id	sid	tid	token	lemma	pos
ejpam-5963	1	1	european	european	PROPN
ejpam-5963	1	2	journal	journal	PROPN
ejpam-5963	1	3	of	of	ADP
ejpam-5963	1	4	pure	pure	ADJ
ejpam-5963	1	5	and	and	CCONJ
ejpam-5963	1	6	applied	applied	ADJ
ejpam-5963	1	7	mathematics	mathematic	NOUN
ejpam-5963	1	8	2025	2025	NUM
ejpam-5963	1	9	,	,	PUNCT
ejpam-5963	1	10	vol	vol	NOUN
ejpam-5963	1	11	.	.	PROPN
ejpam-5963	1	12	18	18	NUM
ejpam-5963	1	13	,	,	PUNCT
ejpam-5963	1	14	issue	issue	NOUN
ejpam-5963	1	15	2	2	NUM
ejpam-5963	1	16	,	,	PUNCT
ejpam-5963	1	17	article	article	NOUN
ejpam-5963	1	18	number	number	NOUN
ejpam-5963	1	19	5963	5963	NUM
ejpam-5963	1	20	issn	issn	PROPN
ejpam-5963	1	21	1307	1307	NUM
ejpam-5963	1	22	-	-	SYM
ejpam-5963	1	23	5543	5543	NUM
ejpam-5963	1	24	–	–	PUNCT
ejpam-5963	1	25	ejpam.com	ejpam.com	X
ejpam-5963	1	26	published	publish	VERB
ejpam-5963	1	27	by	by	ADP
ejpam-5963	1	28	new	new	PROPN
ejpam-5963	1	29	york	york	PROPN
ejpam-5963	1	30	business	business	PROPN
ejpam-5963	1	31	global	global	ADJ
ejpam-5963	1	32	investigation	investigation	NOUN
ejpam-5963	1	33	of	of	ADP
ejpam-5963	1	34	existence	existence	NOUN
ejpam-5963	1	35	and	and	CCONJ
ejpam-5963	1	36	ulam	ulam	PROPN
ejpam-5963	1	37	’s	’s	PART
ejpam-5963	1	38	type	type	NOUN
ejpam-5963	1	39	stability	stability	NOUN
ejpam-5963	1	40	for	for	ADP
ejpam-5963	1	41	coupled	couple	VERB
ejpam-5963	1	42	fractal	fractal	ADJ
ejpam-5963	1	43	fractional	fractional	ADJ
ejpam-5963	1	44	differential	differential	PROPN
ejpam-5963	1	45	equations	equation	NOUN
ejpam-5963	1	46	amjad	amjad	PROPN
ejpam-5963	1	47	ali1	ali1	PROPN
ejpam-5963	1	48	,	,	PUNCT
ejpam-5963	1	49	farha	farha	PROPN
ejpam-5963	1	50	bibi1	bibi1	PROPN
ejpam-5963	1	51	,	,	PUNCT
ejpam-5963	1	52	zeeshan	zeeshan	PROPN
ejpam-5963	1	53	ali2,∗	ali2,∗	PROPN
ejpam-5963	1	54	,	,	PUNCT
ejpam-5963	1	55	kamal	kamal	PROPN
ejpam-5963	1	56	shah3	shah3	PROPN
ejpam-5963	1	57	,	,	PUNCT
ejpam-5963	1	58	bahaaeldin	bahaaeldin	VERB
ejpam-5963	1	59	abdalla3	abdalla3	PROPN
ejpam-5963	1	60	,	,	PUNCT
ejpam-5963	1	61	thabet	thabet	ADJ
ejpam-5963	1	62	abdeljawad3	abdeljawad3	NOUN
ejpam-5963	1	63	1	1	NUM
ejpam-5963	1	64	department	department	NOUN
ejpam-5963	1	65	of	of	ADP
ejpam-5963	1	66	mathematics	mathematic	NOUN
ejpam-5963	1	67	and	and	CCONJ
ejpam-5963	1	68	statistics	statistic	NOUN
ejpam-5963	1	69	,	,	PUNCT
ejpam-5963	1	70	university	university	PROPN
ejpam-5963	1	71	of	of	ADP
ejpam-5963	1	72	swat	swat	PROPN
ejpam-5963	1	73	,	,	PUNCT
ejpam-5963	1	74	kpk	kpk	PROPN
ejpam-5963	1	75	,	,	PUNCT
ejpam-5963	1	76	pakistan	pakistan	PROPN
ejpam-5963	1	77	2	2	NUM
ejpam-5963	1	78	department	department	NOUN
ejpam-5963	1	79	of	of	ADP
ejpam-5963	1	80	information	information	NOUN
ejpam-5963	1	81	management	management	NOUN
ejpam-5963	1	82	,	,	PUNCT
ejpam-5963	1	83	national	national	PROPN
ejpam-5963	1	84	yunlin	yunlin	PROPN
ejpam-5963	1	85	university	university	PROPN
ejpam-5963	1	86	of	of	ADP
ejpam-5963	1	87	science	science	NOUN
ejpam-5963	1	88	and	and	CCONJ
ejpam-5963	1	89	technology	technology	NOUN
ejpam-5963	1	90	douliu	douliu	PROPN
ejpam-5963	1	91	taiwan	taiwan	PROPN
ejpam-5963	1	92	,	,	PUNCT
ejpam-5963	1	93	r.	r.	PROPN
ejpam-5963	1	94	o.c	o.c	PROPN
ejpam-5963	1	95	2	2	NUM
ejpam-5963	1	96	department	department	NOUN
ejpam-5963	1	97	of	of	ADP
ejpam-5963	1	98	mathematics	mathematic	NOUN
ejpam-5963	1	99	and	and	CCONJ
ejpam-5963	1	100	sciences	science	NOUN
ejpam-5963	1	101	,	,	PUNCT
ejpam-5963	1	102	prince	prince	PROPN
ejpam-5963	1	103	sultan	sultan	PROPN
ejpam-5963	1	104	university	university	PROPN
ejpam-5963	1	105	,	,	PUNCT
ejpam-5963	1	106	p.o	p.o	PROPN
ejpam-5963	1	107	.	.	PROPN
ejpam-5963	1	108	box	box	PROPN
ejpam-5963	1	109	66833	66833	NUM
ejpam-5963	1	110	,	,	PUNCT
ejpam-5963	1	111	11586	11586	NUM
ejpam-5963	1	112	riyadh	riyadh	NOUN
ejpam-5963	1	113	,	,	PUNCT
ejpam-5963	1	114	saudi	saudi	PROPN
ejpam-5963	1	115	arabia	arabia	PROPN
ejpam-5963	1	116	abstract	abstract	NOUN
ejpam-5963	1	117	.	.	PUNCT
ejpam-5963	2	1	in	in	ADP
ejpam-5963	2	2	this	this	DET
ejpam-5963	2	3	study	study	NOUN
ejpam-5963	2	4	,	,	PUNCT
ejpam-5963	2	5	we	we	PRON
ejpam-5963	2	6	investigate	investigate	VERB
ejpam-5963	2	7	the	the	DET
ejpam-5963	2	8	coupled	couple	VERB
ejpam-5963	2	9	system	system	NOUN
ejpam-5963	2	10	of	of	ADP
ejpam-5963	2	11	fractal	fractal	ADJ
ejpam-5963	2	12	fractional	fractional	ADJ
ejpam-5963	2	13	differential	differential	ADJ
ejpam-5963	2	14	equations	equation	NOUN
ejpam-5963	2	15	(	(	PUNCT
ejpam-5963	2	16	ffdes	ffdes	PROPN
ejpam-5963	2	17	)	)	PUNCT
ejpam-5963	2	18	from	from	ADP
ejpam-5963	2	19	an	an	DET
ejpam-5963	2	20	existence	existence	NOUN
ejpam-5963	2	21	and	and	CCONJ
ejpam-5963	2	22	stability	stability	NOUN
ejpam-5963	2	23	point	point	NOUN
ejpam-5963	2	24	of	of	ADP
ejpam-5963	2	25	view	view	NOUN
ejpam-5963	2	26	.	.	PUNCT
ejpam-5963	3	1	the	the	DET
ejpam-5963	3	2	area	area	NOUN
ejpam-5963	3	3	related	relate	VERB
ejpam-5963	3	4	to	to	ADP
ejpam-5963	3	5	coupled	couple	VERB
ejpam-5963	3	6	ffdes	ffde	NOUN
ejpam-5963	3	7	is	be	AUX
ejpam-5963	3	8	significant	significant	ADJ
ejpam-5963	3	9	because	because	SCONJ
ejpam-5963	3	10	its	its	PRON
ejpam-5963	3	11	permitting	permit	VERB
ejpam-5963	3	12	us	we	PRON
ejpam-5963	3	13	to	to	PART
ejpam-5963	3	14	analyze	analyze	VERB
ejpam-5963	3	15	and	and	CCONJ
ejpam-5963	3	16	predict	predict	VERB
ejpam-5963	3	17	the	the	DET
ejpam-5963	3	18	relationships	relationship	NOUN
ejpam-5963	3	19	between	between	ADP
ejpam-5963	3	20	several	several	ADJ
ejpam-5963	3	21	variables	variable	NOUN
ejpam-5963	3	22	throughout	throughout	ADP
ejpam-5963	3	23	the	the	DET
ejpam-5963	3	24	real	real	ADJ
ejpam-5963	3	25	-	-	PUNCT
ejpam-5963	3	26	world	world	NOUN
ejpam-5963	3	27	phenomena	phenomenon	NOUN
ejpam-5963	3	28	.	.	PUNCT
ejpam-5963	4	1	coupled	couple	VERB
ejpam-5963	4	2	systems	system	NOUN
ejpam-5963	4	3	have	have	VERB
ejpam-5963	4	4	numerous	numerous	ADJ
ejpam-5963	4	5	applications	application	NOUN
ejpam-5963	4	6	in	in	ADP
ejpam-5963	4	7	different	different	ADJ
ejpam-5963	4	8	fields	field	NOUN
ejpam-5963	4	9	,	,	PUNCT
ejpam-5963	4	10	such	such	ADJ
ejpam-5963	4	11	as	as	ADP
ejpam-5963	4	12	modeling	modeling	NOUN
ejpam-5963	4	13	of	of	ADP
ejpam-5963	4	14	brain	brain	NOUN
ejpam-5963	4	15	activities	activity	NOUN
ejpam-5963	4	16	and	and	CCONJ
ejpam-5963	4	17	spreads	spread	NOUN
ejpam-5963	4	18	of	of	ADP
ejpam-5963	4	19	disease	disease	NOUN
ejpam-5963	4	20	in	in	ADP
ejpam-5963	4	21	biology	biology	NOUN
ejpam-5963	4	22	and	and	CCONJ
ejpam-5963	4	23	medicine	medicine	NOUN
ejpam-5963	4	24	,	,	PUNCT
ejpam-5963	4	25	modeling	modeling	NOUN
ejpam-5963	4	26	of	of	ADP
ejpam-5963	4	27	mechanical	mechanical	ADJ
ejpam-5963	4	28	systems	system	NOUN
ejpam-5963	4	29	,	,	PUNCT
ejpam-5963	4	30	electrical	electrical	ADJ
ejpam-5963	4	31	circuits	circuit	NOUN
ejpam-5963	4	32	in	in	ADP
ejpam-5963	4	33	engineering	engineering	NOUN
ejpam-5963	4	34	,	,	PUNCT
ejpam-5963	4	35	and	and	CCONJ
ejpam-5963	4	36	modeling	modeling	NOUN
ejpam-5963	4	37	of	of	ADP
ejpam-5963	4	38	population	population	NOUN
ejpam-5963	4	39	dynamics	dynamic	NOUN
ejpam-5963	4	40	,	,	PUNCT
ejpam-5963	4	41	predator	predator	NOUN
ejpam-5963	4	42	-	-	PUNCT
ejpam-5963	4	43	prey	prey	NOUN
ejpam-5963	4	44	models	model	NOUN
ejpam-5963	4	45	in	in	ADP
ejpam-5963	4	46	ecology	ecology	NOUN
ejpam-5963	4	47	and	and	CCONJ
ejpam-5963	4	48	financial	financial	ADJ
ejpam-5963	4	49	mathematical	mathematical	NOUN
ejpam-5963	4	50	in	in	ADP
ejpam-5963	4	51	economics	economic	NOUN
ejpam-5963	4	52	.	.	PUNCT
ejpam-5963	5	1	furthermore	furthermore	ADV
ejpam-5963	5	2	,	,	PUNCT
ejpam-5963	5	3	the	the	DET
ejpam-5963	5	4	afore	afore	ADV
ejpam-5963	5	5	mentioned	mention	VERB
ejpam-5963	5	6	area	area	NOUN
ejpam-5963	5	7	is	be	AUX
ejpam-5963	5	8	significant	significant	ADJ
ejpam-5963	5	9	for	for	ADP
ejpam-5963	5	10	environmental	environmental	ADJ
ejpam-5963	5	11	science	science	NOUN
ejpam-5963	5	12	in	in	ADP
ejpam-5963	5	13	pollution	pollution	NOUN
ejpam-5963	5	14	control	control	NOUN
ejpam-5963	5	15	,	,	PUNCT
ejpam-5963	5	16	climate	climate	NOUN
ejpam-5963	5	17	change	change	NOUN
ejpam-5963	5	18	modeling	modeling	NOUN
ejpam-5963	5	19	,	,	PUNCT
ejpam-5963	5	20	artificial	artificial	ADJ
ejpam-5963	5	21	intelligence	intelligence	NOUN
ejpam-5963	5	22	,	,	PUNCT
ejpam-5963	5	23	and	and	CCONJ
ejpam-5963	5	24	control	control	NOUN
ejpam-5963	5	25	systems	system	NOUN
ejpam-5963	5	26	in	in	ADP
ejpam-5963	5	27	technology	technology	NOUN
ejpam-5963	5	28	.	.	PUNCT
ejpam-5963	6	1	we	we	PRON
ejpam-5963	6	2	analysis	analysis	VERB
ejpam-5963	6	3	a	a	DET
ejpam-5963	6	4	coupled	couple	VERB
ejpam-5963	6	5	system	system	NOUN
ejpam-5963	6	6	and	and	CCONJ
ejpam-5963	6	7	make	make	VERB
ejpam-5963	6	8	more	more	ADV
ejpam-5963	6	9	informed	informed	ADJ
ejpam-5963	6	10	choices	choice	NOUN
ejpam-5963	6	11	in	in	ADP
ejpam-5963	6	12	a	a	DET
ejpam-5963	6	13	variety	variety	NOUN
ejpam-5963	6	14	of	of	ADP
ejpam-5963	6	15	fields	field	NOUN
ejpam-5963	6	16	through	through	ADP
ejpam-5963	6	17	coupled	couple	VERB
ejpam-5963	6	18	system	system	NOUN
ejpam-5963	6	19	of	of	ADP
ejpam-5963	6	20	ffdes	ffde	NOUN
ejpam-5963	6	21	.	.	PUNCT
ejpam-5963	7	1	keeping	keep	VERB
ejpam-5963	7	2	these	these	DET
ejpam-5963	7	3	informative	informative	ADJ
ejpam-5963	7	4	aspects	aspect	NOUN
ejpam-5963	7	5	of	of	ADP
ejpam-5963	7	6	coupled	couple	VERB
ejpam-5963	7	7	systems	system	NOUN
ejpam-5963	7	8	in	in	ADP
ejpam-5963	7	9	mind	mind	NOUN
ejpam-5963	7	10	,	,	PUNCT
ejpam-5963	7	11	this	this	DET
ejpam-5963	7	12	article	article	NOUN
ejpam-5963	7	13	aims	aim	VERB
ejpam-5963	7	14	to	to	PART
ejpam-5963	7	15	explore	explore	VERB
ejpam-5963	7	16	the	the	DET
ejpam-5963	7	17	qualitative	qualitative	ADJ
ejpam-5963	7	18	analysis	analysis	NOUN
ejpam-5963	7	19	such	such	ADJ
ejpam-5963	7	20	as	as	ADP
ejpam-5963	7	21	existence	existence	NOUN
ejpam-5963	7	22	,	,	PUNCT
ejpam-5963	7	23	uniqueness	uniqueness	NOUN
ejpam-5963	7	24	,	,	PUNCT
ejpam-5963	7	25	and	and	CCONJ
ejpam-5963	7	26	stability	stability	NOUN
ejpam-5963	7	27	for	for	ADP
ejpam-5963	7	28	the	the	DET
ejpam-5963	7	29	solution	solution	NOUN
ejpam-5963	7	30	of	of	ADP
ejpam-5963	7	31	underlying	underlie	VERB
ejpam-5963	7	32	coupled	couple	VERB
ejpam-5963	7	33	systems	system	NOUN
ejpam-5963	7	34	of	of	ADP
ejpam-5963	7	35	ffdes	ffde	NOUN
ejpam-5963	7	36	.	.	PUNCT
ejpam-5963	8	1	the	the	DET
ejpam-5963	8	2	tools	tool	NOUN
ejpam-5963	8	3	of	of	ADP
ejpam-5963	8	4	functional	functional	ADJ
ejpam-5963	8	5	analysis	analysis	NOUN
ejpam-5963	8	6	(	(	PUNCT
ejpam-5963	8	7	fa	fa	NOUN
ejpam-5963	8	8	)	)	PUNCT
ejpam-5963	8	9	and	and	CCONJ
ejpam-5963	8	10	fixed	fix	VERB
ejpam-5963	8	11	point	point	NOUN
ejpam-5963	8	12	theory	theory	NOUN
ejpam-5963	8	13	(	(	PUNCT
ejpam-5963	8	14	fpt	fpt	PROPN
ejpam-5963	8	15	)	)	PUNCT
ejpam-5963	8	16	have	have	AUX
ejpam-5963	8	17	been	be	AUX
ejpam-5963	8	18	applied	apply	VERB
ejpam-5963	8	19	to	to	PART
ejpam-5963	8	20	deduce	deduce	VERB
ejpam-5963	8	21	our	our	PRON
ejpam-5963	8	22	required	require	VERB
ejpam-5963	8	23	results	result	NOUN
ejpam-5963	8	24	.	.	PUNCT
ejpam-5963	9	1	we	we	PRON
ejpam-5963	9	2	have	have	AUX
ejpam-5963	9	3	used	use	VERB
ejpam-5963	9	4	the	the	DET
ejpam-5963	9	5	banach	banach	NOUN
ejpam-5963	9	6	contraction	contraction	NOUN
ejpam-5963	9	7	principle	principle	NOUN
ejpam-5963	9	8	(	(	PUNCT
ejpam-5963	9	9	bcp	bcp	PROPN
ejpam-5963	9	10	)	)	PUNCT
ejpam-5963	9	11	and	and	CCONJ
ejpam-5963	9	12	the	the	DET
ejpam-5963	9	13	krasnoselskii	krasnoselskii	PROPN
ejpam-5963	9	14	fixed	fix	VERB
ejpam-5963	9	15	point	point	NOUN
ejpam-5963	9	16	theorem	theorem	NOUN
ejpam-5963	9	17	(	(	PUNCT
ejpam-5963	9	18	kfpt	kfpt	PROPN
ejpam-5963	9	19	)	)	PUNCT
ejpam-5963	9	20	to	to	PART
ejpam-5963	9	21	demonstrate	demonstrate	VERB
ejpam-5963	9	22	the	the	DET
ejpam-5963	9	23	conditions	condition	NOUN
ejpam-5963	9	24	for	for	ADP
ejpam-5963	9	25	existence	existence	NOUN
ejpam-5963	9	26	and	and	CCONJ
ejpam-5963	9	27	uniqueness	uniqueness	NOUN
ejpam-5963	9	28	of	of	ADP
ejpam-5963	9	29	a	a	DET
ejpam-5963	9	30	solutions	solution	NOUN
ejpam-5963	9	31	(	(	PUNCT
ejpam-5963	9	32	eus	eus	PROPN
ejpam-5963	9	33	)	)	PUNCT
ejpam-5963	9	34	.	.	PUNCT
ejpam-5963	10	1	additionally	additionally	ADV
ejpam-5963	10	2	,	,	PUNCT
ejpam-5963	10	3	the	the	DET
ejpam-5963	10	4	results	result	NOUN
ejpam-5963	10	5	related	relate	VERB
ejpam-5963	10	6	to	to	ADP
ejpam-5963	10	7	stability	stability	NOUN
ejpam-5963	10	8	have	have	AUX
ejpam-5963	10	9	demonstrated	demonstrate	VERB
ejpam-5963	10	10	by	by	ADP
ejpam-5963	10	11	using	use	VERB
ejpam-5963	10	12	ulam	ulam	PROPN
ejpam-5963	10	13	’s	’s	PART
ejpam-5963	10	14	concept	concept	NOUN
ejpam-5963	10	15	.	.	PUNCT
ejpam-5963	11	1	subsequently	subsequently	ADV
ejpam-5963	11	2	,	,	PUNCT
ejpam-5963	11	3	a	a	DET
ejpam-5963	11	4	suitable	suitable	ADJ
ejpam-5963	11	5	example	example	NOUN
ejpam-5963	11	6	is	be	AUX
ejpam-5963	11	7	given	give	VERB
ejpam-5963	11	8	to	to	PART
ejpam-5963	11	9	illustrates	illustrate	VERB
ejpam-5963	11	10	the	the	DET
ejpam-5963	11	11	validity	validity	NOUN
ejpam-5963	11	12	of	of	ADP
ejpam-5963	11	13	this	this	DET
ejpam-5963	11	14	work	work	NOUN
ejpam-5963	11	15	.	.	PUNCT
ejpam-5963	12	1	2020	2020	NUM
ejpam-5963	12	2	mathematics	mathematic	NOUN
ejpam-5963	12	3	subject	subject	NOUN
ejpam-5963	12	4	classifications	classification	NOUN
ejpam-5963	12	5	:	:	PUNCT
ejpam-5963	12	6	26a33	26a33	NUM
ejpam-5963	12	7	,	,	PUNCT
ejpam-5963	12	8	34a08	34a08	NUM
ejpam-5963	12	9	,	,	PUNCT
ejpam-5963	12	10	35a07	35a07	NUM
ejpam-5963	12	11	key	key	ADJ
ejpam-5963	12	12	words	word	NOUN
ejpam-5963	12	13	and	and	CCONJ
ejpam-5963	12	14	phrases	phrase	NOUN
ejpam-5963	12	15	:	:	PUNCT
ejpam-5963	12	16	coupled	couple	VERB
ejpam-5963	12	17	system	system	NOUN
ejpam-5963	12	18	,	,	PUNCT
ejpam-5963	12	19	fractal	fractal	ADJ
ejpam-5963	12	20	fractional	fractional	ADJ
ejpam-5963	12	21	operator	operator	NOUN
ejpam-5963	12	22	,	,	PUNCT
ejpam-5963	12	23	existence	existence	NOUN
ejpam-5963	12	24	,	,	PUNCT
ejpam-5963	12	25	stability	stability	NOUN
ejpam-5963	12	26	,	,	PUNCT
ejpam-5963	12	27	fixed	fix	VERB
ejpam-5963	12	28	point	point	NOUN
ejpam-5963	12	29	theorems	theorem	NOUN
ejpam-5963	12	30	∗corresponding	∗corresponde	VERB
ejpam-5963	12	31	author	author	NOUN
ejpam-5963	12	32	.	.	PUNCT
ejpam-5963	13	1	doi	doi	NOUN
ejpam-5963	13	2	:	:	PUNCT
ejpam-5963	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5963	https://doi.org/10.29020/nybg.ejpam.v18i2.5963	DET
ejpam-5963	13	4	email	email	NOUN
ejpam-5963	13	5	addresses	address	NOUN
ejpam-5963	13	6	:	:	PUNCT
ejpam-5963	14	1	amjadalijc18@gmail.com	amjadalijc18@gmail.com	NOUN
ejpam-5963	14	2	(	(	PUNCT
ejpam-5963	14	3	a.	a.	PROPN
ejpam-5963	14	4	ali	ali	PROPN
ejpam-5963	14	5	)	)	PUNCT
ejpam-5963	14	6	,	,	PUNCT
ejpam-5963	14	7	farhabibi987@gmail.com	farhabibi987@gmail.com	X
ejpam-5963	14	8	(	(	PUNCT
ejpam-5963	14	9	f.bibi	f.bibi	NOUN
ejpam-5963	14	10	)	)	PUNCT
ejpam-5963	14	11	,	,	PUNCT
ejpam-5963	14	12	zeeshan@yuntech.edu.tw	zeeshan@yuntech.edu.tw	PROPN
ejpam-5963	14	13	(	(	PUNCT
ejpam-5963	14	14	z.	z.	PROPN
ejpam-5963	14	15	ali),kshah@psu.edu.sa	ali),kshah@psu.edu.sa	PROPN
ejpam-5963	14	16	(	(	PUNCT
ejpam-5963	14	17	k.	k.	PROPN
ejpam-5963	14	18	shah	shah	PROPN
ejpam-5963	14	19	)	)	PUNCT
ejpam-5963	14	20	,	,	PUNCT
ejpam-5963	14	21	babdallah@psu.edu.sa	babdallah@psu.edu.sa	PROPN
ejpam-5963	14	22	(	(	PUNCT
ejpam-5963	14	23	b.abdalla	b.abdalla	NOUN
ejpam-5963	14	24	)	)	PUNCT
ejpam-5963	14	25	,	,	PUNCT
ejpam-5963	14	26	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-5963	14	27	(	(	PUNCT
ejpam-5963	14	28	t.	t.	NOUN
ejpam-5963	14	29	abdeljawad	abdeljawad	PROPN
ejpam-5963	14	30	)	)	PUNCT
ejpam-5963	14	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5963	14	32	1	1	NUM
ejpam-5963	14	33	copyright	copyright	NOUN
ejpam-5963	14	34	:	:	PUNCT
ejpam-5963	14	35	©	©	PROPN
ejpam-5963	14	36	2025	2025	NUM
ejpam-5963	14	37	the	the	DET
ejpam-5963	14	38	author(s	author(s	NOUN
ejpam-5963	14	39	)	)	PUNCT
ejpam-5963	14	40	.	.	PUNCT
ejpam-5963	15	1	(	(	PUNCT
ejpam-5963	15	2	cc	cc	NOUN
ejpam-5963	15	3	by	by	ADP
ejpam-5963	15	4	-	-	PUNCT
ejpam-5963	15	5	nc	nc	PROPN
ejpam-5963	15	6	4.0	4.0	NUM
ejpam-5963	15	7	)	)	PUNCT
ejpam-5963	15	8	a.	a.	NOUN
ejpam-5963	15	9	ali	ali	PROPN
ejpam-5963	15	10	et	et	PROPN
ejpam-5963	15	11	al	al	PROPN
ejpam-5963	15	12	.	.	PUNCT
ejpam-5963	15	13	/	/	SYM
ejpam-5963	15	14	eur	eur	PROPN
ejpam-5963	15	15	.	.	PUNCT
ejpam-5963	16	1	j.	j.	PROPN
ejpam-5963	16	2	pure	pure	PROPN
ejpam-5963	16	3	appl	appl	PROPN
ejpam-5963	16	4	.	.	PROPN
ejpam-5963	16	5	math	math	PROPN
ejpam-5963	16	6	,	,	PUNCT
ejpam-5963	16	7	18	18	NUM
ejpam-5963	16	8	(	(	PUNCT
ejpam-5963	16	9	2	2	NUM
ejpam-5963	16	10	)	)	PUNCT
ejpam-5963	16	11	(	(	PUNCT
ejpam-5963	16	12	2025	2025	NUM
ejpam-5963	16	13	)	)	PUNCT
ejpam-5963	16	14	,	,	PUNCT
ejpam-5963	16	15	5963	5963	NUM
ejpam-5963	16	16	2	2	NUM
ejpam-5963	16	17	of	of	ADP
ejpam-5963	16	18	19	19	NUM
ejpam-5963	16	19	1	1	NUM
ejpam-5963	16	20	.	.	PUNCT
ejpam-5963	16	21	introduction	introduction	NOUN
ejpam-5963	16	22	the	the	DET
ejpam-5963	16	23	concept	concept	NOUN
ejpam-5963	16	24	of	of	ADP
ejpam-5963	16	25	fractional	fractional	ADJ
ejpam-5963	16	26	calculus	calculus	NOUN
ejpam-5963	16	27	(	(	PUNCT
ejpam-5963	16	28	fc	fc	INTJ
ejpam-5963	16	29	)	)	PUNCT
ejpam-5963	16	30	is	be	AUX
ejpam-5963	16	31	an	an	DET
ejpam-5963	16	32	emerging	emerge	VERB
ejpam-5963	16	33	area	area	NOUN
ejpam-5963	16	34	of	of	ADP
ejpam-5963	16	35	recent	recent	ADJ
ejpam-5963	16	36	research	research	NOUN
ejpam-5963	16	37	due	due	ADP
ejpam-5963	16	38	to	to	ADP
ejpam-5963	16	39	its	its	PRON
ejpam-5963	16	40	significant	significant	ADJ
ejpam-5963	16	41	implementations	implementation	NOUN
ejpam-5963	16	42	in	in	ADP
ejpam-5963	16	43	different	different	ADJ
ejpam-5963	16	44	field	field	NOUN
ejpam-5963	16	45	of	of	ADP
ejpam-5963	16	46	life	life	NOUN
ejpam-5963	16	47	sciences	science	NOUN
ejpam-5963	16	48	,	,	PUNCT
ejpam-5963	16	49	physical	physical	ADJ
ejpam-5963	16	50	sciences	science	NOUN
ejpam-5963	16	51	,	,	PUNCT
ejpam-5963	16	52	and	and	CCONJ
ejpam-5963	16	53	social	social	ADJ
ejpam-5963	16	54	sciences	science	NOUN
ejpam-5963	17	1	[	[	X
ejpam-5963	17	2	1	1	NUM
ejpam-5963	17	3	]	]	PUNCT
ejpam-5963	17	4	.	.	PUNCT
ejpam-5963	18	1	the	the	DET
ejpam-5963	18	2	idea	idea	NOUN
ejpam-5963	18	3	of	of	ADP
ejpam-5963	18	4	fractional	fractional	ADJ
ejpam-5963	18	5	order	order	NOUN
ejpam-5963	18	6	derivative	derivative	ADJ
ejpam-5963	18	7	(	(	PUNCT
ejpam-5963	18	8	fods	fod	NOUN
ejpam-5963	18	9	)	)	PUNCT
ejpam-5963	18	10	was	be	AUX
ejpam-5963	18	11	initiated	initiate	VERB
ejpam-5963	18	12	from	from	ADP
ejpam-5963	18	13	the	the	DET
ejpam-5963	18	14	well	well	ADV
ejpam-5963	18	15	-	-	PUNCT
ejpam-5963	18	16	known	know	VERB
ejpam-5963	18	17	correspondence	correspondence	NOUN
ejpam-5963	18	18	between	between	ADP
ejpam-5963	18	19	leibniz	leibniz	PROPN
ejpam-5963	18	20	’s	’s	PART
ejpam-5963	18	21	and	and	CCONJ
ejpam-5963	18	22	l’hospital	l’hospital	NOUN
ejpam-5963	18	23	in	in	ADP
ejpam-5963	18	24	the	the	DET
ejpam-5963	18	25	seventeenth	seventeenth	ADJ
ejpam-5963	18	26	hundred	hundred	NUM
ejpam-5963	18	27	century	century	NOUN
ejpam-5963	18	28	[	[	X
ejpam-5963	18	29	2	2	NUM
ejpam-5963	18	30	]	]	PUNCT
ejpam-5963	18	31	.	.	PUNCT
ejpam-5963	19	1	the	the	DET
ejpam-5963	19	2	fods	fod	NOUN
ejpam-5963	19	3	have	have	VERB
ejpam-5963	19	4	some	some	DET
ejpam-5963	19	5	advantages	advantage	NOUN
ejpam-5963	19	6	over	over	ADP
ejpam-5963	19	7	the	the	DET
ejpam-5963	19	8	classical	classical	ADJ
ejpam-5963	19	9	derivatives	derivative	NOUN
ejpam-5963	19	10	,	,	PUNCT
ejpam-5963	19	11	these	these	PRON
ejpam-5963	19	12	are	be	AUX
ejpam-5963	19	13	more	more	ADV
ejpam-5963	19	14	flexible	flexible	ADJ
ejpam-5963	19	15	,	,	PUNCT
ejpam-5963	19	16	non	non	ADJ
ejpam-5963	19	17	-	-	ADJ
ejpam-5963	19	18	local	local	ADJ
ejpam-5963	19	19	in	in	ADP
ejpam-5963	19	20	nature	nature	NOUN
ejpam-5963	19	21	,	,	PUNCT
ejpam-5963	19	22	having	have	VERB
ejpam-5963	19	23	memory	memory	NOUN
ejpam-5963	19	24	effects	effect	NOUN
ejpam-5963	19	25	,	,	PUNCT
ejpam-5963	19	26	great	great	ADJ
ejpam-5963	19	27	degree	degree	NOUN
ejpam-5963	19	28	of	of	ADP
ejpam-5963	19	29	freedom	freedom	NOUN
ejpam-5963	19	30	and	and	CCONJ
ejpam-5963	19	31	more	more	ADV
ejpam-5963	19	32	reliable	reliable	ADJ
ejpam-5963	19	33	[	[	X
ejpam-5963	19	34	3	3	NUM
ejpam-5963	19	35	]	]	PUNCT
ejpam-5963	19	36	.	.	PUNCT
ejpam-5963	20	1	fc	fc	PROPN
ejpam-5963	20	2	is	be	AUX
ejpam-5963	20	3	the	the	DET
ejpam-5963	20	4	capability	capability	NOUN
ejpam-5963	20	5	to	to	PART
ejpam-5963	20	6	describe	describe	VERB
ejpam-5963	20	7	the	the	DET
ejpam-5963	20	8	complex	complex	ADJ
ejpam-5963	20	9	dynamics	dynamic	NOUN
ejpam-5963	20	10	of	of	ADP
ejpam-5963	20	11	all	all	DET
ejpam-5963	20	12	those	those	DET
ejpam-5963	20	13	real	real	ADJ
ejpam-5963	20	14	-	-	PUNCT
ejpam-5963	20	15	world	world	NOUN
ejpam-5963	20	16	scenarios	scenario	NOUN
ejpam-5963	20	17	,	,	PUNCT
ejpam-5963	20	18	which	which	PRON
ejpam-5963	20	19	can	can	AUX
ejpam-5963	20	20	not	not	PART
ejpam-5963	20	21	be	be	AUX
ejpam-5963	20	22	formulated	formulate	VERB
ejpam-5963	20	23	by	by	ADP
ejpam-5963	20	24	conventional	conventional	ADJ
ejpam-5963	20	25	calculus	calculus	NOUN
ejpam-5963	20	26	[	[	X
ejpam-5963	20	27	4	4	NUM
ejpam-5963	20	28	]	]	PUNCT
ejpam-5963	20	29	.	.	PUNCT
ejpam-5963	21	1	furthermore	furthermore	ADV
ejpam-5963	21	2	,	,	PUNCT
ejpam-5963	21	3	fc	fc	PROPN
ejpam-5963	21	4	is	be	AUX
ejpam-5963	21	5	substantial	substantial	ADJ
ejpam-5963	21	6	and	and	CCONJ
ejpam-5963	21	7	has	have	VERB
ejpam-5963	21	8	a	a	DET
ejpam-5963	21	9	multifaceted	multifaceted	ADJ
ejpam-5963	21	10	of	of	ADP
ejpam-5963	21	11	applications	application	NOUN
ejpam-5963	21	12	throughout	throughout	ADP
ejpam-5963	21	13	numerous	numerous	ADJ
ejpam-5963	21	14	fields	field	NOUN
ejpam-5963	21	15	,	,	PUNCT
ejpam-5963	21	16	such	such	ADJ
ejpam-5963	21	17	as	as	ADP
ejpam-5963	21	18	finance	finance	NOUN
ejpam-5963	21	19	,	,	PUNCT
ejpam-5963	21	20	bio	bio	NOUN
ejpam-5963	21	21	-	-	ADJ
ejpam-5963	21	22	engineering	engineering	ADJ
ejpam-5963	21	23	,	,	PUNCT
ejpam-5963	21	24	ecology	ecology	NOUN
ejpam-5963	21	25	,	,	PUNCT
ejpam-5963	21	26	physics	physics	NOUN
ejpam-5963	21	27	and	and	CCONJ
ejpam-5963	21	28	graphics	graphic	NOUN
ejpam-5963	21	29	.	.	PUNCT
ejpam-5963	22	1	of	of	ADV
ejpam-5963	22	2	course	course	ADV
ejpam-5963	22	3	one	one	NUM
ejpam-5963	22	4	of	of	ADP
ejpam-5963	22	5	the	the	DET
ejpam-5963	22	6	significant	significant	ADJ
ejpam-5963	22	7	aspects	aspect	NOUN
ejpam-5963	22	8	of	of	ADP
ejpam-5963	22	9	fc	fc	PROPN
ejpam-5963	22	10	is	be	AUX
ejpam-5963	22	11	that	that	SCONJ
ejpam-5963	22	12	it	it	PRON
ejpam-5963	22	13	can	can	AUX
ejpam-5963	22	14	describe	describe	VERB
ejpam-5963	22	15	and	and	CCONJ
ejpam-5963	22	16	investigate	investigate	VERB
ejpam-5963	22	17	the	the	DET
ejpam-5963	22	18	real	real	ADJ
ejpam-5963	22	19	-	-	PUNCT
ejpam-5963	22	20	world	world	NOUN
ejpam-5963	22	21	situation	situation	NOUN
ejpam-5963	22	22	in	in	ADP
ejpam-5963	22	23	the	the	DET
ejpam-5963	22	24	form	form	NOUN
ejpam-5963	22	25	of	of	ADP
ejpam-5963	22	26	fractional	fractional	ADJ
ejpam-5963	22	27	differential	differential	ADJ
ejpam-5963	22	28	equations	equation	NOUN
ejpam-5963	22	29	(	(	PUNCT
ejpam-5963	22	30	fdes	fde	NOUN
ejpam-5963	22	31	)	)	PUNCT
ejpam-5963	22	32	,	,	PUNCT
ejpam-5963	22	33	or	or	CCONJ
ejpam-5963	22	34	system	system	NOUN
ejpam-5963	22	35	of	of	ADP
ejpam-5963	22	36	fdes	fde	NOUN
ejpam-5963	22	37	[	[	X
ejpam-5963	22	38	5	5	NUM
ejpam-5963	22	39	]	]	PUNCT
ejpam-5963	22	40	.	.	PUNCT
ejpam-5963	23	1	researchers	researcher	NOUN
ejpam-5963	23	2	are	be	AUX
ejpam-5963	23	3	interested	interested	ADJ
ejpam-5963	23	4	to	to	PART
ejpam-5963	23	5	investigate	investigate	VERB
ejpam-5963	23	6	fdes	fde	NOUN
ejpam-5963	23	7	to	to	PART
ejpam-5963	23	8	provides	provide	VERB
ejpam-5963	23	9	a	a	DET
ejpam-5963	23	10	powerful	powerful	ADJ
ejpam-5963	23	11	framework	framework	NOUN
ejpam-5963	23	12	for	for	ADP
ejpam-5963	23	13	formulating	formulate	VERB
ejpam-5963	23	14	those	those	DET
ejpam-5963	23	15	dynamical	dynamical	ADJ
ejpam-5963	23	16	phenomena	phenomenon	NOUN
ejpam-5963	23	17	which	which	PRON
ejpam-5963	23	18	is	be	AUX
ejpam-5963	23	19	not	not	PART
ejpam-5963	23	20	describe	describe	NOUN
ejpam-5963	23	21	by	by	ADP
ejpam-5963	23	22	classical	classical	ADJ
ejpam-5963	23	23	order	order	NOUN
ejpam-5963	23	24	des	des	X
ejpam-5963	23	25	accurately	accurately	ADV
ejpam-5963	23	26	[	[	X
ejpam-5963	23	27	1	1	NUM
ejpam-5963	23	28	]	]	PUNCT
ejpam-5963	23	29	.	.	PUNCT
ejpam-5963	24	1	due	due	ADP
ejpam-5963	24	2	to	to	ADP
ejpam-5963	24	3	aforesaid	aforesaid	ADJ
ejpam-5963	24	4	applications	application	NOUN
ejpam-5963	24	5	,	,	PUNCT
ejpam-5963	24	6	mathematicians	mathematician	NOUN
ejpam-5963	24	7	have	have	AUX
ejpam-5963	24	8	been	be	AUX
ejpam-5963	24	9	taken	take	VERB
ejpam-5963	24	10	keen	keen	ADJ
ejpam-5963	24	11	interest	interest	NOUN
ejpam-5963	24	12	to	to	PART
ejpam-5963	24	13	investigate	investigate	VERB
ejpam-5963	24	14	fdes	fde	NOUN
ejpam-5963	24	15	.	.	PUNCT
ejpam-5963	25	1	consequently	consequently	ADV
ejpam-5963	25	2	,	,	PUNCT
ejpam-5963	25	3	researchers	researcher	NOUN
ejpam-5963	25	4	have	have	AUX
ejpam-5963	25	5	well	well	ADV
ejpam-5963	25	6	explored	explore	VERB
ejpam-5963	25	7	the	the	DET
ejpam-5963	25	8	theory	theory	NOUN
ejpam-5963	25	9	of	of	ADP
ejpam-5963	25	10	fdes	fde	NOUN
ejpam-5963	25	11	from	from	ADP
ejpam-5963	25	12	different	different	ADJ
ejpam-5963	25	13	aspects	aspect	NOUN
ejpam-5963	25	14	,	,	PUNCT
ejpam-5963	25	15	such	such	ADJ
ejpam-5963	25	16	as	as	ADP
ejpam-5963	25	17	stability	stability	NOUN
ejpam-5963	25	18	analysis	analysis	NOUN
ejpam-5963	25	19	,	,	PUNCT
ejpam-5963	25	20	numerical	numerical	ADJ
ejpam-5963	25	21	approximation	approximation	NOUN
ejpam-5963	25	22	,	,	PUNCT
ejpam-5963	25	23	and	and	CCONJ
ejpam-5963	25	24	existence	existence	NOUN
ejpam-5963	25	25	of	of	ADP
ejpam-5963	25	26	solution	solution	NOUN
ejpam-5963	25	27	,	,	PUNCT
ejpam-5963	25	28	and	and	CCONJ
ejpam-5963	25	29	published	publish	VERB
ejpam-5963	25	30	plenty	plenty	NOUN
ejpam-5963	25	31	of	of	ADP
ejpam-5963	25	32	books	book	NOUN
ejpam-5963	25	33	,	,	PUNCT
ejpam-5963	25	34	articles	article	NOUN
ejpam-5963	25	35	,	,	PUNCT
ejpam-5963	25	36	and	and	CCONJ
ejpam-5963	25	37	manographs	manograph	VERB
ejpam-5963	25	38	[	[	X
ejpam-5963	25	39	6	6	NUM
ejpam-5963	25	40	]	]	PUNCT
ejpam-5963	25	41	.	.	PUNCT
ejpam-5963	26	1	meanwhile	meanwhile	ADV
ejpam-5963	26	2	,	,	PUNCT
ejpam-5963	26	3	the	the	DET
ejpam-5963	26	4	researchers	researcher	NOUN
ejpam-5963	26	5	introduced	introduce	VERB
ejpam-5963	26	6	different	different	ADJ
ejpam-5963	26	7	types	type	NOUN
ejpam-5963	26	8	of	of	ADP
ejpam-5963	26	9	fractional	fractional	ADJ
ejpam-5963	26	10	operators	operator	NOUN
ejpam-5963	26	11	(	(	PUNCT
ejpam-5963	26	12	fos	fos	NOUN
ejpam-5963	26	13	)	)	PUNCT
ejpam-5963	26	14	,	,	PUNCT
ejpam-5963	26	15	such	such	ADJ
ejpam-5963	26	16	as	as	ADP
ejpam-5963	26	17	the	the	DET
ejpam-5963	26	18	conformable	conformable	ADJ
ejpam-5963	26	19	fractional	fractional	ADJ
ejpam-5963	26	20	derivatives	derivative	NOUN
ejpam-5963	26	21	(	(	PUNCT
ejpam-5963	26	22	cfds	cfds	NOUN
ejpam-5963	26	23	)	)	PUNCT
ejpam-5963	26	24	,	,	PUNCT
ejpam-5963	26	25	the	the	DET
ejpam-5963	26	26	riemann	riemann	PROPN
ejpam-5963	26	27	-	-	PUNCT
ejpam-5963	26	28	liouville	liouville	VERB
ejpam-5963	26	29	fractional	fractional	ADJ
ejpam-5963	26	30	derivatives	derivative	NOUN
ejpam-5963	26	31	(	(	PUNCT
ejpam-5963	26	32	rlfds	rlfds	PROPN
ejpam-5963	26	33	)	)	PUNCT
ejpam-5963	26	34	,	,	PUNCT
ejpam-5963	26	35	the	the	DET
ejpam-5963	26	36	caputo	caputo	PROPN
ejpam-5963	26	37	fractional	fractional	PROPN
ejpam-5963	26	38	derivative	derivative	PROPN
ejpam-5963	26	39	(	(	PUNCT
ejpam-5963	26	40	cfd	cfd	NOUN
ejpam-5963	26	41	)	)	PUNCT
ejpam-5963	26	42	,	,	PUNCT
ejpam-5963	26	43	the	the	DET
ejpam-5963	26	44	grunwald	grunwald	NOUN
ejpam-5963	26	45	-	-	PUNCT
ejpam-5963	26	46	letnikov	letnikov	NOUN
ejpam-5963	26	47	fractional	fractional	ADJ
ejpam-5963	26	48	derivative	derivative	NOUN
ejpam-5963	26	49	(	(	PUNCT
ejpam-5963	26	50	glfd	glfd	NOUN
ejpam-5963	26	51	)	)	PUNCT
ejpam-5963	27	1	[	[	X
ejpam-5963	27	2	7	7	NUM
ejpam-5963	27	3	]	]	PUNCT
ejpam-5963	27	4	,	,	PUNCT
ejpam-5963	27	5	non	non	ADJ
ejpam-5963	27	6	singular	singular	ADJ
ejpam-5963	27	7	fractional	fractional	ADJ
ejpam-5963	27	8	derivatives	derivative	NOUN
ejpam-5963	27	9	(	(	PUNCT
ejpam-5963	27	10	nsfds	nsfds	NOUN
ejpam-5963	27	11	)	)	PUNCT
ejpam-5963	27	12	like	like	ADP
ejpam-5963	27	13	atangana	atangana	PROPN
ejpam-5963	27	14	-	-	PUNCT
ejpam-5963	27	15	baleanu	baleanu	ADJ
ejpam-5963	27	16	fractional	fractional	ADJ
ejpam-5963	27	17	derivative	derivative	NOUN
ejpam-5963	27	18	(	(	PUNCT
ejpam-5963	27	19	abfd	abfd	PROPN
