id	sid	tid	token	lemma	pos
ejpam-5671	1	1	european	european	PROPN
ejpam-5671	1	2	journal	journal	PROPN
ejpam-5671	1	3	of	of	ADP
ejpam-5671	1	4	pure	pure	ADJ
ejpam-5671	1	5	and	and	CCONJ
ejpam-5671	1	6	applied	applied	ADJ
ejpam-5671	1	7	mathematics	mathematic	NOUN
ejpam-5671	1	8	2025	2025	NUM
ejpam-5671	1	9	,	,	PUNCT
ejpam-5671	1	10	vol	vol	NOUN
ejpam-5671	1	11	.	.	PROPN
ejpam-5671	1	12	18	18	NUM
ejpam-5671	1	13	,	,	PUNCT
ejpam-5671	1	14	issue	issue	NOUN
ejpam-5671	1	15	1	1	NUM
ejpam-5671	1	16	,	,	PUNCT
ejpam-5671	1	17	article	article	NOUN
ejpam-5671	1	18	number	number	NOUN
ejpam-5671	1	19	5671	5671	NUM
ejpam-5671	1	20	issn	issn	PROPN
ejpam-5671	1	21	1307	1307	NUM
ejpam-5671	1	22	-	-	SYM
ejpam-5671	1	23	5543	5543	NUM
ejpam-5671	1	24	–	–	PUNCT
ejpam-5671	1	25	ejpam.com	ejpam.com	X
ejpam-5671	1	26	published	publish	VERB
ejpam-5671	1	27	by	by	ADP
ejpam-5671	1	28	new	new	PROPN
ejpam-5671	1	29	york	york	PROPN
ejpam-5671	1	30	business	business	PROPN
ejpam-5671	1	31	global	global	ADJ
ejpam-5671	1	32	existence	existence	NOUN
ejpam-5671	1	33	of	of	ADP
ejpam-5671	1	34	solutions	solution	NOUN
ejpam-5671	1	35	to	to	ADP
ejpam-5671	1	36	a	a	DET
ejpam-5671	1	37	new	new	ADJ
ejpam-5671	1	38	class	class	NOUN
ejpam-5671	1	39	of	of	ADP
ejpam-5671	1	40	fractional	fractional	ADJ
ejpam-5671	1	41	differential	differential	ADJ
ejpam-5671	1	42	equations	equation	NOUN
ejpam-5671	1	43	with	with	ADP
ejpam-5671	1	44	antiperiodic	antiperiodic	ADJ
ejpam-5671	1	45	boundary	boundary	ADJ
ejpam-5671	1	46	conditions	condition	NOUN
ejpam-5671	1	47	saleh	saleh	PROPN
ejpam-5671	1	48	fahad	fahad	PROPN
ejpam-5671	1	49	aljurbua1,∗	aljurbua1,∗	PROPN
ejpam-5671	1	50	,	,	PUNCT
ejpam-5671	1	51	hasanen	hasanen	PROPN
ejpam-5671	1	52	a.	a.	PROPN
ejpam-5671	1	53	hammad1	hammad1	PROPN
ejpam-5671	1	54	,	,	PUNCT
ejpam-5671	1	55	najat	najat	PROPN
ejpam-5671	1	56	bandar	bandar	PROPN
ejpam-5671	1	57	almutairi1	almutairi1	PROPN
ejpam-5671	1	58	1	1	NUM
ejpam-5671	1	59	department	department	NOUN
ejpam-5671	1	60	of	of	ADP
ejpam-5671	1	61	mathematics	mathematic	NOUN
ejpam-5671	1	62	,	,	PUNCT
ejpam-5671	1	63	college	college	NOUN
ejpam-5671	1	64	of	of	ADP
ejpam-5671	1	65	science	science	NOUN
ejpam-5671	1	66	,	,	PUNCT
ejpam-5671	1	67	qassim	qassim	PROPN
ejpam-5671	1	68	university	university	PROPN
ejpam-5671	1	69	,	,	PUNCT
ejpam-5671	1	70	buraydah	buraydah	NOUN
ejpam-5671	1	71	51452	51452	NUM
ejpam-5671	1	72	,	,	PUNCT
ejpam-5671	1	73	saudi	saudi	PROPN
ejpam-5671	1	74	arabia	arabia	PROPN
ejpam-5671	1	75	abstract	abstract	NOUN
ejpam-5671	1	76	.	.	PUNCT
ejpam-5671	2	1	this	this	DET
ejpam-5671	2	2	study	study	NOUN
ejpam-5671	2	3	introduces	introduce	VERB
ejpam-5671	2	4	a	a	DET
ejpam-5671	2	5	novel	novel	ADJ
ejpam-5671	2	6	class	class	NOUN
ejpam-5671	2	7	of	of	ADP
ejpam-5671	2	8	fractional	fractional	ADJ
ejpam-5671	2	9	differential	differential	ADJ
ejpam-5671	2	10	equations	equation	NOUN
ejpam-5671	2	11	characterized	characterize	VERB
ejpam-5671	2	12	by	by	ADP
ejpam-5671	2	13	antiperiodic	antiperiodic	ADJ
ejpam-5671	2	14	parametric	parametric	ADJ
ejpam-5671	2	15	boundary	boundary	ADJ
ejpam-5671	2	16	conditions	condition	NOUN
ejpam-5671	2	17	of	of	ADP
ejpam-5671	2	18	order	order	NOUN
ejpam-5671	2	19	µ	µ	X
ejpam-5671	2	20	∈	∈	NOUN
ejpam-5671	2	21	(	(	PUNCT
ejpam-5671	2	22	2	2	NUM
ejpam-5671	2	23	,	,	PUNCT
ejpam-5671	2	24	3	3	NUM
ejpam-5671	2	25	]	]	PUNCT
ejpam-5671	2	26	.	.	PUNCT
ejpam-5671	3	1	the	the	DET
ejpam-5671	3	2	parameters	parameter	NOUN
ejpam-5671	3	3	θ	θ	PROPN
ejpam-5671	3	4	and	and	CCONJ
ejpam-5671	3	5	ξ	ξ	PROPN
ejpam-5671	3	6	play	play	VERB
ejpam-5671	3	7	a	a	DET
ejpam-5671	3	8	crucial	crucial	ADJ
ejpam-5671	3	9	role	role	NOUN
ejpam-5671	3	10	in	in	ADP
ejpam-5671	3	11	shaping	shape	VERB
ejpam-5671	3	12	the	the	DET
ejpam-5671	3	13	boundary	boundary	ADJ
ejpam-5671	3	14	conditions	condition	NOUN
ejpam-5671	3	15	by	by	ADP
ejpam-5671	3	16	defining	define	VERB
ejpam-5671	3	17	specific	specific	ADJ
ejpam-5671	3	18	values	value	NOUN
ejpam-5671	3	19	and	and	CCONJ
ejpam-5671	3	20	functional	functional	ADJ
ejpam-5671	3	21	behavior	behavior	NOUN
ejpam-5671	3	22	.	.	PUNCT
ejpam-5671	4	1	by	by	ADP
ejpam-5671	4	2	employing	employ	VERB
ejpam-5671	4	3	fixed	fix	VERB
ejpam-5671	4	4	point	point	NOUN
ejpam-5671	4	5	theorems	theorem	NOUN
ejpam-5671	4	6	,	,	PUNCT
ejpam-5671	4	7	we	we	PRON
ejpam-5671	4	8	establish	establish	VERB
ejpam-5671	4	9	existence	existence	NOUN
ejpam-5671	4	10	results	result	NOUN
ejpam-5671	4	11	for	for	ADP
ejpam-5671	4	12	a	a	DET
ejpam-5671	4	13	fractional	fractional	ADJ
ejpam-5671	4	14	differential	differential	NOUN
ejpam-5671	4	15	equation	equation	NOUN
ejpam-5671	4	16	equipped	equip	VERB
ejpam-5671	4	17	with	with	ADP
ejpam-5671	4	18	nonlocal	nonlocal	ADJ
ejpam-5671	4	19	antiperiodic	antiperiodic	ADJ
ejpam-5671	4	20	boundary	boundary	ADJ
ejpam-5671	4	21	conditions	condition	NOUN
ejpam-5671	4	22	involving	involve	VERB
ejpam-5671	4	23	a	a	DET
ejpam-5671	4	24	caputo	caputo	PROPN
ejpam-5671	4	25	fractional	fractional	PROPN
ejpam-5671	4	26	derivative	derivative	NOUN
ejpam-5671	4	27	at	at	ADP
ejpam-5671	4	28	one	one	NUM
ejpam-5671	4	29	of	of	ADP
ejpam-5671	4	30	the	the	DET
ejpam-5671	4	31	boundaries	boundary	NOUN
ejpam-5671	4	32	.	.	PUNCT
ejpam-5671	5	1	our	our	PRON
ejpam-5671	5	2	investigation	investigation	NOUN
ejpam-5671	5	3	centers	center	VERB
ejpam-5671	5	4	on	on	ADP
ejpam-5671	5	5	a	a	DET
ejpam-5671	5	6	nonlocal	nonlocal	ADJ
ejpam-5671	5	7	point	point	NOUN
ejpam-5671	5	8	0	0	NUM
ejpam-5671	5	9	≤	≤	NUM
ejpam-5671	6	1	θ	θ	PROPN
ejpam-5671	6	2	<	<	X
ejpam-5671	6	3	b	b	X
ejpam-5671	6	4	,	,	PUNCT
ejpam-5671	6	5	in	in	ADP
ejpam-5671	6	6	conjunction	conjunction	NOUN
ejpam-5671	6	7	with	with	ADP
ejpam-5671	6	8	a	a	DET
ejpam-5671	6	9	fixed	fix	VERB
ejpam-5671	6	10	endpoint	endpoint	NOUN
ejpam-5671	6	11	at	at	ADP
ejpam-5671	6	12	the	the	DET
ejpam-5671	6	13	interval	interval	NOUN
ejpam-5671	6	14	’s	’s	PART
ejpam-5671	6	15	extremity	extremity	NOUN
ejpam-5671	6	16	(	(	PUNCT
ejpam-5671	6	17	0	0	NUM
ejpam-5671	6	18	,	,	PUNCT
ejpam-5671	6	19	b	b	NOUN
ejpam-5671	6	20	]	]	X
ejpam-5671	6	21	.	.	PUNCT
ejpam-5671	7	1	this	this	DET
ejpam-5671	7	2	approach	approach	NOUN
ejpam-5671	7	3	enables	enable	VERB
ejpam-5671	7	4	us	we	PRON
ejpam-5671	7	5	to	to	PART
ejpam-5671	7	6	extend	extend	VERB
ejpam-5671	7	7	the	the	DET
ejpam-5671	7	8	interval	interval	NOUN
ejpam-5671	7	9	of	of	ADP
ejpam-5671	7	10	interest	interest	NOUN
ejpam-5671	7	11	to	to	ADP
ejpam-5671	7	12	(	(	PUNCT
ejpam-5671	7	13	−∞	−∞	NOUN
ejpam-5671	7	14	,	,	PUNCT
ejpam-5671	7	15	b	b	NOUN
ejpam-5671	7	16	]	]	X
ejpam-5671	7	17	.	.	PUNCT
ejpam-5671	8	1	the	the	DET
ejpam-5671	8	2	findings	finding	NOUN
ejpam-5671	8	3	presented	present	VERB
ejpam-5671	8	4	in	in	ADP
ejpam-5671	8	5	this	this	DET
ejpam-5671	8	6	study	study	NOUN
ejpam-5671	8	7	serve	serve	VERB
ejpam-5671	8	8	to	to	PART
ejpam-5671	8	9	expand	expand	VERB
ejpam-5671	8	10	and	and	CCONJ
ejpam-5671	8	11	generalize	generalize	VERB
ejpam-5671	8	12	the	the	DET
ejpam-5671	8	13	existing	exist	VERB
ejpam-5671	8	14	body	body	NOUN
ejpam-5671	8	15	of	of	ADP
ejpam-5671	8	16	knowledge	knowledge	NOUN
ejpam-5671	8	17	pertaining	pertain	VERB
ejpam-5671	8	18	to	to	ADP
ejpam-5671	8	19	nonlocal	nonlocal	ADJ
ejpam-5671	8	20	and	and	CCONJ
ejpam-5671	8	21	classical	classical	ADJ
ejpam-5671	8	22	fractional	fractional	ADJ
ejpam-5671	8	23	differential	differential	ADJ
ejpam-5671	8	24	equations	equation	NOUN
ejpam-5671	8	25	.	.	PUNCT
ejpam-5671	9	1	2020	2020	NUM
ejpam-5671	9	2	mathematics	mathematic	NOUN
ejpam-5671	9	3	subject	subject	NOUN
ejpam-5671	9	4	classifications	classification	NOUN
ejpam-5671	9	5	:	:	PUNCT
ejpam-5671	9	6	47h10	47h10	NUM
ejpam-5671	9	7	,	,	PUNCT
ejpam-5671	9	8	47h09	47h09	NUM
ejpam-5671	9	9	,	,	PUNCT
ejpam-5671	9	10	93c27	93c27	NUM
ejpam-5671	9	11	,	,	PUNCT
ejpam-5671	9	12	47a06	47a06	NUM
ejpam-5671	9	13	,	,	PUNCT
ejpam-5671	9	14	34a08	34a08	NUM
ejpam-5671	9	15	,	,	PUNCT
ejpam-5671	9	16	34k35	34k35	NUM
ejpam-5671	9	17	,	,	PUNCT
ejpam-5671	9	18	93b06	93b06	NUM
ejpam-5671	9	19	key	key	ADJ
ejpam-5671	9	20	words	word	NOUN
ejpam-5671	9	21	and	and	CCONJ
ejpam-5671	9	22	phrases	phrase	NOUN
ejpam-5671	9	23	:	:	PUNCT
ejpam-5671	9	24	fractional	fractional	ADJ
ejpam-5671	9	25	derivatives	derivative	NOUN
ejpam-5671	9	26	,	,	PUNCT
ejpam-5671	9	27	differential	differential	ADJ
ejpam-5671	9	28	equations	equation	NOUN
ejpam-5671	9	29	,	,	PUNCT
ejpam-5671	9	30	existence	existence	NOUN
ejpam-5671	9	31	of	of	ADP
ejpam-5671	9	32	solutions	solution	NOUN
ejpam-5671	9	33	,	,	PUNCT
ejpam-5671	9	34	fixed	fix	VERB
ejpam-5671	9	35	-	-	PUNCT
ejpam-5671	9	36	point	point	NOUN
ejpam-5671	9	37	techniques	technique	NOUN
ejpam-5671	9	38	,	,	PUNCT
ejpam-5671	9	39	evaluation	evaluation	NOUN
ejpam-5671	9	40	metrics	metric	NOUN
ejpam-5671	9	41	1	1	NUM
ejpam-5671	9	42	.	.	PUNCT
ejpam-5671	10	1	introduction	introduction	NOUN
ejpam-5671	10	2	in	in	ADP
ejpam-5671	10	3	this	this	DET
ejpam-5671	10	4	paper	paper	NOUN
ejpam-5671	10	5	,	,	PUNCT
ejpam-5671	10	6	we	we	PRON
ejpam-5671	10	7	find	find	VERB
ejpam-5671	10	8	the	the	DET
ejpam-5671	10	9	existence	existence	NOUN
ejpam-5671	10	10	and	and	CCONJ
ejpam-5671	10	11	uniqueness	uniqueness	NOUN
ejpam-5671	10	12	of	of	ADP
ejpam-5671	10	13	a	a	DET
ejpam-5671	10	14	solution	solution	NOUN
ejpam-5671	10	15	to	to	ADP
ejpam-5671	10	16	the	the	DET
ejpam-5671	10	17	following	follow	VERB
ejpam-5671	10	18	fractional	fractional	ADJ
ejpam-5671	10	19	problem	problem	NOUN
ejpam-5671	10	20	:	:	PUNCT
ejpam-5671	10	21	{	{	PUNCT
ejpam-5671	10	22	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	10	23	)	)	PUNCT
ejpam-5671	10	24	=	=	SYM
ejpam-5671	10	25	ω(ρ	ω(ρ	NOUN
ejpam-5671	10	26	,	,	PUNCT
ejpam-5671	10	27	ω(ρ	ω(ρ	NOUN
ejpam-5671	10	28	)	)	PUNCT
ejpam-5671	10	29	)	)	PUNCT
ejpam-5671	10	30	,	,	PUNCT
ejpam-5671	10	31	ρ	ρ	PROPN
ejpam-5671	10	32	∈	∈	PROPN
ejpam-5671	11	1	[	[	X
ejpam-5671	11	2	0	0	NUM
ejpam-5671	11	3	,	,	PUNCT
ejpam-5671	11	4	b	b	NOUN
ejpam-5671	11	5	]	]	X
ejpam-5671	11	6	,	,	PUNCT
ejpam-5671	11	7	2	2	NUM
ejpam-5671	11	8	<	<	X
ejpam-5671	11	9	µ	µ	X
ejpam-5671	11	10	≤	≤	NUM
ejpam-5671	11	11	3	3	NUM
ejpam-5671	11	12	,	,	PUNCT
ejpam-5671	11	13	θ	θ	PROPN
ejpam-5671	11	14	∈	∈	PROPN
ejpam-5671	12	1	[	[	X
ejpam-5671	12	2	0	0	NUM
ejpam-5671	12	3	,	,	PUNCT
ejpam-5671	12	4	b	b	NOUN
ejpam-5671	12	5	)	)	PUNCT
ejpam-5671	12	6	,	,	PUNCT
ejpam-5671	12	7	ω(θ	ω(θ	NUM
ejpam-5671	12	8	)	)	PUNCT
ejpam-5671	12	9	=	=	SYM
ejpam-5671	12	10	−ω(b	−ω(b	X
ejpam-5671	12	11	)	)	PUNCT
ejpam-5671	12	12	,	,	PUNCT
ejpam-5671	13	1	ω	ω	NUM
ejpam-5671	13	2	′	′	NUM
ejpam-5671	13	3	(	(	PUNCT
ejpam-5671	13	4	θ	θ	NOUN
ejpam-5671	13	5	)	)	PUNCT
ejpam-5671	13	6	=	=	SYM
ejpam-5671	13	7	−ω′	−ω′	NOUN
ejpam-5671	13	8	(	(	PUNCT
ejpam-5671	13	9	b	b	NOUN
ejpam-5671	13	10	)	)	PUNCT
ejpam-5671	13	11	,	,	PUNCT
ejpam-5671	13	12	cdξ+1ω(θ	cdξ+1ω(θ	NOUN
ejpam-5671	13	13	)	)	PUNCT
ejpam-5671	13	14	=	=	SYM
ejpam-5671	13	15	−cdξ+1ω(b	−cdξ+1ω(b	PROPN
ejpam-5671	13	16	)	)	PUNCT
ejpam-5671	13	17	,	,	PUNCT
ejpam-5671	13	18	0	0	PUNCT
ejpam-5671	13	19	<	<	X
ejpam-5671	13	20	ξ	ξ	X
ejpam-5671	13	21	<	<	X
ejpam-5671	13	22	1	1	NUM
ejpam-5671	13	23	.	.	NUM
ejpam-5671	13	24	,	,	PUNCT
ejpam-5671	13	25	(	(	PUNCT
ejpam-5671	13	26	1	1	X
ejpam-5671	13	27	)	)	PUNCT
ejpam-5671	13	28	where	where	SCONJ
ejpam-5671	13	29	cdµ	cdµ	PROPN
ejpam-5671	13	30	denotes	denote	VERB
ejpam-5671	13	31	the	the	DET
ejpam-5671	13	32	caputo	caputo	PROPN
ejpam-5671	13	33	fractional	fractional	PROPN
ejpam-5671	13	34	derivative	derivative	NOUN
ejpam-5671	13	35	of	of	ADP
ejpam-5671	13	36	order	order	NOUN
ejpam-5671	13	37	µ	µ	PRON
ejpam-5671	13	38	,	,	PUNCT
ejpam-5671	13	39	ω	ω	NOUN
ejpam-5671	13	40	:	:	PUNCT
ejpam-5671	13	41	[	[	X
ejpam-5671	13	42	0	0	NUM
ejpam-5671	13	43	,	,	PUNCT
ejpam-5671	13	44	b	b	NOUN
ejpam-5671	13	45	]	]	X
ejpam-5671	13	46	×	×	NOUN
ejpam-5671	13	47	r	r	NOUN
ejpam-5671	13	48	−→	−→	NOUN
ejpam-5671	13	49	r	r	NOUN
ejpam-5671	13	50	is	be	AUX
ejpam-5671	13	51	a	a	DET
ejpam-5671	13	52	continuous	continuous	ADJ
ejpam-5671	13	53	function	function	NOUN
ejpam-5671	13	54	,	,	PUNCT
ejpam-5671	13	55	ω(ρ	ω(ρ	NUM
ejpam-5671	13	56	)	)	PUNCT
ejpam-5671	13	57	represents	represent	VERB
ejpam-5671	13	58	the	the	DET
ejpam-5671	13	59	solution	solution	NOUN
ejpam-5671	13	60	of	of	ADP
ejpam-5671	13	61	(	(	PUNCT
ejpam-5671	13	62	1	1	NUM
ejpam-5671	13	63	)	)	PUNCT
ejpam-5671	13	64	for	for	ADP
ejpam-5671	13	65	a	a	DET
ejpam-5671	13	66	variable	variable	ADJ
ejpam-5671	13	67	ρ	ρ	PROPN
ejpam-5671	13	68	∈	∈	PROPN
ejpam-5671	14	1	[	[	X
ejpam-5671	14	2	0	0	NUM
ejpam-5671	14	3	,	,	PUNCT
ejpam-5671	14	4	b	b	NOUN
ejpam-5671	14	5	]	]	X
ejpam-5671	14	6	,	,	PUNCT
ejpam-5671	14	7	and	and	CCONJ
ejpam-5671	14	8	∗corresponding	∗corresponde	VERB
ejpam-5671	14	9	author	author	NOUN
ejpam-5671	14	10	.	.	PUNCT
ejpam-5671	15	1	doi	doi	NOUN
ejpam-5671	15	2	:	:	PUNCT
ejpam-5671	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5671	https://doi.org/10.29020/nybg.ejpam.v18i1.5671	NOUN
ejpam-5671	15	4	email	email	NOUN
ejpam-5671	15	5	addresses	address	NOUN
ejpam-5671	15	6	:	:	PUNCT
ejpam-5671	15	7	s.aljurbua@qu.edu.sa	s.aljurbua@qu.edu.sa	PROPN
ejpam-5671	15	8	(	(	PUNCT
ejpam-5671	15	9	s.f	s.f	PROPN
ejpam-5671	15	10	.	.	PROPN
ejpam-5671	15	11	aljurbua	aljurbua	PROPN
ejpam-5671	15	12	)	)	PUNCT
ejpam-5671	15	13	,	,	PUNCT
ejpam-5671	15	14	h.abdelwareth@qu.edu.sa	h.abdelwareth@qu.edu.sa	PROPN
ejpam-5671	15	15	(	(	PUNCT
ejpam-5671	15	16	h.	h.	PROPN
ejpam-5671	15	17	a.	a.	PROPN
ejpam-5671	15	18	hammad	hammad	PROPN
ejpam-5671	15	19	)	)	PUNCT
ejpam-5671	15	20	,	,	PUNCT
ejpam-5671	15	21	nbalmutairi@qu.edu.sa	nbalmutairi@qu.edu.sa	PROPN
ejpam-5671	15	22	(	(	PUNCT
ejpam-5671	15	23	n.	n.	PROPN
ejpam-5671	15	24	b.	b.	PROPN
ejpam-5671	15	25	almutairi	almutairi	PROPN
ejpam-5671	15	26	)	)	PUNCT
ejpam-5671	15	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5671	16	1	1	1	NUM
ejpam-5671	16	2	copyright	copyright	NOUN
ejpam-5671	16	3	:	:	PUNCT
ejpam-5671	16	4	©	©	PROPN
ejpam-5671	16	5	2025	2025	NUM
ejpam-5671	16	6	the	the	DET
ejpam-5671	16	7	author(s	author(s	NOUN
ejpam-5671	16	8	)	)	PUNCT
ejpam-5671	16	9	.	.	PUNCT
ejpam-5671	17	1	(	(	PUNCT
ejpam-5671	17	2	cc	cc	NOUN
ejpam-5671	17	3	by	by	ADP
ejpam-5671	17	4	-	-	PUNCT
ejpam-5671	17	5	nc	nc	PROPN
ejpam-5671	17	6	4.0	4.0	NUM
ejpam-5671	17	7	)	)	PUNCT
ejpam-5671	17	8	s.	s.	PROPN
ejpam-5671	17	9	f.	f.	PROPN
ejpam-5671	17	10	aljurbua	aljurbua	PROPN
ejpam-5671	17	11	,	,	PUNCT
ejpam-5671	17	12	h.	h.	PROPN
ejpam-5671	17	13	a.	a.	PROPN
ejpam-5671	17	14	hammad	hammad	PROPN
ejpam-5671	17	15	,	,	PUNCT
ejpam-5671	17	16	n.	n.	PROPN
ejpam-5671	17	17	b.	b.	PROPN
ejpam-5671	17	18	almutairi	almutairi	PROPN
ejpam-5671	17	19	/	/	SYM
ejpam-5671	17	20	eur	eur	PROPN
ejpam-5671	17	21	.	.	PUNCT
ejpam-5671	18	1	j.	j.	PROPN
ejpam-5671	18	2	pure	pure	PROPN
ejpam-5671	18	3	appl	appl	PROPN
ejpam-5671	18	4	.	.	PROPN
ejpam-5671	18	5	math	math	PROPN
ejpam-5671	18	6	,	,	PUNCT
ejpam-5671	18	7	18	18	NUM
ejpam-5671	18	8	(	(	PUNCT
ejpam-5671	18	9	1	1	NUM
ejpam-5671	18	10	)	)	PUNCT
ejpam-5671	18	11	(	(	PUNCT
ejpam-5671	18	12	2025	2025	NUM
ejpam-5671	18	13	)	)	PUNCT
ejpam-5671	18	14	,	,	PUNCT
ejpam-5671	18	15	5671	5671	NUM
ejpam-5671	18	16	2	2	NUM
ejpam-5671	18	17	of	of	ADP
ejpam-5671	18	18	18	18	NUM
ejpam-5671	18	19	ω(θ	ω(θ	NUM
ejpam-5671	18	20	)	)	PUNCT
ejpam-5671	18	21	=	=	SYM
ejpam-5671	18	22	−ω(b	−ω(b	X
ejpam-5671	18	23	)	)	PUNCT
ejpam-5671	18	24	,	,	PUNCT
ejpam-5671	18	25	ω′	ω′	X
ejpam-5671	18	26	(	(	PUNCT
ejpam-5671	18	27	θ	θ	NOUN
ejpam-5671	18	28	)	)	PUNCT
ejpam-5671	18	29	=	=	SYM
ejpam-5671	19	1	−ω′	−ω′	NOUN
ejpam-5671	19	2	(	(	PUNCT
ejpam-5671	19	3	b	b	NOUN
ejpam-5671	19	4	)	)	PUNCT
ejpam-5671	19	5	,	,	PUNCT
ejpam-5671	19	6	cdξ+1ω(θ	cdξ+1ω(θ	NOUN
ejpam-5671	19	7	)	)	PUNCT
ejpam-5671	19	8	=	=	SYM
ejpam-5671	19	9	−cdξ+1ω(b	−cdξ+1ω(b	PROPN
ejpam-5671	19	10	)	)	PUNCT
ejpam-5671	19	11	,	,	PUNCT
ejpam-5671	19	12	0	0	PUNCT
ejpam-5671	19	13	<	<	X
ejpam-5671	19	14	ξ	ξ	X
ejpam-5671	19	15	<	<	X
ejpam-5671	19	16	1	1	NUM
ejpam-5671	19	17	represents	represent	VERB
ejpam-5671	19	18	the	the	DET
ejpam-5671	19	19	nonlocal	nonlocal	ADJ
ejpam-5671	19	20	boundary	boundary	ADJ
ejpam-5671	19	21	conditions	condition	NOUN
ejpam-5671	19	22	imposed	impose	VERB
ejpam-5671	19	23	on	on	ADP
ejpam-5671	19	24	the	the	DET
ejpam-5671	19	25	solution	solution	NOUN
ejpam-5671	19	26	ω(ρ	ω(ρ	NUM
ejpam-5671	19	27	)	)	PUNCT
ejpam-5671	19	28	.	.	PUNCT
ejpam-5671	20	1	problem	problem	NOUN
ejpam-5671	20	2	(	(	PUNCT
ejpam-5671	20	3	1	1	X
ejpam-5671	20	4	)	)	PUNCT
ejpam-5671	20	5	describes	describe	VERB
ejpam-5671	20	6	a	a	DET
ejpam-5671	20	7	physical	physical	ADJ
ejpam-5671	20	8	phenomenon	phenomenon	NOUN
ejpam-5671	20	9	based	base	VERB
ejpam-5671	20	10	on	on	ADP
ejpam-5671	20	11	the	the	DET
ejpam-5671	20	12	nonlocal	nonlocal	ADJ
ejpam-5671	20	13	boundary	boundary	ADJ
ejpam-5671	20	14	conditions	condition	NOUN
ejpam-5671	20	15	that	that	PRON
ejpam-5671	20	16	restrict	restrict	VERB
ejpam-5671	20	17	the	the	DET
ejpam-5671	20	18	solution	solution	NOUN
ejpam-5671	20	19	’s	’s	PART
ejpam-5671	20	20	behavior	behavior	NOUN
ejpam-5671	20	21	at	at	ADP
ejpam-5671	20	22	the	the	DET
ejpam-5671	20	23	domain	domain	NOUN
ejpam-5671	20	24	boundaries	boundary	NOUN
ejpam-5671	20	25	.	.	PUNCT
ejpam-5671	21	1	to	to	PART
ejpam-5671	21	2	utilize	utilize	VERB
ejpam-5671	21	3	these	these	DET
ejpam-5671	21	4	conditions	condition	NOUN
ejpam-5671	21	5	,	,	PUNCT
ejpam-5671	21	6	consider	consider	VERB
ejpam-5671	21	7	a	a	DET
ejpam-5671	21	8	fractional	fractional	ADJ
ejpam-5671	21	9	heat	heat	NOUN
ejpam-5671	21	10	conduction	conduction	NOUN
ejpam-5671	21	11	problem	problem	NOUN
ejpam-5671	21	12	.	.	PUNCT
ejpam-5671	22	1	then	then	ADV
ejpam-5671	22	2	,	,	PUNCT
ejpam-5671	22	3	we	we	PRON
ejpam-5671	22	4	can	can	AUX
ejpam-5671	22	5	understand	understand	VERB
ejpam-5671	22	6	these	these	DET
ejpam-5671	22	7	conditions	condition	NOUN
ejpam-5671	22	8	as	as	ADP
ejpam-5671	22	9	defining	define	VERB
ejpam-5671	22	10	specific	specific	ADJ
ejpam-5671	22	11	characteristics	characteristic	NOUN
ejpam-5671	22	12	of	of	ADP
ejpam-5671	22	13	the	the	DET
ejpam-5671	22	14	system	system	NOUN
ejpam-5671	22	15	at	at	ADP
ejpam-5671	22	16	the	the	DET
ejpam-5671	22	17	boundaries	boundary	NOUN
ejpam-5671	22	18	.	.	PUNCT
ejpam-5671	23	1	for	for	ADP
ejpam-5671	23	2	example	example	NOUN
ejpam-5671	23	3	,	,	PUNCT
ejpam-5671	23	4	ω(θ	ω(θ	NUM
ejpam-5671	23	5	)	)	PUNCT
ejpam-5671	23	6	=	=	SYM
ejpam-5671	23	7	−ω(b	−ω(b	X
ejpam-5671	23	8	)	)	PUNCT
ejpam-5671	23	9	indicates	indicate	VERB
ejpam-5671	23	10	a	a	DET
ejpam-5671	23	11	symmetry	symmetry	NOUN
ejpam-5671	23	12	requirement	requirement	NOUN
ejpam-5671	23	13	in	in	ADP
ejpam-5671	23	14	which	which	PRON
ejpam-5671	23	15	the	the	DET
ejpam-5671	23	16	temperature	temperature	NOUN
ejpam-5671	23	17	at	at	ADP
ejpam-5671	23	18	θ	θ	PROPN
ejpam-5671	23	19	is	be	AUX
ejpam-5671	23	20	equal	equal	ADJ
ejpam-5671	23	21	in	in	ADP
ejpam-5671	23	22	magnitude	magnitude	NOUN
ejpam-5671	23	23	but	but	CCONJ
ejpam-5671	23	24	opposite	opposite	ADJ
ejpam-5671	23	25	in	in	ADP
ejpam-5671	23	26	sign	sign	NOUN
ejpam-5671	23	27	to	to	ADP
ejpam-5671	23	28	the	the	DET
ejpam-5671	23	29	temperature	temperature	NOUN
ejpam-5671	23	30	at	at	ADP
ejpam-5671	23	31	b	b	PROPN
ejpam-5671	23	32	,	,	PUNCT
ejpam-5671	23	33	suggesting	suggest	VERB
ejpam-5671	23	34	a	a	DET
ejpam-5671	23	35	reflective	reflective	ADJ
ejpam-5671	23	36	boundary	boundary	NOUN
ejpam-5671	23	37	of	of	ADP
ejpam-5671	23	38	some	some	DET
ejpam-5671	23	39	kind	kind	NOUN
ejpam-5671	23	40	.	.	PUNCT
ejpam-5671	24	1	likewise	likewise	ADV
ejpam-5671	24	2	,	,	PUNCT
ejpam-5671	24	3	the	the	DET
ejpam-5671	24	4	other	other	ADJ
ejpam-5671	24	5	statements	statement	NOUN
ejpam-5671	24	6	could	could	AUX
ejpam-5671	24	7	impose	impose	VERB
ejpam-5671	24	8	further	further	ADJ
ejpam-5671	24	9	restrictions	restriction	NOUN
ejpam-5671	24	10	on	on	ADP
ejpam-5671	24	11	the	the	DET
ejpam-5671	24	12	derivatives	derivative	NOUN
ejpam-5671	24	13	of	of	ADP
ejpam-5671	24	14	ω	ω	NUM
ejpam-5671	24	15	at	at	ADP
ejpam-5671	24	16	these	these	DET
ejpam-5671	24	17	boundaries	boundary	NOUN
ejpam-5671	24	18	.	.	PUNCT
ejpam-5671	25	1	the	the	DET
ejpam-5671	25	2	exploration	exploration	NOUN
ejpam-5671	25	3	of	of	ADP
ejpam-5671	25	4	differential	differential	ADJ
ejpam-5671	25	5	equations	equation	NOUN
ejpam-5671	25	6	with	with	ADP
ejpam-5671	25	7	a	a	DET
ejpam-5671	25	8	fractional	fractional	ADJ
ejpam-5671	25	9	order	order	NOUN
ejpam-5671	25	10	became	became	AUX
ejpam-5671	25	11	extensively	extensively	ADV
ejpam-5671	25	12	researched	research	VERB
ejpam-5671	25	13	.	.	PUNCT
ejpam-5671	26	1	models	model	NOUN
ejpam-5671	26	2	with	with	ADP
ejpam-5671	26	3	non	non	ADJ
ejpam-5671	26	4	-	-	ADJ
ejpam-5671	26	5	integer	integer	ADJ
ejpam-5671	26	6	order	order	NOUN
ejpam-5671	26	7	can	can	AUX
ejpam-5671	26	8	grant	grant	VERB
ejpam-5671	26	9	an	an	DET
ejpam-5671	26	10	astonishing	astonishing	ADJ
ejpam-5671	26	11	description	description	NOUN
ejpam-5671	26	12	of	of	ADP
ejpam-5671	26	13	memory	memory	NOUN
ejpam-5671	26	14	and	and	CCONJ
ejpam-5671	26	15	hereditary	hereditary	ADJ
ejpam-5671	26	16	properties	property	NOUN
ejpam-5671	26	17	of	of	ADP
ejpam-5671	26	18	many	many	ADJ
ejpam-5671	26	19	physical	physical	ADJ
ejpam-5671	26	20	phenomena	phenomenon	NOUN
ejpam-5671	26	21	.	.	PUNCT
ejpam-5671	27	1	moreover	moreover	ADV
ejpam-5671	27	2	,	,	PUNCT
ejpam-5671	27	3	using	use	VERB
ejpam-5671	27	4	fractional	fractional	ADJ
ejpam-5671	27	5	derivatives	derivative	NOUN
ejpam-5671	27	6	in	in	ADP
ejpam-5671	27	7	non	non	ADJ
ejpam-5671	27	8	-	-	ADJ
ejpam-5671	27	9	integer	integer	ADJ
ejpam-5671	27	10	order	order	NOUN
ejpam-5671	27	11	models	model	NOUN
ejpam-5671	27	12	of	of	ADP
ejpam-5671	27	13	real	real	ADJ
ejpam-5671	27	14	systems	system	NOUN
ejpam-5671	27	15	can	can	AUX
ejpam-5671	27	16	be	be	AUX
ejpam-5671	27	17	more	more	ADV
ejpam-5671	27	18	accurate	accurate	ADJ
ejpam-5671	27	19	and	and	CCONJ
ejpam-5671	27	20	adequate	adequate	ADJ
ejpam-5671	27	21	than	than	ADP
ejpam-5671	27	22	the	the	DET
ejpam-5671	27	23	integer	integer	NOUN
ejpam-5671	27	24	order	order	NOUN
ejpam-5671	27	25	models	model	NOUN
ejpam-5671	27	26	.	.	PUNCT
ejpam-5671	28	1	fractional	fractional	ADJ
ejpam-5671	28	2	differential	differential	ADJ
ejpam-5671	28	3	equations	equation	NOUN
ejpam-5671	28	4	can	can	AUX
ejpam-5671	28	5	provide	provide	VERB
ejpam-5671	28	6	a	a	DET
ejpam-5671	28	7	comprehensive	comprehensive	ADJ
ejpam-5671	28	8	scheme	scheme	NOUN
ejpam-5671	28	9	to	to	PART
ejpam-5671	28	10	examine	examine	VERB
ejpam-5671	28	11	complex	complex	ADJ
ejpam-5671	28	12	and	and	CCONJ
ejpam-5671	28	13	regular	regular	ADJ
ejpam-5671	28	14	systems	system	NOUN
ejpam-5671	28	15	in	in	ADP
ejpam-5671	28	16	numerous	numerous	ADJ
ejpam-5671	28	17	fields	field	NOUN
ejpam-5671	28	18	,	,	PUNCT
ejpam-5671	28	19	such	such	ADJ
ejpam-5671	28	20	as	as	ADP
ejpam-5671	28	21	physics	physics	NOUN
ejpam-5671	28	22	,	,	PUNCT
ejpam-5671	28	23	biology	biology	NOUN
ejpam-5671	28	24	,	,	PUNCT
ejpam-5671	28	25	economics	economic	NOUN
ejpam-5671	28	26	,	,	PUNCT
ejpam-5671	28	27	engineering	engineering	NOUN
ejpam-5671	28	28	,	,	PUNCT
ejpam-5671	28	29	social	social	ADJ
ejpam-5671	28	30	sciences	science	NOUN
ejpam-5671	28	31	,	,	PUNCT
ejpam-5671	28	32	and	and	CCONJ
ejpam-5671	28	33	material	material	NOUN
ejpam-5671	28	34	science	science	NOUN
ejpam-5671	28	35	[	[	X
ejpam-5671	28	36	17–19	17–19	NUM
ejpam-5671	28	37	,	,	PUNCT
ejpam-5671	28	38	27	27	NUM
ejpam-5671	28	39	]	]	PUNCT
ejpam-5671	28	40	.	.	PUNCT
ejpam-5671	29	1	for	for	ADP
ejpam-5671	29	2	example	example	NOUN
ejpam-5671	29	3	•	•	ADP
ejpam-5671	29	4	in	in	ADP
ejpam-5671	29	5	physics	physics	NOUN
ejpam-5671	29	6	,	,	PUNCT
ejpam-5671	29	7	the	the	DET
ejpam-5671	29	8	nonlinear	nonlinear	ADJ
ejpam-5671	29	9	fractional	fractional	ADJ
ejpam-5671	29	10	–	–	PUNCT
ejpam-5671	29	11	stochastic	stochastic	ADJ
ejpam-5671	29	12	wave	wave	NOUN
ejpam-5671	29	13	equation	equation	NOUN
ejpam-5671	29	14	can	can	AUX
ejpam-5671	29	15	be	be	AUX
ejpam-5671	29	16	used	use	VERB
ejpam-5671	29	17	to	to	PART
ejpam-5671	29	18	describe	describe	VERB
ejpam-5671	29	19	numerous	numerous	ADJ
ejpam-5671	29	20	nonlinear	nonlinear	ADJ
ejpam-5671	29	21	physical	physical	ADJ
ejpam-5671	29	22	phenomena	phenomenon	NOUN
ejpam-5671	29	23	with	with	ADP
ejpam-5671	29	24	gas	gas	NOUN
ejpam-5671	29	25	bubbles	bubble	NOUN
ejpam-5671	29	26	in	in	ADP
ejpam-5671	29	27	liquids	liquid	NOUN
ejpam-5671	29	28	.	.	PUNCT
ejpam-5671	30	1	moreover	moreover	ADV
ejpam-5671	30	2	,	,	PUNCT
ejpam-5671	30	3	fractional	fractional	ADJ
ejpam-5671	30	4	kinetic	kinetic	ADJ
ejpam-5671	30	5	equations	equation	NOUN
ejpam-5671	30	6	describe	describe	VERB
ejpam-5671	30	7	a	a	DET
ejpam-5671	30	8	system	system	NOUN
ejpam-5671	30	9	’s	’s	PART
ejpam-5671	30	10	evolution	evolution	NOUN
ejpam-5671	30	11	over	over	ADP
ejpam-5671	30	12	time	time	NOUN
ejpam-5671	30	13	and	and	CCONJ
ejpam-5671	30	14	fundamental	fundamental	ADJ
ejpam-5671	30	15	in	in	ADP
ejpam-5671	30	16	modeling	model	VERB
ejpam-5671	30	17	anomalous	anomalous	ADJ
ejpam-5671	30	18	diffusion	diffusion	NOUN
ejpam-5671	31	1	[	[	X
ejpam-5671	31	2	25	25	NUM
ejpam-5671	31	3	]	]	PUNCT
ejpam-5671	31	4	.	.	PUNCT
ejpam-5671	31	5	•	•	NUM
ejpam-5671	31	6	in	in	ADP
ejpam-5671	31	7	biology	biology	NOUN
ejpam-5671	31	8	,	,	PUNCT
ejpam-5671	31	9	models	model	NOUN
ejpam-5671	31	10	of	of	ADP
ejpam-5671	31	11	a	a	DET
ejpam-5671	31	12	fractional	fractional	ADJ
ejpam-5671	31	13	order	order	NOUN
ejpam-5671	31	14	can	can	AUX
ejpam-5671	31	15	be	be	AUX
ejpam-5671	31	16	used	use	VERB
ejpam-5671	31	17	to	to	PART
ejpam-5671	31	18	investigate	investigate	VERB
ejpam-5671	31	19	the	the	DET
ejpam-5671	31	20	spread	spread	NOUN
ejpam-5671	31	21	of	of	ADP
ejpam-5671	31	22	a	a	DET
ejpam-5671	31	23	disease	disease	NOUN
ejpam-5671	31	24	in	in	ADP
ejpam-5671	31	25	communities	community	NOUN
ejpam-5671	31	26	.	.	PUNCT
ejpam-5671	32	1	in	in	ADP
ejpam-5671	32	2	particular	particular	ADJ
ejpam-5671	32	3	,	,	PUNCT
ejpam-5671	32	4	an	an	DET
ejpam-5671	32	5	accurate	accurate	ADJ
ejpam-5671	32	6	and	and	CCONJ
ejpam-5671	32	7	efficient	efficient	ADJ
ejpam-5671	32	8	description	description	NOUN
ejpam-5671	32	9	of	of	ADP
ejpam-5671	32	10	the	the	DET
ejpam-5671	32	11	covid-19	covid-19	PROPN
ejpam-5671	32	12	pandemic	pandemic	NOUN
ejpam-5671	32	13	and	and	CCONJ
ejpam-5671	32	14	its	its	PRON
ejpam-5671	32	15	growing	grow	VERB
ejpam-5671	32	16	variant	variant	NOUN
ejpam-5671	32	17	can	can	AUX
ejpam-5671	32	18	be	be	AUX
ejpam-5671	32	19	obtained	obtain	VERB
ejpam-5671	32	20	by	by	ADP
ejpam-5671	32	21	using	use	VERB
ejpam-5671	32	22	a	a	DET
ejpam-5671	32	23	noninteger	noninteger	NOUN
ejpam-5671	32	24	order	order	NOUN
ejpam-5671	32	25	of	of	ADP
ejpam-5671	32	26	covid-19	covid-19	PROPN
ejpam-5671	32	27	models	model	NOUN
ejpam-5671	32	28	[	[	X
ejpam-5671	32	29	26	26	NUM
ejpam-5671	32	30	]	]	PUNCT
ejpam-5671	32	31	.	.	PUNCT
ejpam-5671	33	1	•	•	NOUN
ejpam-5671	33	2	in	in	ADP
ejpam-5671	33	3	economics	economic	NOUN
ejpam-5671	33	4	,	,	PUNCT
ejpam-5671	33	5	growth	growth	NOUN
ejpam-5671	33	6	model	model	NOUN
ejpam-5671	33	7	of	of	ADP
ejpam-5671	33	8	fractional	fractional	ADJ
ejpam-5671	33	9	order	order	NOUN
ejpam-5671	33	10	with	with	ADP
ejpam-5671	33	11	time	time	NOUN
ejpam-5671	33	12	delay	delay	NOUN
ejpam-5671	33	13	can	can	AUX
ejpam-5671	33	14	effectively	effectively	ADV
ejpam-5671	33	15	describe	describe	VERB
ejpam-5671	33	16	the	the	DET
ejpam-5671	33	17	economic	economic	ADJ
ejpam-5671	33	18	growth	growth	NOUN
ejpam-5671	33	19	by	by	ADP
ejpam-5671	33	20	adding	add	VERB
ejpam-5671	33	21	a	a	DET
ejpam-5671	33	22	time	time	NOUN
ejpam-5671	33	23	lag	lag	NOUN
ejpam-5671	33	24	to	to	ADP
ejpam-5671	33	25	the	the	DET
ejpam-5671	33	26	capital	capital	NOUN
ejpam-5671	33	27	stock	stock	NOUN
ejpam-5671	33	28	[	[	X
ejpam-5671	33	29	23	23	NUM
ejpam-5671	33	30	]	]	PUNCT
ejpam-5671	33	31	.	.	PUNCT
ejpam-5671	34	1	•	•	NOUN
ejpam-5671	34	2	in	in	ADP
ejpam-5671	34	3	engineering	engineering	NOUN
ejpam-5671	34	4	,	,	PUNCT
ejpam-5671	34	5	fractional	fractional	ADJ
ejpam-5671	34	6	order	order	NOUN
ejpam-5671	34	7	sliding	slide	VERB
ejpam-5671	34	8	mode	mode	NOUN
ejpam-5671	34	9	is	be	AUX
ejpam-5671	34	10	used	use	VERB
ejpam-5671	34	11	to	to	PART
ejpam-5671	34	12	progress	progress	VERB
ejpam-5671	34	13	the	the	DET
ejpam-5671	34	14	control	control	NOUN
ejpam-5671	34	15	performance	performance	NOUN
ejpam-5671	34	16	by	by	ADP
ejpam-5671	34	17	reducing	reduce	VERB
ejpam-5671	34	18	the	the	DET
ejpam-5671	34	19	error	error	NOUN
ejpam-5671	34	20	of	of	ADP
ejpam-5671	34	21	steady	steady	ADJ
ejpam-5671	34	22	-	-	PUNCT
ejpam-5671	34	23	state	state	NOUN
ejpam-5671	34	24	and	and	CCONJ
ejpam-5671	34	25	saturate	saturate	VERB
ejpam-5671	34	26	.	.	PUNCT
ejpam-5671	35	1	also	also	ADV
ejpam-5671	35	2	,	,	PUNCT
ejpam-5671	35	3	fractional	fractional	ADJ
ejpam-5671	35	4	-	-	PUNCT
ejpam-5671	35	5	order	order	NOUN
ejpam-5671	35	6	fast	fast	ADJ
ejpam-5671	35	7	adaptive	adaptive	ADJ
ejpam-5671	35	8	sliding	slide	VERB
ejpam-5671	35	9	mode	mode	NOUN
ejpam-5671	35	10	control	control	NOUN
ejpam-5671	35	11	ensure	ensure	VERB
ejpam-5671	35	12	prompt	prompt	ADJ
ejpam-5671	35	13	convergence	convergence	NOUN
ejpam-5671	35	14	of	of	ADP
ejpam-5671	35	15	the	the	DET
ejpam-5671	35	16	human	human	ADJ
ejpam-5671	35	17	knee	knee	NOUN
ejpam-5671	35	18	joint	joint	ADJ
ejpam-5671	35	19	orthosis	orthosis	NOUN
ejpam-5671	35	20	state	state	NOUN
ejpam-5671	35	21	and	and	CCONJ
ejpam-5671	35	22	its	its	PRON
ejpam-5671	35	23	finite	finite	ADJ
ejpam-5671	35	24	-	-	PUNCT
ejpam-5671	35	25	time	time	NOUN
ejpam-5671	35	26	stability	stability	NOUN
ejpam-5671	35	27	to	to	ADP
ejpam-5671	35	28	the	the	DET
ejpam-5671	35	29	intended	intend	VERB
ejpam-5671	35	30	trajectory	trajectory	NOUN
ejpam-5671	35	31	[	[	X
ejpam-5671	35	32	22	22	NUM
ejpam-5671	35	33	]	]	PUNCT
ejpam-5671	35	34	.	.	PUNCT
ejpam-5671	36	1	boundary	boundary	ADJ
ejpam-5671	36	2	conditions	condition	NOUN
ejpam-5671	36	3	have	have	VERB
ejpam-5671	36	4	a	a	DET
ejpam-5671	36	5	significant	significant	ADJ
ejpam-5671	36	6	impact	impact	NOUN
ejpam-5671	36	7	on	on	ADP
ejpam-5671	36	8	comprehending	comprehending	ADJ
ejpam-5671	36	9	physical	physical	ADJ
ejpam-5671	36	10	systems	system	NOUN
ejpam-5671	36	11	and	and	CCONJ
ejpam-5671	36	12	solving	solve	VERB
ejpam-5671	36	13	differential	differential	ADJ
ejpam-5671	36	14	equations	equation	NOUN
ejpam-5671	36	15	.	.	PUNCT
ejpam-5671	37	1	periodic	periodic	ADJ
ejpam-5671	37	2	and	and	CCONJ
ejpam-5671	37	3	antiperiodic	antiperiodic	ADJ
ejpam-5671	37	4	boundary	boundary	ADJ
ejpam-5671	37	5	conditions	condition	NOUN
ejpam-5671	37	6	are	be	AUX
ejpam-5671	37	7	crucial	crucial	ADJ
ejpam-5671	37	8	in	in	ADP
ejpam-5671	37	9	solving	solve	VERB
ejpam-5671	37	10	fractional	fractional	ADJ
ejpam-5671	37	11	differential	differential	ADJ
ejpam-5671	37	12	equations	equation	NOUN
ejpam-5671	37	13	.	.	PUNCT
ejpam-5671	38	1	in	in	ADP
ejpam-5671	38	2	quantum	quantum	ADJ
ejpam-5671	38	3	mechanics	mechanic	NOUN
ejpam-5671	38	4	,	,	PUNCT
ejpam-5671	38	5	antiperiodic	antiperiodic	ADJ
ejpam-5671	38	6	boundary	boundary	ADJ
ejpam-5671	38	7	problems	problem	NOUN
ejpam-5671	38	8	will	will	AUX
ejpam-5671	38	9	give	give	VERB
ejpam-5671	38	10	a	a	DET
ejpam-5671	38	11	meaningful	meaningful	ADJ
ejpam-5671	38	12	description	description	NOUN
ejpam-5671	38	13	of	of	ADP
ejpam-5671	38	14	the	the	DET
ejpam-5671	38	15	system	system	NOUN
ejpam-5671	38	16	and	and	CCONJ
ejpam-5671	38	17	how	how	SCONJ
ejpam-5671	38	18	it	it	PRON
ejpam-5671	38	19	behave	behave	VERB
ejpam-5671	38	20	in	in	ADP
ejpam-5671	38	21	a	a	DET
ejpam-5671	38	22	certain	certain	ADJ
ejpam-5671	38	23	domain	domain	NOUN
ejpam-5671	38	24	.	.	PUNCT
ejpam-5671	39	1	in	in	ADP
ejpam-5671	39	2	spin	spin	NOUN
ejpam-5671	39	3	systems	system	NOUN
ejpam-5671	39	4	,	,	PUNCT
ejpam-5671	39	5	problems	problem	NOUN
ejpam-5671	39	6	with	with	ADP
ejpam-5671	39	7	antiperiodics	antiperiodic	NOUN
ejpam-5671	39	8	can	can	AUX
ejpam-5671	39	9	assist	assist	VERB
ejpam-5671	39	10	in	in	ADP
ejpam-5671	39	11	examining	examine	VERB
ejpam-5671	39	12	the	the	DET
ejpam-5671	39	13	characteristics	characteristic	NOUN
ejpam-5671	39	14	of	of	ADP
ejpam-5671	39	15	spins	spin	NOUN
ejpam-5671	39	16	located	locate	VERB
ejpam-5671	39	17	at	at	ADP
ejpam-5671	39	18	the	the	DET
ejpam-5671	39	19	extremities	extremity	NOUN
ejpam-5671	39	20	of	of	ADP
ejpam-5671	39	21	limited	limited	ADJ
ejpam-5671	39	22	chains	chain	NOUN
ejpam-5671	39	23	.	.	PUNCT
ejpam-5671	40	1	in	in	ADP
ejpam-5671	40	2	general	general	ADJ
ejpam-5671	40	3	,	,	PUNCT
ejpam-5671	40	4	fractional	fractional	ADJ
ejpam-5671	40	5	differential	differential	ADJ
ejpam-5671	40	6	equations	equation	NOUN
ejpam-5671	40	7	with	with	ADP
ejpam-5671	40	8	antiperiodic	antiperiodic	ADJ
ejpam-5671	40	9	boundary	boundary	ADJ
ejpam-5671	40	10	conditions	condition	NOUN
ejpam-5671	40	11	offer	offer	VERB
ejpam-5671	40	12	a	a	DET
ejpam-5671	40	13	flexible	flexible	ADJ
ejpam-5671	40	14	mathematical	mathematical	ADJ
ejpam-5671	40	15	s.	s.	PROPN
ejpam-5671	40	16	f.	f.	PROPN
ejpam-5671	40	17	aljurbua	aljurbua	PROPN
ejpam-5671	40	18	,	,	PUNCT
ejpam-5671	40	19	h.	h.	PROPN
ejpam-5671	40	20	a.	a.	PROPN
ejpam-5671	40	21	hammad	hammad	PROPN
ejpam-5671	40	22	,	,	PUNCT
ejpam-5671	40	23	n.	n.	PROPN
ejpam-5671	40	24	b.	b.	PROPN
ejpam-5671	40	25	almutairi	almutairi	PROPN
ejpam-5671	40	26	/	/	SYM
ejpam-5671	40	27	eur	eur	PROPN
ejpam-5671	40	28	.	.	PUNCT
ejpam-5671	41	1	j.	j.	PROPN
ejpam-5671	41	2	pure	pure	PROPN
ejpam-5671	41	3	appl	appl	PROPN
ejpam-5671	41	4	.	.	PROPN
ejpam-5671	41	5	math	math	PROPN
ejpam-5671	41	6	,	,	PUNCT
ejpam-5671	41	7	18	18	NUM
ejpam-5671	41	8	(	(	PUNCT
ejpam-5671	41	9	1	1	NUM
ejpam-5671	41	10	)	)	PUNCT
ejpam-5671	41	11	(	(	PUNCT
ejpam-5671	41	12	2025	2025	NUM
ejpam-5671	41	13	)	)	PUNCT
ejpam-5671	41	14	,	,	PUNCT
ejpam-5671	41	15	5671	5671	NUM
ejpam-5671	41	16	3	3	NUM
ejpam-5671	41	17	of	of	ADP
ejpam-5671	41	18	18	18	NUM
ejpam-5671	41	19	tool	tool	NOUN
ejpam-5671	41	20	for	for	ADP
ejpam-5671	41	21	comprehending	comprehending	ADJ
ejpam-5671	41	22	and	and	CCONJ
ejpam-5671	41	23	modeling	model	VERB
ejpam-5671	41	24	different	different	ADJ
ejpam-5671	41	25	engineering	engineering	NOUN
ejpam-5671	41	26	and	and	CCONJ
ejpam-5671	41	27	physical	physical	ADJ
ejpam-5671	41	28	systems	system	NOUN
ejpam-5671	41	29	that	that	PRON
ejpam-5671	41	30	display	display	VERB
ejpam-5671	41	31	cyclic	cyclic	NOUN
ejpam-5671	41	32	or	or	CCONJ
ejpam-5671	41	33	alternating	alternate	VERB
ejpam-5671	41	34	behaviors	behavior	NOUN
ejpam-5671	41	35	at	at	ADP
ejpam-5671	41	36	their	their	PRON
ejpam-5671	41	37	boundaries	boundary	NOUN
ejpam-5671	41	38	.	.	PUNCT
ejpam-5671	42	1	fractional	fractional	ADJ
ejpam-5671	42	2	derivatives	derivative	NOUN
ejpam-5671	42	3	have	have	AUX
ejpam-5671	42	4	been	be	AUX
ejpam-5671	42	5	defined	define	VERB
ejpam-5671	42	6	in	in	ADP
ejpam-5671	42	7	various	various	ADJ
ejpam-5671	42	8	ways	way	NOUN
ejpam-5671	42	9	by	by	ADP
ejpam-5671	42	10	mathematicians	mathematician	NOUN
ejpam-5671	42	11	,	,	PUNCT
ejpam-5671	42	12	including	include	VERB
ejpam-5671	42	13	grünwald	grünwald	ADJ
ejpam-5671	42	14	–	–	PUNCT
ejpam-5671	42	15	letnikov	letnikov	ADJ
ejpam-5671	42	16	,	,	PUNCT
ejpam-5671	42	17	liouville	liouville	NOUN
ejpam-5671	42	18	,	,	PUNCT
ejpam-5671	42	19	hadamard	hadamard	ADJ
