id	sid	tid	token	lemma	pos
ejpam-6157	1	1	european	european	PROPN
ejpam-6157	1	2	journal	journal	PROPN
ejpam-6157	1	3	of	of	ADP
ejpam-6157	1	4	pure	pure	ADJ
ejpam-6157	1	5	and	and	CCONJ
ejpam-6157	1	6	applied	applied	ADJ
ejpam-6157	1	7	mathematics	mathematic	NOUN
ejpam-6157	1	8	2025	2025	NUM
ejpam-6157	1	9	,	,	PUNCT
ejpam-6157	1	10	vol	vol	NOUN
ejpam-6157	1	11	.	.	PROPN
ejpam-6157	1	12	18	18	NUM
ejpam-6157	1	13	,	,	PUNCT
ejpam-6157	1	14	issue	issue	NOUN
ejpam-6157	1	15	2	2	NUM
ejpam-6157	1	16	,	,	PUNCT
ejpam-6157	1	17	article	article	NOUN
ejpam-6157	1	18	number	number	NOUN
ejpam-6157	1	19	6157	6157	NUM
ejpam-6157	1	20	issn	issn	VERB
ejpam-6157	1	21	1307	1307	NUM
ejpam-6157	1	22	-	-	SYM
ejpam-6157	1	23	5543	5543	NUM
ejpam-6157	1	24	–	–	PUNCT
ejpam-6157	1	25	ejpam.com	ejpam.com	X
ejpam-6157	1	26	published	publish	VERB
ejpam-6157	1	27	by	by	ADP
ejpam-6157	1	28	new	new	PROPN
ejpam-6157	1	29	york	york	PROPN
ejpam-6157	1	30	business	business	PROPN
ejpam-6157	1	31	global	global	ADJ
ejpam-6157	1	32	on	on	ADP
ejpam-6157	1	33	qualitative	qualitative	ADJ
ejpam-6157	1	34	properties	property	NOUN
ejpam-6157	1	35	of	of	ADP
ejpam-6157	1	36	lθ	lθ	NOUN
ejpam-6157	1	37	-	-	PUNCT
ejpam-6157	1	38	solutions	solution	NOUN
ejpam-6157	1	39	for	for	ADP
ejpam-6157	1	40	coupled	couple	VERB
ejpam-6157	1	41	systems	system	NOUN
ejpam-6157	1	42	of	of	ADP
ejpam-6157	1	43	hadamard	hadamard	ADJ
ejpam-6157	1	44	-	-	PUNCT
ejpam-6157	1	45	type	type	NOUN
ejpam-6157	1	46	fractional	fractional	ADJ
ejpam-6157	1	47	integral	integral	ADJ
ejpam-6157	1	48	equations	equation	NOUN
ejpam-6157	1	49	in	in	ADP
ejpam-6157	1	50	banach	banach	NOUN
ejpam-6157	1	51	spaces	space	NOUN
ejpam-6157	1	52	mohamed	mohamed	PROPN
ejpam-6157	1	53	m.a	m.a	PROPN
ejpam-6157	1	54	.	.	PROPN
ejpam-6157	2	1	metwali1,2,∗	metwali1,2,∗	PROPN
ejpam-6157	2	2	,	,	PUNCT
ejpam-6157	2	3	shami	shami	PROPN
ejpam-6157	2	4	a.	a.	PROPN
ejpam-6157	2	5	m.	m.	PROPN
ejpam-6157	2	6	alsallami3	alsallami3	PROPN
ejpam-6157	3	1	1	1	NUM
ejpam-6157	3	2	department	department	NOUN
ejpam-6157	3	3	of	of	ADP
ejpam-6157	3	4	mathematics	mathematic	NOUN
ejpam-6157	3	5	,	,	PUNCT
ejpam-6157	3	6	college	college	NOUN
ejpam-6157	3	7	of	of	ADP
ejpam-6157	3	8	science	science	NOUN
ejpam-6157	3	9	and	and	CCONJ
ejpam-6157	3	10	humanities	humanity	NOUN
ejpam-6157	3	11	in	in	ADP
ejpam-6157	3	12	alkharj	alkharj	NOUN
ejpam-6157	3	13	,	,	PUNCT
ejpam-6157	3	14	prince	prince	PROPN
ejpam-6157	3	15	sattam	sattam	PROPN
ejpam-6157	3	16	bin	bin	PROPN
ejpam-6157	3	17	abdulaziz	abdulaziz	PROPN
ejpam-6157	3	18	university	university	PROPN
ejpam-6157	3	19	,	,	PUNCT
ejpam-6157	3	20	alkharj	alkharj	VERB
ejpam-6157	3	21	11942	11942	NUM
ejpam-6157	3	22	,	,	PUNCT
ejpam-6157	3	23	saudi	saudi	PROPN
ejpam-6157	3	24	arabia	arabia	PROPN
ejpam-6157	3	25	2	2	NUM
ejpam-6157	3	26	department	department	NOUN
ejpam-6157	3	27	of	of	ADP
ejpam-6157	3	28	mathematics	mathematic	NOUN
ejpam-6157	3	29	and	and	CCONJ
ejpam-6157	3	30	computer	computer	NOUN
ejpam-6157	3	31	science	science	NOUN
ejpam-6157	3	32	,	,	PUNCT
ejpam-6157	3	33	faculty	faculty	NOUN
ejpam-6157	3	34	of	of	ADP
ejpam-6157	3	35	science	science	NOUN
ejpam-6157	3	36	,	,	PUNCT
ejpam-6157	3	37	damanhour	damanhour	NOUN
ejpam-6157	3	38	university	university	NOUN
ejpam-6157	3	39	,	,	PUNCT
ejpam-6157	3	40	damanhour	damanhour	NOUN
ejpam-6157	3	41	,	,	PUNCT
ejpam-6157	3	42	22511	22511	NUM
ejpam-6157	3	43	,	,	PUNCT
ejpam-6157	3	44	egypt	egypt	PROPN
ejpam-6157	3	45	3	3	NUM
ejpam-6157	3	46	mathematics	mathematics	PROPN
ejpam-6157	3	47	department	department	NOUN
ejpam-6157	3	48	,	,	PUNCT
ejpam-6157	3	49	college	college	NOUN
ejpam-6157	3	50	of	of	ADP
ejpam-6157	3	51	sciences	sciences	PROPN
ejpam-6157	3	52	,	,	PUNCT
ejpam-6157	3	53	umm	umm	INTJ
ejpam-6157	3	54	al	al	PROPN
ejpam-6157	3	55	-	-	PUNCT
ejpam-6157	3	56	qura	qura	PROPN
ejpam-6157	3	57	university	university	PROPN
ejpam-6157	3	58	,	,	PUNCT
ejpam-6157	3	59	makkah	makkah	PROPN
ejpam-6157	3	60	24381	24381	NUM
ejpam-6157	3	61	,	,	PUNCT
ejpam-6157	3	62	saudi	saudi	PROPN
ejpam-6157	3	63	arabia	arabia	PROPN
ejpam-6157	3	64	abstract	abstract	NOUN
ejpam-6157	3	65	.	.	PUNCT
ejpam-6157	4	1	in	in	ADP
ejpam-6157	4	2	this	this	DET
ejpam-6157	4	3	manuscript	manuscript	NOUN
ejpam-6157	4	4	,	,	PUNCT
ejpam-6157	4	5	the	the	DET
ejpam-6157	4	6	measure	measure	NOUN
ejpam-6157	4	7	of	of	ADP
ejpam-6157	4	8	noncompactness	noncompactness	ADJ
ejpam-6157	4	9	(	(	PUNCT
ejpam-6157	4	10	mnc	mnc	PROPN
ejpam-6157	4	11	)	)	PUNCT
ejpam-6157	4	12	,	,	PUNCT
ejpam-6157	4	13	darbo	darbo	NOUN
ejpam-6157	4	14	and	and	CCONJ
ejpam-6157	4	15	banach	banach	NOUN
ejpam-6157	4	16	contraction	contraction	NOUN
ejpam-6157	4	17	fixed	fix	VERB
ejpam-6157	4	18	point	point	NOUN
ejpam-6157	4	19	theorems	theorem	NOUN
ejpam-6157	4	20	(	(	PUNCT
ejpam-6157	4	21	fpt	fpt	NOUN
ejpam-6157	4	22	)	)	PUNCT
ejpam-6157	4	23	,	,	PUNCT
ejpam-6157	4	24	as	as	ADV
ejpam-6157	4	25	well	well	ADV
ejpam-6157	4	26	as	as	ADP
ejpam-6157	4	27	fractional	fractional	ADJ
ejpam-6157	4	28	calculus	calculus	NOUN
ejpam-6157	4	29	,	,	PUNCT
ejpam-6157	4	30	are	be	AUX
ejpam-6157	4	31	used	use	VERB
ejpam-6157	4	32	to	to	PART
ejpam-6157	4	33	carry	carry	VERB
ejpam-6157	4	34	out	out	ADP
ejpam-6157	4	35	the	the	DET
ejpam-6157	4	36	analysis	analysis	NOUN
ejpam-6157	4	37	of	of	ADP
ejpam-6157	4	38	the	the	DET
ejpam-6157	4	39	solvability	solvability	NOUN
ejpam-6157	4	40	of	of	ADP
ejpam-6157	4	41	a	a	DET
ejpam-6157	4	42	general	general	ADJ
ejpam-6157	4	43	but	but	CCONJ
ejpam-6157	4	44	abstract	abstract	ADJ
ejpam-6157	4	45	coupled	couple	VERB
ejpam-6157	4	46	system	system	NOUN
ejpam-6157	4	47	of	of	ADP
ejpam-6157	4	48	quadratic	quadratic	ADJ
ejpam-6157	4	49	hadamard	hadamard	ADJ
ejpam-6157	4	50	-	-	PUNCT
ejpam-6157	4	51	fractional	fractional	ADJ
ejpam-6157	4	52	integral	integral	ADJ
ejpam-6157	4	53	equations	equation	NOUN
ejpam-6157	4	54	in	in	ADP
ejpam-6157	4	55	orlicz	orlicz	PROPN
ejpam-6157	4	56	spaces	space	VERB
ejpam-6157	4	57	lθ	lθ	NOUN
ejpam-6157	4	58	.	.	PUNCT
ejpam-6157	5	1	several	several	ADJ
ejpam-6157	5	2	qualitative	qualitative	ADJ
ejpam-6157	5	3	properties	property	NOUN
ejpam-6157	5	4	of	of	ADP
ejpam-6157	5	5	the	the	DET
ejpam-6157	5	6	solution	solution	NOUN
ejpam-6157	5	7	to	to	ADP
ejpam-6157	5	8	the	the	DET
ejpam-6157	5	9	studied	study	VERB
ejpam-6157	5	10	coupled	couple	VERB
ejpam-6157	5	11	system	system	NOUN
ejpam-6157	5	12	are	be	AUX
ejpam-6157	5	13	established	establish	VERB
ejpam-6157	5	14	,	,	PUNCT
ejpam-6157	5	15	such	such	ADJ
ejpam-6157	5	16	as	as	ADP
ejpam-6157	5	17	the	the	DET
ejpam-6157	5	18	existence	existence	NOUN
ejpam-6157	5	19	,	,	PUNCT
ejpam-6157	5	20	monotonicity	monotonicity	NOUN
ejpam-6157	5	21	,	,	PUNCT
ejpam-6157	5	22	and	and	CCONJ
ejpam-6157	5	23	uniqueness	uniqueness	NOUN
ejpam-6157	5	24	,	,	PUNCT
ejpam-6157	5	25	in	in	ADP
ejpam-6157	5	26	addition	addition	NOUN
ejpam-6157	5	27	to	to	ADP
ejpam-6157	5	28	continuous	continuous	ADJ
ejpam-6157	5	29	dependence	dependence	NOUN
ejpam-6157	5	30	on	on	ADP
ejpam-6157	5	31	the	the	DET
ejpam-6157	5	32	data	datum	NOUN
ejpam-6157	5	33	.	.	PUNCT
ejpam-6157	6	1	we	we	PRON
ejpam-6157	6	2	conclude	conclude	VERB
ejpam-6157	6	3	with	with	ADP
ejpam-6157	6	4	some	some	DET
ejpam-6157	6	5	examples	example	NOUN
ejpam-6157	6	6	that	that	PRON
ejpam-6157	6	7	illustrate	illustrate	VERB
ejpam-6157	6	8	our	our	PRON
ejpam-6157	6	9	hypothesis	hypothesis	NOUN
ejpam-6157	6	10	.	.	PUNCT
ejpam-6157	7	1	2020	2020	NUM
ejpam-6157	7	2	mathematics	mathematic	NOUN
ejpam-6157	7	3	subject	subject	NOUN
ejpam-6157	7	4	classifications	classification	NOUN
ejpam-6157	7	5	:	:	PUNCT
ejpam-6157	7	6	47h30	47h30	NUM
ejpam-6157	7	7	,	,	PUNCT
ejpam-6157	7	8	45g10	45g10	NUM
ejpam-6157	7	9	,	,	PUNCT
ejpam-6157	7	10	47n20	47n20	NUM
ejpam-6157	7	11	key	key	ADJ
ejpam-6157	7	12	words	word	NOUN
ejpam-6157	7	13	and	and	CCONJ
ejpam-6157	7	14	phrases	phrase	NOUN
ejpam-6157	7	15	:	:	PUNCT
ejpam-6157	7	16	fixed	fix	VERB
ejpam-6157	7	17	-	-	PUNCT
ejpam-6157	7	18	point	point	NOUN
ejpam-6157	7	19	theorem	theorem	NOUN
ejpam-6157	7	20	(	(	PUNCT
ejpam-6157	7	21	fpt	fpt	PROPN
ejpam-6157	7	22	)	)	PUNCT
ejpam-6157	7	23	,	,	PUNCT
ejpam-6157	7	24	orlicz	orlicz	PROPN
ejpam-6157	7	25	spaces	space	VERB
ejpam-6157	7	26	lθ	lθ	PROPN
ejpam-6157	7	27	,	,	PUNCT
ejpam-6157	7	28	coupled	couple	VERB
ejpam-6157	7	29	system	system	NOUN
ejpam-6157	7	30	of	of	ADP
ejpam-6157	7	31	integral	integral	ADJ
ejpam-6157	7	32	equations	equation	NOUN
ejpam-6157	7	33	,	,	PUNCT
ejpam-6157	7	34	(	(	PUNCT
ejpam-6157	7	35	mnc	mnc	PROPN
ejpam-6157	7	36	)	)	PUNCT
ejpam-6157	7	37	measure	measure	NOUN
ejpam-6157	7	38	of	of	ADP
ejpam-6157	7	39	noncompactness	noncompactness	ADJ
ejpam-6157	7	40	1	1	NUM
ejpam-6157	7	41	.	.	PUNCT
ejpam-6157	7	42	introduction	introduction	NOUN
ejpam-6157	7	43	coupled	couple	VERB
ejpam-6157	7	44	systems	system	NOUN
ejpam-6157	7	45	of	of	ADP
ejpam-6157	7	46	differential	differential	ADJ
ejpam-6157	7	47	and	and	CCONJ
ejpam-6157	7	48	integral	integral	ADJ
ejpam-6157	7	49	equations	equation	NOUN
ejpam-6157	7	50	are	be	AUX
ejpam-6157	7	51	often	often	ADV
ejpam-6157	7	52	used	use	VERB
ejpam-6157	7	53	to	to	PART
ejpam-6157	7	54	formulate	formulate	VERB
ejpam-6157	7	55	physical	physical	ADJ
ejpam-6157	7	56	and	and	CCONJ
ejpam-6157	7	57	biological	biological	ADJ
ejpam-6157	7	58	models	model	NOUN
ejpam-6157	7	59	.	.	PUNCT
ejpam-6157	8	1	the	the	DET
ejpam-6157	8	2	study	study	NOUN
ejpam-6157	8	3	of	of	ADP
ejpam-6157	8	4	coupled	couple	VERB
ejpam-6157	8	5	systems	system	NOUN
ejpam-6157	8	6	of	of	ADP
ejpam-6157	8	7	integral	integral	ADJ
ejpam-6157	8	8	equations	equation	NOUN
ejpam-6157	8	9	is	be	AUX
ejpam-6157	8	10	of	of	ADP
ejpam-6157	8	11	significant	significant	ADJ
ejpam-6157	8	12	interest	interest	NOUN
ejpam-6157	8	13	to	to	ADP
ejpam-6157	8	14	numerous	numerous	ADJ
ejpam-6157	8	15	fields	field	NOUN
ejpam-6157	8	16	of	of	ADP
ejpam-6157	8	17	science	science	NOUN
ejpam-6157	8	18	,	,	PUNCT
ejpam-6157	8	19	such	such	ADJ
ejpam-6157	8	20	as	as	ADP
ejpam-6157	8	21	multimedia	multimedia	NOUN
ejpam-6157	8	22	processing	processing	NOUN
ejpam-6157	8	23	[	[	X
ejpam-6157	8	24	1	1	NUM
ejpam-6157	8	25	]	]	PUNCT
ejpam-6157	8	26	,	,	PUNCT
ejpam-6157	8	27	nuclear	nuclear	ADJ
ejpam-6157	8	28	physics	physics	NOUN
ejpam-6157	9	1	[	[	X
ejpam-6157	9	2	2	2	NUM
ejpam-6157	9	3	]	]	PUNCT
ejpam-6157	9	4	,	,	PUNCT
ejpam-6157	9	5	diffusion	diffusion	NOUN
ejpam-6157	9	6	equations	equation	NOUN
ejpam-6157	10	1	[	[	X
ejpam-6157	10	2	3	3	NUM
ejpam-6157	10	3	]	]	PUNCT
ejpam-6157	10	4	,	,	PUNCT
ejpam-6157	10	5	electromagnetics	electromagnetic	NOUN
ejpam-6157	10	6	[	[	X
ejpam-6157	10	7	4	4	NUM
ejpam-6157	10	8	]	]	PUNCT
ejpam-6157	10	9	,	,	PUNCT
ejpam-6157	10	10	and	and	CCONJ
ejpam-6157	10	11	heat	heat	NOUN
ejpam-6157	10	12	conduction	conduction	NOUN
ejpam-6157	10	13	[	[	X
ejpam-6157	10	14	5	5	NUM
ejpam-6157	10	15	]	]	PUNCT
ejpam-6157	10	16	.	.	PUNCT
ejpam-6157	11	1	the	the	DET
ejpam-6157	11	2	aim	aim	NOUN
ejpam-6157	11	3	of	of	ADP
ejpam-6157	11	4	the	the	DET
ejpam-6157	11	5	present	present	ADJ
ejpam-6157	11	6	paper	paper	NOUN
ejpam-6157	11	7	is	be	AUX
ejpam-6157	11	8	to	to	PART
ejpam-6157	11	9	analyze	analyze	VERB
ejpam-6157	11	10	and	and	CCONJ
ejpam-6157	11	11	demonstrate	demonstrate	VERB
ejpam-6157	11	12	the	the	DET
ejpam-6157	11	13	solutions	solution	NOUN
ejpam-6157	11	14	of	of	ADP
ejpam-6157	11	15	the	the	DET
ejpam-6157	11	16	coupled	couple	VERB
ejpam-6157	11	17	system:	system:	PROPN
ejpam-6157	11	18	x(t	x(t	PROPN
ejpam-6157	11	19	)	)	PUNCT
ejpam-6157	11	20	=	=	PUNCT
ejpam-6157	12	1	h1(t	h1(t	X
ejpam-6157	12	2	)	)	PUNCT
ejpam-6157	13	1	+	+	CCONJ
ejpam-6157	13	2	f1	f1	PROPN
ejpam-6157	13	3	(	(	PUNCT
ejpam-6157	13	4	t	t	PROPN
ejpam-6157	13	5	,	,	PUNCT
ejpam-6157	13	6	λ1(y)(t	λ1(y)(t	PROPN
ejpam-6157	13	7	)	)	PUNCT
ejpam-6157	13	8	,	,	PUNCT
ejpam-6157	13	9	g1(y)(t	g1(y)(t	PROPN
ejpam-6157	13	10	)	)	PUNCT
ejpam-6157	13	11	γ(β	γ(β	PROPN
ejpam-6157	13	12	)	)	PUNCT
ejpam-6157	13	13	·	·	PUNCT
ejpam-6157	14	1	∫	∫	PROPN
ejpam-6157	14	2	t	t	PROPN
ejpam-6157	14	3	1	1	NUM
ejpam-6157	14	4	(	(	PUNCT
ejpam-6157	14	5	log	log	VERB
ejpam-6157	14	6	t	t	PROPN
ejpam-6157	14	7	s	s	PART
ejpam-6157	14	8	)	)	PUNCT
ejpam-6157	14	9	β−1	β−1	SYM
ejpam-6157	14	10	r1(y)(s	r1(y)(s	NOUN
ejpam-6157	14	11	)	)	PUNCT
ejpam-6157	14	12	s	s	VERB
ejpam-6157	14	13	ds	ds	ADJ
ejpam-6157	14	14	)	)	PUNCT
ejpam-6157	14	15	y(t	y(t	NUM
ejpam-6157	14	16	)	)	PUNCT
ejpam-6157	15	1	=	=	PUNCT
ejpam-6157	15	2	h2(t	h2(t	X
ejpam-6157	15	3	)	)	PUNCT
ejpam-6157	16	1	+	+	CCONJ
ejpam-6157	16	2	f2	f2	PROPN
ejpam-6157	16	3	(	(	PUNCT
ejpam-6157	16	4	t	t	PROPN
ejpam-6157	16	5	,	,	PUNCT
ejpam-6157	16	6	λ2(x)(t	λ2(x)(t	PROPN
ejpam-6157	16	7	)	)	PUNCT
ejpam-6157	16	8	,	,	PUNCT
ejpam-6157	16	9	g2(x)(t	g2(x)(t	NOUN
ejpam-6157	16	10	)	)	PUNCT
ejpam-6157	16	11	γ(β	γ(β	PROPN
ejpam-6157	16	12	)	)	PUNCT
ejpam-6157	16	13	·	·	PUNCT
ejpam-6157	17	1	∫	∫	PROPN
ejpam-6157	18	1	t	t	PROPN
ejpam-6157	18	2	1	1	NUM
ejpam-6157	18	3	(	(	PUNCT
ejpam-6157	18	4	log	log	VERB
ejpam-6157	18	5	t	t	PROPN
ejpam-6157	18	6	s	s	PART
ejpam-6157	18	7	)	)	PUNCT
ejpam-6157	18	8	β−1	β−1	SYM
ejpam-6157	18	9	r2(x)(s	r2(x)(s	PROPN
ejpam-6157	18	10	)	)	PUNCT
ejpam-6157	18	11	s	s	PART
ejpam-6157	18	12	ds	ds	NOUN
ejpam-6157	18	13	)	)	PUNCT
ejpam-6157	18	14	,	,	PUNCT
ejpam-6157	18	15	t	t	PROPN
ejpam-6157	18	16	∈	∈	PROPN
ejpam-6157	19	1	[	[	X
ejpam-6157	19	2	1	1	NUM
ejpam-6157	19	3	,	,	PUNCT
ejpam-6157	19	4	e	e	NOUN
ejpam-6157	19	5	]	]	X
ejpam-6157	19	6	,	,	PUNCT
ejpam-6157	19	7	(	(	PUNCT
ejpam-6157	19	8	1	1	X
ejpam-6157	19	9	)	)	PUNCT
ejpam-6157	19	10	∗corresponding	∗corresponde	VERB
ejpam-6157	19	11	author	author	NOUN
ejpam-6157	19	12	.	.	PUNCT
ejpam-6157	20	1	doi	doi	NOUN
ejpam-6157	20	2	:	:	PUNCT
ejpam-6157	20	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6157	https://doi.org/10.29020/nybg.ejpam.v18i2.6157	PROPN
ejpam-6157	20	4	email	email	NOUN
ejpam-6157	20	5	addresses	address	NOUN
ejpam-6157	20	6	:	:	PUNCT
ejpam-6157	20	7	m.metwali@psau.edu.sa	m.metwali@psau.edu.sa	NOUN
ejpam-6157	20	8	(	(	PUNCT
ejpam-6157	20	9	m.	m.	NOUN
ejpam-6157	20	10	metwali	metwali	PROPN
ejpam-6157	20	11	)	)	PUNCT
ejpam-6157	20	12	,	,	PUNCT
ejpam-6157	20	13	sasallami@uqu.edu.sa	sasallami@uqu.edu.sa	PROPN
ejpam-6157	20	14	(	(	PUNCT
ejpam-6157	20	15	s.	s.	PROPN
ejpam-6157	20	16	alsallami	alsallami	PROPN
ejpam-6157	20	17	)	)	PUNCT
ejpam-6157	20	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6157	21	1	1	1	NUM
ejpam-6157	21	2	copyright	copyright	NOUN
ejpam-6157	21	3	:	:	PUNCT
ejpam-6157	21	4	©	©	PROPN
ejpam-6157	21	5	2025	2025	NUM
ejpam-6157	21	6	the	the	DET
ejpam-6157	21	7	author(s	author(s	NOUN
ejpam-6157	21	8	)	)	PUNCT
ejpam-6157	21	9	.	.	PUNCT
ejpam-6157	22	1	(	(	PUNCT
ejpam-6157	22	2	cc	cc	NOUN
ejpam-6157	22	3	by	by	ADP
ejpam-6157	22	4	-	-	PUNCT
ejpam-6157	22	5	nc	nc	PROPN
ejpam-6157	22	6	4.0	4.0	NUM
ejpam-6157	22	7	)	)	PUNCT
ejpam-6157	22	8	m.	m.	NOUN
ejpam-6157	22	9	metwali	metwali	PROPN
ejpam-6157	22	10	,	,	PUNCT
ejpam-6157	22	11	s.	s.	PROPN
ejpam-6157	22	12	alsallami	alsallami	PROPN
ejpam-6157	22	13	/	/	SYM
ejpam-6157	22	14	eur	eur	PROPN
ejpam-6157	22	15	.	.	PUNCT
ejpam-6157	23	1	j.	j.	PROPN
ejpam-6157	23	2	pure	pure	PROPN
ejpam-6157	23	3	appl	appl	PROPN
ejpam-6157	23	4	.	.	PROPN
ejpam-6157	23	5	math	math	PROPN
ejpam-6157	23	6	,	,	PUNCT
ejpam-6157	23	7	18	18	NUM
ejpam-6157	23	8	(	(	PUNCT
ejpam-6157	23	9	2	2	NUM
ejpam-6157	23	10	)	)	PUNCT
ejpam-6157	23	11	(	(	PUNCT
ejpam-6157	23	12	2025	2025	NUM
ejpam-6157	23	13	)	)	PUNCT
ejpam-6157	23	14	,	,	PUNCT
ejpam-6157	23	15	6157	6157	NUM
ejpam-6157	23	16	2	2	NUM
ejpam-6157	23	17	of	of	ADP
ejpam-6157	23	18	15	15	NUM
ejpam-6157	23	19	where	where	SCONJ
ejpam-6157	23	20	0	0	NUM
ejpam-6157	23	21	<	<	X
ejpam-6157	23	22	β	β	X
ejpam-6157	23	23	<	<	X
ejpam-6157	23	24	1	1	NUM
ejpam-6157	23	25	,	,	PUNCT
ejpam-6157	23	26	in	in	ADP
ejpam-6157	23	27	orlicz	orlicz	PROPN
ejpam-6157	23	28	spaces	space	VERB
ejpam-6157	23	29	lθ	lθ	NOUN
ejpam-6157	23	30	,	,	PUNCT
ejpam-6157	23	31	and	and	CCONJ
ejpam-6157	23	32	the	the	DET
ejpam-6157	23	33	operators	operator	NOUN
ejpam-6157	23	34	gi	gi	VERB
ejpam-6157	23	35	,	,	PUNCT
ejpam-6157	23	36	λi	λi	PROPN
ejpam-6157	23	37	,	,	PUNCT
ejpam-6157	23	38	ri	ri	PROPN
ejpam-6157	23	39	,	,	PUNCT
ejpam-6157	23	40	i	i	NOUN
ejpam-6157	23	41	=	=	NOUN
ejpam-6157	23	42	1	1	NUM
ejpam-6157	23	43	,	,	PUNCT
ejpam-6157	23	44	2	2	NUM
ejpam-6157	23	45	,	,	PUNCT
ejpam-6157	23	46	operate	operate	VERB
ejpam-6157	23	47	on	on	ADP
ejpam-6157	23	48	some	some	DET
ejpam-6157	23	49	arbitrary	arbitrary	ADJ
ejpam-6157	23	50	lθ	lθ	NOUN
ejpam-6157	23	51	.	.	PUNCT
ejpam-6157	24	1	we	we	PRON
ejpam-6157	24	2	establish	establish	VERB
ejpam-6157	24	3	and	and	CCONJ
ejpam-6157	24	4	present	present	ADJ
ejpam-6157	24	5	assumptions	assumption	NOUN
ejpam-6157	24	6	that	that	PRON
ejpam-6157	24	7	allow	allow	VERB
ejpam-6157	24	8	us	we	PRON
ejpam-6157	24	9	to	to	PART
ejpam-6157	24	10	solve	solve	VERB
ejpam-6157	24	11	and	and	CCONJ
ejpam-6157	24	12	study	study	VERB
ejpam-6157	24	13	the	the	DET
ejpam-6157	24	14	coupled	couple	VERB
ejpam-6157	24	15	system	system	NOUN
ejpam-6157	24	16	(	(	PUNCT
ejpam-6157	24	17	1	1	NUM
ejpam-6157	24	18	)	)	PUNCT
ejpam-6157	24	19	under	under	ADP
ejpam-6157	24	20	general	general	ADJ
ejpam-6157	24	21	growth	growth	NOUN
ejpam-6157	24	22	conditions	condition	NOUN
ejpam-6157	24	23	.	.	PUNCT
ejpam-6157	25	1	as	as	ADP
ejpam-6157	25	2	a	a	DET
ejpam-6157	25	3	result	result	NOUN
ejpam-6157	25	4	,	,	PUNCT
ejpam-6157	25	5	we	we	PRON
ejpam-6157	25	6	examine	examine	VERB
ejpam-6157	25	7	some	some	DET
ejpam-6157	25	8	qualitative	qualitative	ADJ
ejpam-6157	25	9	properties	property	NOUN
ejpam-6157	25	10	of	of	ADP
ejpam-6157	25	11	the	the	DET
ejpam-6157	25	12	problem	problem	NOUN
ejpam-6157	25	13	(	(	PUNCT
ejpam-6157	25	14	1	1	NUM
ejpam-6157	25	15	)	)	PUNCT
ejpam-6157	25	16	,	,	PUNCT
ejpam-6157	25	17	such	such	ADJ
ejpam-6157	25	18	as	as	ADP
ejpam-6157	25	19	existence	existence	NOUN
ejpam-6157	25	20	,	,	PUNCT
ejpam-6157	25	21	monotonicity	monotonicity	NOUN
ejpam-6157	25	22	,	,	PUNCT
ejpam-6157	25	23	and	and	CCONJ
ejpam-6157	25	24	uniqueness	uniqueness	NOUN
ejpam-6157	25	25	,	,	PUNCT
ejpam-6157	25	26	in	in	ADP
ejpam-6157	25	27	addition	addition	NOUN
ejpam-6157	25	28	to	to	ADP
ejpam-6157	25	29	the	the	DET
ejpam-6157	25	30	continuous	continuous	ADJ
ejpam-6157	25	31	dependence	dependence	NOUN
ejpam-6157	25	32	on	on	ADP
ejpam-6157	25	33	the	the	DET
ejpam-6157	25	34	data	datum	NOUN
ejpam-6157	25	35	in	in	ADP
ejpam-6157	25	36	the	the	DET
ejpam-6157	25	37	spaces	space	NOUN
ejpam-6157	25	38	lθ	lθ	NOUN
ejpam-6157	25	39	(	(	PUNCT
ejpam-6157	25	40	cf	cf	NOUN
ejpam-6157	25	41	.	.	PUNCT
ejpam-6157	26	1	[	[	X
ejpam-6157	26	2	6	6	NUM
ejpam-6157	26	3	]	]	NUM
ejpam-6157	26	4	)	)	PUNCT
ejpam-6157	26	5	.	.	PUNCT
ejpam-6157	27	1	several	several	ADJ
ejpam-6157	27	2	authors	author	NOUN
ejpam-6157	27	3	examined	examine	VERB
ejpam-6157	27	4	various	various	ADJ
ejpam-6157	27	5	types	type	NOUN
ejpam-6157	27	6	of	of	ADP
ejpam-6157	27	7	coupled	couple	VERB
ejpam-6157	27	8	systems	system	NOUN
ejpam-6157	27	9	of	of	ADP
ejpam-6157	27	10	integral	integral	ADJ
ejpam-6157	27	11	equations	equation	NOUN
ejpam-6157	27	12	in	in	ADP
ejpam-6157	27	13	the	the	DET
ejpam-6157	27	14	literature	literature	NOUN
ejpam-6157	27	15	,	,	PUNCT
ejpam-6157	27	16	including	include	VERB
ejpam-6157	27	17	the	the	DET
ejpam-6157	27	18	space	space	NOUN
ejpam-6157	27	19	c(j	c(j	PROPN
ejpam-6157	27	20	)	)	PUNCT
ejpam-6157	27	21	(	(	PUNCT
ejpam-6157	27	22	cf	cf	NOUN
ejpam-6157	27	23	.	.	PUNCT
ejpam-6157	28	1	[	[	X
ejpam-6157	28	2	7–10	7–10	NOUN
ejpam-6157	28	3	]	]	PUNCT
ejpam-6157	28	4	)	)	PUNCT
ejpam-6157	28	5	and	and	CCONJ
ejpam-6157	28	6	the	the	DET
ejpam-6157	28	7	banach	banach	NOUN
ejpam-6157	28	8	algebras	algebras	X
ejpam-6157	28	9	(	(	PUNCT
ejpam-6157	28	10	cf	cf	NOUN
ejpam-6157	28	11	.	.	PUNCT
ejpam-6157	29	1	[	[	X
ejpam-6157	29	2	11	11	NUM
ejpam-6157	29	3	,	,	PUNCT
ejpam-6157	29	4	12	12	NUM
ejpam-6157	29	5	]	]	PUNCT
ejpam-6157	29	6	,	,	PUNCT
ejpam-6157	29	7	for	for	ADP
ejpam-6157	29	8	instance	instance	NOUN
ejpam-6157	29	9	)	)	PUNCT
ejpam-6157	29	10	,	,	PUNCT
ejpam-6157	29	11	where	where	SCONJ
ejpam-6157	29	12	the	the	DET
ejpam-6157	29	13	outcomes	outcome	NOUN
ejpam-6157	29	14	have	have	AUX
ejpam-6157	29	15	been	be	AUX
ejpam-6157	29	16	made	make	VERB
ejpam-6157	29	17	under	under	ADP
ejpam-6157	29	18	conditions	condition	NOUN
ejpam-6157	29	19	that	that	PRON
ejpam-6157	29	20	are	be	AUX
ejpam-6157	29	21	”	"	PUNCT
ejpam-6157	29	22	continuous	continuous	ADJ
ejpam-6157	29	23	,	,	PUNCT
ejpam-6157	29	24	”	"	PUNCT
ejpam-6157	29	25	i.e.	i.e.	X
ejpam-6157	29	26	,	,	PUNCT
ejpam-6157	29	27	stronger	strong	ADJ
ejpam-6157	29	28	than	than	ADP
ejpam-6157	29	29	the	the	DET
ejpam-6157	29	30	ones	one	NOUN
ejpam-6157	29	31	provided	provide	VERB
ejpam-6157	29	32	in	in	ADP
ejpam-6157	29	33	this	this	DET
ejpam-6157	29	34	article	article	NOUN
ejpam-6157	29	35	.	.	PUNCT
ejpam-6157	30	1	additionally	additionally	ADV
ejpam-6157	30	2	,	,	PUNCT
ejpam-6157	30	3	polynomial	polynomial	ADJ
ejpam-6157	30	4	growth	growth	NOUN
ejpam-6157	30	5	was	be	AUX
ejpam-6157	30	6	used	use	VERB
ejpam-6157	30	7	on	on	ADP
ejpam-6157	30	8	the	the	DET
ejpam-6157	30	9	studied	study	VERB
ejpam-6157	30	10	functions	function	NOUN
ejpam-6157	30	11	to	to	PART
ejpam-6157	30	12	obtain	obtain	VERB
ejpam-6157	30	13	lp	lp	NOUN
ejpam-6157	30	14	-	-	NOUN
ejpam-6157	30	15	solutions	solution	NOUN
ejpam-6157	30	16	for	for	ADP
ejpam-6157	30	17	the	the	DET
ejpam-6157	30	18	coupled	couple	VERB
ejpam-6157	30	19	systems	system	NOUN
ejpam-6157	30	20	in	in	ADP
ejpam-6157	30	21	[	[	X
ejpam-6157	30	22	13	13	NUM
ejpam-6157	30	23	,	,	PUNCT
ejpam-6157	30	24	14	14	NUM
ejpam-6157	30	25	]	]	PUNCT
ejpam-6157	30	26	.	.	PUNCT
ejpam-6157	31	1	as	as	ADP
ejpam-6157	31	2	a	a	DET
ejpam-6157	31	3	result	result	NOUN
ejpam-6157	31	4	of	of	ADP
ejpam-6157	31	5	eliminating	eliminate	VERB
ejpam-6157	31	6	these	these	DET
ejpam-6157	31	7	limitations	limitation	NOUN
ejpam-6157	31	8	,	,	PUNCT
ejpam-6157	31	9	we	we	PRON
ejpam-6157	31	10	extended	extend	VERB
ejpam-6157	31	11	these	these	DET
ejpam-6157	31	12	results	result	NOUN
ejpam-6157	31	13	to	to	PART
ejpam-6157	31	14	examine	examine	VERB
ejpam-6157	31	15	the	the	DET
ejpam-6157	31	16	coupled	couple	VERB
ejpam-6157	31	17	system	system	NOUN
ejpam-6157	31	18	(	(	PUNCT
ejpam-6157	31	19	1	1	X
ejpam-6157	31	20	)	)	PUNCT
ejpam-6157	31	21	using	use	VERB
ejpam-6157	31	22	the	the	DET
ejpam-6157	31	23	technique	technique	NOUN
ejpam-6157	31	24	presented	present	VERB
ejpam-6157	31	25	in	in	ADP
ejpam-6157	31	26	[	[	X
ejpam-6157	31	27	15	15	NUM
ejpam-6157	31	28	]	]	PUNCT
ejpam-6157	31	29	that	that	PRON
ejpam-6157	31	30	is	be	AUX
ejpam-6157	31	31	not	not	PART
ejpam-6157	31	32	a	a	DET
ejpam-6157	31	33	banach	banach	NOUN
ejpam-6157	31	34	algebra	algebra	NOUN
ejpam-6157	31	35	,	,	PUNCT
ejpam-6157	31	36	using	use	VERB
ejpam-6157	31	37	appropriately	appropriately	ADV
ejpam-6157	31	38	and	and	CCONJ
ejpam-6157	31	39	various	various	ADJ
ejpam-6157	31	40	orlicz	orlicz	ADJ
ejpam-6157	31	41	spaces	space	NOUN
ejpam-6157	31	42	(	(	PUNCT
ejpam-6157	31	43	lθ1	lθ1	INTJ
ejpam-6157	31	44	,	,	PUNCT
ejpam-6157	31	45	lθ2	lθ2	ADJ
ejpam-6157	31	46	,	,	PUNCT
ejpam-6157	31	47	lθ3	lθ3	X
ejpam-6157	31	48	)	)	PUNCT
ejpam-6157	31	49	,	,	PUNCT
ejpam-6157	31	50	which	which	PRON
ejpam-6157	31	51	are	be	AUX
ejpam-6157	31	52	not	not	PART
ejpam-6157	31	53	a	a	DET
ejpam-6157	31	54	banach	banach	NOUN
ejpam-6157	31	55	algebra	algebra	NOUN
ejpam-6157	31	56	.	.	PUNCT
ejpam-6157	32	1	using	use	VERB
ejpam-6157	32	2	orlicz	orlicz	PROPN
ejpam-6157	32	3	spaces	space	NOUN
ejpam-6157	32	4	lθ	lθ	ADP
ejpam-6157	32	5	as	as	ADP
ejpam-6157	32	6	the	the	DET
ejpam-6157	32	7	solution	solution	NOUN
ejpam-6157	32	8	space	space	NOUN
ejpam-6157	32	9	,	,	PUNCT
ejpam-6157	32	10	we	we	PRON
ejpam-6157	32	11	can	can	AUX
ejpam-6157	32	12	study	study	VERB
ejpam-6157	32	13	operators	operator	NOUN
ejpam-6157	32	14	with	with	ADP
ejpam-6157	32	15	strong	strong	ADJ
ejpam-6157	32	16	nonlinear	nonlinear	ADJ
ejpam-6157	32	17	properties	property	NOUN
ejpam-6157	32	18	(	(	PUNCT
ejpam-6157	32	19	such	such	ADJ
ejpam-6157	32	20	as	as	ADP
ejpam-6157	32	21	exponential	exponential	ADJ
ejpam-6157	32	22	growth	growth	NOUN
ejpam-6157	32	23	,	,	PUNCT
ejpam-6157	32	24	for	for	ADP
ejpam-6157	32	25	example	example	NOUN
ejpam-6157	32	26	)	)	PUNCT
ejpam-6157	32	27	.	.	PUNCT
ejpam-6157	33	1	this	this	PRON
ejpam-6157	33	2	allows	allow	VERB
ejpam-6157	33	3	us	we	PRON
ejpam-6157	33	4	to	to	PART
ejpam-6157	33	5	examine	examine	VERB
ejpam-6157	33	6	the	the	DET
ejpam-6157	33	7	solutions	solution	NOUN
ejpam-6157	33	8	in	in	ADP
ejpam-6157	33	9	lθ	lθ	NOUN
ejpam-6157	33	10	rather	rather	ADV
ejpam-6157	33	11	than	than	ADP
ejpam-6157	33	12	continuous	continuous	ADJ
ejpam-6157	33	13	results	result	NOUN
ejpam-6157	33	14	.	.	PUNCT
ejpam-6157	34	1	statistical	statistical	ADJ
ejpam-6157	34	2	physics	physics	NOUN
ejpam-6157	34	3	and	and	CCONJ
ejpam-6157	34	4	physics	physics	NOUN
ejpam-6157	34	5	models	model	NOUN
ejpam-6157	34	6	may	may	AUX
ejpam-6157	34	7	inspire	inspire	VERB
ejpam-6157	34	8	this	this	PRON
ejpam-6157	34	9	(	(	PUNCT
ejpam-6157	34	10	cf	cf	NOUN
ejpam-6157	34	11	.	.	PUNCT
ejpam-6157	35	1	[	[	X
ejpam-6157	35	2	16	16	NUM
ejpam-6157	35	3	,	,	PUNCT
ejpam-6157	35	4	17	17	NUM
ejpam-6157	35	5	]	]	PUNCT
ejpam-6157	35	6	)	)	PUNCT
ejpam-6157	35	7	.	.	PUNCT
ejpam-6157	36	1	recalling	recall	VERB
ejpam-6157	36	2	the	the	DET
ejpam-6157	36	3	thermodynamics	thermodynamic	NOUN
ejpam-6157	36	4	model	model	NOUN
ejpam-6157	36	5	y(s	y(s	PROPN
ejpam-6157	36	6	)	)	PUNCT
ejpam-6157	37	1	+	+	CCONJ
ejpam-6157	37	2	∫	∫	PROPN
ejpam-6157	37	3	i	i	PRON
ejpam-6157	37	4	a(s	a(s	PROPN
ejpam-6157	37	5	,	,	PUNCT
ejpam-6157	37	6	t)ey(t	t)ey(t	NOUN
ejpam-6157	37	7	)	)	PUNCT
ejpam-6157	37	8	dt	dt	NOUN
ejpam-6157	37	9	=	=	SYM
ejpam-6157	37	10	0	0	NUM
ejpam-6157	37	11	contains	contain	VERB
ejpam-6157	37	12	exponential	exponential	ADJ
ejpam-6157	37	13	nonlinearity	nonlinearity	NOUN
ejpam-6157	37	14	(	(	PUNCT
ejpam-6157	37	15	cf	cf	NOUN
ejpam-6157	37	16	.	.	PUNCT
ejpam-6157	38	1	[	[	X
ejpam-6157	38	2	18	18	NUM
ejpam-6157	38	3	]	]	NUM
ejpam-6157	38	4	)	)	PUNCT
ejpam-6157	38	5	.	.	PUNCT
ejpam-6157	39	1	furthermore	furthermore	ADV
ejpam-6157	39	2	,	,	PUNCT
ejpam-6157	39	3	the	the	DET
ejpam-6157	39	4	quadratic	quadratic	ADJ
ejpam-6157	39	5	integral	integral	ADJ
ejpam-6157	39	6	equations	equation	NOUN
ejpam-6157	39	7	(	(	PUNCT
ejpam-6157	39	8	qie	qie	PROPN
ejpam-6157	39	9	)	)	PUNCT
ejpam-6157	39	10	were	be	AUX
ejpam-6157	39	11	studied	study	VERB
ejpam-6157	39	12	in	in	ADP
ejpam-6157	39	13	the	the	DET
ejpam-6157	39	14	banach	banach	ADV
ejpam-6157	39	15	-	-	PUNCT
ejpam-6157	39	16	orlicz	orlicz	ADJ
ejpam-6157	39	17	algebra	algebra	NOUN
ejpam-6157	39	18	[	[	X
ejpam-6157	39	19	19	19	NUM
ejpam-6157	39	20	]	]	PUNCT
ejpam-6157	39	21	and	and	CCONJ
ejpam-6157	39	22	in	in	ADP
ejpam-6157	39	23	various	various	ADJ
ejpam-6157	39	24	orlicz	orlicz	ADJ
ejpam-6157	39	25	spaces	space	NOUN
ejpam-6157	39	26	in	in	ADP
ejpam-6157	39	27	[	[	X
ejpam-6157	39	28	15	15	NUM
ejpam-6157	39	29	,	,	PUNCT
ejpam-6157	39	30	20	20	NUM
ejpam-6157	39	31	]	]	PUNCT
ejpam-6157	39	32	employing	employ	VERB
ejpam-6157	39	33	the	the	DET
ejpam-6157	39	34	approach	approach	NOUN
ejpam-6157	39	35	of	of	ADP
ejpam-6157	39	36	the	the	DET
ejpam-6157	39	37	fixed	fix	VERB
ejpam-6157	39	38	point	point	NOUN
ejpam-6157	39	39	theorems	theorem	NOUN
ejpam-6157	39	40	(	(	PUNCT
ejpam-6157	39	41	fpt	fpt	X
ejpam-6157	39	42	)	)	PUNCT
ejpam-6157	39	43	in	in	ADP
ejpam-6157	39	44	conjunction	conjunction	NOUN
ejpam-6157	39	45	with	with	ADP
ejpam-6157	39	46	a	a	DET
ejpam-6157	39	47	suitable	suitable	ADJ
ejpam-6157	39	48	(	(	PUNCT
ejpam-6157	39	49	mnc	mnc	PROPN
ejpam-6157	39	50	)	)	PUNCT
ejpam-6157	39	51	measure	measure	NOUN
ejpam-6157	39	52	of	of	ADP
ejpam-6157	39	53	noncompactness	noncompactness	ADJ
ejpam-6157	39	54	(	(	PUNCT
ejpam-6157	39	55	mnc	mnc	PROPN
ejpam-6157	39	56	)	)	PUNCT
ejpam-6157	39	57	concerning	concern	VERB
ejpam-6157	39	58	different	different	ADJ
ejpam-6157	39	59	assumptions	assumption	NOUN
ejpam-6157	39	60	,	,	PUNCT
ejpam-6157	39	61	see	see	VERB
ejpam-6157	39	62	also	also	ADV
ejpam-6157	39	63	[	[	X
ejpam-6157	39	64	21	21	NUM
ejpam-6157	39	65	,	,	PUNCT
ejpam-6157	39	66	22	22	NUM
ejpam-6157	39	67	]	]	PUNCT
ejpam-6157	39	68	.	.	PUNCT
ejpam-6157	40	1	the	the	DET
ejpam-6157	40	2	measures	measure	NOUN
ejpam-6157	40	3	of	of	ADP
ejpam-6157	40	4	noncompactness	noncompactness	ADJ
ejpam-6157	40	5	(	(	PUNCT
ejpam-6157	40	6	mnc	mnc	PROPN
ejpam-6157	40	7	)	)	PUNCT
ejpam-6157	40	8	have	have	AUX
ejpam-6157	40	9	been	be	AUX
ejpam-6157	40	10	employed	employ	VERB
