id	sid	tid	token	lemma	pos
ejpam-3539	1	1	european	european	PROPN
ejpam-3539	1	2	journal	journal	PROPN
ejpam-3539	1	3	of	of	ADP
ejpam-3539	1	4	pure	pure	ADJ
ejpam-3539	1	5	and	and	CCONJ
ejpam-3539	1	6	applied	apply	VERB
ejpam-3539	1	7	mathematics	mathematic	NOUN
ejpam-3539	1	8	vol	vol	NOUN
ejpam-3539	1	9	.	.	PROPN
ejpam-3539	2	1	13	13	NUM
ejpam-3539	2	2	,	,	PUNCT
ejpam-3539	2	3	no	no	INTJ
ejpam-3539	2	4	.	.	NOUN
ejpam-3539	2	5	1	1	NUM
ejpam-3539	2	6	,	,	PUNCT
ejpam-3539	2	7	2020	2020	NUM
ejpam-3539	2	8	,	,	PUNCT
ejpam-3539	2	9	33	33	NUM
ejpam-3539	2	10	-	-	SYM
ejpam-3539	2	11	47	47	NUM
ejpam-3539	2	12	issn	issn	PROPN
ejpam-3539	2	13	1307	1307	NUM
ejpam-3539	2	14	-	-	SYM
ejpam-3539	2	15	5543	5543	NUM
ejpam-3539	2	16	–	–	PUNCT
ejpam-3539	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3539	2	18	published	publish	VERB
ejpam-3539	2	19	by	by	ADP
ejpam-3539	2	20	new	new	PROPN
ejpam-3539	2	21	york	york	PROPN
ejpam-3539	2	22	business	business	PROPN
ejpam-3539	2	23	global	global	ADJ
ejpam-3539	2	24	higher	high	ADJ
ejpam-3539	2	25	order	order	NOUN
ejpam-3539	2	26	nonlocal	nonlocal	ADJ
ejpam-3539	2	27	boundary	boundary	ADJ
ejpam-3539	2	28	value	value	NOUN
ejpam-3539	2	29	problems	problem	NOUN
ejpam-3539	2	30	at	at	ADP
ejpam-3539	2	31	resonance	resonance	NOUN
ejpam-3539	2	32	on	on	ADP
ejpam-3539	2	33	the	the	DET
ejpam-3539	2	34	half	half	ADJ
ejpam-3539	2	35	-	-	PUNCT
ejpam-3539	2	36	line	line	NOUN
ejpam-3539	2	37	s.a	s.a	PROPN
ejpam-3539	2	38	.	.	PROPN
ejpam-3539	2	39	iyase1	iyase1	PROPN
ejpam-3539	2	40	,	,	PUNCT
ejpam-3539	2	41	a.a	a.a	PROPN
ejpam-3539	2	42	.	.	PROPN
ejpam-3539	2	43	opanuga2,∗	opanuga2,∗	VERB
ejpam-3539	2	44	1	1	NUM
ejpam-3539	2	45	department	department	NOUN
ejpam-3539	2	46	of	of	ADP
ejpam-3539	2	47	mathematics	mathematic	NOUN
ejpam-3539	2	48	,	,	PUNCT
ejpam-3539	2	49	college	college	NOUN
ejpam-3539	2	50	of	of	ADP
ejpam-3539	2	51	science	science	NOUN
ejpam-3539	2	52	and	and	CCONJ
ejpam-3539	2	53	technology	technology	NOUN
ejpam-3539	2	54	,	,	PUNCT
ejpam-3539	2	55	covenant	covenant	ADJ
ejpam-3539	2	56	university	university	PROPN
ejpam-3539	2	57	,	,	PUNCT
ejpam-3539	2	58	ota	ota	PROPN
ejpam-3539	2	59	,	,	PUNCT
ejpam-3539	2	60	ogun	ogun	PROPN
ejpam-3539	2	61	state	state	PROPN
ejpam-3539	2	62	,	,	PUNCT
ejpam-3539	2	63	nigeria	nigeria	PROPN
ejpam-3539	2	64	abstract	abstract	ADJ
ejpam-3539	2	65	.	.	PUNCT
ejpam-3539	3	1	this	this	DET
ejpam-3539	3	2	paper	paper	NOUN
ejpam-3539	3	3	investigates	investigate	VERB
ejpam-3539	3	4	the	the	DET
ejpam-3539	3	5	solvability	solvability	NOUN
ejpam-3539	3	6	of	of	ADP
ejpam-3539	3	7	a	a	DET
ejpam-3539	3	8	class	class	NOUN
ejpam-3539	3	9	of	of	ADP
ejpam-3539	3	10	higher	high	ADJ
ejpam-3539	3	11	order	order	NOUN
ejpam-3539	3	12	nonlocal	nonlocal	ADJ
ejpam-3539	3	13	boundary	boundary	ADJ
ejpam-3539	3	14	value	value	NOUN
ejpam-3539	3	15	problems	problem	NOUN
ejpam-3539	3	16	of	of	ADP
ejpam-3539	3	17	the	the	DET
ejpam-3539	3	18	form	form	NOUN
ejpam-3539	3	19	u(n)(t	u(n)(t	NOUN
ejpam-3539	3	20	)	)	PUNCT
ejpam-3539	3	21	=	=	SYM
ejpam-3539	3	22	g(t	g(t	PROPN
ejpam-3539	3	23	,	,	PUNCT
ejpam-3539	3	24	u(t	u(t	NOUN
ejpam-3539	3	25	)	)	PUNCT
ejpam-3539	3	26	,	,	PUNCT
ejpam-3539	3	27	u′(t	u′(t	X
ejpam-3539	3	28	)	)	PUNCT
ejpam-3539	3	29	·	·	PUNCT
ejpam-3539	3	30	·	·	PUNCT
ejpam-3539	3	31	·	·	PUNCT
ejpam-3539	3	32	u(n−1)(t	u(n−1)(t	NOUN
ejpam-3539	3	33	)	)	PUNCT
ejpam-3539	3	34	)	)	PUNCT
ejpam-3539	3	35	,	,	PUNCT
ejpam-3539	3	36	a.e	a.e	PROPN
ejpam-3539	3	37	.	.	PROPN
ejpam-3539	3	38	t	t	PROPN
ejpam-3539	3	39	∈	∈	PROPN
ejpam-3539	3	40	(	(	PUNCT
ejpam-3539	3	41	0,∞	0,∞	NOUN
ejpam-3539	3	42	)	)	PUNCT
ejpam-3539	3	43	subject	subject	NOUN
ejpam-3539	3	44	to	to	ADP
ejpam-3539	3	45	the	the	DET
ejpam-3539	3	46	boundary	boundary	ADJ
ejpam-3539	3	47	conditions	condition	NOUN
ejpam-3539	3	48	u(n−1)(0	u(n−1)(0	PRON
ejpam-3539	3	49	)	)	PUNCT
ejpam-3539	3	50	=	=	PUNCT
ejpam-3539	4	1	(	(	PUNCT
ejpam-3539	4	2	n−	n−	NOUN
ejpam-3539	4	3	1	1	NUM
ejpam-3539	4	4	)	)	PUNCT
ejpam-3539	4	5	!	!	PUNCT
ejpam-3539	5	1	ξn−1	ξn−1	ADJ
ejpam-3539	5	2	u(ξ	u(ξ	NOUN
ejpam-3539	5	3	)	)	PUNCT
ejpam-3539	5	4	,	,	PUNCT
ejpam-3539	5	5	u(i)(0	u(i)(0	PROPN
ejpam-3539	5	6	)	)	PUNCT
ejpam-3539	5	7	=	=	SYM
ejpam-3539	5	8	0	0	NUM
ejpam-3539	5	9	,	,	PUNCT
ejpam-3539	5	10	i	i	PRON
ejpam-3539	5	11	=	=	NOUN
ejpam-3539	5	12	1	1	NUM
ejpam-3539	5	13	,	,	PUNCT
ejpam-3539	5	14	2	2	NUM
ejpam-3539	5	15	,	,	PUNCT
ejpam-3539	5	16	.	.	PUNCT
ejpam-3539	5	17	.	.	PUNCT
ejpam-3539	5	18	.	.	PUNCT
ejpam-3539	6	1	,	,	PUNCT
ejpam-3539	6	2	n−	n−	NOUN
ejpam-3539	6	3	2	2	NUM
ejpam-3539	6	4	,	,	PUNCT
ejpam-3539	6	5	u(n−1)(∞	u(n−1)(∞	NOUN
ejpam-3539	6	6	)	)	PUNCT
ejpam-3539	7	1	=	=	PUNCT
ejpam-3539	7	2	∫	∫	PROPN
ejpam-3539	8	1	ξ	ξ	SYM
ejpam-3539	8	2	0	0	NUM
ejpam-3539	8	3	u(n−1)(s)da(s	u(n−1)(s)da(	NOUN
ejpam-3539	8	4	)	)	PUNCT
ejpam-3539	8	5	where	where	SCONJ
ejpam-3539	8	6	ξ	ξ	X
ejpam-3539	8	7	>	>	X
ejpam-3539	8	8	0	0	NUM
ejpam-3539	8	9	,	,	PUNCT
ejpam-3539	8	10	g	g	NOUN
ejpam-3539	8	11	:	:	PUNCT
ejpam-3539	9	1	[	[	X
ejpam-3539	9	2	0,∞)×<n	0,∞)×<n	VERB
ejpam-3539	9	3	−→	−→	NOUN
ejpam-3539	9	4	<	<	X
ejpam-3539	9	5	is	be	AUX
ejpam-3539	9	6	a	a	DET
ejpam-3539	9	7	caratheodory	caratheodory	NOUN
ejpam-3539	9	8	’s	’s	PART
ejpam-3539	9	9	function	function	NOUN
ejpam-3539	9	10	,	,	PUNCT
ejpam-3539	9	11	a	a	PRON
ejpam-3539	9	12	:	:	PUNCT
ejpam-3539	10	1	[	[	X
ejpam-3539	10	2	0	0	NUM
ejpam-3539	10	3	,	,	PUNCT
ejpam-3539	10	4	ξ	ξ	X
ejpam-3539	10	5	]	]	X
ejpam-3539	10	6	−→	−→	NOUN
ejpam-3539	10	7	[	[	X
ejpam-3539	10	8	0	0	NUM
ejpam-3539	10	9	,	,	PUNCT
ejpam-3539	10	10	1	1	NUM
ejpam-3539	10	11	)	)	PUNCT
ejpam-3539	10	12	is	be	AUX
ejpam-3539	10	13	a	a	DET
ejpam-3539	10	14	non	non	ADJ
ejpam-3539	10	15	-	-	ADJ
ejpam-3539	10	16	decreasing	decrease	VERB
ejpam-3539	10	17	function	function	NOUN
ejpam-3539	10	18	with	with	ADP
ejpam-3539	10	19	a(0	a(0	PROPN
ejpam-3539	10	20	)	)	PUNCT
ejpam-3539	10	21	=	=	SYM
ejpam-3539	10	22	0	0	NUM
ejpam-3539	10	23	,	,	PUNCT
ejpam-3539	10	24	a(ξ	a(ξ	PROPN
ejpam-3539	10	25	)	)	PUNCT
ejpam-3539	10	26	=	=	SYM
ejpam-3539	11	1	1	1	X
ejpam-3539	11	2	.	.	PUNCT
ejpam-3539	12	1	the	the	DET
ejpam-3539	12	2	differential	differential	ADJ
ejpam-3539	12	3	operator	operator	NOUN
ejpam-3539	12	4	is	be	AUX
ejpam-3539	12	5	a	a	DET
ejpam-3539	12	6	fredholm	fredholm	NOUN
ejpam-3539	12	7	map	map	NOUN
ejpam-3539	12	8	of	of	ADP
ejpam-3539	12	9	index	index	NOUN
ejpam-3539	12	10	zero	zero	NUM
ejpam-3539	12	11	and	and	CCONJ
ejpam-3539	12	12	non	non	ADJ
ejpam-3539	12	13	-	-	ADJ
ejpam-3539	12	14	invertible	invertible	ADJ
ejpam-3539	12	15	.	.	PUNCT
ejpam-3539	13	1	we	we	PRON
ejpam-3539	13	2	shall	shall	AUX
ejpam-3539	13	3	employ	employ	VERB
ejpam-3539	13	4	coicidence	coicidence	NOUN
ejpam-3539	13	5	degree	degree	NOUN
ejpam-3539	13	6	arguments	argument	NOUN
ejpam-3539	13	7	and	and	CCONJ
ejpam-3539	13	8	construct	construct	VERB
ejpam-3539	13	9	suitable	suitable	ADJ
ejpam-3539	13	10	operators	operator	NOUN
ejpam-3539	13	11	to	to	PART
ejpam-3539	13	12	establish	establish	VERB
ejpam-3539	13	13	existence	existence	NOUN
ejpam-3539	13	14	of	of	ADP
ejpam-3539	13	15	solutions	solution	NOUN
ejpam-3539	13	16	for	for	ADP
ejpam-3539	13	17	the	the	DET
ejpam-3539	13	18	above	above	ADJ
ejpam-3539	13	19	higher	high	ADJ
ejpam-3539	13	20	order	order	NOUN
ejpam-3539	13	21	nonlocal	nonlocal	ADJ
ejpam-3539	13	22	boundary	boundary	ADJ
ejpam-3539	13	23	value	value	NOUN
ejpam-3539	13	24	problems	problem	NOUN
ejpam-3539	13	25	at	at	ADP
ejpam-3539	13	26	resonance	resonance	NOUN
ejpam-3539	13	27	.	.	PUNCT
ejpam-3539	14	1	2020	2020	NUM
ejpam-3539	14	2	mathematics	mathematic	NOUN
ejpam-3539	14	3	subject	subject	NOUN
ejpam-3539	14	4	classifications	classification	NOUN
ejpam-3539	14	5	:	:	PUNCT
ejpam-3539	14	6	34b40	34b40	NUM
ejpam-3539	14	7	,	,	PUNCT
ejpam-3539	14	8	34b15	34b15	NUM
ejpam-3539	14	9	key	key	ADJ
ejpam-3539	14	10	words	word	NOUN
ejpam-3539	14	11	and	and	CCONJ
ejpam-3539	14	12	phrases	phrase	NOUN
ejpam-3539	14	13	:	:	PUNCT
ejpam-3539	14	14	higher	high	ADJ
ejpam-3539	14	15	order	order	NOUN
ejpam-3539	14	16	,	,	PUNCT
ejpam-3539	14	17	resonance	resonance	NOUN
ejpam-3539	14	18	,	,	PUNCT
ejpam-3539	14	19	coincidence	coincidence	NOUN
ejpam-3539	14	20	degree	degree	NOUN
ejpam-3539	14	21	,	,	PUNCT
ejpam-3539	14	22	nonlocal	nonlocal	ADJ
ejpam-3539	14	23	boundary	boundary	ADJ
ejpam-3539	14	24	value	value	NOUN
ejpam-3539	14	25	problem	problem	NOUN
ejpam-3539	14	26	,	,	PUNCT
ejpam-3539	14	27	half	half	ADJ
ejpam-3539	14	28	-	-	PUNCT
ejpam-3539	14	29	line	line	NOUN
ejpam-3539	14	30	1	1	NUM
ejpam-3539	14	31	.	.	PUNCT
ejpam-3539	14	32	introduction	introduction	NOUN
ejpam-3539	14	33	in	in	ADP
ejpam-3539	14	34	this	this	DET
ejpam-3539	14	35	paper	paper	NOUN
ejpam-3539	14	36	,	,	PUNCT
ejpam-3539	14	37	we	we	PRON
ejpam-3539	14	38	study	study	VERB
ejpam-3539	14	39	the	the	DET
ejpam-3539	14	40	existence	existence	NOUN
ejpam-3539	14	41	of	of	ADP
ejpam-3539	14	42	solutions	solution	NOUN
ejpam-3539	14	43	for	for	ADP
ejpam-3539	14	44	the	the	DET
ejpam-3539	14	45	higher	high	ADJ
ejpam-3539	14	46	order	order	NOUN
ejpam-3539	14	47	boundary	boundary	ADJ
ejpam-3539	14	48	value	value	NOUN
ejpam-3539	14	49	problems	problem	NOUN
ejpam-3539	14	50	.	.	PUNCT
ejpam-3539	15	1	u(n)(t	u(n)(t	X
ejpam-3539	15	2	)	)	PUNCT
ejpam-3539	15	3	=	=	SYM
ejpam-3539	15	4	g(t	g(t	PROPN
ejpam-3539	15	5	,	,	PUNCT
ejpam-3539	15	6	u	u	NOUN
ejpam-3539	15	7	,	,	PUNCT
ejpam-3539	15	8	u′(t)	u′(t)	PROPN
ejpam-3539	15	9	...	...	PUNCT
ejpam-3539	15	10	un−1(t	un−1(t	ADJ
ejpam-3539	15	11	)	)	PUNCT
ejpam-3539	15	12	)	)	PUNCT
ejpam-3539	16	1	a.e	a.e	PROPN
ejpam-3539	16	2	.	.	PROPN
ejpam-3539	16	3	t	t	PROPN
ejpam-3539	16	4	∈	∈	PROPN
ejpam-3539	16	5	(	(	PUNCT
ejpam-3539	16	6	0,∞	0,∞	NOUN
ejpam-3539	16	7	)	)	PUNCT
ejpam-3539	16	8	(	(	PUNCT
ejpam-3539	16	9	1	1	X
ejpam-3539	16	10	)	)	PUNCT
ejpam-3539	16	11	∗corresponding	∗corresponde	VERB
ejpam-3539	16	12	author	author	NOUN
ejpam-3539	16	13	.	.	PUNCT
ejpam-3539	17	1	doi	doi	PROPN
ejpam-3539	17	2	:	:	PUNCT
ejpam-3539	17	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3539	https://doi.org/10.29020/nybg.ejpam.v13i1.3539	PROPN
ejpam-3539	17	4	email	email	NOUN
ejpam-3539	17	5	addresses	address	NOUN
ejpam-3539	17	6	:	:	PUNCT
ejpam-3539	17	7	samuel.iyase@covenantuniversity.edu.ng	samuel.iyase@covenantuniversity.edu.ng	PROPN
ejpam-3539	17	8	(	(	PUNCT
ejpam-3539	17	9	s.a	s.a	PROPN
ejpam-3539	17	10	.	.	PROPN
ejpam-3539	17	11	iyase	iyase	PROPN
ejpam-3539	17	12	)	)	PUNCT
ejpam-3539	17	13	,	,	PUNCT
ejpam-3539	17	14	abiodun.opanuga@covenantuniversity.edu.ng	abiodun.opanuga@covenantuniversity.edu.ng	X
ejpam-3539	17	15	(	(	PUNCT
ejpam-3539	17	16	a.a	a.a	PROPN
ejpam-3539	17	17	.	.	PROPN
ejpam-3539	17	18	opanuga	opanuga	PROPN
ejpam-3539	17	19	)	)	PUNCT
ejpam-3539	17	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3539	18	1	33	33	NUM
ejpam-3539	19	1	c	c	X
ejpam-3539	19	2	©	©	NOUN
ejpam-3539	19	3	2020	2020	NUM
ejpam-3539	19	4	ejpam	ejpam	VERB
ejpam-3539	19	5	all	all	DET
ejpam-3539	19	6	rights	right	NOUN
ejpam-3539	19	7	reserved	reserve	VERB
ejpam-3539	19	8	.	.	PUNCT
ejpam-3539	20	1	samuel	samuel	PROPN
ejpam-3539	20	2	a.	a.	PROPN
ejpam-3539	20	3	iyase	iyase	PROPN
ejpam-3539	20	4	,	,	PUNCT
ejpam-3539	20	5	abiodun	abiodun	PROPN
ejpam-3539	20	6	a.	a.	PROPN
ejpam-3539	20	7	opanuga	opanuga	PROPN
ejpam-3539	20	8	/	/	SYM
ejpam-3539	20	9	eur	eur	PROPN
ejpam-3539	20	10	.	.	PUNCT
ejpam-3539	21	1	j.	j.	PROPN
ejpam-3539	21	2	pure	pure	PROPN
ejpam-3539	21	3	appl	appl	PROPN
ejpam-3539	21	4	.	.	PROPN
ejpam-3539	21	5	math	math	PROPN
ejpam-3539	21	6	,	,	PUNCT
ejpam-3539	21	7	13	13	NUM
ejpam-3539	21	8	(	(	PUNCT
ejpam-3539	21	9	1	1	NUM
ejpam-3539	21	10	)	)	PUNCT
ejpam-3539	21	11	(	(	PUNCT
ejpam-3539	21	12	2020	2020	NUM
ejpam-3539	21	13	)	)	PUNCT
ejpam-3539	21	14	,	,	PUNCT
ejpam-3539	21	15	33	33	NUM
ejpam-3539	21	16	-	-	SYM
ejpam-3539	21	17	47	47	NUM
ejpam-3539	21	18	34	34	NUM
ejpam-3539	21	19	subject	subject	NOUN
ejpam-3539	21	20	to	to	ADP
ejpam-3539	21	21	the	the	DET
ejpam-3539	21	22	boundary	boundary	ADJ
ejpam-3539	21	23	conditions	condition	NOUN
ejpam-3539	21	24	u(n−1)(0	u(n−1)(0	PRON
ejpam-3539	21	25	)	)	PUNCT
ejpam-3539	21	26	=	=	PUNCT
ejpam-3539	21	27	(	(	PUNCT
ejpam-3539	21	28	n−	n−	NOUN
ejpam-3539	21	29	1	1	NUM
ejpam-3539	21	30	)	)	PUNCT
ejpam-3539	21	31	!	!	PUNCT
ejpam-3539	22	1	ξn−1	ξn−1	ADJ
ejpam-3539	22	2	u(ξ	u(ξ	NOUN
ejpam-3539	22	3	)	)	PUNCT
ejpam-3539	22	4	,	,	PUNCT
ejpam-3539	22	5	u(i)(0	u(i)(0	PROPN
ejpam-3539	22	6	)	)	PUNCT
ejpam-3539	22	7	=	=	SYM
ejpam-3539	22	8	0	0	NUM
ejpam-3539	22	9	,	,	PUNCT
ejpam-3539	22	10	i	i	PRON
ejpam-3539	22	11	=	=	NOUN
ejpam-3539	22	12	1	1	NUM
ejpam-3539	22	13	,	,	PUNCT
ejpam-3539	22	14	2	2	NUM
ejpam-3539	22	15	,	,	PUNCT
ejpam-3539	22	16	.	.	PUNCT
ejpam-3539	22	17	.	.	PUNCT
ejpam-3539	22	18	.	.	PUNCT
ejpam-3539	23	1	,	,	PUNCT
ejpam-3539	23	2	n−	n−	NOUN
ejpam-3539	23	3	2	2	NUM
ejpam-3539	23	4	,	,	PUNCT
ejpam-3539	23	5	u(n−1)(∞	u(n−1)(∞	NOUN
ejpam-3539	23	6	)	)	PUNCT
ejpam-3539	24	1	=	=	PUNCT
ejpam-3539	24	2	∫	∫	PROPN
ejpam-3539	25	1	ξ	ξ	SYM
ejpam-3539	25	2	0	0	NUM
ejpam-3539	25	3	u(n−1)(s)da(s	u(n−1)(s)da(	NOUN
ejpam-3539	25	4	)	)	PUNCT
ejpam-3539	25	5	(	(	PUNCT
ejpam-3539	25	6	2	2	X
ejpam-3539	25	7	)	)	PUNCT
ejpam-3539	25	8	where	where	SCONJ
ejpam-3539	25	9	ξ	ξ	X
ejpam-3539	25	10	>	>	X
ejpam-3539	25	11	0	0	NUM
ejpam-3539	25	12	,	,	PUNCT
ejpam-3539	25	13	g	g	NOUN
ejpam-3539	25	14	:	:	PUNCT
ejpam-3539	26	1	[	[	X
ejpam-3539	26	2	0,∞)×<n	0,∞)×<n	VERB
ejpam-3539	26	3	−→	−→	NOUN
ejpam-3539	26	4	<	<	X
ejpam-3539	26	5	is	be	AUX
ejpam-3539	26	6	a	a	DET
ejpam-3539	26	7	caratheodory	caratheodory	NOUN
ejpam-3539	26	8	’s	’s	PART
ejpam-3539	26	9	function	function	NOUN
ejpam-3539	26	10	and	and	CCONJ
ejpam-3539	26	11	a	a	PRON
ejpam-3539	26	12	:	:	PUNCT
ejpam-3539	27	1	[	[	X
ejpam-3539	27	2	0	0	NUM
ejpam-3539	27	3	,	,	PUNCT
ejpam-3539	27	4	ξ	ξ	X
ejpam-3539	27	5	]	]	X
ejpam-3539	27	6	−→	−→	NOUN
ejpam-3539	27	7	[	[	X
ejpam-3539	27	8	0	0	NUM
ejpam-3539	27	9	,	,	PUNCT
ejpam-3539	27	10	1	1	NUM
ejpam-3539	27	11	)	)	PUNCT
ejpam-3539	27	12	is	be	AUX
ejpam-3539	27	13	a	a	DET
ejpam-3539	27	14	non	non	ADJ
ejpam-3539	27	15	-	-	ADJ
ejpam-3539	27	16	decreasing	decrease	VERB
ejpam-3539	27	17	function	function	NOUN
ejpam-3539	27	18	with	with	ADP
ejpam-3539	27	19	a(0	a(0	PROPN
ejpam-3539	27	20	)	)	PUNCT
ejpam-3539	27	21	=	=	SYM
ejpam-3539	27	22	0	0	NUM
ejpam-3539	27	23	,	,	PUNCT
ejpam-3539	27	24	a(ξ	a(ξ	PROPN
ejpam-3539	27	25	)	)	PUNCT
ejpam-3539	27	26	=	=	SYM
ejpam-3539	28	1	1	1	X
ejpam-3539	28	2	.	.	PUNCT
ejpam-3539	29	1	the	the	DET
ejpam-3539	29	2	integral	integral	ADJ
ejpam-3539	29	3	is	be	AUX
ejpam-3539	29	4	the	the	DET
ejpam-3539	29	5	riemann	riemann	PROPN
ejpam-3539	29	6	-	-	PUNCT
ejpam-3539	29	7	stieltjes	stieltjes	PROPN
ejpam-3539	29	8	integral	integral	ADJ
ejpam-3539	29	9	.	.	PUNCT
ejpam-3539	30	1	boundary	boundary	ADJ
ejpam-3539	30	2	value	value	NOUN
ejpam-3539	30	3	problems	problem	NOUN
ejpam-3539	30	4	such	such	ADJ
ejpam-3539	30	5	as	as	ADP
ejpam-3539	30	6	(	(	PUNCT
ejpam-3539	30	7	1)-(2	1)-(2	NUM
ejpam-3539	30	8	)	)	PUNCT
ejpam-3539	30	9	with	with	ADP
ejpam-3539	30	10	nontrivial	nontrivial	ADJ
ejpam-3539	30	11	kernels	kernel	NOUN
ejpam-3539	30	12	are	be	AUX
ejpam-3539	30	13	called	call	VERB
ejpam-3539	30	14	resonance	resonance	NOUN
ejpam-3539	30	15	problems	problem	NOUN
ejpam-3539	30	16	.	.	PUNCT
ejpam-3539	31	1	to	to	ADP
ejpam-3539	31	2	the	the	DET
ejpam-3539	31	3	best	good	ADJ
ejpam-3539	31	4	of	of	ADP
ejpam-3539	31	5	our	our	PRON
ejpam-3539	31	6	knowledge	knowledge	NOUN
ejpam-3539	31	7	higher	high	ADJ
ejpam-3539	31	8	order	order	NOUN
ejpam-3539	31	9	boundary	boundary	ADJ
ejpam-3539	31	10	value	value	NOUN
ejpam-3539	31	11	problems	problem	NOUN
ejpam-3539	31	12	on	on	ADP
ejpam-3539	31	13	infinite	infinite	ADJ
ejpam-3539	31	14	intervals	interval	NOUN
ejpam-3539	31	15	at	at	ADP
ejpam-3539	31	16	resonance	resonance	NOUN
ejpam-3539	31	17	have	have	AUX
ejpam-3539	31	18	not	not	PART
ejpam-3539	31	19	received	receive	VERB
ejpam-3539	31	20	much	much	ADJ
ejpam-3539	31	21	attention	attention	NOUN
ejpam-3539	31	22	in	in	ADP
ejpam-3539	31	23	the	the	DET
ejpam-3539	31	24	literature	literature	NOUN
ejpam-3539	31	25	especially	especially	ADV
ejpam-3539	31	26	those	those	PRON
ejpam-3539	31	27	with	with	ADP
ejpam-3539	31	28	integral	integral	ADJ
ejpam-3539	31	29	boundary	boundary	ADJ
ejpam-3539	31	30	conditions	condition	NOUN
ejpam-3539	31	31	.	.	PUNCT
ejpam-3539	32	1	most	most	ADJ
ejpam-3539	32	2	papers	paper	NOUN
ejpam-3539	32	3	focused	focus	VERB
ejpam-3539	32	4	on	on	ADP
ejpam-3539	32	5	boundary	boundary	ADJ
ejpam-3539	32	6	value	value	NOUN
ejpam-3539	32	7	problems	problem	NOUN
ejpam-3539	32	8	at	at	ADP
ejpam-3539	32	9	resonance	resonance	NOUN
ejpam-3539	32	10	on	on	ADP
ejpam-3539	32	11	finite	finite	ADJ
ejpam-3539	32	12	intervals	interval	NOUN
ejpam-3539	32	13	especially	especially	ADV
ejpam-3539	32	14	for	for	ADP
ejpam-3539	32	15	second	second	ADJ
ejpam-3539	32	16	and	and	CCONJ
ejpam-3539	32	17	third	third	ADJ
ejpam-3539	32	18	order	order	NOUN
ejpam-3539	32	19	boundary	boundary	ADJ
ejpam-3539	32	20	value	value	NOUN
ejpam-3539	32	21	problems	problem	NOUN
ejpam-3539	32	22	.	.	PUNCT
ejpam-3539	33	1	for	for	SCONJ
ejpam-3539	33	2	some	some	DET
ejpam-3539	33	3	results	result	NOUN
ejpam-3539	33	4	in	in	ADP
ejpam-3539	33	5	this	this	DET
ejpam-3539	33	6	direction	direction	NOUN
ejpam-3539	33	7	see	see	VERB
ejpam-3539	33	8	[	[	X
ejpam-3539	33	9	4	4	NUM
ejpam-3539	33	10	,	,	PUNCT
ejpam-3539	33	11	5	5	NUM
ejpam-3539	33	12	,	,	PUNCT
ejpam-3539	33	13	6	6	NUM
ejpam-3539	33	14	,	,	PUNCT
ejpam-3539	33	15	7	7	NUM
ejpam-3539	33	16	,	,	PUNCT
ejpam-3539	33	17	8	8	NUM
ejpam-3539	33	18	,	,	PUNCT
ejpam-3539	33	19	9	9	NUM
ejpam-3539	33	20	,	,	PUNCT
ejpam-3539	33	21	10	10	NUM
ejpam-3539	33	22	,	,	PUNCT
ejpam-3539	33	23	11	11	NUM
ejpam-3539	33	24	,	,	PUNCT
ejpam-3539	33	25	12	12	NUM
ejpam-3539	33	26	,	,	PUNCT
ejpam-3539	33	27	13	13	NUM
ejpam-3539	33	28	,	,	PUNCT
ejpam-3539	33	29	14	14	NUM
ejpam-3539	33	30	,	,	PUNCT
ejpam-3539	33	31	15	15	NUM
ejpam-3539	33	32	,	,	PUNCT
ejpam-3539	33	33	17	17	NUM
ejpam-3539	33	34	,	,	PUNCT
ejpam-3539	33	35	18,19	18,19	NUM
ejpam-3539	33	36	]	]	PUNCT
ejpam-3539	33	37	and	and	CCONJ
ejpam-3539	33	38	references	reference	NOUN
ejpam-3539	33	39	therein	therein	ADV
ejpam-3539	33	40	.	.	PUNCT
ejpam-3539	34	1	nonlocal	nonlocal	ADJ
ejpam-3539	34	2	boundary	boundary	ADJ
ejpam-3539	34	3	value	value	NOUN
ejpam-3539	34	4	problems	problem	NOUN
ejpam-3539	34	5	were	be	AUX
ejpam-3539	34	6	first	first	ADV
ejpam-3539	34	7	studied	study	VERB
ejpam-3539	34	8	in	in	ADP
ejpam-3539	34	9	[	[	X
ejpam-3539	34	10	3	3	NUM
ejpam-3539	34	11	]	]	PUNCT
ejpam-3539	34	12	by	by	ADP
ejpam-3539	34	13	bicadze	bicadze	NOUN
ejpam-3539	34	14	and	and	CCONJ
ejpam-3539	34	15	samarskii	samarskii	NOUN
ejpam-3539	34	16	.	.	PUNCT
ejpam-3539	35	1	in	in	ADP
ejpam-3539	35	2	a	a	DET
ejpam-3539	35	3	recent	recent	ADJ
ejpam-3539	35	4	paper	paper	NOUN
ejpam-3539	35	5	[	[	X
ejpam-3539	35	6	10	10	NUM
ejpam-3539	35	7	]	]	X
ejpam-3539	35	8	karakostas	karakosta	NOUN
ejpam-3539	35	9	and	and	CCONJ
ejpam-3539	35	10	tsamatos	tsamato	NOUN
ejpam-3539	35	11	considered	consider	VERB
ejpam-3539	35	12	the	the	DET
ejpam-3539	35	13	following	follow	VERB
ejpam-3539	35	14	nonlocal	nonlocal	ADJ
ejpam-3539	35	15	boundary	boundary	ADJ
ejpam-3539	35	16	value	value	NOUN
ejpam-3539	35	17	problem	problem	NOUN
ejpam-3539	35	18	.	.	PUNCT
ejpam-3539	36	1	x	x	X
ejpam-3539	36	2	′′	′′	PROPN
ejpam-3539	36	3	(	(	PUNCT
ejpam-3539	36	4	t	t	PROPN
ejpam-3539	36	5	)	)	PUNCT
ejpam-3539	36	6	+	+	PUNCT
ejpam-3539	36	7	q(t)f(x(t	q(t)f(x(t	NOUN
ejpam-3539	36	8	)	)	PUNCT
ejpam-3539	36	9	,	,	PUNCT
ejpam-3539	36	10	x	x	SYM
ejpam-3539	36	11	′	′	NUM
ejpam-3539	36	12	(	(	PUNCT
ejpam-3539	36	13	t	t	NOUN
ejpam-3539	36	14	)	)	PUNCT
ejpam-3539	36	15	)	)	PUNCT
ejpam-3539	37	1	=	=	PUNCT
ejpam-3539	37	2	0	0	NUM
ejpam-3539	37	3	,	,	PUNCT
ejpam-3539	37	4	t	t	PROPN
ejpam-3539	37	5	∈	∈	PROPN
ejpam-3539	37	6	(	(	PUNCT
ejpam-3539	37	7	0	0	NUM
ejpam-3539	37	8	,	,	PUNCT
ejpam-3539	37	9	1	1	NUM
ejpam-3539	37	10	)	)	PUNCT
ejpam-3539	37	11	x(0	x(0	PROPN
ejpam-3539	37	12	)	)	PUNCT
ejpam-3539	37	13	=	=	SYM
ejpam-3539	38	1	0	0	NUM
ejpam-3539	38	2	,	,	PUNCT
ejpam-3539	38	3	x	x	X
ejpam-3539	38	4	′	′	NUM
ejpam-3539	38	5	(	(	PUNCT
ejpam-3539	38	6	1	1	NUM
ejpam-3539	38	7	)	)	PUNCT
ejpam-3539	38	8	=	=	SYM
ejpam-3539	38	9	∫	∫	PROPN
ejpam-3539	38	10	1	1	NUM
ejpam-3539	38	11	0	0	NUM
ejpam-3539	38	12	x	x	SYM
ejpam-3539	38	13	′	′	NUM
ejpam-3539	38	14	(	(	PUNCT
ejpam-3539	38	15	s)dg(s	s)dg(s	NOUN
ejpam-3539	38	16	)	)	PUNCT
ejpam-3539	38	17	under	under	ADP
ejpam-3539	38	18	the	the	DET
ejpam-3539	38	19	nonresonance	nonresonance	NOUN
ejpam-3539	38	20	condition	condition	NOUN
ejpam-3539	38	21	0	0	NUM
ejpam-3539	38	22	=	=	SYM
ejpam-3539	38	23	g(0	g(0	PROPN
ejpam-3539	38	24	)	)	PUNCT
ejpam-3539	38	25	≤	≤	NOUN
ejpam-3539	38	26	g(1	g(1	NOUN
ejpam-3539	38	27	)	)	PUNCT
ejpam-3539	38	28	<	<	X
ejpam-3539	39	1	1	1	X
ejpam-3539	39	2	.	.	PUNCT
ejpam-3539	39	3	they	they	PRON
ejpam-3539	39	4	used	use	VERB
ejpam-3539	39	5	krasnoselskii	krasnoselskii	PROPN
ejpam-3539	39	6	’s	’s	PART
ejpam-3539	39	7	fixed	fix	VERB
ejpam-3539	39	8	point	point	NOUN
ejpam-3539	39	9	theorem	theorem	VERB
ejpam-3539	39	10	in	in	ADP
ejpam-3539	39	11	establishing	establish	VERB
ejpam-3539	39	12	existence	existence	NOUN
ejpam-3539	39	13	of	of	ADP
ejpam-3539	39	14	solutions	solution	NOUN
ejpam-3539	39	15	.	.	PUNCT
ejpam-3539	40	1	in	in	ADP
ejpam-3539	40	2	[	[	X
ejpam-3539	40	3	13	13	NUM
ejpam-3539	40	4	]	]	X
ejpam-3539	40	5	lin	lin	PROPN
ejpam-3539	40	6	derived	derive	VERB
ejpam-3539	40	7	existence	existence	NOUN
ejpam-3539	40	8	results	result	VERB
ejpam-3539	40	9	for	for	ADP
ejpam-3539	40	10	the	the	DET
ejpam-3539	40	11	nonlocal	nonlocal	ADJ
ejpam-3539	40	12	boundary	boundary	ADJ
ejpam-3539	40	13	value	value	NOUN
ejpam-3539	40	14	problem	problem	NOUN
ejpam-3539	40	15	.	.	PUNCT
ejpam-3539	41	1	x	x	X
ejpam-3539	41	2	′′	′′	PROPN
ejpam-3539	41	3	(	(	PUNCT
ejpam-3539	41	4	t	t	PROPN
ejpam-3539	41	5	)	)	PUNCT
ejpam-3539	41	6	=	=	PUNCT
ejpam-3539	41	7	f(t	f(t	NOUN
ejpam-3539	41	8	,	,	PUNCT
ejpam-3539	41	9	x(t	x(t	PROPN
ejpam-3539	41	10	)	)	PUNCT
ejpam-3539	41	11	,	,	PUNCT
ejpam-3539	41	12	x	x	X
ejpam-3539	41	13	′	′	NUM
ejpam-3539	41	14	(	(	PUNCT
ejpam-3539	41	15	t	t	PROPN
ejpam-3539	41	16	)	)	PUNCT
ejpam-3539	41	17	)	)	PUNCT
ejpam-3539	41	18	,	,	PUNCT
ejpam-3539	41	19	t	t	PROPN
