	298	13	set	set	NOUN
ejpam-5280	298	14	[	[	X
ejpam-5280	298	15	0	0	NUM
ejpam-5280	298	16	,	,	PUNCT
ejpam-5280	298	17	1]×	1]×	NUM
ejpam-5280	299	1	[	[	X
ejpam-5280	299	2	0	0	NUM
ejpam-5280	299	3	,	,	PUNCT
ejpam-5280	299	4	1	1	NUM
ejpam-5280	299	5	]	]	PUNCT
ejpam-5280	299	6	,	,	PUNCT
ejpam-5280	299	7	then	then	ADV
ejpam-5280	299	8	|	|	ADV
ejpam-5280	299	9	ωj	ωj	ADP
ejpam-5280	299	10	−	−	PROPN
ejpam-5280	300	1	ωj	ωj	ADP
ejpam-5280	300	2	|	|	ADV
ejpam-5280	300	3	≤	≤	NUM
ejpam-5280	300	4	l1	l1	PROPN
ejpam-5280	300	5	∥	∥	PUNCT
ejpam-5280	300	6	ω−	ω−	PROPN
ejpam-5280	300	7	ωm	ωm	X
ejpam-5280	300	8	∥	∥	X
ejpam-5280	300	9	γ(µ	γ(µ	PROPN
ejpam-5280	300	10	)	)	PUNCT
ejpam-5280	301	1	|	|	ADV
ejpam-5280	301	2	∫	∫	PROPN
ejpam-5280	301	3	tj	tj	PROPN
ejpam-5280	301	4	0	0	NUM
ejpam-5280	302	1	(	(	PUNCT
ejpam-5280	302	2	tj	tj	NOUN
ejpam-5280	302	3	−	−	PROPN
ejpam-5280	302	4	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	303	1	|	|	ADV
ejpam-5280	304	1	+	+	CCONJ
ejpam-5280	304	2	l3q1	l3q1	NOUN
ejpam-5280	304	3	∥	∥	NUM
ejpam-5280	304	4	ω−	ω−	ADJ
ejpam-5280	304	5	ωm	ωm	PUNCT
ejpam-5280	304	6	∥	∥	X
ejpam-5280	304	7	γ(µ	γ(µ	PROPN
ejpam-5280	304	8	)	)	PUNCT
ejpam-5280	305	1	|	|	ADV
ejpam-5280	305	2	∫	∫	PROPN
ejpam-5280	305	3	tj	tj	PROPN
ejpam-5280	305	4	0	0	PROPN
ejpam-5280	305	5	∫	∫	PROPN
ejpam-5280	305	6	z	z	PROPN
ejpam-5280	305	7	0	0	PROPN
ejpam-5280	306	1	ds(tj	ds(tj	NOUN
ejpam-5280	306	2	−	−	PROPN
ejpam-5280	306	3	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	307	1	|	|	ADV
ejpam-5280	308	1	+	+	CCONJ
ejpam-5280	308	2	l4q2	l4q2	NOUN
ejpam-5280	308	3	∥	∥	PUNCT
ejpam-5280	308	4	ω−	ω−	ADJ
ejpam-5280	308	5	ωm	ωm	X
ejpam-5280	308	6	∥	∥	X
ejpam-5280	308	7	γ(µ	γ(µ	PROPN
ejpam-5280	308	8	)	)	PUNCT
ejpam-5280	309	1	|	|	ADV
ejpam-5280	309	2	∫	∫	PROPN
ejpam-5280	309	3	tj	tj	PROPN
ejpam-5280	309	4	0	0	PROPN
ejpam-5280	309	5	∫	∫	PROPN
ejpam-5280	309	6	1	1	NUM
ejpam-5280	309	7	0	0	X
ejpam-5280	309	8	ds(tj	ds(tj	NOUN
ejpam-5280	309	9	−	−	PROPN
ejpam-5280	309	10	z)µ−1dz	z)µ−1dz	PROPN
ejpam-5280	310	1	|	|	ADV
ejpam-5280	310	2	≤	≤	PROPN
ejpam-5280	310	3	(	(	PUNCT
ejpam-5280	310	4	l1tj	l1tj	X
ejpam-5280	310	5	µ	µ	X
ejpam-5280	310	6	γ(µ+	γ(µ+	X
ejpam-5280	310	7	1	1	NUM
ejpam-5280	310	8	)	)	PUNCT
ejpam-5280	310	9	+	+	CCONJ
ejpam-5280	310	10	(	(	PUNCT
ejpam-5280	310	11	l3q1	l3q1	NOUN
ejpam-5280	311	1	+	+	CCONJ
ejpam-5280	311	2	l4q2)tj	l4q2)tj	NOUN
ejpam-5280	311	3	µ+1	µ+1	NOUN
ejpam-5280	311	4	γ(µ+	γ(µ+	X
ejpam-5280	311	5	2	2	NUM
ejpam-5280	311	6	)	)	PUNCT
ejpam-5280	311	7	)	)	PUNCT
ejpam-5280	312	1	∥	∥	PUNCT
ejpam-5280	312	2	ω−	ω−	VERB
ejpam-5280	312	3	ωm	ωm	PUNCT
ejpam-5280	312	4	∥	∥	PUNCT
ejpam-5280	312	5	≤	≤	NOUN
ejpam-5280	312	6	(	(	PUNCT
ejpam-5280	312	7	l1(µ+	l1(µ+	PROPN
ejpam-5280	312	8	1	1	NUM
ejpam-5280	312	9	)	)	PUNCT
ejpam-5280	312	10	+	+	CCONJ
ejpam-5280	312	11	(	(	PUNCT
ejpam-5280	312	12	l3q1	l3q1	X
ejpam-5280	312	13	+	+	CCONJ
ejpam-5280	312	14	l4q2	l4q2	NOUN
ejpam-5280	312	15	)	)	PUNCT
ejpam-5280	312	16	γ(µ+	γ(µ+	X
ejpam-5280	312	17	2	2	NUM
ejpam-5280	312	18	)	)	PUNCT
ejpam-5280	312	19	)	)	PUNCT
ejpam-5280	312	20	∥	∥	PUNCT
ejpam-5280	312	21	ω−	ω−	X
ejpam-5280	312	22	ωm	ωm	PUNCT
ejpam-5280	312	23	∥	∥	X
ejpam-5280	312	24	.	.	PUNCT
ejpam-5280	313	1	(	(	PUNCT
ejpam-5280	313	2	62	62	NUM
ejpam-5280	313	3	)	)	PUNCT
ejpam-5280	313	4	therefore	therefore	ADV
ejpam-5280	313	5	,	,	PUNCT
ejpam-5280	313	6	|	|	ADV
ejpam-5280	313	7	ω(t)−	ω(t)−	PROPN
ejpam-5280	313	8	ωm	ωm	NUM
ejpam-5280	313	9	(	(	PUNCT
ejpam-5280	313	10	t	t	NOUN
ejpam-5280	313	11	)	)	PUNCT
ejpam-5280	314	1	|	|	NOUN
ejpam-5280	315	1	=	=	SYM
ejpam-5280	316	1	∥	∥	PROPN
ejpam-5280	317	1	m−1∑	m−1∑	X
ejpam-5280	318	1	i=0	i=0	X
ejpam-5280	319	1	(	(	PUNCT
ejpam-5280	319	2	ωi	ωi	NOUN
ejpam-5280	319	3	−	−	PROPN
ejpam-5280	319	4	ωi)γi(t	ωi)γi(t	PROPN
ejpam-5280	319	5	)	)	PUNCT
ejpam-5280	320	1	+	+	CCONJ
ejpam-5280	321	1	∞∑	∞∑	NUM
ejpam-5280	321	2	j	j	X
ejpam-5280	321	3	=	=	NOUN
ejpam-5280	321	4	m	m	NOUN
ejpam-5280	321	5	ωjγj(t)∥	ωjγj(t)∥	NOUN
ejpam-5280	321	6	≤	≤	NUM
ejpam-5280	321	7	∥	∥	X
ejpam-5280	321	8	m−1∑	m−1∑	X
ejpam-5280	321	9	i=0	i=0	X
ejpam-5280	321	10	(	(	PUNCT
ejpam-5280	321	11	ωi	ωi	NOUN
ejpam-5280	321	12	−	−	NOUN
ejpam-5280	321	13	ωi)γi(t)∥+	ωi)γi(t)∥+	ADJ
ejpam-5280	321	14	∥	∥	X
ejpam-5280	322	1	∞∑	∞∑	NUM
ejpam-5280	322	2	j	j	NOUN
ejpam-5280	322	3	=	=	NOUN
ejpam-5280	322	4	m	m	PROPN
ejpam-5280	322	5	ωjγj(t)∥	ωjγj(t)∥	NOUN
ejpam-5280	322	6	≤	≤	NUM
ejpam-5280	322	7	m−1∑	m−1∑	NUM
ejpam-5280	322	8	i=0	i=0	PROPN
ejpam-5280	322	9	(	(	PUNCT
ejpam-5280	322	10	l1(µ+	l1(µ+	PROPN
ejpam-5280	322	11	1	1	NUM
ejpam-5280	322	12	)	)	PUNCT
ejpam-5280	322	13	+	+	CCONJ
ejpam-5280	322	14	(	(	PUNCT
ejpam-5280	322	15	l3q1	l3q1	X
ejpam-5280	322	16	+	+	CCONJ
ejpam-5280	322	17	l4q2	l4q2	NOUN
ejpam-5280	322	18	)	)	PUNCT
ejpam-5280	322	19	γ(µ+	γ(µ+	X
ejpam-5280	322	20	2	2	NUM
ejpam-5280	322	21	)	)	PUNCT
ejpam-5280	322	22	)	)	PUNCT
ejpam-5280	322	23	∥	∥	PUNCT
ejpam-5280	322	24	ω−	ω−	X
ejpam-5280	322	25	ωm	ωm	PUNCT
ejpam-5280	322	26	∥	∥	X
ejpam-5280	322	27	+	+	NUM
ejpam-5280	322	28	∥	∥	NOUN
ejpam-5280	322	29	∞∑	∞∑	NUM
ejpam-5280	322	30	j	j	PROPN
ejpam-5280	322	31	=	=	NOUN
ejpam-5280	322	32	m	m	NOUN
ejpam-5280	322	33	ωjγj(t	ωjγj(t	NOUN
ejpam-5280	322	34	)	)	PUNCT
ejpam-5280	322	35	∥	∥	PUNCT
ejpam-5280	322	36	.	.	PUNCT
ejpam-5280	323	1	since	since	SCONJ
ejpam-5280	323	2	the	the	DET
ejpam-5280	323	3	series	series	NOUN
ejpam-5280	323	4	in	in	ADP
ejpam-5280	323	5	equation	equation	NOUN
ejpam-5280	323	6	(	(	PUNCT
ejpam-5280	323	7	55	55	NUM
ejpam-5280	323	8	)	)	PUNCT
ejpam-5280	323	9	converges	converge	VERB
ejpam-5280	323	10	uniformly	uniformly	ADV
ejpam-5280	323	11	in	in	ADP
ejpam-5280	323	12	[	[	X
ejpam-5280	323	13	0	0	NUM
ejpam-5280	323	14	,	,	PUNCT
ejpam-5280	323	15	1	1	NUM
ejpam-5280	323	16	]	]	PUNCT
ejpam-5280	323	17	,	,	PUNCT
ejpam-5280	323	18	then	then	ADV
ejpam-5280	323	19	for	for	ADP
ejpam-5280	323	20	ϵ	ϵ	PROPN
ejpam-5280	323	21	=	=	SYM
ejpam-5280	323	22	1	1	NUM
ejpam-5280	323	23	,	,	PUNCT
ejpam-5280	323	24	there	there	PRON
ejpam-5280	323	25	exist	exist	VERB
ejpam-5280	323	26	positive	positive	ADJ
ejpam-5280	323	27	integer	integer	NOUN
ejpam-5280	323	28	n1	n1	NOUN
ejpam-5280	323	29	such	such	ADJ
ejpam-5280	323	30	that	that	SCONJ
ejpam-5280	323	31	∥	∥	X
ejpam-5280	324	1	∞∑	∞∑	NUM
ejpam-5280	324	2	j	j	X
ejpam-5280	324	3	=	=	NOUN
ejpam-5280	324	4	m	m	NOUN
ejpam-5280	324	5	ωjγj(t	ωjγj(t	NOUN
ejpam-5280	324	6	)	)	PUNCT
ejpam-5280	324	7	∥≤	∥≤	PROPN
ejpam-5280	324	8	1	1	NUM
ejpam-5280	324	9	,	,	PUNCT
ejpam-5280	324	10	m	m	NOUN
ejpam-5280	324	11	≥	≥	NOUN
ejpam-5280	324	12	n1	n1	NOUN
ejpam-5280	324	13	,	,	PUNCT
ejpam-5280	324	14	t	t	PROPN
ejpam-5280	324	15	∈	∈	PROPN
ejpam-5280	325	1	[	[	X
ejpam-5280	325	2	0	0	NUM
ejpam-5280	325	3	,	,	PUNCT
ejpam-5280	325	4	1	1	NUM
ejpam-5280	325	5	]	]	PUNCT
ejpam-5280	325	6	.	.	PUNCT
ejpam-5280	326	1	(	(	PUNCT
ejpam-5280	326	2	63	63	NUM
ejpam-5280	326	3	)	)	PUNCT
ejpam-5280	326	4	therefore	therefore	ADV
ejpam-5280	326	5	,	,	PUNCT
ejpam-5280	326	6	|	|	ADV
ejpam-5280	326	7	ω(t)−	ω(t)−	PROPN
ejpam-5280	326	8	ωm	ωm	NUM
ejpam-5280	326	9	(	(	PUNCT
ejpam-5280	326	10	t	t	NOUN
ejpam-5280	326	11	)	)	PUNCT
ejpam-5280	326	12	|	|	ADV
ejpam-5280	326	13	≤	≤	NUM
ejpam-5280	326	14	(	(	PUNCT
ejpam-5280	326	15	l1(µ+	l1(µ+	PROPN
ejpam-5280	326	16	1	1	NUM
ejpam-5280	326	17	)	)	PUNCT
ejpam-5280	326	18	+	+	CCONJ
ejpam-5280	326	19	(	(	PUNCT
ejpam-5280	326	20	l3q1	l3q1	X
ejpam-5280	326	21	+	+	NUM
ejpam-5280	326	22	l4q2)m	l4q2)m	NOUN
ejpam-5280	326	23	γ(µ+	γ(µ+	X
ejpam-5280	326	24	2	2	NUM
ejpam-5280	326	25	)	)	PUNCT
ejpam-5280	326	26	)	)	PUNCT
ejpam-5280	327	1	∥	∥	PUNCT
ejpam-5280	327	2	ω−	ω−	VERB
ejpam-5280	327	3	ωm	ωm	PUNCT
ejpam-5280	327	4	∥	∥	X
ejpam-5280	327	5	+1	+1	X
ejpam-5280	327	6	.	.	PUNCT
ejpam-5280	328	1	(	(	PUNCT
ejpam-5280	328	2	64	64	NUM
ejpam-5280	328	3	)	)	PUNCT
ejpam-5280	328	4	take	take	VERB
ejpam-5280	328	5	the	the	DET
ejpam-5280	328	6	supreme	supreme	NOUN
ejpam-5280	328	7	over	over	ADP
ejpam-5280	328	8	[	[	X
ejpam-5280	328	9	0	0	NUM
ejpam-5280	328	10	,	,	PUNCT
ejpam-5280	328	11	1	1	NUM
ejpam-5280	328	12	]	]	PUNCT
ejpam-5280	328	13	to	to	PART
ejpam-5280	328	14	get	get	VERB
ejpam-5280	328	15	∥	∥	PRON
ejpam-5280	328	16	ω−	ω−	VERB
ejpam-5280	328	17	ωm	ωm	PUNCT
ejpam-5280	328	18	∥	∥	PUNCT
ejpam-5280	328	19	≤	≤	NOUN
ejpam-5280	328	20	(	(	PUNCT
ejpam-5280	328	21	l1(µ+	l1(µ+	PROPN
ejpam-5280	328	22	1	1	NUM
ejpam-5280	328	23	)	)	PUNCT
ejpam-5280	328	24	+	+	CCONJ
ejpam-5280	328	25	(	(	PUNCT
ejpam-5280	328	26	l3q1	l3q1	X
ejpam-5280	329	1	+	+	NUM
ejpam-5280	329	2	l4q2)m	l4q2)m	NOUN
ejpam-5280	329	3	γ(µ+	γ(µ+	X
ejpam-5280	329	4	2	2	NUM
ejpam-5280	329	5	)	)	PUNCT
ejpam-5280	329	6	)	)	PUNCT
ejpam-5280	329	7	∥	∥	PUNCT
ejpam-5280	329	8	ω−	ω−	VERB
ejpam-5280	329	9	ωm	ωm	PUNCT
ejpam-5280	329	10	∥	∥	X
ejpam-5280	329	11	+1	+1	X
ejpam-5280	329	12	(	(	PUNCT
ejpam-5280	329	13	65	65	NUM
ejpam-5280	329	14	)	)	PUNCT
ejpam-5280	329	15	m.i	m.i	PROPN
ejpam-5280	329	16	.	.	PROPN
ejpam-5280	329	17	syam	syam	PROPN
ejpam-5280	329	18	,	,	PUNCT
ejpam-5280	329	19	m.	m.	NOUN
ejpam-5280	329	20	sharadga	sharadga	PROPN
ejpam-5280	329	21	,	,	PUNCT
ejpam-5280	329	22	i.	i.	PROPN
ejpam-5280	329	23	hashim	hashim	PROPN
ejpam-5280	329	24	/	/	SYM
ejpam-5280	329	25	eur	eur	PROPN
ejpam-5280	329	26	.	.	PUNCT
ejpam-5280	330	1	j.	j.	PROPN
ejpam-5280	330	2	pure	pure	PROPN
ejpam-5280	330	3	appl	appl	PROPN
ejpam-5280	330	4	.	.	PROPN
ejpam-5280	330	5	math	math	PROPN
ejpam-5280	330	6	,	,	PUNCT
ejpam-5280	330	7	17	17	NUM
ejpam-5280	330	8	(	(	PUNCT
ejpam-5280	330	9	3	3	NUM
ejpam-5280	330	10	)	)	PUNCT
ejpam-5280	330	11	(	(	PUNCT
ejpam-5280	330	12	2024	2024	NUM
ejpam-5280	330	13	)	)	PUNCT
ejpam-5280	330	14	,	,	PUNCT
ejpam-5280	330	15	1429	1429	NUM
ejpam-5280	330	16	-	-	SYM
ejpam-5280	330	17	1448	1448	NUM
ejpam-5280	330	18	1442	1442	NUM
ejpam-5280	330	19	which	which	PRON
ejpam-5280	330	20	can	can	AUX
ejpam-5280	330	21	simplify	simplify	VERB
ejpam-5280	330	22	as	as	ADP
ejpam-5280	330	23	∥	∥	NUM
ejpam-5280	330	24	ω−	ω−	ADV
ejpam-5280	330	25	ωm	ωm	X
ejpam-5280	330	26	∥≤	∥≤	PROPN
ejpam-5280	330	27	γ(µ+	γ(µ+	X
ejpam-5280	330	28	2	2	X
ejpam-5280	330	29	)	)	PUNCT
ejpam-5280	330	30	γ(µ+	γ(µ+	PUNCT
ejpam-5280	331	1	2)−	2)−	NUM
ejpam-5280	331	2	l1(µ+	l1(µ+	PROPN
ejpam-5280	331	3	1	1	NUM
ejpam-5280	331	4	)	)	PUNCT
ejpam-5280	331	5	+	+	CCONJ
ejpam-5280	331	6	(	(	PUNCT
ejpam-5280	331	7	l3q1	l3q1	X
ejpam-5280	331	8	+	+	NUM
ejpam-5280	331	9	l4q2)m	l4q2)m	NOUN
ejpam-5280	331	10	→	→	SYM
ejpam-5280	331	11	0	0	NUM
ejpam-5280	331	12	(	(	PUNCT
ejpam-5280	331	13	66	66	NUM
ejpam-5280	331	14	)	)	PUNCT
ejpam-5280	331	15	as	as	ADP
ejpam-5280	331	16	m	m	PROPN
ejpam-5280	331	17	approaches	approach	NOUN
ejpam-5280	331	18	to	to	ADP
ejpam-5280	331	19	infinity	infinity	NOUN
ejpam-5280	331	20	.	.	PUNCT
ejpam-5280	332	1	hence	hence	ADV
ejpam-5280	332	2	,	,	PUNCT
ejpam-5280	332	3	{	{	PUNCT
ejpam-5280	332	4	ωm	ωm	X
ejpam-5280	332	5	(	(	PUNCT
ejpam-5280	332	6	t)}∞m=1	t)}∞m=1	PROPN
ejpam-5280	332	7	converges	converge	VERB
ejpam-5280	332	8	uniformly	uniformly	ADV
ejpam-5280	332	9	to	to	ADP
ejpam-5280	332	10	the	the	DET
ejpam-5280	332	11	unique	unique	ADJ
ejpam-5280	332	12	solution	solution	NOUN
ejpam-5280	332	13	of	of	ADP
ejpam-5280	332	14	problem	problem	NOUN
ejpam-5280	332	15	(	(	PUNCT
ejpam-5280	332	16	1)-(2	1)-(2	NUM
ejpam-5280	332	17	)	)	PUNCT
ejpam-5280	332	18	on	on	ADP
ejpam-5280	332	19	[	[	X
ejpam-5280	332	20	0	0	NUM
ejpam-5280	332	21	,	,	PUNCT
ejpam-5280	332	22	1	1	NUM
ejpam-5280	332	23	]	]	PUNCT
ejpam-5280	332	24	.	.	PUNCT
ejpam-5280	333	1	5	5	X
ejpam-5280	333	2	.	.	X
ejpam-5280	333	3	numerical	numerical	ADJ
ejpam-5280	333	4	results	result	NOUN
ejpam-5280	333	5	in	in	ADP
ejpam-5280	333	6	this	this	DET
ejpam-5280	333	7	section	section	NOUN
ejpam-5280	333	8	,	,	PUNCT
ejpam-5280	333	9	we	we	PRON
ejpam-5280	333	10	will	will	AUX
ejpam-5280	333	11	present	present	VERB