ejpam-6157	40	11	in	in	ADP
ejpam-6157	40	12	the	the	DET
ejpam-6157	40	13	study	study	NOUN
ejpam-6157	40	14	of	of	ADP
ejpam-6157	40	15	numerous	numerous	ADJ
ejpam-6157	40	16	models	model	NOUN
ejpam-6157	40	17	of	of	ADP
ejpam-6157	40	18	integral	integral	ADJ
ejpam-6157	40	19	equations	equation	NOUN
ejpam-6157	40	20	;	;	PUNCT
ejpam-6157	40	21	(	(	PUNCT
ejpam-6157	40	22	cf	cf	NOUN
ejpam-6157	40	23	.	.	PUNCT
ejpam-6157	41	1	[	[	X
ejpam-6157	41	2	23–25	23–25	NUM
ejpam-6157	41	3	]	]	PUNCT
ejpam-6157	41	4	)	)	PUNCT
ejpam-6157	41	5	.	.	PUNCT
ejpam-6157	42	1	these	these	DET
ejpam-6157	42	2	cases	case	NOUN
ejpam-6157	42	3	are	be	AUX
ejpam-6157	42	4	unified	unify	VERB
ejpam-6157	42	5	and	and	CCONJ
ejpam-6157	42	6	included	include	VERB
ejpam-6157	42	7	as	as	ADP
ejpam-6157	42	8	special	special	ADJ
ejpam-6157	42	9	cases	case	NOUN
ejpam-6157	42	10	of	of	ADP
ejpam-6157	42	11	the	the	DET
ejpam-6157	42	12	coupled	couple	VERB
ejpam-6157	42	13	system	system	NOUN
ejpam-6157	42	14	(	(	PUNCT
ejpam-6157	42	15	1	1	NUM
ejpam-6157	42	16	)	)	PUNCT
ejpam-6157	42	17	.	.	PUNCT
ejpam-6157	43	1	let	let	VERB
ejpam-6157	43	2	us	we	PRON
ejpam-6157	43	3	recall	recall	VERB
ejpam-6157	43	4	that	that	SCONJ
ejpam-6157	43	5	,	,	PUNCT
ejpam-6157	43	6	in	in	ADP
ejpam-6157	43	7	[	[	X
ejpam-6157	43	8	26	26	NUM
ejpam-6157	43	9	]	]	X
ejpam-6157	43	10	,	,	PUNCT
ejpam-6157	43	11	two	two	NUM
ejpam-6157	43	12	existence	existence	NOUN
ejpam-6157	43	13	theorems	theorem	NOUN
ejpam-6157	43	14	of	of	ADP
ejpam-6157	43	15	the	the	DET
ejpam-6157	43	16	coupled	couple	VERB
ejpam-6157	43	17	system	system	PROPN
ejpam-6157	43	18	x(t	x(t	PROPN
ejpam-6157	43	19	)	)	PUNCT
ejpam-6157	43	20	=	=	PUNCT
ejpam-6157	44	1	g1(t	g1(t	X
ejpam-6157	44	2	)	)	PUNCT
ejpam-6157	44	3	+	+	NUM
ejpam-6157	44	4	f1	f1	PROPN
ejpam-6157	44	5	(	(	PUNCT
ejpam-6157	44	6	t	t	PROPN
ejpam-6157	44	7	,	,	PUNCT
ejpam-6157	44	8	y(t	y(t	PROPN
ejpam-6157	44	9	)	)	PUNCT
ejpam-6157	44	10	,	,	PUNCT
ejpam-6157	44	11	λ	λ	PROPN
ejpam-6157	44	12	·	·	PUNCT
ejpam-6157	44	13	v1y(t	v1y(t	PROPN
ejpam-6157	44	14	)	)	PUNCT
ejpam-6157	44	15	∫	∫	PROPN
ejpam-6157	45	1	b	b	PROPN
ejpam-6157	45	2	a	a	PRON
ejpam-6157	45	3	k	k	PROPN
ejpam-6157	45	4	(	(	PUNCT
ejpam-6157	45	5	t	t	PROPN
ejpam-6157	45	6	,	,	PUNCT
ejpam-6157	45	7	s	s	PART
ejpam-6157	45	8	)	)	PUNCT
ejpam-6157	45	9	h1(s	h1(s	PROPN
ejpam-6157	45	10	,	,	PUNCT
ejpam-6157	45	11	y(s	y(s	PROPN
ejpam-6157	45	12	)	)	PUNCT
ejpam-6157	45	13	)	)	PUNCT
ejpam-6157	46	1	ds	ds	PROPN
ejpam-6157	46	2	,	,	PUNCT
ejpam-6157	46	3	λ	λ	NOUN
ejpam-6157	46	4	·	·	SYM
ejpam-6157	46	5	g1y(t	g1y(t	PROPN
ejpam-6157	46	6	)	)	PUNCT
ejpam-6157	46	7	∫	∫	PROPN
ejpam-6157	46	8	b	b	PROPN
ejpam-6157	47	1	a	a	DET
ejpam-6157	47	2	u1	u1	NOUN
ejpam-6157	47	3	(	(	PUNCT
ejpam-6157	47	4	t	t	PROPN
ejpam-6157	47	5	,	,	PUNCT
ejpam-6157	47	6	s	s	PROPN
ejpam-6157	47	7	,	,	PUNCT
ejpam-6157	47	8	y(s	y(s	PROPN
ejpam-6157	47	9	)	)	PUNCT
ejpam-6157	47	10	)	)	PUNCT
ejpam-6157	48	1	ds	ds	X
ejpam-6157	48	2	)	)	PUNCT
ejpam-6157	48	3	y(t	y(t	NUM
ejpam-6157	48	4	)	)	PUNCT
ejpam-6157	48	5	=	=	SYM
ejpam-6157	49	1	g2(t	g2(t	PROPN
ejpam-6157	49	2	)	)	PUNCT
ejpam-6157	50	1	+	+	CCONJ
ejpam-6157	50	2	f2	f2	PROPN
ejpam-6157	50	3	(	(	PUNCT
ejpam-6157	50	4	t	t	PROPN
ejpam-6157	50	5	,	,	PUNCT
ejpam-6157	50	6	x(t	x(t	PROPN
ejpam-6157	50	7	)	)	PUNCT
ejpam-6157	50	8	,	,	PUNCT
ejpam-6157	50	9	λ	λ	X
ejpam-6157	50	10	·	·	PUNCT
ejpam-6157	50	11	v2x(t	v2x(t	PROPN
ejpam-6157	50	12	)	)	PUNCT
ejpam-6157	50	13	∫	∫	PROPN
ejpam-6157	51	1	b	b	PROPN
ejpam-6157	51	2	a	a	PRON
ejpam-6157	51	3	k	k	PROPN
ejpam-6157	51	4	(	(	PUNCT
ejpam-6157	51	5	t	t	PROPN
ejpam-6157	51	6	,	,	PUNCT
ejpam-6157	51	7	s	s	PART
ejpam-6157	51	8	)	)	PUNCT
ejpam-6157	51	9	h2(s	h2(s	PROPN
ejpam-6157	51	10	,	,	PUNCT
ejpam-6157	51	11	x(s	x(s	PROPN
ejpam-6157	51	12	)	)	PUNCT
ejpam-6157	51	13	)	)	PUNCT
ejpam-6157	52	1	ds	ds	PROPN
ejpam-6157	52	2	,	,	PUNCT
ejpam-6157	52	3	λ	λ	NOUN
ejpam-6157	52	4	·	·	SYM
ejpam-6157	52	5	g2x(t	g2x(t	PROPN
ejpam-6157	52	6	)	)	PUNCT
ejpam-6157	52	7	∫	∫	PROPN
ejpam-6157	52	8	b	b	PROPN
ejpam-6157	52	9	a	a	DET
ejpam-6157	52	10	u2	u2	NOUN
ejpam-6157	52	11	(	(	PUNCT
ejpam-6157	52	12	t	t	PROPN
ejpam-6157	52	13	,	,	PUNCT
ejpam-6157	52	14	s	s	PROPN
ejpam-6157	52	15	,	,	PUNCT
ejpam-6157	52	16	x(s	x(s	PROPN
ejpam-6157	52	17	)	)	PUNCT
ejpam-6157	52	18	)	)	PUNCT
ejpam-6157	53	1	ds	ds	X
ejpam-6157	53	2	)	)	PUNCT
ejpam-6157	53	3	have	have	AUX
ejpam-6157	53	4	been	be	AUX
ejpam-6157	53	5	studied	study	VERB
ejpam-6157	53	6	in	in	ADP
ejpam-6157	53	7	arbitrary	arbitrary	ADJ
ejpam-6157	53	8	lθ	lθ	NOUN
ejpam-6157	53	9	,	,	PUNCT
ejpam-6157	53	10	in	in	ADP
ejpam-6157	53	11	two	two	NUM
ejpam-6157	53	12	separately	separately	ADJ
ejpam-6157	53	13	cases	case	NOUN
ejpam-6157	53	14	∆′	∆′	PROPN
ejpam-6157	53	15	and	and	CCONJ
ejpam-6157	53	16	∆3	∆3	NOUN
ejpam-6157	53	17	-	-	NOUN
ejpam-6157	53	18	conditions	condition	NOUN
ejpam-6157	53	19	using	use	VERB
ejpam-6157	53	20	darbo’s(fpt	darbo’s(fpt	PUNCT
ejpam-6157	53	21	)	)	PUNCT
ejpam-6157	53	22	with	with	ADP
ejpam-6157	53	23	a	a	DET
ejpam-6157	53	24	(	(	PUNCT
ejpam-6157	53	25	mnc	mnc	PROPN
ejpam-6157	53	26	)	)	PUNCT
ejpam-6157	53	27	.	.	PUNCT
ejpam-6157	54	1	the	the	DET
ejpam-6157	54	2	authors	author	NOUN
ejpam-6157	54	3	in	in	ADP
ejpam-6157	54	4	[	[	X
ejpam-6157	54	5	27	27	NUM
ejpam-6157	54	6	]	]	PUNCT
ejpam-6157	54	7	studied	study	VERB
ejpam-6157	54	8	the	the	DET
ejpam-6157	54	9	existence	existence	NOUN
ejpam-6157	54	10	,	,	PUNCT
ejpam-6157	54	11	in	in	ADP
ejpam-6157	54	12	addition	addition	NOUN
ejpam-6157	54	13	to	to	ADP
ejpam-6157	54	14	the	the	DET
ejpam-6157	54	15	uniqueness	uniqueness	NOUN
ejpam-6157	54	16	of	of	ADP
ejpam-6157	54	17	monotonic	monotonic	ADJ
ejpam-6157	54	18	solutions	solution	NOUN
ejpam-6157	54	19	of	of	ADP
ejpam-6157	54	20	the	the	DET
ejpam-6157	54	21	hadamard	hadamard	ADJ
ejpam-6157	54	22	fraction	fraction	NOUN
ejpam-6157	54	23	equations	equation	NOUN
ejpam-6157	54	24	x(t	x(t	PROPN
ejpam-6157	54	25	)	)	PUNCT
ejpam-6157	55	1	=	=	PUNCT
ejpam-6157	55	2	n∏	n∏	PROPN
ejpam-6157	55	3	i=1	i=1	PROPN
ejpam-6157	56	1	(	(	PUNCT
ejpam-6157	56	2	hi(t)+g2i(x)(t)+	hi(t)+g2i(x)(t)+	NOUN
ejpam-6157	56	3	g1i(x)(t	g1i(x)(t	ADJ
ejpam-6157	56	4	)	)	PUNCT
ejpam-6157	56	5	γ(αi	γ(αi	NOUN
ejpam-6157	56	6	)	)	PUNCT
ejpam-6157	56	7	·	·	PUNCT
ejpam-6157	57	1	∫	∫	PROPN
ejpam-6157	57	2	t	t	PROPN
ejpam-6157	57	3	1	1	NUM
ejpam-6157	57	4	(	(	PUNCT
ejpam-6157	57	5	log	log	VERB
ejpam-6157	57	6	t	t	PROPN
ejpam-6157	57	7	s	s	PART
ejpam-6157	57	8	)	)	PUNCT
ejpam-6157	57	9	αi−1g3i(x)(s	αi−1g3i(x)(s	NUM
ejpam-6157	57	10	)	)	PUNCT
ejpam-6157	57	11	s	s	VERB
ejpam-6157	57	12	ds	ds	NOUN
ejpam-6157	57	13	)	)	PUNCT
ejpam-6157	57	14	,	,	PUNCT
ejpam-6157	57	15	t	t	PROPN
ejpam-6157	57	16	∈	∈	PROPN
ejpam-6157	58	1	[	[	X
ejpam-6157	58	2	1	1	NUM
ejpam-6157	58	3	,	,	PUNCT
ejpam-6157	58	4	e	e	NOUN
ejpam-6157	58	5	]	]	X
ejpam-6157	58	6	,	,	PUNCT
ejpam-6157	58	7	0	0	PUNCT
ejpam-6157	58	8	<	<	X
ejpam-6157	58	9	αi	αi	X
ejpam-6157	58	10	<	<	X
ejpam-6157	58	11	1	1	NUM
ejpam-6157	58	12	m.	m.	NOUN
ejpam-6157	58	13	metwali	metwali	PROPN
ejpam-6157	58	14	,	,	PUNCT
ejpam-6157	58	15	s.	s.	PROPN
ejpam-6157	58	16	alsallami	alsallami	PROPN
ejpam-6157	58	17	/	/	SYM
ejpam-6157	58	18	eur	eur	PROPN
ejpam-6157	58	19	.	.	PUNCT
ejpam-6157	59	1	j.	j.	PROPN
ejpam-6157	59	2	pure	pure	PROPN
ejpam-6157	59	3	appl	appl	PROPN
ejpam-6157	59	4	.	.	PROPN
ejpam-6157	59	5	math	math	PROPN
ejpam-6157	59	6	,	,	PUNCT
ejpam-6157	59	7	18	18	NUM
ejpam-6157	59	8	(	(	PUNCT
ejpam-6157	59	9	2	2	NUM
ejpam-6157	59	10	)	)	PUNCT
ejpam-6157	59	11	(	(	PUNCT
ejpam-6157	59	12	2025	2025	NUM
ejpam-6157	59	13	)	)	PUNCT
ejpam-6157	59	14	,	,	PUNCT
ejpam-6157	59	15	6157	6157	NUM
ejpam-6157	59	16	3	3	NUM
ejpam-6157	59	17	of	of	ADP
ejpam-6157	59	18	15	15	NUM
ejpam-6157	59	19	in	in	ADP
ejpam-6157	59	20	orlicz	orlicz	ADJ
ejpam-6157	59	21	spaces	space	NOUN
ejpam-6157	59	22	see	see	VERB
ejpam-6157	59	23	also	also	ADV
ejpam-6157	59	24	[	[	X
ejpam-6157	59	25	28	28	NUM
ejpam-6157	59	26	]	]	PUNCT
ejpam-6157	59	27	.	.	PUNCT
ejpam-6157	60	1	the	the	DET
ejpam-6157	60	2	current	current	ADJ
ejpam-6157	60	3	manuscript	manuscript	NOUN
ejpam-6157	60	4	is	be	AUX
ejpam-6157	60	5	motivated	motivate	VERB
ejpam-6157	60	6	and	and	CCONJ
ejpam-6157	60	7	induced	induce	VERB
ejpam-6157	60	8	by	by	ADP
ejpam-6157	60	9	the	the	DET
ejpam-6157	60	10	extension	extension	NOUN
ejpam-6157	60	11	and	and	CCONJ
ejpam-6157	60	12	generalization	generalization	NOUN
ejpam-6157	60	13	of	of	ADP
ejpam-6157	60	14	the	the	DET
ejpam-6157	60	15	results	result	NOUN
ejpam-6157	60	16	introduced	introduce	VERB
ejpam-6157	60	17	in	in	ADP
ejpam-6157	60	18	the	the	DET
ejpam-6157	60	19	previous	previous	ADJ
ejpam-6157	60	20	literature	literature	NOUN
ejpam-6157	60	21	to	to	PART
ejpam-6157	60	22	prove	prove	VERB
ejpam-6157	60	23	some	some	DET
ejpam-6157	60	24	qualitative	qualitative	ADJ
ejpam-6157	60	25	properties	property	NOUN
ejpam-6157	60	26	of	of	ADP
ejpam-6157	60	27	the	the	DET
ejpam-6157	60	28	solutions	solution	NOUN
ejpam-6157	60	29	for	for	ADP
ejpam-6157	60	30	an	an	DET
ejpam-6157	60	31	abstract	abstract	ADJ
ejpam-6157	60	32	but	but	CCONJ
ejpam-6157	60	33	general	general	ADJ
ejpam-6157	60	34	coupled	couple	VERB
ejpam-6157	60	35	system	system	NOUN
ejpam-6157	60	36	of	of	ADP
ejpam-6157	60	37	quadratic	quadratic	ADJ
ejpam-6157	60	38	hadamard	hadamard	ADJ
ejpam-6157	60	39	-	-	PUNCT
ejpam-6157	60	40	fractional	fractional	ADJ
ejpam-6157	60	41	integral	integral	ADJ
ejpam-6157	60	42	equations	equation	NOUN
ejpam-6157	60	43	(	(	PUNCT
ejpam-6157	60	44	1	1	NUM
ejpam-6157	60	45	)	)	PUNCT
ejpam-6157	60	46	,	,	PUNCT
ejpam-6157	60	47	including	include	VERB
ejpam-6157	60	48	existence	existence	NOUN
ejpam-6157	60	49	,	,	PUNCT
ejpam-6157	60	50	monotonicity	monotonicity	NOUN
ejpam-6157	60	51	,	,	PUNCT
ejpam-6157	60	52	and	and	CCONJ
ejpam-6157	60	53	uniqueness	uniqueness	NOUN
ejpam-6157	60	54	,	,	PUNCT
ejpam-6157	60	55	in	in	ADP
ejpam-6157	60	56	addition	addition	NOUN
ejpam-6157	60	57	to	to	ADP
ejpam-6157	60	58	continuous	continuous	ADJ
ejpam-6157	60	59	dependence	dependence	NOUN
ejpam-6157	60	60	on	on	ADP
ejpam-6157	60	61	the	the	DET
ejpam-6157	60	62	data	datum	NOUN
ejpam-6157	60	63	in	in	ADP
ejpam-6157	60	64	lθ	lθ	NOUN
ejpam-6157	60	65	-	-	NOUN
ejpam-6157	60	66	spaces	space	NOUN
ejpam-6157	60	67	.	.	PUNCT
ejpam-6157	61	1	we	we	PRON
ejpam-6157	61	2	use	use	VERB
ejpam-6157	61	3	the	the	DET
ejpam-6157	61	4	technique	technique	NOUN
ejpam-6157	61	5	of	of	ADP
ejpam-6157	61	6	(	(	PUNCT
ejpam-6157	61	7	mnc	mnc	PROPN
ejpam-6157	61	8	)	)	PUNCT
ejpam-6157	61	9	concerning	concern	VERB
ejpam-6157	61	10	(	(	PUNCT
ejpam-6157	61	11	fpt	fpt	X
ejpam-6157	61	12	)	)	PUNCT
ejpam-6157	61	13	and	and	CCONJ
ejpam-6157	61	14	the	the	DET
ejpam-6157	61	15	theory	theory	NOUN
ejpam-6157	61	16	of	of	ADP
ejpam-6157	61	17	fractional	fractional	ADJ
ejpam-6157	61	18	calculus	calculus	NOUN
ejpam-6157	61	19	to	to	PART
ejpam-6157	61	20	obtain	obtain	VERB
ejpam-6157	61	21	the	the	DET
ejpam-6157	61	22	findings	finding	NOUN
ejpam-6157	61	23	.	.	PUNCT
ejpam-6157	62	1	we	we	PRON
ejpam-6157	62	2	present	present	VERB
ejpam-6157	62	3	a	a	DET
ejpam-6157	62	4	few	few	ADJ
ejpam-6157	62	5	constructed	construct	VERB
ejpam-6157	62	6	examples	example	NOUN
ejpam-6157	62	7	that	that	PRON
ejpam-6157	62	8	support	support	VERB
ejpam-6157	62	9	and	and	CCONJ
ejpam-6157	62	10	illustrate	illustrate	VERB
ejpam-6157	62	11	our	our	PRON
ejpam-6157	62	12	findings	finding	NOUN
ejpam-6157	62	13	.	.	PUNCT
ejpam-6157	63	1	2	2	X
ejpam-6157	63	2	.	.	X
ejpam-6157	63	3	preliminaries	preliminary	NOUN
ejpam-6157	63	4	let	let	VERB
ejpam-6157	63	5	r+	r+	PUNCT
ejpam-6157	63	6	=	=	PUNCT
ejpam-6157	64	1	[	[	X
ejpam-6157	64	2	0,∞	0,∞	NUM
ejpam-6157	64	3	)	)	PUNCT
ejpam-6157	65	1	⊂	⊂	PROPN
ejpam-6157	65	2	r	r	NOUN
ejpam-6157	65	3	=	=	PUNCT
ejpam-6157	65	4	(	(	PUNCT
ejpam-6157	65	5	−∞,∞	−∞,∞	NOUN
ejpam-6157	65	6	)	)	PUNCT
ejpam-6157	65	7	and	and	CCONJ
ejpam-6157	65	8	j	j	X
ejpam-6157	66	1	=	=	PUNCT
ejpam-6157	67	1	[	[	X
ejpam-6157	67	2	1	1	NUM
ejpam-6157	67	3	,	,	PUNCT
ejpam-6157	67	4	e	e	NOUN
ejpam-6157	67	5	]	]	X
ejpam-6157	67	6	,	,	PUNCT
ejpam-6157	67	7	e	e	PROPN
ejpam-6157	67	8	≈	≈	PROPN
ejpam-6157	67	9	2.718	2.718	NUM
ejpam-6157	67	10	.	.	PUNCT
ejpam-6157	68	1	definition	definition	NOUN
ejpam-6157	68	2	1	1	NUM
ejpam-6157	68	3	.	.	PUNCT
ejpam-6157	69	1	[	[	X
ejpam-6157	69	2	17	17	NUM
ejpam-6157	69	3	]	]	PUNCT
ejpam-6157	69	4	the	the	DET
ejpam-6157	69	5	function	function	NOUN
ejpam-6157	69	6	θ(u	θ(u	PROPN
ejpam-6157	69	7	)	)	PUNCT
ejpam-6157	70	1	=	=	SYM
ejpam-6157	70	2	∫	∫	PROPN
ejpam-6157	70	3	|u|	|u|	ADJ
ejpam-6157	70	4	0	0	NUM
ejpam-6157	70	5	p(t	p(t	NOUN
ejpam-6157	70	6	)	)	PUNCT
ejpam-6157	70	7	dt	dt	NOUN
ejpam-6157	70	8	,	,	PUNCT
ejpam-6157	70	9	defined	define	VERB
ejpam-6157	70	10	on	on	ADP
ejpam-6157	70	11	r+	r+	NOUN
ejpam-6157	70	12	is	be	AUX
ejpam-6157	70	13	called	call	VERB
ejpam-6157	70	14	a	a	DET
ejpam-6157	70	15	young	young	ADJ
ejpam-6157	70	16	function	function	NOUN
ejpam-6157	70	17	(	(	PUNCT
ejpam-6157	70	18	y.f	y.f	PROPN
ejpam-6157	70	19	.	.	PUNCT
ejpam-6157	70	20	)	)	PUNCT
ejpam-6157	71	1	if	if	SCONJ
ejpam-6157	71	2	:	:	PUNCT
ejpam-6157	71	3	•	•	ADP
ejpam-6157	71	4	the	the	DET
ejpam-6157	71	5	function	function	NOUN
ejpam-6157	71	6	p	p	NOUN
ejpam-6157	71	7	is	be	AUX
ejpam-6157	71	8	nondecreasing	nondecrease	VERB
ejpam-6157	71	9	,	,	PUNCT
ejpam-6157	71	10	right	right	ADJ
ejpam-6157	71	11	-	-	PUNCT
ejpam-6157	71	12	continuous	continuous	ADJ
ejpam-6157	71	13	,	,	PUNCT
ejpam-6157	71	14	positive	positive	ADJ
ejpam-6157	71	15	,	,	PUNCT
ejpam-6157	71	16	and	and	CCONJ
ejpam-6157	71	17	defined	define	VERB
ejpam-6157	71	18	on	on	ADP
ejpam-6157	71	19	r+	r+	X
ejpam-6157	71	20	;	;	PUNCT
ejpam-6157	71	21	•	•	NUM
ejpam-6157	71	22	limt→∞θ(t	limt→∞θ(t	PROPN
ejpam-6157	71	23	)	)	PUNCT
ejpam-6157	71	24	=	=	SYM
ejpam-6157	71	25	∞	∞	PROPN
ejpam-6157	71	26	and	and	CCONJ
ejpam-6157	71	27	θ(0	θ(0	PROPN
ejpam-6157	71	28	)	)	PUNCT
ejpam-6157	71	29	=	=	PUNCT
ejpam-6157	71	30	limt→0θ(t	limt→0θ(t	PROPN
ejpam-6157	71	31	)	)	PUNCT
ejpam-6157	72	1	=	=	SYM
ejpam-6157	72	2	0	0	X
ejpam-6157	72	3	.	.	PUNCT
ejpam-6157	73	1	the	the	DET
ejpam-6157	73	2	complementary	complementary	ADJ
ejpam-6157	73	3	(	(	PUNCT
ejpam-6157	73	4	y.f	y.f	PROPN
ejpam-6157	73	5	.	.	PUNCT
ejpam-6157	73	6	)	)	PUNCT
ejpam-6157	74	1	function	function	NOUN
ejpam-6157	75	1	θ∗	θ∗	NOUN
ejpam-6157	75	2	of	of	ADP
ejpam-6157	75	3	the	the	DET
ejpam-6157	75	4	function	function	NOUN
ejpam-6157	75	5	θ	θ	PROPN
ejpam-6157	75	6	is	be	AUX
ejpam-6157	75	7	known	know	VERB
ejpam-6157	75	8	as	as	ADP
ejpam-6157	75	9	θ∗(t	θ∗(t	NOUN
ejpam-6157	75	10	)	)	PUNCT
ejpam-6157	75	11	=	=	SYM
ejpam-6157	75	12	sup	sup	NOUN
ejpam-6157	75	13	s≥0	s≥0	NOUN
ejpam-6157	75	14	(	(	PUNCT
ejpam-6157	75	15	ts−θ(s	ts−θ(s	ADJ
ejpam-6157	75	16	)	)	PUNCT
ejpam-6157	75	17	)	)	PUNCT
ejpam-6157	75	18	,	,	PUNCT
ejpam-6157	75	19	∀	∀	X
ejpam-6157	75	20	t	t	NOUN
ejpam-6157	75	21	≥	≥	NOUN
ejpam-6157	75	22	0	0	NUM
ejpam-6157	75	23	.	.	PUNCT
ejpam-6157	76	1	furthermore	furthermore	ADV
ejpam-6157	76	2	,	,	PUNCT
ejpam-6157	76	3	the	the	DET
ejpam-6157	76	4	function	function	NOUN
ejpam-6157	76	5	θ	θ	PROPN
ejpam-6157	76	6	is	be	AUX
ejpam-6157	76	7	known	know	VERB
ejpam-6157	76	8	as	as	ADP
ejpam-6157	76	9	n	n	NOUN
ejpam-6157	76	10	-function	-function	NOUN
ejpam-6157	76	11	if	if	SCONJ
ejpam-6157	76	12	:	:	PUNCT
ejpam-6157	76	13	•	•	NUM
ejpam-6157	76	14	limt→0	limt→0	NOUN
ejpam-6157	76	15	θ(t	θ(t	PROPN
ejpam-6157	76	16	)	)	PUNCT
ejpam-6157	76	17	t	t	NOUN
ejpam-6157	76	18	=	=	SYM
ejpam-6157	76	19	0	0	NUM
ejpam-6157	76	20	and	and	CCONJ
ejpam-6157	76	21	limt→∞	limt→∞	PROPN
ejpam-6157	76	22	θ(t	θ(t	PROPN
ejpam-6157	76	23	)	)	PUNCT
ejpam-6157	76	24	t	t	NOUN
ejpam-6157	77	1	=	=	SYM
ejpam-6157	77	2	∞	∞	PROPN
ejpam-6157	77	3	;	;	PUNCT
ejpam-6157	77	4	•	•	NUM
ejpam-6157	77	5	θ(s	θ(s	NOUN
ejpam-6157	77	6	)	)	PUNCT
ejpam-6157	77	7	=	=	SYM
ejpam-6157	77	8	0	0	NUM
ejpam-6157	78	1	⇔	⇔	PROPN
ejpam-6157	78	2	s	s	X
ejpam-6157	78	3	=	=	SYM
ejpam-6157	78	4	0	0	NUM
ejpam-6157	78	5	and	and	CCONJ
ejpam-6157	78	6	θ(s	θ(s	PROPN
ejpam-6157	78	7	)	)	PUNCT
ejpam-6157	78	8	>	>	X
ejpam-6157	78	9	0	0	PUNCT
ejpam-6157	79	1	if	if	SCONJ
ejpam-6157	79	2	s	s	VERB
ejpam-6157	79	3	>	>	X
ejpam-6157	79	4	0	0	PROPN
ejpam-6157	79	5	.	.	PUNCT
ejpam-6157	79	6	definition	definition	NOUN
ejpam-6157	79	7	2	2	NUM
ejpam-6157	79	8	.	.	PUNCT
ejpam-6157	80	1	[	[	X
ejpam-6157	80	2	26	26	NUM
ejpam-6157	80	3	]	]	PUNCT
ejpam-6157	80	4	the	the	DET
ejpam-6157	80	5	space	space	NOUN
ejpam-6157	80	6	lx	lx	NOUN
ejpam-6157	80	7	=	=	SYM
ejpam-6157	80	8	lθ(j)×	lθ(j)×	NOUN
ejpam-6157	80	9	lθ(j	lθ(j	X
ejpam-6157	80	10	)	)	PUNCT
ejpam-6157	80	11	is	be	AUX
ejpam-6157	80	12	a	a	DET
ejpam-6157	80	13	banach	banach	NOUN
ejpam-6157	80	14	space	space	NOUN
ejpam-6157	80	15	under	under	ADP
ejpam-6157	80	16	the	the	DET
ejpam-6157	80	17	norm	norm	NOUN
ejpam-6157	80	18	∥(x	∥(x	NOUN
ejpam-6157	80	19	,	,	PUNCT
ejpam-6157	80	20	y)∥x	y)∥x	NOUN
ejpam-6157	80	21	=	=	SYM
ejpam-6157	80	22	∥x∥θ	∥x∥θ	NOUN
ejpam-6157	80	23	+	+	NUM
ejpam-6157	80	24	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	80	25	,	,	PUNCT
ejpam-6157	80	26	where	where	SCONJ
ejpam-6157	80	27	x	x	X
ejpam-6157	80	28	,	,	PUNCT
ejpam-6157	80	29	y	y	PROPN
ejpam-6157	80	30	∈	∈	PROPN
ejpam-6157	80	31	lθ(j	lθ(j	X
ejpam-6157	80	32	)	)	PUNCT
ejpam-6157	80	33	,	,	PUNCT
ejpam-6157	80	34	and	and	CCONJ
ejpam-6157	80	35	lθ	lθ	NOUN
ejpam-6157	80	36	=	=	SYM
ejpam-6157	80	37	lθ(j	lθ(j	X
ejpam-6157	80	38	)	)	PUNCT
ejpam-6157	80	39	is	be	AUX
ejpam-6157	80	40	called	call	VERB
ejpam-6157	80	41	the	the	DET
ejpam-6157	80	42	orlicz	orlicz	ADJ
ejpam-6157	80	43	space	space	NOUN
ejpam-6157	80	44	of	of	ADP
ejpam-6157	80	45	the	the	DET
ejpam-6157	80	46	functions	function	NOUN
ejpam-6157	80	47	f	f	X
ejpam-6157	80	48	under	under	ADP
ejpam-6157	80	49	the	the	DET
ejpam-6157	80	50	norm	norm	NOUN
ejpam-6157	81	1	∥f∥θ	∥f∥θ	NOUN
ejpam-6157	81	2	=	=	SYM
ejpam-6157	81	3	inf	inf	PROPN
ejpam-6157	81	4	ϵ>0	ϵ>0	PROPN
ejpam-6157	81	5	{	{	PUNCT
ejpam-6157	81	6	∫	∫	PROPN
ejpam-6157	81	7	j	j	PROPN
ejpam-6157	81	8	θ	θ	PROPN
ejpam-6157	81	9	(	(	PUNCT
ejpam-6157	81	10	f	f	PROPN
ejpam-6157	81	11	ϵ	ϵ	X
ejpam-6157	81	12	)	)	PUNCT
ejpam-6157	81	13	ds	ds	ADJ
ejpam-6157	81	14	≤	≤	NUM
ejpam-6157	81	15	1	1	NUM
ejpam-6157	81	16	}	}	PUNCT
ejpam-6157	81	17	.	.	PUNCT
ejpam-6157	82	1	let	let	VERB
ejpam-6157	82	2	ex	ex	X
ejpam-6157	82	3	=	=	NOUN
ejpam-6157	82	4	eθ(j	eθ(j	X
ejpam-6157	82	5	)	)	PUNCT
ejpam-6157	82	6	×	×	NOUN
ejpam-6157	82	7	eθ(j	eθ(j	NOUN
ejpam-6157	82	8	)	)	PUNCT
ejpam-6157	82	9	be	be	AUX
ejpam-6157	82	10	the	the	DET
ejpam-6157	82	11	closure	closure	NOUN
ejpam-6157	82	12	in	in	ADP
ejpam-6157	82	13	lx	lx	NOUN
ejpam-6157	82	14	,	,	PUNCT
ejpam-6157	82	15	where	where	SCONJ
ejpam-6157	82	16	eθ	eθ	NOUN
ejpam-6157	82	17	=	=	PRON
ejpam-6157	82	18	eθ(j	eθ(j	X
ejpam-6157	82	19	)	)	PUNCT
ejpam-6157	82	20	be	be	AUX
ejpam-6157	82	21	the	the	DET
ejpam-6157	82	22	closure	closure	NOUN
ejpam-6157	82	23	in	in	ADP
ejpam-6157	82	24	lθ(j	lθ(j	NOUN
ejpam-6157	82	25	)	)	PUNCT
ejpam-6157	82	26	such	such	ADJ
ejpam-6157	82	27	that	that	SCONJ
ejpam-6157	82	28	lim	lim	PROPN
ejpam-6157	82	29	δ→0	δ→0	PUNCT
ejpam-6157	82	30	sup	sup	NOUN
ejpam-6157	82	31	measd	measd	NOUN
ejpam-6157	82	32	<	<	X
ejpam-6157	82	33	δ	δ	PROPN
ejpam-6157	82	34	sup	sup	NOUN
ejpam-6157	82	35	f∈eθ	f∈eθ	PROPN
ejpam-6157	82	36	∥f	∥f	PROPN
ejpam-6157	82	37	·	·	PUNCT
ejpam-6157	82	38	χd∥θ	χd∥θ	PROPN
ejpam-6157	83	1	=	=	PUNCT
ejpam-6157	83	2	0	0	PROPN
ejpam-6157	83	3	,	,	PUNCT
ejpam-6157	83	4	where	where	SCONJ
ejpam-6157	83	5	χd	χd	PROPN
ejpam-6157	83	6	and	and	CCONJ
ejpam-6157	83	7	”	"	PUNCT
ejpam-6157	83	8	meas	mea	NOUN
ejpam-6157	83	9	”	"	PUNCT
ejpam-6157	83	10	are	be	AUX
ejpam-6157	83	11	the	the	DET
ejpam-6157	83	12	characteristic	characteristic	ADJ
ejpam-6157	83	13	function	function	NOUN
ejpam-6157	83	14	of	of	ADP
ejpam-6157	83	15	a	a	DET
ejpam-6157	83	16	measurable	measurable	NOUN
ejpam-6157	83	17	subset	subset	NOUN
ejpam-6157	84	1	d	d	X
ejpam-6157	84	2	⊂	⊂	PROPN
ejpam-6157	84	3	j	j	PROPN
ejpam-6157	84	4	and	and	CCONJ
ejpam-6157	84	5	the	the	DET
ejpam-6157	84	6	lebesgue	lebesgue	NOUN
ejpam-6157	84	7	measure	measure	NOUN
ejpam-6157	84	8	,	,	PUNCT
ejpam-6157	84	9	respectively	respectively	ADV
ejpam-6157	84	10	.	.	PUNCT
ejpam-6157	85	1	for	for	ADP
ejpam-6157	85	2	multiplications	multiplication	NOUN
ejpam-6157	85	3	of	of	ADP
ejpam-6157	85	4	operators	operator	NOUN
ejpam-6157	85	5	,	,	PUNCT
ejpam-6157	85	6	we	we	PRON
ejpam-6157	85	7	have	have	VERB
ejpam-6157	85	8	:	:	PUNCT
ejpam-6157	85	9	m.	m.	NOUN
ejpam-6157	85	10	metwali	metwali	PROPN
ejpam-6157	85	11	,	,	PUNCT
ejpam-6157	85	12	s.	s.	PROPN
ejpam-6157	85	13	alsallami	alsallami	PROPN
ejpam-6157	85	14	/	/	SYM
ejpam-6157	85	15	eur	eur	PROPN
ejpam-6157	85	16	.	.	PUNCT
ejpam-6157	86	1	j.	j.	PROPN
ejpam-6157	86	2	pure	pure	PROPN
ejpam-6157	86	3	appl	appl	PROPN
ejpam-6157	86	4	.	.	PROPN
ejpam-6157	86	5	math	math	PROPN
ejpam-6157	86	6	,	,	PUNCT
ejpam-6157	86	7	18	18	NUM
ejpam-6157	86	8	(	(	PUNCT
ejpam-6157	86	9	2	2	NUM
ejpam-6157	86	10	)	)	PUNCT
ejpam-6157	86	11	(	(	PUNCT
ejpam-6157	86	12	2025	2025	NUM
ejpam-6157	86	13	)	)	PUNCT
ejpam-6157	86	14	,	,	PUNCT
ejpam-6157	86	15	6157	6157	NUM
ejpam-6157	86	16	4	4	NUM
ejpam-6157	86	17	of	of	ADP
ejpam-6157	86	18	15	15	NUM
ejpam-6157	86	19	lemma	lemma	PROPN
ejpam-6157	86	20	1	1	NUM
ejpam-6157	86	21	.	.	PUNCT
ejpam-6157	87	1	(	(	PUNCT
ejpam-6157	87	2	[	[	X
ejpam-6157	87	3	29	29	NUM
ejpam-6157	87	4	,	,	PUNCT
ejpam-6157	87	5	theorem	theorem	VERB
ejpam-6157	87	6	10.2	10.2	NUM
ejpam-6157	87	7	]	]	PUNCT
ejpam-6157	87	8	let	let	VERB
ejpam-6157	87	9	θ1,θ2	θ1,θ2	PROPN
ejpam-6157	87	10	and	and	CCONJ
ejpam-6157	87	11	θ	θ	PROPN
ejpam-6157	87	12	be	be	AUX
ejpam-6157	87	13	arbitrary	arbitrary	ADJ
ejpam-6157	87	14	n	n	CCONJ
ejpam-6157	87	15	-functions	-function	NOUN
ejpam-6157	87	16	.	.	PUNCT
ejpam-6157	88	1	the	the	DET
ejpam-6157	88	2	following	follow	VERB
ejpam-6157	88	3	hypotheses	hypothesis	NOUN
ejpam-6157	88	4	are	be	AUX
ejpam-6157	88	5	identical	identical	ADJ
ejpam-6157	88	6	:	:	PUNCT
ejpam-6157	88	7	(	(	PUNCT
ejpam-6157	88	8	i	i	NOUN
ejpam-6157	88	9	)	)	PUNCT
ejpam-6157	88	10	for	for	ADP
ejpam-6157	88	11	every	every	DET
ejpam-6157	88	12	u1	u1	NOUN
ejpam-6157	88	13	∈	∈	NOUN
ejpam-6157	88	14	lθ1	lθ1	NOUN
ejpam-6157	88	15	and	and	CCONJ
ejpam-6157	88	16	u2	u2	PROPN
ejpam-6157	88	17	∈	∈	PROPN
ejpam-6157	88	18	lθ2	lθ2	ADJ
ejpam-6157	88	19	,	,	PUNCT
ejpam-6157	88	20	u1	u1	NOUN
ejpam-6157	88	21	·	·	PUNCT
ejpam-6157	88	22	u2	u2	PROPN
ejpam-6157	88	23	∈	∈	PROPN
ejpam-6157	88	24	lθ	lθ	X
ejpam-6157	88	25	.	.	PUNCT
ejpam-6157	88	26	(	(	PUNCT
ejpam-6157	88	27	ii	ii	NOUN
ejpam-6157	88	28	)	)	PUNCT
ejpam-6157	88	29	∃	∃	PROPN
ejpam-6157	88	30	k	k	PROPN
ejpam-6157	88	31	>	>	X
ejpam-6157	88	32	0	0	NUM
ejpam-6157	88	33	such	such	ADJ
ejpam-6157	88	34	that	that	SCONJ
ejpam-6157	88	35	for	for	ADP
ejpam-6157	88	36	all	all	DET
ejpam-6157	88	37	measurable	measurable	ADJ
ejpam-6157	88	38	functions	function	NOUN
ejpam-6157	88	39	u1	u1	NOUN
ejpam-6157	88	40	,	,	PUNCT
ejpam-6157	88	41	u2	u2	PROPN
ejpam-6157	88	42	,	,	PUNCT
ejpam-6157	88	43	we	we	PRON
ejpam-6157	88	44	obtain	obtain	VERB
ejpam-6157	88	45	∥u1u2∥θ	∥u1u2∥θ	NOUN
ejpam-6157	88	46	≤	≤	ADJ
ejpam-6157	88	47	k∥u1∥θ1∥u2∥θ2	k∥u1∥θ1∥u2∥θ2	NOUN
ejpam-6157	88	48	.	.	PUNCT
ejpam-6157	89	1	(	(	PUNCT
ejpam-6157	89	2	iii	iii	X
ejpam-6157	89	3	)	)	PUNCT
ejpam-6157	89	4	∃	∃	PROPN
ejpam-6157	89	5	l	l	NOUN
ejpam-6157	89	6	>	>	X
ejpam-6157	89	7	0	0	PROPN
ejpam-6157	89	8	,	,	PUNCT
ejpam-6157	89	9	u0	u0	ADJ
ejpam-6157	89	10	≥	≥	NOUN
ejpam-6157	89	11	0	0	NUM
ejpam-6157	89	12	s.t	s.t	PROPN
ejpam-6157	89	13	.	.	PROPN
ejpam-6157	89	14	∀	∀	PROPN
ejpam-6157	90	1	t	t	PROPN
ejpam-6157	90	2	≥	≥	NOUN
ejpam-6157	90	3	u0	u0	PROPN
ejpam-6157	90	4	,	,	PUNCT
ejpam-6157	90	5	θ	θ	PROPN
ejpam-6157	90	6	(	(	PUNCT
ejpam-6157	90	7	st	st	PROPN
ejpam-6157	90	8	l	l	NOUN
ejpam-6157	90	9	)	)	PUNCT
ejpam-6157	90	10	≤	≤	PROPN
ejpam-6157	90	11	θ1(s	θ1(s	X
ejpam-6157	90	12	)	)	PUNCT
ejpam-6157	90	13	+	+	NUM
ejpam-6157	90	14	θ2(t	θ2(t	PROPN
ejpam-6157	90	15	)	)	PUNCT
ejpam-6157	90	16	.	.	PUNCT
ejpam-6157	91	1	(	(	PUNCT
ejpam-6157	91	2	iv	iv	X
ejpam-6157	91	3	)	)	PUNCT
ejpam-6157	91	4	lim	lim	PROPN
ejpam-6157	91	5	supt→∞	supt→∞	PROPN
ejpam-6157	92	1	θ−1	θ−1	PROPN
ejpam-6157	92	2	1	1	NUM
ejpam-6157	92	3	(	(	PUNCT
ejpam-6157	92	4	t)θ−1	t)θ−1	NOUN
ejpam-6157	92	5	2	2	NUM
ejpam-6157	92	6	(	(	PUNCT
ejpam-6157	92	7	t	t	NOUN
ejpam-6157	92	8	)	)	PUNCT
ejpam-6157	92	9	θ(t	θ(t	PROPN
ejpam-6157	92	10	)	)	PUNCT
ejpam-6157	92	11	<	<	X
ejpam-6157	93	1	∞.	∞.	PROPN
ejpam-6157	93	2	denote	denote	VERB
ejpam-6157	93	3	by	by	ADP
ejpam-6157	93	4	w	w	PROPN
ejpam-6157	93	5	=	=	SYM
ejpam-6157	93	6	w	w	PROPN
ejpam-6157	93	7	(	(	PUNCT
ejpam-6157	93	8	j	j	PROPN
ejpam-6157	93	9	)	)	PUNCT
ejpam-6157	93	10	the	the	DET
ejpam-6157	93	11	set	set	NOUN
ejpam-6157	93	12	of	of	ADP
ejpam-6157	93	13	lebesgue	lebesgue	ADJ
ejpam-6157	93	14	measurable	measurable	ADJ
ejpam-6157	93	15	functions	function	NOUN
ejpam-6157	93	16	on	on	ADP
ejpam-6157	93	17	the	the	DET
ejpam-6157	93	18	interval	interval	NOUN
ejpam-6157	93	19	j	j	PROPN
ejpam-6157	93	20	.	.	PUNCT
ejpam-6157	94	1	the	the	DET
ejpam-6157	94	2	functions	function	NOUN
ejpam-6157	94	3	are	be	AUX
ejpam-6157	94	4	equal	equal	ADJ
ejpam-6157	94	5	almost	almost	ADV
ejpam-6157	94	6	everywhere	everywhere	ADV
ejpam-6157	94	7	in	in	ADP
ejpam-6157	94	8	the	the	DET
ejpam-6157	94	9	set	set	NOUN
ejpam-6157	94	10	w	w	ADP
ejpam-6157	94	11	concerned	concern	VERB
ejpam-6157	94	12	with	with	ADP
ejpam-6157	94	13	the	the	DET
ejpam-6157	94	14	metric	metric	ADJ
ejpam-6157	94	15	d(y	d(y	NOUN
ejpam-6157	94	16	,	,	PUNCT
ejpam-6157	94	17	x	x	NOUN
ejpam-6157	94	18	)	)	PUNCT
ejpam-6157	94	19	=	=	SYM
ejpam-6157	94	20	inf	inf	NOUN
ejpam-6157	94	21	ρ>0	ρ>0	NOUN
ejpam-6157	95	1	[	[	X
ejpam-6157	95	2	ρ+meas{s	ρ+meas{s	X
ejpam-6157	95	3	:	:	PUNCT
ejpam-6157	95	4	|y(s)−	|y(s)−	PROPN
ejpam-6157	95	5	x(s)|	x(s)|	PROPN
ejpam-6157	95	6	≥	≥	PROPN
ejpam-6157	95	7	ρ	ρ	PROPN
ejpam-6157	95	8	}	}	PUNCT
ejpam-6157	95	9	]	]	PUNCT
ejpam-6157	95	10	,	,	PUNCT
ejpam-6157	95	11	becoming	become	VERB
ejpam-6157	95	12	a	a	DET
ejpam-6157	95	13	complete	complete	ADJ
ejpam-6157	95	14	metric	metric	ADJ
ejpam-6157	95	15	space	space	NOUN
ejpam-6157	95	16	.	.	PUNCT
ejpam-6157	96	1	it	it	PRON
ejpam-6157	96	2	should	should	AUX
ejpam-6157	96	3	be	be	AUX
ejpam-6157	96	4	noted	note	VERB
ejpam-6157	96	5	that	that	SCONJ
ejpam-6157	96	6	the	the	DET
ejpam-6157	96	7	convergence	convergence	NOUN
ejpam-6157	96	8	in	in	ADP
ejpam-6157	96	9	measure	measure	NOUN
ejpam-6157	96	10	on	on	ADP
ejpam-6157	96	11	the	the	DET
ejpam-6157	96	12	interval	interval	NOUN
ejpam-6157	96	13	j	j	PROPN
ejpam-6157	96	14	is	be	AUX
ejpam-6157	96	15	the	the	DET
ejpam-6157	96	16	same	same	ADJ
ejpam-6157	96	17	as	as	ADP
ejpam-6157	96	18	the	the	DET
ejpam-6157	96	19	convergence	convergence	NOUN
ejpam-6157	96	20	concerning	concern	VERB
ejpam-6157	96	21	the	the	DET
ejpam-6157	96	22	above	above	ADJ
ejpam-6157	96	23	metric	metric	ADJ
ejpam-6157	96	24	d	d	PROPN
ejpam-6157	96	25	(	(	PUNCT
ejpam-6157	96	26	cf	cf	NOUN
ejpam-6157	96	27	.	.	PUNCT
ejpam-6157	97	1	[	[	X
ejpam-6157	97	2	30	30	NUM
ejpam-6157	97	3	]	]	NUM
ejpam-6157	97	4	)	)	PUNCT
ejpam-6157	97	5	.	.	PUNCT
ejpam-6157	98	1	corollary	corollary	ADJ
ejpam-6157	98	2	1	1	NUM
ejpam-6157	98	3	.	.	PUNCT
ejpam-6157	99	1	[	[	X
ejpam-6157	99	2	26	26	NUM
ejpam-6157	99	3	]	]	PUNCT
ejpam-6157	99	4	assume	assume	VERB
ejpam-6157	99	5	that	that	SCONJ
ejpam-6157	99	6	u	u	PROPN
ejpam-6157	99	7	⊂	⊂	PROPN
ejpam-6157	99	8	lx	lx	PROPN
ejpam-6157	99	9	is	be	AUX
ejpam-6157	99	10	a	a	DET
ejpam-6157	99	11	bounded	bounded	ADJ
ejpam-6157	99	12	set	set	NOUN
ejpam-6157	99	13	and	and	CCONJ
ejpam-6157	99	14	the	the	DET
ejpam-6157	99	15	functions	function	NOUN
ejpam-6157	99	16	x	x	X
ejpam-6157	99	17	,	,	PUNCT
ejpam-6157	99	18	y	y	PROPN
ejpam-6157	99	19	∈	∈	PROPN
ejpam-6157	99	20	lθ	lθ	NOUN
ejpam-6157	99	21	are	be	AUX
ejpam-6157	99	22	almost	almost	ADV
ejpam-6157	99	23	everywhere	everywhere	ADV
ejpam-6157	99	24	.	.	PUNCT
ejpam-6157	100	1	nondecreasing	nondecrease	VERB
ejpam-6157	100	2	(	(	PUNCT
ejpam-6157	100	3	or	or	CCONJ
ejpam-6157	100	4	almost	almost	ADV
ejpam-6157	100	5	everywhere	everywhere	ADV
ejpam-6157	100	6	nonincreasing	nonincrease	VERB
ejpam-6157	100	7	)	)	PUNCT
ejpam-6157	100	8	functions	function	NOUN
ejpam-6157	100	9	on	on	ADP
ejpam-6157	100	10	the	the	DET
ejpam-6157	100	11	interval	interval	NOUN
ejpam-6157	100	12	j	j	PROPN
ejpam-6157	100	13	.	.	PUNCT
ejpam-6157	101	1	therefore	therefore	ADV
ejpam-6157	101	2	,	,	PUNCT
ejpam-6157	101	3	the	the	DET
ejpam-6157	101	4	pair	pair	NOUN