ejpam-5671	42	20	,	,	PUNCT
ejpam-5671	42	21	marchaud	marchaud	ADJ
ejpam-5671	42	22	,	,	PUNCT
ejpam-5671	42	23	riesz	riesz	NOUN
ejpam-5671	42	24	,	,	PUNCT
ejpam-5671	42	25	and	and	CCONJ
ejpam-5671	42	26	caputo	caputo	PROPN
ejpam-5671	42	27	derivatives	derivative	NOUN
ejpam-5671	42	28	.	.	PUNCT
ejpam-5671	43	1	these	these	DET
ejpam-5671	43	2	definitions	definition	NOUN
ejpam-5671	43	3	have	have	AUX
ejpam-5671	43	4	been	be	AUX
ejpam-5671	43	5	used	use	VERB
ejpam-5671	43	6	to	to	PART
ejpam-5671	43	7	investigate	investigate	VERB
ejpam-5671	43	8	solutions	solution	NOUN
ejpam-5671	43	9	and	and	CCONJ
ejpam-5671	43	10	stability	stability	NOUN
ejpam-5671	43	11	of	of	ADP
ejpam-5671	43	12	systems	system	NOUN
ejpam-5671	43	13	,	,	PUNCT
ejpam-5671	43	14	as	as	ADV
ejpam-5671	43	15	well	well	ADV
ejpam-5671	43	16	as	as	ADP
ejpam-5671	43	17	to	to	PART
ejpam-5671	43	18	define	define	VERB
ejpam-5671	43	19	and	and	CCONJ
ejpam-5671	43	20	characterize	characterize	VERB
ejpam-5671	43	21	spaces	space	NOUN
ejpam-5671	43	22	[	[	X
ejpam-5671	43	23	12	12	NUM
ejpam-5671	43	24	,	,	PUNCT
ejpam-5671	43	25	30	30	NUM
ejpam-5671	43	26	]	]	PUNCT
ejpam-5671	43	27	.	.	PUNCT
ejpam-5671	44	1	in	in	ADP
ejpam-5671	44	2	this	this	DET
ejpam-5671	44	3	work	work	NOUN
ejpam-5671	44	4	,	,	PUNCT
ejpam-5671	44	5	we	we	PRON
ejpam-5671	44	6	focus	focus	VERB
ejpam-5671	44	7	on	on	ADP
ejpam-5671	44	8	the	the	DET
ejpam-5671	44	9	caputo	caputo	PROPN
ejpam-5671	44	10	fractional	fractional	PROPN
ejpam-5671	44	11	derivative	derivative	NOUN
ejpam-5671	44	12	because	because	SCONJ
ejpam-5671	44	13	of	of	ADP
ejpam-5671	44	14	its	its	PRON
ejpam-5671	44	15	similarity	similarity	NOUN
ejpam-5671	44	16	to	to	ADP
ejpam-5671	44	17	ordinary	ordinary	ADJ
ejpam-5671	44	18	differential	differential	ADJ
ejpam-5671	44	19	equations	equation	NOUN
ejpam-5671	44	20	and	and	CCONJ
ejpam-5671	44	21	its	its	PRON
ejpam-5671	44	22	effectiveness	effectiveness	NOUN
ejpam-5671	44	23	in	in	ADP
ejpam-5671	44	24	handling	handle	VERB
ejpam-5671	44	25	antiperiodic	antiperiodic	ADJ
ejpam-5671	44	26	boundary	boundary	ADJ
ejpam-5671	44	27	problems	problem	NOUN
ejpam-5671	44	28	.	.	PUNCT
ejpam-5671	45	1	tremendous	tremendous	ADJ
ejpam-5671	45	2	papers	paper	NOUN
ejpam-5671	45	3	discuss	discuss	VERB
ejpam-5671	45	4	the	the	DET
ejpam-5671	45	5	existence	existence	NOUN
ejpam-5671	45	6	and	and	CCONJ
ejpam-5671	45	7	uniqueness	uniqueness	NOUN
ejpam-5671	45	8	of	of	ADP
ejpam-5671	45	9	a	a	DET
ejpam-5671	45	10	solution	solution	NOUN
ejpam-5671	45	11	or	or	CCONJ
ejpam-5671	45	12	solving	solve	VERB
ejpam-5671	45	13	different	different	ADJ
ejpam-5671	45	14	types	type	NOUN
ejpam-5671	45	15	of	of	ADP
ejpam-5671	45	16	the	the	DET
ejpam-5671	45	17	boundary	boundary	ADJ
ejpam-5671	45	18	problems	problem	NOUN
ejpam-5671	45	19	of	of	ADP
ejpam-5671	45	20	fractional	fractional	ADJ
ejpam-5671	45	21	differential	differential	ADJ
ejpam-5671	45	22	equations	equation	NOUN
ejpam-5671	45	23	.	.	PUNCT
ejpam-5671	46	1	for	for	ADP
ejpam-5671	46	2	interesting	interesting	ADJ
ejpam-5671	46	3	results	result	NOUN
ejpam-5671	46	4	see	see	VERB
ejpam-5671	46	5	[	[	X
ejpam-5671	46	6	5	5	NUM
ejpam-5671	46	7	,	,	PUNCT
ejpam-5671	46	8	8	8	NUM
ejpam-5671	46	9	,	,	PUNCT
ejpam-5671	46	10	10	10	NUM
ejpam-5671	46	11	,	,	PUNCT
ejpam-5671	46	12	13	13	NUM
ejpam-5671	46	13	,	,	PUNCT
ejpam-5671	46	14	14	14	NUM
ejpam-5671	46	15	,	,	PUNCT
ejpam-5671	46	16	16	16	NUM
ejpam-5671	46	17	,	,	PUNCT
ejpam-5671	46	18	24	24	NUM
ejpam-5671	46	19	,	,	PUNCT
ejpam-5671	46	20	28	28	NUM
ejpam-5671	46	21	]	]	PUNCT
ejpam-5671	46	22	.	.	PUNCT
ejpam-5671	47	1	in	in	ADP
ejpam-5671	47	2	[	[	X
ejpam-5671	47	3	4	4	NUM
ejpam-5671	47	4	]	]	PUNCT
ejpam-5671	47	5	,	,	PUNCT
ejpam-5671	47	6	the	the	DET
ejpam-5671	47	7	author	author	NOUN
ejpam-5671	47	8	investigated	investigate	VERB
ejpam-5671	47	9	and	and	CCONJ
ejpam-5671	47	10	confirmed	confirm	VERB
ejpam-5671	47	11	the	the	DET
ejpam-5671	47	12	existence	existence	NOUN
ejpam-5671	47	13	of	of	ADP
ejpam-5671	47	14	solutions	solution	NOUN
ejpam-5671	47	15	to	to	ADP
ejpam-5671	47	16	the	the	DET
ejpam-5671	47	17	following	following	ADJ
ejpam-5671	47	18	problem	problem	NOUN
ejpam-5671	47	19	:	:	PUNCT
ejpam-5671	47	20	{	{	PUNCT
ejpam-5671	47	21	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	47	22	)	)	PUNCT
ejpam-5671	47	23	=	=	SYM
ejpam-5671	47	24	ω(ρ	ω(ρ	NOUN
ejpam-5671	47	25	,	,	PUNCT
ejpam-5671	47	26	ω(ρ	ω(ρ	NOUN
ejpam-5671	47	27	)	)	PUNCT
ejpam-5671	47	28	)	)	PUNCT
ejpam-5671	47	29	,	,	PUNCT
ejpam-5671	47	30	ρ	ρ	PROPN
ejpam-5671	47	31	∈	∈	PROPN
ejpam-5671	48	1	[	[	X
ejpam-5671	48	2	0	0	NUM
ejpam-5671	48	3	,	,	PUNCT
ejpam-5671	48	4	b	b	NOUN
ejpam-5671	48	5	]	]	X
ejpam-5671	48	6	,	,	PUNCT
ejpam-5671	48	7	2	2	NUM
ejpam-5671	48	8	<	<	X
ejpam-5671	48	9	µ	µ	X
ejpam-5671	48	10	≤	≤	NOUN
ejpam-5671	48	11	3	3	NUM
ejpam-5671	48	12	,	,	PUNCT
ejpam-5671	48	13	ω(0	ω(0	PROPN
ejpam-5671	48	14	)	)	PUNCT
ejpam-5671	48	15	=	=	SYM
ejpam-5671	48	16	−ω(b	−ω(b	X
ejpam-5671	48	17	)	)	PUNCT
ejpam-5671	48	18	,	,	PUNCT
ejpam-5671	48	19	ω′	ω′	X
ejpam-5671	48	20	(	(	PUNCT
ejpam-5671	48	21	0	0	NUM
ejpam-5671	48	22	)	)	PUNCT
ejpam-5671	49	1	=	=	SYM
ejpam-5671	49	2	−ω′	−ω′	NOUN
ejpam-5671	49	3	(	(	PUNCT
ejpam-5671	49	4	b	b	NOUN
ejpam-5671	49	5	)	)	PUNCT
ejpam-5671	49	6	,	,	PUNCT
ejpam-5671	49	7	ω	ω	X
ejpam-5671	50	1	′′	′′	PROPN
ejpam-5671	50	2	(	(	PUNCT
ejpam-5671	50	3	0	0	NUM
ejpam-5671	50	4	)	)	PUNCT
ejpam-5671	50	5	=	=	SYM
ejpam-5671	50	6	−ω′′	−ω′′	X
ejpam-5671	50	7	(	(	PUNCT
ejpam-5671	50	8	b	b	NOUN
ejpam-5671	50	9	)	)	PUNCT
ejpam-5671	50	10	,	,	PUNCT
ejpam-5671	50	11	(	(	PUNCT
ejpam-5671	50	12	2	2	X
ejpam-5671	50	13	)	)	PUNCT
ejpam-5671	50	14	where	where	SCONJ
ejpam-5671	50	15	ω	ω	X
ejpam-5671	50	16	:	:	PUNCT
ejpam-5671	51	1	[	[	X
ejpam-5671	51	2	0	0	NUM
ejpam-5671	51	3	,	,	PUNCT
ejpam-5671	51	4	b]×	b]×	NOUN
ejpam-5671	51	5	r	r	NOUN
ejpam-5671	51	6	−→	−→	NOUN
ejpam-5671	51	7	r	r	NOUN
ejpam-5671	51	8	,	,	PUNCT
ejpam-5671	51	9	by	by	ADP
ejpam-5671	51	10	using	use	VERB
ejpam-5671	51	11	fixed	fix	VERB
ejpam-5671	51	12	point	point	NOUN
ejpam-5671	51	13	theorem	theorem	NOUN
ejpam-5671	51	14	of	of	ADP
ejpam-5671	51	15	krasnoselskii	krasnoselskii	PROPN
ejpam-5671	51	16	’s	’s	PART
ejpam-5671	51	17	.	.	PUNCT
ejpam-5671	52	1	an	an	DET
ejpam-5671	52	2	interesting	interesting	ADJ
ejpam-5671	52	3	result	result	NOUN
ejpam-5671	52	4	was	be	AUX
ejpam-5671	52	5	proved	prove	VERB
ejpam-5671	52	6	in	in	ADP
ejpam-5671	52	7	[	[	X
ejpam-5671	52	8	2	2	NUM
ejpam-5671	52	9	]	]	PUNCT
ejpam-5671	52	10	,	,	PUNCT
ejpam-5671	52	11	in	in	ADP
ejpam-5671	52	12	which	which	PRON
ejpam-5671	52	13	the	the	DET
ejpam-5671	52	14	domain	domain	NOUN
ejpam-5671	52	15	[	[	X
ejpam-5671	52	16	0	0	NUM
ejpam-5671	52	17	,	,	PUNCT
ejpam-5671	52	18	b	b	NOUN
ejpam-5671	52	19	]	]	PUNCT
ejpam-5671	52	20	was	be	AUX
ejpam-5671	52	21	not	not	PART
ejpam-5671	52	22	considered	consider	VERB
ejpam-5671	52	23	for	for	ADP
ejpam-5671	52	24	both	both	CCONJ
ejpam-5671	52	25	its	its	PRON
ejpam-5671	52	26	boundaries	boundary	NOUN
ejpam-5671	52	27	for	for	ADP
ejpam-5671	52	28	the	the	DET
ejpam-5671	52	29	fractional	fractional	ADJ
ejpam-5671	52	30	differential	differential	ADJ
ejpam-5671	52	31	equation	equation	NOUN
ejpam-5671	52	32	of	of	ADP
ejpam-5671	52	33	order	order	NOUN
ejpam-5671	52	34	µ	µ	X
ejpam-5671	52	35	∈	∈	NOUN
ejpam-5671	52	36	(	(	PUNCT
ejpam-5671	52	37	1	1	NUM
ejpam-5671	52	38	,	,	PUNCT
ejpam-5671	52	39	2	2	NUM
ejpam-5671	52	40	]	]	PUNCT
ejpam-5671	52	41	.	.	PUNCT
ejpam-5671	53	1	they	they	PRON
ejpam-5671	53	2	selected	select	VERB
ejpam-5671	53	3	a	a	DET
ejpam-5671	53	4	nonlocal	nonlocal	ADJ
ejpam-5671	53	5	intermediate	intermediate	ADJ
ejpam-5671	53	6	θ	θ	NOUN
ejpam-5671	53	7	point	point	NOUN
ejpam-5671	53	8	and	and	CCONJ
ejpam-5671	53	9	one	one	NUM
ejpam-5671	53	10	of	of	ADP
ejpam-5671	53	11	the	the	DET
ejpam-5671	53	12	fixed	fix	VERB
ejpam-5671	53	13	endpoints	endpoint	NOUN
ejpam-5671	53	14	of	of	ADP
ejpam-5671	53	15	the	the	DET
ejpam-5671	53	16	interval	interval	NOUN
ejpam-5671	53	17	(	(	PUNCT
ejpam-5671	53	18	0	0	NUM
ejpam-5671	53	19	,	,	PUNCT
ejpam-5671	53	20	b	b	NOUN
ejpam-5671	53	21	]	]	X
ejpam-5671	53	22	for	for	ADP
ejpam-5671	53	23	:	:	PUNCT
ejpam-5671	53	24	{	{	PUNCT
ejpam-5671	53	25	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	53	26	)	)	PUNCT
ejpam-5671	53	27	=	=	SYM
ejpam-5671	53	28	ω(ρ	ω(ρ	NOUN
ejpam-5671	53	29	,	,	PUNCT
ejpam-5671	53	30	ω(ρ	ω(ρ	NOUN
ejpam-5671	53	31	)	)	PUNCT
ejpam-5671	53	32	)	)	PUNCT
ejpam-5671	53	33	,	,	PUNCT
ejpam-5671	53	34	ρ	ρ	PROPN
ejpam-5671	53	35	∈	∈	PROPN
ejpam-5671	54	1	[	[	X
ejpam-5671	54	2	0	0	NUM
ejpam-5671	54	3	,	,	PUNCT
ejpam-5671	54	4	b	b	NOUN
ejpam-5671	54	5	]	]	X
ejpam-5671	54	6	,	,	PUNCT
ejpam-5671	54	7	1	1	NUM
ejpam-5671	54	8	<	<	X
ejpam-5671	54	9	µ	µ	X
ejpam-5671	54	10	≤	≤	NUM
ejpam-5671	54	11	2	2	NUM
ejpam-5671	54	12	,	,	PUNCT
ejpam-5671	54	13	0	0	NUM
ejpam-5671	54	14	<	<	X
ejpam-5671	54	15	θ	θ	X
ejpam-5671	54	16	<	<	X
ejpam-5671	54	17	b	b	PROPN
ejpam-5671	54	18	,	,	PUNCT
ejpam-5671	54	19	ω(θ	ω(θ	NUM
ejpam-5671	54	20	)	)	PUNCT
ejpam-5671	54	21	=	=	SYM
ejpam-5671	54	22	−ω(b	−ω(b	X
ejpam-5671	54	23	)	)	PUNCT
ejpam-5671	54	24	,	,	PUNCT
ejpam-5671	55	1	ω	ω	NUM
ejpam-5671	55	2	′	′	NUM
ejpam-5671	55	3	(	(	PUNCT
ejpam-5671	55	4	θ	θ	NOUN
ejpam-5671	55	5	)	)	PUNCT
ejpam-5671	55	6	=	=	SYM
ejpam-5671	56	1	−ω′	−ω′	NOUN
ejpam-5671	56	2	(	(	PUNCT
ejpam-5671	56	3	b	b	NOUN
ejpam-5671	56	4	)	)	PUNCT
ejpam-5671	56	5	,	,	PUNCT
ejpam-5671	56	6	(	(	PUNCT
ejpam-5671	56	7	3	3	X
ejpam-5671	56	8	)	)	PUNCT
ejpam-5671	56	9	where	where	SCONJ
ejpam-5671	56	10	ω	ω	X
ejpam-5671	56	11	:	:	PUNCT
ejpam-5671	57	1	[	[	X
ejpam-5671	57	2	0	0	NUM
ejpam-5671	57	3	,	,	PUNCT
ejpam-5671	57	4	b	b	NOUN
ejpam-5671	57	5	]	]	X
ejpam-5671	57	6	×	×	NOUN
ejpam-5671	57	7	r	r	NOUN
ejpam-5671	57	8	−→	−→	NOUN
ejpam-5671	57	9	r	r	NOUN
ejpam-5671	57	10	is	be	AUX
ejpam-5671	57	11	a	a	DET
ejpam-5671	57	12	given	give	VERB
ejpam-5671	57	13	function	function	NOUN
ejpam-5671	57	14	.	.	PUNCT
ejpam-5671	58	1	the	the	DET
ejpam-5671	58	2	existence	existence	NOUN
ejpam-5671	58	3	of	of	ADP
ejpam-5671	58	4	a	a	DET
ejpam-5671	58	5	solution	solution	NOUN
ejpam-5671	58	6	for	for	ADP
ejpam-5671	58	7	this	this	DET
ejpam-5671	58	8	type	type	NOUN
ejpam-5671	58	9	of	of	ADP
ejpam-5671	58	10	problems	problem	NOUN
ejpam-5671	58	11	is	be	AUX
ejpam-5671	58	12	based	base	VERB
ejpam-5671	58	13	on	on	ADP
ejpam-5671	58	14	standard	standard	ADJ
ejpam-5671	58	15	fixed	fix	VERB
ejpam-5671	58	16	point	point	NOUN
ejpam-5671	58	17	theorems	theorem	NOUN
ejpam-5671	58	18	.	.	PUNCT
ejpam-5671	59	1	in	in	ADP
ejpam-5671	59	2	[	[	X
ejpam-5671	59	3	6	6	NUM
ejpam-5671	59	4	]	]	PUNCT
ejpam-5671	59	5	,	,	PUNCT
ejpam-5671	59	6	the	the	DET
ejpam-5671	59	7	author	author	NOUN
ejpam-5671	59	8	studied	study	VERB
ejpam-5671	59	9	the	the	DET
ejpam-5671	59	10	existence	existence	NOUN
ejpam-5671	59	11	of	of	ADP
ejpam-5671	59	12	solutions	solution	NOUN
ejpam-5671	59	13	for	for	ADP
ejpam-5671	59	14	the	the	DET
ejpam-5671	59	15	following	follow	VERB
ejpam-5671	59	16	nfde	nfde	NOUN
ejpam-5671	59	17	:	:	PUNCT
ejpam-5671	59	18	{	{	PUNCT
ejpam-5671	59	19	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	59	20	)	)	PUNCT
ejpam-5671	59	21	=	=	SYM
ejpam-5671	59	22	ω(ρ	ω(ρ	NOUN
ejpam-5671	59	23	,	,	PUNCT
ejpam-5671	59	24	ω(ρ	ω(ρ	NOUN
ejpam-5671	59	25	)	)	PUNCT
ejpam-5671	59	26	)	)	PUNCT
ejpam-5671	59	27	,	,	PUNCT
ejpam-5671	59	28	ρ	ρ	PROPN
ejpam-5671	59	29	∈	∈	PROPN
ejpam-5671	60	1	[	[	X
ejpam-5671	60	2	0	0	NUM
ejpam-5671	60	3	,	,	PUNCT
ejpam-5671	60	4	b	b	NOUN
ejpam-5671	60	5	]	]	X
ejpam-5671	60	6	,	,	PUNCT
ejpam-5671	60	7	1	1	NUM
ejpam-5671	60	8	<	<	X
ejpam-5671	60	9	µ	µ	X
ejpam-5671	60	10	≤	≤	NUM
ejpam-5671	60	11	2	2	NUM
ejpam-5671	60	12	,	,	PUNCT
ejpam-5671	60	13	0	0	NUM
ejpam-5671	60	14	<	<	X
ejpam-5671	60	15	θ	θ	X
ejpam-5671	60	16	<	<	X
ejpam-5671	60	17	b	b	PROPN
ejpam-5671	60	18	,	,	PUNCT
ejpam-5671	60	19	a0ω(θ	a0ω(θ	PROPN
ejpam-5671	60	20	)	)	PUNCT
ejpam-5671	60	21	=	=	SYM
ejpam-5671	60	22	−b0ω(b	−b0ω(b	NOUN
ejpam-5671	60	23	)	)	PUNCT
ejpam-5671	60	24	,	,	PUNCT
ejpam-5671	60	25	a1ω	a1ω	PROPN
ejpam-5671	60	26	′	′	NUM
ejpam-5671	60	27	(	(	PUNCT
ejpam-5671	60	28	θ	θ	NOUN
ejpam-5671	60	29	)	)	PUNCT
ejpam-5671	60	30	=	=	SYM
ejpam-5671	60	31	−b1ω	−b1ω	X
ejpam-5671	61	1	′	′	NUM
ejpam-5671	61	2	(	(	PUNCT
ejpam-5671	61	3	b	b	NOUN
ejpam-5671	61	4	)	)	PUNCT
ejpam-5671	61	5	,	,	PUNCT
ejpam-5671	61	6	(	(	PUNCT
ejpam-5671	61	7	4	4	X
ejpam-5671	61	8	)	)	PUNCT
ejpam-5671	61	9	where	where	SCONJ
ejpam-5671	61	10	ai	ai	VERB
ejpam-5671	61	11	,	,	PUNCT
ejpam-5671	61	12	bi	bi	PROPN
ejpam-5671	61	13	∈	∈	PROPN
ejpam-5671	61	14	r+	r+	X
ejpam-5671	61	15	,	,	PUNCT
ejpam-5671	61	16	for	for	ADP
ejpam-5671	61	17	i	i	PROPN
ejpam-5671	61	18	=	=	SYM
ejpam-5671	61	19	0	0	NUM
ejpam-5671	61	20	,	,	PUNCT
ejpam-5671	61	21	1	1	NUM
ejpam-5671	61	22	and	and	CCONJ
ejpam-5671	61	23	a	a	DET
ejpam-5671	61	24	continuous	continuous	ADJ
ejpam-5671	61	25	function	function	NOUN
ejpam-5671	61	26	ω	ω	NOUN
ejpam-5671	61	27	:	:	PUNCT
ejpam-5671	62	1	[	[	X
ejpam-5671	62	2	0	0	NUM
ejpam-5671	62	3	,	,	PUNCT
ejpam-5671	62	4	b]×r	b]×r	NUM
ejpam-5671	62	5	−→	−→	ADJ
ejpam-5671	62	6	r	r	NOUN
ejpam-5671	62	7	,	,	PUNCT
ejpam-5671	62	8	by	by	ADP
ejpam-5671	62	9	using	use	VERB
ejpam-5671	62	10	the	the	DET
ejpam-5671	62	11	krasnoselskii	krasnoselskii	ADJ
ejpam-5671	62	12	fixed	fix	VERB
ejpam-5671	62	13	-	-	PUNCT
ejpam-5671	62	14	point	point	NOUN
ejpam-5671	62	15	theorem	theorem	NOUN
ejpam-5671	62	16	and	and	CCONJ
ejpam-5671	62	17	the	the	DET
ejpam-5671	62	18	contraction	contraction	NOUN
ejpam-5671	62	19	principle	principle	NOUN
ejpam-5671	62	20	.	.	PUNCT
ejpam-5671	63	1	in	in	ADP
ejpam-5671	63	2	recent	recent	ADJ
ejpam-5671	63	3	work	work	NOUN
ejpam-5671	63	4	[	[	X
ejpam-5671	63	5	15	15	NUM
ejpam-5671	63	6	]	]	X
ejpam-5671	63	7	,	,	PUNCT
ejpam-5671	63	8	positive	positive	ADJ
ejpam-5671	63	9	solutions	solution	NOUN
ejpam-5671	63	10	of	of	ADP
ejpam-5671	63	11	fractional	fractional	ADJ
ejpam-5671	63	12	order	order	NOUN
ejpam-5671	63	13	riemann	riemann	PROPN
ejpam-5671	63	14	liouville	liouville	PROPN
ejpam-5671	63	15	and	and	CCONJ
ejpam-5671	63	16	caputo	caputo	PROPN
ejpam-5671	63	17	type	type	PROPN
ejpam-5671	63	18	langevin	langevin	PROPN
ejpam-5671	63	19	equations	equation	NOUN
ejpam-5671	63	20	was	be	AUX
ejpam-5671	63	21	investigated	investigate	VERB
ejpam-5671	63	22	.	.	PUNCT
ejpam-5671	64	1	the	the	DET
ejpam-5671	64	2	results	result	NOUN
ejpam-5671	64	3	was	be	AUX
ejpam-5671	64	4	obtained	obtain	VERB
ejpam-5671	64	5	by	by	ADP
ejpam-5671	64	6	upper	upper	ADJ
ejpam-5671	64	7	and	and	CCONJ
ejpam-5671	64	8	lower	low	ADJ
ejpam-5671	64	9	solution	solution	NOUN
ejpam-5671	64	10	techniques	technique	NOUN
ejpam-5671	64	11	along	along	ADP
ejpam-5671	64	12	with	with	ADP
ejpam-5671	64	13	fixed	fix	VERB
ejpam-5671	64	14	point	point	NOUN
ejpam-5671	64	15	theorems	theorem	NOUN
ejpam-5671	64	16	.	.	PUNCT
ejpam-5671	65	1	the	the	DET
ejpam-5671	65	2	paper	paper	NOUN
ejpam-5671	65	3	is	be	AUX
ejpam-5671	65	4	organized	organize	VERB
ejpam-5671	65	5	into	into	ADP
ejpam-5671	65	6	four	four	NUM
ejpam-5671	65	7	main	main	ADJ
ejpam-5671	65	8	sections	section	NOUN
ejpam-5671	65	9	,	,	PUNCT
ejpam-5671	65	10	each	each	PRON
ejpam-5671	65	11	serving	serve	VERB
ejpam-5671	65	12	a	a	DET
ejpam-5671	65	13	specific	specific	ADJ
ejpam-5671	65	14	purpose	purpose	NOUN
ejpam-5671	65	15	in	in	ADP
ejpam-5671	65	16	presenting	present	VERB
ejpam-5671	65	17	and	and	CCONJ
ejpam-5671	65	18	analyzing	analyze	VERB
ejpam-5671	65	19	the	the	DET
ejpam-5671	65	20	research	research	NOUN
ejpam-5671	65	21	.	.	PUNCT
ejpam-5671	66	1	the	the	DET
ejpam-5671	66	2	introduction	introduction	NOUN
ejpam-5671	66	3	provides	provide	VERB
ejpam-5671	66	4	a	a	DET
ejpam-5671	66	5	general	general	ADJ
ejpam-5671	66	6	overview	overview	NOUN
ejpam-5671	66	7	of	of	ADP
ejpam-5671	66	8	the	the	DET
ejpam-5671	66	9	topic	topic	NOUN
ejpam-5671	66	10	,	,	PUNCT
ejpam-5671	66	11	serving	serve	VERB
ejpam-5671	66	12	as	as	ADP
ejpam-5671	66	13	an	an	DET
ejpam-5671	66	14	entry	entry	NOUN
ejpam-5671	66	15	point	point	NOUN
ejpam-5671	66	16	into	into	ADP
ejpam-5671	66	17	the	the	DET
ejpam-5671	66	18	study	study	NOUN
ejpam-5671	66	19	.	.	PUNCT
ejpam-5671	67	1	the	the	DET
ejpam-5671	67	2	preliminary	preliminary	ADJ
ejpam-5671	67	3	section	section	NOUN
ejpam-5671	67	4	delves	delve	VERB
ejpam-5671	67	5	deeper	deeply	ADV
ejpam-5671	67	6	into	into	ADP
ejpam-5671	67	7	the	the	DET
ejpam-5671	67	8	theoretical	theoretical	ADJ
ejpam-5671	67	9	framework	framework	NOUN
ejpam-5671	67	10	,	,	PUNCT
ejpam-5671	67	11	methodological	methodological	ADJ
ejpam-5671	67	12	approach	approach	NOUN
ejpam-5671	67	13	,	,	PUNCT
ejpam-5671	67	14	and	and	CCONJ
ejpam-5671	67	15	essential	essential	ADJ
ejpam-5671	67	16	background	background	NOUN
ejpam-5671	67	17	information	information	NOUN
ejpam-5671	67	18	,	,	PUNCT
ejpam-5671	67	19	providing	provide	VERB
ejpam-5671	67	20	context	context	NOUN
ejpam-5671	67	21	for	for	ADP
ejpam-5671	67	22	the	the	DET
ejpam-5671	67	23	subsequent	subsequent	ADJ
ejpam-5671	67	24	analysis	analysis	NOUN
ejpam-5671	67	25	.	.	PUNCT
ejpam-5671	68	1	the	the	DET
ejpam-5671	68	2	third	third	ADJ
ejpam-5671	68	3	section	section	NOUN
ejpam-5671	68	4	presents	present	VERB
ejpam-5671	68	5	and	and	CCONJ
ejpam-5671	68	6	demonstrates	demonstrate	VERB
ejpam-5671	68	7	important	important	ADJ
ejpam-5671	68	8	theorems	theorem	NOUN
ejpam-5671	68	9	that	that	PRON
ejpam-5671	68	10	establish	establish	VERB
ejpam-5671	68	11	the	the	DET
ejpam-5671	68	12	existence	existence	NOUN
ejpam-5671	68	13	of	of	ADP
ejpam-5671	68	14	solutions	solution	NOUN
ejpam-5671	68	15	to	to	ADP
ejpam-5671	68	16	equation	equation	NOUN
ejpam-5671	68	17	(	(	PUNCT
ejpam-5671	68	18	1	1	NUM
ejpam-5671	68	19	)	)	PUNCT
ejpam-5671	68	20	.	.	PUNCT
ejpam-5671	69	1	finally	finally	ADV
ejpam-5671	69	2	,	,	PUNCT
ejpam-5671	69	3	the	the	DET
ejpam-5671	69	4	conclusion	conclusion	NOUN
ejpam-5671	69	5	summarizes	summarize	VERB
ejpam-5671	69	6	the	the	DET
ejpam-5671	69	7	key	key	ADJ
ejpam-5671	69	8	findings	finding	NOUN
ejpam-5671	69	9	and	and	CCONJ
ejpam-5671	69	10	contributions	contribution	NOUN
ejpam-5671	69	11	of	of	ADP
ejpam-5671	69	12	the	the	DET
ejpam-5671	69	13	research	research	NOUN
ejpam-5671	69	14	.	.	PUNCT
ejpam-5671	70	1	s.	s.	PROPN
ejpam-5671	70	2	f.	f.	PROPN
ejpam-5671	70	3	aljurbua	aljurbua	PROPN
ejpam-5671	70	4	,	,	PUNCT
ejpam-5671	70	5	h.	h.	PROPN
ejpam-5671	70	6	a.	a.	PROPN
ejpam-5671	70	7	hammad	hammad	PROPN
ejpam-5671	70	8	,	,	PUNCT
ejpam-5671	70	9	n.	n.	PROPN
ejpam-5671	70	10	b.	b.	PROPN
ejpam-5671	70	11	almutairi	almutairi	PROPN
ejpam-5671	70	12	/	/	SYM
ejpam-5671	70	13	eur	eur	PROPN
ejpam-5671	70	14	.	.	PUNCT
ejpam-5671	71	1	j.	j.	PROPN
ejpam-5671	71	2	pure	pure	PROPN
ejpam-5671	71	3	appl	appl	PROPN
ejpam-5671	71	4	.	.	PROPN
ejpam-5671	71	5	math	math	PROPN
ejpam-5671	71	6	,	,	PUNCT
ejpam-5671	71	7	18	18	NUM
ejpam-5671	71	8	(	(	PUNCT
ejpam-5671	71	9	1	1	NUM
ejpam-5671	71	10	)	)	PUNCT
ejpam-5671	71	11	(	(	PUNCT
ejpam-5671	71	12	2025	2025	NUM
ejpam-5671	71	13	)	)	PUNCT
ejpam-5671	71	14	,	,	PUNCT
ejpam-5671	71	15	5671	5671	NUM
ejpam-5671	71	16	4	4	NUM
ejpam-5671	71	17	of	of	ADP
ejpam-5671	71	18	18	18	NUM
ejpam-5671	71	19	2	2	NUM
ejpam-5671	71	20	.	.	PUNCT
ejpam-5671	71	21	basic	basic	ADJ
ejpam-5671	71	22	facts	fact	NOUN
ejpam-5671	71	23	in	in	ADP
ejpam-5671	71	24	this	this	DET
ejpam-5671	71	25	manuscript	manuscript	NOUN
ejpam-5671	71	26	,	,	PUNCT
ejpam-5671	71	27	we	we	PRON
ejpam-5671	71	28	consider	consider	VERB
ejpam-5671	71	29	a	a	DET
ejpam-5671	71	30	=	=	X
ejpam-5671	71	31	c([0	c([0	NOUN
ejpam-5671	71	32	,	,	PUNCT
ejpam-5671	71	33	b],r	b],r	NOUN
ejpam-5671	71	34	)	)	PUNCT
ejpam-5671	71	35	is	be	AUX
ejpam-5671	71	36	the	the	DET
ejpam-5671	71	37	banach	banach	NOUN
ejpam-5671	71	38	space	space	NOUN
ejpam-5671	71	39	of	of	ADP
ejpam-5671	71	40	all	all	DET
ejpam-5671	71	41	continuous	continuous	ADJ
ejpam-5671	71	42	functions	function	NOUN
ejpam-5671	71	43	on	on	ADP
ejpam-5671	71	44	the	the	DET
ejpam-5671	71	45	interval	interval	NOUN
ejpam-5671	72	1	[	[	X
ejpam-5671	72	2	0	0	NUM
ejpam-5671	72	3	,	,	PUNCT
ejpam-5671	72	4	b	b	NOUN
ejpam-5671	72	5	]	]	X
ejpam-5671	72	6	equiped	equiped	NOUN
ejpam-5671	72	7	with	with	ADP
ejpam-5671	72	8	the	the	DET
ejpam-5671	72	9	norm	norm	NOUN
ejpam-5671	72	10	||ω||	||ω||	VERB
ejpam-5671	72	11	=	=	SYM
ejpam-5671	72	12	supρ∈[0,b	supρ∈[0,b	X
ejpam-5671	72	13	]	]	X
ejpam-5671	72	14	|ω(ρ)|	|ω(ρ)|	NOUN
ejpam-5671	72	15	,	,	PUNCT
ejpam-5671	72	16	and	and	CCONJ
ejpam-5671	72	17	l1([0	l1([0	PROPN
ejpam-5671	72	18	,	,	PUNCT
ejpam-5671	72	19	b),r+	b),r+	PROPN
ejpam-5671	72	20	)	)	PUNCT
ejpam-5671	72	21	is	be	AUX
ejpam-5671	72	22	the	the	DET
ejpam-5671	72	23	space	space	NOUN
ejpam-5671	72	24	of	of	ADP
ejpam-5671	72	25	all	all	DET
ejpam-5671	72	26	integrable	integrable	ADJ
ejpam-5671	72	27	functions	function	NOUN
ejpam-5671	72	28	on	on	ADP
ejpam-5671	72	29	the	the	DET
ejpam-5671	72	30	interval	interval	NOUN
ejpam-5671	72	31	[	[	X
ejpam-5671	72	32	0	0	NUM
ejpam-5671	72	33	,	,	PUNCT
ejpam-5671	72	34	b	b	NOUN
ejpam-5671	72	35	]	]	PUNCT
ejpam-5671	72	36	.	.	PUNCT
ejpam-5671	73	1	definition	definition	NOUN
ejpam-5671	73	2	1	1	NUM
ejpam-5671	73	3	.	.	PUNCT
ejpam-5671	74	1	[	[	X
ejpam-5671	74	2	1	1	X
ejpam-5671	74	3	]	]	PUNCT
ejpam-5671	74	4	for	for	ADP
ejpam-5671	74	5	the	the	DET
ejpam-5671	74	6	function	function	NOUN
ejpam-5671	74	7	δ	δ	PROPN
ejpam-5671	74	8	∈	∈	PROPN
ejpam-5671	74	9	l1([0	l1([0	PROPN
ejpam-5671	74	10	,	,	PUNCT
ejpam-5671	74	11	b],r+	b],r+	PROPN
ejpam-5671	74	12	)	)	PUNCT
ejpam-5671	74	13	,	,	PUNCT
ejpam-5671	74	14	the	the	DET
ejpam-5671	74	15	caputo	caputo	PROPN
ejpam-5671	74	16	fractional	fractional	PROPN
ejpam-5671	74	17	derivative	derivative	NOUN
ejpam-5671	74	18	of	of	ADP
ejpam-5671	74	19	order	order	NOUN
ejpam-5671	74	20	µ	µ	X
ejpam-5671	74	21	>	>	X
ejpam-5671	74	22	0	0	NUM
ejpam-5671	74	23	is	be	AUX
ejpam-5671	74	24	described	describe	VERB
ejpam-5671	74	25	as	as	ADP
ejpam-5671	74	26	cdµδ(ρ	cdµδ(ρ	NOUN
ejpam-5671	74	27	)	)	PUNCT
ejpam-5671	74	28	=	=	SYM
ejpam-5671	74	29	1	1	NUM
ejpam-5671	74	30	γ(β	γ(β	PROPN
ejpam-5671	74	31	−	−	PROPN
ejpam-5671	74	32	µ	µ	NUM
ejpam-5671	74	33	)	)	PUNCT
ejpam-5671	74	34	∫	∫	PROPN
ejpam-5671	75	1	ρ	ρ	PROPN
ejpam-5671	75	2	0	0	PUNCT
ejpam-5671	75	3	(	(	PUNCT
ejpam-5671	75	4	ρ−	ρ−	NOUN
ejpam-5671	75	5	ν)β−µ−1δ(β)(ν)dν	ν)β−µ−1δ(β)(ν)dν	PROPN
ejpam-5671	75	6	,	,	PUNCT
ejpam-5671	75	7	β	β	X
ejpam-5671	75	8	−	−	NOUN
ejpam-5671	75	9	1	1	NUM
ejpam-5671	75	10	<	<	X
ejpam-5671	75	11	µ	µ	X
ejpam-5671	75	12	<	<	X
ejpam-5671	75	13	β	β	X
ejpam-5671	75	14	,	,	PUNCT
ejpam-5671	75	15	β	β	X
ejpam-5671	75	16	=	=	PUNCT
ejpam-5671	76	1	[	[	X
ejpam-5671	76	2	µ	µ	X
ejpam-5671	76	3	]	]	X
ejpam-5671	76	4	+	+	NUM
ejpam-5671	76	5	1	1	NUM
ejpam-5671	76	6	,	,	PUNCT
ejpam-5671	76	7	where	where	SCONJ
ejpam-5671	76	8	[	[	X
ejpam-5671	76	9	µ	µ	X
ejpam-5671	76	10	]	]	X
ejpam-5671	76	11	is	be	AUX
ejpam-5671	76	12	the	the	DET
ejpam-5671	76	13	integer	integer	ADJ
ejpam-5671	76	14	part	part	NOUN
ejpam-5671	76	15	of	of	ADP
ejpam-5671	76	16	µ.	µ.	PROPN
ejpam-5671	76	17	definition	definition	NOUN
ejpam-5671	76	18	2	2	NUM
ejpam-5671	76	19	.	.	PUNCT
ejpam-5671	77	1	[	[	X
ejpam-5671	77	2	1	1	X
ejpam-5671	77	3	]	]	PUNCT
ejpam-5671	77	4	for	for	ADP
ejpam-5671	77	5	the	the	DET
ejpam-5671	77	6	function	function	NOUN
ejpam-5671	77	7	δ	δ	PROPN
ejpam-5671	77	8	∈	∈	PROPN
ejpam-5671	77	9	l1([0	l1([0	PROPN
ejpam-5671	77	10	,	,	PUNCT
ejpam-5671	77	11	b],r+	b],r+	PROPN
ejpam-5671	77	12	)	)	PUNCT
ejpam-5671	77	13	,	,	PUNCT
ejpam-5671	77	14	the	the	DET
ejpam-5671	77	15	riemann	riemann	PROPN
ejpam-5671	77	16	-	-	PUNCT
ejpam-5671	77	17	liouville	liouville	VERB
ejpam-5671	77	18	fractional	fractional	ADJ
ejpam-5671	77	19	integral	integral	ADJ
ejpam-5671	77	20	of	of	ADP
ejpam-5671	77	21	order	order	NOUN
ejpam-5671	77	22	µ	µ	X
ejpam-5671	77	23	>	>	X
ejpam-5671	77	24	0	0	NUM
ejpam-5671	77	25	is	be	AUX
ejpam-5671	77	26	defined	define	VERB
ejpam-5671	77	27	by	by	ADP
ejpam-5671	77	28	iµδ(ρ	iµδ(ρ	PROPN
ejpam-5671	77	29	)	)	PUNCT
ejpam-5671	77	30	=	=	NOUN
ejpam-5671	77	31	1	1	NUM
ejpam-5671	77	32	γ(µ	γ(µ	PROPN
ejpam-5671	77	33	)	)	PUNCT
ejpam-5671	77	34	∫	∫	PROPN
ejpam-5671	78	1	ρ	ρ	PROPN
ejpam-5671	78	2	0	0	PUNCT
ejpam-5671	78	3	(	(	PUNCT
ejpam-5671	78	4	ρ−	ρ−	NOUN
ejpam-5671	78	5	ν)µ−1δ(ν)dν	ν)µ−1δ(ν)dν	NOUN
ejpam-5671	78	6	.	.	PUNCT
ejpam-5671	79	1	lemma	lemma	PROPN
ejpam-5671	79	2	1	1	NUM
ejpam-5671	79	3	.	.	PUNCT
ejpam-5671	80	1	[	[	X
ejpam-5671	80	2	1	1	X
ejpam-5671	80	3	]	]	PUNCT
ejpam-5671	80	4	assume	assume	VERB
ejpam-5671	80	5	that	that	SCONJ
ejpam-5671	80	6	µ	µ	X
ejpam-5671	80	7	>	>	X
ejpam-5671	80	8	0	0	NUM
ejpam-5671	80	9	,	,	PUNCT
ejpam-5671	80	10	then	then	ADV
ejpam-5671	80	11	,	,	PUNCT
ejpam-5671	80	12	the	the	DET
ejpam-5671	80	13	solution	solution	NOUN
ejpam-5671	80	14	of	of	ADP
ejpam-5671	80	15	equation	equation	NOUN
ejpam-5671	80	16	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	80	17	)	)	PUNCT
ejpam-5671	80	18	=	=	SYM
ejpam-5671	80	19	0	0	NUM
ejpam-5671	80	20	is	be	AUX
ejpam-5671	80	21	given	give	VERB
ejpam-5671	80	22	by	by	ADP
ejpam-5671	80	23	ω(ρ	ω(ρ	NOUN
ejpam-5671	80	24	)	)	PUNCT
ejpam-5671	80	25	=	=	PUNCT
ejpam-5671	81	1	[	[	X
ejpam-5671	81	2	µ]+1∑	µ]+1∑	X
ejpam-5671	81	3	k=1	k=1	X
ejpam-5671	81	4	τkρ	τkρ	VERB
ejpam-5671	81	5	k−1	k−1	PROPN
ejpam-5671	81	6	,	,	PUNCT
ejpam-5671	81	7	(	(	PUNCT
ejpam-5671	81	8	5	5	NUM
ejpam-5671	81	9	)	)	PUNCT
ejpam-5671	81	10	where	where	SCONJ
ejpam-5671	81	11	τk	τk	ADP
ejpam-5671	81	12	∈	∈	PROPN
ejpam-5671	81	13	r	r	NOUN
ejpam-5671	81	14	,	,	PUNCT
ejpam-5671	81	15	for	for	ADP
ejpam-5671	81	16	k	k	PROPN
ejpam-5671	81	17	=	=	SYM
ejpam-5671	81	18	1	1	NUM
ejpam-5671	81	19	,	,	PUNCT
ejpam-5671	81	20	2	2	NUM
ejpam-5671	81	21	,	,	PUNCT
ejpam-5671	81	22	·	·	PUNCT
ejpam-5671	81	23	·	·	PUNCT
ejpam-5671	81	24	·	·	PUNCT
ejpam-5671	81	25	,	,	PUNCT
ejpam-5671	81	26	[	[	X
ejpam-5671	81	27	µ	µ	X
ejpam-5671	81	28	]	]	X
ejpam-5671	81	29	+	+	NUM
ejpam-5671	81	30	1	1	X
ejpam-5671	81	31	.	.	X
ejpam-5671	81	32	lemma	lemma	PROPN
ejpam-5671	81	33	2	2	X
ejpam-5671	81	34	.	.	PROPN
ejpam-5671	81	35	assume	assume	VERB
ejpam-5671	81	36	that	that	SCONJ
ejpam-5671	81	37	γ	γ	PROPN
ejpam-5671	81	38	∈	∈	PROPN
ejpam-5671	81	39	c[0	c[0	PROPN
ejpam-5671	81	40	,	,	PUNCT
ejpam-5671	81	41	b	b	NOUN
ejpam-5671	81	42	]	]	X
ejpam-5671	81	43	.	.	PUNCT
ejpam-5671	82	1	the	the	DET
ejpam-5671	82	2	solution	solution	NOUN
ejpam-5671	82	3	of	of	ADP
ejpam-5671	82	4	the	the	DET
ejpam-5671	82	5	fractional	fractional	ADJ
ejpam-5671	82	6	differential	differential	ADJ
ejpam-5671	82	7	equation	equation	NOUN
ejpam-5671	82	8	{	{	PUNCT
ejpam-5671	82	9	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	82	10	)	)	PUNCT
ejpam-5671	82	11	=	=	SYM
ejpam-5671	82	12	γ(ρ	γ(ρ	PROPN
ejpam-5671	82	13	)	)	PUNCT
ejpam-5671	82	14	,	,	PUNCT
ejpam-5671	82	15	ρ	ρ	PROPN
ejpam-5671	82	16	∈	∈	PROPN
ejpam-5671	83	1	[	[	X
ejpam-5671	83	2	0	0	NUM
ejpam-5671	83	3	,	,	PUNCT
ejpam-5671	83	4	b	b	NOUN
ejpam-5671	83	5	]	]	X
ejpam-5671	83	6	,	,	PUNCT
ejpam-5671	83	7	2	2	NUM
ejpam-5671	83	8	<	<	X
ejpam-5671	83	9	µ	µ	X
ejpam-5671	83	10	≤	≤	NOUN
ejpam-5671	83	11	3	3	NUM
ejpam-5671	83	12	,	,	PUNCT
ejpam-5671	83	13	0	0	NUM
ejpam-5671	83	14	<	<	X
ejpam-5671	83	15	θ	θ	X
ejpam-5671	83	16	<	<	X
ejpam-5671	83	17	b	b	PROPN
ejpam-5671	83	18	,	,	PUNCT
ejpam-5671	83	19	ω(θ	ω(θ	NUM
ejpam-5671	83	20	)	)	PUNCT
ejpam-5671	83	21	=	=	SYM
ejpam-5671	83	22	−ω(b	−ω(b	X
ejpam-5671	83	23	)	)	PUNCT
ejpam-5671	83	24	,	,	PUNCT
ejpam-5671	83	25	ω′	ω′	X
ejpam-5671	83	26	(	(	PUNCT
ejpam-5671	83	27	θ	θ	NOUN
ejpam-5671	83	28	)	)	PUNCT
ejpam-5671	83	29	=	=	SYM
ejpam-5671	84	1	−ω′	−ω′	NOUN
ejpam-5671	84	2	(	(	PUNCT
ejpam-5671	84	3	b	b	NOUN
ejpam-5671	84	4	)	)	PUNCT
ejpam-5671	84	5	,	,	PUNCT
ejpam-5671	84	6	cdξ+1ω(θ	cdξ+1ω(θ	NOUN
ejpam-5671	84	7	)	)	PUNCT
ejpam-5671	84	8	=	=	SYM
ejpam-5671	84	9	−cdξ+1ω(b	−cdξ+1ω(b	PROPN
ejpam-5671	84	10	)	)	PUNCT
ejpam-5671	84	11	,	,	PUNCT
ejpam-5671	84	12	0	0	PUNCT
ejpam-5671	84	13	<	<	X
ejpam-5671	84	14	ξ	ξ	X
ejpam-5671	84	15	<	<	X
ejpam-5671	84	16	1	1	NUM
ejpam-5671	84	17	,	,	PUNCT
ejpam-5671	84	18	(	(	PUNCT
ejpam-5671	84	19	6	6	NUM
ejpam-5671	84	20	)	)	PUNCT
ejpam-5671	84	21	is	be	AUX
ejpam-5671	84	22	given	give	VERB
ejpam-5671	84	23	by	by	ADP
ejpam-5671	84	24	ω(ρ	ω(ρ	NOUN
ejpam-5671	84	25	)	)	PUNCT
ejpam-5671	85	1	=	=	SYM
ejpam-5671	85	2	∫	∫	PROPN
ejpam-5671	86	1	ρ	ρ	PROPN
ejpam-5671	86	2	0	0	PUNCT
ejpam-5671	87	1	(	(	PUNCT
ejpam-5671	87	2	ρ−	ρ−	NOUN
ejpam-5671	87	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	87	4	γ(µ	γ(µ	PROPN
ejpam-5671	87	5	)	)	PUNCT
ejpam-5671	88	1	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	88	2	−	−	PROPN
ejpam-5671	88	3	1	1	NUM
ejpam-5671	88	4	2	2	NUM
ejpam-5671	88	5	(	(	PUNCT
ejpam-5671	88	6	∫	∫	PROPN
ejpam-5671	88	7	θ	θ	PROPN
ejpam-5671	88	8	0	0	PUNCT
ejpam-5671	88	9	(	(	PUNCT
ejpam-5671	88	10	θ	θ	NOUN
ejpam-5671	88	11	−	−	PROPN
ejpam-5671	88	12	ν)µ−1	ν)µ−1	PROPN
ejpam-5671	88	13	γ(µ	γ(µ	PROPN
ejpam-5671	88	14	)	)	PUNCT
ejpam-5671	88	15	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	88	16	+	+	CCONJ
ejpam-5671	88	17	∫	∫	PROPN
ejpam-5671	88	18	b	b	PROPN
ejpam-5671	88	19	0	0	NUM
ejpam-5671	88	20	(	(	PUNCT
ejpam-5671	88	21	b−	b−	PROPN
ejpam-5671	88	22	ν)µ−1	ν)µ−1	VERB
ejpam-5671	88	23	γ(µ	γ(µ	PROPN
ejpam-5671	88	24	)	)	PUNCT
ejpam-5671	88	25	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	88	26	)	)	PUNCT
ejpam-5671	89	1	+	+	CCONJ
ejpam-5671	89	2	γ(2−	γ(2−	NUM
ejpam-5671	89	3	ξ)[(θ	ξ)[(θ	NOUN
ejpam-5671	90	1	+	+	CCONJ
ejpam-5671	90	2	b)−	b)−	PROPN
ejpam-5671	90	3	2ρ	2ρ	NOUN
ejpam-5671	90	4	]	]	PUNCT
ejpam-5671	91	1	2(θ1−ξ	2(θ1−ξ	PROPN
ejpam-5671	91	2	+	+	CCONJ
ejpam-5671	91	3	b1−ξ	b1−ξ	PROPN
ejpam-5671	91	4	)	)	PUNCT
ejpam-5671	91	5	(	(	PUNCT
ejpam-5671	91	6	∫	∫	PROPN
ejpam-5671	91	7	θ	θ	PROPN
ejpam-5671	91	8	0	0	PUNCT
ejpam-5671	91	9	(	(	PUNCT
ejpam-5671	91	10	θ	θ	X
ejpam-5671	91	11	−	−	PROPN
ejpam-5671	91	12	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	91	13	γ(µ−	γ(µ−	VERB
ejpam-5671	91	14	ξ	ξ	NOUN
ejpam-5671	91	15	)	)	PUNCT
ejpam-5671	91	16	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	91	17	+	+	CCONJ
ejpam-5671	91	18	∫	∫	PROPN
ejpam-5671	91	19	b	b	PROPN
ejpam-5671	91	20	0	0	NUM
ejpam-5671	91	21	(	(	PUNCT
ejpam-5671	91	22	b−	b−	PROPN
ejpam-5671	91	23	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	91	24	γ(µ−	γ(µ−	VERB
ejpam-5671	91	25	ξ	ξ	NUM
ejpam-5671	91	26	)	)	PUNCT
ejpam-5671	91	27	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	91	28	)	)	PUNCT
ejpam-5671	92	1	+	+	CCONJ
ejpam-5671	92	2	γ(2−	γ(2−	PROPN
ejpam-5671	92	3	ξ	ξ	PROPN
ejpam-5671	92	4	)	)	PUNCT
ejpam-5671	93	1	4γ(3−	4γ(3−	NUM
ejpam-5671	93	2	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	93	3	+	+	CCONJ
ejpam-5671	93	4	b1−ξ)2	b1−ξ)2	PROPN
ejpam-5671	93	5			PROPN
ejpam-5671	93	6	4ρ(θ2−ξ	4ρ(θ2−ξ	NUM
ejpam-5671	93	7	+	+	CCONJ
ejpam-5671	93	8	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	93	9	ξ	ξ	PROPN
ejpam-5671	93	10	)	)	PUNCT
ejpam-5671	93	11	−2ρ2γ(3−	−2ρ2γ(3−	NOUN
ejpam-5671	93	12	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	93	13	+	+	CCONJ
ejpam-5671	93	14	b1−ξ	b1−ξ	PROPN
ejpam-5671	93	15	)	)	PUNCT
ejpam-5671	93	16	−2(θ	−2(θ	PUNCT
ejpam-5671	94	1	+	+	CCONJ
ejpam-5671	94	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	94	3	+	+	CCONJ
ejpam-5671	94	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	94	5	ξ	ξ	PROPN
ejpam-5671	94	6	)	)	PUNCT
ejpam-5671	95	1	+	+	PROPN
ejpam-5671	95	2	(	(	PUNCT
ejpam-5671	95	3	θ2	θ2	ADV
ejpam-5671	95	4	+	+	CCONJ
ejpam-5671	95	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	95	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	95	7	+	+	CCONJ
ejpam-5671	95	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	95	9	)	)	PUNCT
ejpam-5671	95	10			NOUN
ejpam-5671	95	11	×	×	NOUN
ejpam-5671	95	12	(	(	PUNCT
ejpam-5671	95	13	∫	∫	PROPN
ejpam-5671	95	14	θ	θ	PROPN
ejpam-5671	95	15	0	0	PUNCT
ejpam-5671	95	16	(	(	PUNCT
ejpam-5671	95	17	θ	θ	NOUN
ejpam-5671	95	18	−	−	NOUN
ejpam-5671	95	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	95	20	γ(µ−	γ(µ−	VERB
ejpam-5671	95	21	ξ	ξ	NOUN
ejpam-5671	95	22	−	−	NOUN
ejpam-5671	95	23	1	1	NUM
ejpam-5671	95	24	)	)	PUNCT
ejpam-5671	95	25	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	95	26	+	+	CCONJ
ejpam-5671	95	27	∫	∫	PROPN
ejpam-5671	95	28	b	b	PROPN
ejpam-5671	95	29	0	0	NUM
ejpam-5671	95	30	(	(	PUNCT
ejpam-5671	95	31	b−	b−	NOUN
ejpam-5671	95	32	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	95	33	γ(µ−	γ(µ−	VERB
ejpam-5671	95	34	ξ	ξ	PRON
ejpam-5671	95	35	−	−	NOUN
ejpam-5671	95	36	1	1	NUM
ejpam-5671	95	37	)	)	PUNCT
ejpam-5671	95	38	γ(ν)dν	γ(ν)dν	ADP
ejpam-5671	95	39	)	)	PUNCT
ejpam-5671	95	40	.	.	PUNCT
ejpam-5671	96	1	(	(	PUNCT
ejpam-5671	96	2	7	7	X
ejpam-5671	96	3	)	)	PUNCT
ejpam-5671	96	4	s.	s.	PROPN
ejpam-5671	96	5	f.	f.	PROPN
ejpam-5671	96	6	aljurbua	aljurbua	PROPN
ejpam-5671	96	7	,	,	PUNCT
ejpam-5671	96	8	h.	h.	PROPN
ejpam-5671	96	9	a.	a.	PROPN
ejpam-5671	96	10	hammad	hammad	PROPN
ejpam-5671	96	11	,	,	PUNCT
ejpam-5671	96	12	n.	n.	PROPN
ejpam-5671	96	13	b.	b.	PROPN
ejpam-5671	96	14	almutairi	almutairi	PROPN
ejpam-5671	96	15	/	/	SYM
ejpam-5671	96	16	eur	eur	PROPN
ejpam-5671	96	17	.	.	PUNCT
ejpam-5671	97	1	j.	j.	PROPN
ejpam-5671	97	2	pure	pure	PROPN
ejpam-5671	97	3	appl	appl	PROPN
ejpam-5671	97	4	.	.	PROPN
ejpam-5671	97	5	math	math	PROPN
ejpam-5671	97	6	,	,	PUNCT
ejpam-5671	97	7	18	18	NUM
ejpam-5671	97	8	(	(	PUNCT
ejpam-5671	97	9	1	1	NUM
ejpam-5671	97	10	)	)	PUNCT
ejpam-5671	97	11	(	(	PUNCT
ejpam-5671	97	12	2025	2025	NUM
ejpam-5671	97	13	)	)	PUNCT
ejpam-5671	97	14	,	,	PUNCT
ejpam-5671	97	15	5671	5671	NUM
ejpam-5671	97	16	5	5	NUM
ejpam-5671	97	17	of	of	ADP
ejpam-5671	97	18	18	18	NUM
ejpam-5671	97	19	proof	proof	NOUN
ejpam-5671	97	20	.	.	PUNCT
ejpam-5671	98	1	by	by	ADP
ejpam-5671	98	2	lemma	lemma	PROPN
ejpam-5671	98	3	1	1	NUM
ejpam-5671	98	4	there	there	PRON
ejpam-5671	98	5	are	be	VERB
ejpam-5671	98	6	constants	constant	NOUN
ejpam-5671	98	7	τj	τj	ADP
ejpam-5671	98	8	∈	∈	PROPN
ejpam-5671	98	9	r	r	NOUN
ejpam-5671	98	10	,	,	PUNCT
ejpam-5671	98	11	for	for	ADP
ejpam-5671	98	12	j	j	PROPN
ejpam-5671	98	13	=	=	SYM
ejpam-5671	98	14	1	1	NUM
ejpam-5671	98	15	,	,	PUNCT
ejpam-5671	98	16	2	2	NUM
ejpam-5671	98	17	,	,	PUNCT
ejpam-5671	98	18	3	3	NUM
ejpam-5671	98	19	such	such	ADJ
ejpam-5671	98	20	that	that	DET
ejpam-5671	98	21	ω(ρ	ω(ρ	NOUN
ejpam-5671	98	22	)	)	PUNCT
ejpam-5671	98	23	=	=	PUNCT
ejpam-5671	99	1	iµ	iµ	PROPN
ejpam-5671	99	2	δ(ρ)−	δ(ρ)−	PROPN
ejpam-5671	99	3	τ1	τ1	ADP
ejpam-5671	99	4	−	−	PROPN
ejpam-5671	99	5	τ2ρ−	τ2ρ−	PROPN
ejpam-5671	99	6	τ3ρ	τ3ρ	PROPN
ejpam-5671	99	7	2	2	NUM
ejpam-5671	99	8	=	=	SYM
ejpam-5671	99	9	∫	∫	PROPN
ejpam-5671	99	10	ρ	ρ	PROPN
ejpam-5671	99	11	0	0	PUNCT
ejpam-5671	100	1	(	(	PUNCT
ejpam-5671	100	2	ρ−	ρ−	NOUN
ejpam-5671	100	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	100	4	γ(µ	γ(µ	PROPN
ejpam-5671	100	5	)	)	PUNCT
ejpam-5671	101	1	δ(ν)dν	δ(ν)dν	CCONJ
ejpam-5671	101	2	−	−	PROPN
ejpam-5671	101	3	τ1	τ1	NOUN
ejpam-5671	101	4	−	−	PROPN
ejpam-5671	101	5	τ2ρ−	τ2ρ−	NOUN
ejpam-5671	101	6	τ3ρ	τ3ρ	PROPN
ejpam-5671	101	7	2	2	NUM
ejpam-5671	101	8	.	.	PUNCT
ejpam-5671	102	1	(	(	PUNCT
ejpam-5671	102	2	8)	8)	NUM
ejpam-5671	102	3	applying	apply	VERB
ejpam-5671	102	4	the	the	DET
ejpam-5671	102	5	conditions	condition	NOUN
ejpam-5671	102	6	(	(	PUNCT
ejpam-5671	102	7	6	6	NUM
ejpam-5671	102	8	)	)	PUNCT