ejpam-3539	41	20	∈	∈	PROPN
ejpam-3539	41	21	(	(	PUNCT
ejpam-3539	41	22	0	0	NUM
ejpam-3539	41	23	,	,	PUNCT
ejpam-3539	41	24	1	1	NUM
ejpam-3539	41	25	)	)	PUNCT
ejpam-3539	41	26	x(0	x(0	PROPN
ejpam-3539	41	27	)	)	PUNCT
ejpam-3539	41	28	=	=	SYM
ejpam-3539	41	29	α(ξ	α(ξ	PROPN
ejpam-3539	41	30	)	)	PUNCT
ejpam-3539	41	31	,	,	PUNCT
ejpam-3539	41	32	x	x	X
ejpam-3539	41	33	′	′	NUM
ejpam-3539	41	34	(	(	PUNCT
ejpam-3539	41	35	1	1	NUM
ejpam-3539	41	36	)	)	PUNCT
ejpam-3539	41	37	=	=	SYM
ejpam-3539	41	38	∫	∫	PROPN
ejpam-3539	41	39	1	1	NUM
ejpam-3539	41	40	0	0	NUM
ejpam-3539	41	41	x	x	SYM
ejpam-3539	41	42	′	′	NUM
ejpam-3539	41	43	(	(	PUNCT
ejpam-3539	41	44	s)dg(s	s)dg(s	NOUN
ejpam-3539	41	45	)	)	PUNCT
ejpam-3539	41	46	under	under	ADP
ejpam-3539	41	47	the	the	DET
ejpam-3539	41	48	resonant	resonant	ADJ
ejpam-3539	41	49	condition	condition	NOUN
ejpam-3539	41	50	g(1	g(1	NOUN
ejpam-3539	41	51	)	)	PUNCT
ejpam-3539	41	52	=	=	PUNCT
ejpam-3539	41	53	1	1	NUM
ejpam-3539	41	54	the	the	DET
ejpam-3539	41	55	main	main	ADJ
ejpam-3539	41	56	purpose	purpose	NOUN
ejpam-3539	41	57	of	of	ADP
ejpam-3539	41	58	this	this	DET
ejpam-3539	41	59	paper	paper	NOUN
ejpam-3539	41	60	is	be	AUX
ejpam-3539	41	61	to	to	PART
ejpam-3539	41	62	provide	provide	VERB
ejpam-3539	41	63	new	new	ADJ
ejpam-3539	41	64	sufficient	sufficient	ADJ
ejpam-3539	41	65	conditions	condition	NOUN
ejpam-3539	41	66	that	that	PRON
ejpam-3539	41	67	guarantees	guarantee	VERB
ejpam-3539	41	68	existence	existence	NOUN
ejpam-3539	41	69	of	of	ADP
ejpam-3539	41	70	solutions	solution	NOUN
ejpam-3539	41	71	to	to	ADP
ejpam-3539	41	72	(	(	PUNCT
ejpam-3539	41	73	1)-(2	1)-(2	NUM
ejpam-3539	41	74	)	)	PUNCT
ejpam-3539	41	75	.	.	PUNCT
ejpam-3539	42	1	our	our	PRON
ejpam-3539	42	2	investigation	investigation	NOUN
ejpam-3539	42	3	will	will	AUX
ejpam-3539	42	4	be	be	AUX
ejpam-3539	42	5	based	base	VERB
ejpam-3539	42	6	on	on	ADP
ejpam-3539	42	7	the	the	DET
ejpam-3539	42	8	coincidence	coincidence	NOUN
ejpam-3539	42	9	degree	degree	NOUN
ejpam-3539	42	10	theory	theory	NOUN
ejpam-3539	42	11	of	of	ADP
ejpam-3539	42	12	mawhin	mawhin	NOUN
ejpam-3539	42	13	[	[	X
ejpam-3539	42	14	17	17	NUM
ejpam-3539	42	15	]	]	PUNCT
ejpam-3539	42	16	.	.	PUNCT
ejpam-3539	43	1	the	the	DET
ejpam-3539	43	2	main	main	ADJ
ejpam-3539	43	3	motivation	motivation	NOUN
ejpam-3539	43	4	for	for	ADP
ejpam-3539	43	5	this	this	DET
ejpam-3539	43	6	article	article	NOUN
ejpam-3539	43	7	is	be	AUX
ejpam-3539	43	8	the	the	DET
ejpam-3539	43	9	recent	recent	ADJ
ejpam-3539	43	10	paper	paper	NOUN
ejpam-3539	43	11	of	of	ADP
ejpam-3539	43	12	frioui	frioui	NOUN
ejpam-3539	43	13	,	,	PUNCT
ejpam-3539	43	14	guezane	guezane	NOUN
ejpam-3539	43	15	-	-	PUNCT
ejpam-3539	43	16	lakoud	lakoud	PROPN
ejpam-3539	43	17	and	and	CCONJ
ejpam-3539	43	18	khaldi	khaldi	VERB
ejpam-3539	43	19	[	[	X
ejpam-3539	43	20	7	7	NUM
ejpam-3539	43	21	]	]	PUNCT
ejpam-3539	43	22	.	.	PUNCT
ejpam-3539	44	1	the	the	DET
ejpam-3539	44	2	authors	author	NOUN
ejpam-3539	44	3	obtained	obtain	VERB
ejpam-3539	44	4	existence	existence	NOUN
ejpam-3539	44	5	results	result	NOUN
ejpam-3539	44	6	for	for	ADP
ejpam-3539	44	7	the	the	DET
ejpam-3539	44	8	problem	problem	NOUN
ejpam-3539	44	9	x(n)(t	x(n)(t	NUM
ejpam-3539	44	10	)	)	PUNCT
ejpam-3539	44	11	=	=	PUNCT
ejpam-3539	44	12	f(t	f(t	NOUN
ejpam-3539	44	13	,	,	PUNCT
ejpam-3539	44	14	x(t	x(t	PROPN
ejpam-3539	44	15	)	)	PUNCT
ejpam-3539	44	16	)	)	PUNCT
ejpam-3539	44	17	,	,	PUNCT
ejpam-3539	44	18	t	t	PROPN
ejpam-3539	44	19	∈	∈	PROPN
ejpam-3539	44	20	(	(	PUNCT
ejpam-3539	44	21	0,∞	0,∞	NOUN
ejpam-3539	44	22	)	)	PUNCT
ejpam-3539	44	23	(	(	PUNCT
ejpam-3539	44	24	3	3	X
ejpam-3539	44	25	)	)	PUNCT
ejpam-3539	44	26	x(i)(0	x(i)(0	PROPN
ejpam-3539	44	27	)	)	PUNCT
ejpam-3539	45	1	=	=	SYM
ejpam-3539	45	2	0	0	NUM
ejpam-3539	45	3	,	,	PUNCT
ejpam-3539	45	4	i	i	PRON
ejpam-3539	45	5	:	:	PUNCT
ejpam-3539	45	6	=	=	SYM
ejpam-3539	45	7	0	0	NUM
ejpam-3539	45	8	,	,	PUNCT
ejpam-3539	45	9	1	1	NUM
ejpam-3539	45	10	.	.	PUNCT
ejpam-3539	45	11	.	.	PUNCT
ejpam-3539	45	12	.	.	PUNCT
ejpam-3539	46	1	n−	n−	NOUN
ejpam-3539	46	2	2	2	NUM
ejpam-3539	46	3	,	,	PUNCT
ejpam-3539	46	4	x(n−1)(∞	x(n−1)(∞	PROPN
ejpam-3539	46	5	)	)	PUNCT
ejpam-3539	46	6	=	=	SYM
ejpam-3539	46	7	n	n	X
ejpam-3539	46	8	!	!	PUNCT
ejpam-3539	47	1	ξn	ξn	PROPN
ejpam-3539	47	2	∫	∫	PROPN
ejpam-3539	47	3	ξ	ξ	SYM
ejpam-3539	47	4	0	0	PUNCT
ejpam-3539	47	5	x(t)dt	x(t)dt	PROPN
ejpam-3539	47	6	(	(	PUNCT
ejpam-3539	47	7	4	4	NUM
ejpam-3539	47	8	)	)	PUNCT
ejpam-3539	48	1	where	where	SCONJ
ejpam-3539	48	2	f	f	NOUN
ejpam-3539	48	3	:	:	PUNCT
ejpam-3539	49	1	[	[	X
ejpam-3539	49	2	0,∞	0,∞	NUM
ejpam-3539	49	3	)	)	PUNCT
ejpam-3539	49	4	×	×	NOUN
ejpam-3539	49	5	<	<	X
ejpam-3539	49	6	−→	−→	NOUN
ejpam-3539	49	7	<	<	X
ejpam-3539	49	8	is	be	AUX
ejpam-3539	49	9	a	a	DET
ejpam-3539	49	10	given	give	VERB
ejpam-3539	49	11	function	function	NOUN
ejpam-3539	49	12	satisfying	satisfy	VERB
ejpam-3539	49	13	certain	certain	ADJ
ejpam-3539	49	14	conditions	condition	NOUN
ejpam-3539	49	15	.	.	PUNCT
ejpam-3539	50	1	there	there	PRON
ejpam-3539	50	2	is	be	VERB
ejpam-3539	50	3	so	so	ADV
ejpam-3539	50	4	far	far	ADV
ejpam-3539	50	5	little	little	ADJ
ejpam-3539	50	6	research	research	NOUN
ejpam-3539	50	7	with	with	ADP
ejpam-3539	50	8	regards	regard	NOUN
ejpam-3539	50	9	to	to	ADP
ejpam-3539	50	10	(	(	PUNCT
ejpam-3539	50	11	1)-(2	1)-(2	NUM
ejpam-3539	50	12	)	)	PUNCT
ejpam-3539	50	13	,	,	PUNCT
ejpam-3539	50	14	therefore	therefore	ADV
ejpam-3539	50	15	it	it	PRON
ejpam-3539	50	16	is	be	AUX
ejpam-3539	50	17	important	important	ADJ
ejpam-3539	50	18	to	to	PART
ejpam-3539	50	19	investigate	investigate	VERB
ejpam-3539	50	20	it	it	PRON
ejpam-3539	50	21	.	.	PUNCT
ejpam-3539	51	1	we	we	PRON
ejpam-3539	51	2	samuel	samuel	PROPN
ejpam-3539	51	3	a.	a.	PROPN
ejpam-3539	51	4	iyase	iyase	PROPN
ejpam-3539	51	5	,	,	PUNCT
ejpam-3539	51	6	abiodun	abiodun	PROPN
ejpam-3539	51	7	a.	a.	PROPN
ejpam-3539	51	8	opanuga	opanuga	PROPN
ejpam-3539	51	9	/	/	SYM
ejpam-3539	51	10	eur	eur	PROPN
ejpam-3539	51	11	.	.	PUNCT
ejpam-3539	52	1	j.	j.	PROPN
ejpam-3539	52	2	pure	pure	PROPN
ejpam-3539	52	3	appl	appl	PROPN
ejpam-3539	52	4	.	.	PROPN
ejpam-3539	52	5	math	math	PROPN
ejpam-3539	52	6	,	,	PUNCT
ejpam-3539	52	7	13	13	NUM
ejpam-3539	52	8	(	(	PUNCT
ejpam-3539	52	9	1	1	NUM
ejpam-3539	52	10	)	)	PUNCT
ejpam-3539	52	11	(	(	PUNCT
ejpam-3539	52	12	2020	2020	NUM
ejpam-3539	52	13	)	)	PUNCT
ejpam-3539	52	14	,	,	PUNCT
ejpam-3539	52	15	33	33	NUM
ejpam-3539	52	16	-	-	SYM
ejpam-3539	52	17	47	47	NUM
ejpam-3539	52	18	35	35	NUM
ejpam-3539	52	19	also	also	ADV
ejpam-3539	52	20	note	note	VERB
ejpam-3539	52	21	that	that	SCONJ
ejpam-3539	52	22	(	(	PUNCT
ejpam-3539	52	23	1)-(2	1)-(2	NUM
ejpam-3539	52	24	)	)	PUNCT
ejpam-3539	52	25	is	be	AUX
ejpam-3539	52	26	more	more	ADV
ejpam-3539	52	27	general	general	ADJ
ejpam-3539	52	28	than	than	ADP
ejpam-3539	52	29	(	(	PUNCT
ejpam-3539	52	30	3)-(4	3)-(4	NUM
ejpam-3539	52	31	)	)	PUNCT
ejpam-3539	52	32	.	.	PUNCT
ejpam-3539	53	1	in	in	ADP
ejpam-3539	53	2	section	section	NOUN
ejpam-3539	53	3	2	2	NUM
ejpam-3539	53	4	,	,	PUNCT
ejpam-3539	53	5	we	we	PRON
ejpam-3539	53	6	provide	provide	VERB
ejpam-3539	53	7	some	some	DET
ejpam-3539	53	8	background	background	NOUN
ejpam-3539	53	9	definitions	definition	NOUN
ejpam-3539	53	10	,	,	PUNCT
ejpam-3539	53	11	lemmas	lemmas	PROPN
ejpam-3539	53	12	and	and	CCONJ
ejpam-3539	53	13	the	the	DET
ejpam-3539	53	14	coincidence	coincidence	NOUN
ejpam-3539	53	15	degree	degree	NOUN
ejpam-3539	53	16	theorem	theorem	NOUN
ejpam-3539	53	17	of	of	ADP
ejpam-3539	53	18	mawhin	mawhin	NOUN
ejpam-3539	54	1	[	[	X
ejpam-3539	54	2	17	17	NUM
ejpam-3539	54	3	]	]	PUNCT
ejpam-3539	54	4	,	,	PUNCT
ejpam-3539	54	5	section	section	NOUN
ejpam-3539	54	6	3	3	NUM
ejpam-3539	54	7	will	will	AUX
ejpam-3539	54	8	be	be	AUX
ejpam-3539	54	9	devoted	devote	VERB
ejpam-3539	54	10	to	to	ADP
ejpam-3539	54	11	proving	prove	VERB
ejpam-3539	54	12	the	the	DET
ejpam-3539	54	13	main	main	ADJ
ejpam-3539	54	14	existence	existence	NOUN
ejpam-3539	54	15	results	result	NOUN
ejpam-3539	54	16	.	.	PUNCT
ejpam-3539	55	1	2	2	X
ejpam-3539	55	2	.	.	X
ejpam-3539	55	3	preliminaries	preliminary	NOUN
ejpam-3539	55	4	in	in	ADP
ejpam-3539	55	5	this	this	DET
ejpam-3539	55	6	section	section	NOUN
ejpam-3539	55	7	,	,	PUNCT
ejpam-3539	55	8	we	we	PRON
ejpam-3539	55	9	recall	recall	VERB
ejpam-3539	55	10	some	some	DET
ejpam-3539	55	11	background	background	NOUN
ejpam-3539	55	12	definitions	definition	NOUN
ejpam-3539	55	13	and	and	CCONJ
ejpam-3539	55	14	the	the	DET
ejpam-3539	55	15	coincidence	coincidence	NOUN
ejpam-3539	55	16	degree	degree	NOUN
ejpam-3539	55	17	theorem	theorem	VERB
ejpam-3539	55	18	[	[	X
ejpam-3539	55	19	17	17	NUM
ejpam-3539	55	20	]	]	PUNCT
ejpam-3539	55	21	.	.	PUNCT
ejpam-3539	56	1	we	we	PRON
ejpam-3539	56	2	shall	shall	AUX
ejpam-3539	56	3	also	also	ADV
ejpam-3539	56	4	provide	provide	VERB
ejpam-3539	56	5	compactness	compactness	NOUN
ejpam-3539	56	6	criterion	criterion	NOUN
ejpam-3539	56	7	for	for	ADP
ejpam-3539	56	8	continuous	continuous	ADJ
ejpam-3539	56	9	vector	vector	NOUN
ejpam-3539	56	10	-	-	PUNCT
ejpam-3539	56	11	valued	value	VERB
ejpam-3539	56	12	functions	function	NOUN
ejpam-3539	56	13	on	on	ADP
ejpam-3539	56	14	unbounded	unbounded	ADJ
ejpam-3539	56	15	domains	domain	NOUN
ejpam-3539	56	16	.	.	PUNCT
ejpam-3539	57	1	first	first	ADV
ejpam-3539	57	2	,	,	PUNCT
ejpam-3539	57	3	we	we	PRON
ejpam-3539	57	4	give	give	VERB
ejpam-3539	57	5	some	some	DET
ejpam-3539	57	6	background	background	NOUN
ejpam-3539	57	7	results	result	NOUN
ejpam-3539	57	8	from	from	ADP
ejpam-3539	57	9	coincidence	coincidence	NOUN
ejpam-3539	57	10	degree	degree	NOUN
ejpam-3539	57	11	theory	theory	NOUN
ejpam-3539	57	12	.	.	PUNCT
ejpam-3539	58	1	definition	definition	NOUN
ejpam-3539	58	2	2.1	2.1	NUM
ejpam-3539	58	3	:	:	PUNCT
ejpam-3539	58	4	definition	definition	NOUN
ejpam-3539	58	5	1	1	NUM
ejpam-3539	58	6	.	.	PUNCT
ejpam-3539	59	1	let	let	VERB
ejpam-3539	59	2	x	x	PRON
ejpam-3539	59	3	and	and	CCONJ
ejpam-3539	59	4	z	z	AUX
ejpam-3539	59	5	be	be	AUX
ejpam-3539	59	6	real	real	ADJ
ejpam-3539	60	1	banach	banach	NOUN
ejpam-3539	60	2	spaces	space	VERB
ejpam-3539	60	3	.	.	PUNCT
ejpam-3539	61	1	a	a	DET
ejpam-3539	61	2	linear	linear	ADJ
ejpam-3539	61	3	mapping	mapping	NOUN
ejpam-3539	61	4	l	l	NOUN
ejpam-3539	61	5	:	:	PUNCT
ejpam-3539	61	6	doml	doml	VERB
ejpam-3539	61	7	⊂	⊂	PROPN
ejpam-3539	61	8	x	x	PUNCT
ejpam-3539	62	1	−→	−→	ADJ
ejpam-3539	62	2	z	z	NOUN
ejpam-3539	62	3	is	be	AUX
ejpam-3539	62	4	said	say	VERB
ejpam-3539	62	5	to	to	PART
ejpam-3539	62	6	be	be	AUX
ejpam-3539	62	7	a	a	DET
ejpam-3539	62	8	fredholm	fredholm	NOUN
ejpam-3539	62	9	mapping	mapping	NOUN
ejpam-3539	62	10	if	if	SCONJ
ejpam-3539	62	11	(	(	PUNCT
ejpam-3539	62	12	i	i	NOUN
ejpam-3539	62	13	)	)	PUNCT
ejpam-3539	62	14	kerl	kerl	PROPN
ejpam-3539	62	15	has	have	VERB
ejpam-3539	62	16	finite	finite	ADJ
ejpam-3539	62	17	dimension	dimension	NOUN
ejpam-3539	62	18	.	.	PUNCT
ejpam-3539	63	1	(	(	PUNCT
ejpam-3539	63	2	ii	ii	NOUN
ejpam-3539	63	3	)	)	PUNCT
ejpam-3539	63	4	iml	iml	NOUN
ejpam-3539	63	5	is	be	AUX
ejpam-3539	63	6	closed	close	VERB
ejpam-3539	63	7	and	and	CCONJ
ejpam-3539	63	8	has	have	VERB
ejpam-3539	63	9	a	a	DET
ejpam-3539	63	10	finite	finite	ADJ
ejpam-3539	63	11	codimension	codimension	NOUN
ejpam-3539	63	12	.	.	PUNCT
ejpam-3539	64	1	in	in	ADP
ejpam-3539	64	2	this	this	DET
ejpam-3539	64	3	case	case	NOUN
ejpam-3539	64	4	,	,	PUNCT
ejpam-3539	64	5	the	the	DET
ejpam-3539	64	6	fredholm	fredholm	NOUN
ejpam-3539	64	7	index	index	NOUN
ejpam-3539	64	8	is	be	AUX
ejpam-3539	64	9	the	the	DET
ejpam-3539	64	10	integer	integer	NOUN
ejpam-3539	64	11	indl	indl	NOUN
ejpam-3539	64	12	=	=	PUNCT
ejpam-3539	64	13	dim	dim	ADJ
ejpam-3539	64	14	kerl−	kerl−	NOUN
ejpam-3539	64	15	codimiml	codimiml	NOUN
ejpam-3539	64	16	.	.	PUNCT
ejpam-3539	65	1	in	in	ADP
ejpam-3539	65	2	this	this	DET
ejpam-3539	65	3	work	work	NOUN
ejpam-3539	65	4	,	,	PUNCT
ejpam-3539	65	5	we	we	PRON
ejpam-3539	65	6	shall	shall	AUX
ejpam-3539	65	7	utilise	utilise	VERB
ejpam-3539	65	8	fredholm	fredholm	NOUN
ejpam-3539	65	9	mappings	mapping	NOUN
ejpam-3539	65	10	of	of	ADP
ejpam-3539	65	11	index	index	NOUN
ejpam-3539	65	12	zero	zero	NUM
ejpam-3539	65	13	.	.	PUNCT
ejpam-3539	66	1	if	if	SCONJ
ejpam-3539	66	2	l	l	NOUN
ejpam-3539	66	3	is	be	AUX
ejpam-3539	66	4	a	a	DET
ejpam-3539	66	5	fredholm	fredholm	NOUN
ejpam-3539	66	6	mapping	mapping	NOUN
ejpam-3539	66	7	of	of	ADP
ejpam-3539	66	8	index	index	NOUN
ejpam-3539	66	9	zero	zero	NUM
ejpam-3539	66	10	,	,	PUNCT
ejpam-3539	66	11	then	then	ADV
ejpam-3539	66	12	there	there	PRON
ejpam-3539	66	13	exist	exist	VERB
ejpam-3539	66	14	continuous	continuous	ADJ
ejpam-3539	66	15	projections	projection	NOUN
ejpam-3539	66	16	p	p	X
ejpam-3539	66	17	:	:	PUNCT
ejpam-3539	66	18	x	x	PUNCT
ejpam-3539	66	19	−→	−→	NOUN
ejpam-3539	66	20	x	x	X
ejpam-3539	66	21	and	and	CCONJ
ejpam-3539	66	22	q	q	NOUN
ejpam-3539	66	23	:	:	PUNCT
ejpam-3539	66	24	z	z	NOUN
ejpam-3539	66	25	−→−→	−→−→	NOUN
ejpam-3539	66	26	z	z	NOUN
ejpam-3539	66	27	such	such	ADJ
ejpam-3539	66	28	that	that	DET
ejpam-3539	66	29	imp	imp	PROPN
ejpam-3539	66	30	=	=	SYM
ejpam-3539	66	31	kerl	kerl	PROPN
ejpam-3539	66	32	,	,	PUNCT
ejpam-3539	66	33	kerq	kerq	NOUN
ejpam-3539	66	34	=	=	SYM
ejpam-3539	66	35	iml	iml	NOUN
ejpam-3539	66	36	and	and	CCONJ
ejpam-3539	66	37	x	x	X
ejpam-3539	67	1	=	=	PUNCT
ejpam-3539	67	2	kerl⊕	kerl⊕	NOUN
ejpam-3539	67	3	kerp	kerp	PROPN
ejpam-3539	67	4	z	z	PROPN
ejpam-3539	68	1	=	=	PUNCT
ejpam-3539	69	1	iml⊕	iml⊕	PROPN
ejpam-3539	69	2	imq	imq	NOUN
ejpam-3539	69	3	and	and	CCONJ
ejpam-3539	69	4	the	the	DET
ejpam-3539	69	5	mapping	mapping	NOUN
ejpam-3539	69	6	l|doml∩kerp	l|doml∩kerp	PROPN
ejpam-3539	69	7	:	:	PUNCT
ejpam-3539	69	8	doml	doml	PROPN
ejpam-3539	69	9	∩	∩	PROPN
ejpam-3539	69	10	kerp	kerp	PROPN
ejpam-3539	69	11	−→	−→	ADJ
ejpam-3539	69	12	iml	iml	NOUN
ejpam-3539	69	13	is	be	AUX
ejpam-3539	69	14	invertible	invertible	ADJ
ejpam-3539	69	15	.	.	PUNCT
ejpam-3539	70	1	‘	'	PUNCT
ejpam-3539	70	2	we	we	PRON
ejpam-3539	70	3	denote	denote	VERB
ejpam-3539	70	4	the	the	DET
ejpam-3539	70	5	inverse	inverse	NOUN
ejpam-3539	70	6	of	of	ADP
ejpam-3539	70	7	l|doml∩kerp	l|doml∩kerp	PROPN
ejpam-3539	70	8	by	by	ADP
ejpam-3539	70	9	kp	kp	PROPN
ejpam-3539	70	10	:	:	PUNCT
ejpam-3539	70	11	iml	iml	PROPN
ejpam-3539	70	12	−→	−→	NOUN
ejpam-3539	70	13	doml	doml	PROPN
ejpam-3539	70	14	∩	∩	PROPN
ejpam-3539	70	15	kerp	kerp	PROPN
ejpam-3539	70	16	.	.	PUNCT
ejpam-3539	71	1	we	we	PRON
ejpam-3539	71	2	designate	designate	VERB
ejpam-3539	71	3	the	the	DET
ejpam-3539	71	4	generalised	generalised	ADJ
ejpam-3539	71	5	inverse	inverse	NOUN
ejpam-3539	71	6	of	of	ADP
ejpam-3539	71	7	l	l	NOUN
ejpam-3539	71	8	given	give	VERB
ejpam-3539	71	9	by	by	ADP
ejpam-3539	71	10	kp	kp	PROPN
ejpam-3539	71	11	,	,	PUNCT
ejpam-3539	71	12	q	q	NOUN
ejpam-3539	71	13	:	:	PUNCT
ejpam-3539	71	14	z	z	NOUN
ejpam-3539	71	15	−→	−→	PROPN
ejpam-3539	71	16	doml	doml	PROPN
ejpam-3539	71	17	∩	∩	ADJ
ejpam-3539	71	18	kerp	kerp	PROPN
ejpam-3539	71	19	as	as	ADP
ejpam-3539	71	20	kp	kp	PROPN
ejpam-3539	71	21	,	,	PUNCT
ejpam-3539	71	22	q	q	PROPN
ejpam-3539	71	23	=	=	PUNCT
ejpam-3539	71	24	kp	kp	X
ejpam-3539	71	25	(	(	PUNCT
ejpam-3539	71	26	i	i	PRON
ejpam-3539	71	27	−q	−q	VERB
ejpam-3539	71	28	)	)	PUNCT
ejpam-3539	71	29	.	.	PUNCT
ejpam-3539	72	1	definition	definition	NOUN
ejpam-3539	72	2	2.2	2.2	NUM
ejpam-3539	72	3	:	:	PUNCT
ejpam-3539	72	4	the	the	DET
ejpam-3539	72	5	map	map	NOUN
ejpam-3539	72	6	g	g	NOUN
ejpam-3539	72	7	:	:	PUNCT
ejpam-3539	72	8	[	[	X
ejpam-3539	72	9	0,∞	0,∞	NUM
ejpam-3539	72	10	)	)	PUNCT
ejpam-3539	72	11	×	×	NOUN
ejpam-3539	72	12	<	<	NOUN
ejpam-3539	72	13	n	n	DET
ejpam-3539	72	14	−→	−→	NOUN
ejpam-3539	72	15	<	<	X
ejpam-3539	72	16	is	be	AUX
ejpam-3539	72	17	l1[0,∞)-caratheodory	l1[0,∞)-caratheodory	ADJ
ejpam-3539	72	18	,	,	PUNCT
ejpam-3539	72	19	if	if	SCONJ
ejpam-3539	72	20	the	the	DET
ejpam-3539	72	21	following	follow	VERB
ejpam-3539	72	22	conditions	condition	NOUN
ejpam-3539	72	23	are	be	AUX
ejpam-3539	72	24	satisfied	satisfied	ADJ
ejpam-3539	72	25	.	.	PUNCT
ejpam-3539	73	1	(	(	PUNCT
ejpam-3539	73	2	i	i	NOUN
ejpam-3539	73	3	)	)	PUNCT
ejpam-3539	73	4	for	for	ADP
ejpam-3539	73	5	each	each	DET
ejpam-3539	73	6	u	u	PROPN
ejpam-3539	73	7	∈	∈	PROPN
ejpam-3539	73	8	<	<	NOUN
ejpam-3539	73	9	n	n	CCONJ
ejpam-3539	73	10	,	,	PUNCT
ejpam-3539	73	11	f(t	f(t	PROPN
ejpam-3539	73	12	,	,	PUNCT
ejpam-3539	73	13	u	u	NOUN
ejpam-3539	73	14	)	)	PUNCT
ejpam-3539	73	15	is	be	AUX
ejpam-3539	73	16	lebesgue	lebesgue	ADJ
ejpam-3539	73	17	measurable	measurable	ADJ
ejpam-3539	73	18	(	(	PUNCT
ejpam-3539	73	19	ii	ii	NOUN
ejpam-3539	73	20	)	)	PUNCT
ejpam-3539	73	21	for	for	ADP
ejpam-3539	73	22	a.e	a.e	PROPN
ejpam-3539	73	23	.	.	PROPN
ejpam-3539	73	24	t	t	PROPN
ejpam-3539	73	25	∈	∈	PROPN
ejpam-3539	74	1	[	[	X
ejpam-3539	74	2	0,∞	0,∞	NUM
ejpam-3539	74	3	)	)	PUNCT
ejpam-3539	74	4	,	,	PUNCT
ejpam-3539	74	5	there	there	PRON
ejpam-3539	74	6	exists	exist	VERB
ejpam-3539	74	7	ϕr	ϕr	PRON
ejpam-3539	74	8	∈	∈	PROPN
ejpam-3539	74	9	l1[0,∞	l1[0,∞	NOUN
ejpam-3539	74	10	)	)	PUNCT
ejpam-3539	74	11	such	such	ADJ
ejpam-3539	74	12	that	that	PRON
ejpam-3539	74	13	for	for	ADP
ejpam-3539	74	14	a.e	a.e	PROPN
ejpam-3539	74	15	.	.	PROPN
ejpam-3539	74	16	t	t	PROPN
ejpam-3539	74	17	∈	∈	PROPN
ejpam-3539	75	1	[	[	X
ejpam-3539	75	2	0,∞	0,∞	NUM
ejpam-3539	75	3	)	)	PUNCT
ejpam-3539	75	4	and	and	CCONJ
ejpam-3539	75	5	every	every	DET
ejpam-3539	75	6	u	u	NOUN
ejpam-3539	75	7	such	such	ADJ
ejpam-3539	75	8	that	that	SCONJ
ejpam-3539	75	9	|u|	|u|	ADJ
ejpam-3539	75	10	≤	≤	NOUN
ejpam-3539	75	11	r	r	NOUN
ejpam-3539	75	12	we	we	PRON
ejpam-3539	75	13	have	have	VERB
ejpam-3539	75	14	|f(t	|f(t	NOUN
ejpam-3539	75	15	,	,	PUNCT
ejpam-3539	75	16	u)|	u)|	NOUN
ejpam-3539	75	17	≤	≤	NOUN
ejpam-3539	75	18	ϕr(t	ϕr(t	PUNCT
ejpam-3539	75	19	)	)	PUNCT
ejpam-3539	75	20	.	.	PUNCT
ejpam-3539	76	1	let	let	VERB
ejpam-3539	76	2	x	x	PUNCT
ejpam-3539	76	3	=	=	PRON
ejpam-3539	76	4	{	{	PUNCT
ejpam-3539	76	5	u	u	NOUN
ejpam-3539	76	6	∈	∈	PROPN
ejpam-3539	76	7	cn−1[0,∞	cn−1[0,∞	NOUN
ejpam-3539	76	8	)	)	PUNCT
ejpam-3539	76	9	,	,	PUNCT
ejpam-3539	76	10	limt→∞	limt→∞	PROPN
ejpam-3539	76	11	e	e	PROPN
ejpam-3539	76	12	−t|u(i)(t)|	−t|u(i)(t)|	ADV
ejpam-3539	76	13	exists	exist	VERB
ejpam-3539	76	14	,	,	PUNCT
ejpam-3539	76	15	0	0	NUM
ejpam-3539	76	16	≤	≤	NUM
ejpam-3539	77	1	i	i	PRON
ejpam-3539	77	2	≤	≤	ADJ
ejpam-3539	77	3	n−	n−	PROPN
ejpam-3539	77	4	1	1	NUM
ejpam-3539	77	5	,	,	PUNCT
ejpam-3539	77	6	u(n)(t	u(n)(t	NOUN
ejpam-3539	77	7	)	)	PUNCT
ejpam-3539	77	8	∈	∈	PROPN
ejpam-3539	77	9	l1[0,∞	l1[0,∞	NOUN
ejpam-3539	77	10	)	)	PUNCT
ejpam-3539	77	11	}	}	PUNCT
ejpam-3539	77	12	endowed	endow	VERB
ejpam-3539	77	13	with	with	ADP
ejpam-3539	77	14	the	the	DET
ejpam-3539	77	15	norm	norm	NOUN
ejpam-3539	77	16	‖x‖	‖x‖	PROPN
ejpam-3539	77	17	=	=	SYM
ejpam-3539	77	18	max	max	PROPN
ejpam-3539	77	19	0≤i≤n−1	0≤i≤n−1	NUM
ejpam-3539	77	20	(	(	PUNCT
ejpam-3539	77	21	sup	sup	NOUN
ejpam-3539	77	22	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	77	23	)	)	PUNCT
ejpam-3539	77	24	e−t|u(i)(t)|	e−t|u(i)(t)|	NOUN
ejpam-3539	77	25	)	)	PUNCT
ejpam-3539	77	26	samuel	samuel	PROPN
ejpam-3539	77	27	a.	a.	PROPN
ejpam-3539	77	28	iyase	iyase	PROPN
ejpam-3539	77	29	,	,	PUNCT
ejpam-3539	77	30	abiodun	abiodun	PROPN
ejpam-3539	77	31	a.	a.	PROPN
ejpam-3539	77	32	opanuga	opanuga	PROPN
ejpam-3539	77	33	/	/	SYM
ejpam-3539	77	34	eur	eur	PROPN
ejpam-3539	77	35	.	.	PUNCT
ejpam-3539	78	1	j.	j.	PROPN
ejpam-3539	78	2	pure	pure	PROPN
ejpam-3539	78	3	appl	appl	PROPN
ejpam-3539	78	4	.	.	PROPN
ejpam-3539	78	5	math	math	PROPN
ejpam-3539	78	6	,	,	PUNCT
ejpam-3539	78	7	13	13	NUM
ejpam-3539	78	8	(	(	PUNCT
ejpam-3539	78	9	1	1	NUM
ejpam-3539	78	10	)	)	PUNCT
ejpam-3539	78	11	(	(	PUNCT
ejpam-3539	78	12	2020	2020	NUM
ejpam-3539	78	13	)	)	PUNCT
ejpam-3539	78	14	,	,	PUNCT
ejpam-3539	78	15	33	33	NUM
ejpam-3539	78	16	-	-	SYM
ejpam-3539	78	17	47	47	NUM
ejpam-3539	78	18	36	36	NUM
ejpam-3539	78	19	then	then	ADV
ejpam-3539	78	20	x	x	PUNCT
ejpam-3539	78	21	is	be	AUX
ejpam-3539	78	22	a	a	DET
ejpam-3539	78	23	banach	banach	NOUN
ejpam-3539	78	24	space	space	NOUN
ejpam-3539	78	25	.	.	PUNCT
ejpam-3539	79	1	theorem	theorem	VERB
ejpam-3539	79	2	2.1	2.1	NUM
ejpam-3539	79	3	[	[	NOUN
ejpam-3539	79	4	2]a	2]a	NOUN
ejpam-3539	79	5	let	let	VERB
ejpam-3539	79	6	f	f	PRON
ejpam-3539	79	7	be	be	AUX
ejpam-3539	79	8	a	a	DET
ejpam-3539	79	9	subset	subset	NOUN
ejpam-3539	79	10	of	of	ADP
ejpam-3539	79	11	c∞	c∞	PROPN
ejpam-3539	79	12	=	=	SYM
ejpam-3539	79	13	{	{	PUNCT
ejpam-3539	79	14	y	y	PROPN
ejpam-3539	79	15	∈	∈	PROPN
ejpam-3539	79	16	c	c	X
ejpam-3539	79	17	(	(	PUNCT
ejpam-3539	79	18	[	[	X
ejpam-3539	79	19	0,∞	0,∞	NOUN
ejpam-3539	79	20	)	)	PUNCT
ejpam-3539	79	21	)	)	PUNCT
ejpam-3539	79	22	,	,	PUNCT
ejpam-3539	79	23	limt→∞	limt→∞	PROPN
ejpam-3539	79	24	)	)	PUNCT
ejpam-3539	79	25	y(t	y(t	NUM
ejpam-3539	79	26	)	)	PUNCT
ejpam-3539	79	27	exists	exist	VERB
ejpam-3539	79	28	that	that	PRON
ejpam-3539	79	29	is	be	AUX
ejpam-3539	79	30	equipped	equip	VERB
ejpam-3539	79	31	with	with	ADP
ejpam-3539	79	32	the	the	DET
ejpam-3539	79	33	norm	norm	NOUN
ejpam-3539	79	34	‖y‖∞	‖y‖∞	PROPN
ejpam-3539	79	35	=	=	SYM
ejpam-3539	79	36	supt∈[0,∞	supt∈[0,∞	PROPN
ejpam-3539	79	37	)	)	PUNCT
ejpam-3539	80	1	|y(t)|	|y(t)|	VERB
ejpam-3539	80	2	then	then	ADV
ejpam-3539	80	3	f	f	PROPN
ejpam-3539	80	4	is	be	AUX
ejpam-3539	80	5	relatively	relatively	ADV
ejpam-3539	80	6	compact	compact	ADJ
ejpam-3539	80	7	if	if	SCONJ
ejpam-3539	80	8	the	the	DET
ejpam-3539	80	9	following	follow	VERB
ejpam-3539	80	10	conditions	condition	NOUN
ejpam-3539	80	11	hold	hold	VERB
ejpam-3539	80	12	.	.	PUNCT
ejpam-3539	81	1	(	(	PUNCT
ejpam-3539	81	2	i	i	NOUN
ejpam-3539	81	3	)	)	PUNCT
ejpam-3539	81	4	f	f	PROPN
ejpam-3539	81	5	is	be	AUX
ejpam-3539	81	6	bounded	bound	VERB
ejpam-3539	81	7	in	in	ADP
ejpam-3539	81	8	x	x	PROPN
ejpam-3539	81	9	(	(	PUNCT
ejpam-3539	81	10	ii	ii	NOUN
ejpam-3539	81	11	)	)	PUNCT
ejpam-3539	81	12	the	the	DET
ejpam-3539	81	13	functions	function	NOUN
ejpam-3539	81	14	belonging	belong	VERB
ejpam-3539	81	15	to	to	ADP
ejpam-3539	81	16	f	f	PROPN
ejpam-3539	81	17	are	be	AUX
ejpam-3539	81	18	equicontinuous	equicontinuous	ADJ
ejpam-3539	81	19	on	on	ADP
ejpam-3539	81	20	any	any	DET
ejpam-3539	81	21	compact	compact	ADJ
ejpam-3539	81	22	subinterval	subinterval	NOUN
ejpam-3539	81	23	of	of	ADP
ejpam-3539	81	24	[	[	X
ejpam-3539	81	25	0,∞	0,∞	NUM
ejpam-3539	81	26	)	)	PUNCT
ejpam-3539	81	27	(	(	PUNCT
ejpam-3539	81	28	iii	iii	X
ejpam-3539	81	29	)	)	PUNCT
ejpam-3539	81	30	the	the	DET