ejpam-6157	101	5	(	(	PUNCT
ejpam-6157	101	6	x	x	NOUN
ejpam-6157	101	7	,	,	PUNCT
ejpam-6157	101	8	y	y	NOUN
ejpam-6157	101	9	)	)	PUNCT
ejpam-6157	101	10	=	=	SYM
ejpam-6157	102	1	u	u	NOUN
ejpam-6157	102	2	∈	∈	NOUN
ejpam-6157	102	3	u	u	NOUN
ejpam-6157	102	4	becomes	become	VERB
ejpam-6157	102	5	almost	almost	ADV
ejpam-6157	102	6	everywhere	everywhere	ADV
ejpam-6157	102	7	nondecreasing	nondecrease	VERB
ejpam-6157	102	8	(	(	PUNCT
ejpam-6157	102	9	or	or	CCONJ
ejpam-6157	102	10	almost	almost	ADV
ejpam-6157	102	11	everywhere	everywhere	ADV
ejpam-6157	102	12	nonincreasing	nonincrease	VERB
ejpam-6157	102	13	)	)	PUNCT
ejpam-6157	102	14	on	on	ADP
ejpam-6157	102	15	the	the	DET
ejpam-6157	102	16	interval	interval	NOUN
ejpam-6157	102	17	j	j	PROPN
ejpam-6157	102	18	,	,	PUNCT
ejpam-6157	102	19	in	in	ADP
ejpam-6157	102	20	addition	addition	NOUN
ejpam-6157	102	21	to	to	ADP
ejpam-6157	102	22	the	the	DET
ejpam-6157	102	23	set	set	NOUN
ejpam-6157	102	24	u	u	NOUN
ejpam-6157	102	25	being	be	AUX
ejpam-6157	102	26	compact	compact	ADJ
ejpam-6157	102	27	in	in	ADP
ejpam-6157	102	28	measure	measure	NOUN
ejpam-6157	102	29	in	in	ADP
ejpam-6157	102	30	lx	lx	NOUN
ejpam-6157	102	31	.	.	PUNCT
ejpam-6157	103	1	definition	definition	NOUN
ejpam-6157	103	2	3	3	NUM
ejpam-6157	103	3	.	.	PUNCT
ejpam-6157	104	1	[	[	X
ejpam-6157	104	2	31	31	NUM
ejpam-6157	104	3	]	]	PUNCT
ejpam-6157	104	4	assume	assume	VERB
ejpam-6157	104	5	that	that	SCONJ
ejpam-6157	104	6	u	u	PROPN
ejpam-6157	104	7	⊂	⊂	PROPN
ejpam-6157	104	8	lx	lx	PROPN
ejpam-6157	104	9	is	be	AUX
ejpam-6157	104	10	a	a	DET
ejpam-6157	104	11	bounded	bounded	ADJ
ejpam-6157	104	12	set	set	NOUN
ejpam-6157	104	13	.	.	PUNCT
ejpam-6157	105	1	the	the	DET
ejpam-6157	105	2	hausdorff	hausdorff	PROPN
ejpam-6157	105	3	mnc	mnc	PROPN
ejpam-6157	105	4	βh(x	βh(x	PUNCT
ejpam-6157	105	5	)	)	PUNCT
ejpam-6157	105	6	(	(	PUNCT
ejpam-6157	105	7	cf	cf	NOUN
ejpam-6157	105	8	.	.	PUNCT
ejpam-6157	106	1	[	[	X
ejpam-6157	106	2	31	31	NUM
ejpam-6157	106	3	]	]	PUNCT
ejpam-6157	106	4	)	)	PUNCT
ejpam-6157	106	5	is	be	AUX
ejpam-6157	106	6	known	know	VERB
ejpam-6157	106	7	as	as	ADP
ejpam-6157	106	8	βh(u	βh(u	X
ejpam-6157	106	9	)	)	PUNCT
ejpam-6157	106	10	=	=	SYM
ejpam-6157	106	11	inf{r	inf{r	PROPN
ejpam-6157	106	12	>	>	X
ejpam-6157	106	13	0	0	PUNCT
ejpam-6157	106	14	:	:	PUNCT
ejpam-6157	107	1	∃	∃	PROPN
ejpam-6157	107	2	y	y	PROPN
ejpam-6157	107	3	⊂	⊂	PROPN
ejpam-6157	107	4	lx	lx	PROPN
ejpam-6157	107	5	s.t	s.t	PROPN
ejpam-6157	107	6	.	.	PROPN
ejpam-6157	107	7	u	u	PROPN
ejpam-6157	107	8	⊂	⊂	PROPN
ejpam-6157	107	9	y	y	PROPN
ejpam-6157	107	10	+	+	CCONJ
ejpam-6157	107	11	br	br	PROPN
ejpam-6157	107	12	}	}	PUNCT
ejpam-6157	107	13	,	,	PUNCT
ejpam-6157	107	14	where	where	SCONJ
ejpam-6157	107	15	br	br	NOUN
ejpam-6157	107	16	=	=	PRON
ejpam-6157	107	17	{	{	PUNCT
ejpam-6157	107	18	x	x	SYM
ejpam-6157	107	19	∈	∈	PROPN
ejpam-6157	107	20	lx	lx	NOUN
ejpam-6157	107	21	:	:	PUNCT
ejpam-6157	107	22	∥x∥x	∥x∥x	PUNCT
ejpam-6157	107	23	≤	≤	NOUN
ejpam-6157	107	24	r	r	X
ejpam-6157	107	25	}	}	PUNCT
ejpam-6157	107	26	,	,	PUNCT
ejpam-6157	107	27	r	r	NOUN
ejpam-6157	107	28	>	>	X
ejpam-6157	107	29	0	0	NUM
ejpam-6157	107	30	.	.	PUNCT
ejpam-6157	108	1	definition	definition	NOUN
ejpam-6157	108	2	4	4	NUM
ejpam-6157	108	3	.	.	PUNCT
ejpam-6157	109	1	[	[	X
ejpam-6157	109	2	26	26	NUM
ejpam-6157	109	3	]	]	PUNCT
ejpam-6157	109	4	assume	assume	VERB
ejpam-6157	109	5	that	that	SCONJ
ejpam-6157	109	6	,	,	PUNCT
ejpam-6157	109	7	∅	∅	NOUN
ejpam-6157	109	8	=	=	NOUN
ejpam-6157	109	9	̸	̸	NUM
ejpam-6157	109	10	u	u	NOUN
ejpam-6157	109	11	=	=	PUNCT
ejpam-6157	109	12	(	(	PUNCT
ejpam-6157	109	13	x1	x1	PROPN
ejpam-6157	109	14	,	,	PUNCT
ejpam-6157	109	15	x2	x2	PROPN
ejpam-6157	109	16	)	)	PUNCT
ejpam-6157	109	17	⊂	⊂	PROPN
ejpam-6157	109	18	lx	lx	NOUN
ejpam-6157	109	19	,	,	PUNCT
ejpam-6157	109	20	with	with	ADP
ejpam-6157	109	21	x1	x1	PROPN
ejpam-6157	109	22	,	,	PUNCT
ejpam-6157	109	23	x2	x2	PROPN
ejpam-6157	109	24	⊂	⊂	PROPN
ejpam-6157	109	25	lθ	lθ	X
ejpam-6157	109	26	are	be	AUX
ejpam-6157	109	27	bounded	bounded	ADJ
ejpam-6157	109	28	sets	set	NOUN
ejpam-6157	109	29	and	and	CCONJ
ejpam-6157	109	30	for	for	ADP
ejpam-6157	109	31	ϵ	ϵ	PROPN
ejpam-6157	109	32	>	>	X
ejpam-6157	109	33	0	0	NUM
ejpam-6157	109	34	,	,	PUNCT
ejpam-6157	109	35	then	then	ADV
ejpam-6157	109	36	c(u	c(u	PROPN
ejpam-6157	109	37	)	)	PUNCT
ejpam-6157	110	1	=	=	SYM
ejpam-6157	110	2	c(x1	c(x1	NOUN
ejpam-6157	110	3	,	,	PUNCT
ejpam-6157	110	4	x2	x2	PROPN
ejpam-6157	110	5	)	)	PUNCT
ejpam-6157	110	6	=	=	SYM
ejpam-6157	110	7	c(x1	c(x1	NOUN
ejpam-6157	110	8	)	)	PUNCT
ejpam-6157	110	9	+	+	NUM
ejpam-6157	110	10	c(x2	c(x2	NOUN
ejpam-6157	110	11	)	)	PUNCT
ejpam-6157	111	1	=	=	SYM
ejpam-6157	111	2	lim	lim	PROPN
ejpam-6157	111	3	sup	sup	NOUN
ejpam-6157	111	4	ε→0	ε→0	NOUN
ejpam-6157	111	5	sup	sup	NOUN
ejpam-6157	111	6	mesd≤ε	mesd≤ε	ADJ
ejpam-6157	111	7	sup	sup	NOUN
ejpam-6157	111	8	x1∈x1	x1∈x1	PROPN
ejpam-6157	111	9	∥x1	∥x1	NOUN
ejpam-6157	111	10	·	·	PUNCT
ejpam-6157	111	11	χd∥θ	χd∥θ	PROPN
ejpam-6157	112	1	+	+	CCONJ
ejpam-6157	112	2	lim	lim	PROPN
ejpam-6157	112	3	sup	sup	NOUN
ejpam-6157	112	4	ε→0	ε→0	NOUN
ejpam-6157	112	5	sup	sup	NOUN
ejpam-6157	112	6	mesd≤ε	mesd≤ε	ADJ
ejpam-6157	112	7	sup	sup	NOUN
ejpam-6157	112	8	x2∈x2	x2∈x2	NUM
ejpam-6157	112	9	∥x2	∥x2	NOUN
ejpam-6157	112	10	·	·	PUNCT
ejpam-6157	112	11	χd∥θ	χd∥θ	PROPN
ejpam-6157	112	12	is	be	AUX
ejpam-6157	112	13	known	know	VERB
ejpam-6157	112	14	as	as	ADP
ejpam-6157	112	15	the	the	DET
ejpam-6157	112	16	measure	measure	NOUN
ejpam-6157	112	17	of	of	ADP
ejpam-6157	112	18	equiintegrability	equiintegrability	NOUN
ejpam-6157	112	19	in	in	ADP
ejpam-6157	112	20	lx	lx	NOUN
ejpam-6157	112	21	.	.	PUNCT
ejpam-6157	113	1	corollary	corollary	ADJ
ejpam-6157	113	2	2	2	NUM
ejpam-6157	113	3	.	.	PUNCT
ejpam-6157	114	1	[	[	X
ejpam-6157	114	2	26	26	NUM
ejpam-6157	114	3	]	]	PUNCT
ejpam-6157	114	4	for	for	ADP
ejpam-6157	114	5	a	a	DET
ejpam-6157	114	6	compact	compact	NOUN
ejpam-6157	114	7	in	in	ADP
ejpam-6157	114	8	measure	measure	NOUN
ejpam-6157	114	9	and	and	CCONJ
ejpam-6157	114	10	bounded	bound	VERB
ejpam-6157	114	11	set	set	NOUN
ejpam-6157	114	12	∅	∅	NOUN
ejpam-6157	114	13	=	=	NOUN
ejpam-6157	114	14	̸	̸	NUM
ejpam-6157	114	15	u	u	NOUN
ejpam-6157	114	16	⊂	⊂	PROPN
ejpam-6157	114	17	lx	lx	PROPN
ejpam-6157	114	18	,	,	PUNCT
ejpam-6157	114	19	we	we	PRON
ejpam-6157	114	20	have	have	VERB
ejpam-6157	114	21	c(u	c(u	PROPN
ejpam-6157	114	22	)	)	PUNCT
ejpam-6157	114	23	=	=	SYM
ejpam-6157	114	24	βh(u	βh(u	PUNCT
ejpam-6157	114	25	)	)	PUNCT
ejpam-6157	114	26	.	.	PUNCT
ejpam-6157	115	1	theorem	theorem	NOUN
ejpam-6157	115	2	1	1	NUM
ejpam-6157	115	3	.	.	PUNCT
ejpam-6157	116	1	[	[	X
ejpam-6157	116	2	26	26	NUM
ejpam-6157	116	3	]	]	PUNCT
ejpam-6157	116	4	assume	assume	VERB
ejpam-6157	116	5	that	that	SCONJ
ejpam-6157	116	6	∅	∅	NOUN
ejpam-6157	116	7	=	=	NOUN
ejpam-6157	116	8	̸	̸	NUM
ejpam-6157	116	9	c	c	X
ejpam-6157	117	1	⊂	⊂	PROPN
ejpam-6157	117	2	lx	lx	PROPN
ejpam-6157	117	3	is	be	AUX
ejpam-6157	117	4	a	a	DET
ejpam-6157	117	5	closed	closed	ADJ
ejpam-6157	117	6	,	,	PUNCT
ejpam-6157	117	7	bounded	bound	VERB
ejpam-6157	117	8	,	,	PUNCT
ejpam-6157	117	9	and	and	CCONJ
ejpam-6157	117	10	convex	convex	VERB
ejpam-6157	117	11	in	in	ADP
ejpam-6157	117	12	addition	addition	NOUN
ejpam-6157	117	13	to	to	ADP
ejpam-6157	117	14	the	the	DET
ejpam-6157	117	15	continuous	continuous	ADJ
ejpam-6157	117	16	map	map	NOUN
ejpam-6157	117	17	t	t	NOUN
ejpam-6157	117	18	:	:	PUNCT
ejpam-6157	117	19	c	c	PROPN
ejpam-6157	117	20	→	→	SYM
ejpam-6157	117	21	c	c	NOUN
ejpam-6157	117	22	verifying	verifying	NOUN
ejpam-6157	117	23	βh(t	βh(t	PUNCT
ejpam-6157	117	24	(	(	PUNCT
ejpam-6157	117	25	u	u	NOUN
ejpam-6157	117	26	)	)	PUNCT
ejpam-6157	117	27	)	)	PUNCT
ejpam-6157	117	28	≤	≤	PUNCT
ejpam-6157	118	1	k	k	X
ejpam-6157	118	2	βh(u	βh(u	X
ejpam-6157	118	3	)	)	PUNCT
ejpam-6157	118	4	,	,	PUNCT
ejpam-6157	118	5	0	0	NUM
ejpam-6157	118	6	≤	≤	X
ejpam-6157	119	1	k	k	X
ejpam-6157	119	2	<	<	X
ejpam-6157	119	3	1	1	NUM
ejpam-6157	119	4	,	,	PUNCT
ejpam-6157	119	5	(	(	PUNCT
ejpam-6157	119	6	contraction	contraction	NOUN
ejpam-6157	119	7	condition	condition	NOUN
ejpam-6157	119	8	)	)	PUNCT
ejpam-6157	119	9	for	for	ADP
ejpam-6157	119	10	any	any	DET
ejpam-6157	119	11	∅	∅	NOUN
ejpam-6157	119	12	=	=	NOUN
ejpam-6157	119	13	̸	̸	NUM
ejpam-6157	119	14	u	u	NOUN
ejpam-6157	119	15	⊂	⊂	PROPN
ejpam-6157	119	16	c.	c.	PROPN
ejpam-6157	119	17	then	then	ADV
ejpam-6157	119	18	t	t	PROPN
ejpam-6157	119	19	has	have	VERB
ejpam-6157	119	20	at	at	ADV
ejpam-6157	119	21	least	least	ADV
ejpam-6157	119	22	one	one	NUM
ejpam-6157	119	23	fixed	fix	VERB
ejpam-6157	119	24	point	point	NOUN
ejpam-6157	119	25	in	in	ADP
ejpam-6157	119	26	c.	c.	PROPN
ejpam-6157	119	27	m.	m.	PROPN
ejpam-6157	119	28	metwali	metwali	PROPN
ejpam-6157	119	29	,	,	PUNCT
ejpam-6157	119	30	s.	s.	PROPN
ejpam-6157	119	31	alsallami	alsallami	PROPN
ejpam-6157	119	32	/	/	SYM
ejpam-6157	119	33	eur	eur	PROPN
ejpam-6157	119	34	.	.	PUNCT
ejpam-6157	120	1	j.	j.	PROPN
ejpam-6157	120	2	pure	pure	PROPN
ejpam-6157	120	3	appl	appl	PROPN
ejpam-6157	120	4	.	.	PROPN
ejpam-6157	120	5	math	math	PROPN
ejpam-6157	120	6	,	,	PUNCT
ejpam-6157	120	7	18	18	NUM
ejpam-6157	120	8	(	(	PUNCT
ejpam-6157	120	9	2	2	NUM
ejpam-6157	120	10	)	)	PUNCT
ejpam-6157	120	11	(	(	PUNCT
ejpam-6157	120	12	2025	2025	NUM
ejpam-6157	120	13	)	)	PUNCT
ejpam-6157	120	14	,	,	PUNCT
ejpam-6157	120	15	6157	6157	NUM
ejpam-6157	120	16	5	5	NUM
ejpam-6157	120	17	of	of	ADP
ejpam-6157	120	18	15	15	NUM
ejpam-6157	120	19	proposition	proposition	NOUN
ejpam-6157	120	20	1	1	NUM
ejpam-6157	120	21	.	.	PUNCT
ejpam-6157	121	1	[	[	X
ejpam-6157	121	2	32	32	NUM
ejpam-6157	121	3	]	]	PUNCT
ejpam-6157	121	4	suppose	suppose	VERB
ejpam-6157	121	5	that	that	SCONJ
ejpam-6157	121	6	β	β	PROPN
ejpam-6157	121	7	∈	∈	PROPN
ejpam-6157	121	8	(	(	PUNCT
ejpam-6157	121	9	0	0	NUM
ejpam-6157	121	10	,	,	PUNCT
ejpam-6157	121	11	1	1	NUM
ejpam-6157	121	12	)	)	PUNCT
ejpam-6157	121	13	,	,	PUNCT
ejpam-6157	121	14	t	t	PROPN
ejpam-6157	121	15	∈	∈	PROPN
ejpam-6157	121	16	r+	r+	X
ejpam-6157	121	17	,	,	PUNCT
ejpam-6157	121	18	and	and	CCONJ
ejpam-6157	121	19	θ	θ	PROPN
ejpam-6157	121	20	is	be	AUX
ejpam-6157	121	21	a	a	DET
ejpam-6157	121	22	young	young	ADJ
ejpam-6157	121	23	function	function	NOUN
ejpam-6157	121	24	(	(	PUNCT
ejpam-6157	121	25	yf	yf	NOUN
ejpam-6157	121	26	)	)	PUNCT
ejpam-6157	121	27	,	,	PUNCT
ejpam-6157	121	28	then	then	ADV
ejpam-6157	121	29	we	we	PRON
ejpam-6157	121	30	get	get	VERB
ejpam-6157	121	31	:	:	PUNCT
ejpam-6157	121	32	(	(	PUNCT
ejpam-6157	121	33	a	a	X
ejpam-6157	121	34	)	)	PUNCT
ejpam-6157	121	35	for	for	ADP
ejpam-6157	121	36	∫	∫	PROPN
ejpam-6157	121	37	t	t	PROPN
ejpam-6157	121	38	0	0	NUM
ejpam-6157	121	39	θ(s−β	θ(s−β	PROPN
ejpam-6157	121	40	)	)	PUNCT
ejpam-6157	121	41	ds	ds	ADP
ejpam-6157	121	42	<	<	X
ejpam-6157	121	43	∞.	∞.	PROPN
ejpam-6157	121	44	if	if	SCONJ
ejpam-6157	121	45	β2	β2	VERB
ejpam-6157	121	46	<	<	X
ejpam-6157	121	47	β	β	NOUN
ejpam-6157	121	48	,	,	PUNCT
ejpam-6157	121	49	then	then	ADV
ejpam-6157	121	50	the	the	DET
ejpam-6157	121	51	integral∫	integral∫	NOUN
ejpam-6157	121	52	t	t	NOUN
ejpam-6157	121	53	0	0	NUM
ejpam-6157	121	54	θ(s−β2	θ(s−β2	NOUN
ejpam-6157	121	55	)	)	PUNCT
ejpam-6157	121	56	ds	ds	PROPN
ejpam-6157	121	57	is	be	AUX
ejpam-6157	121	58	finite	finite	ADJ
ejpam-6157	121	59	as	as	ADV
ejpam-6157	121	60	well	well	ADV
ejpam-6157	121	61	.	.	PUNCT
ejpam-6157	122	1	(	(	PUNCT
ejpam-6157	122	2	b	b	X
ejpam-6157	122	3	)	)	PUNCT
ejpam-6157	122	4	the	the	DET
ejpam-6157	122	5	set	set	NOUN
ejpam-6157	122	6	⋓(t	⋓(t	VERB
ejpam-6157	122	7	)	)	PUNCT
ejpam-6157	122	8	=	=	PUNCT
ejpam-6157	123	1	k	k	X
ejpam-6157	123	2	>	>	X
ejpam-6157	123	3	0	0	PUNCT
ejpam-6157	124	1	:	:	SYM
ejpam-6157	124	2	1	1	NUM
ejpam-6157	124	3	k	k	SYM
ejpam-6157	124	4	1	1	NUM
ejpam-6157	124	5	1−β	1−β	NUM
ejpam-6157	124	6	∫	∫	PROPN
ejpam-6157	124	7	tk	tk	PROPN
ejpam-6157	124	8	1	1	NUM
ejpam-6157	124	9	1−β	1−β	NUM
ejpam-6157	124	10	0	0	NUM
ejpam-6157	124	11	θ(sβ−1	θ(sβ−1	NUM
ejpam-6157	124	12	)	)	PUNCT
ejpam-6157	124	13	ds	ds	ADJ
ejpam-6157	124	14	≤	≤	NUM
ejpam-6157	124	15	1	1	NUM
ejpam-6157	124	16			NOUN
ejpam-6157	124	17	is	be	AUX
ejpam-6157	124	18	increasing	increase	VERB
ejpam-6157	124	19	and	and	CCONJ
ejpam-6157	124	20	continuous	continuous	ADJ
ejpam-6157	124	21	functions	function	NOUN
ejpam-6157	124	22	with	with	ADP
ejpam-6157	124	23	⋓(0	⋓(0	NOUN
ejpam-6157	124	24	)	)	PUNCT
ejpam-6157	124	25	=	=	SYM
ejpam-6157	125	1	0	0	X
ejpam-6157	125	2	.	.	PUNCT
ejpam-6157	125	3	definition	definition	NOUN
ejpam-6157	125	4	5	5	NUM
ejpam-6157	125	5	.	.	PUNCT
ejpam-6157	126	1	[	[	X
ejpam-6157	126	2	33	33	NUM
ejpam-6157	126	3	]	]	PUNCT
ejpam-6157	126	4	the	the	DET
ejpam-6157	126	5	hadamard	hadamard	ADJ
ejpam-6157	126	6	type	type	NOUN
ejpam-6157	126	7	fractional	fractional	ADJ
ejpam-6157	126	8	integral	integral	ADJ
ejpam-6157	126	9	of	of	ADP
ejpam-6157	126	10	order	order	NOUN
ejpam-6157	126	11	β	β	X
ejpam-6157	126	12	>	>	X
ejpam-6157	126	13	0	0	NUM
ejpam-6157	127	1	for	for	ADP
ejpam-6157	127	2	a	a	DET
ejpam-6157	127	3	given	give	VERB
ejpam-6157	127	4	integrable	integrable	ADJ
ejpam-6157	127	5	function	function	NOUN
ejpam-6157	127	6	y	y	PROPN
ejpam-6157	127	7	is	be	AUX
ejpam-6157	127	8	known	know	VERB
ejpam-6157	127	9	as	as	ADP
ejpam-6157	127	10	kβy(t	kβy(t	PROPN
ejpam-6157	127	11	)	)	PUNCT
ejpam-6157	127	12	=	=	NOUN
ejpam-6157	127	13	1	1	NUM
ejpam-6157	127	14	γ(β	γ(β	PROPN
ejpam-6157	127	15	)	)	PUNCT
ejpam-6157	127	16	∫	∫	PROPN
ejpam-6157	127	17	t	t	PROPN
ejpam-6157	127	18	1	1	NUM
ejpam-6157	127	19	(	(	PUNCT
ejpam-6157	127	20	log	log	VERB
ejpam-6157	127	21	t	t	PROPN
ejpam-6157	127	22	s	s	PART
ejpam-6157	127	23	)	)	PUNCT
ejpam-6157	127	24	β−1	β−1	PUNCT
ejpam-6157	127	25	y(s	y(s	PROPN
ejpam-6157	127	26	)	)	PUNCT
ejpam-6157	127	27	s	s	PART
ejpam-6157	127	28	ds	ds	PROPN
ejpam-6157	127	29	,	,	PUNCT
ejpam-6157	127	30	t	t	PROPN
ejpam-6157	127	31	>	>	X
ejpam-6157	127	32	1	1	NUM
ejpam-6157	127	33	,	,	PUNCT
ejpam-6157	127	34	β	β	X
ejpam-6157	127	35	>	>	X
ejpam-6157	127	36	0	0	PROPN
ejpam-6157	127	37	,	,	PUNCT
ejpam-6157	127	38	where	where	SCONJ
ejpam-6157	127	39	γ(β	γ(β	PROPN
ejpam-6157	127	40	)	)	PUNCT
ejpam-6157	128	1	=	=	PUNCT
ejpam-6157	128	2	∫∞	∫∞	NOUN
ejpam-6157	128	3	0	0	PUNCT
ejpam-6157	128	4	e−ννβ−1	e−ννβ−1	VERB
ejpam-6157	128	5	dν	dν	PROPN
ejpam-6157	128	6	.	.	PUNCT
ejpam-6157	129	1	proposition	proposition	NOUN
ejpam-6157	129	2	2	2	NUM
ejpam-6157	129	3	.	.	PUNCT
ejpam-6157	130	1	[	[	X
ejpam-6157	130	2	34	34	NUM
ejpam-6157	130	3	]	]	X
ejpam-6157	130	4	the	the	DET
ejpam-6157	130	5	operator	operator	NOUN
ejpam-6157	130	6	kβ	kβ	NOUN
ejpam-6157	130	7	maps	map	VERB
ejpam-6157	130	8	the	the	DET
ejpam-6157	130	9	a.e	a.e	PROPN
ejpam-6157	130	10	.	.	PUNCT
ejpam-6157	130	11	nonnegative	nonnegative	PROPN
ejpam-6157	130	12	-	-	PUNCT
ejpam-6157	130	13	nondecreasing	nondecrease	VERB
ejpam-6157	130	14	functions	function	NOUN
ejpam-6157	130	15	into	into	ADP
ejpam-6157	130	16	itself	itself	PRON
ejpam-6157	130	17	.	.	PUNCT
ejpam-6157	131	1	lemma	lemma	PROPN
ejpam-6157	131	2	2	2	NUM
ejpam-6157	131	3	.	.	PUNCT
ejpam-6157	132	1	[	[	X
ejpam-6157	132	2	28	28	NUM
ejpam-6157	132	3	]	]	PUNCT
ejpam-6157	132	4	suppose	suppose	VERB
ejpam-6157	132	5	,	,	PUNCT
ejpam-6157	132	6	that	that	SCONJ
ejpam-6157	132	7	m∗	m∗	VERB
ejpam-6157	132	8	and	and	CCONJ
ejpam-6157	132	9	m	m	NOUN
ejpam-6157	132	10	are	be	AUX
ejpam-6157	132	11	complementary	complementary	ADJ
ejpam-6157	132	12	n	n	CCONJ
ejpam-6157	132	13	-functions	-function	NOUN
ejpam-6157	132	14	and	and	CCONJ
ejpam-6157	132	15	θ	θ	PROPN
ejpam-6157	132	16	is	be	AUX
ejpam-6157	132	17	n	n	ADV
ejpam-6157	132	18	function	function	NOUN
ejpam-6157	132	19	with	with	ADP
ejpam-6157	132	20	∫	∫	PROPN
ejpam-6157	132	21	t	t	PROPN
ejpam-6157	132	22	0	0	NUM
ejpam-6157	132	23	m(sβ−1	m(sβ−1	NOUN
ejpam-6157	132	24	)	)	PUNCT
ejpam-6157	132	25	ds	ds	ADP
ejpam-6157	132	26	<	<	X
ejpam-6157	132	27	∞	∞	PROPN
ejpam-6157	132	28	,	,	PUNCT
ejpam-6157	132	29	0	0	PUNCT
ejpam-6157	132	30	<	<	X
ejpam-6157	132	31	β	β	X
ejpam-6157	132	32	<	<	X
ejpam-6157	132	33	1	1	NUM
ejpam-6157	132	34	.	.	PUNCT
ejpam-6157	133	1	moreover	moreover	ADV
ejpam-6157	133	2	,	,	PUNCT
ejpam-6157	133	3	put	put	VERB
ejpam-6157	133	4	k(t	k(t	PROPN
ejpam-6157	133	5	)	)	PUNCT
ejpam-6157	133	6	=	=	SYM
ejpam-6157	134	1	1	1	NUM
ejpam-6157	134	2	ϵ	ϵ	SYM
ejpam-6157	134	3	1	1	NUM
ejpam-6157	134	4	1−β	1−β	NUM
ejpam-6157	134	5	∫	∫	NOUN
ejpam-6157	134	6	tϵ	tϵ	NOUN
ejpam-6157	134	7	1	1	NUM
ejpam-6157	134	8	1−β	1−β	NUM
ejpam-6157	134	9	0	0	NUM
ejpam-6157	134	10	m(sβ−1	m(sβ−1	NOUN
ejpam-6157	134	11	)	)	PUNCT
ejpam-6157	134	12	ds	ds	PROPN
ejpam-6157	134	13	∈	∈	PROPN
ejpam-6157	134	14	eθ	eθ	PROPN
ejpam-6157	134	15	,	,	PUNCT
ejpam-6157	134	16	s	s	PROPN
ejpam-6157	134	17	∈	∈	PROPN
ejpam-6157	134	18	j	j	PROPN
ejpam-6157	134	19	,	,	PUNCT
ejpam-6157	134	20	ϵ	ϵ	X
ejpam-6157	134	21	>	>	X
ejpam-6157	134	22	0	0	PROPN
ejpam-6157	134	23	,	,	PUNCT
ejpam-6157	134	24	then	then	ADV
ejpam-6157	134	25	the	the	DET
ejpam-6157	134	26	hadamard	hadamard	ADJ
ejpam-6157	134	27	operator	operator	NOUN
ejpam-6157	134	28	kβ	kβ	X
ejpam-6157	134	29	:	:	PUNCT
ejpam-6157	134	30	lm∗	lm∗	PROPN
ejpam-6157	135	1	→	→	PUNCT
ejpam-6157	135	2	lθ	lθ	PRON
ejpam-6157	135	3	is	be	AUX
ejpam-6157	135	4	continuous	continuous	ADJ
ejpam-6157	135	5	and	and	CCONJ
ejpam-6157	135	6	verifying	verify	VERB
ejpam-6157	135	7	∥kβx∥θ	∥kβx∥θ	PROPN
ejpam-6157	135	8	≤	≤	ADJ
ejpam-6157	135	9	2	2	NUM
ejpam-6157	135	10	γ(β	γ(β	PROPN
ejpam-6157	135	11	)	)	PUNCT
ejpam-6157	135	12	∥k∥θ∥x∥m∗	∥k∥θ∥x∥m∗	PROPN
ejpam-6157	135	13	.	.	PUNCT
ejpam-6157	136	1	3	3	X
ejpam-6157	136	2	.	.	X
ejpam-6157	136	3	main	main	ADJ
ejpam-6157	136	4	results	result	NOUN
ejpam-6157	136	5	.	.	PUNCT
ejpam-6157	137	1	next	next	ADV
ejpam-6157	137	2	,	,	PUNCT
ejpam-6157	137	3	we	we	PRON
ejpam-6157	137	4	discuss	discuss	VERB
ejpam-6157	137	5	the	the	DET
ejpam-6157	137	6	solvability	solvability	NOUN
ejpam-6157	137	7	of	of	ADP
ejpam-6157	137	8	the	the	DET
ejpam-6157	137	9	coupled	couple	VERB
ejpam-6157	137	10	system	system	NOUN
ejpam-6157	137	11	(	(	PUNCT
ejpam-6157	137	12	1	1	NUM
ejpam-6157	137	13	)	)	PUNCT
ejpam-6157	137	14	in	in	ADP
ejpam-6157	137	15	lθ	lθ	PRON
ejpam-6157	137	16	.	.	PUNCT
ejpam-6157	138	1	define	define	VERB
ejpam-6157	138	2	the	the	DET
ejpam-6157	138	3	operator	operator	NOUN
ejpam-6157	138	4	t	t	PROPN
ejpam-6157	138	5	as	as	SCONJ
ejpam-6157	138	6	follows	follow	VERB
ejpam-6157	138	7	t	t	PROPN
ejpam-6157	138	8	(	(	PUNCT
ejpam-6157	138	9	x	x	NOUN
ejpam-6157	138	10	,	,	PUNCT
ejpam-6157	138	11	y)(t	y)(t	PUNCT
ejpam-6157	138	12	)	)	PUNCT
ejpam-6157	139	1	=	=	SYM
ejpam-6157	139	2	(	(	PUNCT
ejpam-6157	139	3	t1y(t	t1y(t	PROPN
ejpam-6157	139	4	)	)	PUNCT
ejpam-6157	139	5	,	,	PUNCT
ejpam-6157	139	6	t2x(t	t2x(t	PROPN
ejpam-6157	139	7	)	)	PUNCT
ejpam-6157	139	8	)	)	PUNCT
ejpam-6157	139	9	,	,	PUNCT
ejpam-6157	140	1	t	t	PROPN
ejpam-6157	140	2	∈	∈	PROPN
ejpam-6157	140	3	j	j	PROPN
ejpam-6157	140	4	,	,	PUNCT
ejpam-6157	140	5	where	where	SCONJ
ejpam-6157	140	6	t1y	t1y	PROPN
ejpam-6157	140	7	=	=	PUNCT
ejpam-6157	140	8	h1	h1	PROPN
ejpam-6157	140	9	+	+	CCONJ
ejpam-6157	140	10	ff1	ff1	NOUN
ejpam-6157	140	11	(	(	PUNCT
ejpam-6157	140	12	λ1(y	λ1(y	PROPN
ejpam-6157	140	13	)	)	PUNCT
ejpam-6157	140	14	,	,	PUNCT
ejpam-6157	140	15	u1(y	u1(y	PROPN
ejpam-6157	140	16	)	)	PUNCT
ejpam-6157	140	17	)	)	PUNCT
ejpam-6157	140	18	,	,	PUNCT
ejpam-6157	140	19	t2x	t2x	NOUN
ejpam-6157	140	20	=	=	SYM
ejpam-6157	140	21	h2	h2	PROPN
ejpam-6157	140	22	+	+	CCONJ
ejpam-6157	140	23	ff2	ff2	PROPN
ejpam-6157	140	24	(	(	PUNCT
ejpam-6157	140	25	λ2(x	λ2(x	NOUN
ejpam-6157	140	26	)	)	PUNCT
ejpam-6157	140	27	,	,	PUNCT
ejpam-6157	140	28	u2(x	u2(x	X
ejpam-6157	140	29	)	)	PUNCT
ejpam-6157	140	30	)	)	PUNCT
ejpam-6157	140	31	,	,	PUNCT
ejpam-6157	140	32	m.	m.	NOUN
ejpam-6157	140	33	metwali	metwali	PROPN
ejpam-6157	140	34	,	,	PUNCT
ejpam-6157	140	35	s.	s.	PROPN
ejpam-6157	140	36	alsallami	alsallami	PROPN
ejpam-6157	140	37	/	/	SYM
ejpam-6157	140	38	eur	eur	PROPN
ejpam-6157	140	39	.	.	PUNCT
ejpam-6157	141	1	j.	j.	PROPN
ejpam-6157	141	2	pure	pure	PROPN
ejpam-6157	141	3	appl	appl	PROPN
ejpam-6157	141	4	.	.	PROPN
ejpam-6157	141	5	math	math	PROPN
ejpam-6157	141	6	,	,	PUNCT
ejpam-6157	141	7	18	18	NUM
ejpam-6157	141	8	(	(	PUNCT
ejpam-6157	141	9	2	2	NUM
ejpam-6157	141	10	)	)	PUNCT
ejpam-6157	141	11	(	(	PUNCT
ejpam-6157	141	12	2025	2025	NUM
ejpam-6157	141	13	)	)	PUNCT
ejpam-6157	141	14	,	,	PUNCT
ejpam-6157	141	15	6157	6157	NUM
ejpam-6157	141	16	6	6	NUM
ejpam-6157	141	17	of	of	ADP
ejpam-6157	141	18	15	15	NUM
ejpam-6157	141	19	ffi	ffi	PROPN
ejpam-6157	141	20	(	(	PUNCT
ejpam-6157	141	21	λi(w	λi(w	NOUN
ejpam-6157	141	22	)	)	PUNCT
ejpam-6157	141	23	,	,	PUNCT
ejpam-6157	141	24	ui(w	ui(w	NOUN
ejpam-6157	141	25	)	)	PUNCT
ejpam-6157	141	26	)	)	PUNCT
ejpam-6157	142	1	=	=	PUNCT
ejpam-6157	142	2	fi	fi	NOUN
ejpam-6157	142	3	(	(	PUNCT
ejpam-6157	142	4	t	t	PROPN
ejpam-6157	142	5	,	,	PUNCT
ejpam-6157	142	6	λ2(w	λ2(w	NUM
ejpam-6157	142	7	)	)	PUNCT
ejpam-6157	142	8	,	,	PUNCT
ejpam-6157	142	9	ui(w	ui(w	NOUN
ejpam-6157	142	10	)	)	PUNCT
ejpam-6157	142	11	)	)	PUNCT
ejpam-6157	142	12	,	,	PUNCT
ejpam-6157	142	13	ui(w	ui(w	NOUN
ejpam-6157	142	14	)	)	PUNCT
ejpam-6157	142	15	=	=	SYM
ejpam-6157	142	16	gi(w	gi(w	X
ejpam-6157	142	17	)	)	PUNCT
ejpam-6157	142	18	·	·	PUNCT
ejpam-6157	142	19	ai(w	ai(w	NOUN
ejpam-6157	142	20	)	)	PUNCT
ejpam-6157	142	21	,	,	PUNCT
ejpam-6157	142	22	and	and	CCONJ
ejpam-6157	142	23	ai(w)(t	ai(w)(t	NUM
ejpam-6157	142	24	)	)	PUNCT
ejpam-6157	142	25	=	=	SYM
ejpam-6157	142	26	kβri(w	kβri(w	PROPN
ejpam-6157	142	27	)	)	PUNCT
ejpam-6157	142	28	,	,	PUNCT
ejpam-6157	142	29	s.t	s.t	PROPN
ejpam-6157	142	30	.	.	PROPN
ejpam-6157	142	31	kβ	kβ	PROPN
ejpam-6157	142	32	is	be	AUX
ejpam-6157	142	33	hadamard	hadamard	ADJ
ejpam-6157	142	34	operator	operator	NOUN
ejpam-6157	142	35	5	5	NUM
ejpam-6157	142	36	and	and	CCONJ
ejpam-6157	142	37	gi	gi	INTJ
ejpam-6157	142	38	,	,	PUNCT
ejpam-6157	142	39	ffi	ffi	PROPN
ejpam-6157	142	40	,	,	PUNCT
ejpam-6157	142	41	λi	λi	PROPN
ejpam-6157	142	42	,	,	PUNCT
ejpam-6157	142	43	ri	ri	PROPN
ejpam-6157	142	44	,	,	PUNCT
ejpam-6157	142	45	are	be	AUX
ejpam-6157	142	46	different	different	ADJ
ejpam-6157	142	47	operators	operator	NOUN
ejpam-6157	142	48	operate	operate	VERB
ejpam-6157	142	49	on	on	ADP
ejpam-6157	142	50	different	different	ADJ
ejpam-6157	142	51	orlicz	orlicz	NOUN
ejpam-6157	142	52	spaces	space	VERB
ejpam-6157	142	53	i	i	PRON
ejpam-6157	142	54	=	=	NOUN
ejpam-6157	142	55	1	1	NUM
ejpam-6157	142	56	,	,	PUNCT
ejpam-6157	142	57	2	2	NUM
ejpam-6157	142	58	.	.	X
ejpam-6157	143	1	first	first	ADV
ejpam-6157	143	2	,	,	PUNCT
ejpam-6157	143	3	we	we	PRON
ejpam-6157	143	4	inspect	inspect	VERB
ejpam-6157	143	5	the	the	DET
ejpam-6157	143	6	existence	existence	NOUN
ejpam-6157	143	7	of	of	ADP
ejpam-6157	143	8	monotonic	monotonic	ADJ
ejpam-6157	143	9	-	-	PUNCT
ejpam-6157	143	10	lθ	lθ	NOUN
ejpam-6157	143	11	solutions	solution	NOUN
ejpam-6157	143	12	for	for	ADP
ejpam-6157	143	13	the	the	DET
ejpam-6157	143	14	coupled	couple	VERB
ejpam-6157	143	15	system	system	NOUN
ejpam-6157	143	16	(	(	PUNCT
ejpam-6157	143	17	1	1	NUM
ejpam-6157	143	18	)	)	PUNCT
ejpam-6157	143	19	.	.	PUNCT
ejpam-6157	144	1	definition	definition	NOUN
ejpam-6157	144	2	6	6	NUM
ejpam-6157	144	3	.	.	PUNCT
ejpam-6157	145	1	the	the	DET
ejpam-6157	145	2	ordered	order	VERB
ejpam-6157	145	3	pair	pair	NOUN
ejpam-6157	145	4	u	u	NOUN
ejpam-6157	145	5	=	=	PUNCT
ejpam-6157	145	6	(	(	PUNCT
ejpam-6157	145	7	x	x	NOUN
ejpam-6157	145	8	,	,	PUNCT
ejpam-6157	145	9	y	y	NOUN
ejpam-6157	145	10	)	)	PUNCT
ejpam-6157	145	11	∈	∈	PROPN
ejpam-6157	145	12	lx	lx	ADP
ejpam-6157	145	13	s.t	s.t	PROPN
ejpam-6157	145	14	.	.	PROPN
ejpam-6157	145	15	x	x	PROPN
ejpam-6157	145	16	,	,	PUNCT
ejpam-6157	145	17	y	y	PROPN
ejpam-6157	145	18	∈	∈	PROPN
ejpam-6157	145	19	lθ	lθ	NOUN
ejpam-6157	145	20	is	be	AUX
ejpam-6157	145	21	called	call	VERB
ejpam-6157	145	22	a	a	DET
ejpam-6157	145	23	solution	solution	NOUN
ejpam-6157	145	24	of	of	ADP
ejpam-6157	145	25	the	the	DET
ejpam-6157	145	26	coupled	couple	VERB
ejpam-6157	145	27	system	system	NOUN
ejpam-6157	145	28	(	(	PUNCT
ejpam-6157	145	29	1	1	NUM
ejpam-6157	145	30	)	)	PUNCT
ejpam-6157	145	31	,	,	PUNCT
ejpam-6157	145	32	if	if	SCONJ
ejpam-6157	145	33	u	u	PRON
ejpam-6157	145	34	verifies	verify	VERB
ejpam-6157	145	35	the	the	DET
ejpam-6157	145	36	coupled	couple	VERB
ejpam-6157	145	37	system	system	NOUN
ejpam-6157	145	38	(	(	PUNCT
ejpam-6157	145	39	1	1	NUM
ejpam-6157	145	40	)	)	PUNCT
ejpam-6157	145	41	.	.	PUNCT
ejpam-6157	146	1	3.1	3.1	NUM
ejpam-6157	146	2	.	.	PUNCT
ejpam-6157	147	1	the	the	DET
ejpam-6157	147	2	existence	existence	NOUN
ejpam-6157	147	3	of	of	ADP
ejpam-6157	147	4	solutions	solution	NOUN
ejpam-6157	147	5	.	.	PUNCT
ejpam-6157	148	1	let	let	VERB
ejpam-6157	148	2	m	m	PRON
ejpam-6157	148	3	,	,	PUNCT
ejpam-6157	148	4	m∗	m∗	NOUN
ejpam-6157	148	5	be	be	AUX
ejpam-6157	148	6	complementary	complementary	ADJ
ejpam-6157	148	7	n	n	CCONJ
ejpam-6157	148	8	-functions	-functions	PROPN
ejpam-6157	148	9	and	and	CCONJ
ejpam-6157	148	10	θ	θ	PROPN
ejpam-6157	148	11	,	,	PUNCT
ejpam-6157	148	12	θ1,θ2	θ1,θ2	PROPN
ejpam-6157	148	13	be	be	VERB
ejpam-6157	148	14	n	n	DET
ejpam-6157	148	15	-functions	-function	NOUN
ejpam-6157	148	16	.	.	PUNCT
ejpam-6157	149	1	furthermore	furthermore	ADV
ejpam-6157	149	2	,	,	PUNCT
ejpam-6157	149	3	put	put	VERB
ejpam-6157	149	4	the	the	DET
ejpam-6157	149	5	assumptions	assumption	NOUN
ejpam-6157	149	6	for	for	ADP
ejpam-6157	149	7	i	i	PRON
ejpam-6157	149	8	=	=	SYM
ejpam-6157	149	9	1	1	NUM
ejpam-6157	149	10	,	,	PUNCT
ejpam-6157	149	11	2	2	NUM
ejpam-6157	149	12	:	:	PUNCT
ejpam-6157	149	13	(	(	PUNCT
ejpam-6157	149	14	g1	g1	PROPN
ejpam-6157	149	15	)	)	PUNCT
ejpam-6157	149	16	∃	∃	PROPN
ejpam-6157	149	17	k1	k1	PROPN
ejpam-6157	149	18	>	>	X
ejpam-6157	149	19	0	0	NUM
ejpam-6157	150	1	s.t	s.t	PROPN
ejpam-6157	150	2	.	.	PROPN
ejpam-6157	151	1	for	for	ADP
ejpam-6157	151	2	every	every	DET
ejpam-6157	151	3	u1	u1	NOUN
ejpam-6157	151	4	∈	∈	NOUN
ejpam-6157	151	5	lθ1	lθ1	NOUN
ejpam-6157	151	6	and	and	CCONJ
ejpam-6157	151	7	u2	u2	PROPN
ejpam-6157	151	8	∈	∈	PROPN
ejpam-6157	151	9	lθ2	lθ2	ADJ
ejpam-6157	151	10	we	we	PRON
ejpam-6157	151	11	have	have	AUX
ejpam-6157	151	12	∥u1u2∥θ	∥u1u2∥θ	VERB
ejpam-6157	151	13	≤	≤	NUM
ejpam-6157	151	14	k1∥u1∥θ1∥u2∥θ2	k1∥u1∥θ1∥u2∥θ2	PROPN
ejpam-6157	151	15	,	,	PUNCT
ejpam-6157	151	16	(	(	PUNCT
ejpam-6157	151	17	g2	g2	PROPN
ejpam-6157	151	18	)	)	PUNCT
ejpam-6157	152	1	hi	hi	PROPN
ejpam-6157	152	2	∈	∈	PROPN
ejpam-6157	152	3	eθ(j	eθ(j	NOUN
ejpam-6157	152	4	)	)	PUNCT
ejpam-6157	152	5	are	be	AUX
ejpam-6157	152	6	a.e	a.e	PROPN
ejpam-6157	152	7	.	.	PROPN
ejpam-6157	152	8	nondecreasing	nondecrease	VERB
ejpam-6157	152	9	functions	function	NOUN
ejpam-6157	152	10	on	on	ADP
ejpam-6157	152	11	the	the	DET
ejpam-6157	152	12	interval	interval	NOUN
ejpam-6157	152	13	j	j	PROPN
ejpam-6157	152	14	,	,	PUNCT
ejpam-6157	152	15	(	(	PUNCT
ejpam-6157	152	16	g3	g3	NOUN
ejpam-6157	152	17	)	)	PUNCT
ejpam-6157	152	18	fi(t	fi(t	NOUN
ejpam-6157	152	19	,	,	PUNCT
ejpam-6157	152	20	x	x	NOUN
ejpam-6157	152	21	,	,	PUNCT
ejpam-6157	152	22	y	y	PROPN
ejpam-6157	152	23	)	)	PUNCT
ejpam-6157	152	24	:	:	PUNCT
ejpam-6157	153	1	j	j	PROPN
ejpam-6157	153	2	×	×	NOUN
ejpam-6157	153	3	r	r	NOUN
ejpam-6157	153	4	×	×	NOUN
ejpam-6157	153	5	r	r	NOUN
ejpam-6157	153	6	→	→	SYM
ejpam-6157	153	7	r	r	NOUN
ejpam-6157	153	8	be	be	AUX
ejpam-6157	153	9	continuous	continuous	ADJ
ejpam-6157	153	10	in	in	ADP
ejpam-6157	153	11	x	x	X
ejpam-6157	153	12	and	and	CCONJ
ejpam-6157	153	13	y	y	PROPN
ejpam-6157	153	14	for	for	ADP
ejpam-6157	153	15	almost	almost	ADV
ejpam-6157	153	16	all	all	PRON
ejpam-6157	153	17	t	t	NOUN
ejpam-6157	153	18	and	and	CCONJ
ejpam-6157	153	19	measurable	measurable	ADJ
ejpam-6157	153	20	in	in	ADP
ejpam-6157	153	21	t	t	PROPN
ejpam-6157	153	22	∈	∈	PROPN
ejpam-6157	154	1	j	j	PROPN
ejpam-6157	154	2	.	.	PUNCT
ejpam-6157	155	1	furthermore	furthermore	ADV
ejpam-6157	155	2	,	,	PUNCT
ejpam-6157	155	3	suppose	suppose	VERB
ejpam-6157	155	4	that	that	SCONJ
ejpam-6157	155	5	t	t	PROPN
ejpam-6157	155	6	→	→	SYM
ejpam-6157	155	7	fi(t	fi(t	NOUN
ejpam-6157	155	8	,	,	PUNCT
ejpam-6157	155	9	x	x	NOUN
ejpam-6157	155	10	,	,	PUNCT
ejpam-6157	155	11	y	y	NOUN
ejpam-6157	155	12	)	)	PUNCT
ejpam-6157	155	13	are	be	AUX
ejpam-6157	155	14	nondecreasingpositive	nondecreasingpositive	ADJ
ejpam-6157	155	15	function	function	NOUN
ejpam-6157	155	16	and	and	CCONJ
ejpam-6157	155	17	∃	∃	PROPN
ejpam-6157	155	18	α1	α1	PROPN
ejpam-6157	155	19	,	,	PUNCT
ejpam-6157	155	20	α2	α2	PROPN
ejpam-6157	155	21	≥	≥	NOUN
ejpam-6157	155	22	0	0	NUM
ejpam-6157	155	23	,	,	PUNCT
ejpam-6157	155	24	and	and	CCONJ
ejpam-6157	155	25	functions	function	VERB
ejpam-6157	155	26	ci	ci	PROPN
ejpam-6157	155	27	∈	∈	PROPN
