id	sid	tid	token	lemma	pos
ejpam-2714	1	1	compile	compile	NOUN
ejpam-2714	1	2	/	/	SYM
ejpam-2714	1	3	output.dvi	output.dvi	NOUN
ejpam-2714	1	4	european	european	ADJ
ejpam-2714	1	5	journal	journal	NOUN
ejpam-2714	1	6	of	of	ADP
ejpam-2714	1	7	pure	pure	ADJ
ejpam-2714	1	8	and	and	CCONJ
ejpam-2714	1	9	applied	apply	VERB
ejpam-2714	1	10	mathematics	mathematic	NOUN
ejpam-2714	1	11	vol	vol	NOUN
ejpam-2714	1	12	.	.	PROPN
ejpam-2714	2	1	9	9	NUM
ejpam-2714	2	2	,	,	PUNCT
ejpam-2714	2	3	no	no	INTJ
ejpam-2714	2	4	.	.	NOUN
ejpam-2714	2	5	4	4	NUM
ejpam-2714	2	6	,	,	PUNCT
ejpam-2714	2	7	2016	2016	NUM
ejpam-2714	2	8	,	,	PUNCT
ejpam-2714	2	9	346	346	NUM
ejpam-2714	2	10	-	-	SYM
ejpam-2714	2	11	359	359	NUM
ejpam-2714	2	12	issn	issn	PROPN
ejpam-2714	2	13	1307	1307	NUM
ejpam-2714	2	14	-	-	SYM
ejpam-2714	2	15	5543	5543	NUM
ejpam-2714	2	16	–	–	PUNCT
ejpam-2714	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2714	2	18	generalized	generalize	VERB
ejpam-2714	2	19	monotone	monotone	ADJ
ejpam-2714	2	20	iterative	iterative	NOUN
ejpam-2714	2	21	method	method	NOUN
ejpam-2714	2	22	for	for	ADP
ejpam-2714	2	23	caputo	caputo	PROPN
ejpam-2714	2	24	fractional	fractional	PROPN
ejpam-2714	2	25	integro	integro	PROPN
ejpam-2714	2	26	-	-	PUNCT
ejpam-2714	2	27	differential	differential	NOUN
ejpam-2714	2	28	equations	equation	NOUN
ejpam-2714	2	29	j.	j.	PROPN
ejpam-2714	2	30	vasundhara	vasundhara	PROPN
ejpam-2714	2	31	devi∗	devi∗	PROPN
ejpam-2714	2	32	,	,	PUNCT
ejpam-2714	2	33	ch	ch	NOUN
ejpam-2714	2	34	.	.	PROPN
ejpam-2714	3	1	v.	v.	ADP
ejpam-2714	3	2	sreedhar	sreedhar	ADJ
ejpam-2714	3	3	gvp	gvp	NOUN
ejpam-2714	3	4	-	-	PUNCT
ejpam-2714	3	5	prof	prof	NOUN
ejpam-2714	3	6	.	.	PUNCT
ejpam-2714	4	1	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-2714	4	2	institute	institute	PROPN
ejpam-2714	4	3	for	for	ADP
ejpam-2714	4	4	advanced	advanced	ADJ
ejpam-2714	4	5	studies	study	NOUN
ejpam-2714	4	6	,	,	PUNCT
ejpam-2714	4	7	department	department	NOUN
ejpam-2714	4	8	of	of	ADP
ejpam-2714	4	9	mathematics	mathematic	NOUN
ejpam-2714	4	10	,	,	PUNCT
ejpam-2714	4	11	gvp	gvp	PROPN
ejpam-2714	4	12	college	college	PROPN
ejpam-2714	4	13	of	of	ADP
ejpam-2714	4	14	engineering	engineering	PROPN
ejpam-2714	4	15	,	,	PUNCT
ejpam-2714	4	16	visakhapatnam	visakhapatnam	PROPN
ejpam-2714	4	17	,	,	PUNCT
ejpam-2714	4	18	ap	ap	PROPN
ejpam-2714	4	19	,	,	PUNCT
ejpam-2714	4	20	india	india	PROPN
ejpam-2714	4	21	.	.	PUNCT
ejpam-2714	5	1	abstract	abstract	PROPN
ejpam-2714	5	2	.	.	PUNCT
ejpam-2714	6	1	using	use	VERB
ejpam-2714	6	2	coupled	couple	VERB
ejpam-2714	6	3	lower	low	ADJ
ejpam-2714	6	4	and	and	CCONJ
ejpam-2714	6	5	upper	upper	ADJ
ejpam-2714	6	6	solutions	solution	NOUN
ejpam-2714	6	7	we	we	PRON
ejpam-2714	6	8	develop	develop	VERB
ejpam-2714	6	9	the	the	DET
ejpam-2714	6	10	generalized	generalized	ADJ
ejpam-2714	6	11	monotone	monotone	ADJ
ejpam-2714	6	12	iterative	iterative	NOUN
ejpam-2714	6	13	technique	technique	NOUN
ejpam-2714	6	14	to	to	PART
ejpam-2714	6	15	solve	solve	VERB
ejpam-2714	6	16	caputo	caputo	PROPN
ejpam-2714	6	17	fractional	fractional	PROPN
ejpam-2714	6	18	integro	integro	PROPN
ejpam-2714	6	19	-	-	PUNCT
ejpam-2714	6	20	differential	differential	NOUN
ejpam-2714	6	21	equation	equation	NOUN
ejpam-2714	6	22	of	of	ADP
ejpam-2714	6	23	order	order	NOUN
ejpam-2714	6	24	q	q	NOUN
ejpam-2714	6	25	with	with	ADP
ejpam-2714	6	26	periodic	periodic	ADJ
ejpam-2714	6	27	boundary	boundary	ADJ
ejpam-2714	6	28	condition	condition	NOUN
ejpam-2714	6	29	,	,	PUNCT
ejpam-2714	6	30	via	via	ADP
ejpam-2714	6	31	initial	initial	ADJ
ejpam-2714	6	32	value	value	NOUN
ejpam-2714	6	33	problem	problem	NOUN
ejpam-2714	6	34	(	(	PUNCT
ejpam-2714	6	35	ivp	ivp	NOUN
ejpam-2714	6	36	)	)	PUNCT
ejpam-2714	7	1	where	where	SCONJ
ejpam-2714	7	2	0	0	PUNCT
ejpam-2714	7	3	<	<	X
ejpam-2714	7	4	q	q	X
ejpam-2714	7	5	<	<	X
ejpam-2714	7	6	1	1	NUM
ejpam-2714	7	7	.	.	PUNCT
ejpam-2714	7	8	we	we	PRON
ejpam-2714	7	9	construct	construct	VERB
ejpam-2714	7	10	monotone	monotone	ADJ
ejpam-2714	7	11	iterates	iterate	NOUN
ejpam-2714	7	12	which	which	PRON
ejpam-2714	7	13	are	be	AUX
ejpam-2714	7	14	solutions	solution	NOUN
ejpam-2714	7	15	of	of	ADP
ejpam-2714	7	16	initial	initial	ADJ
ejpam-2714	7	17	value	value	NOUN
ejpam-2714	7	18	problems	problem	NOUN
ejpam-2714	7	19	associated	associate	VERB
ejpam-2714	7	20	with	with	ADP
ejpam-2714	7	21	linear	linear	PROPN
ejpam-2714	7	22	integro	integro	ADJ
ejpam-2714	7	23	-	-	PUNCT
ejpam-2714	7	24	differential	differential	NOUN
ejpam-2714	7	25	equations	equation	NOUN
ejpam-2714	7	26	,	,	PUNCT
ejpam-2714	7	27	that	that	PRON
ejpam-2714	7	28	are	be	AUX
ejpam-2714	7	29	easy	easy	ADJ
ejpam-2714	7	30	to	to	PART
ejpam-2714	7	31	obtain	obtain	VERB
ejpam-2714	7	32	.	.	PUNCT
ejpam-2714	8	1	we	we	PRON
ejpam-2714	8	2	show	show	VERB
ejpam-2714	8	3	that	that	SCONJ
ejpam-2714	8	4	these	these	DET
ejpam-2714	8	5	iterates	iterate	NOUN
ejpam-2714	8	6	converge	converge	VERB
ejpam-2714	8	7	uniformly	uniformly	ADV
ejpam-2714	8	8	and	and	CCONJ
ejpam-2714	8	9	monotonically	monotonically	ADV
ejpam-2714	8	10	to	to	PART
ejpam-2714	8	11	coupled	couple	VERB
ejpam-2714	8	12	minimal	minimal	ADJ
ejpam-2714	8	13	and	and	CCONJ
ejpam-2714	8	14	maximal	maximal	ADJ
ejpam-2714	8	15	solutions	solution	NOUN
ejpam-2714	8	16	of	of	ADP
ejpam-2714	8	17	the	the	DET
ejpam-2714	8	18	problem	problem	NOUN
ejpam-2714	8	19	considered	consider	VERB
ejpam-2714	8	20	.	.	PUNCT
ejpam-2714	9	1	we	we	PRON
ejpam-2714	9	2	have	have	AUX
ejpam-2714	9	3	obtained	obtain	VERB
ejpam-2714	9	4	explicit	explicit	ADJ
ejpam-2714	9	5	solution	solution	NOUN
ejpam-2714	9	6	of	of	ADP
ejpam-2714	9	7	the	the	DET
ejpam-2714	9	8	linear	linear	ADJ
ejpam-2714	9	9	ivp	ivp	PROPN
ejpam-2714	9	10	of	of	ADP
ejpam-2714	9	11	caputo	caputo	PROPN
ejpam-2714	9	12	fractional	fractional	PROPN
ejpam-2714	9	13	integro	integro	PROPN
ejpam-2714	9	14	-	-	PUNCT
ejpam-2714	9	15	differential	differential	NOUN
ejpam-2714	9	16	equation	equation	NOUN
ejpam-2714	9	17	.	.	PUNCT
ejpam-2714	10	1	2010	2010	NUM
ejpam-2714	10	2	mathematics	mathematic	NOUN
ejpam-2714	10	3	subject	subject	NOUN
ejpam-2714	10	4	classifications	classification	NOUN
ejpam-2714	10	5	:	:	PUNCT
ejpam-2714	10	6	34a08,34k10,45k99	34a08,34k10,45k99	NUM
ejpam-2714	10	7	key	key	ADJ
ejpam-2714	10	8	words	word	NOUN
ejpam-2714	10	9	and	and	CCONJ
ejpam-2714	10	10	phrases	phrase	NOUN
ejpam-2714	10	11	:	:	PUNCT
ejpam-2714	10	12	caputo	caputo	PROPN
ejpam-2714	10	13	fractional	fractional	PROPN
ejpam-2714	10	14	integro	integro	PROPN
ejpam-2714	10	15	-	-	PUNCT
ejpam-2714	10	16	differential	differential	NOUN
ejpam-2714	10	17	equation	equation	NOUN
ejpam-2714	10	18	,	,	PUNCT
ejpam-2714	10	19	linear	linear	PROPN
ejpam-2714	10	20	integro	integro	ADJ
ejpam-2714	10	21	-	-	PUNCT
ejpam-2714	10	22	differential	differential	NOUN
ejpam-2714	10	23	equations	equation	NOUN
ejpam-2714	10	24	,	,	PUNCT
ejpam-2714	10	25	monotone	monotone	ADJ
ejpam-2714	10	26	iterative	iterative	NOUN
ejpam-2714	10	27	technique	technique	NOUN
ejpam-2714	10	28	,	,	PUNCT
ejpam-2714	10	29	maximal	maximal	ADJ
ejpam-2714	10	30	and	and	CCONJ
ejpam-2714	10	31	minimal	minimal	ADJ
ejpam-2714	10	32	solutions	solution	NOUN
ejpam-2714	10	33	1	1	NUM
ejpam-2714	10	34	.	.	PUNCT
ejpam-2714	10	35	introduction	introduction	NOUN
ejpam-2714	10	36	the	the	DET
ejpam-2714	10	37	theory	theory	NOUN
ejpam-2714	10	38	of	of	ADP
ejpam-2714	10	39	fractional	fractional	ADJ
ejpam-2714	10	40	calculus	calculus	NOUN
ejpam-2714	10	41	[	[	X
ejpam-2714	10	42	3	3	NUM
ejpam-2714	10	43	,	,	PUNCT
ejpam-2714	10	44	8	8	NUM
ejpam-2714	10	45	]	]	PUNCT
ejpam-2714	10	46	is	be	AUX
ejpam-2714	10	47	more	more	ADJ
ejpam-2714	10	48	than	than	ADP
ejpam-2714	10	49	three	three	NUM
ejpam-2714	10	50	centuries	century	NOUN
ejpam-2714	10	51	old	old	ADJ
ejpam-2714	10	52	and	and	CCONJ
ejpam-2714	10	53	but	but	CCONJ
ejpam-2714	10	54	its	its	PRON
ejpam-2714	10	55	study	study	NOUN
ejpam-2714	10	56	has	have	AUX
ejpam-2714	10	57	been	be	AUX
ejpam-2714	10	58	restricted	restrict	VERB
ejpam-2714	10	59	mainly	mainly	ADV
ejpam-2714	10	60	to	to	ADP
ejpam-2714	10	61	mathematicians	mathematician	NOUN
ejpam-2714	10	62	till	till	SCONJ
ejpam-2714	10	63	a	a	DET
ejpam-2714	10	64	few	few	ADJ
ejpam-2714	10	65	decades	decade	NOUN
ejpam-2714	10	66	ago	ago	ADV
ejpam-2714	10	67	.	.	PUNCT
ejpam-2714	11	1	the	the	DET
ejpam-2714	11	2	book	book	NOUN
ejpam-2714	11	3	of	of	ADP
ejpam-2714	11	4	oldham	oldham	PROPN
ejpam-2714	11	5	and	and	CCONJ
ejpam-2714	11	6	spanier	spanier	NOUN
ejpam-2714	11	7	[	[	X
ejpam-2714	11	8	6	6	NUM
ejpam-2714	11	9	]	]	PUNCT
ejpam-2714	11	10	attracted	attract	VERB
ejpam-2714	11	11	the	the	DET
ejpam-2714	11	12	attention	attention	NOUN
ejpam-2714	11	13	of	of	ADP
ejpam-2714	11	14	many	many	ADJ
ejpam-2714	11	15	researchers	researcher	NOUN
ejpam-2714	11	16	and	and	CCONJ
ejpam-2714	11	17	study	study	NOUN
ejpam-2714	11	18	of	of	ADP
ejpam-2714	11	19	various	various	ADJ
ejpam-2714	11	20	areas	area	NOUN
ejpam-2714	11	21	using	use	VERB
ejpam-2714	11	22	fractional	fractional	ADJ
ejpam-2714	11	23	derivatives	derivative	NOUN
ejpam-2714	11	24	quickly	quickly	ADV
ejpam-2714	11	25	gained	gain	VERB
ejpam-2714	11	26	impetus	impetus	NOUN
ejpam-2714	11	27	.	.	PUNCT
ejpam-2714	12	1	with	with	ADP
ejpam-2714	12	2	the	the	DET
ejpam-2714	12	3	monograph	monograph	NOUN
ejpam-2714	12	4	published	publish	VERB
ejpam-2714	12	5	by	by	ADP
ejpam-2714	12	6	prof	prof	NOUN
ejpam-2714	12	7	.	.	PUNCT
ejpam-2714	13	1	v.	v.	INTJ
ejpam-2714	13	2	lakshmikantham	lakshmikantham	INTJ
ejpam-2714	13	3	et	et	PROPN
ejpam-2714	13	4	al	al	PROPN
ejpam-2714	13	5	.	.	PUNCT
ejpam-2714	14	1	[	[	X
ejpam-2714	14	2	4	4	NUM
ejpam-2714	14	3	]	]	PUNCT
ejpam-2714	14	4	,	,	PUNCT
ejpam-2714	14	5	there	there	PRON
ejpam-2714	14	6	has	have	AUX
ejpam-2714	14	7	been	be	AUX
ejpam-2714	14	8	extensive	extensive	ADJ
ejpam-2714	14	9	work	work	NOUN
ejpam-2714	14	10	in	in	ADP
ejpam-2714	14	11	this	this	DET
ejpam-2714	14	12	area	area	NOUN
ejpam-2714	14	13	of	of	ADP
ejpam-2714	14	14	research	research	NOUN
ejpam-2714	14	15	.	.	PUNCT
ejpam-2714	15	1	as	as	SCONJ
ejpam-2714	15	2	the	the	DET
ejpam-2714	15	3	monotone	monotone	ADJ
ejpam-2714	15	4	iterative	iterative	NOUN
ejpam-2714	15	5	technique	technique	NOUN
ejpam-2714	15	6	mit	mit	NOUN
ejpam-2714	15	7	combined	combine	VERB
ejpam-2714	15	8	with	with	ADP
ejpam-2714	15	9	method	method	NOUN
ejpam-2714	15	10	of	of	ADP
ejpam-2714	15	11	lower	low	ADJ
ejpam-2714	15	12	and	and	CCONJ
ejpam-2714	15	13	upper	upper	ADJ
ejpam-2714	15	14	solutions	solution	NOUN
ejpam-2714	15	15	offers	offer	VERB
ejpam-2714	15	16	a	a	DET
ejpam-2714	15	17	flexible	flexible	ADJ
ejpam-2714	15	18	mechanism	mechanism	NOUN
ejpam-2714	15	19	to	to	PART
ejpam-2714	15	20	obtain	obtain	VERB
ejpam-2714	15	21	a	a	DET
ejpam-2714	15	22	solution	solution	NOUN
ejpam-2714	15	23	of	of	ADP
ejpam-2714	15	24	the	the	DET
ejpam-2714	15	25	considered	consider	VERB
ejpam-2714	15	26	mathematical	mathematical	ADJ
ejpam-2714	15	27	model	model	NOUN
ejpam-2714	15	28	,	,	PUNCT
ejpam-2714	15	29	this	this	DET
ejpam-2714	15	30	technique	technique	NOUN
ejpam-2714	15	31	was	be	AUX
ejpam-2714	15	32	developed	develop	VERB
ejpam-2714	15	33	in	in	ADP
ejpam-2714	15	34	various	various	ADJ
ejpam-2714	15	35	setups	setup	NOUN
ejpam-2714	15	36	[	[	X
ejpam-2714	15	37	5	5	NUM
ejpam-2714	15	38	]	]	PUNCT
ejpam-2714	15	39	over	over	ADP
ejpam-2714	15	40	the	the	DET
ejpam-2714	15	41	years	year	NOUN
ejpam-2714	15	42	.	.	PUNCT
ejpam-2714	16	1	the	the	DET
ejpam-2714	16	2	interest	interest	NOUN
ejpam-2714	16	3	in	in	ADP
ejpam-2714	16	4	fractional	fractional	ADJ
ejpam-2714	16	5	differential	differential	ADJ
ejpam-2714	16	6	equations	equation	NOUN
ejpam-2714	16	7	led	lead	VERB
ejpam-2714	16	8	to	to	ADP
ejpam-2714	16	9	developing	develop	VERB
ejpam-2714	16	10	mit	mit	NOUN
ejpam-2714	16	11	for	for	ADP
ejpam-2714	16	12	ivps	ivps	PROPN
ejpam-2714	16	13	and	and	CCONJ
ejpam-2714	16	14	bvps	bvps	VERB
ejpam-2714	16	15	.	.	PUNCT
ejpam-2714	17	1	there	there	PRON
ejpam-2714	17	2	have	have	AUX
ejpam-2714	17	3	been	be	AUX
ejpam-2714	17	4	several	several	ADJ
ejpam-2714	17	5	papers	paper	NOUN
ejpam-2714	17	6	[	[	X
ejpam-2714	17	7	1	1	X
ejpam-2714	17	8	]	]	PUNCT
ejpam-2714	17	9	dealing	deal	VERB
ejpam-2714	17	10	with	with	ADP
ejpam-2714	17	11	iterative	iterative	NOUN
ejpam-2714	17	12	techniques	technique	NOUN
ejpam-2714	17	13	for	for	ADP
ejpam-2714	17	14	systems	system	NOUN
ejpam-2714	17	15	involving	involve	VERB
ejpam-2714	17	16	fractional	fractional	ADJ
ejpam-2714	17	17	derivatives	derivative	NOUN
ejpam-2714	17	18	.	.	PUNCT
ejpam-2714	18	1	it	it	PRON
ejpam-2714	18	2	is	be	AUX
ejpam-2714	18	3	quite	quite	ADV
ejpam-2714	18	4	obvious	obvious	ADJ
ejpam-2714	18	5	that	that	SCONJ
ejpam-2714	18	6	the	the	DET
ejpam-2714	18	7	study	study	NOUN
ejpam-2714	18	8	of	of	ADP
ejpam-2714	18	9	ivps	ivps	PROPN
ejpam-2714	18	10	is	be	AUX
ejpam-2714	18	11	relatively	relatively	ADV
ejpam-2714	18	12	simpler	simple	ADJ
ejpam-2714	18	13	than	than	ADP
ejpam-2714	18	14	the	the	DET
ejpam-2714	18	15	study	study	NOUN
ejpam-2714	18	16	of	of	ADP
ejpam-2714	18	17	bvps	bvps	PROPN
ejpam-2714	18	18	.	.	PUNCT
ejpam-2714	19	1	developing	develop	VERB
ejpam-2714	19	2	iterative	iterative	NOUN
ejpam-2714	19	3	techniques	technique	NOUN
ejpam-2714	19	4	for	for	ADP
ejpam-2714	19	5	bvps	bvps	NOUN
ejpam-2714	19	6	is	be	AUX
ejpam-2714	19	7	quite	quite	ADV
ejpam-2714	19	8	cumbersome	cumbersome	ADJ
ejpam-2714	19	9	.	.	PUNCT
ejpam-2714	20	1	at	at	ADP
ejpam-2714	20	2	this	this	DET
ejpam-2714	20	3	stage	stage	NOUN
ejpam-2714	20	4	pandit	pandit	NOUN
ejpam-2714	20	5	et	et	PROPN
ejpam-2714	20	6	al	al	PROPN
ejpam-2714	20	7	.	.	PUNCT
ejpam-2714	21	1	[	[	X
ejpam-2714	21	2	7	7	NUM
ejpam-2714	21	3	]	]	PUNCT
ejpam-2714	21	4	,	,	PUNCT
ejpam-2714	21	5	obtained	obtain	VERB
ejpam-2714	21	6	the	the	DET
ejpam-2714	21	7	solution	solution	NOUN
ejpam-2714	21	8	of	of	ADP
ejpam-2714	21	9	a	a	DET
ejpam-2714	21	10	bvp	bvp	NOUN
ejpam-2714	21	11	using	use	VERB
ejpam-2714	21	12	the	the	DET
ejpam-2714	21	13	monotone	monotone	ADJ
ejpam-2714	21	14	iterates	iterate	NOUN
ejpam-2714	21	15	of	of	ADP
ejpam-2714	21	16	the	the	DET
ejpam-2714	21	17	corresponding	corresponding	ADJ
ejpam-2714	21	18	ivp	ivp	NOUN
ejpam-2714	21	19	introduced	introduce	VERB
ejpam-2714	21	20	∗corresponding	∗corresponde	VERB
ejpam-2714	21	21	author	author	NOUN
ejpam-2714	21	22	.	.	PUNCT
ejpam-2714	22	1	email	email	NOUN
ejpam-2714	22	2	addresses	address	NOUN
ejpam-2714	22	3	:	:	PUNCT
ejpam-2714	23	1	jvdevi@igmail.com	jvdevi@igmail.com	X
ejpam-2714	23	2	(	(	PUNCT
ejpam-2714	23	3	j.	j.	PROPN
ejpam-2714	23	4	devi	devi	PROPN
ejpam-2714	23	5	)	)	PUNCT
ejpam-2714	23	6	,	,	PUNCT
ejpam-2714	23	7	chaduvulasreedhar@gmail.com	chaduvulasreedhar@gmail.com	PROPN
ejpam-2714	23	8	(	(	PUNCT
ejpam-2714	23	9	ch	ch	NOUN
ejpam-2714	23	10	.	.	PUNCT
ejpam-2714	23	11	sreedhar	sreedhar	PROPN
ejpam-2714	23	12	)	)	PUNCT
ejpam-2714	23	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2714	24	1	346	346	NUM
ejpam-2714	24	2	c	c	X
ejpam-2714	24	3	©	©	PROPN
ejpam-2714	24	4	2016	2016	NUM
ejpam-2714	24	5	ejpam	ejpam	VERB
ejpam-2714	24	6	all	all	DET
ejpam-2714	24	7	rights	right	NOUN
ejpam-2714	24	8	reserved	reserve	VERB
ejpam-2714	24	9	.	.	PUNCT
ejpam-2714	25	1	j.	j.	PROPN
ejpam-2714	25	2	devi	devi	PROPN
ejpam-2714	25	3	,	,	PUNCT
ejpam-2714	25	4	ch	ch	PROPN
ejpam-2714	25	5	.	.	PUNCT
ejpam-2714	25	6	sreedhar	sreedhar	PROPN
ejpam-2714	25	7	/	/	SYM
ejpam-2714	25	8	eur	eur	PROPN
ejpam-2714	25	9	.	.	PUNCT
ejpam-2714	26	1	j.	j.	PROPN
ejpam-2714	26	2	pure	pure	PROPN
ejpam-2714	26	3	appl	appl	PROPN
ejpam-2714	26	4	.	.	PROPN
ejpam-2714	26	5	math	math	PROPN
ejpam-2714	26	6	,	,	PUNCT
ejpam-2714	26	7	9	9	NUM
ejpam-2714	26	8	(	(	PUNCT
ejpam-2714	26	9	2016	2016	NUM
ejpam-2714	26	10	)	)	PUNCT
ejpam-2714	26	11	,	,	PUNCT
ejpam-2714	26	12	346	346	NUM
ejpam-2714	26	13	-	-	SYM
ejpam-2714	26	14	359	359	NUM
ejpam-2714	26	15	347	347	NUM
ejpam-2714	26	16	the	the	DET
ejpam-2714	26	17	development	development	NOUN
ejpam-2714	26	18	of	of	ADP
ejpam-2714	26	19	mit	mit	NOUN
ejpam-2714	26	20	of	of	ADP
ejpam-2714	26	21	a	a	DET
ejpam-2714	26	22	pbvp	pbvp	NOUN
ejpam-2714	26	23	through	through	ADP
ejpam-2714	26	24	the	the	DET
ejpam-2714	26	25	mit	mit	NOUN
ejpam-2714	26	26	of	of	ADP
ejpam-2714	26	27	a	a	DET
ejpam-2714	26	28	ivp	ivp	NOUN
ejpam-2714	26	29	.	.	PUNCT
ejpam-2714	27	1	this	this	DET
ejpam-2714	27	2	work	work	NOUN
ejpam-2714	27	3	has	have	AUX
ejpam-2714	27	4	been	be	AUX
ejpam-2714	27	5	extended	extend	VERB
ejpam-2714	27	6	by	by	ADP
ejpam-2714	27	7	j.	j.	PROPN
ejpam-2714	27	8	d.	d.	PROPN
ejpam-2714	27	9	ramirez	ramirez	PROPN
ejpam-2714	27	10	and	and	CCONJ
ejpam-2714	27	11	a.	a.	PROPN
ejpam-2714	27	12	s.	s.	PROPN
ejpam-2714	27	13	vatsala	vatsala	PROPN
ejpam-2714	27	14	for	for	ADP
ejpam-2714	27	15	caputo	caputo	PROPN
ejpam-2714	27	16	fractional	fractional	PROPN
ejpam-2714	27	17	differential	differential	ADJ
ejpam-2714	27	18	equations	equation	NOUN
ejpam-2714	27	19	in	in	ADP
ejpam-2714	27	20	[	[	X
ejpam-2714	27	21	9	9	NUM
ejpam-2714	27	22	]	]	PUNCT
ejpam-2714	27	23	.	.	PUNCT
ejpam-2714	28	1	wen	wen	PROPN
ejpam-2714	28	2	-	-	PUNCT
ejpam-2714	28	3	li	li	PROPN
ejpam-2714	28	4	wang	wang	PROPN
ejpam-2714	28	5	and	and	CCONJ
ejpam-2714	28	6	jing	jing	PROPN
ejpam-2714	28	7	feng	feng	PROPN
ejpam-2714	28	8	tian	tian	PROPN
ejpam-2714	28	9	proposed	propose	VERB
ejpam-2714	28	10	a	a	DET
ejpam-2714	28	11	different	different	ADJ
ejpam-2714	28	12	approach	approach	NOUN
ejpam-2714	28	13	to	to	PART
ejpam-2714	28	14	obtain	obtain	VERB
ejpam-2714	28	15	a	a	DET
ejpam-2714	28	16	unique	unique	ADJ
ejpam-2714	28	17	solution	solution	NOUN
ejpam-2714	28	18	for	for	ADP
ejpam-2714	28	19	the	the	DET
ejpam-2714	28	20	bvp	bvp	NOUN
ejpam-2714	28	21	in	in	ADP
ejpam-2714	28	22	[	[	X
ejpam-2714	28	23	10	10	NUM
ejpam-2714	28	24	]	]	PUNCT
ejpam-2714	28	25	.	.	PUNCT
ejpam-2714	29	1	in	in	ADP
ejpam-2714	29	2	this	this	DET
ejpam-2714	29	3	paper	paper	NOUN
ejpam-2714	29	4	,	,	PUNCT
ejpam-2714	29	5	we	we	PRON
ejpam-2714	29	6	consider	consider	VERB
ejpam-2714	29	7	the	the	DET
ejpam-2714	29	8	pbvp	pbvp	NOUN
ejpam-2714	29	9	of	of	ADP
ejpam-2714	29	10	caputo	caputo	PROPN
ejpam-2714	29	11	fractional	fractional	PROPN
ejpam-2714	29	12	integro	integro	PROPN
ejpam-2714	29	13	differential	differential	ADJ
ejpam-2714	29	14	equation	equation	NOUN
ejpam-2714	29	15	and	and	CCONJ
ejpam-2714	29	16	obtain	obtain	VERB
ejpam-2714	29	17	its	its	PRON
ejpam-2714	29	18	solution	solution	NOUN
ejpam-2714	29	19	through	through	ADP
ejpam-2714	29	20	a	a	DET
ejpam-2714	29	21	sequence	sequence	NOUN
ejpam-2714	29	22	of	of	ADP
ejpam-2714	29	23	iterates	iterate	NOUN
ejpam-2714	29	24	developed	develop	VERB
ejpam-2714	29	25	for	for	ADP
ejpam-2714	29	26	the	the	DET
ejpam-2714	29	27	corresponding	corresponding	ADJ
ejpam-2714	29	28	ivp	ivp	NOUN
ejpam-2714	29	29	.	.	PUNCT
ejpam-2714	30	1	2	2	X
ejpam-2714	30	2	.	.	X
ejpam-2714	30	3	preliminaries	preliminary	NOUN
ejpam-2714	30	4	in	in	ADP
ejpam-2714	30	5	this	this	DET
ejpam-2714	30	6	section	section	NOUN
ejpam-2714	30	7	,	,	PUNCT
ejpam-2714	30	8	we	we	PRON
ejpam-2714	30	9	state	state	VERB
ejpam-2714	30	10	a	a	DET
ejpam-2714	30	11	few	few	ADJ
ejpam-2714	30	12	definitions	definition	NOUN
ejpam-2714	30	13	,	,	PUNCT
ejpam-2714	30	14	some	some	DET
ejpam-2714	30	15	properties	property	NOUN
ejpam-2714	30	16	of	of	ADP
ejpam-2714	30	17	fractional	fractional	ADJ
ejpam-2714	30	18	derivatives	derivative	NOUN
ejpam-2714	30	19	and	and	CCONJ
ejpam-2714	30	20	recall	recall	VERB
ejpam-2714	30	21	required	require	VERB
ejpam-2714	30	22	results	result	NOUN
ejpam-2714	30	23	pertaining	pertain	VERB
ejpam-2714	30	24	to	to	ADP
ejpam-2714	30	25	caputo	caputo	PROPN
ejpam-2714	30	26	fractional	fractional	PROPN
ejpam-2714	30	27	integro	integro	PROPN
ejpam-2714	30	28	differential	differential	ADJ
ejpam-2714	30	29	equations	equation	NOUN
ejpam-2714	30	30	which	which	PRON
ejpam-2714	30	31	are	be	AUX
ejpam-2714	30	32	useful	useful	ADJ
ejpam-2714	30	33	in	in	ADP
ejpam-2714	30	34	proving	prove	VERB
ejpam-2714	30	35	the	the	DET
ejpam-2714	30	36	main	main	ADJ
ejpam-2714	30	37	result	result	NOUN
ejpam-2714	30	38	.	.	PUNCT
ejpam-2714	31	1	consider	consider	VERB
ejpam-2714	31	2	the	the	DET
ejpam-2714	31	3	caputo	caputo	PROPN
ejpam-2714	31	4	fractional	fractional	PROPN
ejpam-2714	31	5	integro	integro	PROPN
ejpam-2714	31	6	-	-	PUNCT
ejpam-2714	31	7	differential	differential	NOUN
ejpam-2714	31	8	equation	equation	NOUN
ejpam-2714	31	9	of	of	ADP
ejpam-2714	31	10	the	the	DET
ejpam-2714	31	11	type	type	NOUN
ejpam-2714	31	12	c	c	PROPN
ejpam-2714	31	13	dqu=	dqu=	PROPN
ejpam-2714	31	14	f	f	PROPN
ejpam-2714	31	15	(	(	PUNCT
ejpam-2714	31	16	t	t	PROPN
ejpam-2714	31	17	,	,	PUNCT
ejpam-2714	31	18	u	u	NOUN
ejpam-2714	31	19	,	,	PUNCT
ejpam-2714	31	20	iq(u	iq(u	NOUN
ejpam-2714	31	21	)	)	PUNCT
ejpam-2714	31	22	)	)	PUNCT
ejpam-2714	31	23	,	,	PUNCT
ejpam-2714	31	24	(	(	PUNCT
ejpam-2714	31	25	1	1	X
ejpam-2714	31	26	)	)	PUNCT
ejpam-2714	31	27	with	with	ADP
ejpam-2714	31	28	u(0	u(0	NOUN
ejpam-2714	31	29	)	)	PUNCT
ejpam-2714	31	30	=	=	PUNCT
ejpam-2714	32	1	u0	u0	ADJ
ejpam-2714	32	2	,	,	PUNCT
ejpam-2714	32	3	(	(	PUNCT
ejpam-2714	32	4	2	2	X
ejpam-2714	32	5	)	)	PUNCT
ejpam-2714	32	6	where	where	SCONJ
ejpam-2714	32	7	f	f	PROPN
ejpam-2714	32	8	,	,	PUNCT
ejpam-2714	32	9	g	g	PROPN
ejpam-2714	32	10	∈	∈	PROPN
ejpam-2714	32	11	c[j	c[j	ADJ
ejpam-2714	32	12	×r×r+,r	×r×r+,r	PROPN
ejpam-2714	32	13	]	]	PUNCT
ejpam-2714	32	14	,	,	PUNCT
ejpam-2714	32	15	u	u	PROPN
ejpam-2714	32	16	∈	∈	NOUN
ejpam-2714	32	17	c1[j	c1[j	NOUN
ejpam-2714	32	18	,	,	PUNCT
ejpam-2714	32	19	r	r	NOUN
ejpam-2714	32	20	]	]	X
ejpam-2714	32	21	,	,	PUNCT
ejpam-2714	32	22	j	j	X
ejpam-2714	32	23	=	=	PUNCT
ejpam-2714	33	1	[	[	X
ejpam-2714	33	2	0	0	NUM
ejpam-2714	33	3	,	,	PUNCT
ejpam-2714	33	4	t	t	PROPN
ejpam-2714	33	5	]	]	PUNCT
ejpam-2714	33	6	,	,	PUNCT
ejpam-2714	33	7	c	c	PROPN
ejpam-2714	33	8	dqu(t	dqu(t	PROPN
ejpam-2714	33	9	)	)	PUNCT
ejpam-2714	33	10	=	=	SYM
ejpam-2714	33	11	1	1	NUM
ejpam-2714	33	12	γ(1−	γ(1−	NOUN
ejpam-2714	33	13	q	q	X
ejpam-2714	33	14	)	)	PUNCT
ejpam-2714	33	15	∫	∫	PROPN
ejpam-2714	33	16	t	t	PROPN
ejpam-2714	33	17	0	0	NUM
ejpam-2714	34	1	(	(	PUNCT
ejpam-2714	34	2	t	t	PROPN
ejpam-2714	34	3	−	−	PROPN
ejpam-2714	34	4	s)−qu′(s)ds	s)−qu′(s)d	VERB
ejpam-2714	34	5	,	,	PUNCT
ejpam-2714	34	6	(	(	PUNCT
ejpam-2714	34	7	3	3	X
ejpam-2714	34	8	)	)	PUNCT
ejpam-2714	34	9	and	and	CCONJ
ejpam-2714	34	10	iq(u(t	iq(u(t	NUM
ejpam-2714	34	11	)	)	PUNCT
ejpam-2714	34	12	)	)	PUNCT
ejpam-2714	35	1	=	=	SYM
ejpam-2714	35	2	1	1	NUM
ejpam-2714	35	3	γq	γq	ADP
ejpam-2714	35	4	∫	∫	PROPN
ejpam-2714	35	5	t	t	PROPN
ejpam-2714	35	6	0	0	NUM
ejpam-2714	36	1	(	(	PUNCT
ejpam-2714	36	2	t	t	NOUN
ejpam-2714	36	3	−	−	PROPN
ejpam-2714	36	4	s)q−1u(s)ds	s)q−1u(s)ds	PROPN
ejpam-2714	36	5	.	.	PUNCT
ejpam-2714	37	1	(	(	PUNCT
ejpam-2714	37	2	4	4	X
ejpam-2714	37	3	)	)	PUNCT
ejpam-2714	37	4	we	we	PRON
ejpam-2714	37	5	start	start	VERB
ejpam-2714	37	6	by	by	ADP
ejpam-2714	37	7	stating	state	VERB
ejpam-2714	37	8	a	a	DET
ejpam-2714	37	9	couple	couple	NOUN
ejpam-2714	37	10	of	of	ADP
ejpam-2714	37	11	lemmas	lemma	NOUN
ejpam-2714	37	12	from	from	ADP
ejpam-2714	37	13	[	[	X
ejpam-2714	37	14	3	3	NUM
ejpam-2714	37	15	]	]	PUNCT
ejpam-2714	37	16	related	relate	VERB
ejpam-2714	37	17	to	to	ADP
ejpam-2714	37	18	ivps	ivps	PROPN
ejpam-2714	37	19	of	of	ADP
ejpam-2714	37	20	riemann	riemann	PROPN
ejpam-2714	37	21	liouville	liouville	PROPN
ejpam-2714	37	22	and	and	CCONJ
ejpam-2714	37	23	caputo	caputo	PROPN
ejpam-2714	37	24	fractional	fractional	PROPN
ejpam-2714	37	25	derivative	derivative	NOUN
ejpam-2714	37	26	of	of	ADP
ejpam-2714	37	27	order	order	NOUN
ejpam-2714	37	28	q.	q.	PROPN
ejpam-2714	37	29	lemma	lemma	PROPN
ejpam-2714	37	30	1	1	X
ejpam-2714	37	31	.	.	PUNCT
ejpam-2714	38	1	let	let	VERB
ejpam-2714	38	2	m(t	m(t	NOUN
ejpam-2714	38	3	)	)	PUNCT
ejpam-2714	38	4	∈	∈	PROPN
ejpam-2714	38	5	c1([0	c1([0	PROPN
ejpam-2714	38	6	,	,	PUNCT
ejpam-2714	38	7	t]r	t]r	NOUN
ejpam-2714	38	8	)	)	PUNCT
ejpam-2714	38	9	.	.	PUNCT
ejpam-2714	39	1	if	if	SCONJ
ejpam-2714	39	2	there	there	PRON
ejpam-2714	39	3	exists	exist	VERB
ejpam-2714	39	4	t1	t1	PROPN
ejpam-2714	39	5	∈	∈	PROPN
ejpam-2714	40	1	[	[	X
ejpam-2714	40	2	0	0	NUM
ejpam-2714	40	3	,	,	PUNCT
ejpam-2714	40	4	t	t	PROPN
ejpam-2714	40	5	]	]	PUNCT
ejpam-2714	40	6	such	such	ADJ
ejpam-2714	40	7	that	that	DET
ejpam-2714	40	8	m(t1	m(t1	NOUN
ejpam-2714	40	9	)	)	PUNCT
ejpam-2714	40	10	=	=	SYM
ejpam-2714	40	11	0	0	PUNCT
ejpam-2714	40	12	and	and	CCONJ
ejpam-2714	40	13	m(t)≤	m(t)≤	NOUN
ejpam-2714	40	14	0	0	NUM
ejpam-2714	40	15	on	on	ADP
ejpam-2714	40	16	[	[	X
ejpam-2714	40	17	0	0	NUM
ejpam-2714	40	18	,	,	PUNCT
ejpam-2714	40	19	t	t	PROPN
ejpam-2714	40	20	]	]	PUNCT
ejpam-2714	40	21	then	then	ADV
ejpam-2714	40	22	dqm(t1)≥	dqm(t1)≥	PROPN
ejpam-2714	40	23	0	0	NUM
ejpam-2714	40	24	.	.	PUNCT
ejpam-2714	41	1	lemma	lemma	PROPN
ejpam-2714	41	2	2	2	X
ejpam-2714	41	3	.	.	PUNCT
ejpam-2714	41	4	let	let	VERB
ejpam-2714	41	5	m(t	m(t	NOUN
ejpam-2714	41	6	)	)	PUNCT
ejpam-2714	41	7	∈	∈	PROPN
ejpam-2714	41	8	c1([0	c1([0	PROPN
ejpam-2714	41	9	,	,	PUNCT
ejpam-2714	41	10	t],r	t],r	NOUN
ejpam-2714	41	11	)	)	PUNCT
ejpam-2714	41	12	.	.	PUNCT
ejpam-2714	42	1	if	if	SCONJ
ejpam-2714	42	2	there	there	PRON
ejpam-2714	42	3	exists	exist	VERB
ejpam-2714	42	4	t1	t1	PROPN
ejpam-2714	42	5	∈	∈	PROPN
ejpam-2714	43	1	[	[	X
ejpam-2714	43	2	0	0	NUM
ejpam-2714	43	3	,	,	PUNCT
ejpam-2714	43	4	t	t	PROPN
ejpam-2714	43	5	]	]	PUNCT
ejpam-2714	43	6	such	such	ADJ
ejpam-2714	43	7	that	that	DET
ejpam-2714	43	8	m(t1	m(t1	NOUN
ejpam-2714	43	9	)	)	PUNCT
ejpam-2714	43	10	=	=	SYM
ejpam-2714	43	11	0	0	PUNCT
ejpam-2714	43	12	and	and	CCONJ
ejpam-2714	43	13	m(t)≤	m(t)≤	NOUN
ejpam-2714	43	14	0	0	NUM
ejpam-2714	43	15	on	on	ADP
ejpam-2714	43	16	[	[	X
ejpam-2714	43	17	0	0	NUM
ejpam-2714	43	18	,	,	PUNCT
ejpam-2714	43	19	t	t	PROPN
ejpam-2714	43	20	]	]	PUNCT
ejpam-2714	43	21	then	then	ADV
ejpam-2714	43	22	c	c	X
ejpam-2714	43	23	dqm(t1)≥	dqm(t1)≥	PROPN
ejpam-2714	43	24	0	0	NUM
ejpam-2714	43	25	.	.	PUNCT
ejpam-2714	44	1	the	the	DET
ejpam-2714	44	2	following	follow	VERB
ejpam-2714	44	3	theorem	theorem	VERB
ejpam-2714	44	4	,	,	PUNCT
ejpam-2714	44	5	which	which	PRON
ejpam-2714	44	6	is	be	AUX
ejpam-2714	44	7	a	a	DET
ejpam-2714	44	8	new	new	ADJ
ejpam-2714	44	9	result	result	NOUN
ejpam-2714	44	10	,	,	PUNCT
ejpam-2714	44	11	gives	give	VERB
ejpam-2714	44	12	the	the	DET
ejpam-2714	44	13	explicit	explicit	ADJ
ejpam-2714	44	14	solution	solution	NOUN
ejpam-2714	44	15	of	of	ADP
ejpam-2714	44	16	the	the	DET
ejpam-2714	44	17	linear	linear	ADJ
ejpam-2714	44	18	ivp	ivp	PROPN
ejpam-2714	44	19	of	of	ADP
ejpam-2714	44	20	caputo	caputo	PROPN
ejpam-2714	44	21	fractional	fractional	PROPN
ejpam-2714	44	22	integro	integro	PROPN
ejpam-2714	44	23	-	-	PUNCT
ejpam-2714	44	24	differential	differential	NOUN
ejpam-2714	44	25	equation	equation	NOUN
ejpam-2714	44	26	,	,	PUNCT
ejpam-2714	44	27	this	this	PRON
ejpam-2714	44	28	is	be	AUX
ejpam-2714	44	29	the	the	DET
ejpam-2714	44	30	generalization	generalization	NOUN
ejpam-2714	44	31	of	of	ADP
ejpam-2714	44	32	the	the	DET
ejpam-2714	44	33	result	result	NOUN
ejpam-2714	44	34	in	in	ADP
ejpam-2714	44	35	[	[	X
ejpam-2714	44	36	8	8	NUM
ejpam-2714	44	37	]	]	PUNCT
ejpam-2714	44	38	.	.	PUNCT
ejpam-2714	45	1	theorem	theorem	NOUN
ejpam-2714	45	2	1	1	NUM
ejpam-2714	45	3	.	.	PUNCT
ejpam-2714	46	1	if	if	SCONJ
ejpam-2714	46	2	λ	λ	PROPN
ejpam-2714	46	3	∈	∈	PROPN
ejpam-2714	46	4	c1([0	c1([0	NOUN
ejpam-2714	46	5	,	,	PUNCT
ejpam-2714	46	6	t],r	t],r	NOUN
ejpam-2714	46	7	)	)	PUNCT
ejpam-2714	46	8	.	.	PUNCT
ejpam-2714	47	1	the	the	DET
ejpam-2714	47	2	solution	solution	NOUN
ejpam-2714	47	3	of	of	ADP
ejpam-2714	47	4	c	c	NOUN
ejpam-2714	47	5	dqλ(t	dqλ(t	PROPN
ejpam-2714	47	6	)	)	PUNCT
ejpam-2714	47	7	=	=	SYM