ejpam-5963	27	20	)	)	PUNCT
ejpam-5963	27	21	,	,	PUNCT
ejpam-5963	27	22	caputo	caputo	PROPN
ejpam-5963	27	23	-	-	PUNCT
ejpam-5963	27	24	fabrizio	fabrizio	PROPN
ejpam-5963	27	25	fractional	fractional	ADJ
ejpam-5963	27	26	derivative	derivative	NOUN
ejpam-5963	27	27	(	(	PUNCT
ejpam-5963	27	28	cffd	cffd	NOUN
ejpam-5963	27	29	)	)	PUNCT
ejpam-5963	27	30	,	,	PUNCT
ejpam-5963	27	31	etc	etc	X
ejpam-5963	28	1	[	[	X
ejpam-5963	28	2	8	8	NUM
ejpam-5963	28	3	]	]	PUNCT
ejpam-5963	28	4	.	.	PUNCT
ejpam-5963	29	1	the	the	DET
ejpam-5963	29	2	theory	theory	NOUN
ejpam-5963	29	3	of	of	ADP
ejpam-5963	29	4	fractals	fractal	NOUN
ejpam-5963	29	5	derivative	derivative	ADJ
ejpam-5963	29	6	is	be	AUX
ejpam-5963	29	7	old	old	ADJ
ejpam-5963	29	8	as	as	ADP
ejpam-5963	29	9	the	the	DET
ejpam-5963	29	10	fc	fc	PROPN
ejpam-5963	29	11	.	.	PUNCT
ejpam-5963	30	1	in	in	ADP
ejpam-5963	30	2	2017	2017	NUM
ejpam-5963	30	3	,	,	PUNCT
ejpam-5963	30	4	researchers	researcher	NOUN
ejpam-5963	30	5	have	have	AUX
ejpam-5963	30	6	extended	extend	VERB
ejpam-5963	30	7	the	the	DET
ejpam-5963	30	8	concepts	concept	NOUN
ejpam-5963	30	9	of	of	ADP
ejpam-5963	30	10	fractional	fractional	ADJ
ejpam-5963	30	11	derivatives	derivative	NOUN
ejpam-5963	30	12	to	to	PART
ejpam-5963	30	13	fractal	fractal	VERB
ejpam-5963	30	14	and	and	CCONJ
ejpam-5963	30	15	introduced	introduce	VERB
ejpam-5963	30	16	fractals	fractal	NOUN
ejpam-5963	30	17	fractional	fractional	ADJ
ejpam-5963	30	18	derivatives	derivative	NOUN
ejpam-5963	30	19	(	(	PUNCT
ejpam-5963	30	20	ffds	ffds	NOUN
ejpam-5963	30	21	)	)	PUNCT
ejpam-5963	31	1	[	[	X
ejpam-5963	31	2	9	9	NUM
ejpam-5963	31	3	]	]	PUNCT
ejpam-5963	31	4	.	.	PUNCT
ejpam-5963	32	1	the	the	DET
ejpam-5963	32	2	concept	concept	NOUN
ejpam-5963	32	3	of	of	ADP
ejpam-5963	32	4	this	this	DET
ejpam-5963	32	5	new	new	ADJ
ejpam-5963	32	6	type	type	NOUN
ejpam-5963	32	7	of	of	ADP
ejpam-5963	32	8	ffds	ffds	NOUN
ejpam-5963	32	9	was	be	AUX
ejpam-5963	32	10	introduced	introduce	VERB
ejpam-5963	32	11	by	by	ADP
ejpam-5963	32	12	atangana	atangana	NOUN
ejpam-5963	33	1	[	[	X
ejpam-5963	33	2	10	10	NUM
ejpam-5963	33	3	]	]	PUNCT
ejpam-5963	33	4	.	.	PUNCT
ejpam-5963	34	1	this	this	PRON
ejpam-5963	34	2	mentioned	mention	VERB
ejpam-5963	34	3	class	class	NOUN
ejpam-5963	34	4	of	of	ADP
ejpam-5963	34	5	ffds	ffds	ADJ
ejpam-5963	34	6	consist	consist	NOUN
ejpam-5963	34	7	of	of	ADP
ejpam-5963	34	8	two	two	NUM
ejpam-5963	34	9	types	type	NOUN
ejpam-5963	34	10	of	of	ADP
ejpam-5963	34	11	orders	order	NOUN
ejpam-5963	34	12	,	,	PUNCT
ejpam-5963	34	13	the	the	DET
ejpam-5963	34	14	first	first	ADJ
ejpam-5963	34	15	is	be	AUX
ejpam-5963	34	16	usual	usual	ADJ
ejpam-5963	34	17	fractional	fractional	ADJ
ejpam-5963	34	18	order	order	NOUN
ejpam-5963	34	19	,	,	PUNCT
ejpam-5963	34	20	while	while	SCONJ
ejpam-5963	34	21	the	the	DET
ejpam-5963	34	22	second	second	ADJ
ejpam-5963	34	23	part	part	NOUN
ejpam-5963	34	24	is	be	AUX
ejpam-5963	34	25	known	know	VERB
ejpam-5963	34	26	as	as	ADP
ejpam-5963	34	27	fractal	fractal	ADJ
ejpam-5963	34	28	dimension	dimension	NOUN
ejpam-5963	34	29	.	.	PUNCT
ejpam-5963	35	1	an	an	DET
ejpam-5963	35	2	important	important	ADJ
ejpam-5963	35	3	aspect	aspect	NOUN
ejpam-5963	35	4	of	of	ADP
ejpam-5963	35	5	the	the	DET
ejpam-5963	35	6	consider	consider	VERB
ejpam-5963	35	7	derivatives	derivative	NOUN
ejpam-5963	35	8	is	be	AUX
ejpam-5963	35	9	that	that	SCONJ
ejpam-5963	35	10	they	they	PRON
ejpam-5963	35	11	can	can	AUX
ejpam-5963	35	12	investigate	investigate	VERB
ejpam-5963	35	13	both	both	DET
ejpam-5963	35	14	fods	fod	NOUN
ejpam-5963	35	15	and	and	CCONJ
ejpam-5963	35	16	ffds	ffd	VERB
ejpam-5963	35	17	at	at	ADP
ejpam-5963	35	18	same	same	ADJ
ejpam-5963	35	19	stage	stage	NOUN
ejpam-5963	35	20	simultaneously	simultaneously	ADV
ejpam-5963	35	21	in	in	ADP
ejpam-5963	35	22	the	the	DET
ejpam-5963	35	23	same	same	ADJ
ejpam-5963	35	24	problem	problem	NOUN
ejpam-5963	35	25	[	[	X
ejpam-5963	35	26	11	11	NUM
ejpam-5963	35	27	]	]	PUNCT
ejpam-5963	35	28	.	.	PUNCT
ejpam-5963	36	1	the	the	DET
ejpam-5963	36	2	ffds	ffds	NOUN
ejpam-5963	36	3	have	have	AUX
ejpam-5963	36	4	advanced	advance	VERB
ejpam-5963	36	5	over	over	ADP
ejpam-5963	36	6	the	the	DET
ejpam-5963	36	7	traditional	traditional	ADJ
ejpam-5963	36	8	fods	fod	NOUN
ejpam-5963	36	9	to	to	ADP
ejpam-5963	36	10	understanding	understand	VERB
ejpam-5963	36	11	their	their	PRON
ejpam-5963	36	12	geometrical	geometrical	ADJ
ejpam-5963	36	13	meaning	meaning	NOUN
ejpam-5963	36	14	as	as	ADV
ejpam-5963	36	15	well	well	ADV
ejpam-5963	36	16	as	as	ADP
ejpam-5963	36	17	relation	relation	NOUN
ejpam-5963	36	18	with	with	ADP
ejpam-5963	36	19	them	they	PRON
ejpam-5963	37	1	[	[	X
ejpam-5963	37	2	12	12	NUM
ejpam-5963	37	3	]	]	PUNCT
ejpam-5963	37	4	.	.	PUNCT
ejpam-5963	38	1	the	the	DET
ejpam-5963	38	2	ffds	ffds	NOUN
ejpam-5963	38	3	have	have	VERB
ejpam-5963	38	4	very	very	ADV
ejpam-5963	38	5	useful	useful	ADJ
ejpam-5963	38	6	consequences	consequence	NOUN
ejpam-5963	38	7	in	in	ADP
ejpam-5963	38	8	situation	situation	NOUN
ejpam-5963	38	9	,	,	PUNCT
ejpam-5963	38	10	where	where	SCONJ
ejpam-5963	38	11	discontinuity	discontinuity	NOUN
ejpam-5963	38	12	,	,	PUNCT
ejpam-5963	38	13	power	power	NOUN
ejpam-5963	38	14	-	-	PUNCT
ejpam-5963	38	15	law	law	NOUN
ejpam-5963	38	16	,	,	PUNCT
ejpam-5963	38	17	and	and	CCONJ
ejpam-5963	38	18	crossover	crossover	VERB
ejpam-5963	38	19	occur	occur	VERB
ejpam-5963	38	20	,	,	PUNCT
ejpam-5963	38	21	or	or	CCONJ
ejpam-5963	38	22	decaying	decay	VERB
ejpam-5963	38	23	memory	memory	NOUN
ejpam-5963	38	24	fail	fail	VERB
ejpam-5963	38	25	to	to	PART
ejpam-5963	38	26	capture	capture	VERB
ejpam-5963	38	27	the	the	DET
ejpam-5963	38	28	complex	complex	ADJ
ejpam-5963	38	29	behaviors	behavior	NOUN
ejpam-5963	38	30	[	[	X
ejpam-5963	38	31	13	13	NUM
ejpam-5963	38	32	]	]	PUNCT
ejpam-5963	38	33	.	.	PUNCT
ejpam-5963	39	1	the	the	DET
ejpam-5963	39	2	concerned	concerned	ADJ
ejpam-5963	39	3	ffds	ffds	NOUN
ejpam-5963	39	4	has	have	VERB
ejpam-5963	39	5	a	a	DET
ejpam-5963	39	6	accomplished	accomplished	ADJ
ejpam-5963	39	7	form	form	NOUN
ejpam-5963	39	8	of	of	ADP
ejpam-5963	39	9	fods	fod	NOUN
ejpam-5963	39	10	which	which	PRON
ejpam-5963	39	11	combined	combine	VERB
ejpam-5963	39	12	both	both	CCONJ
ejpam-5963	39	13	fractal	fractal	ADJ
ejpam-5963	39	14	and	and	CCONJ
ejpam-5963	39	15	fractional	fractional	ADJ
ejpam-5963	39	16	to	to	ADP
ejpam-5963	39	17	more	more	ADV
ejpam-5963	39	18	compact	compact	ADJ
ejpam-5963	39	19	form	form	NOUN
ejpam-5963	39	20	is	be	AUX
ejpam-5963	39	21	known	know	VERB
ejpam-5963	39	22	as	as	ADP
ejpam-5963	39	23	fractal	fractal	ADJ
ejpam-5963	39	24	fractional	fractional	ADJ
ejpam-5963	39	25	calculus	calculus	NOUN
ejpam-5963	39	26	[	[	X
ejpam-5963	39	27	14	14	NUM
ejpam-5963	39	28	]	]	PUNCT
ejpam-5963	39	29	.	.	PUNCT
ejpam-5963	40	1	this	this	DET
ejpam-5963	40	2	newly	newly	ADV
ejpam-5963	40	3	emerging	emerge	VERB
ejpam-5963	40	4	area	area	NOUN
ejpam-5963	40	5	of	of	ADP
ejpam-5963	40	6	research	research	NOUN
ejpam-5963	40	7	has	have	AUX
ejpam-5963	40	8	attracted	attract	VERB
ejpam-5963	40	9	the	the	DET
ejpam-5963	40	10	attention	attention	NOUN
ejpam-5963	40	11	of	of	ADP
ejpam-5963	40	12	researchers	researcher	NOUN
ejpam-5963	40	13	to	to	PART
ejpam-5963	40	14	investigate	investigate	VERB
ejpam-5963	40	15	various	various	ADJ
ejpam-5963	40	16	features	feature	NOUN
ejpam-5963	40	17	[	[	X
ejpam-5963	40	18	15	15	NUM
ejpam-5963	40	19	]	]	PUNCT
ejpam-5963	40	20	.	.	PUNCT
ejpam-5963	41	1	the	the	DET
ejpam-5963	41	2	coupled	couple	VERB
ejpam-5963	41	3	system	system	NOUN
ejpam-5963	41	4	of	of	ADP
ejpam-5963	41	5	fdes	fde	NOUN
ejpam-5963	41	6	have	have	AUX
ejpam-5963	41	7	been	be	AUX
ejpam-5963	41	8	studied	study	VERB
ejpam-5963	41	9	by	by	ADP
ejpam-5963	41	10	researchers	researcher	NOUN
ejpam-5963	41	11	from	from	ADP
ejpam-5963	41	12	various	various	ADJ
ejpam-5963	41	13	aspects	aspect	NOUN
ejpam-5963	41	14	and	and	CCONJ
ejpam-5963	41	15	furnish	furnish	VERB
ejpam-5963	41	16	theory	theory	NOUN
ejpam-5963	41	17	up	up	ADP
ejpam-5963	41	18	-	-	PUNCT
ejpam-5963	41	19	to	to	ADP
ejpam-5963	41	20	large	large	ADJ
ejpam-5963	41	21	extend	extend	NOUN
ejpam-5963	41	22	in	in	ADP
ejpam-5963	41	23	the	the	DET
ejpam-5963	41	24	sense	sense	NOUN
ejpam-5963	41	25	of	of	ADP
ejpam-5963	41	26	ordinary	ordinary	ADJ
ejpam-5963	41	27	fods	fod	NOUN
ejpam-5963	41	28	,	,	PUNCT
ejpam-5963	41	29	such	such	ADJ
ejpam-5963	41	30	as	as	ADP
ejpam-5963	41	31	existence	existence	NOUN
ejpam-5963	41	32	,	,	PUNCT
ejpam-5963	41	33	numerical	numerical	ADJ
ejpam-5963	41	34	solution	solution	NOUN
ejpam-5963	41	35	and	and	CCONJ
ejpam-5963	41	36	stability	stability	NOUN
ejpam-5963	41	37	analysis	analysis	NOUN
ejpam-5963	41	38	[	[	X
ejpam-5963	41	39	16	16	NUM
ejpam-5963	41	40	]	]	PUNCT
ejpam-5963	41	41	.	.	PUNCT
ejpam-5963	42	1	to	to	PART
ejpam-5963	42	2	best	good	ADJ
ejpam-5963	42	3	to	to	ADP
ejpam-5963	42	4	our	our	PRON
ejpam-5963	42	5	knowledge	knowledge	NOUN
ejpam-5963	42	6	the	the	PRON
ejpam-5963	42	7	consider	consider	VERB
ejpam-5963	42	8	type	type	NOUN
ejpam-5963	42	9	of	of	ADP
ejpam-5963	42	10	coupled	couple	VERB
ejpam-5963	42	11	system	system	NOUN
ejpam-5963	42	12	of	of	ADP
ejpam-5963	42	13	ffdes	ffde	NOUN
ejpam-5963	42	14	are	be	AUX
ejpam-5963	42	15	very	very	ADV
ejpam-5963	42	16	rarely	rarely	ADV
ejpam-5963	42	17	investigated	investigate	VERB
ejpam-5963	42	18	by	by	ADP
ejpam-5963	42	19	researchers	researcher	NOUN
ejpam-5963	42	20	.	.	PUNCT
ejpam-5963	43	1	in	in	ADP
ejpam-5963	43	2	this	this	DET
ejpam-5963	43	3	context	context	NOUN
ejpam-5963	43	4	,	,	PUNCT
ejpam-5963	43	5	the	the	DET
ejpam-5963	43	6	aforementioned	aforementioned	ADJ
ejpam-5963	43	7	research	research	NOUN
ejpam-5963	43	8	directions	direction	NOUN
ejpam-5963	43	9	needs	need	VERB
ejpam-5963	43	10	further	further	ADJ
ejpam-5963	43	11	attention	attention	NOUN
ejpam-5963	43	12	of	of	ADP
ejpam-5963	43	13	researchers	researcher	NOUN
ejpam-5963	43	14	to	to	PART
ejpam-5963	43	15	explore	explore	VERB
ejpam-5963	43	16	a.	a.	PROPN
ejpam-5963	43	17	ali	ali	PROPN
ejpam-5963	43	18	et	et	PROPN
ejpam-5963	43	19	al	al	PROPN
ejpam-5963	43	20	.	.	PUNCT
ejpam-5963	43	21	/	/	SYM
ejpam-5963	43	22	eur	eur	PROPN
ejpam-5963	43	23	.	.	PUNCT
ejpam-5963	44	1	j.	j.	PROPN
ejpam-5963	44	2	pure	pure	PROPN
ejpam-5963	44	3	appl	appl	PROPN
ejpam-5963	44	4	.	.	PROPN
ejpam-5963	44	5	math	math	PROPN
ejpam-5963	44	6	,	,	PUNCT
ejpam-5963	44	7	18	18	NUM
ejpam-5963	44	8	(	(	PUNCT
ejpam-5963	44	9	2	2	NUM
ejpam-5963	44	10	)	)	PUNCT
ejpam-5963	44	11	(	(	PUNCT
ejpam-5963	44	12	2025	2025	NUM
ejpam-5963	44	13	)	)	PUNCT
ejpam-5963	44	14	,	,	PUNCT
ejpam-5963	44	15	5963	5963	NUM
ejpam-5963	44	16	3	3	NUM
ejpam-5963	44	17	of	of	ADP
ejpam-5963	44	18	19	19	NUM
ejpam-5963	44	19	this	this	DET
ejpam-5963	44	20	theory	theory	NOUN
ejpam-5963	44	21	.	.	PUNCT
ejpam-5963	45	1	it	it	PRON
ejpam-5963	45	2	is	be	AUX
ejpam-5963	45	3	worthy	worthy	ADJ
ejpam-5963	45	4	to	to	PART
ejpam-5963	45	5	highlight	highlight	VERB
ejpam-5963	45	6	the	the	DET
ejpam-5963	45	7	key	key	ADJ
ejpam-5963	45	8	features	feature	NOUN
ejpam-5963	45	9	of	of	ADP
ejpam-5963	45	10	underlying	underlie	VERB
ejpam-5963	45	11	coupled	couple	VERB
ejpam-5963	45	12	system	system	NOUN
ejpam-5963	45	13	of	of	ADP
ejpam-5963	45	14	ffdes	ffde	NOUN
ejpam-5963	45	15	,	,	PUNCT
ejpam-5963	45	16	that	that	SCONJ
ejpam-5963	45	17	in	in	ADP
ejpam-5963	45	18	some	some	DET
ejpam-5963	45	19	circumstances	circumstance	NOUN
ejpam-5963	45	20	,	,	PUNCT
ejpam-5963	45	21	the	the	DET
ejpam-5963	45	22	actual	actual	ADJ
ejpam-5963	45	23	dynamics	dynamic	NOUN
ejpam-5963	45	24	behaviors	behavior	NOUN
ejpam-5963	45	25	of	of	ADP
ejpam-5963	45	26	phenomena	phenomenon	NOUN
ejpam-5963	45	27	can	can	AUX
ejpam-5963	45	28	not	not	PART
ejpam-5963	45	29	be	be	AUX
ejpam-5963	45	30	expressed	express	VERB
ejpam-5963	45	31	with	with	ADP
ejpam-5963	45	32	ordinary	ordinary	ADJ
ejpam-5963	45	33	tools	tool	NOUN
ejpam-5963	45	34	of	of	ADP
ejpam-5963	45	35	fdes	fde	NOUN
ejpam-5963	45	36	[	[	X
ejpam-5963	45	37	17	17	NUM
ejpam-5963	45	38	]	]	PUNCT
ejpam-5963	45	39	.	.	PUNCT
ejpam-5963	46	1	while	while	SCONJ
ejpam-5963	46	2	,	,	PUNCT
ejpam-5963	46	3	the	the	DET
ejpam-5963	46	4	proposed	propose	VERB
ejpam-5963	46	5	tools	tool	NOUN
ejpam-5963	46	6	of	of	ADP
ejpam-5963	46	7	coupled	couple	VERB
ejpam-5963	46	8	system	system	NOUN
ejpam-5963	46	9	of	of	ADP
ejpam-5963	46	10	ffdes	ffde	NOUN
ejpam-5963	46	11	are	be	AUX
ejpam-5963	46	12	remarkable	remarkable	ADJ
ejpam-5963	46	13	achievement	achievement	NOUN
ejpam-5963	46	14	for	for	ADP
ejpam-5963	46	15	investigating	investigate	VERB
ejpam-5963	46	16	such	such	ADJ
ejpam-5963	46	17	problems	problem	NOUN
ejpam-5963	46	18	.	.	PUNCT
ejpam-5963	47	1	some	some	DET
ejpam-5963	47	2	well	well	ADV
ejpam-5963	47	3	-	-	PUNCT
ejpam-5963	47	4	known	know	VERB
ejpam-5963	47	5	examples	example	NOUN
ejpam-5963	47	6	of	of	ADP
ejpam-5963	47	7	coupled	couple	VERB
ejpam-5963	47	8	systems	system	NOUN
ejpam-5963	47	9	are	be	AUX
ejpam-5963	47	10	host	host	NOUN
ejpam-5963	47	11	-	-	PUNCT
ejpam-5963	47	12	parasite	parasite	NOUN
ejpam-5963	47	13	,	,	PUNCT
ejpam-5963	47	14	plantpollinator	plantpollinator	NOUN
ejpam-5963	47	15	of	of	ADP
ejpam-5963	47	16	biological	biological	ADJ
ejpam-5963	47	17	process	process	NOUN
ejpam-5963	47	18	,	,	PUNCT
ejpam-5963	47	19	grass	grass	NOUN
ejpam-5963	47	20	land	land	NOUN
ejpam-5963	47	21	-	-	PUNCT
ejpam-5963	47	22	fire	fire	NOUN
ejpam-5963	47	23	,	,	PUNCT
ejpam-5963	47	24	lorenz	lorenz	PROPN
ejpam-5963	47	25	model	model	NOUN
ejpam-5963	48	1	[	[	X
ejpam-5963	48	2	18	18	NUM
ejpam-5963	48	3	]	]	X
ejpam-5963	48	4	,	,	PUNCT
ejpam-5963	48	5	atmosphere	atmosphere	NOUN
ejpam-5963	48	6	-	-	PUNCT
ejpam-5963	48	7	ocean	ocean	NOUN
ejpam-5963	48	8	current	current	NOUN
ejpam-5963	48	9	and	and	CCONJ
ejpam-5963	48	10	tides	tide	NOUN
ejpam-5963	48	11	-	-	PUNCT
ejpam-5963	48	12	coastal	coastal	ADJ
ejpam-5963	48	13	erosion	erosion	NOUN
ejpam-5963	48	14	are	be	AUX
ejpam-5963	48	15	examples	example	NOUN
ejpam-5963	48	16	of	of	ADP
ejpam-5963	48	17	physical	physical	ADJ
ejpam-5963	48	18	systems	system	NOUN
ejpam-5963	48	19	[	[	X
ejpam-5963	48	20	19	19	NUM
ejpam-5963	48	21	]	]	PUNCT
ejpam-5963	48	22	.	.	PUNCT
ejpam-5963	49	1	according	accord	VERB
ejpam-5963	49	2	to	to	ADP
ejpam-5963	49	3	our	our	PRON
ejpam-5963	49	4	study	study	NOUN
ejpam-5963	49	5	the	the	DET
ejpam-5963	49	6	coupled	couple	VERB
ejpam-5963	49	7	system	system	NOUN
ejpam-5963	49	8	of	of	ADP
ejpam-5963	49	9	fdes	fde	NOUN
ejpam-5963	49	10	in	in	ADP
ejpam-5963	49	11	sense	sense	NOUN
ejpam-5963	49	12	of	of	ADP
ejpam-5963	49	13	fractal	fractal	ADJ
ejpam-5963	49	14	derivatives	derivative	NOUN
ejpam-5963	49	15	are	be	AUX
ejpam-5963	49	16	very	very	ADV
ejpam-5963	49	17	rarely	rarely	ADV
ejpam-5963	49	18	studied	study	VERB
ejpam-5963	49	19	by	by	ADP
ejpam-5963	49	20	researchers	researcher	NOUN
ejpam-5963	49	21	and	and	CCONJ
ejpam-5963	49	22	need	need	VERB
ejpam-5963	49	23	more	more	ADJ
ejpam-5963	49	24	attention	attention	NOUN
ejpam-5963	49	25	.	.	PUNCT
ejpam-5963	50	1	therefore	therefore	ADV
ejpam-5963	50	2	,	,	PUNCT
ejpam-5963	50	3	we	we	PRON
ejpam-5963	50	4	investigate	investigate	VERB
ejpam-5963	50	5	the	the	DET
ejpam-5963	50	6	coupled	couple	VERB
ejpam-5963	50	7	system	system	NOUN
ejpam-5963	50	8	of	of	ADP
ejpam-5963	50	9	fdes	fde	NOUN
ejpam-5963	50	10	in	in	ADP
ejpam-5963	50	11	sense	sense	NOUN
ejpam-5963	50	12	of	of	ADP
ejpam-5963	50	13	fractal	fractal	ADJ
ejpam-5963	50	14	operator	operator	NOUN
ejpam-5963	50	15	.	.	PUNCT
ejpam-5963	51	1	researchers	researcher	NOUN
ejpam-5963	51	2	from	from	ADP
ejpam-5963	51	3	different	different	ADJ
ejpam-5963	51	4	fields	field	NOUN
ejpam-5963	51	5	are	be	AUX
ejpam-5963	51	6	interested	interested	ADJ
ejpam-5963	51	7	to	to	PART
ejpam-5963	51	8	investigate	investigate	VERB
ejpam-5963	51	9	numerous	numerous	ADJ
ejpam-5963	51	10	aspects	aspect	NOUN
ejpam-5963	51	11	as	as	SCONJ
ejpam-5963	51	12	this	this	DET
ejpam-5963	51	13	theory	theory	NOUN
ejpam-5963	51	14	has	have	VERB
ejpam-5963	51	15	the	the	DET
ejpam-5963	51	16	potential	potential	NOUN
ejpam-5963	51	17	to	to	PART
ejpam-5963	51	18	address	address	VERB
ejpam-5963	51	19	a	a	DET
ejpam-5963	51	20	variety	variety	NOUN
ejpam-5963	51	21	of	of	ADP
ejpam-5963	51	22	issues	issue	NOUN
ejpam-5963	51	23	and	and	CCONJ
ejpam-5963	51	24	is	be	AUX
ejpam-5963	51	25	a	a	DET
ejpam-5963	51	26	fast	fast	ADJ
ejpam-5963	51	27	growing	grow	VERB
ejpam-5963	51	28	field	field	NOUN
ejpam-5963	51	29	of	of	ADP
ejpam-5963	51	30	research	research	NOUN
ejpam-5963	51	31	[	[	X
ejpam-5963	51	32	20	20	NUM
ejpam-5963	51	33	]	]	PUNCT
ejpam-5963	51	34	.	.	PUNCT
ejpam-5963	52	1	there	there	PRON
ejpam-5963	52	2	are	be	VERB
ejpam-5963	52	3	many	many	ADJ
ejpam-5963	52	4	methods	method	NOUN
ejpam-5963	52	5	to	to	PART
ejpam-5963	52	6	develop	develop	VERB
ejpam-5963	52	7	the	the	DET
ejpam-5963	52	8	eus	eus	NOUN
ejpam-5963	52	9	of	of	ADP
ejpam-5963	52	10	ffdes	ffde	NOUN
ejpam-5963	52	11	,	,	PUNCT
ejpam-5963	52	12	such	such	ADJ
ejpam-5963	52	13	as	as	ADP
ejpam-5963	52	14	fpt	fpt	PROPN
ejpam-5963	52	15	and	and	CCONJ
ejpam-5963	52	16	topological	topological	ADJ
ejpam-5963	52	17	degree	degree	NOUN
ejpam-5963	52	18	theory	theory	NOUN
ejpam-5963	52	19	[	[	X
ejpam-5963	52	20	21	21	NUM
ejpam-5963	52	21	]	]	PUNCT
ejpam-5963	52	22	.	.	PUNCT
ejpam-5963	53	1	another	another	DET
ejpam-5963	53	2	subsequent	subsequent	ADJ
ejpam-5963	53	3	aspect	aspect	NOUN
ejpam-5963	53	4	of	of	ADP
ejpam-5963	53	5	fractal	fractal	ADJ
ejpam-5963	53	6	fractional	fractional	ADJ
ejpam-5963	53	7	calculus	calculus	NOUN
ejpam-5963	53	8	is	be	AUX
ejpam-5963	53	9	investigating	investigate	VERB
ejpam-5963	53	10	stability	stability	NOUN
ejpam-5963	53	11	analysis	analysis	NOUN
ejpam-5963	53	12	of	of	ADP
ejpam-5963	53	13	initial	initial	ADJ
ejpam-5963	53	14	value	value	NOUN
ejpam-5963	53	15	problems	problem	NOUN
ejpam-5963	53	16	of	of	ADP
ejpam-5963	53	17	ffdes	ffde	NOUN
ejpam-5963	53	18	.	.	PUNCT
ejpam-5963	54	1	stability	stability	NOUN
ejpam-5963	54	2	analysis	analysis	NOUN
ejpam-5963	54	3	is	be	AUX
ejpam-5963	54	4	a	a	DET
ejpam-5963	54	5	technique	technique	NOUN
ejpam-5963	54	6	,	,	PUNCT
ejpam-5963	54	7	used	use	VERB
ejpam-5963	54	8	to	to	PART
ejpam-5963	54	9	find	find	VERB
ejpam-5963	54	10	the	the	DET
ejpam-5963	54	11	ability	ability	NOUN
ejpam-5963	54	12	of	of	ADP
ejpam-5963	54	13	the	the	DET
ejpam-5963	54	14	system	system	NOUN
ejpam-5963	54	15	to	to	PART
ejpam-5963	54	16	get	get	VERB
ejpam-5963	54	17	back	back	ADV
ejpam-5963	54	18	to	to	ADP
ejpam-5963	54	19	its	its	PRON
ejpam-5963	54	20	equilibrium	equilibrium	NOUN
ejpam-5963	54	21	position	position	NOUN
ejpam-5963	54	22	after	after	ADP
ejpam-5963	54	23	introducing	introduce	VERB
ejpam-5963	54	24	some	some	DET
ejpam-5963	54	25	changes	change	NOUN
ejpam-5963	54	26	.	.	PUNCT
ejpam-5963	55	1	there	there	PRON
ejpam-5963	55	2	are	be	VERB
ejpam-5963	55	3	different	different	ADJ
ejpam-5963	55	4	kinds	kind	NOUN
ejpam-5963	55	5	of	of	ADP
ejpam-5963	55	6	stability	stability	NOUN
ejpam-5963	55	7	analysis	analysis	NOUN
ejpam-5963	55	8	in	in	ADP
ejpam-5963	55	9	the	the	DET
ejpam-5963	55	10	present	present	ADJ
ejpam-5963	55	11	literature	literature	NOUN
ejpam-5963	55	12	of	of	ADP
ejpam-5963	55	13	fractal	fractal	PROPN
ejpam-5963	55	14	fc	fc	PROPN
ejpam-5963	56	1	[	[	X
ejpam-5963	56	2	22	22	NUM
ejpam-5963	56	3	]	]	PUNCT
ejpam-5963	56	4	.	.	PUNCT
ejpam-5963	57	1	ulam	ulam	PROPN
ejpam-5963	57	2	,	,	PUNCT
ejpam-5963	57	3	raised	raise	VERB
ejpam-5963	57	4	a	a	DET
ejpam-5963	57	5	question	question	NOUN
ejpam-5963	57	6	that	that	SCONJ
ejpam-5963	57	7	under	under	ADP
ejpam-5963	57	8	what	what	DET
ejpam-5963	57	9	condition	condition	NOUN
ejpam-5963	57	10	does	do	AUX
ejpam-5963	57	11	there	there	PRON
ejpam-5963	57	12	exists	exist	VERB
ejpam-5963	57	13	an	an	DET
ejpam-5963	57	14	additive	additive	ADJ
ejpam-5963	57	15	mapping	mapping	NOUN
ejpam-5963	57	16	near	near	ADP
ejpam-5963	57	17	an	an	DET
ejpam-5963	57	18	approximately	approximately	ADV
ejpam-5963	57	19	additive	additive	ADJ
ejpam-5963	57	20	mapping	mapping	NOUN
ejpam-5963	57	21	?	?	PUNCT
ejpam-5963	58	1	in	in	ADP
ejpam-5963	58	2	reply	reply	NOUN
ejpam-5963	58	3	to	to	ADP
ejpam-5963	58	4	this	this	DET
ejpam-5963	58	5	question	question	NOUN
ejpam-5963	58	6	hyres	hyre	NOUN
ejpam-5963	58	7	answered	answer	VERB
ejpam-5963	58	8	ulam	ulam	PROPN
ejpam-5963	58	9	’s	’s	PART
ejpam-5963	58	10	question	question	NOUN
ejpam-5963	58	11	for	for	ADP
ejpam-5963	58	12	the	the	DET
ejpam-5963	58	13	“	"	PUNCT
ejpam-5963	58	14	additive	additive	ADJ
ejpam-5963	58	15	mapping	mapping	NOUN
ejpam-5963	58	16	in	in	ADP
ejpam-5963	58	17	complete	complete	ADJ
ejpam-5963	58	18	norm	norm	NOUN
ejpam-5963	58	19	spaces	space	NOUN
ejpam-5963	58	20	”	"	PUNCT
ejpam-5963	59	1	[	[	X
ejpam-5963	59	2	23	23	NUM
ejpam-5963	59	3	]	]	PUNCT
ejpam-5963	59	4	.	.	PUNCT
ejpam-5963	60	1	after	after	SCONJ
ejpam-5963	60	2	it	it	PRON
ejpam-5963	60	3	was	be	AUX
ejpam-5963	60	4	considered	consider	VERB
ejpam-5963	60	5	a	a	DET
ejpam-5963	60	6	type	type	NOUN
ejpam-5963	60	7	of	of	ADP
ejpam-5963	60	8	stability	stability	NOUN
ejpam-5963	60	9	and	and	CCONJ
ejpam-5963	60	10	called	call	VERB
ejpam-5963	60	11	it	it	PRON
ejpam-5963	60	12	ulam	ulam	PROPN
ejpam-5963	60	13	-hyers	-hyer	NOUN
ejpam-5963	60	14	(	(	PUNCT
ejpam-5963	60	15	uh	uh	INTJ
ejpam-5963	60	16	)	)	PUNCT
ejpam-5963	60	17	stability	stability	NOUN
ejpam-5963	60	18	.	.	PUNCT
ejpam-5963	61	1	the	the	DET
ejpam-5963	61	2	said	say	VERB
ejpam-5963	61	3	concept	concept	NOUN
ejpam-5963	61	4	was	be	AUX
ejpam-5963	61	5	further	far	ADV
ejpam-5963	61	6	extended	extend	VERB
ejpam-5963	61	7	to	to	ADP
ejpam-5963	61	8	generalized	generalize	VERB
ejpam-5963	61	9	(	(	PUNCT
ejpam-5963	61	10	guh	guh	NOUN
ejpam-5963	61	11	)	)	PUNCT
ejpam-5963	61	12	,	,	PUNCT
ejpam-5963	61	13	and	and	CCONJ
ejpam-5963	61	14	ulam	ulam	NOUN
ejpam-5963	61	15	-	-	PUNCT
ejpam-5963	61	16	hyersrassias	hyersrassias	PROPN
ejpam-5963	61	17	(	(	PUNCT
ejpam-5963	61	18	uhr	uhr	NOUN
ejpam-5963	61	19	)	)	PUNCT
ejpam-5963	61	20	and	and	CCONJ
ejpam-5963	61	21	generalized	generalize	VERB
ejpam-5963	61	22	(	(	PUNCT
ejpam-5963	61	23	guhr	guhr	ADJ
ejpam-5963	61	24	)	)	PUNCT
ejpam-5963	61	25	analysis	analysis	NOUN
ejpam-5963	61	26	.	.	PUNCT
ejpam-5963	62	1	this	this	DET
ejpam-5963	62	2	concept	concept	NOUN
ejpam-5963	62	3	has	have	VERB
ejpam-5963	62	4	many	many	ADJ
ejpam-5963	62	5	applications	application	NOUN
ejpam-5963	62	6	in	in	ADP
ejpam-5963	62	7	different	different	ADJ
ejpam-5963	62	8	mathematical	mathematical	ADJ
ejpam-5963	62	9	fields	field	NOUN
ejpam-5963	62	10	,	,	PUNCT
ejpam-5963	62	11	including	include	VERB
ejpam-5963	62	12	des	des	PROPN
ejpam-5963	62	13	,	,	PUNCT
ejpam-5963	62	14	operator	operator	NOUN
ejpam-5963	62	15	theory	theory	NOUN
ejpam-5963	62	16	,	,	PUNCT
ejpam-5963	62	17	physics	physics	NOUN
ejpam-5963	62	18	,	,	PUNCT
ejpam-5963	62	19	engineering	engineering	NOUN
ejpam-5963	62	20	,	,	PUNCT
ejpam-5963	62	21	and	and	CCONJ
ejpam-5963	62	22	computer	computer	NOUN
ejpam-5963	62	23	science	science	NOUN
ejpam-5963	62	24	.	.	PUNCT
ejpam-5963	63	1	the	the	DET
ejpam-5963	63	2	connection	connection	NOUN
ejpam-5963	63	3	between	between	ADP
ejpam-5963	63	4	stability	stability	NOUN
ejpam-5963	63	5	analysis	analysis	NOUN
ejpam-5963	63	6	and	and	CCONJ
ejpam-5963	63	7	hyers	hyer	NOUN
ejpam-5963	63	8	-	-	PUNCT
ejpam-5963	63	9	ulam	ulam	PROPN
ejpam-5963	63	10	stability	stability	NOUN
ejpam-5963	63	11	are	be	AUX
ejpam-5963	63	12	interconnected	interconnected	ADJ
ejpam-5963	63	13	concepts	concept	NOUN
ejpam-5963	63	14	of	of	ADP
ejpam-5963	63	15	understanding	understand	VERB
ejpam-5963	63	16	the	the	DET
ejpam-5963	63	17	strength	strength	NOUN
ejpam-5963	63	18	of	of	ADP
ejpam-5963	63	19	systems	system	NOUN
ejpam-5963	63	20	and	and	CCONJ
ejpam-5963	63	21	equations	equation	NOUN
ejpam-5963	63	22	by	by	ADP
ejpam-5963	63	23	applying	apply	VERB
ejpam-5963	63	24	stability	stability	NOUN
ejpam-5963	63	25	analysis	analysis	NOUN
ejpam-5963	63	26	to	to	ADP
ejpam-5963	63	27	functional	functional	ADJ
ejpam-5963	63	28	equations	equation	NOUN
ejpam-5963	63	29	[	[	X
ejpam-5963	63	30	24	24	NUM
ejpam-5963	63	31	]	]	PUNCT
ejpam-5963	63	32	.	.	PUNCT
ejpam-5963	64	1	this	this	DET
ejpam-5963	64	2	integrated	integrate	VERB
ejpam-5963	64	3	approach	approach	NOUN
ejpam-5963	64	4	can	can	AUX
ejpam-5963	64	5	lead	lead	VERB
ejpam-5963	64	6	to	to	ADP
ejpam-5963	64	7	a	a	DET
ejpam-5963	64	8	deeper	deep	ADJ
ejpam-5963	64	9	understanding	understanding	NOUN
ejpam-5963	64	10	of	of	ADP
ejpam-5963	64	11	complex	complex	ADJ
ejpam-5963	64	12	dynamics	dynamic	NOUN
ejpam-5963	64	13	and	and	CCONJ
ejpam-5963	64	14	their	their	PRON
ejpam-5963	64	15	behavior	behavior	NOUN
ejpam-5963	64	16	.	.	PUNCT
ejpam-5963	65	1	the	the	DET
ejpam-5963	65	2	proposed	propose	VERB
ejpam-5963	65	3	stability	stability	NOUN
ejpam-5963	65	4	has	have	VERB
ejpam-5963	65	5	the	the	DET
ejpam-5963	65	6	main	main	ADJ
ejpam-5963	65	7	concern	concern	NOUN
ejpam-5963	65	8	of	of	ADP
ejpam-5963	65	9	researchers	researcher	NOUN
ejpam-5963	65	10	,	,	PUNCT
ejpam-5963	65	11	due	due	ADP
ejpam-5963	65	12	to	to	ADP
ejpam-5963	65	13	extensive	extensive	ADJ
ejpam-5963	65	14	applications	application	NOUN
ejpam-5963	65	15	in	in	ADP
ejpam-5963	65	16	various	various	ADJ
ejpam-5963	65	17	fields	field	NOUN
ejpam-5963	65	18	.	.	PUNCT
ejpam-5963	66	1	some	some	DET
ejpam-5963	66	2	the	the	DET
ejpam-5963	66	3	major	major	ADJ
ejpam-5963	66	4	contributions	contribution	NOUN
ejpam-5963	66	5	in	in	ADP
ejpam-5963	66	6	proposed	propose	VERB
ejpam-5963	66	7	field	field	NOUN
ejpam-5963	66	8	we	we	PRON
ejpam-5963	66	9	discuss	discuss	VERB
ejpam-5963	66	10	here	here	ADV
ejpam-5963	66	11	.	.	PUNCT
ejpam-5963	67	1	for	for	ADP
ejpam-5963	67	2	instance	instance	NOUN
ejpam-5963	67	3	,	,	PUNCT
ejpam-5963	67	4	xiadjie	xiadjie	PROPN
ejpam-5963	67	5	et	et	PROPN
ejpam-5963	67	6	al	al	PROPN
ejpam-5963	67	7	.	.	PROPN
ejpam-5963	67	8	,	,	PUNCT
ejpam-5963	68	1	[	[	X
ejpam-5963	68	2	25	25	NUM
ejpam-5963	68	3	]	]	PUNCT
ejpam-5963	68	4	studied	study	VERB
ejpam-5963	68	5	the	the	DET
ejpam-5963	68	6	following	follow	VERB
ejpam-5963	68	7	non	non	ADJ
ejpam-5963	68	8	-	-	ADJ
ejpam-5963	68	9	linear	linear	ADJ
ejpam-5963	68	10	problem	problem	NOUN
ejpam-5963	68	11	in	in	ADP
ejpam-5963	68	12	sense	sense	NOUN
ejpam-5963	68	13	of	of	ADP
ejpam-5963	68	14	the	the	DET
ejpam-5963	68	15	caputo	caputo	PROPN
ejpam-5963	68	16	’s	’s	PART
ejpam-5963	68	17	derivative	derivative	NOUN
ejpam-5963	68	18	with	with	ADP
ejpam-5963	68	19	order	order	NOUN
ejpam-5963	68	20	ξ	ξ	NOUN
ejpam-5963	68	21	as	as	ADP
ejpam-5963	68	22	:	:	PUNCT
ejpam-5963	68	23	dξϕ(t	dξϕ(t	PROPN
ejpam-5963	68	24	)	)	PUNCT
ejpam-5963	68	25	=	=	SYM
ejpam-5963	68	26	θ1(t	θ1(t	PROPN
ejpam-5963	68	27	,	,	PUNCT
ejpam-5963	68	28	ϕ(t	ϕ(t	NUM
ejpam-5963	68	29	)	)	PUNCT
ejpam-5963	68	30	)	)	PUNCT
ejpam-5963	68	31	,	,	PUNCT
ejpam-5963	69	1	t	t	PROPN
ejpam-5963	69	2	∈	∈	PROPN
ejpam-5963	69	3	ω	ω	X
ejpam-5963	69	4	=	=	PUNCT
ejpam-5963	70	1	[	[	X
ejpam-5963	70	2	0	0	NUM
ejpam-5963	70	3	,	,	PUNCT
ejpam-5963	70	4	t	t	X
ejpam-5963	70	5	]	]	PUNCT
ejpam-5963	70	6	,	,	PUNCT
ejpam-5963	70	7	ϕ(0	ϕ(0	PROPN
ejpam-5963	70	8	)	)	PUNCT
ejpam-5963	70	9	+	+	CCONJ
ejpam-5963	70	10	ψ(ϕ	ψ(ϕ	PROPN
ejpam-5963	70	11	)	)	PUNCT
ejpam-5963	70	12	=	=	SYM
ejpam-5963	70	13	ϕ0	ϕ0	NOUN
ejpam-5963	70	14	,	,	PUNCT
ejpam-5963	70	15	where	where	SCONJ
ejpam-5963	70	16	f	f	X
ejpam-5963	70	17	:	:	PUNCT
ejpam-5963	70	18	ω	ω	NUM
ejpam-5963	70	19	×	×	NOUN
ejpam-5963	70	20	r	r	NOUN
ejpam-5963	70	21	→	→	SYM
ejpam-5963	70	22	r	r	NOUN
ejpam-5963	70	23	is	be	AUX
ejpam-5963	70	24	continuous	continuous	ADJ
ejpam-5963	70	25	function	function	NOUN
ejpam-5963	70	26	.	.	PUNCT
ejpam-5963	71	1	the	the	DET
ejpam-5963	71	2	investigation	investigation	NOUN
ejpam-5963	71	3	of	of	ADP
ejpam-5963	71	4	coupled	couple	VERB
ejpam-5963	71	5	system	system	NOUN
ejpam-5963	71	6	for	for	ADP
ejpam-5963	71	7	non	non	ADJ
ejpam-5963	71	8	-	-	ADJ
ejpam-5963	71	9	linear	linear	ADJ
ejpam-5963	71	10	fdes	fde	NOUN
ejpam-5963	71	11	has	have	VERB
ejpam-5963	71	12	the	the	DET
ejpam-5963	71	13	main	main	ADJ
ejpam-5963	71	14	focuss	focuss	NOUN
ejpam-5963	71	15	of	of	ADP
ejpam-5963	71	16	researchers	researcher	NOUN
ejpam-5963	71	17	from	from	ADP
ejpam-5963	71	18	existence	existence	NOUN
ejpam-5963	71	19	point	point	NOUN
ejpam-5963	71	20	of	of	ADP
ejpam-5963	71	21	view	view	NOUN
ejpam-5963	71	22	.	.	PUNCT
ejpam-5963	72	1	in	in	ADP
ejpam-5963	72	2	this	this	DET
ejpam-5963	72	3	regards	regard	NOUN
ejpam-5963	72	4	,	,	PUNCT
ejpam-5963	72	5	the	the	DET
ejpam-5963	72	6	author	author	NOUN
ejpam-5963	72	7	’s	’s	PART
ejpam-5963	72	8	[	[	X
ejpam-5963	72	9	26	26	NUM
ejpam-5963	72	10	]	]	PUNCT
ejpam-5963	72	11	studied	study	VERB
ejpam-5963	72	12	the	the	DET
ejpam-5963	72	13	uniqueness	uniqueness	NOUN