ejpam-3539	81	31	functions	function	NOUN
ejpam-3539	81	32	from	from	ADP
ejpam-3539	81	33	f	f	PROPN
ejpam-3539	81	34	are	be	AUX
ejpam-3539	81	35	equiconvergent	equiconvergent	NOUN
ejpam-3539	81	36	at	at	ADP
ejpam-3539	81	37	infinity	infinity	NOUN
ejpam-3539	81	38	.	.	PUNCT
ejpam-3539	82	1	the	the	DET
ejpam-3539	82	2	following	follow	VERB
ejpam-3539	82	3	adaptation	adaptation	NOUN
ejpam-3539	82	4	of	of	ADP
ejpam-3539	82	5	the	the	DET
ejpam-3539	82	6	above	above	ADJ
ejpam-3539	82	7	theorem	theorem	NOUN
ejpam-3539	82	8	will	will	AUX
ejpam-3539	82	9	be	be	AUX
ejpam-3539	82	10	used	use	VERB
ejpam-3539	82	11	to	to	PART
ejpam-3539	82	12	establish	establish	VERB
ejpam-3539	82	13	the	the	DET
ejpam-3539	82	14	compactness	compactness	NOUN
ejpam-3539	82	15	of	of	ADP
ejpam-3539	82	16	kp	kp	PROPN
ejpam-3539	82	17	(	(	PUNCT
ejpam-3539	82	18	i	i	PRON
ejpam-3539	82	19	−q	−q	VERB
ejpam-3539	82	20	)	)	PUNCT
ejpam-3539	82	21	lemma	lemma	PROPN
ejpam-3539	82	22	2.1	2.1	NUM
ejpam-3539	83	1	[	[	X
ejpam-3539	83	2	7	7	NUM
ejpam-3539	83	3	]	]	PUNCT
ejpam-3539	83	4	:	:	PUNCT
ejpam-3539	83	5	let	let	VERB
ejpam-3539	83	6	d	d	X
ejpam-3539	83	7	⊂	⊂	PROPN
ejpam-3539	83	8	x	x	X
ejpam-3539	83	9	,	,	PUNCT
ejpam-3539	83	10	then	then	ADV
ejpam-3539	83	11	d	d	PROPN
ejpam-3539	83	12	is	be	AUX
ejpam-3539	83	13	relatively	relatively	ADV
ejpam-3539	83	14	compact	compact	ADJ
ejpam-3539	83	15	in	in	ADP
ejpam-3539	83	16	x	x	SYM
ejpam-3539	83	17	if	if	SCONJ
ejpam-3539	83	18	the	the	DET
ejpam-3539	83	19	following	follow	VERB
ejpam-3539	83	20	conditions	condition	NOUN
ejpam-3539	83	21	hold	hold	VERB
ejpam-3539	83	22	.	.	PUNCT
ejpam-3539	84	1	(	(	PUNCT
ejpam-3539	84	2	i	i	NOUN
ejpam-3539	84	3	)	)	PUNCT
ejpam-3539	85	1	d	d	NOUN
ejpam-3539	85	2	is	be	AUX
ejpam-3539	85	3	bounded	bound	VERB
ejpam-3539	85	4	in	in	ADP
ejpam-3539	85	5	x	x	PROPN
ejpam-3539	85	6	(	(	PUNCT
ejpam-3539	85	7	ii	ii	NOUN
ejpam-3539	85	8	)	)	PUNCT
ejpam-3539	85	9	the	the	DET
ejpam-3539	85	10	family	family	NOUN
ejpam-3539	85	11	w	w	PROPN
ejpam-3539	85	12	i	i	NOUN
ejpam-3539	85	13	=	=	PUNCT
ejpam-3539	85	14	{	{	PUNCT
ejpam-3539	85	15	ψi	ψi	ADV
ejpam-3539	85	16	:	:	PUNCT
ejpam-3539	85	17	ψi(t	ψi(t	NOUN
ejpam-3539	85	18	)	)	PUNCT
ejpam-3539	85	19	=	=	SYM
ejpam-3539	85	20	e−tu(i)(t	e−tu(i)(t	NOUN
ejpam-3539	85	21	)	)	PUNCT
ejpam-3539	85	22	,	,	PUNCT
ejpam-3539	85	23	t	t	PROPN
ejpam-3539	85	24	≥	≥	NUM
ejpam-3539	85	25	0	0	NUM
ejpam-3539	85	26	,	,	PUNCT
ejpam-3539	85	27	u	u	PROPN
ejpam-3539	85	28	∈	∈	PROPN
ejpam-3539	85	29	d	d	X
ejpam-3539	85	30	}	}	PUNCT
ejpam-3539	85	31	is	be	AUX
ejpam-3539	85	32	equicontinuous	equicontinuous	ADJ
ejpam-3539	85	33	on	on	ADP
ejpam-3539	85	34	any	any	DET
ejpam-3539	85	35	compact	compact	ADJ
ejpam-3539	85	36	subinterval	subinterval	NOUN
ejpam-3539	85	37	of	of	ADP
ejpam-3539	85	38	[	[	X
ejpam-3539	85	39	0,∞	0,∞	NOUN
ejpam-3539	85	40	)	)	PUNCT
ejpam-3539	85	41	for	for	ADP
ejpam-3539	85	42	i	i	PROPN
ejpam-3539	85	43	=	=	NOUN
ejpam-3539	85	44	0	0	NUM
ejpam-3539	85	45	,	,	PUNCT
ejpam-3539	85	46	.	.	PUNCT
ejpam-3539	85	47	.	.	PUNCT
ejpam-3539	86	1	.	.	PUNCT
ejpam-3539	87	1	,	,	PUNCT
ejpam-3539	87	2	n−	n−	NOUN
ejpam-3539	87	3	1	1	NUM
ejpam-3539	87	4	.	.	PUNCT
ejpam-3539	88	1	(	(	PUNCT
ejpam-3539	88	2	iii	iii	X
ejpam-3539	88	3	)	)	PUNCT
ejpam-3539	88	4	the	the	DET
ejpam-3539	88	5	family	family	NOUN
ejpam-3539	88	6	w	w	PROPN
ejpam-3539	88	7	i	i	NOUN
ejpam-3539	88	8	=	=	PUNCT
ejpam-3539	88	9	{	{	PUNCT
ejpam-3539	88	10	ψi	ψi	ADV
ejpam-3539	88	11	:	:	PUNCT
ejpam-3539	88	12	ψi(t	ψi(t	NOUN
ejpam-3539	88	13	)	)	PUNCT
ejpam-3539	88	14	=	=	SYM
ejpam-3539	88	15	e−tu(i)(t	e−tu(i)(t	NOUN
ejpam-3539	88	16	)	)	PUNCT
ejpam-3539	88	17	,	,	PUNCT
ejpam-3539	88	18	t	t	PROPN
ejpam-3539	88	19	≥	≥	NUM
ejpam-3539	88	20	0	0	NUM
ejpam-3539	88	21	,	,	PUNCT
ejpam-3539	88	22	u	u	PROPN
ejpam-3539	88	23	∈	∈	PROPN
ejpam-3539	88	24	d	d	AUX
ejpam-3539	88	25	}	}	PUNCT
ejpam-3539	88	26	is	be	AUX
ejpam-3539	88	27	equiconvergent	equiconvergent	NOUN
ejpam-3539	88	28	at	at	ADP
ejpam-3539	88	29	infinity	infinity	NOUN
ejpam-3539	88	30	for	for	ADP
ejpam-3539	88	31	i	i	PROPN
ejpam-3539	88	32	=	=	SYM
ejpam-3539	88	33	0	0	NUM
ejpam-3539	88	34	,	,	PUNCT
ejpam-3539	88	35	1	1	NUM
ejpam-3539	88	36	,	,	PUNCT
ejpam-3539	88	37	.	.	PUNCT
ejpam-3539	88	38	.	.	PUNCT
ejpam-3539	89	1	.	.	PUNCT
ejpam-3539	90	1	,	,	PUNCT
ejpam-3539	90	2	n−	n−	NOUN
ejpam-3539	90	3	1	1	NUM
ejpam-3539	90	4	.	.	PUNCT
ejpam-3539	91	1	let	let	VERB
ejpam-3539	91	2	z	z	NOUN
ejpam-3539	91	3	=	=	SYM
ejpam-3539	91	4	l1[0,∞	l1[0,∞	NOUN
ejpam-3539	91	5	)	)	PUNCT
ejpam-3539	91	6	with	with	ADP
ejpam-3539	91	7	the	the	DET
ejpam-3539	91	8	norm	norm	NOUN
ejpam-3539	91	9	‖y‖1	‖y‖1	NOUN
ejpam-3539	91	10	=	=	SYM
ejpam-3539	91	11	∫∞	∫∞	NOUN
ejpam-3539	91	12	0	0	PUNCT
ejpam-3539	91	13	|y(t)|dt	|y(t)|dt	X
ejpam-3539	91	14	for	for	ADP
ejpam-3539	91	15	y	y	PROPN
ejpam-3539	91	16	∈	∈	PROPN
ejpam-3539	91	17	z.	z.	PROPN
ejpam-3539	92	1	we	we	PRON
ejpam-3539	92	2	denote	denote	VERB
ejpam-3539	92	3	acloc[0,∞	acloc[0,∞	NOUN
ejpam-3539	92	4	)	)	PUNCT
ejpam-3539	92	5	as	as	ADP
ejpam-3539	92	6	the	the	DET
ejpam-3539	92	7	space	space	NOUN
ejpam-3539	92	8	of	of	ADP
ejpam-3539	92	9	locally	locally	ADV
ejpam-3539	92	10	absolutely	absolutely	ADV
ejpam-3539	92	11	continuous	continuous	ADJ
ejpam-3539	92	12	functions	function	NOUN
ejpam-3539	92	13	on	on	ADP
ejpam-3539	92	14	[	[	X
ejpam-3539	92	15	0,∞	0,∞	NOUN
ejpam-3539	92	16	)	)	PUNCT
ejpam-3539	92	17	.	.	PUNCT
ejpam-3539	93	1	we	we	PRON
ejpam-3539	93	2	define	define	VERB
ejpam-3539	93	3	l	l	NOUN
ejpam-3539	93	4	to	to	PART
ejpam-3539	93	5	be	be	AUX
ejpam-3539	93	6	the	the	DET
ejpam-3539	93	7	linear	linear	ADJ
ejpam-3539	93	8	operator	operator	NOUN
ejpam-3539	93	9	from	from	ADP
ejpam-3539	93	10	doml	doml	PROPN
ejpam-3539	93	11	⊂	⊂	PROPN
ejpam-3539	93	12	x	x	PUNCT
ejpam-3539	94	1	→	→	PUNCT
ejpam-3539	94	2	z	z	NOUN
ejpam-3539	94	3	with	with	ADP
ejpam-3539	94	4	doml	doml	NOUN
ejpam-3539	94	5	=	=	PUNCT
ejpam-3539	94	6	{	{	PUNCT
ejpam-3539	94	7	u	u	NOUN
ejpam-3539	94	8	∈	∈	PROPN
ejpam-3539	94	9	x	x	X
ejpam-3539	94	10	:	:	PUNCT
ejpam-3539	94	11	u(n−1)(t	u(n−1)(t	ADJ
ejpam-3539	94	12	)	)	PUNCT
ejpam-3539	94	13	∈	∈	PROPN
ejpam-3539	94	14	acloc[0,∞	acloc[0,∞	NOUN
ejpam-3539	94	15	)	)	PUNCT
ejpam-3539	94	16	,	,	PUNCT
ejpam-3539	94	17	u(i)(0	u(i)(0	PROPN
ejpam-3539	94	18	)	)	PUNCT
ejpam-3539	94	19	=	=	SYM
ejpam-3539	94	20	0	0	NUM
ejpam-3539	94	21	,	,	PUNCT
ejpam-3539	94	22	i	i	PRON
ejpam-3539	94	23	=	=	NOUN
ejpam-3539	94	24	1	1	NUM
ejpam-3539	94	25	,	,	PUNCT
ejpam-3539	94	26	2	2	NUM
ejpam-3539	94	27	,	,	PUNCT
ejpam-3539	94	28	.	.	PUNCT
ejpam-3539	94	29	.	.	PUNCT
ejpam-3539	95	1	.	.	PUNCT
ejpam-3539	96	1	,	,	PUNCT
ejpam-3539	96	2	n−	n−	NOUN
ejpam-3539	96	3	2	2	NUM
ejpam-3539	96	4	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	96	5	)	)	PUNCT
ejpam-3539	97	1	=	=	PUNCT
ejpam-3539	97	2	(	(	PUNCT
ejpam-3539	97	3	n−	n−	NOUN
ejpam-3539	97	4	1	1	NUM
ejpam-3539	97	5	)	)	PUNCT
ejpam-3539	97	6	!	!	PUNCT
ejpam-3539	98	1	ξn−1	ξn−1	ADJ
ejpam-3539	98	2	u(ξ	u(ξ	NOUN
ejpam-3539	98	3	)	)	PUNCT
ejpam-3539	98	4	,	,	PUNCT
ejpam-3539	98	5	u(n−1)(∞	u(n−1)(∞	PROPN
ejpam-3539	98	6	)	)	PUNCT
ejpam-3539	98	7	=	=	PUNCT
ejpam-3539	99	1	∫	∫	PROPN
ejpam-3539	99	2	ξ	ξ	SYM
ejpam-3539	99	3	0	0	NUM
ejpam-3539	99	4	u(n−1)(s)da(s	u(n−1)(s)da(	NOUN
ejpam-3539	99	5	)	)	PUNCT
ejpam-3539	99	6	,	,	PUNCT
ejpam-3539	99	7	u(n	u(n	PROPN
ejpam-3539	99	8	)	)	PUNCT
ejpam-3539	99	9	∈	∈	PROPN
ejpam-3539	99	10	z	z	NOUN
ejpam-3539	99	11	}	}	PUNCT
ejpam-3539	99	12	and	and	CCONJ
ejpam-3539	99	13	lu(t	lu(t	PROPN
ejpam-3539	99	14	)	)	PUNCT
ejpam-3539	99	15	=	=	SYM
ejpam-3539	100	1	u(n)(t	u(n)(t	X
ejpam-3539	100	2	)	)	PUNCT
ejpam-3539	100	3	,	,	PUNCT
ejpam-3539	100	4	u	u	PROPN
ejpam-3539	100	5	∈	∈	PROPN
ejpam-3539	100	6	doml	doml	PROPN
ejpam-3539	100	7	,	,	PUNCT
ejpam-3539	100	8	t	t	PROPN
ejpam-3539	100	9	∈	∈	PROPN
ejpam-3539	101	1	[	[	X
ejpam-3539	101	2	0,∞	0,∞	NOUN
ejpam-3539	101	3	)	)	PUNCT
ejpam-3539	101	4	.	.	PUNCT
ejpam-3539	102	1	we	we	PRON
ejpam-3539	102	2	define	define	VERB
ejpam-3539	102	3	n	n	X
ejpam-3539	102	4	:	:	PUNCT
ejpam-3539	102	5	x	x	PUNCT
ejpam-3539	102	6	−→	−→	NOUN
ejpam-3539	102	7	z	z	VERB
ejpam-3539	102	8	by	by	ADP
ejpam-3539	102	9	setting	set	VERB
ejpam-3539	102	10	nu(t	nu(t	NUM
ejpam-3539	102	11	)	)	PUNCT
ejpam-3539	102	12	=	=	SYM
ejpam-3539	102	13	g(t	g(t	PROPN
ejpam-3539	102	14	,	,	PUNCT
ejpam-3539	102	15	u(t	u(t	NOUN
ejpam-3539	102	16	)	)	PUNCT
ejpam-3539	102	17	,	,	PUNCT
ejpam-3539	102	18	u′(t	u′(t	X
ejpam-3539	102	19	)	)	PUNCT
ejpam-3539	102	20	·	·	PUNCT
ejpam-3539	102	21	·	·	PUNCT
ejpam-3539	102	22	·	·	PUNCT
ejpam-3539	102	23	u(n−1)(t	u(n−1)(t	NOUN
ejpam-3539	102	24	)	)	PUNCT
ejpam-3539	102	25	)	)	PUNCT
ejpam-3539	102	26	,	,	PUNCT
ejpam-3539	102	27	t	t	PROPN
ejpam-3539	102	28	∈	∈	PROPN
ejpam-3539	103	1	[	[	X
ejpam-3539	103	2	0,∞	0,∞	NUM
ejpam-3539	103	3	)	)	PUNCT
ejpam-3539	103	4	we	we	PRON
ejpam-3539	103	5	can	can	AUX
ejpam-3539	103	6	then	then	ADV
ejpam-3539	103	7	write	write	VERB
ejpam-3539	103	8	(	(	PUNCT
ejpam-3539	103	9	1)-(2	1)-(2	NUM
ejpam-3539	103	10	)	)	PUNCT
ejpam-3539	103	11	as	as	ADP
ejpam-3539	103	12	lu	lu	NOUN
ejpam-3539	103	13	=	=	SYM
ejpam-3539	103	14	nu	nu	X
ejpam-3539	103	15	(	(	PUNCT
ejpam-3539	103	16	5	5	NUM
ejpam-3539	103	17	)	)	PUNCT
ejpam-3539	103	18	definition	definition	NOUN
ejpam-3539	103	19	2.3	2.3	NUM
ejpam-3539	103	20	:	:	PUNCT
ejpam-3539	103	21	definition	definition	NOUN
ejpam-3539	103	22	2	2	NUM
ejpam-3539	103	23	.	.	PUNCT
ejpam-3539	104	1	let	let	VERB
ejpam-3539	104	2	l	l	NOUN
ejpam-3539	104	3	:	:	PUNCT
ejpam-3539	104	4	doml	doml	VERB
ejpam-3539	104	5	⊂	⊂	PROPN
ejpam-3539	104	6	x	x	PUNCT
ejpam-3539	105	1	−→	−→	ADJ
ejpam-3539	105	2	z	z	NOUN
ejpam-3539	105	3	be	be	AUX
ejpam-3539	105	4	a	a	DET
ejpam-3539	105	5	fredholm	fredholm	NOUN
ejpam-3539	105	6	mapping	mapping	NOUN
ejpam-3539	105	7	,	,	PUNCT
ejpam-3539	105	8	e	e	X
ejpam-3539	105	9	a	a	DET
ejpam-3539	105	10	metric	metric	ADJ
ejpam-3539	105	11	space	space	NOUN
ejpam-3539	105	12	and	and	CCONJ
ejpam-3539	105	13	n	n	NOUN
ejpam-3539	105	14	:	:	PUNCT
ejpam-3539	105	15	e	e	AUX
ejpam-3539	105	16	−→	−→	NOUN
ejpam-3539	105	17	z	z	NOUN
ejpam-3539	105	18	be	be	AUX
ejpam-3539	105	19	a	a	DET
ejpam-3539	105	20	mapping	mapping	NOUN
ejpam-3539	105	21	:	:	PUNCT
ejpam-3539	105	22	n	n	PRON
ejpam-3539	105	23	is	be	AUX
ejpam-3539	105	24	said	say	VERB
ejpam-3539	105	25	to	to	PART
ejpam-3539	105	26	be	be	AUX
ejpam-3539	105	27	l	l	NOUN
ejpam-3539	105	28	-	-	ADJ
ejpam-3539	105	29	compact	compact	ADJ
ejpam-3539	105	30	on	on	ADP
ejpam-3539	105	31	e	e	NOUN
ejpam-3539	105	32	if	if	SCONJ
ejpam-3539	105	33	qn	qn	INTJ
ejpam-3539	105	34	:	:	PUNCT
ejpam-3539	105	35	e	e	X
ejpam-3539	105	36	−→	−→	NOUN
ejpam-3539	105	37	z	z	PROPN
ejpam-3539	105	38	and	and	CCONJ
ejpam-3539	105	39	kp	kp	PROPN
ejpam-3539	105	40	,	,	PUNCT
ejpam-3539	105	41	qn	qn	INTJ
ejpam-3539	105	42	:	:	PUNCT
ejpam-3539	105	43	e	e	X
ejpam-3539	105	44	−→	−→	NOUN
ejpam-3539	105	45	z	z	NOUN
ejpam-3539	105	46	are	be	AUX
ejpam-3539	105	47	compact	compact	ADJ
ejpam-3539	105	48	on	on	ADP
ejpam-3539	105	49	e.	e.	PROPN
ejpam-3539	105	50	n	n	PROPN
ejpam-3539	105	51	is	be	AUX
ejpam-3539	105	52	called	call	VERB
ejpam-3539	105	53	completely	completely	ADV
ejpam-3539	105	54	continuous	continuous	ADJ
ejpam-3539	105	55	if	if	SCONJ
ejpam-3539	105	56	it	it	PRON
ejpam-3539	105	57	is	be	AUX
ejpam-3539	105	58	l	l	NOUN
ejpam-3539	105	59	-	-	ADJ
ejpam-3539	105	60	compact	compact	ADJ
ejpam-3539	105	61	on	on	ADP
ejpam-3539	105	62	every	every	DET
ejpam-3539	105	63	bounded	bound	VERB
ejpam-3539	105	64	e	e	PROPN
ejpam-3539	105	65	⊂	⊂	PROPN
ejpam-3539	105	66	x.	x.	PROPN
ejpam-3539	106	1	samuel	samuel	PROPN
ejpam-3539	106	2	a.	a.	PROPN
ejpam-3539	106	3	iyase	iyase	PROPN
ejpam-3539	106	4	,	,	PUNCT
ejpam-3539	106	5	abiodun	abiodun	PROPN
ejpam-3539	106	6	a.	a.	PROPN
ejpam-3539	106	7	opanuga	opanuga	PROPN
ejpam-3539	106	8	/	/	SYM
ejpam-3539	106	9	eur	eur	PROPN
ejpam-3539	106	10	.	.	PUNCT
ejpam-3539	107	1	j.	j.	PROPN
ejpam-3539	107	2	pure	pure	PROPN
ejpam-3539	107	3	appl	appl	PROPN
ejpam-3539	107	4	.	.	PROPN
ejpam-3539	107	5	math	math	PROPN
ejpam-3539	107	6	,	,	PUNCT
ejpam-3539	107	7	13	13	NUM
ejpam-3539	107	8	(	(	PUNCT
ejpam-3539	107	9	1	1	NUM
ejpam-3539	107	10	)	)	PUNCT
ejpam-3539	107	11	(	(	PUNCT
ejpam-3539	107	12	2020	2020	NUM
ejpam-3539	107	13	)	)	PUNCT
ejpam-3539	107	14	,	,	PUNCT
ejpam-3539	107	15	33	33	NUM
ejpam-3539	107	16	-	-	SYM
ejpam-3539	107	17	47	47	NUM
ejpam-3539	107	18	37	37	NUM
ejpam-3539	107	19	the	the	DET
ejpam-3539	107	20	existence	existence	NOUN
ejpam-3539	107	21	of	of	ADP
ejpam-3539	107	22	solution	solution	NOUN
ejpam-3539	107	23	to	to	ADP
ejpam-3539	107	24	(	(	PUNCT
ejpam-3539	107	25	5	5	NUM
ejpam-3539	107	26	)	)	PUNCT
ejpam-3539	107	27	will	will	AUX
ejpam-3539	107	28	be	be	AUX
ejpam-3539	107	29	guaranteed	guarantee	VERB
ejpam-3539	107	30	by	by	ADP
ejpam-3539	107	31	the	the	DET
ejpam-3539	107	32	following	following	ADJ
ejpam-3539	107	33	theorem	theorem	NOUN
ejpam-3539	107	34	of	of	ADP
ejpam-3539	107	35	mawhin	mawhin	NOUN
ejpam-3539	107	36	[	[	X
ejpam-3539	107	37	17	17	NUM
ejpam-3539	107	38	]	]	PUNCT
ejpam-3539	107	39	.	.	PUNCT
ejpam-3539	108	1	theorem	theorem	VERB
ejpam-3539	108	2	2.2	2.2	NUM
ejpam-3539	109	1	[	[	X
ejpam-3539	109	2	16	16	NUM
ejpam-3539	109	3	]	]	X
ejpam-3539	109	4	:	:	PUNCT
ejpam-3539	109	5	let	let	VERB
ejpam-3539	109	6	ω	ω	PROPN
ejpam-3539	109	7	⊂	⊂	PROPN
ejpam-3539	109	8	x	x	PUNCT
ejpam-3539	109	9	be	be	AUX
ejpam-3539	109	10	,	,	PUNCT
ejpam-3539	109	11	and	and	CCONJ
ejpam-3539	109	12	l	l	NOUN
ejpam-3539	109	13	be	be	AUX
ejpam-3539	109	14	a	a	DET
ejpam-3539	109	15	fredholm	fredholm	NOUN
ejpam-3539	109	16	mapping	mapping	NOUN
ejpam-3539	109	17	of	of	ADP
ejpam-3539	109	18	index	index	NOUN
ejpam-3539	109	19	zero	zero	NUM
ejpam-3539	109	20	and	and	CCONJ
ejpam-3539	109	21	n	n	CCONJ
ejpam-3539	109	22	be	be	VERB
ejpam-3539	109	23	l	l	ADJ
ejpam-3539	109	24	-	-	ADJ
ejpam-3539	109	25	compact	compact	ADJ
ejpam-3539	109	26	on	on	ADP
ejpam-3539	109	27	ω̄.	ω̄.	PUNCT
ejpam-3539	109	28	assume	assume	VERB
ejpam-3539	109	29	that	that	SCONJ
ejpam-3539	109	30	the	the	DET
ejpam-3539	109	31	following	follow	VERB
ejpam-3539	109	32	conditions	condition	NOUN
ejpam-3539	109	33	are	be	AUX
ejpam-3539	109	34	satisfied	satisfied	ADJ
ejpam-3539	109	35	.	.	PUNCT
ejpam-3539	110	1	(	(	PUNCT
ejpam-3539	110	2	1	1	X
ejpam-3539	110	3	)	)	PUNCT
ejpam-3539	110	4	lu	lu	PROPN
ejpam-3539	110	5	6=	6=	PROPN
ejpam-3539	110	6	nu	nu	PROPN
ejpam-3539	110	7	for	for	ADP
ejpam-3539	110	8	every	every	DET
ejpam-3539	110	9	(	(	PUNCT
ejpam-3539	110	10	u	u	NOUN
ejpam-3539	110	11	,	,	PUNCT
ejpam-3539	110	12	λ	λ	NOUN
ejpam-3539	110	13	)	)	PUNCT
ejpam-3539	110	14	∈	∈	NOUN
ejpam-3539	111	1	[	[	X
ejpam-3539	111	2	(	(	PUNCT
ejpam-3539	111	3	doml\	doml\	PROPN
ejpam-3539	111	4	kerl	kerl	PROPN
ejpam-3539	111	5	)	)	PUNCT
ejpam-3539	111	6	∩	∩	ADJ
ejpam-3539	111	7	∂ω]×	∂ω]×	X
ejpam-3539	111	8	(	(	PUNCT
ejpam-3539	111	9	0	0	NUM
ejpam-3539	111	10	,	,	PUNCT
ejpam-3539	111	11	1	1	NUM
ejpam-3539	111	12	)	)	PUNCT
ejpam-3539	111	13	(	(	PUNCT
ejpam-3539	111	14	2	2	X
ejpam-3539	111	15	)	)	PUNCT
ejpam-3539	111	16	nu	nu	NOUN
ejpam-3539	111	17	/∈	/∈	SYM
ejpam-3539	111	18	iml	iml	NOUN
ejpam-3539	111	19	for	for	ADP
ejpam-3539	111	20	every	every	DET
ejpam-3539	111	21	u	u	PROPN
ejpam-3539	111	22	∈	∈	PROPN
ejpam-3539	111	23	kerl	kerl	X
ejpam-3539	111	24	∩	∩	ADJ
ejpam-3539	111	25	∂ω	∂ω	PROPN
ejpam-3539	111	26	(	(	PUNCT
ejpam-3539	111	27	3	3	X
ejpam-3539	111	28	)	)	PUNCT
ejpam-3539	111	29	deg(qn	deg(qn	PROPN
ejpam-3539	111	30	|∂ω∩kerl	|∂ω∩kerl	PROPN
ejpam-3539	111	31	,	,	PUNCT
ejpam-3539	111	32	ω	ω	PROPN
ejpam-3539	111	33	∩	∩	ADJ
ejpam-3539	111	34	kerl	kerl	PROPN
ejpam-3539	111	35	,	,	PUNCT
ejpam-3539	111	36	0	0	NUM
ejpam-3539	111	37	)	)	PUNCT
ejpam-3539	111	38	6=	6=	ADP
ejpam-3539	111	39	0	0	NUM
ejpam-3539	111	40	where	where	SCONJ
ejpam-3539	111	41	q	q	NOUN
ejpam-3539	111	42	:	:	PUNCT
ejpam-3539	111	43	z	z	NOUN
ejpam-3539	111	44	−→	−→	NOUN
ejpam-3539	111	45	z	z	NOUN
ejpam-3539	111	46	is	be	AUX
ejpam-3539	111	47	a	a	DET
ejpam-3539	111	48	projection	projection	NOUN
ejpam-3539	111	49	such	such	ADJ
ejpam-3539	111	50	that	that	DET
ejpam-3539	111	51	iml	iml	NOUN
ejpam-3539	111	52	=	=	SYM
ejpam-3539	111	53	kerq	kerq	PROPN
ejpam-3539	111	54	then	then	ADV
ejpam-3539	111	55	the	the	DET
ejpam-3539	111	56	equation	equation	NOUN
ejpam-3539	111	57	lu	lu	PROPN
ejpam-3539	112	1	=	=	NOUN
ejpam-3539	112	2	nu	nu	PROPN
ejpam-3539	112	3	has	have	AUX
ejpam-3539	112	4	at	at	ADV
ejpam-3539	112	5	least	least	ADV
ejpam-3539	112	6	one	one	NUM
ejpam-3539	112	7	solution	solution	NOUN
ejpam-3539	112	8	in	in	ADP
ejpam-3539	112	9	doml	doml	PROPN
ejpam-3539	112	10	∩	∩	PROPN
ejpam-3539	112	11	ω̄.	ω̄.	PUNCT
ejpam-3539	112	12	lemma	lemma	PROPN
ejpam-3539	112	13	2.2	2.2	NUM
ejpam-3539	112	14	:	:	PUNCT
ejpam-3539	112	15	if	if	SCONJ
ejpam-3539	112	16	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	112	17	)	)	PUNCT
ejpam-3539	112	18	=	=	SYM
ejpam-3539	112	19	(	(	PUNCT
ejpam-3539	112	20	n−1	n−1	PROPN
ejpam-3539	112	21	)	)	PUNCT
ejpam-3539	112	22	!	!	PUNCT
ejpam-3539	113	1	ξn−1	ξn−1	ADJ
ejpam-3539	113	2	u(ξ	u(ξ	NOUN
ejpam-3539	113	3	)	)	PUNCT
ejpam-3539	113	4	,	,	PUNCT
ejpam-3539	113	5	a(ξ	a(ξ	PROPN
ejpam-3539	113	6	)	)	PUNCT
ejpam-3539	113	7	=	=	SYM
ejpam-3539	113	8	1	1	NUM
ejpam-3539	113	9	,	,	PUNCT
ejpam-3539	113	10	a(0	a(0	PROPN
ejpam-3539	113	11	)	)	PUNCT
ejpam-3539	113	12	=	=	SYM
ejpam-3539	113	13	0	0	NUM
ejpam-3539	113	14	,	,	PUNCT
ejpam-3539	113	15	u(n−1)(∞	u(n−1)(∞	NOUN
ejpam-3539	113	16	)	)	PUNCT
ejpam-3539	113	17	=	=	PUNCT
ejpam-3539	114	1	∫	∫	PROPN
ejpam-3539	114	2	ξ	ξ	SYM
ejpam-3539	114	3	0	0	NUM
ejpam-3539	114	4	u	u	NOUN
ejpam-3539	114	5	(	(	PUNCT
ejpam-3539	114	6	n−1)(s)da(s	n−1)(s)da(s	PROPN
ejpam-3539	114	7	)	)	PUNCT
ejpam-3539	114	8	,	,	PUNCT
ejpam-3539	114	9	u(i)(0	u(i)(0	PROPN
ejpam-3539	114	10	)	)	PUNCT
ejpam-3539	114	11	=	=	SYM
ejpam-3539	114	12	0	0	NUM
ejpam-3539	114	13	,	,	PUNCT
ejpam-3539	114	14	i	i	PRON
ejpam-3539	114	15	=	=	NOUN
ejpam-3539	114	16	1	1	NUM
ejpam-3539	114	17	,	,	PUNCT
ejpam-3539	114	18	2	2	NUM
ejpam-3539	114	19	,	,	PUNCT
ejpam-3539	114	20	.	.	PUNCT
ejpam-3539	114	21	.	.	PUNCT
ejpam-3539	114	22	.	.	PUNCT
ejpam-3539	115	1	,	,	PUNCT
ejpam-3539	115	2	n−	n−	NOUN
ejpam-3539	115	3	2	2	NUM
ejpam-3539	115	4	then	then	ADV
ejpam-3539	115	5	(	(	PUNCT
ejpam-3539	115	6	i	i	NOUN
ejpam-3539	115	7	)	)	PUNCT
ejpam-3539	115	8	kerl	kerl	PROPN
ejpam-3539	115	9	=	=	PUNCT
ejpam-3539	115	10	{	{	PUNCT
ejpam-3539	115	11	u	u	NOUN
ejpam-3539	115	12	∈	∈	PROPN
ejpam-3539	115	13	doml	doml	NOUN
ejpam-3539	115	14	:	:	PUNCT
ejpam-3539	116	1	u	u	NOUN
ejpam-3539	116	2	=	=	SYM
ejpam-3539	116	3	dtn−1	dtn−1	PROPN
ejpam-3539	116	4	,	,	PUNCT
ejpam-3539	116	5	d	d	PROPN
ejpam-3539	116	6	∈	∈	PROPN
ejpam-3539	116	7	<	<	X
ejpam-3539	116	8	,	,	PUNCT
ejpam-3539	116	9	t	t	PROPN
ejpam-3539	116	10	∈	∈	PROPN
ejpam-3539	116	11	(	(	PUNCT
ejpam-3539	116	12	0,∞	0,∞	NOUN
ejpam-3539	116	13	)	)	PUNCT
ejpam-3539	116	14	}	}	PUNCT
ejpam-3539	116	15	(	(	PUNCT
ejpam-3539	116	16	ii	ii	NOUN
ejpam-3539	116	17	)	)	PUNCT
ejpam-3539	116	18	iml	iml	NOUN
ejpam-3539	116	19	=	=	SYM
ejpam-3539	116	20	{	{	PUNCT
ejpam-3539	116	21	y	y	PROPN
ejpam-3539	116	22	∈	∈	PROPN
ejpam-3539	116	23	z	z	NOUN
ejpam-3539	116	24	:	:	PUNCT
ejpam-3539	116	25	∫∞	∫∞	NOUN
ejpam-3539	116	26	0	0	NUM
ejpam-3539	117	1	y(τ)dτ	y(τ)dτ	PROPN
ejpam-3539	118	1	−	−	PROPN
ejpam-3539	118	2	∫	∫	PROPN
ejpam-3539	119	1	ξ	ξ	SYM
ejpam-3539	119	2	0	0	NUM
ejpam-3539	119	3	∫	∫	PROPN
ejpam-3539	119	4	s	s	PART
ejpam-3539	119	5	0	0	NUM
ejpam-3539	119	6	y(v)dvda(s	y(v)dvda(s	NOUN
ejpam-3539	119	7	)	)	PUNCT
ejpam-3539	119	8	=	=	SYM
ejpam-3539	119	9	0	0	NUM
ejpam-3539	119	10	}	}	PUNCT
ejpam-3539	119	11	.	.	PUNCT
ejpam-3539	120	1	proof	proof	NOUN
ejpam-3539	120	2	:	:	PUNCT
ejpam-3539	120	3	(	(	PUNCT
ejpam-3539	120	4	i	i	NOUN
ejpam-3539	120	5	)	)	PUNCT
ejpam-3539	120	6	let	let	VERB
ejpam-3539	120	7	u	u	PROPN
ejpam-3539	120	8	∈	∈	PROPN
ejpam-3539	120	9	kerl	kerl	PROPN
ejpam-3539	120	10	,	,	PUNCT
ejpam-3539	120	11	then	then	ADV
ejpam-3539	120	12	u(n)(t	u(n)(t	NUM
ejpam-3539	120	13	)	)	PUNCT
ejpam-3539	120	14	=	=	SYM
ejpam-3539	120	15	0	0	NUM
ejpam-3539	121	1	for	for	ADP
ejpam-3539	121	2	a.e	a.e	PROPN
ejpam-3539	121	3	.	.	PROPN
ejpam-3539	121	4	t	t	PROPN
ejpam-3539	121	5	∈	∈	PROPN
ejpam-3539	122	1	[	[	X
ejpam-3539	122	2	0,∞	0,∞	NOUN
ejpam-3539	122	3	)	)	PUNCT
ejpam-3539	122	4	.	.	PUNCT
ejpam-3539	123	1	since	since	SCONJ
ejpam-3539	123	2	u(i)(0	u(i)(0	NUM
ejpam-3539	123	3	)	)	PUNCT
ejpam-3539	123	4	=	=	SYM
ejpam-3539	123	5	0	0	NUM
ejpam-3539	123	6	for	for	ADP
ejpam-3539	123	7	i	i	PRON
ejpam-3539	123	8	=	=	PROPN
ejpam-3539	123	9	1.2	1.2	NUM
ejpam-3539	123	10	.	.	PUNCT
ejpam-3539	123	11	.	.	PUNCT
ejpam-3539	123	12	.	.	PUNCT
ejpam-3539	123	13	.	.	PUNCT
ejpam-3539	124	1	,	,	PUNCT
ejpam-3539	124	2	n−	n−	NOUN
ejpam-3539	124	3	2	2	NUM
ejpam-3539	124	4	and	and	CCONJ
ejpam-3539	124	5	using	use	VERB
ejpam-3539	124	6	(	(	PUNCT
ejpam-3539	124	7	5	5	NUM
ejpam-3539	124	8	)	)	PUNCT
ejpam-3539	124	9	we	we	PRON
ejpam-3539	124	10	derive	derive	VERB
ejpam-3539	124	11	that	that	SCONJ
ejpam-3539	124	12	u(t	u(t	NOUN
ejpam-3539	124	13	)	)	PUNCT
ejpam-3539	124	14	=	=	PUNCT
ejpam-3539	125	1	dtn−1	dtn−1	ADJ
ejpam-3539	125	2	.	.	PUNCT
ejpam-3539	125	3	thus	thus	ADV
ejpam-3539	125	4	kerl	kerl	X
ejpam-3539	125	5	=	=	PUNCT
ejpam-3539	125	6	{	{	PUNCT
ejpam-3539	125	7	u	u	NOUN
ejpam-3539	125	8	∈	∈	PROPN
ejpam-3539	125	9	x	x	X
ejpam-3539	125	10	:	:	PUNCT
ejpam-3539	125	11	u(t	u(t	NOUN
ejpam-3539	125	12	)	)	PUNCT
ejpam-3539	125	13	=	=	PUNCT
ejpam-3539	126	1	dtn−1	dtn−1	ADJ
ejpam-3539	126	2	}	}	PUNCT
ejpam-3539	126	3	(	(	PUNCT
ejpam-3539	126	4	ii	ii	NOUN
ejpam-3539	126	5	)	)	PUNCT
ejpam-3539	126	6	we	we	PRON
ejpam-3539	126	7	next	next	ADV
ejpam-3539	126	8	show	show	VERB
ejpam-3539	126	9	that	that	SCONJ
ejpam-3539	126	10	iml	iml	NOUN
ejpam-3539	126	11	=	=	SYM
ejpam-3539	126	12	{	{	PUNCT
ejpam-3539	126	13	y	y	PROPN
ejpam-3539	126	14	∈	∈	PROPN
ejpam-3539	126	15	z	z	NOUN
ejpam-3539	126	16	:	:	PUNCT
ejpam-3539	126	17	∫	∫	PROPN
ejpam-3539	127	1	∞	∞	NUM
ejpam-3539	127	2	0	0	PUNCT
ejpam-3539	128	1	y(s)ds−	y(s)ds−	NUM
ejpam-3539	128	2	∫	∫	PROPN
ejpam-3539	129	1	ξ	ξ	SYM
ejpam-3539	129	2	0	0	NUM
ejpam-3539	129	3	∫	∫	PROPN
ejpam-3539	129	4	s	s	PART
ejpam-3539	129	5	0	0	NUM
ejpam-3539	129	6	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	129	7	)	)	PUNCT
ejpam-3539	129	8	=	=	SYM