ejpam-5280	333	12	three	three	NUM
ejpam-5280	333	13	examples	example	NOUN
ejpam-5280	333	14	to	to	PART
ejpam-5280	333	15	demonstrate	demonstrate	VERB
ejpam-5280	333	16	the	the	DET
ejpam-5280	333	17	effectiveness	effectiveness	NOUN
ejpam-5280	333	18	of	of	ADP
ejpam-5280	333	19	the	the	DET
ejpam-5280	333	20	proposed	propose	VERB
ejpam-5280	333	21	method	method	NOUN
ejpam-5280	333	22	.	.	PUNCT
ejpam-5280	334	1	example	example	NOUN
ejpam-5280	335	1	1	1	NUM
ejpam-5280	335	2	.	.	X
ejpam-5280	335	3	consider	consider	VERB
ejpam-5280	335	4	the	the	DET
ejpam-5280	335	5	following	follow	VERB
ejpam-5280	335	6	class	class	NOUN
ejpam-5280	335	7	of	of	ADP
ejpam-5280	335	8	integro	integro	ADJ
ejpam-5280	335	9	-	-	PUNCT
ejpam-5280	335	10	differential	differential	NOUN
ejpam-5280	335	11	equations	equation	NOUN
ejpam-5280	335	12	:	:	PUNCT
ejpam-5280	335	13	dµω(t	dµω(t	NOUN
ejpam-5280	335	14	)	)	PUNCT
ejpam-5280	335	15	=	=	SYM
ejpam-5280	335	16	−t2et	−t2et	NUM
ejpam-5280	335	17	3	3	NUM
ejpam-5280	335	18	ω(t	ω(t	NOUN
ejpam-5280	335	19	)	)	PUNCT
ejpam-5280	335	20	+	+	CCONJ
ejpam-5280	335	21	t1−µ	t1−µ	PROPN
ejpam-5280	335	22	γ(2−	γ(2−	PROPN
ejpam-5280	335	23	µ	µ	NOUN
ejpam-5280	335	24	)	)	PUNCT
ejpam-5280	335	25	−	−	PROPN
ejpam-5280	335	26	t2	t2	NOUN
ejpam-5280	335	27	2	2	NUM
ejpam-5280	335	28	+	+	CCONJ
ejpam-5280	335	29	∫	∫	PROPN
ejpam-5280	335	30	t	t	PROPN
ejpam-5280	335	31	0	0	NUM
ejpam-5280	336	1	setω(s)ds+	setω(s)ds+	SYM
ejpam-5280	336	2	∫	∫	PROPN
ejpam-5280	336	3	1	1	NUM
ejpam-5280	336	4	0	0	NUM
ejpam-5280	336	5	t2ω(s)ds	t2ω(s)ds	PROPN
ejpam-5280	336	6	,	,	PUNCT
ejpam-5280	336	7	ω(0	ω(0	PROPN
ejpam-5280	336	8	)	)	PUNCT
ejpam-5280	336	9	=	=	SYM
ejpam-5280	336	10	0	0	NUM
ejpam-5280	336	11	,	,	PUNCT
ejpam-5280	336	12	where	where	SCONJ
ejpam-5280	336	13	t	t	PROPN
ejpam-5280	336	14	∈	∈	PROPN
ejpam-5280	337	1	[	[	X
ejpam-5280	337	2	0	0	NUM
ejpam-5280	337	3	,	,	PUNCT
ejpam-5280	337	4	1	1	NUM
ejpam-5280	337	5	]	]	PUNCT
ejpam-5280	337	6	,	,	PUNCT
ejpam-5280	337	7	and	and	CCONJ
ejpam-5280	337	8	0	0	NUM
ejpam-5280	337	9	<	<	X
ejpam-5280	337	10	µ	µ	X
ejpam-5280	337	11	≤	≤	NUM
ejpam-5280	337	12	1	1	NUM
ejpam-5280	337	13	.	.	PUNCT
ejpam-5280	338	1	then	then	ADV
ejpam-5280	338	2	,	,	PUNCT
ejpam-5280	338	3	the	the	DET
ejpam-5280	338	4	exact	exact	ADJ
ejpam-5280	338	5	solution	solution	NOUN
ejpam-5280	338	6	is	be	AUX
ejpam-5280	338	7	q(t	q(t	ADJ
ejpam-5280	338	8	)	)	PUNCT
ejpam-5280	338	9	=	=	NOUN
ejpam-5280	339	1	t.	t.	NOUN
ejpam-5280	339	2	we	we	PRON
ejpam-5280	339	3	approximate	approximate	VERB
ejpam-5280	339	4	ω(t	ω(t	NOUN
ejpam-5280	339	5	)	)	PUNCT
ejpam-5280	339	6	as	as	SCONJ
ejpam-5280	339	7	follows	follow	VERB
ejpam-5280	339	8	ω(t	ω(t	NOUN
ejpam-5280	339	9	)	)	PUNCT
ejpam-5280	339	10	=	=	SYM
ejpam-5280	339	11	m−1∑	m−1∑	PROPN
ejpam-5280	339	12	i=0	i=0	PROPN
ejpam-5280	339	13	ωjµj(t	ωjµj(t	PROPN
ejpam-5280	339	14	)	)	PUNCT
ejpam-5280	339	15	.	.	PUNCT
ejpam-5280	340	1	then	then	ADV
ejpam-5280	340	2	,	,	PUNCT
ejpam-5280	340	3	g1(t	g1(t	ADP
ejpam-5280	340	4	,	,	PUNCT
ejpam-5280	340	5	ω(t	ω(t	NOUN
ejpam-5280	340	6	)	)	PUNCT
ejpam-5280	340	7	)	)	PUNCT
ejpam-5280	341	1	=	=	PUNCT
ejpam-5280	341	2	−t2et	−t2et	NUM
ejpam-5280	341	3	3	3	NUM
ejpam-5280	341	4	ω(t	ω(t	NOUN
ejpam-5280	341	5	)	)	PUNCT
ejpam-5280	341	6	,	,	PUNCT
ejpam-5280	341	7	g2(t	g2(t	PROPN
ejpam-5280	341	8	)	)	PUNCT
ejpam-5280	341	9	=	=	VERB
ejpam-5280	342	1	t1−µ	t1−µ	PROPN
ejpam-5280	342	2	γ(2−	γ(2−	PROPN
ejpam-5280	342	3	µ	µ	NOUN
ejpam-5280	342	4	)	)	PUNCT
ejpam-5280	342	5	−	−	PROPN
ejpam-5280	342	6	t2	t2	PROPN
ejpam-5280	342	7	2	2	NUM
ejpam-5280	342	8	,	,	PUNCT
ejpam-5280	342	9	g3(ω(s	g3(ω(s	NOUN
ejpam-5280	342	10	)	)	PUNCT
ejpam-5280	342	11	)	)	PUNCT
ejpam-5280	343	1	=	=	SYM
ejpam-5280	343	2	ω(s	ω(s	NOUN
ejpam-5280	343	3	)	)	PUNCT
ejpam-5280	343	4	,	,	PUNCT
ejpam-5280	343	5	g4(ω(s	g4(ω(s	PROPN
ejpam-5280	343	6	)	)	PUNCT
ejpam-5280	343	7	)	)	PUNCT
ejpam-5280	344	1	=	=	SYM
ejpam-5280	344	2	ω(s	ω(s	NOUN
ejpam-5280	344	3	)	)	PUNCT
ejpam-5280	344	4	,	,	PUNCT
ejpam-5280	344	5	π1(t	π1(t	PROPN
ejpam-5280	344	6	,	,	PUNCT
ejpam-5280	344	7	s	s	NOUN
ejpam-5280	344	8	)	)	PUNCT
ejpam-5280	344	9	=	=	VERB
ejpam-5280	345	1	set	set	NOUN
ejpam-5280	345	2	,	,	PUNCT
ejpam-5280	345	3	π2(t	π2(t	PROPN
ejpam-5280	345	4	,	,	PUNCT
ejpam-5280	345	5	s	s	PART
ejpam-5280	345	6	)	)	PUNCT
ejpam-5280	345	7	=	=	SYM
ejpam-5280	345	8	t2	t2	NOUN
ejpam-5280	345	9	,	,	PUNCT
ejpam-5280	345	10	ω0	ω0	ADV
ejpam-5280	345	11	=	=	SYM
ejpam-5280	345	12	0	0	X
ejpam-5280	345	13	.	.	PUNCT
ejpam-5280	346	1	direct	direct	ADJ
ejpam-5280	346	2	calculations	calculation	NOUN
ejpam-5280	346	3	implies	imply	VERB
ejpam-5280	346	4	that	that	SCONJ
ejpam-5280	346	5	p1(ω	p1(ω	PROPN
ejpam-5280	346	6	)	)	PUNCT
ejpam-5280	346	7	=	=	SYM
ejpam-5280	346	8	ω	ω	PROPN
ejpam-5280	346	9	t	t	PROPN
ejpam-5280	346	10	a1	a1	PROPN
ejpam-5280	346	11	,	,	PUNCT
ejpam-5280	346	12	p2(ω	p2(ω	NUM
ejpam-5280	346	13	)	)	PUNCT
ejpam-5280	346	14	=	=	SYM
ejpam-5280	346	15	ω	ω	PROPN
ejpam-5280	346	16	t	t	PROPN
ejpam-5280	346	17	a2	a2	PROPN
ejpam-5280	346	18	,	,	PUNCT
ejpam-5280	346	19	p3(ω	p3(ω	X
ejpam-5280	346	20	)	)	PUNCT
ejpam-5280	346	21	=	=	SYM
ejpam-5280	346	22	ω	ω	PROPN
ejpam-5280	346	23	t	t	NOUN
ejpam-5280	346	24	a3	a3	NOUN
ejpam-5280	346	25	,	,	PUNCT
ejpam-5280	346	26	where	where	SCONJ
ejpam-5280	346	27	a1	a1	NOUN
ejpam-5280	346	28	=	=	NOUN
ejpam-5280	346	29	r	r	NOUN
ejpam-5280	346	30	2	2	NUM
ejpam-5280	346	31			NOUN
ejpam-5280	346	32	f(0	f(0	NOUN
ejpam-5280	346	33	)	)	PUNCT
ejpam-5280	346	34	f(1	f(1	PROPN
ejpam-5280	346	35	)	)	PUNCT
ejpam-5280	346	36	.	.	PUNCT
ejpam-5280	346	37	.	.	PUNCT
ejpam-5280	346	38	.	.	PUNCT
ejpam-5280	347	1	f(m	f(m	PROPN
ejpam-5280	347	2	−	−	PROPN
ejpam-5280	347	3	1	1	NUM
ejpam-5280	347	4	)	)	PUNCT
ejpam-5280	347	5	3f(0	3f(0	NUM
ejpam-5280	347	6	)	)	PUNCT
ejpam-5280	347	7	3f(1	3f(1	NUM
ejpam-5280	347	8	)	)	PUNCT
ejpam-5280	347	9	.	.	PUNCT
ejpam-5280	347	10	.	.	PUNCT
ejpam-5280	348	1	.	.	PUNCT
ejpam-5280	349	1	3f(m	3f(m	NOUN
ejpam-5280	349	2	−	−	NOUN
ejpam-5280	349	3	1	1	NUM
ejpam-5280	349	4	)	)	PUNCT
ejpam-5280	349	5	...	...	PUNCT
ejpam-5280	349	6	...	...	PUNCT
ejpam-5280	349	7	.	.	PUNCT
ejpam-5280	349	8	.	.	PUNCT
ejpam-5280	349	9	.	.	PUNCT
ejpam-5280	350	1	...	...	PUNCT
ejpam-5280	351	1	(	(	PUNCT
ejpam-5280	351	2	2	2	NUM
ejpam-5280	351	3	m	m	NOUN
ejpam-5280	351	4	+	+	NOUN
ejpam-5280	351	5	1)f(0	1)f(0	NUM
ejpam-5280	351	6	)	)	PUNCT
ejpam-5280	351	7	(	(	PUNCT
ejpam-5280	351	8	2	2	NUM
ejpam-5280	351	9	m	m	NOUN
ejpam-5280	351	10	+	+	NUM
ejpam-5280	351	11	1)f(1	1)f(1	NOUN
ejpam-5280	351	12	)	)	PUNCT
ejpam-5280	351	13	.	.	PUNCT
ejpam-5280	351	14	.	.	PUNCT
ejpam-5280	351	15	.	.	PUNCT
ejpam-5280	352	1	(	(	PUNCT
ejpam-5280	352	2	2	2	NUM
ejpam-5280	352	3	m	m	NOUN
ejpam-5280	352	4	+	+	NUM
ejpam-5280	352	5	1)f(m	1)f(m	NUM
ejpam-5280	352	6	−	−	NOUN
ejpam-5280	352	7	1	1	X
ejpam-5280	352	8	)	)	PUNCT
ejpam-5280	352	9			PROPN
ejpam-5280	352	10	a2	a2	NOUN
ejpam-5280	352	11	=	=	SYM
ejpam-5280	352	12	r2	r2	PROPN
ejpam-5280	352	13	3	3	NUM
ejpam-5280	352	14			NOUN
ejpam-5280	352	15	1	1	NUM
ejpam-5280	352	16	23	23	NUM
ejpam-5280	352	17	−	−	NUM
ejpam-5280	352	18	13	13	NUM
ejpam-5280	352	19	.	.	PUNCT
ejpam-5280	352	20	.	.	PUNCT
ejpam-5280	352	21	.	.	PUNCT
ejpam-5280	353	1	m3	m3	PROPN
ejpam-5280	353	2	−	−	PROPN
ejpam-5280	354	1	(	(	PUNCT
ejpam-5280	354	2	m	m	VERB
ejpam-5280	354	3	−	−	PROPN
ejpam-5280	354	4	1)3	1)3	NUM
ejpam-5280	354	5	1	1	NUM
ejpam-5280	354	6	23	23	NUM
ejpam-5280	354	7	−	−	NUM
ejpam-5280	354	8	13	13	NUM
ejpam-5280	354	9	.	.	PUNCT
ejpam-5280	354	10	.	.	PUNCT
ejpam-5280	354	11	.	.	PUNCT
ejpam-5280	355	1	m3	m3	PROPN
ejpam-5280	355	2	−	−	PROPN
ejpam-5280	356	1	(	(	PUNCT
ejpam-5280	356	2	m	m	PROPN
ejpam-5280	356	3	−	−	PROPN
ejpam-5280	356	4	1)3	1)3	NUM
ejpam-5280	356	5	...	...	PUNCT
ejpam-5280	356	6	...	...	PUNCT
ejpam-5280	356	7	.	.	PUNCT
ejpam-5280	356	8	.	.	PUNCT
ejpam-5280	357	1	.	.	PUNCT
ejpam-5280	358	1	...	...	PUNCT
ejpam-5280	359	1	1	1	NUM
ejpam-5280	359	2	23	23	NUM
ejpam-5280	359	3	−	−	NUM
ejpam-5280	359	4	13	13	NUM
ejpam-5280	359	5	.	.	PUNCT
ejpam-5280	359	6	.	.	PUNCT
ejpam-5280	359	7	.	.	PUNCT
ejpam-5280	360	1	m3	m3	PROPN
ejpam-5280	360	2	−	−	PROPN
ejpam-5280	361	1	(	(	PUNCT
ejpam-5280	361	2	m	m	VERB
ejpam-5280	361	3	−	−	PROPN
ejpam-5280	361	4	1)3	1)3	NUM
ejpam-5280	361	5			PROPN
ejpam-5280	361	6	,	,	PUNCT
ejpam-5280	361	7	a3	a3	NOUN
ejpam-5280	361	8	=	=	NOUN
ejpam-5280	361	9	1	1	NUM
ejpam-5280	361	10	r	r	NOUN
ejpam-5280	361	11			NOUN
ejpam-5280	361	12	g(0	g(0	PROPN
ejpam-5280	361	13	)	)	PUNCT
ejpam-5280	361	14	0	0	NUM
ejpam-5280	361	15	.	.	PUNCT
ejpam-5280	361	16	.	.	PUNCT
ejpam-5280	362	1	.	.	PUNCT
ejpam-5280	363	1	0	0	NUM
ejpam-5280	363	2	0	0	NUM
ejpam-5280	363	3	g(1	g(1	NOUN
ejpam-5280	363	4	)	)	PUNCT
ejpam-5280	363	5	.	.	PUNCT
ejpam-5280	363	6	.	.	PUNCT
ejpam-5280	364	1	.	.	PUNCT
ejpam-5280	365	1	0	0	NUM
ejpam-5280	365	2	...	...	PUNCT
ejpam-5280	365	3	...	...	PUNCT
ejpam-5280	365	4	.	.	PUNCT
ejpam-5280	365	5	.	.	PUNCT
ejpam-5280	365	6	.	.	PUNCT
ejpam-5280	366	1	...	...	PUNCT
ejpam-5280	367	1	0	0	NUM
ejpam-5280	367	2	0	0	NUM
ejpam-5280	367	3	.	.	PUNCT
ejpam-5280	367	4	.	.	PUNCT
ejpam-5280	367	5	.	.	PUNCT
ejpam-5280	368	1	g(m	g(m	VERB
ejpam-5280	368	2	−	−	NOUN
ejpam-5280	368	3	1	1	X
ejpam-5280	368	4	)	)	PUNCT
ejpam-5280	368	5			PROPN
ejpam-5280	368	6	,	,	PUNCT
ejpam-5280	368	7	m.i	m.i	PROPN
ejpam-5280	368	8	.	.	PROPN
ejpam-5280	368	9	syam	syam	PROPN
ejpam-5280	368	10	,	,	PUNCT
ejpam-5280	368	11	m.	m.	NOUN
ejpam-5280	368	12	sharadga	sharadga	PROPN
ejpam-5280	368	13	,	,	PUNCT
ejpam-5280	368	14	i.	i.	PROPN
ejpam-5280	368	15	hashim	hashim	PROPN
ejpam-5280	368	16	/	/	SYM
ejpam-5280	368	17	eur	eur	PROPN
ejpam-5280	368	18	.	.	PUNCT
ejpam-5280	369	1	j.	j.	PROPN
ejpam-5280	369	2	pure	pure	PROPN
ejpam-5280	369	3	appl	appl	PROPN
ejpam-5280	369	4	.	.	PROPN
ejpam-5280	369	5	math	math	PROPN
ejpam-5280	369	6	,	,	PUNCT
ejpam-5280	369	7	17	17	NUM
ejpam-5280	369	8	(	(	PUNCT
ejpam-5280	369	9	3	3	NUM
ejpam-5280	369	10	)	)	PUNCT
ejpam-5280	369	11	(	(	PUNCT
ejpam-5280	369	12	2024	2024	NUM
ejpam-5280	369	13	)	)	PUNCT
ejpam-5280	369	14	,	,	PUNCT
ejpam-5280	369	15	1429	1429	NUM
ejpam-5280	369	16	-	-	SYM
ejpam-5280	369	17	1448	1448	NUM
ejpam-5280	369	18	1443	1443	NUM
ejpam-5280	369	19	p4	p4	NOUN
ejpam-5280	369	20	=	=	SYM
ejpam-5280	369	21	(	(	PUNCT
ejpam-5280	369	22	h(0)−	h(0)−	PROPN
ejpam-5280	369	23	h(1	h(1	PROPN
ejpam-5280	369	24	)	)	PUNCT
ejpam-5280	369	25	h(1)−	h(1)−	NOUN
ejpam-5280	369	26	h(2	h(2	NOUN
ejpam-5280	369	27	)	)	PUNCT
ejpam-5280	369	28	.	.	PUNCT
ejpam-5280	369	29	.	.	PUNCT
ejpam-5280	369	30	.	.	PUNCT
ejpam-5280	370	1	h(m	h(m	X
ejpam-5280	370	2	−	−	PROPN
ejpam-5280	370	3	1)−	1)−	PROPN
ejpam-5280	370	4	h(m	h(m	NOUN
ejpam-5280	370	5	)	)	PUNCT
ejpam-5280	370	6	)	)	PUNCT
ejpam-5280	371	1	f(j	f(j	NOUN
ejpam-5280	371	2	)	)	PUNCT
ejpam-5280	371	3	=	=	PUNCT
ejpam-5280	372	1	er(j+1	er(j+1	PROPN
ejpam-5280	372	2	)	)	PUNCT
ejpam-5280	372	3	−	−	PROPN
ejpam-5280	372	4	erj	erj	PROPN
ejpam-5280	372	5	,	,	PUNCT
ejpam-5280	372	6	g(j	g(j	PROPN
ejpam-5280	372	7	)	)	PUNCT
ejpam-5280	373	1	=	=	PUNCT
ejpam-5280	373	2	−1	−1	NOUN
ejpam-5280	373	3	3	3	NUM
ejpam-5280	373	4	(	(	PUNCT
ejpam-5280	373	5	er(j+1)(2−	er(j+1)(2−	NOUN
ejpam-5280	373	6	2(j	2(j	NUM
ejpam-5280	373	7	+	+	CCONJ
ejpam-5280	373	8	1)r	1)r	NUM
ejpam-5280	374	1	+	+	CCONJ
ejpam-5280	374	2	r2(j	r2(j	X
ejpam-5280	374	3	+	+	CCONJ
ejpam-5280	374	4	1)2)−	1)2)−	NUM
ejpam-5280	374	5	erj(2−	erj(2−	NOUN
ejpam-5280	374	6	2rj	2rj	NOUN
ejpam-5280	374	7	+	+	CCONJ
ejpam-5280	374	8	r2j2	r2j2	ADJ
ejpam-5280	374	9	)	)	PUNCT
ejpam-5280	374	10	)	)	PUNCT
ejpam-5280	374	11	,	,	PUNCT
ejpam-5280	374	12	h(j	h(j	ADP
ejpam-5280	374	13	)	)	PUNCT
ejpam-5280	374	14	=	=	SYM
ejpam-5280	374	15	1	1	NUM
ejpam-5280	374	16	r	r	NOUN
ejpam-5280	374	17	(	(	PUNCT
ejpam-5280	374	18	(	(	PUNCT
ejpam-5280	374	19	rj)2−µ	rj)2−µ	NOUN