ejpam-5963	72	14	of	of	ADP
ejpam-5963	72	15	solution	solution	NOUN
ejpam-5963	72	16	for	for	ADP
ejpam-5963	72	17	coupled	couple	VERB
ejpam-5963	72	18	system	system	NOUN
ejpam-5963	72	19	of	of	ADP
ejpam-5963	72	20	fdes	fde	NOUN
ejpam-5963	72	21	with	with	ADP
ejpam-5963	72	22	integral	integral	ADJ
ejpam-5963	72	23	boundary	boundary	ADJ
ejpam-5963	72	24	conditions	condition	NOUN
ejpam-5963	72	25	.	.	PUNCT
ejpam-5963	73	1	in	in	ADP
ejpam-5963	73	2	the	the	DET
ejpam-5963	73	3	same	same	ADJ
ejpam-5963	73	4	way	way	NOUN
ejpam-5963	73	5	,	,	PUNCT
ejpam-5963	73	6	su	su	PROPN
ejpam-5963	74	1	[	[	X
ejpam-5963	74	2	27	27	NUM
ejpam-5963	74	3	]	]	PUNCT
ejpam-5963	74	4	established	establish	VERB
ejpam-5963	74	5	the	the	DET
ejpam-5963	74	6	conditions	condition	NOUN
ejpam-5963	74	7	for	for	ADP
ejpam-5963	74	8	eus	eus	PROPN
ejpam-5963	74	9	for	for	ADP
ejpam-5963	74	10	the	the	DET
ejpam-5963	74	11	following	follow	VERB
ejpam-5963	74	12	coupled	couple	VERB
ejpam-5963	74	13	system	system	NOUN
ejpam-5963	74	14	with	with	ADP
ejpam-5963	74	15	two	two	NUM
ejpam-5963	74	16	-	-	PUNCT
ejpam-5963	74	17	point	point	NOUN
ejpam-5963	74	18	boundary	boundary	ADJ
ejpam-5963	74	19	conditions	condition	NOUN
ejpam-5963	74	20	(	(	PUNCT
ejpam-5963	74	21	bcs	bc	NOUN
ejpam-5963	74	22	)	)	PUNCT
ejpam-5963	74	23	in	in	ADP
ejpam-5963	74	24	sense	sense	NOUN
ejpam-5963	74	25	a.	a.	PROPN
ejpam-5963	74	26	ali	ali	PROPN
ejpam-5963	74	27	et	et	PROPN
ejpam-5963	74	28	al	al	PROPN
ejpam-5963	74	29	.	.	PUNCT
ejpam-5963	74	30	/	/	SYM
ejpam-5963	74	31	eur	eur	PROPN
ejpam-5963	74	32	.	.	PUNCT
ejpam-5963	75	1	j.	j.	PROPN
ejpam-5963	75	2	pure	pure	PROPN
ejpam-5963	75	3	appl	appl	PROPN
ejpam-5963	75	4	.	.	PROPN
ejpam-5963	75	5	math	math	PROPN
ejpam-5963	75	6	,	,	PUNCT
ejpam-5963	75	7	18	18	NUM
ejpam-5963	75	8	(	(	PUNCT
ejpam-5963	75	9	2	2	NUM
ejpam-5963	75	10	)	)	PUNCT
ejpam-5963	75	11	(	(	PUNCT
ejpam-5963	75	12	2025	2025	NUM
ejpam-5963	75	13	)	)	PUNCT
ejpam-5963	75	14	,	,	PUNCT
ejpam-5963	75	15	5963	5963	NUM
ejpam-5963	75	16	4	4	NUM
ejpam-5963	75	17	of	of	ADP
ejpam-5963	75	18	19	19	NUM
ejpam-5963	75	19	of	of	ADP
ejpam-5963	75	20	singular	singular	ADJ
ejpam-5963	75	21	kernel	kernel	NOUN
ejpam-5963	75	22	operator	operator	ADP
ejpam-5963	75	23	dηϕ(t	dηϕ(t	PROPN
ejpam-5963	75	24	)	)	PUNCT
ejpam-5963	75	25	=	=	SYM
ejpam-5963	75	26	θ1(t	θ1(t	PROPN
ejpam-5963	75	27	,	,	PUNCT
ejpam-5963	75	28	ψ(t	ψ(t	PROPN
ejpam-5963	75	29	)	)	PUNCT
ejpam-5963	75	30	,	,	PUNCT
ejpam-5963	75	31	d	d	NOUN
ejpam-5963	75	32	pψ(t	pψ(t	X
ejpam-5963	75	33	)	)	PUNCT
ejpam-5963	75	34	)	)	PUNCT
ejpam-5963	75	35	,	,	PUNCT
ejpam-5963	75	36	t	t	PROPN
ejpam-5963	75	37	∈	∈	PROPN
ejpam-5963	75	38	ω	ω	X
ejpam-5963	76	1	=	=	PUNCT
ejpam-5963	77	1	[	[	X
ejpam-5963	77	2	0	0	NUM
ejpam-5963	77	3	,	,	PUNCT
ejpam-5963	77	4	1	1	NUM
ejpam-5963	77	5	]	]	PUNCT
ejpam-5963	77	6	,	,	PUNCT
ejpam-5963	77	7	dξϕ(t	dξϕ(t	PROPN
ejpam-5963	77	8	)	)	PUNCT
ejpam-5963	77	9	=	=	SYM
ejpam-5963	77	10	θ2(t	θ2(t	PROPN
ejpam-5963	77	11	,	,	PUNCT
ejpam-5963	77	12	ϕ(t	ϕ(t	PROPN
ejpam-5963	77	13	)	)	PUNCT
ejpam-5963	77	14	,	,	PUNCT
ejpam-5963	77	15	d	d	NOUN
ejpam-5963	77	16	qϕ(t	qϕ(t	NOUN
ejpam-5963	77	17	)	)	PUNCT
ejpam-5963	77	18	)	)	PUNCT
ejpam-5963	77	19	,	,	PUNCT
ejpam-5963	77	20	ϕ(0	ϕ(0	PROPN
ejpam-5963	77	21	)	)	PUNCT
ejpam-5963	77	22	=	=	SYM
ejpam-5963	78	1	ϕ(1	ϕ(1	PROPN
ejpam-5963	78	2	)	)	PUNCT
ejpam-5963	78	3	=	=	PUNCT
ejpam-5963	79	1	ψ(0	ψ(0	X
ejpam-5963	79	2	)	)	PUNCT
ejpam-5963	79	3	=	=	SYM
ejpam-5963	79	4	ψ(1	ψ(1	PROPN
ejpam-5963	79	5	)	)	PUNCT
ejpam-5963	79	6	=	=	SYM
ejpam-5963	80	1	0	0	NUM
ejpam-5963	80	2	,	,	PUNCT
ejpam-5963	80	3	where	where	SCONJ
ejpam-5963	80	4	η	η	PROPN
ejpam-5963	80	5	,	,	PUNCT
ejpam-5963	80	6	ξ	ξ	PROPN
ejpam-5963	80	7	∈	∈	PROPN
ejpam-5963	80	8	(	(	PUNCT
ejpam-5963	80	9	1	1	NUM
ejpam-5963	80	10	,	,	PUNCT
ejpam-5963	80	11	2	2	NUM
ejpam-5963	80	12	]	]	PUNCT
ejpam-5963	80	13	,	,	PUNCT
ejpam-5963	80	14	such	such	ADJ
ejpam-5963	80	15	that	that	SCONJ
ejpam-5963	80	16	p	p	PROPN
ejpam-5963	80	17	−	−	PROPN
ejpam-5963	80	18	η	η	PROPN
ejpam-5963	80	19	and	and	CCONJ
ejpam-5963	80	20	q	q	NOUN
ejpam-5963	80	21	−	−	PROPN
ejpam-5963	80	22	ξ	ξ	X
ejpam-5963	80	23	>	>	SYM
ejpam-5963	80	24	0	0	NUM
ejpam-5963	80	25	,	,	PUNCT
ejpam-5963	80	26	θ1	θ1	NOUN
ejpam-5963	80	27	,	,	PUNCT
ejpam-5963	80	28	θ2	θ2	PROPN
ejpam-5963	80	29	∈	∈	PROPN
ejpam-5963	80	30	c([0	c([0	NOUN
ejpam-5963	80	31	,	,	PUNCT
ejpam-5963	80	32	1	1	NUM
ejpam-5963	80	33	]	]	SYM
ejpam-5963	80	34	×	×	NOUN
ejpam-5963	80	35	r2	r2	NOUN
ejpam-5963	80	36	,	,	PUNCT
ejpam-5963	80	37	r	r	NOUN
ejpam-5963	80	38	)	)	PUNCT
ejpam-5963	80	39	.	.	PUNCT
ejpam-5963	81	1	on	on	ADP
ejpam-5963	81	2	the	the	DET
ejpam-5963	81	3	same	same	ADJ
ejpam-5963	81	4	fashion	fashion	NOUN
ejpam-5963	81	5	,	,	PUNCT
ejpam-5963	81	6	wang	wang	PROPN
ejpam-5963	81	7	et	et	PROPN
ejpam-5963	81	8	al	al	PROPN
ejpam-5963	81	9	.	.	PROPN
ejpam-5963	81	10	,	,	PUNCT
ejpam-5963	82	1	[	[	X
ejpam-5963	82	2	28	28	NUM
ejpam-5963	82	3	]	]	PUNCT
ejpam-5963	82	4	have	have	AUX
ejpam-5963	82	5	been	be	AUX
ejpam-5963	82	6	presented	present	VERB
ejpam-5963	82	7	sufficient	sufficient	ADJ
ejpam-5963	82	8	conditions	condition	NOUN
ejpam-5963	82	9	for	for	ADP
ejpam-5963	82	10	the	the	DET
ejpam-5963	82	11	eus	eus	NOUN
ejpam-5963	82	12	to	to	ADP
ejpam-5963	82	13	the	the	DET
ejpam-5963	82	14	following	follow	VERB
ejpam-5963	82	15	non	non	ADJ
ejpam-5963	82	16	-	-	ADJ
ejpam-5963	82	17	linear	linear	ADJ
ejpam-5963	82	18	cs	cs	PROPN
ejpam-5963	82	19	with	with	ADP
ejpam-5963	82	20	three	three	NUM
ejpam-5963	82	21	point	point	NOUN
ejpam-5963	82	22	bcs	bcs	ADP
ejpam-5963	82	23	dηϕ(t	dηϕ(t	PROPN
ejpam-5963	82	24	)	)	PUNCT
ejpam-5963	82	25	=	=	SYM
ejpam-5963	82	26	θ1(t	θ1(t	PROPN
ejpam-5963	82	27	,	,	PUNCT
ejpam-5963	82	28	ψ(t	ψ(t	PROPN
ejpam-5963	82	29	)	)	PUNCT
ejpam-5963	82	30	)	)	PUNCT
ejpam-5963	82	31	,	,	PUNCT
ejpam-5963	82	32	t	t	PROPN
ejpam-5963	82	33	∈	∈	PROPN
ejpam-5963	82	34	ω	ω	X
ejpam-5963	82	35	=	=	PUNCT
ejpam-5963	83	1	[	[	X
ejpam-5963	83	2	0	0	NUM
ejpam-5963	83	3	,	,	PUNCT
ejpam-5963	83	4	1	1	NUM
ejpam-5963	83	5	]	]	PUNCT
ejpam-5963	83	6	,	,	PUNCT
ejpam-5963	83	7	dξϕ(t	dξϕ(t	PROPN
ejpam-5963	83	8	)	)	PUNCT
ejpam-5963	83	9	=	=	SYM
ejpam-5963	83	10	θ2(t	θ2(t	PROPN
ejpam-5963	83	11	,	,	PUNCT
ejpam-5963	83	12	ϕ(t	ϕ(t	NUM
ejpam-5963	83	13	)	)	PUNCT
ejpam-5963	83	14	)	)	PUNCT
ejpam-5963	83	15	,	,	PUNCT
ejpam-5963	83	16	ϕ(0	ϕ(0	PROPN
ejpam-5963	83	17	)	)	PUNCT
ejpam-5963	83	18	=	=	PUNCT
ejpam-5963	84	1	ψ(0	ψ(0	X
ejpam-5963	84	2	)	)	PUNCT
ejpam-5963	84	3	=	=	SYM
ejpam-5963	84	4	0	0	NUM
ejpam-5963	84	5	,	,	PUNCT
ejpam-5963	84	6	ϕ(1	ϕ(1	PROPN
ejpam-5963	84	7	)	)	PUNCT
ejpam-5963	84	8	=	=	SYM
ejpam-5963	84	9	qϕ(p	qϕ(p	X
ejpam-5963	84	10	)	)	PUNCT
ejpam-5963	84	11	,	,	PUNCT
ejpam-5963	84	12	ψ1bψ(p	ψ1bψ(p	ADP
ejpam-5963	84	13	)	)	PUNCT
ejpam-5963	84	14	,	,	PUNCT
ejpam-5963	84	15	where	where	SCONJ
ejpam-5963	84	16	η	η	PROPN
ejpam-5963	84	17	,	,	PUNCT
ejpam-5963	84	18	ξ	ξ	PROPN
ejpam-5963	84	19	∈	∈	PROPN
ejpam-5963	84	20	(	(	PUNCT
ejpam-5963	84	21	1	1	NUM
ejpam-5963	84	22	,	,	PUNCT
ejpam-5963	84	23	2	2	NUM
ejpam-5963	84	24	]	]	PUNCT
ejpam-5963	84	25	and	and	CCONJ
ejpam-5963	84	26	0	0	NUM
ejpam-5963	84	27	≤	≤	NOUN
ejpam-5963	84	28	a	a	PRON
ejpam-5963	84	29	,	,	PUNCT
ejpam-5963	84	30	b	b	PROPN
ejpam-5963	84	31	≤	≤	ADV
ejpam-5963	84	32	1	1	NUM
ejpam-5963	84	33	,	,	PUNCT
ejpam-5963	84	34	0	0	PUNCT
ejpam-5963	84	35	<	<	X
ejpam-5963	84	36	p	p	X
ejpam-5963	84	37	≤	≤	NUM
ejpam-5963	84	38	1	1	NUM
ejpam-5963	84	39	,	,	PUNCT
ejpam-5963	84	40	θ1	θ1	NOUN
ejpam-5963	84	41	,	,	PUNCT
ejpam-5963	84	42	θ2	θ2	PROPN
ejpam-5963	84	43	∈	∈	PROPN
ejpam-5963	84	44	c([0	c([0	PROPN
ejpam-5963	84	45	,	,	PUNCT
ejpam-5963	84	46	1]×r	1]×r	NUM
ejpam-5963	84	47	,	,	PUNCT
ejpam-5963	84	48	r	r	NOUN
ejpam-5963	84	49	)	)	PUNCT
ejpam-5963	84	50	.	.	PUNCT
ejpam-5963	85	1	after	after	ADP
ejpam-5963	85	2	the	the	DET
ejpam-5963	85	3	comprehensive	comprehensive	ADJ
ejpam-5963	85	4	study	study	NOUN
ejpam-5963	85	5	of	of	ADP
ejpam-5963	85	6	present	present	ADJ
ejpam-5963	85	7	literature	literature	NOUN
ejpam-5963	85	8	,	,	PUNCT
ejpam-5963	85	9	it	it	PRON
ejpam-5963	85	10	is	be	AUX
ejpam-5963	85	11	clear	clear	ADJ
ejpam-5963	85	12	that	that	SCONJ
ejpam-5963	85	13	fdes	fde	NOUN
ejpam-5963	85	14	and	and	CCONJ
ejpam-5963	85	15	their	their	PRON
ejpam-5963	85	16	coupled	couple	VERB
ejpam-5963	85	17	systems	system	NOUN
ejpam-5963	85	18	are	be	AUX
ejpam-5963	85	19	well	well	ADV
ejpam-5963	85	20	investigated	investigate	VERB
ejpam-5963	85	21	by	by	ADP
ejpam-5963	85	22	researchers	researcher	NOUN
ejpam-5963	85	23	in	in	ADP
ejpam-5963	85	24	term	term	NOUN
ejpam-5963	85	25	of	of	ADP
ejpam-5963	85	26	singular	singular	ADJ
ejpam-5963	85	27	kernel	kernel	PROPN
ejpam-5963	85	28	fractional	fractional	PROPN
ejpam-5963	85	29	operators	operator	NOUN
ejpam-5963	85	30	.	.	PUNCT
ejpam-5963	86	1	we	we	PRON
ejpam-5963	86	2	felt	feel	VERB
ejpam-5963	86	3	that	that	SCONJ
ejpam-5963	86	4	coupled	couple	VERB
ejpam-5963	86	5	system	system	NOUN
ejpam-5963	86	6	of	of	ADP
ejpam-5963	86	7	ffdes	ffde	NOUN
ejpam-5963	86	8	are	be	AUX
ejpam-5963	86	9	very	very	ADV
ejpam-5963	86	10	rarely	rarely	ADV
ejpam-5963	86	11	investigated	investigate	VERB
ejpam-5963	86	12	by	by	ADP
ejpam-5963	86	13	researchers	researcher	NOUN
ejpam-5963	86	14	.	.	PUNCT
ejpam-5963	87	1	for	for	ADP
ejpam-5963	87	2	the	the	DET
ejpam-5963	87	3	better	well	ADJ
ejpam-5963	87	4	understanding	understanding	NOUN
ejpam-5963	87	5	of	of	ADP
ejpam-5963	87	6	consider	consider	VERB
ejpam-5963	87	7	coupled	couple	VERB
ejpam-5963	87	8	system	system	NOUN
ejpam-5963	87	9	ffdes	ffde	NOUN
ejpam-5963	87	10	,	,	PUNCT
ejpam-5963	87	11	we	we	PRON
ejpam-5963	87	12	carry	carry	VERB
ejpam-5963	87	13	out	out	ADP
ejpam-5963	87	14	investigations	investigation	NOUN
ejpam-5963	87	15	and	and	CCONJ
ejpam-5963	87	16	analysis	analysis	NOUN
ejpam-5963	87	17	for	for	ADP
ejpam-5963	87	18	model	model	NOUN
ejpam-5963	87	19	via	via	ADP
ejpam-5963	87	20	the	the	DET
ejpam-5963	87	21	tools	tool	NOUN
ejpam-5963	87	22	of	of	ADP
ejpam-5963	87	23	mathematical	mathematical	ADJ
ejpam-5963	87	24	analysis	analysis	NOUN
ejpam-5963	87	25	.	.	PUNCT
ejpam-5963	88	1	therefore	therefore	ADV
ejpam-5963	88	2	,	,	PUNCT
ejpam-5963	88	3	main	main	ADJ
ejpam-5963	88	4	focuses	focus	NOUN
ejpam-5963	88	5	of	of	ADP
ejpam-5963	88	6	our	our	PRON
ejpam-5963	88	7	research	research	NOUN
ejpam-5963	88	8	work	work	NOUN
ejpam-5963	88	9	is	be	AUX
ejpam-5963	88	10	to	to	PART
ejpam-5963	88	11	establish	establish	VERB
ejpam-5963	88	12	the	the	DET
ejpam-5963	88	13	conditions	condition	NOUN
ejpam-5963	88	14	of	of	ADP
ejpam-5963	88	15	eus	eus	PROPN
ejpam-5963	88	16	and	and	CCONJ
ejpam-5963	88	17	stability	stability	NOUN
ejpam-5963	88	18	analysis	analysis	NOUN
ejpam-5963	88	19	for	for	ADP
ejpam-5963	88	20	underlying	underlie	VERB
ejpam-5963	88	21	coupled	couple	VERB
ejpam-5963	88	22	system	system	NOUN
ejpam-5963	88	23	of	of	ADP
ejpam-5963	88	24	ffdes	ffde	NOUN
ejpam-5963	88	25	.	.	PUNCT
ejpam-5963	89	1	we	we	PRON
ejpam-5963	89	2	use	use	VERB
ejpam-5963	89	3	the	the	DET
ejpam-5963	89	4	results	result	NOUN
ejpam-5963	89	5	of	of	ADP
ejpam-5963	89	6	the	the	DET
ejpam-5963	89	7	functional	functional	ADJ
ejpam-5963	89	8	analysis	analysis	NOUN
ejpam-5963	89	9	along	along	ADP
ejpam-5963	89	10	with	with	ADP
ejpam-5963	89	11	fpt	fpt	PROPN
ejpam-5963	89	12	[	[	X
ejpam-5963	89	13	29	29	NUM
ejpam-5963	89	14	,	,	PUNCT
ejpam-5963	89	15	30	30	NUM
ejpam-5963	89	16	]	]	PUNCT
ejpam-5963	89	17	to	to	PART
ejpam-5963	89	18	obtain	obtain	VERB
ejpam-5963	89	19	required	required	ADJ
ejpam-5963	89	20	results	result	NOUN
ejpam-5963	89	21	.	.	PUNCT
ejpam-5963	90	1	the	the	DET
ejpam-5963	90	2	considered	consider	VERB
ejpam-5963	90	3	problem	problem	NOUN
ejpam-5963	90	4	is	be	AUX
ejpam-5963	90	5	described	describe	VERB
ejpam-5963	90	6	as	as	SCONJ
ejpam-5963	90	7	follows	follow	VERB
ejpam-5963	90	8	:	:	PUNCT
ejpam-5963	90	9			NOUN
ejpam-5963	90	10	fddηr(t	fddηr(t	NOUN
ejpam-5963	90	11	)	)	PUNCT
ejpam-5963	91	1	=	=	SYM
ejpam-5963	91	2	ξtξ−1f	ξtξ−1f	PROPN
ejpam-5963	91	3	(	(	PUNCT
ejpam-5963	91	4	t	t	PROPN
ejpam-5963	91	5	,	,	PUNCT
ejpam-5963	91	6	r(t	r(t	NOUN
ejpam-5963	91	7	)	)	PUNCT
ejpam-5963	91	8	,	,	PUNCT
ejpam-5963	91	9	p(t	p(t	NOUN
ejpam-5963	91	10	)	)	PUNCT
ejpam-5963	91	11	)	)	PUNCT
ejpam-5963	91	12	,	,	PUNCT
ejpam-5963	92	1	t	t	PROPN
ejpam-5963	92	2	∈	∈	PROPN
ejpam-5963	93	1	i	i	PRON
ejpam-5963	93	2	=	=	PUNCT
ejpam-5963	94	1	[	[	X
ejpam-5963	94	2	0	0	NUM
ejpam-5963	94	3	,	,	PUNCT
ejpam-5963	94	4	t	t	X
ejpam-5963	94	5	]	]	PUNCT
ejpam-5963	94	6	,	,	PUNCT
ejpam-5963	94	7	fddηp(t	fddηp(t	NOUN
ejpam-5963	94	8	)	)	PUNCT
ejpam-5963	94	9	=	=	SYM
ejpam-5963	95	1	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	95	2	,	,	PUNCT
ejpam-5963	95	3	r(t	r(t	NOUN
ejpam-5963	95	4	)	)	PUNCT
ejpam-5963	95	5	,	,	PUNCT
ejpam-5963	95	6	p(t	p(t	NOUN
ejpam-5963	95	7	)	)	PUNCT
ejpam-5963	95	8	)	)	PUNCT
ejpam-5963	95	9	,	,	PUNCT
ejpam-5963	95	10	r(0	r(0	PROPN
ejpam-5963	95	11	)	)	PUNCT
ejpam-5963	95	12	=	=	SYM
ejpam-5963	95	13	r0	r0	NOUN
ejpam-5963	95	14	+	+	CCONJ
ejpam-5963	95	15	ϕ(r	ϕ(r	PROPN
ejpam-5963	95	16	)	)	PUNCT
ejpam-5963	95	17	,	,	PUNCT
ejpam-5963	95	18	p(0	p(0	NOUN
ejpam-5963	95	19	)	)	PUNCT
ejpam-5963	96	1	=	=	SYM
ejpam-5963	96	2	p0	p0	NOUN
ejpam-5963	96	3	+	+	CCONJ
ejpam-5963	96	4	ψ(p	ψ(p	NOUN
ejpam-5963	96	5	)	)	PUNCT
ejpam-5963	96	6	,	,	PUNCT
ejpam-5963	96	7	(	(	PUNCT
ejpam-5963	96	8	1	1	X
ejpam-5963	96	9	)	)	PUNCT
ejpam-5963	96	10	where	where	SCONJ
ejpam-5963	96	11	fddη	fddη	NOUN
ejpam-5963	96	12	is	be	AUX
ejpam-5963	96	13	the	the	DET
ejpam-5963	96	14	caputo	caputo	PROPN
ejpam-5963	96	15	fractional	fractional	PROPN
ejpam-5963	96	16	derivative	derivative	NOUN
ejpam-5963	96	17	and	and	CCONJ
ejpam-5963	96	18	r0	r0	NOUN
ejpam-5963	96	19	,	,	PUNCT
ejpam-5963	96	20	p0	p0	NOUN
ejpam-5963	96	21	∈	∈	PROPN
ejpam-5963	96	22	r	r	PROPN
ejpam-5963	96	23	,	,	PUNCT
ejpam-5963	96	24	η	η	PROPN
ejpam-5963	96	25	,	,	PUNCT
ejpam-5963	96	26	ξ	ξ	PROPN
ejpam-5963	96	27	∈	∈	PROPN
ejpam-5963	96	28	(	(	PUNCT
ejpam-5963	96	29	0	0	NUM
ejpam-5963	96	30	,	,	PUNCT
ejpam-5963	96	31	1	1	NUM
ejpam-5963	96	32	]	]	PUNCT
ejpam-5963	96	33	,	,	PUNCT
ejpam-5963	96	34	f	f	X
ejpam-5963	96	35	,	,	PUNCT
ejpam-5963	96	36	g	g	NOUN
ejpam-5963	96	37	:	:	PUNCT
ejpam-5963	96	38	i	i	PRON
ejpam-5963	96	39	×	×	VERB
ejpam-5963	96	40	r2	r2	PROPN
ejpam-5963	96	41	→	→	SYM
ejpam-5963	96	42	r	r	PROPN
ejpam-5963	96	43	,	,	PUNCT
ejpam-5963	96	44	ϕ	ϕ	NOUN
ejpam-5963	96	45	,	,	PUNCT
ejpam-5963	96	46	ψ	ψ	X
ejpam-5963	96	47	:	:	PUNCT
ejpam-5963	96	48	i	i	PRON
ejpam-5963	96	49	=	=	PUNCT
ejpam-5963	97	1	[	[	X
ejpam-5963	97	2	0	0	NUM
ejpam-5963	97	3	,	,	PUNCT
ejpam-5963	97	4	t	t	X
ejpam-5963	97	5	]	]	PUNCT
ejpam-5963	97	6	×	×	NOUN
ejpam-5963	97	7	r	r	NOUN
ejpam-5963	97	8	→	→	SYM
ejpam-5963	97	9	r	r	NOUN
ejpam-5963	97	10	are	be	AUX
ejpam-5963	97	11	continuous	continuous	ADJ
ejpam-5963	97	12	functions	function	NOUN
ejpam-5963	97	13	.	.	PUNCT
ejpam-5963	98	1	the	the	DET
ejpam-5963	98	2	qualitative	qualitative	ADJ
ejpam-5963	98	3	analysis	analysis	NOUN
ejpam-5963	98	4	of	of	ADP
ejpam-5963	98	5	the	the	DET
ejpam-5963	98	6	proposed	propose	VERB
ejpam-5963	98	7	coupled	couple	VERB
ejpam-5963	98	8	system	system	NOUN
ejpam-5963	98	9	of	of	ADP
ejpam-5963	98	10	ffdes	ffde	NOUN
ejpam-5963	98	11	offer	offer	VERB
ejpam-5963	98	12	deeper	deep	ADJ
ejpam-5963	98	13	understanding	understanding	NOUN
ejpam-5963	98	14	into	into	ADP
ejpam-5963	98	15	the	the	DET
ejpam-5963	98	16	complex	complex	ADJ
ejpam-5963	98	17	dynamics	dynamic	NOUN
ejpam-5963	98	18	systems	system	NOUN
ejpam-5963	98	19	exhibiting	exhibit	VERB
ejpam-5963	98	20	self	self	NOUN
ejpam-5963	98	21	-	-	PUNCT
ejpam-5963	98	22	similarity	similarity	NOUN
ejpam-5963	98	23	and	and	CCONJ
ejpam-5963	98	24	non	non	ADJ
ejpam-5963	98	25	-	-	NOUN
ejpam-5963	98	26	locality	locality	NOUN
ejpam-5963	98	27	.	.	PUNCT
ejpam-5963	99	1	the	the	DET
ejpam-5963	99	2	consider	consider	VERB
ejpam-5963	99	3	class	class	NOUN
ejpam-5963	99	4	have	have	VERB
ejpam-5963	99	5	many	many	ADJ
ejpam-5963	99	6	applications	application	NOUN
ejpam-5963	99	7	in	in	ADP
ejpam-5963	99	8	various	various	ADJ
ejpam-5963	99	9	discipline	discipline	NOUN
ejpam-5963	99	10	that	that	PRON
ejpam-5963	99	11	can	can	AUX
ejpam-5963	99	12	model	model	VERB
ejpam-5963	99	13	complex	complex	ADJ
ejpam-5963	99	14	phenomena	phenomenon	NOUN
ejpam-5963	99	15	.	.	PUNCT
ejpam-5963	100	1	the	the	DET
ejpam-5963	100	2	coupled	couple	VERB
ejpam-5963	100	3	system	system	NOUN
ejpam-5963	100	4	of	of	ADP
ejpam-5963	100	5	ffdes	ffde	NOUN
ejpam-5963	100	6	can	can	AUX
ejpam-5963	100	7	accurately	accurately	ADV
ejpam-5963	100	8	describe	describe	VERB
ejpam-5963	100	9	the	the	DET
ejpam-5963	100	10	behavior	behavior	NOUN
ejpam-5963	100	11	of	of	ADP
ejpam-5963	100	12	complex	complex	ADJ
ejpam-5963	100	13	system	system	NOUN
ejpam-5963	100	14	in	in	ADP
ejpam-5963	100	15	physics	physics	NOUN
ejpam-5963	100	16	,	,	PUNCT
ejpam-5963	100	17	biology	biology	NOUN
ejpam-5963	100	18	,	,	PUNCT
ejpam-5963	100	19	finance	finance	NOUN
ejpam-5963	100	20	and	and	CCONJ
ejpam-5963	100	21	predictive	predictive	ADJ
ejpam-5963	100	22	capabilities	capability	NOUN
ejpam-5963	100	23	and	and	CCONJ
ejpam-5963	100	24	understanding	understand	VERB
ejpam-5963	100	25	the	the	DET
ejpam-5963	100	26	qualitative	qualitative	ADJ
ejpam-5963	100	27	behavior	behavior	NOUN
ejpam-5963	100	28	of	of	ADP
ejpam-5963	100	29	solution	solution	NOUN
ejpam-5963	100	30	.	.	PUNCT
ejpam-5963	101	1	the	the	DET
ejpam-5963	101	2	result	result	NOUN
ejpam-5963	101	3	of	of	ADP
ejpam-5963	101	4	this	this	DET
ejpam-5963	101	5	research	research	NOUN
ejpam-5963	101	6	will	will	AUX
ejpam-5963	101	7	also	also	ADV
ejpam-5963	101	8	provide	provide	VERB
ejpam-5963	101	9	new	new	ADJ
ejpam-5963	101	10	insight	insight	NOUN
ejpam-5963	101	11	into	into	ADP
ejpam-5963	101	12	the	the	DET
ejpam-5963	101	13	behavior	behavior	NOUN
ejpam-5963	101	14	of	of	ADP
ejpam-5963	101	15	coupled	couple	VERB
ejpam-5963	101	16	system	system	NOUN
ejpam-5963	101	17	of	of	ADP
ejpam-5963	101	18	ffdes	ffde	NOUN
ejpam-5963	101	19	and	and	CCONJ
ejpam-5963	101	20	will	will	AUX
ejpam-5963	101	21	have	have	VERB
ejpam-5963	101	22	the	the	DET
ejpam-5963	101	23	ability	ability	NOUN
ejpam-5963	101	24	to	to	PART
ejpam-5963	101	25	inspire	inspire	VERB
ejpam-5963	101	26	new	new	ADJ
ejpam-5963	101	27	applications	application	NOUN
ejpam-5963	101	28	and	and	CCONJ
ejpam-5963	101	29	research	research	NOUN
ejpam-5963	101	30	directions	direction	NOUN
ejpam-5963	101	31	.	.	PUNCT
ejpam-5963	102	1	2	2	X
ejpam-5963	102	2	.	.	X
ejpam-5963	102	3	background	background	NOUN
ejpam-5963	102	4	information	information	NOUN
ejpam-5963	102	5	in	in	ADP
ejpam-5963	102	6	this	this	DET
ejpam-5963	102	7	work	work	NOUN
ejpam-5963	102	8	,	,	PUNCT
ejpam-5963	102	9	we	we	PRON
ejpam-5963	102	10	will	will	AUX
ejpam-5963	102	11	use	use	VERB
ejpam-5963	102	12	the	the	DET
ejpam-5963	102	13	following	following	ADJ
ejpam-5963	102	14	notation	notation	NOUN
ejpam-5963	102	15	:	:	PUNCT
ejpam-5963	102	16	the	the	DET
ejpam-5963	102	17	norm	norm	NOUN
ejpam-5963	102	18	define	define	VERB
ejpam-5963	102	19	by	by	ADP
ejpam-5963	102	20	∥u∥	∥u∥	NOUN
ejpam-5963	103	1	=	=	SYM
ejpam-5963	103	2	sup{|u(t)|	sup{|u(t)|	PROPN
ejpam-5963	103	3	:	:	PUNCT
ejpam-5963	104	1	t	t	PROPN
ejpam-5963	104	2	∈	∈	PROPN
ejpam-5963	105	1	[	[	X
ejpam-5963	105	2	0	0	NUM
ejpam-5963	105	3	,	,	PUNCT
ejpam-5963	105	4	t	t	X
ejpam-5963	105	5	]	]	PUNCT
ejpam-5963	105	6	}	}	PUNCT
ejpam-5963	105	7	for	for	ADP
ejpam-5963	105	8	the	the	DET
ejpam-5963	105	9	banach	banach	NOUN
ejpam-5963	105	10	space	space	NOUN
ejpam-5963	105	11	denoted	denote	VERB
ejpam-5963	105	12	by	by	ADP
ejpam-5963	105	13	u	u	NOUN
ejpam-5963	105	14	,	,	PUNCT
ejpam-5963	105	15	v	v	NOUN
ejpam-5963	105	16	=	=	SYM
ejpam-5963	105	17	c([0	c([0	NOUN
ejpam-5963	105	18	,	,	PUNCT
ejpam-5963	105	19	t	t	X
ejpam-5963	105	20	]	]	PUNCT
ejpam-5963	105	21	,	,	PUNCT
ejpam-5963	105	22	r	r	NOUN
ejpam-5963	105	23	)	)	PUNCT
ejpam-5963	105	24	,	,	PUNCT
ejpam-5963	105	25	where	where	SCONJ
ejpam-5963	105	26	s	s	NOUN
ejpam-5963	105	27	represents	represent	VERB
ejpam-5963	105	28	a	a	DET
ejpam-5963	105	29	a.	a.	NOUN
ejpam-5963	105	30	ali	ali	PROPN
ejpam-5963	105	31	et	et	PROPN
ejpam-5963	105	32	al	al	PROPN
ejpam-5963	105	33	.	.	PUNCT
ejpam-5963	105	34	/	/	SYM
ejpam-5963	105	35	eur	eur	PROPN
ejpam-5963	105	36	.	.	PUNCT
ejpam-5963	106	1	j.	j.	PROPN
ejpam-5963	106	2	pure	pure	PROPN
ejpam-5963	106	3	appl	appl	PROPN
ejpam-5963	106	4	.	.	PROPN
ejpam-5963	106	5	math	math	PROPN
ejpam-5963	106	6	,	,	PUNCT
ejpam-5963	106	7	18	18	NUM
ejpam-5963	106	8	(	(	PUNCT
ejpam-5963	106	9	2	2	NUM
ejpam-5963	106	10	)	)	PUNCT
ejpam-5963	106	11	(	(	PUNCT
ejpam-5963	106	12	2025	2025	NUM
ejpam-5963	106	13	)	)	PUNCT
ejpam-5963	106	14	,	,	PUNCT
ejpam-5963	106	15	5963	5963	NUM
ejpam-5963	106	16	5	5	NUM
ejpam-5963	106	17	of	of	ADP
ejpam-5963	106	18	19	19	NUM
ejpam-5963	106	19	family	family	NOUN
ejpam-5963	106	20	of	of	ADP
ejpam-5963	106	21	all	all	DET
ejpam-5963	106	22	bounded	bound	VERB
ejpam-5963	106	23	subsets	subset	NOUN
ejpam-5963	106	24	of	of	ADP
ejpam-5963	106	25	b(u×v	b(u×v	NOUN
ejpam-5963	106	26	)	)	PUNCT
ejpam-5963	106	27	,	,	PUNCT
ejpam-5963	106	28	and	and	CCONJ
ejpam-5963	106	29	the	the	DET
ejpam-5963	106	30	product	product	NOUN
ejpam-5963	106	31	u×v	u×v	PROPN
ejpam-5963	106	32	is	be	AUX
ejpam-5963	106	33	a	a	DET
ejpam-5963	106	34	banach	banach	NOUN
ejpam-5963	106	35	space	space	NOUN
ejpam-5963	106	36	with	with	ADP
ejpam-5963	106	37	norm	norm	NOUN
ejpam-5963	106	38	∥(u	∥(u	ADJ
ejpam-5963	106	39	,	,	PUNCT
ejpam-5963	106	40	v)∥	v)∥	PUNCT
ejpam-5963	106	41	=	=	PRON
ejpam-5963	106	42	∥u∥+	∥u∥+	VERB
ejpam-5963	106	43	∥v∥.	∥v∥.	ADJ
ejpam-5963	106	44	definition	definition	NOUN
ejpam-5963	106	45	1	1	NUM
ejpam-5963	106	46	.	.	PUNCT
ejpam-5963	107	1	[	[	X
ejpam-5963	107	2	2	2	X
ejpam-5963	107	3	]	]	PUNCT
ejpam-5963	107	4	the	the	DET
ejpam-5963	107	5	riemann	riemann	PROPN
ejpam-5963	107	6	-	-	PUNCT
ejpam-5963	107	7	liouville	liouville	VERB
ejpam-5963	107	8	derivative	derivative	NOUN
ejpam-5963	107	9	is	be	AUX
ejpam-5963	107	10	defined	define	VERB
ejpam-5963	107	11	by	by	ADP
ejpam-5963	107	12	fddηy(t	fddηy(t	NOUN
ejpam-5963	107	13	)	)	PUNCT
ejpam-5963	108	1	=	=	SYM
ejpam-5963	108	2			PROPN
ejpam-5963	108	3	1	1	NUM
ejpam-5963	108	4	γ(m−	γ(m−	PROPN
ejpam-5963	108	5	η	η	PROPN
ejpam-5963	108	6	)	)	PUNCT
ejpam-5963	108	7	(	(	PUNCT
ejpam-5963	108	8	d	d	X
ejpam-5963	108	9	dt	dt	NOUN
ejpam-5963	108	10	)	)	PUNCT
ejpam-5963	108	11	m	m	VERB
ejpam-5963	108	12	∫	∫	PROPN
ejpam-5963	109	1	t	t	NOUN
ejpam-5963	109	2	0	0	NUM
ejpam-5963	110	1	(	(	PUNCT
ejpam-5963	110	2	t−	t−	PROPN
ejpam-5963	110	3	δ)m−η−1y(δ)dδ	δ)m−η−1y(δ)dδ	PROPN
ejpam-5963	110	4	,	,	PUNCT
ejpam-5963	110	5	m−	m−	PROPN
ejpam-5963	110	6	1	1	NUM
ejpam-5963	110	7	<	<	X
ejpam-5963	110	8	η	η	X
ejpam-5963	110	9	<	<	X
ejpam-5963	110	10	m	m	PROPN
ejpam-5963	110	11	,	,	PUNCT
ejpam-5963	110	12	1	1	NUM
ejpam-5963	110	13	γ(1−	γ(1−	PROPN
ejpam-5963	110	14	η	η	PROPN
ejpam-5963	110	15	)	)	PUNCT
ejpam-5963	110	16	d	d	PROPN
ejpam-5963	110	17	dt	dt	X
ejpam-5963	110	18	∫	∫	PROPN
ejpam-5963	110	19	t	t	PROPN
ejpam-5963	110	20	0	0	NUM
ejpam-5963	110	21	(	(	PUNCT
ejpam-5963	110	22	t−	t−	PROPN
ejpam-5963	110	23	δ)−ηy(δ)dδ	δ)−ηy(δ)dδ	PROPN
ejpam-5963	110	24	,	,	PUNCT
ejpam-5963	110	25	0	0	PUNCT
ejpam-5963	110	26	<	<	X
ejpam-5963	110	27	η	η	X
ejpam-5963	110	28	<	<	X
ejpam-5963	110	29	1	1	NUM
ejpam-5963	110	30	,	,	PUNCT
ejpam-5963	110	31	dmy	dmy	PROPN
ejpam-5963	110	32	dtm	dtm	PROPN
ejpam-5963	110	33	,	,	PUNCT
ejpam-5963	110	34	η	η	PROPN
ejpam-5963	110	35	=	=	PUNCT
ejpam-5963	110	36	m.	m.	NOUN
ejpam-5963	110	37	in	in	ADP
ejpam-5963	110	38	the	the	DET
ejpam-5963	110	39	same	same	ADJ
ejpam-5963	110	40	way	way	NOUN
ejpam-5963	110	41	,	,	PUNCT
ejpam-5963	110	42	the	the	DET
ejpam-5963	110	43	caputo	caputo	PROPN
ejpam-5963	110	44	fractional	fractional	PROPN
ejpam-5963	110	45	derivative	derivative	NOUN
ejpam-5963	110	46	is	be	AUX
ejpam-5963	110	47	defined	define	VERB
ejpam-5963	110	48	by	by	ADP
ejpam-5963	110	49	fddηy(t	fddηy(t	NOUN
ejpam-5963	110	50	)	)	PUNCT
ejpam-5963	111	1	=	=	SYM
ejpam-5963	111	2			PROPN
ejpam-5963	111	3	1	1	NUM
ejpam-5963	111	4	γ(m−	γ(m−	PROPN
ejpam-5963	111	5	η	η	PROPN
ejpam-5963	111	6	)	)	PUNCT
ejpam-5963	111	7	∫	∫	PROPN
ejpam-5963	112	1	t	t	PROPN
ejpam-5963	112	2	0	0	NUM
ejpam-5963	112	3	(	(	PUNCT
ejpam-5963	112	4	t−	t−	PROPN
ejpam-5963	112	5	δ)m−η−1	δ)m−η−1	PROPN
ejpam-5963	112	6	(	(	PUNCT
ejpam-5963	112	7	d	d	X
ejpam-5963	112	8	dδ	dδ	ADP
ejpam-5963	112	9	)	)	PUNCT
ejpam-5963	112	10	m	m	PROPN
ejpam-5963	112	11	y(δ)dδ	y(δ)dδ	PROPN
ejpam-5963	112	12	,	,	PUNCT
ejpam-5963	112	13	m−	m−	PROPN
ejpam-5963	112	14	1	1	NUM
ejpam-5963	112	15	<	<	X
ejpam-5963	112	16	η	η	X
ejpam-5963	112	17	<	<	X
ejpam-5963	112	18	m	m	PROPN
ejpam-5963	112	19	,	,	PUNCT
ejpam-5963	112	20	1	1	NUM
ejpam-5963	112	21	γ(1−	γ(1−	PROPN
ejpam-5963	112	22	η	η	PROPN
ejpam-5963	112	23	)	)	PUNCT
ejpam-5963	112	24	∫	∫	PROPN
ejpam-5963	113	1	t	t	PROPN
ejpam-5963	113	2	0	0	NUM
ejpam-5963	113	3	(	(	PUNCT
ejpam-5963	113	4	t−	t−	PROPN
ejpam-5963	113	5	δ)−η	δ)−η	PROPN
ejpam-5963	113	6	d	d	PROPN
ejpam-5963	113	7	dδ	dδ	ADP
ejpam-5963	113	8	y(δ)dδ	y(δ)dδ	PROPN
ejpam-5963	113	9	,	,	PUNCT
ejpam-5963	113	10	0	0	PUNCT
ejpam-5963	113	11	<	<	X
ejpam-5963	113	12	η	η	X
ejpam-5963	113	13	<	<	X
ejpam-5963	113	14	1	1	NUM
ejpam-5963	113	15	,	,	PUNCT
ejpam-5963	113	16	dmy	dmy	PROPN
ejpam-5963	113	17	dtm	dtm	PROPN
ejpam-5963	113	18	,	,	PUNCT
ejpam-5963	113	19	η	η	PROPN
ejpam-5963	113	20	=	=	PROPN
ejpam-5963	113	21	m.	m.	NOUN
ejpam-5963	113	22	the	the	DET
ejpam-5963	113	23	corresponding	corresponding	ADJ
ejpam-5963	113	24	fractional	fractional	ADJ
ejpam-5963	113	25	integral	integral	ADJ
ejpam-5963	113	26	is	be	AUX
ejpam-5963	113	27	defined	define	VERB
ejpam-5963	113	28	by	by	ADP
ejpam-5963	113	29	fiiηy(t	fiiηy(t	PROPN
ejpam-5963	113	30	)	)	PUNCT
ejpam-5963	113	31	=	=	SYM
ejpam-5963	113	32	1	1	NUM
ejpam-5963	113	33	γ(η	γ(η	NOUN
ejpam-5963	113	34	)	)	PUNCT
ejpam-5963	114	1	∫	∫	PROPN
ejpam-5963	114	2	t	t	PROPN
ejpam-5963	114	3	0	0	NUM
ejpam-5963	115	1	(	(	PUNCT
ejpam-5963	115	2	t−	t−	PROPN
ejpam-5963	115	3	δ)η−1y(δ)dδ	δ)η−1y(δ)dδ	NOUN
ejpam-5963	115	4	,	,	PUNCT
ejpam-5963	115	5	provided	provide	VERB
ejpam-5963	115	6	that	that	PRON
ejpam-5963	115	7	integral	integral	ADJ
ejpam-5963	115	8	on	on	ADP
ejpam-5963	115	9	right	right	ADJ
ejpam-5963	115	10	exists	exist	NOUN
ejpam-5963	115	11	.	.	PUNCT
ejpam-5963	116	1	definition	definition	NOUN
ejpam-5963	116	2	2	2	NUM
ejpam-5963	116	3	.	.	PUNCT
ejpam-5963	117	1	[	[	X
ejpam-5963	117	2	10	10	NUM
ejpam-5963	117	3	]	]	PUNCT
ejpam-5963	117	4	the	the	DET
ejpam-5963	117	5	ffd	ffd	NOUN
ejpam-5963	117	6	in	in	ADP
ejpam-5963	117	7	sense	sense	NOUN
ejpam-5963	117	8	of	of	ADP
ejpam-5963	117	9	riemann	riemann	PROPN
ejpam-5963	117	10	-	-	PUNCT
ejpam-5963	117	11	liouville	liouville	NOUN
ejpam-5963	117	12	operator	operator	NOUN
ejpam-5963	117	13	for	for	ADP
ejpam-5963	117	14	function	function	NOUN
ejpam-5963	117	15	y	y	PROPN
ejpam-5963	117	16	which	which	PRON
ejpam-5963	117	17	is	be	AUX
ejpam-5963	117	18	differentiable	differentiable	ADJ
ejpam-5963	117	19	both	both	CCONJ
ejpam-5963	117	20	in	in	ADP
ejpam-5963	117	21	fractional	fractional	ADJ
ejpam-5963	117	22	and	and	CCONJ
ejpam-5963	117	23	in	in	ADP
ejpam-5963	117	24	fractals	fractal	NOUN
ejpam-5963	117	25	sense	sense	NOUN
ejpam-5963	117	26	over	over	ADP
ejpam-5963	117	27	[	[	X
ejpam-5963	117	28	0	0	NUM
ejpam-5963	117	29	,	,	PUNCT
ejpam-5963	117	30	t	t	NOUN
ejpam-5963	117	31	]	]	PUNCT
ejpam-5963	117	32	given	give	VERB
ejpam-5963	117	33	by	by	ADP
ejpam-5963	117	34	rffdη	rffdη	PROPN
ejpam-5963	117	35	,	,	PUNCT
ejpam-5963	117	36	ξy(t	ξy(t	PUNCT
ejpam-5963	117	37	)	)	PUNCT
ejpam-5963	117	38	=	=	SYM
ejpam-5963	117	39			PROPN
ejpam-5963	117	40	1	1	NUM
ejpam-5963	117	41	γ(m−	γ(m−	PROPN
ejpam-5963	117	42	η	η	PROPN
ejpam-5963	117	43	)	)	PUNCT
ejpam-5963	117	44	(	(	PUNCT
ejpam-5963	117	45	d	d	NOUN
ejpam-5963	117	46	dtξ	dtξ	NOUN
ejpam-5963	117	47	)	)	PUNCT
ejpam-5963	117	48	m	m	VERB
ejpam-5963	118	1	∫	∫	PROPN
ejpam-5963	118	2	t	t	NOUN
ejpam-5963	118	3	0	0	NUM
ejpam-5963	119	1	(	(	PUNCT
ejpam-5963	119	2	t−	t−	PROPN
ejpam-5963	119	3	δ)m−η−1y(δ)dδ	δ)m−η−1y(δ)dδ	PROPN
ejpam-5963	119	4	,	,	PUNCT
ejpam-5963	119	5	m−	m−	PROPN
ejpam-5963	119	6	1	1	NUM
ejpam-5963	119	7	<	<	X
ejpam-5963	119	8	η	η	X
ejpam-5963	119	9	<	<	X
ejpam-5963	119	10	m	m	PROPN
ejpam-5963	119	11	,	,	PUNCT
ejpam-5963	119	12	1	1	NUM
ejpam-5963	119	13	γ(1−	γ(1−	PROPN
ejpam-5963	119	14	η	η	PROPN
ejpam-5963	119	15	)	)	PUNCT
ejpam-5963	120	1	d	d	X
ejpam-5963	120	2	dtξ	dtξ	NOUN
ejpam-5963	121	1	∫	∫	PROPN
ejpam-5963	121	2	t	t	PROPN
ejpam-5963	121	3	0	0	NUM
ejpam-5963	121	4	(	(	PUNCT