ejpam-5671	102	9	,	,	PUNCT
ejpam-5671	102	10	we	we	PRON
ejpam-5671	102	11	have	have	VERB
ejpam-5671	102	12	τ1	τ1	NOUN
ejpam-5671	102	13	=	=	SYM
ejpam-5671	102	14	1	1	NUM
ejpam-5671	102	15	2	2	NUM
ejpam-5671	102	16	(	(	PUNCT
ejpam-5671	102	17	∫	∫	PROPN
ejpam-5671	102	18	θ	θ	PROPN
ejpam-5671	102	19	0	0	PUNCT
ejpam-5671	103	1	(	(	PUNCT
ejpam-5671	103	2	θ	θ	NOUN
ejpam-5671	103	3	−	−	PROPN
ejpam-5671	103	4	ν)µ−1	ν)µ−1	X
ejpam-5671	103	5	γ(µ	γ(µ	PROPN
ejpam-5671	103	6	)	)	PUNCT
ejpam-5671	103	7	δ(ν)dν	δ(ν)dν	PART
ejpam-5671	104	1	+	+	NUM
ejpam-5671	104	2	∫	∫	PROPN
ejpam-5671	104	3	b	b	PROPN
ejpam-5671	104	4	0	0	NUM
ejpam-5671	104	5	(	(	PUNCT
ejpam-5671	104	6	b−	b−	PROPN
ejpam-5671	104	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	104	8	γ(µ	γ(µ	PROPN
ejpam-5671	104	9	)	)	PUNCT
ejpam-5671	104	10	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	104	11	)	)	PUNCT
ejpam-5671	104	12	−(θ	−(θ	NOUN
ejpam-5671	105	1	+	+	CCONJ
ejpam-5671	105	2	b)γ(2−	b)γ(2−	PROPN
ejpam-5671	105	3	ξ	ξ	PROPN
ejpam-5671	105	4	)	)	PUNCT
ejpam-5671	105	5	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	106	1	+	+	CCONJ
ejpam-5671	106	2	b1−ξ	b1−ξ	PROPN
ejpam-5671	106	3	)	)	PUNCT
ejpam-5671	106	4	(	(	PUNCT
ejpam-5671	106	5	∫	∫	PROPN
ejpam-5671	106	6	θ	θ	PROPN
ejpam-5671	106	7	0	0	PUNCT
ejpam-5671	106	8	(	(	PUNCT
ejpam-5671	106	9	θ	θ	X
ejpam-5671	106	10	−	−	PROPN
ejpam-5671	106	11	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	106	12	γ(µ−	γ(µ−	VERB
ejpam-5671	106	13	ξ	ξ	NUM
ejpam-5671	106	14	)	)	PUNCT
ejpam-5671	106	15	δ(ν)dν	δ(ν)dν	NOUN
ejpam-5671	107	1	+	+	NUM
ejpam-5671	107	2	∫	∫	PROPN
ejpam-5671	107	3	b	b	PROPN
ejpam-5671	107	4	0	0	NUM
ejpam-5671	107	5	(	(	PUNCT
ejpam-5671	107	6	b−	b−	PROPN
ejpam-5671	107	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	107	8	γ(µ−	γ(µ−	VERB
ejpam-5671	107	9	ξ	ξ	NUM
ejpam-5671	107	10	)	)	PUNCT
ejpam-5671	107	11	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	107	12	)	)	PUNCT
ejpam-5671	108	1	+	+	CCONJ
ejpam-5671	108	2	γ(2−	γ(2−	PROPN
ejpam-5671	108	3	ξ	ξ	PROPN
ejpam-5671	108	4	)	)	PUNCT
ejpam-5671	108	5	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	109	1	+	+	CCONJ
ejpam-5671	109	2	b1−ξ	b1−ξ	PROPN
ejpam-5671	109	3	)	)	PUNCT
ejpam-5671	109	4	(	(	PUNCT
ejpam-5671	109	5	(	(	PUNCT
ejpam-5671	109	6	θ	θ	NOUN
ejpam-5671	109	7	+	+	CCONJ
ejpam-5671	109	8	b)(θ2−ξ	b)(θ2−ξ	PROPN
ejpam-5671	109	9	+	+	CCONJ
ejpam-5671	109	10	b2−ξ)(γ(2−	b2−ξ)(γ(2−	NOUN
ejpam-5671	109	11	ξ	ξ	X
ejpam-5671	109	12	)	)	PUNCT
ejpam-5671	109	13	)	)	PUNCT
ejpam-5671	110	1	γ(3−	γ(3−	ADP
ejpam-5671	110	2	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	110	3	+	+	PROPN
ejpam-5671	110	4	b1−ξ	b1−ξ	PROPN
ejpam-5671	110	5	)	)	PUNCT
ejpam-5671	111	1	−	−	PROPN
ejpam-5671	112	1	(	(	PUNCT
ejpam-5671	112	2	θ2	θ2	NOUN
ejpam-5671	112	3	+	+	CCONJ
ejpam-5671	112	4	b2	b2	NOUN
ejpam-5671	112	5	)	)	PUNCT
ejpam-5671	112	6	2	2	NUM
ejpam-5671	112	7	)	)	PUNCT
ejpam-5671	112	8	×	×	NOUN
ejpam-5671	112	9	(	(	PUNCT
ejpam-5671	112	10	∫	∫	PROPN
ejpam-5671	112	11	θ	θ	PROPN
ejpam-5671	112	12	0	0	PUNCT
ejpam-5671	112	13	(	(	PUNCT
ejpam-5671	112	14	θ	θ	NOUN
ejpam-5671	112	15	−	−	NOUN
ejpam-5671	112	16	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	112	17	γ(µ−	γ(µ−	VERB
ejpam-5671	112	18	ξ	ξ	PRON
ejpam-5671	112	19	−	−	NOUN
ejpam-5671	112	20	1	1	NUM
ejpam-5671	112	21	)	)	PUNCT
ejpam-5671	112	22	δ(ν)dν	δ(ν)dν	NOUN
ejpam-5671	113	1	+	+	NUM
ejpam-5671	113	2	∫	∫	PROPN
ejpam-5671	113	3	b	b	PROPN
ejpam-5671	113	4	0	0	NUM
ejpam-5671	113	5	(	(	PUNCT
ejpam-5671	113	6	b−	b−	NOUN
ejpam-5671	113	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	113	8	γ(µ−	γ(µ−	VERB
ejpam-5671	113	9	ξ	ξ	PRON
ejpam-5671	113	10	−	−	NOUN
ejpam-5671	113	11	1	1	NUM
ejpam-5671	113	12	)	)	PUNCT
ejpam-5671	113	13	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	113	14	)	)	PUNCT
ejpam-5671	113	15	,	,	PUNCT
ejpam-5671	113	16	τ2	τ2	NOUN
ejpam-5671	113	17	=	=	PUNCT
ejpam-5671	113	18	γ(2−	γ(2−	PROPN
ejpam-5671	113	19	ξ	ξ	PROPN
ejpam-5671	113	20	)	)	PUNCT
ejpam-5671	113	21	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	113	22	+	+	PROPN
ejpam-5671	113	23	b1−ξ	b1−ξ	PROPN
ejpam-5671	113	24	(	(	PUNCT
ejpam-5671	113	25	∫	∫	PROPN
ejpam-5671	113	26	θ	θ	PROPN
ejpam-5671	113	27	0	0	PUNCT
ejpam-5671	113	28	(	(	PUNCT
ejpam-5671	113	29	θ	θ	X
ejpam-5671	113	30	−	−	PROPN
ejpam-5671	113	31	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	113	32	γ(µ−	γ(µ−	VERB
ejpam-5671	113	33	ξ	ξ	NUM
ejpam-5671	113	34	)	)	PUNCT
ejpam-5671	113	35	δ(ν)dν	δ(ν)dν	NOUN
ejpam-5671	114	1	+	+	NUM
ejpam-5671	114	2	∫	∫	PROPN
ejpam-5671	114	3	b	b	PROPN
ejpam-5671	114	4	0	0	NUM
ejpam-5671	114	5	(	(	PUNCT
ejpam-5671	114	6	b−	b−	PROPN
ejpam-5671	114	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	114	8	γ(µ−	γ(µ−	VERB
ejpam-5671	114	9	ξ	ξ	NUM
ejpam-5671	114	10	)	)	PUNCT
ejpam-5671	114	11	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	114	12	)	)	PUNCT
ejpam-5671	114	13	−(θ2−ξ	−(θ2−ξ	NOUN
ejpam-5671	114	14	+	+	CCONJ
ejpam-5671	114	15	b2−ξ)(γ(2−	b2−ξ)(γ(2−	NOUN
ejpam-5671	114	16	ξ))2	ξ))2	NOUN
ejpam-5671	114	17	γ(3−	γ(3−	ADP
ejpam-5671	114	18	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	114	19	+	+	CCONJ
ejpam-5671	114	20	b1−ξ)2	b1−ξ)2	PROPN
ejpam-5671	114	21	(	(	PUNCT
ejpam-5671	114	22	∫	∫	PROPN
ejpam-5671	114	23	θ	θ	PROPN
ejpam-5671	114	24	0	0	PUNCT
ejpam-5671	115	1	(	(	PUNCT
ejpam-5671	115	2	θ	θ	NOUN
ejpam-5671	115	3	−	−	NOUN
ejpam-5671	115	4	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	115	5	γ(µ−	γ(µ−	VERB
ejpam-5671	115	6	ξ	ξ	PRON
ejpam-5671	115	7	−	−	NOUN
ejpam-5671	115	8	1	1	NUM
ejpam-5671	115	9	)	)	PUNCT
ejpam-5671	115	10	δ(ν)dν	δ(ν)dν	NOUN
ejpam-5671	116	1	+	+	NUM
ejpam-5671	116	2	∫	∫	PROPN
ejpam-5671	116	3	b	b	PROPN
ejpam-5671	116	4	0	0	NUM
ejpam-5671	116	5	(	(	PUNCT
ejpam-5671	116	6	b−	b−	NOUN
ejpam-5671	116	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	116	8	γ(µ−	γ(µ−	VERB
ejpam-5671	116	9	ξ	ξ	PRON
ejpam-5671	116	10	−	−	NOUN
ejpam-5671	116	11	1	1	NUM
ejpam-5671	116	12	)	)	PUNCT
ejpam-5671	116	13	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	116	14	)	)	PUNCT
ejpam-5671	116	15	,	,	PUNCT
ejpam-5671	116	16	and	and	CCONJ
ejpam-5671	116	17	τ3	τ3	NOUN
ejpam-5671	116	18	=	=	PUNCT
ejpam-5671	116	19	γ(2−	γ(2−	PROPN
ejpam-5671	116	20	ξ	ξ	PROPN
ejpam-5671	116	21	)	)	PUNCT
ejpam-5671	116	22	2(b1−ξ	2(b1−ξ	NUM
ejpam-5671	117	1	+	+	CCONJ
ejpam-5671	117	2	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	117	3	)	)	PUNCT
ejpam-5671	117	4	(	(	PUNCT
ejpam-5671	117	5	∫	∫	PROPN
ejpam-5671	117	6	θ	θ	PROPN
ejpam-5671	117	7	0	0	PUNCT
ejpam-5671	117	8	(	(	PUNCT
ejpam-5671	117	9	θ	θ	NOUN
ejpam-5671	117	10	−	−	NOUN
ejpam-5671	117	11	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	117	12	γ(µ−	γ(µ−	VERB
ejpam-5671	117	13	ξ	ξ	PRON
ejpam-5671	117	14	−	−	NOUN
ejpam-5671	117	15	1	1	NUM
ejpam-5671	117	16	)	)	PUNCT
ejpam-5671	117	17	δ(ν)dν	δ(ν)dν	NOUN
ejpam-5671	118	1	+	+	NUM
ejpam-5671	118	2	∫	∫	PROPN
ejpam-5671	118	3	b	b	PROPN
ejpam-5671	118	4	0	0	NUM
ejpam-5671	118	5	(	(	PUNCT
ejpam-5671	118	6	b−	b−	NOUN
ejpam-5671	118	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	118	8	γ(µ−	γ(µ−	VERB
ejpam-5671	118	9	ξ	ξ	PRON
ejpam-5671	118	10	−	−	NOUN
ejpam-5671	118	11	1	1	NUM
ejpam-5671	118	12	)	)	PUNCT
ejpam-5671	118	13	δ(ν)dν	δ(ν)dν	NUM
ejpam-5671	118	14	)	)	PUNCT
ejpam-5671	118	15	.	.	PUNCT
ejpam-5671	119	1	substituting	substitute	VERB
ejpam-5671	119	2	the	the	DET
ejpam-5671	119	3	values	value	NOUN
ejpam-5671	119	4	of	of	ADP
ejpam-5671	119	5	τ1	τ1	NOUN
ejpam-5671	119	6	,	,	PUNCT
ejpam-5671	119	7	τ2	τ2	NOUN
ejpam-5671	119	8	and	and	CCONJ
ejpam-5671	119	9	τ3	τ3	NOUN
ejpam-5671	119	10	in	in	ADP
ejpam-5671	119	11	(	(	PUNCT
ejpam-5671	119	12	8)	8)	NUM
ejpam-5671	119	13	,	,	PUNCT
ejpam-5671	119	14	we	we	PRON
ejpam-5671	119	15	obtain	obtain	VERB
ejpam-5671	119	16	the	the	DET
ejpam-5671	119	17	result	result	NOUN
ejpam-5671	119	18	.	.	PUNCT
ejpam-5671	120	1	remark	remark	NOUN
ejpam-5671	120	2	1	1	NUM
ejpam-5671	120	3	.	.	PUNCT
ejpam-5671	121	1	it	it	PRON
ejpam-5671	121	2	’s	’	VERB
ejpam-5671	121	3	important	important	ADJ
ejpam-5671	121	4	to	to	PART
ejpam-5671	121	5	note	note	VERB
ejpam-5671	121	6	that	that	SCONJ
ejpam-5671	121	7	when	when	SCONJ
ejpam-5671	121	8	a	a	DET
ejpam-5671	121	9	equals	equal	VERB
ejpam-5671	121	10	0	0	NUM
ejpam-5671	121	11	,	,	PUNCT
ejpam-5671	121	12	the	the	DET
ejpam-5671	121	13	first	first	ADJ
ejpam-5671	121	14	three	three	NUM
ejpam-5671	121	15	terms	term	NOUN
ejpam-5671	121	16	in	in	ADP
ejpam-5671	121	17	equation	equation	NOUN
ejpam-5671	121	18	(	(	PUNCT
ejpam-5671	121	19	7	7	X
ejpam-5671	121	20	)	)	PUNCT
ejpam-5671	121	21	represent	represent	VERB
ejpam-5671	121	22	the	the	DET
ejpam-5671	121	23	solution	solution	NOUN
ejpam-5671	121	24	to	to	ADP
ejpam-5671	121	25	the	the	DET
ejpam-5671	121	26	fractional	fractional	ADJ
ejpam-5671	121	27	problem	problem	NOUN
ejpam-5671	121	28	of	of	ADP
ejpam-5671	121	29	order	order	NOUN
ejpam-5671	121	30	µ	µ	X
ejpam-5671	121	31	∈	∈	NOUN
ejpam-5671	121	32	(	(	PUNCT
ejpam-5671	121	33	1	1	NUM
ejpam-5671	121	34	,	,	PUNCT
ejpam-5671	121	35	2	2	NUM
ejpam-5671	121	36	]	]	PUNCT
ejpam-5671	122	1	[	[	X
ejpam-5671	122	2	3	3	NUM
ejpam-5671	122	3	]	]	PUNCT
ejpam-5671	122	4	.	.	PUNCT
ejpam-5671	123	1	additionally	additionally	ADV
ejpam-5671	123	2	,	,	PUNCT
ejpam-5671	123	3	two	two	NUM
ejpam-5671	123	4	more	more	ADJ
ejpam-5671	123	5	terms	term	NOUN
ejpam-5671	123	6	are	be	AUX
ejpam-5671	123	7	added	add	VERB
ejpam-5671	123	8	to	to	ADP
ejpam-5671	123	9	the	the	DET
ejpam-5671	123	10	solution	solution	NOUN
ejpam-5671	123	11	when	when	SCONJ
ejpam-5671	123	12	the	the	DET
ejpam-5671	123	13	order	order	NOUN
ejpam-5671	123	14	µ	µ	NOUN
ejpam-5671	123	15	is	be	AUX
ejpam-5671	123	16	increased	increase	VERB
ejpam-5671	123	17	to	to	ADP
ejpam-5671	123	18	a	a	DET
ejpam-5671	123	19	number	number	NOUN
ejpam-5671	123	20	in	in	ADP
ejpam-5671	123	21	the	the	DET
ejpam-5671	123	22	interval	interval	NOUN
ejpam-5671	123	23	(	(	PUNCT
ejpam-5671	123	24	2	2	NUM
ejpam-5671	123	25	,	,	PUNCT
ejpam-5671	123	26	3	3	NUM
ejpam-5671	123	27	]	]	PUNCT
ejpam-5671	123	28	,	,	PUNCT
ejpam-5671	123	29	as	as	SCONJ
ejpam-5671	123	30	demonstrated	demonstrate	VERB
ejpam-5671	123	31	in	in	ADP
ejpam-5671	123	32	lemma	lemma	PROPN
ejpam-5671	123	33	2	2	NUM
ejpam-5671	123	34	.	.	NOUN
ejpam-5671	123	35	remark	remark	NOUN
ejpam-5671	123	36	2	2	NUM
ejpam-5671	123	37	.	.	PUNCT
ejpam-5671	124	1	the	the	DET
ejpam-5671	124	2	solution	solution	NOUN
ejpam-5671	124	3	of	of	ADP
ejpam-5671	124	4	the	the	DET
ejpam-5671	124	5	fractional	fractional	ADJ
ejpam-5671	124	6	problem	problem	NOUN
ejpam-5671	124	7	{	{	PUNCT
ejpam-5671	124	8	cdµω(ρ	cdµω(ρ	NOUN
ejpam-5671	124	9	)	)	PUNCT
ejpam-5671	124	10	=	=	SYM
ejpam-5671	124	11	u(ρ	u(ρ	PROPN
ejpam-5671	124	12	)	)	PUNCT
ejpam-5671	124	13	,	,	PUNCT
ejpam-5671	124	14	ρ	ρ	PROPN
ejpam-5671	124	15	∈	∈	PROPN
ejpam-5671	125	1	[	[	X
ejpam-5671	125	2	0	0	NUM
ejpam-5671	125	3	,	,	PUNCT
ejpam-5671	125	4	b	b	NOUN
ejpam-5671	125	5	]	]	X
ejpam-5671	125	6	,	,	PUNCT
ejpam-5671	125	7	2	2	NUM
ejpam-5671	125	8	<	<	X
ejpam-5671	125	9	µ	µ	X
ejpam-5671	125	10	≤	≤	NOUN
ejpam-5671	125	11	3	3	NUM
ejpam-5671	125	12	,	,	PUNCT
ejpam-5671	125	13	ω(0	ω(0	PROPN
ejpam-5671	125	14	)	)	PUNCT
ejpam-5671	125	15	=	=	SYM
ejpam-5671	125	16	−ω(b	−ω(b	X
ejpam-5671	125	17	)	)	PUNCT
ejpam-5671	125	18	,	,	PUNCT
ejpam-5671	125	19	ω′	ω′	X
ejpam-5671	125	20	(	(	PUNCT
ejpam-5671	125	21	0	0	NUM
ejpam-5671	125	22	)	)	PUNCT
ejpam-5671	125	23	=	=	SYM
ejpam-5671	126	1	−ρ′	−ρ′	NUM
ejpam-5671	126	2	(	(	PUNCT
ejpam-5671	126	3	b	b	NOUN
ejpam-5671	126	4	)	)	PUNCT
ejpam-5671	126	5	,	,	PUNCT
ejpam-5671	126	6	ω	ω	X
ejpam-5671	127	1	′′	′′	PROPN
ejpam-5671	127	2	(	(	PUNCT
ejpam-5671	127	3	0	0	NUM
ejpam-5671	127	4	)	)	PUNCT
ejpam-5671	127	5	=	=	SYM
ejpam-5671	127	6	−ω′′	−ω′′	X
ejpam-5671	127	7	(	(	PUNCT
ejpam-5671	127	8	ρ	ρ	PROPN
ejpam-5671	127	9	)	)	PUNCT
ejpam-5671	127	10	,	,	PUNCT
ejpam-5671	127	11	(	(	PUNCT
ejpam-5671	127	12	9	9	X
ejpam-5671	127	13	)	)	PUNCT
ejpam-5671	127	14	is	be	AUX
ejpam-5671	127	15	equivalent	equivalent	ADJ
ejpam-5671	127	16	to	to	ADP
ejpam-5671	127	17	ω(ρ	ω(ρ	NUM
ejpam-5671	127	18	)	)	PUNCT
ejpam-5671	128	1	=	=	SYM
ejpam-5671	128	2	∫	∫	PROPN
ejpam-5671	129	1	ρ	ρ	PROPN
ejpam-5671	129	2	0	0	PUNCT
ejpam-5671	130	1	(	(	PUNCT
ejpam-5671	130	2	ρ−	ρ−	NOUN
ejpam-5671	130	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	130	4	γ(µ	γ(µ	PROPN
ejpam-5671	130	5	)	)	PUNCT
ejpam-5671	131	1	u(ν)dν	u(ν)dν	PART
ejpam-5671	131	2	−	−	NOUN
ejpam-5671	131	3	1	1	NUM
ejpam-5671	131	4	2	2	NUM
ejpam-5671	131	5	∫	∫	NOUN
ejpam-5671	131	6	b	b	SYM
ejpam-5671	131	7	0	0	NUM
ejpam-5671	131	8	(	(	PUNCT
ejpam-5671	131	9	b−	b−	PROPN
ejpam-5671	131	10	ν)µ−1	ν)µ−1	VERB
ejpam-5671	131	11	γ(µ	γ(µ	PROPN
ejpam-5671	131	12	)	)	PUNCT
ejpam-5671	132	1	u(ν)dν	u(ν)dν	ADP
ejpam-5671	133	1	+	+	NUM
ejpam-5671	133	2	b−	b−	NOUN
ejpam-5671	133	3	2ρ	2ρ	NOUN
ejpam-5671	133	4	4	4	NUM
ejpam-5671	133	5	∫	∫	PROPN
ejpam-5671	133	6	b	b	PROPN
ejpam-5671	133	7	0	0	NUM
ejpam-5671	134	1	(	(	PUNCT
ejpam-5671	134	2	b−	b−	NOUN
ejpam-5671	134	3	ν)µ−2	ν)µ−2	PROPN
ejpam-5671	134	4	γ(µ−	γ(µ−	VERB
ejpam-5671	134	5	1	1	NUM
ejpam-5671	134	6	)	)	PUNCT
ejpam-5671	134	7	u(ν)dν	u(ν)dν	NOUN
ejpam-5671	135	1	+	+	CCONJ
ejpam-5671	135	2	ρ(b−	ρ(b−	PROPN
ejpam-5671	135	3	ρ	ρ	NOUN
ejpam-5671	135	4	)	)	PUNCT
ejpam-5671	135	5	4	4	NUM
ejpam-5671	135	6	∫	∫	PROPN
ejpam-5671	135	7	b	b	SYM
ejpam-5671	135	8	0	0	NUM
ejpam-5671	135	9	(	(	PUNCT
ejpam-5671	135	10	b−	b−	NOUN
ejpam-5671	135	11	ν)µ−3	ν)µ−3	X
ejpam-5671	135	12	γ(µ−	γ(µ−	PROPN
ejpam-5671	135	13	2	2	NUM
ejpam-5671	135	14	)	)	PUNCT
ejpam-5671	135	15	u(ν)dν	u(ν)dν	NOUN
ejpam-5671	135	16	,	,	PUNCT
ejpam-5671	135	17	(	(	PUNCT
ejpam-5671	135	18	10	10	NUM
ejpam-5671	135	19	)	)	PUNCT
ejpam-5671	135	20	s.	s.	PROPN
ejpam-5671	135	21	f.	f.	PROPN
ejpam-5671	135	22	aljurbua	aljurbua	PROPN
ejpam-5671	135	23	,	,	PUNCT
ejpam-5671	135	24	h.	h.	PROPN
ejpam-5671	135	25	a.	a.	PROPN
ejpam-5671	135	26	hammad	hammad	PROPN
ejpam-5671	135	27	,	,	PUNCT
ejpam-5671	135	28	n.	n.	PROPN
ejpam-5671	135	29	b.	b.	PROPN
ejpam-5671	135	30	almutairi	almutairi	PROPN
ejpam-5671	135	31	/	/	SYM
ejpam-5671	135	32	eur	eur	PROPN
ejpam-5671	135	33	.	.	PUNCT
ejpam-5671	136	1	j.	j.	PROPN
ejpam-5671	136	2	pure	pure	PROPN
ejpam-5671	136	3	appl	appl	PROPN
ejpam-5671	136	4	.	.	PROPN
ejpam-5671	136	5	math	math	PROPN
ejpam-5671	136	6	,	,	PUNCT
ejpam-5671	136	7	18	18	NUM
ejpam-5671	136	8	(	(	PUNCT
ejpam-5671	136	9	1	1	NUM
ejpam-5671	136	10	)	)	PUNCT
ejpam-5671	136	11	(	(	PUNCT
ejpam-5671	136	12	2025	2025	NUM
ejpam-5671	136	13	)	)	PUNCT
ejpam-5671	136	14	,	,	PUNCT
ejpam-5671	136	15	5671	5671	NUM
ejpam-5671	136	16	6	6	NUM
ejpam-5671	136	17	of	of	ADP
ejpam-5671	136	18	18	18	NUM
ejpam-5671	136	19	which	which	PRON
ejpam-5671	136	20	is	be	AUX
ejpam-5671	136	21	given	give	VERB
ejpam-5671	136	22	in	in	ADP
ejpam-5671	136	23	[	[	X
ejpam-5671	136	24	4	4	NUM
ejpam-5671	136	25	]	]	PUNCT
ejpam-5671	136	26	.	.	PUNCT
ejpam-5671	137	1	observing	observe	VERB
ejpam-5671	137	2	that	that	SCONJ
ejpam-5671	137	3	the	the	DET
ejpam-5671	137	4	solutions	solution	NOUN
ejpam-5671	137	5	(	(	PUNCT
ejpam-5671	137	6	7	7	NUM
ejpam-5671	137	7	)	)	PUNCT
ejpam-5671	137	8	and	and	CCONJ
ejpam-5671	137	9	(	(	PUNCT
ejpam-5671	137	10	10	10	NUM
ejpam-5671	137	11	)	)	PUNCT
ejpam-5671	137	12	,	,	PUNCT
ejpam-5671	137	13	we	we	PRON
ejpam-5671	137	14	notice	notice	VERB
ejpam-5671	137	15	that	that	SCONJ
ejpam-5671	137	16	there	there	PRON
ejpam-5671	137	17	are	be	VERB
ejpam-5671	137	18	additional	additional	ADJ
ejpam-5671	137	19	terms	term	NOUN
ejpam-5671	137	20	in	in	ADP
ejpam-5671	137	21	7	7	NUM
ejpam-5671	137	22	.	.	PUNCT
ejpam-5671	138	1	moreover	moreover	ADV
ejpam-5671	138	2	,	,	PUNCT
ejpam-5671	138	3	when	when	SCONJ
ejpam-5671	138	4	ξ	ξ	X
ejpam-5671	138	5	−→	−→	NOUN
ejpam-5671	138	6	1−	1−	NUM
ejpam-5671	138	7	,	,	PUNCT
ejpam-5671	138	8	it	it	PRON
ejpam-5671	138	9	will	will	AUX
ejpam-5671	138	10	be	be	AUX
ejpam-5671	138	11	the	the	DET
ejpam-5671	138	12	solution	solution	NOUN
ejpam-5671	138	13	of	of	ADP
ejpam-5671	138	14	the	the	DET
ejpam-5671	138	15	nonlocal	nonlocal	ADJ
ejpam-5671	138	16	antiperiodic	antiperiodic	ADJ
ejpam-5671	138	17	boundary	boundary	ADJ
ejpam-5671	138	18	condition	condition	NOUN
ejpam-5671	138	19	of	of	ADP
ejpam-5671	138	20	order	order	NOUN
ejpam-5671	138	21	µ	µ	X
ejpam-5671	138	22	∈	∈	NOUN
ejpam-5671	138	23	(	(	PUNCT
ejpam-5671	138	24	2	2	NUM
ejpam-5671	138	25	,	,	PUNCT
ejpam-5671	138	26	3	3	NUM
ejpam-5671	138	27	]	]	PUNCT
ejpam-5671	138	28	.	.	PUNCT
ejpam-5671	139	1	if	if	SCONJ
ejpam-5671	139	2	we	we	PRON
ejpam-5671	139	3	set	set	VERB
ejpam-5671	139	4	θ	θ	PROPN
ejpam-5671	139	5	=	=	SYM
ejpam-5671	139	6	0	0	PUNCT
ejpam-5671	139	7	then	then	ADV
ejpam-5671	139	8	take	take	VERB
ejpam-5671	139	9	ξ	ξ	PRON
ejpam-5671	139	10	−→	−→	NOUN
ejpam-5671	139	11	1−	1−	NUM
ejpam-5671	139	12	,	,	PUNCT
ejpam-5671	139	13	we	we	PRON
ejpam-5671	139	14	obtain	obtain	VERB
ejpam-5671	139	15	ω(ρ	ω(ρ	NUM
ejpam-5671	139	16	)	)	PUNCT
ejpam-5671	140	1	=	=	SYM
ejpam-5671	140	2	∫	∫	PROPN
ejpam-5671	141	1	ρ	ρ	PROPN
ejpam-5671	141	2	0	0	PUNCT
ejpam-5671	142	1	(	(	PUNCT
ejpam-5671	142	2	ρ−	ρ−	NOUN
ejpam-5671	142	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	142	4	γ(µ	γ(µ	PROPN
ejpam-5671	142	5	)	)	PUNCT
ejpam-5671	143	1	u(ν)dν	u(ν)dν	PART
ejpam-5671	143	2	−	−	NOUN
ejpam-5671	143	3	1	1	NUM
ejpam-5671	143	4	2	2	NUM
ejpam-5671	143	5	∫	∫	NOUN
ejpam-5671	143	6	b	b	SYM
ejpam-5671	143	7	0	0	NUM
ejpam-5671	143	8	(	(	PUNCT
ejpam-5671	143	9	b−	b−	PROPN
ejpam-5671	143	10	ν)ν−1	ν)ν−1	PROPN
ejpam-5671	143	11	γ(ν	γ(ν	PROPN
ejpam-5671	143	12	)	)	PUNCT
ejpam-5671	144	1	u(ν)dν	u(ν)dν	ADP
ejpam-5671	145	1	+	+	NUM
ejpam-5671	145	2	b−	b−	NOUN
ejpam-5671	145	3	2ρ	2ρ	NOUN
ejpam-5671	145	4	2	2	NUM
ejpam-5671	145	5	∫	∫	PROPN
ejpam-5671	145	6	b	b	PROPN
ejpam-5671	145	7	0	0	NUM
ejpam-5671	145	8	(	(	PUNCT
ejpam-5671	145	9	b−	b−	NOUN
ejpam-5671	145	10	ν)µ−2	ν)µ−2	PROPN
ejpam-5671	145	11	γ(µ−	γ(µ−	VERB
ejpam-5671	145	12	1	1	NUM
ejpam-5671	145	13	)	)	PUNCT
ejpam-5671	145	14	u(ν)dν	u(ν)dν	ADP
ejpam-5671	145	15	+	+	NUM
ejpam-5671	145	16	2ρ(2b−	2ρ(2b−	NUM
ejpam-5671	145	17	ρ)−	ρ)−	PROPN
ejpam-5671	145	18	b2	b2	NOUN
ejpam-5671	145	19	4	4	NUM
ejpam-5671	145	20	∫	∫	PROPN
ejpam-5671	145	21	b	b	SYM
ejpam-5671	145	22	0	0	NUM
ejpam-5671	145	23	(	(	PUNCT
ejpam-5671	145	24	b−	b−	PROPN
ejpam-5671	145	25	s)µ−3	s)µ−3	NOUN
ejpam-5671	145	26	γ(µ−	γ(µ−	NOUN
ejpam-5671	145	27	2	2	NUM
ejpam-5671	145	28	)	)	PUNCT
ejpam-5671	145	29	u(ν)dν].(11	u(ν)dν].(11	NOUN
ejpam-5671	145	30	)	)	PUNCT
ejpam-5671	145	31	the	the	DET
ejpam-5671	145	32	solution	solution	NOUN
ejpam-5671	145	33	of	of	ADP
ejpam-5671	145	34	(	(	PUNCT
ejpam-5671	145	35	10	10	NUM
ejpam-5671	145	36	)	)	PUNCT
ejpam-5671	145	37	and	and	CCONJ
ejpam-5671	145	38	(	(	PUNCT
ejpam-5671	145	39	11	11	NUM
ejpam-5671	145	40	)	)	PUNCT
ejpam-5671	145	41	will	will	AUX
ejpam-5671	145	42	be	be	AUX
ejpam-5671	145	43	different	different	ADJ
ejpam-5671	145	44	and	and	CCONJ
ejpam-5671	145	45	contains	contain	VERB
ejpam-5671	145	46	additional	additional	ADJ
ejpam-5671	145	47	different	different	ADJ
ejpam-5671	145	48	terms	term	NOUN
ejpam-5671	145	49	.	.	PUNCT
ejpam-5671	146	1	therefore	therefore	ADV
ejpam-5671	146	2	,	,	PUNCT
ejpam-5671	146	3	the	the	DET
ejpam-5671	146	4	boundary	boundary	ADJ
ejpam-5671	146	5	conditions	condition	NOUN
ejpam-5671	146	6	give	give	VERB
ejpam-5671	146	7	rise	rise	NOUN
ejpam-5671	146	8	to	to	ADP
ejpam-5671	146	9	a	a	DET
ejpam-5671	146	10	new	new	ADJ
ejpam-5671	146	11	class	class	NOUN
ejpam-5671	146	12	of	of	ADP
ejpam-5671	146	13	problems	problem	NOUN
ejpam-5671	146	14	.	.	PUNCT
ejpam-5671	147	1	however	however	ADV
ejpam-5671	147	2	,	,	PUNCT
ejpam-5671	147	3	if	if	SCONJ
ejpam-5671	147	4	we	we	PRON
ejpam-5671	147	5	take	take	VERB
ejpam-5671	147	6	first	first	ADV
ejpam-5671	147	7	ξ	ξ	ADV
ejpam-5671	147	8	−→	−→	NOUN
ejpam-5671	147	9	1−	1−	NUM
ejpam-5671	147	10	and	and	CCONJ
ejpam-5671	147	11	then	then	ADV
ejpam-5671	147	12	set	set	VERB
ejpam-5671	147	13	every	every	DET
ejpam-5671	147	14	a	a	DET
ejpam-5671	147	15	=	=	SYM
ejpam-5671	147	16	0	0	NUM
ejpam-5671	147	17	,	,	PUNCT
ejpam-5671	147	18	the	the	DET
ejpam-5671	147	19	solution	solution	NOUN
ejpam-5671	147	20	will	will	AUX
ejpam-5671	147	21	stay	stay	VERB
ejpam-5671	147	22	the	the	DET
ejpam-5671	147	23	same	same	ADJ
ejpam-5671	147	24	,	,	PUNCT
ejpam-5671	147	25	due	due	ADP
ejpam-5671	147	26	to	to	ADP
ejpam-5671	147	27	the	the	DET
ejpam-5671	147	28	shifting	shifting	NOUN
ejpam-5671	147	29	in	in	ADP
ejpam-5671	147	30	the	the	DET
ejpam-5671	147	31	position	position	NOUN
ejpam-5671	147	32	at	at	ADP
ejpam-5671	147	33	the	the	DET
ejpam-5671	147	34	left	left	ADJ
ejpam-5671	147	35	end	end	NOUN
ejpam-5671	147	36	of	of	ADP
ejpam-5671	147	37	the	the	DET
ejpam-5671	147	38	interval	interval	NOUN
ejpam-5671	147	39	[	[	X
ejpam-5671	147	40	0	0	NUM
ejpam-5671	147	41	,	,	PUNCT
ejpam-5671	147	42	b	b	NOUN
ejpam-5671	147	43	]	]	X
ejpam-5671	147	44	.	.	PUNCT
ejpam-5671	148	1	other	other	ADJ
ejpam-5671	148	2	results	result	NOUN
ejpam-5671	148	3	with	with	ADP
ejpam-5671	148	4	different	different	ADJ
ejpam-5671	148	5	boundary	boundary	ADJ
ejpam-5671	148	6	conditions	condition	NOUN
ejpam-5671	148	7	can	can	AUX
ejpam-5671	148	8	be	be	AUX
ejpam-5671	148	9	found	find	VERB
ejpam-5671	148	10	in	in	ADP
ejpam-5671	148	11	[	[	X
ejpam-5671	148	12	7	7	NUM
ejpam-5671	148	13	,	,	PUNCT
ejpam-5671	148	14	9	9	NUM
ejpam-5671	148	15	,	,	PUNCT
ejpam-5671	148	16	11	11	NUM
ejpam-5671	148	17	,	,	PUNCT
ejpam-5671	148	18	20	20	NUM
ejpam-5671	148	19	,	,	PUNCT
ejpam-5671	148	20	21	21	NUM
ejpam-5671	148	21	]	]	PUNCT
ejpam-5671	148	22	.	.	PUNCT
ejpam-5671	149	1	theorem	theorem	NOUN
ejpam-5671	149	2	1	1	NUM
ejpam-5671	149	3	.	.	PUNCT
ejpam-5671	150	1	[	[	X
ejpam-5671	150	2	29	29	NUM
ejpam-5671	150	3	]	]	PUNCT
ejpam-5671	150	4	assume	assume	VERB
ejpam-5671	150	5	that	that	SCONJ
ejpam-5671	150	6	p	p	NOUN
ejpam-5671	150	7	is	be	AUX
ejpam-5671	150	8	an	an	DET
ejpam-5671	150	9	open	open	ADJ
ejpam-5671	150	10	bounded	bounded	ADJ
ejpam-5671	150	11	subset	subset	NOUN
ejpam-5671	150	12	of	of	ADP
ejpam-5671	150	13	a	a	DET
ejpam-5671	150	14	banach	banach	NOUN
ejpam-5671	150	15	space	space	NOUN
ejpam-5671	150	16	y	y	NOUN
ejpam-5671	150	17	with	with	ADP
ejpam-5671	150	18	0	0	NUM
ejpam-5671	150	19	∈	∈	PROPN
ejpam-5671	150	20	p	p	NOUN
ejpam-5671	150	21	and	and	CCONJ
ejpam-5671	150	22	the	the	DET
ejpam-5671	150	23	operator	operator	NOUN
ejpam-5671	150	24	l	l	NOUN
ejpam-5671	150	25	:	:	PUNCT
ejpam-5671	150	26	p	p	X
ejpam-5671	150	27	−→	−→	NOUN
ejpam-5671	150	28	y	y	PROPN
ejpam-5671	150	29	is	be	AUX
ejpam-5671	150	30	a	a	DET
ejpam-5671	150	31	completely	completely	ADV
ejpam-5671	150	32	continuous	continuous	ADJ
ejpam-5671	150	33	with	with	ADP
ejpam-5671	150	34	||lω||	||lω||	NOUN
ejpam-5671	150	35	≤	≤	NOUN
ejpam-5671	150	36	||ω||	||ω||	VERB
ejpam-5671	150	37	for	for	ADP
ejpam-5671	150	38	every	every	DET
ejpam-5671	150	39	ω	ω	PROPN
ejpam-5671	150	40	∈	∈	PROPN
ejpam-5671	150	41	∂p	∂p	PROPN
ejpam-5671	150	42	.	.	PUNCT
ejpam-5671	151	1	then	then	ADV
ejpam-5671	151	2	,	,	PUNCT
ejpam-5671	151	3	there	there	PRON
ejpam-5671	151	4	is	be	VERB
ejpam-5671	151	5	a	a	DET
ejpam-5671	151	6	fixed	fix	VERB
ejpam-5671	151	7	point	point	NOUN
ejpam-5671	151	8	of	of	ADP
ejpam-5671	151	9	the	the	DET
ejpam-5671	151	10	operator	operator	NOUN
ejpam-5671	151	11	l	l	NOUN
ejpam-5671	151	12	in	in	ADP
ejpam-5671	151	13	∂l	∂l	PROPN
ejpam-5671	151	14	.	.	PUNCT
ejpam-5671	152	1	theorem	theorem	NOUN
ejpam-5671	152	2	2	2	NUM
ejpam-5671	152	3	.	.	PUNCT
ejpam-5671	153	1	[	[	X
ejpam-5671	153	2	29	29	NUM
ejpam-5671	153	3	]	]	PUNCT
ejpam-5671	153	4	suppose	suppose	VERB
ejpam-5671	153	5	that	that	SCONJ
ejpam-5671	153	6	a	a	PRON
ejpam-5671	153	7	is	be	AUX
ejpam-5671	153	8	a	a	DET
ejpam-5671	153	9	non	non	ADJ
ejpam-5671	153	10	-	-	ADJ
ejpam-5671	153	11	empty	empty	ADJ
ejpam-5671	153	12	closed	closed	ADJ
ejpam-5671	153	13	and	and	CCONJ
ejpam-5671	153	14	convex	convex	NOUN
ejpam-5671	153	15	subset	subset	NOUN
ejpam-5671	153	16	of	of	ADP
ejpam-5671	153	17	a	a	DET
ejpam-5671	153	18	banach	banach	NOUN
ejpam-5671	153	19	space	space	NOUN
ejpam-5671	153	20	b	b	NOUN
ejpam-5671	153	21	,	,	PUNCT
ejpam-5671	153	22	w1	w1	NOUN
ejpam-5671	153	23	,	,	PUNCT
ejpam-5671	153	24	and	and	CCONJ
ejpam-5671	153	25	w2	w2	NOUN
ejpam-5671	153	26	are	be	AUX
ejpam-5671	153	27	operators	operator	NOUN
ejpam-5671	153	28	such	such	ADJ
ejpam-5671	153	29	that	that	DET
ejpam-5671	153	30	•	•	NUM
ejpam-5671	153	31	w1ω1	w1ω1	NOUN
ejpam-5671	154	1	+	+	NOUN
ejpam-5671	154	2	w2ω2	w2ω2	PROPN
ejpam-5671	154	3	∈	∈	PROPN
ejpam-5671	154	4	a	a	DET
ejpam-5671	154	5	,	,	PUNCT
ejpam-5671	154	6	whenever	whenever	SCONJ
ejpam-5671	154	7	ω1	ω1	PROPN
ejpam-5671	154	8	,	,	PUNCT
ejpam-5671	154	9	ω2	ω2	NOUN
ejpam-5671	154	10	∈	∈	PROPN
ejpam-5671	154	11	a	a	PRON
ejpam-5671	154	12	;	;	PUNCT
ejpam-5671	154	13	•	•	NUM
ejpam-5671	154	14	w1	w1	NOUN
ejpam-5671	154	15	is	be	AUX
ejpam-5671	154	16	compact	compact	ADJ
ejpam-5671	154	17	and	and	CCONJ
ejpam-5671	154	18	continuous	continuous	ADJ
ejpam-5671	154	19	;	;	PUNCT
ejpam-5671	154	20	•	•	NUM
ejpam-5671	154	21	w2	w2	NOUN
ejpam-5671	154	22	is	be	AUX
ejpam-5671	154	23	a	a	DET
ejpam-5671	154	24	contraction	contraction	NOUN
ejpam-5671	154	25	mapping	mapping	NOUN
ejpam-5671	154	26	.	.	PUNCT
ejpam-5671	155	1	then	then	ADV
ejpam-5671	155	2	there	there	PRON
ejpam-5671	155	3	is	be	VERB
ejpam-5671	155	4	ω̂	ω̂	PROPN
ejpam-5671	155	5	∈	∈	PROPN
ejpam-5671	155	6	a	a	DET
ejpam-5671	155	7	satisfies	satisfie	NOUN
ejpam-5671	155	8	the	the	DET
ejpam-5671	155	9	equation	equation	NOUN
ejpam-5671	155	10	ω̂	ω̂	PUNCT
ejpam-5671	156	1	=	=	SYM
ejpam-5671	156	2	w1ω̂	w1ω̂	NOUN
ejpam-5671	156	3	+	+	NOUN
ejpam-5671	156	4	w2ω̂.	w2ω̂.	PROPN
ejpam-5671	156	5	3	3	NUM
ejpam-5671	156	6	.	.	NOUN
ejpam-5671	156	7	main	main	ADJ
ejpam-5671	156	8	results	result	NOUN
ejpam-5671	156	9	we	we	PRON
ejpam-5671	156	10	begin	begin	VERB
ejpam-5671	156	11	this	this	DET
ejpam-5671	156	12	part	part	NOUN
ejpam-5671	156	13	with	with	ADP
ejpam-5671	156	14	the	the	DET
ejpam-5671	156	15	definition	definition	NOUN
ejpam-5671	156	16	of	of	ADP
ejpam-5671	156	17	the	the	DET
ejpam-5671	156	18	operator	operator	NOUN
ejpam-5671	156	19	l	l	NOUN
ejpam-5671	156	20	:	:	PUNCT
ejpam-5671	156	21	a	a	DET
ejpam-5671	156	22	−→	−→	NOUN
ejpam-5671	156	23	a	a	PRON
ejpam-5671	156	24	by	by	ADP
ejpam-5671	156	25	(	(	PUNCT
ejpam-5671	156	26	lω)ρ	lω)ρ	PROPN
ejpam-5671	156	27	=	=	SYM
ejpam-5671	156	28	∫	∫	PROPN
ejpam-5671	156	29	ρ	ρ	PROPN
ejpam-5671	156	30	0	0	PUNCT
ejpam-5671	157	1	(	(	PUNCT
ejpam-5671	157	2	ρ−	ρ−	NOUN
ejpam-5671	157	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	157	4	γ(µ	γ(µ	PROPN
ejpam-5671	157	5	)	)	PUNCT
ejpam-5671	157	6	ω(ν	ω(ν	NOUN
ejpam-5671	157	7	,	,	PUNCT
ejpam-5671	157	8	ω(ν))dν	ω(ν))dν	NUM
ejpam-5671	157	9	−1	−1	NOUN
ejpam-5671	157	10	2	2	NUM
ejpam-5671	157	11	(	(	PUNCT
ejpam-5671	157	12	∫	∫	PROPN
ejpam-5671	157	13	θ	θ	PROPN
ejpam-5671	157	14	0	0	PUNCT
ejpam-5671	157	15	(	(	PUNCT
ejpam-5671	157	16	θ	θ	NOUN
ejpam-5671	157	17	−	−	PROPN
ejpam-5671	157	18	ν)µ−1	ν)µ−1	NOUN
ejpam-5671	157	19	γ(µ	γ(µ	PROPN
ejpam-5671	157	20	)	)	PUNCT
ejpam-5671	157	21	ω(ν	ω(ν	NOUN
ejpam-5671	157	22	,	,	PUNCT
ejpam-5671	157	23	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	157	24	+	+	CCONJ
ejpam-5671	157	25	∫	∫	PROPN
ejpam-5671	157	26	b	b	PROPN
ejpam-5671	157	27	0	0	NUM
ejpam-5671	157	28	(	(	PUNCT
ejpam-5671	157	29	b−	b−	PROPN
ejpam-5671	157	30	ν)µ−1	ν)µ−1	VERB
ejpam-5671	157	31	γ(µ	γ(µ	PROPN
ejpam-5671	157	32	)	)	PUNCT
ejpam-5671	157	33	ω(ν	ω(ν	NOUN
ejpam-5671	157	34	,	,	PUNCT
ejpam-5671	157	35	ω(ν))dν	ω(ν))dν	PRON
ejpam-5671	157	36	)	)	PUNCT
ejpam-5671	158	1	+	+	CCONJ
ejpam-5671	158	2	γ(2−	γ(2−	NUM
ejpam-5671	158	3	ξ)[(θ	ξ)[(θ	NOUN
ejpam-5671	159	1	+	+	CCONJ
ejpam-5671	159	2	b)−	b)−	PROPN
ejpam-5671	159	3	2ρ	2ρ	NOUN
ejpam-5671	159	4	]	]	PUNCT
ejpam-5671	159	5	2(ρ1−ξ	2(ρ1−ξ	PROPN
ejpam-5671	160	1	+	+	CCONJ
ejpam-5671	160	2	b1−ξ	b1−ξ	PROPN
ejpam-5671	160	3	)	)	PUNCT
ejpam-5671	160	4	(	(	PUNCT
ejpam-5671	160	5	∫	∫	PROPN
ejpam-5671	160	6	θ	θ	PROPN
ejpam-5671	160	7	0	0	PUNCT
ejpam-5671	160	8	(	(	PUNCT
ejpam-5671	160	9	θ	θ	X
ejpam-5671	160	10	−	−	PROPN
ejpam-5671	160	11	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	160	12	γ(µ−	γ(µ−	VERB
ejpam-5671	160	13	ξ	ξ	NUM
ejpam-5671	160	14	)	)	PUNCT
ejpam-5671	160	15	ω(ν	ω(ν	NOUN
ejpam-5671	160	16	,	,	PUNCT
ejpam-5671	160	17	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	160	18	+	+	CCONJ
ejpam-5671	160	19	∫	∫	PROPN
ejpam-5671	160	20	b	b	PROPN
ejpam-5671	160	21	0	0	NUM
ejpam-5671	160	22	(	(	PUNCT
ejpam-5671	160	23	b−	b−	PROPN
ejpam-5671	160	24	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	160	25	γ(µ−	γ(µ−	VERB
ejpam-5671	160	26	ξ	ξ	NUM
ejpam-5671	160	27	)	)	PUNCT
ejpam-5671	160	28	ω(ν	ω(ν	NOUN
ejpam-5671	160	29	,	,	PUNCT
ejpam-5671	160	30	ω(ν))dν	ω(ν))dν	NUM
ejpam-5671	160	31	)	)	PUNCT
ejpam-5671	160	32	s.	s.	PROPN
ejpam-5671	160	33	f.	f.	PROPN
ejpam-5671	160	34	aljurbua	aljurbua	PROPN
ejpam-5671	160	35	,	,	PUNCT
ejpam-5671	160	36	h.	h.	PROPN
ejpam-5671	160	37	a.	a.	PROPN
ejpam-5671	160	38	hammad	hammad	PROPN
ejpam-5671	160	39	,	,	PUNCT
ejpam-5671	160	40	n.	n.	PROPN
ejpam-5671	160	41	b.	b.	PROPN
ejpam-5671	160	42	almutairi	almutairi	PROPN
ejpam-5671	160	43	/	/	SYM
ejpam-5671	160	44	eur	eur	PROPN
ejpam-5671	160	45	.	.	PUNCT
ejpam-5671	161	1	j.	j.	PROPN
ejpam-5671	161	2	pure	pure	PROPN
ejpam-5671	161	3	appl	appl	PROPN
ejpam-5671	161	4	.	.	PROPN
ejpam-5671	161	5	math	math	PROPN
ejpam-5671	161	6	,	,	PUNCT
ejpam-5671	161	7	18	18	NUM
ejpam-5671	161	8	(	(	PUNCT
ejpam-5671	161	9	1	1	NUM
ejpam-5671	161	10	)	)	PUNCT
ejpam-5671	161	11	(	(	PUNCT
ejpam-5671	161	12	2025	2025	NUM
ejpam-5671	161	13	)	)	PUNCT
ejpam-5671	161	14	,	,	PUNCT
ejpam-5671	161	15	5671	5671	NUM
ejpam-5671	161	16	7	7	NUM
ejpam-5671	161	17	of	of	ADP
ejpam-5671	161	18	18	18	NUM
ejpam-5671	161	19	+	+	CCONJ
ejpam-5671	161	20	γ(2−	γ(2−	PROPN
ejpam-5671	161	21	ξ	ξ	PROPN
ejpam-5671	161	22	)	)	PUNCT
ejpam-5671	161	23	4γ(3−	4γ(3−	NUM
ejpam-5671	162	1	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	162	2	+	+	CCONJ
ejpam-5671	162	3	b1−ξ)2	b1−ξ)2	PROPN
ejpam-5671	162	4			PROPN
ejpam-5671	162	5	4ρ(θ2−ξ	4ρ(θ2−ξ	NUM
ejpam-5671	162	6	+	+	CCONJ
ejpam-5671	162	7	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	162	8	ξ	ξ	PROPN
ejpam-5671	162	9	)	)	PUNCT
ejpam-5671	162	10	−4ρ2γ(3−	−4ρ2γ(3−	VERB
ejpam-5671	162	11	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	162	12	+	+	CCONJ
ejpam-5671	162	13	b1−ξ	b1−ξ	PROPN
ejpam-5671	162	14	)	)	PUNCT
ejpam-5671	162	15	−2(θ	−2(θ	PUNCT
ejpam-5671	163	1	+	+	CCONJ
ejpam-5671	163	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	163	3	+	+	CCONJ
ejpam-5671	163	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	163	5	ξ	ξ	PROPN
ejpam-5671	163	6	)	)	PUNCT
ejpam-5671	164	1	+	+	PROPN
ejpam-5671	164	2	(	(	PUNCT
ejpam-5671	164	3	θ2	θ2	ADV
ejpam-5671	164	4	+	+	CCONJ
ejpam-5671	164	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	164	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	164	7	+	+	CCONJ
ejpam-5671	164	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	164	9	)	)	PUNCT
ejpam-5671	164	10			NOUN
ejpam-5671	164	11	×	×	NOUN
ejpam-5671	164	12	(	(	PUNCT
ejpam-5671	164	13	∫	∫	PROPN
ejpam-5671	164	14	θ	θ	PROPN
ejpam-5671	164	15	0	0	PUNCT
ejpam-5671	164	16	(	(	PUNCT
ejpam-5671	164	17	θ	θ	NOUN
ejpam-5671	164	18	−	−	NOUN
ejpam-5671	164	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	164	20	γ(µ−	γ(µ−	VERB
ejpam-5671	164	21	ξ	ξ	PRON
ejpam-5671	164	22	−	−	NOUN
ejpam-5671	164	23	1	1	NUM
ejpam-5671	164	24	)	)	PUNCT
ejpam-5671	164	25	ω(ν	ω(ν	NOUN
ejpam-5671	164	26	,	,	PUNCT
ejpam-5671	164	27	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	165	1	+	+	CCONJ
ejpam-5671	165	2	∫	∫	PROPN
ejpam-5671	165	3	b	b	PROPN
ejpam-5671	165	4	0	0	NUM
ejpam-5671	165	5	(	(	PUNCT
ejpam-5671	165	6	b−	b−	NOUN
ejpam-5671	165	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	165	8	γ(µ−	γ(µ−	VERB
ejpam-5671	165	9	ξ	ξ	PRON
ejpam-5671	165	10	−	−	NOUN
ejpam-5671	165	11	1	1	NUM
ejpam-5671	165	12	)	)	PUNCT
ejpam-5671	165	13	ω(ν	ω(ν	NOUN
ejpam-5671	165	14	,	,	PUNCT
ejpam-5671	165	15	ω(ν))dν	ω(ν))dν	NUM
ejpam-5671	165	16	)	)	PUNCT
ejpam-5671	165	17	.	.	PUNCT
ejpam-5671	166	1	(	(	PUNCT
ejpam-5671	166	2	12	12	NUM
ejpam-5671	166	3	)	)	PUNCT
ejpam-5671	166	4	where	where	SCONJ
ejpam-5671	166	5	a	a	DET
ejpam-5671	166	6	=	=	X
ejpam-5671	166	7	c([0	c([0	X
ejpam-5671	166	8	,	,	PUNCT
ejpam-5671	166	9	b],r	b],r	NOUN
ejpam-5671	166	10	)	)	PUNCT
ejpam-5671	166	11	is	be	AUX
ejpam-5671	166	12	a	a	DET
ejpam-5671	166	13	banach	banach	NOUN
ejpam-5671	166	14	space	space	NOUN
ejpam-5671	166	15	.	.	PUNCT
ejpam-5671	167	1	remark	remark	NOUN
ejpam-5671	167	2	3	3	NUM
ejpam-5671	167	3	.	.	PUNCT
ejpam-5671	168	1	the	the	DET
ejpam-5671	168	2	existence	existence	NOUN
ejpam-5671	168	3	of	of	ADP
ejpam-5671	168	4	the	the	DET
ejpam-5671	168	5	fixed	fix	VERB
ejpam-5671	168	6	point	point	NOUN
ejpam-5671	168	7	of	of	ADP
ejpam-5671	168	8	the	the	DET
ejpam-5671	168	9	operator	operator	NOUN
ejpam-5671	168	10	l	l	NOUN
ejpam-5671	168	11	(	(	PUNCT
ejpam-5671	168	12	lω	lω	PROPN
ejpam-5671	168	13	=	=	PUNCT
ejpam-5671	168	14	ω	ω	PROPN
ejpam-5671	168	15	)	)	PUNCT
ejpam-5671	168	16	is	be	AUX
ejpam-5671	168	17	equivalent	equivalent	ADJ
ejpam-5671	168	18	to	to	ADP
ejpam-5671	168	19	the	the	DET
ejpam-5671	168	20	existence	existence	NOUN
ejpam-5671	168	21	of	of	ADP
ejpam-5671	168	22	the	the	DET
ejpam-5671	168	23	solution	solution	NOUN
ejpam-5671	168	24	to	to	ADP
ejpam-5671	168	25	the	the	DET
ejpam-5671	168	26	problem	problem	NOUN
ejpam-5671	168	27	(	(	PUNCT
ejpam-5671	168	28	1	1	NUM
ejpam-5671	168	29	)	)	PUNCT
ejpam-5671	168	30	.	.	PUNCT
ejpam-5671	169	1	for	for	ADP
ejpam-5671	169	2	simplicity	simplicity	NOUN
ejpam-5671	169	3	,	,	PUNCT
ejpam-5671	169	4	we	we	PRON
ejpam-5671	169	5	consider	consider	VERB
ejpam-5671	169	6	the	the	DET
ejpam-5671	169	7	following	follow	VERB
ejpam-5671	169	8	notations	notation	NOUN
ejpam-5671	169	9	:	:	PUNCT
ejpam-5671	169	10	m1	m1	PROPN
ejpam-5671	169	11	=	=	SYM
ejpam-5671	169	12	max	max	PROPN
ejpam-5671	169	13	ρ∈[0,b]||ω(ρ,0)||=n<∞	ρ∈[0,b]||ω(ρ,0)||=n<∞	X
ejpam-5671	169	14	{	{	PUNCT
ejpam-5671	169	15	3bµ	3bµ	ADJ
ejpam-5671	169	16	+	+	CCONJ
ejpam-5671	169	17	θµ	θµ	NUM
ejpam-5671	169	18	γ(µ+	γ(µ+	NOUN
ejpam-5671	169	19	1	1	NUM
ejpam-5671	169	20	)	)	PUNCT
ejpam-5671	169	21	+	+	CCONJ
ejpam-5671	170	1	γ(2−	γ(2−	PROPN
ejpam-5671	170	2	ξ	ξ	X
ejpam-5671	170	3	)	)	PUNCT
ejpam-5671	170	4	|(θ	|(θ	PROPN
ejpam-5671	171	1	+	+	CCONJ
ejpam-5671	172	1	b)−	b)−	PROPN
ejpam-5671	172	2	2ρ|	2ρ|	NUM
ejpam-5671	172	3	(	(	PUNCT
ejpam-5671	172	4	θµ−ξ−1	θµ−ξ−1	X
ejpam-5671	172	5	+	+	NUM
ejpam-5671	172	6	bµ−ξ−1	bµ−ξ−1	NOUN
ejpam-5671	172	7	)	)	PUNCT
ejpam-5671	172	8	(	(	PUNCT
ejpam-5671	172	9	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	172	10	+	+	CCONJ
ejpam-5671	172	11	b1−ξ)γ(µ−	b1−ξ)γ(µ−	PROPN
ejpam-5671	172	12	ξ	ξ	PROPN
ejpam-5671	172	13	+	+	PROPN
ejpam-5671	172	14	1	1	NUM
ejpam-5671	172	15	)	)	PUNCT
ejpam-5671	172	16	+	+	CCONJ
ejpam-5671	172	17	γ(2−	γ(2−	PROPN
ejpam-5671	172	18	ξ	ξ	PROPN
ejpam-5671	172	19	)	)	PUNCT
ejpam-5671	172	20	2γ(3−	2γ(3−	PROPN
ejpam-5671	172	21	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	172	22	+	+	CCONJ
ejpam-5671	172	23	b1−ξ)2γ(µ−	b1−ξ)2γ(µ−	X
ejpam-5671	172	24	ξ	ξ	X