ejpam-2714	47	8	l1λ(t	l1λ(t	PROPN
ejpam-2714	47	9	)	)	PUNCT
ejpam-2714	48	1	+	+	NOUN
ejpam-2714	48	2	m	m	NOUN
ejpam-2714	48	3	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	48	4	)	)	PUNCT
ejpam-2714	48	5	)	)	PUNCT
ejpam-2714	48	6	is	be	AUX
ejpam-2714	48	7	given	give	VERB
ejpam-2714	48	8	by	by	ADP
ejpam-2714	48	9	λ(t	λ(t	NOUN
ejpam-2714	48	10	)	)	PUNCT
ejpam-2714	48	11	=	=	SYM
ejpam-2714	49	1	σ∞n=0σ	σ∞n=0σ	ADJ
ejpam-2714	49	2	∞	∞	NUM
ejpam-2714	49	3	k=0	k=0	PROPN
ejpam-2714	49	4	2n+km	2n+km	NUM
ejpam-2714	49	5	n	n	CCONJ
ejpam-2714	49	6	lk	lk	NOUN
ejpam-2714	49	7	1	1	NUM
ejpam-2714	49	8	n+kck	n+kck	NUM
ejpam-2714	49	9	t(2n+1)q	t(2n+1)q	NOUN
ejpam-2714	49	10	γ[(2n+	γ[(2n+	X
ejpam-2714	49	11	1)q+	1)q+	NUM
ejpam-2714	49	12	1	1	NUM
ejpam-2714	49	13	]	]	PUNCT
ejpam-2714	49	14	where	where	SCONJ
ejpam-2714	49	15	l1	l1	PROPN
ejpam-2714	49	16	,	,	PUNCT
ejpam-2714	49	17	m	m	VERB
ejpam-2714	49	18	>	>	X
ejpam-2714	49	19	0	0	NUM
ejpam-2714	49	20	.	.	PUNCT
ejpam-2714	50	1	j.	j.	PROPN
ejpam-2714	50	2	devi	devi	PROPN
ejpam-2714	50	3	,	,	PUNCT
ejpam-2714	50	4	ch	ch	PROPN
ejpam-2714	50	5	.	.	PUNCT
ejpam-2714	50	6	sreedhar	sreedhar	PROPN
ejpam-2714	50	7	/	/	SYM
ejpam-2714	50	8	eur	eur	PROPN
ejpam-2714	50	9	.	.	PUNCT
ejpam-2714	51	1	j.	j.	PROPN
ejpam-2714	51	2	pure	pure	PROPN
ejpam-2714	51	3	appl	appl	PROPN
ejpam-2714	51	4	.	.	PROPN
ejpam-2714	51	5	math	math	PROPN
ejpam-2714	51	6	,	,	PUNCT
ejpam-2714	51	7	9	9	NUM
ejpam-2714	51	8	(	(	PUNCT
ejpam-2714	51	9	2016	2016	NUM
ejpam-2714	51	10	)	)	PUNCT
ejpam-2714	51	11	,	,	PUNCT
ejpam-2714	51	12	346	346	NUM
ejpam-2714	51	13	-	-	SYM
ejpam-2714	51	14	359	359	NUM
ejpam-2714	51	15	348	348	NUM
ejpam-2714	51	16	proof	proof	NOUN
ejpam-2714	51	17	.	.	PUNCT
ejpam-2714	52	1	by	by	ADP
ejpam-2714	52	2	hypothesis	hypothesis	NOUN
ejpam-2714	52	3	we	we	PRON
ejpam-2714	52	4	have	have	VERB
ejpam-2714	52	5	c	c	NOUN
ejpam-2714	52	6	dqλ(t	dqλ(t	PROPN
ejpam-2714	52	7	)	)	PUNCT
ejpam-2714	52	8	=	=	SYM
ejpam-2714	52	9	l1λ(t)+m	l1λ(t)+m	PROPN
ejpam-2714	52	10	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	52	11	)	)	PUNCT
ejpam-2714	52	12	)	)	PUNCT
ejpam-2714	52	13	.	.	PUNCT
ejpam-2714	53	1	now	now	ADV
ejpam-2714	53	2	by	by	ADP
ejpam-2714	53	3	applying	apply	VERB
ejpam-2714	53	4	the	the	DET
ejpam-2714	53	5	laplace	laplace	NOUN
ejpam-2714	53	6	transform	transform	NOUN
ejpam-2714	53	7	on	on	ADP
ejpam-2714	53	8	both	both	DET
ejpam-2714	53	9	sides	side	NOUN
ejpam-2714	53	10	we	we	PRON
ejpam-2714	53	11	get	get	VERB
ejpam-2714	53	12	sq	sq	INTJ
ejpam-2714	53	13	¯λ(s)−	¯λ(s)−	X
ejpam-2714	53	14	sq−1λ(0	sq−1λ(0	PROPN
ejpam-2714	53	15	)	)	PUNCT
ejpam-2714	54	1	=	=	PROPN
ejpam-2714	54	2	l1	l1	PROPN
ejpam-2714	54	3	¯λ(s	¯λ(s	PART
ejpam-2714	54	4	)	)	PUNCT
ejpam-2714	55	1	+	+	ADJ
ejpam-2714	55	2	ms−q	ms−q	PROPN
ejpam-2714	55	3	sq	sq	NUM
ejpam-2714	55	4	¯λ(s)[sq	¯λ(s)[sq	ADJ
ejpam-2714	55	5	−ms−q	−ms−q	NOUN
ejpam-2714	55	6	−	−	PROPN
ejpam-2714	55	7	l1	l1	PROPN
ejpam-2714	55	8	]	]	PUNCT
ejpam-2714	56	1	=	=	PUNCT
ejpam-2714	56	2	λ(0)s	λ(0)s	SYM
ejpam-2714	56	3	q−1	q−1	PROPN
ejpam-2714	56	4	¯λ(s	¯λ(s	PROPN
ejpam-2714	56	5	)	)	PUNCT
ejpam-2714	57	1	=	=	SYM
ejpam-2714	57	2	sq−1	sq−1	NOUN
ejpam-2714	57	3	[	[	X
ejpam-2714	57	4	sq	sq	INTJ
ejpam-2714	57	5	−ms−q	−ms−q	PROPN
ejpam-2714	57	6	−	−	PROPN
ejpam-2714	57	7	l1	l1	PROPN
ejpam-2714	57	8	]	]	X
ejpam-2714	57	9	λ(0	λ(0	PROPN
ejpam-2714	57	10	)	)	PUNCT
ejpam-2714	57	11	¯λ(s	¯λ(s	PROPN
ejpam-2714	57	12	)	)	PUNCT
ejpam-2714	58	1	=	=	SYM
ejpam-2714	58	2	sq−1	sq−1	NOUN
ejpam-2714	59	1	[	[	PUNCT
ejpam-2714	59	2	s2q	s2q	PROPN
ejpam-2714	59	3	−m	−m	NOUN
ejpam-2714	59	4	−	−	PROPN
ejpam-2714	59	5	l1sq	l1sq	PROPN
ejpam-2714	59	6	]	]	X
ejpam-2714	59	7	λ(0	λ(0	PROPN
ejpam-2714	59	8	)	)	PUNCT
ejpam-2714	59	9	l−1	l−1	PROPN
ejpam-2714	59	10	(	(	PUNCT
ejpam-2714	59	11	¯λ(s	¯λ(s	NUM
ejpam-2714	59	12	)	)	PUNCT
ejpam-2714	59	13	)	)	PUNCT
ejpam-2714	60	1	=	=	X
ejpam-2714	60	2	l−1	l−1	PROPN
ejpam-2714	60	3	(	(	PUNCT
ejpam-2714	60	4	sq−1	sq−1	NOUN
ejpam-2714	60	5	[	[	X
ejpam-2714	60	6	s2q	s2q	PROPN
ejpam-2714	60	7	−m	−m	NOUN
ejpam-2714	60	8	−	−	PROPN
ejpam-2714	60	9	l1sq	l1sq	PROPN
ejpam-2714	60	10	]	]	PUNCT
ejpam-2714	60	11	)	)	PUNCT
ejpam-2714	60	12	λ(0	λ(0	NOUN
ejpam-2714	60	13	)	)	PUNCT
ejpam-2714	60	14	λ(t	λ(t	NOUN
ejpam-2714	60	15	)	)	PUNCT
ejpam-2714	61	1	=	=	NOUN
ejpam-2714	61	2	σ∞n=0σ	σ∞n=0σ	ADJ
ejpam-2714	61	3	∞	∞	PROPN
ejpam-2714	61	4	k=0	k=0	PROPN
ejpam-2714	61	5	2n+km	2n+km	NUM
ejpam-2714	61	6	n	n	CCONJ
ejpam-2714	61	7	lk	lk	NOUN
ejpam-2714	61	8	1	1	NUM
ejpam-2714	61	9	n+kck	n+kck	NUM
ejpam-2714	61	10	t(2n+1)q	t(2n+1)q	NOUN
ejpam-2714	61	11	γ[(2n+	γ[(2n+	X
ejpam-2714	61	12	1)q+	1)q+	NUM
ejpam-2714	61	13	1	1	NUM
ejpam-2714	61	14	]	]	X
ejpam-2714	61	15	λ(0	λ(0	PROPN
ejpam-2714	61	16	)	)	PUNCT
ejpam-2714	61	17	.	.	PUNCT
ejpam-2714	62	1	next	next	ADV
ejpam-2714	62	2	we	we	PRON
ejpam-2714	62	3	shall	shall	AUX
ejpam-2714	62	4	establish	establish	VERB
ejpam-2714	62	5	the	the	DET
ejpam-2714	62	6	following	follow	VERB
ejpam-2714	62	7	comparison	comparison	NOUN
ejpam-2714	62	8	theorem	theorem	VERB
ejpam-2714	62	9	.	.	PUNCT
ejpam-2714	62	10	theorem	theorem	NOUN
ejpam-2714	62	11	2	2	NUM
ejpam-2714	62	12	.	.	PUNCT
ejpam-2714	63	1	let	let	VERB
ejpam-2714	63	2	j	j	PROPN
ejpam-2714	63	3	=	=	PUNCT
ejpam-2714	64	1	[	[	X
ejpam-2714	64	2	0	0	NUM
ejpam-2714	64	3	,	,	PUNCT
ejpam-2714	64	4	t	t	PROPN
ejpam-2714	64	5	]	]	PUNCT
ejpam-2714	64	6	,	,	PUNCT
ejpam-2714	64	7	f	f	PROPN
ejpam-2714	64	8	∈	∈	PROPN
ejpam-2714	64	9	c[j×r×r+,r	c[j×r×r+,r	PROPN
ejpam-2714	64	10	]	]	PUNCT
ejpam-2714	64	11	,	,	PUNCT
ejpam-2714	64	12	v	v	NOUN
ejpam-2714	64	13	,	,	PUNCT
ejpam-2714	64	14	w	w	PROPN
ejpam-2714	64	15	∈	∈	PROPN
ejpam-2714	64	16	c1[j	c1[j	NOUN
ejpam-2714	64	17	,	,	PUNCT
ejpam-2714	64	18	r	r	NOUN
ejpam-2714	64	19	]	]	PUNCT
ejpam-2714	64	20	and	and	CCONJ
ejpam-2714	64	21	suppose	suppose	VERB
ejpam-2714	64	22	that	that	SCONJ
ejpam-2714	64	23	the	the	DET
ejpam-2714	64	24	following	follow	VERB
ejpam-2714	64	25	inequalities	inequality	NOUN
ejpam-2714	64	26	hold	hold	VERB
ejpam-2714	64	27	,	,	PUNCT
ejpam-2714	64	28	for	for	ADP
ejpam-2714	64	29	all	all	DET
ejpam-2714	64	30	t	t	NOUN
ejpam-2714	64	31	∈	∈	PROPN
ejpam-2714	64	32	j.	j.	PROPN
ejpam-2714	64	33	c	c	PROPN
ejpam-2714	64	34	dqv(t)≤	dqv(t)≤	PROPN
ejpam-2714	65	1	f	f	PROPN
ejpam-2714	65	2	(	(	PUNCT
ejpam-2714	65	3	t	t	PROPN
ejpam-2714	65	4	,	,	PUNCT
ejpam-2714	65	5	v(t	v(t	NOUN
ejpam-2714	65	6	)	)	PUNCT
ejpam-2714	65	7	,	,	PUNCT
ejpam-2714	65	8	iq(v(t	iq(v(t	NOUN
ejpam-2714	65	9	)	)	PUNCT
ejpam-2714	65	10	)	)	PUNCT
ejpam-2714	65	11	)	)	PUNCT
ejpam-2714	65	12	,	,	PUNCT
ejpam-2714	65	13	v(0)≤	v(0)≤	PROPN
ejpam-2714	65	14	u0	u0	ADJ
ejpam-2714	65	15	,	,	PUNCT
ejpam-2714	65	16	(	(	PUNCT
ejpam-2714	65	17	5	5	NUM
ejpam-2714	65	18	)	)	PUNCT
ejpam-2714	65	19	c	c	NOUN
ejpam-2714	65	20	dqw(t)≥	dqw(t)≥	NUM
ejpam-2714	65	21	f	f	PROPN
ejpam-2714	65	22	(	(	PUNCT
ejpam-2714	65	23	t	t	PROPN
ejpam-2714	65	24	,	,	PUNCT
ejpam-2714	65	25	w(t	w(t	PROPN
ejpam-2714	65	26	)	)	PUNCT
ejpam-2714	65	27	,	,	PUNCT
ejpam-2714	65	28	iq(w(t	iq(w(t	X
ejpam-2714	65	29	)	)	PUNCT
ejpam-2714	65	30	)	)	PUNCT
ejpam-2714	65	31	)	)	PUNCT
ejpam-2714	65	32	,	,	PUNCT
ejpam-2714	65	33	w(0)≥	w(0)≥	PROPN
ejpam-2714	65	34	u0	u0	PROPN
ejpam-2714	65	35	.	.	PUNCT
ejpam-2714	66	1	(	(	PUNCT
ejpam-2714	66	2	6	6	X
ejpam-2714	66	3	)	)	PUNCT
ejpam-2714	66	4	suppose	suppose	VERB
ejpam-2714	66	5	further	far	ADV
ejpam-2714	66	6	that	that	SCONJ
ejpam-2714	66	7	f	f	PROPN
ejpam-2714	66	8	(	(	PUNCT
ejpam-2714	66	9	t	t	PROPN
ejpam-2714	66	10	,	,	PUNCT
ejpam-2714	66	11	u(t	u(t	PROPN
ejpam-2714	66	12	)	)	PUNCT
ejpam-2714	66	13	,	,	PUNCT
ejpam-2714	66	14	iq(u(t	iq(u(t	NUM
ejpam-2714	66	15	)	)	PUNCT
ejpam-2714	66	16	)	)	PUNCT
ejpam-2714	66	17	)	)	PUNCT
ejpam-2714	66	18	satisfies	satisfy	VERB
ejpam-2714	66	19	the	the	DET
ejpam-2714	66	20	following	follow	VERB
ejpam-2714	66	21	lipschitz	lipschitz	VERB
ejpam-2714	66	22	-	-	PUNCT
ejpam-2714	66	23	like	like	ADJ
ejpam-2714	66	24	condition	condition	NOUN
ejpam-2714	66	25	,	,	PUNCT
ejpam-2714	66	26	f	f	PROPN
ejpam-2714	66	27	(	(	PUNCT
ejpam-2714	66	28	t	t	PROPN
ejpam-2714	66	29	,	,	PUNCT
ejpam-2714	66	30	x	x	X
ejpam-2714	66	31	,	,	PUNCT
ejpam-2714	66	32	iq(x))−	iq(x))−	PROPN
ejpam-2714	66	33	f	f	PROPN
ejpam-2714	66	34	(	(	PUNCT
ejpam-2714	66	35	t	t	PROPN
ejpam-2714	66	36	,	,	PUNCT
ejpam-2714	66	37	y	y	PROPN
ejpam-2714	66	38	,	,	PUNCT
ejpam-2714	66	39	iq(y))≤	iq(y))≤	ADJ
ejpam-2714	66	40	l(x	l(x	PROPN
ejpam-2714	66	41	−	−	PROPN
ejpam-2714	66	42	y	y	PROPN
ejpam-2714	66	43	)	)	PUNCT
ejpam-2714	67	1	+	+	NOUN
ejpam-2714	67	2	m(iq(x)−	m(iq(x)−	NOUN
ejpam-2714	67	3	iq(y	iq(y	NOUN
ejpam-2714	67	4	)	)	PUNCT
ejpam-2714	67	5	)	)	PUNCT
ejpam-2714	67	6	,	,	PUNCT
ejpam-2714	67	7	(	(	PUNCT
ejpam-2714	67	8	7	7	X
ejpam-2714	67	9	)	)	PUNCT
ejpam-2714	67	10	for	for	ADP
ejpam-2714	67	11	x	x	X
ejpam-2714	67	12	≥	≥	PROPN
ejpam-2714	67	13	y	y	PROPN
ejpam-2714	67	14	,	,	PUNCT
ejpam-2714	67	15	l	l	PROPN
ejpam-2714	67	16	,	,	PUNCT
ejpam-2714	67	17	m	m	VERB
ejpam-2714	67	18	>	>	X
ejpam-2714	67	19	0	0	X
ejpam-2714	67	20	.	.	PUNCT
ejpam-2714	68	1	then	then	ADV
ejpam-2714	68	2	,	,	PUNCT
ejpam-2714	68	3	v(0)≤	v(0)≤	PROPN
ejpam-2714	68	4	w(0	w(0	PROPN
ejpam-2714	68	5	)	)	PUNCT
ejpam-2714	68	6	implies	imply	VERB
ejpam-2714	68	7	that	that	SCONJ
ejpam-2714	68	8	v(t)≤	v(t)≤	NOUN
ejpam-2714	68	9	w(t	w(t	PROPN
ejpam-2714	68	10	)	)	PUNCT
ejpam-2714	68	11	,	,	PUNCT
ejpam-2714	68	12	0≤	0≤	NUM
ejpam-2714	68	13	t	t	NOUN
ejpam-2714	68	14	≤	≤	ADJ
ejpam-2714	68	15	t.	t.	NOUN
ejpam-2714	68	16	(	(	PUNCT
ejpam-2714	68	17	8)	8)	NUM
ejpam-2714	68	18	proof	proof	NOUN
ejpam-2714	68	19	.	.	PUNCT
ejpam-2714	69	1	assume	assume	VERB
ejpam-2714	69	2	without	without	ADP
ejpam-2714	69	3	loss	loss	NOUN
ejpam-2714	69	4	of	of	ADP
ejpam-2714	69	5	generality	generality	NOUN
ejpam-2714	69	6	that	that	PRON
ejpam-2714	69	7	one	one	NUM
ejpam-2714	69	8	of	of	ADP
ejpam-2714	69	9	the	the	DET
ejpam-2714	69	10	inequalities	inequality	NOUN
ejpam-2714	69	11	in	in	ADP
ejpam-2714	69	12	(	(	PUNCT
ejpam-2714	69	13	5	5	NUM
ejpam-2714	69	14	)	)	PUNCT
ejpam-2714	69	15	,	,	PUNCT
ejpam-2714	69	16	(	(	PUNCT
ejpam-2714	69	17	6	6	X
ejpam-2714	69	18	)	)	PUNCT
ejpam-2714	69	19	is	be	AUX
ejpam-2714	69	20	strict	strict	ADJ
ejpam-2714	69	21	,	,	PUNCT
ejpam-2714	69	22	say	say	VERB
ejpam-2714	69	23	c	c	PROPN
ejpam-2714	69	24	dqv(t	dqv(t	PROPN
ejpam-2714	69	25	)	)	PUNCT
ejpam-2714	69	26	<	<	X
ejpam-2714	69	27	f	f	X
ejpam-2714	69	28	(	(	PUNCT
ejpam-2714	69	29	t	t	PROPN
ejpam-2714	69	30	,	,	PUNCT
ejpam-2714	69	31	v(t	v(t	NOUN
ejpam-2714	69	32	)	)	PUNCT
ejpam-2714	69	33	,	,	PUNCT
ejpam-2714	69	34	iq(v(t	iq(v(t	NOUN
ejpam-2714	69	35	)	)	PUNCT
ejpam-2714	69	36	)	)	PUNCT
ejpam-2714	69	37	)	)	PUNCT
ejpam-2714	69	38	and	and	CCONJ
ejpam-2714	69	39	v(0	v(0	PROPN
ejpam-2714	69	40	)	)	PUNCT
ejpam-2714	69	41	<	<	X
ejpam-2714	69	42	w(0	w(0	PROPN
ejpam-2714	69	43	)	)	PUNCT
ejpam-2714	69	44	,	,	PUNCT
ejpam-2714	69	45	where	where	SCONJ
ejpam-2714	69	46	v(0	v(0	NOUN
ejpam-2714	69	47	)	)	PUNCT
ejpam-2714	69	48	=	=	SYM
ejpam-2714	69	49	v0	v0	NOUN
ejpam-2714	69	50	and	and	CCONJ
ejpam-2714	69	51	w(0	w(0	PROPN
ejpam-2714	69	52	)	)	PUNCT
ejpam-2714	69	53	=	=	NOUN
ejpam-2714	69	54	w0	w0	PROPN
ejpam-2714	69	55	.	.	PUNCT
ejpam-2714	70	1	we	we	PRON
ejpam-2714	70	2	claim	claim	VERB
ejpam-2714	70	3	that	that	SCONJ
ejpam-2714	70	4	v(t	v(t	NOUN
ejpam-2714	70	5	)	)	PUNCT
ejpam-2714	70	6	<	<	X
ejpam-2714	70	7	w(t	w(t	PROPN
ejpam-2714	70	8	)	)	PUNCT
ejpam-2714	70	9	for	for	ADP
ejpam-2714	70	10	t	t	PROPN
ejpam-2714	70	11	∈	∈	PROPN
ejpam-2714	70	12	j	j	PROPN
ejpam-2714	70	13	.	.	PUNCT
ejpam-2714	70	14	suppose	suppose	VERB
ejpam-2714	70	15	there	there	PRON
ejpam-2714	70	16	exists	exist	VERB
ejpam-2714	70	17	t1	t1	NOUN
ejpam-2714	70	18	such	such	ADJ
ejpam-2714	70	19	that	that	SCONJ
ejpam-2714	70	20	0	0	NUM
ejpam-2714	70	21	<	<	X
ejpam-2714	70	22	t1	t1	NOUN
ejpam-2714	70	23	≤	≤	X
ejpam-2714	70	24	t	t	PROPN
ejpam-2714	70	25	for	for	ADP
ejpam-2714	70	26	which	which	PRON
ejpam-2714	70	27	v(t1	v(t1	VERB
ejpam-2714	70	28	)	)	PUNCT
ejpam-2714	71	1	=	=	SYM
ejpam-2714	71	2	w(t1	w(t1	PROPN
ejpam-2714	71	3	)	)	PUNCT
ejpam-2714	71	4	,	,	PUNCT
ejpam-2714	71	5	v(t)≤	v(t)≤	NOUN
ejpam-2714	71	6	w(t	w(t	PROPN
ejpam-2714	71	7	)	)	PUNCT
ejpam-2714	71	8	,	,	PUNCT
ejpam-2714	71	9	for	for	ADP
ejpam-2714	71	10	t	t	PROPN
ejpam-2714	71	11	<	<	X
ejpam-2714	71	12	t1	t1	PROPN
ejpam-2714	71	13	.	.	PUNCT
ejpam-2714	72	1	(	(	PUNCT
ejpam-2714	72	2	9	9	X
ejpam-2714	72	3	)	)	PUNCT
ejpam-2714	72	4	if	if	SCONJ
ejpam-2714	72	5	we	we	PRON
ejpam-2714	72	6	set	set	VERB
ejpam-2714	72	7	m(t	m(t	NOUN
ejpam-2714	72	8	)	)	PUNCT
ejpam-2714	72	9	=	=	PUNCT
ejpam-2714	72	10	v(t)−w(t	v(t)−w(t	NUM
ejpam-2714	72	11	)	)	PUNCT
ejpam-2714	72	12	.	.	PUNCT
ejpam-2714	73	1	then	then	ADV
ejpam-2714	73	2	m(t1	m(t1	VERB
ejpam-2714	73	3	)	)	PUNCT
ejpam-2714	73	4	=	=	SYM
ejpam-2714	73	5	0	0	NUM
ejpam-2714	73	6	and	and	CCONJ
ejpam-2714	73	7	m(t	m(t	NOUN
ejpam-2714	73	8	)	)	PUNCT
ejpam-2714	74	1	=	=	SYM
ejpam-2714	74	2	v(t)−w(t)≤	v(t)−w(t)≤	PROPN
ejpam-2714	74	3	0	0	NUM
ejpam-2714	74	4	for	for	ADP
ejpam-2714	74	5	t	t	PROPN
ejpam-2714	74	6	<	<	X
ejpam-2714	74	7	t1	t1	PROPN
ejpam-2714	74	8	.	.	PUNCT
ejpam-2714	75	1	then	then	ADV
ejpam-2714	75	2	by	by	ADP
ejpam-2714	75	3	lemma	lemma	PROPN
ejpam-2714	75	4	2	2	NUM
ejpam-2714	75	5	we	we	PRON
ejpam-2714	75	6	have	have	VERB
ejpam-2714	75	7	c	c	NOUN
ejpam-2714	75	8	dqm(t1)≥	dqm(t1)≥	ADJ
ejpam-2714	75	9	0	0	NUM
ejpam-2714	75	10	.	.	PUNCT
ejpam-2714	76	1	thus	thus	ADV
ejpam-2714	76	2	f	f	X
ejpam-2714	76	3	(	(	PUNCT
ejpam-2714	76	4	t1	t1	PROPN
ejpam-2714	76	5	,	,	PUNCT
ejpam-2714	76	6	v(t1	v(t1	NOUN
ejpam-2714	76	7	)	)	PUNCT
ejpam-2714	76	8	,	,	PUNCT
ejpam-2714	76	9	iq(v(t1	iq(v(t1	PROPN
ejpam-2714	76	10	)	)	PUNCT
ejpam-2714	76	11	)	)	PUNCT
ejpam-2714	76	12	)	)	PUNCT
ejpam-2714	76	13	>	>	X
ejpam-2714	76	14	c	c	PROPN
ejpam-2714	76	15	dqv(t1	dqv(t1	PROPN
ejpam-2714	76	16	)	)	PUNCT
ejpam-2714	76	17	≥c	≥c	X
ejpam-2714	76	18	dqw(t1	dqw(t1	PROPN
ejpam-2714	76	19	)	)	PUNCT
ejpam-2714	76	20	≥	≥	NOUN
ejpam-2714	76	21	f	f	PROPN
ejpam-2714	76	22	(	(	PUNCT
ejpam-2714	76	23	t1	t1	PROPN
ejpam-2714	76	24	,	,	PUNCT
ejpam-2714	76	25	w(t1	w(t1	PROPN
ejpam-2714	76	26	)	)	PUNCT
ejpam-2714	76	27	,	,	PUNCT
ejpam-2714	76	28	iq(w(t1	iq(w(t1	PROPN
ejpam-2714	76	29	)	)	PUNCT
ejpam-2714	76	30	)	)	PUNCT
ejpam-2714	76	31	)	)	PUNCT
ejpam-2714	76	32	,	,	PUNCT
ejpam-2714	76	33	j.	j.	PROPN
ejpam-2714	76	34	devi	devi	PROPN
ejpam-2714	76	35	,	,	PUNCT
ejpam-2714	76	36	ch	ch	PROPN
ejpam-2714	76	37	.	.	PUNCT
ejpam-2714	76	38	sreedhar	sreedhar	PROPN
ejpam-2714	76	39	/	/	SYM
ejpam-2714	76	40	eur	eur	PROPN
ejpam-2714	76	41	.	.	PUNCT
ejpam-2714	77	1	j.	j.	PROPN
ejpam-2714	77	2	pure	pure	PROPN
ejpam-2714	77	3	appl	appl	PROPN
ejpam-2714	77	4	.	.	PROPN
ejpam-2714	77	5	math	math	PROPN
ejpam-2714	77	6	,	,	PUNCT
ejpam-2714	77	7	9	9	NUM
ejpam-2714	77	8	(	(	PUNCT
ejpam-2714	77	9	2016	2016	NUM
ejpam-2714	77	10	)	)	PUNCT
ejpam-2714	77	11	,	,	PUNCT
ejpam-2714	77	12	346	346	NUM
ejpam-2714	77	13	-	-	SYM
ejpam-2714	77	14	359	359	NUM
ejpam-2714	77	15	349	349	NUM
ejpam-2714	77	16	which	which	PRON
ejpam-2714	77	17	is	be	AUX
ejpam-2714	77	18	a	a	DET
ejpam-2714	77	19	contradiction	contradiction	NOUN
ejpam-2714	77	20	.	.	PUNCT
ejpam-2714	78	1	so	so	ADV
ejpam-2714	78	2	v(t	v(t	NUM
ejpam-2714	78	3	)	)	PUNCT
ejpam-2714	78	4	<	<	X
ejpam-2714	78	5	w(t	w(t	PROPN
ejpam-2714	78	6	)	)	PUNCT
ejpam-2714	78	7	for	for	ADP
ejpam-2714	78	8	t	t	PROPN
ejpam-2714	78	9	∈	∈	PROPN
ejpam-2714	78	10	j	j	PROPN
ejpam-2714	78	11	.	.	PUNCT
ejpam-2714	79	1	by	by	ADP
ejpam-2714	79	2	assuming	assume	VERB
ejpam-2714	79	3	that	that	SCONJ
ejpam-2714	79	4	the	the	DET
ejpam-2714	79	5	inequalities	inequality	NOUN
ejpam-2714	79	6	in	in	ADP
ejpam-2714	79	7	(	(	PUNCT
ejpam-2714	79	8	5	5	NUM
ejpam-2714	79	9	)	)	PUNCT
ejpam-2714	79	10	and	and	CCONJ
ejpam-2714	79	11	(	(	PUNCT
ejpam-2714	79	12	6	6	NUM
ejpam-2714	79	13	)	)	PUNCT
ejpam-2714	79	14	are	be	AUX
ejpam-2714	79	15	non	non	ADJ
ejpam-2714	79	16	strict	strict	ADJ
ejpam-2714	79	17	,	,	PUNCT
ejpam-2714	79	18	we	we	PRON
ejpam-2714	79	19	now	now	ADV
ejpam-2714	79	20	prove	prove	VERB
ejpam-2714	79	21	that	that	SCONJ
ejpam-2714	79	22	v(t)≤	v(t)≤	NOUN
ejpam-2714	79	23	w(t	w(t	PROPN
ejpam-2714	79	24	)	)	PUNCT
ejpam-2714	79	25	.	.	PUNCT
ejpam-2714	80	1	set	set	VERB
ejpam-2714	80	2	wε(t	wε(t	NOUN
ejpam-2714	80	3	)	)	PUNCT
ejpam-2714	80	4	=	=	SYM
ejpam-2714	80	5	w(t	w(t	PROPN
ejpam-2714	80	6	)	)	PUNCT
ejpam-2714	81	1	+	+	NUM
ejpam-2714	81	2	ελ(t	ελ(t	NOUN
ejpam-2714	81	3	)	)	PUNCT
ejpam-2714	82	1	where	where	SCONJ
ejpam-2714	82	2	ε	ε	PROPN
ejpam-2714	82	3	>	>	X
ejpam-2714	82	4	0	0	PROPN
ejpam-2714	82	5	and	and	CCONJ
ejpam-2714	82	6	λ(t	λ(t	PRON
ejpam-2714	82	7	)	)	PUNCT
ejpam-2714	82	8	=	=	SYM
ejpam-2714	82	9	σ∞n=0σ	σ∞n=0σ	NOUN
ejpam-2714	82	10	∞	∞	NUM
ejpam-2714	82	11	k=0	k=0	PROPN
ejpam-2714	82	12	2n+km	2n+km	NUM
ejpam-2714	82	13	n	n	PRON
ejpam-2714	82	14	lkn+kck	lkn+kck	VERB
ejpam-2714	82	15	t(2n+1)q	t(2n+1)q	NOUN
ejpam-2714	82	16	γ[(2n+	γ[(2n+	X
ejpam-2714	82	17	1)q+	1)q+	NUM
ejpam-2714	82	18	1	1	NUM
ejpam-2714	82	19	]	]	PUNCT
ejpam-2714	82	20	is	be	AUX
ejpam-2714	82	21	a	a	DET
ejpam-2714	82	22	solution	solution	NOUN
ejpam-2714	82	23	of	of	ADP
ejpam-2714	82	24	the	the	DET
ejpam-2714	82	25	caputo	caputo	PROPN
ejpam-2714	82	26	fractional	fractional	PROPN
ejpam-2714	82	27	integro	integro	PROPN
ejpam-2714	82	28	differential	differential	ADJ
ejpam-2714	82	29	equation	equation	NOUN
ejpam-2714	82	30	c	c	NOUN
ejpam-2714	82	31	dqλ(t	dqλ(t	PROPN
ejpam-2714	82	32	)	)	PUNCT
ejpam-2714	82	33	=	=	SYM
ejpam-2714	82	34	2lλ(t	2lλ(t	NUM
ejpam-2714	82	35	)	)	PUNCT
ejpam-2714	83	1	+	+	CCONJ
ejpam-2714	83	2	2	2	NUM
ejpam-2714	83	3	m	m	NOUN
ejpam-2714	83	4	iqλ(t)withλ(0	iqλ(t)withλ(0	NOUN
ejpam-2714	83	5	)	)	PUNCT
ejpam-2714	83	6	=	=	SYM
ejpam-2714	84	1	1	1	X
ejpam-2714	84	2	.	.	X
ejpam-2714	85	1	we	we	PRON
ejpam-2714	85	2	have	have	VERB
ejpam-2714	85	3	wε(0	wε(0	NOUN
ejpam-2714	85	4	)	)	PUNCT
ejpam-2714	85	5	=	=	SYM
ejpam-2714	85	6	w(0	w(0	PROPN
ejpam-2714	85	7	)	)	PUNCT
ejpam-2714	86	1	+	+	CCONJ
ejpam-2714	86	2	ε	ε	PROPN
ejpam-2714	86	3	>	>	X
ejpam-2714	86	4	w0	w0	PROPN
ejpam-2714	86	5	and	and	CCONJ
ejpam-2714	86	6	wε(t	wε(t	NOUN
ejpam-2714	86	7	)	)	PUNCT
ejpam-2714	86	8	>	>	X
ejpam-2714	86	9	w(t	w(t	PROPN
ejpam-2714	86	10	)	)	PUNCT
ejpam-2714	86	11	for	for	ADP
ejpam-2714	86	12	t	t	PROPN
ejpam-2714	86	13	∈	∈	PROPN
ejpam-2714	86	14	j	j	PROPN
ejpam-2714	86	15	.	.	PUNCT
ejpam-2714	87	1	using	use	VERB
ejpam-2714	87	2	(	(	PUNCT
ejpam-2714	87	3	5	5	NUM
ejpam-2714	87	4	)	)	PUNCT
ejpam-2714	87	5	,	,	PUNCT
ejpam-2714	87	6	(	(	PUNCT
ejpam-2714	87	7	6	6	NUM
ejpam-2714	87	8	)	)	PUNCT
ejpam-2714	87	9	,	,	PUNCT
ejpam-2714	87	10	and	and	CCONJ
ejpam-2714	87	11	(	(	PUNCT
ejpam-2714	87	12	7	7	NUM
ejpam-2714	87	13	)	)	PUNCT
ejpam-2714	87	14	,	,	PUNCT
ejpam-2714	87	15	we	we	PRON
ejpam-2714	87	16	find	find	VERB
ejpam-2714	87	17	that	that	SCONJ
ejpam-2714	87	18	c	c	PROPN
ejpam-2714	87	19	dqwε(t	dqwε(t	PROPN
ejpam-2714	87	20	)	)	PUNCT
ejpam-2714	87	21	=	=	SYM
ejpam-2714	87	22	c	c	X
ejpam-2714	87	23	dqw(t	dqw(t	PROPN
ejpam-2714	87	24	)	)	PUNCT
ejpam-2714	88	1	+	+	CCONJ
ejpam-2714	88	2	εc	εc	NOUN
ejpam-2714	88	3	dqλ(t	dqλ(t	PROPN
ejpam-2714	88	4	)	)	PUNCT
ejpam-2714	88	5	≥	≥	NOUN
ejpam-2714	88	6	f	f	PROPN
ejpam-2714	88	7	(	(	PUNCT
ejpam-2714	88	8	t	t	PROPN
ejpam-2714	88	9	,	,	PUNCT
ejpam-2714	88	10	w(t	w(t	PROPN
ejpam-2714	88	11	)	)	PUNCT
ejpam-2714	88	12	,	,	PUNCT
ejpam-2714	88	13	iq(w(t	iq(w(t	X
ejpam-2714	88	14	)	)	PUNCT
ejpam-2714	88	15	)	)	PUNCT
ejpam-2714	88	16	)	)	PUNCT
ejpam-2714	89	1	+	+	CCONJ
ejpam-2714	89	2	2lλ(t	2lλ(t	NUM
ejpam-2714	89	3	)	)	PUNCT
ejpam-2714	89	4	+	+	CCONJ
ejpam-2714	89	5	2	2	NUM
ejpam-2714	89	6	m	m	NOUN
ejpam-2714	89	7	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	89	8	)	)	PUNCT
ejpam-2714	89	9	)	)	PUNCT
ejpam-2714	90	1	≥	≥	PROPN
ejpam-2714	90	2	f	f	X
ejpam-2714	90	3	(	(	PUNCT
ejpam-2714	90	4	t	t	PROPN
ejpam-2714	90	5	,	,	PUNCT
ejpam-2714	90	6	wε(t	wε(t	NOUN
ejpam-2714	90	7	)	)	PUNCT
ejpam-2714	90	8	,	,	PUNCT
ejpam-2714	90	9	iq(wε(t)))−	iq(wε(t)))−	NUM
ejpam-2714	90	10	lλ(t)−m	lλ(t)−m	NOUN
ejpam-2714	90	11	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	90	12	)	)	PUNCT
ejpam-2714	90	13	)	)	PUNCT
ejpam-2714	91	1	+	+	CCONJ
ejpam-2714	91	2	2lλ(t	2lλ(t	NUM
ejpam-2714	91	3	)	)	PUNCT
ejpam-2714	92	1	+	+	CCONJ
ejpam-2714	92	2	2	2	NUM
ejpam-2714	92	3	m	m	NOUN
ejpam-2714	92	4	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	92	5	)	)	PUNCT
ejpam-2714	92	6	)	)	PUNCT
ejpam-2714	93	1	≥	≥	PROPN
ejpam-2714	93	2	f	f	X
ejpam-2714	93	3	(	(	PUNCT
ejpam-2714	93	4	t	t	PROPN
ejpam-2714	93	5	,	,	PUNCT
ejpam-2714	93	6	wε(t	wε(t	NOUN
ejpam-2714	93	7	)	)	PUNCT
ejpam-2714	93	8	,	,	PUNCT
ejpam-2714	93	9	iq(wε(t	iq(wε(t	NOUN
ejpam-2714	93	10	)	)	PUNCT
ejpam-2714	93	11	)	)	PUNCT
ejpam-2714	93	12	)	)	PUNCT
ejpam-2714	94	1	+	+	CCONJ
ejpam-2714	94	2	lλ(t	lλ(t	NOUN
ejpam-2714	94	3	)	)	PUNCT
ejpam-2714	95	1	+	+	VERB
ejpam-2714	95	2	m	m	NOUN
ejpam-2714	95	3	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	95	4	)	)	PUNCT
ejpam-2714	95	5	)	)	PUNCT
ejpam-2714	95	6	>	>	X
ejpam-2714	96	1	f	f	X
ejpam-2714	96	2	(	(	PUNCT
ejpam-2714	96	3	t	t	PROPN
ejpam-2714	96	4	,	,	PUNCT
ejpam-2714	96	5	wε(t	wε(t	NOUN
ejpam-2714	96	6	)	)	PUNCT
ejpam-2714	96	7	,	,	PUNCT
ejpam-2714	96	8	iq(wε)(t	iq(wε)(t	NOUN
ejpam-2714	96	9	)	)	PUNCT
ejpam-2714	96	10	)	)	PUNCT
ejpam-2714	96	11	,	,	PUNCT
ejpam-2714	96	12	for	for	ADP
ejpam-2714	96	13	0≤	0≤	NUM
ejpam-2714	96	14	t	t	PROPN
ejpam-2714	96	15	≤	≤	NOUN
ejpam-2714	96	16	t	t	NOUN
ejpam-2714	96	17	.	.	PUNCT
ejpam-2714	97	1	applying	apply	VERB
ejpam-2714	97	2	the	the	DET
ejpam-2714	97	3	result	result	NOUN
ejpam-2714	97	4	for	for	ADP
ejpam-2714	97	5	strict	strict	ADJ
ejpam-2714	97	6	inequalities	inequality	NOUN
ejpam-2714	97	7	to	to	ADP
ejpam-2714	97	8	v(t	v(t	NOUN
ejpam-2714	97	9	)	)	PUNCT
ejpam-2714	97	10	,	,	PUNCT
ejpam-2714	97	11	wε(t	wε(t	NOUN
ejpam-2714	97	12	)	)	PUNCT
ejpam-2714	97	13	we	we	PRON
ejpam-2714	97	14	obtain	obtain	VERB
ejpam-2714	97	15	v(t	v(t	ADJ
ejpam-2714	97	16	)	)	PUNCT
ejpam-2714	97	17	<	<	X
ejpam-2714	97	18	wε(t	wε(t	NOUN
ejpam-2714	97	19	)	)	PUNCT
ejpam-2714	97	20	for	for	ADP
ejpam-2714	97	21	t	t	PROPN
ejpam-2714	97	22	∈	∈	PROPN
ejpam-2714	97	23	j	j	PROPN
ejpam-2714	97	24	,	,	PUNCT
ejpam-2714	97	25	for	for	ADP
ejpam-2714	97	26	every	every	DET
ejpam-2714	97	27	ε	ε	PROPN
ejpam-2714	97	28	>	>	X
ejpam-2714	97	29	0	0	PUNCT
ejpam-2714	97	30	and	and	CCONJ
ejpam-2714	97	31	consequently	consequently	ADV
ejpam-2714	97	32	as	as	ADP
ejpam-2714	97	33	ε→	ε→	NUM
ejpam-2714	97	34	0	0	NUM
ejpam-2714	97	35	,	,	PUNCT
ejpam-2714	97	36	we	we	PRON
ejpam-2714	97	37	get	get	VERB
ejpam-2714	97	38	that	that	DET
ejpam-2714	97	39	v(t)≤	v(t)≤	NOUN
ejpam-2714	97	40	w(t	w(t	PROPN
ejpam-2714	97	41	)	)	PUNCT
ejpam-2714	97	42	for	for	ADP
ejpam-2714	97	43	t	t	PROPN
ejpam-2714	97	44	∈	∈	PROPN
ejpam-2714	97	45	j	j	PROPN
ejpam-2714	97	46	.	.	PUNCT
ejpam-2714	98	1	corollary	corollary	ADJ
ejpam-2714	98	2	1	1	NUM
ejpam-2714	98	3	.	.	PUNCT
ejpam-2714	99	1	let	let	VERB
ejpam-2714	99	2	m	m	PRON
ejpam-2714	99	3	∈	∈	NOUN
ejpam-2714	99	4	c1[j	c1[j	NOUN
ejpam-2714	99	5	,	,	PUNCT
ejpam-2714	99	6	r	r	X
ejpam-2714	99	7	]	]	PUNCT
ejpam-2714	99	8	be	be	AUX
ejpam-2714	99	9	such	such	ADJ
ejpam-2714	99	10	that	that	SCONJ
ejpam-2714	99	11	c	c	PROPN
ejpam-2714	99	12	dqm(t)≤	dqm(t)≤	NOUN
ejpam-2714	99	13	lm(t	lm(t	NOUN
ejpam-2714	99	14	)	)	PUNCT
ejpam-2714	100	1	+	+	NOUN
ejpam-2714	100	2	m	m	X
ejpam-2714	100	3	iq(m(t	iq(m(t	NOUN
ejpam-2714	100	4	)	)	PUNCT
ejpam-2714	100	5	)	)	PUNCT
ejpam-2714	100	6	,	,	PUNCT
ejpam-2714	100	7	m(0	m(0	NOUN
ejpam-2714	100	8	)	)	PUNCT
ejpam-2714	100	9	=	=	SYM
ejpam-2714	100	10	m0	m0	NOUN
ejpam-2714	100	11	≤	≤	NUM
ejpam-2714	100	12	1	1	NUM
ejpam-2714	100	13	,	,	PUNCT
ejpam-2714	100	14	then	then	ADV
ejpam-2714	100	15	m(t)≤	m(t)≤	VERB
ejpam-2714	100	16	λ(t	λ(t	NOUN
ejpam-2714	100	17	)	)	PUNCT
ejpam-2714	100	18	,	,	PUNCT
ejpam-2714	100	19	for	for	ADP
ejpam-2714	100	20	0≤	0≤	NUM
ejpam-2714	100	21	t	t	PROPN
ejpam-2714	100	22	≤	≤	NOUN
ejpam-2714	100	23	t	t	PROPN
ejpam-2714	100	24	and	and	CCONJ
ejpam-2714	100	25	l	l	NOUN
ejpam-2714	100	26	,	,	PUNCT
ejpam-2714	100	27	m	m	VERB
ejpam-2714	100	28	>	>	X
ejpam-2714	100	29	0	0	NUM
ejpam-2714	100	30	,	,	PUNCT
ejpam-2714	100	31	λ(0	λ(0	PROPN
ejpam-2714	100	32	)	)	PUNCT
ejpam-2714	101	1	=	=	SYM
ejpam-2714	101	2	1,λ(t	1,λ(t	NUM
ejpam-2714	101	3	)	)	PUNCT
ejpam-2714	101	4	=	=	NOUN
ejpam-2714	102	1	σ∞n=0σ	σ∞n=0σ	PROPN
ejpam-2714	102	2	∞	∞	PROPN
ejpam-2714	102	3	k=0	k=0	PROPN
ejpam-2714	102	4	2n+k	2n+k	NUM
ejpam-2714	102	5	m	m	VERB
ejpam-2714	102	6	n	n	PRON
ejpam-2714	102	7	lkn+kck	lkn+kck	PROPN
ejpam-2714	102	8	t(2n+1)q	t(2n+1)q	NOUN
ejpam-2714	102	9	γ[(2n+1)q+1	γ[(2n+1)q+1	PROPN
ejpam-2714	102	10	]	]	PUNCT
ejpam-2714	102	11	.	.	PUNCT
ejpam-2714	103	1	proof	proof	NOUN
ejpam-2714	103	2	.	.	PUNCT
ejpam-2714	104	1	we	we	PRON
ejpam-2714	104	2	have	have	VERB
ejpam-2714	104	3	c	c	PROPN
ejpam-2714	104	4	dqm(t)≤	dqm(t)≤	NOUN
ejpam-2714	104	5	lm(t	lm(t	NOUN
ejpam-2714	104	6	)	)	PUNCT
ejpam-2714	105	1	+	+	NOUN
ejpam-2714	105	2	m	m	X
ejpam-2714	105	3	iq(m(t	iq(m(t	NOUN
ejpam-2714	105	4	)	)	PUNCT
ejpam-2714	105	5	)	)	PUNCT
ejpam-2714	105	6	and	and	CCONJ
ejpam-2714	105	7	c	c	NOUN
ejpam-2714	105	8	dqλ(t	dqλ(t	ADV
ejpam-2714	105	9	)	)	PUNCT
ejpam-2714	105	10	=	=	NUM
ejpam-2714	105	11	2lλ(t	2lλ(t	NUM
ejpam-2714	105	12	)	)	PUNCT
ejpam-2714	105	13	+	+	CCONJ
ejpam-2714	105	14	2	2	NUM
ejpam-2714	105	15	m	m	NOUN
ejpam-2714	105	16	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	105	17	)	)	PUNCT
ejpam-2714	105	18	)	)	PUNCT
ejpam-2714	105	19	≥lλ(t	≥lλ(t	NUM
ejpam-2714	105	20	)	)	PUNCT
ejpam-2714	106	1	+	+	VERB
ejpam-2714	106	2	m	m	NOUN
ejpam-2714	106	3	iq(λ(t	iq(λ(t	NOUN
ejpam-2714	106	4	)	)	PUNCT
ejpam-2714	106	5	)	)	PUNCT
ejpam-2714	106	6	,	,	PUNCT
ejpam-2714	106	7	for	for	ADP
ejpam-2714	106	8	m(0	m(0	NOUN
ejpam-2714	106	9	)	)	PUNCT
ejpam-2714	106	10	=	=	SYM
ejpam-2714	106	11	m0	m0	NOUN
ejpam-2714	106	12	≤	≤	NUM
ejpam-2714	106	13	1=	1=	NUM
ejpam-2714	106	14	λ(0	λ(0	NOUN
ejpam-2714	106	15	)	)	PUNCT
ejpam-2714	106	16	.	.	PUNCT
ejpam-2714	107	1	hence	hence	ADV
ejpam-2714	107	2	from	from	ADP
ejpam-2714	107	3	theorem	theorem	ADJ
ejpam-2714	107	4	2	2	NUM
ejpam-2714	107	5	we	we	PRON
ejpam-2714	107	6	conclude	conclude	VERB
ejpam-2714	107	7	that	that	SCONJ
ejpam-2714	107	8	m(t)≤	m(t)≤	NOUN
ejpam-2714	107	9	λ(t	λ(t	PROPN
ejpam-2714	107	10	)	)	PUNCT
ejpam-2714	107	11	for	for	ADP
ejpam-2714	107	12	t	t	PROPN
ejpam-2714	107	13	∈	∈	PROPN
ejpam-2714	107	14	j	j	PROPN
ejpam-2714	107	15	.	.	PUNCT
ejpam-2714	108	1	the	the	DET
ejpam-2714	108	2	result	result	NOUN
ejpam-2714	108	3	of	of	ADP
ejpam-2714	108	4	corollary	corollary	ADJ
ejpam-2714	108	5	1	1	NUM
ejpam-2714	108	6	is	be	AUX
ejpam-2714	108	7	still	still	ADV
ejpam-2714	108	8	true	true	ADJ
ejpam-2714	108	9	even	even	ADV
ejpam-2714	108	10	if	if	SCONJ
ejpam-2714	108	11	l	l	NOUN
ejpam-2714	108	12	=	=	PUNCT
ejpam-2714	108	13	m	m	VERB
ejpam-2714	108	14	=	=	SYM
ejpam-2714	108	15	0	0	NUM
ejpam-2714	108	16	,	,	PUNCT
ejpam-2714	108	17	which	which	PRON
ejpam-2714	108	18	is	be	AUX
ejpam-2714	108	19	given	give	VERB
ejpam-2714	108	20	below	below	ADV
ejpam-2714	108	21	.	.	PUNCT
ejpam-2714	109	1	corollary	corollary	ADJ
ejpam-2714	109	2	2	2	NUM
ejpam-2714	109	3	.	.	PUNCT
ejpam-2714	110	1	let	let	VERB
ejpam-2714	110	2	c	c	NOUN
ejpam-2714	110	3	dqm(t)≤	dqm(t)≤	VERB
ejpam-2714	110	4	0	0	PUNCT
ejpam-2714	111	1	on	on	ADP
ejpam-2714	111	2	[	[	X
ejpam-2714	111	3	0	0	NUM
ejpam-2714	111	4	,	,	PUNCT
ejpam-2714	111	5	t	t	PROPN
ejpam-2714	111	6	]	]	PUNCT
ejpam-2714	111	7	.	.	PUNCT