ejpam-5963	121	5	t−	t−	PROPN
ejpam-5963	121	6	δ)−ηy(δ)dδ	δ)−ηy(δ)dδ	PROPN
ejpam-5963	121	7	,	,	PUNCT
ejpam-5963	121	8	0	0	NUM
ejpam-5963	121	9	<	<	X
ejpam-5963	121	10	η	η	PROPN
ejpam-5963	121	11	,	,	PUNCT
ejpam-5963	121	12	ξ	ξ	X
ejpam-5963	121	13	<	<	X
ejpam-5963	121	14	1	1	NUM
ejpam-5963	121	15	,	,	PUNCT
ejpam-5963	121	16	1	1	NUM
ejpam-5963	121	17	γ(m−	γ(m−	PROPN
ejpam-5963	121	18	η	η	PROPN
ejpam-5963	121	19	)	)	PUNCT
ejpam-5963	121	20	(	(	PUNCT
ejpam-5963	121	21	d	d	X
ejpam-5963	121	22	dt	dt	NOUN
ejpam-5963	121	23	)	)	PUNCT
ejpam-5963	121	24	m	m	VERB
ejpam-5963	121	25	∫	∫	PROPN
ejpam-5963	121	26	t	t	NOUN
ejpam-5963	121	27	0	0	NUM
ejpam-5963	121	28	(	(	PUNCT
ejpam-5963	121	29	t−	t−	PROPN
ejpam-5963	121	30	δ)m−η−1y(δ)dδ	δ)m−η−1y(δ)dδ	PROPN
ejpam-5963	121	31	,	,	PUNCT
ejpam-5963	121	32	ξ	ξ	X
ejpam-5963	121	33	=	=	SYM
ejpam-5963	121	34	1,m−	1,m−	NUM
ejpam-5963	121	35	1	1	NUM
ejpam-5963	121	36	<	<	X
ejpam-5963	121	37	η	η	X
ejpam-5963	121	38	<	<	X
ejpam-5963	121	39	m	m	PROPN
ejpam-5963	121	40	,	,	PUNCT
ejpam-5963	121	41	dmy	dmy	PROPN
ejpam-5963	121	42	dtm	dtm	PROPN
ejpam-5963	121	43	,	,	PUNCT
ejpam-5963	121	44	ξ	ξ	X
ejpam-5963	121	45	=	=	SYM
ejpam-5963	121	46	1	1	NUM
ejpam-5963	121	47	,	,	PUNCT
ejpam-5963	121	48	η	η	NOUN
ejpam-5963	121	49	=	=	SYM
ejpam-5963	121	50	m.	m.	NOUN
ejpam-5963	121	51	definition	definition	NOUN
ejpam-5963	121	52	3	3	NUM
ejpam-5963	121	53	.	.	PUNCT
ejpam-5963	122	1	[	[	X
ejpam-5963	122	2	10	10	NUM
ejpam-5963	122	3	]	]	PUNCT
ejpam-5963	122	4	let	let	VERB
ejpam-5963	122	5	y	y	PRON
ejpam-5963	122	6	is	be	AUX
ejpam-5963	122	7	continuous	continuous	ADJ
ejpam-5963	122	8	function	function	NOUN
ejpam-5963	122	9	,	,	PUNCT
ejpam-5963	122	10	then	then	ADV
ejpam-5963	122	11	the	the	DET
ejpam-5963	122	12	fractals	fractal	NOUN
ejpam-5963	122	13	fractional	fractional	ADJ
ejpam-5963	122	14	integral	integral	ADJ
ejpam-5963	122	15	is	be	AUX
ejpam-5963	122	16	defined	define	VERB
ejpam-5963	122	17	as	as	SCONJ
ejpam-5963	122	18	follows	follow	VERB
ejpam-5963	122	19	:	:	PUNCT
ejpam-5963	122	20	rff	rff	NOUN
ejpam-5963	122	21	iη	iη	NOUN
ejpam-5963	122	22	,	,	PUNCT
ejpam-5963	122	23	ξf(t	ξf(t	NOUN
ejpam-5963	122	24	)	)	PUNCT
ejpam-5963	122	25	=	=	SYM
ejpam-5963	123	1	ξ	ξ	PRON
ejpam-5963	123	2	γ(η	γ(η	PROPN
ejpam-5963	123	3	)	)	PUNCT
ejpam-5963	124	1	∫	∫	PROPN
ejpam-5963	125	1	t	t	PROPN
ejpam-5963	125	2	0	0	NUM
ejpam-5963	125	3	(	(	PUNCT
ejpam-5963	125	4	t−	t−	DET
ejpam-5963	125	5	δ)η−1δξ−1f(δ)dδ	δ)η−1δξ−1f(δ)dδ	NOUN
ejpam-5963	125	6	,	,	PUNCT
ejpam-5963	125	7	where	where	SCONJ
ejpam-5963	125	8	ξ	ξ	PROPN
ejpam-5963	125	9	is	be	AUX
ejpam-5963	125	10	fractal	fractal	ADJ
ejpam-5963	125	11	dimension	dimension	NOUN
ejpam-5963	125	12	and	and	CCONJ
ejpam-5963	125	13	η	η	PROPN
ejpam-5963	125	14	is	be	AUX
ejpam-5963	125	15	fractional	fractional	ADJ
ejpam-5963	125	16	order	order	NOUN
ejpam-5963	125	17	.	.	PUNCT
ejpam-5963	126	1	a.	a.	PROPN
ejpam-5963	126	2	ali	ali	PROPN
ejpam-5963	126	3	et	et	PROPN
ejpam-5963	126	4	al	al	PROPN
ejpam-5963	126	5	.	.	PUNCT
ejpam-5963	126	6	/	/	SYM
ejpam-5963	126	7	eur	eur	PROPN
ejpam-5963	126	8	.	.	PUNCT
ejpam-5963	127	1	j.	j.	PROPN
ejpam-5963	127	2	pure	pure	PROPN
ejpam-5963	127	3	appl	appl	PROPN
ejpam-5963	127	4	.	.	PROPN
ejpam-5963	127	5	math	math	PROPN
ejpam-5963	127	6	,	,	PUNCT
ejpam-5963	127	7	18	18	NUM
ejpam-5963	127	8	(	(	PUNCT
ejpam-5963	127	9	2	2	NUM
ejpam-5963	127	10	)	)	PUNCT
ejpam-5963	127	11	(	(	PUNCT
ejpam-5963	127	12	2025	2025	NUM
ejpam-5963	127	13	)	)	PUNCT
ejpam-5963	127	14	,	,	PUNCT
ejpam-5963	127	15	5963	5963	NUM
ejpam-5963	127	16	6	6	NUM
ejpam-5963	127	17	of	of	ADP
ejpam-5963	127	18	19	19	NUM
ejpam-5963	127	19	lemma	lemma	PROPN
ejpam-5963	127	20	1	1	NUM
ejpam-5963	127	21	.	.	PUNCT
ejpam-5963	128	1	[	[	X
ejpam-5963	128	2	2	2	X
ejpam-5963	128	3	]	]	PUNCT
ejpam-5963	128	4	the	the	DET
ejpam-5963	128	5	solution	solution	NOUN
ejpam-5963	128	6	of	of	ADP
ejpam-5963	128	7	fdes	fde	NOUN
ejpam-5963	128	8	fddηr(t)−	fddηr(t)−	PROPN
ejpam-5963	128	9	ξtξ−1e(t	ξtξ−1e(t	ADJ
ejpam-5963	128	10	)	)	PUNCT
ejpam-5963	128	11	=	=	SYM
ejpam-5963	128	12	0	0	NUM
ejpam-5963	128	13	,	,	PUNCT
ejpam-5963	128	14	r(0	r(0	PROPN
ejpam-5963	128	15	)	)	PUNCT
ejpam-5963	128	16	=	=	SYM
ejpam-5963	128	17	r0	r0	NOUN
ejpam-5963	128	18	,	,	PUNCT
ejpam-5963	128	19	is	be	AUX
ejpam-5963	128	20	given	give	VERB
ejpam-5963	128	21	by	by	ADP
ejpam-5963	128	22	r(t	r(t	NOUN
ejpam-5963	128	23	)	)	PUNCT
ejpam-5963	128	24	=	=	SYM
ejpam-5963	128	25	r0	r0	NOUN
ejpam-5963	128	26	+	+	CCONJ
ejpam-5963	128	27	fi	fi	NOUN
ejpam-5963	128	28	iηξtξ−1e(t	iηξtξ−1e(t	NOUN
ejpam-5963	128	29	)	)	PUNCT
ejpam-5963	128	30	.	.	PUNCT
ejpam-5963	129	1	definition	definition	NOUN
ejpam-5963	129	2	4	4	NUM
ejpam-5963	129	3	.	.	PUNCT
ejpam-5963	130	1	(	(	PUNCT
ejpam-5963	130	2	fixed	fix	VERB
ejpam-5963	130	3	point:)[29	point:)[29	NOUN
ejpam-5963	130	4	]	]	X
ejpam-5963	130	5	let	let	VERB
ejpam-5963	130	6	u	u	PRON
ejpam-5963	130	7	×	×	VERB
ejpam-5963	130	8	v	v	INTJ
ejpam-5963	130	9	be	be	AUX
ejpam-5963	130	10	a	a	DET
ejpam-5963	130	11	norm	norm	NOUN
ejpam-5963	130	12	linear	linear	ADJ
ejpam-5963	130	13	space	space	NOUN
ejpam-5963	130	14	and	and	CCONJ
ejpam-5963	130	15	mapping	mapping	NOUN
ejpam-5963	130	16	h	h	NOUN
ejpam-5963	130	17	:	:	PUNCT
ejpam-5963	130	18	u×v	u×v	PROPN
ejpam-5963	130	19	→	→	SYM
ejpam-5963	130	20	u×v	u×v	PROPN
ejpam-5963	130	21	,	,	PUNCT
ejpam-5963	130	22	then	then	ADV
ejpam-5963	130	23	(	(	PUNCT
ejpam-5963	130	24	r	r	NOUN
ejpam-5963	130	25	,	,	PUNCT
ejpam-5963	130	26	p	p	NOUN
ejpam-5963	130	27	)	)	PUNCT
ejpam-5963	130	28	∈	∈	PROPN
ejpam-5963	130	29	u×v	u×v	PROPN
ejpam-5963	130	30	is	be	AUX
ejpam-5963	130	31	be	be	AUX
ejpam-5963	130	32	fixed	fix	VERB
ejpam-5963	130	33	point	point	NOUN
ejpam-5963	130	34	,	,	PUNCT
ejpam-5963	130	35	if	if	SCONJ
ejpam-5963	130	36	h(r	h(r	ADJ
ejpam-5963	130	37	,	,	PUNCT
ejpam-5963	130	38	p	p	NOUN
ejpam-5963	130	39	)	)	PUNCT
ejpam-5963	130	40	=	=	SYM
ejpam-5963	130	41	(	(	PUNCT
ejpam-5963	130	42	r	r	NOUN
ejpam-5963	130	43	,	,	PUNCT
ejpam-5963	130	44	p	p	NOUN
ejpam-5963	130	45	)	)	PUNCT
ejpam-5963	130	46	definition	definition	NOUN
ejpam-5963	130	47	5	5	NUM
ejpam-5963	130	48	.	.	PUNCT
ejpam-5963	131	1	[	[	X
ejpam-5963	131	2	29	29	NUM
ejpam-5963	131	3	]	]	PUNCT
ejpam-5963	131	4	(	(	PUNCT
ejpam-5963	131	5	equi	equi	NOUN
ejpam-5963	131	6	-	-	PUNCT
ejpam-5963	131	7	continuous	continuous	ADJ
ejpam-5963	131	8	:)	:)	INTJ
ejpam-5963	131	9	let	let	VERB
ejpam-5963	131	10	a	a	DET
ejpam-5963	131	11	bounded	bound	VERB
ejpam-5963	131	12	subset	subset	NOUN
ejpam-5963	131	13	b	b	PROPN
ejpam-5963	131	14	of	of	ADP
ejpam-5963	131	15	u	u	PROPN
ejpam-5963	131	16	×	×	PROPN
ejpam-5963	131	17	v	v	NOUN
ejpam-5963	131	18	and	and	CCONJ
ejpam-5963	131	19	(	(	PUNCT
ejpam-5963	131	20	rn	rn	PROPN
ejpam-5963	131	21	,	,	PUNCT
ejpam-5963	131	22	pn	pn	PROPN
ejpam-5963	131	23	)	)	PUNCT
ejpam-5963	131	24	have	have	VERB
ejpam-5963	131	25	a	a	DET
ejpam-5963	131	26	sequence	sequence	NOUN
ejpam-5963	131	27	in	in	ADP
ejpam-5963	131	28	b	b	NOUN
ejpam-5963	131	29	for	for	ADP
ejpam-5963	131	30	several	several	ADJ
ejpam-5963	131	31	(	(	PUNCT
ejpam-5963	131	32	rn	rn	PROPN
ejpam-5963	131	33	,	,	PUNCT
ejpam-5963	131	34	pn	pn	NOUN
ejpam-5963	131	35	)	)	PUNCT
ejpam-5963	131	36	in	in	ADP
ejpam-5963	131	37	b	b	PROPN
ejpam-5963	131	38	and	and	CCONJ
ejpam-5963	131	39	for	for	ADP
ejpam-5963	131	40	all	all	DET
ejpam-5963	131	41	possible	possible	ADJ
ejpam-5963	131	42	ϵ	ϵ	X
ejpam-5963	131	43	>	>	X
ejpam-5963	131	44	0	0	NUM
ejpam-5963	132	1	|ζ(rn	|ζ(rn	PROPN
ejpam-5963	132	2	,	,	PUNCT
ejpam-5963	132	3	pn)(t)−	pn)(t)−	PROPN
ejpam-5963	132	4	ζ(rn	ζ(rn	PROPN
ejpam-5963	132	5	,	,	PUNCT
ejpam-5963	132	6	pn)(τ)|	pn)(τ)|	PROPN
ejpam-5963	132	7	≤	≤	X
ejpam-5963	132	8	ϵ	ϵ	X
ejpam-5963	132	9	theorem	theorem	NOUN
ejpam-5963	132	10	1	1	NUM
ejpam-5963	132	11	.	.	PUNCT
ejpam-5963	133	1	[	[	X
ejpam-5963	133	2	29	29	NUM
ejpam-5963	133	3	]	]	PUNCT
ejpam-5963	133	4	let	let	VERB
ejpam-5963	133	5	u	u	PRON
ejpam-5963	133	6	×	×	VERB
ejpam-5963	133	7	v	v	NOUN
ejpam-5963	133	8	,	,	PUNCT
ejpam-5963	133	9	be	be	AUX
ejpam-5963	133	10	a	a	DET
ejpam-5963	133	11	banach	banach	NOUN
ejpam-5963	133	12	space	space	NOUN
ejpam-5963	133	13	and	and	CCONJ
ejpam-5963	133	14	mapping	mapping	NOUN
ejpam-5963	133	15	h	h	NOUN
ejpam-5963	133	16	:	:	PUNCT
ejpam-5963	133	17	u	u	NOUN
ejpam-5963	133	18	×	×	PROPN
ejpam-5963	133	19	v	v	INTJ
ejpam-5963	133	20	→	→	SYM
ejpam-5963	133	21	u	u	NOUN
ejpam-5963	133	22	×	×	PROPN
ejpam-5963	133	23	v	v	NOUN
ejpam-5963	133	24	,	,	PUNCT
ejpam-5963	133	25	is	be	AUX
ejpam-5963	133	26	contraction	contraction	NOUN
ejpam-5963	133	27	,	,	PUNCT
ejpam-5963	133	28	with	with	ADP
ejpam-5963	133	29	h(r	h(r	PROPN
ejpam-5963	133	30	,	,	PUNCT
ejpam-5963	133	31	p	p	NOUN
ejpam-5963	133	32	)	)	PUNCT
ejpam-5963	133	33	=	=	SYM
ejpam-5963	133	34	(	(	PUNCT
ejpam-5963	133	35	r	r	NOUN
ejpam-5963	133	36	,	,	PUNCT
ejpam-5963	133	37	p	p	NOUN
ejpam-5963	133	38	)	)	PUNCT
ejpam-5963	133	39	,	,	PUNCT
ejpam-5963	133	40	then	then	ADV
ejpam-5963	133	41	h	h	PROPN
ejpam-5963	133	42	has	have	VERB
ejpam-5963	133	43	a	a	DET
ejpam-5963	133	44	unique	unique	ADJ
ejpam-5963	133	45	fixed	fix	VERB
ejpam-5963	133	46	point	point	NOUN
ejpam-5963	133	47	in	in	ADP
ejpam-5963	133	48	u×v	u×v	PROPN
ejpam-5963	133	49	.	.	PUNCT
ejpam-5963	134	1	theorem	theorem	PROPN
ejpam-5963	134	2	2	2	NUM
ejpam-5963	134	3	.	.	PUNCT
ejpam-5963	135	1	(	(	PUNCT
ejpam-5963	135	2	krasnoselskii	krasnoselskii	PROPN
ejpam-5963	135	3	theorem:)[30	theorem:)[30	X
ejpam-5963	135	4	]	]	PUNCT
ejpam-5963	135	5	let	let	VERB
ejpam-5963	135	6	b	b	PRON
ejpam-5963	135	7	be	be	AUX
ejpam-5963	135	8	a	a	DET
ejpam-5963	135	9	banach	banach	NOUN
ejpam-5963	135	10	space	space	NOUN
ejpam-5963	135	11	and	and	CCONJ
ejpam-5963	135	12	h	h	NOUN
ejpam-5963	135	13	and	and	CCONJ
ejpam-5963	135	14	g	g	PROPN
ejpam-5963	135	15	be	be	VERB
ejpam-5963	135	16	two	two	NUM
ejpam-5963	135	17	operators	operator	NOUN
ejpam-5963	135	18	,	,	PUNCT
ejpam-5963	135	19	such	such	ADJ
ejpam-5963	135	20	that	that	SCONJ
ejpam-5963	135	21	•	•	NUM
ejpam-5963	135	22	h	h	NOUN
ejpam-5963	135	23	is	be	AUX
ejpam-5963	135	24	contraction	contraction	NOUN
ejpam-5963	135	25	.	.	PUNCT
ejpam-5963	136	1	•	•	NUM
ejpam-5963	136	2	g	g	PROPN
ejpam-5963	136	3	is	be	AUX
ejpam-5963	136	4	compact	compact	ADJ
ejpam-5963	136	5	operator	operator	NOUN
ejpam-5963	136	6	.	.	PUNCT
ejpam-5963	137	1	•	•	NUM
ejpam-5963	137	2	then	then	ADV
ejpam-5963	137	3	p	p	NOUN
ejpam-5963	137	4	=	=	PUNCT
ejpam-5963	137	5	(	(	PUNCT
ejpam-5963	137	6	h	h	NOUN
ejpam-5963	137	7	+	+	NOUN
ejpam-5963	137	8	g)p	g)p	NOUN
ejpam-5963	137	9	has	have	VERB
ejpam-5963	137	10	a	a	DET
ejpam-5963	137	11	fixed	fix	VERB
ejpam-5963	137	12	point	point	NOUN
ejpam-5963	137	13	.	.	PUNCT
ejpam-5963	138	1	3	3	X
ejpam-5963	138	2	.	.	X
ejpam-5963	138	3	existence	existence	NOUN
ejpam-5963	138	4	of	of	ADP
ejpam-5963	138	5	solution	solution	NOUN
ejpam-5963	138	6	this	this	DET
ejpam-5963	138	7	section	section	NOUN
ejpam-5963	138	8	of	of	ADP
ejpam-5963	138	9	research	research	NOUN
ejpam-5963	138	10	work	work	NOUN
ejpam-5963	138	11	is	be	AUX
ejpam-5963	138	12	devoted	devote	VERB
ejpam-5963	138	13	to	to	ADP
ejpam-5963	138	14	eus	eus	PROPN
ejpam-5963	138	15	for	for	ADP
ejpam-5963	138	16	the	the	DET
ejpam-5963	138	17	proposed	propose	VERB
ejpam-5963	138	18	coupled	couple	VERB
ejpam-5963	138	19	system	system	NOUN
ejpam-5963	138	20	of	of	ADP
ejpam-5963	138	21	ffdes	ffde	NOUN
ejpam-5963	138	22	(	(	PUNCT
ejpam-5963	138	23	1	1	NUM
ejpam-5963	138	24	)	)	PUNCT
ejpam-5963	138	25	.	.	PUNCT
ejpam-5963	139	1	lemma	lemma	PROPN
ejpam-5963	139	2	2	2	X
ejpam-5963	139	3	.	.	PUNCT
ejpam-5963	140	1	let	let	VERB
ejpam-5963	140	2	t	t	PROPN
ejpam-5963	140	3	∈	∈	PROPN
ejpam-5963	141	1	i	i	PROPN
ejpam-5963	141	2	and	and	CCONJ
ejpam-5963	141	3	η	η	PROPN
ejpam-5963	141	4	,	,	PUNCT
ejpam-5963	141	5	ξ	ξ	PROPN
ejpam-5963	141	6	∈	∈	PROPN
ejpam-5963	141	7	(	(	PUNCT
ejpam-5963	141	8	0	0	NUM
ejpam-5963	141	9	,	,	PUNCT
ejpam-5963	141	10	1	1	NUM
ejpam-5963	141	11	]	]	PUNCT
ejpam-5963	141	12	,	,	PUNCT
ejpam-5963	141	13	then	then	ADV
ejpam-5963	141	14	the	the	DET
ejpam-5963	141	15	solution	solution	NOUN
ejpam-5963	141	16	of	of	ADP
ejpam-5963	141	17	coupled	couple	VERB
ejpam-5963	141	18	system	system	NOUN
ejpam-5963	141	19	of	of	ADP
ejpam-5963	141	20	ffdes	ffdes	PROPN
ejpam-5963	141	21	fddηr(t	fddηr(t	NOUN
ejpam-5963	141	22	)	)	PUNCT
ejpam-5963	141	23	=	=	SYM
ejpam-5963	142	1	ξtξ−1f	ξtξ−1f	PROPN
ejpam-5963	142	2	(	(	PUNCT
ejpam-5963	142	3	t	t	PROPN
ejpam-5963	142	4	,	,	PUNCT
ejpam-5963	142	5	r(t	r(t	NOUN
ejpam-5963	142	6	)	)	PUNCT
ejpam-5963	142	7	,	,	PUNCT
ejpam-5963	142	8	p(t	p(t	NOUN
ejpam-5963	142	9	)	)	PUNCT
ejpam-5963	142	10	)	)	PUNCT
ejpam-5963	142	11	,	,	PUNCT
ejpam-5963	142	12	fddηp(t	fddηp(t	NOUN
ejpam-5963	142	13	)	)	PUNCT
ejpam-5963	142	14	=	=	SYM
ejpam-5963	142	15	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	142	16	,	,	PUNCT
ejpam-5963	142	17	r(t	r(t	NOUN
ejpam-5963	142	18	)	)	PUNCT
ejpam-5963	142	19	,	,	PUNCT
ejpam-5963	142	20	p(t	p(t	NOUN
ejpam-5963	142	21	)	)	PUNCT
ejpam-5963	142	22	)	)	PUNCT
ejpam-5963	142	23	,	,	PUNCT
ejpam-5963	142	24	r(0	r(0	PROPN
ejpam-5963	142	25	)	)	PUNCT
ejpam-5963	142	26	=	=	SYM
ejpam-5963	142	27	r0	r0	NOUN
ejpam-5963	142	28	+	+	CCONJ
ejpam-5963	142	29	ϕ(r	ϕ(r	PROPN
ejpam-5963	142	30	)	)	PUNCT
ejpam-5963	142	31	,	,	PUNCT
ejpam-5963	142	32	p(0	p(0	NOUN
ejpam-5963	142	33	)	)	PUNCT
ejpam-5963	142	34	=	=	SYM
ejpam-5963	142	35	p0	p0	NOUN
ejpam-5963	142	36	+	+	CCONJ
ejpam-5963	142	37	ψ(p	ψ(p	NOUN
ejpam-5963	142	38	)	)	PUNCT
ejpam-5963	142	39	,	,	PUNCT
ejpam-5963	142	40	(	(	PUNCT
ejpam-5963	142	41	2	2	X
ejpam-5963	142	42	)	)	PUNCT
ejpam-5963	142	43	is	be	AUX
ejpam-5963	142	44	provided	provide	VERB
ejpam-5963	142	45	by	by	ADP
ejpam-5963	142	46			PROPN
ejpam-5963	142	47	r(t	r(t	NOUN
ejpam-5963	142	48	)	)	PUNCT
ejpam-5963	142	49	=	=	SYM
ejpam-5963	142	50	r0	r0	NOUN
ejpam-5963	142	51	+	+	CCONJ
ejpam-5963	142	52	ϕ(r	ϕ(r	PROPN
ejpam-5963	142	53	)	)	PUNCT
ejpam-5963	143	1	+	+	CCONJ
ejpam-5963	144	1	ξ	ξ	DET
ejpam-5963	144	2	γ(η	γ(η	NOUN
ejpam-5963	144	3	)	)	PUNCT
ejpam-5963	144	4	∫	∫	PROPN
ejpam-5963	144	5	t	t	PROPN
ejpam-5963	144	6	0	0	NUM
ejpam-5963	144	7	(	(	PUNCT
ejpam-5963	144	8	t−	t−	PROPN
ejpam-5963	144	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	144	10	,	,	PUNCT
ejpam-5963	144	11	r(δ	r(δ	PROPN
ejpam-5963	144	12	)	)	PUNCT
ejpam-5963	144	13	,	,	PUNCT
ejpam-5963	144	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	144	15	,	,	PUNCT
ejpam-5963	144	16	p(t	p(t	NOUN
ejpam-5963	144	17	)	)	PUNCT
ejpam-5963	145	1	=	=	SYM
ejpam-5963	145	2	p0	p0	NOUN
ejpam-5963	145	3	+	+	CCONJ
ejpam-5963	145	4	ψ(p	ψ(p	NOUN
ejpam-5963	145	5	)	)	PUNCT
ejpam-5963	146	1	+	+	NUM
ejpam-5963	147	1	ξ	ξ	DET
ejpam-5963	147	2	γ(η	γ(η	NOUN
ejpam-5963	147	3	)	)	PUNCT
ejpam-5963	147	4	∫	∫	PROPN
ejpam-5963	147	5	t	t	PROPN
ejpam-5963	147	6	0	0	NUM
ejpam-5963	147	7	(	(	PUNCT
ejpam-5963	147	8	t−	t−	PROPN
ejpam-5963	147	9	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	147	10	,	,	PUNCT
ejpam-5963	147	11	r(δ	r(δ	PROPN
ejpam-5963	147	12	)	)	PUNCT
ejpam-5963	147	13	,	,	PUNCT
ejpam-5963	147	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	147	15	.	.	PUNCT
ejpam-5963	148	1	(	(	PUNCT
ejpam-5963	148	2	3	3	X
ejpam-5963	148	3	)	)	PUNCT
ejpam-5963	148	4	a.	a.	NOUN
ejpam-5963	148	5	ali	ali	PROPN
ejpam-5963	148	6	et	et	PROPN
ejpam-5963	148	7	al	al	PROPN
ejpam-5963	148	8	.	.	PUNCT
ejpam-5963	148	9	/	/	SYM
ejpam-5963	148	10	eur	eur	PROPN
ejpam-5963	148	11	.	.	PUNCT
ejpam-5963	149	1	j.	j.	PROPN
ejpam-5963	149	2	pure	pure	PROPN
ejpam-5963	149	3	appl	appl	PROPN
ejpam-5963	149	4	.	.	PROPN
ejpam-5963	149	5	math	math	PROPN
ejpam-5963	149	6	,	,	PUNCT
ejpam-5963	149	7	18	18	NUM
ejpam-5963	149	8	(	(	PUNCT
ejpam-5963	149	9	2	2	NUM
ejpam-5963	149	10	)	)	PUNCT
ejpam-5963	149	11	(	(	PUNCT
ejpam-5963	149	12	2025	2025	NUM
ejpam-5963	149	13	)	)	PUNCT
ejpam-5963	149	14	,	,	PUNCT
ejpam-5963	149	15	5963	5963	NUM
ejpam-5963	149	16	7	7	NUM
ejpam-5963	149	17	of	of	ADP
ejpam-5963	149	18	19	19	NUM
ejpam-5963	149	19	proof	proof	NOUN
ejpam-5963	149	20	.	.	PUNCT
ejpam-5963	150	1	let	let	VERB
ejpam-5963	150	2	us	we	PRON
ejpam-5963	150	3	consider	consider	VERB
ejpam-5963	150	4	the	the	DET
ejpam-5963	150	5	coupled	couple	VERB
ejpam-5963	150	6	system	system	NOUN
ejpam-5963	150	7	of	of	ADP
ejpam-5963	150	8	ffdes	ffde	NOUN
ejpam-5963	150	9	(	(	PUNCT
ejpam-5963	150	10	2	2	NUM
ejpam-5963	150	11	)	)	PUNCT
ejpam-5963	150	12	in	in	ADP
ejpam-5963	150	13	the	the	DET
ejpam-5963	150	14	form	form	NOUN
ejpam-5963	150	15	of	of	ADP
ejpam-5963	150	16	linear	linear	ADJ
ejpam-5963	150	17	equations	equation	NOUN
ejpam-5963	150	18	as	as	ADP
ejpam-5963	150	19	:	:	PUNCT
ejpam-5963	150	20			NOUN
ejpam-5963	150	21	fddηr(t	fddηr(t	NOUN
ejpam-5963	150	22	)	)	PUNCT
ejpam-5963	150	23	=	=	SYM
ejpam-5963	151	1	ξtξ−1f	ξtξ−1f	PROPN
ejpam-5963	151	2	(	(	PUNCT
ejpam-5963	151	3	t	t	PROPN
ejpam-5963	151	4	,	,	PUNCT
ejpam-5963	151	5	r(t	r(t	NOUN
ejpam-5963	151	6	)	)	PUNCT
ejpam-5963	151	7	,	,	PUNCT
ejpam-5963	151	8	p(t	p(t	NOUN
ejpam-5963	151	9	)	)	PUNCT
ejpam-5963	151	10	)	)	PUNCT
ejpam-5963	152	1	=	=	SYM
ejpam-5963	152	2	θ1(t	θ1(t	PROPN
ejpam-5963	152	3	)	)	PUNCT
ejpam-5963	152	4	,	,	PUNCT
ejpam-5963	152	5	fddηp(t	fddηp(t	NOUN
ejpam-5963	152	6	)	)	PUNCT
ejpam-5963	152	7	=	=	SYM
ejpam-5963	153	1	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	153	2	,	,	PUNCT
ejpam-5963	153	3	r(t	r(t	NOUN
ejpam-5963	153	4	)	)	PUNCT
ejpam-5963	153	5	,	,	PUNCT
ejpam-5963	153	6	p(t	p(t	NOUN
ejpam-5963	153	7	)	)	PUNCT
ejpam-5963	153	8	)	)	PUNCT
ejpam-5963	154	1	=	=	SYM
ejpam-5963	154	2	θ2(1	θ2(1	NOUN
ejpam-5963	154	3	)	)	PUNCT
ejpam-5963	154	4	,	,	PUNCT
ejpam-5963	154	5	r(0	r(0	PROPN
ejpam-5963	154	6	)	)	PUNCT
ejpam-5963	154	7	=	=	SYM
ejpam-5963	154	8	r0	r0	NOUN
ejpam-5963	154	9	+	+	CCONJ
ejpam-5963	154	10	ϕ(r	ϕ(r	PROPN
ejpam-5963	154	11	)	)	PUNCT
ejpam-5963	154	12	,	,	PUNCT
ejpam-5963	154	13	p(0	p(0	NOUN
ejpam-5963	154	14	)	)	PUNCT
ejpam-5963	154	15	=	=	SYM
ejpam-5963	154	16	p0	p0	NOUN
ejpam-5963	154	17	+	+	CCONJ
ejpam-5963	154	18	ψ(p	ψ(p	NOUN
ejpam-5963	154	19	)	)	PUNCT
ejpam-5963	154	20	,	,	PUNCT
ejpam-5963	154	21	(	(	PUNCT
ejpam-5963	154	22	4	4	X
ejpam-5963	154	23	)	)	PUNCT
ejpam-5963	154	24	where	where	SCONJ
ejpam-5963	154	25	θ1(t	θ1(t	X
ejpam-5963	154	26	)	)	PUNCT
ejpam-5963	154	27	,	,	PUNCT
ejpam-5963	154	28	θ2(t	θ2(t	PROPN
ejpam-5963	154	29	)	)	PUNCT
ejpam-5963	154	30	:	:	PUNCT
ejpam-5963	155	1	i	i	PRON
ejpam-5963	155	2	→	→	PUNCT
ejpam-5963	155	3	r	r	NOUN
ejpam-5963	155	4	are	be	AUX
ejpam-5963	155	5	continuous	continuous	ADJ
ejpam-5963	155	6	functions	function	NOUN
ejpam-5963	155	7	.	.	PUNCT
ejpam-5963	156	1	applying	apply	VERB
ejpam-5963	156	2	fiiη	fiiη	NOUN
ejpam-5963	156	3	on	on	ADP
ejpam-5963	156	4	coupled	couple	VERB
ejpam-5963	156	5	system	system	NOUN
ejpam-5963	156	6	of	of	ADP
ejpam-5963	156	7	ffdes	ffde	NOUN
ejpam-5963	156	8	(	(	PUNCT
ejpam-5963	156	9	4	4	NUM
ejpam-5963	156	10	)	)	PUNCT
ejpam-5963	156	11	and	and	CCONJ
ejpam-5963	156	12	in	in	ADP
ejpam-5963	156	13	view	view	NOUN
ejpam-5963	156	14	of	of	ADP
ejpam-5963	156	15	lemma	lemma	PROPN
ejpam-5963	156	16	1	1	NUM
ejpam-5963	156	17	,	,	PUNCT
ejpam-5963	156	18	we	we	PRON
ejpam-5963	156	19	obtain	obtain	VERB
ejpam-5963	156	20	{	{	PUNCT
ejpam-5963	156	21	r(t	r(t	NOUN
ejpam-5963	156	22	)	)	PUNCT
ejpam-5963	156	23	=	=	PUNCT
ejpam-5963	156	24	h0	h0	NOUN
ejpam-5963	156	25	+	+	CCONJ
ejpam-5963	156	26	fi	fi	NOUN
ejpam-5963	156	27	ipξtξ−1θ1(t	ipξtξ−1θ1(t	NOUN
ejpam-5963	156	28	)	)	PUNCT
ejpam-5963	156	29	,	,	PUNCT
ejpam-5963	156	30	p(t	p(t	NOUN
ejpam-5963	156	31	)	)	PUNCT
ejpam-5963	157	1	=	=	PUNCT
ejpam-5963	157	2	h∗0	h∗0	PROPN
ejpam-5963	158	1	+	+	CCONJ
ejpam-5963	158	2	fi	fi	NOUN
ejpam-5963	158	3	iηξtξ−1θ2(t	iηξtξ−1θ2(t	PROPN
ejpam-5963	158	4	)	)	PUNCT
ejpam-5963	158	5	.	.	PUNCT
ejpam-5963	159	1	(	(	PUNCT
ejpam-5963	159	2	5	5	X
ejpam-5963	159	3	)	)	PUNCT
ejpam-5963	159	4	using	use	VERB
ejpam-5963	159	5	the	the	DET
ejpam-5963	159	6	condition	condition	NOUN
ejpam-5963	159	7	r(0	r(0	PROPN
ejpam-5963	159	8	)	)	PUNCT
ejpam-5963	159	9	=	=	SYM
ejpam-5963	159	10	r0	r0	NOUN
ejpam-5963	159	11	+	+	CCONJ
ejpam-5963	159	12	ϕ(r	ϕ(r	PROPN
ejpam-5963	159	13	)	)	PUNCT
ejpam-5963	159	14	and	and	CCONJ
ejpam-5963	159	15	p(0	p(0	NOUN
ejpam-5963	159	16	)	)	PUNCT
ejpam-5963	160	1	=	=	NOUN
ejpam-5963	160	2	p0	p0	NOUN
ejpam-5963	160	3	+	+	CCONJ
ejpam-5963	160	4	ψ(t	ψ(t	PROPN
ejpam-5963	160	5	,	,	PUNCT
ejpam-5963	160	6	e(t	e(t	NOUN
ejpam-5963	160	7	)	)	PUNCT
ejpam-5963	160	8	)	)	PUNCT
ejpam-5963	160	9	,	,	PUNCT
ejpam-5963	160	10	we	we	PRON
ejpam-5963	160	11	obtain	obtain	VERB
ejpam-5963	160	12	equation	equation	NOUN
ejpam-5963	160	13	(	(	PUNCT
ejpam-5963	160	14	5	5	NUM
ejpam-5963	160	15	)	)	PUNCT
ejpam-5963	160	16	in	in	ADP
ejpam-5963	160	17	the	the	DET
ejpam-5963	160	18	form	form	NOUN
ejpam-5963	160	19	of	of	ADP
ejpam-5963	160	20			PROPN
ejpam-5963	160	21	r(t	r(t	NOUN
ejpam-5963	160	22	)	)	PUNCT
ejpam-5963	160	23	=	=	SYM
ejpam-5963	160	24	r0	r0	NOUN
ejpam-5963	160	25	+	+	CCONJ
ejpam-5963	160	26	ϕ(r	ϕ(r	PROPN
ejpam-5963	160	27	)	)	PUNCT
ejpam-5963	161	1	+	+	CCONJ
ejpam-5963	162	1	ξ	ξ	DET
ejpam-5963	162	2	γ(η	γ(η	NOUN
ejpam-5963	162	3	)	)	PUNCT
ejpam-5963	162	4	∫	∫	PROPN
ejpam-5963	162	5	t	t	PROPN
ejpam-5963	162	6	0	0	NUM
ejpam-5963	162	7	(	(	PUNCT
ejpam-5963	162	8	t−	t−	PROPN
ejpam-5963	162	9	δ)η−1δξ−1θ1(δ)dδ	δ)η−1δξ−1θ1(δ)dδ	PROPN
ejpam-5963	162	10	.	.	PUNCT
ejpam-5963	162	11	p(t	p(t	NOUN
ejpam-5963	162	12	)	)	PUNCT
ejpam-5963	163	1	=	=	SYM
ejpam-5963	163	2	p0	p0	NOUN
ejpam-5963	163	3	+	+	CCONJ
ejpam-5963	163	4	ψ(p	ψ(p	NOUN
ejpam-5963	163	5	)	)	PUNCT
ejpam-5963	164	1	+	+	NUM
ejpam-5963	165	1	ξ	ξ	DET
ejpam-5963	165	2	γ(η	γ(η	NOUN
ejpam-5963	165	3	)	)	PUNCT
ejpam-5963	165	4	∫	∫	PROPN
ejpam-5963	165	5	t	t	PROPN
ejpam-5963	165	6	0	0	NUM
ejpam-5963	165	7	(	(	PUNCT
ejpam-5963	165	8	t−	t−	PROPN
ejpam-5963	165	9	δ)η−1δξ−1θ2(δ)dδ	δ)η−1δξ−1θ2(δ)dδ	PROPN
ejpam-5963	165	10	.	.	PUNCT
ejpam-5963	166	1	(	(	PUNCT
ejpam-5963	166	2	6	6	NUM
ejpam-5963	166	3	)	)	PUNCT
ejpam-5963	166	4	in	in	ADP
ejpam-5963	166	5	-	-	PUNCT
ejpam-5963	166	6	sight	sight	NOUN
ejpam-5963	166	7	of	of	ADP
ejpam-5963	166	8	system	system	NOUN
ejpam-5963	166	9	of	of	ADP
ejpam-5963	166	10	equations	equation	NOUN
ejpam-5963	166	11	(	(	PUNCT
ejpam-5963	166	12	4	4	NUM
ejpam-5963	166	13	)	)	PUNCT
ejpam-5963	166	14	,	,	PUNCT
ejpam-5963	166	15	the	the	DET
ejpam-5963	166	16	system	system	NOUN
ejpam-5963	166	17	of	of	ADP
ejpam-5963	166	18	equations	equation	NOUN
ejpam-5963	166	19	(	(	PUNCT
ejpam-5963	166	20	6	6	NUM
ejpam-5963	166	21	)	)	PUNCT
ejpam-5963	166	22	is	be	AUX
ejpam-5963	166	23	equivalent	equivalent	ADJ
ejpam-5963	166	24	to	to	ADP
ejpam-5963	166	25	the	the	DET
ejpam-5963	166	26	following	following	NOUN
ejpam-5963	166	27	:	:	PUNCT
ejpam-5963	166	28	r(t	r(t	NOUN
ejpam-5963	166	29	)	)	PUNCT
ejpam-5963	167	1	=	=	SYM
ejpam-5963	167	2	r0	r0	NOUN
ejpam-5963	167	3	+	+	CCONJ
ejpam-5963	167	4	ϕ(r	ϕ(r	PROPN
ejpam-5963	167	5	)	)	PUNCT
ejpam-5963	168	1	+	+	CCONJ
ejpam-5963	169	1	ξ	ξ	DET
ejpam-5963	169	2	γ(η	γ(η	NOUN
ejpam-5963	169	3	)	)	PUNCT
ejpam-5963	169	4	∫	∫	PROPN
ejpam-5963	169	5	t	t	PROPN
ejpam-5963	169	6	0	0	NUM
ejpam-5963	169	7	(	(	PUNCT
ejpam-5963	169	8	t−	t−	PROPN
ejpam-5963	169	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	169	10	,	,	PUNCT
ejpam-5963	169	11	r(δ	r(δ	PROPN
ejpam-5963	169	12	)	)	PUNCT
ejpam-5963	169	13	,	,	PUNCT
ejpam-5963	169	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	169	15	.	.	PUNCT
ejpam-5963	169	16	p(t	p(t	NOUN
ejpam-5963	169	17	)	)	PUNCT
ejpam-5963	170	1	=	=	SYM
ejpam-5963	170	2	p0	p0	NOUN
ejpam-5963	170	3	+	+	CCONJ
ejpam-5963	170	4	ψ(p	ψ(p	NOUN
ejpam-5963	170	5	)	)	PUNCT
ejpam-5963	171	1	+	+	NUM
ejpam-5963	172	1	ξ	ξ	DET
ejpam-5963	172	2	γ(η	γ(η	NOUN
ejpam-5963	172	3	)	)	PUNCT
ejpam-5963	172	4	∫	∫	PROPN
ejpam-5963	172	5	t	t	PROPN
ejpam-5963	172	6	0	0	NUM
ejpam-5963	172	7	(	(	PUNCT
ejpam-5963	172	8	t−	t−	PROPN
ejpam-5963	172	9	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	172	10	,	,	PUNCT
ejpam-5963	172	11	r(δ	r(δ	PROPN
ejpam-5963	172	12	)	)	PUNCT
ejpam-5963	172	13	,	,	PUNCT
ejpam-5963	172	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	172	15	.	.	PUNCT
ejpam-5963	173	1	(	(	PUNCT
ejpam-5963	173	2	7	7	X
ejpam-5963	173	3	)	)	PUNCT
ejpam-5963	173	4	the	the	DET
ejpam-5963	173	5	above	above	ADJ
ejpam-5963	173	6	system	system	NOUN
ejpam-5963	173	7	(	(	PUNCT
ejpam-5963	173	8	7	7	NUM
ejpam-5963	173	9	)	)	PUNCT
ejpam-5963	173	10	,	,	PUNCT
ejpam-5963	173	11	represents	represent	VERB
ejpam-5963	173	12	the	the	DET
ejpam-5963	173	13	integral	integral	ADJ
ejpam-5963	173	14	representation	representation	NOUN
ejpam-5963	173	15	for	for	ADP
ejpam-5963	173	16	our	our	PRON
ejpam-5963	173	17	proposed	propose	VERB
ejpam-5963	173	18	problem	problem	NOUN
ejpam-5963	173	19	(	(	PUNCT
ejpam-5963	173	20	2	2	NUM
ejpam-5963	173	21	)	)	PUNCT
ejpam-5963	173	22	.	.	PUNCT
ejpam-5963	174	1	let	let	VERB
ejpam-5963	174	2	us	we	PRON
ejpam-5963	174	3	define	define	VERB
ejpam-5963	174	4	the	the	DET
ejpam-5963	174	5	following	follow	VERB
ejpam-5963	174	6	operators	operator	NOUN
ejpam-5963	174	7	,	,	PUNCT
ejpam-5963	174	8	h	h	NOUN
ejpam-5963	174	9	:	:	PUNCT
ejpam-5963	175	1	u×v	u×v	PROPN
ejpam-5963	175	2	→	→	SYM
ejpam-5963	175	3	u×v	u×v	PROPN
ejpam-5963	175	4	,	,	PUNCT
ejpam-5963	175	5	such	such	ADJ
ejpam-5963	175	6	that	that	DET
ejpam-5963	175	7	h(r	h(r	NOUN
ejpam-5963	175	8	,	,	PUNCT
ejpam-5963	175	9	p)(t	p)(t	NOUN
ejpam-5963	175	10	)	)	PUNCT
ejpam-5963	175	11	=	=	SYM
ejpam-5963	175	12	(	(	PUNCT
ejpam-5963	175	13	h1r(t	h1r(t	PROPN
ejpam-5963	175	14	)	)	PUNCT
ejpam-5963	175	15	,	,	PUNCT
ejpam-5963	175	16	h2p(t	h2p(t	PROPN
ejpam-5963	175	17	)	)	PUNCT
ejpam-5963	175	18	)	)	PUNCT
ejpam-5963	175	19	,	,	PUNCT
ejpam-5963	175	20	(	(	PUNCT
ejpam-5963	175	21	8)	8)	NUM
ejpam-5963	175	22	.	.	PUNCT
ejpam-5963	176	1	where	where	SCONJ
ejpam-5963	176	2	h1r(t	h1r(t	NOUN
ejpam-5963	176	3	)	)	PUNCT
ejpam-5963	176	4	=	=	SYM
ejpam-5963	176	5	r0	r0	NOUN
ejpam-5963	176	6	+	+	CCONJ
ejpam-5963	176	7	ϕ(r	ϕ(r	PROPN
ejpam-5963	176	8	)	)	PUNCT
ejpam-5963	176	9	,	,	PUNCT
ejpam-5963	176	10	h2p(t	h2p(t	PROPN
ejpam-5963	176	11	)	)	PUNCT
ejpam-5963	177	1	=	=	SYM
ejpam-5963	177	2	p0	p0	NOUN
ejpam-5963	177	3	+	+	CCONJ
ejpam-5963	177	4	ψ(p	ψ(p	NOUN
ejpam-5963	177	5	)	)	PUNCT
ejpam-5963	177	6	.	.	PUNCT
ejpam-5963	178	1	also	also	ADV
ejpam-5963	178	2	g∗∗	g∗∗	INTJ
ejpam-5963	178	3	:	:	PUNCT
ejpam-5963	178	4	u×v	u×v	PROPN
ejpam-5963	178	5	→	→	SYM
ejpam-5963	178	6	u×v	u×v	PROPN
ejpam-5963	178	7	,	,	PUNCT
ejpam-5963	178	8	such	such	ADJ
ejpam-5963	178	9	that	that	PRON
ejpam-5963	178	10	g∗∗(r	g∗∗(r	NOUN
ejpam-5963	178	11	,	,	PUNCT
ejpam-5963	178	12	p)(t	p)(t	NOUN
ejpam-5963	178	13	)	)	PUNCT
ejpam-5963	178	14	=	=	SYM
ejpam-5963	178	15	(	(	PUNCT
ejpam-5963	178	16	g∗	g∗	VERB
ejpam-5963	178	17	1(r	1(r	NUM
ejpam-5963	178	18	,	,	PUNCT
ejpam-5963	178	19	p)(t	p)(t	NOUN
ejpam-5963	178	20	)	)	PUNCT
ejpam-5963	178	21	,	,	PUNCT
ejpam-5963	178	22	g	g	PROPN
ejpam-5963	178	23	∗	∗	NOUN
ejpam-5963	178	24	2(r	2(r	NUM
ejpam-5963	178	25	,	,	PUNCT
ejpam-5963	178	26	p)(t	p)(t	NOUN
ejpam-5963	178	27	)	)	PUNCT
ejpam-5963	178	28	)	)	PUNCT
ejpam-5963	178	29	,	,	PUNCT
ejpam-5963	178	30	(	(	PUNCT
ejpam-5963	178	31	9	9	X
ejpam-5963	178	32	)	)	PUNCT
ejpam-5963	178	33	where	where	SCONJ
ejpam-5963	178	34	g∗	g∗	VERB
ejpam-5963	178	35	1(r	1(r	NOUN
ejpam-5963	178	36	,	,	PUNCT
ejpam-5963	178	37	p)(t	p)(t	NOUN
ejpam-5963	178	38	)	)	PUNCT
ejpam-5963	178	39	=	=	SYM
ejpam-5963	179	1	ξ	ξ	PROPN
ejpam-5963	179	2	γ(η	γ(η	PROPN
ejpam-5963	179	3	)	)	PUNCT
ejpam-5963	180	1	∫	∫	PROPN
ejpam-5963	181	1	t	t	PROPN
ejpam-5963	181	2	0	0	NUM
ejpam-5963	181	3	(	(	PUNCT
ejpam-5963	181	4	t−	t−	PROPN
ejpam-5963	181	5	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	181	6	,	,	PUNCT
ejpam-5963	181	7	r(δ	r(δ	PROPN
ejpam-5963	181	8	)	)	PUNCT
ejpam-5963	181	9	,	,	PUNCT
ejpam-5963	181	10	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	181	11	,	,	PUNCT
ejpam-5963	181	12	g∗	g∗	VERB
ejpam-5963	181	13	2(r	2(r	NUM
ejpam-5963	181	14	,	,	PUNCT
ejpam-5963	181	15	p)(t	p)(t	NOUN
ejpam-5963	181	16	)	)	PUNCT
ejpam-5963	181	17	=	=	SYM
ejpam-5963	182	1	ξ	ξ	PROPN
ejpam-5963	182	2	γ(η	γ(η	PROPN
ejpam-5963	182	3	)	)	PUNCT
ejpam-5963	183	1	∫	∫	PROPN
ejpam-5963	183	2	t	t	PROPN
ejpam-5963	183	3	0	0	NUM
ejpam-5963	183	4	(	(	PUNCT
ejpam-5963	183	5	t−	t−	PROPN
ejpam-5963	183	6	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	183	7	,	,	PUNCT
ejpam-5963	183	8	r(δ	r(δ	PROPN
ejpam-5963	183	9	)	)	PUNCT
ejpam-5963	183	10	,	,	PUNCT
ejpam-5963	183	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	183	12	.	.	PUNCT
ejpam-5963	183	13	a.	a.	PROPN
ejpam-5963	183	14	ali	ali	PROPN
ejpam-5963	183	15	et	et	PROPN
ejpam-5963	183	16	al	al	PROPN
ejpam-5963	183	17	.	.	PUNCT