ejpam-5280	374	20	γ(3−	γ(3−	ADP
ejpam-5280	374	21	µ	µ	NOUN
ejpam-5280	374	22	)	)	PUNCT
ejpam-5280	374	23	−	−	PROPN
ejpam-5280	374	24	(	(	PUNCT
ejpam-5280	374	25	rj)3	rj)3	NOUN
ejpam-5280	374	26	3	3	NUM
ejpam-5280	374	27	)	)	PUNCT
ejpam-5280	374	28	.	.	PUNCT
ejpam-5280	375	1	then	then	ADV
ejpam-5280	375	2	,	,	PUNCT
ejpam-5280	375	3	ω	ω	PROPN
ejpam-5280	375	4	t	t	PROPN
ejpam-5280	375	5	(	(	PUNCT
ejpam-5280	375	6	(	(	PUNCT
ejpam-5280	375	7	a1	a1	PROPN
ejpam-5280	375	8	+	+	PROPN
ejpam-5280	375	9	a2	a2	PROPN
ejpam-5280	375	10	+	+	NOUN
ejpam-5280	375	11	a3)oµ	a3)oµ	PROPN
ejpam-5280	375	12	−	−	PROPN
ejpam-5280	375	13	i	i	PRON
ejpam-5280	375	14	m	m	VERB
ejpam-5280	375	15	)	)	PUNCT
ejpam-5280	376	1	=	=	SYM
ejpam-5280	376	2	p4oµ	p4oµ	NOUN
ejpam-5280	376	3	which	which	PRON
ejpam-5280	376	4	can	can	AUX
ejpam-5280	376	5	be	be	AUX
ejpam-5280	376	6	written	write	VERB
ejpam-5280	376	7	as	as	ADP
ejpam-5280	376	8	(	(	PUNCT
ejpam-5280	376	9	(	(	PUNCT
ejpam-5280	376	10	a1	a1	PROPN
ejpam-5280	376	11	+	+	NOUN
ejpam-5280	376	12	a2	a2	PROPN
ejpam-5280	376	13	+	+	NOUN
ejpam-5280	376	14	a3)oµ	a3)oµ	PROPN
ejpam-5280	376	15	−	−	PROPN
ejpam-5280	376	16	i	i	PRON
ejpam-5280	376	17	m	m	PROPN
ejpam-5280	376	18	)	)	PUNCT
ejpam-5280	376	19	t	t	PROPN
ejpam-5280	376	20	ω	ω	NUM
ejpam-5280	376	21	=	=	SYM
ejpam-5280	376	22	(	(	PUNCT
ejpam-5280	376	23	p4oµ	p4oµ	X
ejpam-5280	376	24	)	)	PUNCT
ejpam-5280	376	25	t	t	NOUN
ejpam-5280	376	26	.	.	PUNCT
ejpam-5280	377	1	(	(	PUNCT
ejpam-5280	377	2	67	67	NUM
ejpam-5280	377	3	)	)	PUNCT
ejpam-5280	377	4	one	one	NOUN
ejpam-5280	377	5	can	can	AUX
ejpam-5280	377	6	see	see	VERB
ejpam-5280	377	7	that	that	DET
ejpam-5280	377	8	system	system	NOUN
ejpam-5280	377	9	(	(	PUNCT
ejpam-5280	377	10	67	67	NUM
ejpam-5280	377	11	)	)	PUNCT
ejpam-5280	377	12	is	be	AUX
ejpam-5280	377	13	linear	linear	ADJ
ejpam-5280	377	14	system	system	NOUN
ejpam-5280	377	15	.	.	PUNCT
ejpam-5280	378	1	for	for	ADP
ejpam-5280	378	2	m	m	PROPN
ejpam-5280	378	3	=	=	SYM
ejpam-5280	378	4	500	500	NUM
ejpam-5280	378	5	,	,	PUNCT
ejpam-5280	378	6	we	we	PRON
ejpam-5280	378	7	solve	solve	VERB
ejpam-5280	378	8	the	the	DET
ejpam-5280	378	9	system	system	NOUN
ejpam-5280	378	10	(	(	PUNCT
ejpam-5280	378	11	67	67	NUM
ejpam-5280	378	12	)	)	PUNCT
ejpam-5280	378	13	in	in	ADP
ejpam-5280	378	14	terms	term	NOUN
ejpam-5280	378	15	of	of	ADP
ejpam-5280	378	16	r	r	NOUN
ejpam-5280	378	17	and	and	CCONJ
ejpam-5280	378	18	we	we	PRON
ejpam-5280	378	19	found	find	VERB
ejpam-5280	378	20	that	that	SCONJ
ejpam-5280	378	21	ωj	ωj	ADP
ejpam-5280	378	22	=	=	PUNCT
ejpam-5280	378	23	2j	2j	NOUN
ejpam-5280	379	1	+	+	CCONJ
ejpam-5280	379	2	1	1	NUM
ejpam-5280	379	3	2	2	NUM
ejpam-5280	379	4	r	r	NOUN
ejpam-5280	379	5	,	,	PUNCT
ejpam-5280	379	6	j	j	NOUN
ejpam-5280	379	7	=	=	SYM
ejpam-5280	379	8	0	0	NUM
ejpam-5280	379	9	,	,	PUNCT
ejpam-5280	379	10	1	1	NUM
ejpam-5280	379	11	,	,	PUNCT
ejpam-5280	379	12	.	.	PUNCT
ejpam-5280	379	13	.	.	PUNCT
ejpam-5280	379	14	.	.	PUNCT
ejpam-5280	380	1	,	,	PUNCT
ejpam-5280	380	2	m	m	VERB
ejpam-5280	380	3	−	−	NOUN
ejpam-5280	380	4	1	1	NUM
ejpam-5280	380	5	.	.	PUNCT
ejpam-5280	381	1	thus	thus	ADV
ejpam-5280	381	2	,	,	PUNCT
ejpam-5280	381	3	the	the	DET
ejpam-5280	381	4	approximate	approximate	ADJ
ejpam-5280	381	5	solution	solution	NOUN
ejpam-5280	381	6	is	be	AUX
ejpam-5280	381	7	given	give	VERB
ejpam-5280	381	8	as	as	ADP
ejpam-5280	381	9	r	r	NOUN
ejpam-5280	381	10	m−1∑	m−1∑	NUM
ejpam-5280	381	11	j=0	j=0	PROPN
ejpam-5280	381	12	2j	2j	X
ejpam-5280	381	13	+	+	CCONJ
ejpam-5280	381	14	1	1	NUM
ejpam-5280	381	15	2	2	NUM
ejpam-5280	381	16	µj(t	µj(t	NUM
ejpam-5280	381	17	)	)	PUNCT
ejpam-5280	381	18	→	→	SYM
ejpam-5280	381	19	x	x	X
ejpam-5280	381	20	as	as	SCONJ
ejpam-5280	381	21	m	m	PROPN
ejpam-5280	381	22	approaches	approach	NOUN
ejpam-5280	381	23	to	to	ADP
ejpam-5280	381	24	∞.	∞.	PROPN
ejpam-5280	381	25	thus	thus	ADV
ejpam-5280	381	26	,	,	PUNCT
ejpam-5280	381	27	our	our	PRON
ejpam-5280	381	28	approximate	approximate	ADJ
ejpam-5280	381	29	solution	solution	NOUN
ejpam-5280	381	30	converges	converge	VERB
ejpam-5280	381	31	to	to	ADP
ejpam-5280	381	32	the	the	DET
ejpam-5280	381	33	exact	exact	ADJ
ejpam-5280	381	34	solution	solution	NOUN
ejpam-5280	381	35	.	.	PUNCT
ejpam-5280	382	1	this	this	DET
ejpam-5280	382	2	result	result	NOUN
ejpam-5280	382	3	can	can	AUX
ejpam-5280	382	4	be	be	AUX
ejpam-5280	382	5	obtained	obtain	VERB
ejpam-5280	382	6	using	use	VERB
ejpam-5280	382	7	mathematical	mathematical	NOUN
ejpam-5280	382	8	for	for	ADP
ejpam-5280	382	9	linear	linear	PROPN
ejpam-5280	382	10	cases	case	NOUN
ejpam-5280	382	11	.	.	PUNCT
ejpam-5280	383	1	let	let	VERB
ejpam-5280	383	2	us	we	PRON
ejpam-5280	383	3	study	study	VERB
ejpam-5280	383	4	a	a	DET
ejpam-5280	383	5	nonlinear	nonlinear	ADJ
ejpam-5280	383	6	problem	problem	NOUN
ejpam-5280	383	7	in	in	ADP
ejpam-5280	383	8	the	the	DET
ejpam-5280	383	9	next	next	ADJ
ejpam-5280	383	10	example	example	NOUN
ejpam-5280	383	11	.	.	PUNCT
ejpam-5280	384	1	example	example	NOUN
ejpam-5280	385	1	2	2	NUM
ejpam-5280	385	2	.	.	X
ejpam-5280	385	3	consider	consider	VERB
ejpam-5280	385	4	the	the	DET
ejpam-5280	385	5	following	follow	VERB
ejpam-5280	385	6	class	class	NOUN
ejpam-5280	385	7	of	of	ADP
ejpam-5280	385	8	integro	integro	ADJ
ejpam-5280	385	9	-	-	PUNCT
ejpam-5280	385	10	differential	differential	NOUN
ejpam-5280	385	11	equations	equation	NOUN
ejpam-5280	385	12	:	:	PUNCT
ejpam-5280	385	13	dµω(t	dµω(t	NOUN
ejpam-5280	385	14	)	)	PUNCT
ejpam-5280	385	15	=	=	SYM
ejpam-5280	385	16	ω2(t	ω2(t	NOUN
ejpam-5280	385	17	)	)	PUNCT
ejpam-5280	385	18	+	+	NOUN
ejpam-5280	385	19	g2(t	g2(t	NOUN
ejpam-5280	385	20	)	)	PUNCT
ejpam-5280	386	1	+	+	NUM
ejpam-5280	386	2	∫	∫	PROPN
ejpam-5280	386	3	t	t	PROPN
ejpam-5280	386	4	0	0	NUM
ejpam-5280	386	5	(	(	PUNCT
ejpam-5280	386	6	sµ	sµ	NOUN
ejpam-5280	387	1	+	+	CCONJ
ejpam-5280	387	2	1)(tµ	1)(tµ	NUM
ejpam-5280	388	1	+	+	SYM
ejpam-5280	388	2	1)ω2(s)ds+	1)ω2(s)ds+	NUM
ejpam-5280	388	3	∫	∫	NOUN
ejpam-5280	388	4	1	1	NUM
ejpam-5280	388	5	0	0	NUM
ejpam-5280	388	6	(	(	PUNCT
ejpam-5280	388	7	sµ	sµ	NOUN
ejpam-5280	388	8	+	+	X
ejpam-5280	388	9	1)tµω2(s)ds	1)tµω2(s)ds	NUM
ejpam-5280	388	10	,	,	PUNCT
ejpam-5280	388	11	ω(0	ω(0	PROPN
ejpam-5280	388	12	)	)	PUNCT
ejpam-5280	388	13	=	=	SYM
ejpam-5280	388	14	1	1	NUM
ejpam-5280	388	15	,	,	PUNCT
ejpam-5280	388	16	where	where	SCONJ
ejpam-5280	388	17	t	t	PROPN
ejpam-5280	388	18	∈	∈	PROPN
ejpam-5280	389	1	[	[	X
ejpam-5280	389	2	0	0	NUM
ejpam-5280	389	3	,	,	PUNCT
ejpam-5280	389	4	1	1	NUM
ejpam-5280	389	5	]	]	PUNCT
ejpam-5280	389	6	,	,	PUNCT
ejpam-5280	389	7	0	0	PUNCT
ejpam-5280	389	8	<	<	X
ejpam-5280	389	9	µ	µ	X
ejpam-5280	389	10	≤	≤	NUM
ejpam-5280	389	11	1	1	NUM
ejpam-5280	389	12	,	,	PUNCT
ejpam-5280	389	13	and	and	CCONJ
ejpam-5280	389	14	then	then	ADV
ejpam-5280	389	15	,	,	PUNCT
ejpam-5280	389	16	g2(t	g2(t	PROPN
ejpam-5280	389	17	)	)	PUNCT
ejpam-5280	389	18	=	=	PUNCT
ejpam-5280	390	1	−(5µ+	−(5µ+	PROPN
ejpam-5280	390	2	4)t3µ+2	4)t3µ+2	NOUN
ejpam-5280	390	3	3µ2	3µ2	NUM
ejpam-5280	391	1	+	+	CCONJ
ejpam-5280	392	1	5µ+	5µ+	NUM
ejpam-5280	392	2	2	2	NUM
ejpam-5280	392	3	−	−	NUM
ejpam-5280	392	4	3(3µ+	3(3µ+	NUM
ejpam-5280	392	5	2)t5µ+3	2)t5µ+3	NUM
ejpam-5280	392	6	20µ2	20µ2	NUM
ejpam-5280	392	7	+	+	NUM
ejpam-5280	392	8	27µ+	27µ+	NUM
ejpam-5280	392	9	9	9	NUM
ejpam-5280	392	10	−	−	NOUN
ejpam-5280	392	11	(	(	PUNCT
ejpam-5280	392	12	5µ+	5µ+	NUM
ejpam-5280	392	13	4)(µ(2µ+	4)(µ(2µ+	NOUN
ejpam-5280	392	14	3)(6µ+	3)(6µ+	NUM
ejpam-5280	392	15	23	23	NUM
ejpam-5280	392	16	)	)	PUNCT
ejpam-5280	393	1	+	+	CCONJ
ejpam-5280	394	1	21)tµ	21)tµ	NUM
ejpam-5280	394	2	(	(	PUNCT
ejpam-5280	394	3	µ+	µ+	PROPN
ejpam-5280	394	4	1)(3µ+	1)(3µ+	PROPN
ejpam-5280	394	5	2)(4µ+	2)(4µ+	PROPN
ejpam-5280	395	1	3)(5µ+	3)(5µ+	NOUN
ejpam-5280	395	2	3	3	NUM
ejpam-5280	395	3	)	)	PUNCT
ejpam-5280	395	4	−	−	PROPN
ejpam-5280	395	5	(	(	PUNCT
ejpam-5280	395	6	µ+	µ+	PROPN
ejpam-5280	395	7	2)tµ+1	2)tµ+1	NUM
ejpam-5280	395	8	µ+	µ+	PRON
ejpam-5280	395	9	1	1	NUM
ejpam-5280	395	10	−	−	NOUN
ejpam-5280	395	11	(	(	PUNCT
ejpam-5280	395	12	2µ+	2µ+	NUM
ejpam-5280	395	13	t+	t+	NUM
ejpam-5280	395	14	3)t2µ+1	3)t2µ+1	NUM
ejpam-5280	395	15	µ+	µ+	X
ejpam-5280	395	16	1	1	NUM
ejpam-5280	395	17	−	−	NOUN
ejpam-5280	395	18	(	(	PUNCT
ejpam-5280	395	19	3µ+	3µ+	NUM
ejpam-5280	395	20	4)t4µ+2	4)t4µ+2	NOUN
ejpam-5280	395	21	3µ+	3µ+	NUM
ejpam-5280	395	22	2	2	NUM
ejpam-5280	395	23	−	−	NOUN
ejpam-5280	395	24	t4µ+3	t4µ+3	NOUN
ejpam-5280	395	25	4µ+	4µ+	NUM
ejpam-5280	395	26	3	3	NUM
ejpam-5280	395	27	−	−	NOUN
ejpam-5280	395	28	t6µ+3	t6µ+3	NOUN
ejpam-5280	395	29	5µ+	5µ+	NUM
ejpam-5280	395	30	3	3	NUM
ejpam-5280	395	31	+	+	NUM
ejpam-5280	395	32	γ(2µ+	γ(2µ+	NOUN
ejpam-5280	396	1	2)tµ+1	2)tµ+1	NUM
ejpam-5280	396	2	γ(µ+	γ(µ+	NOUN
ejpam-5280	396	3	2	2	NUM
ejpam-5280	396	4	)	)	PUNCT
ejpam-5280	396	5	−	−	PROPN
ejpam-5280	396	6	t−	t−	PROPN
ejpam-5280	396	7	1	1	NUM
ejpam-5280	396	8	.	.	PUNCT
ejpam-5280	397	1	first	first	ADV
ejpam-5280	397	2	,	,	PUNCT
ejpam-5280	397	3	let	let	VERB
ejpam-5280	397	4	’s	’s	PRON
ejpam-5280	397	5	examine	examine	VERB
ejpam-5280	397	6	the	the	DET
ejpam-5280	397	7	influence	influence	NOUN
ejpam-5280	397	8	of	of	ADP
ejpam-5280	397	9	the	the	DET
ejpam-5280	397	10	fractional	fractional	ADJ
ejpam-5280	397	11	order	order	NOUN
ejpam-5280	397	12	derivative	derivative	NOUN
ejpam-5280	397	13	on	on	ADP
ejpam-5280	397	14	the	the	DET
ejpam-5280	397	15	behavior	behavior	NOUN
ejpam-5280	397	16	of	of	ADP
ejpam-5280	397	17	the	the	DET
ejpam-5280	397	18	solution	solution	NOUN
ejpam-5280	397	19	.	.	PUNCT
ejpam-5280	398	1	figures	figure	NOUN
ejpam-5280	398	2	1	1	NUM
ejpam-5280	398	3	shows	show	VERB
ejpam-5280	398	4	the	the	DET
ejpam-5280	398	5	approximate	approximate	ADJ
ejpam-5280	398	6	solutions	solution	NOUN
ejpam-5280	398	7	ω	ω	X
ejpam-5280	398	8	for	for	ADP
ejpam-5280	398	9	different	different	ADJ
ejpam-5280	398	10	values	value	NOUN
ejpam-5280	398	11	of	of	ADP
ejpam-5280	398	12	µ	µ	X
ejpam-5280	398	13	=	=	SYM
ejpam-5280	398	14	m.i	m.i	PROPN
ejpam-5280	398	15	.	.	PROPN
ejpam-5280	398	16	syam	syam	PROPN
ejpam-5280	398	17	,	,	PUNCT
ejpam-5280	398	18	m.	m.	NOUN
ejpam-5280	398	19	sharadga	sharadga	PROPN
ejpam-5280	398	20	,	,	PUNCT
ejpam-5280	398	21	i.	i.	PROPN
ejpam-5280	398	22	hashim	hashim	PROPN
ejpam-5280	398	23	/	/	SYM
ejpam-5280	398	24	eur	eur	PROPN
ejpam-5280	398	25	.	.	PUNCT
ejpam-5280	399	1	j.	j.	PROPN
ejpam-5280	399	2	pure	pure	PROPN
ejpam-5280	399	3	appl	appl	PROPN
ejpam-5280	399	4	.	.	PROPN
ejpam-5280	399	5	math	math	PROPN
ejpam-5280	399	6	,	,	PUNCT
ejpam-5280	399	7	17	17	NUM
ejpam-5280	399	8	(	(	PUNCT
ejpam-5280	399	9	3	3	NUM
ejpam-5280	399	10	)	)	PUNCT
ejpam-5280	399	11	(	(	PUNCT
ejpam-5280	399	12	2024	2024	NUM
ejpam-5280	399	13	)	)	PUNCT
ejpam-5280	399	14	,	,	PUNCT
ejpam-5280	399	15	1429	1429	NUM
ejpam-5280	399	16	-	-	SYM
ejpam-5280	399	17	1448	1448	NUM
ejpam-5280	399	18	1444	1444	NUM
ejpam-5280	399	19	0.2	0.2	NUM
ejpam-5280	399	20	0.4	0.4	NUM
ejpam-5280	399	21	0.6	0.6	NUM
ejpam-5280	399	22	0.8	0.8	NUM
ejpam-5280	399	23	1.0	1.0	NUM
ejpam-5280	399	24	1.2	1.2	NUM
ejpam-5280	399	25	1.4	1.4	NUM
ejpam-5280	399	26	1.6	1.6	NUM
ejpam-5280	399	27	1.8	1.8	NUM
ejpam-5280	399	28	2.0	2.0	NUM
ejpam-5280	399	29	μ=0.5	μ=0.5	NUM
ejpam-5280	399	30	μ=0.6	μ=0.6	NOUN
ejpam-5280	399	31	μ=0.7	μ=0.7	NOUN
ejpam-5280	399	32	μ=0.8	μ=0.8	NOUN
ejpam-5280	399	33	μ=0.9	μ=0.9	NOUN
ejpam-5280	399	34	μ=1	μ=1	NOUN
ejpam-5280	399	35	figure	figure	NOUN
ejpam-5280	399	36	1	1	NUM
ejpam-5280	399	37	:	:	PUNCT
ejpam-5280	399	38	the	the	DET
ejpam-5280	399	39	approximate	approximate	ADJ
ejpam-5280	399	40	solution	solution	NOUN
ejpam-5280	399	41	ω	ω	PROPN
ejpam-5280	399	42	for	for	ADP
ejpam-5280	399	43	µ	µ	NOUN
ejpam-5280	399	44	=	=	SYM
ejpam-5280	399	45	0.5	0.5	NUM
ejpam-5280	399	46	,	,	PUNCT
ejpam-5280	399	47	0.6	0.6	NUM
ejpam-5280	399	48	,	,	PUNCT
ejpam-5280	399	49	0.7	0.7	NUM
ejpam-5280	399	50	,	,	PUNCT
