id	sid	tid	token	lemma	pos
ejpam-6388	1	1	european	european	PROPN
ejpam-6388	1	2	journal	journal	PROPN
ejpam-6388	1	3	of	of	ADP
ejpam-6388	1	4	pure	pure	ADJ
ejpam-6388	1	5	and	and	CCONJ
ejpam-6388	1	6	applied	applied	ADJ
ejpam-6388	1	7	mathematics	mathematic	NOUN
ejpam-6388	1	8	2025	2025	NUM
ejpam-6388	1	9	,	,	PUNCT
ejpam-6388	1	10	vol	vol	NOUN
ejpam-6388	1	11	.	.	PROPN
ejpam-6388	1	12	18	18	NUM
ejpam-6388	1	13	,	,	PUNCT
ejpam-6388	1	14	issue	issue	NOUN
ejpam-6388	1	15	4	4	NUM
ejpam-6388	1	16	,	,	PUNCT
ejpam-6388	1	17	article	article	NOUN
ejpam-6388	1	18	number	number	NOUN
ejpam-6388	1	19	6388	6388	NUM
ejpam-6388	1	20	issn	issn	PROPN
ejpam-6388	1	21	1307	1307	NUM
ejpam-6388	1	22	-	-	SYM
ejpam-6388	1	23	5543	5543	NUM
ejpam-6388	1	24	–	–	PUNCT
ejpam-6388	1	25	ejpam.com	ejpam.com	X
ejpam-6388	1	26	published	publish	VERB
ejpam-6388	1	27	by	by	ADP
ejpam-6388	1	28	new	new	PROPN
ejpam-6388	1	29	york	york	PROPN
ejpam-6388	1	30	business	business	PROPN
ejpam-6388	1	31	global	global	ADJ
ejpam-6388	1	32	qualitative	qualitative	ADJ
ejpam-6388	1	33	analysis	analysis	NOUN
ejpam-6388	1	34	and	and	CCONJ
ejpam-6388	1	35	simulation	simulation	NOUN
ejpam-6388	1	36	of	of	ADP
ejpam-6388	1	37	fractional	fractional	ADJ
ejpam-6388	1	38	hybrid	hybrid	ADJ
ejpam-6388	1	39	boundary	boundary	ADJ
ejpam-6388	1	40	value	value	NOUN
ejpam-6388	1	41	problems	problem	NOUN
ejpam-6388	1	42	in	in	ADP
ejpam-6388	1	43	orthogonal	orthogonal	ADJ
ejpam-6388	1	44	cone	cone	NOUN
ejpam-6388	1	45	metric	metric	NOUN
ejpam-6388	1	46	spaces	space	NOUN
ejpam-6388	1	47	dumitru	dumitru	PROPN
ejpam-6388	1	48	baleanu1,2	baleanu1,2	PROPN
ejpam-6388	1	49	,	,	PUNCT
ejpam-6388	1	50	mahammad	mahammad	PROPN
ejpam-6388	1	51	khuddush3	khuddush3	PROPN
ejpam-6388	1	52	,	,	PUNCT
ejpam-6388	1	53	b.m.b	b.m.b	ADJ
ejpam-6388	1	54	.	.	PUNCT
ejpam-6388	2	1	krushna4	krushna4	PROPN
ejpam-6388	2	2	,	,	PUNCT
ejpam-6388	2	3	sanket	sanket	VERB
ejpam-6388	2	4	tikare5,∗	tikare5,∗	ADJ
ejpam-6388	2	5	1	1	NUM
ejpam-6388	2	6	department	department	NOUN
ejpam-6388	2	7	of	of	ADP
ejpam-6388	2	8	computer	computer	NOUN
ejpam-6388	2	9	science	science	NOUN
ejpam-6388	2	10	and	and	CCONJ
ejpam-6388	2	11	mathematics	mathematic	NOUN
ejpam-6388	2	12	,	,	PUNCT
ejpam-6388	2	13	lebanese	lebanese	ADJ
ejpam-6388	2	14	american	american	PROPN
ejpam-6388	2	15	university	university	PROPN
ejpam-6388	2	16	,	,	PUNCT
ejpam-6388	2	17	beirut	beirut	PROPN
ejpam-6388	2	18	,	,	PUNCT
ejpam-6388	2	19	1102	1102	NUM
ejpam-6388	2	20	2801	2801	NUM
ejpam-6388	2	21	,	,	PUNCT
ejpam-6388	2	22	lebanon	lebanon	PROPN
ejpam-6388	2	23	2	2	NUM
ejpam-6388	2	24	institute	institute	PROPN
ejpam-6388	2	25	of	of	ADP
ejpam-6388	2	26	space	space	NOUN
ejpam-6388	2	27	sciences	sciences	PROPN
ejpam-6388	2	28	-	-	PUNCT
ejpam-6388	2	29	subsidiary	subsidiary	NOUN
ejpam-6388	2	30	of	of	ADP
ejpam-6388	2	31	inflpr	inflpr	PROPN
ejpam-6388	2	32	,	,	PUNCT
ejpam-6388	2	33	magurele	magurele	PROPN
ejpam-6388	2	34	,	,	PUNCT
ejpam-6388	2	35	bucharest	buchar	ADJ
ejpam-6388	2	36	,	,	PUNCT
ejpam-6388	2	37	077125	077125	NUM
ejpam-6388	2	38	,	,	PUNCT
ejpam-6388	2	39	romania	romania	PROPN
ejpam-6388	2	40	3	3	NUM
ejpam-6388	2	41	applied	apply	VERB
ejpam-6388	2	42	nonlinear	nonlinear	ADJ
ejpam-6388	2	43	science	science	NOUN
ejpam-6388	2	44	lab(ansl	lab(ansl	NOUN
ejpam-6388	2	45	)	)	PUNCT
ejpam-6388	2	46	,	,	PUNCT
ejpam-6388	2	47	anand	anand	PROPN
ejpam-6388	2	48	international	international	PROPN
ejpam-6388	2	49	college	college	PROPN
ejpam-6388	2	50	of	of	ADP
ejpam-6388	2	51	engineering	engineering	PROPN
ejpam-6388	2	52	,	,	PUNCT
ejpam-6388	2	53	jaipur	jaipur	PROPN
ejpam-6388	2	54	303012	303012	NUM
ejpam-6388	2	55	,	,	PUNCT
ejpam-6388	2	56	india	india	PROPN
ejpam-6388	2	57	4	4	NUM
ejpam-6388	2	58	department	department	NOUN
ejpam-6388	2	59	of	of	ADP
ejpam-6388	2	60	mathematics	mathematic	NOUN
ejpam-6388	2	61	,	,	PUNCT
ejpam-6388	2	62	mvgr	mvgr	PROPN
ejpam-6388	2	63	college	college	PROPN
ejpam-6388	2	64	of	of	ADP
ejpam-6388	2	65	engineering	engineering	NOUN
ejpam-6388	2	66	(	(	PUNCT
ejpam-6388	2	67	autonomous	autonomous	ADJ
ejpam-6388	2	68	)	)	PUNCT
ejpam-6388	2	69	,	,	PUNCT
ejpam-6388	2	70	vizianagaram	vizianagaram	PROPN
ejpam-6388	2	71	,	,	PUNCT
ejpam-6388	2	72	535	535	NUM
ejpam-6388	2	73	005	005	NUM
ejpam-6388	2	74	,	,	PUNCT
ejpam-6388	2	75	andhra	andhra	PROPN
ejpam-6388	2	76	pradesh	pradesh	PROPN
ejpam-6388	2	77	,	,	PUNCT
ejpam-6388	2	78	india	india	PROPN
ejpam-6388	2	79	5	5	NUM
ejpam-6388	2	80	department	department	NOUN
ejpam-6388	2	81	of	of	ADP
ejpam-6388	2	82	mathematics	mathematic	NOUN
ejpam-6388	2	83	,	,	PUNCT
ejpam-6388	2	84	ramniranjan	ramniranjan	ADJ
ejpam-6388	2	85	jhunjhunwala	jhunjhunwala	PROPN
ejpam-6388	2	86	college	college	PROPN
ejpam-6388	2	87	,	,	PUNCT
ejpam-6388	2	88	mumbai	mumbai	PROPN
ejpam-6388	2	89	,	,	PUNCT
ejpam-6388	2	90	400	400	NUM
ejpam-6388	2	91	086	086	NUM
ejpam-6388	2	92	,	,	PUNCT
ejpam-6388	2	93	maharashtra	maharashtra	PROPN
ejpam-6388	2	94	,	,	PUNCT
ejpam-6388	2	95	india	india	PROPN
ejpam-6388	2	96	abstract	abstract	NOUN
ejpam-6388	2	97	.	.	PUNCT
ejpam-6388	3	1	this	this	DET
ejpam-6388	3	2	article	article	NOUN
ejpam-6388	3	3	aims	aim	VERB
ejpam-6388	3	4	to	to	PART
ejpam-6388	3	5	advance	advance	VERB
ejpam-6388	3	6	the	the	DET
ejpam-6388	3	7	qualitative	qualitative	ADJ
ejpam-6388	3	8	analysis	analysis	NOUN
ejpam-6388	3	9	of	of	ADP
ejpam-6388	3	10	fractional	fractional	ADJ
ejpam-6388	3	11	hybrid	hybrid	ADJ
ejpam-6388	3	12	boundary	boundary	ADJ
ejpam-6388	3	13	value	value	NOUN
ejpam-6388	3	14	problems	problem	NOUN
ejpam-6388	3	15	(	(	PUNCT
ejpam-6388	3	16	fhbvps	fhbvps	PROPN
ejpam-6388	3	17	)	)	PUNCT
ejpam-6388	3	18	involving	involve	VERB
ejpam-6388	3	19	riemann	riemann	PROPN
ejpam-6388	3	20	–	–	PUNCT
ejpam-6388	3	21	liouville	liouville	VERB
ejpam-6388	3	22	fractional	fractional	ADJ
ejpam-6388	3	23	derivatives	derivative	NOUN
ejpam-6388	3	24	of	of	ADP
ejpam-6388	3	25	order	order	NOUN
ejpam-6388	3	26	1	1	NUM
ejpam-6388	3	27	<	<	X
ejpam-6388	3	28	y	y	PROPN
ejpam-6388	3	29	≤	≤	NUM
ejpam-6388	3	30	2	2	NUM
ejpam-6388	3	31	,	,	PUNCT
ejpam-6388	3	32	with	with	ADP
ejpam-6388	3	33	a	a	DET
ejpam-6388	3	34	focus	focus	NOUN
ejpam-6388	3	35	on	on	ADP
ejpam-6388	3	36	establishing	establish	VERB
ejpam-6388	3	37	the	the	DET
ejpam-6388	3	38	existence	existence	NOUN
ejpam-6388	3	39	,	,	PUNCT
ejpam-6388	3	40	uniqueness	uniqueness	NOUN
ejpam-6388	3	41	,	,	PUNCT
ejpam-6388	3	42	and	and	CCONJ
ejpam-6388	3	43	stability	stability	NOUN
ejpam-6388	3	44	of	of	ADP
ejpam-6388	3	45	solutions	solution	NOUN
ejpam-6388	3	46	in	in	ADP
ejpam-6388	3	47	a	a	DET
ejpam-6388	3	48	novel	novel	ADJ
ejpam-6388	3	49	mathematical	mathematical	ADJ
ejpam-6388	3	50	framework	framework	NOUN
ejpam-6388	3	51	.	.	PUNCT
ejpam-6388	4	1	by	by	ADP
ejpam-6388	4	2	employing	employ	VERB
ejpam-6388	4	3	the	the	DET
ejpam-6388	4	4	extended	extended	ADJ
ejpam-6388	4	5	banach	banach	ADV
ejpam-6388	4	6	fixed	fix	VERB
ejpam-6388	4	7	point	point	NOUN
ejpam-6388	4	8	theorem	theorem	VERB
ejpam-6388	4	9	within	within	ADP
ejpam-6388	4	10	orthogonal	orthogonal	ADJ
ejpam-6388	4	11	cone	cone	NOUN
ejpam-6388	4	12	metric	metric	ADJ
ejpam-6388	4	13	spaces	space	NOUN
ejpam-6388	4	14	,	,	PUNCT
ejpam-6388	4	15	we	we	PRON
ejpam-6388	4	16	prove	prove	VERB
ejpam-6388	4	17	the	the	DET
ejpam-6388	4	18	existence	existence	NOUN
ejpam-6388	4	19	and	and	CCONJ
ejpam-6388	4	20	uniqueness	uniqueness	NOUN
ejpam-6388	4	21	of	of	ADP
ejpam-6388	4	22	solutions	solution	NOUN
ejpam-6388	4	23	for	for	ADP
ejpam-6388	4	24	fhbvps	fhbvps	PROPN
ejpam-6388	4	25	,	,	PUNCT
ejpam-6388	4	26	generalizing	generalize	VERB
ejpam-6388	4	27	prior	prior	ADJ
ejpam-6388	4	28	results	result	NOUN
ejpam-6388	4	29	in	in	ADP
ejpam-6388	4	30	standard	standard	ADJ
ejpam-6388	4	31	metric	metric	ADJ
ejpam-6388	4	32	spaces	space	NOUN
ejpam-6388	4	33	and	and	CCONJ
ejpam-6388	4	34	banach	banach	NOUN
ejpam-6388	4	35	algebras	algebras	X
ejpam-6388	5	1	[	[	X
ejpam-6388	5	2	1	1	NUM
ejpam-6388	5	3	,	,	PUNCT
ejpam-6388	5	4	2	2	NUM
ejpam-6388	5	5	]	]	PUNCT
ejpam-6388	5	6	.	.	PUNCT
ejpam-6388	6	1	additionally	additionally	ADV
ejpam-6388	6	2	,	,	PUNCT
ejpam-6388	6	3	we	we	PRON
ejpam-6388	6	4	investigate	investigate	VERB
ejpam-6388	6	5	the	the	DET
ejpam-6388	6	6	hyers	hyer	NOUN
ejpam-6388	6	7	–	–	PUNCT
ejpam-6388	6	8	ulam	ulam	X
ejpam-6388	6	9	stability	stability	NOUN
ejpam-6388	6	10	to	to	PART
ejpam-6388	6	11	ensure	ensure	VERB
ejpam-6388	6	12	solution	solution	NOUN
ejpam-6388	6	13	robustness	robustness	NOUN
ejpam-6388	6	14	against	against	ADP
ejpam-6388	6	15	perturbations	perturbation	NOUN
ejpam-6388	6	16	,	,	PUNCT
ejpam-6388	6	17	addressing	address	VERB
ejpam-6388	6	18	common	common	ADJ
ejpam-6388	6	19	methodological	methodological	ADJ
ejpam-6388	6	20	errors	error	NOUN
ejpam-6388	6	21	in	in	ADP
ejpam-6388	6	22	prior	prior	ADJ
ejpam-6388	6	23	studies	study	NOUN
ejpam-6388	6	24	[	[	X
ejpam-6388	6	25	3	3	NUM
ejpam-6388	6	26	]	]	PUNCT
ejpam-6388	6	27	.	.	PUNCT
ejpam-6388	7	1	numerical	numerical	PROPN
ejpam-6388	7	2	simulations	simulation	NOUN
ejpam-6388	7	3	complement	complement	VERB
ejpam-6388	7	4	our	our	PRON
ejpam-6388	7	5	theoretical	theoretical	ADJ
ejpam-6388	7	6	findings	finding	NOUN
ejpam-6388	7	7	,	,	PUNCT
ejpam-6388	7	8	demonstrating	demonstrate	VERB
ejpam-6388	7	9	the	the	DET
ejpam-6388	7	10	impact	impact	NOUN
ejpam-6388	7	11	of	of	ADP
ejpam-6388	7	12	fractional	fractional	ADJ
ejpam-6388	7	13	order	order	NOUN
ejpam-6388	7	14	and	and	CCONJ
ejpam-6388	7	15	nonlinear	nonlinear	ADJ
ejpam-6388	7	16	terms	term	NOUN
ejpam-6388	7	17	on	on	ADP
ejpam-6388	7	18	solution	solution	NOUN
ejpam-6388	7	19	behavior	behavior	NOUN
ejpam-6388	7	20	.	.	PUNCT
ejpam-6388	8	1	these	these	DET
ejpam-6388	8	2	results	result	NOUN
ejpam-6388	8	3	provide	provide	VERB
ejpam-6388	8	4	new	new	ADJ
ejpam-6388	8	5	insights	insight	NOUN
ejpam-6388	8	6	into	into	ADP
ejpam-6388	8	7	modeling	model	VERB
ejpam-6388	8	8	complex	complex	ADJ
ejpam-6388	8	9	dynamic	dynamic	ADJ
ejpam-6388	8	10	systems	system	NOUN
ejpam-6388	8	11	with	with	ADP
ejpam-6388	8	12	nonlocal	nonlocal	ADJ
ejpam-6388	8	13	and	and	CCONJ
ejpam-6388	8	14	memory	memory	NOUN
ejpam-6388	8	15	-	-	PUNCT
ejpam-6388	8	16	dependent	dependent	ADJ
ejpam-6388	8	17	behaviors	behavior	NOUN
ejpam-6388	8	18	,	,	PUNCT
ejpam-6388	8	19	applicable	applicable	ADJ
ejpam-6388	8	20	to	to	ADP
ejpam-6388	8	21	fields	field	NOUN
ejpam-6388	8	22	such	such	ADJ
ejpam-6388	8	23	as	as	ADP
ejpam-6388	8	24	viscoelasticity	viscoelasticity	NOUN
ejpam-6388	8	25	,	,	PUNCT
ejpam-6388	8	26	fluid	fluid	ADJ
ejpam-6388	8	27	dynamics	dynamic	NOUN
ejpam-6388	8	28	,	,	PUNCT
ejpam-6388	8	29	and	and	CCONJ
ejpam-6388	8	30	biological	biological	ADJ
ejpam-6388	8	31	modeling	modeling	NOUN
ejpam-6388	8	32	.	.	PUNCT
ejpam-6388	9	1	2020	2020	NUM
ejpam-6388	9	2	mathematics	mathematic	NOUN
ejpam-6388	9	3	subject	subject	NOUN
ejpam-6388	9	4	classifications	classification	NOUN
ejpam-6388	9	5	:	:	PUNCT
ejpam-6388	9	6	34a08	34a08	NUM
ejpam-6388	9	7	,	,	PUNCT
ejpam-6388	9	8	47h10	47h10	NUM
ejpam-6388	9	9	,	,	PUNCT
ejpam-6388	9	10	54h25	54h25	NUM
ejpam-6388	9	11	key	key	ADJ
ejpam-6388	9	12	words	word	NOUN
ejpam-6388	9	13	and	and	CCONJ
ejpam-6388	9	14	phrases	phrase	NOUN
ejpam-6388	9	15	:	:	PUNCT
ejpam-6388	9	16	existence	existence	NOUN
ejpam-6388	9	17	and	and	CCONJ
ejpam-6388	9	18	uniqueness	uniqueness	NOUN
ejpam-6388	9	19	,	,	PUNCT
ejpam-6388	9	20	fractional	fractional	ADJ
ejpam-6388	9	21	derivative	derivative	NOUN
ejpam-6388	9	22	,	,	PUNCT
ejpam-6388	9	23	hyers	hyer	NOUN
ejpam-6388	9	24	–	–	PUNCT
ejpam-6388	9	25	ulam	ulam	X
ejpam-6388	9	26	stability	stability	NOUN
ejpam-6388	9	27	,	,	PUNCT
ejpam-6388	9	28	hybrid	hybrid	ADJ
ejpam-6388	9	29	boundary	boundary	ADJ
ejpam-6388	9	30	value	value	NOUN
ejpam-6388	9	31	problem	problem	NOUN
ejpam-6388	9	32	,	,	PUNCT
ejpam-6388	9	33	orthogonal	orthogonal	ADJ
ejpam-6388	9	34	cone	cone	NOUN
ejpam-6388	9	35	metric	metric	ADJ
ejpam-6388	9	36	space	space	NOUN
ejpam-6388	9	37	∗corresponding	∗corresponde	VERB
ejpam-6388	9	38	author	author	NOUN
ejpam-6388	9	39	.	.	PUNCT
ejpam-6388	10	1	doi	doi	NOUN
ejpam-6388	10	2	:	:	PUNCT
ejpam-6388	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6388	https://doi.org/10.29020/nybg.ejpam.v18i4.6388	PROPN
ejpam-6388	10	4	email	email	NOUN
ejpam-6388	10	5	addresses	address	VERB
ejpam-6388	10	6	:	:	PUNCT
ejpam-6388	10	7	dumitru.baleanu@lau.edu.lb	dumitru.baleanu@lau.edu.lb	PROPN
ejpam-6388	10	8	(	(	PUNCT
ejpam-6388	10	9	d.	d.	PROPN
ejpam-6388	10	10	baleanu	baleanu	PROPN
ejpam-6388	10	11	)	)	PUNCT
ejpam-6388	10	12	,	,	PUNCT
ejpam-6388	10	13	khuddush89@gmail.com	khuddush89@gmail.com	PROPN
ejpam-6388	10	14	(	(	PUNCT
ejpam-6388	10	15	m.	m.	NOUN
ejpam-6388	10	16	khuddush	khuddush	PROPN
ejpam-6388	10	17	)	)	PUNCT
ejpam-6388	10	18	,	,	PUNCT
ejpam-6388	10	19	muraleebalu@yahoo.com	muraleebalu@yahoo.com	X
ejpam-6388	10	20	(	(	PUNCT
ejpam-6388	10	21	b.m.b	b.m.b	ADJ
ejpam-6388	10	22	.	.	PUNCT
ejpam-6388	10	23	krushna	krushna	PROPN
ejpam-6388	10	24	)	)	PUNCT
ejpam-6388	10	25	,	,	PUNCT
ejpam-6388	10	26	sankettikare@rjcollege.edu.in	sankettikare@rjcollege.edu.in	NOUN
ejpam-6388	10	27	(	(	PUNCT
ejpam-6388	10	28	s.	s.	PROPN
ejpam-6388	10	29	tikare	tikare	PROPN
ejpam-6388	10	30	)	)	PUNCT
ejpam-6388	10	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6388	10	32	1	1	NUM
ejpam-6388	10	33	copyright	copyright	NOUN
ejpam-6388	10	34	:	:	PUNCT
ejpam-6388	11	1	©	©	PROPN
ejpam-6388	11	2	2025	2025	NUM
ejpam-6388	11	3	the	the	DET
ejpam-6388	11	4	author(s	author(s	NOUN
ejpam-6388	11	5	)	)	PUNCT
ejpam-6388	11	6	.	.	PUNCT
ejpam-6388	12	1	(	(	PUNCT
ejpam-6388	12	2	cc	cc	NOUN
ejpam-6388	12	3	by	by	ADP
ejpam-6388	12	4	-	-	PUNCT
ejpam-6388	12	5	nc	nc	PROPN
ejpam-6388	12	6	4.0	4.0	NUM
ejpam-6388	12	7	)	)	PUNCT
ejpam-6388	12	8	d.	d.	PROPN
ejpam-6388	12	9	baleanu	baleanu	PROPN
ejpam-6388	12	10	et	et	PROPN
ejpam-6388	12	11	al	al	PROPN
ejpam-6388	12	12	.	.	PUNCT
ejpam-6388	12	13	/	/	SYM
ejpam-6388	12	14	eur	eur	PROPN
ejpam-6388	12	15	.	.	PUNCT
ejpam-6388	13	1	j.	j.	PROPN
ejpam-6388	13	2	pure	pure	PROPN
ejpam-6388	13	3	appl	appl	PROPN
ejpam-6388	13	4	.	.	PROPN
ejpam-6388	13	5	math	math	PROPN
ejpam-6388	13	6	,	,	PUNCT
ejpam-6388	13	7	18	18	NUM
ejpam-6388	13	8	(	(	PUNCT
ejpam-6388	13	9	4	4	NUM
ejpam-6388	13	10	)	)	PUNCT
ejpam-6388	13	11	(	(	PUNCT
ejpam-6388	13	12	2025	2025	NUM
ejpam-6388	13	13	)	)	PUNCT
ejpam-6388	13	14	,	,	PUNCT
ejpam-6388	13	15	6388	6388	NUM
ejpam-6388	13	16	2	2	NUM
ejpam-6388	13	17	of	of	ADP
ejpam-6388	13	18	31	31	NUM
ejpam-6388	13	19	1	1	NUM
ejpam-6388	13	20	.	.	PUNCT
ejpam-6388	14	1	introduction	introduction	NOUN
ejpam-6388	14	2	differential	differential	NOUN
ejpam-6388	14	3	equations	equation	NOUN
ejpam-6388	14	4	(	(	PUNCT
ejpam-6388	14	5	deqs	deq	NOUN
ejpam-6388	14	6	)	)	PUNCT
ejpam-6388	14	7	have	have	AUX
ejpam-6388	14	8	long	long	ADV
ejpam-6388	14	9	been	be	AUX
ejpam-6388	14	10	a	a	DET
ejpam-6388	14	11	cornerstone	cornerstone	NOUN
ejpam-6388	14	12	of	of	ADP
ejpam-6388	14	13	scientific	scientific	ADJ
ejpam-6388	14	14	and	and	CCONJ
ejpam-6388	14	15	engineering	engineering	NOUN
ejpam-6388	14	16	disciplines	discipline	NOUN
ejpam-6388	14	17	due	due	ADP
ejpam-6388	14	18	to	to	ADP
ejpam-6388	14	19	their	their	PRON
ejpam-6388	14	20	ability	ability	NOUN
ejpam-6388	14	21	to	to	PART
ejpam-6388	14	22	model	model	VERB
ejpam-6388	14	23	dynamic	dynamic	ADJ
ejpam-6388	14	24	systems	system	NOUN
ejpam-6388	14	25	and	and	CCONJ
ejpam-6388	14	26	processes	process	NOUN
ejpam-6388	14	27	.	.	PUNCT
ejpam-6388	15	1	however	however	ADV
ejpam-6388	15	2	,	,	PUNCT
ejpam-6388	15	3	classical	classical	ADJ
ejpam-6388	15	4	deqs	deq	NOUN
ejpam-6388	15	5	often	often	ADV
ejpam-6388	15	6	fail	fail	VERB
ejpam-6388	15	7	to	to	PART
ejpam-6388	15	8	capture	capture	VERB
ejpam-6388	15	9	phenomena	phenomenon	NOUN
ejpam-6388	15	10	with	with	ADP
ejpam-6388	15	11	memory	memory	NOUN
ejpam-6388	15	12	effects	effect	NOUN
ejpam-6388	15	13	or	or	CCONJ
ejpam-6388	15	14	nonlocal	nonlocal	ADJ
ejpam-6388	15	15	behavior	behavior	NOUN
ejpam-6388	15	16	.	.	PUNCT
ejpam-6388	16	1	fractional	fractional	ADJ
ejpam-6388	16	2	differential	differential	ADJ
ejpam-6388	16	3	equations	equation	NOUN
ejpam-6388	16	4	(	(	PUNCT
ejpam-6388	16	5	fdeqs	fdeq	NOUN
ejpam-6388	16	6	)	)	PUNCT
ejpam-6388	16	7	,	,	PUNCT
ejpam-6388	16	8	which	which	PRON
ejpam-6388	16	9	extend	extend	VERB
ejpam-6388	16	10	classical	classical	ADJ
ejpam-6388	16	11	deqs	deq	NOUN
ejpam-6388	16	12	by	by	ADP
ejpam-6388	16	13	incorporating	incorporate	VERB
ejpam-6388	16	14	derivatives	derivative	NOUN
ejpam-6388	16	15	of	of	ADP
ejpam-6388	16	16	arbitrary	arbitrary	ADJ
ejpam-6388	16	17	order	order	NOUN
ejpam-6388	16	18	,	,	PUNCT
ejpam-6388	16	19	address	address	VERB
ejpam-6388	16	20	these	these	DET
ejpam-6388	16	21	limitations	limitation	NOUN
ejpam-6388	16	22	by	by	ADP
ejpam-6388	16	23	modeling	model	VERB
ejpam-6388	16	24	multiscale	multiscale	ADJ
ejpam-6388	16	25	dynamics	dynamic	NOUN
ejpam-6388	16	26	,	,	PUNCT
ejpam-6388	16	27	making	make	VERB
ejpam-6388	16	28	them	they	PRON
ejpam-6388	16	29	particularly	particularly	ADV
ejpam-6388	16	30	suitable	suitable	ADJ
ejpam-6388	16	31	for	for	ADP
ejpam-6388	16	32	applications	application	NOUN
ejpam-6388	16	33	in	in	ADP
ejpam-6388	16	34	viscoelasticity	viscoelasticity	NOUN
ejpam-6388	16	35	[	[	X
ejpam-6388	16	36	4	4	NUM
ejpam-6388	16	37	]	]	PUNCT
ejpam-6388	16	38	,	,	PUNCT
ejpam-6388	16	39	fluid	fluid	ADJ
ejpam-6388	16	40	dynamics	dynamic	NOUN
ejpam-6388	16	41	[	[	X
ejpam-6388	16	42	5	5	NUM
ejpam-6388	16	43	]	]	PUNCT
ejpam-6388	16	44	,	,	PUNCT
ejpam-6388	16	45	and	and	CCONJ
ejpam-6388	16	46	biological	biological	ADJ
ejpam-6388	16	47	modeling	modeling	NOUN
ejpam-6388	17	1	[	[	X
ejpam-6388	17	2	6–11	6–11	NOUN
ejpam-6388	17	3	]	]	PUNCT
ejpam-6388	17	4	.	.	PUNCT
ejpam-6388	18	1	the	the	DET
ejpam-6388	18	2	study	study	NOUN
ejpam-6388	18	3	of	of	ADP
ejpam-6388	18	4	fractional	fractional	ADJ
ejpam-6388	18	5	calculus	calculus	NOUN
ejpam-6388	18	6	began	begin	VERB
ejpam-6388	18	7	in	in	ADP
ejpam-6388	18	8	the	the	DET
ejpam-6388	18	9	17th	17th	ADJ
ejpam-6388	18	10	century	century	NOUN
ejpam-6388	18	11	with	with	ADP
ejpam-6388	18	12	discussions	discussion	NOUN
ejpam-6388	18	13	by	by	ADP
ejpam-6388	18	14	leibniz	leibniz	NOUN
ejpam-6388	18	15	and	and	CCONJ
ejpam-6388	18	16	l’hôpital	l’hôpital	ADJ
ejpam-6388	18	17	on	on	ADP
ejpam-6388	18	18	noninteger	noninteger	NOUN
ejpam-6388	18	19	order	order	NOUN
ejpam-6388	18	20	derivatives	derivative	NOUN
ejpam-6388	18	21	,	,	PUNCT
ejpam-6388	18	22	followed	follow	VERB
ejpam-6388	18	23	by	by	ADP
ejpam-6388	18	24	formalization	formalization	NOUN
ejpam-6388	18	25	through	through	ADP
ejpam-6388	18	26	the	the	DET
ejpam-6388	18	27	riemann	riemann	PROPN
ejpam-6388	18	28	–	–	PUNCT
ejpam-6388	18	29	liouville	liouville	VERB
ejpam-6388	18	30	fractional	fractional	ADJ
ejpam-6388	18	31	derivative	derivative	NOUN
ejpam-6388	18	32	in	in	ADP
ejpam-6388	18	33	the	the	DET
ejpam-6388	18	34	19th	19th	ADJ
ejpam-6388	18	35	century	century	NOUN
ejpam-6388	18	36	[	[	X
ejpam-6388	18	37	6	6	NUM
ejpam-6388	18	38	]	]	PUNCT
ejpam-6388	18	39	.	.	PUNCT
ejpam-6388	19	1	the	the	DET
ejpam-6388	19	2	20th	20th	ADJ
ejpam-6388	19	3	century	century	NOUN
ejpam-6388	19	4	marked	mark	VERB
ejpam-6388	19	5	significant	significant	ADJ
ejpam-6388	19	6	advancements	advancement	NOUN
ejpam-6388	19	7	,	,	PUNCT
ejpam-6388	19	8	with	with	ADP
ejpam-6388	19	9	fdeqs	fdeq	NOUN
ejpam-6388	19	10	finding	find	VERB
ejpam-6388	19	11	widespread	widespread	ADJ
ejpam-6388	19	12	applications	application	NOUN
ejpam-6388	19	13	in	in	ADP
ejpam-6388	19	14	real	real	ADJ
ejpam-6388	19	15	-	-	PUNCT
ejpam-6388	19	16	world	world	NOUN
ejpam-6388	19	17	problems	problem	NOUN
ejpam-6388	19	18	.	.	PUNCT
ejpam-6388	20	1	this	this	DET
ejpam-6388	20	2	evolution	evolution	NOUN
ejpam-6388	20	3	led	lead	VERB
ejpam-6388	20	4	to	to	ADP
ejpam-6388	20	5	the	the	DET
ejpam-6388	20	6	development	development	NOUN
ejpam-6388	20	7	of	of	ADP
ejpam-6388	20	8	fractional	fractional	ADJ
ejpam-6388	20	9	boundary	boundary	ADJ
ejpam-6388	20	10	value	value	NOUN
ejpam-6388	20	11	problems	problem	NOUN
ejpam-6388	20	12	(	(	PUNCT
ejpam-6388	20	13	fbvps	fbvps	PROPN
ejpam-6388	20	14	)	)	PUNCT
ejpam-6388	20	15	,	,	PUNCT
ejpam-6388	20	16	which	which	PRON
ejpam-6388	20	17	extend	extend	VERB
ejpam-6388	20	18	classical	classical	ADJ
ejpam-6388	20	19	boundary	boundary	ADJ
ejpam-6388	20	20	value	value	NOUN
ejpam-6388	20	21	problems	problem	NOUN
ejpam-6388	20	22	to	to	PART
ejpam-6388	20	23	model	model	VERB
ejpam-6388	20	24	systems	system	NOUN
ejpam-6388	20	25	with	with	ADP
ejpam-6388	20	26	nonlocal	nonlocal	ADJ
ejpam-6388	20	27	conditions	condition	NOUN
ejpam-6388	20	28	and	and	CCONJ
ejpam-6388	20	29	history	history	NOUN
ejpam-6388	20	30	-	-	PUNCT
ejpam-6388	20	31	dependent	dependent	ADJ
ejpam-6388	20	32	behaviors	behavior	NOUN
ejpam-6388	20	33	[	[	X
ejpam-6388	20	34	12	12	NUM
ejpam-6388	20	35	,	,	PUNCT
ejpam-6388	20	36	13	13	NUM
ejpam-6388	20	37	]	]	PUNCT
ejpam-6388	20	38	.	.	PUNCT
ejpam-6388	21	1	concurrently	concurrently	ADV
ejpam-6388	21	2	,	,	PUNCT
ejpam-6388	21	3	fixed	fixed	ADJ
ejpam-6388	21	4	point	point	NOUN
ejpam-6388	21	5	theory	theory	NOUN
ejpam-6388	21	6	,	,	PUNCT
ejpam-6388	21	7	particularly	particularly	ADV
ejpam-6388	21	8	the	the	DET
ejpam-6388	21	9	banach	banach	ADV
ejpam-6388	21	10	fixed	fix	VERB
ejpam-6388	21	11	point	point	NOUN
ejpam-6388	21	12	theorem	theorem	VERB
ejpam-6388	21	13	,	,	PUNCT
ejpam-6388	21	14	has	have	AUX
ejpam-6388	21	15	been	be	AUX
ejpam-6388	21	16	instrumental	instrumental	ADJ
ejpam-6388	21	17	in	in	ADP
ejpam-6388	21	18	establishing	establish	VERB
ejpam-6388	21	19	the	the	DET
ejpam-6388	21	20	existence	existence	NOUN
ejpam-6388	21	21	and	and	CCONJ
ejpam-6388	21	22	uniqueness	uniqueness	NOUN
ejpam-6388	21	23	of	of	ADP
ejpam-6388	21	24	solutions	solution	NOUN
ejpam-6388	21	25	for	for	ADP
ejpam-6388	21	26	fbvps	fbvps	NOUN
ejpam-6388	21	27	,	,	PUNCT
ejpam-6388	21	28	with	with	ADP
ejpam-6388	21	29	recent	recent	ADJ
ejpam-6388	21	30	extensions	extension	NOUN
ejpam-6388	21	31	to	to	ADP
ejpam-6388	21	32	cone	cone	NOUN
ejpam-6388	21	33	metric	metric	ADJ
ejpam-6388	21	34	spaces	space	NOUN
ejpam-6388	21	35	[	[	X
ejpam-6388	21	36	14	14	NUM
ejpam-6388	21	37	]	]	PUNCT
ejpam-6388	21	38	and	and	CCONJ
ejpam-6388	21	39	orthogonal	orthogonal	ADJ
ejpam-6388	21	40	metric	metric	ADJ
ejpam-6388	21	41	spaces	space	NOUN
ejpam-6388	21	42	[	[	X
ejpam-6388	21	43	15	15	NUM
ejpam-6388	21	44	]	]	PUNCT
ejpam-6388	21	45	providing	provide	VERB
ejpam-6388	21	46	powerful	powerful	ADJ
ejpam-6388	21	47	tools	tool	NOUN
ejpam-6388	21	48	for	for	ADP
ejpam-6388	21	49	addressing	address	VERB
ejpam-6388	21	50	complex	complex	ADJ
ejpam-6388	21	51	nonlinear	nonlinear	ADJ
ejpam-6388	21	52	problems	problem	NOUN
ejpam-6388	21	53	.	.	PUNCT
ejpam-6388	22	1	fractional	fractional	ADJ
ejpam-6388	22	2	hybrid	hybrid	ADJ
ejpam-6388	22	3	boundary	boundary	ADJ
ejpam-6388	22	4	value	value	NOUN
ejpam-6388	22	5	problems	problem	NOUN
ejpam-6388	22	6	(	(	PUNCT
ejpam-6388	22	7	fhbvps	fhbvps	PROPN
ejpam-6388	22	8	)	)	PUNCT
ejpam-6388	22	9	further	far	ADV
ejpam-6388	22	10	generalize	generalize	VERB
ejpam-6388	22	11	fbvps	fbvps	NOUN
ejpam-6388	22	12	by	by	ADP
ejpam-6388	22	13	incorporating	incorporate	VERB
ejpam-6388	22	14	quadratic	quadratic	ADJ
ejpam-6388	22	15	perturbations	perturbation	NOUN
ejpam-6388	22	16	of	of	ADP
ejpam-6388	22	17	nonlinear	nonlinear	ADJ
ejpam-6388	22	18	deqs	deq	NOUN
ejpam-6388	22	19	,	,	PUNCT
ejpam-6388	22	20	combining	combine	VERB
ejpam-6388	22	21	continuous	continuous	ADJ
ejpam-6388	22	22	and	and	CCONJ
ejpam-6388	22	23	discrete	discrete	ADJ
ejpam-6388	22	24	dynamics	dynamic	NOUN
ejpam-6388	22	25	.	.	PUNCT
ejpam-6388	23	1	these	these	DET
ejpam-6388	23	2	equations	equation	NOUN
ejpam-6388	23	3	are	be	AUX
ejpam-6388	23	4	particularly	particularly	ADV
ejpam-6388	23	5	valuable	valuable	ADJ
ejpam-6388	23	6	in	in	ADP
ejpam-6388	23	7	applications	application	NOUN
ejpam-6388	23	8	such	such	ADJ
ejpam-6388	23	9	as	as	ADP
ejpam-6388	23	10	biological	biological	ADJ
ejpam-6388	23	11	systems	system	NOUN
ejpam-6388	23	12	,	,	PUNCT
ejpam-6388	23	13	control	control	NOUN
ejpam-6388	23	14	theory	theory	NOUN
ejpam-6388	23	15	,	,	PUNCT
ejpam-6388	23	16	and	and	CCONJ
ejpam-6388	23	17	economics	economic	NOUN
ejpam-6388	23	18	,	,	PUNCT
ejpam-6388	23	19	where	where	SCONJ
ejpam-6388	23	20	sudden	sudden	ADJ
ejpam-6388	23	21	changes	change	NOUN
ejpam-6388	23	22	interact	interact	VERB
ejpam-6388	23	23	with	with	ADP
ejpam-6388	23	24	continuous	continuous	ADJ
ejpam-6388	23	25	evolution	evolution	NOUN
ejpam-6388	23	26	[	[	X
ejpam-6388	23	27	16–19	16–19	NUM
ejpam-6388	23	28	]	]	PUNCT
ejpam-6388	23	29	.	.	PUNCT
ejpam-6388	24	1	however	however	ADV
ejpam-6388	24	2	,	,	PUNCT
ejpam-6388	24	3	prior	prior	ADJ
ejpam-6388	24	4	studies	study	NOUN
ejpam-6388	24	5	on	on	ADP
ejpam-6388	24	6	fhbvps	fhbvps	PROPN
ejpam-6388	24	7	have	have	VERB
ejpam-6388	24	8	notable	notable	ADJ
ejpam-6388	24	9	limitations	limitation	NOUN
ejpam-6388	24	10	.	.	PUNCT
ejpam-6388	25	1	for	for	ADP
ejpam-6388	25	2	instance	instance	NOUN
ejpam-6388	25	3	,	,	PUNCT
ejpam-6388	25	4	zhao	zhao	PROPN
ejpam-6388	25	5	et	et	PROPN
ejpam-6388	25	6	al	al	PROPN
ejpam-6388	25	7	.	.	PUNCT
ejpam-6388	26	1	[	[	X
ejpam-6388	26	2	1	1	X
ejpam-6388	26	3	]	]	PUNCT
ejpam-6388	26	4	investigated	investigate	VERB
ejpam-6388	26	5	the	the	DET
ejpam-6388	26	6	existence	existence	NOUN
ejpam-6388	26	7	and	and	CCONJ
ejpam-6388	26	8	uniqueness	uniqueness	NOUN
ejpam-6388	26	9	of	of	ADP
ejpam-6388	26	10	solutions	solution	NOUN
ejpam-6388	26	11	for	for	ADP
ejpam-6388	26	12	the	the	DET
ejpam-6388	26	13	riemann	riemann	PROPN
ejpam-6388	26	14	–	–	PUNCT
ejpam-6388	26	15	liouville	liouville	NOUN
ejpam-6388	26	16	-	-	PUNCT
ejpam-6388	26	17	based	base	VERB
ejpam-6388	26	18	fhbvp	fhbvp	NOUN
ejpam-6388	26	19	:	:	PUNCT
ejpam-6388	26	20	rldα	rldα	ADJ
ejpam-6388	26	21	0	0	NUM
ejpam-6388	26	22	+	+	CCONJ
ejpam-6388	26	23	[	[	PUNCT
ejpam-6388	26	24	r(ω	r(ω	ADJ
ejpam-6388	26	25	)	)	PUNCT
ejpam-6388	26	26	f(ω	f(ω	PROPN
ejpam-6388	26	27	,	,	PUNCT
ejpam-6388	26	28	r(ω	r(ω	ADJ
ejpam-6388	26	29	)	)	PUNCT
ejpam-6388	26	30	)	)	PUNCT
ejpam-6388	26	31	]	]	PUNCT
ejpam-6388	27	1	=	=	PUNCT
ejpam-6388	27	2	g(ω	g(ω	PROPN
ejpam-6388	27	3	,	,	PUNCT
ejpam-6388	27	4	r(ω	r(ω	ADJ
ejpam-6388	27	5	)	)	PUNCT
ejpam-6388	27	6	)	)	PUNCT
ejpam-6388	28	1	a.e	a.e	PROPN
ejpam-6388	28	2	.	.	NOUN
ejpam-6388	28	3	0	0	PUNCT
ejpam-6388	28	4	<	<	X
ejpam-6388	28	5	ω	ω	X
ejpam-6388	28	6	<	<	X
ejpam-6388	28	7	ξ	ξ	PROPN
ejpam-6388	28	8	,	,	PUNCT
ejpam-6388	28	9	0	0	NUM
ejpam-6388	28	10	<	<	X
ejpam-6388	28	11	α	α	X
ejpam-6388	28	12	<	<	X
ejpam-6388	28	13	1	1	NUM
ejpam-6388	28	14	,	,	PUNCT
ejpam-6388	28	15	r(0	r(0	PROPN
ejpam-6388	28	16	)	)	PUNCT
ejpam-6388	28	17	=	=	SYM
ejpam-6388	29	1	0	0	X
ejpam-6388	29	2	.	.	PUNCT
ejpam-6388	30	1	their	their	PRON
ejpam-6388	30	2	approach	approach	NOUN
ejpam-6388	30	3	is	be	AUX
ejpam-6388	30	4	constrained	constrain	VERB
ejpam-6388	30	5	by	by	ADP
ejpam-6388	30	6	its	its	PRON
ejpam-6388	30	7	focus	focus	NOUN
ejpam-6388	30	8	on	on	ADP
ejpam-6388	30	9	lower	low	ADJ
ejpam-6388	30	10	-	-	PUNCT
ejpam-6388	30	11	order	order	NOUN
ejpam-6388	30	12	fractional	fractional	ADJ
ejpam-6388	30	13	derivatives	derivative	NOUN
ejpam-6388	30	14	(	(	PUNCT
ejpam-6388	30	15	0	0	NUM
ejpam-6388	30	16	<	<	X
ejpam-6388	30	17	α	α	X
ejpam-6388	30	18	<	<	X
ejpam-6388	30	19	1	1	NUM
ejpam-6388	30	20	)	)	PUNCT
ejpam-6388	30	21	and	and	CCONJ
ejpam-6388	30	22	reliance	reliance	NOUN
ejpam-6388	30	23	on	on	ADP
ejpam-6388	30	24	standard	standard	ADJ
ejpam-6388	30	25	metric	metric	ADJ
ejpam-6388	30	26	spaces	space	NOUN
ejpam-6388	30	27	with	with	ADP
ejpam-6388	30	28	the	the	DET
ejpam-6388	30	29	banach	banach	ADV
ejpam-6388	30	30	fixed	fix	VERB
ejpam-6388	30	31	point	point	NOUN
ejpam-6388	30	32	theorem	theorem	ADJ
ejpam-6388	30	33	,	,	PUNCT
ejpam-6388	30	34	limiting	limit	VERB
ejpam-6388	30	35	its	its	PRON
ejpam-6388	30	36	applicability	applicability	NOUN
ejpam-6388	30	37	to	to	ADP
ejpam-6388	30	38	systems	system	NOUN
ejpam-6388	30	39	with	with	ADP
ejpam-6388	30	40	higher	high	ADJ
ejpam-6388	30	41	-	-	PUNCT
ejpam-6388	30	42	order	order	NOUN
ejpam-6388	30	43	derivatives	derivative	NOUN
ejpam-6388	30	44	or	or	CCONJ
ejpam-6388	30	45	complex	complex	ADJ
ejpam-6388	30	46	nonlocal	nonlocal	ADJ
ejpam-6388	30	47	boundary	boundary	ADJ
ejpam-6388	30	48	conditions	condition	NOUN
ejpam-6388	30	49	.	.	PUNCT
ejpam-6388	31	1	similarly	similarly	ADV
ejpam-6388	31	2	,	,	PUNCT
ejpam-6388	31	3	hilal	hilal	PROPN
ejpam-6388	31	4	and	and	CCONJ
ejpam-6388	31	5	kajouni	kajouni	PROPN
ejpam-6388	32	1	[	[	X
ejpam-6388	32	2	2	2	NUM
ejpam-6388	32	3	]	]	PUNCT
ejpam-6388	32	4	addressed	address	VERB
ejpam-6388	32	5	the	the	DET
ejpam-6388	32	6	caputo	caputo	PROPN
ejpam-6388	32	7	-	-	PUNCT
ejpam-6388	32	8	type	type	NOUN
ejpam-6388	32	9	fhbvp	fhbvp	NOUN
ejpam-6388	32	10	:	:	PUNCT
ejpam-6388	32	11	cdα	cdα	NOUN
ejpam-6388	32	12	0	0	PUNCT
ejpam-6388	33	1	+	+	CCONJ
ejpam-6388	33	2	[	[	PUNCT
ejpam-6388	33	3	r(ω	r(ω	ADJ
ejpam-6388	33	4	)	)	PUNCT
ejpam-6388	33	5	f(ω	f(ω	PROPN
ejpam-6388	33	6	,	,	PUNCT
ejpam-6388	33	7	r(ω	r(ω	ADJ
ejpam-6388	33	8	)	)	PUNCT
ejpam-6388	33	9	)	)	PUNCT
ejpam-6388	33	10	]	]	PUNCT
ejpam-6388	34	1	=	=	PUNCT
ejpam-6388	34	2	g(ω	g(ω	PROPN
ejpam-6388	34	3	,	,	PUNCT
ejpam-6388	34	4	r(ω	r(ω	ADJ
ejpam-6388	34	5	)	)	PUNCT
ejpam-6388	34	6	)	)	PUNCT
ejpam-6388	35	1	a.e	a.e	PROPN
ejpam-6388	35	2	.	.	NOUN
ejpam-6388	35	3	0	0	PUNCT
ejpam-6388	35	4	<	<	X
ejpam-6388	35	5	ω	ω	X
ejpam-6388	35	6	<	<	X
ejpam-6388	35	7	ξ	ξ	PROPN
ejpam-6388	35	8	,	,	PUNCT
ejpam-6388	35	9	0	0	NUM
ejpam-6388	35	10	<	<	X
ejpam-6388	35	11	α	α	X
ejpam-6388	35	12	<	<	X
ejpam-6388	35	13	1	1	NUM
ejpam-6388	35	14	,	,	PUNCT
ejpam-6388	35	15	a	a	DET
ejpam-6388	35	16	r(0	r(0	PROPN
ejpam-6388	35	17	)	)	PUNCT
ejpam-6388	35	18	f(0	f(0	NOUN
ejpam-6388	35	19	,	,	PUNCT
ejpam-6388	35	20	r(0	r(0	PROPN
ejpam-6388	35	21	)	)	PUNCT
ejpam-6388	35	22	)	)	PUNCT
ejpam-6388	36	1	+	+	CCONJ
ejpam-6388	36	2	b	b	X
ejpam-6388	36	3	r(ξ	r(ξ	NOUN
ejpam-6388	36	4	)	)	PUNCT
ejpam-6388	36	5	f(ξ	f(ξ	PROPN
ejpam-6388	36	6	,	,	PUNCT
ejpam-6388	36	7	r(ξ	r(ξ	NOUN
ejpam-6388	36	8	)	)	PUNCT
ejpam-6388	36	9	)	)	PUNCT
ejpam-6388	37	1	=	=	SYM
ejpam-6388	37	2	c.	c.	NOUN
ejpam-6388	37	3	their	their	PRON
ejpam-6388	37	4	framework	framework	NOUN
ejpam-6388	37	5	,	,	PUNCT
ejpam-6388	37	6	based	base	VERB
ejpam-6388	37	7	on	on	ADP
ejpam-6388	37	8	banach	banach	NOUN
ejpam-6388	37	9	algebra	algebra	NOUN
ejpam-6388	37	10	techniques	technique	NOUN
ejpam-6388	37	11	and	and	CCONJ
ejpam-6388	37	12	lipschitz	lipschitz	NOUN
ejpam-6388	37	13	/	/	SYM
ejpam-6388	37	14	carathéodory	carathéodory	NOUN
ejpam-6388	37	15	conditions	condition	NOUN
ejpam-6388	37	16	,	,	PUNCT
ejpam-6388	37	17	is	be	AUX
ejpam-6388	37	18	restricted	restrict	VERB
ejpam-6388	37	19	by	by	ADP
ejpam-6388	37	20	the	the	DET
ejpam-6388	37	21	use	use	NOUN
ejpam-6388	37	22	of	of	ADP
ejpam-6388	37	23	caputo	caputo	PROPN
ejpam-6388	37	24	derivative	derivative	PROPN
ejpam-6388	37	25	and	and	CCONJ
ejpam-6388	37	26	specific	specific	ADJ
ejpam-6388	37	27	algebraic	algebraic	ADJ
ejpam-6388	37	28	structures	structure	NOUN
ejpam-6388	37	29	,	,	PUNCT
ejpam-6388	37	30	reducing	reduce	VERB
ejpam-6388	37	31	its	its	PRON
ejpam-6388	37	32	generality	generality	NOUN
ejpam-6388	37	33	for	for	ADP
ejpam-6388	37	34	broader	broad	ADJ
ejpam-6388	37	35	classes	class	NOUN
ejpam-6388	37	36	of	of	ADP
ejpam-6388	37	37	fhbvps	fhbvps	PROPN
ejpam-6388	37	38	with	with	ADP
ejpam-6388	37	39	higher	high	ADJ
ejpam-6388	37	40	-	-	PUNCT
ejpam-6388	37	41	order	order	NOUN
ejpam-6388	37	42	derivatives	derivative	NOUN
ejpam-6388	37	43	or	or	CCONJ
ejpam-6388	37	44	intricate	intricate	ADJ
ejpam-6388	37	45	boundary	boundary	ADJ
ejpam-6388	37	46	conditions	condition	NOUN
ejpam-6388	37	47	.	.	PUNCT
ejpam-6388	38	1	d.	d.	PROPN
ejpam-6388	38	2	baleanu	baleanu	PROPN
ejpam-6388	38	3	et	et	PROPN
ejpam-6388	38	4	al	al	PROPN
ejpam-6388	38	5	.	.	PUNCT
ejpam-6388	38	6	/	/	SYM
ejpam-6388	38	7	eur	eur	PROPN
ejpam-6388	38	8	.	.	PUNCT
ejpam-6388	39	1	j.	j.	PROPN
ejpam-6388	39	2	pure	pure	PROPN
ejpam-6388	39	3	appl	appl	PROPN
ejpam-6388	39	4	.	.	PROPN
ejpam-6388	39	5	math	math	PROPN
ejpam-6388	39	6	,	,	PUNCT
ejpam-6388	39	7	18	18	NUM
ejpam-6388	39	8	(	(	PUNCT
ejpam-6388	39	9	4	4	NUM
ejpam-6388	39	10	)	)	PUNCT
ejpam-6388	39	11	(	(	PUNCT
ejpam-6388	39	12	2025	2025	NUM
ejpam-6388	39	13	)	)	PUNCT
ejpam-6388	39	14	,	,	PUNCT
ejpam-6388	39	15	6388	6388	NUM
ejpam-6388	39	16	3	3	NUM
ejpam-6388	39	17	of	of	ADP
ejpam-6388	39	18	31	31	NUM
ejpam-6388	39	19	to	to	PART
ejpam-6388	39	20	address	address	VERB
ejpam-6388	39	21	these	these	DET
ejpam-6388	39	22	limitations	limitation	NOUN
ejpam-6388	39	23	,	,	PUNCT
ejpam-6388	39	24	this	this	DET
ejpam-6388	39	25	study	study	NOUN
ejpam-6388	39	26	focuses	focus	VERB
ejpam-6388	39	27	on	on	ADP
ejpam-6388	39	28	the	the	DET
ejpam-6388	39	29	qualitative	qualitative	ADJ
ejpam-6388	39	30	analysis	analysis	NOUN
ejpam-6388	39	31	of	of	ADP
ejpam-6388	39	32	the	the	DET
ejpam-6388	39	33	following	follow	VERB
ejpam-6388	39	34	fractional	fractional	ADJ
ejpam-6388	39	35	hybrid	hybrid	ADJ
ejpam-6388	39	36	boundary	boundary	ADJ
ejpam-6388	39	37	value	value	NOUN
ejpam-6388	39	38	problem	problem	NOUN
ejpam-6388	39	39	(	(	PUNCT
ejpam-6388	39	40	fhbvp	fhbvp	ADJ
ejpam-6388	39	41	):	):	PUNCT
ejpam-6388	39	42	rldy	rldy	NOUN
ejpam-6388	39	43	0	0	NUM
ejpam-6388	39	44	+	+	CCONJ
ejpam-6388	39	45	[	[	PUNCT
ejpam-6388	39	46	r(ω	r(ω	ADJ
ejpam-6388	39	47	)	)	PUNCT
ejpam-6388	39	48	f(ω	f(ω	PROPN
ejpam-6388	39	49	,	,	PUNCT
ejpam-6388	39	50	r(ω	r(ω	ADJ
ejpam-6388	39	51	)	)	PUNCT
ejpam-6388	39	52	)	)	PUNCT
ejpam-6388	39	53	]	]	PUNCT
ejpam-6388	40	1	+	+	CCONJ
ejpam-6388	40	2	g(ω	g(ω	PROPN
ejpam-6388	40	3	,	,	PUNCT
ejpam-6388	40	4	r(ω	r(ω	ADJ
ejpam-6388	40	5	)	)	PUNCT
ejpam-6388	40	6	)	)	PUNCT
ejpam-6388	41	1	=	=	SYM
ejpam-6388	41	2	0	0	NUM
ejpam-6388	42	1	a.e	a.e	PROPN
ejpam-6388	42	2	.	.	PROPN
ejpam-6388	42	3	0	0	NUM
ejpam-6388	42	4	≤	≤	NUM
ejpam-6388	42	5	ω	ω	NUM
ejpam-6388	42	6	≤	≤	NUM
ejpam-6388	42	7	1	1	NUM
ejpam-6388	42	8	,	,	PUNCT
ejpam-6388	42	9	(	(	PUNCT
ejpam-6388	42	10	1	1	X
ejpam-6388	42	11	)	)	PUNCT
ejpam-6388	42	12	with	with	ADP
ejpam-6388	42	13	boundary	boundary	ADJ
ejpam-6388	42	14	conditions	condition	NOUN
ejpam-6388	42	15	(	(	PUNCT
ejpam-6388	42	16	bcs	bcs	NOUN
ejpam-6388	42	17	)	)	PUNCT
ejpam-6388	42	18	r(0	r(0	PROPN
ejpam-6388	42	19	)	)	PUNCT
ejpam-6388	42	20	=	=	SYM
ejpam-6388	42	21	0	0	NUM
ejpam-6388	42	22	and	and	CCONJ
ejpam-6388	42	23	r(1	r(1	PROPN
ejpam-6388	42	24	)	)	PUNCT
ejpam-6388	43	1	=	=	SYM
ejpam-6388	43	2	f	f	PROPN
ejpam-6388	43	3	(	(	PUNCT
ejpam-6388	43	4	1	1	NUM
ejpam-6388	43	5	,	,	PUNCT
ejpam-6388	43	6	r(1	r(1	PROPN
ejpam-6388	43	7	)	)	PUNCT
ejpam-6388	43	8	)	)	PUNCT
ejpam-6388	43	9	,	,	PUNCT
ejpam-6388	43	10	(	(	PUNCT
ejpam-6388	43	11	2	2	X
ejpam-6388	43	12	)	)	PUNCT
ejpam-6388	43	13	where	where	SCONJ
ejpam-6388	43	14	1	1	NUM
ejpam-6388	43	15	<	<	X
ejpam-6388	43	16	y	y	PROPN
ejpam-6388	43	17	≤	≤	ADV
ejpam-6388	43	18	2	2	NUM
ejpam-6388	43	19	,	,	PUNCT
ejpam-6388	43	20	rldy	rldy	NOUN
ejpam-6388	43	21	0	0	NUM
ejpam-6388	43	22	+	+	NUM
ejpam-6388	43	23	is	be	AUX
ejpam-6388	43	24	the	the	DET
ejpam-6388	43	25	riemann	riemann	PROPN
ejpam-6388	43	26	–	–	PUNCT
ejpam-6388	43	27	liouville	liouville	VERB
ejpam-6388	43	28	fractional	fractional	ADJ
ejpam-6388	43	29	derivative	derivative	NOUN
ejpam-6388	43	30	,	,	PUNCT
ejpam-6388	43	31	g	g	PROPN
ejpam-6388	43	32	∈	∈	PROPN
ejpam-6388	43	33	c([0	c([0	NOUN
ejpam-6388	43	34	,	,	PUNCT
ejpam-6388	43	35	1	1	NUM
ejpam-6388	43	36	]	]	X
ejpam-6388	43	37	×	×	NOUN
ejpam-6388	43	38	r	r	NOUN
ejpam-6388	43	39	,	,	PUNCT
ejpam-6388	43	40	r	r	NOUN
ejpam-6388	43	41	)	)	PUNCT
ejpam-6388	43	42	,	,	PUNCT
ejpam-6388	43	43	and	and	CCONJ
ejpam-6388	43	44	f	f	PROPN
ejpam-6388	43	45	∈	∈	PROPN
ejpam-6388	43	46	c([0	c([0	NOUN
ejpam-6388	43	47	,	,	PUNCT
ejpam-6388	43	48	1	1	NUM
ejpam-6388	43	49	]	]	X
ejpam-6388	43	50	×	×	NOUN
ejpam-6388	43	51	r	r	NOUN
ejpam-6388	43	52	,	,	PUNCT
ejpam-6388	43	53	r	r	NOUN
ejpam-6388	43	54	\	\	X
ejpam-6388	43	55	{	{	PUNCT
ejpam-6388	43	56	0	0	NUM
ejpam-6388	43	57	}	}	PUNCT
ejpam-6388	43	58	)	)	PUNCT
ejpam-6388	43	59	.	.	PUNCT
ejpam-6388	44	1	we	we	PRON
ejpam-6388	44	2	aim	aim	VERB
ejpam-6388	44	3	to	to	PART
ejpam-6388	44	4	establish	establish	VERB
ejpam-6388	44	5	the	the	DET
ejpam-6388	44	6	existence	existence	NOUN
ejpam-6388	44	7	,	,	PUNCT
ejpam-6388	44	8	uniqueness	uniqueness	NOUN
ejpam-6388	44	9	,	,	PUNCT
ejpam-6388	44	10	and	and	CCONJ
ejpam-6388	44	11	hyers	hyer	NOUN
ejpam-6388	44	12	–	–	PUNCT
ejpam-6388	44	13	ulam	ulam	X
ejpam-6388	44	14	stability	stability	NOUN
ejpam-6388	44	15	of	of	ADP
ejpam-6388	44	16	solutions	solution	NOUN
ejpam-6388	44	17	using	use	VERB
ejpam-6388	44	18	the	the	DET
ejpam-6388	44	19	extended	extended	ADJ
ejpam-6388	44	20	banach	banach	ADV
ejpam-6388	44	21	fixed	fix	VERB
ejpam-6388	44	22	point	point	NOUN
ejpam-6388	44	23	theorem	theorem	VERB
ejpam-6388	44	24	in	in	ADP
ejpam-6388	44	25	orthogonal	orthogonal	ADJ
ejpam-6388	44	26	cone	cone	NOUN
ejpam-6388	44	27	metric	metric	ADJ
ejpam-6388	44	28	spaces	space	NOUN
ejpam-6388	44	29	[	[	X
ejpam-6388	44	30	20	20	NUM
ejpam-6388	44	31	]	]	PUNCT
ejpam-6388	44	32	,	,	PUNCT
ejpam-6388	44	33	which	which	PRON
ejpam-6388	44	34	provides	provide	VERB
ejpam-6388	44	35	a	a	DET
ejpam-6388	44	36	more	more	ADV
ejpam-6388	44	37	flexible	flexible	ADJ
ejpam-6388	44	38	geometric	geometric	ADJ
ejpam-6388	44	39	framework	framework	NOUN
ejpam-6388	44	40	than	than	ADP
ejpam-6388	44	41	standard	standard	ADJ
ejpam-6388	44	42	metric	metric	ADJ
ejpam-6388	44	43	spaces	space	NOUN
ejpam-6388	44	44	or	or	CCONJ
ejpam-6388	44	45	banach	banach	NOUN
ejpam-6388	44	46	algebras	algebra	NOUN
ejpam-6388	44	47	.	.	PUNCT
ejpam-6388	45	1	recent	recent	ADJ
ejpam-6388	45	2	advancements	advancement	NOUN
ejpam-6388	45	3	in	in	ADP
ejpam-6388	45	4	metric	metric	ADJ
ejpam-6388	45	5	spaces	space	NOUN
ejpam-6388	45	6	have	have	VERB
ejpam-6388	45	7	significantly	significantly	ADV
ejpam-6388	45	8	advanced	advance	VERB
ejpam-6388	45	9	fixed	fix	VERB
ejpam-6388	45	10	point	point	NOUN
ejpam-6388	45	11	theory	theory	NOUN
ejpam-6388	45	12	.	.	PUNCT
ejpam-6388	46	1	traditional	traditional	ADJ
ejpam-6388	46	2	metric	metric	ADJ
ejpam-6388	46	3	spaces	space	NOUN
ejpam-6388	46	4	have	have	AUX
ejpam-6388	46	5	been	be	AUX
ejpam-6388	46	6	extended	extend	VERB
ejpam-6388	46	7	to	to	ADP
ejpam-6388	46	8	cone	cone	NOUN
ejpam-6388	46	9	metric	metric	ADJ
ejpam-6388	46	10	spaces	space	NOUN
ejpam-6388	46	11	by	by	ADP
ejpam-6388	46	12	huang	huang	PROPN
ejpam-6388	46	13	et	et	PROPN
ejpam-6388	46	14	al	al	PROPN
ejpam-6388	46	15	.	.	PUNCT
ejpam-6388	47	1	[	[	X
ejpam-6388	47	2	14	14	NUM
ejpam-6388	47	3	]	]	PUNCT
ejpam-6388	47	4	and	and	CCONJ
ejpam-6388	47	5	orthogonal	orthogonal	ADJ
ejpam-6388	47	6	metric	metric	ADJ
ejpam-6388	47	7	spaces	space	NOUN
ejpam-6388	47	8	by	by	ADP
ejpam-6388	47	9	gordji	gordji	PROPN
ejpam-6388	47	10	et	et	PROPN
ejpam-6388	47	11	al	al	PROPN
ejpam-6388	47	12	.	.	PUNCT
ejpam-6388	48	1	[	[	X
ejpam-6388	48	2	15	15	NUM
ejpam-6388	48	3	]	]	PUNCT
ejpam-6388	48	4	,	,	PUNCT
ejpam-6388	48	5	enabling	enable	VERB
ejpam-6388	48	6	the	the	DET
ejpam-6388	48	7	analysis	analysis	NOUN
ejpam-6388	48	8	of	of	ADP
ejpam-6388	48	9	complex	complex	ADJ
ejpam-6388	48	10	nonlinear	nonlinear	ADJ
ejpam-6388	48	11	problems	problem	NOUN
ejpam-6388	48	12	[	[	X
ejpam-6388	48	13	21–24	21–24	NOUN
ejpam-6388	48	14	]	]	PUNCT
ejpam-6388	48	15	.	.	PUNCT
ejpam-6388	49	1	we	we	PRON
ejpam-6388	49	2	know	know	VERB
ejpam-6388	49	3	that	that	SCONJ
ejpam-6388	49	4	the	the	DET
ejpam-6388	49	5	category	category	NOUN
ejpam-6388	49	6	of	of	ADP
ejpam-6388	49	7	cone	cone	NOUN
ejpam-6388	49	8	metric	metric	ADJ
ejpam-6388	49	9	spaces	space	NOUN
ejpam-6388	49	10	and	and	CCONJ
ejpam-6388	49	11	metric	metric	ADJ
ejpam-6388	49	12	spaces	space	NOUN
ejpam-6388	49	13	are	be	AUX
ejpam-6388	49	14	same	same	ADJ
ejpam-6388	49	15	and	and	CCONJ
ejpam-6388	49	16	most	most	ADV
ejpam-6388	49	17	fixed	fix	VERB
ejpam-6388	49	18	point	point	NOUN
ejpam-6388	49	19	results	result	NOUN
ejpam-6388	49	20	on	on	ADP
ejpam-6388	49	21	cone	cone	NOUN
ejpam-6388	49	22	metric	metric	ADJ
ejpam-6388	49	23	spaces	space	NOUN
ejpam-6388	49	24	are	be	AUX
ejpam-6388	49	25	not	not	PART
ejpam-6388	49	26	real	real	ADJ
ejpam-6388	49	27	generalizations	generalization	NOUN
ejpam-6388	49	28	.	.	PUNCT
ejpam-6388	50	1	but	but	CCONJ
ejpam-6388	50	2	,	,	PUNCT
ejpam-6388	50	3	there	there	PRON
ejpam-6388	50	4	are	be	VERB
ejpam-6388	50	5	some	some	DET
ejpam-6388	50	6	valuable	valuable	ADJ
ejpam-6388	50	7	results	result	NOUN
ejpam-6388	50	8	(	(	PUNCT
ejpam-6388	50	9	such	such	ADJ
ejpam-6388	50	10	results	result	NOUN
ejpam-6388	50	11	of	of	ADP
ejpam-6388	50	12	this	this	DET
ejpam-6388	50	13	work	work	NOUN
ejpam-6388	50	14	)	)	PUNCT
ejpam-6388	50	15	which	which	PRON
ejpam-6388	50	16	researchers	researcher	NOUN
ejpam-6388	50	17	can	can	AUX
ejpam-6388	50	18	work	work	VERB
ejpam-6388	50	19	nowadays	nowadays	ADV
ejpam-6388	50	20	[	[	X
ejpam-6388	50	21	25	25	NUM
ejpam-6388	50	22	]	]	PUNCT
ejpam-6388	50	23	.	.	PUNCT
ejpam-6388	51	1	our	our	PRON
ejpam-6388	51	2	approach	approach	NOUN
ejpam-6388	51	3	generalizes	generalize	VERB
ejpam-6388	51	4	the	the	DET
ejpam-6388	51	5	results	result	NOUN
ejpam-6388	51	6	of	of	ADP
ejpam-6388	51	7	zhao	zhao	PROPN
ejpam-6388	51	8	et	et	PROPN
ejpam-6388	51	9	al	al	PROPN
ejpam-6388	51	10	.	.	PUNCT
ejpam-6388	52	1	[	[	X
ejpam-6388	52	2	1	1	X
ejpam-6388	52	3	]	]	PUNCT
ejpam-6388	52	4	and	and	CCONJ
ejpam-6388	52	5	hilal	hilal	PROPN
ejpam-6388	52	6	and	and	CCONJ
ejpam-6388	52	7	kajouni	kajouni	PROPN
ejpam-6388	52	8	[	[	X
ejpam-6388	52	9	2	2	NUM
ejpam-6388	52	10	]	]	PUNCT
ejpam-6388	52	11	by	by	ADP
ejpam-6388	52	12	addressing	address	VERB
ejpam-6388	52	13	higher	high	ADJ
ejpam-6388	52	14	-	-	PUNCT
ejpam-6388	52	15	order	order	NOUN
ejpam-6388	52	16	fractional	fractional	ADJ
ejpam-6388	52	17	derivatives	derivative	NOUN
ejpam-6388	52	18	and	and	CCONJ
ejpam-6388	52	19	leveraging	leverage	VERB
ejpam-6388	52	20	the	the	DET
ejpam-6388	52	21	orthogonal	orthogonal	ADJ
ejpam-6388	52	22	cone	cone	NOUN
ejpam-6388	52	23	metric	metric	ADJ
ejpam-6388	52	24	space	space	NOUN
ejpam-6388	52	25	framework	framework	NOUN
ejpam-6388	52	26	to	to	PART
ejpam-6388	52	27	accommodate	accommodate	VERB
ejpam-6388	52	28	intricate	intricate	ADJ
ejpam-6388	52	29	nonlinearities	nonlinearitie	NOUN
ejpam-6388	52	30	and	and	CCONJ
ejpam-6388	52	31	nonlocal	nonlocal	ADJ
ejpam-6388	52	32	boundary	boundary	ADJ
ejpam-6388	52	33	conditions	condition	NOUN
ejpam-6388	52	34	,	,	PUNCT
ejpam-6388	52	35	offering	offer	VERB
ejpam-6388	52	36	new	new	ADJ
ejpam-6388	52	37	insights	insight	NOUN
ejpam-6388	52	38	into	into	ADP
ejpam-6388	52	39	the	the	DET
ejpam-6388	52	40	qualitative	qualitative	ADJ
ejpam-6388	52	41	properties	property	NOUN
ejpam-6388	52	42	of	of	ADP
ejpam-6388	52	43	fhbvps	fhbvps	PROPN
ejpam-6388	52	44	across	across	ADP
ejpam-6388	52	45	diverse	diverse	ADJ
ejpam-6388	52	46	scientific	scientific	ADJ
ejpam-6388	52	47	disciplines	discipline	NOUN
ejpam-6388	52	48	.	.	PUNCT
ejpam-6388	53	1	the	the	DET
ejpam-6388	53	2	possible	possible	ADJ
ejpam-6388	53	3	physical	physical	ADJ
ejpam-6388	53	4	interpretations	interpretation	NOUN
ejpam-6388	53	5	of	of	ADP
ejpam-6388	53	6	(	(	PUNCT
ejpam-6388	53	7	1)-(2	1)-(2	NUM
ejpam-6388	53	8	):	):	PUNCT
ejpam-6388	53	9	(	(	PUNCT
ejpam-6388	53	10	i	i	NOUN
ejpam-6388	53	11	)	)	PUNCT
ejpam-6388	53	12	viscoelastic	viscoelastic	ADJ
ejpam-6388	53	13	material	material	NOUN
ejpam-6388	53	14	deformation	deformation	NOUN
ejpam-6388	53	15	:	:	PUNCT
ejpam-6388	53	16	•	•	ADP
ejpam-6388	53	17	meaning	mean	VERB
ejpam-6388	53	18	:	:	PUNCT
ejpam-6388	53	19	the	the	DET
ejpam-6388	53	20	fhbvp	fhbvp	NOUN
ejpam-6388	53	21	can	can	AUX
ejpam-6388	53	22	represent	represent	VERB
ejpam-6388	53	23	the	the	DET
ejpam-6388	53	24	deformation	deformation	NOUN
ejpam-6388	53	25	of	of	ADP
ejpam-6388	53	26	a	a	DET
ejpam-6388	53	27	viscoelastic	viscoelastic	ADJ
ejpam-6388	53	28	material	material	NOUN
ejpam-6388	53	29	(	(	PUNCT
ejpam-6388	53	30	e.g.	e.g.	ADV
ejpam-6388	53	31	,	,	PUNCT
ejpam-6388	53	32	rubber	rubber	NOUN
ejpam-6388	53	33	,	,	PUNCT
ejpam-6388	53	34	biological	biological	ADJ
ejpam-6388	53	35	tissue	tissue	NOUN
ejpam-6388	53	36	)	)	PUNCT
ejpam-6388	53	37	under	under	ADP
ejpam-6388	53	38	a	a	DET
ejpam-6388	53	39	time	time	NOUN
ejpam-6388	53	40	-	-	PUNCT
ejpam-6388	53	41	varying	vary	VERB
ejpam-6388	53	42	load	load	NOUN
ejpam-6388	53	43	.	.	PUNCT
ejpam-6388	54	1	the	the	DET
ejpam-6388	54	2	fractional	fractional	ADJ
ejpam-6388	54	3	derivative	derivative	ADJ
ejpam-6388	54	4	rldy	rldy	NOUN
ejpam-6388	54	5	0	0	NUM
ejpam-6388	54	6	+	+	NUM
ejpam-6388	54	7	captures	capture	VERB
ejpam-6388	54	8	the	the	DET
ejpam-6388	54	9	material	material	NOUN
ejpam-6388	54	10	’s	’s	PART
ejpam-6388	54	11	memory	memory	NOUN
ejpam-6388	54	12	-	-	PUNCT
ejpam-6388	54	13	dependent	dependent	ADJ
ejpam-6388	54	14	stress	stress	NOUN
ejpam-6388	54	15	relaxation	relaxation	NOUN
ejpam-6388	54	16	,	,	PUNCT
ejpam-6388	54	17	where	where	SCONJ
ejpam-6388	54	18	y	y	PROPN
ejpam-6388	54	19	>	>	X
ejpam-6388	54	20	1	1	NUM
ejpam-6388	54	21	accounts	account	NOUN
ejpam-6388	54	22	for	for	ADP
ejpam-6388	54	23	both	both	CCONJ
ejpam-6388	54	24	elastic	elastic	ADJ
ejpam-6388	54	25	and	and	CCONJ
ejpam-6388	54	26	viscous	viscous	ADJ
ejpam-6388	54	27	effects	effect	NOUN
ejpam-6388	54	28	.	.	PUNCT
ejpam-6388	55	1	the	the	DET
ejpam-6388	55	2	term	term	NOUN
ejpam-6388	55	3	r(ω	r(ω	ADV
ejpam-6388	55	4	)	)	PUNCT
ejpam-6388	55	5	f(ω	f(ω	PROPN
ejpam-6388	55	6	,	,	PUNCT
ejpam-6388	55	7	r(ω	r(ω	ADJ
ejpam-6388	55	8	)	)	PUNCT
ejpam-6388	55	9	)	)	PUNCT
ejpam-6388	55	10	might	might	AUX
ejpam-6388	55	11	models	model	VERB
ejpam-6388	55	12	a	a	DET
ejpam-6388	55	13	nonlinear	nonlinear	ADJ
ejpam-6388	55	14	stress	stress	NOUN
ejpam-6388	55	15	-	-	PUNCT
ejpam-6388	55	16	strain	strain	NOUN
ejpam-6388	55	17	relationship	relationship	NOUN
ejpam-6388	55	18	adjusted	adjust	VERB
ejpam-6388	55	19	by	by	ADP
ejpam-6388	55	20	material	material	NOUN
ejpam-6388	55	21	properties	property	NOUN
ejpam-6388	55	22	(	(	PUNCT
ejpam-6388	55	23	f	f	NOUN
ejpam-6388	55	24	)	)	PUNCT
ejpam-6388	55	25	,	,	PUNCT
ejpam-6388	55	26	and	and	CCONJ
ejpam-6388	55	27	g(ω	g(ω	PROPN
ejpam-6388	55	28	,	,	PUNCT
ejpam-6388	55	29	r(ω	r(ω	ADJ
ejpam-6388	55	30	)	)	PUNCT
ejpam-6388	55	31	)	)	PUNCT
ejpam-6388	55	32	could	could	AUX
ejpam-6388	55	33	represent	represent	VERB
ejpam-6388	55	34	an	an	DET
ejpam-6388	55	35	external	external	ADJ
ejpam-6388	55	36	force	force	NOUN
ejpam-6388	55	37	or	or	CCONJ
ejpam-6388	55	38	internal	internal	ADJ
ejpam-6388	55	39	damping	damping	NOUN
ejpam-6388	55	40	.	.	PUNCT
ejpam-6388	56	1	the	the	DET
ejpam-6388	56	2	boundary	boundary	ADJ
ejpam-6388	56	3	condition	condition	NOUN
ejpam-6388	56	4	r(0	r(0	PROPN
ejpam-6388	56	5	)	)	PUNCT
ejpam-6388	56	6	=	=	SYM
ejpam-6388	56	7	0	0	NUM
ejpam-6388	56	8	indicates	indicate	VERB
ejpam-6388	56	9	no	no	DET
ejpam-6388	56	10	initial	initial	ADJ
ejpam-6388	56	11	deformation	deformation	NOUN
ejpam-6388	56	12	,	,	PUNCT
ejpam-6388	56	13	while	while	SCONJ
ejpam-6388	56	14	r(1	r(1	PROPN
ejpam-6388	56	15	)	)	PUNCT
ejpam-6388	57	1	=	=	PUNCT
ejpam-6388	57	2	f(1	f(1	PROPN
ejpam-6388	57	3	,	,	PUNCT
ejpam-6388	57	4	r(1	r(1	PROPN
ejpam-6388	57	5	)	)	PUNCT
ejpam-6388	57	6	)	)	PUNCT
ejpam-6388	57	7	suggests	suggest	VERB
ejpam-6388	57	8	a	a	DET
ejpam-6388	57	9	terminal	terminal	ADJ
ejpam-6388	57	10	state	state	NOUN
ejpam-6388	57	11	dependent	dependent	ADJ
ejpam-6388	57	12	on	on	ADP
ejpam-6388	57	13	the	the	DET
ejpam-6388	57	14	material	material	NOUN
ejpam-6388	57	15	’s	’s	PART
ejpam-6388	57	16	nonlinear	nonlinear	ADJ
ejpam-6388	57	17	response	response	NOUN
ejpam-6388	57	18	,	,	PUNCT
ejpam-6388	57	19	possibly	possibly	ADV
ejpam-6388	57	20	a	a	DET
ejpam-6388	57	21	fixed	fix	VERB
ejpam-6388	57	22	strain	strain	NOUN
ejpam-6388	57	23	at	at	ADP
ejpam-6388	57	24	the	the	DET
ejpam-6388	57	25	end	end	NOUN
ejpam-6388	57	26	of	of	ADP
ejpam-6388	57	27	the	the	DET
ejpam-6388	57	28	interval	interval	NOUN
ejpam-6388	57	29	.	.	PUNCT
ejpam-6388	58	1	•	•	NUM
ejpam-6388	58	2	context	context	NOUN
ejpam-6388	58	3	:	:	PUNCT
ejpam-6388	58	4	applicable	applicable	ADJ
ejpam-6388	58	5	in	in	ADP
ejpam-6388	58	6	engineering	engineering	NOUN
ejpam-6388	58	7	(	(	PUNCT
ejpam-6388	58	8	e.g.	e.g.	ADV
ejpam-6388	58	9	,	,	PUNCT
ejpam-6388	58	10	designing	design	VERB
ejpam-6388	58	11	shock	shock	NOUN
ejpam-6388	58	12	absorbers	absorber	NOUN
ejpam-6388	58	13	)	)	PUNCT
ejpam-6388	58	14	or	or	CCONJ
ejpam-6388	58	15	biomechanics	biomechanic	NOUN
ejpam-6388	58	16	(	(	PUNCT
ejpam-6388	58	17	e.g.	e.g.	ADV
ejpam-6388	58	18	,	,	PUNCT
ejpam-6388	58	19	modeling	model	VERB
ejpam-6388	58	20	soft	soft	ADJ
ejpam-6388	58	21	tissue	tissue	NOUN
ejpam-6388	58	22	)	)	PUNCT
ejpam-6388	58	23	.	.	PUNCT
ejpam-6388	59	1	(	(	PUNCT
ejpam-6388	59	2	ii	ii	NOUN
ejpam-6388	59	3	)	)	PUNCT
ejpam-6388	59	4	anomalous	anomalous	ADJ
ejpam-6388	59	5	diffusion	diffusion	NOUN
ejpam-6388	59	6	in	in	ADP
ejpam-6388	59	7	heterogeneous	heterogeneous	ADJ
ejpam-6388	59	8	media	medium	NOUN
ejpam-6388	59	9	:	:	PUNCT
ejpam-6388	59	10	•	•	ADP
ejpam-6388	59	11	meaning	mean	VERB
ejpam-6388	59	12	:	:	PUNCT
ejpam-6388	59	13	this	this	DET
ejpam-6388	59	14	problem	problem	NOUN
ejpam-6388	59	15	can	can	AUX
ejpam-6388	59	16	describe	describe	VERB
ejpam-6388	59	17	anomalous	anomalous	ADJ
ejpam-6388	59	18	diffusion	diffusion	NOUN
ejpam-6388	59	19	processes	process	NOUN
ejpam-6388	59	20	,	,	PUNCT
ejpam-6388	59	21	such	such	ADJ
ejpam-6388	59	22	as	as	ADP
ejpam-6388	59	23	the	the	DET
ejpam-6388	59	24	spread	spread	NOUN
ejpam-6388	59	25	of	of	ADP
ejpam-6388	59	26	particles	particle	NOUN
ejpam-6388	59	27	in	in	ADP
ejpam-6388	59	28	porous	porous	ADJ
ejpam-6388	59	29	media	medium	NOUN
ejpam-6388	59	30	or	or	CCONJ
ejpam-6388	59	31	fractals	fractal	NOUN
ejpam-6388	59	32	,	,	PUNCT
ejpam-6388	60	1	where	where	SCONJ
ejpam-6388	60	2	classical	classical	ADJ
ejpam-6388	60	3	fick	fick	NOUN
ejpam-6388	60	4	’s	’s	PART
ejpam-6388	60	5	law	law	PROPN
ejpam-6388	60	6	d.	d.	PROPN
ejpam-6388	60	7	baleanu	baleanu	PROPN
ejpam-6388	60	8	et	et	PROPN
ejpam-6388	60	9	al	al	PROPN
ejpam-6388	60	10	.	.	PUNCT
ejpam-6388	60	11	/	/	SYM
ejpam-6388	60	12	eur	eur	PROPN
ejpam-6388	60	13	.	.	PUNCT
ejpam-6388	61	1	j.	j.	PROPN
ejpam-6388	61	2	pure	pure	PROPN
ejpam-6388	61	3	appl	appl	PROPN
ejpam-6388	61	4	.	.	PROPN
ejpam-6388	61	5	math	math	PROPN
ejpam-6388	61	6	,	,	PUNCT
ejpam-6388	61	7	18	18	NUM
ejpam-6388	61	8	(	(	PUNCT
ejpam-6388	61	9	4	4	NUM
ejpam-6388	61	10	)	)	PUNCT
ejpam-6388	61	11	(	(	PUNCT
ejpam-6388	61	12	2025	2025	NUM
ejpam-6388	61	13	)	)	PUNCT
ejpam-6388	61	14	,	,	PUNCT
ejpam-6388	61	15	6388	6388	NUM
ejpam-6388	61	16	4	4	NUM
ejpam-6388	61	17	of	of	ADP
ejpam-6388	61	18	31	31	NUM
ejpam-6388	61	19	fails	fail	VERB
ejpam-6388	61	20	.	.	PUNCT
ejpam-6388	62	1	the	the	DET
ejpam-6388	62	2	fractional	fractional	ADJ
ejpam-6388	62	3	derivative	derivative	NOUN
ejpam-6388	62	4	reflects	reflect	VERB
ejpam-6388	62	5	subdiffusion	subdiffusion	NOUN
ejpam-6388	62	6	or	or	CCONJ
ejpam-6388	62	7	superdiffusion	superdiffusion	NOUN
ejpam-6388	62	8	due	due	ADP
ejpam-6388	62	9	to	to	ADP
ejpam-6388	62	10	memory	memory	NOUN
ejpam-6388	62	11	effects	effect	NOUN
ejpam-6388	62	12	over	over	ADP
ejpam-6388	62	13	the	the	DET
ejpam-6388	62	14	interval	interval	NOUN
ejpam-6388	62	15	[	[	X
ejpam-6388	62	16	0	0	NUM
ejpam-6388	62	17	,	,	PUNCT
ejpam-6388	62	18	1	1	NUM
ejpam-6388	62	19	]	]	PUNCT
ejpam-6388	62	20	(	(	PUNCT
ejpam-6388	62	21	e.g.	e.g.	ADV
ejpam-6388	62	22	,	,	PUNCT
ejpam-6388	62	23	normalized	normalize	VERB
ejpam-6388	62	24	time	time	NOUN
ejpam-6388	62	25	or	or	CCONJ
ejpam-6388	62	26	space	space	NOUN
ejpam-6388	62	27	)	)	PUNCT
ejpam-6388	62	28	.	.	PUNCT
ejpam-6388	63	1	the	the	DET
ejpam-6388	63	2	term	term	NOUN
ejpam-6388	63	3	r(ω	r(ω	ADV
ejpam-6388	63	4	)	)	PUNCT
ejpam-6388	63	5	f(ω	f(ω	PROPN
ejpam-6388	63	6	,	,	PUNCT
ejpam-6388	63	7	r(ω	r(ω	ADJ
ejpam-6388	63	8	)	)	PUNCT
ejpam-6388	63	9	)	)	PUNCT
ejpam-6388	63	10	might	might	AUX
ejpam-6388	63	11	represents	represent	VERB
ejpam-6388	63	12	a	a	DET
ejpam-6388	63	13	concentration	concentration	NOUN
ejpam-6388	63	14	field	field	NOUN
ejpam-6388	63	15	scaled	scale	VERB
ejpam-6388	63	16	by	by	ADP
ejpam-6388	63	17	a	a	DET
ejpam-6388	63	18	nonlinear	nonlinear	ADJ
ejpam-6388	63	19	permeability	permeability	NOUN
ejpam-6388	63	20	or	or	CCONJ
ejpam-6388	63	21	reaction	reaction	NOUN
ejpam-6388	63	22	rate	rate	NOUN
ejpam-6388	63	23	(	(	PUNCT
ejpam-6388	63	24	f	f	NOUN
ejpam-6388	63	25	)	)	PUNCT
ejpam-6388	63	26	,	,	PUNCT
ejpam-6388	63	27	and	and	CCONJ
ejpam-6388	63	28	g(ω	g(ω	PROPN
ejpam-6388	63	29	,	,	PUNCT
ejpam-6388	63	30	r(ω	r(ω	ADJ
ejpam-6388	63	31	)	)	PUNCT
ejpam-6388	63	32	)	)	PUNCT
ejpam-6388	63	33	could	could	AUX
ejpam-6388	63	34	model	model	VERB
ejpam-6388	63	35	source	source	NOUN
ejpam-6388	63	36	/	/	SYM
ejpam-6388	63	37	sink	sink	NOUN
ejpam-6388	63	38	terms	term	NOUN
ejpam-6388	63	39	(	(	PUNCT
ejpam-6388	63	40	e.g.	e.g.	ADV
ejpam-6388	63	41	,	,	PUNCT
ejpam-6388	63	42	injection	injection	NOUN
ejpam-6388	63	43	/	/	SYM
ejpam-6388	63	44	extraction	extraction	NOUN
ejpam-6388	63	45	)	)	PUNCT
ejpam-6388	63	46	.	.	PUNCT
ejpam-6388	64	1	the	the	DET
ejpam-6388	64	2	boundary	boundary	ADJ
ejpam-6388	64	3	conditions	condition	NOUN
ejpam-6388	64	4	r(0	r(0	PROPN
ejpam-6388	64	5	)	)	PUNCT
ejpam-6388	64	6	=	=	SYM
ejpam-6388	64	7	0	0	PUNCT
ejpam-6388	64	8	(	(	PUNCT
ejpam-6388	64	9	no	no	DET
ejpam-6388	64	10	initial	initial	ADJ
