id	sid	tid	token	lemma	pos
ejpam-3529	1	1	european	european	PROPN
ejpam-3529	1	2	journal	journal	PROPN
ejpam-3529	1	3	of	of	ADP
ejpam-3529	1	4	pure	pure	ADJ
ejpam-3529	1	5	and	and	CCONJ
ejpam-3529	1	6	applied	apply	VERB
ejpam-3529	1	7	mathematics	mathematic	NOUN
ejpam-3529	1	8	vol	vol	NOUN
ejpam-3529	1	9	.	.	PROPN
ejpam-3529	2	1	12	12	NUM
ejpam-3529	2	2	,	,	PUNCT
ejpam-3529	2	3	no	no	INTJ
ejpam-3529	2	4	.	.	NOUN
ejpam-3529	2	5	4	4	NUM
ejpam-3529	2	6	,	,	PUNCT
ejpam-3529	2	7	2019	2019	NUM
ejpam-3529	2	8	,	,	PUNCT
ejpam-3529	2	9	1662	1662	NUM
ejpam-3529	2	10	-	-	SYM
ejpam-3529	2	11	1675	1675	NUM
ejpam-3529	2	12	issn	issn	PROPN
ejpam-3529	2	13	1307	1307	NUM
ejpam-3529	2	14	-	-	SYM
ejpam-3529	2	15	5543	5543	NUM
ejpam-3529	2	16	–	–	PUNCT
ejpam-3529	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3529	2	18	published	publish	VERB
ejpam-3529	2	19	by	by	ADP
ejpam-3529	2	20	new	new	PROPN
ejpam-3529	2	21	york	york	PROPN
ejpam-3529	2	22	business	business	PROPN
ejpam-3529	2	23	global	global	ADJ
ejpam-3529	2	24	generalized	generalize	VERB
ejpam-3529	2	25	quasilinearization	quasilinearization	NOUN
ejpam-3529	2	26	using	use	VERB
ejpam-3529	2	27	coupled	couple	VERB
ejpam-3529	2	28	lower	low	ADJ
ejpam-3529	2	29	and	and	CCONJ
ejpam-3529	2	30	upper	upper	ADJ
ejpam-3529	2	31	solutions	solution	NOUN
ejpam-3529	2	32	for	for	ADP
ejpam-3529	2	33	periodic	periodic	ADJ
ejpam-3529	2	34	boundary	boundary	ADJ
ejpam-3529	2	35	value	value	NOUN
ejpam-3529	2	36	problem	problem	NOUN
ejpam-3529	2	37	of	of	ADP
ejpam-3529	2	38	an	an	DET
ejpam-3529	2	39	integro	integro	ADJ
ejpam-3529	2	40	differential	differential	ADJ
ejpam-3529	2	41	equation	equation	NOUN
ejpam-3529	2	42	ch	ch	NOUN
ejpam-3529	2	43	.	.	PUNCT
ejpam-3529	3	1	v.	v.	PROPN
ejpam-3529	3	2	sreedhar1	sreedhar1	PROPN
ejpam-3529	3	3	,	,	PUNCT
ejpam-3529	3	4	j.	j.	PROPN
ejpam-3529	3	5	vasundhara	vasundhara	PROPN
ejpam-3529	3	6	devi1,∗	devi1,∗	PROPN
ejpam-3529	3	7	1	1	NUM
ejpam-3529	3	8	department	department	NOUN
ejpam-3529	3	9	of	of	ADP
ejpam-3529	3	10	mathematics	mathematic	NOUN
ejpam-3529	3	11	,	,	PUNCT
ejpam-3529	3	12	gvp-prof.v.lakshmikantham	gvp-prof.v.lakshmikantham	PROPN
ejpam-3529	3	13	institute	institute	VERB
ejpam-3529	3	14	for	for	ADP
ejpam-3529	3	15	advanced	advanced	ADJ
ejpam-3529	3	16	studies	study	NOUN
ejpam-3529	3	17	,	,	PUNCT
ejpam-3529	3	18	gayatri	gayatri	PROPN
ejpam-3529	3	19	vidya	vidya	PROPN
ejpam-3529	3	20	parishad	parishad	VERB
ejpam-3529	3	21	college	college	PROPN
ejpam-3529	3	22	of	of	ADP
ejpam-3529	3	23	engineering	engineering	NOUN
ejpam-3529	3	24	(	(	PUNCT
ejpam-3529	3	25	autonomous	autonomous	ADJ
ejpam-3529	3	26	)	)	PUNCT
ejpam-3529	3	27	,	,	PUNCT
ejpam-3529	3	28	visakhapatnam	visakhapatnam	PROPN
ejpam-3529	3	29	530048	530048	NUM
ejpam-3529	3	30	,	,	PUNCT
ejpam-3529	3	31	india	india	PROPN
ejpam-3529	3	32	abstract	abstract	NOUN
ejpam-3529	3	33	.	.	PUNCT
ejpam-3529	4	1	in	in	ADP
ejpam-3529	4	2	this	this	DET
ejpam-3529	4	3	paper	paper	NOUN
ejpam-3529	4	4	we	we	PRON
ejpam-3529	4	5	first	first	ADV
ejpam-3529	4	6	develop	develop	VERB
ejpam-3529	4	7	the	the	DET
ejpam-3529	4	8	method	method	NOUN
ejpam-3529	4	9	of	of	ADP
ejpam-3529	4	10	generalized	generalized	ADJ
ejpam-3529	4	11	quasilinearization	quasilinearization	NOUN
ejpam-3529	4	12	for	for	ADP
ejpam-3529	4	13	initial	initial	ADJ
ejpam-3529	4	14	value	value	NOUN
ejpam-3529	4	15	problem	problem	NOUN
ejpam-3529	4	16	of	of	ADP
ejpam-3529	4	17	an	an	DET
ejpam-3529	4	18	integro	integro	ADJ
ejpam-3529	4	19	differential	differential	ADJ
ejpam-3529	4	20	equation	equation	NOUN
ejpam-3529	4	21	and	and	CCONJ
ejpam-3529	4	22	then	then	ADV
ejpam-3529	4	23	use	use	VERB
ejpam-3529	4	24	it	it	PRON
ejpam-3529	4	25	to	to	PART
ejpam-3529	4	26	develop	develop	VERB
ejpam-3529	4	27	quasilinearization	quasilinearization	NOUN
ejpam-3529	4	28	for	for	ADP
ejpam-3529	4	29	the	the	DET
ejpam-3529	4	30	periodic	periodic	ADJ
ejpam-3529	4	31	boundary	boundary	ADJ
ejpam-3529	4	32	value	value	NOUN
ejpam-3529	4	33	problem	problem	NOUN
ejpam-3529	4	34	of	of	ADP
ejpam-3529	4	35	the	the	DET
ejpam-3529	4	36	integro	integro	PROPN
ejpam-3529	4	37	differential	differential	ADJ
ejpam-3529	4	38	equation	equation	NOUN
ejpam-3529	4	39	by	by	ADP
ejpam-3529	4	40	using	use	VERB
ejpam-3529	4	41	the	the	DET
ejpam-3529	4	42	coupled	couple	VERB
ejpam-3529	4	43	lower	low	ADJ
ejpam-3529	4	44	and	and	CCONJ
ejpam-3529	4	45	upper	upper	ADJ
ejpam-3529	4	46	solutions	solution	NOUN
ejpam-3529	4	47	of	of	ADP
ejpam-3529	4	48	type	type	NOUN
ejpam-3529	4	49	-	-	PUNCT
ejpam-3529	4	50	i.	i.	NOUN
ejpam-3529	4	51	2010	2010	NUM
ejpam-3529	4	52	mathematics	mathematic	NOUN
ejpam-3529	4	53	subject	subject	NOUN
ejpam-3529	4	54	classifications	classification	NOUN
ejpam-3529	4	55	:	:	PUNCT
ejpam-3529	4	56	45j05	45j05	NUM
ejpam-3529	4	57	,	,	PUNCT
ejpam-3529	4	58	47g20	47g20	X
ejpam-3529	4	59	key	key	ADJ
ejpam-3529	4	60	words	word	NOUN
ejpam-3529	4	61	and	and	CCONJ
ejpam-3529	4	62	phrases	phrase	NOUN
ejpam-3529	4	63	:	:	PUNCT
ejpam-3529	4	64	periodic	periodic	ADJ
ejpam-3529	4	65	boundary	boundary	ADJ
ejpam-3529	4	66	value	value	NOUN
ejpam-3529	4	67	problem(pbvp	problem(pbvp	NOUN
ejpam-3529	4	68	)	)	PUNCT
ejpam-3529	4	69	,	,	PUNCT
ejpam-3529	4	70	integro	integro	PROPN
ejpam-3529	4	71	differential	differential	NOUN
ejpam-3529	4	72	equation	equation	NOUN
ejpam-3529	4	73	,	,	PUNCT
ejpam-3529	4	74	coupled	couple	VERB
ejpam-3529	4	75	lower	low	ADJ
ejpam-3529	4	76	and	and	CCONJ
ejpam-3529	4	77	upper	upper	ADJ
ejpam-3529	4	78	solutions	solution	NOUN
ejpam-3529	4	79	,	,	PUNCT
ejpam-3529	4	80	existence	existence	NOUN
ejpam-3529	4	81	,	,	PUNCT
ejpam-3529	4	82	quasilinearization	quasilinearization	NOUN
ejpam-3529	4	83	.	.	PUNCT
ejpam-3529	5	1	1	1	X
ejpam-3529	5	2	.	.	X
ejpam-3529	5	3	introduction	introduction	NOUN
ejpam-3529	5	4	integro	integro	PROPN
ejpam-3529	5	5	differential	differential	ADJ
ejpam-3529	5	6	equations	equation	NOUN
ejpam-3529	5	7	[	[	X
ejpam-3529	5	8	1	1	X
ejpam-3529	5	9	]	]	PUNCT
ejpam-3529	5	10	arise	arise	VERB
ejpam-3529	5	11	quite	quite	ADV
ejpam-3529	5	12	frequently	frequently	ADV
ejpam-3529	5	13	as	as	ADP
ejpam-3529	5	14	mathematical	mathematical	ADJ
ejpam-3529	5	15	models	model	NOUN
ejpam-3529	5	16	in	in	ADP
ejpam-3529	5	17	various	various	ADJ
ejpam-3529	5	18	disciplines	discipline	NOUN
ejpam-3529	5	19	of	of	ADP
ejpam-3529	5	20	physical	physical	ADJ
ejpam-3529	5	21	,	,	PUNCT
ejpam-3529	5	22	social	social	ADJ
ejpam-3529	5	23	and	and	CCONJ
ejpam-3529	5	24	biological	biological	ADJ
ejpam-3529	5	25	sciences	science	NOUN
ejpam-3529	5	26	and	and	CCONJ
ejpam-3529	5	27	engineering	engineering	NOUN
ejpam-3529	5	28	.	.	PUNCT
ejpam-3529	6	1	models	model	NOUN
ejpam-3529	6	2	involving	involve	VERB
ejpam-3529	6	3	integro	integro	PROPN
ejpam-3529	6	4	differential	differential	ADJ
ejpam-3529	6	5	equations	equation	NOUN
ejpam-3529	6	6	can	can	AUX
ejpam-3529	6	7	be	be	AUX
ejpam-3529	6	8	found	find	VERB
ejpam-3529	6	9	in	in	ADP
ejpam-3529	6	10	unsteady	unsteady	ADJ
ejpam-3529	6	11	aerodynamics	aerodynamic	NOUN
ejpam-3529	6	12	and	and	CCONJ
ejpam-3529	6	13	aero	aero	ADJ
ejpam-3529	6	14	-	-	ADJ
ejpam-3529	6	15	elastic	elastic	ADJ
ejpam-3529	6	16	phenomena	phenomenon	NOUN
ejpam-3529	6	17	etc	etc	X
ejpam-3529	6	18	.	.	PUNCT
ejpam-3529	7	1	the	the	DET
ejpam-3529	7	2	qualitative	qualitative	ADJ
ejpam-3529	7	3	theory	theory	NOUN
ejpam-3529	7	4	of	of	ADP
ejpam-3529	7	5	integro	integro	PROPN
ejpam-3529	7	6	differential	differential	ADJ
ejpam-3529	7	7	equations	equation	NOUN
ejpam-3529	7	8	deals	deal	VERB
ejpam-3529	7	9	with	with	ADP
ejpam-3529	7	10	existence	existence	NOUN
ejpam-3529	7	11	and	and	CCONJ
ejpam-3529	7	12	uniqueness	uniqueness	NOUN
ejpam-3529	7	13	of	of	ADP
ejpam-3529	7	14	solutions	solution	NOUN
ejpam-3529	7	15	,	,	PUNCT
ejpam-3529	7	16	stability	stability	NOUN
ejpam-3529	7	17	of	of	ADP
ejpam-3529	7	18	solutions	solution	NOUN
ejpam-3529	7	19	etc	etc	X
ejpam-3529	7	20	.	.	X
ejpam-3529	8	1	the	the	DET
ejpam-3529	8	2	existence	existence	NOUN
ejpam-3529	8	3	and	and	CCONJ
ejpam-3529	8	4	uniqueness	uniqueness	NOUN
ejpam-3529	8	5	results	result	NOUN
ejpam-3529	8	6	are	be	AUX
ejpam-3529	8	7	studied	study	VERB
ejpam-3529	8	8	using	use	VERB
ejpam-3529	8	9	various	various	ADJ
ejpam-3529	8	10	approaches	approach	NOUN
ejpam-3529	8	11	like	like	ADP
ejpam-3529	8	12	fixed	fix	VERB
ejpam-3529	8	13	point	point	NOUN
ejpam-3529	8	14	theory	theory	NOUN
ejpam-3529	8	15	and	and	CCONJ
ejpam-3529	8	16	iterative	iterative	NOUN
ejpam-3529	8	17	techniques	technique	NOUN
ejpam-3529	8	18	.	.	PUNCT
ejpam-3529	9	1	there	there	PRON
ejpam-3529	9	2	are	be	VERB
ejpam-3529	9	3	various	various	ADJ
ejpam-3529	9	4	iterative	iterative	NOUN
ejpam-3529	9	5	techniques	technique	NOUN
ejpam-3529	9	6	for	for	ADP
ejpam-3529	9	7	solving	solve	VERB
ejpam-3529	9	8	integro	integro	PROPN
ejpam-3529	9	9	differential	differential	ADJ
ejpam-3529	9	10	equations	equation	NOUN
ejpam-3529	9	11	.	.	PUNCT
ejpam-3529	10	1	some	some	PRON
ejpam-3529	10	2	of	of	ADP
ejpam-3529	10	3	the	the	DET
ejpam-3529	10	4	iterative	iterative	NOUN
ejpam-3529	10	5	methods	method	NOUN
ejpam-3529	10	6	are	be	AUX
ejpam-3529	10	7	monotone	monotone	ADJ
ejpam-3529	10	8	iterative	iterative	NOUN
ejpam-3529	10	9	technique	technique	NOUN
ejpam-3529	10	10	,	,	PUNCT
ejpam-3529	10	11	quasilinearization	quasilinearization	NOUN
ejpam-3529	10	12	and	and	CCONJ
ejpam-3529	10	13	their	their	PRON
ejpam-3529	10	14	generalizations	generalization	NOUN
ejpam-3529	10	15	.	.	PUNCT
ejpam-3529	11	1	the	the	DET
ejpam-3529	11	2	monotone	monotone	ADJ
ejpam-3529	11	3	iterative	iterative	NOUN
ejpam-3529	11	4	technique	technique	NOUN
ejpam-3529	11	5	and	and	CCONJ
ejpam-3529	11	6	quasilinearization	quasilinearization	NOUN
ejpam-3529	11	7	are	be	AUX
ejpam-3529	11	8	two	two	NUM
ejpam-3529	11	9	iterative	iterative	NOUN
ejpam-3529	11	10	techniques	technique	NOUN
ejpam-3529	11	11	that	that	PRON
ejpam-3529	11	12	are	be	AUX
ejpam-3529	11	13	widely	widely	ADV
ejpam-3529	11	14	used	use	VERB
ejpam-3529	11	15	to	to	PART
ejpam-3529	11	16	obtain	obtain	VERB
ejpam-3529	11	17	existence	existence	NOUN
ejpam-3529	11	18	and	and	CCONJ
ejpam-3529	11	19	uniqueness	uniqueness	NOUN
ejpam-3529	11	20	results	result	NOUN
ejpam-3529	11	21	of	of	ADP
ejpam-3529	11	22	various	various	ADJ
ejpam-3529	11	23	types	type	NOUN
ejpam-3529	11	24	of	of	ADP
ejpam-3529	11	25	differential	differential	ADJ
ejpam-3529	11	26	equations	equation	NOUN
ejpam-3529	11	27	.	.	PUNCT
ejpam-3529	12	1	both	both	DET
ejpam-3529	12	2	monotone	monotone	ADJ
ejpam-3529	12	3	iterative	iterative	NOUN
ejpam-3529	12	4	technique	technique	NOUN
ejpam-3529	12	5	and	and	CCONJ
ejpam-3529	12	6	quasilinearization	quasilinearization	NOUN
ejpam-3529	12	7	[	[	X
ejpam-3529	12	8	2	2	NUM
ejpam-3529	12	9	,	,	PUNCT
ejpam-3529	12	10	3	3	NUM
ejpam-3529	12	11	,	,	PUNCT
ejpam-3529	12	12	4	4	NUM
ejpam-3529	12	13	,	,	PUNCT
ejpam-3529	12	14	5	5	NUM
ejpam-3529	12	15	]	]	PUNCT
ejpam-3529	12	16	along	along	ADP
ejpam-3529	12	17	with	with	ADP
ejpam-3529	12	18	the	the	DET
ejpam-3529	12	19	method	method	NOUN
ejpam-3529	12	20	of	of	ADP
ejpam-3529	12	21	upper	upper	ADJ
ejpam-3529	12	22	and	and	CCONJ
ejpam-3529	12	23	lower	low	ADJ
ejpam-3529	12	24	solutions	solution	NOUN
ejpam-3529	12	25	yield	yield	VERB
ejpam-3529	12	26	monotone	monotone	ADJ
ejpam-3529	12	27	iterates	iterate	NOUN
ejpam-3529	12	28	which	which	PRON
ejpam-3529	12	29	are	be	AUX
ejpam-3529	12	30	solutions	solution	NOUN
ejpam-3529	12	31	of	of	ADP
ejpam-3529	12	32	certain	certain	ADJ
ejpam-3529	12	33	linear	linear	PROPN
ejpam-3529	12	34	differential	differential	NOUN
ejpam-3529	12	35	equations	equation	NOUN
ejpam-3529	12	36	obtained	obtain	VERB
ejpam-3529	12	37	from	from	ADP
ejpam-3529	12	38	the	the	DET
ejpam-3529	12	39	hypothesis	hypothesis	NOUN
ejpam-3529	12	40	of	of	ADP
ejpam-3529	12	41	the	the	DET
ejpam-3529	12	42	given	give	VERB
ejpam-3529	12	43	problem	problem	NOUN
ejpam-3529	12	44	.	.	PUNCT
ejpam-3529	13	1	these	these	PRON
ejpam-3529	13	2	iterates	iterate	VERB
ejpam-3529	13	3	converge	converge	VERB
ejpam-3529	13	4	to	to	ADP
ejpam-3529	13	5	a	a	DET
ejpam-3529	13	6	solution	solution	NOUN
ejpam-3529	13	7	of	of	ADP
ejpam-3529	13	8	the	the	DET
ejpam-3529	13	9	original	original	ADJ
ejpam-3529	13	10	problem	problem	NOUN
ejpam-3529	13	11	.	.	PUNCT
ejpam-3529	14	1	∗corresponding	∗corresponde	VERB
ejpam-3529	14	2	author	author	NOUN
ejpam-3529	14	3	.	.	PUNCT
ejpam-3529	15	1	doi	doi	PROPN
ejpam-3529	15	2	:	:	PUNCT
ejpam-3529	15	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3529	https://doi.org/10.29020/nybg.ejpam.v12i4.3529	DET
ejpam-3529	15	4	email	email	NOUN
ejpam-3529	15	5	address	address	NOUN
ejpam-3529	15	6	:	:	PUNCT
ejpam-3529	15	7	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-3529	15	8	(	(	PUNCT
ejpam-3529	15	9	j.	j.	PROPN
ejpam-3529	15	10	vasundhara	vasundhara	PROPN
ejpam-3529	15	11	devi	devi	PROPN
ejpam-3529	15	12	)	)	PUNCT
ejpam-3529	15	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3529	15	14	1662	1662	NUM
ejpam-3529	16	1	c	c	X
ejpam-3529	16	2	©	©	PROPN
ejpam-3529	16	3	2019	2019	NUM
ejpam-3529	16	4	ejpam	ejpam	NOUN
ejpam-3529	16	5	all	all	DET
ejpam-3529	16	6	rights	right	NOUN
ejpam-3529	16	7	reserved	reserve	VERB
ejpam-3529	16	8	.	.	PUNCT
ejpam-3529	17	1	ch	ch	NOUN
ejpam-3529	17	2	.	.	PUNCT
ejpam-3529	18	1	v.	v.	ADP
ejpam-3529	18	2	sreedhar	sreedhar	PROPN
ejpam-3529	18	3	,	,	PUNCT
ejpam-3529	18	4	j.	j.	PROPN
ejpam-3529	18	5	vasundhara	vasundhara	PROPN
ejpam-3529	18	6	devi	devi	PROPN
ejpam-3529	18	7	,	,	PUNCT
ejpam-3529	18	8	/	/	SYM
ejpam-3529	18	9	eur	eur	NOUN
ejpam-3529	18	10	.	.	PUNCT
ejpam-3529	19	1	j.	j.	PROPN
ejpam-3529	19	2	pure	pure	PROPN
ejpam-3529	19	3	appl	appl	PROPN
ejpam-3529	19	4	.	.	PROPN
ejpam-3529	19	5	math	math	PROPN
ejpam-3529	19	6	,	,	PUNCT
ejpam-3529	19	7	12	12	NUM
ejpam-3529	19	8	(	(	PUNCT
ejpam-3529	19	9	4	4	NUM
ejpam-3529	19	10	)	)	PUNCT
ejpam-3529	19	11	(	(	PUNCT
ejpam-3529	19	12	2019	2019	NUM
ejpam-3529	19	13	)	)	PUNCT
ejpam-3529	19	14	,	,	PUNCT
ejpam-3529	19	15	1662	1662	NUM
ejpam-3529	19	16	-	-	SYM
ejpam-3529	19	17	1675	1675	NUM
ejpam-3529	19	18	1663	1663	NUM
ejpam-3529	19	19	the	the	DET
ejpam-3529	19	20	monotone	monotone	ADJ
ejpam-3529	19	21	iterative	iterative	NOUN
ejpam-3529	19	22	technique	technique	NOUN
ejpam-3529	19	23	had	have	AUX
ejpam-3529	19	24	undergone	undergo	VERB
ejpam-3529	19	25	various	various	ADJ
ejpam-3529	19	26	extensions	extension	NOUN
ejpam-3529	19	27	and	and	CCONJ
ejpam-3529	19	28	generalizations	generalization	NOUN
ejpam-3529	19	29	.	.	PUNCT
ejpam-3529	20	1	the	the	DET
ejpam-3529	20	2	right	right	ADJ
ejpam-3529	20	3	hand	hand	NOUN
ejpam-3529	20	4	side	side	NOUN
ejpam-3529	20	5	of	of	ADP
ejpam-3529	20	6	the	the	DET
ejpam-3529	20	7	problem	problem	NOUN
ejpam-3529	20	8	was	be	AUX
ejpam-3529	20	9	considered	consider	VERB
ejpam-3529	20	10	as	as	ADP
ejpam-3529	20	11	a	a	DET
ejpam-3529	20	12	sum	sum	NOUN
ejpam-3529	20	13	of	of	ADP
ejpam-3529	20	14	a	a	DET
ejpam-3529	20	15	nondecreasing	nondecrease	VERB
ejpam-3529	20	16	and	and	CCONJ
ejpam-3529	20	17	nonincreasing	nonincrease	VERB
ejpam-3529	20	18	function	function	NOUN
ejpam-3529	20	19	.	.	PUNCT
ejpam-3529	21	1	this	this	PRON
ejpam-3529	21	2	gave	give	VERB
ejpam-3529	21	3	rise	rise	NOUN
ejpam-3529	21	4	to	to	ADP
ejpam-3529	21	5	various	various	ADJ
ejpam-3529	21	6	notions	notion	NOUN
ejpam-3529	21	7	of	of	ADP
ejpam-3529	21	8	coupled	couple	VERB
ejpam-3529	21	9	solutions	solution	NOUN
ejpam-3529	21	10	and	and	CCONJ
ejpam-3529	21	11	much	much	ADJ
ejpam-3529	21	12	work	work	NOUN
ejpam-3529	21	13	has	have	AUX
ejpam-3529	21	14	been	be	AUX
ejpam-3529	21	15	done	do	VERB
ejpam-3529	21	16	in	in	ADP
ejpam-3529	21	17	this	this	DET
ejpam-3529	21	18	setup	setup	NOUN
ejpam-3529	21	19	for	for	ADP
ejpam-3529	21	20	various	various	ADJ
ejpam-3529	21	21	types	type	NOUN
ejpam-3529	21	22	of	of	ADP
ejpam-3529	21	23	differential	differential	ADJ
ejpam-3529	21	24	equations	equation	NOUN
ejpam-3529	21	25	.	.	PUNCT
ejpam-3529	22	1	in	in	ADP
ejpam-3529	22	2	[	[	X
ejpam-3529	22	3	6	6	NUM
ejpam-3529	22	4	,	,	PUNCT
ejpam-3529	22	5	7	7	NUM
ejpam-3529	22	6	]	]	PUNCT
ejpam-3529	22	7	the	the	DET
ejpam-3529	22	8	authors	author	NOUN
ejpam-3529	22	9	obtained	obtain	VERB
ejpam-3529	22	10	the	the	DET
ejpam-3529	22	11	existence	existence	NOUN
ejpam-3529	22	12	of	of	ADP
ejpam-3529	22	13	solutions	solution	NOUN
ejpam-3529	22	14	for	for	ADP
ejpam-3529	22	15	an	an	DET
ejpam-3529	22	16	integro	integro	ADJ
ejpam-3529	22	17	differential	differential	ADJ
ejpam-3529	22	18	equation	equation	NOUN
ejpam-3529	22	19	with	with	ADP
ejpam-3529	22	20	periodic	periodic	ADJ
ejpam-3529	22	21	boundary	boundary	ADJ
ejpam-3529	22	22	condition	condition	NOUN
ejpam-3529	22	23	using	use	VERB
ejpam-3529	22	24	monotone	monotone	ADJ
ejpam-3529	22	25	iterative	iterative	NOUN
ejpam-3529	22	26	technique	technique	NOUN
ejpam-3529	22	27	.	.	PUNCT
ejpam-3529	23	1	this	this	PRON
ejpam-3529	23	2	was	be	AUX
ejpam-3529	23	3	a	a	DET
ejpam-3529	23	4	very	very	ADV
ejpam-3529	23	5	interesting	interesting	ADJ
ejpam-3529	23	6	result	result	NOUN
ejpam-3529	23	7	because	because	SCONJ
ejpam-3529	23	8	of	of	ADP
ejpam-3529	23	9	two	two	NUM
ejpam-3529	23	10	reasons	reason	NOUN
ejpam-3529	23	11	:	:	PUNCT
ejpam-3529	23	12	1	1	X
ejpam-3529	23	13	)	)	PUNCT
ejpam-3529	23	14	no	no	DET
ejpam-3529	23	15	additional	additional	ADJ
ejpam-3529	23	16	lemmas	lemma	NOUN
ejpam-3529	23	17	were	be	AUX
ejpam-3529	23	18	needed	need	VERB
ejpam-3529	23	19	to	to	PART
ejpam-3529	23	20	prove	prove	VERB
ejpam-3529	23	21	the	the	DET
ejpam-3529	23	22	result	result	NOUN
ejpam-3529	23	23	2	2	NUM
ejpam-3529	23	24	)	)	PUNCT
ejpam-3529	23	25	no	no	DET
ejpam-3529	23	26	extra	extra	ADJ
ejpam-3529	23	27	conditions	condition	NOUN
ejpam-3529	23	28	were	be	AUX
ejpam-3529	23	29	needed	need	VERB
ejpam-3529	23	30	for	for	ADP
ejpam-3529	23	31	uniqueness	uniqueness	NOUN
ejpam-3529	23	32	,	,	PUNCT
ejpam-3529	23	33	as	as	SCONJ
ejpam-3529	23	34	the	the	DET
ejpam-3529	23	35	uniqueness	uniqueness	NOUN
ejpam-3529	23	36	of	of	ADP
ejpam-3529	23	37	solution	solution	NOUN
ejpam-3529	23	38	was	be	AUX
ejpam-3529	23	39	generated	generate	VERB
ejpam-3529	23	40	by	by	ADP
ejpam-3529	23	41	the	the	DET
ejpam-3529	23	42	method	method	NOUN
ejpam-3529	23	43	itself	itself	PRON
ejpam-3529	23	44	.	.	PUNCT
ejpam-3529	24	1	this	this	PRON
ejpam-3529	24	2	led	lead	VERB
ejpam-3529	24	3	to	to	ADP
ejpam-3529	24	4	a	a	DET
ejpam-3529	24	5	spurt	spurt	NOUN
ejpam-3529	24	6	of	of	ADP
ejpam-3529	24	7	publications	publication	NOUN
ejpam-3529	24	8	in	in	ADP
ejpam-3529	24	9	monotone	monotone	ADJ
ejpam-3529	24	10	iterative	iterative	NOUN
ejpam-3529	24	11	technique	technique	NOUN
ejpam-3529	24	12	for	for	ADP
ejpam-3529	24	13	various	various	ADJ
ejpam-3529	24	14	types	type	NOUN
ejpam-3529	24	15	of	of	ADP
ejpam-3529	24	16	differential	differential	ADJ
ejpam-3529	24	17	equations	equation	NOUN
ejpam-3529	24	18	[	[	X
ejpam-3529	24	19	8	8	NUM
ejpam-3529	24	20	,	,	PUNCT
ejpam-3529	24	21	9	9	NUM
ejpam-3529	24	22	]	]	PUNCT
ejpam-3529	24	23	.	.	PUNCT
ejpam-3529	25	1	this	this	DET
ejpam-3529	25	2	idea	idea	NOUN
ejpam-3529	25	3	has	have	AUX
ejpam-3529	25	4	been	be	AUX
ejpam-3529	25	5	extended	extend	VERB
ejpam-3529	25	6	to	to	ADP
ejpam-3529	25	7	quasilinearization	quasilinearization	NOUN
ejpam-3529	25	8	and	and	CCONJ
ejpam-3529	25	9	generalized	generalized	ADJ
ejpam-3529	25	10	quasilinearisation	quasilinearisation	NOUN
ejpam-3529	25	11	had	have	AUX
ejpam-3529	25	12	been	be	AUX
ejpam-3529	25	13	developed	develop	VERB
ejpam-3529	25	14	for	for	ADP
ejpam-3529	25	15	periodic	periodic	ADJ
ejpam-3529	25	16	boundary	boundary	ADJ
ejpam-3529	25	17	value	value	NOUN
ejpam-3529	25	18	problem	problem	NOUN
ejpam-3529	25	19	of	of	ADP
ejpam-3529	25	20	a	a	DET
ejpam-3529	25	21	graph	graph	NOUN
ejpam-3529	25	22	differential	differential	ADJ
ejpam-3529	25	23	equation	equation	NOUN
ejpam-3529	25	24	and	and	CCONJ
ejpam-3529	25	25	a	a	DET
ejpam-3529	25	26	matrix	matrix	NOUN
ejpam-3529	25	27	differential	differential	NOUN
ejpam-3529	25	28	equation	equation	NOUN
ejpam-3529	25	29	through	through	ADP
ejpam-3529	25	30	natural	natural	ADJ
ejpam-3529	25	31	upper	upper	ADJ
ejpam-3529	25	32	and	and	CCONJ
ejpam-3529	25	33	lower	low	ADJ
ejpam-3529	25	34	solutions	solution	NOUN
ejpam-3529	25	35	[	[	X
ejpam-3529	25	36	10	10	NUM
ejpam-3529	25	37	]	]	PUNCT
ejpam-3529	25	38	.	.	PUNCT
ejpam-3529	26	1	in	in	ADP
ejpam-3529	26	2	[	[	X
ejpam-3529	26	3	11	11	NUM
ejpam-3529	26	4	]	]	PUNCT
ejpam-3529	26	5	it	it	PRON
ejpam-3529	26	6	was	be	AUX
ejpam-3529	26	7	observed	observe	VERB
ejpam-3529	26	8	that	that	SCONJ
ejpam-3529	26	9	quasilinearization	quasilinearization	NOUN
ejpam-3529	26	10	for	for	ADP
ejpam-3529	26	11	periodic	periodic	ADJ
ejpam-3529	26	12	boundary	boundary	ADJ
ejpam-3529	26	13	value	value	NOUN
ejpam-3529	26	14	problem	problem	NOUN
ejpam-3529	26	15	through	through	ADP
ejpam-3529	26	16	coupled	couple	VERB
ejpam-3529	26	17	lower	low	ADJ
ejpam-3529	26	18	and	and	CCONJ
ejpam-3529	26	19	upper	upper	ADJ
ejpam-3529	26	20	solutions	solution	NOUN
ejpam-3529	26	21	of	of	ADP
ejpam-3529	26	22	the	the	DET
ejpam-3529	26	23	initial	initial	ADJ
ejpam-3529	26	24	value	value	NOUN
ejpam-3529	26	25	problem	problem	NOUN
ejpam-3529	26	26	can	can	AUX
ejpam-3529	26	27	be	be	AUX
ejpam-3529	26	28	obtained	obtain	VERB
ejpam-3529	26	29	with	with	ADP
ejpam-3529	26	30	certain	certain	ADJ
ejpam-3529	26	31	restrictions	restriction	NOUN
ejpam-3529	26	32	.	.	PUNCT
ejpam-3529	27	1	in	in	ADP
ejpam-3529	27	2	this	this	DET
ejpam-3529	27	3	paper	paper	NOUN
ejpam-3529	27	4	,	,	PUNCT
ejpam-3529	27	5	using	use	VERB
ejpam-3529	27	6	the	the	DET
ejpam-3529	27	7	approach	approach	NOUN
ejpam-3529	27	8	given	give	VERB
ejpam-3529	27	9	in	in	ADP
ejpam-3529	27	10	[	[	NOUN
ejpam-3529	27	11	11	11	NUM
ejpam-3529	27	12	]	]	PUNCT
ejpam-3529	27	13	we	we	PRON
ejpam-3529	27	14	develop	develop	VERB
ejpam-3529	27	15	quasilinearization	quasilinearization	NOUN
ejpam-3529	27	16	technique	technique	NOUN
ejpam-3529	27	17	,	,	PUNCT
ejpam-3529	27	18	using	use	VERB
ejpam-3529	27	19	coupled	couple	VERB
ejpam-3529	27	20	lower	low	ADJ
ejpam-3529	27	21	and	and	CCONJ
ejpam-3529	27	22	upper	upper	ADJ
ejpam-3529	27	23	solutions	solution	NOUN
ejpam-3529	27	24	,	,	PUNCT
ejpam-3529	27	25	for	for	ADP
ejpam-3529	27	26	initial	initial	ADJ
ejpam-3529	27	27	value	value	NOUN
ejpam-3529	27	28	problem	problem	NOUN
ejpam-3529	27	29	of	of	ADP
ejpam-3529	27	30	an	an	DET
ejpam-3529	27	31	integro	integro	ADJ
ejpam-3529	27	32	differential	differential	ADJ
ejpam-3529	27	33	equation	equation	NOUN
ejpam-3529	27	34	and	and	CCONJ
ejpam-3529	27	35	using	use	VERB
ejpam-3529	27	36	this	this	DET
ejpam-3529	27	37	result	result	NOUN
ejpam-3529	27	38	to	to	PART
ejpam-3529	27	39	obtain	obtain	VERB