ejpam-5280	399	51	0.8	0.8	NUM
ejpam-5280	399	52	,	,	PUNCT
ejpam-5280	399	53	0.9	0.9	NUM
ejpam-5280	399	54	,	,	PUNCT
ejpam-5280	399	55	1	1	NUM
ejpam-5280	399	56	.	.	NOUN
ejpam-5280	399	57	0.5	0.5	NUM
ejpam-5280	399	58	,	,	PUNCT
ejpam-5280	399	59	0.6	0.6	NUM
ejpam-5280	399	60	,	,	PUNCT
ejpam-5280	399	61	0.7	0.7	NUM
ejpam-5280	399	62	,	,	PUNCT
ejpam-5280	399	63	0.8	0.8	NUM
ejpam-5280	399	64	,	,	PUNCT
ejpam-5280	399	65	0.9	0.9	NUM
ejpam-5280	399	66	,	,	PUNCT
ejpam-5280	399	67	1	1	NUM
ejpam-5280	399	68	with	with	ADP
ejpam-5280	399	69	r	r	NOUN
ejpam-5280	399	70	=	=	NOUN
ejpam-5280	399	71	0.005	0.005	NUM
ejpam-5280	399	72	.	.	PUNCT
ejpam-5280	400	1	since	since	SCONJ
ejpam-5280	400	2	the	the	DET
ejpam-5280	400	3	exact	exact	ADJ
ejpam-5280	400	4	solution	solution	NOUN
ejpam-5280	400	5	is	be	AUX
ejpam-5280	400	6	not	not	PART
ejpam-5280	400	7	given	give	VERB
ejpam-5280	400	8	,	,	PUNCT
ejpam-5280	400	9	we	we	PRON
ejpam-5280	400	10	assess	assess	VERB
ejpam-5280	400	11	the	the	DET
ejpam-5280	400	12	accuracy	accuracy	NOUN
ejpam-5280	400	13	of	of	ADP
ejpam-5280	400	14	our	our	PRON
ejpam-5280	400	15	approximation	approximation	NOUN
ejpam-5280	400	16	by	by	ADP
ejpam-5280	400	17	computing	compute	VERB
ejpam-5280	400	18	the	the	DET
ejpam-5280	400	19	l2	l2	NOUN
ejpam-5280	400	20	-	-	PUNCT
ejpam-5280	400	21	truncation	truncation	NOUN
ejpam-5280	400	22	errors	error	NOUN
ejpam-5280	400	23	,	,	PUNCT
ejpam-5280	400	24	defined	define	VERB
ejpam-5280	400	25	as	as	ADP
ejpam-5280	400	26	ϵ(µ	ϵ(µ	NOUN
ejpam-5280	400	27	)	)	PUNCT
ejpam-5280	400	28	=	=	PUNCT
ejpam-5280	401	1	(	(	PUNCT
ejpam-5280	401	2	∫	∫	PROPN
ejpam-5280	401	3	1	1	NUM
ejpam-5280	401	4	0	0	NUM
ejpam-5280	401	5	(	(	PUNCT
ejpam-5280	401	6	dµω(t)−	dµω(t)−	PROPN
ejpam-5280	401	7	ω2(t)−g2(t	ω2(t)−g2(t	NUM
ejpam-5280	401	8	)	)	PUNCT
ejpam-5280	402	1	+	+	CCONJ
ejpam-5280	402	2	∫	∫	PROPN
ejpam-5280	402	3	t	t	PROPN
ejpam-5280	402	4	0	0	NUM
ejpam-5280	402	5	(	(	PUNCT
ejpam-5280	402	6	sµ	sµ	NOUN
ejpam-5280	403	1	+	+	CCONJ
ejpam-5280	403	2	1)(tµ	1)(tµ	NUM
ejpam-5280	403	3	+	+	CCONJ
ejpam-5280	403	4	1)ω2(s)ds−	1)ω2(s)ds−	NUM
ejpam-5280	403	5	∫	∫	PROPN
ejpam-5280	403	6	1	1	NUM
ejpam-5280	403	7	0	0	NUM
ejpam-5280	403	8	(	(	PUNCT
ejpam-5280	403	9	sµ	sµ	NOUN
ejpam-5280	403	10	+	+	CCONJ
ejpam-5280	403	11	1)tµω2(s)ds	1)tµω2(s)ds	NUM
ejpam-5280	403	12	)	)	PUNCT
ejpam-5280	403	13	dt	dt	NOUN
ejpam-5280	403	14	)	)	PUNCT
ejpam-5280	403	15	1	1	NUM
ejpam-5280	403	16	2	2	NUM
ejpam-5280	403	17	.	.	PUNCT
ejpam-5280	404	1	the	the	DET
ejpam-5280	404	2	errors	error	NOUN
ejpam-5280	404	3	are	be	AUX
ejpam-5280	404	4	presented	present	VERB
ejpam-5280	404	5	in	in	ADP
ejpam-5280	404	6	table	table	NOUN
ejpam-5280	404	7	1	1	NUM
ejpam-5280	404	8	.	.	PUNCT
ejpam-5280	404	9	table	table	NOUN
ejpam-5280	404	10	1	1	NUM
ejpam-5280	404	11	:	:	PUNCT
ejpam-5280	404	12	the	the	DET
ejpam-5280	404	13	l2	l2	NOUN
ejpam-5280	404	14	-	-	PUNCT
ejpam-5280	404	15	error	error	NOUN
ejpam-5280	404	16	for	for	ADP
ejpam-5280	404	17	µ	µ	NOUN
ejpam-5280	404	18	=	=	SYM
ejpam-5280	404	19	0.5	0.5	NUM
ejpam-5280	404	20	,	,	PUNCT
ejpam-5280	404	21	0.6	0.6	NUM
ejpam-5280	404	22	,	,	PUNCT
ejpam-5280	404	23	0.7	0.7	NUM
ejpam-5280	404	24	,	,	PUNCT
ejpam-5280	404	25	0.8	0.8	NUM
ejpam-5280	404	26	,	,	PUNCT
ejpam-5280	404	27	0.9	0.9	NUM
ejpam-5280	404	28	,	,	PUNCT
ejpam-5280	404	29	1	1	NUM
ejpam-5280	404	30	..	..	PUNCT
ejpam-5280	404	31	µ	µ	X
ejpam-5280	404	32	ϵ(µ	ϵ(µ	NOUN
ejpam-5280	404	33	)	)	PUNCT
ejpam-5280	404	34	0.5	0.5	NUM
ejpam-5280	404	35	1.99×	1.99×	NUM
ejpam-5280	404	36	10−12	10−12	NOUN
ejpam-5280	404	37	0.6	0.6	NUM
ejpam-5280	404	38	1.98×	1.98×	NUM
ejpam-5280	404	39	10−12	10−12	NOUN
ejpam-5280	404	40	0.7	0.7	NUM
ejpam-5280	404	41	1.74×	1.74×	NUM
ejpam-5280	404	42	10−12	10−12	NUM
ejpam-5280	404	43	0.8	0.8	NUM
ejpam-5280	404	44	1.66×	1.66×	NUM
ejpam-5280	404	45	10−12	10−12	NOUN
ejpam-5280	404	46	9	9	NUM
ejpam-5280	404	47	1.23×	1.23×	NUM
ejpam-5280	404	48	10−12	10−12	NOUN
ejpam-5280	404	49	1	1	NUM
ejpam-5280	404	50	1.10×	1.10×	NUM
ejpam-5280	404	51	10−12	10−12	NOUN
ejpam-5280	404	52	example	example	NOUN
ejpam-5280	404	53	3	3	X
ejpam-5280	404	54	.	.	X
ejpam-5280	404	55	consider	consider	VERB
ejpam-5280	404	56	the	the	DET
ejpam-5280	404	57	following	follow	VERB
ejpam-5280	404	58	class	class	NOUN
ejpam-5280	404	59	of	of	ADP
ejpam-5280	404	60	integro	integro	ADJ
ejpam-5280	404	61	-	-	PUNCT
ejpam-5280	404	62	differential	differential	NOUN
ejpam-5280	404	63	equations	equation	NOUN
ejpam-5280	404	64	:	:	PUNCT
ejpam-5280	405	1	dµω(t	dµω(t	NOUN
ejpam-5280	405	2	)	)	PUNCT
ejpam-5280	405	3	=	=	SYM
ejpam-5280	406	1	ω3(t	ω3(t	PROPN
ejpam-5280	406	2	)	)	PUNCT
ejpam-5280	406	3	+	+	NOUN
ejpam-5280	406	4	g2(t	g2(t	NOUN
ejpam-5280	406	5	)	)	PUNCT
ejpam-5280	406	6	+	+	NUM
ejpam-5280	406	7	∫	∫	PROPN
ejpam-5280	406	8	t	t	PROPN
ejpam-5280	406	9	0	0	NUM
ejpam-5280	406	10	(	(	PUNCT
ejpam-5280	406	11	s+	s+	NUM
ejpam-5280	406	12	1)(t+	1)(t+	NUM
ejpam-5280	406	13	1)ω3(s)ds+	1)ω3(s)ds+	NUM
ejpam-5280	406	14	∫	∫	NOUN
ejpam-5280	406	15	1	1	NUM
ejpam-5280	406	16	0	0	NUM
ejpam-5280	406	17	(	(	PUNCT
ejpam-5280	406	18	sµ	sµ	NOUN
ejpam-5280	406	19	+	+	CCONJ
ejpam-5280	406	20	1)t3ω2(s)ds	1)t3ω2(s)ds	NUM
ejpam-5280	406	21	,	,	PUNCT
ejpam-5280	406	22	ω(0	ω(0	PROPN
ejpam-5280	406	23	)	)	PUNCT
ejpam-5280	406	24	=	=	SYM
ejpam-5280	406	25	0	0	NUM
ejpam-5280	406	26	,	,	PUNCT
ejpam-5280	406	27	where	where	SCONJ
ejpam-5280	406	28	t	t	PROPN
ejpam-5280	406	29	∈	∈	PROPN
ejpam-5280	407	1	[	[	X
ejpam-5280	407	2	0	0	NUM
ejpam-5280	407	3	,	,	PUNCT
ejpam-5280	407	4	1	1	NUM
ejpam-5280	407	5	]	]	PUNCT
ejpam-5280	407	6	,	,	PUNCT
ejpam-5280	407	7	0	0	PUNCT
ejpam-5280	407	8	<	<	X
ejpam-5280	407	9	µ	µ	X
ejpam-5280	407	10	≤	≤	NUM
ejpam-5280	407	11	1	1	NUM
ejpam-5280	407	12	,	,	PUNCT
ejpam-5280	407	13	and	and	CCONJ
ejpam-5280	407	14	then	then	ADV
ejpam-5280	407	15	,	,	PUNCT
ejpam-5280	407	16	g2(t	g2(t	PROPN
ejpam-5280	407	17	)	)	PUNCT
ejpam-5280	407	18	=	=	SYM
ejpam-5280	407	19	γ(µ+	γ(µ+	PUNCT
ejpam-5280	408	1	1)−	1)−	NUM
ejpam-5280	408	2	(	(	PUNCT
ejpam-5280	408	3	9µ2	9µ2	NUM
ejpam-5280	408	4	+	+	CCONJ
ejpam-5280	408	5	9µ+	9µ+	NUM
ejpam-5280	408	6	3µt(t+	3µt(t+	NUM
ejpam-5280	408	7	1)2	1)2	NUM
ejpam-5280	408	8	+	+	CCONJ
ejpam-5280	408	9	t(t+	t(t+	NUM
ejpam-5280	408	10	2)(t+	2)(t+	NUM
ejpam-5280	408	11	1	1	NUM
ejpam-5280	408	12	)	)	PUNCT
ejpam-5280	408	13	+	+	CCONJ
ejpam-5280	408	14	2	2	X
ejpam-5280	408	15	)	)	PUNCT
ejpam-5280	408	16	t3µ	t3µ	NOUN
ejpam-5280	408	17	9µ(µ+	9µ(µ+	NUM
ejpam-5280	408	18	1	1	NUM
ejpam-5280	408	19	)	)	PUNCT
ejpam-5280	408	20	+	+	CCONJ
ejpam-5280	408	21	2	2	NUM
ejpam-5280	408	22	−	−	NOUN
ejpam-5280	408	23	3	3	NUM
ejpam-5280	408	24	(	(	PUNCT
ejpam-5280	408	25	16µ2	16µ2	NUM
ejpam-5280	408	26	+	+	NUM
ejpam-5280	408	27	20µ+	20µ+	NUM
ejpam-5280	408	28	4µt(t+	4µt(t+	NUM
ejpam-5280	408	29	1)2	1)2	NUM
ejpam-5280	409	1	+	+	NUM
ejpam-5280	409	2	t(2t+	t(2t+	NOUN
ejpam-5280	409	3	3)(t+	3)(t+	PROPN
ejpam-5280	409	4	1	1	NUM
ejpam-5280	409	5	)	)	PUNCT
ejpam-5280	409	6	+	+	CCONJ
ejpam-5280	409	7	6	6	X
ejpam-5280	409	8	)	)	PUNCT
ejpam-5280	409	9	t4µ+1	t4µ+1	NOUN
ejpam-5280	409	10	2(2µ+	2(2µ+	NUM
ejpam-5280	409	11	1)(4µ+	1)(4µ+	NUM
ejpam-5280	409	12	3	3	NUM
ejpam-5280	409	13	)	)	PUNCT
ejpam-5280	409	14	−	−	NOUN
ejpam-5280	409	15	3	3	NUM
ejpam-5280	409	16	(	(	PUNCT
ejpam-5280	409	17	25µ2	25µ2	NUM
ejpam-5280	410	1	+	+	NUM
ejpam-5280	410	2	35µ+	35µ+	NOUN
ejpam-5280	410	3	5µt(t+	5µt(t+	NUM
ejpam-5280	410	4	1)2	1)2	NUM
ejpam-5280	411	1	+	+	NUM
ejpam-5280	411	2	t(3t+	t(3t+	NOUN
ejpam-5280	411	3	4)(t+	4)(t+	NUM
ejpam-5280	411	4	1	1	NUM
ejpam-5280	411	5	)	)	PUNCT
ejpam-5280	411	6	+	+	CCONJ
ejpam-5280	411	7	12	12	NUM
ejpam-5280	411	8	)	)	PUNCT
ejpam-5280	411	9	t5µ+2	t5µ+2	PROPN
ejpam-5280	411	10	(	(	PUNCT
ejpam-5280	411	11	5µ+	5µ+	NUM
ejpam-5280	411	12	3)(5µ+	3)(5µ+	NOUN
ejpam-5280	411	13	4	4	NUM
ejpam-5280	411	14	)	)	PUNCT
ejpam-5280	411	15	m.i	m.i	PROPN
ejpam-5280	411	16	.	.	PROPN
ejpam-5280	411	17	syam	syam	PROPN
ejpam-5280	411	18	,	,	PUNCT
ejpam-5280	411	19	m.	m.	NOUN
ejpam-5280	411	20	sharadga	sharadga	PROPN
ejpam-5280	411	21	,	,	PUNCT
ejpam-5280	411	22	i.	i.	PROPN
ejpam-5280	411	23	hashim	hashim	PROPN
ejpam-5280	411	24	/	/	SYM
ejpam-5280	411	25	eur	eur	PROPN
ejpam-5280	411	26	.	.	PUNCT
ejpam-5280	412	1	j.	j.	PROPN
ejpam-5280	412	2	pure	pure	PROPN
ejpam-5280	412	3	appl	appl	PROPN
ejpam-5280	412	4	.	.	PROPN
ejpam-5280	412	5	math	math	PROPN
ejpam-5280	412	6	,	,	PUNCT
ejpam-5280	412	7	17	17	NUM
ejpam-5280	412	8	(	(	PUNCT
ejpam-5280	412	9	3	3	NUM
ejpam-5280	412	10	)	)	PUNCT
ejpam-5280	412	11	(	(	PUNCT
ejpam-5280	412	12	2024	2024	NUM
ejpam-5280	412	13	)	)	PUNCT
ejpam-5280	412	14	,	,	PUNCT
ejpam-5280	412	15	1429	1429	NUM
ejpam-5280	412	16	-	-	SYM
ejpam-5280	412	17	1448	1448	NUM
ejpam-5280	412	18	1445	1445	NUM
ejpam-5280	412	19	−	−	PROPN
ejpam-5280	412	20	(	(	PUNCT
ejpam-5280	412	21	36µ2	36µ2	NUM
ejpam-5280	412	22	+	+	NUM
ejpam-5280	412	23	54µ+	54µ+	NUM
ejpam-5280	413	1	6µt(t+	6µt(t+	NUM
ejpam-5280	413	2	1)2	1)2	NUM
ejpam-5280	413	3	+	+	NUM
ejpam-5280	413	4	t(4t+	t(4t+	NOUN
ejpam-5280	413	5	5)(t+	5)(t+	NUM
ejpam-5280	413	6	1	1	NUM
ejpam-5280	413	7	)	)	PUNCT
ejpam-5280	413	8	+	+	NUM
ejpam-5280	413	9	20	20	NUM
ejpam-5280	413	10	)	)	PUNCT
ejpam-5280	413	11	t6µ+3	t6µ+3	VERB
ejpam-5280	413	12	2(3µ+	2(3µ+	NUM
ejpam-5280	413	13	2)(6µ+	2)(6µ+	NUM
ejpam-5280	413	14	5	5	NUM
ejpam-5280	413	15	)	)	PUNCT
ejpam-5280	413	16	−	−	PROPN
ejpam-5280	414	1	(	(	PUNCT
ejpam-5280	414	2	7µ+	7µ+	NUM
ejpam-5280	414	3	4)(µ(7µ(18µ+	4)(µ(7µ(18µ+	NUM
ejpam-5280	414	4	31	31	NUM
ejpam-5280	414	5	)	)	PUNCT
ejpam-5280	414	6	+	+	CCONJ
ejpam-5280	414	7	120	120	NUM
ejpam-5280	414	8	)	)	PUNCT
ejpam-5280	415	1	+	+	CCONJ
ejpam-5280	415	2	21)t3	21)t3	NUM
ejpam-5280	415	3	(	(	PUNCT
ejpam-5280	415	4	2µ+	2µ+	NUM
ejpam-5280	415	5	1)(3µ+	1)(3µ+	NUM
ejpam-5280	416	1	1)(3µ+	1)(3µ+	NUM
ejpam-5280	417	1	2)(4µ+	2)(4µ+	NUM
ejpam-5280	418	1	3)(5µ+	3)(5µ+	NOUN
ejpam-5280	418	2	3	3	NUM
ejpam-5280	418	3	)	)	PUNCT
ejpam-5280	419	1	+	+	NUM
ejpam-5280	419	2	γ(2µ+	γ(2µ+	NOUN
ejpam-5280	419	3	2)tµ+1	2)tµ+1	NUM
ejpam-5280	419	4	γ(µ+	γ(µ+	NOUN
ejpam-5280	419	5	2	2	NUM
ejpam-5280	419	6	)	)	PUNCT
ejpam-5280	419	7	.	.	PUNCT
ejpam-5280	420	1	first	first	ADV
ejpam-5280	420	2	,	,	PUNCT
ejpam-5280	420	3	let	let	VERB
ejpam-5280	420	4	’s	’s	PRON
ejpam-5280	420	5	examine	examine	VERB
ejpam-5280	420	6	the	the	DET
ejpam-5280	420	7	influence	influence	NOUN
ejpam-5280	420	8	of	of	ADP
ejpam-5280	420	9	the	the	DET
ejpam-5280	420	10	fractional	fractional	ADJ
ejpam-5280	420	11	order	order	NOUN
ejpam-5280	420	12	derivative	derivative	NOUN
ejpam-5280	420	13	on	on	ADP
ejpam-5280	420	14	the	the	DET
ejpam-5280	420	15	behavior	behavior	NOUN
ejpam-5280	420	16	of	of	ADP
ejpam-5280	420	17	the	the	DET
ejpam-5280	420	18	solution	solution	NOUN
ejpam-5280	420	19	.	.	PUNCT
ejpam-5280	421	1	figures	figure	NOUN
ejpam-5280	421	2	2	2	NUM
ejpam-5280	421	3	shows	show	VERB
ejpam-5280	421	4	the	the	DET
ejpam-5280	421	5	approximate	approximate	ADJ
ejpam-5280	421	6	solutions	solution	NOUN
ejpam-5280	421	7	ω	ω	X
ejpam-5280	421	8	for	for	ADP
ejpam-5280	421	9	different	different	ADJ
ejpam-5280	421	10	values	value	NOUN
ejpam-5280	421	11	of	of	ADP
ejpam-5280	421	12	µ	µ	NOUN
ejpam-5280	421	13	=	=	SYM
ejpam-5280	421	14	0.5	0.5	NUM
ejpam-5280	421	15	,	,	PUNCT
ejpam-5280	421	16	0.6	0.6	NUM
ejpam-5280	421	17	,	,	PUNCT
ejpam-5280	421	18	0.7	0.7	NUM
ejpam-5280	421	19	,	,	PUNCT
ejpam-5280	421	20	0.8	0.8	NUM
ejpam-5280	421	21	,	,	PUNCT
ejpam-5280	421	22	0.9	0.9	NUM
ejpam-5280	421	23	,	,	PUNCT
ejpam-5280	421	24	1	1	NUM
ejpam-5280	421	25	with	with	ADP
ejpam-5280	421	26	r	r	NOUN
ejpam-5280	421	27	=	=	NOUN
ejpam-5280	421	28	0.005	0.005	NUM
ejpam-5280	421	29	.	.	PUNCT
ejpam-5280	422	1	since	since	SCONJ
ejpam-5280	422	2	the	the	DET
ejpam-5280	422	3	exact	exact	ADJ
ejpam-5280	422	4	solution	solution	NOUN