ejpam-6388	64	11	concentration	concentration	NOUN
ejpam-6388	64	12	)	)	PUNCT
ejpam-6388	64	13	and	and	CCONJ
ejpam-6388	64	14	r(1	r(1	PROPN
ejpam-6388	64	15	)	)	PUNCT
ejpam-6388	64	16	=	=	PUNCT
ejpam-6388	64	17	f(1	f(1	PROPN
ejpam-6388	64	18	,	,	PUNCT
ejpam-6388	64	19	r(1	r(1	PROPN
ejpam-6388	64	20	)	)	PUNCT
ejpam-6388	64	21	)	)	PUNCT
ejpam-6388	64	22	(	(	PUNCT
ejpam-6388	64	23	a	a	DET
ejpam-6388	64	24	nonlinear	nonlinear	ADJ
ejpam-6388	64	25	equilibrium	equilibrium	NOUN
ejpam-6388	64	26	at	at	ADP
ejpam-6388	64	27	the	the	DET
ejpam-6388	64	28	boundary	boundary	NOUN
ejpam-6388	64	29	)	)	PUNCT
ejpam-6388	64	30	suggest	suggest	VERB
ejpam-6388	64	31	a	a	DET
ejpam-6388	64	32	system	system	NOUN
ejpam-6388	64	33	with	with	ADP
ejpam-6388	64	34	controlled	control	VERB
ejpam-6388	64	35	influx	influx	NOUN
ejpam-6388	64	36	or	or	CCONJ
ejpam-6388	64	37	outflow	outflow	NOUN
ejpam-6388	64	38	.	.	PUNCT
ejpam-6388	65	1	•	•	NUM
ejpam-6388	65	2	context	context	NOUN
ejpam-6388	65	3	:	:	PUNCT
ejpam-6388	65	4	relevant	relevant	ADJ
ejpam-6388	65	5	in	in	ADP
ejpam-6388	65	6	environmental	environmental	ADJ
ejpam-6388	65	7	science	science	NOUN
ejpam-6388	65	8	(	(	PUNCT
ejpam-6388	65	9	e.g.	e.g.	ADV
ejpam-6388	65	10	,	,	PUNCT
ejpam-6388	65	11	groundwater	groundwater	NOUN
ejpam-6388	65	12	flow	flow	NOUN
ejpam-6388	65	13	)	)	PUNCT
ejpam-6388	65	14	or	or	CCONJ
ejpam-6388	65	15	material	material	NOUN
ejpam-6388	65	16	science	science	NOUN
ejpam-6388	65	17	(	(	PUNCT
ejpam-6388	65	18	e.g.	e.g.	ADV
ejpam-6388	65	19	,	,	PUNCT
ejpam-6388	65	20	diffusion	diffusion	NOUN
ejpam-6388	65	21	in	in	ADP
ejpam-6388	65	22	nanocomposites	nanocomposite	NOUN
ejpam-6388	65	23	)	)	PUNCT
ejpam-6388	65	24	.	.	PUNCT
ejpam-6388	66	1	the	the	DET
ejpam-6388	66	2	novelty	novelty	NOUN
ejpam-6388	66	3	of	of	ADP
ejpam-6388	66	4	this	this	DET
ejpam-6388	66	5	work	work	NOUN
ejpam-6388	66	6	lies	lie	VERB
ejpam-6388	66	7	in	in	ADP
ejpam-6388	66	8	the	the	DET
ejpam-6388	66	9	following	follow	VERB
ejpam-6388	66	10	contributions	contribution	NOUN
ejpam-6388	66	11	:	:	PUNCT
ejpam-6388	66	12	•	•	NUM
ejpam-6388	66	13	generalization	generalization	NOUN
ejpam-6388	66	14	to	to	ADP
ejpam-6388	66	15	higher	high	ADJ
ejpam-6388	66	16	-	-	PUNCT
ejpam-6388	66	17	order	order	NOUN
ejpam-6388	66	18	fractional	fractional	ADJ
ejpam-6388	66	19	derivatives	derivative	NOUN
ejpam-6388	66	20	:	:	PUNCT
ejpam-6388	66	21	unlike	unlike	ADP
ejpam-6388	66	22	prior	prior	ADJ
ejpam-6388	66	23	studies	study	NOUN
ejpam-6388	66	24	such	such	ADJ
ejpam-6388	66	25	as	as	ADP
ejpam-6388	66	26	zhao	zhao	PROPN
ejpam-6388	66	27	et	et	PROPN
ejpam-6388	66	28	al	al	PROPN
ejpam-6388	66	29	.	.	PUNCT
ejpam-6388	67	1	[	[	X
ejpam-6388	67	2	1	1	NUM
ejpam-6388	67	3	]	]	PUNCT
ejpam-6388	67	4	,	,	PUNCT
ejpam-6388	67	5	which	which	PRON
ejpam-6388	67	6	focus	focus	VERB
ejpam-6388	67	7	on	on	ADP
ejpam-6388	67	8	fhbvps	fhbvps	PROPN
ejpam-6388	67	9	with	with	ADP
ejpam-6388	67	10	riemann	riemann	PROPN
ejpam-6388	67	11	–	–	PUNCT
ejpam-6388	67	12	liouville	liouville	VERB
ejpam-6388	67	13	derivatives	derivative	NOUN
ejpam-6388	67	14	of	of	ADP
ejpam-6388	67	15	order	order	NOUN
ejpam-6388	67	16	0	0	PUNCT
ejpam-6388	67	17	<	<	X
ejpam-6388	67	18	α	α	X
ejpam-6388	67	19	<	<	X
ejpam-6388	67	20	1	1	NUM
ejpam-6388	67	21	,	,	PUNCT
ejpam-6388	67	22	our	our	PRON
ejpam-6388	67	23	work	work	NOUN
ejpam-6388	67	24	extends	extend	VERB
ejpam-6388	67	25	the	the	DET
ejpam-6388	67	26	analysis	analysis	NOUN
ejpam-6388	67	27	to	to	ADP
ejpam-6388	67	28	higher	high	ADJ
ejpam-6388	67	29	-	-	PUNCT
ejpam-6388	67	30	order	order	NOUN
ejpam-6388	67	31	derivatives	derivative	NOUN
ejpam-6388	67	32	(	(	PUNCT
ejpam-6388	67	33	1	1	NUM
ejpam-6388	67	34	<	<	X
ejpam-6388	67	35	y	y	PROPN
ejpam-6388	67	36	≤	≤	NUM
ejpam-6388	67	37	2	2	NUM
ejpam-6388	67	38	)	)	PUNCT
ejpam-6388	67	39	,	,	PUNCT
ejpam-6388	67	40	enabling	enable	VERB
ejpam-6388	67	41	the	the	DET
ejpam-6388	67	42	modeling	modeling	NOUN
ejpam-6388	67	43	of	of	ADP
ejpam-6388	67	44	more	more	ADJ
ejpam-6388	67	45	complex	complex	ADJ
ejpam-6388	67	46	dynamic	dynamic	ADJ
ejpam-6388	67	47	systems	system	NOUN
ejpam-6388	67	48	.	.	PUNCT
ejpam-6388	68	1	•	•	NUM
ejpam-6388	68	2	orthogonal	orthogonal	ADJ
ejpam-6388	68	3	cone	cone	NOUN
ejpam-6388	68	4	metric	metric	ADJ
ejpam-6388	68	5	space	space	NOUN
ejpam-6388	68	6	framework	framework	NOUN
ejpam-6388	68	7	:	:	PUNCT
ejpam-6388	68	8	we	we	PRON
ejpam-6388	68	9	apply	apply	VERB
ejpam-6388	68	10	the	the	DET
ejpam-6388	68	11	extended	extended	ADJ
ejpam-6388	68	12	banach	banach	ADV
ejpam-6388	68	13	fixed	fix	VERB
ejpam-6388	68	14	point	point	NOUN
ejpam-6388	68	15	theorem	theorem	NOUN
ejpam-6388	68	16	(	(	PUNCT
ejpam-6388	68	17	fpt	fpt	PROPN
ejpam-6388	68	18	)	)	PUNCT
ejpam-6388	68	19	in	in	ADP
ejpam-6388	68	20	orthogonal	orthogonal	ADJ
ejpam-6388	68	21	cone	cone	NOUN
ejpam-6388	68	22	metric	metric	ADJ
ejpam-6388	68	23	spaces	space	NOUN
ejpam-6388	68	24	[	[	X
ejpam-6388	68	25	20	20	NUM
ejpam-6388	68	26	]	]	PUNCT
ejpam-6388	68	27	,	,	PUNCT
ejpam-6388	68	28	generalizing	generalize	VERB
ejpam-6388	68	29	the	the	DET
ejpam-6388	68	30	standard	standard	ADJ
ejpam-6388	68	31	metric	metric	ADJ
ejpam-6388	68	32	space	space	NOUN
ejpam-6388	68	33	and	and	CCONJ
ejpam-6388	68	34	banach	banach	NOUN
ejpam-6388	68	35	algebra	algebra	NOUN
ejpam-6388	68	36	approaches	approach	NOUN
ejpam-6388	68	37	of	of	ADP
ejpam-6388	68	38	[	[	X
ejpam-6388	68	39	1	1	NUM
ejpam-6388	68	40	,	,	PUNCT
ejpam-6388	68	41	2	2	NUM
ejpam-6388	68	42	]	]	PUNCT
ejpam-6388	68	43	.	.	PUNCT
ejpam-6388	69	1	this	this	DET
ejpam-6388	69	2	framework	framework	NOUN
ejpam-6388	69	3	accommodates	accommodate	VERB
ejpam-6388	69	4	intricate	intricate	ADJ
ejpam-6388	69	5	nonlinearities	nonlinearitie	NOUN
ejpam-6388	69	6	and	and	CCONJ
ejpam-6388	69	7	nonlocal	nonlocal	ADJ
ejpam-6388	69	8	boundary	boundary	ADJ
ejpam-6388	69	9	conditions	condition	NOUN
ejpam-6388	69	10	,	,	PUNCT
ejpam-6388	69	11	offering	offer	VERB
ejpam-6388	69	12	a	a	DET
ejpam-6388	69	13	more	more	ADV
ejpam-6388	69	14	flexible	flexible	ADJ
ejpam-6388	69	15	geometric	geometric	ADJ
ejpam-6388	69	16	structure	structure	NOUN
ejpam-6388	69	17	.	.	PUNCT
ejpam-6388	70	1	•	•	NUM
ejpam-6388	70	2	hyers	hyer	NOUN
ejpam-6388	70	3	–	–	PUNCT
ejpam-6388	70	4	ulam	ulam	PROPN
ejpam-6388	70	5	stability	stability	NOUN
ejpam-6388	70	6	analysis	analysis	NOUN
ejpam-6388	70	7	:	:	PUNCT
ejpam-6388	70	8	our	our	PRON
ejpam-6388	70	9	study	study	NOUN
ejpam-6388	70	10	provides	provide	VERB
ejpam-6388	70	11	a	a	DET
ejpam-6388	70	12	rigorous	rigorous	ADJ
ejpam-6388	70	13	hyers	hyer	NOUN
ejpam-6388	70	14	–	–	PUNCT
ejpam-6388	70	15	ulam	ulam	PROPN
ejpam-6388	70	16	stability	stability	NOUN
ejpam-6388	70	17	analysis	analysis	NOUN
ejpam-6388	70	18	for	for	ADP
ejpam-6388	70	19	fhbvps	fhbvps	PROPN
ejpam-6388	70	20	,	,	PUNCT
ejpam-6388	70	21	correcting	correct	VERB
ejpam-6388	70	22	common	common	ADJ
ejpam-6388	70	23	misunderstandings	misunderstanding	NOUN
ejpam-6388	70	24	in	in	ADP
ejpam-6388	70	25	prior	prior	ADJ
ejpam-6388	70	26	approaches	approach	NOUN
ejpam-6388	70	27	[	[	X
ejpam-6388	70	28	3	3	X
ejpam-6388	70	29	]	]	PUNCT
ejpam-6388	70	30	by	by	ADP
ejpam-6388	70	31	introducing	introduce	VERB
ejpam-6388	70	32	a	a	DET
ejpam-6388	70	33	parameter	parameter	NOUN
ejpam-6388	70	34	to	to	PART
ejpam-6388	70	35	handle	handle	AUX
ejpam-6388	70	36	perturbed	perturb	VERB
ejpam-6388	70	37	boundary	boundary	ADJ
ejpam-6388	70	38	conditions	condition	NOUN
ejpam-6388	70	39	,	,	PUNCT
ejpam-6388	70	40	ensuring	ensure	VERB
ejpam-6388	70	41	robust	robust	ADJ
ejpam-6388	70	42	solutions	solution	NOUN
ejpam-6388	70	43	.	.	PUNCT
ejpam-6388	71	1	•	•	NUM
ejpam-6388	71	2	numerical	numerical	ADJ
ejpam-6388	71	3	validation	validation	NOUN
ejpam-6388	71	4	:	:	PUNCT
ejpam-6388	71	5	we	we	PRON
ejpam-6388	71	6	complement	complement	VERB
ejpam-6388	71	7	our	our	PRON
ejpam-6388	71	8	theoretical	theoretical	ADJ
ejpam-6388	71	9	results	result	NOUN
ejpam-6388	71	10	with	with	ADP
ejpam-6388	71	11	numerical	numerical	ADJ
ejpam-6388	71	12	simulations	simulation	NOUN
ejpam-6388	71	13	,	,	PUNCT
ejpam-6388	71	14	using	use	VERB
ejpam-6388	71	15	the	the	DET
ejpam-6388	71	16	trapezoidal	trapezoidal	ADJ
ejpam-6388	71	17	rule	rule	NOUN
ejpam-6388	71	18	to	to	PART
ejpam-6388	71	19	approximate	approximate	ADJ
ejpam-6388	71	20	solutions	solution	NOUN
ejpam-6388	71	21	and	and	CCONJ
ejpam-6388	71	22	providing	provide	VERB
ejpam-6388	71	23	graphical	graphical	ADJ
ejpam-6388	71	24	comparisons	comparison	NOUN
ejpam-6388	71	25	(	(	PUNCT
ejpam-6388	71	26	e.g.	e.g.	ADV
ejpam-6388	71	27	,	,	PUNCT
ejpam-6388	71	28	figures	figure	NOUN
ejpam-6388	71	29	1	1	NUM
ejpam-6388	71	30	-	-	SYM
ejpam-6388	71	31	4	4	NUM
ejpam-6388	71	32	)	)	PUNCT
ejpam-6388	71	33	to	to	PART
ejpam-6388	71	34	illustrate	illustrate	VERB
ejpam-6388	71	35	the	the	DET
ejpam-6388	71	36	impact	impact	NOUN
ejpam-6388	71	37	of	of	ADP
ejpam-6388	71	38	fractional	fractional	ADJ
ejpam-6388	71	39	order	order	NOUN
ejpam-6388	71	40	and	and	CCONJ
ejpam-6388	71	41	function	function	NOUN
ejpam-6388	71	42	choices	choice	NOUN
ejpam-6388	71	43	on	on	ADP
ejpam-6388	71	44	solution	solution	NOUN
ejpam-6388	71	45	behavior	behavior	NOUN
ejpam-6388	71	46	.	.	PUNCT
ejpam-6388	72	1	the	the	DET
ejpam-6388	72	2	layout	layout	NOUN
ejpam-6388	72	3	of	of	ADP
ejpam-6388	72	4	this	this	DET
ejpam-6388	72	5	paper	paper	NOUN
ejpam-6388	72	6	is	be	AUX
ejpam-6388	72	7	as	as	SCONJ
ejpam-6388	72	8	follows	follow	VERB
ejpam-6388	72	9	:	:	PUNCT
ejpam-6388	72	10	section	section	NOUN
ejpam-6388	72	11	2	2	NUM
ejpam-6388	72	12	presents	present	VERB
ejpam-6388	72	13	foundational	foundational	ADJ
ejpam-6388	72	14	definitions	definition	NOUN
ejpam-6388	72	15	and	and	CCONJ
ejpam-6388	72	16	key	key	ADJ
ejpam-6388	72	17	results	result	NOUN
ejpam-6388	72	18	required	require	VERB
ejpam-6388	72	19	for	for	ADP
ejpam-6388	72	20	later	later	ADJ
ejpam-6388	72	21	sections	section	NOUN
ejpam-6388	72	22	.	.	PUNCT
ejpam-6388	73	1	in	in	ADP
ejpam-6388	73	2	section	section	NOUN
ejpam-6388	73	3	3	3	NUM
ejpam-6388	73	4	,	,	PUNCT
ejpam-6388	73	5	we	we	PRON
ejpam-6388	73	6	establish	establish	VERB
ejpam-6388	73	7	and	and	CCONJ
ejpam-6388	73	8	prove	prove	VERB
ejpam-6388	73	9	several	several	ADJ
ejpam-6388	73	10	preliminary	preliminary	ADJ
ejpam-6388	73	11	results	result	NOUN
ejpam-6388	73	12	that	that	PRON
ejpam-6388	73	13	provide	provide	VERB
ejpam-6388	73	14	a	a	DET
ejpam-6388	73	15	basis	basis	NOUN
ejpam-6388	73	16	for	for	ADP
ejpam-6388	73	17	the	the	DET
ejpam-6388	73	18	main	main	ADJ
ejpam-6388	73	19	findings	finding	NOUN
ejpam-6388	73	20	.	.	PUNCT
ejpam-6388	74	1	section	section	NOUN
ejpam-6388	74	2	4	4	NUM
ejpam-6388	74	3	is	be	AUX
ejpam-6388	74	4	dedicated	dedicate	VERB
ejpam-6388	74	5	to	to	ADP
ejpam-6388	74	6	an	an	DET
ejpam-6388	74	7	in	in	ADP
ejpam-6388	74	8	-	-	PUNCT
ejpam-6388	74	9	depth	depth	NOUN
ejpam-6388	74	10	examination	examination	NOUN
ejpam-6388	74	11	of	of	ADP
ejpam-6388	74	12	the	the	DET
ejpam-6388	74	13	existence	existence	NOUN
ejpam-6388	74	14	and	and	CCONJ
ejpam-6388	74	15	uniqueness	uniqueness	NOUN
ejpam-6388	74	16	of	of	ADP
ejpam-6388	74	17	solutions	solution	NOUN
ejpam-6388	74	18	for	for	ADP
ejpam-6388	74	19	the	the	DET
ejpam-6388	74	20	fhbvp	fhbvp	NOUN
ejpam-6388	74	21	(	(	PUNCT
ejpam-6388	74	22	1)–(2	1)–(2	NUM
ejpam-6388	74	23	)	)	PUNCT
ejpam-6388	74	24	.	.	PUNCT
ejpam-6388	75	1	section	section	NOUN
ejpam-6388	75	2	5	5	NUM
ejpam-6388	75	3	outlines	outline	VERB
ejpam-6388	75	4	the	the	DET
ejpam-6388	75	5	requirements	requirement	NOUN
ejpam-6388	75	6	for	for	ADP
ejpam-6388	75	7	hyers	hyer	NOUN
ejpam-6388	75	8	–	–	PUNCT
ejpam-6388	75	9	ulam	ulam	PROPN
ejpam-6388	75	10	stability	stability	NOUN
ejpam-6388	75	11	concerning	concern	VERB
ejpam-6388	75	12	(	(	PUNCT
ejpam-6388	75	13	1	1	NUM
ejpam-6388	75	14	)	)	PUNCT
ejpam-6388	75	15	–	–	PUNCT
ejpam-6388	75	16	(	(	PUNCT
ejpam-6388	75	17	2	2	NUM
ejpam-6388	75	18	)	)	PUNCT
ejpam-6388	75	19	.	.	PUNCT
ejpam-6388	76	1	illustrative	illustrative	ADJ
ejpam-6388	76	2	examples	example	NOUN
ejpam-6388	76	3	to	to	PART
ejpam-6388	76	4	support	support	VERB
ejpam-6388	76	5	the	the	DET
ejpam-6388	76	6	obtained	obtain	VERB
ejpam-6388	76	7	results	result	NOUN
ejpam-6388	76	8	are	be	AUX
ejpam-6388	76	9	included	include	VERB
ejpam-6388	76	10	in	in	ADP
ejpam-6388	76	11	section	section	NOUN
ejpam-6388	76	12	6	6	NUM
ejpam-6388	76	13	.	.	PUNCT
ejpam-6388	77	1	in	in	ADP
ejpam-6388	77	2	section	section	NOUN
ejpam-6388	77	3	7	7	NUM
ejpam-6388	77	4	,	,	PUNCT
ejpam-6388	77	5	we	we	PRON
ejpam-6388	77	6	provide	provide	VERB
ejpam-6388	77	7	a	a	DET
ejpam-6388	77	8	conclusion	conclusion	NOUN
ejpam-6388	77	9	of	of	ADP
ejpam-6388	77	10	the	the	DET
ejpam-6388	77	11	work	work	NOUN
ejpam-6388	77	12	done	do	VERB
ejpam-6388	77	13	in	in	ADP
ejpam-6388	77	14	this	this	DET
ejpam-6388	77	15	paper	paper	NOUN
ejpam-6388	77	16	and	and	CCONJ
ejpam-6388	77	17	highlight	highlight	VERB
ejpam-6388	77	18	possible	possible	ADJ
ejpam-6388	77	19	avenues	avenue	NOUN
ejpam-6388	77	20	for	for	ADP
ejpam-6388	77	21	future	future	ADJ
ejpam-6388	77	22	research	research	NOUN
ejpam-6388	77	23	.	.	PUNCT
ejpam-6388	78	1	2	2	X
ejpam-6388	78	2	.	.	X
ejpam-6388	78	3	essential	essential	ADJ
ejpam-6388	78	4	preliminaries	preliminary	NOUN
ejpam-6388	78	5	definition	definition	NOUN
ejpam-6388	78	6	1	1	NUM
ejpam-6388	78	7	.	.	PUNCT
ejpam-6388	79	1	[	[	X
ejpam-6388	79	2	6	6	NUM
ejpam-6388	79	3	]	]	PUNCT
ejpam-6388	79	4	for	for	ADP
ejpam-6388	79	5	a	a	DET
ejpam-6388	79	6	continuous	continuous	ADJ
ejpam-6388	79	7	function	function	NOUN
ejpam-6388	79	8	ψ	ψ	NOUN
ejpam-6388	79	9	:	:	PUNCT
ejpam-6388	79	10	(	(	PUNCT
ejpam-6388	79	11	0,∞	0,∞	NOUN
ejpam-6388	79	12	)	)	PUNCT
ejpam-6388	79	13	→	→	SYM
ejpam-6388	79	14	r	r	NOUN
ejpam-6388	79	15	and	and	CCONJ
ejpam-6388	79	16	an	an	DET
ejpam-6388	79	17	order	order	NOUN
ejpam-6388	79	18	y	y	PROPN
ejpam-6388	79	19	>	>	X
ejpam-6388	79	20	0	0	PROPN
ejpam-6388	79	21	,	,	PUNCT
ejpam-6388	79	22	the	the	DET
ejpam-6388	79	23	d.	d.	PROPN
ejpam-6388	79	24	baleanu	baleanu	PROPN
ejpam-6388	79	25	et	et	PROPN
ejpam-6388	79	26	al	al	PROPN
ejpam-6388	79	27	.	.	PUNCT
ejpam-6388	79	28	/	/	SYM
ejpam-6388	79	29	eur	eur	PROPN
ejpam-6388	79	30	.	.	PUNCT
ejpam-6388	80	1	j.	j.	PROPN
ejpam-6388	80	2	pure	pure	PROPN
ejpam-6388	80	3	appl	appl	PROPN
ejpam-6388	80	4	.	.	PROPN
ejpam-6388	80	5	math	math	PROPN
ejpam-6388	80	6	,	,	PUNCT
ejpam-6388	80	7	18	18	NUM
ejpam-6388	80	8	(	(	PUNCT
ejpam-6388	80	9	4	4	NUM
ejpam-6388	80	10	)	)	PUNCT
ejpam-6388	80	11	(	(	PUNCT
ejpam-6388	80	12	2025	2025	NUM
ejpam-6388	80	13	)	)	PUNCT
ejpam-6388	80	14	,	,	PUNCT
ejpam-6388	80	15	6388	6388	NUM
ejpam-6388	80	16	5	5	NUM
ejpam-6388	80	17	of	of	ADP
ejpam-6388	80	18	31	31	NUM
ejpam-6388	80	19	riemann	riemann	PROPN
ejpam-6388	80	20	–	–	PUNCT
ejpam-6388	80	21	liouville	liouville	VERB
ejpam-6388	80	22	fractional	fractional	ADJ
ejpam-6388	80	23	integral	integral	NOUN
ejpam-6388	80	24	is	be	AUX
ejpam-6388	80	25	described	describe	VERB
ejpam-6388	80	26	as	as	SCONJ
ejpam-6388	80	27	follows	follow	VERB
ejpam-6388	80	28	:	:	PUNCT
ejpam-6388	80	29	i	i	PRON
ejpam-6388	80	30	y	y	PROPN
ejpam-6388	80	31	0	0	NUM
ejpam-6388	80	32	+	+	NUM
ejpam-6388	80	33	ψ(ω	ψ(ω	PROPN
ejpam-6388	80	34	)	)	PUNCT
ejpam-6388	81	1	=	=	SYM
ejpam-6388	81	2	1	1	NUM
ejpam-6388	81	3	γ(y	γ(y	PROPN
ejpam-6388	81	4	)	)	PUNCT
ejpam-6388	81	5	∫	∫	PROPN
ejpam-6388	82	1	ω	ω	NUM
ejpam-6388	82	2	0	0	NUM
ejpam-6388	82	3	(	(	PUNCT
ejpam-6388	82	4	ω	ω	NOUN
ejpam-6388	82	5	−	−	PROPN
ejpam-6388	82	6	ξ)y−1ψ(ξ)dξ	ξ)y−1ψ(ξ)dξ	NOUN
ejpam-6388	82	7	.	.	PUNCT
ejpam-6388	83	1	definition	definition	NOUN
ejpam-6388	83	2	2	2	NUM
ejpam-6388	83	3	.	.	PUNCT
ejpam-6388	84	1	[	[	X
ejpam-6388	84	2	6	6	NUM
ejpam-6388	84	3	]	]	PUNCT
ejpam-6388	84	4	for	for	ADP
ejpam-6388	84	5	a	a	DET
ejpam-6388	84	6	continuous	continuous	ADJ
ejpam-6388	84	7	function	function	NOUN
ejpam-6388	84	8	ψ	ψ	NOUN
ejpam-6388	84	9	:	:	PUNCT
ejpam-6388	84	10	(	(	PUNCT
ejpam-6388	84	11	0,∞	0,∞	NOUN
ejpam-6388	84	12	)	)	PUNCT
ejpam-6388	84	13	→	→	SYM
ejpam-6388	84	14	r	r	NOUN
ejpam-6388	84	15	and	and	CCONJ
ejpam-6388	84	16	an	an	DET
ejpam-6388	84	17	order	order	NOUN
ejpam-6388	84	18	y	y	PROPN
ejpam-6388	84	19	>	>	X
ejpam-6388	84	20	0	0	PROPN
ejpam-6388	84	21	,	,	PUNCT
ejpam-6388	84	22	the	the	DET
ejpam-6388	84	23	riemann	riemann	PROPN
ejpam-6388	84	24	–	–	PUNCT
ejpam-6388	84	25	liouville	liouville	VERB
ejpam-6388	84	26	fractional	fractional	ADJ
ejpam-6388	84	27	derivative	derivative	NOUN
ejpam-6388	84	28	is	be	AUX
ejpam-6388	84	29	formulated	formulate	VERB
ejpam-6388	84	30	as	as	SCONJ
ejpam-6388	84	31	follows	follow	VERB
ejpam-6388	84	32	:	:	PUNCT
ejpam-6388	84	33	dy	dy	NOUN
ejpam-6388	84	34	0	0	PROPN
ejpam-6388	84	35	+	+	NUM
ejpam-6388	84	36	ψ(ω	ψ(ω	X
ejpam-6388	84	37	)	)	PUNCT
ejpam-6388	85	1	=	=	PUNCT
ejpam-6388	85	2	1	1	NUM
ejpam-6388	85	3	γ(m−	γ(m−	PROPN
ejpam-6388	85	4	y	y	PROPN
ejpam-6388	85	5	)	)	PUNCT
ejpam-6388	85	6	(	(	PUNCT
ejpam-6388	86	1	d	d	X
ejpam-6388	86	2	dω	dω	NOUN
ejpam-6388	86	3	)	)	PUNCT
ejpam-6388	86	4	m	m	PROPN
ejpam-6388	86	5	∫	∫	PROPN
ejpam-6388	86	6	ω	ω	NUM
ejpam-6388	86	7	0	0	NUM
ejpam-6388	86	8	ψ(ξ	ψ(ξ	PROPN
ejpam-6388	86	9	)	)	PUNCT
ejpam-6388	86	10	(	(	PUNCT
ejpam-6388	86	11	ω	ω	NUM
ejpam-6388	86	12	−	−	PROPN
ejpam-6388	86	13	ξ)y−m+1	ξ)y−m+1	PROPN
ejpam-6388	86	14	dξ	dξ	PROPN
ejpam-6388	86	15	,	,	PUNCT
ejpam-6388	86	16	m	m	VERB
ejpam-6388	86	17	=	=	PUNCT
ejpam-6388	87	1	[	[	X
ejpam-6388	87	2	y	y	X
ejpam-6388	87	3	]	]	X
ejpam-6388	87	4	+	+	NOUN
ejpam-6388	87	5	1	1	X
ejpam-6388	87	6	.	.	X
ejpam-6388	87	7	remark	remark	NOUN
ejpam-6388	87	8	1	1	NUM
ejpam-6388	87	9	.	.	PUNCT
ejpam-6388	88	1	[	[	X
ejpam-6388	88	2	6	6	NUM
ejpam-6388	88	3	]	]	PUNCT
ejpam-6388	88	4	the	the	DET
ejpam-6388	88	5	following	follow	VERB
ejpam-6388	88	6	composition	composition	NOUN
ejpam-6388	88	7	relations	relation	NOUN
ejpam-6388	88	8	are	be	AUX
ejpam-6388	88	9	necessary	necessary	ADJ
ejpam-6388	88	10	for	for	ADP
ejpam-6388	88	11	the	the	DET
ejpam-6388	88	12	present	present	ADJ
ejpam-6388	88	13	work	work	NOUN
ejpam-6388	88	14	:	:	PUNCT
ejpam-6388	88	15	(	(	PUNCT
ejpam-6388	88	16	i	i	NOUN
ejpam-6388	88	17	)	)	PUNCT
ejpam-6388	88	18	dy	dy	NOUN
ejpam-6388	88	19	0	0	NUM
ejpam-6388	89	1	+	+	NUM
ejpam-6388	89	2	i	i	NOUN
ejpam-6388	89	3	y	y	PROPN
ejpam-6388	89	4	0	0	NUM
ejpam-6388	89	5	+	+	NUM
ejpam-6388	89	6	ψ(ω	ψ(ω	PROPN
ejpam-6388	89	7	)	)	PUNCT
ejpam-6388	90	1	=	=	SYM
ejpam-6388	90	2	ψ(ω	ψ(ω	PROPN
ejpam-6388	90	3	)	)	PUNCT
ejpam-6388	90	4	,	,	PUNCT
ejpam-6388	90	5	y	y	PROPN
ejpam-6388	90	6	>	>	X
ejpam-6388	90	7	0	0	PROPN
ejpam-6388	90	8	,	,	PUNCT
ejpam-6388	90	9	where	where	SCONJ
ejpam-6388	90	10	ψ(ω	ψ(ω	PROPN
ejpam-6388	90	11	)	)	PUNCT
ejpam-6388	90	12	∈	∈	PROPN
ejpam-6388	90	13	l1(0,+∞	l1(0,+∞	PROPN
ejpam-6388	90	14	)	)	PUNCT
ejpam-6388	90	15	.	.	PUNCT
ejpam-6388	91	1	(	(	PUNCT
ejpam-6388	91	2	ii	ii	NOUN
ejpam-6388	91	3	)	)	PUNCT
ejpam-6388	91	4	dδ	dδ	ADP
ejpam-6388	91	5	0+i	0+i	NUM
ejpam-6388	91	6	y	y	PROPN
ejpam-6388	91	7	0	0	NUM
ejpam-6388	91	8	+	+	NUM
ejpam-6388	91	9	ψ(ω	ψ(ω	X
ejpam-6388	91	10	)	)	PUNCT
ejpam-6388	92	1	=	=	PUNCT
ejpam-6388	93	1	i	i	PRON
ejpam-6388	93	2	y−δ	y−δ	NOUN
ejpam-6388	93	3	0	0	PUNCT
ejpam-6388	93	4	+	+	NUM
ejpam-6388	93	5	ψ(ω	ψ(ω	PROPN
ejpam-6388	93	6	)	)	PUNCT
ejpam-6388	93	7	,	,	PUNCT
ejpam-6388	93	8	y	y	PROPN
ejpam-6388	93	9	>	>	X
ejpam-6388	93	10	δ	δ	PROPN
ejpam-6388	93	11	>	>	X
ejpam-6388	93	12	0	0	PROPN
ejpam-6388	93	13	,	,	PUNCT
ejpam-6388	93	14	where	where	SCONJ
ejpam-6388	93	15	ψ(ω	ψ(ω	PROPN
ejpam-6388	93	16	)	)	PUNCT
ejpam-6388	93	17	∈	∈	PROPN
ejpam-6388	93	18	l1(0,+∞	l1(0,+∞	NUM
ejpam-6388	93	19	)	)	PUNCT
ejpam-6388	93	20	.	.	PUNCT
ejpam-6388	94	1	remark	remark	NOUN
ejpam-6388	94	2	2	2	NUM
ejpam-6388	94	3	.	.	PUNCT
ejpam-6388	95	1	[	[	X
ejpam-6388	95	2	26	26	NUM
ejpam-6388	95	3	]	]	PUNCT
ejpam-6388	95	4	for	for	ADP
ejpam-6388	95	5	α	α	PROPN
ejpam-6388	95	6	>	>	X
ejpam-6388	95	7	−1	−1	NOUN
ejpam-6388	95	8	,	,	PUNCT
ejpam-6388	95	9	we	we	PRON
ejpam-6388	95	10	have	have	AUX
ejpam-6388	95	11	dy	dy	NOUN
ejpam-6388	95	12	0	0	NUM
ejpam-6388	96	1	+	+	SYM
ejpam-6388	96	2	ωα	ωα	X
ejpam-6388	96	3	=	=	SYM
ejpam-6388	96	4	γ(α+	γ(α+	PRON
ejpam-6388	96	5	1	1	NUM
ejpam-6388	96	6	)	)	PUNCT
ejpam-6388	96	7	γ(α−	γ(α−	NOUN
ejpam-6388	96	8	y+	y+	NUM
ejpam-6388	96	9	1	1	NUM
ejpam-6388	96	10	)	)	PUNCT
ejpam-6388	96	11	ωα−y	ωα−y	NOUN
ejpam-6388	96	12	,	,	PUNCT
ejpam-6388	96	13	which	which	PRON
ejpam-6388	96	14	precisely	precisely	ADV
ejpam-6388	96	15	yields	yield	VERB
ejpam-6388	96	16	dy	dy	NOUN
ejpam-6388	96	17	0	0	NUM
ejpam-6388	96	18	+	+	SYM
ejpam-6388	96	19	ωy−m	ωy−m	ADJ
ejpam-6388	96	20	=	=	SYM
ejpam-6388	96	21	0	0	NUM
ejpam-6388	96	22	,	,	PUNCT
ejpam-6388	96	23	m	m	VERB
ejpam-6388	96	24	=	=	NOUN
ejpam-6388	96	25	1	1	NUM
ejpam-6388	96	26	,	,	PUNCT
ejpam-6388	96	27	n	n	CCONJ
ejpam-6388	96	28	,	,	PUNCT
ejpam-6388	96	29	where	where	SCONJ
ejpam-6388	96	30	n	n	PRON
ejpam-6388	96	31	≤	≤	X
ejpam-6388	96	32	y	y	PROPN
ejpam-6388	96	33	≤	≤	PROPN
ejpam-6388	96	34	n	n	CCONJ
ejpam-6388	96	35	+	+	CCONJ
ejpam-6388	96	36	1	1	NUM
ejpam-6388	96	37	and	and	CCONJ
ejpam-6388	96	38	n	n	PRON
ejpam-6388	96	39	∈	∈	PROPN
ejpam-6388	96	40	z.	z.	PROPN
ejpam-6388	96	41	here	here	ADV
ejpam-6388	96	42	1	1	NUM
ejpam-6388	96	43	,	,	PUNCT
ejpam-6388	96	44	n	n	NOUN
ejpam-6388	96	45	=	=	SYM
ejpam-6388	96	46	1	1	NUM
ejpam-6388	96	47	,	,	PUNCT
ejpam-6388	96	48	2	2	NUM
ejpam-6388	96	49	,	,	PUNCT
ejpam-6388	96	50	3	3	NUM
ejpam-6388	96	51	,	,	PUNCT
ejpam-6388	96	52	.	.	PUNCT
ejpam-6388	96	53	.	.	PUNCT
ejpam-6388	97	1	.	.	PUNCT
ejpam-6388	98	1	,	,	PUNCT
ejpam-6388	98	2	n.	n.	PROPN
ejpam-6388	98	3	lemma	lemma	PROPN
ejpam-6388	98	4	1	1	NUM
ejpam-6388	98	5	.	.	PUNCT
ejpam-6388	99	1	[	[	X
ejpam-6388	99	2	6	6	NUM
ejpam-6388	99	3	]	]	PUNCT
ejpam-6388	99	4	let	let	VERB
ejpam-6388	99	5	y	y	PROPN
ejpam-6388	99	6	∈	∈	PROPN
ejpam-6388	99	7	(	(	PUNCT
ejpam-6388	99	8	m	m	NOUN
ejpam-6388	99	9	−	−	PROPN
ejpam-6388	99	10	1	1	NUM
ejpam-6388	99	11	,	,	PUNCT
ejpam-6388	99	12	m	m	PROPN
ejpam-6388	99	13	]	]	X
ejpam-6388	99	14	and	and	CCONJ
ejpam-6388	99	15	m	m	VERB
ejpam-6388	99	16	>	>	X
ejpam-6388	100	1	1	1	X
ejpam-6388	100	2	.	.	PUNCT
ejpam-6388	101	1	then	then	ADV
ejpam-6388	101	2	the	the	DET
ejpam-6388	101	3	general	general	ADJ
ejpam-6388	101	4	solution	solution	NOUN
ejpam-6388	101	5	to	to	ADP
ejpam-6388	101	6	dy	dy	NOUN
ejpam-6388	101	7	0	0	NUM
ejpam-6388	101	8	+	+	NOUN
ejpam-6388	101	9	u(ω	u(ω	X
ejpam-6388	101	10	)	)	PUNCT
ejpam-6388	102	1	=	=	SYM
ejpam-6388	102	2	0	0	NUM
ejpam-6388	102	3	is	be	AUX
ejpam-6388	102	4	u(ω	u(ω	PROPN
ejpam-6388	102	5	)	)	PUNCT
ejpam-6388	103	1	=	=	PUNCT
ejpam-6388	103	2	∑m	∑m	PROPN
ejpam-6388	103	3	i=1	i=1	PROPN
ejpam-6388	103	4	kiω	kiω	NOUN
ejpam-6388	103	5	y−i	y−i	PROPN
ejpam-6388	103	6	,	,	PUNCT
ejpam-6388	103	7	where	where	SCONJ
ejpam-6388	103	8	ki	ki	PROPN
ejpam-6388	103	9	∈	∈	PROPN
ejpam-6388	103	10	r	r	PROPN
ejpam-6388	103	11	,	,	PUNCT
ejpam-6388	103	12	i	i	NOUN
ejpam-6388	103	13	=	=	NOUN
ejpam-6388	103	14	1	1	NUM
ejpam-6388	103	15	,	,	PUNCT
ejpam-6388	103	16	m.	m.	NOUN
ejpam-6388	103	17	lemma	lemma	PROPN
ejpam-6388	103	18	2	2	X
ejpam-6388	103	19	.	.	PUNCT
ejpam-6388	104	1	[	[	X
ejpam-6388	104	2	6	6	NUM
ejpam-6388	104	3	]	]	PUNCT
ejpam-6388	104	4	let	let	VERB
ejpam-6388	104	5	y	y	PRON
ejpam-6388	104	6	>	>	X
ejpam-6388	104	7	0	0	PROPN
ejpam-6388	104	8	.	.	PUNCT
ejpam-6388	105	1	then	then	ADV
ejpam-6388	105	2	,	,	PUNCT
ejpam-6388	105	3	for	for	ADP
ejpam-6388	105	4	a	a	DET
ejpam-6388	105	5	given	give	VERB
ejpam-6388	105	6	function	function	NOUN
ejpam-6388	105	7	u	u	NOUN
ejpam-6388	105	8	,	,	PUNCT
ejpam-6388	105	9	we	we	PRON
ejpam-6388	105	10	have	have	VERB
ejpam-6388	105	11	i	i	PRON
ejpam-6388	105	12	y	y	PROPN
ejpam-6388	105	13	0	0	NUM
ejpam-6388	105	14	+	+	NUM
ejpam-6388	105	15	dy	dy	NOUN
ejpam-6388	105	16	0	0	SYM
ejpam-6388	105	17	+	+	NOUN
ejpam-6388	105	18	u(ω	u(ω	X
ejpam-6388	105	19	)	)	PUNCT
ejpam-6388	105	20	=	=	SYM
ejpam-6388	105	21	u(ω	u(ω	PROPN
ejpam-6388	105	22	)	)	PUNCT
ejpam-6388	106	1	+	+	CCONJ
ejpam-6388	106	2	m∑	m∑	CCONJ
ejpam-6388	106	3	i=1	i=1	PROPN
ejpam-6388	106	4	kiω	kiω	PROPN
ejpam-6388	106	5	y−i	y−i	PROPN
ejpam-6388	106	6	,	,	PUNCT
ejpam-6388	106	7	where	where	SCONJ
ejpam-6388	106	8	ki	ki	PROPN
ejpam-6388	106	9	∈	∈	PROPN
ejpam-6388	106	10	r	r	PROPN
ejpam-6388	106	11	,	,	PUNCT
ejpam-6388	106	12	i	i	NOUN
ejpam-6388	106	13	=	=	NOUN
ejpam-6388	106	14	1	1	NUM
ejpam-6388	106	15	,	,	PUNCT
ejpam-6388	106	16	m	m	PROPN
ejpam-6388	106	17	,	,	PUNCT
ejpam-6388	106	18	m	m	VERB
ejpam-6388	106	19	≤	≤	NUM
ejpam-6388	106	20	y	y	NOUN
ejpam-6388	106	21	≤	≤	NUM
ejpam-6388	106	22	m+	m+	NUM
ejpam-6388	106	23	1	1	NUM
ejpam-6388	106	24	and	and	CCONJ
ejpam-6388	106	25	m	m	PROPN
ejpam-6388	106	26	∈	∈	PROPN
ejpam-6388	106	27	z.	z.	PROPN
ejpam-6388	106	28	definition	definition	NOUN
ejpam-6388	106	29	3	3	NUM
ejpam-6388	106	30	.	.	PUNCT
ejpam-6388	107	1	[	[	X
ejpam-6388	107	2	14	14	NUM
ejpam-6388	107	3	]	]	PUNCT
ejpam-6388	107	4	let	let	VERB
ejpam-6388	107	5	e	e	PRON
ejpam-6388	107	6	be	be	AUX
ejpam-6388	107	7	a	a	DET
ejpam-6388	107	8	real	real	ADJ
ejpam-6388	107	9	banach	banach	NOUN
ejpam-6388	107	10	space	space	NOUN
ejpam-6388	107	11	and	and	CCONJ
ejpam-6388	107	12	q	q	AUX
ejpam-6388	107	13	be	be	AUX
ejpam-6388	107	14	a	a	DET
ejpam-6388	107	15	subset	subset	NOUN
ejpam-6388	107	16	of	of	ADP
ejpam-6388	107	17	e.	e.	PROPN
ejpam-6388	107	18	then	then	ADV
ejpam-6388	107	19	q	q	PROPN
ejpam-6388	107	20	is	be	AUX
ejpam-6388	107	21	said	say	VERB
ejpam-6388	107	22	to	to	PART
ejpam-6388	107	23	be	be	AUX
ejpam-6388	107	24	a	a	DET
ejpam-6388	107	25	cone	cone	NOUN
ejpam-6388	107	26	provided	provide	VERB
ejpam-6388	107	27	(	(	PUNCT
ejpam-6388	107	28	i	i	NOUN
ejpam-6388	107	29	)	)	PUNCT
ejpam-6388	107	30	q	q	PUNCT
ejpam-6388	107	31	is	be	AUX
ejpam-6388	107	32	nonempty	nonempty	ADV
ejpam-6388	107	33	closed	close	VERB
ejpam-6388	107	34	,	,	PUNCT
ejpam-6388	107	35	and	and	CCONJ
ejpam-6388	107	36	q	q	PROPN
ejpam-6388	107	37	̸=	̸=	PROPN
ejpam-6388	107	38	{	{	PUNCT
ejpam-6388	107	39	0	0	NUM
ejpam-6388	107	40	}	}	PUNCT
ejpam-6388	107	41	;	;	PUNCT
ejpam-6388	107	42	(	(	PUNCT
ejpam-6388	107	43	ii	ii	NOUN
ejpam-6388	107	44	)	)	PUNCT
ejpam-6388	107	45	for	for	ADP
ejpam-6388	107	46	l	l	NOUN
ejpam-6388	107	47	,	,	PUNCT
ejpam-6388	107	48	m	m	PROPN
ejpam-6388	107	49	∈	∈	ADJ
ejpam-6388	107	50	r	r	NOUN
ejpam-6388	107	51	,	,	PUNCT
ejpam-6388	107	52	l	l	NOUN
ejpam-6388	107	53	,	,	PUNCT
ejpam-6388	107	54	m	m	PROPN
ejpam-6388	107	55	≥	≥	NOUN
ejpam-6388	107	56	0	0	NUM
ejpam-6388	107	57	,	,	PUNCT
ejpam-6388	107	58	z	z	NOUN
ejpam-6388	107	59	,	,	PUNCT
ejpam-6388	107	60	u	u	PROPN
ejpam-6388	107	61	∈	∈	PROPN
ejpam-6388	107	62	q	q	NOUN
ejpam-6388	107	63	,	,	PUNCT
ejpam-6388	107	64	we	we	PRON
ejpam-6388	107	65	have	have	VERB
ejpam-6388	107	66	lz+mu	lz+mu	NOUN
ejpam-6388	107	67	∈	∈	PROPN
ejpam-6388	107	68	q	q	NOUN
ejpam-6388	107	69	;	;	PUNCT
ejpam-6388	107	70	and	and	CCONJ
ejpam-6388	107	71	(	(	PUNCT
ejpam-6388	107	72	iii	iii	X
ejpam-6388	107	73	)	)	PUNCT
ejpam-6388	107	74	z	z	NOUN
ejpam-6388	107	75	∈	∈	PROPN
ejpam-6388	107	76	q	q	NOUN
ejpam-6388	107	77	and	and	CCONJ
ejpam-6388	107	78	−z	−z	NOUN
ejpam-6388	107	79	∈	∈	PROPN
ejpam-6388	107	80	q	q	X
ejpam-6388	107	81	imply	imply	NOUN
ejpam-6388	107	82	z	z	NOUN
ejpam-6388	107	83	=	=	SYM
ejpam-6388	108	1	0	0	X
ejpam-6388	108	2	.	.	PUNCT
ejpam-6388	108	3	definition	definition	NOUN
ejpam-6388	108	4	4	4	NUM
ejpam-6388	108	5	.	.	PUNCT
ejpam-6388	109	1	[	[	X
ejpam-6388	109	2	14	14	NUM
ejpam-6388	109	3	]	]	PUNCT
ejpam-6388	109	4	let	let	VERB
ejpam-6388	109	5	a	a	DET
ejpam-6388	109	6	denote	denote	NOUN
ejpam-6388	109	7	a	a	DET
ejpam-6388	109	8	nonempty	nonempty	ADJ
ejpam-6388	109	9	collection	collection	NOUN
ejpam-6388	109	10	of	of	ADP
ejpam-6388	109	11	elements	element	NOUN
ejpam-6388	109	12	.	.	PUNCT
ejpam-6388	110	1	consider	consider	VERB
ejpam-6388	110	2	the	the	DET
ejpam-6388	110	3	function	function	NOUN
ejpam-6388	110	4	γ	γ	NOUN
ejpam-6388	110	5	:	:	PUNCT
ejpam-6388	110	6	a×a	a×a	PROPN
ejpam-6388	110	7	→	→	SYM
ejpam-6388	110	8	e	e	X
ejpam-6388	110	9	which	which	PRON
ejpam-6388	110	10	fulfills	fulfill	VERB
ejpam-6388	110	11	the	the	DET
ejpam-6388	110	12	following	follow	VERB
ejpam-6388	110	13	criteria	criterion	NOUN
ejpam-6388	110	14	:	:	PUNCT
ejpam-6388	110	15	(	(	PUNCT
ejpam-6388	110	16	c1	c1	NOUN
ejpam-6388	110	17	)	)	PUNCT
ejpam-6388	110	18	for	for	ADP
ejpam-6388	110	19	all	all	DET
ejpam-6388	110	20	m	m	PROPN
ejpam-6388	110	21	,	,	PUNCT
ejpam-6388	110	22	n	n	PROPN
ejpam-6388	110	23	∈	∈	PROPN
ejpam-6388	110	24	a	a	X
ejpam-6388	110	25	,	,	PUNCT
ejpam-6388	110	26	it	it	PRON
ejpam-6388	110	27	holds	hold	VERB
ejpam-6388	110	28	that	that	SCONJ
ejpam-6388	110	29	0	0	NUM
ejpam-6388	110	30	<	<	X
ejpam-6388	110	31	γ(m	γ(m	PROPN
ejpam-6388	110	32	,	,	PUNCT
ejpam-6388	110	33	n	n	CCONJ
ejpam-6388	110	34	)	)	PUNCT
ejpam-6388	110	35	,	,	PUNCT
ejpam-6388	110	36	and	and	CCONJ
ejpam-6388	110	37	γ(m	γ(m	PROPN
ejpam-6388	110	38	,	,	PUNCT
ejpam-6388	110	39	n	n	CCONJ
ejpam-6388	110	40	)	)	PUNCT
ejpam-6388	110	41	=	=	SYM
ejpam-6388	110	42	0	0	PUNCT
ejpam-6388	111	1	if	if	SCONJ
ejpam-6388	111	2	and	and	CCONJ
ejpam-6388	111	3	only	only	ADV
ejpam-6388	111	4	if	if	SCONJ
ejpam-6388	111	5	m	m	PROPN
ejpam-6388	111	6	=	=	VERB
ejpam-6388	111	7	n.	n.	NOUN
ejpam-6388	111	8	(	(	PUNCT
ejpam-6388	111	9	c2	c2	PROPN
ejpam-6388	111	10	)	)	PUNCT
ejpam-6388	111	11	the	the	DET
ejpam-6388	111	12	equality	equality	NOUN
ejpam-6388	111	13	γ(m	γ(m	PROPN
ejpam-6388	111	14	,	,	PUNCT
ejpam-6388	111	15	n	n	CCONJ
ejpam-6388	111	16	)	)	PUNCT
ejpam-6388	111	17	=	=	SYM
ejpam-6388	111	18	γ(n	γ(n	X
ejpam-6388	111	19	,	,	PUNCT
ejpam-6388	111	20	m	m	NOUN
ejpam-6388	111	21	)	)	PUNCT
ejpam-6388	111	22	=	=	SYM
ejpam-6388	111	23	0	0	NUM
ejpam-6388	111	24	is	be	AUX
ejpam-6388	111	25	satisfied	satisfied	ADJ
ejpam-6388	111	26	for	for	ADP
ejpam-6388	111	27	m	m	PROPN
ejpam-6388	111	28	,	,	PUNCT
ejpam-6388	111	29	n	n	PROPN
ejpam-6388	111	30	∈	∈	PROPN
ejpam-6388	111	31	a.	a.	NOUN
ejpam-6388	111	32	d.	d.	PROPN
ejpam-6388	111	33	baleanu	baleanu	PROPN
ejpam-6388	111	34	et	et	PROPN
ejpam-6388	111	35	al	al	PROPN
ejpam-6388	111	36	.	.	PUNCT
ejpam-6388	111	37	/	/	SYM
ejpam-6388	111	38	eur	eur	PROPN
ejpam-6388	111	39	.	.	PUNCT
ejpam-6388	112	1	j.	j.	PROPN
ejpam-6388	112	2	pure	pure	PROPN
ejpam-6388	112	3	appl	appl	PROPN
ejpam-6388	112	4	.	.	PROPN
ejpam-6388	112	5	math	math	PROPN
ejpam-6388	112	6	,	,	PUNCT
ejpam-6388	112	7	18	18	NUM
ejpam-6388	112	8	(	(	PUNCT
ejpam-6388	112	9	4	4	NUM
ejpam-6388	112	10	)	)	PUNCT
ejpam-6388	112	11	(	(	PUNCT
ejpam-6388	112	12	2025	2025	NUM
ejpam-6388	112	13	)	)	PUNCT
ejpam-6388	112	14	,	,	PUNCT
ejpam-6388	112	15	6388	6388	NUM
ejpam-6388	112	16	6	6	NUM
ejpam-6388	112	17	of	of	ADP
ejpam-6388	112	18	31	31	NUM
ejpam-6388	112	19	(	(	PUNCT
ejpam-6388	112	20	c3	c3	PROPN
ejpam-6388	112	21	)	)	PUNCT
ejpam-6388	112	22	the	the	DET
ejpam-6388	112	23	inequality	inequality	NOUN
ejpam-6388	112	24	γ(m	γ(m	PROPN
ejpam-6388	112	25	,	,	PUNCT
ejpam-6388	112	26	n	n	CCONJ
ejpam-6388	112	27	)	)	PUNCT
ejpam-6388	112	28	≤	≤	NOUN
ejpam-6388	112	29	γ(m	γ(m	PROPN
ejpam-6388	112	30	,	,	PUNCT
ejpam-6388	112	31	p	p	NOUN
ejpam-6388	112	32	)	)	PUNCT
ejpam-6388	112	33	+	+	X
ejpam-6388	112	34	γ(p	γ(p	PROPN
ejpam-6388	112	35	,	,	PUNCT
ejpam-6388	112	36	n	n	CCONJ
ejpam-6388	112	37	)	)	PUNCT
ejpam-6388	112	38	is	be	AUX
ejpam-6388	112	39	true	true	ADJ
ejpam-6388	112	40	for	for	ADP
ejpam-6388	112	41	m	m	PROPN
ejpam-6388	112	42	,	,	PUNCT
ejpam-6388	112	43	n	n	CCONJ
ejpam-6388	112	44	,	,	PUNCT
ejpam-6388	112	45	p	p	PROPN
ejpam-6388	112	46	∈	∈	PROPN
ejpam-6388	112	47	a.	a.	NOUN
ejpam-6388	112	48	when	when	SCONJ
ejpam-6388	112	49	the	the	DET
ejpam-6388	112	50	function	function	NOUN
ejpam-6388	112	51	γ	γ	NOUN
ejpam-6388	112	52	satisfies	satisfy	VERB
ejpam-6388	112	53	these	these	DET
ejpam-6388	112	54	properties	property	NOUN
ejpam-6388	112	55	,	,	PUNCT
ejpam-6388	112	56	it	it	PRON
ejpam-6388	112	57	is	be	AUX
ejpam-6388	112	58	referred	refer	VERB
ejpam-6388	112	59	to	to	ADP
ejpam-6388	112	60	as	as	ADP
ejpam-6388	112	61	a	a	DET
ejpam-6388	112	62	cone	cone	NOUN
ejpam-6388	112	63	metric	metric	NOUN
ejpam-6388	112	64	on	on	ADP
ejpam-6388	112	65	a	a	PRON
ejpam-6388	112	66	,	,	PUNCT
ejpam-6388	112	67	and	and	CCONJ
ejpam-6388	112	68	the	the	DET
ejpam-6388	112	69	pair	pair	NOUN
ejpam-6388	112	70	(	(	PUNCT
ejpam-6388	112	71	a	a	PRON
ejpam-6388	112	72	,	,	PUNCT
ejpam-6388	112	73	γ	γ	NOUN
ejpam-6388	112	74	)	)	PUNCT
ejpam-6388	112	75	is	be	AUX
ejpam-6388	112	76	termed	term	VERB
ejpam-6388	112	77	a	a	DET
ejpam-6388	112	78	cone	cone	NOUN
ejpam-6388	112	79	metric	metric	ADJ
ejpam-6388	112	80	space	space	NOUN
ejpam-6388	112	81	.	.	PUNCT
ejpam-6388	113	1	definition	definition	NOUN
ejpam-6388	113	2	5	5	NUM
ejpam-6388	113	3	.	.	PUNCT
ejpam-6388	114	1	[	[	X
ejpam-6388	114	2	14	14	NUM
ejpam-6388	114	3	]	]	X
ejpam-6388	114	4	a	a	DET
ejpam-6388	114	5	cone	cone	NOUN
ejpam-6388	114	6	c	c	NOUN
ejpam-6388	114	7	is	be	AUX
ejpam-6388	114	8	termed	term	VERB
ejpam-6388	114	9	normal	normal	ADJ
ejpam-6388	114	10	provided	provide	VERB
ejpam-6388	114	11	there	there	PRON
ejpam-6388	114	12	exists	exist	VERB
ejpam-6388	114	13	a	a	DET
ejpam-6388	114	14	positive	positive	ADJ
ejpam-6388	114	15	constant	constant	ADJ
ejpam-6388	115	1	k	k	NOUN
ejpam-6388	115	2	>	>	X
ejpam-6388	115	3	0	0	NUM
ejpam-6388	115	4	such	such	ADJ
ejpam-6388	115	5	that	that	PRON
ejpam-6388	115	6	for	for	ADP
ejpam-6388	115	7	every	every	DET
ejpam-6388	115	8	ℓ1	ℓ1	NOUN
ejpam-6388	115	9	,	,	PUNCT
ejpam-6388	115	10	ℓ2	ℓ2	PROPN
ejpam-6388	115	11	∈	∈	PROPN
ejpam-6388	115	12	e	e	NOUN
ejpam-6388	115	13	,	,	PUNCT
ejpam-6388	115	14	0	0	NUM
ejpam-6388	115	15	≤	≤	NOUN
ejpam-6388	115	16	ℓ1	ℓ1	NOUN
ejpam-6388	115	17	≤	≤	NOUN
ejpam-6388	115	18	ℓ2	ℓ2	NOUN
ejpam-6388	115	19	implies	imply	VERB
ejpam-6388	115	20	∥ℓ1∥	∥ℓ1∥	PROPN
ejpam-6388	115	21	≤	≤	NOUN
ejpam-6388	115	22	k∥ℓ2∥.	k∥ℓ2∥.	VERB
ejpam-6388	115	23	the	the	DET
ejpam-6388	115	24	normality	normality	NOUN
ejpam-6388	115	25	constant	constant	ADJ
ejpam-6388	115	26	associated	associate	VERB
ejpam-6388	115	27	with	with	ADP
ejpam-6388	115	28	c	c	PROPN
ejpam-6388	115	29	is	be	AUX
ejpam-6388	115	30	the	the	DET
ejpam-6388	115	31	smallest	small	ADJ
ejpam-6388	115	32	positive	positive	ADJ
ejpam-6388	115	33	value	value	NOUN
ejpam-6388	115	34	of	of	ADP
ejpam-6388	115	35	k	k	PROPN
ejpam-6388	115	36	that	that	PRON
ejpam-6388	115	37	satisfies	satisfy	VERB
ejpam-6388	115	38	this	this	DET
ejpam-6388	115	39	condition	condition	NOUN
ejpam-6388	115	40	.	.	PUNCT
ejpam-6388	116	1	theorem	theorem	NOUN
ejpam-6388	116	2	1	1	NUM
ejpam-6388	116	3	.	.	PUNCT
ejpam-6388	117	1	[	[	X
ejpam-6388	117	2	14	14	NUM
ejpam-6388	117	3	]	]	X
ejpam-6388	117	4	let	let	VERB
ejpam-6388	117	5	(	(	PUNCT
ejpam-6388	117	6	a	a	DET
ejpam-6388	117	7	,	,	PUNCT
ejpam-6388	117	8	γ	γ	NOUN
ejpam-6388	117	9	)	)	PUNCT
ejpam-6388	117	10	denote	denote	VERB
ejpam-6388	117	11	a	a	DET
ejpam-6388	117	12	complete	complete	ADJ
ejpam-6388	117	13	cone	cone	NOUN
ejpam-6388	117	14	metric	metric	ADJ
ejpam-6388	117	15	space	space	NOUN
ejpam-6388	117	16	,	,	PUNCT
ejpam-6388	117	17	and	and	CCONJ
ejpam-6388	117	18	let	let	VERB
ejpam-6388	117	19	c	c	PRON
ejpam-6388	117	20	be	be	AUX
ejpam-6388	117	21	a	a	DET
ejpam-6388	117	22	normal	normal	ADJ
ejpam-6388	117	23	cone	cone	NOUN
ejpam-6388	117	24	characterized	characterize	VERB
ejpam-6388	117	25	by	by	ADP
ejpam-6388	117	26	its	its	PRON
ejpam-6388	117	27	normality	normality	NOUN
ejpam-6388	117	28	constant	constant	ADJ
ejpam-6388	117	29	k.	k.	PROPN
ejpam-6388	117	30	suppose	suppose	VERB
ejpam-6388	117	31	the	the	DET
ejpam-6388	117	32	function	function	NOUN
ejpam-6388	117	33	g	g	NOUN
ejpam-6388	117	34	:	:	PUNCT
ejpam-6388	117	35	a	a	PRON
ejpam-6388	117	36	→	→	X
ejpam-6388	117	37	a	a	DET
ejpam-6388	117	38	fulfills	fulfill	VERB
ejpam-6388	117	39	the	the	DET
ejpam-6388	117	40	contractive	contractive	ADJ
ejpam-6388	117	41	property	property	NOUN
ejpam-6388	117	42	γ(gu	γ(gu	PROPN
ejpam-6388	117	43	,	,	PUNCT
ejpam-6388	117	44	gv	gv	NOUN
ejpam-6388	117	45	)	)	PUNCT
ejpam-6388	117	46	≤	≤	NUM
ejpam-6388	117	47	cγ(u	cγ(u	ADJ
ejpam-6388	117	48	,	,	PUNCT
ejpam-6388	117	49	v	v	NOUN
ejpam-6388	117	50	)	)	PUNCT
ejpam-6388	117	51	for	for	ADP
ejpam-6388	117	52	any	any	DET
ejpam-6388	117	53	u	u	NOUN
ejpam-6388	117	54	,	,	PUNCT
ejpam-6388	117	55	v	v	ADP
ejpam-6388	117	56	∈	∈	PROPN
ejpam-6388	117	57	a	a	PRON
ejpam-6388	117	58	,	,	PUNCT
ejpam-6388	117	59	where	where	SCONJ
ejpam-6388	117	60	c	c	NOUN
ejpam-6388	117	61	is	be	AUX
ejpam-6388	117	62	a	a	DET
ejpam-6388	117	63	constant	constant	ADJ
ejpam-6388	118	1	such	such	ADJ
ejpam-6388	118	2	that	that	SCONJ
ejpam-6388	118	3	0	0	NUM
ejpam-6388	118	4	≤	≤	NUM
ejpam-6388	118	5	c	c	X
ejpam-6388	118	6	<	<	X
ejpam-6388	118	7	1	1	NUM
ejpam-6388	118	8	.	.	PUNCT
ejpam-6388	118	9	given	give	VERB
ejpam-6388	118	10	these	these	DET
ejpam-6388	118	11	assumptions	assumption	NOUN
ejpam-6388	118	12	,	,	PUNCT
ejpam-6388	118	13	the	the	DET
ejpam-6388	118	14	mapping	mapping	NOUN
ejpam-6388	118	15	g	g	NOUN
ejpam-6388	118	16	possesses	possess	VERB
ejpam-6388	118	17	a	a	DET
ejpam-6388	118	18	unique	unique	ADJ
ejpam-6388	118	19	fixed	fix	VERB
ejpam-6388	118	20	point	point	NOUN
ejpam-6388	118	21	within	within	ADP
ejpam-6388	118	22	a.	a.	NOUN
ejpam-6388	118	23	additionally	additionally	ADV
ejpam-6388	118	24	,	,	PUNCT
ejpam-6388	118	25	for	for	ADP
ejpam-6388	118	26	any	any	DET
ejpam-6388	118	27	element	element	NOUN
ejpam-6388	118	28	u	u	NOUN
ejpam-6388	118	29	∈	∈	PROPN
ejpam-6388	118	30	a	a	PRON
ejpam-6388	118	31	,	,	PUNCT
ejpam-6388	118	32	the	the	DET
ejpam-6388	118	33	sequence	sequence	NOUN
ejpam-6388	118	34	defined	define	VERB
ejpam-6388	118	35	by	by	ADP
ejpam-6388	118	36	iterating	iterate	VERB
ejpam-6388	118	37	g	g	NOUN
ejpam-6388	118	38	,	,	PUNCT
ejpam-6388	118	39	denoted	denote	VERB
ejpam-6388	118	40	as	as	ADP
ejpam-6388	118	41	{	{	PUNCT
ejpam-6388	118	42	gnu	gnu	NOUN
ejpam-6388	118	43	}	}	PUNCT
ejpam-6388	118	44	,	,	PUNCT
ejpam-6388	118	45	converges	converge	VERB
ejpam-6388	118	46	to	to	ADP
ejpam-6388	118	47	this	this	DET
ejpam-6388	118	48	distinct	distinct	ADJ
ejpam-6388	118	49	fixed	fix	VERB
ejpam-6388	118	50	point	point	NOUN
ejpam-6388	118	51	.	.	PUNCT
ejpam-6388	119	1	definition	definition	NOUN
ejpam-6388	119	2	6	6	NUM
ejpam-6388	119	3	.	.	PUNCT
ejpam-6388	120	1	[	[	X
ejpam-6388	120	2	15	15	NUM
ejpam-6388	120	3	]	]	PUNCT
ejpam-6388	120	4	let	let	VERB
ejpam-6388	120	5	a	a	DET
ejpam-6388	120	6	̸=	̸=	PROPN
ejpam-6388	120	7	∅	∅	NOUN
ejpam-6388	120	8	and	and	CCONJ
ejpam-6388	120	9	⊥⊆	⊥⊆	DET
ejpam-6388	120	10	a	a	DET
ejpam-6388	120	11	×	×	NOUN
ejpam-6388	120	12	a	a	DET
ejpam-6388	120	13	be	be	AUX
ejpam-6388	120	14	a	a	DET
ejpam-6388	120	15	binary	binary	ADJ
ejpam-6388	120	16	relation	relation	NOUN
ejpam-6388	120	17	.	.	PUNCT
ejpam-6388	121	1	the	the	DET
ejpam-6388	121	2	relation	relation	NOUN
ejpam-6388	121	3	⊥	⊥	PROPN
ejpam-6388	121	4	is	be	AUX
ejpam-6388	121	5	referred	refer	VERB
ejpam-6388	121	6	to	to	ADP
ejpam-6388	121	7	as	as	ADP
ejpam-6388	121	8	an	an	DET
ejpam-6388	121	9	orthogonal	orthogonal	ADJ
ejpam-6388	121	10	set	set	NOUN
ejpam-6388	121	11	(	(	PUNCT
ejpam-6388	121	12	or	or	CCONJ
ejpam-6388	121	13	simply	simply	ADV
ejpam-6388	121	14	an	an	DET
ejpam-6388	121	15	o	o	NOUN
ejpam-6388	121	16	-	-	NOUN
ejpam-6388	121	17	set	set	NOUN
ejpam-6388	121	18	)	)	PUNCT
ejpam-6388	121	19	provided	provide	VERB
ejpam-6388	121	20	there	there	PRON
ejpam-6388	121	21	exists	exist	VERB
ejpam-6388	121	22	an	an	DET
ejpam-6388	121	23	element	element	NOUN
ejpam-6388	121	24	α0	α0	PROPN
ejpam-6388	121	25	∈	∈	PROPN
ejpam-6388	121	26	a	a	DET
ejpam-6388	121	27	such	such	ADJ
ejpam-6388	121	28	that	that	PRON
ejpam-6388	121	29	for	for	ADP
ejpam-6388	121	30	every	every	DET
ejpam-6388	121	31	β	β	X
ejpam-6388	121	32	∈	∈	PROPN
ejpam-6388	121	33	a	a	PRON
ejpam-6388	121	34	,	,	PUNCT
ejpam-6388	121	35	either	either	CCONJ
ejpam-6388	121	36	β	β	X
ejpam-6388	121	37	⊥	⊥	NOUN
ejpam-6388	121	38	α0	α0	ADJ
ejpam-6388	121	39	or	or	CCONJ
ejpam-6388	121	40	α0	α0	PROPN
ejpam-6388	121	41	⊥	⊥	PROPN
ejpam-6388	121	42	β	β	X
ejpam-6388	121	43	.	.	PUNCT
ejpam-6388	122	1	we	we	PRON
ejpam-6388	122	2	denote	denote	VERB
ejpam-6388	122	3	this	this	DET
ejpam-6388	122	4	o	o	NOUN
ejpam-6388	122	5	-	-	PUNCT
ejpam-6388	122	6	set	set	VERB
ejpam-6388	122	7	by	by	ADP
ejpam-6388	122	8	(	(	PUNCT
ejpam-6388	122	9	a,⊥	a,⊥	PROPN
ejpam-6388	122	10	)	)	PUNCT
ejpam-6388	122	11	.	.	PUNCT
ejpam-6388	123	1	definition	definition	NOUN
ejpam-6388	123	2	7	7	NUM
ejpam-6388	123	3	.	.	PUNCT
ejpam-6388	124	1	[	[	X
ejpam-6388	124	2	15	15	NUM
ejpam-6388	124	3	]	]	X
ejpam-6388	124	4	let	let	NOUN
ejpam-6388	124	5	(	(	PUNCT
ejpam-6388	124	6	a,⊥	a,⊥	PUNCT
ejpam-6388	124	7	)	)	PUNCT
ejpam-6388	124	8	be	be	VERB
ejpam-6388	124	9	an	an	DET
ejpam-6388	124	10	o	o	NOUN
ejpam-6388	124	11	-	-	NOUN
ejpam-6388	124	12	set	set	NOUN
ejpam-6388	124	13	.	.	PUNCT
ejpam-6388	125	1	a	a	DET
ejpam-6388	125	2	sequence	sequence	NOUN
ejpam-6388	125	3	{	{	PUNCT
ejpam-6388	125	4	αn}n∈n	αn}n∈n	INTJ
ejpam-6388	125	5	in	in	ADP
ejpam-6388	125	6	a	a	PRON
ejpam-6388	125	7	is	be	AUX
ejpam-6388	125	8	termed	term	VERB
ejpam-6388	125	9	an	an	DET
ejpam-6388	125	10	orthogonal	orthogonal	ADJ
ejpam-6388	125	11	sequence	sequence	NOUN
ejpam-6388	125	12	(	(	PUNCT
ejpam-6388	125	13	or	or	CCONJ
ejpam-6388	125	14	briefly	briefly	ADV
ejpam-6388	125	15	an	an	DET
ejpam-6388	125	16	o	o	NOUN
ejpam-6388	125	17	-	-	NOUN
ejpam-6388	125	18	sequence	sequence	NOUN
ejpam-6388	125	19	)	)	PUNCT
ejpam-6388	125	20	provided	provide	VERB
ejpam-6388	125	21	for	for	ADP
ejpam-6388	125	22	all	all	PRON
ejpam-6388	125	23	n	n	PRON
ejpam-6388	125	24	∈	∈	PROPN
ejpam-6388	125	25	n	n	CCONJ
ejpam-6388	125	26	,	,	PUNCT
ejpam-6388	125	27	either	either	CCONJ
ejpam-6388	125	28	αn	αn	NOUN
ejpam-6388	125	29	⊥	⊥	NUM
ejpam-6388	125	30	αn+1	αn+1	NUM
ejpam-6388	125	31	or	or	CCONJ
ejpam-6388	125	32	αn	αn	NOUN
ejpam-6388	125	33	⊥	⊥	NOUN
ejpam-6388	125	34	αn+1	αn+1	NUM
ejpam-6388	125	35	.	.	PUNCT
ejpam-6388	125	36	definition	definition	NOUN
ejpam-6388	125	37	8	8	NUM
ejpam-6388	125	38	.	.	PUNCT
ejpam-6388	126	1	[	[	X
ejpam-6388	126	2	15	15	NUM
ejpam-6388	126	3	]	]	X
ejpam-6388	126	4	let	let	VERB
ejpam-6388	126	5	(	(	PUNCT
ejpam-6388	126	6	a	a	DET
ejpam-6388	126	7	,	,	PUNCT
ejpam-6388	126	8	γ,⊥	γ,⊥	NOUN
ejpam-6388	126	9	)	)	PUNCT
ejpam-6388	126	10	be	be	AUX
ejpam-6388	126	11	an	an	DET
ejpam-6388	126	12	orthogonal	orthogonal	ADJ
ejpam-6388	126	13	metric	metric	ADJ
ejpam-6388	126	14	space	space	NOUN
ejpam-6388	126	15	(	(	PUNCT
ejpam-6388	126	16	where	where	SCONJ
ejpam-6388	126	17	(	(	PUNCT
ejpam-6388	126	18	a,⊥	a,⊥	PROPN
ejpam-6388	126	19	)	)	PUNCT
ejpam-6388	126	20	is	be	AUX
ejpam-6388	126	21	an	an	DET
ejpam-6388	126	22	oset	oset	NOUN
ejpam-6388	126	23	and	and	CCONJ
ejpam-6388	126	24	(	(	PUNCT
ejpam-6388	126	25	a	a	DET
ejpam-6388	126	26	,	,	PUNCT
ejpam-6388	126	27	γ	γ	NOUN
ejpam-6388	126	28	)	)	PUNCT
ejpam-6388	126	29	is	be	AUX
ejpam-6388	126	30	a	a	DET
ejpam-6388	126	31	metric	metric	ADJ
ejpam-6388	126	32	space	space	NOUN
ejpam-6388	126	33	)	)	PUNCT
ejpam-6388	126	34	.	.	PUNCT
ejpam-6388	127	1	the	the	DET
ejpam-6388	127	2	space	space	NOUN
ejpam-6388	127	3	a	a	PRON
ejpam-6388	127	4	is	be	AUX
ejpam-6388	127	5	said	say	VERB
ejpam-6388	127	6	to	to	PART
ejpam-6388	127	7	be	be	AUX
ejpam-6388	127	8	orthogonally	orthogonally	ADV
ejpam-6388	127	9	complete	complete	ADJ
ejpam-6388	127	10	(	(	PUNCT
ejpam-6388	127	11	or	or	CCONJ
ejpam-6388	127	12	briefly	briefly	ADV
ejpam-6388	127	13	,	,	PUNCT
ejpam-6388	127	14	o	o	NOUN
ejpam-6388	127	15	-	-	NOUN
ejpam-6388	127	16	complete	complete	ADJ
ejpam-6388	127	17	)	)	PUNCT
ejpam-6388	127	18	provided	provide	VERB
ejpam-6388	127	19	every	every	DET
ejpam-6388	127	20	cauchy	cauchy	ADJ
ejpam-6388	127	21	o	o	ADJ
ejpam-6388	127	22	-	-	ADJ
ejpam-6388	127	23	sequence	sequence	NOUN
ejpam-6388	127	24	converges	converge	NOUN
ejpam-6388	127	25	.	.	PUNCT
ejpam-6388	128	1	remark	remark	NOUN
ejpam-6388	128	2	3	3	NUM
ejpam-6388	128	3	.	.	PUNCT
ejpam-6388	129	1	it	it	PRON
ejpam-6388	129	2	is	be	AUX
ejpam-6388	129	3	important	important	ADJ
ejpam-6388	129	4	to	to	PART
ejpam-6388	129	5	observe	observe	VERB
ejpam-6388	129	6	that	that	SCONJ
ejpam-6388	129	7	while	while	SCONJ
ejpam-6388	129	8	every	every	DET
ejpam-6388	129	9	complete	complete	ADJ
ejpam-6388	129	10	metric	metric	ADJ
ejpam-6388	129	11	space	space	NOUN
ejpam-6388	129	12	qualifies	qualifie	NOUN
ejpam-6388	129	13	as	as	ADP
ejpam-6388	129	14	o	o	NOUN
ejpam-6388	129	15	-	-	NOUN
ejpam-6388	129	16	complete	complete	ADJ
ejpam-6388	129	17	,	,	PUNCT
ejpam-6388	129	18	the	the	DET
ejpam-6388	129	19	reverse	reverse	ADJ
ejpam-6388	129	20	statement	statement	NOUN
ejpam-6388	129	21	does	do	AUX
ejpam-6388	129	22	not	not	PART
ejpam-6388	129	23	hold	hold	VERB
ejpam-6388	129	24	true	true	ADJ
ejpam-6388	129	25	(	(	PUNCT
ejpam-6388	129	26	refer	refer	VERB
ejpam-6388	129	27	to	to	ADP
ejpam-6388	129	28	[	[	X
ejpam-6388	129	29	15	15	NUM
ejpam-6388	129	30	]	]	NUM
ejpam-6388	129	31	)	)	PUNCT
ejpam-6388	129	32	.	.	PUNCT
ejpam-6388	130	1	definition	definition	NOUN
ejpam-6388	130	2	9	9	NUM
ejpam-6388	130	3	.	.	PUNCT
ejpam-6388	131	1	[	[	X
ejpam-6388	131	2	15	15	NUM
ejpam-6388	131	3	]	]	X
ejpam-6388	131	4	let	let	VERB
ejpam-6388	131	5	(	(	PUNCT
ejpam-6388	131	6	a	a	DET
ejpam-6388	131	7	,	,	PUNCT
ejpam-6388	131	8	γ,⊥	γ,⊥	NOUN
ejpam-6388	131	9	)	)	PUNCT
ejpam-6388	131	10	be	be	AUX
ejpam-6388	131	11	an	an	DET
ejpam-6388	131	12	orthogonal	orthogonal	ADJ
ejpam-6388	131	13	metric	metric	ADJ
ejpam-6388	131	14	space	space	NOUN
ejpam-6388	131	15	,	,	PUNCT
ejpam-6388	131	16	and	and	CCONJ
ejpam-6388	131	17	let	let	VERB
ejpam-6388	131	18	0	0	NUM
ejpam-6388	131	19	<	<	X
ejpam-6388	131	20	c	c	X
ejpam-6388	131	21	<	<	X
ejpam-6388	131	22	1	1	NUM
ejpam-6388	131	23	.	.	PUNCT
ejpam-6388	132	1	then	then	ADV
ejpam-6388	132	2	we	we	PRON
ejpam-6388	132	3	have	have	VERB
ejpam-6388	132	4	the	the	DET
ejpam-6388	132	5	following	following	NOUN
ejpam-6388	132	6	:	:	PUNCT
ejpam-6388	132	7	1	1	X
ejpam-6388	132	8	.	.	PUNCT
ejpam-6388	132	9	orthogonal	orthogonal	ADJ
ejpam-6388	132	10	contractive	contractive	ADJ
ejpam-6388	132	11	function	function	NOUN
ejpam-6388	132	12	:	:	PUNCT
ejpam-6388	132	13	a	a	DET
ejpam-6388	132	14	function	function	NOUN
ejpam-6388	132	15	g	g	NOUN
ejpam-6388	132	16	:	:	PUNCT
ejpam-6388	132	17	a	a	PRON
ejpam-6388	132	18	→	→	X
ejpam-6388	132	19	a	a	PRON
ejpam-6388	132	20	is	be	AUX
ejpam-6388	132	21	called	call	VERB
ejpam-6388	132	22	an	an	DET
ejpam-6388	132	23	orthogonal	orthogonal	ADJ
ejpam-6388	132	24	contractive	contractive	ADJ
ejpam-6388	132	25	(	(	PUNCT
ejpam-6388	132	26	or	or	CCONJ
ejpam-6388	132	27	⊥-contractive	⊥-contractive	ADJ
ejpam-6388	132	28	)	)	PUNCT
ejpam-6388	132	29	function	function	NOUN
ejpam-6388	132	30	with	with	ADP
ejpam-6388	132	31	lipschitz	lipschitz	NOUN
ejpam-6388	132	32	constant	constant	ADJ
ejpam-6388	132	33	c	c	NOUN
ejpam-6388	132	34	provided	provide	VERB
ejpam-6388	132	35	it	it	PRON
ejpam-6388	132	36	satisfies	satisfy	VERB
ejpam-6388	132	37	γ(gu	γ(gu	PROPN
ejpam-6388	132	38	,	,	PUNCT
ejpam-6388	132	39	gv	gv	ADP
ejpam-6388	132	40	)	)	PUNCT
ejpam-6388	132	41	≤	≤	NUM
ejpam-6388	132	42	cγ(u	cγ(u	NOUN
ejpam-6388	132	43	,	,	PUNCT
ejpam-6388	132	44	v	v	NOUN
ejpam-6388	132	45	)	)	PUNCT
ejpam-6388	132	46	,	,	PUNCT
ejpam-6388	132	47	where	where	SCONJ
ejpam-6388	132	48	u	u	PROPN
ejpam-6388	132	49	⊥	⊥	PROPN
ejpam-6388	132	50	v.	v.	ADP
ejpam-6388	132	51	2	2	NUM
ejpam-6388	132	52	.	.	PUNCT
ejpam-6388	132	53	orthogonal	orthogonal	ADJ
ejpam-6388	132	54	preserving	preserve	VERB
ejpam-6388	132	55	function	function	NOUN
ejpam-6388	132	56	:	:	PUNCT
ejpam-6388	132	57	a	a	DET
ejpam-6388	132	58	function	function	NOUN
ejpam-6388	132	59	g	g	NOUN
ejpam-6388	132	60	:	:	PUNCT
ejpam-6388	132	61	a	a	DET
ejpam-6388	132	62	→	→	X
ejpam-6388	132	63	a	a	PRON
ejpam-6388	132	64	is	be	AUX
ejpam-6388	132	65	termed	term	VERB
ejpam-6388	132	66	an	an	DET
ejpam-6388	132	67	orthogonal	orthogonal	ADJ
ejpam-6388	132	68	preserving	preserve	VERB
ejpam-6388	132	69	(	(	PUNCT
ejpam-6388	132	70	or	or	CCONJ
ejpam-6388	132	71	⊥-preserving	⊥-preserving	NOUN
ejpam-6388	132	72	)	)	PUNCT
ejpam-6388	132	73	function	function	NOUN
ejpam-6388	132	74	provided	provide	VERB
ejpam-6388	132	75	g(u	g(u	PROPN
ejpam-6388	132	76	)	)	PUNCT
ejpam-6388	132	77	⊥	⊥	ADJ
ejpam-6388	132	78	g(v	g(v	X
ejpam-6388	132	79	)	)	PUNCT
ejpam-6388	132	80	whenever	whenever	SCONJ
ejpam-6388	132	81	u	u	PROPN
ejpam-6388	132	82	⊥	⊥	PROPN
ejpam-6388	132	83	v.	v.	ADP
ejpam-6388	132	84	3	3	X
ejpam-6388	132	85	.	.	NOUN
ejpam-6388	132	86	orthogonally	orthogonally	ADV
ejpam-6388	132	87	continuous	continuous	ADJ
ejpam-6388	132	88	function	function	NOUN
ejpam-6388	132	89	:	:	PUNCT
ejpam-6388	132	90	a	a	DET
ejpam-6388	132	91	function	function	NOUN
ejpam-6388	132	92	g	g	NOUN
ejpam-6388	132	93	:	:	PUNCT
ejpam-6388	132	94	a	a	PRON
ejpam-6388	132	95	→	→	X
ejpam-6388	132	96	a	a	PRON
ejpam-6388	132	97	is	be	AUX
ejpam-6388	132	98	classified	classify	VERB
ejpam-6388	132	99	as	as	ADP
ejpam-6388	132	100	orthogonally	orthogonally	ADV
ejpam-6388	132	101	continuous	continuous	ADJ
ejpam-6388	132	102	(	(	PUNCT
ejpam-6388	132	103	or	or	CCONJ
ejpam-6388	132	104	⊥-continuous	⊥-continuous	ADJ
ejpam-6388	132	105	)	)	PUNCT
ejpam-6388	132	106	at	at	ADP
ejpam-6388	132	107	a	a	DET
ejpam-6388	132	108	point	point	NOUN
ejpam-6388	132	109	b	b	X
ejpam-6388	132	110	∈	∈	PROPN
ejpam-6388	132	111	a	a	DET
ejpam-6388	132	112	provided	provide	VERB
ejpam-6388	132	113	for	for	ADP
ejpam-6388	132	114	any	any	DET
ejpam-6388	132	115	osequence	osequence	NOUN
ejpam-6388	132	116	{	{	PUNCT
ejpam-6388	132	117	bn}n∈n	bn}n∈n	ADP
ejpam-6388	132	118	in	in	ADP
ejpam-6388	132	119	a	a	PRON
ejpam-6388	132	120	,	,	PUNCT
ejpam-6388	132	121	the	the	DET
ejpam-6388	132	122	convergence	convergence	NOUN
ejpam-6388	132	123	bn	bn	NOUN
ejpam-6388	132	124	→	→	SYM
ejpam-6388	132	125	b	b	PROPN
ejpam-6388	132	126	implies	imply	VERB
ejpam-6388	132	127	that	that	SCONJ
ejpam-6388	132	128	g(bn	g(bn	PROPN
ejpam-6388	132	129	)	)	PUNCT
ejpam-6388	132	130	→	→	SYM
ejpam-6388	132	131	g(b	g(b	X
ejpam-6388	132	132	)	)	PUNCT
ejpam-6388	132	133	.	.	PUNCT
ejpam-6388	133	1	furthermore	furthermore	ADV
ejpam-6388	133	2	,	,	PUNCT
ejpam-6388	133	3	g	g	PROPN
ejpam-6388	133	4	is	be	AUX
ejpam-6388	133	5	regarded	regard	VERB
ejpam-6388	133	6	as	as	ADP
ejpam-6388	133	7	⊥-continuous	⊥-continuous	ADJ
ejpam-6388	133	8	on	on	ADP
ejpam-6388	133	9	a	a	DET
ejpam-6388	133	10	provided	provide	VERB
ejpam-6388	133	11	it	it	PRON
ejpam-6388	133	12	maintains	maintain	VERB
ejpam-6388	133	13	⊥-continuity	⊥-continuity	NOUN
ejpam-6388	133	14	at	at	ADP
ejpam-6388	133	15	every	every	DET
ejpam-6388	133	16	b	b	PROPN
ejpam-6388	133	17	∈	∈	PROPN
ejpam-6388	133	18	a.	a.	NOUN
ejpam-6388	133	19	d.	d.	PROPN
ejpam-6388	133	20	baleanu	baleanu	PROPN
ejpam-6388	133	21	et	et	PROPN
ejpam-6388	133	22	al	al	PROPN
ejpam-6388	133	23	.	.	PUNCT
ejpam-6388	133	24	/	/	SYM
ejpam-6388	133	25	eur	eur	PROPN
ejpam-6388	133	26	.	.	PUNCT
ejpam-6388	134	1	j.	j.	PROPN
ejpam-6388	134	2	pure	pure	PROPN
ejpam-6388	134	3	appl	appl	PROPN
ejpam-6388	134	4	.	.	PROPN
ejpam-6388	134	5	math	math	PROPN
ejpam-6388	134	6	,	,	PUNCT
ejpam-6388	134	7	18	18	NUM
ejpam-6388	134	8	(	(	PUNCT
ejpam-6388	134	9	4	4	NUM
ejpam-6388	134	10	)	)	PUNCT
ejpam-6388	134	11	(	(	PUNCT
ejpam-6388	134	12	2025	2025	NUM
ejpam-6388	134	13	)	)	PUNCT
ejpam-6388	134	14	,	,	PUNCT
ejpam-6388	134	15	6388	6388	NUM
ejpam-6388	134	16	7	7	NUM
ejpam-6388	134	17	of	of	ADP
ejpam-6388	134	18	31	31	NUM
ejpam-6388	134	19	definition	definition	NOUN
ejpam-6388	134	20	10	10	NUM
ejpam-6388	134	21	.	.	PUNCT
ejpam-6388	135	1	[	[	X
ejpam-6388	135	2	20	20	NUM
ejpam-6388	135	3	]	]	X
ejpam-6388	135	4	let	let	VERB
ejpam-6388	135	5	(	(	PUNCT
ejpam-6388	135	6	a,⊥	a,⊥	PUNCT
ejpam-6388	135	7	)	)	PUNCT
ejpam-6388	135	8	be	be	AUX
ejpam-6388	135	9	a	a	DET
ejpam-6388	135	10	nonempty	nonempty	ADJ
ejpam-6388	135	11	orthogonal	orthogonal	ADJ
ejpam-6388	135	12	set	set	NOUN
ejpam-6388	135	13	.	.	PUNCT
ejpam-6388	136	1	assume	assume	VERB
ejpam-6388	136	2	the	the	DET
ejpam-6388	136	3	function	function	NOUN
ejpam-6388	136	4	γ	γ	NOUN
ejpam-6388	136	5	:	:	PUNCT
ejpam-6388	136	6	a×a	a×a	PROPN
ejpam-6388	136	7	→	→	SYM
ejpam-6388	136	8	e	e	NOUN
ejpam-6388	136	9	satisfies	satisfy	VERB
ejpam-6388	136	10	the	the	DET
ejpam-6388	136	11	following	follow	VERB
ejpam-6388	136	12	conditions	condition	NOUN
ejpam-6388	136	13	:	:	PUNCT
ejpam-6388	136	14	(	(	PUNCT
ejpam-6388	136	15	p1	p1	NOUN
ejpam-6388	136	16	)	)	PUNCT
ejpam-6388	136	17	0	0	PUNCT
ejpam-6388	136	18	<	<	X
ejpam-6388	136	19	γ(u	γ(u	PROPN
ejpam-6388	136	20	,	,	PUNCT
ejpam-6388	136	21	v	v	NOUN
ejpam-6388	136	22	)	)	PUNCT
ejpam-6388	136	23	for	for	ADP
ejpam-6388	136	24	all	all	DET
ejpam-6388	136	25	u	u	NOUN
ejpam-6388	136	26	,	,	PUNCT
ejpam-6388	136	27	v	v	ADP
ejpam-6388	136	28	∈	∈	PROPN
ejpam-6388	136	29	a	a	PRON
ejpam-6388	136	30	and	and	CCONJ
ejpam-6388	136	31	γ(u	γ(u	PROPN
ejpam-6388	136	32	,	,	PUNCT
ejpam-6388	136	33	v	v	NOUN
ejpam-6388	136	34	)	)	PUNCT
ejpam-6388	136	35	=	=	SYM
ejpam-6388	136	36	0	0	NUM
ejpam-6388	137	1	⇐	⇐	ADJ
ejpam-6388	137	2	⇒	⇒	PROPN
ejpam-6388	137	3	u	u	NOUN
ejpam-6388	137	4	=	=	PROPN
ejpam-6388	137	5	v	v	NOUN
ejpam-6388	137	6	;	;	PUNCT
ejpam-6388	137	7	(	(	PUNCT
ejpam-6388	137	8	p2	p2	X
ejpam-6388	137	9	)	)	PUNCT
ejpam-6388	137	10	γ(u	γ(u	NOUN
ejpam-6388	137	11	,	,	PUNCT
ejpam-6388	137	12	v	v	NOUN
ejpam-6388	137	13	)	)	PUNCT
ejpam-6388	137	14	=	=	SYM
ejpam-6388	137	15	γ(v	γ(v	PROPN
ejpam-6388	137	16	,	,	PUNCT
ejpam-6388	137	17	u	u	NOUN
ejpam-6388	137	18	)	)	PUNCT
ejpam-6388	137	19	=	=	SYM
ejpam-6388	137	20	0	0	NUM
ejpam-6388	137	21	for	for	ADP