ejpam-3539	129	9	0	0	NUM
ejpam-3539	129	10	}	}	PUNCT
ejpam-3539	129	11	.	.	PUNCT
ejpam-3539	130	1	we	we	PRON
ejpam-3539	130	2	consider	consider	VERB
ejpam-3539	130	3	the	the	DET
ejpam-3539	130	4	problem	problem	NOUN
ejpam-3539	130	5	u(n)(t	u(n)(t	NUM
ejpam-3539	130	6	)	)	PUNCT
ejpam-3539	130	7	=	=	SYM
ejpam-3539	130	8	y(t	y(t	PROPN
ejpam-3539	130	9	)	)	PUNCT
ejpam-3539	130	10	,	,	PUNCT
ejpam-3539	130	11	y	y	PROPN
ejpam-3539	130	12	∈	∈	PROPN
ejpam-3539	130	13	z	z	X
ejpam-3539	130	14	(	(	PUNCT
ejpam-3539	130	15	6	6	NUM
ejpam-3539	130	16	)	)	PUNCT
ejpam-3539	130	17	we	we	PRON
ejpam-3539	130	18	prove	prove	VERB
ejpam-3539	130	19	that	that	SCONJ
ejpam-3539	130	20	(	(	PUNCT
ejpam-3539	130	21	6	6	NUM
ejpam-3539	130	22	)	)	PUNCT
ejpam-3539	130	23	has	have	VERB
ejpam-3539	130	24	a	a	DET
ejpam-3539	130	25	solution	solution	NOUN
ejpam-3539	130	26	u(t	u(t	NOUN
ejpam-3539	130	27	)	)	PUNCT
ejpam-3539	130	28	satisfying	satisfy	VERB
ejpam-3539	130	29	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	130	30	)	)	PUNCT
ejpam-3539	130	31	=	=	PUNCT
ejpam-3539	131	1	(	(	PUNCT
ejpam-3539	131	2	n−	n−	NOUN
ejpam-3539	131	3	1	1	NUM
ejpam-3539	131	4	)	)	PUNCT
ejpam-3539	131	5	!	!	PUNCT
ejpam-3539	132	1	ξn−1	ξn−1	ADJ
ejpam-3539	132	2	u(ξ	u(ξ	NOUN
ejpam-3539	132	3	)	)	PUNCT
ejpam-3539	132	4	,	,	PUNCT
ejpam-3539	132	5	u(i)(0	u(i)(0	PROPN
ejpam-3539	132	6	)	)	PUNCT
ejpam-3539	132	7	=	=	SYM
ejpam-3539	132	8	0	0	NUM
ejpam-3539	132	9	,	,	PUNCT
ejpam-3539	132	10	i	i	PRON
ejpam-3539	132	11	=	=	NOUN
ejpam-3539	132	12	1	1	NUM
ejpam-3539	132	13	,	,	PUNCT
ejpam-3539	132	14	2	2	NUM
ejpam-3539	132	15	,	,	PUNCT
ejpam-3539	132	16	.	.	PUNCT
ejpam-3539	132	17	.	.	PUNCT
ejpam-3539	132	18	.	.	PUNCT
ejpam-3539	133	1	,	,	PUNCT
ejpam-3539	133	2	n−	n−	NOUN
ejpam-3539	133	3	2	2	NUM
ejpam-3539	133	4	,	,	PUNCT
ejpam-3539	133	5	un−1(∞	un−1(∞	X
ejpam-3539	133	6	)	)	PUNCT
ejpam-3539	133	7	=	=	SYM
ejpam-3539	134	1	∫	∫	PROPN
ejpam-3539	134	2	ξ	ξ	SYM
ejpam-3539	134	3	0	0	NUM
ejpam-3539	134	4	u(n−1)(s)da(s	u(n−1)(s)da(	NOUN
ejpam-3539	134	5	)	)	PUNCT
ejpam-3539	134	6	if	if	SCONJ
ejpam-3539	134	7	and	and	CCONJ
ejpam-3539	134	8	only	only	ADV
ejpam-3539	135	1	if	if	SCONJ
ejpam-3539	135	2	∫	∫	PROPN
ejpam-3539	135	3	∞	∞	NUM
ejpam-3539	135	4	0	0	NUM
ejpam-3539	135	5	y(τ)dτ	y(τ)dτ	NOUN
ejpam-3539	135	6	−	−	PROPN
ejpam-3539	135	7	∫	∫	PROPN
ejpam-3539	136	1	ξ	ξ	SYM
ejpam-3539	136	2	0	0	NUM
ejpam-3539	136	3	∫	∫	PROPN
ejpam-3539	136	4	s	s	PART
ejpam-3539	136	5	0	0	NUM
ejpam-3539	136	6	y(v)dvda(s	y(v)dvda(s	NOUN
ejpam-3539	136	7	)	)	PUNCT
ejpam-3539	136	8	=	=	SYM
ejpam-3539	136	9	0	0	NUM
ejpam-3539	136	10	(	(	PUNCT
ejpam-3539	136	11	7	7	X
ejpam-3539	136	12	)	)	PUNCT
ejpam-3539	136	13	samuel	samuel	PROPN
ejpam-3539	136	14	a.	a.	PROPN
ejpam-3539	136	15	iyase	iyase	PROPN
ejpam-3539	136	16	,	,	PUNCT
ejpam-3539	136	17	abiodun	abiodun	PROPN
ejpam-3539	136	18	a.	a.	PROPN
ejpam-3539	136	19	opanuga	opanuga	PROPN
ejpam-3539	136	20	/	/	SYM
ejpam-3539	136	21	eur	eur	PROPN
ejpam-3539	136	22	.	.	PUNCT
ejpam-3539	137	1	j.	j.	PROPN
ejpam-3539	137	2	pure	pure	PROPN
ejpam-3539	137	3	appl	appl	PROPN
ejpam-3539	137	4	.	.	PROPN
ejpam-3539	137	5	math	math	PROPN
ejpam-3539	137	6	,	,	PUNCT
ejpam-3539	137	7	13	13	NUM
ejpam-3539	137	8	(	(	PUNCT
ejpam-3539	137	9	1	1	NUM
ejpam-3539	137	10	)	)	PUNCT
ejpam-3539	137	11	(	(	PUNCT
ejpam-3539	137	12	2020	2020	NUM
ejpam-3539	137	13	)	)	PUNCT
ejpam-3539	137	14	,	,	PUNCT
ejpam-3539	137	15	33	33	NUM
ejpam-3539	137	16	-	-	SYM
ejpam-3539	137	17	47	47	NUM
ejpam-3539	137	18	38	38	NUM
ejpam-3539	137	19	suppose	suppose	VERB
ejpam-3539	137	20	(	(	PUNCT
ejpam-3539	137	21	6	6	NUM
ejpam-3539	137	22	)	)	PUNCT
ejpam-3539	137	23	has	have	VERB
ejpam-3539	137	24	a	a	DET
ejpam-3539	137	25	solution	solution	NOUN
ejpam-3539	137	26	u(t	u(t	NOUN
ejpam-3539	137	27	)	)	PUNCT
ejpam-3539	137	28	satisfying	satisfying	NOUN
ejpam-3539	137	29	(	(	PUNCT
ejpam-3539	137	30	5	5	NUM
ejpam-3539	137	31	)	)	PUNCT
ejpam-3539	137	32	.	.	PUNCT
ejpam-3539	138	1	we	we	PRON
ejpam-3539	138	2	show	show	VERB
ejpam-3539	138	3	that	that	SCONJ
ejpam-3539	138	4	this	this	DET
ejpam-3539	138	5	solution	solution	NOUN
ejpam-3539	138	6	satisfies	satisfie	NOUN
ejpam-3539	138	7	(	(	PUNCT
ejpam-3539	138	8	7	7	NUM
ejpam-3539	138	9	)	)	PUNCT
ejpam-3539	138	10	.	.	PUNCT
ejpam-3539	139	1	from	from	ADP
ejpam-3539	139	2	(	(	PUNCT
ejpam-3539	139	3	5	5	X
ejpam-3539	139	4	)	)	PUNCT
ejpam-3539	139	5	we	we	PRON
ejpam-3539	139	6	obtain	obtain	VERB
ejpam-3539	139	7	u(t	u(t	NOUN
ejpam-3539	139	8	)	)	PUNCT
ejpam-3539	139	9	=	=	SYM
ejpam-3539	139	10	u(0	u(0	NOUN
ejpam-3539	139	11	)	)	PUNCT
ejpam-3539	140	1	+	+	CCONJ
ejpam-3539	140	2	u(n−1	u(n−1	NOUN
ejpam-3539	140	3	)	)	PUNCT
ejpam-3539	140	4	(	(	PUNCT
ejpam-3539	140	5	n−	n−	NOUN
ejpam-3539	140	6	1	1	NUM
ejpam-3539	140	7	)	)	PUNCT
ejpam-3539	140	8	!	!	PUNCT
ejpam-3539	141	1	tn−1	tn−1	PROPN
ejpam-3539	142	1	+	+	CCONJ
ejpam-3539	142	2	∫	∫	PROPN
ejpam-3539	142	3	t	t	PROPN
ejpam-3539	142	4	0	0	NUM
ejpam-3539	142	5	∫	∫	PROPN
ejpam-3539	142	6	τn	τn	ADP
ejpam-3539	142	7	0	0	NUM
ejpam-3539	142	8	·	·	PUNCT
ejpam-3539	142	9	·	·	PUNCT
ejpam-3539	143	1	·	·	PUNCT
ejpam-3539	143	2	∫	∫	PROPN
ejpam-3539	144	1	τ2	τ2	NOUN
ejpam-3539	144	2	0	0	NUM
ejpam-3539	144	3	y(τ)dτ1	y(τ)dτ1	NOUN
ejpam-3539	144	4	,	,	PUNCT
ejpam-3539	144	5	.	.	PUNCT
ejpam-3539	144	6	.	.	PUNCT
ejpam-3539	144	7	.	.	PUNCT
ejpam-3539	145	1	,	,	PUNCT
ejpam-3539	145	2	dτn	dτn	PROPN
ejpam-3539	145	3	u(n−1)(t	u(n−1)(t	ADJ
ejpam-3539	145	4	)	)	PUNCT
ejpam-3539	145	5	=	=	SYM
ejpam-3539	145	6	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	145	7	)	)	PUNCT
ejpam-3539	146	1	+	+	CCONJ
ejpam-3539	146	2	∫	∫	PROPN
ejpam-3539	146	3	t	t	NOUN
ejpam-3539	146	4	0	0	NUM
ejpam-3539	146	5	y(τ)dτ	y(τ)dτ	PROPN
ejpam-3539	146	6	u(n−1)(∞	u(n−1)(∞	PROPN
ejpam-3539	146	7	)	)	PUNCT
ejpam-3539	146	8	=	=	SYM
ejpam-3539	146	9	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	146	10	)	)	PUNCT
ejpam-3539	147	1	+	+	CCONJ
ejpam-3539	147	2	∫	∫	PROPN
ejpam-3539	147	3	∞	∞	NUM
ejpam-3539	147	4	0	0	NUM
ejpam-3539	148	1	y(τ)dτ	y(τ)dτ	PROPN
ejpam-3539	149	1	=	=	SYM
ejpam-3539	149	2	∫	∫	PROPN
ejpam-3539	149	3	ξ	ξ	SYM
ejpam-3539	149	4	0	0	PUNCT
ejpam-3539	149	5	[	[	PUNCT
ejpam-3539	149	6	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	149	7	)	)	PUNCT
ejpam-3539	149	8	+	+	CCONJ
ejpam-3539	149	9	∫	∫	PROPN
ejpam-3539	149	10	s	s	PART
ejpam-3539	149	11	0	0	NUM
ejpam-3539	149	12	y(τ)dτ	y(τ)dτ	NOUN
ejpam-3539	149	13	]	]	PUNCT
ejpam-3539	149	14	da(s	da(s	X
ejpam-3539	149	15	)	)	PUNCT
ejpam-3539	149	16	=	=	SYM
ejpam-3539	149	17	u(n−1)(0)a(ξ	u(n−1)(0)a(ξ	ADJ
ejpam-3539	149	18	)	)	PUNCT
ejpam-3539	150	1	+	+	CCONJ
ejpam-3539	150	2	∫	∫	X
ejpam-3539	150	3	ξ	ξ	SYM
ejpam-3539	150	4	0	0	NUM
ejpam-3539	150	5	∫	∫	PROPN
ejpam-3539	150	6	s	s	PART
ejpam-3539	150	7	0	0	NUM
ejpam-3539	150	8	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	150	9	)	)	PUNCT
ejpam-3539	150	10	=	=	SYM
ejpam-3539	150	11	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	150	12	)	)	PUNCT
ejpam-3539	151	1	+	+	CCONJ
ejpam-3539	152	1	∫	∫	X
ejpam-3539	153	1	ξ	ξ	SYM
ejpam-3539	153	2	0	0	NUM
ejpam-3539	153	3	∫	∫	PROPN
ejpam-3539	153	4	s	s	PART
ejpam-3539	153	5	0	0	NUM
ejpam-3539	153	6	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	153	7	)	)	PUNCT
ejpam-3539	153	8	and	and	CCONJ
ejpam-3539	153	9	hence	hence	ADV
ejpam-3539	153	10	∫	∫	PROPN
ejpam-3539	153	11	∞	∞	NUM
ejpam-3539	153	12	0	0	NUM
ejpam-3539	153	13	y(τ)dτ	y(τ)dτ	PROPN
ejpam-3539	153	14	−	−	PROPN
ejpam-3539	153	15	∫	∫	PROPN
ejpam-3539	154	1	ξ	ξ	SYM
ejpam-3539	154	2	0	0	NUM
ejpam-3539	154	3	∫	∫	PROPN
ejpam-3539	154	4	s	s	PART
ejpam-3539	154	5	0	0	NUM
ejpam-3539	154	6	y(v)dvda(s	y(v)dvda(s	NOUN
ejpam-3539	154	7	)	)	PUNCT
ejpam-3539	154	8	=	=	SYM
ejpam-3539	155	1	0	0	X
ejpam-3539	155	2	.	.	PUNCT
ejpam-3539	156	1	if	if	SCONJ
ejpam-3539	156	2	however	however	ADV
ejpam-3539	156	3	,	,	PUNCT
ejpam-3539	156	4	(	(	PUNCT
ejpam-3539	156	5	7	7	X
ejpam-3539	156	6	)	)	PUNCT
ejpam-3539	156	7	holds	hold	VERB
ejpam-3539	156	8	then	then	ADV
ejpam-3539	156	9	setting	set	VERB
ejpam-3539	156	10	u(t	u(t	NOUN
ejpam-3539	156	11	)	)	PUNCT
ejpam-3539	156	12	=	=	SYM
ejpam-3539	156	13	u(n−1)(0	u(n−1)(0	PROPN
ejpam-3539	156	14	)	)	PUNCT
ejpam-3539	156	15	(	(	PUNCT
ejpam-3539	156	16	n−	n−	NOUN
ejpam-3539	156	17	1	1	NUM
ejpam-3539	156	18	)	)	PUNCT
ejpam-3539	156	19	!	!	PUNCT
ejpam-3539	157	1	tn−1	tn−1	PROPN
ejpam-3539	158	1	+	+	CCONJ
ejpam-3539	158	2	∫	∫	PROPN
ejpam-3539	158	3	t	t	PROPN
ejpam-3539	158	4	0	0	NUM
ejpam-3539	158	5	∫	∫	PROPN
ejpam-3539	158	6	τn	τn	ADP
ejpam-3539	158	7	0	0	NUM
ejpam-3539	158	8	·	·	PUNCT
ejpam-3539	158	9	·	·	PUNCT
ejpam-3539	159	1	·	·	PUNCT
ejpam-3539	159	2	∫	∫	PROPN
ejpam-3539	160	1	τ2	τ2	NOUN
ejpam-3539	160	2	0	0	NUM
ejpam-3539	160	3	y(τ1)dτ1	y(τ1)dτ1	PROPN
ejpam-3539	160	4	,	,	PUNCT
ejpam-3539	160	5	·	·	PUNCT
ejpam-3539	160	6	·	·	PUNCT
ejpam-3539	160	7	·	·	PUNCT
ejpam-3539	160	8	,	,	PUNCT
ejpam-3539	160	9	dτn	dτn	INTJ
ejpam-3539	160	10	we	we	PRON
ejpam-3539	160	11	conclude	conclude	VERB
ejpam-3539	160	12	that	that	SCONJ
ejpam-3539	160	13	u(t	u(t	NOUN
ejpam-3539	160	14	)	)	PUNCT
ejpam-3539	160	15	is	be	AUX
ejpam-3539	160	16	a	a	DET
ejpam-3539	160	17	solution	solution	NOUN
ejpam-3539	160	18	of	of	ADP
ejpam-3539	160	19	(	(	PUNCT
ejpam-3539	160	20	6	6	NUM
ejpam-3539	160	21	)	)	PUNCT
ejpam-3539	160	22	satisfying	satisfying	NOUN
ejpam-3539	160	23	(	(	PUNCT
ejpam-3539	160	24	7	7	NUM
ejpam-3539	160	25	)	)	PUNCT
ejpam-3539	160	26	.	.	PUNCT
ejpam-3539	161	1	lemma	lemma	PROPN
ejpam-3539	161	2	2.3	2.3	NUM
ejpam-3539	161	3	the	the	DET
ejpam-3539	161	4	mapping	mapping	NOUN
ejpam-3539	161	5	l	l	NOUN
ejpam-3539	161	6	:	:	PUNCT
ejpam-3539	161	7	doml	doml	VERB
ejpam-3539	161	8	⊂	⊂	PROPN
ejpam-3539	161	9	x	x	PUNCT
ejpam-3539	162	1	−→	−→	ADJ
ejpam-3539	162	2	z	z	NOUN
ejpam-3539	162	3	is	be	AUX
ejpam-3539	162	4	a	a	DET
ejpam-3539	162	5	fredholm	fredholm	NOUN
ejpam-3539	162	6	mapping	mapping	NOUN
ejpam-3539	162	7	of	of	ADP
ejpam-3539	162	8	index	index	NOUN
ejpam-3539	162	9	zero	zero	NUM
ejpam-3539	162	10	and	and	CCONJ
ejpam-3539	162	11	furthermore	furthermore	ADV
ejpam-3539	162	12	the	the	DET
ejpam-3539	162	13	linear	linear	ADJ
ejpam-3539	162	14	continuous	continuous	ADJ
ejpam-3539	162	15	projector	projector	NOUN
ejpam-3539	162	16	q	q	NOUN
ejpam-3539	163	1	:	:	PUNCT
ejpam-3539	163	2	z	z	NOUN
ejpam-3539	163	3	−→	−→	NOUN
ejpam-3539	163	4	z	z	NOUN
ejpam-3539	163	5	can	can	AUX
ejpam-3539	163	6	be	be	AUX
ejpam-3539	163	7	defined	define	VERB
ejpam-3539	163	8	as	as	ADP
ejpam-3539	163	9	qy	qy	NOUN
ejpam-3539	163	10	=	=	SYM
ejpam-3539	163	11	h(t	h(t	PROPN
ejpam-3539	163	12	)	)	PUNCT
ejpam-3539	164	1	[	[	X
ejpam-3539	164	2	∫	∫	X
ejpam-3539	164	3	∞	∞	NUM
ejpam-3539	164	4	0	0	PUNCT
ejpam-3539	165	1	y(s)ds−	y(s)ds−	NUM
ejpam-3539	165	2	∫	∫	PROPN
ejpam-3539	166	1	ξ	ξ	SYM
ejpam-3539	166	2	0	0	NUM
ejpam-3539	166	3	∫	∫	PROPN
ejpam-3539	166	4	s	s	PART
ejpam-3539	166	5	0	0	NUM
ejpam-3539	166	6	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	166	7	)	)	PUNCT
ejpam-3539	166	8	]	]	PUNCT
ejpam-3539	166	9	where	where	SCONJ
ejpam-3539	166	10	h(t	h(t	X
ejpam-3539	166	11	)	)	PUNCT
ejpam-3539	166	12	=	=	PUNCT
ejpam-3539	167	1	e−t∫	e−t∫	NOUN
ejpam-3539	167	2	ξ	ξ	SYM
ejpam-3539	167	3	0	0	PUNCT
ejpam-3539	167	4	e	e	PROPN
ejpam-3539	167	5	−sda(s	−sda(s	PROPN
ejpam-3539	167	6	)	)	PUNCT
ejpam-3539	167	7	the	the	DET
ejpam-3539	167	8	linear	linear	ADJ
ejpam-3539	167	9	operator	operator	NOUN
ejpam-3539	167	10	kp	kp	NOUN
ejpam-3539	167	11	:	:	PUNCT
ejpam-3539	167	12	iml	iml	X
ejpam-3539	167	13	→	→	SYM
ejpam-3539	167	14	doml	doml	NOUN
ejpam-3539	167	15	∩	∩	PROPN
ejpam-3539	167	16	kerp	kerp	PROPN
ejpam-3539	167	17	,	,	PUNCT
ejpam-3539	167	18	the	the	DET
ejpam-3539	167	19	inverse	inverse	NOUN
ejpam-3539	167	20	of	of	ADP
ejpam-3539	167	21	l|doml	l|doml	PROPN
ejpam-3539	167	22	∩	∩	NOUN
ejpam-3539	167	23	kerp	kerp	PROPN
ejpam-3539	167	24	can	can	AUX
ejpam-3539	167	25	be	be	AUX
ejpam-3539	167	26	defined	define	VERB
ejpam-3539	167	27	as	as	ADP
ejpam-3539	167	28	kpy	kpy	PROPN
ejpam-3539	167	29	=	=	SYM
ejpam-3539	167	30	∫	∫	PROPN
ejpam-3539	168	1	t	t	PROPN
ejpam-3539	168	2	0	0	NUM
ejpam-3539	168	3	∫	∫	PROPN
ejpam-3539	168	4	τn	τn	ADP
ejpam-3539	168	5	0	0	NUM
ejpam-3539	168	6	·	·	PUNCT
ejpam-3539	168	7	·	·	PUNCT
ejpam-3539	168	8	·	·	PUNCT
ejpam-3539	168	9	∫	∫	PROPN
ejpam-3539	169	1	τ2	τ2	NOUN
ejpam-3539	169	2	0	0	NUM
ejpam-3539	169	3	y(τ1	y(τ1	NOUN
ejpam-3539	169	4	)	)	PUNCT
ejpam-3539	169	5	,	,	PUNCT
ejpam-3539	169	6	dτ1	dτ1	PROPN
ejpam-3539	169	7	.	.	PUNCT
ejpam-3539	169	8	.	.	PUNCT
ejpam-3539	169	9	.	.	PUNCT
ejpam-3539	170	1	dτn	dτn	PROPN
ejpam-3539	171	1	−	−	PROPN
ejpam-3539	171	2	∫	∫	PROPN
ejpam-3539	171	3	ξ	ξ	SYM
ejpam-3539	171	4	0	0	NUM
ejpam-3539	171	5	∫	∫	NOUN
ejpam-3539	171	6	τn	τn	ADP
ejpam-3539	171	7	0	0	NUM
ejpam-3539	171	8	·	·	PUNCT
ejpam-3539	171	9	·	·	PUNCT
ejpam-3539	171	10	·	·	PUNCT
ejpam-3539	171	11	∫	∫	PROPN
ejpam-3539	172	1	τ2	τ2	NOUN
ejpam-3539	172	2	0	0	NUM
ejpam-3539	172	3	y(τ1)dτ1	y(τ1)dτ1	NOUN
ejpam-3539	172	4	·	·	PUNCT
ejpam-3539	172	5	·	·	PUNCT
ejpam-3539	172	6	·	·	PUNCT
ejpam-3539	172	7	dτn	dτn	VERB
ejpam-3539	172	8	with	with	ADP
ejpam-3539	172	9	‖kpy‖	‖kpy‖	PRON
ejpam-3539	172	10	≤	≤	NUM
ejpam-3539	172	11	dn‖y‖1	dn‖y‖1	PROPN
ejpam-3539	172	12	(	(	PUNCT
ejpam-3539	172	13	8)	8)	NUM
ejpam-3539	172	14	samuel	samuel	PROPN
ejpam-3539	172	15	a.	a.	NOUN
ejpam-3539	172	16	iyase	iyase	PROPN
ejpam-3539	172	17	,	,	PUNCT
ejpam-3539	172	18	abiodun	abiodun	PROPN
ejpam-3539	172	19	a.	a.	PROPN
ejpam-3539	172	20	opanuga	opanuga	PROPN
ejpam-3539	172	21	/	/	SYM
ejpam-3539	172	22	eur	eur	PROPN
ejpam-3539	172	23	.	.	PUNCT
ejpam-3539	173	1	j.	j.	PROPN
ejpam-3539	173	2	pure	pure	PROPN
ejpam-3539	173	3	appl	appl	PROPN
ejpam-3539	173	4	.	.	PROPN
ejpam-3539	173	5	math	math	PROPN
ejpam-3539	173	6	,	,	PUNCT
ejpam-3539	173	7	13	13	NUM
ejpam-3539	173	8	(	(	PUNCT
ejpam-3539	173	9	1	1	NUM
ejpam-3539	173	10	)	)	PUNCT
ejpam-3539	173	11	(	(	PUNCT
ejpam-3539	173	12	2020	2020	NUM
ejpam-3539	173	13	)	)	PUNCT
ejpam-3539	173	14	,	,	PUNCT
ejpam-3539	173	15	33	33	NUM
ejpam-3539	173	16	-	-	SYM
ejpam-3539	173	17	47	47	NUM
ejpam-3539	173	18	39	39	NUM
ejpam-3539	173	19	where	where	SCONJ
ejpam-3539	173	20	dn	dn	PROPN
ejpam-3539	173	21	=	=	SYM
ejpam-3539	173	22	max	max	PROPN
ejpam-3539	173	23	[	[	PUNCT
ejpam-3539	173	24	2	2	NUM
ejpam-3539	173	25	sup	sup	NOUN
ejpam-3539	173	26	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	173	27	)	)	PUNCT
ejpam-3539	173	28	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	173	29	,	,	PUNCT
ejpam-3539	173	30	max	max	PROPN
ejpam-3539	173	31	1∈i≤n−1	1∈i≤n−1	NUM
ejpam-3539	173	32	(	(	PUNCT
ejpam-3539	173	33	sup	sup	NOUN
ejpam-3539	173	34	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	173	35	)	)	PUNCT
ejpam-3539	173	36	e−ttn−1−i	e−ttn−1−i	NOUN
ejpam-3539	173	37	)	)	PUNCT
ejpam-3539	173	38	]	]	PUNCT
ejpam-3539	174	1	proof	proof	NOUN
ejpam-3539	174	2	:	:	PUNCT
ejpam-3539	174	3	for	for	ADP
ejpam-3539	174	4	y	y	PROPN
ejpam-3539	174	5	∈	∈	PROPN
ejpam-3539	174	6	z	z	PROPN
ejpam-3539	174	7	,	,	PUNCT
ejpam-3539	174	8	we	we	PRON
ejpam-3539	174	9	define	define	VERB
ejpam-3539	174	10	the	the	DET
ejpam-3539	174	11	projection	projection	NOUN
ejpam-3539	174	12	qy	qy	PROPN
ejpam-3539	174	13	as	as	ADP
ejpam-3539	174	14	:	:	PUNCT
ejpam-3539	174	15	qy	qy	NOUN
ejpam-3539	174	16	=	=	SYM
ejpam-3539	174	17	h(t	h(t	PROPN
ejpam-3539	174	18	)	)	PUNCT
ejpam-3539	175	1	[	[	X
ejpam-3539	175	2	∫	∫	X
ejpam-3539	175	3	∞	∞	NUM
ejpam-3539	175	4	0	0	PROPN
ejpam-3539	175	5	y(v)dv	y(v)dv	NOUN
ejpam-3539	175	6	−	−	NOUN
ejpam-3539	175	7	∫	∫	PROPN
ejpam-3539	175	8	ξ	ξ	SYM
ejpam-3539	175	9	0	0	NUM
ejpam-3539	175	10	∫	∫	PROPN
ejpam-3539	175	11	s	s	PART
ejpam-3539	175	12	0	0	NUM
ejpam-3539	175	13	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	175	14	)	)	PUNCT
ejpam-3539	175	15	]	]	PUNCT
ejpam-3539	175	16	where	where	SCONJ
ejpam-3539	175	17	h(t	h(t	X
ejpam-3539	175	18	)	)	PUNCT
ejpam-3539	175	19	=	=	PUNCT
ejpam-3539	176	1	e−t∫	e−t∫	NOUN
ejpam-3539	176	2	ξ	ξ	SYM
ejpam-3539	176	3	0	0	PUNCT
ejpam-3539	176	4	e	e	PROPN
ejpam-3539	176	5	−sda(s	−sda(s	PROPN
ejpam-3539	176	6	)	)	PUNCT
ejpam-3539	176	7	6=	6=	ADP
ejpam-3539	176	8	0	0	NUM
ejpam-3539	177	1	then	then	ADV
ejpam-3539	177	2	we	we	PRON
ejpam-3539	177	3	have	have	VERB
ejpam-3539	177	4	q2y	q2y	NOUN
ejpam-3539	177	5	=	=	SYM
ejpam-3539	177	6	q(qy	q(qy	ADV
ejpam-3539	177	7	)	)	PUNCT
ejpam-3539	177	8	=	=	SYM
ejpam-3539	177	9	h(t	h(t	PROPN
ejpam-3539	177	10	)	)	PUNCT
ejpam-3539	178	1	[	[	X
ejpam-3539	178	2	∫	∫	X
ejpam-3539	178	3	∞	∞	NUM
ejpam-3539	178	4	0	0	PROPN
ejpam-3539	178	5	y(v)dv	y(v)dv	NOUN
ejpam-3539	178	6	−	−	NOUN
ejpam-3539	178	7	∫	∫	PROPN
ejpam-3539	178	8	ξ	ξ	SYM
ejpam-3539	178	9	0	0	NUM
ejpam-3539	178	10	∫	∫	PROPN
ejpam-3539	178	11	s	s	PART
ejpam-3539	178	12	0	0	NUM
ejpam-3539	178	13	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	178	14	)	)	PUNCT
ejpam-3539	178	15	]	]	PUNCT
ejpam-3539	178	16	·	·	PUNCT
ejpam-3539	178	17	∫	∫	PUNCT
ejpam-3539	179	1	ξ	ξ	X
ejpam-3539	179	2	0	0	PUNCT
ejpam-3539	179	3	e	e	NOUN
ejpam-3539	179	4	−sda(s)∫	−sda(s)∫	NOUN
ejpam-3539	179	5	ξ	ξ	SYM
ejpam-3539	179	6	0	0	NUM
ejpam-3539	179	7	e	e	NOUN
ejpam-3539	179	8	−sda(s	−sda(s	PROPN
ejpam-3539	179	9	)	)	PUNCT
ejpam-3539	179	10	=	=	SYM
ejpam-3539	179	11	qy	qy	NOUN
ejpam-3539	179	12	this	this	PRON
ejpam-3539	179	13	implies	imply	VERB
ejpam-3539	179	14	that	that	SCONJ
ejpam-3539	179	15	q	q	NOUN
ejpam-3539	179	16	is	be	AUX
ejpam-3539	179	17	a	a	DET
ejpam-3539	179	18	projection	projection	NOUN
ejpam-3539	179	19	.	.	PUNCT
ejpam-3539	180	1	let	let	VERB
ejpam-3539	180	2	y1	y1	INTJ
ejpam-3539	180	3	=	=	SYM
ejpam-3539	180	4	y	y	PROPN
ejpam-3539	180	5	−qy	−qy	PROPN
ejpam-3539	180	6	i.e.	i.e.	X
ejpam-3539	180	7	y1	y1	PROPN
ejpam-3539	180	8	∈	∈	PROPN
ejpam-3539	180	9	kerq	kerq	NOUN
ejpam-3539	181	1	then∫	then∫	NOUN
ejpam-3539	181	2	∞	∞	NOUN
ejpam-3539	181	3	0	0	NUM
ejpam-3539	182	1	y1(v)dv	y1(v)dv	NOUN
ejpam-3539	182	2	−	−	PROPN
ejpam-3539	182	3	∫	∫	PROPN
ejpam-3539	183	1	ξ	ξ	SYM
ejpam-3539	183	2	0	0	NUM
ejpam-3539	183	3	∫	∫	PROPN
ejpam-3539	183	4	s	s	PART
ejpam-3539	183	5	0	0	NUM
ejpam-3539	183	6	y1(τ)dτda(s	y1(τ)dτda(s	NOUN
ejpam-3539	183	7	)	)	PUNCT
ejpam-3539	183	8	=	=	PUNCT
ejpam-3539	184	1	[	[	X
ejpam-3539	184	2	∫	∫	X
ejpam-3539	184	3	∞	∞	NUM
ejpam-3539	184	4	0	0	PROPN
ejpam-3539	184	5	y(v)dv	y(v)dv	NOUN
ejpam-3539	184	6	−	−	NOUN
ejpam-3539	184	7	∫	∫	PROPN
ejpam-3539	184	8	ξ	ξ	SYM
ejpam-3539	184	9	0	0	NUM
ejpam-3539	184	10	∫	∫	PROPN
ejpam-3539	184	11	s	s	PART
ejpam-3539	184	12	0	0	NUM
ejpam-3539	184	13	y(τ)dτda(s	y(τ)dτda(	NOUN
ejpam-3539	184	14	)	)	PUNCT
ejpam-3539	184	15	]	]	PUNCT
ejpam-3539	184	16	[	[	PUNCT
ejpam-3539	184	17	1−	1−	NUM
ejpam-3539	184	18	∫	∫	NOUN
ejpam-3539	184	19	ξ	ξ	SYM
ejpam-3539	184	20	0	0	PUNCT
ejpam-3539	184	21	e	e	NOUN
ejpam-3539	184	22	−sda(s)∫	−sda(s)∫	NOUN
ejpam-3539	184	23	ξ	ξ	SYM
ejpam-3539	184	24	0	0	NUM
ejpam-3539	184	25	e	e	NOUN
ejpam-3539	184	26	−sda(s	−sda(s	PROPN
ejpam-3539	184	27	)	)	PUNCT
ejpam-3539	184	28	]	]	PUNCT
ejpam-3539	185	1	=	=	PUNCT
ejpam-3539	185	2	0	0	PUNCT
ejpam-3539	185	3	therefore	therefore	ADV
ejpam-3539	185	4	,	,	PUNCT
ejpam-3539	185	5	y1	y1	PROPN
ejpam-3539	185	6	∈	∈	NOUN
ejpam-3539	185	7	iml	iml	NOUN
ejpam-3539	185	8	and	and	CCONJ
ejpam-3539	185	9	hence	hence	ADV
ejpam-3539	185	10	z	z	NOUN
ejpam-3539	185	11	=	=	PUNCT
ejpam-3539	185	12	iml+	iml+	PROPN
ejpam-3539	185	13	imq	imq	PROPN
ejpam-3539	185	14	.	.	PUNCT
ejpam-3539	186	1	since	since	SCONJ
ejpam-3539	186	2	iml	iml	NOUN
ejpam-3539	186	3	∩	∩	NOUN
ejpam-3539	186	4	imq	imq	NOUN
ejpam-3539	186	5	=	=	SYM
ejpam-3539	186	6	{	{	PUNCT
ejpam-3539	186	7	0	0	NUM
ejpam-3539	186	8	}	}	PUNCT
ejpam-3539	186	9	we	we	PRON
ejpam-3539	186	10	obtain	obtain	VERB
ejpam-3539	186	11	z	z	NOUN
ejpam-3539	186	12	=	=	SYM
ejpam-3539	186	13	imq⊕	imq⊕	PROPN
ejpam-3539	186	14	iml	iml	NOUN
ejpam-3539	186	15	.	.	PUNCT
ejpam-3539	187	1	this	this	PRON
ejpam-3539	187	2	implies	imply	VERB
ejpam-3539	187	3	that	that	SCONJ
ejpam-3539	187	4	dim	dim	ADJ
ejpam-3539	187	5	kerl	kerl	NOUN
ejpam-3539	187	6	=	=	SYM
ejpam-3539	187	7	dim	dim	ADJ
ejpam-3539	187	8	imq	imq	NOUN
ejpam-3539	187	9	=	=	NOUN
ejpam-3539	187	10	1	1	X
ejpam-3539	187	11	.	.	PUNCT
ejpam-3539	188	1	hence	hence	ADV
ejpam-3539	188	2	,	,	PUNCT
ejpam-3539	188	3	l	l	NOUN
ejpam-3539	188	4	is	be	AUX
ejpam-3539	188	5	a	a	DET
ejpam-3539	188	6	fredholm	fredholm	NOUN
ejpam-3539	188	7	operator	operator	NOUN
ejpam-3539	188	8	of	of	ADP
ejpam-3539	188	9	index	index	NOUN
ejpam-3539	188	10	zero	zero	NUM
ejpam-3539	188	11	.	.	PUNCT
ejpam-3539	189	1	let	let	VERB
ejpam-3539	189	2	p	p	NOUN
ejpam-3539	189	3	:	:	PUNCT
ejpam-3539	189	4	x	x	PUNCT
ejpam-3539	189	5	−→	−→	NOUN
ejpam-3539	189	6	x	x	AUX
ejpam-3539	189	7	be	be	AUX
ejpam-3539	189	8	defined	define	VERB
ejpam-3539	189	9	by	by	ADP
ejpam-3539	189	10	pu	pu	PROPN
ejpam-3539	189	11	=	=	SYM
ejpam-3539	189	12	u(n−1)(0)tn−1	u(n−1)(0)tn−1	PROPN
ejpam-3539	189	13	(	(	PUNCT
ejpam-3539	189	14	n−	n−	NOUN
ejpam-3539	189	15	1	1	NUM
ejpam-3539	189	16	)	)	PUNCT
ejpam-3539	189	17	!	!	PUNCT
ejpam-3539	190	1	(	(	PUNCT
ejpam-3539	190	2	9	9	X
ejpam-3539	190	3	)	)	PUNCT
ejpam-3539	190	4	we	we	PRON
ejpam-3539	190	5	define	define	VERB
ejpam-3539	190	6	kp	kp	PROPN
ejpam-3539	190	7	:	:	PUNCT
ejpam-3539	190	8	iml	iml	PROPN
ejpam-3539	190	9	−→	−→	NOUN
ejpam-3539	190	10	doml	doml	PROPN
ejpam-3539	190	11	∩	∩	ADJ
ejpam-3539	190	12	kerp	kerp	PROPN
ejpam-3539	190	13	as	as	ADP
ejpam-3539	190	14	kpy	kpy	PROPN
ejpam-3539	191	1	=	=	SYM
ejpam-3539	191	2	∫	∫	PROPN
ejpam-3539	192	1	t	t	PROPN
ejpam-3539	192	2	0	0	NUM
ejpam-3539	192	3	∫	∫	PROPN
ejpam-3539	192	4	τn	τn	ADP
ejpam-3539	192	5	0	0	NUM
ejpam-3539	192	6	·	·	PUNCT
ejpam-3539	192	7	·	·	PUNCT
ejpam-3539	192	8	·	·	PUNCT
ejpam-3539	193	1	∫	∫	PROPN
ejpam-3539	193	2	τn	τn	NOUN
ejpam-3539	193	3	0	0	NUM
ejpam-3539	193	4	y(τ1)dτ1	y(τ1)dτ1	NOUN
ejpam-3539	193	5	·	·	PUNCT
ejpam-3539	193	6	·	·	PUNCT
ejpam-3539	193	7	·	·	PUNCT
ejpam-3539	193	8	dτn	dτn	INTJ
ejpam-3539	193	9	−	−	PROPN
ejpam-3539	194	1	∫	∫	PROPN
ejpam-3539	195	1	ξ	ξ	SYM
ejpam-3539	195	2	0	0	NUM
ejpam-3539	195	3	∫	∫	NOUN
ejpam-3539	195	4	τn	τn	ADP
ejpam-3539	195	5	0	0	NUM
ejpam-3539	195	6	·	·	PUNCT
ejpam-3539	195	7	·	·	PUNCT
ejpam-3539	195	8	·	·	PUNCT
ejpam-3539	195	9	∫	∫	PROPN
ejpam-3539	196	1	τ2	τ2	NOUN
ejpam-3539	196	2	0	0	NUM
ejpam-3539	196	3	y(τ1)dτ1	y(τ1)dτ1	NOUN
ejpam-3539	196	4	·	·	PUNCT
ejpam-3539	196	5	·	·	PUNCT
ejpam-3539	196	6	·	·	PUNCT