ejpam-3529	27	40	existence	existence	NOUN
ejpam-3529	27	41	and	and	CCONJ
ejpam-3529	27	42	uniqueness	uniqueness	NOUN
ejpam-3529	27	43	of	of	ADP
ejpam-3529	27	44	solutions	solution	NOUN
ejpam-3529	27	45	for	for	ADP
ejpam-3529	27	46	periodic	periodic	ADJ
ejpam-3529	27	47	boundary	boundary	ADJ
ejpam-3529	27	48	value	value	NOUN
ejpam-3529	27	49	problem	problem	NOUN
ejpam-3529	27	50	of	of	ADP
ejpam-3529	27	51	an	an	DET
ejpam-3529	27	52	integro	integro	ADJ
ejpam-3529	27	53	differential	differential	ADJ
ejpam-3529	27	54	equation	equation	NOUN
ejpam-3529	27	55	.	.	PUNCT
ejpam-3529	28	1	2	2	X
ejpam-3529	28	2	.	.	X
ejpam-3529	28	3	preliminaries	preliminary	NOUN
ejpam-3529	28	4	consider	consider	VERB
ejpam-3529	28	5	the	the	DET
ejpam-3529	28	6	periodic	periodic	ADJ
ejpam-3529	28	7	boundary	boundary	ADJ
ejpam-3529	28	8	value	value	NOUN
ejpam-3529	28	9	problem	problem	NOUN
ejpam-3529	28	10	of	of	ADP
ejpam-3529	28	11	an	an	DET
ejpam-3529	28	12	integro	integro	ADJ
ejpam-3529	28	13	differential	differential	ADJ
ejpam-3529	28	14	equation	equation	NOUN
ejpam-3529	28	15	given	give	VERB
ejpam-3529	28	16	by	by	ADP
ejpam-3529	28	17	x′	x′	PROPN
ejpam-3529	28	18	=	=	SYM
ejpam-3529	28	19	f1(t	f1(t	PROPN
ejpam-3529	28	20	,	,	PUNCT
ejpam-3529	28	21	x	x	NOUN
ejpam-3529	28	22	,	,	PUNCT
ejpam-3529	28	23	sx	sx	PROPN
ejpam-3529	28	24	)	)	PUNCT
ejpam-3529	28	25	+	+	CCONJ
ejpam-3529	28	26	f2(t	f2(t	PROPN
ejpam-3529	28	27	,	,	PUNCT
ejpam-3529	28	28	x	x	NOUN
ejpam-3529	28	29	,	,	PUNCT
ejpam-3529	28	30	sx	sx	PROPN
ejpam-3529	28	31	)	)	PUNCT
ejpam-3529	28	32	,	,	PUNCT
ejpam-3529	28	33	(	(	PUNCT
ejpam-3529	28	34	1	1	X
ejpam-3529	28	35	)	)	PUNCT
ejpam-3529	28	36	x(0	x(0	PROPN
ejpam-3529	28	37	)	)	PUNCT
ejpam-3529	29	1	=	=	SYM
ejpam-3529	29	2	x(t	x(t	PROPN
ejpam-3529	29	3	)	)	PUNCT
ejpam-3529	29	4	.	.	PUNCT
ejpam-3529	30	1	(	(	PUNCT
ejpam-3529	30	2	2	2	X
ejpam-3529	30	3	)	)	PUNCT
ejpam-3529	30	4	to	to	PART
ejpam-3529	30	5	develop	develop	VERB
ejpam-3529	30	6	the	the	DET
ejpam-3529	30	7	method	method	NOUN
ejpam-3529	30	8	of	of	ADP
ejpam-3529	30	9	the	the	DET
ejpam-3529	30	10	quasilinearization	quasilinearization	NOUN
ejpam-3529	30	11	technique	technique	NOUN
ejpam-3529	30	12	(	(	PUNCT
ejpam-3529	30	13	1	1	NUM
ejpam-3529	30	14	)	)	PUNCT
ejpam-3529	30	15	and	and	CCONJ
ejpam-3529	30	16	(	(	PUNCT
ejpam-3529	30	17	2	2	NUM
ejpam-3529	30	18	)	)	PUNCT
ejpam-3529	30	19	,	,	PUNCT
ejpam-3529	30	20	we	we	PRON
ejpam-3529	30	21	first	first	ADV
ejpam-3529	30	22	develop	develop	VERB
ejpam-3529	30	23	quasilinearization	quasilinearization	NOUN
ejpam-3529	30	24	technique	technique	NOUN
ejpam-3529	30	25	for	for	ADP
ejpam-3529	30	26	the	the	DET
ejpam-3529	30	27	corresponding	corresponding	ADJ
ejpam-3529	30	28	initial	initial	ADJ
ejpam-3529	30	29	value	value	NOUN
ejpam-3529	30	30	problem	problem	NOUN
ejpam-3529	30	31	of	of	ADP
ejpam-3529	30	32	an	an	DET
ejpam-3529	30	33	integro	integro	ADJ
ejpam-3529	30	34	differential	differential	ADJ
ejpam-3529	30	35	equation	equation	NOUN
ejpam-3529	30	36	given	give	VERB
ejpam-3529	30	37	by	by	ADP
ejpam-3529	30	38	x′	x′	PROPN
ejpam-3529	30	39	=	=	SYM
ejpam-3529	30	40	f1(t	f1(t	PROPN
ejpam-3529	30	41	,	,	PUNCT
ejpam-3529	30	42	x	x	NOUN
ejpam-3529	30	43	,	,	PUNCT
ejpam-3529	30	44	sx	sx	PROPN
ejpam-3529	30	45	)	)	PUNCT
ejpam-3529	30	46	+	+	CCONJ
ejpam-3529	30	47	f2(t	f2(t	PROPN
ejpam-3529	30	48	,	,	PUNCT
ejpam-3529	30	49	x	x	NOUN
ejpam-3529	30	50	,	,	PUNCT
ejpam-3529	30	51	sx	sx	PROPN
ejpam-3529	30	52	)	)	PUNCT
ejpam-3529	30	53	,	,	PUNCT
ejpam-3529	30	54	(	(	PUNCT
ejpam-3529	30	55	3	3	X
ejpam-3529	30	56	)	)	PUNCT
ejpam-3529	30	57	x(0	x(0	PROPN
ejpam-3529	30	58	)	)	PUNCT
ejpam-3529	31	1	=	=	PUNCT
ejpam-3529	31	2	x0	x0	PROPN
ejpam-3529	31	3	,	,	PUNCT
ejpam-3529	31	4	(	(	PUNCT
ejpam-3529	31	5	4	4	X
ejpam-3529	31	6	)	)	PUNCT
ejpam-3529	31	7	where	where	SCONJ
ejpam-3529	31	8	f1	f1	NOUN
ejpam-3529	31	9	,	,	PUNCT
ejpam-3529	31	10	f2	f2	PROPN
ejpam-3529	31	11	∈	∈	PROPN
ejpam-3529	31	12	c[i	c[i	NOUN
ejpam-3529	31	13	×	×	PROPN
ejpam-3529	31	14	rn	rn	PROPN
ejpam-3529	31	15	×	×	PROPN
ejpam-3529	31	16	rn	rn	PROPN
ejpam-3529	31	17	,	,	PUNCT
ejpam-3529	31	18	rn	rn	PROPN
ejpam-3529	31	19	]	]	NOUN
ejpam-3529	31	20	,	,	PUNCT
ejpam-3529	31	21	sx(t	sx(t	X
ejpam-3529	31	22	)	)	PUNCT
ejpam-3529	31	23	=	=	SYM
ejpam-3529	32	1	t∫	t∫	NOUN
ejpam-3529	32	2	0	0	NUM
ejpam-3529	32	3	k(t	k(t	NOUN
ejpam-3529	32	4	,	,	PUNCT
ejpam-3529	32	5	s)x(s)ds	s)x(s)ds	NOUN
ejpam-3529	32	6	,	,	PUNCT
ejpam-3529	32	7	with	with	ADP
ejpam-3529	32	8	k	k	PROPN
ejpam-3529	32	9	∈	∈	PROPN
ejpam-3529	32	10	c[i	c[i	NOUN
ejpam-3529	32	11	×	×	NOUN
ejpam-3529	32	12	i	i	NOUN
ejpam-3529	32	13	,	,	PUNCT
ejpam-3529	32	14	r+	r+	X
ejpam-3529	32	15	]	]	PUNCT
ejpam-3529	32	16	and	and	CCONJ
ejpam-3529	32	17	i=[0,t	i=[0,t	PROPN
ejpam-3529	32	18	]	]	PUNCT
ejpam-3529	32	19	.	.	PUNCT
ejpam-3529	33	1	to	to	PART
ejpam-3529	33	2	do	do	VERB
ejpam-3529	33	3	so	so	ADV
ejpam-3529	33	4	we	we	PRON
ejpam-3529	33	5	first	first	ADV
ejpam-3529	33	6	define	define	VERB
ejpam-3529	33	7	the	the	DET
ejpam-3529	33	8	various	various	ADJ
ejpam-3529	33	9	types	type	NOUN
ejpam-3529	33	10	of	of	ADP
ejpam-3529	33	11	lower	low	ADJ
ejpam-3529	33	12	and	and	CCONJ
ejpam-3529	33	13	upper	upper	ADJ
ejpam-3529	33	14	solution	solution	NOUN
ejpam-3529	33	15	for	for	ADP
ejpam-3529	33	16	(	(	PUNCT
ejpam-3529	33	17	3	3	NUM
ejpam-3529	33	18	)	)	PUNCT
ejpam-3529	33	19	and	and	CCONJ
ejpam-3529	33	20	(	(	PUNCT
ejpam-3529	33	21	4	4	NUM
ejpam-3529	33	22	)	)	PUNCT
ejpam-3529	33	23	,	,	PUNCT
ejpam-3529	33	24	definition	definition	NOUN
ejpam-3529	33	25	1	1	NUM
ejpam-3529	33	26	.	.	PUNCT
ejpam-3529	34	1	let	let	VERB
ejpam-3529	34	2	α0	α0	ADJ
ejpam-3529	34	3	,	,	PUNCT
ejpam-3529	34	4	β0	β0	PROPN
ejpam-3529	34	5	∈	∈	PROPN
ejpam-3529	34	6	c1[i	c1[i	PROPN
ejpam-3529	34	7	,	,	PUNCT
ejpam-3529	34	8	rn	rn	PROPN
ejpam-3529	34	9	]	]	PUNCT
ejpam-3529	34	10	.	.	PUNCT
ejpam-3529	35	1	then	then	ADV
ejpam-3529	35	2	α0	α0	ADJ
ejpam-3529	35	3	,	,	PUNCT
ejpam-3529	35	4	β0	β0	PROPN
ejpam-3529	35	5	are	be	AUX
ejpam-3529	35	6	said	say	VERB
ejpam-3529	35	7	to	to	PART
ejpam-3529	35	8	be	be	AUX
ejpam-3529	35	9	(	(	PUNCT
ejpam-3529	35	10	a	a	DET
ejpam-3529	35	11	)	)	PUNCT
ejpam-3529	35	12	natural	natural	ADJ
ejpam-3529	35	13	lower	low	ADJ
ejpam-3529	35	14	and	and	CCONJ
ejpam-3529	35	15	upper	upper	ADJ
ejpam-3529	35	16	solutions	solution	NOUN
ejpam-3529	35	17	of	of	ADP
ejpam-3529	35	18	(	(	PUNCT
ejpam-3529	35	19	3	3	NUM
ejpam-3529	35	20	)	)	PUNCT
ejpam-3529	35	21	and	and	CCONJ
ejpam-3529	35	22	(	(	PUNCT
ejpam-3529	35	23	4	4	X
ejpam-3529	35	24	)	)	PUNCT
ejpam-3529	35	25	if	if	SCONJ
ejpam-3529	35	26	α′0	α′0	NOUN
ejpam-3529	35	27	≤	≤	PROPN
ejpam-3529	35	28	f1(t	f1(t	PROPN
ejpam-3529	35	29	,	,	PUNCT
ejpam-3529	35	30	α0	α0	ADJ
ejpam-3529	35	31	,	,	PUNCT
ejpam-3529	35	32	sα0	sα0	NOUN
ejpam-3529	35	33	)	)	PUNCT
ejpam-3529	36	1	+	+	CCONJ
ejpam-3529	36	2	f2(t	f2(t	PROPN
ejpam-3529	36	3	,	,	PUNCT
ejpam-3529	36	4	α0	α0	ADJ
ejpam-3529	36	5	,	,	PUNCT
ejpam-3529	36	6	sα0	sα0	NOUN
ejpam-3529	36	7	)	)	PUNCT
ejpam-3529	36	8	,	,	PUNCT
ejpam-3529	36	9	α0(0	α0(0	PROPN
ejpam-3529	36	10	)	)	PUNCT
ejpam-3529	36	11	≤	≤	NOUN
ejpam-3529	36	12	x0	x0	PROPN
ejpam-3529	36	13	,	,	PUNCT
ejpam-3529	36	14	β′0	β′0	PRON
ejpam-3529	36	15	≥	≥	NOUN
ejpam-3529	36	16	f1(t	f1(t	PROPN
ejpam-3529	36	17	,	,	PUNCT
ejpam-3529	36	18	β0	β0	NOUN
ejpam-3529	36	19	,	,	PUNCT
ejpam-3529	36	20	sβ0	sβ0	NOUN
ejpam-3529	36	21	)	)	PUNCT
ejpam-3529	36	22	+	+	CCONJ
ejpam-3529	36	23	f2(t	f2(t	PROPN
ejpam-3529	36	24	,	,	PUNCT
ejpam-3529	36	25	β0	β0	NOUN
ejpam-3529	36	26	,	,	PUNCT
ejpam-3529	36	27	sβ0	sβ0	NOUN
ejpam-3529	36	28	)	)	PUNCT
ejpam-3529	36	29	,	,	PUNCT
ejpam-3529	36	30	β0(0	β0(0	PROPN
ejpam-3529	36	31	)	)	PUNCT
ejpam-3529	36	32	≥	≥	NOUN
ejpam-3529	36	33	x0	x0	PROPN
ejpam-3529	36	34	,	,	PUNCT
ejpam-3529	36	35	t	t	PROPN
ejpam-3529	36	36	∈	∈	PROPN
ejpam-3529	37	1	i	i	PRON
ejpam-3529	37	2	;	;	PUNCT
ejpam-3529	37	3	}	}	PUNCT
ejpam-3529	37	4	(	(	PUNCT
ejpam-3529	37	5	5	5	X
ejpam-3529	37	6	)	)	PUNCT
ejpam-3529	37	7	ch	ch	NOUN
ejpam-3529	37	8	.	.	PUNCT
ejpam-3529	38	1	v.	v.	ADP
ejpam-3529	38	2	sreedhar	sreedhar	PROPN
ejpam-3529	38	3	,	,	PUNCT
ejpam-3529	38	4	j.	j.	PROPN
ejpam-3529	38	5	vasundhara	vasundhara	PROPN
ejpam-3529	38	6	devi	devi	PROPN
ejpam-3529	38	7	,	,	PUNCT
ejpam-3529	38	8	/	/	SYM
ejpam-3529	38	9	eur	eur	NOUN
ejpam-3529	38	10	.	.	PUNCT
ejpam-3529	39	1	j.	j.	PROPN
ejpam-3529	39	2	pure	pure	PROPN
ejpam-3529	39	3	appl	appl	PROPN
ejpam-3529	39	4	.	.	PROPN
ejpam-3529	39	5	math	math	PROPN
ejpam-3529	39	6	,	,	PUNCT
ejpam-3529	39	7	12	12	NUM
ejpam-3529	39	8	(	(	PUNCT
ejpam-3529	39	9	4	4	NUM
ejpam-3529	39	10	)	)	PUNCT
ejpam-3529	39	11	(	(	PUNCT
ejpam-3529	39	12	2019	2019	NUM
ejpam-3529	39	13	)	)	PUNCT
ejpam-3529	39	14	,	,	PUNCT
ejpam-3529	39	15	1662	1662	NUM
ejpam-3529	39	16	-	-	SYM
ejpam-3529	39	17	1675	1675	NUM
ejpam-3529	39	18	1664	1664	NUM
ejpam-3529	39	19	(	(	PUNCT
ejpam-3529	39	20	b	b	NOUN
ejpam-3529	39	21	)	)	PUNCT
ejpam-3529	39	22	coupled	couple	VERB
ejpam-3529	39	23	lower	low	ADJ
ejpam-3529	39	24	and	and	CCONJ
ejpam-3529	39	25	upper	upper	ADJ
ejpam-3529	39	26	solutions	solution	NOUN
ejpam-3529	39	27	of	of	ADP
ejpam-3529	39	28	type	type	NOUN
ejpam-3529	39	29	i	i	PRON
ejpam-3529	39	30	of	of	ADP
ejpam-3529	39	31	(	(	PUNCT
ejpam-3529	39	32	3	3	NUM
ejpam-3529	39	33	)	)	PUNCT
ejpam-3529	39	34	and	and	CCONJ
ejpam-3529	39	35	(	(	PUNCT
ejpam-3529	39	36	4	4	X
ejpam-3529	39	37	)	)	PUNCT
ejpam-3529	39	38	if	if	SCONJ
ejpam-3529	39	39	α′0	α′0	NOUN
ejpam-3529	39	40	≤	≤	PROPN
ejpam-3529	39	41	f1(t	f1(t	PROPN
ejpam-3529	39	42	,	,	PUNCT
ejpam-3529	39	43	α0	α0	ADJ
ejpam-3529	39	44	,	,	PUNCT
ejpam-3529	39	45	sα0	sα0	NOUN
ejpam-3529	39	46	)	)	PUNCT
ejpam-3529	39	47	+	+	CCONJ
ejpam-3529	40	1	f2(t	f2(t	PROPN
ejpam-3529	40	2	,	,	PUNCT
ejpam-3529	40	3	β0	β0	NOUN
ejpam-3529	40	4	,	,	PUNCT
ejpam-3529	40	5	sβ0	sβ0	NOUN
ejpam-3529	40	6	)	)	PUNCT
ejpam-3529	40	7	,	,	PUNCT
ejpam-3529	40	8	α0(0	α0(0	PROPN
ejpam-3529	40	9	)	)	PUNCT
ejpam-3529	40	10	≤	≤	NOUN
ejpam-3529	40	11	x0	x0	PROPN
ejpam-3529	40	12	,	,	PUNCT
ejpam-3529	40	13	β′0	β′0	PRON
ejpam-3529	40	14	≥	≥	NOUN
ejpam-3529	40	15	f1(t	f1(t	PROPN
ejpam-3529	40	16	,	,	PUNCT
ejpam-3529	40	17	β0	β0	NOUN
ejpam-3529	40	18	,	,	PUNCT
ejpam-3529	40	19	sβ0	sβ0	NOUN
ejpam-3529	40	20	)	)	PUNCT
ejpam-3529	40	21	+	+	CCONJ
ejpam-3529	40	22	f2(t	f2(t	PROPN
ejpam-3529	40	23	,	,	PUNCT
ejpam-3529	40	24	α0	α0	ADJ
ejpam-3529	40	25	,	,	PUNCT
ejpam-3529	40	26	sα0	sα0	NOUN
ejpam-3529	40	27	)	)	PUNCT
ejpam-3529	40	28	,	,	PUNCT
ejpam-3529	40	29	β0(0	β0(0	PROPN
ejpam-3529	40	30	)	)	PUNCT
ejpam-3529	40	31	≥	≥	NOUN
ejpam-3529	40	32	x0	x0	PROPN
ejpam-3529	40	33	,	,	PUNCT
ejpam-3529	40	34	t	t	PROPN
ejpam-3529	40	35	∈	∈	PROPN
ejpam-3529	41	1	i	i	PRON
ejpam-3529	41	2	;	;	PUNCT
ejpam-3529	41	3	}	}	PUNCT
ejpam-3529	41	4	(	(	PUNCT
ejpam-3529	41	5	6	6	NUM
ejpam-3529	41	6	)	)	PUNCT
ejpam-3529	41	7	(	(	PUNCT
ejpam-3529	41	8	c	c	X
ejpam-3529	41	9	)	)	PUNCT
ejpam-3529	41	10	coupled	couple	VERB
ejpam-3529	41	11	lower	low	ADJ
ejpam-3529	41	12	and	and	CCONJ
ejpam-3529	41	13	upper	upper	ADJ
ejpam-3529	41	14	solutions	solution	NOUN
ejpam-3529	41	15	of	of	ADP
ejpam-3529	41	16	type	type	NOUN
ejpam-3529	41	17	ii	ii	PROPN
ejpam-3529	41	18	of	of	ADP
ejpam-3529	41	19	(	(	PUNCT
ejpam-3529	41	20	3	3	NUM
ejpam-3529	41	21	)	)	PUNCT
ejpam-3529	41	22	and	and	CCONJ
ejpam-3529	41	23	(	(	PUNCT
ejpam-3529	41	24	4	4	X
ejpam-3529	41	25	)	)	PUNCT
ejpam-3529	41	26	if	if	SCONJ
ejpam-3529	41	27	α′0	α′0	NOUN
ejpam-3529	41	28	≤	≤	PROPN
ejpam-3529	41	29	f1(t	f1(t	PROPN
ejpam-3529	41	30	,	,	PUNCT
ejpam-3529	41	31	β0	β0	NOUN
ejpam-3529	41	32	,	,	PUNCT
ejpam-3529	41	33	sβ0	sβ0	NOUN
ejpam-3529	41	34	)	)	PUNCT
ejpam-3529	42	1	+	+	CCONJ
ejpam-3529	42	2	f2(t	f2(t	PROPN
ejpam-3529	42	3	,	,	PUNCT
ejpam-3529	42	4	α0	α0	ADJ
ejpam-3529	42	5	,	,	PUNCT
ejpam-3529	42	6	sα0	sα0	NOUN
ejpam-3529	42	7	)	)	PUNCT
ejpam-3529	42	8	,	,	PUNCT
ejpam-3529	42	9	α0(0	α0(0	PROPN
ejpam-3529	42	10	)	)	PUNCT
ejpam-3529	42	11	≤	≤	NOUN
ejpam-3529	42	12	x0	x0	PROPN
ejpam-3529	42	13	,	,	PUNCT
ejpam-3529	42	14	β′0	β′0	PRON
ejpam-3529	42	15	≥	≥	NOUN
ejpam-3529	42	16	f1(t	f1(t	PROPN
ejpam-3529	42	17	,	,	PUNCT
ejpam-3529	42	18	α0	α0	ADJ
ejpam-3529	42	19	,	,	PUNCT
ejpam-3529	42	20	sα0	sα0	NOUN
ejpam-3529	42	21	)	)	PUNCT
ejpam-3529	43	1	+	+	CCONJ
ejpam-3529	43	2	f2(t	f2(t	PROPN
ejpam-3529	43	3	,	,	PUNCT
ejpam-3529	43	4	β0	β0	NOUN
ejpam-3529	43	5	,	,	PUNCT
ejpam-3529	43	6	sβ0	sβ0	NOUN
ejpam-3529	43	7	)	)	PUNCT
ejpam-3529	43	8	,	,	PUNCT
ejpam-3529	43	9	β0(0	β0(0	PROPN
ejpam-3529	43	10	)	)	PUNCT
ejpam-3529	43	11	≥	≥	NOUN
ejpam-3529	43	12	x0	x0	PROPN
ejpam-3529	43	13	,	,	PUNCT
ejpam-3529	43	14	t	t	PROPN
ejpam-3529	43	15	∈	∈	PROPN
ejpam-3529	44	1	i	i	PRON
ejpam-3529	44	2	;	;	PUNCT
ejpam-3529	44	3	}	}	PUNCT
ejpam-3529	44	4	(	(	PUNCT
ejpam-3529	44	5	7	7	NUM
ejpam-3529	44	6	)	)	PUNCT
ejpam-3529	44	7	(	(	PUNCT
ejpam-3529	44	8	d	d	X
ejpam-3529	44	9	)	)	PUNCT
ejpam-3529	44	10	coupled	couple	VERB
ejpam-3529	44	11	lower	low	ADJ
ejpam-3529	44	12	and	and	CCONJ
ejpam-3529	44	13	upper	upper	ADJ
ejpam-3529	44	14	solutions	solution	NOUN
ejpam-3529	44	15	of	of	ADP
ejpam-3529	44	16	type	type	NOUN
ejpam-3529	44	17	iii	iii	PROPN
ejpam-3529	44	18	of	of	ADP
ejpam-3529	44	19	(	(	PUNCT
ejpam-3529	44	20	3	3	NUM
ejpam-3529	44	21	)	)	PUNCT
ejpam-3529	44	22	and	and	CCONJ
ejpam-3529	44	23	(	(	PUNCT
ejpam-3529	44	24	4	4	X
ejpam-3529	44	25	)	)	PUNCT
ejpam-3529	44	26	if	if	SCONJ
ejpam-3529	44	27	α′0	α′0	NOUN
ejpam-3529	44	28	≤	≤	PROPN
ejpam-3529	44	29	f1(t	f1(t	PROPN
ejpam-3529	44	30	,	,	PUNCT
ejpam-3529	44	31	β0	β0	NOUN
ejpam-3529	44	32	,	,	PUNCT
ejpam-3529	44	33	sβ0	sβ0	NOUN
ejpam-3529	44	34	)	)	PUNCT
ejpam-3529	45	1	+	+	CCONJ
ejpam-3529	45	2	f2(t	f2(t	PROPN
ejpam-3529	45	3	,	,	PUNCT
ejpam-3529	45	4	β0	β0	NOUN
ejpam-3529	45	5	,	,	PUNCT
ejpam-3529	45	6	sβ0	sβ0	NOUN
ejpam-3529	45	7	)	)	PUNCT
ejpam-3529	45	8	,	,	PUNCT
ejpam-3529	45	9	α0(0	α0(0	PROPN
ejpam-3529	45	10	)	)	PUNCT
ejpam-3529	45	11	≤	≤	NOUN
ejpam-3529	45	12	x0	x0	PROPN
ejpam-3529	45	13	,	,	PUNCT
ejpam-3529	45	14	β′0	β′0	PRON
ejpam-3529	45	15	≥	≥	NOUN
ejpam-3529	45	16	f1(t	f1(t	PROPN
ejpam-3529	45	17	,	,	PUNCT
ejpam-3529	45	18	α0	α0	ADJ
ejpam-3529	45	19	,	,	PUNCT
ejpam-3529	45	20	sα0	sα0	NOUN
ejpam-3529	45	21	)	)	PUNCT
ejpam-3529	46	1	+	+	CCONJ
ejpam-3529	46	2	f2(t	f2(t	PROPN
ejpam-3529	46	3	,	,	PUNCT
ejpam-3529	46	4	α0	α0	ADJ
ejpam-3529	46	5	,	,	PUNCT
ejpam-3529	46	6	sα0	sα0	NOUN
ejpam-3529	46	7	)	)	PUNCT
ejpam-3529	46	8	,	,	PUNCT
ejpam-3529	46	9	β0(0	β0(0	PROPN
ejpam-3529	46	10	)	)	PUNCT
ejpam-3529	46	11	≥	≥	NOUN
ejpam-3529	46	12	x0	x0	PROPN
ejpam-3529	46	13	,	,	PUNCT
ejpam-3529	46	14	t	t	PROPN
ejpam-3529	46	15	∈	∈	PROPN
ejpam-3529	46	16	i.	i.	PROPN
ejpam-3529	46	17	}	}	PUNCT
ejpam-3529	46	18	(	(	PUNCT
ejpam-3529	46	19	8)	8)	NUM
ejpam-3529	46	20	we	we	PRON
ejpam-3529	46	21	observe	observe	VERB
ejpam-3529	46	22	that	that	SCONJ
ejpam-3529	46	23	whenever	whenever	SCONJ
ejpam-3529	46	24	we	we	PRON
ejpam-3529	46	25	have	have	VERB
ejpam-3529	46	26	α(t	α(t	NOUN
ejpam-3529	46	27	)	)	PUNCT
ejpam-3529	46	28	≤	≤	NOUN
ejpam-3529	46	29	β(t	β(t	PROPN
ejpam-3529	46	30	)	)	PUNCT
ejpam-3529	46	31	,	,	PUNCT
ejpam-3529	46	32	t	t	PROPN
ejpam-3529	46	33	∈	∈	PROPN
ejpam-3529	47	1	i	i	PRON
ejpam-3529	47	2	,	,	PUNCT
ejpam-3529	47	3	f1(t	f1(t	PROPN
ejpam-3529	47	4	,	,	PUNCT
ejpam-3529	47	5	x	x	NOUN
ejpam-3529	47	6	,	,	PUNCT
ejpam-3529	47	7	sx	sx	PROPN
ejpam-3529	47	8	)	)	PUNCT
ejpam-3529	47	9	is	be	AUX
ejpam-3529	47	10	nondecreasing	nondecrease	VERB
ejpam-3529	47	11	in	in	ADP
ejpam-3529	47	12	x	x	PUNCT
ejpam-3529	47	13	and	and	CCONJ
ejpam-3529	47	14	y	y	PROPN
ejpam-3529	47	15	and	and	CCONJ
ejpam-3529	47	16	f2(t	f2(t	PROPN
ejpam-3529	47	17	,	,	PUNCT
ejpam-3529	47	18	x	x	NOUN
ejpam-3529	47	19	,	,	PUNCT
ejpam-3529	47	20	sx	sx	PROPN
ejpam-3529	47	21	)	)	PUNCT
ejpam-3529	47	22	is	be	AUX
ejpam-3529	47	23	nonincreasing	nonincrease	VERB
ejpam-3529	47	24	in	in	ADP
ejpam-3529	47	25	x	x	PUNCT
ejpam-3529	47	26	and	and	CCONJ
ejpam-3529	47	27	y	y	PROPN
ejpam-3529	47	28	for	for	ADP
ejpam-3529	47	29	each	each	DET
ejpam-3529	47	30	t	t	NOUN
ejpam-3529	47	31	∈	∈	PROPN
ejpam-3529	48	1	i	i	PRON
ejpam-3529	48	2	,	,	PUNCT
ejpam-3529	48	3	the	the	DET
ejpam-3529	48	4	lower	low	ADJ
ejpam-3529	48	5	and	and	CCONJ
ejpam-3529	48	6	upper	upper	ADJ
ejpam-3529	48	7	solutions	solution	NOUN
ejpam-3529	48	8	defined	define	VERB
ejpam-3529	48	9	by	by	ADP
ejpam-3529	48	10	(	(	PUNCT
ejpam-3529	48	11	5	5	NUM
ejpam-3529	48	12	)	)	PUNCT
ejpam-3529	48	13	and	and	CCONJ
ejpam-3529	48	14	(	(	PUNCT
ejpam-3529	48	15	8)	8)	NUM
ejpam-3529	48	16	reduce	reduce	VERB
ejpam-3529	48	17	to	to	ADP
ejpam-3529	48	18	(	(	PUNCT
ejpam-3529	48	19	6	6	NUM
ejpam-3529	48	20	)	)	PUNCT
ejpam-3529	48	21	and	and	CCONJ
ejpam-3529	48	22	(	(	PUNCT
ejpam-3529	48	23	7	7	X
ejpam-3529	48	24	)	)	PUNCT
ejpam-3529	48	25	consequently	consequently	ADV
ejpam-3529	48	26	,	,	PUNCT
ejpam-3529	48	27	hence	hence	ADV
ejpam-3529	48	28	it	it	PRON
ejpam-3529	48	29	is	be	AUX
ejpam-3529	48	30	sufficient	sufficient	ADJ
ejpam-3529	48	31	to	to	PART
ejpam-3529	48	32	investigate	investigate	VERB
ejpam-3529	48	33	the	the	DET
ejpam-3529	48	34	cases	case	NOUN
ejpam-3529	48	35	(	(	PUNCT
ejpam-3529	48	36	6	6	NUM
ejpam-3529	48	37	)	)	PUNCT
ejpam-3529	48	38	and	and	CCONJ
ejpam-3529	48	39	(	(	PUNCT
ejpam-3529	48	40	7	7	NUM
ejpam-3529	48	41	)	)	PUNCT
ejpam-3529	48	42	.	.	PUNCT
ejpam-3529	49	1	3	3	X
ejpam-3529	49	2	.	.	NUM
ejpam-3529	49	3	generalized	generalized	ADJ
ejpam-3529	49	4	quasilinearization	quasilinearization	NOUN
ejpam-3529	49	5	for	for	ADP
ejpam-3529	49	6	initial	initial	ADJ
ejpam-3529	49	7	value	value	NOUN
ejpam-3529	49	8	problem	problem	NOUN
ejpam-3529	49	9	of	of	ADP
ejpam-3529	49	10	an	an	DET
ejpam-3529	49	11	integro	integro	ADJ
ejpam-3529	49	12	differential	differential	ADJ
ejpam-3529	49	13	equation	equation	NOUN
ejpam-3529	49	14	.	.	PUNCT
ejpam-3529	50	1	in	in	ADP
ejpam-3529	50	2	this	this	DET
ejpam-3529	50	3	section	section	NOUN
ejpam-3529	50	4	we	we	PRON
ejpam-3529	50	5	develop	develop	VERB
ejpam-3529	50	6	the	the	DET
ejpam-3529	50	7	method	method	NOUN
ejpam-3529	50	8	of	of	ADP
ejpam-3529	50	9	generalized	generalized	ADJ
ejpam-3529	50	10	quasilinearization	quasilinearization	NOUN
ejpam-3529	50	11	for	for	ADP
ejpam-3529	50	12	the	the	DET
ejpam-3529	50	13	initial	initial	ADJ
ejpam-3529	50	14	value	value	NOUN
ejpam-3529	50	15	problem	problem	NOUN
ejpam-3529	50	16	of	of	ADP
ejpam-3529	50	17	an	an	DET
ejpam-3529	50	18	integro	integro	ADJ
ejpam-3529	50	19	differential	differential	ADJ
ejpam-3529	50	20	equation	equation	NOUN
ejpam-3529	50	21	and	and	CCONJ
ejpam-3529	50	22	use	use	VERB
ejpam-3529	50	23	it	it	PRON
ejpam-3529	50	24	in	in	ADP
ejpam-3529	50	25	the	the	DET
ejpam-3529	50	26	next	next	ADJ
ejpam-3529	50	27	section	section	NOUN
ejpam-3529	50	28	.	.	PUNCT
ejpam-3529	51	1	we	we	PRON
ejpam-3529	51	2	first	first	ADV
ejpam-3529	51	3	state	state	VERB
ejpam-3529	51	4	a	a	DET
ejpam-3529	51	5	known	know	VERB
ejpam-3529	51	6	result	result	NOUN
ejpam-3529	51	7	from	from	ADP
ejpam-3529	51	8	[	[	X
ejpam-3529	51	9	1	1	NUM
ejpam-3529	51	10	]	]	PUNCT
ejpam-3529	51	11	corresponding	correspond	VERB
ejpam-3529	51	12	to	to	ADP
ejpam-3529	51	13	an	an	DET
ejpam-3529	51	14	integro	integro	ADJ
ejpam-3529	51	15	differential	differential	ADJ
ejpam-3529	51	16	equation	equation	NOUN
ejpam-3529	51	17	which	which	PRON
ejpam-3529	51	18	is	be	AUX
ejpam-3529	51	19	useful	useful	ADJ
ejpam-3529	51	20	in	in	ADP
ejpam-3529	51	21	developing	develop	VERB
ejpam-3529	51	22	a	a	DET
ejpam-3529	51	23	sequence	sequence	NOUN
ejpam-3529	51	24	of	of	ADP
ejpam-3529	51	25	iterates	iterate	NOUN
ejpam-3529	51	26	to	to	PART
ejpam-3529	51	27	be	be	AUX
ejpam-3529	51	28	constructed	construct	VERB
ejpam-3529	51	29	while	while	SCONJ
ejpam-3529	51	30	developing	develop	VERB
ejpam-3529	51	31	the	the	DET
ejpam-3529	51	32	quasilinearization	quasilinearization	NOUN
ejpam-3529	51	33	.	.	PUNCT
ejpam-3529	52	1	lemma	lemma	PROPN
ejpam-3529	52	2	1	1	X
ejpam-3529	52	3	.	.	PUNCT
ejpam-3529	53	1	let	let	VERB
ejpam-3529	53	2	p	p	PROPN
ejpam-3529	53	3	∈	∈	PROPN
ejpam-3529	53	4	c1[i	c1[i	NOUN
ejpam-3529	53	5	,	,	PUNCT
ejpam-3529	53	6	r	r	X
ejpam-3529	53	7	]	]	X
ejpam-3529	53	8	,	,	PUNCT
ejpam-3529	53	9	where	where	SCONJ
ejpam-3529	53	10	i	i	PRON
ejpam-3529	53	11	=	=	PUNCT
ejpam-3529	54	1	[	[	X
ejpam-3529	54	2	0	0	NUM
ejpam-3529	54	3	,	,	PUNCT
ejpam-3529	54	4	t	t	PROPN
ejpam-3529	54	5	]	]	PUNCT
ejpam-3529	54	6	is	be	AUX
ejpam-3529	54	7	such	such	ADJ
ejpam-3529	54	8	that	that	PRON
ejpam-3529	54	9	and	and	CCONJ
ejpam-3529	54	10	p	p	NOUN
ejpam-3529	54	11	′(t	′(t	PROPN
ejpam-3529	54	12	)	)	PUNCT
ejpam-3529	54	13	≤	≤	NUM
ejpam-3529	54	14	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	54	15	)	)	PUNCT
ejpam-3529	54	16	on	on	ADP
ejpam-3529	54	17	i	i	PRON
ejpam-3529	54	18	,	,	PUNCT
ejpam-3529	54	19	p(0	p(0	PROPN
ejpam-3529	54	20	)	)	PUNCT
ejpam-3529	54	21	≤	≤	NOUN
ejpam-3529	54	22	0	0	NUM
ejpam-3529	54	23	,	,	PUNCT
ejpam-3529	54	24	(	(	PUNCT
ejpam-3529	54	25	9	9	X
ejpam-3529	54	26	)	)	PUNCT
ejpam-3529	54	27	where	where	SCONJ
ejpam-3529	54	28	m	m	VERB
ejpam-3529	54	29	>	>	X
ejpam-3529	54	30	0	0	NUM
ejpam-3529	54	31	,	,	PUNCT
ejpam-3529	54	32	n	n	PRON
ejpam-3529	54	33	≥	≥	NOUN
ejpam-3529	54	34	0	0	NUM
ejpam-3529	54	35	are	be	AUX
ejpam-3529	54	36	constants	constant	NOUN
ejpam-3529	54	37	such	such	ADJ
ejpam-3529	54	38	that	that	PRON
ejpam-3529	54	39	nk1	nk1	PROPN
ejpam-3529	54	40	t	t	PROPN
ejpam-3529	54	41	(	(	PUNCT
ejpam-3529	54	42	emt	emt	PROPN
ejpam-3529	54	43	−	−	PROPN
ejpam-3529	54	44	1	1	NUM
ejpam-3529	54	45	)	)	PUNCT
ejpam-3529	54	46	≤m	≤m	NOUN
ejpam-3529	54	47	,	,	PUNCT
ejpam-3529	54	48	(	(	PUNCT
ejpam-3529	54	49	10	10	NUM
ejpam-3529	54	50	)	)	PUNCT
ejpam-3529	54	51	where	where	SCONJ
ejpam-3529	54	52	k1	k1	NOUN
ejpam-3529	54	53	=	=	PROPN
ejpam-3529	54	54	maxt∈i	maxt∈i	PROPN
ejpam-3529	54	55	k(t	k(t	PROPN
ejpam-3529	54	56	,	,	PUNCT
ejpam-3529	54	57	s	s	PART
ejpam-3529	54	58	)	)	PUNCT
ejpam-3529	54	59	.	.	PUNCT
ejpam-3529	55	1	then	then	ADV
ejpam-3529	55	2	p(t	p(t	VERB
ejpam-3529	55	3	)	)	PUNCT
ejpam-3529	55	4	≤	≤	NOUN
ejpam-3529	55	5	0	0	NUM
ejpam-3529	56	1	on	on	ADP
ejpam-3529	56	2	i.	i.	NOUN
ejpam-3529	56	3	to	to	PART
ejpam-3529	56	4	prove	prove	VERB
ejpam-3529	56	5	the	the	DET
ejpam-3529	56	6	main	main	ADJ
ejpam-3529	56	7	theorem	theorem	NOUN
ejpam-3529	56	8	we	we	PRON
ejpam-3529	56	9	need	need	VERB
ejpam-3529	56	10	the	the	DET
ejpam-3529	56	11	following	follow	VERB
ejpam-3529	56	12	assumptions	assumption	NOUN
ejpam-3529	56	13	which	which	PRON
ejpam-3529	56	14	are	be	AUX
ejpam-3529	56	15	listed	list	VERB
ejpam-3529	56	16	below	below	ADP
ejpam-3529	56	17	for	for	ADP
ejpam-3529	56	18	convenience	convenience	NOUN