ejpam-5671	172	25	)	)	PUNCT
ejpam-5671	172	26	×	×	NOUN
ejpam-5671	172	27	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	172	28	+	+	CCONJ
ejpam-5671	172	29	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	172	30	ξ)−	ξ)−	PROPN
ejpam-5671	172	31	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	172	32	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	172	33	+	+	CCONJ
ejpam-5671	172	34	b1−ξ	b1−ξ	PROPN
ejpam-5671	172	35	)	)	PUNCT
ejpam-5671	172	36	−	−	ADP
ejpam-5671	172	37	2(θ	2(θ	NUM
ejpam-5671	173	1	+	+	CCONJ
ejpam-5671	173	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	173	3	+	+	CCONJ
ejpam-5671	173	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	173	5	ξ	ξ	PROPN
ejpam-5671	173	6	)	)	PUNCT
ejpam-5671	174	1	+	+	CCONJ
ejpam-5671	174	2	(	(	PUNCT
ejpam-5671	174	3	θ2	θ2	ADV
ejpam-5671	174	4	+	+	CCONJ
ejpam-5671	174	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	174	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	174	7	+	+	CCONJ
ejpam-5671	174	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	174	9	)	)	PUNCT
ejpam-5671	174	10	∣∣∣	∣∣∣	ADJ
ejpam-5671	174	11	}	}	PUNCT
ejpam-5671	174	12	.	.	PUNCT
ejpam-5671	175	1	(	(	PUNCT
ejpam-5671	175	2	13	13	NUM
ejpam-5671	175	3	)	)	PUNCT
ejpam-5671	175	4	m2	m2	PROPN
ejpam-5671	175	5	=	=	SYM
ejpam-5671	175	6	max	max	PROPN
ejpam-5671	175	7	ρ∈[0,b]||ω(ρ,0)||=m<∞	ρ∈[0,b]||ω(ρ,0)||=m<∞	CCONJ
ejpam-5671	175	8	{	{	PUNCT
ejpam-5671	175	9	bµ	bµ	PROPN
ejpam-5671	175	10	+	+	NUM
ejpam-5671	175	11	θµ	θµ	NUM
ejpam-5671	175	12	γ(µ+	γ(µ+	NOUN
ejpam-5671	175	13	1	1	NUM
ejpam-5671	175	14	)	)	PUNCT
ejpam-5671	175	15	+	+	CCONJ
ejpam-5671	175	16	γ(2−	γ(2−	PROPN
ejpam-5671	175	17	ξ	ξ	X
ejpam-5671	175	18	)	)	PUNCT
ejpam-5671	175	19	|(θ	|(θ	PROPN
ejpam-5671	176	1	+	+	CCONJ
ejpam-5671	176	2	b)−	b)−	PROPN
ejpam-5671	176	3	2ρ|	2ρ|	NUM
ejpam-5671	176	4	(	(	PUNCT
ejpam-5671	176	5	θµ−ξ−1	θµ−ξ−1	X
ejpam-5671	176	6	+	+	NUM
ejpam-5671	176	7	bµ−θ−1	bµ−θ−1	NOUN
ejpam-5671	176	8	)	)	PUNCT
ejpam-5671	176	9	(	(	PUNCT
ejpam-5671	176	10	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	176	11	+	+	CCONJ
ejpam-5671	176	12	b1−ξ)γ(µ−	b1−ξ)γ(µ−	PROPN
ejpam-5671	176	13	ξ	ξ	PROPN
ejpam-5671	176	14	+	+	PROPN
ejpam-5671	176	15	1	1	NUM
ejpam-5671	176	16	)	)	PUNCT
ejpam-5671	176	17	+	+	CCONJ
ejpam-5671	176	18	γ(2−	γ(2−	PROPN
ejpam-5671	176	19	ξ	ξ	PROPN
ejpam-5671	176	20	)	)	PUNCT
ejpam-5671	177	1	2γ(3−	2γ(3−	PROPN
ejpam-5671	177	2	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	177	3	+	+	CCONJ
ejpam-5671	177	4	b1−ξ)2γ(µ−	b1−ξ)2γ(µ−	X
ejpam-5671	177	5	ξ	ξ	X
ejpam-5671	177	6	)	)	PUNCT
ejpam-5671	177	7	×	×	NOUN
ejpam-5671	177	8	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	177	9	+	+	CCONJ
ejpam-5671	177	10	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	177	11	ξ)−	ξ)−	PROPN
ejpam-5671	177	12	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	177	13	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	177	14	+	+	CCONJ
ejpam-5671	177	15	b1−ξ	b1−ξ	PROPN
ejpam-5671	177	16	)	)	PUNCT
ejpam-5671	177	17	−2(θ	−2(θ	PUNCT
ejpam-5671	178	1	+	+	CCONJ
ejpam-5671	178	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	178	3	+	+	CCONJ
ejpam-5671	178	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	178	5	ξ	ξ	PROPN
ejpam-5671	178	6	)	)	PUNCT
ejpam-5671	179	1	+	+	CCONJ
ejpam-5671	179	2	(	(	PUNCT
ejpam-5671	179	3	θ2	θ2	ADV
ejpam-5671	179	4	+	+	CCONJ
ejpam-5671	179	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	179	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	179	7	+	+	CCONJ
ejpam-5671	179	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	179	9	)	)	PUNCT
ejpam-5671	179	10	∣∣∣	∣∣∣	ADJ
ejpam-5671	179	11	}	}	PUNCT
ejpam-5671	179	12	.	.	PUNCT
ejpam-5671	180	1	(	(	PUNCT
ejpam-5671	180	2	14	14	X
ejpam-5671	180	3	)	)	PUNCT
ejpam-5671	180	4	lemma	lemma	PROPN
ejpam-5671	180	5	3	3	NUM
ejpam-5671	180	6	.	.	PUNCT
ejpam-5671	181	1	the	the	DET
ejpam-5671	181	2	operator	operator	NOUN
ejpam-5671	181	3	l	l	NOUN
ejpam-5671	181	4	:	:	PUNCT
ejpam-5671	181	5	a	a	DET
ejpam-5671	181	6	−→	−→	NOUN
ejpam-5671	181	7	a	a	PRON
ejpam-5671	181	8	is	be	AUX
ejpam-5671	181	9	completely	completely	ADV
ejpam-5671	181	10	continuous	continuous	ADJ
ejpam-5671	181	11	.	.	PUNCT
ejpam-5671	182	1	proof	proof	NOUN
ejpam-5671	182	2	.	.	PUNCT
ejpam-5671	183	1	suppose	suppose	VERB
ejpam-5671	183	2	s	s	VERB
ejpam-5671	183	3	⊂	⊂	PROPN
ejpam-5671	183	4	a	a	PRON
ejpam-5671	183	5	be	be	AUX
ejpam-5671	183	6	bounded	bound	VERB
ejpam-5671	183	7	.	.	PUNCT
ejpam-5671	184	1	then	then	ADV
ejpam-5671	184	2	there	there	PRON
ejpam-5671	184	3	existsk1	existsk1	NOUN
ejpam-5671	184	4	>	>	X
ejpam-5671	184	5	0	0	NUM
ejpam-5671	185	1	such	such	ADJ
ejpam-5671	185	2	that	that	PRON
ejpam-5671	185	3	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	185	4	,	,	PUNCT
ejpam-5671	185	5	ω)|	ω)|	ADJ
ejpam-5671	185	6	≤	≤	NUM
ejpam-5671	185	7	k1	k1	NOUN
ejpam-5671	185	8	,	,	PUNCT
ejpam-5671	185	9	∀ρ	∀ρ	NOUN
ejpam-5671	185	10	∈	∈	PROPN
ejpam-5671	186	1	[	[	X
ejpam-5671	186	2	0	0	NUM
ejpam-5671	186	3	,	,	PUNCT
ejpam-5671	186	4	b	b	NOUN
ejpam-5671	186	5	]	]	PUNCT
ejpam-5671	186	6	and	and	CCONJ
ejpam-5671	186	7	ω	ω	PROPN
ejpam-5671	186	8	∈	∈	PROPN
ejpam-5671	186	9	s.	s.	PROPN
ejpam-5671	186	10	let	let	VERB
ejpam-5671	186	11	l	l	NOUN
ejpam-5671	186	12	be	be	AUX
ejpam-5671	186	13	the	the	DET
ejpam-5671	186	14	operator	operator	NOUN
ejpam-5671	186	15	defined	define	VERB
ejpam-5671	186	16	in	in	ADP
ejpam-5671	186	17	(	(	PUNCT
ejpam-5671	186	18	12	12	NUM
ejpam-5671	186	19	)	)	PUNCT
ejpam-5671	186	20	,	,	PUNCT
ejpam-5671	186	21	then	then	ADV
ejpam-5671	186	22	,	,	PUNCT
ejpam-5671	186	23	we	we	PRON
ejpam-5671	186	24	have	have	VERB
ejpam-5671	186	25	|(lω)ρ|	|(lω)ρ|	PROPN
ejpam-5671	186	26	=	=	SYM
ejpam-5671	186	27	∫	∫	PROPN
ejpam-5671	186	28	ρ	ρ	PROPN
ejpam-5671	186	29	0	0	PUNCT
ejpam-5671	187	1	(	(	PUNCT
ejpam-5671	187	2	ρ−	ρ−	NOUN
ejpam-5671	187	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	187	4	γ(µ	γ(µ	PROPN
ejpam-5671	187	5	)	)	PUNCT
ejpam-5671	188	1	|ω(ν	|ω(ν	PROPN
ejpam-5671	188	2	,	,	PUNCT
ejpam-5671	188	3	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	189	1	+	+	CCONJ
ejpam-5671	189	2	1	1	NUM
ejpam-5671	189	3	2	2	NUM
ejpam-5671	189	4	(	(	PUNCT
ejpam-5671	189	5	∫	∫	PROPN
ejpam-5671	189	6	θ	θ	PROPN
ejpam-5671	189	7	0	0	PUNCT
ejpam-5671	189	8	(	(	PUNCT
ejpam-5671	189	9	θ	θ	NOUN
ejpam-5671	189	10	−	−	PROPN
ejpam-5671	189	11	ν)µ−1	ν)µ−1	NOUN
ejpam-5671	189	12	γ(µ	γ(µ	PROPN
ejpam-5671	189	13	)	)	PUNCT
ejpam-5671	190	1	|ω(ν	|ω(ν	PROPN
ejpam-5671	190	2	,	,	PUNCT
ejpam-5671	190	3	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	191	1	+	+	CCONJ
ejpam-5671	191	2	∫	∫	PROPN
ejpam-5671	191	3	b	b	PROPN
ejpam-5671	191	4	0	0	NUM
ejpam-5671	191	5	(	(	PUNCT
ejpam-5671	191	6	b−	b−	PROPN
ejpam-5671	191	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	191	8	γ(µ	γ(µ	PROPN
ejpam-5671	191	9	)	)	PUNCT
ejpam-5671	192	1	|ω(ν	|ω(ν	PROPN
ejpam-5671	192	2	,	,	PUNCT
ejpam-5671	192	3	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	192	4	)	)	PUNCT
ejpam-5671	193	1	+	+	CCONJ
ejpam-5671	193	2	γ(2−	γ(2−	NOUN
ejpam-5671	193	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	193	4	+	+	CCONJ
ejpam-5671	193	5	b)−	b)−	PROPN
ejpam-5671	193	6	2ρ|	2ρ|	NUM
ejpam-5671	193	7	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	193	8	+	+	CCONJ
ejpam-5671	193	9	b1−ξ	b1−ξ	PROPN
ejpam-5671	193	10	)	)	PUNCT
ejpam-5671	193	11	(	(	PUNCT
ejpam-5671	193	12	∫	∫	PROPN
ejpam-5671	193	13	θ	θ	PROPN
ejpam-5671	193	14	0	0	PUNCT
ejpam-5671	193	15	(	(	PUNCT
ejpam-5671	193	16	θ	θ	X
ejpam-5671	193	17	−	−	PROPN
ejpam-5671	193	18	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	193	19	γ(µ−	γ(µ−	VERB
ejpam-5671	193	20	ξ	ξ	NOUN
ejpam-5671	193	21	)	)	PUNCT
ejpam-5671	193	22	|ω(ν	|ω(ν	ADJ
ejpam-5671	193	23	,	,	PUNCT
ejpam-5671	193	24	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	194	1	+	+	CCONJ
ejpam-5671	194	2	∫	∫	PROPN
ejpam-5671	194	3	b	b	PROPN
ejpam-5671	194	4	0	0	NUM
ejpam-5671	194	5	(	(	PUNCT
ejpam-5671	194	6	b−	b−	PROPN
ejpam-5671	194	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	194	8	γ(µ−	γ(µ−	VERB
ejpam-5671	194	9	ξ	ξ	NOUN
ejpam-5671	194	10	)	)	PUNCT
ejpam-5671	194	11	|ω(ν	|ω(ν	ADJ
ejpam-5671	194	12	,	,	PUNCT
ejpam-5671	194	13	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	194	14	)	)	PUNCT
ejpam-5671	195	1	s.	s.	PROPN
ejpam-5671	195	2	f.	f.	PROPN
ejpam-5671	195	3	aljurbua	aljurbua	PROPN
ejpam-5671	195	4	,	,	PUNCT
ejpam-5671	195	5	h.	h.	PROPN
ejpam-5671	195	6	a.	a.	PROPN
ejpam-5671	195	7	hammad	hammad	PROPN
ejpam-5671	195	8	,	,	PUNCT
ejpam-5671	195	9	n.	n.	PROPN
ejpam-5671	195	10	b.	b.	PROPN
ejpam-5671	195	11	almutairi	almutairi	PROPN
ejpam-5671	195	12	/	/	SYM
ejpam-5671	195	13	eur	eur	PROPN
ejpam-5671	195	14	.	.	PUNCT
ejpam-5671	196	1	j.	j.	PROPN
ejpam-5671	196	2	pure	pure	PROPN
ejpam-5671	196	3	appl	appl	PROPN
ejpam-5671	196	4	.	.	PROPN
ejpam-5671	196	5	math	math	PROPN
ejpam-5671	196	6	,	,	PUNCT
ejpam-5671	196	7	18	18	NUM
ejpam-5671	196	8	(	(	PUNCT
ejpam-5671	196	9	1	1	NUM
ejpam-5671	196	10	)	)	PUNCT
ejpam-5671	196	11	(	(	PUNCT
ejpam-5671	196	12	2025	2025	NUM
ejpam-5671	196	13	)	)	PUNCT
ejpam-5671	196	14	,	,	PUNCT
ejpam-5671	196	15	5671	5671	NUM
ejpam-5671	196	16	8	8	NUM
ejpam-5671	196	17	of	of	ADP
ejpam-5671	196	18	18	18	NUM
ejpam-5671	196	19	+	+	CCONJ
ejpam-5671	196	20	γ(2−	γ(2−	PROPN
ejpam-5671	196	21	ξ	ξ	PROPN
ejpam-5671	196	22	)	)	PUNCT
ejpam-5671	196	23	4γ(3−	4γ(3−	NUM
ejpam-5671	196	24	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	197	1	+	+	CCONJ
ejpam-5671	197	2	b1−ξ)2	b1−ξ)2	VERB
ejpam-5671	197	3	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	NOUN
ejpam-5671	197	4	+	+	CCONJ
ejpam-5671	197	5	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	197	6	ξ)−	ξ)−	PROPN
ejpam-5671	197	7	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	197	8	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	197	9	+	+	CCONJ
ejpam-5671	197	10	b1−ξ	b1−ξ	PROPN
ejpam-5671	197	11	)	)	PUNCT
ejpam-5671	197	12	−2(θ	−2(θ	PUNCT
ejpam-5671	198	1	+	+	CCONJ
ejpam-5671	198	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	198	3	+	+	CCONJ
ejpam-5671	198	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	198	5	ξ	ξ	PROPN
ejpam-5671	198	6	)	)	PUNCT
ejpam-5671	199	1	+	+	CCONJ
ejpam-5671	199	2	(	(	PUNCT
ejpam-5671	199	3	θ2	θ2	ADV
ejpam-5671	199	4	+	+	CCONJ
ejpam-5671	199	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	199	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	199	7	+	+	CCONJ
ejpam-5671	199	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	199	9	)	)	PUNCT
ejpam-5671	199	10	∣∣∣	∣∣∣	ADP
ejpam-5671	199	11	×	×	PROPN
ejpam-5671	199	12	(	(	PUNCT
ejpam-5671	199	13	∫	∫	PROPN
ejpam-5671	199	14	θ	θ	PROPN
ejpam-5671	199	15	0	0	PUNCT
ejpam-5671	199	16	(	(	PUNCT
ejpam-5671	199	17	θ	θ	NOUN
ejpam-5671	199	18	−	−	NOUN
ejpam-5671	199	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	199	20	γ(µ−	γ(µ−	VERB
ejpam-5671	199	21	ξ	ξ	PRON
ejpam-5671	199	22	−	−	NOUN
ejpam-5671	199	23	1	1	NUM
ejpam-5671	199	24	)	)	PUNCT
ejpam-5671	199	25	|ω(ν	|ω(ν	ADJ
ejpam-5671	199	26	,	,	PUNCT
ejpam-5671	199	27	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	200	1	+	+	CCONJ
ejpam-5671	200	2	∫	∫	PROPN
ejpam-5671	200	3	b	b	PROPN
ejpam-5671	200	4	0	0	NUM
ejpam-5671	200	5	(	(	PUNCT
ejpam-5671	200	6	b−	b−	NOUN
ejpam-5671	200	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	200	8	γ(µ−	γ(µ−	VERB
ejpam-5671	200	9	ξ	ξ	PRON
ejpam-5671	200	10	−	−	NOUN
ejpam-5671	200	11	1	1	NUM
ejpam-5671	200	12	)	)	PUNCT
ejpam-5671	200	13	|ω(ν	|ω(ν	ADJ
ejpam-5671	200	14	,	,	PUNCT
ejpam-5671	200	15	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	200	16	)	)	PUNCT
ejpam-5671	200	17	≤	≤	NUM
ejpam-5671	200	18	k1	k1	NOUN
ejpam-5671	200	19	2	2	NUM
ejpam-5671	200	20	[	[	PUNCT
ejpam-5671	200	21	2	2	NUM
ejpam-5671	200	22	∫	∫	NOUN
ejpam-5671	200	23	ρ	ρ	NOUN
ejpam-5671	200	24	0	0	PUNCT
ejpam-5671	201	1	(	(	PUNCT
ejpam-5671	201	2	ρ−	ρ−	NOUN
ejpam-5671	201	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	201	4	γ(µ	γ(µ	PROPN
ejpam-5671	201	5	)	)	PUNCT
ejpam-5671	202	1	dν	dν	VERB
ejpam-5671	203	1	+	+	CCONJ
ejpam-5671	203	2	∫	∫	PROPN
ejpam-5671	203	3	θ	θ	NOUN
ejpam-5671	203	4	0	0	PUNCT
ejpam-5671	203	5	(	(	PUNCT
ejpam-5671	203	6	θ	θ	NOUN
ejpam-5671	203	7	−	−	PROPN
ejpam-5671	203	8	ν)µ−1	ν)µ−1	X
ejpam-5671	203	9	γ(µ	γ(µ	PROPN
ejpam-5671	203	10	)	)	PUNCT
ejpam-5671	203	11	dν	dν	VERB
ejpam-5671	204	1	+	+	CCONJ
ejpam-5671	204	2	∫	∫	PROPN
ejpam-5671	204	3	b	b	PROPN
ejpam-5671	204	4	0	0	NUM
ejpam-5671	204	5	(	(	PUNCT
ejpam-5671	204	6	b−	b−	PROPN
ejpam-5671	204	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	204	8	γ(µ	γ(µ	PROPN
ejpam-5671	204	9	)	)	PUNCT
ejpam-5671	205	1	dν	dν	VERB
ejpam-5671	206	1	+	+	CCONJ
ejpam-5671	206	2	γ(2−	γ(2−	NOUN
ejpam-5671	206	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	206	4	+	+	CCONJ
ejpam-5671	206	5	b)−	b)−	PROPN
ejpam-5671	206	6	2ρ|	2ρ|	NUM
ejpam-5671	206	7	(	(	PUNCT
ejpam-5671	206	8	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	206	9	+	+	CCONJ
ejpam-5671	206	10	b1−ξ	b1−ξ	PROPN
ejpam-5671	206	11	)	)	PUNCT
ejpam-5671	207	1	[	[	X
ejpam-5671	207	2	∫	∫	X
ejpam-5671	207	3	θ	θ	X
ejpam-5671	207	4	0	0	PUNCT
ejpam-5671	207	5	(	(	PUNCT
ejpam-5671	207	6	θ	θ	X
ejpam-5671	207	7	−	−	PROPN
ejpam-5671	207	8	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	207	9	γ(µ−	γ(µ−	VERB
ejpam-5671	207	10	ξ	ξ	X
ejpam-5671	207	11	)	)	PUNCT
ejpam-5671	207	12	dν	dν	VERB
ejpam-5671	208	1	+	+	CCONJ
ejpam-5671	208	2	∫	∫	PROPN
ejpam-5671	208	3	b	b	PROPN
ejpam-5671	208	4	0	0	NUM
ejpam-5671	208	5	(	(	PUNCT
ejpam-5671	208	6	b−	b−	PROPN
ejpam-5671	208	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	208	8	γ(µ−	γ(µ−	VERB
ejpam-5671	208	9	ξ	ξ	X
ejpam-5671	208	10	)	)	PUNCT
ejpam-5671	208	11	dν	dν	VERB
ejpam-5671	208	12	]	]	PUNCT
ejpam-5671	209	1	+	+	CCONJ
ejpam-5671	209	2	γ(2−	γ(2−	PROPN
ejpam-5671	209	3	ξ	ξ	PROPN
ejpam-5671	209	4	)	)	PUNCT
ejpam-5671	209	5	2γ(3−	2γ(3−	PROPN
ejpam-5671	209	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	210	1	+	+	CCONJ
ejpam-5671	210	2	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	210	3	4	4	NUM
ejpam-5671	210	4	∣∣∣ρ(θ2−ξ	∣∣∣ρ(θ2−ξ	VERB
ejpam-5671	210	5	+	+	CCONJ
ejpam-5671	210	6	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	210	7	ξ)−	ξ)−	PROPN
ejpam-5671	210	8	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	210	9	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	210	10	+	+	CCONJ
ejpam-5671	210	11	b1−ξ	b1−ξ	PROPN
ejpam-5671	210	12	)	)	PUNCT
ejpam-5671	210	13	−2(θ	−2(θ	PUNCT
ejpam-5671	211	1	+	+	CCONJ
ejpam-5671	211	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	211	3	+	+	CCONJ
ejpam-5671	211	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	211	5	ξ	ξ	PROPN
ejpam-5671	211	6	)	)	PUNCT
ejpam-5671	212	1	+	+	CCONJ
ejpam-5671	212	2	(	(	PUNCT
ejpam-5671	212	3	θ2	θ2	ADV
ejpam-5671	212	4	+	+	CCONJ
ejpam-5671	212	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	212	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	212	7	+	+	CCONJ
ejpam-5671	212	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	212	9	)	)	PUNCT
ejpam-5671	212	10	∣∣∣	∣∣∣	ADP
ejpam-5671	212	11	×	×	PROPN
ejpam-5671	212	12	(	(	PUNCT
ejpam-5671	212	13	∫	∫	PROPN
ejpam-5671	212	14	θ	θ	PROPN
ejpam-5671	212	15	0	0	PUNCT
ejpam-5671	212	16	(	(	PUNCT
ejpam-5671	212	17	θ	θ	NOUN
ejpam-5671	212	18	−	−	NOUN
ejpam-5671	212	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	212	20	γ(µ−	γ(µ−	VERB
ejpam-5671	212	21	ξ	ξ	PRON
ejpam-5671	212	22	−	−	NOUN
ejpam-5671	212	23	1	1	NUM
ejpam-5671	212	24	)	)	PUNCT
ejpam-5671	212	25	dν	dν	VERB
ejpam-5671	213	1	+	+	CCONJ
ejpam-5671	213	2	∫	∫	PROPN
ejpam-5671	213	3	b	b	PROPN
ejpam-5671	213	4	0	0	NUM
ejpam-5671	213	5	(	(	PUNCT
ejpam-5671	213	6	b−	b−	NOUN
ejpam-5671	213	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	213	8	γ(µ−	γ(µ−	VERB
ejpam-5671	213	9	ξ	ξ	PRON
ejpam-5671	213	10	−	−	NOUN
ejpam-5671	213	11	1	1	NUM
ejpam-5671	213	12	)	)	PUNCT
ejpam-5671	213	13	dν	dν	ADJ
ejpam-5671	213	14	)	)	PUNCT
ejpam-5671	213	15	]	]	PUNCT
ejpam-5671	214	1	≤	≤	NUM
ejpam-5671	214	2	k1m1	k1m1	X
ejpam-5671	214	3	2	2	NUM
ejpam-5671	214	4	=	=	SYM
ejpam-5671	214	5	k2	k2	PROPN
ejpam-5671	214	6	,	,	PUNCT
ejpam-5671	214	7	which	which	PRON
ejpam-5671	214	8	implies	imply	VERB
ejpam-5671	214	9	that	that	SCONJ
ejpam-5671	214	10	||(lω)||	||(lω)||	NOUN
ejpam-5671	214	11	≤	≤	ADJ
ejpam-5671	214	12	k2	k2	NOUN
ejpam-5671	214	13	,	,	PUNCT
ejpam-5671	214	14	now	now	ADV
ejpam-5671	214	15	,	,	PUNCT
ejpam-5671	214	16	|(lω)′(ρ)|	|(lω)′(ρ)|	PROPN
ejpam-5671	214	17	≤	≤	NUM
ejpam-5671	214	18	∫	∫	PROPN
ejpam-5671	214	19	ρ	ρ	PROPN
ejpam-5671	214	20	0	0	PUNCT
ejpam-5671	215	1	(	(	PUNCT
ejpam-5671	215	2	ρ−	ρ−	NOUN
ejpam-5671	215	3	ν)µ−2	ν)µ−2	PROPN
ejpam-5671	215	4	γ(µ−	γ(µ−	VERB
ejpam-5671	215	5	1	1	NUM
ejpam-5671	215	6	)	)	PUNCT
ejpam-5671	215	7	|ω(ν	|ω(ν	ADJ
ejpam-5671	215	8	,	,	PUNCT
ejpam-5671	215	9	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	216	1	+	+	CCONJ
ejpam-5671	216	2	γ(2−	γ(2−	PROPN
ejpam-5671	216	3	ξ	ξ	PROPN
ejpam-5671	216	4	)	)	PUNCT
ejpam-5671	216	5	(	(	PUNCT
ejpam-5671	216	6	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	216	7	+	+	CCONJ
ejpam-5671	216	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	216	9	)	)	PUNCT
ejpam-5671	216	10	(	(	PUNCT
ejpam-5671	216	11	∫	∫	PROPN
ejpam-5671	216	12	θ	θ	PROPN
ejpam-5671	216	13	0	0	PUNCT
ejpam-5671	216	14	(	(	PUNCT
ejpam-5671	216	15	θ	θ	NOUN
ejpam-5671	216	16	−	−	NOUN
ejpam-5671	216	17	ν)µ−2	ν)µ−2	PROPN
ejpam-5671	216	18	γ(µ−	γ(µ−	VERB
ejpam-5671	216	19	1	1	NUM
ejpam-5671	216	20	)	)	PUNCT
ejpam-5671	216	21	|ω(ν	|ω(ν	ADJ
ejpam-5671	216	22	,	,	PUNCT
ejpam-5671	216	23	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	217	1	+	+	CCONJ
ejpam-5671	217	2	∫	∫	PROPN
ejpam-5671	217	3	b	b	PROPN
ejpam-5671	217	4	0	0	NUM
ejpam-5671	217	5	(	(	PUNCT
ejpam-5671	217	6	b−	b−	NOUN
ejpam-5671	217	7	ν)µ−2	ν)µ−2	PROPN
ejpam-5671	217	8	γ(µ−	γ(µ−	VERB
ejpam-5671	217	9	1	1	NUM
ejpam-5671	217	10	)	)	PUNCT
ejpam-5671	217	11	|ω(ν	|ω(ν	ADJ
ejpam-5671	217	12	,	,	PUNCT
ejpam-5671	217	13	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	217	14	)	)	PUNCT
ejpam-5671	218	1	+	+	CCONJ
ejpam-5671	219	1	γ(2−	γ(2−	PROPN
ejpam-5671	219	2	ξ	ξ	X
ejpam-5671	219	3	)	)	PUNCT
ejpam-5671	219	4	γ(3−	γ(3−	ADP
ejpam-5671	219	5	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	219	6	+	+	CCONJ
ejpam-5671	219	7	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	219	8	∣∣∣(θ2−ξ	∣∣∣(θ2−ξ	PROPN
ejpam-5671	219	9	+	+	CCONJ
ejpam-5671	219	10	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	219	11	ξ)−	ξ)−	PROPN
ejpam-5671	219	12	2ργ(3−	2ργ(3−	NUM
ejpam-5671	219	13	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	219	14	+	+	CCONJ
ejpam-5671	219	15	b1−ξ	b1−ξ	PROPN
ejpam-5671	219	16	)	)	PUNCT
ejpam-5671	219	17	∣∣∣	∣∣∣	ADP
ejpam-5671	219	18	×	×	PROPN
ejpam-5671	219	19	(	(	PUNCT
ejpam-5671	219	20	∫	∫	PROPN
ejpam-5671	219	21	θ	θ	PROPN
ejpam-5671	219	22	0	0	PUNCT
ejpam-5671	220	1	(	(	PUNCT
ejpam-5671	220	2	θ	θ	NOUN
ejpam-5671	220	3	−	−	NOUN
ejpam-5671	220	4	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	220	5	γ(µ−	γ(µ−	VERB
ejpam-5671	220	6	ξ	ξ	PRON
ejpam-5671	220	7	−	−	NOUN
ejpam-5671	220	8	1	1	NUM
ejpam-5671	220	9	)	)	PUNCT
ejpam-5671	220	10	|ω(ν	|ω(ν	ADJ
ejpam-5671	220	11	,	,	PUNCT
ejpam-5671	220	12	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	221	1	+	+	CCONJ
ejpam-5671	221	2	∫	∫	PROPN
ejpam-5671	221	3	b	b	PROPN
ejpam-5671	221	4	0	0	NUM
ejpam-5671	221	5	(	(	PUNCT
ejpam-5671	221	6	b−	b−	NOUN
ejpam-5671	221	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	221	8	γ(µ−	γ(µ−	VERB
ejpam-5671	221	9	ξ	ξ	PRON
ejpam-5671	221	10	−	−	NOUN
ejpam-5671	221	11	1	1	NUM
ejpam-5671	221	12	)	)	PUNCT
ejpam-5671	221	13	|ω(ν	|ω(ν	ADJ
ejpam-5671	221	14	,	,	PUNCT
ejpam-5671	221	15	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	221	16	)	)	PUNCT
ejpam-5671	221	17	≤	≤	NUM
ejpam-5671	221	18	k1	k1	NOUN
ejpam-5671	221	19	max	max	PROPN
ejpam-5671	221	20	ρ∈[0,b	ρ∈[0,b	PROPN
ejpam-5671	221	21	]	]	X
ejpam-5671	221	22	2|ρµ−1|+	2|ρµ−1|+	NOUN
ejpam-5671	221	23	γ(2−ξ	γ(2−ξ	NOUN
ejpam-5671	221	24	)	)	PUNCT
ejpam-5671	221	25	(	(	PUNCT
ejpam-5671	221	26	a1−ξ+b1−ξ	a1−ξ+b1−ξ	NOUN
ejpam-5671	221	27	)	)	PUNCT
ejpam-5671	221	28	(	(	PUNCT
ejpam-5671	221	29	θµ−1	θµ−1	NOUN
ejpam-5671	221	30	+	+	CCONJ
ejpam-5671	221	31	bµ−1	bµ−1	ADJ
ejpam-5671	221	32	)	)	PUNCT
ejpam-5671	221	33	2γ(µ	2γ(µ	NUM
ejpam-5671	221	34	)	)	PUNCT
ejpam-5671	222	1	+	+	CCONJ
ejpam-5671	222	2	|γ(2−	|γ(2−	PROPN
ejpam-5671	222	3	ξ)|	ξ)|	NOUN
ejpam-5671	222	4	γ(3−	γ(3−	ADP
ejpam-5671	222	5	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	222	6	+	+	CCONJ
ejpam-5671	222	7	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	222	8	|(θ2−ξ	|(θ2−ξ	NOUN
ejpam-5671	222	9	+	+	CCONJ
ejpam-5671	222	10	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	222	11	ξ)−	ξ)−	PROPN
ejpam-5671	222	12	2ργ(3−	2ργ(3−	NUM
ejpam-5671	222	13	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	222	14	+	+	PUNCT
ejpam-5671	222	15	b1−ξ)|	b1−ξ)|	X
ejpam-5671	222	16	}	}	PUNCT
ejpam-5671	222	17	)	)	PUNCT
ejpam-5671	223	1	=	=	PRON
ejpam-5671	223	2	k3	k3	PROPN
ejpam-5671	223	3	.	.	PUNCT
ejpam-5671	224	1	hence	hence	ADV
ejpam-5671	224	2	,	,	PUNCT
ejpam-5671	224	3	for	for	ADP
ejpam-5671	224	4	any	any	DET
ejpam-5671	224	5	ρ1	ρ1	NOUN
ejpam-5671	224	6	,	,	PUNCT
ejpam-5671	224	7	ρ2	ρ2	PROPN
ejpam-5671	224	8	∈	∈	PROPN
ejpam-5671	224	9	[	[	X
ejpam-5671	224	10	0	0	NUM
ejpam-5671	224	11	,	,	PUNCT
ejpam-5671	224	12	b	b	NOUN
ejpam-5671	224	13	]	]	X
ejpam-5671	224	14	,	,	PUNCT
ejpam-5671	224	15	we	we	PRON
ejpam-5671	224	16	have	have	VERB
ejpam-5671	224	17	|(lω)(ρ2)−	|(lω)(ρ2)−	ADJ
ejpam-5671	224	18	(	(	PUNCT
ejpam-5671	224	19	lω)(ρ1)|	lω)(ρ1)|	PRON
ejpam-5671	224	20	≤	≤	NUM
ejpam-5671	224	21	∫	∫	PROPN
ejpam-5671	224	22	ρ2	ρ2	PROPN
ejpam-5671	224	23	ρ1	ρ1	NOUN
ejpam-5671	224	24	|(lρ)′(ν)|dν	|(lρ)′(ν)|dν	NOUN
ejpam-5671	224	25	≤	≤	ADV
ejpam-5671	224	26	k3(ρ2	k3(ρ2	NOUN
ejpam-5671	224	27	−	−	PROPN
ejpam-5671	224	28	ρ1	ρ1	NOUN
ejpam-5671	224	29	)	)	PUNCT
ejpam-5671	224	30	.	.	PUNCT
ejpam-5671	225	1	therefore	therefore	ADV
ejpam-5671	225	2	,	,	PUNCT
ejpam-5671	225	3	l	l	NOUN
ejpam-5671	225	4	satisfies	satisfy	VERB
ejpam-5671	225	5	equuicontinuity	equuicontinuity	NOUN
ejpam-5671	225	6	on	on	ADP
ejpam-5671	225	7	[	[	X
ejpam-5671	225	8	0	0	NUM
ejpam-5671	225	9	,	,	PUNCT
ejpam-5671	225	10	b	b	NOUN
ejpam-5671	225	11	]	]	PUNCT
ejpam-5671	225	12	.	.	PUNCT
ejpam-5671	226	1	by	by	ADP
ejpam-5671	226	2	arzelá-ascoli	arzelá-ascoli	NOUN
ejpam-5671	226	3	theorem	theorem	VERB
ejpam-5671	226	4	,	,	PUNCT
ejpam-5671	226	5	we	we	PRON
ejpam-5671	226	6	conclude	conclude	VERB
ejpam-5671	226	7	that	that	SCONJ
ejpam-5671	226	8	l	l	NOUN
ejpam-5671	226	9	is	be	AUX
ejpam-5671	226	10	completely	completely	ADV
ejpam-5671	226	11	continuous	continuous	ADJ
ejpam-5671	226	12	.	.	PUNCT
ejpam-5671	227	1	s.	s.	PROPN
ejpam-5671	227	2	f.	f.	PROPN
ejpam-5671	227	3	aljurbua	aljurbua	PROPN
ejpam-5671	227	4	,	,	PUNCT
ejpam-5671	227	5	h.	h.	PROPN
ejpam-5671	227	6	a.	a.	PROPN
ejpam-5671	227	7	hammad	hammad	PROPN
ejpam-5671	227	8	,	,	PUNCT
ejpam-5671	227	9	n.	n.	PROPN
ejpam-5671	227	10	b.	b.	PROPN
ejpam-5671	227	11	almutairi	almutairi	PROPN
ejpam-5671	227	12	/	/	SYM
ejpam-5671	227	13	eur	eur	PROPN
ejpam-5671	227	14	.	.	PUNCT
ejpam-5671	228	1	j.	j.	PROPN
ejpam-5671	228	2	pure	pure	PROPN
ejpam-5671	228	3	appl	appl	PROPN
ejpam-5671	228	4	.	.	PROPN
ejpam-5671	228	5	math	math	PROPN
ejpam-5671	228	6	,	,	PUNCT
ejpam-5671	228	7	18	18	NUM
ejpam-5671	228	8	(	(	PUNCT
ejpam-5671	228	9	1	1	NUM
ejpam-5671	228	10	)	)	PUNCT
ejpam-5671	228	11	(	(	PUNCT
ejpam-5671	228	12	2025	2025	NUM
ejpam-5671	228	13	)	)	PUNCT
ejpam-5671	228	14	,	,	PUNCT
ejpam-5671	228	15	5671	5671	NUM
ejpam-5671	228	16	9	9	NUM
ejpam-5671	228	17	of	of	ADP
ejpam-5671	228	18	18	18	NUM
ejpam-5671	228	19	theorem	theorem	NOUN
ejpam-5671	228	20	3	3	NUM
ejpam-5671	228	21	.	.	PUNCT
ejpam-5671	228	22	assume	assume	VERB
ejpam-5671	229	1	that	that	SCONJ
ejpam-5671	229	2	ω	ω	X
ejpam-5671	229	3	:	:	PUNCT
ejpam-5671	230	1	[	[	X
ejpam-5671	230	2	0	0	NUM
ejpam-5671	230	3	,	,	PUNCT
ejpam-5671	230	4	b]×	b]×	NOUN
ejpam-5671	230	5	r	r	NOUN
ejpam-5671	230	6	−→	−→	NOUN
ejpam-5671	230	7	r	r	NOUN
ejpam-5671	230	8	is	be	AUX
ejpam-5671	230	9	jointly	jointly	ADV
ejpam-5671	230	10	continuous	continuous	ADJ
ejpam-5671	230	11	function	function	NOUN
ejpam-5671	230	12	such	such	ADJ
ejpam-5671	230	13	that	that	DET
ejpam-5671	230	14	||ω(ρ	||ω(ρ	NOUN
ejpam-5671	230	15	,	,	PUNCT
ejpam-5671	230	16	ω1)−	ω1)−	PROPN
ejpam-5671	230	17	ω(ρ	ω(ρ	PROPN
ejpam-5671	230	18	,	,	PUNCT
ejpam-5671	230	19	ω2)||	ω2)||	NUM
ejpam-5671	230	20	≤	≤	NUM
ejpam-5671	230	21	l||ω1	l||ω1	PROPN
ejpam-5671	230	22	−	−	PROPN
ejpam-5671	230	23	ω2||	ω2||	PROPN
ejpam-5671	230	24	,	,	PUNCT
ejpam-5671	230	25	for	for	ADP
ejpam-5671	230	26	all	all	DET
ejpam-5671	230	27	ρ	ρ	NOUN
ejpam-5671	230	28	∈	∈	PROPN
ejpam-5671	231	1	[	[	X
ejpam-5671	231	2	0	0	NUM
ejpam-5671	231	3	,	,	PUNCT
ejpam-5671	231	4	b	b	NOUN
ejpam-5671	231	5	]	]	X
ejpam-5671	231	6	and	and	CCONJ
ejpam-5671	231	7	ω1	ω1	PROPN
ejpam-5671	231	8	,	,	PUNCT
ejpam-5671	231	9	ω2	ω2	NOUN
ejpam-5671	231	10	∈	∈	PROPN
ejpam-5671	231	11	r	r	NOUN
ejpam-5671	231	12	,	,	PUNCT
ejpam-5671	231	13	where	where	SCONJ
ejpam-5671	231	14	m1	m1	PROPN
ejpam-5671	231	15	is	be	AUX
ejpam-5671	231	16	defined	define	VERB
ejpam-5671	231	17	in	in	ADP
ejpam-5671	231	18	(	(	PUNCT
ejpam-5671	231	19	13	13	NUM
ejpam-5671	231	20	)	)	PUNCT
ejpam-5671	231	21	.	.	PUNCT
ejpam-5671	232	1	the	the	DET
ejpam-5671	232	2	problem	problem	NOUN
ejpam-5671	232	3	(	(	PUNCT
ejpam-5671	232	4	1	1	X
ejpam-5671	232	5	)	)	PUNCT
ejpam-5671	232	6	has	have	VERB
ejpam-5671	232	7	a	a	DET
ejpam-5671	232	8	solution	solution	NOUN
ejpam-5671	232	9	,	,	PUNCT
ejpam-5671	232	10	provided	provide	VERB
ejpam-5671	232	11	that	that	DET
ejpam-5671	232	12	lm1	lm1	NOUN
ejpam-5671	232	13	<	<	X
ejpam-5671	232	14	1	1	X
ejpam-5671	232	15	.	.	PUNCT
ejpam-5671	232	16	proof	proof	NOUN
ejpam-5671	232	17	.	.	PUNCT
ejpam-5671	233	1	assume	assume	VERB
ejpam-5671	233	2	that	that	SCONJ
ejpam-5671	233	3	maxρ∈[0,b	maxρ∈[0,b	X
ejpam-5671	233	4	]	]	X
ejpam-5671	233	5	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	233	6	,	,	PUNCT
ejpam-5671	233	7	0)||	0)||	NOUN
ejpam-5671	233	8	=	=	SYM
ejpam-5671	233	9	η	η	X
ejpam-5671	233	10	<	<	X
ejpam-5671	233	11	∞	∞	PROPN
ejpam-5671	233	12	and	and	CCONJ
ejpam-5671	233	13	selecting	select	VERB
ejpam-5671	233	14	r	r	NOUN
ejpam-5671	233	15	≥	≥	NOUN
ejpam-5671	233	16	κ1	κ1	NOUN
ejpam-5671	233	17	1−κ2	1−κ2	NUM
ejpam-5671	233	18	where	where	SCONJ
ejpam-5671	233	19	κ1	κ1	NOUN
ejpam-5671	233	20	=	=	PUNCT
ejpam-5671	233	21	ηm1	ηm1	NOUN
ejpam-5671	233	22	2	2	NUM
ejpam-5671	233	23	and	and	CCONJ
ejpam-5671	233	24	κ2	κ2	NOUN
ejpam-5671	233	25	=	=	PUNCT
ejpam-5671	233	26	lm1	lm1	NOUN
ejpam-5671	233	27	2	2	NUM
ejpam-5671	233	28	,	,	PUNCT
ejpam-5671	233	29	we	we	PRON
ejpam-5671	233	30	will	will	AUX
ejpam-5671	233	31	demonstrate	demonstrate	VERB
ejpam-5671	233	32	that	that	SCONJ
ejpam-5671	233	33	lbr	lbr	NOUN
ejpam-5671	233	34	⊂	⊂	PROPN
ejpam-5671	233	35	br	br	X
ejpam-5671	233	36	where	where	SCONJ
ejpam-5671	233	37	br	br	NOUN
ejpam-5671	233	38	=	=	SYM
ejpam-5671	233	39	{	{	PUNCT
ejpam-5671	233	40	ω	ω	PROPN
ejpam-5671	233	41	∈	∈	PROPN
ejpam-5671	233	42	c[0	c[0	PROPN
ejpam-5671	233	43	,	,	PUNCT
ejpam-5671	233	44	b	b	NOUN
ejpam-5671	233	45	]	]	X
ejpam-5671	233	46	:	:	PUNCT
ejpam-5671	233	47	||ω||	||ω||	VERB
ejpam-5671	233	48	≤	≤	NUM
ejpam-5671	233	49	r	r	NOUN
ejpam-5671	233	50	}	}	PUNCT
ejpam-5671	233	51	.	.	PUNCT
ejpam-5671	234	1	now	now	ADV
ejpam-5671	234	2	,	,	PUNCT
ejpam-5671	234	3	for	for	ADP
ejpam-5671	234	4	ω	ω	PROPN
ejpam-5671	234	5	∈	∈	PROPN
ejpam-5671	234	6	br	br	NOUN
ejpam-5671	234	7	,	,	PUNCT
ejpam-5671	234	8	we	we	PRON
ejpam-5671	234	9	have	have	VERB
ejpam-5671	234	10	||(lω)(ρ)||	||(lω)(ρ)||	NOUN
ejpam-5671	234	11	≤	≤	NUM
ejpam-5671	234	12	∫	∫	PROPN
ejpam-5671	234	13	ρ	ρ	PROPN
ejpam-5671	234	14	0	0	PROPN
ejpam-5671	235	1	(	(	PUNCT
ejpam-5671	235	2	ρ−	ρ−	NOUN
ejpam-5671	235	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	235	4	γ(µ	γ(µ	PROPN
ejpam-5671	235	5	)	)	PUNCT
ejpam-5671	236	1	|	|	CCONJ
ejpam-5671	236	2	(	(	PUNCT
ejpam-5671	236	3	|ω(ν	|ω(ν	ADV
ejpam-5671	236	4	,	,	PUNCT
ejpam-5671	236	5	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	236	6	ω(ν	ω(ν	NOUN
ejpam-5671	236	7	,	,	PUNCT
ejpam-5671	236	8	0)||+	0)||+	NOUN
ejpam-5671	236	9	||ω(ν	||ω(ν	ADV
ejpam-5671	236	10	,	,	PUNCT
ejpam-5671	236	11	0)||	0)||	NOUN
ejpam-5671	236	12	)	)	PUNCT
ejpam-5671	236	13	dν	dν	VERB
ejpam-5671	237	1	+	+	CCONJ
ejpam-5671	237	2	1	1	NUM
ejpam-5671	237	3	2	2	NUM
ejpam-5671	237	4	(	(	PUNCT
ejpam-5671	237	5	∫	∫	PROPN
ejpam-5671	237	6	θ	θ	PROPN
ejpam-5671	237	7	0	0	PUNCT
ejpam-5671	237	8	(	(	PUNCT
ejpam-5671	237	9	θ	θ	NOUN
ejpam-5671	237	10	−	−	PROPN
ejpam-5671	237	11	ν)µ−1	ν)µ−1	X
ejpam-5671	237	12	γ(µ	γ(µ	PROPN
ejpam-5671	237	13	)	)	PUNCT
ejpam-5671	238	1	[	[	X
ejpam-5671	238	2	||ω(ν	||ω(ν	ADP
ejpam-5671	238	3	,	,	PUNCT
ejpam-5671	238	4	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	238	5	ω(ν	ω(ν	NOUN
ejpam-5671	238	6	,	,	PUNCT
ejpam-5671	238	7	0)||+	0)||+	NOUN
ejpam-5671	238	8	||ω(ν	||ω(ν	ADV
ejpam-5671	238	9	,	,	PUNCT
ejpam-5671	238	10	0)||dν	0)||dν	PROPN
ejpam-5671	238	11	]	]	PUNCT
ejpam-5671	239	1	+	+	NUM
ejpam-5671	240	1	∫	∫	PROPN
ejpam-5671	240	2	b	b	PROPN
ejpam-5671	240	3	0	0	NUM
ejpam-5671	240	4	(	(	PUNCT
ejpam-5671	240	5	b−	b−	PROPN
ejpam-5671	240	6	ν)µ−1	ν)µ−1	VERB
ejpam-5671	240	7	γ(µ	γ(µ	PROPN
ejpam-5671	240	8	)	)	PUNCT
ejpam-5671	240	9	(	(	PUNCT
ejpam-5671	240	10	||ω(ν	||ω(ν	ADV
ejpam-5671	240	11	,	,	PUNCT
ejpam-5671	240	12	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	240	13	ω(ν	ω(ν	NOUN
ejpam-5671	240	14	,	,	PUNCT
ejpam-5671	240	15	0)||+	0)||+	NOUN
ejpam-5671	240	16	||ω(ν	||ω(ν	ADV
ejpam-5671	240	17	,	,	PUNCT
ejpam-5671	240	18	0)||	0)||	NOUN
ejpam-5671	240	19	)	)	PUNCT
ejpam-5671	240	20	dν	dν	VERB
ejpam-5671	240	21	)	)	PUNCT
ejpam-5671	241	1	+	+	CCONJ
ejpam-5671	241	2	γ(2−	γ(2−	NOUN
ejpam-5671	241	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	241	4	+	+	CCONJ
ejpam-5671	241	5	b)−	b)−	PROPN
ejpam-5671	241	6	2ρ|	2ρ|	NUM
ejpam-5671	241	7	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	241	8	+	+	CCONJ
ejpam-5671	241	9	b1−ξ	b1−ξ	PROPN
ejpam-5671	241	10	)	)	PUNCT
ejpam-5671	241	11	(	(	PUNCT
ejpam-5671	241	12	∫	∫	PROPN
ejpam-5671	241	13	θ	θ	PROPN
ejpam-5671	241	14	0	0	PUNCT
ejpam-5671	241	15	(	(	PUNCT
ejpam-5671	241	16	θ	θ	X
ejpam-5671	241	17	−	−	PROPN
ejpam-5671	241	18	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	241	19	γ(µ−	γ(µ−	VERB
ejpam-5671	241	20	ξ	ξ	NUM
ejpam-5671	241	21	)	)	PUNCT
ejpam-5671	241	22	(	(	PUNCT
ejpam-5671	241	23	||ω(ν	||ω(ν	ADV
ejpam-5671	241	24	,	,	PUNCT
ejpam-5671	241	25	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	241	26	ω(ν	ω(ν	NOUN
ejpam-5671	241	27	,	,	PUNCT
ejpam-5671	241	28	0)||+	0)||+	NOUN
ejpam-5671	241	29	||ω(ν	||ω(ν	ADV
ejpam-5671	241	30	,	,	PUNCT
ejpam-5671	241	31	0)||	0)||	NOUN
ejpam-5671	241	32	)	)	PUNCT
ejpam-5671	241	33	dν	dν	VERB
ejpam-5671	242	1	+	+	CCONJ
ejpam-5671	243	1	∫	∫	PROPN
ejpam-5671	243	2	b	b	PROPN
ejpam-5671	243	3	0	0	NUM
ejpam-5671	243	4	(	(	PUNCT
ejpam-5671	243	5	b−	b−	PROPN
ejpam-5671	243	6	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	243	7	γ(µ−	γ(µ−	VERB
ejpam-5671	243	8	ξ	ξ	NUM
ejpam-5671	243	9	)	)	PUNCT
ejpam-5671	243	10	(	(	PUNCT
ejpam-5671	243	11	||ω(ν	||ω(ν	ADV
ejpam-5671	243	12	,	,	PUNCT
ejpam-5671	243	13	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	243	14	ω(ν	ω(ν	NOUN
ejpam-5671	243	15	,	,	PUNCT
ejpam-5671	243	16	0)||+	0)||+	NOUN
ejpam-5671	243	17	||ω(ν	||ω(ν	ADV
ejpam-5671	243	18	,	,	PUNCT
ejpam-5671	243	19	0)||	0)||	NOUN
ejpam-5671	243	20	)	)	PUNCT
ejpam-5671	243	21	dν	dν	VERB
ejpam-5671	243	22	)	)	PUNCT
ejpam-5671	244	1	+	+	CCONJ
ejpam-5671	244	2	γ(2−	γ(2−	PROPN
ejpam-5671	244	3	ξ	ξ	PROPN
ejpam-5671	244	4	)	)	PUNCT
ejpam-5671	244	5	4γ(3−	4γ(3−	NUM
ejpam-5671	244	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	244	7	+	+	CCONJ
ejpam-5671	244	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	244	9	)	)	PUNCT
ejpam-5671	244	10	)	)	PUNCT
ejpam-5671	245	1	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	245	2	+	+	CCONJ
ejpam-5671	245	3	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	245	4	ξ)−	ξ)−	PROPN
ejpam-5671	245	5	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	245	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	245	7	+	+	CCONJ
ejpam-5671	245	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	245	9	)	)	PUNCT
ejpam-5671	245	10	−2(θ	−2(θ	PUNCT
ejpam-5671	245	11	+	+	CCONJ
ejpam-5671	245	12	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	245	13	+	+	CCONJ
ejpam-5671	245	14	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	245	15	ξ	ξ	PROPN
ejpam-5671	245	16	)	)	PUNCT
ejpam-5671	245	17	)	)	PUNCT
ejpam-5671	246	1	+	+	CCONJ
ejpam-5671	246	2	(	(	PUNCT
ejpam-5671	246	3	θ2	θ2	ADV
ejpam-5671	246	4	+	+	CCONJ
ejpam-5671	246	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	246	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	246	7	+	+	CCONJ
ejpam-5671	246	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	246	9	)	)	PUNCT
ejpam-5671	246	10	∣∣∣	∣∣∣	ADP
ejpam-5671	246	11	×	×	PROPN
ejpam-5671	246	12	(	(	PUNCT
ejpam-5671	246	13	∫	∫	PROPN
ejpam-5671	246	14	θ	θ	PROPN
ejpam-5671	246	15	0	0	PUNCT
ejpam-5671	246	16	(	(	PUNCT
ejpam-5671	246	17	θ	θ	NOUN
ejpam-5671	246	18	−	−	NOUN
ejpam-5671	246	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	246	20	γ(µ−	γ(µ−	VERB
ejpam-5671	246	21	ξ	ξ	PRON
ejpam-5671	246	22	−	−	NOUN
ejpam-5671	246	23	1	1	NUM
ejpam-5671	246	24	)	)	PUNCT
ejpam-5671	246	25	||ω(ν	||ω(ν	ADV
ejpam-5671	246	26	,	,	PUNCT
ejpam-5671	246	27	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	246	28	ω(ν	ω(ν	NOUN
ejpam-5671	246	29	,	,	PUNCT
ejpam-5671	246	30	0)||+	0)||+	NOUN
ejpam-5671	246	31	||ω(ν	||ω(ν	ADV
ejpam-5671	246	32	,	,	PUNCT
ejpam-5671	246	33	0)||	0)||	NOUN
ejpam-5671	246	34	)	)	PUNCT
ejpam-5671	246	35	dν	dν	VERB
ejpam-5671	247	1	+	+	CCONJ
ejpam-5671	247	2	∫	∫	PROPN
ejpam-5671	247	3	b	b	PROPN
ejpam-5671	247	4	0	0	NUM
ejpam-5671	247	5	(	(	PUNCT
ejpam-5671	247	6	b−	b−	NOUN
ejpam-5671	247	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	247	8	γ(µ−	γ(µ−	VERB
ejpam-5671	247	9	ξ	ξ	PRON
ejpam-5671	247	10	−	−	NOUN
ejpam-5671	247	11	1	1	NUM
ejpam-5671	247	12	)	)	PUNCT
ejpam-5671	247	13	(	(	PUNCT
ejpam-5671	247	14	||ω(ν	||ω(ν	ADV
ejpam-5671	247	15	,	,	PUNCT
ejpam-5671	247	16	ω(ν))−	ω(ν))−	NOUN
ejpam-5671	247	17	ω(ν	ω(ν	NOUN
ejpam-5671	247	18	,	,	PUNCT
ejpam-5671	247	19	0)||+	0)||+	NOUN
ejpam-5671	247	20	||ω(ν	||ω(ν	ADV
ejpam-5671	247	21	,	,	PUNCT
ejpam-5671	247	22	0)||	0)||	NOUN
ejpam-5671	247	23	)	)	PUNCT
ejpam-5671	247	24	dν	dν	PROPN
ejpam-5671	247	25	)	)	PUNCT
ejpam-5671	247	26	≤	≤	NOUN
ejpam-5671	247	27	(	(	PUNCT
ejpam-5671	247	28	lr	lr	X
ejpam-5671	247	29	+	+	CCONJ
ejpam-5671	247	30	η	η	NOUN
ejpam-5671	247	31	)	)	PUNCT
ejpam-5671	247	32	2	2	NUM
ejpam-5671	247	33	(	(	PUNCT
ejpam-5671	247	34	2	2	NUM
ejpam-5671	247	35	∫	∫	NOUN
ejpam-5671	247	36	ρ	ρ	NOUN
ejpam-5671	247	37	0	0	PUNCT
ejpam-5671	248	1	(	(	PUNCT
ejpam-5671	248	2	ρ−	ρ−	NOUN
ejpam-5671	248	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	248	4	γ(µ	γ(µ	PROPN
ejpam-5671	248	5	)	)	PUNCT
ejpam-5671	249	1	dν	dν	VERB
ejpam-5671	250	1	+	+	CCONJ
ejpam-5671	250	2	∫	∫	PROPN