ejpam-3539	197	1	dτn	dτn	PROPN
ejpam-3539	197	2	samuel	samuel	PROPN
ejpam-3539	197	3	a.	a.	PROPN
ejpam-3539	197	4	iyase	iyase	PROPN
ejpam-3539	197	5	,	,	PUNCT
ejpam-3539	197	6	abiodun	abiodun	PROPN
ejpam-3539	197	7	a.	a.	PROPN
ejpam-3539	197	8	opanuga	opanuga	PROPN
ejpam-3539	197	9	/	/	SYM
ejpam-3539	197	10	eur	eur	PROPN
ejpam-3539	197	11	.	.	PUNCT
ejpam-3539	198	1	j.	j.	PROPN
ejpam-3539	198	2	pure	pure	PROPN
ejpam-3539	198	3	appl	appl	PROPN
ejpam-3539	198	4	.	.	PROPN
ejpam-3539	198	5	math	math	PROPN
ejpam-3539	198	6	,	,	PUNCT
ejpam-3539	198	7	13	13	NUM
ejpam-3539	198	8	(	(	PUNCT
ejpam-3539	198	9	1	1	NUM
ejpam-3539	198	10	)	)	PUNCT
ejpam-3539	198	11	(	(	PUNCT
ejpam-3539	198	12	2020	2020	NUM
ejpam-3539	198	13	)	)	PUNCT
ejpam-3539	198	14	,	,	PUNCT
ejpam-3539	198	15	33	33	NUM
ejpam-3539	198	16	-	-	SYM
ejpam-3539	198	17	47	47	NUM
ejpam-3539	198	18	40	40	NUM
ejpam-3539	198	19	for	for	ADP
ejpam-3539	198	20	y	y	PROPN
ejpam-3539	198	21	∈	∈	PROPN
ejpam-3539	198	22	iml	iml	NOUN
ejpam-3539	198	23	,	,	PUNCT
ejpam-3539	198	24	(	(	PUNCT
ejpam-3539	198	25	lkp)y(t	lkp)y(t	PROPN
ejpam-3539	198	26	)	)	PUNCT
ejpam-3539	198	27	=	=	PUNCT
ejpam-3539	199	1	[	[	X
ejpam-3539	199	2	(	(	PUNCT
ejpam-3539	199	3	kpy)(t)]n	kpy)(t)]n	PROPN
ejpam-3539	199	4	=	=	SYM
ejpam-3539	199	5	y(t	y(t	PROPN
ejpam-3539	199	6	)	)	PUNCT
ejpam-3539	199	7	and	and	CCONJ
ejpam-3539	199	8	for	for	ADP
ejpam-3539	199	9	u	u	PROPN
ejpam-3539	199	10	∈	∈	PROPN
ejpam-3539	199	11	doml	doml	PROPN
ejpam-3539	199	12	∩	∩	PROPN
ejpam-3539	199	13	kerp	kerp	PROPN
ejpam-3539	199	14	and	and	CCONJ
ejpam-3539	199	15	noting	note	VERB
ejpam-3539	199	16	that	that	SCONJ
ejpam-3539	199	17	u(i)(0	u(i)(0	PROPN
ejpam-3539	199	18	)	)	PUNCT
ejpam-3539	199	19	=	=	SYM
ejpam-3539	199	20	0	0	NUM
ejpam-3539	199	21	,	,	PUNCT
ejpam-3539	199	22	i	i	PRON
ejpam-3539	199	23	=	=	NOUN
ejpam-3539	199	24	1.2	1.2	NUM
ejpam-3539	199	25	,	,	PUNCT
ejpam-3539	199	26	.	.	PUNCT
ejpam-3539	199	27	.	.	PUNCT
ejpam-3539	199	28	.	.	PUNCT
ejpam-3539	200	1	,	,	PUNCT
ejpam-3539	200	2	n−	n−	NOUN
ejpam-3539	200	3	2	2	NUM
ejpam-3539	200	4	(	(	PUNCT
ejpam-3539	200	5	kpl)u(t	kpl)u(t	PROPN
ejpam-3539	200	6	)	)	PUNCT
ejpam-3539	200	7	=	=	PUNCT
ejpam-3539	201	1	u(t)−	u(t)−	PROPN
ejpam-3539	201	2	u(n−1)(0)tn−1	u(n−1)(0)tn−1	PROPN
ejpam-3539	201	3	(	(	PUNCT
ejpam-3539	201	4	n−	n−	NOUN
ejpam-3539	201	5	1	1	NUM
ejpam-3539	201	6	)	)	PUNCT
ejpam-3539	201	7	!	!	PUNCT
ejpam-3539	202	1	−	−	NOUN
ejpam-3539	202	2	u(ξ	u(ξ	NOUN
ejpam-3539	202	3	)	)	PUNCT
ejpam-3539	203	1	+	+	NUM
ejpam-3539	203	2	u(n−1)(0)ξn−1	u(n−1)(0)ξn−1	PROPN
ejpam-3539	203	3	(	(	PUNCT
ejpam-3539	203	4	n−	n−	NOUN
ejpam-3539	203	5	1	1	NUM
ejpam-3539	203	6	)	)	PUNCT
ejpam-3539	203	7	!	!	PUNCT
ejpam-3539	204	1	since	since	SCONJ
ejpam-3539	204	2	u	u	PROPN
ejpam-3539	204	3	∈	∈	PROPN
ejpam-3539	204	4	doml	doml	PROPN
ejpam-3539	204	5	∩	∩	PROPN
ejpam-3539	204	6	kerp	kerp	PROPN
ejpam-3539	204	7	,	,	PUNCT
ejpam-3539	204	8	pu	pu	PROPN
ejpam-3539	204	9	=	=	SYM
ejpam-3539	204	10	u(n−1)(0	u(n−1)(0	PROPN
ejpam-3539	204	11	)	)	PUNCT
ejpam-3539	204	12	(	(	PUNCT
ejpam-3539	204	13	n−1	n−1	PROPN
ejpam-3539	204	14	)	)	PUNCT
ejpam-3539	204	15	!	!	PUNCT
ejpam-3539	205	1	t	t	PROPN
ejpam-3539	205	2	n−1	n−1	PROPN
ejpam-3539	206	1	=	=	SYM
ejpam-3539	206	2	0	0	X
ejpam-3539	206	3	.	.	PUNCT
ejpam-3539	207	1	also	also	ADV
ejpam-3539	207	2	since	since	SCONJ
ejpam-3539	207	3	u(n−1)(0	u(n−1)(0	ADJ
ejpam-3539	207	4	)	)	PUNCT
ejpam-3539	207	5	=	=	SYM
ejpam-3539	207	6	(	(	PUNCT
ejpam-3539	207	7	n−1	n−1	PROPN
ejpam-3539	207	8	)	)	PUNCT
ejpam-3539	207	9	!	!	PUNCT
ejpam-3539	208	1	ξn−1	ξn−1	ADJ
ejpam-3539	208	2	u(ξ	u(ξ	NOUN
ejpam-3539	208	3	)	)	PUNCT
ejpam-3539	208	4	we	we	PRON
ejpam-3539	208	5	derive	derive	VERB
ejpam-3539	208	6	(	(	PUNCT
ejpam-3539	208	7	kpl)u(t	kpl)u(t	PROPN
ejpam-3539	208	8	)	)	PUNCT
ejpam-3539	208	9	=	=	SYM
ejpam-3539	208	10	u(t	u(t	NOUN
ejpam-3539	208	11	)	)	PUNCT
ejpam-3539	208	12	thus	thus	ADV
ejpam-3539	208	13	kp	kp	X
ejpam-3539	208	14	=	=	SYM
ejpam-3539	208	15	(	(	PUNCT
ejpam-3539	208	16	l|doml∩kerp	l|doml∩kerp	PROPN
ejpam-3539	208	17	)	)	PUNCT
ejpam-3539	208	18	−1	−1	NOUN
ejpam-3539	209	1	e−t|(kpy)(t)|	e−t|(kpy)(t)|	NUM
ejpam-3539	209	2	=	=	SYM
ejpam-3539	209	3	e−t	e−t	X
ejpam-3539	209	4	∣∣∣∣[∫	∣∣∣∣[∫	PROPN
ejpam-3539	209	5	t	t	PROPN
ejpam-3539	209	6	0	0	NUM
ejpam-3539	209	7	∫	∫	NOUN
ejpam-3539	209	8	τn	τn	ADP
ejpam-3539	209	9	0	0	NUM
ejpam-3539	209	10	·	·	PUNCT
ejpam-3539	209	11	·	·	PUNCT
ejpam-3539	209	12	·	·	PUNCT
ejpam-3539	210	1	∫	∫	PROPN
ejpam-3539	210	2	τn	τn	NOUN
ejpam-3539	210	3	0	0	NUM
ejpam-3539	210	4	y(τ1)dτ1	y(τ1)dτ1	NOUN
ejpam-3539	210	5	·	·	PUNCT
ejpam-3539	210	6	·	·	PUNCT
ejpam-3539	210	7	·	·	PUNCT
ejpam-3539	210	8	dτn	dτn	INTJ
ejpam-3539	210	9	−	−	PROPN
ejpam-3539	211	1	∫	∫	PROPN
ejpam-3539	212	1	ξ	ξ	SYM
ejpam-3539	212	2	0	0	NUM
ejpam-3539	212	3	∫	∫	NOUN
ejpam-3539	212	4	τn	τn	ADP
ejpam-3539	212	5	0	0	NUM
ejpam-3539	212	6	·	·	PUNCT
ejpam-3539	212	7	·	·	PUNCT
ejpam-3539	212	8	·	·	PUNCT
ejpam-3539	212	9	∫	∫	PROPN
ejpam-3539	213	1	τ2	τ2	NOUN
ejpam-3539	213	2	0	0	NUM
ejpam-3539	213	3	y(τ)dτ1	y(τ)dτ1	X
ejpam-3539	213	4	·	·	PUNCT
ejpam-3539	213	5	·	·	PUNCT
ejpam-3539	213	6	·	·	PUNCT
ejpam-3539	213	7	dτn	dτn	X
ejpam-3539	213	8	]	]	PUNCT
ejpam-3539	213	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	213	10	≤	≤	NUM
ejpam-3539	213	11	e−t	e−t	NOUN
ejpam-3539	214	1	[	[	X
ejpam-3539	214	2	∫	∫	X
ejpam-3539	214	3	t	t	PROPN
ejpam-3539	214	4	0	0	NUM
ejpam-3539	214	5	∫	∫	PROPN
ejpam-3539	214	6	τn	τn	ADP
ejpam-3539	214	7	0	0	NUM
ejpam-3539	214	8	·	·	PUNCT
ejpam-3539	214	9	·	·	PUNCT
ejpam-3539	214	10	·	·	PUNCT
ejpam-3539	214	11	∫	∫	PROPN
ejpam-3539	215	1	τ2	τ2	NOUN
ejpam-3539	215	2	0	0	NUM
ejpam-3539	215	3	|y(τ1)|dτ1	|y(τ1)|dτ1	X
ejpam-3539	215	4	·	·	PUNCT
ejpam-3539	215	5	·	·	PUNCT
ejpam-3539	215	6	·	·	PUNCT
ejpam-3539	215	7	dτn	dτn	PROPN
ejpam-3539	216	1	+	+	CCONJ
ejpam-3539	216	2	∫	∫	PROPN
ejpam-3539	216	3	ξ	ξ	SYM
ejpam-3539	216	4	0	0	NUM
ejpam-3539	216	5	∫	∫	NOUN
ejpam-3539	216	6	τn	τn	ADP
ejpam-3539	216	7	0	0	NUM
ejpam-3539	216	8	·	·	PUNCT
ejpam-3539	216	9	·	·	PUNCT
ejpam-3539	216	10	·	·	PUNCT
ejpam-3539	216	11	∫	∫	PROPN
ejpam-3539	216	12	τ2	τ2	NOUN
ejpam-3539	216	13	0	0	NUM
ejpam-3539	216	14	|y(τ1)|dτ1	|y(τ1)|dτ1	X
ejpam-3539	216	15	·	·	PUNCT
ejpam-3539	216	16	·	·	PUNCT
ejpam-3539	216	17	·	·	PUNCT
ejpam-3539	216	18	dτn	dτn	X
ejpam-3539	216	19	]	]	PUNCT
ejpam-3539	216	20	≤	≤	NUM
ejpam-3539	216	21	sup	sup	NOUN
ejpam-3539	216	22	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	216	23	)	)	PUNCT
ejpam-3539	216	24	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	216	25	∫	∫	PROPN
ejpam-3539	216	26	∞	∞	PROPN
ejpam-3539	216	27	0	0	NUM
ejpam-3539	216	28	|y(s)|ds+	|y(s)|ds+	PROPN
ejpam-3539	216	29	sup	sup	NOUN
ejpam-3539	216	30	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	216	31	)	)	PUNCT
ejpam-3539	216	32	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	216	33	∫	∫	PROPN
ejpam-3539	216	34	∞	∞	PROPN
ejpam-3539	216	35	0	0	NUM
ejpam-3539	216	36	|y(s)|ds	|y(s)|ds	NOUN
ejpam-3539	216	37	≤	≤	ADJ
ejpam-3539	216	38	2	2	NUM
ejpam-3539	216	39	sup	sup	NOUN
ejpam-3539	216	40	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	216	41	)	)	PUNCT
ejpam-3539	216	42	e−ttn−1‖y‖1	e−ttn−1‖y‖1	ADJ
ejpam-3539	216	43	for	for	ADP
ejpam-3539	216	44	1	1	NUM
ejpam-3539	216	45	≤	≤	NUM
ejpam-3539	216	46	i	i	PRON
ejpam-3539	216	47	≤	≤	ADJ
ejpam-3539	216	48	n−	n−	NOUN
ejpam-3539	216	49	1	1	NUM
ejpam-3539	216	50	we	we	PRON
ejpam-3539	216	51	have	have	VERB
ejpam-3539	216	52	e−t|(kpy)(i)(t)|	e−t|(kpy)(i)(t)|	NOUN
ejpam-3539	216	53	=	=	NOUN
ejpam-3539	216	54	e−t	e−t	NOUN
ejpam-3539	216	55	(	(	PUNCT
ejpam-3539	216	56	n−	n−	NOUN
ejpam-3539	216	57	1−	1−	NUM
ejpam-3539	216	58	i	i	NOUN
ejpam-3539	216	59	)	)	PUNCT
ejpam-3539	216	60	!	!	PUNCT
ejpam-3539	217	1	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3539	217	2	t	t	NOUN
ejpam-3539	217	3	0	0	NUM
ejpam-3539	218	1	(	(	PUNCT
ejpam-3539	218	2	t−	t−	PROPN
ejpam-3539	218	3	s)n−1−iy(s)ds	s)n−1−iy(s)ds	VERB
ejpam-3539	218	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	218	5	≤	≤	NUM
ejpam-3539	218	6	e−ttn−1−i	e−ttn−1−i	ADJ
ejpam-3539	218	7	∫	∫	PROPN
ejpam-3539	218	8	∞	∞	NUM
ejpam-3539	218	9	0	0	NUM
ejpam-3539	219	1	|y(s)|ds	|y(s)|ds	NOUN
ejpam-3539	220	1	we	we	PRON
ejpam-3539	220	2	therefore	therefore	ADV
ejpam-3539	220	3	conclude	conclude	VERB
ejpam-3539	220	4	that	that	SCONJ
ejpam-3539	220	5	‖kpy‖	‖kpy‖	DET
ejpam-3539	220	6	≤	≤	NUM
ejpam-3539	220	7	max	max	NOUN
ejpam-3539	220	8	[	[	PUNCT
ejpam-3539	220	9	2	2	NUM
ejpam-3539	220	10	sup	sup	NOUN
ejpam-3539	220	11	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	220	12	)	)	PUNCT
ejpam-3539	220	13	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	220	14	,	,	PUNCT
ejpam-3539	220	15	max	max	PROPN
ejpam-3539	220	16	1≤i≤n−1	1≤i≤n−1	PROPN
ejpam-3539	220	17	(	(	PUNCT
ejpam-3539	220	18	sup	sup	NOUN
ejpam-3539	220	19	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	220	20	)	)	PUNCT
ejpam-3539	220	21	e−ttn−1−i	e−ttn−1−i	NOUN
ejpam-3539	220	22	)	)	PUNCT
ejpam-3539	220	23	]	]	PUNCT
ejpam-3539	220	24	‖y‖1	‖y‖1	PROPN
ejpam-3539	220	25	=	=	SYM
ejpam-3539	220	26	dn‖y‖1	dn‖y‖1	PROPN
ejpam-3539	220	27	(	(	PUNCT
ejpam-3539	220	28	10	10	NUM
ejpam-3539	220	29	)	)	PUNCT
ejpam-3539	220	30	where	where	SCONJ
ejpam-3539	220	31	dn	dn	NOUN
ejpam-3539	220	32	=	=	SYM
ejpam-3539	220	33	max	max	PROPN
ejpam-3539	220	34	[	[	PUNCT
ejpam-3539	220	35	2	2	NUM
ejpam-3539	220	36	supt∈[0,∞	supt∈[0,∞	NOUN
ejpam-3539	220	37	)	)	PUNCT
ejpam-3539	220	38	e	e	PROPN
ejpam-3539	220	39	−ttn−1,max1≤i≤n−1	−ttn−1,max1≤i≤n−1	PROPN
ejpam-3539	220	40	(	(	PUNCT
ejpam-3539	220	41	supt∈[0,∞	supt∈[0,∞	PROPN
ejpam-3539	220	42	)	)	PUNCT
ejpam-3539	220	43	e	e	NOUN
ejpam-3539	220	44	−ttn−1−i	−ttn−1−i	NOUN
ejpam-3539	220	45	)	)	PUNCT
ejpam-3539	220	46	]	]	PUNCT
ejpam-3539	220	47	�	�	PROPN
ejpam-3539	220	48	lemma	lemma	PROPN
ejpam-3539	220	49	2.4	2.4	NUM
ejpam-3539	220	50	if	if	SCONJ
ejpam-3539	220	51	g	g	PROPN
ejpam-3539	220	52	is	be	AUX
ejpam-3539	220	53	a	a	DET
ejpam-3539	220	54	caratheodory	caratheodory	NOUN
ejpam-3539	220	55	’s	’s	PART
ejpam-3539	220	56	function	function	NOUN
ejpam-3539	220	57	and	and	CCONJ
ejpam-3539	220	58	e	e	X
ejpam-3539	220	59	⊂	⊂	PROPN
ejpam-3539	220	60	x	x	X
ejpam-3539	220	61	is	be	AUX
ejpam-3539	220	62	a	a	DET
ejpam-3539	220	63	bounded	bounded	ADJ
ejpam-3539	220	64	open	open	ADJ
ejpam-3539	220	65	subset	subset	NOUN
ejpam-3539	220	66	of	of	ADP
ejpam-3539	220	67	x	x	PRON
ejpam-3539	220	68	,	,	PUNCT
ejpam-3539	220	69	such	such	ADJ
ejpam-3539	220	70	that	that	DET
ejpam-3539	220	71	doml	doml	PROPN
ejpam-3539	220	72	∩	∩	PROPN
ejpam-3539	220	73	ē	ē	ADV
ejpam-3539	220	74	6=	6=	PROPN
ejpam-3539	220	75	φ	φ	PROPN
ejpam-3539	220	76	then	then	ADV
ejpam-3539	220	77	n	n	PROPN
ejpam-3539	220	78	is	be	AUX
ejpam-3539	220	79	l	l	NOUN
ejpam-3539	220	80	-	-	ADJ
ejpam-3539	220	81	compact	compact	ADJ
ejpam-3539	220	82	,	,	PUNCT
ejpam-3539	220	83	where	where	SCONJ
ejpam-3539	220	84	e	e	PROPN
ejpam-3539	220	85	denotes	denote	VERB
ejpam-3539	220	86	the	the	DET
ejpam-3539	220	87	closure	closure	NOUN
ejpam-3539	220	88	of	of	ADP
ejpam-3539	220	89	e	e	NOUN
ejpam-3539	220	90	proof	proof	NOUN
ejpam-3539	220	91	:	:	PUNCT
ejpam-3539	220	92	let	let	VERB
ejpam-3539	220	93	e	e	PROPN
ejpam-3539	220	94	⊂	⊂	PROPN
ejpam-3539	220	95	x	x	PUNCT
ejpam-3539	220	96	with	with	ADP
ejpam-3539	220	97	r	r	NOUN
ejpam-3539	220	98	=	=	NOUN
ejpam-3539	220	99	sup{‖u‖	sup{‖u‖	NOUN
ejpam-3539	220	100	:	:	PUNCT
ejpam-3539	220	101	u	u	NOUN
ejpam-3539	220	102	∈	∈	NOUN
ejpam-3539	220	103	ē	ē	ADV
ejpam-3539	220	104	}	}	PUNCT
ejpam-3539	220	105	.	.	PUNCT
ejpam-3539	221	1	we	we	PRON
ejpam-3539	221	2	consider	consider	VERB
ejpam-3539	221	3	kp(i	kp(i	NOUN
ejpam-3539	221	4	−q)n(ē	−q)n(ē	PROPN
ejpam-3539	221	5	)	)	PUNCT
ejpam-3539	221	6	.	.	PUNCT
ejpam-3539	222	1	since	since	SCONJ
ejpam-3539	222	2	g	g	NOUN
ejpam-3539	222	3	:	:	PUNCT
ejpam-3539	222	4	[	[	X
ejpam-3539	222	5	0,∞	0,∞	NUM
ejpam-3539	222	6	)	)	PUNCT
ejpam-3539	222	7	×	×	NOUN
ejpam-3539	222	8	<	<	NOUN
ejpam-3539	222	9	n	n	DET
ejpam-3539	222	10	−→	−→	NOUN
ejpam-3539	222	11	<	<	X
ejpam-3539	222	12	satisfies	satisfie	NOUN
ejpam-3539	222	13	caratheodory	caratheodory	NOUN
ejpam-3539	222	14	’s	’s	PART
ejpam-3539	222	15	conditions	condition	NOUN
ejpam-3539	222	16	with	with	ADP
ejpam-3539	222	17	respect	respect	NOUN
ejpam-3539	222	18	to	to	ADP
ejpam-3539	222	19	l1[0,∞	l1[0,∞	NOUN
ejpam-3539	222	20	)	)	PUNCT
ejpam-3539	222	21	,	,	PUNCT
ejpam-3539	222	22	there	there	PRON
ejpam-3539	222	23	exist	exist	VERB
ejpam-3539	222	24	a	a	DET
ejpam-3539	222	25	lebesgue	lebesgue	ADJ
ejpam-3539	222	26	integrable	integrable	ADJ
ejpam-3539	222	27	function	function	NOUN
ejpam-3539	222	28	ϕr	ϕr	ADP
ejpam-3539	222	29	such	such	ADJ
ejpam-3539	222	30	that	that	SCONJ
ejpam-3539	222	31	|nu(t)|	|nu(t)|	PROPN
ejpam-3539	222	32	=	=	SYM
ejpam-3539	222	33	|g(t	|g(t	PROPN
ejpam-3539	222	34	,	,	PUNCT
ejpam-3539	222	35	u(t	u(t	PROPN
ejpam-3539	222	36	)	)	PUNCT
ejpam-3539	222	37	,	,	PUNCT
ejpam-3539	222	38	u′(t	u′(t	X
ejpam-3539	222	39	)	)	PUNCT
ejpam-3539	222	40	·	·	PUNCT
ejpam-3539	222	41	·	·	PUNCT
ejpam-3539	223	1	·	·	PUNCT
ejpam-3539	223	2	u(n−1)(t)|	u(n−1)(t)|	ADJ
ejpam-3539	223	3	≤	≤	NOUN
ejpam-3539	223	4	ϕr(t	ϕr(t	NOUN
ejpam-3539	223	5	)	)	PUNCT
ejpam-3539	224	1	a.e	a.e	PROPN
ejpam-3539	224	2	.	.	PROPN
ejpam-3539	224	3	t	t	PROPN
ejpam-3539	224	4	∈	∈	PROPN
ejpam-3539	224	5	(	(	PUNCT
ejpam-3539	224	6	0,∞	0,∞	NOUN
ejpam-3539	224	7	)	)	PUNCT
ejpam-3539	224	8	samuel	samuel	PROPN
ejpam-3539	224	9	a.	a.	PROPN
ejpam-3539	224	10	iyase	iyase	PROPN
ejpam-3539	224	11	,	,	PUNCT
ejpam-3539	224	12	abiodun	abiodun	PROPN
ejpam-3539	224	13	a.	a.	PROPN
ejpam-3539	224	14	opanuga	opanuga	PROPN
ejpam-3539	224	15	/	/	SYM
ejpam-3539	224	16	eur	eur	PROPN
ejpam-3539	224	17	.	.	PUNCT
ejpam-3539	225	1	j.	j.	PROPN
ejpam-3539	225	2	pure	pure	PROPN
ejpam-3539	225	3	appl	appl	PROPN
ejpam-3539	225	4	.	.	PROPN
ejpam-3539	225	5	math	math	PROPN
ejpam-3539	225	6	,	,	PUNCT
ejpam-3539	225	7	13	13	NUM
ejpam-3539	225	8	(	(	PUNCT
ejpam-3539	225	9	1	1	NUM
ejpam-3539	225	10	)	)	PUNCT
ejpam-3539	225	11	(	(	PUNCT
ejpam-3539	225	12	2020	2020	NUM
ejpam-3539	225	13	)	)	PUNCT
ejpam-3539	225	14	,	,	PUNCT
ejpam-3539	225	15	33	33	NUM
ejpam-3539	225	16	-	-	SYM
ejpam-3539	225	17	47	47	NUM
ejpam-3539	225	18	41	41	NUM
ejpam-3539	225	19	‖nu‖1	‖nu‖1	NOUN
ejpam-3539	225	20	≤	≤	NUM
ejpam-3539	225	21	∫	∫	PROPN
ejpam-3539	225	22	∞	∞	PROPN
ejpam-3539	225	23	0	0	NUM
ejpam-3539	225	24	ϕr(t)dt	ϕr(t)dt	PROPN
ejpam-3539	225	25	=	=	PUNCT
ejpam-3539	226	1	‖ϕr‖1	‖ϕr‖1	PROPN
ejpam-3539	226	2	(	(	PUNCT
ejpam-3539	226	3	11	11	NUM
ejpam-3539	226	4	)	)	PUNCT
ejpam-3539	226	5	‖qnu‖1	‖qnu‖1	VERB
ejpam-3539	226	6	≤	≤	NUM
ejpam-3539	227	1	∫	∫	PROPN
ejpam-3539	228	1	∞	∞	NOUN
ejpam-3539	228	2	0	0	PUNCT
ejpam-3539	229	1	|qnu(s)|ds	|qnu(s)|ds	PROPN
ejpam-3539	229	2	=	=	SYM
ejpam-3539	230	1	∫	∫	PROPN
ejpam-3539	230	2	∞	∞	PROPN
ejpam-3539	230	3	0	0	NUM
ejpam-3539	231	1	∣∣∣∣h(t	∣∣∣∣h(t	CCONJ
ejpam-3539	231	2	)	)	PUNCT
ejpam-3539	232	1	[	[	X
ejpam-3539	232	2	∫	∫	X
ejpam-3539	232	3	∞	∞	NUM
ejpam-3539	232	4	0	0	NUM
ejpam-3539	232	5	(	(	PUNCT
ejpam-3539	232	6	g(τ	g(τ	PROPN
ejpam-3539	232	7	,	,	PUNCT
ejpam-3539	232	8	u(τ	u(τ	ADJ
ejpam-3539	232	9	)	)	PUNCT
ejpam-3539	232	10	,	,	PUNCT
ejpam-3539	232	11	u′(τ	u′(τ	NUM
ejpam-3539	232	12	)	)	PUNCT
ejpam-3539	232	13	.	.	PUNCT
ejpam-3539	232	14	.	.	PUNCT
ejpam-3539	232	15	.	.	PUNCT
ejpam-3539	233	1	u(n−1)(τ))dτ	u(n−1)(τ))dτ	PROPN
ejpam-3539	233	2	−	−	PROPN
ejpam-3539	233	3	∫	∫	PROPN
ejpam-3539	234	1	ξ	ξ	SYM
ejpam-3539	234	2	0	0	NUM
ejpam-3539	234	3	∫	∫	PROPN
ejpam-3539	234	4	s	s	PART
ejpam-3539	234	5	0	0	NUM
ejpam-3539	234	6	(	(	PUNCT
ejpam-3539	234	7	g(τ	g(τ	PROPN
ejpam-3539	234	8	,	,	PUNCT
ejpam-3539	234	9	u(τ	u(τ	ADJ
ejpam-3539	234	10	)	)	PUNCT
ejpam-3539	234	11	,	,	PUNCT
ejpam-3539	234	12	u′(τ	u′(τ	NUM
ejpam-3539	234	13	)	)	PUNCT
ejpam-3539	234	14	·	·	PUNCT
ejpam-3539	234	15	·	·	PUNCT
ejpam-3539	234	16	·	·	PUNCT
ejpam-3539	234	17	u(n−1)(τ))dτda(s	u(n−1)(τ))dτda(s	NOUN
ejpam-3539	234	18	)	)	PUNCT
ejpam-3539	234	19	]	]	PUNCT
ejpam-3539	234	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	234	21	dt	dt	X
ejpam-3539	234	22	≤	≤	NUM
ejpam-3539	234	23	∫	∫	PROPN
ejpam-3539	235	1	∞	∞	NUM
ejpam-3539	235	2	0	0	PUNCT
ejpam-3539	236	1	|h(t)|	|h(t)|	NOUN
ejpam-3539	237	1	[	[	X
ejpam-3539	237	2	∫	∫	PROPN
ejpam-3539	237	3	∞	∞	PROPN
ejpam-3539	237	4	0	0	PROPN
ejpam-3539	237	5	|g(τ	|g(τ	PROPN
ejpam-3539	237	6	,	,	PUNCT
ejpam-3539	237	7	u(τ	u(τ	ADJ
ejpam-3539	237	8	)	)	PUNCT
ejpam-3539	237	9	,	,	PUNCT
ejpam-3539	237	10	u′(τ	u′(τ	NUM
ejpam-3539	237	11	)	)	PUNCT
ejpam-3539	237	12	.	.	PUNCT
ejpam-3539	237	13	.	.	PUNCT
ejpam-3539	237	14	.	.	PUNCT
ejpam-3539	238	1	u(n−1)(τ))|dτ	u(n−1)(τ))|dτ	PROPN
ejpam-3539	239	1	+	+	CCONJ
ejpam-3539	239	2	∫	∫	X
ejpam-3539	239	3	ξ	ξ	SYM
ejpam-3539	239	4	0	0	NUM
ejpam-3539	239	5	∫	∫	PROPN
ejpam-3539	239	6	s	s	PART
ejpam-3539	239	7	0	0	NUM
ejpam-3539	239	8	|g(τ	|g(τ	PROPN
ejpam-3539	239	9	,	,	PUNCT
ejpam-3539	239	10	u(τ	u(τ	ADJ
ejpam-3539	239	11	)	)	PUNCT
ejpam-3539	239	12	,	,	PUNCT
ejpam-3539	239	13	u′(τ	u′(τ	NUM
ejpam-3539	239	14	)	)	PUNCT
ejpam-3539	239	15	.	.	PUNCT
ejpam-3539	239	16	.	.	PUNCT
ejpam-3539	239	17	.	.	PUNCT
ejpam-3539	240	1	u(n−1)(τ))|dτda(s	u(n−1)(τ))|dτda(s	PROPN
ejpam-3539	240	2	)	)	PUNCT
ejpam-3539	240	3	]	]	PUNCT
ejpam-3539	240	4	dt	dt	X
ejpam-3539	241	1	≤	≤	NUM
ejpam-3539	241	2	∫	∫	PROPN
ejpam-3539	241	3	∞	∞	PROPN
ejpam-3539	241	4	0	0	PROPN
ejpam-3539	241	5	|h(t	|h(t	NOUN
ejpam-3539	241	6	)	)	PUNCT
ejpam-3539	242	1	[	[	X
ejpam-3539	242	2	∫	∫	X
ejpam-3539	242	3	∞	∞	NUM
ejpam-3539	242	4	0	0	NUM
ejpam-3539	243	1	ϕr(τ)dτ	ϕr(τ)dτ	PUNCT
ejpam-3539	244	1	+	+	NUM
ejpam-3539	244	2	∫	∫	PROPN
ejpam-3539	244	3	ξ	ξ	SYM
ejpam-3539	244	4	0	0	NUM
ejpam-3539	244	5	∫	∫	PROPN
ejpam-3539	244	6	s	s	PART
ejpam-3539	244	7	0	0	NUM
ejpam-3539	244	8	ϕ(τ)dτda(s	ϕ(τ)dτda(s	NOUN
ejpam-3539	244	9	)	)	PUNCT
ejpam-3539	244	10	]	]	PUNCT
ejpam-3539	245	1	dt	dt	X
ejpam-3539	245	2	≤	≤	NUM
ejpam-3539	245	3	‖h‖1[‖ϕr‖1	‖h‖1[‖ϕr‖1	NOUN
ejpam-3539	245	4	+	+	CCONJ
ejpam-3539	245	5	‖ϕr‖1a(ξ	‖ϕr‖1a(ξ	NUM
ejpam-3539	245	6	)	)	PUNCT
ejpam-3539	245	7	]	]	PUNCT
ejpam-3539	246	1	=	=	PUNCT
ejpam-3539	246	2	2‖ϕr‖1‖h‖1	2‖ϕr‖1‖h‖1	NUM
ejpam-3539	246	3	(	(	PUNCT
ejpam-3539	246	4	12	12	NUM
ejpam-3539	246	5	)	)	PUNCT
ejpam-3539	246	6	this	this	PRON
ejpam-3539	246	7	shows	show	VERB
ejpam-3539	246	8	that	that	SCONJ
ejpam-3539	246	9	qn(ē	qn(ē	PROPN
ejpam-3539	246	10	)	)	PUNCT
ejpam-3539	246	11	is	be	AUX
ejpam-3539	246	12	bounded	bound	VERB
ejpam-3539	246	13	.	.	PUNCT
ejpam-3539	247	1	we	we	PRON
ejpam-3539	247	2	now	now	ADV
ejpam-3539	247	3	apply	apply	VERB
ejpam-3539	247	4	lemma	lemma	PROPN
ejpam-3539	247	5	2.1	2.1	NUM
ejpam-3539	247	6	to	to	PART
ejpam-3539	247	7	prove	prove	VERB
ejpam-3539	247	8	the	the	DET
ejpam-3539	247	9	compactness	compactness	NOUN
ejpam-3539	247	10	of	of	ADP
ejpam-3539	247	11	kp(i	kp(i	PROPN
ejpam-3539	247	12	−q)n(ē	−q)n(ē	PROPN
ejpam-3539	247	13	)	)	PUNCT
ejpam-3539	247	14	.	.	PUNCT
ejpam-3539	248	1	let	let	VERB
ejpam-3539	248	2	u	u	PRON
ejpam-3539	248	3	∈	∈	PROPN
ejpam-3539	248	4	ē	ē	ADV
ejpam-3539	248	5	then	then	ADV
ejpam-3539	248	6	from	from	ADP
ejpam-3539	248	7	the	the	DET
ejpam-3539	248	8	definition	definition	NOUN
ejpam-3539	248	9	of	of	ADP
ejpam-3539	248	10	kp(i	kp(i	X
ejpam-3539	248	11	−q)n(u	−q)n(u	NOUN
ejpam-3539	248	12	)	)	PUNCT
ejpam-3539	248	13	together	together	ADV
ejpam-3539	248	14	with	with	ADP
ejpam-3539	248	15	(	(	PUNCT
ejpam-3539	248	16	10	10	NUM
ejpam-3539	248	17	)	)	PUNCT
ejpam-3539	248	18	,	,	PUNCT
ejpam-3539	248	19	(	(	PUNCT
ejpam-3539	248	20	11	11	NUM
ejpam-3539	248	21	)	)	PUNCT
ejpam-3539	248	22	and	and	CCONJ
ejpam-3539	248	23	(	(	PUNCT
ejpam-3539	248	24	12	12	NUM
ejpam-3539	248	25	)	)	PUNCT
ejpam-3539	248	26	we	we	PRON
ejpam-3539	248	27	derive	derive	VERB
ejpam-3539	248	28	‖kp(i	‖kp(i	PUNCT
ejpam-3539	249	1	−q)nu‖	−q)nu‖	PUNCT
ejpam-3539	249	2	≤	≤	NUM
ejpam-3539	249	3	dn‖(i	dn‖(i	NOUN
ejpam-3539	249	4	−q)nu‖1	−q)nu‖1	NOUN
ejpam-3539	249	5	≤	≤	NUM
ejpam-3539	249	6	dn‖nu‖1	dn‖nu‖1	VERB
ejpam-3539	249	7	+	+	SYM
ejpam-3539	249	8	‖qnu‖1	‖qnu‖1	NOUN
ejpam-3539	249	9	≤	≤	NUM
ejpam-3539	249	10	dn‖ϕr‖1	dn‖ϕr‖1	VERB
ejpam-3539	249	11	+	+	CCONJ
ejpam-3539	249	12	2‖ϕr‖1‖h‖1	2‖ϕr‖1‖h‖1	NUM
ejpam-3539	249	13	(	(	PUNCT
ejpam-3539	249	14	13	13	NUM
ejpam-3539	249	15	)	)	PUNCT
ejpam-3539	249	16	kp(i−q)n(ē	kp(i−q)n(ē	PROPN
ejpam-3539	249	17	)	)	PUNCT
ejpam-3539	249	18	is	be	AUX
ejpam-3539	249	19	therefore	therefore	ADV
ejpam-3539	249	20	uniformly	uniformly	ADV
ejpam-3539	249	21	bounded	bound	VERB
ejpam-3539	249	22	in	in	ADP
ejpam-3539	249	23	x.	x.	NOUN
ejpam-3539	249	24	let	let	VERB
ejpam-3539	249	25	u	u	PRON
ejpam-3539	249	26	∈	∈	PROPN
ejpam-3539	249	27	e	e	NOUN
ejpam-3539	249	28	and	and	CCONJ
ejpam-3539	249	29	t1	t1	NOUN
ejpam-3539	249	30	,	,	PUNCT
ejpam-3539	249	31	t2	t2	PROPN
ejpam-3539	249	32	∈	∈	PROPN
ejpam-3539	250	1	[	[	X
ejpam-3539	250	2	0	0	NUM
ejpam-3539	250	3	,	,	PUNCT
ejpam-3539	250	4	t	t	X
ejpam-3539	250	5	]	]	PUNCT
ejpam-3539	250	6	,	,	PUNCT
ejpam-3539	250	7	t1	t1	NOUN
ejpam-3539	250	8	<	<	X
ejpam-3539	250	9	t2	t2	PROPN
ejpam-3539	250	10	with	with	ADP
ejpam-3539	250	11	t	t	PROPN
ejpam-3539	250	12	∈	∈	PROPN
ejpam-3539	250	13	(	(	PUNCT
ejpam-3539	250	14	0,∞	0,∞	NUM
ejpam-3539	250	15	)	)	PUNCT
ejpam-3539	250	16	.	.	PUNCT
ejpam-3539	251	1	we	we	PRON
ejpam-3539	251	2	prove	prove	VERB
ejpam-3539	251	3	that	that	SCONJ
ejpam-3539	251	4	kp(i	kp(i	PUNCT
ejpam-3539	251	5	−	−	PROPN
ejpam-3539	251	6	q)n(ē	q)n(ē	PROPN
ejpam-3539	251	7	)	)	PUNCT
ejpam-3539	251	8	is	be	AUX
ejpam-3539	251	9	equicontinuous	equicontinuous	ADJ
ejpam-3539	251	10	on	on	ADP
ejpam-3539	251	11	every	every	DET
ejpam-3539	251	12	compact	compact	ADJ
ejpam-3539	251	13	subset	subset	NOUN
ejpam-3539	252	1	[	[	X
ejpam-3539	252	2	0	0	NUM
ejpam-3539	252	3	,	,	PUNCT
ejpam-3539	252	4	t	t	NOUN
ejpam-3539	252	5	]	]	PUNCT
ejpam-3539	252	6	of	of	ADP
ejpam-3539	252	7	[	[	X
ejpam-3539	252	8	0,∞	0,∞	NOUN
ejpam-3539	252	9	)	)	PUNCT
ejpam-3539	252	10	.	.	PUNCT
ejpam-3539	253	1	we	we	PRON
ejpam-3539	253	2	have	have	VERB
ejpam-3539	253	3	|e−t2(kp(i	|e−t2(kp(i	NOUN
ejpam-3539	253	4	−q)nu)(i)(t2)−	−q)nu)(i)(t2)−	ADJ
ejpam-3539	253	5	e−t1(kp(i	e−t1(kp(i	X
ejpam-3539	253	6	−q)nu)(i)(t1)|	−q)nu)(i)(t1)|	ADJ
ejpam-3539	253	7	,	,	PUNCT
ejpam-3539	253	8	0	0	NUM
ejpam-3539	253	9	≤	≤	NUM
ejpam-3539	254	1	i	i	PRON