ejpam-6157	155	28	lθ	lθ	PROPN
ejpam-6157	155	29	s.t	s.t	PROPN
ejpam-6157	155	30	.	.	PROPN
ejpam-6157	155	31	|fi(t	|fi(t	PROPN
ejpam-6157	155	32	,	,	PUNCT
ejpam-6157	155	33	x	x	PRON
ejpam-6157	155	34	,	,	PUNCT
ejpam-6157	155	35	y)|	y)|	PROPN
ejpam-6157	155	36	≤	≤	NOUN
ejpam-6157	155	37	ci(t	ci(t	ADV
ejpam-6157	155	38	)	)	PUNCT
ejpam-6157	156	1	+	+	CCONJ
ejpam-6157	156	2	α1|x|+	α1|x|+	PROPN
ejpam-6157	156	3	α2|y|	α2|y|	NUM
ejpam-6157	156	4	.	.	PUNCT
ejpam-6157	157	1	(	(	PUNCT
ejpam-6157	157	2	2	2	NUM
ejpam-6157	157	3	)	)	PUNCT
ejpam-6157	157	4	(	(	PUNCT
ejpam-6157	157	5	g4	g4	NOUN
ejpam-6157	157	6	)	)	PUNCT
ejpam-6157	157	7	the	the	DET
ejpam-6157	157	8	operators	operator	NOUN
ejpam-6157	157	9	λi	λi	X
ejpam-6157	157	10	:	:	PUNCT
ejpam-6157	157	11	eθ	eθ	PROPN
ejpam-6157	157	12	→	→	SYM
ejpam-6157	157	13	eθ	eθ	PROPN
ejpam-6157	157	14	,	,	PUNCT
ejpam-6157	157	15	gi	gi	INTJ
ejpam-6157	157	16	:	:	PUNCT
ejpam-6157	157	17	eθ	eθ	PROPN
ejpam-6157	157	18	→	→	SYM
ejpam-6157	157	19	eθ1	eθ1	NOUN
ejpam-6157	157	20	,	,	PUNCT
ejpam-6157	157	21	and	and	CCONJ
ejpam-6157	157	22	ri	ri	INTJ
ejpam-6157	157	23	:	:	PUNCT
ejpam-6157	157	24	eθ	eθ	PROPN
ejpam-6157	157	25	→	→	SYM
ejpam-6157	157	26	em∗	em∗	NOUN
ejpam-6157	157	27	,	,	PUNCT
ejpam-6157	157	28	and	and	CCONJ
ejpam-6157	157	29	they	they	PRON
ejpam-6157	157	30	are	be	AUX
ejpam-6157	157	31	continuous	continuous	ADJ
ejpam-6157	157	32	.	.	PUNCT
ejpam-6157	158	1	moreover	moreover	ADV
ejpam-6157	158	2	,	,	PUNCT
ejpam-6157	158	3	let	let	VERB
ejpam-6157	158	4	λi	λi	INTJ
ejpam-6157	158	5	,	,	PUNCT
ejpam-6157	158	6	gi	gi	INTJ
ejpam-6157	158	7	,	,	PUNCT
ejpam-6157	158	8	ri	ri	PROPN
ejpam-6157	158	9	take	take	VERB
ejpam-6157	158	10	the	the	DET
ejpam-6157	158	11	set	set	NOUN
ejpam-6157	158	12	of	of	ADP
ejpam-6157	158	13	all	all	DET
ejpam-6157	158	14	a.e	a.e	PROPN
ejpam-6157	158	15	.	.	NOUN
ejpam-6157	158	16	nondecreasing	nondecrease	VERB
ejpam-6157	158	17	functions	function	NOUN
ejpam-6157	158	18	into	into	ADP
ejpam-6157	158	19	itself	itself	PRON
ejpam-6157	158	20	and	and	CCONJ
ejpam-6157	158	21	assume	assume	VERB
ejpam-6157	158	22	that	that	SCONJ
ejpam-6157	158	23	for	for	ADP
ejpam-6157	158	24	any	any	DET
ejpam-6157	158	25	w	w	PROPN
ejpam-6157	158	26	∈	∈	PROPN
ejpam-6157	158	27	eθ	eθ	SCONJ
ejpam-6157	158	28	we	we	PRON
ejpam-6157	158	29	get	get	VERB
ejpam-6157	158	30	λi(w	λi(w	PUNCT
ejpam-6157	158	31	)	)	PUNCT
ejpam-6157	158	32	∈	∈	PROPN
ejpam-6157	158	33	eθ	eθ	PROPN
ejpam-6157	158	34	,	,	PUNCT
ejpam-6157	158	35	gi(w	gi(w	PUNCT
ejpam-6157	158	36	)	)	PUNCT
ejpam-6157	158	37	∈	∈	PROPN
ejpam-6157	158	38	eθ1	eθ1	NOUN
ejpam-6157	158	39	,	,	PUNCT
ejpam-6157	158	40	and	and	CCONJ
ejpam-6157	158	41	ri(w	ri(w	PUNCT
ejpam-6157	158	42	)	)	PUNCT
ejpam-6157	158	43	∈	∈	PROPN
ejpam-6157	158	44	em∗	em∗	NOUN
ejpam-6157	158	45	.	.	PUNCT
ejpam-6157	159	1	(	(	PUNCT
ejpam-6157	159	2	g5	g5	NOUN
ejpam-6157	159	3	)	)	PUNCT
ejpam-6157	159	4	there	there	PRON
ejpam-6157	159	5	exist	exist	VERB
ejpam-6157	159	6	positive	positive	ADJ
ejpam-6157	159	7	functions	function	NOUN
ejpam-6157	159	8	ai	ai	VERB
ejpam-6157	159	9	∈	∈	PROPN
ejpam-6157	159	10	lθ	lθ	NOUN
ejpam-6157	159	11	,	,	PUNCT
ejpam-6157	159	12	gi	gi	NOUN
ejpam-6157	159	13	∈	∈	NOUN
ejpam-6157	159	14	lθ1	lθ1	NOUN
ejpam-6157	159	15	,	,	PUNCT
ejpam-6157	159	16	bi	bi	PROPN
ejpam-6157	159	17	∈	∈	PROPN
ejpam-6157	159	18	lm∗	lm∗	PROPN
ejpam-6157	159	19	s.t	s.t	PROPN
ejpam-6157	159	20	.	.	PROPN
ejpam-6157	160	1	for	for	ADP
ejpam-6157	160	2	t	t	PROPN
ejpam-6157	160	3	∈	∈	PROPN
ejpam-6157	160	4	j	j	PROPN
ejpam-6157	160	5	,	,	PUNCT
ejpam-6157	160	6	|λi(w)(t)|	|λi(w)(t)|	ADP
ejpam-6157	160	7	≤	≤	NOUN
ejpam-6157	160	8	ai(t)∥w∥θ	ai(t)∥w∥θ	ADJ
ejpam-6157	160	9	,	,	PUNCT
ejpam-6157	160	10	|gi(w)(t)|	|gi(w)(t)|	ADJ
ejpam-6157	160	11	≤	≤	NUM
ejpam-6157	160	12	gi(t)∥w∥θ	gi(t)∥w∥θ	NOUN
ejpam-6157	160	13	,	,	PUNCT
ejpam-6157	160	14	|ri(w)(t)|	|ri(w)(t)|	ADJ
ejpam-6157	160	15	≤	≤	NUM
ejpam-6157	160	16	bi(t)∥w∥θ	bi(t)∥w∥θ	NOUN
ejpam-6157	160	17	.	.	PUNCT
ejpam-6157	161	1	(	(	PUNCT
ejpam-6157	161	2	g6	g6	ADJ
ejpam-6157	161	3	)	)	PUNCT
ejpam-6157	161	4	assume	assume	VERB
ejpam-6157	161	5	that	that	SCONJ
ejpam-6157	161	6	k(t	k(t	NOUN
ejpam-6157	161	7	)	)	PUNCT
ejpam-6157	161	8	=	=	SYM
ejpam-6157	161	9	1	1	NUM
ejpam-6157	161	10	ϵ	ϵ	SYM
ejpam-6157	161	11	1	1	NUM
ejpam-6157	161	12	1−β	1−β	NUM
ejpam-6157	161	13	∫	∫	NOUN
ejpam-6157	161	14	tϵ	tϵ	NOUN
ejpam-6157	161	15	1	1	NUM
ejpam-6157	161	16	1−β	1−β	NUM
ejpam-6157	161	17	0	0	NUM
ejpam-6157	161	18	m(sβ−1	m(sβ−1	NOUN
ejpam-6157	161	19	)	)	PUNCT
ejpam-6157	161	20	ds	ds	PRON
ejpam-6157	161	21	∈	∈	NOUN
ejpam-6157	161	22	eθ2	eθ2	NOUN
ejpam-6157	161	23	for	for	ADP
ejpam-6157	161	24	a.e	a.e	PROPN
ejpam-6157	161	25	.	.	PROPN
ejpam-6157	161	26	s	s	PART
ejpam-6157	161	27	∈	∈	PROPN
ejpam-6157	161	28	j	j	PROPN
ejpam-6157	161	29	and	and	CCONJ
ejpam-6157	161	30	ϵ	ϵ	X
ejpam-6157	161	31	>	>	X
ejpam-6157	161	32	0	0	NUM
ejpam-6157	161	33	.	.	PUNCT
ejpam-6157	162	1	(	(	PUNCT
ejpam-6157	162	2	g7	g7	PROPN
ejpam-6157	162	3	)	)	PUNCT
ejpam-6157	162	4	let	let	VERB
ejpam-6157	162	5	(	(	PUNCT
ejpam-6157	162	6	α1∥a∗∥	α1∥a∗∥	NOUN
ejpam-6157	162	7	−	−	PROPN
ejpam-6157	162	8	1	1	NUM
ejpam-6157	162	9	)	)	SYM
ejpam-6157	162	10	2	2	NUM
ejpam-6157	162	11	>	>	SYM
ejpam-6157	162	12	8α2k1∥k∥θ2	8α2k1∥k∥θ2	NUM
ejpam-6157	162	13	γ(β	γ(β	PROPN
ejpam-6157	162	14	)	)	PUNCT
ejpam-6157	162	15	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	162	16	(	(	PUNCT
ejpam-6157	162	17	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	162	18	+	+	CCONJ
ejpam-6157	162	19	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	162	20	+	+	CCONJ
ejpam-6157	162	21	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	162	22	+	+	X
ejpam-6157	162	23	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	162	24	)	)	PUNCT
ejpam-6157	162	25	,	,	PUNCT
ejpam-6157	162	26	and	and	CCONJ
ejpam-6157	162	27	(	(	PUNCT
ejpam-6157	162	28	α1∥a∗∥θ	α1∥a∗∥θ	INTJ
ejpam-6157	162	29	+	+	ADJ
ejpam-6157	162	30	2	2	NUM
ejpam-6157	162	31	·	·	PUNCT
ejpam-6157	162	32	r	r	NOUN
ejpam-6157	162	33	·	·	PUNCT
ejpam-6157	162	34	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	162	35	γ(β	γ(β	PROPN
ejpam-6157	162	36	)	)	PUNCT
ejpam-6157	162	37	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	162	38	)	)	PUNCT
ejpam-6157	162	39	<	<	X
ejpam-6157	163	1	1	1	NUM
ejpam-6157	163	2	,	,	PUNCT
ejpam-6157	163	3	where	where	SCONJ
ejpam-6157	163	4	r	r	NOUN
ejpam-6157	163	5	is	be	AUX
ejpam-6157	163	6	the	the	DET
ejpam-6157	163	7	positive	positive	ADJ
ejpam-6157	163	8	solution	solution	NOUN
ejpam-6157	163	9	of	of	ADP
ejpam-6157	163	10	the	the	DET
ejpam-6157	163	11	equation	equation	NOUN
ejpam-6157	163	12	∥h1∥θ+∥h2∥θ+∥c1∥θ+	∥h1∥θ+∥h2∥θ+∥c1∥θ+	X
ejpam-6157	163	13	∥c2∥θ−	∥c2∥θ−	ADV
ejpam-6157	163	14	(	(	PUNCT
ejpam-6157	163	15	1−α1∥a∗∥θ	1−α1∥a∗∥θ	NUM
ejpam-6157	163	16	)	)	PUNCT
ejpam-6157	163	17	·	·	PUNCT
ejpam-6157	163	18	r+2α2k1∥k∥θ2	r+2α2k1∥k∥θ2	PROPN
ejpam-6157	163	19	γ(β	γ(β	PROPN
ejpam-6157	163	20	)	)	PUNCT
ejpam-6157	163	21	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	163	22	·	·	SYM
ejpam-6157	163	23	r2	r2	PROPN
ejpam-6157	163	24	=	=	SYM
ejpam-6157	163	25	0	0	NUM
ejpam-6157	163	26	and	and	CCONJ
ejpam-6157	163	27	∥a∗∥θ	∥a∗∥θ	PROPN
ejpam-6157	163	28	=	=	SYM
ejpam-6157	163	29	max	max	PROPN
ejpam-6157	163	30	{	{	PUNCT
ejpam-6157	163	31	∥ai∥θ	∥ai∥θ	PROPN
ejpam-6157	163	32	}	}	PUNCT
ejpam-6157	163	33	,	,	PUNCT
ejpam-6157	163	34	∥b∗∥m∗	∥b∗∥m∗	PROPN
ejpam-6157	163	35	=	=	SYM
ejpam-6157	163	36	max	max	PROPN
ejpam-6157	163	37	{	{	PUNCT
ejpam-6157	163	38	∥bi∥m∗	∥bi∥m∗	NOUN
ejpam-6157	163	39	}	}	PUNCT
ejpam-6157	163	40	and	and	CCONJ
ejpam-6157	163	41	∥g∗∥θ1	∥g∗∥θ1	PROPN
ejpam-6157	163	42	=	=	SYM
ejpam-6157	163	43	max	max	PROPN
ejpam-6157	163	44	{	{	PUNCT
ejpam-6157	163	45	∥gi∥θ1	∥gi∥θ1	PROPN
ejpam-6157	163	46	}	}	PUNCT
ejpam-6157	163	47	.	.	PUNCT
ejpam-6157	164	1	m.	m.	PROPN
ejpam-6157	164	2	metwali	metwali	PROPN
ejpam-6157	164	3	,	,	PUNCT
ejpam-6157	164	4	s.	s.	PROPN
ejpam-6157	164	5	alsallami	alsallami	PROPN
ejpam-6157	164	6	/	/	SYM
ejpam-6157	164	7	eur	eur	PROPN
ejpam-6157	164	8	.	.	PUNCT
ejpam-6157	165	1	j.	j.	PROPN
ejpam-6157	165	2	pure	pure	PROPN
ejpam-6157	165	3	appl	appl	PROPN
ejpam-6157	165	4	.	.	PROPN
ejpam-6157	165	5	math	math	PROPN
ejpam-6157	165	6	,	,	PUNCT
ejpam-6157	165	7	18	18	NUM
ejpam-6157	165	8	(	(	PUNCT
ejpam-6157	165	9	2	2	NUM
ejpam-6157	165	10	)	)	PUNCT
ejpam-6157	165	11	(	(	PUNCT
ejpam-6157	165	12	2025	2025	NUM
ejpam-6157	165	13	)	)	PUNCT
ejpam-6157	165	14	,	,	PUNCT
ejpam-6157	165	15	6157	6157	NUM
ejpam-6157	165	16	7	7	NUM
ejpam-6157	165	17	of	of	ADP
ejpam-6157	165	18	15	15	NUM
ejpam-6157	165	19	theorem	theorem	NOUN
ejpam-6157	165	20	2	2	NUM
ejpam-6157	165	21	.	.	PUNCT
ejpam-6157	166	1	let	let	VERB
ejpam-6157	166	2	the	the	DET
ejpam-6157	166	3	assumptions	assumption	NOUN
ejpam-6157	166	4	(	(	PUNCT
ejpam-6157	166	5	g1)-(g7	g1)-(g7	NOUN
ejpam-6157	166	6	)	)	PUNCT
ejpam-6157	166	7	hold	hold	VERB
ejpam-6157	166	8	,	,	PUNCT
ejpam-6157	166	9	then	then	ADV
ejpam-6157	166	10	there	there	PRON
ejpam-6157	166	11	exists	exist	VERB
ejpam-6157	166	12	a.e	a.e	PROPN
ejpam-6157	166	13	.	.	PROPN
ejpam-6157	166	14	nondecreasingsolution	nondecreasingsolution	PROPN
ejpam-6157	166	15	u	u	PROPN
ejpam-6157	166	16	=	=	PUNCT
ejpam-6157	166	17	(	(	PUNCT
ejpam-6157	166	18	x	x	NOUN
ejpam-6157	166	19	,	,	PUNCT
ejpam-6157	166	20	y	y	PROPN
ejpam-6157	166	21	)	)	PUNCT
ejpam-6157	166	22	∈	∈	PROPN
ejpam-6157	166	23	eθ	eθ	PROPN
ejpam-6157	166	24	of	of	ADP
ejpam-6157	166	25	(	(	PUNCT
ejpam-6157	166	26	1	1	NUM
ejpam-6157	166	27	)	)	PUNCT
ejpam-6157	166	28	.	.	PUNCT
ejpam-6157	167	1	proof	proof	NOUN
ejpam-6157	167	2	.	.	PUNCT
ejpam-6157	168	1	step	step	NOUN
ejpam-6157	168	2	i.	i.	NOUN
ejpam-6157	168	3	in	in	ADP
ejpam-6157	168	4	what	what	PRON
ejpam-6157	168	5	follows	follow	VERB
ejpam-6157	168	6	,	,	PUNCT
ejpam-6157	168	7	put	put	VERB
ejpam-6157	168	8	i	i	PRON
ejpam-6157	168	9	=	=	NOUN
ejpam-6157	168	10	1	1	NUM
ejpam-6157	168	11	,	,	PUNCT
ejpam-6157	168	12	2	2	NUM
ejpam-6157	168	13	.	.	PUNCT
ejpam-6157	168	14	lemma	lemma	PROPN
ejpam-6157	168	15	2	2	NUM
ejpam-6157	168	16	and	and	CCONJ
ejpam-6157	168	17	assumption	assumption	NOUN
ejpam-6157	168	18	(	(	PUNCT
ejpam-6157	168	19	g6	g6	ADJ
ejpam-6157	168	20	)	)	PUNCT
ejpam-6157	168	21	imply	imply	VERB
ejpam-6157	168	22	that	that	SCONJ
ejpam-6157	168	23	the	the	DET
ejpam-6157	168	24	operator	operator	NOUN
ejpam-6157	168	25	kβ	kβ	INTJ
ejpam-6157	168	26	:	:	PUNCT
ejpam-6157	168	27	lm∗	lm∗	PROPN
ejpam-6157	168	28	→	→	PUNCT
ejpam-6157	168	29	lθ2	lθ2	ADJ
ejpam-6157	168	30	is	be	AUX
ejpam-6157	168	31	continuous	continuous	ADJ
ejpam-6157	168	32	and	and	CCONJ
ejpam-6157	168	33	assumptions	assumption	NOUN
ejpam-6157	168	34	(	(	PUNCT
ejpam-6157	168	35	g3	g3	NOUN
ejpam-6157	168	36	)	)	PUNCT
ejpam-6157	168	37	and	and	CCONJ
ejpam-6157	168	38	(	(	PUNCT
ejpam-6157	168	39	g4	g4	NOUN
ejpam-6157	168	40	)	)	PUNCT
ejpam-6157	168	41	indicate	indicate	VERB
ejpam-6157	168	42	that	that	SCONJ
ejpam-6157	168	43	ffi	ffi	PROPN
ejpam-6157	168	44	,	,	PUNCT
ejpam-6157	168	45	λi	λi	NOUN
ejpam-6157	168	46	:	:	PUNCT
ejpam-6157	168	47	eθ	eθ	PROPN
ejpam-6157	168	48	→	→	SYM
ejpam-6157	168	49	eθ	eθ	PROPN
ejpam-6157	168	50	,	,	PUNCT
ejpam-6157	168	51	gi	gi	INTJ
ejpam-6157	168	52	:	:	PUNCT
ejpam-6157	168	53	eθ	eθ	PROPN
ejpam-6157	168	54	→	→	SYM
ejpam-6157	168	55	eθ1	eθ1	PROPN
ejpam-6157	168	56	and	and	CCONJ
ejpam-6157	168	57	ri	ri	PROPN
ejpam-6157	168	58	:	:	PUNCT
ejpam-6157	168	59	eθ	eθ	PROPN
ejpam-6157	168	60	→	→	SYM
ejpam-6157	168	61	em∗	em∗	PROPN
ejpam-6157	168	62	.	.	PUNCT
ejpam-6157	169	1	then	then	ADV
ejpam-6157	169	2	the	the	DET
ejpam-6157	169	3	operators	operator	NOUN
ejpam-6157	169	4	ai	ai	VERB
ejpam-6157	169	5	=	=	VERB
ejpam-6157	169	6	kβri	kβri	NOUN
ejpam-6157	169	7	:	:	PUNCT
ejpam-6157	169	8	eθ	eθ	PROPN
ejpam-6157	169	9	→	→	SYM
ejpam-6157	169	10	eθ2	eθ2	PROPN
ejpam-6157	169	11	is	be	AUX
ejpam-6157	169	12	continuous	continuous	ADJ
ejpam-6157	169	13	.	.	PUNCT
ejpam-6157	170	1	by	by	ADP
ejpam-6157	170	2	assumptions	assumption	NOUN
ejpam-6157	170	3	(	(	PUNCT
ejpam-6157	170	4	g1	g1	PROPN
ejpam-6157	170	5	)	)	PUNCT
ejpam-6157	170	6	and	and	CCONJ
ejpam-6157	170	7	(	(	PUNCT
ejpam-6157	170	8	g4	g4	NOUN
ejpam-6157	170	9	)	)	PUNCT
ejpam-6157	170	10	the	the	DET
ejpam-6157	170	11	operators	operator	NOUN
ejpam-6157	170	12	ui	ui	PROPN
ejpam-6157	171	1	=	=	PUNCT
ejpam-6157	171	2	gi·ai	gi·ai	ADJ
ejpam-6157	171	3	:	:	PUNCT
ejpam-6157	171	4	eθ	eθ	PROPN
ejpam-6157	171	5	→	→	SYM
ejpam-6157	171	6	eθ	eθ	PROPN
ejpam-6157	171	7	is	be	AUX
ejpam-6157	171	8	continuous	continuous	ADJ
ejpam-6157	171	9	.	.	PUNCT
ejpam-6157	172	1	assumption	assumption	NOUN
ejpam-6157	172	2	(	(	PUNCT
ejpam-6157	172	3	g2	g2	PROPN
ejpam-6157	172	4	)	)	PUNCT
ejpam-6157	172	5	gives	give	VERB
ejpam-6157	172	6	that	that	PRON
ejpam-6157	172	7	,	,	PUNCT
ejpam-6157	172	8	the	the	DET
ejpam-6157	172	9	operators	operator	NOUN
ejpam-6157	172	10	ti	ti	VERB
ejpam-6157	172	11	:	:	PUNCT
ejpam-6157	172	12	eθ	eθ	PROPN
ejpam-6157	172	13	→	→	SYM
ejpam-6157	172	14	eθ	eθ	PROPN
ejpam-6157	172	15	are	be	AUX
ejpam-6157	172	16	continuous	continuous	ADJ
ejpam-6157	172	17	.	.	PUNCT
ejpam-6157	173	1	therefore	therefore	ADV
ejpam-6157	173	2	,	,	PUNCT
ejpam-6157	173	3	t	t	PROPN
ejpam-6157	173	4	=	=	SYM
ejpam-6157	173	5	(	(	PUNCT
ejpam-6157	173	6	t1	t1	NOUN
ejpam-6157	173	7	,	,	PUNCT
ejpam-6157	173	8	t2	t2	NOUN
ejpam-6157	173	9	)	)	PUNCT
ejpam-6157	173	10	acts	act	VERB
ejpam-6157	173	11	from	from	ADP
ejpam-6157	173	12	ex	ex	PRON
ejpam-6157	173	13	into	into	ADP
ejpam-6157	173	14	itself	itself	PRON
ejpam-6157	173	15	and	and	CCONJ
ejpam-6157	173	16	is	be	AUX
ejpam-6157	173	17	continuous	continuous	ADJ
ejpam-6157	173	18	.	.	PUNCT
ejpam-6157	174	1	step	step	NOUN
ejpam-6157	174	2	ii	ii	PROPN
ejpam-6157	174	3	.	.	PUNCT
ejpam-6157	175	1	we	we	PRON
ejpam-6157	175	2	shall	shall	AUX
ejpam-6157	175	3	prove	prove	VERB
ejpam-6157	175	4	that	that	SCONJ
ejpam-6157	175	5	t	t	NOUN
ejpam-6157	175	6	:	:	PUNCT
ejpam-6157	175	7	br(ex	br(ex	PROPN
ejpam-6157	175	8	)	)	PUNCT
ejpam-6157	176	1	→	→	PUNCT
ejpam-6157	176	2	ex	ex	X
ejpam-6157	176	3	is	be	AUX
ejpam-6157	176	4	continuous	continuous	ADJ
ejpam-6157	176	5	,	,	PUNCT
ejpam-6157	176	6	where	where	SCONJ
ejpam-6157	176	7	br(ex	br(ex	NOUN
ejpam-6157	176	8	)	)	PUNCT
ejpam-6157	177	1	=	=	PRON
ejpam-6157	177	2	{	{	PUNCT
ejpam-6157	177	3	u	u	NOUN
ejpam-6157	177	4	=	=	SYM
ejpam-6157	177	5	(	(	PUNCT
ejpam-6157	177	6	x	x	NOUN
ejpam-6157	177	7	,	,	PUNCT
ejpam-6157	177	8	y	y	NOUN
ejpam-6157	177	9	)	)	PUNCT
ejpam-6157	177	10	∈	∈	PROPN
ejpam-6157	177	11	lx	lx	NOUN
ejpam-6157	177	12	:	:	PUNCT
ejpam-6157	177	13	x	x	X
ejpam-6157	177	14	,	,	PUNCT
ejpam-6157	177	15	y	y	PROPN
ejpam-6157	177	16	∈	∈	PROPN
ejpam-6157	177	17	eθ	eθ	PROPN
ejpam-6157	177	18	,	,	PUNCT
ejpam-6157	177	19	∥u∥x	∥u∥x	ADJ
ejpam-6157	177	20	≤	≤	NOUN
ejpam-6157	177	21	r	r	NOUN
ejpam-6157	177	22	}	}	PUNCT
ejpam-6157	177	23	.	.	PUNCT
ejpam-6157	178	1	for	for	ADP
ejpam-6157	178	2	arbitrary	arbitrary	ADJ
ejpam-6157	178	3	u	u	NOUN
ejpam-6157	178	4	=	=	SYM
ejpam-6157	178	5	(	(	PUNCT
ejpam-6157	178	6	x	x	NOUN
ejpam-6157	178	7	,	,	PUNCT
ejpam-6157	178	8	y	y	NOUN
ejpam-6157	178	9	)	)	PUNCT
ejpam-6157	178	10	∈	∈	PROPN
ejpam-6157	178	11	br(ex	br(ex	NOUN
ejpam-6157	178	12	)	)	PUNCT
ejpam-6157	178	13	,	,	PUNCT
ejpam-6157	178	14	x	x	X
ejpam-6157	178	15	,	,	PUNCT
ejpam-6157	178	16	y	y	PROPN
ejpam-6157	178	17	∈	∈	PROPN
ejpam-6157	178	18	eθ	eθ	PROPN
ejpam-6157	178	19	,	,	PUNCT
ejpam-6157	178	20	and	and	CCONJ
ejpam-6157	178	21	recalling	recall	VERB
ejpam-6157	178	22	remark	remark	NOUN
ejpam-6157	178	23	2	2	NUM
ejpam-6157	178	24	,	,	PUNCT
ejpam-6157	178	25	we	we	PRON
ejpam-6157	178	26	have	have	VERB
ejpam-6157	178	27	∥t1y∥θ	∥t1y∥θ	NOUN
ejpam-6157	178	28	≤	≤	NUM
ejpam-6157	178	29	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	178	30	+	+	CCONJ
ejpam-6157	178	31	∥f1(t	∥f1(t	PROPN
ejpam-6157	178	32	,	,	PUNCT
ejpam-6157	178	33	λ1(y	λ1(y	PROPN
ejpam-6157	178	34	)	)	PUNCT
ejpam-6157	178	35	,	,	PUNCT
ejpam-6157	178	36	u1(y))∥θ	u1(y))∥θ	PROPN
ejpam-6157	178	37	≤	≤	NUM
ejpam-6157	178	38	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	178	39	+	+	CCONJ
ejpam-6157	178	40	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	178	41	+	+	CCONJ
ejpam-6157	178	42	α1∥λ1(y)∥θ	α1∥λ1(y)∥θ	X
ejpam-6157	178	43	+	+	CCONJ
ejpam-6157	178	44	α2∥u1y∥θ	α2∥u1y∥θ	PROPN
ejpam-6157	178	45	≤	≤	NOUN
ejpam-6157	178	46	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	178	47	+	+	CCONJ
ejpam-6157	178	48	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	178	49	+	+	CCONJ
ejpam-6157	178	50	α1	α1	PROPN
ejpam-6157	178	51	∥∥∥a1	∥∥∥a1	VERB
ejpam-6157	178	52	·	·	PUNCT
ejpam-6157	178	53	∥y∥θ∥∥∥	∥y∥θ∥∥∥	NUM
ejpam-6157	178	54	θ	θ	PROPN
ejpam-6157	178	55	+	+	CCONJ
ejpam-6157	178	56	α2∥g1(y	α2∥g1(y	NUM
ejpam-6157	178	57	)	)	PUNCT
ejpam-6157	178	58	·	·	PUNCT
ejpam-6157	178	59	a1(y)∥θ	a1(y)∥θ	VERB
ejpam-6157	178	60	≤	≤	NUM
ejpam-6157	178	61	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	178	62	+	+	CCONJ
ejpam-6157	178	63	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	178	64	+	+	CCONJ
ejpam-6157	178	65	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	178	66	·	·	PUNCT
ejpam-6157	179	1	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	180	1	+	+	PUNCT
ejpam-6157	180	2	α2k1∥g1(y)∥θ1	α2k1∥g1(y)∥θ1	PROPN
ejpam-6157	180	3	·	·	PUNCT
ejpam-6157	180	4	∥a1(y)∥θ2	∥a1(y)∥θ2	NOUN
ejpam-6157	180	5	≤	≤	PRON
ejpam-6157	180	6	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	180	7	+	+	CCONJ
ejpam-6157	180	8	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	180	9	+	+	CCONJ
ejpam-6157	180	10	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	180	11	·	·	PUNCT
ejpam-6157	180	12	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	180	13	+	+	PUNCT
ejpam-6157	180	14	α2k1	α2k1	PRON
ejpam-6157	180	15	∥∥∥g1	∥∥∥g1	NUM
ejpam-6157	180	16	·	·	PUNCT
ejpam-6157	180	17	∥y∥θ∥∥∥	∥y∥θ∥∥∥	NUM
ejpam-6157	180	18	θ1	θ1	NOUN
ejpam-6157	180	19	∥∥∥kβr1(y	∥∥∥kβr1(y	NOUN
ejpam-6157	180	20	)	)	PUNCT
ejpam-6157	180	21	∥∥∥	∥∥∥	PROPN
ejpam-6157	180	22	θ2	θ2	ADP
ejpam-6157	180	23	≤	≤	NUM
ejpam-6157	180	24	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	180	25	+	+	CCONJ
ejpam-6157	180	26	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	180	27	+	+	CCONJ
ejpam-6157	180	28	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	180	29	·	·	PUNCT
ejpam-6157	180	30	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	180	31	+	+	CCONJ
ejpam-6157	180	32	α2k1∥g1∥θ1	α2k1∥g1∥θ1	PROPN
ejpam-6157	180	33	·	·	PUNCT
ejpam-6157	180	34	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	180	35	2∥k∥θ2	2∥k∥θ2	NUM
ejpam-6157	180	36	γ(β	γ(β	PROPN
ejpam-6157	180	37	)	)	PUNCT
ejpam-6157	180	38	∥r1(y)∥m∗	∥r1(y)∥m∗	PROPN
ejpam-6157	180	39	≤	≤	NUM
ejpam-6157	180	40	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	180	41	+	+	CCONJ
ejpam-6157	180	42	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	180	43	+	+	CCONJ
ejpam-6157	180	44	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	180	45	·	·	PUNCT
ejpam-6157	180	46	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	181	1	+	+	NUM
ejpam-6157	181	2	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	181	3	γ(β	γ(β	PROPN
ejpam-6157	181	4	)	)	PUNCT
ejpam-6157	181	5	∥g1∥θ1	∥g1∥θ1	PROPN
ejpam-6157	181	6	·	·	PUNCT
ejpam-6157	181	7	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	181	8	·	·	PUNCT
ejpam-6157	181	9	∥b1∥m∗∥y∥θ	∥b1∥m∗∥y∥θ	PROPN
ejpam-6157	181	10	=	=	SYM
ejpam-6157	181	11	∥h1∥θ	∥h1∥θ	PROPN
ejpam-6157	181	12	+	+	CCONJ
ejpam-6157	181	13	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	181	14	+	+	CCONJ
ejpam-6157	181	15	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	181	16	·	·	PUNCT
ejpam-6157	181	17	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	181	18	+	+	NUM
ejpam-6157	181	19	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	181	20	γ(β	γ(β	PROPN
ejpam-6157	181	21	)	)	PUNCT
ejpam-6157	181	22	∥g1∥θ1∥b1∥m∗	∥g1∥θ1∥b1∥m∗	X
ejpam-6157	181	23	·	·	PUNCT
ejpam-6157	181	24	∥y∥2θ	∥y∥2θ	PROPN
ejpam-6157	181	25	.	.	NOUN
ejpam-6157	181	26	similarly	similarly	ADV
ejpam-6157	181	27	,	,	PUNCT
ejpam-6157	181	28	for	for	ADP
ejpam-6157	181	29	x	x	PROPN
ejpam-6157	181	30	∈	∈	PROPN
ejpam-6157	181	31	eθ	eθ	PROPN
ejpam-6157	181	32	,	,	PUNCT
ejpam-6157	181	33	we	we	PRON
ejpam-6157	181	34	have	have	VERB
ejpam-6157	181	35	∥t2x∥θ	∥t2x∥θ	NOUN
ejpam-6157	181	36	≤	≤	PROPN
ejpam-6157	182	1	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	182	2	+	+	PROPN
ejpam-6157	182	3	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	182	4	+	+	CCONJ
ejpam-6157	182	5	α1∥a2∥θ	α1∥a2∥θ	ADJ
ejpam-6157	182	6	·	·	PUNCT
ejpam-6157	182	7	∥x∥θ	∥x∥θ	NOUN
ejpam-6157	182	8	+	+	NUM
ejpam-6157	182	9	2α2k1∥k∥θ2	2α2k1∥k∥θ2	ADJ
ejpam-6157	182	10	γ(β	γ(β	PROPN
ejpam-6157	182	11	)	)	PUNCT
ejpam-6157	182	12	∥g2∥θ1∥b2∥m∗	∥g2∥θ1∥b2∥m∗	X
ejpam-6157	182	13	·	·	PUNCT
ejpam-6157	182	14	∥x∥2θ	∥x∥2θ	PROPN
ejpam-6157	182	15	.	.	PUNCT
ejpam-6157	183	1	then	then	ADV
ejpam-6157	183	2	for	for	ADP
ejpam-6157	183	3	u	u	PROPN
ejpam-6157	183	4	∈	∈	PROPN
ejpam-6157	183	5	ex	ex	NOUN
ejpam-6157	183	6	,	,	PUNCT
ejpam-6157	183	7	we	we	PRON
ejpam-6157	183	8	have	have	AUX
ejpam-6157	183	9	∥tu∥x	∥tu∥x	VERB
ejpam-6157	183	10	=	=	SYM
ejpam-6157	183	11	∥t1y∥θ	∥t1y∥θ	PROPN
ejpam-6157	183	12	+	+	CCONJ
ejpam-6157	183	13	∥t2x∥θ	∥t2x∥θ	PROPN
ejpam-6157	183	14	≤	≤	NUM
ejpam-6157	183	15	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	183	16	+	+	CCONJ
ejpam-6157	183	17	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	183	18	+	+	CCONJ
ejpam-6157	183	19	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	183	20	+	+	CCONJ
ejpam-6157	183	21	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	183	22	+	+	CCONJ
ejpam-6157	183	23	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	183	24	·	·	PUNCT
ejpam-6157	184	1	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	185	1	+	+	NUM
ejpam-6157	185	2	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	185	3	γ(β	γ(β	PROPN
ejpam-6157	185	4	)	)	PUNCT
ejpam-6157	185	5	∥g1∥θ1∥b1∥m∗	∥g1∥θ1∥b1∥m∗	NOUN
ejpam-6157	185	6	·	·	PUNCT
ejpam-6157	186	1	∥y∥2θ	∥y∥2θ	PUNCT
ejpam-6157	186	2	+	+	ADV
ejpam-6157	186	3	α1∥a2∥θ	α1∥a2∥θ	ADJ
ejpam-6157	186	4	·	·	PUNCT
ejpam-6157	186	5	∥x∥θ	∥x∥θ	NOUN
ejpam-6157	186	6	+	+	NUM
ejpam-6157	186	7	2α2k1∥k∥θ2	2α2k1∥k∥θ2	ADJ
ejpam-6157	186	8	γ(β	γ(β	PROPN
ejpam-6157	186	9	)	)	PUNCT
ejpam-6157	186	10	∥g2∥θ1∥b2∥m∗	∥g2∥θ1∥b2∥m∗	NOUN
ejpam-6157	186	11	·	·	PUNCT
ejpam-6157	187	1	∥x∥2θ	∥x∥2θ	PROPN
ejpam-6157	187	2	≤	≤	NUM
ejpam-6157	187	3	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	187	4	+	+	CCONJ
ejpam-6157	187	5	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	187	6	+	+	CCONJ
ejpam-6157	187	7	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	187	8	+	+	CCONJ
ejpam-6157	187	9	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	187	10	+	+	CCONJ
ejpam-6157	187	11	α1∥a∗∥θ	α1∥a∗∥θ	ADJ
ejpam-6157	187	12	(	(	PUNCT
ejpam-6157	187	13	∥x∥θ	∥x∥θ	NOUN
ejpam-6157	187	14	+	+	NUM
ejpam-6157	187	15	∥y∥θ	∥y∥θ	PROPN
ejpam-6157	187	16	)	)	PUNCT
ejpam-6157	187	17	m.	m.	NOUN
ejpam-6157	187	18	metwali	metwali	PROPN
ejpam-6157	187	19	,	,	PUNCT
ejpam-6157	187	20	s.	s.	PROPN
ejpam-6157	187	21	alsallami	alsallami	PROPN
ejpam-6157	187	22	/	/	SYM
ejpam-6157	187	23	eur	eur	PROPN
ejpam-6157	187	24	.	.	PUNCT
ejpam-6157	188	1	j.	j.	PROPN
ejpam-6157	188	2	pure	pure	PROPN
ejpam-6157	188	3	appl	appl	PROPN
ejpam-6157	188	4	.	.	PROPN
ejpam-6157	188	5	math	math	PROPN
ejpam-6157	188	6	,	,	PUNCT
ejpam-6157	188	7	18	18	NUM
ejpam-6157	188	8	(	(	PUNCT
ejpam-6157	188	9	2	2	NUM
ejpam-6157	188	10	)	)	PUNCT
ejpam-6157	188	11	(	(	PUNCT
ejpam-6157	188	12	2025	2025	NUM
ejpam-6157	188	13	)	)	PUNCT
ejpam-6157	188	14	,	,	PUNCT
ejpam-6157	188	15	6157	6157	NUM
ejpam-6157	188	16	8	8	NUM
ejpam-6157	188	17	of	of	ADP
ejpam-6157	188	18	15	15	NUM
ejpam-6157	188	19	+	+	CCONJ
ejpam-6157	188	20	2α2k1∥k∥θ2	2α2k1∥k∥θ2	ADJ
ejpam-6157	188	21	γ(β	γ(β	PROPN
ejpam-6157	188	22	)	)	PUNCT
ejpam-6157	188	23	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	188	24	(	(	PUNCT
ejpam-6157	188	25	∥x∥θ	∥x∥θ	NOUN
ejpam-6157	188	26	+	+	X
ejpam-6157	188	27	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	188	28	)	)	PUNCT
ejpam-6157	188	29	2	2	NUM
ejpam-6157	188	30	≤	≤	NOUN
ejpam-6157	188	31	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	188	32	+	+	CCONJ
ejpam-6157	188	33	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	188	34	+	+	CCONJ
ejpam-6157	188	35	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	188	36	+	+	CCONJ
ejpam-6157	188	37	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	188	38	+	+	CCONJ
ejpam-6157	188	39	α1∥a∗∥θ	α1∥a∗∥θ	ADJ
ejpam-6157	188	40	·	·	PUNCT
ejpam-6157	188	41	∥u∥x	∥u∥x	ADJ
ejpam-6157	188	42	+	+	CCONJ
ejpam-6157	188	43	2α2k1∥k∥θ2	2α2k1∥k∥θ2	ADJ
ejpam-6157	188	44	γ(β	γ(β	PROPN
ejpam-6157	188	45	)	)	PUNCT
ejpam-6157	188	46	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	188	47	·	·	PUNCT
ejpam-6157	189	1	∥u∥2x	∥u∥2x	PROPN
ejpam-6157	189	2	≤	≤	NUM
ejpam-6157	189	3	∥h1∥θ	∥h1∥θ	NOUN
ejpam-6157	189	4	+	+	CCONJ
ejpam-6157	189	5	∥h2∥θ	∥h2∥θ	PROPN
ejpam-6157	189	6	+	+	CCONJ
ejpam-6157	189	7	∥c1∥θ	∥c1∥θ	PROPN
ejpam-6157	189	8	+	+	CCONJ
ejpam-6157	189	9	∥c2∥θ	∥c2∥θ	PROPN
ejpam-6157	189	10	+	+	PUNCT
ejpam-6157	189	11	α1∥a∗∥θ	α1∥a∗∥θ	ADJ
ejpam-6157	189	12	·	·	PUNCT
ejpam-6157	189	13	r	r	NOUN
ejpam-6157	190	1	+	+	NUM
ejpam-6157	190	2	2α2k1∥k∥θ2	2α2k1∥k∥θ2	ADJ
ejpam-6157	190	3	γ(β	γ(β	PROPN
ejpam-6157	190	4	)	)	PUNCT
ejpam-6157	190	5	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	190	6	·	·	PUNCT
ejpam-6157	190	7	r2	r2	PROPN
ejpam-6157	190	8	≤	≤	ADJ
ejpam-6157	190	9	r	r	NOUN
ejpam-6157	190	10	,	,	PUNCT
ejpam-6157	190	11	where	where	SCONJ
ejpam-6157	190	12	∥a∗∥θ	∥a∗∥θ	NOUN
ejpam-6157	190	13	=	=	SYM
ejpam-6157	190	14	max	max	PROPN
ejpam-6157	190	15	{	{	PUNCT
ejpam-6157	190	16	∥ai∥θ	∥ai∥θ	PROPN
ejpam-6157	190	17	}	}	PUNCT
ejpam-6157	190	18	,	,	PUNCT
ejpam-6157	190	19	∥b∗∥m∗	∥b∗∥m∗	PROPN
ejpam-6157	190	20	=	=	SYM
ejpam-6157	190	21	max	max	PROPN
ejpam-6157	190	22	{	{	PUNCT
ejpam-6157	190	23	∥bi∥m∗	∥bi∥m∗	NOUN
ejpam-6157	190	24	}	}	PUNCT
ejpam-6157	190	25	and	and	CCONJ
ejpam-6157	190	26	∥g∗∥θ1	∥g∗∥θ1	PROPN
ejpam-6157	190	27	=	=	SYM
ejpam-6157	190	28	max	max	PROPN
ejpam-6157	190	29	{	{	PUNCT
ejpam-6157	190	30	∥gi∥θ1	∥gi∥θ1	PROPN
ejpam-6157	190	31	}	}	PUNCT
ejpam-6157	190	32	,	,	PUNCT
ejpam-6157	190	33	i	i	PRON
ejpam-6157	190	34	=	=	NOUN
ejpam-6157	190	35	1	1	NUM
ejpam-6157	190	36	,	,	PUNCT
ejpam-6157	190	37	2	2	NUM
ejpam-6157	190	38	.	.	PUNCT
ejpam-6157	190	39	recalling	recall	VERB
ejpam-6157	190	40	assumption	assumption	NOUN
ejpam-6157	190	41	(	(	PUNCT
ejpam-6157	190	42	g7	g7	PROPN
ejpam-6157	190	43	)	)	PUNCT
ejpam-6157	190	44	,	,	PUNCT
ejpam-6157	190	45	we	we	PRON
ejpam-6157	190	46	have	have	VERB
ejpam-6157	190	47	t	t	NOUN
ejpam-6157	190	48	:	:	PUNCT
ejpam-6157	190	49	br(ex	br(ex	PROPN
ejpam-6157	190	50	)	)	PUNCT
ejpam-6157	191	1	→	→	PUNCT
ejpam-6157	191	2	ex	ex	X
ejpam-6157	191	3	is	be	AUX
ejpam-6157	191	4	continuous	continuous	ADJ
ejpam-6157	191	5	.	.	PUNCT
ejpam-6157	192	1	step	step	NOUN
ejpam-6157	192	2	iii	iii	PROPN
ejpam-6157	192	3	.	.	PUNCT
ejpam-6157	193	1	let	let	VERB
ejpam-6157	193	2	qr	qr	PROPN
ejpam-6157	193	3	⊂	⊂	ADV
ejpam-6157	193	4	br(ex	br(ex	PROPN
ejpam-6157	193	5	)	)	PUNCT
ejpam-6157	193	6	include	include	VERB
ejpam-6157	193	7	all	all	DET
ejpam-6157	193	8	monotonic	monotonic	ADJ
ejpam-6157	193	9	(	(	PUNCT
ejpam-6157	193	10	a.e	a.e	PROPN
ejpam-6157	193	11	.	.	PROPN
ejpam-6157	193	12	nondecreasing	nondecrease	VERB
ejpam-6157	193	13	)	)	PUNCT
ejpam-6157	193	14	functions	function	NOUN
ejpam-6157	193	15	on	on	ADP
ejpam-6157	193	16	the	the	DET
ejpam-6157	193	17	interval	interval	NOUN
ejpam-6157	193	18	j	j	PROPN
ejpam-6157	193	19	.	.	PUNCT
ejpam-6157	194	1	then	then	ADV
ejpam-6157	194	2	∅	∅	NOUN
ejpam-6157	194	3	=	=	NOUN
ejpam-6157	194	4	̸	̸	ADV
ejpam-6157	194	5	qr	qr	NOUN
ejpam-6157	194	6	is	be	AUX
ejpam-6157	194	7	closed	closed	ADJ
ejpam-6157	194	8	,	,	PUNCT
ejpam-6157	194	9	convex	convex	NOUN
ejpam-6157	194	10	,	,	PUNCT
ejpam-6157	194	11	and	and	CCONJ
ejpam-6157	194	12	bounded	bound	VERB
ejpam-6157	194	13	,	,	PUNCT
ejpam-6157	194	14	in	in	ADP
ejpam-6157	194	15	ex	ex	PRON
ejpam-6157	194	16	in	in	ADP
ejpam-6157	194	17	addition	addition	NOUN
ejpam-6157	194	18	to	to	PART
ejpam-6157	194	19	be	be	AUX
ejpam-6157	194	20	compact	compact	ADJ
ejpam-6157	194	21	in	in	ADP
ejpam-6157	194	22	measure	measure	NOUN
ejpam-6157	194	23	regarding	regard	VERB
ejpam-6157	194	24	corollary	corollary	ADJ
ejpam-6157	194	25	1	1	NUM
ejpam-6157	194	26	.	.	PUNCT
ejpam-6157	194	27	step	step	NOUN
ejpam-6157	194	28	iv	iv	NUM
ejpam-6157	194	29	.	.	PUNCT