ejpam-2714	112	1	if	if	SCONJ
ejpam-2714	112	2	m(0)≤	m(0)≤	PROPN
ejpam-2714	112	3	0	0	PUNCT
ejpam-2714	112	4	then	then	ADV
ejpam-2714	112	5	m(t)≤	m(t)≤	NOUN
ejpam-2714	112	6	0	0	NUM
ejpam-2714	112	7	,	,	PUNCT
ejpam-2714	112	8	t	t	PROPN
ejpam-2714	112	9	≤	≤	NUM
ejpam-2714	112	10	j	j	PROPN
ejpam-2714	112	11	.	.	PUNCT
ejpam-2714	113	1	proof	proof	NOUN
ejpam-2714	113	2	.	.	PUNCT
ejpam-2714	114	1	by	by	ADP
ejpam-2714	114	2	definition	definition	NOUN
ejpam-2714	114	3	of	of	ADP
ejpam-2714	114	4	c	c	PROPN
ejpam-2714	114	5	dqm(t	dqm(t	PROPN
ejpam-2714	114	6	)	)	PUNCT
ejpam-2714	114	7	and	and	CCONJ
ejpam-2714	114	8	by	by	ADP
ejpam-2714	114	9	hypothesis	hypothesis	NOUN
ejpam-2714	114	10	,	,	PUNCT
ejpam-2714	114	11	c	c	PROPN
ejpam-2714	114	12	dqm(t	dqm(t	PROPN
ejpam-2714	114	13	)	)	PUNCT
ejpam-2714	114	14	=	=	SYM
ejpam-2714	114	15	1	1	NUM
ejpam-2714	114	16	γ(1−	γ(1−	NOUN
ejpam-2714	114	17	q	q	X
ejpam-2714	114	18	)	)	PUNCT
ejpam-2714	114	19	∫	∫	PROPN
ejpam-2714	114	20	t	t	PROPN
ejpam-2714	114	21	0	0	NUM
ejpam-2714	115	1	(	(	PUNCT
ejpam-2714	115	2	t	t	PROPN
ejpam-2714	115	3	−	−	PROPN
ejpam-2714	115	4	s)−qm′(s)ds	s)−qm′(s)ds	NOUN
ejpam-2714	115	5	≤	≤	NOUN
ejpam-2714	115	6	0	0	NUM
ejpam-2714	115	7	,	,	PUNCT
ejpam-2714	115	8	which	which	PRON
ejpam-2714	115	9	implies	imply	VERB
ejpam-2714	115	10	that	that	SCONJ
ejpam-2714	115	11	m′(t	m′(t	NOUN
ejpam-2714	115	12	)	)	PUNCT
ejpam-2714	115	13	≤	≤	NOUN
ejpam-2714	115	14	0	0	NUM
ejpam-2714	115	15	on	on	ADP
ejpam-2714	115	16	[	[	X
ejpam-2714	115	17	0	0	NUM
ejpam-2714	115	18	,	,	PUNCT
ejpam-2714	115	19	t	t	PROPN
ejpam-2714	115	20	]	]	PUNCT
ejpam-2714	115	21	.	.	PUNCT
ejpam-2714	116	1	therefore	therefore	ADV
ejpam-2714	116	2	m(t	m(t	NOUN
ejpam-2714	116	3	)	)	PUNCT
ejpam-2714	116	4	≤	≤	NOUN
ejpam-2714	117	1	m(0	m(0	NOUN
ejpam-2714	117	2	)	)	PUNCT
ejpam-2714	117	3	≤	≤	NOUN
ejpam-2714	117	4	0	0	NUM
ejpam-2714	117	5	on	on	ADP
ejpam-2714	117	6	[	[	X
ejpam-2714	117	7	0	0	NUM
ejpam-2714	117	8	,	,	PUNCT
ejpam-2714	117	9	t	t	PROPN
ejpam-2714	117	10	]	]	PUNCT
ejpam-2714	117	11	.	.	PUNCT
ejpam-2714	118	1	the	the	DET
ejpam-2714	118	2	proof	proof	NOUN
ejpam-2714	118	3	is	be	AUX
ejpam-2714	118	4	complete	complete	ADJ
ejpam-2714	118	5	.	.	PUNCT
ejpam-2714	119	1	j.	j.	PROPN
ejpam-2714	119	2	devi	devi	PROPN
ejpam-2714	119	3	,	,	PUNCT
ejpam-2714	119	4	ch	ch	PROPN
ejpam-2714	119	5	.	.	PUNCT
ejpam-2714	119	6	sreedhar	sreedhar	PROPN
ejpam-2714	119	7	/	/	SYM
ejpam-2714	119	8	eur	eur	PROPN
ejpam-2714	119	9	.	.	PUNCT
ejpam-2714	120	1	j.	j.	PROPN
ejpam-2714	120	2	pure	pure	PROPN
ejpam-2714	120	3	appl	appl	PROPN
ejpam-2714	120	4	.	.	PROPN
ejpam-2714	120	5	math	math	PROPN
ejpam-2714	120	6	,	,	PUNCT
ejpam-2714	120	7	9	9	NUM
ejpam-2714	120	8	(	(	PUNCT
ejpam-2714	120	9	2016	2016	NUM
ejpam-2714	120	10	)	)	PUNCT
ejpam-2714	120	11	,	,	PUNCT
ejpam-2714	120	12	346	346	NUM
ejpam-2714	120	13	-	-	SYM
ejpam-2714	120	14	359	359	NUM
ejpam-2714	120	15	350	350	NUM
ejpam-2714	120	16	3	3	NUM
ejpam-2714	120	17	.	.	PUNCT
ejpam-2714	121	1	the	the	DET
ejpam-2714	121	2	technique	technique	NOUN
ejpam-2714	121	3	in	in	ADP
ejpam-2714	121	4	this	this	DET
ejpam-2714	121	5	section	section	NOUN
ejpam-2714	121	6	,	,	PUNCT
ejpam-2714	121	7	we	we	PRON
ejpam-2714	121	8	develop	develop	VERB
ejpam-2714	121	9	generalized	generalized	ADJ
ejpam-2714	121	10	monotone	monotone	ADJ
ejpam-2714	121	11	iterative	iterative	NOUN
ejpam-2714	121	12	technique	technique	NOUN
ejpam-2714	121	13	to	to	PART
ejpam-2714	121	14	obtain	obtain	VERB
ejpam-2714	121	15	a	a	DET
ejpam-2714	121	16	coupled	couple	VERB
ejpam-2714	121	17	minimal	minimal	ADJ
ejpam-2714	121	18	and	and	CCONJ
ejpam-2714	121	19	maximal	maximal	ADJ
ejpam-2714	121	20	solutions	solution	NOUN
ejpam-2714	121	21	for	for	ADP
ejpam-2714	121	22	the	the	DET
ejpam-2714	121	23	caputo	caputo	PROPN
ejpam-2714	121	24	fractional	fractional	PROPN
ejpam-2714	121	25	integro	integro	PROPN
ejpam-2714	121	26	-	-	PUNCT
ejpam-2714	121	27	differential	differential	NOUN
ejpam-2714	121	28	equation	equation	NOUN
ejpam-2714	121	29	of	of	ADP
ejpam-2714	121	30	the	the	DET
ejpam-2714	121	31	form	form	NOUN
ejpam-2714	121	32	c	c	PROPN
ejpam-2714	121	33	dqu=	dqu=	PROPN
ejpam-2714	121	34	f(t	f(t	PROPN
ejpam-2714	121	35	,	,	PUNCT
ejpam-2714	121	36	u	u	NOUN
ejpam-2714	121	37	,	,	PUNCT
ejpam-2714	121	38	iq(u	iq(u	NOUN
ejpam-2714	121	39	)	)	PUNCT
ejpam-2714	121	40	)	)	PUNCT
ejpam-2714	122	1	+	+	CCONJ
ejpam-2714	122	2	g(t	g(t	PROPN
ejpam-2714	122	3	,	,	PUNCT
ejpam-2714	122	4	u	u	NOUN
ejpam-2714	122	5	,	,	PUNCT
ejpam-2714	122	6	iq(u	iq(u	NOUN
ejpam-2714	122	7	)	)	PUNCT
ejpam-2714	122	8	)	)	PUNCT
ejpam-2714	122	9	,	,	PUNCT
ejpam-2714	122	10	(	(	PUNCT
ejpam-2714	122	11	10	10	NUM
ejpam-2714	122	12	)	)	PUNCT
ejpam-2714	122	13	with	with	ADP
ejpam-2714	122	14	the	the	DET
ejpam-2714	122	15	boundary	boundary	ADJ
ejpam-2714	122	16	condition	condition	NOUN
ejpam-2714	122	17	g(u(0),u(t	g(u(0),u(t	NOUN
ejpam-2714	122	18	)	)	PUNCT
ejpam-2714	122	19	)	)	PUNCT
ejpam-2714	123	1	=	=	SYM
ejpam-2714	123	2	0	0	NUM
ejpam-2714	123	3	,	,	PUNCT
ejpam-2714	123	4	(	(	PUNCT
ejpam-2714	123	5	11	11	NUM
ejpam-2714	123	6	)	)	PUNCT
ejpam-2714	123	7	where	where	SCONJ
ejpam-2714	123	8	f	f	X
ejpam-2714	123	9	,	,	PUNCT
ejpam-2714	123	10	g	g	PROPN
ejpam-2714	123	11	∈	∈	PROPN
ejpam-2714	123	12	c[j	c[j	ADJ
ejpam-2714	123	13	×	×	NOUN
ejpam-2714	123	14	r	r	NOUN
ejpam-2714	123	15	×	×	PROPN
ejpam-2714	123	16	r+,r	r+,r	NOUN
ejpam-2714	123	17	]	]	PUNCT
ejpam-2714	123	18	,	,	PUNCT
ejpam-2714	123	19	u	u	PROPN
ejpam-2714	123	20	∈	∈	NOUN
ejpam-2714	123	21	c1[j	c1[j	NOUN
ejpam-2714	123	22	,	,	PUNCT
ejpam-2714	123	23	r	r	NOUN
ejpam-2714	123	24	]	]	PUNCT
ejpam-2714	123	25	.	.	PUNCT
ejpam-2714	124	1	we	we	PRON
ejpam-2714	124	2	begin	begin	VERB
ejpam-2714	124	3	with	with	ADP
ejpam-2714	124	4	various	various	ADJ
ejpam-2714	124	5	definitions	definition	NOUN
ejpam-2714	124	6	of	of	ADP
ejpam-2714	124	7	coupled	couple	VERB
ejpam-2714	124	8	lower	low	ADJ
ejpam-2714	124	9	and	and	CCONJ
ejpam-2714	124	10	upper	upper	ADJ
ejpam-2714	124	11	solutions	solution	NOUN
ejpam-2714	124	12	of	of	ADP
ejpam-2714	124	13	(	(	PUNCT
ejpam-2714	124	14	10	10	NUM
ejpam-2714	124	15	)	)	PUNCT
ejpam-2714	124	16	and	and	CCONJ
ejpam-2714	124	17	(	(	PUNCT
ejpam-2714	124	18	11	11	NUM
ejpam-2714	124	19	)	)	PUNCT
ejpam-2714	124	20	.	.	PUNCT
ejpam-2714	125	1	definition	definition	NOUN
ejpam-2714	125	2	1	1	NUM
ejpam-2714	125	3	.	.	PUNCT
ejpam-2714	126	1	let	let	VERB
ejpam-2714	126	2	v0	v0	NOUN
ejpam-2714	126	3	,	,	PUNCT
ejpam-2714	126	4	w0	w0	PROPN
ejpam-2714	126	5	∈	∈	PROPN
ejpam-2714	126	6	c1[j	c1[j	NOUN
ejpam-2714	126	7	,	,	PUNCT
ejpam-2714	126	8	r	r	NOUN
ejpam-2714	126	9	]	]	PUNCT
ejpam-2714	126	10	.	.	PUNCT
ejpam-2714	127	1	then	then	ADV
ejpam-2714	127	2	v0	v0	PROPN
ejpam-2714	127	3	and	and	CCONJ
ejpam-2714	127	4	w0	w0	PROPN
ejpam-2714	127	5	are	be	AUX
ejpam-2714	127	6	said	say	VERB
ejpam-2714	127	7	to	to	PART
ejpam-2714	127	8	be	be	AUX
ejpam-2714	127	9	(	(	PUNCT
ejpam-2714	127	10	i	i	NOUN
ejpam-2714	127	11	)	)	PUNCT
ejpam-2714	127	12	natural	natural	ADJ
ejpam-2714	127	13	lower	low	ADJ
ejpam-2714	127	14	and	and	CCONJ
ejpam-2714	127	15	upper	upper	ADJ
ejpam-2714	127	16	solutions	solution	NOUN
ejpam-2714	127	17	of	of	ADP
ejpam-2714	127	18	(	(	PUNCT
ejpam-2714	127	19	10	10	NUM
ejpam-2714	127	20	)	)	PUNCT
ejpam-2714	127	21	,	,	PUNCT
ejpam-2714	127	22	(	(	PUNCT
ejpam-2714	127	23	11	11	NUM
ejpam-2714	127	24	)	)	PUNCT
ejpam-2714	127	25	if	if	SCONJ
ejpam-2714	127	26	,	,	PUNCT
ejpam-2714	127	27	c	c	NOUN
ejpam-2714	127	28	dqv0(t)≤f(t	dqv0(t)≤f(t	PROPN
ejpam-2714	127	29	,	,	PUNCT
ejpam-2714	127	30	v0(t	v0(t	PROPN
ejpam-2714	127	31	)	)	PUNCT
ejpam-2714	127	32	,	,	PUNCT
ejpam-2714	127	33	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	127	34	)	)	PUNCT
ejpam-2714	127	35	)	)	PUNCT
ejpam-2714	127	36	)	)	PUNCT
ejpam-2714	128	1	+	+	CCONJ
ejpam-2714	128	2	g(t	g(t	PROPN
ejpam-2714	128	3	,	,	PUNCT
ejpam-2714	128	4	v0(t	v0(t	PROPN
ejpam-2714	128	5	)	)	PUNCT
ejpam-2714	128	6	,	,	PUNCT
ejpam-2714	128	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	128	8	)	)	PUNCT
ejpam-2714	128	9	)	)	PUNCT
ejpam-2714	128	10	)	)	PUNCT
ejpam-2714	128	11	,	,	PUNCT
ejpam-2714	128	12	g(v0(0	g(v0(0	NOUN
ejpam-2714	128	13	)	)	PUNCT
ejpam-2714	128	14	,	,	PUNCT
ejpam-2714	128	15	v0(t	v0(t	PROPN
ejpam-2714	128	16	)	)	PUNCT
ejpam-2714	128	17	)	)	PUNCT
ejpam-2714	128	18	≤	≤	NOUN
ejpam-2714	128	19	0	0	NUM
ejpam-2714	128	20	,	,	PUNCT
ejpam-2714	128	21	(	(	PUNCT
ejpam-2714	128	22	12	12	NUM
ejpam-2714	128	23	)	)	PUNCT
ejpam-2714	128	24	c	c	NOUN
ejpam-2714	128	25	dqw0(t)≥f(t	dqw0(t)≥f(t	NOUN
ejpam-2714	128	26	,	,	PUNCT
ejpam-2714	128	27	w0(t	w0(t	PROPN
ejpam-2714	128	28	)	)	PUNCT
ejpam-2714	128	29	,	,	PUNCT
ejpam-2714	128	30	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	128	31	)	)	PUNCT
ejpam-2714	128	32	)	)	PUNCT
ejpam-2714	128	33	)	)	PUNCT
ejpam-2714	129	1	+	+	CCONJ
ejpam-2714	129	2	g(t	g(t	PROPN
ejpam-2714	129	3	,	,	PUNCT
ejpam-2714	129	4	w0(t	w0(t	PROPN
ejpam-2714	129	5	)	)	PUNCT
ejpam-2714	129	6	,	,	PUNCT
ejpam-2714	129	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	129	8	)	)	PUNCT
ejpam-2714	129	9	)	)	PUNCT
ejpam-2714	129	10	)	)	PUNCT
ejpam-2714	129	11	,	,	PUNCT
ejpam-2714	129	12	g(w0(0	g(w0(0	NOUN
ejpam-2714	129	13	)	)	PUNCT
ejpam-2714	129	14	,	,	PUNCT
ejpam-2714	129	15	w0(t	w0(t	PROPN
ejpam-2714	129	16	)	)	PUNCT
ejpam-2714	129	17	)	)	PUNCT
ejpam-2714	129	18	≥	≥	NOUN
ejpam-2714	129	19	0	0	NUM
ejpam-2714	129	20	,	,	PUNCT
ejpam-2714	129	21	(	(	PUNCT
ejpam-2714	129	22	13	13	NUM
ejpam-2714	129	23	)	)	PUNCT
ejpam-2714	129	24	(	(	PUNCT
ejpam-2714	129	25	ii	ii	NOUN
ejpam-2714	129	26	)	)	PUNCT
ejpam-2714	129	27	coupled	couple	VERB
ejpam-2714	129	28	lower	low	ADJ
ejpam-2714	129	29	and	and	CCONJ
ejpam-2714	129	30	upper	upper	ADJ
ejpam-2714	129	31	solutions	solution	NOUN
ejpam-2714	129	32	of	of	ADP
ejpam-2714	129	33	type	type	NOUN
ejpam-2714	129	34	i	i	PRON
ejpam-2714	129	35	of	of	ADP
ejpam-2714	129	36	(	(	PUNCT
ejpam-2714	129	37	10	10	NUM
ejpam-2714	129	38	)	)	PUNCT
ejpam-2714	129	39	,	,	PUNCT
ejpam-2714	129	40	(	(	PUNCT
ejpam-2714	129	41	11	11	NUM
ejpam-2714	129	42	)	)	PUNCT
ejpam-2714	129	43	if	if	SCONJ
ejpam-2714	129	44	c	c	PROPN
ejpam-2714	129	45	dqv0(t)≤f(t	dqv0(t)≤f(t	PROPN
ejpam-2714	129	46	,	,	PUNCT
ejpam-2714	129	47	v0(t	v0(t	PROPN
ejpam-2714	129	48	)	)	PUNCT
ejpam-2714	129	49	,	,	PUNCT
ejpam-2714	129	50	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	129	51	)	)	PUNCT
ejpam-2714	129	52	)	)	PUNCT
ejpam-2714	129	53	)	)	PUNCT
ejpam-2714	130	1	+	+	CCONJ
ejpam-2714	130	2	g(t	g(t	PROPN
ejpam-2714	130	3	,	,	PUNCT
ejpam-2714	130	4	w0(t	w0(t	PROPN
ejpam-2714	130	5	)	)	PUNCT
ejpam-2714	130	6	,	,	PUNCT
ejpam-2714	130	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	130	8	)	)	PUNCT
ejpam-2714	130	9	)	)	PUNCT
ejpam-2714	130	10	)	)	PUNCT
ejpam-2714	130	11	,	,	PUNCT
ejpam-2714	130	12	g(v0(0	g(v0(0	NOUN
ejpam-2714	130	13	)	)	PUNCT
ejpam-2714	130	14	,	,	PUNCT
ejpam-2714	130	15	v0(t	v0(t	PROPN
ejpam-2714	130	16	)	)	PUNCT
ejpam-2714	130	17	)	)	PUNCT
ejpam-2714	130	18	≤	≤	NOUN
ejpam-2714	130	19	0	0	NUM
ejpam-2714	130	20	,	,	PUNCT
ejpam-2714	130	21	(	(	PUNCT
ejpam-2714	130	22	14	14	NUM
ejpam-2714	130	23	)	)	PUNCT
ejpam-2714	130	24	c	c	NOUN
ejpam-2714	130	25	dqw0(t)≥f(t	dqw0(t)≥f(t	NOUN
ejpam-2714	130	26	,	,	PUNCT
ejpam-2714	130	27	w0(t	w0(t	PROPN
ejpam-2714	130	28	)	)	PUNCT
ejpam-2714	130	29	,	,	PUNCT
ejpam-2714	130	30	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	130	31	)	)	PUNCT
ejpam-2714	130	32	)	)	PUNCT
ejpam-2714	130	33	)	)	PUNCT
ejpam-2714	131	1	+	+	CCONJ
ejpam-2714	131	2	g(t	g(t	PROPN
ejpam-2714	131	3	,	,	PUNCT
ejpam-2714	131	4	v0(t	v0(t	PROPN
ejpam-2714	131	5	)	)	PUNCT
ejpam-2714	131	6	,	,	PUNCT
ejpam-2714	131	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	131	8	)	)	PUNCT
ejpam-2714	131	9	)	)	PUNCT
ejpam-2714	131	10	)	)	PUNCT
ejpam-2714	131	11	,	,	PUNCT
ejpam-2714	131	12	g(w0(0	g(w0(0	NOUN
ejpam-2714	131	13	)	)	PUNCT
ejpam-2714	131	14	,	,	PUNCT
ejpam-2714	131	15	w0(t	w0(t	PROPN
ejpam-2714	131	16	)	)	PUNCT
ejpam-2714	131	17	)	)	PUNCT
ejpam-2714	131	18	≥	≥	NOUN
ejpam-2714	131	19	0	0	NUM
ejpam-2714	131	20	,	,	PUNCT
ejpam-2714	131	21	(	(	PUNCT
ejpam-2714	131	22	15	15	NUM
ejpam-2714	131	23	)	)	PUNCT
ejpam-2714	131	24	(	(	PUNCT
ejpam-2714	131	25	iii	iii	NOUN
ejpam-2714	131	26	)	)	PUNCT
ejpam-2714	131	27	coupled	couple	VERB
ejpam-2714	131	28	lower	low	ADJ
ejpam-2714	131	29	and	and	CCONJ
ejpam-2714	131	30	upper	upper	ADJ
ejpam-2714	131	31	solutions	solution	NOUN
ejpam-2714	131	32	of	of	ADP
ejpam-2714	131	33	type	type	NOUN
ejpam-2714	131	34	ii	ii	PROPN
ejpam-2714	131	35	of	of	ADP
ejpam-2714	131	36	(	(	PUNCT
ejpam-2714	131	37	10	10	NUM
ejpam-2714	131	38	)	)	PUNCT
ejpam-2714	131	39	,	,	PUNCT
ejpam-2714	131	40	(	(	PUNCT
ejpam-2714	131	41	11	11	NUM
ejpam-2714	131	42	)	)	PUNCT
ejpam-2714	131	43	if	if	SCONJ
ejpam-2714	131	44	c	c	PROPN
ejpam-2714	131	45	dqv0(t)≤f(t	dqv0(t)≤f(t	PROPN
ejpam-2714	131	46	,	,	PUNCT
ejpam-2714	131	47	w0(t	w0(t	PROPN
ejpam-2714	131	48	)	)	PUNCT
ejpam-2714	131	49	,	,	PUNCT
ejpam-2714	131	50	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	131	51	)	)	PUNCT
ejpam-2714	131	52	)	)	PUNCT
ejpam-2714	131	53	)	)	PUNCT
ejpam-2714	132	1	+	+	CCONJ
ejpam-2714	132	2	g(t	g(t	PROPN
ejpam-2714	132	3	,	,	PUNCT
ejpam-2714	132	4	v0(t	v0(t	PROPN
ejpam-2714	132	5	)	)	PUNCT
ejpam-2714	132	6	,	,	PUNCT
ejpam-2714	132	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	132	8	)	)	PUNCT
ejpam-2714	132	9	)	)	PUNCT
ejpam-2714	132	10	)	)	PUNCT
ejpam-2714	132	11	,	,	PUNCT
ejpam-2714	132	12	g(v0(0	g(v0(0	NOUN
ejpam-2714	132	13	)	)	PUNCT
ejpam-2714	132	14	,	,	PUNCT
ejpam-2714	132	15	v0(t	v0(t	PROPN
ejpam-2714	132	16	)	)	PUNCT
ejpam-2714	132	17	)	)	PUNCT
ejpam-2714	132	18	≤	≤	NOUN
ejpam-2714	132	19	0	0	NUM
ejpam-2714	132	20	,	,	PUNCT
ejpam-2714	132	21	(	(	PUNCT
ejpam-2714	132	22	16	16	NUM
ejpam-2714	132	23	)	)	PUNCT
ejpam-2714	132	24	c	c	NOUN
ejpam-2714	132	25	dqw0(t)≥f(t	dqw0(t)≥f(t	NOUN
ejpam-2714	132	26	,	,	PUNCT
ejpam-2714	132	27	v0(t	v0(t	PROPN
ejpam-2714	132	28	)	)	PUNCT
ejpam-2714	132	29	,	,	PUNCT
ejpam-2714	132	30	iqv0(t	iqv0(t	NOUN
ejpam-2714	132	31	)	)	PUNCT
ejpam-2714	132	32	)	)	PUNCT
ejpam-2714	133	1	+	+	CCONJ
ejpam-2714	133	2	g(t	g(t	PROPN
ejpam-2714	133	3	,	,	PUNCT
ejpam-2714	133	4	w0(t	w0(t	PROPN
ejpam-2714	133	5	)	)	PUNCT
ejpam-2714	133	6	,	,	PUNCT
ejpam-2714	133	7	iqw0(t	iqw0(t	NOUN
ejpam-2714	133	8	)	)	PUNCT
ejpam-2714	133	9	)	)	PUNCT
ejpam-2714	133	10	,	,	PUNCT
ejpam-2714	133	11	g(w0(0	g(w0(0	NOUN
ejpam-2714	133	12	)	)	PUNCT
ejpam-2714	133	13	,	,	PUNCT
ejpam-2714	133	14	w0(t	w0(t	PROPN
ejpam-2714	133	15	)	)	PUNCT
ejpam-2714	133	16	)	)	PUNCT
ejpam-2714	133	17	≥	≥	NOUN
ejpam-2714	133	18	0	0	NUM
ejpam-2714	133	19	,	,	PUNCT
ejpam-2714	133	20	(	(	PUNCT
ejpam-2714	133	21	17	17	NUM
ejpam-2714	133	22	)	)	PUNCT
ejpam-2714	133	23	(	(	PUNCT
ejpam-2714	133	24	iv	iv	X
ejpam-2714	133	25	)	)	PUNCT
ejpam-2714	133	26	coupled	couple	VERB
ejpam-2714	133	27	lower	low	ADJ
ejpam-2714	133	28	and	and	CCONJ
ejpam-2714	133	29	upper	upper	ADJ
ejpam-2714	133	30	solutions	solution	NOUN
ejpam-2714	133	31	of	of	ADP
ejpam-2714	133	32	type	type	NOUN
ejpam-2714	133	33	iii	iii	PROPN
ejpam-2714	133	34	of	of	ADP
ejpam-2714	133	35	(	(	PUNCT
ejpam-2714	133	36	10	10	NUM
ejpam-2714	133	37	)	)	PUNCT
ejpam-2714	133	38	,	,	PUNCT
ejpam-2714	133	39	(	(	PUNCT
ejpam-2714	133	40	11	11	NUM
ejpam-2714	133	41	)	)	PUNCT
ejpam-2714	133	42	if	if	SCONJ
ejpam-2714	133	43	c	c	PROPN
ejpam-2714	133	44	dqv0(t)≤f(t	dqv0(t)≤f(t	PROPN
ejpam-2714	133	45	,	,	PUNCT
ejpam-2714	133	46	w0(t	w0(t	PROPN
ejpam-2714	133	47	)	)	PUNCT
ejpam-2714	133	48	,	,	PUNCT
ejpam-2714	133	49	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	133	50	)	)	PUNCT
ejpam-2714	133	51	)	)	PUNCT
ejpam-2714	133	52	)	)	PUNCT
ejpam-2714	134	1	+	+	CCONJ
ejpam-2714	134	2	g(t	g(t	PROPN
ejpam-2714	134	3	,	,	PUNCT
ejpam-2714	134	4	w0(t	w0(t	PROPN
ejpam-2714	134	5	)	)	PUNCT
ejpam-2714	134	6	,	,	PUNCT
ejpam-2714	134	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	134	8	)	)	PUNCT
ejpam-2714	134	9	)	)	PUNCT
ejpam-2714	134	10	)	)	PUNCT
ejpam-2714	134	11	,	,	PUNCT
ejpam-2714	134	12	g(v0(0	g(v0(0	NOUN
ejpam-2714	134	13	)	)	PUNCT
ejpam-2714	134	14	,	,	PUNCT
ejpam-2714	134	15	v0(t	v0(t	PROPN
ejpam-2714	134	16	)	)	PUNCT
ejpam-2714	134	17	)	)	PUNCT
ejpam-2714	134	18	≤	≤	NOUN
ejpam-2714	134	19	0	0	NUM
ejpam-2714	134	20	,	,	PUNCT
ejpam-2714	134	21	(	(	PUNCT
ejpam-2714	134	22	18	18	NUM
ejpam-2714	134	23	)	)	PUNCT
ejpam-2714	134	24	c	c	NOUN
ejpam-2714	134	25	dqw0(t)≥f(t	dqw0(t)≥f(t	NOUN
ejpam-2714	134	26	,	,	PUNCT
ejpam-2714	134	27	v0(t	v0(t	PROPN
ejpam-2714	134	28	)	)	PUNCT
ejpam-2714	134	29	,	,	PUNCT
ejpam-2714	134	30	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	134	31	)	)	PUNCT
ejpam-2714	134	32	)	)	PUNCT
ejpam-2714	134	33	)	)	PUNCT
ejpam-2714	135	1	+	+	CCONJ
ejpam-2714	135	2	g(t	g(t	PROPN
ejpam-2714	135	3	,	,	PUNCT
ejpam-2714	135	4	v0(t	v0(t	PROPN
ejpam-2714	135	5	)	)	PUNCT
ejpam-2714	135	6	,	,	PUNCT
ejpam-2714	135	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	135	8	)	)	PUNCT
ejpam-2714	135	9	)	)	PUNCT
ejpam-2714	135	10	)	)	PUNCT
ejpam-2714	135	11	,	,	PUNCT
ejpam-2714	135	12	g(w0(0	g(w0(0	NOUN
ejpam-2714	135	13	)	)	PUNCT
ejpam-2714	135	14	,	,	PUNCT
ejpam-2714	135	15	w0(t	w0(t	PROPN
ejpam-2714	135	16	)	)	PUNCT
ejpam-2714	135	17	)	)	PUNCT
ejpam-2714	135	18	≥	≥	NOUN
ejpam-2714	135	19	0	0	NUM
ejpam-2714	135	20	.	.	PUNCT
ejpam-2714	136	1	(	(	PUNCT
ejpam-2714	136	2	19	19	NUM
ejpam-2714	136	3	)	)	PUNCT
ejpam-2714	136	4	we	we	PRON
ejpam-2714	136	5	note	note	VERB
ejpam-2714	136	6	that	that	SCONJ
ejpam-2714	136	7	whenever	whenever	SCONJ
ejpam-2714	136	8	v(t	v(t	NOUN
ejpam-2714	136	9	)	)	PUNCT
ejpam-2714	136	10	≤	≤	NOUN
ejpam-2714	136	11	w(t	w(t	PROPN
ejpam-2714	136	12	)	)	PUNCT
ejpam-2714	136	13	,	,	PUNCT
ejpam-2714	136	14	t	t	PROPN
ejpam-2714	136	15	∈	∈	PROPN
ejpam-2714	136	16	j	j	PROPN
ejpam-2714	136	17	,	,	PUNCT
ejpam-2714	136	18	if	if	SCONJ
ejpam-2714	136	19	f(t	f(t	NOUN
ejpam-2714	136	20	,	,	PUNCT
ejpam-2714	136	21	x1	x1	PROPN
ejpam-2714	136	22	,	,	PUNCT
ejpam-2714	136	23	x2	x2	PROPN
ejpam-2714	136	24	)	)	PUNCT
ejpam-2714	136	25	is	be	AUX
ejpam-2714	136	26	nondecreasing	nondecrease	VERB
ejpam-2714	136	27	in	in	ADP
ejpam-2714	136	28	x1	x1	PROPN
ejpam-2714	136	29	for	for	ADP
ejpam-2714	136	30	each	each	DET
ejpam-2714	136	31	(	(	PUNCT
ejpam-2714	136	32	t	t	PROPN
ejpam-2714	136	33	,	,	PUNCT
ejpam-2714	136	34	x2	x2	PROPN
ejpam-2714	136	35	)	)	PUNCT
ejpam-2714	136	36	∈	∈	PROPN
ejpam-2714	136	37	j×r+	j×r+	NOUN
ejpam-2714	136	38	and	and	CCONJ
ejpam-2714	136	39	is	be	AUX
ejpam-2714	136	40	nondecreasing	nondecrease	VERB
ejpam-2714	136	41	in	in	ADP
ejpam-2714	136	42	x2	x2	PROPN
ejpam-2714	136	43	for	for	ADP
ejpam-2714	136	44	each	each	DET
ejpam-2714	136	45	(	(	PUNCT
ejpam-2714	136	46	t	t	PROPN
ejpam-2714	136	47	,	,	PUNCT
ejpam-2714	136	48	x1	x1	PROPN
ejpam-2714	136	49	)	)	PUNCT
ejpam-2714	136	50	∈	∈	PROPN
ejpam-2714	136	51	j×r	j×r	PROPN
ejpam-2714	136	52	,	,	PUNCT
ejpam-2714	136	53	further	far	ADV
ejpam-2714	136	54	,	,	PUNCT
ejpam-2714	136	55	if	if	SCONJ
ejpam-2714	136	56	g(t	g(t	PROPN
ejpam-2714	136	57	,	,	PUNCT
ejpam-2714	136	58	y1	y1	NOUN
ejpam-2714	136	59	,	,	PUNCT
ejpam-2714	136	60	y2	y2	PROPN
ejpam-2714	136	61	)	)	PUNCT
ejpam-2714	136	62	is	be	AUX
ejpam-2714	136	63	non	non	ADJ
ejpam-2714	136	64	increasing	increase	VERB
ejpam-2714	136	65	in	in	ADP
ejpam-2714	136	66	y1	y1	NOUN
ejpam-2714	136	67	for	for	ADP
ejpam-2714	136	68	each	each	PRON
ejpam-2714	136	69	(	(	PUNCT
ejpam-2714	136	70	t	t	PROPN
ejpam-2714	136	71	,	,	PUNCT
ejpam-2714	136	72	y2	y2	PROPN
ejpam-2714	136	73	)	)	PUNCT
ejpam-2714	136	74	∈	∈	PROPN
ejpam-2714	137	1	j	j	PROPN
ejpam-2714	137	2	×r+	×r+	ADV
ejpam-2714	137	3	and	and	CCONJ
ejpam-2714	137	4	is	be	AUX
ejpam-2714	137	5	non	non	PRON
ejpam-2714	137	6	increasing	increase	VERB
ejpam-2714	137	7	in	in	ADP
ejpam-2714	137	8	y2	y2	PROPN
ejpam-2714	137	9	for	for	ADP
ejpam-2714	137	10	each	each	DET
ejpam-2714	137	11	(	(	PUNCT
ejpam-2714	137	12	t	t	PROPN
ejpam-2714	137	13	,	,	PUNCT
ejpam-2714	137	14	y1	y1	PROPN
ejpam-2714	137	15	)	)	PUNCT
ejpam-2714	137	16	∈	∈	PROPN
ejpam-2714	137	17	j	j	PROPN
ejpam-2714	137	18	×r	×r	PROPN
ejpam-2714	137	19	,	,	PUNCT
ejpam-2714	137	20	then	then	ADV
ejpam-2714	137	21	the	the	DET
ejpam-2714	137	22	lower	low	ADJ
ejpam-2714	137	23	and	and	CCONJ
ejpam-2714	137	24	upper	upper	ADJ
ejpam-2714	137	25	solutions	solution	NOUN
ejpam-2714	137	26	defined	define	VERB
ejpam-2714	137	27	by	by	ADP
ejpam-2714	137	28	(	(	PUNCT
ejpam-2714	137	29	12	12	NUM
ejpam-2714	137	30	)	)	PUNCT
ejpam-2714	137	31	,	,	PUNCT
ejpam-2714	137	32	(	(	PUNCT
ejpam-2714	137	33	13	13	NUM
ejpam-2714	137	34	)	)	PUNCT
ejpam-2714	137	35	and	and	CCONJ
ejpam-2714	137	36	those	those	PRON
ejpam-2714	137	37	defined	define	VERB
ejpam-2714	137	38	by	by	ADP
ejpam-2714	137	39	(	(	PUNCT
ejpam-2714	137	40	18	18	NUM
ejpam-2714	137	41	)	)	PUNCT
ejpam-2714	137	42	and	and	CCONJ
ejpam-2714	137	43	(	(	PUNCT
ejpam-2714	137	44	19	19	NUM
ejpam-2714	137	45	)	)	PUNCT
ejpam-2714	137	46	reduce	reduce	VERB
ejpam-2714	137	47	to	to	ADP
ejpam-2714	137	48	(	(	PUNCT
ejpam-2714	137	49	14	14	NUM
ejpam-2714	137	50	)	)	PUNCT
ejpam-2714	137	51	,	,	PUNCT
ejpam-2714	137	52	(	(	PUNCT
ejpam-2714	137	53	15	15	NUM
ejpam-2714	137	54	)	)	PUNCT
ejpam-2714	137	55	,	,	PUNCT
ejpam-2714	137	56	and	and	CCONJ
ejpam-2714	137	57	(	(	PUNCT
ejpam-2714	137	58	16	16	NUM
ejpam-2714	137	59	)	)	PUNCT
ejpam-2714	137	60	,	,	PUNCT
ejpam-2714	137	61	(	(	PUNCT
ejpam-2714	137	62	17	17	NUM
ejpam-2714	137	63	)	)	PUNCT
ejpam-2714	137	64	respectively	respectively	ADV
ejpam-2714	137	65	.	.	PUNCT
ejpam-2714	138	1	hence	hence	ADV
ejpam-2714	138	2	it	it	PRON
ejpam-2714	138	3	is	be	AUX
ejpam-2714	138	4	sufficient	sufficient	ADJ
ejpam-2714	138	5	to	to	PART
ejpam-2714	138	6	investigate	investigate	VERB
ejpam-2714	138	7	the	the	DET
ejpam-2714	138	8	cases	case	NOUN
ejpam-2714	138	9	(	(	PUNCT
ejpam-2714	138	10	14	14	NUM
ejpam-2714	138	11	)	)	PUNCT
ejpam-2714	138	12	,	,	PUNCT
ejpam-2714	138	13	(	(	PUNCT
ejpam-2714	138	14	15	15	NUM
ejpam-2714	138	15	)	)	PUNCT
ejpam-2714	138	16	and	and	CCONJ
ejpam-2714	138	17	(	(	PUNCT
ejpam-2714	138	18	16	16	NUM
ejpam-2714	138	19	)	)	PUNCT
ejpam-2714	138	20	,	,	PUNCT
ejpam-2714	138	21	(	(	PUNCT
ejpam-2714	138	22	17	17	NUM
ejpam-2714	138	23	)	)	PUNCT
ejpam-2714	138	24	.	.	PUNCT
ejpam-2714	139	1	based	base	VERB
ejpam-2714	139	2	on	on	ADP
ejpam-2714	139	3	the	the	DET
ejpam-2714	139	4	concepts	concept	NOUN
ejpam-2714	139	5	defined	define	VERB
ejpam-2714	139	6	above	above	ADV
ejpam-2714	139	7	,	,	PUNCT
ejpam-2714	139	8	we	we	PRON
ejpam-2714	139	9	now	now	ADV
ejpam-2714	139	10	develop	develop	VERB
ejpam-2714	139	11	the	the	DET
ejpam-2714	139	12	monotone	monotone	ADJ
ejpam-2714	139	13	iterative	iterative	NOUN
ejpam-2714	139	14	technique	technique	NOUN
ejpam-2714	139	15	for	for	ADP
ejpam-2714	139	16	the	the	DET
ejpam-2714	139	17	considered	consider	VERB
ejpam-2714	139	18	problem	problem	NOUN
ejpam-2714	139	19	.	.	PUNCT
ejpam-2714	140	1	to	to	PART
ejpam-2714	140	2	do	do	VERB
ejpam-2714	140	3	so	so	ADV
ejpam-2714	140	4	we	we	PRON
ejpam-2714	140	5	use	use	VERB
ejpam-2714	140	6	sequences	sequence	NOUN
ejpam-2714	140	7	of	of	ADP
ejpam-2714	140	8	iterates	iterate	NOUN
ejpam-2714	140	9	which	which	PRON
ejpam-2714	140	10	are	be	AUX
ejpam-2714	140	11	solutions	solution	NOUN
ejpam-2714	140	12	sequences	sequence	NOUN
ejpam-2714	140	13	of	of	ADP
ejpam-2714	140	14	ivp	ivp	NUM
ejpam-2714	140	15	of	of	ADP
ejpam-2714	140	16	linear	linear	PROPN
ejpam-2714	140	17	caputo	caputo	PROPN
ejpam-2714	140	18	fractional	fractional	PROPN
ejpam-2714	140	19	integro	integro	PROPN
ejpam-2714	140	20	-	-	PUNCT
ejpam-2714	140	21	differential	differential	NOUN
ejpam-2714	140	22	equations	equation	NOUN
ejpam-2714	140	23	.	.	PUNCT
ejpam-2714	141	1	since	since	SCONJ
ejpam-2714	141	2	the	the	DET
ejpam-2714	141	3	solution	solution	NOUN
ejpam-2714	141	4	of	of	ADP
ejpam-2714	141	5	the	the	DET
ejpam-2714	141	6	linear	linear	PROPN
ejpam-2714	141	7	caputo	caputo	PROPN
ejpam-2714	141	8	fractional	fractional	PROPN
ejpam-2714	141	9	differential	differential	NOUN
ejpam-2714	141	10	equation	equation	NOUN
ejpam-2714	141	11	is	be	AUX
ejpam-2714	141	12	unique	unique	ADJ
ejpam-2714	141	13	,	,	PUNCT
ejpam-2714	141	14	the	the	DET
ejpam-2714	141	15	sequence	sequence	NOUN
ejpam-2714	141	16	of	of	ADP
ejpam-2714	141	17	iterates	iterate	NOUN
ejpam-2714	141	18	is	be	AUX
ejpam-2714	141	19	a	a	DET
ejpam-2714	141	20	unique	unique	ADJ
ejpam-2714	141	21	j.	j.	PROPN
ejpam-2714	141	22	devi	devi	PROPN
ejpam-2714	141	23	,	,	PUNCT
ejpam-2714	141	24	ch	ch	PROPN
ejpam-2714	141	25	.	.	PUNCT
ejpam-2714	141	26	sreedhar	sreedhar	PROPN
ejpam-2714	141	27	/	/	SYM
ejpam-2714	141	28	eur	eur	PROPN
ejpam-2714	141	29	.	.	PUNCT
ejpam-2714	142	1	j.	j.	PROPN
ejpam-2714	142	2	pure	pure	PROPN
ejpam-2714	142	3	appl	appl	PROPN
ejpam-2714	142	4	.	.	PROPN
ejpam-2714	142	5	math	math	PROPN
ejpam-2714	142	6	,	,	PUNCT
ejpam-2714	142	7	9	9	NUM
ejpam-2714	142	8	(	(	PUNCT
ejpam-2714	142	9	2016	2016	NUM
ejpam-2714	142	10	)	)	PUNCT
ejpam-2714	142	11	,	,	PUNCT
ejpam-2714	142	12	346	346	NUM
ejpam-2714	142	13	-	-	SYM
ejpam-2714	142	14	359	359	NUM
ejpam-2714	142	15	351	351	NUM
ejpam-2714	142	16	sequence	sequence	NOUN
ejpam-2714	142	17	converging	converge	VERB
ejpam-2714	142	18	to	to	ADP
ejpam-2714	142	19	a	a	DET
ejpam-2714	142	20	solution	solution	NOUN
ejpam-2714	142	21	of	of	ADP
ejpam-2714	142	22	the	the	DET
ejpam-2714	142	23	considered	consider	VERB
ejpam-2714	142	24	problem	problem	NOUN
ejpam-2714	142	25	defined	define	VERB
ejpam-2714	142	26	by	by	ADP
ejpam-2714	142	27	(	(	PUNCT
ejpam-2714	142	28	10	10	NUM
ejpam-2714	142	29	)	)	PUNCT
ejpam-2714	142	30	and	and	CCONJ
ejpam-2714	142	31	(	(	PUNCT
ejpam-2714	142	32	11	11	NUM
ejpam-2714	142	33	)	)	PUNCT
ejpam-2714	142	34	.	.	PUNCT
ejpam-2714	143	1	in	in	ADP
ejpam-2714	143	2	this	this	DET
ejpam-2714	143	3	approach	approach	NOUN
ejpam-2714	143	4	,	,	PUNCT
ejpam-2714	143	5	we	we	PRON
ejpam-2714	143	6	do	do	AUX
ejpam-2714	143	7	not	not	PART
ejpam-2714	143	8	need	need	VERB
ejpam-2714	143	9	to	to	PART
ejpam-2714	143	10	prove	prove	VERB
ejpam-2714	143	11	the	the	DET
ejpam-2714	143	12	existence	existence	NOUN
ejpam-2714	143	13	of	of	ADP
ejpam-2714	143	14	solution	solution	NOUN
ejpam-2714	143	15	for	for	ADP
ejpam-2714	143	16	bvp	bvp	NOUN
ejpam-2714	143	17	of	of	ADP
ejpam-2714	143	18	nonlinear	nonlinear	PROPN
ejpam-2714	143	19	caputo	caputo	PROPN
ejpam-2714	143	20	fractional	fractional	PROPN
ejpam-2714	143	21	integro	integro	PROPN
ejpam-2714	143	22	differential	differential	NOUN
ejpam-2714	143	23	equation	equation	NOUN
ejpam-2714	143	24	,	,	PUNCT
ejpam-2714	143	25	as	as	SCONJ
ejpam-2714	143	26	it	it	PRON
ejpam-2714	143	27	follows	follow	VERB
ejpam-2714	143	28	from	from	ADP
ejpam-2714	143	29	the	the	DET
ejpam-2714	143	30	construction	construction	NOUN
ejpam-2714	143	31	of	of	ADP
ejpam-2714	143	32	the	the	DET
ejpam-2714	143	33	monotone	monotone	ADJ
ejpam-2714	143	34	sequences	sequence	NOUN
ejpam-2714	143	35	.	.	PUNCT
ejpam-2714	144	1	in	in	ADP
ejpam-2714	144	2	the	the	DET
ejpam-2714	144	3	following	following	NOUN
ejpam-2714	144	4	theorem	theorem	NOUN
ejpam-2714	144	5	,	,	PUNCT
ejpam-2714	144	6	we	we	PRON
ejpam-2714	144	7	use	use	VERB
ejpam-2714	144	8	coupled	couple	VERB
ejpam-2714	144	9	lower	low	ADJ
ejpam-2714	144	10	and	and	CCONJ
ejpam-2714	144	11	upper	upper	ADJ
ejpam-2714	144	12	solutions	solution	NOUN
ejpam-2714	144	13	of	of	ADP
ejpam-2714	144	14	type	type	NOUN
ejpam-2714	144	15	i	i	PRON
ejpam-2714	144	16	and	and	CCONJ
ejpam-2714	144	17	obtain	obtain	VERB
ejpam-2714	144	18	monotone	monotone	ADJ
ejpam-2714	144	19	sequences	sequence	NOUN