ejpam-3539	254	2	≤	≤	ADJ
ejpam-3539	254	3	n−	n−	NOUN
ejpam-3539	254	4	2	2	NUM
ejpam-3539	254	5	=	=	SYM
ejpam-3539	254	6	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3539	254	7	t2	t2	NOUN
ejpam-3539	254	8	t1	t1	NOUN
ejpam-3539	255	1	[	[	X
ejpam-3539	255	2	e−s(kp(i	e−s(kp(i	NOUN
ejpam-3539	255	3	−q)nu)(i)(s)]′ds	−q)nu)(i)(s)]′ds	X
ejpam-3539	255	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	255	5	=	=	SYM
ejpam-3539	255	6	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3539	255	7	t2	t2	PROPN
ejpam-3539	255	8	t1	t1	NOUN
ejpam-3539	256	1	[	[	X
ejpam-3539	256	2	−e−s(kp(i	−e−s(kp(i	NOUN
ejpam-3539	256	3	−q)nu)(i)(s	−q)nu)(i)(s	NOUN
ejpam-3539	256	4	)	)	PUNCT
ejpam-3539	257	1	+	+	CCONJ
ejpam-3539	258	1	e−s(kp(i	e−s(kp(i	NOUN
ejpam-3539	258	2	−q)nu)i+1(s)]ds	−q)nu)i+1(s)]ds	ADP
ejpam-3539	258	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	258	4	≤	≤	NUM
ejpam-3539	258	5	2|	2|	NUM
ejpam-3539	258	6	(	(	PUNCT
ejpam-3539	258	7	t1	t1	NOUN
ejpam-3539	258	8	−	−	PROPN
ejpam-3539	258	9	t2	t2	NOUN
ejpam-3539	258	10	)	)	PUNCT
ejpam-3539	258	11	|‖kp(i	|‖kp(i	NOUN
ejpam-3539	259	1	−q)nu‖	−q)nu‖	PROPN
ejpam-3539	259	2	≤	≤	NOUN
ejpam-3539	260	1	2|t1	2|t1	ADV
ejpam-3539	260	2	−	−	NOUN
ejpam-3539	260	3	t2|[dn‖ϕr‖1	t2|[dn‖ϕr‖1	NOUN
ejpam-3539	261	1	+	+	NOUN
ejpam-3539	262	1	2‖ϕr‖1‖h‖1	2‖ϕr‖1‖h‖1	NUM
ejpam-3539	262	2	]	]	X
ejpam-3539	262	3	−→	−→	NOUN
ejpam-3539	262	4	0	0	NUM
ejpam-3539	262	5	as	as	ADP
ejpam-3539	262	6	t1	t1	NOUN
ejpam-3539	262	7	→	→	SYM
ejpam-3539	262	8	t2	t2	NOUN
ejpam-3539	262	9	for	for	ADP
ejpam-3539	262	10	i	i	PRON
ejpam-3539	262	11	=	=	PUNCT
ejpam-3539	262	12	n−	n−	NOUN
ejpam-3539	262	13	1	1	NUM
ejpam-3539	262	14	,	,	PUNCT
ejpam-3539	262	15	we	we	PRON
ejpam-3539	262	16	obtain∣∣∣e−t2(kp(i	obtain∣∣∣e−t2(kp(i	ADJ
ejpam-3539	262	17	−q)nu)(n−1)(t2)−	−q)nu)(n−1)(t2)−	PROPN
ejpam-3539	262	18	e−t1(kp(i	e−t1(kp(i	PRON
ejpam-3539	262	19	−q)nu)(n−1)(t1	−q)nu)(n−1)(t1	NOUN
ejpam-3539	262	20	)	)	PUNCT
ejpam-3539	262	21	∣∣∣	∣∣∣	NOUN
ejpam-3539	262	22	=	=	SYM
ejpam-3539	262	23	∣∣∣∣e−t2	∣∣∣∣e−t2	PROPN
ejpam-3539	262	24	∫	∫	NOUN
ejpam-3539	262	25	t2	t2	PROPN
ejpam-3539	262	26	0	0	PUNCT
ejpam-3539	263	1	(	(	PUNCT
ejpam-3539	263	2	i	i	PROPN
ejpam-3539	263	3	−q)nu(s)ds−	−q)nu(s)ds−	VERB
ejpam-3539	263	4	e−t1	e−t1	X
ejpam-3539	263	5	∫	∫	PROPN
ejpam-3539	263	6	t1	t1	NOUN
ejpam-3539	263	7	0	0	NUM
ejpam-3539	264	1	(	(	PUNCT
ejpam-3539	264	2	i	i	PRON
ejpam-3539	264	3	−q)nu(s)ds	−q)nu(s)ds	VERB
ejpam-3539	264	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	264	5	≤	≤	NUM
ejpam-3539	264	6	∫	∫	PROPN
ejpam-3539	264	7	t2	t2	PROPN
ejpam-3539	264	8	0	0	NUM
ejpam-3539	264	9	(	(	PUNCT
ejpam-3539	264	10	e−t1	e−t1	NUM
ejpam-3539	264	11	−	−	PROPN
ejpam-3539	264	12	e−t2	e−t2	PROPN
ejpam-3539	264	13	)	)	PUNCT
ejpam-3539	264	14	∣∣∣∣(i	∣∣∣∣(i	ADV
ejpam-3539	264	15	−q)nu(s)|ds+	−q)nu(s)|ds+	VERB
ejpam-3539	264	16	∫	∫	PROPN
ejpam-3539	264	17	t2	t2	PROPN
ejpam-3539	264	18	t1	t1	PROPN
ejpam-3539	264	19	e−t1	e−t1	NOUN
ejpam-3539	264	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3539	264	21	(	(	PUNCT
ejpam-3539	264	22	i	i	NOUN
ejpam-3539	264	23	−q)nu(s)|ds	−q)nu(s)|ds	PROPN
ejpam-3539	264	24	]	]	X
ejpam-3539	264	25	samuel	samuel	PROPN
ejpam-3539	264	26	a.	a.	PROPN
ejpam-3539	264	27	iyase	iyase	PROPN
ejpam-3539	264	28	,	,	PUNCT
ejpam-3539	264	29	abiodun	abiodun	PROPN
ejpam-3539	264	30	a.	a.	PROPN
ejpam-3539	264	31	opanuga	opanuga	PROPN
ejpam-3539	264	32	/	/	SYM
ejpam-3539	264	33	eur	eur	PROPN
ejpam-3539	264	34	.	.	PUNCT
ejpam-3539	265	1	j.	j.	PROPN
ejpam-3539	265	2	pure	pure	PROPN
ejpam-3539	265	3	appl	appl	PROPN
ejpam-3539	265	4	.	.	PROPN
ejpam-3539	265	5	math	math	PROPN
ejpam-3539	265	6	,	,	PUNCT
ejpam-3539	265	7	13	13	NUM
ejpam-3539	265	8	(	(	PUNCT
ejpam-3539	265	9	1	1	NUM
ejpam-3539	265	10	)	)	PUNCT
ejpam-3539	265	11	(	(	PUNCT
ejpam-3539	265	12	2020	2020	NUM
ejpam-3539	265	13	)	)	PUNCT
ejpam-3539	265	14	,	,	PUNCT
ejpam-3539	265	15	33	33	NUM
ejpam-3539	265	16	-	-	SYM
ejpam-3539	265	17	47	47	NUM
ejpam-3539	265	18	42	42	NUM
ejpam-3539	265	19	−→	−→	NOUN
ejpam-3539	265	20	0	0	NUM
ejpam-3539	265	21	las	las	PROPN
ejpam-3539	265	22	t1	t1	PROPN
ejpam-3539	265	23	→	→	PUNCT
ejpam-3539	265	24	t2	t2	NOUN
ejpam-3539	265	25	it	it	PRON
ejpam-3539	265	26	follows	follow	VERB
ejpam-3539	265	27	that	that	PRON
ejpam-3539	265	28	kp(i	kp(i	PUNCT
ejpam-3539	266	1	−q)n(ē	−q)n(ē	PROPN
ejpam-3539	266	2	)	)	PUNCT
ejpam-3539	266	3	is	be	AUX
ejpam-3539	266	4	equicontinuous	equicontinuous	ADJ
ejpam-3539	266	5	on	on	ADP
ejpam-3539	266	6	every	every	DET
ejpam-3539	266	7	compact	compact	ADJ
ejpam-3539	266	8	subset	subset	NOUN
ejpam-3539	266	9	of	of	ADP
ejpam-3539	266	10	[	[	X
ejpam-3539	266	11	0,∞	0,∞	NOUN
ejpam-3539	266	12	)	)	PUNCT
ejpam-3539	266	13	.	.	PUNCT
ejpam-3539	267	1	next	next	ADV
ejpam-3539	267	2	,	,	PUNCT
ejpam-3539	267	3	we	we	PRON
ejpam-3539	267	4	prove	prove	VERB
ejpam-3539	267	5	that	that	SCONJ
ejpam-3539	267	6	kp(i	kp(i	PUNCT
ejpam-3539	267	7	−q)n(ē	−q)n(ē	PROPN
ejpam-3539	267	8	)	)	PUNCT
ejpam-3539	267	9	is	be	AUX
ejpam-3539	267	10	equicontinuous	equicontinuous	ADJ
ejpam-3539	267	11	at	at	ADP
ejpam-3539	267	12	infinity	infinity	NOUN
ejpam-3539	267	13	.	.	PUNCT
ejpam-3539	268	1	for	for	ADP
ejpam-3539	268	2	u	u	PROPN
ejpam-3539	268	3	∈	∈	PROPN
ejpam-3539	268	4	ē	ē	NOUN
ejpam-3539	268	5	we	we	PRON
ejpam-3539	268	6	have	have	VERB
ejpam-3539	268	7	|e−t(kp(i	|e−t(kp(i	PROPN
ejpam-3539	268	8	−q)nu)(t)|	−q)nu)(t)|	NOUN
ejpam-3539	268	9	=	=	NOUN
ejpam-3539	268	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	268	11	e−t	e−t	NOUN
ejpam-3539	268	12	(	(	PUNCT
ejpam-3539	268	13	n−	n−	NOUN
ejpam-3539	268	14	1	1	NUM
ejpam-3539	268	15	)	)	PUNCT
ejpam-3539	268	16	!	!	PUNCT
ejpam-3539	269	1	∫	∫	PROPN
ejpam-3539	269	2	t	t	PROPN
ejpam-3539	269	3	0	0	NUM
ejpam-3539	270	1	(	(	PUNCT
ejpam-3539	270	2	t−	t−	PRON
ejpam-3539	270	3	s)n−1(i	s)n−1(i	NOUN
ejpam-3539	270	4	−q)nu(s)ds	−q)nu(s)ds	NOUN
ejpam-3539	270	5	−	−	NOUN
ejpam-3539	270	6	e−t	e−t	NOUN
ejpam-3539	270	7	(	(	PUNCT
ejpam-3539	270	8	n−	n−	NOUN
ejpam-3539	270	9	1	1	NUM
ejpam-3539	270	10	)	)	PUNCT
ejpam-3539	270	11	!	!	PUNCT
ejpam-3539	271	1	∫	∫	PROPN
ejpam-3539	272	1	ξ	ξ	X
ejpam-3539	272	2	0	0	PUNCT
ejpam-3539	272	3	(	(	PUNCT
ejpam-3539	272	4	t−	t−	PRON
ejpam-3539	272	5	s)n−1(i	s)n−1(i	NOUN
ejpam-3539	272	6	−q)nu(s)ds	−q)nu(s)ds	NOUN
ejpam-3539	272	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	272	8	≤	≤	PUNCT
ejpam-3539	272	9	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	272	10	∫	∫	PROPN
ejpam-3539	272	11	∞	∞	PROPN
ejpam-3539	272	12	0	0	NUM
ejpam-3539	272	13	|(i	|(i	NUM
ejpam-3539	272	14	−q)nu(s)|ds+	−q)nu(s)|ds+	ADJ
ejpam-3539	272	15	e−ttn−1	e−ttn−1	PROPN
ejpam-3539	272	16	∫	∫	PROPN
ejpam-3539	272	17	∞	∞	PROPN
ejpam-3539	272	18	0	0	PUNCT
ejpam-3539	273	1	|(i	|(i	NUM
ejpam-3539	273	2	−q)nu(s)|ds	−q)nu(s)|ds	NUM
ejpam-3539	273	3	≤	≤	NOUN
ejpam-3539	273	4	2e−ttn−1(‖nu‖1	2e−ttn−1(‖nu‖1	NUM
ejpam-3539	273	5	+	+	NUM
ejpam-3539	273	6	‖qnu‖1	‖qnu‖1	NOUN
ejpam-3539	273	7	)	)	PUNCT
ejpam-3539	273	8	≤	≤	NOUN
ejpam-3539	274	1	2e−ttn−1[‖ϕr‖+	2e−ttn−1[‖ϕr‖+	NUM
ejpam-3539	274	2	2‖ϕr‖1‖h‖1	2‖ϕr‖1‖h‖1	NOUN
ejpam-3539	274	3	]	]	X
ejpam-3539	274	4	−→	−→	NOUN
ejpam-3539	274	5	0	0	NUM
ejpam-3539	274	6	as	as	ADP
ejpam-3539	274	7	t→∞.	t→∞.	NOUN
ejpam-3539	274	8	for	for	ADP
ejpam-3539	274	9	i	i	PROPN
ejpam-3539	274	10	=	=	SYM
ejpam-3539	274	11	1	1	NUM
ejpam-3539	274	12	,	,	PUNCT
ejpam-3539	274	13	2	2	NUM
ejpam-3539	274	14	,	,	PUNCT
ejpam-3539	274	15	.	.	PUNCT
ejpam-3539	274	16	.	.	PUNCT
ejpam-3539	274	17	.	.	PUNCT
ejpam-3539	275	1	,	,	PUNCT
ejpam-3539	275	2	n−	n−	NOUN
ejpam-3539	275	3	1	1	NUM
ejpam-3539	275	4	we	we	PRON
ejpam-3539	275	5	have	have	VERB
ejpam-3539	275	6	|e−t(kp(i	|e−t(kp(i	PROPN
ejpam-3539	275	7	−q)nu)(i)(t)|	−q)nu)(i)(t)|	VERB
ejpam-3539	275	8	≤	≤	NUM
ejpam-3539	275	9	e−t	e−t	NOUN
ejpam-3539	275	10	(	(	PUNCT
ejpam-3539	275	11	n−	n−	NOUN
ejpam-3539	275	12	1−	1−	NUM
ejpam-3539	275	13	i	i	NOUN
ejpam-3539	275	14	)	)	PUNCT
ejpam-3539	275	15	!	!	PUNCT
ejpam-3539	276	1	∫	∫	PROPN
ejpam-3539	276	2	t	t	PROPN
ejpam-3539	276	3	0	0	NUM
ejpam-3539	277	1	(	(	PUNCT
ejpam-3539	277	2	t−	t−	PROPN
ejpam-3539	277	3	s)n−1−i|(i	s)n−1−i|(i	PROPN
ejpam-3539	277	4	−q)nu(s)|ds	−q)nu(s)|ds	SYM
ejpam-3539	277	5	≤	≤	NUM
ejpam-3539	277	6	e−ttn−1−i	e−ttn−1−i	ADJ
ejpam-3539	277	7	∫	∫	PROPN
ejpam-3539	277	8	t	t	PROPN
ejpam-3539	277	9	0	0	X
ejpam-3539	278	1	|(i	|(i	SYM
ejpam-3539	278	2	−q)nu(s)|ds	−q)nu(s)|ds	NUM
ejpam-3539	278	3	≤	≤	NUM
ejpam-3539	278	4	e−ttn−1−i‖(i	e−ttn−1−i‖(i	NOUN
ejpam-3539	278	5	−q)nu‖1	−q)nu‖1	NOUN
ejpam-3539	278	6	≤	≤	NUM
ejpam-3539	278	7	e−ttn−1−i[‖ϕr‖1	e−ttn−1−i[‖ϕr‖1	NOUN
ejpam-3539	278	8	+	+	X
ejpam-3539	279	1	2‖ϕr‖1‖h‖1	2‖ϕr‖1‖h‖1	NUM
ejpam-3539	279	2	]	]	X
ejpam-3539	279	3	−→	−→	NOUN
ejpam-3539	279	4	0	0	NUM
ejpam-3539	279	5	as	as	ADP
ejpam-3539	279	6	t→∞.	t→∞.	X
ejpam-3539	279	7	we	we	PRON
ejpam-3539	279	8	conclude	conclude	VERB
ejpam-3539	279	9	that	that	PRON
ejpam-3539	279	10	kp(i	kp(i	PUNCT
ejpam-3539	280	1	−q)n(ē	−q)n(ē	PROPN
ejpam-3539	280	2	)	)	PUNCT
ejpam-3539	280	3	is	be	AUX
ejpam-3539	280	4	equiconvergence	equiconvergence	NOUN
ejpam-3539	280	5	at	at	ADP
ejpam-3539	280	6	∞.	∞.	PROPN
ejpam-3539	280	7	�	�	PROPN
ejpam-3539	281	1	3	3	NUM
ejpam-3539	281	2	.	.	PUNCT
ejpam-3539	281	3	existence	existence	NOUN
ejpam-3539	281	4	results	result	VERB
ejpam-3539	281	5	to	to	PART
ejpam-3539	281	6	establish	establish	VERB
ejpam-3539	281	7	the	the	DET
ejpam-3539	281	8	main	main	ADJ
ejpam-3539	281	9	existence	existence	NOUN
ejpam-3539	281	10	results	result	NOUN
ejpam-3539	281	11	,	,	PUNCT
ejpam-3539	281	12	we	we	PRON
ejpam-3539	281	13	assume	assume	VERB
ejpam-3539	281	14	the	the	DET
ejpam-3539	281	15	following	follow	VERB
ejpam-3539	281	16	conditions	condition	NOUN
ejpam-3539	281	17	(	(	PUNCT
ejpam-3539	281	18	r1	r1	PROPN
ejpam-3539	281	19	)	)	PUNCT
ejpam-3539	281	20	there	there	PRON
ejpam-3539	281	21	exists	exist	VERB
ejpam-3539	281	22	functions	function	NOUN
ejpam-3539	281	23	ai(i	ai(i	PUNCT
ejpam-3539	281	24	=	=	SYM
ejpam-3539	281	25	0	0	NUM
ejpam-3539	281	26	,	,	PUNCT
ejpam-3539	281	27	1	1	NUM
ejpam-3539	281	28	,	,	PUNCT
ejpam-3539	281	29	.	.	PUNCT
ejpam-3539	281	30	.	.	PUNCT
ejpam-3539	282	1	.	.	PUNCT
ejpam-3539	283	1	,	,	PUNCT
ejpam-3539	284	1	n	n	CCONJ
ejpam-3539	284	2	−	−	PROPN
ejpam-3539	284	3	1	1	NUM
ejpam-3539	284	4	)	)	PUNCT
ejpam-3539	284	5	,	,	PUNCT
ejpam-3539	284	6	b	b	X
ejpam-3539	284	7	,	,	PUNCT
ejpam-3539	284	8	r	r	NOUN
ejpam-3539	284	9	∈	∈	PROPN
ejpam-3539	284	10	l1[0,∞	l1[0,∞	NOUN
ejpam-3539	284	11	)	)	PUNCT
ejpam-3539	284	12	and	and	CCONJ
ejpam-3539	284	13	constant	constant	ADJ
ejpam-3539	284	14	θ	θ	PROPN
ejpam-3539	284	15	∈	∈	PROPN
ejpam-3539	285	1	[	[	X
ejpam-3539	285	2	0	0	NUM
ejpam-3539	285	3	,	,	PUNCT
ejpam-3539	285	4	1	1	NUM
ejpam-3539	285	5	)	)	PUNCT
ejpam-3539	285	6	where	where	SCONJ
ejpam-3539	285	7	ai	ai	VERB
ejpam-3539	285	8	,	,	PUNCT
ejpam-3539	285	9	b	b	NOUN
ejpam-3539	285	10	,	,	PUNCT
ejpam-3539	285	11	r	r	NOUN
ejpam-3539	285	12	:	:	PUNCT
ejpam-3539	285	13	[	[	X
ejpam-3539	285	14	0,∞	0,∞	X
ejpam-3539	285	15	)	)	PUNCT
ejpam-3539	286	1	−→	−→	NOUN
ejpam-3539	287	1	[	[	X
ejpam-3539	287	2	0,∞	0,∞	NUM
ejpam-3539	287	3	)	)	PUNCT
ejpam-3539	287	4	are	be	AUX
ejpam-3539	287	5	such	such	ADJ
ejpam-3539	287	6	that	that	SCONJ
ejpam-3539	287	7	for	for	ADP
ejpam-3539	287	8	all	all	PRON
ejpam-3539	287	9	(	(	PUNCT
ejpam-3539	287	10	u0	u0	ADJ
ejpam-3539	287	11	,	,	PUNCT
ejpam-3539	287	12	u1	u1	NOUN
ejpam-3539	287	13	,	,	PUNCT
ejpam-3539	287	14	.	.	PUNCT
ejpam-3539	287	15	.	.	PUNCT
ejpam-3539	288	1	.	.	PUNCT
ejpam-3539	289	1	,	,	PUNCT
ejpam-3539	289	2	un−1	un−1	ADJ
ejpam-3539	289	3	)	)	PUNCT
ejpam-3539	289	4	∈	∈	PROPN
ejpam-3539	289	5	<	<	NOUN
ejpam-3539	289	6	n	n	CCONJ
ejpam-3539	289	7	,	,	PUNCT
ejpam-3539	289	8	the	the	DET
ejpam-3539	289	9	following	follow	VERB
ejpam-3539	289	10	inequality	inequality	NOUN
ejpam-3539	289	11	is	be	AUX
ejpam-3539	289	12	satisfied	satisfied	ADJ
ejpam-3539	289	13	|g(t	|g(t	PROPN
ejpam-3539	289	14	,	,	PUNCT
ejpam-3539	289	15	u0(t	u0(t	ADJ
ejpam-3539	289	16	)	)	PUNCT
ejpam-3539	289	17	·	·	PUNCT
ejpam-3539	289	18	·	·	PUNCT
ejpam-3539	289	19	·	·	PUNCT
ejpam-3539	289	20	un−1(t)|	un−1(t)|	NUM
ejpam-3539	289	21	≤	≤	ADJ
ejpam-3539	289	22	e−t	e−t	NOUN
ejpam-3539	289	23	(	(	PUNCT
ejpam-3539	289	24	n−1∑	n−1∑	PROPN
ejpam-3539	289	25	i=0	i=0	PROPN
ejpam-3539	289	26	ai(t)|ui(t)|+	ai(t)|ui(t)|+	NUM
ejpam-3539	289	27	b(t)|un−1(t)|θ	b(t)|un−1(t)|θ	NUM
ejpam-3539	289	28	)	)	PUNCT
ejpam-3539	290	1	+	+	CCONJ
ejpam-3539	290	2	r(t	r(t	NOUN
ejpam-3539	290	3	)	)	PUNCT
ejpam-3539	290	4	(	(	PUNCT
ejpam-3539	290	5	14	14	NUM
ejpam-3539	290	6	)	)	PUNCT
ejpam-3539	290	7	(	(	PUNCT
ejpam-3539	290	8	r2	r2	PROPN
ejpam-3539	290	9	)	)	PUNCT
ejpam-3539	290	10	there	there	PRON
ejpam-3539	290	11	exists	exist	VERB
ejpam-3539	290	12	a	a	DET
ejpam-3539	290	13	constant	constant	ADJ
ejpam-3539	290	14	b1	b1	NOUN
ejpam-3539	290	15	>	>	X
ejpam-3539	290	16	0	0	NUM
ejpam-3539	290	17	such	such	ADJ
ejpam-3539	290	18	that	that	PRON
ejpam-3539	290	19	for	for	ADP
ejpam-3539	290	20	u	u	PROPN
ejpam-3539	290	21	∈	∈	PROPN
ejpam-3539	290	22	doml	doml	NOUN
ejpam-3539	290	23	if	if	SCONJ
ejpam-3539	290	24	u(n−1)(t	u(n−1)(t	NOUN
ejpam-3539	290	25	)	)	PUNCT
ejpam-3539	290	26	>	>	X
ejpam-3539	290	27	b1	b1	NOUN
ejpam-3539	290	28	for	for	ADP
ejpam-3539	290	29	all	all	DET
ejpam-3539	290	30	t	t	NOUN
ejpam-3539	290	31	∈	∈	PROPN
ejpam-3539	291	1	[	[	X
ejpam-3539	291	2	0,∞	0,∞	NUM
ejpam-3539	291	3	)	)	PUNCT
ejpam-3539	291	4	we	we	PRON
ejpam-3539	291	5	have	have	VERB
ejpam-3539	291	6	qnu	qnu	NUM
ejpam-3539	291	7	6=	6=	NUM
ejpam-3539	291	8	0	0	NUM
ejpam-3539	291	9	(	(	PUNCT
ejpam-3539	291	10	r3	r3	PROPN
ejpam-3539	291	11	)	)	PUNCT
ejpam-3539	291	12	there	there	PRON
ejpam-3539	291	13	exists	exist	VERB
ejpam-3539	291	14	a	a	DET
ejpam-3539	291	15	constant	constant	ADJ
ejpam-3539	291	16	b2	b2	NOUN
ejpam-3539	291	17	>	>	X
ejpam-3539	291	18	0	0	NUM
ejpam-3539	291	19	such	such	ADJ
ejpam-3539	291	20	that	that	PRON
ejpam-3539	291	21	for	for	ADP
ejpam-3539	291	22	u(t	u(t	NOUN
ejpam-3539	291	23	)	)	PUNCT
ejpam-3539	291	24	=	=	PUNCT
ejpam-3539	291	25	dtn−1	dtn−1	PROPN
ejpam-3539	291	26	∈	∈	PROPN
ejpam-3539	291	27	kerl	kerl	NOUN
ejpam-3539	291	28	,	,	PUNCT
ejpam-3539	291	29	d	d	PROPN
ejpam-3539	291	30	∈	∈	PROPN
ejpam-3539	291	31	<	<	X
ejpam-3539	291	32	with	with	ADP
ejpam-3539	291	33	|d|	|d|	PROPN
ejpam-3539	291	34	>	>	X
ejpam-3539	291	35	b2	b2	PROPN
ejpam-3539	291	36	(	(	PUNCT
ejpam-3539	291	37	n−1	n−1	PROPN
ejpam-3539	291	38	)	)	PUNCT
ejpam-3539	291	39	!	!	PUNCT
ejpam-3539	292	1	then	then	ADV
ejpam-3539	292	2	either	either	CCONJ
ejpam-3539	292	3	samuel	samuel	PROPN
ejpam-3539	292	4	a.	a.	PROPN
ejpam-3539	292	5	iyase	iyase	PROPN
ejpam-3539	292	6	,	,	PUNCT
ejpam-3539	292	7	abiodun	abiodun	PROPN
ejpam-3539	292	8	a.	a.	PROPN
ejpam-3539	292	9	opanuga	opanuga	PROPN
ejpam-3539	292	10	/	/	SYM
ejpam-3539	292	11	eur	eur	PROPN
ejpam-3539	292	12	.	.	PUNCT
ejpam-3539	293	1	j.	j.	PROPN
ejpam-3539	293	2	pure	pure	PROPN
ejpam-3539	293	3	appl	appl	PROPN
ejpam-3539	293	4	.	.	PROPN
ejpam-3539	293	5	math	math	PROPN
ejpam-3539	293	6	,	,	PUNCT
ejpam-3539	293	7	13	13	NUM
ejpam-3539	293	8	(	(	PUNCT
ejpam-3539	293	9	1	1	NUM
ejpam-3539	293	10	)	)	PUNCT
ejpam-3539	293	11	(	(	PUNCT
ejpam-3539	293	12	2020	2020	NUM
ejpam-3539	293	13	)	)	PUNCT
ejpam-3539	293	14	,	,	PUNCT
ejpam-3539	293	15	33	33	NUM
ejpam-3539	293	16	-	-	SYM
ejpam-3539	293	17	47	47	NUM
ejpam-3539	293	18	43	43	NUM
ejpam-3539	293	19	d	d	NOUN
ejpam-3539	293	20	·	·	PUNCT
ejpam-3539	293	21	h(t	h(t	NUM
ejpam-3539	293	22	)	)	PUNCT
ejpam-3539	294	1	[	[	X
ejpam-3539	294	2	∫	∫	X
ejpam-3539	294	3	∞	∞	NUM
ejpam-3539	294	4	0	0	NUM
ejpam-3539	295	1	g	g	PROPN
ejpam-3539	295	2	(	(	PUNCT
ejpam-3539	295	3	v	v	NOUN
ejpam-3539	295	4	,	,	PUNCT
ejpam-3539	295	5	dvn−1	dvn−1	PROPN
ejpam-3539	295	6	,	,	PUNCT
ejpam-3539	295	7	d(n−	d(n−	PROPN
ejpam-3539	295	8	1)vn−2	1)vn−2	NUM
ejpam-3539	295	9	·	·	PUNCT
ejpam-3539	295	10	·	·	PUNCT
ejpam-3539	295	11	·	·	PUNCT
ejpam-3539	296	1	(	(	PUNCT
ejpam-3539	296	2	n−	n−	NOUN
ejpam-3539	296	3	1)!d	1)!d	NUM
ejpam-3539	296	4	)	)	PUNCT
ejpam-3539	297	1	dv	dv	PROPN
ejpam-3539	297	2	−	−	PROPN
ejpam-3539	297	3	∫	∫	PROPN
ejpam-3539	298	1	ξ	ξ	SYM
ejpam-3539	298	2	0	0	NUM
ejpam-3539	298	3	∫	∫	PROPN
ejpam-3539	298	4	s	s	PART
ejpam-3539	298	5	0	0	NUM
ejpam-3539	298	6	g	g	PROPN
ejpam-3539	298	7	(	(	PUNCT
ejpam-3539	298	8	τ	τ	PROPN
ejpam-3539	298	9	,	,	PUNCT
ejpam-3539	298	10	dτn−1	dτn−1	PROPN
ejpam-3539	298	11	,	,	PUNCT
ejpam-3539	298	12	d(n−	d(n−	PROPN
ejpam-3539	298	13	1)τn−2	1)τn−2	PROPN
ejpam-3539	298	14	·	·	PUNCT
ejpam-3539	298	15	·	·	PUNCT
ejpam-3539	298	16	·	·	PUNCT
ejpam-3539	298	17	(	(	PUNCT
ejpam-3539	298	18	n−	n−	NOUN
ejpam-3539	298	19	1)!d	1)!d	NUM
ejpam-3539	298	20	)	)	PUNCT
ejpam-3539	298	21	dτda(s	dτda(s	PROPN
ejpam-3539	298	22	)	)	PUNCT
ejpam-3539	298	23	>	>	X
ejpam-3539	298	24	0	0	PUNCT
ejpam-3539	298	25	(	(	PUNCT
ejpam-3539	298	26	15	15	NUM
ejpam-3539	298	27	)	)	PUNCT
ejpam-3539	298	28	or	or	CCONJ
ejpam-3539	298	29	d	d	X
ejpam-3539	298	30	·	·	PUNCT
ejpam-3539	298	31	h(t	h(t	NUM
ejpam-3539	298	32	)	)	PUNCT
ejpam-3539	299	1	[	[	X
ejpam-3539	299	2	∫∞	∫∞	NOUN
ejpam-3539	299	3	0	0	PUNCT
ejpam-3539	299	4	g	g	PROPN
ejpam-3539	299	5	(	(	PUNCT
ejpam-3539	299	6	v	v	NOUN
ejpam-3539	299	7	,	,	PUNCT
ejpam-3539	299	8	dvn−1	dvn−1	PROPN
ejpam-3539	299	9	,	,	PUNCT
ejpam-3539	299	10	d(n−	d(n−	PROPN
ejpam-3539	299	11	1)vn−2	1)vn−2	NUM
ejpam-3539	299	12	·	·	PUNCT
ejpam-3539	299	13	·	·	PUNCT
ejpam-3539	299	14	·	·	PUNCT
ejpam-3539	299	15	(	(	PUNCT
ejpam-3539	299	16	n−	n−	NOUN
ejpam-3539	299	17	1)!d	1)!d	NUM
ejpam-3539	299	18	)	)	PUNCT
ejpam-3539	300	1	dv	dv	PROPN
ejpam-3539	300	2	−	−	PROPN
ejpam-3539	300	3	∫	∫	PROPN
ejpam-3539	301	1	ξ	ξ	SYM
ejpam-3539	301	2	0	0	NUM
ejpam-3539	301	3	∫	∫	PROPN
ejpam-3539	301	4	s	s	PART
ejpam-3539	301	5	0	0	NUM
ejpam-3539	301	6	g	g	PROPN
ejpam-3539	301	7	(	(	PUNCT
ejpam-3539	301	8	τ	τ	PROPN
ejpam-3539	301	9	,	,	PUNCT
ejpam-3539	301	10	dτn−1	dτn−1	PROPN
ejpam-3539	301	11	,	,	PUNCT
ejpam-3539	301	12	d(n−	d(n−	PROPN
ejpam-3539	301	13	1)τn−2	1)τn−2	PROPN
ejpam-3539	301	14	·	·	PUNCT
ejpam-3539	301	15	·	·	PUNCT
ejpam-3539	301	16	·	·	PUNCT
ejpam-3539	301	17	(	(	PUNCT
ejpam-3539	301	18	n−	n−	NOUN
ejpam-3539	301	19	1)!d	1)!d	NUM
ejpam-3539	301	20	)	)	PUNCT
ejpam-3539	301	21	dτda(s	dτda(s	PROPN
ejpam-3539	301	22	)	)	PUNCT
ejpam-3539	301	23	<	<	X
ejpam-3539	301	24	0	0	NUM
ejpam-3539	301	25	(	(	PUNCT
ejpam-3539	301	26	16	16	NUM
ejpam-3539	301	27	)	)	PUNCT
ejpam-3539	301	28	theorem	theorem	VERB
ejpam-3539	301	29	3.1	3.1	NUM
ejpam-3539	301	30	:	:	PUNCT
ejpam-3539	301	31	if	if	SCONJ
ejpam-3539	301	32	(	(	PUNCT
ejpam-3539	301	33	r1	r1	NOUN
ejpam-3539	301	34	)	)	PUNCT
ejpam-3539	301	35	−	−	PROPN
ejpam-3539	301	36	(	(	PUNCT
ejpam-3539	301	37	r3	r3	PROPN
ejpam-3539	301	38	)	)	PUNCT
ejpam-3539	301	39	hold	hold	VERB
ejpam-3539	301	40	,	,	PUNCT
ejpam-3539	301	41	then	then	ADV
ejpam-3539	301	42	the	the	DET
ejpam-3539	301	43	boundary	boundary	ADJ
ejpam-3539	301	44	value	value	NOUN
ejpam-3539	301	45	problem	problem	NOUN
ejpam-3539	301	46	(	(	PUNCT
ejpam-3539	301	47	1)-(2	1)-(2	NUM
ejpam-3539	301	48	)	)	PUNCT
ejpam-3539	301	49	has	have	AUX
ejpam-3539	301	50	at	at	ADV
ejpam-3539	301	51	least	least	ADV
ejpam-3539	301	52	one	one	NUM
ejpam-3539	301	53	solution	solution	NOUN
ejpam-3539	301	54	in	in	ADP
ejpam-3539	301	55	cn−1[0,∞	cn−1[0,∞	NOUN
ejpam-3539	301	56	)	)	PUNCT
ejpam-3539	301	57	provided	provide	VERB
ejpam-3539	301	58	n−1∑	n−1∑	NUM
ejpam-3539	301	59	i=0	i=0	PROPN
ejpam-3539	301	60	‖ai‖1	‖ai‖1	PROPN
ejpam-3539	301	61	<	<	X
ejpam-3539	301	62	1	1	NUM
ejpam-3539	301	63	2dn	2dn	NOUN
ejpam-3539	301	64	(	(	PUNCT
ejpam-3539	301	65	17	17	NUM
ejpam-3539	301	66	)	)	PUNCT
ejpam-3539	301	67	proof	proof	NOUN
ejpam-3539	301	68	:	:	PUNCT
ejpam-3539	301	69	our	our	PRON
ejpam-3539	301	70	goal	goal	NOUN
ejpam-3539	301	71	is	be	AUX
ejpam-3539	301	72	to	to	PART
ejpam-3539	301	73	construct	construct	VERB
ejpam-3539	301	74	an	an	DET
ejpam-3539	301	75	open	open	ADJ
ejpam-3539	301	76	bounded	bounded	ADJ
ejpam-3539	301	77	set	set	NOUN
ejpam-3539	301	78	ω	ω	PROPN
ejpam-3539	301	79	⊂	⊂	PROPN
ejpam-3539	301	80	x	x	PUNCT
ejpam-3539	301	81	that	that	SCONJ
ejpam-3539	301	82	satisfies	satisfy	VERB
ejpam-3539	301	83	assumption	assumption	NOUN
ejpam-3539	301	84	(	(	PUNCT
ejpam-3539	301	85	1)-(3	1)-(3	NUM
ejpam-3539	301	86	)	)	PUNCT
ejpam-3539	301	87	of	of	ADP
ejpam-3539	301	88	theorem	theorem	NOUN
ejpam-3539	301	89	2.2	2.2	NUM
ejpam-3539	301	90	.	.	PUNCT
ejpam-3539	302	1	let	let	VERB
ejpam-3539	302	2	ω1	ω1	PROPN
ejpam-3539	302	3	=	=	PUNCT
ejpam-3539	302	4	{	{	PUNCT
ejpam-3539	302	5	u	u	NOUN
ejpam-3539	302	6	∈	∈	PROPN
ejpam-3539	302	7	doml\	doml\	NOUN
ejpam-3539	302	8	kerl	kerl	PROPN
ejpam-3539	302	9	,	,	PUNCT
ejpam-3539	302	10	lu	lu	PROPN
ejpam-3539	302	11	=	=	NOUN
ejpam-3539	302	12	λnu	λnu	NOUN
ejpam-3539	302	13	for	for	ADP
ejpam-3539	302	14	λ	λ	PROPN
ejpam-3539	302	15	∈	∈	PROPN
ejpam-3539	302	16	(	(	PUNCT
ejpam-3539	302	17	0	0	NUM
ejpam-3539	302	18	,	,	PUNCT
ejpam-3539	302	19	1	1	NUM
ejpam-3539	302	20	]	]	PUNCT
ejpam-3539	302	21	}	}	PUNCT
ejpam-3539	302	22	.	.	PUNCT
ejpam-3539	303	1	for	for	ADP
ejpam-3539	303	2	u	u	PROPN
ejpam-3539	303	3	∈	∈	PROPN
ejpam-3539	303	4	ω1	ω1	PROPN
ejpam-3539	303	5	,	,	PUNCT
ejpam-3539	303	6	u	u	NOUN
ejpam-3539	303	7	/∈	/∈	PROPN
ejpam-3539	303	8	kerl	kerl	PROPN
ejpam-3539	303	9	and	and	CCONJ
ejpam-3539	303	10	therefore	therefore	ADV
ejpam-3539	303	11	nu	nu	PROPN
ejpam-3539	303	12	∈	∈	PROPN
ejpam-3539	303	13	iml	iml	NOUN
ejpam-3539	303	14	=	=	SYM
ejpam-3539	303	15	kerq	kerq	PROPN
ejpam-3539	303	16	.	.	PUNCT
ejpam-3539	304	1	thus	thus	ADV
ejpam-3539	304	2	qnu	qnu	NUM
ejpam-3539	304	3	=	=	NOUN
ejpam-3539	304	4	0	0	NUM
ejpam-3539	304	5	and	and	CCONJ
ejpam-3539	304	6	by	by	ADP
ejpam-3539	304	7	(	(	PUNCT
ejpam-3539	304	8	r2	r2	PROPN
ejpam-3539	304	9	)	)	PUNCT
ejpam-3539	304	10	there	there	PRON
ejpam-3539	304	11	exist	exist	VERB
ejpam-3539	304	12	t0	t0	PROPN
ejpam-3539	304	13	∈	∈	PROPN
ejpam-3539	305	1	[	[	X
ejpam-3539	305	2	0,∞	0,∞	NOUN
ejpam-3539	305	3	)	)	PUNCT
ejpam-3539	305	4	such	such	ADJ
ejpam-3539	305	5	that	that	DET
ejpam-3539	305	6	|u(n−1)(t0)|	|u(n−1)(t0)|	ADJ
ejpam-3539	305	7	≤	≤	NUM
ejpam-3539	305	8	b1	b1	NOUN
ejpam-3539	305	9	.	.	PUNCT
ejpam-3539	306	1	we	we	PRON
ejpam-3539	306	2	have	have	VERB
ejpam-3539	306	3	|u(n−1)(0)|	|u(n−1)(0)|	NOUN
ejpam-3539	306	4	=	=	SYM