ejpam-6388	137	22	all	all	DET
ejpam-6388	137	23	u	u	NOUN
ejpam-6388	137	24	,	,	PUNCT
ejpam-6388	137	25	v	v	ADP
ejpam-6388	137	26	∈	∈	PROPN
ejpam-6388	137	27	a	a	PRON
ejpam-6388	137	28	;	;	PUNCT
ejpam-6388	137	29	(	(	PUNCT
ejpam-6388	137	30	p3	p3	NOUN
ejpam-6388	137	31	)	)	PUNCT
ejpam-6388	137	32	γ(u	γ(u	PROPN
ejpam-6388	137	33	,	,	PUNCT
ejpam-6388	137	34	v	v	NOUN
ejpam-6388	137	35	)	)	PUNCT
ejpam-6388	137	36	≤	≤	NOUN
ejpam-6388	137	37	γ(u	γ(u	PROPN
ejpam-6388	137	38	,	,	PUNCT
ejpam-6388	137	39	w	w	NOUN
ejpam-6388	137	40	)	)	PUNCT
ejpam-6388	137	41	+	+	CCONJ
ejpam-6388	137	42	γ(w	γ(w	PROPN
ejpam-6388	137	43	,	,	PUNCT
ejpam-6388	137	44	v	v	NOUN
ejpam-6388	137	45	)	)	PUNCT
ejpam-6388	137	46	for	for	ADP
ejpam-6388	137	47	all	all	DET
ejpam-6388	137	48	u	u	NOUN
ejpam-6388	137	49	,	,	PUNCT
ejpam-6388	137	50	v	v	NOUN
ejpam-6388	137	51	,	,	PUNCT
ejpam-6388	137	52	w	w	PROPN
ejpam-6388	137	53	∈	∈	PROPN
ejpam-6388	137	54	a.	a.	NOUN
ejpam-6388	137	55	then	then	ADV
ejpam-6388	137	56	γ	γ	PROPN
ejpam-6388	137	57	is	be	AUX
ejpam-6388	137	58	referred	refer	VERB
ejpam-6388	137	59	to	to	ADP
ejpam-6388	137	60	as	as	ADP
ejpam-6388	137	61	a	a	DET
ejpam-6388	137	62	cone	cone	NOUN
ejpam-6388	137	63	metric	metric	NOUN
ejpam-6388	137	64	on	on	ADP
ejpam-6388	137	65	(	(	PUNCT
ejpam-6388	137	66	a,⊥	a,⊥	NOUN
ejpam-6388	137	67	)	)	PUNCT
ejpam-6388	137	68	,	,	PUNCT
ejpam-6388	137	69	and	and	CCONJ
ejpam-6388	137	70	(	(	PUNCT
ejpam-6388	137	71	a	a	DET
ejpam-6388	137	72	,	,	PUNCT
ejpam-6388	137	73	γ,⊥	γ,⊥	NOUN
ejpam-6388	137	74	)	)	PUNCT
ejpam-6388	137	75	is	be	AUX
ejpam-6388	137	76	classified	classify	VERB
ejpam-6388	137	77	as	as	ADP
ejpam-6388	137	78	an	an	DET
ejpam-6388	137	79	orthogonal	orthogonal	ADJ
ejpam-6388	137	80	cone	cone	NOUN
ejpam-6388	137	81	metric	metric	ADJ
ejpam-6388	137	82	space	space	NOUN
ejpam-6388	137	83	.	.	PUNCT
ejpam-6388	138	1	definition	definition	NOUN
ejpam-6388	138	2	11	11	NUM
ejpam-6388	138	3	.	.	PUNCT
ejpam-6388	139	1	[	[	X
ejpam-6388	139	2	20	20	NUM
ejpam-6388	139	3	]	]	X
ejpam-6388	139	4	let	let	VERB
ejpam-6388	139	5	(	(	PUNCT
ejpam-6388	139	6	a	a	DET
ejpam-6388	139	7	,	,	PUNCT
ejpam-6388	139	8	γ,⊥	γ,⊥	NOUN
ejpam-6388	139	9	)	)	PUNCT
ejpam-6388	139	10	be	be	AUX
ejpam-6388	139	11	an	an	DET
ejpam-6388	139	12	orthogonal	orthogonal	ADJ
ejpam-6388	139	13	cone	cone	NOUN
ejpam-6388	139	14	metric	metric	ADJ
ejpam-6388	139	15	space	space	NOUN
ejpam-6388	139	16	.	.	PUNCT
ejpam-6388	140	1	the	the	DET
ejpam-6388	140	2	space	space	NOUN
ejpam-6388	140	3	a	a	PRON
ejpam-6388	140	4	is	be	AUX
ejpam-6388	140	5	considered	consider	VERB
ejpam-6388	140	6	an	an	DET
ejpam-6388	140	7	orthogonally	orthogonally	ADV
ejpam-6388	140	8	complete	complete	ADJ
ejpam-6388	140	9	cone	cone	NOUN
ejpam-6388	140	10	metric	metric	ADJ
ejpam-6388	140	11	space	space	NOUN
ejpam-6388	140	12	provided	provide	VERB
ejpam-6388	140	13	every	every	DET
ejpam-6388	140	14	cauchy	cauchy	ADJ
ejpam-6388	140	15	o	o	ADJ
ejpam-6388	140	16	-	-	NOUN
ejpam-6388	140	17	sequence	sequence	NOUN
ejpam-6388	140	18	converges	converge	VERB
ejpam-6388	140	19	within	within	ADP
ejpam-6388	140	20	a.	a.	NOUN
ejpam-6388	140	21	remark	remark	NOUN
ejpam-6388	140	22	4	4	NUM
ejpam-6388	140	23	.	.	PUNCT
ejpam-6388	141	1	it	it	PRON
ejpam-6388	141	2	is	be	AUX
ejpam-6388	141	3	important	important	ADJ
ejpam-6388	141	4	to	to	PART
ejpam-6388	141	5	note	note	VERB
ejpam-6388	141	6	that	that	SCONJ
ejpam-6388	141	7	every	every	DET
ejpam-6388	141	8	complete	complete	ADJ
ejpam-6388	141	9	cone	cone	NOUN
ejpam-6388	141	10	metric	metric	ADJ
ejpam-6388	141	11	space	space	NOUN
ejpam-6388	141	12	qualifies	qualify	VERB
ejpam-6388	141	13	as	as	ADP
ejpam-6388	141	14	an	an	DET
ejpam-6388	141	15	o	o	NOUN
ejpam-6388	141	16	-	-	ADJ
ejpam-6388	141	17	complete	complete	ADJ
ejpam-6388	141	18	space	space	NOUN
ejpam-6388	141	19	;	;	PUNCT
ejpam-6388	141	20	however	however	ADV
ejpam-6388	141	21	,	,	PUNCT
ejpam-6388	141	22	the	the	DET
ejpam-6388	141	23	reverse	reverse	NOUN
ejpam-6388	141	24	is	be	AUX
ejpam-6388	141	25	not	not	PART
ejpam-6388	141	26	necessarily	necessarily	ADV
ejpam-6388	141	27	valid	valid	ADJ
ejpam-6388	141	28	(	(	PUNCT
ejpam-6388	141	29	see	see	VERB
ejpam-6388	141	30	[	[	X
ejpam-6388	141	31	20	20	NUM
ejpam-6388	141	32	]	]	NUM
ejpam-6388	141	33	)	)	PUNCT
ejpam-6388	141	34	.	.	PUNCT
ejpam-6388	142	1	below	below	ADP
ejpam-6388	142	2	we	we	PRON
ejpam-6388	142	3	state	state	VERB
ejpam-6388	142	4	the	the	DET
ejpam-6388	142	5	banach	banach	NOUN
ejpam-6388	142	6	fpt	fpt	NOUN
ejpam-6388	142	7	on	on	ADP
ejpam-6388	142	8	an	an	DET
ejpam-6388	142	9	orthogonal	orthogonal	ADJ
ejpam-6388	142	10	cone	cone	NOUN
ejpam-6388	142	11	metric	metric	ADJ
ejpam-6388	142	12	space	space	NOUN
ejpam-6388	142	13	.	.	PUNCT
ejpam-6388	143	1	theorem	theorem	NOUN
ejpam-6388	143	2	2	2	NUM
ejpam-6388	143	3	.	.	PUNCT
ejpam-6388	144	1	[	[	X
ejpam-6388	144	2	20	20	NUM
ejpam-6388	144	3	]	]	X
ejpam-6388	144	4	let	let	VERB
ejpam-6388	144	5	(	(	PUNCT
ejpam-6388	144	6	a	a	DET
ejpam-6388	144	7	,	,	PUNCT
ejpam-6388	144	8	γ,⊥	γ,⊥	NOUN
ejpam-6388	144	9	)	)	PUNCT
ejpam-6388	144	10	be	be	AUX
ejpam-6388	144	11	an	an	DET
ejpam-6388	144	12	o	o	NOUN
ejpam-6388	144	13	-	-	ADJ
ejpam-6388	144	14	complete	complete	ADJ
ejpam-6388	144	15	metric	metric	ADJ
ejpam-6388	144	16	space	space	NOUN
ejpam-6388	144	17	(	(	PUNCT
ejpam-6388	144	18	which	which	PRON
ejpam-6388	144	19	may	may	AUX
ejpam-6388	144	20	not	not	PART
ejpam-6388	144	21	necessarily	necessarily	ADV
ejpam-6388	144	22	be	be	AUX
ejpam-6388	144	23	complete	complete	ADJ
ejpam-6388	144	24	)	)	PUNCT
ejpam-6388	144	25	.	.	PUNCT
ejpam-6388	145	1	consider	consider	VERB
ejpam-6388	145	2	a	a	DET
ejpam-6388	145	3	mapping	mapping	NOUN
ejpam-6388	145	4	g	g	NOUN
ejpam-6388	145	5	:	:	PUNCT
ejpam-6388	145	6	a	a	DET
ejpam-6388	145	7	→	→	PUNCT
ejpam-6388	145	8	a	a	PRON
ejpam-6388	145	9	that	that	PRON
ejpam-6388	145	10	satisfies	satisfy	VERB
ejpam-6388	145	11	the	the	DET
ejpam-6388	145	12	following	follow	VERB
ejpam-6388	145	13	conditions	condition	NOUN
ejpam-6388	146	1	:	:	PUNCT
ejpam-6388	146	2	1	1	X
ejpam-6388	146	3	.	.	X
ejpam-6388	146	4	⊥-continuity	⊥-continuity	NOUN
ejpam-6388	146	5	:	:	PUNCT
ejpam-6388	146	6	the	the	DET
ejpam-6388	146	7	mapping	mapping	NOUN
ejpam-6388	146	8	g	g	NOUN
ejpam-6388	146	9	is	be	AUX
ejpam-6388	146	10	continuous	continuous	ADJ
ejpam-6388	146	11	with	with	ADP
ejpam-6388	146	12	respect	respect	NOUN
ejpam-6388	146	13	to	to	ADP
ejpam-6388	146	14	the	the	DET
ejpam-6388	146	15	orthogonal	orthogonal	ADJ
ejpam-6388	146	16	structure	structure	NOUN
ejpam-6388	146	17	present	present	ADJ
ejpam-6388	146	18	in	in	ADP
ejpam-6388	146	19	the	the	DET
ejpam-6388	146	20	space	space	NOUN
ejpam-6388	146	21	.	.	PUNCT
ejpam-6388	147	1	2	2	X
ejpam-6388	147	2	.	.	X
ejpam-6388	147	3	⊥-contraction	⊥-contraction	NOUN
ejpam-6388	147	4	:	:	PUNCT
ejpam-6388	147	5	there	there	PRON
ejpam-6388	147	6	exists	exist	VERB
ejpam-6388	147	7	a	a	DET
ejpam-6388	147	8	lipschitz	lipschitz	NOUN
ejpam-6388	147	9	constant	constant	ADJ
ejpam-6388	147	10	c	c	NOUN
ejpam-6388	147	11	such	such	ADJ
ejpam-6388	147	12	that	that	PRON
ejpam-6388	147	13	for	for	ADP
ejpam-6388	147	14	all	all	DET
ejpam-6388	147	15	u	u	NOUN
ejpam-6388	147	16	,	,	PUNCT
ejpam-6388	147	17	v	v	ADP
ejpam-6388	147	18	∈	∈	PROPN
ejpam-6388	147	19	a	a	PRON
ejpam-6388	147	20	,	,	PUNCT
ejpam-6388	147	21	the	the	DET
ejpam-6388	147	22	inequality	inequality	NOUN
ejpam-6388	147	23	γ(g(u),g(v	γ(g(u),g(v	PROPN
ejpam-6388	147	24	)	)	PUNCT
ejpam-6388	147	25	)	)	PUNCT
ejpam-6388	147	26	≤	≤	PUNCT
ejpam-6388	147	27	c	c	NOUN
ejpam-6388	147	28	·	·	PUNCT
ejpam-6388	147	29	γ(u	γ(u	X
ejpam-6388	147	30	,	,	PUNCT
ejpam-6388	147	31	v	v	NOUN
ejpam-6388	147	32	)	)	PUNCT
ejpam-6388	147	33	holds	hold	NOUN
ejpam-6388	147	34	,	,	PUNCT
ejpam-6388	147	35	where	where	SCONJ
ejpam-6388	147	36	c	c	PROPN
ejpam-6388	147	37	is	be	AUX
ejpam-6388	147	38	constrained	constrain	VERB
ejpam-6388	147	39	within	within	ADP
ejpam-6388	147	40	the	the	DET
ejpam-6388	147	41	interval	interval	NOUN
ejpam-6388	147	42	[	[	X
ejpam-6388	147	43	0	0	NUM
ejpam-6388	147	44	,	,	PUNCT
ejpam-6388	147	45	1	1	NUM
ejpam-6388	147	46	)	)	PUNCT
ejpam-6388	147	47	.	.	PUNCT
ejpam-6388	148	1	3	3	X
ejpam-6388	148	2	.	.	X
ejpam-6388	148	3	⊥-preserving	⊥-preserve	VERB
ejpam-6388	148	4	:	:	PUNCT
ejpam-6388	148	5	the	the	DET
ejpam-6388	148	6	mapping	mapping	NOUN
ejpam-6388	148	7	g	g	NOUN
ejpam-6388	148	8	maintains	maintain	VERB
ejpam-6388	148	9	the	the	DET
ejpam-6388	148	10	orthogonality	orthogonality	NOUN
ejpam-6388	148	11	relation	relation	NOUN
ejpam-6388	148	12	within	within	ADP
ejpam-6388	148	13	the	the	DET
ejpam-6388	148	14	space	space	NOUN
ejpam-6388	148	15	.	.	PUNCT
ejpam-6388	149	1	given	give	VERB
ejpam-6388	149	2	these	these	DET
ejpam-6388	149	3	criteria	criterion	NOUN
ejpam-6388	149	4	,	,	PUNCT
ejpam-6388	149	5	the	the	DET
ejpam-6388	149	6	mapping	mapping	NOUN
ejpam-6388	149	7	g	g	NOUN
ejpam-6388	149	8	possesses	possess	VERB
ejpam-6388	149	9	a	a	DET
ejpam-6388	149	10	unique	unique	ADJ
ejpam-6388	149	11	fixed	fix	VERB
ejpam-6388	149	12	point	point	NOUN
ejpam-6388	149	13	u∗	u∗	ADV
ejpam-6388	149	14	in	in	ADP
ejpam-6388	149	15	the	the	DET
ejpam-6388	149	16	set	set	NOUN
ejpam-6388	149	17	a.	a.	NOUN
ejpam-6388	149	18	furthermore	furthermore	ADV
ejpam-6388	149	19	,	,	PUNCT
ejpam-6388	149	20	g	g	PROPN
ejpam-6388	149	21	qualifies	qualify	VERB
ejpam-6388	149	22	as	as	ADP
ejpam-6388	149	23	a	a	DET
ejpam-6388	149	24	picard	picard	NOUN
ejpam-6388	149	25	operator	operator	NOUN
ejpam-6388	149	26	,	,	PUNCT
ejpam-6388	149	27	which	which	PRON
ejpam-6388	149	28	implies	imply	VERB
ejpam-6388	149	29	that	that	SCONJ
ejpam-6388	149	30	limr→∞	limr→∞	PROPN
ejpam-6388	149	31	gr(u	gr(u	PRON
ejpam-6388	149	32	)	)	PUNCT
ejpam-6388	149	33	=	=	VERB
ejpam-6388	150	1	u∗	u∗	ADJ
ejpam-6388	150	2	for	for	ADP
ejpam-6388	150	3	every	every	DET
ejpam-6388	150	4	u	u	PROPN
ejpam-6388	150	5	∈	∈	PROPN
ejpam-6388	150	6	a.	a.	NOUN
ejpam-6388	150	7	3	3	X
ejpam-6388	150	8	.	.	PUNCT
ejpam-6388	150	9	auxiliary	auxiliary	ADJ
ejpam-6388	150	10	results	result	NOUN
ejpam-6388	150	11	in	in	ADP
ejpam-6388	150	12	this	this	DET
ejpam-6388	150	13	section	section	NOUN
ejpam-6388	150	14	,	,	PUNCT
ejpam-6388	150	15	we	we	PRON
ejpam-6388	150	16	shall	shall	AUX
ejpam-6388	150	17	state	state	NOUN
ejpam-6388	150	18	and	and	CCONJ
ejpam-6388	150	19	prove	prove	VERB
ejpam-6388	150	20	certain	certain	ADJ
ejpam-6388	150	21	auxiliary	auxiliary	ADJ
ejpam-6388	150	22	results	result	NOUN
ejpam-6388	150	23	which	which	PRON
ejpam-6388	150	24	serve	serve	VERB
ejpam-6388	150	25	as	as	ADP
ejpam-6388	150	26	basis	basis	NOUN
ejpam-6388	150	27	material	material	NOUN
ejpam-6388	150	28	for	for	ADP
ejpam-6388	150	29	our	our	PRON
ejpam-6388	150	30	main	main	ADJ
ejpam-6388	150	31	results	result	NOUN
ejpam-6388	150	32	.	.	PUNCT
ejpam-6388	151	1	lemma	lemma	PROPN
ejpam-6388	151	2	3	3	NUM
ejpam-6388	151	3	.	.	PUNCT
ejpam-6388	152	1	the	the	DET
ejpam-6388	152	2	function	function	NOUN
ejpam-6388	152	3	r	r	NOUN
ejpam-6388	152	4	is	be	AUX
ejpam-6388	152	5	a	a	DET
ejpam-6388	152	6	solution	solution	NOUN
ejpam-6388	152	7	of	of	ADP
ejpam-6388	152	8	the	the	DET
ejpam-6388	152	9	fhbvp	fhbvp	NOUN
ejpam-6388	152	10	(	(	PUNCT
ejpam-6388	152	11	1)–(2	1)–(2	NUM
ejpam-6388	152	12	)	)	PUNCT
ejpam-6388	152	13	if	if	SCONJ
ejpam-6388	153	1	and	and	CCONJ
ejpam-6388	153	2	only	only	ADV
ejpam-6388	153	3	if	if	SCONJ
ejpam-6388	153	4	r	r	NOUN
ejpam-6388	153	5	is	be	AUX
ejpam-6388	153	6	a	a	DET
ejpam-6388	153	7	solution	solution	NOUN
ejpam-6388	153	8	to	to	ADP
ejpam-6388	153	9	the	the	DET
ejpam-6388	153	10	integral	integral	ADJ
ejpam-6388	153	11	equation	equation	NOUN
ejpam-6388	153	12	r(ω	r(ω	ADV
ejpam-6388	153	13	)	)	PUNCT
ejpam-6388	154	1	=	=	SYM
ejpam-6388	154	2	f	f	PROPN
ejpam-6388	154	3	(	(	PUNCT
ejpam-6388	154	4	ω	ω	PROPN
ejpam-6388	154	5	,	,	PUNCT
ejpam-6388	154	6	r(ω	r(ω	ADJ
ejpam-6388	154	7	)	)	PUNCT
ejpam-6388	154	8	)	)	PUNCT
ejpam-6388	155	1	ωy−1	ωy−1	ADV
ejpam-6388	156	1	+	+	CCONJ
ejpam-6388	156	2	f	f	X
ejpam-6388	156	3	(	(	PUNCT
ejpam-6388	156	4	ω	ω	PROPN
ejpam-6388	156	5	,	,	PUNCT
ejpam-6388	156	6	r(ω	r(ω	ADJ
ejpam-6388	156	7	)	)	PUNCT
ejpam-6388	156	8	)	)	PUNCT
ejpam-6388	157	1	∫	∫	PROPN
ejpam-6388	157	2	1	1	NUM
ejpam-6388	157	3	0	0	NUM
ejpam-6388	157	4	0	0	NUM
ejpam-6388	158	1	(	(	PUNCT
ejpam-6388	158	2	ω	ω	PROPN
ejpam-6388	158	3	,	,	PUNCT
ejpam-6388	158	4	ξ	ξ	PROPN
ejpam-6388	158	5	)	)	PUNCT
ejpam-6388	158	6	g(ξ	g(ξ	PROPN
ejpam-6388	158	7	,	,	PUNCT
ejpam-6388	158	8	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	158	9	,	,	PUNCT
ejpam-6388	158	10	(	(	PUNCT
ejpam-6388	158	11	3	3	X
ejpam-6388	158	12	)	)	PUNCT
ejpam-6388	158	13	where	where	SCONJ
ejpam-6388	158	14	0(ω	0(ω	NOUN
ejpam-6388	158	15	,	,	PUNCT
ejpam-6388	158	16	ξ	ξ	X
ejpam-6388	158	17	)	)	PUNCT
ejpam-6388	158	18	=	=	SYM
ejpam-6388	158	19	1	1	NUM
ejpam-6388	158	20	γ(y	γ(y	PROPN
ejpam-6388	158	21	)	)	PUNCT
ejpam-6388	158	22	{	{	PUNCT
ejpam-6388	159	1	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	159	2	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	159	3	−	−	PROPN
ejpam-6388	159	4	(	(	PUNCT
ejpam-6388	159	5	ω	ω	NUM
ejpam-6388	159	6	−	−	PROPN
ejpam-6388	159	7	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	159	8	,	,	PUNCT
ejpam-6388	159	9	ξ	ξ	PROPN
ejpam-6388	159	10	≤	≤	PROPN
ejpam-6388	159	11	ω	ω	NUM
ejpam-6388	159	12	,	,	PUNCT
ejpam-6388	159	13	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	159	14	ξ)y−1	ξ)y−1	PROPN
ejpam-6388	159	15	,	,	PUNCT
ejpam-6388	159	16	ω	ω	NUM
ejpam-6388	159	17	≤	≤	NUM
ejpam-6388	159	18	ξ	ξ	NUM
ejpam-6388	159	19	.	.	PUNCT
ejpam-6388	160	1	(	(	PUNCT
ejpam-6388	160	2	4	4	X
ejpam-6388	160	3	)	)	PUNCT
ejpam-6388	160	4	d.	d.	PROPN
ejpam-6388	160	5	baleanu	baleanu	PROPN
ejpam-6388	160	6	et	et	PROPN
ejpam-6388	160	7	al	al	PROPN
ejpam-6388	160	8	.	.	PUNCT
ejpam-6388	160	9	/	/	SYM
ejpam-6388	160	10	eur	eur	PROPN
ejpam-6388	160	11	.	.	PUNCT
ejpam-6388	161	1	j.	j.	PROPN
ejpam-6388	161	2	pure	pure	PROPN
ejpam-6388	161	3	appl	appl	PROPN
ejpam-6388	161	4	.	.	PROPN
ejpam-6388	161	5	math	math	PROPN
ejpam-6388	161	6	,	,	PUNCT
ejpam-6388	161	7	18	18	NUM
ejpam-6388	161	8	(	(	PUNCT
ejpam-6388	161	9	4	4	NUM
ejpam-6388	161	10	)	)	PUNCT
ejpam-6388	161	11	(	(	PUNCT
ejpam-6388	161	12	2025	2025	NUM
ejpam-6388	161	13	)	)	PUNCT
ejpam-6388	161	14	,	,	PUNCT
ejpam-6388	161	15	6388	6388	NUM
ejpam-6388	161	16	8	8	NUM
ejpam-6388	161	17	of	of	ADP
ejpam-6388	161	18	31	31	NUM
ejpam-6388	161	19	proof	proof	NOUN
ejpam-6388	161	20	.	.	PUNCT
ejpam-6388	162	1	let	let	VERB
ejpam-6388	162	2	r	r	PRON
ejpam-6388	162	3	be	be	AUX
ejpam-6388	162	4	a	a	DET
ejpam-6388	162	5	solution	solution	NOUN
ejpam-6388	162	6	of	of	ADP
ejpam-6388	162	7	the	the	DET
ejpam-6388	162	8	fhbvp	fhbvp	NOUN
ejpam-6388	162	9	(	(	PUNCT
ejpam-6388	162	10	1)–(2	1)–(2	NUM
ejpam-6388	162	11	)	)	PUNCT
ejpam-6388	162	12	.	.	PUNCT
ejpam-6388	163	1	then	then	ADV
ejpam-6388	163	2	employing	employ	VERB
ejpam-6388	163	3	lemma	lemma	PROPN
ejpam-6388	163	4	2	2	NUM
ejpam-6388	163	5	,	,	PUNCT
ejpam-6388	163	6	we	we	PRON
ejpam-6388	163	7	have	have	VERB
ejpam-6388	163	8	r(ω	r(ω	ADV
ejpam-6388	163	9	)	)	PUNCT
ejpam-6388	163	10	f	f	PROPN
ejpam-6388	163	11	(	(	PUNCT
ejpam-6388	163	12	ω	ω	NOUN
ejpam-6388	163	13	,	,	PUNCT
ejpam-6388	163	14	r(ω	r(ω	ADJ
ejpam-6388	163	15	)	)	PUNCT
ejpam-6388	163	16	)	)	PUNCT
ejpam-6388	164	1	=	=	PUNCT
ejpam-6388	165	1	2∑	2∑	X
ejpam-6388	165	2	i=1	i=1	X
ejpam-6388	165	3	aiω	aiω	NOUN
ejpam-6388	165	4	y−i	y−i	PROPN
ejpam-6388	165	5	−	−	PROPN
ejpam-6388	165	6	∫	∫	PROPN
ejpam-6388	165	7	ω	ω	PROPN
ejpam-6388	165	8	0	0	NUM
ejpam-6388	165	9	(	(	PUNCT
ejpam-6388	165	10	ω	ω	NUM
ejpam-6388	165	11	−	−	PROPN
ejpam-6388	165	12	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	165	13	γ(y	γ(y	PROPN
ejpam-6388	165	14	)	)	PUNCT
ejpam-6388	166	1	g(ξ	g(ξ	PROPN
ejpam-6388	166	2	,	,	PUNCT
ejpam-6388	166	3	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	166	4	,	,	PUNCT
ejpam-6388	166	5	(	(	PUNCT
ejpam-6388	166	6	5	5	NUM
ejpam-6388	166	7	)	)	PUNCT
ejpam-6388	166	8	where	where	SCONJ
ejpam-6388	166	9	a1	a1	NOUN
ejpam-6388	166	10	,	,	PUNCT
ejpam-6388	166	11	a2	a2	PROPN
ejpam-6388	166	12	are	be	AUX
ejpam-6388	166	13	real	real	ADJ
ejpam-6388	166	14	constants	constant	NOUN
ejpam-6388	166	15	.	.	PUNCT
ejpam-6388	167	1	applying	apply	VERB
ejpam-6388	167	2	the	the	DET
ejpam-6388	167	3	stipulations	stipulation	NOUN
ejpam-6388	167	4	(	(	PUNCT
ejpam-6388	167	5	2	2	NUM
ejpam-6388	167	6	)	)	PUNCT
ejpam-6388	167	7	,	,	PUNCT
ejpam-6388	167	8	it	it	PRON
ejpam-6388	167	9	can	can	AUX
ejpam-6388	167	10	be	be	AUX
ejpam-6388	167	11	concluded	conclude	VERB
ejpam-6388	167	12	that	that	SCONJ
ejpam-6388	167	13	a2	a2	PROPN
ejpam-6388	167	14	=	=	NOUN
ejpam-6388	167	15	0	0	PUNCT
ejpam-6388	167	16	as	as	ADV
ejpam-6388	167	17	well	well	ADV
ejpam-6388	167	18	as	as	ADP
ejpam-6388	167	19	a1	a1	NOUN
ejpam-6388	167	20	=	=	SYM
ejpam-6388	167	21	1	1	NUM
ejpam-6388	167	22	+	+	NUM
ejpam-6388	167	23	∫	∫	PROPN
ejpam-6388	167	24	1	1	NUM
ejpam-6388	167	25	0	0	NUM
ejpam-6388	167	26	(	(	PUNCT
ejpam-6388	167	27	1−	1−	NUM
ejpam-6388	167	28	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	167	29	γ(y	γ(y	PROPN
ejpam-6388	167	30	)	)	PUNCT
ejpam-6388	168	1	g(ξ	g(ξ	PROPN
ejpam-6388	168	2	,	,	PUNCT
ejpam-6388	168	3	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	168	4	.	.	PUNCT
ejpam-6388	169	1	now	now	ADV
ejpam-6388	169	2	,	,	PUNCT
ejpam-6388	169	3	putting	put	VERB
ejpam-6388	169	4	a1	a1	NOUN
ejpam-6388	169	5	and	and	CCONJ
ejpam-6388	169	6	a2	a2	PROPN
ejpam-6388	169	7	in	in	ADP
ejpam-6388	169	8	(	(	PUNCT
ejpam-6388	169	9	5	5	NUM
ejpam-6388	169	10	)	)	PUNCT
ejpam-6388	169	11	,	,	PUNCT
ejpam-6388	169	12	we	we	PRON
ejpam-6388	169	13	get	get	VERB
ejpam-6388	169	14	r(ω	r(ω	ADV
ejpam-6388	169	15	)	)	PUNCT
ejpam-6388	170	1	f	f	PROPN
ejpam-6388	170	2	(	(	PUNCT
ejpam-6388	170	3	ω	ω	NOUN
ejpam-6388	170	4	,	,	PUNCT
ejpam-6388	170	5	r(ω	r(ω	ADJ
ejpam-6388	170	6	)	)	PUNCT
ejpam-6388	170	7	)	)	PUNCT
ejpam-6388	171	1	=	=	PUNCT
ejpam-6388	172	1	ωy−1	ωy−1	INTJ
ejpam-6388	172	2	+	+	CCONJ
ejpam-6388	172	3	∫	∫	PROPN
ejpam-6388	172	4	1	1	NUM
ejpam-6388	172	5	0	0	NUM
ejpam-6388	172	6	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	172	7	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	172	8	γ(y	γ(y	PROPN
ejpam-6388	172	9	)	)	PUNCT
ejpam-6388	172	10	g(ξ	g(ξ	PROPN
ejpam-6388	172	11	,	,	PUNCT
ejpam-6388	172	12	r(ξ))dξ−	r(ξ))dξ−	PROPN
ejpam-6388	172	13	∫	∫	PROPN
ejpam-6388	172	14	ω	ω	PROPN
ejpam-6388	172	15	0	0	NUM
ejpam-6388	173	1	(	(	PUNCT
ejpam-6388	173	2	ω	ω	NUM
ejpam-6388	173	3	−	−	PROPN
ejpam-6388	173	4	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	173	5	γ(y	γ(y	PROPN
ejpam-6388	173	6	)	)	PUNCT
ejpam-6388	174	1	g(ξ	g(ξ	PROPN
ejpam-6388	174	2	,	,	PUNCT
ejpam-6388	174	3	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	174	4	.	.	PUNCT
ejpam-6388	175	1	therefore	therefore	ADV
ejpam-6388	175	2	r(ω	r(ω	ADV
ejpam-6388	175	3	)	)	PUNCT
ejpam-6388	176	1	=	=	SYM
ejpam-6388	176	2	f	f	PROPN
ejpam-6388	176	3	(	(	PUNCT
ejpam-6388	176	4	ω	ω	PROPN
ejpam-6388	176	5	,	,	PUNCT
ejpam-6388	176	6	r(ω	r(ω	ADJ
ejpam-6388	176	7	)	)	PUNCT
ejpam-6388	176	8	)	)	PUNCT
ejpam-6388	177	1	ωy−1	ωy−1	ADV
ejpam-6388	178	1	+	+	CCONJ
ejpam-6388	178	2	f	f	X
ejpam-6388	178	3	(	(	PUNCT
ejpam-6388	178	4	ω	ω	PROPN
ejpam-6388	178	5	,	,	PUNCT
ejpam-6388	178	6	r(ω	r(ω	ADJ
ejpam-6388	178	7	)	)	PUNCT
ejpam-6388	178	8	)	)	PUNCT
ejpam-6388	179	1	∫	∫	PROPN
ejpam-6388	179	2	1	1	NUM
ejpam-6388	179	3	0	0	NUM
ejpam-6388	179	4	0	0	NUM
ejpam-6388	180	1	(	(	PUNCT
ejpam-6388	180	2	ω	ω	PROPN
ejpam-6388	180	3	,	,	PUNCT
ejpam-6388	180	4	ξ	ξ	PROPN
ejpam-6388	180	5	)	)	PUNCT
ejpam-6388	180	6	g(ξ	g(ξ	PROPN
ejpam-6388	180	7	,	,	PUNCT
ejpam-6388	180	8	r(ξ))dξ	r(ξ))dξ	PROPN
ejpam-6388	180	9	.	.	PUNCT
ejpam-6388	181	1	assume	assume	VERB
ejpam-6388	181	2	,	,	PUNCT
ejpam-6388	181	3	on	on	ADP
ejpam-6388	181	4	the	the	DET
ejpam-6388	181	5	other	other	ADJ
ejpam-6388	181	6	hand	hand	NOUN
ejpam-6388	181	7	,	,	PUNCT
ejpam-6388	181	8	that	that	SCONJ
ejpam-6388	181	9	r	r	NOUN
ejpam-6388	181	10	is	be	AUX
ejpam-6388	181	11	a	a	DET
ejpam-6388	181	12	solution	solution	NOUN
ejpam-6388	181	13	to	to	ADP
ejpam-6388	181	14	(	(	PUNCT
ejpam-6388	181	15	3	3	NUM
ejpam-6388	181	16	)	)	PUNCT
ejpam-6388	181	17	.	.	PUNCT
ejpam-6388	182	1	then	then	ADV
ejpam-6388	182	2	r(ω	r(ω	ADV
ejpam-6388	182	3	)	)	PUNCT
ejpam-6388	182	4	f	f	PROPN
ejpam-6388	182	5	(	(	PUNCT
ejpam-6388	182	6	ω	ω	NOUN
ejpam-6388	182	7	,	,	PUNCT
ejpam-6388	182	8	r(ω	r(ω	ADJ
ejpam-6388	182	9	)	)	PUNCT
ejpam-6388	182	10	)	)	PUNCT
ejpam-6388	183	1	=	=	PUNCT
ejpam-6388	184	1	ωy−1	ωy−1	INTJ
ejpam-6388	184	2	+	+	CCONJ
ejpam-6388	184	3	∫	∫	PROPN
ejpam-6388	184	4	1	1	NUM
ejpam-6388	184	5	0	0	NUM
ejpam-6388	184	6	0(ω	0(ω	NUM
ejpam-6388	184	7	,	,	PUNCT
ejpam-6388	184	8	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	184	9	,	,	PUNCT
ejpam-6388	184	10	r(ξ))dξ	r(ξ))dξ	X
ejpam-6388	184	11	=	=	SYM
ejpam-6388	184	12	ωy−1	ωy−1	ADJ
ejpam-6388	184	13	[	[	PUNCT
ejpam-6388	184	14	1	1	NUM
ejpam-6388	184	15	+	+	NUM
ejpam-6388	184	16	∫	∫	PROPN
ejpam-6388	184	17	1	1	NUM
ejpam-6388	184	18	0	0	NUM
ejpam-6388	184	19	(	(	PUNCT
ejpam-6388	184	20	1−	1−	NUM
ejpam-6388	184	21	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	184	22	γ(y	γ(y	PROPN
ejpam-6388	184	23	)	)	PUNCT
ejpam-6388	185	1	g(ξ	g(ξ	PROPN
ejpam-6388	185	2	,	,	PUNCT
ejpam-6388	185	3	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	185	4	]	]	PUNCT
ejpam-6388	185	5	−	−	PROPN
ejpam-6388	185	6	∫	∫	PROPN
ejpam-6388	185	7	ω	ω	PROPN
ejpam-6388	185	8	0	0	NUM
ejpam-6388	185	9	(	(	PUNCT
ejpam-6388	185	10	ω	ω	NUM
ejpam-6388	185	11	−	−	PROPN
ejpam-6388	185	12	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	185	13	γ(y	γ(y	PROPN
ejpam-6388	185	14	)	)	PUNCT
ejpam-6388	186	1	g(ξ	g(ξ	PROPN
ejpam-6388	186	2	,	,	PUNCT
ejpam-6388	186	3	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	186	4	.	.	PUNCT
ejpam-6388	187	1	keeping	keep	VERB
ejpam-6388	187	2	in	in	ADP
ejpam-6388	187	3	mind	mind	NOUN
ejpam-6388	187	4	remarks	remark	NOUN
ejpam-6388	187	5	1	1	NUM
ejpam-6388	187	6	and	and	CCONJ
ejpam-6388	187	7	2	2	NUM
ejpam-6388	187	8	,	,	PUNCT
ejpam-6388	187	9	the	the	DET
ejpam-6388	187	10	operator	operator	NOUN
ejpam-6388	187	11	rld	rld	NOUN
ejpam-6388	187	12	y	y	PROPN
ejpam-6388	187	13	0	0	PROPN
ejpam-6388	187	14	+	+	CCONJ
ejpam-6388	187	15	is	be	AUX
ejpam-6388	187	16	applied	apply	VERB
ejpam-6388	187	17	to	to	ADP
ejpam-6388	187	18	each	each	DET
ejpam-6388	187	19	part	part	NOUN
ejpam-6388	187	20	of	of	ADP
ejpam-6388	187	21	the	the	DET
ejpam-6388	187	22	aforementioned	aforementioned	ADJ
ejpam-6388	187	23	equation	equation	NOUN
ejpam-6388	187	24	to	to	PART
ejpam-6388	187	25	arrive	arrive	VERB
ejpam-6388	187	26	at	at	ADP
ejpam-6388	187	27	rldy	rldy	NOUN
ejpam-6388	187	28	0	0	NUM
ejpam-6388	188	1	+	+	CCONJ
ejpam-6388	188	2	[	[	PUNCT
ejpam-6388	188	3	r(ω	r(ω	ADJ
ejpam-6388	188	4	)	)	PUNCT
ejpam-6388	188	5	f(ω	f(ω	PROPN
ejpam-6388	188	6	,	,	PUNCT
ejpam-6388	188	7	r(ω	r(ω	ADJ
ejpam-6388	188	8	)	)	PUNCT
ejpam-6388	188	9	)	)	PUNCT
ejpam-6388	188	10	]	]	PUNCT
ejpam-6388	189	1	=	=	PUNCT
ejpam-6388	189	2	−g(ω	−g(ω	PROPN
ejpam-6388	189	3	,	,	PUNCT
ejpam-6388	189	4	r(ω	r(ω	ADJ
ejpam-6388	189	5	)	)	PUNCT
ejpam-6388	189	6	)	)	PUNCT
ejpam-6388	189	7	.	.	PUNCT
ejpam-6388	190	1	given	give	VERB
ejpam-6388	190	2	f(ω	f(ω	PROPN
ejpam-6388	190	3	,	,	PUNCT
ejpam-6388	190	4	r(ω	r(ω	ADJ
ejpam-6388	190	5	)	)	PUNCT
ejpam-6388	190	6	)	)	PUNCT
ejpam-6388	191	1	̸=	̸=	NOUN
ejpam-6388	191	2	0	0	NUM
ejpam-6388	191	3	for	for	ADP
ejpam-6388	191	4	ω	ω	PROPN
ejpam-6388	191	5	∈	∈	PROPN
ejpam-6388	192	1	[	[	X
ejpam-6388	192	2	0	0	NUM
ejpam-6388	192	3	,	,	PUNCT
ejpam-6388	192	4	1	1	NUM
ejpam-6388	192	5	]	]	PUNCT
ejpam-6388	192	6	,	,	PUNCT
ejpam-6388	192	7	it	it	PRON
ejpam-6388	192	8	implies	imply	VERB
ejpam-6388	192	9	from	from	ADP
ejpam-6388	192	10	(	(	PUNCT
ejpam-6388	192	11	3	3	NUM
ejpam-6388	192	12	)	)	PUNCT
ejpam-6388	192	13	that	that	PRON
ejpam-6388	192	14	r(0	r(0	PROPN
ejpam-6388	192	15	)	)	PUNCT
ejpam-6388	192	16	=	=	SYM
ejpam-6388	192	17	0	0	NUM
ejpam-6388	192	18	and	and	CCONJ
ejpam-6388	192	19	r(1	r(1	PROPN
ejpam-6388	192	20	)	)	PUNCT
ejpam-6388	193	1	=	=	SYM
ejpam-6388	193	2	f	f	PROPN
ejpam-6388	193	3	(	(	PUNCT
ejpam-6388	193	4	1	1	NUM
ejpam-6388	193	5	,	,	PUNCT
ejpam-6388	193	6	r(1	r(1	PROPN
ejpam-6388	193	7	)	)	PUNCT
ejpam-6388	193	8	)	)	PUNCT
ejpam-6388	193	9	.	.	PUNCT
ejpam-6388	194	1	consequently	consequently	ADV
ejpam-6388	194	2	,	,	PUNCT
ejpam-6388	194	3	the	the	DET
ejpam-6388	194	4	proof	proof	NOUN
ejpam-6388	194	5	is	be	AUX
ejpam-6388	194	6	now	now	ADV
ejpam-6388	194	7	concluded	conclude	VERB
ejpam-6388	194	8	.	.	PUNCT
ejpam-6388	195	1	lemma	lemma	PROPN
ejpam-6388	195	2	4	4	NUM
ejpam-6388	195	3	.	.	PUNCT
ejpam-6388	196	1	the	the	DET
ejpam-6388	196	2	kernel	kernel	NOUN
ejpam-6388	196	3	0(ω	0(ω	PRON
ejpam-6388	196	4	,	,	PUNCT
ejpam-6388	196	5	ξ	ξ	X
ejpam-6388	196	6	)	)	PUNCT
ejpam-6388	196	7	possesses	possess	VERB
ejpam-6388	196	8	the	the	DET
ejpam-6388	196	9	following	follow	VERB
ejpam-6388	196	10	characteristics	characteristic	NOUN
ejpam-6388	196	11	:	:	PUNCT
ejpam-6388	196	12	(	(	PUNCT
ejpam-6388	196	13	κ1	κ1	NOUN
ejpam-6388	196	14	)	)	PUNCT
ejpam-6388	196	15	0(ω	0(ω	ADV
ejpam-6388	196	16	,	,	PUNCT
ejpam-6388	196	17	ξ	ξ	X
ejpam-6388	196	18	)	)	PUNCT
ejpam-6388	196	19	nonnegative	nonnegative	ADJ
ejpam-6388	196	20	and	and	CCONJ
ejpam-6388	196	21	continuous	continuous	ADJ
ejpam-6388	196	22	on	on	ADP
ejpam-6388	196	23	[	[	X
ejpam-6388	196	24	0	0	NUM
ejpam-6388	196	25	,	,	PUNCT
ejpam-6388	196	26	1]×	1]×	NUM
ejpam-6388	197	1	[	[	X
ejpam-6388	197	2	0	0	NUM
ejpam-6388	197	3	,	,	PUNCT
ejpam-6388	197	4	1	1	NUM
ejpam-6388	197	5	]	]	PUNCT
ejpam-6388	197	6	.	.	PUNCT
ejpam-6388	198	1	(	(	PUNCT
ejpam-6388	198	2	κ2	κ2	PROPN
ejpam-6388	198	3	)	)	PUNCT
ejpam-6388	198	4	0(ω	0(ω	ADV
ejpam-6388	198	5	,	,	PUNCT
ejpam-6388	198	6	ξ	ξ	X
ejpam-6388	198	7	)	)	PUNCT
ejpam-6388	198	8	≤	≤	NOUN
ejpam-6388	198	9	0(ξ	0(ξ	NUM
ejpam-6388	198	10	,	,	PUNCT
ejpam-6388	198	11	ξ	ξ	NOUN
ejpam-6388	198	12	)	)	PUNCT
ejpam-6388	198	13	for	for	ADP
ejpam-6388	198	14	ω	ω	PROPN
ejpam-6388	198	15	,	,	PUNCT
ejpam-6388	198	16	ξ	ξ	PROPN
ejpam-6388	198	17	∈	∈	PROPN
ejpam-6388	199	1	[	[	X
ejpam-6388	199	2	0	0	NUM
ejpam-6388	199	3	,	,	PUNCT
ejpam-6388	199	4	1	1	NUM
ejpam-6388	199	5	]	]	PUNCT
ejpam-6388	199	6	.	.	PUNCT
ejpam-6388	200	1	proof	proof	NOUN
ejpam-6388	200	2	.	.	PUNCT
ejpam-6388	201	1	(	(	PUNCT
ejpam-6388	201	2	κ1	κ1	NOUN
ejpam-6388	201	3	)	)	PUNCT
ejpam-6388	201	4	from	from	ADP
ejpam-6388	201	5	(	(	PUNCT
ejpam-6388	201	6	4	4	NUM
ejpam-6388	201	7	)	)	PUNCT
ejpam-6388	201	8	,	,	PUNCT
ejpam-6388	201	9	we	we	PRON
ejpam-6388	201	10	see	see	VERB
ejpam-6388	201	11	that	that	SCONJ
ejpam-6388	201	12	0(ω	0(ω	NOUN
ejpam-6388	201	13	,	,	PUNCT
ejpam-6388	201	14	ξ	ξ	X
ejpam-6388	201	15	)	)	PUNCT
ejpam-6388	201	16	is	be	AUX
ejpam-6388	201	17	continuous	continuous	ADJ
ejpam-6388	201	18	for	for	ADP
ejpam-6388	201	19	ω	ω	PROPN
ejpam-6388	201	20	,	,	PUNCT
ejpam-6388	201	21	ξ	ξ	PROPN
ejpam-6388	201	22	∈	∈	PROPN
ejpam-6388	202	1	[	[	X
ejpam-6388	202	2	0	0	NUM
ejpam-6388	202	3	,	,	PUNCT
ejpam-6388	202	4	1	1	NUM
ejpam-6388	202	5	]	]	PUNCT
ejpam-6388	202	6	.	.	PUNCT
ejpam-6388	203	1	next	next	ADV
ejpam-6388	203	2	,	,	PUNCT
ejpam-6388	203	3	for	for	ADP
ejpam-6388	203	4	0	0	NUM
ejpam-6388	203	5	≤	≤	NUM
ejpam-6388	203	6	ξ	ξ	PROPN
ejpam-6388	203	7	≤	≤	NUM
ejpam-6388	203	8	ω	ω	NUM
ejpam-6388	203	9	≤	≤	NUM
ejpam-6388	203	10	1	1	NUM
ejpam-6388	203	11	,	,	PUNCT
ejpam-6388	203	12	we	we	PRON
ejpam-6388	203	13	have	have	AUX
ejpam-6388	203	14	0(ω	0(ω	VERB
ejpam-6388	203	15	,	,	PUNCT
ejpam-6388	203	16	ξ	ξ	X
ejpam-6388	203	17	)	)	PUNCT
ejpam-6388	203	18	=	=	SYM
ejpam-6388	203	19	1	1	NUM
ejpam-6388	203	20	γ(y	γ(y	PROPN
ejpam-6388	203	21	)	)	PUNCT
ejpam-6388	204	1	[	[	PUNCT
ejpam-6388	204	2	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	204	3	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	204	4	−	−	PROPN
ejpam-6388	205	1	(	(	PUNCT
ejpam-6388	205	2	ω	ω	NUM
ejpam-6388	205	3	−	−	PROPN
ejpam-6388	205	4	ξ)y−1	ξ)y−1	X
ejpam-6388	205	5	]	]	PUNCT
ejpam-6388	205	6	d.	d.	PROPN
ejpam-6388	205	7	baleanu	baleanu	PROPN
ejpam-6388	205	8	et	et	PROPN
ejpam-6388	205	9	al	al	PROPN
ejpam-6388	205	10	.	.	PUNCT
ejpam-6388	205	11	/	/	SYM
ejpam-6388	205	12	eur	eur	PROPN
ejpam-6388	205	13	.	.	PUNCT
ejpam-6388	206	1	j.	j.	PROPN
ejpam-6388	206	2	pure	pure	PROPN
ejpam-6388	206	3	appl	appl	PROPN
ejpam-6388	206	4	.	.	PROPN
ejpam-6388	206	5	math	math	PROPN
ejpam-6388	206	6	,	,	PUNCT
ejpam-6388	206	7	18	18	NUM
ejpam-6388	206	8	(	(	PUNCT
ejpam-6388	206	9	4	4	NUM
ejpam-6388	206	10	)	)	PUNCT
ejpam-6388	206	11	(	(	PUNCT
ejpam-6388	206	12	2025	2025	NUM
ejpam-6388	206	13	)	)	PUNCT
ejpam-6388	206	14	,	,	PUNCT
ejpam-6388	206	15	6388	6388	NUM
ejpam-6388	206	16	9	9	NUM
ejpam-6388	206	17	of	of	ADP
ejpam-6388	206	18	31	31	NUM
ejpam-6388	206	19	=	=	SYM
ejpam-6388	206	20	1	1	NUM
ejpam-6388	206	21	γ(y	γ(y	PROPN
ejpam-6388	206	22	)	)	PUNCT
ejpam-6388	207	1	[	[	PUNCT
ejpam-6388	207	2	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	207	3	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	207	4	−	−	PROPN
ejpam-6388	207	5	ωy−1	ωy−1	ADV
ejpam-6388	207	6	(	(	PUNCT
ejpam-6388	207	7	1−	1−	NUM
ejpam-6388	207	8	ξ	ξ	PROPN
ejpam-6388	207	9	ω	ω	PROPN
ejpam-6388	207	10	)	)	PUNCT
ejpam-6388	207	11	y−1	y−1	PROPN
ejpam-6388	207	12	]	]	PUNCT
ejpam-6388	207	13	≥	≥	PROPN
ejpam-6388	207	14	1	1	NUM
ejpam-6388	207	15	γ(y	γ(y	PROPN
ejpam-6388	207	16	)	)	PUNCT
ejpam-6388	207	17	[	[	PUNCT
ejpam-6388	207	18	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	207	19	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	207	20	−	−	PROPN
ejpam-6388	207	21	ωy−1(1−	ωy−1(1−	PROPN
ejpam-6388	207	22	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	207	23	]	]	PUNCT
ejpam-6388	207	24	=	=	PUNCT
ejpam-6388	207	25	0	0	X
ejpam-6388	207	26	.	.	PUNCT
ejpam-6388	208	1	similarly	similarly	ADV
ejpam-6388	208	2	,	,	PUNCT
ejpam-6388	208	3	for	for	ADP
ejpam-6388	208	4	0	0	NUM
ejpam-6388	208	5	≤	≤	NUM
ejpam-6388	208	6	ω	ω	NUM
ejpam-6388	208	7	≤	≤	NUM
ejpam-6388	208	8	ξ	ξ	X
ejpam-6388	208	9	≤	≤	NUM
ejpam-6388	208	10	1	1	NUM
ejpam-6388	208	11	,	,	PUNCT
ejpam-6388	208	12	we	we	PRON
ejpam-6388	208	13	find	find	VERB
ejpam-6388	208	14	that	that	SCONJ
ejpam-6388	208	15	0(ω	0(ω	NOUN
ejpam-6388	208	16	,	,	PUNCT
ejpam-6388	208	17	ξ	ξ	X
ejpam-6388	208	18	)	)	PUNCT
ejpam-6388	208	19	≥	≥	NOUN
ejpam-6388	208	20	0	0	NUM
ejpam-6388	208	21	.	.	PUNCT
ejpam-6388	209	1	thus	thus	ADV
ejpam-6388	209	2	,	,	PUNCT
ejpam-6388	209	3	0(ω	0(ω	ADV
ejpam-6388	209	4	,	,	PUNCT
ejpam-6388	209	5	ξ	ξ	X
ejpam-6388	209	6	)	)	PUNCT
ejpam-6388	209	7	≥	≥	NOUN
ejpam-6388	209	8	0	0	NUM
ejpam-6388	209	9	for	for	ADP
ejpam-6388	209	10	all	all	DET
ejpam-6388	209	11	ω	ω	PROPN
ejpam-6388	209	12	,	,	PUNCT
ejpam-6388	209	13	ξ	ξ	PROPN
ejpam-6388	209	14	∈	∈	PROPN
ejpam-6388	210	1	[	[	X
ejpam-6388	210	2	0	0	NUM
ejpam-6388	210	3	,	,	PUNCT
ejpam-6388	210	4	1	1	NUM
ejpam-6388	210	5	]	]	PUNCT
ejpam-6388	210	6	.	.	PUNCT
ejpam-6388	211	1	(	(	PUNCT
ejpam-6388	211	2	κ2	κ2	PROPN
ejpam-6388	211	3	)	)	PUNCT
ejpam-6388	211	4	for	for	ADP
ejpam-6388	211	5	0	0	NUM
ejpam-6388	211	6	≤	≤	NUM
ejpam-6388	211	7	ξ	ξ	PROPN
ejpam-6388	211	8	≤	≤	NUM
ejpam-6388	211	9	ω	ω	NUM
ejpam-6388	211	10	≤	≤	NUM
ejpam-6388	211	11	1	1	NUM
ejpam-6388	211	12	,	,	PUNCT
ejpam-6388	211	13	we	we	PRON
ejpam-6388	211	14	have	have	VERB
ejpam-6388	211	15	∂0(ω	∂0(ω	PROPN
ejpam-6388	211	16	,	,	PUNCT
ejpam-6388	211	17	ξ	ξ	X
ejpam-6388	211	18	)	)	PUNCT
ejpam-6388	211	19	∂ω	∂ω	ADJ
ejpam-6388	211	20	=	=	SYM
ejpam-6388	211	21	1	1	NUM
ejpam-6388	211	22	γ(y	γ(y	PROPN
ejpam-6388	211	23	)	)	PUNCT
ejpam-6388	212	1	[	[	PUNCT
ejpam-6388	212	2	(	(	PUNCT
ejpam-6388	212	3	y−	y−	X
ejpam-6388	212	4	1)ωy−2(1−	1)ωy−2(1−	PROPN
ejpam-6388	212	5	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	212	6	−	−	PROPN
ejpam-6388	212	7	(	(	PUNCT
ejpam-6388	212	8	y−	y−	X
ejpam-6388	212	9	1)(ω	1)(ω	NUM
ejpam-6388	212	10	−	−	NOUN
ejpam-6388	212	11	ξ)y−2	ξ)y−2	NOUN
ejpam-6388	212	12	]	]	X
ejpam-6388	212	13	=	=	PUNCT
ejpam-6388	212	14	ωy−1	ωy−1	ADJ
ejpam-6388	212	15	γ(y−	γ(y−	PROPN
ejpam-6388	212	16	1	1	NUM
ejpam-6388	212	17	)	)	PUNCT
ejpam-6388	212	18	[	[	PUNCT
ejpam-6388	212	19	(	(	PUNCT
ejpam-6388	212	20	1−	1−	NUM
ejpam-6388	212	21	ξ)y−2	ξ)y−2	NOUN
ejpam-6388	212	22	−	−	PROPN
ejpam-6388	212	23	(	(	PUNCT
ejpam-6388	212	24	1−	1−	NUM
ejpam-6388	212	25	ξ	ξ	PROPN
ejpam-6388	212	26	ω	ω	PROPN
ejpam-6388	212	27	)	)	PUNCT
ejpam-6388	213	1	y−2	y−2	PROPN
ejpam-6388	213	2	]	]	PUNCT
ejpam-6388	213	3	≤	≤	NUM
ejpam-6388	213	4	0	0	NUM
ejpam-6388	213	5	,	,	PUNCT
ejpam-6388	213	6	1	1	NUM
ejpam-6388	213	7	<	<	X
ejpam-6388	213	8	y	y	PROPN
ejpam-6388	213	9	≤	≤	ADV
ejpam-6388	213	10	2	2	NUM
ejpam-6388	213	11	.	.	PUNCT
ejpam-6388	214	1	this	this	PRON
ejpam-6388	214	2	implies	imply	VERB
ejpam-6388	214	3	that	that	SCONJ
ejpam-6388	214	4	0(ω	0(ω	NOUN
ejpam-6388	214	5	,	,	PUNCT
ejpam-6388	214	6	ξ	ξ	X
ejpam-6388	214	7	)	)	PUNCT
ejpam-6388	214	8	is	be	AUX
ejpam-6388	214	9	nonincreasing	nonincrease	VERB
ejpam-6388	214	10	with	with	ADP
ejpam-6388	214	11	respect	respect	NOUN
ejpam-6388	214	12	to	to	ADP
ejpam-6388	214	13	ω	ω	NOUN
ejpam-6388	214	14	on	on	ADP
ejpam-6388	214	15	[	[	X
ejpam-6388	214	16	ξ	ξ	X
ejpam-6388	214	17	,	,	PUNCT
ejpam-6388	214	18	1	1	NUM
ejpam-6388	214	19	]	]	PUNCT
ejpam-6388	214	20	.	.	PUNCT
ejpam-6388	215	1	hence	hence	ADV
ejpam-6388	215	2	,	,	PUNCT
ejpam-6388	215	3	for	for	ADP
ejpam-6388	215	4	0	0	NUM
ejpam-6388	215	5	≤	≤	NUM
ejpam-6388	215	6	ξ	ξ	PROPN
ejpam-6388	215	7	≤	≤	NUM
ejpam-6388	215	8	ω	ω	NUM
ejpam-6388	215	9	≤	≤	NUM
ejpam-6388	215	10	1	1	NUM
ejpam-6388	215	11	,	,	PUNCT
ejpam-6388	215	12	0(ω	0(ω	PRON
ejpam-6388	215	13	,	,	PUNCT
ejpam-6388	215	14	ξ	ξ	NOUN
ejpam-6388	215	15	)	)	PUNCT
ejpam-6388	215	16	≤	≤	NOUN
ejpam-6388	215	17	0(ξ	0(ξ	NUM
ejpam-6388	215	18	,	,	PUNCT
ejpam-6388	215	19	ξ	ξ	NOUN
ejpam-6388	215	20	)	)	PUNCT
ejpam-6388	215	21	.	.	PUNCT
ejpam-6388	216	1	also	also	ADV
ejpam-6388	216	2	,	,	PUNCT
ejpam-6388	216	3	for	for	ADP
ejpam-6388	216	4	0	0	NUM
ejpam-6388	216	5	≤	≤	NUM
ejpam-6388	216	6	ω	ω	NUM
ejpam-6388	216	7	≤	≤	NUM
ejpam-6388	216	8	ξ	ξ	X
ejpam-6388	216	9	≤	≤	NUM
ejpam-6388	216	10	1	1	NUM
ejpam-6388	216	11	,	,	PUNCT
ejpam-6388	216	12	we	we	PRON
ejpam-6388	216	13	have	have	VERB
ejpam-6388	216	14	∂0(ω	∂0(ω	PROPN
ejpam-6388	216	15	,	,	PUNCT
ejpam-6388	216	16	ξ	ξ	X
ejpam-6388	216	17	)	)	PUNCT
ejpam-6388	216	18	∂ω	∂ω	ADJ
ejpam-6388	216	19	=	=	SYM
ejpam-6388	216	20	1	1	NUM
ejpam-6388	216	21	γ(y	γ(y	PROPN
ejpam-6388	216	22	)	)	PUNCT
ejpam-6388	217	1	[	[	PUNCT
ejpam-6388	217	2	(	(	PUNCT
ejpam-6388	217	3	y−	y−	X
ejpam-6388	217	4	1)ωy−2(1−	1)ωy−2(1−	PROPN
ejpam-6388	217	5	ξ)y−1	ξ)y−1	NOUN
ejpam-6388	217	6	]	]	PUNCT
ejpam-6388	217	7	≥	≥	X
ejpam-6388	217	8	0	0	NUM
ejpam-6388	217	9	,	,	PUNCT
ejpam-6388	217	10	1	1	NUM
ejpam-6388	217	11	<	<	X
ejpam-6388	217	12	y	y	PROPN
ejpam-6388	217	13	≤	≤	NUM
ejpam-6388	217	14	2	2	NUM
ejpam-6388	217	15	,	,	PUNCT
ejpam-6388	217	16	which	which	PRON
ejpam-6388	217	17	implies	imply	VERB
ejpam-6388	217	18	that	that	SCONJ
ejpam-6388	217	19	0(ω	0(ω	NOUN
ejpam-6388	217	20	,	,	PUNCT
ejpam-6388	217	21	ξ	ξ	X
ejpam-6388	217	22	)	)	PUNCT
ejpam-6388	217	23	is	be	AUX
ejpam-6388	217	24	nondecreasing	nondecrease	VERB
ejpam-6388	217	25	with	with	ADP
ejpam-6388	217	26	respect	respect	NOUN
ejpam-6388	217	27	to	to	ADP
ejpam-6388	217	28	ω	ω	NOUN
ejpam-6388	217	29	on	on	ADP
ejpam-6388	217	30	[	[	X
ejpam-6388	217	31	0	0	NUM
ejpam-6388	217	32	,	,	PUNCT
ejpam-6388	217	33	ξ	ξ	NOUN
ejpam-6388	217	34	]	]	PUNCT
ejpam-6388	217	35	.	.	PUNCT
ejpam-6388	218	1	hence	hence	ADV
ejpam-6388	218	2	,	,	PUNCT
ejpam-6388	218	3	for	for	ADP
ejpam-6388	218	4	0	0	NUM
ejpam-6388	218	5	≤	≤	NUM
ejpam-6388	218	6	ω	ω	NUM
ejpam-6388	218	7	≤	≤	NUM
ejpam-6388	218	8	ξ	ξ	X
ejpam-6388	218	9	≤	≤	NUM
ejpam-6388	218	10	1	1	NUM
ejpam-6388	218	11	,	,	PUNCT
ejpam-6388	218	12	0(ω	0(ω	PRON
ejpam-6388	218	13	,	,	PUNCT
ejpam-6388	218	14	ξ	ξ	NOUN
ejpam-6388	218	15	)	)	PUNCT
ejpam-6388	218	16	≤	≤	NOUN
ejpam-6388	218	17	0(ξ	0(ξ	NUM
ejpam-6388	218	18	,	,	PUNCT
ejpam-6388	218	19	ξ	ξ	NOUN
ejpam-6388	218	20	)	)	PUNCT
ejpam-6388	218	21	.	.	PUNCT
ejpam-6388	219	1	thus	thus	ADV
ejpam-6388	219	2	,	,	PUNCT
ejpam-6388	219	3	we	we	PRON
ejpam-6388	219	4	conclude	conclude	VERB
ejpam-6388	219	5	that	that	SCONJ
ejpam-6388	219	6	0(ω	0(ω	NOUN
ejpam-6388	219	7	,	,	PUNCT
ejpam-6388	219	8	ξ	ξ	NOUN
ejpam-6388	219	9	)	)	PUNCT
ejpam-6388	219	10	≤	≤	NOUN
ejpam-6388	219	11	0(ξ	0(ξ	NUM
ejpam-6388	219	12	,	,	PUNCT
ejpam-6388	219	13	ξ	ξ	NOUN
ejpam-6388	219	14	)	)	PUNCT
ejpam-6388	219	15	for	for	ADP
ejpam-6388	219	16	ω	ω	PROPN
ejpam-6388	219	17	,	,	PUNCT
ejpam-6388	219	18	ξ	ξ	PROPN
ejpam-6388	219	19	∈	∈	PROPN
ejpam-6388	220	1	[	[	X
ejpam-6388	220	2	0	0	NUM
ejpam-6388	220	3	,	,	PUNCT
ejpam-6388	220	4	1	1	NUM
ejpam-6388	220	5	]	]	PUNCT
ejpam-6388	220	6	.	.	PUNCT
ejpam-6388	221	1	this	this	PRON
ejpam-6388	221	2	completes	complete	VERB
ejpam-6388	221	3	the	the	DET
ejpam-6388	221	4	proof	proof	NOUN
ejpam-6388	221	5	.	.	PUNCT
ejpam-6388	222	1	next	next	ADV
ejpam-6388	222	2	,	,	PUNCT
ejpam-6388	222	3	we	we	PRON
ejpam-6388	222	4	will	will	AUX
ejpam-6388	222	5	proceed	proceed	VERB
ejpam-6388	222	6	to	to	PART
ejpam-6388	222	7	outline	outline	VERB
ejpam-6388	222	8	and	and	CCONJ
ejpam-6388	222	9	validate	validate	VERB
ejpam-6388	222	10	our	our	PRON
ejpam-6388	222	11	next	next	ADJ
ejpam-6388	222	12	auxiliary	auxiliary	ADJ
ejpam-6388	222	13	finding	finding	NOUN
ejpam-6388	222	14	,	,	PUNCT
ejpam-6388	222	15	which	which	PRON
ejpam-6388	222	16	acts	act	VERB
ejpam-6388	222	17	as	as	ADP
ejpam-6388	222	18	the	the	DET
ejpam-6388	222	19	central	central	ADJ
ejpam-6388	222	20	component	component	NOUN
ejpam-6388	222	21	of	of	ADP
ejpam-6388	222	22	this	this	DET
ejpam-6388	222	23	paper	paper	NOUN
ejpam-6388	222	24	.	.	PUNCT
ejpam-6388	223	1	theorem	theorem	NOUN
ejpam-6388	223	2	3	3	X
ejpam-6388	223	3	.	.	PUNCT
ejpam-6388	223	4	consider	consider	VERB
ejpam-6388	223	5	an	an	DET
ejpam-6388	223	6	orthogonal	orthogonal	ADJ
ejpam-6388	223	7	complete	complete	ADJ
ejpam-6388	223	8	cone	cone	NOUN
ejpam-6388	223	9	metric	metric	ADJ
ejpam-6388	223	10	space	space	NOUN
ejpam-6388	223	11	(	(	PUNCT
ejpam-6388	223	12	a	a	DET
ejpam-6388	223	13	,	,	PUNCT
ejpam-6388	223	14	γ,⊥	γ,⊥	NOUN
ejpam-6388	223	15	)	)	PUNCT
ejpam-6388	223	16	.	.	PUNCT
ejpam-6388	224	1	let	let	VERB
ejpam-6388	224	2	there	there	PRON
ejpam-6388	224	3	be	be	AUX
ejpam-6388	224	4	a	a	DET
ejpam-6388	224	5	mapping	mapping	NOUN
ejpam-6388	224	6	f	f	NOUN
ejpam-6388	225	1	:	:	PUNCT
ejpam-6388	225	2	a	a	DET
ejpam-6388	225	3	→	→	PUNCT
ejpam-6388	225	4	a	a	PRON
ejpam-6388	225	5	that	that	PRON
ejpam-6388	225	6	maintains	maintain	VERB
ejpam-6388	225	7	the	the	DET
ejpam-6388	225	8	orthogonality	orthogonality	NOUN
ejpam-6388	225	9	property	property	NOUN
ejpam-6388	225	10	and	and	CCONJ
ejpam-6388	225	11	exhibits	exhibit	VERB
ejpam-6388	225	12	continuity	continuity	NOUN
ejpam-6388	225	13	with	with	ADP
ejpam-6388	225	14	respect	respect	NOUN
ejpam-6388	225	15	to	to	ADP
ejpam-6388	225	16	this	this	DET
ejpam-6388	225	17	structure	structure	NOUN
ejpam-6388	225	18	.	.	PUNCT
ejpam-6388	226	1	suppose	suppose	VERB
ejpam-6388	226	2	f	f	PROPN
ejpam-6388	226	3	fulfills	fulfill	VERB
ejpam-6388	226	4	a	a	DET
ejpam-6388	226	5	specific	specific	ADJ
ejpam-6388	226	6	contractive	contractive	ADJ
ejpam-6388	226	7	condition	condition	NOUN
ejpam-6388	226	8	,	,	PUNCT
ejpam-6388	226	9	referred	refer	VERB
ejpam-6388	226	10	to	to	ADP
ejpam-6388	226	11	as	as	ADP
ejpam-6388	226	12	γ(fz	γ(fz	NOUN
ejpam-6388	226	13	,	,	PUNCT
ejpam-6388	226	14	fu	fu	NOUN
ejpam-6388	226	15	)	)	PUNCT
ejpam-6388	226	16	≤	≤	NOUN
ejpam-6388	226	17	aγ(u	aγ(u	NUM
ejpam-6388	226	18	,	,	PUNCT
ejpam-6388	226	19	fu	fu	NOUN
ejpam-6388	226	20	)	)	PUNCT
ejpam-6388	226	21	[	[	PUNCT
ejpam-6388	226	22	1	1	NUM
ejpam-6388	226	23	+	+	CCONJ
ejpam-6388	226	24	γ(z	γ(z	PROPN
ejpam-6388	226	25	,	,	PUNCT
ejpam-6388	226	26	fz	fz	PROPN
ejpam-6388	226	27	)	)	PUNCT
ejpam-6388	226	28	]	]	PUNCT
ejpam-6388	227	1	1	1	NUM
ejpam-6388	227	2	+	+	CCONJ
ejpam-6388	227	3	γ(z	γ(z	ADJ
ejpam-6388	227	4	,	,	PUNCT
ejpam-6388	227	5	u	u	NOUN
ejpam-6388	227	6	)	)	PUNCT
ejpam-6388	228	1	+	+	CCONJ
ejpam-6388	228	2	bγ(z	bγ(z	NUM
ejpam-6388	228	3	,	,	PUNCT
ejpam-6388	228	4	u	u	NOUN
ejpam-6388	228	5	)	)	PUNCT
ejpam-6388	228	6	,	,	PUNCT
ejpam-6388	229	1	applicable	applicable	ADJ
ejpam-6388	229	2	to	to	ADP
ejpam-6388	229	3	any	any	DET
ejpam-6388	229	4	two	two	NUM
ejpam-6388	229	5	elements	element	NOUN
ejpam-6388	229	6	z	z	NOUN
ejpam-6388	229	7	and	and	CCONJ
ejpam-6388	229	8	u	u	NOUN
ejpam-6388	229	9	from	from	ADP
ejpam-6388	229	10	a	a	PRON
ejpam-6388	229	11	that	that	PRON
ejpam-6388	229	12	are	be	AUX
ejpam-6388	229	13	orthogonal	orthogonal	ADJ
ejpam-6388	229	14	,	,	PUNCT
ejpam-6388	229	15	alongside	alongside	ADP
ejpam-6388	229	16	constants	constant	NOUN
ejpam-6388	229	17	a	a	PRON
ejpam-6388	229	18	and	and	CCONJ
ejpam-6388	229	19	b	b	NOUN
ejpam-6388	229	20	that	that	PRON
ejpam-6388	229	21	fall	fall	VERB
ejpam-6388	229	22	within	within	ADP
ejpam-6388	229	23	the	the	DET
ejpam-6388	229	24	range	range	NOUN
ejpam-6388	229	25	[	[	X
ejpam-6388	229	26	0	0	NUM
ejpam-6388	229	27	,	,	PUNCT
ejpam-6388	229	28	1	1	NUM
ejpam-6388	229	29	)	)	PUNCT
ejpam-6388	229	30	,	,	PUNCT
ejpam-6388	229	31	and	and	CCONJ
ejpam-6388	229	32	satisfy	satisfy	VERB
ejpam-6388	229	33	the	the	DET
ejpam-6388	229	34	condition	condition	NOUN
ejpam-6388	229	35	a+	a+	PUNCT
ejpam-6388	230	1	b	b	X
ejpam-6388	230	2	<	<	X
ejpam-6388	230	3	1	1	NUM
ejpam-6388	230	4	.	.	PUNCT
ejpam-6388	231	1	under	under	ADP
ejpam-6388	231	2	these	these	DET
ejpam-6388	231	3	stipulated	stipulate	VERB
ejpam-6388	231	4	conditions	condition	NOUN
ejpam-6388	231	5	,	,	PUNCT
ejpam-6388	231	6	it	it	PRON
ejpam-6388	231	7	follows	follow	VERB
ejpam-6388	231	8	that	that	SCONJ
ejpam-6388	231	9	f	f	PROPN
ejpam-6388	231	10	has	have	VERB
ejpam-6388	231	11	exactly	exactly	ADV
ejpam-6388	231	12	one	one	NUM
ejpam-6388	231	13	fixed	fix	VERB
ejpam-6388	231	14	point	point	NOUN
ejpam-6388	231	15	in	in	ADP
ejpam-6388	231	16	the	the	DET
ejpam-6388	231	17	set	set	NOUN
ejpam-6388	231	18	a.	a.	NOUN
ejpam-6388	231	19	proof	proof	NOUN
ejpam-6388	231	20	.	.	PUNCT
ejpam-6388	232	1	by	by	ADP
ejpam-6388	232	2	the	the	DET
ejpam-6388	232	3	definition	definition	NOUN
ejpam-6388	232	4	of	of	ADP
ejpam-6388	232	5	orthogonality	orthogonality	NOUN
ejpam-6388	232	6	,	,	PUNCT
ejpam-6388	232	7	there	there	PRON
ejpam-6388	232	8	exists	exist	VERB
ejpam-6388	232	9	an	an	DET
ejpam-6388	232	10	element	element	NOUN
ejpam-6388	232	11	z0	z0	PROPN
ejpam-6388	232	12	∈	∈	PROPN
ejpam-6388	232	13	a	a	PRON
ejpam-6388	232	14	,	,	PUNCT
ejpam-6388	232	15	where	where	SCONJ
ejpam-6388	232	16	for	for	ADP
ejpam-6388	232	17	every	every	DET
ejpam-6388	232	18	z	z	NOUN
ejpam-6388	232	19	∈	∈	PROPN
ejpam-6388	232	20	a	a	PRON
ejpam-6388	232	21	,	,	PUNCT
ejpam-6388	232	22	either	either	CCONJ
ejpam-6388	232	23	z	z	NOUN
ejpam-6388	232	24	is	be	AUX
ejpam-6388	232	25	orthogonal	orthogonal	ADJ
ejpam-6388	232	26	to	to	ADP
ejpam-6388	232	27	z0	z0	PROPN
ejpam-6388	232	28	or	or	CCONJ
ejpam-6388	232	29	z0	z0	PROPN
ejpam-6388	232	30	is	be	AUX
ejpam-6388	232	31	orthogonal	orthogonal	ADJ
ejpam-6388	232	32	to	to	ADP
ejpam-6388	232	33	z.	z.	PROPN
ejpam-6388	232	34	this	this	PRON
ejpam-6388	232	35	leads	lead	VERB
ejpam-6388	232	36	us	we	PRON
ejpam-6388	232	37	to	to	ADP
ejpam-6388	232	38	d.	d.	PROPN
ejpam-6388	232	39	baleanu	baleanu	PROPN
ejpam-6388	232	40	et	et	PROPN
ejpam-6388	232	41	al	al	PROPN
ejpam-6388	232	42	.	.	PUNCT
ejpam-6388	232	43	/	/	SYM
ejpam-6388	232	44	eur	eur	PROPN
ejpam-6388	232	45	.	.	PUNCT
ejpam-6388	233	1	j.	j.	PROPN
ejpam-6388	233	2	pure	pure	PROPN
ejpam-6388	233	3	appl	appl	PROPN
ejpam-6388	233	4	.	.	PROPN
ejpam-6388	233	5	math	math	PROPN
ejpam-6388	233	6	,	,	PUNCT
ejpam-6388	233	7	18	18	NUM
ejpam-6388	233	8	(	(	PUNCT
ejpam-6388	233	9	4	4	NUM
ejpam-6388	233	10	)	)	PUNCT
ejpam-6388	233	11	(	(	PUNCT
ejpam-6388	233	12	2025	2025	NUM
ejpam-6388	233	13	)	)	PUNCT
ejpam-6388	233	14	,	,	PUNCT
ejpam-6388	233	15	6388	6388	NUM
ejpam-6388	233	16	10	10	NUM
ejpam-6388	233	17	of	of	ADP
ejpam-6388	233	18	31	31	NUM
ejpam-6388	233	19	conclude	conclude	NOUN
ejpam-6388	233	20	that	that	SCONJ
ejpam-6388	233	21	either	either	CCONJ
ejpam-6388	233	22	z0	z0	PROPN
ejpam-6388	233	23	⊥	⊥	PROPN
ejpam-6388	233	24	f(z0	f(z0	NOUN
ejpam-6388	233	25	)	)	PUNCT
ejpam-6388	233	26	or	or	CCONJ
ejpam-6388	233	27	f(z0	f(z0	NOUN
ejpam-6388	233	28	)	)	PUNCT
ejpam-6388	233	29	⊥	⊥	PROPN
ejpam-6388	233	30	z0	z0	PROPN
ejpam-6388	233	31	.	.	PUNCT
ejpam-6388	234	1	now	now	ADV
ejpam-6388	234	2	,	,	PUNCT
ejpam-6388	234	3	we	we	PRON
ejpam-6388	234	4	can	can	AUX
ejpam-6388	234	5	define	define	VERB
ejpam-6388	234	6	a	a	DET
ejpam-6388	234	7	sequence	sequence	NOUN
ejpam-6388	234	8	of	of	ADP
ejpam-6388	234	9	elements	element	NOUN
ejpam-6388	234	10	as	as	SCONJ
ejpam-6388	234	11	follows	follow	VERB
ejpam-6388	234	12	:	:	PUNCT
ejpam-6388	234	13	z1	z1	PROPN
ejpam-6388	234	14	=	=	SYM
ejpam-6388	234	15	f(z0	f(z0	NOUN
ejpam-6388	234	16	)	)	PUNCT
ejpam-6388	234	17	,	,	PUNCT
ejpam-6388	234	18	z2	z2	NOUN
ejpam-6388	234	19	=	=	SYM
ejpam-6388	234	20	f(z1	f(z1	NOUN
ejpam-6388	234	21	)	)	PUNCT
ejpam-6388	234	22	=	=	PUNCT
ejpam-6388	234	23	f2(z0	f2(z0	NOUN
ejpam-6388	234	24	)	)	PUNCT
ejpam-6388	234	25	,	,	PUNCT
ejpam-6388	234	26	...	...	PUNCT
ejpam-6388	235	1	zn+1	zn+1	X
ejpam-6388	235	2	=	=	SYM
ejpam-6388	235	3	f(zn	f(zn	PROPN
ejpam-6388	235	4	)	)	PUNCT
ejpam-6388	235	5	=	=	SYM
ejpam-6388	235	6	fn(z0	fn(z0	NOUN
ejpam-6388	235	7	)	)	PUNCT
ejpam-6388	235	8	,	,	PUNCT
ejpam-6388	235	9	n	n	PROPN
ejpam-6388	235	10	∈	∈	PROPN
ejpam-6388	235	11	n.	n.	NOUN
ejpam-6388	235	12	then	then	ADV
ejpam-6388	235	13	γ(zn	γ(zn	PROPN
ejpam-6388	235	14	,	,	PUNCT
ejpam-6388	235	15	zn+1	zn+1	X
ejpam-6388	235	16	)	)	PUNCT
ejpam-6388	235	17	=	=	SYM
ejpam-6388	235	18	γ(fzn−1	γ(fzn−1	PROPN
ejpam-6388	235	19	,	,	PUNCT
ejpam-6388	235	20	fzn	fzn	NOUN
ejpam-6388	235	21	)	)	PUNCT
ejpam-6388	235	22	≤	≤	NOUN
ejpam-6388	235	23	aγ(zn	aγ(zn	PROPN
ejpam-6388	235	24	,	,	PUNCT
ejpam-6388	235	25	fzn	fzn	NOUN
ejpam-6388	235	26	)	)	PUNCT
ejpam-6388	235	27	[	[	PUNCT
ejpam-6388	235	28	1	1	NUM
ejpam-6388	235	29	+	+	CCONJ
ejpam-6388	235	30	γ(zn−1	γ(zn−1	NUM
ejpam-6388	235	31	,	,	PUNCT
ejpam-6388	235	32	fzn−1	fzn−1	PROPN
ejpam-6388	235	33	)	)	PUNCT
ejpam-6388	235	34	]	]	PUNCT
ejpam-6388	235	35	1	1	NUM
ejpam-6388	235	36	+	+	CCONJ
ejpam-6388	235	37	γ(zn−1	γ(zn−1	NUM
ejpam-6388	235	38	,	,	PUNCT
ejpam-6388	235	39	zn	zn	NOUN
ejpam-6388	235	40	)	)	PUNCT
ejpam-6388	236	1	+	+	CCONJ
ejpam-6388	236	2	bγ(zn−1	bγ(zn−1	PROPN
ejpam-6388	236	3	,	,	PUNCT
ejpam-6388	236	4	zn	zn	NOUN
ejpam-6388	236	5	)	)	PUNCT
ejpam-6388	236	6	≤	≤	NOUN
ejpam-6388	236	7	aγ(zn	aγ(zn	PROPN
ejpam-6388	236	8	,	,	PUNCT
ejpam-6388	236	9	zn+1	zn+1	X
ejpam-6388	236	10	)	)	PUNCT
ejpam-6388	236	11	[	[	PUNCT
ejpam-6388	236	12	1	1	NUM
ejpam-6388	236	13	+	+	CCONJ
ejpam-6388	236	14	γ(zn−1	γ(zn−1	NUM
ejpam-6388	236	15	,	,	PUNCT
ejpam-6388	236	16	zn	zn	PROPN
ejpam-6388	236	17	)	)	PUNCT
ejpam-6388	236	18	]	]	PUNCT
ejpam-6388	236	19	1	1	NUM
ejpam-6388	236	20	+	+	CCONJ
ejpam-6388	236	21	γ(zn−1	γ(zn−1	NUM
ejpam-6388	236	22	,	,	PUNCT
ejpam-6388	236	23	zn	zn	NOUN
ejpam-6388	236	24	)	)	PUNCT
ejpam-6388	236	25	+	+	CCONJ
ejpam-6388	236	26	bγ(zn−1	bγ(zn−1	PROPN
ejpam-6388	236	27	,	,	PUNCT
ejpam-6388	236	28	zn	zn	PROPN
ejpam-6388	236	29	)	)	PUNCT
ejpam-6388	236	30	,	,	PUNCT
ejpam-6388	236	31	which	which	PRON
ejpam-6388	236	32	implies	imply	VERB
ejpam-6388	236	33	(	(	PUNCT
ejpam-6388	236	34	1	1	NUM
ejpam-6388	236	35	−	−	NOUN
ejpam-6388	236	36	a)γ(zn	a)γ(zn	NOUN
ejpam-6388	236	37	,	,	PUNCT
ejpam-6388	236	38	zn+1	zn+1	NOUN
ejpam-6388	236	39	)	)	PUNCT
ejpam-6388	236	40	≤	≤	NOUN
ejpam-6388	236	41	bγ(zn−1	bγ(zn−1	PROPN
ejpam-6388	236	42	,	,	PUNCT
ejpam-6388	236	43	zn	zn	PROPN
ejpam-6388	236	44	)	)	PUNCT
ejpam-6388	236	45	,	,	PUNCT
ejpam-6388	236	46	n	n	PROPN
ejpam-6388	236	47	∈	∈	PROPN
ejpam-6388	236	48	n.	n.	NOUN
ejpam-6388	236	49	from	from	ADP
ejpam-6388	236	50	this	this	PRON
ejpam-6388	236	51	,	,	PUNCT
ejpam-6388	236	52	taking	take	VERB
ejpam-6388	236	53	r	r	NOUN
ejpam-6388	236	54	=	=	SYM
ejpam-6388	236	55	b	b	SYM
ejpam-6388	236	56	1−a	1−a	NUM
ejpam-6388	236	57	<	<	X
ejpam-6388	236	58	1	1	NUM
ejpam-6388	236	59	,	,	PUNCT
ejpam-6388	236	60	we	we	PRON
ejpam-6388	236	61	can	can	AUX
ejpam-6388	236	62	write	write	VERB
ejpam-6388	236	63	that	that	PRON
ejpam-6388	236	64	γ(zn	γ(zn	NOUN
ejpam-6388	236	65	,	,	PUNCT
ejpam-6388	236	66	zn+1	zn+1	NUM
ejpam-6388	236	67	)	)	PUNCT
ejpam-6388	236	68	≤	≤	NOUN
ejpam-6388	236	69	rγ(zn−1	rγ(zn−1	PROPN
ejpam-6388	236	70	,	,	PUNCT
ejpam-6388	236	71	zn	zn	NOUN
ejpam-6388	236	72	)	)	PUNCT
ejpam-6388	236	73	,	,	PUNCT
ejpam-6388	236	74	≤	≤	NOUN
ejpam-6388	236	75	·	·	PUNCT
ejpam-6388	236	76	·	·	PUNCT
ejpam-6388	236	77	·	·	PUNCT
ejpam-6388	237	1	≤	≤	NUM
ejpam-6388	237	2	rnγ(z0	rnγ(z0	NOUN
ejpam-6388	237	3	,	,	PUNCT
ejpam-6388	237	4	z1	z1	NOUN
ejpam-6388	237	5	)	)	PUNCT
ejpam-6388	237	6	.	.	PUNCT
ejpam-6388	238	1	for	for	ADP
ejpam-6388	238	2	p	p	PRON
ejpam-6388	238	3	,	,	PUNCT
ejpam-6388	238	4	q	q	X
ejpam-6388	238	5	≥	≥	NOUN
ejpam-6388	238	6	1	1	NUM
ejpam-6388	238	7	,	,	PUNCT
ejpam-6388	238	8	we	we	PRON
ejpam-6388	238	9	have	have	VERB
ejpam-6388	238	10	γ(zp	γ(zp	ADJ
ejpam-6388	238	11	,	,	PUNCT
ejpam-6388	238	12	zp+q	zp+q	NOUN
ejpam-6388	238	13	)	)	PUNCT
ejpam-6388	238	14	≤	≤	NOUN
ejpam-6388	239	1	γ(zp	γ(zp	ADJ
ejpam-6388	239	2	,	,	PUNCT
ejpam-6388	239	3	zp+1	zp+1	NUM
ejpam-6388	239	4	)	)	PUNCT
ejpam-6388	240	1	+	+	X
ejpam-6388	240	2	γ(zp+1	γ(zp+1	ADJ
ejpam-6388	240	3	,	,	PUNCT
ejpam-6388	240	4	zp+q	zp+q	NOUN
ejpam-6388	240	5	)	)	PUNCT
ejpam-6388	240	6	≤	≤	NOUN
ejpam-6388	241	1	γ(zp	γ(zp	ADJ
ejpam-6388	241	2	,	,	PUNCT
ejpam-6388	241	3	zp+1	zp+1	NUM
ejpam-6388	241	4	)	)	PUNCT
ejpam-6388	242	1	+	+	CCONJ
ejpam-6388	242	2	γ(zp+1	γ(zp+1	ADJ
ejpam-6388	242	3	,	,	PUNCT
ejpam-6388	242	4	zp+2	zp+2	NOUN
ejpam-6388	242	5	)	)	PUNCT
ejpam-6388	242	6	+	+	CCONJ
ejpam-6388	242	7	γ(zp+2	γ(zp+2	ADJ
ejpam-6388	242	8	,	,	PUNCT
ejpam-6388	242	9	zp+q	zp+q	NOUN
ejpam-6388	242	10	)	)	PUNCT
ejpam-6388	242	11	≤	≤	NOUN
ejpam-6388	243	1	γ(zp	γ(zp	ADJ
ejpam-6388	243	2	,	,	PUNCT
ejpam-6388	243	3	zp+1	zp+1	NUM
ejpam-6388	243	4	)	)	PUNCT
ejpam-6388	244	1	+	+	CCONJ
ejpam-6388	244	2	γ(zp+1	γ(zp+1	ADJ
ejpam-6388	244	3	,	,	PUNCT
ejpam-6388	244	4	zp+2	zp+2	NOUN
ejpam-6388	244	5	)	)	PUNCT
ejpam-6388	244	6	+	+	CCONJ
ejpam-6388	244	7	γ(zp+2	γ(zp+2	ADJ
ejpam-6388	244	8	,	,	PUNCT
ejpam-6388	244	9	zp+3	zp+3	NOUN
ejpam-6388	244	10	)	)	PUNCT
ejpam-6388	244	11	+	+	CCONJ
ejpam-6388	244	12	·	·	PUNCT
ejpam-6388	244	13	·	·	PUNCT
ejpam-6388	244	14	·	·	PUNCT
ejpam-6388	244	15	+	+	CCONJ
ejpam-6388	244	16	γ(zp+q−3	γ(zp+q−3	ADJ
ejpam-6388	244	17	,	,	PUNCT
ejpam-6388	244	18	zp+q−2	zp+q−2	PROPN
ejpam-6388	244	19	)	)	PUNCT
ejpam-6388	244	20	+	+	NUM
ejpam-6388	244	21	γ(zp+q−2	γ(zp+q−2	NOUN
ejpam-6388	244	22	,	,	PUNCT
ejpam-6388	244	23	zp+q−1	zp+q−1	NOUN
ejpam-6388	244	24	)	)	PUNCT
ejpam-6388	244	25	+	+	CCONJ
ejpam-6388	245	1	γ(zp+q−1	γ(zp+q−1	NOUN
ejpam-6388	245	2	,	,	PUNCT
ejpam-6388	245	3	zp+q	zp+q	NOUN
ejpam-6388	245	4	)	)	PUNCT
ejpam-6388	245	5	≤	≤	NOUN
ejpam-6388	245	6	rpγ(z0	rpγ(z0	NOUN
ejpam-6388	245	7	,	,	PUNCT
ejpam-6388	245	8	z1	z1	NOUN
ejpam-6388	245	9	)	)	PUNCT
ejpam-6388	245	10	+	+	CCONJ
ejpam-6388	245	11	rp+1γ(z0	rp+1γ(z0	ADJ
ejpam-6388	245	12	,	,	PUNCT
ejpam-6388	245	13	z1	z1	NOUN
ejpam-6388	245	14	)	)	PUNCT
ejpam-6388	245	15	+	+	NUM
ejpam-6388	245	16	·	·	PUNCT
ejpam-6388	245	17	·	·	PUNCT
ejpam-6388	245	18	·	·	PUNCT
ejpam-6388	245	19	+	+	PUNCT
ejpam-6388	245	20	rp+q−1γ(z0	rp+q−1γ(z0	NOUN
ejpam-6388	245	21	,	,	PUNCT
ejpam-6388	245	22	z1	z1	NOUN
ejpam-6388	245	23	)	)	PUNCT
ejpam-6388	245	24	≤	≤	NOUN
ejpam-6388	245	25	rp	rp	NOUN
ejpam-6388	245	26	1−	1−	NUM
ejpam-6388	245	27	r	r	NOUN
ejpam-6388	245	28	γ(z0	γ(z0	NOUN
ejpam-6388	245	29	,	,	PUNCT
ejpam-6388	245	30	z1	z1	NOUN
ejpam-6388	245	31	)	)	PUNCT
ejpam-6388	245	32	.	.	PUNCT
ejpam-6388	246	1	thus	thus	ADV
ejpam-6388	246	2	,	,	PUNCT
ejpam-6388	246	3	γ(zp	γ(zp	ADJ
ejpam-6388	246	4	,	,	PUNCT
ejpam-6388	246	5	zp+q	zp+q	NOUN
ejpam-6388	246	6	)	)	PUNCT
ejpam-6388	246	7	≤	≤	NOUN
ejpam-6388	246	8	rp	rp	NOUN
ejpam-6388	246	9	1−rγ(z0	1−rγ(z0	NUM
ejpam-6388	246	10	,	,	PUNCT
ejpam-6388	246	11	z1	z1	PROPN
ejpam-6388	246	12	)	)	PUNCT
ejpam-6388	246	13	.	.	PUNCT
ejpam-6388	247	1	as	as	ADP
ejpam-6388	247	2	p→	p→	NOUN
ejpam-6388	247	3	∞	∞	PROPN
ejpam-6388	247	4	,	,	PUNCT
ejpam-6388	247	5	we	we	PRON
ejpam-6388	247	6	deduce	deduce	VERB
ejpam-6388	247	7	{	{	PUNCT
ejpam-6388	247	8	zn	zn	NOUN
ejpam-6388	247	9	}	}	PUNCT
ejpam-6388	247	10	forms	form	VERB
ejpam-6388	247	11	a	a	DET
ejpam-6388	247	12	cauchy	cauchy	ADJ
ejpam-6388	247	13	o	o	NOUN
ejpam-6388	247	14	-	-	NOUN
ejpam-6388	247	15	sequence	sequence	NOUN
ejpam-6388	247	16	.	.	PUNCT
ejpam-6388	248	1	since	since	SCONJ
ejpam-6388	248	2	(	(	PUNCT
ejpam-6388	248	3	a	a	PRON
ejpam-6388	248	4	,	,	PUNCT
ejpam-6388	248	5	γ	γ	NOUN
ejpam-6388	248	6	)	)	PUNCT
ejpam-6388	248	7	is	be	AUX
ejpam-6388	248	8	a	a	DET
ejpam-6388	248	9	complete	complete	ADJ
ejpam-6388	248	10	orthogonal	orthogonal	ADJ
ejpam-6388	248	11	cone	cone	NOUN
ejpam-6388	248	12	metric	metric	ADJ
ejpam-6388	248	13	space	space	NOUN
ejpam-6388	248	14	,	,	PUNCT
ejpam-6388	248	15	we	we	PRON
ejpam-6388	248	16	can	can	AUX
ejpam-6388	248	17	find	find	VERB
ejpam-6388	248	18	an	an	DET
ejpam-6388	248	19	element	element	NOUN
ejpam-6388	248	20	z⋆	z⋆	NUM
ejpam-6388	248	21	∈	∈	PROPN
ejpam-6388	248	22	a	a	PRON
ejpam-6388	248	23	where	where	SCONJ