ejpam-3529	56	19	.	.	PUNCT
ejpam-3529	57	1	ch	ch	NOUN
ejpam-3529	57	2	.	.	PUNCT
ejpam-3529	58	1	v.	v.	ADP
ejpam-3529	58	2	sreedhar	sreedhar	PROPN
ejpam-3529	58	3	,	,	PUNCT
ejpam-3529	58	4	j.	j.	PROPN
ejpam-3529	58	5	vasundhara	vasundhara	PROPN
ejpam-3529	58	6	devi	devi	PROPN
ejpam-3529	58	7	,	,	PUNCT
ejpam-3529	58	8	/	/	SYM
ejpam-3529	58	9	eur	eur	NOUN
ejpam-3529	58	10	.	.	PUNCT
ejpam-3529	59	1	j.	j.	PROPN
ejpam-3529	59	2	pure	pure	PROPN
ejpam-3529	59	3	appl	appl	PROPN
ejpam-3529	59	4	.	.	PROPN
ejpam-3529	59	5	math	math	PROPN
ejpam-3529	59	6	,	,	PUNCT
ejpam-3529	59	7	12	12	NUM
ejpam-3529	59	8	(	(	PUNCT
ejpam-3529	59	9	4	4	NUM
ejpam-3529	59	10	)	)	PUNCT
ejpam-3529	59	11	(	(	PUNCT
ejpam-3529	59	12	2019	2019	NUM
ejpam-3529	59	13	)	)	PUNCT
ejpam-3529	59	14	,	,	PUNCT
ejpam-3529	59	15	1662	1662	NUM
ejpam-3529	59	16	-	-	SYM
ejpam-3529	59	17	1675	1675	NUM
ejpam-3529	59	18	1665	1665	NUM
ejpam-3529	59	19	h1	h1	NOUN
ejpam-3529	59	20	:	:	PUNCT
ejpam-3529	59	21	(	(	PUNCT
ejpam-3529	59	22	i	i	NOUN
ejpam-3529	59	23	)	)	PUNCT
ejpam-3529	59	24	second	second	ADJ
ejpam-3529	59	25	order	order	NOUN
ejpam-3529	59	26	frechet	frechet	NOUN
ejpam-3529	59	27	derivatives	derivative	NOUN
ejpam-3529	59	28	of	of	ADP
ejpam-3529	59	29	f1(t	f1(t	PROPN
ejpam-3529	59	30	,	,	PUNCT
ejpam-3529	59	31	x	x	NOUN
ejpam-3529	59	32	,	,	PUNCT
ejpam-3529	59	33	ξ	ξ	NOUN
ejpam-3529	59	34	)	)	PUNCT
ejpam-3529	59	35	,	,	PUNCT
ejpam-3529	59	36	f2(t	f2(t	PROPN
ejpam-3529	59	37	,	,	PUNCT
ejpam-3529	59	38	x	x	NOUN
ejpam-3529	59	39	,	,	PUNCT
ejpam-3529	59	40	ξ	ξ	NOUN
ejpam-3529	59	41	)	)	PUNCT
ejpam-3529	59	42	with	with	ADP
ejpam-3529	59	43	respect	respect	NOUN
ejpam-3529	59	44	to	to	ADP
ejpam-3529	59	45	all	all	DET
ejpam-3529	59	46	variables	variable	NOUN
ejpam-3529	59	47	exist	exist	VERB
ejpam-3529	59	48	and	and	CCONJ
ejpam-3529	59	49	are	be	AUX
ejpam-3529	59	50	bounded	bound	VERB
ejpam-3529	59	51	;	;	PUNCT
ejpam-3529	59	52	(	(	PUNCT
ejpam-3529	59	53	ii	ii	NOUN
ejpam-3529	59	54	)	)	PUNCT
ejpam-3529	59	55	f1(t	f1(t	PROPN
ejpam-3529	59	56	,	,	PUNCT
ejpam-3529	59	57	x	x	NOUN
ejpam-3529	59	58	,	,	PUNCT
ejpam-3529	59	59	ξ	ξ	X
ejpam-3529	59	60	)	)	PUNCT
ejpam-3529	59	61	is	be	AUX
ejpam-3529	59	62	convex	convex	ADJ
ejpam-3529	59	63	in	in	ADP
ejpam-3529	59	64	x	x	PROPN
ejpam-3529	59	65	,	,	PUNCT
ejpam-3529	59	66	ξ	ξ	PROPN
ejpam-3529	59	67	;	;	PUNCT
ejpam-3529	59	68	(	(	PUNCT
ejpam-3529	59	69	iii	iii	X
ejpam-3529	59	70	)	)	PUNCT
ejpam-3529	59	71	f1x(t	f1x(t	PROPN
ejpam-3529	59	72	,	,	PUNCT
ejpam-3529	59	73	x	x	NOUN
ejpam-3529	59	74	,	,	PUNCT
ejpam-3529	59	75	ξ	ξ	X
ejpam-3529	59	76	)	)	PUNCT
ejpam-3529	59	77	is	be	AUX
ejpam-3529	59	78	nondecreasing	nondecrease	VERB
ejpam-3529	59	79	in	in	ADP
ejpam-3529	59	80	ξ	ξ	PROPN
ejpam-3529	59	81	for	for	ADP
ejpam-3529	59	82	each	each	PRON
ejpam-3529	59	83	(	(	PUNCT
ejpam-3529	59	84	t	t	PROPN
ejpam-3529	59	85	,	,	PUNCT
ejpam-3529	59	86	x	x	NOUN
ejpam-3529	59	87	)	)	PUNCT
ejpam-3529	59	88	;	;	PUNCT
ejpam-3529	59	89	(	(	PUNCT
ejpam-3529	59	90	iv	iv	X
ejpam-3529	59	91	)	)	PUNCT
ejpam-3529	59	92	f1	f1	NOUN
ejpam-3529	59	93	is	be	AUX
ejpam-3529	59	94	nondecreasing	nondecrease	VERB
ejpam-3529	59	95	function	function	NOUN
ejpam-3529	59	96	in	in	ADP
ejpam-3529	59	97	x	x	PROPN
ejpam-3529	59	98	,	,	PUNCT
ejpam-3529	59	99	ξ	ξ	PROPN
ejpam-3529	59	100	for	for	ADP
ejpam-3529	59	101	each	each	DET
ejpam-3529	59	102	t	t	NOUN
ejpam-3529	59	103	∈	∈	PROPN
ejpam-3529	60	1	i	i	PRON
ejpam-3529	60	2	and	and	CCONJ
ejpam-3529	60	3	f2	f2	PROPN
ejpam-3529	60	4	is	be	AUX
ejpam-3529	60	5	nonincreasing	nonincrease	VERB
ejpam-3529	60	6	function	function	NOUN
ejpam-3529	60	7	in	in	ADP
ejpam-3529	60	8	x	x	PROPN
ejpam-3529	60	9	,	,	PUNCT
ejpam-3529	60	10	ξ	ξ	PROPN
ejpam-3529	60	11	for	for	ADP
ejpam-3529	60	12	each	each	DET
ejpam-3529	60	13	t	t	PROPN
ejpam-3529	60	14	∈	∈	PROPN
ejpam-3529	60	15	i.	i.	PROPN
ejpam-3529	60	16	h2	h2	PROPN
ejpam-3529	60	17	:	:	PUNCT
ejpam-3529	60	18	(	(	PUNCT
ejpam-3529	60	19	i	i	NOUN
ejpam-3529	60	20	)	)	PUNCT
ejpam-3529	60	21	−m1	−m1	PROPN
ejpam-3529	60	22	≤	≤	NUM
ejpam-3529	60	23	f1x(t	f1x(t	PROPN
ejpam-3529	60	24	,	,	PUNCT
ejpam-3529	60	25	x	x	NOUN
ejpam-3529	60	26	,	,	PUNCT
ejpam-3529	60	27	ξ	ξ	NOUN
ejpam-3529	60	28	)	)	PUNCT
ejpam-3529	60	29	≤	≤	NOUN
ejpam-3529	60	30	−m	−m	NOUN
ejpam-3529	60	31	,	,	PUNCT
ejpam-3529	60	32	0	0	PUNCT
ejpam-3529	60	33	<	<	X
ejpam-3529	60	34	m	m	VERB
ejpam-3529	60	35	<	<	X
ejpam-3529	60	36	m1	m1	NOUN
ejpam-3529	60	37	;	;	PUNCT
ejpam-3529	60	38	(	(	PUNCT
ejpam-3529	60	39	ii	ii	NOUN
ejpam-3529	60	40	)	)	PUNCT
ejpam-3529	60	41	−m2	−m2	NOUN
ejpam-3529	60	42	≤	≤	ADJ
ejpam-3529	60	43	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	60	44	,	,	PUNCT
ejpam-3529	60	45	x	x	X
ejpam-3529	60	46	,	,	PUNCT
ejpam-3529	60	47	ξ	ξ	NOUN
ejpam-3529	60	48	)	)	PUNCT
ejpam-3529	60	49	≤	≤	NOUN
ejpam-3529	60	50	−n	−n	NOUN
ejpam-3529	60	51	,	,	PUNCT
ejpam-3529	60	52	0	0	PUNCT
ejpam-3529	60	53	<	<	X
ejpam-3529	60	54	n	n	X
ejpam-3529	60	55	<	<	X
ejpam-3529	60	56	m2	m2	PROPN
ejpam-3529	60	57	;	;	PUNCT
ejpam-3529	60	58	(	(	PUNCT
ejpam-3529	60	59	iii	iii	X
ejpam-3529	60	60	)	)	PUNCT
ejpam-3529	60	61	nk1	nk1	NOUN
ejpam-3529	60	62	t	t	NOUN
ejpam-3529	60	63	<	<	X
ejpam-3529	60	64	m	m	PROPN
ejpam-3529	60	65	;	;	PUNCT
ejpam-3529	60	66	where	where	SCONJ
ejpam-3529	60	67	m	m	VERB
ejpam-3529	60	68	>	>	X
ejpam-3529	60	69	0	0	NUM
ejpam-3529	60	70	,	,	PUNCT
ejpam-3529	60	71	n	n	PRON
ejpam-3529	60	72	≥	≥	NOUN
ejpam-3529	60	73	0	0	NUM
ejpam-3529	60	74	.	.	PUNCT
ejpam-3529	61	1	h3	h3	NOUN
ejpam-3529	61	2	:	:	PUNCT
ejpam-3529	62	1	α0	α0	ADJ
ejpam-3529	62	2	,	,	PUNCT
ejpam-3529	62	3	β0	β0	NOUN
ejpam-3529	62	4	are	be	AUX
ejpam-3529	62	5	coupled	couple	VERB
ejpam-3529	62	6	lower	low	ADJ
ejpam-3529	62	7	and	and	CCONJ
ejpam-3529	62	8	upper	upper	ADJ
ejpam-3529	62	9	solutions	solution	NOUN
ejpam-3529	62	10	of	of	ADP
ejpam-3529	62	11	(	(	PUNCT
ejpam-3529	62	12	3	3	NUM
ejpam-3529	62	13	)	)	PUNCT
ejpam-3529	62	14	and	and	CCONJ
ejpam-3529	62	15	(	(	PUNCT
ejpam-3529	62	16	4	4	NUM
ejpam-3529	62	17	)	)	PUNCT
ejpam-3529	62	18	.	.	PUNCT
ejpam-3529	63	1	h4	h4	NOUN
ejpam-3529	63	2	:	:	PUNCT
ejpam-3529	63	3	(	(	PUNCT
ejpam-3529	63	4	i	i	NOUN
ejpam-3529	63	5	)	)	PUNCT
ejpam-3529	63	6	f1(t	f1(t	PROPN
ejpam-3529	63	7	,	,	PUNCT
ejpam-3529	63	8	x	x	NOUN
ejpam-3529	63	9	,	,	PUNCT
ejpam-3529	63	10	sx	sx	PROPN
ejpam-3529	63	11	)	)	PUNCT
ejpam-3529	63	12	≥	≥	NOUN
ejpam-3529	63	13	f1(t	f1(t	PROPN
ejpam-3529	63	14	,	,	PUNCT
ejpam-3529	63	15	y	y	PROPN
ejpam-3529	63	16	,	,	PUNCT
ejpam-3529	63	17	sy	sy	PROPN
ejpam-3529	63	18	)	)	PUNCT
ejpam-3529	63	19	+	+	CCONJ
ejpam-3529	63	20	f1x(t	f1x(t	PROPN
ejpam-3529	63	21	,	,	PUNCT
ejpam-3529	63	22	y	y	PROPN
ejpam-3529	63	23	,	,	PUNCT
ejpam-3529	63	24	sy)(x−	sy)(x−	NOUN
ejpam-3529	63	25	y	y	NOUN
ejpam-3529	63	26	)	)	PUNCT
ejpam-3529	64	1	+	+	CCONJ
ejpam-3529	64	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	64	3	,	,	PUNCT
ejpam-3529	64	4	y	y	PROPN
ejpam-3529	64	5	,	,	PUNCT
ejpam-3529	64	6	sy)(sx−	sy)(sx−	PROPN
ejpam-3529	64	7	sy	sy	PROPN
ejpam-3529	64	8	)	)	PUNCT
ejpam-3529	64	9	;	;	PUNCT
ejpam-3529	64	10	(	(	PUNCT
ejpam-3529	64	11	ii	ii	NOUN
ejpam-3529	64	12	)	)	PUNCT
ejpam-3529	64	13	|f1x(t	|f1x(t	PROPN
ejpam-3529	64	14	,	,	PUNCT
ejpam-3529	64	15	x	x	NOUN
ejpam-3529	64	16	,	,	PUNCT
ejpam-3529	64	17	sx)−	sx)−	NOUN
ejpam-3529	64	18	f1x(t	f1x(t	PROPN
ejpam-3529	64	19	,	,	PUNCT
ejpam-3529	64	20	y	y	PROPN
ejpam-3529	64	21	,	,	PUNCT
ejpam-3529	64	22	sy)|	sy)|	PROPN
ejpam-3529	64	23	≤	≤	PROPN
ejpam-3529	64	24	l1(x−	l1(x−	PRON
ejpam-3529	64	25	y	y	NOUN
ejpam-3529	64	26	)	)	PUNCT
ejpam-3529	65	1	+	+	NOUN
ejpam-3529	65	2	m1(sx−	m1(sx−	PROPN
ejpam-3529	65	3	sy	sy	NOUN
ejpam-3529	65	4	)	)	PUNCT
ejpam-3529	65	5	,	,	PUNCT
ejpam-3529	65	6	l1,m1	l1,m1	PROPN
ejpam-3529	65	7	≥	≥	NOUN
ejpam-3529	65	8	0	0	NUM
ejpam-3529	65	9	.	.	PUNCT
ejpam-3529	65	10	theorem	theorem	NOUN
ejpam-3529	65	11	1	1	NUM
ejpam-3529	65	12	.	.	PUNCT
ejpam-3529	65	13	suppose	suppose	VERB
ejpam-3529	65	14	that	that	SCONJ
ejpam-3529	65	15	the	the	DET
ejpam-3529	65	16	assumptions	assumption	NOUN
ejpam-3529	65	17	h1	h1	VERB
ejpam-3529	65	18	to	to	ADP
ejpam-3529	65	19	h4	h4	PROPN
ejpam-3529	65	20	are	be	AUX
ejpam-3529	65	21	satisfied	satisfied	ADJ
ejpam-3529	65	22	.	.	PUNCT
ejpam-3529	66	1	then	then	ADV
ejpam-3529	66	2	there	there	PRON
ejpam-3529	66	3	exists	exist	VERB
ejpam-3529	66	4	monotone	monotone	ADJ
ejpam-3529	66	5	sequence	sequence	NOUN
ejpam-3529	66	6	{	{	PUNCT
ejpam-3529	66	7	αn	αn	NOUN
ejpam-3529	66	8	}	}	PUNCT
ejpam-3529	66	9	,	,	PUNCT
ejpam-3529	66	10	such	such	ADJ
ejpam-3529	66	11	that	that	DET
ejpam-3529	66	12	αn	αn	NOUN
ejpam-3529	66	13	→	→	SYM
ejpam-3529	66	14	ρ	ρ	PROPN
ejpam-3529	66	15	,	,	PUNCT
ejpam-3529	66	16	as	as	ADP
ejpam-3529	66	17	n	n	NUM
ejpam-3529	66	18	→	→	SYM
ejpam-3529	66	19	∞	∞	X
ejpam-3529	66	20	uniformly	uniformly	ADV
ejpam-3529	66	21	and	and	CCONJ
ejpam-3529	66	22	monotonically	monotonically	ADV
ejpam-3529	66	23	to	to	ADP
ejpam-3529	66	24	the	the	DET
ejpam-3529	66	25	unique	unique	ADJ
ejpam-3529	66	26	solution	solution	NOUN
ejpam-3529	66	27	ρ	ρ	NOUN
ejpam-3529	66	28	=	=	SYM
ejpam-3529	66	29	u	u	PROPN
ejpam-3529	66	30	of	of	ADP
ejpam-3529	66	31	an	an	DET
ejpam-3529	66	32	integro	integro	ADJ
ejpam-3529	66	33	differential	differential	ADJ
ejpam-3529	66	34	equation	equation	NOUN
ejpam-3529	66	35	(	(	PUNCT
ejpam-3529	66	36	3	3	NUM
ejpam-3529	66	37	)	)	PUNCT
ejpam-3529	66	38	and	and	CCONJ
ejpam-3529	66	39	(	(	PUNCT
ejpam-3529	66	40	4)on	4)on	PROPN
ejpam-3529	66	41	i	i	PROPN
ejpam-3529	66	42	and	and	CCONJ
ejpam-3529	66	43	the	the	DET
ejpam-3529	66	44	convergence	convergence	NOUN
ejpam-3529	66	45	is	be	AUX
ejpam-3529	66	46	quadratic	quadratic	ADJ
ejpam-3529	66	47	.	.	PUNCT
ejpam-3529	67	1	proof	proof	NOUN
ejpam-3529	67	2	:	:	PUNCT
ejpam-3529	67	3	in	in	ADP
ejpam-3529	67	4	order	order	NOUN
ejpam-3529	67	5	to	to	PART
ejpam-3529	67	6	construct	construct	VERB
ejpam-3529	67	7	a	a	DET
ejpam-3529	67	8	sequence	sequence	NOUN
ejpam-3529	67	9	of	of	ADP
ejpam-3529	67	10	lower	low	ADJ
ejpam-3529	67	11	iterates	iterate	NOUN
ejpam-3529	67	12	that	that	PRON
ejpam-3529	67	13	converge	converge	NOUN
ejpam-3529	67	14	to	to	ADP
ejpam-3529	67	15	the	the	DET
ejpam-3529	67	16	solution	solution	NOUN
ejpam-3529	67	17	of	of	ADP
ejpam-3529	67	18	the	the	DET
ejpam-3529	67	19	ivp	ivp	NOUN
ejpam-3529	67	20	we	we	PRON
ejpam-3529	67	21	fix	fix	VERB
ejpam-3529	67	22	the	the	DET
ejpam-3529	67	23	upper	upper	ADJ
ejpam-3529	67	24	solution	solution	NOUN
ejpam-3529	67	25	β0	β0	NOUN
ejpam-3529	67	26	.	.	PUNCT
ejpam-3529	68	1	now	now	ADV
ejpam-3529	68	2	consider	consider	VERB
ejpam-3529	68	3	the	the	DET
ejpam-3529	68	4	following	follow	VERB
ejpam-3529	68	5	linear	linear	ADJ
ejpam-3529	68	6	problem	problem	NOUN
ejpam-3529	68	7	for	for	ADP
ejpam-3529	68	8	n	n	NOUN
ejpam-3529	68	9	=	=	SYM
ejpam-3529	68	10	0	0	NUM
ejpam-3529	68	11	,	,	PUNCT
ejpam-3529	68	12	1	1	NUM
ejpam-3529	68	13	,	,	PUNCT
ejpam-3529	68	14	2	2	NUM
ejpam-3529	68	15	,	,	PUNCT
ejpam-3529	68	16	3	3	NUM
ejpam-3529	68	17	,	,	PUNCT
ejpam-3529	68	18	...	...	PUNCT
ejpam-3529	69	1	α′n+1	α′n+1	X
ejpam-3529	69	2	=	=	SYM
ejpam-3529	69	3	f1(t	f1(t	PROPN
ejpam-3529	69	4	,	,	PUNCT
ejpam-3529	69	5	αn	αn	NOUN
ejpam-3529	69	6	,	,	PUNCT
ejpam-3529	69	7	sαn	sαn	NOUN
ejpam-3529	69	8	)	)	PUNCT
ejpam-3529	70	1	+	+	CCONJ
ejpam-3529	70	2	f1x(t	f1x(t	PROPN
ejpam-3529	70	3	,	,	PUNCT
ejpam-3529	70	4	αn	αn	NOUN
ejpam-3529	70	5	,	,	PUNCT
ejpam-3529	70	6	sαn)[αn+1	sαn)[αn+1	NOUN
ejpam-3529	70	7	−	−	NOUN
ejpam-3529	70	8	αn	αn	NOUN
ejpam-3529	70	9	]	]	X
ejpam-3529	71	1	+	+	CCONJ
ejpam-3529	71	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	71	3	,	,	PUNCT
ejpam-3529	71	4	αn	αn	NOUN
ejpam-3529	71	5	,	,	PUNCT
ejpam-3529	71	6	sαn)[sαn+1	sαn)[sαn+1	ADJ
ejpam-3529	71	7	−	−	NOUN
ejpam-3529	71	8	sαn	sαn	NOUN
ejpam-3529	71	9	]	]	PUNCT
ejpam-3529	72	1	+	+	PUNCT
ejpam-3529	72	2	f2(t	f2(t	PROPN
ejpam-3529	72	3	,	,	PUNCT
ejpam-3529	72	4	β0	β0	NOUN
ejpam-3529	72	5	,	,	PUNCT
ejpam-3529	72	6	sβ0	sβ0	NOUN
ejpam-3529	72	7	)	)	PUNCT
ejpam-3529	72	8	,	,	PUNCT
ejpam-3529	72	9	}	}	PUNCT
ejpam-3529	72	10	(	(	PUNCT
ejpam-3529	72	11	11	11	NUM
ejpam-3529	72	12	)	)	PUNCT
ejpam-3529	72	13	αn+1(0	αn+1(0	NUM
ejpam-3529	72	14	)	)	PUNCT
ejpam-3529	72	15	=	=	SYM
ejpam-3529	72	16	x0	x0	PROPN
ejpam-3529	72	17	.	.	PUNCT
ejpam-3529	73	1	(	(	PUNCT
ejpam-3529	73	2	12	12	NUM
ejpam-3529	73	3	)	)	PUNCT
ejpam-3529	73	4	since	since	SCONJ
ejpam-3529	73	5	the	the	DET
ejpam-3529	73	6	above	above	ADJ
ejpam-3529	73	7	equation	equation	NOUN
ejpam-3529	73	8	is	be	AUX
ejpam-3529	73	9	a	a	DET
ejpam-3529	73	10	linear	linear	ADJ
ejpam-3529	73	11	integro	integro	PROPN
ejpam-3529	73	12	differential	differential	NOUN
ejpam-3529	73	13	equation	equation	NOUN
ejpam-3529	73	14	,	,	PUNCT
ejpam-3529	73	15	it	it	PRON
ejpam-3529	73	16	has	have	VERB
ejpam-3529	73	17	unique	unique	ADJ
ejpam-3529	73	18	solution	solution	NOUN
ejpam-3529	73	19	αn+1(t	αn+1(t	PROPN
ejpam-3529	73	20	)	)	PUNCT
ejpam-3529	73	21	on	on	ADP
ejpam-3529	73	22	i	i	PRON
ejpam-3529	73	23	for	for	ADP
ejpam-3529	73	24	each	each	DET
ejpam-3529	73	25	n.	n.	NOUN
ejpam-3529	73	26	now	now	ADV
ejpam-3529	73	27	we	we	PRON
ejpam-3529	73	28	claim	claim	VERB
ejpam-3529	73	29	that	that	SCONJ
ejpam-3529	73	30	α0	α0	ADJ
ejpam-3529	73	31	≤	≤	ADJ
ejpam-3529	73	32	α1	α1	PROPN
ejpam-3529	73	33	≤	≤	ADV
ejpam-3529	73	34	α2	α2	ADJ
ejpam-3529	73	35	≤	≤	NOUN
ejpam-3529	73	36	...	...	PUNCT
ejpam-3529	74	1	≤	≤	NUM
ejpam-3529	75	1	αn−1	αn−1	ADJ
ejpam-3529	75	2	≤	≤	NUM
ejpam-3529	75	3	αn	αn	NOUN
ejpam-3529	75	4	≤	≤	NUM
ejpam-3529	75	5	...	...	PUNCT
ejpam-3529	76	1	≤	≤	NUM
ejpam-3529	76	2	β0	β0	NOUN
ejpam-3529	76	3	(	(	PUNCT
ejpam-3529	76	4	13	13	NUM
ejpam-3529	76	5	)	)	PUNCT
ejpam-3529	76	6	on	on	ADP
ejpam-3529	76	7	i.	i.	PROPN
ejpam-3529	76	8	ch	ch	PROPN
ejpam-3529	76	9	.	.	PUNCT
ejpam-3529	77	1	v.	v.	ADP
ejpam-3529	77	2	sreedhar	sreedhar	PROPN
ejpam-3529	77	3	,	,	PUNCT
ejpam-3529	77	4	j.	j.	PROPN
ejpam-3529	77	5	vasundhara	vasundhara	PROPN
ejpam-3529	77	6	devi	devi	PROPN
ejpam-3529	77	7	,	,	PUNCT
ejpam-3529	77	8	/	/	SYM
ejpam-3529	77	9	eur	eur	NOUN
ejpam-3529	77	10	.	.	PUNCT
ejpam-3529	78	1	j.	j.	PROPN
ejpam-3529	78	2	pure	pure	PROPN
ejpam-3529	78	3	appl	appl	PROPN
ejpam-3529	78	4	.	.	PROPN
ejpam-3529	78	5	math	math	PROPN
ejpam-3529	78	6	,	,	PUNCT
ejpam-3529	78	7	12	12	NUM
ejpam-3529	78	8	(	(	PUNCT
ejpam-3529	78	9	4	4	NUM
ejpam-3529	78	10	)	)	PUNCT
ejpam-3529	78	11	(	(	PUNCT
ejpam-3529	78	12	2019	2019	NUM
ejpam-3529	78	13	)	)	PUNCT
ejpam-3529	78	14	,	,	PUNCT
ejpam-3529	78	15	1662	1662	NUM
ejpam-3529	78	16	-	-	SYM
ejpam-3529	78	17	1675	1675	NUM
ejpam-3529	78	18	1666	1666	NUM
ejpam-3529	78	19	we	we	PRON
ejpam-3529	78	20	begin	begin	VERB
ejpam-3529	78	21	by	by	ADP
ejpam-3529	78	22	setting	set	VERB
ejpam-3529	78	23	p	p	X
ejpam-3529	78	24	=	=	PUNCT
ejpam-3529	78	25	α0	α0	ADJ
ejpam-3529	78	26	−	−	PROPN
ejpam-3529	78	27	α1	α1	PROPN
ejpam-3529	78	28	.	.	PUNCT
ejpam-3529	79	1	then	then	ADV
ejpam-3529	79	2	p′	p′	X
ejpam-3529	79	3	=	=	SYM
ejpam-3529	80	1	α′0	α′0	NOUN
ejpam-3529	81	1	−	−	NUM
ejpam-3529	81	2	α′1	α′1	X
ejpam-3529	81	3	≤	≤	PROPN
ejpam-3529	81	4	{	{	PUNCT
ejpam-3529	81	5	f1(t	f1(t	PROPN
ejpam-3529	81	6	,	,	PUNCT
ejpam-3529	81	7	α0	α0	ADJ
ejpam-3529	81	8	,	,	PUNCT
ejpam-3529	81	9	sα0	sα0	NOUN
ejpam-3529	81	10	)	)	PUNCT
ejpam-3529	82	1	+	+	CCONJ
ejpam-3529	82	2	f2(t	f2(t	PROPN
ejpam-3529	82	3	,	,	PUNCT
ejpam-3529	82	4	β0	β0	NOUN
ejpam-3529	82	5	,	,	PUNCT
ejpam-3529	82	6	sβ0	sβ0	NOUN
ejpam-3529	82	7	)	)	PUNCT
ejpam-3529	82	8	}	}	PUNCT
ejpam-3529	83	1	−{f1(t	−{f1(t	ADJ
ejpam-3529	83	2	,	,	PUNCT
ejpam-3529	83	3	α0	α0	ADJ
ejpam-3529	83	4	,	,	PUNCT
ejpam-3529	83	5	sα0	sα0	NOUN
ejpam-3529	83	6	)	)	PUNCT
ejpam-3529	84	1	+	+	CCONJ
ejpam-3529	84	2	f1x(t	f1x(t	PROPN
ejpam-3529	84	3	,	,	PUNCT
ejpam-3529	84	4	α0	α0	ADJ
ejpam-3529	84	5	,	,	PUNCT
ejpam-3529	84	6	sα0)[α1	sα0)[α1	NOUN
ejpam-3529	84	7	−	−	PROPN
ejpam-3529	84	8	α0	α0	ADJ
ejpam-3529	84	9	]	]	X
ejpam-3529	84	10	+	+	CCONJ
ejpam-3529	84	11	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	84	12	,	,	PUNCT
ejpam-3529	84	13	α0	α0	ADJ
ejpam-3529	84	14	,	,	PUNCT
ejpam-3529	84	15	sα0)[sα1	sα0)[sα1	NOUN
ejpam-3529	85	1	−	−	PROPN
ejpam-3529	85	2	sα0	sα0	NOUN
ejpam-3529	85	3	]	]	PUNCT
ejpam-3529	86	1	+	+	CCONJ
ejpam-3529	86	2	f2(t	f2(t	PROPN
ejpam-3529	86	3	,	,	PUNCT
ejpam-3529	86	4	β0	β0	NOUN
ejpam-3529	86	5	,	,	PUNCT
ejpam-3529	86	6	sβ0	sβ0	NOUN
ejpam-3529	86	7	)	)	PUNCT
ejpam-3529	86	8	}	}	PUNCT
ejpam-3529	86	9	≤	≤	NUM
ejpam-3529	86	10	f1x(t	f1x(t	PROPN
ejpam-3529	86	11	,	,	PUNCT
ejpam-3529	86	12	α0	α0	ADJ
ejpam-3529	86	13	,	,	PUNCT
ejpam-3529	86	14	sα0)[α0	sα0)[α0	ADJ
ejpam-3529	86	15	−	−	PROPN
ejpam-3529	86	16	α1	α1	PROPN
ejpam-3529	86	17	]	]	PUNCT
ejpam-3529	86	18	+	+	CCONJ
ejpam-3529	86	19	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	86	20	,	,	PUNCT
ejpam-3529	86	21	α0	α0	ADJ
ejpam-3529	86	22	,	,	PUNCT
ejpam-3529	86	23	sα0)[sα0	sα0)[sα0	NOUN
ejpam-3529	86	24	−	−	ADP
ejpam-3529	86	25	sα1	sα1	NOUN
ejpam-3529	86	26	]	]	X
ejpam-3529	86	27	p′(t	p′(t	NOUN
ejpam-3529	86	28	)	)	PUNCT
ejpam-3529	86	29	≤	≤	NUM
ejpam-3529	86	30	−mp(t)−nsp(t	−mp(t)−nsp(t	PROPN
ejpam-3529	86	31	)	)	PUNCT
ejpam-3529	86	32	.	.	PUNCT
ejpam-3529	87	1	also	also	ADV
ejpam-3529	87	2	p(0	p(0	VERB
ejpam-3529	87	3	)	)	PUNCT
ejpam-3529	87	4	=	=	SYM
ejpam-3529	87	5	α0(0	α0(0	PROPN
ejpam-3529	87	6	)	)	PUNCT
ejpam-3529	87	7	−	−	PROPN
ejpam-3529	87	8	α1(0	α1(0	PROPN
ejpam-3529	87	9	)	)	PUNCT
ejpam-3529	87	10	≤	≤	NOUN
ejpam-3529	87	11	0	0	NUM
ejpam-3529	87	12	.	.	PUNCT
ejpam-3529	88	1	hence	hence	ADV
ejpam-3529	88	2	by	by	ADP
ejpam-3529	88	3	lemma	lemma	PROPN
ejpam-3529	88	4	1	1	NUM
ejpam-3529	88	5	we	we	PRON
ejpam-3529	88	6	have	have	VERB
ejpam-3529	88	7	p(t	p(t	NOUN
ejpam-3529	88	8	)	)	PUNCT
ejpam-3529	88	9	≤	≤	NOUN
ejpam-3529	88	10	0	0	NUM
ejpam-3529	88	11	.	.	PUNCT
ejpam-3529	89	1	so	so	ADV
ejpam-3529	89	2	α0	α0	ADJ
ejpam-3529	89	3	≤	≤	ADJ
ejpam-3529	89	4	α1	α1	PROPN
ejpam-3529	89	5	on	on	ADP
ejpam-3529	89	6	i.	i.	PROPN
ejpam-3529	89	7	next	next	ADV
ejpam-3529	89	8	,	,	PUNCT
ejpam-3529	89	9	we	we	PRON
ejpam-3529	89	10	show	show	VERB
ejpam-3529	89	11	that	that	SCONJ
ejpam-3529	89	12	α1	α1	PROPN
ejpam-3529	89	13	≤	≤	ADV
ejpam-3529	89	14	α2	α2	PROPN
ejpam-3529	89	15	on	on	ADP
ejpam-3529	89	16	i.	i.	NOUN
ejpam-3529	89	17	for	for	ADP
ejpam-3529	89	18	this	this	DET
ejpam-3529	89	19	set	set	NOUN
ejpam-3529	89	20	p	p	PROPN
ejpam-3529	89	21	=	=	PROPN
ejpam-3529	89	22	α1	α1	PROPN
ejpam-3529	89	23	−	−	PROPN
ejpam-3529	89	24	α2	α2	PROPN
ejpam-3529	89	25	.	.	PUNCT
ejpam-3529	90	1	then	then	ADV
ejpam-3529	90	2	p′	p′	NUM
ejpam-3529	91	1	=	=	SYM
ejpam-3529	91	2	α′1	α′1	NOUN
ejpam-3529	91	3	−	−	PROPN
ejpam-3529	91	4	α′2	α′2	NOUN
ejpam-3529	91	5	≤	≤	PROPN
ejpam-3529	91	6	f1(t	f1(t	PROPN
ejpam-3529	91	7	,	,	PUNCT
ejpam-3529	91	8	α1	α1	PROPN
ejpam-3529	91	9	,	,	PUNCT
ejpam-3529	91	10	sα1)−	sα1)−	NOUN
ejpam-3529	91	11	{	{	PUNCT
ejpam-3529	91	12	f1(t	f1(t	PROPN
ejpam-3529	91	13	,	,	PUNCT
ejpam-3529	91	14	α1	α1	PROPN
ejpam-3529	91	15	,	,	PUNCT
ejpam-3529	91	16	sα1	sα1	PROPN
ejpam-3529	91	17	)	)	PUNCT
ejpam-3529	91	18	+	+	CCONJ
ejpam-3529	91	19	f1x(t	f1x(t	PROPN
ejpam-3529	91	20	,	,	PUNCT
ejpam-3529	91	21	α1	α1	PROPN
ejpam-3529	91	22	,	,	PUNCT
ejpam-3529	91	23	sα1)[α2	sα1)[α2	VERB
ejpam-3529	91	24	−	−	PROPN
ejpam-3529	91	25	α1	α1	PROPN
ejpam-3529	91	26	]	]	PUNCT
ejpam-3529	91	27	+	+	CCONJ
ejpam-3529	91	28	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	91	29	,	,	PUNCT
ejpam-3529	91	30	α1	α1	PROPN
ejpam-3529	91	31	,	,	PUNCT
ejpam-3529	91	32	sα1)[sα2	sα1)[sα2	NOUN
ejpam-3529	91	33	−	−	PROPN
ejpam-3529	91	34	sα1	sα1	NOUN
ejpam-3529	91	35	]	]	X
ejpam-3529	91	36	}	}	PUNCT
ejpam-3529	91	37	=	=	SYM
ejpam-3529	91	38	f1x(t	f1x(t	PROPN
ejpam-3529	91	39	,	,	PUNCT
ejpam-3529	91	40	α1	α1	PROPN
ejpam-3529	91	41	,	,	PUNCT
ejpam-3529	91	42	sα1)[α1	sα1)[α1	NOUN
ejpam-3529	91	43	−	−	PROPN
ejpam-3529	91	44	α2	α2	PROPN
ejpam-3529	91	45	]	]	PUNCT
ejpam-3529	92	1	+	+	CCONJ
ejpam-3529	92	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	92	3	,	,	PUNCT
ejpam-3529	92	4	α1	α1	PROPN
ejpam-3529	92	5	,	,	PUNCT
ejpam-3529	92	6	sα1)[sα1	sα1)[sα1	NOUN
ejpam-3529	93	1	−	−	PROPN
ejpam-3529	93	2	sα2	sα2	X
ejpam-3529	93	3	]	]	X
ejpam-3529	93	4	≤	≤	NUM
ejpam-3529	93	5	−mp(t)−nsp(t	−mp(t)−nsp(t	PROPN
ejpam-3529	93	6	)	)	PUNCT
ejpam-3529	93	7	.	.	PUNCT
ejpam-3529	94	1	also	also	ADV
ejpam-3529	94	2	p(0	p(0	VERB
ejpam-3529	94	3	)	)	PUNCT
ejpam-3529	94	4	=	=	SYM
ejpam-3529	94	5	α1(0	α1(0	PROPN
ejpam-3529	94	6	)	)	PUNCT
ejpam-3529	94	7	−	−	PROPN
ejpam-3529	94	8	α2(0	α2(0	NOUN
ejpam-3529	94	9	)	)	PUNCT
ejpam-3529	94	10	=	=	PUNCT
ejpam-3529	95	1	0	0	X
ejpam-3529	95	2	.	.	PUNCT
ejpam-3529	95	3	hence	hence	ADV
ejpam-3529	95	4	by	by	ADP
ejpam-3529	95	5	lemma	lemma	PROPN
ejpam-3529	95	6	1	1	NUM
ejpam-3529	95	7	we	we	PRON
ejpam-3529	95	8	have	have	VERB
ejpam-3529	95	9	p(t	p(t	NOUN
ejpam-3529	95	10	)	)	PUNCT
ejpam-3529	95	11	≤	≤	NOUN
ejpam-3529	95	12	0	0	NUM
ejpam-3529	95	13	.	.	PUNCT
ejpam-3529	96	1	thus	thus	ADV
ejpam-3529	96	2	α1	α1	PROPN
ejpam-3529	96	3	≤	≤	ADV
ejpam-3529	96	4	α2	α2	PROPN
ejpam-3529	96	5	on	on	ADP
ejpam-3529	96	6	i.	i.	PROPN
ejpam-3529	96	7	now	now	ADV
ejpam-3529	96	8	we	we	PRON
ejpam-3529	96	9	show	show	VERB
ejpam-3529	96	10	α1	α1	PROPN
ejpam-3529	96	11	≤	≤	PROPN
ejpam-3529	96	12	β0	β0	ADV
ejpam-3529	96	13	on	on	ADP
ejpam-3529	96	14	i	i	PRON
ejpam-3529	96	15	by	by	ADP
ejpam-3529	96	16	setting	set	VERB
ejpam-3529	96	17	p	p	X
ejpam-3529	96	18	=	=	PUNCT
ejpam-3529	96	19	α1	α1	PROPN
ejpam-3529	96	20	−	−	PROPN
ejpam-3529	96	21	β0	β0	PROPN
ejpam-3529	96	22	.	.	PUNCT
ejpam-3529	97	1	then	then	ADV
ejpam-3529	97	2	,	,	PUNCT
ejpam-3529	97	3	p′	p′	PROPN
ejpam-3529	97	4	=	=	SYM
ejpam-3529	97	5	α′1	α′1	ADV
ejpam-3529	97	6	−	−	PROPN
ejpam-3529	97	7	β′0	β′0	SYM
ejpam-3529	97	8	≤	≤	PROPN
ejpam-3529	97	9	{	{	PUNCT
ejpam-3529	97	10	f1(t	f1(t	PROPN
ejpam-3529	97	11	,	,	PUNCT
ejpam-3529	97	12	α0	α0	ADJ
ejpam-3529	97	13	,	,	PUNCT
ejpam-3529	97	14	sα0)−	sα0)−	PROPN
ejpam-3529	97	15	f1(t	f1(t	PROPN
ejpam-3529	97	16	,	,	PUNCT
ejpam-3529	97	17	β0	β0	NOUN
ejpam-3529	97	18	,	,	PUNCT
ejpam-3529	97	19	sβ0)}+	sβ0)}+	PROPN
ejpam-3529	97	20	{	{	PUNCT
ejpam-3529	97	21	f1x(t	f1x(t	PROPN
ejpam-3529	97	22	,	,	PUNCT
ejpam-3529	97	23	α0	α0	ADJ
ejpam-3529	97	24	,	,	PUNCT
ejpam-3529	97	25	sα0)[α1	sα0)[α1	NOUN
ejpam-3529	97	26	−	−	PROPN
ejpam-3529	97	27	α0	α0	ADJ
ejpam-3529	97	28	]	]	X
ejpam-3529	97	29	+	+	CCONJ
ejpam-3529	97	30	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	97	31	,	,	PUNCT
ejpam-3529	97	32	α0	α0	ADJ
ejpam-3529	97	33	,	,	PUNCT
ejpam-3529	97	34	sα0)[sα1	sα0)[sα1	PROPN
ejpam-3529	98	1	−	−	PROPN
ejpam-3529	98	2	sα0]}+	sα0]}+	PROPN
ejpam-3529	98	3	{	{	PUNCT
ejpam-3529	98	4	f2(t	f2(t	PROPN