ejpam-6157	195	1	the	the	DET
ejpam-6157	195	2	operator	operator	NOUN
ejpam-6157	195	3	t	t	PROPN
ejpam-6157	195	4	keeps	keep	VERB
ejpam-6157	195	5	the	the	DET
ejpam-6157	195	6	monotonicity	monotonicity	NOUN
ejpam-6157	195	7	property	property	NOUN
ejpam-6157	195	8	for	for	ADP
ejpam-6157	195	9	the	the	DET
ejpam-6157	195	10	functions	function	NOUN
ejpam-6157	195	11	.	.	PUNCT
ejpam-6157	196	1	for	for	ADP
ejpam-6157	196	2	i	i	PRON
ejpam-6157	196	3	=	=	NOUN
ejpam-6157	196	4	1	1	NUM
ejpam-6157	196	5	,	,	PUNCT
ejpam-6157	196	6	2	2	NUM
ejpam-6157	196	7	,	,	PUNCT
ejpam-6157	196	8	let	let	VERB
ejpam-6157	196	9	us	we	PRON
ejpam-6157	196	10	choose	choose	VERB
ejpam-6157	196	11	u	u	NOUN
ejpam-6157	196	12	=	=	PUNCT
ejpam-6157	196	13	(	(	PUNCT
ejpam-6157	196	14	x	x	NOUN
ejpam-6157	196	15	,	,	PUNCT
ejpam-6157	196	16	y	y	NOUN
ejpam-6157	196	17	)	)	PUNCT
ejpam-6157	196	18	∈	∈	PROPN
ejpam-6157	196	19	qr	qr	NOUN
ejpam-6157	196	20	,	,	PUNCT
ejpam-6157	196	21	where	where	SCONJ
ejpam-6157	196	22	x	x	PUNCT
ejpam-6157	196	23	and	and	CCONJ
ejpam-6157	196	24	y	y	PROPN
ejpam-6157	196	25	are	be	AUX
ejpam-6157	196	26	nondecreasing	nondecrease	VERB
ejpam-6157	196	27	on	on	ADP
ejpam-6157	196	28	j	j	PROPN
ejpam-6157	196	29	.	.	PUNCT
ejpam-6157	197	1	proposition	proposition	NOUN
ejpam-6157	197	2	2	2	NUM
ejpam-6157	197	3	implies	imply	VERB
ejpam-6157	197	4	that	that	SCONJ
ejpam-6157	197	5	the	the	DET
ejpam-6157	197	6	operator	operator	NOUN
ejpam-6157	197	7	kβ	kβ	NOUN
ejpam-6157	197	8	takes	take	VERB
ejpam-6157	197	9	the	the	DET
ejpam-6157	197	10	a.e	a.e	PROPN
ejpam-6157	197	11	.	.	PUNCT
ejpam-6157	197	12	nonnegative	nonnegative	PROPN
ejpam-6157	197	13	-	-	PUNCT
ejpam-6157	197	14	nondecreasing	nondecrease	VERB
ejpam-6157	197	15	functions	function	NOUN
ejpam-6157	197	16	into	into	ADP
ejpam-6157	197	17	itself	itself	PRON
ejpam-6157	197	18	.	.	PUNCT
ejpam-6157	198	1	therefore	therefore	ADV
ejpam-6157	198	2	,	,	PUNCT
ejpam-6157	198	3	the	the	DET
ejpam-6157	198	4	operators	operator	NOUN
ejpam-6157	198	5	ai	ai	VERB
ejpam-6157	198	6	=	=	NOUN
ejpam-6157	198	7	kβri	kβri	NOUN
ejpam-6157	198	8	and	and	CCONJ
ejpam-6157	198	9	λi	λi	CCONJ
ejpam-6157	198	10	,	,	PUNCT
ejpam-6157	198	11	and	and	CCONJ
ejpam-6157	198	12	ui	ui	NOUN
ejpam-6157	198	13	=	=	NOUN
ejpam-6157	198	14	gi	gi	X
ejpam-6157	198	15	·	·	PUNCT
ejpam-6157	198	16	ai	ai	VERB
ejpam-6157	198	17	are	be	AUX
ejpam-6157	198	18	a.e	a.e	PROPN
ejpam-6157	198	19	.	.	PROPN
ejpam-6157	198	20	nondecreasing	nondecrease	VERB
ejpam-6157	198	21	on	on	ADP
ejpam-6157	198	22	the	the	DET
ejpam-6157	198	23	interval	interval	NOUN
ejpam-6157	198	24	j	j	PROPN
ejpam-6157	198	25	(	(	PUNCT
ejpam-6157	198	26	by	by	ADP
ejpam-6157	198	27	using	use	VERB
ejpam-6157	198	28	(	(	PUNCT
ejpam-6157	198	29	g4	g4	NOUN
ejpam-6157	198	30	)	)	PUNCT
ejpam-6157	198	31	)	)	PUNCT
ejpam-6157	198	32	.	.	PUNCT
ejpam-6157	199	1	assumptions	assumption	NOUN
ejpam-6157	199	2	(	(	PUNCT
ejpam-6157	199	3	g2	g2	PROPN
ejpam-6157	199	4	)	)	PUNCT
ejpam-6157	199	5	and	and	CCONJ
ejpam-6157	199	6	(	(	PUNCT
ejpam-6157	199	7	g3	g3	NOUN
ejpam-6157	199	8	)	)	PUNCT
ejpam-6157	199	9	grant	grant	VERB
ejpam-6157	199	10	us	we	PRON
ejpam-6157	199	11	that	that	SCONJ
ejpam-6157	199	12	the	the	DET
ejpam-6157	199	13	operators	operator	NOUN
ejpam-6157	199	14	t1	t1	VERB
ejpam-6157	199	15	,	,	PUNCT
ejpam-6157	199	16	t2	t2	PROPN
ejpam-6157	199	17	are	be	AUX
ejpam-6157	199	18	a.e	a.e	PROPN
ejpam-6157	199	19	.	.	PROPN
ejpam-6157	199	20	nondecreasing	nondecrease	VERB
ejpam-6157	199	21	on	on	ADP
ejpam-6157	199	22	j	j	PROPN
ejpam-6157	199	23	.	.	PUNCT
ejpam-6157	200	1	those	those	PRON
ejpam-6157	200	2	grant	grant	VERB
ejpam-6157	200	3	us	we	PRON
ejpam-6157	200	4	that	that	DET
ejpam-6157	200	5	t	t	NOUN
ejpam-6157	200	6	=	=	SYM
ejpam-6157	200	7	(	(	PUNCT
ejpam-6157	200	8	t1	t1	NOUN
ejpam-6157	200	9	,	,	PUNCT
ejpam-6157	200	10	t2	t2	PROPN
ejpam-6157	200	11	)	)	PUNCT
ejpam-6157	200	12	:	:	PUNCT
ejpam-6157	200	13	qr	qr	PROPN
ejpam-6157	200	14	→	→	SYM
ejpam-6157	200	15	qr	qr	PROPN
ejpam-6157	200	16	is	be	AUX
ejpam-6157	200	17	continuous	continuous	ADJ
ejpam-6157	200	18	.	.	PUNCT
ejpam-6157	201	1	step	step	NOUN
ejpam-6157	201	2	v.	v.	CCONJ
ejpam-6157	201	3	we	we	PRON
ejpam-6157	201	4	need	need	VERB
ejpam-6157	201	5	to	to	PART
ejpam-6157	201	6	show	show	VERB
ejpam-6157	201	7	that	that	SCONJ
ejpam-6157	201	8	βh(tx	βh(tx	NOUN
ejpam-6157	201	9	)	)	PUNCT
ejpam-6157	201	10	≤	≤	NUM
ejpam-6157	201	11	kβh(x	kβh(x	PROPN
ejpam-6157	201	12	)	)	PUNCT
ejpam-6157	201	13	,	,	PUNCT
ejpam-6157	201	14	k	k	PROPN
ejpam-6157	201	15	∈	∈	PROPN
ejpam-6157	202	1	[	[	X
ejpam-6157	202	2	0	0	NUM
ejpam-6157	202	3	,	,	PUNCT
ejpam-6157	202	4	1	1	NUM
ejpam-6157	202	5	)	)	PUNCT
ejpam-6157	202	6	.	.	PUNCT
ejpam-6157	203	1	for	for	ADP
ejpam-6157	203	2	any	any	DET
ejpam-6157	203	3	u	u	NOUN
ejpam-6157	203	4	=	=	PUNCT
ejpam-6157	203	5	(	(	PUNCT
ejpam-6157	203	6	x	x	NOUN
ejpam-6157	203	7	,	,	PUNCT
ejpam-6157	203	8	y	y	NOUN
ejpam-6157	203	9	)	)	PUNCT
ejpam-6157	203	10	∈	∈	PROPN
ejpam-6157	203	11	u	u	PROPN
ejpam-6157	203	12	⊂	⊂	PROPN
ejpam-6157	203	13	qr	qr	PROPN
ejpam-6157	203	14	and	and	CCONJ
ejpam-6157	203	15	a	a	DET
ejpam-6157	203	16	set	set	NOUN
ejpam-6157	203	17	d	d	X
ejpam-6157	203	18	⊂	⊂	PROPN
ejpam-6157	203	19	j	j	PROPN
ejpam-6157	203	20	,	,	PUNCT
ejpam-6157	203	21	with	with	ADP
ejpam-6157	203	22	measd	measd	NOUN
ejpam-6157	203	23	≤	≤	X
ejpam-6157	203	24	ε	ε	PROPN
ejpam-6157	203	25	,	,	PUNCT
ejpam-6157	203	26	ε	ε	PROPN
ejpam-6157	203	27	>	>	X
ejpam-6157	203	28	0	0	PROPN
ejpam-6157	203	29	.	.	PUNCT
ejpam-6157	204	1	by	by	ADP
ejpam-6157	204	2	assumption	assumption	NOUN
ejpam-6157	204	3	(	(	PUNCT
ejpam-6157	204	4	g5	g5	NOUN
ejpam-6157	204	5	)	)	PUNCT
ejpam-6157	204	6	,	,	PUNCT
ejpam-6157	204	7	we	we	PRON
ejpam-6157	204	8	have	have	VERB
ejpam-6157	204	9	∥λi(z	∥λi(z	NOUN
ejpam-6157	204	10	)	)	PUNCT
ejpam-6157	204	11	·	·	PUNCT
ejpam-6157	205	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	205	2	≤	≤	PROPN
ejpam-6157	205	3	∥λi(x	∥λi(x	NOUN
ejpam-6157	205	4	·	·	PUNCT
ejpam-6157	205	5	χd)∥θ	χd)∥θ	VERB
ejpam-6157	205	6	≤	≤	NOUN
ejpam-6157	205	7	∥∥a1	∥∥a1	NOUN
ejpam-6157	205	8	·	·	PUNCT
ejpam-6157	206	1	∥x	∥x	NOUN
ejpam-6157	206	2	·	·	PUNCT
ejpam-6157	206	3	χd∥θ	χd∥θ	PROPN
ejpam-6157	206	4	∥∥	∥∥	X
ejpam-6157	206	5	θ	θ	PROPN
ejpam-6157	206	6	≤	≤	PROPN
ejpam-6157	206	7	∥ai∥θ∥x	∥ai∥θ∥x	PROPN
ejpam-6157	206	8	·	·	PUNCT
ejpam-6157	206	9	χd∥θ	χd∥θ	X
ejpam-6157	206	10	and	and	CCONJ
ejpam-6157	206	11	similarly	similarly	ADV
ejpam-6157	206	12	∥gi(z	∥gi(z	X
ejpam-6157	206	13	)	)	PUNCT
ejpam-6157	206	14	·	·	PUNCT
ejpam-6157	207	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	207	2	≤	≤	PROPN
ejpam-6157	207	3	∥∥gi∥∥θ∥x	∥∥gi∥∥θ∥x	PROPN
ejpam-6157	207	4	·	·	PUNCT
ejpam-6157	208	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	208	2	.	.	PUNCT
ejpam-6157	209	1	therefore	therefore	ADV
ejpam-6157	209	2	,	,	PUNCT
ejpam-6157	209	3	we	we	PRON
ejpam-6157	209	4	have	have	AUX
ejpam-6157	209	5	∥t1(y	∥t1(y	VERB
ejpam-6157	209	6	)	)	PUNCT
ejpam-6157	209	7	·	·	PUNCT
ejpam-6157	210	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	210	2	≤	≤	PROPN
ejpam-6157	210	3	∥h1	∥h1	VERB
ejpam-6157	210	4	·	·	PUNCT
ejpam-6157	210	5	χd∥θ	χd∥θ	PROPN
ejpam-6157	211	1	+	+	PUNCT
ejpam-6157	211	2	∥∥∥ff1	∥∥∥ff1	X
ejpam-6157	211	3	(	(	PUNCT
ejpam-6157	211	4	λ1(y	λ1(y	NUM
ejpam-6157	211	5	)	)	PUNCT
ejpam-6157	211	6	,	,	PUNCT
ejpam-6157	211	7	u1(y	u1(y	PROPN
ejpam-6157	211	8	)	)	PUNCT
ejpam-6157	211	9	)	)	PUNCT
ejpam-6157	211	10	·	·	PUNCT
ejpam-6157	212	1	χd	χd	PROPN
ejpam-6157	212	2	∥∥∥	∥∥∥	NUM
ejpam-6157	212	3	θ	θ	PROPN
ejpam-6157	212	4	≤	≤	PROPN
ejpam-6157	212	5	∥h1	∥h1	VERB
ejpam-6157	212	6	·	·	PUNCT
ejpam-6157	212	7	χd∥θ	χd∥θ	X
ejpam-6157	213	1	+	+	PUNCT
ejpam-6157	213	2	∥c1	∥c1	NOUN
ejpam-6157	213	3	·	·	PUNCT
ejpam-6157	213	4	χd∥θ	χd∥θ	PROPN
ejpam-6157	214	1	+	+	CCONJ
ejpam-6157	214	2	α1	α1	PROPN
ejpam-6157	214	3	∥∥∥λ1(y	∥∥∥λ1(y	NUM
ejpam-6157	214	4	)	)	PUNCT
ejpam-6157	214	5	·	·	PUNCT
ejpam-6157	214	6	χd	χd	PROPN
ejpam-6157	214	7	∥∥∥	∥∥∥	PROPN
ejpam-6157	214	8	θ	θ	PROPN
ejpam-6157	214	9	+	+	CCONJ
ejpam-6157	214	10	α2∥g1(y	α2∥g1(y	NUM
ejpam-6157	214	11	)	)	PUNCT
ejpam-6157	214	12	·	·	PUNCT
ejpam-6157	214	13	a1(y	a1(y	PROPN
ejpam-6157	214	14	)	)	PUNCT
ejpam-6157	214	15	·	·	PUNCT
ejpam-6157	215	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	215	2	≤	≤	PROPN
ejpam-6157	215	3	∥h1	∥h1	VERB
ejpam-6157	215	4	·	·	PUNCT
ejpam-6157	215	5	χd∥θ	χd∥θ	PROPN
ejpam-6157	216	1	+	+	PUNCT
ejpam-6157	216	2	∥c1	∥c1	NOUN
ejpam-6157	216	3	·	·	PUNCT
ejpam-6157	216	4	χd∥θ	χd∥θ	X
ejpam-6157	217	1	+	+	NUM
ejpam-6157	217	2	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	217	3	·	·	PUNCT
ejpam-6157	217	4	∥y	∥y	NOUN
ejpam-6157	217	5	·	·	PUNCT
ejpam-6157	217	6	χd∥θ	χd∥θ	PROPN
ejpam-6157	218	1	+	+	CCONJ
ejpam-6157	218	2	α2k1∥g1(y	α2k1∥g1(y	PROPN
ejpam-6157	218	3	)	)	PUNCT
ejpam-6157	218	4	·	·	PUNCT
ejpam-6157	219	1	χd∥θ1	χd∥θ1	PROPN
ejpam-6157	219	2	·	·	PUNCT
ejpam-6157	219	3	∥a1(y)∥θ2	∥a1(y)∥θ2	NOUN
ejpam-6157	219	4	≤	≤	PROPN
ejpam-6157	219	5	∥h1	∥h1	VERB
ejpam-6157	219	6	·	·	PUNCT
ejpam-6157	219	7	χd∥θ	χd∥θ	X
ejpam-6157	220	1	+	+	PUNCT
ejpam-6157	220	2	∥c1	∥c1	NOUN
ejpam-6157	220	3	·	·	PUNCT
ejpam-6157	220	4	χd∥θ	χd∥θ	X
ejpam-6157	221	1	+	+	NUM
ejpam-6157	221	2	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	221	3	·	·	PUNCT
ejpam-6157	221	4	∥y	∥y	NOUN
ejpam-6157	221	5	·	·	PUNCT
ejpam-6157	221	6	χd∥θ	χd∥θ	PROPN
ejpam-6157	222	1	+	+	CCONJ
ejpam-6157	222	2	α2k1∥g1∥θ1	α2k1∥g1∥θ1	PROPN
ejpam-6157	222	3	·	·	PUNCT
ejpam-6157	222	4	∥y	∥y	PROPN
ejpam-6157	222	5	·	·	PUNCT
ejpam-6157	223	1	χd∥θ	χd∥θ	PROPN
ejpam-6157	223	2	2∥k∥θ2	2∥k∥θ2	NUM
ejpam-6157	223	3	γ(β	γ(β	PROPN
ejpam-6157	223	4	)	)	PUNCT
ejpam-6157	223	5	∥b1∥m∗∥y∥θ	∥b1∥m∗∥y∥θ	PROPN
ejpam-6157	223	6	≤	≤	NOUN
ejpam-6157	223	7	∥h1	∥h1	VERB
ejpam-6157	223	8	·	·	PUNCT
ejpam-6157	223	9	χd∥θ	χd∥θ	X
ejpam-6157	224	1	+	+	PUNCT
ejpam-6157	224	2	∥c1	∥c1	NOUN
ejpam-6157	224	3	·	·	PUNCT
ejpam-6157	224	4	χd∥θ	χd∥θ	X
ejpam-6157	225	1	+	+	NUM
ejpam-6157	225	2	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	225	3	·	·	PUNCT
ejpam-6157	225	4	∥y	∥y	NOUN
ejpam-6157	225	5	·	·	PUNCT
ejpam-6157	225	6	χd∥θ	χd∥θ	PROPN
ejpam-6157	226	1	+	+	CCONJ
ejpam-6157	226	2	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	226	3	γ(β	γ(β	PROPN
ejpam-6157	226	4	)	)	PUNCT
ejpam-6157	226	5	∥g1∥θ1	∥g1∥θ1	X
ejpam-6157	226	6	·	·	PUNCT
ejpam-6157	226	7	∥y	∥y	PROPN
ejpam-6157	226	8	·	·	SYM
ejpam-6157	226	9	χd∥θ∥b1∥m∗	χd∥θ∥b1∥m∗	PROPN
ejpam-6157	226	10	·	·	PUNCT
ejpam-6157	226	11	r.	r.	PROPN
ejpam-6157	226	12	similarly	similarly	ADV
ejpam-6157	226	13	,	,	PUNCT
ejpam-6157	226	14	we	we	PRON
ejpam-6157	226	15	have	have	VERB
ejpam-6157	226	16	∥t2x·χd∥θ	∥t2x·χd∥θ	NOUN
ejpam-6157	226	17	≤	≤	NUM
ejpam-6157	226	18	∥h2·χd∥θ+∥c2·χd∥θ+	∥h2·χd∥θ+∥c2·χd∥θ+	NOUN
ejpam-6157	226	19	α1∥a2∥θ·∥x·χd∥θ+	α1∥a2∥θ·∥x·χd∥θ+	NOUN
ejpam-6157	226	20	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	226	21	γ(β	γ(β	PROPN
ejpam-6157	226	22	)	)	PUNCT
ejpam-6157	226	23	∥g2∥θ1	∥g2∥θ1	X
ejpam-6157	226	24	·	·	SYM
ejpam-6157	226	25	∥x·χd∥θ∥b1∥m∗	∥x·χd∥θ∥b1∥m∗	X
ejpam-6157	226	26	·	·	SYM
ejpam-6157	226	27	r.	r.	PROPN
ejpam-6157	226	28	m.	m.	PROPN
ejpam-6157	226	29	metwali	metwali	PROPN
ejpam-6157	226	30	,	,	PUNCT
ejpam-6157	226	31	s.	s.	PROPN
ejpam-6157	226	32	alsallami	alsallami	PROPN
ejpam-6157	226	33	/	/	SYM
ejpam-6157	226	34	eur	eur	PROPN
ejpam-6157	226	35	.	.	PUNCT
ejpam-6157	227	1	j.	j.	PROPN
ejpam-6157	227	2	pure	pure	PROPN
ejpam-6157	227	3	appl	appl	PROPN
ejpam-6157	227	4	.	.	PROPN
ejpam-6157	227	5	math	math	PROPN
ejpam-6157	227	6	,	,	PUNCT
ejpam-6157	227	7	18	18	NUM
ejpam-6157	227	8	(	(	PUNCT
ejpam-6157	227	9	2	2	NUM
ejpam-6157	227	10	)	)	PUNCT
ejpam-6157	227	11	(	(	PUNCT
ejpam-6157	227	12	2025	2025	NUM
ejpam-6157	227	13	)	)	PUNCT
ejpam-6157	227	14	,	,	PUNCT
ejpam-6157	227	15	6157	6157	NUM
ejpam-6157	227	16	9	9	NUM
ejpam-6157	227	17	of	of	ADP
ejpam-6157	227	18	15	15	NUM
ejpam-6157	227	19	then	then	ADV
ejpam-6157	227	20	∥tu	∥tu	PROPN
ejpam-6157	227	21	·	·	PUNCT
ejpam-6157	227	22	χd∥x	χd∥x	PROPN
ejpam-6157	228	1	=	=	SYM
ejpam-6157	228	2	∥t1y	∥t1y	PROPN
ejpam-6157	228	3	·	·	PUNCT
ejpam-6157	228	4	χd∥θ	χd∥θ	PROPN
ejpam-6157	229	1	+	+	CCONJ
ejpam-6157	229	2	∥t2x	∥t2x	PROPN
ejpam-6157	229	3	·	·	PUNCT
ejpam-6157	229	4	χd∥θ	χd∥θ	PROPN
ejpam-6157	229	5	≤	≤	PROPN
ejpam-6157	229	6	∥h1	∥h1	VERB
ejpam-6157	229	7	·	·	PUNCT
ejpam-6157	229	8	χd∥θ	χd∥θ	PROPN
ejpam-6157	230	1	+	+	CCONJ
ejpam-6157	230	2	∥h2	∥h2	X
ejpam-6157	230	3	·	·	PUNCT
ejpam-6157	230	4	χd∥θ	χd∥θ	X
ejpam-6157	231	1	+	+	PUNCT
ejpam-6157	231	2	∥c1	∥c1	NOUN
ejpam-6157	231	3	·	·	PUNCT
ejpam-6157	231	4	χd∥θ	χd∥θ	X
ejpam-6157	231	5	+	+	PUNCT
ejpam-6157	231	6	∥c2	∥c2	NOUN
ejpam-6157	231	7	·	·	PUNCT
ejpam-6157	231	8	χd∥θ	χd∥θ	PROPN
ejpam-6157	232	1	+	+	CCONJ
ejpam-6157	232	2	α1∥a∗∥θ	α1∥a∗∥θ	PROPN
ejpam-6157	232	3	·	·	PUNCT
ejpam-6157	232	4	(	(	PUNCT
ejpam-6157	232	5	∥x	∥x	PROPN
ejpam-6157	232	6	·	·	PUNCT
ejpam-6157	232	7	χd∥θ	χd∥θ	PROPN
ejpam-6157	233	1	+	+	CCONJ
ejpam-6157	233	2	∥y	∥y	PROPN
ejpam-6157	233	3	·	·	PUNCT
ejpam-6157	233	4	χd∥θ	χd∥θ	PUNCT
ejpam-6157	233	5	)	)	PUNCT
ejpam-6157	234	1	+	+	CCONJ
ejpam-6157	234	2	2	2	NUM
ejpam-6157	234	3	·	·	PUNCT
ejpam-6157	234	4	rα2k1∥k∥θ2	rα2k1∥k∥θ2	NOUN
ejpam-6157	235	1	γ(β	γ(β	NOUN
ejpam-6157	235	2	)	)	PUNCT
ejpam-6157	235	3	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	235	4	·	·	PUNCT
ejpam-6157	235	5	(	(	PUNCT
ejpam-6157	235	6	∥x	∥x	PROPN
ejpam-6157	235	7	·	·	PUNCT
ejpam-6157	235	8	χd∥θ	χd∥θ	PROPN
ejpam-6157	236	1	+	+	CCONJ
ejpam-6157	236	2	∥y	∥y	PROPN
ejpam-6157	236	3	·	·	PUNCT
ejpam-6157	236	4	χd∥θ	χd∥θ	PROPN
ejpam-6157	236	5	)	)	PUNCT
ejpam-6157	236	6	≤	≤	PROPN
ejpam-6157	236	7	∥h1	∥h1	VERB
ejpam-6157	236	8	·	·	PUNCT
ejpam-6157	236	9	χd∥θ	χd∥θ	PROPN
ejpam-6157	237	1	+	+	CCONJ
ejpam-6157	237	2	∥h2	∥h2	X
ejpam-6157	237	3	·	·	PUNCT
ejpam-6157	237	4	χd∥θ	χd∥θ	X
ejpam-6157	238	1	+	+	PUNCT
ejpam-6157	238	2	∥c1	∥c1	NOUN
ejpam-6157	238	3	·	·	PUNCT
ejpam-6157	238	4	χd∥θ	χd∥θ	X
ejpam-6157	238	5	+	+	PUNCT
ejpam-6157	238	6	∥c2	∥c2	NOUN
ejpam-6157	238	7	·	·	PUNCT
ejpam-6157	238	8	χd∥θ	χd∥θ	PROPN
ejpam-6157	239	1	+	+	CCONJ
ejpam-6157	239	2	α1∥a∗∥θ	α1∥a∗∥θ	PROPN
ejpam-6157	239	3	·	·	PUNCT
ejpam-6157	239	4	∥u	∥u	PROPN
ejpam-6157	239	5	·	·	PUNCT
ejpam-6157	239	6	χd∥x	χd∥x	PROPN
ejpam-6157	239	7	+	+	CCONJ
ejpam-6157	239	8	2	2	NUM
ejpam-6157	239	9	·	·	PUNCT
ejpam-6157	239	10	rα2k1∥k∥θ2	rα2k1∥k∥θ2	NOUN
ejpam-6157	239	11	γ(β	γ(β	NOUN
ejpam-6157	239	12	)	)	PUNCT
ejpam-6157	239	13	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	239	14	·	·	PUNCT
ejpam-6157	240	1	∥u	∥u	PROPN
ejpam-6157	240	2	·	·	PUNCT
ejpam-6157	240	3	χd∥x	χd∥x	PROPN
ejpam-6157	240	4	.	.	PUNCT
ejpam-6157	241	1	since	since	SCONJ
ejpam-6157	241	2	hi	hi	PROPN
ejpam-6157	241	3	,	,	PUNCT
ejpam-6157	241	4	ci	ci	PROPN
ejpam-6157	241	5	∈	∈	PROPN
ejpam-6157	241	6	eθ	eθ	PROPN
ejpam-6157	241	7	,	,	PUNCT
ejpam-6157	241	8	i	i	PRON
ejpam-6157	241	9	=	=	NOUN
ejpam-6157	241	10	1	1	NUM
ejpam-6157	241	11	,	,	PUNCT
ejpam-6157	241	12	2	2	NUM
ejpam-6157	241	13	,	,	PUNCT
ejpam-6157	241	14	we	we	PRON
ejpam-6157	241	15	get	get	VERB
ejpam-6157	241	16	lim	lim	NOUN
ejpam-6157	241	17	ε→0	ε→0	NOUN
ejpam-6157	241	18	{	{	PUNCT
ejpam-6157	241	19	sup	sup	NOUN
ejpam-6157	241	20	mes	me	NOUN
ejpam-6157	241	21	d≤ε	d≤ε	X
ejpam-6157	241	22	[	[	PUNCT
ejpam-6157	241	23	sup	sup	NOUN
ejpam-6157	241	24	u∈x	u∈x	NOUN
ejpam-6157	241	25	{	{	PUNCT
ejpam-6157	241	26	∥hiχd∥θ	∥hiχd∥θ	NOUN
ejpam-6157	241	27	+	+	CCONJ
ejpam-6157	241	28	∥ciχd∥θ	∥ciχd∥θ	NOUN
ejpam-6157	241	29	=	=	SYM
ejpam-6157	241	30	0	0	NUM
ejpam-6157	241	31	}	}	PUNCT
ejpam-6157	241	32	]	]	PUNCT
ejpam-6157	241	33	}	}	PUNCT
ejpam-6157	241	34	.	.	PUNCT
ejpam-6157	242	1	recalling	recall	VERB
ejpam-6157	242	2	definition	definition	NOUN
ejpam-6157	242	3	4	4	NUM
ejpam-6157	242	4	,	,	PUNCT
ejpam-6157	242	5	we	we	PRON
ejpam-6157	242	6	obtain	obtain	VERB
ejpam-6157	242	7	c(t	c(t	PROPN
ejpam-6157	242	8	(	(	PUNCT
ejpam-6157	242	9	u	u	NOUN
ejpam-6157	242	10	)	)	PUNCT
ejpam-6157	242	11	)	)	PUNCT
ejpam-6157	242	12	≤	≤	NOUN
ejpam-6157	242	13	(	(	PUNCT
ejpam-6157	242	14	α1∥a∗∥θ	α1∥a∗∥θ	NOUN
ejpam-6157	242	15	+	+	ADJ
ejpam-6157	242	16	2	2	NUM
ejpam-6157	242	17	·	·	PUNCT
ejpam-6157	242	18	rα2k1∥k∥θ2	rα2k1∥k∥θ2	NOUN
ejpam-6157	242	19	γ(β	γ(β	PROPN
ejpam-6157	242	20	)	)	PUNCT
ejpam-6157	242	21	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	242	22	)	)	PUNCT
ejpam-6157	242	23	·	·	PUNCT
ejpam-6157	242	24	c(u	c(u	PROPN
ejpam-6157	242	25	)	)	PUNCT
ejpam-6157	242	26	.	.	PUNCT
ejpam-6157	243	1	since	since	SCONJ
ejpam-6157	243	2	∅	∅	NOUN
ejpam-6157	243	3	̸=	̸=	PROPN
ejpam-6157	243	4	u	u	NOUN
ejpam-6157	243	5	⊂	⊂	PROPN
ejpam-6157	243	6	qr	qr	PROPN
ejpam-6157	243	7	is	be	AUX
ejpam-6157	243	8	bounded	bound	VERB
ejpam-6157	243	9	in	in	ADP
ejpam-6157	243	10	addition	addition	NOUN
ejpam-6157	243	11	to	to	ADP
ejpam-6157	243	12	compact	compact	VERB
ejpam-6157	243	13	in	in	ADP
ejpam-6157	243	14	measure	measure	NOUN
ejpam-6157	243	15	,	,	PUNCT
ejpam-6157	243	16	then	then	ADV
ejpam-6157	243	17	we	we	PRON
ejpam-6157	243	18	shall	shall	AUX
ejpam-6157	243	19	apply	apply	VERB
ejpam-6157	243	20	corollary	corollary	ADJ
ejpam-6157	243	21	2	2	NUM
ejpam-6157	243	22	to	to	PART
ejpam-6157	243	23	obtain	obtain	VERB
ejpam-6157	243	24	βh(t	βh(t	PUNCT
ejpam-6157	243	25	(	(	PUNCT
ejpam-6157	243	26	u	u	NOUN
ejpam-6157	243	27	)	)	PUNCT
ejpam-6157	243	28	)	)	PUNCT
ejpam-6157	243	29	≤	≤	NOUN
ejpam-6157	244	1	(	(	PUNCT
ejpam-6157	244	2	α1∥a∗∥θ	α1∥a∗∥θ	NOUN
ejpam-6157	244	3	+	+	ADJ
ejpam-6157	244	4	2	2	NUM
ejpam-6157	244	5	·	·	PUNCT
ejpam-6157	244	6	rα2k1∥k∥θ2	rα2k1∥k∥θ2	NOUN
ejpam-6157	244	7	γ(β	γ(β	PROPN
ejpam-6157	244	8	)	)	PUNCT
ejpam-6157	244	9	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	244	10	)	)	PUNCT
ejpam-6157	244	11	·	·	PUNCT
ejpam-6157	245	1	βh(u	βh(u	X
ejpam-6157	245	2	)	)	PUNCT
ejpam-6157	245	3	.	.	PUNCT
ejpam-6157	246	1	since	since	SCONJ
ejpam-6157	246	2	(	(	PUNCT
ejpam-6157	246	3	α1∥a∗∥θ	α1∥a∗∥θ	PROPN
ejpam-6157	246	4	+	+	NUM
ejpam-6157	246	5	2·rα2k1∥k∥θ2	2·rα2k1∥k∥θ2	NOUN
ejpam-6157	246	6	γ(β	γ(β	PROPN
ejpam-6157	246	7	)	)	PUNCT
ejpam-6157	246	8	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	246	9	)	)	PUNCT
ejpam-6157	246	10	<	<	X
ejpam-6157	246	11	1	1	NUM
ejpam-6157	246	12	,	,	PUNCT
ejpam-6157	246	13	we	we	PRON
ejpam-6157	246	14	get	get	VERB
ejpam-6157	246	15	our	our	PRON
ejpam-6157	246	16	verification	verification	NOUN
ejpam-6157	246	17	and	and	CCONJ
ejpam-6157	246	18	theorem	theorem	ADJ
ejpam-6157	246	19	1	1	NUM
ejpam-6157	246	20	achieves	achieve	VERB
ejpam-6157	246	21	our	our	PRON
ejpam-6157	246	22	proof	proof	NOUN
ejpam-6157	246	23	.	.	PUNCT
ejpam-6157	247	1	3.2	3.2	NUM
ejpam-6157	247	2	.	.	PUNCT
ejpam-6157	247	3	uniqueness	uniqueness	NOUN
ejpam-6157	247	4	of	of	ADP
ejpam-6157	247	5	the	the	DET
ejpam-6157	247	6	solution	solution	NOUN
ejpam-6157	247	7	.	.	PUNCT
ejpam-6157	248	1	next	next	ADV
ejpam-6157	248	2	,	,	PUNCT
ejpam-6157	248	3	we	we	PRON
ejpam-6157	248	4	demonstrate	demonstrate	VERB
ejpam-6157	248	5	that	that	SCONJ
ejpam-6157	248	6	the	the	DET
ejpam-6157	248	7	coupled	couple	VERB
ejpam-6157	248	8	system	system	NOUN
ejpam-6157	248	9	(	(	PUNCT
ejpam-6157	248	10	1	1	X
ejpam-6157	248	11	)	)	PUNCT
ejpam-6157	248	12	has	have	VERB
ejpam-6157	248	13	exactly	exactly	ADV
ejpam-6157	248	14	one	one	NUM
ejpam-6157	248	15	solution	solution	NOUN
ejpam-6157	248	16	.	.	PUNCT
ejpam-6157	249	1	theorem	theorem	NOUN
ejpam-6157	249	2	3	3	NUM
ejpam-6157	249	3	.	.	PUNCT
ejpam-6157	249	4	assume	assume	VERB
ejpam-6157	249	5	that	that	SCONJ
ejpam-6157	249	6	the	the	DET
ejpam-6157	249	7	assumptions	assumption	NOUN
ejpam-6157	249	8	of	of	ADP
ejpam-6157	249	9	theorem	theorem	ADJ
ejpam-6157	249	10	2	2	NUM
ejpam-6157	249	11	hold	hold	NOUN
ejpam-6157	249	12	with	with	ADP
ejpam-6157	249	13	replacing	replace	VERB
ejpam-6157	249	14	the	the	DET
ejpam-6157	249	15	inequality	inequality	NOUN
ejpam-6157	249	16	(	(	PUNCT
ejpam-6157	249	17	2	2	NUM
ejpam-6157	249	18	)	)	PUNCT
ejpam-6157	249	19	with	with	ADP
ejpam-6157	249	20	the	the	DET
ejpam-6157	249	21	following	follow	VERB
ejpam-6157	249	22	|fi(t	|fi(t	PROPN
ejpam-6157	249	23	,	,	PUNCT
ejpam-6157	249	24	0	0	NUM
ejpam-6157	249	25	,	,	PUNCT
ejpam-6157	249	26	0)|	0)|	VERB
ejpam-6157	249	27	≤	≤	NUM
ejpam-6157	249	28	ci(t	ci(t	ADV
ejpam-6157	249	29	)	)	PUNCT
ejpam-6157	249	30	,	,	PUNCT
ejpam-6157	249	31	|fi(t	|fi(t	PROPN
ejpam-6157	249	32	,	,	PUNCT
ejpam-6157	249	33	x	x	X
ejpam-6157	249	34	,	,	PUNCT
ejpam-6157	249	35	y)−fi(t	y)−fi(t	PROPN
ejpam-6157	249	36	,	,	PUNCT
ejpam-6157	249	37	x̄	x̄	PROPN
ejpam-6157	249	38	,	,	PUNCT
ejpam-6157	249	39	ȳ)|	ȳ)|	PROPN
ejpam-6157	249	40	≤	≤	PROPN
ejpam-6157	249	41	α1|x−x̄|+α2|y−ȳ|	α1|x−x̄|+α2|y−ȳ|	NOUN
ejpam-6157	249	42	,	,	PUNCT
ejpam-6157	249	43	u	u	NOUN
ejpam-6157	249	44	=	=	PUNCT
ejpam-6157	249	45	(	(	PUNCT
ejpam-6157	249	46	x	x	NOUN
ejpam-6157	249	47	,	,	PUNCT
ejpam-6157	249	48	y	y	PROPN
ejpam-6157	249	49	)	)	PUNCT
ejpam-6157	249	50	,	,	PUNCT
ejpam-6157	249	51	ū	ū	NOUN
ejpam-6157	250	1	=	=	SYM
ejpam-6157	250	2	(	(	PUNCT
ejpam-6157	250	3	x̄	x̄	PROPN
ejpam-6157	250	4	,	,	PUNCT
ejpam-6157	250	5	ȳ	ȳ	PROPN
ejpam-6157	250	6	)	)	PUNCT
ejpam-6157	250	7	∈	∈	PROPN
ejpam-6157	250	8	qr	qr	PROPN
ejpam-6157	250	9	,	,	PUNCT
ejpam-6157	250	10	(	(	PUNCT
ejpam-6157	250	11	3	3	X
ejpam-6157	250	12	)	)	PUNCT
ejpam-6157	250	13	for	for	ADP
ejpam-6157	250	14	i	i	PRON
ejpam-6157	250	15	=	=	SYM
ejpam-6157	250	16	1	1	NUM
ejpam-6157	250	17	,	,	PUNCT
ejpam-6157	250	18	2	2	NUM
ejpam-6157	250	19	,	,	PUNCT
ejpam-6157	250	20	and	and	CCONJ
ejpam-6157	250	21	in	in	ADP
ejpam-6157	250	22	addition	addition	NOUN
ejpam-6157	250	23	,	,	PUNCT
ejpam-6157	250	24	assume	assume	VERB
ejpam-6157	250	25	that	that	SCONJ
ejpam-6157	250	26	c	c	AUX
ejpam-6157	250	27	=	=	PUNCT
ejpam-6157	250	28	(	(	PUNCT
ejpam-6157	250	29	α1∥a∗∥θ	α1∥a∗∥θ	X
ejpam-6157	250	30	+	+	CCONJ
ejpam-6157	250	31	4r	4r	NUM
ejpam-6157	250	32	·	·	PUNCT
ejpam-6157	250	33	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	250	34	γ(β	γ(β	PROPN
ejpam-6157	250	35	)	)	PUNCT
ejpam-6157	250	36	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	250	37	)	)	PUNCT
ejpam-6157	250	38	<	<	X
ejpam-6157	251	1	1	1	NUM
ejpam-6157	251	2	,	,	PUNCT
ejpam-6157	251	3	(	(	PUNCT
ejpam-6157	251	4	4	4	X
ejpam-6157	251	5	)	)	PUNCT
ejpam-6157	251	6	where	where	SCONJ
ejpam-6157	251	7	r	r	NOUN
ejpam-6157	251	8	,	,	PUNCT
ejpam-6157	251	9	qr	qr	PROPN
ejpam-6157	251	10	are	be	AUX
ejpam-6157	251	11	defined	define	VERB
ejpam-6157	251	12	in	in	ADP
ejpam-6157	251	13	theorem	theorem	NOUN
ejpam-6157	251	14	2	2	NUM
ejpam-6157	251	15	.	.	PUNCT
ejpam-6157	252	1	then	then	ADV
ejpam-6157	252	2	the	the	DET
ejpam-6157	252	3	coupled	couple	VERB
ejpam-6157	252	4	system	system	NOUN
ejpam-6157	252	5	(	(	PUNCT
ejpam-6157	252	6	1	1	X
ejpam-6157	252	7	)	)	PUNCT
ejpam-6157	252	8	has	have	VERB
ejpam-6157	252	9	a	a	DET
ejpam-6157	252	10	unique	unique	ADJ
ejpam-6157	252	11	solution	solution	NOUN
ejpam-6157	252	12	u	u	NOUN
ejpam-6157	252	13	∈	∈	NOUN
ejpam-6157	252	14	lx	lx	NOUN
ejpam-6157	252	15	in	in	ADP
ejpam-6157	252	16	qr	qr	PROPN
ejpam-6157	252	17	.	.	PUNCT
ejpam-6157	252	18	m.	m.	PROPN
ejpam-6157	252	19	metwali	metwali	PROPN
ejpam-6157	252	20	,	,	PUNCT
ejpam-6157	252	21	s.	s.	PROPN
ejpam-6157	252	22	alsallami	alsallami	PROPN
ejpam-6157	252	23	/	/	SYM
ejpam-6157	252	24	eur	eur	PROPN
ejpam-6157	252	25	.	.	PUNCT
ejpam-6157	253	1	j.	j.	PROPN
ejpam-6157	253	2	pure	pure	PROPN
ejpam-6157	253	3	appl	appl	PROPN
ejpam-6157	253	4	.	.	PROPN
ejpam-6157	253	5	math	math	PROPN
ejpam-6157	253	6	,	,	PUNCT
ejpam-6157	253	7	18	18	NUM
ejpam-6157	253	8	(	(	PUNCT
ejpam-6157	253	9	2	2	NUM
ejpam-6157	253	10	)	)	PUNCT
ejpam-6157	253	11	(	(	PUNCT
ejpam-6157	253	12	2025	2025	NUM
ejpam-6157	253	13	)	)	PUNCT
ejpam-6157	253	14	,	,	PUNCT
ejpam-6157	253	15	6157	6157	NUM
ejpam-6157	253	16	10	10	NUM
ejpam-6157	253	17	of	of	ADP
ejpam-6157	253	18	15	15	NUM
ejpam-6157	253	19	proof	proof	NOUN
ejpam-6157	253	20	.	.	PUNCT
ejpam-6157	254	1	using	use	VERB
ejpam-6157	254	2	the	the	DET
ejpam-6157	254	3	inequalities	inequality	NOUN
ejpam-6157	254	4	(	(	PUNCT
ejpam-6157	254	5	3	3	NUM
ejpam-6157	254	6	)	)	PUNCT
ejpam-6157	254	7	for	for	ADP
ejpam-6157	254	8	i	i	PRON
ejpam-6157	254	9	=	=	SYM
ejpam-6157	254	10	1	1	NUM
ejpam-6157	254	11	,	,	PUNCT
ejpam-6157	254	12	2	2	NUM
ejpam-6157	254	13	,	,	PUNCT
ejpam-6157	254	14	we	we	PRON
ejpam-6157	254	15	obtain∣∣∣∣|fi(t	obtain∣∣∣∣|fi(t	VERB
ejpam-6157	254	16	,	,	PUNCT
ejpam-6157	254	17	x	x	AUX
ejpam-6157	254	18	,	,	PUNCT
ejpam-6157	254	19	y)|	y)|	INTJ
ejpam-6157	254	20	−	−	PROPN
ejpam-6157	254	21	|fi(t	|fi(t	PROPN
ejpam-6157	254	22	,	,	PUNCT
ejpam-6157	254	23	0	0	NUM
ejpam-6157	254	24	,	,	PUNCT
ejpam-6157	254	25	0)|	0)|	NOUN
ejpam-6157	254	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6157	254	27	≤	≤	NOUN
ejpam-6157	254	28	|fi(t	|fi(t	ADP
ejpam-6157	254	29	,	,	PUNCT
ejpam-6157	254	30	x	x	PRON
ejpam-6157	254	31	,	,	PUNCT
ejpam-6157	254	32	y)−	y)−	PROPN
ejpam-6157	254	33	fi(t	fi(t	NOUN
ejpam-6157	254	34	,	,	PUNCT
ejpam-6157	254	35	0	0	NUM
ejpam-6157	254	36	,	,	PUNCT
ejpam-6157	254	37	0)|	0)|	VERB
ejpam-6157	254	38	≤	≤	NUM
ejpam-6157	254	39	α1|x|+	α1|x|+	PUNCT
ejpam-6157	254	40	α2|y|	α2|y|	X
ejpam-6157	254	41	⇒	⇒	NOUN
ejpam-6157	254	42	|fi(t	|fi(t	NUM
ejpam-6157	254	43	,	,	PUNCT
ejpam-6157	254	44	x	x	PRON
ejpam-6157	254	45	,	,	PUNCT
ejpam-6157	254	46	y)|	y)|	PROPN
ejpam-6157	254	47	≤	≤	PROPN
ejpam-6157	254	48	|fi(t	|fi(t	PROPN
ejpam-6157	254	49	,	,	PUNCT
ejpam-6157	254	50	0	0	NUM
ejpam-6157	254	51	,	,	PUNCT
ejpam-6157	254	52	0)|+	0)|+	NUM
ejpam-6157	254	53	α1|x|+	α1|x|+	PROPN
ejpam-6157	254	54	α2|y|	α2|y|	PROPN
ejpam-6157	254	55	≤	≤	NOUN
ejpam-6157	254	56	ci(t	ci(t	ADV
ejpam-6157	254	57	)	)	PUNCT
ejpam-6157	255	1	+	+	CCONJ
ejpam-6157	255	2	α1|x|+	α1|x|+	PROPN
ejpam-6157	255	3	α2|y|	α2|y|	NUM
ejpam-6157	255	4	.	.	PUNCT
ejpam-6157	256	1	thus	thus	ADV
ejpam-6157	256	2	,	,	PUNCT
ejpam-6157	256	3	theorem	theorem	ADJ
ejpam-6157	256	4	2	2	NUM
ejpam-6157	256	5	indicates	indicate	VERB
ejpam-6157	256	6	that	that	SCONJ
ejpam-6157	256	7	,	,	PUNCT
ejpam-6157	256	8	there	there	PRON
ejpam-6157	256	9	is	be	VERB
ejpam-6157	256	10	a.e	a.e	PROPN
ejpam-6157	256	11	.	.	PROPN
ejpam-6157	256	12	nondecreasing	nondecrease	VERB
ejpam-6157	256	13	solution	solution	NOUN
ejpam-6157	256	14	u	u	NOUN
ejpam-6157	256	15	∈	∈	PROPN
ejpam-6157	256	16	ex	ex	X
ejpam-6157	256	17	of	of	ADP
ejpam-6157	256	18	(	(	PUNCT
ejpam-6157	256	19	1	1	NUM
ejpam-6157	256	20	)	)	PUNCT
ejpam-6157	256	21	in	in	ADP
ejpam-6157	256	22	qr	qr	PROPN
ejpam-6157	256	23	.	.	PUNCT
ejpam-6157	257	1	now	now	ADV
ejpam-6157	257	2	,	,	PUNCT
ejpam-6157	257	3	let	let	VERB
ejpam-6157	257	4	u	u	PRON
ejpam-6157	257	5	=	=	SYM
ejpam-6157	257	6	(	(	PUNCT
ejpam-6157	257	7	x	x	NOUN
ejpam-6157	257	8	,	,	PUNCT
ejpam-6157	257	9	y	y	PROPN
ejpam-6157	257	10	)	)	PUNCT
ejpam-6157	257	11	,	,	PUNCT
ejpam-6157	257	12	ū	ū	NOUN
ejpam-6157	257	13	=	=	SYM
ejpam-6157	257	14	(	(	PUNCT
ejpam-6157	257	15	x̄	x̄	PROPN
ejpam-6157	257	16	,	,	PUNCT
ejpam-6157	257	17	ȳ	ȳ	PROPN
ejpam-6157	257	18	)	)	PUNCT
ejpam-6157	257	19	∈	∈	PROPN
ejpam-6157	257	20	qr	qr	PROPN
ejpam-6157	257	21	be	be	AUX
ejpam-6157	257	22	any	any	DET
ejpam-6157	257	23	two	two	NUM
ejpam-6157	257	24	distinct	distinct	ADJ
ejpam-6157	257	25	solutions	solution	NOUN
ejpam-6157	257	26	of	of	ADP
ejpam-6157	257	27	the	the	DET
ejpam-6157	257	28	coupled	couple	VERB
ejpam-6157	257	29	system	system	NOUN
ejpam-6157	257	30	(	(	PUNCT
ejpam-6157	257	31	1	1	NUM
ejpam-6157	257	32	)	)	PUNCT
ejpam-6157	257	33	,	,	PUNCT
ejpam-6157	257	34	then	then	ADV
ejpam-6157	257	35	we	we	PRON
ejpam-6157	257	36	have	have	VERB
ejpam-6157	257	37	∥x−	∥x−	PROPN
ejpam-6157	257	38	x̄∥θ	x̄∥θ	PROPN
ejpam-6157	257	39	≤	≤	PROPN
ejpam-6157	257	40	∥∥∥f1(t	∥∥∥f1(t	PROPN
ejpam-6157	257	41	,	,	PUNCT
ejpam-6157	257	42	λ1(y	λ1(y	PROPN
ejpam-6157	257	43	)	)	PUNCT
ejpam-6157	257	44	,	,	PUNCT
ejpam-6157	257	45	u1(y	u1(y	PROPN
ejpam-6157	257	46	)	)	PUNCT
ejpam-6157	257	47	)	)	PUNCT
ejpam-6157	258	1	−	−	PROPN
ejpam-6157	258	2	f1	f1	PROPN
ejpam-6157	258	3	(	(	PUNCT
ejpam-6157	258	4	t	t	PROPN
ejpam-6157	258	5	,	,	PUNCT
ejpam-6157	258	6	λ1(ȳ	λ1(ȳ	NOUN
ejpam-6157	258	7	)	)	PUNCT
ejpam-6157	258	8	,	,	PUNCT
ejpam-6157	258	9	u1(ȳ	u1(ȳ	NUM
ejpam-6157	258	10	)	)	PUNCT
ejpam-6157	258	11	)	)	PUNCT
ejpam-6157	258	12	∥∥∥	∥∥∥	NUM
ejpam-6157	258	13	θ	θ	X
ejpam-6157	258	14	≤	≤	NUM
ejpam-6157	259	1	α1∥λ1(y)−	α1∥λ1(y)−	NUM
ejpam-6157	259	2	λ1(ȳ)∥θ	λ1(ȳ)∥θ	NOUN
ejpam-6157	259	3	+	+	CCONJ
ejpam-6157	259	4	α2∥u1(y)−	α2∥u1(y)−	X
ejpam-6157	259	5	u1(ȳ)∥θ	u1(ȳ)∥θ	PROPN
ejpam-6157	259	6	≤	≤	PROPN
ejpam-6157	259	7	α1	α1	PROPN
ejpam-6157	259	8	∥∥∥a1∥y∥θ	∥∥∥a1∥y∥θ	NOUN
ejpam-6157	259	9	−	−	ADP