ejpam-6388	248	24	zn	zn	PROPN
ejpam-6388	248	25	converges	converge	VERB
ejpam-6388	248	26	to	to	ADP
ejpam-6388	248	27	z⋆	z⋆	NOUN
ejpam-6388	248	28	as	as	ADP
ejpam-6388	248	29	n→	n→	PUNCT
ejpam-6388	248	30	∞.	∞.	PROPN
ejpam-6388	248	31	our	our	PRON
ejpam-6388	248	32	next	next	ADJ
ejpam-6388	248	33	objective	objective	NOUN
ejpam-6388	248	34	is	be	AUX
ejpam-6388	248	35	to	to	PART
ejpam-6388	248	36	demonstrate	demonstrate	VERB
ejpam-6388	248	37	that	that	SCONJ
ejpam-6388	248	38	z⋆	z⋆	NOUN
ejpam-6388	248	39	serves	serve	VERB
ejpam-6388	248	40	as	as	ADP
ejpam-6388	248	41	a	a	DET
ejpam-6388	248	42	fixed	fix	VERB
ejpam-6388	248	43	point	point	NOUN
ejpam-6388	248	44	of	of	ADP
ejpam-6388	248	45	f.	f.	PROPN
ejpam-6388	248	46	for	for	ADP
ejpam-6388	248	47	this	this	DET
ejpam-6388	248	48	,	,	PUNCT
ejpam-6388	248	49	γ(z⋆	γ(z⋆	NOUN
ejpam-6388	248	50	,	,	PUNCT
ejpam-6388	248	51	fz⋆	fz⋆	PROPN
ejpam-6388	248	52	)	)	PUNCT
ejpam-6388	248	53	≤	≤	NUM
ejpam-6388	248	54	γ(z⋆	γ(z⋆	NOUN
ejpam-6388	248	55	,	,	PUNCT
ejpam-6388	248	56	fzn	fzn	NOUN
ejpam-6388	248	57	)	)	PUNCT
ejpam-6388	249	1	+	+	CCONJ
ejpam-6388	249	2	γ(fzn	γ(fzn	PROPN
ejpam-6388	249	3	,	,	PUNCT
ejpam-6388	249	4	fz	fz	VERB
ejpam-6388	249	5	⋆	⋆	NOUN
ejpam-6388	249	6	)	)	PUNCT
ejpam-6388	250	1	≤	≤	NUM
ejpam-6388	250	2	γ(z⋆	γ(z⋆	NOUN
ejpam-6388	250	3	,	,	PUNCT
ejpam-6388	250	4	fzn	fzn	NOUN
ejpam-6388	250	5	)	)	PUNCT
ejpam-6388	250	6	+	+	CCONJ
ejpam-6388	250	7	aγ(z⋆	aγ(z⋆	PROPN
ejpam-6388	250	8	,	,	PUNCT
ejpam-6388	250	9	fz⋆	fz⋆	PROPN
ejpam-6388	250	10	)	)	PUNCT
ejpam-6388	250	11	[	[	PUNCT
ejpam-6388	250	12	1	1	NUM
ejpam-6388	250	13	+	+	NUM
ejpam-6388	250	14	γ(zn	γ(zn	NOUN
ejpam-6388	250	15	,	,	PUNCT
ejpam-6388	250	16	fzn	fzn	NOUN
ejpam-6388	250	17	)	)	PUNCT
ejpam-6388	250	18	]	]	PUNCT
ejpam-6388	250	19	1	1	NUM
ejpam-6388	250	20	+	+	NUM
ejpam-6388	250	21	γ(zn	γ(zn	NOUN
ejpam-6388	250	22	,	,	PUNCT
ejpam-6388	250	23	z⋆	z⋆	NOUN
ejpam-6388	250	24	)	)	PUNCT
ejpam-6388	250	25	+	+	CCONJ
ejpam-6388	250	26	bγ(zn	bγ(zn	PROPN
ejpam-6388	250	27	,	,	PUNCT
ejpam-6388	250	28	z	z	PROPN
ejpam-6388	250	29	⋆	⋆	NOUN
ejpam-6388	250	30	)	)	PUNCT
ejpam-6388	250	31	≤	≤	NUM
ejpam-6388	250	32	1	1	NUM
ejpam-6388	250	33	+	+	NUM
ejpam-6388	250	34	γ(zn	γ(zn	NOUN
ejpam-6388	250	35	,	,	PUNCT
ejpam-6388	250	36	z	z	PROPN
ejpam-6388	250	37	⋆	⋆	NOUN
ejpam-6388	250	38	)	)	PUNCT
ejpam-6388	250	39	(	(	PUNCT
ejpam-6388	250	40	1−	1−	NUM
ejpam-6388	250	41	a	a	NOUN
ejpam-6388	250	42	)	)	PUNCT
ejpam-6388	250	43	+	+	NUM
ejpam-6388	250	44	γ(zn	γ(zn	NOUN
ejpam-6388	250	45	,	,	PUNCT
ejpam-6388	250	46	z⋆)−	z⋆)−	PROPN
ejpam-6388	250	47	aγ(zn	aγ(zn	PROPN
ejpam-6388	250	48	,	,	PUNCT
ejpam-6388	250	49	zn+1	zn+1	X
ejpam-6388	250	50	)	)	PUNCT
ejpam-6388	250	51	[	[	PUNCT
ejpam-6388	250	52	γ(z⋆	γ(z⋆	NOUN
ejpam-6388	250	53	,	,	PUNCT
ejpam-6388	250	54	zn+1	zn+1	X
ejpam-6388	250	55	)	)	PUNCT
ejpam-6388	250	56	+	+	CCONJ
ejpam-6388	250	57	bγ(zn	bγ(zn	PROPN
ejpam-6388	250	58	,	,	PUNCT
ejpam-6388	250	59	z	z	PROPN
ejpam-6388	250	60	⋆	⋆	NOUN
ejpam-6388	250	61	)	)	PUNCT
ejpam-6388	250	62	]	]	PUNCT
ejpam-6388	251	1	d.	d.	PROPN
ejpam-6388	251	2	baleanu	baleanu	PROPN
ejpam-6388	251	3	et	et	PROPN
ejpam-6388	251	4	al	al	PROPN
ejpam-6388	251	5	.	.	PUNCT
ejpam-6388	251	6	/	/	SYM
ejpam-6388	251	7	eur	eur	PROPN
ejpam-6388	251	8	.	.	PUNCT
ejpam-6388	252	1	j.	j.	PROPN
ejpam-6388	252	2	pure	pure	PROPN
ejpam-6388	252	3	appl	appl	PROPN
ejpam-6388	252	4	.	.	PROPN
ejpam-6388	252	5	math	math	PROPN
ejpam-6388	252	6	,	,	PUNCT
ejpam-6388	252	7	18	18	NUM
ejpam-6388	252	8	(	(	PUNCT
ejpam-6388	252	9	4	4	NUM
ejpam-6388	252	10	)	)	PUNCT
ejpam-6388	252	11	(	(	PUNCT
ejpam-6388	252	12	2025	2025	NUM
ejpam-6388	252	13	)	)	PUNCT
ejpam-6388	252	14	,	,	PUNCT
ejpam-6388	252	15	6388	6388	NUM
ejpam-6388	252	16	11	11	NUM
ejpam-6388	252	17	of	of	ADP
ejpam-6388	252	18	31	31	NUM
ejpam-6388	252	19	→	→	SYM
ejpam-6388	252	20	0	0	NUM
ejpam-6388	252	21	as	as	ADP
ejpam-6388	252	22	n→	n→	PUNCT
ejpam-6388	252	23	∞.	∞.	PROPN
ejpam-6388	252	24	hence	hence	ADV
ejpam-6388	252	25	fz⋆	fz⋆	PROPN
ejpam-6388	252	26	=	=	PUNCT
ejpam-6388	252	27	z⋆	z⋆	NOUN
ejpam-6388	252	28	,	,	PUNCT
ejpam-6388	252	29	that	that	ADV
ejpam-6388	252	30	is	is	ADV
ejpam-6388	252	31	,	,	PUNCT
ejpam-6388	252	32	z⋆	z⋆	NUM
ejpam-6388	252	33	is	be	AUX
ejpam-6388	252	34	a	a	DET
ejpam-6388	252	35	fixed	fix	VERB
ejpam-6388	252	36	point	point	NOUN
ejpam-6388	252	37	of	of	ADP
ejpam-6388	252	38	f.	f.	PROPN
ejpam-6388	252	39	finally	finally	ADV
ejpam-6388	252	40	,	,	PUNCT
ejpam-6388	252	41	we	we	PRON
ejpam-6388	252	42	prove	prove	VERB
ejpam-6388	252	43	that	that	SCONJ
ejpam-6388	252	44	z⋆	z⋆	NOUN
ejpam-6388	252	45	is	be	AUX
ejpam-6388	252	46	a	a	DET
ejpam-6388	252	47	unique	unique	ADJ
ejpam-6388	252	48	fixed	fix	VERB
ejpam-6388	252	49	point	point	NOUN
ejpam-6388	252	50	of	of	ADP
ejpam-6388	252	51	f.	f.	PROPN
ejpam-6388	252	52	if	if	SCONJ
ejpam-6388	252	53	u⋆	u⋆	ADV
ejpam-6388	252	54	is	be	AUX
ejpam-6388	252	55	also	also	ADV
ejpam-6388	252	56	a	a	DET
ejpam-6388	252	57	fixed	fix	VERB
ejpam-6388	252	58	point	point	NOUN
ejpam-6388	252	59	of	of	ADP
ejpam-6388	252	60	f	f	PROPN
ejpam-6388	252	61	,	,	PUNCT
ejpam-6388	252	62	i.e.	i.e.	X
ejpam-6388	252	63	,	,	PUNCT
ejpam-6388	252	64	fu⋆	fu⋆	PROPN
ejpam-6388	252	65	=	=	NOUN
ejpam-6388	252	66	u⋆.	u⋆.	NOUN
ejpam-6388	252	67	then	then	ADV
ejpam-6388	252	68	γ(u⋆	γ(u⋆	NOUN
ejpam-6388	252	69	,	,	PUNCT
ejpam-6388	252	70	z⋆	z⋆	NOUN
ejpam-6388	252	71	)	)	PUNCT
ejpam-6388	253	1	=	=	PUNCT
ejpam-6388	253	2	γ(fu⋆	γ(fu⋆	PROPN
ejpam-6388	253	3	,	,	PUNCT
ejpam-6388	253	4	fz⋆	fz⋆	PROPN
ejpam-6388	253	5	)	)	PUNCT
ejpam-6388	253	6	≤	≤	NUM
ejpam-6388	253	7	aγ(z⋆	aγ(z⋆	PROPN
ejpam-6388	253	8	,	,	PUNCT
ejpam-6388	253	9	fz⋆	fz⋆	PROPN
ejpam-6388	253	10	)	)	PUNCT
ejpam-6388	253	11	[	[	PUNCT
ejpam-6388	253	12	1	1	NUM
ejpam-6388	253	13	+	+	SYM
ejpam-6388	253	14	γ(u⋆	γ(u⋆	NOUN
ejpam-6388	253	15	,	,	PUNCT
ejpam-6388	253	16	fu⋆	fu⋆	PROPN
ejpam-6388	253	17	)	)	PUNCT
ejpam-6388	253	18	]	]	PUNCT
ejpam-6388	253	19	1	1	NUM
ejpam-6388	254	1	+	+	SYM
ejpam-6388	254	2	γ(u⋆	γ(u⋆	NOUN
ejpam-6388	254	3	,	,	PUNCT
ejpam-6388	254	4	z⋆	z⋆	NOUN
ejpam-6388	254	5	)	)	PUNCT
ejpam-6388	254	6	+	+	X
ejpam-6388	254	7	bγ(u⋆	bγ(u⋆	NUM
ejpam-6388	254	8	,	,	PUNCT
ejpam-6388	254	9	z⋆	z⋆	NOUN
ejpam-6388	254	10	)	)	PUNCT
ejpam-6388	254	11	=	=	SYM
ejpam-6388	254	12	bγ(u⋆	bγ(u⋆	PROPN
ejpam-6388	254	13	,	,	PUNCT
ejpam-6388	254	14	z⋆	z⋆	NOUN
ejpam-6388	254	15	)	)	PUNCT
ejpam-6388	254	16	.	.	PUNCT
ejpam-6388	255	1	since	since	SCONJ
ejpam-6388	255	2	b	b	PROPN
ejpam-6388	255	3	<	<	X
ejpam-6388	255	4	1	1	NUM
ejpam-6388	255	5	,	,	PUNCT
ejpam-6388	255	6	it	it	PRON
ejpam-6388	255	7	follows	follow	VERB
ejpam-6388	255	8	that	that	DET
ejpam-6388	255	9	γ(u⋆	γ(u⋆	NOUN
ejpam-6388	255	10	,	,	PUNCT
ejpam-6388	255	11	z⋆	z⋆	NOUN
ejpam-6388	255	12	)	)	PUNCT
ejpam-6388	255	13	=	=	SYM
ejpam-6388	256	1	0	0	NUM
ejpam-6388	256	2	,	,	PUNCT
ejpam-6388	256	3	which	which	PRON
ejpam-6388	256	4	yields	yield	VERB
ejpam-6388	256	5	u⋆	u⋆	ADV
ejpam-6388	256	6	=	=	SYM
ejpam-6388	256	7	z⋆.	z⋆.	X
ejpam-6388	256	8	this	this	PRON
ejpam-6388	256	9	establishes	establish	VERB
ejpam-6388	256	10	the	the	DET
ejpam-6388	256	11	uniqueness	uniqueness	NOUN
ejpam-6388	256	12	of	of	ADP
ejpam-6388	256	13	the	the	DET
ejpam-6388	256	14	fixed	fix	VERB
ejpam-6388	256	15	point	point	NOUN
ejpam-6388	256	16	of	of	ADP
ejpam-6388	256	17	f	f	PROPN
ejpam-6388	256	18	and	and	CCONJ
ejpam-6388	256	19	completes	complete	VERB
ejpam-6388	256	20	the	the	DET
ejpam-6388	256	21	proof	proof	NOUN
ejpam-6388	256	22	.	.	PUNCT
ejpam-6388	257	1	remark	remark	NOUN
ejpam-6388	257	2	5	5	NUM
ejpam-6388	257	3	.	.	PUNCT
ejpam-6388	258	1	for	for	ADP
ejpam-6388	258	2	a	a	DET
ejpam-6388	258	3	=	=	SYM
ejpam-6388	258	4	0	0	NUM
ejpam-6388	258	5	,	,	PUNCT
ejpam-6388	258	6	theorem	theorem	VERB
ejpam-6388	258	7	3	3	NUM
ejpam-6388	258	8	reduces	reduce	VERB
ejpam-6388	258	9	the	the	DET
ejpam-6388	258	10	banach	banach	NOUN
ejpam-6388	258	11	fpt	fpt	NOUN
ejpam-6388	258	12	on	on	ADP
ejpam-6388	258	13	orthogonal	orthogonal	ADJ
ejpam-6388	258	14	cone	cone	NOUN
ejpam-6388	258	15	metric	metric	ADJ
ejpam-6388	258	16	space	space	NOUN
ejpam-6388	258	17	,	,	PUNCT
ejpam-6388	258	18	i.e.	i.e.	X
ejpam-6388	258	19	,	,	PUNCT
ejpam-6388	258	20	theorem	theorem	ADJ
ejpam-6388	258	21	2	2	NUM
ejpam-6388	258	22	.	.	NOUN
ejpam-6388	258	23	4	4	NUM
ejpam-6388	258	24	.	.	NOUN
ejpam-6388	259	1	existence	existence	NOUN
ejpam-6388	259	2	and	and	CCONJ
ejpam-6388	259	3	uniqueness	uniqueness	NOUN
ejpam-6388	259	4	of	of	ADP
ejpam-6388	259	5	solutions	solution	NOUN
ejpam-6388	259	6	consider	consider	VERB
ejpam-6388	259	7	the	the	DET
ejpam-6388	259	8	set	set	NOUN
ejpam-6388	259	9	a	a	PRON
ejpam-6388	259	10	=	=	SYM
ejpam-6388	259	11	{	{	PUNCT
ejpam-6388	259	12	r	r	NOUN
ejpam-6388	259	13	∈	∈	PROPN
ejpam-6388	259	14	c(i	c(i	NOUN
ejpam-6388	259	15	,	,	PUNCT
ejpam-6388	259	16	r	r	NOUN
ejpam-6388	259	17	)	)	PUNCT
ejpam-6388	259	18	:	:	PUNCT
ejpam-6388	259	19	r(ω	r(ω	X
ejpam-6388	259	20	)	)	PUNCT
ejpam-6388	259	21	≥	≥	NOUN
ejpam-6388	259	22	0	0	NUM
ejpam-6388	259	23	for	for	ADP
ejpam-6388	259	24	almost	almost	ADV
ejpam-6388	259	25	every	every	PRON
ejpam-6388	259	26	ω	ω	NOUN
ejpam-6388	259	27	∈	∈	PROPN
ejpam-6388	259	28	i	i	X
ejpam-6388	259	29	}	}	PUNCT
ejpam-6388	259	30	,	,	PUNCT
ejpam-6388	259	31	where	where	SCONJ
ejpam-6388	259	32	i	i	PRON
ejpam-6388	259	33	:	:	PUNCT
ejpam-6388	259	34	=	=	PUNCT
ejpam-6388	260	1	[	[	X
ejpam-6388	260	2	0	0	NUM
ejpam-6388	260	3	,	,	PUNCT
ejpam-6388	260	4	1	1	NUM
ejpam-6388	260	5	]	]	PUNCT
ejpam-6388	260	6	.	.	PUNCT
ejpam-6388	261	1	define	define	VERB
ejpam-6388	261	2	the	the	DET
ejpam-6388	261	3	banach	banach	NOUN
ejpam-6388	261	4	space	space	NOUN
ejpam-6388	261	5	e	e	NOUN
ejpam-6388	261	6	=	=	SYM
ejpam-6388	261	7	r	r	NOUN
ejpam-6388	261	8	and	and	CCONJ
ejpam-6388	261	9	the	the	DET
ejpam-6388	261	10	subset	subset	NOUN
ejpam-6388	261	11	q	q	X
ejpam-6388	262	1	=	=	PUNCT
ejpam-6388	262	2	[	[	X
ejpam-6388	262	3	0,∞	0,∞	NUM
ejpam-6388	262	4	)	)	PUNCT
ejpam-6388	262	5	within	within	ADP
ejpam-6388	262	6	e.	e.	PROPN
ejpam-6388	262	7	we	we	PRON
ejpam-6388	262	8	introduce	introduce	VERB
ejpam-6388	262	9	a	a	DET
ejpam-6388	262	10	partial	partial	ADJ
ejpam-6388	262	11	ordering	ordering	NOUN
ejpam-6388	262	12	⪯	⪯	NOUN
ejpam-6388	262	13	on	on	ADP
ejpam-6388	262	14	e	e	NOUN
ejpam-6388	262	15	with	with	ADP
ejpam-6388	262	16	respect	respect	NOUN
ejpam-6388	262	17	to	to	ADP
ejpam-6388	262	18	q	q	NOUN
ejpam-6388	262	19	,	,	PUNCT
ejpam-6388	262	20	where	where	SCONJ
ejpam-6388	262	21	u	u	PRON
ejpam-6388	262	22	⪯	⪯	VERB
ejpam-6388	262	23	v	v	INTJ
ejpam-6388	262	24	if	if	SCONJ
ejpam-6388	262	25	and	and	CCONJ
ejpam-6388	262	26	only	only	ADV
ejpam-6388	262	27	if	if	SCONJ
ejpam-6388	262	28	v	v	NUM
ejpam-6388	262	29	−	−	PROPN
ejpam-6388	262	30	u	u	PROPN
ejpam-6388	262	31	∈	∈	PROPN
ejpam-6388	262	32	q.	q.	NOUN
ejpam-6388	262	33	now	now	ADV
ejpam-6388	262	34	,	,	PUNCT
ejpam-6388	262	35	consider	consider	VERB
ejpam-6388	262	36	a	a	DET
ejpam-6388	262	37	functional	functional	ADJ
ejpam-6388	262	38	γ	γ	NOUN
ejpam-6388	262	39	:	:	PUNCT
ejpam-6388	262	40	a×a	a×a	PROPN
ejpam-6388	262	41	→	→	SYM
ejpam-6388	262	42	e	e	NOUN
ejpam-6388	262	43	given	give	VERB
ejpam-6388	262	44	by	by	ADP
ejpam-6388	262	45	γ(r1	γ(r1	NOUN
ejpam-6388	262	46	,	,	PUNCT
ejpam-6388	262	47	r2	r2	PROPN
ejpam-6388	262	48	)	)	PUNCT
ejpam-6388	263	1	=	=	SYM
ejpam-6388	263	2	sup	sup	NOUN
ejpam-6388	263	3	ω∈i	ω∈i	NOUN
ejpam-6388	263	4	|r1(ω)−	|r1(ω)−	ADJ
ejpam-6388	264	1	r2(ω)|	r2(ω)|	PROPN
ejpam-6388	264	2	for	for	ADP
ejpam-6388	264	3	r1	r1	PROPN
ejpam-6388	264	4	,	,	PUNCT
ejpam-6388	264	5	r2	r2	PROPN
ejpam-6388	264	6	∈	∈	PROPN
ejpam-6388	264	7	a.	a.	NOUN
ejpam-6388	264	8	theorem	theorem	NOUN
ejpam-6388	264	9	4	4	X
ejpam-6388	264	10	.	.	PUNCT
ejpam-6388	264	11	suppose	suppose	VERB
ejpam-6388	264	12	the	the	DET
ejpam-6388	264	13	subsequent	subsequent	ADJ
ejpam-6388	264	14	assertions	assertion	NOUN
ejpam-6388	264	15	hold	hold	VERB
ejpam-6388	264	16	true	true	ADJ
ejpam-6388	264	17	:	:	PUNCT
ejpam-6388	264	18	(	(	PUNCT
ejpam-6388	264	19	b1	b1	NOUN
ejpam-6388	264	20	)	)	PUNCT
ejpam-6388	264	21	a	a	DET
ejpam-6388	264	22	function	function	NOUN
ejpam-6388	264	23	℘	℘	PROPN
ejpam-6388	264	24	∈	∈	PROPN
ejpam-6388	264	25	l1(i	l1(i	PROPN
ejpam-6388	264	26	,	,	PUNCT
ejpam-6388	264	27	r	r	NOUN
ejpam-6388	264	28	)	)	PUNCT
ejpam-6388	264	29	can	can	AUX
ejpam-6388	264	30	be	be	AUX
ejpam-6388	264	31	found	find	VERB
ejpam-6388	264	32	satisfying	satisfy	VERB
ejpam-6388	264	33	|g(ω	|g(ω	PROPN
ejpam-6388	264	34	,	,	PUNCT
ejpam-6388	264	35	r)−	r)−	PROPN
ejpam-6388	264	36	g(ω	g(ω	PROPN
ejpam-6388	264	37	,	,	PUNCT
ejpam-6388	264	38	u)|	u)|	NOUN
ejpam-6388	264	39	≤	≤	ADJ
ejpam-6388	264	40	℘(ω	℘(ω	NOUN
ejpam-6388	264	41	)	)	PUNCT
ejpam-6388	264	42	≤	≤	NOUN
ejpam-6388	264	43	|g(ω	|g(ω	PROPN
ejpam-6388	264	44	,	,	PUNCT
ejpam-6388	264	45	0)|	0)|	NOUN
ejpam-6388	264	46	for	for	ADP
ejpam-6388	264	47	all	all	DET
ejpam-6388	264	48	ω	ω	NUM
ejpam-6388	264	49	∈	∈	NOUN
ejpam-6388	264	50	i	i	PRON
ejpam-6388	264	51	and	and	CCONJ
ejpam-6388	264	52	r	r	NOUN
ejpam-6388	264	53	,	,	PUNCT
ejpam-6388	264	54	u	u	PROPN
ejpam-6388	264	55	∈	∈	PROPN
ejpam-6388	264	56	a.	a.	NOUN
ejpam-6388	264	57	(	(	PUNCT
ejpam-6388	264	58	b2	b2	NOUN
ejpam-6388	264	59	)	)	PUNCT
ejpam-6388	264	60	a	a	DET
ejpam-6388	264	61	constant	constant	ADJ
ejpam-6388	264	62	0	0	NUM
ejpam-6388	264	63	<	<	X
ejpam-6388	264	64	b	b	X
ejpam-6388	264	65	<	<	X
ejpam-6388	264	66	1	1	NUM
ejpam-6388	264	67	exists	exist	VERB
ejpam-6388	264	68	so	so	SCONJ
ejpam-6388	264	69	that	that	SCONJ
ejpam-6388	264	70	|f(ω	|f(ω	NOUN
ejpam-6388	264	71	,	,	PUNCT
ejpam-6388	264	72	r)−	r)−	PROPN
ejpam-6388	264	73	f(ω	f(ω	PROPN
ejpam-6388	264	74	,	,	PUNCT
ejpam-6388	264	75	u)|	u)|	NOUN
ejpam-6388	264	76	≤	≤	PUNCT
ejpam-6388	264	77	b|r−	b|r−	NOUN
ejpam-6388	264	78	u|[1	u|[1	PROPN
ejpam-6388	264	79	+	+	CCONJ
ejpam-6388	264	80	|r−	|r−	ADV
ejpam-6388	264	81	u|	u|	PROPN
ejpam-6388	264	82	]	]	X
ejpam-6388	264	83	1	1	NUM
ejpam-6388	265	1	+	+	NUM
ejpam-6388	265	2	2	2	NUM
ejpam-6388	265	3	m	m	NOUN
ejpam-6388	265	4	for	for	ADP
ejpam-6388	265	5	ω	ω	PROPN
ejpam-6388	265	6	∈	∈	PROPN
ejpam-6388	266	1	i	i	PRON
ejpam-6388	266	2	and	and	CCONJ
ejpam-6388	266	3	r	r	NOUN
ejpam-6388	266	4	,	,	PUNCT
ejpam-6388	266	5	u	u	NOUN
ejpam-6388	266	6	∈	∈	PROPN
ejpam-6388	266	7	a	a	PRON
ejpam-6388	266	8	,	,	PUNCT
ejpam-6388	266	9	where	where	SCONJ
ejpam-6388	266	10	m	m	VERB
ejpam-6388	266	11	:	:	PUNCT
ejpam-6388	266	12	=	=	SYM
ejpam-6388	266	13	∫	∫	PROPN
ejpam-6388	266	14	1	1	NUM
ejpam-6388	266	15	0	0	NUM
ejpam-6388	266	16	0(ω	0(ω	NUM
ejpam-6388	266	17	,	,	PUNCT
ejpam-6388	266	18	ω)℘(ω	ω)℘(ω	NUM
ejpam-6388	266	19	)	)	PUNCT
ejpam-6388	266	20	dω	dω	ADJ
ejpam-6388	266	21	.	.	PUNCT
ejpam-6388	267	1	under	under	ADP
ejpam-6388	267	2	these	these	DET
ejpam-6388	267	3	conditions	condition	NOUN
ejpam-6388	267	4	,	,	PUNCT
ejpam-6388	267	5	the	the	DET
ejpam-6388	267	6	fhbvp	fhbvp	NOUN
ejpam-6388	267	7	(	(	PUNCT
ejpam-6388	267	8	1)–(2	1)–(2	NUM
ejpam-6388	267	9	)	)	PUNCT
ejpam-6388	267	10	has	have	VERB
ejpam-6388	267	11	a	a	DET
ejpam-6388	267	12	unique	unique	ADJ
ejpam-6388	267	13	solution	solution	NOUN
ejpam-6388	267	14	.	.	PUNCT
ejpam-6388	268	1	d.	d.	PROPN
ejpam-6388	268	2	baleanu	baleanu	PROPN
ejpam-6388	268	3	et	et	PROPN
ejpam-6388	268	4	al	al	PROPN
ejpam-6388	268	5	.	.	PUNCT
ejpam-6388	268	6	/	/	SYM
ejpam-6388	268	7	eur	eur	PROPN
ejpam-6388	268	8	.	.	PUNCT
ejpam-6388	269	1	j.	j.	PROPN
ejpam-6388	269	2	pure	pure	PROPN
ejpam-6388	269	3	appl	appl	PROPN
ejpam-6388	269	4	.	.	PROPN
ejpam-6388	269	5	math	math	PROPN
ejpam-6388	269	6	,	,	PUNCT
ejpam-6388	269	7	18	18	NUM
ejpam-6388	269	8	(	(	PUNCT
ejpam-6388	269	9	4	4	NUM
ejpam-6388	269	10	)	)	PUNCT
ejpam-6388	269	11	(	(	PUNCT
ejpam-6388	269	12	2025	2025	NUM
ejpam-6388	269	13	)	)	PUNCT
ejpam-6388	269	14	,	,	PUNCT
ejpam-6388	269	15	6388	6388	NUM
ejpam-6388	269	16	12	12	NUM
ejpam-6388	269	17	of	of	ADP
ejpam-6388	269	18	31	31	NUM
ejpam-6388	269	19	proof	proof	NOUN
ejpam-6388	269	20	.	.	PUNCT
ejpam-6388	270	1	define	define	VERB
ejpam-6388	270	2	an	an	DET
ejpam-6388	270	3	orthogonality	orthogonality	NOUN
ejpam-6388	270	4	relation	relation	NOUN
ejpam-6388	270	5	⊥	⊥	NOUN
ejpam-6388	270	6	on	on	ADP
ejpam-6388	270	7	the	the	DET
ejpam-6388	270	8	set	set	NOUN
ejpam-6388	270	9	a	a	PRON
ejpam-6388	270	10	as	as	SCONJ
ejpam-6388	270	11	follows	follow	VERB
ejpam-6388	270	12	z	z	PROPN
ejpam-6388	270	13	⊥	⊥	NOUN
ejpam-6388	270	14	u	u	NOUN
ejpam-6388	270	15	if	if	SCONJ
ejpam-6388	270	16	and	and	CCONJ
ejpam-6388	270	17	only	only	ADV
ejpam-6388	270	18	if	if	SCONJ
ejpam-6388	270	19	z(ω	z(ω	NUM
ejpam-6388	270	20	)	)	PUNCT
ejpam-6388	270	21	·	·	PUNCT
ejpam-6388	271	1	u(ω	u(ω	PROPN
ejpam-6388	271	2	)	)	PUNCT
ejpam-6388	271	3	≥	≥	NOUN
ejpam-6388	271	4	0	0	NUM
ejpam-6388	271	5	for	for	ADP
ejpam-6388	271	6	almost	almost	ADV
ejpam-6388	271	7	all	all	PRON
ejpam-6388	271	8	ω	ω	NOUN
ejpam-6388	271	9	within	within	ADP
ejpam-6388	271	10	the	the	DET
ejpam-6388	271	11	interval	interval	NOUN
ejpam-6388	271	12	i.	i.	NOUN
ejpam-6388	271	13	this	this	DET
ejpam-6388	271	14	relation	relation	NOUN
ejpam-6388	271	15	demonstrates	demonstrate	VERB
ejpam-6388	271	16	that	that	SCONJ
ejpam-6388	271	17	(	(	PUNCT
ejpam-6388	271	18	a	a	DET
ejpam-6388	271	19	,	,	PUNCT
ejpam-6388	271	20	γ,⊥	γ,⊥	NOUN
ejpam-6388	271	21	)	)	PUNCT
ejpam-6388	271	22	satisfies	satisfy	VERB
ejpam-6388	271	23	the	the	DET
ejpam-6388	271	24	conditions	condition	NOUN
ejpam-6388	271	25	for	for	ADP
ejpam-6388	271	26	a	a	DET
ejpam-6388	271	27	cone	cone	NOUN
ejpam-6388	271	28	metric	metric	ADJ
ejpam-6388	271	29	space	space	NOUN
ejpam-6388	271	30	.	.	PUNCT
ejpam-6388	272	1	additionally	additionally	ADV
ejpam-6388	272	2	,	,	PUNCT
ejpam-6388	272	3	because	because	SCONJ
ejpam-6388	272	4	each	each	DET
ejpam-6388	272	5	function	function	NOUN
ejpam-6388	272	6	z	z	NOUN
ejpam-6388	272	7	in	in	ADP
ejpam-6388	272	8	a	a	PRON
ejpam-6388	272	9	is	be	AUX
ejpam-6388	272	10	continuous	continuous	ADJ
ejpam-6388	272	11	over	over	ADP
ejpam-6388	272	12	a	a	DET
ejpam-6388	272	13	closed	closed	ADJ
ejpam-6388	272	14	and	and	CCONJ
ejpam-6388	272	15	bounded	bound	VERB
ejpam-6388	272	16	subset	subset	NOUN
ejpam-6388	272	17	of	of	ADP
ejpam-6388	272	18	euclidean	euclidean	ADJ
ejpam-6388	272	19	space	space	NOUN
ejpam-6388	272	20	,	,	PUNCT
ejpam-6388	272	21	it	it	PRON
ejpam-6388	272	22	attains	attain	VERB
ejpam-6388	272	23	a	a	DET
ejpam-6388	272	24	supremum	supremum	NOUN
ejpam-6388	272	25	in	in	ADP
ejpam-6388	272	26	(	(	PUNCT
ejpam-6388	272	27	a	a	DET
ejpam-6388	272	28	,	,	PUNCT
ejpam-6388	272	29	γ,⊥	γ,⊥	NOUN
ejpam-6388	272	30	)	)	PUNCT
ejpam-6388	272	31	.	.	PUNCT
ejpam-6388	273	1	as	as	ADP
ejpam-6388	273	2	a	a	DET
ejpam-6388	273	3	result	result	NOUN
ejpam-6388	273	4	,	,	PUNCT
ejpam-6388	273	5	we	we	PRON
ejpam-6388	273	6	conclude	conclude	VERB
ejpam-6388	273	7	that	that	SCONJ
ejpam-6388	273	8	(	(	PUNCT
ejpam-6388	273	9	a	a	DET
ejpam-6388	273	10	,	,	PUNCT
ejpam-6388	273	11	γ,⊥	γ,⊥	NOUN
ejpam-6388	273	12	)	)	PUNCT
ejpam-6388	273	13	is	be	AUX
ejpam-6388	273	14	a	a	DET
ejpam-6388	273	15	complete	complete	ADJ
ejpam-6388	273	16	space	space	NOUN
ejpam-6388	273	17	.	.	PUNCT
ejpam-6388	274	1	now	now	ADV
ejpam-6388	274	2	,	,	PUNCT
ejpam-6388	274	3	we	we	PRON
ejpam-6388	274	4	introduce	introduce	VERB
ejpam-6388	274	5	a	a	DET
ejpam-6388	274	6	function	function	NOUN
ejpam-6388	274	7	f	f	NOUN
ejpam-6388	274	8	:	:	PUNCT
ejpam-6388	274	9	(	(	PUNCT
ejpam-6388	274	10	a	a	DET
ejpam-6388	274	11	,	,	PUNCT
ejpam-6388	274	12	γ,⊥	γ,⊥	NOUN
ejpam-6388	274	13	)	)	PUNCT
ejpam-6388	274	14	→	→	PUNCT
ejpam-6388	274	15	(	(	PUNCT
ejpam-6388	274	16	a	a	DET
ejpam-6388	274	17	,	,	PUNCT
ejpam-6388	274	18	γ,⊥	γ,⊥	NOUN
ejpam-6388	274	19	)	)	PUNCT
ejpam-6388	274	20	defined	define	VERB
ejpam-6388	274	21	by	by	ADP
ejpam-6388	274	22	fr(ω	fr(ω	ADJ
ejpam-6388	274	23	)	)	PUNCT
ejpam-6388	275	1	=	=	SYM
ejpam-6388	275	2	f(ω	f(ω	PROPN
ejpam-6388	275	3	,	,	PUNCT
ejpam-6388	275	4	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	275	5	+	+	CCONJ
ejpam-6388	275	6	f(ω	f(ω	PROPN
ejpam-6388	275	7	,	,	PUNCT
ejpam-6388	275	8	r(ω	r(ω	ADJ
ejpam-6388	275	9	)	)	PUNCT
ejpam-6388	275	10	)	)	PUNCT
ejpam-6388	275	11	∫	∫	PROPN
ejpam-6388	276	1	1	1	NUM
ejpam-6388	276	2	0	0	NUM
ejpam-6388	276	3	0(ω	0(ω	NUM
ejpam-6388	276	4	,	,	PUNCT
ejpam-6388	276	5	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	276	6	,	,	PUNCT
ejpam-6388	276	7	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	276	8	,	,	PUNCT
ejpam-6388	276	9	for	for	ADP
ejpam-6388	276	10	all	all	DET
ejpam-6388	276	11	ω	ω	PROPN
ejpam-6388	276	12	∈	∈	PROPN
ejpam-6388	276	13	i.	i.	NOUN
ejpam-6388	276	14	we	we	PRON
ejpam-6388	276	15	observe	observe	VERB
ejpam-6388	276	16	that	that	SCONJ
ejpam-6388	276	17	r	r	NOUN
ejpam-6388	276	18	∈	∈	PROPN
ejpam-6388	276	19	a	a	PRON
ejpam-6388	276	20	is	be	AUX
ejpam-6388	276	21	a	a	DET
ejpam-6388	276	22	solution	solution	NOUN
ejpam-6388	276	23	to	to	ADP
ejpam-6388	276	24	fhbvp	fhbvp	PROPN
ejpam-6388	276	25	(	(	PUNCT
ejpam-6388	276	26	1)–(2	1)–(2	NUM
ejpam-6388	276	27	)	)	PUNCT
ejpam-6388	277	1	if	if	SCONJ
ejpam-6388	277	2	and	and	CCONJ
ejpam-6388	277	3	only	only	ADV
ejpam-6388	277	4	if	if	SCONJ
ejpam-6388	277	5	r	r	NOUN
ejpam-6388	277	6	is	be	AUX
ejpam-6388	277	7	a	a	DET
ejpam-6388	277	8	fixed	fix	VERB
ejpam-6388	277	9	point	point	NOUN
ejpam-6388	277	10	of	of	ADP
ejpam-6388	277	11	f.	f.	PROPN
ejpam-6388	277	12	firstly	firstly	ADV
ejpam-6388	277	13	,	,	PUNCT
ejpam-6388	277	14	we	we	PRON
ejpam-6388	277	15	prove	prove	VERB
ejpam-6388	277	16	that	that	SCONJ
ejpam-6388	277	17	f	f	PROPN
ejpam-6388	277	18	is	be	AUX
ejpam-6388	277	19	a	a	DET
ejpam-6388	277	20	self	self	NOUN
ejpam-6388	277	21	-	-	PUNCT
ejpam-6388	277	22	mapping	mapping	NOUN
ejpam-6388	277	23	on	on	ADP
ejpam-6388	277	24	z.	z.	PROPN
ejpam-6388	277	25	to	to	PART
ejpam-6388	277	26	prove	prove	VERB
ejpam-6388	277	27	this	this	PRON
ejpam-6388	277	28	,	,	PUNCT
ejpam-6388	277	29	let	let	VERB
ejpam-6388	277	30	ω	ω	NUM
ejpam-6388	277	31	∈	∈	VERB
ejpam-6388	277	32	i	i	PRON
ejpam-6388	277	33	and	and	CCONJ
ejpam-6388	277	34	r	r	NOUN
ejpam-6388	277	35	∈	∈	PROPN
ejpam-6388	277	36	a.	a.	NOUN
ejpam-6388	277	37	then	then	ADV
ejpam-6388	277	38	,	,	PUNCT
ejpam-6388	277	39	fr(ω	fr(ω	ADV
ejpam-6388	277	40	)	)	PUNCT
ejpam-6388	278	1	=	=	SYM
ejpam-6388	278	2	f(ω	f(ω	PROPN
ejpam-6388	278	3	,	,	PUNCT
ejpam-6388	278	4	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	278	5	+	+	CCONJ
ejpam-6388	278	6	f(ω	f(ω	PROPN
ejpam-6388	278	7	,	,	PUNCT
ejpam-6388	278	8	r(ω	r(ω	ADJ
ejpam-6388	278	9	)	)	PUNCT
ejpam-6388	278	10	)	)	PUNCT
ejpam-6388	278	11	∫	∫	PROPN
ejpam-6388	279	1	1	1	NUM
ejpam-6388	279	2	0	0	NUM
ejpam-6388	279	3	0(ω	0(ω	NUM
ejpam-6388	279	4	,	,	PUNCT
ejpam-6388	279	5	ξ)g(ξ	ξ)g(ξ	PROPN
ejpam-6388	279	6	,	,	PUNCT
ejpam-6388	279	7	r(ξ))dξ	r(ξ))dξ	X
ejpam-6388	279	8	≥	≥	NOUN
ejpam-6388	279	9	f(ω	f(ω	PROPN
ejpam-6388	279	10	,	,	PUNCT
ejpam-6388	279	11	r(ω	r(ω	ADJ
ejpam-6388	279	12	)	)	PUNCT
ejpam-6388	279	13	)	)	PUNCT
ejpam-6388	280	1	∫	∫	PROPN
ejpam-6388	280	2	1	1	NUM
ejpam-6388	280	3	0	0	NUM
ejpam-6388	280	4	0(ω	0(ω	NUM
ejpam-6388	280	5	,	,	PUNCT
ejpam-6388	280	6	ξ)g(ξ	ξ)g(ξ	PROPN
ejpam-6388	280	7	,	,	PUNCT
ejpam-6388	280	8	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	280	9	≥	≥	NOUN
ejpam-6388	280	10	0	0	NUM
ejpam-6388	280	11	.	.	PUNCT
ejpam-6388	281	1	(	(	PUNCT
ejpam-6388	281	2	6	6	NUM
ejpam-6388	281	3	)	)	PUNCT
ejpam-6388	281	4	therefore	therefore	ADV
ejpam-6388	281	5	,	,	PUNCT
ejpam-6388	281	6	we	we	PRON
ejpam-6388	281	7	have	have	AUX
ejpam-6388	281	8	f(z	f(z	NOUN
ejpam-6388	281	9	)	)	PUNCT
ejpam-6388	282	1	⊆	⊆	NUM
ejpam-6388	282	2	a.	a.	NOUN
ejpam-6388	282	3	next	next	ADV
ejpam-6388	282	4	,	,	PUNCT
ejpam-6388	282	5	we	we	PRON
ejpam-6388	282	6	verify	verify	VERB
ejpam-6388	282	7	that	that	SCONJ
ejpam-6388	282	8	the	the	DET
ejpam-6388	282	9	conditions	condition	NOUN
ejpam-6388	282	10	of	of	ADP
ejpam-6388	282	11	theorem	theorem	ADJ
ejpam-6388	282	12	2	2	NUM
ejpam-6388	282	13	are	be	AUX
ejpam-6388	282	14	met	meet	VERB
ejpam-6388	282	15	.	.	PUNCT
ejpam-6388	283	1	f	f	PROPN
ejpam-6388	283	2	is	be	AUX
ejpam-6388	283	3	⊥-preserving	⊥-preserve	VERB
ejpam-6388	283	4	:	:	PUNCT
ejpam-6388	283	5	let	let	VERB
ejpam-6388	283	6	r(ω	r(ω	ADV
ejpam-6388	283	7	)	)	PUNCT
ejpam-6388	283	8	⊥	⊥	NOUN
ejpam-6388	283	9	u(ω	u(ω	PROPN
ejpam-6388	283	10	)	)	PUNCT
ejpam-6388	283	11	for	for	ADP
ejpam-6388	283	12	all	all	DET
ejpam-6388	283	13	ω	ω	PROPN
ejpam-6388	283	14	∈	∈	PROPN
ejpam-6388	283	15	i.	i.	NOUN
ejpam-6388	283	16	from	from	ADP
ejpam-6388	283	17	(	(	PUNCT
ejpam-6388	283	18	6	6	NUM
ejpam-6388	283	19	)	)	PUNCT
ejpam-6388	283	20	,	,	PUNCT
ejpam-6388	283	21	fr(ω	fr(ω	X
ejpam-6388	283	22	)	)	PUNCT
ejpam-6388	283	23	≥	≥	X
ejpam-6388	283	24	0	0	NUM
ejpam-6388	283	25	for	for	ADP
ejpam-6388	283	26	all	all	PRON
ejpam-6388	283	27	ω	ω	NUM
ejpam-6388	283	28	∈	∈	PROPN
ejpam-6388	284	1	i	i	PRON
ejpam-6388	284	2	,	,	PUNCT
ejpam-6388	284	3	which	which	PRON
ejpam-6388	284	4	implies	imply	VERB
ejpam-6388	284	5	that	that	SCONJ
ejpam-6388	284	6	fr	fr	PROPN
ejpam-6388	284	7	⊥	⊥	PROPN
ejpam-6388	284	8	fu	fu	NOUN
ejpam-6388	284	9	,	,	PUNCT
ejpam-6388	284	10	i.e.	i.e.	X
ejpam-6388	284	11	,	,	PUNCT
ejpam-6388	284	12	f	f	PROPN
ejpam-6388	284	13	is	be	AUX
ejpam-6388	284	14	⊥-preserving	⊥-preserve	VERB
ejpam-6388	284	15	.	.	PUNCT
ejpam-6388	285	1	f	f	PROPN
ejpam-6388	285	2	is	be	AUX
ejpam-6388	285	3	⊥-rational	⊥-rational	ADJ
ejpam-6388	285	4	contraction	contraction	NOUN
ejpam-6388	285	5	:	:	PUNCT
ejpam-6388	285	6	let	let	VERB
ejpam-6388	285	7	r	r	VERB
ejpam-6388	285	8	,	,	PUNCT
ejpam-6388	285	9	u	u	NOUN
ejpam-6388	285	10	∈	∈	PROPN
ejpam-6388	285	11	a	a	PRON
ejpam-6388	285	12	and	and	CCONJ
ejpam-6388	285	13	r	r	NOUN
ejpam-6388	285	14	⊥	⊥	PROPN
ejpam-6388	285	15	u.	u.	NOUN
ejpam-6388	286	1	then	then	ADV
ejpam-6388	286	2	,	,	PUNCT
ejpam-6388	286	3	we	we	PRON
ejpam-6388	286	4	have	have	VERB
ejpam-6388	286	5	|fr(ω)−	|fr(ω)−	NOUN
ejpam-6388	286	6	fu(ω)|	fu(ω)|	PRON
ejpam-6388	286	7	≤	≤	NUM
ejpam-6388	286	8	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	286	9	,	,	PUNCT
ejpam-6388	286	10	r(ω))−	r(ω))−	PROPN
ejpam-6388	286	11	f(ω	f(ω	PROPN
ejpam-6388	286	12	,	,	PUNCT
ejpam-6388	286	13	u(ω))|	u(ω))|	NOUN
ejpam-6388	286	14	+	+	CCONJ
ejpam-6388	286	15	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	286	16	,	,	PUNCT
ejpam-6388	286	17	r(ω	r(ω	ADJ
ejpam-6388	286	18	)	)	PUNCT
ejpam-6388	286	19	)	)	PUNCT
ejpam-6388	287	1	∫	∫	PROPN
ejpam-6388	287	2	1	1	NUM
ejpam-6388	287	3	0	0	NUM
ejpam-6388	287	4	0(ω	0(ω	NUM
ejpam-6388	287	5	,	,	PUNCT
ejpam-6388	287	6	ξ)g(ξ	ξ)g(ξ	PROPN
ejpam-6388	287	7	,	,	PUNCT
ejpam-6388	287	8	r(ξ))dξ	r(ξ))dξ	ADP
ejpam-6388	287	9	−	−	PROPN
ejpam-6388	287	10	f(ω	f(ω	PROPN
ejpam-6388	287	11	,	,	PUNCT
ejpam-6388	287	12	u(ω	u(ω	PROPN
ejpam-6388	287	13	)	)	PUNCT
ejpam-6388	287	14	)	)	PUNCT
ejpam-6388	288	1	∫	∫	PROPN
ejpam-6388	288	2	1	1	NUM
ejpam-6388	288	3	0	0	NUM
ejpam-6388	288	4	0(ω	0(ω	NUM
ejpam-6388	288	5	,	,	PUNCT
ejpam-6388	288	6	ξ)g(ξ	ξ)g(ξ	PROPN
ejpam-6388	288	7	,	,	PUNCT
ejpam-6388	288	8	u(ξ))dξ	u(ξ))dξ	PROPN
ejpam-6388	288	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	288	10	≤	≤	NUM
ejpam-6388	288	11	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	288	12	,	,	PUNCT
ejpam-6388	288	13	r(ω))−	r(ω))−	PROPN
ejpam-6388	288	14	f(ω	f(ω	PROPN
ejpam-6388	288	15	,	,	PUNCT
ejpam-6388	288	16	u(ω))|+	u(ω))|+	PROPN
ejpam-6388	288	17	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	288	18	,	,	PUNCT
ejpam-6388	288	19	r(ω))∫	r(ω))∫	NOUN
ejpam-6388	288	20	1	1	NUM
ejpam-6388	288	21	0	0	NUM
ejpam-6388	288	22	0(ω	0(ω	NUM
ejpam-6388	288	23	,	,	PUNCT
ejpam-6388	288	24	ξ)[g(ξ	ξ)[g(ξ	PROPN
ejpam-6388	288	25	,	,	PUNCT
ejpam-6388	288	26	r(ξ))−	r(ξ))−	PROPN
ejpam-6388	288	27	g(ξ	g(ξ	PROPN
ejpam-6388	288	28	,	,	PUNCT
ejpam-6388	288	29	0)]dξ	0)]dξ	PUNCT
ejpam-6388	288	30	−	−	PROPN
ejpam-6388	289	1	[	[	PUNCT
ejpam-6388	289	2	f(ω	f(ω	PROPN
ejpam-6388	289	3	,	,	PUNCT
ejpam-6388	289	4	u(ω	u(ω	PROPN
ejpam-6388	289	5	)	)	PUNCT
ejpam-6388	289	6	)	)	PUNCT
ejpam-6388	289	7	∫	∫	PROPN
ejpam-6388	289	8	1	1	NUM
ejpam-6388	289	9	0	0	NUM
ejpam-6388	289	10	0(ω	0(ω	NUM
ejpam-6388	289	11	,	,	PUNCT
ejpam-6388	289	12	ξ)[g(ξ	ξ)[g(ξ	ADJ
ejpam-6388	289	13	,	,	PUNCT
ejpam-6388	289	14	u(ξ))−	u(ξ))−	ADJ
ejpam-6388	289	15	g(ξ	g(ξ	PROPN
ejpam-6388	289	16	,	,	PUNCT
ejpam-6388	289	17	0)]dξ	0)]dξ	PUNCT
ejpam-6388	289	18	−	−	PROPN
ejpam-6388	289	19	f(ω	f(ω	PROPN
ejpam-6388	289	20	,	,	PUNCT
ejpam-6388	289	21	r(ω	r(ω	ADJ
ejpam-6388	289	22	)	)	PUNCT
ejpam-6388	289	23	)	)	PUNCT
ejpam-6388	289	24	∫	∫	PROPN
ejpam-6388	290	1	1	1	NUM
ejpam-6388	290	2	0	0	NUM
ejpam-6388	290	3	0(ω	0(ω	NUM
ejpam-6388	290	4	,	,	PUNCT
ejpam-6388	290	5	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	290	6	,	,	PUNCT
ejpam-6388	290	7	0)dξ	0)dξ	NUM
ejpam-6388	290	8	]	]	PUNCT
ejpam-6388	290	9	−f(ω	−f(ω	NOUN
ejpam-6388	290	10	,	,	PUNCT
ejpam-6388	290	11	u(ω	u(ω	PROPN
ejpam-6388	290	12	)	)	PUNCT
ejpam-6388	290	13	)	)	PUNCT
ejpam-6388	291	1	∫	∫	PROPN
ejpam-6388	291	2	1	1	NUM
ejpam-6388	291	3	0	0	NUM
ejpam-6388	291	4	0(ω	0(ω	NUM
ejpam-6388	291	5	,	,	PUNCT
ejpam-6388	291	6	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	291	7	,	,	PUNCT
ejpam-6388	291	8	0)dξ	0)dξ	ADJ
ejpam-6388	291	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	291	10	≤	≤	NUM
ejpam-6388	291	11	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	291	12	,	,	PUNCT
ejpam-6388	291	13	r(ω))−	r(ω))−	PROPN
ejpam-6388	291	14	f(ω	f(ω	PROPN
ejpam-6388	291	15	,	,	PUNCT
ejpam-6388	291	16	u(ω))|	u(ω))|	NOUN
ejpam-6388	291	17	+	+	CCONJ
ejpam-6388	291	18	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	291	19	,	,	PUNCT
ejpam-6388	291	20	r(ω))∫	r(ω))∫	NOUN
ejpam-6388	291	21	1	1	NUM
ejpam-6388	291	22	0	0	NUM
ejpam-6388	291	23	0(ω	0(ω	NUM
ejpam-6388	291	24	,	,	PUNCT
ejpam-6388	291	25	ξ)[g(ξ	ξ)[g(ξ	PROPN
ejpam-6388	291	26	,	,	PUNCT
ejpam-6388	291	27	r(ξ))−	r(ξ))−	PROPN
ejpam-6388	291	28	g(ξ	g(ξ	PROPN
ejpam-6388	291	29	,	,	PUNCT
ejpam-6388	291	30	0)]dξ	0)]dξ	NUM
ejpam-6388	291	31	−	−	PROPN
ejpam-6388	291	32	f(ω	f(ω	PROPN
ejpam-6388	291	33	,	,	PUNCT
ejpam-6388	291	34	u(ω	u(ω	PROPN
ejpam-6388	291	35	)	)	PUNCT
ejpam-6388	291	36	)	)	PUNCT
ejpam-6388	292	1	∫	∫	PROPN
ejpam-6388	292	2	1	1	NUM
ejpam-6388	292	3	0	0	NUM
ejpam-6388	292	4	0(ω	0(ω	NUM
ejpam-6388	292	5	,	,	PUNCT
ejpam-6388	292	6	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	292	7	,	,	PUNCT
ejpam-6388	292	8	0)dξ	0)dξ	ADJ
ejpam-6388	292	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	292	10	+	+	X
ejpam-6388	292	11	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	292	12	,	,	PUNCT
ejpam-6388	292	13	u(ω))∫	u(ω))∫	PROPN
ejpam-6388	292	14	1	1	NUM
ejpam-6388	292	15	0	0	NUM
ejpam-6388	292	16	0(ω	0(ω	NUM
ejpam-6388	292	17	,	,	PUNCT
ejpam-6388	292	18	ξ)[g(ξ	ξ)[g(ξ	ADJ
ejpam-6388	292	19	,	,	PUNCT
ejpam-6388	292	20	u(ξ))−	u(ξ))−	ADJ
ejpam-6388	292	21	g(ξ	g(ξ	PROPN
ejpam-6388	292	22	,	,	PUNCT
ejpam-6388	292	23	0)]dξ−f(ω	0)]dξ−f(ω	NUM
ejpam-6388	292	24	,	,	PUNCT
ejpam-6388	292	25	r(ω	r(ω	ADV
ejpam-6388	292	26	)	)	PUNCT
ejpam-6388	292	27	)	)	PUNCT
ejpam-6388	293	1	∫	∫	PROPN
ejpam-6388	293	2	1	1	NUM
ejpam-6388	293	3	0	0	NUM
ejpam-6388	293	4	0(ω	0(ω	NUM
ejpam-6388	293	5	,	,	PUNCT
ejpam-6388	293	6	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	293	7	,	,	PUNCT
ejpam-6388	293	8	0)dξ	0)dξ	ADJ
ejpam-6388	293	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	293	10	d.	d.	PROPN
ejpam-6388	293	11	baleanu	baleanu	PROPN
ejpam-6388	293	12	et	et	PROPN
ejpam-6388	293	13	al	al	PROPN
ejpam-6388	293	14	.	.	PUNCT
ejpam-6388	293	15	/	/	SYM
ejpam-6388	293	16	eur	eur	PROPN
ejpam-6388	293	17	.	.	PUNCT
ejpam-6388	294	1	j.	j.	PROPN
ejpam-6388	294	2	pure	pure	PROPN
ejpam-6388	294	3	appl	appl	PROPN
ejpam-6388	294	4	.	.	PROPN
ejpam-6388	294	5	math	math	PROPN
ejpam-6388	294	6	,	,	PUNCT
ejpam-6388	294	7	18	18	NUM
ejpam-6388	294	8	(	(	PUNCT
ejpam-6388	294	9	4	4	NUM
ejpam-6388	294	10	)	)	PUNCT
ejpam-6388	294	11	(	(	PUNCT
ejpam-6388	294	12	2025	2025	NUM
ejpam-6388	294	13	)	)	PUNCT
ejpam-6388	294	14	,	,	PUNCT
ejpam-6388	294	15	6388	6388	NUM
ejpam-6388	294	16	13	13	NUM
ejpam-6388	294	17	of	of	ADP
ejpam-6388	294	18	31	31	NUM
ejpam-6388	294	19	≤	≤	NUM
ejpam-6388	294	20	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	294	21	,	,	PUNCT
ejpam-6388	294	22	r(ω))−	r(ω))−	PROPN
ejpam-6388	294	23	f(ω	f(ω	PROPN
ejpam-6388	294	24	,	,	PUNCT
ejpam-6388	294	25	u(ω))|	u(ω))|	NOUN
ejpam-6388	294	26	+	+	CCONJ
ejpam-6388	294	27	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	294	28	,	,	PUNCT
ejpam-6388	294	29	r(ω	r(ω	ADJ
ejpam-6388	294	30	)	)	PUNCT
ejpam-6388	294	31	)	)	PUNCT
ejpam-6388	295	1	∫	∫	PROPN
ejpam-6388	296	1	1	1	NUM
ejpam-6388	296	2	0	0	NUM
ejpam-6388	296	3	0(ω	0(ω	NUM
ejpam-6388	296	4	,	,	PUNCT
ejpam-6388	296	5	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADV
ejpam-6388	297	1	−	−	PROPN
ejpam-6388	297	2	f(ω	f(ω	PROPN
ejpam-6388	297	3	,	,	PUNCT
ejpam-6388	297	4	u(ω	u(ω	PROPN
ejpam-6388	297	5	)	)	PUNCT
ejpam-6388	297	6	)	)	PUNCT
ejpam-6388	297	7	∫	∫	PROPN
ejpam-6388	297	8	1	1	NUM
ejpam-6388	297	9	0	0	NUM
ejpam-6388	297	10	0(ω	0(ω	NUM
ejpam-6388	297	11	,	,	PUNCT
ejpam-6388	297	12	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADJ
ejpam-6388	297	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	297	14	+	+	CCONJ
ejpam-6388	297	15	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	297	16	,	,	PUNCT
ejpam-6388	297	17	r(ω	r(ω	ADJ
ejpam-6388	297	18	)	)	PUNCT
ejpam-6388	297	19	)	)	PUNCT
ejpam-6388	297	20	∫	∫	PROPN
ejpam-6388	297	21	1	1	NUM
ejpam-6388	297	22	0	0	NUM
ejpam-6388	297	23	0(ω	0(ω	NUM
ejpam-6388	297	24	,	,	PUNCT
ejpam-6388	297	25	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADV
ejpam-6388	297	26	−	−	PROPN
ejpam-6388	297	27	f(ω	f(ω	PROPN
ejpam-6388	297	28	,	,	PUNCT
ejpam-6388	297	29	u(ω	u(ω	PROPN
ejpam-6388	297	30	)	)	PUNCT
ejpam-6388	297	31	)	)	PUNCT
ejpam-6388	297	32	∫	∫	PROPN
ejpam-6388	297	33	1	1	NUM
ejpam-6388	297	34	0	0	NUM
ejpam-6388	297	35	0(ω	0(ω	NUM
ejpam-6388	297	36	,	,	PUNCT
ejpam-6388	297	37	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADJ
ejpam-6388	297	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	297	39	≤	≤	NUM
ejpam-6388	297	40	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	297	41	,	,	PUNCT
ejpam-6388	297	42	r(ω))−	r(ω))−	PROPN
ejpam-6388	297	43	f(ω	f(ω	PROPN
ejpam-6388	297	44	,	,	PUNCT
ejpam-6388	297	45	u(ω))|	u(ω))|	NOUN
ejpam-6388	297	46	+	+	CCONJ
ejpam-6388	297	47	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	297	48	,	,	PUNCT
ejpam-6388	297	49	r(ω	r(ω	ADJ
ejpam-6388	297	50	)	)	PUNCT
ejpam-6388	297	51	)	)	PUNCT
ejpam-6388	298	1	∫	∫	PROPN
ejpam-6388	299	1	1	1	NUM
ejpam-6388	299	2	0	0	NUM
ejpam-6388	299	3	0(ω	0(ω	NUM
ejpam-6388	299	4	,	,	PUNCT
ejpam-6388	299	5	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADV
ejpam-6388	300	1	−	−	PROPN
ejpam-6388	300	2	f(ω	f(ω	PROPN
ejpam-6388	300	3	,	,	PUNCT
ejpam-6388	300	4	u(ω	u(ω	PROPN
ejpam-6388	300	5	)	)	PUNCT
ejpam-6388	300	6	)	)	PUNCT
ejpam-6388	300	7	∫	∫	PROPN
ejpam-6388	300	8	1	1	NUM
ejpam-6388	300	9	0	0	NUM
ejpam-6388	300	10	0(ω	0(ω	NUM
ejpam-6388	300	11	,	,	PUNCT
ejpam-6388	300	12	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADJ
ejpam-6388	300	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	300	14	+	+	CCONJ
ejpam-6388	300	15	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	300	16	,	,	PUNCT
ejpam-6388	300	17	r(ω	r(ω	ADJ
ejpam-6388	300	18	)	)	PUNCT
ejpam-6388	300	19	)	)	PUNCT
ejpam-6388	300	20	∫	∫	PROPN
ejpam-6388	300	21	1	1	NUM
ejpam-6388	300	22	0	0	NUM
ejpam-6388	300	23	0(ω	0(ω	NUM
ejpam-6388	300	24	,	,	PUNCT
ejpam-6388	300	25	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADV
ejpam-6388	300	26	−	−	PROPN
ejpam-6388	300	27	f(ω	f(ω	PROPN
ejpam-6388	300	28	,	,	PUNCT
ejpam-6388	300	29	u(ω	u(ω	PROPN
ejpam-6388	300	30	)	)	PUNCT
ejpam-6388	300	31	)	)	PUNCT
ejpam-6388	300	32	∫	∫	PROPN
ejpam-6388	300	33	1	1	NUM
ejpam-6388	300	34	0	0	NUM
ejpam-6388	300	35	0(ω	0(ω	NUM
ejpam-6388	300	36	,	,	PUNCT
ejpam-6388	300	37	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADJ
ejpam-6388	300	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	300	39	≤	≤	NUM
ejpam-6388	300	40	|ω|y−1|f(ω	|ω|y−1|f(ω	NOUN
ejpam-6388	300	41	,	,	PUNCT
ejpam-6388	300	42	r(ω))−	r(ω))−	PROPN
ejpam-6388	300	43	f(ω	f(ω	PROPN
ejpam-6388	300	44	,	,	PUNCT
ejpam-6388	300	45	u(ω))|+	u(ω))|+	PROPN
ejpam-6388	300	46	2|f(ω	2|f(ω	NOUN
ejpam-6388	300	47	,	,	PUNCT
ejpam-6388	300	48	r(ω))−	r(ω))−	PROPN
ejpam-6388	300	49	f(ω	f(ω	PROPN
ejpam-6388	300	50	,	,	PUNCT
ejpam-6388	300	51	u(ω))|	u(ω))|	PROPN
ejpam-6388	300	52	∫	∫	PROPN
ejpam-6388	300	53	1	1	NUM
ejpam-6388	300	54	0	0	NUM
ejpam-6388	300	55	0(ξ	0(ξ	NUM
ejpam-6388	300	56	,	,	PUNCT
ejpam-6388	300	57	ξ)℘(ξ)dξ	ξ)℘(ξ)dξ	ADJ
ejpam-6388	300	58	≤	≤	NUM
ejpam-6388	300	59	|f(ω	|f(ω	NOUN
ejpam-6388	300	60	,	,	PUNCT
ejpam-6388	300	61	r(ω))−	r(ω))−	PROPN
ejpam-6388	300	62	f(ω	f(ω	PROPN
ejpam-6388	300	63	,	,	PUNCT
ejpam-6388	300	64	u(ω))|+	u(ω))|+	PROPN
ejpam-6388	300	65	2|f(ω	2|f(ω	NOUN
ejpam-6388	300	66	,	,	PUNCT
ejpam-6388	300	67	r(ω))−	r(ω))−	PROPN
ejpam-6388	300	68	f(ω	f(ω	PROPN
ejpam-6388	300	69	,	,	PUNCT
ejpam-6388	300	70	u(ω))|m	u(ω))|m	PROPN
ejpam-6388	300	71	≤	≤	ADJ
ejpam-6388	300	72	|f(ω	|f(ω	NOUN
ejpam-6388	300	73	,	,	PUNCT
ejpam-6388	300	74	r(ω))−	r(ω))−	PROPN
ejpam-6388	300	75	f(ω	f(ω	PROPN
ejpam-6388	300	76	,	,	PUNCT
ejpam-6388	300	77	u(ω))|	u(ω))|	PROPN
ejpam-6388	300	78	(	(	PUNCT
ejpam-6388	300	79	1	1	NUM
ejpam-6388	300	80	+	+	NUM
ejpam-6388	300	81	2	2	NUM
ejpam-6388	300	82	m	m	NOUN
ejpam-6388	300	83	)	)	PUNCT
ejpam-6388	300	84	≤	≤	NUM
ejpam-6388	300	85	b|r−	b|r−	NOUN
ejpam-6388	300	86	u|[1	u|[1	NOUN
ejpam-6388	300	87	+	+	CCONJ
ejpam-6388	300	88	|r−	|r−	ADV
ejpam-6388	300	89	u|	u|	PROPN
ejpam-6388	300	90	]	]	X
ejpam-6388	300	91	1	1	NUM
ejpam-6388	300	92	+	+	NUM
ejpam-6388	300	93	2	2	NUM
ejpam-6388	300	94	m	m	NOUN
ejpam-6388	300	95	(	(	PUNCT
ejpam-6388	300	96	1	1	NUM
ejpam-6388	300	97	+	+	NUM
ejpam-6388	300	98	2	2	NUM
ejpam-6388	300	99	m	m	NOUN
ejpam-6388	300	100	)	)	PUNCT
ejpam-6388	300	101	=	=	PUNCT
ejpam-6388	301	1	b|r−	b|r−	NOUN
ejpam-6388	301	2	u|[1	u|[1	VERB
ejpam-6388	301	3	+	+	CCONJ
ejpam-6388	301	4	|r−	|r−	ADV
ejpam-6388	301	5	u|	u|	PROPN
ejpam-6388	301	6	]	]	PUNCT
ejpam-6388	301	7	.	.	PUNCT
ejpam-6388	302	1	but	but	CCONJ
ejpam-6388	302	2	,	,	PUNCT
ejpam-6388	302	3	for	for	ADP
ejpam-6388	302	4	any	any	DET
ejpam-6388	302	5	0	0	PUNCT
ejpam-6388	302	6	<	<	X
ejpam-6388	302	7	a	a	DET
ejpam-6388	302	8	<	<	X
ejpam-6388	302	9	1	1	NUM
ejpam-6388	302	10	,	,	PUNCT
ejpam-6388	302	11	we	we	PRON
ejpam-6388	302	12	have	have	VERB
ejpam-6388	302	13	|fr−	|fr−	NUM
ejpam-6388	302	14	fu|(1	fu|(1	NOUN
ejpam-6388	302	15	+	+	NOUN
ejpam-6388	302	16	|r−	|r−	ADJ
ejpam-6388	302	17	u|)−	u|)−	NOUN
ejpam-6388	302	18	a|r−	a|r−	PROPN
ejpam-6388	302	19	fr|(1	fr|(1	NOUN
ejpam-6388	302	20	+	+	CCONJ
ejpam-6388	302	21	|u−	|u−	ADJ
ejpam-6388	302	22	fu|	fu|	NOUN
ejpam-6388	302	23	)	)	PUNCT
ejpam-6388	302	24	≤	≤	NOUN
ejpam-6388	302	25	|fr−	|fr−	NOUN
ejpam-6388	302	26	fu|	fu|	ADJ
ejpam-6388	302	27	≤	≤	NOUN
ejpam-6388	302	28	b|r−	b|r−	NOUN
ejpam-6388	302	29	u|	u|	PROPN
ejpam-6388	302	30	[	[	PUNCT
ejpam-6388	302	31	1	1	NUM
ejpam-6388	302	32	+	+	NOUN
ejpam-6388	302	33	|r−	|r−	NOUN
ejpam-6388	302	34	u|	u|	PROPN
ejpam-6388	302	35	]	]	PUNCT
ejpam-6388	302	36	which	which	DET
ejpam-6388	302	37	implies∣∣fr(ω)−	implies∣∣fr(ω)−	NOUN
ejpam-6388	302	38	fu(ω	fu(ω	X
ejpam-6388	302	39	)	)	PUNCT
ejpam-6388	303	1	∣∣	∣∣	NUM
ejpam-6388	303	2	≤	≤	NOUN
ejpam-6388	303	3	a|r(ω)−	a|r(ω)−	VERB
ejpam-6388	303	4	fr(ω)|(1	fr(ω)|(1	NOUN
ejpam-6388	303	5	+	+	CCONJ
ejpam-6388	303	6	|u(ω)−	|u(ω)−	NOUN
ejpam-6388	303	7	fu(ω)|	fu(ω)|	ADJ
ejpam-6388	303	8	)	)	PUNCT
ejpam-6388	303	9	1	1	NUM
ejpam-6388	303	10	+	+	NUM
ejpam-6388	303	11	|r(ω)−	|r(ω)−	NOUN
ejpam-6388	303	12	u(ω)|	u(ω)|	X
ejpam-6388	303	13	+	+	X
ejpam-6388	303	14	b|r(ω)−	b|r(ω)−	NOUN
ejpam-6388	303	15	u(ω)|	u(ω)|	INTJ
ejpam-6388	303	16	.	.	PUNCT
ejpam-6388	304	1	taking	take	VERB
ejpam-6388	304	2	supremum	supremum	ADV
ejpam-6388	304	3	on	on	ADP
ejpam-6388	304	4	both	both	DET
ejpam-6388	304	5	sides	side	NOUN
ejpam-6388	304	6	over	over	ADP
ejpam-6388	304	7	ω	ω	PROPN
ejpam-6388	304	8	,	,	PUNCT
ejpam-6388	304	9	we	we	PRON
ejpam-6388	304	10	get	get	VERB
ejpam-6388	304	11	γ(fr	γ(fr	NOUN
ejpam-6388	304	12	,	,	PUNCT
ejpam-6388	304	13	fu	fu	NOUN
ejpam-6388	304	14	)	)	PUNCT
ejpam-6388	304	15	≤	≤	NOUN
ejpam-6388	304	16	aγ(r	aγ(r	PUNCT
ejpam-6388	304	17	,	,	PUNCT
ejpam-6388	304	18	fr)[1	fr)[1	PROPN
ejpam-6388	304	19	+	+	CCONJ
ejpam-6388	304	20	γ(u	γ(u	PROPN
ejpam-6388	304	21	,	,	PUNCT
ejpam-6388	304	22	fu	fu	NOUN
ejpam-6388	304	23	)	)	PUNCT
ejpam-6388	304	24	]	]	PUNCT
ejpam-6388	305	1	1	1	NUM
ejpam-6388	305	2	+	+	CCONJ
ejpam-6388	305	3	γ(r	γ(r	PROPN
ejpam-6388	305	4	,	,	PUNCT
ejpam-6388	305	5	u	u	NOUN
ejpam-6388	305	6	)	)	PUNCT
ejpam-6388	305	7	+	+	CCONJ
ejpam-6388	305	8	bγ(r	bγ(r	NUM
ejpam-6388	305	9	,	,	PUNCT
ejpam-6388	305	10	u	u	NOUN
ejpam-6388	305	11	)	)	PUNCT
ejpam-6388	305	12	,	,	PUNCT
ejpam-6388	305	13	(	(	PUNCT
ejpam-6388	305	14	7	7	X
ejpam-6388	305	15	)	)	PUNCT
ejpam-6388	305	16	which	which	PRON
ejpam-6388	305	17	shows	show	VERB
ejpam-6388	305	18	that	that	SCONJ
ejpam-6388	305	19	f	f	PROPN
ejpam-6388	305	20	is	be	AUX
ejpam-6388	305	21	⊥-rational	⊥-rational	ADJ
ejpam-6388	305	22	contractive	contractive	ADJ
ejpam-6388	305	23	,	,	PUNCT
ejpam-6388	305	24	since	since	SCONJ
ejpam-6388	305	25	a+	a+	PRON
ejpam-6388	305	26	b	b	X
ejpam-6388	305	27	<	<	X
ejpam-6388	305	28	1	1	NUM
ejpam-6388	305	29	.	.	PUNCT
ejpam-6388	305	30	f	f	PROPN
ejpam-6388	305	31	is	be	AUX
ejpam-6388	305	32	⊥-continuous	⊥-continuous	ADJ
ejpam-6388	305	33	:	:	PUNCT
ejpam-6388	305	34	consider	consider	VERB
ejpam-6388	305	35	an	an	DET
ejpam-6388	305	36	o	o	NOUN
ejpam-6388	305	37	-	-	NOUN
ejpam-6388	305	38	sequence	sequence	NOUN
ejpam-6388	305	39	{	{	PUNCT
ejpam-6388	305	40	rn	rn	NOUN
ejpam-6388	305	41	}	}	PUNCT
ejpam-6388	305	42	in	in	ADP
ejpam-6388	305	43	z	z	NOUN
ejpam-6388	305	44	that	that	PRON
ejpam-6388	305	45	converges	converge	VERB
ejpam-6388	305	46	to	to	ADP
ejpam-6388	305	47	a	a	DET
ejpam-6388	305	48	point	point	NOUN
ejpam-6388	305	49	r	r	NOUN
ejpam-6388	305	50	∈	∈	NOUN
ejpam-6388	305	51	a.	a.	NOUN
ejpam-6388	305	52	since	since	SCONJ
ejpam-6388	305	53	f	f	PROPN
ejpam-6388	305	54	preserves	preserve	VERB
ejpam-6388	305	55	the	the	DET
ejpam-6388	305	56	⊥-orthogonality	⊥-orthogonality	NOUN
ejpam-6388	305	57	property	property	NOUN
ejpam-6388	305	58	,	,	PUNCT
ejpam-6388	305	59	the	the	DET
ejpam-6388	305	60	sequence	sequence	NOUN
ejpam-6388	305	61	{	{	PUNCT
ejpam-6388	305	62	f(rn	f(rn	PROPN
ejpam-6388	305	63	)	)	PUNCT
ejpam-6388	305	64	}	}	PUNCT
ejpam-6388	305	65	also	also	ADV
ejpam-6388	305	66	qualifies	qualify	VERB
ejpam-6388	305	67	as	as	ADP
ejpam-6388	305	68	an	an	DET
ejpam-6388	305	69	o	o	NOUN
ejpam-6388	305	70	-	-	NOUN
ejpam-6388	305	71	sequence	sequence	NOUN
ejpam-6388	305	72	.	.	PUNCT
ejpam-6388	306	1	for	for	ADP
ejpam-6388	306	2	any	any	DET
ejpam-6388	306	3	natural	natural	ADJ
ejpam-6388	306	4	number	number	NOUN
ejpam-6388	306	5	n	n	CCONJ
ejpam-6388	306	6	,	,	PUNCT
ejpam-6388	306	7	setting	set	VERB
ejpam-6388	306	8	r	r	NOUN
ejpam-6388	306	9	=	=	SYM
ejpam-6388	306	10	rn	rn	PROPN
ejpam-6388	306	11	,	,	PUNCT
ejpam-6388	306	12	u	u	NOUN
ejpam-6388	306	13	=	=	SYM
ejpam-6388	306	14	r	r	NOUN
ejpam-6388	306	15	,	,	PUNCT
ejpam-6388	306	16	and	and	CCONJ
ejpam-6388	306	17	a	a	DET
ejpam-6388	306	18	=	=	NOUN
ejpam-6388	306	19	0	0	NUM
ejpam-6388	306	20	in	in	ADP
ejpam-6388	306	21	equation	equation	NOUN
ejpam-6388	306	22	(	(	PUNCT
ejpam-6388	306	23	7	7	X
ejpam-6388	306	24	)	)	PUNCT
ejpam-6388	306	25	yields	yield	NOUN
ejpam-6388	306	26	∣∣f(rn)−	∣∣f(rn)−	NOUN
ejpam-6388	306	27	f(r	f(r	NOUN
ejpam-6388	306	28	)	)	PUNCT
ejpam-6388	306	29	∣∣	∣∣	NUM
ejpam-6388	306	30	≤	≤	NUM
ejpam-6388	306	31	b|rn	b|rn	X
ejpam-6388	306	32	−	−	X
ejpam-6388	306	33	r|	r|	NOUN
ejpam-6388	306	34	.	.	PUNCT
ejpam-6388	307	1	taking	take	VERB
ejpam-6388	307	2	the	the	DET
ejpam-6388	307	3	limit	limit	NOUN
ejpam-6388	307	4	as	as	ADP
ejpam-6388	307	5	n	n	NUM
ejpam-6388	307	6	approaches	approach	NOUN
ejpam-6388	307	7	infinity	infinity	NOUN
ejpam-6388	307	8	,	,	PUNCT
ejpam-6388	307	9	it	it	PRON
ejpam-6388	307	10	follows	follow	VERB
ejpam-6388	307	11	that	that	SCONJ
ejpam-6388	307	12	f	f	PROPN
ejpam-6388	307	13	is	be	AUX
ejpam-6388	307	14	⊥-continuous	⊥-continuous	ADJ
ejpam-6388	307	15	.	.	PUNCT
ejpam-6388	308	1	by	by	ADP
ejpam-6388	308	2	applying	apply	VERB
ejpam-6388	308	3	theorem	theorem	NOUN
ejpam-6388	308	4	3	3	NUM
ejpam-6388	308	5	,	,	PUNCT
ejpam-6388	308	6	we	we	PRON
ejpam-6388	308	7	conclude	conclude	VERB
ejpam-6388	308	8	that	that	SCONJ
ejpam-6388	308	9	r	r	NOUN
ejpam-6388	308	10	is	be	AUX
ejpam-6388	308	11	the	the	DET
ejpam-6388	308	12	unique	unique	ADJ
ejpam-6388	308	13	fixed	fix	VERB
ejpam-6388	308	14	point	point	NOUN
ejpam-6388	308	15	of	of	ADP
ejpam-6388	308	16	f	f	PROPN
ejpam-6388	308	17	,	,	PUNCT
ejpam-6388	308	18	which	which	PRON
ejpam-6388	308	19	represents	represent	VERB
ejpam-6388	308	20	the	the	DET
ejpam-6388	308	21	solution	solution	NOUN
ejpam-6388	308	22	for	for	ADP
ejpam-6388	308	23	the	the	DET
ejpam-6388	308	24	fhbvp	fhbvp	NOUN
ejpam-6388	308	25	specified	specify	VERB
ejpam-6388	308	26	in	in	ADP
ejpam-6388	308	27	(	(	PUNCT
ejpam-6388	308	28	1)-(2	1)-(2	NUM
ejpam-6388	308	29	)	)	PUNCT
ejpam-6388	308	30	.	.	PUNCT
ejpam-6388	309	1	this	this	PRON
ejpam-6388	309	2	completes	complete	VERB
ejpam-6388	309	3	the	the	DET
ejpam-6388	309	4	proof	proof	NOUN
ejpam-6388	309	5	.	.	PUNCT
ejpam-6388	310	1	d.	d.	PROPN
ejpam-6388	310	2	baleanu	baleanu	PROPN
ejpam-6388	310	3	et	et	PROPN
ejpam-6388	310	4	al	al	PROPN
ejpam-6388	310	5	.	.	PUNCT
ejpam-6388	310	6	/	/	SYM
ejpam-6388	310	7	eur	eur	PROPN
ejpam-6388	310	8	.	.	PUNCT
ejpam-6388	311	1	j.	j.	PROPN
ejpam-6388	311	2	pure	pure	PROPN
ejpam-6388	311	3	appl	appl	PROPN
ejpam-6388	311	4	.	.	PROPN
ejpam-6388	311	5	math	math	PROPN
ejpam-6388	311	6	,	,	PUNCT
ejpam-6388	311	7	18	18	NUM
ejpam-6388	311	8	(	(	PUNCT
ejpam-6388	311	9	4	4	NUM
ejpam-6388	311	10	)	)	PUNCT
ejpam-6388	311	11	(	(	PUNCT
ejpam-6388	311	12	2025	2025	NUM
ejpam-6388	311	13	)	)	PUNCT
ejpam-6388	311	14	,	,	PUNCT
ejpam-6388	311	15	6388	6388	NUM
ejpam-6388	311	16	14	14	NUM
ejpam-6388	311	17	of	of	ADP
ejpam-6388	311	18	31	31	NUM
ejpam-6388	311	19	5	5	NUM
ejpam-6388	311	20	.	.	PUNCT
ejpam-6388	312	1	hyers	hyer	NOUN
ejpam-6388	312	2	–	–	PUNCT
ejpam-6388	312	3	ulam	ulam	PROPN
ejpam-6388	312	4	stability	stability	NOUN
ejpam-6388	312	5	analysis	analysis	NOUN
ejpam-6388	312	6	for	for	ADP
ejpam-6388	312	7	some	some	DET
ejpam-6388	312	8	positive	positive	ADJ
ejpam-6388	312	9	ε	ε	NOUN
ejpam-6388	312	10	,	,	PUNCT
ejpam-6388	312	11	consider	consider	VERB
ejpam-6388	312	12	the	the	DET
ejpam-6388	312	13	inequality∣∣∣∣rldy	inequality∣∣∣∣rldy	NUM
ejpam-6388	312	14	0	0	NUM
ejpam-6388	312	15	+	+	CCONJ
ejpam-6388	312	16	[	[	PUNCT
ejpam-6388	312	17	r(ω	r(ω	ADJ
ejpam-6388	312	18	)	)	PUNCT
ejpam-6388	312	19	f(ω	f(ω	PROPN
ejpam-6388	312	20	,	,	PUNCT
ejpam-6388	312	21	r(ω	r(ω	ADJ
ejpam-6388	312	22	)	)	PUNCT
ejpam-6388	312	23	)	)	PUNCT
ejpam-6388	312	24	]	]	PUNCT
ejpam-6388	313	1	+	+	CCONJ
ejpam-6388	313	2	g(ω	g(ω	PROPN
ejpam-6388	313	3	,	,	PUNCT
ejpam-6388	313	4	r(ω	r(ω	ADJ
ejpam-6388	313	5	)	)	PUNCT
ejpam-6388	313	6	)	)	PUNCT
ejpam-6388	313	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	313	8	≤	≤	NUM
ejpam-6388	313	9	ε	ε	PROPN
ejpam-6388	313	10	(	(	PUNCT
ejpam-6388	313	11	8)	8)	NUM
ejpam-6388	313	12	for	for	ADP
ejpam-6388	313	13	ω	ω	PROPN
ejpam-6388	313	14	∈	∈	PROPN
ejpam-6388	314	1	[	[	X
ejpam-6388	314	2	0	0	NUM
ejpam-6388	314	3	,	,	PUNCT
ejpam-6388	314	4	1	1	NUM
ejpam-6388	314	5	]	]	PUNCT
ejpam-6388	314	6	.	.	PUNCT
ejpam-6388	315	1	the	the	DET
ejpam-6388	315	2	fractional	fractional	ADJ
ejpam-6388	315	3	hybrid	hybrid	ADJ
ejpam-6388	315	4	boundary	boundary	ADJ
ejpam-6388	315	5	value	value	NOUN
ejpam-6388	315	6	problem	problem	NOUN
ejpam-6388	315	7	(	(	PUNCT
ejpam-6388	315	8	fhbvp	fhbvp	PROPN
ejpam-6388	315	9	)	)	PUNCT
ejpam-6388	315	10	(	(	PUNCT
ejpam-6388	315	11	1)–(2	1)–(2	NUM
ejpam-6388	315	12	)	)	PUNCT
ejpam-6388	315	13	is	be	AUX
ejpam-6388	315	14	susceptible	susceptible	ADJ
ejpam-6388	315	15	to	to	ADP
ejpam-6388	315	16	misunderstandings	misunderstanding	NOUN
ejpam-6388	315	17	when	when	SCONJ
ejpam-6388	315	18	applying	apply	VERB
ejpam-6388	315	19	hyers	hyer	NOUN
ejpam-6388	315	20	–	–	PUNCT
ejpam-6388	315	21	ulam	ulam	X
ejpam-6388	315	22	stability	stability	NOUN
ejpam-6388	315	23	,	,	PUNCT
ejpam-6388	315	24	as	as	SCONJ
ejpam-6388	315	25	noted	note	VERB
ejpam-6388	315	26	by	by	ADP
ejpam-6388	315	27	agarwal	agarwal	PROPN
ejpam-6388	315	28	et	et	PROPN
ejpam-6388	315	29	al	al	PROPN
ejpam-6388	315	30	.	.	PUNCT
ejpam-6388	316	1	[	[	X
ejpam-6388	316	2	3	3	NUM
ejpam-6388	316	3	]	]	PUNCT
ejpam-6388	316	4	.	.	PUNCT
ejpam-6388	317	1	they	they	PRON
ejpam-6388	317	2	identify	identify	VERB
ejpam-6388	317	3	two	two	NUM
ejpam-6388	317	4	main	main	ADJ
ejpam-6388	317	5	issues	issue	NOUN
ejpam-6388	317	6	:	:	PUNCT
ejpam-6388	317	7	(	(	PUNCT
ejpam-6388	317	8	p1	p1	NOUN
ejpam-6388	317	9	)	)	PUNCT
ejpam-6388	317	10	treating	treat	VERB
ejpam-6388	317	11	the	the	DET
ejpam-6388	317	12	exact	exact	ADJ
ejpam-6388	317	13	solution	solution	NOUN
ejpam-6388	317	14	as	as	SCONJ
ejpam-6388	317	15	fixed	fix	VERB
ejpam-6388	317	16	and	and	CCONJ
ejpam-6388	317	17	independent	independent	ADJ
ejpam-6388	317	18	of	of	ADP
ejpam-6388	317	19	the	the	DET
ejpam-6388	317	20	approximate	approximate	ADJ
ejpam-6388	317	21	solution	solution	NOUN
ejpam-6388	317	22	,	,	PUNCT
ejpam-6388	317	23	and	and	CCONJ
ejpam-6388	317	24	(	(	PUNCT
ejpam-6388	317	25	p2	p2	X
ejpam-6388	317	26	)	)	PUNCT
ejpam-6388	317	27	assuming	assume	VERB
ejpam-6388	317	28	the	the	DET
ejpam-6388	317	29	approximate	approximate	ADJ
ejpam-6388	317	30	solution	solution	NOUN
ejpam-6388	317	31	satisfies	satisfy	VERB
ejpam-6388	317	32	the	the	DET
ejpam-6388	317	33	original	original	ADJ
ejpam-6388	317	34	boundary	boundary	ADJ
ejpam-6388	317	35	conditions	condition	NOUN
ejpam-6388	317	36	,	,	PUNCT
ejpam-6388	317	37	leading	lead	VERB
ejpam-6388	317	38	to	to	ADP
ejpam-6388	317	39	invalid	invalid	ADJ
ejpam-6388	317	40	stability	stability	NOUN
ejpam-6388	317	41	claims	claim	NOUN
ejpam-6388	317	42	(	(	PUNCT
ejpam-6388	317	43	see	see	VERB
ejpam-6388	317	44	[	[	X
ejpam-6388	317	45	3	3	NUM
ejpam-6388	317	46	]	]	PUNCT
ejpam-6388	317	47	,	,	PUNCT
ejpam-6388	317	48	section	section	NOUN
ejpam-6388	317	49	2.2.1	2.2.1	NUM
ejpam-6388	317	50	)	)	PUNCT
ejpam-6388	317	51	.	.	PUNCT
ejpam-6388	318	1	to	to	PART
ejpam-6388	318	2	address	address	VERB
ejpam-6388	318	3	these	these	PRON
ejpam-6388	318	4	,	,	PUNCT
ejpam-6388	318	5	we	we	PRON
ejpam-6388	318	6	modify	modify	VERB
ejpam-6388	318	7	the	the	DET
ejpam-6388	318	8	approach	approach	NOUN
ejpam-6388	318	9	by	by	ADP
ejpam-6388	318	10	introducing	introduce	VERB
ejpam-6388	318	11	a	a	DET
ejpam-6388	318	12	parameter	parameter	NOUN
ejpam-6388	318	13	θ	θ	PROPN
ejpam-6388	318	14	.	.	PUNCT
ejpam-6388	319	1	thus	thus	ADV
ejpam-6388	319	2	,	,	PUNCT
ejpam-6388	319	3	the	the	DET
ejpam-6388	319	4	fhbvp	fhbvp	NOUN
ejpam-6388	319	5	is	be	AUX
ejpam-6388	319	6	regarded	regard	VERB
ejpam-6388	319	7	as	as	ADP
ejpam-6388	319	8	hyers	hyer	NOUN
ejpam-6388	319	9	–	–	PUNCT
ejpam-6388	319	10	ulam	ulam	X
ejpam-6388	319	11	stable	stable	ADJ
ejpam-6388	319	12	provided	provide	VERB
ejpam-6388	319	13	for	for	ADP
ejpam-6388	319	14	any	any	DET
ejpam-6388	319	15	r	r	NOUN
ejpam-6388	319	16	∈	∈	PROPN
ejpam-6388	319	17	a	a	DET
ejpam-6388	319	18	satisfying	satisfy	VERB
ejpam-6388	319	19	inequality	inequality	NOUN
ejpam-6388	319	20	(	(	PUNCT
ejpam-6388	319	21	8)	8)	NUM
ejpam-6388	319	22	,	,	PUNCT
ejpam-6388	319	23	there	there	PRON
ejpam-6388	319	24	exists	exist	VERB
ejpam-6388	319	25	a	a	DET
ejpam-6388	319	26	parameter	parameter	NOUN
ejpam-6388	319	27	θ	θ	NOUN
ejpam-6388	319	28	=	=	PUNCT
ejpam-6388	319	29	θ(r	θ(r	X
ejpam-6388	319	30	,	,	PUNCT
ejpam-6388	319	31	ε	ε	PROPN
ejpam-6388	319	32	)	)	PUNCT
ejpam-6388	319	33	=	=	SYM
ejpam-6388	319	34	r(1)−	r(1)−	PROPN
ejpam-6388	319	35	f(1	f(1	PROPN
ejpam-6388	319	36	,	,	PUNCT
ejpam-6388	319	37	r(1	r(1	PROPN
ejpam-6388	319	38	)	)	PUNCT
ejpam-6388	319	39	)	)	PUNCT
ejpam-6388	319	40	and	and	CCONJ
ejpam-6388	319	41	a	a	DET
ejpam-6388	319	42	corresponding	corresponding	ADJ
ejpam-6388	319	43	solution	solution	NOUN
ejpam-6388	319	44	u(ω	u(ω	PROPN
ejpam-6388	319	45	,	,	PUNCT
ejpam-6388	319	46	θ	θ	NOUN
ejpam-6388	319	47	)	)	PUNCT
ejpam-6388	319	48	∈	∈	PROPN
ejpam-6388	319	49	a	a	PRON
ejpam-6388	319	50	of	of	ADP
ejpam-6388	319	51	the	the	DET
ejpam-6388	319	52	modified	modified	ADJ
ejpam-6388	319	53	problem	problem	NOUN
ejpam-6388	319	54	r(0	r(0	PROPN
ejpam-6388	319	55	)	)	PUNCT
ejpam-6388	319	56	=	=	SYM
ejpam-6388	319	57	0	0	NUM
ejpam-6388	319	58	and	and	CCONJ
ejpam-6388	319	59	r(1	r(1	PROPN
ejpam-6388	319	60	)	)	PUNCT
ejpam-6388	320	1	=	=	PUNCT
ejpam-6388	320	2	f(1	f(1	PROPN
ejpam-6388	320	3	,	,	PUNCT
ejpam-6388	320	4	r(1	r(1	PROPN
ejpam-6388	320	5	)	)	PUNCT
ejpam-6388	320	6	)	)	PUNCT
ejpam-6388	321	1	+	+	CCONJ
ejpam-6388	322	1	θ	θ	NOUN
ejpam-6388	322	2	,	,	PUNCT
ejpam-6388	322	3	(	(	PUNCT
ejpam-6388	322	4	9	9	X
ejpam-6388	322	5	)	)	PUNCT
ejpam-6388	322	6	such	such	ADJ
ejpam-6388	322	7	that	that	DET
ejpam-6388	322	8	|r(ω)−	|r(ω)−	PROPN
ejpam-6388	322	9	u(ω	u(ω	PROPN
ejpam-6388	322	10	,	,	PUNCT
ejpam-6388	322	11	θ)|	θ)|	PROPN
ejpam-6388	322	12	≤	≤	PROPN
ejpam-6388	322	13	kε	kε	X
ejpam-6388	322	14	(	(	PUNCT
ejpam-6388	322	15	10	10	NUM
ejpam-6388	322	16	)	)	PUNCT
ejpam-6388	322	17	for	for	ADP