ejpam-3529	98	5	,	,	PUNCT
ejpam-3529	98	6	β0	β0	NOUN
ejpam-3529	98	7	,	,	PUNCT
ejpam-3529	98	8	sβ0)−	sβ0)−	PROPN
ejpam-3529	98	9	f2(t	f2(t	PROPN
ejpam-3529	98	10	,	,	PUNCT
ejpam-3529	98	11	α0	α0	ADJ
ejpam-3529	98	12	,	,	PUNCT
ejpam-3529	98	13	sα0	sα0	NOUN
ejpam-3529	98	14	)	)	PUNCT
ejpam-3529	98	15	}	}	PUNCT
ejpam-3529	98	16	≤	≤	NUM
ejpam-3529	98	17	f1x(t	f1x(t	PROPN
ejpam-3529	98	18	,	,	PUNCT
ejpam-3529	98	19	α0	α0	ADJ
ejpam-3529	98	20	,	,	PUNCT
ejpam-3529	98	21	sα0)[α1	sα0)[α1	NOUN
ejpam-3529	98	22	−	−	PROPN
ejpam-3529	98	23	β0	β0	NOUN
ejpam-3529	98	24	]	]	X
ejpam-3529	98	25	+	+	CCONJ
ejpam-3529	98	26	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	98	27	,	,	PUNCT
ejpam-3529	98	28	α0	α0	ADJ
ejpam-3529	98	29	,	,	PUNCT
ejpam-3529	98	30	sα0)[sα1	sα0)[sα1	NOUN
ejpam-3529	98	31	−	−	PROPN
ejpam-3529	98	32	sβ0	sβ0	PROPN
ejpam-3529	98	33	]	]	PUNCT
ejpam-3529	98	34	≤	≤	NUM
ejpam-3529	98	35	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	98	36	)	)	PUNCT
ejpam-3529	98	37	.	.	PUNCT
ejpam-3529	99	1	also	also	ADV
ejpam-3529	99	2	p(0	p(0	VERB
ejpam-3529	99	3	)	)	PUNCT
ejpam-3529	99	4	=	=	SYM
ejpam-3529	99	5	α1(0	α1(0	PROPN
ejpam-3529	99	6	)	)	PUNCT
ejpam-3529	99	7	−	−	PROPN
ejpam-3529	99	8	β0(0	β0(0	PROPN
ejpam-3529	99	9	)	)	PUNCT
ejpam-3529	99	10	≤	≤	NOUN
ejpam-3529	99	11	0	0	NUM
ejpam-3529	99	12	.	.	PUNCT
ejpam-3529	100	1	hence	hence	ADV
ejpam-3529	100	2	by	by	ADP
ejpam-3529	100	3	lemma	lemma	PROPN
ejpam-3529	100	4	1	1	NUM
ejpam-3529	100	5	we	we	PRON
ejpam-3529	100	6	have	have	VERB
ejpam-3529	100	7	p(t	p(t	NOUN
ejpam-3529	100	8	)	)	PUNCT
ejpam-3529	100	9	≤	≤	NOUN
ejpam-3529	100	10	0	0	NUM
ejpam-3529	100	11	.	.	PUNCT
ejpam-3529	101	1	which	which	PRON
ejpam-3529	101	2	means	mean	VERB
ejpam-3529	101	3	that	that	SCONJ
ejpam-3529	101	4	α1	α1	PROPN
ejpam-3529	101	5	≤	≤	PUNCT
ejpam-3529	101	6	β0	β0	PROPN
ejpam-3529	101	7	on	on	ADP
ejpam-3529	101	8	i.	i.	NOUN
ejpam-3529	101	9	similarly	similarly	ADV
ejpam-3529	101	10	we	we	PRON
ejpam-3529	101	11	can	can	AUX
ejpam-3529	101	12	show	show	VERB
ejpam-3529	101	13	α2	α2	ADJ
ejpam-3529	101	14	≤	≤	PROPN
ejpam-3529	101	15	β0	β0	ADV
ejpam-3529	101	16	on	on	ADP
ejpam-3529	101	17	i.	i.	NOUN
ejpam-3529	101	18	thus	thus	ADV
ejpam-3529	101	19	α0	α0	ADJ
ejpam-3529	101	20	≤	≤	ADJ
ejpam-3529	101	21	α1	α1	PROPN
ejpam-3529	101	22	≤	≤	VERB
ejpam-3529	101	23	α2	α2	PROPN
ejpam-3529	101	24	≤	≤	PROPN
ejpam-3529	101	25	β0	β0	NOUN
ejpam-3529	101	26	,	,	PUNCT
ejpam-3529	101	27	on	on	ADP
ejpam-3529	101	28	i.	i.	PROPN
ejpam-3529	101	29	now	now	ADV
ejpam-3529	101	30	we	we	PRON
ejpam-3529	101	31	assume	assume	VERB
ejpam-3529	101	32	that	that	SCONJ
ejpam-3529	101	33	the	the	DET
ejpam-3529	101	34	result	result	NOUN
ejpam-3529	101	35	holds	hold	VERB
ejpam-3529	101	36	for	for	ADP
ejpam-3529	101	37	n	n	NOUN
ejpam-3529	101	38	=	=	SYM
ejpam-3529	101	39	k	k	PROPN
ejpam-3529	101	40	and	and	CCONJ
ejpam-3529	101	41	prove	prove	VERB
ejpam-3529	101	42	it	it	PRON
ejpam-3529	101	43	for	for	ADP
ejpam-3529	101	44	n	n	PROPN
ejpam-3529	101	45	=	=	SYM
ejpam-3529	101	46	k+1	k+1	X
ejpam-3529	101	47	.	.	X
ejpam-3529	102	1	we	we	PRON
ejpam-3529	102	2	now	now	ADV
ejpam-3529	102	3	consider	consider	VERB
ejpam-3529	102	4	the	the	DET
ejpam-3529	102	5	following	follow	VERB
ejpam-3529	102	6	linear	linear	PROPN
ejpam-3529	102	7	integro	integro	PROPN
ejpam-3529	102	8	differential	differential	NOUN
ejpam-3529	102	9	equation	equation	NOUN
ejpam-3529	102	10	,	,	PUNCT
ejpam-3529	102	11	α′k+1	α′k+1	X
ejpam-3529	102	12	=	=	SYM
ejpam-3529	102	13	f1(t	f1(t	PROPN
ejpam-3529	102	14	,	,	PUNCT
ejpam-3529	102	15	αk	αk	INTJ
ejpam-3529	102	16	,	,	PUNCT
ejpam-3529	102	17	sαk)+f1x(t	sαk)+f1x(t	NOUN
ejpam-3529	102	18	,	,	PUNCT
ejpam-3529	102	19	αk	αk	NOUN
ejpam-3529	102	20	,	,	PUNCT
ejpam-3529	102	21	sαk)[αk+1−αk]+f1ξ(t	sαk)[αk+1−αk]+f1ξ(t	PRON
ejpam-3529	102	22	,	,	PUNCT
ejpam-3529	102	23	αk	αk	INTJ
ejpam-3529	102	24	,	,	PUNCT
ejpam-3529	102	25	sαk)[sαk+1−sαk]+f2(t	sαk)[sαk+1−sαk]+f2(t	PROPN
ejpam-3529	102	26	,	,	PUNCT
ejpam-3529	102	27	β0	β0	NOUN
ejpam-3529	102	28	,	,	PUNCT
ejpam-3529	102	29	sβ0	sβ0	NOUN
ejpam-3529	102	30	)	)	PUNCT
ejpam-3529	102	31	,	,	PUNCT
ejpam-3529	102	32	αk+1(0	αk+1(0	NUM
ejpam-3529	102	33	)	)	PUNCT
ejpam-3529	102	34	=	=	SYM
ejpam-3529	103	1	x0	x0	PROPN
ejpam-3529	103	2	.	.	PUNCT
ejpam-3529	104	1	ch	ch	NOUN
ejpam-3529	104	2	.	.	PUNCT
ejpam-3529	105	1	v.	v.	ADP
ejpam-3529	105	2	sreedhar	sreedhar	PROPN
ejpam-3529	105	3	,	,	PUNCT
ejpam-3529	105	4	j.	j.	PROPN
ejpam-3529	105	5	vasundhara	vasundhara	PROPN
ejpam-3529	105	6	devi	devi	PROPN
ejpam-3529	105	7	,	,	PUNCT
ejpam-3529	105	8	/	/	SYM
ejpam-3529	105	9	eur	eur	NOUN
ejpam-3529	105	10	.	.	PUNCT
ejpam-3529	106	1	j.	j.	PROPN
ejpam-3529	106	2	pure	pure	PROPN
ejpam-3529	106	3	appl	appl	PROPN
ejpam-3529	106	4	.	.	PROPN
ejpam-3529	106	5	math	math	PROPN
ejpam-3529	106	6	,	,	PUNCT
ejpam-3529	106	7	12	12	NUM
ejpam-3529	106	8	(	(	PUNCT
ejpam-3529	106	9	4	4	NUM
ejpam-3529	106	10	)	)	PUNCT
ejpam-3529	106	11	(	(	PUNCT
ejpam-3529	106	12	2019	2019	NUM
ejpam-3529	106	13	)	)	PUNCT
ejpam-3529	106	14	,	,	PUNCT
ejpam-3529	106	15	1662	1662	NUM
ejpam-3529	106	16	-	-	SYM
ejpam-3529	106	17	1675	1675	NUM
ejpam-3529	106	18	1667	1667	NUM
ejpam-3529	106	19	the	the	DET
ejpam-3529	106	20	above	above	ADJ
ejpam-3529	106	21	linear	linear	PROPN
ejpam-3529	106	22	integro	integro	PROPN
ejpam-3529	106	23	differential	differential	ADJ
ejpam-3529	106	24	equation	equation	NOUN
ejpam-3529	106	25	has	have	VERB
ejpam-3529	106	26	the	the	DET
ejpam-3529	106	27	unique	unique	ADJ
ejpam-3529	106	28	solution	solution	NOUN
ejpam-3529	106	29	αk+1	αk+1	NUM
ejpam-3529	106	30	where	where	SCONJ
ejpam-3529	106	31	αk	αk	NOUN
ejpam-3529	106	32	and	and	CCONJ
ejpam-3529	106	33	β0	β0	NOUN
ejpam-3529	106	34	are	be	AUX
ejpam-3529	106	35	known	know	VERB
ejpam-3529	106	36	lower	low	ADJ
ejpam-3529	106	37	and	and	CCONJ
ejpam-3529	106	38	upper	upper	ADJ
ejpam-3529	106	39	solutions	solution	NOUN
ejpam-3529	106	40	of	of	ADP
ejpam-3529	106	41	(	(	PUNCT
ejpam-3529	106	42	3	3	NUM
ejpam-3529	106	43	)	)	PUNCT
ejpam-3529	106	44	and	and	CCONJ
ejpam-3529	106	45	(	(	PUNCT
ejpam-3529	106	46	4	4	NUM
ejpam-3529	106	47	)	)	PUNCT
ejpam-3529	106	48	.	.	PUNCT
ejpam-3529	107	1	further	far	ADV
ejpam-3529	107	2	αk	αk	PRON
ejpam-3529	107	3	is	be	AUX
ejpam-3529	107	4	the	the	DET
ejpam-3529	107	5	solution	solution	NOUN
ejpam-3529	107	6	of	of	ADP
ejpam-3529	107	7	the	the	DET
ejpam-3529	107	8	linear	linear	PROPN
ejpam-3529	107	9	integro	integro	PROPN
ejpam-3529	107	10	differential	differential	ADJ
ejpam-3529	107	11	equation	equation	NOUN
ejpam-3529	107	12	α′k	α′k	X
ejpam-3529	107	13	=	=	SYM
ejpam-3529	107	14	f1(t	f1(t	PROPN
ejpam-3529	107	15	,	,	PUNCT
ejpam-3529	107	16	αk−1	αk−1	NOUN
ejpam-3529	107	17	,	,	PUNCT
ejpam-3529	107	18	sαk−1	sαk−1	PROPN
ejpam-3529	107	19	)	)	PUNCT
ejpam-3529	107	20	+	+	CCONJ
ejpam-3529	107	21	f1x(t	f1x(t	PROPN
ejpam-3529	107	22	,	,	PUNCT
ejpam-3529	107	23	αk−1	αk−1	NOUN
ejpam-3529	107	24	,	,	PUNCT
ejpam-3529	107	25	sαk−1)[αk	sαk−1)[αk	NOUN
ejpam-3529	107	26	−	−	NOUN
ejpam-3529	107	27	αk−1	αk−1	NOUN
ejpam-3529	107	28	]	]	X
ejpam-3529	108	1	+	+	ADJ
ejpam-3529	108	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	108	3	,	,	PUNCT
ejpam-3529	108	4	αk−1	αk−1	NOUN
ejpam-3529	108	5	,	,	PUNCT
ejpam-3529	108	6	sαk−1)[sαk	sαk−1)[sαk	VERB
ejpam-3529	108	7	−	−	PROPN
ejpam-3529	108	8	sαk−1	sαk−1	PROPN
ejpam-3529	108	9	]	]	X
ejpam-3529	108	10	+	+	CCONJ
ejpam-3529	108	11	f2(t	f2(t	PROPN
ejpam-3529	108	12	,	,	PUNCT
ejpam-3529	108	13	β0	β0	NOUN
ejpam-3529	108	14	,	,	PUNCT
ejpam-3529	108	15	sβ0	sβ0	NOUN
ejpam-3529	108	16	)	)	PUNCT
ejpam-3529	108	17	,	,	PUNCT
ejpam-3529	108	18	αk(0	αk(0	PROPN
ejpam-3529	108	19	)	)	PUNCT
ejpam-3529	108	20	=	=	SYM
ejpam-3529	108	21	x0	x0	PROPN
ejpam-3529	108	22	.	.	PUNCT
ejpam-3529	109	1	we	we	PRON
ejpam-3529	109	2	now	now	ADV
ejpam-3529	109	3	consider	consider	VERB
ejpam-3529	109	4	p	p	NOUN
ejpam-3529	109	5	=	=	NOUN
ejpam-3529	110	1	αk	αk	ADP
ejpam-3529	110	2	−	−	NUM
ejpam-3529	111	1	αk+1	αk+1	NUM
ejpam-3529	111	2	p′	p′	NOUN
ejpam-3529	111	3	=	=	SYM
ejpam-3529	111	4	α′k	α′k	NOUN
ejpam-3529	112	1	−	−	NOUN
ejpam-3529	112	2	α′k+1	α′k+1	SYM
ejpam-3529	112	3	≤	≤	NUM
ejpam-3529	112	4	{	{	PUNCT
ejpam-3529	112	5	f1x(t	f1x(t	PROPN
ejpam-3529	112	6	,	,	PUNCT
ejpam-3529	112	7	αk	αk	NOUN
ejpam-3529	112	8	,	,	PUNCT
ejpam-3529	112	9	sαk)[αk	sαk)[αk	ADV
ejpam-3529	112	10	−	−	NOUN
ejpam-3529	112	11	αk+1	αk+1	X
ejpam-3529	112	12	]	]	X
ejpam-3529	112	13	+	+	CCONJ
ejpam-3529	112	14	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	112	15	,	,	PUNCT
ejpam-3529	112	16	αk	αk	NOUN
ejpam-3529	112	17	,	,	PUNCT
ejpam-3529	112	18	sαk)[sαk	sαk)[sαk	NUM
ejpam-3529	112	19	−	−	PROPN
ejpam-3529	112	20	sαk+1	sαk+1	VERB
ejpam-3529	112	21	]	]	PUNCT
ejpam-3529	112	22	≤	≤	NUM
ejpam-3529	112	23	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	112	24	)	)	PUNCT
ejpam-3529	112	25	.	.	PUNCT
ejpam-3529	113	1	also	also	ADV
ejpam-3529	113	2	p(0	p(0	VERB
ejpam-3529	113	3	)	)	PUNCT
ejpam-3529	113	4	=	=	SYM
ejpam-3529	113	5	αk(0)−αk+1(0	αk(0)−αk+1(0	X
ejpam-3529	113	6	)	)	PUNCT
ejpam-3529	113	7	=	=	SYM
ejpam-3529	114	1	0	0	X
ejpam-3529	114	2	.	.	PUNCT
ejpam-3529	114	3	hence	hence	ADV
ejpam-3529	114	4	by	by	ADP
ejpam-3529	114	5	lemma	lemma	PROPN
ejpam-3529	114	6	1	1	NUM
ejpam-3529	114	7	we	we	PRON
ejpam-3529	114	8	have	have	VERB
ejpam-3529	114	9	p(t	p(t	NOUN
ejpam-3529	114	10	)	)	PUNCT
ejpam-3529	114	11	≤	≤	NOUN
ejpam-3529	114	12	0	0	NUM
ejpam-3529	114	13	.	.	PUNCT
ejpam-3529	115	1	thus	thus	ADV
ejpam-3529	115	2	αk	αk	ADP
ejpam-3529	115	3	≤	≤	NUM
ejpam-3529	115	4	αk+1	αk+1	NUM
ejpam-3529	115	5	on	on	ADP
ejpam-3529	115	6	i.	i.	NOUN
ejpam-3529	115	7	to	to	PART
ejpam-3529	115	8	show	show	VERB
ejpam-3529	115	9	αk+1	αk+1	NUM
ejpam-3529	115	10	≤	≤	NUM
ejpam-3529	115	11	β0	β0	ADV
ejpam-3529	115	12	on	on	ADP
ejpam-3529	115	13	i.	i.	PROPN
ejpam-3529	115	14	set	set	VERB
ejpam-3529	115	15	p	p	NOUN
ejpam-3529	115	16	=	=	NUM
ejpam-3529	115	17	αk+1	αk+1	NUM
ejpam-3529	116	1	−	−	ADP
ejpam-3529	116	2	β0	β0	NOUN
ejpam-3529	116	3	p′	p′	NOUN
ejpam-3529	116	4	=	=	PUNCT
ejpam-3529	117	1	α′k+1	α′k+1	X
ejpam-3529	117	2	−	−	X
ejpam-3529	117	3	β′0	β′0	SYM
ejpam-3529	117	4	≤	≤	NUM
ejpam-3529	117	5	{	{	PUNCT
ejpam-3529	117	6	f1x(t	f1x(t	PROPN
ejpam-3529	117	7	,	,	PUNCT
ejpam-3529	117	8	αk	αk	NOUN
ejpam-3529	117	9	,	,	PUNCT
ejpam-3529	117	10	sαk)[αk	sαk)[αk	VERB
ejpam-3529	117	11	−	−	PROPN
ejpam-3529	117	12	β0	β0	NOUN
ejpam-3529	117	13	]	]	X
ejpam-3529	117	14	+	+	CCONJ
ejpam-3529	117	15	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	117	16	,	,	PUNCT
ejpam-3529	117	17	αk	αk	NOUN
ejpam-3529	117	18	,	,	PUNCT
ejpam-3529	117	19	sαk)[sαk	sαk)[sαk	NUM
ejpam-3529	117	20	−	−	PROPN
ejpam-3529	117	21	sβ0	sβ0	NOUN
ejpam-3529	117	22	]	]	PUNCT
ejpam-3529	117	23	}	}	PUNCT
ejpam-3529	117	24	]	]	PUNCT
ejpam-3529	118	1	+	+	CCONJ
ejpam-3529	118	2	{	{	PUNCT
ejpam-3529	118	3	f1x(t	f1x(t	PROPN
ejpam-3529	118	4	,	,	PUNCT
ejpam-3529	118	5	αk	αk	NOUN
ejpam-3529	118	6	,	,	PUNCT
ejpam-3529	118	7	sαk)[αk+1	sαk)[αk+1	PROPN
ejpam-3529	118	8	−	−	NOUN
ejpam-3529	118	9	αk	αk	NOUN
ejpam-3529	118	10	]	]	X
ejpam-3529	118	11	+	+	CCONJ
ejpam-3529	118	12	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	118	13	,	,	PUNCT
ejpam-3529	118	14	αk	αk	NOUN
ejpam-3529	118	15	,	,	PUNCT
ejpam-3529	118	16	sαk)[sαk+1	sαk)[sαk+1	VERB
ejpam-3529	118	17	−	−	NUM
ejpam-3529	118	18	sαk	sαk	PROPN
ejpam-3529	118	19	]	]	PUNCT
ejpam-3529	118	20	}	}	PUNCT
ejpam-3529	118	21	+	+	CCONJ
ejpam-3529	118	22	{	{	PUNCT
ejpam-3529	118	23	f2(t	f2(t	PROPN
ejpam-3529	118	24	,	,	PUNCT
ejpam-3529	118	25	β0	β0	NOUN
ejpam-3529	118	26	,	,	PUNCT
ejpam-3529	118	27	sβ0)−	sβ0)−	PROPN
ejpam-3529	118	28	f2(t	f2(t	PROPN
ejpam-3529	118	29	,	,	PUNCT
ejpam-3529	118	30	α0	α0	ADJ
ejpam-3529	118	31	,	,	PUNCT
ejpam-3529	118	32	sα0	sα0	NOUN
ejpam-3529	118	33	)	)	PUNCT
ejpam-3529	118	34	}	}	PUNCT
ejpam-3529	118	35	≤	≤	NOUN
ejpam-3529	118	36	{	{	PUNCT
ejpam-3529	118	37	f1x(t	f1x(t	PROPN
ejpam-3529	118	38	,	,	PUNCT
ejpam-3529	118	39	αk	αk	NOUN
ejpam-3529	118	40	,	,	PUNCT
ejpam-3529	118	41	sαk)[αk+1	sαk)[αk+1	PROPN
ejpam-3529	118	42	−	−	NOUN
ejpam-3529	118	43	αk	αk	NOUN
ejpam-3529	118	44	]	]	X
ejpam-3529	119	1	+	+	CCONJ
ejpam-3529	119	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	119	3	,	,	PUNCT
ejpam-3529	119	4	αk	αk	NOUN
ejpam-3529	119	5	,	,	PUNCT
ejpam-3529	119	6	sαk)[sαk+1	sαk)[sαk+1	VERB
ejpam-3529	119	7	−	−	NUM
ejpam-3529	119	8	sαk	sαk	PROPN
ejpam-3529	119	9	]	]	PUNCT
ejpam-3529	119	10	}	}	PUNCT
ejpam-3529	119	11	≤	≤	NUM
ejpam-3529	119	12	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	119	13	)	)	PUNCT
ejpam-3529	119	14	.	.	PUNCT
ejpam-3529	120	1	also	also	ADV
ejpam-3529	120	2	p(0	p(0	VERB
ejpam-3529	120	3	)	)	PUNCT
ejpam-3529	120	4	=	=	SYM
ejpam-3529	120	5	αk+1(0	αk+1(0	X
ejpam-3529	120	6	)	)	PUNCT
ejpam-3529	120	7	−	−	PROPN
ejpam-3529	120	8	β0(0	β0(0	PROPN
ejpam-3529	120	9	)	)	PUNCT
ejpam-3529	120	10	≤	≤	NOUN
ejpam-3529	120	11	0	0	NUM
ejpam-3529	120	12	.	.	PUNCT
ejpam-3529	121	1	hence	hence	ADV
ejpam-3529	121	2	by	by	ADP
ejpam-3529	121	3	lemma	lemma	PROPN
ejpam-3529	121	4	1	1	NUM
ejpam-3529	121	5	we	we	PRON
ejpam-3529	121	6	have	have	VERB
ejpam-3529	121	7	p(t	p(t	NOUN
ejpam-3529	121	8	)	)	PUNCT
ejpam-3529	121	9	≤	≤	NOUN
ejpam-3529	121	10	0	0	NUM
ejpam-3529	122	1	which	which	PRON
ejpam-3529	122	2	implies	imply	VERB
ejpam-3529	122	3	that	that	SCONJ
ejpam-3529	122	4	αk+1	αk+1	NUM
ejpam-3529	122	5	≤	≤	NOUN
ejpam-3529	122	6	β0	β0	ADJ
ejpam-3529	122	7	on	on	ADP
ejpam-3529	122	8	i.	i.	NOUN
ejpam-3529	122	9	thus	thus	ADV
ejpam-3529	122	10	αk	αk	CCONJ
ejpam-3529	122	11	≤	≤	NUM
ejpam-3529	122	12	αk+1	αk+1	VERB
ejpam-3529	122	13	≤	≤	NUM
ejpam-3529	122	14	β0	β0	NOUN
ejpam-3529	122	15	,	,	PUNCT
ejpam-3529	122	16	on	on	ADP
ejpam-3529	122	17	i.	i.	PROPN
ejpam-3529	122	18	now	now	ADV
ejpam-3529	122	19	using	use	VERB
ejpam-3529	122	20	the	the	DET
ejpam-3529	122	21	principle	principle	NOUN
ejpam-3529	122	22	of	of	ADP
ejpam-3529	122	23	mathematical	mathematical	ADJ
ejpam-3529	122	24	induction	induction	NOUN
ejpam-3529	122	25	,	,	PUNCT
ejpam-3529	122	26	we	we	PRON
ejpam-3529	122	27	deduce	deduce	VERB
ejpam-3529	122	28	the	the	DET
ejpam-3529	122	29	relation	relation	NOUN
ejpam-3529	122	30	(	(	PUNCT
ejpam-3529	122	31	13	13	NUM
ejpam-3529	122	32	)	)	PUNCT
ejpam-3529	122	33	and	and	CCONJ
ejpam-3529	122	34	our	our	PRON
ejpam-3529	122	35	claim	claim	NOUN
ejpam-3529	122	36	holds	hold	VERB
ejpam-3529	122	37	.	.	PUNCT
ejpam-3529	123	1	also	also	ADV
ejpam-3529	123	2	from	from	ADP
ejpam-3529	123	3	relation	relation	NOUN
ejpam-3529	123	4	(	(	PUNCT
ejpam-3529	123	5	13	13	NUM
ejpam-3529	123	6	)	)	PUNCT
ejpam-3529	123	7	,	,	PUNCT
ejpam-3529	123	8	we	we	PRON
ejpam-3529	123	9	can	can	AUX
ejpam-3529	123	10	seen	see	VERB
ejpam-3529	123	11	that	that	SCONJ
ejpam-3529	123	12	the	the	DET
ejpam-3529	123	13	sequences	sequence	NOUN
ejpam-3529	123	14	are	be	AUX
ejpam-3529	123	15	uniformly	uniformly	ADV
ejpam-3529	123	16	bounded	bound	VERB
ejpam-3529	123	17	.	.	PUNCT
ejpam-3529	124	1	since	since	SCONJ
ejpam-3529	124	2	f1	f1	NOUN
ejpam-3529	124	3	,	,	PUNCT
ejpam-3529	124	4	f2	f2	PROPN
ejpam-3529	124	5	are	be	AUX
ejpam-3529	124	6	uniformly	uniformly	ADV
ejpam-3529	124	7	bounded	bound	VERB
ejpam-3529	124	8	,	,	PUNCT
ejpam-3529	124	9	the	the	DET
ejpam-3529	124	10	sequence	sequence	NOUN
ejpam-3529	124	11	{	{	PUNCT
ejpam-3529	124	12	αn	αn	NOUN
ejpam-3529	124	13	}	}	PUNCT
ejpam-3529	124	14	is	be	AUX
ejpam-3529	124	15	equicontinuous	equicontinuous	ADJ
ejpam-3529	124	16	on	on	ADP
ejpam-3529	124	17	[	[	X
ejpam-3529	124	18	0	0	NUM
ejpam-3529	124	19	,	,	PUNCT
ejpam-3529	124	20	t	t	NOUN
ejpam-3529	124	21	]	]	PUNCT
ejpam-3529	124	22	and	and	CCONJ
ejpam-3529	124	23	therefore	therefore	ADV
ejpam-3529	124	24	by	by	ADP
ejpam-3529	124	25	using	use	VERB
ejpam-3529	124	26	ascoli	ascoli	PROPN
ejpam-3529	124	27	-	-	PUNCT
ejpam-3529	124	28	arzela	arzela	PROPN
ejpam-3529	124	29	theorem	theorem	VERB
ejpam-3529	124	30	,	,	PUNCT
ejpam-3529	124	31	there	there	PRON
ejpam-3529	124	32	exists	exist	VERB
ejpam-3529	124	33	a	a	DET
ejpam-3529	124	34	subsequence	subsequence	NOUN
ejpam-3529	124	35	{	{	PUNCT
ejpam-3529	124	36	αnk	αnk	NOUN
ejpam-3529	124	37	}	}	PUNCT
ejpam-3529	124	38	that	that	PRON
ejpam-3529	124	39	converges	converge	VERB
ejpam-3529	124	40	uniformly	uniformly	ADV
ejpam-3529	124	41	on	on	ADP
ejpam-3529	124	42	[	[	X
ejpam-3529	124	43	0	0	NUM
ejpam-3529	124	44	,	,	PUNCT
ejpam-3529	124	45	t	t	NOUN
ejpam-3529	124	46	]	]	PUNCT
ejpam-3529	124	47	.	.	PUNCT
ejpam-3529	125	1	in	in	ADP
ejpam-3529	125	2	view	view	NOUN
ejpam-3529	125	3	of	of	ADP
ejpam-3529	125	4	(	(	PUNCT
ejpam-3529	125	5	13	13	NUM
ejpam-3529	125	6	)	)	PUNCT
ejpam-3529	125	7	it	it	PRON
ejpam-3529	125	8	also	also	ADV
ejpam-3529	125	9	follows	follow	VERB
ejpam-3529	125	10	that	that	SCONJ
ejpam-3529	125	11	the	the	DET
ejpam-3529	125	12	entire	entire	ADJ
ejpam-3529	125	13	sequence	sequence	NOUN
ejpam-3529	125	14	{	{	PUNCT
ejpam-3529	125	15	αn	αn	NOUN
ejpam-3529	125	16	}	}	PUNCT
ejpam-3529	125	17	converges	converge	VERB
ejpam-3529	125	18	uniformly	uniformly	ADV
ejpam-3529	125	19	to	to	ADP
ejpam-3529	125	20	ρ	ρ	PROPN
ejpam-3529	125	21	.	.	PUNCT
ejpam-3529	126	1	since	since	SCONJ
ejpam-3529	126	2	f1x	f1x	PROPN
ejpam-3529	126	3	exists	exist	VERB
ejpam-3529	126	4	and	and	CCONJ
ejpam-3529	126	5	is	be	AUX
ejpam-3529	126	6	bounded	bound	VERB
ejpam-3529	126	7	on	on	ADP
ejpam-3529	126	8	[	[	X
ejpam-3529	126	9	0	0	NUM
ejpam-3529	126	10	,	,	PUNCT
ejpam-3529	126	11	t	t	X
ejpam-3529	126	12	]	]	PUNCT
ejpam-3529	126	13	,	,	PUNCT
ejpam-3529	126	14	we	we	PRON
ejpam-3529	126	15	obtain	obtain	VERB
ejpam-3529	126	16	that	that	DET
ejpam-3529	126	17	f1	f1	NOUN
ejpam-3529	126	18	is	be	AUX
ejpam-3529	126	19	lipschitz	lipschitz	NOUN
ejpam-3529	126	20	and	and	CCONJ
ejpam-3529	126	21	hence	hence	ADV
ejpam-3529	126	22	the	the	DET
ejpam-3529	126	23	solution	solution	NOUN
ejpam-3529	126	24	u	u	NOUN
ejpam-3529	126	25	is	be	AUX
ejpam-3529	126	26	unique	unique	ADJ
ejpam-3529	126	27	.	.	PUNCT
ejpam-3529	127	1	to	to	PART
ejpam-3529	127	2	show	show	VERB
ejpam-3529	127	3	that	that	SCONJ
ejpam-3529	127	4	the	the	DET
ejpam-3529	127	5	convergence	convergence	NOUN
ejpam-3529	127	6	is	be	AUX
ejpam-3529	127	7	quadratic	quadratic	ADJ
ejpam-3529	127	8	,	,	PUNCT
ejpam-3529	127	9	we	we	PRON
ejpam-3529	127	10	begin	begin	VERB
ejpam-3529	127	11	by	by	ADP
ejpam-3529	127	12	writing	write	VERB
ejpam-3529	127	13	pn+1	pn+1	PROPN
ejpam-3529	127	14	=	=	SYM
ejpam-3529	127	15	u−	u−	NUM
ejpam-3529	127	16	αn+1	αn+1	NUM
ejpam-3529	127	17	and	and	CCONJ
ejpam-3529	127	18	consider	consider	VERB
ejpam-3529	127	19	p′n+1	p′n+1	NOUN
ejpam-3529	127	20	=	=	PUNCT
ejpam-3529	127	21	u′	u′	X
ejpam-3529	127	22	−	−	ADP
ejpam-3529	127	23	α′n+1	α′n+1	NOUN
ejpam-3529	127	24	ch	ch	NOUN
ejpam-3529	127	25	.	.	PUNCT
ejpam-3529	128	1	v.	v.	ADP
ejpam-3529	128	2	sreedhar	sreedhar	PROPN
ejpam-3529	128	3	,	,	PUNCT
ejpam-3529	128	4	j.	j.	PROPN
ejpam-3529	128	5	vasundhara	vasundhara	PROPN
ejpam-3529	128	6	devi	devi	PROPN
ejpam-3529	128	7	,	,	PUNCT
ejpam-3529	128	8	/	/	SYM
ejpam-3529	128	9	eur	eur	NOUN
ejpam-3529	128	10	.	.	PUNCT
ejpam-3529	129	1	j.	j.	PROPN
ejpam-3529	129	2	pure	pure	PROPN
ejpam-3529	129	3	appl	appl	PROPN
ejpam-3529	129	4	.	.	PROPN
ejpam-3529	129	5	math	math	PROPN
ejpam-3529	129	6	,	,	PUNCT
ejpam-3529	129	7	12	12	NUM
ejpam-3529	129	8	(	(	PUNCT
ejpam-3529	129	9	4	4	NUM
ejpam-3529	129	10	)	)	PUNCT
ejpam-3529	129	11	(	(	PUNCT
ejpam-3529	129	12	2019	2019	NUM
ejpam-3529	129	13	)	)	PUNCT
ejpam-3529	129	14	,	,	PUNCT
ejpam-3529	129	15	1662	1662	NUM
ejpam-3529	129	16	-	-	SYM
ejpam-3529	129	17	1675	1675	NUM
ejpam-3529	129	18	1668	1668	NUM
ejpam-3529	129	19	=	=	PUNCT
ejpam-3529	130	1	[	[	X
ejpam-3529	130	2	f1(t	f1(t	PROPN
ejpam-3529	130	3	,	,	PUNCT
ejpam-3529	130	4	u	u	NOUN
ejpam-3529	130	5	,	,	PUNCT
ejpam-3529	130	6	su	su	PROPN
ejpam-3529	130	7	)	)	PUNCT
ejpam-3529	131	1	+	+	CCONJ
ejpam-3529	131	2	f2(t	f2(t	PROPN
ejpam-3529	131	3	,	,	PUNCT
ejpam-3529	131	4	u	u	NOUN
ejpam-3529	131	5	,	,	PUNCT
ejpam-3529	131	6	su	su	PROPN
ejpam-3529	131	7	)	)	PUNCT
ejpam-3529	131	8	]	]	PUNCT
ejpam-3529	132	1	−	−	PUNCT
ejpam-3529	133	1	[	[	X
ejpam-3529	133	2	{	{	PUNCT
ejpam-3529	133	3	f1(t	f1(t	PROPN
ejpam-3529	133	4	,	,	PUNCT
ejpam-3529	133	5	αn	αn	NOUN
ejpam-3529	133	6	,	,	PUNCT
ejpam-3529	133	7	sαn	sαn	NOUN
ejpam-3529	133	8	)	)	PUNCT
ejpam-3529	134	1	+	+	CCONJ
ejpam-3529	134	2	f1x(t	f1x(t	PROPN
ejpam-3529	134	3	,	,	PUNCT
ejpam-3529	134	4	αn	αn	NOUN
ejpam-3529	134	5	,	,	PUNCT
ejpam-3529	134	6	sαn)[αn+1	sαn)[αn+1	NOUN
ejpam-3529	134	7	−	−	NOUN
ejpam-3529	134	8	αn	αn	NOUN
ejpam-3529	134	9	]	]	X
ejpam-3529	135	1	+	+	CCONJ
ejpam-3529	135	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	135	3	,	,	PUNCT
ejpam-3529	135	4	αn	αn	NOUN
ejpam-3529	135	5	,	,	PUNCT
ejpam-3529	135	6	sαn)[sαn+1	sαn)[sαn+1	ADJ
ejpam-3529	135	7	−	−	NOUN
ejpam-3529	135	8	sαn	sαn	NOUN
ejpam-3529	135	9	]	]	PUNCT
ejpam-3529	135	10	+	+	CCONJ
ejpam-3529	135	11	f2(t	f2(t	PROPN
ejpam-3529	135	12	,	,	PUNCT
ejpam-3529	135	13	β0	β0	NOUN
ejpam-3529	135	14	,	,	PUNCT
ejpam-3529	135	15	sβ0	sβ0	NOUN
ejpam-3529	135	16	)	)	PUNCT
ejpam-3529	135	17	}	}	PUNCT
ejpam-3529	135	18	]	]	PUNCT
ejpam-3529	135	19	p′n+1	p′n+1	PROPN
ejpam-3529	135	20	≤	≤	PROPN
ejpam-3529	135	21	a+b	a+b	PUNCT
ejpam-3529	135	22	+	+	CCONJ
ejpam-3529	135	23	f1x(t	f1x(t	PROPN
ejpam-3529	135	24	,	,	PUNCT
ejpam-3529	135	25	αn	αn	NOUN
ejpam-3529	135	26	,	,	PUNCT
ejpam-3529	135	27	sαn)pn+1	sαn)pn+1	ADJ
ejpam-3529	135	28	+	+	CCONJ
ejpam-3529	135	29	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	135	30	,	,	PUNCT
ejpam-3529	135	31	αn	αn	NOUN
ejpam-3529	135	32	,	,	PUNCT
ejpam-3529	135	33	sαn)spn+1	sαn)spn+1	ADV
ejpam-3529	135	34	(	(	PUNCT
ejpam-3529	135	35	14	14	NUM
ejpam-3529	135	36	)	)	PUNCT
ejpam-3529	135	37	where	where	SCONJ
ejpam-3529	135	38	a	a	DET
ejpam-3529	135	39	=	=	SYM
ejpam-3529	135	40	f1(t	f1(t	PROPN
ejpam-3529	135	41	,	,	PUNCT
ejpam-3529	135	42	u	u	NOUN
ejpam-3529	135	43	,	,	PUNCT
ejpam-3529	135	44	su)−	su)−	X
ejpam-3529	135	45	f1(t	f1(t	PROPN
ejpam-3529	135	46	,	,	PUNCT
ejpam-3529	135	47	αn	αn	NOUN
ejpam-3529	135	48	,	,	PUNCT
ejpam-3529	135	49	su)−	su)−	VERB
ejpam-3529	135	50	f1x(t	f1x(t	PROPN
ejpam-3529	135	51	,	,	PUNCT
ejpam-3529	135	52	αn	αn	NOUN
ejpam-3529	135	53	,	,	PUNCT
ejpam-3529	135	54	sαn)[u−	sαn)[u−	NOUN
ejpam-3529	135	55	αn	αn	NOUN
ejpam-3529	135	56	]	]	X
ejpam-3529	135	57	;	;	PUNCT
ejpam-3529	135	58	b	b	X
ejpam-3529	135	59	=	=	SYM
ejpam-3529	135	60	f1(t	f1(t	PROPN
ejpam-3529	135	61	,	,	PUNCT
ejpam-3529	135	62	αn	αn	NOUN
ejpam-3529	135	63	,	,	PUNCT
ejpam-3529	135	64	su)−	su)−	NOUN
ejpam-3529	135	65	f1(t	f1(t	PROPN
ejpam-3529	135	66	,	,	PUNCT
ejpam-3529	135	67	αn	αn	NOUN