ejpam-3539	306	5	∣∣∣∣u(n−1)(t0)−	∣∣∣∣u(n−1)(t0)−	NOUN
ejpam-3539	306	6	∫	∫	PROPN
ejpam-3539	306	7	t0	t0	PROPN
ejpam-3539	306	8	0	0	NUM
ejpam-3539	307	1	u(n)(s)ds	u(n)(s)ds	PROPN
ejpam-3539	307	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3539	307	3	≤	≤	NOUN
ejpam-3539	307	4	b1	b1	NOUN
ejpam-3539	307	5	+	+	CCONJ
ejpam-3539	307	6	∫	∫	PROPN
ejpam-3539	307	7	∞	∞	NOUN
ejpam-3539	307	8	0	0	NUM
ejpam-3539	308	1	|nu(s)|ds	|nu(s)|ds	PROPN
ejpam-3539	308	2	=	=	PROPN
ejpam-3539	308	3	b1	b1	NOUN
ejpam-3539	308	4	+	+	CCONJ
ejpam-3539	308	5	‖nu‖1	‖nu‖1	NOUN
ejpam-3539	308	6	(	(	PUNCT
ejpam-3539	308	7	18	18	NUM
ejpam-3539	308	8	)	)	PUNCT
ejpam-3539	308	9	for	for	ADP
ejpam-3539	308	10	u	u	PROPN
ejpam-3539	308	11	∈	∈	PROPN
ejpam-3539	308	12	ω1	ω1	PROPN
ejpam-3539	308	13	,	,	PUNCT
ejpam-3539	308	14	u	u	PROPN
ejpam-3539	308	15	∈	∈	PROPN
ejpam-3539	308	16	doml\	doml\	VERB
ejpam-3539	308	17	kerl	kerl	PROPN
ejpam-3539	308	18	and	and	CCONJ
ejpam-3539	308	19	hence	hence	ADV
ejpam-3539	308	20	(	(	PUNCT
ejpam-3539	308	21	i	i	PRON
ejpam-3539	308	22	−	−	PROPN
ejpam-3539	308	23	p	p	NOUN
ejpam-3539	308	24	)	)	PUNCT
ejpam-3539	308	25	u	u	PROPN
ejpam-3539	308	26	∈	∈	PROPN
ejpam-3539	308	27	doml	doml	PROPN
ejpam-3539	308	28	∩	∩	PROPN
ejpam-3539	308	29	kerp	kerp	PROPN
ejpam-3539	308	30	with	with	ADP
ejpam-3539	308	31	lpu	lpu	NOUN
ejpam-3539	308	32	=	=	SYM
ejpam-3539	308	33	0	0	NUM
ejpam-3539	308	34	.	.	PUNCT
ejpam-3539	309	1	thus	thus	ADV
ejpam-3539	309	2	from	from	ADP
ejpam-3539	309	3	(	(	PUNCT
ejpam-3539	309	4	10	10	NUM
ejpam-3539	309	5	)	)	PUNCT
ejpam-3539	309	6	we	we	PRON
ejpam-3539	309	7	obtain	obtain	VERB
ejpam-3539	309	8	‖(i	‖(i	NOUN
ejpam-3539	309	9	−	−	NOUN
ejpam-3539	309	10	p	p	NOUN
ejpam-3539	309	11	)	)	PUNCT
ejpam-3539	309	12	u‖	u‖	NOUN
ejpam-3539	309	13	=	=	PUNCT
ejpam-3539	309	14	‖kpl(i	‖kpl(i	NOUN
ejpam-3539	309	15	−	−	PROPN
ejpam-3539	309	16	p	p	NOUN
ejpam-3539	309	17	)	)	PUNCT
ejpam-3539	309	18	u‖	u‖	ADJ
ejpam-3539	309	19	≤	≤	ADJ
ejpam-3539	309	20	dn‖l(i	dn‖l(i	NOUN
ejpam-3539	310	1	−	−	PROPN
ejpam-3539	310	2	p	p	NOUN
ejpam-3539	310	3	)	)	PUNCT
ejpam-3539	310	4	u‖1	u‖1	NOUN
ejpam-3539	310	5	≤	≤	NUM
ejpam-3539	310	6	dn‖lu‖1	dn‖lu‖1	VERB
ejpam-3539	310	7	≤	≤	NUM
ejpam-3539	310	8	dn‖nu‖1	dn‖nu‖1	NOUN
ejpam-3539	310	9	(	(	PUNCT
ejpam-3539	310	10	19	19	NUM
ejpam-3539	310	11	)	)	PUNCT
ejpam-3539	310	12	using	use	VERB
ejpam-3539	310	13	(	(	PUNCT
ejpam-3539	310	14	18	18	NUM
ejpam-3539	310	15	)	)	PUNCT
ejpam-3539	310	16	and	and	CCONJ
ejpam-3539	310	17	(	(	PUNCT
ejpam-3539	310	18	19	19	NUM
ejpam-3539	310	19	)	)	PUNCT
ejpam-3539	310	20	we	we	PRON
ejpam-3539	310	21	get	get	VERB
ejpam-3539	311	1	‖u‖	‖u‖	PROPN
ejpam-3539	311	2	=	=	PUNCT
ejpam-3539	311	3	‖pu+	‖pu+	INTJ
ejpam-3539	311	4	(	(	PUNCT
ejpam-3539	311	5	i	i	PRON
ejpam-3539	311	6	−	−	PROPN
ejpam-3539	311	7	p	p	NOUN
ejpam-3539	311	8	)	)	PUNCT
ejpam-3539	311	9	u‖	u‖	ADJ
ejpam-3539	311	10	≤	≤	ADJ
ejpam-3539	311	11	‖pu‖+	‖pu‖+	ADJ
ejpam-3539	311	12	‖‖(i	‖‖(i	NOUN
ejpam-3539	311	13	−	−	PROPN
ejpam-3539	311	14	pu)‖	pu)‖	PROPN
ejpam-3539	311	15	≤	≤	NUM
ejpam-3539	311	16	dn|u(n−1)(0)|+dn‖nu‖1	dn|u(n−1)(0)|+dn‖nu‖1	VERB
ejpam-3539	311	17	=	=	PRON
ejpam-3539	311	18	dn(b1	dn(b1	NOUN
ejpam-3539	311	19	+	+	CCONJ
ejpam-3539	311	20	‖nu‖1	‖nu‖1	NOUN
ejpam-3539	311	21	)	)	PUNCT
ejpam-3539	312	1	+	+	SYM
ejpam-3539	312	2	dn‖nu‖1	dn‖nu‖1	NOUN
ejpam-3539	312	3	=	=	SYM
ejpam-3539	312	4	dnb1	dnb1	PROPN
ejpam-3539	312	5	+	+	CCONJ
ejpam-3539	312	6	2dn‖nu‖1	2dn‖nu‖1	NUM
ejpam-3539	312	7	(	(	PUNCT
ejpam-3539	312	8	20	20	NUM
ejpam-3539	312	9	)	)	PUNCT
ejpam-3539	312	10	samuel	samuel	PROPN
ejpam-3539	312	11	a.	a.	PROPN
ejpam-3539	312	12	iyase	iyase	PROPN
ejpam-3539	312	13	,	,	PUNCT
ejpam-3539	312	14	abiodun	abiodun	PROPN
ejpam-3539	312	15	a.	a.	PROPN
ejpam-3539	312	16	opanuga	opanuga	PROPN
ejpam-3539	312	17	/	/	SYM
ejpam-3539	312	18	eur	eur	PROPN
ejpam-3539	312	19	.	.	PUNCT
ejpam-3539	313	1	j.	j.	PROPN
ejpam-3539	313	2	pure	pure	PROPN
ejpam-3539	313	3	appl	appl	PROPN
ejpam-3539	313	4	.	.	PROPN
ejpam-3539	313	5	math	math	PROPN
ejpam-3539	313	6	,	,	PUNCT
ejpam-3539	313	7	13	13	NUM
ejpam-3539	313	8	(	(	PUNCT
ejpam-3539	313	9	1	1	NUM
ejpam-3539	313	10	)	)	PUNCT
ejpam-3539	313	11	(	(	PUNCT
ejpam-3539	313	12	2020	2020	NUM
ejpam-3539	313	13	)	)	PUNCT
ejpam-3539	313	14	,	,	PUNCT
ejpam-3539	313	15	33	33	NUM
ejpam-3539	313	16	-	-	SYM
ejpam-3539	313	17	47	47	NUM
ejpam-3539	313	18	44	44	NUM
ejpam-3539	313	19	using	use	VERB
ejpam-3539	313	20	(	(	PUNCT
ejpam-3539	313	21	14	14	NUM
ejpam-3539	313	22	)	)	PUNCT
ejpam-3539	313	23	we	we	PRON
ejpam-3539	313	24	have	have	VERB
ejpam-3539	313	25	‖nu‖1	‖nu‖1	NOUN
ejpam-3539	313	26	=	=	SYM
ejpam-3539	313	27	∫	∫	PROPN
ejpam-3539	313	28	∞	∞	PROPN
ejpam-3539	313	29	0	0	PROPN
ejpam-3539	313	30	|g(s	|g(s	PROPN
ejpam-3539	313	31	,	,	PUNCT
ejpam-3539	313	32	u(s	u(s	NUM
ejpam-3539	313	33	)	)	PUNCT
ejpam-3539	313	34	·	·	PUNCT
ejpam-3539	313	35	·	·	PUNCT
ejpam-3539	313	36	·	·	PUNCT
ejpam-3539	314	1	un−1(s)|ds	un−1(s)|ds	ADP
ejpam-3539	314	2	≤	≤	ADV
ejpam-3539	314	3	n−1∑	n−1∑	NUM
ejpam-3539	314	4	i=0	i=0	PROPN
ejpam-3539	314	5	∫	∫	PROPN
ejpam-3539	314	6	∞	∞	NUM
ejpam-3539	314	7	0	0	NUM
ejpam-3539	314	8	|ai|e−s|u(i)(s)|ds+	|ai|e−s|u(i)(s)|ds+	ADJ
ejpam-3539	314	9	∫	∫	PROPN
ejpam-3539	314	10	∞	∞	NUM
ejpam-3539	314	11	0	0	NUM
ejpam-3539	314	12	|b(s)|e−s|un−1(s)|θds+	|b(s)|e−s|un−1(s)|θds+	NOUN
ejpam-3539	314	13	∫	∫	NOUN
ejpam-3539	314	14	∞	∞	NUM
ejpam-3539	314	15	0	0	NUM
ejpam-3539	314	16	|r(s)|ds	|r(s)|ds	NOUN
ejpam-3539	314	17	≤	≤	X
ejpam-3539	314	18	n−1∑	n−1∑	NUM
ejpam-3539	314	19	i=0	i=0	PROPN
ejpam-3539	314	20	‖ai‖1	‖ai‖1	PROPN
ejpam-3539	314	21	,	,	PUNCT
ejpam-3539	314	22	‖u‖+	‖u‖+	PROPN
ejpam-3539	314	23	‖b‖1	‖b‖1	NOUN
ejpam-3539	314	24	,	,	PUNCT
ejpam-3539	314	25	‖u‖θ	‖u‖θ	NOUN
ejpam-3539	314	26	+	+	CCONJ
ejpam-3539	314	27	‖r‖1	‖r‖1	ADJ
ejpam-3539	314	28	(	(	PUNCT
ejpam-3539	314	29	21	21	NUM
ejpam-3539	314	30	)	)	PUNCT
ejpam-3539	314	31	from	from	ADP
ejpam-3539	314	32	(	(	PUNCT
ejpam-3539	314	33	20	20	NUM
ejpam-3539	314	34	)	)	PUNCT
ejpam-3539	314	35	we	we	PRON
ejpam-3539	314	36	derive	derive	VERB
ejpam-3539	314	37	‖u‖	‖u‖	PROPN
ejpam-3539	314	38	≤	≤	ADJ
ejpam-3539	314	39	dnb1	dnb1	NOUN
ejpam-3539	314	40	+	+	CCONJ
ejpam-3539	314	41	2dn	2dn	NOUN
ejpam-3539	314	42	[	[	PUNCT
ejpam-3539	314	43	n−1∑	n−1∑	ADJ
ejpam-3539	314	44	i=0	i=0	PROPN
ejpam-3539	314	45	‖ai‖1‖u(i)‖∞|‖b‖1‖u(n−1)‖θ∞	‖ai‖1‖u(i)‖∞|‖b‖1‖u(n−1)‖θ∞	X
ejpam-3539	314	46	+	+	CCONJ
ejpam-3539	314	47	‖r‖1	‖r‖1	ADJ
ejpam-3539	314	48	]	]	PUNCT
ejpam-3539	314	49	≤	≤	NUM
ejpam-3539	314	50	dnb1	dnb1	NOUN
ejpam-3539	314	51	+	+	CCONJ
ejpam-3539	315	1	2dn	2dn	NOUN
ejpam-3539	316	1	[	[	PUNCT
ejpam-3539	316	2	n−1∑	n−1∑	PROPN
ejpam-3539	316	3	i=0	i=0	PROPN
ejpam-3539	316	4	‖ai‖1‖u‖+	‖ai‖1‖u‖+	NUM
ejpam-3539	316	5	‖b‖1‖u‖θ	‖b‖1‖u‖θ	CCONJ
ejpam-3539	316	6	+	+	NUM
ejpam-3539	316	7	‖r‖1	‖r‖1	ADJ
ejpam-3539	316	8	]	]	PUNCT
ejpam-3539	316	9	i.e.	i.e.	X
ejpam-3539	316	10	(	(	PUNCT
ejpam-3539	316	11	1−	1−	NUM
ejpam-3539	316	12	2dn	2dn	NOUN
ejpam-3539	316	13	∑n−1	∑n−1	ADP
ejpam-3539	316	14	i=0	i=0	PROPN
ejpam-3539	316	15	‖ai‖1	‖ai‖1	PROPN
ejpam-3539	316	16	)	)	PUNCT
ejpam-3539	317	1	‖u‖	‖u‖	PROPN
ejpam-3539	317	2	≤	≤	NOUN
ejpam-3539	317	3	2dn‖b‖1‖u‖θ	2dn‖b‖1‖u‖θ	NUM
ejpam-3539	318	1	+	+	ADJ
ejpam-3539	318	2	dnb1	dnb1	NOUN
ejpam-3539	318	3	+	+	CCONJ
ejpam-3539	318	4	2dn‖r‖1	2dn‖r‖1	NUM
ejpam-3539	318	5	since	since	SCONJ
ejpam-3539	318	6	θ	θ	PROPN
ejpam-3539	318	7	∈	∈	PROPN
ejpam-3539	319	1	[	[	X
ejpam-3539	319	2	0	0	NUM
ejpam-3539	319	3	,	,	PUNCT
ejpam-3539	319	4	1	1	NUM
ejpam-3539	319	5	)	)	PUNCT
ejpam-3539	319	6	and	and	CCONJ
ejpam-3539	319	7	condition	condition	NOUN
ejpam-3539	319	8	(	(	PUNCT
ejpam-3539	319	9	17	17	NUM
ejpam-3539	319	10	)	)	PUNCT
ejpam-3539	319	11	,	,	PUNCT
ejpam-3539	319	12	we	we	PRON
ejpam-3539	319	13	conclude	conclude	VERB
ejpam-3539	319	14	that	that	SCONJ
ejpam-3539	319	15	there	there	PRON
ejpam-3539	319	16	exists	exist	VERB
ejpam-3539	319	17	constant	constant	ADJ
ejpam-3539	319	18	m	m	VERB
ejpam-3539	319	19	>	>	X
ejpam-3539	319	20	0	0	NUM
ejpam-3539	319	21	such	such	ADJ
ejpam-3539	319	22	that	that	SCONJ
ejpam-3539	319	23	‖u‖	‖u‖	PROPN
ejpam-3539	319	24	≤m	≤m	PROPN
ejpam-3539	319	25	.	.	PUNCT
ejpam-3539	320	1	therefore	therefore	ADV
ejpam-3539	320	2	,	,	PUNCT
ejpam-3539	320	3	ω1	ω1	PROPN
ejpam-3539	320	4	bounded	bound	VERB
ejpam-3539	320	5	.	.	PUNCT
ejpam-3539	321	1	let	let	VERB
ejpam-3539	321	2	ω2	ω2	ADV
ejpam-3539	321	3	=	=	SYM
ejpam-3539	321	4	{	{	PUNCT
ejpam-3539	321	5	u	u	NOUN
ejpam-3539	321	6	∈	∈	PROPN
ejpam-3539	321	7	kerl	kerl	PROPN
ejpam-3539	321	8	:	:	PUNCT
ejpam-3539	321	9	nu	nu	PROPN
ejpam-3539	321	10	∈	∈	PROPN
ejpam-3539	321	11	iml	iml	NOUN
ejpam-3539	321	12	}	}	PUNCT
ejpam-3539	321	13	.	.	PUNCT
ejpam-3539	322	1	for	for	ADP
ejpam-3539	322	2	u	u	PROPN
ejpam-3539	322	3	∈	∈	PROPN
ejpam-3539	322	4	ω2	ω2	PROPN
ejpam-3539	322	5	,	,	PUNCT
ejpam-3539	322	6	u	u	PROPN
ejpam-3539	322	7	∈	∈	PROPN
ejpam-3539	322	8	kerl	kerl	NOUN
ejpam-3539	322	9	=	=	PUNCT
ejpam-3539	322	10	{	{	PUNCT
ejpam-3539	322	11	u	u	NOUN
ejpam-3539	322	12	∈	∈	PROPN
ejpam-3539	322	13	doml	doml	NOUN
ejpam-3539	322	14	:	:	PUNCT
ejpam-3539	323	1	u	u	NOUN
ejpam-3539	324	1	=	=	SYM
ejpam-3539	324	2	dtn−1	dtn−1	PROPN
ejpam-3539	324	3	,	,	PUNCT
ejpam-3539	324	4	d	d	PROPN
ejpam-3539	324	5	∈	∈	PROPN
ejpam-3539	324	6	<	<	X
ejpam-3539	324	7	,	,	PUNCT
ejpam-3539	324	8	t	t	PROPN
ejpam-3539	324	9	∈	∈	PROPN
ejpam-3539	325	1	[	[	X
ejpam-3539	325	2	0,∞	0,∞	NOUN
ejpam-3539	325	3	)	)	PUNCT
ejpam-3539	325	4	}	}	PUNCT
ejpam-3539	325	5	and	and	CCONJ
ejpam-3539	325	6	qnu	qnu	NOUN
ejpam-3539	325	7	=	=	NOUN
ejpam-3539	325	8	0	0	X
ejpam-3539	325	9	.	.	PUNCT
ejpam-3539	325	10	therefore	therefore	ADV
ejpam-3539	325	11	from	from	ADP
ejpam-3539	325	12	(	(	PUNCT
ejpam-3539	325	13	r2	r2	PROPN
ejpam-3539	325	14	)	)	PUNCT
ejpam-3539	325	15	there	there	PRON
ejpam-3539	325	16	exist	exist	VERB
ejpam-3539	325	17	t0	t0	PROPN
ejpam-3539	325	18	∈	∈	PROPN
ejpam-3539	326	1	[	[	X
ejpam-3539	326	2	0,∞	0,∞	NOUN
ejpam-3539	326	3	)	)	PUNCT
ejpam-3539	326	4	such	such	ADJ
ejpam-3539	326	5	that	that	DET
ejpam-3539	326	6	|u(n−1)(t0)|	|u(n−1)(t0)|	NOUN
ejpam-3539	326	7	<	<	X
ejpam-3539	326	8	b1	b1	PROPN
ejpam-3539	326	9	i.e	i.e	PRON
ejpam-3539	326	10	,	,	PUNCT
ejpam-3539	326	11	(	(	PUNCT
ejpam-3539	326	12	n−	n−	NOUN
ejpam-3539	326	13	1)!d	1)!d	NOUN
ejpam-3539	326	14	≤	≤	NUM
ejpam-3539	326	15	b1	b1	NOUN
ejpam-3539	326	16	which	which	PRON
ejpam-3539	326	17	implies	imply	VERB
ejpam-3539	326	18	that	that	SCONJ
ejpam-3539	326	19	|d|	|d|	PROPN
ejpam-3539	326	20	≤	≤	PROPN
ejpam-3539	326	21	b1	b1	PROPN
ejpam-3539	326	22	(	(	PUNCT
ejpam-3539	326	23	n−1	n−1	PROPN
ejpam-3539	326	24	)	)	PUNCT
ejpam-3539	326	25	!	!	PUNCT
ejpam-3539	326	26	.	.	PUNCT
ejpam-3539	327	1	now	now	ADV
ejpam-3539	327	2	for	for	ADP
ejpam-3539	327	3	u	u	PROPN
ejpam-3539	327	4	∈	∈	PROPN
ejpam-3539	327	5	ω2	ω2	NOUN
ejpam-3539	327	6	‖u‖	‖u‖	PROPN
ejpam-3539	327	7	=	=	PUNCT
ejpam-3539	327	8	|d|max	|d|max	CCONJ
ejpam-3539	327	9	(	(	PUNCT
ejpam-3539	327	10	sup	sup	NOUN
ejpam-3539	327	11	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3539	327	12	)	)	PUNCT
ejpam-3539	327	13	e−t|(tn−1)(i)|	e−t|(tn−1)(i)|	NOUN
ejpam-3539	327	14	)	)	PUNCT
ejpam-3539	327	15	≤	≤	NOUN
ejpam-3539	327	16	b1dn	b1dn	PUNCT
ejpam-3539	327	17	<	<	X
ejpam-3539	327	18	∞	∞	PROPN
ejpam-3539	327	19	(	(	PUNCT
ejpam-3539	327	20	22	22	NUM
ejpam-3539	327	21	)	)	PUNCT
ejpam-3539	327	22	therefore	therefore	ADV
ejpam-3539	327	23	ω2	ω2	PROPN
ejpam-3539	327	24	is	be	AUX
ejpam-3539	327	25	bounded	bound	VERB
ejpam-3539	327	26	in	in	ADP
ejpam-3539	327	27	x.	x.	NOUN
ejpam-3539	327	28	if	if	SCONJ
ejpam-3539	327	29	(	(	PUNCT
ejpam-3539	327	30	15	15	NUM
ejpam-3539	327	31	)	)	PUNCT
ejpam-3539	327	32	holds	hold	VERB
ejpam-3539	327	33	,	,	PUNCT
ejpam-3539	327	34	we	we	PRON
ejpam-3539	327	35	set	set	VERB
ejpam-3539	327	36	ω3	ω3	NOUN
ejpam-3539	327	37	=	=	PUNCT
ejpam-3539	327	38	{	{	PUNCT
ejpam-3539	327	39	u	u	NOUN
ejpam-3539	327	40	∈	∈	PROPN
ejpam-3539	327	41	kerl	kerl	NOUN
ejpam-3539	327	42	:	:	PUNCT
ejpam-3539	328	1	λju+	λju+	ADJ
ejpam-3539	328	2	(	(	PUNCT
ejpam-3539	328	3	1−	1−	NUM
ejpam-3539	328	4	λ)qnu	λ)qnu	NOUN
ejpam-3539	328	5	=	=	NOUN
ejpam-3539	328	6	0	0	NUM
ejpam-3539	328	7	}	}	PUNCT
ejpam-3539	328	8	(	(	PUNCT
ejpam-3539	328	9	23	23	NUM
ejpam-3539	328	10	)	)	PUNCT
ejpam-3539	328	11	where	where	SCONJ
ejpam-3539	328	12	j	j	PROPN
ejpam-3539	328	13	is	be	AUX
ejpam-3539	328	14	the	the	DET
ejpam-3539	328	15	isomorphism	isomorphism	NOUN
ejpam-3539	328	16	,	,	PUNCT
ejpam-3539	328	17	j	j	NOUN
ejpam-3539	328	18	:	:	PUNCT
ejpam-3539	328	19	kerl→	kerl→	VERB
ejpam-3539	328	20	imq	imq	NOUN
ejpam-3539	328	21	defined	define	VERB
ejpam-3539	328	22	by	by	ADP
ejpam-3539	328	23	j(dtn−1	j(dtn−1	ADJ
ejpam-3539	328	24	)	)	PUNCT
ejpam-3539	329	1	=	=	SYM
ejpam-3539	329	2	de−t	de−t	NOUN
ejpam-3539	329	3	;	;	PUNCT
ejpam-3539	329	4	d	d	X
ejpam-3539	329	5	∈	∈	PROPN
ejpam-3539	330	1	<	<	X
ejpam-3539	330	2	.	.	PUNCT
ejpam-3539	331	1	for	for	ADP
ejpam-3539	331	2	u	u	PROPN
ejpam-3539	331	3	∈	∈	PROPN
ejpam-3539	331	4	ω3	ω3	NOUN
ejpam-3539	331	5	,	,	PUNCT
ejpam-3539	331	6	u	u	NOUN
ejpam-3539	331	7	=	=	PUNCT
ejpam-3539	331	8	dtn−1	dtn−1	PROPN
ejpam-3539	331	9	and	and	CCONJ
ejpam-3539	331	10	from	from	ADP
ejpam-3539	331	11	(	(	PUNCT
ejpam-3539	331	12	23	23	NUM
ejpam-3539	331	13	)	)	PUNCT
ejpam-3539	331	14	we	we	PRON
ejpam-3539	331	15	get	get	VERB
ejpam-3539	331	16	−λju	−λju	PUNCT
ejpam-3539	331	17	=	=	PUNCT
ejpam-3539	331	18	(	(	PUNCT
ejpam-3539	331	19	1−	1−	NUM
ejpam-3539	331	20	λ)qnu	λ)qnu	NOUN
ejpam-3539	331	21	−λde−t	−λde−t	NOUN
ejpam-3539	331	22	=	=	SYM
ejpam-3539	331	23	(	(	PUNCT
ejpam-3539	331	24	1−	1−	NUM
ejpam-3539	331	25	λ)h(t	λ)h(t	NOUN
ejpam-3539	331	26	)	)	PUNCT
ejpam-3539	332	1	[	[	X
ejpam-3539	332	2	∫∞	∫∞	NOUN
ejpam-3539	332	3	0	0	SYM
ejpam-3539	332	4	nu(v)dv	nu(v)dv	PROPN
ejpam-3539	332	5	−	−	PROPN
ejpam-3539	332	6	∫	∫	PROPN
ejpam-3539	333	1	ξ	ξ	SYM
ejpam-3539	333	2	0	0	NUM
ejpam-3539	333	3	∫	∫	PROPN
ejpam-3539	333	4	s	s	PART
ejpam-3539	333	5	0	0	NUM
ejpam-3539	333	6	nu(τ)dτda(s	nu(τ)dτda(s	PROPN
ejpam-3539	333	7	)	)	PUNCT
ejpam-3539	333	8	]	]	PUNCT
ejpam-3539	333	9	references	reference	VERB
ejpam-3539	333	10	45	45	NUM
ejpam-3539	333	11	if	if	SCONJ
ejpam-3539	333	12	λ	λ	NOUN
ejpam-3539	333	13	=	=	SYM
ejpam-3539	333	14	1	1	NUM
ejpam-3539	333	15	,	,	PUNCT
ejpam-3539	333	16	then	then	ADV
ejpam-3539	333	17	d	d	PROPN
ejpam-3539	333	18	=	=	SYM
ejpam-3539	333	19	0	0	X
ejpam-3539	333	20	.	.	PUNCT
ejpam-3539	334	1	however	however	ADV
ejpam-3539	334	2	if	if	SCONJ
ejpam-3539	334	3	|d|	|d|	PROPN
ejpam-3539	334	4	>	>	X
ejpam-3539	334	5	b1	b1	PROPN
ejpam-3539	334	6	(	(	PUNCT
ejpam-3539	334	7	n−1	n−1	PROPN
ejpam-3539	334	8	)	)	PUNCT
ejpam-3539	334	9	!	!	PUNCT
ejpam-3539	335	1	and	and	CCONJ
ejpam-3539	335	2	0	0	NUM
ejpam-3539	335	3	<	<	X
ejpam-3539	335	4	λ	λ	X
ejpam-3539	335	5	<	<	X
ejpam-3539	335	6	1	1	NUM
ejpam-3539	335	7	then	then	ADV
ejpam-3539	335	8	from	from	ADP
ejpam-3539	335	9	(	(	PUNCT
ejpam-3539	335	10	15	15	NUM
ejpam-3539	335	11	)	)	PUNCT
ejpam-3539	335	12	we	we	PRON
ejpam-3539	335	13	obtain	obtain	VERB
ejpam-3539	335	14	−λd2e−t	−λd2e−t	NOUN
ejpam-3539	335	15	=	=	PUNCT
ejpam-3539	335	16	(	(	PUNCT
ejpam-3539	335	17	1−	1−	NUM
ejpam-3539	335	18	λ)h(t)d	λ)h(t)d	NUM
ejpam-3539	335	19	·	·	PUNCT
ejpam-3539	336	1	[	[	X
ejpam-3539	336	2	∫	∫	X
ejpam-3539	336	3	∞	∞	PROPN
ejpam-3539	336	4	0	0	PROPN
ejpam-3539	336	5	nu(v)dv	nu(v)dv	PROPN
ejpam-3539	336	6	−	−	PROPN
ejpam-3539	336	7	∫	∫	PROPN
ejpam-3539	337	1	ξ	ξ	SYM
ejpam-3539	337	2	0	0	NUM
ejpam-3539	337	3	∫	∫	PROPN
ejpam-3539	337	4	s	s	PART
ejpam-3539	337	5	0	0	NUM
ejpam-3539	337	6	nu(τ)dτda(s	nu(τ)dτda(s	PROPN
ejpam-3539	337	7	)	)	PUNCT
ejpam-3539	337	8	]	]	PUNCT
ejpam-3539	338	1	>	>	X
ejpam-3539	338	2	0	0	NUM
ejpam-3539	338	3	which	which	PRON
ejpam-3539	338	4	is	be	AUX
ejpam-3539	338	5	a	a	DET
ejpam-3539	338	6	contradiction	contradiction	NOUN
ejpam-3539	338	7	.	.	PUNCT
ejpam-3539	339	1	similarly	similarly	ADV
ejpam-3539	339	2	if	if	SCONJ
ejpam-3539	339	3	ω3	ω3	NOUN
ejpam-3539	339	4	=	=	PUNCT
ejpam-3539	339	5	{	{	PUNCT
ejpam-3539	339	6	u	u	NOUN
ejpam-3539	339	7	∈	∈	PROPN
ejpam-3539	339	8	kerl	kerl	NOUN
ejpam-3539	339	9	:	:	PUNCT
ejpam-3539	339	10	−λju+	−λju+	PRON
ejpam-3539	339	11	(	(	PUNCT
ejpam-3539	339	12	1−	1−	NUM
ejpam-3539	339	13	λ)qnu	λ)qnu	NOUN
ejpam-3539	339	14	=	=	NOUN
ejpam-3539	339	15	0	0	NUM
ejpam-3539	339	16	}	}	PUNCT
ejpam-3539	339	17	we	we	PRON
ejpam-3539	339	18	arrive	arrive	VERB
ejpam-3539	339	19	at	at	ADP
ejpam-3539	339	20	a	a	DET
ejpam-3539	339	21	similar	similar	ADJ
ejpam-3539	339	22	contradiction	contradiction	NOUN
ejpam-3539	339	23	using	use	VERB
ejpam-3539	339	24	(	(	PUNCT
ejpam-3539	339	25	16	16	NUM
ejpam-3539	339	26	)	)	PUNCT
ejpam-3539	339	27	.	.	PUNCT
ejpam-3539	340	1	therefore	therefore	ADV
ejpam-3539	340	2	,	,	PUNCT
ejpam-3539	340	3	ω3	ω3	PROPN
ejpam-3539	340	4	is	be	AUX
ejpam-3539	340	5	bounded	bound	VERB
ejpam-3539	340	6	.	.	PUNCT
ejpam-3539	341	1	let	let	VERB
ejpam-3539	341	2	ω	ω	NOUN
ejpam-3539	341	3	be	be	AUX
ejpam-3539	341	4	open	open	ADJ
ejpam-3539	341	5	and	and	CCONJ
ejpam-3539	341	6	bounded	bound	VERB
ejpam-3539	341	7	such	such	DET
ejpam-3539	341	8	that	that	SCONJ
ejpam-3539	341	9	∪3	∪3	PROPN
ejpam-3539	341	10	i=1ωi	i=1ωi	PRON
ejpam-3539	342	1	⊂	⊂	PROPN
ejpam-3539	342	2	ω	ω	PROPN
ejpam-3539	342	3	.	.	PUNCT
ejpam-3539	343	1	it	it	PRON
ejpam-3539	343	2	is	be	AUX
ejpam-3539	343	3	easily	easily	ADV
ejpam-3539	343	4	seen	see	VERB
ejpam-3539	343	5	that	that	SCONJ
ejpam-3539	343	6	assumptions	assumption	NOUN
ejpam-3539	343	7	(	(	PUNCT
ejpam-3539	343	8	1	1	NUM
ejpam-3539	343	9	)	)	PUNCT
ejpam-3539	343	10	and	and	CCONJ
ejpam-3539	343	11	(	(	PUNCT
ejpam-3539	343	12	2	2	X
ejpam-3539	343	13	)	)	PUNCT
ejpam-3539	343	14	of	of	ADP
ejpam-3539	343	15	theorem	theorem	ADJ
ejpam-3539	343	16	2.2	2.2	NUM
ejpam-3539	343	17	are	be	AUX
ejpam-3539	343	18	satisfied	satisfied	ADJ
ejpam-3539	343	19	.	.	PUNCT
ejpam-3539	344	1	we	we	PRON
ejpam-3539	344	2	now	now	ADV
ejpam-3539	344	3	verify	verify	VERB
ejpam-3539	344	4	the	the	DET
ejpam-3539	344	5	third	third	ADJ
ejpam-3539	344	6	assumption	assumption	NOUN
ejpam-3539	344	7	.	.	PUNCT
ejpam-3539	345	1	to	to	PART
ejpam-3539	345	2	do	do	VERB
ejpam-3539	345	3	this	this	PRON
ejpam-3539	345	4	,	,	PUNCT
ejpam-3539	345	5	we	we	PRON
ejpam-3539	345	6	apply	apply	VERB
ejpam-3539	345	7	the	the	DET
ejpam-3539	345	8	invariance	invariance	NOUN
ejpam-3539	345	9	under	under	ADP
ejpam-3539	345	10	a	a	DET
ejpam-3539	345	11	homotopy	homotopy	NOUN
ejpam-3539	345	12	of	of	ADP
ejpam-3539	345	13	the	the	DET
ejpam-3539	345	14	degree	degree	NOUN
ejpam-3539	345	15	.	.	PUNCT
ejpam-3539	346	1	we	we	PRON
ejpam-3539	346	2	define	define	VERB
ejpam-3539	346	3	h(u	h(u	PROPN
ejpam-3539	346	4	,	,	PUNCT
ejpam-3539	346	5	λ	λ	NOUN
ejpam-3539	346	6	)	)	PUNCT
ejpam-3539	346	7	=	=	VERB
ejpam-3539	346	8	±λju+	±λju+	PRON
ejpam-3539	346	9	(	(	PUNCT
ejpam-3539	346	10	1−	1−	NUM
ejpam-3539	346	11	λ)qnu	λ)qnu	NOUN
ejpam-3539	346	12	since	since	SCONJ
ejpam-3539	346	13	∪3	∪3	PROPN
ejpam-3539	346	14	i=1ωi	i=1ωi	PRON
ejpam-3539	347	1	⊂	⊂	PROPN
ejpam-3539	347	2	ω	ω	PROPN
ejpam-3539	347	3	,	,	PUNCT
ejpam-3539	347	4	we	we	PRON
ejpam-3539	347	5	have	have	VERB
ejpam-3539	347	6	that	that	SCONJ
ejpam-3539	347	7	h(u	h(u	PROPN
ejpam-3539	347	8	,	,	PUNCT
ejpam-3539	347	9	λ	λ	PROPN
ejpam-3539	347	10	)	)	PUNCT
ejpam-3539	347	11	6=	6=	ADP
ejpam-3539	347	12	0	0	NUM
ejpam-3539	347	13	for	for	ADP
ejpam-3539	347	14	u	u	PROPN
ejpam-3539	347	15	∈	∈	PROPN
ejpam-3539	347	16	kerl	kerl	X
ejpam-3539	347	17	∩	∩	ADJ
ejpam-3539	347	18	∂ω	∂ω	PROPN
ejpam-3539	347	19	.	.	PUNCT
ejpam-3539	348	1	hence	hence	ADV
ejpam-3539	348	2	deg(qn	deg(qn	PROPN
ejpam-3539	348	3	|kerl∩∂ω	|kerl∩∂ω	PROPN
ejpam-3539	348	4	,	,	PUNCT
ejpam-3539	348	5	ω	ω	NUM
ejpam-3539	348	6	∩	∩	ADJ
ejpam-3539	348	7	kerl	kerl	PROPN
ejpam-3539	348	8	,	,	PUNCT
ejpam-3539	348	9	0	0	NUM
ejpam-3539	348	10	)	)	PUNCT
ejpam-3539	348	11	=	=	PUNCT
ejpam-3539	348	12	deg(h(0	deg(h(0	NOUN
ejpam-3539	348	13	,	,	PUNCT
ejpam-3539	348	14	1),ω	1),ω	NUM
ejpam-3539	348	15	∩	∩	ADJ
ejpam-3539	348	16	kerl	kerl	PROPN
ejpam-3539	348	17	,	,	PUNCT
ejpam-3539	348	18	0	0	NUM
ejpam-3539	348	19	)	)	PUNCT
ejpam-3539	348	20	=	=	PUNCT
ejpam-3539	348	21	deg(±j	deg(±j	NOUN
ejpam-3539	348	22	,	,	PUNCT
ejpam-3539	348	23	ω	ω	NUM
ejpam-3539	348	24	∩	∩	ADJ
ejpam-3539	348	25	kerl	kerl	PROPN
ejpam-3539	348	26	,	,	PUNCT
ejpam-3539	348	27	0	0	NUM
ejpam-3539	348	28	)	)	PUNCT
ejpam-3539	348	29	6=	6=	ADP
ejpam-3539	348	30	0	0	NUM
ejpam-3539	348	31	therefore	therefore	ADV
ejpam-3539	348	32	by	by	ADP
ejpam-3539	348	33	theorem	theorem	NOUN
ejpam-3539	348	34	2.1	2.1	NUM
ejpam-3539	348	35	lu	lu	NOUN
ejpam-3539	348	36	=	=	SYM
ejpam-3539	348	37	nu	nu	NOUN
ejpam-3539	348	38	has	have	VERB
ejpam-3539	348	39	at	at	ADV
ejpam-3539	348	40	least	least	ADV
ejpam-3539	348	41	one	one	NUM
ejpam-3539	348	42	solution	solution	NOUN
ejpam-3539	348	43	in	in	ADP
ejpam-3539	348	44	doml	doml	PROPN
ejpam-3539	348	45	∩	∩	PROPN
ejpam-3539	348	46	ω̄	ω̄	ADP
ejpam-3539	348	47	i.e.	i.e.	X
ejpam-3539	348	48	(	(	PUNCT
ejpam-3539	348	49	1	1	NUM
ejpam-3539	348	50	)	)	PUNCT
ejpam-3539	348	51	(	(	PUNCT
ejpam-3539	348	52	2	2	X
ejpam-3539	348	53	)	)	PUNCT
ejpam-3539	348	54	has	have	VERB
ejpam-3539	348	55	at	at	ADV
ejpam-3539	348	56	least	least	ADV
ejpam-3539	348	57	one	one	NUM
ejpam-3539	348	58	solution	solution	NOUN
ejpam-3539	348	59	in	in	ADP
ejpam-3539	348	60	x	x	PROPN
ejpam-3539	348	61	�	�	PROPN
ejpam-3539	348	62	4	4	NUM
ejpam-3539	348	63	.	.	PUNCT
ejpam-3539	348	64	conclusion	conclusion	NOUN
ejpam-3539	348	65	this	this	DET
ejpam-3539	348	66	paper	paper	NOUN
ejpam-3539	348	67	has	have	AUX
ejpam-3539	348	68	established	establish	VERB
ejpam-3539	348	69	conditions	condition	NOUN
ejpam-3539	348	70	for	for	ADP
ejpam-3539	348	71	the	the	DET
ejpam-3539	348	72	existence	existence	NOUN
ejpam-3539	348	73	of	of	ADP
ejpam-3539	348	74	solutions	solution	NOUN
ejpam-3539	348	75	for	for	ADP
ejpam-3539	348	76	the	the	DET
ejpam-3539	348	77	resonant	resonant	ADJ
ejpam-3539	348	78	boundary	boundary	ADJ
ejpam-3539	348	79	value	value	NOUN
ejpam-3539	348	80	problems	problem	NOUN
ejpam-3539	348	81	(	(	PUNCT
ejpam-3539	348	82	1	1	NUM
ejpam-3539	348	83	)	)	PUNCT
ejpam-3539	348	84	(	(	PUNCT
ejpam-3539	348	85	2	2	NUM
ejpam-3539	348	86	)	)	PUNCT
ejpam-3539	348	87	;	;	PUNCT
ejpam-3539	348	88	using	use	VERB
ejpam-3539	348	89	coincidence	coincidence	NOUN