ejpam-6388	322	18	some	some	PRON
ejpam-6388	322	19	k	k	PROPN
ejpam-6388	322	20	>	>	X
ejpam-6388	322	21	0	0	PROPN
ejpam-6388	322	22	independent	independent	ADJ
ejpam-6388	322	23	of	of	ADP
ejpam-6388	322	24	ε	ε	PROPN
ejpam-6388	322	25	,	,	PUNCT
ejpam-6388	322	26	aligning	align	VERB
ejpam-6388	322	27	with	with	ADP
ejpam-6388	322	28	the	the	DET
ejpam-6388	322	29	methodology	methodology	NOUN
ejpam-6388	322	30	proposed	propose	VERB
ejpam-6388	322	31	in	in	ADP
ejpam-6388	322	32	[	[	X
ejpam-6388	322	33	3	3	NUM
ejpam-6388	322	34	]	]	PUNCT
ejpam-6388	322	35	(	(	PUNCT
ejpam-6388	322	36	section	section	NOUN
ejpam-6388	322	37	2.2.2	2.2.2	NUM
ejpam-6388	322	38	)	)	PUNCT
ejpam-6388	322	39	.	.	PUNCT
ejpam-6388	323	1	remark	remark	NOUN
ejpam-6388	323	2	6	6	NUM
ejpam-6388	323	3	.	.	PUNCT
ejpam-6388	324	1	we	we	PRON
ejpam-6388	324	2	say	say	VERB
ejpam-6388	324	3	that	that	SCONJ
ejpam-6388	324	4	r	r	NOUN
ejpam-6388	324	5	∈	∈	PROPN
ejpam-6388	324	6	a	a	PRON
ejpam-6388	324	7	is	be	AUX
ejpam-6388	324	8	a	a	DET
ejpam-6388	324	9	solution	solution	NOUN
ejpam-6388	324	10	of	of	ADP
ejpam-6388	324	11	the	the	DET
ejpam-6388	324	12	inequality	inequality	NOUN
ejpam-6388	324	13	(	(	PUNCT
ejpam-6388	324	14	8)	8)	NUM
ejpam-6388	324	15	provided	provide	VERB
ejpam-6388	324	16	there	there	PRON
ejpam-6388	324	17	exists	exist	VERB
ejpam-6388	324	18	a	a	DET
ejpam-6388	324	19	function	function	NOUN
ejpam-6388	324	20	ψ	ψ	X
ejpam-6388	324	21	∈	∈	PROPN
ejpam-6388	324	22	a	a	PRON
ejpam-6388	324	23	,	,	PUNCT
ejpam-6388	324	24	which	which	PRON
ejpam-6388	324	25	depends	depend	VERB
ejpam-6388	324	26	upon	upon	SCONJ
ejpam-6388	324	27	r	r	NOUN
ejpam-6388	324	28	,	,	PUNCT
ejpam-6388	324	29	such	such	ADJ
ejpam-6388	324	30	that	that	SCONJ
ejpam-6388	324	31	|ψ(ω)|	|ψ(ω)|	PROPN
ejpam-6388	324	32	≤	≤	ADJ
ejpam-6388	324	33	ε	ε	PROPN
ejpam-6388	324	34	and	and	CCONJ
ejpam-6388	324	35	rldy	rldy	NOUN
ejpam-6388	324	36	0	0	NUM
ejpam-6388	325	1	+	+	CCONJ
ejpam-6388	325	2	[	[	PUNCT
ejpam-6388	325	3	r(ω	r(ω	ADJ
ejpam-6388	325	4	)	)	PUNCT
ejpam-6388	325	5	f(ω	f(ω	PROPN
ejpam-6388	325	6	,	,	PUNCT
ejpam-6388	325	7	r(ω	r(ω	ADJ
ejpam-6388	325	8	)	)	PUNCT
ejpam-6388	325	9	)	)	PUNCT
ejpam-6388	325	10	]	]	PUNCT
ejpam-6388	326	1	+	+	CCONJ
ejpam-6388	326	2	g(ω	g(ω	PROPN
ejpam-6388	326	3	,	,	PUNCT
ejpam-6388	326	4	r(ω	r(ω	ADJ
ejpam-6388	326	5	)	)	PUNCT
ejpam-6388	326	6	)	)	PUNCT
ejpam-6388	327	1	=	=	SYM
ejpam-6388	327	2	ψ(ω	ψ(ω	PROPN
ejpam-6388	327	3	)	)	PUNCT
ejpam-6388	327	4	for	for	ADP
ejpam-6388	327	5	ω	ω	PROPN
ejpam-6388	327	6	∈	∈	PROPN
ejpam-6388	328	1	[	[	X
ejpam-6388	328	2	0	0	NUM
ejpam-6388	328	3	,	,	PUNCT
ejpam-6388	328	4	1	1	NUM
ejpam-6388	328	5	]	]	PUNCT
ejpam-6388	328	6	.	.	PUNCT
ejpam-6388	329	1	(	(	PUNCT
ejpam-6388	329	2	11	11	NUM
ejpam-6388	329	3	)	)	PUNCT
ejpam-6388	329	4	note	note	NOUN
ejpam-6388	329	5	that	that	SCONJ
ejpam-6388	329	6	r	r	NOUN
ejpam-6388	329	7	is	be	AUX
ejpam-6388	329	8	not	not	PART
ejpam-6388	329	9	required	require	VERB
ejpam-6388	329	10	to	to	PART
ejpam-6388	329	11	satisfy	satisfy	VERB
ejpam-6388	329	12	the	the	DET
ejpam-6388	329	13	original	original	ADJ
ejpam-6388	329	14	boundary	boundary	ADJ
ejpam-6388	329	15	condition	condition	NOUN
ejpam-6388	329	16	r(1	r(1	PROPN
ejpam-6388	329	17	)	)	PUNCT
ejpam-6388	330	1	=	=	PUNCT
ejpam-6388	330	2	f(1	f(1	PROPN
ejpam-6388	330	3	,	,	PUNCT
ejpam-6388	330	4	r(1	r(1	PROPN
ejpam-6388	330	5	)	)	PUNCT
ejpam-6388	330	6	)	)	PUNCT
ejpam-6388	330	7	,	,	PUNCT
ejpam-6388	330	8	avoiding	avoid	VERB
ejpam-6388	330	9	the	the	DET
ejpam-6388	330	10	mistake	mistake	NOUN
ejpam-6388	330	11	(	(	PUNCT
ejpam-6388	330	12	p2	p2	PROPN
ejpam-6388	330	13	)	)	PUNCT
ejpam-6388	330	14	highlighted	highlight	VERB
ejpam-6388	330	15	in	in	ADP
ejpam-6388	330	16	[	[	X
ejpam-6388	330	17	3	3	NUM
ejpam-6388	330	18	]	]	PUNCT
ejpam-6388	330	19	.	.	PUNCT
ejpam-6388	331	1	lemma	lemma	PROPN
ejpam-6388	331	2	5	5	X
ejpam-6388	331	3	.	.	PUNCT
ejpam-6388	332	1	let	let	VERB
ejpam-6388	332	2	r	r	NOUN
ejpam-6388	332	3	∈	∈	PROPN
ejpam-6388	332	4	a	a	DET
ejpam-6388	332	5	be	be	AUX
ejpam-6388	332	6	a	a	DET
ejpam-6388	332	7	solution	solution	NOUN
ejpam-6388	332	8	of	of	ADP
ejpam-6388	332	9	(	(	PUNCT
ejpam-6388	332	10	8)	8)	NUM
ejpam-6388	332	11	.	.	PUNCT
ejpam-6388	333	1	suppose	suppose	VERB
ejpam-6388	333	2	sup	sup	NOUN
ejpam-6388	333	3	ω∈[0,1	ω∈[0,1	ADV
ejpam-6388	333	4	]	]	PUNCT
ejpam-6388	333	5	|f(ω	|f(ω	NOUN
ejpam-6388	333	6	,	,	PUNCT
ejpam-6388	333	7	r(ω))|	r(ω))|	NOUN
ejpam-6388	333	8	≤	≤	X
ejpam-6388	333	9	q	q	NOUN
ejpam-6388	333	10	for	for	ADP
ejpam-6388	333	11	some	some	DET
ejpam-6388	333	12	q	q	NOUN
ejpam-6388	333	13	>	>	X
ejpam-6388	333	14	0	0	NUM
ejpam-6388	333	15	,	,	PUNCT
ejpam-6388	333	16	and	and	CCONJ
ejpam-6388	333	17	n	n	CCONJ
ejpam-6388	333	18	=	=	SYM
ejpam-6388	333	19	∫	∫	PROPN
ejpam-6388	333	20	1	1	NUM
ejpam-6388	333	21	0	0	NUM
ejpam-6388	333	22	0(ω	0(ω	NUM
ejpam-6388	333	23	,	,	PUNCT
ejpam-6388	333	24	ω	ω	NOUN
ejpam-6388	333	25	)	)	PUNCT
ejpam-6388	334	1	dω	dω	PROPN
ejpam-6388	334	2	.	.	PUNCT
ejpam-6388	335	1	then	then	ADV
ejpam-6388	335	2	the	the	DET
ejpam-6388	335	3	inequality∣∣∣∣r(ω)−	inequality∣∣∣∣r(ω)−	PROPN
ejpam-6388	335	4	f(ω	f(ω	PROPN
ejpam-6388	335	5	,	,	PUNCT
ejpam-6388	335	6	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	335	7	−	−	PROPN
ejpam-6388	335	8	f(ω	f(ω	PROPN
ejpam-6388	335	9	,	,	PUNCT
ejpam-6388	335	10	r(ω	r(ω	ADJ
ejpam-6388	335	11	)	)	PUNCT
ejpam-6388	335	12	)	)	PUNCT
ejpam-6388	335	13	∫	∫	PROPN
ejpam-6388	336	1	1	1	NUM
ejpam-6388	336	2	0	0	NUM
ejpam-6388	336	3	0(ω	0(ω	NUM
ejpam-6388	336	4	,	,	PUNCT
ejpam-6388	336	5	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	336	6	,	,	PUNCT
ejpam-6388	336	7	r(ξ	r(ξ	PROPN
ejpam-6388	336	8	)	)	PUNCT
ejpam-6388	336	9	)	)	PUNCT
ejpam-6388	337	1	dξ	dξ	PROPN
ejpam-6388	337	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	337	3	≤	≤	PROPN
ejpam-6388	337	4	nqε	nqε	NOUN
ejpam-6388	337	5	(	(	PUNCT
ejpam-6388	337	6	12	12	NUM
ejpam-6388	337	7	)	)	PUNCT
ejpam-6388	337	8	holds	hold	VERB
ejpam-6388	337	9	for	for	ADP
ejpam-6388	337	10	ω	ω	PROPN
ejpam-6388	337	11	∈	∈	PROPN
ejpam-6388	338	1	[	[	X
ejpam-6388	338	2	0	0	NUM
ejpam-6388	338	3	,	,	PUNCT
ejpam-6388	338	4	1	1	NUM
ejpam-6388	338	5	]	]	PUNCT
ejpam-6388	338	6	.	.	PUNCT
ejpam-6388	339	1	d.	d.	PROPN
ejpam-6388	339	2	baleanu	baleanu	PROPN
ejpam-6388	339	3	et	et	PROPN
ejpam-6388	339	4	al	al	PROPN
ejpam-6388	339	5	.	.	PUNCT
ejpam-6388	339	6	/	/	SYM
ejpam-6388	339	7	eur	eur	PROPN
ejpam-6388	339	8	.	.	PUNCT
ejpam-6388	340	1	j.	j.	PROPN
ejpam-6388	340	2	pure	pure	PROPN
ejpam-6388	340	3	appl	appl	PROPN
ejpam-6388	340	4	.	.	PROPN
ejpam-6388	340	5	math	math	PROPN
ejpam-6388	340	6	,	,	PUNCT
ejpam-6388	340	7	18	18	NUM
ejpam-6388	340	8	(	(	PUNCT
ejpam-6388	340	9	4	4	NUM
ejpam-6388	340	10	)	)	PUNCT
ejpam-6388	340	11	(	(	PUNCT
ejpam-6388	340	12	2025	2025	NUM
ejpam-6388	340	13	)	)	PUNCT
ejpam-6388	340	14	,	,	PUNCT
ejpam-6388	340	15	6388	6388	NUM
ejpam-6388	340	16	15	15	NUM
ejpam-6388	340	17	of	of	ADP
ejpam-6388	340	18	31	31	NUM
ejpam-6388	340	19	proof	proof	NOUN
ejpam-6388	340	20	.	.	PUNCT
ejpam-6388	341	1	from	from	ADP
ejpam-6388	341	2	remark	remark	NOUN
ejpam-6388	341	3	6	6	NUM
ejpam-6388	341	4	,	,	PUNCT
ejpam-6388	341	5	there	there	PRON
ejpam-6388	341	6	exists	exist	VERB
ejpam-6388	341	7	ψ(ω	ψ(ω	PROPN
ejpam-6388	341	8	)	)	PUNCT
ejpam-6388	341	9	with	with	ADP
ejpam-6388	341	10	|ψ(ω)|	|ψ(ω)|	PROPN
ejpam-6388	341	11	≤	≤	NUM
ejpam-6388	341	12	ε	ε	PROPN
ejpam-6388	341	13	such	such	ADJ
ejpam-6388	341	14	that	that	SCONJ
ejpam-6388	341	15	(	(	PUNCT
ejpam-6388	341	16	11	11	NUM
ejpam-6388	341	17	)	)	PUNCT
ejpam-6388	341	18	holds	hold	VERB
ejpam-6388	341	19	.	.	PUNCT
ejpam-6388	342	1	the	the	DET
ejpam-6388	342	2	integral	integral	ADJ
ejpam-6388	342	3	representation	representation	NOUN
ejpam-6388	342	4	for	for	ADP
ejpam-6388	342	5	a	a	DET
ejpam-6388	342	6	solution	solution	NOUN
ejpam-6388	342	7	z	z	X
ejpam-6388	342	8	of	of	ADP
ejpam-6388	342	9	(	(	PUNCT
ejpam-6388	342	10	11	11	NUM
ejpam-6388	342	11	)	)	PUNCT
ejpam-6388	342	12	with	with	ADP
ejpam-6388	342	13	boundary	boundary	ADJ
ejpam-6388	342	14	condition	condition	NOUN
ejpam-6388	342	15	z(0	z(0	NOUN
ejpam-6388	342	16	)	)	PUNCT
ejpam-6388	342	17	=	=	SYM
ejpam-6388	342	18	0	0	NUM
ejpam-6388	342	19	and	and	CCONJ
ejpam-6388	342	20	z(1	z(1	PROPN
ejpam-6388	342	21	)	)	PUNCT
ejpam-6388	342	22	=	=	SYM
ejpam-6388	342	23	f(1	f(1	PROPN
ejpam-6388	342	24	,	,	PUNCT
ejpam-6388	342	25	z(1	z(1	PROPN
ejpam-6388	342	26	)	)	PUNCT
ejpam-6388	342	27	)	)	PUNCT
ejpam-6388	343	1	+	+	CCONJ
ejpam-6388	343	2	θ	θ	NOUN
ejpam-6388	343	3	(	(	PUNCT
ejpam-6388	343	4	for	for	ADP
ejpam-6388	343	5	some	some	DET
ejpam-6388	343	6	θ	θ	NOUN
ejpam-6388	343	7	)	)	PUNCT
ejpam-6388	343	8	is	be	AUX
ejpam-6388	343	9	given	give	VERB
ejpam-6388	343	10	by	by	ADP
ejpam-6388	343	11	z(ω	z(ω	NUM
ejpam-6388	343	12	)	)	PUNCT
ejpam-6388	343	13	=	=	SYM
ejpam-6388	343	14	f(ω	f(ω	PROPN
ejpam-6388	343	15	,	,	PUNCT
ejpam-6388	343	16	z(ω))ωy−1+f(ω	z(ω))ωy−1+f(ω	NOUN
ejpam-6388	343	17	,	,	PUNCT
ejpam-6388	343	18	z(ω	z(ω	NUM
ejpam-6388	343	19	)	)	PUNCT
ejpam-6388	343	20	)	)	PUNCT
ejpam-6388	343	21	∫	∫	PROPN
ejpam-6388	344	1	1	1	NUM
ejpam-6388	344	2	0	0	NUM
ejpam-6388	344	3	0(ω	0(ω	NUM
ejpam-6388	344	4	,	,	PUNCT
ejpam-6388	344	5	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	344	6	,	,	PUNCT
ejpam-6388	344	7	z(ξ	z(ξ	NOUN
ejpam-6388	344	8	)	)	PUNCT
ejpam-6388	344	9	)	)	PUNCT
ejpam-6388	345	1	dξ−f(ω	dξ−f(ω	NOUN
ejpam-6388	345	2	,	,	PUNCT
ejpam-6388	345	3	z(ω	z(ω	NUM
ejpam-6388	345	4	)	)	PUNCT
ejpam-6388	345	5	)	)	PUNCT
ejpam-6388	346	1	∫	∫	PROPN
ejpam-6388	347	1	1	1	NUM
ejpam-6388	347	2	0	0	NUM
ejpam-6388	347	3	0(ω	0(ω	NUM
ejpam-6388	347	4	,	,	PUNCT
ejpam-6388	347	5	ξ)ψ(ξ	ξ)ψ(ξ	NUM
ejpam-6388	347	6	)	)	PUNCT
ejpam-6388	348	1	dξ	dξ	PROPN
ejpam-6388	348	2	.	.	PUNCT
ejpam-6388	349	1	since	since	SCONJ
ejpam-6388	349	2	r	r	NOUN
ejpam-6388	349	3	does	do	AUX
ejpam-6388	349	4	not	not	PART
ejpam-6388	349	5	necessarily	necessarily	ADV
ejpam-6388	349	6	satisfy	satisfy	VERB
ejpam-6388	349	7	the	the	DET
ejpam-6388	349	8	original	original	ADJ
ejpam-6388	349	9	bc	bc	PROPN
ejpam-6388	349	10	,	,	PUNCT
ejpam-6388	349	11	we	we	PRON
ejpam-6388	349	12	consider	consider	VERB
ejpam-6388	349	13	the	the	DET
ejpam-6388	349	14	perturbation	perturbation	NOUN
ejpam-6388	349	15	.	.	PUNCT
ejpam-6388	350	1	substituting	substitute	VERB
ejpam-6388	350	2	ψ(ω	ψ(ω	PROPN
ejpam-6388	350	3	)	)	PUNCT
ejpam-6388	350	4	into	into	ADP
ejpam-6388	350	5	the	the	DET
ejpam-6388	350	6	integral	integral	ADJ
ejpam-6388	350	7	form	form	NOUN
ejpam-6388	350	8	and	and	CCONJ
ejpam-6388	350	9	using	use	VERB
ejpam-6388	350	10	the	the	DET
ejpam-6388	350	11	bound	bound	ADJ
ejpam-6388	350	12	|ψ(ξ)|	|ψ(ξ)|	PROPN
ejpam-6388	350	13	≤	≤	NUM
ejpam-6388	350	14	ε	ε	PROPN
ejpam-6388	350	15	,	,	PUNCT
ejpam-6388	350	16	we	we	PRON
ejpam-6388	350	17	get∣∣∣∣r(ω)−	get∣∣∣∣r(ω)−	AUX
ejpam-6388	350	18	f(ω	f(ω	PROPN
ejpam-6388	350	19	,	,	PUNCT
ejpam-6388	350	20	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	350	21	−	−	PROPN
ejpam-6388	350	22	f(ω	f(ω	PROPN
ejpam-6388	350	23	,	,	PUNCT
ejpam-6388	350	24	r(ω	r(ω	ADJ
ejpam-6388	350	25	)	)	PUNCT
ejpam-6388	350	26	)	)	PUNCT
ejpam-6388	351	1	∫	∫	PROPN
ejpam-6388	351	2	1	1	NUM
ejpam-6388	351	3	0	0	NUM
ejpam-6388	351	4	0(ω	0(ω	NUM
ejpam-6388	351	5	,	,	PUNCT
ejpam-6388	351	6	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	351	7	,	,	PUNCT
ejpam-6388	351	8	r(ξ	r(ξ	PROPN
ejpam-6388	351	9	)	)	PUNCT
ejpam-6388	351	10	)	)	PUNCT
ejpam-6388	352	1	dξ	dξ	PROPN
ejpam-6388	352	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	352	3	≤	≤	PROPN
ejpam-6388	352	4	|f(ω	|f(ω	NOUN
ejpam-6388	352	5	,	,	PUNCT
ejpam-6388	352	6	r(ω))|	r(ω))|	X
ejpam-6388	352	7	∫	∫	PROPN
ejpam-6388	352	8	1	1	NUM
ejpam-6388	352	9	0	0	NUM
ejpam-6388	353	1	|0(ω	|0(ω	ADJ
ejpam-6388	353	2	,	,	PUNCT
ejpam-6388	353	3	ξ)||ψ(ξ)|	ξ)||ψ(ξ)|	PROPN
ejpam-6388	353	4	dξ	dξ	NOUN
ejpam-6388	353	5	.	.	PUNCT
ejpam-6388	354	1	using	use	VERB
ejpam-6388	354	2	|0(ω	|0(ω	ADJ
ejpam-6388	354	3	,	,	PUNCT
ejpam-6388	354	4	ξ)|	ξ)|	ADJ
ejpam-6388	354	5	≤	≤	NOUN
ejpam-6388	354	6	0(ξ	0(ξ	NUM
ejpam-6388	354	7	,	,	PUNCT
ejpam-6388	354	8	ξ	ξ	X
ejpam-6388	354	9	)	)	PUNCT
ejpam-6388	354	10	(	(	PUNCT
ejpam-6388	354	11	by	by	ADP
ejpam-6388	354	12	the	the	DET
ejpam-6388	354	13	definition	definition	NOUN
ejpam-6388	354	14	of	of	ADP
ejpam-6388	354	15	0	0	NUM
ejpam-6388	354	16	)	)	PUNCT
ejpam-6388	354	17	and	and	CCONJ
ejpam-6388	354	18	|ψ(ξ)|	|ψ(ξ)|	PROPN
ejpam-6388	354	19	≤	≤	NUM
ejpam-6388	354	20	ε	ε	PROPN
ejpam-6388	354	21	,	,	PUNCT
ejpam-6388	354	22	we	we	PRON
ejpam-6388	354	23	have∫	have∫	VERB
ejpam-6388	354	24	1	1	NUM
ejpam-6388	354	25	0	0	NUM
ejpam-6388	354	26	|0(ω	|0(ω	ADJ
ejpam-6388	354	27	,	,	PUNCT
ejpam-6388	354	28	ξ)||ψ(ξ)|	ξ)||ψ(ξ)|	PROPN
ejpam-6388	354	29	dξ	dξ	PROPN
ejpam-6388	354	30	≤	≤	PROPN
ejpam-6388	354	31	ε	ε	PROPN
ejpam-6388	354	32	∫	∫	PROPN
ejpam-6388	354	33	1	1	NUM
ejpam-6388	354	34	0	0	NUM
ejpam-6388	354	35	0(ξ	0(ξ	NUM
ejpam-6388	354	36	,	,	PUNCT
ejpam-6388	354	37	ξ	ξ	X
ejpam-6388	354	38	)	)	PUNCT
ejpam-6388	354	39	dξ	dξ	PROPN
ejpam-6388	355	1	=	=	PUNCT
ejpam-6388	355	2	nε	nε	PROPN
ejpam-6388	355	3	.	.	PUNCT
ejpam-6388	356	1	thus	thus	ADV
ejpam-6388	356	2	,	,	PUNCT
ejpam-6388	356	3	∣∣∣∣r(ω)−	∣∣∣∣r(ω)−	ADP
ejpam-6388	356	4	f(ω	f(ω	PROPN
ejpam-6388	356	5	,	,	PUNCT
ejpam-6388	356	6	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	356	7	−	−	PROPN
ejpam-6388	356	8	f(ω	f(ω	PROPN
ejpam-6388	356	9	,	,	PUNCT
ejpam-6388	356	10	r(ω	r(ω	ADJ
ejpam-6388	356	11	)	)	PUNCT
ejpam-6388	356	12	)	)	PUNCT
ejpam-6388	356	13	∫	∫	PROPN
ejpam-6388	357	1	1	1	NUM
ejpam-6388	357	2	0	0	NUM
ejpam-6388	357	3	0(ω	0(ω	NUM
ejpam-6388	357	4	,	,	PUNCT
ejpam-6388	357	5	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	357	6	,	,	PUNCT
ejpam-6388	357	7	r(ξ	r(ξ	PROPN
ejpam-6388	357	8	)	)	PUNCT
ejpam-6388	357	9	)	)	PUNCT
ejpam-6388	358	1	dξ	dξ	PROPN
ejpam-6388	358	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	358	3	≤	≤	NUM
ejpam-6388	358	4	qnε	qnε	NOUN
ejpam-6388	358	5	,	,	PUNCT
ejpam-6388	358	6	completing	complete	VERB
ejpam-6388	358	7	the	the	DET
ejpam-6388	358	8	proof	proof	NOUN
ejpam-6388	358	9	.	.	PUNCT
ejpam-6388	359	1	theorem	theorem	ADJ
ejpam-6388	359	2	5	5	NUM
ejpam-6388	359	3	.	.	PUNCT
ejpam-6388	360	1	suppose	suppose	VERB
ejpam-6388	360	2	(	(	PUNCT
ejpam-6388	360	3	b1	b1	NOUN
ejpam-6388	360	4	)	)	PUNCT
ejpam-6388	360	5	and	and	CCONJ
ejpam-6388	360	6	(	(	PUNCT
ejpam-6388	360	7	b2	b2	NOUN
ejpam-6388	360	8	)	)	PUNCT
ejpam-6388	360	9	hold	hold	NOUN
ejpam-6388	360	10	,	,	PUNCT
ejpam-6388	360	11	where	where	SCONJ
ejpam-6388	360	12	(	(	PUNCT
ejpam-6388	360	13	b1	b1	NOUN
ejpam-6388	360	14	)	)	PUNCT
ejpam-6388	360	15	ensures	ensure	VERB
ejpam-6388	360	16	the	the	DET
ejpam-6388	360	17	existence	existence	NOUN
ejpam-6388	360	18	and	and	CCONJ
ejpam-6388	360	19	uniqueness	uniqueness	NOUN
ejpam-6388	360	20	of	of	ADP
ejpam-6388	360	21	u(ω	u(ω	PROPN
ejpam-6388	360	22	,	,	PUNCT
ejpam-6388	360	23	θ	θ	NOUN
ejpam-6388	360	24	)	)	PUNCT
ejpam-6388	360	25	for	for	ADP
ejpam-6388	360	26	the	the	DET
ejpam-6388	360	27	modified	modify	VERB
ejpam-6388	360	28	fhbvp	fhbvp	NOUN
ejpam-6388	360	29	(	(	PUNCT
ejpam-6388	360	30	1)–(9	1)–(9	NOUN
ejpam-6388	360	31	)	)	PUNCT
ejpam-6388	360	32	for	for	ADP
ejpam-6388	360	33	any	any	DET
ejpam-6388	360	34	θ	θ	NOUN
ejpam-6388	360	35	,	,	PUNCT
ejpam-6388	360	36	and	and	CCONJ
ejpam-6388	360	37	(	(	PUNCT
ejpam-6388	360	38	b2	b2	NOUN
ejpam-6388	360	39	)	)	PUNCT
ejpam-6388	360	40	provides	provide	VERB
ejpam-6388	360	41	lipschitz	lipschitz	NOUN
ejpam-6388	360	42	conditions	condition	NOUN
ejpam-6388	360	43	on	on	ADP
ejpam-6388	360	44	f	f	PROPN
ejpam-6388	360	45	and	and	CCONJ
ejpam-6388	360	46	g	g	NOUN
ejpam-6388	360	47	with	with	ADP
ejpam-6388	360	48	constants	constant	NOUN
ejpam-6388	360	49	lf	lf	ADP
ejpam-6388	360	50	and	and	CCONJ
ejpam-6388	360	51	lg	lg	PROPN
ejpam-6388	360	52	.	.	PROPN
ejpam-6388	360	53	further	far	ADV
ejpam-6388	360	54	,	,	PUNCT
ejpam-6388	360	55	suppose	suppose	VERB
ejpam-6388	360	56	nq	nq	X
ejpam-6388	360	57	<	<	X
ejpam-6388	360	58	1	1	NUM
ejpam-6388	360	59	,	,	PUNCT
ejpam-6388	360	60	where	where	SCONJ
ejpam-6388	360	61	q	q	NOUN
ejpam-6388	360	62	=	=	NOUN
ejpam-6388	360	63	sup	sup	NOUN
ejpam-6388	360	64	ω∈[0,1	ω∈[0,1	NUM
ejpam-6388	360	65	]	]	X
ejpam-6388	360	66	|f(ω	|f(ω	NOUN
ejpam-6388	360	67	,	,	PUNCT
ejpam-6388	360	68	r(ω))|	r(ω))|	NOUN
ejpam-6388	360	69	and	and	CCONJ
ejpam-6388	360	70	n	n	NOUN
ejpam-6388	360	71	=	=	SYM
ejpam-6388	360	72	∫	∫	PROPN
ejpam-6388	360	73	1	1	NUM
ejpam-6388	360	74	0	0	NUM
ejpam-6388	360	75	0(ω	0(ω	NUM
ejpam-6388	360	76	,	,	PUNCT
ejpam-6388	360	77	ω	ω	NOUN
ejpam-6388	360	78	)	)	PUNCT
ejpam-6388	360	79	dω	dω	PROPN
ejpam-6388	360	80	.	.	PUNCT
ejpam-6388	361	1	then	then	ADV
ejpam-6388	361	2	the	the	DET
ejpam-6388	361	3	fhbvp	fhbvp	NOUN
ejpam-6388	361	4	(	(	PUNCT
ejpam-6388	361	5	1)–(2	1)–(2	NUM
ejpam-6388	361	6	)	)	PUNCT
ejpam-6388	361	7	is	be	AUX
ejpam-6388	361	8	hyers	hyer	NOUN
ejpam-6388	361	9	–	–	PUNCT
ejpam-6388	361	10	ulam	ulam	X
ejpam-6388	361	11	stable	stable	ADJ
ejpam-6388	361	12	.	.	PUNCT
ejpam-6388	362	1	proof	proof	NOUN
ejpam-6388	362	2	.	.	PUNCT
ejpam-6388	363	1	assume	assume	VERB
ejpam-6388	363	2	r	r	NOUN
ejpam-6388	363	3	∈	∈	PROPN
ejpam-6388	363	4	a	a	DET
ejpam-6388	363	5	fulfills	fulfill	VERB
ejpam-6388	363	6	the	the	DET
ejpam-6388	363	7	condition	condition	NOUN
ejpam-6388	363	8	given	give	VERB
ejpam-6388	363	9	in	in	ADP
ejpam-6388	363	10	inequality	inequality	NOUN
ejpam-6388	363	11	(	(	PUNCT
ejpam-6388	363	12	8)	8)	NUM
ejpam-6388	363	13	,	,	PUNCT
ejpam-6388	363	14	and	and	CCONJ
ejpam-6388	363	15	let	let	VERB
ejpam-6388	363	16	u(ω	u(ω	PROPN
ejpam-6388	363	17	,	,	PUNCT
ejpam-6388	363	18	θ	θ	NOUN
ejpam-6388	363	19	)	)	PUNCT
ejpam-6388	363	20	∈	∈	PROPN
ejpam-6388	363	21	a	a	DET
ejpam-6388	363	22	denote	denote	NOUN
ejpam-6388	363	23	the	the	DET
ejpam-6388	363	24	unique	unique	ADJ
ejpam-6388	363	25	solution	solution	NOUN
ejpam-6388	363	26	to	to	ADP
ejpam-6388	363	27	the	the	DET
ejpam-6388	363	28	modified	modify	VERB
ejpam-6388	363	29	fhbvp	fhbvp	NOUN
ejpam-6388	363	30	(	(	PUNCT
ejpam-6388	363	31	1)–(9	1)–(9	NOUN
ejpam-6388	363	32	)	)	PUNCT
ejpam-6388	363	33	with	with	ADP
ejpam-6388	363	34	θ	θ	PROPN
ejpam-6388	363	35	=	=	SYM
ejpam-6388	363	36	r(1	r(1	PROPN
ejpam-6388	363	37	)	)	PUNCT
ejpam-6388	364	1	−	−	PROPN
ejpam-6388	365	1	f(1	f(1	PROPN
ejpam-6388	365	2	,	,	PUNCT
ejpam-6388	365	3	r(1	r(1	PROPN
ejpam-6388	365	4	)	)	PUNCT
ejpam-6388	365	5	)	)	PUNCT
ejpam-6388	365	6	.	.	PUNCT
ejpam-6388	366	1	in	in	ADP
ejpam-6388	366	2	the	the	DET
ejpam-6388	366	3	view	view	NOUN
ejpam-6388	366	4	of	of	ADP
ejpam-6388	366	5	lemma	lemma	PROPN
ejpam-6388	366	6	5	5	NUM
ejpam-6388	366	7	,	,	PUNCT
ejpam-6388	366	8	we	we	PRON
ejpam-6388	366	9	have∣∣∣∣r(ω)−	have∣∣∣∣r(ω)−	PROPN
ejpam-6388	366	10	f(ω	f(ω	PROPN
ejpam-6388	366	11	,	,	PUNCT
ejpam-6388	366	12	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	366	13	−	−	PROPN
ejpam-6388	366	14	f(ω	f(ω	PROPN
ejpam-6388	366	15	,	,	PUNCT
ejpam-6388	366	16	r(ω	r(ω	ADJ
ejpam-6388	366	17	)	)	PUNCT
ejpam-6388	366	18	)	)	PUNCT
ejpam-6388	366	19	∫	∫	PROPN
ejpam-6388	367	1	1	1	NUM
ejpam-6388	367	2	0	0	NUM
ejpam-6388	367	3	0(ω	0(ω	NUM
ejpam-6388	367	4	,	,	PUNCT
ejpam-6388	367	5	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	367	6	,	,	PUNCT
ejpam-6388	367	7	r(ξ	r(ξ	PROPN
ejpam-6388	367	8	)	)	PUNCT
ejpam-6388	367	9	)	)	PUNCT
ejpam-6388	368	1	dξ	dξ	PROPN
ejpam-6388	368	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6388	368	3	≤	≤	PUNCT
ejpam-6388	368	4	nqε	nqε	PROPN
ejpam-6388	368	5	.	.	PUNCT
ejpam-6388	369	1	the	the	DET
ejpam-6388	369	2	exact	exact	ADJ
ejpam-6388	369	3	solution	solution	NOUN
ejpam-6388	369	4	u(ω	u(ω	PROPN
ejpam-6388	369	5	,	,	PUNCT
ejpam-6388	369	6	θ	θ	NOUN
ejpam-6388	369	7	)	)	PUNCT
ejpam-6388	369	8	satisfies	satisfie	NOUN
ejpam-6388	369	9	u(ω	u(ω	PROPN
ejpam-6388	369	10	,	,	PUNCT
ejpam-6388	369	11	θ	θ	NOUN
ejpam-6388	369	12	)	)	PUNCT
ejpam-6388	369	13	=	=	SYM
ejpam-6388	369	14	f(ω	f(ω	PROPN
ejpam-6388	369	15	,	,	PUNCT
ejpam-6388	369	16	u(ω	u(ω	PROPN
ejpam-6388	369	17	,	,	PUNCT
ejpam-6388	369	18	θ))ωy−1	θ))ωy−1	PROPN
ejpam-6388	369	19	+	+	CCONJ
ejpam-6388	369	20	f(ω	f(ω	PROPN
ejpam-6388	369	21	,	,	PUNCT
ejpam-6388	369	22	u(ω	u(ω	PROPN
ejpam-6388	369	23	,	,	PUNCT
ejpam-6388	369	24	θ	θ	NOUN
ejpam-6388	369	25	)	)	PUNCT
ejpam-6388	369	26	)	)	PUNCT
ejpam-6388	369	27	∫	∫	PROPN
ejpam-6388	370	1	1	1	NUM
ejpam-6388	370	2	0	0	NUM
ejpam-6388	370	3	0(ω	0(ω	NUM
ejpam-6388	370	4	,	,	PUNCT
ejpam-6388	370	5	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	370	6	,	,	PUNCT
ejpam-6388	370	7	u(ξ	u(ξ	NOUN
ejpam-6388	370	8	,	,	PUNCT
ejpam-6388	370	9	θ	θ	NOUN
ejpam-6388	370	10	)	)	PUNCT
ejpam-6388	370	11	)	)	PUNCT
ejpam-6388	371	1	dξ	dξ	PROPN
ejpam-6388	371	2	.	.	PUNCT
ejpam-6388	372	1	d.	d.	PROPN
ejpam-6388	372	2	baleanu	baleanu	PROPN
ejpam-6388	372	3	et	et	PROPN
ejpam-6388	372	4	al	al	PROPN
ejpam-6388	372	5	.	.	PUNCT
ejpam-6388	372	6	/	/	SYM
ejpam-6388	372	7	eur	eur	PROPN
ejpam-6388	372	8	.	.	PUNCT
ejpam-6388	373	1	j.	j.	PROPN
ejpam-6388	373	2	pure	pure	PROPN
ejpam-6388	373	3	appl	appl	PROPN
ejpam-6388	373	4	.	.	PROPN
ejpam-6388	373	5	math	math	PROPN
ejpam-6388	373	6	,	,	PUNCT
ejpam-6388	373	7	18	18	NUM
ejpam-6388	373	8	(	(	PUNCT
ejpam-6388	373	9	4	4	NUM
ejpam-6388	373	10	)	)	PUNCT
ejpam-6388	373	11	(	(	PUNCT
ejpam-6388	373	12	2025	2025	NUM
ejpam-6388	373	13	)	)	PUNCT
ejpam-6388	373	14	,	,	PUNCT
ejpam-6388	373	15	6388	6388	NUM
ejpam-6388	373	16	16	16	NUM
ejpam-6388	373	17	of	of	ADP
ejpam-6388	373	18	31	31	NUM
ejpam-6388	373	19	consider	consider	VERB
ejpam-6388	373	20	the	the	DET
ejpam-6388	373	21	difference	difference	NOUN
ejpam-6388	373	22	|r(ω)−	|r(ω)−	NOUN
ejpam-6388	373	23	u(ω	u(ω	PROPN
ejpam-6388	373	24	,	,	PUNCT
ejpam-6388	373	25	θ)|	θ)|	PROPN
ejpam-6388	373	26	≤	≤	NOUN
ejpam-6388	373	27	∣∣∣∣r(ω)−	∣∣∣∣r(ω)−	ADP
ejpam-6388	373	28	f(ω	f(ω	PROPN
ejpam-6388	373	29	,	,	PUNCT
ejpam-6388	373	30	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	373	31	−	−	PROPN
ejpam-6388	373	32	f(ω	f(ω	PROPN
ejpam-6388	373	33	,	,	PUNCT
ejpam-6388	373	34	r(ω	r(ω	ADJ
ejpam-6388	373	35	)	)	PUNCT
ejpam-6388	373	36	)	)	PUNCT
ejpam-6388	374	1	∫	∫	PROPN
ejpam-6388	374	2	1	1	NUM
ejpam-6388	374	3	0	0	NUM
ejpam-6388	374	4	0(ω	0(ω	NUM
ejpam-6388	374	5	,	,	PUNCT
ejpam-6388	374	6	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	374	7	,	,	PUNCT
ejpam-6388	374	8	r(ξ	r(ξ	PROPN
ejpam-6388	374	9	)	)	PUNCT
ejpam-6388	374	10	)	)	PUNCT
ejpam-6388	375	1	dξ	dξ	PROPN
ejpam-6388	375	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	375	3	+	+	CCONJ
ejpam-6388	375	4	∣∣∣∣f(ω	∣∣∣∣f(ω	PROPN
ejpam-6388	375	5	,	,	PUNCT
ejpam-6388	375	6	r(ω))ωy−1	r(ω))ωy−1	PROPN
ejpam-6388	375	7	+	+	CCONJ
ejpam-6388	375	8	f(ω	f(ω	PROPN
ejpam-6388	375	9	,	,	PUNCT
ejpam-6388	375	10	r(ω	r(ω	ADJ
ejpam-6388	375	11	)	)	PUNCT
ejpam-6388	375	12	)	)	PUNCT
ejpam-6388	376	1	∫	∫	PROPN
ejpam-6388	376	2	1	1	NUM
ejpam-6388	376	3	0	0	NUM
ejpam-6388	376	4	0(ω	0(ω	NUM
ejpam-6388	376	5	,	,	PUNCT
ejpam-6388	376	6	ξ)g(ξ	ξ)g(ξ	NOUN
ejpam-6388	376	7	,	,	PUNCT
ejpam-6388	376	8	r(ξ	r(ξ	PROPN
ejpam-6388	376	9	)	)	PUNCT
ejpam-6388	376	10	)	)	PUNCT
ejpam-6388	377	1	dξ	dξ	PROPN
ejpam-6388	377	2	−f(ω	−f(ω	PROPN
ejpam-6388	377	3	,	,	PUNCT
ejpam-6388	377	4	u(ω	u(ω	PROPN
ejpam-6388	377	5	,	,	PUNCT
ejpam-6388	377	6	θ))ωy−1	θ))ωy−1	PROPN
ejpam-6388	377	7	−	−	PROPN
ejpam-6388	377	8	f(ω	f(ω	PROPN
ejpam-6388	377	9	,	,	PUNCT
ejpam-6388	377	10	u(ω	u(ω	PROPN
ejpam-6388	377	11	,	,	PUNCT
ejpam-6388	377	12	θ	θ	NOUN
ejpam-6388	377	13	)	)	PUNCT
ejpam-6388	377	14	)	)	PUNCT
ejpam-6388	377	15	∫	∫	PROPN
ejpam-6388	378	1	1	1	NUM
ejpam-6388	378	2	0	0	NUM
ejpam-6388	378	3	0(ω	0(ω	NUM
ejpam-6388	378	4	,	,	PUNCT
ejpam-6388	378	5	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	378	6	,	,	PUNCT
ejpam-6388	378	7	u(ξ	u(ξ	NOUN
ejpam-6388	378	8	,	,	PUNCT
ejpam-6388	378	9	θ	θ	NOUN
ejpam-6388	378	10	)	)	PUNCT
ejpam-6388	378	11	)	)	PUNCT
ejpam-6388	379	1	dξ	dξ	PROPN
ejpam-6388	379	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	379	3	.	.	PUNCT
ejpam-6388	380	1	using	use	VERB
ejpam-6388	380	2	the	the	DET
ejpam-6388	380	3	lipschitz	lipschitz	NOUN
ejpam-6388	380	4	condition	condition	NOUN
ejpam-6388	380	5	|f(ω	|f(ω	NOUN
ejpam-6388	380	6	,	,	PUNCT
ejpam-6388	380	7	r	r	NOUN
ejpam-6388	380	8	)	)	PUNCT
ejpam-6388	380	9	−	−	PROPN
ejpam-6388	381	1	f(ω	f(ω	PROPN
ejpam-6388	381	2	,	,	PUNCT
ejpam-6388	381	3	u)|	u)|	NOUN
ejpam-6388	381	4	≤	≤	NUM
ejpam-6388	381	5	lf|r	lf|r	PUNCT
ejpam-6388	382	1	−	−	PROPN
ejpam-6388	383	1	u|	u|	PROPN
ejpam-6388	383	2	and	and	CCONJ
ejpam-6388	383	3	|g(ξ	|g(ξ	NOUN
ejpam-6388	383	4	,	,	PUNCT
ejpam-6388	383	5	r	r	NOUN
ejpam-6388	383	6	)	)	PUNCT
ejpam-6388	383	7	−	−	PROPN
ejpam-6388	384	1	g(ξ	g(ξ	PROPN
ejpam-6388	384	2	,	,	PUNCT
ejpam-6388	384	3	u)|	u)|	NOUN
ejpam-6388	384	4	≤	≤	NOUN
ejpam-6388	384	5	lg|r−	lg|r−	PUNCT
ejpam-6388	384	6	u|	u|	NOUN
ejpam-6388	384	7	,	,	PUNCT
ejpam-6388	384	8	and	and	CCONJ
ejpam-6388	384	9	bounding	bound	VERB
ejpam-6388	384	10	the	the	DET
ejpam-6388	384	11	integral	integral	ADJ
ejpam-6388	384	12	term	term	NOUN
ejpam-6388	384	13	,	,	PUNCT
ejpam-6388	384	14	we	we	PRON
ejpam-6388	384	15	get∣∣∣∣f(ω	get∣∣∣∣f(ω	VERB
ejpam-6388	384	16	,	,	PUNCT
ejpam-6388	384	17	r(ω	r(ω	ADJ
ejpam-6388	384	18	)	)	PUNCT
ejpam-6388	384	19	)	)	PUNCT
ejpam-6388	385	1	∫	∫	PROPN
ejpam-6388	385	2	1	1	NUM
ejpam-6388	385	3	0	0	NUM
ejpam-6388	385	4	0(ω	0(ω	NUM
ejpam-6388	385	5	,	,	PUNCT
ejpam-6388	385	6	ξ)[g(ξ	ξ)[g(ξ	PROPN
ejpam-6388	385	7	,	,	PUNCT
ejpam-6388	385	8	r(ξ))−	r(ξ))−	PROPN
ejpam-6388	385	9	g(ξ	g(ξ	PROPN
ejpam-6388	385	10	,	,	PUNCT
ejpam-6388	385	11	u(ξ	u(ξ	NOUN
ejpam-6388	385	12	,	,	PUNCT
ejpam-6388	385	13	θ	θ	NOUN
ejpam-6388	385	14	)	)	PUNCT
ejpam-6388	385	15	)	)	PUNCT
ejpam-6388	385	16	]	]	PUNCT
ejpam-6388	386	1	dξ	dξ	PROPN
ejpam-6388	386	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6388	386	3	≤	≤	PROPN
ejpam-6388	386	4	qlgn|r−	qlgn|r−	NOUN
ejpam-6388	386	5	u|	u|	PROPN
ejpam-6388	386	6	.	.	PUNCT
ejpam-6388	387	1	thus	thus	ADV
ejpam-6388	387	2	,	,	PUNCT
ejpam-6388	387	3	|r(ω)−	|r(ω)−	PROPN
ejpam-6388	387	4	u(ω	u(ω	PROPN
ejpam-6388	387	5	,	,	PUNCT
ejpam-6388	387	6	θ)|	θ)|	PROPN
ejpam-6388	387	7	≤	≤	PROPN
ejpam-6388	387	8	nqε+	nqε+	NOUN
ejpam-6388	387	9	lfω	lfω	VERB
ejpam-6388	387	10	y−1|r−	y−1|r−	PROPN
ejpam-6388	387	11	u|+	u|+	PROPN
ejpam-6388	387	12	qlgn|r−	qlgn|r−	NOUN
ejpam-6388	387	13	u|	u|	PROPN
ejpam-6388	387	14	.	.	PUNCT
ejpam-6388	388	1	now	now	ADV
ejpam-6388	388	2	,	,	PUNCT
ejpam-6388	388	3	taking	take	VERB
ejpam-6388	388	4	supremum	supremum	ADV
ejpam-6388	388	5	over	over	ADP
ejpam-6388	388	6	ω	ω	PROPN
ejpam-6388	388	7	∈	∈	PROPN
ejpam-6388	389	1	[	[	X
ejpam-6388	389	2	0	0	NUM
ejpam-6388	389	3	,	,	PUNCT
ejpam-6388	389	4	1	1	NUM
ejpam-6388	389	5	]	]	PUNCT
ejpam-6388	389	6	,	,	PUNCT
ejpam-6388	389	7	we	we	PRON
ejpam-6388	389	8	get	get	VERB
ejpam-6388	389	9	∥r−	∥r−	PRON
ejpam-6388	389	10	u∥	u∥	PROPN
ejpam-6388	389	11	≤	≤	NUM
ejpam-6388	389	12	nqε+m∥r−	nqε+m∥r−	PROPN
ejpam-6388	389	13	u∥	u∥	NOUN
ejpam-6388	389	14	,	,	PUNCT
ejpam-6388	389	15	where	where	SCONJ
ejpam-6388	389	16	m	m	VERB
ejpam-6388	389	17	=	=	VERB
ejpam-6388	389	18	supω(lfω	supω(lfω	PROPN
ejpam-6388	389	19	y−1	y−1	PROPN
ejpam-6388	389	20	+	+	CCONJ
ejpam-6388	389	21	qlgn	qlgn	PROPN
ejpam-6388	389	22	)	)	PUNCT
ejpam-6388	389	23	.	.	PUNCT
ejpam-6388	390	1	since	since	SCONJ
ejpam-6388	390	2	nq	nq	PROPN
ejpam-6388	390	3	<	<	X
ejpam-6388	390	4	1	1	NUM
ejpam-6388	390	5	,	,	PUNCT
ejpam-6388	390	6	we	we	PRON
ejpam-6388	390	7	have	have	VERB
ejpam-6388	390	8	∥r−	∥r−	NUM
ejpam-6388	390	9	u∥(1−m	u∥(1−m	NOUN
ejpam-6388	390	10	)	)	PUNCT
ejpam-6388	390	11	≤	≤	NOUN
ejpam-6388	390	12	nqε	nqε	NOUN
ejpam-6388	390	13	,	,	PUNCT
ejpam-6388	390	14	which	which	PRON
ejpam-6388	390	15	yields	yield	VERB
ejpam-6388	390	16	∥r−	∥r−	PRON
ejpam-6388	390	17	u∥	u∥	PROPN
ejpam-6388	390	18	≤	≤	NUM
ejpam-6388	390	19	nq	nq	PROPN
ejpam-6388	390	20	1−m	1−m	NUM
ejpam-6388	390	21	ε	ε	PROPN
ejpam-6388	390	22	,	,	PUNCT
ejpam-6388	390	23	where	where	SCONJ
ejpam-6388	390	24	k	k	PROPN
ejpam-6388	390	25	=	=	PUNCT
ejpam-6388	390	26	nq	nq	PROPN
ejpam-6388	390	27	1−m	1−m	NUM
ejpam-6388	390	28	>	>	X
ejpam-6388	390	29	0	0	PUNCT
ejpam-6388	391	1	if	if	SCONJ
ejpam-6388	391	2	m	m	VERB
ejpam-6388	391	3	<	<	X
ejpam-6388	391	4	1	1	X
ejpam-6388	391	5	.	.	PUNCT
ejpam-6388	392	1	under	under	ADP
ejpam-6388	392	2	(	(	PUNCT
ejpam-6388	392	3	b2	b2	NOUN
ejpam-6388	392	4	)	)	PUNCT
ejpam-6388	392	5	,	,	PUNCT
ejpam-6388	392	6	ensure	ensure	VERB
ejpam-6388	392	7	m	m	PRON
ejpam-6388	392	8	<	<	X
ejpam-6388	392	9	1	1	NUM
ejpam-6388	392	10	(	(	PUNCT
ejpam-6388	392	11	e.g.	e.g.	ADV
ejpam-6388	392	12	,	,	PUNCT
ejpam-6388	392	13	by	by	ADP
ejpam-6388	392	14	bounding	bound	VERB
ejpam-6388	392	15	lf	lf	ADP
ejpam-6388	392	16	and	and	CCONJ
ejpam-6388	392	17	lg	lg	NOUN
ejpam-6388	392	18	)	)	PUNCT
ejpam-6388	392	19	.	.	PUNCT
ejpam-6388	393	1	this	this	PRON
ejpam-6388	393	2	completes	complete	VERB
ejpam-6388	393	3	the	the	DET
ejpam-6388	393	4	proof	proof	NOUN
ejpam-6388	393	5	,	,	PUNCT
ejpam-6388	393	6	correcting	correct	VERB
ejpam-6388	393	7	the	the	DET
ejpam-6388	393	8	fixed	fix	VERB
ejpam-6388	393	9	-	-	PUNCT
ejpam-6388	393	10	solution	solution	NOUN
ejpam-6388	393	11	error	error	NOUN
ejpam-6388	393	12	(	(	PUNCT
ejpam-6388	393	13	p1	p1	NOUN
ejpam-6388	393	14	)	)	PUNCT
ejpam-6388	393	15	as	as	ADP
ejpam-6388	393	16	per	per	ADP
ejpam-6388	393	17	[	[	X
ejpam-6388	393	18	3	3	NUM
ejpam-6388	393	19	]	]	PUNCT
ejpam-6388	393	20	.	.	PUNCT
ejpam-6388	394	1	6	6	NUM
ejpam-6388	394	2	.	.	X
ejpam-6388	394	3	numerical	numerical	PROPN
ejpam-6388	394	4	illustrations	illustrations	PROPN
ejpam-6388	394	5	example	example	NOUN
ejpam-6388	394	6	1	1	X
ejpam-6388	394	7	.	.	X
ejpam-6388	395	1	consider	consider	VERB
ejpam-6388	395	2	the	the	DET
ejpam-6388	395	3	fhbvp	fhbvp	NOUN
ejpam-6388	395	4	rldy	rldy	VERB
ejpam-6388	395	5	0	0	NUM
ejpam-6388	396	1	+	+	CCONJ
ejpam-6388	396	2	[	[	PUNCT
ejpam-6388	396	3	r(ω	r(ω	ADJ
ejpam-6388	396	4	)	)	PUNCT
ejpam-6388	396	5	f(ω	f(ω	PROPN
ejpam-6388	396	6	,	,	PUNCT
ejpam-6388	396	7	r(ω	r(ω	ADJ
ejpam-6388	396	8	)	)	PUNCT
ejpam-6388	396	9	)	)	PUNCT
ejpam-6388	396	10	]	]	PUNCT
ejpam-6388	397	1	+	+	CCONJ
ejpam-6388	397	2	g(ω	g(ω	PROPN
ejpam-6388	397	3	,	,	PUNCT
ejpam-6388	397	4	r(ω	r(ω	ADJ
ejpam-6388	397	5	)	)	PUNCT
ejpam-6388	397	6	)	)	PUNCT
ejpam-6388	398	1	=	=	PUNCT
ejpam-6388	398	2	0	0	NUM
ejpam-6388	398	3	,	,	PUNCT
ejpam-6388	398	4	0	0	NUM
ejpam-6388	398	5	<	<	X
ejpam-6388	398	6	ω	ω	X
ejpam-6388	398	7	<	<	X
ejpam-6388	398	8	1	1	NUM
ejpam-6388	398	9	,	,	PUNCT
ejpam-6388	398	10	(	(	PUNCT
ejpam-6388	398	11	13	13	NUM
ejpam-6388	398	12	)	)	PUNCT
ejpam-6388	398	13	r(0	r(0	PROPN
ejpam-6388	398	14	)	)	PUNCT
ejpam-6388	398	15	=	=	SYM
ejpam-6388	398	16	0	0	NUM
ejpam-6388	398	17	,	,	PUNCT
ejpam-6388	398	18	r(1	r(1	PROPN
ejpam-6388	398	19	)	)	PUNCT
ejpam-6388	399	1	=	=	PUNCT
ejpam-6388	399	2	f(1	f(1	PROPN
ejpam-6388	399	3	,	,	PUNCT
ejpam-6388	399	4	r(1	r(1	PROPN
ejpam-6388	399	5	)	)	PUNCT
ejpam-6388	399	6	)	)	PUNCT
ejpam-6388	399	7	,	,	PUNCT
ejpam-6388	399	8	(	(	PUNCT
ejpam-6388	399	9	14	14	NUM
ejpam-6388	399	10	)	)	PUNCT
ejpam-6388	399	11	where	where	SCONJ
ejpam-6388	399	12	y	y	NOUN
ejpam-6388	399	13	=	=	NOUN
ejpam-6388	399	14	3	3	NUM
ejpam-6388	399	15	2	2	NUM
ejpam-6388	399	16	,	,	PUNCT
ejpam-6388	399	17	g(ω	g(ω	PROPN
ejpam-6388	399	18	,	,	PUNCT
ejpam-6388	399	19	r	r	NOUN
ejpam-6388	399	20	)	)	PUNCT
ejpam-6388	399	21	=	=	SYM
ejpam-6388	399	22	2(1	2(1	NUM
ejpam-6388	399	23	+	+	NUM
ejpam-6388	399	24	ω	ω	NUM
ejpam-6388	399	25	)	)	PUNCT
ejpam-6388	399	26	+	+	CCONJ
ejpam-6388	399	27	(	(	PUNCT
ejpam-6388	399	28	1	1	NUM
ejpam-6388	399	29	+	+	NUM
ejpam-6388	399	30	ω	ω	X
ejpam-6388	399	31	)	)	PUNCT
ejpam-6388	399	32	sin(r	sin(r	PROPN
ejpam-6388	399	33	)	)	PUNCT
ejpam-6388	399	34	,	,	PUNCT
ejpam-6388	399	35	and	and	CCONJ
ejpam-6388	399	36	f(ω	f(ω	PROPN
ejpam-6388	399	37	,	,	PUNCT
ejpam-6388	399	38	r	r	NOUN
ejpam-6388	399	39	)	)	PUNCT
ejpam-6388	399	40	=	=	SYM
ejpam-6388	399	41	ω	ω	PROPN
ejpam-6388	399	42	+	+	NUM
ejpam-6388	399	43	4	4	NUM
ejpam-6388	399	44	cos(r	cos(r	NUM
ejpam-6388	399	45	)	)	PUNCT
ejpam-6388	399	46	19	19	NUM
ejpam-6388	399	47	+	+	NUM
ejpam-6388	399	48	38	38	NUM
ejpam-6388	399	49	m	m	NOUN
ejpam-6388	399	50	.	.	PUNCT
ejpam-6388	400	1	d.	d.	PROPN
ejpam-6388	400	2	baleanu	baleanu	PROPN
ejpam-6388	400	3	et	et	PROPN
ejpam-6388	400	4	al	al	PROPN
ejpam-6388	400	5	.	.	PUNCT
ejpam-6388	400	6	/	/	SYM
ejpam-6388	400	7	eur	eur	PROPN
ejpam-6388	400	8	.	.	PUNCT
ejpam-6388	401	1	j.	j.	PROPN
ejpam-6388	401	2	pure	pure	PROPN
ejpam-6388	401	3	appl	appl	PROPN
ejpam-6388	401	4	.	.	PROPN
ejpam-6388	401	5	math	math	PROPN
ejpam-6388	401	6	,	,	PUNCT
ejpam-6388	401	7	18	18	NUM
ejpam-6388	401	8	(	(	PUNCT
ejpam-6388	401	9	4	4	NUM
ejpam-6388	401	10	)	)	PUNCT
ejpam-6388	401	11	(	(	PUNCT
ejpam-6388	401	12	2025	2025	NUM
ejpam-6388	401	13	)	)	PUNCT
ejpam-6388	401	14	,	,	PUNCT
ejpam-6388	401	15	6388	6388	NUM
ejpam-6388	401	16	17	17	NUM
ejpam-6388	401	17	of	of	ADP
ejpam-6388	401	18	31	31	NUM
ejpam-6388	401	19	let	let	VERB
ejpam-6388	401	20	℘(ω	℘(ω	PRON
ejpam-6388	401	21	)	)	PUNCT
ejpam-6388	401	22	=	=	PUNCT
ejpam-6388	402	1	2(1	2(1	NUM
ejpam-6388	402	2	+	+	NUM
ejpam-6388	402	3	ω	ω	NUM
ejpam-6388	402	4	)	)	PUNCT
ejpam-6388	402	5	.	.	PUNCT
ejpam-6388	403	1	to	to	PART
ejpam-6388	403	2	verify	verify	VERB
ejpam-6388	403	3	condition	condition	NOUN
ejpam-6388	403	4	(	(	PUNCT
ejpam-6388	403	5	b1	b1	NOUN
ejpam-6388	403	6	)	)	PUNCT
ejpam-6388	403	7	,	,	PUNCT
ejpam-6388	403	8	compute	compute	NOUN
ejpam-6388	403	9	:	:	PUNCT
ejpam-6388	403	10	g(ω	g(ω	PROPN
ejpam-6388	403	11	,	,	PUNCT
ejpam-6388	403	12	r)−	r)−	PROPN
ejpam-6388	403	13	g(ω	g(ω	PROPN
ejpam-6388	403	14	,	,	PUNCT
ejpam-6388	403	15	u	u	NOUN
ejpam-6388	403	16	)	)	PUNCT
ejpam-6388	403	17	=	=	PUNCT
ejpam-6388	404	1	[	[	X
ejpam-6388	404	2	2(1	2(1	NUM
ejpam-6388	404	3	+	+	NUM
ejpam-6388	404	4	ω	ω	NUM
ejpam-6388	404	5	)	)	PUNCT
ejpam-6388	404	6	+	+	CCONJ
ejpam-6388	404	7	(	(	PUNCT
ejpam-6388	404	8	1	1	NUM
ejpam-6388	404	9	+	+	NUM
ejpam-6388	404	10	ω	ω	NUM
ejpam-6388	404	11	)	)	PUNCT
ejpam-6388	404	12	sin(r)]−	sin(r)]−	PUNCT
ejpam-6388	405	1	[	[	X
ejpam-6388	405	2	2(1	2(1	NUM
ejpam-6388	405	3	+	+	NUM
ejpam-6388	405	4	ω	ω	NUM
ejpam-6388	405	5	)	)	PUNCT
ejpam-6388	405	6	+	+	CCONJ
ejpam-6388	405	7	(	(	PUNCT
ejpam-6388	405	8	1	1	NUM
ejpam-6388	405	9	+	+	NUM
ejpam-6388	405	10	ω	ω	X
ejpam-6388	405	11	)	)	PUNCT
ejpam-6388	405	12	sin(u	sin(u	NOUN
ejpam-6388	405	13	)	)	PUNCT
ejpam-6388	405	14	]	]	PUNCT
ejpam-6388	406	1	=	=	PUNCT
ejpam-6388	406	2	(	(	PUNCT
ejpam-6388	406	3	1	1	NUM
ejpam-6388	406	4	+	+	NUM
ejpam-6388	406	5	ω)(sin(r)−	ω)(sin(r)−	PROPN
ejpam-6388	406	6	sin(u	sin(u	PROPN
ejpam-6388	406	7	)	)	PUNCT
ejpam-6388	406	8	)	)	PUNCT
ejpam-6388	406	9	,	,	PUNCT
ejpam-6388	406	10	so	so	ADV
ejpam-6388	406	11	|g(ω	|g(ω	PROPN
ejpam-6388	406	12	,	,	PUNCT
ejpam-6388	406	13	r)−	r)−	PROPN
ejpam-6388	406	14	g(ω	g(ω	PROPN
ejpam-6388	406	15	,	,	PUNCT
ejpam-6388	406	16	u)|	u)|	NOUN
ejpam-6388	406	17	=	=	SYM
ejpam-6388	406	18	(	(	PUNCT
ejpam-6388	406	19	1	1	X
ejpam-6388	406	20	+	+	CCONJ
ejpam-6388	406	21	ω)|	ω)|	PRON
ejpam-6388	406	22	sin(r)−	sin(r)−	PROPN
ejpam-6388	406	23	sin(u)|	sin(u)|	PROPN
ejpam-6388	406	24	.	.	PUNCT
ejpam-6388	407	1	using	use	VERB
ejpam-6388	407	2	the	the	DET
ejpam-6388	407	3	mean	mean	ADJ
ejpam-6388	407	4	value	value	NOUN
ejpam-6388	407	5	theorem	theorem	VERB
ejpam-6388	407	6	,	,	PUNCT
ejpam-6388	407	7	we	we	PRON
ejpam-6388	407	8	have	have	VERB
ejpam-6388	407	9	|	|	ADV
ejpam-6388	407	10	sin(r)−	sin(r)−	PROPN
ejpam-6388	407	11	sin(u)|	sin(u)|	PROPN
ejpam-6388	407	12	≤	≤	PROPN
ejpam-6388	407	13	|r−	|r−	NOUN
ejpam-6388	407	14	u|	u|	PROPN
ejpam-6388	407	15	,	,	PUNCT
ejpam-6388	407	16	and	and	CCONJ
ejpam-6388	407	17	thus	thus	ADV
ejpam-6388	407	18	|g(ω	|g(ω	PROPN
ejpam-6388	407	19	,	,	PUNCT
ejpam-6388	407	20	r)−	r)−	PROPN
ejpam-6388	407	21	g(ω	g(ω	PROPN
ejpam-6388	407	22	,	,	PUNCT
ejpam-6388	407	23	u)|	u)|	NOUN
ejpam-6388	407	24	≤	≤	NUM
ejpam-6388	407	25	(	(	PUNCT
ejpam-6388	407	26	1	1	NUM
ejpam-6388	407	27	+	+	NUM
ejpam-6388	407	28	ω)|r−	ω)|r−	NOUN
ejpam-6388	408	1	u|	u|	NOUN
ejpam-6388	408	2	≤	≤	NUM
ejpam-6388	408	3	2(1	2(1	NUM
ejpam-6388	408	4	+	+	CCONJ
ejpam-6388	408	5	ω	ω	NUM
ejpam-6388	408	6	)	)	PUNCT
ejpam-6388	408	7	=	=	SYM
ejpam-6388	408	8	℘(ω	℘(ω	NOUN
ejpam-6388	408	9	)	)	PUNCT
ejpam-6388	408	10	,	,	PUNCT
ejpam-6388	408	11	since	since	SCONJ
ejpam-6388	408	12	ω	ω	PROPN
ejpam-6388	408	13	∈	∈	PROPN
ejpam-6388	409	1	[	[	X
ejpam-6388	409	2	0	0	NUM
ejpam-6388	409	3	,	,	PUNCT
ejpam-6388	409	4	1	1	NUM
ejpam-6388	409	5	]	]	PUNCT
ejpam-6388	409	6	.	.	PUNCT
ejpam-6388	410	1	also	also	ADV
ejpam-6388	410	2	,	,	PUNCT
ejpam-6388	410	3	g(ω	g(ω	PROPN
ejpam-6388	410	4	,	,	PUNCT
ejpam-6388	410	5	0	0	NUM
ejpam-6388	410	6	)	)	PUNCT
ejpam-6388	410	7	=	=	SYM
ejpam-6388	410	8	2(1	2(1	NUM
ejpam-6388	410	9	+	+	NUM
ejpam-6388	410	10	ω	ω	NUM
ejpam-6388	410	11	)	)	PUNCT
ejpam-6388	410	12	=	=	SYM
ejpam-6388	410	13	℘(ω	℘(ω	PROPN
ejpam-6388	410	14	)	)	PUNCT
ejpam-6388	410	15	,	,	PUNCT
ejpam-6388	410	16	so	so	CCONJ
ejpam-6388	410	17	(	(	PUNCT
ejpam-6388	410	18	b1	b1	NOUN
ejpam-6388	410	19	)	)	PUNCT
ejpam-6388	410	20	holds	hold	VERB
ejpam-6388	410	21	.	.	PUNCT
ejpam-6388	411	1	next	next	ADV
ejpam-6388	411	2	,	,	PUNCT
ejpam-6388	411	3	compute	compute	VERB
ejpam-6388	411	4	the	the	DET
ejpam-6388	411	5	constants	constant	NOUN
ejpam-6388	411	6	using	use	VERB
ejpam-6388	411	7	green	green	PROPN
ejpam-6388	411	8	’s	’s	PART
ejpam-6388	411	9	function	function	NOUN
ejpam-6388	411	10	0(ω	0(ω	PRON
ejpam-6388	411	11	,	,	PUNCT
ejpam-6388	411	12	ξ	ξ	X
ejpam-6388	411	13	)	)	PUNCT
ejpam-6388	411	14	as	as	ADP
ejpam-6388	411	15	0(ω	0(ω	NOUN
ejpam-6388	411	16	,	,	PUNCT
ejpam-6388	411	17	ω	ω	NOUN
ejpam-6388	411	18	)	)	PUNCT
ejpam-6388	411	19	=	=	SYM
ejpam-6388	412	1	ω	ω	NUM
ejpam-6388	412	2	1	1	NUM
ejpam-6388	412	3	2	2	NUM
ejpam-6388	412	4	(	(	PUNCT
ejpam-6388	412	5	1−	1−	NUM
ejpam-6388	412	6	ω	ω	NUM
ejpam-6388	412	7	)	)	PUNCT
ejpam-6388	412	8	1	1	NUM
ejpam-6388	412	9	2	2	NUM
ejpam-6388	412	10	γ(32	γ(32	NUM
ejpam-6388	412	11	)	)	PUNCT
ejpam-6388	412	12	,	,	PUNCT
ejpam-6388	412	13	where	where	SCONJ
ejpam-6388	412	14	γ(32	γ(32	VERB
ejpam-6388	412	15	)	)	PUNCT
ejpam-6388	412	16	=	=	SYM
ejpam-6388	413	1	√	√	NUM
ejpam-6388	413	2	π	π	NOUN
ejpam-6388	413	3	2	2	NUM
ejpam-6388	413	4	.	.	PUNCT
ejpam-6388	414	1	then	then	ADV
ejpam-6388	414	2	n	n	PROPN
ejpam-6388	414	3	=	=	SYM
ejpam-6388	414	4	∫	∫	PROPN
ejpam-6388	414	5	1	1	NUM
ejpam-6388	414	6	0	0	NUM
ejpam-6388	414	7	0(ω	0(ω	ADJ
ejpam-6388	414	8	,	,	PUNCT
ejpam-6388	414	9	ω)dω	ω)dω	PROPN
ejpam-6388	414	10	=	=	SYM
ejpam-6388	414	11	2√	2√	PROPN
ejpam-6388	414	12	π	π	NOUN
ejpam-6388	414	13	∫	∫	PROPN
ejpam-6388	414	14	1	1	NUM
ejpam-6388	414	15	0	0	NUM
ejpam-6388	414	16	ω	ω	NUM
ejpam-6388	414	17	1	1	NUM
ejpam-6388	414	18	2	2	NUM
ejpam-6388	414	19	(	(	PUNCT
ejpam-6388	414	20	1−	1−	NUM
ejpam-6388	414	21	ω	ω	NUM
ejpam-6388	414	22	)	)	PUNCT
ejpam-6388	414	23	1	1	NUM
ejpam-6388	414	24	2dω	2dω	NOUN
ejpam-6388	414	25	=	=	SYM
ejpam-6388	414	26	2√	2√	PROPN
ejpam-6388	414	27	π	π	X
ejpam-6388	414	28	b	b	X
ejpam-6388	414	29	(	(	PUNCT
ejpam-6388	414	30	3	3	NUM
ejpam-6388	414	31	2	2	NUM
ejpam-6388	414	32	,	,	PUNCT
ejpam-6388	414	33	3	3	NUM
ejpam-6388	414	34	2	2	NUM
ejpam-6388	414	35	)	)	PUNCT
ejpam-6388	414	36	.	.	PUNCT
ejpam-6388	415	1	since	since	SCONJ
ejpam-6388	415	2	b	b	PROPN
ejpam-6388	415	3	(	(	PUNCT
ejpam-6388	415	4	3	3	NUM
ejpam-6388	415	5	2	2	NUM
ejpam-6388	415	6	,	,	PUNCT
ejpam-6388	415	7	3	3	NUM
ejpam-6388	415	8	2	2	NUM
ejpam-6388	415	9	)	)	PUNCT
ejpam-6388	415	10	=	=	PUNCT
ejpam-6388	415	11	π	π	SYM
ejpam-6388	415	12	8	8	NUM
ejpam-6388	415	13	,	,	PUNCT
ejpam-6388	415	14	n	n	NOUN
ejpam-6388	415	15	=	=	SYM
ejpam-6388	415	16	2√	2√	PROPN
ejpam-6388	415	17	π	π	X
ejpam-6388	415	18	·	·	PUNCT
ejpam-6388	415	19	π	π	NOUN
ejpam-6388	415	20	8	8	NUM
ejpam-6388	415	21	=	=	SYM
ejpam-6388	415	22	√	√	NUM
ejpam-6388	415	23	π	π	PROPN
ejpam-6388	415	24	4	4	NUM
ejpam-6388	415	25	.	.	PUNCT
ejpam-6388	416	1	next	next	ADJ
ejpam-6388	416	2	,	,	PUNCT
ejpam-6388	416	3	m	m	VERB
ejpam-6388	416	4	=	=	SYM
ejpam-6388	416	5	∫	∫	PROPN
ejpam-6388	416	6	1	1	NUM
ejpam-6388	416	7	0	0	NUM
ejpam-6388	416	8	0(ω	0(ω	NUM
ejpam-6388	416	9	,	,	PUNCT
ejpam-6388	416	10	ω)℘(ω)dω	ω)℘(ω)dω	NOUN
ejpam-6388	416	11	=	=	SYM
ejpam-6388	416	12	2√	2√	PROPN
ejpam-6388	416	13	π	π	NOUN
ejpam-6388	416	14	∫	∫	PROPN
ejpam-6388	416	15	1	1	NUM
ejpam-6388	416	16	0	0	NUM
ejpam-6388	416	17	ω	ω	NUM
ejpam-6388	416	18	1	1	NUM
ejpam-6388	416	19	2	2	NUM
ejpam-6388	416	20	(	(	PUNCT
ejpam-6388	416	21	1−	1−	NUM
ejpam-6388	416	22	ω	ω	NUM
ejpam-6388	416	23	)	)	PUNCT
ejpam-6388	416	24	1	1	NUM
ejpam-6388	416	25	2	2	NUM
ejpam-6388	416	26	·	·	SYM
ejpam-6388	416	27	2(1	2(1	NUM
ejpam-6388	416	28	+	+	PUNCT
ejpam-6388	416	29	ω)dω	ω)dω	PROPN
ejpam-6388	416	30	.	.	PUNCT
ejpam-6388	417	1	but	but	CCONJ
ejpam-6388	417	2	∫	∫	PROPN
ejpam-6388	417	3	1	1	NUM
ejpam-6388	417	4	0	0	NUM
ejpam-6388	417	5	ω	ω	NUM
ejpam-6388	417	6	1	1	NUM
ejpam-6388	417	7	2	2	NUM
ejpam-6388	417	8	(	(	PUNCT
ejpam-6388	417	9	1−	1−	NUM
ejpam-6388	417	10	ω	ω	NUM
ejpam-6388	417	11	)	)	PUNCT
ejpam-6388	417	12	1	1	NUM
ejpam-6388	417	13	2	2	NUM
ejpam-6388	417	14	(	(	PUNCT
ejpam-6388	417	15	1	1	NUM
ejpam-6388	417	16	+	+	NUM
ejpam-6388	417	17	ω)dω	ω)dω	PROPN
ejpam-6388	417	18	=	=	SYM
ejpam-6388	417	19	∫	∫	PROPN
ejpam-6388	418	1	1	1	NUM
ejpam-6388	418	2	0	0	NUM
ejpam-6388	418	3	ω	ω	NUM
ejpam-6388	418	4	1	1	NUM
ejpam-6388	418	5	2	2	NUM
ejpam-6388	418	6	(	(	PUNCT
ejpam-6388	418	7	1−	1−	NUM
ejpam-6388	418	8	ω	ω	NUM
ejpam-6388	418	9	)	)	PUNCT
ejpam-6388	418	10	1	1	NUM
ejpam-6388	418	11	2dω	2dω	NOUN
ejpam-6388	419	1	+	+	CCONJ
ejpam-6388	419	2	∫	∫	PROPN
ejpam-6388	419	3	1	1	NUM
ejpam-6388	419	4	0	0	NUM
ejpam-6388	419	5	ω	ω	NUM
ejpam-6388	419	6	3	3	NUM
ejpam-6388	419	7	2	2	NUM
ejpam-6388	419	8	(	(	PUNCT
ejpam-6388	419	9	1−	1−	NUM
ejpam-6388	419	10	ω	ω	NUM
ejpam-6388	419	11	)	)	PUNCT
ejpam-6388	419	12	1	1	NUM
ejpam-6388	419	13	2dω	2dω	NOUN
ejpam-6388	419	14	=	=	SYM
ejpam-6388	419	15	b	b	PROPN
ejpam-6388	419	16	(	(	PUNCT
ejpam-6388	419	17	3	3	NUM
ejpam-6388	419	18	2	2	NUM
ejpam-6388	419	19	,	,	PUNCT
ejpam-6388	419	20	3	3	NUM
ejpam-6388	419	21	2	2	NUM
ejpam-6388	419	22	)	)	PUNCT
ejpam-6388	420	1	+	+	NOUN
ejpam-6388	420	2	b	b	NOUN
ejpam-6388	420	3	(	(	PUNCT
ejpam-6388	420	4	5	5	NUM
ejpam-6388	420	5	2	2	NUM
ejpam-6388	420	6	,	,	PUNCT
ejpam-6388	420	7	3	3	NUM
ejpam-6388	420	8	2	2	NUM
ejpam-6388	420	9	)	)	PUNCT
ejpam-6388	420	10	=	=	PUNCT
ejpam-6388	421	1	π	π	NOUN
ejpam-6388	421	2	8	8	NUM
ejpam-6388	422	1	+	+	CCONJ
ejpam-6388	422	2	π	π	PROPN
ejpam-6388	422	3	16	16	NUM
ejpam-6388	422	4	=	=	SYM
ejpam-6388	422	5	3π	3π	NOUN
ejpam-6388	422	6	16	16	NUM
ejpam-6388	422	7	.	.	PUNCT
ejpam-6388	423	1	hence	hence	ADV
ejpam-6388	423	2	m	m	VERB
ejpam-6388	423	3	=	=	SYM
ejpam-6388	424	1	4√	4√	PROPN
ejpam-6388	424	2	π	π	X
ejpam-6388	424	3	·	·	PUNCT
ejpam-6388	424	4	3π	3π	NUM
ejpam-6388	424	5	16	16	NUM
ejpam-6388	424	6	=	=	NOUN
ejpam-6388	424	7	12π	12π	NUM
ejpam-6388	424	8	16	16	NUM
ejpam-6388	425	1	√	√	NUM
ejpam-6388	425	2	π	π	X
ejpam-6388	425	3	=	=	SYM
ejpam-6388	425	4	3	3	NUM
ejpam-6388	425	5	√	√	NUM
ejpam-6388	425	6	π	π	PROPN
ejpam-6388	425	7	4	4	NUM
ejpam-6388	425	8	.	.	PUNCT
ejpam-6388	426	1	let	let	VERB
ejpam-6388	426	2	q	q	NOUN
ejpam-6388	427	1	=	=	SYM
ejpam-6388	427	2	9	9	NUM
ejpam-6388	427	3	+	+	NUM
ejpam-6388	427	4	10	10	NUM
ejpam-6388	427	5	m	m	NUM
ejpam-6388	427	6	19	19	NUM
ejpam-6388	427	7	+	+	NUM
ejpam-6388	427	8	38	38	NUM
ejpam-6388	427	9	m	m	NOUN
ejpam-6388	427	10	=	=	NOUN
ejpam-6388	427	11	9	9	NUM
ejpam-6388	428	1	+	+	CCONJ
ejpam-6388	428	2	10	10	NUM
ejpam-6388	428	3	·	·	SYM
ejpam-6388	428	4	3	3	NUM
ejpam-6388	428	5	√	√	NUM
ejpam-6388	428	6	π	π	PROPN
ejpam-6388	428	7	4	4	NUM
ejpam-6388	428	8	19	19	NUM
ejpam-6388	428	9	+	+	NUM
ejpam-6388	428	10	38	38	NUM
ejpam-6388	428	11	·	·	SYM
ejpam-6388	428	12	3	3	NUM
ejpam-6388	428	13	√	√	NUM
ejpam-6388	428	14	π	π	PROPN
ejpam-6388	428	15	4	4	NUM
ejpam-6388	428	16	≈	≈	PROPN
ejpam-6388	428	17	0.3207	0.3207	NUM
ejpam-6388	428	18	.	.	PUNCT
ejpam-6388	429	1	d.	d.	PROPN
ejpam-6388	429	2	baleanu	baleanu	PROPN
ejpam-6388	429	3	et	et	PROPN
ejpam-6388	429	4	al	al	PROPN
ejpam-6388	429	5	.	.	PUNCT
ejpam-6388	429	6	/	/	SYM
ejpam-6388	429	7	eur	eur	PROPN
ejpam-6388	429	8	.	.	PUNCT
ejpam-6388	430	1	j.	j.	PROPN
ejpam-6388	430	2	pure	pure	PROPN
ejpam-6388	430	3	appl	appl	PROPN
ejpam-6388	430	4	.	.	PROPN
ejpam-6388	430	5	math	math	PROPN
ejpam-6388	430	6	,	,	PUNCT
ejpam-6388	430	7	18	18	NUM
ejpam-6388	430	8	(	(	PUNCT
ejpam-6388	430	9	4	4	NUM
ejpam-6388	430	10	)	)	PUNCT
ejpam-6388	430	11	(	(	PUNCT
ejpam-6388	430	12	2025	2025	NUM
ejpam-6388	430	13	)	)	PUNCT
ejpam-6388	430	14	,	,	PUNCT
ejpam-6388	430	15	6388	6388	NUM
ejpam-6388	430	16	18	18	NUM
ejpam-6388	430	17	of	of	ADP
ejpam-6388	430	18	31	31	NUM
ejpam-6388	430	19	for	for	ADP
ejpam-6388	430	20	condition	condition	NOUN
ejpam-6388	430	21	(	(	PUNCT
ejpam-6388	430	22	b2	b2	NOUN
ejpam-6388	430	23	)	)	PUNCT
ejpam-6388	430	24	,	,	PUNCT
ejpam-6388	430	25	compute	compute	PROPN
ejpam-6388	430	26	|f(ω	|f(ω	PROPN
ejpam-6388	430	27	,	,	PUNCT
ejpam-6388	430	28	r)−	r)−	PROPN
ejpam-6388	430	29	f(ω	f(ω	PROPN
ejpam-6388	430	30	,	,	PUNCT
ejpam-6388	430	31	u)|	u)|	NOUN
ejpam-6388	431	1	=	=	NOUN
ejpam-6388	431	2	4	4	NUM
ejpam-6388	431	3	19	19	NUM
ejpam-6388	431	4	+	+	NUM
ejpam-6388	431	5	38	38	NUM
ejpam-6388	431	6	m	m	VERB
ejpam-6388	431	7	|	|	ADV
ejpam-6388	431	8	cos(r)−	cos(r)−	ADJ
ejpam-6388	431	9	cos(u)|	cos(u)|	PROPN
ejpam-6388	431	10	,	,	PUNCT
ejpam-6388	431	11	|	|	ADV
ejpam-6388	431	12	cos(r)−	cos(r)−	PROPN
ejpam-6388	431	13	cos(u)|	cos(u)|	PROPN
ejpam-6388	431	14	≤	≤	NOUN
ejpam-6388	431	15	|r−	|r−	NOUN
ejpam-6388	431	16	u|	u|	PROPN
ejpam-6388	431	17	,	,	PUNCT
ejpam-6388	431	18	|f(ω	|f(ω	NOUN
ejpam-6388	431	19	,	,	PUNCT
ejpam-6388	431	20	r)−	r)−	PROPN
ejpam-6388	431	21	f(ω	f(ω	PROPN
ejpam-6388	431	22	,	,	PUNCT
ejpam-6388	431	23	u)|	u)|	NOUN
ejpam-6388	431	24	≤	≤	NUM
ejpam-6388	431	25	4	4	NUM
ejpam-6388	431	26	19	19	NUM
ejpam-6388	431	27	+	+	NUM
ejpam-6388	431	28	38	38	NUM
ejpam-6388	431	29	·	·	SYM
ejpam-6388	431	30	3	3	NUM
ejpam-6388	431	31	√	√	NUM
ejpam-6388	431	32	π	π	PROPN
ejpam-6388	431	33	4	4	NUM
ejpam-6388	431	34	|r−	|r−	ADV
ejpam-6388	431	35	u|	u|	PROPN
ejpam-6388	432	1	≈	≈	PROPN
ejpam-6388	432	2	4	4	NUM
ejpam-6388	432	3	69.5144	69.5144	NUM
ejpam-6388	432	4	|r−	|r−	NOUN
ejpam-6388	432	5	u|	u|	PROPN
ejpam-6388	432	6	≈	≈	PROPN
ejpam-6388	432	7	0.0575|r−	0.0575|r−	PROPN
ejpam-6388	432	8	u|	u|	NOUN
ejpam-6388	432	9	,	,	PUNCT
ejpam-6388	432	10	with	with	ADP
ejpam-6388	432	11	b	b	NOUN
ejpam-6388	432	12	=	=	SYM
ejpam-6388	432	13	0.0575	0.0575	NUM
ejpam-6388	432	14	<	<	X
ejpam-6388	432	15	1	1	NUM
ejpam-6388	432	16	.	.	PUNCT
ejpam-6388	432	17	thus	thus	ADV
ejpam-6388	432	18	,	,	PUNCT
ejpam-6388	432	19	by	by	ADP
ejpam-6388	432	20	theorem	theorem	NOUN
ejpam-6388	432	21	4	4	NUM
ejpam-6388	432	22	,	,	PUNCT
ejpam-6388	432	23	the	the	DET
ejpam-6388	432	24	fhbvp	fhbvp	NOUN
ejpam-6388	432	25	(	(	PUNCT
ejpam-6388	432	26	13)–(14	13)–(14	NUM
ejpam-6388	432	27	)	)	PUNCT
ejpam-6388	432	28	has	have	VERB
ejpam-6388	432	29	a	a	DET
ejpam-6388	432	30	unique	unique	ADJ
ejpam-6388	432	31	solution	solution	NOUN
ejpam-6388	432	32	.	.	PUNCT
ejpam-6388	433	1	now	now	ADV
ejpam-6388	433	2	,	,	PUNCT
ejpam-6388	433	3	for	for	ADP
ejpam-6388	433	4	hyers	hyer	NOUN
ejpam-6388	433	5	–	–	PUNCT
ejpam-6388	433	6	ulam	ulam	X
ejpam-6388	433	7	stability	stability	NOUN
ejpam-6388	433	8	,	,	PUNCT
ejpam-6388	433	9	we	we	PRON
ejpam-6388	433	10	find	find	VERB
ejpam-6388	433	11	the	the	DET
ejpam-6388	433	12	roots	root	NOUN
ejpam-6388	433	13	of	of	ADP
ejpam-6388	433	14	−	−	NUM
ejpam-6388	433	15	4	4	NUM
ejpam-6388	433	16	19	19	NUM
ejpam-6388	433	17	z2	z2	NOUN
ejpam-6388	433	18	+	+	CCONJ
ejpam-6388	433	19	15	15	NUM
ejpam-6388	433	20	19	19	NUM
ejpam-6388	433	21	z−	z−	NOUN
ejpam-6388	433	22	√	√	PROPN
ejpam-6388	433	23	π	π	NOUN
ejpam-6388	433	24	4	4	NUM
ejpam-6388	433	25	[	[	SYM
ejpam-6388	433	26	18	18	NUM
ejpam-6388	433	27	+	+	NUM
ejpam-6388	433	28	15	15	NUM
ejpam-6388	433	29	√	√	PROPN
ejpam-6388	433	30	π	π	PROPN
ejpam-6388	433	31	10	10	NUM
ejpam-6388	433	32	+	+	CCONJ
ejpam-6388	433	33	15	15	NUM
ejpam-6388	433	34	√	√	PROPN
ejpam-6388	433	35	π	π	X
ejpam-6388	433	36	]	]	X
ejpam-6388	434	1	=	=	PUNCT
ejpam-6388	434	2	0	0	NUM
ejpam-6388	434	3	,	,	PUNCT
ejpam-6388	434	4	that	that	ADV
ejpam-6388	434	5	is	is	ADV
ejpam-6388	434	6	,	,	PUNCT
ejpam-6388	434	7	−0.2105z2	−0.2105z2	PROPN
ejpam-6388	434	8	+	+	CCONJ
ejpam-6388	434	9	0.7895z−	0.7895z−	X
ejpam-6388	434	10	0.5400	0.5400	NUM
ejpam-6388	434	11	=	=	SYM
ejpam-6388	434	12	0	0	NUM
ejpam-6388	434	13	,	,	PUNCT
ejpam-6388	434	14	which	which	PRON
ejpam-6388	434	15	are	be	AUX
ejpam-6388	434	16	z1	z1	ADJ
ejpam-6388	434	17	≈	≈	PROPN
ejpam-6388	434	18	0.9	0.9	NUM
ejpam-6388	434	19	,	,	PUNCT
ejpam-6388	434	20	z2	z2	PROPN
ejpam-6388	434	21	≈	≈	PROPN
ejpam-6388	434	22	2.85	2.85	NUM
ejpam-6388	434	23	.	.	PUNCT
ejpam-6388	435	1	also	also	ADV
ejpam-6388	435	2	,	,	PUNCT
ejpam-6388	435	3	nq	nq	PROPN
ejpam-6388	435	4	≈	≈	PROPN
ejpam-6388	435	5	√	√	PROPN
ejpam-6388	435	6	π	π	PROPN
ejpam-6388	435	7	4	4	NUM
ejpam-6388	435	8	·	·	SYM
ejpam-6388	435	9	0.3207	0.3207	NUM
ejpam-6388	435	10	≈	≈	NUM
ejpam-6388	435	11	0.14210648	0.14210648	NUM
ejpam-6388	435	12	.	.	PUNCT
ejpam-6388	435	13	thus	thus	ADV
ejpam-6388	435	14	,	,	PUNCT
ejpam-6388	435	15	by	by	ADP
ejpam-6388	435	16	theorem	theorem	NOUN
ejpam-6388	435	17	5	5	NUM
ejpam-6388	435	18	,	,	PUNCT
ejpam-6388	435	19	the	the	DET
ejpam-6388	435	20	fhbvp	fhbvp	NOUN
ejpam-6388	435	21	is	be	AUX
ejpam-6388	435	22	hyers	hyer	NOUN
ejpam-6388	435	23	–	–	PUNCT
ejpam-6388	435	24	ulam	ulam	X
ejpam-6388	435	25	stable	stable	PROPN
ejpam-6388	435	26	.	.	PUNCT
ejpam-6388	436	1	numerical	numerical	ADJ
ejpam-6388	436	2	approximation	approximation	NOUN
ejpam-6388	436	3	of	of	ADP
ejpam-6388	436	4	the	the	DET
ejpam-6388	436	5	solution	solution	NOUN
ejpam-6388	436	6	:	:	PUNCT
ejpam-6388	436	7	the	the	DET
ejpam-6388	436	8	integral	integral	ADJ
ejpam-6388	436	9	equation	equation	NOUN
ejpam-6388	436	10	for	for	ADP
ejpam-6388	436	11	r	r	NOUN
ejpam-6388	436	12	is	be	AUX
ejpam-6388	436	13	approximated	approximate	VERB
ejpam-6388	436	14	numerically	numerically	ADV
ejpam-6388	436	15	using	use	VERB
ejpam-6388	436	16	the	the	DET
ejpam-6388	436	17	form	form	NOUN
ejpam-6388	436	18	(	(	PUNCT
ejpam-6388	436	19	3	3	NUM
ejpam-6388	436	20	)	)	PUNCT
ejpam-6388	436	21	.	.	PUNCT
ejpam-6388	437	1	to	to	PART
ejpam-6388	437	2	compute	compute	VERB
ejpam-6388	437	3	the	the	DET
ejpam-6388	437	4	integral	integral	ADJ
ejpam-6388	437	5	term∫	term∫	INTJ
ejpam-6388	437	6	1	1	NUM
ejpam-6388	437	7	0	0	NUM
ejpam-6388	437	8	0(ω	0(ω	NUM
ejpam-6388	437	9	,	,	PUNCT
ejpam-6388	437	10	ξ)g(ξ	ξ)g(ξ	ADJ
ejpam-6388	437	11	,	,	PUNCT
ejpam-6388	437	12	r(ξ))dξ	r(ξ))dξ	ADV
ejpam-6388	437	13	,	,	PUNCT
ejpam-6388	437	14	we	we	PRON
ejpam-6388	437	15	employed	employ	VERB
ejpam-6388	437	16	the	the	DET
ejpam-6388	437	17	trapezoidal	trapezoidal	ADJ
ejpam-6388	437	18	rule	rule	NOUN
ejpam-6388	437	19	for	for	ADP
ejpam-6388	437	20	numerical	numerical	ADJ
ejpam-6388	437	21	integration	integration	NOUN
ejpam-6388	437	22	.	.	PUNCT
ejpam-6388	438	1	the	the	DET
ejpam-6388	438	2	kernel	kernel	PROPN
ejpam-6388	438	3	function	function	PROPN
ejpam-6388	438	4	0(ω	0(ω	PRON
ejpam-6388	438	5	,	,	PUNCT
ejpam-6388	438	6	ξ	ξ	X
ejpam-6388	438	7	)	)	PUNCT
ejpam-6388	438	8	is	be	AUX
ejpam-6388	438	9	computed	compute	VERB
ejpam-6388	438	10	at	at	ADP
ejpam-6388	438	11	discrete	discrete	ADJ
ejpam-6388	438	12	values	value	NOUN
ejpam-6388	438	13	of	of	ADP
ejpam-6388	438	14	ξ	ξ	PROPN
ejpam-6388	438	15	,	,	PUNCT
ejpam-6388	438	16	and	and	CCONJ
ejpam-6388	438	17	the	the	DET
ejpam-6388	438	18	integration	integration	NOUN
ejpam-6388	438	19	is	be	AUX
ejpam-6388	438	20	performed	perform	VERB
ejpam-6388	438	21	over	over	ADP
ejpam-6388	438	22	the	the	DET
ejpam-6388	438	23	interval	interval	NOUN
ejpam-6388	438	24	[	[	X
ejpam-6388	438	25	0	0	NUM
ejpam-6388	438	26	,	,	PUNCT
ejpam-6388	438	27	1	1	NUM
ejpam-6388	438	28	]	]	PUNCT
ejpam-6388	438	29	using	use	VERB
ejpam-6388	438	30	the	the	DET
ejpam-6388	438	31	np.trapezoid	np.trapezoid	NOUN
ejpam-6388	438	32	(	(	PUNCT
ejpam-6388	438	33	)	)	PUNCT
ejpam-6388	438	34	function	function	NOUN
ejpam-6388	438	35	from	from	ADP
ejpam-6388	438	36	the	the	DET
ejpam-6388	438	37	python	python	NOUN
ejpam-6388	438	38	numpy	numpy	NOUN
ejpam-6388	438	39	library	library	NOUN
ejpam-6388	438	40	.	.	PUNCT
ejpam-6388	439	1	creation	creation	NOUN
ejpam-6388	439	2	of	of	ADP
ejpam-6388	439	3	the	the	DET
ejpam-6388	439	4	numerical	numerical	ADJ
ejpam-6388	439	5	table	table	NOUN
ejpam-6388	439	6	:	:	PUNCT
ejpam-6388	439	7	the	the	DET
ejpam-6388	439	8	functional	functional	ADJ
ejpam-6388	439	9	value	value	NOUN
ejpam-6388	439	10	r(ω	r(ω	ADV
ejpam-6388	439	11	)	)	PUNCT
ejpam-6388	439	12	is	be	AUX
ejpam-6388	439	13	computed	compute	VERB
ejpam-6388	439	14	for	for	ADP
ejpam-6388	439	15	100	100	NUM
ejpam-6388	439	16	discrete	discrete	ADJ
ejpam-6388	439	17	values	value	NOUN
ejpam-6388	439	18	of	of	ADP
ejpam-6388	439	19	ω	ω	PROPN
ejpam-6388	439	20	in	in	ADP
ejpam-6388	439	21	the	the	DET
ejpam-6388	439	22	interval	interval	NOUN
ejpam-6388	439	23	[	[	X
ejpam-6388	439	24	0	0	NUM
ejpam-6388	439	25	,	,	PUNCT
ejpam-6388	439	26	1	1	NUM
ejpam-6388	439	27	]	]	PUNCT
ejpam-6388	439	28	,	,	PUNCT
ejpam-6388	439	29	starting	start	VERB
ejpam-6388	439	30	from	from	ADP
ejpam-6388	439	31	the	the	DET
ejpam-6388	439	32	initial	initial	ADJ