ejpam-3529	135	68	,	,	PUNCT
ejpam-3529	135	69	sαn)−	sαn)−	PROPN
ejpam-3529	135	70	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	135	71	,	,	PUNCT
ejpam-3529	135	72	αn	αn	NOUN
ejpam-3529	135	73	,	,	PUNCT
ejpam-3529	135	74	sαn)[su−	sαn)[su−	PROPN
ejpam-3529	135	75	sαn	sαn	NOUN
ejpam-3529	135	76	]	]	PUNCT
ejpam-3529	135	77	.	.	PUNCT
ejpam-3529	136	1	our	our	PRON
ejpam-3529	136	2	aim	aim	NOUN
ejpam-3529	136	3	is	be	AUX
ejpam-3529	136	4	to	to	PART
ejpam-3529	136	5	simplify	simplify	VERB
ejpam-3529	136	6	each	each	PRON
ejpam-3529	136	7	of	of	ADP
ejpam-3529	136	8	the	the	DET
ejpam-3529	136	9	term	term	NOUN
ejpam-3529	136	10	a	a	DET
ejpam-3529	136	11	,	,	PUNCT
ejpam-3529	136	12	b	b	NOUN
ejpam-3529	136	13	and	and	CCONJ
ejpam-3529	136	14	substitute	substitute	NOUN
ejpam-3529	136	15	in	in	ADP
ejpam-3529	136	16	(	(	PUNCT
ejpam-3529	136	17	14	14	NUM
ejpam-3529	136	18	)	)	PUNCT
ejpam-3529	136	19	.	.	PUNCT
ejpam-3529	137	1	in	in	ADP
ejpam-3529	137	2	this	this	DET
ejpam-3529	137	3	direction	direction	NOUN
ejpam-3529	137	4	,	,	PUNCT
ejpam-3529	137	5	consider	consider	VERB
ejpam-3529	137	6	a	a	DET
ejpam-3529	137	7	=	=	SYM
ejpam-3529	137	8	f1(t	f1(t	PROPN
ejpam-3529	137	9	,	,	PUNCT
ejpam-3529	137	10	u	u	NOUN
ejpam-3529	137	11	,	,	PUNCT
ejpam-3529	137	12	su)−	su)−	X
ejpam-3529	137	13	f1(t	f1(t	PROPN
ejpam-3529	137	14	,	,	PUNCT
ejpam-3529	137	15	αn	αn	NOUN
ejpam-3529	137	16	,	,	PUNCT
ejpam-3529	137	17	su)−	su)−	VERB
ejpam-3529	137	18	f1x(t	f1x(t	PROPN
ejpam-3529	137	19	,	,	PUNCT
ejpam-3529	137	20	αn	αn	NOUN
ejpam-3529	137	21	,	,	PUNCT
ejpam-3529	137	22	sαn)[u−	sαn)[u−	NOUN
ejpam-3529	137	23	αn	αn	NOUN
ejpam-3529	137	24	]	]	X
ejpam-3529	137	25	;	;	PUNCT
ejpam-3529	137	26	=	=	SYM
ejpam-3529	137	27	[	[	X
ejpam-3529	137	28	f1x(t	f1x(t	PROPN
ejpam-3529	137	29	,	,	PUNCT
ejpam-3529	137	30	η1	η1	NOUN
ejpam-3529	137	31	,	,	PUNCT
ejpam-3529	137	32	su)(u−	su)(u−	ADJ
ejpam-3529	137	33	αn	αn	NOUN
ejpam-3529	137	34	)	)	PUNCT
ejpam-3529	137	35	−	−	ADP
ejpam-3529	137	36	f1x(t	f1x(t	PROPN
ejpam-3529	137	37	,	,	PUNCT
ejpam-3529	137	38	αn	αn	NOUN
ejpam-3529	137	39	,	,	PUNCT
ejpam-3529	137	40	sαn)](u−	sαn)](u−	X
ejpam-3529	137	41	αn	αn	VERB
ejpam-3529	137	42	)	)	PUNCT
ejpam-3529	137	43	=	=	PUNCT
ejpam-3529	138	1	[	[	X
ejpam-3529	138	2	f1x(t	f1x(t	PROPN
ejpam-3529	138	3	,	,	PUNCT
ejpam-3529	138	4	η1	η1	NOUN
ejpam-3529	138	5	,	,	PUNCT
ejpam-3529	138	6	su	su	PROPN
ejpam-3529	138	7	)	)	PUNCT
ejpam-3529	138	8	−	−	ADP
ejpam-3529	139	1	f1x(t	f1x(t	PROPN
ejpam-3529	139	2	,	,	PUNCT
ejpam-3529	139	3	αn	αn	NOUN
ejpam-3529	139	4	,	,	PUNCT
ejpam-3529	139	5	sαn)](u−	sαn)](u−	X
ejpam-3529	139	6	αn	αn	VERB
ejpam-3529	139	7	)	)	PUNCT
ejpam-3529	139	8	=	=	PUNCT
ejpam-3529	140	1	[	[	X
ejpam-3529	140	2	f1x(t	f1x(t	PROPN
ejpam-3529	140	3	,	,	PUNCT
ejpam-3529	140	4	η1	η1	NOUN
ejpam-3529	140	5	,	,	PUNCT
ejpam-3529	140	6	su)−	su)−	VERB
ejpam-3529	140	7	f1x(t	f1x(t	PROPN
ejpam-3529	140	8	,	,	PUNCT
ejpam-3529	140	9	αn	αn	NOUN
ejpam-3529	140	10	,	,	PUNCT
ejpam-3529	140	11	su	su	PROPN
ejpam-3529	140	12	)	)	PUNCT
ejpam-3529	141	1	+	+	NOUN
ejpam-3529	141	2	f1x(t	f1x(t	PROPN
ejpam-3529	141	3	,	,	PUNCT
ejpam-3529	141	4	αn	αn	NOUN
ejpam-3529	141	5	,	,	PUNCT
ejpam-3529	141	6	su)−	su)−	VERB
ejpam-3529	142	1	[	[	X
ejpam-3529	142	2	f1x(t	f1x(t	PROPN
ejpam-3529	142	3	,	,	PUNCT
ejpam-3529	142	4	αn	αn	NOUN
ejpam-3529	142	5	,	,	PUNCT
ejpam-3529	142	6	sαn)]pn(t	sαn)]pn(t	NOUN
ejpam-3529	142	7	)	)	PUNCT
ejpam-3529	142	8	=	=	SYM
ejpam-3529	142	9	f1xx(t	f1xx(t	PROPN
ejpam-3529	142	10	,	,	PUNCT
ejpam-3529	142	11	τ1	τ1	NOUN
ejpam-3529	142	12	,	,	PUNCT
ejpam-3529	142	13	su)pn[η1	su)pn[η1	PROPN
ejpam-3529	142	14	−	−	NOUN
ejpam-3529	143	1	αn	αn	NOUN
ejpam-3529	143	2	]	]	X
ejpam-3529	144	1	+	+	CCONJ
ejpam-3529	144	2	1∫	1∫	NUM
ejpam-3529	144	3	0	0	NUM
ejpam-3529	144	4	f1xξ(t	f1xξ(t	PROPN
ejpam-3529	144	5	,	,	PUNCT
ejpam-3529	144	6	αn	αn	NOUN
ejpam-3529	144	7	,	,	PUNCT
ejpam-3529	144	8	ssu+	ssu+	NOUN
ejpam-3529	144	9	(	(	PUNCT
ejpam-3529	144	10	1−	1−	NUM
ejpam-3529	144	11	s)sαn)[su−	s)sαn)[su−	NOUN
ejpam-3529	144	12	sαn]pnds	sαn]pnd	VERB
ejpam-3529	144	13	≤	≤	ADJ
ejpam-3529	144	14	f1xx(t	f1xx(t	PROPN
ejpam-3529	144	15	,	,	PUNCT
ejpam-3529	144	16	τ1	τ1	NOUN
ejpam-3529	144	17	,	,	PUNCT
ejpam-3529	144	18	su)pn	su)pn	NOUN
ejpam-3529	144	19	2	2	NUM
ejpam-3529	144	20	+	+	CCONJ
ejpam-3529	144	21	1∫	1∫	NUM
ejpam-3529	144	22	0	0	NUM
ejpam-3529	144	23	f1xξ(t	f1xξ(t	PROPN
ejpam-3529	144	24	,	,	PUNCT
ejpam-3529	144	25	αn	αn	NOUN
ejpam-3529	144	26	,	,	PUNCT
ejpam-3529	144	27	ssu+	ssu+	NOUN
ejpam-3529	144	28	(	(	PUNCT
ejpam-3529	144	29	1−	1−	NUM
ejpam-3529	144	30	s)sαn)[spn]pnds	s)sαn)[spn]pnd	VERB
ejpam-3529	144	31	≤	≤	NOUN
ejpam-3529	144	32	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	144	33	+	+	CCONJ
ejpam-3529	145	1	l2k1	l2k1	AUX
ejpam-3529	145	2	t	t	X
ejpam-3529	145	3	|pn||pn|	|pn||pn|	NUM
ejpam-3529	145	4	1∫	1∫	NUM
ejpam-3529	145	5	0	0	NUM
ejpam-3529	145	6	ds	ds	ADJ
ejpam-3529	145	7	≤	≤	NOUN
ejpam-3529	145	8	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	145	9	+	+	CCONJ
ejpam-3529	145	10	l2k1	l2k1	PROPN
ejpam-3529	145	11	t	t	NOUN
ejpam-3529	145	12	|pn|2	|pn|2	PUNCT
ejpam-3529	145	13	next	next	ADV
ejpam-3529	145	14	consider	consider	VERB
ejpam-3529	145	15	b	b	PROPN
ejpam-3529	145	16	=	=	SYM
ejpam-3529	145	17	f1(t	f1(t	PROPN
ejpam-3529	145	18	,	,	PUNCT
ejpam-3529	145	19	αn	αn	NOUN
ejpam-3529	145	20	,	,	PUNCT
ejpam-3529	145	21	su)−	su)−	NOUN
ejpam-3529	145	22	f1(t	f1(t	PROPN
ejpam-3529	145	23	,	,	PUNCT
ejpam-3529	145	24	αn	αn	NOUN
ejpam-3529	145	25	,	,	PUNCT
ejpam-3529	145	26	sαn)−	sαn)−	PROPN
ejpam-3529	145	27	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	145	28	,	,	PUNCT
ejpam-3529	145	29	αn	αn	NOUN
ejpam-3529	145	30	,	,	PUNCT
ejpam-3529	145	31	sαn)[su−	sαn)[su−	PROPN
ejpam-3529	145	32	sαn	sαn	NOUN
ejpam-3529	145	33	]	]	PUNCT
ejpam-3529	145	34	;	;	PUNCT
ejpam-3529	145	35	=	=	SYM
ejpam-3529	146	1	1∫	1∫	NUM
ejpam-3529	146	2	0	0	NUM
ejpam-3529	147	1	[	[	X
ejpam-3529	147	2	f1ξ(t	f1ξ(t	ADP
ejpam-3529	147	3	,	,	PUNCT
ejpam-3529	147	4	αn	αn	NOUN
ejpam-3529	147	5	,	,	PUNCT
ejpam-3529	147	6	s(su	s(su	NUM
ejpam-3529	147	7	)	)	PUNCT
ejpam-3529	147	8	+	+	CCONJ
ejpam-3529	147	9	(	(	PUNCT
ejpam-3529	147	10	1−	1−	NUM
ejpam-3529	147	11	s)sαn)−	s)sαn)−	NOUN
ejpam-3529	147	12	[	[	X
ejpam-3529	147	13	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	147	14	,	,	PUNCT
ejpam-3529	147	15	αn	αn	NOUN
ejpam-3529	147	16	,	,	PUNCT
ejpam-3529	147	17	sαn)](su−	sαn)](su−	PROPN
ejpam-3529	147	18	sαn)ds	sαn)ds	ADV
ejpam-3529	147	19	.	.	PUNCT
ejpam-3529	148	1	let	let	VERB
ejpam-3529	148	2	η2(s	η2(s	NOUN
ejpam-3529	148	3	)	)	PUNCT
ejpam-3529	149	1	=	=	PUNCT
ejpam-3529	149	2	s(su	s(su	PROPN
ejpam-3529	149	3	)	)	PUNCT
ejpam-3529	149	4	+	+	CCONJ
ejpam-3529	149	5	(	(	PUNCT
ejpam-3529	149	6	1−	1−	NUM
ejpam-3529	149	7	s)sαn	s)sαn	NOUN
ejpam-3529	149	8	.	.	PUNCT
ejpam-3529	150	1	then	then	ADV
ejpam-3529	150	2	b	b	X
ejpam-3529	150	3	=	=	SYM
ejpam-3529	151	1	1∫	1∫	NUM
ejpam-3529	151	2	0	0	NUM
ejpam-3529	152	1	[	[	X
ejpam-3529	152	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	152	3	,	,	PUNCT
ejpam-3529	152	4	αn	αn	NOUN
ejpam-3529	152	5	,	,	PUNCT
ejpam-3529	152	6	η2(s))−	η2(s))−	ADJ
ejpam-3529	152	7	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	152	8	,	,	PUNCT
ejpam-3529	152	9	αn	αn	NOUN
ejpam-3529	152	10	,	,	PUNCT
ejpam-3529	152	11	sαn)](su−	sαn)](su−	NOUN
ejpam-3529	152	12	sαn)ds	sαn)ds	ADV
ejpam-3529	152	13	=	=	NOUN
ejpam-3529	153	1	1∫	1∫	NUM
ejpam-3529	153	2	0	0	NUM
ejpam-3529	153	3	1∫	1∫	NUM
ejpam-3529	153	4	0	0	NUM
ejpam-3529	153	5	f1ξξ(t	f1ξξ(t	PROPN
ejpam-3529	153	6	,	,	PUNCT
ejpam-3529	153	7	αn	αn	NOUN
ejpam-3529	153	8	,	,	PUNCT
ejpam-3529	153	9	σ	σ	PROPN
ejpam-3529	153	10	η2(s	η2(s	PROPN
ejpam-3529	153	11	)	)	PUNCT
ejpam-3529	154	1	+	+	CCONJ
ejpam-3529	154	2	(	(	PUNCT
ejpam-3529	154	3	1−	1−	NUM
ejpam-3529	154	4	σ)sαn)s(spn)(su−	σ)sαn)s(spn)(su−	PROPN
ejpam-3529	154	5	sαn)dsdσ	sαn)dsdσ	PROPN
ejpam-3529	154	6	=	=	PROPN
ejpam-3529	155	1	1∫	1∫	NUM
ejpam-3529	155	2	0	0	NUM
ejpam-3529	155	3	1∫	1∫	NUM
ejpam-3529	155	4	0	0	NUM
ejpam-3529	155	5	f1ξξ(t	f1ξξ(t	PROPN
ejpam-3529	155	6	,	,	PUNCT
ejpam-3529	155	7	αn	αn	NOUN
ejpam-3529	155	8	,	,	PUNCT
ejpam-3529	155	9	σ	σ	PROPN
ejpam-3529	155	10	η2(s	η2(s	PROPN
ejpam-3529	155	11	)	)	PUNCT
ejpam-3529	156	1	+	+	CCONJ
ejpam-3529	156	2	(	(	PUNCT
ejpam-3529	156	3	1−	1−	NUM
ejpam-3529	156	4	σ)sαn)s(spn)(spn)dsdσ	σ)sαn)s(spn)(spn)dsdσ	PROPN
ejpam-3529	156	5	ch	ch	NOUN
ejpam-3529	156	6	.	.	PUNCT
ejpam-3529	157	1	v.	v.	ADP
ejpam-3529	157	2	sreedhar	sreedhar	PROPN
ejpam-3529	157	3	,	,	PUNCT
ejpam-3529	157	4	j.	j.	PROPN
ejpam-3529	157	5	vasundhara	vasundhara	PROPN
ejpam-3529	157	6	devi	devi	PROPN
ejpam-3529	157	7	,	,	PUNCT
ejpam-3529	157	8	/	/	SYM
ejpam-3529	157	9	eur	eur	NOUN
ejpam-3529	157	10	.	.	PUNCT
ejpam-3529	158	1	j.	j.	PROPN
ejpam-3529	158	2	pure	pure	PROPN
ejpam-3529	158	3	appl	appl	PROPN
ejpam-3529	158	4	.	.	PROPN
ejpam-3529	158	5	math	math	PROPN
ejpam-3529	158	6	,	,	PUNCT
ejpam-3529	158	7	12	12	NUM
ejpam-3529	158	8	(	(	PUNCT
ejpam-3529	158	9	4	4	NUM
ejpam-3529	158	10	)	)	PUNCT
ejpam-3529	158	11	(	(	PUNCT
ejpam-3529	158	12	2019	2019	NUM
ejpam-3529	158	13	)	)	PUNCT
ejpam-3529	158	14	,	,	PUNCT
ejpam-3529	158	15	1662	1662	NUM
ejpam-3529	158	16	-	-	SYM
ejpam-3529	158	17	1675	1675	NUM
ejpam-3529	158	18	1669	1669	NUM
ejpam-3529	158	19	=	=	SYM
ejpam-3529	159	1	1∫	1∫	NUM
ejpam-3529	159	2	0	0	NUM
ejpam-3529	159	3	1∫	1∫	NUM
ejpam-3529	159	4	0	0	NUM
ejpam-3529	159	5	f1ξξ(t	f1ξξ(t	PROPN
ejpam-3529	159	6	,	,	PUNCT
ejpam-3529	159	7	αn	αn	NOUN
ejpam-3529	159	8	,	,	PUNCT
ejpam-3529	159	9	σ	σ	PROPN
ejpam-3529	159	10	η2(s	η2(s	PROPN
ejpam-3529	159	11	)	)	PUNCT
ejpam-3529	160	1	+	+	CCONJ
ejpam-3529	160	2	(	(	PUNCT
ejpam-3529	160	3	1−	1−	NUM
ejpam-3529	160	4	σ)sαn)s(spn)2dsdσ	σ)sαn)s(spn)2dsdσ	PROPN
ejpam-3529	160	5	≤	≤	PROPN
ejpam-3529	161	1	l3k21	l3k21	PROPN
ejpam-3529	161	2	t	t	NOUN
ejpam-3529	161	3	2|p2n|	2|p2n|	NUM
ejpam-3529	161	4	1∫	1∫	NUM
ejpam-3529	161	5	0	0	NUM
ejpam-3529	162	1	1∫	1∫	NUM
ejpam-3529	162	2	0	0	NUM
ejpam-3529	162	3	s	s	PART
ejpam-3529	162	4	dsdσ	dsdσ	NOUN
ejpam-3529	162	5	≤	≤	NUM
ejpam-3529	162	6	l3k21	l3k21	PROPN
ejpam-3529	162	7	t	t	NOUN
ejpam-3529	162	8	2|p2n|	2|p2n|	NUM
ejpam-3529	162	9	p′n+1	p′n+1	PROPN
ejpam-3529	162	10	≤	≤	PROPN
ejpam-3529	162	11	{	{	PUNCT
ejpam-3529	162	12	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	162	13	+	+	CCONJ
ejpam-3529	162	14	l2k1	l2k1	NOUN
ejpam-3529	162	15	t	t	NOUN
ejpam-3529	162	16	|pn|2}+	|pn|2}+	NUM
ejpam-3529	162	17	{	{	PUNCT
ejpam-3529	162	18	l3k21	l3k21	NOUN
ejpam-3529	162	19	t	t	NOUN
ejpam-3529	162	20	2|p2n|	2|p2n|	NUM
ejpam-3529	162	21	}	}	SYM
ejpam-3529	162	22	−mpn+1(t)−nspn+1(t	−mpn+1(t)−nspn+1(t	PROPN
ejpam-3529	162	23	)	)	PUNCT
ejpam-3529	162	24	≤	≤	NUM
ejpam-3529	162	25	l	l	NOUN
ejpam-3529	162	26	−mpn+1(t)−nspn+1(t	−mpn+1(t)−nspn+1(t	PROPN
ejpam-3529	162	27	)	)	PUNCT
ejpam-3529	162	28	where	where	SCONJ
ejpam-3529	162	29	l	l	NOUN
ejpam-3529	162	30	=	=	PUNCT
ejpam-3529	162	31	{	{	PUNCT
ejpam-3529	162	32	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	162	33	+	+	CCONJ
ejpam-3529	162	34	l2k1	l2k1	PROPN
ejpam-3529	162	35	t	t	NOUN
ejpam-3529	162	36	|pn|2	|pn|2	VERB
ejpam-3529	162	37	}	}	PUNCT
ejpam-3529	162	38	+	+	CCONJ
ejpam-3529	162	39	{	{	PUNCT
ejpam-3529	162	40	l3k21	l3k21	X
ejpam-3529	162	41	t	t	NOUN
ejpam-3529	162	42	2|p2n|	2|p2n|	NUM
ejpam-3529	162	43	}	}	PUNCT
ejpam-3529	162	44	.	.	PUNCT
ejpam-3529	163	1	now	now	ADV
ejpam-3529	163	2	multiplying	multiply	VERB
ejpam-3529	163	3	throughout	throughout	ADP
ejpam-3529	163	4	by	by	ADP
ejpam-3529	163	5	emt	emt	NOUN
ejpam-3529	163	6	and	and	CCONJ
ejpam-3529	163	7	setting	set	VERB
ejpam-3529	163	8	p̃n+1	p̃n+1	PROPN
ejpam-3529	163	9	=	=	SYM
ejpam-3529	163	10	emtpn+1	emtpn+1	PROPN
ejpam-3529	163	11	,	,	PUNCT
ejpam-3529	163	12	we	we	PRON
ejpam-3529	163	13	get	get	VERB
ejpam-3529	163	14	(	(	PUNCT
ejpam-3529	163	15	pn+1(t)e	pn+1(t)e	X
ejpam-3529	163	16	mt)′	mt)′	NOUN
ejpam-3529	163	17	≤	≤	PROPN
ejpam-3529	163	18	nk1	nk1	PROPN
ejpam-3529	163	19	h2∫	h2∫	NOUN
ejpam-3529	163	20	0	0	NUM
ejpam-3529	164	1	pn+1(s)e	pn+1(s)e	NOUN
ejpam-3529	164	2	mtds+	mtds+	X
ejpam-3529	164	3	lemt	lemt	PROPN
ejpam-3529	164	4	≤	≤	PROPN
ejpam-3529	164	5	nk1	nk1	PROPN
ejpam-3529	164	6	∫	∫	PROPN
ejpam-3529	164	7	t	t	PROPN
ejpam-3529	164	8	0	0	NUM
ejpam-3529	165	1	p̃n+1(s)e	p̃n+1(s)e	ADV
ejpam-3529	165	2	m(t−s)ds+	m(t−s)ds+	PROPN
ejpam-3529	165	3	lemt	lemt	NOUN
ejpam-3529	165	4	=	=	SYM
ejpam-3529	165	5	w′(t	w′(t	NOUN
ejpam-3529	165	6	)	)	PUNCT
ejpam-3529	165	7	(	(	PUNCT
ejpam-3529	165	8	say	say	INTJ
ejpam-3529	165	9	)	)	PUNCT
ejpam-3529	165	10	then	then	ADV
ejpam-3529	165	11	choosing	choose	VERB
ejpam-3529	165	12	w(0)=0	w(0)=0	NUM
ejpam-3529	165	13	,	,	PUNCT
ejpam-3529	165	14	we	we	PRON
ejpam-3529	165	15	get	get	VERB
ejpam-3529	165	16	p̃n+1	p̃n+1	PROPN
ejpam-3529	165	17	≤	≤	NOUN
ejpam-3529	165	18	w(t	w(t	PROPN
ejpam-3529	165	19	)	)	PUNCT
ejpam-3529	165	20	on	on	ADP
ejpam-3529	165	21	i.	i.	PROPN
ejpam-3529	165	22	clearly	clearly	ADV
ejpam-3529	165	23	w′(t	w′(t	NOUN
ejpam-3529	165	24	)	)	PUNCT
ejpam-3529	165	25	≥	≥	NOUN
ejpam-3529	165	26	0	0	NUM
ejpam-3529	165	27	,	,	PUNCT
ejpam-3529	165	28	which	which	PRON
ejpam-3529	165	29	means	mean	VERB
ejpam-3529	165	30	that	that	SCONJ
ejpam-3529	165	31	w(t	w(t	PROPN
ejpam-3529	165	32	)	)	PUNCT
ejpam-3529	165	33	is	be	AUX
ejpam-3529	165	34	nondecreasing	nondecrease	VERB
ejpam-3529	165	35	on	on	ADP
ejpam-3529	165	36	i.	i.	PROPN
ejpam-3529	165	37	now	now	ADV
ejpam-3529	165	38	for	for	ADP
ejpam-3529	165	39	t	t	PROPN
ejpam-3529	165	40	∈	∈	PROPN
ejpam-3529	165	41	i	i	PROPN
ejpam-3529	165	42	,	,	PUNCT
ejpam-3529	165	43	w(t	w(t	PROPN
ejpam-3529	165	44	)	)	PUNCT
ejpam-3529	165	45	≤	≤	PUNCT
ejpam-3529	165	46	nk1	nk1	NOUN
ejpam-3529	165	47	t∫	t∫	PRON
ejpam-3529	165	48	0	0	NUM
ejpam-3529	165	49	z∫	z∫	NOUN
ejpam-3529	165	50	0	0	PUNCT
ejpam-3529	166	1	p̃n+1(s)e	p̃n+1(s)e	VERB
ejpam-3529	166	2	m(z−s)dsdz	m(z−s)dsdz	PROPN
ejpam-3529	166	3	+	+	CCONJ
ejpam-3529	166	4	t∫	t∫	ADJ
ejpam-3529	166	5	0	0	NUM
ejpam-3529	166	6	lemudu	lemudu	NOUN
ejpam-3529	166	7	≤	≤	NUM
ejpam-3529	166	8	nk1	nk1	NOUN
ejpam-3529	166	9	t∫	t∫	PRON
ejpam-3529	166	10	0	0	NUM
ejpam-3529	166	11	z∫	z∫	NOUN
ejpam-3529	166	12	0	0	NUM
ejpam-3529	166	13	w(z)em(z−s)dsdz	w(z)em(z−s)dsdz	PROPN
ejpam-3529	166	14	+	+	CCONJ
ejpam-3529	166	15	l[max[0,t	l[max[0,t	NOUN
ejpam-3529	166	16	]	]	X
ejpam-3529	166	17	{	{	PUNCT
ejpam-3529	166	18	e	e	PROPN
ejpam-3529	166	19	mt	mt	PROPN
ejpam-3529	166	20	m	m	PROPN
ejpam-3529	166	21	−	−	PROPN
ejpam-3529	166	22	1	1	NUM
ejpam-3529	166	23	m	m	NOUN
ejpam-3529	166	24	}	}	PUNCT
ejpam-3529	166	25	]	]	PUNCT
ejpam-3529	166	26	≤	≤	NUM
ejpam-3529	166	27	nk1	nk1	NOUN
ejpam-3529	166	28	t∫	t∫	PRON
ejpam-3529	166	29	0	0	NUM
ejpam-3529	166	30	z∫	z∫	NOUN
ejpam-3529	166	31	0	0	NUM
ejpam-3529	166	32	w(z)em(z−s)dsdz	w(z)em(z−s)dsdz	PROPN
ejpam-3529	166	33	+	+	CCONJ
ejpam-3529	166	34	l[max[0,t	l[max[0,t	NOUN
ejpam-3529	166	35	]	]	X
ejpam-3529	166	36	{	{	PUNCT
ejpam-3529	166	37	e	e	X
ejpam-3529	166	38	mt	mt	PROPN
ejpam-3529	166	39	m	m	PROPN
ejpam-3529	166	40	}	}	PUNCT
ejpam-3529	166	41	]	]	PUNCT
ejpam-3529	166	42	≤	≤	NUM
ejpam-3529	166	43	nk1	nk1	NOUN
ejpam-3529	166	44	t∫	t∫	PRON
ejpam-3529	166	45	0	0	NUM
ejpam-3529	166	46	z∫	z∫	NOUN
ejpam-3529	166	47	0	0	NUM
ejpam-3529	166	48	w(z)em(z−s)dsdz	w(z)em(z−s)dsdz	X
ejpam-3529	166	49	+	+	SYM
ejpam-3529	166	50	l	l	NOUN
ejpam-3529	166	51	{	{	PUNCT
ejpam-3529	166	52	emt	emt	PROPN
ejpam-3529	166	53	m	m	VERB
ejpam-3529	166	54	}	}	PUNCT
ejpam-3529	166	55	by	by	ADP
ejpam-3529	166	56	setting	set	VERB
ejpam-3529	166	57	c2	c2	PROPN
ejpam-3529	166	58	=	=	SYM
ejpam-3529	166	59	l	l	PROPN
ejpam-3529	166	60	{	{	PUNCT
ejpam-3529	166	61	emt	emt	PROPN
ejpam-3529	166	62	m	m	PROPN
ejpam-3529	166	63	}	}	PUNCT
ejpam-3529	166	64	and	and	CCONJ
ejpam-3529	166	65	c1	c1	PROPN
ejpam-3529	166	66	=	=	PUNCT
ejpam-3529	166	67	n	n	CCONJ
ejpam-3529	166	68	m	m	PROPN
ejpam-3529	166	69	k1e	k1e	PROPN
ejpam-3529	166	70	mt	mt	PROPN
ejpam-3529	166	71	we	we	PRON
ejpam-3529	166	72	get	get	VERB
ejpam-3529	166	73	w(t	w(t	PROPN
ejpam-3529	166	74	)	)	PUNCT
ejpam-3529	167	1	≤	≤	PROPN
ejpam-3529	167	2	c1	c1	PROPN
ejpam-3529	167	3	t∫	t∫	PROPN
ejpam-3529	167	4	0	0	NUM
ejpam-3529	167	5	w(z)dz	w(z)dz	PROPN
ejpam-3529	167	6	+	+	PROPN
ejpam-3529	167	7	c2	c2	PROPN
ejpam-3529	167	8	.	.	PUNCT
ejpam-3529	168	1	now	now	ADV
ejpam-3529	168	2	by	by	ADP
ejpam-3529	168	3	using	use	VERB
ejpam-3529	168	4	gronwall	gronwall	PROPN
ejpam-3529	168	5	’s	’s	PART
ejpam-3529	168	6	inequality	inequality	NOUN
ejpam-3529	168	7	we	we	PRON
ejpam-3529	168	8	get	get	VERB
ejpam-3529	168	9	w(t	w(t	PROPN
ejpam-3529	168	10	)	)	PUNCT
ejpam-3529	168	11	≤	≤	NUM
ejpam-3529	168	12	c2e	c2e	NOUN
ejpam-3529	168	13	t∫	t∫	ADJ
ejpam-3529	168	14	0	0	NUM
ejpam-3529	168	15	c1ds	c1ds	NOUN
ejpam-3529	168	16	ch	ch	NOUN
ejpam-3529	168	17	.	.	PROPN
ejpam-3529	169	1	v.	v.	ADP
ejpam-3529	169	2	sreedhar	sreedhar	PROPN
ejpam-3529	169	3	,	,	PUNCT
ejpam-3529	169	4	j.	j.	PROPN
ejpam-3529	169	5	vasundhara	vasundhara	PROPN
ejpam-3529	169	6	devi	devi	PROPN
ejpam-3529	169	7	,	,	PUNCT
ejpam-3529	169	8	/	/	SYM
ejpam-3529	169	9	eur	eur	NOUN
ejpam-3529	169	10	.	.	PUNCT
ejpam-3529	170	1	j.	j.	PROPN
ejpam-3529	170	2	pure	pure	PROPN
ejpam-3529	170	3	appl	appl	PROPN
ejpam-3529	170	4	.	.	PROPN
ejpam-3529	170	5	math	math	PROPN
ejpam-3529	170	6	,	,	PUNCT
ejpam-3529	170	7	12	12	NUM
ejpam-3529	170	8	(	(	PUNCT
ejpam-3529	170	9	4	4	NUM
ejpam-3529	170	10	)	)	PUNCT
ejpam-3529	170	11	(	(	PUNCT
ejpam-3529	170	12	2019	2019	NUM
ejpam-3529	170	13	)	)	PUNCT
ejpam-3529	170	14	,	,	PUNCT
ejpam-3529	170	15	1662	1662	NUM
ejpam-3529	170	16	-	-	SYM
ejpam-3529	170	17	1675	1675	NUM
ejpam-3529	170	18	1670	1670	NUM
ejpam-3529	170	19	≤	≤	NUM
ejpam-3529	170	20	c2ec1	c2ec1	NOUN
ejpam-3529	170	21	t	t	PROPN
ejpam-3529	170	22	≤	≤	NUM
ejpam-3529	170	23	c2ec1	c2ec1	PROPN
ejpam-3529	170	24	t	t	PROPN
ejpam-3529	170	25	.	.	PUNCT
ejpam-3529	171	1	hence	hence	ADV
ejpam-3529	171	2	p̃n+1(t	p̃n+1(t	ADJ
ejpam-3529	171	3	)	)	PUNCT
ejpam-3529	171	4	≤	≤	NUM
ejpam-3529	171	5	w(t	w(t	PROPN
ejpam-3529	171	6	)	)	PUNCT
ejpam-3529	171	7	≤	≤	PUNCT
ejpam-3529	172	1	max[0,t	max[0,t	PROPN
ejpam-3529	172	2	]	]	PUNCT
ejpam-3529	172	3	l(t)[emt]ec1	l(t)[emt]ec1	PROPN
ejpam-3529	172	4	t	t	PROPN
ejpam-3529	172	5	p̃n+1(t	p̃n+1(t	NOUN
ejpam-3529	172	6	)	)	PUNCT
ejpam-3529	172	7	≤	≤	NUM
ejpam-3529	172	8	w(t	w(t	PROPN
ejpam-3529	172	9	)	)	PUNCT
ejpam-3529	172	10	≤	≤	PUNCT
ejpam-3529	173	1	max[0,t	max[0,t	PROPN
ejpam-3529	173	2	]	]	X
ejpam-3529	173	3	l(t)[e(m+c1)t	l(t)[e(m+c1)t	X
ejpam-3529	173	4	]	]	X
ejpam-3529	173	5	|pn+1|	|pn+1|	X
ejpam-3529	173	6	≤	≤	NOUN
ejpam-3529	173	7	(	(	PUNCT
ejpam-3529	173	8	e(n1+c1)t	e(n1+c1)t	NOUN
ejpam-3529	173	9	)	)	PUNCT
ejpam-3529	174	1	[	[	X
ejpam-3529	174	2	m	m	NOUN
ejpam-3529	174	3	|pn|2	|pn|2	ADP
ejpam-3529	174	4	]	]	X
ejpam-3529	174	5	,	,	PUNCT
ejpam-3529	174	6	therefore	therefore	ADV
ejpam-3529	174	7	the	the	DET
ejpam-3529	174	8	sequence	sequence	NOUN
ejpam-3529	174	9	{	{	PUNCT
ejpam-3529	174	10	αn	αn	NOUN
ejpam-3529	174	11	}	}	PUNCT
ejpam-3529	174	12	converges	converge	VERB
ejpam-3529	174	13	quadratically	quadratically	ADV
ejpam-3529	174	14	on	on	ADP
ejpam-3529	174	15	i.	i.	NOUN
ejpam-3529	174	16	hence	hence	ADV
ejpam-3529	174	17	the	the	DET
ejpam-3529	174	18	theorem	theorem	NOUN
ejpam-3529	174	19	.	.	PROPN
ejpam-3529	174	20	4	4	NUM
ejpam-3529	174	21	.	.	NOUN
ejpam-3529	174	22	generalized	generalize	VERB
ejpam-3529	174	23	quasilinearization	quasilinearization	NOUN
ejpam-3529	174	24	for	for	ADP
ejpam-3529	174	25	periodic	periodic	ADJ
ejpam-3529	174	26	boundary	boundary	ADJ
ejpam-3529	174	27	value	value	NOUN
ejpam-3529	174	28	problem	problem	NOUN
ejpam-3529	174	29	in	in	ADP
ejpam-3529	174	30	this	this	DET
ejpam-3529	174	31	section	section	NOUN
ejpam-3529	174	32	an	an	DET
ejpam-3529	174	33	existence	existence	NOUN
ejpam-3529	174	34	and	and	CCONJ
ejpam-3529	174	35	uniqueness	uniqueness	NOUN
ejpam-3529	174	36	result	result	NOUN
ejpam-3529	174	37	is	be	AUX
ejpam-3529	174	38	obtained	obtain	VERB
ejpam-3529	174	39	for	for	ADP
ejpam-3529	174	40	an	an	DET
ejpam-3529	174	41	pbvp	pbvp	NOUN
ejpam-3529	174	42	of	of	ADP
ejpam-3529	174	43	an	an	DET
ejpam-3529	174	44	integro	integro	ADJ
ejpam-3529	174	45	differential	differential	ADJ
ejpam-3529	174	46	equation	equation	NOUN
ejpam-3529	174	47	using	use	VERB
ejpam-3529	174	48	the	the	DET
ejpam-3529	174	49	method	method	NOUN
ejpam-3529	174	50	of	of	ADP
ejpam-3529	174	51	generalized	generalized	ADJ
ejpam-3529	174	52	quasilinearization	quasilinearization	NOUN
ejpam-3529	174	53	.	.	PUNCT
ejpam-3529	175	1	for	for	ADP
ejpam-3529	175	2	this	this	DET
ejpam-3529	175	3	first	first	ADV
ejpam-3529	175	4	we	we	PRON
ejpam-3529	175	5	define	define	VERB
ejpam-3529	175	6	the	the	DET
ejpam-3529	175	7	various	various	ADJ
ejpam-3529	175	8	types	type	NOUN
ejpam-3529	175	9	of	of	ADP
ejpam-3529	175	10	lower	low	ADJ
ejpam-3529	175	11	and	and	CCONJ
ejpam-3529	175	12	upper	upper	ADJ
ejpam-3529	175	13	solutions	solution	NOUN
ejpam-3529	175	14	for	for	ADP
ejpam-3529	175	15	the	the	DET
ejpam-3529	175	16	periodic	periodic	ADJ
ejpam-3529	175	17	boundary	boundary	ADJ
ejpam-3529	175	18	value	value	NOUN
ejpam-3529	175	19	problem	problem	NOUN
ejpam-3529	175	20	of	of	ADP
ejpam-3529	175	21	an	an	DET
ejpam-3529	175	22	integro	integro	ADJ
ejpam-3529	175	23	differential	differential	ADJ
ejpam-3529	175	24	equation	equation	NOUN
ejpam-3529	175	25	given	give	VERB
ejpam-3529	175	26	by	by	ADP
ejpam-3529	175	27	x′	x′	PROPN
ejpam-3529	175	28	=	=	SYM
ejpam-3529	175	29	f1(t	f1(t	PROPN
ejpam-3529	175	30	,	,	PUNCT
ejpam-3529	175	31	x	x	NOUN
ejpam-3529	175	32	,	,	PUNCT
ejpam-3529	175	33	sx	sx	PROPN
ejpam-3529	175	34	)	)	PUNCT
ejpam-3529	175	35	+	+	CCONJ
ejpam-3529	175	36	f2(t	f2(t	PROPN
ejpam-3529	175	37	,	,	PUNCT
ejpam-3529	175	38	x	x	NOUN
ejpam-3529	175	39	,	,	PUNCT
ejpam-3529	175	40	sx	sx	PROPN
ejpam-3529	175	41	)	)	PUNCT
ejpam-3529	175	42	,	,	PUNCT
ejpam-3529	175	43	(	(	PUNCT
ejpam-3529	175	44	15	15	NUM
ejpam-3529	175	45	)	)	PUNCT
ejpam-3529	175	46	x(0	x(0	PROPN
ejpam-3529	175	47	)	)	PUNCT
ejpam-3529	175	48	=	=	SYM
ejpam-3529	175	49	x(t	x(t	PROPN
ejpam-3529	175	50	)	)	PUNCT
ejpam-3529	175	51	,	,	PUNCT
ejpam-3529	175	52	(	(	PUNCT
ejpam-3529	175	53	16	16	NUM
ejpam-3529	175	54	)	)	PUNCT
ejpam-3529	175	55	where	where	SCONJ
ejpam-3529	175	56	f1	f1	NOUN
ejpam-3529	175	57	,	,	PUNCT
ejpam-3529	175	58	f2	f2	PROPN
ejpam-3529	175	59	∈	∈	PROPN
ejpam-3529	175	60	c[i×rn×rn	c[i×rn×rn	NOUN
ejpam-3529	175	61	,	,	PUNCT
ejpam-3529	175	62	rn	rn	NOUN
ejpam-3529	175	63	]	]	NOUN
ejpam-3529	175	64	,	,	PUNCT
ejpam-3529	175	65	sx(t	sx(t	X
ejpam-3529	175	66	)	)	PUNCT
ejpam-3529	175	67	=	=	SYM