ejpam-6157	259	10	a1∥ȳ∥θ	a1∥ȳ∥θ	PROPN
ejpam-6157	259	11	∥∥∥	∥∥∥	PROPN
ejpam-6157	259	12	θ	θ	NOUN
ejpam-6157	259	13	+	+	CCONJ
ejpam-6157	259	14	α2∥g1(y)a1(y)−g1(ȳ)a1(ȳ)∥θ	α2∥g1(y)a1(y)−g1(ȳ)a1(ȳ)∥θ	NOUN
ejpam-6157	259	15	≤	≤	NUM
ejpam-6157	259	16	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	259	17	∣∣∥y∥θ	∣∣∥y∥θ	PROPN
ejpam-6157	259	18	−	−	PROPN
ejpam-6157	259	19	∥ȳ∥θ	∥ȳ∥θ	ADJ
ejpam-6157	259	20	∣∣+	∣∣+	PROPN
ejpam-6157	259	21	α2	α2	PROPN
ejpam-6157	259	22	∥∥g1(y)a1(y)−g1(ȳ)a1(y	∥∥g1(y)a1(y)−g1(ȳ)a1(y	PROPN
ejpam-6157	259	23	)	)	PUNCT
ejpam-6157	259	24	∥∥	∥∥	X
ejpam-6157	259	25	θ	θ	PROPN
ejpam-6157	259	26	+	+	CCONJ
ejpam-6157	259	27	α2	α2	PROPN
ejpam-6157	259	28	∥∥g1(ȳ)a1(y)−g1(ȳ)a1(ȳ	∥∥g1(ȳ)a1(y)−g1(ȳ)a1(ȳ	NOUN
ejpam-6157	259	29	)	)	PUNCT
ejpam-6157	259	30	∥∥	∥∥	X
ejpam-6157	259	31	θ	θ	PROPN
ejpam-6157	259	32	≤	≤	NUM
ejpam-6157	259	33	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	259	34	∥∥y	∥∥y	ADV
ejpam-6157	259	35	−	−	PROPN
ejpam-6157	259	36	ȳ	ȳ	NOUN
ejpam-6157	259	37	∥∥	∥∥	X
ejpam-6157	259	38	θ	θ	NOUN
ejpam-6157	259	39	+	+	PUNCT
ejpam-6157	259	40	α2k1	α2k1	PROPN
ejpam-6157	259	41	∥∥g1(y)−g1(ȳ	∥∥g1(y)−g1(ȳ	NUM
ejpam-6157	259	42	)	)	PUNCT
ejpam-6157	259	43	∥∥	∥∥	PROPN
ejpam-6157	259	44	θ1	θ1	PROPN
ejpam-6157	259	45	∥a1(y)∥θ2	∥a1(y)∥θ2	NOUN
ejpam-6157	259	46	+	+	CCONJ
ejpam-6157	259	47	α2k1	α2k1	PROPN
ejpam-6157	259	48	∥∥g1(ȳ)∥θ1	∥∥g1(ȳ)∥θ1	PROPN
ejpam-6157	259	49	∥∥a1(y)−a1(ȳ	∥∥a1(y)−a1(ȳ	X
ejpam-6157	259	50	)	)	PUNCT
ejpam-6157	259	51	∥∥	∥∥	PROPN
ejpam-6157	259	52	θ2	θ2	ADP
ejpam-6157	259	53	≤	≤	NUM
ejpam-6157	259	54	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	259	55	∥∥y	∥∥y	ADV
ejpam-6157	259	56	−	−	PROPN
ejpam-6157	259	57	ȳ	ȳ	NOUN
ejpam-6157	259	58	∥∥	∥∥	X
ejpam-6157	259	59	θ	θ	NOUN
ejpam-6157	260	1	+	+	PUNCT
ejpam-6157	260	2	α2k1	α2k1	VERB
ejpam-6157	260	3	∥∥g1∥∥θ1	∥∥g1∥∥θ1	ADJ
ejpam-6157	260	4	∥y	∥y	PROPN
ejpam-6157	260	5	−	−	PROPN
ejpam-6157	260	6	ȳ∥θ	ȳ∥θ	PROPN
ejpam-6157	260	7	2∥k∥θ2	2∥k∥θ2	NUM
ejpam-6157	260	8	γ(β	γ(β	PROPN
ejpam-6157	260	9	)	)	PUNCT
ejpam-6157	260	10	∥b1∥m∗∥y∥θ	∥b1∥m∗∥y∥θ	PROPN
ejpam-6157	260	11	+	+	CCONJ
ejpam-6157	260	12	α2k1	α2k1	NUM
ejpam-6157	260	13	∥∥g1∥∥θ1	∥∥g1∥∥θ1	ADJ
ejpam-6157	260	14	∥y∥θ	∥y∥θ	NOUN
ejpam-6157	260	15	2∥k∥θ2	2∥k∥θ2	NUM
ejpam-6157	260	16	γ(β	γ(β	PROPN
ejpam-6157	260	17	)	)	PUNCT
ejpam-6157	260	18	∥r1(y)−r1(ȳ	∥r1(y)−r1(ȳ	NUM
ejpam-6157	260	19	)	)	PUNCT
ejpam-6157	260	20	∥∥	∥∥	PRON
ejpam-6157	260	21	m∗	m∗	VERB
ejpam-6157	260	22	≤	≤	ADJ
ejpam-6157	260	23	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	260	24	∥∥y	∥∥y	ADV
ejpam-6157	260	25	−	−	PROPN
ejpam-6157	260	26	ȳ	ȳ	NOUN
ejpam-6157	261	1	∥∥	∥∥	X
ejpam-6157	261	2	θ	θ	PROPN
ejpam-6157	261	3	+	+	PUNCT
ejpam-6157	261	4	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	261	5	γ(β	γ(β	PROPN
ejpam-6157	261	6	)	)	PUNCT
ejpam-6157	261	7	∥∥g1∥∥θ1	∥∥g1∥∥θ1	PROPN
ejpam-6157	261	8	∥b1∥m∗∥y∥θ∥y	∥b1∥m∗∥y∥θ∥y	NOUN
ejpam-6157	261	9	−	−	PROPN
ejpam-6157	261	10	ȳ∥θ	ȳ∥θ	PROPN
ejpam-6157	261	11	+	+	CCONJ
ejpam-6157	261	12	2α2k1∥k∥θ2	2α2k1∥k∥θ2	NUM
ejpam-6157	261	13	γ(β	γ(β	PROPN
ejpam-6157	261	14	)	)	PUNCT
ejpam-6157	262	1	∥∥g1∥∥θ1	∥∥g1∥∥θ1	PROPN
ejpam-6157	262	2	∥y∥θ∥b1∥m∗	∥y∥θ∥b1∥m∗	NOUN
ejpam-6157	262	3	∥∥y	∥∥y	PROPN
ejpam-6157	262	4	−	−	PROPN
ejpam-6157	262	5	ȳ	ȳ	NOUN
ejpam-6157	263	1	∥∥	∥∥	X
ejpam-6157	263	2	θ	θ	NOUN
ejpam-6157	263	3	=	=	PUNCT
ejpam-6157	263	4	(	(	PUNCT
ejpam-6157	263	5	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	263	6	+	+	CCONJ
ejpam-6157	263	7	4r	4r	NUM
ejpam-6157	263	8	·	·	PUNCT
ejpam-6157	263	9	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	263	10	γ(β	γ(β	PROPN
ejpam-6157	263	11	)	)	PUNCT
ejpam-6157	263	12	∥g1∥θ1∥b1∥m∗	∥g1∥θ1∥b1∥m∗	PROPN
ejpam-6157	263	13	)	)	PUNCT
ejpam-6157	263	14	∥∥y	∥∥y	ADV
ejpam-6157	263	15	−	−	PROPN
ejpam-6157	263	16	ȳ	ȳ	PROPN
ejpam-6157	263	17	∥∥	∥∥	PROPN
ejpam-6157	263	18	θ	θ	PROPN
ejpam-6157	263	19	.	.	PUNCT
ejpam-6157	264	1	similarly	similarly	ADV
ejpam-6157	264	2	,	,	PUNCT
ejpam-6157	264	3	∥y	∥y	PROPN
ejpam-6157	264	4	−	−	PROPN
ejpam-6157	264	5	ȳ∥θ	ȳ∥θ	PROPN
ejpam-6157	264	6	≤	≤	NOUN
ejpam-6157	264	7	(	(	PUNCT
ejpam-6157	264	8	α1∥a2∥θ	α1∥a2∥θ	ADJ
ejpam-6157	264	9	+	+	CCONJ
ejpam-6157	264	10	4r	4r	NUM
ejpam-6157	264	11	·	·	PUNCT
ejpam-6157	264	12	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	264	13	γ(β	γ(β	PROPN
ejpam-6157	264	14	)	)	PUNCT
ejpam-6157	264	15	∥∥g2∥∥θ1	∥∥g2∥∥θ1	PROPN
ejpam-6157	264	16	∥b2∥m∗	∥b2∥m∗	PROPN
ejpam-6157	264	17	)	)	PUNCT
ejpam-6157	264	18	∥∥x−	∥∥x−	NOUN
ejpam-6157	264	19	x̄	x̄	NOUN
ejpam-6157	264	20	∥∥	∥∥	PUNCT
ejpam-6157	264	21	θ	θ	X
ejpam-6157	264	22	.	.	PUNCT
ejpam-6157	265	1	therefore	therefore	ADV
ejpam-6157	265	2	,	,	PUNCT
ejpam-6157	265	3	∥u−	∥u−	PROPN
ejpam-6157	265	4	ū∥x	ū∥x	PROPN
ejpam-6157	265	5	=	=	PUNCT
ejpam-6157	265	6	∥∥(x−	∥∥(x−	X
ejpam-6157	265	7	x̄	x̄	PROPN
ejpam-6157	265	8	,	,	PUNCT
ejpam-6157	265	9	y	y	PROPN
ejpam-6157	265	10	−	−	PROPN
ejpam-6157	265	11	ȳ	ȳ	PROPN
ejpam-6157	265	12	)	)	PUNCT
ejpam-6157	265	13	∥∥	∥∥	X
ejpam-6157	265	14	x	x	X
ejpam-6157	265	15	=	=	PUNCT
ejpam-6157	265	16	∥x−	∥x−	NUM
ejpam-6157	265	17	x̄∥θ	x̄∥θ	PROPN
ejpam-6157	265	18	+	+	PUNCT
ejpam-6157	265	19	∥y	∥y	ADJ
ejpam-6157	265	20	−	−	PROPN
ejpam-6157	265	21	ȳ∥θ	ȳ∥θ	PROPN
ejpam-6157	265	22	≤	≤	NOUN
ejpam-6157	265	23	(	(	PUNCT
ejpam-6157	265	24	α1∥a1∥θ	α1∥a1∥θ	NOUN
ejpam-6157	265	25	+	+	CCONJ
ejpam-6157	265	26	4r	4r	NUM
ejpam-6157	265	27	·	·	PUNCT
ejpam-6157	265	28	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	265	29	γ(β	γ(β	PROPN
ejpam-6157	265	30	)	)	PUNCT
ejpam-6157	265	31	∥g1∥θ1∥b1∥m∗	∥g1∥θ1∥b1∥m∗	PROPN
ejpam-6157	265	32	)	)	PUNCT
ejpam-6157	265	33	∥∥y	∥∥y	ADV
ejpam-6157	265	34	−	−	PROPN
ejpam-6157	265	35	ȳ	ȳ	PROPN
ejpam-6157	265	36	∥∥	∥∥	PROPN
ejpam-6157	265	37	θ	θ	NOUN
ejpam-6157	265	38	+	+	CCONJ
ejpam-6157	265	39	(	(	PUNCT
ejpam-6157	265	40	α1∥a2∥θ	α1∥a2∥θ	X
ejpam-6157	265	41	+	+	CCONJ
ejpam-6157	265	42	4r	4r	NUM
ejpam-6157	265	43	·	·	PUNCT
ejpam-6157	265	44	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	265	45	γ(β	γ(β	PROPN
ejpam-6157	265	46	)	)	PUNCT
ejpam-6157	265	47	∥∥g2∥∥θ1	∥∥g2∥∥θ1	PROPN
ejpam-6157	265	48	∥b2∥m∗	∥b2∥m∗	PROPN
ejpam-6157	265	49	)	)	PUNCT
ejpam-6157	265	50	∥∥x−	∥∥x−	NOUN
ejpam-6157	265	51	x̄	x̄	NOUN
ejpam-6157	265	52	∥∥	∥∥	X
ejpam-6157	265	53	θ	θ	NOUN
ejpam-6157	265	54	≤	≤	NUM
ejpam-6157	265	55	(	(	PUNCT
ejpam-6157	265	56	α1∥a∗∥θ	α1∥a∗∥θ	NOUN
ejpam-6157	265	57	+	+	CCONJ
ejpam-6157	265	58	4r	4r	NUM
ejpam-6157	265	59	·	·	PUNCT
ejpam-6157	265	60	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	265	61	γ(β	γ(β	PROPN
ejpam-6157	265	62	)	)	PUNCT
ejpam-6157	265	63	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	265	64	)	)	PUNCT
ejpam-6157	265	65	(	(	PUNCT
ejpam-6157	265	66	∥∥y	∥∥y	PROPN
ejpam-6157	265	67	−	−	PROPN
ejpam-6157	265	68	ȳ	ȳ	PROPN
ejpam-6157	265	69	∥∥	∥∥	X
ejpam-6157	265	70	θ	θ	PROPN
ejpam-6157	265	71	+	+	CCONJ
ejpam-6157	265	72	∥∥x−	∥∥x−	PROPN
ejpam-6157	265	73	x̄	x̄	X
ejpam-6157	265	74	∥∥	∥∥	PUNCT
ejpam-6157	265	75	θ	θ	NOUN
ejpam-6157	265	76	)	)	PUNCT
ejpam-6157	265	77	=	=	PUNCT
ejpam-6157	266	1	c	c	X
ejpam-6157	266	2	·	·	PUNCT
ejpam-6157	266	3	∥u−	∥u−	PROPN
ejpam-6157	266	4	ū∥x	ū∥x	PROPN
ejpam-6157	266	5	.	.	PUNCT
ejpam-6157	266	6	equation	equation	NOUN
ejpam-6157	266	7	(	(	PUNCT
ejpam-6157	266	8	4	4	X
ejpam-6157	266	9	)	)	PUNCT
ejpam-6157	266	10	grants	grant	VERB
ejpam-6157	266	11	us	we	PRON
ejpam-6157	266	12	that	that	DET
ejpam-6157	266	13	u	u	NOUN
ejpam-6157	266	14	=	=	X
ejpam-6157	266	15	ū	ū	X
ejpam-6157	266	16	(	(	PUNCT
ejpam-6157	266	17	a.e	a.e	PROPN
ejpam-6157	266	18	.	.	PROPN
ejpam-6157	266	19	)	)	PUNCT
ejpam-6157	266	20	,	,	PUNCT
ejpam-6157	266	21	and	and	CCONJ
ejpam-6157	266	22	we	we	PRON
ejpam-6157	266	23	get	get	VERB
ejpam-6157	266	24	our	our	PRON
ejpam-6157	266	25	verification	verification	NOUN
ejpam-6157	266	26	.	.	PUNCT
ejpam-6157	267	1	m.	m.	PROPN
ejpam-6157	267	2	metwali	metwali	PROPN
ejpam-6157	267	3	,	,	PUNCT
ejpam-6157	267	4	s.	s.	PROPN
ejpam-6157	267	5	alsallami	alsallami	PROPN
ejpam-6157	267	6	/	/	SYM
ejpam-6157	267	7	eur	eur	PROPN
ejpam-6157	267	8	.	.	PUNCT
ejpam-6157	268	1	j.	j.	PROPN
ejpam-6157	268	2	pure	pure	PROPN
ejpam-6157	268	3	appl	appl	PROPN
ejpam-6157	268	4	.	.	PROPN
ejpam-6157	268	5	math	math	PROPN
ejpam-6157	268	6	,	,	PUNCT
ejpam-6157	268	7	18	18	NUM
ejpam-6157	268	8	(	(	PUNCT
ejpam-6157	268	9	2	2	NUM
ejpam-6157	268	10	)	)	PUNCT
ejpam-6157	268	11	(	(	PUNCT
ejpam-6157	268	12	2025	2025	NUM
ejpam-6157	268	13	)	)	PUNCT
ejpam-6157	268	14	,	,	PUNCT
ejpam-6157	268	15	6157	6157	NUM
ejpam-6157	268	16	11	11	NUM
ejpam-6157	268	17	of	of	ADP
ejpam-6157	268	18	15	15	NUM
ejpam-6157	268	19	3.3	3.3	NUM
ejpam-6157	268	20	.	.	PUNCT
ejpam-6157	269	1	continuous	continuous	ADJ
ejpam-6157	269	2	dependence	dependence	NOUN
ejpam-6157	269	3	on	on	ADP
ejpam-6157	269	4	the	the	DET
ejpam-6157	269	5	functions	function	NOUN
ejpam-6157	269	6	h1	h1	VERB
ejpam-6157	269	7	,	,	PUNCT
ejpam-6157	269	8	and	and	CCONJ
ejpam-6157	269	9	h2	h2	NOUN
ejpam-6157	269	10	.	.	PUNCT
ejpam-6157	270	1	next	next	ADV
ejpam-6157	270	2	,	,	PUNCT
ejpam-6157	270	3	we	we	PRON
ejpam-6157	270	4	may	may	AUX
ejpam-6157	270	5	discuss	discuss	VERB
ejpam-6157	270	6	the	the	DET
ejpam-6157	270	7	continuous	continuous	ADJ
ejpam-6157	270	8	dependence	dependence	NOUN
ejpam-6157	270	9	of	of	ADP
ejpam-6157	270	10	the	the	DET
ejpam-6157	270	11	obtained	obtain	VERB
ejpam-6157	270	12	solutions	solution	NOUN
ejpam-6157	270	13	for	for	ADP
ejpam-6157	270	14	the	the	DET
ejpam-6157	270	15	coupled	couple	VERB
ejpam-6157	270	16	system	system	NOUN
ejpam-6157	270	17	(	(	PUNCT
ejpam-6157	270	18	1	1	NUM
ejpam-6157	270	19	)	)	PUNCT
ejpam-6157	270	20	on	on	ADP
ejpam-6157	270	21	the	the	DET
ejpam-6157	270	22	functions	function	NOUN
ejpam-6157	270	23	hi	hi	INTJ
ejpam-6157	270	24	,	,	PUNCT
ejpam-6157	270	25	i	i	PRON
ejpam-6157	270	26	=	=	NOUN
ejpam-6157	270	27	1	1	NUM
ejpam-6157	270	28	,	,	PUNCT
ejpam-6157	270	29	2	2	NUM
ejpam-6157	270	30	.	.	X
ejpam-6157	270	31	definition	definition	NOUN
ejpam-6157	270	32	7	7	NUM
ejpam-6157	270	33	.	.	PUNCT
ejpam-6157	270	34	a	a	DET
ejpam-6157	270	35	solution	solution	NOUN
ejpam-6157	270	36	u	u	NOUN
ejpam-6157	270	37	=	=	SYM
ejpam-6157	270	38	(	(	PUNCT
ejpam-6157	270	39	x	x	NOUN
ejpam-6157	270	40	,	,	PUNCT
ejpam-6157	270	41	y	y	NOUN
ejpam-6157	270	42	)	)	PUNCT
ejpam-6157	270	43	∈	∈	PROPN
ejpam-6157	270	44	lx	lx	NOUN
ejpam-6157	270	45	of	of	ADP
ejpam-6157	270	46	(	(	PUNCT
ejpam-6157	270	47	1	1	X
ejpam-6157	270	48	)	)	PUNCT
ejpam-6157	270	49	is	be	AUX
ejpam-6157	270	50	continuously	continuously	ADV
ejpam-6157	270	51	dependent	dependent	ADJ
ejpam-6157	270	52	on	on	ADP
ejpam-6157	270	53	the	the	DET
ejpam-6157	270	54	function	function	NOUN
ejpam-6157	270	55	h1	h1	PROPN
ejpam-6157	270	56	,	,	PUNCT
ejpam-6157	270	57	h2	h2	PROPN
ejpam-6157	270	58	if	if	SCONJ
ejpam-6157	270	59	∀	∀	NOUN
ejpam-6157	270	60	ϵ	ϵ	X
ejpam-6157	270	61	>	>	X
ejpam-6157	270	62	0	0	PROPN
ejpam-6157	270	63	,	,	PUNCT
ejpam-6157	270	64	∃δ	∃δ	PROPN
ejpam-6157	270	65	>	>	X
ejpam-6157	270	66	o	o	NOUN
ejpam-6157	271	1	such	such	ADJ
ejpam-6157	271	2	that	that	SCONJ
ejpam-6157	271	3	∥h1−	∥h1−	PROPN
ejpam-6157	271	4	h̄1∥θ+∥h2−	h̄1∥θ+∥h2−	PROPN
ejpam-6157	271	5	h̄2∥θ	h̄2∥θ	VERB
ejpam-6157	271	6	≤	≤	NUM
ejpam-6157	271	7	δ	δ	PROPN
ejpam-6157	271	8	implies	imply	VERB
ejpam-6157	272	1	that	that	SCONJ
ejpam-6157	272	2	∥u−	∥u−	PROPN
ejpam-6157	272	3	ū∥θ	ū∥θ	ADJ
ejpam-6157	272	4	≤	≤	PROPN
ejpam-6157	272	5	ϵ	ϵ	ADP
ejpam-6157	272	6	,	,	PUNCT
ejpam-6157	272	7	where	where	PROPN
ejpam-6157	272	8	x̄(t	x̄(t	PROPN
ejpam-6157	272	9	)	)	PUNCT
ejpam-6157	272	10	=	=	SYM
ejpam-6157	272	11	h̄1(t	h̄1(t	X
ejpam-6157	272	12	)	)	PUNCT
ejpam-6157	272	13	+	+	NUM
ejpam-6157	272	14	f1	f1	NOUN
ejpam-6157	272	15	(	(	PUNCT
ejpam-6157	272	16	λ1(ȳ)(t	λ1(ȳ)(t	NOUN
ejpam-6157	272	17	)	)	PUNCT
ejpam-6157	272	18	+	+	CCONJ
ejpam-6157	272	19	g1(ȳ)(t	g1(ȳ)(t	X
ejpam-6157	272	20	)	)	PUNCT
ejpam-6157	272	21	γ(β	γ(β	PROPN
ejpam-6157	272	22	)	)	PUNCT
ejpam-6157	272	23	·	·	PUNCT
ejpam-6157	272	24	∫	∫	PROPN
ejpam-6157	273	1	t	t	PROPN
ejpam-6157	273	2	1	1	NUM
ejpam-6157	273	3	(	(	PUNCT
ejpam-6157	273	4	log	log	VERB
ejpam-6157	273	5	t	t	PROPN
ejpam-6157	273	6	s	s	PART
ejpam-6157	273	7	)	)	PUNCT
ejpam-6157	273	8	β−1	β−1	PUNCT
ejpam-6157	273	9	r1(ȳ)(s	r1(ȳ)(s	VERB
ejpam-6157	273	10	)	)	PUNCT
ejpam-6157	273	11	s	s	PART
ejpam-6157	273	12	ds	ds	ADJ
ejpam-6157	273	13	)	)	PUNCT
ejpam-6157	273	14	ȳ(t	ȳ(t	NOUN
ejpam-6157	273	15	)	)	PUNCT
ejpam-6157	273	16	=	=	SYM
ejpam-6157	273	17	h̄2(t	h̄2(t	X
ejpam-6157	273	18	)	)	PUNCT
ejpam-6157	274	1	+	+	CCONJ
ejpam-6157	274	2	f2	f2	PROPN
ejpam-6157	274	3	(	(	PUNCT
ejpam-6157	274	4	λ2(x̄)(t	λ2(x̄)(t	X
ejpam-6157	274	5	)	)	PUNCT
ejpam-6157	274	6	+	+	CCONJ
ejpam-6157	274	7	g2(x̄)(t	g2(x̄)(t	X
ejpam-6157	274	8	)	)	PUNCT
ejpam-6157	274	9	γ(β	γ(β	PROPN
ejpam-6157	274	10	)	)	PUNCT
ejpam-6157	274	11	·	·	PUNCT
ejpam-6157	275	1	∫	∫	PROPN
ejpam-6157	276	1	t	t	PROPN
ejpam-6157	276	2	1	1	NUM
ejpam-6157	276	3	(	(	PUNCT
ejpam-6157	276	4	log	log	VERB
ejpam-6157	276	5	t	t	PROPN
ejpam-6157	276	6	s	s	PART
ejpam-6157	276	7	)	)	PUNCT
ejpam-6157	276	8	β−1	β−1	SYM
ejpam-6157	276	9	r2(x̄)(s	r2(x̄)(s	NOUN
ejpam-6157	276	10	)	)	PUNCT
ejpam-6157	276	11	s	s	VERB
ejpam-6157	276	12	ds	ds	PROPN
ejpam-6157	276	13	)	)	PUNCT
ejpam-6157	276	14	,	,	PUNCT
ejpam-6157	276	15	t	t	PROPN
ejpam-6157	276	16	∈	∈	PROPN
ejpam-6157	277	1	[	[	X
ejpam-6157	277	2	1	1	NUM
ejpam-6157	277	3	,	,	PUNCT
ejpam-6157	277	4	e	e	NOUN
ejpam-6157	277	5	]	]	X
ejpam-6157	277	6	.	.	PUNCT
ejpam-6157	278	1	(	(	PUNCT
ejpam-6157	278	2	5	5	X
ejpam-6157	278	3	)	)	PUNCT
ejpam-6157	278	4	theorem	theorem	NOUN
ejpam-6157	278	5	4	4	NUM
ejpam-6157	278	6	.	.	PUNCT
ejpam-6157	278	7	assume	assume	VERB
ejpam-6157	278	8	that	that	SCONJ
ejpam-6157	278	9	the	the	DET
ejpam-6157	278	10	assumptions	assumption	NOUN
ejpam-6157	278	11	of	of	ADP
ejpam-6157	278	12	theorem	theorem	ADJ
ejpam-6157	278	13	3	3	NUM
ejpam-6157	278	14	hold	hold	NOUN
ejpam-6157	278	15	.	.	PUNCT
ejpam-6157	279	1	then	then	ADV
ejpam-6157	279	2	the	the	DET
ejpam-6157	279	3	solutions	solution	NOUN
ejpam-6157	279	4	u	u	NOUN
ejpam-6157	279	5	∈	∈	NOUN
ejpam-6157	279	6	lx	lx	NOUN
ejpam-6157	279	7	of	of	ADP
ejpam-6157	279	8	the	the	DET
ejpam-6157	279	9	system	system	NOUN
ejpam-6157	279	10	(	(	PUNCT
ejpam-6157	279	11	1	1	X
ejpam-6157	279	12	)	)	PUNCT
ejpam-6157	279	13	depend	depend	VERB
ejpam-6157	279	14	continuously	continuously	ADV
ejpam-6157	279	15	on	on	ADP
ejpam-6157	279	16	the	the	DET
ejpam-6157	279	17	functions	function	NOUN
ejpam-6157	279	18	h1	h1	PROPN
ejpam-6157	279	19	,	,	PUNCT
ejpam-6157	279	20	h2	h2	NOUN
ejpam-6157	279	21	.	.	PUNCT
ejpam-6157	280	1	proof	proof	NOUN
ejpam-6157	280	2	.	.	PUNCT
ejpam-6157	281	1	let	let	VERB
ejpam-6157	281	2	u	u	NOUN
ejpam-6157	281	3	,	,	PUNCT
ejpam-6157	281	4	ū	ū	PROPN
ejpam-6157	281	5	be	be	VERB
ejpam-6157	281	6	any	any	DET
ejpam-6157	281	7	two	two	NUM
ejpam-6157	281	8	different	different	ADJ
ejpam-6157	281	9	solutions	solution	NOUN
ejpam-6157	281	10	of	of	ADP
ejpam-6157	281	11	(	(	PUNCT
ejpam-6157	281	12	1	1	NUM
ejpam-6157	281	13	)	)	PUNCT
ejpam-6157	281	14	,	,	PUNCT
ejpam-6157	281	15	then	then	ADV
ejpam-6157	281	16	similarly	similarly	ADV
ejpam-6157	281	17	as	as	SCONJ
ejpam-6157	281	18	done	do	VERB
ejpam-6157	281	19	in	in	ADP
ejpam-6157	281	20	theorem	theorem	NOUN
ejpam-6157	281	21	3	3	NUM
ejpam-6157	281	22	,	,	PUNCT
ejpam-6157	281	23	we	we	PRON
ejpam-6157	281	24	have	have	AUX
ejpam-6157	281	25	∥u−	∥u−	NUM
ejpam-6157	281	26	ū∥x	ū∥x	PROPN
ejpam-6157	281	27	≤	≤	PROPN
ejpam-6157	281	28	∥h1	∥h1	VERB
ejpam-6157	281	29	−	−	PROPN
ejpam-6157	281	30	h̄1∥θ	h̄1∥θ	NOUN
ejpam-6157	281	31	+	+	CCONJ
ejpam-6157	281	32	∥h2	∥h2	X
ejpam-6157	282	1	−	−	PROPN
ejpam-6157	282	2	h̄2∥θ	h̄2∥θ	PROPN
ejpam-6157	282	3	+	+	CCONJ
ejpam-6157	283	1	(	(	PUNCT
ejpam-6157	283	2	α1∥a∗∥θ	α1∥a∗∥θ	ADJ
ejpam-6157	283	3	+	+	CCONJ
ejpam-6157	283	4	4r	4r	NUM
ejpam-6157	283	5	·	·	PUNCT
ejpam-6157	283	6	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	283	7	γ(β	γ(β	PROPN
ejpam-6157	283	8	)	)	PUNCT
ejpam-6157	283	9	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	283	10	)	)	PUNCT
ejpam-6157	283	11	(	(	PUNCT
ejpam-6157	283	12	∥∥y	∥∥y	PROPN
ejpam-6157	283	13	−	−	PROPN
ejpam-6157	283	14	ȳ	ȳ	PROPN
ejpam-6157	283	15	∥∥	∥∥	X
ejpam-6157	283	16	θ	θ	PROPN
ejpam-6157	284	1	+	+	CCONJ
ejpam-6157	284	2	∥∥x−	∥∥x−	PROPN
ejpam-6157	284	3	x̄	x̄	X
ejpam-6157	284	4	∥∥	∥∥	PUNCT
ejpam-6157	284	5	θ	θ	X
ejpam-6157	284	6	)	)	PUNCT
ejpam-6157	285	1	=	=	PRON
ejpam-6157	285	2	∥h1	∥h1	VERB
ejpam-6157	285	3	−	−	PROPN
ejpam-6157	285	4	h̄1∥θ	h̄1∥θ	NOUN
ejpam-6157	285	5	+	+	CCONJ
ejpam-6157	285	6	∥h2	∥h2	X
ejpam-6157	285	7	−	−	PROPN
ejpam-6157	285	8	h̄2∥θ	h̄2∥θ	PROPN
ejpam-6157	285	9	+	+	CCONJ
ejpam-6157	286	1	(	(	PUNCT
ejpam-6157	286	2	α1∥a∗∥θ	α1∥a∗∥θ	ADJ
ejpam-6157	286	3	+	+	CCONJ
ejpam-6157	286	4	4r	4r	NUM
ejpam-6157	286	5	·	·	PUNCT
ejpam-6157	286	6	α2k1∥k∥θ2	α2k1∥k∥θ2	ADJ
ejpam-6157	286	7	γ(β	γ(β	PROPN
ejpam-6157	286	8	)	)	PUNCT
ejpam-6157	286	9	∥g∗∥θ1∥b∗∥m∗	∥g∗∥θ1∥b∗∥m∗	PROPN
ejpam-6157	286	10	)	)	PUNCT
ejpam-6157	286	11	∥u−	∥u−	PROPN
ejpam-6157	286	12	ū∥x	ū∥x	PROPN
ejpam-6157	286	13	≤	≤	PROPN
ejpam-6157	286	14	∥h1	∥h1	VERB
ejpam-6157	286	15	−	−	PROPN
ejpam-6157	286	16	h̄1∥θ	h̄1∥θ	NOUN
ejpam-6157	286	17	+	+	CCONJ
ejpam-6157	286	18	∥h2	∥h2	X
ejpam-6157	286	19	−	−	PROPN
ejpam-6157	286	20	h̄2∥θ	h̄2∥θ	PROPN
ejpam-6157	286	21	+	+	CCONJ
ejpam-6157	286	22	c∥u−	c∥u−	PROPN
ejpam-6157	286	23	ū∥x	ū∥x	PROPN
ejpam-6157	286	24	,	,	PUNCT
ejpam-6157	286	25	where	where	SCONJ
ejpam-6157	286	26	c	c	PROPN
ejpam-6157	286	27	is	be	AUX
ejpam-6157	286	28	given	give	VERB
ejpam-6157	286	29	by	by	ADP
ejpam-6157	286	30	(	(	PUNCT
ejpam-6157	286	31	4	4	NUM
ejpam-6157	286	32	)	)	PUNCT
ejpam-6157	286	33	.	.	PUNCT
ejpam-6157	287	1	then	then	ADV
ejpam-6157	287	2	,	,	PUNCT
ejpam-6157	287	3	we	we	PRON
ejpam-6157	287	4	get	get	VERB
ejpam-6157	287	5	∥u−	∥u−	PROPN
ejpam-6157	287	6	ū∥x	ū∥x	PROPN
ejpam-6157	287	7	≤	≤	NOUN
ejpam-6157	287	8	(	(	PUNCT
ejpam-6157	287	9	1−	1−	NUM
ejpam-6157	287	10	c	c	NOUN
ejpam-6157	287	11	)	)	PUNCT
ejpam-6157	287	12	−1	−1	NOUN
ejpam-6157	287	13	(	(	PUNCT
ejpam-6157	287	14	∥h1	∥h1	VERB
ejpam-6157	287	15	−	−	PROPN
ejpam-6157	287	16	h̄1∥θ	h̄1∥θ	NOUN
ejpam-6157	287	17	+	+	CCONJ
ejpam-6157	287	18	∥h2	∥h2	X
ejpam-6157	287	19	−	−	PROPN
ejpam-6157	287	20	h̄2∥θ	h̄2∥θ	PROPN
ejpam-6157	287	21	)	)	PUNCT
ejpam-6157	287	22	.	.	PUNCT
ejpam-6157	288	1	therefore	therefore	ADV
ejpam-6157	288	2	,	,	PUNCT
ejpam-6157	288	3	if	if	SCONJ
ejpam-6157	288	4	∥h1	∥h1	AUX
ejpam-6157	288	5	−	−	PROPN
ejpam-6157	288	6	h̄1∥θ	h̄1∥θ	NOUN
ejpam-6157	288	7	+	+	CCONJ
ejpam-6157	288	8	∥h2	∥h2	X
ejpam-6157	288	9	−	−	PUNCT
ejpam-6157	288	10	h̄2∥θ+	h̄2∥θ+	NOUN
ejpam-6157	288	11	≤	≤	PROPN
ejpam-6157	288	12	δ(ϵ	δ(ϵ	PROPN
ejpam-6157	288	13	)	)	PUNCT
ejpam-6157	288	14	,	,	PUNCT
ejpam-6157	288	15	then	then	ADV
ejpam-6157	288	16	∥u−	∥u−	PROPN
ejpam-6157	288	17	ū∥θ	ū∥θ	ADJ
ejpam-6157	288	18	≤	≤	NOUN
ejpam-6157	288	19	ϵ	ϵ	ADP
ejpam-6157	288	20	,	,	PUNCT
ejpam-6157	288	21	where	where	SCONJ
ejpam-6157	288	22	δ(ϵ	δ(ϵ	PROPN
ejpam-6157	288	23	)	)	PUNCT
ejpam-6157	288	24	=	=	SYM
ejpam-6157	289	1	ϵ	ϵ	X
ejpam-6157	289	2	·	·	PUNCT
ejpam-6157	289	3	(	(	PUNCT
ejpam-6157	289	4	1−	1−	NUM
ejpam-6157	289	5	c	c	NOUN
ejpam-6157	289	6	)	)	PUNCT
ejpam-6157	289	7	.	.	PUNCT
ejpam-6157	290	1	4	4	X
ejpam-6157	290	2	.	.	NUM
ejpam-6157	290	3	remarks	remark	NOUN
ejpam-6157	290	4	and	and	CCONJ
ejpam-6157	290	5	example	example	NOUN
ejpam-6157	290	6	we	we	PRON
ejpam-6157	290	7	would	would	AUX
ejpam-6157	290	8	like	like	VERB
ejpam-6157	290	9	to	to	PART
ejpam-6157	290	10	conclude	conclude	VERB
ejpam-6157	290	11	with	with	ADP
ejpam-6157	290	12	some	some	DET
ejpam-6157	290	13	significant	significant	ADJ
ejpam-6157	290	14	remarks	remark	NOUN
ejpam-6157	290	15	and	and	CCONJ
ejpam-6157	290	16	examples	example	NOUN
ejpam-6157	290	17	that	that	PRON
ejpam-6157	290	18	highlight	highlight	VERB
ejpam-6157	290	19	the	the	DET
ejpam-6157	290	20	applicability	applicability	NOUN
ejpam-6157	290	21	of	of	ADP
ejpam-6157	290	22	the	the	DET
ejpam-6157	290	23	results	result	NOUN
ejpam-6157	290	24	we	we	PRON
ejpam-6157	290	25	have	have	AUX
ejpam-6157	290	26	found	find	VERB
ejpam-6157	290	27	.	.	PUNCT
ejpam-6157	291	1	remark	remark	PROPN
ejpam-6157	291	2	1	1	NUM
ejpam-6157	291	3	.	.	PUNCT
ejpam-6157	292	1	the	the	DET
ejpam-6157	292	2	neutron	neutron	NOUN
ejpam-6157	292	3	transport	transport	NOUN
ejpam-6157	292	4	[	[	X
ejpam-6157	292	5	35	35	NUM
ejpam-6157	292	6	]	]	PUNCT
ejpam-6157	292	7	,	,	PUNCT
ejpam-6157	292	8	the	the	DET
ejpam-6157	292	9	traffic	traffic	NOUN
ejpam-6157	292	10	theory	theory	NOUN
ejpam-6157	292	11	[	[	X
ejpam-6157	292	12	36	36	NUM
ejpam-6157	292	13	]	]	PUNCT
ejpam-6157	292	14	,	,	PUNCT
ejpam-6157	292	15	the	the	DET
ejpam-6157	292	16	kinetic	kinetic	ADJ
ejpam-6157	292	17	theory	theory	NOUN
ejpam-6157	292	18	of	of	ADP
ejpam-6157	292	19	gases	gas	NOUN
ejpam-6157	292	20	[	[	X
ejpam-6157	292	21	37	37	NUM
ejpam-6157	292	22	]	]	PUNCT
ejpam-6157	292	23	,	,	PUNCT
ejpam-6157	292	24	and	and	CCONJ
ejpam-6157	292	25	astrophysics	astrophysic	NOUN
ejpam-6157	293	1	[	[	X
ejpam-6157	293	2	38	38	NUM
ejpam-6157	293	3	]	]	PUNCT
ejpam-6157	293	4	are	be	AUX
ejpam-6157	293	5	more	more	ADV
ejpam-6157	293	6	efficient	efficient	ADJ
ejpam-6157	293	7	utilization	utilization	NOUN
ejpam-6157	293	8	of	of	ADP
ejpam-6157	293	9	the	the	DET
ejpam-6157	293	10	quadratic	quadratic	ADJ
ejpam-6157	293	11	integral	integral	ADJ
ejpam-6157	293	12	equation	equation	NOUN
ejpam-6157	293	13	through	through	ADP
ejpam-6157	293	14	hadamard	hadamard	ADJ
ejpam-6157	293	15	fractional	fractional	ADJ
ejpam-6157	293	16	operators	operator	NOUN
ejpam-6157	293	17	.	.	PUNCT
ejpam-6157	294	1	m.	m.	PROPN
ejpam-6157	294	2	metwali	metwali	PROPN
ejpam-6157	294	3	,	,	PUNCT
ejpam-6157	294	4	s.	s.	PROPN
ejpam-6157	294	5	alsallami	alsallami	PROPN
ejpam-6157	294	6	/	/	SYM
ejpam-6157	294	7	eur	eur	PROPN
ejpam-6157	294	8	.	.	PUNCT
ejpam-6157	295	1	j.	j.	PROPN
ejpam-6157	295	2	pure	pure	PROPN
ejpam-6157	295	3	appl	appl	PROPN
ejpam-6157	295	4	.	.	PROPN
ejpam-6157	295	5	math	math	PROPN
ejpam-6157	295	6	,	,	PUNCT
ejpam-6157	295	7	18	18	NUM
ejpam-6157	295	8	(	(	PUNCT
ejpam-6157	295	9	2	2	NUM
ejpam-6157	295	10	)	)	PUNCT
ejpam-6157	295	11	(	(	PUNCT
ejpam-6157	295	12	2025	2025	NUM
ejpam-6157	295	13	)	)	PUNCT
ejpam-6157	295	14	,	,	PUNCT
ejpam-6157	295	15	6157	6157	NUM
ejpam-6157	295	16	12	12	NUM
ejpam-6157	295	17	of	of	ADP
ejpam-6157	295	18	15	15	NUM
ejpam-6157	295	19	remark	remark	NOUN
ejpam-6157	295	20	2	2	NUM
ejpam-6157	295	21	.	.	PUNCT
ejpam-6157	296	1	we	we	PRON
ejpam-6157	296	2	can	can	AUX
ejpam-6157	296	3	determine	determine	VERB
ejpam-6157	296	4	the	the	DET
ejpam-6157	296	5	acting	acting	NOUN
ejpam-6157	296	6	and	and	CCONJ
ejpam-6157	296	7	continuation	continuation	NOUN
ejpam-6157	296	8	assumptions	assumption	NOUN
ejpam-6157	296	9	for	for	ADP
ejpam-6157	296	10	the	the	DET
ejpam-6157	296	11	operators	operator	NOUN
ejpam-6157	296	12	of	of	ADP
ejpam-6157	296	13	the	the	DET
ejpam-6157	296	14	form	form	NOUN
ejpam-6157	296	15	gi(w	gi(w	PUNCT
ejpam-6157	296	16	)	)	PUNCT
ejpam-6157	296	17	=	=	SYM
ejpam-6157	296	18	li(t	li(t	X
ejpam-6157	296	19	)	)	PUNCT
ejpam-6157	296	20	·	·	PUNCT
ejpam-6157	296	21	w(t	w(t	PROPN
ejpam-6157	296	22	)	)	PUNCT
ejpam-6157	296	23	,	,	PUNCT
ejpam-6157	296	24	li	li	PROPN
ejpam-6157	296	25	∈	∈	PROPN
ejpam-6157	296	26	lθ	lθ	NOUN
ejpam-6157	296	27	,	,	PUNCT
ejpam-6157	296	28	over	over	ADP
ejpam-6157	296	29	several	several	ADJ
ejpam-6157	296	30	orlicz	orlicz	ADJ
ejpam-6157	296	31	spaces	space	NOUN
ejpam-6157	296	32	in	in	ADP
ejpam-6157	296	33	(	(	PUNCT
ejpam-6157	296	34	cf	cf	NOUN
ejpam-6157	296	35	.	.	PUNCT
ejpam-6157	297	1	[	[	X
ejpam-6157	297	2	17	17	NUM
ejpam-6157	297	3	]	]	PUNCT
ejpam-6157	297	4	and	and	CCONJ
ejpam-6157	297	5	assumption	assumption	NOUN
ejpam-6157	297	6	(	(	PUNCT
ejpam-6157	297	7	g3	g3	NOUN
ejpam-6157	297	8	)	)	PUNCT
ejpam-6157	297	9	)	)	PUNCT
ejpam-6157	297	10	.	.	PUNCT
ejpam-6157	297	11	example	example	NOUN
ejpam-6157	297	12	1	1	NUM
ejpam-6157	297	13	.	.	X
ejpam-6157	297	14	select	select	VERB
ejpam-6157	297	15	the	the	DET
ejpam-6157	297	16	n	n	PRON
ejpam-6157	297	17	-functions	-functions	PROPN
ejpam-6157	297	18	m(s	m(s	PROPN
ejpam-6157	297	19	)	)	PUNCT
ejpam-6157	297	20	=	=	SYM
ejpam-6157	297	21	m∗(s	m∗(s	NOUN
ejpam-6157	297	22	)	)	PUNCT
ejpam-6157	297	23	=	=	SYM
ejpam-6157	297	24	s2	s2	NOUN
ejpam-6157	297	25	and	and	CCONJ
ejpam-6157	297	26	θ2(s	θ2(s	NOUN
ejpam-6157	297	27	)	)	PUNCT
ejpam-6157	297	28	=	=	NOUN
ejpam-6157	297	29	exp	exp	NOUN
ejpam-6157	297	30	|s|	|s|	PROPN
ejpam-6157	297	31	−	−	PROPN
ejpam-6157	297	32	|s|	|s|	PROPN
ejpam-6157	297	33	−	−	PROPN
ejpam-6157	297	34	1	1	NUM
ejpam-6157	297	35	.	.	PUNCT
ejpam-6157	298	1	we	we	PRON
ejpam-6157	298	2	need	need	VERB
ejpam-6157	298	3	to	to	PART
ejpam-6157	298	4	show	show	VERB
ejpam-6157	298	5	that	that	SCONJ
ejpam-6157	298	6	,	,	PUNCT
ejpam-6157	298	7	the	the	DET
ejpam-6157	298	8	operator	operator	NOUN
ejpam-6157	298	9	kβ	kβ	INTJ
ejpam-6157	298	10	:	:	PUNCT
ejpam-6157	298	11	lm∗	lm∗	PROPN
ejpam-6157	298	12	→	→	PUNCT
ejpam-6157	298	13	lθ2	lθ2	ADJ
ejpam-6157	298	14	is	be	AUX
ejpam-6157	298	15	continuous	continuous	ADJ
ejpam-6157	298	16	and	and	CCONJ
ejpam-6157	298	17	the	the	DET
ejpam-6157	298	18	outcomes	outcome	NOUN
ejpam-6157	298	19	of	of	ADP
ejpam-6157	298	20	lemma	lemma	PROPN
ejpam-6157	298	21	2	2	NUM
ejpam-6157	298	22	is	be	AUX
ejpam-6157	298	23	verified	verify	VERB
ejpam-6157	298	24	.	.	PUNCT
ejpam-6157	299	1	indeed	indeed	ADV
ejpam-6157	299	2	:	:	PUNCT
ejpam-6157	299	3	let	let	VERB
ejpam-6157	299	4	t	t	X
ejpam-6157	299	5	∈	∈	PROPN
ejpam-6157	300	1	[	[	X
ejpam-6157	300	2	1	1	NUM
ejpam-6157	300	3	,	,	PUNCT
ejpam-6157	300	4	e	e	NOUN
ejpam-6157	300	5	]	]	PUNCT
ejpam-6157	300	6	and	and	CCONJ
ejpam-6157	300	7	for	for	ADP
ejpam-6157	300	8	any	any	DET
ejpam-6157	300	9	β	β	X
ejpam-6157	300	10	∈	∈	PROPN
ejpam-6157	300	11	(	(	PUNCT
ejpam-6157	300	12	0	0	NUM
ejpam-6157	300	13	,	,	PUNCT
ejpam-6157	300	14	1	1	NUM
ejpam-6157	300	15	)	)	PUNCT
ejpam-6157	300	16	,	,	PUNCT
ejpam-6157	300	17	we	we	PRON
ejpam-6157	300	18	get	get	VERB
ejpam-6157	300	19	k(t	k(t	X
ejpam-6157	300	20	)	)	PUNCT
ejpam-6157	301	1	=	=	SYM
ejpam-6157	302	1	∫	∫	PROPN
ejpam-6157	303	1	t	t	PROPN
ejpam-6157	303	2	0	0	NUM
ejpam-6157	303	3	m	m	VERB
ejpam-6157	303	4	(	(	PUNCT
ejpam-6157	303	5	uβ−1	uβ−1	PROPN
ejpam-6157	303	6	)	)	PUNCT
ejpam-6157	303	7	du	du	PROPN
ejpam-6157	303	8	=	=	SYM
ejpam-6157	303	9	∫	∫	PROPN
ejpam-6157	303	10	t	t	PROPN
ejpam-6157	303	11	0	0	NUM
ejpam-6157	303	12	u2β−2	u2β−2	PROPN
ejpam-6157	303	13	du	du	X
ejpam-6157	303	14	=	=	PUNCT
ejpam-6157	303	15	t2β−1	t2β−1	PROPN
ejpam-6157	303	16	2β	2β	NOUN
ejpam-6157	303	17	−	−	NOUN
ejpam-6157	303	18	1	1	NUM
ejpam-6157	303	19	.	.	PUNCT
ejpam-6157	304	1	that	that	PRON
ejpam-6157	304	2	gives	give	VERB
ejpam-6157	304	3	us	we	PRON
ejpam-6157	304	4	the	the	DET
ejpam-6157	304	5	verification	verification	NOUN
ejpam-6157	304	6	of	of	ADP
ejpam-6157	304	7	proposition	proposition	NOUN
ejpam-6157	304	8	1	1	NUM
ejpam-6157	304	9	.	.	PUNCT
ejpam-6157	304	10	furthermore,∫	furthermore,∫	NUM
ejpam-6157	305	1	e	e	PROPN
ejpam-6157	305	2	1	1	NUM
ejpam-6157	305	3	θ2	θ2	PROPN
ejpam-6157	305	4	(	(	PUNCT
ejpam-6157	305	5	k(t	k(t	PROPN
ejpam-6157	305	6	)	)	PUNCT
ejpam-6157	305	7	)	)	PUNCT
ejpam-6157	306	1	ds	ds	PROPN
ejpam-6157	306	2	=	=	SYM
ejpam-6157	306	3	∫	∫	PROPN
ejpam-6157	306	4	e	e	NOUN
ejpam-6157	306	5	1	1	NUM
ejpam-6157	306	6	(	(	PUNCT
ejpam-6157	306	7	e	e	X
ejpam-6157	306	8	t2β−1	t2β−1	PROPN
ejpam-6157	306	9	2β−1	2β−1	NUM
ejpam-6157	306	10	−	−	ADP
ejpam-6157	306	11	t2β−1	t2β−1	NOUN
ejpam-6157	306	12	2β	2β	NOUN
ejpam-6157	306	13	−	−	NOUN
ejpam-6157	306	14	1	1	NUM
ejpam-6157	306	15	−	−	NOUN
ejpam-6157	306	16	1	1	NUM
ejpam-6157	306	17	)	)	PUNCT
ejpam-6157	306	18	dt	dt	PROPN
ejpam-6157	306	19	,	,	PUNCT
ejpam-6157	306	20	which	which	PRON
ejpam-6157	306	21	is	be	AUX
ejpam-6157	306	22	finite	finite	ADJ
ejpam-6157	306	23	.	.	PUNCT
ejpam-6157	307	1	then	then	ADV
ejpam-6157	307	2	for	for	ADP
ejpam-6157	307	3	x	x	PROPN
ejpam-6157	307	4	∈	∈	PROPN
ejpam-6157	307	5	lm∗	lm∗	PROPN
ejpam-6157	307	6	,	,	PUNCT
ejpam-6157	307	7	we	we	PRON
ejpam-6157	307	8	have	have	VERB
ejpam-6157	307	9	jβ	jβ	NOUN
ejpam-6157	307	10	:	:	PUNCT
ejpam-6157	307	11	lm∗	lm∗	PROPN
ejpam-6157	307	12	→	→	PUNCT
ejpam-6157	307	13	lθ2	lθ2	ADJ
ejpam-6157	307	14	is	be	AUX
ejpam-6157	307	15	continuous	continuous	ADJ
ejpam-6157	307	16	.	.	PUNCT
ejpam-6157	308	1	for	for	ADP
ejpam-6157	308	2	additional	additional	ADJ
ejpam-6157	308	3	details	detail	NOUN
ejpam-6157	308	4	and	and	CCONJ
ejpam-6157	308	5	many	many	ADJ
ejpam-6157	308	6	instances	instance	NOUN