ejpam-5280	422	5	is	be	AUX
ejpam-5280	422	6	not	not	PART
ejpam-5280	422	7	given	give	VERB
ejpam-5280	422	8	,	,	PUNCT
ejpam-5280	422	9	we	we	PRON
ejpam-5280	422	10	assess	assess	VERB
ejpam-5280	422	11	the	the	DET
ejpam-5280	422	12	0.2	0.2	NUM
ejpam-5280	422	13	0.4	0.4	NUM
ejpam-5280	422	14	0.6	0.6	NUM
ejpam-5280	422	15	0.8	0.8	NUM
ejpam-5280	422	16	1.0	1.0	NUM
ejpam-5280	422	17	0.5	0.5	NUM
ejpam-5280	422	18	1.0	1.0	NUM
ejpam-5280	422	19	1.5	1.5	NUM
ejpam-5280	422	20	2.0	2.0	NUM
ejpam-5280	422	21	μ=0.5	μ=0.5	ADJ
ejpam-5280	422	22	μ=0.6	μ=0.6	NOUN
ejpam-5280	422	23	μ=0.7	μ=0.7	NOUN
ejpam-5280	422	24	μ=0.8	μ=0.8	NOUN
ejpam-5280	422	25	μ=0.9	μ=0.9	NOUN
ejpam-5280	422	26	μ=1	μ=1	NOUN
ejpam-5280	422	27	figure	figure	NOUN
ejpam-5280	422	28	2	2	NUM
ejpam-5280	422	29	:	:	PUNCT
ejpam-5280	422	30	the	the	DET
ejpam-5280	422	31	approximate	approximate	ADJ
ejpam-5280	422	32	solution	solution	NOUN
ejpam-5280	422	33	ω	ω	PROPN
ejpam-5280	422	34	for	for	ADP
ejpam-5280	422	35	µ	µ	NOUN
ejpam-5280	422	36	=	=	SYM
ejpam-5280	422	37	0.5	0.5	NUM
ejpam-5280	422	38	,	,	PUNCT
ejpam-5280	422	39	0.6	0.6	NUM
ejpam-5280	422	40	,	,	PUNCT
ejpam-5280	422	41	0.7	0.7	NUM
ejpam-5280	422	42	,	,	PUNCT
ejpam-5280	422	43	0.8	0.8	NUM
ejpam-5280	422	44	,	,	PUNCT
ejpam-5280	422	45	0.9	0.9	NUM
ejpam-5280	422	46	,	,	PUNCT
ejpam-5280	422	47	1	1	NUM
ejpam-5280	422	48	.	.	X
ejpam-5280	422	49	accuracy	accuracy	NOUN
ejpam-5280	422	50	of	of	ADP
ejpam-5280	422	51	our	our	PRON
ejpam-5280	422	52	approximation	approximation	NOUN
ejpam-5280	422	53	by	by	ADP
ejpam-5280	422	54	computing	compute	VERB
ejpam-5280	422	55	the	the	DET
ejpam-5280	422	56	l2	l2	NOUN
ejpam-5280	422	57	-	-	PUNCT
ejpam-5280	422	58	truncation	truncation	NOUN
ejpam-5280	422	59	errors	error	NOUN
ejpam-5280	422	60	,	,	PUNCT
ejpam-5280	422	61	defined	define	VERB
ejpam-5280	422	62	as	as	ADP
ejpam-5280	422	63	ϵ(µ	ϵ(µ	NOUN
ejpam-5280	422	64	)	)	PUNCT
ejpam-5280	422	65	=	=	PUNCT
ejpam-5280	423	1	(	(	PUNCT
ejpam-5280	423	2	∫	∫	PROPN
ejpam-5280	423	3	1	1	NUM
ejpam-5280	423	4	0	0	NUM
ejpam-5280	423	5	(	(	PUNCT
ejpam-5280	423	6	dµω(t)−	dµω(t)−	PROPN
ejpam-5280	423	7	ω2(t)−g2(t	ω2(t)−g2(t	NUM
ejpam-5280	423	8	)	)	PUNCT
ejpam-5280	424	1	+	+	CCONJ
ejpam-5280	424	2	∫	∫	PROPN
ejpam-5280	424	3	t	t	PROPN
ejpam-5280	424	4	0	0	NUM
ejpam-5280	424	5	(	(	PUNCT
ejpam-5280	424	6	sµ	sµ	NOUN
ejpam-5280	425	1	+	+	CCONJ
ejpam-5280	425	2	1)(tµ	1)(tµ	NUM
ejpam-5280	425	3	+	+	CCONJ
ejpam-5280	425	4	1)ω2(s)ds−	1)ω2(s)ds−	NUM
ejpam-5280	425	5	∫	∫	PROPN
ejpam-5280	425	6	1	1	NUM
ejpam-5280	425	7	0	0	NUM
ejpam-5280	425	8	(	(	PUNCT
ejpam-5280	425	9	sµ	sµ	NOUN
ejpam-5280	425	10	+	+	CCONJ
ejpam-5280	425	11	1)tµω2(s)ds	1)tµω2(s)ds	NUM
ejpam-5280	425	12	)	)	PUNCT
ejpam-5280	425	13	dt	dt	NOUN
ejpam-5280	425	14	)	)	PUNCT
ejpam-5280	425	15	1	1	NUM
ejpam-5280	425	16	2	2	NUM
ejpam-5280	425	17	.	.	PUNCT
ejpam-5280	426	1	the	the	DET
ejpam-5280	426	2	errors	error	NOUN
ejpam-5280	426	3	are	be	AUX
ejpam-5280	426	4	presented	present	VERB
ejpam-5280	426	5	in	in	ADP
ejpam-5280	426	6	table	table	NOUN
ejpam-5280	426	7	2	2	NUM
ejpam-5280	426	8	.	.	PUNCT
ejpam-5280	426	9	table	table	NOUN
ejpam-5280	426	10	2	2	NUM
ejpam-5280	426	11	:	:	PUNCT
ejpam-5280	426	12	the	the	DET
ejpam-5280	426	13	l2	l2	NOUN
ejpam-5280	426	14	-	-	PUNCT
ejpam-5280	426	15	error	error	NOUN
ejpam-5280	426	16	for	for	ADP
ejpam-5280	426	17	µ	µ	NOUN
ejpam-5280	426	18	=	=	SYM
ejpam-5280	426	19	0.5	0.5	NUM
ejpam-5280	426	20	,	,	PUNCT
ejpam-5280	426	21	0.6	0.6	NUM
ejpam-5280	426	22	,	,	PUNCT
ejpam-5280	426	23	0.7	0.7	NUM
ejpam-5280	426	24	,	,	PUNCT
ejpam-5280	426	25	0.8	0.8	NUM
ejpam-5280	426	26	,	,	PUNCT
ejpam-5280	426	27	0.9	0.9	NUM
ejpam-5280	426	28	,	,	PUNCT
ejpam-5280	426	29	1	1	NUM
ejpam-5280	426	30	.	.	X
ejpam-5280	426	31	µ	µ	X
ejpam-5280	426	32	ϵ(µ	ϵ(µ	NOUN
ejpam-5280	426	33	)	)	PUNCT
ejpam-5280	426	34	0.5	0.5	NUM
ejpam-5280	426	35	2.34×	2.34×	NUM
ejpam-5280	426	36	10−12	10−12	NOUN
ejpam-5280	426	37	0.6	0.6	NUM
ejpam-5280	426	38	2.21×	2.21×	NUM
ejpam-5280	426	39	10−12	10−12	NOUN
ejpam-5280	426	40	0.7	0.7	NUM
ejpam-5280	426	41	2.01×	2.01×	NUM
ejpam-5280	426	42	10−12	10−12	NOUN
ejpam-5280	426	43	0.8	0.8	NUM
ejpam-5280	426	44	1.98×	1.98×	NUM
ejpam-5280	426	45	10−12	10−12	NOUN
ejpam-5280	426	46	9	9	NUM
ejpam-5280	426	47	1.95×	1.95×	NUM
ejpam-5280	426	48	10−12	10−12	NOUN
ejpam-5280	426	49	1	1	NUM
ejpam-5280	426	50	1.82×	1.82×	NUM
ejpam-5280	426	51	10−12	10−12	PROPN
ejpam-5280	426	52	6	6	NUM
ejpam-5280	426	53	.	.	PUNCT
ejpam-5280	427	1	conclusion	conclusion	NOUN
ejpam-5280	427	2	the	the	DET
ejpam-5280	427	3	operational	operational	ADJ
ejpam-5280	427	4	matrix	matrix	NOUN
ejpam-5280	427	5	method	method	NOUN
ejpam-5280	427	6	is	be	AUX
ejpam-5280	427	7	a	a	DET
ejpam-5280	427	8	useful	useful	ADJ
ejpam-5280	427	9	approach	approach	NOUN
ejpam-5280	427	10	for	for	ADP
ejpam-5280	427	11	solving	solve	VERB
ejpam-5280	427	12	fractional	fractional	ADJ
ejpam-5280	427	13	volterrafredholm	volterrafredholm	NOUN
ejpam-5280	427	14	integro	integro	ADJ
ejpam-5280	427	15	-	-	PUNCT
ejpam-5280	427	16	differential	differential	NOUN
ejpam-5280	427	17	equations	equation	NOUN
ejpam-5280	427	18	.	.	PUNCT
ejpam-5280	428	1	it	it	PRON
ejpam-5280	428	2	involves	involve	VERB
ejpam-5280	428	3	converting	convert	VERB
ejpam-5280	428	4	the	the	DET
ejpam-5280	428	5	differential	differential	ADJ
ejpam-5280	428	6	system	system	NOUN
ejpam-5280	428	7	into	into	ADP
ejpam-5280	428	8	a	a	DET
ejpam-5280	428	9	system	system	NOUN
ejpam-5280	428	10	of	of	ADP
ejpam-5280	428	11	algebraic	algebraic	ADJ
ejpam-5280	428	12	equations	equation	NOUN
ejpam-5280	428	13	to	to	PART
ejpam-5280	428	14	determine	determine	VERB
ejpam-5280	428	15	the	the	DET
ejpam-5280	428	16	coefficients	coefficient	NOUN
ejpam-5280	428	17	of	of	ADP
ejpam-5280	428	18	the	the	DET
ejpam-5280	428	19	approximating	approximate	VERB
ejpam-5280	428	20	solution	solution	NOUN
ejpam-5280	428	21	.	.	PUNCT
ejpam-5280	429	1	references	reference	NOUN
ejpam-5280	429	2	1446	1446	NUM
ejpam-5280	429	3	typically	typically	ADV
ejpam-5280	429	4	,	,	PUNCT
ejpam-5280	429	5	these	these	DET
ejpam-5280	429	6	coefficients	coefficient	NOUN
ejpam-5280	429	7	are	be	AUX
ejpam-5280	429	8	computed	compute	VERB
ejpam-5280	429	9	by	by	ADP
ejpam-5280	429	10	establishing	establish	VERB
ejpam-5280	429	11	operational	operational	ADJ
ejpam-5280	429	12	matrices	matrix	NOUN
ejpam-5280	429	13	corresponding	correspond	VERB
ejpam-5280	429	14	to	to	ADP
ejpam-5280	429	15	integral	integral	ADJ
ejpam-5280	429	16	,	,	PUNCT
ejpam-5280	429	17	derivative	derivative	ADJ
ejpam-5280	429	18	,	,	PUNCT
ejpam-5280	429	19	and	and	CCONJ
ejpam-5280	429	20	product	product	NOUN
ejpam-5280	429	21	operators	operator	NOUN
ejpam-5280	429	22	.	.	PUNCT
ejpam-5280	430	1	the	the	DET
ejpam-5280	430	2	block	block	NOUN
ejpam-5280	430	3	pulse	pulse	NOUN
ejpam-5280	430	4	functions	function	NOUN
ejpam-5280	430	5	,	,	PUNCT
ejpam-5280	430	6	upon	upon	SCONJ
ejpam-5280	430	7	which	which	PRON
ejpam-5280	430	8	our	our	PRON
ejpam-5280	430	9	approximation	approximation	NOUN
ejpam-5280	430	10	basis	basis	NOUN
ejpam-5280	430	11	,	,	PUNCT
ejpam-5280	430	12	possess	possess	VERB
ejpam-5280	430	13	three	three	NUM
ejpam-5280	430	14	key	key	ADJ
ejpam-5280	430	15	properties	property	NOUN
ejpam-5280	430	16	—	—	PUNCT
ejpam-5280	430	17	disjointness	disjointness	NOUN
ejpam-5280	430	18	,	,	PUNCT
ejpam-5280	430	19	orthogonality	orthogonality	NOUN
ejpam-5280	430	20	,	,	PUNCT
ejpam-5280	430	21	and	and	CCONJ
ejpam-5280	430	22	completeness	completeness	NOUN
ejpam-5280	430	23	—	—	PUNCT
ejpam-5280	430	24	that	that	PRON
ejpam-5280	430	25	facilitate	facilitate	VERB
ejpam-5280	430	26	the	the	DET
ejpam-5280	430	27	computations	computation	NOUN
ejpam-5280	430	28	.	.	PUNCT
ejpam-5280	431	1	in	in	ADP
ejpam-5280	431	2	this	this	DET
ejpam-5280	431	3	paper	paper	NOUN
ejpam-5280	431	4	,	,	PUNCT
ejpam-5280	431	5	we	we	PRON
ejpam-5280	431	6	investigate	investigate	VERB
ejpam-5280	431	7	fractional	fractional	ADJ
ejpam-5280	431	8	volterra	volterra	NOUN
ejpam-5280	431	9	-	-	PUNCT
ejpam-5280	431	10	fredholm	fredholm	NOUN
ejpam-5280	431	11	integro	integro	ADJ
ejpam-5280	431	12	-	-	PUNCT
ejpam-5280	431	13	differential	differential	NOUN
ejpam-5280	431	14	equations	equation	NOUN
ejpam-5280	431	15	,	,	PUNCT
ejpam-5280	431	16	a	a	DET
ejpam-5280	431	17	fundamental	fundamental	ADJ
ejpam-5280	431	18	problem	problem	NOUN
ejpam-5280	431	19	in	in	ADP
ejpam-5280	431	20	various	various	ADJ
ejpam-5280	431	21	fields	field	NOUN
ejpam-5280	431	22	such	such	ADJ
ejpam-5280	431	23	as	as	ADP
ejpam-5280	431	24	control	control	NOUN
ejpam-5280	431	25	theory	theory	NOUN
ejpam-5280	431	26	,	,	PUNCT
ejpam-5280	431	27	biology	biology	NOUN
ejpam-5280	431	28	,	,	PUNCT
ejpam-5280	431	29	and	and	CCONJ
ejpam-5280	431	30	particle	particle	NOUN
ejpam-5280	431	31	dynamics	dynamic	NOUN
ejpam-5280	431	32	in	in	ADP
ejpam-5280	431	33	physics	physics	NOUN
ejpam-5280	431	34	.	.	PUNCT
ejpam-5280	432	1	we	we	PRON
ejpam-5280	432	2	develop	develop	VERB
ejpam-5280	432	3	a	a	DET
ejpam-5280	432	4	numerical	numerical	ADJ
ejpam-5280	432	5	method	method	NOUN
ejpam-5280	432	6	based	base	VERB
ejpam-5280	432	7	on	on	ADP
ejpam-5280	432	8	the	the	DET
ejpam-5280	432	9	operational	operational	ADJ
ejpam-5280	432	10	matrix	matrix	NOUN
ejpam-5280	432	11	method	method	NOUN
ejpam-5280	432	12	to	to	PART
ejpam-5280	432	13	solve	solve	VERB
ejpam-5280	432	14	these	these	DET
ejpam-5280	432	15	equations	equation	NOUN
ejpam-5280	432	16	,	,	PUNCT
ejpam-5280	432	17	proving	prove	VERB
ejpam-5280	432	18	the	the	DET
ejpam-5280	432	19	existence	existence	NOUN
ejpam-5280	432	20	and	and	CCONJ
ejpam-5280	432	21	uniqueness	uniqueness	NOUN
ejpam-5280	432	22	of	of	ADP
ejpam-5280	432	23	the	the	DET
ejpam-5280	432	24	exact	exact	ADJ
ejpam-5280	432	25	solution	solution	NOUN
ejpam-5280	432	26	.	.	PUNCT
ejpam-5280	433	1	additionally	additionally	ADV
ejpam-5280	433	2	,	,	PUNCT
ejpam-5280	433	3	we	we	PRON
ejpam-5280	433	4	demonstrate	demonstrate	VERB
ejpam-5280	433	5	the	the	DET
ejpam-5280	433	6	uniform	uniform	ADJ
ejpam-5280	433	7	convergence	convergence	NOUN
ejpam-5280	433	8	of	of	ADP
ejpam-5280	433	9	numerical	numerical	ADJ
ejpam-5280	433	10	solutions	solution	NOUN
ejpam-5280	433	11	to	to	ADP
ejpam-5280	433	12	the	the	DET
ejpam-5280	433	13	exact	exact	ADJ
ejpam-5280	433	14	solution	solution	NOUN
ejpam-5280	433	15	and	and	CCONJ
ejpam-5280	433	16	present	present	VERB
ejpam-5280	433	17	several	several	ADJ
ejpam-5280	433	18	numerical	numerical	ADJ
ejpam-5280	433	19	examples	example	NOUN
ejpam-5280	433	20	illustrating	illustrate	VERB
ejpam-5280	433	21	the	the	DET
ejpam-5280	433	22	method	method	NOUN
ejpam-5280	433	23	’s	’s	PART
ejpam-5280	433	24	efficiency	efficiency	NOUN
ejpam-5280	433	25	.	.	PUNCT
ejpam-5280	434	1	in	in	ADP
ejpam-5280	434	2	one	one	NUM
ejpam-5280	434	3	example	example	NOUN
ejpam-5280	434	4	,	,	PUNCT
ejpam-5280	434	5	for	for	ADP
ejpam-5280	434	6	a	a	DET
ejpam-5280	434	7	linear	linear	ADJ
ejpam-5280	434	8	problem	problem	NOUN
ejpam-5280	434	9	,	,	PUNCT
ejpam-5280	434	10	we	we	PRON
ejpam-5280	434	11	observe	observe	VERB
ejpam-5280	434	12	convergence	convergence	NOUN
ejpam-5280	434	13	of	of	ADP
ejpam-5280	434	14	the	the	DET
ejpam-5280	434	15	approximate	approximate	ADJ
ejpam-5280	434	16	solution	solution	NOUN
ejpam-5280	434	17	to	to	ADP
ejpam-5280	434	18	the	the	DET
ejpam-5280	434	19	exact	exact	ADJ
ejpam-5280	434	20	solution	solution	NOUN
ejpam-5280	434	21	as	as	ADP
ejpam-5280	434	22	the	the	DET
ejpam-5280	434	23	number	number	NOUN
ejpam-5280	434	24	of	of	ADP
ejpam-5280	434	25	block	block	NOUN
ejpam-5280	434	26	pulse	pulse	NOUN
ejpam-5280	434	27	functions	function	NOUN
ejpam-5280	434	28	increases	increase	NOUN
ejpam-5280	434	29	.	.	PUNCT
ejpam-5280	435	1	in	in	ADP
ejpam-5280	435	2	nonlinear	nonlinear	ADJ
ejpam-5280	435	3	cases	case	NOUN
ejpam-5280	435	4	,	,	PUNCT