ejpam-5671	250	3	θ	θ	NOUN
ejpam-5671	250	4	0	0	PUNCT
ejpam-5671	250	5	(	(	PUNCT
ejpam-5671	250	6	θ	θ	NOUN
ejpam-5671	250	7	−	−	PROPN
ejpam-5671	250	8	ν)µ−1	ν)µ−1	X
ejpam-5671	250	9	γ(µ	γ(µ	PROPN
ejpam-5671	250	10	)	)	PUNCT
ejpam-5671	250	11	dν	dν	VERB
ejpam-5671	251	1	+	+	CCONJ
ejpam-5671	251	2	∫	∫	PROPN
ejpam-5671	251	3	b	b	PROPN
ejpam-5671	251	4	0	0	NUM
ejpam-5671	251	5	(	(	PUNCT
ejpam-5671	251	6	b−	b−	PROPN
ejpam-5671	251	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	251	8	γ(µ	γ(µ	PROPN
ejpam-5671	251	9	)	)	PUNCT
ejpam-5671	252	1	dν	dν	VERB
ejpam-5671	252	2	)	)	PUNCT
ejpam-5671	253	1	+	+	CCONJ
ejpam-5671	253	2	γ(2−	γ(2−	NOUN
ejpam-5671	253	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	253	4	+	+	CCONJ
ejpam-5671	253	5	b)−	b)−	PROPN
ejpam-5671	253	6	2ρ|	2ρ|	NUM
ejpam-5671	253	7	(	(	PUNCT
ejpam-5671	253	8	θ1−ξ	θ1−ξ	PROPN
ejpam-5671	253	9	+	+	CCONJ
ejpam-5671	253	10	b1−ξ	b1−ξ	PROPN
ejpam-5671	253	11	)	)	PUNCT
ejpam-5671	253	12	(	(	PUNCT
ejpam-5671	253	13	∫	∫	PROPN
ejpam-5671	253	14	θ	θ	PROPN
ejpam-5671	253	15	0	0	PUNCT
ejpam-5671	253	16	(	(	PUNCT
ejpam-5671	253	17	θ	θ	X
ejpam-5671	253	18	−	−	PROPN
ejpam-5671	253	19	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	253	20	γ(µ−	γ(µ−	VERB
ejpam-5671	253	21	ξ	ξ	X
ejpam-5671	253	22	)	)	PUNCT
ejpam-5671	253	23	dν	dν	VERB
ejpam-5671	254	1	+	+	CCONJ
ejpam-5671	254	2	∫	∫	PROPN
ejpam-5671	254	3	b	b	PROPN
ejpam-5671	254	4	0	0	NUM
ejpam-5671	254	5	(	(	PUNCT
ejpam-5671	254	6	b−	b−	PROPN
ejpam-5671	254	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	254	8	γ(µ−	γ(µ−	VERB
ejpam-5671	254	9	ξ	ξ	X
ejpam-5671	254	10	)	)	PUNCT
ejpam-5671	254	11	dν	dν	VERB
ejpam-5671	254	12	)	)	PUNCT
ejpam-5671	255	1	+	+	CCONJ
ejpam-5671	255	2	γ(2−	γ(2−	PROPN
ejpam-5671	255	3	ξ	ξ	PROPN
ejpam-5671	255	4	)	)	PUNCT
ejpam-5671	255	5	2γ(3−	2γ(3−	PROPN
ejpam-5671	255	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	255	7	+	+	CCONJ
ejpam-5671	255	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	255	9	)	)	PUNCT
ejpam-5671	255	10	)	)	PUNCT
ejpam-5671	256	1	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	256	2	+	+	CCONJ
ejpam-5671	256	3	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	256	4	ξ)−	ξ)−	PROPN
ejpam-5671	256	5	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	256	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	256	7	+	+	CCONJ
ejpam-5671	256	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	256	9	)	)	PUNCT
ejpam-5671	256	10	−2(θ	−2(θ	PUNCT
ejpam-5671	256	11	+	+	CCONJ
ejpam-5671	256	12	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	256	13	+	+	CCONJ
ejpam-5671	256	14	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	256	15	ξ	ξ	PROPN
ejpam-5671	256	16	)	)	PUNCT
ejpam-5671	256	17	)	)	PUNCT
ejpam-5671	257	1	+	+	CCONJ
ejpam-5671	257	2	(	(	PUNCT
ejpam-5671	257	3	θ2	θ2	ADV
ejpam-5671	257	4	+	+	CCONJ
ejpam-5671	257	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	257	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	257	7	+	+	CCONJ
ejpam-5671	257	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	257	9	)	)	PUNCT
ejpam-5671	257	10	∣∣∣	∣∣∣	ADP
ejpam-5671	257	11	×	×	PROPN
ejpam-5671	257	12	(	(	PUNCT
ejpam-5671	257	13	∫	∫	PROPN
ejpam-5671	257	14	θ	θ	PROPN
ejpam-5671	257	15	0	0	PUNCT
ejpam-5671	257	16	(	(	PUNCT
ejpam-5671	257	17	θ	θ	NOUN
ejpam-5671	257	18	−	−	NOUN
ejpam-5671	257	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	257	20	γ(µ−	γ(µ−	VERB
ejpam-5671	257	21	ξ	ξ	PRON
ejpam-5671	257	22	−	−	NOUN
ejpam-5671	257	23	1	1	NUM
ejpam-5671	257	24	)	)	PUNCT
ejpam-5671	257	25	dν	dν	VERB
ejpam-5671	258	1	+	+	CCONJ
ejpam-5671	258	2	∫	∫	PROPN
ejpam-5671	258	3	b	b	PROPN
ejpam-5671	258	4	0	0	NUM
ejpam-5671	258	5	(	(	PUNCT
ejpam-5671	258	6	b−	b−	NOUN
ejpam-5671	258	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	258	8	γ(µ−	γ(µ−	VERB
ejpam-5671	258	9	ξ	ξ	PRON
ejpam-5671	258	10	−	−	NOUN
ejpam-5671	258	11	1	1	NUM
ejpam-5671	258	12	)	)	PUNCT
ejpam-5671	258	13	dν	dν	ADJ
ejpam-5671	258	14	)	)	PUNCT
ejpam-5671	258	15	≤	≤	NOUN
ejpam-5671	258	16	(	(	PUNCT
ejpam-5671	258	17	lr	lr	X
ejpam-5671	258	18	+	+	CCONJ
ejpam-5671	258	19	η	η	NOUN
ejpam-5671	258	20	)	)	PUNCT
ejpam-5671	258	21	2	2	NUM
ejpam-5671	258	22	[	[	PUNCT
ejpam-5671	258	23	2|ρ|µ	2|ρ|µ	NUM
ejpam-5671	258	24	+	+	NUM
ejpam-5671	258	25	bµ	bµ	PROPN
ejpam-5671	258	26	+	+	CCONJ
ejpam-5671	258	27	θµ	θµ	NUM
ejpam-5671	258	28	γ(µ+	γ(µ+	NOUN
ejpam-5671	258	29	1	1	NUM
ejpam-5671	258	30	)	)	PUNCT
ejpam-5671	259	1	+	+	CCONJ
ejpam-5671	259	2	γ(2−	γ(2−	NOUN
ejpam-5671	259	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	259	4	+	+	CCONJ
ejpam-5671	259	5	b)−	b)−	PROPN
ejpam-5671	259	6	2ρ|(θµ−ξ	2ρ|(θµ−ξ	PROPN
ejpam-5671	259	7	+	+	CCONJ
ejpam-5671	259	8	bµ−ξ	bµ−ξ	NOUN
ejpam-5671	259	9	)	)	PUNCT
ejpam-5671	259	10	2γ(µ−	2γ(µ−	NUM
ejpam-5671	260	1	ξ	ξ	X
ejpam-5671	260	2	+	+	NUM
ejpam-5671	260	3	1	1	X
ejpam-5671	260	4	)	)	PUNCT
ejpam-5671	260	5	s.	s.	PROPN
ejpam-5671	260	6	f.	f.	PROPN
ejpam-5671	260	7	aljurbua	aljurbua	PROPN
ejpam-5671	260	8	,	,	PUNCT
ejpam-5671	260	9	h.	h.	PROPN
ejpam-5671	260	10	a.	a.	PROPN
ejpam-5671	260	11	hammad	hammad	PROPN
ejpam-5671	260	12	,	,	PUNCT
ejpam-5671	260	13	n.	n.	PROPN
ejpam-5671	260	14	b.	b.	PROPN
ejpam-5671	260	15	almutairi	almutairi	PROPN
ejpam-5671	260	16	/	/	SYM
ejpam-5671	260	17	eur	eur	PROPN
ejpam-5671	260	18	.	.	PUNCT
ejpam-5671	261	1	j.	j.	PROPN
ejpam-5671	261	2	pure	pure	PROPN
ejpam-5671	261	3	appl	appl	PROPN
ejpam-5671	261	4	.	.	PROPN
ejpam-5671	261	5	math	math	PROPN
ejpam-5671	261	6	,	,	PUNCT
ejpam-5671	261	7	18	18	NUM
ejpam-5671	261	8	(	(	PUNCT
ejpam-5671	261	9	1	1	NUM
ejpam-5671	261	10	)	)	PUNCT
ejpam-5671	261	11	(	(	PUNCT
ejpam-5671	261	12	2025	2025	NUM
ejpam-5671	261	13	)	)	PUNCT
ejpam-5671	261	14	,	,	PUNCT
ejpam-5671	261	15	5671	5671	NUM
ejpam-5671	261	16	10	10	NUM
ejpam-5671	261	17	of	of	ADP
ejpam-5671	261	18	18	18	NUM
ejpam-5671	261	19	+	+	CCONJ
ejpam-5671	261	20	γ(2−	γ(2−	NOUN
ejpam-5671	261	21	ξ)(θµ−ξ−1	ξ)(θµ−ξ−1	ADJ
ejpam-5671	261	22	+	+	CCONJ
ejpam-5671	261	23	bµ−ξ−1	bµ−ξ−1	NOUN
ejpam-5671	261	24	)	)	PUNCT
ejpam-5671	261	25	2γ(µ−	2γ(µ−	NUM
ejpam-5671	261	26	ξ	ξ	X
ejpam-5671	261	27	)	)	PUNCT
ejpam-5671	261	28	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	261	29	+	+	CCONJ
ejpam-5671	261	30	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	261	31	ξ)−	ξ)−	PROPN
ejpam-5671	261	32	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	261	33	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	261	34	+	+	CCONJ
ejpam-5671	261	35	b1−ξ	b1−ξ	PROPN
ejpam-5671	261	36	)	)	PUNCT
ejpam-5671	262	1	−	−	ADP
ejpam-5671	262	2	2(θ	2(θ	NUM
ejpam-5671	263	1	+	+	CCONJ
ejpam-5671	263	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	263	3	+	+	CCONJ
ejpam-5671	263	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	263	5	ξ	ξ	PROPN
ejpam-5671	263	6	)	)	PUNCT
ejpam-5671	263	7	)	)	PUNCT
ejpam-5671	264	1	+	+	CCONJ
ejpam-5671	264	2	(	(	PUNCT
ejpam-5671	264	3	θ2	θ2	ADV
ejpam-5671	264	4	+	+	CCONJ
ejpam-5671	264	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	264	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	264	7	+	+	CCONJ
ejpam-5671	264	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	264	9	)	)	PUNCT
ejpam-5671	264	10	∣∣∣	∣∣∣	ADP
ejpam-5671	264	11	]	]	PUNCT
ejpam-5671	264	12	≤	≤	NUM
ejpam-5671	264	13	(	(	PUNCT
ejpam-5671	264	14	lr	lr	X
ejpam-5671	264	15	+	+	CCONJ
ejpam-5671	264	16	η	η	NOUN
ejpam-5671	264	17	)	)	PUNCT
ejpam-5671	264	18	m1	m1	NOUN
ejpam-5671	264	19	2	2	NUM
ejpam-5671	264	20	≤	≤	PROPN
ejpam-5671	264	21	r.	r.	NOUN
ejpam-5671	264	22	this	this	PRON
ejpam-5671	264	23	proves	prove	VERB
ejpam-5671	264	24	that	that	SCONJ
ejpam-5671	264	25	lbr	lbr	NOUN
ejpam-5671	264	26	⊂	⊂	X
ejpam-5671	264	27	br	br	PROPN
ejpam-5671	264	28	.	.	PUNCT
ejpam-5671	265	1	now	now	ADV
ejpam-5671	265	2	,	,	PUNCT
ejpam-5671	265	3	we	we	PRON
ejpam-5671	265	4	prove	prove	VERB
ejpam-5671	265	5	that	that	SCONJ
ejpam-5671	265	6	the	the	DET
ejpam-5671	265	7	operator	operator	NOUN
ejpam-5671	265	8	l	l	NOUN
ejpam-5671	265	9	is	be	AUX
ejpam-5671	265	10	a	a	DET
ejpam-5671	265	11	contraction	contraction	NOUN
ejpam-5671	265	12	.	.	PUNCT
ejpam-5671	266	1	for	for	ADP
ejpam-5671	266	2	ω1	ω1	PROPN
ejpam-5671	266	3	,	,	PUNCT
ejpam-5671	266	4	ω2	ω2	PROPN
ejpam-5671	266	5	∈	∈	PROPN
ejpam-5671	266	6	br	br	NOUN
ejpam-5671	266	7	,	,	PUNCT
ejpam-5671	266	8	we	we	PRON
ejpam-5671	266	9	can	can	AUX
ejpam-5671	266	10	write	write	VERB
ejpam-5671	266	11	||(lω1)(ρ)−	||(lω1)(ρ)−	PROPN
ejpam-5671	266	12	(	(	PUNCT
ejpam-5671	266	13	lω2)(ρ)||	lω2)(ρ)||	PROPN
ejpam-5671	266	14	≤	≤	NUM
ejpam-5671	266	15	∫	∫	PROPN
ejpam-5671	267	1	ρ	ρ	PROPN
ejpam-5671	267	2	0	0	PROPN
ejpam-5671	268	1	(	(	PUNCT
ejpam-5671	268	2	ρ−	ρ−	NOUN
ejpam-5671	268	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	268	4	γ(µ	γ(µ	PROPN
ejpam-5671	268	5	)	)	PUNCT
ejpam-5671	269	1	||ω(ν	||ω(ν	ADV
ejpam-5671	269	2	,	,	PUNCT
ejpam-5671	269	3	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	269	4	ω(ν	ω(ν	ADJ
ejpam-5671	269	5	,	,	PUNCT
ejpam-5671	269	6	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	269	7	+	+	CCONJ
ejpam-5671	269	8	1	1	NUM
ejpam-5671	269	9	2	2	NUM
ejpam-5671	269	10	[	[	X
ejpam-5671	269	11	∫	∫	X
ejpam-5671	269	12	θ	θ	X
ejpam-5671	269	13	0	0	PUNCT
ejpam-5671	269	14	(	(	PUNCT
ejpam-5671	269	15	θ	θ	NOUN
ejpam-5671	269	16	−	−	PROPN
ejpam-5671	269	17	ν)µ−1	ν)µ−1	PROPN
ejpam-5671	269	18	γ(µ	γ(µ	PROPN
ejpam-5671	269	19	)	)	PUNCT
ejpam-5671	269	20	||ω(ν	||ω(ν	ADP
ejpam-5671	269	21	,	,	PUNCT
ejpam-5671	269	22	y1(ν))−	y1(ν))−	PROPN
ejpam-5671	269	23	ω(ν	ω(ν	NOUN
ejpam-5671	269	24	,	,	PUNCT
ejpam-5671	269	25	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	269	26	+	+	CCONJ
ejpam-5671	269	27	∫	∫	PROPN
ejpam-5671	269	28	b	b	PROPN
ejpam-5671	269	29	0	0	NUM
ejpam-5671	269	30	(	(	PUNCT
ejpam-5671	269	31	b−	b−	PROPN
ejpam-5671	269	32	ν)µ−1	ν)µ−1	VERB
ejpam-5671	269	33	γ(µ	γ(µ	PROPN
ejpam-5671	269	34	)	)	PUNCT
ejpam-5671	269	35	||ω(ν	||ω(ν	ADV
ejpam-5671	269	36	,	,	PUNCT
ejpam-5671	269	37	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	269	38	ω(ν	ω(ν	ADJ
ejpam-5671	269	39	,	,	PUNCT
ejpam-5671	269	40	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	269	41	]	]	PUNCT
ejpam-5671	269	42	+	+	CCONJ
ejpam-5671	269	43	γ(2−	γ(2−	PROPN
ejpam-5671	269	44	ξ	ξ	PROPN
ejpam-5671	269	45	)	)	PUNCT
ejpam-5671	269	46	|[(θ	|[(θ	NOUN
ejpam-5671	269	47	+	+	CCONJ
ejpam-5671	269	48	b)−	b)−	PROPN
ejpam-5671	269	49	2ρ]|	2ρ]|	NUM
ejpam-5671	269	50	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	269	51	+	+	CCONJ
ejpam-5671	269	52	b1−ξ	b1−ξ	PROPN
ejpam-5671	269	53	)	)	PUNCT
ejpam-5671	269	54	(	(	PUNCT
ejpam-5671	269	55	∫	∫	PROPN
ejpam-5671	269	56	θ	θ	PROPN
ejpam-5671	269	57	0	0	PUNCT
ejpam-5671	269	58	(	(	PUNCT
ejpam-5671	269	59	θ	θ	X
ejpam-5671	269	60	−	−	PROPN
ejpam-5671	269	61	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	269	62	γ(µ−	γ(µ−	VERB
ejpam-5671	269	63	ξ	ξ	NOUN
ejpam-5671	269	64	)	)	PUNCT
ejpam-5671	269	65	||ω(ν	||ω(ν	ADV
ejpam-5671	269	66	,	,	PUNCT
ejpam-5671	269	67	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	269	68	ω(ν	ω(ν	ADJ
ejpam-5671	269	69	,	,	PUNCT
ejpam-5671	269	70	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	269	71	+	+	CCONJ
ejpam-5671	269	72	∫	∫	PROPN
ejpam-5671	269	73	b	b	PROPN
ejpam-5671	269	74	0	0	NUM
ejpam-5671	269	75	(	(	PUNCT
ejpam-5671	269	76	b−	b−	PROPN
ejpam-5671	269	77	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	269	78	γ(µ−	γ(µ−	VERB
ejpam-5671	269	79	ξ	ξ	NUM
ejpam-5671	269	80	)	)	PUNCT
ejpam-5671	269	81	||ω(ν	||ω(ν	ADV
ejpam-5671	269	82	,	,	PUNCT
ejpam-5671	269	83	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	269	84	ω(ν	ω(ν	ADJ
ejpam-5671	269	85	,	,	PUNCT
ejpam-5671	269	86	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	269	87	)	)	PUNCT
ejpam-5671	270	1	+	+	CCONJ
ejpam-5671	270	2	γ(2−	γ(2−	PROPN
ejpam-5671	270	3	ξ	ξ	PROPN
ejpam-5671	270	4	)	)	PUNCT
ejpam-5671	271	1	4γ(3−	4γ(3−	NUM
ejpam-5671	271	2	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	271	3	+	+	NUM
ejpam-5671	271	4	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	271	5	[	[	PUNCT
ejpam-5671	271	6	|4ρ(θ2−ξ	|4ρ(θ2−ξ	PROPN
ejpam-5671	271	7	+	+	CCONJ
ejpam-5671	271	8	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	271	9	ξ)−	ξ)−	PROPN
ejpam-5671	271	10	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	271	11	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	271	12	+	+	CCONJ
ejpam-5671	271	13	b1−ξ	b1−ξ	PROPN
ejpam-5671	271	14	)	)	PUNCT
ejpam-5671	271	15	−2(θ	−2(θ	PUNCT
ejpam-5671	271	16	+	+	CCONJ
ejpam-5671	271	17	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	271	18	+	+	CCONJ
ejpam-5671	271	19	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	271	20	ξ	ξ	PROPN
ejpam-5671	271	21	)	)	PUNCT
ejpam-5671	271	22	+	+	CCONJ
ejpam-5671	271	23	(	(	PUNCT
ejpam-5671	271	24	θ2	θ2	ADV
ejpam-5671	271	25	+	+	CCONJ
ejpam-5671	271	26	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	271	27	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	271	28	+	+	CCONJ
ejpam-5671	271	29	b1−ξ	b1−ξ	PROPN
ejpam-5671	271	30	)	)	PUNCT
ejpam-5671	271	31	∣∣∣	∣∣∣	ADP
ejpam-5671	271	32	]	]	X
ejpam-5671	271	33	×	×	NOUN
ejpam-5671	272	1	[	[	X
ejpam-5671	272	2	∫	∫	PROPN
ejpam-5671	272	3	θ	θ	X
ejpam-5671	272	4	0	0	PUNCT
ejpam-5671	272	5	(	(	PUNCT
ejpam-5671	272	6	θ	θ	NOUN
ejpam-5671	272	7	−	−	NOUN
ejpam-5671	272	8	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	272	9	γ(µ−	γ(µ−	VERB
ejpam-5671	272	10	ξ	ξ	PRON
ejpam-5671	272	11	−	−	NOUN
ejpam-5671	272	12	1	1	NUM
ejpam-5671	272	13	)	)	PUNCT
ejpam-5671	272	14	||ω(ν	||ω(ν	ADV
ejpam-5671	272	15	,	,	PUNCT
ejpam-5671	272	16	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	272	17	ω(ν	ω(ν	ADJ
ejpam-5671	272	18	,	,	PUNCT
ejpam-5671	272	19	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	272	20	+	+	CCONJ
ejpam-5671	272	21	∫	∫	PROPN
ejpam-5671	272	22	b	b	PROPN
ejpam-5671	272	23	0	0	NUM
ejpam-5671	272	24	(	(	PUNCT
ejpam-5671	272	25	b−	b−	NOUN
ejpam-5671	272	26	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	272	27	γ(µ−	γ(µ−	VERB
ejpam-5671	272	28	ξ	ξ	PRON
ejpam-5671	272	29	−	−	NOUN
ejpam-5671	272	30	1	1	NUM
ejpam-5671	272	31	)	)	PUNCT
ejpam-5671	272	32	||ω(ν	||ω(ν	ADV
ejpam-5671	272	33	,	,	PUNCT
ejpam-5671	272	34	ω1(ν))−	ω1(ν))−	ADV
ejpam-5671	272	35	ω(ν	ω(ν	ADJ
ejpam-5671	272	36	,	,	PUNCT
ejpam-5671	272	37	ω2(ν))||dν	ω2(ν))||dν	NOUN
ejpam-5671	272	38	]	]	PUNCT
ejpam-5671	272	39	≤	≤	NUM
ejpam-5671	273	1	l||ω1	l||ω1	NOUN
ejpam-5671	273	2	−	−	PROPN
ejpam-5671	273	3	ω2||	ω2||	PROPN
ejpam-5671	274	1	[	[	X
ejpam-5671	274	2	∫	∫	PROPN
ejpam-5671	274	3	ρ	ρ	PROPN
ejpam-5671	274	4	0	0	PROPN
ejpam-5671	274	5	(	(	PUNCT
ejpam-5671	274	6	ρ−	ρ−	NOUN
ejpam-5671	274	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	274	8	γ(µ	γ(µ	PROPN
ejpam-5671	274	9	)	)	PUNCT
ejpam-5671	274	10	dν	dν	VERB
ejpam-5671	275	1	+	+	CCONJ
ejpam-5671	275	2	1	1	NUM
ejpam-5671	275	3	2	2	NUM
ejpam-5671	275	4	(	(	PUNCT
ejpam-5671	275	5	∫	∫	PROPN
ejpam-5671	275	6	θ	θ	PROPN
ejpam-5671	275	7	0	0	PUNCT
ejpam-5671	275	8	(	(	PUNCT
ejpam-5671	275	9	θ	θ	NOUN
ejpam-5671	275	10	−	−	PROPN
ejpam-5671	275	11	ν)µ−1	ν)µ−1	X
ejpam-5671	275	12	γ(µ	γ(µ	PROPN
ejpam-5671	275	13	)	)	PUNCT
ejpam-5671	275	14	dν	dν	VERB
ejpam-5671	276	1	+	+	CCONJ
ejpam-5671	276	2	∫	∫	PROPN
ejpam-5671	276	3	b	b	PROPN
ejpam-5671	276	4	0	0	NUM
ejpam-5671	276	5	(	(	PUNCT
ejpam-5671	276	6	b−	b−	PROPN
ejpam-5671	276	7	ν)µ−1	ν)µ−1	VERB
ejpam-5671	276	8	γ(µ	γ(µ	PROPN
ejpam-5671	276	9	)	)	PUNCT
ejpam-5671	277	1	dν	dν	VERB
ejpam-5671	277	2	)	)	PUNCT
ejpam-5671	278	1	+	+	CCONJ
ejpam-5671	278	2	γ(2−	γ(2−	PROPN
ejpam-5671	278	3	ξ	ξ	X
ejpam-5671	278	4	)	)	PUNCT
ejpam-5671	278	5	|(θ	|(θ	PROPN
ejpam-5671	279	1	+	+	CCONJ
ejpam-5671	279	2	b)−	b)−	PROPN
ejpam-5671	279	3	2ρ|	2ρ|	NUM
ejpam-5671	279	4	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	279	5	+	+	CCONJ
ejpam-5671	279	6	b1−ξ	b1−ξ	PROPN
ejpam-5671	279	7	)	)	PUNCT
ejpam-5671	279	8	(	(	PUNCT
ejpam-5671	279	9	∫	∫	PROPN
ejpam-5671	279	10	θ	θ	PROPN
ejpam-5671	279	11	0	0	PUNCT
ejpam-5671	279	12	(	(	PUNCT
ejpam-5671	279	13	θ	θ	X
ejpam-5671	279	14	−	−	PROPN
ejpam-5671	279	15	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	279	16	γ(µ−	γ(µ−	VERB
ejpam-5671	279	17	ξ	ξ	X
ejpam-5671	279	18	)	)	PUNCT
ejpam-5671	279	19	dν	dν	VERB
ejpam-5671	280	1	+	+	CCONJ
ejpam-5671	280	2	∫	∫	PROPN
ejpam-5671	280	3	b	b	PROPN
ejpam-5671	280	4	0	0	NUM
ejpam-5671	280	5	(	(	PUNCT
ejpam-5671	280	6	b−	b−	PROPN
ejpam-5671	280	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	280	8	γ(µ−	γ(µ−	VERB
ejpam-5671	280	9	ξ	ξ	X
ejpam-5671	280	10	)	)	PUNCT
ejpam-5671	280	11	dν	dν	VERB
ejpam-5671	280	12	)	)	PUNCT
ejpam-5671	281	1	+	+	CCONJ
ejpam-5671	282	1	γ(2−	γ(2−	PROPN
ejpam-5671	282	2	ξ	ξ	PROPN
ejpam-5671	282	3	)	)	PUNCT
ejpam-5671	282	4	4γ(3−	4γ(3−	NUM
ejpam-5671	282	5	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	283	1	+	+	CCONJ
ejpam-5671	283	2	b1−ξ)2	b1−ξ)2	VERB
ejpam-5671	283	3	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	NOUN
ejpam-5671	283	4	+	+	CCONJ
ejpam-5671	283	5	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	283	6	ξ)−	ξ)−	PROPN
ejpam-5671	283	7	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	283	8	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	283	9	+	+	CCONJ
ejpam-5671	283	10	b1−ξ	b1−ξ	PROPN
ejpam-5671	283	11	)	)	PUNCT
ejpam-5671	283	12	−2(θ	−2(θ	PUNCT
ejpam-5671	284	1	+	+	CCONJ
ejpam-5671	284	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	284	3	+	+	CCONJ
ejpam-5671	284	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	284	5	ξ	ξ	PROPN
ejpam-5671	284	6	)	)	PUNCT
ejpam-5671	285	1	+	+	CCONJ
ejpam-5671	285	2	(	(	PUNCT
ejpam-5671	285	3	θ2	θ2	ADV
ejpam-5671	285	4	+	+	CCONJ
ejpam-5671	285	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	285	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	285	7	+	+	CCONJ
ejpam-5671	285	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	285	9	)	)	PUNCT
ejpam-5671	285	10	∣∣∣	∣∣∣	ADP
ejpam-5671	285	11	×	×	PROPN
ejpam-5671	285	12	(	(	PUNCT
ejpam-5671	285	13	∫	∫	PROPN
ejpam-5671	285	14	θ	θ	PROPN
ejpam-5671	285	15	0	0	PUNCT
ejpam-5671	285	16	(	(	PUNCT
ejpam-5671	285	17	θ	θ	NOUN
ejpam-5671	285	18	−	−	NOUN
ejpam-5671	285	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	285	20	γ(µ−	γ(µ−	VERB
ejpam-5671	285	21	ξ	ξ	PRON
ejpam-5671	285	22	−	−	NOUN
ejpam-5671	285	23	1	1	NUM
ejpam-5671	285	24	)	)	PUNCT
ejpam-5671	285	25	dν	dν	VERB
ejpam-5671	286	1	+	+	CCONJ
ejpam-5671	286	2	∫	∫	PROPN
ejpam-5671	286	3	b	b	PROPN
ejpam-5671	286	4	0	0	NUM
ejpam-5671	286	5	(	(	PUNCT
ejpam-5671	286	6	b−	b−	NOUN
ejpam-5671	286	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	286	8	γ(µ−	γ(µ−	VERB
ejpam-5671	286	9	ξ	ξ	PRON
ejpam-5671	286	10	−	−	NOUN
ejpam-5671	286	11	1	1	NUM
ejpam-5671	286	12	)	)	PUNCT
ejpam-5671	286	13	dν	dν	ADJ
ejpam-5671	286	14	)	)	PUNCT
ejpam-5671	286	15	]	]	PUNCT
ejpam-5671	286	16	≤	≤	NUM
ejpam-5671	286	17	lm1||ω1	lm1||ω1	NOUN
ejpam-5671	286	18	−	−	PROPN
ejpam-5671	286	19	ω2||	ω2||	PROPN
ejpam-5671	286	20	.	.	PUNCT
ejpam-5671	287	1	since	since	SCONJ
ejpam-5671	287	2	lm1	lm1	NOUN
ejpam-5671	287	3	<	<	X
ejpam-5671	287	4	1	1	NUM
ejpam-5671	287	5	,	,	PUNCT
ejpam-5671	287	6	we	we	PRON
ejpam-5671	287	7	conclude	conclude	VERB
ejpam-5671	287	8	that	that	SCONJ
ejpam-5671	287	9	l	l	NOUN
ejpam-5671	287	10	is	be	AUX
ejpam-5671	287	11	a	a	DET
ejpam-5671	287	12	contraction	contraction	NOUN
ejpam-5671	287	13	operator	operator	NOUN
ejpam-5671	287	14	.	.	PUNCT
ejpam-5671	288	1	according	accord	VERB
ejpam-5671	288	2	to	to	ADP
ejpam-5671	288	3	lemma	lemma	PROPN
ejpam-5671	288	4	3	3	NUM
ejpam-5671	288	5	and	and	CCONJ
ejpam-5671	288	6	s.	s.	PROPN
ejpam-5671	288	7	f.	f.	PROPN
ejpam-5671	288	8	aljurbua	aljurbua	PROPN
ejpam-5671	288	9	,	,	PUNCT
ejpam-5671	288	10	h.	h.	PROPN
ejpam-5671	288	11	a.	a.	PROPN
ejpam-5671	288	12	hammad	hammad	PROPN
ejpam-5671	288	13	,	,	PUNCT
ejpam-5671	288	14	n.	n.	PROPN
ejpam-5671	288	15	b.	b.	PROPN
ejpam-5671	288	16	almutairi	almutairi	PROPN
ejpam-5671	288	17	/	/	SYM
ejpam-5671	288	18	eur	eur	PROPN
ejpam-5671	288	19	.	.	PUNCT
ejpam-5671	289	1	j.	j.	PROPN
ejpam-5671	289	2	pure	pure	PROPN
ejpam-5671	289	3	appl	appl	PROPN
ejpam-5671	289	4	.	.	PROPN
ejpam-5671	289	5	math	math	PROPN
ejpam-5671	289	6	,	,	PUNCT
ejpam-5671	289	7	18	18	NUM
ejpam-5671	289	8	(	(	PUNCT
ejpam-5671	289	9	1	1	NUM
ejpam-5671	289	10	)	)	PUNCT
ejpam-5671	289	11	(	(	PUNCT
ejpam-5671	289	12	2025	2025	NUM
ejpam-5671	289	13	)	)	PUNCT
ejpam-5671	289	14	,	,	PUNCT
ejpam-5671	289	15	5671	5671	NUM
ejpam-5671	289	16	11	11	NUM
ejpam-5671	289	17	of	of	ADP
ejpam-5671	289	18	18	18	NUM
ejpam-5671	289	19	theorem	theorem	ADJ
ejpam-5671	289	20	1	1	NUM
ejpam-5671	289	21	,	,	PUNCT
ejpam-5671	289	22	l	l	NOUN
ejpam-5671	289	23	has	have	VERB
ejpam-5671	289	24	a	a	DET
ejpam-5671	289	25	fixed	fix	VERB
ejpam-5671	289	26	point	point	NOUN
ejpam-5671	289	27	,	,	PUNCT
ejpam-5671	289	28	which	which	PRON
ejpam-5671	289	29	is	be	AUX
ejpam-5671	289	30	a	a	DET
ejpam-5671	289	31	solution	solution	NOUN
ejpam-5671	289	32	to	to	ADP
ejpam-5671	289	33	the	the	DET
ejpam-5671	289	34	problem	problem	NOUN
ejpam-5671	289	35	(	(	PUNCT
ejpam-5671	289	36	1	1	NUM
ejpam-5671	289	37	)	)	PUNCT
ejpam-5671	289	38	.	.	PUNCT
ejpam-5671	290	1	theorem	theorem	ADJ
ejpam-5671	290	2	4	4	NUM
ejpam-5671	290	3	.	.	PUNCT
ejpam-5671	290	4	assume	assume	VERB
ejpam-5671	290	5	that	that	SCONJ
ejpam-5671	290	6	ω	ω	X
ejpam-5671	290	7	:	:	PUNCT
ejpam-5671	291	1	[	[	X
ejpam-5671	291	2	0	0	NUM
ejpam-5671	291	3	,	,	PUNCT
ejpam-5671	291	4	b]×	b]×	NOUN
ejpam-5671	291	5	r	r	NOUN
ejpam-5671	291	6	−→	−→	NOUN
ejpam-5671	291	7	r	r	NOUN
ejpam-5671	291	8	is	be	AUX
ejpam-5671	291	9	continuous	continuous	ADJ
ejpam-5671	291	10	such	such	ADJ
ejpam-5671	291	11	that	that	DET
ejpam-5671	291	12	||ω(ρ	||ω(ρ	NOUN
ejpam-5671	291	13	,	,	PUNCT
ejpam-5671	291	14	ω1)−	ω1)−	PROPN
ejpam-5671	291	15	ω(ρ	ω(ρ	PROPN
ejpam-5671	291	16	,	,	PUNCT
ejpam-5671	291	17	ω2)||	ω2)||	NUM
ejpam-5671	291	18	≤	≤	NUM
ejpam-5671	291	19	l||ω1	l||ω1	PROPN
ejpam-5671	291	20	−	−	PROPN
ejpam-5671	291	21	ω2||	ω2||	PROPN
ejpam-5671	291	22	,	,	PUNCT
ejpam-5671	291	23	for	for	ADP
ejpam-5671	291	24	all	all	DET
ejpam-5671	291	25	ρ	ρ	NOUN
ejpam-5671	291	26	∈	∈	PROPN
ejpam-5671	292	1	[	[	X
ejpam-5671	292	2	0	0	NUM
ejpam-5671	292	3	,	,	PUNCT
ejpam-5671	292	4	b	b	NOUN
ejpam-5671	292	5	]	]	X
ejpam-5671	292	6	and	and	CCONJ
ejpam-5671	292	7	ω1	ω1	PROPN
ejpam-5671	292	8	,	,	PUNCT
ejpam-5671	292	9	ω2	ω2	PROPN
ejpam-5671	292	10	∈	∈	PROPN
ejpam-5671	292	11	r.	r.	PROPN
ejpam-5671	292	12	if	if	SCONJ
ejpam-5671	292	13	for	for	ADP
ejpam-5671	292	14	all	all	DET
ejpam-5671	292	15	(	(	PUNCT
ejpam-5671	292	16	ρ	ρ	PROPN
ejpam-5671	292	17	,	,	PUNCT
ejpam-5671	292	18	ω	ω	NOUN
ejpam-5671	292	19	)	)	PUNCT
ejpam-5671	292	20	∈	∈	PROPN
ejpam-5671	292	21	[	[	X
ejpam-5671	292	22	0	0	NUM
ejpam-5671	292	23	,	,	PUNCT
ejpam-5671	292	24	1]×	1]×	NUM
ejpam-5671	292	25	r	r	NOUN
ejpam-5671	292	26	and	and	CCONJ
ejpam-5671	292	27	ψ	ψ	NOUN
ejpam-5671	292	28	∈	∈	PROPN
ejpam-5671	292	29	l1([0	l1([0	NOUN
ejpam-5671	292	30	,	,	PUNCT
ejpam-5671	292	31	b],r+	b],r+	PROPN
ejpam-5671	292	32	)	)	PUNCT
ejpam-5671	292	33	,	,	PUNCT
ejpam-5671	292	34	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	292	35	,	,	PUNCT
ejpam-5671	292	36	ω)|	ω)|	ADJ
ejpam-5671	292	37	≤	≤	ADJ
ejpam-5671	292	38	ψ(ρ	ψ(ρ	PROPN
ejpam-5671	292	39	)	)	PUNCT
ejpam-5671	292	40	.	.	PUNCT
ejpam-5671	293	1	then	then	ADV
ejpam-5671	293	2	,	,	PUNCT
ejpam-5671	293	3	the	the	DET
ejpam-5671	293	4	problem	problem	NOUN
ejpam-5671	293	5	(	(	PUNCT
ejpam-5671	293	6	1	1	X
ejpam-5671	293	7	)	)	PUNCT
ejpam-5671	293	8	has	have	VERB
ejpam-5671	293	9	at	at	ADV
ejpam-5671	293	10	least	least	ADV
ejpam-5671	293	11	one	one	NUM
ejpam-5671	293	12	solution	solution	NOUN
ejpam-5671	293	13	on	on	ADP
ejpam-5671	293	14	[	[	X
ejpam-5671	293	15	0	0	NUM
ejpam-5671	293	16	,	,	PUNCT
ejpam-5671	293	17	b	b	NOUN
ejpam-5671	293	18	]	]	X
ejpam-5671	293	19	,	,	PUNCT
ejpam-5671	293	20	provided	provide	VERB
ejpam-5671	293	21	that	that	DET
ejpam-5671	293	22	lm2	lm2	NOUN
ejpam-5671	293	23	<	<	X
ejpam-5671	293	24	1	1	NUM
ejpam-5671	293	25	,	,	PUNCT
ejpam-5671	293	26	where	where	SCONJ
ejpam-5671	293	27	m2	m2	PROPN
ejpam-5671	293	28	is	be	AUX
ejpam-5671	293	29	defined	define	VERB
ejpam-5671	293	30	in	in	ADP
ejpam-5671	293	31	(	(	PUNCT
ejpam-5671	293	32	14	14	NUM
ejpam-5671	293	33	)	)	PUNCT
ejpam-5671	293	34	.	.	PUNCT
ejpam-5671	294	1	proof	proof	NOUN
ejpam-5671	294	2	.	.	PUNCT
ejpam-5671	295	1	define	define	VERB
ejpam-5671	295	2	the	the	DET
ejpam-5671	295	3	operators	operator	NOUN
ejpam-5671	295	4	l1	l1	PROPN
ejpam-5671	295	5	and	and	CCONJ
ejpam-5671	295	6	l2	l2	NOUN
ejpam-5671	295	7	by	by	ADP
ejpam-5671	295	8	(	(	PUNCT
ejpam-5671	295	9	l1ω)(ρ	l1ω)(ρ	PROPN
ejpam-5671	295	10	)	)	PUNCT
ejpam-5671	296	1	=	=	SYM
ejpam-5671	296	2	∫	∫	PROPN
ejpam-5671	297	1	ρ	ρ	PROPN
ejpam-5671	297	2	0	0	PUNCT
ejpam-5671	298	1	(	(	PUNCT
ejpam-5671	298	2	ρ−	ρ−	NOUN
ejpam-5671	298	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	298	4	γ(µ	γ(µ	PROPN
ejpam-5671	298	5	)	)	PUNCT
ejpam-5671	298	6	ω(ν	ω(ν	NOUN
ejpam-5671	298	7	,	,	PUNCT
ejpam-5671	298	8	ω(ν))dν	ω(ν))dν	NOUN
ejpam-5671	298	9	,	,	PUNCT
ejpam-5671	298	10	and	and	CCONJ
ejpam-5671	298	11	(	(	PUNCT
ejpam-5671	298	12	l2ω)(ρ	l2ω)(ρ	PROPN
ejpam-5671	298	13	)	)	PUNCT
ejpam-5671	299	1	=	=	SYM
ejpam-5671	299	2	−1	−1	NOUN
ejpam-5671	299	3	2	2	NUM
ejpam-5671	299	4	(	(	PUNCT
ejpam-5671	299	5	∫	∫	PROPN
ejpam-5671	299	6	θ	θ	PROPN
ejpam-5671	299	7	0	0	PUNCT
ejpam-5671	299	8	(	(	PUNCT
ejpam-5671	299	9	θ	θ	NOUN
ejpam-5671	299	10	−	−	PROPN
ejpam-5671	299	11	ν)µ−1	ν)µ−1	NOUN
ejpam-5671	299	12	γ(µ	γ(µ	PROPN
ejpam-5671	299	13	)	)	PUNCT
ejpam-5671	299	14	ω(ν	ω(ν	NOUN
ejpam-5671	299	15	,	,	PUNCT
ejpam-5671	299	16	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	299	17	+	+	CCONJ
ejpam-5671	299	18	∫	∫	PROPN
ejpam-5671	299	19	b	b	PROPN
ejpam-5671	299	20	0	0	NUM
ejpam-5671	299	21	(	(	PUNCT
ejpam-5671	299	22	b−	b−	PROPN
ejpam-5671	299	23	ν)µ−1	ν)µ−1	VERB
ejpam-5671	299	24	γ(µ	γ(µ	PROPN
ejpam-5671	299	25	)	)	PUNCT
ejpam-5671	299	26	ω(ν	ω(ν	NOUN
ejpam-5671	299	27	,	,	PUNCT
ejpam-5671	299	28	ω(ν))dν	ω(ν))dν	PRON
ejpam-5671	299	29	)	)	PUNCT
ejpam-5671	300	1	+	+	CCONJ
ejpam-5671	300	2	γ(2−	γ(2−	NUM
ejpam-5671	300	3	ξ)[(θ	ξ)[(θ	NOUN
ejpam-5671	301	1	+	+	CCONJ
ejpam-5671	301	2	b)−	b)−	PROPN
ejpam-5671	301	3	2ρ	2ρ	NOUN
ejpam-5671	301	4	]	]	PUNCT
ejpam-5671	302	1	2(θ1−ξ	2(θ1−ξ	PROPN
ejpam-5671	302	2	+	+	CCONJ
ejpam-5671	302	3	b1−ξ	b1−ξ	PROPN
ejpam-5671	302	4	)	)	PUNCT
ejpam-5671	302	5	×	×	NOUN
ejpam-5671	302	6	(	(	PUNCT
ejpam-5671	302	7	∫	∫	PROPN
ejpam-5671	302	8	θ	θ	PROPN
ejpam-5671	302	9	0	0	PUNCT
ejpam-5671	302	10	(	(	PUNCT
ejpam-5671	302	11	θ	θ	X
ejpam-5671	302	12	−	−	PROPN
ejpam-5671	302	13	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	302	14	γ(µ−	γ(µ−	VERB
ejpam-5671	302	15	ξ	ξ	NUM
ejpam-5671	302	16	)	)	PUNCT
ejpam-5671	302	17	ω(ν	ω(ν	NOUN
ejpam-5671	302	18	,	,	PUNCT
ejpam-5671	302	19	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	302	20	+	+	CCONJ
ejpam-5671	302	21	∫	∫	PROPN
ejpam-5671	302	22	b	b	PROPN
ejpam-5671	302	23	0	0	NUM
ejpam-5671	302	24	(	(	PUNCT
ejpam-5671	302	25	b−	b−	PROPN
ejpam-5671	302	26	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	302	27	γ(µ−	γ(µ−	VERB
ejpam-5671	302	28	ξ	ξ	NUM
ejpam-5671	302	29	)	)	PUNCT
ejpam-5671	302	30	ω(ν	ω(ν	NOUN
ejpam-5671	302	31	,	,	PUNCT
ejpam-5671	302	32	ω(ν))dν	ω(ν))dν	PRON
ejpam-5671	302	33	)	)	PUNCT
ejpam-5671	303	1	+	+	CCONJ
ejpam-5671	303	2	γ(2−	γ(2−	PROPN
ejpam-5671	303	3	ξ	ξ	PROPN
ejpam-5671	303	4	)	)	PUNCT
ejpam-5671	304	1	4γ(3−	4γ(3−	NUM
ejpam-5671	304	2	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	304	3	+	+	CCONJ
ejpam-5671	304	4	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	304	5	[	[	PUNCT
ejpam-5671	304	6	4ρ(θ2−ξ	4ρ(θ2−ξ	NUM
ejpam-5671	304	7	+	+	CCONJ
ejpam-5671	304	8	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	304	9	ξ)−	ξ)−	PROPN
ejpam-5671	304	10	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	304	11	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	304	12	+	+	CCONJ
ejpam-5671	304	13	b1−ξ	b1−ξ	PROPN
ejpam-5671	304	14	)	)	PUNCT
ejpam-5671	304	15	−2(θ	−2(θ	PUNCT
ejpam-5671	304	16	+	+	CCONJ
ejpam-5671	304	17	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	304	18	+	+	CCONJ
ejpam-5671	304	19	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	304	20	ξ	ξ	PROPN
ejpam-5671	304	21	)	)	PUNCT
ejpam-5671	304	22	+	+	CCONJ
ejpam-5671	304	23	(	(	PUNCT
ejpam-5671	304	24	θ2	θ2	ADV
ejpam-5671	304	25	+	+	CCONJ
ejpam-5671	304	26	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	304	27	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	304	28	+	+	CCONJ
ejpam-5671	304	29	b1−ξ	b1−ξ	PROPN
ejpam-5671	304	30	)	)	PUNCT
ejpam-5671	304	31	]	]	PUNCT
ejpam-5671	304	32	×	×	NOUN
ejpam-5671	304	33	(	(	PUNCT
ejpam-5671	304	34	∫	∫	PROPN
ejpam-5671	304	35	θ	θ	PROPN
ejpam-5671	304	36	0	0	PUNCT
ejpam-5671	304	37	(	(	PUNCT
ejpam-5671	304	38	θ	θ	NOUN
ejpam-5671	304	39	−	−	NOUN
ejpam-5671	304	40	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	304	41	γ(µ−	γ(µ−	VERB
ejpam-5671	304	42	ξ	ξ	PRON
ejpam-5671	304	43	−	−	NOUN
ejpam-5671	304	44	1	1	NUM
ejpam-5671	304	45	)	)	PUNCT
ejpam-5671	304	46	ω(ν	ω(ν	NOUN
ejpam-5671	304	47	,	,	PUNCT
ejpam-5671	304	48	ω(ν))dν	ω(ν))dν	VERB
ejpam-5671	305	1	+	+	CCONJ
ejpam-5671	305	2	∫	∫	PROPN
ejpam-5671	305	3	b	b	PROPN
ejpam-5671	305	4	0	0	NUM
ejpam-5671	305	5	(	(	PUNCT
ejpam-5671	305	6	b−	b−	NOUN
ejpam-5671	305	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	305	8	γ(µ−	γ(µ−	VERB
ejpam-5671	305	9	ξ	ξ	PRON
ejpam-5671	305	10	−	−	NOUN
ejpam-5671	305	11	1	1	NUM
ejpam-5671	305	12	)	)	PUNCT
ejpam-5671	305	13	ω(ν	ω(ν	NOUN
ejpam-5671	305	14	,	,	PUNCT
ejpam-5671	305	15	ω(ν))dν	ω(ν))dν	X
ejpam-5671	305	16	)	)	PUNCT
ejpam-5671	305	17	on	on	ADP
ejpam-5671	305	18	br	br	NOUN
ejpam-5671	305	19	=	=	SYM
ejpam-5671	305	20	{	{	PUNCT
ejpam-5671	305	21	ω	ω	NUM
ejpam-5671	305	22	∈	∈	PROPN
ejpam-5671	305	23	l	l	NOUN
ejpam-5671	305	24	:	:	PUNCT
ejpam-5671	305	25	||ω||	||ω||	VERB
ejpam-5671	305	26	≤	≤	NUM
ejpam-5671	305	27	r	r	NOUN
ejpam-5671	305	28	}	}	PUNCT
ejpam-5671	305	29	where	where	SCONJ
ejpam-5671	305	30	r	r	NOUN
ejpam-5671	305	31	≥	≥	NOUN
ejpam-5671	305	32	||µ||m1	||µ||m1	NOUN
ejpam-5671	305	33	2	2	NUM
ejpam-5671	305	34	.	.	PUNCT
ejpam-5671	306	1	clearly	clearly	ADV
ejpam-5671	306	2	,	,	PUNCT
ejpam-5671	306	3	for	for	ADP
ejpam-5671	306	4	ω1	ω1	PROPN
ejpam-5671	306	5	,	,	PUNCT
ejpam-5671	306	6	ω2	ω2	PROPN
ejpam-5671	306	7	∈	∈	PROPN
ejpam-5671	306	8	br	br	PROPN
ejpam-5671	306	9	,	,	PUNCT
ejpam-5671	306	10	||l1ω1	||l1ω1	AUX
ejpam-5671	306	11	+	+	CCONJ
ejpam-5671	306	12	l2ω2||	l2ω2||	ADJ
ejpam-5671	306	13	≤	≤	NUM
ejpam-5671	306	14	||ψ||m1	||ψ||m1	PROPN
ejpam-5671	306	15	2	2	NUM
ejpam-5671	306	16	≤	≤	NOUN
ejpam-5671	306	17	r	r	NOUN
ejpam-5671	306	18	,	,	PUNCT
ejpam-5671	306	19	which	which	PRON
ejpam-5671	306	20	implies	imply	VERB
ejpam-5671	306	21	that	that	SCONJ
ejpam-5671	306	22	l1ω1+l2ω2	l1ω1+l2ω2	PROPN
ejpam-5671	306	23	∈	∈	PROPN
ejpam-5671	306	24	br	br	NOUN
ejpam-5671	306	25	.	.	PUNCT
ejpam-5671	307	1	by	by	ADP
ejpam-5671	307	2	the	the	DET
ejpam-5671	307	3	same	same	ADJ
ejpam-5671	307	4	steps	step	NOUN
ejpam-5671	307	5	of	of	ADP
ejpam-5671	307	6	theorem	theorem	NOUN
ejpam-5671	307	7	4	4	NUM
ejpam-5671	307	8	and	and	CCONJ
ejpam-5671	307	9	the	the	DET
ejpam-5671	307	10	assumption	assumption	NOUN
ejpam-5671	307	11	lm2	lm2	NOUN
ejpam-5671	307	12	<	<	X
ejpam-5671	307	13	1	1	NUM
ejpam-5671	307	14	,	,	PUNCT
ejpam-5671	307	15	we	we	PRON
ejpam-5671	307	16	have	have	AUX
ejpam-5671	307	17	l2	l2	NOUN
ejpam-5671	307	18	is	be	AUX
ejpam-5671	307	19	a	a	DET
ejpam-5671	307	20	contraction	contraction	NOUN
ejpam-5671	307	21	mapping	mapping	NOUN
ejpam-5671	307	22	.	.	PUNCT
ejpam-5671	308	1	further	far	ADV
ejpam-5671	308	2	,	,	PUNCT
ejpam-5671	308	3	the	the	DET
ejpam-5671	308	4	continuity	continuity	NOUN
ejpam-5671	308	5	of	of	ADP
ejpam-5671	308	6	ω	ω	PROPN
ejpam-5671	308	7	implies	imply	VERB
ejpam-5671	308	8	that	that	SCONJ
ejpam-5671	308	9	the	the	DET
ejpam-5671	308	10	continuity	continuity	NOUN
ejpam-5671	308	11	of	of	ADP
ejpam-5671	308	12	l1	l1	PROPN
ejpam-5671	308	13	.	.	PUNCT
ejpam-5671	309	1	since	since	SCONJ
ejpam-5671	309	2	||(l1ω(ρ)||	||(l1ω(ρ)||	VERB
ejpam-5671	309	3	≤	≤	NOUN
ejpam-5671	309	4	||ψ||	||ψ||	ADJ
ejpam-5671	309	5	γ(µ+	γ(µ+	NOUN
ejpam-5671	309	6	1	1	X
ejpam-5671	309	7	)	)	PUNCT
ejpam-5671	309	8	bµ	bµ	PROPN
ejpam-5671	309	9	,	,	PUNCT
ejpam-5671	309	10	s.	s.	PROPN
ejpam-5671	309	11	f.	f.	PROPN
ejpam-5671	309	12	aljurbua	aljurbua	PROPN
ejpam-5671	309	13	,	,	PUNCT
ejpam-5671	309	14	h.	h.	PROPN
ejpam-5671	309	15	a.	a.	PROPN
ejpam-5671	309	16	hammad	hammad	PROPN
ejpam-5671	309	17	,	,	PUNCT
ejpam-5671	309	18	n.	n.	PROPN
ejpam-5671	309	19	b.	b.	PROPN
ejpam-5671	309	20	almutairi	almutairi	PROPN
ejpam-5671	309	21	/	/	SYM
ejpam-5671	309	22	eur	eur	PROPN
ejpam-5671	309	23	.	.	PUNCT
ejpam-5671	310	1	j.	j.	PROPN
ejpam-5671	310	2	pure	pure	PROPN
ejpam-5671	310	3	appl	appl	PROPN
ejpam-5671	310	4	.	.	PROPN
ejpam-5671	310	5	math	math	PROPN
ejpam-5671	310	6	,	,	PUNCT
ejpam-5671	310	7	18	18	NUM
ejpam-5671	310	8	(	(	PUNCT
ejpam-5671	310	9	1	1	NUM
ejpam-5671	310	10	)	)	PUNCT
ejpam-5671	310	11	(	(	PUNCT
ejpam-5671	310	12	2025	2025	NUM
ejpam-5671	310	13	)	)	PUNCT
ejpam-5671	310	14	,	,	PUNCT
ejpam-5671	310	15	5671	5671	NUM
ejpam-5671	310	16	12	12	NUM
ejpam-5671	310	17	of	of	ADP
ejpam-5671	310	18	18	18	NUM
ejpam-5671	310	19	then	then	ADV
ejpam-5671	310	20	,	,	PUNCT
ejpam-5671	310	21	l1	l1	PROPN
ejpam-5671	310	22	is	be	AUX
ejpam-5671	310	23	uniformly	uniformly	ADV
ejpam-5671	310	24	bounded	bound	VERB
ejpam-5671	310	25	on	on	ADP
ejpam-5671	310	26	br	br	PROPN
ejpam-5671	310	27	.	.	PUNCT
ejpam-5671	311	1	in	in	ADP
ejpam-5671	311	2	a	a	DET
ejpam-5671	311	3	view	view	NOUN
ejpam-5671	311	4	of	of	ADP
ejpam-5671	311	5	the	the	DET
ejpam-5671	311	6	second	second	ADJ
ejpam-5671	311	7	assumption	assumption	NOUN
ejpam-5671	311	8	,	,	PUNCT
ejpam-5671	311	9	for	for	ADP
ejpam-5671	311	10	all	all	DET
ejpam-5671	311	11	(	(	PUNCT
ejpam-5671	311	12	ρ	ρ	PROPN
ejpam-5671	311	13	,	,	PUNCT
ejpam-5671	311	14	ω	ω	NOUN
ejpam-5671	311	15	)	)	PUNCT
ejpam-5671	311	16	∈	∈	PROPN
ejpam-5671	311	17	[	[	X
ejpam-5671	311	18	0	0	NUM
ejpam-5671	311	19	,	,	PUNCT
ejpam-5671	311	20	b]×br	b]×br	PROPN
ejpam-5671	311	21	,	,	PUNCT
ejpam-5671	311	22	we	we	PRON
ejpam-5671	311	23	have	have	VERB
ejpam-5671	311	24	||(l1ω)(ρ1)−	||(l1ω)(ρ1)−	NUM
ejpam-5671	311	25	(	(	PUNCT
ejpam-5671	311	26	l1ω)(ρ2)||	l1ω)(ρ2)||	NOUN
ejpam-5671	311	27	=	=	NOUN
ejpam-5671	311	28	1	1	NUM
ejpam-5671	311	29	γ(µ	γ(µ	PROPN
ejpam-5671	311	30	)	)	PUNCT
ejpam-5671	311	31	∥∥∥∥∫	∥∥∥∥∫	NOUN
ejpam-5671	311	32	ρ1	ρ1	NOUN
ejpam-5671	311	33	0	0	PUNCT
ejpam-5671	312	1	[	[	X
ejpam-5671	312	2	(	(	PUNCT
ejpam-5671	312	3	ρ1	ρ1	NOUN
ejpam-5671	312	4	−	−	PROPN
ejpam-5671	312	5	ν)µ−1	ν)µ−1	X
ejpam-5671	312	6	−	−	PROPN
ejpam-5671	312	7	(	(	PUNCT
ejpam-5671	312	8	ρ2	ρ2	NOUN
ejpam-5671	312	9	−	−	NOUN
ejpam-5671	312	10	ν)µ−1]ω(ν	ν)µ−1]ω(ν	ADJ
ejpam-5671	312	11	,	,	PUNCT
ejpam-5671	312	12	ω(ν))dν	ω(ν))dν	ADJ
ejpam-5671	312	13	+	+	CCONJ
ejpam-5671	312	14	∫	∫	NOUN
ejpam-5671	312	15	ρ2	ρ2	NOUN
ejpam-5671	312	16	ρ1	ρ1	NOUN
ejpam-5671	312	17	(	(	PUNCT
ejpam-5671	312	18	ρ2	ρ2	NOUN
ejpam-5671	312	19	−	−	PROPN
ejpam-5671	312	20	ν)µ−1ω(ν	ν)µ−1ω(ν	AUX
ejpam-5671	312	21	,	,	PUNCT
ejpam-5671	312	22	ω(ν))dν|	ω(ν))dν|	NOUN
ejpam-5671	312	23	∥∥∥∥	∥∥∥∥	NUM