ejpam-5963	183	18	/	/	SYM
ejpam-5963	183	19	eur	eur	PROPN
ejpam-5963	183	20	.	.	PUNCT
ejpam-5963	184	1	j.	j.	PROPN
ejpam-5963	184	2	pure	pure	PROPN
ejpam-5963	184	3	appl	appl	PROPN
ejpam-5963	184	4	.	.	PROPN
ejpam-5963	184	5	math	math	PROPN
ejpam-5963	184	6	,	,	PUNCT
ejpam-5963	184	7	18	18	NUM
ejpam-5963	184	8	(	(	PUNCT
ejpam-5963	184	9	2	2	NUM
ejpam-5963	184	10	)	)	PUNCT
ejpam-5963	184	11	(	(	PUNCT
ejpam-5963	184	12	2025	2025	NUM
ejpam-5963	184	13	)	)	PUNCT
ejpam-5963	184	14	,	,	PUNCT
ejpam-5963	184	15	5963	5963	NUM
ejpam-5963	184	16	8	8	NUM
ejpam-5963	184	17	of	of	ADP
ejpam-5963	184	18	19	19	NUM
ejpam-5963	184	19	furthermore	furthermore	ADV
ejpam-5963	184	20	,	,	PUNCT
ejpam-5963	184	21	let	let	VERB
ejpam-5963	184	22	us	we	PRON
ejpam-5963	184	23	define	define	VERB
ejpam-5963	184	24	k	k	NOUN
ejpam-5963	184	25	=	=	PUNCT
ejpam-5963	184	26	h	h	PROPN
ejpam-5963	185	1	+	+	CCONJ
ejpam-5963	185	2	g∗∗	g∗∗	PROPN
ejpam-5963	185	3	,	,	PUNCT
ejpam-5963	185	4	then	then	ADV
ejpam-5963	185	5	the	the	DET
ejpam-5963	185	6	operator	operator	NOUN
ejpam-5963	185	7	equation	equation	NOUN
ejpam-5963	185	8	corresponding	correspond	VERB
ejpam-5963	185	9	to	to	ADP
ejpam-5963	185	10	system	system	NOUN
ejpam-5963	185	11	of	of	ADP
ejpam-5963	185	12	equation	equation	NOUN
ejpam-5963	185	13	(	(	PUNCT
ejpam-5963	185	14	6	6	NUM
ejpam-5963	185	15	)	)	PUNCT
ejpam-5963	185	16	as	as	ADP
ejpam-5963	185	17	:	:	PUNCT
ejpam-5963	185	18	(	(	PUNCT
ejpam-5963	185	19	r	r	NOUN
ejpam-5963	185	20	,	,	PUNCT
ejpam-5963	185	21	p	p	NOUN
ejpam-5963	185	22	)	)	PUNCT
ejpam-5963	185	23	=	=	SYM
ejpam-5963	185	24	k(r	k(r	NOUN
ejpam-5963	185	25	,	,	PUNCT
ejpam-5963	185	26	p)(t	p)(t	NOUN
ejpam-5963	185	27	)	)	PUNCT
ejpam-5963	185	28	=	=	SYM
ejpam-5963	185	29	h(r	h(r	NOUN
ejpam-5963	185	30	,	,	PUNCT
ejpam-5963	185	31	p)(t	p)(t	NOUN
ejpam-5963	185	32	)	)	PUNCT
ejpam-5963	185	33	+	+	ADJ
ejpam-5963	185	34	g∗∗(r	g∗∗(r	NOUN
ejpam-5963	185	35	,	,	PUNCT
ejpam-5963	185	36	p)(t	p)(t	NOUN
ejpam-5963	185	37	)	)	PUNCT
ejpam-5963	185	38	,	,	PUNCT
ejpam-5963	185	39	which	which	PRON
ejpam-5963	185	40	is	be	AUX
ejpam-5963	185	41	a	a	DET
ejpam-5963	185	42	solution	solution	NOUN
ejpam-5963	185	43	of	of	ADP
ejpam-5963	185	44	the	the	DET
ejpam-5963	185	45	system	system	NOUN
ejpam-5963	185	46	in	in	ADP
ejpam-5963	185	47	operator	operator	NOUN
ejpam-5963	185	48	form	form	NOUN
ejpam-5963	185	49	.	.	PUNCT
ejpam-5963	186	1	now	now	ADV
ejpam-5963	186	2	we	we	PRON
ejpam-5963	186	3	present	present	VERB
ejpam-5963	186	4	some	some	DET
ejpam-5963	186	5	hypothesis	hypothesis	NOUN
ejpam-5963	186	6	which	which	PRON
ejpam-5963	186	7	are	be	AUX
ejpam-5963	186	8	helpful	helpful	ADJ
ejpam-5963	186	9	in	in	ADP
ejpam-5963	186	10	building	build	VERB
ejpam-5963	186	11	our	our	PRON
ejpam-5963	186	12	main	main	ADJ
ejpam-5963	186	13	existence	existence	NOUN
ejpam-5963	186	14	result	result	NOUN
ejpam-5963	186	15	.	.	PUNCT
ejpam-5963	187	1	(	(	PUNCT
ejpam-5963	187	2	m1	m1	NOUN
ejpam-5963	187	3	)	)	PUNCT
ejpam-5963	187	4	there	there	PRON
ejpam-5963	187	5	exist	exist	VERB
ejpam-5963	187	6	some	some	DET
ejpam-5963	187	7	constant	constant	ADJ
ejpam-5963	187	8	lϕ	lϕ	NOUN
ejpam-5963	187	9	and	and	CCONJ
ejpam-5963	187	10	lψ	lψ	PROPN
ejpam-5963	187	11	∈	∈	PROPN
ejpam-5963	187	12	(	(	PUNCT
ejpam-5963	187	13	0	0	NUM
ejpam-5963	187	14	,	,	PUNCT
ejpam-5963	187	15	1	1	NUM
ejpam-5963	187	16	]	]	PUNCT
ejpam-5963	187	17	such	such	ADJ
ejpam-5963	187	18	that	that	DET
ejpam-5963	187	19	|ϕ(r)−	|ϕ(r)−	PROPN
ejpam-5963	187	20	ϕ(r)|	ϕ(r)|	PROPN
ejpam-5963	187	21	≤	≤	PROPN
ejpam-5963	187	22	lϕ|r	lϕ|r	PROPN
ejpam-5963	188	1	−	−	PROPN
ejpam-5963	188	2	r|	r|	PROPN
ejpam-5963	188	3	,	,	PUNCT
ejpam-5963	188	4	|ψ(p)−	|ψ(p)−	NOUN
ejpam-5963	188	5	ψ(p)|	ψ(p)|	NOUN
ejpam-5963	188	6	≤	≤	NUM
ejpam-5963	188	7	lψ|p−	lψ|p−	PUNCT
ejpam-5963	188	8	p|	p|	NOUN
ejpam-5963	188	9	.	.	PUNCT
ejpam-5963	189	1	(	(	PUNCT
ejpam-5963	189	2	m2	m2	PROPN
ejpam-5963	189	3	)	)	PUNCT
ejpam-5963	189	4	there	there	PRON
ejpam-5963	189	5	exist	exist	VERB
ejpam-5963	189	6	some	some	DET
ejpam-5963	189	7	constant	constant	ADJ
ejpam-5963	189	8	c1	c1	NOUN
ejpam-5963	189	9	,	,	PUNCT
ejpam-5963	189	10	c2	c2	PROPN
ejpam-5963	189	11	,	,	PUNCT
ejpam-5963	189	12	d1	d1	PROPN
ejpam-5963	189	13	,	,	PUNCT
ejpam-5963	189	14	d2	d2	PROPN
ejpam-5963	189	15	>	>	X
ejpam-5963	189	16	0	0	PROPN
ejpam-5963	190	1	and	and	CCONJ
ejpam-5963	190	2	c3	c3	PROPN
ejpam-5963	190	3	,	,	PUNCT
ejpam-5963	190	4	d3	d3	PROPN
ejpam-5963	190	5	⩾	⩾	PROPN
ejpam-5963	190	6	0	0	NUM
ejpam-5963	190	7	,	,	PUNCT
ejpam-5963	190	8	with	with	ADP
ejpam-5963	190	9	|f(t	|f(t	NOUN
ejpam-5963	190	10	,	,	PUNCT
ejpam-5963	190	11	r(t	r(t	NOUN
ejpam-5963	190	12	)	)	PUNCT
ejpam-5963	190	13	,	,	PUNCT
ejpam-5963	190	14	p(t))|	p(t))|	VERB
ejpam-5963	190	15	≤	≤	PUNCT
ejpam-5963	190	16	c1|r|+	c1|r|+	PROPN
ejpam-5963	190	17	c2|p|+	c2|p|+	PROPN
ejpam-5963	190	18	c3	c3	PROPN
ejpam-5963	190	19	,	,	PUNCT
ejpam-5963	190	20	|g(t	|g(t	NOUN
ejpam-5963	190	21	,	,	PUNCT
ejpam-5963	190	22	r(t	r(t	NOUN
ejpam-5963	190	23	)	)	PUNCT
ejpam-5963	190	24	,	,	PUNCT
ejpam-5963	190	25	p(t)|	p(t)|	ADV
ejpam-5963	190	26	≤	≤	NUM
ejpam-5963	190	27	d1|r|+	d1|r|+	PROPN
ejpam-5963	190	28	d2|p|+	d2|p|+	NUM
ejpam-5963	190	29	d3	d3	PROPN
ejpam-5963	190	30	.	.	PUNCT
ejpam-5963	191	1	(	(	PUNCT
ejpam-5963	191	2	m3	m3	PROPN
ejpam-5963	191	3	)	)	PUNCT
ejpam-5963	191	4	there	there	PRON
ejpam-5963	191	5	exist	exist	VERB
ejpam-5963	191	6	lf	lf	ADP
ejpam-5963	191	7	and	and	CCONJ
ejpam-5963	191	8	lg	lg	NOUN
ejpam-5963	191	9	such	such	ADJ
ejpam-5963	191	10	that	that	DET
ejpam-5963	191	11	||f(t	||f(t	NOUN
ejpam-5963	191	12	,	,	PUNCT
ejpam-5963	191	13	r	r	NOUN
ejpam-5963	191	14	,	,	PUNCT
ejpam-5963	191	15	p)(t)−	p)(t)−	PROPN
ejpam-5963	191	16	f(t	f(t	NOUN
ejpam-5963	191	17	,	,	PUNCT
ejpam-5963	191	18	r(t	r(t	NOUN
ejpam-5963	191	19	)	)	PUNCT
ejpam-5963	191	20	,	,	PUNCT
ejpam-5963	191	21	r(t)||	r(t)||	NOUN
ejpam-5963	191	22	≤	≤	NUM
ejpam-5963	191	23	lf	lf	ADP
ejpam-5963	191	24	(	(	PUNCT
ejpam-5963	191	25	||r	||r	NOUN
ejpam-5963	191	26	−	−	NOUN
ejpam-5963	191	27	r||+	r||+	ADJ
ejpam-5963	191	28	||p−	||p−	PROPN
ejpam-5963	191	29	p||	p||	NOUN
ejpam-5963	191	30	)	)	PUNCT
ejpam-5963	191	31	,	,	PUNCT
ejpam-5963	191	32	||g(t	||g(t	X
ejpam-5963	191	33	,	,	PUNCT
ejpam-5963	191	34	r	r	NOUN
ejpam-5963	191	35	,	,	PUNCT
ejpam-5963	191	36	p)(t)−	p)(t)−	PROPN
ejpam-5963	191	37	g(t	g(t	PROPN
ejpam-5963	191	38	,	,	PUNCT
ejpam-5963	191	39	r(t	r(t	NOUN
ejpam-5963	191	40	)	)	PUNCT
ejpam-5963	191	41	,	,	PUNCT
ejpam-5963	191	42	p(t)||	p(t)||	VERB
ejpam-5963	191	43	≤	≤	NOUN
ejpam-5963	191	44	lg	lg	NOUN
ejpam-5963	191	45	(	(	PUNCT
ejpam-5963	191	46	||r	||r	NOUN
ejpam-5963	191	47	−	−	NOUN
ejpam-5963	191	48	r||+	r||+	ADJ
ejpam-5963	191	49	||p−	||p−	NOUN
ejpam-5963	191	50	p||	p||	NOUN
ejpam-5963	191	51	)	)	PUNCT
ejpam-5963	191	52	.	.	PUNCT
ejpam-5963	192	1	theorem	theorem	NOUN
ejpam-5963	192	2	3	3	NUM
ejpam-5963	192	3	.	.	PUNCT
ejpam-5963	193	1	under	under	ADP
ejpam-5963	193	2	the	the	DET
ejpam-5963	193	3	assumption	assumption	NOUN
ejpam-5963	193	4	(	(	PUNCT
ejpam-5963	193	5	m1	m1	NOUN
ejpam-5963	193	6	)	)	PUNCT
ejpam-5963	193	7	and	and	CCONJ
ejpam-5963	193	8	(	(	PUNCT
ejpam-5963	193	9	m2	m2	PROPN
ejpam-5963	193	10	)	)	PUNCT
ejpam-5963	193	11	the	the	DET
ejpam-5963	193	12	coupled	couple	VERB
ejpam-5963	193	13	system	system	NOUN
ejpam-5963	193	14	of	of	ADP
ejpam-5963	193	15	ffde	ffde	NOUN
ejpam-5963	193	16	(	(	PUNCT
ejpam-5963	193	17	2	2	NUM
ejpam-5963	193	18	)	)	PUNCT
ejpam-5963	193	19	has	have	VERB
ejpam-5963	193	20	at	at	ADP
ejpam-5963	193	21	lest	lest	ADP
ejpam-5963	193	22	one	one	NUM
ejpam-5963	193	23	solution	solution	NOUN
ejpam-5963	193	24	.	.	PUNCT
ejpam-5963	194	1	proof	proof	NOUN
ejpam-5963	194	2	.	.	PUNCT
ejpam-5963	195	1	to	to	PART
ejpam-5963	195	2	obtained	obtain	VERB
ejpam-5963	195	3	results	result	NOUN
ejpam-5963	195	4	,	,	PUNCT
ejpam-5963	195	5	we	we	PRON
ejpam-5963	195	6	needs	need	VERB
ejpam-5963	195	7	the	the	DET
ejpam-5963	195	8	following	following	NOUN
ejpam-5963	195	9	:	:	PUNCT
ejpam-5963	196	1	step1	step1	PROPN
ejpam-5963	196	2	:	:	PUNCT
ejpam-5963	196	3	we	we	PRON
ejpam-5963	196	4	need	need	VERB
ejpam-5963	196	5	to	to	PART
ejpam-5963	196	6	show	show	VERB
ejpam-5963	196	7	that	that	SCONJ
ejpam-5963	196	8	h	h	NOUN
ejpam-5963	196	9	is	be	AUX
ejpam-5963	196	10	contraction	contraction	NOUN
ejpam-5963	196	11	mapping	mapping	NOUN
ejpam-5963	196	12	,	,	PUNCT
ejpam-5963	196	13	so	so	SCONJ
ejpam-5963	196	14	for	for	ADP
ejpam-5963	196	15	any	any	DET
ejpam-5963	196	16	(	(	PUNCT
ejpam-5963	196	17	r	r	NOUN
ejpam-5963	196	18	,	,	PUNCT
ejpam-5963	196	19	p	p	NOUN
ejpam-5963	196	20	)	)	PUNCT
ejpam-5963	196	21	,	,	PUNCT
ejpam-5963	196	22	(	(	PUNCT
ejpam-5963	196	23	r	r	NOUN
ejpam-5963	196	24	,	,	PUNCT
ejpam-5963	196	25	p	p	NOUN
ejpam-5963	196	26	)	)	PUNCT
ejpam-5963	196	27	.	.	PUNCT
ejpam-5963	197	1	||h(r	||h(r	ADJ
ejpam-5963	197	2	,	,	PUNCT
ejpam-5963	197	3	p)(t)−h(r	p)(t)−h(r	NOUN
ejpam-5963	197	4	,	,	PUNCT
ejpam-5963	197	5	p)(t)||	p)(t)||	NOUN
ejpam-5963	197	6	≤	≤	PUNCT
ejpam-5963	198	1	||ϕ(r)−	||ϕ(r)−	PROPN
ejpam-5963	198	2	ϕ(r)||+	ϕ(r)||+	PROPN
ejpam-5963	198	3	||ψ(p)−	||ψ(p)−	PROPN
ejpam-5963	198	4	ψ(p||	ψ(p||	NOUN
ejpam-5963	198	5	≤	≤	NOUN
ejpam-5963	198	6	lϕ|r	lϕ|r	PROPN
ejpam-5963	199	1	−	−	PROPN
ejpam-5963	199	2	r|+	r|+	NOUN
ejpam-5963	199	3	lψ|p−	lψ|p−	PUNCT
ejpam-5963	199	4	p|	p|	NOUN
ejpam-5963	199	5	,	,	PUNCT
ejpam-5963	199	6	which	which	PRON
ejpam-5963	199	7	implies	imply	VERB
ejpam-5963	199	8	that	that	PRON
ejpam-5963	199	9	||h(r	||h(r	NOUN
ejpam-5963	199	10	,	,	PUNCT
ejpam-5963	199	11	p)(t)−h(r	p)(t)−h(r	NOUN
ejpam-5963	199	12	,	,	PUNCT
ejpam-5963	199	13	p)(t)||	p)(t)||	NOUN
ejpam-5963	199	14	≤	≤	NUM
ejpam-5963	199	15	l||(r	l||(r	PROPN
ejpam-5963	199	16	,	,	PUNCT
ejpam-5963	199	17	p)−	p)−	NOUN
ejpam-5963	199	18	(	(	PUNCT
ejpam-5963	199	19	r	r	NOUN
ejpam-5963	199	20	,	,	PUNCT
ejpam-5963	199	21	p)||	p)||	NOUN
ejpam-5963	199	22	,	,	PUNCT
ejpam-5963	199	23	(	(	PUNCT
ejpam-5963	199	24	10	10	NUM
ejpam-5963	199	25	)	)	PUNCT
ejpam-5963	199	26	where	where	SCONJ
ejpam-5963	199	27	l	l	NOUN
ejpam-5963	199	28	=	=	SYM
ejpam-5963	199	29	max(lϕ	max(lϕ	NOUN
ejpam-5963	199	30	,	,	PUNCT
ejpam-5963	199	31	lψ	lψ	NOUN
ejpam-5963	199	32	)	)	PUNCT
ejpam-5963	199	33	.	.	PUNCT
ejpam-5963	200	1	hence	hence	ADV
ejpam-5963	200	2	h	h	PROPN
ejpam-5963	200	3	is	be	AUX
ejpam-5963	200	4	contraction	contraction	NOUN
ejpam-5963	200	5	.	.	PUNCT
ejpam-5963	201	1	step2	step2	PROPN
ejpam-5963	201	2	:	:	PUNCT
ejpam-5963	201	3	next	next	ADV
ejpam-5963	201	4	,	,	PUNCT
ejpam-5963	201	5	we	we	PRON
ejpam-5963	201	6	will	will	AUX
ejpam-5963	201	7	to	to	PART
ejpam-5963	201	8	prove	prove	VERB
ejpam-5963	201	9	g∗∗	g∗∗	PROPN
ejpam-5963	201	10	is	be	AUX
ejpam-5963	201	11	bounded	bound	VERB
ejpam-5963	201	12	,	,	PUNCT
ejpam-5963	201	13	for	for	SCONJ
ejpam-5963	201	14	this	this	PRON
ejpam-5963	201	15	let	let	VERB
ejpam-5963	201	16	s	s	VERB
ejpam-5963	201	17	=	=	NOUN
ejpam-5963	201	18	{	{	PUNCT
ejpam-5963	201	19	||(r	||(r	NOUN
ejpam-5963	201	20	,	,	PUNCT
ejpam-5963	201	21	p)||	p)||	ADJ
ejpam-5963	201	22	≤	≤	ADJ
ejpam-5963	201	23	r	r	NOUN
ejpam-5963	201	24	;	;	PUNCT
ejpam-5963	201	25	(	(	PUNCT
ejpam-5963	201	26	r	r	NOUN
ejpam-5963	201	27	,	,	PUNCT
ejpam-5963	201	28	p	p	NOUN
ejpam-5963	201	29	)	)	PUNCT
ejpam-5963	201	30	}	}	PUNCT
ejpam-5963	201	31	be	be	AUX
ejpam-5963	201	32	closed	close	VERB
ejpam-5963	201	33	and	and	CCONJ
ejpam-5963	201	34	bounded	bound	VERB
ejpam-5963	201	35	set	set	NOUN
ejpam-5963	201	36	,	,	PUNCT
ejpam-5963	201	37	then	then	ADV
ejpam-5963	201	38	∥g∗∗(r	∥g∗∗(r	NUM
ejpam-5963	201	39	,	,	PUNCT
ejpam-5963	201	40	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	201	41	=	=	SYM
ejpam-5963	201	42	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	201	43	ξ	ξ	X
ejpam-5963	201	44	γ(η	γ(η	PROPN
ejpam-5963	201	45	)	)	PUNCT
ejpam-5963	202	1	∫	∫	PROPN
ejpam-5963	202	2	t	t	PROPN
ejpam-5963	202	3	0	0	NUM
ejpam-5963	202	4	(	(	PUNCT
ejpam-5963	202	5	t−	t−	PROPN
ejpam-5963	202	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	202	7	,	,	PUNCT
ejpam-5963	202	8	r(δ	r(δ	PROPN
ejpam-5963	202	9	)	)	PUNCT
ejpam-5963	202	10	,	,	PUNCT
ejpam-5963	202	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	202	12	+	+	CCONJ
ejpam-5963	202	13	ξ	ξ	PROPN
ejpam-5963	202	14	γ(η	γ(η	PROPN
ejpam-5963	202	15	)	)	PUNCT
ejpam-5963	203	1	∫	∫	PROPN
ejpam-5963	203	2	t	t	PROPN
ejpam-5963	203	3	0	0	NUM
ejpam-5963	203	4	(	(	PUNCT
ejpam-5963	203	5	t−	t−	PROPN
ejpam-5963	203	6	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	203	7	,	,	PUNCT
ejpam-5963	203	8	r(δ	r(δ	PROPN
ejpam-5963	203	9	)	)	PUNCT
ejpam-5963	203	10	,	,	PUNCT
ejpam-5963	203	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	203	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	203	13	≤	≤	NUM
ejpam-5963	203	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	203	15	ξ	ξ	PROPN
ejpam-5963	203	16	γ(η	γ(η	PROPN
ejpam-5963	203	17	)	)	PUNCT
ejpam-5963	204	1	∫	∫	PROPN
ejpam-5963	204	2	t	t	PROPN
ejpam-5963	204	3	0	0	NUM
ejpam-5963	204	4	(	(	PUNCT
ejpam-5963	204	5	t−	t−	PROPN
ejpam-5963	204	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	204	7	,	,	PUNCT
ejpam-5963	204	8	r(δ	r(δ	PROPN
ejpam-5963	204	9	)	)	PUNCT
ejpam-5963	204	10	,	,	PUNCT
ejpam-5963	204	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	204	12	∥∥∥∥+	∥∥∥∥+	PROPN
ejpam-5963	204	13	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	204	14	ξ	ξ	PROPN
ejpam-5963	204	15	γ(η	γ(η	PROPN
ejpam-5963	204	16	)	)	PUNCT
ejpam-5963	205	1	∫	∫	PROPN
ejpam-5963	205	2	t	t	PROPN
ejpam-5963	205	3	0	0	NUM
ejpam-5963	205	4	(	(	PUNCT
ejpam-5963	205	5	t−	t−	PROPN
ejpam-5963	205	6	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	205	7	,	,	PUNCT
ejpam-5963	205	8	r(δ	r(δ	PROPN
ejpam-5963	205	9	)	)	PUNCT
ejpam-5963	205	10	,	,	PUNCT
ejpam-5963	205	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	205	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	205	13	≤	≤	PROPN
ejpam-5963	205	14	t	t	PROPN
ejpam-5963	205	15	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	205	16	,	,	PUNCT
ejpam-5963	205	17	ξ)(c1|r|+	ξ)(c1|r|+	PROPN
ejpam-5963	205	18	c2|p|+	c2|p|+	PROPN
ejpam-5963	205	19	c3	c3	PROPN
ejpam-5963	205	20	)	)	PUNCT
ejpam-5963	206	1	+	+	NUM
ejpam-5963	206	2	t	t	PROPN
ejpam-5963	206	3	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	206	4	,	,	PUNCT
ejpam-5963	206	5	ξ)(d1|r|+	ξ)(d1|r|+	PROPN
ejpam-5963	206	6	d2|p|+	d2|p|+	PROPN
ejpam-5963	206	7	d3	d3	PROPN
ejpam-5963	206	8	)	)	PUNCT
ejpam-5963	206	9	,	,	PUNCT
ejpam-5963	206	10	=	=	PROPN
ejpam-5963	206	11	t	t	PROPN
ejpam-5963	206	12	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	206	13	,	,	PUNCT
ejpam-5963	206	14	ξ	ξ	X
ejpam-5963	206	15	)	)	PUNCT
ejpam-5963	207	1	[	[	X
ejpam-5963	207	2	(	(	PUNCT
ejpam-5963	207	3	c1	c1	NOUN
ejpam-5963	207	4	+	+	CCONJ
ejpam-5963	207	5	d1)|r|+	d1)|r|+	PROPN
ejpam-5963	207	6	(	(	PUNCT
ejpam-5963	207	7	c2	c2	PROPN
ejpam-5963	207	8	+	+	CCONJ
ejpam-5963	207	9	d2)|p|+	d2)|p|+	PROPN
ejpam-5963	207	10	(	(	PUNCT
ejpam-5963	207	11	c3	c3	PROPN
ejpam-5963	207	12	+	+	CCONJ
ejpam-5963	207	13	d3	d3	PROPN
ejpam-5963	207	14	)	)	PUNCT
ejpam-5963	207	15	]	]	PUNCT
ejpam-5963	207	16	≤	≤	NUM
ejpam-5963	207	17	∞.	∞.	PROPN
ejpam-5963	207	18	a.	a.	PROPN
ejpam-5963	207	19	ali	ali	PROPN
ejpam-5963	207	20	et	et	PROPN
ejpam-5963	207	21	al	al	PROPN
ejpam-5963	207	22	.	.	PUNCT
ejpam-5963	207	23	/	/	SYM
ejpam-5963	207	24	eur	eur	PROPN
ejpam-5963	207	25	.	.	PUNCT
ejpam-5963	208	1	j.	j.	PROPN
ejpam-5963	208	2	pure	pure	PROPN
ejpam-5963	208	3	appl	appl	PROPN
ejpam-5963	208	4	.	.	PROPN
ejpam-5963	208	5	math	math	PROPN
ejpam-5963	208	6	,	,	PUNCT
ejpam-5963	208	7	18	18	NUM
ejpam-5963	208	8	(	(	PUNCT
ejpam-5963	208	9	2	2	NUM
ejpam-5963	208	10	)	)	PUNCT
ejpam-5963	208	11	(	(	PUNCT
ejpam-5963	208	12	2025	2025	NUM
ejpam-5963	208	13	)	)	PUNCT
ejpam-5963	208	14	,	,	PUNCT
ejpam-5963	208	15	5963	5963	NUM
ejpam-5963	208	16	9	9	NUM
ejpam-5963	208	17	of	of	ADP
ejpam-5963	208	18	19	19	NUM
ejpam-5963	208	19	thus	thus	ADV
ejpam-5963	208	20	,	,	PUNCT
ejpam-5963	208	21	g∗∗	g∗∗	PROPN
ejpam-5963	208	22	is	be	AUX
ejpam-5963	208	23	bounded	bound	VERB
ejpam-5963	208	24	.	.	PUNCT
ejpam-5963	209	1	for	for	ADP
ejpam-5963	209	2	the	the	DET
ejpam-5963	209	3	equi	equi	NOUN
ejpam-5963	209	4	-	-	PUNCT
ejpam-5963	209	5	continuity	continuity	NOUN
ejpam-5963	209	6	of	of	ADP
ejpam-5963	209	7	g	g	NOUN
ejpam-5963	209	8	,	,	PUNCT
ejpam-5963	209	9	let	let	VERB
ejpam-5963	209	10	τ	τ	X
ejpam-5963	209	11	<	<	X
ejpam-5963	209	12	t	t	X
ejpam-5963	209	13	∈	∈	PROPN
ejpam-5963	210	1	i	i	PRON
ejpam-5963	210	2	,	,	PUNCT
ejpam-5963	210	3	and	and	CCONJ
ejpam-5963	210	4	∥g∗	∥g∗	PROPN
ejpam-5963	210	5	1(r	1(r	NUM
ejpam-5963	210	6	,	,	PUNCT
ejpam-5963	210	7	p)(t)−g∗	p)(t)−g∗	NUM
ejpam-5963	210	8	1(r	1(r	NUM
ejpam-5963	210	9	,	,	PUNCT
ejpam-5963	210	10	p)(τ)∥	p)(τ)∥	PROPN
ejpam-5963	210	11	=	=	SYM
ejpam-5963	210	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	210	13	ξ	ξ	X
ejpam-5963	210	14	γ(η	γ(η	PROPN
ejpam-5963	210	15	)	)	PUNCT
ejpam-5963	211	1	∫	∫	PROPN
ejpam-5963	211	2	t	t	PROPN
ejpam-5963	211	3	0	0	NUM
ejpam-5963	211	4	(	(	PUNCT
ejpam-5963	211	5	t−	t−	PROPN
ejpam-5963	211	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	211	7	,	,	PUNCT
ejpam-5963	211	8	r(δ	r(δ	PROPN
ejpam-5963	211	9	)	)	PUNCT
ejpam-5963	211	10	,	,	PUNCT
ejpam-5963	211	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	211	12	−	−	PROPN
ejpam-5963	211	13	ξ	ξ	PROPN
ejpam-5963	211	14	γ(η	γ(η	PROPN
ejpam-5963	211	15	)	)	PUNCT
ejpam-5963	211	16	∫	∫	PROPN
ejpam-5963	212	1	τ	τ	PROPN
ejpam-5963	212	2	0	0	NUM
ejpam-5963	212	3	(	(	PUNCT
ejpam-5963	212	4	τ	τ	X
ejpam-5963	212	5	−	−	PROPN
ejpam-5963	212	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	212	7	,	,	PUNCT
ejpam-5963	212	8	r(δ	r(δ	PROPN
ejpam-5963	212	9	)	)	PUNCT
ejpam-5963	212	10	,	,	PUNCT
ejpam-5963	212	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	212	12	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-5963	212	13	≤	≤	NUM
ejpam-5963	212	14	∥f(δ	∥f(δ	NOUN
ejpam-5963	212	15	,	,	PUNCT
ejpam-5963	212	16	r(δ	r(δ	PROPN
ejpam-5963	212	17	)	)	PUNCT
ejpam-5963	212	18	,	,	PUNCT
ejpam-5963	212	19	p(δ))∥	p(δ))∥	X
ejpam-5963	212	20	(	(	PUNCT
ejpam-5963	212	21	∫	∫	PROPN
ejpam-5963	212	22	t	t	PROPN
ejpam-5963	212	23	0	0	NUM
ejpam-5963	212	24	(	(	PUNCT
ejpam-5963	212	25	t−	t−	PROPN
ejpam-5963	212	26	δ)η−1δξ−1dδ	δ)η−1δξ−1dδ	PROPN
ejpam-5963	213	1	−	−	PROPN
ejpam-5963	213	2	∫	∫	PROPN
ejpam-5963	213	3	τ	τ	X
ejpam-5963	213	4	0	0	NUM
ejpam-5963	214	1	(	(	PUNCT
ejpam-5963	214	2	τ	τ	PROPN
ejpam-5963	214	3	−	−	PROPN
ejpam-5963	214	4	δ)η−1δξ−1dδ	δ)η−1δξ−1dδ	PROPN
ejpam-5963	214	5	)	)	PUNCT
ejpam-5963	214	6	≤	≤	PUNCT
ejpam-5963	214	7	∥f(δ	∥f(δ	PROPN
ejpam-5963	214	8	,	,	PUNCT
ejpam-5963	214	9	r(δ	r(δ	PROPN
ejpam-5963	214	10	)	)	PUNCT
ejpam-5963	214	11	,	,	PUNCT
ejpam-5963	214	12	p(δ))∥b(η	p(δ))∥b(η	NOUN
ejpam-5963	214	13	,	,	PUNCT
ejpam-5963	214	14	ξ)(tη+ξ−1	ξ)(tη+ξ−1	PROPN
ejpam-5963	214	15	−	−	NUM
ejpam-5963	214	16	τη+ξ−1	τη+ξ−1	NOUN
ejpam-5963	214	17	)	)	PUNCT
ejpam-5963	214	18	→	→	SYM
ejpam-5963	214	19	0	0	NUM
ejpam-5963	214	20	as	as	ADP
ejpam-5963	214	21	t→	t→	X
ejpam-5963	214	22	τ	τ	X
ejpam-5963	214	23	.	.	PUNCT
ejpam-5963	215	1	it	it	PRON
ejpam-5963	215	2	follow	follow	VERB
ejpam-5963	215	3	that	that	SCONJ
ejpam-5963	215	4	∥g∗	∥g∗	PROPN
ejpam-5963	215	5	1(r	1(r	NOUN
ejpam-5963	215	6	,	,	PUNCT
ejpam-5963	215	7	p)(t)−g∗	p)(t)−g∗	NUM
ejpam-5963	215	8	1(r	1(r	NUM
ejpam-5963	215	9	,	,	PUNCT
ejpam-5963	215	10	p)(τ)∥	p)(τ)∥	PROPN
ejpam-5963	215	11	→	→	SYM
ejpam-5963	215	12	0	0	NUM
ejpam-5963	215	13	as	as	SCONJ
ejpam-5963	215	14	t→	t→	X
ejpam-5963	215	15	τ	τ	X
ejpam-5963	215	16	.	.	PUNCT
ejpam-5963	215	17	similarly	similarly	ADV
ejpam-5963	215	18	,	,	PUNCT
ejpam-5963	215	19	one	one	PRON
ejpam-5963	215	20	can	can	AUX
ejpam-5963	215	21	obtained	obtain	VERB
ejpam-5963	215	22	the	the	DET
ejpam-5963	215	23	following	following	ADJ
ejpam-5963	215	24	result	result	NOUN
ejpam-5963	215	25	for	for	ADP
ejpam-5963	215	26	:	:	PUNCT
ejpam-5963	215	27	∥g∗	∥g∗	PROPN
ejpam-5963	215	28	2(r	2(r	NUM
ejpam-5963	215	29	,	,	PUNCT
ejpam-5963	215	30	p)(t)−g∗	p)(t)−g∗	PROPN
ejpam-5963	215	31	2(r	2(r	NUM
ejpam-5963	215	32	,	,	PUNCT
ejpam-5963	215	33	p)(τ)∥	p)(τ)∥	PROPN
ejpam-5963	215	34	→	→	SYM
ejpam-5963	215	35	0	0	NUM
ejpam-5963	215	36	as	as	SCONJ
ejpam-5963	215	37	t→	t→	PRON
ejpam-5963	215	38	τ	τ	X
ejpam-5963	215	39	.	.	PUNCT
ejpam-5963	215	40	therefore	therefore	ADV
ejpam-5963	215	41	g∗	g∗	VERB
ejpam-5963	215	42	1	1	NUM
ejpam-5963	215	43	and	and	CCONJ
ejpam-5963	215	44	g∗	g∗	VERB
ejpam-5963	215	45	1	1	NUM
ejpam-5963	215	46	are	be	AUX
ejpam-5963	215	47	continuous	continuous	ADJ
ejpam-5963	215	48	and	and	CCONJ
ejpam-5963	215	49	hence	hence	ADV
ejpam-5963	215	50	g∗∗	g∗∗	PROPN
ejpam-5963	215	51	is	be	AUX
ejpam-5963	215	52	continuous	continuous	ADJ
ejpam-5963	215	53	and	and	CCONJ
ejpam-5963	215	54	also	also	ADV
ejpam-5963	215	55	bounded	bound	VERB
ejpam-5963	215	56	.	.	PUNCT
ejpam-5963	216	1	thanks	thank	NOUN
ejpam-5963	216	2	to	to	ADP
ejpam-5963	216	3	krasnoselskii	krasnoselskii	PROPN
ejpam-5963	216	4	’s	’s	PART
ejpam-5963	216	5	fpt	fpt	VERB
ejpam-5963	216	6	the	the	DET
ejpam-5963	216	7	system	system	NOUN
ejpam-5963	216	8	(	(	PUNCT
ejpam-5963	216	9	2	2	X
ejpam-5963	216	10	)	)	PUNCT
ejpam-5963	216	11	has	have	VERB
ejpam-5963	216	12	at	at	ADP
ejpam-5963	216	13	lest	lest	ADP
ejpam-5963	216	14	one	one	NUM
ejpam-5963	216	15	solution	solution	NOUN
ejpam-5963	216	16	.	.	PUNCT
ejpam-5963	217	1	theorem	theorem	ADJ
ejpam-5963	217	2	4	4	NUM
ejpam-5963	217	3	.	.	PUNCT
ejpam-5963	218	1	under	under	ADP
ejpam-5963	218	2	the	the	DET
ejpam-5963	218	3	assumptions	assumption	NOUN
ejpam-5963	218	4	(	(	PUNCT
ejpam-5963	218	5	m1	m1	NOUN
ejpam-5963	218	6	)	)	PUNCT
ejpam-5963	218	7	and	and	CCONJ
ejpam-5963	218	8	(	(	PUNCT
ejpam-5963	218	9	m3	m3	PROPN
ejpam-5963	218	10	)	)	PUNCT
ejpam-5963	218	11	and	and	CCONJ
ejpam-5963	218	12	such	such	ADJ
ejpam-5963	218	13	υ	υ	NOUN
ejpam-5963	218	14	=	=	SYM
ejpam-5963	218	15	l+wt	l+wt	NOUN
ejpam-5963	218	16	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	218	17	,	,	PUNCT
ejpam-5963	218	18	ξ	ξ	X
ejpam-5963	218	19	)	)	PUNCT
ejpam-5963	218	20	≤	≤	NUM
ejpam-5963	218	21	1	1	NUM
ejpam-5963	218	22	holds	hold	NOUN
ejpam-5963	218	23	,	,	PUNCT
ejpam-5963	218	24	then	then	ADV
ejpam-5963	218	25	the	the	DET
ejpam-5963	218	26	consider	consider	VERB
ejpam-5963	218	27	system	system	NOUN
ejpam-5963	218	28	ffde	ffde	NOUN
ejpam-5963	218	29	have	have	VERB
ejpam-5963	218	30	unique	unique	ADJ
ejpam-5963	218	31	solution	solution	NOUN
ejpam-5963	218	32	.	.	PUNCT
ejpam-5963	219	1	proof	proof	NOUN
ejpam-5963	219	2	.	.	PUNCT
ejpam-5963	220	1	for	for	ADP
ejpam-5963	220	2	this	this	PRON
ejpam-5963	220	3	let	let	NOUN
ejpam-5963	220	4	(	(	PUNCT
ejpam-5963	220	5	r	r	NOUN
ejpam-5963	220	6	,	,	PUNCT
ejpam-5963	220	7	p	p	NOUN
ejpam-5963	220	8	)	)	PUNCT
ejpam-5963	220	9	,	,	PUNCT
ejpam-5963	220	10	(	(	PUNCT
ejpam-5963	220	11	r	r	X
ejpam-5963	220	12	,	,	PUNCT
ejpam-5963	220	13	p	p	NOUN
ejpam-5963	220	14	)	)	PUNCT
ejpam-5963	220	15	∈	∈	PROPN
ejpam-5963	220	16	u×v	u×v	PROPN
ejpam-5963	220	17	,	,	PUNCT
ejpam-5963	220	18	then	then	ADV
ejpam-5963	220	19	from	from	ADP
ejpam-5963	220	20	equation	equation	NOUN
ejpam-5963	220	21	(	(	PUNCT
ejpam-5963	220	22	10	10	NUM
ejpam-5963	220	23	)	)	PUNCT
ejpam-5963	220	24	,	,	PUNCT
ejpam-5963	220	25	one	one	PRON
ejpam-5963	220	26	have	have	VERB
ejpam-5963	220	27	||h(r	||h(r	PROPN
ejpam-5963	220	28	,	,	PUNCT
ejpam-5963	220	29	p)(t)−h(r	p)(t)−h(r	NOUN
ejpam-5963	220	30	,	,	PUNCT
ejpam-5963	220	31	p)(t)||	p)(t)||	NOUN
ejpam-5963	220	32	≤	≤	NUM
ejpam-5963	220	33	l||(r	l||(r	PROPN
ejpam-5963	220	34	,	,	PUNCT
ejpam-5963	220	35	p)−	p)−	NOUN
ejpam-5963	220	36	(	(	PUNCT
ejpam-5963	220	37	r	r	NOUN
ejpam-5963	220	38	,	,	PUNCT
ejpam-5963	220	39	p)||	p)||	NOUN
ejpam-5963	220	40	,	,	PUNCT
ejpam-5963	220	41	(	(	PUNCT
ejpam-5963	220	42	11	11	NUM
ejpam-5963	220	43	)	)	PUNCT
ejpam-5963	220	44	and	and	CCONJ
ejpam-5963	220	45	∥g∗	∥g∗	PROPN
ejpam-5963	220	46	1(r	1(r	NUM
ejpam-5963	220	47	,	,	PUNCT
ejpam-5963	220	48	p)(t)−g∗	p)(t)−g∗	PROPN
ejpam-5963	220	49	1(r	1(r	NUM
ejpam-5963	220	50	,	,	PUNCT
ejpam-5963	220	51	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	220	52	=	=	SYM
ejpam-5963	220	53	∥∥∥∥	∥∥∥∥	NUM
ejpam-5963	220	54	ξ	ξ	X
ejpam-5963	220	55	γ(η	γ(η	PROPN
ejpam-5963	220	56	)	)	PUNCT
ejpam-5963	221	1	∫	∫	PROPN
ejpam-5963	221	2	t	t	PROPN
ejpam-5963	221	3	0	0	NUM
ejpam-5963	221	4	(	(	PUNCT
ejpam-5963	221	5	t−	t−	PROPN
ejpam-5963	221	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	221	7	,	,	PUNCT
ejpam-5963	221	8	r(δ	r(δ	PROPN
ejpam-5963	221	9	)	)	PUNCT
ejpam-5963	221	10	,	,	PUNCT
ejpam-5963	221	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	221	12	−	−	PROPN
ejpam-5963	221	13	ξ	ξ	PROPN
ejpam-5963	221	14	γ(η	γ(η	PROPN
ejpam-5963	221	15	)	)	PUNCT
ejpam-5963	222	1	∫	∫	PROPN
ejpam-5963	222	2	t	t	PROPN
ejpam-5963	222	3	0	0	NUM
ejpam-5963	222	4	(	(	PUNCT
ejpam-5963	222	5	t−	t−	PROPN
ejpam-5963	222	6	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	222	7	,	,	PUNCT
ejpam-5963	222	8	r(δ	r(δ	PROPN
ejpam-5963	222	9	)	)	PUNCT
ejpam-5963	222	10	,	,	PUNCT
ejpam-5963	222	11	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	222	12	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5963	222	13	,	,	PUNCT
ejpam-5963	222	14	=	=	SYM
ejpam-5963	222	15	ξ	ξ	PROPN
ejpam-5963	222	16	γ(η	γ(η	PROPN
ejpam-5963	222	17	)	)	PUNCT
ejpam-5963	223	1	∫	∫	PROPN
ejpam-5963	223	2	t	t	PROPN
ejpam-5963	223	3	0	0	NUM
ejpam-5963	224	1	(	(	PUNCT
ejpam-5963	224	2	t−	t−	PROPN
ejpam-5963	224	3	δ)η−1δξ−1∥f(δ	δ)η−1δξ−1∥f(δ	PROPN
ejpam-5963	224	4	,	,	PUNCT
ejpam-5963	224	5	r(δ	r(δ	PROPN
ejpam-5963	224	6	)	)	PUNCT
ejpam-5963	224	7	,	,	PUNCT
ejpam-5963	224	8	p(δ))−	p(δ))−	PROPN
ejpam-5963	224	9	f(δ	f(δ	PROPN
ejpam-5963	224	10	,	,	PUNCT
ejpam-5963	224	11	r(δ	r(δ	PROPN
ejpam-5963	224	12	)	)	PUNCT
ejpam-5963	224	13	,	,	PUNCT
ejpam-5963	224	14	p(δ))∥dδ	p(δ))∥dδ	ADV
ejpam-5963	224	15	,	,	PUNCT
ejpam-5963	224	16	≤	≤	NUM
ejpam-5963	224	17	ξ	ξ	PRON
ejpam-5963	224	18	γ(η	γ(η	PROPN
ejpam-5963	224	19	)	)	PUNCT
ejpam-5963	224	20	t	t	PROPN
ejpam-5963	224	21	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	224	22	,	,	PUNCT
ejpam-5963	224	23	ξ)lf	ξ)lf	PROPN
ejpam-5963	224	24	(	(	PUNCT
ejpam-5963	224	25	||r	||r	NOUN
ejpam-5963	224	26	−	−	ADP
ejpam-5963	224	27	r||+	r||+	ADJ
ejpam-5963	224	28	||p−	||p−	PROPN
ejpam-5963	224	29	p||	p||	NOUN
ejpam-5963	224	30	,	,	PUNCT
ejpam-5963	224	31	which	which	PRON
ejpam-5963	224	32	implies	imply	VERB
ejpam-5963	224	33	that	that	SCONJ
ejpam-5963	224	34	∥g∗	∥g∗	PROPN
ejpam-5963	224	35	1(r	1(r	NOUN
ejpam-5963	224	36	,	,	PUNCT
ejpam-5963	224	37	p)(t)−g∗	p)(t)−g∗	PROPN
ejpam-5963	224	38	1(r	1(r	NUM
ejpam-5963	224	39	,	,	PUNCT
ejpam-5963	224	40	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	224	41	≤	≤	PROPN
ejpam-5963	224	42	t	t	PROPN
ejpam-5963	224	43	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	224	44	,	,	PUNCT
ejpam-5963	224	45	ξ)lf∥(r	ξ)lf∥(r	NOUN
ejpam-5963	224	46	,	,	PUNCT
ejpam-5963	224	47	p)(t)−	p)(t)−	NOUN
ejpam-5963	224	48	(	(	PUNCT
ejpam-5963	224	49	r	r	NOUN
ejpam-5963	224	50	,	,	PUNCT
ejpam-5963	224	51	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	224	52	,	,	PUNCT
ejpam-5963	224	53	(	(	PUNCT
ejpam-5963	224	54	12	12	NUM
ejpam-5963	224	55	)	)	PUNCT
ejpam-5963	224	56	and	and	CCONJ
ejpam-5963	224	57	∥g∗	∥g∗	PROPN
ejpam-5963	224	58	2(r	2(r	NUM
ejpam-5963	224	59	,	,	PUNCT
ejpam-5963	224	60	p)(t)−g∗	p)(t)−g∗	PROPN
ejpam-5963	224	61	2(r	2(r	NUM
ejpam-5963	224	62	,	,	PUNCT
ejpam-5963	224	63	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	224	64	≤	≤	PROPN
ejpam-5963	224	65	t	t	PROPN
ejpam-5963	224	66	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	224	67	,	,	PUNCT
ejpam-5963	224	68	ξ)lg∥(r	ξ)lg∥(r	NOUN
ejpam-5963	224	69	,	,	PUNCT
ejpam-5963	224	70	p)(t)−	p)(t)−	NOUN
ejpam-5963	224	71	(	(	PUNCT
ejpam-5963	224	72	r	r	NOUN
ejpam-5963	224	73	,	,	PUNCT
ejpam-5963	224	74	p)(t)∥.	p)(t)∥.	ADJ
ejpam-5963	224	75	(	(	PUNCT
ejpam-5963	224	76	13	13	NUM
ejpam-5963	224	77	)	)	PUNCT
ejpam-5963	224	78	a.	a.	NOUN
ejpam-5963	224	79	ali	ali	PROPN
ejpam-5963	224	80	et	et	PROPN
ejpam-5963	224	81	al	al	PROPN
ejpam-5963	224	82	.	.	PUNCT
ejpam-5963	224	83	/	/	SYM
ejpam-5963	224	84	eur	eur	PROPN
ejpam-5963	224	85	.	.	PUNCT
ejpam-5963	225	1	j.	j.	PROPN
ejpam-5963	225	2	pure	pure	PROPN
ejpam-5963	225	3	appl	appl	PROPN
ejpam-5963	225	4	.	.	PROPN
ejpam-5963	225	5	math	math	PROPN
ejpam-5963	225	6	,	,	PUNCT
ejpam-5963	225	7	18	18	NUM
ejpam-5963	225	8	(	(	PUNCT
ejpam-5963	225	9	2	2	NUM
ejpam-5963	225	10	)	)	PUNCT
ejpam-5963	225	11	(	(	PUNCT
ejpam-5963	225	12	2025	2025	NUM
ejpam-5963	225	13	)	)	PUNCT
ejpam-5963	225	14	,	,	PUNCT
ejpam-5963	225	15	5963	5963	NUM