ejpam-3529	176	1	t∫	t∫	NOUN
ejpam-3529	176	2	0	0	NUM
ejpam-3529	176	3	k(t	k(t	NOUN
ejpam-3529	176	4	,	,	PUNCT
ejpam-3529	176	5	s)x(s)ds	s)x(s)ds	NOUN
ejpam-3529	176	6	,	,	PUNCT
ejpam-3529	176	7	and	and	CCONJ
ejpam-3529	176	8	k	k	PROPN
ejpam-3529	176	9	∈	∈	PROPN
ejpam-3529	176	10	c[i×i	c[i×i	PROPN
ejpam-3529	176	11	,	,	PUNCT
ejpam-3529	176	12	r+	r+	X
ejpam-3529	176	13	]	]	PUNCT
ejpam-3529	176	14	,	,	PUNCT
ejpam-3529	176	15	i=[0,t	i=[0,t	PROPN
ejpam-3529	176	16	]	]	PUNCT
ejpam-3529	176	17	.	.	PUNCT
ejpam-3529	177	1	definition	definition	NOUN
ejpam-3529	177	2	2	2	NUM
ejpam-3529	177	3	.	.	PUNCT
ejpam-3529	177	4	let	let	VERB
ejpam-3529	177	5	α0	α0	ADJ
ejpam-3529	177	6	,	,	PUNCT
ejpam-3529	177	7	β0	β0	PROPN
ejpam-3529	177	8	∈	∈	PROPN
ejpam-3529	177	9	c1[i	c1[i	PROPN
ejpam-3529	177	10	,	,	PUNCT
ejpam-3529	177	11	rn	rn	PROPN
ejpam-3529	177	12	]	]	PUNCT
ejpam-3529	177	13	.	.	PUNCT
ejpam-3529	178	1	then	then	ADV
ejpam-3529	178	2	α0	α0	ADJ
ejpam-3529	178	3	,	,	PUNCT
ejpam-3529	178	4	β0	β0	PROPN
ejpam-3529	178	5	are	be	AUX
ejpam-3529	178	6	said	say	VERB
ejpam-3529	178	7	to	to	PART
ejpam-3529	178	8	be	be	AUX
ejpam-3529	178	9	(	(	PUNCT
ejpam-3529	178	10	a	a	PRON
ejpam-3529	178	11	)	)	PUNCT
ejpam-3529	178	12	natural	natural	ADJ
ejpam-3529	178	13	lower	low	ADJ
ejpam-3529	178	14	and	and	CCONJ
ejpam-3529	178	15	upper	upper	ADJ
ejpam-3529	178	16	solutions	solution	NOUN
ejpam-3529	178	17	of	of	ADP
ejpam-3529	178	18	(	(	PUNCT
ejpam-3529	178	19	15	15	NUM
ejpam-3529	178	20	)	)	PUNCT
ejpam-3529	178	21	and	and	CCONJ
ejpam-3529	178	22	(	(	PUNCT
ejpam-3529	178	23	16	16	NUM
ejpam-3529	178	24	)	)	PUNCT
ejpam-3529	178	25	if	if	SCONJ
ejpam-3529	178	26	α′0	α′0	NOUN
ejpam-3529	178	27	≤	≤	PROPN
ejpam-3529	178	28	f1(t	f1(t	PROPN
ejpam-3529	178	29	,	,	PUNCT
ejpam-3529	178	30	α0	α0	ADJ
ejpam-3529	178	31	,	,	PUNCT
ejpam-3529	178	32	sα0	sα0	NOUN
ejpam-3529	178	33	)	)	PUNCT
ejpam-3529	179	1	+	+	CCONJ
ejpam-3529	179	2	f2(t	f2(t	PROPN
ejpam-3529	179	3	,	,	PUNCT
ejpam-3529	179	4	α0	α0	ADJ
ejpam-3529	179	5	,	,	PUNCT
ejpam-3529	179	6	sα0	sα0	NOUN
ejpam-3529	179	7	)	)	PUNCT
ejpam-3529	179	8	,	,	PUNCT
ejpam-3529	179	9	α0(0	α0(0	PROPN
ejpam-3529	179	10	)	)	PUNCT
ejpam-3529	179	11	≤	≤	NOUN
ejpam-3529	179	12	α0(t	α0(t	NUM
ejpam-3529	179	13	)	)	PUNCT
ejpam-3529	179	14	,	,	PUNCT
ejpam-3529	179	15	β′0	β′0	PRON
ejpam-3529	179	16	≥	≥	NOUN
ejpam-3529	179	17	f1(t	f1(t	PROPN
ejpam-3529	179	18	,	,	PUNCT
ejpam-3529	179	19	β0	β0	NOUN
ejpam-3529	179	20	,	,	PUNCT
ejpam-3529	179	21	sβ0	sβ0	NOUN
ejpam-3529	179	22	)	)	PUNCT
ejpam-3529	179	23	+	+	CCONJ
ejpam-3529	179	24	f2(t	f2(t	PROPN
ejpam-3529	179	25	,	,	PUNCT
ejpam-3529	179	26	β0	β0	NOUN
ejpam-3529	179	27	,	,	PUNCT
ejpam-3529	179	28	sβ0	sβ0	NOUN
ejpam-3529	179	29	)	)	PUNCT
ejpam-3529	179	30	,	,	PUNCT
ejpam-3529	179	31	β0(0	β0(0	PROPN
ejpam-3529	179	32	)	)	PUNCT
ejpam-3529	179	33	≥	≥	NOUN
ejpam-3529	179	34	β0(t	β0(t	X
ejpam-3529	179	35	)	)	PUNCT
ejpam-3529	179	36	,	,	PUNCT
ejpam-3529	179	37	t	t	PROPN
ejpam-3529	179	38	∈	∈	PROPN
ejpam-3529	180	1	i	i	PRON
ejpam-3529	180	2	;	;	PUNCT
ejpam-3529	180	3	}	}	PUNCT
ejpam-3529	180	4	(	(	PUNCT
ejpam-3529	180	5	17	17	NUM
ejpam-3529	180	6	)	)	PUNCT
ejpam-3529	180	7	(	(	PUNCT
ejpam-3529	180	8	b	b	X
ejpam-3529	180	9	)	)	PUNCT
ejpam-3529	180	10	coupled	couple	VERB
ejpam-3529	180	11	lower	low	ADJ
ejpam-3529	180	12	and	and	CCONJ
ejpam-3529	180	13	upper	upper	ADJ
ejpam-3529	180	14	solutions	solution	NOUN
ejpam-3529	180	15	of	of	ADP
ejpam-3529	180	16	type	type	NOUN
ejpam-3529	180	17	i	i	PRON
ejpam-3529	180	18	of	of	ADP
ejpam-3529	180	19	(	(	PUNCT
ejpam-3529	180	20	15	15	NUM
ejpam-3529	180	21	)	)	PUNCT
ejpam-3529	180	22	and	and	CCONJ
ejpam-3529	180	23	(	(	PUNCT
ejpam-3529	180	24	16	16	NUM
ejpam-3529	180	25	)	)	PUNCT
ejpam-3529	180	26	if	if	SCONJ
ejpam-3529	180	27	α′0	α′0	NOUN
ejpam-3529	180	28	≤	≤	PROPN
ejpam-3529	180	29	f1(t	f1(t	PROPN
ejpam-3529	180	30	,	,	PUNCT
ejpam-3529	180	31	α0	α0	ADJ
ejpam-3529	180	32	,	,	PUNCT
ejpam-3529	180	33	sα0	sα0	NOUN
ejpam-3529	180	34	)	)	PUNCT
ejpam-3529	181	1	+	+	CCONJ
ejpam-3529	181	2	f2(t	f2(t	PROPN
ejpam-3529	181	3	,	,	PUNCT
ejpam-3529	181	4	β0	β0	NOUN
ejpam-3529	181	5	,	,	PUNCT
ejpam-3529	181	6	sβ0	sβ0	NOUN
ejpam-3529	181	7	)	)	PUNCT
ejpam-3529	181	8	,	,	PUNCT
ejpam-3529	181	9	α0(0	α0(0	PROPN
ejpam-3529	181	10	)	)	PUNCT
ejpam-3529	181	11	≤	≤	NOUN
ejpam-3529	181	12	α0(t	α0(t	NUM
ejpam-3529	181	13	)	)	PUNCT
ejpam-3529	181	14	,	,	PUNCT
ejpam-3529	181	15	β′0	β′0	PRON
ejpam-3529	181	16	≥	≥	NOUN
ejpam-3529	181	17	f1(t	f1(t	PROPN
ejpam-3529	181	18	,	,	PUNCT
ejpam-3529	181	19	β0	β0	NOUN
ejpam-3529	181	20	,	,	PUNCT
ejpam-3529	181	21	sβ0	sβ0	NOUN
ejpam-3529	181	22	)	)	PUNCT
ejpam-3529	181	23	+	+	CCONJ
ejpam-3529	181	24	f2(t	f2(t	PROPN
ejpam-3529	181	25	,	,	PUNCT
ejpam-3529	181	26	α0	α0	ADJ
ejpam-3529	181	27	,	,	PUNCT
ejpam-3529	181	28	sα0	sα0	NOUN
ejpam-3529	181	29	)	)	PUNCT
ejpam-3529	181	30	,	,	PUNCT
ejpam-3529	181	31	β0(0	β0(0	PROPN
ejpam-3529	181	32	)	)	PUNCT
ejpam-3529	181	33	≥	≥	NOUN
ejpam-3529	181	34	β0(t	β0(t	X
ejpam-3529	181	35	)	)	PUNCT
ejpam-3529	181	36	,	,	PUNCT
ejpam-3529	181	37	t	t	PROPN
ejpam-3529	181	38	∈	∈	PROPN
ejpam-3529	182	1	i	i	PRON
ejpam-3529	182	2	;	;	PUNCT
ejpam-3529	182	3	}	}	PUNCT
ejpam-3529	182	4	(	(	PUNCT
ejpam-3529	182	5	18	18	NUM
ejpam-3529	182	6	)	)	PUNCT
ejpam-3529	182	7	(	(	PUNCT
ejpam-3529	182	8	c	c	X
ejpam-3529	182	9	)	)	PUNCT
ejpam-3529	182	10	coupled	couple	VERB
ejpam-3529	182	11	lower	low	ADJ
ejpam-3529	182	12	and	and	CCONJ
ejpam-3529	182	13	upper	upper	ADJ
ejpam-3529	182	14	solutions	solution	NOUN
ejpam-3529	182	15	of	of	ADP
ejpam-3529	182	16	type	type	NOUN
ejpam-3529	182	17	ii	ii	PROPN
ejpam-3529	182	18	of	of	ADP
ejpam-3529	182	19	(	(	PUNCT
ejpam-3529	182	20	15	15	NUM
ejpam-3529	182	21	)	)	PUNCT
ejpam-3529	182	22	and	and	CCONJ
ejpam-3529	182	23	(	(	PUNCT
ejpam-3529	182	24	16	16	NUM
ejpam-3529	182	25	)	)	PUNCT
ejpam-3529	182	26	if	if	SCONJ
ejpam-3529	182	27	α′0	α′0	NOUN
ejpam-3529	182	28	≤	≤	PROPN
ejpam-3529	182	29	f1(t	f1(t	PROPN
ejpam-3529	182	30	,	,	PUNCT
ejpam-3529	182	31	β0	β0	NOUN
ejpam-3529	182	32	,	,	PUNCT
ejpam-3529	182	33	sβ0	sβ0	NOUN
ejpam-3529	182	34	)	)	PUNCT
ejpam-3529	183	1	+	+	CCONJ
ejpam-3529	183	2	f2(t	f2(t	PROPN
ejpam-3529	183	3	,	,	PUNCT
ejpam-3529	183	4	α0	α0	ADJ
ejpam-3529	183	5	,	,	PUNCT
ejpam-3529	183	6	sα0	sα0	NOUN
ejpam-3529	183	7	)	)	PUNCT
ejpam-3529	183	8	,	,	PUNCT
ejpam-3529	183	9	α0(0	α0(0	PROPN
ejpam-3529	183	10	)	)	PUNCT
ejpam-3529	183	11	≤	≤	NOUN
ejpam-3529	183	12	α0(t	α0(t	NUM
ejpam-3529	183	13	)	)	PUNCT
ejpam-3529	183	14	,	,	PUNCT
ejpam-3529	183	15	β′0	β′0	PRON
ejpam-3529	183	16	≥	≥	NOUN
ejpam-3529	183	17	f1(t	f1(t	PROPN
ejpam-3529	183	18	,	,	PUNCT
ejpam-3529	183	19	α0	α0	ADJ
ejpam-3529	183	20	,	,	PUNCT
ejpam-3529	183	21	sα0	sα0	NOUN
ejpam-3529	183	22	)	)	PUNCT
ejpam-3529	184	1	+	+	CCONJ
ejpam-3529	184	2	f2(t	f2(t	PROPN
ejpam-3529	184	3	,	,	PUNCT
ejpam-3529	184	4	β0	β0	NOUN
ejpam-3529	184	5	,	,	PUNCT
ejpam-3529	184	6	sβ0	sβ0	NOUN
ejpam-3529	184	7	)	)	PUNCT
ejpam-3529	184	8	,	,	PUNCT
ejpam-3529	184	9	β0(0	β0(0	PROPN
ejpam-3529	184	10	)	)	PUNCT
ejpam-3529	184	11	≥	≥	NOUN
ejpam-3529	184	12	β0(t	β0(t	X
ejpam-3529	184	13	)	)	PUNCT
ejpam-3529	184	14	,	,	PUNCT
ejpam-3529	184	15	t	t	PROPN
ejpam-3529	184	16	∈	∈	PROPN
ejpam-3529	185	1	i	i	PRON
ejpam-3529	185	2	;	;	PUNCT
ejpam-3529	185	3	}	}	PUNCT
ejpam-3529	185	4	(	(	PUNCT
ejpam-3529	185	5	19	19	NUM
ejpam-3529	185	6	)	)	PUNCT
ejpam-3529	185	7	(	(	PUNCT
ejpam-3529	185	8	d	d	X
ejpam-3529	185	9	)	)	PUNCT
ejpam-3529	185	10	coupled	couple	VERB
ejpam-3529	185	11	lower	low	ADJ
ejpam-3529	185	12	and	and	CCONJ
ejpam-3529	185	13	upper	upper	ADJ
ejpam-3529	185	14	solutions	solution	NOUN
ejpam-3529	185	15	of	of	ADP
ejpam-3529	185	16	type	type	NOUN
ejpam-3529	185	17	iii	iii	PROPN
ejpam-3529	185	18	of	of	ADP
ejpam-3529	185	19	(	(	PUNCT
ejpam-3529	185	20	15	15	NUM
ejpam-3529	185	21	)	)	PUNCT
ejpam-3529	185	22	and	and	CCONJ
ejpam-3529	185	23	(	(	PUNCT
ejpam-3529	185	24	16	16	NUM
ejpam-3529	185	25	)	)	PUNCT
ejpam-3529	185	26	if	if	SCONJ
ejpam-3529	185	27	α′0	α′0	NOUN
ejpam-3529	185	28	≤	≤	PROPN
ejpam-3529	185	29	f1(t	f1(t	PROPN
ejpam-3529	185	30	,	,	PUNCT
ejpam-3529	185	31	β0	β0	NOUN
ejpam-3529	185	32	,	,	PUNCT
ejpam-3529	185	33	sβ0	sβ0	NOUN
ejpam-3529	185	34	)	)	PUNCT
ejpam-3529	186	1	+	+	CCONJ
ejpam-3529	186	2	f2(t	f2(t	PROPN
ejpam-3529	186	3	,	,	PUNCT
ejpam-3529	186	4	β0	β0	NOUN
ejpam-3529	186	5	,	,	PUNCT
ejpam-3529	186	6	sβ0	sβ0	NOUN
ejpam-3529	186	7	)	)	PUNCT
ejpam-3529	186	8	,	,	PUNCT
ejpam-3529	186	9	α0(0	α0(0	PROPN
ejpam-3529	186	10	)	)	PUNCT
ejpam-3529	186	11	≤	≤	NOUN
ejpam-3529	187	1	α0(t	α0(t	NUM
ejpam-3529	187	2	)	)	PUNCT
ejpam-3529	187	3	,	,	PUNCT
ejpam-3529	187	4	β′0	β′0	PRON
ejpam-3529	187	5	≥	≥	NOUN
ejpam-3529	187	6	f1(t	f1(t	PROPN
ejpam-3529	187	7	,	,	PUNCT
ejpam-3529	187	8	α0	α0	ADJ
ejpam-3529	187	9	,	,	PUNCT
ejpam-3529	187	10	sα0	sα0	NOUN
ejpam-3529	187	11	)	)	PUNCT
ejpam-3529	187	12	+	+	CCONJ
ejpam-3529	187	13	f2(t	f2(t	PROPN
ejpam-3529	187	14	,	,	PUNCT
ejpam-3529	187	15	α0	α0	ADJ
ejpam-3529	187	16	,	,	PUNCT
ejpam-3529	187	17	sα0	sα0	NOUN
ejpam-3529	187	18	)	)	PUNCT
ejpam-3529	187	19	,	,	PUNCT
ejpam-3529	187	20	β0(0	β0(0	PROPN
ejpam-3529	187	21	)	)	PUNCT
ejpam-3529	187	22	≥	≥	NOUN
ejpam-3529	187	23	β0(t	β0(t	X
ejpam-3529	187	24	)	)	PUNCT
ejpam-3529	187	25	,	,	PUNCT
ejpam-3529	187	26	t	t	PROPN
ejpam-3529	187	27	∈	∈	PROPN
ejpam-3529	187	28	i.	i.	PROPN
ejpam-3529	187	29	}	}	PUNCT
ejpam-3529	187	30	(	(	PUNCT
ejpam-3529	187	31	20	20	NUM
ejpam-3529	187	32	)	)	PUNCT
ejpam-3529	187	33	ch	ch	NOUN
ejpam-3529	187	34	.	.	PUNCT
ejpam-3529	188	1	v.	v.	ADP
ejpam-3529	188	2	sreedhar	sreedhar	PROPN
ejpam-3529	188	3	,	,	PUNCT
ejpam-3529	188	4	j.	j.	PROPN
ejpam-3529	188	5	vasundhara	vasundhara	PROPN
ejpam-3529	188	6	devi	devi	PROPN
ejpam-3529	188	7	,	,	PUNCT
ejpam-3529	188	8	/	/	SYM
ejpam-3529	188	9	eur	eur	NOUN
ejpam-3529	188	10	.	.	PUNCT
ejpam-3529	189	1	j.	j.	PROPN
ejpam-3529	189	2	pure	pure	PROPN
ejpam-3529	189	3	appl	appl	PROPN
ejpam-3529	189	4	.	.	PROPN
ejpam-3529	189	5	math	math	PROPN
ejpam-3529	189	6	,	,	PUNCT
ejpam-3529	189	7	12	12	NUM
ejpam-3529	189	8	(	(	PUNCT
ejpam-3529	189	9	4	4	NUM
ejpam-3529	189	10	)	)	PUNCT
ejpam-3529	189	11	(	(	PUNCT
ejpam-3529	189	12	2019	2019	NUM
ejpam-3529	189	13	)	)	PUNCT
ejpam-3529	189	14	,	,	PUNCT
ejpam-3529	189	15	1662	1662	NUM
ejpam-3529	189	16	-	-	SYM
ejpam-3529	189	17	1675	1675	NUM
ejpam-3529	189	18	1671	1671	NUM
ejpam-3529	189	19	now	now	ADV
ejpam-3529	189	20	we	we	PRON
ejpam-3529	189	21	will	will	AUX
ejpam-3529	189	22	prove	prove	VERB
ejpam-3529	189	23	the	the	DET
ejpam-3529	189	24	following	follow	VERB
ejpam-3529	189	25	theorem	theorem	NOUN
ejpam-3529	189	26	related	relate	VERB
ejpam-3529	189	27	to	to	ADP
ejpam-3529	189	28	coupled	couple	VERB
ejpam-3529	189	29	lower	low	ADJ
ejpam-3529	189	30	and	and	CCONJ
ejpam-3529	189	31	upper	upper	ADJ
ejpam-3529	189	32	solutions	solution	NOUN
ejpam-3529	189	33	of	of	ADP
ejpam-3529	189	34	type	type	NOUN
ejpam-3529	190	1	i	i	PRON
ejpam-3529	190	2	and	and	CCONJ
ejpam-3529	190	3	we	we	PRON
ejpam-3529	190	4	develop	develop	VERB
ejpam-3529	190	5	the	the	DET
ejpam-3529	190	6	generalized	generalized	ADJ
ejpam-3529	190	7	quasilinearization	quasilinearization	NOUN
ejpam-3529	190	8	method	method	NOUN
ejpam-3529	190	9	for	for	ADP
ejpam-3529	190	10	the	the	DET
ejpam-3529	190	11	periodic	periodic	ADJ
ejpam-3529	190	12	boundary	boundary	ADJ
ejpam-3529	190	13	value	value	NOUN
ejpam-3529	190	14	problem	problem	NOUN
ejpam-3529	190	15	of	of	ADP
ejpam-3529	190	16	an	an	DET
ejpam-3529	190	17	integro	integro	ADJ
ejpam-3529	190	18	diffential	diffential	ADJ
ejpam-3529	190	19	equation	equation	NOUN
ejpam-3529	190	20	via	via	ADP
ejpam-3529	190	21	the	the	DET
ejpam-3529	190	22	initial	initial	ADJ
ejpam-3529	190	23	value	value	NOUN
ejpam-3529	190	24	problem	problem	NOUN
ejpam-3529	190	25	approach	approach	NOUN
ejpam-3529	190	26	.	.	PUNCT
ejpam-3529	191	1	theorem	theorem	NOUN
ejpam-3529	191	2	2	2	NUM
ejpam-3529	191	3	.	.	PUNCT
ejpam-3529	191	4	suppose	suppose	VERB
ejpam-3529	191	5	that	that	SCONJ
ejpam-3529	191	6	the	the	DET
ejpam-3529	191	7	assumptions	assumption	NOUN
ejpam-3529	191	8	of	of	ADP
ejpam-3529	191	9	theorem	theorem	ADJ
ejpam-3529	191	10	1	1	NUM
ejpam-3529	191	11	are	be	AUX
ejpam-3529	191	12	satisfied	satisfied	ADJ
ejpam-3529	191	13	.	.	PUNCT
ejpam-3529	192	1	then	then	ADV
ejpam-3529	192	2	there	there	PRON
ejpam-3529	192	3	exists	exist	VERB
ejpam-3529	192	4	monotone	monotone	ADJ
ejpam-3529	192	5	sequence	sequence	NOUN
ejpam-3529	192	6	{	{	PUNCT
ejpam-3529	192	7	αn	αn	NOUN
ejpam-3529	192	8	}	}	PUNCT
ejpam-3529	192	9	,	,	PUNCT
ejpam-3529	192	10	such	such	ADJ
ejpam-3529	192	11	that	that	DET
ejpam-3529	192	12	αn	αn	NOUN
ejpam-3529	192	13	→	→	SYM
ejpam-3529	192	14	ρ	ρ	PROPN
ejpam-3529	192	15	,	,	PUNCT
ejpam-3529	192	16	as	as	ADP
ejpam-3529	192	17	n	n	NUM
ejpam-3529	192	18	→	→	SYM
ejpam-3529	192	19	∞	∞	X
ejpam-3529	192	20	uniformly	uniformly	ADV
ejpam-3529	192	21	and	and	CCONJ
ejpam-3529	192	22	monotonically	monotonically	ADV
ejpam-3529	192	23	to	to	ADP
ejpam-3529	192	24	the	the	DET
ejpam-3529	192	25	unique	unique	ADJ
ejpam-3529	192	26	solution	solution	NOUN
ejpam-3529	192	27	ρ	ρ	NOUN
ejpam-3529	192	28	=	=	SYM
ejpam-3529	192	29	u	u	PROPN
ejpam-3529	192	30	for	for	ADP
ejpam-3529	192	31	pbvp	pbvp	NOUN
ejpam-3529	192	32	of	of	ADP
ejpam-3529	192	33	an	an	DET
ejpam-3529	192	34	integro	integro	ADJ
ejpam-3529	192	35	differential	differential	ADJ
ejpam-3529	192	36	equation	equation	NOUN
ejpam-3529	192	37	(	(	PUNCT
ejpam-3529	192	38	15	15	NUM
ejpam-3529	192	39	)	)	PUNCT
ejpam-3529	192	40	and	and	CCONJ
ejpam-3529	192	41	(	(	PUNCT
ejpam-3529	192	42	16)on	16)on	NUM
ejpam-3529	192	43	i	i	PRON
ejpam-3529	192	44	and	and	CCONJ
ejpam-3529	192	45	the	the	DET
ejpam-3529	192	46	convergence	convergence	NOUN
ejpam-3529	192	47	is	be	AUX
ejpam-3529	192	48	quadratic	quadratic	ADJ
ejpam-3529	192	49	.	.	PUNCT
ejpam-3529	193	1	proof	proof	NOUN
ejpam-3529	193	2	:	:	PUNCT
ejpam-3529	193	3	in	in	ADP
ejpam-3529	193	4	order	order	NOUN
ejpam-3529	193	5	to	to	PART
ejpam-3529	193	6	construct	construct	VERB
ejpam-3529	193	7	a	a	DET
ejpam-3529	193	8	sequence	sequence	NOUN
ejpam-3529	193	9	of	of	ADP
ejpam-3529	193	10	lower	low	ADJ
ejpam-3529	193	11	and	and	CCONJ
ejpam-3529	193	12	upper	upper	ADJ
ejpam-3529	193	13	iterates	iterate	NOUN
ejpam-3529	193	14	that	that	PRON
ejpam-3529	193	15	converge	converge	VERB
ejpam-3529	193	16	to	to	ADP
ejpam-3529	193	17	the	the	DET
ejpam-3529	193	18	solution	solution	NOUN
ejpam-3529	193	19	of	of	ADP
ejpam-3529	193	20	the	the	DET
ejpam-3529	193	21	pbvp	pbvp	NOUN
ejpam-3529	193	22	we	we	PRON
ejpam-3529	193	23	fix	fix	VERB
ejpam-3529	193	24	the	the	DET
ejpam-3529	193	25	upper	upper	ADJ
ejpam-3529	193	26	solution	solution	NOUN
ejpam-3529	193	27	β0	β0	NOUN
ejpam-3529	193	28	.	.	PUNCT
ejpam-3529	193	29	now	now	ADV
ejpam-3529	193	30	consider	consider	VERB
ejpam-3529	193	31	the	the	DET
ejpam-3529	193	32	following	follow	VERB
ejpam-3529	193	33	linear	linear	PROPN
ejpam-3529	193	34	problem	problem	NOUN
ejpam-3529	193	35	for	for	ADP
ejpam-3529	193	36	n=	n=	ADJ
ejpam-3529	193	37	0,1,2,3	0,1,2,3	NUM
ejpam-3529	193	38	...	...	PUNCT
ejpam-3529	194	1	α′n+1	α′n+1	X
ejpam-3529	194	2	=	=	SYM
ejpam-3529	194	3	f1(t	f1(t	PROPN
ejpam-3529	194	4	,	,	PUNCT
ejpam-3529	194	5	αn	αn	NOUN
ejpam-3529	194	6	,	,	PUNCT
ejpam-3529	194	7	sαn)+f1x(t	sαn)+f1x(t	PROPN
ejpam-3529	194	8	,	,	PUNCT
ejpam-3529	194	9	αn	αn	NOUN
ejpam-3529	194	10	,	,	PUNCT
ejpam-3529	194	11	sαn)[αn+1−αn]+f1ξ(t	sαn)[αn+1−αn]+f1ξ(t	NUM
ejpam-3529	194	12	,	,	PUNCT
ejpam-3529	194	13	αn	αn	NOUN
ejpam-3529	194	14	,	,	PUNCT
ejpam-3529	194	15	sαn)[sαn+1−sαn]+f2(t	sαn)[sαn+1−sαn]+f2(t	NOUN
ejpam-3529	194	16	,	,	PUNCT
ejpam-3529	194	17	β0	β0	NOUN
ejpam-3529	194	18	,	,	PUNCT
ejpam-3529	194	19	sβ0	sβ0	NOUN
ejpam-3529	194	20	)	)	PUNCT
ejpam-3529	194	21	,	,	PUNCT
ejpam-3529	194	22	αn+1(0	αn+1(0	X
ejpam-3529	194	23	)	)	PUNCT
ejpam-3529	194	24	=	=	SYM
ejpam-3529	194	25	αn(t	αn(t	NUM
ejpam-3529	194	26	)	)	PUNCT
ejpam-3529	194	27	.	.	PUNCT
ejpam-3529	195	1	since	since	SCONJ
ejpam-3529	195	2	the	the	DET
ejpam-3529	195	3	above	above	ADJ
ejpam-3529	195	4	equation	equation	NOUN
ejpam-3529	195	5	is	be	AUX
ejpam-3529	195	6	a	a	DET
ejpam-3529	195	7	linear	linear	ADJ
ejpam-3529	195	8	integro	integro	ADJ
ejpam-3529	195	9	differential	differential	NOUN
ejpam-3529	195	10	equation	equation	NOUN
ejpam-3529	195	11	,	,	PUNCT
ejpam-3529	195	12	so	so	SCONJ
ejpam-3529	195	13	it	it	PRON
ejpam-3529	195	14	has	have	VERB
ejpam-3529	195	15	unique	unique	ADJ
ejpam-3529	195	16	solution	solution	NOUN
ejpam-3529	195	17	αn+1(t	αn+1(t	PROPN
ejpam-3529	195	18	)	)	PUNCT
ejpam-3529	195	19	on	on	ADP
ejpam-3529	195	20	i.	i.	PROPN
ejpam-3529	195	21	now	now	ADV
ejpam-3529	195	22	we	we	PRON
ejpam-3529	195	23	claim	claim	VERB
ejpam-3529	195	24	that	that	SCONJ
ejpam-3529	195	25	α0	α0	ADJ
ejpam-3529	195	26	≤	≤	ADJ
ejpam-3529	195	27	α1	α1	PROPN
ejpam-3529	195	28	≤	≤	ADV
ejpam-3529	195	29	α2	α2	ADJ
ejpam-3529	195	30	≤	≤	NOUN
ejpam-3529	195	31	...	...	PUNCT
ejpam-3529	196	1	≤	≤	NUM
ejpam-3529	197	1	αn−1	αn−1	ADJ
ejpam-3529	197	2	≤	≤	NUM
ejpam-3529	197	3	αn	αn	NOUN
ejpam-3529	197	4	≤	≤	NUM
ejpam-3529	197	5	...	...	PUNCT
ejpam-3529	198	1	≤	≤	NUM
ejpam-3529	198	2	β0	β0	NOUN
ejpam-3529	198	3	(	(	PUNCT
ejpam-3529	198	4	21	21	NUM
ejpam-3529	198	5	)	)	PUNCT
ejpam-3529	198	6	on	on	ADP
ejpam-3529	198	7	i.	i.	NOUN
ejpam-3529	198	8	we	we	PRON
ejpam-3529	198	9	begin	begin	VERB
ejpam-3529	198	10	by	by	ADP
ejpam-3529	198	11	setting	set	VERB
ejpam-3529	198	12	p	p	X
ejpam-3529	198	13	=	=	PUNCT
ejpam-3529	198	14	α0	α0	ADJ
ejpam-3529	198	15	−	−	PROPN
ejpam-3529	198	16	α1	α1	PROPN
ejpam-3529	198	17	.	.	PUNCT
ejpam-3529	199	1	then	then	ADV
ejpam-3529	199	2	p′	p′	X
ejpam-3529	199	3	=	=	SYM
ejpam-3529	200	1	α′0	α′0	NOUN
ejpam-3529	201	1	−	−	NUM
ejpam-3529	201	2	α′1	α′1	NOUN
ejpam-3529	201	3	=	=	SYM
ejpam-3529	201	4	f1x(t	f1x(t	PROPN
ejpam-3529	201	5	,	,	PUNCT
ejpam-3529	201	6	α0	α0	ADJ
ejpam-3529	201	7	,	,	PUNCT
ejpam-3529	201	8	sα0)p(t	sα0)p(t	ADJ
ejpam-3529	201	9	)	)	PUNCT
ejpam-3529	201	10	+	+	CCONJ
ejpam-3529	201	11	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	201	12	,	,	PUNCT
ejpam-3529	201	13	α0	α0	ADJ
ejpam-3529	201	14	,	,	PUNCT
ejpam-3529	201	15	sα0)sp(t	sα0)sp(t	NOUN
ejpam-3529	201	16	)	)	PUNCT
ejpam-3529	201	17	p′(t	p′(t	PROPN
ejpam-3529	201	18	)	)	PUNCT
ejpam-3529	201	19	≤	≤	NUM
ejpam-3529	201	20	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	201	21	)	)	PUNCT
ejpam-3529	201	22	also	also	ADV
ejpam-3529	201	23	p(0	p(0	PROPN
ejpam-3529	201	24	)	)	PUNCT
ejpam-3529	201	25	=	=	SYM
ejpam-3529	201	26	α0(0	α0(0	PROPN
ejpam-3529	201	27	)	)	PUNCT
ejpam-3529	201	28	−	−	PROPN
ejpam-3529	201	29	α1(0	α1(0	PROPN
ejpam-3529	201	30	)	)	PUNCT
ejpam-3529	201	31	≤	≤	NOUN
ejpam-3529	201	32	0	0	NUM
ejpam-3529	201	33	.	.	PUNCT
ejpam-3529	202	1	hence	hence	ADV
ejpam-3529	202	2	by	by	ADP
ejpam-3529	202	3	lemma	lemma	PROPN
ejpam-3529	202	4	1	1	NUM
ejpam-3529	202	5	we	we	PRON
ejpam-3529	202	6	have	have	VERB
ejpam-3529	202	7	p(t	p(t	NOUN
ejpam-3529	202	8	)	)	PUNCT
ejpam-3529	202	9	≤	≤	NOUN
ejpam-3529	202	10	0	0	NUM
ejpam-3529	202	11	.	.	PUNCT
ejpam-3529	203	1	thus	thus	ADV
ejpam-3529	203	2	α0	α0	ADJ
ejpam-3529	203	3	≤	≤	ADJ
ejpam-3529	203	4	α1	α1	PROPN
ejpam-3529	203	5	on	on	ADP
ejpam-3529	203	6	i.	i.	PROPN
ejpam-3529	203	7	now	now	ADV
ejpam-3529	203	8	we	we	PRON
ejpam-3529	203	9	show	show	VERB
ejpam-3529	203	10	α1	α1	PROPN
ejpam-3529	203	11	≤	≤	PROPN
ejpam-3529	203	12	β0	β0	ADV
ejpam-3529	203	13	on	on	ADP
ejpam-3529	203	14	i	i	PRON
ejpam-3529	203	15	by	by	ADP
ejpam-3529	203	16	setting	set	VERB
ejpam-3529	203	17	p	p	X
ejpam-3529	203	18	=	=	PUNCT
ejpam-3529	203	19	α1	α1	PROPN
ejpam-3529	203	20	−	−	PROPN
ejpam-3529	203	21	β0	β0	PROPN
ejpam-3529	203	22	.	.	PUNCT
ejpam-3529	204	1	then	then	ADV
ejpam-3529	204	2	,	,	PUNCT
ejpam-3529	204	3	p′	p′	PROPN
ejpam-3529	204	4	=	=	SYM
ejpam-3529	204	5	α′1	α′1	ADV
ejpam-3529	204	6	−	−	PROPN
ejpam-3529	204	7	β′0	β′0	SYM
ejpam-3529	204	8	≤	≤	PROPN
ejpam-3529	204	9	{	{	PUNCT
ejpam-3529	204	10	f1(t	f1(t	PROPN
ejpam-3529	204	11	,	,	PUNCT
ejpam-3529	204	12	α0	α0	ADJ
ejpam-3529	204	13	,	,	PUNCT
ejpam-3529	204	14	sα0)−	sα0)−	PROPN
ejpam-3529	204	15	f1(t	f1(t	PROPN
ejpam-3529	204	16	,	,	PUNCT
ejpam-3529	204	17	β0	β0	NOUN
ejpam-3529	204	18	,	,	PUNCT
ejpam-3529	204	19	sβ0)}+	sβ0)}+	PROPN
ejpam-3529	204	20	{	{	PUNCT
ejpam-3529	204	21	f1x(t	f1x(t	PROPN
ejpam-3529	204	22	,	,	PUNCT
ejpam-3529	204	23	α0	α0	ADJ
ejpam-3529	204	24	,	,	PUNCT
ejpam-3529	204	25	sα0)[α1	sα0)[α1	NOUN
ejpam-3529	204	26	−	−	PROPN
ejpam-3529	204	27	α0	α0	ADJ
ejpam-3529	204	28	]	]	X
ejpam-3529	204	29	+	+	CCONJ
ejpam-3529	204	30	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	204	31	,	,	PUNCT
ejpam-3529	204	32	α0	α0	ADJ
ejpam-3529	204	33	,	,	PUNCT
ejpam-3529	204	34	sα0)[sα1	sα0)[sα1	PROPN
ejpam-3529	205	1	−	−	PROPN
ejpam-3529	205	2	sα0]}+	sα0]}+	PROPN
ejpam-3529	205	3	{	{	PUNCT
ejpam-3529	205	4	f2(t	f2(t	PROPN
ejpam-3529	205	5	,	,	PUNCT
ejpam-3529	205	6	β0	β0	NOUN
ejpam-3529	205	7	,	,	PUNCT
ejpam-3529	205	8	sβ0)−	sβ0)−	PROPN
ejpam-3529	205	9	f2(t	f2(t	PROPN
ejpam-3529	205	10	,	,	PUNCT
ejpam-3529	205	11	α0	α0	ADJ
ejpam-3529	205	12	,	,	PUNCT
ejpam-3529	205	13	sα0	sα0	NOUN
ejpam-3529	205	14	)	)	PUNCT
ejpam-3529	205	15	}	}	PUNCT
ejpam-3529	205	16	≤	≤	NUM
ejpam-3529	205	17	f1x(t	f1x(t	PROPN
ejpam-3529	205	18	,	,	PUNCT
ejpam-3529	205	19	α0	α0	ADJ
ejpam-3529	205	20	,	,	PUNCT
ejpam-3529	205	21	sα0)[α1	sα0)[α1	NOUN
ejpam-3529	205	22	−	−	PROPN
ejpam-3529	205	23	β0	β0	NOUN
ejpam-3529	205	24	]	]	X
ejpam-3529	205	25	+	+	CCONJ
ejpam-3529	205	26	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	205	27	,	,	PUNCT
ejpam-3529	205	28	α0	α0	ADJ
ejpam-3529	205	29	,	,	PUNCT
ejpam-3529	205	30	sα0)[sα1	sα0)[sα1	NOUN
ejpam-3529	205	31	−	−	PROPN
ejpam-3529	205	32	sβ0	sβ0	PROPN
ejpam-3529	205	33	]	]	PUNCT
ejpam-3529	205	34	≤	≤	NUM
ejpam-3529	205	35	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	205	36	)	)	PUNCT
ejpam-3529	205	37	.	.	PUNCT
ejpam-3529	206	1	also	also	ADV
ejpam-3529	206	2	p(0	p(0	VERB
ejpam-3529	206	3	)	)	PUNCT
ejpam-3529	206	4	=	=	SYM
ejpam-3529	206	5	α1(0	α1(0	PROPN
ejpam-3529	206	6	)	)	PUNCT
ejpam-3529	206	7	−	−	PROPN
ejpam-3529	206	8	β0(0	β0(0	PROPN
ejpam-3529	206	9	)	)	PUNCT
ejpam-3529	206	10	≤	≤	NOUN
ejpam-3529	206	11	0	0	NUM
ejpam-3529	206	12	.	.	PUNCT
ejpam-3529	207	1	hence	hence	ADV
ejpam-3529	207	2	by	by	ADP
ejpam-3529	207	3	lemma	lemma	PROPN
ejpam-3529	207	4	1	1	NUM
ejpam-3529	207	5	we	we	PRON
ejpam-3529	207	6	have	have	VERB
ejpam-3529	207	7	p(t	p(t	NOUN
ejpam-3529	207	8	)	)	PUNCT
ejpam-3529	207	9	≤	≤	NOUN
ejpam-3529	207	10	0	0	NUM
ejpam-3529	207	11	.	.	PUNCT
ejpam-3529	208	1	hence	hence	ADV