ejpam-6157	308	7	of	of	ADP
ejpam-6157	308	8	the	the	DET
ejpam-6157	308	9	n	n	CCONJ
ejpam-6157	308	10	-functions	-functions	PROPN
ejpam-6157	308	11	m	m	PROPN
ejpam-6157	308	12	,	,	PUNCT
ejpam-6157	308	13	m∗	m∗	NOUN
ejpam-6157	308	14	,	,	PUNCT
ejpam-6157	308	15	and	and	CCONJ
ejpam-6157	308	16	θ2	θ2	NOUN
ejpam-6157	308	17	that	that	PRON
ejpam-6157	308	18	satisfy	satisfy	VERB
ejpam-6157	308	19	lemma	lemma	PROPN
ejpam-6157	308	20	2	2	NUM
ejpam-6157	308	21	,	,	PUNCT
ejpam-6157	308	22	refer	refer	VERB
ejpam-6157	308	23	to	to	ADP
ejpam-6157	308	24	[	[	X
ejpam-6157	308	25	17	17	NUM
ejpam-6157	308	26	,	,	PUNCT
ejpam-6157	308	27	theorem	theorem	VERB
ejpam-6157	308	28	15.4	15.4	NUM
ejpam-6157	308	29	]	]	PUNCT
ejpam-6157	308	30	.	.	PUNCT
ejpam-6157	308	31	example	example	NOUN
ejpam-6157	309	1	2	2	NUM
ejpam-6157	309	2	.	.	X
ejpam-6157	310	1	for	for	ADP
ejpam-6157	310	2	i	i	PRON
ejpam-6157	310	3	=	=	NOUN
ejpam-6157	310	4	1	1	NUM
ejpam-6157	310	5	,	,	PUNCT
ejpam-6157	310	6	2	2	NUM
ejpam-6157	310	7	,	,	PUNCT
ejpam-6157	310	8	let	let	VERB
ejpam-6157	310	9	β	β	X
ejpam-6157	310	10	=	=	SYM
ejpam-6157	310	11	1	1	NUM
ejpam-6157	310	12	2	2	NUM
ejpam-6157	310	13	,	,	PUNCT
ejpam-6157	310	14	λi(z	λi(z	NOUN
ejpam-6157	310	15	)	)	PUNCT
ejpam-6157	310	16	=	=	SYM
ejpam-6157	310	17	ai(t	ai(t	NOUN
ejpam-6157	310	18	)	)	PUNCT
ejpam-6157	310	19	·	·	PUNCT
ejpam-6157	311	1	z(t	z(t	NOUN
ejpam-6157	311	2	)	)	PUNCT
ejpam-6157	311	3	,	,	PUNCT
ejpam-6157	311	4	gi(z	gi(z	NOUN
ejpam-6157	311	5	)	)	PUNCT
ejpam-6157	311	6	=	=	SYM
ejpam-6157	311	7	gi(t	gi(t	X
ejpam-6157	311	8	)	)	PUNCT
ejpam-6157	311	9	·	·	PUNCT
ejpam-6157	311	10	z(t	z(t	NOUN
ejpam-6157	311	11	)	)	PUNCT
ejpam-6157	311	12	,	,	PUNCT
ejpam-6157	311	13	and	and	CCONJ
ejpam-6157	311	14	ri(z	ri(z	NOUN
ejpam-6157	311	15	)	)	PUNCT
ejpam-6157	311	16	=	=	SYM
ejpam-6157	311	17	ai(t	ai(t	NOUN
ejpam-6157	311	18	)	)	PUNCT
ejpam-6157	311	19	·	·	PUNCT
ejpam-6157	312	1	z(t	z(t	NOUN
ejpam-6157	312	2	)	)	PUNCT
ejpam-6157	312	3	,	,	PUNCT
ejpam-6157	312	4	where	where	SCONJ
ejpam-6157	312	5	hi	hi	INTJ
ejpam-6157	312	6	∈	∈	PROPN
ejpam-6157	312	7	lθ	lθ	NOUN
ejpam-6157	312	8	,	,	PUNCT
ejpam-6157	312	9	ai	ai	VERB
ejpam-6157	312	10	∈	∈	PROPN
ejpam-6157	312	11	lθ	lθ	NOUN
ejpam-6157	312	12	,	,	PUNCT
ejpam-6157	312	13	gi	gi	NOUN
ejpam-6157	312	14	∈	∈	PROPN
ejpam-6157	312	15	lθ1	lθ1	PROPN
ejpam-6157	312	16	,	,	PUNCT
ejpam-6157	312	17	and	and	CCONJ
ejpam-6157	312	18	bi	bi	PROPN
ejpam-6157	312	19	∈	∈	PROPN
ejpam-6157	312	20	lm∗	lm∗	PROPN
ejpam-6157	312	21	,	,	PUNCT
ejpam-6157	312	22	then	then	ADV
ejpam-6157	312	23	the	the	DET
ejpam-6157	312	24	coupled	couple	VERB
ejpam-6157	312	25	system	system	NOUN
ejpam-6157	312	26			X
ejpam-6157	312	27	x(t	x(t	PROPN
ejpam-6157	312	28	)	)	PUNCT
ejpam-6157	312	29	=	=	PUNCT
ejpam-6157	313	1	h1(t	h1(t	X
ejpam-6157	313	2	)	)	PUNCT
ejpam-6157	314	1	+	+	CCONJ
ejpam-6157	314	2	f1	f1	PROPN
ejpam-6157	314	3	(	(	PUNCT
ejpam-6157	314	4	t	t	PROPN
ejpam-6157	314	5	,	,	PUNCT
ejpam-6157	314	6	a1(t	a1(t	PROPN
ejpam-6157	314	7	)	)	PUNCT
ejpam-6157	314	8	·	·	PUNCT
ejpam-6157	314	9	y(t	y(t	NUM
ejpam-6157	314	10	)	)	PUNCT
ejpam-6157	314	11	,	,	PUNCT
ejpam-6157	314	12	g1(t)·y(t	g1(t)·y(t	PROPN
ejpam-6157	314	13	)	)	PUNCT
ejpam-6157	314	14	γ	γ	PROPN
ejpam-6157	314	15	(	(	PUNCT
ejpam-6157	314	16	1	1	NUM
ejpam-6157	314	17	2	2	NUM
ejpam-6157	314	18	)	)	PUNCT
ejpam-6157	314	19	∫	∫	PROPN
ejpam-6157	315	1	t	t	PROPN
ejpam-6157	315	2	0	0	NUM
ejpam-6157	315	3	√	√	PROPN
ejpam-6157	315	4	log	log	PROPN
ejpam-6157	315	5	t	t	PROPN
ejpam-6157	315	6	s	s	PART
ejpam-6157	315	7	b1(t)·y(t	b1(t)·y(t	PROPN
ejpam-6157	315	8	)	)	PUNCT
ejpam-6157	315	9	s	s	PART
ejpam-6157	315	10	ds	ds	ADJ
ejpam-6157	315	11	)	)	PUNCT
ejpam-6157	315	12	y(t	y(t	NUM
ejpam-6157	315	13	)	)	PUNCT
ejpam-6157	316	1	=	=	PUNCT
ejpam-6157	316	2	h2(t	h2(t	X
ejpam-6157	316	3	)	)	PUNCT
ejpam-6157	317	1	+	+	CCONJ
ejpam-6157	317	2	f2	f2	PROPN
ejpam-6157	317	3	(	(	PUNCT
ejpam-6157	317	4	t	t	PROPN
ejpam-6157	317	5	,	,	PUNCT
ejpam-6157	317	6	a2(t	a2(t	PROPN
ejpam-6157	317	7	)	)	PUNCT
ejpam-6157	317	8	·	·	PUNCT
ejpam-6157	317	9	x(t	x(t	PROPN
ejpam-6157	317	10	)	)	PUNCT
ejpam-6157	317	11	,	,	PUNCT
ejpam-6157	317	12	g1(t)·x(t	g1(t)·x(t	PROPN
ejpam-6157	317	13	)	)	PUNCT
ejpam-6157	317	14	γ	γ	PROPN
ejpam-6157	317	15	(	(	PUNCT
ejpam-6157	317	16	1	1	NUM
ejpam-6157	317	17	2	2	NUM
ejpam-6157	317	18	)	)	PUNCT
ejpam-6157	317	19	∫	∫	PROPN
ejpam-6157	317	20	t	t	PROPN
ejpam-6157	317	21	0	0	NUM
ejpam-6157	317	22	√	√	PROPN
ejpam-6157	317	23	log	log	PROPN
ejpam-6157	317	24	t	t	PROPN
ejpam-6157	317	25	s	s	PART
ejpam-6157	317	26	b2(t)·x(t	b2(t)·x(t	PROPN
ejpam-6157	317	27	)	)	PUNCT
ejpam-6157	317	28	s	s	AUX
ejpam-6157	317	29	ds	ds	NOUN
ejpam-6157	317	30	)	)	PUNCT
ejpam-6157	317	31	,	,	PUNCT
ejpam-6157	317	32	have	have	VERB
ejpam-6157	317	33	a	a	DET
ejpam-6157	317	34	solution	solution	NOUN
ejpam-6157	317	35	u	u	NOUN
ejpam-6157	317	36	=	=	SYM
ejpam-6157	317	37	(	(	PUNCT
ejpam-6157	317	38	x	x	NOUN
ejpam-6157	317	39	,	,	PUNCT
ejpam-6157	317	40	y	y	NOUN
ejpam-6157	317	41	)	)	PUNCT
ejpam-6157	317	42	∈	∈	PROPN
ejpam-6157	317	43	lx	lx	NOUN
ejpam-6157	317	44	,	,	PUNCT
ejpam-6157	317	45	where	where	SCONJ
ejpam-6157	317	46	t	t	PROPN
ejpam-6157	317	47	∈	∈	PROPN
ejpam-6157	317	48	j	j	PROPN
ejpam-6157	317	49	.	.	PUNCT
ejpam-6157	318	1	5	5	X
ejpam-6157	318	2	.	.	X
ejpam-6157	318	3	conclusion	conclusion	NOUN
ejpam-6157	318	4	there	there	PRON
ejpam-6157	318	5	have	have	AUX
ejpam-6157	318	6	been	be	AUX
ejpam-6157	318	7	several	several	ADJ
ejpam-6157	318	8	qualitative	qualitative	ADJ
ejpam-6157	318	9	properties	property	NOUN
ejpam-6157	318	10	developed	develop	VERB
ejpam-6157	318	11	in	in	ADP
ejpam-6157	318	12	this	this	DET
ejpam-6157	318	13	paper	paper	NOUN
ejpam-6157	318	14	,	,	PUNCT
ejpam-6157	318	15	consisting	consist	VERB
ejpam-6157	318	16	of	of	ADP
ejpam-6157	318	17	existence	existence	NOUN
ejpam-6157	318	18	,	,	PUNCT
ejpam-6157	318	19	monotonicity	monotonicity	NOUN
ejpam-6157	318	20	,	,	PUNCT
ejpam-6157	318	21	and	and	CCONJ
ejpam-6157	318	22	uniqueness	uniqueness	NOUN
ejpam-6157	318	23	,	,	PUNCT
ejpam-6157	318	24	in	in	ADP
ejpam-6157	318	25	addition	addition	NOUN
ejpam-6157	318	26	to	to	ADP
ejpam-6157	318	27	the	the	DET
ejpam-6157	318	28	continuous	continuous	ADJ
ejpam-6157	318	29	dependence	dependence	NOUN
ejpam-6157	318	30	of	of	ADP
ejpam-6157	318	31	the	the	DET
ejpam-6157	318	32	data	datum	NOUN
ejpam-6157	318	33	,	,	PUNCT
ejpam-6157	318	34	which	which	PRON
ejpam-6157	318	35	are	be	AUX
ejpam-6157	318	36	all	all	PRON
ejpam-6157	318	37	indications	indication	NOUN
ejpam-6157	318	38	for	for	ADP
ejpam-6157	318	39	an	an	DET
ejpam-6157	318	40	abstract	abstract	ADJ
ejpam-6157	318	41	and	and	CCONJ
ejpam-6157	318	42	general	general	ADJ
ejpam-6157	318	43	coupled	couple	VERB
ejpam-6157	318	44	system	system	NOUN
ejpam-6157	318	45	of	of	ADP
ejpam-6157	318	46	quadratic	quadratic	ADJ
ejpam-6157	318	47	hadamard	hadamard	ADJ
ejpam-6157	318	48	-	-	PUNCT
ejpam-6157	318	49	fractional	fractional	ADJ
ejpam-6157	318	50	integral	integral	ADJ
ejpam-6157	318	51	equations	equation	NOUN
ejpam-6157	318	52	.	.	PUNCT
ejpam-6157	319	1	to	to	PART
ejpam-6157	319	2	perform	perform	VERB
ejpam-6157	319	3	our	our	PRON
ejpam-6157	319	4	analysis	analysis	NOUN
ejpam-6157	319	5	,	,	PUNCT
ejpam-6157	319	6	we	we	PRON
ejpam-6157	319	7	used	use	VERB
ejpam-6157	319	8	the	the	DET
ejpam-6157	319	9	(	(	PUNCT
ejpam-6157	319	10	mnc	mnc	PROPN
ejpam-6157	319	11	)	)	PUNCT
ejpam-6157	319	12	measure	measure	NOUN
ejpam-6157	319	13	of	of	ADP
ejpam-6157	319	14	noncompactness	noncompactness	ADJ
ejpam-6157	319	15	,	,	PUNCT
ejpam-6157	319	16	as	as	ADV
ejpam-6157	319	17	well	well	ADV
ejpam-6157	319	18	as	as	ADP
ejpam-6157	319	19	the	the	DET
ejpam-6157	319	20	(	(	PUNCT
ejpam-6157	319	21	fpt	fpt	NOUN
ejpam-6157	319	22	)	)	PUNCT
ejpam-6157	319	23	fixed	fix	VERB
ejpam-6157	319	24	-	-	PUNCT
ejpam-6157	319	25	point	point	NOUN
ejpam-6157	319	26	theorem	theorem	NOUN
ejpam-6157	319	27	and	and	CCONJ
ejpam-6157	319	28	the	the	DET
ejpam-6157	319	29	fractional	fractional	ADJ
ejpam-6157	319	30	calculus	calculus	NOUN
ejpam-6157	319	31	in	in	ADP
ejpam-6157	319	32	the	the	DET
ejpam-6157	319	33	orlicz	orlicz	NOUN
ejpam-6157	319	34	spaces	space	VERB
ejpam-6157	319	35	lθ	lθ	NOUN
ejpam-6157	319	36	.	.	PUNCT
ejpam-6157	320	1	finally	finally	ADV
ejpam-6157	320	2	,	,	PUNCT
ejpam-6157	320	3	we	we	PRON
ejpam-6157	320	4	concluded	conclude	VERB
ejpam-6157	320	5	with	with	ADP
ejpam-6157	320	6	a	a	DET
ejpam-6157	320	7	few	few	ADJ
ejpam-6157	320	8	remarks	remark	NOUN
ejpam-6157	320	9	as	as	ADV
ejpam-6157	320	10	well	well	ADV
ejpam-6157	320	11	as	as	ADP
ejpam-6157	320	12	a	a	DET
ejpam-6157	320	13	few	few	ADJ
ejpam-6157	320	14	examples	example	NOUN
ejpam-6157	320	15	that	that	PRON
ejpam-6157	320	16	illustrate	illustrate	VERB
ejpam-6157	320	17	and	and	CCONJ
ejpam-6157	320	18	support	support	VERB
ejpam-6157	320	19	our	our	PRON
ejpam-6157	320	20	hypothesis	hypothesis	NOUN
ejpam-6157	320	21	.	.	PUNCT
ejpam-6157	321	1	future	future	ADJ
ejpam-6157	321	2	research	research	NOUN
ejpam-6157	321	3	will	will	AUX
ejpam-6157	321	4	concentrate	concentrate	VERB
ejpam-6157	321	5	on	on	ADP
ejpam-6157	321	6	the	the	DET
ejpam-6157	321	7	qualitative	qualitative	ADJ
ejpam-6157	321	8	properties	property	NOUN
ejpam-6157	321	9	of	of	ADP
ejpam-6157	321	10	the	the	DET
ejpam-6157	321	11	solutions	solution	NOUN
ejpam-6157	321	12	for	for	ADP
ejpam-6157	321	13	numerous	numerous	ADJ
ejpam-6157	321	14	fractional	fractional	ADJ
ejpam-6157	321	15	problems	problem	NOUN
ejpam-6157	321	16	in	in	ADP
ejpam-6157	321	17	distinct	distinct	ADJ
ejpam-6157	321	18	function	function	NOUN
ejpam-6157	321	19	spaces	space	NOUN
ejpam-6157	321	20	,	,	PUNCT
ejpam-6157	321	21	such	such	ADJ
ejpam-6157	321	22	as	as	ADP
ejpam-6157	321	23	lebesgue	lebesgue	NOUN
ejpam-6157	321	24	spaces	space	NOUN
ejpam-6157	321	25	or	or	CCONJ
ejpam-6157	321	26	orlicz	orlicz	ADJ
ejpam-6157	321	27	spaces	space	NOUN
ejpam-6157	321	28	.	.	PUNCT
ejpam-6157	322	1	furthermore	furthermore	ADV
ejpam-6157	322	2	,	,	PUNCT
ejpam-6157	322	3	we	we	PRON
ejpam-6157	322	4	shall	shall	AUX
ejpam-6157	322	5	check	check	VERB
ejpam-6157	322	6	the	the	DET
ejpam-6157	322	7	numerical	numerical	ADJ
ejpam-6157	322	8	results	result	NOUN
ejpam-6157	322	9	for	for	ADP
ejpam-6157	322	10	the	the	DET
ejpam-6157	322	11	issues	issue	NOUN
ejpam-6157	322	12	considered	consider	VERB
ejpam-6157	322	13	.	.	PUNCT
ejpam-6157	323	1	m.	m.	PROPN
ejpam-6157	323	2	metwali	metwali	PROPN
ejpam-6157	323	3	,	,	PUNCT
ejpam-6157	323	4	s.	s.	PROPN
ejpam-6157	323	5	alsallami	alsallami	PROPN
ejpam-6157	323	6	/	/	SYM
ejpam-6157	323	7	eur	eur	PROPN
ejpam-6157	323	8	.	.	PUNCT
ejpam-6157	324	1	j.	j.	PROPN
ejpam-6157	324	2	pure	pure	PROPN
ejpam-6157	324	3	appl	appl	PROPN
ejpam-6157	324	4	.	.	PROPN
ejpam-6157	324	5	math	math	PROPN
ejpam-6157	324	6	,	,	PUNCT
ejpam-6157	324	7	18	18	NUM
ejpam-6157	324	8	(	(	PUNCT
ejpam-6157	324	9	2	2	NUM
ejpam-6157	324	10	)	)	PUNCT
ejpam-6157	324	11	(	(	PUNCT
ejpam-6157	324	12	2025	2025	NUM
ejpam-6157	324	13	)	)	PUNCT
ejpam-6157	324	14	,	,	PUNCT
ejpam-6157	324	15	6157	6157	NUM
ejpam-6157	324	16	13	13	NUM
ejpam-6157	324	17	of	of	ADP
ejpam-6157	324	18	15	15	NUM
ejpam-6157	324	19	acknowledgements	acknowledgement	NOUN
ejpam-6157	324	20	the	the	DET
ejpam-6157	324	21	authors	author	NOUN
ejpam-6157	324	22	extend	extend	VERB
ejpam-6157	324	23	their	their	PRON
ejpam-6157	324	24	appreciation	appreciation	NOUN
ejpam-6157	324	25	to	to	ADP
ejpam-6157	324	26	umm	umm	INTJ
ejpam-6157	324	27	al	al	PROPN
ejpam-6157	324	28	-	-	PUNCT
ejpam-6157	324	29	qura	qura	PROPN
ejpam-6157	324	30	university	university	PROPN
ejpam-6157	324	31	,	,	PUNCT
ejpam-6157	324	32	saudi	saudi	PROPN
ejpam-6157	324	33	arabia	arabia	PROPN
ejpam-6157	324	34	for	for	ADP
ejpam-6157	324	35	funding	fund	VERB
ejpam-6157	324	36	this	this	DET
ejpam-6157	324	37	research	research	NOUN
ejpam-6157	324	38	work	work	NOUN
ejpam-6157	324	39	through	through	ADP
ejpam-6157	324	40	grant	grant	NOUN
ejpam-6157	324	41	number	number	NOUN
ejpam-6157	324	42	:	:	PUNCT
ejpam-6157	324	43	25uqu4290491gssr03	25uqu4290491gssr03	NUM
ejpam-6157	324	44	.	.	PUNCT
ejpam-6157	325	1	author	author	NOUN
ejpam-6157	325	2	contributions	contribution	VERB
ejpam-6157	325	3	all	all	DET
ejpam-6157	325	4	the	the	DET
ejpam-6157	325	5	authors	author	NOUN
ejpam-6157	325	6	contributed	contribute	VERB
ejpam-6157	325	7	equally	equally	ADV
ejpam-6157	325	8	in	in	ADP
ejpam-6157	325	9	preparing	prepare	VERB
ejpam-6157	325	10	,	,	PUNCT
ejpam-6157	325	11	writing	writing	NOUN
ejpam-6157	325	12	,	,	PUNCT
ejpam-6157	325	13	and	and	CCONJ
ejpam-6157	325	14	obtaining	obtain	VERB
ejpam-6157	325	15	the	the	DET
ejpam-6157	325	16	paper	paper	NOUN
ejpam-6157	325	17	’s	’s	PART
ejpam-6157	325	18	results	result	NOUN
ejpam-6157	325	19	.	.	PUNCT
ejpam-6157	326	1	funding	fund	VERB
ejpam-6157	326	2	this	this	DET
ejpam-6157	326	3	research	research	NOUN
ejpam-6157	326	4	work	work	NOUN
ejpam-6157	326	5	was	be	AUX
ejpam-6157	326	6	funded	fund	VERB
ejpam-6157	326	7	by	by	ADP
ejpam-6157	326	8	umm	umm	INTJ
ejpam-6157	326	9	al	al	PROPN
ejpam-6157	326	10	-	-	PUNCT
ejpam-6157	326	11	qura	qura	PROPN
ejpam-6157	326	12	university	university	PROPN
ejpam-6157	326	13	,	,	PUNCT
ejpam-6157	326	14	saudi	saudi	PROPN
ejpam-6157	326	15	arabia	arabia	PROPN
ejpam-6157	326	16	,	,	PUNCT
ejpam-6157	326	17	under	under	ADP
ejpam-6157	326	18	grant	grant	NOUN
ejpam-6157	326	19	number	number	NOUN
ejpam-6157	326	20	:	:	PUNCT
ejpam-6157	326	21	25uqu4290491gssr03	25uqu4290491gssr03	NUM
ejpam-6157	326	22	.	.	PUNCT
ejpam-6157	327	1	references	reference	NOUN
ejpam-6157	327	2	[	[	X
ejpam-6157	327	3	1	1	NUM
ejpam-6157	327	4	]	]	PUNCT
ejpam-6157	327	5	e	e	X
ejpam-6157	327	6	cuesta	cuesta	X
ejpam-6157	327	7	;	;	PUNCT
ejpam-6157	327	8	m	m	VERB
ejpam-6157	327	9	kirance	kirance	NOUN
ejpam-6157	327	10	;	;	PUNCT
ejpam-6157	327	11	and	and	CCONJ
ejpam-6157	327	12	s	s	VERB
ejpam-6157	327	13	a	a	DET
ejpam-6157	327	14	malik	malik	PROPN
ejpam-6157	327	15	.	.	PUNCT
ejpam-6157	328	1	image	image	NOUN
ejpam-6157	328	2	structure	structure	NOUN
ejpam-6157	328	3	preseving	preseve	VERB
ejpam-6157	328	4	denoising	denoise	VERB
ejpam-6157	328	5	generalized	generalize	VERB
ejpam-6157	328	6	fractional	fractional	ADJ
ejpam-6157	328	7	time	time	NOUN
ejpam-6157	328	8	integrals	integral	NOUN
ejpam-6157	328	9	.	.	PUNCT
ejpam-6157	329	1	signal	signal	ADJ
ejpam-6157	329	2	process	process	NOUN
ejpam-6157	329	3	.	.	PUNCT
ejpam-6157	329	4	,	,	PUNCT
ejpam-6157	329	5	92:553–563	92:553–563	NUM
ejpam-6157	329	6	,	,	PUNCT
ejpam-6157	329	7	2012	2012	NUM
ejpam-6157	329	8	.	.	PUNCT
ejpam-6157	330	1	[	[	X
ejpam-6157	330	2	2	2	NUM
ejpam-6157	330	3	]	]	X
ejpam-6157	330	4	m	m	VERB
ejpam-6157	330	5	a	a	DET
ejpam-6157	330	6	polo	polo	NOUN
ejpam-6157	330	7	-	-	PUNCT
ejpam-6157	330	8	labarrios	labarrio	NOUN
ejpam-6157	330	9	;	;	PUNCT
ejpam-6157	330	10	s	s	VERB
ejpam-6157	330	11	q	q	PROPN
ejpam-6157	330	12	garcia	garcia	PROPN
ejpam-6157	330	13	;	;	PUNCT
ejpam-6157	330	14	g	g	PROPN
ejpam-6157	330	15	e	e	PROPN
ejpam-6157	330	16	paredes	parede	NOUN
ejpam-6157	330	17	;	;	PUNCT
ejpam-6157	330	18	l	l	PROPN
ejpam-6157	330	19	f	f	PROPN
ejpam-6157	330	20	perez	perez	PROPN
ejpam-6157	330	21	;	;	PUNCT
ejpam-6157	330	22	and	and	CCONJ
ejpam-6157	330	23	j	j	PROPN
ejpam-6157	330	24	o	o	PROPN
ejpam-6157	330	25	villafuerta	villafuerta	PROPN
ejpam-6157	330	26	.	.	PUNCT
ejpam-6157	331	1	novel	novel	ADJ
ejpam-6157	331	2	numerical	numerical	ADJ
ejpam-6157	331	3	solution	solution	NOUN
ejpam-6157	331	4	to	to	ADP
ejpam-6157	331	5	the	the	DET
ejpam-6157	331	6	fractional	fractional	ADJ
ejpam-6157	331	7	neutron	neutron	NOUN
ejpam-6157	331	8	point	point	NOUN
ejpam-6157	331	9	kinetic	kinetic	ADJ
ejpam-6157	331	10	equation	equation	NOUN
ejpam-6157	331	11	in	in	ADP
ejpam-6157	331	12	nuclear	nuclear	ADJ
ejpam-6157	331	13	reactor	reactor	NOUN
ejpam-6157	331	14	dynamics	dynamic	NOUN
ejpam-6157	331	15	.	.	PUNCT
ejpam-6157	332	1	ann	ann	PROPN
ejpam-6157	332	2	.	.	PUNCT
ejpam-6157	332	3	nucl	nucl	PROPN
ejpam-6157	332	4	.	.	PUNCT
ejpam-6157	333	1	energy	energy	NOUN
ejpam-6157	333	2	,	,	PUNCT
ejpam-6157	333	3	137(10717	137(10717	NUM
ejpam-6157	333	4	)	)	PUNCT
ejpam-6157	333	5	,	,	PUNCT
ejpam-6157	333	6	2020	2020	NUM
ejpam-6157	333	7	.	.	PUNCT
ejpam-6157	334	1	[	[	X
ejpam-6157	334	2	3	3	NUM
ejpam-6157	334	3	]	]	SYM
ejpam-6157	334	4	v	v	ADP
ejpam-6157	334	5	gafiychuk	gafiychuk	NOUN
ejpam-6157	334	6	;	;	PUNCT
ejpam-6157	334	7	b	b	X
ejpam-6157	334	8	datsko	datsko	ADV
ejpam-6157	334	9	;	;	PUNCT
ejpam-6157	334	10	v	v	X
ejpam-6157	334	11	meleshko	meleshko	VERB
ejpam-6157	334	12	;	;	PUNCT
ejpam-6157	334	13	and	and	CCONJ
ejpam-6157	334	14	d	d	X
ejpam-6157	334	15	blackmore	blackmore	NOUN
ejpam-6157	334	16	.	.	PUNCT
ejpam-6157	335	1	chaos	chaos	NOUN
ejpam-6157	335	2	solitons	soliton	NOUN
ejpam-6157	335	3	and	and	CCONJ
ejpam-6157	335	4	fract	fract	NOUN
ejpam-6157	335	5	.	.	PUNCT
ejpam-6157	336	1	southern	southern	ADJ
ejpam-6157	336	2	economic	economic	ADJ
ejpam-6157	336	3	journal	journal	PROPN
ejpam-6157	336	4	,	,	PUNCT
ejpam-6157	336	5	41:1095–1104	41:1095–1104	PROPN
ejpam-6157	336	6	,	,	PUNCT
ejpam-6157	336	7	2009	2009	NUM
ejpam-6157	336	8	.	.	PUNCT
ejpam-6157	337	1	[	[	X
ejpam-6157	337	2	4	4	X
ejpam-6157	337	3	]	]	X
ejpam-6157	337	4	t	t	PROPN
ejpam-6157	337	5	e	e	PROPN
ejpam-6157	337	6	roth	roth	PROPN
ejpam-6157	337	7	and	and	CCONJ
ejpam-6157	337	8	w	w	PROPN
ejpam-6157	337	9	c	c	NOUN
ejpam-6157	337	10	chew	chew	VERB
ejpam-6157	337	11	.	.	PUNCT
ejpam-6157	338	1	stability	stability	NOUN
ejpam-6157	338	2	analysis	analysis	NOUN
ejpam-6157	338	3	and	and	CCONJ
ejpam-6157	338	4	discretization	discretization	NOUN
ejpam-6157	338	5	of	of	ADP
ejpam-6157	338	6	a-ϕ	a-ϕ	NOUN
ejpam-6157	338	7	time	time	NOUN
ejpam-6157	338	8	domain	domain	VERB
ejpam-6157	338	9	integral	integral	ADJ
ejpam-6157	338	10	equations	equation	NOUN
ejpam-6157	338	11	for	for	ADP
ejpam-6157	338	12	multiscale	multiscale	ADJ
ejpam-6157	338	13	electromagnetic	electromagnetic	NOUN
ejpam-6157	338	14	.	.	PUNCT
ejpam-6157	339	1	j.	j.	PROPN
ejpam-6157	339	2	comput	comput	PROPN
ejpam-6157	339	3	.	.	PUNCT
ejpam-6157	340	1	phys	phy	NOUN
ejpam-6157	340	2	.	.	PUNCT
ejpam-6157	340	3	,	,	PUNCT
ejpam-6157	340	4	408(109102):705	408(109102):705	NOUN
ejpam-6157	340	5	–	–	PUNCT
ejpam-6157	340	6	717	717	NUM
ejpam-6157	340	7	,	,	PUNCT
ejpam-6157	340	8	2020	2020	NUM
ejpam-6157	340	9	.	.	PUNCT
ejpam-6157	341	1	[	[	X
ejpam-6157	341	2	5	5	NUM
ejpam-6157	341	3	]	]	X
ejpam-6157	341	4	h	h	NOUN
ejpam-6157	341	5	chen	chen	PROPN
ejpam-6157	341	6	;	;	PUNCT
ejpam-6157	341	7	j	j	PROPN
ejpam-6157	341	8	i	i	PRON
ejpam-6157	341	9	frankel	frankel	PROPN
ejpam-6157	341	10	;	;	PUNCT
ejpam-6157	341	11	and	and	CCONJ
ejpam-6157	341	12	m	m	PROPN
ejpam-6157	341	13	keyhani	keyhani	ADJ
ejpam-6157	341	14	.	.	PUNCT
ejpam-6157	342	1	two	two	NUM
ejpam-6157	342	2	-	-	PUNCT
ejpam-6157	342	3	probe	probe	NOUN
ejpam-6157	342	4	calibration	calibration	NOUN
ejpam-6157	342	5	integral	integral	ADJ
ejpam-6157	342	6	equation	equation	NOUN
ejpam-6157	342	7	method	method	NOUN
ejpam-6157	342	8	for	for	ADP
ejpam-6157	342	9	nonlinear	nonlinear	ADJ
ejpam-6157	342	10	inverse	inverse	ADJ
ejpam-6157	342	11	heat	heat	NOUN
ejpam-6157	342	12	conduction	conduction	NOUN
ejpam-6157	342	13	problem	problem	NOUN
ejpam-6157	342	14	of	of	ADP
ejpam-6157	342	15	surface	surface	NOUN
ejpam-6157	342	16	heat	heat	NOUN
ejpam-6157	342	17	flux	flux	PROPN
ejpam-6157	342	18	estimation	estimation	PROPN
ejpam-6157	342	19	.	.	PUNCT
ejpam-6157	343	1	int	int	NOUN
ejpam-6157	343	2	.	.	PUNCT
ejpam-6157	344	1	j.	j.	PROPN
ejpam-6157	344	2	heat	heat	PROPN
ejpam-6157	344	3	mass	mass	PROPN
ejpam-6157	344	4	transf	transf	PROPN
ejpam-6157	344	5	.	.	PUNCT
ejpam-6157	344	6	,	,	PUNCT
ejpam-6157	344	7	121:246–264	121:246–264	NUM
ejpam-6157	344	8	,	,	PUNCT
ejpam-6157	344	9	2018	2018	NUM
ejpam-6157	344	10	.	.	PUNCT
ejpam-6157	345	1	[	[	X
ejpam-6157	345	2	6	6	NUM
ejpam-6157	345	3	]	]	PUNCT
ejpam-6157	345	4	a.	a.	NOUN
ejpam-6157	345	5	m.	m.	NOUN
ejpam-6157	345	6	alotaibi	alotaibi	PROPN
ejpam-6157	345	7	;	;	PUNCT
ejpam-6157	345	8	m.	m.	NOUN
ejpam-6157	345	9	metwali	metwali	PROPN
ejpam-6157	345	10	;	;	PUNCT
ejpam-6157	345	11	h.	h.	PROPN
ejpam-6157	345	12	taha	taha	PROPN
ejpam-6157	345	13	;	;	PUNCT
ejpam-6157	345	14	r.	r.	PROPN
ejpam-6157	345	15	p.	p.	PROPN
ejpam-6157	345	16	agarwal	agarwal	PROPN
ejpam-6157	345	17	.	.	PUNCT
ejpam-6157	346	1	existence	existence	NOUN
ejpam-6157	346	2	,	,	PUNCT
ejpam-6157	346	3	uniqueness	uniqueness	NOUN
ejpam-6157	346	4	,	,	PUNCT
ejpam-6157	346	5	continuous	continuous	ADJ
ejpam-6157	346	6	dependence	dependence	NOUN
ejpam-6157	346	7	on	on	ADP
ejpam-6157	346	8	the	the	DET
ejpam-6157	346	9	data	datum	NOUN
ejpam-6157	346	10	for	for	ADP
ejpam-6157	346	11	the	the	DET
ejpam-6157	346	12	product	product	NOUN
ejpam-6157	346	13	of	of	ADP
ejpam-6157	346	14	n	n	CCONJ
ejpam-6157	346	15	-	-	PUNCT
ejpam-6157	346	16	fractional	fractional	ADJ
ejpam-6157	346	17	integral	integral	ADJ
ejpam-6157	346	18	equations	equation	NOUN
ejpam-6157	346	19	in	in	ADP
ejpam-6157	346	20	orlicz	orlicz	ADJ
ejpam-6157	346	21	spaces	space	NOUN
ejpam-6157	346	22	.	.	PUNCT
ejpam-6157	347	1	aims	aim	VERB
ejpam-6157	347	2	mathematics	mathematic	NOUN
ejpam-6157	347	3	,	,	PUNCT
ejpam-6157	347	4	10(4):8382–8397	10(4):8382–8397	NUM
ejpam-6157	347	5	,	,	PUNCT
ejpam-6157	347	6	2025	2025	NUM
ejpam-6157	347	7	.	.	PUNCT
ejpam-6157	348	1	[	[	X
ejpam-6157	348	2	7	7	NUM
ejpam-6157	348	3	]	]	X
ejpam-6157	348	4	r	r	NOUN
ejpam-6157	348	5	arab	arab	PROPN
ejpam-6157	348	6	.	.	PUNCT
ejpam-6157	348	7	application	application	NOUN
ejpam-6157	348	8	of	of	ADP
ejpam-6157	348	9	measure	measure	NOUN
ejpam-6157	348	10	of	of	ADP
ejpam-6157	348	11	noncompactness	noncompactness	NOUN
ejpam-6157	348	12	for	for	ADP
ejpam-6157	348	13	the	the	DET
ejpam-6157	348	14	system	system	NOUN
ejpam-6157	348	15	of	of	ADP
ejpam-6157	348	16	functional	functional	ADJ
ejpam-6157	348	17	integral	integral	ADJ
ejpam-6157	348	18	equations	equation	NOUN
ejpam-6157	348	19	.	.	PUNCT
ejpam-6157	349	1	filomat	filomat	PROPN
ejpam-6157	349	2	,	,	PUNCT
ejpam-6157	349	3	30:3063–3073	30:3063–3073	NUM
ejpam-6157	349	4	,	,	PUNCT
ejpam-6157	349	5	2016	2016	NUM
ejpam-6157	349	6	.	.	PUNCT
ejpam-6157	350	1	[	[	X
ejpam-6157	350	2	8	8	NUM
ejpam-6157	350	3	]	]	SYM
ejpam-6157	350	4	b	b	X
ejpam-6157	350	5	ahmad	ahmad	PROPN
ejpam-6157	350	6	;	;	PUNCT
ejpam-6157	350	7	s	s	PART
ejpam-6157	350	8	k	k	NOUN
ejpam-6157	350	9	ntouyas	ntouyas	NOUN
ejpam-6157	350	10	;	;	PUNCT
ejpam-6157	350	11	a	a	DET
ejpam-6157	350	12	alsaedi	alsaedi	NOUN
ejpam-6157	350	13	;	;	PUNCT
ejpam-6157	350	14	and	and	CCONJ
ejpam-6157	350	15	a	a	DET
ejpam-6157	350	16	f	f	NOUN
ejpam-6157	350	17	albideewi	albideewi	NOUN
ejpam-6157	350	18	.	.	PUNCT
ejpam-6157	351	1	a	a	DET
ejpam-6157	351	2	study	study	NOUN
ejpam-6157	351	3	of	of	ADP
ejpam-6157	351	4	a	a	DET
ejpam-6157	351	5	coupled	couple	VERB
ejpam-6157	351	6	system	system	NOUN
ejpam-6157	351	7	of	of	ADP
ejpam-6157	351	8	hadamard	hadamard	ADJ
ejpam-6157	351	9	fractional	fractional	ADJ
ejpam-6157	351	10	differential	differential	NOUN
ejpam-6157	351	11	equations	equation	NOUN
ejpam-6157	351	12	with	with	ADP
ejpam-6157	351	13	nonlocal	nonlocal	ADJ
ejpam-6157	351	14	coupled	couple	VERB
ejpam-6157	351	15	initial	initial	ADJ
ejpam-6157	351	16	-	-	PUNCT
ejpam-6157	351	17	multipoint	multipoint	NOUN
ejpam-6157	351	18	conditions	condition	NOUN
ejpam-6157	351	19	.	.	PUNCT
ejpam-6157	352	1	adv	adv	PROPN
ejpam-6157	352	2	.	.	PROPN
ejpam-6157	352	3	differ	differ	VERB
ejpam-6157	352	4	.	.	PUNCT
ejpam-6157	353	1	equ	equ	PROPN
ejpam-6157	353	2	.	.	PROPN
ejpam-6157	353	3	,	,	PUNCT
ejpam-6157	353	4	33(2021	33(2021	NUM
ejpam-6157	353	5	)	)	PUNCT
ejpam-6157	353	6	,	,	PUNCT
ejpam-6157	353	7	2021	2021	NUM
ejpam-6157	353	8	.	.	PUNCT
ejpam-6157	354	1	[	[	X
ejpam-6157	354	2	9	9	NUM
ejpam-6157	354	3	]	]	SYM
ejpam-6157	354	4	m	m	VERB
ejpam-6157	354	5	i	i	PROPN
ejpam-6157	354	6	youssef	youssef	PROPN
ejpam-6157	354	7	.	.	PUNCT
ejpam-6157	355	1	on	on	ADP
ejpam-6157	355	2	the	the	DET
ejpam-6157	355	3	solvability	solvability	NOUN
ejpam-6157	355	4	of	of	ADP
ejpam-6157	355	5	a	a	DET
ejpam-6157	355	6	general	general	ADJ
ejpam-6157	355	7	class	class	NOUN
ejpam-6157	355	8	of	of	ADP
ejpam-6157	355	9	a	a	DET
ejpam-6157	355	10	coupled	couple	VERB
ejpam-6157	355	11	system	system	NOUN
ejpam-6157	355	12	of	of	ADP
ejpam-6157	355	13	stochastic	stochastic	ADJ
ejpam-6157	355	14	functional	functional	ADJ
ejpam-6157	355	15	integral	integral	ADJ
ejpam-6157	355	16	equations	equation	NOUN
ejpam-6157	355	17	.	.	PUNCT
ejpam-6157	356	1	arab	arab	PROPN
ejpam-6157	356	2	journal	journal	PROPN
ejpam-6157	356	3	of	of	ADP
ejpam-6157	356	4	basic	basic	ADJ
ejpam-6157	356	5	and	and	CCONJ
ejpam-6157	356	6	applied	applied	ADJ
ejpam-6157	356	7	sciences	science	NOUN
ejpam-6157	356	8	,	,	PUNCT
ejpam-6157	356	9	27:142	27:142	NUM
ejpam-6157	356	10	–	–	PUNCT
ejpam-6157	356	11	148	148	NUM
ejpam-6157	356	12	,	,	PUNCT
ejpam-6157	356	13	2020	2020	NUM
ejpam-6157	356	14	.	.	PUNCT
ejpam-6157	357	1	[	[	X
ejpam-6157	357	2	10	10	NUM
ejpam-6157	357	3	]	]	X
ejpam-6157	357	4	j	j	PROPN
ejpam-6157	357	5	west	west	PROPN
ejpam-6157	357	6	and	and	CCONJ
ejpam-6157	357	7	linster	linster	PROPN
ejpam-6157	357	8	.	.	PUNCT
ejpam-6157	358	1	boundary	boundary	ADJ
ejpam-6157	358	2	value	value	NOUN
ejpam-6157	358	3	problem	problem	NOUN
ejpam-6157	358	4	for	for	ADP
ejpam-6157	358	5	a	a	DET
ejpam-6157	358	6	coupled	couple	VERB
ejpam-6157	358	7	system	system	NOUN
ejpam-6157	358	8	of	of	ADP
ejpam-6157	358	9	nonlinear	nonlinear	ADJ
ejpam-6157	358	10	fractional	fractional	ADJ
ejpam-6157	358	11	differential	differential	ADJ
ejpam-6157	358	12	equations	equation	NOUN
ejpam-6157	358	13	.	.	PUNCT
ejpam-6157	359	1	appl	appl	PROPN
ejpam-6157	359	2	.	.	PROPN
ejpam-6157	359	3	math	math	PROPN
ejpam-6157	359	4	.	.	PUNCT
ejpam-6157	360	1	lett	lett	PROPN
ejpam-6157	360	2	.	.	PROPN
ejpam-6157	360	3	,	,	PUNCT
ejpam-6157	360	4	22:64–69	22:64–69	NUM
ejpam-6157	360	5	,	,	PUNCT
ejpam-6157	360	6	2009	2009	NUM
ejpam-6157	360	7	.	.	PUNCT
ejpam-6157	361	1	m.	m.	PROPN
ejpam-6157	361	2	metwali	metwali	PROPN
ejpam-6157	361	3	,	,	PUNCT
ejpam-6157	361	4	s.	s.	PROPN
ejpam-6157	361	5	alsallami	alsallami	PROPN
ejpam-6157	361	6	/	/	SYM
ejpam-6157	361	7	eur	eur	PROPN
ejpam-6157	361	8	.	.	PUNCT
ejpam-6157	362	1	j.	j.	PROPN
ejpam-6157	362	2	pure	pure	PROPN
ejpam-6157	362	3	appl	appl	PROPN
ejpam-6157	362	4	.	.	PROPN
ejpam-6157	362	5	math	math	PROPN
ejpam-6157	362	6	,	,	PUNCT
ejpam-6157	362	7	18	18	NUM
ejpam-6157	362	8	(	(	PUNCT
ejpam-6157	362	9	2	2	NUM
ejpam-6157	362	10	)	)	PUNCT
ejpam-6157	362	11	(	(	PUNCT
ejpam-6157	362	12	2025	2025	NUM
ejpam-6157	362	13	)	)	PUNCT
ejpam-6157	362	14	,	,	PUNCT
ejpam-6157	362	15	6157	6157	NUM
ejpam-6157	362	16	14	14	NUM
ejpam-6157	362	17	of	of	ADP
ejpam-6157	362	18	15	15	NUM
ejpam-6157	362	19	[	[	X
ejpam-6157	362	20	11	11	NUM
ejpam-6157	362	21	]	]	SYM
ejpam-6157	362	22	b	b	PROPN
ejpam-6157	362	23	d	d	X
ejpam-6157	362	24	karande	karande	PROPN
ejpam-6157	362	25	and	and	CCONJ
ejpam-6157	362	26	s	s	NOUN
ejpam-6157	362	27	n	n	PRON
ejpam-6157	362	28	kondekar	kondekar	NOUN
ejpam-6157	362	29	.	.	PUNCT
ejpam-6157	363	1	existence	existence	VERB
ejpam-6157	363	2	the	the	DET
ejpam-6157	363	3	solution	solution	NOUN
ejpam-6157	363	4	of	of	ADP
ejpam-6157	363	5	coupled	couple	VERB
ejpam-6157	363	6	system	system	NOUN
ejpam-6157	363	7	of	of	ADP
ejpam-6157	363	8	quadratic	quadratic	ADJ
ejpam-6157	363	9	hybrid	hybrid	ADJ
ejpam-6157	363	10	functional	functional	ADJ
ejpam-6157	363	11	integral	integral	ADJ
ejpam-6157	363	12	equation	equation	NOUN
ejpam-6157	363	13	in	in	ADP
ejpam-6157	363	14	banach	banach	NOUN
ejpam-6157	363	15	algebras	algebras	PROPN
ejpam-6157	363	16	.	.	PUNCT
ejpam-6157	364	1	journal	journal	PROPN
ejpam-6157	364	2	of	of	ADP
ejpam-6157	364	3	mechanics	mechanic	NOUN
ejpam-6157	364	4	of	of	ADP
ejpam-6157	364	5	continua	continua	PROPN
ejpam-6157	364	6	and	and	CCONJ
ejpam-6157	364	7	mathematical	mathematical	ADJ
ejpam-6157	364	8	sciences	science	NOUN
ejpam-6157	364	9	,	,	PUNCT
ejpam-6157	364	10	15:243–255	15:243–255	PROPN
ejpam-6157	364	11	,	,	PUNCT
ejpam-6157	364	12	2020	2020	NUM
ejpam-6157	364	13	.	.	PUNCT
ejpam-6157	365	1	[	[	X
ejpam-6157	365	2	12	12	NUM
ejpam-6157	365	3	]	]	X
ejpam-6157	365	4	s	s	PART
ejpam-6157	365	5	baghdad	baghdad	PROPN
ejpam-6157	365	6	.	.	PUNCT
ejpam-6157	366	1	existence	existence	NOUN
ejpam-6157	366	2	and	and	CCONJ
ejpam-6157	366	3	stability	stability	NOUN
ejpam-6157	366	4	of	of	ADP
ejpam-6157	366	5	solutions	solution	NOUN
ejpam-6157	366	6	for	for	ADP
ejpam-6157	366	7	a	a	DET
ejpam-6157	366	8	system	system	NOUN