ejpam-2714	144	20	which	which	PRON
ejpam-2714	144	21	converge	converge	VERB
ejpam-2714	144	22	uniformly	uniformly	ADV
ejpam-2714	144	23	and	and	CCONJ
ejpam-2714	144	24	monotonically	monotonically	ADV
ejpam-2714	144	25	to	to	PART
ejpam-2714	144	26	coupled	couple	VERB
ejpam-2714	144	27	minimal	minimal	ADJ
ejpam-2714	144	28	and	and	CCONJ
ejpam-2714	144	29	maximal	maximal	ADJ
ejpam-2714	144	30	solutions	solution	NOUN
ejpam-2714	144	31	of	of	ADP
ejpam-2714	144	32	the	the	DET
ejpam-2714	144	33	problem	problem	NOUN
ejpam-2714	144	34	defined	define	VERB
ejpam-2714	144	35	by	by	ADP
ejpam-2714	144	36	(	(	PUNCT
ejpam-2714	144	37	10	10	NUM
ejpam-2714	144	38	)	)	PUNCT
ejpam-2714	144	39	and	and	CCONJ
ejpam-2714	144	40	(	(	PUNCT
ejpam-2714	144	41	11	11	NUM
ejpam-2714	144	42	)	)	PUNCT
ejpam-2714	144	43	.	.	PUNCT
ejpam-2714	145	1	theorem	theorem	NOUN
ejpam-2714	145	2	3	3	X
ejpam-2714	145	3	.	.	PUNCT
ejpam-2714	145	4	suppose	suppose	VERB
ejpam-2714	145	5	that	that	SCONJ
ejpam-2714	145	6	(	(	PUNCT
ejpam-2714	145	7	a1	a1	PROPN
ejpam-2714	145	8	)	)	PUNCT
ejpam-2714	145	9	v0	v0	NOUN
ejpam-2714	145	10	,	,	PUNCT
ejpam-2714	145	11	w0	w0	PROPN
ejpam-2714	145	12	are	be	AUX
ejpam-2714	145	13	coupled	couple	VERB
ejpam-2714	145	14	lower	low	ADJ
ejpam-2714	145	15	and	and	CCONJ
ejpam-2714	145	16	upper	upper	ADJ
ejpam-2714	145	17	solutions	solution	NOUN
ejpam-2714	145	18	of	of	ADP
ejpam-2714	145	19	type	type	NOUN
ejpam-2714	145	20	i	i	PRON
ejpam-2714	145	21	for	for	ADP
ejpam-2714	145	22	problem	problem	NOUN
ejpam-2714	145	23	defined	define	VERB
ejpam-2714	145	24	by	by	ADP
ejpam-2714	145	25	(	(	PUNCT
ejpam-2714	145	26	10	10	NUM
ejpam-2714	145	27	)	)	PUNCT
ejpam-2714	145	28	,	,	PUNCT
ejpam-2714	145	29	(	(	PUNCT
ejpam-2714	145	30	11	11	NUM
ejpam-2714	145	31	)	)	PUNCT
ejpam-2714	145	32	with	with	ADP
ejpam-2714	145	33	v0(t)≤	v0(t)≤	PROPN
ejpam-2714	145	34	w0(t	w0(t	PROPN
ejpam-2714	145	35	)	)	PUNCT
ejpam-2714	145	36	on	on	ADP
ejpam-2714	145	37	j	j	PROPN
ejpam-2714	145	38	,	,	PUNCT
ejpam-2714	145	39	(	(	PUNCT
ejpam-2714	145	40	a2	a2	PROPN
ejpam-2714	145	41	)	)	PUNCT
ejpam-2714	145	42	the	the	DET
ejpam-2714	145	43	function	function	NOUN
ejpam-2714	145	44	g(u	g(u	PROPN
ejpam-2714	145	45	,	,	PUNCT
ejpam-2714	145	46	v	v	NOUN
ejpam-2714	145	47	)	)	PUNCT
ejpam-2714	145	48	∈	∈	PROPN
ejpam-2714	146	1	c[r2,r	c[r2,r	NOUN
ejpam-2714	146	2	]	]	X
ejpam-2714	146	3	is	be	AUX
ejpam-2714	146	4	nonincreasing	nonincrease	VERB
ejpam-2714	146	5	in	in	ADP
ejpam-2714	146	6	v	v	NOUN
ejpam-2714	146	7	for	for	ADP
ejpam-2714	146	8	each	each	DET
ejpam-2714	146	9	u	u	NOUN
ejpam-2714	146	10	and	and	CCONJ
ejpam-2714	146	11	there	there	PRON
ejpam-2714	146	12	exists	exist	VERB
ejpam-2714	146	13	a	a	DET
ejpam-2714	146	14	constant	constant	ADJ
ejpam-2714	146	15	m	m	NOUN
ejpam-2714	146	16	>	>	X
ejpam-2714	146	17	0	0	NUM
ejpam-2714	146	18	such	such	ADJ
ejpam-2714	146	19	that	that	DET
ejpam-2714	146	20	g(u1	g(u1	NOUN
ejpam-2714	146	21	,	,	PUNCT
ejpam-2714	146	22	v)−	v)−	PROPN
ejpam-2714	146	23	g(u2	g(u2	NOUN
ejpam-2714	146	24	,	,	PUNCT
ejpam-2714	146	25	v)≤	v)≤	NOUN
ejpam-2714	146	26	m(u1	m(u1	NOUN
ejpam-2714	146	27	−	−	PROPN
ejpam-2714	146	28	u2	u2	PROPN
ejpam-2714	146	29	)	)	PUNCT
ejpam-2714	146	30	,	,	PUNCT
ejpam-2714	146	31	(	(	PUNCT
ejpam-2714	146	32	20	20	NUM
ejpam-2714	146	33	)	)	PUNCT
ejpam-2714	146	34	for	for	ADP
ejpam-2714	146	35	v0(0)≤	v0(0)≤	PROPN
ejpam-2714	146	36	u2	u2	PROPN
ejpam-2714	146	37	≤	≤	PROPN
ejpam-2714	146	38	u1	u1	NOUN
ejpam-2714	146	39	≤	≤	PROPN
ejpam-2714	146	40	w0(0	w0(0	PROPN
ejpam-2714	146	41	)	)	PUNCT
ejpam-2714	146	42	,	,	PUNCT
ejpam-2714	147	1	v0(t	v0(t	VERB
ejpam-2714	147	2	)	)	PUNCT
ejpam-2714	147	3	≤	≤	NOUN
ejpam-2714	147	4	v	v	ADP
ejpam-2714	147	5	≤	≤	NUM
ejpam-2714	147	6	w0(t	w0(t	PROPN
ejpam-2714	147	7	)	)	PUNCT
ejpam-2714	147	8	,	,	PUNCT
ejpam-2714	147	9	(	(	PUNCT
ejpam-2714	147	10	a3	a3	NOUN
ejpam-2714	147	11	)	)	PUNCT
ejpam-2714	148	1	f	f	X
ejpam-2714	148	2	,	,	PUNCT
ejpam-2714	148	3	g	g	PROPN
ejpam-2714	148	4	∈	∈	PROPN
ejpam-2714	148	5	c[j	c[j	ADJ
ejpam-2714	148	6	×r×r+,r	×r×r+,r	NOUN
ejpam-2714	148	7	]	]	PUNCT
ejpam-2714	148	8	and	and	CCONJ
ejpam-2714	148	9	f(t	f(t	NOUN
ejpam-2714	148	10	,	,	PUNCT
ejpam-2714	148	11	x1	x1	PROPN
ejpam-2714	148	12	,	,	PUNCT
ejpam-2714	148	13	x2	x2	PROPN
ejpam-2714	148	14	)	)	PUNCT
ejpam-2714	148	15	is	be	AUX
ejpam-2714	148	16	non	non	ADJ
ejpam-2714	148	17	-	-	ADJ
ejpam-2714	148	18	decreasing	decrease	VERB
ejpam-2714	148	19	in	in	ADP
ejpam-2714	148	20	x1	x1	PROPN
ejpam-2714	148	21	for	for	ADP
ejpam-2714	148	22	each	each	DET
ejpam-2714	148	23	(	(	PUNCT
ejpam-2714	148	24	t	t	PROPN
ejpam-2714	148	25	,	,	PUNCT
ejpam-2714	148	26	x2	x2	PROPN
ejpam-2714	148	27	)	)	PUNCT
ejpam-2714	148	28	∈	∈	PROPN
ejpam-2714	148	29	j	j	PROPN
ejpam-2714	148	30	×r+	×r+	ADV
ejpam-2714	148	31	and	and	CCONJ
ejpam-2714	148	32	is	be	AUX
ejpam-2714	148	33	nondecreasing	nondecrease	VERB
ejpam-2714	148	34	in	in	ADP
ejpam-2714	148	35	x2	x2	PROPN
ejpam-2714	148	36	for	for	ADP
ejpam-2714	148	37	each	each	DET
ejpam-2714	148	38	(	(	PUNCT
ejpam-2714	148	39	t	t	PROPN
ejpam-2714	148	40	,	,	PUNCT
ejpam-2714	148	41	x1	x1	PROPN
ejpam-2714	148	42	)	)	PUNCT
ejpam-2714	148	43	∈	∈	PROPN
ejpam-2714	148	44	j	j	PROPN
ejpam-2714	148	45	×r	×r	PROPN
ejpam-2714	148	46	.	.	PUNCT
ejpam-2714	149	1	further	far	ADV
ejpam-2714	149	2	,	,	PUNCT
ejpam-2714	149	3	g(t	g(t	PROPN
ejpam-2714	149	4	,	,	PUNCT
ejpam-2714	149	5	y1	y1	NOUN
ejpam-2714	149	6	,	,	PUNCT
ejpam-2714	149	7	y2	y2	PROPN
ejpam-2714	149	8	)	)	PUNCT
ejpam-2714	149	9	is	be	AUX
ejpam-2714	149	10	nonincreasing	nonincrease	VERB
ejpam-2714	149	11	in	in	ADP
ejpam-2714	149	12	y1	y1	NOUN
ejpam-2714	149	13	for	for	ADP
ejpam-2714	149	14	each	each	DET
ejpam-2714	149	15	(	(	PUNCT
ejpam-2714	149	16	t	t	PROPN
ejpam-2714	149	17	,	,	PUNCT
ejpam-2714	149	18	y2	y2	PROPN
ejpam-2714	149	19	)	)	PUNCT
ejpam-2714	149	20	∈	∈	PROPN
ejpam-2714	149	21	j	j	PROPN
ejpam-2714	149	22	×r+	×r+	ADV
ejpam-2714	149	23	and	and	CCONJ
ejpam-2714	149	24	is	be	AUX
ejpam-2714	149	25	nonincreasing	nonincrease	VERB
ejpam-2714	149	26	in	in	ADP
ejpam-2714	149	27	y2	y2	PROPN
ejpam-2714	149	28	for	for	ADP
ejpam-2714	149	29	each	each	DET
ejpam-2714	149	30	(	(	PUNCT
ejpam-2714	149	31	t	t	PROPN
ejpam-2714	149	32	,	,	PUNCT
ejpam-2714	149	33	y1	y1	PROPN
ejpam-2714	149	34	)	)	PUNCT
ejpam-2714	149	35	∈	∈	PROPN
ejpam-2714	149	36	j	j	PROPN
ejpam-2714	149	37	×r	×r	PROPN
ejpam-2714	149	38	.	.	PUNCT
ejpam-2714	150	1	then	then	ADV
ejpam-2714	150	2	the	the	DET
ejpam-2714	150	3	iterative	iterative	NOUN
ejpam-2714	150	4	scheme	scheme	NOUN
ejpam-2714	150	5	given	give	VERB
ejpam-2714	150	6	by	by	ADP
ejpam-2714	150	7	c	c	PROPN
ejpam-2714	150	8	dqvn+1	dqvn+1	PROPN
ejpam-2714	151	1	=	=	NOUN
ejpam-2714	151	2	f(t	f(t	NOUN
ejpam-2714	151	3	,	,	PUNCT
ejpam-2714	151	4	vn	vn	NOUN
ejpam-2714	151	5	,	,	PUNCT
ejpam-2714	151	6	iq(vn	iq(vn	PROPN
ejpam-2714	151	7	)	)	PUNCT
ejpam-2714	151	8	)	)	PUNCT
ejpam-2714	152	1	+	+	CCONJ
ejpam-2714	153	1	g(t	g(t	PROPN
ejpam-2714	153	2	,	,	PUNCT
ejpam-2714	153	3	wn	wn	PROPN
ejpam-2714	153	4	,	,	PUNCT
ejpam-2714	153	5	iq(wn	iq(wn	PROPN
ejpam-2714	153	6	)	)	PUNCT
ejpam-2714	153	7	)	)	PUNCT
ejpam-2714	153	8	,	,	PUNCT
ejpam-2714	153	9	(	(	PUNCT
ejpam-2714	153	10	21	21	NUM
ejpam-2714	153	11	)	)	PUNCT
ejpam-2714	153	12	vn+1(0	vn+1(0	PUNCT
ejpam-2714	153	13	)	)	PUNCT
ejpam-2714	154	1	=	=	SYM
ejpam-2714	154	2	vn(0)−	vn(0)−	VERB
ejpam-2714	154	3	1	1	NUM
ejpam-2714	154	4	m	m	NOUN
ejpam-2714	154	5	g(vn(0	g(vn(0	PROPN
ejpam-2714	154	6	)	)	PUNCT
ejpam-2714	154	7	,	,	PUNCT
ejpam-2714	154	8	vn(t	vn(t	NUM
ejpam-2714	154	9	)	)	PUNCT
ejpam-2714	154	10	)	)	PUNCT
ejpam-2714	154	11	,	,	PUNCT
ejpam-2714	154	12	(	(	PUNCT
ejpam-2714	154	13	22	22	NUM
ejpam-2714	154	14	)	)	PUNCT
ejpam-2714	154	15	c	c	NOUN
ejpam-2714	155	1	dqwn+1	dqwn+1	NOUN
ejpam-2714	155	2	=	=	PRON
ejpam-2714	155	3	f(t	f(t	NOUN
ejpam-2714	155	4	,	,	PUNCT
ejpam-2714	155	5	wn	wn	PROPN
ejpam-2714	155	6	,	,	PUNCT
ejpam-2714	155	7	iq(wn	iq(wn	PROPN
ejpam-2714	155	8	)	)	PUNCT
ejpam-2714	155	9	)	)	PUNCT
ejpam-2714	156	1	+	+	CCONJ
ejpam-2714	157	1	g(t	g(t	PROPN
ejpam-2714	157	2	,	,	PUNCT
ejpam-2714	157	3	vn	vn	NOUN
ejpam-2714	157	4	,	,	PUNCT
ejpam-2714	157	5	iq(vn	iq(vn	PROPN
ejpam-2714	157	6	)	)	PUNCT
ejpam-2714	157	7	)	)	PUNCT
ejpam-2714	157	8	,	,	PUNCT
ejpam-2714	157	9	(	(	PUNCT
ejpam-2714	157	10	23	23	NUM
ejpam-2714	157	11	)	)	PUNCT
ejpam-2714	157	12	wn+1(0	wn+1(0	PUNCT
ejpam-2714	157	13	)	)	PUNCT
ejpam-2714	158	1	=	=	SYM
ejpam-2714	158	2	wn(0)−	wn(0)−	NOUN
ejpam-2714	158	3	1	1	NUM
ejpam-2714	158	4	m	m	NOUN
ejpam-2714	158	5	g(wn(0	g(wn(0	PROPN
ejpam-2714	158	6	)	)	PUNCT
ejpam-2714	158	7	,	,	PUNCT
ejpam-2714	158	8	wn(t	wn(t	NUM
ejpam-2714	158	9	)	)	PUNCT
ejpam-2714	158	10	)	)	PUNCT
ejpam-2714	158	11	,	,	PUNCT
ejpam-2714	158	12	(	(	PUNCT
ejpam-2714	158	13	24	24	NUM
ejpam-2714	158	14	)	)	PUNCT
ejpam-2714	158	15	yields	yield	VERB
ejpam-2714	158	16	two	two	NUM
ejpam-2714	158	17	monotone	monotone	ADJ
ejpam-2714	158	18	sequences	sequence	NOUN
ejpam-2714	158	19	{	{	PUNCT
ejpam-2714	158	20	vn(t	vn(t	NUM
ejpam-2714	158	21	)	)	PUNCT
ejpam-2714	158	22	}	}	PUNCT
ejpam-2714	158	23	and	and	CCONJ
ejpam-2714	158	24	{	{	PUNCT
ejpam-2714	158	25	wn(t	wn(t	NUM
ejpam-2714	158	26	)	)	PUNCT
ejpam-2714	158	27	}	}	PUNCT
ejpam-2714	158	28	such	such	ADJ
ejpam-2714	158	29	that	that	DET
ejpam-2714	158	30	v0	v0	NOUN
ejpam-2714	158	31	≤	≤	NOUN
ejpam-2714	158	32	v1	v1	NOUN
ejpam-2714	158	33	≤	≤	NUM
ejpam-2714	158	34	.	.	PUNCT
ejpam-2714	158	35	.	.	PUNCT
ejpam-2714	159	1	.≤	.≤	PUNCT
ejpam-2714	160	1	vn	vn	PROPN
ejpam-2714	160	2	≤	≤	NUM
ejpam-2714	160	3	wn	wn	PROPN
ejpam-2714	160	4	≤	≤	PROPN
ejpam-2714	160	5	.	.	PUNCT
ejpam-2714	160	6	.	.	PUNCT
ejpam-2714	161	1	.≤	.≤	PUNCT
ejpam-2714	162	1	w1	w1	NOUN
ejpam-2714	162	2	≤	≤	PROPN
ejpam-2714	162	3	w0	w0	NOUN
ejpam-2714	162	4	.	.	PUNCT
ejpam-2714	163	1	further	far	ADV
ejpam-2714	163	2	,	,	PUNCT
ejpam-2714	163	3	vn	vn	PROPN
ejpam-2714	163	4	→	→	SYM
ejpam-2714	163	5	ρ	ρ	PROPN
ejpam-2714	163	6	and	and	CCONJ
ejpam-2714	163	7	wn	wn	PROPN
ejpam-2714	163	8	→	→	SYM
ejpam-2714	163	9	r	r	NOUN
ejpam-2714	163	10	in	in	ADP
ejpam-2714	163	11	c1[j	c1[j	NOUN
ejpam-2714	163	12	,	,	PUNCT
ejpam-2714	163	13	r	r	X
ejpam-2714	163	14	]	]	X
ejpam-2714	163	15	uniformly	uniformly	ADV
ejpam-2714	163	16	and	and	CCONJ
ejpam-2714	163	17	monotonically	monotonically	ADV
ejpam-2714	163	18	,	,	PUNCT
ejpam-2714	163	19	such	such	ADJ
ejpam-2714	163	20	that	that	SCONJ
ejpam-2714	163	21	ρ	ρ	NOUN
ejpam-2714	163	22	and	and	CCONJ
ejpam-2714	163	23	r	r	NOUN
ejpam-2714	163	24	are	be	AUX
ejpam-2714	163	25	respectively	respectively	ADV
ejpam-2714	163	26	the	the	DET
ejpam-2714	163	27	coupled	couple	VERB
ejpam-2714	163	28	minimal	minimal	ADJ
ejpam-2714	163	29	and	and	CCONJ
ejpam-2714	163	30	maximal	maximal	ADJ
ejpam-2714	163	31	solutions	solution	NOUN
ejpam-2714	163	32	of	of	ADP
ejpam-2714	163	33	the	the	DET
ejpam-2714	163	34	problem	problem	NOUN
ejpam-2714	163	35	defined	define	VERB
ejpam-2714	163	36	by	by	ADP
ejpam-2714	163	37	(	(	PUNCT
ejpam-2714	163	38	10	10	NUM
ejpam-2714	163	39	)	)	PUNCT
ejpam-2714	163	40	and	and	CCONJ
ejpam-2714	163	41	(	(	PUNCT
ejpam-2714	163	42	11	11	NUM
ejpam-2714	163	43	)	)	PUNCT
ejpam-2714	163	44	,	,	PUNCT
ejpam-2714	163	45	that	that	ADV
ejpam-2714	163	46	is	is	ADV
ejpam-2714	163	47	,	,	PUNCT
ejpam-2714	163	48	ρ	ρ	PROPN
ejpam-2714	163	49	and	and	CCONJ
ejpam-2714	163	50	r	r	NOUN
ejpam-2714	163	51	satisfy	satisfy	NOUN
ejpam-2714	163	52	the	the	DET
ejpam-2714	163	53	coupled	couple	VERB
ejpam-2714	163	54	system	system	NOUN
ejpam-2714	163	55	c	c	AUX
ejpam-2714	163	56	dqρ	dqρ	VERB
ejpam-2714	163	57	=	=	NOUN
ejpam-2714	163	58	f(t	f(t	NOUN
ejpam-2714	163	59	,	,	PUNCT
ejpam-2714	163	60	ρ	ρ	NOUN
ejpam-2714	163	61	,	,	PUNCT
ejpam-2714	163	62	iq(ρ	iq(ρ	NOUN
ejpam-2714	163	63	)	)	PUNCT
ejpam-2714	163	64	)	)	PUNCT
ejpam-2714	164	1	+	+	CCONJ
ejpam-2714	165	1	g(t	g(t	PROPN
ejpam-2714	165	2	,	,	PUNCT
ejpam-2714	165	3	r	r	NOUN
ejpam-2714	165	4	,	,	PUNCT
ejpam-2714	165	5	iq(r	iq(r	NOUN
ejpam-2714	165	6	)	)	PUNCT
ejpam-2714	165	7	)	)	PUNCT
ejpam-2714	165	8	,	,	PUNCT
ejpam-2714	165	9	g(ρ(0),ρ(t	g(ρ(0),ρ(t	NOUN
ejpam-2714	165	10	)	)	PUNCT
ejpam-2714	165	11	)	)	PUNCT
ejpam-2714	166	1	=	=	PUNCT
ejpam-2714	166	2	0	0	NUM
ejpam-2714	166	3	,	,	PUNCT
ejpam-2714	166	4	c	c	PROPN
ejpam-2714	166	5	dqr	dqr	PROPN
ejpam-2714	166	6	=	=	SYM
ejpam-2714	166	7	f(t	f(t	NOUN
ejpam-2714	166	8	,	,	PUNCT
ejpam-2714	166	9	r	r	NOUN
ejpam-2714	166	10	,	,	PUNCT
ejpam-2714	166	11	iq(r	iq(r	NOUN
ejpam-2714	166	12	)	)	PUNCT
ejpam-2714	166	13	)	)	PUNCT
ejpam-2714	167	1	+	+	CCONJ
ejpam-2714	167	2	g(t	g(t	PROPN
ejpam-2714	167	3	,	,	PUNCT
ejpam-2714	167	4	ρ	ρ	NOUN
ejpam-2714	167	5	,	,	PUNCT
ejpam-2714	167	6	iq(ρ	iq(ρ	NOUN
ejpam-2714	167	7	)	)	PUNCT
ejpam-2714	167	8	)	)	PUNCT
ejpam-2714	167	9	,	,	PUNCT
ejpam-2714	167	10	g(r(0	g(r(0	PROPN
ejpam-2714	167	11	)	)	PUNCT
ejpam-2714	167	12	,	,	PUNCT
ejpam-2714	167	13	r(t	r(t	NOUN
ejpam-2714	167	14	)	)	PUNCT
ejpam-2714	167	15	)	)	PUNCT
ejpam-2714	168	1	=	=	PUNCT
ejpam-2714	168	2	0	0	X
ejpam-2714	168	3	.	.	PUNCT
ejpam-2714	168	4	j.	j.	PROPN
ejpam-2714	168	5	devi	devi	PROPN
ejpam-2714	168	6	,	,	PUNCT
ejpam-2714	168	7	ch	ch	PROPN
ejpam-2714	168	8	.	.	PUNCT
ejpam-2714	168	9	sreedhar	sreedhar	PROPN
ejpam-2714	168	10	/	/	SYM
ejpam-2714	168	11	eur	eur	PROPN
ejpam-2714	168	12	.	.	PUNCT
ejpam-2714	169	1	j.	j.	PROPN
ejpam-2714	169	2	pure	pure	PROPN
ejpam-2714	169	3	appl	appl	PROPN
ejpam-2714	169	4	.	.	PROPN
ejpam-2714	169	5	math	math	PROPN
ejpam-2714	169	6	,	,	PUNCT
ejpam-2714	169	7	9	9	NUM
ejpam-2714	169	8	(	(	PUNCT
ejpam-2714	169	9	2016	2016	NUM
ejpam-2714	169	10	)	)	PUNCT
ejpam-2714	169	11	,	,	PUNCT
ejpam-2714	169	12	346	346	NUM
ejpam-2714	169	13	-	-	SYM
ejpam-2714	169	14	359	359	NUM
ejpam-2714	169	15	352	352	NUM
ejpam-2714	169	16	proof	proof	NOUN
ejpam-2714	169	17	.	.	PUNCT
ejpam-2714	170	1	putting	put	VERB
ejpam-2714	170	2	n=	n=	ADJ
ejpam-2714	170	3	0	0	PUNCT
ejpam-2714	171	1	in	in	ADP
ejpam-2714	171	2	(	(	PUNCT
ejpam-2714	171	3	21	21	NUM
ejpam-2714	171	4	)	)	PUNCT
ejpam-2714	171	5	,	,	PUNCT
ejpam-2714	171	6	(	(	PUNCT
ejpam-2714	171	7	22	22	NUM
ejpam-2714	171	8	)	)	PUNCT
ejpam-2714	171	9	,	,	PUNCT
ejpam-2714	171	10	we	we	PRON
ejpam-2714	171	11	get	get	VERB
ejpam-2714	171	12	c	c	NOUN
ejpam-2714	171	13	dqv1(t	dqv1(t	X
ejpam-2714	171	14	)	)	PUNCT
ejpam-2714	172	1	=	=	NOUN
ejpam-2714	172	2	f(t	f(t	NOUN
ejpam-2714	172	3	,	,	PUNCT
ejpam-2714	172	4	v0(t	v0(t	NOUN
ejpam-2714	172	5	)	)	PUNCT
ejpam-2714	172	6	,	,	PUNCT
ejpam-2714	172	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	172	8	)	)	PUNCT
ejpam-2714	172	9	)	)	PUNCT
ejpam-2714	172	10	)	)	PUNCT
ejpam-2714	173	1	+	+	CCONJ
ejpam-2714	173	2	g(t	g(t	PROPN
ejpam-2714	173	3	,	,	PUNCT
ejpam-2714	173	4	w0(t	w0(t	PROPN
ejpam-2714	173	5	)	)	PUNCT
ejpam-2714	173	6	,	,	PUNCT
ejpam-2714	173	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	173	8	)	)	PUNCT
ejpam-2714	173	9	)	)	PUNCT
ejpam-2714	173	10	)	)	PUNCT
ejpam-2714	173	11	,	,	PUNCT
ejpam-2714	173	12	v1(0	v1(0	NOUN
ejpam-2714	173	13	)	)	PUNCT
ejpam-2714	173	14	=	=	SYM
ejpam-2714	173	15	v0(0)−	v0(0)−	ADJ
ejpam-2714	173	16	1	1	NUM
ejpam-2714	173	17	m	m	NOUN
ejpam-2714	173	18	g(v0(0	g(v0(0	NOUN
ejpam-2714	173	19	)	)	PUNCT
ejpam-2714	173	20	,	,	PUNCT
ejpam-2714	173	21	v0(t	v0(t	PROPN
ejpam-2714	173	22	)	)	PUNCT
ejpam-2714	173	23	)	)	PUNCT
ejpam-2714	173	24	.	.	PUNCT
ejpam-2714	174	1	clearly	clearly	ADV
ejpam-2714	174	2	the	the	DET
ejpam-2714	174	3	above	above	ADJ
ejpam-2714	174	4	ivp	ivp	NOUN
ejpam-2714	174	5	has	have	VERB
ejpam-2714	174	6	a	a	DET
ejpam-2714	174	7	unique	unique	ADJ
ejpam-2714	174	8	solution	solution	NOUN
ejpam-2714	174	9	denoted	denote	VERB
ejpam-2714	174	10	by	by	ADP
ejpam-2714	174	11	v1(t	v1(t	NOUN
ejpam-2714	174	12	)	)	PUNCT
ejpam-2714	174	13	,	,	PUNCT
ejpam-2714	174	14	t	t	PROPN
ejpam-2714	174	15	∈	∈	PROPN
ejpam-2714	174	16	j	j	PROPN
ejpam-2714	174	17	.	.	PUNCT
ejpam-2714	175	1	we	we	PRON
ejpam-2714	175	2	use	use	VERB
ejpam-2714	175	3	induction	induction	NOUN
ejpam-2714	175	4	on	on	ADP
ejpam-2714	175	5	n	n	PART
ejpam-2714	175	6	to	to	PART
ejpam-2714	175	7	establish	establish	VERB
ejpam-2714	175	8	the	the	DET
ejpam-2714	175	9	relation	relation	NOUN
ejpam-2714	175	10	v0	v0	NOUN
ejpam-2714	175	11	≤	≤	NOUN
ejpam-2714	175	12	v1	v1	NOUN
ejpam-2714	175	13	≤	≤	NUM
ejpam-2714	175	14	.	.	PUNCT
ejpam-2714	175	15	.	.	PUNCT
ejpam-2714	175	16	.	.	PUNCT
ejpam-2714	176	1	≤	≤	PROPN
ejpam-2714	176	2	vn	vn	VERB
ejpam-2714	176	3	≤	≤	NUM
ejpam-2714	176	4	wn	wn	PROPN
ejpam-2714	176	5	≤	≤	PROPN
ejpam-2714	176	6	.	.	PUNCT
ejpam-2714	176	7	.	.	PUNCT
ejpam-2714	176	8	.	.	PUNCT
ejpam-2714	177	1	≤	≤	NUM
ejpam-2714	177	2	w1	w1	NOUN
ejpam-2714	177	3	≤	≤	NOUN
ejpam-2714	177	4	w0	w0	NOUN
ejpam-2714	177	5	.	.	PUNCT
ejpam-2714	178	1	we	we	PRON
ejpam-2714	178	2	start	start	VERB
ejpam-2714	178	3	by	by	ADP
ejpam-2714	178	4	showing	show	VERB
ejpam-2714	178	5	v0	v0	NOUN
ejpam-2714	178	6	≤	≤	NOUN
ejpam-2714	178	7	v1	v1	PROPN
ejpam-2714	178	8	≤	≤	NOUN
ejpam-2714	178	9	w1	w1	NOUN
ejpam-2714	178	10	≤	≤	NOUN
ejpam-2714	178	11	w0	w0	PROPN
ejpam-2714	178	12	.	.	PUNCT
ejpam-2714	179	1	for	for	ADP
ejpam-2714	179	2	this	this	DET
ejpam-2714	179	3	set	set	NOUN
ejpam-2714	179	4	p(t	p(t	NOUN
ejpam-2714	179	5	)	)	PUNCT
ejpam-2714	179	6	=	=	SYM
ejpam-2714	179	7	v0(t)−	v0(t)−	PROPN
ejpam-2714	179	8	v1(t	v1(t	NUM
ejpam-2714	179	9	)	)	PUNCT
ejpam-2714	179	10	,	,	PUNCT
ejpam-2714	179	11	then	then	ADV
ejpam-2714	179	12	c	c	PROPN
ejpam-2714	179	13	dqp(t	dqp(t	PROPN
ejpam-2714	179	14	)	)	PUNCT
ejpam-2714	180	1	=	=	PROPN
ejpam-2714	180	2	c	c	NOUN
ejpam-2714	180	3	dqv0(t)−	dqv0(t)−	PROPN
ejpam-2714	180	4	c	c	PROPN
ejpam-2714	180	5	dqv1(t	dqv1(t	X
ejpam-2714	180	6	)	)	PUNCT
ejpam-2714	180	7	,	,	PUNCT
ejpam-2714	180	8	≤f(t	≤f(t	NOUN
ejpam-2714	180	9	,	,	PUNCT
ejpam-2714	180	10	v0(t	v0(t	PROPN
ejpam-2714	180	11	)	)	PUNCT
ejpam-2714	180	12	,	,	PUNCT
ejpam-2714	180	13	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	180	14	)	)	PUNCT
ejpam-2714	180	15	)	)	PUNCT
ejpam-2714	180	16	)	)	PUNCT
ejpam-2714	181	1	+	+	CCONJ
ejpam-2714	181	2	g(t	g(t	PROPN
ejpam-2714	181	3	,	,	PUNCT
ejpam-2714	181	4	w0(t	w0(t	PROPN
ejpam-2714	181	5	)	)	PUNCT
ejpam-2714	181	6	,	,	PUNCT
ejpam-2714	181	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	181	8	)	)	PUNCT
ejpam-2714	181	9	)	)	PUNCT
ejpam-2714	181	10	)	)	PUNCT
ejpam-2714	182	1	−	−	PUNCT
ejpam-2714	183	1	[	[	X
ejpam-2714	183	2	f(t	f(t	PROPN
ejpam-2714	183	3	,	,	PUNCT
ejpam-2714	183	4	v0(t	v0(t	PROPN
ejpam-2714	183	5	)	)	PUNCT
ejpam-2714	183	6	,	,	PUNCT
ejpam-2714	183	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	183	8	)	)	PUNCT
ejpam-2714	183	9	)	)	PUNCT
ejpam-2714	183	10	)	)	PUNCT
ejpam-2714	184	1	+	+	CCONJ
ejpam-2714	184	2	g(t	g(t	PROPN
ejpam-2714	184	3	,	,	PUNCT
ejpam-2714	184	4	w0(t	w0(t	PROPN
ejpam-2714	184	5	)	)	PUNCT
ejpam-2714	184	6	,	,	PUNCT
ejpam-2714	184	7	iq)(w0(t	iq)(w0(t	PROPN
ejpam-2714	184	8	)	)	PUNCT
ejpam-2714	184	9	)	)	PUNCT
ejpam-2714	184	10	)	)	PUNCT
ejpam-2714	184	11	]	]	PUNCT
ejpam-2714	184	12	=	=	SYM
ejpam-2714	184	13	0	0	NUM
ejpam-2714	184	14	and	and	CCONJ
ejpam-2714	184	15	p(0	p(0	PROPN
ejpam-2714	184	16	)	)	PUNCT
ejpam-2714	184	17	=	=	PUNCT
ejpam-2714	184	18	v0(0)−v0(0)+	v0(0)−v0(0)+	PROPN
ejpam-2714	184	19	1	1	NUM
ejpam-2714	184	20	m	m	NOUN
ejpam-2714	184	21	g(v0(0	g(v0(0	NOUN
ejpam-2714	184	22	)	)	PUNCT
ejpam-2714	184	23	,	,	PUNCT
ejpam-2714	184	24	v0(t	v0(t	PROPN
ejpam-2714	184	25	)	)	PUNCT
ejpam-2714	184	26	)	)	PUNCT
ejpam-2714	184	27	≤	≤	NOUN
ejpam-2714	184	28	0	0	NUM
ejpam-2714	184	29	.	.	PUNCT
ejpam-2714	185	1	thus	thus	ADV
ejpam-2714	185	2	the	the	DET
ejpam-2714	185	3	hypothesis	hypothesis	NOUN
ejpam-2714	185	4	of	of	ADP
ejpam-2714	185	5	corollary	corollary	ADJ
ejpam-2714	185	6	2	2	NUM
ejpam-2714	185	7	is	be	AUX
ejpam-2714	185	8	satisfied	satisfied	ADJ
ejpam-2714	185	9	and	and	CCONJ
ejpam-2714	185	10	we	we	PRON
ejpam-2714	185	11	conclude	conclude	VERB
ejpam-2714	185	12	that	that	SCONJ
ejpam-2714	185	13	p(t	p(t	NOUN
ejpam-2714	185	14	)	)	PUNCT
ejpam-2714	185	15	≤	≤	NOUN
ejpam-2714	185	16	0	0	NUM
ejpam-2714	186	1	on	on	ADP
ejpam-2714	186	2	j	j	PROPN
ejpam-2714	186	3	,	,	PUNCT
ejpam-2714	186	4	and	and	CCONJ
ejpam-2714	186	5	obtain	obtain	VERB
ejpam-2714	186	6	.	.	PUNCT
ejpam-2714	187	1	similarly	similarly	ADV
ejpam-2714	187	2	we	we	PRON
ejpam-2714	187	3	can	can	AUX
ejpam-2714	187	4	show	show	VERB
ejpam-2714	187	5	that	that	SCONJ
ejpam-2714	187	6	w1	w1	NOUN
ejpam-2714	187	7	≤	≤	NOUN
ejpam-2714	187	8	w0	w0	PROPN
ejpam-2714	187	9	on	on	ADP
ejpam-2714	187	10	j	j	PROPN
ejpam-2714	187	11	.	.	PUNCT
ejpam-2714	188	1	next	next	ADV
ejpam-2714	188	2	we	we	PRON
ejpam-2714	188	3	consider	consider	VERB
ejpam-2714	188	4	p(t	p(t	NOUN
ejpam-2714	188	5	)	)	PUNCT
ejpam-2714	188	6	=	=	PUNCT
ejpam-2714	189	1	v1(t	v1(t	PROPN
ejpam-2714	189	2	)	)	PUNCT
ejpam-2714	189	3	−	−	PROPN
ejpam-2714	190	1	w1(t	w1(t	PROPN
ejpam-2714	190	2	)	)	PUNCT
ejpam-2714	190	3	,	,	PUNCT
ejpam-2714	190	4	then	then	ADV
ejpam-2714	190	5	by	by	ADP
ejpam-2714	190	6	adding	add	VERB
ejpam-2714	190	7	and	and	CCONJ
ejpam-2714	190	8	subtracting	subtract	VERB
ejpam-2714	190	9	suitable	suitable	ADJ
ejpam-2714	190	10	terms	term	NOUN
ejpam-2714	190	11	,	,	PUNCT
ejpam-2714	190	12	and	and	CCONJ
ejpam-2714	190	13	using	use	VERB
ejpam-2714	190	14	the	the	DET
ejpam-2714	190	15	fact	fact	NOUN
ejpam-2714	190	16	that	that	SCONJ
ejpam-2714	190	17	f	f	PROPN
ejpam-2714	190	18	is	be	AUX
ejpam-2714	190	19	nondecreasing	nondecrease	VERB
ejpam-2714	190	20	in	in	ADP
ejpam-2714	190	21	second	second	ADJ
ejpam-2714	190	22	and	and	CCONJ
ejpam-2714	190	23	third	third	ADJ
ejpam-2714	190	24	variables	variable	NOUN
ejpam-2714	190	25	,	,	PUNCT
ejpam-2714	190	26	g	g	PROPN
ejpam-2714	190	27	is	be	AUX
ejpam-2714	190	28	nonincreasing	nonincrease	VERB
ejpam-2714	190	29	in	in	ADP
ejpam-2714	190	30	second	second	ADJ
ejpam-2714	190	31	and	and	CCONJ
ejpam-2714	190	32	third	third	ADJ
ejpam-2714	190	33	variables	variable	NOUN
ejpam-2714	190	34	,	,	PUNCT
ejpam-2714	190	35	and	and	CCONJ
ejpam-2714	190	36	by	by	ADP
ejpam-2714	190	37	taking	take	VERB
ejpam-2714	190	38	caputo	caputo	PROPN
ejpam-2714	190	39	fractional	fractional	PROPN
ejpam-2714	190	40	derivative	derivative	NOUN
ejpam-2714	190	41	we	we	PRON
ejpam-2714	190	42	arrive	arrive	VERB
ejpam-2714	190	43	at	at	ADP
ejpam-2714	190	44	,	,	PUNCT
ejpam-2714	190	45	c	c	PROPN
ejpam-2714	190	46	dqp(t	dqp(t	PROPN
ejpam-2714	190	47	)	)	PUNCT
ejpam-2714	191	1	=	=	PROPN
ejpam-2714	191	2	c	c	PROPN
ejpam-2714	191	3	dqv1(t)−	dqv1(t)−	PROPN
ejpam-2714	191	4	c	c	PROPN
ejpam-2714	191	5	dqw1(t	dqw1(t	PRON
ejpam-2714	191	6	)	)	PUNCT
ejpam-2714	191	7	,	,	PUNCT
ejpam-2714	191	8	=	=	SYM
ejpam-2714	191	9	f(t	f(t	NOUN
ejpam-2714	191	10	,	,	PUNCT
ejpam-2714	191	11	v0(t	v0(t	NOUN
ejpam-2714	191	12	)	)	PUNCT
ejpam-2714	191	13	,	,	PUNCT
ejpam-2714	191	14	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	191	15	)	)	PUNCT
ejpam-2714	191	16	)	)	PUNCT
ejpam-2714	191	17	)	)	PUNCT
ejpam-2714	192	1	+	+	CCONJ
ejpam-2714	192	2	g(t	g(t	PROPN
ejpam-2714	192	3	,	,	PUNCT
ejpam-2714	192	4	w0(t	w0(t	PROPN
ejpam-2714	192	5	)	)	PUNCT
ejpam-2714	192	6	,	,	PUNCT
ejpam-2714	192	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	192	8	)	)	PUNCT
ejpam-2714	192	9	)	)	PUNCT
ejpam-2714	192	10	)	)	PUNCT
ejpam-2714	193	1	−	−	PUNCT
ejpam-2714	194	1	[	[	X
ejpam-2714	194	2	f(t	f(t	PROPN
ejpam-2714	194	3	,	,	PUNCT
ejpam-2714	194	4	w0(t	w0(t	PROPN
ejpam-2714	194	5	)	)	PUNCT
ejpam-2714	194	6	,	,	PUNCT
ejpam-2714	194	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	194	8	)	)	PUNCT
ejpam-2714	194	9	)	)	PUNCT
ejpam-2714	194	10	)	)	PUNCT
ejpam-2714	195	1	+	+	CCONJ
ejpam-2714	195	2	g(t	g(t	PROPN
ejpam-2714	195	3	,	,	PUNCT
ejpam-2714	195	4	v0(t	v0(t	PROPN
ejpam-2714	195	5	)	)	PUNCT
ejpam-2714	195	6	,	,	PUNCT
ejpam-2714	195	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	195	8	)	)	PUNCT
ejpam-2714	195	9	)	)	PUNCT
ejpam-2714	195	10	)	)	PUNCT
ejpam-2714	195	11	]	]	PUNCT
ejpam-2714	196	1	≤0	≤0	PROPN
ejpam-2714	196	2	,	,	PUNCT
ejpam-2714	196	3	and	and	CCONJ
ejpam-2714	196	4	p(0	p(0	NOUN
ejpam-2714	196	5	)	)	PUNCT
ejpam-2714	197	1	=	=	NOUN
ejpam-2714	197	2	v0(0)−w0(0)−	v0(0)−w0(0)−	NOUN
ejpam-2714	197	3	1	1	NUM
ejpam-2714	197	4	m	m	PROPN
ejpam-2714	197	5	[	[	X
ejpam-2714	197	6	g(v0(0	g(v0(0	NOUN
ejpam-2714	197	7	)	)	PUNCT
ejpam-2714	197	8	,	,	PUNCT
ejpam-2714	197	9	v0(t	v0(t	PROPN
ejpam-2714	197	10	)	)	PUNCT
ejpam-2714	197	11	)	)	PUNCT
ejpam-2714	197	12	−	−	PROPN
ejpam-2714	197	13	g(w0(0	g(w0(0	PROPN
ejpam-2714	197	14	)	)	PUNCT
ejpam-2714	197	15	,	,	PUNCT
ejpam-2714	197	16	w0(t	w0(t	PROPN
ejpam-2714	197	17	)	)	PUNCT
ejpam-2714	197	18	)	)	PUNCT
ejpam-2714	198	1	≤v0(0)−w0(0)−	≤v0(0)−w0(0)−	NOUN
ejpam-2714	199	1	[	[	X
ejpam-2714	199	2	v0(0)−w0(0	v0(0)−w0(0	NOUN
ejpam-2714	199	3	)	)	PUNCT
ejpam-2714	199	4	]	]	PUNCT
ejpam-2714	200	1	=	=	PUNCT
ejpam-2714	200	2	0	0	X
ejpam-2714	200	3	.	.	PUNCT
ejpam-2714	200	4	hence	hence	ADV
ejpam-2714	200	5	by	by	ADP
ejpam-2714	200	6	corollary	corollary	ADJ
ejpam-2714	200	7	2	2	NUM
ejpam-2714	200	8	we	we	PRON
ejpam-2714	200	9	have	have	VERB
ejpam-2714	200	10	p(t	p(t	NOUN
ejpam-2714	200	11	)	)	PUNCT
ejpam-2714	200	12	≤	≤	NOUN
ejpam-2714	200	13	0	0	NUM
ejpam-2714	201	1	on	on	ADP
ejpam-2714	201	2	j	j	PROPN
ejpam-2714	201	3	that	that	ADV
ejpam-2714	201	4	is	be	AUX
ejpam-2714	201	5	,	,	PUNCT
ejpam-2714	201	6	v1(t	v1(t	CCONJ
ejpam-2714	201	7	)	)	PUNCT
ejpam-2714	201	8	≤	≤	NOUN
ejpam-2714	201	9	w1(t	w1(t	PROPN
ejpam-2714	201	10	)	)	PUNCT
ejpam-2714	201	11	,	,	PUNCT
ejpam-2714	201	12	on	on	ADP
ejpam-2714	201	13	j	j	PROPN
ejpam-2714	201	14	.	.	PUNCT
ejpam-2714	202	1	thus	thus	ADV
ejpam-2714	202	2	the	the	DET
ejpam-2714	202	3	claim	claim	NOUN
ejpam-2714	202	4	v0	v0	NOUN
ejpam-2714	202	5	≤	≤	NUM
ejpam-2714	202	6	v1	v1	PROPN
ejpam-2714	202	7	≤	≤	NOUN
ejpam-2714	202	8	w1	w1	NOUN
ejpam-2714	202	9	≤	≤	NOUN
ejpam-2714	202	10	w0	w0	PROPN
ejpam-2714	202	11	on	on	ADP
ejpam-2714	202	12	j	j	PROPN
ejpam-2714	202	13	is	be	AUX
ejpam-2714	202	14	proved	prove	VERB
ejpam-2714	202	15	.	.	PUNCT
ejpam-2714	203	1	we	we	PRON
ejpam-2714	203	2	now	now	ADV
ejpam-2714	203	3	show	show	VERB
ejpam-2714	203	4	that	that	SCONJ
ejpam-2714	203	5	v1	v1	NOUN
ejpam-2714	203	6	,	,	PUNCT
ejpam-2714	203	7	w1	w1	NOUN
ejpam-2714	203	8	are	be	AUX
ejpam-2714	203	9	the	the	DET
ejpam-2714	203	10	coupled	couple	VERB
ejpam-2714	203	11	lower	low	ADJ
ejpam-2714	203	12	and	and	CCONJ
ejpam-2714	203	13	upper	upper	ADJ
ejpam-2714	203	14	solutions	solution	NOUN
ejpam-2714	203	15	of	of	ADP
ejpam-2714	203	16	type	type	NOUN
ejpam-2714	203	17	i	i	PRON
ejpam-2714	203	18	for	for	ADP
ejpam-2714	203	19	(	(	PUNCT
ejpam-2714	203	20	10	10	NUM
ejpam-2714	203	21	)	)	PUNCT
ejpam-2714	203	22	,	,	PUNCT
ejpam-2714	203	23	(	(	PUNCT
ejpam-2714	203	24	11	11	NUM
ejpam-2714	203	25	)	)	PUNCT
ejpam-2714	203	26	,	,	PUNCT
ejpam-2714	203	27	using	use	VERB
ejpam-2714	203	28	the	the	DET
ejpam-2714	203	29	fact	fact	NOUN
ejpam-2714	203	30	that	that	SCONJ
ejpam-2714	203	31	v0	v0	NOUN
ejpam-2714	203	32	≤	≤	NUM
ejpam-2714	203	33	v1	v1	NOUN
ejpam-2714	203	34	,	,	PUNCT
ejpam-2714	203	35	w1	w1	NOUN
ejpam-2714	203	36	≤	≤	NOUN
ejpam-2714	203	37	w0	w0	PROPN
ejpam-2714	203	38	and	and	CCONJ
ejpam-2714	203	39	from	from	ADP
ejpam-2714	203	40	the	the	DET
ejpam-2714	203	41	assumption	assumption	NOUN
ejpam-2714	203	42	(	(	PUNCT
ejpam-2714	203	43	a3	a3	NOUN
ejpam-2714	203	44	)	)	PUNCT
ejpam-2714	203	45	,	,	PUNCT
ejpam-2714	203	46	proceeding	proceed	VERB
ejpam-2714	203	47	as	as	ADP
ejpam-2714	203	48	earlier	early	ADV
ejpam-2714	203	49	we	we	PRON
ejpam-2714	203	50	obtain	obtain	VERB
ejpam-2714	203	51	c	c	PROPN
ejpam-2714	203	52	dqv1(t)≤	dqv1(t)≤	NOUN
ejpam-2714	203	53	0	0	NUM
ejpam-2714	203	54	.	.	PUNCT