ejpam-5671	312	24	≤	≤	NUM
ejpam-5671	312	25	max	max	NOUN
ejpam-5671	312	26	(	(	PUNCT
ejpam-5671	312	27	ρ	ρ	PROPN
ejpam-5671	312	28	,	,	PUNCT
ejpam-5671	312	29	ω)∈[0,b]×br	ω)∈[0,b]×br	PROPN
ejpam-5671	312	30	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	312	31	,	,	PUNCT
ejpam-5671	312	32	ω)|	ω)|	ADJ
ejpam-5671	312	33	γ(µ+	γ(µ+	X
ejpam-5671	312	34	1	1	X
ejpam-5671	312	35	)	)	PUNCT
ejpam-5671	312	36	|2(ρ2	|2(ρ2	NOUN
ejpam-5671	312	37	−	−	NOUN
ejpam-5671	312	38	ρ1	ρ1	NOUN
ejpam-5671	312	39	)	)	PUNCT
ejpam-5671	312	40	µ	µ	X
ejpam-5671	312	41	+	+	NOUN
ejpam-5671	312	42	ρµ1	ρµ1	PROPN
ejpam-5671	312	43	−	−	X
ejpam-5671	313	1	ρµ2	ρµ2	NOUN
ejpam-5671	314	1	|	|	ADV
ejpam-5671	314	2	.	.	PUNCT
ejpam-5671	315	1	when	when	SCONJ
ejpam-5671	315	2	ρ1	ρ1	NOUN
ejpam-5671	315	3	→	→	SYM
ejpam-5671	315	4	ρ2	ρ2	NOUN
ejpam-5671	315	5	,	,	PUNCT
ejpam-5671	315	6	then	then	ADV
ejpam-5671	315	7	||(l1ω)(ρ1	||(l1ω)(ρ1	NUM
ejpam-5671	315	8	)	)	PUNCT
ejpam-5671	316	1	−	−	PROPN
ejpam-5671	317	1	(	(	PUNCT
ejpam-5671	317	2	l1ω)(ρ2)||	l1ω)(ρ2)||	NOUN
ejpam-5671	317	3	→	→	SYM
ejpam-5671	317	4	0	0	X
ejpam-5671	317	5	.	.	PUNCT
ejpam-5671	317	6	by	by	ADP
ejpam-5671	317	7	using	use	VERB
ejpam-5671	317	8	arzelá-ascoli	arzelá-ascoli	NOUN
ejpam-5671	317	9	theorem	theorem	VERB
ejpam-5671	317	10	,	,	PUNCT
ejpam-5671	317	11	l1	l1	PROPN
ejpam-5671	317	12	is	be	AUX
ejpam-5671	317	13	compact	compact	ADJ
ejpam-5671	317	14	on	on	ADP
ejpam-5671	317	15	br	br	PROPN
ejpam-5671	317	16	.	.	PUNCT
ejpam-5671	318	1	based	base	VERB
ejpam-5671	318	2	on	on	ADP
ejpam-5671	318	3	theorem	theorem	NOUN
ejpam-5671	318	4	2	2	NUM
ejpam-5671	318	5	,	,	PUNCT
ejpam-5671	318	6	there	there	PRON
ejpam-5671	318	7	exists	exist	VERB
ejpam-5671	318	8	at	at	ADP
ejpam-5671	318	9	least	least	ADV
ejpam-5671	318	10	one	one	NUM
ejpam-5671	318	11	solution	solution	NOUN
ejpam-5671	318	12	to	to	ADP
ejpam-5671	318	13	the	the	DET
ejpam-5671	318	14	problem	problem	NOUN
ejpam-5671	318	15	(	(	PUNCT
ejpam-5671	318	16	1	1	NUM
ejpam-5671	318	17	)	)	PUNCT
ejpam-5671	318	18	.	.	PUNCT
ejpam-5671	319	1	theorem	theorem	ADJ
ejpam-5671	319	2	5	5	NUM
ejpam-5671	319	3	.	.	PUNCT
ejpam-5671	319	4	assume	assume	VERB
ejpam-5671	319	5	that	that	SCONJ
ejpam-5671	319	6	ω	ω	X
ejpam-5671	319	7	:	:	PUNCT
ejpam-5671	320	1	[	[	X
ejpam-5671	320	2	0	0	NUM
ejpam-5671	320	3	,	,	PUNCT
ejpam-5671	320	4	b]×r	b]×r	NUM
ejpam-5671	320	5	−→	−→	NOUN
ejpam-5671	320	6	r	r	NOUN
ejpam-5671	320	7	is	be	AUX
ejpam-5671	320	8	a	a	DET
ejpam-5671	320	9	continuous	continuous	ADJ
ejpam-5671	320	10	function	function	NOUN
ejpam-5671	320	11	and	and	CCONJ
ejpam-5671	320	12	there	there	PRON
ejpam-5671	320	13	exists	exist	VERB
ejpam-5671	320	14	a	a	DET
ejpam-5671	320	15	constant	constant	ADJ
ejpam-5671	320	16	0	0	NUM
ejpam-5671	320	17	<	<	X
ejpam-5671	320	18	χ	χ	X
ejpam-5671	320	19	<	<	X
ejpam-5671	320	20	1	1	NUM
ejpam-5671	320	21	m	m	NOUN
ejpam-5671	320	22	and	and	CCONJ
ejpam-5671	320	23	δ	δ	X
ejpam-5671	320	24	>	>	X
ejpam-5671	320	25	0	0	NUM
ejpam-5671	321	1	such	such	ADJ
ejpam-5671	321	2	that	that	DET
ejpam-5671	321	3	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	321	4	,	,	PUNCT
ejpam-5671	321	5	ω)|	ω)|	ADJ
ejpam-5671	321	6	≤	≤	ADJ
ejpam-5671	321	7	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	321	8	δ	δ	PROPN
ejpam-5671	321	9	,	,	PUNCT
ejpam-5671	321	10	for	for	ADP
ejpam-5671	321	11	all	all	DET
ejpam-5671	321	12	ρ	ρ	NOUN
ejpam-5671	321	13	∈	∈	PROPN
ejpam-5671	322	1	[	[	X
ejpam-5671	322	2	0	0	NUM
ejpam-5671	322	3	,	,	PUNCT
ejpam-5671	322	4	b	b	NOUN
ejpam-5671	322	5	]	]	X
ejpam-5671	322	6	,	,	PUNCT
ejpam-5671	322	7	and	and	CCONJ
ejpam-5671	322	8	ω	ω	NUM
ejpam-5671	322	9	∈	∈	PROPN
ejpam-5671	322	10	r.	r.	PROPN
ejpam-5671	322	11	then	then	ADV
ejpam-5671	322	12	,	,	PUNCT
ejpam-5671	322	13	the	the	DET
ejpam-5671	322	14	problem	problem	NOUN
ejpam-5671	322	15	(	(	PUNCT
ejpam-5671	322	16	1	1	X
ejpam-5671	322	17	)	)	PUNCT
ejpam-5671	322	18	has	have	VERB
ejpam-5671	322	19	at	at	ADV
ejpam-5671	322	20	least	least	ADV
ejpam-5671	322	21	one	one	NUM
ejpam-5671	322	22	solution	solution	NOUN
ejpam-5671	322	23	,	,	PUNCT
ejpam-5671	322	24	where	where	SCONJ
ejpam-5671	322	25	m	m	PROPN
ejpam-5671	322	26	=	=	SYM
ejpam-5671	322	27	max	max	PROPN
ejpam-5671	322	28	ρ∈[0,b]||ω(ρ,0)||=n<∞	ρ∈[0,b]||ω(ρ,0)||=n<∞	NOUN
ejpam-5671	322	29	{	{	PUNCT
ejpam-5671	322	30	3bµ	3bµ	ADJ
ejpam-5671	322	31	+	+	CCONJ
ejpam-5671	322	32	θµ	θµ	PROPN
ejpam-5671	322	33	2γ(µ+	2γ(µ+	PROPN
ejpam-5671	322	34	1	1	NUM
ejpam-5671	322	35	)	)	PUNCT
ejpam-5671	322	36	+	+	CCONJ
ejpam-5671	322	37	γ(2−	γ(2−	NOUN
ejpam-5671	322	38	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	322	39	+	+	CCONJ
ejpam-5671	322	40	b)−	b)−	PROPN
ejpam-5671	322	41	2ρ|(θµ−ξ−1	2ρ|(θµ−ξ−1	NUM
ejpam-5671	322	42	+	+	NOUN
ejpam-5671	322	43	bµ−ξ−1	bµ−ξ−1	NOUN
ejpam-5671	322	44	)	)	PUNCT
ejpam-5671	323	1	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	324	1	+	+	CCONJ
ejpam-5671	324	2	b1−ξ)γ(µ−	b1−ξ)γ(µ−	PROPN
ejpam-5671	324	3	ξ	ξ	PROPN
ejpam-5671	324	4	+	+	PROPN
ejpam-5671	324	5	1	1	NUM
ejpam-5671	324	6	)	)	PUNCT
ejpam-5671	324	7	+	+	CCONJ
ejpam-5671	324	8	γ(2−	γ(2−	PROPN
ejpam-5671	324	9	ξ	ξ	PROPN
ejpam-5671	324	10	)	)	PUNCT
ejpam-5671	324	11	4γ(3−	4γ(3−	NUM
ejpam-5671	325	1	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	326	1	+	+	CCONJ
ejpam-5671	326	2	b1−ξ)2γ(µ−	b1−ξ)2γ(µ−	X
ejpam-5671	326	3	ξ	ξ	X
ejpam-5671	326	4	)	)	PUNCT
ejpam-5671	326	5	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	326	6	+	+	CCONJ
ejpam-5671	326	7	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	326	8	ξ)−	ξ)−	PROPN
ejpam-5671	326	9	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	326	10	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	326	11	+	+	CCONJ
ejpam-5671	326	12	b1−ξ	b1−ξ	PROPN
ejpam-5671	326	13	)	)	PUNCT
ejpam-5671	326	14	−2(θ	−2(θ	PUNCT
ejpam-5671	326	15	+	+	CCONJ
ejpam-5671	326	16	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	326	17	+	+	CCONJ
ejpam-5671	326	18	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	326	19	ξ	ξ	PROPN
ejpam-5671	326	20	)	)	PUNCT
ejpam-5671	327	1	+	+	CCONJ
ejpam-5671	327	2	(	(	PUNCT
ejpam-5671	327	3	θ2	θ2	ADV
ejpam-5671	327	4	+	+	CCONJ
ejpam-5671	327	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	327	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	327	7	+	+	CCONJ
ejpam-5671	327	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	327	9	)	)	PUNCT
ejpam-5671	327	10	∣∣∣	∣∣∣	ADJ
ejpam-5671	327	11	}	}	PUNCT
ejpam-5671	327	12	.	.	PUNCT
ejpam-5671	328	1	proof	proof	NOUN
ejpam-5671	328	2	.	.	PUNCT
ejpam-5671	329	1	define	define	VERB
ejpam-5671	329	2	the	the	DET
ejpam-5671	329	3	operator	operator	NOUN
ejpam-5671	329	4	l	l	NOUN
ejpam-5671	329	5	:	:	PUNCT
ejpam-5671	329	6	a	a	DET
ejpam-5671	329	7	−→	−→	NOUN
ejpam-5671	329	8	a	a	PRON
ejpam-5671	329	9	as	as	ADP
ejpam-5671	329	10	in	in	ADP
ejpam-5671	329	11	(	(	PUNCT
ejpam-5671	329	12	12	12	NUM
ejpam-5671	329	13	)	)	PUNCT
ejpam-5671	329	14	,	,	PUNCT
ejpam-5671	329	15	then	then	ADV
ejpam-5671	329	16	(	(	PUNCT
ejpam-5671	329	17	lω)ρ	lω)ρ	PROPN
ejpam-5671	329	18	fulfills	fulfill	VERB
ejpam-5671	329	19	a	a	DET
ejpam-5671	329	20	fixed	fix	VERB
ejpam-5671	329	21	point	point	NOUN
ejpam-5671	329	22	problem	problem	NOUN
ejpam-5671	329	23	ω	ω	X
ejpam-5671	330	1	=	=	SYM
ejpam-5671	330	2	lω	lω	AUX
ejpam-5671	330	3	.	.	NOUN
ejpam-5671	330	4	define	define	VERB
ejpam-5671	330	5	a	a	DET
ejpam-5671	330	6	ball	ball	NOUN
ejpam-5671	330	7	br	br	PROPN
ejpam-5671	330	8	⊂	⊂	PROPN
ejpam-5671	330	9	c[0	c[0	PROPN
ejpam-5671	330	10	,	,	PUNCT
ejpam-5671	330	11	b	b	X
ejpam-5671	330	12	]	]	X
ejpam-5671	330	13	with	with	ADP
ejpam-5671	330	14	a	a	DET
ejpam-5671	330	15	suitable	suitable	ADJ
ejpam-5671	330	16	radius	radius	NOUN
ejpam-5671	330	17	r	r	NOUN
ejpam-5671	330	18	>	>	X
ejpam-5671	330	19	0	0	NUM
ejpam-5671	330	20	,	,	PUNCT
ejpam-5671	330	21	where	where	SCONJ
ejpam-5671	330	22	r	r	NOUN
ejpam-5671	330	23	>	>	X
ejpam-5671	330	24	δm	δm	PROPN
ejpam-5671	330	25	1−χm	1−χm	NUM
ejpam-5671	330	26	,	,	PUNCT
ejpam-5671	330	27	such	such	ADJ
ejpam-5671	330	28	that	that	DET
ejpam-5671	330	29	br	br	NOUN
ejpam-5671	330	30	=	=	SYM
ejpam-5671	330	31	{	{	PUNCT
ejpam-5671	330	32	ω	ω	PROPN
ejpam-5671	330	33	∈	∈	PROPN
ejpam-5671	330	34	c[0	c[0	PROPN
ejpam-5671	330	35	,	,	PUNCT
ejpam-5671	330	36	b	b	NOUN
ejpam-5671	330	37	]	]	X
ejpam-5671	330	38	:	:	PUNCT
ejpam-5671	330	39	||ω||	||ω||	VERB
ejpam-5671	330	40	<	<	X
ejpam-5671	330	41	r	r	NOUN
ejpam-5671	330	42	}	}	PUNCT
ejpam-5671	330	43	.	.	PUNCT
ejpam-5671	331	1	we	we	PRON
ejpam-5671	331	2	want	want	VERB
ejpam-5671	331	3	to	to	PART
ejpam-5671	331	4	show	show	VERB
ejpam-5671	331	5	that	that	SCONJ
ejpam-5671	331	6	lω	lω	ADP
ejpam-5671	331	7	:	:	PUNCT
ejpam-5671	331	8	br	br	ADP
ejpam-5671	331	9	−→	−→	ADJ
ejpam-5671	331	10	c[0	c[0	PROPN
ejpam-5671	331	11	,	,	PUNCT
ejpam-5671	332	1	b	b	NOUN
ejpam-5671	332	2	]	]	PUNCT
ejpam-5671	332	3	satisfies	satisfie	NOUN
ejpam-5671	332	4	ω	ω	NUM
ejpam-5671	332	5	̸=	̸=	PROPN
ejpam-5671	332	6	λlω	λlω	PROPN
ejpam-5671	332	7	,	,	PUNCT
ejpam-5671	332	8	for	for	ADP
ejpam-5671	332	9	all	all	DET
ejpam-5671	332	10	ω	ω	PROPN
ejpam-5671	332	11	∈	∈	PROPN
ejpam-5671	332	12	∂br	∂br	PROPN
ejpam-5671	332	13	and	and	CCONJ
ejpam-5671	332	14	all	all	DET
ejpam-5671	332	15	λ	λ	X
ejpam-5671	332	16	∈	∈	PROPN
ejpam-5671	333	1	[	[	X
ejpam-5671	333	2	0	0	NUM
ejpam-5671	333	3	,	,	PUNCT
ejpam-5671	333	4	b	b	NOUN
ejpam-5671	333	5	]	]	X
ejpam-5671	333	6	.	.	PUNCT
ejpam-5671	334	1	(	(	PUNCT
ejpam-5671	334	2	15	15	NUM
ejpam-5671	334	3	)	)	PUNCT
ejpam-5671	334	4	for	for	ADP
ejpam-5671	334	5	ω	ω	PROPN
ejpam-5671	334	6	∈	∈	PROPN
ejpam-5671	334	7	c(r	c(r	NOUN
ejpam-5671	334	8	)	)	PUNCT
ejpam-5671	334	9	,	,	PUNCT
ejpam-5671	334	10	λ	λ	PROPN
ejpam-5671	334	11	∈	∈	PROPN
ejpam-5671	335	1	[	[	X
ejpam-5671	335	2	0	0	NUM
ejpam-5671	335	3	,	,	PUNCT
ejpam-5671	335	4	1	1	NUM
ejpam-5671	335	5	]	]	PUNCT
ejpam-5671	335	6	,	,	PUNCT
ejpam-5671	335	7	setting	set	VERB
ejpam-5671	335	8	h(λ	h(λ	PROPN
ejpam-5671	335	9	,	,	PUNCT
ejpam-5671	335	10	ω	ω	NOUN
ejpam-5671	335	11	)	)	PUNCT
ejpam-5671	335	12	=	=	SYM
ejpam-5671	335	13	λlω	λlω	PROPN
ejpam-5671	335	14	.	.	PUNCT
ejpam-5671	336	1	consequently	consequently	ADV
ejpam-5671	336	2	,	,	PUNCT
ejpam-5671	336	3	the	the	DET
ejpam-5671	336	4	complete	complete	ADJ
ejpam-5671	336	5	continuity	continuity	NOUN
ejpam-5671	336	6	of	of	ADP
ejpam-5671	336	7	hλ(ω	hλ(ω	PUNCT
ejpam-5671	336	8	)	)	PUNCT
ejpam-5671	336	9	=	=	PUNCT
ejpam-5671	337	1	ω	ω	NUM
ejpam-5671	337	2	−h(λ	−h(λ	PROPN
ejpam-5671	337	3	,	,	PUNCT
ejpam-5671	337	4	ω	ω	NOUN
ejpam-5671	337	5	)	)	PUNCT
ejpam-5671	338	1	=	=	SYM
ejpam-5671	338	2	ω	ω	NOUN
ejpam-5671	339	1	−	−	NOUN
ejpam-5671	339	2	λlω	λlω	NOUN
ejpam-5671	339	3	can	can	AUX
ejpam-5671	339	4	be	be	AUX
ejpam-5671	339	5	deduced	deduce	VERB
ejpam-5671	339	6	via	via	ADP
ejpam-5671	339	7	the	the	DET
ejpam-5671	339	8	arzelá-ascoli	arzelá-ascoli	NOUN
ejpam-5671	339	9	theorem	theorem	VERB
ejpam-5671	339	10	.	.	PUNCT
ejpam-5671	340	1	if	if	SCONJ
ejpam-5671	340	2	(	(	PUNCT
ejpam-5671	340	3	15	15	NUM
ejpam-5671	340	4	)	)	PUNCT
ejpam-5671	340	5	is	be	AUX
ejpam-5671	340	6	satisfied	satisfied	ADJ
ejpam-5671	340	7	,	,	PUNCT
ejpam-5671	340	8	and	and	CCONJ
ejpam-5671	340	9	since	since	SCONJ
ejpam-5671	340	10	deg(hλ	deg(hλ	NOUN
ejpam-5671	340	11	,	,	PUNCT
ejpam-5671	340	12	br	br	NOUN
ejpam-5671	340	13	,	,	PUNCT
ejpam-5671	340	14	0	0	NUM
ejpam-5671	340	15	)	)	PUNCT
ejpam-5671	341	1	=	=	SYM
ejpam-5671	341	2	deg(h1	deg(h1	PROPN
ejpam-5671	341	3	,	,	PUNCT
ejpam-5671	341	4	br	br	PROPN
ejpam-5671	341	5	,	,	PUNCT
ejpam-5671	341	6	0	0	NUM
ejpam-5671	341	7	)	)	PUNCT
ejpam-5671	341	8	=	=	SYM
ejpam-5671	341	9	deg(h0	deg(h0	PROPN
ejpam-5671	341	10	,	,	PUNCT
ejpam-5671	341	11	br	br	PROPN
ejpam-5671	341	12	,	,	PUNCT
ejpam-5671	341	13	0	0	NUM
ejpam-5671	341	14	)	)	PUNCT
ejpam-5671	341	15	=	=	SYM
ejpam-5671	342	1	1	1	NUM
ejpam-5671	342	2	̸=	̸=	PROPN
ejpam-5671	342	3	0	0	NUM
ejpam-5671	342	4	∈	∈	PROPN
ejpam-5671	342	5	br	br	PROPN
ejpam-5671	342	6	,	,	PUNCT
ejpam-5671	342	7	s.	s.	PROPN
ejpam-5671	342	8	f.	f.	PROPN
ejpam-5671	342	9	aljurbua	aljurbua	PROPN
ejpam-5671	342	10	,	,	PUNCT
ejpam-5671	342	11	h.	h.	PROPN
ejpam-5671	342	12	a.	a.	PROPN
ejpam-5671	342	13	hammad	hammad	PROPN
ejpam-5671	342	14	,	,	PUNCT
ejpam-5671	342	15	n.	n.	PROPN
ejpam-5671	342	16	b.	b.	PROPN
ejpam-5671	342	17	almutairi	almutairi	PROPN
ejpam-5671	342	18	/	/	SYM
ejpam-5671	342	19	eur	eur	PROPN
ejpam-5671	342	20	.	.	PUNCT
ejpam-5671	343	1	j.	j.	PROPN
ejpam-5671	343	2	pure	pure	PROPN
ejpam-5671	343	3	appl	appl	PROPN
ejpam-5671	343	4	.	.	PROPN
ejpam-5671	343	5	math	math	PROPN
ejpam-5671	343	6	,	,	PUNCT
ejpam-5671	343	7	18	18	NUM
ejpam-5671	343	8	(	(	PUNCT
ejpam-5671	343	9	1	1	NUM
ejpam-5671	343	10	)	)	PUNCT
ejpam-5671	343	11	(	(	PUNCT
ejpam-5671	343	12	2025	2025	NUM
ejpam-5671	343	13	)	)	PUNCT
ejpam-5671	343	14	,	,	PUNCT
ejpam-5671	343	15	5671	5671	NUM
ejpam-5671	343	16	13	13	NUM
ejpam-5671	343	17	of	of	ADP
ejpam-5671	343	18	18	18	NUM
ejpam-5671	343	19	then	then	ADV
ejpam-5671	343	20	by	by	ADP
ejpam-5671	343	21	leray	leray	ADJ
ejpam-5671	343	22	-	-	PUNCT
ejpam-5671	343	23	schauder	schauder	NOUN
ejpam-5671	343	24	degree	degree	NOUN
ejpam-5671	343	25	there	there	PRON
ejpam-5671	343	26	is	be	VERB
ejpam-5671	343	27	at	at	ADV
ejpam-5671	343	28	least	least	ADV
ejpam-5671	343	29	one	one	NUM
ejpam-5671	343	30	ω	ω	NOUN
ejpam-5671	343	31	∈	∈	NOUN
ejpam-5671	343	32	br	br	NOUN
ejpam-5671	343	33	such	such	ADJ
ejpam-5671	343	34	that	that	DET
ejpam-5671	343	35	h1(ω	h1(ω	PROPN
ejpam-5671	343	36	)	)	PUNCT
ejpam-5671	343	37	=	=	NOUN
ejpam-5671	343	38	ω−λlω	ω−λlω	NOUN
ejpam-5671	343	39	=	=	NOUN
ejpam-5671	344	1	0	0	X
ejpam-5671	344	2	.	.	PUNCT
ejpam-5671	345	1	so	so	ADV
ejpam-5671	345	2	for	for	ADP
ejpam-5671	345	3	some	some	DET
ejpam-5671	345	4	λ	λ	X
ejpam-5671	345	5	∈	∈	PROPN
ejpam-5671	345	6	[	[	X
ejpam-5671	345	7	0	0	NUM
ejpam-5671	345	8	,	,	PUNCT
ejpam-5671	345	9	1	1	NUM
ejpam-5671	345	10	]	]	PUNCT
ejpam-5671	345	11	and	and	CCONJ
ejpam-5671	345	12	for	for	ADP
ejpam-5671	345	13	all	all	DET
ejpam-5671	345	14	ρ	ρ	NOUN
ejpam-5671	345	15	∈	∈	PROPN
ejpam-5671	345	16	[	[	X
ejpam-5671	345	17	0	0	NUM
ejpam-5671	345	18	,	,	PUNCT
ejpam-5671	345	19	b	b	NOUN
ejpam-5671	345	20	]	]	X
ejpam-5671	345	21	we	we	PRON
ejpam-5671	345	22	conclude	conclude	VERB
ejpam-5671	345	23	that	that	PRON
ejpam-5671	345	24	ω	ω	PROPN
ejpam-5671	345	25	=	=	X
ejpam-5671	345	26	λlω	λlω	PROPN
ejpam-5671	345	27	.	.	PUNCT
ejpam-5671	346	1	now	now	ADV
ejpam-5671	346	2	,	,	PUNCT
ejpam-5671	346	3	|ω(ρ)|	|ω(ρ)|	PROPN
ejpam-5671	346	4	=	=	PUNCT
ejpam-5671	346	5	|λlω(ρ)|	|λlω(ρ)|	NOUN
ejpam-5671	346	6	≤	≤	NUM
ejpam-5671	346	7	∫	∫	PROPN
ejpam-5671	346	8	ρ	ρ	PROPN
ejpam-5671	346	9	0	0	PROPN
ejpam-5671	346	10	(	(	PUNCT
ejpam-5671	346	11	ρ−	ρ−	NOUN
ejpam-5671	346	12	ν)µ−1	ν)µ−1	VERB
ejpam-5671	346	13	γ(µ	γ(µ	PROPN
ejpam-5671	346	14	)	)	PUNCT
ejpam-5671	346	15	|ω(ν	|ω(ν	PROPN
ejpam-5671	346	16	,	,	PUNCT
ejpam-5671	346	17	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	347	1	+	+	CCONJ
ejpam-5671	347	2	1	1	NUM
ejpam-5671	347	3	2	2	NUM
ejpam-5671	347	4	(	(	PUNCT
ejpam-5671	347	5	∫	∫	PROPN
ejpam-5671	347	6	θ	θ	PROPN
ejpam-5671	347	7	0	0	PUNCT
ejpam-5671	347	8	(	(	PUNCT
ejpam-5671	347	9	θ	θ	NOUN
ejpam-5671	347	10	−	−	PROPN
ejpam-5671	347	11	ν)µ−1	ν)µ−1	NOUN
ejpam-5671	347	12	γ(µ	γ(µ	PROPN
ejpam-5671	347	13	)	)	PUNCT
ejpam-5671	348	1	|ω(ν	|ω(ν	ADJ
ejpam-5671	348	2	,	,	PUNCT
ejpam-5671	348	3	ω(ν))dν|+	ω(ν))dν|+	PROPN
ejpam-5671	348	4	∫	∫	PROPN
ejpam-5671	348	5	b	b	PROPN
ejpam-5671	348	6	0	0	NUM
ejpam-5671	348	7	(	(	PUNCT
ejpam-5671	348	8	b−	b−	PROPN
ejpam-5671	348	9	ν)µ−1	ν)µ−1	VERB
ejpam-5671	348	10	γ(µ	γ(µ	PROPN
ejpam-5671	348	11	)	)	PUNCT
ejpam-5671	349	1	|ω(ν	|ω(ν	PROPN
ejpam-5671	349	2	,	,	PUNCT
ejpam-5671	349	3	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	349	4	)	)	PUNCT
ejpam-5671	350	1	+	+	CCONJ
ejpam-5671	350	2	γ(2−	γ(2−	NOUN
ejpam-5671	350	3	ξ)|(θ	ξ)|(θ	NOUN
ejpam-5671	350	4	+	+	CCONJ
ejpam-5671	350	5	b)−	b)−	PROPN
ejpam-5671	350	6	2ρ|	2ρ|	NUM
ejpam-5671	350	7	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	350	8	+	+	CCONJ
ejpam-5671	350	9	b1−ξ	b1−ξ	PROPN
ejpam-5671	350	10	)	)	PUNCT
ejpam-5671	350	11	(	(	PUNCT
ejpam-5671	350	12	∫	∫	PROPN
ejpam-5671	350	13	θ	θ	PROPN
ejpam-5671	350	14	0	0	PUNCT
ejpam-5671	350	15	(	(	PUNCT
ejpam-5671	350	16	θ	θ	X
ejpam-5671	350	17	−	−	PROPN
ejpam-5671	350	18	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	350	19	γ(µ−	γ(µ−	VERB
ejpam-5671	350	20	ξ	ξ	NOUN
ejpam-5671	350	21	)	)	PUNCT
ejpam-5671	350	22	|ω(ν	|ω(ν	ADJ
ejpam-5671	350	23	,	,	PUNCT
ejpam-5671	350	24	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	351	1	+	+	CCONJ
ejpam-5671	351	2	∫	∫	PROPN
ejpam-5671	351	3	b	b	PROPN
ejpam-5671	351	4	0	0	NUM
ejpam-5671	351	5	(	(	PUNCT
ejpam-5671	351	6	b−	b−	PROPN
ejpam-5671	351	7	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	351	8	γ(µ−	γ(µ−	VERB
ejpam-5671	351	9	ξ	ξ	NOUN
ejpam-5671	351	10	)	)	PUNCT
ejpam-5671	351	11	|ω(ν	|ω(ν	ADJ
ejpam-5671	351	12	,	,	PUNCT
ejpam-5671	351	13	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	351	14	)	)	PUNCT
ejpam-5671	352	1	γ(2−	γ(2−	PROPN
ejpam-5671	352	2	ξ	ξ	X
ejpam-5671	352	3	)	)	PUNCT
ejpam-5671	352	4	4γ(3−	4γ(3−	NUM
ejpam-5671	352	5	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	353	1	+	+	CCONJ
ejpam-5671	353	2	b1−ξ)2	b1−ξ)2	VERB
ejpam-5671	353	3	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	NOUN
ejpam-5671	353	4	+	+	CCONJ
ejpam-5671	353	5	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	353	6	ξ)−	ξ)−	PROPN
ejpam-5671	353	7	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	353	8	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	353	9	+	+	CCONJ
ejpam-5671	353	10	b1−ξ	b1−ξ	PROPN
ejpam-5671	353	11	)	)	PUNCT
ejpam-5671	353	12	−	−	ADP
ejpam-5671	353	13	2(θ	2(θ	NUM
ejpam-5671	354	1	+	+	CCONJ
ejpam-5671	354	2	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	354	3	+	+	CCONJ
ejpam-5671	354	4	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	354	5	ξ	ξ	PROPN
ejpam-5671	354	6	)	)	PUNCT
ejpam-5671	355	1	+	+	CCONJ
ejpam-5671	355	2	(	(	PUNCT
ejpam-5671	355	3	θ2	θ2	ADV
ejpam-5671	355	4	+	+	CCONJ
ejpam-5671	355	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	355	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	355	7	+	+	CCONJ
ejpam-5671	355	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	355	9	)	)	PUNCT
ejpam-5671	355	10	∣∣∣	∣∣∣	ADP
ejpam-5671	355	11	×	×	PROPN
ejpam-5671	355	12	(	(	PUNCT
ejpam-5671	355	13	∫	∫	PROPN
ejpam-5671	355	14	θ	θ	PROPN
ejpam-5671	355	15	0	0	PUNCT
ejpam-5671	355	16	(	(	PUNCT
ejpam-5671	355	17	θ	θ	NOUN
ejpam-5671	355	18	−	−	NOUN
ejpam-5671	355	19	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	355	20	γ(µ−	γ(µ−	VERB
ejpam-5671	355	21	ξ	ξ	PRON
ejpam-5671	355	22	−	−	NOUN
ejpam-5671	355	23	1	1	NUM
ejpam-5671	355	24	)	)	PUNCT
ejpam-5671	355	25	|ω(ν	|ω(ν	ADJ
ejpam-5671	355	26	,	,	PUNCT
ejpam-5671	355	27	ω(ν))|dν	ω(ν))|dν	X
ejpam-5671	356	1	+	+	CCONJ
ejpam-5671	356	2	∫	∫	PROPN
ejpam-5671	356	3	b	b	PROPN
ejpam-5671	356	4	0	0	NUM
ejpam-5671	356	5	(	(	PUNCT
ejpam-5671	356	6	b−	b−	NOUN
ejpam-5671	356	7	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	356	8	γ(µ−	γ(µ−	VERB
ejpam-5671	356	9	ξ	ξ	PRON
ejpam-5671	356	10	−	−	NOUN
ejpam-5671	356	11	1	1	NUM
ejpam-5671	356	12	)	)	PUNCT
ejpam-5671	356	13	|ω(ν	|ω(ν	ADJ
ejpam-5671	356	14	,	,	PUNCT
ejpam-5671	356	15	ω(ν))|dν	ω(ν))|dν	NUM
ejpam-5671	356	16	)	)	PUNCT
ejpam-5671	357	1	≤	≤	NUM
ejpam-5671	358	1	∫	∫	PROPN
ejpam-5671	359	1	ρ	ρ	PROPN
ejpam-5671	359	2	0	0	PROPN
ejpam-5671	360	1	(	(	PUNCT
ejpam-5671	360	2	ρ−	ρ−	NOUN
ejpam-5671	360	3	ν)µ−1	ν)µ−1	VERB
ejpam-5671	360	4	γ(µ	γ(µ	PROPN
ejpam-5671	360	5	)	)	PUNCT
ejpam-5671	361	1	(	(	PUNCT
ejpam-5671	361	2	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	361	3	δ)dν	δ)dν	PROPN
ejpam-5671	361	4	+	+	CCONJ
ejpam-5671	361	5	1	1	NUM
ejpam-5671	361	6	2	2	NUM
ejpam-5671	361	7	(	(	PUNCT
ejpam-5671	361	8	∫	∫	PROPN
ejpam-5671	361	9	θ	θ	PROPN
ejpam-5671	361	10	0	0	PUNCT
ejpam-5671	361	11	(	(	PUNCT
ejpam-5671	361	12	θ	θ	NOUN
ejpam-5671	361	13	−	−	PROPN
ejpam-5671	361	14	ν)µ−1	ν)µ−1	NOUN
ejpam-5671	361	15	γ(µ	γ(µ	PROPN
ejpam-5671	361	16	)	)	PUNCT
ejpam-5671	361	17	(	(	PUNCT
ejpam-5671	362	1	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	362	2	δ)dν	δ)dν	PROPN
ejpam-5671	362	3	+	+	NUM
ejpam-5671	362	4	∫	∫	PROPN
ejpam-5671	362	5	b	b	PROPN
ejpam-5671	362	6	0	0	NUM
ejpam-5671	362	7	(	(	PUNCT
ejpam-5671	362	8	b−	b−	PROPN
ejpam-5671	362	9	ν)µ−1	ν)µ−1	VERB
ejpam-5671	362	10	γ(µ	γ(µ	PROPN
ejpam-5671	362	11	)	)	PUNCT
ejpam-5671	362	12	(	(	PUNCT
ejpam-5671	362	13	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	362	14	δ)dν	δ)dν	PROPN
ejpam-5671	362	15	)	)	PUNCT
ejpam-5671	363	1	+	+	CCONJ
ejpam-5671	363	2	γ(2−	γ(2−	PROPN
ejpam-5671	363	3	ξ	ξ	X
ejpam-5671	363	4	)	)	PUNCT
ejpam-5671	363	5	|(θ	|(θ	PROPN
ejpam-5671	364	1	+	+	CCONJ
ejpam-5671	364	2	b)−	b)−	PROPN
ejpam-5671	364	3	2ρ|	2ρ|	NUM
ejpam-5671	364	4	2(θ1−ξ	2(θ1−ξ	NUM
ejpam-5671	364	5	+	+	CCONJ
ejpam-5671	364	6	b1−ξ	b1−ξ	PROPN
ejpam-5671	364	7	)	)	PUNCT
ejpam-5671	364	8	(	(	PUNCT
ejpam-5671	364	9	∫	∫	PROPN
ejpam-5671	364	10	θ	θ	PROPN
ejpam-5671	364	11	0	0	PUNCT
ejpam-5671	364	12	(	(	PUNCT
ejpam-5671	364	13	θ	θ	X
ejpam-5671	364	14	−	−	PROPN
ejpam-5671	364	15	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	364	16	γ(µ−	γ(µ−	VERB
ejpam-5671	364	17	ξ	ξ	NUM
ejpam-5671	364	18	)	)	PUNCT
ejpam-5671	364	19	(	(	PUNCT
ejpam-5671	365	1	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	365	2	δ)dν	δ)dν	PROPN
ejpam-5671	365	3	+	+	NUM
ejpam-5671	365	4	∫	∫	PROPN
ejpam-5671	365	5	b	b	PROPN
ejpam-5671	365	6	0	0	NUM
ejpam-5671	365	7	(	(	PUNCT
ejpam-5671	365	8	b−	b−	PROPN
ejpam-5671	365	9	ν)µ−ξ−1	ν)µ−ξ−1	ADJ
ejpam-5671	365	10	γ(µ−	γ(µ−	VERB
ejpam-5671	365	11	ξ	ξ	NUM
ejpam-5671	365	12	)	)	PUNCT
ejpam-5671	365	13	(	(	PUNCT
ejpam-5671	365	14	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	365	15	δ)dν	δ)dν	PROPN
ejpam-5671	365	16	)	)	PUNCT
ejpam-5671	366	1	+	+	CCONJ
ejpam-5671	367	1	γ(2−	γ(2−	PROPN
ejpam-5671	367	2	ξ	ξ	PROPN
ejpam-5671	367	3	)	)	PUNCT
ejpam-5671	367	4	4γ(3−	4γ(3−	NUM
ejpam-5671	367	5	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	367	6	+	+	CCONJ
ejpam-5671	367	7	b1−ξ)2	b1−ξ)2	NOUN
ejpam-5671	367	8	(	(	PUNCT
ejpam-5671	367	9	∣∣∣4ρ(θ2−ξ	∣∣∣4ρ(θ2−ξ	PROPN
ejpam-5671	367	10	+	+	NUM
ejpam-5671	367	11	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	367	12	ξ)−	ξ)−	PROPN
ejpam-5671	367	13	4ρ2γ(3−	4ρ2γ(3−	NUM
ejpam-5671	367	14	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	367	15	+	+	CCONJ
ejpam-5671	367	16	b1−ξ	b1−ξ	PROPN
ejpam-5671	367	17	)	)	PUNCT
ejpam-5671	367	18	−2(θ	−2(θ	PUNCT
ejpam-5671	367	19	+	+	CCONJ
ejpam-5671	367	20	b)(θ2−ξ	b)(θ2−ξ	NOUN
ejpam-5671	367	21	+	+	CCONJ
ejpam-5671	367	22	b2−ξ)γ(2−	b2−ξ)γ(2−	PROPN
ejpam-5671	367	23	ξ	ξ	PROPN
ejpam-5671	367	24	)	)	PUNCT
ejpam-5671	368	1	+	+	CCONJ
ejpam-5671	368	2	(	(	PUNCT
ejpam-5671	368	3	θ2	θ2	ADV
ejpam-5671	368	4	+	+	CCONJ
ejpam-5671	368	5	b2)γ(3−	b2)γ(3−	ADJ
ejpam-5671	368	6	ξ)(θ1−ξ	ξ)(θ1−ξ	PROPN
ejpam-5671	368	7	+	+	CCONJ
ejpam-5671	368	8	b1−ξ	b1−ξ	PROPN
ejpam-5671	368	9	)	)	PUNCT
ejpam-5671	368	10	∣∣∣	∣∣∣	ADP
ejpam-5671	368	11	]	]	X
ejpam-5671	368	12	×	×	NOUN
ejpam-5671	368	13	(	(	PUNCT
ejpam-5671	368	14	∫	∫	PROPN
ejpam-5671	368	15	θ	θ	PROPN
ejpam-5671	368	16	0	0	PUNCT
ejpam-5671	369	1	(	(	PUNCT
ejpam-5671	369	2	θ	θ	NOUN
ejpam-5671	369	3	−	−	NOUN
ejpam-5671	369	4	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	369	5	γ(µ−	γ(µ−	VERB
ejpam-5671	369	6	ξ	ξ	NOUN
ejpam-5671	369	7	−	−	NOUN
ejpam-5671	369	8	1	1	NUM
ejpam-5671	369	9	)	)	PUNCT
ejpam-5671	369	10	(	(	PUNCT
ejpam-5671	370	1	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	370	2	δ)dν	δ)dν	PROPN
ejpam-5671	370	3	+	+	NUM
ejpam-5671	370	4	∫	∫	PROPN
ejpam-5671	370	5	b	b	PROPN
ejpam-5671	370	6	0	0	NUM
ejpam-5671	370	7	(	(	PUNCT
ejpam-5671	370	8	b−	b−	NOUN
ejpam-5671	370	9	ν)µ−ξ−2	ν)µ−ξ−2	NOUN
ejpam-5671	370	10	γ(µ−	γ(µ−	VERB
ejpam-5671	370	11	ξ	ξ	PRON
ejpam-5671	370	12	−	−	NOUN
ejpam-5671	370	13	1	1	NUM
ejpam-5671	370	14	)	)	PUNCT
ejpam-5671	370	15	(	(	PUNCT
ejpam-5671	370	16	χ|ω|+	χ|ω|+	PROPN
ejpam-5671	370	17	δ)dν	δ)dν	PROPN
ejpam-5671	370	18	)	)	PUNCT
ejpam-5671	370	19	,	,	PUNCT
ejpam-5671	370	20	which	which	PRON
ejpam-5671	370	21	implies	imply	VERB
ejpam-5671	370	22	that	that	SCONJ
ejpam-5671	370	23	|ω|	|ω|	VERB
ejpam-5671	370	24	≤	≤	NUM
ejpam-5671	370	25	(	(	PUNCT
ejpam-5671	370	26	χ||ω||+	χ||ω||+	NOUN
ejpam-5671	370	27	δ)m	δ)m	NOUN
ejpam-5671	370	28	.	.	PUNCT
ejpam-5671	371	1	hence	hence	ADV
ejpam-5671	371	2	,	,	PUNCT
ejpam-5671	371	3	||ω||	||ω||	VERB
ejpam-5671	371	4	≤	≤	NUM
ejpam-5671	371	5	δm	δm	ADP
ejpam-5671	371	6	1−	1−	NUM
ejpam-5671	371	7	χm	χm	NOUN
ejpam-5671	371	8	.	.	PUNCT
ejpam-5671	372	1	this	this	PRON
ejpam-5671	372	2	proves	prove	VERB
ejpam-5671	372	3	that	that	SCONJ
ejpam-5671	372	4	the	the	DET
ejpam-5671	372	5	relation	relation	NOUN
ejpam-5671	372	6	(	(	PUNCT
ejpam-5671	372	7	15	15	NUM
ejpam-5671	372	8	)	)	PUNCT
ejpam-5671	372	9	is	be	AUX
ejpam-5671	372	10	satisfied	satisfied	ADJ
ejpam-5671	372	11	.	.	PUNCT
ejpam-5671	373	1	by	by	ADP
ejpam-5671	373	2	applying	apply	VERB
ejpam-5671	373	3	theorem	theorem	NOUN
ejpam-5671	373	4	1	1	NUM
ejpam-5671	373	5	,	,	PUNCT
ejpam-5671	373	6	we	we	PRON
ejpam-5671	373	7	get	get	VERB
ejpam-5671	373	8	the	the	DET
ejpam-5671	373	9	desired	desire	VERB
ejpam-5671	373	10	result	result	NOUN
ejpam-5671	373	11	.	.	PUNCT
ejpam-5671	374	1	4	4	X
ejpam-5671	374	2	.	.	X
ejpam-5671	374	3	illustrative	illustrative	ADJ
ejpam-5671	374	4	examples	example	NOUN
ejpam-5671	374	5	this	this	DET
ejpam-5671	374	6	section	section	NOUN
ejpam-5671	374	7	is	be	AUX
ejpam-5671	374	8	devoted	devote	VERB
ejpam-5671	374	9	to	to	ADP
ejpam-5671	374	10	studying	study	VERB
ejpam-5671	374	11	some	some	DET
ejpam-5671	374	12	illustrative	illustrative	ADJ
ejpam-5671	374	13	examples	example	NOUN
ejpam-5671	374	14	that	that	PRON
ejpam-5671	374	15	support	support	VERB
ejpam-5671	374	16	the	the	DET
ejpam-5671	374	17	theoretical	theoretical	ADJ
ejpam-5671	374	18	results	result	NOUN
ejpam-5671	374	19	.	.	PUNCT
ejpam-5671	375	1	s.	s.	PROPN
ejpam-5671	375	2	f.	f.	PROPN
ejpam-5671	375	3	aljurbua	aljurbua	PROPN
ejpam-5671	375	4	,	,	PUNCT
ejpam-5671	375	5	h.	h.	PROPN
ejpam-5671	375	6	a.	a.	PROPN
ejpam-5671	375	7	hammad	hammad	PROPN
ejpam-5671	375	8	,	,	PUNCT
ejpam-5671	375	9	n.	n.	PROPN
ejpam-5671	375	10	b.	b.	PROPN
ejpam-5671	375	11	almutairi	almutairi	PROPN
ejpam-5671	375	12	/	/	SYM
ejpam-5671	375	13	eur	eur	PROPN
ejpam-5671	375	14	.	.	PUNCT
ejpam-5671	376	1	j.	j.	PROPN
ejpam-5671	376	2	pure	pure	PROPN
ejpam-5671	376	3	appl	appl	PROPN
ejpam-5671	376	4	.	.	PROPN
ejpam-5671	376	5	math	math	PROPN
ejpam-5671	376	6	,	,	PUNCT
ejpam-5671	376	7	18	18	NUM
ejpam-5671	376	8	(	(	PUNCT
ejpam-5671	376	9	1	1	NUM
ejpam-5671	376	10	)	)	PUNCT
ejpam-5671	376	11	(	(	PUNCT
ejpam-5671	376	12	2025	2025	NUM
ejpam-5671	376	13	)	)	PUNCT
ejpam-5671	376	14	,	,	PUNCT
ejpam-5671	376	15	5671	5671	NUM
ejpam-5671	376	16	14	14	NUM
ejpam-5671	376	17	of	of	ADP
ejpam-5671	376	18	18	18	NUM
ejpam-5671	376	19	example	example	NOUN
ejpam-5671	376	20	1	1	NUM
ejpam-5671	376	21	.	.	PUNCT
ejpam-5671	376	22	consider	consider	VERB
ejpam-5671	376	23	the	the	DET
ejpam-5671	376	24	following	follow	VERB
ejpam-5671	376	25	fractional	fractional	ADJ
ejpam-5671	376	26	problem	problem	NOUN
ejpam-5671	376	27	{	{	PUNCT
ejpam-5671	376	28	cd	cd	NOUN
ejpam-5671	376	29	5	5	NUM
ejpam-5671	376	30	2ω(ρ	2ω(ρ	NUM
ejpam-5671	376	31	)	)	PUNCT
ejpam-5671	377	1	=	=	SYM
ejpam-5671	377	2	1	1	NUM
ejpam-5671	377	3	(	(	PUNCT
ejpam-5671	377	4	ρ−3)4	ρ−3)4	NOUN
ejpam-5671	377	5	|ω|	|ω|	PROPN
ejpam-5671	377	6	1+|ω|	1+|ω|	NUM
ejpam-5671	377	7	,	,	PUNCT
ejpam-5671	377	8	ρ	ρ	PROPN
ejpam-5671	377	9	∈	∈	PROPN
ejpam-5671	378	1	[	[	X
ejpam-5671	378	2	0	0	NUM
ejpam-5671	378	3	,	,	PUNCT
ejpam-5671	378	4	2	2	NUM
ejpam-5671	378	5	]	]	PUNCT
ejpam-5671	378	6	,	,	PUNCT
ejpam-5671	378	7	ω(θ	ω(θ	NUM
ejpam-5671	378	8	)	)	PUNCT
ejpam-5671	378	9	=	=	SYM
ejpam-5671	378	10	−ω(2	−ω(2	NOUN
ejpam-5671	378	11	)	)	PUNCT
ejpam-5671	378	12	,	,	PUNCT
ejpam-5671	378	13	ω′(θ	ω′(θ	NOUN
ejpam-5671	378	14	)	)	PUNCT
ejpam-5671	378	15	=	=	SYM
ejpam-5671	378	16	−ω′(2	−ω′(2	PROPN
ejpam-5671	378	17	)	)	PUNCT
ejpam-5671	378	18	,	,	PUNCT
ejpam-5671	378	19	cd	cd	PROPN
ejpam-5671	378	20	3	3	NUM
ejpam-5671	378	21	2ω(θ	2ω(θ	NUM
ejpam-5671	378	22	)	)	PUNCT
ejpam-5671	379	1	=	=	SYM
ejpam-5671	379	2	−cd	−cd	NOUN
ejpam-5671	379	3	3	3	NUM
ejpam-5671	379	4	2ω(2	2ω(2	NUM
ejpam-5671	379	5	)	)	PUNCT
ejpam-5671	379	6	,	,	PUNCT
ejpam-5671	379	7	θ	θ	X
ejpam-5671	379	8	=	=	SYM
ejpam-5671	379	9	1	1	NUM
ejpam-5671	379	10	(	(	PUNCT
ejpam-5671	379	11	16	16	NUM
ejpam-5671	379	12	)	)	PUNCT
ejpam-5671	379	13	clearly	clearly	ADV
ejpam-5671	379	14	,	,	PUNCT
ejpam-5671	379	15	the	the	DET
ejpam-5671	379	16	problem	problem	NOUN
ejpam-5671	379	17	(	(	PUNCT
ejpam-5671	379	18	16	16	NUM
ejpam-5671	379	19	)	)	PUNCT
ejpam-5671	379	20	is	be	AUX
ejpam-5671	379	21	a	a	DET
ejpam-5671	379	22	special	special	ADJ
ejpam-5671	379	23	case	case	NOUN
ejpam-5671	379	24	of	of	ADP
ejpam-5671	379	25	the	the	DET
ejpam-5671	379	26	problem	problem	NOUN
ejpam-5671	379	27	(	(	PUNCT
ejpam-5671	379	28	1	1	NUM
ejpam-5671	379	29	)	)	PUNCT
ejpam-5671	379	30	with	with	ADP
ejpam-5671	379	31	µ	µ	NOUN
ejpam-5671	379	32	=	=	SYM
ejpam-5671	379	33	5	5	NUM
ejpam-5671	379	34	2	2	NUM
ejpam-5671	379	35	∈	∈	NOUN
ejpam-5671	379	36	(	(	PUNCT
ejpam-5671	379	37	2	2	NUM
ejpam-5671	379	38	,	,	PUNCT
ejpam-5671	379	39	3	3	NUM
ejpam-5671	379	40	]	]	PUNCT
ejpam-5671	379	41	,	,	PUNCT
ejpam-5671	379	42	ξ	ξ	X
ejpam-5671	379	43	=	=	SYM
ejpam-5671	379	44	1	1	NUM
ejpam-5671	379	45	2	2	NUM
ejpam-5671	379	46	∈	∈	NOUN
ejpam-5671	379	47	(	(	PUNCT
ejpam-5671	379	48	0	0	NUM
ejpam-5671	379	49	,	,	PUNCT
ejpam-5671	379	50	1	1	NUM
ejpam-5671	379	51	)	)	PUNCT
ejpam-5671	379	52	,	,	PUNCT
ejpam-5671	379	53	b	b	X
ejpam-5671	379	54	=	=	SYM
ejpam-5671	379	55	2	2	NUM
ejpam-5671	379	56	>	>	SYM
ejpam-5671	379	57	0	0	NUM
ejpam-5671	379	58	,	,	PUNCT
ejpam-5671	379	59	θ	θ	PROPN
ejpam-5671	379	60	∈	∈	PROPN
ejpam-5671	380	1	[	[	X
ejpam-5671	380	2	0	0	NUM
ejpam-5671	380	3	,	,	PUNCT
ejpam-5671	380	4	2	2	NUM
ejpam-5671	380	5	)	)	PUNCT
ejpam-5671	381	1	,	,	PUNCT
ejpam-5671	381	2	ρ	ρ	PROPN
ejpam-5671	381	3	∈	∈	PROPN
ejpam-5671	382	1	[	[	X
ejpam-5671	382	2	0	0	NUM
ejpam-5671	382	3	,	,	PUNCT
ejpam-5671	382	4	2	2	NUM
ejpam-5671	382	5	]	]	PUNCT
ejpam-5671	382	6	,	,	PUNCT
ejpam-5671	382	7	and	and	CCONJ
ejpam-5671	382	8	ω	ω	NUM
ejpam-5671	382	9	(	(	PUNCT
ejpam-5671	382	10	ρ	ρ	PROPN
ejpam-5671	382	11	,	,	PUNCT
ejpam-5671	382	12	ω	ω	PROPN
ejpam-5671	382	13	(	(	PUNCT
ejpam-5671	382	14	ρ	ρ	NOUN
ejpam-5671	382	15	)	)	PUNCT
ejpam-5671	382	16	)	)	PUNCT
ejpam-5671	382	17	=	=	SYM
ejpam-5671	382	18	1	1	NUM
ejpam-5671	382	19	(	(	PUNCT
ejpam-5671	382	20	ρ−3)4	ρ−3)4	NOUN
ejpam-5671	382	21	|ω|	|ω|	PROPN
ejpam-5671	382	22	1+|ω|	1+|ω|	NUM
ejpam-5671	382	23	.	.	PUNCT
ejpam-5671	383	1	now	now	ADV
ejpam-5671	383	2	,	,	PUNCT
ejpam-5671	383	3	for	for	ADP
ejpam-5671	383	4	each	each	DET
ejpam-5671	383	5	ω1	ω1	PROPN
ejpam-5671	383	6	,	,	PUNCT
ejpam-5671	383	7	ω2	ω2	NOUN
ejpam-5671	383	8	∈	∈	PROPN
ejpam-5671	383	9	r	r	X
ejpam-5671	383	10	,	,	PUNCT
ejpam-5671	383	11	we	we	PRON
ejpam-5671	383	12	have	have	VERB
ejpam-5671	383	13	∥ω1(ρ	∥ω1(ρ	PROPN
ejpam-5671	383	14	,	,	PUNCT
ejpam-5671	383	15	ω1)−	ω1)−	PROPN
ejpam-5671	383	16	ω1(ρ	ω1(ρ	PROPN
ejpam-5671	383	17	,	,	PUNCT
ejpam-5671	383	18	ω2)∥	ω2)∥	PRON
ejpam-5671	383	19	=	=	SYM
ejpam-5671	383	20	1	1	NUM
ejpam-5671	383	21	(	(	PUNCT
ejpam-5671	383	22	ρ−	ρ−	NOUN
ejpam-5671	383	23	3)4	3)4	NUM
ejpam-5671	383	24	∥∥∥∥	∥∥∥∥	NUM
ejpam-5671	383	25	|ω1|	|ω1|	NOUN
ejpam-5671	383	26	1	1	NUM
ejpam-5671	383	27	+	+	NUM
ejpam-5671	383	28	|ω1|	|ω1|	NOUN
ejpam-5671	383	29	−	−	NOUN
ejpam-5671	383	30	|ω2|	|ω2|	NOUN
ejpam-5671	383	31	1	1	NUM
ejpam-5671	383	32	+	+	NUM
ejpam-5671	383	33	|ω2|	|ω2|	NOUN
ejpam-5671	383	34	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5671	383	35	≤	≤	NUM
ejpam-5671	383	36	1	1	NUM
ejpam-5671	383	37	81	81	NUM
ejpam-5671	383	38	∥ω1	∥ω1	PUNCT
ejpam-5671	383	39	−	−	PROPN
ejpam-5671	383	40	ω2∥	ω2∥	PROPN
ejpam-5671	383	41	.	.	PUNCT
ejpam-5671	384	1	hence	hence	ADV
ejpam-5671	384	2	,	,	PUNCT
ejpam-5671	384	3	l	l	NOUN
ejpam-5671	384	4	=	=	SYM
ejpam-5671	384	5	1	1	NUM
ejpam-5671	384	6	81	81	NUM
ejpam-5671	384	7	.	.	PUNCT
ejpam-5671	385	1	by	by	ADP
ejpam-5671	385	2	simple	simple	ADJ
ejpam-5671	385	3	calculations	calculation	NOUN
ejpam-5671	385	4	,	,	PUNCT
ejpam-5671	385	5	according	accord	VERB
ejpam-5671	385	6	to	to	ADP
ejpam-5671	385	7	eq	eq	PROPN
ejpam-5671	385	8	.	.	PUNCT
ejpam-5671	386	1	(	(	PUNCT
ejpam-5671	386	2	13	13	NUM
ejpam-5671	386	3	)	)	PUNCT
ejpam-5671	386	4	,	,	PUNCT
ejpam-5671	386	5	if	if	SCONJ
ejpam-5671	386	6	we	we	PRON
ejpam-5671	386	7	choose	choose	VERB
ejpam-5671	386	8	θ	θ	X
ejpam-5671	386	9	=	=	SYM
ejpam-5671	386	10	1	1	NUM
ejpam-5671	386	11	∈	∈	NOUN
ejpam-5671	387	1	[	[	X
ejpam-5671	387	2	0	0	NUM
ejpam-5671	387	3	,	,	PUNCT
ejpam-5671	387	4	2	2	NUM
ejpam-5671	387	5	)	)	PUNCT
ejpam-5671	387	6	,	,	PUNCT
ejpam-5671	387	7	we	we	PRON
ejpam-5671	387	8	get	get	VERB
ejpam-5671	387	9	m1	m1	PROPN
ejpam-5671	388	1	≈	≈	PROPN
ejpam-5671	388	2	7.59	7.59	NUM
ejpam-5671	388	3	.	.	PUNCT
ejpam-5671	389	1	thus	thus	ADV
ejpam-5671	389	2	,	,	PUNCT
ejpam-5671	389	3	lm1	lm1	NOUN
ejpam-5671	389	4	=	=	SYM
ejpam-5671	389	5	(	(	PUNCT
ejpam-5671	389	6	1	1	NUM
ejpam-5671	389	7	81)(7.59	81)(7.59	NUM
ejpam-5671	389	8	)	)	PUNCT
ejpam-5671	390	1	≈	≈	PROPN
ejpam-5671	390	2	0.0937	0.0937	NUM
ejpam-5671	390	3	<	<	X
ejpam-5671	390	4	1	1	NUM
ejpam-5671	390	5	.	.	PUNCT
ejpam-5671	390	6	therefore	therefore	ADV
ejpam-5671	390	7	,	,	PUNCT
ejpam-5671	390	8	all	all	DET
ejpam-5671	390	9	conditions	condition	NOUN
ejpam-5671	390	10	of	of	ADP
ejpam-5671	390	11	theorem	theorem	ADJ
ejpam-5671	390	12	3	3	NUM
ejpam-5671	390	13	are	be	AUX
ejpam-5671	390	14	fulfilled	fulfil	VERB
ejpam-5671	390	15	.	.	PUNCT
ejpam-5671	391	1	then	then	ADV
ejpam-5671	391	2	the	the	DET
ejpam-5671	391	3	problem	problem	NOUN
ejpam-5671	391	4	(	(	PUNCT
ejpam-5671	391	5	16	16	NUM
ejpam-5671	391	6	)	)	PUNCT
ejpam-5671	391	7	has	have	VERB
ejpam-5671	391	8	a	a	DET
ejpam-5671	391	9	solution	solution	NOUN
ejpam-5671	391	10	on	on	ADP
ejpam-5671	391	11	[	[	X
ejpam-5671	391	12	0	0	NUM
ejpam-5671	391	13	,	,	PUNCT
ejpam-5671	391	14	2	2	NUM
ejpam-5671	391	15	]	]	PUNCT
ejpam-5671	391	16	.	.	PUNCT
ejpam-5671	391	17	example	example	NOUN
ejpam-5671	392	1	2	2	NUM
ejpam-5671	392	2	.	.	X
ejpam-5671	392	3	assume	assume	VERB
ejpam-5671	392	4	the	the	DET
ejpam-5671	392	5	boundary	boundary	ADJ
ejpam-5671	392	6	value	value	NOUN
ejpam-5671	392	7	problem	problem	NOUN
ejpam-5671	392	8	below	below	ADV
ejpam-5671	392	9	{	{	PUNCT
ejpam-5671	392	10	cd	cd	PROPN
ejpam-5671	392	11	5	5	NUM
ejpam-5671	392	12	2ω(ρ	2ω(ρ	NUM
ejpam-5671	392	13	)	)	PUNCT
ejpam-5671	393	1	=	=	SYM
ejpam-5671	393	2	1	1	NUM
ejpam-5671	393	3	9ω(ρ	9ω(ρ	NUM
ejpam-5671	393	4	)	)	PUNCT
ejpam-5671	393	5	cos(ρ	cos(ρ	PROPN
ejpam-5671	393	6	)	)	PUNCT
ejpam-5671	393	7	,	,	PUNCT
ejpam-5671	393	8	ρ	ρ	PROPN
ejpam-5671	393	9	∈	∈	PROPN
ejpam-5671	394	1	[	[	X
ejpam-5671	394	2	0	0	NUM
ejpam-5671	394	3	,	,	PUNCT
ejpam-5671	394	4	1	1	NUM
ejpam-5671	394	5	]	]	PUNCT
ejpam-5671	394	6	,	,	PUNCT
ejpam-5671	394	7	ω(θ	ω(θ	NUM
ejpam-5671	394	8	)	)	PUNCT
ejpam-5671	394	9	=	=	SYM