ejpam-6157	366	9	of	of	ADP
ejpam-6157	366	10	quadratic	quadratic	ADJ
ejpam-6157	366	11	integral	integral	ADJ
ejpam-6157	366	12	equations	equation	NOUN
ejpam-6157	366	13	in	in	ADP
ejpam-6157	366	14	banach	banach	NOUN
ejpam-6157	366	15	algebras	algebra	NOUN
ejpam-6157	366	16	.	.	PUNCT
ejpam-6157	367	1	ann	ann	PROPN
ejpam-6157	367	2	.	.	PROPN
ejpam-6157	367	3	univ	univ	PROPN
ejpam-6157	367	4	.	.	PUNCT
ejpam-6157	368	1	paedagog	paedagog	PROPN
ejpam-6157	368	2	.	.	PUNCT
ejpam-6157	369	1	crac	crac	PROPN
ejpam-6157	369	2	.	.	PROPN
ejpam-6157	369	3	stud	stud	PROPN
ejpam-6157	369	4	.	.	PUNCT
ejpam-6157	370	1	math	math	NOUN
ejpam-6157	370	2	.	.	PUNCT
ejpam-6157	370	3	,	,	PUNCT
ejpam-6157	371	1	19:203–218	19:203–218	NUM
ejpam-6157	371	2	,	,	PUNCT
ejpam-6157	371	3	2020	2020	NUM
ejpam-6157	371	4	.	.	PUNCT
ejpam-6157	372	1	[	[	X
ejpam-6157	372	2	13	13	NUM
ejpam-6157	372	3	]	]	SYM
ejpam-6157	372	4	h	h	NOUN
ejpam-6157	372	5	a	a	DET
ejpam-6157	372	6	hammad	hammad	PROPN
ejpam-6157	372	7	;	;	PUNCT
ejpam-6157	372	8	h	h	NOUN
ejpam-6157	372	9	aydi	aydi	ADJ
ejpam-6157	372	10	;	;	PUNCT
ejpam-6157	372	11	and	and	CCONJ
ejpam-6157	372	12	c	c	PROPN
ejpam-6157	372	13	park	park	NOUN
ejpam-6157	372	14	.	.	PUNCT
ejpam-6157	373	1	fixed	fix	VERB
ejpam-6157	373	2	point	point	NOUN
ejpam-6157	373	3	approach	approach	NOUN
ejpam-6157	373	4	for	for	ADP
ejpam-6157	373	5	solving	solve	VERB
ejpam-6157	373	6	a	a	DET
ejpam-6157	373	7	system	system	NOUN
ejpam-6157	373	8	of	of	ADP
ejpam-6157	373	9	volterra	volterra	PROPN
ejpam-6157	373	10	integral	integral	ADJ
ejpam-6157	373	11	equations	equation	NOUN
ejpam-6157	373	12	and	and	CCONJ
ejpam-6157	373	13	lebesgue	lebesgue	VERB
ejpam-6157	373	14	integral	integral	ADJ
ejpam-6157	373	15	concept	concept	NOUN
ejpam-6157	373	16	in	in	ADP
ejpam-6157	373	17	fcm	fcm	PROPN
ejpam-6157	373	18	-spaces	-space	NOUN
ejpam-6157	373	19	.	.	PUNCT
ejpam-6157	374	1	aims	aim	VERB
ejpam-6157	374	2	mathematics	mathematic	NOUN
ejpam-6157	374	3	,	,	PUNCT
ejpam-6157	374	4	7:9003–9022	7:9003–9022	NOUN
ejpam-6157	374	5	,	,	PUNCT
ejpam-6157	374	6	2022	2022	NUM
ejpam-6157	374	7	.	.	PUNCT
ejpam-6157	375	1	[	[	X
ejpam-6157	375	2	14	14	NUM
ejpam-6157	375	3	]	]	PUNCT
ejpam-6157	375	4	a	a	DET
ejpam-6157	375	5	el	el	PROPN
ejpam-6157	375	6	-	-	PUNCT
ejpam-6157	375	7	sayed	say	VERB
ejpam-6157	375	8	and	and	CCONJ
ejpam-6157	375	9	s	s	PROPN
ejpam-6157	375	10	abd	abd	PROPN
ejpam-6157	375	11	el	el	PROPN
ejpam-6157	375	12	-	-	PROPN
ejpam-6157	375	13	salam	salam	PROPN
ejpam-6157	375	14	.	.	PUNCT
ejpam-6157	375	15	coupled	couple	VERB
ejpam-6157	375	16	system	system	NOUN
ejpam-6157	375	17	of	of	ADP
ejpam-6157	375	18	a	a	DET
ejpam-6157	375	19	fractional	fractional	ADJ
ejpam-6157	375	20	order	order	NOUN
ejpam-6157	375	21	differential	differential	ADJ
ejpam-6157	375	22	equations	equation	NOUN
ejpam-6157	375	23	with	with	ADP
ejpam-6157	375	24	weighted	weight	VERB
ejpam-6157	375	25	initial	initial	ADJ
ejpam-6157	375	26	conditions	condition	NOUN
ejpam-6157	375	27	.	.	PUNCT
ejpam-6157	376	1	open	open	ADJ
ejpam-6157	376	2	math	math	NOUN
ejpam-6157	376	3	.	.	PUNCT
ejpam-6157	376	4	,	,	PUNCT
ejpam-6157	376	5	17:1737–1749	17:1737–1749	NUM
ejpam-6157	376	6	,	,	PUNCT
ejpam-6157	376	7	2019	2019	NUM
ejpam-6157	376	8	.	.	PUNCT
ejpam-6157	377	1	[	[	X
ejpam-6157	377	2	15	15	NUM
ejpam-6157	377	3	]	]	X
ejpam-6157	377	4	m	m	VERB
ejpam-6157	377	5	cichoń	cichoń	NOUN
ejpam-6157	377	6	and	and	CCONJ
ejpam-6157	377	7	m	m	PROPN
ejpam-6157	377	8	metwali	metwali	ADJ
ejpam-6157	377	9	.	.	PUNCT
ejpam-6157	378	1	on	on	ADP
ejpam-6157	378	2	a	a	DET
ejpam-6157	378	3	fixed	fix	VERB
ejpam-6157	378	4	point	point	NOUN
ejpam-6157	378	5	theorem	theorem	NOUN
ejpam-6157	378	6	for	for	ADP
ejpam-6157	378	7	the	the	DET
ejpam-6157	378	8	product	product	NOUN
ejpam-6157	378	9	of	of	ADP
ejpam-6157	378	10	operators	operator	NOUN
ejpam-6157	378	11	.	.	PUNCT
ejpam-6157	379	1	j.	j.	PROPN
ejpam-6157	379	2	fixed	fix	VERB
ejpam-6157	379	3	point	point	PROPN
ejpam-6157	379	4	theory	theory	NOUN
ejpam-6157	379	5	appl	appl	PROPN
ejpam-6157	379	6	.	.	PROPN
ejpam-6157	379	7	,	,	PUNCT
ejpam-6157	380	1	18:753–770	18:753–770	NUM
ejpam-6157	380	2	,	,	PUNCT
ejpam-6157	380	3	2016	2016	NUM
ejpam-6157	380	4	.	.	PUNCT
ejpam-6157	381	1	[	[	X
ejpam-6157	381	2	16	16	NUM
ejpam-6157	381	3	]	]	X
ejpam-6157	381	4	j	j	PROPN
ejpam-6157	381	5	berger	berger	PROPN
ejpam-6157	381	6	and	and	CCONJ
ejpam-6157	381	7	j	j	PROPN
ejpam-6157	381	8	robert	robert	PROPN
ejpam-6157	381	9	.	.	PROPN
ejpam-6157	381	10	strongly	strongly	ADV
ejpam-6157	381	11	nonlinear	nonlinear	ADJ
ejpam-6157	381	12	equations	equation	NOUN
ejpam-6157	381	13	of	of	ADP
ejpam-6157	381	14	hammerstein	hammerstein	PROPN
ejpam-6157	381	15	type	type	PROPN
ejpam-6157	381	16	.	.	PUNCT
ejpam-6157	382	1	j.	j.	PROPN
ejpam-6157	382	2	lond	lond	PROPN
ejpam-6157	382	3	.	.	PUNCT
ejpam-6157	383	1	math	math	PROPN
ejpam-6157	383	2	.	.	PUNCT
ejpam-6157	384	1	soc	soc	PROPN
ejpam-6157	384	2	.	.	PUNCT
ejpam-6157	384	3	,	,	PUNCT
ejpam-6157	384	4	15:277–287	15:277–287	PROPN
ejpam-6157	384	5	,	,	PUNCT
ejpam-6157	384	6	1977	1977	NUM
ejpam-6157	384	7	.	.	PUNCT
ejpam-6157	385	1	[	[	X
ejpam-6157	385	2	17	17	NUM
ejpam-6157	385	3	]	]	X
ejpam-6157	385	4	m	m	VERB
ejpam-6157	385	5	a	a	DET
ejpam-6157	385	6	krasnosel’skii	krasnosel’skii	PROPN
ejpam-6157	385	7	and	and	CCONJ
ejpam-6157	385	8	yu	yu	PROPN
ejpam-6157	385	9	rutitskii	rutitskii	PROPN
ejpam-6157	385	10	.	.	PUNCT
ejpam-6157	386	1	convex	convex	NOUN
ejpam-6157	386	2	functions	function	NOUN
ejpam-6157	386	3	and	and	CCONJ
ejpam-6157	386	4	orlicz	orlicz	ADJ
ejpam-6157	386	5	spaces	space	NOUN
ejpam-6157	386	6	.	.	PUNCT
ejpam-6157	387	1	gröningen	gröningen	NOUN
ejpam-6157	387	2	,	,	PUNCT
ejpam-6157	387	3	noordhoff	noordhoff	NOUN
ejpam-6157	387	4	,	,	PUNCT
ejpam-6157	387	5	1961	1961	NUM
ejpam-6157	387	6	.	.	PUNCT
ejpam-6157	388	1	[	[	X
ejpam-6157	388	2	18	18	NUM
ejpam-6157	388	3	]	]	X
ejpam-6157	388	4	i	i	PROPN
ejpam-6157	388	5	-	-	PUNCT
ejpam-6157	388	6	y	y	PROPN
ejpam-6157	388	7	s	s	PROPN
ejpam-6157	388	8	cheng	cheng	PROPN
ejpam-6157	388	9	and	and	CCONJ
ejpam-6157	388	10	j	j	PROPN
ejpam-6157	388	11	j	j	PROPN
ejpam-6157	388	12	kozak	kozak	PROPN
ejpam-6157	388	13	.	.	PUNCT
ejpam-6157	389	1	application	application	NOUN
ejpam-6157	389	2	of	of	ADP
ejpam-6157	389	3	the	the	DET
ejpam-6157	389	4	theory	theory	NOUN
ejpam-6157	389	5	of	of	ADP
ejpam-6157	389	6	orlicz	orlicz	PROPN
ejpam-6157	389	7	spaces	space	NOUN
ejpam-6157	389	8	to	to	ADP
ejpam-6157	389	9	statistical	statistical	ADJ
ejpam-6157	389	10	mechanics	mechanic	NOUN
ejpam-6157	389	11	.	.	PUNCT
ejpam-6157	390	1	i.	i.	PROPN
ejpam-6157	390	2	integral	integral	ADJ
ejpam-6157	390	3	equations	equation	NOUN
ejpam-6157	390	4	.	.	PUNCT
ejpam-6157	391	1	j.	j.	PROPN
ejpam-6157	391	2	math	math	PROPN
ejpam-6157	391	3	.	.	PUNCT
ejpam-6157	392	1	phys	phy	NOUN
ejpam-6157	392	2	.	.	PUNCT
ejpam-6157	392	3	,	,	PUNCT
ejpam-6157	392	4	13:51–58	13:51–58	PROPN
ejpam-6157	392	5	,	,	PUNCT
ejpam-6157	392	6	1972	1972	NUM
ejpam-6157	392	7	.	.	PUNCT
ejpam-6157	393	1	[	[	X
ejpam-6157	393	2	19	19	NUM
ejpam-6157	393	3	]	]	X
ejpam-6157	393	4	m	m	VERB
ejpam-6157	393	5	cichoń	cichoń	NOUN
ejpam-6157	393	6	and	and	CCONJ
ejpam-6157	393	7	m	m	PROPN
ejpam-6157	393	8	metwali	metwali	ADJ
ejpam-6157	393	9	.	.	PUNCT
ejpam-6157	394	1	on	on	ADP
ejpam-6157	394	2	quadratic	quadratic	ADJ
ejpam-6157	394	3	integral	integral	ADJ
ejpam-6157	394	4	equations	equation	NOUN
ejpam-6157	394	5	in	in	ADP
ejpam-6157	394	6	orlicz	orlicz	ADJ
ejpam-6157	394	7	spaces	space	NOUN
ejpam-6157	394	8	.	.	PUNCT
ejpam-6157	395	1	j.	j.	PROPN
ejpam-6157	395	2	math	math	PROPN
ejpam-6157	395	3	.	.	PUNCT
ejpam-6157	396	1	anal	anal	PROPN
ejpam-6157	396	2	.	.	PUNCT
ejpam-6157	397	1	appl	appl	PROPN
ejpam-6157	397	2	.	.	PROPN
ejpam-6157	397	3	,	,	PUNCT
ejpam-6157	397	4	387:419–432	387:419–432	NUM
ejpam-6157	397	5	,	,	PUNCT
ejpam-6157	397	6	2012	2012	NUM
ejpam-6157	397	7	.	.	PUNCT
ejpam-6157	398	1	[	[	X
ejpam-6157	398	2	20	20	NUM
ejpam-6157	398	3	]	]	PUNCT
ejpam-6157	398	4	m	m	VERB
ejpam-6157	398	5	cichoń	cichoń	NOUN
ejpam-6157	398	6	and	and	CCONJ
ejpam-6157	398	7	m	m	PROPN
ejpam-6157	398	8	metwali	metwali	ADJ
ejpam-6157	398	9	.	.	PUNCT
ejpam-6157	399	1	on	on	ADP
ejpam-6157	399	2	solutions	solution	NOUN
ejpam-6157	399	3	of	of	ADP
ejpam-6157	399	4	quadratic	quadratic	ADJ
ejpam-6157	399	5	integral	integral	ADJ
ejpam-6157	399	6	equations	equation	NOUN
ejpam-6157	399	7	in	in	ADP
ejpam-6157	399	8	orlicz	orlicz	ADJ
ejpam-6157	399	9	spaces	space	NOUN
ejpam-6157	399	10	.	.	PUNCT
ejpam-6157	400	1	mediterr	mediterr	PROPN
ejpam-6157	400	2	.	.	PUNCT
ejpam-6157	401	1	j.	j.	PROPN
ejpam-6157	401	2	math	math	PROPN
ejpam-6157	401	3	.	.	PUNCT
ejpam-6157	401	4	,	,	PUNCT
ejpam-6157	401	5	12:901–920	12:901–920	NUM
ejpam-6157	401	6	,	,	PUNCT
ejpam-6157	401	7	2015	2015	NUM
ejpam-6157	401	8	.	.	PUNCT
ejpam-6157	402	1	[	[	X
ejpam-6157	402	2	21	21	NUM
ejpam-6157	402	3	]	]	X
ejpam-6157	402	4	m	m	VERB
ejpam-6157	402	5	metwali	metwali	ADJ
ejpam-6157	402	6	.	.	PUNCT
ejpam-6157	403	1	on	on	ADP
ejpam-6157	403	2	some	some	DET
ejpam-6157	403	3	properties	property	NOUN
ejpam-6157	403	4	of	of	ADP
ejpam-6157	403	5	riemann	riemann	PROPN
ejpam-6157	403	6	-	-	PUNCT
ejpam-6157	403	7	liouville	liouville	VERB
ejpam-6157	403	8	fractional	fractional	ADJ
ejpam-6157	403	9	operator	operator	NOUN
ejpam-6157	403	10	in	in	ADP
ejpam-6157	403	11	orlicz	orlicz	ADJ
ejpam-6157	403	12	spaces	space	NOUN
ejpam-6157	403	13	and	and	CCONJ
ejpam-6157	403	14	applications	application	NOUN
ejpam-6157	403	15	to	to	ADP
ejpam-6157	403	16	quadratic	quadratic	ADJ
ejpam-6157	403	17	integral	integral	ADJ
ejpam-6157	403	18	equations	equation	NOUN
ejpam-6157	403	19	.	.	PUNCT
ejpam-6157	404	1	filomat	filomat	PROPN
ejpam-6157	404	2	,	,	PUNCT
ejpam-6157	404	3	36(17):6009–6020	36(17):6009–6020	NUM
ejpam-6157	404	4	,	,	PUNCT
ejpam-6157	404	5	2022	2022	NUM
ejpam-6157	404	6	.	.	PUNCT
ejpam-6157	405	1	[	[	X
ejpam-6157	405	2	22	22	NUM
ejpam-6157	405	3	]	]	X
ejpam-6157	405	4	m	m	VERB
ejpam-6157	405	5	metwali	metwali	ADJ
ejpam-6157	405	6	and	and	CCONJ
ejpam-6157	405	7	s	s	VERB
ejpam-6157	405	8	a	a	DET
ejpam-6157	405	9	m	m	NOUN
ejpam-6157	405	10	alsallami	alsallami	NOUN
ejpam-6157	405	11	.	.	PUNCT
ejpam-6157	406	1	on	on	ADP
ejpam-6157	406	2	erdélyi	erdélyi	PROPN
ejpam-6157	406	3	–	–	PUNCT
ejpam-6157	406	4	kober	kober	NOUN
ejpam-6157	406	5	fractional	fractional	ADJ
ejpam-6157	406	6	operator	operator	NOUN
ejpam-6157	406	7	and	and	CCONJ
ejpam-6157	406	8	quadratic	quadratic	ADJ
ejpam-6157	406	9	integral	integral	ADJ
ejpam-6157	406	10	equations	equation	NOUN
ejpam-6157	406	11	in	in	ADP
ejpam-6157	406	12	orlicz	orlicz	ADJ
ejpam-6157	406	13	spaces	space	NOUN
ejpam-6157	406	14	.	.	PUNCT
ejpam-6157	407	1	mathematics	mathematic	NOUN
ejpam-6157	407	2	,	,	PUNCT
ejpam-6157	407	3	11(3901	11(3901	NUM
ejpam-6157	407	4	)	)	PUNCT
ejpam-6157	407	5	,	,	PUNCT
ejpam-6157	407	6	2023	2023	NUM
ejpam-6157	407	7	.	.	PUNCT
ejpam-6157	408	1	[	[	X
ejpam-6157	408	2	23	23	NUM
ejpam-6157	408	3	]	]	PUNCT
ejpam-6157	408	4	a	a	DET
ejpam-6157	408	5	samadi	samadi	NOUN
ejpam-6157	408	6	.	.	PUNCT
ejpam-6157	409	1	applications	application	NOUN
ejpam-6157	409	2	of	of	ADP
ejpam-6157	409	3	measure	measure	NOUN
ejpam-6157	409	4	of	of	ADP
ejpam-6157	409	5	noncompactness	noncompactness	ADV
ejpam-6157	409	6	to	to	ADP
ejpam-6157	409	7	coupled	couple	VERB
ejpam-6157	409	8	fixed	fix	VERB
ejpam-6157	409	9	points	point	NOUN
ejpam-6157	409	10	and	and	CCONJ
ejpam-6157	409	11	systems	system	NOUN
ejpam-6157	409	12	of	of	ADP
ejpam-6157	409	13	integral	integral	ADJ
ejpam-6157	409	14	equations	equation	NOUN
ejpam-6157	409	15	.	.	PUNCT
ejpam-6157	410	1	miskolc	miskolc	ADJ
ejpam-6157	410	2	mathematical	mathematical	ADJ
ejpam-6157	410	3	notes	note	NOUN
ejpam-6157	410	4	,	,	PUNCT
ejpam-6157	410	5	19(537):537–5530	19(537):537–5530	NUM
ejpam-6157	410	6	,	,	PUNCT
ejpam-6157	410	7	2018	2018	NUM
ejpam-6157	410	8	.	.	PUNCT
ejpam-6157	411	1	[	[	X
ejpam-6157	411	2	24	24	NUM
ejpam-6157	411	3	]	]	X
ejpam-6157	411	4	k	k	PROPN
ejpam-6157	411	5	kavitha	kavitha	PROPN
ejpam-6157	411	6	;	;	PUNCT
ejpam-6157	411	7	v	v	PROPN
ejpam-6157	411	8	vijayakumar	vijayakumar	NOUN
ejpam-6157	411	9	;	;	PUNCT
ejpam-6157	411	10	r	r	NOUN
ejpam-6157	411	11	udhayakumar	udhayakumar	NOUN
ejpam-6157	411	12	;	;	PUNCT
ejpam-6157	411	13	and	and	CCONJ
ejpam-6157	411	14	c	c	NOUN
ejpam-6157	411	15	ravichandran	ravichandran	NOUN
ejpam-6157	411	16	.	.	PUNCT
ejpam-6157	412	1	results	result	NOUN
ejpam-6157	412	2	on	on	ADP
ejpam-6157	412	3	controllability	controllability	NOUN
ejpam-6157	412	4	of	of	ADP
ejpam-6157	412	5	hilfer	hilfer	NOUN
ejpam-6157	412	6	fractional	fractional	ADJ
ejpam-6157	412	7	differential	differential	ADJ
ejpam-6157	412	8	equations	equation	NOUN
ejpam-6157	412	9	with	with	ADP
ejpam-6157	412	10	infinite	infinite	ADJ
ejpam-6157	412	11	delay	delay	NOUN
ejpam-6157	412	12	via	via	ADP
ejpam-6157	412	13	measures	measure	NOUN
ejpam-6157	412	14	of	of	ADP
ejpam-6157	412	15	noncompactness	noncompactness	NOUN
ejpam-6157	412	16	.	.	PUNCT
ejpam-6157	413	1	asian	asian	PROPN
ejpam-6157	413	2	j.	j.	PROPN
ejpam-6157	413	3	control	control	PROPN
ejpam-6157	413	4	.	.	PUNCT
ejpam-6157	413	5	,	,	PUNCT
ejpam-6157	413	6	2021:1–10	2021:1–10	NOUN
ejpam-6157	413	7	,	,	PUNCT
ejpam-6157	413	8	2021	2021	NUM
ejpam-6157	413	9	.	.	PUNCT
ejpam-6157	414	1	[	[	X
ejpam-6157	414	2	25	25	NUM
ejpam-6157	414	3	]	]	X
ejpam-6157	414	4	s	s	VERB
ejpam-6157	414	5	singh	singh	NOUN
ejpam-6157	414	6	;	;	PUNCT
ejpam-6157	414	7	s	s	PROPN
ejpam-6157	414	8	kumar	kumar	PROPN
ejpam-6157	414	9	;	;	PUNCT
ejpam-6157	414	10	m	m	PROPN
ejpam-6157	414	11	metwali	metwali	ADJ
ejpam-6157	414	12	;	;	PUNCT
ejpam-6157	414	13	s	s	VERB
ejpam-6157	414	14	aldosary	aldosary	ADJ
ejpam-6157	414	15	;	;	PUNCT
ejpam-6157	414	16	and	and	CCONJ
ejpam-6157	414	17	k	k	PROPN
ejpam-6157	414	18	nisar	nisar	PROPN
ejpam-6157	414	19	.	.	PUNCT
ejpam-6157	415	1	an	an	DET
ejpam-6157	415	2	existence	existence	NOUN
ejpam-6157	415	3	theorem	theorem	VERB
ejpam-6157	415	4	for	for	ADP
ejpam-6157	415	5	nonlinear	nonlinear	ADJ
ejpam-6157	415	6	functional	functional	ADJ
ejpam-6157	415	7	volterra	volterra	PROPN
ejpam-6157	415	8	integral	integral	ADJ
ejpam-6157	415	9	equations	equation	NOUN
ejpam-6157	415	10	via	via	ADP
ejpam-6157	415	11	petryshyn	petryshyn	PROPN
ejpam-6157	415	12	’s	’s	PART
ejpam-6157	415	13	fixed	fix	VERB
ejpam-6157	415	14	point	point	NOUN
ejpam-6157	415	15	theorem	theorem	VERB
ejpam-6157	415	16	.	.	PUNCT
ejpam-6157	416	1	aims	aim	VERB
ejpam-6157	416	2	mathematics	mathematic	NOUN
ejpam-6157	416	3	,	,	PUNCT
ejpam-6157	416	4	7:5594–5604	7:5594–5604	NUM
ejpam-6157	416	5	,	,	PUNCT
ejpam-6157	416	6	2022	2022	NUM
ejpam-6157	416	7	.	.	PUNCT
ejpam-6157	417	1	[	[	X
ejpam-6157	417	2	26	26	NUM
ejpam-6157	417	3	]	]	PUNCT
ejpam-6157	417	4	a	a	DET
ejpam-6157	417	5	alsaadi	alsaadi	NOUN
ejpam-6157	417	6	and	and	CCONJ
ejpam-6157	417	7	m	m	AUX
ejpam-6157	417	8	metwali	metwali	ADJ
ejpam-6157	417	9	.	.	PUNCT
ejpam-6157	418	1	on	on	ADP
ejpam-6157	418	2	existence	existence	NOUN
ejpam-6157	418	3	theorems	theorem	NOUN
ejpam-6157	418	4	for	for	ADP
ejpam-6157	418	5	coupled	couple	VERB
ejpam-6157	418	6	systems	system	NOUN
ejpam-6157	418	7	of	of	ADP
ejpam-6157	418	8	quadratic	quadratic	ADJ
ejpam-6157	418	9	hammerstein	hammerstein	PROPN
ejpam-6157	418	10	-	-	PUNCT
ejpam-6157	418	11	urysohn	urysohn	ADJ
ejpam-6157	418	12	integral	integral	ADJ
ejpam-6157	418	13	equations	equation	NOUN
ejpam-6157	418	14	in	in	ADP
ejpam-6157	418	15	orlicz	orlicz	ADJ
ejpam-6157	418	16	spaces	space	NOUN
ejpam-6157	418	17	.	.	PUNCT
ejpam-6157	419	1	aims	aim	VERB
ejpam-6157	419	2	mathematics	mathematic	NOUN
ejpam-6157	419	3	,	,	PUNCT
ejpam-6157	419	4	7(9):16278–16295	7(9):16278–16295	PROPN
ejpam-6157	419	5	,	,	PUNCT
ejpam-6157	419	6	2022	2022	NUM
ejpam-6157	419	7	.	.	PUNCT
ejpam-6157	420	1	[	[	X
ejpam-6157	420	2	27	27	NUM
ejpam-6157	420	3	]	]	SYM
ejpam-6157	420	4	s	s	X
ejpam-6157	420	5	f	f	X
ejpam-6157	420	6	aldosary	aldosary	ADJ
ejpam-6157	420	7	and	and	CCONJ
ejpam-6157	420	8	m	m	PROPN
ejpam-6157	420	9	metwali	metwali	ADJ
ejpam-6157	420	10	.	.	PUNCT
ejpam-6157	421	1	solvability	solvability	NOUN
ejpam-6157	421	2	of	of	ADP
ejpam-6157	421	3	product	product	NOUN
ejpam-6157	421	4	of	of	ADP
ejpam-6157	421	5	n	n	CCONJ
ejpam-6157	421	6	-	-	PUNCT
ejpam-6157	421	7	quadratic	quadratic	ADJ
ejpam-6157	421	8	hadamard	hadamard	ADJ
ejpam-6157	421	9	-	-	PUNCT
ejpam-6157	421	10	type	type	NOUN
ejpam-6157	421	11	fractional	fractional	ADJ
ejpam-6157	421	12	integral	integral	ADJ
ejpam-6157	421	13	equations	equation	NOUN
ejpam-6157	421	14	in	in	ADP
ejpam-6157	421	15	orlicz	orlicz	ADJ
ejpam-6157	421	16	spaces	space	NOUN
ejpam-6157	421	17	.	.	PUNCT
ejpam-6157	422	1	aims	aim	VERB
ejpam-6157	422	2	mathematics	mathematic	NOUN
ejpam-6157	422	3	,	,	PUNCT
ejpam-6157	422	4	9(5):11039–11050	9(5):11039–11050	PROPN
ejpam-6157	422	5	,	,	PUNCT
ejpam-6157	422	6	2024	2024	NUM
ejpam-6157	422	7	.	.	PUNCT
ejpam-6157	423	1	[	[	X
ejpam-6157	423	2	28	28	NUM
ejpam-6157	423	3	]	]	X
ejpam-6157	423	4	m	m	VERB
ejpam-6157	423	5	metwali	metwali	ADJ
ejpam-6157	423	6	.	.	PUNCT
ejpam-6157	424	1	solvability	solvability	NOUN
ejpam-6157	424	2	of	of	ADP
ejpam-6157	424	3	quadratic	quadratic	ADJ
ejpam-6157	424	4	hadamard	hadamard	ADJ
ejpam-6157	424	5	-	-	PUNCT
ejpam-6157	424	6	type	type	NOUN
ejpam-6157	424	7	fractional	fractional	ADJ
ejpam-6157	424	8	integral	integral	ADJ
ejpam-6157	424	9	equations	equation	NOUN
ejpam-6157	424	10	in	in	ADP
ejpam-6157	424	11	m.	m.	PROPN
ejpam-6157	424	12	metwali	metwali	PROPN
ejpam-6157	424	13	,	,	PUNCT
ejpam-6157	424	14	s.	s.	PROPN
ejpam-6157	424	15	alsallami	alsallami	PROPN
ejpam-6157	424	16	/	/	SYM
ejpam-6157	424	17	eur	eur	PROPN
ejpam-6157	424	18	.	.	PUNCT
ejpam-6157	425	1	j.	j.	PROPN
ejpam-6157	425	2	pure	pure	PROPN
ejpam-6157	425	3	appl	appl	PROPN
ejpam-6157	425	4	.	.	PROPN
ejpam-6157	425	5	math	math	PROPN
ejpam-6157	425	6	,	,	PUNCT
ejpam-6157	425	7	18	18	NUM
ejpam-6157	425	8	(	(	PUNCT
ejpam-6157	425	9	2	2	NUM
ejpam-6157	425	10	)	)	PUNCT
ejpam-6157	425	11	(	(	PUNCT
ejpam-6157	425	12	2025	2025	NUM
ejpam-6157	425	13	)	)	PUNCT
ejpam-6157	425	14	,	,	PUNCT
ejpam-6157	425	15	6157	6157	NUM
ejpam-6157	425	16	15	15	NUM
ejpam-6157	425	17	of	of	ADP
ejpam-6157	425	18	15	15	NUM
ejpam-6157	425	19	orlicz	orlicz	ADJ
ejpam-6157	425	20	spaces	space	NOUN
ejpam-6157	425	21	.	.	PUNCT
ejpam-6157	426	1	rocky	rocky	ADJ
ejpam-6157	426	2	mountain	mountain	PROPN
ejpam-6157	426	3	j.	j.	PROPN
ejpam-6157	426	4	math	math	PROPN
ejpam-6157	426	5	.	.	PUNCT
ejpam-6157	426	6	,	,	PUNCT
ejpam-6157	426	7	53(2):531–540	53(2):531–540	PROPN
ejpam-6157	426	8	,	,	PUNCT
ejpam-6157	426	9	2023	2023	NUM
ejpam-6157	426	10	.	.	PUNCT
ejpam-6157	427	1	[	[	X
ejpam-6157	427	2	29	29	NUM
ejpam-6157	427	3	]	]	X
ejpam-6157	427	4	l	l	NOUN
ejpam-6157	427	5	maligranda	maligranda	PROPN
ejpam-6157	427	6	.	.	PUNCT
ejpam-6157	428	1	orlicz	orlicz	PROPN
ejpam-6157	428	2	spaces	space	NOUN
ejpam-6157	428	3	and	and	CCONJ
ejpam-6157	428	4	interpolation	interpolation	NOUN
ejpam-6157	428	5	.	.	PUNCT
ejpam-6157	429	1	campinas	campinas	PROPN
ejpam-6157	429	2	sp	sp	ADP
ejpam-6157	429	3	brazil	brazil	PROPN
ejpam-6157	429	4	,	,	PUNCT
ejpam-6157	429	5	campinas	campinas	PROPN
ejpam-6157	429	6	sp	sp	ADP
ejpam-6157	429	7	brazil	brazil	PROPN
ejpam-6157	429	8	:	:	PUNCT
ejpam-6157	429	9	departamento	departamento	PROPN
ejpam-6157	429	10	de	de	PROPN
ejpam-6157	429	11	matemática	matemática	PROPN
ejpam-6157	429	12	,	,	PUNCT
ejpam-6157	429	13	universidade	universidade	PROPN
ejpam-6157	429	14	estadual	estadual	PROPN
ejpam-6157	429	15	de	de	PROPN
ejpam-6157	429	16	campinas	campinas	PROPN
ejpam-6157	429	17	,	,	PUNCT
ejpam-6157	429	18	1989	1989	NUM
ejpam-6157	429	19	.	.	PUNCT
ejpam-6157	430	1	[	[	X
ejpam-6157	430	2	30	30	NUM
ejpam-6157	430	3	]	]	X
ejpam-6157	430	4	m	m	VERB
ejpam-6157	430	5	väth	väth	ADJ
ejpam-6157	430	6	.	.	PUNCT
ejpam-6157	431	1	volterra	volterra	NOUN
ejpam-6157	431	2	and	and	CCONJ
ejpam-6157	431	3	integral	integral	ADJ
ejpam-6157	431	4	equations	equation	NOUN
ejpam-6157	431	5	of	of	ADP
ejpam-6157	431	6	vector	vector	NOUN
ejpam-6157	431	7	functions	function	NOUN
ejpam-6157	431	8	.	.	PUNCT
ejpam-6157	432	1	marcel	marcel	PROPN
ejpam-6157	432	2	dekker	dekker	PROPN
ejpam-6157	432	3	,	,	PUNCT
ejpam-6157	432	4	new	new	PROPN
ejpam-6157	432	5	york	york	PROPN
ejpam-6157	432	6	,	,	PUNCT
ejpam-6157	432	7	basel	basel	PROPN
ejpam-6157	432	8	,	,	PUNCT
ejpam-6157	432	9	2000	2000	NUM
ejpam-6157	432	10	.	.	PUNCT
ejpam-6157	433	1	[	[	X
ejpam-6157	433	2	31	31	NUM
ejpam-6157	433	3	]	]	X
ejpam-6157	433	4	j	j	PROPN
ejpam-6157	433	5	banaś	banaś	PROPN
ejpam-6157	433	6	and	and	CCONJ
ejpam-6157	433	7	k	k	PROPN
ejpam-6157	433	8	goebel	goebel	NOUN
ejpam-6157	433	9	.	.	PUNCT
ejpam-6157	434	1	measures	measure	NOUN
ejpam-6157	434	2	of	of	ADP
ejpam-6157	434	3	noncompactness	noncompactness	ADJ
ejpam-6157	434	4	in	in	ADP
ejpam-6157	434	5	banach	banach	NOUN
ejpam-6157	434	6	spaces	space	NOUN
ejpam-6157	434	7	.	.	PUNCT
ejpam-6157	435	1	lect	lect	PROPN
ejpam-6157	435	2	.	.	PUNCT
ejpam-6157	436	1	notes	note	NOUN
ejpam-6157	436	2	in	in	ADP
ejpam-6157	436	3	math	math	NOUN
ejpam-6157	436	4	.	.	PUNCT
ejpam-6157	437	1	60	60	NUM
ejpam-6157	437	2	,	,	PUNCT
ejpam-6157	437	3	m.	m.	NOUN
ejpam-6157	437	4	dekker	dekker	PROPN
ejpam-6157	437	5	,	,	PUNCT
ejpam-6157	437	6	new	new	PROPN
ejpam-6157	437	7	york	york	PROPN
ejpam-6157	437	8	,	,	PUNCT
ejpam-6157	437	9	basel	basel	PROPN
ejpam-6157	437	10	,	,	PUNCT
ejpam-6157	437	11	1980	1980	NUM
ejpam-6157	437	12	.	.	PUNCT
ejpam-6157	438	1	[	[	X
ejpam-6157	438	2	32	32	NUM
ejpam-6157	438	3	]	]	PUNCT
ejpam-6157	438	4	m	m	VERB
ejpam-6157	438	5	cichoń	cichoń	NOUN
ejpam-6157	438	6	and	and	CCONJ
ejpam-6157	438	7	h	h	DET
ejpam-6157	438	8	a	a	DET
ejpam-6157	438	9	h	h	NOUN
ejpam-6157	438	10	salem	salem	NOUN
ejpam-6157	438	11	.	.	PUNCT
ejpam-6157	439	1	on	on	ADP
ejpam-6157	439	2	the	the	DET
ejpam-6157	439	3	solutions	solution	NOUN
ejpam-6157	439	4	of	of	ADP
ejpam-6157	439	5	caputo	caputo	PROPN
ejpam-6157	439	6	-	-	PUNCT
ejpam-6157	439	7	hadamard	hadamard	PROPN
ejpam-6157	439	8	pettis	pettis	NOUN
ejpam-6157	439	9	-	-	PUNCT
ejpam-6157	439	10	type	type	NOUN
ejpam-6157	439	11	fractional	fractional	ADJ
ejpam-6157	439	12	differential	differential	NOUN
ejpam-6157	439	13	equations	equation	NOUN
ejpam-6157	439	14	.	.	PUNCT
ejpam-6157	440	1	racsam	racsam	PROPN
ejpam-6157	440	2	,	,	PUNCT
ejpam-6157	440	3	2019:1–23	2019:1–23	NUM
ejpam-6157	440	4	,	,	PUNCT
ejpam-6157	440	5	2019	2019	NUM
ejpam-6157	440	6	.	.	PUNCT
ejpam-6157	441	1	[	[	X
ejpam-6157	441	2	33	33	NUM
ejpam-6157	441	3	]	]	PUNCT
ejpam-6157	441	4	a	a	DET
ejpam-6157	441	5	a	a	DET
ejpam-6157	441	6	kilbas	kilbas	NOUN
ejpam-6157	441	7	;	;	PUNCT
ejpam-6157	441	8	h	h	PROPN
ejpam-6157	441	9	m	m	PROPN
ejpam-6157	441	10	srivastava	srivastava	PROPN
ejpam-6157	441	11	;	;	PUNCT
ejpam-6157	441	12	and	and	CCONJ
ejpam-6157	441	13	j	j	PROPN
ejpam-6157	441	14	j	j	PROPN
ejpam-6157	441	15	trujillo	trujillo	PROPN
ejpam-6157	441	16	.	.	PUNCT
ejpam-6157	441	17	theory	theory	NOUN
ejpam-6157	441	18	and	and	CCONJ
ejpam-6157	441	19	applications	application	NOUN
ejpam-6157	441	20	of	of	ADP
ejpam-6157	441	21	fractional	fractional	ADJ
ejpam-6157	441	22	differential	differential	ADJ
ejpam-6157	441	23	equations	equation	NOUN
ejpam-6157	441	24	.	.	PUNCT
ejpam-6157	442	1	elsevier	elsevier	NOUN
ejpam-6157	442	2	:	:	PUNCT
ejpam-6157	443	1	amsterdam	amsterdam	PROPN
ejpam-6157	443	2	,	,	PUNCT
ejpam-6157	443	3	the	the	DET
ejpam-6157	443	4	netherlands	netherlands	PROPN
ejpam-6157	443	5	,	,	PUNCT
ejpam-6157	443	6	2006	2006	NUM
ejpam-6157	443	7	.	.	PUNCT
ejpam-6157	444	1	[	[	X
ejpam-6157	444	2	34	34	NUM
ejpam-6157	444	3	]	]	X
ejpam-6157	444	4	a	a	DET
ejpam-6157	444	5	m	m	NOUN
ejpam-6157	444	6	abdalla	abdalla	NOUN
ejpam-6157	444	7	and	and	CCONJ
ejpam-6157	444	8	h	h	DET
ejpam-6157	444	9	a	a	DET
ejpam-6157	444	10	h	h	NOUN
ejpam-6157	444	11	salem	salem	NOUN
ejpam-6157	444	12	.	.	PUNCT
ejpam-6157	445	1	on	on	ADP
ejpam-6157	445	2	the	the	DET
ejpam-6157	445	3	monotonic	monotonic	ADJ
ejpam-6157	445	4	solutions	solution	NOUN
ejpam-6157	445	5	of	of	ADP
ejpam-6157	445	6	quadratic	quadratic	ADJ
ejpam-6157	445	7	integral	integral	ADJ
ejpam-6157	445	8	equations	equation	NOUN
ejpam-6157	445	9	in	in	ADP
ejpam-6157	445	10	orlicz	orlicz	ADJ
ejpam-6157	445	11	space	space	NOUN
ejpam-6157	445	12	.	.	PUNCT
ejpam-6157	446	1	journal	journal	NOUN
ejpam-6157	446	2	of	of	ADP
ejpam-6157	446	3	advances	advance	NOUN
ejpam-6157	446	4	in	in	ADP
ejpam-6157	446	5	mathematics	mathematic	NOUN
ejpam-6157	446	6	and	and	CCONJ
ejpam-6157	446	7	computer	computer	NOUN
ejpam-6157	446	8	science	science	NOUN
ejpam-6157	446	9	.	.	PUNCT
ejpam-6157	446	10	,	,	PUNCT
ejpam-6157	446	11	30:1–11	30:1–11	PROPN
ejpam-6157	446	12	,	,	PUNCT
ejpam-6157	446	13	2019	2019	NUM
ejpam-6157	446	14	.	.	PUNCT
ejpam-6157	447	1	[	[	X
ejpam-6157	447	2	35	35	NUM
ejpam-6157	447	3	]	]	X
ejpam-6157	447	4	c	c	PROPN
ejpam-6157	447	5	t	t	PROPN
ejpam-6157	447	6	kelly	kelly	PROPN
ejpam-6157	447	7	.	.	PUNCT
ejpam-6157	448	1	approximation	approximation	NOUN
ejpam-6157	448	2	of	of	ADP
ejpam-6157	448	3	solutions	solution	NOUN
ejpam-6157	448	4	of	of	ADP
ejpam-6157	448	5	some	some	DET
ejpam-6157	448	6	quadratic	quadratic	ADJ
ejpam-6157	448	7	integral	integral	ADJ
ejpam-6157	448	8	equations	equation	NOUN
ejpam-6157	448	9	in	in	ADP
ejpam-6157	448	10	transport	transport	NOUN
ejpam-6157	448	11	theory	theory	NOUN
ejpam-6157	448	12	.	.	PUNCT
ejpam-6157	449	1	j.	j.	PROPN
ejpam-6157	449	2	integral	integral	PROPN
ejpam-6157	449	3	equ	equ	PROPN
ejpam-6157	449	4	.	.	PROPN
ejpam-6157	449	5	,	,	PUNCT
ejpam-6157	449	6	4:221–237	4:221–237	NUM
ejpam-6157	449	7	,	,	PUNCT
ejpam-6157	449	8	1982	1982	NUM
ejpam-6157	449	9	.	.	PUNCT
ejpam-6157	450	1	[	[	X
ejpam-6157	450	2	36	36	NUM
ejpam-6157	450	3	]	]	X
ejpam-6157	450	4	s	s	PART
ejpam-6157	450	5	chandrasekhar	chandrasekhar	PROPN
ejpam-6157	450	6	.	.	PUNCT
ejpam-6157	451	1	radiative	radiative	ADJ
ejpam-6157	451	2	transfer	transfer	NOUN
ejpam-6157	451	3	.	.	PUNCT
ejpam-6157	452	1	dover	dover	PROPN
ejpam-6157	452	2	publ	publ	PROPN
ejpam-6157	452	3	.	.	PUNCT
ejpam-6157	452	4	,	,	PUNCT
ejpam-6157	452	5	new	new	PROPN
ejpam-6157	452	6	york	york	PROPN
ejpam-6157	452	7	,	,	PUNCT
ejpam-6157	452	8	1960	1960	NUM
ejpam-6157	452	9	.	.	PUNCT
ejpam-6157	453	1	[	[	X
ejpam-6157	453	2	37	37	NUM
ejpam-6157	453	3	]	]	X
ejpam-6157	453	4	s	s	PART
ejpam-6157	453	5	hu	hu	PROPN
ejpam-6157	453	6	;	;	PUNCT
ejpam-6157	453	7	m	m	VERB
ejpam-6157	453	8	khavanin	khavanin	NOUN
ejpam-6157	453	9	;	;	PUNCT
ejpam-6157	453	10	and	and	CCONJ
ejpam-6157	453	11	w.	w.	PROPN
ejpam-6157	453	12	zhuang	zhuang	PROPN
ejpam-6157	453	13	.	.	PUNCT
ejpam-6157	454	1	integral	integral	ADJ
ejpam-6157	454	2	equations	equation	NOUN
ejpam-6157	454	3	arising	arise	VERB
ejpam-6157	454	4	in	in	ADP
ejpam-6157	454	5	the	the	DET
ejpam-6157	454	6	kinetic	kinetic	ADJ
ejpam-6157	454	7	theory	theory	NOUN
ejpam-6157	454	8	of	of	ADP
ejpam-6157	454	9	gases	gas	NOUN
ejpam-6157	454	10	.	.	PUNCT
ejpam-6157	455	1	appl	appl	PROPN
ejpam-6157	455	2	.	.	PUNCT
ejpam-6157	456	1	anal	anal	PROPN
ejpam-6157	456	2	.	.	PUNCT
ejpam-6157	456	3	,	,	PUNCT
ejpam-6157	457	1	34(2):261–266	34(2):261–266	NUM
ejpam-6157	457	2	,	,	PUNCT
ejpam-6157	457	3	1989	1989	NUM
ejpam-6157	457	4	.	.	PUNCT
ejpam-6157	458	1	[	[	X
ejpam-6157	458	2	38	38	NUM
ejpam-6157	458	3	]	]	X
ejpam-6157	458	4	j	j	PROPN
ejpam-6157	458	5	caballero	caballero	PROPN
ejpam-6157	458	6	;	;	PUNCT
ejpam-6157	458	7	a	a	DET
ejpam-6157	458	8	b	b	NOUN
ejpam-6157	458	9	mingarelli	mingarelli	NOUN
ejpam-6157	458	10	;	;	PUNCT
ejpam-6157	458	11	and	and	CCONJ
ejpam-6157	458	12	k.	k.	PROPN
ejpam-6157	458	13	sadarangani	sadarangani	PROPN
ejpam-6157	458	14	.	.	PUNCT
ejpam-6157	459	1	existence	existence	NOUN
ejpam-6157	459	2	of	of	ADP
ejpam-6157	459	3	solutions	solution	NOUN
ejpam-6157	459	4	of	of	ADP
ejpam-6157	459	5	an	an	DET
ejpam-6157	459	6	integral	integral	ADJ
ejpam-6157	459	7	equation	equation	NOUN
ejpam-6157	459	8	of	of	ADP
ejpam-6157	459	9	chandrasekhar	chandrasekhar	PROPN
ejpam-6157	459	10	type	type	NOUN
ejpam-6157	459	11	in	in	ADP
ejpam-6157	459	12	the	the	DET
ejpam-6157	459	13	theory	theory	NOUN
ejpam-6157	459	14	of	of	ADP
ejpam-6157	459	15	radiative	radiative	ADJ
ejpam-6157	459	16	transfer	transfer	NOUN
ejpam-6157	459	17	.	.	PUNCT
ejpam-6157	460	1	electron	electron	PROPN
ejpam-6157	460	2	.	.	PUNCT
ejpam-6157	461	1	j.	j.	PROPN
ejpam-6157	461	2	differential	differential	PROPN
ejpam-6157	461	3	equations	equations	PROPN
ejpam-6157	461	4	,	,	PUNCT
ejpam-6157	461	5	57:1–11	57:1–11	NUM
ejpam-6157	461	6	,	,	PUNCT
ejpam-6157	461	7	2006	2006	NUM
ejpam-6157	461	8	.	.	PUNCT