ejpam-2714	204	1	also	also	ADV
ejpam-2714	204	2	,	,	PUNCT
ejpam-2714	204	3	g(v1(0	g(v1(0	PROPN
ejpam-2714	204	4	)	)	PUNCT
ejpam-2714	204	5	,	,	PUNCT
ejpam-2714	204	6	v1(t	v1(t	CCONJ
ejpam-2714	204	7	)	)	PUNCT
ejpam-2714	204	8	)	)	PUNCT
ejpam-2714	205	1	=	=	NOUN
ejpam-2714	205	2	g(v1(0	g(v1(0	NOUN
ejpam-2714	205	3	)	)	PUNCT
ejpam-2714	205	4	,	,	PUNCT
ejpam-2714	205	5	v1(t	v1(t	CCONJ
ejpam-2714	205	6	)	)	PUNCT
ejpam-2714	205	7	)	)	PUNCT
ejpam-2714	205	8	−	−	PROPN
ejpam-2714	205	9	g(v0(0	g(v0(0	NOUN
ejpam-2714	205	10	)	)	PUNCT
ejpam-2714	205	11	,	,	PUNCT
ejpam-2714	205	12	v0(t	v0(t	PROPN
ejpam-2714	205	13	)	)	PUNCT
ejpam-2714	205	14	)	)	PUNCT
ejpam-2714	205	15	−m	−m	ADJ
ejpam-2714	205	16	v1(0	v1(0	PROPN
ejpam-2714	205	17	)	)	PUNCT
ejpam-2714	206	1	+	+	NOUN
ejpam-2714	206	2	m	m	PROPN
ejpam-2714	206	3	v0(0	v0(0	NOUN
ejpam-2714	206	4	)	)	PUNCT
ejpam-2714	206	5	≤m(v1(0)−	≤m(v1(0)−	PROPN
ejpam-2714	206	6	v0(0))−m(v1(0)−	v0(0))−m(v1(0)−	PROPN
ejpam-2714	206	7	v0(0	v0(0	PROPN
ejpam-2714	206	8	)	)	PUNCT
ejpam-2714	206	9	)	)	PUNCT
ejpam-2714	207	1	=	=	PUNCT
ejpam-2714	207	2	0	0	X
ejpam-2714	207	3	.	.	PUNCT
ejpam-2714	208	1	similarly	similarly	ADV
ejpam-2714	208	2	we	we	PRON
ejpam-2714	208	3	can	can	AUX
ejpam-2714	208	4	show	show	VERB
ejpam-2714	208	5	that	that	SCONJ
ejpam-2714	208	6	w1	w1	NOUN
ejpam-2714	208	7	satisfies	satisfie	NOUN
ejpam-2714	208	8	reverse	reverse	VERB
ejpam-2714	208	9	inequalities	inequality	NOUN
ejpam-2714	208	10	.	.	PUNCT
ejpam-2714	209	1	hence	hence	ADV
ejpam-2714	209	2	v1	v1	PROPN
ejpam-2714	209	3	,	,	PUNCT
ejpam-2714	209	4	w1	w1	NOUN
ejpam-2714	209	5	are	be	AUX
ejpam-2714	209	6	coupled	couple	VERB
ejpam-2714	209	7	lower	low	ADJ
ejpam-2714	209	8	and	and	CCONJ
ejpam-2714	209	9	upper	upper	ADJ
ejpam-2714	209	10	solutions	solution	NOUN
ejpam-2714	209	11	of	of	ADP
ejpam-2714	209	12	(	(	PUNCT
ejpam-2714	209	13	10	10	NUM
ejpam-2714	209	14	)	)	PUNCT
ejpam-2714	209	15	,	,	PUNCT
ejpam-2714	209	16	(	(	PUNCT
ejpam-2714	209	17	11	11	NUM
ejpam-2714	209	18	)	)	PUNCT
ejpam-2714	209	19	.	.	PUNCT
ejpam-2714	210	1	assume	assume	VERB
ejpam-2714	210	2	that	that	SCONJ
ejpam-2714	210	3	vk−1	vk−1	VERB
ejpam-2714	210	4	≤	≤	NUM
ejpam-2714	210	5	vk	vk	ADP
ejpam-2714	210	6	≤	≤	NUM
ejpam-2714	210	7	wk	wk	NOUN
ejpam-2714	210	8	≤	≤	NUM
ejpam-2714	210	9	wk−1	wk−1	PROPN
ejpam-2714	210	10	on	on	ADP
ejpam-2714	210	11	j	j	PROPN
ejpam-2714	210	12	for	for	ADP
ejpam-2714	210	13	k	k	PROPN
ejpam-2714	210	14	>	>	X
ejpam-2714	210	15	1	1	NUM
ejpam-2714	210	16	,	,	PUNCT
ejpam-2714	210	17	where	where	SCONJ
ejpam-2714	210	18	vk−1	vk−1	NOUN
ejpam-2714	210	19	,	,	PUNCT
ejpam-2714	210	20	vk	vk	NOUN
ejpam-2714	210	21	are	be	AUX
ejpam-2714	210	22	the	the	DET
ejpam-2714	210	23	solutions	solution	NOUN
ejpam-2714	210	24	of	of	ADP
ejpam-2714	210	25	the	the	DET
ejpam-2714	210	26	ivp	ivp	NOUN
ejpam-2714	210	27	(	(	PUNCT
ejpam-2714	210	28	21	21	NUM
ejpam-2714	210	29	)	)	PUNCT
ejpam-2714	210	30	,	,	PUNCT
ejpam-2714	210	31	(	(	PUNCT
ejpam-2714	210	32	22	22	NUM
ejpam-2714	210	33	)	)	PUNCT
ejpam-2714	210	34	and	and	CCONJ
ejpam-2714	210	35	wk−1	wk−1	PROPN
ejpam-2714	210	36	,	,	PUNCT
ejpam-2714	210	37	wk	wk	X
ejpam-2714	210	38	are	be	AUX
ejpam-2714	210	39	the	the	DET
ejpam-2714	210	40	solutions	solution	NOUN
ejpam-2714	210	41	of	of	ADP
ejpam-2714	210	42	the	the	DET
ejpam-2714	210	43	ivp	ivp	NOUN
ejpam-2714	210	44	(	(	PUNCT
ejpam-2714	210	45	23	23	NUM
ejpam-2714	210	46	)	)	PUNCT
ejpam-2714	210	47	,	,	PUNCT
ejpam-2714	210	48	(	(	PUNCT
ejpam-2714	210	49	24	24	NUM
ejpam-2714	210	50	)	)	PUNCT
ejpam-2714	210	51	for	for	ADP
ejpam-2714	210	52	n	n	NOUN
ejpam-2714	210	53	=	=	SYM
ejpam-2714	210	54	k	k	NOUN
ejpam-2714	211	1	−	−	PROPN
ejpam-2714	211	2	1	1	NUM
ejpam-2714	211	3	,	,	PUNCT
ejpam-2714	211	4	n	n	PROPN
ejpam-2714	211	5	=	=	SYM
ejpam-2714	211	6	k	k	NOUN
ejpam-2714	211	7	respectively	respectively	ADV
ejpam-2714	211	8	.	.	PUNCT
ejpam-2714	212	1	we	we	PRON
ejpam-2714	212	2	claim	claim	VERB
ejpam-2714	212	3	that	that	SCONJ
ejpam-2714	212	4	the	the	DET
ejpam-2714	212	5	following	follow	VERB
ejpam-2714	212	6	relation	relation	NOUN
ejpam-2714	212	7	holds	hold	VERB
ejpam-2714	212	8	.	.	PUNCT
ejpam-2714	213	1	vk	vk	NOUN
ejpam-2714	213	2	≤	≤	NUM
ejpam-2714	213	3	vk+1	vk+1	VERB
ejpam-2714	213	4	≤	≤	NUM
ejpam-2714	213	5	wk+1	wk+1	NOUN
ejpam-2714	213	6	≤	≤	NUM
ejpam-2714	213	7	wk	wk	ADP
ejpam-2714	213	8	j.	j.	PROPN
ejpam-2714	213	9	devi	devi	PROPN
ejpam-2714	213	10	,	,	PUNCT
ejpam-2714	213	11	ch	ch	PROPN
ejpam-2714	213	12	.	.	PUNCT
ejpam-2714	213	13	sreedhar	sreedhar	PROPN
ejpam-2714	213	14	/	/	SYM
ejpam-2714	213	15	eur	eur	PROPN
ejpam-2714	213	16	.	.	PUNCT
ejpam-2714	214	1	j.	j.	PROPN
ejpam-2714	214	2	pure	pure	PROPN
ejpam-2714	214	3	appl	appl	PROPN
ejpam-2714	214	4	.	.	PROPN
ejpam-2714	214	5	math	math	PROPN
ejpam-2714	214	6	,	,	PUNCT
ejpam-2714	214	7	9	9	NUM
ejpam-2714	214	8	(	(	PUNCT
ejpam-2714	214	9	2016	2016	NUM
ejpam-2714	214	10	)	)	PUNCT
ejpam-2714	214	11	,	,	PUNCT
ejpam-2714	214	12	346	346	NUM
ejpam-2714	214	13	-	-	SYM
ejpam-2714	214	14	359	359	NUM
ejpam-2714	214	15	353	353	NUM
ejpam-2714	214	16	on	on	ADP
ejpam-2714	214	17	j	j	PROPN
ejpam-2714	214	18	.	.	PUNCT
ejpam-2714	215	1	to	to	PART
ejpam-2714	215	2	prove	prove	VERB
ejpam-2714	215	3	this	this	PRON
ejpam-2714	215	4	we	we	PRON
ejpam-2714	215	5	take	take	VERB
ejpam-2714	215	6	p(t	p(t	NOUN
ejpam-2714	215	7	)	)	PUNCT
ejpam-2714	216	1	=	=	SYM
ejpam-2714	216	2	vk(t	vk(t	NOUN
ejpam-2714	216	3	)	)	PUNCT
ejpam-2714	216	4	−	−	PROPN
ejpam-2714	216	5	vk+1(t	vk+1(t	PROPN
ejpam-2714	216	6	)	)	PUNCT
ejpam-2714	216	7	,	,	PUNCT
ejpam-2714	216	8	then	then	ADV
ejpam-2714	216	9	by	by	ADP
ejpam-2714	216	10	adding	add	VERB
ejpam-2714	216	11	and	and	CCONJ
ejpam-2714	216	12	subtracting	subtract	VERB
ejpam-2714	216	13	suitable	suitable	ADJ
ejpam-2714	216	14	terms	term	NOUN
ejpam-2714	216	15	and	and	CCONJ
ejpam-2714	216	16	working	work	VERB
ejpam-2714	216	17	as	as	ADP
ejpam-2714	216	18	earlier	early	ADV
ejpam-2714	216	19	we	we	PRON
ejpam-2714	216	20	arrive	arrive	VERB
ejpam-2714	216	21	at	at	ADP
ejpam-2714	216	22	,	,	PUNCT
ejpam-2714	216	23	c	c	PROPN
ejpam-2714	216	24	dqp(t	dqp(t	PROPN
ejpam-2714	216	25	)	)	PUNCT
ejpam-2714	217	1	=	=	PROPN
ejpam-2714	217	2	c	c	PROPN
ejpam-2714	217	3	dqvk(t)−	dqvk(t)−	PROPN
ejpam-2714	217	4	c	c	PROPN
ejpam-2714	217	5	dqvk+1(t	dqvk+1(t	PROPN
ejpam-2714	217	6	)	)	PUNCT
ejpam-2714	217	7	≤[f(t	≤[f(t	NOUN
ejpam-2714	217	8	,	,	PUNCT
ejpam-2714	217	9	vk−1(t	vk−1(t	ADJ
ejpam-2714	217	10	)	)	PUNCT
ejpam-2714	217	11	,	,	PUNCT
ejpam-2714	217	12	iq(vk−1(t	iq(vk−1(t	NUM
ejpam-2714	217	13	)	)	PUNCT
ejpam-2714	217	14	)	)	PUNCT
ejpam-2714	217	15	)	)	PUNCT
ejpam-2714	218	1	+	+	CCONJ
ejpam-2714	218	2	g(t	g(t	PROPN
ejpam-2714	218	3	,	,	PUNCT
ejpam-2714	218	4	wk−1(t	wk−1(t	PROPN
ejpam-2714	218	5	)	)	PUNCT
ejpam-2714	218	6	,	,	PUNCT
ejpam-2714	218	7	iq(wk−1)(t	iq(wk−1)(t	NOUN
ejpam-2714	218	8	)	)	PUNCT
ejpam-2714	218	9	)	)	PUNCT
ejpam-2714	218	10	]	]	PUNCT
ejpam-2714	219	1	−	−	PUNCT
ejpam-2714	220	1	[	[	X
ejpam-2714	220	2	f(t	f(t	NOUN
ejpam-2714	220	3	,	,	PUNCT
ejpam-2714	220	4	vk(t	vk(t	NOUN
ejpam-2714	220	5	)	)	PUNCT
ejpam-2714	220	6	,	,	PUNCT
ejpam-2714	220	7	iq(vk(t	iq(vk(t	ADJ
ejpam-2714	220	8	)	)	PUNCT
ejpam-2714	220	9	)	)	PUNCT
ejpam-2714	220	10	)	)	PUNCT
ejpam-2714	221	1	+	+	CCONJ
ejpam-2714	221	2	g(t	g(t	PROPN
ejpam-2714	221	3	,	,	PUNCT
ejpam-2714	221	4	wk(t	wk(t	NUM
ejpam-2714	221	5	)	)	PUNCT
ejpam-2714	221	6	,	,	PUNCT
ejpam-2714	221	7	iq(wk(t)))]≤	iq(wk(t)))]≤	NOUN
ejpam-2714	221	8	0	0	NUM
ejpam-2714	221	9	.	.	PUNCT
ejpam-2714	222	1	further	far	ADV
ejpam-2714	222	2	,	,	PUNCT
ejpam-2714	222	3	p(0	p(0	NOUN
ejpam-2714	222	4	)	)	PUNCT
ejpam-2714	222	5	=	=	PUNCT
ejpam-2714	222	6	vk(0	vk(0	PROPN
ejpam-2714	222	7	)	)	PUNCT
ejpam-2714	222	8	−	−	NOUN
ejpam-2714	222	9	vk+1(0	vk+1(0	PUNCT
ejpam-2714	222	10	)	)	PUNCT
ejpam-2714	222	11	=	=	PUNCT
ejpam-2714	223	1	vk(0	vk(0	PROPN
ejpam-2714	223	2	)	)	PUNCT
ejpam-2714	223	3	−	−	PROPN
ejpam-2714	224	1	vk(0	vk(0	NOUN
ejpam-2714	224	2	)	)	PUNCT
ejpam-2714	224	3	+	+	CCONJ
ejpam-2714	224	4	1	1	NUM
ejpam-2714	224	5	m	m	NOUN
ejpam-2714	224	6	g(vk(0	g(vk(0	PROPN
ejpam-2714	224	7	)	)	PUNCT
ejpam-2714	224	8	,	,	PUNCT
ejpam-2714	224	9	vk(t	vk(t	X
ejpam-2714	224	10	)	)	PUNCT
ejpam-2714	224	11	)	)	PUNCT
ejpam-2714	225	1	≤	≤	ADV
ejpam-2714	225	2	0	0	X
ejpam-2714	225	3	.	.	PUNCT
ejpam-2714	226	1	an	an	DET
ejpam-2714	226	2	application	application	NOUN
ejpam-2714	226	3	of	of	ADP
ejpam-2714	226	4	corollary	corollary	ADJ
ejpam-2714	226	5	2	2	NUM
ejpam-2714	226	6	yields	yield	NOUN
ejpam-2714	226	7	that	that	PRON
ejpam-2714	226	8	p(t	p(t	VERB
ejpam-2714	226	9	)	)	PUNCT
ejpam-2714	226	10	≤	≤	NOUN
ejpam-2714	226	11	0	0	NUM
ejpam-2714	226	12	and	and	CCONJ
ejpam-2714	226	13	consequently	consequently	ADV
ejpam-2714	226	14	,	,	PUNCT
ejpam-2714	226	15	vk(t	vk(t	NOUN
ejpam-2714	226	16	)	)	PUNCT
ejpam-2714	226	17	≤	≤	NOUN
ejpam-2714	226	18	vk+1(t	vk+1(t	PROPN
ejpam-2714	226	19	)	)	PUNCT
ejpam-2714	226	20	,	,	PUNCT
ejpam-2714	226	21	on	on	ADP
ejpam-2714	226	22	j	j	PROPN
ejpam-2714	226	23	.	.	PUNCT
ejpam-2714	227	1	in	in	ADP
ejpam-2714	227	2	a	a	DET
ejpam-2714	227	3	similar	similar	ADJ
ejpam-2714	227	4	manner	manner	NOUN
ejpam-2714	227	5	we	we	PRON
ejpam-2714	227	6	can	can	AUX
ejpam-2714	227	7	prove	prove	VERB
ejpam-2714	227	8	that	that	DET
ejpam-2714	227	9	wk+1(t)≤	wk+1(t)≤	PROPN
ejpam-2714	227	10	wk(t	wk(t	NOUN
ejpam-2714	227	11	)	)	PUNCT
ejpam-2714	227	12	.	.	PUNCT
ejpam-2714	228	1	next	next	ADJ
ejpam-2714	228	2	to	to	PART
ejpam-2714	228	3	prove	prove	VERB
ejpam-2714	228	4	vk+1(t	vk+1(t	PROPN
ejpam-2714	228	5	)	)	PUNCT
ejpam-2714	228	6	≤	≤	NOUN
ejpam-2714	228	7	wk+1(t	wk+1(t	PROPN
ejpam-2714	228	8	)	)	PUNCT
ejpam-2714	228	9	,	,	PUNCT
ejpam-2714	228	10	on	on	ADP
ejpam-2714	228	11	j	j	PROPN
ejpam-2714	228	12	,	,	PUNCT
ejpam-2714	228	13	consider	consider	VERB
ejpam-2714	228	14	p(t	p(t	NOUN
ejpam-2714	228	15	)	)	PUNCT
ejpam-2714	228	16	=	=	PUNCT
ejpam-2714	229	1	vk+1(t)−	vk+1(t)−	VERB
ejpam-2714	229	2	wk+1(t	wk+1(t	PRON
ejpam-2714	229	3	)	)	PUNCT
ejpam-2714	229	4	and	and	CCONJ
ejpam-2714	229	5	again	again	ADV
ejpam-2714	229	6	following	follow	VERB
ejpam-2714	229	7	the	the	DET
ejpam-2714	229	8	earlier	early	ADJ
ejpam-2714	229	9	approach	approach	NOUN
ejpam-2714	229	10	we	we	PRON
ejpam-2714	229	11	deduce	deduce	VERB
ejpam-2714	229	12	that	that	SCONJ
ejpam-2714	229	13	c	c	PROPN
ejpam-2714	229	14	dqp(t	dqp(t	PROPN
ejpam-2714	229	15	)	)	PUNCT
ejpam-2714	230	1	=	=	NOUN
ejpam-2714	230	2	c	c	X
ejpam-2714	230	3	dqvk+1(t)−	dqvk+1(t)−	PROPN
ejpam-2714	230	4	c	c	PROPN
ejpam-2714	230	5	dqwk+1(t)≤	dqwk+1(t)≤	PROPN
ejpam-2714	230	6	0	0	PROPN
ejpam-2714	230	7	and	and	CCONJ
ejpam-2714	230	8	p(0	p(0	PROPN
ejpam-2714	230	9	)	)	PUNCT
ejpam-2714	230	10	=	=	NOUN
ejpam-2714	230	11	vk+1(0)−wk+1(0	vk+1(0)−wk+1(0	NOUN
ejpam-2714	230	12	)	)	PUNCT
ejpam-2714	231	1	=	=	SYM
ejpam-2714	231	2	vk(0)−	vk(0)−	NOUN
ejpam-2714	231	3	1	1	NUM
ejpam-2714	231	4	m	m	NOUN
ejpam-2714	231	5	g(vk(0	g(vk(0	PROPN
ejpam-2714	231	6	)	)	PUNCT
ejpam-2714	231	7	,	,	PUNCT
ejpam-2714	231	8	vk(t	vk(t	X
ejpam-2714	231	9	)	)	PUNCT
ejpam-2714	231	10	)	)	PUNCT
ejpam-2714	232	1	−wk(0	−wk(0	NOUN
ejpam-2714	232	2	)	)	PUNCT
ejpam-2714	232	3	+	+	CCONJ
ejpam-2714	232	4	1	1	NUM
ejpam-2714	232	5	m	m	NOUN
ejpam-2714	232	6	g(wk(0	g(wk(0	ADJ
ejpam-2714	232	7	)	)	PUNCT
ejpam-2714	232	8	,	,	PUNCT
ejpam-2714	232	9	wk(t	wk(t	NUM
ejpam-2714	232	10	)	)	PUNCT
ejpam-2714	232	11	)	)	PUNCT
ejpam-2714	233	1	≤vk(0)−wk(0	≤vk(0)−wk(0	NOUN
ejpam-2714	233	2	)	)	PUNCT
ejpam-2714	234	1	+	+	CCONJ
ejpam-2714	234	2	1	1	NUM
ejpam-2714	234	3	m	m	VERB
ejpam-2714	235	1	[	[	X
ejpam-2714	235	2	g(wk(0	g(wk(0	ADJ
ejpam-2714	235	3	)	)	PUNCT
ejpam-2714	235	4	,	,	PUNCT
ejpam-2714	235	5	wk(t	wk(t	PUNCT
ejpam-2714	235	6	)	)	PUNCT
ejpam-2714	235	7	)	)	PUNCT
ejpam-2714	235	8	−	−	PROPN
ejpam-2714	235	9	g(vk(0	g(vk(0	PROPN
ejpam-2714	235	10	)	)	PUNCT
ejpam-2714	235	11	,	,	PUNCT
ejpam-2714	235	12	vk(t	vk(t	X
ejpam-2714	235	13	)	)	PUNCT
ejpam-2714	235	14	)	)	PUNCT
ejpam-2714	235	15	≤	≤	NOUN
ejpam-2714	235	16	0	0	NUM
ejpam-2714	235	17	.	.	PUNCT
ejpam-2714	236	1	which	which	PRON
ejpam-2714	236	2	yields	yield	VERB
ejpam-2714	236	3	p(t)≤	p(t)≤	NOUN
ejpam-2714	236	4	0	0	NUM
ejpam-2714	236	5	on	on	ADP
ejpam-2714	236	6	using	use	VERB
ejpam-2714	236	7	corollary	corollary	ADJ
ejpam-2714	236	8	2	2	NUM
ejpam-2714	236	9	.	.	PUNCT
ejpam-2714	237	1	thus	thus	ADV
ejpam-2714	237	2	we	we	PRON
ejpam-2714	237	3	obtain	obtain	VERB
ejpam-2714	237	4	two	two	NUM
ejpam-2714	237	5	monotone	monotone	ADJ
ejpam-2714	237	6	sequences	sequence	NOUN
ejpam-2714	237	7	{	{	PUNCT
ejpam-2714	237	8	vn	vn	NOUN
ejpam-2714	237	9	}	}	PUNCT
ejpam-2714	237	10	and	and	CCONJ
ejpam-2714	237	11	{	{	PUNCT
ejpam-2714	237	12	wn	wn	AUX
ejpam-2714	237	13	}	}	PUNCT
ejpam-2714	237	14	satisfying	satisfy	VERB
ejpam-2714	237	15	v0	v0	NOUN
ejpam-2714	237	16	≤	≤	NOUN
ejpam-2714	237	17	v1	v1	NOUN
ejpam-2714	237	18	≤	≤	NUM
ejpam-2714	237	19	.	.	PUNCT
ejpam-2714	237	20	.	.	PUNCT
ejpam-2714	238	1	.≤	.≤	PUNCT
ejpam-2714	239	1	vn	vn	PROPN
ejpam-2714	239	2	≤	≤	NUM
ejpam-2714	239	3	wn	wn	PROPN
ejpam-2714	239	4	≤	≤	PROPN
ejpam-2714	239	5	.	.	PUNCT
ejpam-2714	239	6	.	.	PUNCT
ejpam-2714	240	1	.≤	.≤	PUNCT
ejpam-2714	241	1	w1	w1	NOUN
ejpam-2714	241	2	≤	≤	PROPN
ejpam-2714	241	3	w0	w0	PROPN
ejpam-2714	241	4	.	.	PUNCT
ejpam-2714	242	1	now	now	ADV
ejpam-2714	242	2	we	we	PRON
ejpam-2714	242	3	claim	claim	VERB
ejpam-2714	242	4	that	that	SCONJ
ejpam-2714	242	5	these	these	DET
ejpam-2714	242	6	sequences	sequence	NOUN
ejpam-2714	242	7	are	be	AUX
ejpam-2714	242	8	equicontinuous	equicontinuous	ADJ
ejpam-2714	242	9	and	and	CCONJ
ejpam-2714	242	10	uniformly	uniformly	ADV
ejpam-2714	242	11	bounded	bound	VERB
ejpam-2714	242	12	.	.	PUNCT
ejpam-2714	243	1	by	by	ADP
ejpam-2714	243	2	hypothesis	hypothesis	NOUN
ejpam-2714	243	3	both	both	PRON
ejpam-2714	243	4	v0(t	v0(t	PROPN
ejpam-2714	243	5	)	)	PUNCT
ejpam-2714	243	6	,	,	PUNCT
ejpam-2714	243	7	w0(t	w0(t	PROPN
ejpam-2714	243	8	)	)	PUNCT
ejpam-2714	243	9	are	be	AUX
ejpam-2714	243	10	bounded	bound	VERB
ejpam-2714	243	11	on	on	ADP
ejpam-2714	243	12	[	[	X
ejpam-2714	243	13	0	0	NUM
ejpam-2714	243	14	,	,	PUNCT
ejpam-2714	243	15	t	t	PROPN
ejpam-2714	243	16	]	]	PUNCT
ejpam-2714	243	17	and	and	CCONJ
ejpam-2714	243	18	the	the	DET
ejpam-2714	243	19	sequences	sequence	NOUN
ejpam-2714	243	20	{	{	PUNCT
ejpam-2714	243	21	vn	vn	NOUN
ejpam-2714	243	22	}	}	PUNCT
ejpam-2714	243	23	and	and	CCONJ
ejpam-2714	243	24	{	{	PUNCT
ejpam-2714	243	25	wn	wn	NOUN
ejpam-2714	243	26	}	}	PUNCT
ejpam-2714	243	27	are	be	AUX
ejpam-2714	243	28	such	such	ADJ
ejpam-2714	243	29	that	that	DET
ejpam-2714	243	30	v0	v0	NOUN
ejpam-2714	243	31	≤	≤	NOUN
ejpam-2714	243	32	v1	v1	NOUN
ejpam-2714	243	33	≤	≤	NUM
ejpam-2714	243	34	.	.	PUNCT
ejpam-2714	243	35	.	.	PUNCT
ejpam-2714	244	1	.≤	.≤	PUNCT
ejpam-2714	245	1	vn	vn	PROPN
ejpam-2714	245	2	≤	≤	NUM
ejpam-2714	245	3	wn	wn	PROPN
ejpam-2714	245	4	≤	≤	PROPN
ejpam-2714	245	5	.	.	PUNCT
ejpam-2714	245	6	.	.	PUNCT
ejpam-2714	246	1	.≤	.≤	PUNCT
ejpam-2714	247	1	w1	w1	NOUN
ejpam-2714	247	2	≤	≤	PROPN
ejpam-2714	247	3	w0	w0	PROPN
ejpam-2714	247	4	.	.	PUNCT
ejpam-2714	248	1	therefore	therefore	ADV
ejpam-2714	248	2	{	{	PUNCT
ejpam-2714	248	3	vn	vn	NOUN
ejpam-2714	248	4	}	}	PUNCT
ejpam-2714	248	5	and	and	CCONJ
ejpam-2714	248	6	{	{	PUNCT
ejpam-2714	248	7	wn	wn	NOUN
ejpam-2714	248	8	}	}	PUNCT
ejpam-2714	248	9	are	be	AUX
ejpam-2714	248	10	uniformly	uniformly	ADV
ejpam-2714	248	11	bounded	bound	VERB
ejpam-2714	248	12	.	.	PUNCT
ejpam-2714	249	1	next	next	ADV
ejpam-2714	249	2	we	we	PRON
ejpam-2714	249	3	prove	prove	VERB
ejpam-2714	249	4	that	that	SCONJ
ejpam-2714	249	5	{	{	PUNCT
ejpam-2714	249	6	vn	vn	NOUN
ejpam-2714	249	7	}	}	PUNCT
ejpam-2714	249	8	is	be	AUX
ejpam-2714	249	9	equicontinous	equicontinous	ADJ
ejpam-2714	249	10	.	.	PUNCT
ejpam-2714	250	1	to	to	PART
ejpam-2714	250	2	do	do	VERB
ejpam-2714	250	3	so	so	ADV
ejpam-2714	250	4	for	for	ADP
ejpam-2714	250	5	given	give	VERB
ejpam-2714	250	6	ε	ε	PROPN
ejpam-2714	250	7	>	>	X
ejpam-2714	250	8	0	0	PUNCT
ejpam-2714	250	9	choose	choose	VERB
ejpam-2714	250	10	δ	δ	X
ejpam-2714	250	11	=	=	SYM
ejpam-2714	250	12	(	(	PUNCT
ejpam-2714	250	13	(	(	PUNCT
ejpam-2714	250	14	εγ(q+1	εγ(q+1	PROPN
ejpam-2714	250	15	)	)	PUNCT
ejpam-2714	250	16	)	)	PUNCT
ejpam-2714	250	17	2m2	2m2	NUM
ejpam-2714	250	18	)	)	PUNCT
ejpam-2714	250	19	1	1	NUM
ejpam-2714	250	20	q	q	NOUN
ejpam-2714	250	21	.	.	PUNCT
ejpam-2714	251	1	next	next	ADV
ejpam-2714	251	2	for	for	ADP
ejpam-2714	251	3	t1	t1	NOUN
ejpam-2714	251	4	,	,	PUNCT
ejpam-2714	251	5	t2	t2	PROPN
ejpam-2714	251	6	∈	∈	PROPN
ejpam-2714	251	7	j	j	PROPN
ejpam-2714	252	1	such	such	ADJ
ejpam-2714	252	2	that	that	SCONJ
ejpam-2714	252	3	t2	t2	PROPN
ejpam-2714	252	4	>	>	X
ejpam-2714	252	5	t1	t1	PROPN
ejpam-2714	252	6	consider	consider	VERB
ejpam-2714	252	7	|vn(t1)−	|vn(t1)−	PROPN
ejpam-2714	252	8	vn(t2)|	vn(t2)|	PROPN
ejpam-2714	252	9	=	=	SYM
ejpam-2714	252	10	|vn(0	|vn(0	PROPN
ejpam-2714	252	11	)	)	PUNCT
ejpam-2714	253	1	+	+	CCONJ
ejpam-2714	253	2	1	1	NUM
ejpam-2714	253	3	γq	γq	ADP
ejpam-2714	253	4	∫	∫	PROPN
ejpam-2714	253	5	t1	t1	NOUN
ejpam-2714	253	6	0	0	NUM
ejpam-2714	254	1	(	(	PUNCT
ejpam-2714	254	2	t1	t1	NOUN
ejpam-2714	254	3	−	−	NOUN
ejpam-2714	254	4	s)q−1[f(s	s)q−1[f(	NOUN
ejpam-2714	254	5	,	,	PUNCT
ejpam-2714	254	6	vn−1(s	vn−1(s	NOUN
ejpam-2714	254	7	)	)	PUNCT
ejpam-2714	254	8	,	,	PUNCT
ejpam-2714	254	9	iq(vn−1(s	iq(vn−1(s	X
ejpam-2714	254	10	)	)	PUNCT
ejpam-2714	254	11	)	)	PUNCT
ejpam-2714	255	1	+	+	CCONJ
ejpam-2714	255	2	g(s	g(s	NOUN
ejpam-2714	255	3	,	,	PUNCT
ejpam-2714	255	4	wn−1(s	wn−1(s	PROPN
ejpam-2714	255	5	)	)	PUNCT
ejpam-2714	255	6	,	,	PUNCT
ejpam-2714	255	7	iq(wn−1(s)))]ds	iq(wn−1(s)))]ds	ADP
ejpam-2714	255	8	−	−	PROPN
ejpam-2714	255	9	vn(0	vn(0	NOUN
ejpam-2714	255	10	)	)	PUNCT
ejpam-2714	255	11	+	+	CCONJ
ejpam-2714	255	12	1	1	NUM
ejpam-2714	255	13	γq	γq	ADP
ejpam-2714	255	14	∫	∫	PROPN
ejpam-2714	255	15	t2	t2	PROPN
ejpam-2714	255	16	0	0	NUM
ejpam-2714	255	17	(	(	PUNCT
ejpam-2714	255	18	t2	t2	NOUN
ejpam-2714	255	19	−	−	PROPN
ejpam-2714	255	20	s)q−1[f(s	s)q−1[f(	NOUN
ejpam-2714	255	21	,	,	PUNCT
ejpam-2714	255	22	vn−1(s	vn−1(s	NOUN
ejpam-2714	255	23	)	)	PUNCT
ejpam-2714	255	24	,	,	PUNCT
ejpam-2714	255	25	iq(vn−1(s	iq(vn−1(s	X
ejpam-2714	255	26	)	)	PUNCT
ejpam-2714	255	27	)	)	PUNCT
ejpam-2714	255	28	)	)	PUNCT
ejpam-2714	256	1	+	+	CCONJ
ejpam-2714	256	2	g(s	g(s	NOUN
ejpam-2714	256	3	,	,	PUNCT
ejpam-2714	256	4	wn−1(s	wn−1(s	PROPN
ejpam-2714	256	5	)	)	PUNCT
ejpam-2714	256	6	,	,	PUNCT
ejpam-2714	256	7	iq(wn−1(s)))]ds|	iq(wn−1(s)))]ds|	VERB
ejpam-2714	256	8	≤	≤	NUM
ejpam-2714	256	9	1	1	NUM
ejpam-2714	256	10	γq	γq	ADP
ejpam-2714	256	11	∫	∫	PROPN
ejpam-2714	256	12	t1	t1	NOUN
ejpam-2714	256	13	0	0	PUNCT
ejpam-2714	257	1	[	[	X
ejpam-2714	257	2	(	(	PUNCT
ejpam-2714	257	3	t1	t1	NOUN
ejpam-2714	257	4	−	−	PROPN
ejpam-2714	257	5	s)q−1	s)q−1	PRON
ejpam-2714	257	6	−	−	PROPN
ejpam-2714	258	1	(	(	PUNCT
ejpam-2714	258	2	t2	t2	PROPN
ejpam-2714	258	3	−	−	PROPN
ejpam-2714	258	4	s)q−1]|f(s	s)q−1]|f(	VERB
ejpam-2714	258	5	,	,	PUNCT
ejpam-2714	258	6	vn−1(s	vn−1(s	NOUN
ejpam-2714	258	7	)	)	PUNCT
ejpam-2714	258	8	,	,	PUNCT
ejpam-2714	258	9	iq(vn−1(s	iq(vn−1(s	X
ejpam-2714	258	10	)	)	PUNCT
ejpam-2714	258	11	)	)	PUNCT
ejpam-2714	258	12	)	)	PUNCT
ejpam-2714	259	1	+	+	CCONJ
ejpam-2714	259	2	g(s	g(s	NOUN
ejpam-2714	259	3	,	,	PUNCT
ejpam-2714	259	4	wn−1(s	wn−1(s	PROPN
ejpam-2714	259	5	)	)	PUNCT
ejpam-2714	259	6	,	,	PUNCT
ejpam-2714	259	7	iq(wn−1(s)))|ds	iq(wn−1(s)))|ds	PROPN
ejpam-2714	259	8	+	+	CCONJ
ejpam-2714	259	9	∫	∫	PROPN
ejpam-2714	259	10	t2	t2	PROPN
ejpam-2714	259	11	t1	t1	NOUN
ejpam-2714	259	12	(	(	PUNCT
ejpam-2714	259	13	t2	t2	PROPN
ejpam-2714	259	14	−	−	PROPN
ejpam-2714	259	15	s)q−1|f(s	s)q−1|f(	NOUN
ejpam-2714	259	16	,	,	PUNCT
ejpam-2714	259	17	vn−1(s	vn−1(s	PROPN
ejpam-2714	259	18	)	)	PUNCT
ejpam-2714	259	19	,	,	PUNCT
ejpam-2714	259	20	iq(vn−1(s	iq(vn−1(s	X
ejpam-2714	259	21	)	)	PUNCT
ejpam-2714	259	22	)	)	PUNCT
ejpam-2714	259	23	)	)	PUNCT
ejpam-2714	260	1	+	+	CCONJ
ejpam-2714	260	2	g(s	g(s	NOUN
ejpam-2714	260	3	,	,	PUNCT
ejpam-2714	260	4	wn−1(s	wn−1(s	PROPN
ejpam-2714	260	5	)	)	PUNCT
ejpam-2714	260	6	,	,	PUNCT
ejpam-2714	260	7	iq(wn−1(s)))|ds	iq(wn−1(s)))|ds	PROPN
ejpam-2714	260	8	j.	j.	PROPN
ejpam-2714	260	9	devi	devi	PROPN
ejpam-2714	260	10	,	,	PUNCT
ejpam-2714	260	11	ch	ch	PROPN
ejpam-2714	260	12	.	.	PUNCT
ejpam-2714	260	13	sreedhar	sreedhar	PROPN
ejpam-2714	260	14	/	/	SYM
ejpam-2714	260	15	eur	eur	PROPN
ejpam-2714	260	16	.	.	PUNCT
ejpam-2714	261	1	j.	j.	PROPN
ejpam-2714	261	2	pure	pure	PROPN
ejpam-2714	261	3	appl	appl	PROPN
ejpam-2714	261	4	.	.	PROPN
ejpam-2714	261	5	math	math	PROPN
ejpam-2714	261	6	,	,	PUNCT
ejpam-2714	261	7	9	9	NUM
ejpam-2714	261	8	(	(	PUNCT
ejpam-2714	261	9	2016	2016	NUM
ejpam-2714	261	10	)	)	PUNCT
ejpam-2714	261	11	,	,	PUNCT
ejpam-2714	261	12	346	346	NUM
ejpam-2714	261	13	-	-	SYM
ejpam-2714	261	14	359	359	NUM
ejpam-2714	261	15	354	354	NUM
ejpam-2714	261	16	≤	≤	NOUN
ejpam-2714	261	17	m2	m2	PROPN
ejpam-2714	262	1	γq	γq	ADP
ejpam-2714	262	2	{	{	PUNCT
ejpam-2714	262	3	∫	∫	PROPN
ejpam-2714	262	4	t1	t1	NOUN
ejpam-2714	262	5	0	0	PUNCT
ejpam-2714	263	1	[	[	X
ejpam-2714	263	2	(	(	PUNCT
ejpam-2714	263	3	t1	t1	NOUN
ejpam-2714	263	4	−	−	PROPN
ejpam-2714	263	5	s)q−1	s)q−1	PRON
ejpam-2714	263	6	−	−	PROPN
ejpam-2714	264	1	(	(	PUNCT
ejpam-2714	264	2	t2	t2	PROPN
ejpam-2714	264	3	−	−	PROPN
ejpam-2714	264	4	s)q−1]ds+	s)q−1]ds+	PROPN
ejpam-2714	264	5	∫	∫	PROPN
ejpam-2714	265	1	t2	t2	PROPN
ejpam-2714	265	2	t1	t1	PROPN
ejpam-2714	265	3	(	(	PUNCT
ejpam-2714	265	4	t2	t2	PROPN
ejpam-2714	265	5	−	−	PROPN
ejpam-2714	265	6	s)q−1ds	s)q−1ds	PROPN
ejpam-2714	265	7	}	}	PUNCT
ejpam-2714	265	8	≤	≤	NUM
ejpam-2714	265	9	m2	m2	PROPN
ejpam-2714	265	10	γq+	γq+	NOUN
ejpam-2714	265	11	1	1	NUM
ejpam-2714	266	1	[	[	X
ejpam-2714	266	2	(	(	PUNCT
ejpam-2714	266	3	t1	t1	NOUN
ejpam-2714	266	4	)	)	PUNCT
ejpam-2714	266	5	q	q	NOUN
ejpam-2714	267	1	+	+	CCONJ
ejpam-2714	267	2	(	(	PUNCT
ejpam-2714	267	3	t2	t2	PROPN
ejpam-2714	267	4	−	−	PROPN
ejpam-2714	267	5	t1	t1	PROPN
ejpam-2714	267	6	)	)	PUNCT
ejpam-2714	267	7	q	q	NOUN
ejpam-2714	267	8	−	−	PROPN
ejpam-2714	267	9	(	(	PUNCT
ejpam-2714	267	10	t2	t2	NOUN
ejpam-2714	267	11	)	)	PUNCT
ejpam-2714	267	12	q	q	NOUN
ejpam-2714	268	1	+	+	CCONJ
ejpam-2714	268	2	(	(	PUNCT
ejpam-2714	268	3	t2	t2	PROPN
ejpam-2714	268	4	−	−	PROPN
ejpam-2714	268	5	t1	t1	PROPN
ejpam-2714	268	6	)	)	PUNCT
ejpam-2714	268	7	q	q	X
ejpam-2714	268	8	]	]	PUNCT
ejpam-2714	268	9	≤	≤	NUM
ejpam-2714	268	10	m2	m2	PROPN
ejpam-2714	268	11	γq+	γq+	NOUN
ejpam-2714	268	12	1	1	NUM
ejpam-2714	269	1	[	[	X
ejpam-2714	269	2	t	t	X
ejpam-2714	269	3	q	q	NOUN
ejpam-2714	269	4	1	1	NUM
ejpam-2714	269	5	−	−	PROPN
ejpam-2714	269	6	t	t	NOUN
ejpam-2714	269	7	q	q	PROPN
ejpam-2714	269	8	2	2	NUM
ejpam-2714	269	9	]	]	PUNCT
ejpam-2714	269	10	+	+	CCONJ
ejpam-2714	269	11	2m2	2m2	NUM
ejpam-2714	269	12	γq+	γq+	NOUN
ejpam-2714	269	13	1	1	NUM
ejpam-2714	269	14	(	(	PUNCT
ejpam-2714	269	15	t2	t2	PROPN
ejpam-2714	269	16	−	−	PROPN
ejpam-2714	269	17	t1	t1	PROPN
ejpam-2714	269	18	)	)	PUNCT
ejpam-2714	269	19	q	q	PROPN
ejpam-2714	269	20	≤	≤	NOUN
ejpam-2714	269	21	2m2	2m2	NUM
ejpam-2714	269	22	γq+	γq+	NOUN
ejpam-2714	269	23	1	1	NUM
ejpam-2714	269	24	(	(	PUNCT
ejpam-2714	269	25	t2	t2	PROPN
ejpam-2714	269	26	−	−	PROPN
ejpam-2714	269	27	t1	t1	PROPN
ejpam-2714	269	28	)	)	PUNCT
ejpam-2714	269	29	q	q	NOUN
ejpam-2714	269	30	,	,	PUNCT
ejpam-2714	269	31	here	here	ADV
ejpam-2714	269	32	we	we	PRON
ejpam-2714	269	33	have	have	AUX
ejpam-2714	269	34	used	use	VERB
ejpam-2714	269	35	the	the	DET
ejpam-2714	269	36	fact	fact	NOUN
ejpam-2714	269	37	that	that	SCONJ
ejpam-2714	269	38	{	{	PUNCT
ejpam-2714	269	39	vn	vn	NOUN
ejpam-2714	269	40	}	}	PUNCT
ejpam-2714	269	41	,	,	PUNCT
ejpam-2714	269	42	{	{	PUNCT
ejpam-2714	269	43	i	i	PRON
ejpam-2714	269	44	qvn	qvn	VERB
ejpam-2714	269	45	}	}	PUNCT
ejpam-2714	269	46	,	,	PUNCT
ejpam-2714	269	47	{	{	PUNCT
ejpam-2714	269	48	wn	wn	X
ejpam-2714	269	49	}	}	PUNCT
ejpam-2714	269	50	,	,	PUNCT
ejpam-2714	269	51	{	{	PUNCT
ejpam-2714	269	52	i	i	PRON
ejpam-2714	269	53	qvn	qvn	VERB
ejpam-2714	269	54	}	}	PUNCT
ejpam-2714	269	55	are	be	AUX
ejpam-2714	269	56	uniformly	uniformly	ADV
ejpam-2714	269	57	bounded	bound	VERB
ejpam-2714	269	58	and	and	CCONJ
ejpam-2714	269	59	f(t	f(t	NOUN
ejpam-2714	269	60	,	,	PUNCT
ejpam-2714	269	61	x1	x1	PROPN
ejpam-2714	269	62	,	,	PUNCT
ejpam-2714	269	63	x2	x2	PROPN
ejpam-2714	269	64	)	)	PUNCT
ejpam-2714	269	65	,	,	PUNCT
ejpam-2714	269	66	g(t	g(t	PROPN
ejpam-2714	269	67	,	,	PUNCT
ejpam-2714	269	68	y1	y1	NOUN
ejpam-2714	269	69	,	,	PUNCT
ejpam-2714	269	70	y2	y2	PROPN
ejpam-2714	269	71	)	)	PUNCT
ejpam-2714	269	72	are	be	AUX
ejpam-2714	269	73	continuous	continuous	ADJ
ejpam-2714	269	74	on	on	ADP
ejpam-2714	269	75	[	[	X
ejpam-2714	269	76	0	0	NUM
ejpam-2714	269	77	,	,	PUNCT
ejpam-2714	269	78	t	t	PROPN
ejpam-2714	269	79	]	]	PUNCT
ejpam-2714	269	80	.	.	PUNCT
ejpam-2714	270	1	thus	thus	ADV
ejpam-2714	270	2	for	for	ADP
ejpam-2714	270	3	any	any	DET
ejpam-2714	270	4	given	give	VERB
ejpam-2714	270	5	ε	ε	PROPN
ejpam-2714	270	6	>	>	X
ejpam-2714	270	7	0	0	PUNCT
ejpam-2714	270	8	there	there	PRON
ejpam-2714	270	9	exists	exist	VERB
ejpam-2714	270	10	δ	δ	PROPN
ejpam-2714	270	11	>	>	X
ejpam-2714	270	12	0	0	PUNCT
ejpam-2714	270	13	independent	independent	ADJ
ejpam-2714	270	14	of	of	ADP
ejpam-2714	270	15	n	n	PRON
ejpam-2714	270	16	such	such	ADJ
ejpam-2714	270	17	that	that	PRON
ejpam-2714	270	18	for	for	ADP
ejpam-2714	270	19	each	each	DET
ejpam-2714	270	20	n	n	CCONJ
ejpam-2714	270	21	,	,	PUNCT
ejpam-2714	270	22	|vn(t1)−	|vn(t1)−	PROPN
ejpam-2714	270	23	vn(t2)|	vn(t2)|	PROPN
ejpam-2714	270	24	<	<	X
ejpam-2714	270	25	ε	ε	PROPN
ejpam-2714	271	1	whenever	whenever	SCONJ
ejpam-2714	271	2	δ	δ	X
ejpam-2714	271	3	=	=	PRON
ejpam-2714	271	4	(	(	PUNCT
ejpam-2714	271	5	(	(	PUNCT
ejpam-2714	271	6	εγ(q+1	εγ(q+1	PROPN
ejpam-2714	271	7	)	)	PUNCT
ejpam-2714	271	8	)	)	PUNCT
ejpam-2714	271	9	2m2	2m2	NUM
ejpam-2714	271	10	)	)	PUNCT
ejpam-2714	271	11	1	1	NUM
ejpam-2714	271	12	q	q	NOUN
ejpam-2714	271	13	.	.	PUNCT
ejpam-2714	272	1	therefore	therefore	ADV
ejpam-2714	272	2	{	{	PUNCT
ejpam-2714	272	3	vn	vn	NOUN
ejpam-2714	272	4	}	}	PUNCT
ejpam-2714	272	5	is	be	AUX
ejpam-2714	272	6	equicontinuous	equicontinuous	ADJ
ejpam-2714	272	7	.	.	PUNCT
ejpam-2714	273	1	similarly	similarly	ADV
ejpam-2714	273	2	we	we	PRON
ejpam-2714	273	3	can	can	AUX
ejpam-2714	273	4	prove	prove	VERB
ejpam-2714	273	5	that	that	SCONJ
ejpam-2714	273	6	{	{	PUNCT
ejpam-2714	273	7	wn	wn	NOUN
ejpam-2714	273	8	}	}	PUNCT
ejpam-2714	273	9	is	be	AUX
ejpam-2714	273	10	equicontinuous	equicontinuous	ADJ
ejpam-2714	273	11	.	.	PUNCT
ejpam-2714	274	1	hence	hence	ADV
ejpam-2714	274	2	by	by	ADP
ejpam-2714	274	3	arzela	arzela	PROPN
ejpam-2714	274	4	-	-	PUNCT
ejpam-2714	274	5	ascoli	ascoli	PROPN
ejpam-2714	274	6	’s	’s	PART
ejpam-2714	274	7	theorem	theorem	NOUN
ejpam-2714	274	8	there	there	PRON
ejpam-2714	274	9	exist	exist	VERB
ejpam-2714	274	10	subsequences	subsequence	NOUN
ejpam-2714	274	11	{	{	PUNCT
ejpam-2714	274	12	vnk	vnk	NOUN
ejpam-2714	274	13	}	}	PUNCT
ejpam-2714	274	14	and	and	CCONJ
ejpam-2714	274	15	{	{	PUNCT
ejpam-2714	274	16	wnk	wnk	X
ejpam-2714	274	17	}	}	PUNCT
ejpam-2714	274	18	which	which	PRON
ejpam-2714	274	19	converge	converge	VERB
ejpam-2714	274	20	uniformly	uniformly	ADV
ejpam-2714	274	21	to	to	ADP
ejpam-2714	274	22	ρ(t	ρ(t	NUM
ejpam-2714	274	23	)	)	PUNCT
ejpam-2714	274	24	and	and	CCONJ
ejpam-2714	274	25	r(t	r(t	NOUN
ejpam-2714	274	26	)	)	PUNCT
ejpam-2714	274	27	respectively	respectively	ADV
ejpam-2714	274	28	.	.	PUNCT
ejpam-2714	275	1	since	since	SCONJ
ejpam-2714	275	2	the	the	DET
ejpam-2714	275	3	sequences	sequence	NOUN