ejpam-3539	348	90	degree	degree	NOUN
ejpam-3539	348	91	theory	theory	NOUN
ejpam-3539	348	92	.	.	PUNCT
ejpam-3539	349	1	the	the	DET
ejpam-3539	349	2	results	result	NOUN
ejpam-3539	349	3	obtained	obtain	VERB
ejpam-3539	349	4	here	here	ADV
ejpam-3539	349	5	are	be	AUX
ejpam-3539	349	6	new	new	ADJ
ejpam-3539	349	7	and	and	CCONJ
ejpam-3539	349	8	complements	complement	VERB
ejpam-3539	349	9	existing	exist	VERB
ejpam-3539	349	10	results	result	NOUN
ejpam-3539	349	11	for	for	ADP
ejpam-3539	349	12	higher	high	ADJ
ejpam-3539	349	13	order	order	NOUN
ejpam-3539	349	14	boundary	boundary	ADJ
ejpam-3539	349	15	value	value	NOUN
ejpam-3539	349	16	problems	problem	NOUN
ejpam-3539	349	17	on	on	ADP
ejpam-3539	349	18	infinite	infinite	ADJ
ejpam-3539	349	19	intervals	interval	NOUN
ejpam-3539	349	20	.	.	PUNCT
ejpam-3539	350	1	acknowledgements	acknowledgement	NOUN
ejpam-3539	350	2	authors	author	NOUN
ejpam-3539	350	3	are	be	AUX
ejpam-3539	350	4	grateful	grateful	ADJ
ejpam-3539	350	5	to	to	ADP
ejpam-3539	350	6	covenant	covenant	ADJ
ejpam-3539	350	7	university	university	NOUN
ejpam-3539	350	8	for	for	ADP
ejpam-3539	350	9	financial	financial	ADJ
ejpam-3539	350	10	assistance	assistance	NOUN
ejpam-3539	350	11	and	and	CCONJ
ejpam-3539	350	12	the	the	DET
ejpam-3539	350	13	reviewers	reviewer	NOUN
ejpam-3539	350	14	for	for	ADP
ejpam-3539	350	15	their	their	PRON
ejpam-3539	350	16	useful	useful	ADJ
ejpam-3539	350	17	comments	comment	NOUN
ejpam-3539	350	18	.	.	PUNCT
ejpam-3539	351	1	references	reference	NOUN
ejpam-3539	351	2	[	[	X
ejpam-3539	351	3	1	1	NUM
ejpam-3539	351	4	]	]	X
ejpam-3539	351	5	r.p	r.p	PROPN
ejpam-3539	351	6	.	.	PROPN
ejpam-3539	351	7	agarwal	agarwal	PROPN
ejpam-3539	351	8	.	.	PUNCT
ejpam-3539	352	1	boundary	boundary	ADJ
ejpam-3539	352	2	value	value	NOUN
ejpam-3539	352	3	problem	problem	NOUN
ejpam-3539	352	4	for	for	ADP
ejpam-3539	352	5	higher	high	ADJ
ejpam-3539	352	6	order	order	NOUN
ejpam-3539	352	7	differential	differential	ADJ
ejpam-3539	352	8	equations	equation	NOUN
ejpam-3539	352	9	,	,	PUNCT
ejpam-3539	352	10	world	world	NOUN
ejpam-3539	352	11	scientific	scientific	PROPN
ejpam-3539	352	12	,	,	PUNCT
ejpam-3539	352	13	singapore	singapore	PROPN
ejpam-3539	352	14	1986	1986	NUM
ejpam-3539	352	15	.	.	PUNCT
ejpam-3539	353	1	[	[	X
ejpam-3539	353	2	2	2	NUM
ejpam-3539	353	3	]	]	X
ejpam-3539	353	4	r.p	r.p	PROPN
ejpam-3539	353	5	.	.	PROPN
ejpam-3539	353	6	agarwal	agarwal	PROPN
ejpam-3539	353	7	,	,	PUNCT
ejpam-3539	353	8	d.o	d.o	PROPN
ejpam-3539	353	9	.	.	PROPN
ejpam-3539	353	10	o’regan	o’regan	PROPN
ejpam-3539	353	11	.	.	PROPN
ejpam-3539	353	12	infinity	infinity	NOUN
ejpam-3539	353	13	interval	interval	NOUN
ejpam-3539	353	14	problems	problem	NOUN
ejpam-3539	353	15	for	for	ADP
ejpam-3539	353	16	difference	difference	NOUN
ejpam-3539	353	17	and	and	CCONJ
ejpam-3539	353	18	integral	integral	ADJ
ejpam-3539	353	19	equations	equation	NOUN
ejpam-3539	353	20	,	,	PUNCT
ejpam-3539	353	21	kluwer	kluwer	NOUN
ejpam-3539	353	22	academic	academic	ADJ
ejpam-3539	353	23	publisher	publisher	NOUN
ejpam-3539	353	24	.	.	PUNCT
ejpam-3539	354	1	derdrecht	derdrecht	NOUN
ejpam-3539	354	2	2001	2001	NUM
ejpam-3539	354	3	.	.	PUNCT
ejpam-3539	355	1	[	[	X
ejpam-3539	355	2	3	3	X
ejpam-3539	355	3	]	]	X
ejpam-3539	355	4	a.v	a.v	PROPN
ejpam-3539	355	5	.	.	PROPN
ejpam-3539	355	6	bicadze	bicadze	PROPN
ejpam-3539	355	7	and	and	CCONJ
ejpam-3539	355	8	a.a	a.a	PROPN
ejpam-3539	355	9	.	.	PROPN
ejpam-3539	355	10	samarskii	samarskii	PROPN
ejpam-3539	355	11	.	.	PUNCT
ejpam-3539	356	1	some	some	DET
ejpam-3539	356	2	elementary	elementary	ADJ
ejpam-3539	356	3	generalisations	generalisation	NOUN
ejpam-3539	356	4	of	of	ADP
ejpam-3539	356	5	linear	linear	PROPN
ejpam-3539	356	6	elliptic	elliptic	ADJ
ejpam-3539	356	7	boundary	boundary	ADJ
ejpam-3539	356	8	value	value	NOUN
ejpam-3539	356	9	problems	problem	NOUN
ejpam-3539	356	10	,	,	PUNCT
ejpam-3539	356	11	dokhady	dokhady	ADJ
ejpam-3539	356	12	nauk	nauk	PROPN
ejpam-3539	356	13	sssr	sssr	NOUN
ejpam-3539	356	14	,	,	PUNCT
ejpam-3539	356	15	185(1969	185(1969	NUM
ejpam-3539	356	16	)	)	PUNCT
ejpam-3539	356	17	739–749	739–749	NUM
ejpam-3539	356	18	.	.	PUNCT
ejpam-3539	357	1	references	reference	NOUN
ejpam-3539	357	2	46	46	NUM
ejpam-3539	358	1	[	[	X
ejpam-3539	358	2	4	4	NUM
ejpam-3539	358	3	]	]	X
ejpam-3539	358	4	y.	y.	PROPN
ejpam-3539	358	5	cui	cui	PROPN
ejpam-3539	358	6	.	.	PUNCT
ejpam-3539	359	1	solvability	solvability	NOUN
ejpam-3539	359	2	of	of	ADP
ejpam-3539	359	3	second	second	ADJ
ejpam-3539	359	4	order	order	NOUN
ejpam-3539	359	5	boundary	boundary	ADJ
ejpam-3539	359	6	value	value	NOUN
ejpam-3539	359	7	problems	problem	NOUN
ejpam-3539	359	8	at	at	ADP
ejpam-3539	359	9	resonance	resonance	NOUN
ejpam-3539	359	10	involving	involve	VERB
ejpam-3539	359	11	integral	integral	ADJ
ejpam-3539	359	12	conditions	condition	NOUN
ejpam-3539	359	13	,	,	PUNCT
ejpam-3539	359	14	electron	electron	NOUN
ejpam-3539	359	15	j.	j.	PROPN
ejpam-3539	359	16	differential	differential	PROPN
ejpam-3539	359	17	equation	equation	PROPN
ejpam-3539	359	18	,	,	PUNCT
ejpam-3539	359	19	45(2012	45(2012	NUM
ejpam-3539	359	20	)	)	PUNCT
ejpam-3539	359	21	1–9	1–9	NOUN
ejpam-3539	359	22	.	.	PUNCT
ejpam-3539	360	1	[	[	X
ejpam-3539	360	2	5	5	X
ejpam-3539	360	3	]	]	PUNCT
ejpam-3539	360	4	z.	z.	PROPN
ejpam-3539	360	5	i.	i.	PROPN
ejpam-3539	360	6	du	du	PROPN
ejpam-3539	360	7	,	,	PUNCT
ejpam-3539	360	8	x.i	x.i	PROPN
ejpam-3539	360	9	.	.	PROPN
ejpam-3539	360	10	lin	lin	PROPN
ejpam-3539	360	11	,	,	PUNCT
ejpam-3539	360	12	h.g	h.g	PROPN
ejpam-3539	360	13	.	.	PROPN
ejpam-3539	360	14	ge	ge	PROPN
ejpam-3539	360	15	.	.	PUNCT
ejpam-3539	361	1	some	some	DET
ejpam-3539	361	2	higher	high	ADJ
ejpam-3539	361	3	-	-	PUNCT
ejpam-3539	361	4	order	order	NOUN
ejpam-3539	361	5	multipoint	multipoint	NOUN
ejpam-3539	361	6	boundary	boundary	ADJ
ejpam-3539	361	7	value	value	NOUN
ejpam-3539	361	8	problems	problem	NOUN
ejpam-3539	361	9	at	at	ADP
ejpam-3539	361	10	resonance	resonance	NOUN
ejpam-3539	361	11	,	,	PUNCT
ejpam-3539	361	12	j.	j.	PROPN
ejpam-3539	361	13	comput	comput	PROPN
ejpam-3539	361	14	.	.	PUNCT
ejpam-3539	362	1	appl	appl	PROPN
ejpam-3539	362	2	.	.	PROPN
ejpam-3539	362	3	math	math	NOUN
ejpam-3539	362	4	.	.	PUNCT
ejpam-3539	363	1	177	177	NUM
ejpam-3539	363	2	(	(	PUNCT
ejpam-3539	363	3	2015	2015	NUM
ejpam-3539	363	4	)	)	PUNCT
ejpam-3539	363	5	,	,	PUNCT
ejpam-3539	363	6	55–65	55–65	NUM
ejpam-3539	363	7	.	.	PUNCT
ejpam-3539	364	1	[	[	X
ejpam-3539	364	2	6	6	NUM
ejpam-3539	364	3	]	]	PUNCT
ejpam-3539	364	4	d.	d.	PROPN
ejpam-3539	364	5	franco	franco	PROPN
ejpam-3539	364	6	,	,	PUNCT
ejpam-3539	364	7	g.	g.	PROPN
ejpam-3539	364	8	infante	infante	PROPN
ejpam-3539	364	9	,	,	PUNCT
ejpam-3539	364	10	m.	m.	PROPN
ejpam-3539	364	11	zima	zima	PROPN
ejpam-3539	364	12	.	.	PUNCT
ejpam-3539	365	1	second	second	ADJ
ejpam-3539	365	2	order	order	NOUN
ejpam-3539	365	3	nonlocal	nonlocal	ADJ
ejpam-3539	365	4	boundary	boundary	ADJ
ejpam-3539	365	5	value	value	NOUN
ejpam-3539	365	6	problems	problem	NOUN
ejpam-3539	365	7	at	at	ADP
ejpam-3539	365	8	resonance	resonance	NOUN
ejpam-3539	365	9	math	math	NOUN
ejpam-3539	365	10	.	.	PUNCT
ejpam-3539	366	1	nachr	nachr	PROPN
ejpam-3539	366	2	.	.	PUNCT
ejpam-3539	367	1	284	284	NUM
ejpam-3539	367	2	(	(	PUNCT
ejpam-3539	367	3	7	7	NUM
ejpam-3539	367	4	)	)	PUNCT
ejpam-3539	367	5	(	(	PUNCT
ejpam-3539	367	6	2011	2011	NUM
ejpam-3539	367	7	)	)	PUNCT
ejpam-3539	367	8	.	.	PUNCT
ejpam-3539	368	1	[	[	X
ejpam-3539	368	2	7	7	X
ejpam-3539	368	3	]	]	PUNCT
ejpam-3539	368	4	a.	a.	NOUN
ejpam-3539	368	5	frioui	frioui	PROPN
ejpam-3539	368	6	,	,	PUNCT
ejpam-3539	368	7	a	a	DET
ejpam-3539	368	8	guezane	guezane	NOUN
ejpam-3539	368	9	-	-	PUNCT
ejpam-3539	368	10	lakoud	lakoud	NOUN
ejpam-3539	368	11	,	,	PUNCT
ejpam-3539	368	12	r.	r.	PROPN
ejpam-3539	368	13	khaldi	khaldi	PROPN
ejpam-3539	368	14	.	.	PUNCT
ejpam-3539	369	1	higher	high	ADJ
ejpam-3539	369	2	order	order	NOUN
ejpam-3539	369	3	boundary	boundary	ADJ
ejpam-3539	369	4	value	value	NOUN
ejpam-3539	369	5	problems	problem	NOUN
ejpam-3539	369	6	at	at	ADP
ejpam-3539	369	7	resonance	resonance	NOUN
ejpam-3539	369	8	on	on	ADP
ejpam-3539	369	9	an	an	DET
ejpam-3539	369	10	unbounded	unbounded	ADJ
ejpam-3539	369	11	interval	interval	NOUN
ejpam-3539	369	12	electronic	electronic	NOUN
ejpam-3539	369	13	,	,	PUNCT
ejpam-3539	369	14	j.	j.	PROPN
ejpam-3539	369	15	diff	diff	PROPN
ejpam-3539	369	16	.	.	PUNCT
ejpam-3539	370	1	equation	equation	NOUN
ejpam-3539	370	2	,	,	PUNCT
ejpam-3539	370	3	29(2016	29(2016	NUM
ejpam-3539	370	4	)	)	PUNCT
ejpam-3539	370	5	,	,	PUNCT
ejpam-3539	370	6	1–10	1–10	NOUN
ejpam-3539	370	7	.	.	PUNCT
ejpam-3539	371	1	[	[	X
ejpam-3539	371	2	8	8	NUM
ejpam-3539	371	3	]	]	X
ejpam-3539	371	4	s.a	s.a	PROPN
ejpam-3539	371	5	.	.	PROPN
ejpam-3539	371	6	iyase	iyase	PROPN
ejpam-3539	371	7	on	on	ADP
ejpam-3539	371	8	a	a	DET
ejpam-3539	371	9	third	third	ADJ
ejpam-3539	371	10	-	-	PUNCT
ejpam-3539	371	11	order	order	NOUN
ejpam-3539	371	12	boundary	boundary	ADJ
ejpam-3539	371	13	value	value	NOUN
ejpam-3539	371	14	problem	problem	NOUN
ejpam-3539	371	15	at	at	ADP
ejpam-3539	371	16	resonance	resonance	NOUN
ejpam-3539	371	17	on	on	ADP
ejpam-3539	371	18	the	the	DET
ejpam-3539	371	19	half	half	ADJ
ejpam-3539	371	20	-	-	PUNCT
ejpam-3539	371	21	line	line	NOUN
ejpam-3539	371	22	,	,	PUNCT
ejpam-3539	371	23	arabian	arabian	ADJ
ejpam-3539	371	24	journal	journal	NOUN
ejpam-3539	371	25	of	of	ADP
ejpam-3539	371	26	mathematics	mathematic	NOUN
ejpam-3539	371	27	,	,	PUNCT
ejpam-3539	371	28	8(2019	8(2019	NUM
ejpam-3539	371	29	)	)	PUNCT
ejpam-3539	371	30	,	,	PUNCT
ejpam-3539	371	31	43–53	43–53	NOUN
ejpam-3539	371	32	.	.	PUNCT
ejpam-3539	372	1	https://doi.org/10.1007/s40065018-0209-5	https://doi.org/10.1007/s40065018-0209-5	PROPN
ejpam-3539	372	2	.	.	PUNCT
ejpam-3539	373	1	[	[	X
ejpam-3539	373	2	9	9	NUM
ejpam-3539	373	3	]	]	X
ejpam-3539	373	4	s.a	s.a	PROPN
ejpam-3539	373	5	.	.	PROPN
ejpam-3539	373	6	iyase	iyase	PROPN
ejpam-3539	373	7	and	and	CCONJ
ejpam-3539	373	8	o.f	o.f	PROPN
ejpam-3539	373	9	.	.	PROPN
ejpam-3539	373	10	imaga	imaga	PROPN
ejpam-3539	373	11	.	.	PUNCT
ejpam-3539	374	1	on	on	ADP
ejpam-3539	374	2	a	a	DET
ejpam-3539	374	3	singular	singular	ADJ
ejpam-3539	374	4	second	second	ADJ
ejpam-3539	374	5	-	-	PUNCT
ejpam-3539	374	6	order	order	NOUN
ejpam-3539	374	7	multipoint	multipoint	NOUN
ejpam-3539	374	8	boundary	boundary	ADJ
ejpam-3539	374	9	value	value	NOUN
ejpam-3539	374	10	problem	problem	NOUN
ejpam-3539	374	11	at	at	ADP
ejpam-3539	374	12	resonance	resonance	NOUN
ejpam-3539	374	13	,	,	PUNCT
ejpam-3539	374	14	international	international	ADJ
ejpam-3539	374	15	journal	journal	NOUN
ejpam-3539	374	16	of	of	ADP
ejpam-3539	374	17	differential	differential	ADJ
ejpam-3539	374	18	equations	equation	NOUN
ejpam-3539	374	19	,	,	PUNCT
ejpam-3539	374	20	(	(	PUNCT
ejpam-3539	374	21	2017	2017	NUM
ejpam-3539	374	22	)	)	PUNCT
ejpam-3539	374	23	,	,	PUNCT
ejpam-3539	374	24	1–6	1–6	X
ejpam-3539	374	25	.	.	PUNCT
ejpam-3539	375	1	id8579065	id8579065	PROPN
ejpam-3539	375	2	.	.	PUNCT
ejpam-3539	376	1	[	[	X
ejpam-3539	376	2	10	10	NUM
ejpam-3539	376	3	]	]	X
ejpam-3539	376	4	g.l	g.l	PROPN
ejpam-3539	376	5	.	.	PROPN
ejpam-3539	376	6	karakistas	karakistas	PROPN
ejpam-3539	376	7	and	and	CCONJ
ejpam-3539	376	8	p.isamatos	p.isamato	NOUN
ejpam-3539	376	9	.	.	PUNCT
ejpam-3539	377	1	sufficient	sufficient	ADJ
ejpam-3539	377	2	conditions	condition	NOUN
ejpam-3539	377	3	for	for	ADP
ejpam-3539	377	4	the	the	DET
ejpam-3539	377	5	existence	existence	NOUN
ejpam-3539	377	6	of	of	ADP
ejpam-3539	377	7	nonnegative	nonnegative	ADJ
ejpam-3539	377	8	solutions	solution	NOUN
ejpam-3539	377	9	of	of	ADP
ejpam-3539	377	10	a	a	DET
ejpam-3539	377	11	nonlcal	nonlcal	ADJ
ejpam-3539	377	12	boundary	boundary	ADJ
ejpam-3539	377	13	value	value	NOUN
ejpam-3539	377	14	problem	problem	NOUN
ejpam-3539	377	15	,	,	PUNCT
ejpam-3539	377	16	applied	apply	VERB
ejpam-3539	377	17	mathematics	mathematics	NOUN
ejpam-3539	377	18	letters	letter	NOUN
ejpam-3539	377	19	,	,	PUNCT
ejpam-3539	377	20	15(4)(2002	15(4)(2002	NUM
ejpam-3539	377	21	)	)	PUNCT
ejpam-3539	377	22	,	,	PUNCT
ejpam-3539	377	23	401–407	401–407	NUM
ejpam-3539	377	24	.	.	PUNCT
ejpam-3539	378	1	[	[	X
ejpam-3539	378	2	11	11	NUM
ejpam-3539	378	3	]	]	PUNCT
ejpam-3539	378	4	a.m.	a.m.	PROPN
ejpam-3539	378	5	krosnosel’skii	krosnosel’skii	PROPN
ejpam-3539	378	6	,	,	PUNCT
ejpam-3539	378	7	j.	j.	PROPN
ejpam-3539	378	8	mawhin	mawhin	PROPN
ejpam-3539	378	9	.	.	PUNCT
ejpam-3539	379	1	on	on	ADP
ejpam-3539	379	2	some	some	DET
ejpam-3539	379	3	higher	high	ADJ
ejpam-3539	379	4	order	order	NOUN
ejpam-3539	379	5	boundary	boundary	ADJ
ejpam-3539	379	6	value	value	NOUN
ejpam-3539	379	7	problems	problem	NOUN
ejpam-3539	379	8	at	at	ADP
ejpam-3539	379	9	resonance	resonance	NOUN
ejpam-3539	379	10	,	,	PUNCT
ejpam-3539	379	11	nonlinear	nonlinear	ADJ
ejpam-3539	379	12	anal	anal	NOUN
ejpam-3539	379	13	.	.	PUNCT
ejpam-3539	380	1	24	24	NUM
ejpam-3539	380	2	(	(	PUNCT
ejpam-3539	380	3	1995	1995	NUM
ejpam-3539	380	4	)	)	PUNCT
ejpam-3539	380	5	,	,	PUNCT
ejpam-3539	380	6	1411–1148	1411–1148	NUM
ejpam-3539	380	7	.	.	PUNCT
ejpam-3539	381	1	[	[	X
ejpam-3539	381	2	12	12	NUM
ejpam-3539	381	3	]	]	X
ejpam-3539	381	4	h.r	h.r	PROPN
ejpam-3539	381	5	.	.	PROPN
ejpam-3539	381	6	lian	lian	PROPN
ejpam-3539	381	7	,	,	PUNCT
ejpam-3539	381	8	h.h	h.h	PROPN
ejpam-3539	381	9	.	.	PROPN
ejpam-3539	381	10	pang	pang	PROPN
ejpam-3539	381	11	,	,	PUNCT
ejpam-3539	381	12	w.g	w.g	PROPN
ejpam-3539	381	13	.	.	PROPN
ejpam-3539	381	14	ge	ge	PROPN
ejpam-3539	381	15	.	.	PROPN
ejpam-3539	381	16	solvability	solvability	PROPN
ejpam-3539	381	17	for	for	ADP
ejpam-3539	381	18	second	second	ADJ
ejpam-3539	381	19	order	order	NOUN
ejpam-3539	381	20	three	three	NUM
ejpam-3539	381	21	point	point	NOUN
ejpam-3539	381	22	boundaryvalue	boundaryvalue	NOUN
ejpam-3539	381	23	problems	problem	NOUN
ejpam-3539	381	24	at	at	ADP
ejpam-3539	381	25	resonance	resonance	NOUN
ejpam-3539	381	26	on	on	ADP
ejpam-3539	381	27	a	a	DET
ejpam-3539	381	28	half	half	ADJ
ejpam-3539	381	29	-	-	PUNCT
ejpam-3539	381	30	line	line	NOUN
ejpam-3539	381	31	.	.	PUNCT
ejpam-3539	382	1	j.	j.	PROPN
ejpam-3539	382	2	math	math	PROPN
ejpam-3539	382	3	.	.	PUNCT
ejpam-3539	383	1	anal	anal	PROPN
ejpam-3539	383	2	.	.	PUNCT
ejpam-3539	383	3	appl	appl	PROPN
ejpam-3539	383	4	.	.	PUNCT
ejpam-3539	384	1	337	337	NUM
ejpam-3539	384	2	(	(	PUNCT
ejpam-3539	384	3	2008	2008	NUM
ejpam-3539	384	4	)	)	PUNCT
ejpam-3539	384	5	,	,	PUNCT
ejpam-3539	384	6	1171–1181	1171–1181	NUM
ejpam-3539	384	7	.	.	PUNCT
ejpam-3539	385	1	[	[	X
ejpam-3539	385	2	13	13	NUM
ejpam-3539	385	3	]	]	SYM
ejpam-3539	385	4	x.j	x.j	PROPN
ejpam-3539	385	5	.	.	PROPN
ejpam-3539	385	6	lin	lin	PROPN
ejpam-3539	385	7	,	,	PUNCT
ejpam-3539	385	8	z.j	z.j	PROPN
ejpam-3539	385	9	.	.	PROPN
ejpam-3539	385	10	du	du	PROPN
ejpam-3539	385	11	,	,	PUNCT
ejpam-3539	385	12	w.g	w.g	PROPN
ejpam-3539	385	13	.	.	PROPN
ejpam-3539	385	14	ge	ge	PROPN
ejpam-3539	385	15	.	.	PROPN
ejpam-3539	386	1	solvability	solvability	PROPN
ejpam-3539	386	2	of	of	ADP
ejpam-3539	386	3	multipoint	multipoint	PROPN
ejpam-3539	386	4	boundary	boundary	ADJ
ejpam-3539	386	5	value	value	NOUN
ejpam-3539	386	6	problems	problem	NOUN
ejpam-3539	386	7	at	at	ADP
ejpam-3539	386	8	resonance	resonance	NOUN
ejpam-3539	386	9	for	for	ADP
ejpam-3539	386	10	higher	high	ADJ
ejpam-3539	386	11	order	order	NOUN
ejpam-3539	386	12	ordinary	ordinary	ADJ
ejpam-3539	386	13	differential	differential	ADJ
ejpam-3539	386	14	equations	equation	NOUN
ejpam-3539	386	15	,	,	PUNCT
ejpam-3539	386	16	comput	comput	NOUN
ejpam-3539	386	17	.	.	PUNCT
ejpam-3539	387	1	math	math	NOUN
ejpam-3539	387	2	.	.	PUNCT
ejpam-3539	388	1	appl	appl	PROPN
ejpam-3539	388	2	.	.	PROPN
ejpam-3539	389	1	49	49	NUM
ejpam-3539	389	2	(	(	PUNCT
ejpam-3539	389	3	2005	2005	NUM
ejpam-3539	389	4	)	)	PUNCT
ejpam-3539	389	5	,	,	PUNCT
ejpam-3539	389	6	1–11	1–11	PROPN
ejpam-3539	389	7	.	.	PUNCT
ejpam-3539	390	1	[	[	X
ejpam-3539	390	2	14	14	NUM
ejpam-3539	390	3	]	]	PUNCT
ejpam-3539	390	4	x.	x.	NOUN
ejpam-3539	390	5	lin	lin	PROPN
ejpam-3539	390	6	.	.	PUNCT
ejpam-3539	391	1	existence	existence	NOUN
ejpam-3539	391	2	of	of	ADP
ejpam-3539	391	3	solutions	solution	NOUN
ejpam-3539	391	4	to	to	ADP
ejpam-3539	391	5	a	a	DET
ejpam-3539	391	6	nonlocal	nonlocal	ADJ
ejpam-3539	391	7	boundary	boundary	ADJ
ejpam-3539	391	8	value	value	NOUN
ejpam-3539	391	9	problem	problem	NOUN
ejpam-3539	391	10	with	with	ADP
ejpam-3539	391	11	nonlinear	nonlinear	ADJ
ejpam-3539	391	12	growth	growth	NOUN
ejpam-3539	391	13	.	.	PUNCT
ejpam-3539	392	1	boundary	boundary	ADJ
ejpam-3539	392	2	value	value	NOUN
ejpam-3539	392	3	problems.(2011	problems.(2011	NOUN
ejpam-3539	392	4	)	)	PUNCT
ejpam-3539	392	5	doi	doi	NOUN
ejpam-3539	392	6	:	:	PUNCT
ejpam-3539	392	7	10.1155/2011/416416	10.1155/2011/416416	NUM
ejpam-3539	392	8	.	.	PUNCT
ejpam-3539	393	1	[	[	X
ejpam-3539	393	2	15	15	NUM
ejpam-3539	393	3	]	]	X
ejpam-3539	393	4	y.	y.	PROPN
ejpam-3539	393	5	liu	liu	PROPN
ejpam-3539	393	6	.	.	PUNCT
ejpam-3539	394	1	w.ge	w.ge	PROPN
ejpam-3539	394	2	solutions	solution	NOUN
ejpam-3539	394	3	of	of	ADP
ejpam-3539	394	4	a	a	DET
ejpam-3539	394	5	multipoint	multipoint	NOUN
ejpam-3539	394	6	boundary	boundary	ADJ
ejpam-3539	394	7	value	value	NOUN
ejpam-3539	394	8	problem	problem	NOUN
ejpam-3539	394	9	for	for	ADP
ejpam-3539	394	10	higher	high	ADJ
ejpam-3539	394	11	order	order	NOUN
ejpam-3539	394	12	differential	differential	ADJ
ejpam-3539	394	13	equations	equation	NOUN
ejpam-3539	394	14	at	at	ADP
ejpam-3539	394	15	resonance	resonance	NOUN
ejpam-3539	394	16	.	.	PUNCT
ejpam-3539	395	1	tamakang	tamakang	PROPN
ejpam-3539	395	2	.	.	PUNCT
ejpam-3539	396	1	journal	journal	PROPN
ejpam-3539	396	2	of	of	ADP
ejpam-3539	396	3	maths	math	NOUN
ejpam-3539	396	4	36(2)(2005	36(2)(2005	NUM
ejpam-3539	396	5	)	)	PUNCT
ejpam-3539	396	6	,	,	PUNCT
ejpam-3539	396	7	119–130	119–130	NUM
ejpam-3539	396	8	.	.	PUNCT
ejpam-3539	397	1	[	[	X
ejpam-3539	397	2	16	16	NUM
ejpam-3539	397	3	]	]	X
ejpam-3539	397	4	y.	y.	PROPN
ejpam-3539	397	5	liu	liu	PROPN
ejpam-3539	397	6	,	,	PUNCT
ejpam-3539	397	7	d.li	d.li	PROPN
ejpam-3539	397	8	,	,	PUNCT
ejpam-3539	397	9	m.	m.	NOUN
ejpam-3539	397	10	fang	fang	PROPN
ejpam-3539	397	11	.	.	PUNCT
ejpam-3539	397	12	solvability	solvability	NOUN
ejpam-3539	397	13	for	for	ADP
ejpam-3539	397	14	second	second	ADJ
ejpam-3539	397	15	order	order	NOUN
ejpam-3539	397	16	m	m	NOUN
ejpam-3539	397	17	-	-	PUNCT
ejpam-3539	397	18	point	point	NOUN
ejpam-3539	397	19	boundary	boundary	ADJ
ejpam-3539	397	20	value	value	NOUN
ejpam-3539	397	21	problems	problem	NOUN
ejpam-3539	397	22	on	on	ADP
ejpam-3539	397	23	the	the	DET
ejpam-3539	397	24	half	half	ADJ
ejpam-3539	397	25	-	-	PUNCT
ejpam-3539	397	26	line	line	NOUN
ejpam-3539	397	27	.	.	PUNCT
ejpam-3539	398	1	electron	electron	PROPN
ejpam-3539	398	2	j.	j.	PROPN
ejpam-3539	398	3	of	of	ADP
ejpam-3539	398	4	diff	diff	PROPN
ejpam-3539	398	5	.	.	PUNCT
ejpam-3539	399	1	equation	equation	NOUN
ejpam-3539	399	2	,	,	PUNCT
ejpam-3539	399	3	13(2009	13(2009	NUM
ejpam-3539	399	4	)	)	PUNCT
ejpam-3539	399	5	,	,	PUNCT
ejpam-3539	399	6	1–11	1–11	PROPN
ejpam-3539	399	7	.	.	PUNCT
ejpam-3539	400	1	[	[	X
ejpam-3539	400	2	17	17	NUM
ejpam-3539	400	3	]	]	PUNCT
ejpam-3539	400	4	j.	j.	PROPN
ejpam-3539	400	5	mawhin	mawhin	PROPN
ejpam-3539	400	6	.	.	PUNCT
ejpam-3539	401	1	topological	topological	ADJ
ejpam-3539	401	2	degree	degree	NOUN
ejpam-3539	401	3	methods	method	NOUN
ejpam-3539	401	4	in	in	ADP
ejpam-3539	401	5	nonlinear	nonlinear	ADJ
ejpam-3539	401	6	boundary	boundary	ADJ
ejpam-3539	401	7	value	value	NOUN
ejpam-3539	401	8	problems	problem	NOUN
ejpam-3539	401	9	.	.	PUNCT
ejpam-3539	402	1	nsfcbms	nsfcbms	NOUN
ejpam-3539	402	2	.	.	PUNCT
ejpam-3539	403	1	regional	regional	ADJ
ejpam-3539	403	2	conference	conference	NOUN
ejpam-3539	403	3	series	series	NOUN
ejpam-3539	403	4	in	in	ADP
ejpam-3539	403	5	math	math	NOUN
ejpam-3539	403	6	.	.	PUNCT
ejpam-3539	404	1	vol	vol	NOUN
ejpam-3539	404	2	.	.	PROPN
ejpam-3539	405	1	40	40	NUM
ejpam-3539	405	2	.	.	PUNCT
ejpam-3539	406	1	americ	americ	PROPN
ejpam-3539	406	2	.	.	PUNCT
ejpam-3539	406	3	math	math	NOUN
ejpam-3539	406	4	.	.	PUNCT
ejpam-3539	407	1	soc	soc	PROPN
ejpam-3539	407	2	.	.	PUNCT
ejpam-3539	408	1	providence	providence	NOUN
ejpam-3539	408	2	ri	ri	PROPN
ejpam-3539	408	3	1979	1979	NUM
ejpam-3539	408	4	.	.	PUNCT
ejpam-3539	409	1	references	reference	NOUN
ejpam-3539	409	2	47	47	NUM
ejpam-3539	409	3	[	[	X
ejpam-3539	409	4	18	18	NUM
ejpam-3539	409	5	]	]	SYM
ejpam-3539	409	6	j.r.l	j.r.l	NOUN
ejpam-3539	409	7	.	.	PUNCT
ejpam-3539	409	8	webb	webb	PROPN
ejpam-3539	409	9	,	,	PUNCT
ejpam-3539	409	10	g.	g.	PROPN
ejpam-3539	409	11	infante	infante	PROPN
ejpam-3539	409	12	.	.	PUNCT
ejpam-3539	410	1	positive	positive	ADJ
ejpam-3539	410	2	solutions	solution	NOUN
ejpam-3539	410	3	of	of	ADP
ejpam-3539	410	4	nonlocal	nonlocal	ADJ
ejpam-3539	410	5	boundary	boundary	ADJ
ejpam-3539	410	6	value	value	NOUN
ejpam-3539	410	7	problems	problem	NOUN
ejpam-3539	410	8	involving	involve	VERB
ejpam-3539	410	9	integral	integral	ADJ
ejpam-3539	410	10	conditions	condition	NOUN
ejpam-3539	410	11	.	.	PUNCT
ejpam-3539	411	1	nonlinear	nonlinear	ADJ
ejpam-3539	411	2	differential	differential	ADJ
ejpam-3539	411	3	equations	equation	NOUN
ejpam-3539	411	4	.	.	PUNCT
ejpam-3539	412	1	appl	appl	PROPN
ejpam-3539	412	2	.	.	PUNCT
ejpam-3539	413	1	15(2008	15(2008	NUM
ejpam-3539	413	2	)	)	PUNCT
ejpam-3539	413	3	,	,	PUNCT
ejpam-3539	413	4	45–67	45–67	NUM
ejpam-3539	413	5	.	.	PUNCT
ejpam-3539	414	1	[	[	X
ejpam-3539	414	2	19	19	NUM
ejpam-3539	414	3	]	]	PUNCT
ejpam-3539	414	4	m.	m.	NOUN
ejpam-3539	414	5	zima	zima	PROPN
ejpam-3539	414	6	.	.	PUNCT
ejpam-3539	415	1	on	on	ADP
ejpam-3539	415	2	positive	positive	ADJ
ejpam-3539	415	3	solutions	solution	NOUN
ejpam-3539	415	4	of	of	ADP
ejpam-3539	415	5	boundary	boundary	ADJ
ejpam-3539	415	6	value	value	NOUN
ejpam-3539	415	7	problems	problem	NOUN
ejpam-3539	415	8	on	on	ADP
ejpam-3539	415	9	the	the	DET
ejpam-3539	415	10	half	half	ADJ
ejpam-3539	415	11	-	-	PUNCT
ejpam-3539	415	12	line	line	NOUN
ejpam-3539	415	13	.	.	PUNCT
ejpam-3539	416	1	j.	j.	PROPN
ejpam-3539	416	2	math	math	PROPN
ejpam-3539	416	3	.	.	PUNCT
ejpam-3539	417	1	anal	anal	PROPN
ejpam-3539	417	2	.	.	PUNCT
ejpam-3539	417	3	appl	appl	PROPN
ejpam-3539	417	4	.	.	PUNCT
ejpam-3539	418	1	259	259	NUM
ejpam-3539	418	2	(	(	PUNCT
ejpam-3539	418	3	2001	2001	NUM
ejpam-3539	418	4	)	)	PUNCT
ejpam-3539	418	5	,	,	PUNCT
ejpam-3539	418	6	127–136	127–136	NUM