ejpam-5963	225	16	10	10	NUM
ejpam-5963	225	17	of	of	ADP
ejpam-5963	225	18	19	19	NUM
ejpam-5963	225	19	hence	hence	ADV
ejpam-5963	225	20	from	from	ADP
ejpam-5963	225	21	(	(	PUNCT
ejpam-5963	225	22	12	12	NUM
ejpam-5963	225	23	)	)	PUNCT
ejpam-5963	225	24	and	and	CCONJ
ejpam-5963	225	25	(	(	PUNCT
ejpam-5963	225	26	13	13	NUM
ejpam-5963	225	27	)	)	PUNCT
ejpam-5963	225	28	,	,	PUNCT
ejpam-5963	225	29	we	we	PRON
ejpam-5963	225	30	have	have	VERB
ejpam-5963	225	31	∥g∗∗(r	∥g∗∗(r	NUM
ejpam-5963	225	32	,	,	PUNCT
ejpam-5963	225	33	p)(t)−g∗∗(r	p)(t)−g∗∗(r	NOUN
ejpam-5963	225	34	,	,	PUNCT
ejpam-5963	225	35	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	225	36	≤	≤	PROPN
ejpam-5963	225	37	t	t	PROPN
ejpam-5963	225	38	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	225	39	,	,	PUNCT
ejpam-5963	225	40	ξ)lf∥(r	ξ)lf∥(r	NOUN
ejpam-5963	225	41	,	,	PUNCT
ejpam-5963	225	42	p)(t)−	p)(t)−	NOUN
ejpam-5963	225	43	(	(	PUNCT
ejpam-5963	225	44	r	r	NOUN
ejpam-5963	225	45	,	,	PUNCT
ejpam-5963	225	46	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	225	47	+	+	NOUN
ejpam-5963	225	48	t	t	PROPN
ejpam-5963	225	49	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	225	50	,	,	PUNCT
ejpam-5963	225	51	ξ)lg∥(r	ξ)lg∥(r	NOUN
ejpam-5963	225	52	,	,	PUNCT
ejpam-5963	225	53	p)(t)−	p)(t)−	NOUN
ejpam-5963	225	54	(	(	PUNCT
ejpam-5963	225	55	r	r	NOUN
ejpam-5963	225	56	,	,	PUNCT
ejpam-5963	225	57	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	225	58	,	,	PUNCT
ejpam-5963	225	59	≤	≤	PROPN
ejpam-5963	225	60	t	t	PROPN
ejpam-5963	225	61	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	225	62	,	,	PUNCT
ejpam-5963	225	63	ξ)(lf	ξ)(lf	PROPN
ejpam-5963	225	64	+	+	CCONJ
ejpam-5963	225	65	lg)|(r	lg)|(r	PROPN
ejpam-5963	225	66	,	,	PUNCT
ejpam-5963	225	67	p)(t)−	p)(t)−	PROPN
ejpam-5963	225	68	(	(	PUNCT
ejpam-5963	225	69	r	r	NOUN
ejpam-5963	225	70	,	,	PUNCT
ejpam-5963	225	71	p)(t)|	p)(t)|	PROPN
ejpam-5963	225	72	.	.	PUNCT
ejpam-5963	226	1	which	which	PRON
ejpam-5963	226	2	implies	imply	VERB
ejpam-5963	226	3	that	that	SCONJ
ejpam-5963	226	4	∥g∗∗(r	∥g∗∗(r	ADJ
ejpam-5963	226	5	,	,	PUNCT
ejpam-5963	226	6	p)(t)−g∗∗(r	p)(t)−g∗∗(r	NOUN
ejpam-5963	226	7	,	,	PUNCT
ejpam-5963	226	8	p)(t)∥	p)(t)∥	PROPN
ejpam-5963	226	9	≤	≤	PROPN
ejpam-5963	226	10	t	t	PROPN
ejpam-5963	226	11	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	226	12	,	,	PUNCT
ejpam-5963	226	13	ξ)w∥(r	ξ)w∥(r	PROPN
ejpam-5963	226	14	,	,	PUNCT
ejpam-5963	226	15	p)(t)−	p)(t)−	NOUN
ejpam-5963	226	16	(	(	PUNCT
ejpam-5963	226	17	r	r	NOUN
ejpam-5963	226	18	,	,	PUNCT
ejpam-5963	226	19	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	226	20	,	,	PUNCT
ejpam-5963	226	21	(	(	PUNCT
ejpam-5963	226	22	14	14	NUM
ejpam-5963	226	23	)	)	PUNCT
ejpam-5963	226	24	where	where	SCONJ
ejpam-5963	226	25	w	w	NOUN
ejpam-5963	226	26	=	=	VERB
ejpam-5963	226	27	lf	lf	PROPN
ejpam-5963	226	28	+	+	X
ejpam-5963	226	29	lg	lg	PROPN
ejpam-5963	226	30	.	.	PROPN
ejpam-5963	226	31	therefore	therefore	ADV
ejpam-5963	226	32	,	,	PUNCT
ejpam-5963	226	33	from	from	ADP
ejpam-5963	226	34	(	(	PUNCT
ejpam-5963	226	35	11	11	NUM
ejpam-5963	226	36	)	)	PUNCT
ejpam-5963	226	37	and	and	CCONJ
ejpam-5963	226	38	(	(	PUNCT
ejpam-5963	226	39	14	14	NUM
ejpam-5963	226	40	)	)	PUNCT
ejpam-5963	226	41	,	,	PUNCT
ejpam-5963	226	42	we	we	PRON
ejpam-5963	226	43	have	have	VERB
ejpam-5963	226	44	∥k(r	∥k(r	NOUN
ejpam-5963	226	45	,	,	PUNCT
ejpam-5963	226	46	p)(t)−k(r	p)(t)−k(r	VERB
ejpam-5963	226	47	,	,	PUNCT
ejpam-5963	226	48	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	226	49	≤	≤	NOUN
ejpam-5963	226	50	l∥(r	l∥(r	PROPN
ejpam-5963	226	51	,	,	PUNCT
ejpam-5963	226	52	p)(t)−	p)(t)−	PROPN
ejpam-5963	226	53	(	(	PUNCT
ejpam-5963	226	54	r	r	NOUN
ejpam-5963	226	55	,	,	PUNCT
ejpam-5963	226	56	p)(t)∥+wt	p)(t)∥+wt	NOUN
ejpam-5963	226	57	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	226	58	,	,	PUNCT
ejpam-5963	226	59	ξ)∥(r	ξ)∥(r	NOUN
ejpam-5963	226	60	,	,	PUNCT
ejpam-5963	226	61	p)(t)−	p)(t)−	NOUN
ejpam-5963	226	62	(	(	PUNCT
ejpam-5963	226	63	r	r	NOUN
ejpam-5963	226	64	,	,	PUNCT
ejpam-5963	226	65	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	226	66	≤	≤	NOUN
ejpam-5963	226	67	υ∥(r	υ∥(r	ADV
ejpam-5963	226	68	,	,	PUNCT
ejpam-5963	226	69	p)(t)−	p)(t)−	NOUN
ejpam-5963	226	70	(	(	PUNCT
ejpam-5963	226	71	r	r	NOUN
ejpam-5963	226	72	,	,	PUNCT
ejpam-5963	226	73	p)(t)∥	p)(t)∥	NOUN
ejpam-5963	226	74	,	,	PUNCT
ejpam-5963	226	75	where	where	SCONJ
ejpam-5963	226	76	υ	υ	NOUN
ejpam-5963	226	77	=	=	PUNCT
ejpam-5963	227	1	l	l	NOUN
ejpam-5963	228	1	+	+	NOUN
ejpam-5963	228	2	wt	wt	PROPN
ejpam-5963	228	3	η+ξ−1b(η	η+ξ−1b(η	PROPN
ejpam-5963	228	4	,	,	PUNCT
ejpam-5963	228	5	ξ	ξ	PROPN
ejpam-5963	228	6	)	)	PUNCT
ejpam-5963	228	7	.	.	PUNCT
ejpam-5963	229	1	therefore	therefore	ADV
ejpam-5963	229	2	,	,	PUNCT
ejpam-5963	229	3	k	k	PROPN
ejpam-5963	229	4	is	be	AUX
ejpam-5963	229	5	contraction	contraction	NOUN
ejpam-5963	229	6	,	,	PUNCT
ejpam-5963	229	7	thus	thus	ADV
ejpam-5963	229	8	the	the	DET
ejpam-5963	229	9	system	system	NOUN
ejpam-5963	229	10	(	(	PUNCT
ejpam-5963	229	11	2	2	X
ejpam-5963	229	12	)	)	PUNCT
ejpam-5963	229	13	has	have	VERB
ejpam-5963	229	14	a	a	DET
ejpam-5963	229	15	unique	unique	ADJ
ejpam-5963	229	16	solution	solution	NOUN
ejpam-5963	229	17	.	.	PUNCT
ejpam-5963	230	1	4	4	X
ejpam-5963	230	2	.	.	X
ejpam-5963	230	3	stability	stability	NOUN
ejpam-5963	230	4	analysis	analysis	NOUN
ejpam-5963	230	5	this	this	DET
ejpam-5963	230	6	section	section	NOUN
ejpam-5963	230	7	,	,	PUNCT
ejpam-5963	230	8	is	be	AUX
ejpam-5963	230	9	devoted	devote	VERB
ejpam-5963	230	10	to	to	ADP
ejpam-5963	230	11	establishing	establish	VERB
ejpam-5963	230	12	stability	stability	NOUN
ejpam-5963	230	13	results	result	NOUN
ejpam-5963	230	14	for	for	ADP
ejpam-5963	230	15	the	the	DET
ejpam-5963	230	16	considered	consider	VERB
ejpam-5963	230	17	coupled	couple	VERB
ejpam-5963	230	18	system	system	NOUN
ejpam-5963	230	19	of	of	ADP
ejpam-5963	230	20	ffdes	ffde	NOUN
ejpam-5963	230	21	(	(	PUNCT
ejpam-5963	230	22	2	2	NUM
ejpam-5963	230	23	)	)	PUNCT
ejpam-5963	230	24	.	.	PUNCT
ejpam-5963	231	1	we	we	PRON
ejpam-5963	231	2	contend	contend	VERB
ejpam-5963	231	3	that	that	SCONJ
ejpam-5963	231	4	uh	uh	INTJ
ejpam-5963	231	5	stability	stability	NOUN
ejpam-5963	231	6	idea	idea	NOUN
ejpam-5963	231	7	is	be	AUX
ejpam-5963	231	8	important	important	ADJ
ejpam-5963	231	9	for	for	ADP
ejpam-5963	231	10	practical	practical	ADJ
ejpam-5963	231	11	issues	issue	NOUN
ejpam-5963	231	12	in	in	ADP
ejpam-5963	231	13	analysis	analysis	NOUN
ejpam-5963	231	14	.	.	PUNCT
ejpam-5963	232	1	the	the	DET
ejpam-5963	232	2	interesting	interesting	ADJ
ejpam-5963	232	3	feature	feature	NOUN
ejpam-5963	232	4	of	of	ADP
ejpam-5963	232	5	stability	stability	NOUN
ejpam-5963	232	6	is	be	AUX
ejpam-5963	232	7	that	that	PRON
ejpam-5963	232	8	to	to	PART
ejpam-5963	232	9	search	search	VERB
ejpam-5963	232	10	a	a	DET
ejpam-5963	232	11	uh	uh	INTJ
ejpam-5963	232	12	stability	stability	NOUN
ejpam-5963	232	13	of	of	ADP
ejpam-5963	232	14	a	a	DET
ejpam-5963	232	15	system	system	NOUN
ejpam-5963	232	16	,	,	PUNCT
ejpam-5963	232	17	who	who	PRON
ejpam-5963	232	18	exact	exact	VERB
ejpam-5963	232	19	solution	solution	NOUN
ejpam-5963	232	20	does	do	AUX
ejpam-5963	232	21	not	not	PART
ejpam-5963	232	22	exist	exist	VERB
ejpam-5963	232	23	,	,	PUNCT
ejpam-5963	232	24	which	which	PRON
ejpam-5963	232	25	is	be	AUX
ejpam-5963	232	26	typically	typically	ADV
ejpam-5963	232	27	challenging	challenging	ADJ
ejpam-5963	232	28	or	or	CCONJ
ejpam-5963	232	29	time	time	NOUN
ejpam-5963	232	30	consuming	consume	VERB
ejpam-5963	232	31	.	.	PUNCT
ejpam-5963	233	1	according	accord	VERB
ejpam-5963	233	2	to	to	ADP
ejpam-5963	233	3	uh	uh	INTJ
ejpam-5963	233	4	stability	stability	NOUN
ejpam-5963	233	5	,	,	PUNCT
ejpam-5963	233	6	there	there	PRON
ejpam-5963	233	7	exist	exist	VERB
ejpam-5963	233	8	a	a	DET
ejpam-5963	233	9	close	close	ADJ
ejpam-5963	233	10	approximate	approximate	ADJ
ejpam-5963	233	11	solution	solution	NOUN
ejpam-5963	233	12	of	of	ADP
ejpam-5963	233	13	system	system	NOUN
ejpam-5963	233	14	to	to	PART
ejpam-5963	233	15	exact	exact	VERB
ejpam-5963	233	16	solution	solution	NOUN
ejpam-5963	233	17	.	.	PUNCT
ejpam-5963	234	1	as	as	SCONJ
ejpam-5963	234	2	we	we	PRON
ejpam-5963	234	3	know	know	VERB
ejpam-5963	234	4	that	that	SCONJ
ejpam-5963	234	5	mostly	mostly	ADV
ejpam-5963	234	6	a	a	DET
ejpam-5963	234	7	mathematical	mathematical	ADJ
ejpam-5963	234	8	models	model	NOUN
ejpam-5963	234	9	are	be	AUX
ejpam-5963	234	10	non	non	ADJ
ejpam-5963	234	11	-	-	ADJ
ejpam-5963	234	12	linear	linear	ADJ
ejpam-5963	234	13	in	in	ADP
ejpam-5963	234	14	nature	nature	NOUN
ejpam-5963	234	15	and	and	CCONJ
ejpam-5963	234	16	some	some	DET
ejpam-5963	234	17	time	time	NOUN
ejpam-5963	234	18	its	its	PRON
ejpam-5963	234	19	exact	exact	ADJ
ejpam-5963	234	20	solution	solution	NOUN
ejpam-5963	234	21	does	do	AUX
ejpam-5963	234	22	not	not	PART
ejpam-5963	234	23	exist	exist	VERB
ejpam-5963	234	24	or	or	CCONJ
ejpam-5963	234	25	difficult	difficult	ADJ
ejpam-5963	234	26	to	to	PART
ejpam-5963	234	27	be	be	AUX
ejpam-5963	234	28	obtained	obtain	VERB
ejpam-5963	234	29	.	.	PUNCT
ejpam-5963	235	1	therefore	therefore	ADV
ejpam-5963	235	2	,	,	PUNCT
ejpam-5963	235	3	we	we	PRON
ejpam-5963	235	4	need	need	VERB
ejpam-5963	235	5	to	to	PART
ejpam-5963	235	6	find	find	VERB
ejpam-5963	235	7	best	good	ADJ
ejpam-5963	235	8	approximate	approximate	ADJ
ejpam-5963	235	9	solution	solution	NOUN
ejpam-5963	235	10	for	for	ADP
ejpam-5963	235	11	such	such	ADJ
ejpam-5963	235	12	problems	problem	NOUN
ejpam-5963	235	13	.	.	PUNCT
ejpam-5963	236	1	definition	definition	NOUN
ejpam-5963	236	2	6	6	NUM
ejpam-5963	236	3	.	.	PUNCT
ejpam-5963	236	4	to	to	PART
ejpam-5963	236	5	obtained	obtain	VERB
ejpam-5963	236	6	the	the	DET
ejpam-5963	236	7	uh	uh	INTJ
ejpam-5963	236	8	stability	stability	NOUN
ejpam-5963	236	9	of	of	ADP
ejpam-5963	236	10	the	the	DET
ejpam-5963	236	11	system	system	NOUN
ejpam-5963	236	12	(	(	PUNCT
ejpam-5963	236	13	2	2	NUM
ejpam-5963	236	14	)	)	PUNCT
ejpam-5963	236	15	,	,	PUNCT
ejpam-5963	236	16	suppose	suppose	VERB
ejpam-5963	236	17	that	that	SCONJ
ejpam-5963	236	18	exist	exist	VERB
ejpam-5963	236	19	ϵ	ϵ	NOUN
ejpam-5963	236	20	=	=	SYM
ejpam-5963	236	21	max	max	PROPN
ejpam-5963	236	22	(	(	PUNCT
ejpam-5963	236	23	ϵ1	ϵ1	ADJ
ejpam-5963	236	24	,	,	PUNCT
ejpam-5963	236	25	ϵ2	ϵ2	ADJ
ejpam-5963	236	26	)	)	PUNCT
ejpam-5963	236	27	>	>	X
ejpam-5963	236	28	0	0	NUM
ejpam-5963	236	29	,	,	PUNCT
ejpam-5963	236	30	and	and	CCONJ
ejpam-5963	236	31	the	the	DET
ejpam-5963	236	32	system	system	NOUN
ejpam-5963	236	33	of	of	ADP
ejpam-5963	236	34	inequality	inequality	NOUN
ejpam-5963	236	35	given	give	VERB
ejpam-5963	236	36	by	by	ADP
ejpam-5963	236	37	{	{	PUNCT
ejpam-5963	236	38	|fddηr(t)−	|fddηr(t)−	PROPN
ejpam-5963	236	39	ξtξ−1f(t	ξtξ−1f(t	NOUN
ejpam-5963	236	40	,	,	PUNCT
ejpam-5963	236	41	r(t	r(t	NOUN
ejpam-5963	236	42	)	)	PUNCT
ejpam-5963	236	43	,	,	PUNCT
ejpam-5963	236	44	p(t))|	p(t))|	VERB
ejpam-5963	236	45	≤	≤	NOUN
ejpam-5963	236	46	ϵ1	ϵ1	VERB
ejpam-5963	236	47	,	,	PUNCT
ejpam-5963	236	48	|fddηp(t)−	|fddηp(t)−	PRON
ejpam-5963	236	49	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	236	50	,	,	PUNCT
ejpam-5963	236	51	r(t	r(t	NOUN
ejpam-5963	236	52	)	)	PUNCT
ejpam-5963	236	53	,	,	PUNCT
ejpam-5963	236	54	p(t))|	p(t))|	VERB
ejpam-5963	236	55	≤	≤	X
ejpam-5963	236	56	ϵ2	ϵ2	ADJ
ejpam-5963	236	57	.	.	PUNCT
ejpam-5963	237	1	(	(	PUNCT
ejpam-5963	237	2	15	15	NUM
ejpam-5963	237	3	)	)	PUNCT
ejpam-5963	237	4	then	then	ADV
ejpam-5963	237	5	our	our	PRON
ejpam-5963	237	6	system	system	NOUN
ejpam-5963	237	7	(	(	PUNCT
ejpam-5963	237	8	2	2	X
ejpam-5963	237	9	)	)	PUNCT
ejpam-5963	237	10	is	be	AUX
ejpam-5963	237	11	uh	uh	INTJ
ejpam-5963	237	12	stable	stable	ADJ
ejpam-5963	237	13	,	,	PUNCT
ejpam-5963	237	14	∃c(1,2	∃c(1,2	NUM
ejpam-5963	237	15	)	)	PUNCT
ejpam-5963	237	16	>	>	X
ejpam-5963	237	17	0	0	NUM
ejpam-5963	237	18	,	,	PUNCT
ejpam-5963	237	19	with	with	ADP
ejpam-5963	237	20	every	every	DET
ejpam-5963	237	21	solution	solution	NOUN
ejpam-5963	237	22	(	(	PUNCT
ejpam-5963	237	23	r	r	NOUN
ejpam-5963	237	24	,	,	PUNCT
ejpam-5963	237	25	p	p	NOUN
ejpam-5963	237	26	)	)	PUNCT
ejpam-5963	237	27	of	of	ADP
ejpam-5963	237	28	inequality	inequality	NOUN
ejpam-5963	237	29	equation	equation	NOUN
ejpam-5963	237	30	(	(	PUNCT
ejpam-5963	237	31	15	15	NUM
ejpam-5963	237	32	)	)	PUNCT
ejpam-5963	237	33	there	there	PRON
ejpam-5963	237	34	exist	exist	VERB
ejpam-5963	237	35	unique	unique	ADJ
ejpam-5963	237	36	solution	solution	NOUN
ejpam-5963	237	37	(	(	PUNCT
ejpam-5963	237	38	r	r	NOUN
ejpam-5963	237	39	,	,	PUNCT
ejpam-5963	237	40	p	p	NOUN
ejpam-5963	237	41	)	)	PUNCT
ejpam-5963	237	42	with	with	ADP
ejpam-5963	237	43	|(r	|(r	PROPN
ejpam-5963	237	44	,	,	PUNCT
ejpam-5963	237	45	p)(t)−	p)(t)−	NOUN
ejpam-5963	237	46	(	(	PUNCT
ejpam-5963	237	47	r	r	NOUN
ejpam-5963	237	48	,	,	PUNCT
ejpam-5963	237	49	p)(t)|	p)(t)|	PROPN
ejpam-5963	237	50	≤	≤	NOUN
ejpam-5963	237	51	ϵc(1,2	ϵc(1,2	NOUN
ejpam-5963	237	52	)	)	PUNCT
ejpam-5963	237	53	.	.	PUNCT
ejpam-5963	238	1	(	(	PUNCT
ejpam-5963	238	2	16	16	X
ejpam-5963	238	3	)	)	PUNCT
ejpam-5963	238	4	remark	remark	NOUN
ejpam-5963	238	5	:	:	PUNCT
ejpam-5963	238	6	we	we	PRON
ejpam-5963	238	7	say	say	VERB
ejpam-5963	238	8	that	that	SCONJ
ejpam-5963	238	9	(	(	PUNCT
ejpam-5963	238	10	r	r	NOUN
ejpam-5963	238	11	,	,	PUNCT
ejpam-5963	238	12	p	p	NOUN
ejpam-5963	238	13	)	)	PUNCT
ejpam-5963	238	14	is	be	AUX
ejpam-5963	238	15	a	a	DET
ejpam-5963	238	16	solution	solution	NOUN
ejpam-5963	238	17	of	of	ADP
ejpam-5963	238	18	the	the	DET
ejpam-5963	238	19	system	system	NOUN
ejpam-5963	238	20	(	(	PUNCT
ejpam-5963	238	21	15	15	NUM
ejpam-5963	238	22	)	)	PUNCT
ejpam-5963	238	23	,	,	PUNCT
ejpam-5963	238	24	if	if	SCONJ
ejpam-5963	238	25	there	there	PRON
ejpam-5963	238	26	exist	exist	VERB
ejpam-5963	238	27	ω1	ω1	PROPN
ejpam-5963	238	28	,	,	PUNCT
ejpam-5963	238	29	ω2	ω2	PROPN
ejpam-5963	238	30	∈	∈	PROPN
ejpam-5963	238	31	c(i	c(i	PROPN
ejpam-5963	238	32	,	,	PUNCT
ejpam-5963	238	33	r	r	NOUN
ejpam-5963	238	34	)	)	PUNCT
ejpam-5963	238	35	which	which	PRON
ejpam-5963	238	36	defend	defend	VERB
ejpam-5963	238	37	upon	upon	SCONJ
ejpam-5963	238	38	(	(	PUNCT
ejpam-5963	238	39	r	r	NOUN
ejpam-5963	238	40	,	,	PUNCT
ejpam-5963	238	41	p	p	NOUN
ejpam-5963	238	42	)	)	PUNCT
ejpam-5963	238	43	,	,	PUNCT
ejpam-5963	238	44	such	such	ADJ
ejpam-5963	238	45	that	that	DET
ejpam-5963	238	46	•	•	NUM
ejpam-5963	238	47	|ω1(t)|	|ω1(t)|	NUM
ejpam-5963	238	48	≤	≤	NUM
ejpam-5963	238	49	ϵ1	ϵ1	NOUN
ejpam-5963	238	50	,	,	PUNCT
ejpam-5963	238	51	a.	a.	PROPN
ejpam-5963	238	52	ali	ali	PROPN
ejpam-5963	238	53	et	et	PROPN
ejpam-5963	238	54	al	al	PROPN
ejpam-5963	238	55	.	.	PUNCT
ejpam-5963	238	56	/	/	SYM
ejpam-5963	238	57	eur	eur	PROPN
ejpam-5963	238	58	.	.	PUNCT
ejpam-5963	239	1	j.	j.	PROPN
ejpam-5963	239	2	pure	pure	PROPN
ejpam-5963	239	3	appl	appl	PROPN
ejpam-5963	239	4	.	.	PROPN
ejpam-5963	239	5	math	math	PROPN
ejpam-5963	239	6	,	,	PUNCT
ejpam-5963	239	7	18	18	NUM
ejpam-5963	239	8	(	(	PUNCT
ejpam-5963	239	9	2	2	NUM
ejpam-5963	239	10	)	)	PUNCT
ejpam-5963	239	11	(	(	PUNCT
ejpam-5963	239	12	2025	2025	NUM
ejpam-5963	239	13	)	)	PUNCT
ejpam-5963	239	14	,	,	PUNCT
ejpam-5963	239	15	5963	5963	NUM
ejpam-5963	239	16	11	11	NUM
ejpam-5963	239	17	of	of	ADP
ejpam-5963	239	18	19	19	NUM
ejpam-5963	239	19	•	•	NOUN
ejpam-5963	239	20	|ω2(t)|	|ω2(t)|	NUM
ejpam-5963	239	21	≤	≤	PUNCT
ejpam-5963	239	22	ϵ2	ϵ2	ADJ
ejpam-5963	239	23	.	.	PUNCT
ejpam-5963	240	1	and	and	CCONJ
ejpam-5963	240	2	the	the	DET
ejpam-5963	240	3	perturbed	perturb	VERB
ejpam-5963	240	4	system	system	NOUN
ejpam-5963	240	5	of	of	ADP
ejpam-5963	240	6	coupled	couple	VERB
ejpam-5963	240	7	system	system	NOUN
ejpam-5963	240	8	of	of	ADP
ejpam-5963	240	9	ffdes	ffde	NOUN
ejpam-5963	240	10	as	as	ADP
ejpam-5963	240	11	:	:	PUNCT
ejpam-5963	240	12	{	{	PUNCT
ejpam-5963	240	13	fddηr(t	fddηr(t	NOUN
ejpam-5963	240	14	)	)	PUNCT
ejpam-5963	240	15	=	=	SYM
ejpam-5963	240	16	ξtξ−1f(t	ξtξ−1f(t	NOUN
ejpam-5963	240	17	,	,	PUNCT
ejpam-5963	240	18	r(t	r(t	NOUN
ejpam-5963	240	19	)	)	PUNCT
ejpam-5963	240	20	,	,	PUNCT
ejpam-5963	240	21	p(t	p(t	NOUN
ejpam-5963	240	22	)	)	PUNCT
ejpam-5963	240	23	)	)	PUNCT
ejpam-5963	241	1	+	+	CCONJ
ejpam-5963	241	2	ξtξ−1ω1(t	ξtξ−1ω1(t	ADJ
ejpam-5963	241	3	)	)	PUNCT
ejpam-5963	241	4	,	,	PUNCT
ejpam-5963	241	5	fddηp(t	fddηp(t	NOUN
ejpam-5963	241	6	)	)	PUNCT
ejpam-5963	241	7	=	=	SYM
ejpam-5963	241	8	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	241	9	,	,	PUNCT
ejpam-5963	241	10	r(t	r(t	NOUN
ejpam-5963	241	11	)	)	PUNCT
ejpam-5963	241	12	,	,	PUNCT
ejpam-5963	241	13	p(t	p(t	NOUN
ejpam-5963	241	14	)	)	PUNCT
ejpam-5963	241	15	)	)	PUNCT
ejpam-5963	242	1	+	+	CCONJ
ejpam-5963	242	2	ξtξ−1ω2(t	ξtξ−1ω2(t	NUM
ejpam-5963	242	3	)	)	PUNCT
ejpam-5963	242	4	.	.	PUNCT
ejpam-5963	243	1	(	(	PUNCT
ejpam-5963	243	2	17	17	NUM
ejpam-5963	243	3	)	)	PUNCT
ejpam-5963	243	4	lemma	lemma	PROPN
ejpam-5963	243	5	3	3	X
ejpam-5963	243	6	.	.	PUNCT
ejpam-5963	243	7	suppose	suppose	VERB
ejpam-5963	243	8	that	that	SCONJ
ejpam-5963	243	9	(	(	PUNCT
ejpam-5963	243	10	r	r	NOUN
ejpam-5963	243	11	,	,	PUNCT
ejpam-5963	243	12	p	p	NOUN
ejpam-5963	243	13	)	)	PUNCT
ejpam-5963	243	14	be	be	AUX
ejpam-5963	243	15	the	the	DET
ejpam-5963	243	16	solution	solution	NOUN
ejpam-5963	243	17	of	of	ADP
ejpam-5963	243	18	the	the	DET
ejpam-5963	243	19	inequality	inequality	NOUN
ejpam-5963	243	20	(	(	PUNCT
ejpam-5963	243	21	15	15	NUM
ejpam-5963	243	22	)	)	PUNCT
ejpam-5963	243	23	,	,	PUNCT
ejpam-5963	243	24	then	then	ADV
ejpam-5963	243	25	the	the	DET
ejpam-5963	243	26	following	follow	VERB
ejpam-5963	243	27	system	system	NOUN
ejpam-5963	243	28	of	of	ADP
ejpam-5963	243	29	inequality	inequality	PROPN
ejpam-5963	243	30	hold.∣∣∣∣r(t)−	hold.∣∣∣∣r(t)−	PROPN
ejpam-5963	243	31	(	(	PUNCT
ejpam-5963	243	32	(	(	PUNCT
ejpam-5963	243	33	r0	r0	NOUN
ejpam-5963	243	34	+	+	CCONJ
ejpam-5963	243	35	ϕ(r	ϕ(r	PROPN
ejpam-5963	243	36	)	)	PUNCT
ejpam-5963	244	1	+	+	CCONJ
ejpam-5963	245	1	ξ	ξ	DET
ejpam-5963	245	2	γ(η	γ(η	NOUN
ejpam-5963	245	3	)	)	PUNCT
ejpam-5963	245	4	∫	∫	PROPN
ejpam-5963	245	5	t	t	PROPN
ejpam-5963	245	6	0	0	NUM
ejpam-5963	245	7	(	(	PUNCT
ejpam-5963	245	8	t−	t−	PROPN
ejpam-5963	245	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	245	10	,	,	PUNCT
ejpam-5963	245	11	ri(δ	ri(δ	NOUN
ejpam-5963	245	12	)	)	PUNCT
ejpam-5963	245	13	,	,	PUNCT
ejpam-5963	245	14	pi(δ))dδ	pi(δ))dδ	PROPN
ejpam-5963	245	15	)	)	PUNCT
ejpam-5963	245	16	)	)	PUNCT
ejpam-5963	245	17	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	245	18	≤	≤	PROPN
ejpam-5963	245	19	δϵ1,∣∣∣∣p(t)−	δϵ1,∣∣∣∣p(t)−	PROPN
ejpam-5963	245	20	(	(	PUNCT
ejpam-5963	245	21	(	(	PUNCT
ejpam-5963	245	22	p0	p0	NOUN
ejpam-5963	245	23	+	+	CCONJ
ejpam-5963	245	24	ψ(p	ψ(p	NOUN
ejpam-5963	245	25	)	)	PUNCT
ejpam-5963	245	26	+	+	NUM
ejpam-5963	245	27	ξ	ξ	DET
ejpam-5963	245	28	γ(η	γ(η	NOUN
ejpam-5963	245	29	)	)	PUNCT
ejpam-5963	245	30	∫	∫	PROPN
ejpam-5963	246	1	t	t	PROPN
ejpam-5963	246	2	0	0	NUM
ejpam-5963	246	3	(	(	PUNCT
ejpam-5963	246	4	t−	t−	PROPN
ejpam-5963	246	5	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	246	6	,	,	PUNCT
ejpam-5963	246	7	xi(δ	xi(δ	NUM
ejpam-5963	246	8	)	)	PUNCT
ejpam-5963	246	9	,	,	PUNCT
ejpam-5963	246	10	pi(δ))dδ	pi(δ))dδ	PROPN
ejpam-5963	246	11	)	)	PUNCT
ejpam-5963	246	12	)	)	PUNCT
ejpam-5963	246	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5963	246	14	≤	≤	NUM
ejpam-5963	246	15	δϵ2	δϵ2	NOUN
ejpam-5963	246	16	.	.	PUNCT
ejpam-5963	247	1	proof	proof	NOUN
ejpam-5963	247	2	.	.	PUNCT
ejpam-5963	248	1	in	in	ADP
ejpam-5963	248	2	-	-	PUNCT
ejpam-5963	248	3	view	view	NOUN
ejpam-5963	248	4	of	of	ADP
ejpam-5963	248	5	remark(4	remark(4	NOUN
ejpam-5963	248	6	)	)	PUNCT
ejpam-5963	248	7	,	,	PUNCT
ejpam-5963	248	8	we	we	PRON
ejpam-5963	248	9	can	can	AUX
ejpam-5963	248	10	express	express	VERB
ejpam-5963	248	11	the	the	DET
ejpam-5963	248	12	consider	consider	NOUN
ejpam-5963	248	13	system	system	NOUN
ejpam-5963	248	14	as:	as:	NOUN
ejpam-5963	248	15	fddηr(t	fddηr(t	NOUN
ejpam-5963	248	16	)	)	PUNCT
ejpam-5963	248	17	=	=	SYM
ejpam-5963	249	1	ξtξ−1f(t	ξtξ−1f(t	NOUN
ejpam-5963	249	2	,	,	PUNCT
ejpam-5963	249	3	r(t	r(t	NOUN
ejpam-5963	249	4	)	)	PUNCT
ejpam-5963	249	5	,	,	PUNCT
ejpam-5963	249	6	p(t	p(t	NOUN
ejpam-5963	249	7	)	)	PUNCT
ejpam-5963	249	8	)	)	PUNCT
ejpam-5963	250	1	+	+	CCONJ
ejpam-5963	250	2	ξtξ−1ω1(t	ξtξ−1ω1(t	ADJ
ejpam-5963	250	3	)	)	PUNCT
ejpam-5963	250	4	,	,	PUNCT
ejpam-5963	250	5	fddηp(t	fddηp(t	NOUN
ejpam-5963	250	6	)	)	PUNCT
ejpam-5963	250	7	=	=	SYM
ejpam-5963	250	8	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	250	9	,	,	PUNCT
ejpam-5963	250	10	r(t	r(t	NOUN
ejpam-5963	250	11	)	)	PUNCT
ejpam-5963	250	12	,	,	PUNCT
ejpam-5963	250	13	p(t	p(t	NOUN
ejpam-5963	250	14	)	)	PUNCT
ejpam-5963	250	15	)	)	PUNCT
ejpam-5963	251	1	+	+	CCONJ
ejpam-5963	251	2	ξtξ−1ω2(t	ξtξ−1ω2(t	NOUN
ejpam-5963	251	3	)	)	PUNCT
ejpam-5963	251	4	,	,	PUNCT
ejpam-5963	251	5	r(0	r(0	PROPN
ejpam-5963	251	6	)	)	PUNCT
ejpam-5963	251	7	=	=	PUNCT
ejpam-5963	251	8	(	(	PUNCT
ejpam-5963	251	9	r0	r0	NOUN
ejpam-5963	251	10	+	+	CCONJ
ejpam-5963	251	11	ϕ(r	ϕ(r	PROPN
ejpam-5963	251	12	)	)	PUNCT
ejpam-5963	251	13	)	)	PUNCT
ejpam-5963	251	14	,	,	PUNCT
ejpam-5963	251	15	p(0	p(0	NOUN
ejpam-5963	251	16	)	)	PUNCT
ejpam-5963	251	17	=	=	SYM
ejpam-5963	251	18	(	(	PUNCT
ejpam-5963	251	19	p0	p0	NOUN
ejpam-5963	251	20	+	+	CCONJ
ejpam-5963	251	21	ψ(p	ψ(p	NOUN
ejpam-5963	251	22	)	)	PUNCT
ejpam-5963	251	23	)	)	PUNCT
ejpam-5963	251	24	.	.	PUNCT
ejpam-5963	252	1	in	in	ADP
ejpam-5963	252	2	light	light	NOUN
ejpam-5963	252	3	of	of	ADP
ejpam-5963	252	4	lemma	lemma	PROPN
ejpam-5963	252	5	2	2	NUM
ejpam-5963	252	6	,	,	PUNCT
ejpam-5963	252	7	we	we	PRON
ejpam-5963	252	8	can	can	AUX
ejpam-5963	252	9	obtained	obtain	VERB
ejpam-5963	252	10	the	the	DET
ejpam-5963	252	11	following	follow	VERB
ejpam-5963	252	12	results	result	NOUN
ejpam-5963	252	13	:	:	PUNCT
ejpam-5963	252	14	r(t	r(t	NOUN
ejpam-5963	252	15	)	)	PUNCT
ejpam-5963	252	16	=	=	PUNCT
ejpam-5963	253	1	(	(	PUNCT
ejpam-5963	253	2	r0	r0	NOUN
ejpam-5963	253	3	+	+	CCONJ
ejpam-5963	253	4	ϕ(r	ϕ(r	PROPN
ejpam-5963	253	5	)	)	PUNCT
ejpam-5963	253	6	)	)	PUNCT
ejpam-5963	254	1	+	+	CCONJ
ejpam-5963	255	1	ξ	ξ	DET
ejpam-5963	255	2	γ(η	γ(η	NOUN
ejpam-5963	255	3	)	)	PUNCT
ejpam-5963	255	4	∫	∫	PROPN
ejpam-5963	255	5	t	t	PROPN
ejpam-5963	255	6	0	0	NUM
ejpam-5963	255	7	(	(	PUNCT
ejpam-5963	255	8	t−	t−	PROPN
ejpam-5963	255	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	255	10	,	,	PUNCT
ejpam-5963	255	11	r(δ	r(δ	PROPN
ejpam-5963	255	12	)	)	PUNCT
ejpam-5963	255	13	,	,	PUNCT
ejpam-5963	255	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	255	15	)	)	PUNCT
ejpam-5963	256	1	+	+	NUM
ejpam-5963	256	2	ξ	ξ	PROPN
ejpam-5963	256	3	γ(η	γ(η	NOUN
ejpam-5963	256	4	)	)	PUNCT
ejpam-5963	257	1	∫	∫	PROPN
ejpam-5963	257	2	t	t	PROPN
ejpam-5963	257	3	0	0	NUM
ejpam-5963	257	4	(	(	PUNCT
ejpam-5963	257	5	t−	t−	PROPN
ejpam-5963	257	6	δ)η−1δξ−1ω1(δ)dδ	δ)η−1δξ−1ω1(δ)dδ	PROPN
ejpam-5963	257	7	,	,	PUNCT
ejpam-5963	257	8	p(t	p(t	NOUN
ejpam-5963	257	9	)	)	PUNCT
ejpam-5963	257	10	=	=	SYM
ejpam-5963	257	11	(	(	PUNCT
ejpam-5963	257	12	p0	p0	NOUN
ejpam-5963	257	13	+	+	CCONJ
ejpam-5963	257	14	ψ(p	ψ(p	NOUN
ejpam-5963	257	15	)	)	PUNCT
ejpam-5963	257	16	)	)	PUNCT
ejpam-5963	258	1	+	+	CCONJ
ejpam-5963	259	1	ξ	ξ	DET
ejpam-5963	259	2	γ(η	γ(η	NOUN
ejpam-5963	259	3	)	)	PUNCT
ejpam-5963	259	4	∫	∫	PROPN
ejpam-5963	259	5	t	t	PROPN
ejpam-5963	259	6	0	0	NUM
ejpam-5963	259	7	(	(	PUNCT
ejpam-5963	259	8	t−	t−	PROPN
ejpam-5963	259	9	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	259	10	,	,	PUNCT
ejpam-5963	259	11	r(δ	r(δ	PROPN
ejpam-5963	259	12	)	)	PUNCT
ejpam-5963	259	13	,	,	PUNCT
ejpam-5963	259	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	259	15	)	)	PUNCT
ejpam-5963	260	1	+	+	NUM
ejpam-5963	260	2	ξ	ξ	PROPN
ejpam-5963	260	3	γ(η	γ(η	NOUN
ejpam-5963	260	4	)	)	PUNCT
ejpam-5963	261	1	∫	∫	PROPN
ejpam-5963	261	2	t	t	PROPN
ejpam-5963	261	3	0	0	NUM
ejpam-5963	261	4	(	(	PUNCT
ejpam-5963	261	5	t−	t−	PROPN
ejpam-5963	261	6	δ)η−1δξ−1ω2(δ)dδ	δ)η−1δξ−1ω2(δ)dδ	PROPN
ejpam-5963	261	7	.	.	PUNCT
ejpam-5963	262	1	now∣∣∣∣r(t)−	now∣∣∣∣r(t)−	PROPN
ejpam-5963	262	2	(	(	PUNCT
ejpam-5963	262	3	r0	r0	NOUN
ejpam-5963	262	4	+	+	CCONJ
ejpam-5963	262	5	ϕ(r	ϕ(r	PROPN
ejpam-5963	262	6	)	)	PUNCT
ejpam-5963	262	7	+	+	CCONJ
ejpam-5963	262	8	ξ	ξ	PRON
ejpam-5963	262	9	γ(η	γ(η	NOUN
ejpam-5963	262	10	)	)	PUNCT
ejpam-5963	262	11	∫	∫	PROPN
ejpam-5963	262	12	t	t	PROPN
ejpam-5963	262	13	0	0	NUM
ejpam-5963	262	14	(	(	PUNCT
ejpam-5963	262	15	t−	t−	PROPN
ejpam-5963	262	16	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	262	17	,	,	PUNCT
ejpam-5963	262	18	r(δ	r(δ	PROPN
ejpam-5963	262	19	)	)	PUNCT
ejpam-5963	262	20	,	,	PUNCT
ejpam-5963	262	21	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	262	22	)	)	PUNCT
ejpam-5963	262	23	)	)	PUNCT
ejpam-5963	262	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	262	25	=	=	SYM
ejpam-5963	262	26	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	262	27	ξ	ξ	PROPN
ejpam-5963	262	28	γ(η	γ(η	PROPN
ejpam-5963	262	29	)	)	PUNCT
ejpam-5963	262	30	∫	∫	PROPN
ejpam-5963	262	31	t	t	PROPN
ejpam-5963	262	32	0	0	NUM
ejpam-5963	262	33	(	(	PUNCT
ejpam-5963	262	34	t−	t−	PROPN
ejpam-5963	262	35	δ)η−1δξ−1ω1(δ)dδ	δ)η−1δξ−1ω1(δ)dδ	PROPN
ejpam-5963	262	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	262	37	≤	≤	NUM
ejpam-5963	262	38	ξ	ξ	PRON
ejpam-5963	262	39	γ(η	γ(η	PROPN
ejpam-5963	262	40	)	)	PUNCT
ejpam-5963	262	41	∫	∫	PROPN
ejpam-5963	262	42	t	t	PROPN
ejpam-5963	262	43	0	0	NUM
ejpam-5963	262	44	(	(	PUNCT
ejpam-5963	262	45	t−	t−	PRON
ejpam-5963	262	46	δ)η−1δξ−1ϵ1dδ	δ)η−1δξ−1ϵ1dδ	PROPN
ejpam-5963	262	47	≤	≤	ADJ
ejpam-5963	262	48	b(η	b(η	NOUN
ejpam-5963	262	49	,	,	PUNCT
ejpam-5963	262	50	ξ)t	ξ)t	PUNCT
ejpam-5963	262	51	η+ξ−1ϵ1	η+ξ−1ϵ1	NOUN
ejpam-5963	262	52	=	=	SYM
ejpam-5963	262	53	δϵ1	δϵ1	NOUN
ejpam-5963	262	54	,	,	PUNCT
ejpam-5963	262	55	where	where	SCONJ
ejpam-5963	262	56	δ	δ	PROPN
ejpam-5963	262	57	=	=	SYM
ejpam-5963	262	58	b(η	b(η	PROPN
ejpam-5963	262	59	,	,	PUNCT
ejpam-5963	262	60	ξ)t	ξ)t	X
ejpam-5963	262	61	η+ξ−1	η+ξ−1	PROPN
ejpam-5963	262	62	.	.	PROPN
ejpam-5963	262	63	similarly	similarly	ADV
ejpam-5963	262	64	,	,	PUNCT
ejpam-5963	262	65	one	one	PRON
ejpam-5963	262	66	can	can	AUX
ejpam-5963	262	67	obtain	obtain	VERB
ejpam-5963	262	68	the	the	DET
ejpam-5963	262	69	following	following	ADJ
ejpam-5963	262	70	result	result	NOUN
ejpam-5963	262	71	for	for	ADP
ejpam-5963	262	72	second	second	ADJ
ejpam-5963	262	73	compartment	compartment	NOUN
ejpam-5963	262	74	of	of	ADP
ejpam-5963	262	75	proposed	propose	VERB
ejpam-5963	262	76	model:∣∣∣∣p(t)−	model:∣∣∣∣p(t)−	PROPN
ejpam-5963	262	77	(	(	PUNCT
ejpam-5963	262	78	p0	p0	NOUN
ejpam-5963	262	79	+	+	CCONJ
ejpam-5963	262	80	ψ(p	ψ(p	NOUN
ejpam-5963	262	81	)	)	PUNCT
ejpam-5963	262	82	+	+	NUM
ejpam-5963	263	1	ξ	ξ	DET
ejpam-5963	263	2	γ(η	γ(η	NOUN
ejpam-5963	263	3	)	)	PUNCT
ejpam-5963	263	4	∫	∫	PROPN
ejpam-5963	263	5	t	t	PROPN
ejpam-5963	263	6	0	0	NUM
ejpam-5963	263	7	(	(	PUNCT
ejpam-5963	263	8	t−	t−	PROPN
ejpam-5963	263	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	263	10	,	,	PUNCT
ejpam-5963	263	11	r(δ	r(δ	PROPN
ejpam-5963	263	12	)	)	PUNCT
ejpam-5963	263	13	,	,	PUNCT
ejpam-5963	263	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	263	15	)	)	PUNCT
ejpam-5963	263	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	263	17	≤	≤	NUM
ejpam-5963	263	18	δϵ2	δϵ2	NOUN
ejpam-5963	263	19	,	,	PUNCT
ejpam-5963	263	20	which	which	PRON
ejpam-5963	263	21	completes	complete	VERB
ejpam-5963	263	22	the	the	DET
ejpam-5963	263	23	proof	proof	NOUN
ejpam-5963	263	24	a.	a.	PROPN
ejpam-5963	263	25	ali	ali	PROPN
ejpam-5963	263	26	et	et	PROPN
ejpam-5963	263	27	al	al	PROPN
ejpam-5963	263	28	.	.	PUNCT
ejpam-5963	263	29	/	/	SYM
ejpam-5963	263	30	eur	eur	PROPN
ejpam-5963	263	31	.	.	PUNCT
ejpam-5963	264	1	j.	j.	PROPN
ejpam-5963	264	2	pure	pure	PROPN
ejpam-5963	264	3	appl	appl	PROPN
ejpam-5963	264	4	.	.	PROPN
ejpam-5963	264	5	math	math	PROPN
ejpam-5963	264	6	,	,	PUNCT
ejpam-5963	264	7	18	18	NUM
ejpam-5963	264	8	(	(	PUNCT
ejpam-5963	264	9	2	2	NUM
ejpam-5963	264	10	)	)	PUNCT
ejpam-5963	264	11	(	(	PUNCT
ejpam-5963	264	12	2025	2025	NUM
ejpam-5963	264	13	)	)	PUNCT
ejpam-5963	264	14	,	,	PUNCT
ejpam-5963	264	15	5963	5963	NUM
ejpam-5963	264	16	12	12	NUM
ejpam-5963	264	17	of	of	ADP
ejpam-5963	264	18	19	19	NUM
ejpam-5963	264	19	theorem	theorem	NOUN
ejpam-5963	264	20	5	5	NUM
ejpam-5963	264	21	.	.	PUNCT
ejpam-5963	265	1	under	under	ADP
ejpam-5963	265	2	the	the	DET
ejpam-5963	265	3	assumptions	assumption	NOUN
ejpam-5963	265	4	(	(	PUNCT
ejpam-5963	265	5	m1)-(m3	m1)-(m3	PROPN
ejpam-5963	265	6	)	)	PUNCT
ejpam-5963	265	7	,	,	PUNCT
ejpam-5963	265	8	the	the	DET
ejpam-5963	265	9	solution	solution	NOUN
ejpam-5963	265	10	of	of	ADP
ejpam-5963	265	11	coupled	couple	VERB
ejpam-5963	265	12	system	system	NOUN
ejpam-5963	265	13	(	(	PUNCT