ejpam-2714	275	4	are	be	AUX
ejpam-2714	275	5	monotone	monotone	ADJ
ejpam-2714	275	6	,	,	PUNCT
ejpam-2714	275	7	the	the	DET
ejpam-2714	275	8	entire	entire	ADJ
ejpam-2714	275	9	sequences	sequence	NOUN
ejpam-2714	275	10	converge	converge	VERB
ejpam-2714	275	11	uniformly	uniformly	ADV
ejpam-2714	275	12	to	to	ADP
ejpam-2714	275	13	ρ	ρ	PROPN
ejpam-2714	275	14	and	and	CCONJ
ejpam-2714	275	15	r	r	NOUN
ejpam-2714	275	16	respectively	respectively	ADV
ejpam-2714	275	17	on	on	ADP
ejpam-2714	275	18	j	j	PROPN
ejpam-2714	275	19	.	.	PUNCT
ejpam-2714	276	1	to	to	PART
ejpam-2714	276	2	prove	prove	VERB
ejpam-2714	276	3	that	that	SCONJ
ejpam-2714	276	4	ρ	ρ	PROPN
ejpam-2714	276	5	and	and	CCONJ
ejpam-2714	276	6	r	r	NOUN
ejpam-2714	276	7	are	be	AUX
ejpam-2714	276	8	coupled	couple	VERB
ejpam-2714	276	9	minimal	minimal	ADJ
ejpam-2714	276	10	and	and	CCONJ
ejpam-2714	276	11	maximal	maximal	ADJ
ejpam-2714	276	12	solutions	solution	NOUN
ejpam-2714	276	13	of	of	ADP
ejpam-2714	276	14	(	(	PUNCT
ejpam-2714	276	15	10	10	NUM
ejpam-2714	276	16	)	)	PUNCT
ejpam-2714	276	17	and	and	CCONJ
ejpam-2714	276	18	(	(	PUNCT
ejpam-2714	276	19	11	11	NUM
ejpam-2714	276	20	)	)	PUNCT
ejpam-2714	276	21	respectively	respectively	ADV
ejpam-2714	276	22	,	,	PUNCT
ejpam-2714	276	23	we	we	PRON
ejpam-2714	276	24	need	need	VERB
ejpam-2714	276	25	to	to	PART
ejpam-2714	276	26	show	show	VERB
ejpam-2714	276	27	that	that	SCONJ
ejpam-2714	276	28	if	if	SCONJ
ejpam-2714	276	29	u	u	NOUN
ejpam-2714	276	30	is	be	AUX
ejpam-2714	276	31	any	any	DET
ejpam-2714	276	32	solution	solution	NOUN
ejpam-2714	276	33	of	of	ADP
ejpam-2714	276	34	(	(	PUNCT
ejpam-2714	276	35	10	10	NUM
ejpam-2714	276	36	)	)	PUNCT
ejpam-2714	276	37	and	and	CCONJ
ejpam-2714	276	38	(	(	PUNCT
ejpam-2714	276	39	11	11	NUM
ejpam-2714	276	40	)	)	PUNCT
ejpam-2714	276	41	,	,	PUNCT
ejpam-2714	276	42	such	such	ADJ
ejpam-2714	276	43	that	that	DET
ejpam-2714	276	44	v0	v0	NOUN
ejpam-2714	276	45	≤	≤	NOUN
ejpam-2714	276	46	u	u	NOUN
ejpam-2714	276	47	≤	≤	NOUN
ejpam-2714	276	48	w0	w0	NOUN
ejpam-2714	276	49	,	,	PUNCT
ejpam-2714	276	50	then	then	ADV
ejpam-2714	276	51	ρ	ρ	PROPN
ejpam-2714	276	52	≤	≤	PROPN
ejpam-2714	276	53	u1	u1	NOUN
ejpam-2714	276	54	,	,	PUNCT
ejpam-2714	276	55	u2	u2	PROPN
ejpam-2714	276	56	≤	≤	PROPN
ejpam-2714	276	57	r.	r.	PROPN
ejpam-2714	276	58	assume	assume	VERB
ejpam-2714	276	59	that	that	SCONJ
ejpam-2714	276	60	there	there	PRON
ejpam-2714	276	61	exists	exist	VERB
ejpam-2714	276	62	a	a	DET
ejpam-2714	276	63	positive	positive	ADJ
ejpam-2714	276	64	integer	integer	NOUN
ejpam-2714	276	65	n	n	CCONJ
ejpam-2714	276	66	such	such	ADJ
ejpam-2714	276	67	that	that	PRON
ejpam-2714	276	68	vn	vn	PROPN
ejpam-2714	276	69	≤	≤	X
ejpam-2714	276	70	u≤	u≤	PROPN
ejpam-2714	276	71	wn	wn	NOUN
ejpam-2714	276	72	on	on	ADP
ejpam-2714	276	73	j	j	PROPN
ejpam-2714	276	74	.	.	PUNCT
ejpam-2714	277	1	then	then	ADV
ejpam-2714	277	2	using	use	VERB
ejpam-2714	277	3	the	the	DET
ejpam-2714	277	4	monotone	monotone	ADJ
ejpam-2714	277	5	nature	nature	NOUN
ejpam-2714	277	6	of	of	ADP
ejpam-2714	277	7	f	f	PROPN
ejpam-2714	277	8	,	,	PUNCT
ejpam-2714	277	9	g	g	PROPN
ejpam-2714	277	10	we	we	PRON
ejpam-2714	277	11	have	have	VERB
ejpam-2714	277	12	c	c	PROPN
ejpam-2714	277	13	dqp(t	dqp(t	PROPN
ejpam-2714	277	14	)	)	PUNCT
ejpam-2714	278	1	=	=	PROPN
ejpam-2714	278	2	c	c	X
ejpam-2714	278	3	dqvn+1(t)−	dqvn+1(t)−	PROPN
ejpam-2714	278	4	c	c	PROPN
ejpam-2714	278	5	dqu(t	dqu(t	PROPN
ejpam-2714	278	6	)	)	PUNCT
ejpam-2714	278	7	,	,	PUNCT
ejpam-2714	278	8	≤[f(t	≤[f(t	NOUN
ejpam-2714	278	9	,	,	PUNCT
ejpam-2714	278	10	vn(t	vn(t	NUM
ejpam-2714	278	11	)	)	PUNCT
ejpam-2714	278	12	,	,	PUNCT
ejpam-2714	278	13	iq(vn(t	iq(vn(t	NUM
ejpam-2714	278	14	)	)	PUNCT
ejpam-2714	278	15	)	)	PUNCT
ejpam-2714	278	16	)	)	PUNCT
ejpam-2714	279	1	+	+	CCONJ
ejpam-2714	279	2	g(t	g(t	PROPN
ejpam-2714	279	3	,	,	PUNCT
ejpam-2714	279	4	wn(t	wn(t	NUM
ejpam-2714	279	5	)	)	PUNCT
ejpam-2714	279	6	,	,	PUNCT
ejpam-2714	279	7	iq(wn(t	iq(wn(t	X
ejpam-2714	279	8	)	)	PUNCT
ejpam-2714	279	9	)	)	PUNCT
ejpam-2714	279	10	)	)	PUNCT
ejpam-2714	279	11	]	]	PUNCT
ejpam-2714	280	1	−	−	PUNCT
ejpam-2714	281	1	[	[	X
ejpam-2714	281	2	f(t	f(t	NOUN
ejpam-2714	281	3	,	,	PUNCT
ejpam-2714	281	4	u(t	u(t	NOUN
ejpam-2714	281	5	)	)	PUNCT
ejpam-2714	281	6	,	,	PUNCT
ejpam-2714	281	7	iq(u(t	iq(u(t	NUM
ejpam-2714	281	8	)	)	PUNCT
ejpam-2714	281	9	)	)	PUNCT
ejpam-2714	281	10	)	)	PUNCT
ejpam-2714	282	1	+	+	CCONJ
ejpam-2714	282	2	g(t	g(t	PROPN
ejpam-2714	282	3	,	,	PUNCT
ejpam-2714	282	4	u(t	u(t	NOUN
ejpam-2714	282	5	)	)	PUNCT
ejpam-2714	282	6	,	,	PUNCT
ejpam-2714	282	7	iq(u(t	iq(u(t	NUM
ejpam-2714	282	8	)	)	PUNCT
ejpam-2714	282	9	)	)	PUNCT
ejpam-2714	282	10	)	)	PUNCT
ejpam-2714	282	11	]	]	PUNCT
ejpam-2714	283	1	c	c	NOUN
ejpam-2714	283	2	dqp(t)≤0	dqp(t)≤0	NUM
ejpam-2714	283	3	and	and	CCONJ
ejpam-2714	283	4	p(0	p(0	NOUN
ejpam-2714	283	5	)	)	PUNCT
ejpam-2714	284	1	=	=	PROPN
ejpam-2714	284	2	vn+1(0)−	vn+1(0)−	PROPN
ejpam-2714	284	3	u(0	u(0	PROPN
ejpam-2714	284	4	)	)	PUNCT
ejpam-2714	284	5	=	=	SYM
ejpam-2714	284	6	vn(0)−	vn(0)−	VERB
ejpam-2714	284	7	1	1	NUM
ejpam-2714	284	8	m	m	NOUN
ejpam-2714	284	9	g(vn(0	g(vn(0	PROPN
ejpam-2714	284	10	)	)	PUNCT
ejpam-2714	284	11	,	,	PUNCT
ejpam-2714	284	12	vn(t	vn(t	PUNCT
ejpam-2714	284	13	)	)	PUNCT
ejpam-2714	284	14	)	)	PUNCT
ejpam-2714	285	1	−	−	PROPN
ejpam-2714	286	1	u(0	u(0	PROPN
ejpam-2714	286	2	)	)	PUNCT
ejpam-2714	286	3	≤vn(0)−	≤vn(0)−	PROPN
ejpam-2714	286	4	u(0)−	u(0)−	PROPN
ejpam-2714	286	5	1	1	NUM
ejpam-2714	286	6	m	m	NOUN
ejpam-2714	286	7	[	[	X
ejpam-2714	286	8	g(vn(0	g(vn(0	NOUN
ejpam-2714	286	9	)	)	PUNCT
ejpam-2714	286	10	,	,	PUNCT
ejpam-2714	286	11	vn(t	vn(t	NUM
ejpam-2714	286	12	)	)	PUNCT
ejpam-2714	286	13	)	)	PUNCT
ejpam-2714	286	14	−	−	PROPN
ejpam-2714	286	15	g(u(0),u(t	g(u(0),u(t	PROPN
ejpam-2714	286	16	)	)	PUNCT
ejpam-2714	286	17	)	)	PUNCT
ejpam-2714	287	1	]	]	PUNCT
ejpam-2714	287	2	≤	≤	NUM
ejpam-2714	287	3	0	0	PUNCT
ejpam-2714	288	1	so	so	ADV
ejpam-2714	288	2	vn+1(t)≤	vn+1(t)≤	PROPN
ejpam-2714	288	3	u1(t	u1(t	PROPN
ejpam-2714	288	4	)	)	PUNCT
ejpam-2714	288	5	,	,	PUNCT
ejpam-2714	288	6	on	on	ADP
ejpam-2714	288	7	j	j	PROPN
ejpam-2714	288	8	follows	follow	VERB
ejpam-2714	288	9	from	from	ADP
ejpam-2714	288	10	corollary	corollary	ADJ
ejpam-2714	288	11	2	2	NUM
ejpam-2714	288	12	.	.	PUNCT
ejpam-2714	289	1	similarly	similarly	ADV
ejpam-2714	289	2	we	we	PRON
ejpam-2714	289	3	can	can	AUX
ejpam-2714	289	4	show	show	VERB
ejpam-2714	289	5	that	that	SCONJ
ejpam-2714	289	6	u(t)≤	u(t)≤	PROPN
ejpam-2714	289	7	wn+1(t	wn+1(t	PROPN
ejpam-2714	289	8	)	)	PUNCT
ejpam-2714	289	9	,	,	PUNCT
ejpam-2714	289	10	on	on	ADP
ejpam-2714	289	11	j	j	PROPN
ejpam-2714	289	12	.	.	PUNCT
ejpam-2714	290	1	by	by	ADP
ejpam-2714	290	2	applying	apply	VERB
ejpam-2714	290	3	induction	induction	NOUN
ejpam-2714	290	4	on	on	ADP
ejpam-2714	290	5	n	n	CCONJ
ejpam-2714	290	6	we	we	PRON
ejpam-2714	290	7	conclude	conclude	VERB
ejpam-2714	290	8	that	that	SCONJ
ejpam-2714	290	9	vn+1	vn+1	PROPN
ejpam-2714	290	10	≤	≤	NUM
ejpam-2714	290	11	u	u	NOUN
ejpam-2714	290	12	≤	≤	NOUN
ejpam-2714	290	13	wn+1	wn+1	VERB
ejpam-2714	290	14	on	on	ADP
ejpam-2714	290	15	j	j	PROPN
ejpam-2714	290	16	.	.	PUNCT
ejpam-2714	291	1	taking	take	VERB
ejpam-2714	291	2	limit	limit	NOUN
ejpam-2714	291	3	as	as	ADP
ejpam-2714	291	4	n→∞	n→∞	NUM
ejpam-2714	291	5	,	,	PUNCT
ejpam-2714	291	6	we	we	PRON
ejpam-2714	291	7	get	get	VERB
ejpam-2714	291	8	ρ	ρ	NOUN
ejpam-2714	291	9	≤	≤	NUM
ejpam-2714	291	10	u≤	u≤	PROPN
ejpam-2714	291	11	r	r	NOUN
ejpam-2714	291	12	,	,	PUNCT
ejpam-2714	292	1	t	t	PROPN
ejpam-2714	292	2	∈	∈	PROPN
ejpam-2714	292	3	j	j	PROPN
ejpam-2714	292	4	.	.	PUNCT
ejpam-2714	293	1	hence	hence	ADV
ejpam-2714	293	2	v0	v0	VERB
ejpam-2714	293	3	≤	≤	NUM
ejpam-2714	293	4	v1	v1	PROPN
ejpam-2714	293	5	≤	≤	PUNCT
ejpam-2714	293	6	v2	v2	NOUN
ejpam-2714	293	7	≤	≤	NOUN
ejpam-2714	293	8	.	.	PUNCT
ejpam-2714	293	9	.	.	PUNCT
ejpam-2714	294	1	.≤	.≤	PUNCT
ejpam-2714	295	1	vn	vn	VERB
ejpam-2714	295	2	≤	≤	NUM
ejpam-2714	295	3	.	.	PUNCT
ejpam-2714	295	4	.	.	PUNCT
ejpam-2714	296	1	.≤	.≤	PUNCT
ejpam-2714	297	1	ρ	ρ	PROPN
ejpam-2714	297	2	≤	≤	NUM
ejpam-2714	297	3	u≤	u≤	NUM
ejpam-2714	297	4	r	r	NOUN
ejpam-2714	297	5	≤	≤	NUM
ejpam-2714	297	6	.	.	PUNCT
ejpam-2714	297	7	.	.	PUNCT
ejpam-2714	298	1	.≤	.≤	PUNCT
ejpam-2714	299	1	wn	wn	PROPN
ejpam-2714	299	2	≤	≤	PROPN
ejpam-2714	299	3	.	.	PUNCT
ejpam-2714	299	4	.	.	PUNCT
ejpam-2714	299	5	.	.	PUNCT
ejpam-2714	300	1	w1	w1	NOUN
ejpam-2714	300	2	≤	≤	PROPN
ejpam-2714	300	3	w0	w0	NOUN
ejpam-2714	300	4	,	,	PUNCT
ejpam-2714	300	5	on	on	ADP
ejpam-2714	300	6	j	j	PROPN
ejpam-2714	300	7	,	,	PUNCT
ejpam-2714	300	8	where	where	SCONJ
ejpam-2714	300	9	ρ	ρ	NOUN
ejpam-2714	300	10	and	and	CCONJ
ejpam-2714	300	11	r	r	NOUN
ejpam-2714	300	12	are	be	AUX
ejpam-2714	300	13	coupled	couple	VERB
ejpam-2714	300	14	minimal	minimal	ADJ
ejpam-2714	300	15	and	and	CCONJ
ejpam-2714	300	16	maximal	maximal	ADJ
ejpam-2714	300	17	solutions	solution	NOUN
ejpam-2714	300	18	of	of	ADP
ejpam-2714	300	19	(	(	PUNCT
ejpam-2714	300	20	10	10	NUM
ejpam-2714	300	21	)	)	PUNCT
ejpam-2714	300	22	and	and	CCONJ
ejpam-2714	300	23	(	(	PUNCT
ejpam-2714	300	24	11	11	NUM
ejpam-2714	300	25	)	)	PUNCT
ejpam-2714	300	26	.	.	PUNCT
ejpam-2714	301	1	thus	thus	ADV
ejpam-2714	301	2	the	the	DET
ejpam-2714	301	3	proof	proof	NOUN
ejpam-2714	301	4	is	be	AUX
ejpam-2714	301	5	complete	complete	ADJ
ejpam-2714	301	6	.	.	PUNCT
ejpam-2714	302	1	j.	j.	PROPN
ejpam-2714	302	2	devi	devi	PROPN
ejpam-2714	302	3	,	,	PUNCT
ejpam-2714	302	4	ch	ch	PROPN
ejpam-2714	302	5	.	.	PUNCT
ejpam-2714	302	6	sreedhar	sreedhar	PROPN
ejpam-2714	302	7	/	/	SYM
ejpam-2714	302	8	eur	eur	PROPN
ejpam-2714	302	9	.	.	PUNCT
ejpam-2714	303	1	j.	j.	PROPN
ejpam-2714	303	2	pure	pure	PROPN
ejpam-2714	303	3	appl	appl	PROPN
ejpam-2714	303	4	.	.	PROPN
ejpam-2714	303	5	math	math	PROPN
ejpam-2714	303	6	,	,	PUNCT
ejpam-2714	303	7	9	9	NUM
ejpam-2714	303	8	(	(	PUNCT
ejpam-2714	303	9	2016	2016	NUM
ejpam-2714	303	10	)	)	PUNCT
ejpam-2714	303	11	,	,	PUNCT
ejpam-2714	303	12	346	346	NUM
ejpam-2714	303	13	-	-	SYM
ejpam-2714	303	14	359	359	NUM
ejpam-2714	303	15	355	355	NUM
ejpam-2714	303	16	remark	remark	NOUN
ejpam-2714	303	17	1	1	NUM
ejpam-2714	303	18	.	.	PUNCT
ejpam-2714	304	1	(	(	PUNCT
ejpam-2714	304	2	i	i	NOUN
ejpam-2714	304	3	)	)	PUNCT
ejpam-2714	304	4	in	in	ADP
ejpam-2714	304	5	theorem	theorem	NOUN
ejpam-2714	304	6	3	3	NUM
ejpam-2714	304	7	,	,	PUNCT
ejpam-2714	304	8	if	if	SCONJ
ejpam-2714	304	9	g(t	g(t	PROPN
ejpam-2714	304	10	,	,	PUNCT
ejpam-2714	304	11	u	u	NOUN
ejpam-2714	304	12	,	,	PUNCT
ejpam-2714	304	13	iq(u	iq(u	NOUN
ejpam-2714	304	14	)	)	PUNCT
ejpam-2714	304	15	)	)	PUNCT
ejpam-2714	305	1	=	=	PUNCT
ejpam-2714	305	2	0	0	NUM
ejpam-2714	305	3	,	,	PUNCT
ejpam-2714	305	4	then	then	ADV
ejpam-2714	305	5	we	we	PRON
ejpam-2714	305	6	get	get	VERB
ejpam-2714	305	7	a	a	DET
ejpam-2714	305	8	result	result	NOUN
ejpam-2714	305	9	when	when	SCONJ
ejpam-2714	305	10	f	f	PROPN
ejpam-2714	305	11	is	be	AUX
ejpam-2714	305	12	nondecreasing	nondecrease	VERB
ejpam-2714	305	13	in	in	ADP
ejpam-2714	305	14	first	first	ADJ
ejpam-2714	305	15	and	and	CCONJ
ejpam-2714	305	16	second	second	ADJ
ejpam-2714	305	17	variables	variable	NOUN
ejpam-2714	305	18	,	,	PUNCT
ejpam-2714	305	19	(	(	PUNCT
ejpam-2714	305	20	ii	ii	NOUN
ejpam-2714	305	21	)	)	PUNCT
ejpam-2714	305	22	if	if	SCONJ
ejpam-2714	305	23	f(t	f(t	NOUN
ejpam-2714	305	24	,	,	PUNCT
ejpam-2714	305	25	u	u	NOUN
ejpam-2714	305	26	,	,	PUNCT
ejpam-2714	305	27	iqu	iqu	NOUN
ejpam-2714	305	28	)	)	PUNCT
ejpam-2714	305	29	=	=	SYM
ejpam-2714	306	1	0	0	NUM
ejpam-2714	306	2	,	,	PUNCT
ejpam-2714	306	3	in	in	ADP
ejpam-2714	306	4	theorem	theorem	NOUN
ejpam-2714	306	5	3	3	NUM
ejpam-2714	306	6	then	then	ADV
ejpam-2714	306	7	we	we	PRON
ejpam-2714	306	8	obtain	obtain	VERB
ejpam-2714	306	9	the	the	DET
ejpam-2714	306	10	results	result	NOUN
ejpam-2714	306	11	for	for	ADP
ejpam-2714	306	12	g	g	NOUN
ejpam-2714	306	13	nonincreasing	nonincrease	VERB
ejpam-2714	306	14	in	in	ADP
ejpam-2714	306	15	first	first	ADJ
ejpam-2714	306	16	and	and	CCONJ
ejpam-2714	306	17	second	second	ADJ
ejpam-2714	306	18	variables	variable	NOUN
ejpam-2714	306	19	.	.	PUNCT
ejpam-2714	307	1	theorem	theorem	ADJ
ejpam-2714	307	2	4	4	NUM
ejpam-2714	307	3	.	.	PUNCT
ejpam-2714	307	4	assume	assume	VERB
ejpam-2714	307	5	that	that	SCONJ
ejpam-2714	307	6	conditions	condition	NOUN
ejpam-2714	307	7	(	(	PUNCT
ejpam-2714	307	8	a1	a1	NOUN
ejpam-2714	307	9	)	)	PUNCT
ejpam-2714	307	10	,	,	PUNCT
ejpam-2714	307	11	(	(	PUNCT
ejpam-2714	307	12	a2	a2	PROPN
ejpam-2714	307	13	)	)	PUNCT
ejpam-2714	307	14	,	,	PUNCT
ejpam-2714	307	15	and	and	CCONJ
ejpam-2714	307	16	(	(	PUNCT
ejpam-2714	307	17	a3	a3	NOUN
ejpam-2714	307	18	)	)	PUNCT
ejpam-2714	307	19	of	of	ADP
ejpam-2714	307	20	theorem	theorem	ADJ
ejpam-2714	307	21	3	3	NUM
ejpam-2714	307	22	are	be	AUX
ejpam-2714	307	23	true	true	ADJ
ejpam-2714	307	24	.	.	PUNCT
ejpam-2714	308	1	then	then	ADV
ejpam-2714	308	2	for	for	ADP
ejpam-2714	308	3	any	any	DET
ejpam-2714	308	4	solution	solution	NOUN
ejpam-2714	308	5	u(t	u(t	NOUN
ejpam-2714	308	6	)	)	PUNCT
ejpam-2714	308	7	of	of	ADP
ejpam-2714	308	8	(	(	PUNCT
ejpam-2714	308	9	10	10	NUM
ejpam-2714	308	10	)	)	PUNCT
ejpam-2714	308	11	,	,	PUNCT
ejpam-2714	308	12	(	(	PUNCT
ejpam-2714	308	13	11	11	NUM
ejpam-2714	308	14	)	)	PUNCT
ejpam-2714	308	15	with	with	ADP
ejpam-2714	308	16	v0	v0	NOUN
ejpam-2714	308	17	≤	≤	NOUN
ejpam-2714	308	18	u	u	NOUN
ejpam-2714	308	19	≤	≤	NOUN
ejpam-2714	308	20	w0	w0	NOUN
ejpam-2714	308	21	.	.	PUNCT
ejpam-2714	309	1	on	on	ADP
ejpam-2714	309	2	j	j	PROPN
ejpam-2714	309	3	,	,	PUNCT
ejpam-2714	309	4	we	we	PRON
ejpam-2714	309	5	have	have	VERB
ejpam-2714	309	6	the	the	DET
ejpam-2714	309	7	iterates	iterate	NOUN
ejpam-2714	309	8	{	{	PUNCT
ejpam-2714	309	9	v2n	v2n	NOUN
ejpam-2714	309	10	,	,	PUNCT
ejpam-2714	309	11	w2n+1	w2n+1	NOUN
ejpam-2714	309	12	}	}	PUNCT
ejpam-2714	309	13	and	and	CCONJ
ejpam-2714	309	14	{	{	PUNCT
ejpam-2714	309	15	v2n+1	v2n+1	PROPN
ejpam-2714	309	16	,	,	PUNCT
ejpam-2714	309	17	w2n	w2n	PRON
ejpam-2714	309	18	}	}	PUNCT
ejpam-2714	309	19	satisfying	satisfy	VERB
ejpam-2714	309	20	v0	v0	NOUN
ejpam-2714	309	21	≤	≤	NOUN
ejpam-2714	309	22	w1	w1	NOUN
ejpam-2714	309	23	≤	≤	NOUN
ejpam-2714	309	24	.	.	PUNCT
ejpam-2714	309	25	.	.	PUNCT
ejpam-2714	310	1	.≤	.≤	PUNCT
ejpam-2714	311	1	v2n	v2n	PROPN
ejpam-2714	311	2	≤	≤	PROPN
ejpam-2714	311	3	w2n+1	w2n+1	PROPN
ejpam-2714	311	4	≤	≤	PUNCT
ejpam-2714	311	5	u≤	u≤	PROPN
ejpam-2714	311	6	v2n+1	v2n+1	PROPN
ejpam-2714	311	7	≤	≤	NOUN
ejpam-2714	311	8	w2n	w2n	PRON
ejpam-2714	311	9	≤	≤	NUM
ejpam-2714	311	10	.	.	PUNCT
ejpam-2714	311	11	.	.	PUNCT
ejpam-2714	312	1	.≤	.≤	NOUN
ejpam-2714	313	1	v1	v1	PROPN
ejpam-2714	313	2	≤	≤	NUM
ejpam-2714	313	3	w0	w0	NOUN
ejpam-2714	313	4	.	.	PUNCT
ejpam-2714	314	1	(	(	PUNCT
ejpam-2714	314	2	25	25	NUM
ejpam-2714	314	3	)	)	PUNCT
ejpam-2714	314	4	for	for	ADP
ejpam-2714	314	5	each	each	DET
ejpam-2714	314	6	n≥	n≥	NOUN
ejpam-2714	314	7	1	1	NUM
ejpam-2714	314	8	on	on	ADP
ejpam-2714	314	9	j	j	PROPN
ejpam-2714	314	10	,	,	PUNCT
ejpam-2714	314	11	further	far	ADV
ejpam-2714	314	12	more	more	ADV
ejpam-2714	314	13	{	{	PUNCT
ejpam-2714	314	14	v2n	v2n	NOUN
ejpam-2714	314	15	,	,	PUNCT
ejpam-2714	314	16	w2n+1	w2n+1	NOUN
ejpam-2714	314	17	}	}	PUNCT
ejpam-2714	314	18	→	→	SYM
ejpam-2714	314	19	ρ	ρ	PROPN
ejpam-2714	314	20	and	and	CCONJ
ejpam-2714	314	21	{	{	PUNCT
ejpam-2714	314	22	v2n+1	v2n+1	PROPN
ejpam-2714	314	23	,	,	PUNCT
ejpam-2714	314	24	w2n	w2n	X
ejpam-2714	314	25	}	}	PUNCT
ejpam-2714	314	26	→	→	SYM
ejpam-2714	314	27	r	r	NOUN
ejpam-2714	314	28	in	in	ADP
ejpam-2714	314	29	c1[j	c1[j	NOUN
ejpam-2714	314	30	,	,	PUNCT
ejpam-2714	314	31	r	r	X
ejpam-2714	314	32	]	]	X
ejpam-2714	314	33	uniformly	uniformly	ADV
ejpam-2714	314	34	and	and	CCONJ
ejpam-2714	314	35	monotonically	monotonically	ADV
ejpam-2714	314	36	,	,	PUNCT
ejpam-2714	314	37	such	such	ADJ
ejpam-2714	314	38	that	that	SCONJ
ejpam-2714	314	39	ρ	ρ	NOUN
ejpam-2714	314	40	and	and	CCONJ
ejpam-2714	314	41	r	r	NOUN
ejpam-2714	314	42	are	be	AUX
ejpam-2714	314	43	coupled	couple	VERB
ejpam-2714	314	44	minimal	minimal	ADJ
ejpam-2714	314	45	and	and	CCONJ
ejpam-2714	314	46	maximal	maximal	ADJ
ejpam-2714	314	47	solutions	solution	NOUN
ejpam-2714	314	48	of	of	ADP
ejpam-2714	314	49	(	(	PUNCT
ejpam-2714	314	50	10	10	NUM
ejpam-2714	314	51	)	)	PUNCT
ejpam-2714	314	52	and	and	CCONJ
ejpam-2714	314	53	(	(	PUNCT
ejpam-2714	314	54	11	11	NUM
ejpam-2714	314	55	)	)	PUNCT
ejpam-2714	314	56	,	,	PUNCT
ejpam-2714	314	57	respectively	respectively	ADV
ejpam-2714	314	58	,	,	PUNCT
ejpam-2714	314	59	that	that	ADV
ejpam-2714	314	60	is	is	ADV
ejpam-2714	314	61	,	,	PUNCT
ejpam-2714	314	62	ρ	ρ	PROPN
ejpam-2714	314	63	≤	≤	NUM
ejpam-2714	314	64	u≤	u≤	NUM
ejpam-2714	314	65	r	r	NOUN
ejpam-2714	314	66	,	,	PUNCT
ejpam-2714	314	67	ρ	ρ	NOUN
ejpam-2714	314	68	and	and	CCONJ
ejpam-2714	314	69	r	r	NOUN
ejpam-2714	314	70	satisfy	satisfy	NOUN
ejpam-2714	314	71	the	the	DET
ejpam-2714	314	72	coupled	couple	VERB
ejpam-2714	314	73	system	system	NOUN
ejpam-2714	314	74	c	c	AUX
ejpam-2714	314	75	dqρ	dqρ	VERB
ejpam-2714	314	76	=	=	NOUN
ejpam-2714	314	77	f(t	f(t	NOUN
ejpam-2714	314	78	,	,	PUNCT
ejpam-2714	314	79	ρ	ρ	NOUN
ejpam-2714	314	80	,	,	PUNCT
ejpam-2714	314	81	iq(ρ	iq(ρ	NOUN
ejpam-2714	314	82	)	)	PUNCT
ejpam-2714	314	83	)	)	PUNCT
ejpam-2714	315	1	+	+	CCONJ
ejpam-2714	316	1	g(t	g(t	PROPN
ejpam-2714	316	2	,	,	PUNCT
ejpam-2714	316	3	r	r	NOUN
ejpam-2714	316	4	,	,	PUNCT
ejpam-2714	316	5	iq(r	iq(r	NOUN
ejpam-2714	316	6	)	)	PUNCT
ejpam-2714	316	7	)	)	PUNCT
ejpam-2714	316	8	,	,	PUNCT
ejpam-2714	316	9	g(ρ(0),ρ(t	g(ρ(0),ρ(t	NOUN
ejpam-2714	316	10	)	)	PUNCT
ejpam-2714	316	11	)	)	PUNCT
ejpam-2714	317	1	=	=	PUNCT
ejpam-2714	317	2	0	0	NUM
ejpam-2714	317	3	,	,	PUNCT
ejpam-2714	317	4	c	c	PROPN
ejpam-2714	317	5	dqr	dqr	PROPN
ejpam-2714	317	6	=	=	SYM
ejpam-2714	317	7	f(t	f(t	NOUN
ejpam-2714	317	8	,	,	PUNCT
ejpam-2714	317	9	r	r	NOUN
ejpam-2714	317	10	,	,	PUNCT
ejpam-2714	317	11	iq(r	iq(r	NOUN
ejpam-2714	317	12	)	)	PUNCT
ejpam-2714	317	13	)	)	PUNCT
ejpam-2714	318	1	+	+	CCONJ
ejpam-2714	318	2	g(t	g(t	PROPN
ejpam-2714	318	3	,	,	PUNCT
ejpam-2714	318	4	ρ	ρ	NOUN
ejpam-2714	318	5	,	,	PUNCT
ejpam-2714	318	6	iq(ρ	iq(ρ	NUM
ejpam-2714	318	7	)	)	PUNCT
ejpam-2714	318	8	)	)	PUNCT
ejpam-2714	318	9	g(r(0	g(r(0	PROPN
ejpam-2714	318	10	)	)	PUNCT
ejpam-2714	318	11	,	,	PUNCT
ejpam-2714	318	12	r(t	r(t	NOUN
ejpam-2714	318	13	)	)	PUNCT
ejpam-2714	318	14	)	)	PUNCT
ejpam-2714	319	1	=	=	PUNCT
ejpam-2714	319	2	0	0	X
ejpam-2714	319	3	.	.	PUNCT
ejpam-2714	320	1	proof	proof	NOUN
ejpam-2714	320	2	.	.	PUNCT
ejpam-2714	321	1	consider	consider	VERB
ejpam-2714	321	2	the	the	DET
ejpam-2714	321	3	following	follow	VERB
ejpam-2714	321	4	ivp	ivp	X
ejpam-2714	321	5	c	c	PROPN
ejpam-2714	321	6	dqvn+1	dqvn+1	PROPN
ejpam-2714	322	1	=	=	NOUN
ejpam-2714	322	2	f(t	f(t	PROPN
ejpam-2714	322	3	,	,	PUNCT
ejpam-2714	322	4	wn	wn	PROPN
ejpam-2714	322	5	,	,	PUNCT
ejpam-2714	322	6	iq(wn	iq(wn	PROPN
ejpam-2714	322	7	)	)	PUNCT
ejpam-2714	322	8	)	)	PUNCT
ejpam-2714	323	1	+	+	CCONJ
ejpam-2714	324	1	g(t	g(t	PROPN
ejpam-2714	324	2	,	,	PUNCT
ejpam-2714	324	3	vn	vn	NOUN
ejpam-2714	324	4	,	,	PUNCT
ejpam-2714	324	5	iq(vn	iq(vn	PROPN
ejpam-2714	324	6	)	)	PUNCT
ejpam-2714	324	7	)	)	PUNCT
ejpam-2714	324	8	,	,	PUNCT
ejpam-2714	324	9	(	(	PUNCT
ejpam-2714	324	10	26	26	NUM
ejpam-2714	324	11	)	)	PUNCT
ejpam-2714	324	12	vn+1(0	vn+1(0	PUNCT
ejpam-2714	324	13	)	)	PUNCT
ejpam-2714	325	1	=	=	SYM
ejpam-2714	325	2	wn(0)−	wn(0)−	NOUN
ejpam-2714	325	3	1	1	NUM
ejpam-2714	325	4	m	m	NOUN
ejpam-2714	325	5	g(wn(0	g(wn(0	PROPN
ejpam-2714	325	6	)	)	PUNCT
ejpam-2714	325	7	,	,	PUNCT
ejpam-2714	325	8	wn(t	wn(t	NUM
ejpam-2714	325	9	)	)	PUNCT
ejpam-2714	325	10	)	)	PUNCT
ejpam-2714	325	11	,	,	PUNCT
ejpam-2714	325	12	(	(	PUNCT
ejpam-2714	325	13	27	27	NUM
ejpam-2714	325	14	)	)	PUNCT
ejpam-2714	325	15	c	c	NOUN
ejpam-2714	325	16	dqwn+1	dqwn+1	NOUN
ejpam-2714	325	17	=	=	SYM
ejpam-2714	325	18	f(t	f(t	NOUN
ejpam-2714	325	19	,	,	PUNCT
ejpam-2714	325	20	vn	vn	NOUN
ejpam-2714	325	21	,	,	PUNCT
ejpam-2714	325	22	iq(vn	iq(vn	PROPN
ejpam-2714	325	23	)	)	PUNCT
ejpam-2714	325	24	)	)	PUNCT
ejpam-2714	326	1	+	+	CCONJ
ejpam-2714	327	1	g(t	g(t	PROPN
ejpam-2714	327	2	,	,	PUNCT
ejpam-2714	327	3	wn	wn	PROPN
ejpam-2714	327	4	,	,	PUNCT
ejpam-2714	327	5	iq(wn	iq(wn	PROPN
ejpam-2714	327	6	)	)	PUNCT
ejpam-2714	327	7	)	)	PUNCT
ejpam-2714	327	8	,	,	PUNCT
ejpam-2714	327	9	(	(	PUNCT
ejpam-2714	327	10	28	28	NUM
ejpam-2714	327	11	)	)	PUNCT
ejpam-2714	327	12	wn+1(0	wn+1(0	PUNCT
ejpam-2714	327	13	)	)	PUNCT
ejpam-2714	328	1	=	=	SYM
ejpam-2714	328	2	vn(0)−	vn(0)−	VERB
ejpam-2714	328	3	1	1	NUM
ejpam-2714	328	4	m	m	NOUN
ejpam-2714	328	5	g(vn(0	g(vn(0	PROPN
ejpam-2714	328	6	)	)	PUNCT
ejpam-2714	328	7	,	,	PUNCT
ejpam-2714	328	8	vn(t	vn(t	NUM
ejpam-2714	328	9	)	)	PUNCT
ejpam-2714	328	10	)	)	PUNCT
ejpam-2714	328	11	,	,	PUNCT
ejpam-2714	328	12	(	(	PUNCT
ejpam-2714	328	13	29	29	NUM
ejpam-2714	328	14	)	)	PUNCT
ejpam-2714	328	15	where	where	SCONJ
ejpam-2714	328	16	v0	v0	NOUN
ejpam-2714	328	17	≤	≤	NUM
ejpam-2714	328	18	w0	w0	NOUN
ejpam-2714	328	19	.	.	PUNCT
ejpam-2714	329	1	our	our	PRON
ejpam-2714	329	2	aim	aim	NOUN
ejpam-2714	329	3	is	be	AUX
ejpam-2714	329	4	to	to	PART
ejpam-2714	329	5	show	show	VERB
ejpam-2714	329	6	that	that	SCONJ
ejpam-2714	329	7	the	the	DET
ejpam-2714	329	8	solutions	solution	NOUN
ejpam-2714	329	9	vn+1	vn+1	PROPN
ejpam-2714	329	10	,	,	PUNCT
ejpam-2714	329	11	wn+1	wn+1	VERB
ejpam-2714	329	12	of	of	ADP
ejpam-2714	329	13	(	(	PUNCT
ejpam-2714	329	14	26	26	NUM
ejpam-2714	329	15	)	)	PUNCT
ejpam-2714	329	16	,	,	PUNCT
ejpam-2714	329	17	(	(	PUNCT
ejpam-2714	329	18	27	27	NUM
ejpam-2714	329	19	)	)	PUNCT
ejpam-2714	329	20	,	,	PUNCT
ejpam-2714	329	21	and	and	CCONJ
ejpam-2714	329	22	(	(	PUNCT
ejpam-2714	329	23	28	28	NUM
ejpam-2714	329	24	)	)	PUNCT
ejpam-2714	329	25	,	,	PUNCT
ejpam-2714	329	26	(	(	PUNCT
ejpam-2714	329	27	29	29	NUM
ejpam-2714	329	28	)	)	PUNCT
ejpam-2714	329	29	satisfy	satisfy	NOUN
ejpam-2714	329	30	v0	v0	NOUN
ejpam-2714	329	31	≤	≤	ADJ
ejpam-2714	329	32	w1	w1	NOUN
ejpam-2714	329	33	≤	≤	NOUN
ejpam-2714	329	34	.	.	PUNCT
ejpam-2714	329	35	.	.	PUNCT
ejpam-2714	329	36	.≤	.≤	PUNCT
ejpam-2714	330	1	v2n	v2n	PROPN
ejpam-2714	330	2	≤	≤	PROPN
ejpam-2714	330	3	w2n+1	w2n+1	PROPN
ejpam-2714	330	4	≤	≤	PUNCT
ejpam-2714	330	5	u≤	u≤	PROPN
ejpam-2714	330	6	v2n+1	v2n+1	PROPN
ejpam-2714	330	7	≤	≤	NOUN
ejpam-2714	330	8	w2n	w2n	PRON
ejpam-2714	330	9	≤	≤	NUM
ejpam-2714	330	10	.	.	PUNCT
ejpam-2714	330	11	.	.	PUNCT
ejpam-2714	331	1	.≤	.≤	NOUN
ejpam-2714	332	1	v1	v1	PROPN
ejpam-2714	332	2	≤	≤	NUM
ejpam-2714	332	3	w0	w0	NOUN
ejpam-2714	332	4	.	.	PUNCT
ejpam-2714	333	1	clearly	clearly	ADV
ejpam-2714	333	2	the	the	DET
ejpam-2714	333	3	ivps	ivps	PROPN
ejpam-2714	333	4	(	(	PUNCT
ejpam-2714	333	5	26	26	NUM
ejpam-2714	333	6	)	)	PUNCT
ejpam-2714	333	7	,	,	PUNCT
ejpam-2714	333	8	(	(	PUNCT
ejpam-2714	333	9	27	27	NUM
ejpam-2714	333	10	)	)	PUNCT
ejpam-2714	333	11	,	,	PUNCT
ejpam-2714	333	12	and	and	CCONJ
ejpam-2714	333	13	(	(	PUNCT
ejpam-2714	333	14	28	28	NUM
ejpam-2714	333	15	)	)	PUNCT
ejpam-2714	333	16	,	,	PUNCT
ejpam-2714	333	17	(	(	PUNCT
ejpam-2714	333	18	29	29	NUM
ejpam-2714	333	19	)	)	PUNCT
ejpam-2714	333	20	have	have	VERB
ejpam-2714	333	21	unique	unique	ADJ
ejpam-2714	333	22	solutions	solution	NOUN
ejpam-2714	333	23	for	for	ADP
ejpam-2714	333	24	each	each	DET
ejpam-2714	333	25	n	n	NOUN
ejpam-2714	333	26	=	=	NOUN
ejpam-2714	333	27	0,1,2	0,1,2	NUM
ejpam-2714	333	28	,	,	PUNCT
ejpam-2714	333	29	.	.	PUNCT
ejpam-2714	333	30	.	.	PUNCT
ejpam-2714	334	1	.	.	PUNCT
ejpam-2714	335	1	denoted	denote	VERB
ejpam-2714	335	2	by	by	ADP
ejpam-2714	335	3	vn+1	vn+1	PROPN
ejpam-2714	335	4	,	,	PUNCT
ejpam-2714	335	5	wn+1	wn+1	AUX
ejpam-2714	335	6	.	.	PUNCT
ejpam-2714	336	1	first	first	ADV
ejpam-2714	336	2	we	we	PRON
ejpam-2714	336	3	show	show	VERB
ejpam-2714	336	4	that	that	SCONJ
ejpam-2714	336	5	v0	v0	NOUN
ejpam-2714	336	6	≤	≤	NOUN
ejpam-2714	336	7	v1	v1	PROPN
ejpam-2714	336	8	≤	≤	NOUN
ejpam-2714	336	9	w1	w1	NOUN
ejpam-2714	336	10	≤	≤	NOUN
ejpam-2714	336	11	w0	w0	NOUN
ejpam-2714	336	12	.	.	PUNCT
ejpam-2714	337	1	since	since	SCONJ
ejpam-2714	337	2	v0	v0	NOUN
ejpam-2714	337	3	is	be	AUX
ejpam-2714	337	4	a	a	DET
ejpam-2714	337	5	coupled	couple	VERB
ejpam-2714	337	6	lower	low	ADJ
ejpam-2714	337	7	solution	solution	NOUN
ejpam-2714	337	8	of	of	ADP
ejpam-2714	337	9	type	type	NOUN
ejpam-2714	337	10	i	i	PRON
ejpam-2714	337	11	for	for	ADP
ejpam-2714	337	12	(	(	PUNCT
ejpam-2714	337	13	10	10	NUM
ejpam-2714	337	14	)	)	PUNCT
ejpam-2714	337	15	,	,	PUNCT
ejpam-2714	337	16	(	(	PUNCT
ejpam-2714	337	17	11	11	X
ejpam-2714	337	18	)	)	PUNCT
ejpam-2714	337	19	we	we	PRON
ejpam-2714	337	20	have	have	VERB
ejpam-2714	337	21	c	c	PROPN
ejpam-2714	337	22	dqv0(t)≤	dqv0(t)≤	PROPN
ejpam-2714	337	23	f(t	f(t	PROPN
ejpam-2714	337	24	,	,	PUNCT
ejpam-2714	337	25	v0(t	v0(t	PROPN
ejpam-2714	337	26	)	)	PUNCT
ejpam-2714	337	27	,	,	PUNCT
ejpam-2714	337	28	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	337	29	)	)	PUNCT
ejpam-2714	337	30	)	)	PUNCT
ejpam-2714	337	31	)	)	PUNCT
ejpam-2714	338	1	+	+	CCONJ
ejpam-2714	338	2	g(t	g(t	PROPN
ejpam-2714	338	3	,	,	PUNCT
ejpam-2714	338	4	w0(t	w0(t	PROPN
ejpam-2714	338	5	)	)	PUNCT
ejpam-2714	338	6	,	,	PUNCT
ejpam-2714	338	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	338	8	)	)	PUNCT
ejpam-2714	338	9	)	)	PUNCT
ejpam-2714	338	10	)	)	PUNCT
ejpam-2714	338	11	,	,	PUNCT
ejpam-2714	338	12	g(v0(0	g(v0(0	NOUN
ejpam-2714	338	13	)	)	PUNCT
ejpam-2714	338	14	,	,	PUNCT
ejpam-2714	338	15	v0(t	v0(t	PROPN
ejpam-2714	338	16	)	)	PUNCT
ejpam-2714	338	17	)	)	PUNCT
ejpam-2714	338	18	≤	≤	NOUN
ejpam-2714	338	19	0	0	NUM
ejpam-2714	338	20	.	.	PUNCT
ejpam-2714	338	21	setting	set	VERB
ejpam-2714	338	22	n=	n=	ADJ
ejpam-2714	338	23	0	0	PUNCT
ejpam-2714	339	1	in	in	ADP
ejpam-2714	339	2	(	(	PUNCT
ejpam-2714	339	3	26	26	NUM
ejpam-2714	339	4	)	)	PUNCT
ejpam-2714	339	5	,	,	PUNCT
ejpam-2714	339	6	(	(	PUNCT
ejpam-2714	339	7	27	27	NUM
ejpam-2714	339	8	)	)	PUNCT
ejpam-2714	339	9	,	,	PUNCT
ejpam-2714	339	10	we	we	PRON
ejpam-2714	339	11	get	get	VERB
ejpam-2714	339	12	that	that	DET
ejpam-2714	339	13	v1	v1	NOUN
ejpam-2714	339	14	is	be	AUX
ejpam-2714	339	15	a	a	DET
ejpam-2714	339	16	solution	solution	NOUN
ejpam-2714	339	17	of	of	ADP
ejpam-2714	339	18	the	the	DET
ejpam-2714	339	19	boundary	boundary	ADJ
ejpam-2714	339	20	value	value	NOUN
ejpam-2714	339	21	problem	problem	NOUN
ejpam-2714	339	22	,	,	PUNCT
ejpam-2714	339	23	c	c	NOUN
ejpam-2714	339	24	dqv1(t	dqv1(t	X
ejpam-2714	339	25	)	)	PUNCT
ejpam-2714	340	1	=	=	NOUN
ejpam-2714	340	2	f(t	f(t	NOUN
ejpam-2714	340	3	,	,	PUNCT
ejpam-2714	340	4	w0(t	w0(t	PROPN
ejpam-2714	340	5	)	)	PUNCT
ejpam-2714	340	6	,	,	PUNCT
ejpam-2714	340	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	340	8	)	)	PUNCT
ejpam-2714	340	9	)	)	PUNCT
ejpam-2714	340	10	)	)	PUNCT
ejpam-2714	341	1	+	+	CCONJ
ejpam-2714	341	2	g(t	g(t	PROPN
ejpam-2714	341	3	,	,	PUNCT
ejpam-2714	341	4	v0(t	v0(t	PROPN
ejpam-2714	341	5	)	)	PUNCT
ejpam-2714	341	6	,	,	PUNCT
ejpam-2714	341	7	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	341	8	)	)	PUNCT
ejpam-2714	341	9	)	)	PUNCT
ejpam-2714	341	10	)	)	PUNCT
ejpam-2714	341	11	,	,	PUNCT
ejpam-2714	341	12	v1(0	v1(0	NOUN
ejpam-2714	341	13	)	)	PUNCT
ejpam-2714	342	1	=	=	SYM
ejpam-2714	342	2	w0(0)−	w0(0)−	NOUN
ejpam-2714	342	3	1	1	NUM
ejpam-2714	342	4	m	m	PROPN
ejpam-2714	342	5	g(w0(0	g(w0(0	NOUN
ejpam-2714	342	6	)	)	PUNCT
ejpam-2714	342	7	,	,	PUNCT
ejpam-2714	342	8	w0(t	w0(t	PROPN
ejpam-2714	342	9	)	)	PUNCT
ejpam-2714	342	10	)	)	PUNCT
ejpam-2714	342	11	.	.	PUNCT
ejpam-2714	343	1	j.	j.	PROPN
ejpam-2714	343	2	devi	devi	PROPN
ejpam-2714	343	3	,	,	PUNCT
ejpam-2714	343	4	ch	ch	PROPN
ejpam-2714	343	5	.	.	PUNCT
ejpam-2714	343	6	sreedhar	sreedhar	PROPN
ejpam-2714	343	7	/	/	SYM