ejpam-3529	208	2	α1	α1	PROPN
ejpam-3529	208	3	≤	≤	PUNCT
ejpam-3529	208	4	β0	β0	NOUN
ejpam-3529	208	5	on	on	ADP
ejpam-3529	208	6	i.	i.	NOUN
ejpam-3529	208	7	thus	thus	ADV
ejpam-3529	208	8	α0	α0	ADJ
ejpam-3529	208	9	≤	≤	ADJ
ejpam-3529	208	10	α1	α1	PROPN
ejpam-3529	208	11	≤	≤	PROPN
ejpam-3529	208	12	β0	β0	PROPN
ejpam-3529	208	13	ch	ch	NOUN
ejpam-3529	208	14	.	.	PUNCT
ejpam-3529	209	1	v.	v.	ADP
ejpam-3529	209	2	sreedhar	sreedhar	PROPN
ejpam-3529	209	3	,	,	PUNCT
ejpam-3529	209	4	j.	j.	PROPN
ejpam-3529	209	5	vasundhara	vasundhara	PROPN
ejpam-3529	209	6	devi	devi	PROPN
ejpam-3529	209	7	,	,	PUNCT
ejpam-3529	209	8	/	/	SYM
ejpam-3529	209	9	eur	eur	NOUN
ejpam-3529	209	10	.	.	PUNCT
ejpam-3529	210	1	j.	j.	PROPN
ejpam-3529	210	2	pure	pure	PROPN
ejpam-3529	210	3	appl	appl	PROPN
ejpam-3529	210	4	.	.	PROPN
ejpam-3529	210	5	math	math	PROPN
ejpam-3529	210	6	,	,	PUNCT
ejpam-3529	210	7	12	12	NUM
ejpam-3529	210	8	(	(	PUNCT
ejpam-3529	210	9	4	4	NUM
ejpam-3529	210	10	)	)	PUNCT
ejpam-3529	210	11	(	(	PUNCT
ejpam-3529	210	12	2019	2019	NUM
ejpam-3529	210	13	)	)	PUNCT
ejpam-3529	210	14	,	,	PUNCT
ejpam-3529	210	15	1662	1662	NUM
ejpam-3529	210	16	-	-	SYM
ejpam-3529	210	17	1675	1675	NUM
ejpam-3529	210	18	1672	1672	NUM
ejpam-3529	210	19	on	on	ADP
ejpam-3529	210	20	i.	i.	PROPN
ejpam-3529	210	21	now	now	ADV
ejpam-3529	210	22	assuming	assume	VERB
ejpam-3529	210	23	that	that	SCONJ
ejpam-3529	210	24	the	the	DET
ejpam-3529	210	25	result	result	NOUN
ejpam-3529	210	26	is	be	AUX
ejpam-3529	210	27	true	true	ADJ
ejpam-3529	210	28	for	for	ADP
ejpam-3529	210	29	n	n	NOUN
ejpam-3529	210	30	=	=	SYM
ejpam-3529	210	31	k	k	PROPN
ejpam-3529	210	32	and	and	CCONJ
ejpam-3529	210	33	prove	prove	VERB
ejpam-3529	210	34	it	it	PRON
ejpam-3529	210	35	for	for	ADP
ejpam-3529	210	36	n	n	NOUN
ejpam-3529	210	37	=	=	SYM
ejpam-3529	210	38	k	k	PROPN
ejpam-3529	211	1	+	+	NOUN
ejpam-3529	211	2	1	1	X
ejpam-3529	211	3	.	.	PUNCT
ejpam-3529	212	1	in	in	ADP
ejpam-3529	212	2	order	order	NOUN
ejpam-3529	212	3	to	to	PART
ejpam-3529	212	4	prove	prove	VERB
ejpam-3529	212	5	our	our	PRON
ejpam-3529	212	6	claim	claim	NOUN
ejpam-3529	212	7	we	we	PRON
ejpam-3529	212	8	consider	consider	VERB
ejpam-3529	212	9	the	the	DET
ejpam-3529	212	10	following	follow	VERB
ejpam-3529	212	11	linear	linear	PROPN
ejpam-3529	212	12	integro	integro	PROPN
ejpam-3529	212	13	differential	differential	ADJ
ejpam-3529	212	14	equation	equation	NOUN
ejpam-3529	212	15	.	.	PUNCT
ejpam-3529	213	1	α′k+1	α′k+1	X
ejpam-3529	213	2	=	=	SYM
ejpam-3529	213	3	f1(t	f1(t	PROPN
ejpam-3529	213	4	,	,	PUNCT
ejpam-3529	213	5	αk	αk	INTJ
ejpam-3529	213	6	,	,	PUNCT
ejpam-3529	213	7	sαk)+f1x(t	sαk)+f1x(t	NOUN
ejpam-3529	213	8	,	,	PUNCT
ejpam-3529	213	9	αk	αk	NOUN
ejpam-3529	213	10	,	,	PUNCT
ejpam-3529	213	11	sαk)[αk+1−αk]+f1ξ(t	sαk)[αk+1−αk]+f1ξ(t	PRON
ejpam-3529	213	12	,	,	PUNCT
ejpam-3529	213	13	αk	αk	INTJ
ejpam-3529	213	14	,	,	PUNCT
ejpam-3529	213	15	sαk)[sαk+1−sαk]+f2(t	sαk)[sαk+1−sαk]+f2(t	PROPN
ejpam-3529	213	16	,	,	PUNCT
ejpam-3529	213	17	β0	β0	NOUN
ejpam-3529	213	18	,	,	PUNCT
ejpam-3529	213	19	sβ0	sβ0	NOUN
ejpam-3529	213	20	)	)	PUNCT
ejpam-3529	213	21	,	,	PUNCT
ejpam-3529	213	22	αk+1(0	αk+1(0	NUM
ejpam-3529	213	23	)	)	PUNCT
ejpam-3529	213	24	=	=	SYM
ejpam-3529	213	25	αk(t	αk(t	NUM
ejpam-3529	213	26	)	)	PUNCT
ejpam-3529	213	27	.	.	PUNCT
ejpam-3529	214	1	the	the	DET
ejpam-3529	214	2	above	above	ADJ
ejpam-3529	214	3	linear	linear	PROPN
ejpam-3529	214	4	integro	integro	PROPN
ejpam-3529	214	5	differential	differential	ADJ
ejpam-3529	214	6	equation	equation	NOUN
ejpam-3529	214	7	has	have	VERB
ejpam-3529	214	8	unique	unique	ADJ
ejpam-3529	214	9	solution	solution	NOUN
ejpam-3529	214	10	αk+1	αk+1	NUM
ejpam-3529	214	11	,	,	PUNCT
ejpam-3529	214	12	where	where	SCONJ
ejpam-3529	214	13	αk	αk	NOUN
ejpam-3529	215	1	and	and	CCONJ
ejpam-3529	215	2	β0	β0	NOUN
ejpam-3529	215	3	are	be	AUX
ejpam-3529	215	4	known	know	VERB
ejpam-3529	215	5	lower	low	ADJ
ejpam-3529	215	6	and	and	CCONJ
ejpam-3529	215	7	upper	upper	ADJ
ejpam-3529	215	8	solutions	solution	NOUN
ejpam-3529	215	9	of	of	ADP
ejpam-3529	215	10	(	(	PUNCT
ejpam-3529	215	11	15	15	NUM
ejpam-3529	215	12	)	)	PUNCT
ejpam-3529	215	13	and	and	CCONJ
ejpam-3529	215	14	(	(	PUNCT
ejpam-3529	215	15	16	16	NUM
ejpam-3529	215	16	)	)	PUNCT
ejpam-3529	215	17	.	.	PUNCT
ejpam-3529	216	1	further	far	ADV
ejpam-3529	216	2	αk	αk	PRON
ejpam-3529	216	3	is	be	AUX
ejpam-3529	216	4	the	the	DET
ejpam-3529	216	5	solution	solution	NOUN
ejpam-3529	216	6	of	of	ADP
ejpam-3529	216	7	the	the	DET
ejpam-3529	216	8	linear	linear	PROPN
ejpam-3529	216	9	integro	integro	PROPN
ejpam-3529	216	10	differential	differential	ADJ
ejpam-3529	216	11	equation	equation	NOUN
ejpam-3529	216	12	α′k	α′k	X
ejpam-3529	216	13	=	=	SYM
ejpam-3529	216	14	f1(t	f1(t	PROPN
ejpam-3529	216	15	,	,	PUNCT
ejpam-3529	216	16	αk−1	αk−1	NOUN
ejpam-3529	216	17	,	,	PUNCT
ejpam-3529	216	18	sαk−1)+f1x(t	sαk−1)+f1x(t	ADJ
ejpam-3529	216	19	,	,	PUNCT
ejpam-3529	216	20	αk−1	αk−1	NOUN
ejpam-3529	216	21	,	,	PUNCT
ejpam-3529	216	22	sαk−1)[αk−αk−1]+f1ξ(t	sαk−1)[αk−αk−1]+f1ξ(t	NOUN
ejpam-3529	216	23	,	,	PUNCT
ejpam-3529	216	24	αk−1	αk−1	NOUN
ejpam-3529	216	25	,	,	PUNCT
ejpam-3529	216	26	sαk−1)[sαk−sαk−1	sαk−1)[sαk−sαk−1	ADV
ejpam-3529	216	27	]	]	PUNCT
ejpam-3529	217	1	+	+	ADJ
ejpam-3529	217	2	f2(t	f2(t	PROPN
ejpam-3529	217	3	,	,	PUNCT
ejpam-3529	217	4	β0	β0	NOUN
ejpam-3529	217	5	,	,	PUNCT
ejpam-3529	217	6	sβ0	sβ0	NOUN
ejpam-3529	217	7	)	)	PUNCT
ejpam-3529	217	8	,	,	PUNCT
ejpam-3529	217	9	αk(0	αk(0	PROPN
ejpam-3529	217	10	)	)	PUNCT
ejpam-3529	217	11	=	=	PUNCT
ejpam-3529	217	12	αk−1(t	αk−1(t	ADJ
ejpam-3529	217	13	)	)	PUNCT
ejpam-3529	217	14	.	.	PUNCT
ejpam-3529	218	1	we	we	PRON
ejpam-3529	218	2	now	now	ADV
ejpam-3529	218	3	claim	claim	VERB
ejpam-3529	218	4	that	that	SCONJ
ejpam-3529	218	5	αk	αk	NOUN
ejpam-3529	218	6	≤	≤	NUM
ejpam-3529	218	7	αk+1	αk+1	NUM
ejpam-3529	218	8	on	on	ADP
ejpam-3529	218	9	i.	i.	NOUN
ejpam-3529	218	10	for	for	ADP
ejpam-3529	218	11	this	this	DET
ejpam-3529	218	12	set	set	NOUN
ejpam-3529	218	13	p	p	NOUN
ejpam-3529	218	14	=	=	X
ejpam-3529	218	15	αk	αk	ADP
ejpam-3529	218	16	−	−	NUM
ejpam-3529	218	17	αk+1	αk+1	NUM
ejpam-3529	218	18	p′	p′	NOUN
ejpam-3529	218	19	=	=	SYM
ejpam-3529	218	20	α′k	α′k	NOUN
ejpam-3529	219	1	−	−	NOUN
ejpam-3529	219	2	α′k+1	α′k+1	SYM
ejpam-3529	219	3	≤	≤	NUM
ejpam-3529	219	4	{	{	PUNCT
ejpam-3529	219	5	f1x(t	f1x(t	PROPN
ejpam-3529	219	6	,	,	PUNCT
ejpam-3529	219	7	αk	αk	NOUN
ejpam-3529	219	8	,	,	PUNCT
ejpam-3529	219	9	sαk)[αk	sαk)[αk	ADV
ejpam-3529	219	10	−	−	NOUN
ejpam-3529	219	11	αk+1	αk+1	X
ejpam-3529	219	12	]	]	X
ejpam-3529	219	13	+	+	CCONJ
ejpam-3529	219	14	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	219	15	,	,	PUNCT
ejpam-3529	219	16	αk	αk	NOUN
ejpam-3529	219	17	,	,	PUNCT
ejpam-3529	219	18	sαk)[sαk	sαk)[sαk	NUM
ejpam-3529	219	19	−	−	PROPN
ejpam-3529	219	20	sαk+1	sαk+1	VERB
ejpam-3529	219	21	]	]	PUNCT
ejpam-3529	219	22	≤	≤	NUM
ejpam-3529	219	23	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	219	24	)	)	PUNCT
ejpam-3529	219	25	also	also	ADV
ejpam-3529	219	26	p(0	p(0	VERB
ejpam-3529	219	27	)	)	PUNCT
ejpam-3529	219	28	=	=	SYM
ejpam-3529	220	1	αk(0)−	αk(0)−	NOUN
ejpam-3529	220	2	αk+1(0	αk+1(0	NOUN
ejpam-3529	220	3	)	)	PUNCT
ejpam-3529	220	4	≤	≤	NOUN
ejpam-3529	220	5	0	0	NUM
ejpam-3529	220	6	.	.	PUNCT
ejpam-3529	221	1	then	then	ADV
ejpam-3529	221	2	by	by	ADP
ejpam-3529	221	3	lemma	lemma	PROPN
ejpam-3529	221	4	1	1	NUM
ejpam-3529	221	5	thus	thus	ADV
ejpam-3529	221	6	p(t	p(t	NOUN
ejpam-3529	221	7	)	)	PUNCT
ejpam-3529	221	8	≤	≤	NOUN
ejpam-3529	221	9	0	0	NUM
ejpam-3529	221	10	.	.	PUNCT
ejpam-3529	222	1	so	so	ADV
ejpam-3529	222	2	αk	αk	SCONJ
ejpam-3529	222	3	≤	≤	NUM
ejpam-3529	222	4	αk+1	αk+1	NUM
ejpam-3529	222	5	on	on	ADP
ejpam-3529	222	6	i.	i.	PROPN
ejpam-3529	222	7	next	next	ADV
ejpam-3529	222	8	to	to	PART
ejpam-3529	222	9	show	show	VERB
ejpam-3529	222	10	αk+1	αk+1	NUM
ejpam-3529	222	11	≤	≤	NUM
ejpam-3529	222	12	β0	β0	ADV
ejpam-3529	222	13	on	on	ADP
ejpam-3529	222	14	i	i	PRON
ejpam-3529	222	15	,	,	PUNCT
ejpam-3529	222	16	set	set	VERB
ejpam-3529	222	17	p	p	NOUN
ejpam-3529	222	18	=	=	NUM
ejpam-3529	222	19	αk+1	αk+1	NUM
ejpam-3529	223	1	−	−	ADP
ejpam-3529	223	2	β0	β0	NOUN
ejpam-3529	223	3	p′	p′	NOUN
ejpam-3529	223	4	=	=	PUNCT
ejpam-3529	224	1	α′k+1	α′k+1	X
ejpam-3529	224	2	−	−	X
ejpam-3529	224	3	β′0	β′0	SYM
ejpam-3529	224	4	≤	≤	NUM
ejpam-3529	224	5	{	{	PUNCT
ejpam-3529	224	6	f1x(t	f1x(t	PROPN
ejpam-3529	224	7	,	,	PUNCT
ejpam-3529	224	8	αk	αk	NOUN
ejpam-3529	224	9	,	,	PUNCT
ejpam-3529	224	10	sαk)[αk+1	sαk)[αk+1	PROPN
ejpam-3529	224	11	−	−	NOUN
ejpam-3529	224	12	αk	αk	NOUN
ejpam-3529	224	13	]	]	X
ejpam-3529	224	14	+	+	CCONJ
ejpam-3529	224	15	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	224	16	,	,	PUNCT
ejpam-3529	224	17	αk	αk	NOUN
ejpam-3529	224	18	,	,	PUNCT
ejpam-3529	224	19	sαk)[sαk+1	sαk)[sαk+1	VERB
ejpam-3529	224	20	−	−	NUM
ejpam-3529	224	21	sαk	sαk	PROPN
ejpam-3529	224	22	]	]	PUNCT
ejpam-3529	224	23	}	}	PUNCT
ejpam-3529	224	24	≤	≤	NUM
ejpam-3529	224	25	−mp(t)−nsp(t	−mp(t)−nsp(t	NOUN
ejpam-3529	224	26	)	)	PUNCT
ejpam-3529	224	27	also	also	ADV
ejpam-3529	224	28	p(0	p(0	PROPN
ejpam-3529	224	29	)	)	PUNCT
ejpam-3529	224	30	=	=	SYM
ejpam-3529	224	31	αk+1(0	αk+1(0	X
ejpam-3529	224	32	)	)	PUNCT
ejpam-3529	224	33	−	−	PROPN
ejpam-3529	224	34	β0(0	β0(0	PROPN
ejpam-3529	224	35	)	)	PUNCT
ejpam-3529	224	36	≤	≤	NOUN
ejpam-3529	224	37	0	0	NUM
ejpam-3529	224	38	.	.	PUNCT
ejpam-3529	225	1	using	use	VERB
ejpam-3529	225	2	lemma	lemma	PROPN
ejpam-3529	225	3	1	1	NUM
ejpam-3529	225	4	we	we	PRON
ejpam-3529	225	5	get	get	VERB
ejpam-3529	225	6	p(t	p(t	NOUN
ejpam-3529	225	7	)	)	PUNCT
ejpam-3529	225	8	≤	≤	NOUN
ejpam-3529	225	9	0	0	NUM
ejpam-3529	225	10	.	.	PUNCT
ejpam-3529	225	11	which	which	PRON
ejpam-3529	225	12	means	mean	VERB
ejpam-3529	225	13	that	that	SCONJ
ejpam-3529	225	14	αk+1	αk+1	ADJ
ejpam-3529	225	15	≤	≤	NOUN
ejpam-3529	225	16	β0	β0	ADJ
ejpam-3529	225	17	on	on	ADP
ejpam-3529	225	18	i.	i.	PROPN
ejpam-3529	225	19	now	now	ADV
ejpam-3529	225	20	using	use	VERB
ejpam-3529	225	21	the	the	DET
ejpam-3529	225	22	principle	principle	NOUN
ejpam-3529	225	23	of	of	ADP
ejpam-3529	225	24	mathematical	mathematical	ADJ
ejpam-3529	225	25	induction	induction	NOUN
ejpam-3529	225	26	,	,	PUNCT
ejpam-3529	225	27	we	we	PRON
ejpam-3529	225	28	deduce	deduce	VERB
ejpam-3529	225	29	the	the	DET
ejpam-3529	225	30	relation	relation	NOUN
ejpam-3529	225	31	(	(	PUNCT
ejpam-3529	225	32	21	21	NUM
ejpam-3529	225	33	)	)	PUNCT
ejpam-3529	225	34	and	and	CCONJ
ejpam-3529	225	35	our	our	PRON
ejpam-3529	225	36	claim	claim	NOUN
ejpam-3529	225	37	holds	hold	VERB
ejpam-3529	225	38	.	.	PUNCT
ejpam-3529	226	1	also	also	ADV
ejpam-3529	226	2	from	from	ADP
ejpam-3529	226	3	relation	relation	NOUN
ejpam-3529	226	4	(	(	PUNCT
ejpam-3529	226	5	21	21	NUM
ejpam-3529	226	6	)	)	PUNCT
ejpam-3529	226	7	,	,	PUNCT
ejpam-3529	226	8	we	we	PRON
ejpam-3529	226	9	can	can	AUX
ejpam-3529	226	10	seen	see	VERB
ejpam-3529	226	11	that	that	SCONJ
ejpam-3529	226	12	the	the	DET
ejpam-3529	226	13	sequences	sequence	NOUN
ejpam-3529	226	14	are	be	AUX
ejpam-3529	226	15	uniformly	uniformly	ADV
ejpam-3529	226	16	bounded	bound	VERB
ejpam-3529	226	17	.	.	PUNCT
ejpam-3529	227	1	since	since	SCONJ
ejpam-3529	227	2	f1	f1	NOUN
ejpam-3529	227	3	,	,	PUNCT
ejpam-3529	227	4	f2	f2	PROPN
ejpam-3529	227	5	are	be	AUX
ejpam-3529	227	6	uniformly	uniformly	ADV
ejpam-3529	227	7	bounded	bound	VERB
ejpam-3529	227	8	so	so	SCONJ
ejpam-3529	227	9	the	the	DET
ejpam-3529	227	10	sequence	sequence	NOUN
ejpam-3529	227	11	{	{	PUNCT
ejpam-3529	227	12	αn	αn	NOUN
ejpam-3529	227	13	}	}	PUNCT
ejpam-3529	227	14	equicontinuous	equicontinuous	ADJ
ejpam-3529	227	15	on	on	ADP
ejpam-3529	227	16	[	[	X
ejpam-3529	227	17	0	0	NUM
ejpam-3529	227	18	,	,	PUNCT
ejpam-3529	227	19	t	t	NOUN
ejpam-3529	227	20	]	]	PUNCT
ejpam-3529	227	21	and	and	CCONJ
ejpam-3529	227	22	therefore	therefore	ADV
ejpam-3529	227	23	by	by	ADP
ejpam-3529	227	24	using	use	VERB
ejpam-3529	227	25	ascoli	ascoli	PROPN
ejpam-3529	227	26	-	-	PUNCT
ejpam-3529	227	27	arzela	arzela	PROPN
ejpam-3529	227	28	theorem	theorem	VERB
ejpam-3529	227	29	,	,	PUNCT
ejpam-3529	227	30	there	there	PRON
ejpam-3529	227	31	exists	exist	VERB
ejpam-3529	227	32	subsequence	subsequence	NOUN
ejpam-3529	227	33	{	{	PUNCT
ejpam-3529	227	34	αnk	αnk	NOUN
ejpam-3529	227	35	}	}	PUNCT
ejpam-3529	227	36	that	that	PRON
ejpam-3529	227	37	converges	converge	VERB
ejpam-3529	227	38	uniformly	uniformly	ADV
ejpam-3529	227	39	on	on	ADP
ejpam-3529	227	40	[	[	X
ejpam-3529	227	41	0	0	NUM
ejpam-3529	227	42	,	,	PUNCT
ejpam-3529	227	43	t	t	NOUN
ejpam-3529	227	44	]	]	PUNCT
ejpam-3529	227	45	.	.	PUNCT
ejpam-3529	228	1	in	in	ADP
ejpam-3529	228	2	view	view	NOUN
ejpam-3529	228	3	of	of	ADP
ejpam-3529	228	4	(	(	PUNCT
ejpam-3529	228	5	21	21	NUM
ejpam-3529	228	6	)	)	PUNCT
ejpam-3529	228	7	it	it	PRON
ejpam-3529	228	8	also	also	ADV
ejpam-3529	228	9	follows	follow	VERB
ejpam-3529	228	10	that	that	SCONJ
ejpam-3529	228	11	the	the	DET
ejpam-3529	228	12	entire	entire	ADJ
ejpam-3529	228	13	sequence	sequence	NOUN
ejpam-3529	228	14	{	{	PUNCT
ejpam-3529	228	15	αn	αn	NOUN
ejpam-3529	228	16	}	}	PUNCT
ejpam-3529	228	17	converges	converge	VERB
ejpam-3529	228	18	uniformly	uniformly	ADV
ejpam-3529	228	19	to	to	ADP
ejpam-3529	228	20	ρ	ρ	PROPN
ejpam-3529	228	21	.	.	PUNCT
ejpam-3529	229	1	since	since	SCONJ
ejpam-3529	229	2	f1x	f1x	PROPN
ejpam-3529	229	3	exists	exist	VERB
ejpam-3529	229	4	and	and	CCONJ
ejpam-3529	229	5	is	be	AUX
ejpam-3529	229	6	bounded	bound	VERB
ejpam-3529	229	7	on	on	ADP
ejpam-3529	229	8	[	[	X
ejpam-3529	229	9	0	0	NUM
ejpam-3529	229	10	,	,	PUNCT
ejpam-3529	229	11	t	t	X
ejpam-3529	229	12	]	]	PUNCT
ejpam-3529	229	13	,	,	PUNCT
ejpam-3529	229	14	we	we	PRON
ejpam-3529	229	15	obtain	obtain	VERB
ejpam-3529	229	16	that	that	DET
ejpam-3529	229	17	f1	f1	NOUN
ejpam-3529	229	18	is	be	AUX
ejpam-3529	229	19	lipschitz	lipschitz	NOUN
ejpam-3529	229	20	and	and	CCONJ
ejpam-3529	229	21	hence	hence	ADV
ejpam-3529	229	22	the	the	DET
ejpam-3529	229	23	solution	solution	NOUN
ejpam-3529	229	24	u	u	NOUN
ejpam-3529	229	25	is	be	AUX
ejpam-3529	229	26	unique	unique	ADJ
ejpam-3529	229	27	.	.	PUNCT
ejpam-3529	230	1	ch	ch	NOUN
ejpam-3529	230	2	.	.	PUNCT
ejpam-3529	231	1	v.	v.	ADP
ejpam-3529	231	2	sreedhar	sreedhar	PROPN
ejpam-3529	231	3	,	,	PUNCT
ejpam-3529	231	4	j.	j.	PROPN
ejpam-3529	231	5	vasundhara	vasundhara	PROPN
ejpam-3529	231	6	devi	devi	PROPN
ejpam-3529	231	7	,	,	PUNCT
ejpam-3529	231	8	/	/	SYM
ejpam-3529	231	9	eur	eur	NOUN
ejpam-3529	231	10	.	.	PUNCT
ejpam-3529	232	1	j.	j.	PROPN
ejpam-3529	232	2	pure	pure	PROPN
ejpam-3529	232	3	appl	appl	PROPN
ejpam-3529	232	4	.	.	PROPN
ejpam-3529	232	5	math	math	PROPN
ejpam-3529	232	6	,	,	PUNCT
ejpam-3529	232	7	12	12	NUM
ejpam-3529	232	8	(	(	PUNCT
ejpam-3529	232	9	4	4	NUM
ejpam-3529	232	10	)	)	PUNCT
ejpam-3529	232	11	(	(	PUNCT
ejpam-3529	232	12	2019	2019	NUM
ejpam-3529	232	13	)	)	PUNCT
ejpam-3529	232	14	,	,	PUNCT
ejpam-3529	232	15	1662	1662	NUM
ejpam-3529	232	16	-	-	SYM
ejpam-3529	232	17	1675	1675	NUM
ejpam-3529	232	18	1673	1673	NUM
ejpam-3529	232	19	to	to	PART
ejpam-3529	232	20	show	show	VERB
ejpam-3529	232	21	that	that	SCONJ
ejpam-3529	232	22	the	the	DET
ejpam-3529	232	23	convergence	convergence	NOUN
ejpam-3529	232	24	is	be	AUX
ejpam-3529	232	25	quadratic	quadratic	ADJ
ejpam-3529	232	26	,	,	PUNCT
ejpam-3529	232	27	we	we	PRON
ejpam-3529	232	28	begin	begin	VERB
ejpam-3529	232	29	by	by	ADP
ejpam-3529	232	30	writing	write	VERB
ejpam-3529	232	31	pn+1	pn+1	NOUN
ejpam-3529	232	32	=	=	SYM
ejpam-3529	232	33	u−αn+1	u−αn+1	PROPN
ejpam-3529	232	34	.	.	PUNCT
ejpam-3529	233	1	then	then	ADV
ejpam-3529	233	2	p′n+1	p′n+1	PROPN
ejpam-3529	233	3	=	=	PUNCT
ejpam-3529	233	4	u′	u′	X
ejpam-3529	233	5	−	−	ADP
ejpam-3529	233	6	α′n+1	α′n+1	NOUN
ejpam-3529	233	7	≤	≤	NOUN
ejpam-3529	234	1	[	[	X
ejpam-3529	234	2	f1(t	f1(t	PROPN
ejpam-3529	234	3	,	,	PUNCT
ejpam-3529	234	4	u	u	NOUN
ejpam-3529	234	5	,	,	PUNCT
ejpam-3529	234	6	su	su	PROPN
ejpam-3529	234	7	)	)	PUNCT
ejpam-3529	235	1	+	+	CCONJ
ejpam-3529	235	2	f2(t	f2(t	PROPN
ejpam-3529	235	3	,	,	PUNCT
ejpam-3529	235	4	u	u	NOUN
ejpam-3529	235	5	,	,	PUNCT
ejpam-3529	235	6	su	su	PROPN
ejpam-3529	235	7	)	)	PUNCT
ejpam-3529	235	8	]	]	PUNCT
ejpam-3529	236	1	−	−	PUNCT
ejpam-3529	237	1	[	[	X
ejpam-3529	237	2	{	{	PUNCT
ejpam-3529	237	3	f1(t	f1(t	PROPN
ejpam-3529	237	4	,	,	PUNCT
ejpam-3529	237	5	αn	αn	NOUN
ejpam-3529	237	6	,	,	PUNCT
ejpam-3529	237	7	sαn	sαn	NOUN
ejpam-3529	237	8	)	)	PUNCT
ejpam-3529	238	1	+	+	CCONJ
ejpam-3529	238	2	f1x(t	f1x(t	PROPN
ejpam-3529	238	3	,	,	PUNCT
ejpam-3529	238	4	αn	αn	NOUN
ejpam-3529	238	5	,	,	PUNCT
ejpam-3529	238	6	sαn)[αn+1	sαn)[αn+1	NOUN
ejpam-3529	238	7	−	−	NOUN
ejpam-3529	238	8	αn	αn	NOUN
ejpam-3529	238	9	]	]	X
ejpam-3529	239	1	+	+	CCONJ
ejpam-3529	239	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	239	3	,	,	PUNCT
ejpam-3529	239	4	αn	αn	NOUN
ejpam-3529	239	5	,	,	PUNCT
ejpam-3529	239	6	sαn)[sαn+1	sαn)[sαn+1	ADJ
ejpam-3529	239	7	−	−	NOUN
ejpam-3529	239	8	sαn	sαn	NOUN
ejpam-3529	239	9	]	]	PUNCT
ejpam-3529	239	10	+	+	CCONJ
ejpam-3529	239	11	f2(t	f2(t	PROPN
ejpam-3529	239	12	,	,	PUNCT
ejpam-3529	239	13	β0	β0	NOUN
ejpam-3529	239	14	,	,	PUNCT
ejpam-3529	239	15	sβ0	sβ0	NOUN
ejpam-3529	239	16	)	)	PUNCT
ejpam-3529	239	17	}	}	PUNCT
ejpam-3529	239	18	]	]	PUNCT
ejpam-3529	239	19	=	=	SYM
ejpam-3529	239	20	a+b	a+b	NUM
ejpam-3529	239	21	+	+	CCONJ
ejpam-3529	239	22	fx(t	fx(t	NOUN
ejpam-3529	239	23	,	,	PUNCT
ejpam-3529	239	24	αn	αn	NOUN
ejpam-3529	239	25	,	,	PUNCT
ejpam-3529	239	26	sαn)pn+1	sαn)pn+1	ADJ
ejpam-3529	239	27	+	+	NOUN
ejpam-3529	239	28	fξ(t	fξ(t	NOUN
ejpam-3529	239	29	,	,	PUNCT
ejpam-3529	239	30	αn	αn	NOUN
ejpam-3529	239	31	,	,	PUNCT
ejpam-3529	239	32	sαn	sαn	ADJ
ejpam-3529	239	33	,	,	PUNCT
ejpam-3529	239	34	αnt	αnt	NOUN
ejpam-3529	239	35	,	,	PUNCT
ejpam-3529	239	36	α	α	PROPN
ejpam-3529	239	37	t	t	NOUN
ejpam-3529	239	38	n)spn+1	n)spn+1	PROPN
ejpam-3529	239	39	=	=	SYM
ejpam-3529	239	40	a+b	a+b	X
ejpam-3529	239	41	+	+	CCONJ
ejpam-3529	239	42	f1x(t	f1x(t	PROPN
ejpam-3529	239	43	,	,	PUNCT
ejpam-3529	239	44	αn	αn	NOUN
ejpam-3529	239	45	,	,	PUNCT
ejpam-3529	239	46	sαn)pn+1	sαn)pn+1	ADJ
ejpam-3529	239	47	+	+	CCONJ
ejpam-3529	239	48	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	239	49	,	,	PUNCT
ejpam-3529	239	50	αn	αn	NOUN
ejpam-3529	239	51	,	,	PUNCT
ejpam-3529	239	52	sαn)spn+1	sαn)spn+1	ADV
ejpam-3529	239	53	(	(	PUNCT
ejpam-3529	239	54	22	22	NUM
ejpam-3529	239	55	)	)	PUNCT
ejpam-3529	239	56	where	where	SCONJ
ejpam-3529	239	57	a	a	DET
ejpam-3529	239	58	=	=	SYM
ejpam-3529	239	59	f1(t	f1(t	PROPN
ejpam-3529	239	60	,	,	PUNCT
ejpam-3529	239	61	u	u	NOUN
ejpam-3529	239	62	,	,	PUNCT
ejpam-3529	239	63	su)−	su)−	X
ejpam-3529	239	64	f1(t	f1(t	PROPN
ejpam-3529	239	65	,	,	PUNCT
ejpam-3529	239	66	αn	αn	NOUN
ejpam-3529	239	67	,	,	PUNCT
ejpam-3529	239	68	su)−	su)−	VERB
ejpam-3529	239	69	f1x(t	f1x(t	PROPN
ejpam-3529	239	70	,	,	PUNCT
ejpam-3529	239	71	αn	αn	NOUN
ejpam-3529	239	72	,	,	PUNCT
ejpam-3529	239	73	sαn)[u−	sαn)[u−	NOUN
ejpam-3529	239	74	αn	αn	NOUN
ejpam-3529	239	75	]	]	X
ejpam-3529	239	76	;	;	PUNCT
ejpam-3529	239	77	b	b	X
ejpam-3529	239	78	=	=	SYM
ejpam-3529	239	79	f1(t	f1(t	PROPN
ejpam-3529	239	80	,	,	PUNCT
ejpam-3529	239	81	αn	αn	NOUN
ejpam-3529	239	82	,	,	PUNCT
ejpam-3529	239	83	su)−	su)−	NOUN
ejpam-3529	239	84	f1(t	f1(t	PROPN
ejpam-3529	239	85	,	,	PUNCT
ejpam-3529	239	86	αn	αn	NOUN
ejpam-3529	239	87	,	,	PUNCT
ejpam-3529	239	88	sαn)−	sαn)−	PROPN
ejpam-3529	239	89	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	239	90	,	,	PUNCT
ejpam-3529	239	91	αn)[su−	αn)[su−	NUM
ejpam-3529	239	92	sαn	sαn	PROPN
ejpam-3529	239	93	]	]	PUNCT
ejpam-3529	239	94	.	.	PUNCT
ejpam-3529	240	1	our	our	PRON
ejpam-3529	240	2	aim	aim	NOUN
ejpam-3529	240	3	is	be	AUX
ejpam-3529	240	4	to	to	PART
ejpam-3529	240	5	simplify	simplify	VERB
ejpam-3529	240	6	each	each	PRON
ejpam-3529	240	7	of	of	ADP
ejpam-3529	240	8	the	the	DET
ejpam-3529	240	9	term	term	NOUN
ejpam-3529	240	10	a	a	DET
ejpam-3529	240	11	,	,	PUNCT
ejpam-3529	240	12	b	b	NOUN
ejpam-3529	240	13	and	and	CCONJ
ejpam-3529	240	14	substitute	substitute	NOUN
ejpam-3529	240	15	in	in	ADP
ejpam-3529	240	16	(	(	PUNCT
ejpam-3529	240	17	22	22	NUM
ejpam-3529	240	18	)	)	PUNCT
ejpam-3529	240	19	.	.	PUNCT
ejpam-3529	241	1	in	in	ADP
ejpam-3529	241	2	this	this	DET
ejpam-3529	241	3	direction	direction	NOUN
ejpam-3529	241	4	,	,	PUNCT
ejpam-3529	241	5	consider	consider	VERB
ejpam-3529	241	6	a	a	DET
ejpam-3529	241	7	=	=	SYM
ejpam-3529	241	8	f1(t	f1(t	PROPN
ejpam-3529	241	9	,	,	PUNCT
ejpam-3529	241	10	u	u	NOUN
ejpam-3529	241	11	,	,	PUNCT
ejpam-3529	241	12	su)−	su)−	X
ejpam-3529	241	13	f1(t	f1(t	PROPN
ejpam-3529	241	14	,	,	PUNCT
ejpam-3529	241	15	αn	αn	NOUN
ejpam-3529	241	16	,	,	PUNCT
ejpam-3529	241	17	su)−	su)−	VERB
ejpam-3529	241	18	f1x(t	f1x(t	PROPN
ejpam-3529	241	19	,	,	PUNCT
ejpam-3529	241	20	αn	αn	NOUN
ejpam-3529	241	21	,	,	PUNCT
ejpam-3529	241	22	sαn)[u−	sαn)[u−	NOUN
ejpam-3529	241	23	αn	αn	NOUN
ejpam-3529	241	24	]	]	X
ejpam-3529	241	25	;	;	PUNCT
ejpam-3529	241	26	≤	≤	NUM
ejpam-3529	241	27	f1xx(t	f1xx(t	PROPN
ejpam-3529	241	28	,	,	PUNCT
ejpam-3529	241	29	τ1	τ1	NOUN
ejpam-3529	241	30	,	,	PUNCT
ejpam-3529	241	31	su)pn	su)pn	NOUN
ejpam-3529	241	32	2	2	NUM
ejpam-3529	241	33	+	+	CCONJ
ejpam-3529	241	34	1∫	1∫	NUM
ejpam-3529	241	35	0	0	NUM
ejpam-3529	241	36	f1xξ(t	f1xξ(t	PROPN
ejpam-3529	241	37	,	,	PUNCT
ejpam-3529	241	38	αn	αn	NOUN
ejpam-3529	241	39	,	,	PUNCT
ejpam-3529	241	40	ssu+	ssu+	NOUN
ejpam-3529	241	41	(	(	PUNCT
ejpam-3529	241	42	1−	1−	NUM
ejpam-3529	241	43	s)sαn)[spn]pnds	s)sαn)[spn]pnd	VERB
ejpam-3529	241	44	≤	≤	NOUN
ejpam-3529	241	45	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	241	46	+	+	CCONJ
ejpam-3529	242	1	l2k1	l2k1	AUX
ejpam-3529	242	2	t	t	X
ejpam-3529	242	3	|pn||pn|	|pn||pn|	NUM
ejpam-3529	242	4	1∫	1∫	NUM
ejpam-3529	242	5	0	0	NUM
ejpam-3529	242	6	ds	ds	ADJ
ejpam-3529	242	7	≤	≤	NOUN
ejpam-3529	242	8	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	242	9	+	+	CCONJ
ejpam-3529	242	10	l2k1	l2k1	PROPN
ejpam-3529	242	11	t	t	NOUN
ejpam-3529	242	12	|pn|2	|pn|2	PUNCT
ejpam-3529	242	13	next	next	ADV
ejpam-3529	242	14	consider	consider	VERB
ejpam-3529	242	15	b	b	PROPN
ejpam-3529	242	16	=	=	SYM
ejpam-3529	242	17	f1(t	f1(t	PROPN
ejpam-3529	242	18	,	,	PUNCT
ejpam-3529	242	19	αn	αn	NOUN
ejpam-3529	242	20	,	,	PUNCT
ejpam-3529	242	21	su)−	su)−	NOUN
ejpam-3529	242	22	f1(t	f1(t	PROPN
ejpam-3529	242	23	,	,	PUNCT
ejpam-3529	242	24	αn	αn	NOUN
ejpam-3529	242	25	,	,	PUNCT
ejpam-3529	242	26	sαn)−	sαn)−	PROPN
ejpam-3529	242	27	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	242	28	,	,	PUNCT
ejpam-3529	242	29	αn)[su−	αn)[su−	NUM
ejpam-3529	242	30	sαn	sαn	PROPN
ejpam-3529	242	31	]	]	PUNCT
ejpam-3529	242	32	;	;	PUNCT
ejpam-3529	242	33	=	=	SYM
ejpam-3529	243	1	1∫	1∫	NUM