ejpam-5963	265	14	2	2	NUM
ejpam-5963	265	15	)	)	PUNCT
ejpam-5963	265	16	is	be	AUX
ejpam-5963	265	17	uh	uh	INTJ
ejpam-5963	265	18	and	and	CCONJ
ejpam-5963	265	19	guh	guh	PROPN
ejpam-5963	265	20	stable	stable	ADJ
ejpam-5963	265	21	,	,	PUNCT
ejpam-5963	265	22	if	if	SCONJ
ejpam-5963	265	23	c1c2lflg	c1c2lflg	ADV
ejpam-5963	265	24	̸=	̸=	PROPN
ejpam-5963	265	25	1	1	NUM
ejpam-5963	265	26	.	.	PUNCT
ejpam-5963	266	1	proof	proof	NOUN
ejpam-5963	266	2	.	.	PUNCT
ejpam-5963	267	1	let	let	AUX
ejpam-5963	267	2	(	(	PUNCT
ejpam-5963	267	3	r	r	AUX
ejpam-5963	267	4	,	,	PUNCT
ejpam-5963	267	5	p	p	NOUN
ejpam-5963	267	6	)	)	PUNCT
ejpam-5963	267	7	be	be	AUX
ejpam-5963	267	8	the	the	DET
ejpam-5963	267	9	arbitrary	arbitrary	ADJ
ejpam-5963	267	10	solution	solution	NOUN
ejpam-5963	267	11	and	and	CCONJ
ejpam-5963	267	12	(	(	PUNCT
ejpam-5963	267	13	τ	τ	PROPN
ejpam-5963	267	14	,	,	PUNCT
ejpam-5963	267	15	κ	κ	NOUN
ejpam-5963	267	16	)	)	PUNCT
ejpam-5963	267	17	be	be	VERB
ejpam-5963	267	18	the	the	DET
ejpam-5963	267	19	unique	unique	ADJ
ejpam-5963	267	20	solution	solution	NOUN
ejpam-5963	267	21	of	of	ADP
ejpam-5963	267	22	(	(	PUNCT
ejpam-5963	267	23	18):	18):	NUM
ejpam-5963	267	24	fddη	fddη	NOUN
ejpam-5963	267	25	,	,	PUNCT
ejpam-5963	267	26	ξr(t	ξr(t	NUM
ejpam-5963	267	27	)	)	PUNCT
ejpam-5963	267	28	=	=	SYM
ejpam-5963	267	29	ξtξ−1f(t	ξtξ−1f(t	NOUN
ejpam-5963	267	30	,	,	PUNCT
ejpam-5963	267	31	r(t	r(t	NOUN
ejpam-5963	267	32	)	)	PUNCT
ejpam-5963	267	33	,	,	PUNCT
ejpam-5963	267	34	p(t	p(t	NOUN
ejpam-5963	267	35	)	)	PUNCT
ejpam-5963	267	36	)	)	PUNCT
ejpam-5963	267	37	,	,	PUNCT
ejpam-5963	267	38	fddη	fddη	NOUN
ejpam-5963	267	39	,	,	PUNCT
ejpam-5963	267	40	ξp(t	ξp(t	NOUN
ejpam-5963	267	41	)	)	PUNCT
ejpam-5963	267	42	=	=	SYM
ejpam-5963	267	43	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	267	44	,	,	PUNCT
ejpam-5963	267	45	r(t	r(t	NOUN
ejpam-5963	267	46	)	)	PUNCT
ejpam-5963	267	47	,	,	PUNCT
ejpam-5963	267	48	p(t	p(t	NOUN
ejpam-5963	267	49	)	)	PUNCT
ejpam-5963	267	50	)	)	PUNCT
ejpam-5963	267	51	,	,	PUNCT
ejpam-5963	267	52	r(0	r(0	PROPN
ejpam-5963	267	53	)	)	PUNCT
ejpam-5963	267	54	=	=	SYM
ejpam-5963	267	55	r0	r0	NOUN
ejpam-5963	267	56	+	+	CCONJ
ejpam-5963	267	57	ϕ(r	ϕ(r	PROPN
ejpam-5963	267	58	)	)	PUNCT
ejpam-5963	267	59	,	,	PUNCT
ejpam-5963	267	60	p(0	p(0	NOUN
ejpam-5963	267	61	)	)	PUNCT
ejpam-5963	268	1	=	=	SYM
ejpam-5963	268	2	p0	p0	NOUN
ejpam-5963	268	3	+	+	CCONJ
ejpam-5963	268	4	ψ(p	ψ(p	NOUN
ejpam-5963	268	5	)	)	PUNCT
ejpam-5963	268	6	.	.	PUNCT
ejpam-5963	269	1	(	(	PUNCT
ejpam-5963	269	2	18	18	NUM
ejpam-5963	269	3	)	)	PUNCT
ejpam-5963	269	4	the	the	DET
ejpam-5963	269	5	solution	solution	NOUN
ejpam-5963	269	6	of	of	ADP
ejpam-5963	269	7	system	system	NOUN
ejpam-5963	269	8	(	(	PUNCT
ejpam-5963	269	9	18	18	NUM
ejpam-5963	269	10	)	)	PUNCT
ejpam-5963	269	11	is	be	AUX
ejpam-5963	269	12	given	give	VERB
ejpam-5963	269	13	by	by	ADP
ejpam-5963	269	14	:	:	PUNCT
ejpam-5963	269	15	τ(t	τ(t	NUM
ejpam-5963	269	16	)	)	PUNCT
ejpam-5963	269	17	=	=	SYM
ejpam-5963	269	18	(	(	PUNCT
ejpam-5963	269	19	r0	r0	NOUN
ejpam-5963	269	20	+	+	CCONJ
ejpam-5963	269	21	ϕ(τ	ϕ(τ	PROPN
ejpam-5963	269	22	)	)	PUNCT
ejpam-5963	269	23	)	)	PUNCT
ejpam-5963	270	1	+	+	CCONJ
ejpam-5963	271	1	ξ	ξ	DET
ejpam-5963	271	2	γ(η	γ(η	NOUN
ejpam-5963	271	3	)	)	PUNCT
ejpam-5963	271	4	∫	∫	PROPN
ejpam-5963	271	5	t	t	PROPN
ejpam-5963	271	6	0	0	NUM
ejpam-5963	271	7	(	(	PUNCT
ejpam-5963	271	8	t−	t−	PROPN
ejpam-5963	271	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	271	10	,	,	PUNCT
ejpam-5963	271	11	τ(δ	τ(δ	PROPN
ejpam-5963	271	12	)	)	PUNCT
ejpam-5963	271	13	,	,	PUNCT
ejpam-5963	271	14	κ(δ))dδ	κ(δ))dδ	PROPN
ejpam-5963	271	15	)	)	PUNCT
ejpam-5963	271	16	,	,	PUNCT
ejpam-5963	271	17	κ(t	κ(t	X
ejpam-5963	271	18	)	)	PUNCT
ejpam-5963	271	19	=	=	SYM
ejpam-5963	271	20	(	(	PUNCT
ejpam-5963	271	21	p0	p0	NOUN
ejpam-5963	271	22	+	+	CCONJ
ejpam-5963	271	23	ψ(κ	ψ(κ	NOUN
ejpam-5963	271	24	)	)	PUNCT
ejpam-5963	271	25	)	)	PUNCT
ejpam-5963	272	1	+	+	CCONJ
ejpam-5963	273	1	ξ	ξ	DET
ejpam-5963	273	2	γ(η	γ(η	NOUN
ejpam-5963	273	3	)	)	PUNCT
ejpam-5963	273	4	∫	∫	PROPN
ejpam-5963	273	5	t	t	PROPN
ejpam-5963	273	6	0	0	NUM
ejpam-5963	273	7	(	(	PUNCT
ejpam-5963	273	8	t−	t−	PROPN
ejpam-5963	273	9	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	273	10	,	,	PUNCT
ejpam-5963	273	11	τ(δ	τ(δ	PROPN
ejpam-5963	273	12	)	)	PUNCT
ejpam-5963	273	13	,	,	PUNCT
ejpam-5963	273	14	κ(δ))dδ	κ(δ))dδ	PROPN
ejpam-5963	273	15	)	)	PUNCT
ejpam-5963	273	16	.	.	PUNCT
ejpam-5963	274	1	now	now	ADV
ejpam-5963	274	2	|r(t)−	|r(t)−	X
ejpam-5963	274	3	τ(t)|	τ(t)|	PUNCT
ejpam-5963	274	4	=	=	PUNCT
ejpam-5963	274	5	∣∣∣∣(r0	∣∣∣∣(r0	X
ejpam-5963	274	6	+	+	CCONJ
ejpam-5963	274	7	ϕ(r	ϕ(r	PROPN
ejpam-5963	274	8	)	)	PUNCT
ejpam-5963	275	1	+	+	CCONJ
ejpam-5963	276	1	ξ	ξ	DET
ejpam-5963	276	2	γ(η	γ(η	NOUN
ejpam-5963	276	3	)	)	PUNCT
ejpam-5963	276	4	∫	∫	PROPN
ejpam-5963	276	5	t	t	PROPN
ejpam-5963	276	6	0	0	NUM
ejpam-5963	276	7	(	(	PUNCT
ejpam-5963	276	8	t−	t−	PROPN
ejpam-5963	276	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	276	10	,	,	PUNCT
ejpam-5963	276	11	r(δ	r(δ	PROPN
ejpam-5963	276	12	)	)	PUNCT
ejpam-5963	276	13	,	,	PUNCT
ejpam-5963	276	14	p(δ))dδ)−	p(δ))dδ)−	NOUN
ejpam-5963	276	15	(	(	PUNCT
ejpam-5963	276	16	r0	r0	NOUN
ejpam-5963	276	17	+	+	CCONJ
ejpam-5963	276	18	ϕ(τ	ϕ(τ	PROPN
ejpam-5963	276	19	)	)	PUNCT
ejpam-5963	276	20	+	+	NUM
ejpam-5963	276	21	ξ	ξ	DET
ejpam-5963	276	22	γ(η	γ(η	NOUN
ejpam-5963	276	23	)	)	PUNCT
ejpam-5963	276	24	∫	∫	PROPN
ejpam-5963	277	1	t	t	PROPN
ejpam-5963	277	2	0	0	NUM
ejpam-5963	277	3	(	(	PUNCT
ejpam-5963	277	4	t−	t−	PROPN
ejpam-5963	277	5	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	277	6	,	,	PUNCT
ejpam-5963	277	7	τ(δ	τ(δ	PROPN
ejpam-5963	277	8	)	)	PUNCT
ejpam-5963	277	9	,	,	PUNCT
ejpam-5963	277	10	κ(δ))dδ	κ(δ))dδ	PROPN
ejpam-5963	277	11	)	)	PUNCT
ejpam-5963	277	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	277	13	,	,	PUNCT
ejpam-5963	277	14	=	=	SYM
ejpam-5963	277	15	∣∣∣∣r(t)−	∣∣∣∣r(t)−	PROPN
ejpam-5963	277	16	(	(	PUNCT
ejpam-5963	277	17	r0	r0	NOUN
ejpam-5963	277	18	+	+	CCONJ
ejpam-5963	277	19	ϕ(r	ϕ(r	PROPN
ejpam-5963	277	20	)	)	PUNCT
ejpam-5963	278	1	+	+	CCONJ
ejpam-5963	279	1	ξ	ξ	DET
ejpam-5963	279	2	γ(η	γ(η	NOUN
ejpam-5963	279	3	)	)	PUNCT
ejpam-5963	279	4	∫	∫	PROPN
ejpam-5963	279	5	t	t	PROPN
ejpam-5963	279	6	0	0	NUM
ejpam-5963	279	7	(	(	PUNCT
ejpam-5963	279	8	t−	t−	PROPN
ejpam-5963	279	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	279	10	,	,	PUNCT
ejpam-5963	279	11	r(δ	r(δ	PROPN
ejpam-5963	279	12	)	)	PUNCT
ejpam-5963	279	13	,	,	PUNCT
ejpam-5963	279	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	279	15	)	)	PUNCT
ejpam-5963	280	1	+	+	CCONJ
ejpam-5963	280	2	(	(	PUNCT
ejpam-5963	280	3	r0	r0	NOUN
ejpam-5963	280	4	+	+	CCONJ
ejpam-5963	280	5	ϕ(r	ϕ(r	PROPN
ejpam-5963	280	6	)	)	PUNCT
ejpam-5963	281	1	+	+	CCONJ
ejpam-5963	282	1	ξ	ξ	DET
ejpam-5963	282	2	γ(η	γ(η	NOUN
ejpam-5963	282	3	)	)	PUNCT
ejpam-5963	282	4	∫	∫	PROPN
ejpam-5963	282	5	t	t	PROPN
ejpam-5963	282	6	0	0	NUM
ejpam-5963	282	7	(	(	PUNCT
ejpam-5963	282	8	t−	t−	PROPN
ejpam-5963	282	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	282	10	,	,	PUNCT
ejpam-5963	282	11	r(δ	r(δ	PROPN
ejpam-5963	282	12	)	)	PUNCT
ejpam-5963	282	13	,	,	PUNCT
ejpam-5963	282	14	p(δ))dδ)|	p(δ))dδ)|	VERB
ejpam-5963	282	15	−	−	PROPN
ejpam-5963	282	16	(	(	PUNCT
ejpam-5963	282	17	r0	r0	NOUN
ejpam-5963	282	18	+	+	CCONJ
ejpam-5963	282	19	ϕ(τ	ϕ(τ	PROPN
ejpam-5963	282	20	)	)	PUNCT
ejpam-5963	283	1	+	+	NUM
ejpam-5963	284	1	ξ	ξ	DET
ejpam-5963	284	2	γ(η	γ(η	NOUN
ejpam-5963	284	3	)	)	PUNCT
ejpam-5963	284	4	∫	∫	PROPN
ejpam-5963	284	5	t	t	PROPN
ejpam-5963	284	6	0	0	NUM
ejpam-5963	284	7	(	(	PUNCT
ejpam-5963	284	8	t−	t−	PROPN
ejpam-5963	284	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	284	10	,	,	PUNCT
ejpam-5963	284	11	τ(δ	τ(δ	PROPN
ejpam-5963	284	12	)	)	PUNCT
ejpam-5963	284	13	,	,	PUNCT
ejpam-5963	284	14	κ(δ)dδ	κ(δ)dδ	PROPN
ejpam-5963	284	15	)	)	PUNCT
ejpam-5963	284	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	284	17	,	,	PUNCT
ejpam-5963	284	18	≤	≤	NUM
ejpam-5963	284	19	δϵ1	δϵ1	NOUN
ejpam-5963	284	20	+	+	CCONJ
ejpam-5963	284	21	|ϕ(r)−	|ϕ(r)−	NOUN
ejpam-5963	284	22	ϕ(τ)|+	ϕ(τ)|+	ADV
ejpam-5963	284	23	β(η	β(η	PROPN
ejpam-5963	284	24	,	,	PUNCT
ejpam-5963	284	25	ξ)t	ξ)t	X
ejpam-5963	285	1	η+ξ−1|f(δ	η+ξ−1|f(δ	PROPN
ejpam-5963	285	2	,	,	PUNCT
ejpam-5963	285	3	t(δ	t(δ	PROPN
ejpam-5963	285	4	)	)	PUNCT
ejpam-5963	285	5	,	,	PUNCT
ejpam-5963	285	6	p(δ))dδ)−	p(δ))dδ)−	X
ejpam-5963	286	1	f(δ	f(δ	NOUN
ejpam-5963	286	2	,	,	PUNCT
ejpam-5963	286	3	τ(δ	τ(δ	PROPN
ejpam-5963	286	4	)	)	PUNCT
ejpam-5963	286	5	,	,	PUNCT
ejpam-5963	286	6	κ(δ)dδ|	κ(δ)dδ|	NOUN
ejpam-5963	286	7	,	,	PUNCT
ejpam-5963	286	8	≤	≤	NUM
ejpam-5963	286	9	δϵ1	δϵ1	NOUN
ejpam-5963	286	10	+	+	CCONJ
ejpam-5963	286	11	(	(	PUNCT
ejpam-5963	286	12	lϕ	lϕ	ADP
ejpam-5963	286	13	+	+	CCONJ
ejpam-5963	286	14	δlf	δlf	NOUN
ejpam-5963	286	15	)	)	PUNCT
ejpam-5963	286	16	|r(t)−	|r(t)−	PROPN
ejpam-5963	286	17	τ(t)|+	τ(t)|+	PUNCT
ejpam-5963	287	1	δlf	δlf	PROPN
ejpam-5963	287	2	|p(t)−	|p(t)−	PROPN
ejpam-5963	287	3	κ(t)|	κ(t)|	PROPN
ejpam-5963	287	4	,	,	PUNCT
ejpam-5963	287	5	hence	hence	ADV
ejpam-5963	287	6	,	,	PUNCT
ejpam-5963	287	7	we	we	PRON
ejpam-5963	287	8	have	have	VERB
ejpam-5963	287	9	|r(t)−	|r(t)−	PROPN
ejpam-5963	287	10	τ(t)|	τ(t)|	ADP
ejpam-5963	287	11	−	−	PROPN
ejpam-5963	287	12	δlf	δlf	NOUN
ejpam-5963	287	13	1−	1−	NUM
ejpam-5963	288	1	(	(	PUNCT
ejpam-5963	288	2	lϕ	lϕ	ADP
ejpam-5963	288	3	+	+	CCONJ
ejpam-5963	288	4	δlf	δlf	PROPN
ejpam-5963	288	5	)	)	PUNCT
ejpam-5963	288	6	|p(t)−	|p(t)−	PROPN
ejpam-5963	288	7	κ(t)|	κ(t)|	ADV
ejpam-5963	288	8	≤	≤	NUM
ejpam-5963	288	9	δϵ1	δϵ1	NOUN
ejpam-5963	288	10	1−	1−	NUM
ejpam-5963	288	11	(	(	PUNCT
ejpam-5963	288	12	lϕ	lϕ	ADP
ejpam-5963	288	13	+	+	CCONJ
ejpam-5963	288	14	δlf	δlf	NOUN
ejpam-5963	288	15	)	)	PUNCT
ejpam-5963	288	16	.	.	PUNCT
ejpam-5963	289	1	(	(	PUNCT
ejpam-5963	289	2	19	19	NUM
ejpam-5963	289	3	)	)	PUNCT
ejpam-5963	289	4	similarly	similarly	ADV
ejpam-5963	289	5	,	,	PUNCT
ejpam-5963	289	6	one	one	PRON
ejpam-5963	289	7	can	can	AUX
ejpam-5963	289	8	obtain	obtain	VERB
ejpam-5963	289	9	the	the	DET
ejpam-5963	289	10	following	following	ADJ
ejpam-5963	289	11	result	result	PROPN
ejpam-5963	289	12	|p(t)−	|p(t)−	PROPN
ejpam-5963	289	13	κ(t)|	κ(t)|	ADV
ejpam-5963	290	1	−	−	PRON
ejpam-5963	290	2	δlg	δlg	VERB
ejpam-5963	290	3	1−	1−	NUM
ejpam-5963	290	4	(	(	PUNCT
ejpam-5963	290	5	lψ	lψ	PROPN
ejpam-5963	290	6	+	+	CCONJ
ejpam-5963	290	7	δlg	δlg	VERB
ejpam-5963	290	8	)	)	PUNCT
ejpam-5963	290	9	|r(t)−	|r(t)−	PROPN
ejpam-5963	290	10	τ(t)|	τ(t)|	PUNCT
ejpam-5963	290	11	≤	≤	NUM
ejpam-5963	290	12	δϵ2	δϵ2	NOUN
ejpam-5963	290	13	1−	1−	NUM
ejpam-5963	291	1	(	(	PUNCT
ejpam-5963	291	2	lψ	lψ	PROPN
ejpam-5963	291	3	+	+	CCONJ
ejpam-5963	291	4	δlg	δlg	VERB
ejpam-5963	291	5	)	)	PUNCT
ejpam-5963	291	6	.	.	PUNCT
ejpam-5963	292	1	(	(	PUNCT
ejpam-5963	292	2	20	20	NUM
ejpam-5963	292	3	)	)	PUNCT
ejpam-5963	292	4	the	the	DET
ejpam-5963	292	5	matrix	matrix	NOUN
ejpam-5963	292	6	representation	representation	NOUN
ejpam-5963	292	7	the	the	DET
ejpam-5963	292	8	above	above	ADJ
ejpam-5963	292	9	inequalities	inequality	NOUN
ejpam-5963	292	10	as	as	ADP
ejpam-5963	292	11	:	:	PUNCT
ejpam-5963	292	12	a.	a.	PROPN
ejpam-5963	292	13	ali	ali	PROPN
ejpam-5963	292	14	et	et	PROPN
ejpam-5963	292	15	al	al	PROPN
ejpam-5963	292	16	.	.	PUNCT
ejpam-5963	292	17	/	/	SYM
ejpam-5963	292	18	eur	eur	PROPN
ejpam-5963	292	19	.	.	PUNCT
ejpam-5963	293	1	j.	j.	PROPN
ejpam-5963	293	2	pure	pure	PROPN
ejpam-5963	293	3	appl	appl	PROPN
ejpam-5963	293	4	.	.	PROPN
ejpam-5963	293	5	math	math	PROPN
ejpam-5963	293	6	,	,	PUNCT
ejpam-5963	293	7	18	18	NUM
ejpam-5963	293	8	(	(	PUNCT
ejpam-5963	293	9	2	2	NUM
ejpam-5963	293	10	)	)	PUNCT
ejpam-5963	293	11	(	(	PUNCT
ejpam-5963	293	12	2025	2025	NUM
ejpam-5963	293	13	)	)	PUNCT
ejpam-5963	293	14	,	,	PUNCT
ejpam-5963	293	15	5963	5963	NUM
ejpam-5963	293	16	13	13	NUM
ejpam-5963	293	17	of	of	ADP
ejpam-5963	293	18	19	19	NUM
ejpam-5963	293	19	(	(	PUNCT
ejpam-5963	293	20	1	1	NUM
ejpam-5963	293	21	−lfc1	−lfc1	PROPN
ejpam-5963	293	22	−lgc2	−lgc2	PROPN
ejpam-5963	293	23	1	1	NUM
ejpam-5963	293	24	)	)	PUNCT
ejpam-5963	293	25	×	×	NOUN
ejpam-5963	293	26	(	(	PUNCT
ejpam-5963	293	27	|r	|r	PROPN
ejpam-5963	293	28	−	−	PROPN
ejpam-5963	293	29	τ	τ	PROPN
ejpam-5963	293	30	|	|	ADV
ejpam-5963	293	31	|p−	|p−	ADJ
ejpam-5963	293	32	κ|	κ|	NOUN
ejpam-5963	293	33	)	)	PUNCT
ejpam-5963	293	34	≤	≤	NOUN
ejpam-5963	293	35	(	(	PUNCT
ejpam-5963	293	36	c1ϵ1	c1ϵ1	X
ejpam-5963	293	37	c2ϵ2	c2ϵ2	X
ejpam-5963	293	38	,	,	PUNCT
ejpam-5963	293	39	)	)	PUNCT
ejpam-5963	293	40	,	,	PUNCT
ejpam-5963	293	41	where	where	SCONJ
ejpam-5963	293	42	c1	c1	PROPN
ejpam-5963	293	43	=	=	PROPN
ejpam-5963	293	44	δ	δ	PROPN
ejpam-5963	293	45	1−(lϕ+δlf	1−(lϕ+δlf	NUM
ejpam-5963	293	46	)	)	PUNCT
ejpam-5963	293	47	and	and	CCONJ
ejpam-5963	293	48	c2	c2	PROPN
ejpam-5963	293	49	=	=	SYM
ejpam-5963	293	50	δ	δ	PROPN
ejpam-5963	293	51	1−(lψ+δlg	1−(lψ+δlg	NUM
ejpam-5963	293	52	)	)	PUNCT
ejpam-5963	293	53	,	,	PUNCT
ejpam-5963	293	54	then	then	ADV
ejpam-5963	293	55	solving	solve	VERB
ejpam-5963	293	56	the	the	DET
ejpam-5963	293	57	above	above	ADJ
ejpam-5963	293	58	matrix	matrix	NOUN
ejpam-5963	293	59	,	,	PUNCT
ejpam-5963	293	60	we	we	PRON
ejpam-5963	293	61	have	have	VERB
ejpam-5963	293	62	|r	|r	PROPN
ejpam-5963	294	1	−	−	PROPN
ejpam-5963	294	2	τ	τ	PROPN
ejpam-5963	295	1	|	|	ADV
ejpam-5963	295	2	≤	≤	X
ejpam-5963	295	3	c1ϵ1	c1ϵ1	X
ejpam-5963	295	4	1−	1−	NUM
ejpam-5963	295	5	(	(	PUNCT
ejpam-5963	295	6	c1c2lflg	c1c2lflg	ADV
ejpam-5963	295	7	)	)	PUNCT
ejpam-5963	296	1	+	+	CCONJ
ejpam-5963	296	2	c1c2lf	c1c2lf	ADJ
ejpam-5963	296	3	ϵ2	ϵ2	PROPN
ejpam-5963	296	4	1−	1−	NUM
ejpam-5963	296	5	(	(	PUNCT
ejpam-5963	296	6	c1c2lflg	c1c2lflg	ADV
ejpam-5963	296	7	)	)	PUNCT
ejpam-5963	296	8	,	,	PUNCT
ejpam-5963	296	9	(	(	PUNCT
ejpam-5963	296	10	21	21	NUM
ejpam-5963	296	11	)	)	PUNCT
ejpam-5963	296	12	and	and	CCONJ
ejpam-5963	296	13	|p−	|p−	NOUN
ejpam-5963	296	14	κ|	κ|	NOUN
ejpam-5963	296	15	≤	≤	NUM
ejpam-5963	296	16	c2ϵ2	c2ϵ2	X
ejpam-5963	296	17	1−	1−	NUM
ejpam-5963	296	18	(	(	PUNCT
ejpam-5963	296	19	c1c2lflg	c1c2lflg	ADV
ejpam-5963	296	20	)	)	PUNCT
ejpam-5963	296	21	+	+	CCONJ
ejpam-5963	296	22	c1c2lgϵ1	c1c2lgϵ1	VERB
ejpam-5963	296	23	1−	1−	NUM
ejpam-5963	296	24	(	(	PUNCT
ejpam-5963	296	25	c1c2lflg	c1c2lflg	ADV
ejpam-5963	296	26	)	)	PUNCT
ejpam-5963	296	27	(	(	PUNCT
ejpam-5963	296	28	22	22	X
ejpam-5963	296	29	)	)	PUNCT
ejpam-5963	296	30	adding	add	VERB
ejpam-5963	296	31	(	(	PUNCT
ejpam-5963	296	32	21	21	NUM
ejpam-5963	296	33	)	)	PUNCT
ejpam-5963	296	34	and	and	CCONJ
ejpam-5963	296	35	(	(	PUNCT
ejpam-5963	296	36	22	22	NUM
ejpam-5963	296	37	)	)	PUNCT
ejpam-5963	296	38	,	,	PUNCT
ejpam-5963	296	39	we	we	PRON
ejpam-5963	296	40	gets	get	VERB
ejpam-5963	296	41	|r	|r	PROPN
ejpam-5963	296	42	−	−	PROPN
ejpam-5963	297	1	τ	τ	PROPN
ejpam-5963	297	2	|+	|+	NOUN
ejpam-5963	297	3	|p−	|p−	NOUN
ejpam-5963	297	4	κ|	κ|	NOUN
ejpam-5963	297	5	≤	≤	NUM
ejpam-5963	298	1	c1ϵ1	c1ϵ1	X
ejpam-5963	298	2	1−	1−	NUM
ejpam-5963	298	3	(	(	PUNCT
ejpam-5963	298	4	c1c2lflg	c1c2lflg	ADV
ejpam-5963	298	5	)	)	PUNCT
ejpam-5963	298	6	+	+	CCONJ
ejpam-5963	298	7	c1c2lf	c1c2lf	ADJ
ejpam-5963	298	8	ϵ2	ϵ2	PROPN
ejpam-5963	298	9	1−	1−	NUM
ejpam-5963	298	10	(	(	PUNCT
ejpam-5963	298	11	c1c2lflg	c1c2lflg	ADV
ejpam-5963	298	12	)	)	PUNCT
ejpam-5963	299	1	+	+	CCONJ
ejpam-5963	299	2	c2ϵ2	c2ϵ2	X
ejpam-5963	299	3	1−	1−	NUM
ejpam-5963	299	4	(	(	PUNCT
ejpam-5963	299	5	c1c2lflg	c1c2lflg	ADV
ejpam-5963	299	6	)	)	PUNCT
ejpam-5963	300	1	+	+	CCONJ
ejpam-5963	300	2	c1c2lgϵ1	c1c2lgϵ1	VERB
ejpam-5963	300	3	1−	1−	NUM
ejpam-5963	300	4	(	(	PUNCT
ejpam-5963	300	5	c1c2lflg	c1c2lflg	ADV
ejpam-5963	300	6	)	)	PUNCT
ejpam-5963	300	7	,	,	PUNCT
ejpam-5963	300	8	≤	≤	X
ejpam-5963	300	9	(	(	PUNCT
ejpam-5963	300	10	c1	c1	PROPN
ejpam-5963	300	11	+	+	CCONJ
ejpam-5963	300	12	c2	c2	PROPN
ejpam-5963	300	13	+	+	CCONJ
ejpam-5963	300	14	c1c2(lf	c1c2(lf	PROPN
ejpam-5963	301	1	+	+	CCONJ
ejpam-5963	301	2	lg))ϵ	lg))ϵ	PROPN
ejpam-5963	301	3	1−	1−	NUM
ejpam-5963	301	4	(	(	PUNCT
ejpam-5963	301	5	c1c2lflg	c1c2lflg	ADV
ejpam-5963	301	6	)	)	PUNCT
ejpam-5963	301	7	,	,	PUNCT
ejpam-5963	301	8	which	which	PRON
ejpam-5963	301	9	implies	imply	VERB
ejpam-5963	301	10	that	that	SCONJ
ejpam-5963	301	11	|(r	|(r	PROPN
ejpam-5963	301	12	,	,	PUNCT
ejpam-5963	301	13	p)−	p)−	NOUN
ejpam-5963	301	14	(	(	PUNCT
ejpam-5963	301	15	τ	τ	PROPN
ejpam-5963	301	16	,	,	PUNCT
ejpam-5963	301	17	κ)|	κ)|	VERB
ejpam-5963	301	18	≤	≤	NUM
ejpam-5963	301	19	c(1,2)ϵ	c(1,2)ϵ	PROPN
ejpam-5963	301	20	,	,	PUNCT
ejpam-5963	301	21	(	(	PUNCT
ejpam-5963	301	22	23	23	NUM
ejpam-5963	301	23	)	)	PUNCT
ejpam-5963	301	24	where	where	SCONJ
ejpam-5963	301	25	c(1,2	c(1,2	ADJ
ejpam-5963	301	26	)	)	PUNCT
ejpam-5963	301	27	=	=	SYM
ejpam-5963	301	28	(	(	PUNCT
ejpam-5963	301	29	c1	c1	PROPN
ejpam-5963	301	30	+	+	CCONJ
ejpam-5963	301	31	c2	c2	PROPN
ejpam-5963	301	32	+	+	CCONJ
ejpam-5963	301	33	c1c2(lf	c1c2(lf	PROPN
ejpam-5963	301	34	+	+	CCONJ
ejpam-5963	301	35	lg	lg	NOUN
ejpam-5963	301	36	)	)	PUNCT
ejpam-5963	301	37	)	)	PUNCT
ejpam-5963	301	38	1−	1−	NUM
ejpam-5963	301	39	(	(	PUNCT
ejpam-5963	301	40	c1c2lflg	c1c2lflg	ADV
ejpam-5963	301	41	)	)	PUNCT
ejpam-5963	301	42	,	,	PUNCT
ejpam-5963	301	43	thus	thus	ADV
ejpam-5963	301	44	,	,	PUNCT
ejpam-5963	301	45	the	the	DET
ejpam-5963	301	46	solution	solution	NOUN
ejpam-5963	301	47	of	of	ADP
ejpam-5963	301	48	(	(	PUNCT
ejpam-5963	301	49	2	2	NUM
ejpam-5963	301	50	)	)	PUNCT
ejpam-5963	301	51	is	be	AUX
ejpam-5963	301	52	uh	uh	INTJ
ejpam-5963	301	53	stable	stable	ADJ
ejpam-5963	301	54	.	.	PUNCT
ejpam-5963	302	1	further	far	ADV
ejpam-5963	302	2	,	,	PUNCT
ejpam-5963	302	3	the	the	DET
ejpam-5963	302	4	solution	solution	NOUN
ejpam-5963	302	5	of	of	ADP
ejpam-5963	302	6	coupled	couple	VERB
ejpam-5963	302	7	system	system	NOUN
ejpam-5963	302	8	of	of	ADP
ejpam-5963	302	9	ffdes	ffde	NOUN
ejpam-5963	302	10	(	(	PUNCT
ejpam-5963	302	11	2	2	NUM
ejpam-5963	302	12	)	)	PUNCT
ejpam-5963	302	13	is	be	AUX
ejpam-5963	302	14	guh	guh	ADJ
ejpam-5963	302	15	stable	stable	ADJ
ejpam-5963	302	16	,	,	PUNCT
ejpam-5963	302	17	if	if	SCONJ
ejpam-5963	302	18	ψ	ψ	X
ejpam-5963	302	19	:	:	PUNCT
ejpam-5963	302	20	(	(	PUNCT
ejpam-5963	302	21	0	0	NUM
ejpam-5963	302	22	,	,	PUNCT
ejpam-5963	302	23	1	1	NUM
ejpam-5963	302	24	)	)	PUNCT
ejpam-5963	302	25	→	→	X
ejpam-5963	302	26	(	(	PUNCT
ejpam-5963	302	27	0,∞	0,∞	NUM
ejpam-5963	302	28	)	)	PUNCT
ejpam-5963	302	29	such	such	ADJ
ejpam-5963	302	30	that	that	SCONJ
ejpam-5963	302	31	ψ(ϵ	ψ(ϵ	VERB
ejpam-5963	302	32	)	)	PUNCT
ejpam-5963	302	33	=	=	PUNCT
ejpam-5963	303	1	ϵ,be	ϵ,be	PUNCT
ejpam-5963	303	2	a	a	DET
ejpam-5963	303	3	non	non	ADJ
ejpam-5963	303	4	decreasing	decrease	VERB
ejpam-5963	303	5	function	function	NOUN
ejpam-5963	303	6	,	,	PUNCT
ejpam-5963	303	7	then	then	ADV
ejpam-5963	303	8	we	we	PRON
ejpam-5963	303	9	have	have	VERB
ejpam-5963	303	10	|(r	|(r	PROPN
ejpam-5963	303	11	,	,	PUNCT
ejpam-5963	303	12	p)−	p)−	NOUN
ejpam-5963	303	13	(	(	PUNCT
ejpam-5963	303	14	τ	τ	PROPN
ejpam-5963	303	15	,	,	PUNCT
ejpam-5963	303	16	κ)|	κ)|	VERB
ejpam-5963	303	17	≤	≤	NUM
ejpam-5963	303	18	c(1,2)ψ(ϵ	c(1,2)ψ(ϵ	PROPN
ejpam-5963	303	19	)	)	PUNCT
ejpam-5963	303	20	,	,	PUNCT
ejpam-5963	303	21	where	where	SCONJ
ejpam-5963	303	22	ψ(0	ψ(0	NOUN
ejpam-5963	303	23	)	)	PUNCT
ejpam-5963	303	24	=	=	SYM
ejpam-5963	304	1	0	0	X
ejpam-5963	304	2	.	.	PUNCT
ejpam-5963	305	1	(	(	PUNCT
ejpam-5963	305	2	24	24	NUM
ejpam-5963	305	3	)	)	PUNCT
ejpam-5963	305	4	thus	thus	ADV
ejpam-5963	305	5	cs	cs	X
ejpam-5963	305	6	is	be	AUX
ejpam-5963	305	7	(	(	PUNCT
ejpam-5963	305	8	2	2	NUM
ejpam-5963	305	9	)	)	PUNCT
ejpam-5963	305	10	guh	guh	NOUN
ejpam-5963	305	11	stable	stable	ADJ
ejpam-5963	305	12	for	for	ADP
ejpam-5963	305	13	any	any	DET
ejpam-5963	305	14	function	function	NOUN
ejpam-5963	305	15	b	b	NOUN
ejpam-5963	305	16	,	,	PUNCT
ejpam-5963	305	17	we	we	PRON
ejpam-5963	305	18	assume	assume	VERB
ejpam-5963	305	19	the	the	DET
ejpam-5963	305	20	following	follow	VERB
ejpam-5963	305	21	inequalities	inequality	NOUN
ejpam-5963	305	22	holds	hold	VERB
ejpam-5963	305	23	iηbi(t	iηbi(t	NOUN
ejpam-5963	305	24	)	)	PUNCT
ejpam-5963	305	25	≤	≤	NOUN
ejpam-5963	305	26	λinbi(t),where	λinbi(t),where	ADP
ejpam-5963	305	27	bi	bi	NOUN
ejpam-5963	305	28	=	=	PUNCT
ejpam-5963	305	29	{	{	PUNCT
ejpam-5963	305	30	1	1	NUM
ejpam-5963	305	31	,	,	PUNCT
ejpam-5963	305	32	2	2	NUM
ejpam-5963	305	33	}	}	PUNCT
ejpam-5963	305	34	lemma	lemma	PROPN
ejpam-5963	305	35	4	4	NUM
ejpam-5963	305	36	.	.	PUNCT
ejpam-5963	306	1	the	the	DET
ejpam-5963	306	2	solution	solution	NOUN
ejpam-5963	306	3	(	(	PUNCT
ejpam-5963	306	4	r	r	NOUN
ejpam-5963	306	5	,	,	PUNCT
ejpam-5963	306	6	p	p	NOUN
ejpam-5963	306	7	)	)	PUNCT
ejpam-5963	306	8	for	for	ADP
ejpam-5963	306	9	the	the	DET
ejpam-5963	306	10	selected	select	VERB
ejpam-5963	306	11	coupled	couple	VERB
ejpam-5963	306	12	system	system	NOUN
ejpam-5963	306	13	of	of	ADP
ejpam-5963	306	14	ffdes	ffde	NOUN
ejpam-5963	306	15	{	{	PUNCT
ejpam-5963	306	16	fddηr(t	fddηr(t	NOUN
ejpam-5963	306	17	)	)	PUNCT
ejpam-5963	306	18	=	=	SYM
ejpam-5963	306	19	ξtξ−1f(t	ξtξ−1f(t	NOUN
ejpam-5963	306	20	,	,	PUNCT
ejpam-5963	306	21	r(t	r(t	NOUN
ejpam-5963	306	22	)	)	PUNCT
ejpam-5963	306	23	,	,	PUNCT
ejpam-5963	306	24	p(t	p(t	NOUN
ejpam-5963	306	25	)	)	PUNCT
ejpam-5963	306	26	)	)	PUNCT
ejpam-5963	307	1	+	+	CCONJ
ejpam-5963	307	2	ξtξ−1b1(t	ξtξ−1b1(t	ADJ
ejpam-5963	307	3	)	)	PUNCT
ejpam-5963	307	4	,	,	PUNCT
ejpam-5963	307	5	fddηp(t	fddηp(t	NOUN
ejpam-5963	307	6	)	)	PUNCT
ejpam-5963	307	7	=	=	SYM
ejpam-5963	307	8	ξtξ−1g(t	ξtξ−1g(t	NOUN
ejpam-5963	307	9	,	,	PUNCT
ejpam-5963	307	10	r(t	r(t	NOUN
ejpam-5963	307	11	)	)	PUNCT
ejpam-5963	307	12	,	,	PUNCT
ejpam-5963	307	13	p(t	p(t	NOUN
ejpam-5963	307	14	)	)	PUNCT
ejpam-5963	307	15	)	)	PUNCT
ejpam-5963	308	1	+	+	CCONJ
ejpam-5963	308	2	ξtξ−1b2(t	ξtξ−1b2(t	NOUN
ejpam-5963	308	3	)	)	PUNCT
ejpam-5963	308	4	,	,	PUNCT
ejpam-5963	308	5	will	will	AUX
ejpam-5963	308	6	obeys	obey	VERB
ejpam-5963	308	7	the	the	DET
ejpam-5963	308	8	following:∣∣∣∣r(t)−	following:∣∣∣∣r(t)−	PROPN
ejpam-5963	308	9	(	(	PUNCT
ejpam-5963	308	10	(	(	PUNCT
ejpam-5963	308	11	r0	r0	NOUN
ejpam-5963	308	12	+	+	CCONJ
ejpam-5963	308	13	ϕ(r	ϕ(r	PROPN
ejpam-5963	308	14	)	)	PUNCT
ejpam-5963	309	1	+	+	CCONJ
ejpam-5963	310	1	ξ	ξ	DET
ejpam-5963	310	2	γ(η	γ(η	NOUN
ejpam-5963	310	3	)	)	PUNCT
ejpam-5963	310	4	∫	∫	PROPN
ejpam-5963	310	5	t	t	PROPN
ejpam-5963	310	6	0	0	NUM
ejpam-5963	310	7	(	(	PUNCT
ejpam-5963	310	8	t−	t−	PROPN
ejpam-5963	310	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	310	10	,	,	PUNCT
ejpam-5963	310	11	ri(δ	ri(δ	NOUN
ejpam-5963	310	12	)	)	PUNCT
ejpam-5963	310	13	,	,	PUNCT
ejpam-5963	310	14	pi(δ))dδ	pi(δ))dδ	PROPN
ejpam-5963	310	15	)	)	PUNCT
ejpam-5963	310	16	)	)	PUNCT
ejpam-5963	310	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5963	310	18	≤	≤	NUM
ejpam-5963	310	19	λ1nb1(t)ϵ1,∣∣∣∣p(t)−	λ1nb1(t)ϵ1,∣∣∣∣p(t)−	PUNCT
ejpam-5963	310	20	(	(	PUNCT
ejpam-5963	310	21	(	(	PUNCT
ejpam-5963	310	22	p0	p0	NOUN
ejpam-5963	310	23	+	+	CCONJ
ejpam-5963	310	24	ψ(p	ψ(p	NOUN
ejpam-5963	310	25	)	)	PUNCT
ejpam-5963	310	26	+	+	NUM
ejpam-5963	310	27	ξ	ξ	DET
ejpam-5963	310	28	γ(η	γ(η	NOUN
ejpam-5963	310	29	)	)	PUNCT
ejpam-5963	310	30	∫	∫	PROPN
ejpam-5963	311	1	t	t	PROPN
ejpam-5963	311	2	0	0	NUM
ejpam-5963	311	3	(	(	PUNCT
ejpam-5963	311	4	t−	t−	PROPN
ejpam-5963	311	5	δ)η−1δξ−1g(δ	δ)η−1δξ−1g(δ	PROPN
ejpam-5963	311	6	,	,	PUNCT
ejpam-5963	311	7	ri(δ	ri(δ	NUM
ejpam-5963	311	8	)	)	PUNCT
ejpam-5963	311	9	,	,	PUNCT
ejpam-5963	311	10	pi(δ))dδ	pi(δ))dδ	PROPN
ejpam-5963	311	11	)	)	PUNCT
ejpam-5963	311	12	)	)	PUNCT
ejpam-5963	311	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5963	311	14	≤	≤	NOUN
ejpam-5963	311	15	λ2nb2(t)ϵ2	λ2nb2(t)ϵ2	NOUN
ejpam-5963	311	16	.	.	PUNCT
ejpam-5963	312	1	(	(	PUNCT
ejpam-5963	312	2	25	25	NUM
ejpam-5963	312	3	)	)	PUNCT
ejpam-5963	312	4	a.	a.	NOUN
ejpam-5963	312	5	ali	ali	PROPN
ejpam-5963	312	6	et	et	PROPN
ejpam-5963	312	7	al	al	PROPN
ejpam-5963	312	8	.	.	PUNCT
ejpam-5963	312	9	/	/	SYM
ejpam-5963	312	10	eur	eur	PROPN
ejpam-5963	312	11	.	.	PUNCT
ejpam-5963	313	1	j.	j.	PROPN
ejpam-5963	313	2	pure	pure	PROPN
ejpam-5963	313	3	appl	appl	PROPN
ejpam-5963	313	4	.	.	PROPN
ejpam-5963	313	5	math	math	PROPN
ejpam-5963	313	6	,	,	PUNCT
ejpam-5963	313	7	18	18	NUM
ejpam-5963	313	8	(	(	PUNCT
ejpam-5963	313	9	2	2	NUM
ejpam-5963	313	10	)	)	PUNCT
ejpam-5963	313	11	(	(	PUNCT
ejpam-5963	313	12	2025	2025	NUM
ejpam-5963	313	13	)	)	PUNCT
ejpam-5963	313	14	,	,	PUNCT
ejpam-5963	313	15	5963	5963	NUM
ejpam-5963	313	16	14	14	NUM
ejpam-5963	313	17	of	of	ADP
ejpam-5963	313	18	19	19	NUM
ejpam-5963	313	19	proof	proof	NOUN
ejpam-5963	313	20	.	.	PUNCT
ejpam-5963	314	1	using	use	VERB
ejpam-5963	314	2	remark	remark	NOUN
ejpam-5963	314	3	4	4	NUM
ejpam-5963	314	4	,	,	PUNCT
ejpam-5963	314	5	its	its	PRON
ejpam-5963	314	6	proof	proof	NOUN
ejpam-5963	314	7	is	be	AUX
ejpam-5963	314	8	similar	similar	ADJ
ejpam-5963	314	9	to	to	ADP
ejpam-5963	314	10	(	(	PUNCT
ejpam-5963	314	11	3	3	NUM
ejpam-5963	314	12	)	)	PUNCT
ejpam-5963	314	13	theorem	theorem	NOUN
ejpam-5963	314	14	6	6	NUM
ejpam-5963	314	15	.	.	PUNCT
ejpam-5963	315	1	under	under	ADP
ejpam-5963	315	2	the	the	DET
ejpam-5963	315	3	assumptions	assumption	NOUN
ejpam-5963	315	4	(	(	PUNCT
ejpam-5963	315	5	m1)-(m3	m1)-(m3	PROPN
ejpam-5963	315	6	)	)	PUNCT
ejpam-5963	315	7	and	and	CCONJ
ejpam-5963	315	8	consider	consider	VERB
ejpam-5963	315	9	lemma	lemma	PROPN
ejpam-5963	315	10	4	4	NUM
ejpam-5963	315	11	with	with	ADP
ejpam-5963	315	12	the	the	DET
ejpam-5963	315	13	condition	condition	NOUN
ejpam-5963	315	14	c1c2lflg	c1c2lflg	ADV
ejpam-5963	315	15	̸=	̸=	PROPN
ejpam-5963	315	16	1	1	NUM
ejpam-5963	315	17	,	,	PUNCT
ejpam-5963	315	18	then	then	ADV
ejpam-5963	315	19	the	the	DET
ejpam-5963	315	20	selected	select	VERB
ejpam-5963	315	21	system	system	NOUN
ejpam-5963	315	22	is	be	AUX
ejpam-5963	315	23	both	both	CCONJ
ejpam-5963	315	24	uhr	uhr	NOUN
ejpam-5963	315	25	and	and	CCONJ
ejpam-5963	315	26	guhr	guhr	VERB
ejpam-5963	315	27	stable	stable	ADJ
ejpam-5963	315	28	.	.	PUNCT
ejpam-5963	316	1	proof	proof	NOUN
ejpam-5963	316	2	.	.	PUNCT
ejpam-5963	317	1	let	let	VERB
ejpam-5963	317	2	(	(	PUNCT
ejpam-5963	317	3	r	r	NOUN
ejpam-5963	317	4	,	,	PUNCT
ejpam-5963	317	5	p	p	NOUN
ejpam-5963	317	6	)	)	PUNCT
ejpam-5963	317	7	be	be	AUX
ejpam-5963	317	8	the	the	DET
ejpam-5963	317	9	arbitrary	arbitrary	ADJ
ejpam-5963	317	10	and	and	CCONJ
ejpam-5963	317	11	(	(	PUNCT
ejpam-5963	317	12	τ	τ	PROPN
ejpam-5963	317	13	,	,	PUNCT
ejpam-5963	317	14	κ	κ	NOUN
ejpam-5963	317	15	)	)	PUNCT
ejpam-5963	317	16	unique	unique	ADJ
ejpam-5963	317	17	solution	solution	NOUN
ejpam-5963	317	18	of	of	ADP
ejpam-5963	317	19	the	the	DET
ejpam-5963	317	20	coupled	couple	VERB
ejpam-5963	317	21	system	system	NOUN
ejpam-5963	317	22	of	of	ADP
ejpam-5963	317	23	ffdes	ffde	NOUN
ejpam-5963	317	24	,	,	PUNCT
ejpam-5963	317	25	then	then	ADV
ejpam-5963	317	26	one	one	PRON
ejpam-5963	317	27	have	have	VERB
ejpam-5963	317	28	|r(t)−	|r(t)−	PROPN
ejpam-5963	317	29	τ(t)|	τ(t)|	PUNCT
ejpam-5963	317	30	=	=	PUNCT
ejpam-5963	317	31	∣∣∣∣(r0	∣∣∣∣(r0	X
ejpam-5963	318	1	+	+	CCONJ
ejpam-5963	318	2	ϕ(r	ϕ(r	PROPN
ejpam-5963	318	3	)	)	PUNCT
ejpam-5963	319	1	+	+	CCONJ
ejpam-5963	320	1	ξ	ξ	DET
ejpam-5963	320	2	γ(η	γ(η	NOUN
ejpam-5963	320	3	)	)	PUNCT
ejpam-5963	320	4	∫	∫	PROPN
ejpam-5963	320	5	t	t	PROPN
ejpam-5963	320	6	0	0	NUM
ejpam-5963	320	7	(	(	PUNCT
ejpam-5963	320	8	t−	t−	PROPN
ejpam-5963	320	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	320	10	,	,	PUNCT
ejpam-5963	320	11	r(δ	r(δ	PROPN
ejpam-5963	320	12	)	)	PUNCT
ejpam-5963	320	13	,	,	PUNCT
ejpam-5963	320	14	p(δ))dδ)−	p(δ))dδ)−	NOUN
ejpam-5963	320	15	(	(	PUNCT
ejpam-5963	320	16	r0	r0	NOUN
ejpam-5963	320	17	+	+	CCONJ
ejpam-5963	320	18	ϕ(τ	ϕ(τ	PROPN
ejpam-5963	320	19	)	)	PUNCT
ejpam-5963	320	20	+	+	NUM
ejpam-5963	320	21	ξ	ξ	DET
ejpam-5963	320	22	γ(η	γ(η	NOUN
ejpam-5963	320	23	)	)	PUNCT
ejpam-5963	320	24	∫	∫	PROPN
ejpam-5963	321	1	t	t	PROPN
ejpam-5963	321	2	0	0	NUM
ejpam-5963	321	3	(	(	PUNCT
ejpam-5963	321	4	t−	t−	PROPN
ejpam-5963	321	5	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	321	6	,	,	PUNCT
ejpam-5963	321	7	τ(δ	τ(δ	PROPN
ejpam-5963	321	8	)	)	PUNCT
ejpam-5963	321	9	,	,	PUNCT
ejpam-5963	321	10	κ(δ))dδ	κ(δ))dδ	PROPN
ejpam-5963	321	11	)	)	PUNCT
ejpam-5963	321	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	321	13	,	,	PUNCT
ejpam-5963	321	14	=	=	SYM
ejpam-5963	321	15	∣∣∣∣r(t)−	∣∣∣∣r(t)−	PROPN
ejpam-5963	321	16	(	(	PUNCT
ejpam-5963	321	17	r0	r0	NOUN
ejpam-5963	321	18	+	+	CCONJ
ejpam-5963	321	19	ϕ(r	ϕ(r	PROPN
ejpam-5963	321	20	)	)	PUNCT
ejpam-5963	322	1	+	+	CCONJ
ejpam-5963	323	1	ξ	ξ	DET
ejpam-5963	323	2	γ(η	γ(η	NOUN
ejpam-5963	323	3	)	)	PUNCT
ejpam-5963	323	4	∫	∫	PROPN
ejpam-5963	323	5	t	t	PROPN
ejpam-5963	323	6	0	0	NUM
ejpam-5963	323	7	(	(	PUNCT