ejpam-6388	439	33	approximation	approximation	NOUN
ejpam-6388	439	34	r(ω	r(ω	ADV
ejpam-6388	439	35	)	)	PUNCT
ejpam-6388	439	36	=	=	SYM
ejpam-6388	440	1	0	0	X
ejpam-6388	440	2	.	.	PUNCT
ejpam-6388	441	1	the	the	DET
ejpam-6388	441	2	numerical	numerical	ADJ
ejpam-6388	441	3	solution	solution	NOUN
ejpam-6388	441	4	is	be	AUX
ejpam-6388	441	5	obtained	obtain	VERB
ejpam-6388	441	6	for	for	ADP
ejpam-6388	441	7	two	two	NUM
ejpam-6388	441	8	different	different	ADJ
ejpam-6388	441	9	values	value	NOUN
ejpam-6388	441	10	of	of	ADP
ejpam-6388	441	11	the	the	DET
ejpam-6388	441	12	fractional	fractional	ADJ
ejpam-6388	441	13	order	order	NOUN
ejpam-6388	441	14	y	y	NOUN
ejpam-6388	441	15	=	=	SYM
ejpam-6388	441	16	1.5	1.5	NUM
ejpam-6388	441	17	and	and	CCONJ
ejpam-6388	441	18	y	y	NOUN
ejpam-6388	441	19	=	=	SYM
ejpam-6388	441	20	2	2	X
ejpam-6388	441	21	.	.	X
ejpam-6388	442	1	for	for	ADP
ejpam-6388	442	2	each	each	DET
ejpam-6388	442	3	value	value	NOUN
ejpam-6388	442	4	of	of	ADP
ejpam-6388	442	5	ω	ω	PROPN
ejpam-6388	442	6	,	,	PUNCT
ejpam-6388	442	7	the	the	DET
ejpam-6388	442	8	corresponding	corresponding	ADJ
ejpam-6388	442	9	values	value	NOUN
ejpam-6388	442	10	of	of	ADP
ejpam-6388	442	11	r(ω	r(ω	ADJ
ejpam-6388	442	12	)	)	PUNCT
ejpam-6388	442	13	are	be	AUX
ejpam-6388	442	14	calculated	calculate	VERB
ejpam-6388	442	15	iteratively	iteratively	ADV
ejpam-6388	442	16	by	by	ADP
ejpam-6388	442	17	solving	solve	VERB
ejpam-6388	442	18	the	the	DET
ejpam-6388	442	19	integral	integral	ADJ
ejpam-6388	442	20	equation	equation	NOUN
ejpam-6388	442	21	(	(	PUNCT
ejpam-6388	442	22	3	3	NUM
ejpam-6388	442	23	)	)	PUNCT
ejpam-6388	442	24	,	,	PUNCT
ejpam-6388	442	25	and	and	CCONJ
ejpam-6388	442	26	the	the	DET
ejpam-6388	442	27	results	result	NOUN
ejpam-6388	442	28	are	be	AUX
ejpam-6388	442	29	tabulated	tabulate	VERB
ejpam-6388	442	30	in	in	ADP
ejpam-6388	442	31	table	table	NOUN
ejpam-6388	442	32	4	4	NUM
ejpam-6388	442	33	,	,	PUNCT
ejpam-6388	442	34	see	see	VERB
ejpam-6388	442	35	appendix	appendix	NOUN
ejpam-6388	442	36	.	.	PUNCT
ejpam-6388	443	1	graphical	graphical	ADJ
ejpam-6388	443	2	representation	representation	NOUN
ejpam-6388	443	3	of	of	ADP
ejpam-6388	443	4	the	the	DET
ejpam-6388	443	5	results	result	NOUN
ejpam-6388	443	6	:	:	PUNCT
ejpam-6388	443	7	for	for	SCONJ
ejpam-6388	443	8	better	well	ADV
ejpam-6388	443	9	understand	understand	VERB
ejpam-6388	443	10	the	the	DET
ejpam-6388	443	11	behavior	behavior	NOUN
ejpam-6388	443	12	of	of	ADP
ejpam-6388	443	13	r	r	NOUN
ejpam-6388	443	14	across	across	ADP
ejpam-6388	443	15	different	different	ADJ
ejpam-6388	443	16	values	value	NOUN
ejpam-6388	443	17	of	of	ADP
ejpam-6388	443	18	y	y	PROPN
ejpam-6388	443	19	,	,	PUNCT
ejpam-6388	443	20	the	the	DET
ejpam-6388	443	21	computed	computed	ADJ
ejpam-6388	443	22	values	value	NOUN
ejpam-6388	443	23	of	of	ADP
ejpam-6388	443	24	r(ω	r(ω	ADJ
ejpam-6388	443	25	)	)	PUNCT
ejpam-6388	443	26	are	be	AUX
ejpam-6388	443	27	plotted	plot	VERB
ejpam-6388	443	28	for	for	ADP
ejpam-6388	443	29	both	both	PRON
ejpam-6388	443	30	y	y	PROPN
ejpam-6388	443	31	=	=	SYM
ejpam-6388	443	32	1.5	1.5	NUM
ejpam-6388	443	33	and	and	CCONJ
ejpam-6388	443	34	y	y	NOUN
ejpam-6388	443	35	=	=	PROPN
ejpam-6388	443	36	2.0	2.0	NUM
ejpam-6388	443	37	.	.	PUNCT
ejpam-6388	444	1	the	the	DET
ejpam-6388	444	2	plots	plot	NOUN
ejpam-6388	444	3	are	be	AUX
ejpam-6388	444	4	generated	generate	VERB
ejpam-6388	444	5	using	use	VERB
ejpam-6388	444	6	the	the	DET
ejpam-6388	444	7	matplotlib	matplotlib	PROPN
ejpam-6388	444	8	library	library	NOUN
ejpam-6388	444	9	in	in	ADP
ejpam-6388	444	10	python	python	PROPN
ejpam-6388	444	11	,	,	PUNCT
ejpam-6388	444	12	providing	provide	VERB
ejpam-6388	444	13	a	a	DET
ejpam-6388	444	14	visual	visual	ADJ
ejpam-6388	444	15	comparison	comparison	NOUN
ejpam-6388	444	16	of	of	ADP
ejpam-6388	444	17	the	the	DET
ejpam-6388	444	18	two	two	NUM
ejpam-6388	444	19	scenarios	scenario	NOUN
ejpam-6388	444	20	.	.	PUNCT
ejpam-6388	445	1	the	the	DET
ejpam-6388	445	2	first	first	ADJ
ejpam-6388	445	3	plot	plot	NOUN
ejpam-6388	445	4	(	(	PUNCT
ejpam-6388	445	5	figure	figure	NOUN
ejpam-6388	445	6	1	1	NUM
ejpam-6388	445	7	)	)	PUNCT
ejpam-6388	445	8	shows	show	VERB
ejpam-6388	445	9	the	the	DET
ejpam-6388	445	10	behavior	behavior	NOUN
ejpam-6388	445	11	of	of	ADP
ejpam-6388	445	12	r	r	NOUN
ejpam-6388	445	13	for	for	ADP
ejpam-6388	445	14	y	y	NOUN
ejpam-6388	445	15	=	=	SYM
ejpam-6388	445	16	1.5	1.5	NUM
ejpam-6388	445	17	,	,	PUNCT
ejpam-6388	445	18	while	while	SCONJ
ejpam-6388	445	19	the	the	DET
ejpam-6388	445	20	second	second	ADJ
ejpam-6388	445	21	plot	plot	NOUN
ejpam-6388	445	22	(	(	PUNCT
ejpam-6388	445	23	figure	figure	NOUN
ejpam-6388	445	24	2	2	NUM
ejpam-6388	445	25	)	)	PUNCT
ejpam-6388	445	26	compares	compare	VERB
ejpam-6388	445	27	the	the	DET
ejpam-6388	445	28	solutions	solution	NOUN
ejpam-6388	445	29	for	for	ADP
ejpam-6388	445	30	both	both	PRON
ejpam-6388	445	31	y	y	PROPN
ejpam-6388	445	32	=	=	SYM
ejpam-6388	445	33	1.5	1.5	NUM
ejpam-6388	445	34	and	and	CCONJ
ejpam-6388	445	35	y	y	NOUN
ejpam-6388	445	36	=	=	SYM
ejpam-6388	445	37	2.0	2.0	NUM
ejpam-6388	445	38	.	.	PUNCT
ejpam-6388	446	1	d.	d.	PROPN
ejpam-6388	446	2	baleanu	baleanu	PROPN
ejpam-6388	446	3	et	et	PROPN
ejpam-6388	446	4	al	al	PROPN
ejpam-6388	446	5	.	.	PUNCT
ejpam-6388	446	6	/	/	SYM
ejpam-6388	446	7	eur	eur	PROPN
ejpam-6388	446	8	.	.	PUNCT
ejpam-6388	447	1	j.	j.	PROPN
ejpam-6388	447	2	pure	pure	PROPN
ejpam-6388	447	3	appl	appl	PROPN
ejpam-6388	447	4	.	.	PROPN
ejpam-6388	447	5	math	math	PROPN
ejpam-6388	447	6	,	,	PUNCT
ejpam-6388	447	7	18	18	NUM
ejpam-6388	447	8	(	(	PUNCT
ejpam-6388	447	9	4	4	NUM
ejpam-6388	447	10	)	)	PUNCT
ejpam-6388	447	11	(	(	PUNCT
ejpam-6388	447	12	2025	2025	NUM
ejpam-6388	447	13	)	)	PUNCT
ejpam-6388	447	14	,	,	PUNCT
ejpam-6388	447	15	6388	6388	NUM
ejpam-6388	447	16	19	19	NUM
ejpam-6388	447	17	of	of	ADP
ejpam-6388	447	18	31	31	NUM
ejpam-6388	447	19	plot	plot	NOUN
ejpam-6388	447	20	for	for	ADP
ejpam-6388	447	21	y	y	NOUN
ejpam-6388	447	22	=	=	NOUN
ejpam-6388	447	23	1.5	1.5	NUM
ejpam-6388	447	24	:	:	PUNCT
ejpam-6388	447	25	the	the	DET
ejpam-6388	447	26	graph	graph	NOUN
ejpam-6388	447	27	of	of	ADP
ejpam-6388	447	28	r(ω	r(ω	ADJ
ejpam-6388	447	29	)	)	PUNCT
ejpam-6388	447	30	for	for	ADP
ejpam-6388	447	31	y	y	PROPN
ejpam-6388	447	32	=	=	SYM
ejpam-6388	447	33	1.5	1.5	NUM
ejpam-6388	447	34	is	be	AUX
ejpam-6388	447	35	plotted	plot	VERB
ejpam-6388	447	36	in	in	ADP
ejpam-6388	447	37	figure	figure	NOUN
ejpam-6388	447	38	1	1	NUM
ejpam-6388	447	39	,	,	PUNCT
ejpam-6388	447	40	showing	show	VERB
ejpam-6388	447	41	how	how	SCONJ
ejpam-6388	447	42	the	the	DET
ejpam-6388	447	43	function	function	NOUN
ejpam-6388	447	44	evolves	evolve	VERB
ejpam-6388	447	45	over	over	ADP
ejpam-6388	447	46	the	the	DET
ejpam-6388	447	47	interval	interval	NOUN
ejpam-6388	447	48	[	[	X
ejpam-6388	447	49	0	0	NUM
ejpam-6388	447	50	,	,	PUNCT
ejpam-6388	447	51	1	1	NUM
ejpam-6388	447	52	]	]	PUNCT
ejpam-6388	447	53	.	.	PUNCT
ejpam-6388	448	1	the	the	DET
ejpam-6388	448	2	results	result	NOUN
ejpam-6388	448	3	indicate	indicate	VERB
ejpam-6388	448	4	a	a	DET
ejpam-6388	448	5	smooth	smooth	ADJ
ejpam-6388	448	6	increase	increase	NOUN
ejpam-6388	448	7	in	in	ADP
ejpam-6388	448	8	r(ω	r(ω	ADJ
ejpam-6388	448	9	)	)	PUNCT
ejpam-6388	448	10	as	as	ADP
ejpam-6388	448	11	ω	ω	PROPN
ejpam-6388	448	12	approaches	approach	VERB
ejpam-6388	448	13	1	1	NUM
ejpam-6388	448	14	.	.	PUNCT
ejpam-6388	448	15	figure	figure	NOUN
ejpam-6388	448	16	1	1	NUM
ejpam-6388	448	17	:	:	PUNCT
ejpam-6388	448	18	numerical	numerical	ADJ
ejpam-6388	448	19	values	value	NOUN
ejpam-6388	448	20	of	of	ADP
ejpam-6388	448	21	r(ω	r(ω	ADJ
ejpam-6388	448	22	)	)	PUNCT
ejpam-6388	448	23	for	for	ADP
ejpam-6388	448	24	y	y	PROPN
ejpam-6388	448	25	=	=	PROPN
ejpam-6388	448	26	1.5	1.5	NUM
ejpam-6388	448	27	.	.	PUNCT
ejpam-6388	449	1	the	the	DET
ejpam-6388	449	2	plot	plot	NOUN
ejpam-6388	449	3	shows	show	VERB
ejpam-6388	449	4	how	how	SCONJ
ejpam-6388	449	5	the	the	DET
ejpam-6388	449	6	solution	solution	NOUN
ejpam-6388	449	7	r(ω	r(ω	ADV
ejpam-6388	449	8	)	)	PUNCT
ejpam-6388	449	9	evolves	evolve	VERB
ejpam-6388	449	10	smoothly	smoothly	ADV
ejpam-6388	449	11	as	as	SCONJ
ejpam-6388	449	12	ω	ω	NOUN
ejpam-6388	449	13	increases	increase	VERB
ejpam-6388	449	14	from	from	ADP
ejpam-6388	449	15	0	0	NUM
ejpam-6388	449	16	to	to	ADP
ejpam-6388	449	17	1	1	NUM
ejpam-6388	449	18	,	,	PUNCT
ejpam-6388	449	19	illustrating	illustrate	VERB
ejpam-6388	449	20	the	the	DET
ejpam-6388	449	21	behavior	behavior	NOUN
ejpam-6388	449	22	of	of	ADP
ejpam-6388	449	23	the	the	DET
ejpam-6388	449	24	system	system	NOUN
ejpam-6388	449	25	for	for	ADP
ejpam-6388	449	26	this	this	DET
ejpam-6388	449	27	fractional	fractional	ADJ
ejpam-6388	449	28	order	order	NOUN
ejpam-6388	449	29	.	.	PUNCT
ejpam-6388	450	1	comparative	comparative	ADJ
ejpam-6388	450	2	plot	plot	NOUN
ejpam-6388	450	3	for	for	ADP
ejpam-6388	450	4	y	y	PROPN
ejpam-6388	450	5	=	=	PROPN
ejpam-6388	450	6	1.5	1.5	NUM
ejpam-6388	450	7	and	and	CCONJ
ejpam-6388	450	8	y	y	NOUN
ejpam-6388	450	9	=	=	NOUN
ejpam-6388	450	10	2.0	2.0	NUM
ejpam-6388	450	11	:	:	PUNCT
ejpam-6388	450	12	the	the	DET
ejpam-6388	450	13	second	second	ADJ
ejpam-6388	450	14	plot	plot	NOUN
ejpam-6388	450	15	compares	compare	VERB
ejpam-6388	450	16	the	the	DET
ejpam-6388	450	17	two	two	NUM
ejpam-6388	450	18	solutions	solution	NOUN
ejpam-6388	450	19	.	.	PUNCT
ejpam-6388	451	1	for	for	ADP
ejpam-6388	451	2	both	both	DET
ejpam-6388	451	3	values	value	NOUN
ejpam-6388	451	4	of	of	ADP
ejpam-6388	451	5	y	y	PROPN
ejpam-6388	451	6	,	,	PUNCT
ejpam-6388	451	7	the	the	DET
ejpam-6388	451	8	function	function	NOUN
ejpam-6388	451	9	r	r	NOUN
ejpam-6388	451	10	exhibits	exhibit	VERB
ejpam-6388	451	11	a	a	DET
ejpam-6388	451	12	similar	similar	ADJ
ejpam-6388	451	13	overall	overall	ADJ
ejpam-6388	451	14	trend	trend	NOUN
ejpam-6388	451	15	;	;	PUNCT
ejpam-6388	451	16	however	however	ADV
ejpam-6388	451	17	,	,	PUNCT
ejpam-6388	451	18	for	for	ADP
ejpam-6388	451	19	y	y	PROPN
ejpam-6388	451	20	=	=	SYM
ejpam-6388	451	21	2.0	2.0	NUM
ejpam-6388	451	22	,	,	PUNCT
ejpam-6388	451	23	the	the	DET
ejpam-6388	451	24	values	value	NOUN
ejpam-6388	451	25	of	of	ADP
ejpam-6388	451	26	r(ω	r(ω	ADJ
ejpam-6388	451	27	)	)	PUNCT
ejpam-6388	451	28	are	be	AUX
ejpam-6388	451	29	slightly	slightly	ADV
ejpam-6388	451	30	higher	high	ADJ
ejpam-6388	451	31	,	,	PUNCT
ejpam-6388	451	32	indicating	indicate	VERB
ejpam-6388	451	33	the	the	DET
ejpam-6388	451	34	effect	effect	NOUN
ejpam-6388	451	35	of	of	ADP
ejpam-6388	451	36	the	the	DET
ejpam-6388	451	37	increased	increase	VERB
ejpam-6388	451	38	fractional	fractional	ADJ
ejpam-6388	451	39	order	order	NOUN
ejpam-6388	451	40	on	on	ADP
ejpam-6388	451	41	the	the	DET
ejpam-6388	451	42	solution	solution	NOUN
ejpam-6388	451	43	behavior	behavior	NOUN
ejpam-6388	451	44	.	.	PUNCT
ejpam-6388	452	1	this	this	PRON
ejpam-6388	452	2	is	be	AUX
ejpam-6388	452	3	given	give	VERB
ejpam-6388	452	4	in	in	ADP
ejpam-6388	452	5	figure	figure	NOUN
ejpam-6388	452	6	2	2	NUM
ejpam-6388	452	7	.	.	PUNCT
ejpam-6388	452	8	d.	d.	PROPN
ejpam-6388	452	9	baleanu	baleanu	PROPN
ejpam-6388	453	1	et	et	PROPN
ejpam-6388	453	2	al	al	PROPN
ejpam-6388	453	3	.	.	PUNCT
ejpam-6388	453	4	/	/	SYM
ejpam-6388	453	5	eur	eur	PROPN
ejpam-6388	453	6	.	.	PUNCT
ejpam-6388	454	1	j.	j.	PROPN
ejpam-6388	454	2	pure	pure	PROPN
ejpam-6388	454	3	appl	appl	PROPN
ejpam-6388	454	4	.	.	PROPN
ejpam-6388	454	5	math	math	PROPN
ejpam-6388	454	6	,	,	PUNCT
ejpam-6388	454	7	18	18	NUM
ejpam-6388	454	8	(	(	PUNCT
ejpam-6388	454	9	4	4	NUM
ejpam-6388	454	10	)	)	PUNCT
ejpam-6388	454	11	(	(	PUNCT
ejpam-6388	454	12	2025	2025	NUM
ejpam-6388	454	13	)	)	PUNCT
ejpam-6388	454	14	,	,	PUNCT
ejpam-6388	454	15	6388	6388	NUM
ejpam-6388	454	16	20	20	NUM
ejpam-6388	454	17	of	of	ADP
ejpam-6388	454	18	31	31	NUM
ejpam-6388	454	19	figure	figure	NOUN
ejpam-6388	454	20	2	2	NUM
ejpam-6388	454	21	:	:	PUNCT
ejpam-6388	454	22	comparison	comparison	NOUN
ejpam-6388	454	23	of	of	ADP
ejpam-6388	454	24	the	the	DET
ejpam-6388	454	25	numerical	numerical	ADJ
ejpam-6388	454	26	values	value	NOUN
ejpam-6388	454	27	of	of	ADP
ejpam-6388	454	28	r(ω	r(ω	ADJ
ejpam-6388	454	29	)	)	PUNCT
ejpam-6388	454	30	for	for	ADP
ejpam-6388	454	31	y	y	PROPN
ejpam-6388	454	32	=	=	PROPN
ejpam-6388	454	33	1.5	1.5	NUM
ejpam-6388	454	34	and	and	CCONJ
ejpam-6388	454	35	y	y	NOUN
ejpam-6388	454	36	=	=	PROPN
ejpam-6388	454	37	2.0	2.0	NUM
ejpam-6388	454	38	.	.	PUNCT
ejpam-6388	455	1	the	the	DET
ejpam-6388	455	2	plot	plot	NOUN
ejpam-6388	455	3	shows	show	VERB
ejpam-6388	455	4	that	that	SCONJ
ejpam-6388	455	5	while	while	SCONJ
ejpam-6388	455	6	both	both	DET
ejpam-6388	455	7	solutions	solution	NOUN
ejpam-6388	455	8	follow	follow	VERB
ejpam-6388	455	9	a	a	DET
ejpam-6388	455	10	similar	similar	ADJ
ejpam-6388	455	11	trend	trend	NOUN
ejpam-6388	455	12	,	,	PUNCT
ejpam-6388	455	13	the	the	DET
ejpam-6388	455	14	solution	solution	NOUN
ejpam-6388	455	15	for	for	ADP
ejpam-6388	455	16	y	y	PROPN
ejpam-6388	455	17	=	=	PROPN
ejpam-6388	455	18	2.0	2.0	NUM
ejpam-6388	455	19	is	be	AUX
ejpam-6388	455	20	slightly	slightly	ADV
ejpam-6388	455	21	higher	high	ADJ
ejpam-6388	455	22	,	,	PUNCT
ejpam-6388	455	23	indicating	indicate	VERB
ejpam-6388	455	24	the	the	DET
ejpam-6388	455	25	impact	impact	NOUN
ejpam-6388	455	26	of	of	ADP
ejpam-6388	455	27	the	the	DET
ejpam-6388	455	28	increased	increase	VERB
ejpam-6388	455	29	fractional	fractional	ADJ
ejpam-6388	455	30	order	order	NOUN
ejpam-6388	455	31	on	on	ADP
ejpam-6388	455	32	the	the	DET
ejpam-6388	455	33	behavior	behavior	NOUN
ejpam-6388	455	34	of	of	ADP
ejpam-6388	455	35	the	the	DET
ejpam-6388	455	36	system	system	NOUN
ejpam-6388	455	37	.	.	PUNCT
ejpam-6388	456	1	example	example	NOUN
ejpam-6388	457	1	2	2	NUM
ejpam-6388	457	2	.	.	X
ejpam-6388	457	3	consider	consider	VERB
ejpam-6388	457	4	the	the	DET
ejpam-6388	457	5	fhbvp	fhbvp	NOUN
ejpam-6388	457	6	(	(	PUNCT
ejpam-6388	457	7	1)–(2	1)–(2	NUM
ejpam-6388	457	8	)	)	PUNCT
ejpam-6388	457	9	with	with	ADP
ejpam-6388	457	10	y	y	PROPN
ejpam-6388	457	11	=	=	SYM
ejpam-6388	457	12	1.5	1.5	NUM
ejpam-6388	457	13	and	and	CCONJ
ejpam-6388	457	14	g(ω	g(ω	PROPN
ejpam-6388	457	15	,	,	PUNCT
ejpam-6388	457	16	r	r	NOUN
ejpam-6388	457	17	)	)	PUNCT
ejpam-6388	457	18	=	=	SYM
ejpam-6388	457	19	2(1	2(1	NUM
ejpam-6388	457	20	+	+	NUM
ejpam-6388	457	21	ω	ω	NUM
ejpam-6388	457	22	)	)	PUNCT
ejpam-6388	458	1	+	+	CCONJ
ejpam-6388	458	2	(	(	PUNCT
ejpam-6388	458	3	1	1	NUM
ejpam-6388	458	4	+	+	NUM
ejpam-6388	458	5	ω	ω	X
ejpam-6388	458	6	)	)	PUNCT
ejpam-6388	458	7	sin(r	sin(r	PROPN
ejpam-6388	458	8	)	)	PUNCT
ejpam-6388	458	9	.	.	PUNCT
ejpam-6388	459	1	let	let	VERB
ejpam-6388	459	2	f1(ω	f1(ω	SYM
ejpam-6388	459	3	,	,	PUNCT
ejpam-6388	459	4	r	r	NOUN
ejpam-6388	459	5	)	)	PUNCT
ejpam-6388	459	6	=	=	SYM
ejpam-6388	460	1	ω	ω	PROPN
ejpam-6388	460	2	+	+	NUM
ejpam-6388	460	3	4	4	NUM
ejpam-6388	460	4	cos(r	cos(r	NUM
ejpam-6388	460	5	)	)	PUNCT
ejpam-6388	460	6	19	19	NUM
ejpam-6388	461	1	+	+	NUM
ejpam-6388	461	2	38	38	NUM
ejpam-6388	461	3	m	m	NOUN
ejpam-6388	461	4	and	and	CCONJ
ejpam-6388	461	5	f1(ω	f1(ω	NOUN
ejpam-6388	461	6	,	,	PUNCT
ejpam-6388	461	7	r	r	NOUN
ejpam-6388	461	8	)	)	PUNCT
ejpam-6388	461	9	=	=	VERB
ejpam-6388	461	10	eω	eω	NOUN
ejpam-6388	461	11	+	+	NOUN
ejpam-6388	461	12	4	4	NUM
ejpam-6388	461	13	sin(r	sin(r	NOUN
ejpam-6388	461	14	)	)	PUNCT
ejpam-6388	461	15	19	19	NUM
ejpam-6388	462	1	+	+	NUM
ejpam-6388	462	2	38	38	NUM
ejpam-6388	462	3	m	m	NOUN
ejpam-6388	462	4	.	.	PUNCT
ejpam-6388	463	1	d.	d.	PROPN
ejpam-6388	463	2	baleanu	baleanu	PROPN
ejpam-6388	463	3	et	et	PROPN
ejpam-6388	463	4	al	al	PROPN
ejpam-6388	463	5	.	.	PUNCT
ejpam-6388	463	6	/	/	SYM
ejpam-6388	463	7	eur	eur	PROPN
ejpam-6388	463	8	.	.	PUNCT
ejpam-6388	464	1	j.	j.	PROPN
ejpam-6388	464	2	pure	pure	PROPN
ejpam-6388	464	3	appl	appl	PROPN
ejpam-6388	464	4	.	.	PROPN
ejpam-6388	464	5	math	math	PROPN
ejpam-6388	464	6	,	,	PUNCT
ejpam-6388	464	7	18	18	NUM
ejpam-6388	464	8	(	(	PUNCT
ejpam-6388	464	9	4	4	NUM
ejpam-6388	464	10	)	)	PUNCT
ejpam-6388	464	11	(	(	PUNCT
ejpam-6388	464	12	2025	2025	NUM
ejpam-6388	464	13	)	)	PUNCT
ejpam-6388	464	14	,	,	PUNCT
ejpam-6388	464	15	6388	6388	NUM
ejpam-6388	464	16	21	21	NUM
ejpam-6388	464	17	of	of	ADP
ejpam-6388	464	18	31	31	NUM
ejpam-6388	464	19	figure	figure	NOUN
ejpam-6388	464	20	3	3	NUM
ejpam-6388	464	21	:	:	PUNCT
ejpam-6388	464	22	comparison	comparison	NOUN
ejpam-6388	464	23	of	of	ADP
ejpam-6388	464	24	solutions	solution	NOUN
ejpam-6388	464	25	of	of	ADP
ejpam-6388	464	26	r(ω	r(ω	ADV
ejpam-6388	464	27	)	)	PUNCT
ejpam-6388	464	28	using	use	VERB
ejpam-6388	464	29	two	two	NUM
ejpam-6388	464	30	different	different	ADJ
ejpam-6388	464	31	f	f	PROPN
ejpam-6388	464	32	functions	function	NOUN
ejpam-6388	464	33	:	:	PUNCT
ejpam-6388	464	34	f1(ω	f1(ω	NUM
ejpam-6388	464	35	,	,	PUNCT
ejpam-6388	464	36	r	r	NOUN
ejpam-6388	464	37	)	)	PUNCT
ejpam-6388	464	38	=	=	SYM
ejpam-6388	464	39	ω	ω	PROPN
ejpam-6388	465	1	+	+	NUM
ejpam-6388	465	2	4	4	NUM
ejpam-6388	465	3	cos(r	cos(r	NUM
ejpam-6388	465	4	)	)	PUNCT
ejpam-6388	465	5	19	19	NUM
ejpam-6388	466	1	+	+	NUM
ejpam-6388	466	2	38	38	NUM
ejpam-6388	466	3	m	m	NOUN
ejpam-6388	466	4	and	and	CCONJ
ejpam-6388	466	5	f2(ω	f2(ω	ADJ
ejpam-6388	466	6	,	,	PUNCT
ejpam-6388	466	7	r	r	NOUN
ejpam-6388	466	8	)	)	PUNCT
ejpam-6388	466	9	=	=	VERB
ejpam-6388	466	10	eω	eω	NOUN
ejpam-6388	466	11	+	+	NOUN
ejpam-6388	466	12	4	4	NUM
ejpam-6388	466	13	sin(r	sin(r	NOUN
ejpam-6388	466	14	)	)	PUNCT
ejpam-6388	466	15	19	19	NUM
ejpam-6388	467	1	+	+	NUM
ejpam-6388	467	2	38	38	NUM
ejpam-6388	467	3	m	m	NOUN
ejpam-6388	467	4	,	,	PUNCT
ejpam-6388	467	5	with	with	ADP
ejpam-6388	467	6	y	y	PROPN
ejpam-6388	467	7	=	=	SYM
ejpam-6388	467	8	1.5	1.5	NUM
ejpam-6388	467	9	and	and	CCONJ
ejpam-6388	467	10	g(ω	g(ω	PROPN
ejpam-6388	467	11	,	,	PUNCT
ejpam-6388	467	12	r	r	NOUN
ejpam-6388	467	13	)	)	PUNCT
ejpam-6388	467	14	=	=	SYM
ejpam-6388	467	15	2(1	2(1	NUM
ejpam-6388	467	16	+	+	NUM
ejpam-6388	467	17	ω	ω	NUM
ejpam-6388	467	18	)	)	PUNCT
ejpam-6388	467	19	+	+	CCONJ
ejpam-6388	467	20	(	(	PUNCT
ejpam-6388	467	21	1	1	NUM
ejpam-6388	467	22	+	+	NUM
ejpam-6388	467	23	ω	ω	X
ejpam-6388	467	24	)	)	PUNCT
ejpam-6388	467	25	sin(r	sin(r	PROPN
ejpam-6388	467	26	)	)	PUNCT
ejpam-6388	467	27	.	.	PUNCT
ejpam-6388	468	1	the	the	DET
ejpam-6388	468	2	plot	plot	NOUN
ejpam-6388	468	3	,	,	PUNCT
ejpam-6388	468	4	in	in	ADP
ejpam-6388	468	5	figure	figure	NOUN
ejpam-6388	468	6	3	3	NUM
ejpam-6388	468	7	,	,	PUNCT
ejpam-6388	468	8	comparing	compare	VERB
ejpam-6388	468	9	the	the	DET
ejpam-6388	468	10	values	value	NOUN
ejpam-6388	468	11	of	of	ADP
ejpam-6388	468	12	solutions	solution	NOUN
ejpam-6388	468	13	r(ω	r(ω	ADV
ejpam-6388	468	14	)	)	PUNCT
ejpam-6388	468	15	for	for	ADP
ejpam-6388	468	16	the	the	DET
ejpam-6388	468	17	two	two	NUM
ejpam-6388	468	18	f	f	PROPN
ejpam-6388	468	19	functions	function	NOUN
ejpam-6388	468	20	(	(	PUNCT
ejpam-6388	468	21	f1	f1	NOUN
ejpam-6388	468	22	and	and	CCONJ
ejpam-6388	468	23	f2	f2	PROPN
ejpam-6388	468	24	)	)	PUNCT
ejpam-6388	468	25	reveals	reveal	VERB
ejpam-6388	468	26	several	several	ADJ
ejpam-6388	468	27	key	key	ADJ
ejpam-6388	468	28	observations	observation	NOUN
ejpam-6388	468	29	.	.	PUNCT
ejpam-6388	469	1	both	both	DET
ejpam-6388	469	2	functions	function	NOUN
ejpam-6388	469	3	show	show	VERB
ejpam-6388	469	4	a	a	DET
ejpam-6388	469	5	similar	similar	ADJ
ejpam-6388	469	6	increasing	increase	VERB
ejpam-6388	469	7	trend	trend	NOUN
ejpam-6388	469	8	in	in	ADP
ejpam-6388	469	9	r(ω	r(ω	ADV
ejpam-6388	469	10	)	)	PUNCT
ejpam-6388	469	11	as	as	ADP
ejpam-6388	469	12	ω	ω	X
ejpam-6388	469	13	increases	increase	VERB
ejpam-6388	469	14	from	from	ADP
ejpam-6388	469	15	0	0	NUM
ejpam-6388	469	16	to	to	ADP
ejpam-6388	469	17	1	1	NUM
ejpam-6388	469	18	,	,	PUNCT
ejpam-6388	469	19	indicating	indicate	VERB
ejpam-6388	469	20	a	a	DET
ejpam-6388	469	21	positive	positive	ADJ
ejpam-6388	469	22	correlation	correlation	NOUN
ejpam-6388	469	23	.	.	PUNCT
ejpam-6388	470	1	however	however	ADV
ejpam-6388	470	2	,	,	PUNCT
ejpam-6388	470	3	f1	f1	PROPN
ejpam-6388	470	4	(	(	PUNCT
ejpam-6388	470	5	blue	blue	ADJ
ejpam-6388	470	6	line	line	NOUN
ejpam-6388	470	7	)	)	PUNCT
ejpam-6388	470	8	consistently	consistently	ADV
ejpam-6388	470	9	exhibits	exhibit	VERB
ejpam-6388	470	10	a	a	DET
ejpam-6388	470	11	higher	high	ADJ
ejpam-6388	470	12	magnitude	magnitude	NOUN
ejpam-6388	470	13	than	than	ADP
ejpam-6388	470	14	f2	f2	PROPN
ejpam-6388	470	15	(	(	PUNCT
ejpam-6388	470	16	orange	orange	ADJ
ejpam-6388	470	17	line	line	NOUN
ejpam-6388	470	18	)	)	PUNCT
ejpam-6388	470	19	,	,	PUNCT
ejpam-6388	470	20	highlighting	highlight	VERB
ejpam-6388	470	21	the	the	DET
ejpam-6388	470	22	significant	significant	ADJ
ejpam-6388	470	23	impact	impact	NOUN
ejpam-6388	470	24	of	of	ADP
ejpam-6388	470	25	the	the	DET
ejpam-6388	470	26	chosen	choose	VERB
ejpam-6388	470	27	f	f	PROPN
ejpam-6388	470	28	function	function	NOUN
ejpam-6388	470	29	on	on	ADP
ejpam-6388	470	30	the	the	DET
ejpam-6388	470	31	resulting	result	VERB
ejpam-6388	470	32	r(ω	r(ω	ADJ
ejpam-6388	470	33	)	)	PUNCT
ejpam-6388	470	34	values	value	NOUN
ejpam-6388	470	35	.	.	PUNCT
ejpam-6388	471	1	while	while	SCONJ
ejpam-6388	471	2	f1	f1	NOUN
ejpam-6388	471	3	produces	produce	VERB
ejpam-6388	471	4	a	a	DET
ejpam-6388	471	5	smoother	smooth	ADJ
ejpam-6388	471	6	curve	curve	NOUN
ejpam-6388	471	7	,	,	PUNCT
ejpam-6388	471	8	f2	f2	PROPN
ejpam-6388	471	9	introduces	introduce	VERB
ejpam-6388	471	10	more	more	ADJ
ejpam-6388	471	11	fluctuations	fluctuation	NOUN
ejpam-6388	471	12	.	.	PUNCT
ejpam-6388	472	1	this	this	PRON
ejpam-6388	472	2	can	can	AUX
ejpam-6388	472	3	be	be	AUX
ejpam-6388	472	4	attributed	attribute	VERB
ejpam-6388	472	5	to	to	ADP
ejpam-6388	472	6	f1	f1	NOUN
ejpam-6388	472	7	including	include	VERB
ejpam-6388	472	8	a	a	DET
ejpam-6388	472	9	term	term	NOUN
ejpam-6388	472	10	proportional	proportional	ADJ
ejpam-6388	472	11	to	to	ADP
ejpam-6388	472	12	ω	ω	NUM
ejpam-6388	472	13	,	,	PUNCT
ejpam-6388	472	14	while	while	SCONJ
ejpam-6388	472	15	f2	f2	PROPN
ejpam-6388	472	16	relies	rely	VERB
ejpam-6388	472	17	on	on	ADP
ejpam-6388	472	18	sin(r	sin(r	PROPN
ejpam-6388	472	19	)	)	PUNCT
ejpam-6388	472	20	,	,	PUNCT
ejpam-6388	472	21	which	which	PRON
ejpam-6388	472	22	may	may	AUX
ejpam-6388	472	23	have	have	VERB
ejpam-6388	472	24	a	a	DET
ejpam-6388	472	25	lesser	less	ADJ
ejpam-6388	472	26	effect	effect	NOUN
ejpam-6388	472	27	on	on	ADP
ejpam-6388	472	28	magnitude	magnitude	NOUN
ejpam-6388	472	29	.	.	PUNCT
ejpam-6388	473	1	overall	overall	ADV
ejpam-6388	473	2	,	,	PUNCT
ejpam-6388	473	3	the	the	DET
ejpam-6388	473	4	plot	plot	NOUN
ejpam-6388	473	5	illustrates	illustrate	VERB
ejpam-6388	473	6	how	how	SCONJ
ejpam-6388	473	7	variations	variation	NOUN
ejpam-6388	473	8	in	in	ADP
ejpam-6388	473	9	the	the	DET
ejpam-6388	473	10	f	f	PROPN
ejpam-6388	473	11	function	function	NOUN
ejpam-6388	473	12	influence	influence	NOUN
ejpam-6388	473	13	both	both	CCONJ
ejpam-6388	473	14	the	the	DET
ejpam-6388	473	15	magnitude	magnitude	NOUN
ejpam-6388	473	16	and	and	CCONJ
ejpam-6388	473	17	shape	shape	NOUN
ejpam-6388	473	18	of	of	ADP
ejpam-6388	473	19	the	the	DET
ejpam-6388	473	20	solutions	solution	NOUN
ejpam-6388	473	21	for	for	ADP
ejpam-6388	473	22	r(ω	r(ω	ADJ
ejpam-6388	473	23	)	)	PUNCT
ejpam-6388	473	24	.	.	PUNCT
ejpam-6388	474	1	example	example	NOUN
ejpam-6388	475	1	3	3	X
ejpam-6388	475	2	.	.	X
ejpam-6388	475	3	consider	consider	VERB
ejpam-6388	475	4	the	the	DET
ejpam-6388	475	5	fhbvp	fhbvp	NOUN
ejpam-6388	475	6	(	(	PUNCT
ejpam-6388	475	7	1)-(2	1)-(2	NUM
ejpam-6388	475	8	)	)	PUNCT
ejpam-6388	475	9	with	with	ADP
ejpam-6388	475	10	y	y	PROPN
ejpam-6388	475	11	=	=	SYM
ejpam-6388	475	12	1.5	1.5	NUM
ejpam-6388	475	13	and	and	CCONJ
ejpam-6388	475	14	f(ω	f(ω	PROPN
ejpam-6388	475	15	,	,	PUNCT
ejpam-6388	475	16	r	r	NOUN
ejpam-6388	475	17	)	)	PUNCT
ejpam-6388	476	1	=	=	SYM
ejpam-6388	476	2	ω	ω	PROPN
ejpam-6388	476	3	+	+	NUM
ejpam-6388	476	4	4	4	NUM
ejpam-6388	476	5	cos(r	cos(r	NUM
ejpam-6388	476	6	)	)	PUNCT
ejpam-6388	476	7	19	19	NUM
ejpam-6388	477	1	+	+	NUM
ejpam-6388	477	2	38	38	NUM
ejpam-6388	477	3	m	m	NOUN
ejpam-6388	477	4	.	.	PUNCT
ejpam-6388	478	1	let	let	VERB
ejpam-6388	478	2	g1(ω	g1(ω	PRON
ejpam-6388	478	3	,	,	PUNCT
ejpam-6388	478	4	r	r	NOUN
ejpam-6388	478	5	)	)	PUNCT
ejpam-6388	478	6	=	=	SYM
ejpam-6388	478	7	2(1	2(1	NUM
ejpam-6388	478	8	+	+	NUM
ejpam-6388	478	9	ω	ω	NUM
ejpam-6388	478	10	)	)	PUNCT
ejpam-6388	479	1	+	+	CCONJ
ejpam-6388	479	2	(	(	PUNCT
ejpam-6388	479	3	1	1	NUM
ejpam-6388	479	4	+	+	NUM
ejpam-6388	479	5	ω	ω	X
ejpam-6388	479	6	)	)	PUNCT
ejpam-6388	479	7	sin(r	sin(r	PROPN
ejpam-6388	479	8	)	)	PUNCT
ejpam-6388	479	9	and	and	CCONJ
ejpam-6388	479	10	g2(ω	g2(ω	PROPN
ejpam-6388	479	11	,	,	PUNCT
ejpam-6388	479	12	r	r	NOUN
ejpam-6388	479	13	)	)	PUNCT
ejpam-6388	479	14	=	=	SYM
ejpam-6388	479	15	(	(	PUNCT
ejpam-6388	479	16	1	1	NUM
ejpam-6388	479	17	−	−	PROPN
ejpam-6388	479	18	ω	ω	NUM
ejpam-6388	479	19	)	)	PUNCT
ejpam-6388	479	20	cos(r	cos(r	PROPN
ejpam-6388	479	21	)	)	PUNCT
ejpam-6388	479	22	.	.	PUNCT
ejpam-6388	480	1	the	the	DET
ejpam-6388	480	2	plot	plot	NOUN
ejpam-6388	480	3	,	,	PUNCT
ejpam-6388	480	4	in	in	ADP
ejpam-6388	480	5	figure	figure	NOUN
ejpam-6388	480	6	4	4	NUM
ejpam-6388	480	7	,	,	PUNCT
ejpam-6388	480	8	compares	compare	VERB
ejpam-6388	480	9	the	the	DET
ejpam-6388	480	10	value	value	NOUN
ejpam-6388	480	11	of	of	ADP
ejpam-6388	480	12	r(ω	r(ω	ADV
ejpam-6388	480	13	)	)	PUNCT
ejpam-6388	480	14	using	use	VERB
ejpam-6388	480	15	two	two	NUM
ejpam-6388	480	16	different	different	ADJ
ejpam-6388	480	17	g	g	NOUN
ejpam-6388	480	18	functions	function	NOUN
ejpam-6388	480	19	(	(	PUNCT
ejpam-6388	480	20	g1	g1	PROPN
ejpam-6388	480	21	and	and	CCONJ
ejpam-6388	480	22	g2	g2	PROPN
ejpam-6388	480	23	)	)	PUNCT
ejpam-6388	480	24	while	while	SCONJ
ejpam-6388	480	25	keeping	keep	VERB
ejpam-6388	480	26	the	the	DET
ejpam-6388	480	27	same	same	ADJ
ejpam-6388	480	28	f	f	PROPN
ejpam-6388	480	29	function	function	NOUN
ejpam-6388	480	30	.	.	PUNCT
ejpam-6388	481	1	both	both	DET
ejpam-6388	481	2	solutions	solution	NOUN
ejpam-6388	481	3	show	show	VERB
ejpam-6388	481	4	a	a	DET
ejpam-6388	481	5	similar	similar	ADJ
ejpam-6388	481	6	increasing	increase	VERB
ejpam-6388	481	7	trend	trend	NOUN
ejpam-6388	481	8	as	as	ADP
ejpam-6388	481	9	ω	ω	NOUN
ejpam-6388	481	10	moves	move	NOUN
ejpam-6388	481	11	from	from	ADP
ejpam-6388	481	12	0	0	NUM
ejpam-6388	481	13	to	to	ADP
ejpam-6388	481	14	1	1	NUM
ejpam-6388	481	15	,	,	PUNCT
ejpam-6388	481	16	indicating	indicate	VERB
ejpam-6388	481	17	a	a	DET
ejpam-6388	481	18	positive	positive	ADJ
ejpam-6388	481	19	correlation	correlation	NOUN
ejpam-6388	481	20	.	.	PUNCT
ejpam-6388	482	1	however	however	ADV
ejpam-6388	482	2	,	,	PUNCT
ejpam-6388	482	3	g1	g1	PROPN
ejpam-6388	482	4	(	(	PUNCT
ejpam-6388	482	5	blue	blue	ADJ
ejpam-6388	482	6	line	line	NOUN
ejpam-6388	482	7	)	)	PUNCT
ejpam-6388	482	8	yields	yield	NOUN
ejpam-6388	482	9	consistently	consistently	ADV
ejpam-6388	482	10	higher	high	ADJ
ejpam-6388	482	11	magnitudes	magnitude	NOUN
ejpam-6388	482	12	than	than	ADP
ejpam-6388	482	13	g2	g2	PROPN
ejpam-6388	482	14	(	(	PUNCT
ejpam-6388	482	15	orange	orange	PROPN
ejpam-6388	482	16	line	line	NOUN
ejpam-6388	482	17	)	)	PUNCT
ejpam-6388	482	18	.	.	PUNCT
ejpam-6388	483	1	the	the	DET
ejpam-6388	483	2	curve	curve	NOUN
ejpam-6388	483	3	for	for	ADP
ejpam-6388	483	4	g1	g1	PROPN
ejpam-6388	483	5	is	be	AUX
ejpam-6388	483	6	smoother	smooth	ADJ
ejpam-6388	483	7	with	with	ADP
ejpam-6388	483	8	a	a	DET
ejpam-6388	483	9	steeper	steep	ADJ
ejpam-6388	483	10	upward	upward	ADJ
ejpam-6388	483	11	slope	slope	NOUN
ejpam-6388	483	12	,	,	PUNCT
ejpam-6388	483	13	while	while	SCONJ
ejpam-6388	483	14	g2	g2	PROPN
ejpam-6388	483	15	introduces	introduce	VERB
ejpam-6388	483	16	more	more	ADJ
ejpam-6388	483	17	fluctuations	fluctuation	NOUN
ejpam-6388	483	18	and	and	CCONJ
ejpam-6388	483	19	a	a	DET
ejpam-6388	483	20	less	less	ADV
ejpam-6388	483	21	pronounced	pronounced	ADJ
ejpam-6388	483	22	increase	increase	NOUN
ejpam-6388	483	23	.	.	PUNCT
ejpam-6388	484	1	these	these	DET
ejpam-6388	484	2	differences	difference	NOUN
ejpam-6388	484	3	arise	arise	VERB
ejpam-6388	484	4	from	from	ADP
ejpam-6388	484	5	the	the	DET
ejpam-6388	484	6	terms	term	NOUN
ejpam-6388	484	7	in	in	ADP
ejpam-6388	484	8	each	each	DET
ejpam-6388	484	9	g	g	PROPN
ejpam-6388	484	10	function	function	NOUN
ejpam-6388	484	11	,	,	PUNCT
ejpam-6388	484	12	with	with	ADP
ejpam-6388	484	13	g1	g1	PROPN
ejpam-6388	484	14	contributing	contribute	VERB
ejpam-6388	484	15	positively	positively	ADV
ejpam-6388	484	16	d.	d.	PROPN
ejpam-6388	484	17	baleanu	baleanu	PROPN
ejpam-6388	484	18	et	et	PROPN
ejpam-6388	484	19	al	al	PROPN
ejpam-6388	484	20	.	.	PUNCT
ejpam-6388	484	21	/	/	SYM
ejpam-6388	484	22	eur	eur	PROPN
ejpam-6388	484	23	.	.	PUNCT
ejpam-6388	485	1	j.	j.	PROPN
ejpam-6388	485	2	pure	pure	PROPN
ejpam-6388	485	3	appl	appl	PROPN
ejpam-6388	485	4	.	.	PROPN
ejpam-6388	485	5	math	math	PROPN
ejpam-6388	485	6	,	,	PUNCT
ejpam-6388	485	7	18	18	NUM
ejpam-6388	485	8	(	(	PUNCT
ejpam-6388	485	9	4	4	NUM
ejpam-6388	485	10	)	)	PUNCT
ejpam-6388	485	11	(	(	PUNCT
ejpam-6388	485	12	2025	2025	NUM
ejpam-6388	485	13	)	)	PUNCT
ejpam-6388	485	14	,	,	PUNCT
ejpam-6388	485	15	6388	6388	NUM
ejpam-6388	485	16	22	22	NUM
ejpam-6388	485	17	of	of	ADP
ejpam-6388	485	18	31	31	NUM
ejpam-6388	485	19	to	to	PART
ejpam-6388	485	20	magnitude	magnitude	VERB
ejpam-6388	485	21	through	through	ADP
ejpam-6388	485	22	2(1+ω	2(1+ω	NUM
ejpam-6388	485	23	)	)	PUNCT
ejpam-6388	485	24	and	and	CCONJ
ejpam-6388	485	25	(	(	PUNCT
ejpam-6388	485	26	1+ω	1+ω	NUM
ejpam-6388	485	27	)	)	PUNCT
ejpam-6388	485	28	sin(r	sin(r	PROPN
ejpam-6388	485	29	)	)	PUNCT
ejpam-6388	485	30	,	,	PUNCT
ejpam-6388	485	31	while	while	SCONJ
ejpam-6388	485	32	g2	g2	PROPN
ejpam-6388	485	33	relies	rely	VERB
ejpam-6388	485	34	on	on	ADP
ejpam-6388	485	35	(	(	PUNCT
ejpam-6388	485	36	1−ω	1−ω	NUM
ejpam-6388	485	37	)	)	PUNCT
ejpam-6388	485	38	cos(r	cos(r	PROPN
ejpam-6388	485	39	)	)	PUNCT
ejpam-6388	485	40	,	,	PUNCT
ejpam-6388	485	41	which	which	PRON
ejpam-6388	485	42	can	can	AUX
ejpam-6388	485	43	lead	lead	VERB
ejpam-6388	485	44	to	to	ADP
ejpam-6388	485	45	lower	low	ADJ
ejpam-6388	485	46	magnitudes	magnitude	NOUN
ejpam-6388	485	47	and	and	CCONJ
ejpam-6388	485	48	more	more	ADJ
ejpam-6388	485	49	oscillations	oscillation	NOUN
ejpam-6388	485	50	.	.	PUNCT
ejpam-6388	486	1	overall	overall	ADV
ejpam-6388	486	2	,	,	PUNCT
ejpam-6388	486	3	the	the	DET
ejpam-6388	486	4	plot	plot	NOUN
ejpam-6388	486	5	highlights	highlight	NOUN
ejpam-6388	486	6	how	how	SCONJ
ejpam-6388	486	7	variations	variation	NOUN
ejpam-6388	486	8	in	in	ADP
ejpam-6388	486	9	the	the	DET
ejpam-6388	486	10	g	g	PROPN
ejpam-6388	486	11	function	function	NOUN
ejpam-6388	486	12	affect	affect	VERB
ejpam-6388	486	13	the	the	DET
ejpam-6388	486	14	solutions	solution	NOUN
ejpam-6388	486	15	for	for	ADP
ejpam-6388	486	16	r(ω	r(ω	ADJ
ejpam-6388	486	17	)	)	PUNCT
ejpam-6388	486	18	.	.	PUNCT
ejpam-6388	487	1	figure	figure	VERB
ejpam-6388	487	2	4	4	NUM
ejpam-6388	487	3	:	:	PUNCT
ejpam-6388	487	4	comparison	comparison	NOUN
ejpam-6388	487	5	of	of	ADP
ejpam-6388	487	6	solutions	solution	NOUN
ejpam-6388	487	7	r(ω	r(ω	ADV
ejpam-6388	487	8	)	)	PUNCT
ejpam-6388	487	9	using	use	VERB
ejpam-6388	487	10	two	two	NUM
ejpam-6388	487	11	different	different	ADJ
ejpam-6388	487	12	g	g	NOUN
ejpam-6388	487	13	functions	function	NOUN
ejpam-6388	487	14	:	:	PUNCT
ejpam-6388	487	15	g1(ω	g1(ω	NUM
ejpam-6388	487	16	,	,	PUNCT
ejpam-6388	487	17	r	r	NOUN
ejpam-6388	487	18	)	)	PUNCT
ejpam-6388	487	19	=	=	SYM
ejpam-6388	487	20	2(1	2(1	NUM
ejpam-6388	487	21	+	+	NUM
ejpam-6388	487	22	ω	ω	NUM
ejpam-6388	487	23	)	)	PUNCT
ejpam-6388	488	1	+	+	CCONJ
ejpam-6388	488	2	(	(	PUNCT
ejpam-6388	488	3	1	1	NUM
ejpam-6388	488	4	+	+	NUM
ejpam-6388	488	5	ω	ω	X
ejpam-6388	488	6	)	)	PUNCT
ejpam-6388	488	7	sin(r	sin(r	PROPN
ejpam-6388	488	8	)	)	PUNCT
ejpam-6388	488	9	and	and	CCONJ
ejpam-6388	488	10	g2(ω	g2(ω	PROPN
ejpam-6388	488	11	,	,	PUNCT
ejpam-6388	488	12	r	r	NOUN
ejpam-6388	488	13	)	)	PUNCT
ejpam-6388	488	14	=	=	SYM
ejpam-6388	488	15	(	(	PUNCT
ejpam-6388	488	16	1−	1−	NUM
ejpam-6388	488	17	ω	ω	NUM
ejpam-6388	488	18	)	)	PUNCT
ejpam-6388	488	19	cos(r	cos(r	PROPN
ejpam-6388	488	20	)	)	PUNCT
ejpam-6388	488	21	,	,	PUNCT
ejpam-6388	488	22	with	with	ADP
ejpam-6388	488	23	y	y	PROPN
ejpam-6388	488	24	=	=	SYM
ejpam-6388	488	25	1.5	1.5	NUM
ejpam-6388	488	26	and	and	CCONJ
ejpam-6388	488	27	f(ω	f(ω	PROPN
ejpam-6388	488	28	,	,	PUNCT
ejpam-6388	488	29	r	r	NOUN
ejpam-6388	488	30	)	)	PUNCT
ejpam-6388	488	31	=	=	SYM
ejpam-6388	488	32	4	4	NUM
ejpam-6388	488	33	sin(r	sin(r	NOUN
ejpam-6388	488	34	)	)	PUNCT
ejpam-6388	488	35	19	19	NUM
ejpam-6388	489	1	+	+	NUM
ejpam-6388	489	2	38	38	NUM
ejpam-6388	489	3	m	m	NOUN
ejpam-6388	489	4	.	.	PUNCT
ejpam-6388	490	1	example	example	NOUN
ejpam-6388	491	1	4	4	NUM
ejpam-6388	491	2	.	.	PUNCT
ejpam-6388	491	3	consider	consider	VERB
ejpam-6388	491	4	the	the	DET
ejpam-6388	491	5	fhbvp	fhbvp	NOUN
ejpam-6388	491	6	(	(	PUNCT
ejpam-6388	491	7	1)–(2	1)–(2	NUM
ejpam-6388	491	8	)	)	PUNCT
ejpam-6388	491	9	with	with	ADP
ejpam-6388	491	10	fractional	fractional	ADJ
ejpam-6388	491	11	order	order	NOUN
ejpam-6388	491	12	y	y	NOUN
ejpam-6388	491	13	=	=	SYM
ejpam-6388	491	14	1.5	1.5	NUM
ejpam-6388	491	15	and	and	CCONJ
ejpam-6388	491	16	f(ω	f(ω	PROPN
ejpam-6388	491	17	,	,	PUNCT
ejpam-6388	491	18	r	r	NOUN
ejpam-6388	491	19	)	)	PUNCT
ejpam-6388	491	20	=	=	SYM
ejpam-6388	492	1	1	1	NUM
ejpam-6388	492	2	+	+	NUM
ejpam-6388	492	3	ω	ω	NUM
ejpam-6388	492	4	+	+	CCONJ
ejpam-6388	492	5	sin(r	sin(r	PROPN
ejpam-6388	492	6	)	)	PUNCT
ejpam-6388	492	7	,	,	PUNCT
ejpam-6388	492	8	g4(ω	g4(ω	PROPN
ejpam-6388	492	9	,	,	PUNCT
ejpam-6388	492	10	r	r	NOUN
ejpam-6388	492	11	)	)	PUNCT
ejpam-6388	492	12	=	=	SYM
ejpam-6388	492	13	(	(	PUNCT
ejpam-6388	492	14	1	1	NUM
ejpam-6388	492	15	+	+	NUM
ejpam-6388	492	16	ω	ω	NUM
ejpam-6388	492	17	)	)	PUNCT
ejpam-6388	492	18	+	+	CCONJ
ejpam-6388	492	19	0.1	0.1	NUM
ejpam-6388	492	20	r2	r2	NOUN
ejpam-6388	492	21	.	.	PUNCT
ejpam-6388	493	1	this	this	DET
ejpam-6388	493	2	choice	choice	NOUN
ejpam-6388	493	3	introduces	introduce	VERB
ejpam-6388	493	4	a	a	DET
ejpam-6388	493	5	quadratic	quadratic	ADJ
ejpam-6388	493	6	nonlinearity	nonlinearity	NOUN
ejpam-6388	493	7	with	with	ADP
ejpam-6388	493	8	a	a	DET
ejpam-6388	493	9	small	small	ADJ
ejpam-6388	493	10	scaling	scale	VERB
ejpam-6388	493	11	factor	factor	NOUN
ejpam-6388	493	12	to	to	PART
ejpam-6388	493	13	control	control	VERB
ejpam-6388	493	14	growth	growth	NOUN
ejpam-6388	493	15	.	.	PUNCT
ejpam-6388	494	1	the	the	DET
ejpam-6388	494	2	conditions	condition	NOUN
ejpam-6388	494	3	(	(	PUNCT
ejpam-6388	494	4	b1)–(b2	b1)–(b2	NOUN
ejpam-6388	494	5	)	)	PUNCT
ejpam-6388	494	6	are	be	AUX
ejpam-6388	494	7	satisfied	satisfied	ADJ
ejpam-6388	494	8	since	since	SCONJ
ejpam-6388	494	9	|g4(ω	|g4(ω	PROPN
ejpam-6388	494	10	,	,	PUNCT
ejpam-6388	494	11	r)−	r)−	PROPN
ejpam-6388	494	12	g4(ω	g4(ω	PROPN
ejpam-6388	494	13	,	,	PUNCT
ejpam-6388	495	1	u)|	u)|	NOUN
ejpam-6388	495	2	=	=	NOUN
ejpam-6388	495	3	0.1	0.1	NUM
ejpam-6388	495	4	|r2	|r2	NOUN
ejpam-6388	495	5	−	−	PROPN
ejpam-6388	495	6	u2|	u2|	ADJ
ejpam-6388	495	7	≤	≤	NOUN
ejpam-6388	495	8	0.2	0.2	NUM
ejpam-6388	495	9	m	m	NOUN
ejpam-6388	495	10	|r−	|r−	NOUN
ejpam-6388	495	11	u|	u|	ADJ
ejpam-6388	495	12	for	for	ADP
ejpam-6388	495	13	some	some	DET
ejpam-6388	495	14	m	m	NOUN
ejpam-6388	495	15	>	>	X
ejpam-6388	495	16	0	0	NUM
ejpam-6388	495	17	,	,	PUNCT
ejpam-6388	495	18	and	and	CCONJ
ejpam-6388	495	19	|f(ω	|f(ω	NOUN
ejpam-6388	495	20	,	,	PUNCT
ejpam-6388	495	21	r)−	r)−	PROPN
ejpam-6388	495	22	f(ω	f(ω	PROPN
ejpam-6388	495	23	,	,	PUNCT
ejpam-6388	496	1	u)|	u)|	NOUN
ejpam-6388	496	2	=	=	NOUN
ejpam-6388	497	1	|	|	ADV
ejpam-6388	497	2	sin(r)−	sin(r)−	PROPN
ejpam-6388	497	3	sin(u)|	sin(u)|	PROPN
ejpam-6388	497	4	≤	≤	PROPN
ejpam-6388	497	5	|r−	|r−	NOUN
ejpam-6388	497	6	u|	u|	PROPN
ejpam-6388	497	7	,	,	PUNCT
ejpam-6388	497	8	ensuring	ensure	VERB
ejpam-6388	497	9	lipschitz	lipschitz	NOUN
ejpam-6388	497	10	continuity	continuity	NOUN
ejpam-6388	497	11	.	.	PUNCT
ejpam-6388	498	1	numerical	numerical	ADJ
ejpam-6388	498	2	solutions	solution	NOUN
ejpam-6388	498	3	were	be	AUX
ejpam-6388	498	4	obtained	obtain	VERB
ejpam-6388	498	5	with	with	ADP
ejpam-6388	498	6	the	the	DET
ejpam-6388	498	7	trapezoidal	trapezoidal	ADJ
ejpam-6388	498	8	rule	rule	NOUN
ejpam-6388	498	9	on	on	ADP
ejpam-6388	498	10	a	a	DET
ejpam-6388	498	11	uniform	uniform	ADJ
ejpam-6388	498	12	grid	grid	NOUN
ejpam-6388	498	13	of	of	ADP
ejpam-6388	498	14	200	200	NUM
ejpam-6388	498	15	points	point	NOUN
ejpam-6388	498	16	.	.	PUNCT
ejpam-6388	499	1	table	table	NOUN
ejpam-6388	499	2	1	1	NUM
ejpam-6388	499	3	lists	list	NOUN
ejpam-6388	499	4	representative	representative	ADJ
ejpam-6388	499	5	values	value	NOUN
ejpam-6388	499	6	of	of	ADP
ejpam-6388	499	7	r(ω	r(ω	ADJ
ejpam-6388	499	8	)	)	PUNCT
ejpam-6388	499	9	,	,	PUNCT
ejpam-6388	499	10	and	and	CCONJ
ejpam-6388	499	11	figure	figure	VERB
ejpam-6388	499	12	5	5	NUM
ejpam-6388	499	13	compares	compare	VERB
ejpam-6388	499	14	g4	g4	NOUN
ejpam-6388	499	15	against	against	ADP
ejpam-6388	499	16	g1(ω	g1(ω	NOUN
ejpam-6388	499	17	,	,	PUNCT
ejpam-6388	499	18	r	r	NOUN
ejpam-6388	499	19	)	)	PUNCT
ejpam-6388	499	20	=	=	SYM
ejpam-6388	499	21	2(1	2(1	NUM
ejpam-6388	499	22	+	+	NUM
ejpam-6388	499	23	ω	ω	NUM
ejpam-6388	499	24	)	)	PUNCT
ejpam-6388	500	1	+	+	CCONJ
ejpam-6388	500	2	(	(	PUNCT
ejpam-6388	500	3	1	1	NUM
ejpam-6388	500	4	+	+	NUM
ejpam-6388	500	5	ω	ω	X
ejpam-6388	500	6	)	)	PUNCT
ejpam-6388	500	7	sin(r	sin(r	PROPN
ejpam-6388	500	8	)	)	PUNCT
ejpam-6388	500	9	from	from	ADP
ejpam-6388	500	10	example	example	NOUN
ejpam-6388	501	1	1	1	X
ejpam-6388	501	2	.	.	PUNCT
ejpam-6388	502	1	we	we	PRON
ejpam-6388	502	2	observe	observe	VERB
ejpam-6388	502	3	that	that	SCONJ
ejpam-6388	502	4	g4	g4	NOUN
ejpam-6388	502	5	grows	grow	VERB
ejpam-6388	502	6	more	more	ADV
ejpam-6388	502	7	moderately	moderately	ADV
ejpam-6388	502	8	than	than	ADP
ejpam-6388	502	9	g1	g1	NOUN
ejpam-6388	502	10	,	,	PUNCT
ejpam-6388	502	11	with	with	ADP
ejpam-6388	502	12	values	value	NOUN
ejpam-6388	502	13	reaching	reach	VERB
ejpam-6388	502	14	about	about	ADV
ejpam-6388	502	15	3.22	3.22	NUM
ejpam-6388	502	16	at	at	ADP
ejpam-6388	502	17	ω	ω	PROPN
ejpam-6388	502	18	=	=	SYM
ejpam-6388	502	19	1	1	NUM
ejpam-6388	502	20	,	,	PUNCT
ejpam-6388	502	21	compared	compare	VERB
ejpam-6388	502	22	with	with	ADP
ejpam-6388	502	23	3.91	3.91	NUM
ejpam-6388	502	24	for	for	ADP
ejpam-6388	502	25	g1	g1	NOUN
ejpam-6388	502	26	.	.	PUNCT
ejpam-6388	503	1	the	the	DET
ejpam-6388	503	2	quadratic	quadratic	ADJ
ejpam-6388	503	3	term	term	NOUN
ejpam-6388	503	4	thus	thus	ADV
ejpam-6388	503	5	produces	produce	VERB
ejpam-6388	503	6	smoother	smooth	ADJ
ejpam-6388	503	7	profiles	profile	NOUN
ejpam-6388	503	8	while	while	SCONJ
ejpam-6388	503	9	still	still	ADV
ejpam-6388	503	10	increasing	increase	VERB
ejpam-6388	503	11	steeply	steeply	ADV
ejpam-6388	503	12	near	near	ADP
ejpam-6388	503	13	ω	ω	PROPN
ejpam-6388	503	14	=	=	SYM
ejpam-6388	503	15	1	1	X
ejpam-6388	503	16	.	.	X
ejpam-6388	503	17	d.	d.	PROPN
ejpam-6388	503	18	baleanu	baleanu	PROPN
ejpam-6388	503	19	et	et	PROPN
ejpam-6388	503	20	al	al	PROPN
ejpam-6388	503	21	.	.	PUNCT
ejpam-6388	503	22	/	/	SYM
ejpam-6388	503	23	eur	eur	PROPN
ejpam-6388	503	24	.	.	PUNCT
ejpam-6388	504	1	j.	j.	PROPN
ejpam-6388	504	2	pure	pure	PROPN
ejpam-6388	504	3	appl	appl	PROPN
ejpam-6388	504	4	.	.	PROPN
ejpam-6388	504	5	math	math	PROPN
ejpam-6388	504	6	,	,	PUNCT
ejpam-6388	504	7	18	18	NUM
ejpam-6388	504	8	(	(	PUNCT
ejpam-6388	504	9	4	4	NUM
ejpam-6388	504	10	)	)	PUNCT
ejpam-6388	504	11	(	(	PUNCT
ejpam-6388	504	12	2025	2025	NUM
ejpam-6388	504	13	)	)	PUNCT
ejpam-6388	504	14	,	,	PUNCT
ejpam-6388	504	15	6388	6388	NUM
ejpam-6388	504	16	23	23	NUM
ejpam-6388	504	17	of	of	ADP
ejpam-6388	504	18	31	31	NUM
ejpam-6388	504	19	ω	ω	NUM
ejpam-6388	504	20	r(ω	r(ω	ADV
ejpam-6388	504	21	)	)	PUNCT
ejpam-6388	504	22	(	(	PUNCT
ejpam-6388	504	23	g1	g1	PROPN
ejpam-6388	504	24	)	)	PUNCT
ejpam-6388	504	25	r(ω	r(ω	ADV
ejpam-6388	504	26	)	)	PUNCT
ejpam-6388	504	27	(	(	PUNCT
ejpam-6388	504	28	g4	g4	NOUN
ejpam-6388	504	29	)	)	PUNCT
ejpam-6388	504	30	0.00	0.00	NUM
ejpam-6388	504	31	0.0000	0.0000	NUM
ejpam-6388	504	32	0.0000	0.0000	NUM
ejpam-6388	504	33	0.20	0.20	NUM
ejpam-6388	505	1	1.1218	1.1218	NUM
ejpam-6388	505	2	0.9875	0.9875	NUM
ejpam-6388	505	3	0.40	0.40	NUM
ejpam-6388	505	4	2.0504	2.0504	NUM
ejpam-6388	505	5	1.7512	1.7512	NUM
ejpam-6388	505	6	0.60	0.60	NUM
ejpam-6388	505	7	2.7247	2.7247	NUM
ejpam-6388	505	8	2.2987	2.2987	NUM
ejpam-6388	505	9	0.80	0.80	NUM
ejpam-6388	505	10	3.3183	3.3183	NUM
ejpam-6388	505	11	2.7703	2.7703	NUM
ejpam-6388	505	12	1.00	1.00	NUM
ejpam-6388	505	13	3.9071	3.9071	NUM
ejpam-6388	505	14	3.2210	3.2210	NUM
ejpam-6388	505	15	table	table	NOUN
ejpam-6388	505	16	1	1	NUM
ejpam-6388	505	17	:	:	PUNCT
ejpam-6388	505	18	example	example	NOUN
ejpam-6388	505	19	4	4	NUM
ejpam-6388	505	20	:	:	PUNCT
ejpam-6388	505	21	comparison	comparison	NOUN
ejpam-6388	505	22	of	of	ADP
ejpam-6388	505	23	r(ω	r(ω	ADJ
ejpam-6388	505	24	)	)	PUNCT
ejpam-6388	505	25	for	for	ADP
ejpam-6388	505	26	g1	g1	NOUN
ejpam-6388	505	27	and	and	CCONJ
ejpam-6388	505	28	g4	g4	NOUN
ejpam-6388	505	29	with	with	ADP
ejpam-6388	505	30	y	y	PROPN
ejpam-6388	505	31	=	=	PROPN
ejpam-6388	505	32	1.5	1.5	NUM
ejpam-6388	505	33	and	and	CCONJ
ejpam-6388	505	34	f(ω	f(ω	PROPN
ejpam-6388	505	35	,	,	PUNCT
ejpam-6388	505	36	r	r	NOUN
ejpam-6388	505	37	)	)	PUNCT
ejpam-6388	505	38	=	=	SYM
ejpam-6388	505	39	1	1	NUM
ejpam-6388	506	1	+	+	NUM
ejpam-6388	506	2	ω	ω	NUM
ejpam-6388	506	3	+	+	NUM
ejpam-6388	506	4	sin(r	sin(r	PROPN
ejpam-6388	506	5	)	)	PUNCT
ejpam-6388	506	6	.	.	PUNCT
ejpam-6388	507	1	figure	figure	VERB
ejpam-6388	507	2	5	5	NUM
ejpam-6388	507	3	:	:	PUNCT
ejpam-6388	507	4	example	example	NOUN
ejpam-6388	507	5	4	4	NUM
ejpam-6388	507	6	:	:	PUNCT
ejpam-6388	507	7	comparison	comparison	NOUN
ejpam-6388	507	8	of	of	ADP
ejpam-6388	507	9	r(ω	r(ω	ADJ
ejpam-6388	507	10	)	)	PUNCT
ejpam-6388	507	11	for	for	ADP
ejpam-6388	507	12	g1	g1	PROPN
ejpam-6388	507	13	(	(	PUNCT
ejpam-6388	507	14	blue	blue	ADJ
ejpam-6388	507	15	)	)	PUNCT
ejpam-6388	507	16	and	and	CCONJ
ejpam-6388	507	17	g4	g4	NOUN
ejpam-6388	507	18	(	(	PUNCT
ejpam-6388	507	19	orange	orange	NOUN
ejpam-6388	507	20	)	)	PUNCT
ejpam-6388	507	21	under	under	ADP
ejpam-6388	507	22	y	y	PROPN
ejpam-6388	507	23	=	=	PROPN
ejpam-6388	507	24	1.5	1.5	NUM
ejpam-6388	507	25	.	.	PUNCT
ejpam-6388	508	1	the	the	DET
ejpam-6388	508	2	quadratic	quadratic	ADJ
ejpam-6388	508	3	nonlinearity	nonlinearity	NOUN
ejpam-6388	508	4	in	in	ADP
ejpam-6388	508	5	g4	g4	NOUN
ejpam-6388	508	6	reduces	reduce	VERB
ejpam-6388	508	7	overall	overall	ADJ
ejpam-6388	508	8	growth	growth	NOUN
ejpam-6388	508	9	compared	compare	VERB
ejpam-6388	508	10	with	with	ADP
ejpam-6388	508	11	g1	g1	PROPN
ejpam-6388	508	12	.	.	PUNCT
ejpam-6388	509	1	example	example	NOUN
ejpam-6388	509	2	5	5	NUM
ejpam-6388	509	3	.	.	X
ejpam-6388	510	1	consider	consider	VERB
ejpam-6388	510	2	(	(	PUNCT
ejpam-6388	510	3	1)–(2	1)–(2	NUM
ejpam-6388	510	4	)	)	PUNCT
ejpam-6388	510	5	with	with	ADP
ejpam-6388	510	6	y	y	PROPN
ejpam-6388	510	7	=	=	PROPN
ejpam-6388	510	8	1.8	1.8	NUM
ejpam-6388	510	9	and	and	CCONJ
ejpam-6388	510	10	f3(ω	f3(ω	PROPN
ejpam-6388	510	11	,	,	PUNCT
ejpam-6388	510	12	r	r	NOUN
ejpam-6388	510	13	)	)	PUNCT
ejpam-6388	510	14	=	=	SYM
ejpam-6388	511	1	1	1	NUM
ejpam-6388	511	2	+	+	NUM
ejpam-6388	511	3	sin(r	sin(r	PROPN
ejpam-6388	511	4	)	)	PUNCT
ejpam-6388	511	5	,	,	PUNCT
ejpam-6388	511	6	g5(ω	g5(ω	NOUN
ejpam-6388	511	7	,	,	PUNCT
ejpam-6388	511	8	r	r	NOUN
ejpam-6388	511	9	)	)	PUNCT
ejpam-6388	511	10	=	=	SYM
ejpam-6388	511	11	(	(	PUNCT
ejpam-6388	511	12	1	1	NUM
ejpam-6388	511	13	+	+	CCONJ
ejpam-6388	511	14	ω)r	ω)r	NOUN
ejpam-6388	511	15	.	.	PUNCT
ejpam-6388	512	1	here	here	ADV
ejpam-6388	512	2	,	,	PUNCT
ejpam-6388	512	3	g5	g5	NOUN
ejpam-6388	512	4	is	be	AUX
ejpam-6388	512	5	linear	linear	ADJ
ejpam-6388	512	6	in	in	ADP
ejpam-6388	512	7	r	r	NOUN
ejpam-6388	512	8	while	while	SCONJ
ejpam-6388	512	9	f3	f3	PROPN
ejpam-6388	512	10	removes	remove	VERB
ejpam-6388	512	11	the	the	DET
ejpam-6388	512	12	direct	direct	ADJ
ejpam-6388	512	13	ω	ω	PROPN
ejpam-6388	512	14	dependence	dependence	NOUN
ejpam-6388	512	15	,	,	PUNCT
ejpam-6388	512	16	yielding	yield	VERB
ejpam-6388	512	17	a	a	DET
ejpam-6388	512	18	smoother	smoother	ADJ
ejpam-6388	512	19	forcing	force	VERB
ejpam-6388	512	20	term	term	NOUN
ejpam-6388	512	21	.	.	PUNCT
ejpam-6388	513	1	both	both	PRON
ejpam-6388	513	2	(	(	PUNCT
ejpam-6388	513	3	b1	b1	NOUN
ejpam-6388	513	4	)	)	PUNCT
ejpam-6388	513	5	and	and	CCONJ
ejpam-6388	513	6	(	(	PUNCT
ejpam-6388	513	7	b2	b2	NOUN
ejpam-6388	513	8	)	)	PUNCT
ejpam-6388	513	9	are	be	AUX
ejpam-6388	513	10	satisfied	satisfied	ADJ
ejpam-6388	513	11	,	,	PUNCT
ejpam-6388	513	12	since	since	SCONJ
ejpam-6388	513	13	|g5(ω	|g5(ω	PROPN
ejpam-6388	513	14	,	,	PUNCT
ejpam-6388	513	15	r)−	r)−	PROPN
ejpam-6388	513	16	g5(ω	g5(ω	NOUN
ejpam-6388	513	17	,	,	PUNCT
ejpam-6388	513	18	u)|	u)|	NOUN
ejpam-6388	514	1	=	=	SYM
ejpam-6388	514	2	(	(	PUNCT
ejpam-6388	514	3	1	1	NUM
ejpam-6388	514	4	+	+	NUM
ejpam-6388	514	5	ω)|r−	ω)|r−	NOUN
ejpam-6388	514	6	u|	u|	NOUN
ejpam-6388	514	7	≤	≤	NUM
ejpam-6388	514	8	2|r−	2|r−	NUM
ejpam-6388	514	9	u|	u|	NOUN
ejpam-6388	514	10	,	,	PUNCT
ejpam-6388	514	11	and	and	CCONJ
ejpam-6388	514	12	f3	f3	PROPN
ejpam-6388	514	13	is	be	AUX
ejpam-6388	514	14	lipschitz	lipschitz	NOUN
ejpam-6388	514	15	with	with	ADP
ejpam-6388	514	16	constant	constant	ADJ
ejpam-6388	514	17	lf	lf	ADP
ejpam-6388	514	18	=	=	SYM
ejpam-6388	514	19	1	1	PROPN
ejpam-6388	514	20	.	.	PUNCT
ejpam-6388	515	1	numerical	numerical	ADJ
ejpam-6388	515	2	solutions	solution	NOUN
ejpam-6388	515	3	are	be	AUX
ejpam-6388	515	4	summarized	summarize	VERB
ejpam-6388	515	5	in	in	ADP
ejpam-6388	515	6	table	table	NOUN
ejpam-6388	515	7	2	2	NUM
ejpam-6388	515	8	.	.	PUNCT
ejpam-6388	515	9	compared	compare	VERB
ejpam-6388	515	10	with	with	ADP
ejpam-6388	515	11	example	example	NOUN
ejpam-6388	515	12	4	4	NUM
ejpam-6388	515	13	,	,	PUNCT
ejpam-6388	515	14	values	value	NOUN
ejpam-6388	515	15	of	of	ADP
ejpam-6388	515	16	r(ω	r(ω	ADJ
ejpam-6388	515	17	)	)	PUNCT
ejpam-6388	515	18	under	under	ADP
ejpam-6388	515	19	f3	f3	PROPN
ejpam-6388	515	20	are	be	AUX
ejpam-6388	515	21	consistently	consistently	ADV
ejpam-6388	515	22	smaller	small	ADJ
ejpam-6388	515	23	,	,	PUNCT
ejpam-6388	515	24	reaching	reach	VERB
ejpam-6388	515	25	only	only	ADV
ejpam-6388	515	26	2.42	2.42	NUM
ejpam-6388	515	27	at	at	ADP
ejpam-6388	515	28	ω	ω	NUM
ejpam-6388	515	29	=	=	SYM
ejpam-6388	515	30	1	1	NUM
ejpam-6388	515	31	versus	versus	ADP
ejpam-6388	515	32	3.22	3.22	NUM
ejpam-6388	515	33	for	for	ADP
ejpam-6388	515	34	f.	f.	PROPN
ejpam-6388	515	35	this	this	PRON
ejpam-6388	515	36	demonstrates	demonstrate	VERB
ejpam-6388	515	37	that	that	SCONJ
ejpam-6388	515	38	removing	remove	VERB
ejpam-6388	515	39	the	the	DET
ejpam-6388	515	40	ω	ω	NUM
ejpam-6388	515	41	term	term	NOUN
ejpam-6388	515	42	in	in	ADP
ejpam-6388	515	43	f	f	PROPN
ejpam-6388	515	44	reduces	reduce	VERB
ejpam-6388	515	45	growth	growth	NOUN
ejpam-6388	515	46	.	.	PUNCT
ejpam-6388	516	1	figure	figure	VERB
ejpam-6388	516	2	6	6	NUM
ejpam-6388	516	3	highlights	highlight	NOUN
ejpam-6388	516	4	the	the	DET
ejpam-6388	516	5	difference	difference	NOUN
ejpam-6388	516	6	in	in	ADP
ejpam-6388	516	7	magnitudes	magnitude	NOUN
ejpam-6388	516	8	,	,	PUNCT
ejpam-6388	516	9	with	with	ADP
ejpam-6388	516	10	f3	f3	ADJ
ejpam-6388	516	11	producing	produce	VERB
ejpam-6388	516	12	smoother	smooth	ADJ
ejpam-6388	516	13	and	and	CCONJ
ejpam-6388	516	14	more	more	ADV
ejpam-6388	516	15	subdued	subdued	ADJ
ejpam-6388	516	16	solutions	solution	NOUN
ejpam-6388	516	17	.	.	PUNCT
ejpam-6388	517	1	d.	d.	PROPN
ejpam-6388	517	2	baleanu	baleanu	PROPN
ejpam-6388	517	3	et	et	PROPN
ejpam-6388	517	4	al	al	PROPN
ejpam-6388	517	5	.	.	PUNCT
ejpam-6388	517	6	/	/	SYM
ejpam-6388	517	7	eur	eur	PROPN
ejpam-6388	517	8	.	.	PUNCT
ejpam-6388	518	1	j.	j.	PROPN
ejpam-6388	518	2	pure	pure	PROPN
ejpam-6388	518	3	appl	appl	PROPN
ejpam-6388	518	4	.	.	PROPN
ejpam-6388	518	5	math	math	PROPN
ejpam-6388	518	6	,	,	PUNCT
ejpam-6388	518	7	18	18	NUM
ejpam-6388	518	8	(	(	PUNCT
ejpam-6388	518	9	4	4	NUM
ejpam-6388	518	10	)	)	PUNCT
ejpam-6388	518	11	(	(	PUNCT
ejpam-6388	518	12	2025	2025	NUM
ejpam-6388	518	13	)	)	PUNCT
ejpam-6388	518	14	,	,	PUNCT
ejpam-6388	518	15	6388	6388	NUM
ejpam-6388	518	16	24	24	NUM
ejpam-6388	518	17	of	of	ADP
ejpam-6388	518	18	31	31	NUM
ejpam-6388	518	19	ω	ω	NUM
ejpam-6388	518	20	r(ω	r(ω	ADV
ejpam-6388	518	21	)	)	PUNCT
ejpam-6388	518	22	(	(	PUNCT
ejpam-6388	518	23	f	f	X
ejpam-6388	518	24	,	,	PUNCT
ejpam-6388	518	25	y	y	PROPN
ejpam-6388	518	26	=	=	SYM
ejpam-6388	518	27	1.5	1.5	NUM
ejpam-6388	518	28	)	)	PUNCT
ejpam-6388	518	29	r(ω	r(ω	ADV
ejpam-6388	518	30	)	)	PUNCT
ejpam-6388	518	31	(	(	PUNCT
ejpam-6388	518	32	f3	f3	ADJ
ejpam-6388	518	33	,	,	PUNCT
ejpam-6388	518	34	y	y	PROPN
ejpam-6388	518	35	=	=	PROPN
ejpam-6388	518	36	1.8	1.8	NUM
ejpam-6388	518	37	)	)	PUNCT
ejpam-6388	518	38	0.00	0.00	NUM
ejpam-6388	518	39	0.0000	0.0000	NUM
ejpam-6388	518	40	0.0000	0.0000	NUM
ejpam-6388	518	41	0.20	0.20	NUM
ejpam-6388	518	42	0.9875	0.9875	NUM
ejpam-6388	518	43	0.3866	0.3866	NUM
ejpam-6388	518	44	0.40	0.40	NUM
ejpam-6388	518	45	1.7512	1.7512	NUM
ejpam-6388	518	46	0.9004	0.9004	NUM
ejpam-6388	518	47	0.60	0.60	NUM
ejpam-6388	518	48	2.2987	2.2987	NUM
ejpam-6388	518	49	1.4634	1.4634	NUM
ejpam-6388	518	50	0.80	0.80	NUM
ejpam-6388	518	51	2.7703	2.7703	NUM
ejpam-6388	518	52	1.9698	1.9698	NUM
ejpam-6388	518	53	1.00	1.00	NUM
ejpam-6388	518	54	3.2210	3.2210	NUM
ejpam-6388	518	55	2.4181	2.4181	NUM
ejpam-6388	518	56	table	table	NOUN
ejpam-6388	518	57	2	2	NUM
ejpam-6388	518	58	:	:	PUNCT
ejpam-6388	518	59	example	example	NOUN
ejpam-6388	518	60	5	5	NUM
ejpam-6388	518	61	:	:	PUNCT
ejpam-6388	518	62	comparison	comparison	NOUN
ejpam-6388	518	63	of	of	ADP
ejpam-6388	518	64	r(ω	r(ω	PROPN
ejpam-6388	518	65	)	)	PUNCT
ejpam-6388	518	66	for	for	ADP
ejpam-6388	518	67	f	f	PROPN
ejpam-6388	518	68	(	(	PUNCT
ejpam-6388	518	69	y	y	NOUN
ejpam-6388	518	70	=	=	NOUN
ejpam-6388	518	71	1.5	1.5	NUM
ejpam-6388	518	72	)	)	PUNCT
ejpam-6388	518	73	and	and	CCONJ
ejpam-6388	518	74	f3	f3	PROPN
ejpam-6388	518	75	(	(	PUNCT
ejpam-6388	518	76	y	y	NOUN
ejpam-6388	518	77	=	=	PROPN
ejpam-6388	518	78	1.8	1.8	NUM
ejpam-6388	518	79	)	)	PUNCT
ejpam-6388	518	80	under	under	ADP
ejpam-6388	518	81	g5(ω	g5(ω	PROPN
ejpam-6388	518	82	,	,	PUNCT
ejpam-6388	518	83	r	r	NOUN
ejpam-6388	518	84	)	)	PUNCT
ejpam-6388	518	85	=	=	SYM
ejpam-6388	518	86	(	(	PUNCT
ejpam-6388	518	87	1	1	NUM
ejpam-6388	518	88	+	+	CCONJ
ejpam-6388	518	89	ω)r	ω)r	NOUN
ejpam-6388	518	90	.	.	PUNCT
ejpam-6388	518	91	figure	figure	VERB
ejpam-6388	518	92	6	6	NUM
ejpam-6388	518	93	:	:	PUNCT
ejpam-6388	518	94	example	example	NOUN
ejpam-6388	518	95	5	5	NUM
ejpam-6388	518	96	:	:	PUNCT
ejpam-6388	518	97	comparison	comparison	NOUN
ejpam-6388	518	98	of	of	ADP
ejpam-6388	518	99	r(ω	r(ω	PROPN
ejpam-6388	518	100	)	)	PUNCT
ejpam-6388	518	101	for	for	ADP
ejpam-6388	518	102	f	f	PROPN
ejpam-6388	518	103	(	(	PUNCT
ejpam-6388	518	104	y	y	NOUN
ejpam-6388	518	105	=	=	SYM
ejpam-6388	518	106	1.5	1.5	NUM
ejpam-6388	518	107	,	,	PUNCT
ejpam-6388	518	108	blue	blue	ADJ
ejpam-6388	518	109	)	)	PUNCT
ejpam-6388	518	110	and	and	CCONJ
ejpam-6388	518	111	f3	f3	PROPN
ejpam-6388	518	112	(	(	PUNCT
ejpam-6388	518	113	y	y	NOUN
ejpam-6388	518	114	=	=	SYM
ejpam-6388	518	115	1.8	1.8	NUM
ejpam-6388	518	116	,	,	PUNCT
ejpam-6388	518	117	orange	orange	PROPN
ejpam-6388	518	118	)	)	PUNCT
ejpam-6388	518	119	.	.	PUNCT
ejpam-6388	519	1	the	the	DET
ejpam-6388	519	2	removal	removal	NOUN
ejpam-6388	519	3	of	of	ADP
ejpam-6388	519	4	ω	ω	PROPN
ejpam-6388	519	5	in	in	ADP
ejpam-6388	519	6	f3	f3	ADJ
ejpam-6388	519	7	reduces	reduce	VERB
ejpam-6388	519	8	solution	solution	NOUN
ejpam-6388	519	9	magnitudes	magnitude	NOUN
ejpam-6388	519	10	.	.	PUNCT
ejpam-6388	519	11	example	example	NOUN
ejpam-6388	520	1	6	6	NUM
ejpam-6388	520	2	.	.	PUNCT
ejpam-6388	521	1	finally	finally	ADV
ejpam-6388	521	2	,	,	PUNCT
ejpam-6388	521	3	we	we	PRON
ejpam-6388	521	4	compare	compare	VERB
ejpam-6388	521	5	our	our	PRON
ejpam-6388	521	6	formulation	formulation	NOUN
ejpam-6388	521	7	with	with	ADP
ejpam-6388	521	8	related	related	ADJ
ejpam-6388	521	9	works	work	NOUN
ejpam-6388	521	10	by	by	ADP
ejpam-6388	521	11	zhao	zhao	PROPN
ejpam-6388	521	12	et	et	PROPN
ejpam-6388	521	13	al	al	PROPN
ejpam-6388	521	14	.	.	PUNCT
ejpam-6388	522	1	[	[	X
ejpam-6388	522	2	1	1	X
ejpam-6388	522	3	]	]	PUNCT
ejpam-6388	522	4	and	and	CCONJ
ejpam-6388	522	5	hilal	hilal	PROPN
ejpam-6388	522	6	–	–	PUNCT
ejpam-6388	522	7	kajouni	kajouni	PROPN
ejpam-6388	522	8	[	[	X
ejpam-6388	522	9	2	2	NUM
ejpam-6388	522	10	]	]	PUNCT
ejpam-6388	522	11	,	,	PUNCT
ejpam-6388	522	12	both	both	CCONJ
ejpam-6388	522	13	with	with	ADP
ejpam-6388	522	14	α	α	NOUN
ejpam-6388	522	15	=	=	SYM
ejpam-6388	522	16	0.75	0.75	NUM
ejpam-6388	522	17	.	.	PUNCT
ejpam-6388	523	1	zhao	zhao	PROPN
ejpam-6388	523	2	et	et	PROPN
ejpam-6388	523	3	al	al	PROPN
ejpam-6388	523	4	.	.	PUNCT
ejpam-6388	524	1	[	[	X
ejpam-6388	524	2	1	1	X
ejpam-6388	524	3	]	]	PUNCT
ejpam-6388	524	4	considered	consider	VERB
ejpam-6388	524	5	the	the	DET
ejpam-6388	524	6	riemann	riemann	PROPN
ejpam-6388	524	7	–	–	PUNCT
ejpam-6388	524	8	liouville	liouville	VERB
ejpam-6388	524	9	formulation	formulation	NOUN
ejpam-6388	524	10	rldα	rldα	VERB
ejpam-6388	524	11	0	0	NUM
ejpam-6388	525	1	+	+	CCONJ
ejpam-6388	525	2	[	[	PUNCT
ejpam-6388	525	3	r(ω	r(ω	ADJ
ejpam-6388	525	4	)	)	PUNCT
ejpam-6388	525	5	f(ω	f(ω	PROPN
ejpam-6388	525	6	,	,	PUNCT
ejpam-6388	525	7	r(ω	r(ω	ADJ
ejpam-6388	525	8	)	)	PUNCT
ejpam-6388	525	9	)	)	PUNCT
ejpam-6388	525	10	]	]	PUNCT
ejpam-6388	526	1	=	=	PUNCT
ejpam-6388	526	2	g(ω	g(ω	PROPN
ejpam-6388	526	3	,	,	PUNCT