ejpam-3529	243	2	0	0	NUM
ejpam-3529	244	1	[	[	X
ejpam-3529	244	2	f1ξ(t	f1ξ(t	ADP
ejpam-3529	244	3	,	,	PUNCT
ejpam-3529	244	4	αn	αn	NOUN
ejpam-3529	244	5	,	,	PUNCT
ejpam-3529	244	6	s(su	s(su	NUM
ejpam-3529	244	7	)	)	PUNCT
ejpam-3529	244	8	+	+	CCONJ
ejpam-3529	244	9	(	(	PUNCT
ejpam-3529	244	10	1−	1−	NUM
ejpam-3529	244	11	s)sαn)−	s)sαn)−	NOUN
ejpam-3529	244	12	[	[	X
ejpam-3529	244	13	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	244	14	,	,	PUNCT
ejpam-3529	244	15	αn	αn	NOUN
ejpam-3529	244	16	,	,	PUNCT
ejpam-3529	244	17	sαn)](su−	sαn)](su−	PROPN
ejpam-3529	244	18	sαn)ds	sαn)ds	ADV
ejpam-3529	244	19	.	.	PUNCT
ejpam-3529	245	1	let	let	VERB
ejpam-3529	245	2	η2(s	η2(s	NOUN
ejpam-3529	245	3	)	)	PUNCT
ejpam-3529	246	1	=	=	PUNCT
ejpam-3529	246	2	s(su	s(su	PROPN
ejpam-3529	246	3	)	)	PUNCT
ejpam-3529	246	4	+	+	CCONJ
ejpam-3529	246	5	(	(	PUNCT
ejpam-3529	246	6	1−	1−	NUM
ejpam-3529	246	7	s)sαn	s)sαn	NOUN
ejpam-3529	246	8	.	.	PUNCT
ejpam-3529	247	1	then	then	ADV
ejpam-3529	247	2	b	b	X
ejpam-3529	247	3	=	=	SYM
ejpam-3529	248	1	1∫	1∫	NUM
ejpam-3529	248	2	0	0	NUM
ejpam-3529	249	1	[	[	X
ejpam-3529	249	2	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	249	3	,	,	PUNCT
ejpam-3529	249	4	αn	αn	NOUN
ejpam-3529	249	5	,	,	PUNCT
ejpam-3529	249	6	η2(s))−	η2(s))−	ADJ
ejpam-3529	249	7	f1ξ(t	f1ξ(t	PROPN
ejpam-3529	249	8	,	,	PUNCT
ejpam-3529	249	9	αn	αn	NOUN
ejpam-3529	249	10	,	,	PUNCT
ejpam-3529	249	11	sαn)](su−	sαn)](su−	PROPN
ejpam-3529	249	12	sαn)ds	sαn)ds	ADV
ejpam-3529	249	13	≤	≤	NUM
ejpam-3529	249	14	l3k21	l3k21	PROPN
ejpam-3529	249	15	t	t	NOUN
ejpam-3529	249	16	2|p2n|	2|p2n|	NUM
ejpam-3529	249	17	1∫	1∫	NUM
ejpam-3529	249	18	0	0	NUM
ejpam-3529	250	1	1∫	1∫	NUM
ejpam-3529	250	2	0	0	NUM
ejpam-3529	250	3	s	s	PART
ejpam-3529	250	4	dsdσ	dsdσ	NOUN
ejpam-3529	250	5	≤	≤	NUM
ejpam-3529	250	6	l3k21	l3k21	PROPN
ejpam-3529	250	7	t	t	NOUN
ejpam-3529	250	8	2|p2n|	2|p2n|	NUM
ejpam-3529	250	9	p′n+1	p′n+1	PROPN
ejpam-3529	250	10	≤	≤	PROPN
ejpam-3529	250	11	{	{	PUNCT
ejpam-3529	250	12	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	250	13	+	+	CCONJ
ejpam-3529	250	14	l2k1	l2k1	NOUN
ejpam-3529	250	15	t	t	NOUN
ejpam-3529	250	16	|pn|2}+	|pn|2}+	NUM
ejpam-3529	250	17	{	{	PUNCT
ejpam-3529	250	18	l3k21	l3k21	NOUN
ejpam-3529	250	19	t	t	NOUN
ejpam-3529	250	20	2|p2n|	2|p2n|	NUM
ejpam-3529	250	21	}	}	SYM
ejpam-3529	250	22	−mpn+1(t)−nspn+1(t	−mpn+1(t)−nspn+1(t	PROPN
ejpam-3529	250	23	)	)	PUNCT
ejpam-3529	250	24	≤	≤	NUM
ejpam-3529	250	25	l	l	NOUN
ejpam-3529	250	26	−mpn+1(t)−nspn+1(t	−mpn+1(t)−nspn+1(t	PROPN
ejpam-3529	250	27	)	)	PUNCT
ejpam-3529	250	28	references	reference	NOUN
ejpam-3529	250	29	1674	1674	NUM
ejpam-3529	250	30	where	where	SCONJ
ejpam-3529	250	31	l	l	NOUN
ejpam-3529	250	32	=	=	PUNCT
ejpam-3529	250	33	{	{	PUNCT
ejpam-3529	250	34	l1|pn|2	l1|pn|2	NOUN
ejpam-3529	250	35	+	+	CCONJ
ejpam-3529	250	36	l2k1	l2k1	PROPN
ejpam-3529	250	37	t	t	NOUN
ejpam-3529	250	38	|pn|2	|pn|2	VERB
ejpam-3529	250	39	}	}	PUNCT
ejpam-3529	250	40	+	+	CCONJ
ejpam-3529	250	41	{	{	PUNCT
ejpam-3529	250	42	l3k21	l3k21	X
ejpam-3529	250	43	t	t	NOUN
ejpam-3529	250	44	2|p2n|	2|p2n|	NUM
ejpam-3529	250	45	}	}	PUNCT
ejpam-3529	250	46	.	.	PUNCT
ejpam-3529	251	1	now	now	ADV
ejpam-3529	251	2	multiplying	multiply	VERB
ejpam-3529	251	3	throughout	throughout	ADP
ejpam-3529	251	4	by	by	ADP
ejpam-3529	251	5	emt	emt	NOUN
ejpam-3529	251	6	and	and	CCONJ
ejpam-3529	251	7	setting	set	VERB
ejpam-3529	251	8	p̃n+1	p̃n+1	PROPN
ejpam-3529	251	9	=	=	SYM
ejpam-3529	251	10	emtpn+1	emtpn+1	PROPN
ejpam-3529	251	11	,	,	PUNCT
ejpam-3529	251	12	we	we	PRON
ejpam-3529	251	13	get	get	VERB
ejpam-3529	251	14	(	(	PUNCT
ejpam-3529	251	15	pn+1(t)e	pn+1(t)e	X
ejpam-3529	251	16	mt)′	mt)′	NOUN
ejpam-3529	251	17	≤	≤	PROPN
ejpam-3529	251	18	nk1	nk1	PROPN
ejpam-3529	251	19	h2∫	h2∫	NOUN
ejpam-3529	251	20	0	0	NUM
ejpam-3529	252	1	pn+1(s)e	pn+1(s)e	NOUN
ejpam-3529	252	2	mtds+	mtds+	X
ejpam-3529	252	3	lemt	lemt	PROPN
ejpam-3529	252	4	≤	≤	PROPN
ejpam-3529	252	5	nk1	nk1	PROPN
ejpam-3529	252	6	∫	∫	PROPN
ejpam-3529	252	7	t	t	PROPN
ejpam-3529	252	8	0	0	NUM
ejpam-3529	253	1	p̃n+1(s)e	p̃n+1(s)e	ADV
ejpam-3529	253	2	m(t−s)ds+	m(t−s)ds+	PROPN
ejpam-3529	253	3	lemt	lemt	NOUN
ejpam-3529	253	4	=	=	SYM
ejpam-3529	253	5	w′(t	w′(t	NOUN
ejpam-3529	253	6	)	)	PUNCT
ejpam-3529	253	7	(	(	PUNCT
ejpam-3529	253	8	say	say	INTJ
ejpam-3529	253	9	)	)	PUNCT
ejpam-3529	253	10	then	then	ADV
ejpam-3529	253	11	choosing	choose	VERB
ejpam-3529	253	12	w(0)=0	w(0)=0	NUM
ejpam-3529	253	13	,	,	PUNCT
ejpam-3529	253	14	we	we	PRON
ejpam-3529	253	15	get	get	VERB
ejpam-3529	253	16	p̃n+1	p̃n+1	PROPN
ejpam-3529	253	17	≤	≤	NOUN
ejpam-3529	253	18	w(t	w(t	PROPN
ejpam-3529	253	19	)	)	PUNCT
ejpam-3529	253	20	on	on	ADP
ejpam-3529	253	21	i.	i.	PROPN
ejpam-3529	253	22	clearly	clearly	ADV
ejpam-3529	253	23	w′(t	w′(t	NOUN
ejpam-3529	253	24	)	)	PUNCT
ejpam-3529	253	25	≥	≥	NOUN
ejpam-3529	253	26	0	0	NUM
ejpam-3529	253	27	,	,	PUNCT
ejpam-3529	253	28	which	which	PRON
ejpam-3529	253	29	means	mean	VERB
ejpam-3529	253	30	that	that	SCONJ
ejpam-3529	253	31	w(t	w(t	PROPN
ejpam-3529	253	32	)	)	PUNCT
ejpam-3529	253	33	is	be	AUX
ejpam-3529	253	34	nondecreasing	nondecrease	VERB
ejpam-3529	253	35	on	on	ADP
ejpam-3529	253	36	i.	i.	PROPN
ejpam-3529	253	37	now	now	ADV
ejpam-3529	253	38	for	for	ADP
ejpam-3529	253	39	t	t	PROPN
ejpam-3529	253	40	∈	∈	PROPN
ejpam-3529	253	41	i	i	PROPN
ejpam-3529	253	42	,	,	PUNCT
ejpam-3529	253	43	w(t	w(t	PROPN
ejpam-3529	253	44	)	)	PUNCT
ejpam-3529	253	45	≤	≤	PUNCT
ejpam-3529	253	46	nk1	nk1	NOUN
ejpam-3529	253	47	t∫	t∫	PRON
ejpam-3529	253	48	0	0	NUM
ejpam-3529	253	49	z∫	z∫	NOUN
ejpam-3529	253	50	0	0	PUNCT
ejpam-3529	254	1	p̃n+1(s)e	p̃n+1(s)e	VERB
ejpam-3529	254	2	m(z−s)dsdz	m(z−s)dsdz	PROPN
ejpam-3529	254	3	+	+	CCONJ
ejpam-3529	254	4	t∫	t∫	PROPN
ejpam-3529	254	5	0	0	NUM
ejpam-3529	254	6	lemudu	lemudu	NOUN
ejpam-3529	254	7	by	by	ADP
ejpam-3529	254	8	setting	set	VERB
ejpam-3529	254	9	c2	c2	PROPN
ejpam-3529	254	10	=	=	SYM
ejpam-3529	254	11	l	l	PROPN
ejpam-3529	254	12	{	{	PUNCT
ejpam-3529	254	13	emt	emt	PROPN
ejpam-3529	254	14	m	m	PROPN
ejpam-3529	254	15	}	}	PUNCT
ejpam-3529	254	16	and	and	CCONJ
ejpam-3529	254	17	c1	c1	PROPN
ejpam-3529	254	18	=	=	PUNCT
ejpam-3529	254	19	n	n	CCONJ
ejpam-3529	254	20	m	m	PROPN
ejpam-3529	254	21	k1e	k1e	PROPN
ejpam-3529	254	22	mt	mt	PROPN
ejpam-3529	254	23	we	we	PRON
ejpam-3529	254	24	get	get	VERB
ejpam-3529	254	25	w(t	w(t	PROPN
ejpam-3529	254	26	)	)	PUNCT
ejpam-3529	254	27	≤	≤	PROPN
ejpam-3529	254	28	c1	c1	PROPN
ejpam-3529	254	29	t∫	t∫	PROPN
ejpam-3529	254	30	0	0	NUM
ejpam-3529	254	31	w(z)dz	w(z)dz	PROPN
ejpam-3529	254	32	+	+	PROPN
ejpam-3529	254	33	c2	c2	PROPN
ejpam-3529	254	34	.	.	PUNCT
ejpam-3529	255	1	now	now	ADV
ejpam-3529	255	2	by	by	ADP
ejpam-3529	255	3	using	use	VERB
ejpam-3529	255	4	gronwall	gronwall	PROPN
ejpam-3529	255	5	’s	’s	PART
ejpam-3529	255	6	inequality	inequality	NOUN
ejpam-3529	255	7	we	we	PRON
ejpam-3529	255	8	get	get	VERB
ejpam-3529	255	9	w(t	w(t	PROPN
ejpam-3529	255	10	)	)	PUNCT
ejpam-3529	255	11	≤	≤	NUM
ejpam-3529	255	12	c2e	c2e	NOUN
ejpam-3529	255	13	t∫	t∫	ADJ
ejpam-3529	255	14	0	0	NUM
ejpam-3529	255	15	c1ds	c1ds	NOUN
ejpam-3529	255	16	≤	≤	NUM
ejpam-3529	255	17	c2ec1	c2ec1	PROPN
ejpam-3529	255	18	t	t	PROPN
ejpam-3529	255	19	≤	≤	NUM
ejpam-3529	255	20	c2ec1	c2ec1	PROPN
ejpam-3529	255	21	t	t	PROPN
ejpam-3529	255	22	hence	hence	ADV
ejpam-3529	255	23	p̃n+1(t	p̃n+1(t	ADJ
ejpam-3529	255	24	)	)	PUNCT
ejpam-3529	255	25	≤	≤	NUM
ejpam-3529	256	1	w(t	w(t	PROPN
ejpam-3529	256	2	)	)	PUNCT
ejpam-3529	256	3	≤	≤	PUNCT
ejpam-3529	257	1	max[0,t	max[0,t	PROPN
ejpam-3529	257	2	]	]	PUNCT
ejpam-3529	257	3	l(t)[emt]ec1	l(t)[emt]ec1	PROPN
ejpam-3529	257	4	t	t	PROPN
ejpam-3529	257	5	p̃n+1(t	p̃n+1(t	NOUN
ejpam-3529	257	6	)	)	PUNCT
ejpam-3529	257	7	≤	≤	NUM
ejpam-3529	257	8	w(t	w(t	PROPN
ejpam-3529	257	9	)	)	PUNCT
ejpam-3529	257	10	≤	≤	PUNCT
ejpam-3529	258	1	max[0,t	max[0,t	PROPN
ejpam-3529	258	2	]	]	X
ejpam-3529	258	3	l(t)[e(m+c1)t	l(t)[e(m+c1)t	X
ejpam-3529	258	4	]	]	X
ejpam-3529	258	5	|pn+1|	|pn+1|	X
ejpam-3529	258	6	≤	≤	NOUN
ejpam-3529	258	7	(	(	PUNCT
ejpam-3529	258	8	e(n1+c1)t	e(n1+c1)t	NOUN
ejpam-3529	258	9	)	)	PUNCT
ejpam-3529	259	1	[	[	X
ejpam-3529	259	2	m	m	NOUN
ejpam-3529	259	3	|pn|2	|pn|2	ADP
ejpam-3529	259	4	]	]	X
ejpam-3529	259	5	,	,	PUNCT
ejpam-3529	259	6	therefore	therefore	ADV
ejpam-3529	259	7	the	the	DET
ejpam-3529	259	8	sequence	sequence	NOUN
ejpam-3529	259	9	{	{	PUNCT
ejpam-3529	259	10	αn	αn	NOUN
ejpam-3529	259	11	}	}	PUNCT
ejpam-3529	259	12	converges	converge	VERB
ejpam-3529	259	13	quadratically	quadratically	ADV
ejpam-3529	259	14	on	on	ADP
ejpam-3529	259	15	i.	i.	NOUN
ejpam-3529	259	16	hence	hence	ADV
ejpam-3529	259	17	the	the	DET
ejpam-3529	259	18	theorem	theorem	PROPN
ejpam-3529	259	19	.	.	PUNCT
ejpam-3529	260	1	references	reference	NOUN
ejpam-3529	260	2	[	[	X
ejpam-3529	260	3	1	1	NUM
ejpam-3529	260	4	]	]	SYM
ejpam-3529	260	5	lakshmikantham	lakshmikantham	ADV
ejpam-3529	260	6	,	,	PUNCT
ejpam-3529	260	7	v.	v.	ADP
ejpam-3529	260	8	and	and	CCONJ
ejpam-3529	260	9	rama	rama	PROPN
ejpam-3529	260	10	mohana	mohana	PROPN
ejpam-3529	260	11	rao	rao	PROPN
ejpam-3529	260	12	,	,	PUNCT
ejpam-3529	260	13	m.	m.	NOUN
ejpam-3529	260	14	,	,	PUNCT
ejpam-3529	260	15	theory	theory	NOUN
ejpam-3529	260	16	of	of	ADP
ejpam-3529	260	17	integro	integro	PROPN
ejpam-3529	260	18	differential	differential	ADJ
ejpam-3529	260	19	equations	equation	NOUN
ejpam-3529	260	20	.	.	PUNCT
ejpam-3529	261	1	gordon	gordon	PROPN
ejpam-3529	261	2	and	and	CCONJ
ejpam-3529	261	3	breach	breach	VERB
ejpam-3529	261	4	science	science	NOUN
ejpam-3529	261	5	publishers	publisher	NOUN
ejpam-3529	261	6	,	,	PUNCT
ejpam-3529	261	7	s.a	s.a	PROPN
ejpam-3529	261	8	,	,	PUNCT
ejpam-3529	261	9	1995	1995	NUM
ejpam-3529	261	10	.	.	PUNCT
ejpam-3529	262	1	[	[	X
ejpam-3529	262	2	2	2	X
ejpam-3529	262	3	]	]	X
ejpam-3529	262	4	g.	g.	PROPN
ejpam-3529	262	5	s.	s.	PROPN
ejpam-3529	262	6	ladde	ladde	PROPN
ejpam-3529	262	7	,	,	PUNCT
ejpam-3529	262	8	lakshmikantham	lakshmikantham	INTJ
ejpam-3529	262	9	,	,	PUNCT
ejpam-3529	262	10	v.	v.	ADV
ejpam-3529	262	11	,	,	PUNCT
ejpam-3529	262	12	a.	a.	PROPN
ejpam-3529	262	13	s.	s.	PROPN
ejpam-3529	262	14	vatsala.monotone	vatsala.monotone	NUM
ejpam-3529	262	15	iterative	iterative	NOUN
ejpam-3529	262	16	technique	technique	NOUN
ejpam-3529	262	17	for	for	ADP
ejpam-3529	262	18	nonlinear	nonlinear	ADJ
ejpam-3529	262	19	differential	differential	ADJ
ejpam-3529	262	20	equations	equation	NOUN
ejpam-3529	262	21	,	,	PUNCT
ejpam-3529	262	22	pitman	pitman	NOUN
ejpam-3529	262	23	publishing	publishing	PROPN
ejpam-3529	262	24	ltd	ltd	PROPN
ejpam-3529	262	25	,	,	PUNCT
ejpam-3529	262	26	1985	1985	NUM
ejpam-3529	262	27	.	.	PUNCT
ejpam-3529	263	1	references	reference	NOUN
ejpam-3529	263	2	1675	1675	NUM
ejpam-3529	263	3	[	[	X
ejpam-3529	263	4	3	3	NUM
ejpam-3529	263	5	]	]	PUNCT
ejpam-3529	263	6	m.	m.	NOUN
ejpam-3529	263	7	sokol	sokol	PROPN
ejpam-3529	263	8	and	and	CCONJ
ejpam-3529	263	9	a.s	a.s	PROPN
ejpam-3529	263	10	.	.	PROPN
ejpam-3529	263	11	vatsala	vatsala	PROPN
ejpam-3529	263	12	,	,	PUNCT
ejpam-3529	263	13	a	a	DET
ejpam-3529	263	14	unified	unified	ADJ
ejpam-3529	263	15	exhaustive	exhaustive	ADJ
ejpam-3529	263	16	study	study	NOUN
ejpam-3529	263	17	of	of	ADP
ejpam-3529	263	18	monotone	monotone	ADJ
ejpam-3529	263	19	iterative	iterative	NOUN
ejpam-3529	263	20	method	method	NOUN
ejpam-3529	263	21	for	for	ADP
ejpam-3529	263	22	initial	initial	ADJ
ejpam-3529	263	23	value	value	NOUN
ejpam-3529	263	24	problems	problem	NOUN
ejpam-3529	263	25	,	,	PUNCT
ejpam-3529	263	26	nonlinear	nonlinear	ADJ
ejpam-3529	263	27	studies	study	NOUN
ejpam-3529	263	28	8	8	NUM
ejpam-3529	263	29	(	(	PUNCT
ejpam-3529	263	30	4	4	NUM
ejpam-3529	263	31	)	)	PUNCT
ejpam-3529	263	32	,	,	PUNCT
ejpam-3529	263	33	429	429	NUM
ejpam-3529	263	34	-	-	SYM
ejpam-3529	263	35	438	438	NUM
ejpam-3529	263	36	,	,	PUNCT
ejpam-3529	263	37	2001	2001	NUM
ejpam-3529	263	38	.	.	PUNCT
ejpam-3529	264	1	[	[	X
ejpam-3529	264	2	4	4	X
ejpam-3529	264	3	]	]	X
ejpam-3529	264	4	v.	v.	ADP
ejpam-3529	264	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3529	264	6	,	,	PUNCT
ejpam-3529	264	7	a.s.vatsala	a.s.vatsala	NOUN
ejpam-3529	264	8	,	,	PUNCT
ejpam-3529	264	9	generalized	generalized	ADJ
ejpam-3529	264	10	quasilinearization	quasilinearization	NOUN
ejpam-3529	264	11	for	for	ADP
ejpam-3529	264	12	nonlinear	nonlinear	ADJ
ejpam-3529	264	13	problems	problem	NOUN
ejpam-3529	264	14	,	,	PUNCT
ejpam-3529	264	15	academic	academic	ADJ
ejpam-3529	264	16	publications	publication	NOUN
ejpam-3529	264	17	,	,	PUNCT
ejpam-3529	264	18	dordrechet	dordrechet	PROPN
ejpam-3529	264	19	,	,	PUNCT
ejpam-3529	264	20	1998	1998	NUM
ejpam-3529	264	21	.	.	PUNCT
ejpam-3529	265	1	[	[	X
ejpam-3529	265	2	5	5	NUM
ejpam-3529	265	3	]	]	PUNCT
ejpam-3529	265	4	i.	i.	PROPN
ejpam-3529	265	5	h.	h.	PROPN
ejpam-3529	265	6	west	west	PROPN
ejpam-3529	265	7	and	and	CCONJ
ejpam-3529	265	8	a.	a.	PROPN
ejpam-3529	265	9	s.	s.	PROPN
ejpam-3529	265	10	vatsala	vatsala	PROPN
ejpam-3529	265	11	.	.	PUNCT
ejpam-3529	266	1	generalized	generalize	VERB
ejpam-3529	266	2	monotone	monotone	ADJ
ejpam-3529	266	3	iterative	iterative	NOUN
ejpam-3529	266	4	method	method	NOUN
ejpam-3529	266	5	for	for	ADP
ejpam-3529	266	6	initial	initial	ADJ
ejpam-3529	266	7	value	value	NOUN
ejpam-3529	266	8	problems	problem	NOUN
ejpam-3529	266	9	.	.	PUNCT
ejpam-3529	267	1	appl	appl	PROPN
ejpam-3529	267	2	.	.	PROPN
ejpam-3529	267	3	math	math	PROPN
ejpam-3529	267	4	.	.	PUNCT
ejpam-3529	268	1	lett	lett	PROPN
ejpam-3529	268	2	,	,	PUNCT
ejpam-3529	268	3	17	17	NUM
ejpam-3529	268	4	:	:	SYM
ejpam-3529	268	5	1231	1231	NUM
ejpam-3529	268	6	-	-	SYM
ejpam-3529	268	7	1237	1237	NUM
ejpam-3529	268	8	,	,	PUNCT
ejpam-3529	268	9	2004	2004	NUM
ejpam-3529	268	10	.	.	PUNCT
ejpam-3529	269	1	[	[	X
ejpam-3529	269	2	6	6	NUM
ejpam-3529	269	3	]	]	PUNCT
ejpam-3529	269	4	i.	i.	PROPN
ejpam-3529	269	5	h.	h.	PROPN
ejpam-3529	269	6	west	west	PROPN
ejpam-3529	269	7	and	and	CCONJ
ejpam-3529	269	8	a.	a.	PROPN
ejpam-3529	269	9	s.	s.	PROPN
ejpam-3529	269	10	vatsala	vatsala	PROPN
ejpam-3529	269	11	.	.	PUNCT
ejpam-3529	270	1	generalized	generalize	VERB
ejpam-3529	270	2	monotone	monotone	ADJ
ejpam-3529	270	3	iterative	iterative	NOUN
ejpam-3529	270	4	method	method	NOUN
ejpam-3529	270	5	for	for	ADP
ejpam-3529	270	6	integro	integro	PROPN
ejpam-3529	270	7	differential	differential	ADJ
ejpam-3529	270	8	equations	equation	NOUN
ejpam-3529	270	9	with	with	ADP
ejpam-3529	270	10	periodic	periodic	ADJ
ejpam-3529	270	11	boundary	boundary	ADJ
ejpam-3529	270	12	conditions	condition	NOUN
ejpam-3529	270	13	.	.	PUNCT
ejpam-3529	271	1	math	math	NOUN
ejpam-3529	271	2	.	.	PUNCT
ejpam-3529	272	1	inequal	inequal	PROPN
ejpam-3529	272	2	.	.	PUNCT
ejpam-3529	273	1	appl	appl	PROPN
ejpam-3529	273	2	.	.	PROPN
ejpam-3529	273	3	,	,	PUNCT
ejpam-3529	273	4	10	10	NUM
ejpam-3529	273	5	:	:	SYM
ejpam-3529	273	6	151	151	NUM
ejpam-3529	273	7	-	-	SYM
ejpam-3529	273	8	163	163	NUM
ejpam-3529	273	9	,	,	PUNCT
ejpam-3529	273	10	2007	2007	NUM
ejpam-3529	273	11	.	.	PUNCT
ejpam-3529	274	1	[	[	X
ejpam-3529	274	2	7	7	NUM
ejpam-3529	274	3	]	]	X
ejpam-3529	274	4	s.g.pandit	s.g.pandit	NOUN
ejpam-3529	274	5	,	,	PUNCT
ejpam-3529	274	6	d.h.dezern	d.h.dezern	NOUN
ejpam-3529	274	7	and	and	CCONJ
ejpam-3529	274	8	j.o.adeyeye	j.o.adeyeye	NOUN
ejpam-3529	274	9	,	,	PUNCT
ejpam-3529	274	10	periodic	periodic	ADJ
ejpam-3529	274	11	boundary	boundary	ADJ
ejpam-3529	274	12	value	value	NOUN
ejpam-3529	274	13	problems	problem	NOUN
ejpam-3529	274	14	for	for	ADP
ejpam-3529	274	15	nonlinear	nonlinear	ADJ
ejpam-3529	274	16	integro	integro	PROPN
ejpam-3529	274	17	differential	differential	PROPN
ejpam-3529	274	18	equations	equation	NOUN
ejpam-3529	274	19	,	,	PUNCT
ejpam-3529	274	20	proceedings	proceeding	NOUN
ejpam-3529	274	21	of	of	ADP
ejpam-3529	274	22	neural	neural	ADJ
ejpam-3529	274	23	;	;	PUNCT
ejpam-3529	274	24	parallel	parallel	ADJ
ejpam-3529	274	25	;	;	PUNCT
ejpam-3529	274	26	and	and	CCONJ
ejpam-3529	274	27	scientific	scientific	ADJ
ejpam-3529	274	28	computations	computation	NOUN
ejpam-3529	274	29	;	;	PUNCT
ejpam-3529	274	30	vol	vol	NOUN
ejpam-3529	274	31	:	:	PUNCT
ejpam-3529	274	32	4	4	NUM
ejpam-3529	274	33	;	;	PUNCT
ejpam-3529	274	34	pp	pp	CCONJ
ejpam-3529	274	35	:	:	PUNCT
ejpam-3529	274	36	316	316	NUM
ejpam-3529	274	37	-	-	SYM
ejpam-3529	274	38	320	320	NUM
ejpam-3529	274	39	,	,	PUNCT
ejpam-3529	274	40	dynamic	dynamic	ADJ
ejpam-3529	274	41	,	,	PUNCT
ejpam-3529	274	42	atlanta	atlanta	PROPN
ejpam-3529	274	43	,	,	PUNCT
ejpam-3529	274	44	ga	ga	PROPN
ejpam-3529	274	45	,	,	PUNCT
ejpam-3529	274	46	usa	usa	PROPN
ejpam-3529	274	47	,	,	PUNCT
ejpam-3529	274	48	2010	2010	NUM
ejpam-3529	274	49	.	.	PUNCT
ejpam-3529	275	1	[	[	X
ejpam-3529	275	2	8	8	NUM
ejpam-3529	275	3	]	]	X
ejpam-3529	275	4	wen	wen	PROPN
ejpam-3529	275	5	-	-	PUNCT
ejpam-3529	275	6	li	li	PROPN
ejpam-3529	275	7	wang	wang	PROPN
ejpam-3529	275	8	and	and	CCONJ
ejpam-3529	275	9	jing	jing	PROPN
ejpam-3529	275	10	-	-	PUNCT
ejpam-3529	275	11	feng	feng	PROPN
ejpam-3529	275	12	tian	tian	PROPN
ejpam-3529	275	13	,	,	PUNCT
ejpam-3529	275	14	generalized	generalize	VERB
ejpam-3529	275	15	monotone	monotone	ADJ
ejpam-3529	275	16	iterative	iterative	NOUN
ejpam-3529	275	17	method	method	NOUN
ejpam-3529	275	18	for	for	ADP
ejpam-3529	275	19	nonlinear	nonlinear	ADJ
ejpam-3529	275	20	boundary	boundary	ADJ
ejpam-3529	275	21	value	value	NOUN
ejpam-3529	275	22	problems	problem	NOUN
ejpam-3529	275	23	with	with	ADP
ejpam-3529	275	24	causal	causal	NOUN
ejpam-3529	275	25	operators	operator	NOUN
ejpam-3529	275	26	,	,	PUNCT
ejpam-3529	275	27	boundary	boundary	ADJ
ejpam-3529	275	28	value	value	NOUN
ejpam-3529	275	29	problems	problem	NOUN
ejpam-3529	275	30	,	,	PUNCT
ejpam-3529	275	31	volume	volume	NOUN
ejpam-3529	275	32	192	192	NUM
ejpam-3529	275	33	,	,	PUNCT
ejpam-3529	275	34	1	1	NUM
ejpam-3529	275	35	-	-	SYM
ejpam-3529	275	36	12	12	NUM
ejpam-3529	275	37	,	,	PUNCT
ejpam-3529	275	38	2014	2014	NUM
ejpam-3529	275	39	.	.	PUNCT
ejpam-3529	276	1	[	[	X
ejpam-3529	276	2	9	9	NUM
ejpam-3529	276	3	]	]	PUNCT
ejpam-3529	276	4	j.vasundhara	j.vasundhara	X
ejpam-3529	276	5	devi	devi	PROPN
ejpam-3529	276	6	,	,	PUNCT
ejpam-3529	276	7	s.srinivasa	s.srinivasa	PROPN
ejpam-3529	276	8	rao	rao	PROPN
ejpam-3529	276	9	,	,	PUNCT
ejpam-3529	276	10	s.n.r.g.bharat	s.n.r.g.bharat	PROPN
ejpam-3529	276	11	iragavarapu	iragavarapu	PROPN
ejpam-3529	276	12	,	,	PUNCT
ejpam-3529	276	13	periodic	periodic	ADJ
ejpam-3529	276	14	boundary	boundary	ADJ
ejpam-3529	276	15	value	value	NOUN
ejpam-3529	276	16	problem	problem	NOUN
ejpam-3529	276	17	for	for	ADP
ejpam-3529	276	18	graph	graph	NOUN
ejpam-3529	276	19	differential	differential	ADJ
ejpam-3529	276	20	equations	equation	NOUN
ejpam-3529	276	21	through	through	ADP
ejpam-3529	276	22	its	its	PRON
ejpam-3529	276	23	associated	associated	ADJ
ejpam-3529	276	24	matrix	matrix	NOUN
ejpam-3529	276	25	differential	differential	NOUN
ejpam-3529	276	26	equations	equation	NOUN
ejpam-3529	276	27	,	,	PUNCT
ejpam-3529	276	28	malaya	malaya	PROPN
ejpam-3529	276	29	journal	journal	PROPN
ejpam-3529	276	30	of	of	ADP
ejpam-3529	276	31	mathematik	mathematik	PROPN
ejpam-3529	276	32	3(4	3(4	NUM
ejpam-3529	276	33	)	)	PUNCT
ejpam-3529	276	34	,	,	PUNCT
ejpam-3529	276	35	pg	pg	INTJ
ejpam-3529	276	36	.	.	PUNCT
ejpam-3529	277	1	598	598	NUM
ejpam-3529	277	2	-	-	SYM
ejpam-3529	277	3	606	606	NUM
ejpam-3529	277	4	,	,	PUNCT
ejpam-3529	277	5	2015	2015	NUM
ejpam-3529	277	6	.	.	PUNCT
ejpam-3529	278	1	[	[	X
ejpam-3529	278	2	10	10	NUM
ejpam-3529	278	3	]	]	PUNCT
ejpam-3529	278	4	j.vasundhara	j.vasundhara	X
ejpam-3529	278	5	devi	devi	PROPN
ejpam-3529	278	6	,	,	PUNCT
ejpam-3529	278	7	s.n.r.g.bharat	s.n.r.g.bharat	NOUN
ejpam-3529	278	8	iragavarapu	iragavarapu	PROPN
ejpam-3529	278	9	,	,	PUNCT
ejpam-3529	278	10	s.srinivasa	s.srinivasa	PROPN
ejpam-3529	278	11	rao	rao	NOUN
ejpam-3529	278	12	,	,	PUNCT
ejpam-3529	278	13	quasilinearization	quasilinearization	NOUN
ejpam-3529	278	14	technique	technique	NOUN
ejpam-3529	278	15	for	for	ADP
ejpam-3529	278	16	periodic	periodic	ADJ
ejpam-3529	278	17	boundary	boundary	ADJ
ejpam-3529	278	18	value	value	NOUN
ejpam-3529	278	19	problem	problem	NOUN
ejpam-3529	278	20	of	of	ADP
ejpam-3529	278	21	graph	graph	NOUN
ejpam-3529	278	22	differential	differential	ADJ
ejpam-3529	278	23	equations	equation	NOUN
ejpam-3529	278	24	and	and	CCONJ
ejpam-3529	278	25	tts	tts	PROPN
ejpam-3529	278	26	associated	associate	VERB
ejpam-3529	278	27	matrix	matrix	NOUN
ejpam-3529	278	28	differential	differential	NOUN
ejpam-3529	278	29	equations	equation	NOUN
ejpam-3529	278	30	,	,	PUNCT
ejpam-3529	278	31	dynamics	dynamic	NOUN
ejpam-3529	278	32	of	of	ADP
ejpam-3529	278	33	continuous	continuous	ADJ
ejpam-3529	278	34	,	,	PUNCT
ejpam-3529	278	35	discrete	discrete	ADJ
ejpam-3529	278	36	and	and	CCONJ
ejpam-3529	278	37	impulsive	impulsive	ADJ
ejpam-3529	278	38	systems	system	NOUN
ejpam-3529	278	39	,	,	PUNCT
ejpam-3529	278	40	series	series	NOUN
ejpam-3529	278	41	b	b	PROPN
ejpam-3529	278	42	:	:	PUNCT
ejpam-3529	278	43	applications	application	NOUN
ejpam-3529	278	44	and	and	CCONJ
ejpam-3529	278	45	algorithms	algorithm	NOUN
ejpam-3529	278	46	23	23	NUM
ejpam-3529	278	47	,	,	PUNCT
ejpam-3529	278	48	pg.287300	pg.287300	VERB
ejpam-3529	278	49	,	,	PUNCT
ejpam-3529	278	50	2016	2016	NUM
ejpam-3529	278	51	,	,	PUNCT
ejpam-3529	278	52	watam	watam	NOUN
ejpam-3529	278	53	press	press	NOUN
ejpam-3529	278	54	.	.	PUNCT
ejpam-3529	279	1	[	[	X
ejpam-3529	279	2	11	11	NUM
ejpam-3529	279	3	]	]	SYM
ejpam-3529	279	4	i.s.n.r.g.bharat	i.s.n.r.g.bharat	NOUN
ejpam-3529	279	5	and	and	CCONJ
ejpam-3529	279	6	j.vasundhara	j.vasundhara	ADJ
ejpam-3529	279	7	devi	devi	PROPN
ejpam-3529	279	8	,	,	PUNCT
ejpam-3529	279	9	generalized	generalized	ADJ
ejpam-3529	279	10	quasilinearization	quasilinearization	NOUN
ejpam-3529	279	11	for	for	ADP
ejpam-3529	279	12	pbvp	pbvp	NOUN
ejpam-3529	279	13	through	through	ADP
ejpam-3529	279	14	coupled	couple	VERB
ejpam-3529	279	15	lower	low	ADJ
ejpam-3529	279	16	and	and	CCONJ
ejpam-3529	279	17	upper	upper	ADJ
ejpam-3529	279	18	solutions	solution	NOUN
ejpam-3529	279	19	of	of	ADP
ejpam-3529	279	20	the	the	DET
ejpam-3529	279	21	ivp	ivp	NOUN
ejpam-3529	279	22	,	,	PUNCT
ejpam-3529	279	23	dynamics	dynamic	NOUN
ejpam-3529	279	24	of	of	ADP
ejpam-3529	279	25	continuous	continuous	ADJ
ejpam-3529	279	26	,	,	PUNCT
ejpam-3529	279	27	discrete	discrete	ADJ
ejpam-3529	279	28	and	and	CCONJ
ejpam-3529	279	29	impulsive	impulsive	ADJ
ejpam-3529	279	30	systems	system	NOUN
ejpam-3529	279	31	,	,	PUNCT
ejpam-3529	279	32	vol	vol	NOUN
ejpam-3529	279	33	.	.	PROPN
ejpam-3529	279	34	26	26	NUM
ejpam-3529	279	35	,	,	PUNCT
ejpam-3529	279	36	371	371	NUM
ejpam-3529	279	37	-	-	SYM
ejpam-3529	279	38	380	380	NUM
ejpam-3529	279	39	.	.	PUNCT