ejpam-5671	394	10	−ω(1	−ω(1	PROPN
ejpam-5671	394	11	)	)	PUNCT
ejpam-5671	394	12	,	,	PUNCT
ejpam-5671	394	13	ω′(θ	ω′(θ	NOUN
ejpam-5671	394	14	)	)	PUNCT
ejpam-5671	394	15	=	=	SYM
ejpam-5671	394	16	−ω′(1	−ω′(1	PROPN
ejpam-5671	394	17	)	)	PUNCT
ejpam-5671	394	18	,	,	PUNCT
ejpam-5671	394	19	cd	cd	PROPN
ejpam-5671	394	20	3	3	NUM
ejpam-5671	394	21	2ω(θ	2ω(θ	NUM
ejpam-5671	394	22	)	)	PUNCT
ejpam-5671	395	1	=	=	SYM
ejpam-5671	395	2	−cd	−cd	NOUN
ejpam-5671	395	3	3	3	NUM
ejpam-5671	395	4	2ω(1	2ω(1	NUM
ejpam-5671	395	5	)	)	PUNCT
ejpam-5671	395	6	,	,	PUNCT
ejpam-5671	395	7	θ	θ	X
ejpam-5671	395	8	=	=	SYM
ejpam-5671	395	9	1	1	NUM
ejpam-5671	395	10	2	2	NUM
ejpam-5671	395	11	(	(	PUNCT
ejpam-5671	395	12	17	17	NUM
ejpam-5671	395	13	)	)	PUNCT
ejpam-5671	395	14	it	it	PRON
ejpam-5671	395	15	is	be	AUX
ejpam-5671	395	16	clear	clear	ADJ
ejpam-5671	395	17	that	that	SCONJ
ejpam-5671	395	18	,	,	PUNCT
ejpam-5671	395	19	the	the	DET
ejpam-5671	395	20	problem	problem	NOUN
ejpam-5671	395	21	(	(	PUNCT
ejpam-5671	395	22	17	17	NUM
ejpam-5671	395	23	)	)	PUNCT
ejpam-5671	395	24	is	be	AUX
ejpam-5671	395	25	a	a	DET
ejpam-5671	395	26	special	special	ADJ
ejpam-5671	395	27	form	form	NOUN
ejpam-5671	395	28	of	of	ADP
ejpam-5671	395	29	the	the	DET
ejpam-5671	395	30	problem	problem	NOUN
ejpam-5671	395	31	(	(	PUNCT
ejpam-5671	395	32	1	1	NUM
ejpam-5671	395	33	)	)	PUNCT
ejpam-5671	395	34	with	with	ADP
ejpam-5671	395	35	µ	µ	NOUN
ejpam-5671	395	36	=	=	SYM
ejpam-5671	395	37	5	5	NUM
ejpam-5671	395	38	2	2	NUM
ejpam-5671	395	39	∈	∈	NOUN
ejpam-5671	395	40	(	(	PUNCT
ejpam-5671	395	41	2	2	NUM
ejpam-5671	395	42	,	,	PUNCT
ejpam-5671	395	43	3	3	NUM
ejpam-5671	395	44	]	]	PUNCT
ejpam-5671	395	45	,	,	PUNCT
ejpam-5671	395	46	ξ	ξ	X
ejpam-5671	395	47	=	=	SYM
ejpam-5671	395	48	1	1	NUM
ejpam-5671	395	49	2	2	NUM
ejpam-5671	395	50	∈	∈	NOUN
ejpam-5671	395	51	(	(	PUNCT
ejpam-5671	395	52	0	0	NUM
ejpam-5671	395	53	,	,	PUNCT
ejpam-5671	395	54	1	1	NUM
ejpam-5671	395	55	)	)	PUNCT
ejpam-5671	395	56	,	,	PUNCT
ejpam-5671	396	1	b	b	X
ejpam-5671	396	2	=	=	SYM
ejpam-5671	396	3	1	1	NUM
ejpam-5671	396	4	>	>	SYM
ejpam-5671	396	5	0	0	NUM
ejpam-5671	396	6	,	,	PUNCT
ejpam-5671	396	7	θ	θ	PROPN
ejpam-5671	396	8	∈	∈	PROPN
ejpam-5671	397	1	[	[	X
ejpam-5671	397	2	0	0	NUM
ejpam-5671	397	3	,	,	PUNCT
ejpam-5671	397	4	1	1	NUM
ejpam-5671	397	5	)	)	PUNCT
ejpam-5671	398	1	,	,	PUNCT
ejpam-5671	398	2	ρ	ρ	PROPN
ejpam-5671	398	3	∈	∈	PROPN
ejpam-5671	399	1	[	[	X
ejpam-5671	399	2	0	0	NUM
ejpam-5671	399	3	,	,	PUNCT
ejpam-5671	399	4	1	1	NUM
ejpam-5671	399	5	]	]	PUNCT
ejpam-5671	399	6	,	,	PUNCT
ejpam-5671	399	7	and	and	CCONJ
ejpam-5671	399	8	ω	ω	NUM
ejpam-5671	399	9	(	(	PUNCT
ejpam-5671	399	10	ρ	ρ	PROPN
ejpam-5671	399	11	,	,	PUNCT
ejpam-5671	399	12	ω	ω	PROPN
ejpam-5671	399	13	(	(	PUNCT
ejpam-5671	399	14	ρ	ρ	NOUN
ejpam-5671	399	15	)	)	PUNCT
ejpam-5671	399	16	)	)	PUNCT
ejpam-5671	399	17	=	=	SYM
ejpam-5671	399	18	1	1	NUM
ejpam-5671	399	19	9ω(ρ	9ω(ρ	NUM
ejpam-5671	399	20	)	)	PUNCT
ejpam-5671	399	21	cos(ρ	cos(ρ	X
ejpam-5671	399	22	)	)	PUNCT
ejpam-5671	399	23	.	.	PUNCT
ejpam-5671	400	1	now	now	ADV
ejpam-5671	400	2	,	,	PUNCT
ejpam-5671	400	3	for	for	ADP
ejpam-5671	400	4	each	each	DET
ejpam-5671	400	5	ω1	ω1	PROPN
ejpam-5671	400	6	,	,	PUNCT
ejpam-5671	400	7	ω2	ω2	NOUN
ejpam-5671	400	8	∈	∈	PROPN
ejpam-5671	400	9	r	r	NOUN
ejpam-5671	400	10	,	,	PUNCT
ejpam-5671	400	11	we	we	PRON
ejpam-5671	400	12	get	get	VERB
ejpam-5671	400	13	∥ω1(ρ	∥ω1(ρ	PROPN
ejpam-5671	400	14	,	,	PUNCT
ejpam-5671	400	15	ω1)−	ω1)−	PROPN
ejpam-5671	400	16	ω1(ρ	ω1(ρ	PROPN
ejpam-5671	400	17	,	,	PUNCT
ejpam-5671	400	18	ω2)∥	ω2)∥	PRON
ejpam-5671	400	19	=	=	SYM
ejpam-5671	400	20	1	1	NUM
ejpam-5671	400	21	9	9	NUM
ejpam-5671	400	22	|cos(ρ)|	|cos(ρ)|	PROPN
ejpam-5671	400	23	∥ω1(ρ)−	∥ω1(ρ)−	PROPN
ejpam-5671	400	24	ω1(ρ)∥	ω1(ρ)∥	X
ejpam-5671	400	25	≤	≤	NUM
ejpam-5671	400	26	1	1	NUM
ejpam-5671	400	27	9	9	NUM
ejpam-5671	400	28	∥ω1	∥ω1	PUNCT
ejpam-5671	400	29	−	−	PROPN
ejpam-5671	400	30	ω2∥	ω2∥	PROPN
ejpam-5671	400	31	.	.	PUNCT
ejpam-5671	401	1	thus	thus	ADV
ejpam-5671	401	2	,	,	PUNCT
ejpam-5671	401	3	l	l	NOUN
ejpam-5671	401	4	=	=	SYM
ejpam-5671	401	5	1	1	NUM
ejpam-5671	401	6	9	9	NUM
ejpam-5671	401	7	.	.	PUNCT
ejpam-5671	402	1	further	far	ADV
ejpam-5671	402	2	,	,	PUNCT
ejpam-5671	402	3	for	for	ADP
ejpam-5671	402	4	all	all	DET
ejpam-5671	402	5	(	(	PUNCT
ejpam-5671	402	6	ρ	ρ	PROPN
ejpam-5671	402	7	,	,	PUNCT
ejpam-5671	402	8	ω	ω	NOUN
ejpam-5671	402	9	)	)	PUNCT
ejpam-5671	402	10	∈	∈	PROPN
ejpam-5671	403	1	[	[	X
ejpam-5671	403	2	0	0	NUM
ejpam-5671	403	3	,	,	PUNCT
ejpam-5671	403	4	1]×	1]×	NUM
ejpam-5671	403	5	r+	r+	NOUN
ejpam-5671	403	6	,	,	PUNCT
ejpam-5671	403	7	we	we	PRON
ejpam-5671	403	8	have	have	VERB
ejpam-5671	403	9	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	403	10	,	,	PUNCT
ejpam-5671	403	11	ω)|	ω)|	ADJ
ejpam-5671	403	12	=	=	SYM
ejpam-5671	403	13	1	1	NUM
ejpam-5671	403	14	9	9	NUM
ejpam-5671	403	15	|ω(ρ	|ω(ρ	NOUN
ejpam-5671	403	16	)	)	PUNCT
ejpam-5671	404	1	cos(ρ)|	cos(ρ)|	NOUN
ejpam-5671	404	2	≤	≤	NUM
ejpam-5671	404	3	1	1	NUM
ejpam-5671	404	4	9	9	NUM
ejpam-5671	404	5	ω(ρ	ω(ρ	NUM
ejpam-5671	404	6	)	)	PUNCT
ejpam-5671	404	7	,	,	PUNCT
ejpam-5671	404	8	which	which	PRON
ejpam-5671	404	9	implies	imply	VERB
ejpam-5671	404	10	that	that	SCONJ
ejpam-5671	404	11	ψ(ρ	ψ(ρ	PROPN
ejpam-5671	404	12	)	)	PUNCT
ejpam-5671	404	13	=	=	SYM
ejpam-5671	404	14	1	1	NUM
ejpam-5671	404	15	9ω(ρ	9ω(ρ	NUM
ejpam-5671	404	16	)	)	PUNCT
ejpam-5671	404	17	∈	∈	PROPN
ejpam-5671	404	18	l1([0	l1([0	NOUN
ejpam-5671	404	19	,	,	PUNCT
ejpam-5671	404	20	1],r+	1],r+	NUM
ejpam-5671	404	21	)	)	PUNCT
ejpam-5671	404	22	.	.	PUNCT
ejpam-5671	405	1	utilizing	utilize	VERB
ejpam-5671	405	2	eq	eq	ADP
ejpam-5671	405	3	.	.	PUNCT
ejpam-5671	406	1	(	(	PUNCT
ejpam-5671	406	2	14	14	NUM
ejpam-5671	406	3	)	)	PUNCT
ejpam-5671	406	4	.	.	PUNCT
ejpam-5671	407	1	since	since	SCONJ
ejpam-5671	407	2	θ	θ	PROPN
ejpam-5671	407	3	=	=	SYM
ejpam-5671	407	4	1	1	NUM
ejpam-5671	407	5	2	2	NUM
ejpam-5671	407	6	∈	∈	NOUN
ejpam-5671	407	7	[	[	X
ejpam-5671	407	8	0	0	NUM
ejpam-5671	407	9	,	,	PUNCT
ejpam-5671	407	10	1	1	NUM
ejpam-5671	407	11	)	)	PUNCT
ejpam-5671	407	12	,	,	PUNCT
ejpam-5671	407	13	we	we	PRON
ejpam-5671	407	14	get	get	VERB
ejpam-5671	407	15	m2	m2	PROPN
ejpam-5671	407	16	≈	≈	PROPN
ejpam-5671	407	17	1.13	1.13	NUM
ejpam-5671	407	18	.	.	PUNCT
ejpam-5671	408	1	thus	thus	ADV
ejpam-5671	408	2	,	,	PUNCT
ejpam-5671	408	3	lm2	lm2	NOUN
ejpam-5671	408	4	=	=	SYM
ejpam-5671	408	5	(	(	PUNCT
ejpam-5671	408	6	19)(1.13	19)(1.13	NUM
ejpam-5671	408	7	)	)	PUNCT
ejpam-5671	409	1	≈	≈	PROPN
ejpam-5671	409	2	0.1256	0.1256	NUM
ejpam-5671	409	3	<	<	X
ejpam-5671	409	4	1	1	NUM
ejpam-5671	409	5	.	.	PUNCT
ejpam-5671	410	1	therefore	therefore	ADV
ejpam-5671	410	2	,	,	PUNCT
ejpam-5671	410	3	all	all	DET
ejpam-5671	410	4	conditions	condition	NOUN
ejpam-5671	410	5	of	of	ADP
ejpam-5671	410	6	theorem	theorem	ADJ
ejpam-5671	410	7	4	4	NUM
ejpam-5671	410	8	are	be	AUX
ejpam-5671	410	9	satisfied	satisfied	ADJ
ejpam-5671	410	10	.	.	PUNCT
ejpam-5671	411	1	then	then	ADV
ejpam-5671	411	2	the	the	DET
ejpam-5671	411	3	problem	problem	NOUN
ejpam-5671	411	4	(	(	PUNCT
ejpam-5671	411	5	17	17	NUM
ejpam-5671	411	6	)	)	PUNCT
ejpam-5671	411	7	has	have	VERB
ejpam-5671	411	8	a	a	DET
ejpam-5671	411	9	unique	unique	ADJ
ejpam-5671	411	10	solution	solution	NOUN
ejpam-5671	411	11	on	on	ADP
ejpam-5671	411	12	[	[	X
ejpam-5671	411	13	0	0	NUM
ejpam-5671	411	14	,	,	PUNCT
ejpam-5671	411	15	1	1	NUM
ejpam-5671	411	16	]	]	PUNCT
ejpam-5671	411	17	.	.	PUNCT
ejpam-5671	412	1	example	example	NOUN
ejpam-5671	413	1	3	3	X
ejpam-5671	413	2	.	.	X
ejpam-5671	413	3	assume	assume	VERB
ejpam-5671	413	4	the	the	DET
ejpam-5671	413	5	following	follow	VERB
ejpam-5671	413	6	fractional	fractional	ADJ
ejpam-5671	413	7	problem	problem	NOUN
ejpam-5671	413	8	:	:	PUNCT
ejpam-5671	413	9	{	{	PUNCT
ejpam-5671	413	10	cd	cd	PROPN
ejpam-5671	413	11	7	7	NUM
ejpam-5671	413	12	3ω(ρ	3ω(ρ	NOUN
ejpam-5671	413	13	)	)	PUNCT
ejpam-5671	413	14	=	=	SYM
ejpam-5671	413	15	1	1	NUM
ejpam-5671	413	16	15	15	NUM
ejpam-5671	413	17	(	(	PUNCT
ejpam-5671	413	18	e−ρ	e−ρ	PROPN
ejpam-5671	413	19	+	+	PROPN
ejpam-5671	413	20	tan−1(ω(ρ	tan−1(ω(ρ	NOUN
ejpam-5671	413	21	)	)	PUNCT
ejpam-5671	413	22	)	)	PUNCT
ejpam-5671	413	23	1+ω2(ρ	1+ω2(ρ	NOUN
ejpam-5671	413	24	)	)	PUNCT
ejpam-5671	413	25	)	)	PUNCT
ejpam-5671	413	26	,	,	PUNCT
ejpam-5671	413	27	ρ	ρ	PROPN
ejpam-5671	413	28	∈	∈	PROPN
ejpam-5671	414	1	[	[	X
ejpam-5671	414	2	0	0	NUM
ejpam-5671	414	3	,	,	PUNCT
ejpam-5671	414	4	2	2	NUM
ejpam-5671	414	5	]	]	PUNCT
ejpam-5671	414	6	,	,	PUNCT
ejpam-5671	414	7	ω(θ	ω(θ	NUM
ejpam-5671	414	8	)	)	PUNCT
ejpam-5671	414	9	=	=	SYM
ejpam-5671	414	10	−ω(2	−ω(2	NOUN
ejpam-5671	414	11	)	)	PUNCT
ejpam-5671	414	12	,	,	PUNCT
ejpam-5671	414	13	ω′(θ	ω′(θ	NOUN
ejpam-5671	414	14	)	)	PUNCT
ejpam-5671	414	15	=	=	SYM
ejpam-5671	414	16	−ω′(2	−ω′(2	PROPN
ejpam-5671	414	17	)	)	PUNCT
ejpam-5671	414	18	,	,	PUNCT
ejpam-5671	414	19	cd	cd	PROPN
ejpam-5671	414	20	5	5	NUM
ejpam-5671	414	21	4ω(θ	4ω(θ	NUM
ejpam-5671	414	22	)	)	PUNCT
ejpam-5671	415	1	=	=	PRON
ejpam-5671	415	2	−cd	−cd	NOUN
ejpam-5671	415	3	5	5	NUM
ejpam-5671	415	4	4ω(2	4ω(2	NUM
ejpam-5671	415	5	)	)	PUNCT
ejpam-5671	415	6	,	,	PUNCT
ejpam-5671	415	7	θ	θ	X
ejpam-5671	415	8	=	=	SYM
ejpam-5671	415	9	3	3	NUM
ejpam-5671	415	10	2	2	NUM
ejpam-5671	415	11	(	(	PUNCT
ejpam-5671	415	12	18	18	NUM
ejpam-5671	415	13	)	)	PUNCT
ejpam-5671	415	14	s.	s.	PROPN
ejpam-5671	415	15	f.	f.	PROPN
ejpam-5671	415	16	aljurbua	aljurbua	PROPN
ejpam-5671	415	17	,	,	PUNCT
ejpam-5671	415	18	h.	h.	PROPN
ejpam-5671	415	19	a.	a.	PROPN
ejpam-5671	415	20	hammad	hammad	PROPN
ejpam-5671	415	21	,	,	PUNCT
ejpam-5671	415	22	n.	n.	PROPN
ejpam-5671	415	23	b.	b.	PROPN
ejpam-5671	415	24	almutairi	almutairi	PROPN
ejpam-5671	415	25	/	/	SYM
ejpam-5671	415	26	eur	eur	PROPN
ejpam-5671	415	27	.	.	PUNCT
ejpam-5671	416	1	j.	j.	PROPN
ejpam-5671	416	2	pure	pure	PROPN
ejpam-5671	416	3	appl	appl	PROPN
ejpam-5671	416	4	.	.	PROPN
ejpam-5671	416	5	math	math	PROPN
ejpam-5671	416	6	,	,	PUNCT
ejpam-5671	416	7	18	18	NUM
ejpam-5671	416	8	(	(	PUNCT
ejpam-5671	416	9	1	1	NUM
ejpam-5671	416	10	)	)	PUNCT
ejpam-5671	416	11	(	(	PUNCT
ejpam-5671	416	12	2025	2025	NUM
ejpam-5671	416	13	)	)	PUNCT
ejpam-5671	416	14	,	,	PUNCT
ejpam-5671	416	15	5671	5671	NUM
ejpam-5671	416	16	15	15	NUM
ejpam-5671	416	17	of	of	ADP
ejpam-5671	416	18	18	18	NUM
ejpam-5671	416	19	obviousely	obviousely	ADJ
ejpam-5671	416	20	,	,	PUNCT
ejpam-5671	416	21	problems	problem	NOUN
ejpam-5671	416	22	(	(	PUNCT
ejpam-5671	416	23	17	17	NUM
ejpam-5671	416	24	)	)	PUNCT
ejpam-5671	416	25	and	and	CCONJ
ejpam-5671	416	26	(	(	PUNCT
ejpam-5671	416	27	1	1	X
ejpam-5671	416	28	)	)	PUNCT
ejpam-5671	416	29	are	be	AUX
ejpam-5671	416	30	identical	identical	ADJ
ejpam-5671	416	31	with	with	ADP
ejpam-5671	416	32	µ	µ	NOUN
ejpam-5671	416	33	=	=	SYM
ejpam-5671	416	34	7	7	NUM
ejpam-5671	416	35	2	2	NUM
ejpam-5671	416	36	∈	∈	NOUN
ejpam-5671	416	37	(	(	PUNCT
ejpam-5671	416	38	2	2	NUM
ejpam-5671	416	39	,	,	PUNCT
ejpam-5671	416	40	3	3	NUM
ejpam-5671	416	41	]	]	PUNCT
ejpam-5671	416	42	,	,	PUNCT
ejpam-5671	416	43	ξ	ξ	X
ejpam-5671	416	44	=	=	SYM
ejpam-5671	416	45	1	1	NUM
ejpam-5671	416	46	4	4	NUM
ejpam-5671	416	47	∈	∈	NOUN
ejpam-5671	416	48	(	(	PUNCT
ejpam-5671	416	49	0	0	NUM
ejpam-5671	416	50	,	,	PUNCT
ejpam-5671	416	51	1	1	NUM
ejpam-5671	416	52	)	)	PUNCT
ejpam-5671	416	53	,	,	PUNCT
ejpam-5671	416	54	b	b	X
ejpam-5671	417	1	=	=	SYM
ejpam-5671	417	2	2	2	NUM
ejpam-5671	417	3	>	>	SYM
ejpam-5671	417	4	0	0	NUM
ejpam-5671	417	5	,	,	PUNCT
ejpam-5671	417	6	θ	θ	PROPN
ejpam-5671	417	7	∈	∈	PROPN
ejpam-5671	418	1	[	[	X
ejpam-5671	418	2	0	0	NUM
ejpam-5671	418	3	,	,	PUNCT
ejpam-5671	418	4	2	2	NUM
ejpam-5671	418	5	)	)	PUNCT
ejpam-5671	419	1	,	,	PUNCT
ejpam-5671	419	2	ρ	ρ	PROPN
ejpam-5671	419	3	∈	∈	PROPN
ejpam-5671	420	1	[	[	X
ejpam-5671	420	2	0	0	NUM
ejpam-5671	420	3	,	,	PUNCT
ejpam-5671	420	4	2	2	NUM
ejpam-5671	420	5	]	]	PUNCT
ejpam-5671	420	6	,	,	PUNCT
ejpam-5671	420	7	and	and	CCONJ
ejpam-5671	420	8	ω	ω	NUM
ejpam-5671	420	9	(	(	PUNCT
ejpam-5671	420	10	ρ	ρ	PROPN
ejpam-5671	420	11	,	,	PUNCT
ejpam-5671	420	12	ω	ω	PROPN
ejpam-5671	420	13	(	(	PUNCT
ejpam-5671	420	14	ρ	ρ	NOUN
ejpam-5671	420	15	)	)	PUNCT
ejpam-5671	420	16	)	)	PUNCT
ejpam-5671	420	17	=	=	SYM
ejpam-5671	420	18	1	1	NUM
ejpam-5671	420	19	15	15	NUM
ejpam-5671	420	20	(	(	PUNCT
ejpam-5671	420	21	e−ρ	e−ρ	PROPN
ejpam-5671	420	22	+	+	PROPN
ejpam-5671	420	23	tan−1(ω(ρ	tan−1(ω(ρ	NOUN
ejpam-5671	420	24	)	)	PUNCT
ejpam-5671	420	25	)	)	PUNCT
ejpam-5671	420	26	1+ω2(ρ	1+ω2(ρ	NOUN
ejpam-5671	420	27	)	)	PUNCT
ejpam-5671	420	28	)	)	PUNCT
ejpam-5671	420	29	.	.	PUNCT
ejpam-5671	421	1	now	now	ADV
ejpam-5671	421	2	,	,	PUNCT
ejpam-5671	421	3	for	for	ADP
ejpam-5671	421	4	each	each	DET
ejpam-5671	421	5	ω1	ω1	PROPN
ejpam-5671	421	6	,	,	PUNCT
ejpam-5671	421	7	ω2	ω2	NOUN
ejpam-5671	421	8	∈	∈	PROPN
ejpam-5671	421	9	r	r	NOUN
ejpam-5671	421	10	,	,	PUNCT
ejpam-5671	421	11	we	we	PRON
ejpam-5671	421	12	get	get	VERB
ejpam-5671	421	13	∥ω1(ρ	∥ω1(ρ	PROPN
ejpam-5671	421	14	,	,	PUNCT
ejpam-5671	421	15	ω1)−	ω1)−	PROPN
ejpam-5671	421	16	ω1(ρ	ω1(ρ	PROPN
ejpam-5671	421	17	,	,	PUNCT
ejpam-5671	421	18	ω2)∥	ω2)∥	PRON
ejpam-5671	421	19	=	=	SYM
ejpam-5671	421	20	1	1	NUM
ejpam-5671	421	21	15	15	NUM
ejpam-5671	421	22	∥∥∥∥e−ρ	∥∥∥∥e−ρ	NOUN
ejpam-5671	421	23	+	+	CCONJ
ejpam-5671	421	24	tan−1(ω1	tan−1(ω1	NOUN
ejpam-5671	421	25	)	)	PUNCT
ejpam-5671	421	26	1	1	NUM
ejpam-5671	422	1	+	+	CCONJ
ejpam-5671	422	2	ω2	ω2	ADJ
ejpam-5671	422	3	1	1	NUM
ejpam-5671	422	4	−	−	PROPN
ejpam-5671	422	5	e−ρ	e−ρ	PROPN
ejpam-5671	422	6	−	−	PROPN
ejpam-5671	422	7	tan−1(ω2	tan−1(ω2	NOUN
ejpam-5671	422	8	)	)	PUNCT
ejpam-5671	422	9	1	1	NUM
ejpam-5671	423	1	+	+	CCONJ
ejpam-5671	423	2	ω2	ω2	ADJ
ejpam-5671	423	3	2	2	NUM
ejpam-5671	423	4	∥∥∥∥	∥∥∥∥	NOUN
ejpam-5671	423	5	≤	≤	NUM
ejpam-5671	423	6	1	1	NUM
ejpam-5671	423	7	15	15	NUM
ejpam-5671	423	8	∥ω1	∥ω1	PUNCT
ejpam-5671	423	9	−	−	PROPN
ejpam-5671	423	10	ω2∥	ω2∥	PROPN
ejpam-5671	423	11	.	.	PUNCT
ejpam-5671	424	1	therefore	therefore	ADV
ejpam-5671	424	2	,	,	PUNCT
ejpam-5671	424	3	l	l	NOUN
ejpam-5671	424	4	=	=	SYM
ejpam-5671	424	5	1	1	NUM
ejpam-5671	424	6	15	15	NUM
ejpam-5671	424	7	.	.	PUNCT
ejpam-5671	425	1	additionally	additionally	ADV
ejpam-5671	425	2	,	,	PUNCT
ejpam-5671	425	3	for	for	ADP
ejpam-5671	425	4	all	all	DET
ejpam-5671	425	5	(	(	PUNCT
ejpam-5671	425	6	ρ	ρ	PROPN
ejpam-5671	425	7	,	,	PUNCT
ejpam-5671	425	8	ω	ω	NOUN
ejpam-5671	425	9	)	)	PUNCT
ejpam-5671	425	10	∈	∈	PROPN
ejpam-5671	426	1	[	[	X
ejpam-5671	426	2	0	0	NUM
ejpam-5671	426	3	,	,	PUNCT
ejpam-5671	426	4	2]×	2]×	NUM
ejpam-5671	426	5	r+	r+	NOUN
ejpam-5671	426	6	,	,	PUNCT
ejpam-5671	426	7	we	we	PRON
ejpam-5671	426	8	have	have	VERB
ejpam-5671	426	9	|ω(ρ	|ω(ρ	PROPN
ejpam-5671	426	10	,	,	PUNCT
ejpam-5671	426	11	ω)|	ω)|	ADJ
ejpam-5671	426	12	=	=	SYM
ejpam-5671	426	13	1	1	NUM
ejpam-5671	426	14	15	15	NUM
ejpam-5671	426	15	∣∣∣∣e−ρ	∣∣∣∣e−ρ	ADJ
ejpam-5671	426	16	+	+	CCONJ
ejpam-5671	426	17	tan−1(ω	tan−1(ω	X
ejpam-5671	426	18	)	)	PUNCT
ejpam-5671	426	19	1	1	NUM
ejpam-5671	427	1	+	+	PUNCT
ejpam-5671	427	2	ω2(ρ	ω2(ρ	NUM
ejpam-5671	427	3	)	)	PUNCT
ejpam-5671	427	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5671	427	5	≤	≤	NUM
ejpam-5671	427	6	1	1	NUM
ejpam-5671	427	7	15	15	NUM
ejpam-5671	427	8	(	(	PUNCT
ejpam-5671	427	9	1	1	NUM
ejpam-5671	427	10	+	+	CCONJ
ejpam-5671	427	11	tan−1(ω	tan−1(ω	PUNCT
ejpam-5671	427	12	)	)	PUNCT
ejpam-5671	427	13	1	1	NUM
ejpam-5671	428	1	+	+	PUNCT
ejpam-5671	428	2	ω2(ρ	ω2(ρ	NUM
ejpam-5671	428	3	)	)	PUNCT
ejpam-5671	428	4	)	)	PUNCT
ejpam-5671	429	1	,	,	PUNCT
ejpam-5671	429	2	which	which	PRON
ejpam-5671	429	3	implies	imply	VERB
ejpam-5671	429	4	that	that	SCONJ
ejpam-5671	429	5	ψ(ρ	ψ(ρ	PROPN
ejpam-5671	429	6	)	)	PUNCT
ejpam-5671	429	7	=	=	SYM
ejpam-5671	429	8	1	1	NUM
ejpam-5671	429	9	15	15	NUM
ejpam-5671	429	10	(	(	PUNCT
ejpam-5671	429	11	1	1	NUM
ejpam-5671	429	12	+	+	CCONJ
ejpam-5671	429	13	tan−1(ω	tan−1(ω	NOUN
ejpam-5671	429	14	)	)	PUNCT
ejpam-5671	429	15	1+ω2(ρ	1+ω2(ρ	NOUN
ejpam-5671	429	16	)	)	PUNCT
ejpam-5671	429	17	)	)	PUNCT
ejpam-5671	430	1	∈	∈	PROPN
ejpam-5671	430	2	l1([0	l1([0	NOUN
ejpam-5671	430	3	,	,	PUNCT
ejpam-5671	430	4	2],r+	2],r+	NUM
ejpam-5671	430	5	)	)	PUNCT
ejpam-5671	430	6	.	.	PUNCT
ejpam-5671	431	1	utilizing	utilize	VERB
ejpam-5671	431	2	eq	eq	ADP
ejpam-5671	431	3	.	.	PUNCT
ejpam-5671	432	1	(	(	PUNCT
ejpam-5671	432	2	14	14	NUM
ejpam-5671	432	3	)	)	PUNCT
ejpam-5671	432	4	,	,	PUNCT
ejpam-5671	432	5	if	if	SCONJ
ejpam-5671	432	6	we	we	PRON
ejpam-5671	432	7	select	select	VERB
ejpam-5671	432	8	θ	θ	NOUN
ejpam-5671	432	9	=	=	SYM
ejpam-5671	432	10	3	3	NUM
ejpam-5671	432	11	2	2	NUM
ejpam-5671	432	12	∈	∈	NOUN
ejpam-5671	432	13	[	[	X
ejpam-5671	432	14	0	0	NUM
ejpam-5671	432	15	,	,	PUNCT
ejpam-5671	432	16	2	2	NUM
ejpam-5671	432	17	)	)	PUNCT
ejpam-5671	432	18	,	,	PUNCT
ejpam-5671	432	19	we	we	PRON
ejpam-5671	432	20	get	get	VERB
ejpam-5671	432	21	m2	m2	PROPN
ejpam-5671	432	22	≈	≈	PROPN
ejpam-5671	432	23	4.18	4.18	NUM
ejpam-5671	432	24	and	and	CCONJ
ejpam-5671	432	25	lm2	lm2	NOUN
ejpam-5671	432	26	=	=	SYM
ejpam-5671	432	27	(	(	PUNCT
ejpam-5671	432	28	1	1	NUM
ejpam-5671	432	29	15)(4.18	15)(4.18	NUM
ejpam-5671	432	30	)	)	PUNCT
ejpam-5671	433	1	≈	≈	PROPN
ejpam-5671	433	2	0.2787	0.2787	NUM
ejpam-5671	433	3	<	<	X
ejpam-5671	433	4	1	1	NUM
ejpam-5671	433	5	.	.	PUNCT
ejpam-5671	434	1	hence	hence	ADV
ejpam-5671	434	2	,	,	PUNCT
ejpam-5671	434	3	the	the	DET
ejpam-5671	434	4	requirements	requirement	NOUN
ejpam-5671	434	5	of	of	ADP
ejpam-5671	434	6	theorem	theorem	ADJ
ejpam-5671	434	7	4	4	NUM
ejpam-5671	434	8	are	be	AUX
ejpam-5671	434	9	satisfied	satisfied	ADJ
ejpam-5671	434	10	.	.	PUNCT
ejpam-5671	435	1	then	then	ADV
ejpam-5671	435	2	the	the	DET
ejpam-5671	435	3	problem	problem	NOUN
ejpam-5671	435	4	(	(	PUNCT
ejpam-5671	435	5	18	18	NUM
ejpam-5671	435	6	)	)	PUNCT
ejpam-5671	435	7	has	have	VERB
ejpam-5671	435	8	a	a	DET
ejpam-5671	435	9	unique	unique	ADJ
ejpam-5671	435	10	solution	solution	NOUN
ejpam-5671	435	11	on	on	ADP
ejpam-5671	435	12	[	[	X
ejpam-5671	435	13	0	0	NUM
ejpam-5671	435	14	,	,	PUNCT
ejpam-5671	435	15	2	2	NUM
ejpam-5671	435	16	]	]	PUNCT
ejpam-5671	435	17	.	.	PUNCT
ejpam-5671	436	1	moreover	moreover	ADV
ejpam-5671	436	2	,	,	PUNCT
ejpam-5671	436	3	the	the	DET
ejpam-5671	436	4	same	same	ADJ
ejpam-5671	436	5	result	result	NOUN
ejpam-5671	436	6	can	can	AUX
ejpam-5671	436	7	be	be	AUX
ejpam-5671	436	8	obtained	obtain	VERB
ejpam-5671	436	9	by	by	ADP
ejpam-5671	436	10	theorem	theorem	NOUN
ejpam-5671	436	11	5	5	NUM
ejpam-5671	436	12	as	as	SCONJ
ejpam-5671	436	13	follows	follow	VERB
ejpam-5671	436	14	:	:	PUNCT
ejpam-5671	436	15	for	for	ADP
ejpam-5671	436	16	all	all	DET
ejpam-5671	436	17	(	(	PUNCT
ejpam-5671	436	18	ρ	ρ	PROPN
ejpam-5671	436	19	,	,	PUNCT
ejpam-5671	436	20	ω	ω	NOUN
ejpam-5671	436	21	)	)	PUNCT
ejpam-5671	436	22	∈	∈	PROPN
ejpam-5671	437	1	[	[	X
ejpam-5671	437	2	0	0	NUM
ejpam-5671	437	3	,	,	PUNCT
ejpam-5671	437	4	2]×	2]×	NUM
ejpam-5671	437	5	r	r	NOUN
ejpam-5671	437	6	,	,	PUNCT
ejpam-5671	437	7	we	we	PRON
ejpam-5671	437	8	can	can	AUX
ejpam-5671	437	9	write	write	VERB
ejpam-5671	437	10	|ω	|ω	NOUN
ejpam-5671	437	11	(	(	PUNCT
ejpam-5671	437	12	ρ	ρ	PROPN
ejpam-5671	437	13	,	,	PUNCT
ejpam-5671	437	14	ω	ω	PROPN
ejpam-5671	437	15	(	(	PUNCT
ejpam-5671	437	16	ρ))|	ρ))|	PROPN
ejpam-5671	437	17	=	=	SYM
ejpam-5671	437	18	1	1	NUM
ejpam-5671	437	19	15	15	NUM
ejpam-5671	437	20	∣∣∣∣e−ρ	∣∣∣∣e−ρ	NOUN
ejpam-5671	437	21	+	+	CCONJ
ejpam-5671	437	22	tan−1(ω(ρ	tan−1(ω(ρ	NOUN
ejpam-5671	437	23	)	)	PUNCT
ejpam-5671	437	24	)	)	PUNCT
ejpam-5671	438	1	1	1	NUM
ejpam-5671	439	1	+	+	PUNCT
ejpam-5671	439	2	ω2(ρ	ω2(ρ	NUM
ejpam-5671	439	3	)	)	PUNCT
ejpam-5671	439	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5671	439	5	≤	≤	NOUN
ejpam-5671	439	6	eρ	eρ	ADP
ejpam-5671	440	1	+	+	CCONJ
ejpam-5671	440	2	1	1	NUM
ejpam-5671	440	3	3	3	NUM
ejpam-5671	440	4	|ω(ρ)|	|ω(ρ)|	PROPN
ejpam-5671	440	5	,	,	PUNCT
ejpam-5671	440	6	which	which	PRON
ejpam-5671	440	7	implies	imply	VERB
ejpam-5671	440	8	that	that	SCONJ
ejpam-5671	440	9	δ	δ	PROPN
ejpam-5671	440	10	=	=	PUNCT
ejpam-5671	440	11	eρ	eρ	ADP
ejpam-5671	440	12	>	>	X
ejpam-5671	440	13	0	0	PUNCT
ejpam-5671	441	1	and	and	CCONJ
ejpam-5671	441	2	χ	χ	X
ejpam-5671	441	3	=	=	SYM
ejpam-5671	441	4	1	1	NUM
ejpam-5671	441	5	3	3	NUM
ejpam-5671	441	6	.	.	PUNCT
ejpam-5671	442	1	by	by	ADP
ejpam-5671	442	2	simple	simple	ADJ
ejpam-5671	442	3	caculations	caculation	NOUN
ejpam-5671	442	4	,	,	PUNCT
ejpam-5671	442	5	we	we	PRON
ejpam-5671	442	6	have	have	VERB
ejpam-5671	442	7	m	m	NOUN
ejpam-5671	442	8	=	=	NOUN
ejpam-5671	442	9	1.28	1.28	NUM
ejpam-5671	442	10	.	.	PUNCT
ejpam-5671	443	1	clearly	clearly	ADV
ejpam-5671	443	2	,	,	PUNCT
ejpam-5671	443	3	0	0	PUNCT
ejpam-5671	443	4	<	<	X
ejpam-5671	444	1	χ	χ	X
ejpam-5671	445	1	=	=	SYM
ejpam-5671	445	2	1	1	NUM
ejpam-5671	445	3	3	3	NUM
ejpam-5671	445	4	<	<	SYM
ejpam-5671	445	5	1	1	NUM
ejpam-5671	445	6	1.28	1.28	NUM
ejpam-5671	445	7	=	=	SYM
ejpam-5671	445	8	1	1	NUM
ejpam-5671	445	9	m	m	NOUN
ejpam-5671	445	10	.	.	PUNCT
ejpam-5671	445	11	example	example	NOUN
ejpam-5671	445	12	4	4	X
ejpam-5671	445	13	.	.	PUNCT
ejpam-5671	446	1	assume	assume	VERB
ejpam-5671	446	2	the	the	DET
ejpam-5671	446	3	following	follow	VERB
ejpam-5671	446	4	problem	problem	NOUN
ejpam-5671	446	5	{	{	PUNCT
ejpam-5671	446	6	cd	cd	PROPN
ejpam-5671	446	7	7	7	NUM
ejpam-5671	446	8	3ω(ρ	3ω(ρ	NOUN
ejpam-5671	446	9	)	)	PUNCT
ejpam-5671	447	1	=	=	SYM
ejpam-5671	447	2	cos(2πω(ρ	cos(2πω(ρ	NOUN
ejpam-5671	447	3	)	)	PUNCT
ejpam-5671	447	4	)	)	PUNCT
ejpam-5671	447	5	12π	12π	PUNCT
ejpam-5671	448	1	+	+	CCONJ
ejpam-5671	448	2	|sin(ω(ρ))|	|sin(ω(ρ))|	X
ejpam-5671	448	3	1+|sin(ω(ρ))|	1+|sin(ω(ρ))|	INTJ
ejpam-5671	448	4	,	,	PUNCT
ejpam-5671	448	5	ρ	ρ	PROPN
ejpam-5671	448	6	∈	∈	PROPN
ejpam-5671	449	1	[	[	X
ejpam-5671	449	2	0	0	NUM
ejpam-5671	449	3	,	,	PUNCT
ejpam-5671	449	4	1	1	NUM
ejpam-5671	449	5	]	]	PUNCT
ejpam-5671	449	6	,	,	PUNCT
ejpam-5671	449	7	ω(θ	ω(θ	NUM
ejpam-5671	449	8	)	)	PUNCT
ejpam-5671	449	9	=	=	SYM
ejpam-5671	449	10	−ω(1	−ω(1	PROPN
ejpam-5671	449	11	)	)	PUNCT
ejpam-5671	449	12	,	,	PUNCT
ejpam-5671	449	13	ω′(θ	ω′(θ	NOUN
ejpam-5671	449	14	)	)	PUNCT
ejpam-5671	449	15	=	=	SYM
ejpam-5671	449	16	−ω′(1	−ω′(1	PROPN
ejpam-5671	449	17	)	)	PUNCT
ejpam-5671	449	18	,	,	PUNCT
ejpam-5671	449	19	cd	cd	PROPN
ejpam-5671	449	20	4	4	NUM
ejpam-5671	449	21	3ω(θ	3ω(θ	NUM
ejpam-5671	449	22	)	)	PUNCT
ejpam-5671	450	1	=	=	PRON
ejpam-5671	450	2	−cd	−cd	NOUN
ejpam-5671	450	3	4	4	NUM
ejpam-5671	450	4	3ω(1	3ω(1	NUM
ejpam-5671	450	5	)	)	PUNCT
ejpam-5671	450	6	,	,	PUNCT
ejpam-5671	450	7	θ	θ	X
ejpam-5671	450	8	=	=	SYM
ejpam-5671	450	9	0	0	NUM
ejpam-5671	450	10	(	(	PUNCT
ejpam-5671	450	11	19	19	NUM
ejpam-5671	450	12	)	)	PUNCT
ejpam-5671	450	13	the	the	DET
ejpam-5671	450	14	problems	problem	NOUN
ejpam-5671	450	15	(	(	PUNCT
ejpam-5671	450	16	17	17	NUM
ejpam-5671	450	17	)	)	PUNCT
ejpam-5671	450	18	and	and	CCONJ
ejpam-5671	450	19	(	(	PUNCT
ejpam-5671	450	20	1	1	X
ejpam-5671	450	21	)	)	PUNCT
ejpam-5671	450	22	are	be	AUX
ejpam-5671	450	23	the	the	DET
ejpam-5671	450	24	same	same	ADJ
ejpam-5671	450	25	with	with	ADP
ejpam-5671	450	26	µ	µ	NOUN
ejpam-5671	450	27	=	=	SYM
ejpam-5671	450	28	7	7	NUM
ejpam-5671	450	29	2	2	NUM
ejpam-5671	450	30	∈	∈	NOUN
ejpam-5671	450	31	(	(	PUNCT
ejpam-5671	450	32	2	2	NUM
ejpam-5671	450	33	,	,	PUNCT
ejpam-5671	450	34	3	3	NUM
ejpam-5671	450	35	]	]	PUNCT
ejpam-5671	450	36	,	,	PUNCT
ejpam-5671	450	37	ξ	ξ	X
ejpam-5671	450	38	=	=	SYM
ejpam-5671	450	39	1	1	NUM
ejpam-5671	450	40	3	3	NUM
ejpam-5671	450	41	∈	∈	NOUN
ejpam-5671	450	42	(	(	PUNCT
ejpam-5671	450	43	0	0	NUM
ejpam-5671	450	44	,	,	PUNCT
ejpam-5671	450	45	1	1	NUM
ejpam-5671	450	46	)	)	PUNCT
ejpam-5671	450	47	,	,	PUNCT
ejpam-5671	450	48	b	b	X
ejpam-5671	450	49	=	=	SYM
ejpam-5671	450	50	2	2	NUM
ejpam-5671	450	51	>	>	SYM
ejpam-5671	450	52	0	0	NUM
ejpam-5671	450	53	,	,	PUNCT
ejpam-5671	450	54	θ	θ	X
ejpam-5671	450	55	=	=	SYM
ejpam-5671	450	56	0	0	PUNCT
ejpam-5671	450	57	∈	∈	PROPN
ejpam-5671	451	1	[	[	X
ejpam-5671	451	2	0	0	NUM
ejpam-5671	451	3	,	,	PUNCT
ejpam-5671	451	4	2	2	NUM
ejpam-5671	451	5	)	)	PUNCT
ejpam-5671	451	6	,	,	PUNCT
ejpam-5671	451	7	ρ	ρ	PROPN
ejpam-5671	451	8	∈	∈	PROPN
ejpam-5671	452	1	[	[	X
ejpam-5671	452	2	0	0	NUM
ejpam-5671	452	3	,	,	PUNCT
ejpam-5671	452	4	2	2	NUM
ejpam-5671	452	5	]	]	PUNCT
ejpam-5671	452	6	,	,	PUNCT
ejpam-5671	452	7	and	and	CCONJ
ejpam-5671	452	8	ω	ω	NUM
ejpam-5671	452	9	(	(	PUNCT
ejpam-5671	452	10	ρ	ρ	PROPN
ejpam-5671	452	11	,	,	PUNCT
ejpam-5671	452	12	ω	ω	PROPN
ejpam-5671	452	13	(	(	PUNCT
ejpam-5671	452	14	ρ	ρ	NOUN
ejpam-5671	452	15	)	)	PUNCT
ejpam-5671	452	16	)	)	PUNCT
ejpam-5671	452	17	=	=	SYM
ejpam-5671	452	18	cos(2πω(ρ	cos(2πω(ρ	NOUN
ejpam-5671	452	19	)	)	PUNCT
ejpam-5671	452	20	)	)	PUNCT
ejpam-5671	452	21	12π	12π	PUNCT
ejpam-5671	453	1	+	+	CCONJ
ejpam-5671	453	2	|sin(ω(ρ))|	|sin(ω(ρ))|	X
ejpam-5671	453	3	1+|sin(ω(ρ))|	1+|sin(ω(ρ))|	INTJ
ejpam-5671	453	4	.	.	PUNCT
ejpam-5671	454	1	according	accord	VERB
ejpam-5671	454	2	these	these	DET
ejpam-5671	454	3	values	value	NOUN
ejpam-5671	454	4	,	,	PUNCT
ejpam-5671	454	5	we	we	PRON
ejpam-5671	454	6	have	have	VERB
ejpam-5671	454	7	m	m	NOUN
ejpam-5671	454	8	=	=	NOUN
ejpam-5671	454	9	1.17	1.17	NUM
ejpam-5671	454	10	and	and	CCONJ
ejpam-5671	454	11	|ω	|ω	NOUN
ejpam-5671	454	12	(	(	PUNCT
ejpam-5671	454	13	ρ	ρ	PROPN
ejpam-5671	454	14	,	,	PUNCT
ejpam-5671	454	15	ω	ω	PROPN
ejpam-5671	454	16	(	(	PUNCT
ejpam-5671	454	17	ρ))|	ρ))|	PROPN
ejpam-5671	454	18	=	=	SYM
ejpam-5671	454	19	∣∣∣∣cos(2πω(ρ))12π	∣∣∣∣cos(2πω(ρ))12π	ADP
ejpam-5671	454	20	+	+	CCONJ
ejpam-5671	454	21	|sin(ω(ρ))|	|sin(ω(ρ))|	PROPN
ejpam-5671	454	22	1	1	NUM
ejpam-5671	455	1	+	+	NUM
ejpam-5671	455	2	|sin(ω(ρ))|	|sin(ω(ρ))|	PROPN
ejpam-5671	455	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5671	455	4	≤	≤	NOUN
ejpam-5671	455	5	1	1	NUM
ejpam-5671	455	6	+	+	CCONJ
ejpam-5671	455	7	1	1	NUM
ejpam-5671	455	8	2	2	NUM
ejpam-5671	455	9	|ω(ρ)|	|ω(ρ)|	PROPN
ejpam-5671	455	10	,	,	PUNCT
ejpam-5671	455	11	ω	ω	PROPN
ejpam-5671	455	12	∈	∈	PROPN
ejpam-5671	455	13	r.	r.	PROPN
ejpam-5671	455	14	thus	thus	ADV
ejpam-5671	455	15	,	,	PUNCT
ejpam-5671	455	16	δ	δ	PROPN
ejpam-5671	455	17	=	=	SYM
ejpam-5671	455	18	1	1	NUM
ejpam-5671	455	19	,	,	PUNCT
ejpam-5671	455	20	χ	χ	NOUN
ejpam-5671	455	21	=	=	SYM
ejpam-5671	455	22	1	1	NUM
ejpam-5671	455	23	2	2	NUM
ejpam-5671	455	24	,	,	PUNCT
ejpam-5671	455	25	and	and	CCONJ
ejpam-5671	455	26	the	the	DET
ejpam-5671	455	27	inequality	inequality	NOUN
ejpam-5671	455	28	0	0	PUNCT
ejpam-5671	455	29	<	<	X
ejpam-5671	455	30	χ	χ	X
ejpam-5671	455	31	<	<	X
ejpam-5671	455	32	1	1	NUM
ejpam-5671	455	33	m	m	NOUN
ejpam-5671	455	34	holds	hold	NOUN
ejpam-5671	455	35	.	.	PUNCT
ejpam-5671	456	1	therefore	therefore	ADV
ejpam-5671	456	2	,	,	PUNCT
ejpam-5671	456	3	the	the	DET
ejpam-5671	456	4	assertions	assertion	NOUN
ejpam-5671	456	5	of	of	ADP
ejpam-5671	456	6	theorem	theorem	NOUN
ejpam-5671	456	7	5	5	NUM
ejpam-5671	456	8	are	be	AUX
ejpam-5671	456	9	fulfilled	fulfil	VERB
ejpam-5671	456	10	.	.	PUNCT
ejpam-5671	457	1	then	then	ADV
ejpam-5671	457	2	,	,	PUNCT
ejpam-5671	457	3	the	the	DET
ejpam-5671	457	4	problem	problem	NOUN
ejpam-5671	457	5	(	(	PUNCT
ejpam-5671	457	6	18	18	NUM
ejpam-5671	457	7	)	)	PUNCT
ejpam-5671	457	8	has	have	VERB
ejpam-5671	457	9	at	at	ADV
ejpam-5671	457	10	least	least	ADV
ejpam-5671	457	11	one	one	NUM
ejpam-5671	457	12	solution	solution	NOUN
ejpam-5671	457	13	on	on	ADP
ejpam-5671	457	14	[	[	X
ejpam-5671	457	15	0	0	NUM
ejpam-5671	457	16	,	,	PUNCT
ejpam-5671	457	17	2	2	NUM
ejpam-5671	457	18	]	]	PUNCT
ejpam-5671	457	19	.	.	PUNCT
ejpam-5671	458	1	5	5	X
ejpam-5671	458	2	.	.	X
ejpam-5671	458	3	conclusion	conclusion	NOUN
ejpam-5671	458	4	the	the	DET
ejpam-5671	458	5	paper	paper	NOUN
ejpam-5671	458	6	introduces	introduce	VERB
ejpam-5671	458	7	a	a	DET
ejpam-5671	458	8	new	new	ADJ
ejpam-5671	458	9	approach	approach	NOUN
ejpam-5671	458	10	to	to	ADP
ejpam-5671	458	11	nonlinear	nonlinear	ADJ
ejpam-5671	458	12	fractional	fractional	ADJ
ejpam-5671	458	13	order	order	NOUN
ejpam-5671	458	14	nonlocal	nonlocal	ADJ
ejpam-5671	458	15	antiperiodic	antiperiodic	ADJ
ejpam-5671	458	16	boundary	boundary	ADJ
ejpam-5671	458	17	conditions	condition	NOUN
ejpam-5671	458	18	.	.	PUNCT
ejpam-5671	459	1	the	the	DET
ejpam-5671	459	2	study	study	NOUN
ejpam-5671	459	3	reveals	reveal	VERB
ejpam-5671	459	4	additional	additional	ADJ
ejpam-5671	459	5	terms	term	NOUN
ejpam-5671	459	6	in	in	ADP
ejpam-5671	459	7	the	the	DET
ejpam-5671	459	8	integral	integral	ADJ
ejpam-5671	459	9	solutions	solution	NOUN
ejpam-5671	459	10	that	that	PRON
ejpam-5671	459	11	s.	s.	PROPN
ejpam-5671	459	12	f.	f.	PROPN
ejpam-5671	459	13	aljurbua	aljurbua	PROPN
ejpam-5671	459	14	,	,	PUNCT
ejpam-5671	459	15	h.	h.	PROPN
ejpam-5671	459	16	a.	a.	PROPN
ejpam-5671	459	17	hammad	hammad	PROPN
ejpam-5671	459	18	,	,	PUNCT
ejpam-5671	459	19	n.	n.	PROPN
ejpam-5671	459	20	b.	b.	PROPN
ejpam-5671	459	21	almutairi	almutairi	PROPN
ejpam-5671	459	22	/	/	SYM
ejpam-5671	459	23	eur	eur	PROPN
ejpam-5671	459	24	.	.	PUNCT
ejpam-5671	460	1	j.	j.	PROPN
ejpam-5671	460	2	pure	pure	PROPN
ejpam-5671	460	3	appl	appl	PROPN
ejpam-5671	460	4	.	.	PROPN
ejpam-5671	460	5	math	math	PROPN
ejpam-5671	460	6	,	,	PUNCT
ejpam-5671	460	7	18	18	NUM
ejpam-5671	460	8	(	(	PUNCT
ejpam-5671	460	9	1	1	NUM
ejpam-5671	460	10	)	)	PUNCT
ejpam-5671	460	11	(	(	PUNCT
ejpam-5671	460	12	2025	2025	NUM
ejpam-5671	460	13	)	)	PUNCT
ejpam-5671	460	14	,	,	PUNCT
ejpam-5671	460	15	5671	5671	NUM
ejpam-5671	460	16	16	16	NUM
ejpam-5671	460	17	of	of	ADP
ejpam-5671	460	18	18	18	NUM
ejpam-5671	460	19	differ	differ	VERB
ejpam-5671	460	20	from	from	ADP
ejpam-5671	460	21	classical	classical	ADJ
ejpam-5671	460	22	antiperiodic	antiperiodic	ADJ
ejpam-5671	460	23	boundary	boundary	ADJ
ejpam-5671	460	24	conditions	condition	NOUN
ejpam-5671	460	25	.	.	PUNCT
ejpam-5671	461	1	it	it	PRON
ejpam-5671	461	2	is	be	AUX
ejpam-5671	461	3	observed	observe	VERB
ejpam-5671	461	4	that	that	SCONJ
ejpam-5671	461	5	under	under	ADP
ejpam-5671	461	6	certain	certain	ADJ
ejpam-5671	461	7	conditions	condition	NOUN
ejpam-5671	461	8	,	,	PUNCT
ejpam-5671	461	9	the	the	DET
ejpam-5671	461	10	resulting	result	VERB
ejpam-5671	461	11	solution	solution	NOUN
ejpam-5671	461	12	aligns	align	VERB
ejpam-5671	461	13	with	with	ADP
ejpam-5671	461	14	that	that	PRON
ejpam-5671	461	15	of	of	ADP
ejpam-5671	461	16	classical	classical	ADJ
ejpam-5671	461	17	antiperiodic	antiperiodic	ADJ
ejpam-5671	461	18	boundary	boundary	ADJ
ejpam-5671	461	19	conditions	condition	NOUN
ejpam-5671	461	20	,	,	PUNCT
ejpam-5671	461	21	extending	extend	VERB
ejpam-5671	461	22	the	the	DET
ejpam-5671	461	23	existing	exist	VERB
ejpam-5671	461	24	results	result	NOUN
ejpam-5671	461	25	,	,	PUNCT
ejpam-5671	461	26	specifically	specifically	ADV
ejpam-5671	461	27	as	as	ADP
ejpam-5671	461	28	ξ	ξ	PROPN
ejpam-5671	461	29	approaches	approach	NOUN
ejpam-5671	461	30	1−	1−	NUM
ejpam-5671	461	31	before	before	ADP
ejpam-5671	461	32	θ	θ	PROPN
ejpam-5671	461	33	approaches	approach	VERB
ejpam-5671	461	34	0+.however	0+.however	NUM
ejpam-5671	461	35	,	,	PUNCT
ejpam-5671	461	36	a	a	DET
ejpam-5671	461	37	distinct	distinct	ADJ
ejpam-5671	461	38	solution	solution	NOUN
ejpam-5671	461	39	for	for	ADP
ejpam-5671	461	40	this	this	DET
ejpam-5671	461	41	problem	problem	NOUN
ejpam-5671	461	42	type	type	NOUN
ejpam-5671	461	43	is	be	AUX
ejpam-5671	461	44	encountered	encounter	VERB
ejpam-5671	461	45	under	under	ADP
ejpam-5671	461	46	different	different	ADJ
ejpam-5671	461	47	conditions	condition	NOUN
ejpam-5671	461	48	.	.	PUNCT
ejpam-5671	462	1	this	this	PRON
ejpam-5671	462	2	offers	offer	VERB
ejpam-5671	462	3	a	a	DET
ejpam-5671	462	4	fresh	fresh	ADJ
ejpam-5671	462	5	perspective	perspective	NOUN
ejpam-5671	462	6	on	on	ADP
ejpam-5671	462	7	the	the	DET
ejpam-5671	462	8	behavior	behavior	NOUN
ejpam-5671	462	9	of	of	ADP
ejpam-5671	462	10	fractional	fractional	ADJ
ejpam-5671	462	11	differential	differential	ADJ
ejpam-5671	462	12	equations	equation	NOUN
ejpam-5671	462	13	under	under	ADP
ejpam-5671	462	14	specific	specific	ADJ
ejpam-5671	462	15	boundary	boundary	ADJ
ejpam-5671	462	16	conditions	condition	NOUN
ejpam-5671	462	17	,	,	PUNCT
ejpam-5671	462	18	potentially	potentially	ADV
ejpam-5671	462	19	leading	lead	VERB
ejpam-5671	462	20	to	to	ADP
ejpam-5671	462	21	novel	novel	ADJ
ejpam-5671	462	22	solutions	solution	NOUN
ejpam-5671	462	23	in	in	ADP
ejpam-5671	462	24	various	various	ADJ
ejpam-5671	462	25	scientific	scientific	ADJ
ejpam-5671	462	26	fields	field	NOUN
ejpam-5671	462	27	.	.	PUNCT
ejpam-5671	463	1	these	these	DET
ejpam-5671	463	2	new	new	ADJ
ejpam-5671	463	3	solutions	solution	NOUN
ejpam-5671	463	4	could	could	AUX
ejpam-5671	463	5	significantly	significantly	ADV
ejpam-5671	463	6	impact	impact	VERB
ejpam-5671	463	7	resolving	resolve	VERB
ejpam-5671	463	8	complex	complex	ADJ
ejpam-5671	463	9	problems	problem	NOUN
ejpam-5671	463	10	where	where	SCONJ
ejpam-5671	463	11	traditional	traditional	ADJ
ejpam-5671	463	12	approaches	approach	NOUN
ejpam-5671	463	13	fall	fall	VERB
ejpam-5671	463	14	short	short	ADJ
ejpam-5671	463	15	.	.	PUNCT
ejpam-5671	464	1	acknowledgements	acknowledgement	NOUN
ejpam-5671	464	2	the	the	DET
ejpam-5671	464	3	researchers	researcher	NOUN
ejpam-5671	464	4	would	would	AUX
ejpam-5671	464	5	like	like	VERB
ejpam-5671	464	6	to	to	PART
ejpam-5671	464	7	thank	thank	VERB
ejpam-5671	464	8	the	the	DET
ejpam-5671	464	9	deanship	deanship	NOUN
ejpam-5671	464	10	of	of	ADP
ejpam-5671	464	11	graduate	graduate	NOUN
ejpam-5671	464	12	studies	study	NOUN
ejpam-5671	464	13	and	and	CCONJ
ejpam-5671	464	14	scientific	scientific	ADJ
ejpam-5671	464	15	research	research	NOUN
ejpam-5671	464	16	at	at	ADP
ejpam-5671	464	17	qassim	qassim	PROPN
ejpam-5671	464	18	university	university	PROPN
ejpam-5671	464	19	for	for	ADP
ejpam-5671	464	20	financial	financial	ADJ
ejpam-5671	464	21	support	support	NOUN
ejpam-5671	464	22	(	(	PUNCT
ejpam-5671	464	23	qu	qu	NOUN
ejpam-5671	464	24	-	-	ADJ
ejpam-5671	464	25	apc-2025	apc-2025	ADJ
ejpam-5671	464	26	)	)	PUNCT
ejpam-5671	464	27	data	datum	NOUN
ejpam-5671	464	28	availability	availability	NOUN
ejpam-5671	464	29	the	the	DET
ejpam-5671	464	30	article	article	NOUN
ejpam-5671	464	31	contains	contain	VERB
ejpam-5671	464	32	all	all	DET
ejpam-5671	464	33	the	the	DET
ejpam-5671	464	34	necessary	necessary	ADJ
ejpam-5671	464	35	data	datum	NOUN
ejpam-5671	464	36	that	that	PRON
ejpam-5671	464	37	was	be	AUX
ejpam-5671	464	38	utilized	utilize	VERB
ejpam-5671	464	39	to	to	PART
ejpam-5671	464	40	back	back	VERB
ejpam-5671	464	41	up	up	ADP
ejpam-5671	464	42	the	the	DET
ejpam-5671	464	43	findings	finding	NOUN
ejpam-5671	464	44	of	of	ADP
ejpam-5671	464	45	this	this	DET
ejpam-5671	464	46	work	work	NOUN
ejpam-5671	464	47	.	.	PUNCT
ejpam-5671	465	1	conflict	conflict	NOUN
ejpam-5671	465	2	of	of	ADP
ejpam-5671	465	3	interest	interest	NOUN
ejpam-5671	465	4	the	the	DET
ejpam-5671	465	5	author	author	NOUN
ejpam-5671	465	6	does	do	AUX
ejpam-5671	465	7	not	not	PART
ejpam-5671	465	8	have	have	VERB
ejpam-5671	465	9	any	any	DET
ejpam-5671	465	10	conflict	conflict	NOUN
ejpam-5671	465	11	of	of	ADP
ejpam-5671	465	12	interest	interest	NOUN
ejpam-5671	465	13	.	.	PUNCT
ejpam-5671	466	1	references	reference	NOUN
ejpam-5671	466	2	[	[	X
ejpam-5671	466	3	1	1	NUM
ejpam-5671	466	4	]	]	X
ejpam-5671	466	5	s	s	VERB
ejpam-5671	466	6	abbas	abbas	NOUN
ejpam-5671	466	7	,	,	PUNCT
ejpam-5671	466	8	m	m	NOUN
ejpam-5671	466	9	benchohra	benchohra	NOUN
ejpam-5671	466	10	,	,	PUNCT