ejpam-2714	343	8	eur	eur	PROPN
ejpam-2714	343	9	.	.	PUNCT
ejpam-2714	344	1	j.	j.	PROPN
ejpam-2714	344	2	pure	pure	PROPN
ejpam-2714	344	3	appl	appl	PROPN
ejpam-2714	344	4	.	.	PROPN
ejpam-2714	344	5	math	math	PROPN
ejpam-2714	344	6	,	,	PUNCT
ejpam-2714	344	7	9	9	NUM
ejpam-2714	344	8	(	(	PUNCT
ejpam-2714	344	9	2016	2016	NUM
ejpam-2714	344	10	)	)	PUNCT
ejpam-2714	344	11	,	,	PUNCT
ejpam-2714	344	12	346	346	NUM
ejpam-2714	344	13	-	-	SYM
ejpam-2714	344	14	359	359	NUM
ejpam-2714	344	15	356	356	NUM
ejpam-2714	344	16	set	set	VERB
ejpam-2714	344	17	p(t	p(t	NOUN
ejpam-2714	344	18	)	)	PUNCT
ejpam-2714	344	19	=	=	SYM
ejpam-2714	344	20	v0(t)−	v0(t)−	PROPN
ejpam-2714	344	21	v1(t	v1(t	NUM
ejpam-2714	344	22	)	)	PUNCT
ejpam-2714	344	23	,	,	PUNCT
ejpam-2714	344	24	then	then	ADV
ejpam-2714	344	25	by	by	ADP
ejpam-2714	344	26	taking	take	VERB
ejpam-2714	344	27	the	the	DET
ejpam-2714	344	28	caputo	caputo	PROPN
ejpam-2714	344	29	fractional	fractional	PROPN
ejpam-2714	344	30	derivative	derivative	NOUN
ejpam-2714	344	31	on	on	ADP
ejpam-2714	344	32	both	both	DET
ejpam-2714	344	33	sides	side	NOUN
ejpam-2714	344	34	and	and	CCONJ
ejpam-2714	344	35	due	due	ADP
ejpam-2714	344	36	to	to	ADP
ejpam-2714	344	37	the	the	DET
ejpam-2714	344	38	fact	fact	NOUN
ejpam-2714	344	39	that	that	SCONJ
ejpam-2714	344	40	f	f	PROPN
ejpam-2714	344	41	and	and	CCONJ
ejpam-2714	344	42	g	g	PROPN
ejpam-2714	344	43	are	be	AUX
ejpam-2714	344	44	in	in	ADP
ejpam-2714	344	45	monotonic	monotonic	ADJ
ejpam-2714	344	46	in	in	ADP
ejpam-2714	344	47	the	the	DET
ejpam-2714	344	48	second	second	ADJ
ejpam-2714	344	49	and	and	CCONJ
ejpam-2714	344	50	third	third	ADJ
ejpam-2714	344	51	variable	variable	NOUN
ejpam-2714	344	52	we	we	PRON
ejpam-2714	344	53	get	get	VERB
ejpam-2714	344	54	that	that	PRON
ejpam-2714	344	55	c	c	PROPN
ejpam-2714	344	56	dqp(t	dqp(t	PROPN
ejpam-2714	344	57	)	)	PUNCT
ejpam-2714	345	1	=	=	PROPN
ejpam-2714	345	2	c	c	NOUN
ejpam-2714	345	3	dqv0(t)−	dqv0(t)−	PROPN
ejpam-2714	345	4	c	c	PROPN
ejpam-2714	345	5	dqv1(t	dqv1(t	X
ejpam-2714	345	6	)	)	PUNCT
ejpam-2714	345	7	≤[f(t	≤[f(t	NOUN
ejpam-2714	345	8	,	,	PUNCT
ejpam-2714	345	9	v0(t	v0(t	PROPN
ejpam-2714	345	10	)	)	PUNCT
ejpam-2714	345	11	,	,	PUNCT
ejpam-2714	345	12	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	345	13	)	)	PUNCT
ejpam-2714	345	14	)	)	PUNCT
ejpam-2714	345	15	)	)	PUNCT
ejpam-2714	346	1	+	+	CCONJ
ejpam-2714	346	2	g(t	g(t	PROPN
ejpam-2714	346	3	,	,	PUNCT
ejpam-2714	346	4	w0(t	w0(t	PROPN
ejpam-2714	346	5	)	)	PUNCT
ejpam-2714	346	6	,	,	PUNCT
ejpam-2714	346	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	346	8	)	)	PUNCT
ejpam-2714	346	9	)	)	PUNCT
ejpam-2714	346	10	)	)	PUNCT
ejpam-2714	346	11	]	]	PUNCT
ejpam-2714	347	1	−	−	PUNCT
ejpam-2714	348	1	[	[	X
ejpam-2714	348	2	f(t	f(t	PROPN
ejpam-2714	348	3	,	,	PUNCT
ejpam-2714	348	4	w0(t	w0(t	PROPN
ejpam-2714	348	5	)	)	PUNCT
ejpam-2714	348	6	,	,	PUNCT
ejpam-2714	348	7	iq(w0(t	iq(w0(t	PROPN
ejpam-2714	348	8	)	)	PUNCT
ejpam-2714	348	9	)	)	PUNCT
ejpam-2714	348	10	)	)	PUNCT
ejpam-2714	349	1	+	+	CCONJ
ejpam-2714	350	1	g(t	g(t	PROPN
ejpam-2714	350	2	,	,	PUNCT
ejpam-2714	350	3	v0(t	v0(t	PROPN
ejpam-2714	350	4	)	)	PUNCT
ejpam-2714	350	5	,	,	PUNCT
ejpam-2714	350	6	iq(v0(t	iq(v0(t	PROPN
ejpam-2714	350	7	)	)	PUNCT
ejpam-2714	350	8	)	)	PUNCT
ejpam-2714	350	9	)	)	PUNCT
ejpam-2714	350	10	]	]	PUNCT
ejpam-2714	350	11	which	which	PRON
ejpam-2714	350	12	means	mean	VERB
ejpam-2714	350	13	that	that	SCONJ
ejpam-2714	350	14	c	c	PROPN
ejpam-2714	350	15	dqp(t)≤	dqp(t)≤	NOUN
ejpam-2714	350	16	0	0	PUNCT
ejpam-2714	350	17	.	.	PUNCT
ejpam-2714	351	1	now	now	ADV
ejpam-2714	351	2	p(0	p(0	NOUN
ejpam-2714	351	3	)	)	PUNCT
ejpam-2714	351	4	=	=	SYM
ejpam-2714	351	5	v0(0)−	v0(0)−	PROPN
ejpam-2714	351	6	w0(0	w0(0	PROPN
ejpam-2714	351	7	)	)	PUNCT
ejpam-2714	352	1	+	+	CCONJ
ejpam-2714	352	2	1	1	NUM
ejpam-2714	352	3	m	m	PROPN
ejpam-2714	352	4	g(w0(0	g(w0(0	NOUN
ejpam-2714	352	5	)	)	PUNCT
ejpam-2714	352	6	,	,	PUNCT
ejpam-2714	352	7	w0(t	w0(t	PROPN
ejpam-2714	352	8	)	)	PUNCT
ejpam-2714	352	9	)	)	PUNCT
ejpam-2714	353	1	≤	≤	NUM
ejpam-2714	353	2	1	1	NUM
ejpam-2714	353	3	m	m	NOUN
ejpam-2714	353	4	g(v0(0	g(v0(0	NOUN
ejpam-2714	353	5	)	)	PUNCT
ejpam-2714	353	6	,	,	PUNCT
ejpam-2714	353	7	v0(t	v0(t	PROPN
ejpam-2714	353	8	)	)	PUNCT
ejpam-2714	353	9	)	)	PUNCT
ejpam-2714	353	10	≤	≤	ADV
ejpam-2714	353	11	0	0	X
ejpam-2714	353	12	.	.	PUNCT
ejpam-2714	354	1	on	on	ADP
ejpam-2714	354	2	applying	apply	VERB
ejpam-2714	354	3	corollary	corollary	ADJ
ejpam-2714	354	4	2	2	NUM
ejpam-2714	354	5	we	we	PRON
ejpam-2714	354	6	arrive	arrive	VERB
ejpam-2714	354	7	at	at	ADP
ejpam-2714	354	8	v0(t	v0(t	NOUN
ejpam-2714	354	9	)	)	PUNCT
ejpam-2714	354	10	≤	≤	NOUN
ejpam-2714	354	11	v1(t	v1(t	PRON
ejpam-2714	354	12	)	)	PUNCT
ejpam-2714	354	13	,	,	PUNCT
ejpam-2714	354	14	on	on	ADP
ejpam-2714	354	15	j	j	PROPN
ejpam-2714	354	16	.	.	PUNCT
ejpam-2714	355	1	in	in	ADP
ejpam-2714	355	2	a	a	DET
ejpam-2714	355	3	similar	similar	ADJ
ejpam-2714	355	4	fashion	fashion	NOUN
ejpam-2714	355	5	we	we	PRON
ejpam-2714	355	6	get	get	VERB
ejpam-2714	355	7	w1(t	w1(t	NOUN
ejpam-2714	355	8	)	)	PUNCT
ejpam-2714	355	9	≤	≤	NUM
ejpam-2714	355	10	w0(t	w0(t	PROPN
ejpam-2714	355	11	)	)	PUNCT
ejpam-2714	355	12	,	,	PUNCT
ejpam-2714	355	13	on	on	ADP
ejpam-2714	355	14	j	j	PROPN
ejpam-2714	355	15	.	.	PUNCT
ejpam-2714	356	1	next	next	ADV
ejpam-2714	356	2	we	we	PRON
ejpam-2714	356	3	proceed	proceed	VERB
ejpam-2714	356	4	to	to	PART
ejpam-2714	356	5	show	show	VERB
ejpam-2714	356	6	that	that	DET
ejpam-2714	356	7	v0	v0	NOUN
ejpam-2714	356	8	≤	≤	NOUN
ejpam-2714	356	9	w1	w1	NOUN
ejpam-2714	356	10	≤	≤	PUNCT
ejpam-2714	356	11	v2	v2	NOUN
ejpam-2714	356	12	≤	≤	NUM
ejpam-2714	356	13	w3	w3	PROPN
ejpam-2714	356	14	≤	≤	PROPN
ejpam-2714	356	15	u≤	u≤	PROPN
ejpam-2714	356	16	v3	v3	PROPN
ejpam-2714	356	17	≤	≤	PROPN
ejpam-2714	356	18	w2	w2	NOUN
ejpam-2714	356	19	≤	≤	PROPN
ejpam-2714	356	20	v1	v1	PROPN
ejpam-2714	356	21	≤	≤	NUM
ejpam-2714	356	22	w0	w0	NOUN
ejpam-2714	356	23	.	.	PUNCT
ejpam-2714	357	1	(	(	PUNCT
ejpam-2714	357	2	30	30	NUM
ejpam-2714	357	3	)	)	PUNCT
ejpam-2714	357	4	writing	write	VERB
ejpam-2714	357	5	p	p	X
ejpam-2714	357	6	=	=	PUNCT
ejpam-2714	357	7	u	u	NOUN
ejpam-2714	357	8	−	−	PROPN
ejpam-2714	357	9	v1	v1	NOUN
ejpam-2714	357	10	,	,	PUNCT
ejpam-2714	357	11	and	and	CCONJ
ejpam-2714	357	12	working	work	VERB
ejpam-2714	357	13	as	as	ADP
ejpam-2714	357	14	earlier	early	ADV
ejpam-2714	357	15	,	,	PUNCT
ejpam-2714	357	16	we	we	PRON
ejpam-2714	357	17	get	get	VERB
ejpam-2714	357	18	c	c	PROPN
ejpam-2714	357	19	dqp(t	dqp(t	PROPN
ejpam-2714	357	20	)	)	PUNCT
ejpam-2714	357	21	≤	≤	NOUN
ejpam-2714	357	22	0	0	NUM
ejpam-2714	357	23	and	and	CCONJ
ejpam-2714	357	24	p(t	p(t	NOUN
ejpam-2714	357	25	)	)	PUNCT
ejpam-2714	357	26	≤	≤	NOUN
ejpam-2714	357	27	0	0	NUM
ejpam-2714	358	1	again	again	ADV
ejpam-2714	358	2	an	an	DET
ejpam-2714	358	3	application	application	NOUN
ejpam-2714	358	4	of	of	ADP
ejpam-2714	358	5	corollary	corollary	ADJ
ejpam-2714	358	6	2	2	NUM
ejpam-2714	358	7	gives	give	VERB
ejpam-2714	358	8	u(t	u(t	NOUN
ejpam-2714	358	9	)	)	PUNCT
ejpam-2714	358	10	≤	≤	NOUN
ejpam-2714	359	1	v1(t	v1(t	PRON
ejpam-2714	359	2	)	)	PUNCT
ejpam-2714	359	3	,	,	PUNCT
ejpam-2714	359	4	on	on	ADP
ejpam-2714	359	5	j	j	PROPN
ejpam-2714	359	6	.	.	PUNCT
ejpam-2714	360	1	a	a	DET
ejpam-2714	360	2	similar	similar	ADJ
ejpam-2714	360	3	argument	argument	NOUN
ejpam-2714	360	4	yields	yield	VERB
ejpam-2714	360	5	w1	w1	NOUN
ejpam-2714	360	6	≤	≤	PROPN
ejpam-2714	360	7	u	u	PROPN
ejpam-2714	360	8	,	,	PUNCT
ejpam-2714	360	9	v2	v2	PROPN
ejpam-2714	360	10	≤	≤	NUM
ejpam-2714	360	11	u	u	NOUN
ejpam-2714	360	12	,	,	PUNCT
ejpam-2714	360	13	u	u	PROPN
ejpam-2714	360	14	≤	≤	PUNCT
ejpam-2714	360	15	w2	w2	NOUN
ejpam-2714	360	16	,	,	PUNCT
ejpam-2714	360	17	u	u	PROPN
ejpam-2714	360	18	≤	≤	X
ejpam-2714	360	19	v3	v3	PROPN
ejpam-2714	360	20	and	and	CCONJ
ejpam-2714	360	21	w3	w3	PROPN
ejpam-2714	360	22	≤	≤	PROPN
ejpam-2714	360	23	u.	u.	VERB
ejpam-2714	360	24	our	our	PRON
ejpam-2714	360	25	next	next	ADJ
ejpam-2714	360	26	claim	claim	NOUN
ejpam-2714	360	27	is	be	AUX
ejpam-2714	360	28	that	that	SCONJ
ejpam-2714	360	29	v0	v0	NOUN
ejpam-2714	360	30	≤	≤	ADJ
ejpam-2714	360	31	w1	w1	NOUN
ejpam-2714	360	32	≤	≤	PUNCT
ejpam-2714	360	33	v2	v2	PROPN
ejpam-2714	360	34	≤	≤	NUM
ejpam-2714	360	35	w3	w3	PROPN
ejpam-2714	360	36	and	and	CCONJ
ejpam-2714	360	37	v3	v3	PROPN
ejpam-2714	360	38	≤	≤	PROPN
ejpam-2714	360	39	w2	w2	NOUN
ejpam-2714	360	40	≤	≤	PROPN
ejpam-2714	360	41	v1	v1	PROPN
ejpam-2714	360	42	≤	≤	NUM
ejpam-2714	360	43	w0	w0	NOUN
ejpam-2714	360	44	.	.	PUNCT
ejpam-2714	361	1	for	for	ADP
ejpam-2714	361	2	this	this	PRON
ejpam-2714	361	3	,	,	PUNCT
ejpam-2714	361	4	let	let	VERB
ejpam-2714	361	5	p(t	p(t	NOUN
ejpam-2714	361	6	)	)	PUNCT
ejpam-2714	362	1	=	=	SYM
ejpam-2714	362	2	v0(t)−	v0(t)−	X
ejpam-2714	362	3	w1(t	w1(t	PUNCT
ejpam-2714	362	4	)	)	PUNCT
ejpam-2714	362	5	,	,	PUNCT
ejpam-2714	362	6	then	then	ADV
ejpam-2714	362	7	c	c	PROPN
ejpam-2714	362	8	dqp(t	dqp(t	PROPN
ejpam-2714	362	9	)	)	PUNCT
ejpam-2714	362	10	≤	≤	NOUN
ejpam-2714	362	11	0	0	NUM
ejpam-2714	363	1	due	due	ADP
ejpam-2714	363	2	to	to	ADP
ejpam-2714	363	3	the	the	DET
ejpam-2714	363	4	fact	fact	NOUN
ejpam-2714	363	5	that	that	SCONJ
ejpam-2714	363	6	v0	v0	NOUN
ejpam-2714	363	7	≤	≤	NUM
ejpam-2714	363	8	w0	w0	NOUN
ejpam-2714	363	9	,	,	PUNCT
ejpam-2714	363	10	also	also	ADV
ejpam-2714	363	11	p0	p0	VERB
ejpam-2714	363	12	≤	≤	NUM
ejpam-2714	363	13	0	0	NUM
ejpam-2714	363	14	.	.	PUNCT
ejpam-2714	364	1	by	by	ADP
ejpam-2714	364	2	applying	apply	VERB
ejpam-2714	364	3	corollary	corollary	ADJ
ejpam-2714	364	4	2	2	NUM
ejpam-2714	364	5	we	we	PRON
ejpam-2714	364	6	get	get	VERB
ejpam-2714	364	7	p(t	p(t	NOUN
ejpam-2714	364	8	)	)	PUNCT
ejpam-2714	364	9	≤	≤	NOUN
ejpam-2714	364	10	0	0	NUM
ejpam-2714	364	11	.	.	PUNCT
ejpam-2714	365	1	thus	thus	ADV
ejpam-2714	365	2	v0	v0	VERB
ejpam-2714	365	3	≤	≤	ADJ
ejpam-2714	365	4	w1	w1	NOUN
ejpam-2714	365	5	.	.	PUNCT
ejpam-2714	366	1	proceeding	proceed	VERB
ejpam-2714	366	2	in	in	ADP
ejpam-2714	366	3	the	the	DET
ejpam-2714	366	4	same	same	ADJ
ejpam-2714	366	5	way	way	NOUN
ejpam-2714	366	6	we	we	PRON
ejpam-2714	366	7	can	can	AUX
ejpam-2714	366	8	obtain	obtain	VERB
ejpam-2714	366	9	w1	w1	NOUN
ejpam-2714	366	10	≤	≤	NOUN
ejpam-2714	366	11	v2	v2	PROPN
ejpam-2714	366	12	,	,	PUNCT
ejpam-2714	366	13	v1	v1	ADJ
ejpam-2714	366	14	≤	≤	NUM
ejpam-2714	366	15	w0	w0	NOUN
ejpam-2714	366	16	,	,	PUNCT
ejpam-2714	366	17	v2	v2	PROPN
ejpam-2714	366	18	≤	≤	NUM
ejpam-2714	366	19	w3	w3	PROPN
ejpam-2714	366	20	,	,	PUNCT
ejpam-2714	366	21	v3	v3	PROPN
ejpam-2714	366	22	≤	≤	PROPN
ejpam-2714	366	23	w2	w2	NOUN
ejpam-2714	366	24	,	,	PUNCT
ejpam-2714	366	25	w2	w2	NOUN
ejpam-2714	366	26	≤	≤	NOUN
ejpam-2714	366	27	v1	v1	NOUN
ejpam-2714	366	28	on	on	ADP
ejpam-2714	366	29	j	j	PROPN
ejpam-2714	366	30	.	.	PUNCT
ejpam-2714	367	1	thus	thus	ADV
ejpam-2714	367	2	we	we	PRON
ejpam-2714	367	3	arrive	arrive	VERB
ejpam-2714	367	4	at	at	ADP
ejpam-2714	367	5	relation	relation	NOUN
ejpam-2714	367	6	(	(	PUNCT
ejpam-2714	367	7	30	30	NUM
ejpam-2714	367	8	)	)	PUNCT
ejpam-2714	367	9	.	.	PUNCT
ejpam-2714	368	1	suppose	suppose	VERB
ejpam-2714	368	2	there	there	PRON
ejpam-2714	368	3	exists	exist	VERB
ejpam-2714	368	4	an	an	DET
ejpam-2714	368	5	integer	integer	NOUN
ejpam-2714	368	6	k	k	PROPN
ejpam-2714	368	7	≥	≥	NUM
ejpam-2714	368	8	2	2	NUM
ejpam-2714	368	9	such	such	ADJ
ejpam-2714	368	10	that	that	SCONJ
ejpam-2714	368	11	w2k−1	w2k−1	PROPN
ejpam-2714	368	12	≤	≤	NUM
ejpam-2714	368	13	v2k	v2k	X
ejpam-2714	368	14	≤	≤	NUM
ejpam-2714	368	15	w2k+1	w2k+1	NOUN
ejpam-2714	368	16	≤	≤	NUM
ejpam-2714	369	1	u≤	u≤	NUM
ejpam-2714	369	2	v2k+1	v2k+1	ADJ
ejpam-2714	369	3	≤	≤	ADJ
ejpam-2714	369	4	w2k	w2k	PROPN
ejpam-2714	369	5	≤	≤	PUNCT
ejpam-2714	369	6	v2k−1	v2k−1	PROPN
ejpam-2714	369	7	holds	hold	VERB
ejpam-2714	369	8	,	,	PUNCT
ejpam-2714	369	9	then	then	ADV
ejpam-2714	369	10	we	we	PRON
ejpam-2714	369	11	claim	claim	VERB
ejpam-2714	369	12	that	that	SCONJ
ejpam-2714	369	13	w2k+1	w2k+1	VERB
ejpam-2714	369	14	≤	≤	NUM
ejpam-2714	369	15	v2k+2	v2k+2	NOUN
ejpam-2714	369	16	≤	≤	NOUN
ejpam-2714	369	17	w2k+3	w2k+3	PUNCT
ejpam-2714	369	18	≤	≤	NUM
ejpam-2714	370	1	u≤	u≤	NUM
ejpam-2714	371	1	v2k+3	v2k+3	PRON
ejpam-2714	371	2	≤	≤	PROPN
ejpam-2714	371	3	w2k+2	w2k+2	ADJ
ejpam-2714	371	4	≤	≤	NOUN
ejpam-2714	371	5	v2k+1	v2k+1	NOUN
ejpam-2714	371	6	.	.	PUNCT
ejpam-2714	372	1	setting	set	VERB
ejpam-2714	372	2	p(t	p(t	NOUN
ejpam-2714	372	3	)	)	PUNCT
ejpam-2714	373	1	=	=	PRON
ejpam-2714	373	2	w2k+1(t)−	w2k+1(t)−	PUNCT
ejpam-2714	373	3	v2k+2(t	v2k+2(t	NUM
ejpam-2714	373	4	)	)	PUNCT
ejpam-2714	373	5	.	.	PUNCT
ejpam-2714	374	1	c	c	PROPN
ejpam-2714	374	2	dqp(t	dqp(t	PROPN
ejpam-2714	374	3	)	)	PUNCT
ejpam-2714	375	1	=	=	SYM
ejpam-2714	375	2	c	c	PROPN
ejpam-2714	375	3	dqw2k+1(t)−	dqw2k+1(t)−	PROPN
ejpam-2714	375	4	c	c	PROPN
ejpam-2714	375	5	dqv2k+2(t	dqv2k+2(t	PROPN
ejpam-2714	375	6	)	)	PUNCT
ejpam-2714	375	7	≤[f(t	≤[f(t	NOUN
ejpam-2714	375	8	,	,	PUNCT
ejpam-2714	375	9	v2k(t	v2k(t	PROPN
ejpam-2714	375	10	)	)	PUNCT
ejpam-2714	375	11	,	,	PUNCT
ejpam-2714	375	12	iq(v2k(t	iq(v2k(t	NOUN
ejpam-2714	375	13	)	)	PUNCT
ejpam-2714	375	14	)	)	PUNCT
ejpam-2714	375	15	)	)	PUNCT
ejpam-2714	376	1	+	+	CCONJ
ejpam-2714	376	2	g(t	g(t	PROPN
ejpam-2714	376	3	,	,	PUNCT
ejpam-2714	376	4	w2k(t	w2k(t	PROPN
ejpam-2714	376	5	)	)	PUNCT
ejpam-2714	376	6	,	,	PUNCT
ejpam-2714	376	7	iq(w2k(t	iq(w2k(t	NOUN
ejpam-2714	376	8	)	)	PUNCT
ejpam-2714	376	9	)	)	PUNCT
ejpam-2714	376	10	)	)	PUNCT
ejpam-2714	376	11	]	]	PUNCT
ejpam-2714	377	1	−	−	PUNCT
ejpam-2714	378	1	[	[	X
ejpam-2714	378	2	f(t	f(t	NOUN
ejpam-2714	378	3	,	,	PUNCT
ejpam-2714	378	4	w2k+1(t	w2k+1(t	NUM
ejpam-2714	378	5	)	)	PUNCT
ejpam-2714	378	6	,	,	PUNCT
ejpam-2714	378	7	iq(w2k+1(t	iq(w2k+1(t	PROPN
ejpam-2714	378	8	)	)	PUNCT
ejpam-2714	378	9	)	)	PUNCT
ejpam-2714	378	10	)	)	PUNCT
ejpam-2714	379	1	+	+	CCONJ
ejpam-2714	379	2	g(t	g(t	PROPN
ejpam-2714	379	3	,	,	PUNCT
ejpam-2714	379	4	v2k+1(t	v2k+1(t	NUM
ejpam-2714	379	5	)	)	PUNCT
ejpam-2714	379	6	,	,	PUNCT
ejpam-2714	379	7	iq(v2k+1(t	iq(v2k+1(t	PRON
ejpam-2714	379	8	)	)	PUNCT
ejpam-2714	379	9	)	)	PUNCT
ejpam-2714	379	10	)	)	PUNCT
ejpam-2714	379	11	]	]	PUNCT
ejpam-2714	380	1	≤0	≤0	PROPN
ejpam-2714	380	2	,	,	PUNCT
ejpam-2714	380	3	which	which	PRON
ejpam-2714	380	4	is	be	AUX
ejpam-2714	380	5	obtained	obtain	VERB
ejpam-2714	380	6	by	by	ADP
ejpam-2714	380	7	adding	add	VERB
ejpam-2714	380	8	and	and	CCONJ
ejpam-2714	380	9	subtracting	subtract	VERB
ejpam-2714	380	10	suitable	suitable	ADJ
ejpam-2714	380	11	terms	term	NOUN
ejpam-2714	380	12	and	and	CCONJ
ejpam-2714	380	13	on	on	ADP
ejpam-2714	380	14	using	use	VERB
ejpam-2714	380	15	the	the	DET
ejpam-2714	380	16	monotone	monotone	ADJ
ejpam-2714	380	17	nature	nature	NOUN
ejpam-2714	380	18	of	of	ADP
ejpam-2714	380	19	f	f	PROPN
ejpam-2714	380	20	,	,	PUNCT
ejpam-2714	380	21	g.	g.	PROPN
ejpam-2714	380	22	next	next	ADJ
ejpam-2714	380	23	p(0	p(0	PROPN
ejpam-2714	380	24	)	)	PUNCT
ejpam-2714	381	1	=	=	NOUN
ejpam-2714	381	2	w2k+1(0)−	w2k+1(0)−	PROPN
ejpam-2714	381	3	v2k+2(0	v2k+2(0	NOUN
ejpam-2714	381	4	)	)	PUNCT
ejpam-2714	381	5	=	=	NOUN
ejpam-2714	381	6	v2k(0)−w2k+1(0	v2k(0)−w2k+1(0	X
ejpam-2714	381	7	)	)	PUNCT
ejpam-2714	381	8	+	+	CCONJ
ejpam-2714	381	9	1	1	NUM
ejpam-2714	381	10	m	m	NOUN
ejpam-2714	381	11	[	[	X
ejpam-2714	381	12	g(w2k+1(0	g(w2k+1(0	NOUN
ejpam-2714	381	13	)	)	PUNCT
ejpam-2714	381	14	,	,	PUNCT
ejpam-2714	381	15	w2k+1(t	w2k+1(t	NUM
ejpam-2714	381	16	)	)	PUNCT
ejpam-2714	381	17	)	)	PUNCT
ejpam-2714	382	1	−	−	PROPN
ejpam-2714	383	1	g(v2k(0	g(v2k(0	PROPN
ejpam-2714	383	2	)	)	PUNCT
ejpam-2714	383	3	,	,	PUNCT
ejpam-2714	383	4	v2k(t	v2k(t	PROPN
ejpam-2714	383	5	)	)	PUNCT
ejpam-2714	383	6	)	)	PUNCT
ejpam-2714	383	7	≤0	≤0	PROPN
ejpam-2714	383	8	.	.	PUNCT
ejpam-2714	384	1	j.	j.	PROPN
ejpam-2714	384	2	devi	devi	PROPN
ejpam-2714	384	3	,	,	PUNCT
ejpam-2714	384	4	ch	ch	PROPN
ejpam-2714	384	5	.	.	PUNCT
ejpam-2714	384	6	sreedhar	sreedhar	PROPN
ejpam-2714	384	7	/	/	SYM
ejpam-2714	384	8	eur	eur	PROPN
ejpam-2714	384	9	.	.	PUNCT
ejpam-2714	385	1	j.	j.	PROPN
ejpam-2714	385	2	pure	pure	PROPN
ejpam-2714	385	3	appl	appl	PROPN
ejpam-2714	385	4	.	.	PROPN
ejpam-2714	385	5	math	math	PROPN
ejpam-2714	385	6	,	,	PUNCT
ejpam-2714	385	7	9	9	NUM
ejpam-2714	385	8	(	(	PUNCT
ejpam-2714	385	9	2016	2016	NUM
ejpam-2714	385	10	)	)	PUNCT
ejpam-2714	385	11	,	,	PUNCT
ejpam-2714	385	12	346	346	NUM
ejpam-2714	385	13	-	-	SYM
ejpam-2714	385	14	359	359	NUM
ejpam-2714	385	15	357	357	NUM
ejpam-2714	385	16	corollary	corollary	ADJ
ejpam-2714	385	17	2	2	NUM
ejpam-2714	385	18	yields	yield	NOUN
ejpam-2714	385	19	that	that	PRON
ejpam-2714	385	20	p(t	p(t	VERB
ejpam-2714	385	21	)	)	PUNCT
ejpam-2714	385	22	≤	≤	NOUN
ejpam-2714	385	23	0	0	NUM
ejpam-2714	385	24	and	and	CCONJ
ejpam-2714	385	25	consequently	consequently	ADV
ejpam-2714	385	26	,	,	PUNCT
ejpam-2714	385	27	w2k+1	w2k+1	VERB
ejpam-2714	385	28	≤	≤	NOUN
ejpam-2714	385	29	v2k+2	v2k+2	NOUN
ejpam-2714	385	30	,	,	PUNCT
ejpam-2714	385	31	on	on	ADP
ejpam-2714	385	32	j	j	PROPN
ejpam-2714	385	33	.	.	PUNCT
ejpam-2714	386	1	similarly	similarly	ADV
ejpam-2714	386	2	,	,	PUNCT
ejpam-2714	386	3	we	we	PRON
ejpam-2714	386	4	obtain	obtain	VERB
ejpam-2714	386	5	w2k+2	w2k+2	ADJ
ejpam-2714	386	6	≤	≤	NOUN
ejpam-2714	386	7	v2k+1	v2k+1	NOUN
ejpam-2714	386	8	,	,	PUNCT
ejpam-2714	386	9	v2k+2	v2k+2	NOUN
ejpam-2714	386	10	≤	≤	ADV
ejpam-2714	386	11	w2k+3	w2k+3	ADV
ejpam-2714	386	12	,	,	PUNCT
ejpam-2714	386	13	v2k+3	v2k+3	ADP
ejpam-2714	386	14	≤	≤	PROPN
ejpam-2714	386	15	w2k+2	w2k+2	NOUN
ejpam-2714	386	16	.	.	PROPN
ejpam-2714	387	1	finally	finally	ADV
ejpam-2714	387	2	consider	consider	VERB
ejpam-2714	387	3	p(t	p(t	NOUN
ejpam-2714	387	4	)	)	PUNCT
ejpam-2714	387	5	=	=	SYM
ejpam-2714	387	6	v2k+2(t	v2k+2(t	NUM
ejpam-2714	387	7	)	)	PUNCT
ejpam-2714	387	8	−	−	PROPN
ejpam-2714	387	9	u(t	u(t	NOUN
ejpam-2714	387	10	)	)	PUNCT
ejpam-2714	387	11	,	,	PUNCT
ejpam-2714	387	12	and	and	CCONJ
ejpam-2714	387	13	working	work	VERB
ejpam-2714	387	14	in	in	ADP
ejpam-2714	387	15	a	a	DET
ejpam-2714	387	16	similar	similar	ADJ
ejpam-2714	387	17	fashion	fashion	NOUN
ejpam-2714	387	18	we	we	PRON
ejpam-2714	387	19	arrive	arrive	VERB
ejpam-2714	387	20	at	at	ADP
ejpam-2714	387	21	c	c	PROPN
ejpam-2714	387	22	dqp(t	dqp(t	PROPN
ejpam-2714	387	23	)	)	PUNCT
ejpam-2714	388	1	=	=	NOUN
ejpam-2714	388	2	c	c	NOUN
ejpam-2714	388	3	dqv2k+2(t)−	dqv2k+2(t)−	PROPN
ejpam-2714	388	4	c	c	PROPN
ejpam-2714	388	5	dqu(t	dqu(t	PROPN
ejpam-2714	388	6	)	)	PUNCT
ejpam-2714	388	7	≤f(t	≤f(t	NOUN
ejpam-2714	388	8	,	,	PUNCT
ejpam-2714	388	9	w2k+1(t	w2k+1(t	NUM
ejpam-2714	388	10	)	)	PUNCT
ejpam-2714	388	11	,	,	PUNCT
ejpam-2714	388	12	iq(w2k+1(t	iq(w2k+1(t	PROPN
ejpam-2714	388	13	)	)	PUNCT
ejpam-2714	388	14	)	)	PUNCT
ejpam-2714	388	15	)	)	PUNCT
ejpam-2714	389	1	+	+	CCONJ
ejpam-2714	389	2	g(t	g(t	PROPN
ejpam-2714	389	3	,	,	PUNCT
ejpam-2714	389	4	v2k+1(t	v2k+1(t	NUM
ejpam-2714	389	5	)	)	PUNCT
ejpam-2714	389	6	,	,	PUNCT
ejpam-2714	389	7	iq(v2k+1(t	iq(v2k+1(t	PRON
ejpam-2714	389	8	)	)	PUNCT
ejpam-2714	389	9	)	)	PUNCT
ejpam-2714	389	10	)	)	PUNCT
ejpam-2714	390	1	−	−	PUNCT
ejpam-2714	391	1	[	[	X
ejpam-2714	391	2	f(t	f(t	NOUN
ejpam-2714	391	3	,	,	PUNCT
ejpam-2714	391	4	u(t	u(t	NOUN
ejpam-2714	391	5	)	)	PUNCT
ejpam-2714	391	6	,	,	PUNCT
ejpam-2714	391	7	iq(u(t	iq(u(t	NUM
ejpam-2714	391	8	)	)	PUNCT
ejpam-2714	391	9	)	)	PUNCT
ejpam-2714	391	10	)	)	PUNCT
ejpam-2714	392	1	+	+	CCONJ
ejpam-2714	392	2	g(t	g(t	PROPN
ejpam-2714	392	3	,	,	PUNCT
ejpam-2714	392	4	u(t	u(t	NOUN
ejpam-2714	392	5	)	)	PUNCT
ejpam-2714	392	6	,	,	PUNCT
ejpam-2714	392	7	iq(u(t	iq(u(t	NUM
ejpam-2714	392	8	)	)	PUNCT
ejpam-2714	392	9	)	)	PUNCT
ejpam-2714	392	10	)	)	PUNCT
ejpam-2714	392	11	]	]	PUNCT
ejpam-2714	393	1	≤0	≤0	PROPN
ejpam-2714	393	2	,	,	PUNCT
ejpam-2714	393	3	and	and	CCONJ
ejpam-2714	393	4	p(0	p(0	PROPN
ejpam-2714	393	5	)	)	PUNCT
ejpam-2714	393	6	≤	≤	NOUN
ejpam-2714	393	7	0	0	NUM
ejpam-2714	393	8	.	.	PUNCT
ejpam-2714	394	1	so	so	ADV
ejpam-2714	394	2	by	by	ADP
ejpam-2714	394	3	applying	apply	VERB
ejpam-2714	394	4	corollary	corollary	ADJ
ejpam-2714	394	5	2	2	NUM
ejpam-2714	394	6	we	we	PRON
ejpam-2714	394	7	get	get	VERB
ejpam-2714	394	8	u(t	u(t	NOUN
ejpam-2714	394	9	)	)	PUNCT
ejpam-2714	394	10	≤	≤	NOUN
ejpam-2714	394	11	v2k+1(t	v2k+1(t	NUM
ejpam-2714	394	12	)	)	PUNCT
ejpam-2714	394	13	.	.	PUNCT
ejpam-2714	395	1	the	the	DET
ejpam-2714	395	2	relations	relation	NOUN
ejpam-2714	395	3	u	u	PROPN
ejpam-2714	395	4	≤	≤	X
ejpam-2714	395	5	v2k+2	v2k+2	NOUN
ejpam-2714	395	6	,	,	PUNCT
ejpam-2714	395	7	w2k+3	w2k+3	PUNCT
ejpam-2714	395	8	≤	≤	NUM
ejpam-2714	395	9	u	u	NOUN
ejpam-2714	395	10	,	,	PUNCT
ejpam-2714	395	11	w2k+2	w2k+2	VERB
ejpam-2714	395	12	≤	≤	PROPN
ejpam-2714	395	13	u	u	PROPN
ejpam-2714	395	14	,	,	PUNCT
ejpam-2714	395	15	u≤	u≤	NUM
ejpam-2714	395	16	v2k+3	v2k+3	NOUN
ejpam-2714	395	17	can	can	AUX
ejpam-2714	395	18	be	be	AUX
ejpam-2714	395	19	proved	prove	VERB
ejpam-2714	395	20	by	by	ADP
ejpam-2714	395	21	working	work	VERB
ejpam-2714	395	22	as	as	ADP
ejpam-2714	395	23	in	in	ADP
ejpam-2714	395	24	the	the	DET
ejpam-2714	395	25	previous	previous	ADJ
ejpam-2714	395	26	case	case	NOUN
ejpam-2714	395	27	.	.	PUNCT
ejpam-2714	396	1	now	now	ADV
ejpam-2714	396	2	by	by	ADP
ejpam-2714	396	3	induction	induction	NOUN
ejpam-2714	396	4	we	we	PRON
ejpam-2714	396	5	have	have	AUX
ejpam-2714	396	6	v0	v0	NOUN
ejpam-2714	396	7	≤	≤	ADJ
ejpam-2714	396	8	w1	w1	NOUN
ejpam-2714	396	9	≤	≤	NOUN
ejpam-2714	396	10	.	.	PUNCT
ejpam-2714	396	11	.	.	PUNCT
ejpam-2714	397	1	.≤	.≤	PUNCT
ejpam-2714	398	1	v2n	v2n	PROPN
ejpam-2714	398	2	≤	≤	PROPN
ejpam-2714	398	3	w2n+1	w2n+1	PROPN
ejpam-2714	398	4	≤	≤	PUNCT
ejpam-2714	398	5	u≤	u≤	PROPN
ejpam-2714	398	6	v2n+1	v2n+1	PROPN
ejpam-2714	398	7	≤	≤	NOUN
ejpam-2714	398	8	w2n	w2n	PRON
ejpam-2714	398	9	≤	≤	NUM
ejpam-2714	398	10	.	.	PUNCT
ejpam-2714	398	11	.	.	PUNCT
ejpam-2714	399	1	.≤	.≤	NOUN
ejpam-2714	400	1	v1	v1	PROPN
ejpam-2714	400	2	≤	≤	NUM
ejpam-2714	400	3	w0	w0	NOUN
ejpam-2714	400	4	.	.	PUNCT
ejpam-2714	401	1	by	by	ADP
ejpam-2714	401	2	arguing	argue	VERB
ejpam-2714	401	3	as	as	ADP
ejpam-2714	401	4	in	in	ADP
ejpam-2714	401	5	theorem	theorem	NOUN
ejpam-2714	401	6	3	3	NUM
ejpam-2714	401	7	,	,	PUNCT
ejpam-2714	401	8	we	we	PRON
ejpam-2714	401	9	get	get	VERB
ejpam-2714	401	10	the	the	DET
ejpam-2714	401	11	sequences	sequence	NOUN
ejpam-2714	401	12	{	{	PUNCT
ejpam-2714	401	13	v2n	v2n	NOUN
ejpam-2714	401	14	,	,	PUNCT
ejpam-2714	401	15	w2n+1	w2n+1	NOUN
ejpam-2714	401	16	}	}	PUNCT
ejpam-2714	401	17	→	→	SYM
ejpam-2714	401	18	ρ	ρ	PROPN
ejpam-2714	401	19	and	and	CCONJ
ejpam-2714	401	20	{	{	PUNCT
ejpam-2714	401	21	v2n+1	v2n+1	PROPN
ejpam-2714	401	22	,	,	PUNCT
ejpam-2714	401	23	w2n	w2n	X
ejpam-2714	401	24	}	}	PUNCT
ejpam-2714	401	25	→	→	SYM
ejpam-2714	401	26	r	r	NOUN
ejpam-2714	401	27	in	in	ADP
ejpam-2714	401	28	c1[j	c1[j	NOUN
ejpam-2714	401	29	,	,	PUNCT
ejpam-2714	401	30	r	r	X
ejpam-2714	401	31	]	]	X
ejpam-2714	401	32	uniformly	uniformly	ADV
ejpam-2714	401	33	and	and	CCONJ
ejpam-2714	401	34	monotonically	monotonically	ADV
ejpam-2714	401	35	,	,	PUNCT
ejpam-2714	401	36	such	such	ADJ
ejpam-2714	401	37	that	that	SCONJ
ejpam-2714	401	38	ρ	ρ	NOUN
ejpam-2714	401	39	and	and	CCONJ
ejpam-2714	401	40	r	r	NOUN
ejpam-2714	401	41	are	be	AUX
ejpam-2714	401	42	coupled	couple	VERB
ejpam-2714	401	43	minimal	minimal	ADJ
ejpam-2714	401	44	and	and	CCONJ
ejpam-2714	401	45	maximal	maximal	ADJ
ejpam-2714	401	46	solutions	solution	NOUN
ejpam-2714	401	47	of	of	ADP
ejpam-2714	401	48	type	type	NOUN
ejpam-2714	401	49	i	i	PRON
ejpam-2714	401	50	for	for	ADP
ejpam-2714	401	51	(	(	PUNCT
ejpam-2714	401	52	10	10	NUM
ejpam-2714	401	53	)	)	PUNCT
ejpam-2714	401	54	,	,	PUNCT
ejpam-2714	401	55	(	(	PUNCT
ejpam-2714	401	56	11	11	NUM
ejpam-2714	401	57	)	)	PUNCT
ejpam-2714	401	58	.	.	PUNCT
ejpam-2714	402	1	hence	hence	ADV
ejpam-2714	402	2	the	the	DET
ejpam-2714	402	3	proof	proof	NOUN
ejpam-2714	402	4	of	of	ADP
ejpam-2714	402	5	the	the	DET
ejpam-2714	402	6	theorem	theorem	NOUN
ejpam-2714	402	7	.	.	PUNCT
ejpam-2714	402	8	to	to	PART
ejpam-2714	402	9	avoid	avoid	VERB
ejpam-2714	402	10	repetition	repetition	NOUN
ejpam-2714	402	11	,	,	PUNCT
ejpam-2714	402	12	we	we	PRON
ejpam-2714	402	13	will	will	AUX
ejpam-2714	402	14	state	state	VERB
ejpam-2714	402	15	next	next	ADJ
ejpam-2714	402	16	two	two	NUM
ejpam-2714	402	17	theorems	theorem	NOUN
ejpam-2714	402	18	without	without	ADP
ejpam-2714	402	19	proof	proof	NOUN
ejpam-2714	402	20	since	since	SCONJ
ejpam-2714	402	21	it	it	PRON
ejpam-2714	402	22	follows	follow	VERB
ejpam-2714	402	23	the	the	DET
ejpam-2714	402	24	same	same	ADJ
ejpam-2714	402	25	of	of	ADP
ejpam-2714	402	26	pattern	pattern	NOUN
ejpam-2714	402	27	as	as	ADP
ejpam-2714	402	28	that	that	PRON
ejpam-2714	402	29	for	for	ADP
ejpam-2714	402	30	theorem	theorem	ADJ
ejpam-2714	402	31	3	3	NUM
ejpam-2714	402	32	and	and	CCONJ
ejpam-2714	402	33	theorem	theorem	VERB
ejpam-2714	402	34	4	4	NUM
ejpam-2714	402	35	.	.	PUNCT
ejpam-2714	402	36	theorem	theorem	NOUN
ejpam-2714	402	37	5	5	NUM
ejpam-2714	402	38	.	.	PUNCT
ejpam-2714	402	39	assume	assume	VERB
ejpam-2714	402	40	that	that	SCONJ
ejpam-2714	402	41	the	the	DET
ejpam-2714	402	42	hypothesis	hypothesis	NOUN
ejpam-2714	402	43	(	(	PUNCT
ejpam-2714	402	44	a1	a1	NOUN
ejpam-2714	402	45	)	)	PUNCT
ejpam-2714	402	46	,	,	PUNCT
ejpam-2714	402	47	(	(	PUNCT
ejpam-2714	402	48	a2	a2	PROPN
ejpam-2714	402	49	)	)	PUNCT
ejpam-2714	402	50	,	,	PUNCT
ejpam-2714	402	51	(	(	PUNCT
ejpam-2714	402	52	a3	a3	NOUN
ejpam-2714	402	53	)	)	PUNCT
ejpam-2714	402	54	of	of	ADP
ejpam-2714	402	55	theorem	theorem	ADJ
ejpam-2714	402	56	3	3	NUM
ejpam-2714	402	57	hold	hold	NOUN
ejpam-2714	402	58	and	and	CCONJ
ejpam-2714	402	59	v0	v0	NOUN
ejpam-2714	402	60	,	,	PUNCT
ejpam-2714	402	61	w0	w0	PROPN
ejpam-2714	402	62	are	be	AUX
ejpam-2714	402	63	coupled	couple	VERB
ejpam-2714	402	64	lower	low	ADJ
ejpam-2714	402	65	and	and	CCONJ
ejpam-2714	402	66	upper	upper	ADJ
ejpam-2714	402	67	solutions	solution	NOUN
ejpam-2714	402	68	of	of	ADP
ejpam-2714	402	69	type	type	NOUN
ejpam-2714	402	70	ii	ii	PROPN
ejpam-2714	402	71	for	for	ADP
ejpam-2714	402	72	(	(	PUNCT
ejpam-2714	402	73	10	10	NUM
ejpam-2714	402	74	)	)	PUNCT
ejpam-2714	402	75	,	,	PUNCT
ejpam-2714	402	76	(	(	PUNCT
ejpam-2714	402	77	11	11	NUM
ejpam-2714	402	78	)	)	PUNCT
ejpam-2714	402	79	with	with	ADP
ejpam-2714	402	80	v0(t	v0(t	NOUN
ejpam-2714	402	81	)	)	PUNCT
ejpam-2714	402	82	≤	≤	NUM
ejpam-2714	402	83	w0(t	w0(t	PROPN
ejpam-2714	402	84	)	)	PUNCT
ejpam-2714	402	85	on	on	ADP
ejpam-2714	402	86	j.	j.	PROPN
ejpam-2714	402	87	then	then	ADV
ejpam-2714	402	88	the	the	DET
ejpam-2714	402	89	iterative	iterative	NOUN
ejpam-2714	402	90	scheme	scheme	NOUN
ejpam-2714	402	91	given	give	VERB
ejpam-2714	402	92	by	by	ADP
ejpam-2714	402	93	c	c	PROPN
ejpam-2714	402	94	dqvn+1	dqvn+1	PROPN
ejpam-2714	403	1	=	=	NOUN
ejpam-2714	403	2	f(t	f(t	NOUN
ejpam-2714	403	3	,	,	PUNCT
ejpam-2714	403	4	vn	vn	NOUN
ejpam-2714	403	5	,	,	PUNCT
ejpam-2714	403	6	iq(vn	iq(vn	PROPN
ejpam-2714	403	7	)	)	PUNCT
ejpam-2714	403	8	)	)	PUNCT
ejpam-2714	404	1	+	+	CCONJ
ejpam-2714	405	1	g(t	g(t	PROPN
ejpam-2714	405	2	,	,	PUNCT
ejpam-2714	405	3	wn	wn	PROPN
ejpam-2714	405	4	,	,	PUNCT
ejpam-2714	405	5	iq(wn	iq(wn	PROPN
ejpam-2714	405	6	)	)	PUNCT
ejpam-2714	405	7	)	)	PUNCT
ejpam-2714	405	8	,	,	PUNCT
ejpam-2714	405	9	vn+1(0	vn+1(0	PUNCT
ejpam-2714	405	10	)	)	PUNCT
ejpam-2714	406	1	=	=	SYM
ejpam-2714	406	2	vn(0)−	vn(0)−	VERB
ejpam-2714	406	3	1	1	NUM
ejpam-2714	406	4	m	m	NOUN
ejpam-2714	406	5	g(vn(0	g(vn(0	PROPN
ejpam-2714	406	6	)	)	PUNCT
ejpam-2714	406	7	,	,	PUNCT
ejpam-2714	406	8	vn(t	vn(t	NUM
ejpam-2714	406	9	)	)	PUNCT
ejpam-2714	406	10	)	)	PUNCT
ejpam-2714	406	11	,	,	PUNCT
ejpam-2714	407	1	c	c	X
ejpam-2714	407	2	dqwn+1	dqwn+1	NOUN
ejpam-2714	407	3	=	=	SYM
ejpam-2714	407	4	f(t	f(t	NOUN
ejpam-2714	407	5	,	,	PUNCT