ejpam-6388	526	4	r(ω	r(ω	ADJ
ejpam-6388	526	5	)	)	PUNCT
ejpam-6388	526	6	)	)	PUNCT
ejpam-6388	526	7	,	,	PUNCT
ejpam-6388	526	8	r(0	r(0	PROPN
ejpam-6388	526	9	)	)	PUNCT
ejpam-6388	526	10	=	=	SYM
ejpam-6388	526	11	0	0	NUM
ejpam-6388	526	12	,	,	PUNCT
ejpam-6388	526	13	with	with	ADP
ejpam-6388	526	14	f(ω	f(ω	PROPN
ejpam-6388	526	15	,	,	PUNCT
ejpam-6388	526	16	r	r	NOUN
ejpam-6388	526	17	)	)	PUNCT
ejpam-6388	526	18	=	=	SYM
ejpam-6388	526	19	1	1	NUM
ejpam-6388	526	20	+	+	CCONJ
ejpam-6388	526	21	cos(r	cos(r	X
ejpam-6388	526	22	)	)	PUNCT
ejpam-6388	526	23	and	and	CCONJ
ejpam-6388	526	24	g(ω	g(ω	PROPN
ejpam-6388	526	25	,	,	PUNCT
ejpam-6388	526	26	r	r	NOUN
ejpam-6388	526	27	)	)	PUNCT
ejpam-6388	526	28	=	=	SYM
ejpam-6388	526	29	ω	ω	PROPN
ejpam-6388	526	30	+	+	NUM
ejpam-6388	526	31	sin(r	sin(r	PROPN
ejpam-6388	526	32	)	)	PUNCT
ejpam-6388	526	33	.	.	PUNCT
ejpam-6388	527	1	hilal	hilal	PROPN
ejpam-6388	527	2	and	and	CCONJ
ejpam-6388	527	3	kajouni	kajouni	PROPN
ejpam-6388	527	4	[	[	X
ejpam-6388	527	5	2	2	NUM
ejpam-6388	527	6	]	]	PUNCT
ejpam-6388	527	7	studied	study	VERB
ejpam-6388	527	8	the	the	DET
ejpam-6388	527	9	caputo	caputo	PROPN
ejpam-6388	527	10	version	version	PROPN
ejpam-6388	527	11	,	,	PUNCT
ejpam-6388	527	12	cdα	cdα	NOUN
ejpam-6388	527	13	0	0	NUM
ejpam-6388	528	1	+	+	CCONJ
ejpam-6388	528	2	[	[	PUNCT
ejpam-6388	528	3	r(ω	r(ω	ADJ
ejpam-6388	528	4	)	)	PUNCT
ejpam-6388	528	5	f(ω	f(ω	PROPN
ejpam-6388	528	6	,	,	PUNCT
ejpam-6388	528	7	r(ω	r(ω	ADJ
ejpam-6388	528	8	)	)	PUNCT
ejpam-6388	528	9	)	)	PUNCT
ejpam-6388	528	10	]	]	PUNCT
ejpam-6388	529	1	=	=	PUNCT
ejpam-6388	529	2	g(ω	g(ω	PROPN
ejpam-6388	529	3	,	,	PUNCT
ejpam-6388	529	4	r(ω	r(ω	ADJ
ejpam-6388	529	5	)	)	PUNCT
ejpam-6388	529	6	)	)	PUNCT
ejpam-6388	529	7	,	,	PUNCT
ejpam-6388	529	8	a	a	DET
ejpam-6388	529	9	r(0	r(0	PROPN
ejpam-6388	529	10	)	)	PUNCT
ejpam-6388	529	11	f(0,r(0	f(0,r(0	PROPN
ejpam-6388	529	12	)	)	PUNCT
ejpam-6388	529	13	)	)	PUNCT
ejpam-6388	530	1	+	+	CCONJ
ejpam-6388	530	2	b	b	X
ejpam-6388	530	3	r(1	r(1	PROPN
ejpam-6388	530	4	)	)	PUNCT
ejpam-6388	530	5	f(1,r(1	f(1,r(1	NUM
ejpam-6388	530	6	)	)	PUNCT
ejpam-6388	530	7	)	)	PUNCT
ejpam-6388	531	1	=	=	PUNCT
ejpam-6388	532	1	c	c	X
ejpam-6388	532	2	,	,	PUNCT
ejpam-6388	532	3	with	with	ADP
ejpam-6388	532	4	a	a	DET
ejpam-6388	532	5	=	=	SYM
ejpam-6388	532	6	b	b	NOUN
ejpam-6388	532	7	=	=	SYM
ejpam-6388	532	8	c	c	NOUN
ejpam-6388	532	9	=	=	SYM
ejpam-6388	532	10	1	1	X
ejpam-6388	532	11	.	.	PUNCT
ejpam-6388	532	12	using	use	VERB
ejpam-6388	532	13	the	the	DET
ejpam-6388	532	14	caputo	caputo	PROPN
ejpam-6388	532	15	integral	integral	ADJ
ejpam-6388	532	16	representation	representation	NOUN
ejpam-6388	532	17	and	and	CCONJ
ejpam-6388	532	18	enforcing	enforce	VERB
ejpam-6388	532	19	the	the	DET
ejpam-6388	532	20	boundary	boundary	ADJ
ejpam-6388	532	21	condition	condition	NOUN
ejpam-6388	532	22	at	at	ADP
ejpam-6388	532	23	each	each	DET
ejpam-6388	532	24	iteration	iteration	NOUN
ejpam-6388	532	25	,	,	PUNCT
ejpam-6388	532	26	we	we	PRON
ejpam-6388	532	27	obtained	obtain	VERB
ejpam-6388	532	28	the	the	DET
ejpam-6388	532	29	values	value	NOUN
ejpam-6388	532	30	in	in	ADP
ejpam-6388	532	31	table	table	NOUN
ejpam-6388	532	32	3	3	NUM
ejpam-6388	532	33	.	.	PUNCT
ejpam-6388	532	34	d.	d.	PROPN
ejpam-6388	532	35	baleanu	baleanu	PROPN
ejpam-6388	532	36	et	et	PROPN
ejpam-6388	532	37	al	al	PROPN
ejpam-6388	532	38	.	.	PUNCT
ejpam-6388	532	39	/	/	SYM
ejpam-6388	532	40	eur	eur	PROPN
ejpam-6388	532	41	.	.	PUNCT
ejpam-6388	533	1	j.	j.	PROPN
ejpam-6388	533	2	pure	pure	PROPN
ejpam-6388	533	3	appl	appl	PROPN
ejpam-6388	533	4	.	.	PROPN
ejpam-6388	533	5	math	math	PROPN
ejpam-6388	533	6	,	,	PUNCT
ejpam-6388	533	7	18	18	NUM
ejpam-6388	533	8	(	(	PUNCT
ejpam-6388	533	9	4	4	NUM
ejpam-6388	533	10	)	)	PUNCT
ejpam-6388	533	11	(	(	PUNCT
ejpam-6388	533	12	2025	2025	NUM
ejpam-6388	533	13	)	)	PUNCT
ejpam-6388	533	14	,	,	PUNCT
ejpam-6388	533	15	6388	6388	NUM
ejpam-6388	533	16	25	25	NUM
ejpam-6388	533	17	of	of	ADP
ejpam-6388	533	18	31	31	NUM
ejpam-6388	533	19	compared	compare	VERB
ejpam-6388	533	20	with	with	ADP
ejpam-6388	533	21	example	example	NOUN
ejpam-6388	533	22	4	4	NUM
ejpam-6388	533	23	,	,	PUNCT
ejpam-6388	533	24	both	both	PRON
ejpam-6388	533	25	zhao	zhao	PROPN
ejpam-6388	533	26	and	and	CCONJ
ejpam-6388	533	27	hilal	hilal	PROPN
ejpam-6388	533	28	solutions	solution	NOUN
ejpam-6388	533	29	are	be	AUX
ejpam-6388	533	30	smaller	small	ADJ
ejpam-6388	533	31	in	in	ADP
ejpam-6388	533	32	magnitude	magnitude	NOUN
ejpam-6388	533	33	,	,	PUNCT
ejpam-6388	533	34	with	with	ADP
ejpam-6388	533	35	zhao	zhao	PROPN
ejpam-6388	533	36	reaching	reach	VERB
ejpam-6388	533	37	about	about	ADV
ejpam-6388	533	38	2.19	2.19	NUM
ejpam-6388	533	39	at	at	ADP
ejpam-6388	533	40	ω	ω	PROPN
ejpam-6388	533	41	=	=	SYM
ejpam-6388	533	42	1	1	NUM
ejpam-6388	533	43	versus	versus	ADP
ejpam-6388	533	44	3.22	3.22	NUM
ejpam-6388	533	45	for	for	ADP
ejpam-6388	533	46	example	example	NOUN
ejpam-6388	533	47	4	4	NUM
ejpam-6388	533	48	.	.	PUNCT
ejpam-6388	534	1	the	the	DET
ejpam-6388	534	2	hilal	hilal	PROPN
ejpam-6388	534	3	profile	profile	NOUN
ejpam-6388	534	4	is	be	AUX
ejpam-6388	534	5	further	far	ADV
ejpam-6388	534	6	constrained	constrain	VERB
ejpam-6388	534	7	by	by	ADP
ejpam-6388	534	8	the	the	DET
ejpam-6388	534	9	boundary	boundary	ADJ
ejpam-6388	534	10	condition	condition	NOUN
ejpam-6388	534	11	,	,	PUNCT
ejpam-6388	534	12	starting	start	VERB
ejpam-6388	534	13	at	at	ADP
ejpam-6388	534	14	0	0	NUM
ejpam-6388	534	15	and	and	CCONJ
ejpam-6388	534	16	attaining	attain	VERB
ejpam-6388	534	17	1.95	1.95	NUM
ejpam-6388	534	18	at	at	ADP
ejpam-6388	534	19	ω	ω	PROPN
ejpam-6388	534	20	=	=	SYM
ejpam-6388	534	21	1	1	X
ejpam-6388	534	22	.	.	X
ejpam-6388	534	23	figure	figure	VERB
ejpam-6388	534	24	7	7	NUM
ejpam-6388	534	25	plots	plot	NOUN
ejpam-6388	534	26	these	these	DET
ejpam-6388	534	27	curves	curve	NOUN
ejpam-6388	534	28	on	on	ADP
ejpam-6388	534	29	a	a	DET
ejpam-6388	534	30	logarithmic	logarithmic	ADJ
ejpam-6388	534	31	scale	scale	NOUN
ejpam-6388	534	32	,	,	PUNCT
ejpam-6388	534	33	clearly	clearly	ADV
ejpam-6388	534	34	separating	separate	VERB
ejpam-6388	534	35	the	the	DET
ejpam-6388	534	36	profiles	profile	NOUN
ejpam-6388	534	37	across	across	ADP
ejpam-6388	534	38	orders	order	NOUN
ejpam-6388	534	39	of	of	ADP
ejpam-6388	534	40	magnitude	magnitude	NOUN
ejpam-6388	534	41	.	.	PUNCT
ejpam-6388	535	1	the	the	DET
ejpam-6388	535	2	differences	difference	NOUN
ejpam-6388	535	3	illustrate	illustrate	VERB
ejpam-6388	535	4	how	how	SCONJ
ejpam-6388	535	5	fractional	fractional	ADJ
ejpam-6388	535	6	order	order	NOUN
ejpam-6388	535	7	(	(	PUNCT
ejpam-6388	535	8	α	α	NOUN
ejpam-6388	535	9	=	=	SYM
ejpam-6388	535	10	0.75	0.75	NUM
ejpam-6388	535	11	vs.	vs.	ADP
ejpam-6388	535	12	y	y	PROPN
ejpam-6388	535	13	=	=	PROPN
ejpam-6388	535	14	1.5	1.5	NUM
ejpam-6388	535	15	)	)	PUNCT
ejpam-6388	535	16	and	and	CCONJ
ejpam-6388	535	17	boundary	boundary	ADJ
ejpam-6388	535	18	conditions	condition	NOUN
ejpam-6388	535	19	influence	influence	VERB
ejpam-6388	535	20	the	the	DET
ejpam-6388	535	21	growth	growth	NOUN
ejpam-6388	535	22	and	and	CCONJ
ejpam-6388	535	23	shape	shape	NOUN
ejpam-6388	535	24	of	of	ADP
ejpam-6388	535	25	solutions	solution	NOUN
ejpam-6388	535	26	.	.	PUNCT
ejpam-6388	536	1	ω	ω	PROPN
ejpam-6388	536	2	r(ω	r(ω	ADV
ejpam-6388	536	3	)	)	PUNCT
ejpam-6388	536	4	(	(	PUNCT
ejpam-6388	536	5	ex	ex	X
ejpam-6388	536	6	.	.	NOUN
ejpam-6388	536	7	4	4	NUM
ejpam-6388	536	8	)	)	PUNCT
ejpam-6388	536	9	r(ω	r(ω	ADV
ejpam-6388	536	10	)	)	PUNCT
ejpam-6388	536	11	(	(	PUNCT
ejpam-6388	536	12	zhao	zhao	NOUN
ejpam-6388	536	13	)	)	PUNCT
ejpam-6388	536	14	r(ω	r(ω	ADV
ejpam-6388	536	15	)	)	PUNCT
ejpam-6388	536	16	(	(	PUNCT
ejpam-6388	536	17	hilal	hilal	PROPN
ejpam-6388	536	18	)	)	PUNCT
ejpam-6388	536	19	0.00	0.00	NUM
ejpam-6388	536	20	0.0000	0.0000	NUM
ejpam-6388	536	21	0.0000	0.0000	NUM
ejpam-6388	536	22	0.0000	0.0000	NUM
ejpam-6388	536	23	0.20	0.20	NUM
ejpam-6388	536	24	0.9875	0.9875	NUM
ejpam-6388	536	25	2.1354	2.1354	NUM
ejpam-6388	536	26	0.0000	0.0000	NUM
ejpam-6388	536	27	0.40	0.40	NUM
ejpam-6388	536	28	1.7512	1.7512	NUM
ejpam-6388	536	29	2.2120	2.2120	NUM
ejpam-6388	537	1	2.0102	2.0102	NUM
ejpam-6388	537	2	0.60	0.60	NUM
ejpam-6388	537	3	2.2987	2.2987	NUM
ejpam-6388	537	4	2.2731	2.2731	NUM
ejpam-6388	537	5	2.1198	2.1198	NUM
ejpam-6388	537	6	0.80	0.80	NUM
ejpam-6388	537	7	2.7703	2.7703	NUM
ejpam-6388	537	8	2.3258	2.3258	NUM
ejpam-6388	537	9	2.2040	2.2040	NUM
ejpam-6388	537	10	1.00	1.00	NUM
ejpam-6388	537	11	3.2210	3.2210	NUM
ejpam-6388	537	12	2.1856	2.1856	NUM
ejpam-6388	537	13	1.9523	1.9523	NUM
ejpam-6388	537	14	table	table	NOUN
ejpam-6388	537	15	3	3	NUM
ejpam-6388	537	16	:	:	PUNCT
ejpam-6388	537	17	example	example	NOUN
ejpam-6388	537	18	6	6	NUM
ejpam-6388	537	19	:	:	PUNCT
ejpam-6388	537	20	comparison	comparison	NOUN
ejpam-6388	537	21	of	of	ADP
ejpam-6388	537	22	r(ω	r(ω	ADJ
ejpam-6388	537	23	)	)	PUNCT
ejpam-6388	537	24	for	for	ADP
ejpam-6388	537	25	example	example	NOUN
ejpam-6388	537	26	4	4	NUM
ejpam-6388	537	27	(	(	PUNCT
ejpam-6388	537	28	y	y	NOUN
ejpam-6388	537	29	=	=	NOUN
ejpam-6388	537	30	1.5	1.5	NUM
ejpam-6388	537	31	)	)	PUNCT
ejpam-6388	537	32	,	,	PUNCT
ejpam-6388	537	33	zhao	zhao	PROPN
ejpam-6388	537	34	et	et	PROPN
ejpam-6388	537	35	al	al	PROPN
ejpam-6388	537	36	.	.	PUNCT
ejpam-6388	538	1	(	(	PUNCT
ejpam-6388	538	2	α	α	X
ejpam-6388	538	3	=	=	NOUN
ejpam-6388	538	4	0.75	0.75	NUM
ejpam-6388	538	5	)	)	PUNCT
ejpam-6388	538	6	,	,	PUNCT
ejpam-6388	538	7	and	and	CCONJ
ejpam-6388	538	8	hilal	hilal	PROPN
ejpam-6388	538	9	–	–	PUNCT
ejpam-6388	538	10	kajouni	kajouni	PROPN
ejpam-6388	538	11	(	(	PUNCT
ejpam-6388	538	12	α	α	X
ejpam-6388	538	13	=	=	SYM
ejpam-6388	538	14	0.75	0.75	NUM
ejpam-6388	538	15	,	,	PUNCT
ejpam-6388	538	16	caputo	caputo	PROPN
ejpam-6388	538	17	+	+	CCONJ
ejpam-6388	538	18	bc	bc	PROPN
ejpam-6388	538	19	)	)	PUNCT
ejpam-6388	538	20	.	.	PUNCT
ejpam-6388	539	1	figure	figure	VERB
ejpam-6388	539	2	7	7	NUM
ejpam-6388	539	3	:	:	PUNCT
ejpam-6388	539	4	example	example	NOUN
ejpam-6388	539	5	6	6	NUM
ejpam-6388	539	6	:	:	PUNCT
ejpam-6388	539	7	log	log	NOUN
ejpam-6388	539	8	-	-	PUNCT
ejpam-6388	539	9	scale	scale	NOUN
ejpam-6388	539	10	comparison	comparison	NOUN
ejpam-6388	539	11	of	of	ADP
ejpam-6388	539	12	r(ω	r(ω	PROPN
ejpam-6388	539	13	)	)	PUNCT
ejpam-6388	539	14	for	for	ADP
ejpam-6388	539	15	example	example	NOUN
ejpam-6388	539	16	4	4	NUM
ejpam-6388	539	17	(	(	PUNCT
ejpam-6388	539	18	y	y	NOUN
ejpam-6388	539	19	=	=	NOUN
ejpam-6388	539	20	1.5	1.5	NUM
ejpam-6388	539	21	)	)	PUNCT
ejpam-6388	539	22	(	(	PUNCT
ejpam-6388	539	23	blue	blue	ADJ
ejpam-6388	539	24	)	)	PUNCT
ejpam-6388	539	25	,	,	PUNCT
ejpam-6388	539	26	zhao	zhao	PROPN
ejpam-6388	539	27	et	et	PROPN
ejpam-6388	539	28	al	al	PROPN
ejpam-6388	539	29	.	.	PUNCT
ejpam-6388	540	1	(	(	PUNCT
ejpam-6388	540	2	α	α	X
ejpam-6388	540	3	=	=	SYM
ejpam-6388	540	4	0.75	0.75	NUM
ejpam-6388	540	5	,	,	PUNCT
ejpam-6388	540	6	orange	orange	ADJ
ejpam-6388	540	7	)	)	PUNCT
ejpam-6388	540	8	,	,	PUNCT
ejpam-6388	540	9	and	and	CCONJ
ejpam-6388	540	10	hilal	hilal	PROPN
ejpam-6388	540	11	–	–	PUNCT
ejpam-6388	540	12	kajouni	kajouni	PROPN
ejpam-6388	540	13	(	(	PUNCT
ejpam-6388	540	14	α	α	X
ejpam-6388	540	15	=	=	SYM
ejpam-6388	540	16	0.75	0.75	NUM
ejpam-6388	540	17	,	,	PUNCT
ejpam-6388	540	18	green	green	ADJ
ejpam-6388	540	19	)	)	PUNCT
ejpam-6388	540	20	.	.	PUNCT
ejpam-6388	541	1	zhao	zhao	PROPN
ejpam-6388	541	2	and	and	CCONJ
ejpam-6388	541	3	hilal	hilal	PROPN
ejpam-6388	541	4	yield	yield	VERB
ejpam-6388	541	5	smaller	small	ADJ
ejpam-6388	541	6	magnitudes	magnitude	NOUN
ejpam-6388	541	7	,	,	PUNCT
ejpam-6388	541	8	while	while	SCONJ
ejpam-6388	541	9	hilal	hilal	PROPN
ejpam-6388	541	10	is	be	AUX
ejpam-6388	541	11	further	far	ADV
ejpam-6388	541	12	constrained	constrain	VERB
ejpam-6388	541	13	near	near	ADP
ejpam-6388	541	14	the	the	DET
ejpam-6388	541	15	boundary	boundary	ADJ
ejpam-6388	541	16	due	due	ADP
ejpam-6388	541	17	to	to	ADP
ejpam-6388	541	18	the	the	DET
ejpam-6388	541	19	algebraic	algebraic	ADJ
ejpam-6388	541	20	condition	condition	NOUN
ejpam-6388	541	21	.	.	PUNCT
ejpam-6388	542	1	the	the	DET
ejpam-6388	542	2	numerical	numerical	ADJ
ejpam-6388	542	3	investigations	investigation	NOUN
ejpam-6388	542	4	highlight	highlight	VERB
ejpam-6388	542	5	the	the	DET
ejpam-6388	542	6	sensitivity	sensitivity	NOUN
ejpam-6388	542	7	of	of	ADP
ejpam-6388	542	8	fractional	fractional	PROPN
ejpam-6388	542	9	hammerstein	hammerstein	PROPN
ejpam-6388	542	10	boundary	boundary	PROPN
ejpam-6388	542	11	value	value	NOUN
ejpam-6388	542	12	problems	problem	NOUN
ejpam-6388	542	13	to	to	ADP
ejpam-6388	542	14	both	both	CCONJ
ejpam-6388	542	15	the	the	DET
ejpam-6388	542	16	choice	choice	NOUN
ejpam-6388	542	17	of	of	ADP
ejpam-6388	542	18	nonlinearities	nonlinearitie	NOUN
ejpam-6388	542	19	and	and	CCONJ
ejpam-6388	542	20	the	the	DET
ejpam-6388	542	21	fractional	fractional	ADJ
ejpam-6388	542	22	order	order	NOUN
ejpam-6388	542	23	.	.	PUNCT
ejpam-6388	543	1	in	in	ADP
ejpam-6388	543	2	example	example	NOUN
ejpam-6388	543	3	4	4	NUM
ejpam-6388	543	4	,	,	PUNCT
ejpam-6388	543	5	the	the	DET
ejpam-6388	543	6	quadratic	quadratic	ADJ
ejpam-6388	543	7	term	term	NOUN
ejpam-6388	543	8	in	in	ADP
ejpam-6388	543	9	g4	g4	NOUN
ejpam-6388	543	10	moderated	moderate	VERB
ejpam-6388	543	11	the	the	DET
ejpam-6388	543	12	growth	growth	NOUN
ejpam-6388	543	13	of	of	ADP
ejpam-6388	543	14	solutions	solution	NOUN
ejpam-6388	543	15	compared	compare	VERB
ejpam-6388	543	16	with	with	ADP
ejpam-6388	543	17	g1	g1	NOUN
ejpam-6388	543	18	,	,	PUNCT
ejpam-6388	543	19	while	while	SCONJ
ejpam-6388	543	20	example	example	NOUN
ejpam-6388	543	21	5	5	NUM
ejpam-6388	543	22	showed	show	VERB
ejpam-6388	543	23	that	that	SCONJ
ejpam-6388	543	24	removing	remove	VERB
ejpam-6388	543	25	the	the	DET
ejpam-6388	543	26	explicit	explicit	ADJ
ejpam-6388	543	27	ω	ω	NOUN
ejpam-6388	543	28	-	-	NOUN
ejpam-6388	543	29	dependence	dependence	NOUN
ejpam-6388	543	30	in	in	ADP
ejpam-6388	543	31	f3	f3	PROPN
ejpam-6388	543	32	reduced	reduce	VERB
ejpam-6388	543	33	d.	d.	PROPN
ejpam-6388	543	34	baleanu	baleanu	PROPN
ejpam-6388	543	35	et	et	PROPN
ejpam-6388	543	36	al	al	PROPN
ejpam-6388	543	37	.	.	PUNCT
ejpam-6388	543	38	/	/	SYM
ejpam-6388	543	39	eur	eur	PROPN
ejpam-6388	543	40	.	.	PUNCT
ejpam-6388	544	1	j.	j.	PROPN
ejpam-6388	544	2	pure	pure	PROPN
ejpam-6388	544	3	appl	appl	PROPN
ejpam-6388	544	4	.	.	PROPN
ejpam-6388	544	5	math	math	PROPN
ejpam-6388	544	6	,	,	PUNCT
ejpam-6388	544	7	18	18	NUM
ejpam-6388	544	8	(	(	PUNCT
ejpam-6388	544	9	4	4	NUM
ejpam-6388	544	10	)	)	PUNCT
ejpam-6388	544	11	(	(	PUNCT
ejpam-6388	544	12	2025	2025	NUM
ejpam-6388	544	13	)	)	PUNCT
ejpam-6388	544	14	,	,	PUNCT
ejpam-6388	544	15	6388	6388	NUM
ejpam-6388	544	16	26	26	NUM
ejpam-6388	544	17	of	of	ADP
ejpam-6388	544	18	31	31	NUM
ejpam-6388	544	19	the	the	DET
ejpam-6388	544	20	overall	overall	ADJ
ejpam-6388	544	21	amplitude	amplitude	NOUN
ejpam-6388	544	22	of	of	ADP
ejpam-6388	544	23	solutions	solution	NOUN
ejpam-6388	544	24	.	.	PUNCT
ejpam-6388	545	1	example	example	NOUN
ejpam-6388	545	2	6	6	NUM
ejpam-6388	545	3	demonstrated	demonstrate	VERB
ejpam-6388	545	4	that	that	SCONJ
ejpam-6388	545	5	lowering	lower	VERB
ejpam-6388	545	6	the	the	DET
ejpam-6388	545	7	fractional	fractional	ADJ
ejpam-6388	545	8	order	order	NOUN
ejpam-6388	545	9	from	from	ADP
ejpam-6388	545	10	y	y	PROPN
ejpam-6388	545	11	=	=	PROPN
ejpam-6388	545	12	1.5	1.5	NUM
ejpam-6388	545	13	to	to	ADP
ejpam-6388	545	14	α	α	NOUN
ejpam-6388	545	15	=	=	NOUN
ejpam-6388	545	16	0.75	0.75	NUM
ejpam-6388	545	17	significantly	significantly	ADV
ejpam-6388	545	18	decreased	decrease	VERB
ejpam-6388	545	19	the	the	DET
ejpam-6388	545	20	magnitude	magnitude	NOUN
ejpam-6388	545	21	of	of	ADP
ejpam-6388	545	22	solutions	solution	NOUN
ejpam-6388	545	23	,	,	PUNCT
ejpam-6388	545	24	with	with	ADP
ejpam-6388	545	25	hilal	hilal	PROPN
ejpam-6388	545	26	’s	’s	PART
ejpam-6388	545	27	caputo	caputo	PROPN
ejpam-6388	545	28	formulation	formulation	NOUN
ejpam-6388	545	29	further	far	ADV
ejpam-6388	545	30	constrained	constrain	VERB
ejpam-6388	545	31	by	by	ADP
ejpam-6388	545	32	the	the	DET
ejpam-6388	545	33	algebraic	algebraic	ADJ
ejpam-6388	545	34	boundary	boundary	ADJ
ejpam-6388	545	35	condition	condition	NOUN
ejpam-6388	545	36	.	.	PUNCT
ejpam-6388	546	1	tables	table	NOUN
ejpam-6388	546	2	1–3	1–3	NUM
ejpam-6388	546	3	and	and	CCONJ
ejpam-6388	546	4	figures	figure	VERB
ejpam-6388	546	5	5–7	5–7	NOUN
ejpam-6388	546	6	together	together	ADV
ejpam-6388	546	7	confirm	confirm	VERB
ejpam-6388	546	8	that	that	PRON
ejpam-6388	546	9	nonlinear	nonlinear	ADJ
ejpam-6388	546	10	structure	structure	NOUN
ejpam-6388	546	11	,	,	PUNCT
ejpam-6388	546	12	fractional	fractional	ADJ
ejpam-6388	546	13	order	order	NOUN
ejpam-6388	546	14	,	,	PUNCT
ejpam-6388	546	15	and	and	CCONJ
ejpam-6388	546	16	boundary	boundary	ADJ
ejpam-6388	546	17	conditions	condition	NOUN
ejpam-6388	546	18	jointly	jointly	ADV
ejpam-6388	546	19	govern	govern	VERB
ejpam-6388	546	20	the	the	DET
ejpam-6388	546	21	qualitative	qualitative	ADJ
ejpam-6388	546	22	and	and	CCONJ
ejpam-6388	546	23	quantitative	quantitative	ADJ
ejpam-6388	546	24	behavior	behavior	NOUN
ejpam-6388	546	25	of	of	ADP
ejpam-6388	546	26	solutions	solution	NOUN
ejpam-6388	546	27	.	.	PUNCT
ejpam-6388	547	1	7	7	X
ejpam-6388	547	2	.	.	X
ejpam-6388	547	3	conclusions	conclusion	NOUN
ejpam-6388	547	4	the	the	DET
ejpam-6388	547	5	primary	primary	ADJ
ejpam-6388	547	6	aim	aim	NOUN
ejpam-6388	547	7	of	of	ADP
ejpam-6388	547	8	this	this	DET
ejpam-6388	547	9	study	study	NOUN
ejpam-6388	547	10	is	be	AUX
ejpam-6388	547	11	to	to	PART
ejpam-6388	547	12	develop	develop	VERB
ejpam-6388	547	13	a	a	DET
ejpam-6388	547	14	robust	robust	ADJ
ejpam-6388	547	15	mathematical	mathematical	ADJ
ejpam-6388	547	16	framework	framework	NOUN
ejpam-6388	547	17	for	for	ADP
ejpam-6388	547	18	analyzing	analyze	VERB
ejpam-6388	547	19	fractional	fractional	ADJ
ejpam-6388	547	20	hybrid	hybrid	ADJ
ejpam-6388	547	21	boundary	boundary	ADJ
ejpam-6388	547	22	value	value	NOUN
ejpam-6388	547	23	problems	problem	NOUN
ejpam-6388	547	24	(	(	PUNCT
ejpam-6388	547	25	fhbvps	fhbvps	PROPN
ejpam-6388	547	26	)	)	PUNCT
ejpam-6388	547	27	with	with	ADP
ejpam-6388	547	28	riemann	riemann	PROPN
ejpam-6388	547	29	–	–	PUNCT
ejpam-6388	547	30	liouville	liouville	VERB
ejpam-6388	547	31	fractional	fractional	ADJ
ejpam-6388	547	32	derivatives	derivative	NOUN
ejpam-6388	547	33	of	of	ADP
ejpam-6388	547	34	order	order	NOUN
ejpam-6388	547	35	1	1	NUM
ejpam-6388	547	36	<	<	X
ejpam-6388	547	37	y	y	PROPN
ejpam-6388	547	38	≤	≤	NUM
ejpam-6388	547	39	2	2	NUM
ejpam-6388	547	40	,	,	PUNCT
ejpam-6388	547	41	focusing	focus	VERB
ejpam-6388	547	42	on	on	ADP
ejpam-6388	547	43	establishing	establish	VERB
ejpam-6388	547	44	the	the	DET
ejpam-6388	547	45	existence	existence	NOUN
ejpam-6388	547	46	,	,	PUNCT
ejpam-6388	547	47	uniqueness	uniqueness	NOUN
ejpam-6388	547	48	,	,	PUNCT
ejpam-6388	547	49	and	and	CCONJ
ejpam-6388	547	50	stability	stability	NOUN
ejpam-6388	547	51	of	of	ADP
ejpam-6388	547	52	solutions	solution	NOUN
ejpam-6388	547	53	.	.	PUNCT
ejpam-6388	548	1	by	by	ADP
ejpam-6388	548	2	leveraging	leverage	VERB
ejpam-6388	548	3	the	the	DET
ejpam-6388	548	4	extended	extended	ADJ
ejpam-6388	548	5	banach	banach	ADV
ejpam-6388	548	6	fixed	fix	VERB
ejpam-6388	548	7	point	point	NOUN
ejpam-6388	548	8	theorem	theorem	VERB
ejpam-6388	548	9	in	in	ADP
ejpam-6388	548	10	orthogonal	orthogonal	ADJ
ejpam-6388	548	11	cone	cone	NOUN
ejpam-6388	548	12	metric	metric	ADJ
ejpam-6388	548	13	spaces	space	NOUN
ejpam-6388	548	14	,	,	PUNCT
ejpam-6388	548	15	we	we	PRON
ejpam-6388	548	16	successfully	successfully	ADV
ejpam-6388	548	17	proved	prove	VERB
ejpam-6388	548	18	the	the	DET
ejpam-6388	548	19	existence	existence	NOUN
ejpam-6388	548	20	and	and	CCONJ
ejpam-6388	548	21	uniqueness	uniqueness	NOUN
ejpam-6388	548	22	of	of	ADP
ejpam-6388	548	23	solutions	solution	NOUN
ejpam-6388	548	24	for	for	ADP
ejpam-6388	548	25	fhbvps	fhbvps	PROPN
ejpam-6388	548	26	,	,	PUNCT
ejpam-6388	548	27	extending	extend	VERB
ejpam-6388	548	28	prior	prior	ADJ
ejpam-6388	548	29	results	result	NOUN
ejpam-6388	548	30	in	in	ADP
ejpam-6388	548	31	standard	standard	ADJ
ejpam-6388	548	32	metric	metric	ADJ
ejpam-6388	548	33	spaces	space	NOUN
ejpam-6388	548	34	and	and	CCONJ
ejpam-6388	548	35	banach	banach	NOUN
ejpam-6388	548	36	algebras	algebras	X
ejpam-6388	549	1	[	[	X
ejpam-6388	549	2	1	1	NUM
ejpam-6388	549	3	,	,	PUNCT
ejpam-6388	549	4	2	2	NUM
ejpam-6388	549	5	]	]	PUNCT
ejpam-6388	549	6	.	.	PUNCT
ejpam-6388	550	1	our	our	PRON
ejpam-6388	550	2	investigation	investigation	NOUN
ejpam-6388	550	3	of	of	ADP
ejpam-6388	550	4	hyers	hyer	NOUN
ejpam-6388	550	5	–	–	PUNCT
ejpam-6388	550	6	ulam	ulam	X
ejpam-6388	550	7	stability	stability	NOUN
ejpam-6388	550	8	,	,	PUNCT
ejpam-6388	550	9	incorporating	incorporate	VERB
ejpam-6388	550	10	a	a	DET
ejpam-6388	550	11	parameter	parameter	NOUN
ejpam-6388	550	12	to	to	PART
ejpam-6388	550	13	address	address	VERB
ejpam-6388	550	14	perturbed	perturb	VERB
ejpam-6388	550	15	boundary	boundary	ADJ
ejpam-6388	550	16	conditions	condition	NOUN
ejpam-6388	550	17	,	,	PUNCT
ejpam-6388	550	18	ensures	ensure	VERB
ejpam-6388	550	19	the	the	DET
ejpam-6388	550	20	robustness	robustness	NOUN
ejpam-6388	550	21	of	of	ADP
ejpam-6388	550	22	solutions	solution	NOUN
ejpam-6388	550	23	and	and	CCONJ
ejpam-6388	550	24	corrects	correct	NOUN
ejpam-6388	550	25	methodological	methodological	ADJ
ejpam-6388	550	26	issues	issue	NOUN
ejpam-6388	550	27	noted	note	VERB
ejpam-6388	550	28	in	in	ADP
ejpam-6388	550	29	the	the	DET
ejpam-6388	550	30	literature	literature	NOUN
ejpam-6388	550	31	[	[	X
ejpam-6388	550	32	3	3	NUM
ejpam-6388	550	33	]	]	PUNCT
ejpam-6388	550	34	.	.	PUNCT
ejpam-6388	551	1	numerical	numerical	ADJ
ejpam-6388	551	2	simulations	simulation	NOUN
ejpam-6388	551	3	,	,	PUNCT
ejpam-6388	551	4	implemented	implement	VERB
ejpam-6388	551	5	via	via	ADP
ejpam-6388	551	6	the	the	DET
ejpam-6388	551	7	trapezoidal	trapezoidal	ADJ
ejpam-6388	551	8	rule	rule	NOUN
ejpam-6388	551	9	,	,	PUNCT
ejpam-6388	551	10	validated	validate	VERB
ejpam-6388	551	11	our	our	PRON
ejpam-6388	551	12	theoretical	theoretical	ADJ
ejpam-6388	551	13	findings	finding	NOUN
ejpam-6388	551	14	by	by	ADP
ejpam-6388	551	15	illustrating	illustrate	VERB
ejpam-6388	551	16	the	the	DET
ejpam-6388	551	17	influence	influence	NOUN
ejpam-6388	551	18	of	of	ADP
ejpam-6388	551	19	fractional	fractional	ADJ
ejpam-6388	551	20	order	order	NOUN
ejpam-6388	551	21	and	and	CCONJ
ejpam-6388	551	22	nonlinear	nonlinear	ADJ
ejpam-6388	551	23	terms	term	NOUN
ejpam-6388	551	24	on	on	ADP
ejpam-6388	551	25	solution	solution	NOUN
ejpam-6388	551	26	behavior	behavior	NOUN
ejpam-6388	551	27	,	,	PUNCT
ejpam-6388	551	28	as	as	SCONJ
ejpam-6388	551	29	demonstrated	demonstrate	VERB
ejpam-6388	551	30	in	in	ADP
ejpam-6388	551	31	figures	figure	NOUN
ejpam-6388	551	32	1–4	1–4	NUM
ejpam-6388	551	33	.	.	PUNCT
ejpam-6388	552	1	these	these	DET
ejpam-6388	552	2	results	result	NOUN
ejpam-6388	552	3	advance	advance	VERB
ejpam-6388	552	4	the	the	DET
ejpam-6388	552	5	theoretical	theoretical	ADJ
ejpam-6388	552	6	understanding	understanding	NOUN
ejpam-6388	552	7	of	of	ADP
ejpam-6388	552	8	fhbvps	fhbvps	PROPN
ejpam-6388	552	9	and	and	CCONJ
ejpam-6388	552	10	offer	offer	VERB
ejpam-6388	552	11	practical	practical	ADJ
ejpam-6388	552	12	tools	tool	NOUN
ejpam-6388	552	13	for	for	ADP
ejpam-6388	552	14	modeling	model	VERB
ejpam-6388	552	15	complex	complex	ADJ
ejpam-6388	552	16	systems	system	NOUN
ejpam-6388	552	17	with	with	ADP
ejpam-6388	552	18	nonlocal	nonlocal	ADJ
ejpam-6388	552	19	and	and	CCONJ
ejpam-6388	552	20	memory	memory	NOUN
ejpam-6388	552	21	-	-	PUNCT
ejpam-6388	552	22	dependent	dependent	ADJ
ejpam-6388	552	23	dynamics	dynamic	NOUN
ejpam-6388	552	24	in	in	ADP
ejpam-6388	552	25	fields	field	NOUN
ejpam-6388	552	26	such	such	ADJ
ejpam-6388	552	27	as	as	ADP
ejpam-6388	552	28	engineering	engineering	NOUN
ejpam-6388	552	29	,	,	PUNCT
ejpam-6388	552	30	physics	physics	NOUN
ejpam-6388	552	31	,	,	PUNCT
ejpam-6388	552	32	and	and	CCONJ
ejpam-6388	552	33	biology	biology	NOUN
ejpam-6388	552	34	.	.	PUNCT
ejpam-6388	553	1	future	future	ADJ
ejpam-6388	553	2	research	research	NOUN
ejpam-6388	553	3	directions	direction	NOUN
ejpam-6388	553	4	include	include	VERB
ejpam-6388	553	5	the	the	DET
ejpam-6388	553	6	following	follow	VERB
ejpam-6388	553	7	:	:	PUNCT
ejpam-6388	553	8	•	•	NUM
ejpam-6388	553	9	higher	high	ADJ
ejpam-6388	553	10	-	-	PUNCT
ejpam-6388	553	11	order	order	NOUN
ejpam-6388	553	12	and	and	CCONJ
ejpam-6388	553	13	multivariable	multivariable	ADJ
ejpam-6388	553	14	systems	system	NOUN
ejpam-6388	553	15	:	:	PUNCT
ejpam-6388	553	16	extend	extend	VERB
ejpam-6388	553	17	the	the	DET
ejpam-6388	553	18	analysis	analysis	NOUN
ejpam-6388	553	19	to	to	PART
ejpam-6388	553	20	fhbvps	fhbvps	VERB
ejpam-6388	553	21	with	with	ADP
ejpam-6388	553	22	fractional	fractional	ADJ
ejpam-6388	553	23	orders	order	NOUN
ejpam-6388	553	24	beyond	beyond	ADP
ejpam-6388	553	25	1	1	NUM
ejpam-6388	553	26	<	<	X
ejpam-6388	553	27	y	y	PROPN
ejpam-6388	553	28	≤	≤	ADV
ejpam-6388	553	29	2	2	NUM
ejpam-6388	553	30	or	or	CCONJ
ejpam-6388	553	31	multivariable	multivariable	ADJ
ejpam-6388	553	32	hybrid	hybrid	NOUN
ejpam-6388	553	33	systems	system	NOUN
ejpam-6388	553	34	to	to	PART
ejpam-6388	553	35	capture	capture	VERB
ejpam-6388	553	36	richer	rich	ADJ
ejpam-6388	553	37	dynamics	dynamic	NOUN
ejpam-6388	553	38	in	in	ADP
ejpam-6388	553	39	applications	application	NOUN
ejpam-6388	553	40	like	like	ADP
ejpam-6388	553	41	control	control	NOUN
ejpam-6388	553	42	theory	theory	NOUN
ejpam-6388	553	43	and	and	CCONJ
ejpam-6388	553	44	biological	biological	ADJ
ejpam-6388	553	45	networks	network	NOUN
ejpam-6388	553	46	.	.	PUNCT
ejpam-6388	554	1	•	•	NUM
ejpam-6388	554	2	diverse	diverse	ADJ
ejpam-6388	554	3	boundary	boundary	ADJ
ejpam-6388	554	4	conditions	condition	NOUN
ejpam-6388	554	5	:	:	PUNCT
ejpam-6388	554	6	investigate	investigate	VERB
ejpam-6388	554	7	the	the	DET
ejpam-6388	554	8	impact	impact	NOUN
ejpam-6388	554	9	of	of	ADP
ejpam-6388	554	10	alternative	alternative	ADJ
ejpam-6388	554	11	boundary	boundary	ADJ
ejpam-6388	554	12	conditions	condition	NOUN
ejpam-6388	554	13	,	,	PUNCT
ejpam-6388	554	14	such	such	ADJ
ejpam-6388	554	15	as	as	ADP
ejpam-6388	554	16	multi	multi	ADJ
ejpam-6388	554	17	-	-	NOUN
ejpam-6388	554	18	point	point	NOUN
ejpam-6388	554	19	or	or	CCONJ
ejpam-6388	554	20	integral	integral	ADJ
ejpam-6388	554	21	conditions	condition	NOUN
ejpam-6388	554	22	,	,	PUNCT
ejpam-6388	554	23	on	on	ADP
ejpam-6388	554	24	the	the	DET
ejpam-6388	554	25	existence	existence	NOUN
ejpam-6388	554	26	,	,	PUNCT
ejpam-6388	554	27	uniqueness	uniqueness	NOUN
ejpam-6388	554	28	,	,	PUNCT
ejpam-6388	554	29	and	and	CCONJ
ejpam-6388	554	30	stability	stability	NOUN
ejpam-6388	554	31	of	of	ADP
ejpam-6388	554	32	solutions	solution	NOUN
ejpam-6388	554	33	to	to	PART
ejpam-6388	554	34	broaden	broaden	VERB
ejpam-6388	554	35	the	the	DET
ejpam-6388	554	36	applicability	applicability	NOUN
ejpam-6388	554	37	of	of	ADP
ejpam-6388	554	38	the	the	DET
ejpam-6388	554	39	framework	framework	NOUN
ejpam-6388	554	40	.	.	PUNCT
ejpam-6388	555	1	•	•	NUM
ejpam-6388	555	2	advanced	advanced	ADJ
ejpam-6388	555	3	numerical	numerical	ADJ
ejpam-6388	555	4	methods	method	NOUN
ejpam-6388	555	5	:	:	PUNCT
ejpam-6388	555	6	develop	develop	VERB
ejpam-6388	555	7	more	more	ADV
ejpam-6388	555	8	sophisticated	sophisticated	ADJ
ejpam-6388	555	9	numerical	numerical	ADJ
ejpam-6388	555	10	techniques	technique	NOUN
ejpam-6388	555	11	,	,	PUNCT
ejpam-6388	555	12	such	such	ADJ
ejpam-6388	555	13	as	as	ADP
ejpam-6388	555	14	adaptive	adaptive	ADJ
ejpam-6388	555	15	algorithms	algorithm	NOUN
ejpam-6388	555	16	or	or	CCONJ
ejpam-6388	555	17	machine	machine	NOUN
ejpam-6388	555	18	learning	learning	NOUN
ejpam-6388	555	19	-	-	PUNCT
ejpam-6388	555	20	based	base	VERB
ejpam-6388	555	21	approaches	approach	NOUN
ejpam-6388	555	22	,	,	PUNCT
ejpam-6388	555	23	to	to	PART
ejpam-6388	555	24	enhance	enhance	VERB
ejpam-6388	555	25	the	the	DET
ejpam-6388	555	26	accuracy	accuracy	NOUN
ejpam-6388	555	27	and	and	CCONJ
ejpam-6388	555	28	scalability	scalability	NOUN
ejpam-6388	555	29	of	of	ADP
ejpam-6388	555	30	simulations	simulation	NOUN
ejpam-6388	555	31	for	for	ADP
ejpam-6388	555	32	large	large	ADJ
ejpam-6388	555	33	-	-	PUNCT
ejpam-6388	555	34	scale	scale	NOUN
ejpam-6388	555	35	fhbvps	fhbvps	PROPN
ejpam-6388	555	36	.	.	PROPN
ejpam-6388	555	37	•	•	NUM
ejpam-6388	555	38	real	real	ADJ
ejpam-6388	555	39	-	-	PUNCT
ejpam-6388	555	40	world	world	NOUN
ejpam-6388	555	41	applications	application	NOUN
ejpam-6388	555	42	:	:	PUNCT
ejpam-6388	555	43	apply	apply	VERB
ejpam-6388	555	44	the	the	DET
ejpam-6388	555	45	proposed	propose	VERB
ejpam-6388	555	46	framework	framework	NOUN
ejpam-6388	555	47	to	to	ADP
ejpam-6388	555	48	specific	specific	ADJ
ejpam-6388	555	49	problems	problem	NOUN
ejpam-6388	555	50	in	in	ADP
ejpam-6388	555	51	viscoelasticity	viscoelasticity	NOUN
ejpam-6388	555	52	,	,	PUNCT
ejpam-6388	555	53	anomalous	anomalous	ADJ
ejpam-6388	555	54	diffusion	diffusion	NOUN
ejpam-6388	555	55	,	,	PUNCT
ejpam-6388	555	56	or	or	CCONJ
ejpam-6388	555	57	biological	biological	ADJ
ejpam-6388	555	58	systems	system	NOUN
ejpam-6388	555	59	,	,	PUNCT
ejpam-6388	555	60	validating	validate	VERB
ejpam-6388	555	61	the	the	DET
ejpam-6388	555	62	model	model	NOUN
ejpam-6388	555	63	with	with	ADP
ejpam-6388	555	64	experimental	experimental	ADJ
ejpam-6388	555	65	data	datum	NOUN
ejpam-6388	555	66	to	to	PART
ejpam-6388	555	67	bridge	bridge	VERB
ejpam-6388	555	68	theoretical	theoretical	ADJ
ejpam-6388	555	69	and	and	CCONJ
ejpam-6388	555	70	practical	practical	ADJ
ejpam-6388	555	71	domains	domain	NOUN
ejpam-6388	555	72	.	.	PUNCT
ejpam-6388	556	1	•	•	NUM
ejpam-6388	556	2	generalized	generalize	VERB
ejpam-6388	556	3	metric	metric	ADJ
ejpam-6388	556	4	spaces	space	NOUN
ejpam-6388	556	5	:	:	PUNCT
ejpam-6388	556	6	explore	explore	VERB
ejpam-6388	556	7	other	other	ADJ
ejpam-6388	556	8	generalized	generalized	ADJ
ejpam-6388	556	9	metric	metric	ADJ
ejpam-6388	556	10	spaces	space	NOUN
ejpam-6388	556	11	,	,	PUNCT
ejpam-6388	556	12	such	such	ADJ
ejpam-6388	556	13	as	as	ADP
ejpam-6388	556	14	partial	partial	ADJ
ejpam-6388	556	15	metric	metric	ADJ
ejpam-6388	556	16	spaces	space	NOUN
ejpam-6388	556	17	or	or	CCONJ
ejpam-6388	556	18	fuzzy	fuzzy	ADJ
ejpam-6388	556	19	metric	metric	ADJ
ejpam-6388	556	20	spaces	space	NOUN
ejpam-6388	556	21	,	,	PUNCT
ejpam-6388	556	22	to	to	PART
ejpam-6388	556	23	further	far	ADV
ejpam-6388	556	24	extend	extend	VERB
ejpam-6388	556	25	the	the	DET
ejpam-6388	556	26	fixed	fix	VERB
ejpam-6388	556	27	point	point	NOUN
ejpam-6388	556	28	techniques	technique	NOUN
ejpam-6388	556	29	for	for	ADP
ejpam-6388	556	30	fhbvps	fhbvps	ADJ
ejpam-6388	556	31	and	and	CCONJ
ejpam-6388	556	32	related	related	ADJ
ejpam-6388	556	33	problems	problem	NOUN
ejpam-6388	556	34	.	.	PUNCT
ejpam-6388	557	1	these	these	DET
ejpam-6388	557	2	avenues	avenue	NOUN
ejpam-6388	557	3	promise	promise	VERB
ejpam-6388	557	4	to	to	PART
ejpam-6388	557	5	deepen	deepen	VERB
ejpam-6388	557	6	the	the	DET
ejpam-6388	557	7	understanding	understanding	NOUN
ejpam-6388	557	8	of	of	ADP
ejpam-6388	557	9	fractional	fractional	ADJ
ejpam-6388	557	10	hybrid	hybrid	ADJ
ejpam-6388	557	11	systems	system	NOUN
ejpam-6388	557	12	and	and	CCONJ
ejpam-6388	557	13	enhance	enhance	VERB
ejpam-6388	557	14	their	their	PRON
ejpam-6388	557	15	applicability	applicability	NOUN
ejpam-6388	557	16	across	across	ADP
ejpam-6388	557	17	diverse	diverse	ADJ
ejpam-6388	557	18	scientific	scientific	ADJ
ejpam-6388	557	19	disciplines	discipline	NOUN
ejpam-6388	557	20	.	.	PUNCT
ejpam-6388	558	1	d.	d.	PROPN
ejpam-6388	558	2	baleanu	baleanu	PROPN
ejpam-6388	558	3	et	et	PROPN
ejpam-6388	558	4	al	al	PROPN
ejpam-6388	558	5	.	.	PUNCT
ejpam-6388	558	6	/	/	SYM
ejpam-6388	558	7	eur	eur	PROPN
ejpam-6388	558	8	.	.	PUNCT
ejpam-6388	559	1	j.	j.	PROPN
ejpam-6388	559	2	pure	pure	PROPN
ejpam-6388	559	3	appl	appl	PROPN
ejpam-6388	559	4	.	.	PROPN
ejpam-6388	559	5	math	math	PROPN
ejpam-6388	559	6	,	,	PUNCT
ejpam-6388	559	7	18	18	NUM
ejpam-6388	559	8	(	(	PUNCT
ejpam-6388	559	9	4	4	NUM
ejpam-6388	559	10	)	)	PUNCT
ejpam-6388	559	11	(	(	PUNCT
ejpam-6388	559	12	2025	2025	NUM
ejpam-6388	559	13	)	)	PUNCT
ejpam-6388	559	14	,	,	PUNCT
ejpam-6388	559	15	6388	6388	NUM
ejpam-6388	559	16	27	27	NUM
ejpam-6388	559	17	of	of	ADP
ejpam-6388	559	18	31	31	NUM
ejpam-6388	559	19	acknowledgements	acknowledgement	NOUN
ejpam-6388	559	20	we	we	PRON
ejpam-6388	559	21	would	would	AUX
ejpam-6388	559	22	like	like	VERB
ejpam-6388	559	23	to	to	PART
ejpam-6388	559	24	thank	thank	VERB
ejpam-6388	559	25	the	the	DET
ejpam-6388	559	26	reviewers	reviewer	NOUN
ejpam-6388	559	27	for	for	ADP
ejpam-6388	559	28	their	their	PRON
ejpam-6388	559	29	valuable	valuable	ADJ
ejpam-6388	559	30	comments	comment	NOUN
ejpam-6388	559	31	and	and	CCONJ
ejpam-6388	559	32	constructive	constructive	ADJ
ejpam-6388	559	33	feedback	feedback	NOUN
ejpam-6388	559	34	,	,	PUNCT
ejpam-6388	559	35	which	which	PRON
ejpam-6388	559	36	have	have	AUX
ejpam-6388	559	37	significantly	significantly	ADV
ejpam-6388	559	38	contributed	contribute	VERB
ejpam-6388	559	39	to	to	ADP
ejpam-6388	559	40	the	the	DET
ejpam-6388	559	41	improvement	improvement	NOUN
ejpam-6388	559	42	of	of	ADP
ejpam-6388	559	43	this	this	DET
ejpam-6388	559	44	manuscript	manuscript	NOUN
ejpam-6388	559	45	.	.	PUNCT
ejpam-6388	560	1	the	the	DET
ejpam-6388	560	2	authors	author	NOUN
ejpam-6388	560	3	would	would	AUX
ejpam-6388	560	4	like	like	VERB
ejpam-6388	560	5	to	to	PART
ejpam-6388	560	6	express	express	VERB
ejpam-6388	560	7	their	their	PRON
ejpam-6388	560	8	sincere	sincere	ADJ
ejpam-6388	560	9	gratitude	gratitude	NOUN
ejpam-6388	560	10	to	to	ADP
ejpam-6388	560	11	the	the	DET
ejpam-6388	560	12	respective	respective	ADJ
ejpam-6388	560	13	institutions	institution	NOUN
ejpam-6388	560	14	and	and	CCONJ
ejpam-6388	560	15	collaborators	collaborator	NOUN
ejpam-6388	560	16	for	for	ADP
ejpam-6388	560	17	their	their	PRON
ejpam-6388	560	18	support	support	NOUN
ejpam-6388	560	19	in	in	ADP
ejpam-6388	560	20	this	this	DET
ejpam-6388	560	21	research	research	NOUN
ejpam-6388	560	22	.	.	PUNCT
ejpam-6388	561	1	specifically	specifically	ADV
ejpam-6388	561	2	,	,	PUNCT
ejpam-6388	561	3	m.	m.	NOUN
ejpam-6388	561	4	khuddush	khuddush	PROPN
ejpam-6388	561	5	is	be	AUX
ejpam-6388	561	6	thankful	thankful	ADJ
ejpam-6388	561	7	to	to	ADP
ejpam-6388	561	8	the	the	DET
ejpam-6388	561	9	applied	apply	VERB
ejpam-6388	561	10	nonlinear	nonlinear	ADJ
ejpam-6388	561	11	science	science	NOUN
ejpam-6388	561	12	lab	lab	NOUN
ejpam-6388	561	13	(	(	PUNCT
ejpam-6388	561	14	ansl	ansl	ADV
ejpam-6388	561	15	)	)	PUNCT
ejpam-6388	561	16	for	for	ADP
ejpam-6388	561	17	providing	provide	VERB
ejpam-6388	561	18	the	the	DET
ejpam-6388	561	19	necessary	necessary	ADJ
ejpam-6388	561	20	research	research	NOUN
ejpam-6388	561	21	facilities	facility	NOUN
ejpam-6388	561	22	and	and	CCONJ
ejpam-6388	561	23	environment	environment	NOUN
ejpam-6388	561	24	at	at	ADP
ejpam-6388	561	25	aice	aice	NOUN
ejpam-6388	561	26	,	,	PUNCT
ejpam-6388	561	27	jaipur	jaipur	PROPN
ejpam-6388	561	28	,	,	PUNCT
ejpam-6388	561	29	india	india	PROPN
ejpam-6388	562	1	.	.	PUNCT
ejpam-6388	562	2	b.	b.	PROPN
ejpam-6388	562	3	m.	m.	PROPN
ejpam-6388	562	4	b.	b.	PROPN
ejpam-6388	562	5	krushna	krushna	PROPN
ejpam-6388	562	6	is	be	AUX
ejpam-6388	562	7	thankful	thankful	ADJ
ejpam-6388	562	8	to	to	ADP
ejpam-6388	562	9	mvgr	mvgr	PROPN
ejpam-6388	562	10	college	college	PROPN
ejpam-6388	562	11	of	of	ADP
ejpam-6388	562	12	engineering	engineering	PROPN
ejpam-6388	562	13	,	,	PUNCT
ejpam-6388	562	14	vizianagaram	vizianagaram	PROPN
ejpam-6388	562	15	,	,	PUNCT
ejpam-6388	562	16	india	india	PROPN
ejpam-6388	562	17	,	,	PUNCT
ejpam-6388	562	18	for	for	ADP
ejpam-6388	562	19	the	the	DET
ejpam-6388	562	20	support	support	NOUN
ejpam-6388	562	21	during	during	ADP
ejpam-6388	562	22	the	the	DET
ejpam-6388	562	23	preparation	preparation	NOUN
ejpam-6388	562	24	of	of	ADP
ejpam-6388	562	25	this	this	DET
ejpam-6388	562	26	paper	paper	NOUN
ejpam-6388	562	27	.	.	PUNCT
ejpam-6388	563	1	references	reference	NOUN
ejpam-6388	563	2	[	[	X
ejpam-6388	563	3	1	1	NUM
ejpam-6388	563	4	]	]	PUNCT
ejpam-6388	563	5	y	y	PROPN
ejpam-6388	563	6	zhao	zhao	PROPN
ejpam-6388	563	7	,	,	PUNCT
ejpam-6388	563	8	s	s	PROPN
ejpam-6388	563	9	sun	sun	NOUN
ejpam-6388	563	10	,	,	PUNCT
ejpam-6388	563	11	z	z	PROPN
ejpam-6388	563	12	han	han	PROPN
ejpam-6388	563	13	,	,	PUNCT
ejpam-6388	563	14	and	and	CCONJ
ejpam-6388	563	15	q	q	PROPN
ejpam-6388	563	16	li	li	PROPN
ejpam-6388	563	17	.	.	PROPN
ejpam-6388	563	18	theory	theory	NOUN
ejpam-6388	563	19	of	of	ADP
ejpam-6388	563	20	fractional	fractional	ADJ
ejpam-6388	563	21	hybrid	hybrid	ADJ
ejpam-6388	563	22	differential	differential	NOUN
ejpam-6388	563	23	equations	equation	NOUN
ejpam-6388	563	24	.	.	PUNCT
ejpam-6388	564	1	comput	comput	NOUN
ejpam-6388	564	2	.	.	PUNCT
ejpam-6388	565	1	math	math	NOUN
ejpam-6388	565	2	.	.	PUNCT
ejpam-6388	566	1	appl	appl	PROPN
ejpam-6388	566	2	.	.	PROPN
ejpam-6388	566	3	,	,	PUNCT
ejpam-6388	567	1	62(3):1312–1324	62(3):1312–1324	NUM
ejpam-6388	567	2	,	,	PUNCT
ejpam-6388	567	3	2011	2011	NUM
ejpam-6388	567	4	.	.	PUNCT
ejpam-6388	568	1	[	[	X
ejpam-6388	568	2	2	2	NUM
ejpam-6388	568	3	]	]	X
ejpam-6388	568	4	k	k	PROPN
ejpam-6388	568	5	hilal	hilal	PROPN
ejpam-6388	568	6	and	and	CCONJ
ejpam-6388	568	7	a	a	DET
ejpam-6388	568	8	kajouni	kajouni	PROPN
ejpam-6388	568	9	.	.	PUNCT
ejpam-6388	569	1	boundary	boundary	ADJ
ejpam-6388	569	2	value	value	NOUN
ejpam-6388	569	3	problems	problem	NOUN
ejpam-6388	569	4	for	for	ADP
ejpam-6388	569	5	hybrid	hybrid	ADJ
ejpam-6388	569	6	differential	differential	ADJ
ejpam-6388	569	7	equations	equation	NOUN
ejpam-6388	569	8	with	with	ADP
ejpam-6388	569	9	fractional	fractional	ADJ
ejpam-6388	569	10	order	order	NOUN
ejpam-6388	569	11	.	.	PUNCT
ejpam-6388	570	1	adv	adv	PROPN
ejpam-6388	570	2	.	.	PUNCT
ejpam-6388	570	3	difference	difference	PROPN
ejpam-6388	570	4	equ	equ	PROPN
ejpam-6388	570	5	.	.	PROPN
ejpam-6388	570	6	,	,	PUNCT
ejpam-6388	570	7	2015(183):1–19	2015(183):1–19	NUM
ejpam-6388	570	8	,	,	PUNCT
ejpam-6388	570	9	2015	2015	NUM
ejpam-6388	570	10	.	.	PUNCT
ejpam-6388	571	1	[	[	X
ejpam-6388	571	2	3	3	X
ejpam-6388	571	3	]	]	X
ejpam-6388	571	4	rp	rp	NOUN
ejpam-6388	571	5	agarwal	agarwal	PROPN
ejpam-6388	571	6	,	,	PUNCT
ejpam-6388	571	7	s	s	PART
ejpam-6388	571	8	hristova	hristova	PROPN
ejpam-6388	571	9	,	,	PUNCT
ejpam-6388	571	10	and	and	CCONJ
ejpam-6388	571	11	d	d	X
ejpam-6388	571	12	o’regan	o’regan	PROPN
ejpam-6388	571	13	.	.	PUNCT
ejpam-6388	572	1	ulam	ulam	PROPN
ejpam-6388	572	2	stability	stability	PROPN
ejpam-6388	572	3	for	for	ADP
ejpam-6388	572	4	boundary	boundary	ADJ
ejpam-6388	572	5	value	value	NOUN
ejpam-6388	572	6	problems	problem	NOUN
ejpam-6388	572	7	of	of	ADP
ejpam-6388	572	8	differential	differential	ADJ
ejpam-6388	572	9	equations	equation	NOUN
ejpam-6388	572	10	—	—	PUNCT
ejpam-6388	572	11	main	main	ADJ
ejpam-6388	572	12	misunderstandings	misunderstanding	NOUN
ejpam-6388	572	13	and	and	CCONJ
ejpam-6388	572	14	how	how	SCONJ
ejpam-6388	572	15	to	to	PART
ejpam-6388	572	16	avoid	avoid	VERB
ejpam-6388	572	17	them	they	PRON
ejpam-6388	572	18	.	.	PUNCT
ejpam-6388	573	1	mathematics	mathematic	NOUN
ejpam-6388	573	2	,	,	PUNCT
ejpam-6388	573	3	12:1626	12:1626	NUM
ejpam-6388	573	4	,	,	PUNCT
ejpam-6388	573	5	2024	2024	NUM
ejpam-6388	573	6	.	.	PUNCT
ejpam-6388	574	1	[	[	X
ejpam-6388	574	2	4	4	X
ejpam-6388	574	3	]	]	PUNCT
ejpam-6388	574	4	tm	tm	PROPN
ejpam-6388	574	5	atanackovic	atanackovic	PROPN
ejpam-6388	574	6	,	,	PUNCT
ejpam-6388	574	7	s	s	NOUN
ejpam-6388	574	8	pilipovic	pilipovic	ADJ
ejpam-6388	574	9	,	,	PUNCT
ejpam-6388	574	10	and	and	CCONJ
ejpam-6388	574	11	b	b	X
ejpam-6388	574	12	stankovic	stankovic	PROPN
ejpam-6388	574	13	d	d	PROPN
ejpam-6388	574	14	zorica	zorica	PROPN
ejpam-6388	574	15	.	.	PUNCT
ejpam-6388	575	1	fractional	fractional	ADJ
ejpam-6388	575	2	calculus	calculus	NOUN
ejpam-6388	575	3	with	with	ADP
ejpam-6388	575	4	applications	application	NOUN
ejpam-6388	575	5	in	in	ADP
ejpam-6388	575	6	mechanics	mechanic	NOUN
ejpam-6388	575	7	:	:	PUNCT
ejpam-6388	575	8	vibrations	vibration	NOUN
ejpam-6388	575	9	and	and	CCONJ
ejpam-6388	575	10	diffusion	diffusion	NOUN
ejpam-6388	575	11	processes	process	NOUN
ejpam-6388	575	12	.	.	PUNCT
ejpam-6388	576	1	john	john	PROPN
ejpam-6388	576	2	wiley	wiley	PROPN
ejpam-6388	576	3	&	&	CCONJ
ejpam-6388	576	4	sons	sons	PROPN
ejpam-6388	576	5	,	,	PUNCT
ejpam-6388	576	6	nj	nj	PROPN
ejpam-6388	576	7	,	,	PUNCT
ejpam-6388	576	8	usa	usa	PROPN
ejpam-6388	576	9	,	,	PUNCT
ejpam-6388	576	10	2014	2014	NUM
ejpam-6388	576	11	.	.	PUNCT
ejpam-6388	577	1	[	[	X
ejpam-6388	577	2	5	5	X
ejpam-6388	577	3	]	]	PUNCT
ejpam-6388	577	4	wg	wg	PROPN
ejpam-6388	577	5	glöckle	glöckle	PROPN
ejpam-6388	577	6	and	and	CCONJ
ejpam-6388	577	7	tf	tf	PROPN
ejpam-6388	577	8	nonnenmacher	nonnenmacher	NOUN
ejpam-6388	577	9	.	.	PUNCT
ejpam-6388	578	1	a	a	DET
ejpam-6388	578	2	fractional	fractional	ADJ
ejpam-6388	578	3	calculus	calculus	NOUN
ejpam-6388	578	4	approach	approach	NOUN
ejpam-6388	578	5	to	to	ADP
ejpam-6388	578	6	self	self	NOUN
ejpam-6388	578	7	-	-	PUNCT
ejpam-6388	578	8	similar	similar	ADJ
ejpam-6388	578	9	protein	protein	NOUN
ejpam-6388	578	10	dynamics	dynamic	NOUN
ejpam-6388	578	11	.	.	PUNCT
ejpam-6388	579	1	biophys	biophys	PROPN
ejpam-6388	579	2	j.	j.	PROPN
ejpam-6388	579	3	,	,	PUNCT
ejpam-6388	579	4	68(1):46–53	68(1):46–53	NUM
ejpam-6388	579	5	,	,	PUNCT
ejpam-6388	579	6	1995	1995	NUM
ejpam-6388	579	7	.	.	PUNCT
ejpam-6388	580	1	[	[	X
ejpam-6388	580	2	6	6	NUM
ejpam-6388	580	3	]	]	X
ejpam-6388	580	4	aa	aa	PROPN
ejpam-6388	580	5	kilbas	kilbas	PROPN
ejpam-6388	580	6	,	,	PUNCT
ejpam-6388	580	7	hm	hm	X
ejpam-6388	580	8	srivastava	srivastava	PROPN
ejpam-6388	580	9	,	,	PUNCT
ejpam-6388	580	10	and	and	CCONJ
ejpam-6388	580	11	jj	jj	PROPN
ejpam-6388	580	12	trujillo	trujillo	PROPN
ejpam-6388	580	13	.	.	PUNCT
ejpam-6388	580	14	theory	theory	NOUN
ejpam-6388	580	15	and	and	CCONJ
ejpam-6388	580	16	applications	application	NOUN
ejpam-6388	580	17	of	of	ADP
ejpam-6388	580	18	fractional	fractional	ADJ
ejpam-6388	580	19	differential	differential	ADJ
ejpam-6388	580	20	equations	equation	NOUN
ejpam-6388	580	21	.	.	PUNCT
ejpam-6388	581	1	elsevier	elsevier	PROPN
ejpam-6388	581	2	bv	bv	PROPN
ejpam-6388	581	3	,	,	PUNCT
ejpam-6388	581	4	amsterdam	amsterdam	PROPN
ejpam-6388	581	5	,	,	PUNCT
ejpam-6388	581	6	the	the	DET
ejpam-6388	581	7	netherlands	netherlands	PROPN
ejpam-6388	581	8	,	,	PUNCT
ejpam-6388	581	9	2006	2006	NUM
ejpam-6388	581	10	.	.	PUNCT
ejpam-6388	582	1	[	[	X
ejpam-6388	582	2	7	7	X
ejpam-6388	582	3	]	]	PUNCT
ejpam-6388	582	4	rl	rl	X
ejpam-6388	582	5	magin	magin	NOUN
ejpam-6388	582	6	.	.	PUNCT
ejpam-6388	583	1	fractional	fractional	ADJ
ejpam-6388	583	2	calculus	calculus	NOUN
ejpam-6388	583	3	models	model	NOUN
ejpam-6388	583	4	of	of	ADP
ejpam-6388	583	5	complex	complex	ADJ
ejpam-6388	583	6	dynamics	dynamic	NOUN
ejpam-6388	583	7	in	in	ADP
ejpam-6388	583	8	biological	biological	ADJ
ejpam-6388	583	9	tissues	tissue	NOUN
ejpam-6388	583	10	.	.	PUNCT
ejpam-6388	584	1	comput	comput	NOUN
ejpam-6388	584	2	.	.	PUNCT
ejpam-6388	585	1	math	math	NOUN
ejpam-6388	585	2	.	.	PUNCT
ejpam-6388	586	1	appl	appl	PROPN
ejpam-6388	586	2	.	.	PROPN
ejpam-6388	586	3	,	,	PUNCT
ejpam-6388	587	1	59(5):1586–1593	59(5):1586–1593	NUM
ejpam-6388	587	2	,	,	PUNCT
ejpam-6388	587	3	2010	2010	NUM
ejpam-6388	587	4	.	.	PUNCT
ejpam-6388	588	1	[	[	X
ejpam-6388	588	2	8	8	NUM
ejpam-6388	588	3	]	]	PUNCT
ejpam-6388	588	4	sr	sr	PROPN
ejpam-6388	588	5	manam	manam	PROPN
ejpam-6388	588	6	.	.	PUNCT
ejpam-6388	589	1	multiple	multiple	ADJ
ejpam-6388	589	2	integral	integral	ADJ
ejpam-6388	589	3	equations	equation	NOUN
ejpam-6388	589	4	arising	arise	VERB
ejpam-6388	589	5	in	in	ADP
ejpam-6388	589	6	the	the	DET
ejpam-6388	589	7	theory	theory	NOUN
ejpam-6388	589	8	of	of	ADP
ejpam-6388	589	9	water	water	NOUN
ejpam-6388	589	10	waves	wave	NOUN
ejpam-6388	589	11	.	.	PUNCT
ejpam-6388	590	1	appl	appl	PROPN
ejpam-6388	590	2	.	.	PROPN
ejpam-6388	590	3	math	math	PROPN
ejpam-6388	590	4	.	.	PUNCT
ejpam-6388	591	1	lett	lett	PROPN
ejpam-6388	591	2	.	.	PROPN
ejpam-6388	591	3	,	,	PUNCT
ejpam-6388	591	4	24(8):1369–1373	24(8):1369–1373	NUM
ejpam-6388	591	5	,	,	PUNCT
ejpam-6388	591	6	2011	2011	NUM
ejpam-6388	591	7	.	.	PUNCT
ejpam-6388	592	1	[	[	X
ejpam-6388	592	2	9	9	NUM
ejpam-6388	592	3	]	]	X
ejpam-6388	592	4	ks	ks	PROPN
ejpam-6388	592	5	miller	miller	PROPN
ejpam-6388	592	6	and	and	CCONJ
ejpam-6388	592	7	b	b	PROPN
ejpam-6388	592	8	ross	ross	PROPN
ejpam-6388	592	9	.	.	PUNCT
ejpam-6388	593	1	an	an	DET
ejpam-6388	593	2	introduction	introduction	NOUN
ejpam-6388	593	3	to	to	ADP
ejpam-6388	593	4	the	the	DET
ejpam-6388	593	5	fractional	fractional	ADJ
ejpam-6388	593	6	calculus	calculus	NOUN
ejpam-6388	593	7	and	and	CCONJ
ejpam-6388	593	8	fractional	fractional	ADJ
ejpam-6388	593	9	differential	differential	ADJ
ejpam-6388	593	10	equations	equation	NOUN
ejpam-6388	593	11	.	.	PUNCT
ejpam-6388	594	1	john	john	PROPN
ejpam-6388	594	2	wiley	wiley	PROPN
ejpam-6388	594	3	&	&	CCONJ
ejpam-6388	594	4	sons	son	NOUN
ejpam-6388	594	5	,	,	PUNCT
ejpam-6388	594	6	new	new	PROPN
ejpam-6388	594	7	york	york	PROPN
ejpam-6388	594	8	,	,	PUNCT
ejpam-6388	594	9	usa	usa	PROPN
ejpam-6388	594	10	,	,	PUNCT
ejpam-6388	594	11	1993	1993	NUM
ejpam-6388	594	12	.	.	PUNCT
ejpam-6388	595	1	[	[	X
ejpam-6388	595	2	10	10	NUM
ejpam-6388	595	3	]	]	X
ejpam-6388	595	4	h	h	NOUN
ejpam-6388	595	5	mohammadi	mohammadi	NOUN
ejpam-6388	595	6	,	,	PUNCT
ejpam-6388	595	7	mka	mka	PROPN
ejpam-6388	595	8	kaabar	kaabar	PROPN
ejpam-6388	595	9	,	,	PUNCT
ejpam-6388	595	10	j	j	PROPN
ejpam-6388	595	11	alzabut	alzabut	PROPN
ejpam-6388	595	12	,	,	PUNCT
ejpam-6388	595	13	agm	agm	PROPN
ejpam-6388	595	14	selvam	selvam	PROPN
ejpam-6388	595	15	,	,	PUNCT
ejpam-6388	595	16	and	and	CCONJ
ejpam-6388	595	17	s	s	AUX
ejpam-6388	595	18	rezapour	rezapour	NOUN
ejpam-6388	595	19	.	.	PUNCT
ejpam-6388	596	1	a	a	DET
ejpam-6388	596	2	complete	complete	ADJ
ejpam-6388	596	3	model	model	NOUN
ejpam-6388	596	4	of	of	ADP
ejpam-6388	596	5	crimean	crimean	ADJ
ejpam-6388	596	6	-	-	PUNCT
ejpam-6388	596	7	congo	congo	NOUN
ejpam-6388	596	8	hemorrhagic	hemorrhagic	ADJ
ejpam-6388	596	9	fever	fever	NOUN
ejpam-6388	596	10	(	(	PUNCT
ejpam-6388	596	11	cchf	cchf	NOUN
ejpam-6388	596	12	)	)	PUNCT
ejpam-6388	596	13	transmission	transmission	NOUN
ejpam-6388	596	14	cycle	cycle	NOUN
ejpam-6388	596	15	with	with	ADP
ejpam-6388	596	16	nonlocal	nonlocal	ADJ
ejpam-6388	596	17	fractional	fractional	ADJ
ejpam-6388	596	18	derivative	derivative	NOUN
ejpam-6388	596	19	.	.	PUNCT
ejpam-6388	597	1	j.	j.	PROPN
ejpam-6388	597	2	funct	funct	PROPN
ejpam-6388	597	3	.	.	PUNCT
ejpam-6388	598	1	spaces	space	NOUN
ejpam-6388	598	2	,	,	PUNCT
ejpam-6388	598	3	2021(1):1273405	2021(1):1273405	NOUN
ejpam-6388	598	4	,	,	PUNCT
ejpam-6388	598	5	2021	2021	NUM
ejpam-6388	598	6	.	.	PUNCT
ejpam-6388	599	1	[	[	X
ejpam-6388	599	2	11	11	NUM
ejpam-6388	599	3	]	]	X
ejpam-6388	599	4	kr	kr	PROPN
ejpam-6388	599	5	prasad	prasad	PROPN
ejpam-6388	599	6	,	,	PUNCT
ejpam-6388	599	7	bmb	bmb	NOUN
ejpam-6388	599	8	krushna	krushna	PROPN
ejpam-6388	599	9	,	,	PUNCT
ejpam-6388	599	10	vvrrb	vvrrb	PROPN
ejpam-6388	599	11	raju	raju	PROPN
ejpam-6388	599	12	,	,	PUNCT
ejpam-6388	599	13	and	and	CCONJ
ejpam-6388	599	14	y	y	PROPN
ejpam-6388	599	15	narasimhulu	narasimhulu	VERB
ejpam-6388	599	16	.	.	PUNCT
ejpam-6388	600	1	existence	existence	NOUN
ejpam-6388	600	2	of	of	ADP
ejpam-6388	600	3	positive	positive	ADJ
ejpam-6388	600	4	solutions	solution	NOUN
ejpam-6388	600	5	for	for	ADP
ejpam-6388	600	6	systems	system	NOUN
ejpam-6388	600	7	of	of	ADP
ejpam-6388	600	8	fractional	fractional	ADJ
ejpam-6388	600	9	order	order	NOUN
ejpam-6388	600	10	boundary	boundary	ADJ
ejpam-6388	600	11	value	value	NOUN
ejpam-6388	600	12	problems	problem	NOUN
ejpam-6388	600	13	with	with	ADP
ejpam-6388	600	14	riemann	riemann	PROPN
ejpam-6388	600	15	–	–	PUNCT
ejpam-6388	600	16	liouville	liouville	VERB
ejpam-6388	600	17	derivative	derivative	NOUN
ejpam-6388	600	18	.	.	PUNCT
ejpam-6388	601	1	nonlinear	nonlinear	ADJ
ejpam-6388	601	2	stud	stud	NOUN
ejpam-6388	601	3	.	.	PUNCT
ejpam-6388	601	4	,	,	PUNCT
ejpam-6388	601	5	24(3):619–629	24(3):619–629	PROPN
ejpam-6388	601	6	,	,	PUNCT
ejpam-6388	601	7	2017	2017	NUM
ejpam-6388	601	8	.	.	PUNCT
ejpam-6388	602	1	[	[	X
ejpam-6388	602	2	12	12	NUM
ejpam-6388	602	3	]	]	X
ejpam-6388	602	4	m	m	VERB
ejpam-6388	602	5	feng	feng	X
ejpam-6388	602	6	,	,	PUNCT
ejpam-6388	602	7	x	x	PROPN
ejpam-6388	602	8	zhang	zhang	PROPN
ejpam-6388	602	9	,	,	PUNCT
ejpam-6388	602	10	and	and	CCONJ
ejpam-6388	602	11	w	w	PROPN
ejpam-6388	602	12	ge	ge	PROPN
ejpam-6388	602	13	.	.	PUNCT
ejpam-6388	603	1	new	new	ADJ
ejpam-6388	603	2	existence	existence	NOUN
ejpam-6388	603	3	results	result	VERB
ejpam-6388	603	4	for	for	ADP
ejpam-6388	603	5	higher	high	ADJ
ejpam-6388	603	6	-	-	PUNCT
ejpam-6388	603	7	order	order	NOUN
ejpam-6388	603	8	nonlinear	nonlinear	ADJ
ejpam-6388	603	9	fractional	fractional	ADJ
ejpam-6388	603	10	differential	differential	ADJ
ejpam-6388	603	11	equation	equation	NOUN
ejpam-6388	603	12	with	with	ADP
ejpam-6388	603	13	integral	integral	ADJ
ejpam-6388	603	14	boundary	boundary	ADJ
ejpam-6388	603	15	conditions	condition	NOUN
ejpam-6388	603	16	.	.	PUNCT
ejpam-6388	604	1	bound	bind	VERB
ejpam-6388	604	2	.	.	PUNCT
ejpam-6388	605	1	value	value	PROPN
ejpam-6388	605	2	probl	probl	NOUN
ejpam-6388	605	3	.	.	PUNCT
ejpam-6388	605	4	,	,	PUNCT
ejpam-6388	605	5	720702:1–20	720702:1–20	NUM
ejpam-6388	605	6	,	,	PUNCT
ejpam-6388	605	7	2011	2011	NUM
ejpam-6388	605	8	.	.	PUNCT
ejpam-6388	606	1	[	[	X
ejpam-6388	606	2	13	13	NUM
ejpam-6388	606	3	]	]	PUNCT
ejpam-6388	606	4	fj	fj	PROPN
ejpam-6388	606	5	torres	torre	NOUN
ejpam-6388	606	6	.	.	PUNCT
ejpam-6388	607	1	existence	existence	NOUN
ejpam-6388	607	2	of	of	ADP
ejpam-6388	607	3	a	a	DET
ejpam-6388	607	4	positive	positive	ADJ
ejpam-6388	607	5	solution	solution	NOUN
ejpam-6388	607	6	for	for	ADP
ejpam-6388	607	7	a	a	DET
ejpam-6388	607	8	boundary	boundary	ADJ
ejpam-6388	607	9	value	value	NOUN
ejpam-6388	607	10	problem	problem	NOUN
ejpam-6388	607	11	of	of	ADP
ejpam-6388	607	12	a	a	DET
ejpam-6388	607	13	d.	d.	PROPN
ejpam-6388	607	14	baleanu	baleanu	PROPN
ejpam-6388	607	15	et	et	PROPN
ejpam-6388	607	16	al	al	PROPN
ejpam-6388	607	17	.	.	PUNCT
ejpam-6388	607	18	/	/	SYM
ejpam-6388	607	19	eur	eur	PROPN
ejpam-6388	607	20	.	.	PUNCT
ejpam-6388	608	1	j.	j.	PROPN
ejpam-6388	608	2	pure	pure	PROPN
ejpam-6388	608	3	appl	appl	PROPN
ejpam-6388	608	4	.	.	PROPN
ejpam-6388	608	5	math	math	PROPN
ejpam-6388	608	6	,	,	PUNCT
ejpam-6388	608	7	18	18	NUM
ejpam-6388	608	8	(	(	PUNCT
ejpam-6388	608	9	4	4	NUM
ejpam-6388	608	10	)	)	PUNCT
ejpam-6388	608	11	(	(	PUNCT
ejpam-6388	608	12	2025	2025	NUM
ejpam-6388	608	13	)	)	PUNCT
ejpam-6388	608	14	,	,	PUNCT
ejpam-6388	608	15	6388	6388	NUM
ejpam-6388	608	16	28	28	NUM
ejpam-6388	608	17	of	of	ADP
ejpam-6388	608	18	31	31	NUM
ejpam-6388	608	19	nonlinear	nonlinear	ADJ
ejpam-6388	608	20	fractional	fractional	ADJ
ejpam-6388	608	21	differential	differential	NOUN
ejpam-6388	608	22	equation	equation	NOUN
ejpam-6388	608	23	.	.	PUNCT
ejpam-6388	609	1	bull	bull	NOUN
ejpam-6388	609	2	.	.	PUNCT
ejpam-6388	610	1	iran	iran	PROPN
ejpam-6388	610	2	.	.	PUNCT
ejpam-6388	611	1	math	math	NOUN
ejpam-6388	611	2	.	.	PUNCT
ejpam-6388	612	1	soc	soc	PROPN
ejpam-6388	612	2	.	.	PUNCT
ejpam-6388	612	3	,	,	PUNCT
ejpam-6388	612	4	39(2):307–323	39(2):307–323	PROPN
ejpam-6388	612	5	,	,	PUNCT
ejpam-6388	612	6	2013	2013	NUM
ejpam-6388	612	7	.	.	PUNCT
ejpam-6388	613	1	[	[	X
ejpam-6388	613	2	14	14	NUM
ejpam-6388	613	3	]	]	X
ejpam-6388	613	4	lg	lg	PROPN
ejpam-6388	613	5	huang	huang	PROPN
ejpam-6388	613	6	and	and	CCONJ
ejpam-6388	613	7	x	x	PROPN
ejpam-6388	613	8	zhang	zhang	PROPN
ejpam-6388	613	9	.	.	PUNCT
ejpam-6388	614	1	cone	cone	PROPN
ejpam-6388	614	2	metric	metric	ADJ
ejpam-6388	614	3	spaces	space	NOUN
ejpam-6388	614	4	and	and	CCONJ
ejpam-6388	614	5	fixed	fix	VERB
ejpam-6388	614	6	point	point	NOUN
ejpam-6388	614	7	theorems	theorem	NOUN
ejpam-6388	614	8	of	of	ADP
ejpam-6388	614	9	contractive	contractive	ADJ
ejpam-6388	614	10	mappings	mapping	NOUN
ejpam-6388	614	11	.	.	PUNCT
ejpam-6388	615	1	j.	j.	PROPN
ejpam-6388	615	2	math	math	PROPN
ejpam-6388	615	3	.	.	PUNCT
ejpam-6388	616	1	anal	anal	PROPN
ejpam-6388	616	2	.	.	PUNCT
ejpam-6388	617	1	appl	appl	PROPN
ejpam-6388	617	2	.	.	PROPN
ejpam-6388	617	3	,	,	PUNCT
ejpam-6388	617	4	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-6388	617	5	,	,	PUNCT
ejpam-6388	617	6	2007	2007	NUM
ejpam-6388	617	7	.	.	PUNCT
ejpam-6388	618	1	[	[	X
ejpam-6388	618	2	15	15	NUM
ejpam-6388	618	3	]	]	X
ejpam-6388	618	4	me	i	PRON
ejpam-6388	618	5	gordji	gordji	PROPN
ejpam-6388	618	6	,	,	PUNCT
ejpam-6388	618	7	m	m	VERB
ejpam-6388	618	8	ramezani	ramezani	NOUN
ejpam-6388	618	9	,	,	PUNCT
ejpam-6388	618	10	m	m	VERB
ejpam-6388	618	11	de	de	X
ejpam-6388	618	12	la	la	X
ejpam-6388	618	13	sen	sen	PROPN
ejpam-6388	618	14	,	,	PUNCT
ejpam-6388	618	15	and	and	CCONJ
ejpam-6388	618	16	yj	yj	PROPN
ejpam-6388	618	17	cho	cho	PROPN
ejpam-6388	618	18	.	.	PUNCT
ejpam-6388	619	1	on	on	ADP
ejpam-6388	619	2	orthogonal	orthogonal	ADJ
ejpam-6388	619	3	sets	set	NOUN
ejpam-6388	619	4	and	and	CCONJ
ejpam-6388	619	5	banach	banach	ADV
ejpam-6388	619	6	fixed	fix	VERB
ejpam-6388	619	7	point	point	NOUN
ejpam-6388	619	8	theorem	theorem	VERB
ejpam-6388	619	9	.	.	PUNCT
ejpam-6388	620	1	fixed	fix	VERB
ejpam-6388	620	2	point	point	NOUN
ejpam-6388	620	3	theory	theory	NOUN
ejpam-6388	620	4	,	,	PUNCT
ejpam-6388	620	5	18(2):569–578	18(2):569–578	PROPN
ejpam-6388	620	6	,	,	PUNCT
ejpam-6388	620	7	2017	2017	NUM