ejpam-5671	466	11	j	j	PROPN
ejpam-5671	466	12	r	r	NOUN
ejpam-5671	466	13	graef	graef	NOUN
ejpam-5671	466	14	,	,	PUNCT
ejpam-5671	466	15	and	and	CCONJ
ejpam-5671	466	16	j	j	PROPN
ejpam-5671	466	17	henderson	henderson	PROPN
ejpam-5671	466	18	.	.	PUNCT
ejpam-5671	467	1	implicit	implicit	ADJ
ejpam-5671	467	2	fractional	fractional	ADJ
ejpam-5671	467	3	differential	differential	NOUN
ejpam-5671	467	4	and	and	CCONJ
ejpam-5671	467	5	integral	integral	ADJ
ejpam-5671	467	6	equations	equation	NOUN
ejpam-5671	467	7	:	:	PUNCT
ejpam-5671	467	8	existence	existence	NOUN
ejpam-5671	467	9	and	and	CCONJ
ejpam-5671	467	10	stability	stability	NOUN
ejpam-5671	467	11	.	.	PUNCT
ejpam-5671	468	1	walter	walter	PROPN
ejpam-5671	468	2	de	de	PROPN
ejpam-5671	468	3	gruyter	gruyter	PROPN
ejpam-5671	468	4	gmbh	gmbh	PROPN
ejpam-5671	468	5	,	,	PUNCT
ejpam-5671	468	6	co	co	NOUN
ejpam-5671	468	7	kg	kg	PROPN
ejpam-5671	468	8	.	.	PROPN
ejpam-5671	468	9	,	,	PUNCT
ejpam-5671	468	10	26	26	NUM
ejpam-5671	468	11	,	,	PUNCT
ejpam-5671	468	12	2018	2018	NUM
ejpam-5671	468	13	.	.	PUNCT
ejpam-5671	469	1	[	[	X
ejpam-5671	469	2	2	2	NUM
ejpam-5671	469	3	]	]	X
ejpam-5671	469	4	r	r	NOUN
ejpam-5671	469	5	p	p	PROPN
ejpam-5671	469	6	agarwal	agarwal	PROPN
ejpam-5671	469	7	,	,	PUNCT
ejpam-5671	469	8	b	b	NOUN
ejpam-5671	469	9	ahmad	ahmad	PROPN
ejpam-5671	469	10	,	,	PUNCT
ejpam-5671	469	11	and	and	CCONJ
ejpam-5671	469	12	j	j	PROPN
ejpam-5671	469	13	j	j	PROPN
ejpam-5671	469	14	nieto	nieto	PROPN
ejpam-5671	469	15	.	.	PUNCT
ejpam-5671	470	1	fractional	fractional	ADJ
ejpam-5671	470	2	differential	differential	ADJ
ejpam-5671	470	3	equations	equation	NOUN
ejpam-5671	470	4	with	with	ADP
ejpam-5671	470	5	nonlocal	nonlocal	ADJ
ejpam-5671	470	6	(	(	PUNCT
ejpam-5671	470	7	parametric	parametric	ADJ
ejpam-5671	470	8	type	type	NOUN
ejpam-5671	470	9	)	)	PUNCT
ejpam-5671	470	10	anti	anti	ADJ
ejpam-5671	470	11	-	-	ADJ
ejpam-5671	470	12	periodic	periodic	ADJ
ejpam-5671	470	13	boundary	boundary	ADJ
ejpam-5671	470	14	conditions	condition	NOUN
ejpam-5671	470	15	.	.	PUNCT
ejpam-5671	471	1	filomat	filomat	NOUN
ejpam-5671	471	2	,	,	PUNCT
ejpam-5671	471	3	31(5):1207–1214	31(5):1207–1214	NUM
ejpam-5671	471	4	,	,	PUNCT
ejpam-5671	471	5	2017	2017	NUM
ejpam-5671	471	6	.	.	PUNCT
ejpam-5671	472	1	[	[	X
ejpam-5671	472	2	3	3	NUM
ejpam-5671	472	3	]	]	SYM
ejpam-5671	472	4	b	b	NOUN
ejpam-5671	472	5	ahmad	ahmad	PROPN
ejpam-5671	472	6	and	and	CCONJ
ejpam-5671	472	7	j	j	PROPN
ejpam-5671	472	8	j	j	PROPN
ejpam-5671	472	9	nieto	nieto	PROPN
ejpam-5671	472	10	.	.	PUNCT
ejpam-5671	473	1	anti	anti	ADJ
ejpam-5671	473	2	-	-	ADJ
ejpam-5671	473	3	periodic	periodic	ADJ
ejpam-5671	473	4	fractional	fractional	ADJ
ejpam-5671	473	5	boundary	boundary	ADJ
ejpam-5671	473	6	value	value	NOUN
ejpam-5671	473	7	problems	problem	NOUN
ejpam-5671	473	8	.	.	PUNCT
ejpam-5671	474	1	computers	computer	NOUN
ejpam-5671	474	2	math	math	PROPN
ejpam-5671	474	3	.	.	PUNCT
ejpam-5671	475	1	appl	appl	PROPN
ejpam-5671	475	2	.	.	PROPN
ejpam-5671	475	3	,	,	PUNCT
ejpam-5671	475	4	62(3):1150–1156	62(3):1150–1156	NUM
ejpam-5671	475	5	,	,	PUNCT
ejpam-5671	475	6	2011	2011	NUM
ejpam-5671	475	7	.	.	PUNCT
ejpam-5671	476	1	[	[	X
ejpam-5671	476	2	4	4	NUM
ejpam-5671	476	3	]	]	X
ejpam-5671	476	4	b	b	X
ejpam-5671	476	5	ahmed	ahme	VERB
ejpam-5671	476	6	.	.	PUNCT
ejpam-5671	477	1	existence	existence	NOUN
ejpam-5671	477	2	of	of	ADP
ejpam-5671	477	3	solutions	solution	NOUN
ejpam-5671	477	4	for	for	ADP
ejpam-5671	477	5	fractional	fractional	ADJ
ejpam-5671	477	6	differential	differential	ADJ
ejpam-5671	477	7	equations	equation	NOUN
ejpam-5671	477	8	of	of	ADP
ejpam-5671	477	9	order	order	NOUN
ejpam-5671	477	10	q	q	X
ejpam-5671	477	11	in	in	ADP
ejpam-5671	477	12	(	(	PUNCT
ejpam-5671	477	13	2	2	NUM
ejpam-5671	477	14	,	,	PUNCT
ejpam-5671	477	15	3	3	NUM
ejpam-5671	477	16	]	]	PUNCT
ejpam-5671	477	17	with	with	ADP
ejpam-5671	477	18	anti	anti	ADJ
ejpam-5671	477	19	-	-	ADJ
ejpam-5671	477	20	periodic	periodic	ADJ
ejpam-5671	477	21	boundary	boundary	ADJ
ejpam-5671	477	22	conditions	condition	NOUN
ejpam-5671	477	23	.	.	PUNCT
ejpam-5671	478	1	j.	j.	PROPN
ejpam-5671	478	2	vib	vib	PROPN
ejpam-5671	478	3	.	.	PUNCT
ejpam-5671	478	4	control	control	PROPN
ejpam-5671	478	5	.	.	PUNCT
ejpam-5671	478	6	,	,	PUNCT
ejpam-5671	479	1	34:385–391	34:385–391	NUM
ejpam-5671	479	2	,	,	PUNCT
ejpam-5671	479	3	2010	2010	NUM
ejpam-5671	479	4	.	.	PUNCT
ejpam-5671	480	1	[	[	X
ejpam-5671	480	2	5	5	NUM
ejpam-5671	480	3	]	]	SYM
ejpam-5671	480	4	s	s	X
ejpam-5671	480	5	f	f	PROPN
ejpam-5671	480	6	aljurbua	aljurbua	PROPN
ejpam-5671	480	7	.	.	PUNCT
ejpam-5671	481	1	exploring	explore	VERB
ejpam-5671	481	2	solutions	solution	NOUN
ejpam-5671	481	3	to	to	ADP
ejpam-5671	481	4	specific	specific	ADJ
ejpam-5671	481	5	class	class	NOUN
ejpam-5671	481	6	of	of	ADP
ejpam-5671	481	7	fractional	fractional	ADJ
ejpam-5671	481	8	differential	differential	ADJ
ejpam-5671	481	9	equations	equation	NOUN
ejpam-5671	481	10	of	of	ADP
ejpam-5671	481	11	order	order	NOUN
ejpam-5671	481	12	3	3	NUM
ejpam-5671	481	13	<	<	X
ejpam-5671	481	14	u	u	X
ejpam-5671	481	15	≤	≤	ADV
ejpam-5671	481	16	4	4	NUM
ejpam-5671	481	17	.	.	PUNCT
ejpam-5671	481	18	bound	bind	VERB
ejpam-5671	481	19	.	.	PUNCT
ejpam-5671	482	1	value	value	PROPN
ejpam-5671	482	2	prob	prob	PROPN
ejpam-5671	482	3	.	.	PROPN
ejpam-5671	482	4	,	,	PUNCT
ejpam-5671	482	5	1:71	1:71	NUM
ejpam-5671	482	6	,	,	PUNCT
ejpam-5671	482	7	2024	2024	NUM
ejpam-5671	482	8	.	.	PUNCT
ejpam-5671	483	1	[	[	X
ejpam-5671	483	2	6	6	NUM
ejpam-5671	483	3	]	]	SYM
ejpam-5671	483	4	s	s	X
ejpam-5671	483	5	f	f	PROPN
ejpam-5671	483	6	aljurbua	aljurbua	PROPN
ejpam-5671	483	7	.	.	PUNCT
ejpam-5671	483	8	extended	extended	ADJ
ejpam-5671	483	9	existence	existence	NOUN
ejpam-5671	483	10	results	result	NOUN
ejpam-5671	483	11	for	for	ADP
ejpam-5671	483	12	fdes	fde	NOUN
ejpam-5671	483	13	with	with	ADP
ejpam-5671	483	14	nonlocal	nonlocal	ADJ
ejpam-5671	483	15	conditions	condition	NOUN
ejpam-5671	483	16	.	.	PUNCT
ejpam-5671	484	1	aims	aim	VERB
ejpam-5671	484	2	math	math	NOUN
ejpam-5671	484	3	.	.	PUNCT
ejpam-5671	484	4	,	,	PUNCT
ejpam-5671	484	5	9(4):9049–9058	9(4):9049–9058	PROPN
ejpam-5671	484	6	,	,	PUNCT
ejpam-5671	484	7	2024	2024	NUM
ejpam-5671	484	8	.	.	PUNCT
ejpam-5671	485	1	[	[	X
ejpam-5671	485	2	7	7	NUM
ejpam-5671	485	3	]	]	SYM
ejpam-5671	485	4	s	s	X
ejpam-5671	485	5	f	f	PROPN
ejpam-5671	485	6	aljurbua	aljurbua	PROPN
ejpam-5671	485	7	.	.	PUNCT
ejpam-5671	485	8	extended	extended	ADJ
ejpam-5671	485	9	existence	existence	NOUN
ejpam-5671	485	10	results	result	NOUN
ejpam-5671	485	11	of	of	ADP
ejpam-5671	485	12	solutions	solution	NOUN
ejpam-5671	485	13	for	for	ADP
ejpam-5671	485	14	fdes	fde	NOUN
ejpam-5671	485	15	of	of	ADP
ejpam-5671	485	16	order	order	NOUN
ejpam-5671	485	17	gamma	gamma	NOUN
ejpam-5671	485	18	in	in	ADP
ejpam-5671	485	19	(	(	PUNCT
ejpam-5671	485	20	1	1	NUM
ejpam-5671	485	21	,	,	PUNCT
ejpam-5671	485	22	2	2	NUM
ejpam-5671	485	23	]	]	PUNCT
ejpam-5671	485	24	.	.	PUNCT
ejpam-5671	486	1	aims	aim	VERB
ejpam-5671	486	2	math	math	NOUN
ejpam-5671	486	3	.	.	PUNCT
ejpam-5671	486	4	,	,	PUNCT
ejpam-5671	486	5	9(5):13077–13086	9(5):13077–13086	NOUN
ejpam-5671	486	6	,	,	PUNCT
ejpam-5671	486	7	2024	2024	NUM
ejpam-5671	486	8	.	.	PUNCT
ejpam-5671	487	1	[	[	X
ejpam-5671	487	2	8	8	NUM
ejpam-5671	487	3	]	]	SYM
ejpam-5671	487	4	s	s	X
ejpam-5671	487	5	f	f	PROPN
ejpam-5671	487	6	aljurbua	aljurbua	PROPN
ejpam-5671	487	7	.	.	PUNCT
ejpam-5671	488	1	generalized	generalized	ADJ
ejpam-5671	488	2	existence	existence	NOUN
ejpam-5671	488	3	results	result	NOUN
ejpam-5671	488	4	for	for	ADP
ejpam-5671	488	5	solutions	solution	NOUN
ejpam-5671	488	6	of	of	ADP
ejpam-5671	488	7	nonlinear	nonlinear	ADJ
ejpam-5671	488	8	fractional	fractional	ADJ
ejpam-5671	488	9	differential	differential	ADJ
ejpam-5671	488	10	equations	equation	NOUN
ejpam-5671	488	11	with	with	ADP
ejpam-5671	488	12	nonlocal	nonlocal	ADJ
ejpam-5671	488	13	boundary	boundary	ADJ
ejpam-5671	488	14	conditions	condition	NOUN
ejpam-5671	488	15	.	.	PUNCT
ejpam-5671	489	1	ain	ain	PROPN
ejpam-5671	489	2	shams	shams	PROPN
ejpam-5671	489	3	eng	eng	PROPN
ejpam-5671	489	4	.	.	PUNCT
ejpam-5671	490	1	j.	j.	PROPN
ejpam-5671	490	2	,	,	PUNCT
ejpam-5671	490	3	2024:103035	2024:103035	NUM
ejpam-5671	490	4	,	,	PUNCT
ejpam-5671	490	5	2024	2024	NUM
ejpam-5671	490	6	.	.	PUNCT
ejpam-5671	491	1	s.	s.	PROPN
ejpam-5671	491	2	f.	f.	PROPN
ejpam-5671	491	3	aljurbua	aljurbua	PROPN
ejpam-5671	491	4	,	,	PUNCT
ejpam-5671	491	5	h.	h.	PROPN
ejpam-5671	491	6	a.	a.	PROPN
ejpam-5671	491	7	hammad	hammad	PROPN
ejpam-5671	491	8	,	,	PUNCT
ejpam-5671	491	9	n.	n.	PROPN
ejpam-5671	491	10	b.	b.	PROPN
ejpam-5671	491	11	almutairi	almutairi	PROPN
ejpam-5671	491	12	/	/	SYM
ejpam-5671	491	13	eur	eur	PROPN
ejpam-5671	491	14	.	.	PUNCT
ejpam-5671	492	1	j.	j.	PROPN
ejpam-5671	492	2	pure	pure	PROPN
ejpam-5671	492	3	appl	appl	PROPN
ejpam-5671	492	4	.	.	PROPN
ejpam-5671	492	5	math	math	PROPN
ejpam-5671	492	6	,	,	PUNCT
ejpam-5671	492	7	18	18	NUM
ejpam-5671	492	8	(	(	PUNCT
ejpam-5671	492	9	1	1	NUM
ejpam-5671	492	10	)	)	PUNCT
ejpam-5671	492	11	(	(	PUNCT
ejpam-5671	492	12	2025	2025	NUM
ejpam-5671	492	13	)	)	PUNCT
ejpam-5671	492	14	,	,	PUNCT
ejpam-5671	492	15	5671	5671	NUM
ejpam-5671	492	16	17	17	NUM
ejpam-5671	492	17	of	of	ADP
ejpam-5671	492	18	18	18	NUM
ejpam-5671	493	1	[	[	SYM
ejpam-5671	493	2	9	9	NUM
ejpam-5671	493	3	]	]	PUNCT
ejpam-5671	493	4	n	n	PRON
ejpam-5671	493	5	allouch	allouch	NOUN
ejpam-5671	493	6	,	,	PUNCT
ejpam-5671	493	7	j	j	PROPN
ejpam-5671	493	8	r	r	NOUN
ejpam-5671	493	9	graef	graef	NOUN
ejpam-5671	493	10	,	,	PUNCT
ejpam-5671	493	11	and	and	CCONJ
ejpam-5671	493	12	s	s	VERB
ejpam-5671	493	13	hamani	hamani	NOUN
ejpam-5671	493	14	.	.	PUNCT
ejpam-5671	494	1	boundary	boundary	ADJ
ejpam-5671	494	2	value	value	NOUN
ejpam-5671	494	3	problem	problem	NOUN
ejpam-5671	494	4	for	for	ADP
ejpam-5671	494	5	fractional	fractional	ADJ
ejpam-5671	494	6	q−difference	q−difference	NOUN
ejpam-5671	494	7	equations	equation	NOUN
ejpam-5671	494	8	with	with	ADP
ejpam-5671	494	9	integral	integral	ADJ
ejpam-5671	494	10	conditions	condition	NOUN
ejpam-5671	494	11	in	in	ADP
ejpam-5671	494	12	banach	banach	NOUN
ejpam-5671	494	13	spaces	space	NOUN
ejpam-5671	494	14	.	.	PUNCT
ejpam-5671	495	1	fractal	fractal	ADJ
ejpam-5671	495	2	fract	fract	PROPN
ejpam-5671	495	3	.	.	PUNCT
ejpam-5671	495	4	,	,	PUNCT
ejpam-5671	495	5	6(5):237	6(5):237	NUM
ejpam-5671	495	6	,	,	PUNCT
ejpam-5671	495	7	2022	2022	NUM
ejpam-5671	495	8	.	.	PUNCT
ejpam-5671	496	1	[	[	X
ejpam-5671	496	2	10	10	NUM
ejpam-5671	496	3	]	]	X
ejpam-5671	496	4	o	o	NOUN
ejpam-5671	496	5	abu	abu	PROPN
ejpam-5671	496	6	arqub	arqub	NOUN
ejpam-5671	496	7	,	,	PUNCT
ejpam-5671	496	8	r	r	NOUN
ejpam-5671	496	9	mezghiche	mezghiche	NOUN
ejpam-5671	496	10	,	,	PUNCT
ejpam-5671	496	11	and	and	CCONJ
ejpam-5671	496	12	b	b	X
ejpam-5671	496	13	maayah	maayah	NOUN
ejpam-5671	496	14	.	.	PUNCT
ejpam-5671	497	1	fuzzy	fuzzy	ADJ
ejpam-5671	497	2	m−fractional	m−fractional	ADJ
ejpam-5671	497	3	integrodifferential	integrodifferential	ADJ
ejpam-5671	497	4	models	model	NOUN
ejpam-5671	497	5	:	:	PUNCT
ejpam-5671	497	6	theoretical	theoretical	ADJ
ejpam-5671	497	7	existence	existence	NOUN
ejpam-5671	497	8	and	and	CCONJ
ejpam-5671	497	9	uniqueness	uniqueness	NOUN
ejpam-5671	497	10	results	result	NOUN
ejpam-5671	497	11	,	,	PUNCT
ejpam-5671	497	12	and	and	CCONJ
ejpam-5671	497	13	approximate	approximate	ADJ
ejpam-5671	497	14	solutions	solution	NOUN
ejpam-5671	497	15	utilizing	utilize	VERB
ejpam-5671	497	16	the	the	DET
ejpam-5671	497	17	hilbert	hilbert	NOUN
ejpam-5671	497	18	reproducing	reproduce	VERB
ejpam-5671	497	19	kernel	kernel	PROPN
ejpam-5671	497	20	algorithm	algorithm	PROPN
ejpam-5671	497	21	.	.	PUNCT
ejpam-5671	498	1	frontiers	frontier	NOUN
ejpam-5671	498	2	in	in	ADP
ejpam-5671	498	3	physics	physics	PROPN
ejpam-5671	498	4	,	,	PUNCT
ejpam-5671	498	5	11:1252919	11:1252919	NUM
ejpam-5671	498	6	,	,	PUNCT
ejpam-5671	498	7	2023	2023	NUM
ejpam-5671	498	8	.	.	PUNCT
ejpam-5671	499	1	[	[	X
ejpam-5671	499	2	11	11	NUM
ejpam-5671	499	3	]	]	PUNCT
ejpam-5671	499	4	m	m	NOUN
ejpam-5671	499	5	benchohra	benchohra	NOUN
ejpam-5671	499	6	,	,	PUNCT
ejpam-5671	499	7	a	a	DET
ejpam-5671	499	8	cabada	cabada	NOUN
ejpam-5671	499	9	,	,	PUNCT
ejpam-5671	499	10	and	and	CCONJ
ejpam-5671	499	11	d	d	PROPN
ejpam-5671	499	12	seba	seba	PROPN
ejpam-5671	499	13	.	.	PUNCT
ejpam-5671	500	1	an	an	DET
ejpam-5671	500	2	existence	existence	NOUN
ejpam-5671	500	3	result	result	NOUN
ejpam-5671	500	4	for	for	ADP
ejpam-5671	500	5	nonlinear	nonlinear	ADJ
ejpam-5671	500	6	fractional	fractional	ADJ
ejpam-5671	500	7	differential	differential	ADJ
ejpam-5671	500	8	equations	equation	NOUN
ejpam-5671	500	9	on	on	ADP
ejpam-5671	500	10	banach	banach	NOUN
ejpam-5671	500	11	spaces	space	NOUN
ejpam-5671	500	12	.	.	PUNCT
ejpam-5671	501	1	bound	bind	VERB
ejpam-5671	501	2	.	.	PUNCT
ejpam-5671	501	3	value	value	PROPN
ejpam-5671	501	4	prob	prob	PROPN
ejpam-5671	501	5	.	.	PROPN
ejpam-5671	501	6	,	,	PUNCT
ejpam-5671	501	7	2009:1–11	2009:1–11	NUM
ejpam-5671	501	8	,	,	PUNCT
ejpam-5671	501	9	2009	2009	NUM
ejpam-5671	501	10	.	.	PUNCT
ejpam-5671	502	1	[	[	X
ejpam-5671	502	2	12	12	NUM
ejpam-5671	502	3	]	]	X
ejpam-5671	502	4	f	f	X
ejpam-5671	502	5	bouzeffour	bouzeffour	NOUN
ejpam-5671	502	6	.	.	PUNCT
ejpam-5671	503	1	advancing	advance	VERB
ejpam-5671	503	2	fractional	fractional	ADJ
ejpam-5671	503	3	riesz	riesz	NOUN
ejpam-5671	503	4	derivatives	derivative	NOUN
ejpam-5671	503	5	through	through	ADP
ejpam-5671	503	6	dunkl	dunkl	NOUN
ejpam-5671	503	7	operators	operator	NOUN
ejpam-5671	503	8	.	.	PUNCT
ejpam-5671	504	1	mathematics	mathematic	NOUN
ejpam-5671	504	2	,	,	PUNCT
ejpam-5671	504	3	11(19):4073	11(19):4073	NUM
ejpam-5671	504	4	,	,	PUNCT
ejpam-5671	504	5	2023	2023	NUM
ejpam-5671	504	6	.	.	PUNCT
ejpam-5671	505	1	[	[	X
ejpam-5671	505	2	13	13	NUM
ejpam-5671	505	3	]	]	PUNCT
ejpam-5671	505	4	a	a	DET
ejpam-5671	505	5	guezane	guezane	NOUN
ejpam-5671	505	6	-	-	PUNCT
ejpam-5671	505	7	lakoud	lakoud	NOUN
ejpam-5671	505	8	and	and	CCONJ
ejpam-5671	505	9	r	r	NOUN
ejpam-5671	505	10	khaldi	khaldi	NOUN
ejpam-5671	505	11	.	.	PUNCT
ejpam-5671	506	1	solvability	solvability	NOUN
ejpam-5671	506	2	of	of	ADP
ejpam-5671	506	3	a	a	DET
ejpam-5671	506	4	fractional	fractional	ADJ
ejpam-5671	506	5	boundary	boundary	ADJ
ejpam-5671	506	6	value	value	NOUN
ejpam-5671	506	7	problem	problem	NOUN
ejpam-5671	506	8	with	with	ADP
ejpam-5671	506	9	fractional	fractional	ADJ
ejpam-5671	506	10	integral	integral	ADJ
ejpam-5671	506	11	condition	condition	NOUN
ejpam-5671	506	12	.	.	PUNCT
ejpam-5671	507	1	nonlinear	nonlinear	ADJ
ejpam-5671	507	2	anal	anal	PROPN
ejpam-5671	507	3	.	.	PUNCT
ejpam-5671	507	4	,	,	PUNCT
ejpam-5671	507	5	75(4):2692–2700	75(4):2692–2700	NUM
ejpam-5671	507	6	,	,	PUNCT
ejpam-5671	507	7	2012	2012	NUM
ejpam-5671	507	8	.	.	PUNCT
ejpam-5671	508	1	[	[	X
ejpam-5671	508	2	14	14	NUM
ejpam-5671	508	3	]	]	X
ejpam-5671	508	4	h	h	NOUN
ejpam-5671	508	5	a	a	DET
ejpam-5671	508	6	hammad	hammad	PROPN
ejpam-5671	508	7	and	and	CCONJ
ejpam-5671	508	8	m	m	PROPN
ejpam-5671	508	9	de	de	X
ejpam-5671	508	10	la	la	PROPN
ejpam-5671	508	11	sen	sen	PROPN
ejpam-5671	508	12	.	.	PROPN
ejpam-5671	508	13	stability	stability	PROPN
ejpam-5671	508	14	and	and	CCONJ
ejpam-5671	508	15	controllability	controllability	NOUN
ejpam-5671	508	16	study	study	NOUN
ejpam-5671	508	17	for	for	ADP
ejpam-5671	508	18	mixed	mixed	ADJ
ejpam-5671	508	19	integral	integral	ADJ
ejpam-5671	508	20	fractional	fractional	ADJ
ejpam-5671	508	21	delay	delay	NOUN
ejpam-5671	508	22	dynamic	dynamic	ADJ
ejpam-5671	508	23	systems	system	NOUN
ejpam-5671	508	24	endowed	endow	VERB
ejpam-5671	508	25	with	with	ADP
ejpam-5671	508	26	impulsive	impulsive	ADJ
ejpam-5671	508	27	effects	effect	NOUN
ejpam-5671	508	28	on	on	ADP
ejpam-5671	508	29	time	time	NOUN
ejpam-5671	508	30	scales	scale	NOUN
ejpam-5671	508	31	.	.	PUNCT
ejpam-5671	509	1	fractal	fractal	ADJ
ejpam-5671	509	2	fract	fract	PROPN
ejpam-5671	509	3	.	.	PUNCT
ejpam-5671	509	4	,	,	PUNCT
ejpam-5671	509	5	7:92	7:92	NUM
ejpam-5671	509	6	,	,	PUNCT
ejpam-5671	509	7	2023	2023	NUM
ejpam-5671	509	8	.	.	PUNCT
ejpam-5671	510	1	[	[	X
ejpam-5671	510	2	15	15	NUM
ejpam-5671	510	3	]	]	X
ejpam-5671	510	4	h	h	NOUN
ejpam-5671	510	5	a	a	DET
ejpam-5671	510	6	hammad	hammad	PROPN
ejpam-5671	510	7	,	,	PUNCT
ejpam-5671	510	8	m	m	VERB
ejpam-5671	510	9	qasymeh	qasymeh	NOUN
ejpam-5671	510	10	,	,	PUNCT
ejpam-5671	510	11	and	and	CCONJ
ejpam-5671	510	12	m.	m.	PROPN
ejpam-5671	510	13	abdel	abdel	PROPN
ejpam-5671	510	14	-	-	PUNCT
ejpam-5671	510	15	aty	aty	PROPN
ejpam-5671	510	16	.	.	PROPN
ejpam-5671	511	1	existence	existence	NOUN
ejpam-5671	511	2	and	and	CCONJ
ejpam-5671	511	3	stability	stability	NOUN
ejpam-5671	511	4	results	result	VERB
ejpam-5671	511	5	for	for	ADP
ejpam-5671	511	6	a	a	DET
ejpam-5671	511	7	langevin	langevin	ADJ
ejpam-5671	511	8	system	system	NOUN
ejpam-5671	511	9	with	with	ADP
ejpam-5671	511	10	caputo	caputo	PROPN
ejpam-5671	511	11	–	–	PUNCT
ejpam-5671	511	12	hadamard	hadamard	ADJ
ejpam-5671	511	13	fractional	fractional	ADJ
ejpam-5671	511	14	operators	operator	NOUN
ejpam-5671	511	15	.	.	PUNCT
ejpam-5671	512	1	int	int	NOUN
ejpam-5671	512	2	.	.	PUNCT
ejpam-5671	513	1	j.	j.	PROPN
ejpam-5671	513	2	geometric	geometric	ADJ
ejpam-5671	513	3	methods	method	NOUN
ejpam-5671	513	4	modern	modern	ADJ
ejpam-5671	513	5	phy	phy	PROPN
ejpam-5671	513	6	.	.	PROPN
ejpam-5671	513	7	,	,	PUNCT
ejpam-5671	513	8	2450218:1–24	2450218:1–24	NUM
ejpam-5671	513	9	,	,	PUNCT
ejpam-5671	513	10	2024	2024	NUM
ejpam-5671	513	11	.	.	PUNCT
ejpam-5671	514	1	[	[	X
ejpam-5671	514	2	16	16	NUM
ejpam-5671	514	3	]	]	X
ejpam-5671	514	4	h	h	NOUN
ejpam-5671	514	5	a	a	DET
ejpam-5671	514	6	hammad	hammad	PROPN
ejpam-5671	514	7	,	,	PUNCT
ejpam-5671	514	8	r	r	NOUN
ejpam-5671	514	9	a	a	DET
ejpam-5671	514	10	rashwan	rashwan	NOUN
ejpam-5671	514	11	,	,	PUNCT
ejpam-5671	514	12	a	a	DET
ejpam-5671	514	13	nafea	nafea	ADJ
ejpam-5671	514	14	,	,	PUNCT
ejpam-5671	514	15	m	m	PROPN
ejpam-5671	514	16	e	e	NOUN
ejpam-5671	514	17	samei	samei	NOUN
ejpam-5671	514	18	,	,	PUNCT
ejpam-5671	514	19	and	and	CCONJ
ejpam-5671	514	20	de	de	PROPN
ejpam-5671	514	21	la	la	X
ejpam-5671	514	22	sen	sen	PROPN
ejpam-5671	514	23	.	.	PROPN
ejpam-5671	514	24	stability	stability	NOUN
ejpam-5671	514	25	and	and	CCONJ
ejpam-5671	514	26	existence	existence	NOUN
ejpam-5671	514	27	of	of	ADP
ejpam-5671	514	28	solutions	solution	NOUN
ejpam-5671	514	29	for	for	ADP
ejpam-5671	514	30	a	a	DET
ejpam-5671	514	31	tripled	triple	VERB
ejpam-5671	514	32	problem	problem	NOUN
ejpam-5671	514	33	of	of	ADP
ejpam-5671	514	34	fractional	fractional	ADJ
ejpam-5671	514	35	hybrid	hybrid	ADJ
ejpam-5671	514	36	delay	delay	NOUN
ejpam-5671	514	37	differential	differential	ADJ
ejpam-5671	514	38	equations	equation	NOUN
ejpam-5671	514	39	.	.	PUNCT
ejpam-5671	515	1	symmetry	symmetry	PROPN
ejpam-5671	515	2	.	.	PUNCT
ejpam-5671	515	3	,	,	PUNCT
ejpam-5671	515	4	14:2579	14:2579	NUM
ejpam-5671	515	5	,	,	PUNCT
ejpam-5671	515	6	2022	2022	NUM
ejpam-5671	515	7	.	.	PUNCT
ejpam-5671	516	1	[	[	X
ejpam-5671	516	2	17	17	NUM
ejpam-5671	516	3	]	]	X
ejpam-5671	516	4	r	r	NOUN
ejpam-5671	516	5	hilfer	hilfer	NOUN
ejpam-5671	516	6	.	.	PUNCT
ejpam-5671	517	1	applications	application	NOUN
ejpam-5671	517	2	of	of	ADP
ejpam-5671	517	3	fractional	fractional	ADJ
ejpam-5671	517	4	calculus	calculus	NOUN
ejpam-5671	517	5	in	in	ADP
ejpam-5671	517	6	physics	physics	PROPN
ejpam-5671	517	7	.	.	PUNCT
ejpam-5671	518	1	world	world	PROPN
ejpam-5671	518	2	scientific	scientific	PROPN
ejpam-5671	518	3	,	,	PUNCT
ejpam-5671	518	4	2000	2000	NUM
ejpam-5671	518	5	.	.	PUNCT
ejpam-5671	519	1	[	[	X
ejpam-5671	519	2	18	18	NUM
ejpam-5671	519	3	]	]	PUNCT
ejpam-5671	519	4	a	a	DET
ejpam-5671	519	5	kilbas	kilbas	NOUN
ejpam-5671	519	6	,	,	PUNCT
ejpam-5671	519	7	o	o	PROPN
ejpam-5671	520	1	i	i	PRON
ejpam-5671	520	2	marichev	marichev	VERB
ejpam-5671	520	3	,	,	PUNCT
ejpam-5671	520	4	and	and	CCONJ
ejpam-5671	520	5	s	s	VERB
ejpam-5671	520	6	g	g	NOUN
ejpam-5671	520	7	samko	samko	NOUN
ejpam-5671	520	8	.	.	PUNCT
ejpam-5671	521	1	fractional	fractional	ADJ
ejpam-5671	521	2	integrals	integral	NOUN
ejpam-5671	521	3	and	and	CCONJ
ejpam-5671	521	4	derivatives	derivative	NOUN
ejpam-5671	521	5	(	(	PUNCT
ejpam-5671	521	6	theory	theory	NOUN
ejpam-5671	521	7	and	and	CCONJ
ejpam-5671	521	8	applications	application	NOUN
ejpam-5671	521	9	)	)	PUNCT
ejpam-5671	521	10	.	.	PUNCT
ejpam-5671	522	1	gordon	gordon	PROPN
ejpam-5671	522	2	and	and	CCONJ
ejpam-5671	522	3	breach	breach	PROPN
ejpam-5671	522	4	,	,	PUNCT
ejpam-5671	522	5	switzerland	switzerland	PROPN
ejpam-5671	522	6	,	,	PUNCT
ejpam-5671	522	7	1993	1993	NUM
ejpam-5671	522	8	.	.	PUNCT
ejpam-5671	523	1	[	[	X
ejpam-5671	523	2	19	19	NUM
ejpam-5671	523	3	]	]	X
ejpam-5671	523	4	a	a	DET
ejpam-5671	523	5	a	a	DET
ejpam-5671	523	6	kilbas	kilbas	NOUN
ejpam-5671	523	7	,	,	PUNCT
ejpam-5671	523	8	h	h	PROPN
ejpam-5671	523	9	m	m	PROPN
ejpam-5671	523	10	srivastava	srivastava	PROPN
ejpam-5671	523	11	,	,	PUNCT
ejpam-5671	523	12	and	and	CCONJ
ejpam-5671	523	13	j	j	PROPN
ejpam-5671	523	14	j	j	PROPN
ejpam-5671	523	15	trujillo	trujillo	PROPN
ejpam-5671	523	16	.	.	PUNCT
ejpam-5671	523	17	theory	theory	NOUN
ejpam-5671	523	18	and	and	CCONJ
ejpam-5671	523	19	applications	application	NOUN
ejpam-5671	523	20	of	of	ADP
ejpam-5671	523	21	fractional	fractional	ADJ
ejpam-5671	523	22	differential	differential	ADJ
ejpam-5671	523	23	equations	equation	NOUN
ejpam-5671	523	24	.	.	PUNCT
ejpam-5671	524	1	amsterdam	amsterdam	PROPN
ejpam-5671	524	2	:	:	PUNCT
ejpam-5671	524	3	elsevier	elsevier	PROPN
ejpam-5671	524	4	b.v	b.v	PROPN
ejpam-5671	524	5	,	,	PUNCT
ejpam-5671	524	6	2006	2006	NUM
ejpam-5671	524	7	.	.	PUNCT
ejpam-5671	525	1	[	[	X
ejpam-5671	525	2	20	20	NUM
ejpam-5671	525	3	]	]	SYM
ejpam-5671	525	4	v	v	X
ejpam-5671	525	5	lakshmikantham	lakshmikantham	NOUN
ejpam-5671	525	6	.	.	PUNCT
ejpam-5671	526	1	theory	theory	NOUN
ejpam-5671	526	2	of	of	ADP
ejpam-5671	526	3	fractional	fractional	ADJ
ejpam-5671	526	4	functional	functional	ADJ
ejpam-5671	526	5	differential	differential	NOUN
ejpam-5671	526	6	equations	equation	NOUN
ejpam-5671	526	7	.	.	PUNCT
ejpam-5671	527	1	nonlinear	nonlinear	ADJ
ejpam-5671	527	2	anal	anal	PROPN
ejpam-5671	527	3	.	.	PUNCT
ejpam-5671	528	1	theory	theory	NOUN
ejpam-5671	528	2	methods	method	NOUN
ejpam-5671	528	3	appl	appl	PROPN
ejpam-5671	528	4	.	.	PROPN
ejpam-5671	528	5	,	,	PUNCT
ejpam-5671	529	1	69(10):3337–3343	69(10):3337–3343	NOUN
ejpam-5671	529	2	,	,	PUNCT
ejpam-5671	529	3	2008	2008	NUM
ejpam-5671	529	4	.	.	PUNCT
ejpam-5671	530	1	[	[	X
ejpam-5671	530	2	21	21	NUM
ejpam-5671	530	3	]	]	X
ejpam-5671	530	4	s	s	PROPN
ejpam-5671	530	5	c	c	NOUN
ejpam-5671	530	6	lim	lim	PROPN
ejpam-5671	530	7	,	,	PUNCT
ejpam-5671	530	8	m	m	PROPN
ejpam-5671	530	9	li	li	PROPN
ejpam-5671	530	10	,	,	PUNCT
ejpam-5671	530	11	ming	ming	PROPN
ejpam-5671	530	12	,	,	PUNCT
ejpam-5671	530	13	and	and	CCONJ
ejpam-5671	531	1	l	l	NOUN
ejpam-5671	531	2	p	p	PROPN
ejpam-5671	531	3	teo	teo	PROPN
ejpam-5671	531	4	.	.	PUNCT
ejpam-5671	532	1	langevin	langevin	PROPN
ejpam-5671	532	2	equation	equation	NOUN
ejpam-5671	532	3	with	with	ADP
ejpam-5671	532	4	two	two	NUM
ejpam-5671	532	5	fractional	fractional	ADJ
ejpam-5671	532	6	orders	order	NOUN
ejpam-5671	532	7	.	.	PUNCT
ejpam-5671	533	1	phy	phy	NOUN
ejpam-5671	533	2	.	.	PUNCT
ejpam-5671	534	1	lett	lett	PROPN
ejpam-5671	534	2	.	.	PUNCT
ejpam-5671	535	1	a	a	DET
ejpam-5671	535	2	,	,	PUNCT
ejpam-5671	535	3	372(42):6309–6320	372(42):6309–6320	NUM
ejpam-5671	535	4	,	,	PUNCT
ejpam-5671	535	5	2008	2008	NUM
ejpam-5671	535	6	.	.	PUNCT
ejpam-5671	536	1	[	[	X
ejpam-5671	536	2	22	22	NUM
ejpam-5671	536	3	]	]	X
ejpam-5671	536	4	z	z	PROPN
ejpam-5671	536	5	lin	lin	PROPN
ejpam-5671	536	6	and	and	CCONJ
ejpam-5671	536	7	h	h	PROPN
ejpam-5671	536	8	wang	wang	PROPN
ejpam-5671	536	9	.	.	PUNCT
ejpam-5671	537	1	aerodynamic	aerodynamic	ADJ
ejpam-5671	537	2	heating	heating	NOUN
ejpam-5671	537	3	ground	ground	NOUN
ejpam-5671	537	4	simulation	simulation	NOUN
ejpam-5671	537	5	of	of	ADP
ejpam-5671	537	6	hypersonic	hypersonic	ADJ
ejpam-5671	537	7	vehicles	vehicle	NOUN
ejpam-5671	537	8	based	base	VERB
ejpam-5671	537	9	on	on	ADP
ejpam-5671	537	10	model	model	ADJ
ejpam-5671	537	11	-	-	PUNCT
ejpam-5671	537	12	free	free	ADJ
ejpam-5671	537	13	control	control	NOUN
ejpam-5671	537	14	using	use	VERB
ejpam-5671	537	15	super	super	ADJ
ejpam-5671	537	16	twisting	twist	VERB
ejpam-5671	537	17	nonlinear	nonlinear	ADJ
ejpam-5671	537	18	fractional	fractional	ADJ
ejpam-5671	537	19	order	order	NOUN
ejpam-5671	537	20	sliding	slide	VERB
ejpam-5671	537	21	mode	mode	NOUN
ejpam-5671	537	22	.	.	PUNCT
ejpam-5671	538	1	mathematics	mathematic	NOUN
ejpam-5671	538	2	,	,	PUNCT
ejpam-5671	538	3	10(10):1664	10(10):1664	NUM
ejpam-5671	538	4	,	,	PUNCT
ejpam-5671	538	5	2022	2022	NUM
ejpam-5671	538	6	.	.	PUNCT
ejpam-5671	539	1	[	[	X
ejpam-5671	539	2	23	23	NUM
ejpam-5671	539	3	]	]	PUNCT
ejpam-5671	539	4	x	x	X
ejpam-5671	539	5	lv	lv	PROPN
ejpam-5671	539	6	,	,	PUNCT
ejpam-5671	539	7	g	g	PROPN
ejpam-5671	539	8	zhang	zhang	PROPN
ejpam-5671	539	9	,	,	PUNCT
ejpam-5671	539	10	m	m	PROPN
ejpam-5671	539	11	zhu	zhu	PROPN
ejpam-5671	539	12	,	,	PUNCT
ejpam-5671	539	13	z	z	PROPN
ejpam-5671	539	14	shi	shi	PROPN
ejpam-5671	539	15	,	,	PUNCT
ejpam-5671	539	16	z	z	PROPN
ejpam-5671	539	17	bai	bai	PROPN
ejpam-5671	539	18	,	,	PUNCT
ejpam-5671	539	19	and	and	CCONJ
ejpam-5671	539	20	i	i	PRON
ejpam-5671	539	21	v	v	VERB
ejpam-5671	539	22	alexandrov	alexandrov	NOUN
ejpam-5671	539	23	.	.	PUNCT
ejpam-5671	540	1	modeling	modeling	NOUN
ejpam-5671	540	2	and	and	CCONJ
ejpam-5671	540	3	application	application	NOUN
ejpam-5671	540	4	of	of	ADP
ejpam-5671	540	5	fractional	fractional	ADJ
ejpam-5671	540	6	-	-	PUNCT
ejpam-5671	540	7	order	order	NOUN
ejpam-5671	540	8	economic	economic	ADJ
ejpam-5671	540	9	growth	growth	NOUN
ejpam-5671	540	10	model	model	NOUN
ejpam-5671	540	11	with	with	ADP
ejpam-5671	540	12	time	time	NOUN
ejpam-5671	540	13	delay	delay	NOUN
ejpam-5671	540	14	.	.	PUNCT
ejpam-5671	541	1	fractal	fractal	ADJ
ejpam-5671	541	2	fract	fract	PROPN
ejpam-5671	541	3	.	.	PUNCT
ejpam-5671	542	1	,	,	PUNCT
ejpam-5671	542	2	,	,	PUNCT
ejpam-5671	542	3	537):74	537):74	NOUN
ejpam-5671	542	4	,	,	PUNCT
ejpam-5671	542	5	2021	2021	NUM
ejpam-5671	542	6	.	.	PUNCT
ejpam-5671	543	1	[	[	X
ejpam-5671	543	2	24	24	NUM
ejpam-5671	543	3	]	]	SYM
ejpam-5671	543	4	b	b	X
ejpam-5671	543	5	maayah	maayah	NOUN
ejpam-5671	543	6	and	and	CCONJ
ejpam-5671	543	7	o	o	X
ejpam-5671	543	8	a	a	DET
ejpam-5671	543	9	arqub	arqub	NOUN
ejpam-5671	543	10	.	.	PUNCT
ejpam-5671	544	1	uncertain	uncertain	ADJ
ejpam-5671	544	2	m−fractional	m−fractional	ADJ
ejpam-5671	544	3	differential	differential	ADJ
ejpam-5671	544	4	problems	problem	NOUN
ejpam-5671	544	5	:	:	PUNCT
ejpam-5671	545	1	existence	existence	NOUN
ejpam-5671	545	2	,	,	PUNCT
ejpam-5671	545	3	uniqueness	uniqueness	NOUN
ejpam-5671	545	4	,	,	PUNCT
ejpam-5671	545	5	and	and	CCONJ
ejpam-5671	545	6	approximations	approximation	NOUN
ejpam-5671	545	7	using	use	VERB
ejpam-5671	545	8	hilbert	hilbert	NOUN
ejpam-5671	545	9	reproducing	reproducing	NOUN
ejpam-5671	545	10	technique	technique	NOUN
ejpam-5671	545	11	provisioner	provisioner	NOUN
ejpam-5671	545	12	with	with	ADP
ejpam-5671	545	13	the	the	DET
ejpam-5671	545	14	case	case	NOUN
ejpam-5671	545	15	application	application	NOUN
ejpam-5671	545	16	:	:	PUNCT
ejpam-5671	545	17	series	series	NOUN
ejpam-5671	545	18	resistor	resistor	NOUN
ejpam-5671	545	19	-	-	PUNCT
ejpam-5671	545	20	inductor	inductor	NOUN
ejpam-5671	545	21	circuit	circuit	NOUN
ejpam-5671	545	22	.	.	PUNCT
ejpam-5671	546	1	physica	physica	PROPN
ejpam-5671	546	2	scripta	scripta	PROPN
ejpam-5671	546	3	,	,	PUNCT
ejpam-5671	546	4	99(2):025220	99(2):025220	NOUN
ejpam-5671	546	5	,	,	PUNCT
ejpam-5671	546	6	2024	2024	NUM
ejpam-5671	546	7	.	.	PUNCT
ejpam-5671	547	1	[	[	X
ejpam-5671	547	2	25	25	NUM
ejpam-5671	547	3	]	]	X
ejpam-5671	547	4	w	w	PROPN
ejpam-5671	547	5	w	w	PROPN
ejpam-5671	547	6	mohammed	mohammed	PROPN
ejpam-5671	547	7	,	,	PUNCT
ejpam-5671	547	8	f	f	PROPN
ejpam-5671	547	9	m	m	PROPN
ejpam-5671	547	10	al	al	PROPN
ejpam-5671	547	11	-	-	PUNCT
ejpam-5671	547	12	askar	askar	PROPN
ejpam-5671	547	13	,	,	PUNCT
ejpam-5671	547	14	c	c	NOUN
ejpam-5671	547	15	cesarano	cesarano	ADJ
ejpam-5671	547	16	,	,	PUNCT
ejpam-5671	547	17	and	and	CCONJ
ejpam-5671	547	18	m	m	PROPN
ejpam-5671	547	19	el	el	PROPN
ejpam-5671	547	20	-	-	PUNCT
ejpam-5671	547	21	morshedy	morshedy	PROPN
ejpam-5671	547	22	.	.	PUNCT
ejpam-5671	548	1	solitary	solitary	ADJ
ejpam-5671	548	2	wave	wave	NOUN
ejpam-5671	548	3	solution	solution	NOUN
ejpam-5671	548	4	of	of	ADP
ejpam-5671	548	5	a	a	DET
ejpam-5671	548	6	generalized	generalize	VERB
ejpam-5671	548	7	fractional	fractional	ADJ
ejpam-5671	548	8	–	–	PUNCT
ejpam-5671	548	9	stochastic	stochastic	ADJ
ejpam-5671	548	10	nonlinear	nonlinear	ADJ
ejpam-5671	548	11	wave	wave	NOUN
ejpam-5671	548	12	equation	equation	NOUN
ejpam-5671	548	13	for	for	ADP
ejpam-5671	548	14	a	a	DET
ejpam-5671	548	15	liquid	liquid	ADJ
ejpam-5671	548	16	s.	s.	PROPN
ejpam-5671	548	17	f.	f.	PROPN
ejpam-5671	548	18	aljurbua	aljurbua	PROPN
ejpam-5671	548	19	,	,	PUNCT
ejpam-5671	548	20	h.	h.	PROPN
ejpam-5671	548	21	a.	a.	PROPN
ejpam-5671	548	22	hammad	hammad	PROPN
ejpam-5671	548	23	,	,	PUNCT
ejpam-5671	548	24	n.	n.	PROPN
ejpam-5671	548	25	b.	b.	PROPN
ejpam-5671	548	26	almutairi	almutairi	PROPN
ejpam-5671	548	27	/	/	SYM
ejpam-5671	548	28	eur	eur	PROPN
ejpam-5671	548	29	.	.	PUNCT
ejpam-5671	549	1	j.	j.	PROPN
ejpam-5671	549	2	pure	pure	PROPN
ejpam-5671	549	3	appl	appl	PROPN
ejpam-5671	549	4	.	.	PROPN
ejpam-5671	549	5	math	math	PROPN
ejpam-5671	549	6	,	,	PUNCT
ejpam-5671	549	7	18	18	NUM
ejpam-5671	549	8	(	(	PUNCT
ejpam-5671	549	9	1	1	NUM
ejpam-5671	549	10	)	)	PUNCT
ejpam-5671	549	11	(	(	PUNCT
ejpam-5671	549	12	2025	2025	NUM
ejpam-5671	549	13	)	)	PUNCT
ejpam-5671	549	14	,	,	PUNCT
ejpam-5671	549	15	5671	5671	NUM
ejpam-5671	549	16	18	18	NUM
ejpam-5671	549	17	of	of	ADP
ejpam-5671	549	18	18	18	NUM
ejpam-5671	549	19	with	with	ADP
ejpam-5671	549	20	gas	gas	NOUN
ejpam-5671	549	21	bubbles	bubble	NOUN
ejpam-5671	549	22	.	.	PUNCT
ejpam-5671	550	1	mathematics	mathematic	NOUN
ejpam-5671	550	2	,	,	PUNCT
ejpam-5671	550	3	11(7):1692	11(7):1692	NUM
ejpam-5671	550	4	,	,	PUNCT
ejpam-5671	550	5	2023	2023	NUM
ejpam-5671	550	6	.	.	PUNCT
ejpam-5671	551	1	[	[	X
ejpam-5671	551	2	26	26	NUM
ejpam-5671	551	3	]	]	SYM
ejpam-5671	551	4	s	s	VERB
ejpam-5671	551	5	okyere	okyere	PROPN
ejpam-5671	551	6	,	,	PUNCT
ejpam-5671	551	7	j	j	PROPN
ejpam-5671	551	8	ackora	ackora	PROPN
ejpam-5671	551	9	-	-	PUNCT
ejpam-5671	551	10	prah	prah	PROPN
ejpam-5671	551	11	,	,	PUNCT
ejpam-5671	551	12	k	k	PROPN
ejpam-5671	551	13	f	f	PROPN
ejpam-5671	551	14	darkwah	darkwah	PROPN
ejpam-5671	551	15	,	,	PUNCT
ejpam-5671	551	16	f	f	PROPN
ejpam-5671	551	17	tabi	tabi	NOUN
ejpam-5671	551	18	oduro	oduro	NOUN
ejpam-5671	551	19	,	,	PUNCT
ejpam-5671	551	20	and	and	CCONJ
ejpam-5671	551	21	e	e	PROPN
ejpam-5671	551	22	bonyah	bonyah	NOUN
ejpam-5671	551	23	.	.	PUNCT
ejpam-5671	552	1	fractional	fractional	ADJ
ejpam-5671	552	2	optimal	optimal	ADJ
ejpam-5671	552	3	control	control	NOUN
ejpam-5671	552	4	model	model	NOUN
ejpam-5671	552	5	of	of	ADP
ejpam-5671	552	6	sars	sar	NOUN
ejpam-5671	552	7	-	-	PUNCT
ejpam-5671	552	8	cov-2	cov-2	PART
ejpam-5671	552	9	(	(	PUNCT
ejpam-5671	552	10	covid-19	covid-19	PROPN
ejpam-5671	552	11	)	)	PUNCT
ejpam-5671	552	12	disease	disease	NOUN
ejpam-5671	552	13	in	in	ADP
ejpam-5671	552	14	ghana	ghana	PROPN
ejpam-5671	552	15	.	.	PUNCT
ejpam-5671	553	1	j.	j.	PROPN
ejpam-5671	553	2	math	math	PROPN
ejpam-5671	553	3	.	.	PUNCT
ejpam-5671	553	4	,	,	PUNCT
ejpam-5671	553	5	https://doi.org/10.1155/2023/3308529	https://doi.org/10.1155/2023/3308529	PROPN
ejpam-5671	553	6	.	.	PROPN
ejpam-5671	553	7	,	,	PUNCT
ejpam-5671	553	8	2023	2023	NUM
ejpam-5671	553	9	.	.	PUNCT
ejpam-5671	554	1	[	[	X
ejpam-5671	554	2	27	27	NUM
ejpam-5671	554	3	]	]	X
ejpam-5671	554	4	i	i	PRON
ejpam-5671	554	5	podlubny	podlubny	NOUN
ejpam-5671	554	6	.	.	PUNCT
ejpam-5671	555	1	fractional	fractional	ADJ
ejpam-5671	555	2	differential	differential	ADJ
ejpam-5671	555	3	equations	equation	NOUN
ejpam-5671	555	4	,	,	PUNCT
ejpam-5671	555	5	mathematics	mathematic	NOUN
ejpam-5671	555	6	in	in	ADP
ejpam-5671	555	7	science	science	NOUN
ejpam-5671	555	8	and	and	CCONJ
ejpam-5671	555	9	engineering	engineering	NOUN
ejpam-5671	555	10	.	.	PUNCT
ejpam-5671	556	1	academic	academic	ADJ
ejpam-5671	556	2	press	press	PROPN
ejpam-5671	556	3	new	new	PROPN
ejpam-5671	556	4	york	york	PROPN
ejpam-5671	556	5	,	,	PUNCT
ejpam-5671	556	6	1999	1999	NUM
ejpam-5671	556	7	.	.	PUNCT
ejpam-5671	557	1	[	[	X
ejpam-5671	557	2	28	28	NUM
ejpam-5671	557	3	]	]	X
ejpam-5671	557	4	k	k	PROPN
ejpam-5671	557	5	k	k	PROPN
ejpam-5671	557	6	saha	saha	PROPN
ejpam-5671	557	7	,	,	PUNCT
ejpam-5671	557	8	k	k	PROPN
ejpam-5671	557	9	kiran	kiran	PROPN
ejpam-5671	557	10	,	,	PUNCT
ejpam-5671	557	11	n	n	PRON
ejpam-5671	557	12	sukavanam	sukavanam	NOUN
ejpam-5671	557	13	,	,	PUNCT
ejpam-5671	557	14	and	and	CCONJ
ejpam-5671	557	15	s	s	VERB
ejpam-5671	557	16	pan	pan	PROPN
ejpam-5671	557	17	.	.	PROPN
ejpam-5671	557	18	existence	existence	NOUN
ejpam-5671	557	19	and	and	CCONJ
ejpam-5671	557	20	uniqueness	uniqueness	NOUN
ejpam-5671	557	21	of	of	ADP
ejpam-5671	557	22	solutions	solution	NOUN
ejpam-5671	557	23	to	to	ADP
ejpam-5671	557	24	fractional	fractional	ADJ
ejpam-5671	557	25	differential	differential	ADJ
ejpam-5671	557	26	equations	equation	NOUN
ejpam-5671	557	27	with	with	ADP
ejpam-5671	557	28	fractional	fractional	ADJ
ejpam-5671	557	29	boundary	boundary	ADJ
ejpam-5671	557	30	conditions	condition	NOUN
ejpam-5671	557	31	.	.	PUNCT
ejpam-5671	558	1	alex	alex	PROPN
ejpam-5671	558	2	.	.	PUNCT
ejpam-5671	559	1	eng	eng	PROPN
ejpam-5671	559	2	.	.	PUNCT
ejpam-5671	560	1	j.	j.	PROPN
ejpam-5671	560	2	,	,	PUNCT
ejpam-5671	560	3	72:147–155	72:147–155	NUM
ejpam-5671	560	4	,	,	PUNCT
ejpam-5671	560	5	2023	2023	NUM
ejpam-5671	560	6	.	.	PUNCT
ejpam-5671	561	1	[	[	X
ejpam-5671	561	2	29	29	NUM
ejpam-5671	561	3	]	]	X
ejpam-5671	561	4	d	d	NOUN
ejpam-5671	561	5	r	r	NOUN
ejpam-5671	561	6	smart	smart	ADJ
ejpam-5671	561	7	.	.	PUNCT
ejpam-5671	562	1	fixed	fix	VERB
ejpam-5671	562	2	point	point	NOUN
ejpam-5671	562	3	theorems	theorem	NOUN
ejpam-5671	562	4	.	.	PUNCT
ejpam-5671	562	5	cup	cup	PROPN
ejpam-5671	562	6	archive	archive	NOUN
ejpam-5671	562	7	66	66	NUM
ejpam-5671	562	8	,	,	PUNCT
ejpam-5671	562	9	1980	1980	NUM
ejpam-5671	562	10	.	.	PUNCT
ejpam-5671	563	1	[	[	X
ejpam-5671	563	2	30	30	NUM
ejpam-5671	563	3	]	]	X
ejpam-5671	563	4	m	m	PROPN
ejpam-5671	563	5	yamamoto	yamamoto	NOUN
ejpam-5671	563	6	.	.	PUNCT
ejpam-5671	563	7	fractional	fractional	ADJ
ejpam-5671	563	8	calculus	calculus	NOUN
ejpam-5671	563	9	and	and	CCONJ
ejpam-5671	563	10	time	time	NOUN
ejpam-5671	563	11	-	-	PUNCT
ejpam-5671	563	12	fractional	fractional	ADJ
ejpam-5671	563	13	differential	differential	ADJ
ejpam-5671	563	14	equations	equation	NOUN
ejpam-5671	563	15	:	:	PUNCT
ejpam-5671	563	16	revisit	revisit	NOUN
ejpam-5671	563	17	and	and	CCONJ
ejpam-5671	563	18	construction	construction	NOUN
ejpam-5671	563	19	of	of	ADP
ejpam-5671	563	20	a	a	DET
ejpam-5671	563	21	theory	theory	NOUN
ejpam-5671	563	22	.	.	PUNCT
ejpam-5671	564	1	mathematics	mathematic	NOUN
ejpam-5671	564	2	,	,	PUNCT
ejpam-5671	564	3	10(5):698	10(5):698	NUM
ejpam-5671	564	4	,	,	PUNCT
ejpam-5671	564	5	2022	2022	NUM
ejpam-5671	564	6	.	.	PUNCT