ejpam-5280	435	5	where	where	SCONJ
ejpam-5280	435	6	exact	exact	ADJ
ejpam-5280	435	7	solutions	solution	NOUN
ejpam-5280	435	8	are	be	AUX
ejpam-5280	435	9	unavailable	unavailable	ADJ
ejpam-5280	435	10	,	,	PUNCT
ejpam-5280	435	11	we	we	PRON
ejpam-5280	435	12	compute	compute	VERB
ejpam-5280	435	13	the	the	DET
ejpam-5280	435	14	l2	l2	NOUN
ejpam-5280	435	15	-	-	PUNCT
ejpam-5280	435	16	local	local	ADJ
ejpam-5280	435	17	truncation	truncation	NOUN
ejpam-5280	435	18	error	error	NOUN
ejpam-5280	435	19	,	,	PUNCT
ejpam-5280	435	20	which	which	PRON
ejpam-5280	435	21	is	be	AUX
ejpam-5280	435	22	on	on	ADP
ejpam-5280	435	23	the	the	DET
ejpam-5280	435	24	order	order	NOUN
ejpam-5280	435	25	of	of	ADP
ejpam-5280	435	26	10−12	10−12	NOUN
ejpam-5280	435	27	.	.	PUNCT
ejpam-5280	436	1	we	we	PRON
ejpam-5280	436	2	also	also	ADV
ejpam-5280	436	3	examine	examine	VERB
ejpam-5280	436	4	the	the	DET
ejpam-5280	436	5	influence	influence	NOUN
ejpam-5280	436	6	of	of	ADP
ejpam-5280	436	7	the	the	DET
ejpam-5280	436	8	fractional	fractional	ADJ
ejpam-5280	436	9	derivative	derivative	NOUN
ejpam-5280	436	10	on	on	ADP
ejpam-5280	436	11	solution	solution	NOUN
ejpam-5280	436	12	profiles	profile	NOUN
ejpam-5280	436	13	through	through	ADP
ejpam-5280	436	14	graph	graph	NOUN
ejpam-5280	436	15	sketches	sketch	NOUN
ejpam-5280	436	16	.	.	PUNCT
ejpam-5280	437	1	theoretical	theoretical	ADJ
ejpam-5280	437	2	and	and	CCONJ
ejpam-5280	437	3	numerical	numerical	ADJ
ejpam-5280	437	4	results	result	NOUN
ejpam-5280	437	5	affirm	affirm	VERB
ejpam-5280	437	6	the	the	DET
ejpam-5280	437	7	accuracy	accuracy	NOUN
ejpam-5280	437	8	and	and	CCONJ
ejpam-5280	437	9	applicability	applicability	NOUN
ejpam-5280	437	10	of	of	ADP
ejpam-5280	437	11	our	our	PRON
ejpam-5280	437	12	proposed	propose	VERB
ejpam-5280	437	13	method	method	NOUN
ejpam-5280	437	14	to	to	PART
ejpam-5280	437	15	nonlinear	nonlinear	ADJ
ejpam-5280	437	16	problems	problem	NOUN
ejpam-5280	437	17	in	in	ADP
ejpam-5280	437	18	science	science	NOUN
ejpam-5280	437	19	.	.	PUNCT
ejpam-5280	438	1	concluding	conclude	VERB
ejpam-5280	438	2	this	this	DET
ejpam-5280	438	3	paper	paper	NOUN
ejpam-5280	438	4	,	,	PUNCT
ejpam-5280	438	5	we	we	PRON
ejpam-5280	438	6	highlight	highlight	VERB
ejpam-5280	438	7	the	the	DET
ejpam-5280	438	8	following	follow	VERB
ejpam-5280	438	9	observations	observation	NOUN
ejpam-5280	438	10	:	:	PUNCT
ejpam-5280	438	11	(	(	PUNCT
ejpam-5280	438	12	i	i	NOUN
ejpam-5280	438	13	)	)	PUNCT
ejpam-5280	438	14	example	example	NOUN
ejpam-5280	438	15	1	1	NUM
ejpam-5280	438	16	demonstrates	demonstrate	VERB
ejpam-5280	438	17	that	that	SCONJ
ejpam-5280	438	18	in	in	ADP
ejpam-5280	438	19	linear	linear	ADJ
ejpam-5280	438	20	cases	case	NOUN
ejpam-5280	438	21	,	,	PUNCT
ejpam-5280	438	22	the	the	DET
ejpam-5280	438	23	approximate	approximate	ADJ
ejpam-5280	438	24	solution	solution	NOUN
ejpam-5280	438	25	converges	converge	VERB
ejpam-5280	438	26	to	to	ADP
ejpam-5280	438	27	the	the	DET
ejpam-5280	438	28	exact	exact	ADJ
ejpam-5280	438	29	solution	solution	NOUN
ejpam-5280	438	30	with	with	ADP
ejpam-5280	438	31	increasing	increase	VERB
ejpam-5280	438	32	numbers	number	NOUN
ejpam-5280	438	33	of	of	ADP
ejpam-5280	438	34	block	block	NOUN
ejpam-5280	438	35	pulse	pulse	NOUN
ejpam-5280	438	36	functions	function	NOUN
ejpam-5280	438	37	,	,	PUNCT
ejpam-5280	438	38	yielding	yield	VERB
ejpam-5280	438	39	solutions	solution	NOUN
ejpam-5280	438	40	in	in	ADP
ejpam-5280	438	41	closed	closed	ADJ
ejpam-5280	438	42	form	form	NOUN
ejpam-5280	438	43	.	.	PUNCT
ejpam-5280	439	1	(	(	PUNCT
ejpam-5280	439	2	ii	ii	NOUN
ejpam-5280	439	3	)	)	PUNCT
ejpam-5280	439	4	example	example	NOUN
ejpam-5280	439	5	2	2	NUM
ejpam-5280	439	6	illustrates	illustrate	VERB
ejpam-5280	439	7	the	the	DET
ejpam-5280	439	8	decreasing	decrease	VERB
ejpam-5280	439	9	influence	influence	NOUN
ejpam-5280	439	10	of	of	ADP
ejpam-5280	439	11	the	the	DET
ejpam-5280	439	12	fractional	fractional	ADJ
ejpam-5280	439	13	order	order	NOUN
ejpam-5280	439	14	on	on	ADP
ejpam-5280	439	15	solution	solution	NOUN
ejpam-5280	439	16	profiles	profile	NOUN
ejpam-5280	439	17	as	as	ADP
ejpam-5280	439	18	the	the	DET
ejpam-5280	439	19	fractional	fractional	ADJ
ejpam-5280	439	20	derivative	derivative	ADJ
ejpam-5280	439	21	increases	increase	NOUN
ejpam-5280	439	22	.	.	PUNCT
ejpam-5280	440	1	the	the	DET
ejpam-5280	440	2	l2	l2	NOUN
ejpam-5280	440	3	-	-	PUNCT
ejpam-5280	440	4	truncation	truncation	NOUN
ejpam-5280	440	5	error	error	NOUN
ejpam-5280	440	6	is	be	AUX
ejpam-5280	440	7	of	of	ADP
ejpam-5280	440	8	order	order	NOUN
ejpam-5280	440	9	10−12	10−12	NOUN
ejpam-5280	440	10	,	,	PUNCT
ejpam-5280	440	11	as	as	SCONJ
ejpam-5280	440	12	shown	show	VERB
ejpam-5280	440	13	in	in	ADP
ejpam-5280	440	14	table	table	NOUN
ejpam-5280	440	15	1	1	NUM
ejpam-5280	440	16	and	and	CCONJ
ejpam-5280	440	17	figure	figure	VERB
ejpam-5280	440	18	1	1	NUM
ejpam-5280	440	19	.	.	PUNCT
ejpam-5280	441	1	(	(	PUNCT
ejpam-5280	441	2	iii	iii	NOUN
ejpam-5280	441	3	)	)	PUNCT
ejpam-5280	441	4	similar	similar	ADJ
ejpam-5280	441	5	results	result	NOUN
ejpam-5280	441	6	are	be	AUX
ejpam-5280	441	7	obtained	obtain	VERB
ejpam-5280	441	8	in	in	ADP
ejpam-5280	441	9	example	example	NOUN
ejpam-5280	441	10	3	3	NUM
ejpam-5280	441	11	,	,	PUNCT
ejpam-5280	441	12	as	as	SCONJ
ejpam-5280	441	13	presented	present	VERB
ejpam-5280	441	14	in	in	ADP
ejpam-5280	441	15	table	table	NOUN
ejpam-5280	441	16	2	2	NUM
ejpam-5280	441	17	and	and	CCONJ
ejpam-5280	441	18	figure	figure	NOUN
ejpam-5280	441	19	2	2	NUM
ejpam-5280	441	20	.	.	PUNCT
ejpam-5280	441	21	(	(	PUNCT
ejpam-5280	441	22	iv	iv	X
ejpam-5280	441	23	)	)	PUNCT
ejpam-5280	441	24	our	our	PRON
ejpam-5280	441	25	findings	finding	NOUN
ejpam-5280	441	26	suggest	suggest	VERB
ejpam-5280	441	27	that	that	SCONJ
ejpam-5280	441	28	our	our	PRON
ejpam-5280	441	29	proposed	propose	VERB
ejpam-5280	441	30	method	method	NOUN
ejpam-5280	441	31	is	be	AUX
ejpam-5280	441	32	promising	promise	VERB
ejpam-5280	441	33	and	and	CCONJ
ejpam-5280	441	34	applicable	applicable	ADJ
ejpam-5280	441	35	across	across	ADP
ejpam-5280	441	36	diverse	diverse	ADJ
ejpam-5280	441	37	models	model	NOUN
ejpam-5280	441	38	in	in	ADP
ejpam-5280	441	39	physics	physics	NOUN
ejpam-5280	441	40	and	and	CCONJ
ejpam-5280	441	41	engineering	engineering	NOUN
ejpam-5280	441	42	,	,	PUNCT
ejpam-5280	441	43	even	even	ADV
ejpam-5280	441	44	in	in	ADP
ejpam-5280	441	45	the	the	DET
ejpam-5280	441	46	presence	presence	NOUN
ejpam-5280	441	47	of	of	ADP
ejpam-5280	441	48	significant	significant	ADJ
ejpam-5280	441	49	nonlinearity	nonlinearity	NOUN
ejpam-5280	441	50	.	.	PUNCT
ejpam-5280	442	1	acknowledgements	acknowledgement	NOUN
ejpam-5280	442	2	the	the	DET
ejpam-5280	442	3	authors	author	NOUN
ejpam-5280	442	4	express	express	VERB
ejpam-5280	442	5	their	their	PRON
ejpam-5280	442	6	gratitude	gratitude	NOUN
ejpam-5280	442	7	to	to	ADP
ejpam-5280	442	8	the	the	DET
ejpam-5280	442	9	editor	editor	NOUN
ejpam-5280	442	10	and	and	CCONJ
ejpam-5280	442	11	the	the	DET
ejpam-5280	442	12	reviewers	reviewer	NOUN
ejpam-5280	442	13	for	for	ADP
ejpam-5280	442	14	their	their	PRON
ejpam-5280	442	15	valuable	valuable	ADJ
ejpam-5280	442	16	comments	comment	NOUN
ejpam-5280	442	17	.	.	PUNCT
ejpam-5280	443	1	references	reference	NOUN
ejpam-5280	443	2	[	[	X
ejpam-5280	443	3	1	1	NUM
ejpam-5280	443	4	]	]	X
ejpam-5280	443	5	d	d	NOUN
ejpam-5280	443	6	baleanu	baleanu	NOUN
ejpam-5280	443	7	,	,	PUNCT
ejpam-5280	443	8	k	k	PROPN
ejpam-5280	443	9	diethelm	diethelm	PROPN
ejpam-5280	443	10	,	,	PUNCT
ejpam-5280	443	11	e	e	PROPN
ejpam-5280	443	12	scalas	scalas	PROPN
ejpam-5280	443	13	,	,	PUNCT
ejpam-5280	443	14	and	and	CCONJ
ejpam-5280	443	15	j.j	j.j	PROPN
ejpam-5280	443	16	.	.	PROPN
ejpam-5280	443	17	trujillo	trujillo	PROPN
ejpam-5280	443	18	,	,	PUNCT
ejpam-5280	443	19	editors	editor	NOUN
ejpam-5280	443	20	.	.	PUNCT
ejpam-5280	444	1	fractional	fractional	ADJ
ejpam-5280	444	2	calculus	calculus	NOUN
ejpam-5280	444	3	:	:	PUNCT
ejpam-5280	444	4	models	model	NOUN
ejpam-5280	444	5	and	and	CCONJ
ejpam-5280	444	6	numerical	numerical	ADJ
ejpam-5280	444	7	methods	method	NOUN
ejpam-5280	444	8	.	.	PUNCT
ejpam-5280	444	9	,	,	PUNCT
ejpam-5280	444	10	volume	volume	NOUN
ejpam-5280	444	11	3	3	NUM
ejpam-5280	444	12	.	.	PUNCT
ejpam-5280	445	1	world	world	PROPN
ejpam-5280	445	2	scientific	scientific	ADJ
ejpam-5280	445	3	,	,	PUNCT
ejpam-5280	445	4	2012	2012	NUM
ejpam-5280	445	5	.	.	PUNCT
ejpam-5280	446	1	[	[	X
ejpam-5280	446	2	2	2	NUM
ejpam-5280	446	3	]	]	PUNCT
ejpam-5280	446	4	a	a	DET
ejpam-5280	446	5	h	h	NOUN
ejpam-5280	446	6	bhrawy	bhrawy	NOUN
ejpam-5280	446	7	and	and	CCONJ
ejpam-5280	446	8	a	a	DET
ejpam-5280	446	9	s	s	NOUN
ejpam-5280	446	10	alofi	alofi	ADJ
ejpam-5280	446	11	.	.	PUNCT
ejpam-5280	447	1	operational	operational	ADJ
ejpam-5280	447	2	matrix	matrix	NOUN
ejpam-5280	447	3	method	method	NOUN
ejpam-5280	447	4	for	for	ADP
ejpam-5280	447	5	solving	solve	VERB
ejpam-5280	447	6	fractional	fractional	ADJ
ejpam-5280	447	7	differential	differential	ADJ
ejpam-5280	447	8	equations	equation	NOUN
ejpam-5280	447	9	:	:	PUNCT
ejpam-5280	447	10	a	a	DET
ejpam-5280	447	11	review	review	NOUN
ejpam-5280	447	12	.	.	PUNCT
ejpam-5280	448	1	journal	journal	PROPN
ejpam-5280	448	2	of	of	ADP
ejpam-5280	448	3	computational	computational	ADJ
ejpam-5280	448	4	and	and	CCONJ
ejpam-5280	448	5	applied	applied	ADJ
ejpam-5280	448	6	mathematics	mathematic	NOUN
ejpam-5280	448	7	,	,	PUNCT
ejpam-5280	448	8	330:1056–1066	330:1056–1066	NUM
ejpam-5280	448	9	,	,	PUNCT
ejpam-5280	448	10	2017	2017	NUM
ejpam-5280	448	11	.	.	PUNCT
ejpam-5280	449	1	references	reference	NOUN
ejpam-5280	449	2	1447	1447	NUM
ejpam-5280	450	1	[	[	X
ejpam-5280	450	2	3	3	X
ejpam-5280	450	3	]	]	PUNCT
ejpam-5280	450	4	a	a	DET
ejpam-5280	450	5	ghorbani	ghorbani	NOUN
ejpam-5280	450	6	and	and	CCONJ
ejpam-5280	450	7	s	s	VERB
ejpam-5280	450	8	a	a	DET
ejpam-5280	450	9	yousefi	yousefi	NOUN
ejpam-5280	450	10	.	.	PUNCT
ejpam-5280	451	1	numerical	numerical	ADJ
ejpam-5280	451	2	solution	solution	NOUN
ejpam-5280	451	3	of	of	ADP
ejpam-5280	451	4	nonlinear	nonlinear	ADJ
ejpam-5280	451	5	fractional	fractional	ADJ
ejpam-5280	451	6	differential	differential	ADJ
ejpam-5280	451	7	equations	equation	NOUN
ejpam-5280	451	8	by	by	ADP
ejpam-5280	451	9	operational	operational	ADJ
ejpam-5280	451	10	matrix	matrix	NOUN
ejpam-5280	451	11	method	method	NOUN
ejpam-5280	451	12	based	base	VERB
ejpam-5280	451	13	on	on	ADP
ejpam-5280	451	14	difference	difference	NOUN
ejpam-5280	451	15	basis	basis	NOUN
ejpam-5280	451	16	.	.	PUNCT
ejpam-5280	452	1	journal	journal	NOUN
ejpam-5280	452	2	of	of	ADP
ejpam-5280	452	3	computational	computational	ADJ
ejpam-5280	452	4	and	and	CCONJ
ejpam-5280	452	5	applied	applied	ADJ
ejpam-5280	452	6	mathematics	mathematic	NOUN
ejpam-5280	452	7	,	,	PUNCT
ejpam-5280	452	8	347:603–618	347:603–618	NUM
ejpam-5280	452	9	,	,	PUNCT
ejpam-5280	452	10	2019	2019	NUM
ejpam-5280	452	11	.	.	PUNCT
ejpam-5280	453	1	[	[	X
ejpam-5280	453	2	4	4	X
ejpam-5280	453	3	]	]	PUNCT
ejpam-5280	453	4	a	a	DET
ejpam-5280	453	5	ghorbani	ghorbani	NOUN
ejpam-5280	453	6	and	and	CCONJ
ejpam-5280	453	7	s	s	VERB
ejpam-5280	453	8	a	a	DET
ejpam-5280	453	9	yousefi	yousefi	NOUN
ejpam-5280	453	10	.	.	PUNCT
ejpam-5280	454	1	solving	solve	VERB
ejpam-5280	454	2	fractional	fractional	ADJ
ejpam-5280	454	3	differential	differential	ADJ
ejpam-5280	454	4	equations	equation	NOUN
ejpam-5280	454	5	by	by	ADP
ejpam-5280	454	6	operational	operational	ADJ
ejpam-5280	454	7	matrix	matrix	NOUN
ejpam-5280	454	8	method	method	NOUN
ejpam-5280	454	9	based	base	VERB
ejpam-5280	454	10	on	on	ADP
ejpam-5280	454	11	difference	difference	NOUN
ejpam-5280	454	12	basis	basis	NOUN
ejpam-5280	454	13	.	.	PUNCT
ejpam-5280	455	1	communications	communication	NOUN
ejpam-5280	455	2	in	in	ADP
ejpam-5280	455	3	nonlinear	nonlinear	ADJ
ejpam-5280	455	4	science	science	NOUN
ejpam-5280	455	5	and	and	CCONJ