ejpam-6388	620	8	.	.	PUNCT
ejpam-6388	621	1	[	[	X
ejpam-6388	621	2	16	16	NUM
ejpam-6388	621	3	]	]	X
ejpam-6388	621	4	b	b	X
ejpam-6388	621	5	ahmad	ahmad	PROPN
ejpam-6388	621	6	,	,	PUNCT
ejpam-6388	621	7	sk	sk	NOUN
ejpam-6388	621	8	ntouyas	ntouyas	NOUN
ejpam-6388	621	9	,	,	PUNCT
ejpam-6388	621	10	and	and	CCONJ
ejpam-6388	621	11	j	j	PROPN
ejpam-6388	621	12	tariboon	tariboon	NOUN
ejpam-6388	621	13	.	.	PUNCT
ejpam-6388	622	1	a	a	DET
ejpam-6388	622	2	nonlocal	nonlocal	ADJ
ejpam-6388	622	3	hybrid	hybrid	ADJ
ejpam-6388	622	4	boundary	boundary	ADJ
ejpam-6388	622	5	value	value	NOUN
ejpam-6388	622	6	problem	problem	NOUN
ejpam-6388	622	7	of	of	ADP
ejpam-6388	622	8	caputo	caputo	PROPN
ejpam-6388	622	9	fractional	fractional	PROPN
ejpam-6388	622	10	integro	integro	PROPN
ejpam-6388	622	11	-	-	PUNCT
ejpam-6388	622	12	differential	differential	NOUN
ejpam-6388	622	13	equations	equation	NOUN
ejpam-6388	622	14	.	.	PUNCT
ejpam-6388	623	1	acta	acta	PROPN
ejpam-6388	623	2	math	math	PROPN
ejpam-6388	623	3	.	.	PUNCT
ejpam-6388	624	1	sci	sci	PROPN
ejpam-6388	624	2	.	.	PROPN
ejpam-6388	624	3	,	,	PUNCT
ejpam-6388	624	4	36:1631–1640	36:1631–1640	NUM
ejpam-6388	624	5	,	,	PUNCT
ejpam-6388	624	6	2016	2016	NUM
ejpam-6388	624	7	.	.	PUNCT
ejpam-6388	625	1	[	[	X
ejpam-6388	625	2	17	17	NUM
ejpam-6388	625	3	]	]	PUNCT
ejpam-6388	625	4	bc	bc	PROPN
ejpam-6388	625	5	dhage	dhage	NOUN
ejpam-6388	625	6	and	and	CCONJ
ejpam-6388	625	7	v	v	AUX
ejpam-6388	625	8	lakshmikantham	lakshmikantham	NOUN
ejpam-6388	625	9	.	.	PUNCT
ejpam-6388	626	1	basic	basic	ADJ
ejpam-6388	626	2	results	result	NOUN
ejpam-6388	626	3	on	on	ADP
ejpam-6388	626	4	hybrid	hybrid	ADJ
ejpam-6388	626	5	differential	differential	ADJ
ejpam-6388	626	6	equations	equation	NOUN
ejpam-6388	626	7	.	.	PUNCT
ejpam-6388	627	1	nonlinear	nonlinear	ADJ
ejpam-6388	627	2	anal	anal	PROPN
ejpam-6388	627	3	.	.	PUNCT
ejpam-6388	628	1	hybrid	hybrid	ADJ
ejpam-6388	628	2	syst	syst	PROPN
ejpam-6388	628	3	.	.	PROPN
ejpam-6388	628	4	,	,	PUNCT
ejpam-6388	628	5	4(3):414–424	4(3):414–424	PROPN
ejpam-6388	628	6	,	,	PUNCT
ejpam-6388	628	7	2010	2010	NUM
ejpam-6388	628	8	.	.	PUNCT
ejpam-6388	629	1	[	[	X
ejpam-6388	629	2	18	18	NUM
ejpam-6388	629	3	]	]	PUNCT
ejpam-6388	629	4	aem	aem	PROPN
ejpam-6388	629	5	herzallah	herzallah	PROPN
ejpam-6388	629	6	and	and	CCONJ
ejpam-6388	629	7	d	d	NOUN
ejpam-6388	629	8	baleanu	baleanu	NOUN
ejpam-6388	629	9	.	.	PUNCT
ejpam-6388	630	1	on	on	ADP
ejpam-6388	630	2	fractional	fractional	ADJ
ejpam-6388	630	3	order	order	NOUN
ejpam-6388	630	4	hybrid	hybrid	ADJ
ejpam-6388	630	5	differential	differential	NOUN
ejpam-6388	630	6	equations	equation	NOUN
ejpam-6388	630	7	.	.	PUNCT
ejpam-6388	631	1	abstr	abstr	PROPN
ejpam-6388	631	2	.	.	PUNCT
ejpam-6388	631	3	appl	appl	PROPN
ejpam-6388	631	4	.	.	PUNCT
ejpam-6388	632	1	anal	anal	PROPN
ejpam-6388	632	2	.	.	PROPN
ejpam-6388	632	3	,	,	PUNCT
ejpam-6388	632	4	2014(1):389386	2014(1):389386	NUM
ejpam-6388	632	5	,	,	PUNCT
ejpam-6388	632	6	2014	2014	NUM
ejpam-6388	632	7	.	.	PUNCT
ejpam-6388	633	1	[	[	X
ejpam-6388	633	2	19	19	NUM
ejpam-6388	633	3	]	]	X
ejpam-6388	633	4	z	z	PROPN
ejpam-6388	633	5	ullah	ullah	PROPN
ejpam-6388	633	6	,	,	PUNCT
ejpam-6388	633	7	a	a	DET
ejpam-6388	633	8	ali	ali	PROPN
ejpam-6388	633	9	,	,	PUNCT
ejpam-6388	633	10	ra	ra	PROPN
ejpam-6388	633	11	khan	khan	PROPN
ejpam-6388	633	12	,	,	PUNCT
ejpam-6388	633	13	and	and	CCONJ
ejpam-6388	633	14	m	m	PROPN
ejpam-6388	633	15	iqbal	iqbal	PROPN
ejpam-6388	633	16	.	.	PUNCT
ejpam-6388	634	1	existence	existence	NOUN
ejpam-6388	634	2	results	result	VERB
ejpam-6388	634	3	to	to	ADP
ejpam-6388	634	4	a	a	DET
ejpam-6388	634	5	class	class	NOUN
ejpam-6388	634	6	of	of	ADP
ejpam-6388	634	7	hybrid	hybrid	ADJ
ejpam-6388	634	8	fractional	fractional	ADJ
ejpam-6388	634	9	differential	differential	NOUN
ejpam-6388	634	10	equations	equation	NOUN
ejpam-6388	634	11	.	.	PUNCT
ejpam-6388	635	1	matriks	matriks	PROPN
ejpam-6388	635	2	sains	sains	PROPN
ejpam-6388	635	3	mat	mat	PROPN
ejpam-6388	635	4	.	.	PROPN
ejpam-6388	635	5	,	,	PUNCT
ejpam-6388	635	6	2(1):13–17	2(1):13–17	NUM
ejpam-6388	635	7	,	,	PUNCT
ejpam-6388	635	8	2018	2018	NUM
ejpam-6388	635	9	.	.	PUNCT
ejpam-6388	636	1	[	[	X
ejpam-6388	636	2	20	20	NUM
ejpam-6388	636	3	]	]	X
ejpam-6388	636	4	zedd	zedd	PROPN
ejpam-6388	636	5	olia	olia	PROPN
ejpam-6388	636	6	,	,	PUNCT
ejpam-6388	636	7	me	i	PRON
ejpam-6388	636	8	gordji	gordji	NOUN
ejpam-6388	636	9	,	,	PUNCT
ejpam-6388	636	10	and	and	CCONJ
ejpam-6388	636	11	de	de	ADP
ejpam-6388	636	12	bagha	bagha	PROPN
ejpam-6388	636	13	.	.	PUNCT
ejpam-6388	637	1	banach	banach	ADV
ejpam-6388	637	2	fixed	fix	VERB
ejpam-6388	637	3	point	point	NOUN
ejpam-6388	637	4	theorem	theorem	VERB
ejpam-6388	637	5	on	on	ADP
ejpam-6388	637	6	orthogonal	orthogonal	ADJ
ejpam-6388	637	7	cone	cone	NOUN
ejpam-6388	637	8	metric	metric	ADJ
ejpam-6388	637	9	spaces	space	NOUN
ejpam-6388	637	10	.	.	PUNCT
ejpam-6388	638	1	facta	facta	PROPN
ejpam-6388	638	2	univ	univ	PROPN
ejpam-6388	638	3	.	.	PROPN
ejpam-6388	638	4	,	,	PUNCT
ejpam-6388	638	5	ser	ser	PROPN
ejpam-6388	638	6	.	.	PROPN
ejpam-6388	638	7	math	math	PROPN
ejpam-6388	638	8	.	.	PUNCT
ejpam-6388	639	1	inf	inf	PROPN
ejpam-6388	639	2	.	.	PROPN
ejpam-6388	639	3	,	,	PUNCT
ejpam-6388	639	4	35(5):1239–1250	35(5):1239–1250	NUM
ejpam-6388	639	5	,	,	PUNCT
ejpam-6388	639	6	2020	2020	NUM
ejpam-6388	639	7	.	.	PUNCT
ejpam-6388	640	1	[	[	X
ejpam-6388	640	2	21	21	NUM
ejpam-6388	640	3	]	]	SYM
ejpam-6388	640	4	lb	lb	PRON
ejpam-6388	640	5	ćirić.	ćirić.	X
ejpam-6388	640	6	a	a	DET
ejpam-6388	640	7	generalization	generalization	NOUN
ejpam-6388	640	8	of	of	ADP
ejpam-6388	640	9	banach	banach	NOUN
ejpam-6388	640	10	’s	’s	PART
ejpam-6388	640	11	contraction	contraction	NOUN
ejpam-6388	640	12	principle	principle	NOUN
ejpam-6388	640	13	.	.	PUNCT
ejpam-6388	641	1	proc	proc	PROPN
ejpam-6388	641	2	.	.	PUNCT
ejpam-6388	642	1	amer	amer	PROPN
ejpam-6388	642	2	.	.	PUNCT
ejpam-6388	642	3	math	math	PROPN
ejpam-6388	642	4	.	.	PUNCT
ejpam-6388	643	1	soc	soc	PROPN
ejpam-6388	643	2	.	.	PROPN
ejpam-6388	643	3	,	,	PUNCT
ejpam-6388	643	4	45(2):267–273	45(2):267–273	PROPN
ejpam-6388	643	5	,	,	PUNCT
ejpam-6388	643	6	1974	1974	NUM
ejpam-6388	643	7	.	.	PUNCT
ejpam-6388	644	1	[	[	X
ejpam-6388	644	2	22	22	NUM
ejpam-6388	644	3	]	]	PUNCT
ejpam-6388	644	4	bk	bk	VERB
ejpam-6388	644	5	lahiri	lahiri	PROPN
ejpam-6388	644	6	,	,	PUNCT
ejpam-6388	644	7	p	p	PROPN
ejpam-6388	644	8	das	das	PROPN
ejpam-6388	644	9	,	,	PUNCT
ejpam-6388	644	10	and	and	CCONJ
ejpam-6388	644	11	lk	lk	PROPN
ejpam-6388	644	12	dey	dey	PROPN
ejpam-6388	644	13	.	.	PROPN
ejpam-6388	644	14	cantor	cantor	PROPN
ejpam-6388	644	15	’s	’s	PART
ejpam-6388	644	16	theorem	theorem	NOUN
ejpam-6388	644	17	in	in	ADP
ejpam-6388	644	18	2	2	NUM
ejpam-6388	644	19	-	-	PUNCT
ejpam-6388	644	20	metric	metric	ADJ
ejpam-6388	644	21	spaces	space	NOUN
ejpam-6388	644	22	and	and	CCONJ
ejpam-6388	644	23	its	its	PRON
ejpam-6388	644	24	applications	application	NOUN
ejpam-6388	644	25	to	to	ADP
ejpam-6388	644	26	fixed	fix	VERB
ejpam-6388	644	27	point	point	NOUN
ejpam-6388	644	28	problems	problem	NOUN
ejpam-6388	644	29	.	.	PUNCT
ejpam-6388	645	1	taiwanese	taiwanese	ADJ
ejpam-6388	645	2	j.	j.	PROPN
ejpam-6388	645	3	math	math	PROPN
ejpam-6388	645	4	.	.	PUNCT
ejpam-6388	645	5	,	,	PUNCT
ejpam-6388	645	6	15(1):337–352	15(1):337–352	PROPN
ejpam-6388	645	7	,	,	PUNCT
ejpam-6388	645	8	2011	2011	NUM
ejpam-6388	645	9	.	.	PUNCT
ejpam-6388	646	1	[	[	X
ejpam-6388	646	2	23	23	NUM
ejpam-6388	646	3	]	]	X
ejpam-6388	646	4	kr	kr	PROPN
ejpam-6388	646	5	prasad	prasad	PROPN
ejpam-6388	646	6	,	,	PUNCT
ejpam-6388	646	7	m	m	VERB
ejpam-6388	646	8	khuddush	khuddush	NOUN
ejpam-6388	646	9	,	,	PUNCT
ejpam-6388	646	10	and	and	CCONJ
ejpam-6388	646	11	d	d	PROPN
ejpam-6388	646	12	leela	leela	PROPN
ejpam-6388	646	13	.	.	PUNCT
ejpam-6388	647	1	existence	existence	PROPN
ejpam-6388	647	2	,	,	PUNCT
ejpam-6388	647	3	uniqueness	uniqueness	NOUN
ejpam-6388	647	4	and	and	CCONJ
ejpam-6388	647	5	hyers	hyer	NOUN
ejpam-6388	647	6	–	–	PUNCT
ejpam-6388	647	7	ulam	ulam	X
ejpam-6388	647	8	stability	stability	NOUN
ejpam-6388	647	9	of	of	ADP
ejpam-6388	647	10	a	a	DET
ejpam-6388	647	11	fractional	fractional	ADJ
ejpam-6388	647	12	order	order	NOUN
ejpam-6388	647	13	iterative	iterative	NOUN
ejpam-6388	647	14	two	two	NUM
ejpam-6388	647	15	-	-	PUNCT
ejpam-6388	647	16	point	point	NOUN
ejpam-6388	647	17	boundary	boundary	ADJ
ejpam-6388	647	18	value	value	NOUN
ejpam-6388	647	19	problems	problem	NOUN
ejpam-6388	647	20	.	.	PUNCT
ejpam-6388	648	1	afr	afr	PROPN
ejpam-6388	648	2	.	.	PUNCT
ejpam-6388	649	1	mat	mat	PROPN
ejpam-6388	649	2	.	.	PROPN
ejpam-6388	649	3	,	,	PUNCT
ejpam-6388	649	4	32:1227–1237	32:1227–1237	NUM
ejpam-6388	649	5	,	,	PUNCT
ejpam-6388	649	6	2021	2021	NUM
ejpam-6388	649	7	.	.	PUNCT
ejpam-6388	650	1	[	[	X
ejpam-6388	650	2	24	24	NUM
ejpam-6388	650	3	]	]	PUNCT
ejpam-6388	650	4	t	t	NOUN
ejpam-6388	650	5	senapati	senapati	PROPN
ejpam-6388	650	6	,	,	PUNCT
ejpam-6388	650	7	lk	lk	PROPN
ejpam-6388	650	8	dey	dey	PROPN
ejpam-6388	650	9	,	,	PUNCT
ejpam-6388	650	10	and	and	CCONJ
ejpam-6388	650	11	d	d	ADP
ejpam-6388	650	12	dolicanin	dolicanin	NOUN
ejpam-6388	650	13	-	-	PUNCT
ejpam-6388	650	14	dekic	dekic	NOUN
ejpam-6388	650	15	.	.	PUNCT
ejpam-6388	651	1	extension	extension	NOUN
ejpam-6388	651	2	of	of	ADP
ejpam-6388	651	3	ciric	ciric	ADJ
ejpam-6388	651	4	and	and	CCONJ
ejpam-6388	651	5	wardowski	wardowski	PROPN
ejpam-6388	651	6	type	type	NOUN
ejpam-6388	651	7	fixed	fix	VERB
ejpam-6388	651	8	point	point	NOUN
ejpam-6388	651	9	theorems	theorem	NOUN
ejpam-6388	651	10	in	in	ADP
ejpam-6388	651	11	d	d	ADJ
ejpam-6388	651	12	-	-	ADJ
ejpam-6388	651	13	generalized	generalize	VERB
ejpam-6388	651	14	metric	metric	ADJ
ejpam-6388	651	15	spaces	space	NOUN
ejpam-6388	651	16	.	.	PUNCT
ejpam-6388	652	1	fixed	fix	VERB
ejpam-6388	652	2	point	point	NOUN
ejpam-6388	652	3	theory	theory	NOUN
ejpam-6388	652	4	appl	appl	PROPN
ejpam-6388	652	5	.	.	PUNCT
ejpam-6388	652	6	,	,	PUNCT
ejpam-6388	653	1	2016(33):1–14	2016(33):1–14	PROPN
ejpam-6388	653	2	,	,	PUNCT
ejpam-6388	653	3	2016	2016	NUM
ejpam-6388	653	4	.	.	PUNCT
ejpam-6388	654	1	[	[	X
ejpam-6388	654	2	25	25	NUM
ejpam-6388	654	3	]	]	X
ejpam-6388	654	4	s.	s.	PROPN
ejpam-6388	654	5	rezapour	rezapour	PROPN
ejpam-6388	654	6	.	.	PUNCT
ejpam-6388	655	1	lights	light	NOUN
ejpam-6388	655	2	and	and	CCONJ
ejpam-6388	655	3	shadows	shadow	NOUN
ejpam-6388	655	4	on	on	ADP
ejpam-6388	655	5	generalizations	generalization	NOUN
ejpam-6388	655	6	in	in	ADP
ejpam-6388	655	7	fixed	fix	VERB
ejpam-6388	655	8	point	point	NOUN
ejpam-6388	655	9	theory	theory	NOUN
ejpam-6388	655	10	.	.	PUNCT
ejpam-6388	656	1	crc	crc	PROPN
ejpam-6388	656	2	press	press	PROPN
ejpam-6388	656	3	,	,	PUNCT
ejpam-6388	656	4	taylor	taylor	PROPN
ejpam-6388	656	5	and	and	CCONJ
ejpam-6388	656	6	francis	francis	PROPN
ejpam-6388	656	7	,	,	PUNCT
ejpam-6388	656	8	2025	2025	NUM
ejpam-6388	656	9	.	.	PUNCT
ejpam-6388	657	1	[	[	X
ejpam-6388	657	2	26	26	NUM
ejpam-6388	657	3	]	]	X
ejpam-6388	657	4	z	z	NOUN
ejpam-6388	657	5	bai	bai	PROPN
ejpam-6388	657	6	and	and	CCONJ
ejpam-6388	657	7	h	h	NOUN
ejpam-6388	657	8	lü.	lü.	VERB
ejpam-6388	657	9	positive	positive	ADJ
ejpam-6388	657	10	solutions	solution	NOUN
ejpam-6388	657	11	for	for	ADP
ejpam-6388	657	12	a	a	DET
ejpam-6388	657	13	boundary	boundary	ADJ
ejpam-6388	657	14	value	value	NOUN
ejpam-6388	657	15	problem	problem	NOUN
ejpam-6388	657	16	of	of	ADP
ejpam-6388	657	17	nonlinear	nonlinear	ADJ
ejpam-6388	657	18	fractional	fractional	ADJ
ejpam-6388	657	19	differential	differential	ADJ
ejpam-6388	657	20	equations	equation	NOUN
ejpam-6388	657	21	.	.	PUNCT
ejpam-6388	658	1	j.	j.	PROPN
ejpam-6388	658	2	math	math	PROPN
ejpam-6388	658	3	.	.	PUNCT
ejpam-6388	659	1	anal	anal	PROPN
ejpam-6388	659	2	.	.	PUNCT
ejpam-6388	660	1	appl	appl	PROPN
ejpam-6388	660	2	.	.	PROPN
ejpam-6388	660	3	,	,	PUNCT
ejpam-6388	660	4	311(2):495–505	311(2):495–505	PROPN
ejpam-6388	660	5	,	,	PUNCT
ejpam-6388	660	6	2005	2005	NUM
ejpam-6388	660	7	.	.	PUNCT
ejpam-6388	661	1	appendix	appendix	ADJ
ejpam-6388	661	2	table	table	NOUN
ejpam-6388	661	3	4	4	NUM
ejpam-6388	661	4	,	,	PUNCT
ejpam-6388	661	5	compares	compare	VERB
ejpam-6388	661	6	the	the	DET
ejpam-6388	661	7	values	value	NOUN
ejpam-6388	661	8	of	of	ADP
ejpam-6388	661	9	r(ω	r(ω	ADJ
ejpam-6388	661	10	)	)	PUNCT
ejpam-6388	661	11	for	for	ADP
ejpam-6388	661	12	y	y	PROPN
ejpam-6388	661	13	=	=	PROPN
ejpam-6388	661	14	1.5	1.5	NUM
ejpam-6388	661	15	and	and	CCONJ
ejpam-6388	661	16	y	y	PROPN
ejpam-6388	661	17	=	=	PROPN
ejpam-6388	661	18	2.0	2.0	NUM
ejpam-6388	661	19	given	give	VERB
ejpam-6388	661	20	in	in	ADP
ejpam-6388	661	21	example	example	NOUN
ejpam-6388	661	22	1	1	NUM
ejpam-6388	661	23	.	.	PUNCT
ejpam-6388	661	24	table	table	NOUN
ejpam-6388	661	25	5	5	NUM
ejpam-6388	661	26	,	,	PUNCT
ejpam-6388	661	27	compares	compare	VERB
ejpam-6388	661	28	the	the	DET
ejpam-6388	661	29	solutions	solution	NOUN
ejpam-6388	661	30	r(ω	r(ω	ADV
ejpam-6388	661	31	)	)	PUNCT
ejpam-6388	661	32	for	for	ADP
ejpam-6388	661	33	both	both	DET
ejpam-6388	661	34	functions	function	NOUN
ejpam-6388	661	35	f1	f1	NOUN
ejpam-6388	661	36	and	and	CCONJ
ejpam-6388	661	37	f2	f2	PROPN
ejpam-6388	661	38	given	give	VERB
ejpam-6388	661	39	in	in	ADP
ejpam-6388	661	40	example	example	NOUN
ejpam-6388	661	41	2	2	NUM
ejpam-6388	661	42	.	.	PUNCT
ejpam-6388	661	43	table	table	NOUN
ejpam-6388	661	44	6	6	NUM
ejpam-6388	661	45	,	,	PUNCT
ejpam-6388	661	46	compares	compare	VERB
ejpam-6388	661	47	the	the	DET
ejpam-6388	661	48	solutions	solution	NOUN
ejpam-6388	661	49	r(ω	r(ω	ADV
ejpam-6388	661	50	)	)	PUNCT
ejpam-6388	661	51	for	for	ADP
ejpam-6388	661	52	both	both	DET
ejpam-6388	661	53	functions	function	NOUN
ejpam-6388	661	54	g1	g1	NOUN
ejpam-6388	661	55	and	and	CCONJ
ejpam-6388	661	56	g2	g2	PROPN
ejpam-6388	661	57	given	give	VERB
ejpam-6388	661	58	in	in	ADP
ejpam-6388	661	59	example	example	NOUN
ejpam-6388	661	60	3	3	X
ejpam-6388	661	61	.	.	X
ejpam-6388	661	62	d.	d.	PROPN
ejpam-6388	661	63	baleanu	baleanu	PROPN
ejpam-6388	661	64	et	et	PROPN
ejpam-6388	661	65	al	al	PROPN
ejpam-6388	661	66	.	.	PUNCT
ejpam-6388	661	67	/	/	SYM
ejpam-6388	661	68	eur	eur	PROPN
ejpam-6388	661	69	.	.	PUNCT
ejpam-6388	662	1	j.	j.	PROPN
ejpam-6388	662	2	pure	pure	PROPN
ejpam-6388	662	3	appl	appl	PROPN
ejpam-6388	662	4	.	.	PROPN
ejpam-6388	662	5	math	math	PROPN
ejpam-6388	662	6	,	,	PUNCT
ejpam-6388	662	7	18	18	NUM
ejpam-6388	662	8	(	(	PUNCT
ejpam-6388	662	9	4	4	NUM
ejpam-6388	662	10	)	)	PUNCT
ejpam-6388	662	11	(	(	PUNCT
ejpam-6388	662	12	2025	2025	NUM
ejpam-6388	662	13	)	)	PUNCT
ejpam-6388	662	14	,	,	PUNCT
ejpam-6388	662	15	6388	6388	NUM
ejpam-6388	662	16	29	29	NUM
ejpam-6388	662	17	of	of	ADP
ejpam-6388	662	18	31	31	NUM
ejpam-6388	662	19	ω	ω	NUM
ejpam-6388	662	20	r(ω	r(ω	ADV
ejpam-6388	662	21	)	)	PUNCT
ejpam-6388	662	22	(	(	PUNCT
ejpam-6388	662	23	y	y	NOUN
ejpam-6388	662	24	=	=	SYM
ejpam-6388	662	25	1.5	1.5	NUM
ejpam-6388	662	26	)	)	PUNCT
ejpam-6388	662	27	r(ω	r(ω	ADV
ejpam-6388	662	28	)	)	PUNCT
ejpam-6388	662	29	(	(	PUNCT
ejpam-6388	663	1	y	y	NOUN
ejpam-6388	663	2	=	=	SYM
ejpam-6388	663	3	2.0	2.0	NUM
ejpam-6388	663	4	)	)	PUNCT
ejpam-6388	663	5	ω	ω	PROPN
ejpam-6388	663	6	r(ω	r(ω	ADV
ejpam-6388	663	7	)	)	PUNCT
ejpam-6388	663	8	(	(	PUNCT
ejpam-6388	663	9	y	y	NOUN
ejpam-6388	663	10	=	=	SYM
ejpam-6388	663	11	1.5	1.5	NUM
ejpam-6388	663	12	)	)	PUNCT
ejpam-6388	663	13	r(ω	r(ω	ADV
ejpam-6388	663	14	)	)	PUNCT
ejpam-6388	663	15	(	(	PUNCT
ejpam-6388	663	16	y	y	NOUN
ejpam-6388	663	17	=	=	SYM
ejpam-6388	663	18	2.0	2.0	NUM
ejpam-6388	663	19	)	)	PUNCT
ejpam-6388	663	20	ω	ω	PROPN
ejpam-6388	663	21	r(ω	r(ω	ADV
ejpam-6388	663	22	)	)	PUNCT
ejpam-6388	663	23	(	(	PUNCT
ejpam-6388	663	24	y	y	NOUN
ejpam-6388	663	25	=	=	SYM
ejpam-6388	663	26	1.5	1.5	NUM
ejpam-6388	663	27	)	)	PUNCT
ejpam-6388	663	28	r(ω	r(ω	ADV
ejpam-6388	663	29	)	)	PUNCT
ejpam-6388	663	30	(	(	PUNCT
ejpam-6388	663	31	y	y	NOUN
ejpam-6388	663	32	=	=	SYM
ejpam-6388	663	33	2.0	2.0	NUM
ejpam-6388	663	34	)	)	PUNCT
ejpam-6388	663	35	0.00	0.00	NUM
ejpam-6388	663	36	0.0000	0.0000	NUM
ejpam-6388	663	37	0.0000	0.0000	NUM
ejpam-6388	663	38	0.34	0.34	NUM
ejpam-6388	663	39	0.5919	0.5919	NUM
ejpam-6388	663	40	0.2686	0.2686	NUM
ejpam-6388	663	41	0.68	0.68	NUM
ejpam-6388	663	42	1.0949	1.0949	NUM
ejpam-6388	663	43	0.7474	0.7474	NUM
ejpam-6388	663	44	0.01	0.01	NUM
ejpam-6388	663	45	0.0210	0.0210	NUM
ejpam-6388	663	46	0.0016	0.0016	NUM
ejpam-6388	663	47	0.35	0.35	NUM
ejpam-6388	663	48	0.6109	0.6109	NUM
ejpam-6388	663	49	0.2817	0.2817	NUM
ejpam-6388	663	50	0.69	0.69	NUM
ejpam-6388	663	51	1.1037	1.1037	NUM
ejpam-6388	663	52	0.7614	0.7614	NUM
ejpam-6388	663	53	0.02	0.02	NUM
ejpam-6388	663	54	0.0340	0.0340	NUM
ejpam-6388	663	55	0.0036	0.0036	NUM
ejpam-6388	663	56	0.36	0.36	NUM
ejpam-6388	663	57	0.6298	0.6298	NUM
ejpam-6388	663	58	0.2949	0.2949	NUM
ejpam-6388	663	59	0.70	0.70	NUM
ejpam-6388	663	60	1.1120	1.1120	NUM
ejpam-6388	663	61	0.7754	0.7754	NUM
ejpam-6388	663	62	0.03	0.03	NUM
ejpam-6388	663	63	0.0468	0.0468	NUM
ejpam-6388	663	64	0.0061	0.0061	NUM
ejpam-6388	663	65	0.37	0.37	NUM
ejpam-6388	663	66	0.6486	0.6486	NUM
ejpam-6388	663	67	0.3084	0.3084	NUM
ejpam-6388	663	68	0.71	0.71	NUM
ejpam-6388	663	69	1.1198	1.1198	NUM
ejpam-6388	663	70	0.7891	0.7891	NUM
ejpam-6388	663	71	0.04	0.04	NUM
ejpam-6388	663	72	0.0600	0.0600	NUM
ejpam-6388	663	73	0.0091	0.0091	NUM
ejpam-6388	663	74	0.38	0.38	NUM
ejpam-6388	663	75	0.6673	0.6673	NUM
ejpam-6388	663	76	0.3220	0.3220	NUM
ejpam-6388	663	77	0.72	0.72	NUM
ejpam-6388	663	78	1.1270	1.1270	NUM
ejpam-6388	663	79	0.8027	0.8027	NUM
ejpam-6388	663	80	0.05	0.05	NUM
ejpam-6388	663	81	0.0736	0.0736	NUM
ejpam-6388	663	82	0.0125	0.0125	NUM
ejpam-6388	663	83	0.39	0.39	NUM
ejpam-6388	663	84	0.6858	0.6858	NUM
ejpam-6388	663	85	0.3357	0.3357	NUM
ejpam-6388	663	86	0.73	0.73	NUM
ejpam-6388	663	87	1.1337	1.1337	NUM
ejpam-6388	663	88	0.8161	0.8161	NUM
ejpam-6388	663	89	0.06	0.06	NUM
ejpam-6388	663	90	0.0877	0.0877	NUM
ejpam-6388	663	91	0.0163	0.0163	NUM
ejpam-6388	663	92	0.40	0.40	NUM
ejpam-6388	663	93	0.7042	0.7042	NUM
ejpam-6388	663	94	0.3497	0.3497	NUM
ejpam-6388	663	95	0.74	0.74	NUM
ejpam-6388	663	96	1.1397	1.1397	NUM
ejpam-6388	663	97	0.8292	0.8292	NUM
ejpam-6388	663	98	0.07	0.07	NUM
ejpam-6388	663	99	0.1022	0.1022	NUM
ejpam-6388	663	100	0.0205	0.0205	NUM
ejpam-6388	663	101	0.41	0.41	NUM
ejpam-6388	663	102	0.7225	0.7225	NUM
ejpam-6388	663	103	0.3637	0.3637	NUM
ejpam-6388	663	104	0.75	0.75	NUM
ejpam-6388	663	105	1.1452	1.1452	NUM
ejpam-6388	663	106	0.8422	0.8422	NUM
ejpam-6388	663	107	0.08	0.08	NUM
ejpam-6388	663	108	0.1173	0.1173	NUM
ejpam-6388	663	109	0.0252	0.0252	NUM
ejpam-6388	663	110	0.42	0.42	NUM
ejpam-6388	663	111	0.7405	0.7405	NUM
ejpam-6388	663	112	0.3779	0.3779	NUM
ejpam-6388	664	1	0.76	0.76	NUM
ejpam-6388	664	2	1.1502	1.1502	NUM
ejpam-6388	664	3	0.8549	0.8549	NUM
ejpam-6388	664	4	0.09	0.09	NUM
ejpam-6388	664	5	0.1327	0.1327	NUM
ejpam-6388	664	6	0.0302	0.0302	NUM
ejpam-6388	664	7	0.43	0.43	NUM
ejpam-6388	664	8	0.7584	0.7584	NUM
ejpam-6388	664	9	0.3923	0.3923	NUM
ejpam-6388	664	10	0.77	0.77	NUM
ejpam-6388	664	11	1.1545	1.1545	NUM
ejpam-6388	664	12	0.8674	0.8674	NUM
ejpam-6388	664	13	0.10	0.10	NUM
ejpam-6388	664	14	0.1486	0.1486	NUM
ejpam-6388	664	15	0.0357	0.0357	NUM
ejpam-6388	664	16	0.44	0.44	NUM
ejpam-6388	664	17	0.7760	0.7760	NUM
ejpam-6388	664	18	0.4067	0.4067	NUM
ejpam-6388	664	19	0.78	0.78	NUM
ejpam-6388	664	20	1.1581	1.1581	NUM
ejpam-6388	664	21	0.8796	0.8796	NUM
ejpam-6388	664	22	0.11	0.11	NUM
ejpam-6388	664	23	0.1648	0.1648	NUM
ejpam-6388	664	24	0.0416	0.0416	NUM
ejpam-6388	664	25	0.45	0.45	NUM
ejpam-6388	664	26	0.7934	0.7934	NUM
ejpam-6388	664	27	0.4213	0.4213	NUM
ejpam-6388	664	28	0.79	0.79	NUM
ejpam-6388	664	29	1.1612	1.1612	NUM
ejpam-6388	664	30	0.8916	0.8916	NUM
ejpam-6388	664	31	0.12	0.12	NUM
ejpam-6388	664	32	0.1815	0.1815	NUM
ejpam-6388	664	33	0.0478	0.0478	NUM
ejpam-6388	664	34	0.46	0.46	NUM
ejpam-6388	664	35	0.8106	0.8106	NUM
ejpam-6388	664	36	0.4359	0.4359	NUM
ejpam-6388	664	37	0.80	0.80	NUM
ejpam-6388	664	38	1.1636	1.1636	NUM
ejpam-6388	664	39	0.9033	0.9033	NUM
ejpam-6388	664	40	0.13	0.13	NUM
ejpam-6388	664	41	0.1984	0.1984	NUM
ejpam-6388	664	42	0.0545	0.0545	NUM
ejpam-6388	664	43	0.47	0.47	NUM
ejpam-6388	664	44	0.8276	0.8276	NUM
ejpam-6388	664	45	0.4507	0.4507	NUM
ejpam-6388	664	46	0.81	0.81	NUM
ejpam-6388	664	47	1.1653	1.1653	NUM
ejpam-6388	664	48	0.9146	0.9146	NUM
ejpam-6388	664	49	0.14	0.14	NUM
ejpam-6388	664	50	0.2156	0.2156	NUM
ejpam-6388	664	51	0.0615	0.0615	NUM
ejpam-6388	664	52	0.48	0.48	NUM
ejpam-6388	664	53	0.8443	0.8443	NUM
ejpam-6388	664	54	0.4655	0.4655	NUM
ejpam-6388	664	55	0.82	0.82	NUM
ejpam-6388	664	56	1.1664	1.1664	NUM
ejpam-6388	664	57	0.9257	0.9257	NUM
ejpam-6388	664	58	0.15	0.15	NUM
ejpam-6388	664	59	0.2331	0.2331	NUM
ejpam-6388	664	60	0.0689	0.0689	NUM
ejpam-6388	664	61	0.49	0.49	NUM
ejpam-6388	664	62	0.8607	0.8607	NUM
ejpam-6388	664	63	0.4804	0.4804	NUM
ejpam-6388	664	64	0.83	0.83	NUM
ejpam-6388	664	65	1.1668	1.1668	NUM
ejpam-6388	664	66	0.9365	0.9365	NUM
ejpam-6388	664	67	0.16	0.16	NUM
ejpam-6388	664	68	0.2509	0.2509	NUM
ejpam-6388	664	69	0.0766	0.0766	NUM
ejpam-6388	664	70	0.50	0.50	NUM
ejpam-6388	664	71	0.8768	0.8768	NUM
ejpam-6388	664	72	0.4953	0.4953	NUM
ejpam-6388	664	73	0.84	0.84	NUM
ejpam-6388	664	74	1.1665	1.1665	NUM
ejpam-6388	664	75	0.9469	0.9469	NUM
ejpam-6388	664	76	0.17	0.17	NUM
ejpam-6388	664	77	0.2689	0.2689	NUM
ejpam-6388	664	78	0.0847	0.0847	NUM
ejpam-6388	664	79	0.51	0.51	NUM
ejpam-6388	664	80	0.8926	0.8926	NUM
ejpam-6388	664	81	0.5103	0.5103	NUM
ejpam-6388	664	82	0.85	0.85	NUM
ejpam-6388	664	83	1.1655	1.1655	NUM
ejpam-6388	664	84	0.9570	0.9570	NUM
ejpam-6388	664	85	0.18	0.18	NUM
ejpam-6388	664	86	0.2871	0.2871	NUM
ejpam-6388	664	87	0.0932	0.0932	NUM
ejpam-6388	664	88	0.52	0.52	NUM
ejpam-6388	664	89	0.9081	0.9081	NUM
ejpam-6388	664	90	0.5253	0.5253	NUM
ejpam-6388	664	91	0.86	0.86	NUM
ejpam-6388	664	92	1.1638	1.1638	NUM
ejpam-6388	664	93	0.9667	0.9667	NUM
ejpam-6388	664	94	0.19	0.19	NUM
ejpam-6388	664	95	0.3055	0.3055	NUM
ejpam-6388	664	96	0.1019	0.1019	NUM
ejpam-6388	664	97	0.53	0.53	NUM
ejpam-6388	664	98	0.9233	0.9233	NUM
ejpam-6388	664	99	0.5404	0.5404	NUM
ejpam-6388	664	100	0.87	0.87	NUM
ejpam-6388	664	101	1.1613	1.1613	NUM
ejpam-6388	664	102	0.9761	0.9761	NUM
ejpam-6388	664	103	0.20	0.20	NUM
ejpam-6388	664	104	0.3241	0.3241	NUM
ejpam-6388	664	105	0.1110	0.1110	NUM
ejpam-6388	664	106	0.54	0.54	NUM
ejpam-6388	664	107	0.9382	0.9382	NUM
ejpam-6388	664	108	0.5554	0.5554	NUM
ejpam-6388	664	109	0.88	0.88	NUM
ejpam-6388	664	110	1.1581	1.1581	NUM
ejpam-6388	664	111	0.9850	0.9850	NUM
ejpam-6388	664	112	0.21	0.21	NUM
ejpam-6388	664	113	0.3428	0.3428	NUM
ejpam-6388	664	114	0.1205	0.1205	NUM
ejpam-6388	664	115	0.55	0.55	NUM
ejpam-6388	664	116	0.9527	0.9527	NUM
ejpam-6388	664	117	0.5705	0.5705	NUM
ejpam-6388	664	118	0.89	0.89	NUM
ejpam-6388	664	119	1.1542	1.1542	NUM
ejpam-6388	664	120	0.9936	0.9936	NUM
ejpam-6388	664	121	0.22	0.22	NUM
ejpam-6388	664	122	0.3617	0.3617	NUM
ejpam-6388	664	123	0.1302	0.1302	NUM
ejpam-6388	664	124	0.56	0.56	NUM
ejpam-6388	664	125	0.9668	0.9668	NUM
ejpam-6388	664	126	0.5855	0.5855	NUM
ejpam-6388	664	127	0.90	0.90	NUM
ejpam-6388	664	128	1.1495	1.1495	NUM
ejpam-6388	664	129	1.0018	1.0018	NUM
ejpam-6388	664	130	0.23	0.23	NUM
ejpam-6388	664	131	0.3807	0.3807	NUM
ejpam-6388	664	132	0.1403	0.1403	NUM
ejpam-6388	664	133	0.57	0.57	NUM
ejpam-6388	664	134	0.9806	0.9806	NUM
ejpam-6388	664	135	0.6006	0.6006	NUM
ejpam-6388	664	136	0.91	0.91	NUM
ejpam-6388	664	137	1.1440	1.1440	NUM
ejpam-6388	664	138	1.0095	1.0095	NUM
ejpam-6388	664	139	0.24	0.24	NUM
ejpam-6388	664	140	0.3997	0.3997	NUM
ejpam-6388	664	141	0.1506	0.1506	NUM
ejpam-6388	664	142	0.58	0.58	NUM
ejpam-6388	664	143	0.9940	0.9940	NUM
ejpam-6388	664	144	0.6156	0.6156	NUM
ejpam-6388	664	145	0.92	0.92	NUM
ejpam-6388	664	146	1.1377	1.1377	NUM
ejpam-6388	664	147	1.0168	1.0168	NUM
ejpam-6388	664	148	0.25	0.25	NUM
ejpam-6388	664	149	0.4189	0.4189	NUM
ejpam-6388	665	1	0.1613	0.1613	NUM
ejpam-6388	665	2	0.59	0.59	NUM
ejpam-6388	665	3	1.0070	1.0070	NUM
ejpam-6388	665	4	0.6305	0.6305	NUM
ejpam-6388	665	5	0.93	0.93	NUM
ejpam-6388	665	6	1.1306	1.1306	NUM
ejpam-6388	665	7	1.0236	1.0236	NUM
ejpam-6388	665	8	0.26	0.26	NUM
ejpam-6388	665	9	0.4381	0.4381	NUM
ejpam-6388	665	10	0.1722	0.1722	NUM
ejpam-6388	665	11	0.60	0.60	NUM
ejpam-6388	665	12	1.0195	1.0195	NUM
ejpam-6388	665	13	0.6454	0.6454	NUM
ejpam-6388	665	14	0.94	0.94	NUM
ejpam-6388	665	15	1.1227	1.1227	NUM
ejpam-6388	665	16	1.0300	1.0300	NUM
ejpam-6388	665	17	0.27	0.27	NUM
ejpam-6388	665	18	0.4573	0.4573	NUM
ejpam-6388	665	19	0.1834	0.1834	NUM
ejpam-6388	665	20	0.61	0.61	NUM
ejpam-6388	665	21	1.0317	1.0317	NUM
ejpam-6388	665	22	0.6603	0.6603	NUM
ejpam-6388	665	23	0.95	0.95	NUM
ejpam-6388	665	24	1.1140	1.1140	NUM
ejpam-6388	665	25	1.0358	1.0358	NUM
ejpam-6388	665	26	0.28	0.28	NUM
ejpam-6388	665	27	0.4766	0.4766	NUM
ejpam-6388	665	28	0.1948	0.1948	NUM
ejpam-6388	665	29	0.62	0.62	NUM
ejpam-6388	665	30	1.0434	1.0434	NUM
ejpam-6388	665	31	0.6751	0.6751	NUM
ejpam-6388	665	32	0.96	0.96	NUM
ejpam-6388	665	33	1.1044	1.1044	NUM
ejpam-6388	666	1	1.0412	1.0412	NUM
ejpam-6388	666	2	0.29	0.29	NUM
ejpam-6388	666	3	0.4959	0.4959	NUM
ejpam-6388	666	4	0.2065	0.2065	NUM
ejpam-6388	666	5	0.63	0.63	NUM
ejpam-6388	666	6	1.0546	1.0546	NUM
ejpam-6388	666	7	0.6897	0.6897	NUM
ejpam-6388	666	8	0.97	0.97	NUM
ejpam-6388	666	9	1.0940	1.0940	NUM
ejpam-6388	666	10	1.0461	1.0461	NUM
ejpam-6388	666	11	0.30	0.30	NUM
ejpam-6388	666	12	0.5151	0.5151	NUM
ejpam-6388	666	13	0.2185	0.2185	NUM
ejpam-6388	666	14	0.64	0.64	NUM
ejpam-6388	666	15	1.0654	1.0654	NUM
ejpam-6388	666	16	0.7043	0.7043	NUM
ejpam-6388	666	17	0.98	0.98	NUM
ejpam-6388	666	18	1.0827	1.0827	NUM
ejpam-6388	666	19	1.0505	1.0505	NUM
ejpam-6388	666	20	0.31	0.31	NUM
ejpam-6388	666	21	0.5344	0.5344	NUM
ejpam-6388	666	22	0.2307	0.2307	NUM
ejpam-6388	666	23	0.65	0.65	NUM
ejpam-6388	666	24	1.0757	1.0757	NUM
ejpam-6388	666	25	0.7188	0.7188	NUM
ejpam-6388	666	26	0.99	0.99	NUM
ejpam-6388	666	27	1.0706	1.0706	NUM
ejpam-6388	666	28	1.0543	1.0543	NUM
ejpam-6388	666	29	0.32	0.32	NUM
ejpam-6388	666	30	0.5536	0.5536	NUM
ejpam-6388	666	31	0.2431	0.2431	NUM
ejpam-6388	666	32	0.66	0.66	NUM
ejpam-6388	666	33	1.0856	1.0856	NUM
ejpam-6388	666	34	0.7331	0.7331	NUM
ejpam-6388	666	35	1.00	1.00	NUM
ejpam-6388	666	36	1.0575	1.0575	NUM
ejpam-6388	666	37	1.0575	1.0575	NUM
ejpam-6388	666	38	0.33	0.33	NUM
ejpam-6388	666	39	0.5728	0.5728	NUM
ejpam-6388	666	40	0.2558	0.2558	NUM
ejpam-6388	666	41	0.67	0.67	NUM
ejpam-6388	666	42	1.0949	1.0949	NUM
ejpam-6388	666	43	0.7474	0.7474	NUM
ejpam-6388	666	44	table	table	NOUN
ejpam-6388	666	45	4	4	NUM
ejpam-6388	666	46	:	:	PUNCT
ejpam-6388	666	47	comparison	comparison	NOUN
ejpam-6388	666	48	of	of	ADP
ejpam-6388	666	49	r(ω	r(ω	PROPN
ejpam-6388	666	50	)	)	PUNCT
ejpam-6388	666	51	for	for	ADP
ejpam-6388	666	52	y	y	PROPN
ejpam-6388	666	53	=	=	PROPN
ejpam-6388	666	54	1.5	1.5	NUM
ejpam-6388	666	55	and	and	CCONJ
ejpam-6388	666	56	y	y	PROPN
ejpam-6388	666	57	=	=	PROPN
ejpam-6388	666	58	2.0	2.0	NUM
ejpam-6388	666	59	d.	d.	PROPN
ejpam-6388	666	60	baleanu	baleanu	PROPN
ejpam-6388	666	61	et	et	PROPN
ejpam-6388	666	62	al	al	PROPN
ejpam-6388	666	63	.	.	PUNCT
ejpam-6388	666	64	/	/	SYM
ejpam-6388	666	65	eur	eur	PROPN
ejpam-6388	666	66	.	.	PUNCT
ejpam-6388	667	1	j.	j.	PROPN
ejpam-6388	667	2	pure	pure	PROPN
ejpam-6388	667	3	appl	appl	PROPN
ejpam-6388	667	4	.	.	PROPN
ejpam-6388	667	5	math	math	PROPN
ejpam-6388	667	6	,	,	PUNCT
ejpam-6388	667	7	18	18	NUM
ejpam-6388	667	8	(	(	PUNCT
ejpam-6388	667	9	4	4	NUM
ejpam-6388	667	10	)	)	PUNCT
ejpam-6388	667	11	(	(	PUNCT
ejpam-6388	667	12	2025	2025	NUM
ejpam-6388	667	13	)	)	PUNCT
ejpam-6388	667	14	,	,	PUNCT
ejpam-6388	667	15	6388	6388	NUM
ejpam-6388	667	16	30	30	NUM
ejpam-6388	667	17	of	of	ADP
ejpam-6388	667	18	31	31	NUM
ejpam-6388	667	19	ω	ω	NUM
ejpam-6388	667	20	(	(	PUNCT
ejpam-6388	667	21	f1	f1	NOUN
ejpam-6388	667	22	)	)	PUNCT
ejpam-6388	667	23	(	(	PUNCT
ejpam-6388	667	24	f2	f2	PROPN
ejpam-6388	667	25	)	)	PUNCT
ejpam-6388	667	26	ω	ω	PROPN
ejpam-6388	667	27	(	(	PUNCT
ejpam-6388	667	28	f1	f1	NOUN
ejpam-6388	667	29	)	)	PUNCT
ejpam-6388	667	30	(	(	PUNCT
ejpam-6388	667	31	f2	f2	PROPN
ejpam-6388	667	32	)	)	PUNCT
ejpam-6388	667	33	ω	ω	PROPN
ejpam-6388	667	34	(	(	PUNCT
ejpam-6388	667	35	f1	f1	NOUN
ejpam-6388	667	36	)	)	PUNCT
ejpam-6388	667	37	(	(	PUNCT
ejpam-6388	667	38	f2	f2	PROPN
ejpam-6388	667	39	)	)	PUNCT
ejpam-6388	667	40	0.00	0.00	NUM
ejpam-6388	667	41	0.0000	0.0000	NUM
ejpam-6388	667	42	0.0000	0.0000	NUM
ejpam-6388	667	43	0.34	0.34	NUM
ejpam-6388	667	44	2.1659	2.1659	NUM
ejpam-6388	667	45	0.1741	0.1741	NUM
ejpam-6388	667	46	0.68	0.68	NUM
ejpam-6388	667	47	3.0195	3.0195	NUM
ejpam-6388	667	48	0.6829	0.6829	NUM
ejpam-6388	667	49	0.01	0.01	NUM
ejpam-6388	667	50	0.3320	0.3320	NUM
ejpam-6388	667	51	0.0000	0.0000	NUM
ejpam-6388	667	52	0.35	0.35	NUM
ejpam-6388	667	53	2.2018	2.2018	NUM
ejpam-6388	667	54	0.1857	0.1857	NUM
ejpam-6388	667	55	0.69	0.69	NUM
ejpam-6388	667	56	3.0321	3.0321	NUM
ejpam-6388	667	57	0.6995	0.6995	NUM
ejpam-6388	667	58	0.02	0.02	NUM
ejpam-6388	667	59	0.4715	0.4715	NUM
ejpam-6388	667	60	0.0002	0.0002	NUM
ejpam-6388	667	61	0.36	0.36	NUM
ejpam-6388	667	62	2.2372	2.2372	NUM
ejpam-6388	667	63	0.1977	0.1977	NUM
ejpam-6388	667	64	0.70	0.70	NUM
ejpam-6388	667	65	3.0438	3.0438	NUM
ejpam-6388	667	66	0.7159	0.7159	NUM
ejpam-6388	667	67	0.03	0.03	NUM
ejpam-6388	667	68	0.5800	0.5800	NUM
ejpam-6388	667	69	0.0005	0.0005	NUM
ejpam-6388	667	70	0.37	0.37	NUM
ejpam-6388	667	71	2.2720	2.2720	NUM
ejpam-6388	667	72	0.2101	0.2101	NUM
ejpam-6388	667	73	0.71	0.71	NUM
ejpam-6388	667	74	3.0544	3.0544	NUM
ejpam-6388	667	75	0.7322	0.7322	NUM
ejpam-6388	667	76	0.04	0.04	NUM
ejpam-6388	667	77	0.6727	0.6727	NUM
ejpam-6388	668	1	0.0010	0.0010	NUM
ejpam-6388	668	2	0.38	0.38	NUM
ejpam-6388	668	3	2.3063	2.3063	NUM
ejpam-6388	668	4	0.2227	0.2227	NUM
ejpam-6388	668	5	0.72	0.72	NUM
ejpam-6388	668	6	3.0639	3.0639	NUM
ejpam-6388	668	7	0.7482	0.7482	NUM
ejpam-6388	668	8	0.05	0.05	NUM
ejpam-6388	668	9	0.7554	0.7554	NUM
ejpam-6388	668	10	0.0017	0.0017	NUM
ejpam-6388	668	11	0.39	0.39	NUM
ejpam-6388	668	12	2.3400	2.3400	NUM
ejpam-6388	668	13	0.2357	0.2357	NUM
ejpam-6388	668	14	0.73	0.73	NUM
ejpam-6388	668	15	3.0724	3.0724	NUM
ejpam-6388	668	16	0.7640	0.7640	NUM
ejpam-6388	668	17	0.06	0.06	NUM
ejpam-6388	668	18	0.8310	0.8310	NUM
ejpam-6388	668	19	0.0027	0.0027	NUM
ejpam-6388	668	20	0.40	0.40	NUM
ejpam-6388	668	21	2.3731	2.3731	NUM
ejpam-6388	668	22	0.2491	0.2491	NUM
ejpam-6388	668	23	0.74	0.74	NUM
ejpam-6388	668	24	3.0798	3.0798	NUM
ejpam-6388	668	25	0.7796	0.7796	NUM
ejpam-6388	668	26	0.07	0.07	NUM
ejpam-6388	668	27	0.9014	0.9014	NUM
ejpam-6388	668	28	0.0040	0.0040	NUM
ejpam-6388	668	29	0.41	0.41	NUM
ejpam-6388	668	30	2.4057	2.4057	NUM
ejpam-6388	668	31	0.2627	0.2627	NUM
ejpam-6388	668	32	0.75	0.75	NUM
ejpam-6388	668	33	3.0860	3.0860	NUM
ejpam-6388	668	34	0.7949	0.7949	NUM
ejpam-6388	668	35	0.08	0.08	NUM
ejpam-6388	668	36	0.9677	0.9677	NUM
ejpam-6388	668	37	0.0055	0.0055	NUM
ejpam-6388	668	38	0.42	0.42	NUM
ejpam-6388	668	39	2.4377	2.4377	NUM
ejpam-6388	668	40	0.2766	0.2766	NUM
ejpam-6388	668	41	0.76	0.76	NUM
ejpam-6388	668	42	3.0911	3.0911	NUM
ejpam-6388	668	43	0.8098	0.8098	NUM
ejpam-6388	668	44	0.09	0.09	NUM
ejpam-6388	668	45	1.0306	1.0306	NUM
ejpam-6388	668	46	0.0074	0.0074	NUM
ejpam-6388	668	47	0.43	0.43	NUM
ejpam-6388	668	48	2.4691	2.4691	NUM
ejpam-6388	668	49	0.2909	0.2909	NUM
ejpam-6388	668	50	0.77	0.77	NUM
ejpam-6388	668	51	3.0949	3.0949	NUM
ejpam-6388	668	52	0.8244	0.8244	NUM
ejpam-6388	668	53	0.10	0.10	NUM
ejpam-6388	668	54	1.0907	1.0907	NUM
ejpam-6388	668	55	0.0096	0.0096	NUM
ejpam-6388	668	56	0.44	0.44	NUM
ejpam-6388	668	57	2.5000	2.5000	NUM
ejpam-6388	668	58	0.3054	0.3054	NUM
ejpam-6388	668	59	0.78	0.78	NUM
ejpam-6388	668	60	3.0976	3.0976	NUM
ejpam-6388	668	61	0.8387	0.8387	NUM
ejpam-6388	668	62	0.11	0.11	NUM
ejpam-6388	668	63	1.1485	1.1485	NUM
ejpam-6388	668	64	0.0121	0.0121	NUM
ejpam-6388	668	65	0.45	0.45	NUM
ejpam-6388	668	66	2.5302	2.5302	NUM
ejpam-6388	668	67	0.3201	0.3201	NUM
ejpam-6388	668	68	0.79	0.79	NUM
ejpam-6388	668	69	3.0990	3.0990	NUM
ejpam-6388	668	70	0.8526	0.8526	NUM
ejpam-6388	668	71	0.12	0.12	NUM
ejpam-6388	668	72	1.2043	1.2043	NUM
ejpam-6388	668	73	0.0149	0.0149	NUM
ejpam-6388	668	74	0.46	0.46	NUM
ejpam-6388	668	75	2.5599	2.5599	NUM
ejpam-6388	668	76	0.3352	0.3352	NUM
ejpam-6388	668	77	0.80	0.80	NUM
ejpam-6388	668	78	3.0991	3.0991	NUM
ejpam-6388	668	79	0.8661	0.8661	NUM
ejpam-6388	668	80	0.13	0.13	NUM
ejpam-6388	668	81	1.2583	1.2583	NUM
ejpam-6388	668	82	0.0181	0.0181	NUM
ejpam-6388	668	83	0.47	0.47	NUM
ejpam-6388	668	84	2.5889	2.5889	NUM
ejpam-6388	668	85	0.3504	0.3504	NUM
ejpam-6388	668	86	0.81	0.81	NUM
ejpam-6388	668	87	3.0978	3.0978	NUM
ejpam-6388	668	88	0.8791	0.8791	NUM
ejpam-6388	668	89	0.14	0.14	NUM
ejpam-6388	668	90	1.3107	1.3107	NUM
ejpam-6388	668	91	0.0217	0.0217	NUM
ejpam-6388	668	92	0.48	0.48	NUM
ejpam-6388	668	93	2.6173	2.6173	NUM
ejpam-6388	668	94	0.3659	0.3659	NUM
ejpam-6388	668	95	0.82	0.82	NUM
ejpam-6388	668	96	3.0953	3.0953	NUM
ejpam-6388	668	97	0.8916	0.8916	NUM
ejpam-6388	668	98	0.15	0.15	NUM
ejpam-6388	668	99	1.3618	1.3618	NUM
ejpam-6388	668	100	0.0256	0.0256	NUM
ejpam-6388	668	101	0.49	0.49	NUM
ejpam-6388	668	102	2.6451	2.6451	NUM
ejpam-6388	668	103	0.3816	0.3816	NUM
ejpam-6388	668	104	0.83	0.83	NUM
ejpam-6388	668	105	3.0913	3.0913	NUM
ejpam-6388	668	106	0.9037	0.9037	NUM
ejpam-6388	668	107	0.16	0.16	NUM
ejpam-6388	668	108	1.4116	1.4116	NUM
ejpam-6388	668	109	0.0299	0.0299	NUM
ejpam-6388	668	110	0.50	0.50	NUM
ejpam-6388	668	111	2.6722	2.6722	NUM
ejpam-6388	668	112	0.3975	0.3975	NUM
ejpam-6388	668	113	0.84	0.84	NUM
ejpam-6388	668	114	3.0859	3.0859	NUM
ejpam-6388	668	115	0.9152	0.9152	NUM
ejpam-6388	668	116	0.17	0.17	NUM
ejpam-6388	668	117	1.4602	1.4602	NUM
ejpam-6388	668	118	0.0346	0.0346	NUM
ejpam-6388	668	119	0.51	0.51	NUM
ejpam-6388	668	120	2.6987	2.6987	NUM
ejpam-6388	668	121	0.4136	0.4136	NUM
ejpam-6388	668	122	0.85	0.85	NUM
ejpam-6388	668	123	3.0791	3.0791	NUM
ejpam-6388	668	124	0.9261	0.9261	NUM
ejpam-6388	668	125	0.18	0.18	NUM
ejpam-6388	668	126	1.5078	1.5078	NUM
ejpam-6388	668	127	0.0397	0.0397	NUM
ejpam-6388	668	128	0.52	0.52	NUM
ejpam-6388	668	129	2.7245	2.7245	NUM
ejpam-6388	668	130	0.4299	0.4299	NUM
ejpam-6388	668	131	0.86	0.86	NUM
ejpam-6388	668	132	3.0708	3.0708	NUM
ejpam-6388	668	133	0.9364	0.9364	NUM
ejpam-6388	668	134	0.19	0.19	NUM
ejpam-6388	668	135	1.5544	1.5544	NUM
ejpam-6388	668	136	0.0451	0.0451	NUM
ejpam-6388	668	137	0.53	0.53	NUM
ejpam-6388	668	138	2.7496	2.7496	NUM
ejpam-6388	668	139	0.4463	0.4463	NUM
ejpam-6388	668	140	0.87	0.87	NUM
ejpam-6388	668	141	3.0609	3.0609	NUM
ejpam-6388	668	142	0.9461	0.9461	NUM
ejpam-6388	668	143	0.20	0.20	NUM
ejpam-6388	668	144	1.6000	1.6000	NUM
ejpam-6388	668	145	0.0510	0.0510	NUM
ejpam-6388	668	146	0.54	0.54	NUM
ejpam-6388	668	147	2.7740	2.7740	NUM
ejpam-6388	668	148	0.4629	0.4629	NUM
ejpam-6388	668	149	0.88	0.88	NUM
ejpam-6388	668	150	3.0495	3.0495	NUM
ejpam-6388	668	151	0.9552	0.9552	NUM
ejpam-6388	668	152	0.21	0.21	NUM
ejpam-6388	668	153	1.6449	1.6449	NUM
ejpam-6388	668	154	0.0572	0.0572	NUM
ejpam-6388	668	155	0.55	0.55	NUM
ejpam-6388	668	156	2.7977	2.7977	NUM
ejpam-6388	668	157	0.4796	0.4796	NUM
ejpam-6388	668	158	0.89	0.89	NUM
ejpam-6388	668	159	3.0365	3.0365	NUM
ejpam-6388	668	160	0.9636	0.9636	NUM
ejpam-6388	668	161	0.22	0.22	NUM
ejpam-6388	668	162	1.6889	1.6889	NUM
ejpam-6388	668	163	0.0638	0.0638	NUM
ejpam-6388	668	164	0.56	0.56	NUM
ejpam-6388	668	165	2.8207	2.8207	NUM
ejpam-6388	668	166	0.4964	0.4964	NUM
ejpam-6388	668	167	0.90	0.90	NUM
ejpam-6388	668	168	3.0218	3.0218	NUM
ejpam-6388	668	169	0.9712	0.9712	NUM
ejpam-6388	668	170	0.23	0.23	NUM
ejpam-6388	668	171	1.7322	1.7322	NUM
ejpam-6388	668	172	0.0709	0.0709	NUM
ejpam-6388	668	173	0.57	0.57	NUM
ejpam-6388	668	174	2.8429	2.8429	NUM
ejpam-6388	668	175	0.5133	0.5133	NUM
ejpam-6388	668	176	0.91	0.91	NUM
ejpam-6388	668	177	3.0055	3.0055	NUM
ejpam-6388	668	178	0.9781	0.9781	NUM
ejpam-6388	668	179	0.24	0.24	NUM
ejpam-6388	668	180	1.7748	1.7748	NUM
ejpam-6388	668	181	0.0783	0.0783	NUM
ejpam-6388	668	182	0.58	0.58	NUM
ejpam-6388	668	183	2.8643	2.8643	NUM
ejpam-6388	668	184	0.5302	0.5302	NUM
ejpam-6388	668	185	0.92	0.92	NUM
ejpam-6388	668	186	2.9875	2.9875	NUM
ejpam-6388	668	187	0.9841	0.9841	NUM
ejpam-6388	668	188	0.25	0.25	NUM
ejpam-6388	668	189	1.8167	1.8167	NUM
ejpam-6388	668	190	0.0861	0.0861	NUM
ejpam-6388	668	191	0.59	0.59	NUM
ejpam-6388	668	192	2.8850	2.8850	NUM
ejpam-6388	668	193	0.5473	0.5473	NUM
ejpam-6388	668	194	0.93	0.93	NUM
ejpam-6388	668	195	2.9676	2.9676	NUM
ejpam-6388	668	196	0.9894	0.9894	NUM
ejpam-6388	668	197	0.26	0.26	NUM
ejpam-6388	668	198	1.8579	1.8579	NUM
ejpam-6388	668	199	0.0944	0.0944	NUM
ejpam-6388	668	200	0.60	0.60	NUM
ejpam-6388	668	201	2.9048	2.9048	NUM
ejpam-6388	668	202	0.5643	0.5643	NUM
ejpam-6388	668	203	0.94	0.94	NUM
ejpam-6388	668	204	2.9460	2.9460	NUM
ejpam-6388	668	205	0.9938	0.9938	NUM
ejpam-6388	668	206	0.27	0.27	NUM
ejpam-6388	668	207	1.8985	1.8985	NUM
ejpam-6388	668	208	0.1030	0.1030	NUM
ejpam-6388	668	209	0.61	0.61	NUM
ejpam-6388	668	210	2.9238	2.9238	NUM
ejpam-6388	668	211	0.5814	0.5814	NUM
ejpam-6388	668	212	0.95	0.95	NUM
ejpam-6388	668	213	2.9225	2.9225	NUM
ejpam-6388	668	214	0.9973	0.9973	NUM
ejpam-6388	668	215	0.28	0.28	NUM
ejpam-6388	668	216	1.9384	1.9384	NUM
ejpam-6388	668	217	0.1120	0.1120	NUM
ejpam-6388	668	218	0.62	0.62	NUM
ejpam-6388	668	219	2.9420	2.9420	NUM
ejpam-6388	668	220	0.5984	0.5984	NUM
ejpam-6388	668	221	0.96	0.96	NUM
ejpam-6388	668	222	2.8971	2.8971	NUM
ejpam-6388	668	223	0.9998	0.9998	NUM
ejpam-6388	668	224	0.29	0.29	NUM
ejpam-6388	668	225	1.9778	1.9778	NUM
ejpam-6388	668	226	0.1214	0.1214	NUM
ejpam-6388	668	227	0.63	0.63	NUM
ejpam-6388	668	228	2.9593	2.9593	NUM
ejpam-6388	668	229	0.6155	0.6155	NUM
ejpam-6388	668	230	0.97	0.97	NUM
ejpam-6388	668	231	2.8698	2.8698	NUM
ejpam-6388	668	232	1.0014	1.0014	NUM
ejpam-6388	668	233	0.30	0.30	NUM
ejpam-6388	668	234	2.0165	2.0165	NUM
ejpam-6388	668	235	0.1312	0.1312	NUM
ejpam-6388	668	236	0.64	0.64	NUM
ejpam-6388	668	237	2.9757	2.9757	NUM
ejpam-6388	668	238	0.6325	0.6325	NUM
ejpam-6388	668	239	0.98	0.98	NUM
ejpam-6388	668	240	2.8405	2.8405	NUM
ejpam-6388	668	241	1.0020	1.0020	NUM
ejpam-6388	668	242	0.31	0.31	NUM
ejpam-6388	668	243	2.0547	2.0547	NUM
ejpam-6388	668	244	0.1414	0.1414	NUM
ejpam-6388	668	245	0.65	0.65	NUM
ejpam-6388	668	246	2.9913	2.9913	NUM
ejpam-6388	668	247	0.6494	0.6494	NUM
ejpam-6388	668	248	0.99	0.99	NUM
ejpam-6388	668	249	2.8092	2.8092	NUM
ejpam-6388	668	250	1.0015	1.0015	NUM
ejpam-6388	668	251	0.32	0.32	NUM
ejpam-6388	668	252	2.0923	2.0923	NUM
ejpam-6388	668	253	0.1519	0.1519	NUM
ejpam-6388	668	254	0.66	0.66	NUM
ejpam-6388	668	255	3.0058	3.0058	NUM
ejpam-6388	668	256	0.6662	0.6662	NUM
ejpam-6388	668	257	1.00	1.00	NUM
ejpam-6388	668	258	2.7758	2.7758	NUM
ejpam-6388	668	259	1.0000	1.0000	NUM
ejpam-6388	668	260	0.33	0.33	NUM
ejpam-6388	668	261	2.1294	2.1294	NUM
ejpam-6388	668	262	0.1628	0.1628	NUM
ejpam-6388	668	263	0.67	0.67	NUM
ejpam-6388	668	264	3.0058	3.0058	NUM
ejpam-6388	668	265	0.6662	0.6662	NUM
ejpam-6388	668	266	table	table	NOUN
ejpam-6388	668	267	5	5	NUM
ejpam-6388	668	268	:	:	PUNCT
ejpam-6388	668	269	comparison	comparison	NOUN
ejpam-6388	668	270	of	of	ADP
ejpam-6388	668	271	r(ω	r(ω	ADJ
ejpam-6388	668	272	)	)	PUNCT
ejpam-6388	668	273	for	for	ADP
ejpam-6388	668	274	f1(ω	f1(ω	SYM
ejpam-6388	668	275	,	,	PUNCT
ejpam-6388	668	276	r	r	NOUN
ejpam-6388	668	277	)	)	PUNCT
ejpam-6388	668	278	=	=	SYM
ejpam-6388	668	279	ω	ω	PROPN
ejpam-6388	668	280	+	+	NUM
ejpam-6388	668	281	4	4	NUM
ejpam-6388	668	282	cos(r	cos(r	NUM
ejpam-6388	668	283	)	)	PUNCT
ejpam-6388	668	284	19	19	NUM
ejpam-6388	668	285	+	+	NUM
ejpam-6388	668	286	38	38	NUM
ejpam-6388	668	287	m	m	NOUN
ejpam-6388	668	288	and	and	CCONJ
ejpam-6388	668	289	f2(ω	f2(ω	ADJ
ejpam-6388	668	290	,	,	PUNCT
ejpam-6388	668	291	r	r	NOUN
ejpam-6388	668	292	)	)	PUNCT
ejpam-6388	668	293	=	=	VERB
ejpam-6388	668	294	eω	eω	NOUN
ejpam-6388	668	295	+	+	NOUN
ejpam-6388	668	296	4	4	NUM
ejpam-6388	668	297	sin(r	sin(r	NOUN
ejpam-6388	668	298	)	)	PUNCT
ejpam-6388	668	299	19	19	NUM
ejpam-6388	669	1	+	+	NUM
ejpam-6388	669	2	38	38	NUM
ejpam-6388	669	3	m	m	PROPN
ejpam-6388	669	4	d.	d.	PROPN
ejpam-6388	669	5	baleanu	baleanu	PROPN
ejpam-6388	669	6	et	et	PROPN
ejpam-6388	669	7	al	al	PROPN
ejpam-6388	669	8	.	.	PUNCT
ejpam-6388	669	9	/	/	SYM
ejpam-6388	669	10	eur	eur	PROPN
ejpam-6388	669	11	.	.	PUNCT
ejpam-6388	670	1	j.	j.	PROPN
ejpam-6388	670	2	pure	pure	PROPN
ejpam-6388	670	3	appl	appl	PROPN
ejpam-6388	670	4	.	.	PROPN
ejpam-6388	670	5	math	math	PROPN
ejpam-6388	670	6	,	,	PUNCT
ejpam-6388	670	7	18	18	NUM
ejpam-6388	670	8	(	(	PUNCT
ejpam-6388	670	9	4	4	NUM
ejpam-6388	670	10	)	)	PUNCT
ejpam-6388	670	11	(	(	PUNCT
ejpam-6388	670	12	2025	2025	NUM
ejpam-6388	670	13	)	)	PUNCT
ejpam-6388	670	14	,	,	PUNCT
ejpam-6388	670	15	6388	6388	NUM
ejpam-6388	670	16	31	31	NUM
ejpam-6388	670	17	of	of	ADP
ejpam-6388	670	18	31	31	NUM
ejpam-6388	670	19	ω	ω	NOUN
ejpam-6388	670	20	(	(	PUNCT
ejpam-6388	670	21	g1	g1	PROPN
ejpam-6388	670	22	)	)	PUNCT
ejpam-6388	670	23	(	(	PUNCT
ejpam-6388	670	24	g2	g2	PROPN
ejpam-6388	670	25	)	)	PUNCT
ejpam-6388	670	26	ω	ω	PROPN
ejpam-6388	670	27	(	(	PUNCT
ejpam-6388	670	28	g1	g1	PROPN
ejpam-6388	670	29	)	)	PUNCT
ejpam-6388	670	30	(	(	PUNCT
ejpam-6388	670	31	g2	g2	PROPN
ejpam-6388	670	32	)	)	PUNCT
ejpam-6388	670	33	ω	ω	PROPN
ejpam-6388	670	34	(	(	PUNCT
ejpam-6388	670	35	g1	g1	PROPN
ejpam-6388	670	36	)	)	PUNCT
ejpam-6388	670	37	(	(	PUNCT
ejpam-6388	670	38	g2	g2	PROPN
ejpam-6388	670	39	)	)	PUNCT
ejpam-6388	670	40	0.00	0.00	NUM
ejpam-6388	670	41	0.0000	0.0000	NUM
ejpam-6388	670	42	0.0000	0.0000	NUM
ejpam-6388	670	43	0.34	0.34	NUM
ejpam-6388	670	44	0.0087	0.0087	NUM
ejpam-6388	670	45	0.0041	0.0041	NUM
ejpam-6388	670	46	0.68	0.68	NUM
ejpam-6388	670	47	0.0088	0.0088	NUM
ejpam-6388	670	48	0.0051	0.0051	NUM
ejpam-6388	670	49	0.01	0.01	NUM
ejpam-6388	670	50	0.0018	0.0018	NUM
ejpam-6388	670	51	0.0008	0.0008	NUM
ejpam-6388	670	52	0.35	0.35	NUM
ejpam-6388	670	53	0.0088	0.0088	NUM
ejpam-6388	671	1	0.0042	0.0042	NUM
ejpam-6388	671	2	0.69	0.69	NUM
ejpam-6388	671	3	0.0087	0.0087	NUM
ejpam-6388	671	4	0.0051	0.0051	NUM
ejpam-6388	671	5	0.02	0.02	NUM
ejpam-6388	671	6	0.0026	0.0026	NUM
ejpam-6388	671	7	0.0012	0.0012	NUM
ejpam-6388	671	8	0.36	0.36	NUM
ejpam-6388	671	9	0.0088	0.0088	NUM
ejpam-6388	671	10	0.0042	0.0042	NUM
ejpam-6388	671	11	0.70	0.70	NUM
ejpam-6388	671	12	0.0086	0.0086	NUM
ejpam-6388	671	13	0.0051	0.0051	NUM
ejpam-6388	671	14	0.03	0.03	NUM
ejpam-6388	671	15	0.0032	0.0032	NUM
ejpam-6388	671	16	0.0014	0.0014	NUM
ejpam-6388	671	17	0.37	0.37	NUM
ejpam-6388	671	18	0.0088	0.0088	NUM
ejpam-6388	671	19	0.0043	0.0043	NUM
ejpam-6388	671	20	0.71	0.71	NUM
ejpam-6388	671	21	0.0086	0.0086	NUM
ejpam-6388	671	22	0.0052	0.0052	NUM
ejpam-6388	671	23	0.04	0.04	NUM
ejpam-6388	671	24	0.0036	0.0036	NUM
ejpam-6388	671	25	0.0016	0.0016	NUM
ejpam-6388	671	26	0.38	0.38	NUM
ejpam-6388	671	27	0.0089	0.0089	NUM
ejpam-6388	671	28	0.0043	0.0043	NUM
ejpam-6388	671	29	0.72	0.72	NUM
ejpam-6388	671	30	0.0085	0.0085	NUM
ejpam-6388	671	31	0.0052	0.0052	NUM
ejpam-6388	671	32	0.05	0.05	NUM
ejpam-6388	671	33	0.0040	0.0040	NUM
ejpam-6388	671	34	0.0018	0.0018	NUM
ejpam-6388	671	35	0.39	0.39	NUM
ejpam-6388	671	36	0.0089	0.0089	NUM
ejpam-6388	671	37	0.0043	0.0043	NUM
ejpam-6388	671	38	0.73	0.73	NUM
ejpam-6388	671	39	0.0085	0.0085	NUM
ejpam-6388	671	40	0.0052	0.0052	NUM
ejpam-6388	671	41	0.06	0.06	NUM
ejpam-6388	671	42	0.0044	0.0044	NUM
ejpam-6388	671	43	0.0020	0.0020	NUM
ejpam-6388	671	44	0.40	0.40	NUM
ejpam-6388	671	45	0.0090	0.0090	NUM
ejpam-6388	671	46	0.0044	0.0044	NUM
ejpam-6388	671	47	0.74	0.74	NUM
ejpam-6388	671	48	0.0084	0.0084	NUM
ejpam-6388	671	49	0.0052	0.0052	NUM
ejpam-6388	671	50	0.07	0.07	NUM
ejpam-6388	671	51	0.0047	0.0047	NUM
ejpam-6388	671	52	0.0021	0.0021	NUM
ejpam-6388	671	53	0.41	0.41	NUM
ejpam-6388	671	54	0.0091	0.0091	NUM
ejpam-6388	671	55	0.0044	0.0044	NUM
ejpam-6388	671	56	0.75	0.75	NUM
ejpam-6388	671	57	0.0083	0.0083	NUM
ejpam-6388	671	58	0.0052	0.0052	NUM
ejpam-6388	671	59	0.08	0.08	NUM
ejpam-6388	671	60	0.0050	0.0050	NUM
ejpam-6388	671	61	0.0023	0.0023	NUM
ejpam-6388	671	62	0.42	0.42	NUM
ejpam-6388	671	63	0.0091	0.0091	NUM
ejpam-6388	671	64	0.0044	0.0044	NUM
ejpam-6388	671	65	0.76	0.76	NUM
ejpam-6388	671	66	0.0083	0.0083	NUM
ejpam-6388	671	67	0.0053	0.0053	NUM
ejpam-6388	671	68	0.09	0.09	NUM
ejpam-6388	671	69	0.0053	0.0053	NUM
ejpam-6388	671	70	0.0024	0.0024	NUM
ejpam-6388	671	71	0.43	0.43	NUM
ejpam-6388	671	72	0.0091	0.0091	NUM
ejpam-6388	671	73	0.0045	0.0045	NUM
ejpam-6388	671	74	0.77	0.77	NUM
ejpam-6388	671	75	0.0082	0.0082	NUM
ejpam-6388	671	76	0.0053	0.0053	NUM
ejpam-6388	671	77	0.10	0.10	NUM
ejpam-6388	671	78	0.0056	0.0056	NUM
ejpam-6388	671	79	0.0025	0.0025	NUM
ejpam-6388	671	80	0.44	0.44	NUM
ejpam-6388	671	81	0.0091	0.0091	NUM
ejpam-6388	671	82	0.0045	0.0045	NUM
ejpam-6388	671	83	0.78	0.78	NUM
ejpam-6388	671	84	0.0081	0.0081	NUM
ejpam-6388	671	85	0.0053	0.0053	NUM
ejpam-6388	671	86	0.11	0.11	NUM
ejpam-6388	671	87	0.0058	0.0058	NUM
ejpam-6388	671	88	0.0026	0.0026	NUM
ejpam-6388	671	89	0.45	0.45	NUM
ejpam-6388	671	90	0.0092	0.0092	NUM
ejpam-6388	671	91	0.0045	0.0045	NUM
ejpam-6388	671	92	0.79	0.79	NUM
ejpam-6388	671	93	0.0080	0.0080	NUM
ejpam-6388	671	94	0.0053	0.0053	NUM
ejpam-6388	671	95	0.12	0.12	NUM
ejpam-6388	671	96	0.0060	0.0060	NUM
ejpam-6388	671	97	0.0027	0.0027	NUM
ejpam-6388	671	98	0.46	0.46	NUM
ejpam-6388	671	99	0.0092	0.0092	NUM
ejpam-6388	671	100	0.0046	0.0046	NUM
ejpam-6388	671	101	0.80	0.80	NUM
ejpam-6388	671	102	0.0079	0.0079	NUM
ejpam-6388	671	103	0.0053	0.0053	NUM
ejpam-6388	671	104	0.13	0.13	NUM
ejpam-6388	671	105	0.0062	0.0062	NUM
ejpam-6388	671	106	0.0028	0.0028	NUM
ejpam-6388	671	107	0.47	0.47	NUM
ejpam-6388	671	108	0.0092	0.0092	NUM
ejpam-6388	671	109	0.0046	0.0046	NUM
ejpam-6388	671	110	0.81	0.81	NUM
ejpam-6388	671	111	0.0079	0.0079	NUM
ejpam-6388	671	112	0.0054	0.0054	NUM
ejpam-6388	671	113	0.14	0.14	NUM
ejpam-6388	671	114	0.0064	0.0064	NUM
ejpam-6388	671	115	0.0029	0.0029	NUM
ejpam-6388	671	116	0.48	0.48	NUM
ejpam-6388	671	117	0.0092	0.0092	NUM
ejpam-6388	671	118	0.0046	0.0046	NUM
ejpam-6388	671	119	0.82	0.82	NUM
ejpam-6388	671	120	0.0078	0.0078	NUM
ejpam-6388	671	121	0.0054	0.0054	NUM
ejpam-6388	671	122	0.15	0.15	NUM
ejpam-6388	671	123	0.0066	0.0066	NUM
ejpam-6388	671	124	0.0030	0.0030	NUM
ejpam-6388	671	125	0.49	0.49	NUM
ejpam-6388	671	126	0.0092	0.0092	NUM
ejpam-6388	671	127	0.0047	0.0047	NUM
ejpam-6388	671	128	0.83	0.83	NUM
ejpam-6388	671	129	0.0077	0.0077	NUM
ejpam-6388	671	130	0.0054	0.0054	NUM
ejpam-6388	671	131	0.16	0.16	NUM
ejpam-6388	671	132	0.0068	0.0068	NUM
ejpam-6388	671	133	0.0031	0.0031	NUM
ejpam-6388	671	134	0.50	0.50	NUM
ejpam-6388	671	135	0.0092	0.0092	NUM
ejpam-6388	671	136	0.0047	0.0047	NUM
ejpam-6388	671	137	0.84	0.84	NUM
ejpam-6388	671	138	0.0076	0.0076	NUM
ejpam-6388	671	139	0.0054	0.0054	NUM
ejpam-6388	671	140	0.17	0.17	NUM
ejpam-6388	671	141	0.0070	0.0070	NUM
ejpam-6388	671	142	0.0032	0.0032	NUM
ejpam-6388	671	143	0.51	0.51	NUM
ejpam-6388	671	144	0.0092	0.0092	NUM
ejpam-6388	671	145	0.0047	0.0047	NUM
ejpam-6388	671	146	0.85	0.85	NUM
ejpam-6388	671	147	0.0075	0.0075	NUM
ejpam-6388	671	148	0.0054	0.0054	NUM
ejpam-6388	671	149	0.18	0.18	NUM
ejpam-6388	671	150	0.0071	0.0071	NUM
ejpam-6388	671	151	0.0032	0.0032	NUM
ejpam-6388	671	152	0.52	0.52	NUM
ejpam-6388	671	153	0.0092	0.0092	NUM
ejpam-6388	671	154	0.0047	0.0047	NUM
ejpam-6388	671	155	0.86	0.86	NUM
ejpam-6388	671	156	0.0074	0.0074	NUM
ejpam-6388	671	157	0.0055	0.0055	NUM
ejpam-6388	671	158	0.19	0.19	NUM
ejpam-6388	671	159	0.0073	0.0073	NUM
ejpam-6388	671	160	0.0033	0.0033	NUM
ejpam-6388	671	161	0.53	0.53	NUM
ejpam-6388	671	162	0.0092	0.0092	NUM
ejpam-6388	671	163	0.0047	0.0047	NUM
ejpam-6388	671	164	0.87	0.87	NUM
ejpam-6388	671	165	0.0073	0.0073	NUM
ejpam-6388	671	166	0.0055	0.0055	NUM
ejpam-6388	671	167	0.20	0.20	NUM
ejpam-6388	671	168	0.0074	0.0074	NUM
ejpam-6388	671	169	0.0034	0.0034	NUM
ejpam-6388	671	170	0.54	0.54	NUM
ejpam-6388	671	171	0.0092	0.0092	NUM
ejpam-6388	671	172	0.0048	0.0048	NUM
ejpam-6388	671	173	0.88	0.88	NUM
ejpam-6388	671	174	0.0072	0.0072	NUM
ejpam-6388	671	175	0.0055	0.0055	NUM
ejpam-6388	671	176	0.21	0.21	NUM
ejpam-6388	671	177	0.0075	0.0075	NUM
ejpam-6388	671	178	0.0035	0.0035	NUM
ejpam-6388	671	179	0.55	0.55	NUM
ejpam-6388	671	180	0.0092	0.0092	NUM
ejpam-6388	671	181	0.0048	0.0048	NUM
ejpam-6388	671	182	0.89	0.89	NUM
ejpam-6388	671	183	0.0071	0.0071	NUM
ejpam-6388	671	184	0.0055	0.0055	NUM
ejpam-6388	671	185	0.22	0.22	NUM
ejpam-6388	671	186	0.0077	0.0077	NUM
ejpam-6388	671	187	0.0035	0.0035	NUM
ejpam-6388	671	188	0.56	0.56	NUM
ejpam-6388	671	189	0.0092	0.0092	NUM
ejpam-6388	671	190	0.0048	0.0048	NUM
ejpam-6388	671	191	0.90	0.90	NUM
ejpam-6388	671	192	0.0070	0.0070	NUM
ejpam-6388	671	193	0.0055	0.0055	NUM
ejpam-6388	671	194	0.23	0.23	NUM
ejpam-6388	671	195	0.0078	0.0078	NUM
ejpam-6388	671	196	0.0036	0.0036	NUM
ejpam-6388	671	197	0.57	0.57	NUM
ejpam-6388	671	198	0.0092	0.0092	NUM
ejpam-6388	671	199	0.0048	0.0048	NUM
ejpam-6388	671	200	0.91	0.91	NUM
ejpam-6388	671	201	0.0069	0.0069	NUM
ejpam-6388	671	202	0.0056	0.0056	NUM
ejpam-6388	671	203	0.24	0.24	NUM
ejpam-6388	671	204	0.0079	0.0079	NUM
ejpam-6388	671	205	0.0036	0.0036	NUM
ejpam-6388	671	206	0.58	0.58	NUM
ejpam-6388	671	207	0.0091	0.0091	NUM
ejpam-6388	671	208	0.0048	0.0048	NUM
ejpam-6388	671	209	0.92	0.92	NUM
ejpam-6388	671	210	0.0068	0.0068	NUM
ejpam-6388	671	211	0.0056	0.0056	NUM
ejpam-6388	671	212	0.25	0.25	NUM
ejpam-6388	671	213	0.0080	0.0080	NUM
ejpam-6388	671	214	0.0037	0.0037	NUM
ejpam-6388	671	215	0.59	0.59	NUM
ejpam-6388	671	216	0.0091	0.0091	NUM
ejpam-6388	671	217	0.0049	0.0049	NUM
ejpam-6388	671	218	0.93	0.93	NUM
ejpam-6388	671	219	0.0066	0.0066	NUM
ejpam-6388	671	220	0.0056	0.0056	NUM
ejpam-6388	671	221	0.26	0.26	NUM
ejpam-6388	671	222	0.0081	0.0081	NUM
ejpam-6388	671	223	0.0037	0.0037	NUM
ejpam-6388	671	224	0.60	0.60	NUM
ejpam-6388	671	225	0.0091	0.0091	NUM
ejpam-6388	671	226	0.0049	0.0049	NUM
ejpam-6388	671	227	0.94	0.94	NUM
ejpam-6388	671	228	0.0065	0.0065	NUM
ejpam-6388	671	229	0.0056	0.0056	NUM
ejpam-6388	671	230	0.27	0.27	NUM
ejpam-6388	671	231	0.0082	0.0082	NUM
ejpam-6388	671	232	0.0038	0.0038	NUM
ejpam-6388	671	233	0.61	0.61	NUM
ejpam-6388	671	234	0.0090	0.0090	NUM
ejpam-6388	671	235	0.0049	0.0049	NUM
ejpam-6388	671	236	0.95	0.95	NUM
ejpam-6388	671	237	0.0064	0.0064	NUM
ejpam-6388	671	238	0.0056	0.0056	NUM
ejpam-6388	671	239	0.28	0.28	NUM
ejpam-6388	671	240	0.0083	0.0083	NUM
ejpam-6388	671	241	0.0039	0.0039	NUM
ejpam-6388	671	242	0.62	0.62	NUM
ejpam-6388	671	243	0.0090	0.0090	NUM
ejpam-6388	671	244	0.0049	0.0049	NUM
ejpam-6388	671	245	0.96	0.96	NUM
ejpam-6388	671	246	0.0063	0.0063	NUM
ejpam-6388	671	247	0.0056	0.0056	NUM
ejpam-6388	671	248	0.29	0.29	NUM
ejpam-6388	671	249	0.0084	0.0084	NUM
ejpam-6388	671	250	0.0039	0.0039	NUM
ejpam-6388	671	251	0.63	0.63	NUM
ejpam-6388	671	252	0.0090	0.0090	NUM
ejpam-6388	671	253	0.0049	0.0049	NUM
ejpam-6388	671	254	0.97	0.97	NUM
ejpam-6388	671	255	0.0062	0.0062	NUM
ejpam-6388	671	256	0.0056	0.0056	NUM
ejpam-6388	671	257	0.30	0.30	NUM
ejpam-6388	671	258	0.0085	0.0085	NUM
ejpam-6388	671	259	0.0040	0.0040	NUM
ejpam-6388	671	260	0.64	0.64	NUM
ejpam-6388	671	261	0.0090	0.0090	NUM
ejpam-6388	671	262	0.0049	0.0049	NUM
ejpam-6388	671	263	0.98	0.98	NUM
ejpam-6388	671	264	0.0061	0.0061	NUM
ejpam-6388	671	265	0.0056	0.0056	NUM
ejpam-6388	671	266	0.31	0.31	NUM
ejpam-6388	671	267	0.0086	0.0086	NUM
ejpam-6388	671	268	0.0040	0.0040	NUM
ejpam-6388	671	269	0.65	0.65	NUM
ejpam-6388	671	270	0.0089	0.0089	NUM
ejpam-6388	671	271	0.0049	0.0049	NUM
ejpam-6388	671	272	0.99	0.99	NUM
ejpam-6388	671	273	0.0060	0.0060	NUM
ejpam-6388	671	274	0.0057	0.0057	NUM
ejpam-6388	671	275	0.32	0.32	NUM
ejpam-6388	671	276	0.0087	0.0087	NUM
ejpam-6388	671	277	0.0041	0.0041	NUM
ejpam-6388	671	278	0.66	0.66	NUM
ejpam-6388	671	279	0.0089	0.0089	NUM
ejpam-6388	671	280	0.0049	0.0049	NUM
ejpam-6388	671	281	1.00	1.00	NUM
ejpam-6388	671	282	0.0059	0.0059	NUM
ejpam-6388	671	283	0.0057	0.0057	NUM
ejpam-6388	671	284	0.33	0.33	NUM
ejpam-6388	671	285	0.0087	0.0087	NUM
ejpam-6388	671	286	0.0041	0.0041	NUM
ejpam-6388	671	287	0.67	0.67	NUM
ejpam-6388	671	288	0.0088	0.0088	NUM
ejpam-6388	671	289	0.0050	0.0050	NUM
ejpam-6388	671	290	table	table	NOUN
ejpam-6388	671	291	6	6	NUM
ejpam-6388	671	292	:	:	PUNCT
ejpam-6388	671	293	values	value	NOUN
ejpam-6388	671	294	of	of	ADP
ejpam-6388	671	295	r(ω	r(ω	ADJ
ejpam-6388	671	296	)	)	PUNCT
ejpam-6388	671	297	for	for	ADP
ejpam-6388	671	298	ω	ω	NUM
ejpam-6388	671	299	=	=	SYM
ejpam-6388	671	300	0	0	PROPN
ejpam-6388	671	301	to	to	ADP
ejpam-6388	671	302	ω	ω	NUM
ejpam-6388	671	303	=	=	SYM
ejpam-6388	671	304	1.00	1.00	NUM
ejpam-6388	671	305	introduction	introduction	NOUN
ejpam-6388	671	306	essential	essential	ADJ
ejpam-6388	671	307	preliminaries	preliminary	NOUN
ejpam-6388	671	308	auxiliary	auxiliary	ADJ
ejpam-6388	671	309	results	result	VERB
ejpam-6388	671	310	existence	existence	NOUN
ejpam-6388	671	311	and	and	CCONJ
ejpam-6388	671	312	uniqueness	uniqueness	NOUN
ejpam-6388	671	313	of	of	ADP
ejpam-6388	671	314	solutions	solution	NOUN
ejpam-6388	671	315	hyers	hyer	NOUN
ejpam-6388	671	316	–	–	PUNCT
ejpam-6388	671	317	ulam	ulam	PROPN
ejpam-6388	671	318	stability	stability	PROPN
ejpam-6388	671	319	analysis	analysis	NOUN
ejpam-6388	671	320	numerical	numerical	ADJ
ejpam-6388	671	321	illustrations	illustration	NOUN
ejpam-6388	671	322	conclusions	conclusion	NOUN