ejpam-2714	407	6	wn	wn	PROPN
ejpam-2714	407	7	,	,	PUNCT
ejpam-2714	407	8	iq(wn	iq(wn	PROPN
ejpam-2714	407	9	)	)	PUNCT
ejpam-2714	407	10	)	)	PUNCT
ejpam-2714	408	1	+	+	CCONJ
ejpam-2714	409	1	g(t	g(t	PROPN
ejpam-2714	409	2	,	,	PUNCT
ejpam-2714	409	3	vn	vn	NOUN
ejpam-2714	409	4	,	,	PUNCT
ejpam-2714	409	5	iq(vn	iq(vn	PROPN
ejpam-2714	409	6	)	)	PUNCT
ejpam-2714	409	7	)	)	PUNCT
ejpam-2714	409	8	,	,	PUNCT
ejpam-2714	409	9	wn+1(0	wn+1(0	PUNCT
ejpam-2714	409	10	)	)	PUNCT
ejpam-2714	410	1	=	=	SYM
ejpam-2714	410	2	wn(0)−	wn(0)−	NOUN
ejpam-2714	410	3	1	1	NUM
ejpam-2714	410	4	m	m	NOUN
ejpam-2714	410	5	g(wn(0	g(wn(0	PROPN
ejpam-2714	410	6	)	)	PUNCT
ejpam-2714	410	7	,	,	PUNCT
ejpam-2714	410	8	wn(t	wn(t	NUM
ejpam-2714	410	9	)	)	PUNCT
ejpam-2714	410	10	)	)	PUNCT
ejpam-2714	410	11	,	,	PUNCT
ejpam-2714	410	12	result	result	VERB
ejpam-2714	410	13	in	in	ADP
ejpam-2714	410	14	two	two	NUM
ejpam-2714	410	15	monotone	monotone	ADJ
ejpam-2714	410	16	sequences	sequence	NOUN
ejpam-2714	410	17	{	{	PUNCT
ejpam-2714	410	18	vn(t	vn(t	NUM
ejpam-2714	410	19	)	)	PUNCT
ejpam-2714	410	20	}	}	PUNCT
ejpam-2714	410	21	,	,	PUNCT
ejpam-2714	410	22	{	{	PUNCT
ejpam-2714	410	23	wn(t	wn(t	NUM
ejpam-2714	410	24	)	)	PUNCT
ejpam-2714	410	25	}	}	PUNCT
ejpam-2714	410	26	satisfying	satisfy	VERB
ejpam-2714	410	27	v0	v0	NOUN
ejpam-2714	410	28	≤	≤	NOUN
ejpam-2714	410	29	v1	v1	NOUN
ejpam-2714	410	30	≤	≤	NUM
ejpam-2714	410	31	.	.	PUNCT
ejpam-2714	410	32	.	.	PUNCT
ejpam-2714	411	1	.≤	.≤	PUNCT
ejpam-2714	412	1	vn	vn	PROPN
ejpam-2714	412	2	≤	≤	NUM
ejpam-2714	412	3	wn	wn	PROPN
ejpam-2714	412	4	≤	≤	PROPN
ejpam-2714	412	5	.	.	PUNCT
ejpam-2714	412	6	.	.	PUNCT
ejpam-2714	413	1	.≤	.≤	PUNCT
ejpam-2714	414	1	w1	w1	NOUN
ejpam-2714	414	2	≤	≤	PROPN
ejpam-2714	414	3	w0	w0	PROPN
ejpam-2714	414	4	.	.	PUNCT
ejpam-2714	415	1	further	far	ADV
ejpam-2714	415	2	more	more	ADJ
ejpam-2714	415	3	vn	vn	PROPN
ejpam-2714	415	4	→	→	SYM
ejpam-2714	415	5	ρ	ρ	PROPN
ejpam-2714	415	6	and	and	CCONJ
ejpam-2714	415	7	wn	wn	PROPN
ejpam-2714	415	8	→	→	SYM
ejpam-2714	415	9	r	r	NOUN
ejpam-2714	415	10	in	in	ADP
ejpam-2714	415	11	c1[j	c1[j	NOUN
ejpam-2714	415	12	,	,	PUNCT
ejpam-2714	415	13	r	r	X
ejpam-2714	415	14	]	]	X
ejpam-2714	415	15	uniformly	uniformly	ADV
ejpam-2714	415	16	and	and	CCONJ
ejpam-2714	415	17	monotonically	monotonically	ADV
ejpam-2714	415	18	,	,	PUNCT
ejpam-2714	415	19	such	such	ADJ
ejpam-2714	415	20	that	that	SCONJ
ejpam-2714	415	21	ρ	ρ	NOUN
ejpam-2714	415	22	and	and	CCONJ
ejpam-2714	415	23	r	r	NOUN
ejpam-2714	415	24	are	be	AUX
ejpam-2714	415	25	coupled	couple	VERB
ejpam-2714	415	26	minimal	minimal	ADJ
ejpam-2714	415	27	and	and	CCONJ
ejpam-2714	415	28	maximal	maximal	ADJ
ejpam-2714	415	29	solutions	solution	NOUN
ejpam-2714	415	30	of	of	ADP
ejpam-2714	415	31	type	type	NOUN
ejpam-2714	415	32	ii	ii	PROPN
ejpam-2714	415	33	for	for	ADP
ejpam-2714	415	34	(	(	PUNCT
ejpam-2714	415	35	10	10	NUM
ejpam-2714	415	36	)	)	PUNCT
ejpam-2714	415	37	,	,	PUNCT
ejpam-2714	415	38	(	(	PUNCT
ejpam-2714	415	39	11	11	NUM
ejpam-2714	415	40	)	)	PUNCT
ejpam-2714	415	41	,	,	PUNCT
ejpam-2714	415	42	respectively	respectively	ADV
ejpam-2714	415	43	,	,	PUNCT
ejpam-2714	415	44	provided	provide	VERB
ejpam-2714	415	45	that	that	DET
ejpam-2714	415	46	v0	v0	NOUN
ejpam-2714	415	47	≤	≤	NUM
ejpam-2714	415	48	w0	w0	NOUN
ejpam-2714	415	49	.	.	PUNCT
ejpam-2714	416	1	thus	thus	ADV
ejpam-2714	416	2	ρ	ρ	NUM
ejpam-2714	416	3	and	and	CCONJ
ejpam-2714	416	4	r	r	NOUN
ejpam-2714	416	5	satisfy	satisfy	NOUN
ejpam-2714	416	6	the	the	DET
ejpam-2714	416	7	coupled	couple	VERB
ejpam-2714	416	8	system	system	NOUN
ejpam-2714	416	9	c	c	AUX
ejpam-2714	416	10	dqρ	dqρ	VERB
ejpam-2714	416	11	=	=	NOUN
ejpam-2714	416	12	f(t	f(t	NOUN
ejpam-2714	416	13	,	,	PUNCT
ejpam-2714	416	14	ρ	ρ	NOUN
ejpam-2714	416	15	,	,	PUNCT
ejpam-2714	416	16	iq(ρ	iq(ρ	NOUN
ejpam-2714	416	17	)	)	PUNCT
ejpam-2714	416	18	)	)	PUNCT
ejpam-2714	417	1	+	+	CCONJ
ejpam-2714	418	1	g(t	g(t	PROPN
ejpam-2714	418	2	,	,	PUNCT
ejpam-2714	418	3	r	r	NOUN
ejpam-2714	418	4	,	,	PUNCT
ejpam-2714	418	5	iq(r	iq(r	NOUN
ejpam-2714	418	6	)	)	PUNCT
ejpam-2714	418	7	)	)	PUNCT
ejpam-2714	418	8	,	,	PUNCT
ejpam-2714	418	9	g(ρ(0),ρ(t	g(ρ(0),ρ(t	NOUN
ejpam-2714	418	10	)	)	PUNCT
ejpam-2714	418	11	)	)	PUNCT
ejpam-2714	419	1	=	=	PUNCT
ejpam-2714	419	2	0	0	NUM
ejpam-2714	419	3	,	,	PUNCT
ejpam-2714	419	4	c	c	PROPN
ejpam-2714	419	5	dqr	dqr	PROPN
ejpam-2714	419	6	=	=	SYM
ejpam-2714	419	7	f(t	f(t	NOUN
ejpam-2714	419	8	,	,	PUNCT
ejpam-2714	419	9	ρ	ρ	NOUN
ejpam-2714	419	10	,	,	PUNCT
ejpam-2714	419	11	iq(ρ	iq(ρ	NOUN
ejpam-2714	419	12	)	)	PUNCT
ejpam-2714	419	13	)	)	PUNCT
ejpam-2714	420	1	+	+	CCONJ
ejpam-2714	421	1	g(t	g(t	PROPN
ejpam-2714	421	2	,	,	PUNCT
ejpam-2714	421	3	r	r	NOUN
ejpam-2714	421	4	,	,	PUNCT
ejpam-2714	421	5	iq(r	iq(r	NOUN
ejpam-2714	421	6	)	)	PUNCT
ejpam-2714	421	7	)	)	PUNCT
ejpam-2714	421	8	,	,	PUNCT
ejpam-2714	421	9	g(r(0	g(r(0	PROPN
ejpam-2714	421	10	)	)	PUNCT
ejpam-2714	421	11	,	,	PUNCT
ejpam-2714	421	12	r(t	r(t	NOUN
ejpam-2714	421	13	)	)	PUNCT
ejpam-2714	421	14	)	)	PUNCT
ejpam-2714	422	1	=	=	PUNCT
ejpam-2714	422	2	0	0	X
ejpam-2714	422	3	.	.	PUNCT
ejpam-2714	423	1	references	reference	NOUN
ejpam-2714	423	2	358	358	NUM
ejpam-2714	423	3	theorem	theorem	VERB
ejpam-2714	423	4	6	6	NUM
ejpam-2714	423	5	.	.	PUNCT
ejpam-2714	424	1	let	let	VERB
ejpam-2714	424	2	(	(	PUNCT
ejpam-2714	424	3	a2	a2	PROPN
ejpam-2714	424	4	)	)	PUNCT
ejpam-2714	424	5	,	,	PUNCT
ejpam-2714	424	6	(	(	PUNCT
ejpam-2714	424	7	a3	a3	NOUN
ejpam-2714	424	8	)	)	PUNCT
ejpam-2714	424	9	of	of	ADP
ejpam-2714	424	10	theroem	theroem	NOUN
ejpam-2714	424	11	3	3	NUM
ejpam-2714	424	12	hold	hold	NOUN
ejpam-2714	424	13	and	and	CCONJ
ejpam-2714	424	14	v0	v0	NOUN
ejpam-2714	424	15	,	,	PUNCT
ejpam-2714	424	16	w0	w0	PROPN
ejpam-2714	424	17	are	be	AUX
ejpam-2714	424	18	coupled	couple	VERB
ejpam-2714	424	19	lower	low	ADJ
ejpam-2714	424	20	and	and	CCONJ
ejpam-2714	424	21	upper	upper	ADJ
ejpam-2714	424	22	solutions	solution	NOUN
ejpam-2714	424	23	of	of	ADP
ejpam-2714	424	24	type	type	NOUN
ejpam-2714	424	25	ii	ii	PROPN
ejpam-2714	424	26	for	for	ADP
ejpam-2714	424	27	(	(	PUNCT
ejpam-2714	424	28	10	10	NUM
ejpam-2714	424	29	)	)	PUNCT
ejpam-2714	424	30	,	,	PUNCT
ejpam-2714	424	31	(	(	PUNCT
ejpam-2714	424	32	11	11	NUM
ejpam-2714	424	33	)	)	PUNCT
ejpam-2714	424	34	with	with	ADP
ejpam-2714	424	35	v0(t)≤	v0(t)≤	PROPN
ejpam-2714	424	36	w0(t	w0(t	PROPN
ejpam-2714	424	37	)	)	PUNCT
ejpam-2714	424	38	on	on	ADP
ejpam-2714	424	39	j.	j.	PROPN
ejpam-2714	424	40	then	then	ADV
ejpam-2714	424	41	the	the	DET
ejpam-2714	424	42	iterative	iterative	NOUN
ejpam-2714	424	43	scheme	scheme	NOUN
ejpam-2714	424	44	given	give	VERB
ejpam-2714	424	45	by	by	ADP
ejpam-2714	424	46	c	c	PROPN
ejpam-2714	424	47	dqvn+1	dqvn+1	PROPN
ejpam-2714	425	1	=	=	NOUN
ejpam-2714	425	2	f(t	f(t	PROPN
ejpam-2714	425	3	,	,	PUNCT
ejpam-2714	425	4	wn	wn	PROPN
ejpam-2714	425	5	,	,	PUNCT
ejpam-2714	425	6	iq(wn	iq(wn	PROPN
ejpam-2714	425	7	)	)	PUNCT
ejpam-2714	425	8	)	)	PUNCT
ejpam-2714	426	1	+	+	CCONJ
ejpam-2714	427	1	g(t	g(t	PROPN
ejpam-2714	427	2	,	,	PUNCT
ejpam-2714	427	3	vn	vn	NOUN
ejpam-2714	427	4	,	,	PUNCT
ejpam-2714	427	5	iq(vn	iq(vn	PROPN
ejpam-2714	427	6	)	)	PUNCT
ejpam-2714	427	7	)	)	PUNCT
ejpam-2714	427	8	,	,	PUNCT
ejpam-2714	427	9	vn+1(0	vn+1(0	PUNCT
ejpam-2714	427	10	)	)	PUNCT
ejpam-2714	428	1	=	=	SYM
ejpam-2714	428	2	wn(0)−	wn(0)−	NOUN
ejpam-2714	428	3	1	1	NUM
ejpam-2714	428	4	m	m	NOUN
ejpam-2714	428	5	g(wn(0	g(wn(0	PROPN
ejpam-2714	428	6	)	)	PUNCT
ejpam-2714	428	7	,	,	PUNCT
ejpam-2714	428	8	wn(t	wn(t	NUM
ejpam-2714	428	9	)	)	PUNCT
ejpam-2714	428	10	)	)	PUNCT
ejpam-2714	428	11	,	,	PUNCT
ejpam-2714	428	12	c	c	X
ejpam-2714	428	13	dqwn+1	dqwn+1	NOUN
ejpam-2714	428	14	=	=	SYM
ejpam-2714	428	15	f(t	f(t	NOUN
ejpam-2714	428	16	,	,	PUNCT
ejpam-2714	428	17	vn	vn	NOUN
ejpam-2714	428	18	,	,	PUNCT
ejpam-2714	428	19	iq(vn	iq(vn	PROPN
ejpam-2714	428	20	)	)	PUNCT
ejpam-2714	428	21	)	)	PUNCT
ejpam-2714	429	1	+	+	CCONJ
ejpam-2714	430	1	g(t	g(t	PROPN
ejpam-2714	430	2	,	,	PUNCT
ejpam-2714	430	3	wn	wn	PROPN
ejpam-2714	430	4	,	,	PUNCT
ejpam-2714	430	5	iq(wn	iq(wn	PROPN
ejpam-2714	430	6	)	)	PUNCT
ejpam-2714	430	7	)	)	PUNCT
ejpam-2714	430	8	,	,	PUNCT
ejpam-2714	430	9	wn+1(0	wn+1(0	PUNCT
ejpam-2714	430	10	)	)	PUNCT
ejpam-2714	431	1	=	=	SYM
ejpam-2714	431	2	vn(0)−	vn(0)−	VERB
ejpam-2714	431	3	1	1	NUM
ejpam-2714	431	4	m	m	NOUN
ejpam-2714	431	5	g(vn(0	g(vn(0	PROPN
ejpam-2714	431	6	)	)	PUNCT
ejpam-2714	431	7	,	,	PUNCT
ejpam-2714	431	8	vn(t	vn(t	NUM
ejpam-2714	431	9	)	)	PUNCT
ejpam-2714	431	10	)	)	PUNCT
ejpam-2714	431	11	,	,	PUNCT
ejpam-2714	431	12	yields	yield	NOUN
ejpam-2714	431	13	alternating	alternate	VERB
ejpam-2714	431	14	monotone	monotone	ADJ
ejpam-2714	431	15	sequences	sequence	NOUN
ejpam-2714	431	16	{	{	PUNCT
ejpam-2714	431	17	v2n	v2n	NOUN
ejpam-2714	431	18	,	,	PUNCT
ejpam-2714	431	19	w2n+1	w2n+1	NOUN
ejpam-2714	431	20	}	}	PUNCT
ejpam-2714	431	21	and	and	CCONJ
ejpam-2714	431	22	{	{	PUNCT
ejpam-2714	431	23	v2n+1	v2n+1	PROPN
ejpam-2714	431	24	,	,	PUNCT
ejpam-2714	431	25	w2n	w2n	PRON
ejpam-2714	431	26	}	}	PUNCT
ejpam-2714	431	27	satisfying	satisfy	VERB
ejpam-2714	431	28	v0	v0	NOUN
ejpam-2714	431	29	≤	≤	NOUN
ejpam-2714	431	30	w1	w1	NOUN
ejpam-2714	431	31	≤	≤	NOUN
ejpam-2714	431	32	.	.	PUNCT
ejpam-2714	431	33	.	.	PUNCT
ejpam-2714	432	1	.≤	.≤	PUNCT
ejpam-2714	433	1	v2n	v2n	PROPN
ejpam-2714	433	2	≤	≤	PROPN
ejpam-2714	433	3	w2n+1	w2n+1	PROPN
ejpam-2714	433	4	≤	≤	PUNCT
ejpam-2714	433	5	u≤	u≤	PROPN
ejpam-2714	433	6	v2n+1	v2n+1	PROPN
ejpam-2714	433	7	≤	≤	NOUN
ejpam-2714	433	8	w2n	w2n	PRON
ejpam-2714	433	9	≤	≤	NUM
ejpam-2714	433	10	.	.	PUNCT
ejpam-2714	433	11	.	.	PUNCT
ejpam-2714	434	1	.≤	.≤	NOUN
ejpam-2714	435	1	v1	v1	PROPN
ejpam-2714	435	2	≤	≤	NUM
ejpam-2714	435	3	w0	w0	NOUN
ejpam-2714	435	4	,	,	PUNCT
ejpam-2714	435	5	for	for	ADP
ejpam-2714	435	6	each	each	DET
ejpam-2714	435	7	n≥	n≥	NOUN
ejpam-2714	435	8	1	1	NUM
ejpam-2714	435	9	on	on	ADP
ejpam-2714	435	10	j	j	PROPN
ejpam-2714	435	11	,	,	PUNCT
ejpam-2714	435	12	provided	provide	VERB
ejpam-2714	435	13	that	that	DET
ejpam-2714	435	14	v0	v0	NOUN
ejpam-2714	435	15	≤	≤	NOUN
ejpam-2714	435	16	u≤	u≤	NOUN
ejpam-2714	435	17	w0	w0	NOUN
ejpam-2714	435	18	.	.	PUNCT
ejpam-2714	436	1	furthermore	furthermore	ADV
ejpam-2714	436	2	{	{	PUNCT
ejpam-2714	436	3	v2n	v2n	NOUN
ejpam-2714	436	4	,	,	PUNCT
ejpam-2714	436	5	w2n+1	w2n+1	NOUN
ejpam-2714	436	6	}	}	PUNCT
ejpam-2714	436	7	→	→	SYM
ejpam-2714	436	8	ρ	ρ	PROPN
ejpam-2714	436	9	and	and	CCONJ
ejpam-2714	436	10	{	{	PUNCT
ejpam-2714	436	11	v2n+1	v2n+1	PROPN
ejpam-2714	436	12	,	,	PUNCT
ejpam-2714	436	13	w2n	w2n	X
ejpam-2714	436	14	}	}	PUNCT
ejpam-2714	436	15	→	→	SYM
ejpam-2714	436	16	r	r	NOUN
ejpam-2714	436	17	in	in	ADP
ejpam-2714	436	18	c1[j	c1[j	NOUN
ejpam-2714	436	19	,	,	PUNCT
ejpam-2714	436	20	r	r	X
ejpam-2714	436	21	]	]	X
ejpam-2714	436	22	uniformly	uniformly	ADV
ejpam-2714	436	23	and	and	CCONJ
ejpam-2714	436	24	monotonically	monotonically	ADV
ejpam-2714	436	25	,	,	PUNCT
ejpam-2714	436	26	such	such	ADJ
ejpam-2714	436	27	that	that	SCONJ
ejpam-2714	436	28	ρ	ρ	NOUN
ejpam-2714	436	29	and	and	CCONJ
ejpam-2714	436	30	r	r	NOUN
ejpam-2714	436	31	are	be	AUX
ejpam-2714	436	32	coupled	couple	VERB
ejpam-2714	436	33	minimal	minimal	ADJ
ejpam-2714	436	34	and	and	CCONJ
ejpam-2714	436	35	maximal	maximal	ADJ
ejpam-2714	436	36	solutions	solution	NOUN
ejpam-2714	436	37	of	of	ADP
ejpam-2714	436	38	(	(	PUNCT
ejpam-2714	436	39	10	10	NUM
ejpam-2714	436	40	)	)	PUNCT
ejpam-2714	436	41	,	,	PUNCT
ejpam-2714	436	42	(	(	PUNCT
ejpam-2714	436	43	11	11	NUM
ejpam-2714	436	44	)	)	PUNCT
ejpam-2714	436	45	,	,	PUNCT
ejpam-2714	436	46	respectively	respectively	ADV
ejpam-2714	436	47	,	,	PUNCT
ejpam-2714	436	48	that	that	ADV
ejpam-2714	436	49	is	is	ADV
ejpam-2714	436	50	,	,	PUNCT
ejpam-2714	436	51	if	if	SCONJ
ejpam-2714	436	52	v0	v0	NOUN
ejpam-2714	436	53	≤	≤	NOUN
ejpam-2714	436	54	u	u	PROPN
ejpam-2714	436	55	≤	≤	NOUN
ejpam-2714	436	56	w0	w0	PROPN
ejpam-2714	436	57	then	then	ADV
ejpam-2714	436	58	ρ	ρ	PROPN
ejpam-2714	436	59	≤	≤	NUM
ejpam-2714	436	60	u	u	NOUN
ejpam-2714	436	61	≤	≤	X
ejpam-2714	436	62	r	r	NOUN
ejpam-2714	436	63	,	,	PUNCT
ejpam-2714	436	64	and	and	CCONJ
ejpam-2714	436	65	ρ	ρ	NOUN
ejpam-2714	436	66	and	and	CCONJ
ejpam-2714	436	67	r	r	NOUN
ejpam-2714	436	68	satisfy	satisfy	NOUN
ejpam-2714	436	69	the	the	DET
ejpam-2714	436	70	coupled	couple	VERB
ejpam-2714	436	71	system	system	NOUN
ejpam-2714	436	72	.	.	PUNCT
ejpam-2714	437	1	c	c	PROPN
ejpam-2714	437	2	dqρ	dqρ	ADJ
ejpam-2714	437	3	=	=	ADJ
ejpam-2714	437	4	f(t	f(t	NOUN
ejpam-2714	437	5	,	,	PUNCT
ejpam-2714	437	6	ρ	ρ	NOUN
ejpam-2714	437	7	,	,	PUNCT
ejpam-2714	437	8	iq(ρ	iq(ρ	NOUN
ejpam-2714	437	9	)	)	PUNCT
ejpam-2714	437	10	)	)	PUNCT
ejpam-2714	438	1	+	+	CCONJ
ejpam-2714	439	1	g(t	g(t	PROPN
ejpam-2714	439	2	,	,	PUNCT
ejpam-2714	439	3	r	r	NOUN
ejpam-2714	439	4	,	,	PUNCT
ejpam-2714	439	5	iq(r	iq(r	NOUN
ejpam-2714	439	6	)	)	PUNCT
ejpam-2714	439	7	)	)	PUNCT
ejpam-2714	439	8	,	,	PUNCT
ejpam-2714	439	9	g(ρ(0),ρ(t	g(ρ(0),ρ(t	NOUN
ejpam-2714	439	10	)	)	PUNCT
ejpam-2714	439	11	)	)	PUNCT
ejpam-2714	440	1	=	=	PUNCT
ejpam-2714	440	2	0	0	NUM
ejpam-2714	440	3	,	,	PUNCT
ejpam-2714	440	4	c	c	PROPN
ejpam-2714	440	5	dqr	dqr	PROPN
ejpam-2714	440	6	=	=	SYM
ejpam-2714	440	7	f(t	f(t	NOUN
ejpam-2714	440	8	,	,	PUNCT
ejpam-2714	440	9	ρ	ρ	NOUN
ejpam-2714	440	10	,	,	PUNCT
ejpam-2714	440	11	iq(ρ	iq(ρ	NOUN
ejpam-2714	440	12	)	)	PUNCT
ejpam-2714	440	13	)	)	PUNCT
ejpam-2714	441	1	+	+	CCONJ
ejpam-2714	442	1	g(t	g(t	PROPN
ejpam-2714	442	2	,	,	PUNCT
ejpam-2714	442	3	r	r	NOUN
ejpam-2714	442	4	,	,	PUNCT
ejpam-2714	442	5	iq(r	iq(r	NOUN
ejpam-2714	442	6	)	)	PUNCT
ejpam-2714	442	7	)	)	PUNCT
ejpam-2714	442	8	,	,	PUNCT
ejpam-2714	442	9	g(r(0	g(r(0	PROPN
ejpam-2714	442	10	)	)	PUNCT
ejpam-2714	442	11	,	,	PUNCT
ejpam-2714	442	12	r(t	r(t	NOUN
ejpam-2714	442	13	)	)	PUNCT
ejpam-2714	442	14	)	)	PUNCT
ejpam-2714	443	1	=	=	PUNCT
ejpam-2714	443	2	0	0	X
ejpam-2714	443	3	.	.	NOUN
ejpam-2714	443	4	4	4	NUM
ejpam-2714	443	5	.	.	X
ejpam-2714	443	6	conclusion	conclusion	NOUN
ejpam-2714	443	7	we	we	PRON
ejpam-2714	443	8	consider	consider	VERB
ejpam-2714	443	9	periodic	periodic	ADJ
ejpam-2714	443	10	boundary	boundary	ADJ
ejpam-2714	443	11	value	value	NOUN
ejpam-2714	443	12	problem	problem	NOUN
ejpam-2714	443	13	of	of	ADP
ejpam-2714	443	14	caputo	caputo	PROPN
ejpam-2714	443	15	fractional	fractional	PROPN
ejpam-2714	443	16	integro	integro	PROPN
ejpam-2714	443	17	differential	differential	ADJ
ejpam-2714	443	18	equation	equation	NOUN
ejpam-2714	443	19	and	and	CCONJ
ejpam-2714	443	20	obtained	obtain	VERB
ejpam-2714	443	21	its	its	PRON
ejpam-2714	443	22	maximal	maximal	ADJ
ejpam-2714	443	23	and	and	CCONJ
ejpam-2714	443	24	minimal	minimal	ADJ
ejpam-2714	443	25	solutions	solution	NOUN
ejpam-2714	443	26	.	.	PUNCT
ejpam-2714	444	1	we	we	PRON
ejpam-2714	444	2	obtained	obtain	VERB
ejpam-2714	444	3	this	this	PRON
ejpam-2714	444	4	by	by	ADP
ejpam-2714	444	5	using	use	VERB
ejpam-2714	444	6	monotone	monotone	ADJ
ejpam-2714	444	7	iterative	iterative	NOUN
ejpam-2714	444	8	technique	technique	NOUN
ejpam-2714	444	9	of	of	ADP
ejpam-2714	444	10	initial	initial	ADJ
ejpam-2714	444	11	value	value	NOUN
ejpam-2714	444	12	problems	problem	NOUN
ejpam-2714	444	13	.	.	PUNCT
ejpam-2714	445	1	references	reference	NOUN
ejpam-2714	445	2	[	[	X
ejpam-2714	445	3	1	1	NUM
ejpam-2714	445	4	]	]	PUNCT
ejpam-2714	445	5	z.	z.	PROPN
ejpam-2714	445	6	denton	denton	PROPN
ejpam-2714	445	7	and	and	CCONJ
ejpam-2714	445	8	a.s	a.s	PROPN
ejpam-2714	445	9	.	.	PROPN
ejpam-2714	445	10	vatsala	vatsala	PROPN
ejpam-2714	445	11	.	.	PUNCT
ejpam-2714	446	1	monotone	monotone	ADJ
ejpam-2714	446	2	iterative	iterative	NOUN
ejpam-2714	446	3	technique	technique	NOUN
ejpam-2714	446	4	for	for	ADP
ejpam-2714	446	5	finite	finite	ADJ
ejpam-2714	446	6	systems	system	NOUN
ejpam-2714	446	7	of	of	ADP
ejpam-2714	446	8	nonlinear	nonlinear	PROPN
ejpam-2714	446	9	riemann	riemann	PROPN
ejpam-2714	446	10	liouville	liouville	PROPN
ejpam-2714	446	11	fractional	fractional	ADJ
ejpam-2714	446	12	differential	differential	NOUN
ejpam-2714	446	13	equations	equation	NOUN
ejpam-2714	446	14	,	,	PUNCT
ejpam-2714	446	15	opuscula	opuscula	PROPN
ejpam-2714	446	16	mathematica	mathematica	PROPN
ejpam-2714	446	17	,	,	PUNCT
ejpam-2714	446	18	vol	vol	NOUN
ejpam-2714	446	19	.	.	PUNCT
ejpam-2714	447	1	31(3	31(3	NUM
ejpam-2714	447	2	)	)	PUNCT
ejpam-2714	447	3	,	,	PUNCT
ejpam-2714	448	1	pps	pps	PROPN
ejpam-2714	448	2	.	.	PROPN
ejpam-2714	448	3	327	327	NUM
ejpam-2714	448	4	-	-	SYM
ejpam-2714	448	5	339	339	NUM
ejpam-2714	448	6	.	.	PUNCT
ejpam-2714	448	7	2011	2011	NUM
ejpam-2714	448	8	.	.	PUNCT
ejpam-2714	449	1	[	[	X
ejpam-2714	449	2	2	2	X
ejpam-2714	449	3	]	]	PUNCT
ejpam-2714	449	4	s.	s.	PROPN
ejpam-2714	449	5	kazem	kazem	PROPN
ejpam-2714	449	6	.	.	PUNCT
ejpam-2714	450	1	exact	exact	ADJ
ejpam-2714	450	2	solution	solution	NOUN
ejpam-2714	450	3	of	of	ADP
ejpam-2714	450	4	some	some	DET
ejpam-2714	450	5	linear	linear	ADJ
ejpam-2714	450	6	fractional	fractional	ADJ
ejpam-2714	450	7	differential	differential	ADJ
ejpam-2714	450	8	equations	equation	NOUN
ejpam-2714	450	9	by	by	ADP
ejpam-2714	450	10	laplace	laplace	NOUN
ejpam-2714	450	11	transform	transform	NOUN
ejpam-2714	450	12	,	,	PUNCT
ejpam-2714	450	13	international	international	ADJ
ejpam-2714	450	14	journal	journal	NOUN
ejpam-2714	450	15	of	of	ADP
ejpam-2714	450	16	nonlinear	nonlinear	ADJ
ejpam-2714	450	17	science	science	NOUN
ejpam-2714	450	18	,	,	PUNCT
ejpam-2714	450	19	vol	vol	NOUN
ejpam-2714	450	20	.	.	PUNCT
ejpam-2714	450	21	16(1	16(1	NUM
ejpam-2714	450	22	)	)	PUNCT
ejpam-2714	450	23	,	,	PUNCT
ejpam-2714	450	24	pps	pps	NOUN
ejpam-2714	450	25	3	3	NUM
ejpam-2714	450	26	-	-	SYM
ejpam-2714	450	27	11	11	NUM
ejpam-2714	450	28	.	.	PUNCT
ejpam-2714	451	1	2013	2013	NUM
ejpam-2714	451	2	.	.	PUNCT
ejpam-2714	452	1	[	[	X
ejpam-2714	452	2	3	3	NUM
ejpam-2714	452	3	]	]	X
ejpam-2714	452	4	a.a	a.a	PROPN
ejpam-2714	452	5	.	.	PROPN
ejpam-2714	452	6	kilbas	kilbas	PROPN
ejpam-2714	452	7	,	,	PUNCT
ejpam-2714	452	8	h.m	h.m	PROPN
ejpam-2714	452	9	.	.	PROPN
ejpam-2714	452	10	srivatsava	srivatsava	PROPN
ejpam-2714	452	11	,	,	PUNCT
ejpam-2714	452	12	and	and	CCONJ
ejpam-2714	452	13	j.j	j.j	PROPN
ejpam-2714	452	14	.	.	PROPN
ejpam-2714	452	15	trujillo	trujillo	PROPN
ejpam-2714	452	16	.	.	PUNCT
ejpam-2714	452	17	theory	theory	NOUN
ejpam-2714	452	18	and	and	CCONJ
ejpam-2714	452	19	applications	application	NOUN
ejpam-2714	452	20	of	of	ADP
ejpam-2714	452	21	fractional	fractional	ADJ
ejpam-2714	452	22	differential	differential	ADJ
ejpam-2714	452	23	equations	equation	NOUN
ejpam-2714	452	24	,	,	PUNCT
ejpam-2714	452	25	elsevier	elsevier	NOUN
ejpam-2714	452	26	,	,	PUNCT
ejpam-2714	452	27	amsterdam	amsterdam	PROPN
ejpam-2714	452	28	,	,	PUNCT
ejpam-2714	452	29	2006	2006	NUM
ejpam-2714	452	30	.	.	PUNCT
ejpam-2714	453	1	[	[	X
ejpam-2714	453	2	4	4	NUM
ejpam-2714	453	3	]	]	X
ejpam-2714	453	4	v.s.l	v.s.l	NOUN
ejpam-2714	453	5	.	.	PUNCT
ejpam-2714	454	1	lakshmikantham	lakshmikantham	PROPN
ejpam-2714	454	2	and	and	CCONJ
ejpam-2714	454	3	j.v	j.v	PROPN
ejpam-2714	454	4	.	.	PUNCT
ejpam-2714	455	1	devi	devi	PROPN
ejpam-2714	455	2	.	.	PUNCT
ejpam-2714	455	3	theory	theory	NOUN
ejpam-2714	455	4	of	of	ADP
ejpam-2714	455	5	fractional	fractional	ADJ
ejpam-2714	455	6	dynamic	dynamic	ADJ
ejpam-2714	455	7	systems	system	NOUN
ejpam-2714	455	8	,	,	PUNCT
ejpam-2714	455	9	cambridge	cambridge	NOUN
ejpam-2714	455	10	scientific	scientific	ADJ
ejpam-2714	455	11	publishers	publisher	NOUN
ejpam-2714	455	12	,	,	PUNCT
ejpam-2714	455	13	colterham	colterham	NOUN
ejpam-2714	455	14	,	,	PUNCT
ejpam-2714	455	15	2009	2009	NUM
ejpam-2714	455	16	.	.	PUNCT
ejpam-2714	456	1	references	reference	NOUN
ejpam-2714	456	2	359	359	NUM
ejpam-2714	457	1	[	[	X
ejpam-2714	457	2	5	5	NUM
ejpam-2714	457	3	]	]	X
ejpam-2714	457	4	f.a	f.a	PROPN
ejpam-2714	457	5	.	.	PROPN
ejpam-2714	457	6	mcrae	mcrae	PROPN
ejpam-2714	457	7	,	,	PUNCT
ejpam-2714	457	8	j.v	j.v	PROPN
ejpam-2714	457	9	.	.	PUNCT
ejpam-2714	457	10	devi	devi	PROPN
ejpam-2714	457	11	,	,	PUNCT
ejpam-2714	457	12	and	and	CCONJ
ejpam-2714	457	13	z.	z.	PROPN
ejpam-2714	457	14	drici	drici	PROPN
ejpam-2714	457	15	.	.	PUNCT
ejpam-2714	458	1	existence	existence	NOUN
ejpam-2714	458	2	result	result	VERB
ejpam-2714	458	3	for	for	ADP
ejpam-2714	458	4	periodic	periodic	ADJ
ejpam-2714	458	5	boundary	boundary	ADJ
ejpam-2714	458	6	value	value	NOUN
ejpam-2714	458	7	problem	problem	NOUN
ejpam-2714	458	8	of	of	ADP
ejpam-2714	458	9	set	set	VERB
ejpam-2714	458	10	differential	differential	ADJ
ejpam-2714	458	11	equations	equation	NOUN
ejpam-2714	458	12	using	use	VERB
ejpam-2714	458	13	monotone	monotone	ADJ
ejpam-2714	458	14	iterative	iterative	NOUN
ejpam-2714	458	15	technique	technique	NOUN
ejpam-2714	458	16	,	,	PUNCT
ejpam-2714	458	17	communications	communication	NOUN
ejpam-2714	458	18	in	in	ADP
ejpam-2714	458	19	applied	apply	VERB
ejpam-2714	458	20	analysis	analysis	NOUN
ejpam-2714	458	21	,	,	PUNCT
ejpam-2714	458	22	vol	vol	NOUN
ejpam-2714	458	23	.	.	PUNCT
ejpam-2714	459	1	19(2015	19(2015	NUM
ejpam-2714	459	2	)	)	PUNCT
ejpam-2714	459	3	,	,	PUNCT
ejpam-2714	460	1	pps	pps	PROPN
ejpam-2714	460	2	.	.	PROPN
ejpam-2714	460	3	245	245	NUM
ejpam-2714	460	4	-	-	SYM
ejpam-2714	460	5	256	256	NUM
ejpam-2714	460	6	.	.	NOUN
ejpam-2714	460	7	2015	2015	NUM
ejpam-2714	460	8	.	.	PUNCT
ejpam-2714	461	1	[	[	X
ejpam-2714	461	2	6	6	NUM
ejpam-2714	461	3	]	]	X
ejpam-2714	461	4	k.b	k.b	PROPN
ejpam-2714	461	5	.	.	PROPN
ejpam-2714	461	6	oldham	oldham	PROPN
ejpam-2714	461	7	and	and	CCONJ
ejpam-2714	461	8	j.	j.	PROPN
ejpam-2714	461	9	spanier	spanier	PROPN
ejpam-2714	461	10	.	.	PUNCT
ejpam-2714	462	1	the	the	DET
ejpam-2714	462	2	fractional	fractional	ADJ
ejpam-2714	462	3	calculus	calculus	NOUN
ejpam-2714	462	4	:	:	PUNCT
ejpam-2714	462	5	theory	theory	NOUN
ejpam-2714	462	6	and	and	CCONJ
ejpam-2714	462	7	applications	application	NOUN
ejpam-2714	462	8	of	of	ADP
ejpam-2714	462	9	differentiation	differentiation	NOUN
ejpam-2714	462	10	and	and	CCONJ
ejpam-2714	462	11	integration	integration	NOUN
ejpam-2714	462	12	to	to	ADP
ejpam-2714	462	13	arbitrary	arbitrary	ADJ
ejpam-2714	462	14	order	order	NOUN
ejpam-2714	462	15	,	,	PUNCT
ejpam-2714	462	16	dover	dover	PROPN
ejpam-2714	462	17	publications	publication	NOUN
ejpam-2714	462	18	,	,	PUNCT
ejpam-2714	462	19	new	new	PROPN
ejpam-2714	462	20	york	york	PROPN
ejpam-2714	462	21	,	,	PUNCT
ejpam-2714	462	22	2006	2006	NUM
ejpam-2714	462	23	.	.	PUNCT
ejpam-2714	463	1	[	[	X
ejpam-2714	463	2	7	7	X
ejpam-2714	463	3	]	]	X
ejpam-2714	463	4	s.g	s.g	PROPN
ejpam-2714	463	5	.	.	PROPN
ejpam-2714	463	6	pandit	pandit	PROPN
ejpam-2714	463	7	,	,	PUNCT
ejpam-2714	463	8	d.h	d.h	PROPN
ejpam-2714	463	9	.	.	PROPN
ejpam-2714	463	10	dezem	dezem	PROPN
ejpam-2714	463	11	,	,	PUNCT
ejpam-2714	463	12	and	and	CCONJ
ejpam-2714	463	13	j.o	j.o	PROPN
ejpam-2714	463	14	.	.	PROPN
ejpam-2714	463	15	adeyeye	adeyeye	PROPN
ejpam-2714	463	16	.	.	PUNCT
ejpam-2714	464	1	periodic	periodic	ADJ
ejpam-2714	464	2	boundary	boundary	ADJ
ejpam-2714	464	3	value	value	NOUN
ejpam-2714	464	4	problems	problem	NOUN
ejpam-2714	464	5	for	for	ADP
ejpam-2714	464	6	nonlinear	nonlinear	ADJ
ejpam-2714	464	7	integro	integro	ADJ
ejpam-2714	464	8	-	-	PUNCT
ejpam-2714	464	9	differential	differential	NOUN
ejpam-2714	464	10	equations	equation	NOUN
ejpam-2714	464	11	,	,	PUNCT
ejpam-2714	464	12	in	in	ADP
ejpam-2714	464	13	proceedings	proceeding	NOUN
ejpam-2714	464	14	of	of	ADP
ejpam-2714	464	15	neural	neural	ADJ
ejpam-2714	464	16	,	,	PUNCT
ejpam-2714	464	17	parallel	parallel	ADJ
ejpam-2714	464	18	and	and	CCONJ
ejpam-2714	464	19	scientific	scientific	ADJ
ejpam-2714	464	20	computations	computation	NOUN
ejpam-2714	464	21	,	,	PUNCT
ejpam-2714	464	22	vol	vol	NOUN
ejpam-2714	464	23	.	.	PUNCT
ejpam-2714	465	1	4(2010	4(2010	NUM
ejpam-2714	465	2	)	)	PUNCT
ejpam-2714	465	3	,	,	PUNCT
ejpam-2714	465	4	pps	pps	NOUN
ejpam-2714	465	5	316	316	NUM
ejpam-2714	465	6	-	-	SYM
ejpam-2714	465	7	320	320	NUM
ejpam-2714	465	8	,	,	PUNCT
ejpam-2714	465	9	dynamic	dynamic	ADJ
ejpam-2714	465	10	publishing	publishing	NOUN
ejpam-2714	465	11	,	,	PUNCT
ejpam-2714	465	12	atlanta	atlanta	PROPN
ejpam-2714	465	13	.	.	PUNCT
ejpam-2714	466	1	2010	2010	NUM
ejpam-2714	466	2	.	.	PUNCT
ejpam-2714	467	1	[	[	X
ejpam-2714	467	2	8	8	NUM
ejpam-2714	467	3	]	]	X
ejpam-2714	467	4	i.	i.	NOUN
ejpam-2714	467	5	podlubny	podlubny	PROPN
ejpam-2714	467	6	.	.	PUNCT
ejpam-2714	468	1	fractional	fractional	ADJ
ejpam-2714	468	2	differential	differential	ADJ
ejpam-2714	468	3	equations	equation	NOUN
ejpam-2714	468	4	,	,	PUNCT
ejpam-2714	468	5	academic	academic	ADJ
ejpam-2714	468	6	press	press	NOUN
ejpam-2714	468	7	,	,	PUNCT
ejpam-2714	468	8	san	san	PROPN
ejpam-2714	468	9	diego	diego	PROPN
ejpam-2714	468	10	,	,	PUNCT
ejpam-2714	468	11	1999	1999	NUM
ejpam-2714	468	12	.	.	PUNCT
ejpam-2714	469	1	[	[	X
ejpam-2714	469	2	9	9	NUM
ejpam-2714	469	3	]	]	PUNCT
ejpam-2714	469	4	j.	j.	PROPN
ejpam-2714	469	5	d.	d.	PROPN
ejpam-2714	469	6	ramirez	ramirez	PROPN
ejpam-2714	469	7	and	and	CCONJ
ejpam-2714	469	8	a.	a.	PROPN
ejpam-2714	469	9	s.	s.	PROPN
ejpam-2714	469	10	vatsala	vatsala	PROPN
ejpam-2714	469	11	.	.	PUNCT
ejpam-2714	470	1	generalized	generalize	VERB
ejpam-2714	470	2	monotone	monotone	ADJ
ejpam-2714	470	3	iterative	iterative	NOUN
ejpam-2714	470	4	technique	technique	NOUN
ejpam-2714	470	5	for	for	ADP
ejpam-2714	470	6	caputo	caputo	PROPN
ejpam-2714	470	7	fractional	fractional	PROPN
ejpam-2714	470	8	differential	differential	NOUN
ejpam-2714	470	9	equation	equation	NOUN
ejpam-2714	470	10	with	with	ADP
ejpam-2714	470	11	periodic	periodic	ADJ
ejpam-2714	470	12	boundary	boundary	ADJ
ejpam-2714	470	13	condition	condition	NOUN
ejpam-2714	470	14	via	via	ADP
ejpam-2714	470	15	initial	initial	ADJ
ejpam-2714	470	16	value	value	NOUN
ejpam-2714	470	17	problem	problem	NOUN
ejpam-2714	470	18	,	,	PUNCT
ejpam-2714	470	19	international	international	ADJ
ejpam-2714	470	20	journal	journal	NOUN
ejpam-2714	470	21	of	of	ADP
ejpam-2714	470	22	differential	differential	ADJ
ejpam-2714	470	23	equations	equation	NOUN
ejpam-2714	470	24	,	,	PUNCT
ejpam-2714	470	25	vol	vol	NOUN
ejpam-2714	470	26	.	.	PROPN
ejpam-2714	470	27	2012	2012	NUM
ejpam-2714	470	28	,	,	PUNCT
ejpam-2714	470	29	pps	pps	NOUN
ejpam-2714	470	30	1	1	NUM
ejpam-2714	470	31	-	-	SYM
ejpam-2714	470	32	17	17	NUM
ejpam-2714	470	33	.	.	PUNCT
ejpam-2714	470	34	2012	2012	NUM
ejpam-2714	470	35	.	.	PUNCT
ejpam-2714	471	1	[	[	X
ejpam-2714	471	2	10	10	NUM
ejpam-2714	471	3	]	]	X
ejpam-2714	471	4	w	w	PROPN
ejpam-2714	471	5	-	-	PUNCT
ejpam-2714	471	6	l.	l.	PROPN
ejpam-2714	471	7	wang	wang	PROPN
ejpam-2714	471	8	,	,	PUNCT
ejpam-2714	471	9	j	j	PROPN
ejpam-2714	471	10	-	-	PROPN
ejpam-2714	471	11	f.	f.	PROPN
ejpam-2714	471	12	tian	tian	PROPN
ejpam-2714	471	13	.	.	PUNCT
ejpam-2714	472	1	generalized	generalize	VERB
ejpam-2714	472	2	monotone	monotone	ADJ
ejpam-2714	472	3	iterative	iterative	NOUN
ejpam-2714	472	4	menthod	menthod	NOUN
ejpam-2714	472	5	for	for	ADP
ejpam-2714	472	6	nonlinear	nonlinear	ADJ
ejpam-2714	472	7	boundary	boundary	ADJ
ejpam-2714	472	8	value	value	NOUN
ejpam-2714	472	9	problems	problem	NOUN
ejpam-2714	472	10	with	with	ADP
ejpam-2714	472	11	causal	causal	NOUN
ejpam-2714	472	12	operators	operator	NOUN
ejpam-2714	472	13	,	,	PUNCT
ejpam-2714	472	14	boundary	boundary	ADJ
ejpam-2714	472	15	value	value	NOUN
ejpam-2714	472	16	problems	problem	NOUN
ejpam-2714	472	17	,	,	PUNCT
ejpam-2714	472	18	vol	vol	NOUN
ejpam-2714	472	19	.	.	PUNCT
ejpam-2714	473	1	2014(192	2014(192	NUM
ejpam-2714	473	2	)	)	PUNCT
ejpam-2714	474	1	,	,	PUNCT
ejpam-2714	474	2	pps	pps	NOUN
ejpam-2714	474	3	1	1	NUM
ejpam-2714	474	4	-	-	SYM
ejpam-2714	474	5	12	12	NUM
ejpam-2714	474	6	.	.	PUNCT
ejpam-2714	474	7	2014	2014	NUM
ejpam-2714	474	8	.	.	PUNCT