ejpam-5280	455	6	numerical	numerical	PROPN
ejpam-5280	455	7	simulation	simulation	PROPN
ejpam-5280	455	8	,	,	PUNCT
ejpam-5280	455	9	67:416–433	67:416–433	NUM
ejpam-5280	455	10	,	,	PUNCT
ejpam-5280	455	11	2019	2019	NUM
ejpam-5280	455	12	.	.	PUNCT
ejpam-5280	456	1	[	[	X
ejpam-5280	456	2	5	5	NUM
ejpam-5280	456	3	]	]	PUNCT
ejpam-5280	456	4	m	m	VERB
ejpam-5280	456	5	khashan	khashan	NOUN
ejpam-5280	456	6	and	and	CCONJ
ejpam-5280	456	7	m	m	PROPN
ejpam-5280	456	8	i	i	PROPN
ejpam-5280	456	9	syam	syam	NOUN
ejpam-5280	456	10	.	.	PUNCT
ejpam-5280	457	1	an	an	DET
ejpam-5280	457	2	efficient	efficient	ADJ
ejpam-5280	457	3	method	method	NOUN
ejpam-5280	457	4	for	for	ADP
ejpam-5280	457	5	solving	solve	VERB
ejpam-5280	457	6	fractional	fractional	ADJ
ejpam-5280	457	7	ricatti	ricatti	NOUN
ejpam-5280	457	8	equations	equation	NOUN
ejpam-5280	457	9	.	.	PUNCT
ejpam-5280	458	1	advances	advance	NOUN
ejpam-5280	458	2	in	in	ADP
ejpam-5280	458	3	difference	difference	NOUN
ejpam-5280	458	4	equations	equation	NOUN
ejpam-5280	458	5	,	,	PUNCT
ejpam-5280	458	6	2019(1):1–12	2019(1):1–12	NOUN
ejpam-5280	458	7	,	,	PUNCT
ejpam-5280	458	8	2019	2019	NUM
ejpam-5280	458	9	.	.	PUNCT
ejpam-5280	459	1	[	[	X
ejpam-5280	459	2	6	6	NUM
ejpam-5280	459	3	]	]	PUNCT
ejpam-5280	459	4	a	a	DET
ejpam-5280	459	5	kilbas	kilbas	PROPN
ejpam-5280	459	6	,	,	PUNCT
ejpam-5280	459	7	h	h	PROPN
ejpam-5280	459	8	m	m	PROPN
ejpam-5280	459	9	srivastava	srivastava	PROPN
ejpam-5280	459	10	,	,	PUNCT
ejpam-5280	459	11	and	and	CCONJ
ejpam-5280	459	12	j	j	PROPN
ejpam-5280	459	13	j	j	PROPN
ejpam-5280	459	14	trujillo	trujillo	PROPN
ejpam-5280	459	15	.	.	PUNCT
ejpam-5280	459	16	theory	theory	NOUN
ejpam-5280	459	17	and	and	CCONJ
ejpam-5280	459	18	application	application	NOUN
ejpam-5280	459	19	of	of	ADP
ejpam-5280	459	20	fractional	fractional	ADJ
ejpam-5280	459	21	differential	differential	ADJ
ejpam-5280	459	22	equations	equation	NOUN
ejpam-5280	459	23	.	.	PUNCT
ejpam-5280	460	1	,	,	PUNCT
ejpam-5280	460	2	volume	volume	NOUN
ejpam-5280	460	3	204	204	NUM
ejpam-5280	460	4	of	of	ADP
ejpam-5280	460	5	north	north	PROPN
ejpam-5280	460	6	holland	holland	PROPN
ejpam-5280	460	7	mathematics	mathematic	NOUN
ejpam-5280	460	8	studies	study	NOUN
ejpam-5280	460	9	.	.	PUNCT
ejpam-5280	461	1	elsevier	elsevier	PROPN
ejpam-5280	461	2	,	,	PUNCT
ejpam-5280	461	3	amsterdam	amsterdam	PROPN
ejpam-5280	461	4	,	,	PUNCT
ejpam-5280	461	5	2006	2006	NUM
ejpam-5280	461	6	.	.	PUNCT
ejpam-5280	462	1	[	[	X
ejpam-5280	462	2	7	7	X
ejpam-5280	462	3	]	]	X
ejpam-5280	462	4	p	p	PROPN
ejpam-5280	462	5	kumar	kumar	PROPN
ejpam-5280	462	6	and	and	CCONJ
ejpam-5280	462	7	d	d	PROPN
ejpam-5280	462	8	kumar	kumar	PROPN
ejpam-5280	462	9	.	.	PROPN
ejpam-5280	462	10	numerical	numerical	PROPN
ejpam-5280	462	11	solution	solution	NOUN
ejpam-5280	462	12	of	of	ADP
ejpam-5280	462	13	fractional	fractional	ADJ
ejpam-5280	462	14	differential	differential	ADJ
ejpam-5280	462	15	equations	equation	NOUN
ejpam-5280	462	16	using	use	VERB
ejpam-5280	462	17	difference	difference	NOUN
ejpam-5280	462	18	operational	operational	ADJ
ejpam-5280	462	19	matrix	matrix	NOUN
ejpam-5280	462	20	.	.	PUNCT
ejpam-5280	463	1	results	result	NOUN
ejpam-5280	463	2	in	in	ADP
ejpam-5280	463	3	physics	physics	NOUN
ejpam-5280	463	4	,	,	PUNCT
ejpam-5280	463	5	15:102616	15:102616	NUM
ejpam-5280	463	6	,	,	PUNCT
ejpam-5280	463	7	2019	2019	NUM
ejpam-5280	463	8	.	.	PUNCT
ejpam-5280	464	1	[	[	X
ejpam-5280	464	2	8	8	NUM
ejpam-5280	464	3	]	]	SYM
ejpam-5280	464	4	s	s	X
ejpam-5280	464	5	momani	momani	NOUN
ejpam-5280	464	6	and	and	CCONJ
ejpam-5280	464	7	z	z	NOUN
ejpam-5280	464	8	odibat	odibat	NOUN
ejpam-5280	464	9	.	.	PUNCT
ejpam-5280	465	1	analytical	analytical	ADJ
ejpam-5280	465	2	solution	solution	NOUN
ejpam-5280	465	3	of	of	ADP
ejpam-5280	465	4	a	a	DET
ejpam-5280	465	5	time	time	NOUN
ejpam-5280	465	6	-	-	PUNCT
ejpam-5280	465	7	fractional	fractional	ADJ
ejpam-5280	465	8	navier	navier	NOUN
ejpam-5280	465	9	–	–	PUNCT
ejpam-5280	465	10	stokes	stoke	NOUN
ejpam-5280	465	11	equation	equation	NOUN
ejpam-5280	465	12	by	by	ADP
ejpam-5280	465	13	adomian	adomian	NOUN
ejpam-5280	465	14	decomposition	decomposition	NOUN
ejpam-5280	465	15	method	method	NOUN
ejpam-5280	465	16	.	.	PUNCT
ejpam-5280	466	1	applied	apply	VERB
ejpam-5280	466	2	mathematics	mathematic	NOUN
ejpam-5280	466	3	and	and	CCONJ
ejpam-5280	466	4	computation	computation	NOUN
ejpam-5280	466	5	,	,	PUNCT
ejpam-5280	466	6	190(1):102–110	190(1):102–110	NUM
ejpam-5280	466	7	,	,	PUNCT
ejpam-5280	466	8	2008	2008	NUM
ejpam-5280	466	9	.	.	PUNCT
ejpam-5280	467	1	[	[	X
ejpam-5280	467	2	9	9	NUM
ejpam-5280	467	3	]	]	X
ejpam-5280	467	4	a	a	DET
ejpam-5280	467	5	-	-	PUNCT
ejpam-5280	467	6	h	h	NOUN
ejpam-5280	467	7	i	i	PROPN
ejpam-5280	467	8	mourad	mourad	PROPN
ejpam-5280	467	9	,	,	PUNCT
ejpam-5280	467	10	a	a	DET
ejpam-5280	467	11	m	m	PROPN
ejpam-5280	467	12	ghazal	ghazal	PROPN
ejpam-5280	467	13	,	,	PUNCT
ejpam-5280	467	14	m	m	PROPN
ejpam-5280	467	15	m	m	VERB
ejpam-5280	467	16	syam	syam	NOUN
ejpam-5280	467	17	,	,	PUNCT
ejpam-5280	467	18	o	o	PROPN
ejpam-5280	467	19	d	d	X
ejpam-5280	467	20	al	al	PROPN
ejpam-5280	467	21	qadi	qadi	PROPN
ejpam-5280	467	22	,	,	PUNCT
ejpam-5280	467	23	and	and	CCONJ
ejpam-5280	467	24	h	h	PROPN
ejpam-5280	467	25	al	al	PROPN
ejpam-5280	467	26	jassmi	jassmi	PROPN
ejpam-5280	467	27	.	.	PUNCT
ejpam-5280	468	1	utilization	utilization	NOUN
ejpam-5280	468	2	of	of	ADP
ejpam-5280	468	3	additive	additive	ADJ
ejpam-5280	468	4	manufacturing	manufacturing	NOUN
ejpam-5280	468	5	in	in	ADP
ejpam-5280	468	6	evaluating	evaluate	VERB
ejpam-5280	468	7	the	the	DET
ejpam-5280	468	8	performance	performance	NOUN
ejpam-5280	468	9	of	of	ADP
ejpam-5280	468	10	internally	internally	ADV
ejpam-5280	468	11	defected	defect	VERB
ejpam-5280	468	12	materials	material	NOUN
ejpam-5280	468	13	.	.	PUNCT
ejpam-5280	469	1	in	in	ADP
ejpam-5280	469	2	iop	iop	PROPN
ejpam-5280	469	3	conf	conf	NOUN
ejpam-5280	469	4	.	.	PUNCT
ejpam-5280	470	1	ser	ser	PROPN
ejpam-5280	470	2	.	.	PUNCT
ejpam-5280	470	3	:	:	PUNCT
ejpam-5280	471	1	mater	mater	NOUN
ejpam-5280	471	2	.	.	PUNCT
ejpam-5280	472	1	sci	sci	PROPN
ejpam-5280	472	2	.	.	PUNCT
ejpam-5280	473	1	eng	eng	PROPN
ejpam-5280	473	2	.	.	PROPN
ejpam-5280	473	3	,	,	PUNCT
ejpam-5280	473	4	volume	volume	NOUN
ejpam-5280	473	5	362	362	NUM
ejpam-5280	473	6	,	,	PUNCT
ejpam-5280	473	7	page	page	NOUN
ejpam-5280	473	8	012026	012026	NUM
ejpam-5280	473	9	,	,	PUNCT
ejpam-5280	473	10	2018	2018	NUM
ejpam-5280	473	11	.	.	PUNCT
ejpam-5280	474	1	[	[	X
ejpam-5280	474	2	10	10	NUM
ejpam-5280	474	3	]	]	X
ejpam-5280	474	4	s	s	PROPN
ejpam-5280	474	5	al	al	PROPN
ejpam-5280	474	6	omari	omari	PROPN
ejpam-5280	474	7	,	,	PUNCT
ejpam-5280	474	8	a	a	DET
ejpam-5280	474	9	m	m	PROPN
ejpam-5280	474	10	ghazal	ghazal	NOUN
ejpam-5280	474	11	,	,	PUNCT
ejpam-5280	474	12	m	m	VERB
ejpam-5280	474	13	syam	syam	NOUN
ejpam-5280	474	14	,	,	PUNCT
ejpam-5280	474	15	r	r	PROPN
ejpam-5280	474	16	al	al	PROPN
ejpam-5280	474	17	najjar	najjar	PROPN
ejpam-5280	474	18	,	,	PUNCT
ejpam-5280	474	19	and	and	CCONJ
ejpam-5280	474	20	m	m	PROPN
ejpam-5280	474	21	y	y	PROPN
ejpam-5280	474	22	selim	selim	PROPN
ejpam-5280	474	23	.	.	PUNCT
ejpam-5280	475	1	an	an	DET
ejpam-5280	475	2	investigation	investigation	NOUN
ejpam-5280	475	3	on	on	ADP
ejpam-5280	475	4	the	the	DET
ejpam-5280	475	5	thermal	thermal	ADJ
ejpam-5280	475	6	degradation	degradation	NOUN
ejpam-5280	475	7	performance	performance	NOUN
ejpam-5280	475	8	of	of	ADP
ejpam-5280	475	9	crude	crude	ADJ
ejpam-5280	475	10	glycerol	glycerol	NOUN
ejpam-5280	475	11	and	and	CCONJ
ejpam-5280	475	12	date	date	NOUN
ejpam-5280	475	13	seeds	seed	NOUN
ejpam-5280	475	14	blends	blend	NOUN
ejpam-5280	475	15	using	use	VERB
ejpam-5280	475	16	thermogravimetric	thermogravimetric	ADJ
ejpam-5280	475	17	analysis	analysis	NOUN
ejpam-5280	475	18	(	(	PUNCT
ejpam-5280	475	19	tga	tga	NOUN
ejpam-5280	475	20	)	)	PUNCT
ejpam-5280	475	21	.	.	PUNCT
ejpam-5280	476	1	in	in	ADP
ejpam-5280	476	2	5th	5th	ADJ
ejpam-5280	476	3	international	international	ADJ
ejpam-5280	476	4	conference	conference	NOUN
ejpam-5280	476	5	on	on	ADP
ejpam-5280	476	6	renewable	renewable	ADJ
ejpam-5280	476	7	energy	energy	NOUN
ejpam-5280	476	8	:	:	PUNCT
ejpam-5280	476	9	generation	generation	NOUN
ejpam-5280	476	10	and	and	CCONJ
ejpam-5280	476	11	application	application	NOUN
ejpam-5280	476	12	,	,	PUNCT
ejpam-5280	476	13	icrega	icrega	PROPN
ejpam-5280	476	14	2018	2018	NUM
ejpam-5280	476	15	,	,	PUNCT
ejpam-5280	476	16	pages	page	NOUN
ejpam-5280	476	17	102–106	102–106	NUM
ejpam-5280	476	18	,	,	PUNCT
ejpam-5280	476	19	2018	2018	NUM
ejpam-5280	476	20	.	.	PUNCT
ejpam-5280	477	1	[	[	X
ejpam-5280	477	2	11	11	NUM
ejpam-5280	477	3	]	]	X
ejpam-5280	477	4	i	i	PRON
ejpam-5280	477	5	podlubny	podlubny	NOUN
ejpam-5280	477	6	.	.	PUNCT
ejpam-5280	478	1	fractional	fractional	ADJ
ejpam-5280	478	2	differential	differential	ADJ
ejpam-5280	478	3	equations	equation	NOUN
ejpam-5280	478	4	.	.	PUNCT
ejpam-5280	479	1	academic	academic	ADJ
ejpam-5280	479	2	press	press	NOUN
ejpam-5280	479	3	,	,	PUNCT
ejpam-5280	479	4	san	san	PROPN
ejpam-5280	479	5	diego	diego	PROPN
ejpam-5280	479	6	,	,	PUNCT
ejpam-5280	479	7	1999	1999	NUM
ejpam-5280	479	8	.	.	PUNCT
ejpam-5280	480	1	[	[	X
ejpam-5280	480	2	12	12	NUM
ejpam-5280	480	3	]	]	X
ejpam-5280	480	4	s	s	PART
ejpam-5280	480	5	g	g	NOUN
ejpam-5280	480	6	samko	samko	NOUN
ejpam-5280	480	7	,	,	PUNCT
ejpam-5280	480	8	a	a	DET
ejpam-5280	480	9	a	a	DET
ejpam-5280	480	10	kilbas	kilbas	NOUN
ejpam-5280	480	11	,	,	PUNCT
ejpam-5280	480	12	and	and	CCONJ
ejpam-5280	481	1	o	o	INTJ
ejpam-5280	481	2	i	i	PRON
ejpam-5280	481	3	marichev	marichev	PROPN
ejpam-5280	481	4	.	.	PUNCT
ejpam-5280	482	1	fractional	fractional	ADJ
ejpam-5280	482	2	integrals	integral	NOUN
ejpam-5280	482	3	and	and	CCONJ
ejpam-5280	482	4	derivatives	derivative	NOUN
ejpam-5280	482	5	:	:	PUNCT
ejpam-5280	482	6	theory	theory	NOUN
ejpam-5280	482	7	and	and	CCONJ
ejpam-5280	482	8	applications	application	NOUN
ejpam-5280	482	9	.	.	PUNCT
ejpam-5280	483	1	gordon	gordon	PROPN
ejpam-5280	483	2	and	and	CCONJ
ejpam-5280	483	3	breach	breach	NOUN
ejpam-5280	483	4	,	,	PUNCT
ejpam-5280	483	5	yverdon	yverdon	PROPN
ejpam-5280	483	6	,	,	PUNCT
ejpam-5280	483	7	1993	1993	NUM
ejpam-5280	483	8	.	.	PUNCT
ejpam-5280	484	1	[	[	X
ejpam-5280	484	2	13	13	NUM
ejpam-5280	484	3	]	]	SYM
ejpam-5280	484	4	m	m	VERB
ejpam-5280	484	5	i	i	PRON
ejpam-5280	484	6	syam	syam	NOUN
ejpam-5280	484	7	,	,	PUNCT
ejpam-5280	484	8	mn	mn	PROPN
ejpam-5280	484	9	y	y	PROPN
ejpam-5280	484	10	anwar	anwar	PROPN
ejpam-5280	484	11	,	,	PUNCT
ejpam-5280	484	12	a	a	DET
ejpam-5280	484	13	yildirim	yildirim	NOUN
ejpam-5280	484	14	,	,	PUNCT
ejpam-5280	484	15	and	and	CCONJ
ejpam-5280	484	16	et	et	PROPN
ejpam-5280	484	17	al	al	PROPN
ejpam-5280	484	18	.	.	PUNCT
ejpam-5280	485	1	the	the	DET
ejpam-5280	485	2	modified	modify	VERB
ejpam-5280	485	3	fractional	fractional	ADJ
ejpam-5280	485	4	power	power	NOUN
ejpam-5280	485	5	series	series	NOUN
ejpam-5280	485	6	method	method	NOUN
ejpam-5280	485	7	for	for	ADP
ejpam-5280	485	8	solving	solve	VERB
ejpam-5280	485	9	fractional	fractional	ADJ
ejpam-5280	485	10	non	non	ADJ
ejpam-5280	485	11	-	-	ADJ
ejpam-5280	485	12	isothermal	isothermal	ADJ
ejpam-5280	485	13	reaction	reaction	NOUN
ejpam-5280	485	14	–	–	PUNCT
ejpam-5280	485	15	diffusion	diffusion	NOUN
ejpam-5280	485	16	model	model	NOUN
ejpam-5280	485	17	equations	equation	NOUN
ejpam-5280	485	18	in	in	ADP
ejpam-5280	485	19	a	a	DET
ejpam-5280	485	20	spherical	spherical	ADJ
ejpam-5280	485	21	catalyst	catalyst	NOUN
ejpam-5280	485	22	.	.	PUNCT
ejpam-5280	486	1	international	international	ADJ
ejpam-5280	486	2	journal	journal	PROPN
ejpam-5280	486	3	of	of	ADP
ejpam-5280	486	4	applied	applied	ADJ
ejpam-5280	486	5	and	and	CCONJ
ejpam-5280	486	6	computational	computational	ADJ
ejpam-5280	486	7	mathematics	mathematic	NOUN
ejpam-5280	486	8	,	,	PUNCT
ejpam-5280	486	9	5:38	5:38	NUM
ejpam-5280	486	10	,	,	PUNCT
ejpam-5280	486	11	2019	2019	NUM
ejpam-5280	486	12	.	.	PUNCT
ejpam-5280	487	1	[	[	X
ejpam-5280	487	2	14	14	NUM
ejpam-5280	487	3	]	]	X
ejpam-5280	487	4	m	m	VERB
ejpam-5280	487	5	i	i	PRON
ejpam-5280	487	6	syam	syam	NOUN
ejpam-5280	487	7	,	,	PUNCT
ejpam-5280	487	8	m	m	VERB
ejpam-5280	487	9	a	a	DET
ejpam-5280	487	10	raja	raja	PROPN
ejpam-5280	487	11	,	,	PUNCT
ejpam-5280	487	12	m	m	PROPN
ejpam-5280	487	13	m	m	NOUN
ejpam-5280	487	14	syam	syam	NOUN
ejpam-5280	487	15	,	,	PUNCT
ejpam-5280	487	16	and	and	CCONJ
ejpam-5280	487	17	et	et	PROPN
ejpam-5280	487	18	al	al	PROPN
ejpam-5280	487	19	.	.	PUNCT
ejpam-5280	488	1	an	an	DET
ejpam-5280	488	2	accurate	accurate	ADJ
ejpam-5280	488	3	method	method	NOUN
ejpam-5280	488	4	for	for	ADP
ejpam-5280	488	5	solving	solve	VERB
ejpam-5280	488	6	the	the	DET
ejpam-5280	488	7	undamped	undampe	VERB
ejpam-5280	488	8	duffing	duffing	NOUN
ejpam-5280	488	9	equation	equation	NOUN
ejpam-5280	488	10	with	with	ADP
ejpam-5280	488	11	cubic	cubic	ADJ
ejpam-5280	488	12	nonlinearity	nonlinearity	NOUN
ejpam-5280	488	13	.	.	PUNCT
ejpam-5280	489	1	international	international	ADJ
ejpam-5280	489	2	journal	journal	PROPN
ejpam-5280	489	3	of	of	ADP
ejpam-5280	489	4	applied	applied	ADJ
ejpam-5280	489	5	and	and	CCONJ
ejpam-5280	489	6	computational	computational	ADJ
ejpam-5280	489	7	mathematics	mathematic	NOUN
ejpam-5280	489	8	,	,	PUNCT
ejpam-5280	489	9	4:69	4:69	NUM
ejpam-5280	489	10	,	,	PUNCT
ejpam-5280	489	11	2018	2018	NUM
ejpam-5280	489	12	.	.	PUNCT
ejpam-5280	490	1	[	[	X
ejpam-5280	490	2	15	15	NUM
ejpam-5280	490	3	]	]	X
ejpam-5280	490	4	m	m	VERB
ejpam-5280	490	5	i	i	PRON
ejpam-5280	490	6	syam	syam	NOUN
ejpam-5280	490	7	,	,	PUNCT
ejpam-5280	490	8	m	m	VERB
ejpam-5280	490	9	sharadga	sharadga	ADJ
ejpam-5280	490	10	,	,	PUNCT
ejpam-5280	490	11	and	and	CCONJ
ejpam-5280	490	12	i	i	PRON
ejpam-5280	490	13	hashim	hashim	PROPN
ejpam-5280	490	14	.	.	PUNCT
ejpam-5280	491	1	a	a	DET
ejpam-5280	491	2	numerical	numerical	ADJ
ejpam-5280	491	3	method	method	NOUN
ejpam-5280	491	4	for	for	ADP
ejpam-5280	491	5	solving	solve	VERB
ejpam-5280	491	6	fractional	fractional	ADJ
ejpam-5280	491	7	delay	delay	NOUN
ejpam-5280	491	8	differential	differential	ADJ
ejpam-5280	491	9	equations	equation	NOUN
ejpam-5280	491	10	based	base	VERB
ejpam-5280	491	11	on	on	ADP
ejpam-5280	491	12	the	the	DET
ejpam-5280	491	13	operational	operational	ADJ
ejpam-5280	491	14	matrix	matrix	NOUN
ejpam-5280	491	15	method	method	NOUN
ejpam-5280	491	16	.	.	PUNCT
ejpam-5280	492	1	chaos	chaos	NOUN
ejpam-5280	492	2	,	,	PUNCT
ejpam-5280	492	3	solitons	soliton	NOUN
ejpam-5280	492	4	&	&	CCONJ
ejpam-5280	492	5	fractals	fractal	NOUN
ejpam-5280	492	6	,	,	PUNCT
ejpam-5280	492	7	147:110977	147:110977	NUM
ejpam-5280	492	8	,	,	PUNCT
ejpam-5280	492	9	2021	2021	NUM
ejpam-5280	492	10	.	.	PUNCT
ejpam-5280	493	1	references	reference	NOUN
ejpam-5280	493	2	1448	1448	NUM
ejpam-5280	493	3	[	[	X
ejpam-5280	493	4	16	16	NUM
ejpam-5280	493	5	]	]	X
ejpam-5280	493	6	m	m	VERB
ejpam-5280	493	7	m	m	VERB
ejpam-5280	493	8	syam	syam	NOUN
ejpam-5280	493	9	,	,	PUNCT
ejpam-5280	493	10	s	s	VERB
ejpam-5280	493	11	cabrera	cabrera	NOUN
ejpam-5280	493	12	-	-	PUNCT
ejpam-5280	493	13	calderon	calderon	PROPN
ejpam-5280	493	14	,	,	PUNCT
ejpam-5280	493	15	k	k	PROPN
ejpam-5280	493	16	a	a	DET
ejpam-5280	493	17	vijayan	vijayan	PROPN
ejpam-5280	493	18	,	,	PUNCT
ejpam-5280	493	19	v	v	X
ejpam-5280	493	20	balaji	balaji	PROPN
ejpam-5280	493	21	,	,	PUNCT
ejpam-5280	493	22	p	p	PROPN
ejpam-5280	493	23	e	e	PROPN
ejpam-5280	493	24	phelan	phelan	PROPN
ejpam-5280	493	25	,	,	PUNCT
ejpam-5280	493	26	and	and	CCONJ
ejpam-5280	493	27	j	j	PROPN
ejpam-5280	493	28	r	r	PROPN
ejpam-5280	493	29	villalobos	villalobos	PROPN
ejpam-5280	493	30	.	.	PUNCT
ejpam-5280	493	31	mini	mini	ADJ
ejpam-5280	493	32	containers	container	NOUN
ejpam-5280	493	33	to	to	PART
ejpam-5280	493	34	improve	improve	VERB
ejpam-5280	493	35	the	the	DET
ejpam-5280	493	36	cold	cold	ADJ
ejpam-5280	493	37	chain	chain	NOUN
ejpam-5280	493	38	energy	energy	NOUN
ejpam-5280	493	39	efficiency	efficiency	NOUN
ejpam-5280	493	40	and	and	CCONJ
ejpam-5280	493	41	carbon	carbon	NOUN
ejpam-5280	493	42	footprint	footprint	NOUN
ejpam-5280	493	43	.	.	PUNCT
ejpam-5280	494	1	climate	climate	NOUN
ejpam-5280	494	2	,	,	PUNCT
ejpam-5280	494	3	10:76	10:76	NUM
ejpam-5280	494	4	,	,	PUNCT
ejpam-5280	494	5	2022	2022	NUM
ejpam-5280	494	6	.	.	PUNCT
ejpam-5280	495	1	[	[	X
ejpam-5280	495	2	17	17	NUM
ejpam-5280	495	3	]	]	SYM
ejpam-5280	495	4	s	s	NOUN
ejpam-5280	495	5	m	m	NOUN
ejpam-5280	495	6	syam	syam	NOUN
ejpam-5280	495	7	,	,	PUNCT
ejpam-5280	495	8	z	z	NOUN
ejpam-5280	495	9	siri	siri	NOUN
ejpam-5280	495	10	,	,	PUNCT
ejpam-5280	495	11	s	s	NOUN
ejpam-5280	495	12	h	h	NOUN
ejpam-5280	495	13	altoum	altoum	NOUN
ejpam-5280	495	14	,	,	PUNCT
ejpam-5280	495	15	m	m	VERB
ejpam-5280	495	16	a	a	DET
ejpam-5280	495	17	aigo	aigo	ADJ
ejpam-5280	495	18	,	,	PUNCT
ejpam-5280	495	19	and	and	CCONJ
ejpam-5280	495	20	r	r	NOUN
ejpam-5280	495	21	md	md	PROPN
ejpam-5280	495	22	kasmani	kasmani	PROPN
ejpam-5280	495	23	.	.	PUNCT
ejpam-5280	496	1	a	a	DET
ejpam-5280	496	2	novel	novel	ADJ
ejpam-5280	496	3	study	study	NOUN
ejpam-5280	496	4	for	for	ADP
ejpam-5280	496	5	solving	solve	VERB
ejpam-5280	496	6	systems	system	NOUN
ejpam-5280	496	7	of	of	ADP
ejpam-5280	496	8	nonlinear	nonlinear	ADJ
ejpam-5280	496	9	fractional	fractional	ADJ
ejpam-5280	496	10	integral	integral	ADJ
ejpam-5280	496	11	equations	equation	NOUN
ejpam-5280	496	12	.	.	PUNCT
ejpam-5280	497	1	applied	apply	VERB
ejpam-5280	497	2	mathematics	mathematic	NOUN
ejpam-5280	497	3	in	in	ADP
ejpam-5280	497	4	science	science	NOUN
ejpam-5280	497	5	and	and	CCONJ
ejpam-5280	497	6	engineering	engineering	NOUN
ejpam-5280	497	7	,	,	PUNCT
ejpam-5280	497	8	31(1	31(1	NUM
ejpam-5280	497	9	)	)	PUNCT
ejpam-5280	497	10	,	,	PUNCT
ejpam-5280	497	11	2023	2023	NUM
ejpam-5280	497	12	.	.	PUNCT
ejpam-5280	498	1	[	[	X
ejpam-5280	498	2	18	18	NUM
ejpam-5280	498	3	]	]	SYM
ejpam-5280	498	4	s	s	NOUN
ejpam-5280	498	5	m	m	NOUN
ejpam-5280	498	6	syam	syam	NOUN
ejpam-5280	498	7	,	,	PUNCT
ejpam-5280	498	8	z	z	NOUN
ejpam-5280	498	9	siri	siri	NOUN
ejpam-5280	498	10	,	,	PUNCT
ejpam-5280	498	11	s	s	NOUN
ejpam-5280	498	12	h	h	NOUN
ejpam-5280	498	13	altoum	altoum	NOUN
ejpam-5280	498	14	,	,	PUNCT
ejpam-5280	498	15	and	and	CCONJ
ejpam-5280	498	16	r	r	NOUN
ejpam-5280	498	17	m	m	PROPN
ejpam-5280	498	18	kasmani	kasmani	NOUN
ejpam-5280	498	19	.	.	PUNCT
ejpam-5280	499	1	an	an	DET
ejpam-5280	499	2	efficient	efficient	ADJ
ejpam-5280	499	3	numerical	numerical	ADJ
ejpam-5280	499	4	approach	approach	NOUN
ejpam-5280	499	5	for	for	ADP
ejpam-5280	499	6	solving	solve	VERB
ejpam-5280	499	7	systems	system	NOUN
ejpam-5280	499	8	of	of	ADP
ejpam-5280	499	9	fractional	fractional	ADJ
ejpam-5280	499	10	problems	problem	NOUN
ejpam-5280	499	11	and	and	CCONJ
ejpam-5280	499	12	their	their	PRON
ejpam-5280	499	13	applications	application	NOUN
ejpam-5280	499	14	in	in	ADP
ejpam-5280	499	15	science	science	NOUN
ejpam-5280	499	16	.	.	PUNCT
ejpam-5280	500	1	mathematics	mathematic	NOUN
ejpam-5280	500	2	,	,	PUNCT
ejpam-5280	500	3	11:3132	11:3132	NUM
ejpam-5280	500	4	,	,	PUNCT
ejpam-5280	500	5	2023	2023	NUM
ejpam-5280	500	6	.	.	PUNCT
ejpam-5280	501	1	[	[	X
ejpam-5280	501	2	19	19	NUM
ejpam-5280	501	3	]	]	SYM
ejpam-5280	501	4	s	s	NOUN
ejpam-5280	501	5	m	m	NOUN
ejpam-5280	501	6	syam	syam	NOUN
ejpam-5280	501	7	,	,	PUNCT
ejpam-5280	501	8	z	z	NOUN
ejpam-5280	501	9	siri	siri	NOUN
ejpam-5280	501	10	,	,	PUNCT
ejpam-5280	501	11	s	s	NOUN
ejpam-5280	501	12	h	h	NOUN
ejpam-5280	501	13	altoum	altoum	NOUN
ejpam-5280	501	14	,	,	PUNCT
ejpam-5280	501	15	and	and	CCONJ
ejpam-5280	501	16	r	r	NOUN
ejpam-5280	501	17	md	md	PROPN
ejpam-5280	501	18	kasmani	kasmani	PROPN
ejpam-5280	501	19	.	.	PUNCT
ejpam-5280	502	1	analytical	analytical	ADJ
ejpam-5280	502	2	and	and	CCONJ
ejpam-5280	502	3	numerical	numerical	ADJ
ejpam-5280	502	4	methods	method	NOUN
ejpam-5280	502	5	for	for	ADP
ejpam-5280	502	6	solving	solve	VERB
ejpam-5280	502	7	second	second	ADJ
ejpam-5280	502	8	-	-	PUNCT
ejpam-5280	502	9	order	order	NOUN
ejpam-5280	502	10	two	two	NUM
ejpam-5280	502	11	-	-	PUNCT
ejpam-5280	502	12	dimensional	dimensional	ADJ
ejpam-5280	502	13	symmetric	symmetric	ADJ
ejpam-5280	502	14	sequential	sequential	ADJ
ejpam-5280	502	15	fractional	fractional	ADJ
ejpam-5280	502	16	integro	integro	ADJ
ejpam-5280	502	17	-	-	PUNCT
ejpam-5280	502	18	differential	differential	NOUN
ejpam-5280	502	19	equations	equation	NOUN
ejpam-5280	502	20	.	.	PUNCT
ejpam-5280	503	1	symmetry	symmetry	NOUN
ejpam-5280	503	2	,	,	PUNCT
ejpam-5280	503	3	15:1263	15:1263	NUM
ejpam-5280	503	4	,	,	PUNCT
ejpam-5280	503	5	2023	2023	NUM
ejpam-5280	503	6	.	.	PUNCT
ejpam-5280	504	1	[	[	X
ejpam-5280	504	2	20	20	NUM
ejpam-5280	504	3	]	]	SYM
ejpam-5280	504	4	s	s	NOUN
ejpam-5280	504	5	m	m	NOUN
ejpam-5280	504	6	syam	syam	NOUN
ejpam-5280	504	7	,	,	PUNCT
ejpam-5280	504	8	z	z	NOUN
ejpam-5280	504	9	siri	siri	NOUN
ejpam-5280	504	10	,	,	PUNCT
ejpam-5280	504	11	and	and	CCONJ
ejpam-5280	504	12	r	r	NOUN
ejpam-5280	504	13	m	m	PROPN
ejpam-5280	504	14	kasmani	kasmani	NOUN
ejpam-5280	504	15	.	.	PUNCT
ejpam-5280	504	16	operational	operational	ADJ
ejpam-5280	504	17	matrix	matrix	NOUN
ejpam-5280	504	18	method	method	NOUN
ejpam-5280	504	19	for	for	ADP
ejpam-5280	504	20	solving	solve	VERB
ejpam-5280	504	21	fractional	fractional	ADJ
ejpam-5280	504	22	system	system	NOUN
ejpam-5280	504	23	of	of	ADP
ejpam-5280	504	24	riccati	riccati	PROPN
ejpam-5280	504	25	equations	equation	NOUN
ejpam-5280	504	26	.	.	PUNCT
ejpam-5280	505	1	in	in	ADP
ejpam-5280	505	2	2023	2023	NUM
ejpam-5280	505	3	international	international	ADJ
ejpam-5280	505	4	conference	conference	NOUN
ejpam-5280	505	5	on	on	ADP
ejpam-5280	505	6	fractional	fractional	ADJ
ejpam-5280	505	7	differentiation	differentiation	NOUN
ejpam-5280	505	8	and	and	CCONJ
ejpam-5280	505	9	its	its	PRON
ejpam-5280	505	10	applications	application	NOUN
ejpam-5280	505	11	(	(	PUNCT
ejpam-5280	505	12	icfda	icfda	PROPN
ejpam-5280	505	13	)	)	PUNCT
ejpam-5280	505	14	,	,	PUNCT
ejpam-5280	505	15	pages	page	NOUN
ejpam-5280	505	16	1–6	1–6	NUM
ejpam-5280	505	17	,	,	PUNCT
ejpam-5280	505	18	ajman	ajman	PROPN
ejpam-5280	505	19	,	,	PUNCT
ejpam-5280	505	20	united	united	PROPN
ejpam-5280	505	21	arab	arab	PROPN
ejpam-5280	505	22	emirates	emirates	PROPN
ejpam-5280	505	23	,	,	PUNCT
ejpam-5280	505	24	2023	2023	NUM
ejpam-5280	505	25	.	.	PUNCT
ejpam-5280	506	1	[	[	X
ejpam-5280	506	2	21	21	NUM
ejpam-5280	506	3	]	]	X
ejpam-5280	506	4	s	s	NOUN
ejpam-5280	506	5	m	m	NOUN
ejpam-5280	506	6	syam	syam	NOUN
ejpam-5280	506	7	,	,	PUNCT
ejpam-5280	506	8	z	z	NOUN
ejpam-5280	506	9	siri	siri	NOUN
ejpam-5280	506	10	,	,	PUNCT
ejpam-5280	506	11	r	r	NOUN
ejpam-5280	506	12	md	md	PROPN
ejpam-5280	506	13	kasmani	kasmani	NOUN
ejpam-5280	506	14	,	,	PUNCT
ejpam-5280	506	15	and	and	CCONJ
ejpam-5280	506	16	kenan	kenan	PROPN
ejpam-5280	506	17	yildirim	yildirim	PROPN
ejpam-5280	506	18	.	.	PUNCT
ejpam-5280	507	1	a	a	DET
ejpam-5280	507	2	new	new	ADJ
ejpam-5280	507	3	method	method	NOUN
ejpam-5280	507	4	for	for	ADP
ejpam-5280	507	5	solving	solve	VERB
ejpam-5280	507	6	sequential	sequential	ADJ
ejpam-5280	507	7	fractional	fractional	ADJ
ejpam-5280	507	8	wave	wave	NOUN
ejpam-5280	507	9	equations	equation	NOUN
ejpam-5280	507	10	.	.	PUNCT
ejpam-5280	508	1	journal	journal	NOUN
ejpam-5280	508	2	of	of	ADP
ejpam-5280	508	3	mathematics	mathematic	NOUN
ejpam-5280	508	4	,	,	PUNCT
ejpam-5280	508	5	2023	2023	NUM
ejpam-5280	508	6	:	:	PUNCT
ejpam-5280	508	7	article	article	NOUN
ejpam-5280	508	8	i	i	PROPN
ejpam-5280	508	9	d	d	PROPN
ejpam-5280	508	10	5888010	5888010	NUM
ejpam-5280	508	11	,	,	PUNCT
ejpam-5280	508	12	16	16	NUM
ejpam-5280	508	13	pages	page	NOUN
ejpam-5280	508	14	,	,	PUNCT
ejpam-5280	508	15	2023	2023	NUM
ejpam-5280	508	16	.	.	PUNCT