ejpam-5963	323	8	t−	t−	PROPN
ejpam-5963	323	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	323	10	,	,	PUNCT
ejpam-5963	323	11	r(δ	r(δ	PROPN
ejpam-5963	323	12	)	)	PUNCT
ejpam-5963	323	13	,	,	PUNCT
ejpam-5963	323	14	p(δ))dδ	p(δ))dδ	PROPN
ejpam-5963	323	15	)	)	PUNCT
ejpam-5963	324	1	+	+	CCONJ
ejpam-5963	324	2	(	(	PUNCT
ejpam-5963	324	3	r0	r0	NOUN
ejpam-5963	324	4	+	+	CCONJ
ejpam-5963	324	5	ϕ(r	ϕ(r	PROPN
ejpam-5963	324	6	)	)	PUNCT
ejpam-5963	325	1	+	+	CCONJ
ejpam-5963	326	1	ξ	ξ	DET
ejpam-5963	326	2	γ(η	γ(η	NOUN
ejpam-5963	326	3	)	)	PUNCT
ejpam-5963	326	4	∫	∫	PROPN
ejpam-5963	326	5	t	t	PROPN
ejpam-5963	326	6	0	0	NUM
ejpam-5963	326	7	(	(	PUNCT
ejpam-5963	326	8	t−	t−	PROPN
ejpam-5963	326	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	326	10	,	,	PUNCT
ejpam-5963	326	11	r(δ	r(δ	PROPN
ejpam-5963	326	12	)	)	PUNCT
ejpam-5963	326	13	,	,	PUNCT
ejpam-5963	326	14	p(δ))dδ)|	p(δ))dδ)|	VERB
ejpam-5963	326	15	−	−	PROPN
ejpam-5963	326	16	(	(	PUNCT
ejpam-5963	326	17	r0	r0	NOUN
ejpam-5963	326	18	+	+	CCONJ
ejpam-5963	326	19	ϕ(τ	ϕ(τ	PROPN
ejpam-5963	326	20	)	)	PUNCT
ejpam-5963	327	1	+	+	NUM
ejpam-5963	328	1	ξ	ξ	DET
ejpam-5963	328	2	γ(η	γ(η	NOUN
ejpam-5963	328	3	)	)	PUNCT
ejpam-5963	328	4	∫	∫	PROPN
ejpam-5963	328	5	t	t	PROPN
ejpam-5963	328	6	0	0	NUM
ejpam-5963	328	7	(	(	PUNCT
ejpam-5963	328	8	t−	t−	PROPN
ejpam-5963	328	9	δ)η−1δξ−1f(δ	δ)η−1δξ−1f(δ	PROPN
ejpam-5963	328	10	,	,	PUNCT
ejpam-5963	328	11	τ(δ	τ(δ	PROPN
ejpam-5963	328	12	)	)	PUNCT
ejpam-5963	328	13	,	,	PUNCT
ejpam-5963	328	14	κ(δ)ds	κ(δ)d	NOUN
ejpam-5963	328	15	)	)	PUNCT
ejpam-5963	328	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5963	328	17	,	,	PUNCT
ejpam-5963	328	18	≤	≤	NOUN
ejpam-5963	328	19	λinb(t)ϵ1	λinb(t)ϵ1	PROPN
ejpam-5963	329	1	+	+	CCONJ
ejpam-5963	329	2	|(ϕ(r	|(ϕ(r	NUM
ejpam-5963	329	3	−	−	NOUN
ejpam-5963	329	4	ϕ(t	ϕ(t	PROPN
ejpam-5963	329	5	,	,	PUNCT
ejpam-5963	329	6	τ(v))|+	τ(v))|+	PROPN
ejpam-5963	329	7	β(η	β(η	NOUN
ejpam-5963	329	8	,	,	PUNCT
ejpam-5963	329	9	ξ)t	ξ)t	X
ejpam-5963	329	10	η+ξ−1|f(δ	η+ξ−1|f(δ	PROPN
ejpam-5963	329	11	,	,	PUNCT
ejpam-5963	329	12	r(δ	r(δ	PROPN
ejpam-5963	329	13	)	)	PUNCT
ejpam-5963	329	14	,	,	PUNCT
ejpam-5963	329	15	p(δ)))−	p(δ)))−	PROPN
ejpam-5963	329	16	f(δ	f(δ	PROPN
ejpam-5963	329	17	,	,	PUNCT
ejpam-5963	329	18	τ(δ	τ(δ	PROPN
ejpam-5963	329	19	)	)	PUNCT
ejpam-5963	329	20	,	,	PUNCT
ejpam-5963	329	21	κ(δ)|	κ(δ)|	NOUN
ejpam-5963	329	22	,	,	PUNCT
ejpam-5963	329	23	≤	≤	NOUN
ejpam-5963	329	24	λinb1(t)ϵ1	λinb1(t)ϵ1	CCONJ
ejpam-5963	329	25	+	+	NUM
ejpam-5963	329	26	lϕ|r(t)−	lϕ|r(t)−	PROPN
ejpam-5963	329	27	τ(t)|+	τ(t)|+	PROPN
ejpam-5963	329	28	δlf	δlf	PROPN
ejpam-5963	329	29	(	(	PUNCT
ejpam-5963	329	30	||p(t)−	||p(t)−	PROPN
ejpam-5963	329	31	τ(t)|+	τ(t)|+	PROPN
ejpam-5963	329	32	|p(t)−	|p(t)−	PROPN
ejpam-5963	329	33	κ(t)|	κ(t)|	PROPN
ejpam-5963	329	34	)	)	PUNCT
ejpam-5963	329	35	.	.	PUNCT
ejpam-5963	330	1	from	from	ADP
ejpam-5963	330	2	the	the	DET
ejpam-5963	330	3	above	above	NOUN
ejpam-5963	330	4	,	,	PUNCT
ejpam-5963	330	5	we	we	PRON
ejpam-5963	330	6	gets	get	VERB
ejpam-5963	330	7	|r(t)−	|r(t)−	PROPN
ejpam-5963	330	8	τ(t)|	τ(t)|	ADP
ejpam-5963	330	9	−	−	PROPN
ejpam-5963	330	10	δlf	δlf	NOUN
ejpam-5963	330	11	1−	1−	NUM
ejpam-5963	331	1	(	(	PUNCT
ejpam-5963	331	2	lϕ	lϕ	ADP
ejpam-5963	331	3	+	+	CCONJ
ejpam-5963	331	4	δlf	δlf	PROPN
ejpam-5963	331	5	)	)	PUNCT
ejpam-5963	331	6	|p(t)−	|p(t)−	PROPN
ejpam-5963	331	7	κ(t)|	κ(t)|	ADV
ejpam-5963	331	8	≤	≤	PROPN
ejpam-5963	331	9	λinb1(t)ϵ1	λinb1(t)ϵ1	CCONJ
ejpam-5963	331	10	1−	1−	NUM
ejpam-5963	331	11	(	(	PUNCT
ejpam-5963	331	12	lϕ	lϕ	ADP
ejpam-5963	331	13	+	+	CCONJ
ejpam-5963	331	14	δlf	δlf	NOUN
ejpam-5963	331	15	)	)	PUNCT
ejpam-5963	331	16	.	.	PUNCT
ejpam-5963	332	1	(	(	PUNCT
ejpam-5963	332	2	26	26	NUM
ejpam-5963	332	3	)	)	PUNCT
ejpam-5963	332	4	similarly	similarly	ADV
ejpam-5963	332	5	,	,	PUNCT
ejpam-5963	332	6	one	one	PRON
ejpam-5963	332	7	can	can	AUX
ejpam-5963	332	8	obtain	obtain	VERB
ejpam-5963	332	9	the	the	DET
ejpam-5963	332	10	following	following	ADJ
ejpam-5963	332	11	result	result	PROPN
ejpam-5963	332	12	|p(t)−	|p(t)−	PROPN
ejpam-5963	332	13	κ(t)|	κ(t)|	ADV
ejpam-5963	333	1	−	−	PRON
ejpam-5963	333	2	δlg	δlg	VERB
ejpam-5963	333	3	1−	1−	NUM
ejpam-5963	333	4	(	(	PUNCT
ejpam-5963	333	5	lψ	lψ	PROPN
ejpam-5963	333	6	+	+	CCONJ
ejpam-5963	333	7	δlg	δlg	VERB
ejpam-5963	333	8	)	)	PUNCT
ejpam-5963	333	9	|r(t)−	|r(t)−	PROPN
ejpam-5963	333	10	τ(t)|	τ(t)|	PUNCT
ejpam-5963	333	11	≤	≤	NUM
ejpam-5963	333	12	λinb2(t)ϵ2	λinb2(t)ϵ2	PRON
ejpam-5963	333	13	1−	1−	NUM
ejpam-5963	334	1	(	(	PUNCT
ejpam-5963	334	2	lψ	lψ	PROPN
ejpam-5963	334	3	+	+	CCONJ
ejpam-5963	334	4	δlg	δlg	VERB
ejpam-5963	334	5	)	)	PUNCT
ejpam-5963	334	6	.	.	PUNCT
ejpam-5963	335	1	(	(	PUNCT
ejpam-5963	335	2	27	27	NUM
ejpam-5963	335	3	)	)	PUNCT
ejpam-5963	335	4	in	in	ADP
ejpam-5963	335	5	matrix	matrix	NOUN
ejpam-5963	335	6	form	form	NOUN
ejpam-5963	335	7	,	,	PUNCT
ejpam-5963	335	8	the	the	DET
ejpam-5963	335	9	inequalities	inequality	NOUN
ejpam-5963	335	10	(	(	PUNCT
ejpam-5963	335	11	26	26	NUM
ejpam-5963	335	12	)	)	PUNCT
ejpam-5963	335	13	and	and	CCONJ
ejpam-5963	335	14	(	(	PUNCT
ejpam-5963	335	15	27	27	NUM
ejpam-5963	335	16	)	)	PUNCT
ejpam-5963	335	17	can	can	AUX
ejpam-5963	335	18	be	be	AUX
ejpam-5963	335	19	expressed	express	VERB
ejpam-5963	335	20	as	as	ADP
ejpam-5963	335	21	(	(	PUNCT
ejpam-5963	335	22	1	1	NUM
ejpam-5963	335	23	−lfc1	−lfc1	PROPN
ejpam-5963	335	24	−lgc2	−lgc2	PROPN
ejpam-5963	335	25	1	1	NUM
ejpam-5963	335	26	)	)	PUNCT
ejpam-5963	335	27	×	×	NOUN
ejpam-5963	335	28	(	(	PUNCT
ejpam-5963	335	29	|r	|r	PROPN
ejpam-5963	335	30	−	−	PROPN
ejpam-5963	335	31	τ	τ	PROPN
ejpam-5963	335	32	|	|	ADV
ejpam-5963	335	33	|p−	|p−	ADJ
ejpam-5963	335	34	κ|	κ|	NOUN
ejpam-5963	335	35	)	)	PUNCT
ejpam-5963	335	36	≤	≤	NOUN
ejpam-5963	335	37	(	(	PUNCT
ejpam-5963	335	38	c1λinb1(t)ϵ1	c1λinb1(t)ϵ1	NOUN
ejpam-5963	335	39	c2λinb2(t)ϵ2	c2λinb2(t)ϵ2	ADJ
ejpam-5963	335	40	)	)	PUNCT
ejpam-5963	335	41	,	,	PUNCT
ejpam-5963	335	42	let	let	VERB
ejpam-5963	335	43	max{λinb1(t	max{λinb1(t	NOUN
ejpam-5963	335	44	)	)	PUNCT
ejpam-5963	335	45	,	,	PUNCT
ejpam-5963	335	46	λinb2(t	λinb2(t	NOUN
ejpam-5963	335	47	)	)	PUNCT
ejpam-5963	335	48	}	}	PUNCT
ejpam-5963	335	49	=	=	SYM
ejpam-5963	335	50	λb(t	λb(t	NOUN
ejpam-5963	335	51	)	)	PUNCT
ejpam-5963	335	52	,	,	PUNCT
ejpam-5963	335	53	max{ϵ1	max{ϵ1	NOUN
ejpam-5963	335	54	,	,	PUNCT
ejpam-5963	335	55	ϵ2	ϵ2	ADJ
ejpam-5963	335	56	}	}	PUNCT
ejpam-5963	335	57	=	=	SYM
ejpam-5963	335	58	ϵ	ϵ	NOUN
ejpam-5963	335	59	and	and	CCONJ
ejpam-5963	335	60	solving	solve	VERB
ejpam-5963	335	61	the	the	DET
ejpam-5963	335	62	above	above	ADJ
ejpam-5963	335	63	matrix	matrix	NOUN
ejpam-5963	335	64	,	,	PUNCT
ejpam-5963	335	65	we	we	PRON
ejpam-5963	335	66	get	get	VERB
ejpam-5963	335	67	|(r	|(r	PROPN
ejpam-5963	335	68	,	,	PUNCT
ejpam-5963	335	69	p)−	p)−	NOUN
ejpam-5963	335	70	(	(	PUNCT
ejpam-5963	335	71	τ	τ	PROPN
ejpam-5963	335	72	,	,	PUNCT
ejpam-5963	335	73	κ)|	κ)|	VERB
ejpam-5963	335	74	≤	≤	NUM
ejpam-5963	335	75	d(1,2)ϵλb(t	d(1,2)ϵλb(t	ADV
ejpam-5963	335	76	)	)	PUNCT
ejpam-5963	335	77	,	,	PUNCT
ejpam-5963	335	78	(	(	PUNCT
ejpam-5963	335	79	28	28	NUM
ejpam-5963	335	80	)	)	PUNCT
ejpam-5963	335	81	where	where	SCONJ
ejpam-5963	335	82	d(1,2	d(1,2	NOUN
ejpam-5963	335	83	)	)	PUNCT
ejpam-5963	335	84	=	=	SYM
ejpam-5963	335	85	(	(	PUNCT
ejpam-5963	335	86	c1	c1	PROPN
ejpam-5963	335	87	+	+	CCONJ
ejpam-5963	335	88	c2	c2	PROPN
ejpam-5963	335	89	+	+	CCONJ
ejpam-5963	335	90	c1c2(lf	c1c2(lf	PROPN
ejpam-5963	335	91	+	+	CCONJ
ejpam-5963	335	92	lg))λ	lg))λ	PROPN
ejpam-5963	335	93	1−	1−	PROPN
ejpam-5963	335	94	(	(	PUNCT
ejpam-5963	335	95	c1c2lflg	c1c2lflg	ADV
ejpam-5963	335	96	)	)	PUNCT
ejpam-5963	335	97	,	,	PUNCT
ejpam-5963	335	98	hence	hence	ADV
ejpam-5963	335	99	,	,	PUNCT
ejpam-5963	335	100	the	the	DET
ejpam-5963	335	101	solution	solution	NOUN
ejpam-5963	335	102	of	of	ADP
ejpam-5963	335	103	coupled	couple	VERB
ejpam-5963	335	104	system	system	NOUN
ejpam-5963	335	105	of	of	ADP
ejpam-5963	335	106	ffdes	ffde	NOUN
ejpam-5963	335	107	(	(	PUNCT
ejpam-5963	335	108	2	2	X
ejpam-5963	335	109	)	)	PUNCT
ejpam-5963	335	110	is	be	AUX
ejpam-5963	335	111	uhr	uhr	NOUN
ejpam-5963	335	112	stable	stable	ADJ
ejpam-5963	335	113	.	.	PUNCT
ejpam-5963	336	1	now	now	ADV
ejpam-5963	336	2	,	,	PUNCT
ejpam-5963	336	3	by	by	ADP
ejpam-5963	336	4	using	use	VERB
ejpam-5963	336	5	above	above	ADP
ejpam-5963	336	6	inequality	inequality	NOUN
ejpam-5963	336	7	with	with	ADP
ejpam-5963	336	8	d(1,2,ϵ	d(1,2,ϵ	NOUN
ejpam-5963	336	9	)	)	PUNCT
ejpam-5963	336	10	=	=	SYM
ejpam-5963	336	11	(	(	PUNCT
ejpam-5963	336	12	c1	c1	PROPN
ejpam-5963	336	13	+	+	CCONJ
ejpam-5963	336	14	c2	c2	PROPN
ejpam-5963	336	15	+	+	CCONJ
ejpam-5963	336	16	c1c2(lf	c1c2(lf	PROPN
ejpam-5963	336	17	+	+	CCONJ
ejpam-5963	336	18	lg))λϵ	lg))λϵ	PROPN
ejpam-5963	336	19	1−	1−	NUM
ejpam-5963	336	20	(	(	PUNCT
ejpam-5963	336	21	c1c2lflg	c1c2lflg	ADV
ejpam-5963	336	22	)	)	PUNCT
ejpam-5963	336	23	,	,	PUNCT
ejpam-5963	336	24	a.	a.	PROPN
ejpam-5963	336	25	ali	ali	PROPN
ejpam-5963	336	26	et	et	PROPN
ejpam-5963	336	27	al	al	PROPN
ejpam-5963	336	28	.	.	PUNCT
ejpam-5963	336	29	/	/	SYM
ejpam-5963	336	30	eur	eur	PROPN
ejpam-5963	336	31	.	.	PUNCT
ejpam-5963	337	1	j.	j.	PROPN
ejpam-5963	337	2	pure	pure	PROPN
ejpam-5963	337	3	appl	appl	PROPN
ejpam-5963	337	4	.	.	PROPN
ejpam-5963	337	5	math	math	PROPN
ejpam-5963	337	6	,	,	PUNCT
ejpam-5963	337	7	18	18	NUM
ejpam-5963	337	8	(	(	PUNCT
ejpam-5963	337	9	2	2	NUM
ejpam-5963	337	10	)	)	PUNCT
ejpam-5963	337	11	(	(	PUNCT
ejpam-5963	337	12	2025	2025	NUM
ejpam-5963	337	13	)	)	PUNCT
ejpam-5963	337	14	,	,	PUNCT
ejpam-5963	337	15	5963	5963	NUM
ejpam-5963	337	16	15	15	NUM
ejpam-5963	337	17	of	of	ADP
ejpam-5963	337	18	19	19	NUM
ejpam-5963	337	19	we	we	PRON
ejpam-5963	337	20	have	have	VERB
ejpam-5963	337	21	|(r	|(r	PROPN
ejpam-5963	337	22	,	,	PUNCT
ejpam-5963	337	23	p)−	p)−	NOUN
ejpam-5963	337	24	(	(	PUNCT
ejpam-5963	337	25	τ	τ	PROPN
ejpam-5963	337	26	,	,	PUNCT
ejpam-5963	337	27	κ)|	κ)|	VERB
ejpam-5963	337	28	≤	≤	NUM
ejpam-5963	337	29	d(1,2,ϵ)λb(t	d(1,2,ϵ)λb(t	PROPN
ejpam-5963	337	30	)	)	PUNCT
ejpam-5963	337	31	.	.	PUNCT
ejpam-5963	338	1	(	(	PUNCT
ejpam-5963	338	2	29	29	NUM
ejpam-5963	338	3	)	)	PUNCT
ejpam-5963	338	4	so	so	ADV
ejpam-5963	338	5	the	the	DET
ejpam-5963	338	6	coupled	couple	VERB
ejpam-5963	338	7	system	system	NOUN
ejpam-5963	338	8	of	of	ADP
ejpam-5963	338	9	ffdes	ffde	NOUN
ejpam-5963	338	10	(	(	PUNCT
ejpam-5963	338	11	2	2	NUM
ejpam-5963	338	12	)	)	PUNCT
ejpam-5963	338	13	is	be	AUX
ejpam-5963	338	14	guhr	guhr	ADV
ejpam-5963	338	15	stable	stable	ADJ
ejpam-5963	338	16	.	.	PUNCT
ejpam-5963	339	1	5	5	X
ejpam-5963	339	2	.	.	X
ejpam-5963	339	3	numerical	numerical	ADJ
ejpam-5963	339	4	application	application	NOUN
ejpam-5963	339	5	this	this	DET
ejpam-5963	339	6	section	section	NOUN
ejpam-5963	339	7	of	of	ADP
ejpam-5963	339	8	our	our	PRON
ejpam-5963	339	9	work	work	NOUN
ejpam-5963	339	10	,	,	PUNCT
ejpam-5963	339	11	is	be	AUX
ejpam-5963	339	12	committed	commit	VERB
ejpam-5963	339	13	to	to	ADP
ejpam-5963	339	14	numerical	numerical	ADJ
ejpam-5963	339	15	application	application	NOUN
ejpam-5963	339	16	of	of	ADP
ejpam-5963	339	17	our	our	PRON
ejpam-5963	339	18	finding	finding	NOUN
ejpam-5963	339	19	.	.	PUNCT
ejpam-5963	340	1	we	we	PRON
ejpam-5963	340	2	present	present	VERB
ejpam-5963	340	3	a	a	DET
ejpam-5963	340	4	numerical	numerical	ADJ
ejpam-5963	340	5	example	example	NOUN
ejpam-5963	340	6	to	to	PART
ejpam-5963	340	7	elaborate	elaborate	VERB
ejpam-5963	340	8	the	the	DET
ejpam-5963	340	9	main	main	ADJ
ejpam-5963	340	10	finding	finding	NOUN
ejpam-5963	340	11	of	of	ADP
ejpam-5963	340	12	this	this	DET
ejpam-5963	340	13	work	work	NOUN
ejpam-5963	340	14	.	.	PUNCT
ejpam-5963	341	1	example	example	NOUN
ejpam-5963	342	1	1	1	NUM
ejpam-5963	342	2	.	.	X
ejpam-5963	342	3	consider	consider	VERB
ejpam-5963	342	4	the	the	DET
ejpam-5963	342	5	coupled	couple	VERB
ejpam-5963	342	6	system	system	NOUN
ejpam-5963	342	7	of	of	ADP
ejpam-5963	342	8	ffdes	ffde	NOUN
ejpam-5963	342	9	with	with	ADP
ejpam-5963	342	10	t	t	PROPN
ejpam-5963	342	11	∈	∈	PROPN
ejpam-5963	343	1	[	[	X
ejpam-5963	343	2	0	0	NUM
ejpam-5963	343	3	,	,	PUNCT
ejpam-5963	343	4	t	t	X
ejpam-5963	343	5	]	]	PUNCT
ejpam-5963	343	6	as	as	ADP
ejpam-5963	343	7	follows	follows	PROPN
ejpam-5963	343	8	fddηr(t	fddηr(t	NOUN
ejpam-5963	343	9	)	)	PUNCT
ejpam-5963	343	10	=	=	SYM
ejpam-5963	344	1	ξtξ−1	ξtξ−1	PROPN
ejpam-5963	344	2	[	[	PUNCT
ejpam-5963	344	3	e−πt	e−πt	NOUN
ejpam-5963	344	4	42	42	NUM
ejpam-5963	344	5	+	+	NUM
ejpam-5963	344	6	t2	t2	NOUN
ejpam-5963	344	7	+	+	CCONJ
ejpam-5963	344	8	|r(t)|	|r(t)|	PROPN
ejpam-5963	344	9	et(50	et(50	NOUN
ejpam-5963	344	10	+	+	CCONJ
ejpam-5963	344	11	t3	t3	NOUN
ejpam-5963	344	12	)	)	PUNCT
ejpam-5963	345	1	+	+	CCONJ
ejpam-5963	345	2	t2|sinp(t)|	t2|sinp(t)|	PROPN
ejpam-5963	345	3	51	51	NUM
ejpam-5963	345	4	]	]	PUNCT
ejpam-5963	345	5	,	,	PUNCT
ejpam-5963	345	6	fddηp(t	fddηp(t	NOUN
ejpam-5963	345	7	)	)	PUNCT
ejpam-5963	345	8	=	=	SYM
ejpam-5963	346	1	ξtξ−1	ξtξ−1	PROPN
ejpam-5963	346	2	[	[	PUNCT
ejpam-5963	346	3	t3	t3	NOUN
ejpam-5963	346	4	75	75	NUM
ejpam-5963	346	5	+	+	CCONJ
ejpam-5963	346	6	e−tcos|r(t)|	e−tcos|r(t)|	NUM
ejpam-5963	346	7	39	39	NUM
ejpam-5963	346	8	+	+	CCONJ
ejpam-5963	346	9	t5	t5	PROPN
ejpam-5963	346	10	+	+	CCONJ
ejpam-5963	346	11	|p(t)|	|p(t)|	NOUN
ejpam-5963	346	12	39	39	NUM
ejpam-5963	346	13	+	+	CCONJ
ejpam-5963	346	14	|cosp(t)|	|cosp(t)|	PROPN
ejpam-5963	346	15	]	]	PUNCT
ejpam-5963	346	16	,	,	PUNCT
ejpam-5963	346	17	r(0	r(0	PROPN
ejpam-5963	346	18	)	)	PUNCT
ejpam-5963	346	19	=	=	PUNCT
ejpam-5963	347	1	3	3	NUM
ejpam-5963	347	2	73	73	NUM
ejpam-5963	347	3	+	+	CCONJ
ejpam-5963	347	4	sin(r	sin(r	PROPN
ejpam-5963	347	5	)	)	PUNCT
ejpam-5963	347	6	76	76	NUM
ejpam-5963	347	7	,	,	PUNCT
ejpam-5963	347	8	p(0	p(0	NOUN
ejpam-5963	347	9	)	)	PUNCT
ejpam-5963	347	10	=	=	SYM
ejpam-5963	348	1	17	17	NUM
ejpam-5963	348	2	49	49	NUM
ejpam-5963	348	3	+	+	CCONJ
ejpam-5963	348	4	√	√	PROPN
ejpam-5963	348	5	p	p	NOUN
ejpam-5963	348	6	45	45	NUM
ejpam-5963	348	7	(	(	PUNCT
ejpam-5963	348	8	30	30	NUM
ejpam-5963	348	9	)	)	PUNCT
ejpam-5963	348	10	from	from	ADP
ejpam-5963	348	11	(	(	PUNCT
ejpam-5963	348	12	30	30	NUM
ejpam-5963	348	13	)	)	PUNCT
ejpam-5963	348	14	,	,	PUNCT
ejpam-5963	348	15	we	we	PRON
ejpam-5963	348	16	have	have	VERB
ejpam-5963	348	17	the	the	DET
ejpam-5963	348	18	following	follow	VERB
ejpam-5963	348	19	f(t	f(t	NOUN
ejpam-5963	348	20	)	)	PUNCT
ejpam-5963	348	21	=	=	SYM
ejpam-5963	349	1	ξtξ−1	ξtξ−1	PROPN
ejpam-5963	349	2	[	[	PUNCT
ejpam-5963	349	3	e−πt	e−πt	NOUN
ejpam-5963	349	4	42	42	NUM
ejpam-5963	349	5	+	+	NUM
ejpam-5963	349	6	t2	t2	NOUN
ejpam-5963	349	7	+	+	CCONJ
ejpam-5963	349	8	|r(t)|	|r(t)|	ADJ
ejpam-5963	349	9	et(500	et(500	NOUN
ejpam-5963	349	10	+	+	CCONJ
ejpam-5963	349	11	t3	t3	NOUN
ejpam-5963	349	12	)	)	PUNCT
ejpam-5963	349	13	+	+	CCONJ
ejpam-5963	349	14	t2|sinp(t)|	t2|sinp(t)|	PROPN
ejpam-5963	349	15	500	500	NUM
ejpam-5963	349	16	]	]	PUNCT
ejpam-5963	349	17	,	,	PUNCT
ejpam-5963	349	18	g(t	g(t	PROPN
ejpam-5963	349	19	)	)	PUNCT
ejpam-5963	350	1	=	=	SYM
ejpam-5963	351	1	ξtξ−1	ξtξ−1	PROPN
ejpam-5963	351	2	[	[	PUNCT
ejpam-5963	351	3	t3	t3	NOUN
ejpam-5963	351	4	75	75	NUM
ejpam-5963	351	5	+	+	CCONJ
ejpam-5963	351	6	e−tcos|(t)|	e−tcos|(t)|	NOUN
ejpam-5963	351	7	400	400	NUM
ejpam-5963	351	8	+	+	CCONJ
ejpam-5963	351	9	t5	t5	PROPN
ejpam-5963	351	10	+	+	CCONJ
ejpam-5963	351	11	|p(t)|	|p(t)|	NOUN
ejpam-5963	351	12	400	400	NUM
ejpam-5963	351	13	+	+	CCONJ
ejpam-5963	351	14	|cosp(t)|	|cosp(t)|	ADJ
ejpam-5963	351	15	]	]	PUNCT
ejpam-5963	351	16	,	,	PUNCT
ejpam-5963	351	17	ϕ(0	ϕ(0	PROPN
ejpam-5963	351	18	)	)	PUNCT
ejpam-5963	351	19	=	=	PUNCT
ejpam-5963	351	20	sin(r	sin(r	PROPN
ejpam-5963	351	21	)	)	PUNCT
ejpam-5963	351	22	76	76	NUM
ejpam-5963	351	23	,	,	PUNCT
ejpam-5963	351	24	ψ(0	ψ(0	NOUN
ejpam-5963	351	25	)	)	PUNCT
ejpam-5963	351	26	=	=	PUNCT
ejpam-5963	352	1	√	√	PROPN
ejpam-5963	352	2	p	p	NOUN
ejpam-5963	352	3	45	45	NUM
ejpam-5963	352	4	.	.	PUNCT
ejpam-5963	353	1	from	from	ADP
ejpam-5963	353	2	coupled	couple	VERB
ejpam-5963	353	3	system	system	NOUN
ejpam-5963	353	4	(	(	PUNCT
ejpam-5963	353	5	30	30	NUM
ejpam-5963	353	6	)	)	PUNCT
ejpam-5963	353	7	,	,	PUNCT
ejpam-5963	353	8	we	we	PRON
ejpam-5963	353	9	can	can	AUX
ejpam-5963	353	10	easily	easily	ADV
ejpam-5963	353	11	obtained	obtain	VERB
ejpam-5963	353	12	,	,	PUNCT
ejpam-5963	353	13	lϕ	lϕ	ADP
ejpam-5963	353	14	=	=	SYM
ejpam-5963	353	15	1	1	NUM
ejpam-5963	353	16	76	76	NUM
ejpam-5963	353	17	,	,	PUNCT
ejpam-5963	353	18	lψ	lψ	NOUN
ejpam-5963	353	19	=	=	NOUN
ejpam-5963	353	20	1	1	NUM
ejpam-5963	353	21	45	45	NUM
ejpam-5963	353	22	,	,	PUNCT
ejpam-5963	354	1	c1	c1	PROPN
ejpam-5963	354	2	=	=	PROPN
ejpam-5963	354	3	c2	c2	PROPN
ejpam-5963	354	4	=	=	SYM
ejpam-5963	354	5	1	1	NUM
ejpam-5963	354	6	500	500	NUM
ejpam-5963	354	7	,	,	PUNCT
ejpam-5963	354	8	c3	c3	PROPN
ejpam-5963	354	9	=	=	PUNCT
ejpam-5963	354	10	1	1	NUM
ejpam-5963	354	11	42d1	42d1	NUM
ejpam-5963	354	12	=	=	SYM
ejpam-5963	354	13	d2	d2	PROPN
ejpam-5963	354	14	=	=	SYM
ejpam-5963	354	15	1	1	NUM
ejpam-5963	354	16	400	400	NUM
ejpam-5963	354	17	,	,	PUNCT
ejpam-5963	354	18	d3	d3	PROPN
ejpam-5963	354	19	=	=	SYM
ejpam-5963	354	20	1	1	NUM
ejpam-5963	354	21	75	75	NUM
ejpam-5963	354	22	and	and	CCONJ
ejpam-5963	354	23	lf	lf	ADP
ejpam-5963	354	24	=	=	SYM
ejpam-5963	354	25	1	1	NUM
ejpam-5963	354	26	500	500	NUM
ejpam-5963	354	27	,	,	PUNCT
ejpam-5963	354	28	lg	lg	NOUN
ejpam-5963	354	29	=	=	NOUN
ejpam-5963	354	30	1	1	NUM
ejpam-5963	354	31	400	400	NUM
ejpam-5963	354	32	.	.	PUNCT
ejpam-5963	355	1	also	also	ADV
ejpam-5963	355	2	,	,	PUNCT
ejpam-5963	355	3	l	l	NOUN
ejpam-5963	355	4	=	=	SYM
ejpam-5963	355	5	max{lϕ	max{lϕ	X
ejpam-5963	355	6	,	,	PUNCT
ejpam-5963	355	7	lψ	lψ	ADJ
ejpam-5963	355	8	}	}	PUNCT
ejpam-5963	355	9	=	=	SYM
ejpam-5963	355	10	1	1	NUM
ejpam-5963	355	11	45	45	NUM
ejpam-5963	355	12	<	<	SYM
ejpam-5963	355	13	1	1	NUM
ejpam-5963	355	14	.	.	PUNCT
ejpam-5963	355	15	let	let	AUX
ejpam-5963	355	16	particularly	particularly	ADV
ejpam-5963	355	17	use	use	VERB
ejpam-5963	355	18	t	t	NOUN
ejpam-5963	355	19	=	=	SYM
ejpam-5963	355	20	1	1	NUM
ejpam-5963	355	21	,	,	PUNCT
ejpam-5963	355	22	2	2	NUM
ejpam-5963	355	23	,	,	PUNCT
ejpam-5963	355	24	we	we	PRON
ejpam-5963	355	25	have	have	AUX
ejpam-5963	355	26	hence	hence	ADV
ejpam-5963	355	27	,	,	PUNCT
ejpam-5963	355	28	the	the	DET
ejpam-5963	355	29	given	give	VERB
ejpam-5963	355	30	coupled	couple	VERB
ejpam-5963	355	31	system	system	NOUN
ejpam-5963	355	32	of	of	ADP
ejpam-5963	355	33	ffde	ffde	NOUN
ejpam-5963	355	34	(	(	PUNCT
ejpam-5963	355	35	30	30	NUM
ejpam-5963	355	36	)	)	PUNCT
ejpam-5963	355	37	has	have	VERB
ejpam-5963	355	38	at	at	ADV
ejpam-5963	355	39	least	least	ADJ
ejpam-5963	355	40	one	one	NUM
ejpam-5963	355	41	solution	solution	NOUN
ejpam-5963	355	42	.	.	PUNCT
ejpam-5963	356	1	now	now	ADV
ejpam-5963	356	2	further	far	ADV
ejpam-5963	356	3	we	we	PRON
ejpam-5963	356	4	have	have	VERB
ejpam-5963	356	5	l+wt	l+wt	NOUN
ejpam-5963	356	6	η+ξ−1β(η	η+ξ−1β(η	NOUN
ejpam-5963	356	7	,	,	PUNCT
ejpam-5963	356	8	ξ	ξ	NOUN
ejpam-5963	356	9	)	)	PUNCT
ejpam-5963	356	10	=	=	SYM
ejpam-5963	357	1	1	1	NUM
ejpam-5963	357	2	45	45	NUM
ejpam-5963	357	3	+	+	NUM
ejpam-5963	357	4	t	t	PROPN
ejpam-5963	357	5	η+ξ−1	η+ξ−1	PROPN
ejpam-5963	357	6	(	(	PUNCT
ejpam-5963	357	7	1	1	NUM
ejpam-5963	357	8	500	500	NUM
ejpam-5963	357	9	+	+	CCONJ
ejpam-5963	357	10	1	1	NUM
ejpam-5963	357	11	400	400	NUM
ejpam-5963	357	12	)	)	PUNCT
ejpam-5963	357	13	b	b	PROPN
ejpam-5963	357	14	(	(	PUNCT
ejpam-5963	357	15	η	η	PROPN
ejpam-5963	357	16	,	,	PUNCT
ejpam-5963	357	17	ξ	ξ	X
ejpam-5963	357	18	)	)	PUNCT
ejpam-5963	357	19	<	<	X
ejpam-5963	357	20	1	1	NUM
ejpam-5963	357	21	.	.	PUNCT
ejpam-5963	357	22	(	(	PUNCT
ejpam-5963	357	23	31	31	NUM
ejpam-5963	357	24	)	)	PUNCT
ejpam-5963	357	25	here	here	ADV
ejpam-5963	357	26	,	,	PUNCT
ejpam-5963	357	27	we	we	PRON
ejpam-5963	357	28	demonstrate	demonstrate	VERB
ejpam-5963	357	29	graphically	graphically	ADV
ejpam-5963	357	30	to	to	PART
ejpam-5963	357	31	show	show	VERB
ejpam-5963	357	32	that	that	SCONJ
ejpam-5963	357	33	the	the	DET
ejpam-5963	357	34	quantity	quantity	NOUN
ejpam-5963	357	35	υ	υ	NOUN
ejpam-5963	357	36	=	=	PUNCT
ejpam-5963	357	37	l+wt	l+wt	NOUN
ejpam-5963	357	38	η+ξ−1b	η+ξ−1b	X
ejpam-5963	357	39	(	(	PUNCT
ejpam-5963	357	40	η	η	PROPN
ejpam-5963	357	41	,	,	PUNCT
ejpam-5963	357	42	ξ	ξ	X
ejpam-5963	357	43	)	)	PUNCT
ejpam-5963	357	44	<	<	X
ejpam-5963	357	45	1	1	NUM
ejpam-5963	357	46	for	for	ADP
ejpam-5963	357	47	η	η	PROPN
ejpam-5963	357	48	,	,	PUNCT
ejpam-5963	357	49	ξ	ξ	PROPN
ejpam-5963	357	50	∈	∈	PROPN
ejpam-5963	357	51	(	(	PUNCT
ejpam-5963	357	52	0	0	NUM
ejpam-5963	357	53	,	,	PUNCT
ejpam-5963	357	54	1	1	NUM
ejpam-5963	357	55	]	]	PUNCT
ejpam-5963	357	56	in	in	ADP
ejpam-5963	357	57	figure	figure	NOUN
ejpam-5963	357	58	1	1	NUM
ejpam-5963	357	59	a.	a.	NOUN
ejpam-5963	357	60	ali	ali	PROPN
ejpam-5963	357	61	et	et	PROPN
ejpam-5963	357	62	al	al	PROPN
ejpam-5963	357	63	.	.	PUNCT
ejpam-5963	357	64	/	/	SYM
ejpam-5963	357	65	eur	eur	PROPN
ejpam-5963	357	66	.	.	PUNCT
ejpam-5963	358	1	j.	j.	PROPN
ejpam-5963	358	2	pure	pure	PROPN
ejpam-5963	358	3	appl	appl	PROPN
ejpam-5963	358	4	.	.	PROPN
ejpam-5963	358	5	math	math	PROPN
ejpam-5963	358	6	,	,	PUNCT
ejpam-5963	358	7	18	18	NUM
ejpam-5963	358	8	(	(	PUNCT
ejpam-5963	358	9	2	2	NUM
ejpam-5963	358	10	)	)	PUNCT
ejpam-5963	358	11	(	(	PUNCT
ejpam-5963	358	12	2025	2025	NUM
ejpam-5963	358	13	)	)	PUNCT
ejpam-5963	358	14	,	,	PUNCT
ejpam-5963	358	15	5963	5963	NUM
ejpam-5963	358	16	16	16	NUM
ejpam-5963	358	17	of	of	ADP
ejpam-5963	358	18	19	19	NUM
ejpam-5963	358	19	figure	figure	NOUN
ejpam-5963	358	20	1	1	NUM
ejpam-5963	358	21	:	:	PUNCT
ejpam-5963	358	22	graphical	graphical	ADJ
ejpam-5963	358	23	illustration	illustration	NOUN
ejpam-5963	358	24	of	of	ADP
ejpam-5963	358	25	quantity	quantity	NOUN
ejpam-5963	358	26	υ	υ	NOUN
ejpam-5963	358	27	in	in	ADP
ejpam-5963	358	28	η	η	PROPN
ejpam-5963	358	29	,	,	PUNCT
ejpam-5963	358	30	ξ	ξ	PRON
ejpam-5963	358	31	space	space	NOUN
ejpam-5963	358	32	by	by	ADP
ejpam-5963	358	33	using	use	VERB
ejpam-5963	358	34	t	t	PROPN
ejpam-5963	358	35	=	=	SYM
ejpam-5963	358	36	1	1	NUM
ejpam-5963	358	37	,	,	PUNCT
ejpam-5963	358	38	2	2	NUM
ejpam-5963	358	39	.	.	X
ejpam-5963	359	1	from	from	ADP
ejpam-5963	359	2	figure	figure	NOUN
ejpam-5963	359	3	1	1	NUM
ejpam-5963	359	4	,	,	PUNCT
ejpam-5963	359	5	we	we	PRON
ejpam-5963	359	6	see	see	VERB
ejpam-5963	359	7	that	that	SCONJ
ejpam-5963	359	8	as	as	SCONJ
ejpam-5963	359	9	the	the	DET
ejpam-5963	359	10	values	value	NOUN
ejpam-5963	359	11	of	of	ADP
ejpam-5963	359	12	ξ	ξ	PROPN
ejpam-5963	359	13	,	,	PUNCT
ejpam-5963	359	14	η	η	X
ejpam-5963	359	15	increase	increase	NOUN
ejpam-5963	359	16	over	over	ADP
ejpam-5963	359	17	(	(	PUNCT
ejpam-5963	359	18	0	0	NUM
ejpam-5963	359	19	,	,	PUNCT
ejpam-5963	359	20	1	1	NUM
ejpam-5963	359	21	]	]	PUNCT
ejpam-5963	359	22	,	,	PUNCT
ejpam-5963	359	23	the	the	DET
ejpam-5963	359	24	value	value	NOUN
ejpam-5963	359	25	of	of	ADP
ejpam-5963	359	26	υ	υ	NOUN
ejpam-5963	359	27	does	do	AUX
ejpam-5963	359	28	not	not	PART
ejpam-5963	359	29	exceed	exceed	VERB
ejpam-5963	359	30	1	1	NUM
ejpam-5963	359	31	,	,	PUNCT
ejpam-5963	359	32	which	which	PRON
ejpam-5963	359	33	authenticate	authenticate	VERB
ejpam-5963	359	34	the	the	DET
ejpam-5963	359	35	result	result	NOUN
ejpam-5963	359	36	(	(	PUNCT
ejpam-5963	359	37	31	31	NUM
ejpam-5963	359	38	)	)	PUNCT
ejpam-5963	359	39	for	for	ADP
ejpam-5963	359	40	all	all	DET
ejpam-5963	359	41	values	value	NOUN
ejpam-5963	359	42	η	η	PROPN
ejpam-5963	359	43	,	,	PUNCT
ejpam-5963	359	44	ξ	ξ	PROPN
ejpam-5963	359	45	∈	∈	PROPN
ejpam-5963	359	46	(	(	PUNCT
ejpam-5963	359	47	0	0	NUM
ejpam-5963	359	48	,	,	PUNCT
ejpam-5963	359	49	1	1	NUM
ejpam-5963	359	50	]	]	PUNCT
ejpam-5963	359	51	.	.	PUNCT
ejpam-5963	360	1	hence	hence	ADV
ejpam-5963	360	2	,	,	PUNCT
ejpam-5963	360	3	the	the	DET
ejpam-5963	360	4	coupled	couple	VERB
ejpam-5963	360	5	system	system	NOUN
ejpam-5963	360	6	(	(	PUNCT
ejpam-5963	360	7	30	30	NUM
ejpam-5963	360	8	)	)	PUNCT
ejpam-5963	360	9	has	have	VERB
ejpam-5963	360	10	a	a	DET
ejpam-5963	360	11	unique	unique	ADJ
ejpam-5963	360	12	solution	solution	NOUN
ejpam-5963	360	13	.	.	PUNCT
ejpam-5963	361	1	the	the	DET
ejpam-5963	361	2	problem	problem	NOUN
ejpam-5963	361	3	(	(	PUNCT
ejpam-5963	361	4	30	30	NUM
ejpam-5963	361	5	)	)	PUNCT
ejpam-5963	361	6	is	be	AUX
ejpam-5963	361	7	uh	uh	INTJ
ejpam-5963	361	8	and	and	CCONJ
ejpam-5963	361	9	guh	guh	NOUN
ejpam-5963	361	10	stable	stable	ADJ
ejpam-5963	361	11	,	,	PUNCT
ejpam-5963	361	12	since	since	SCONJ
ejpam-5963	361	13	c1c2lflg	c1c2lflg	ADV
ejpam-5963	361	14	̸=	̸=	PROPN
ejpam-5963	361	15	1	1	NUM
ejpam-5963	361	16	for	for	ADP
ejpam-5963	361	17	c1	c1	PROPN
ejpam-5963	361	18	,	,	PUNCT
ejpam-5963	361	19	c2	c2	PROPN
ejpam-5963	361	20	.	.	PUNCT
ejpam-5963	362	1	similarly	similarly	ADV
ejpam-5963	362	2	,	,	PUNCT
ejpam-5963	362	3	by	by	ADP
ejpam-5963	362	4	the	the	DET
ejpam-5963	362	5	same	same	ADJ
ejpam-5963	362	6	procedure	procedure	NOUN
ejpam-5963	362	7	the	the	DET
ejpam-5963	362	8	coupled	couple	VERB
ejpam-5963	362	9	system	system	NOUN
ejpam-5963	362	10	(	(	PUNCT
ejpam-5963	362	11	30	30	NUM
ejpam-5963	362	12	)	)	PUNCT
ejpam-5963	362	13	is	be	AUX
ejpam-5963	362	14	uhr	uhr	NOUN
ejpam-5963	362	15	and	and	CCONJ
ejpam-5963	362	16	guhr	guhr	VERB
ejpam-5963	362	17	stable	stable	ADJ
ejpam-5963	362	18	with	with	ADP
ejpam-5963	362	19	w(t	w(t	PROPN
ejpam-5963	362	20	)	)	PUNCT
ejpam-5963	362	21	=	=	SYM
ejpam-5963	362	22	s(t	s(t	PROPN
ejpam-5963	362	23	)	)	PUNCT
ejpam-5963	363	1	=	=	SYM
ejpam-5963	363	2	t	t	PROPN
ejpam-5963	363	3	for	for	ADP
ejpam-5963	363	4	t	t	PROPN
ejpam-5963	363	5	∈	∈	PROPN
ejpam-5963	363	6	(	(	PUNCT
ejpam-5963	363	7	0	0	NUM
ejpam-5963	363	8	,	,	PUNCT
ejpam-5963	363	9	1	1	NUM
ejpam-5963	363	10	)	)	PUNCT
ejpam-5963	363	11	.	.	PUNCT
ejpam-5963	364	1	6	6	X
ejpam-5963	364	2	.	.	X
ejpam-5963	364	3	conclusion	conclusion	NOUN
ejpam-5963	364	4	in	in	ADP
ejpam-5963	364	5	this	this	DET
ejpam-5963	364	6	research	research	NOUN
ejpam-5963	364	7	work	work	NOUN
ejpam-5963	364	8	,	,	PUNCT
ejpam-5963	364	9	we	we	PRON
ejpam-5963	364	10	have	have	AUX
ejpam-5963	364	11	investigated	investigate	VERB
ejpam-5963	364	12	a	a	DET
ejpam-5963	364	13	coupled	couple	VERB
ejpam-5963	364	14	system	system	NOUN
ejpam-5963	364	15	of	of	ADP
ejpam-5963	364	16	ffdes	ffde	NOUN
ejpam-5963	364	17	for	for	ADP
ejpam-5963	364	18	existence	existence	NOUN
ejpam-5963	364	19	theory	theory	NOUN
ejpam-5963	364	20	and	and	CCONJ
ejpam-5963	364	21	stability	stability	NOUN
ejpam-5963	364	22	analysis	analysis	NOUN
ejpam-5963	364	23	.	.	PUNCT
ejpam-5963	365	1	we	we	PRON
ejpam-5963	365	2	have	have	AUX
ejpam-5963	365	3	deduced	deduce	VERB
ejpam-5963	365	4	sufficient	sufficient	ADJ
ejpam-5963	365	5	conditions	condition	NOUN
ejpam-5963	365	6	for	for	ADP
ejpam-5963	365	7	the	the	DET
ejpam-5963	365	8	existence	existence	NOUN
ejpam-5963	365	9	,	,	PUNCT
ejpam-5963	365	10	uniqueness	uniqueness	NOUN
ejpam-5963	365	11	of	of	ADP
ejpam-5963	365	12	solution	solution	NOUN
ejpam-5963	365	13	to	to	ADP
ejpam-5963	365	14	the	the	DET
ejpam-5963	365	15	mentioned	mention	VERB
ejpam-5963	365	16	problem	problem	NOUN
ejpam-5963	365	17	by	by	ADP
ejpam-5963	365	18	using	use	VERB
ejpam-5963	365	19	fpt	fpt	PROPN
ejpam-5963	365	20	.	.	PUNCT
ejpam-5963	366	1	in	in	ADP
ejpam-5963	366	2	addition	addition	NOUN
ejpam-5963	366	3	,	,	PUNCT
ejpam-5963	366	4	appropriate	appropriate	ADJ
ejpam-5963	366	5	results	result	NOUN
ejpam-5963	366	6	devoted	devote	VERB
ejpam-5963	366	7	to	to	ADP
ejpam-5963	366	8	uh	uh	INTJ
ejpam-5963	366	9	stability	stability	NOUN
ejpam-5963	366	10	has	have	AUX
ejpam-5963	366	11	also	also	ADV
ejpam-5963	366	12	been	be	AUX
ejpam-5963	366	13	developed	develop	VERB
ejpam-5963	366	14	.	.	PUNCT
ejpam-5963	367	1	different	different	ADJ
ejpam-5963	367	2	kinds	kind	NOUN
ejpam-5963	367	3	of	of	ADP
ejpam-5963	367	4	uh	uh	INTJ
ejpam-5963	367	5	stability	stability	NOUN
ejpam-5963	367	6	were	be	AUX
ejpam-5963	367	7	deduced	deduce	VERB
ejpam-5963	367	8	for	for	ADP
ejpam-5963	367	9	the	the	DET
ejpam-5963	367	10	considered	consider	VERB
ejpam-5963	367	11	problem	problem	NOUN
ejpam-5963	367	12	.	.	PUNCT
ejpam-5963	368	1	here	here	ADV
ejpam-5963	368	2	,	,	PUNCT
ejpam-5963	368	3	it	it	PRON
ejpam-5963	368	4	is	be	AUX
ejpam-5963	368	5	remarkable	remarkable	ADJ
ejpam-5963	368	6	that	that	SCONJ
ejpam-5963	368	7	coupled	couple	VERB
ejpam-5963	368	8	systems	system	NOUN
ejpam-5963	368	9	have	have	AUX
ejpam-5963	368	10	very	very	ADV
ejpam-5963	368	11	rarely	rarely	ADV
ejpam-5963	368	12	investigated	investigate	VERB
ejpam-5963	368	13	for	for	ADP
ejpam-5963	368	14	the	the	DET
ejpam-5963	368	15	existence	existence	NOUN
ejpam-5963	368	16	theory	theory	NOUN
ejpam-5963	368	17	of	of	ADP
ejpam-5963	368	18	solution	solution	NOUN
ejpam-5963	368	19	and	and	CCONJ
ejpam-5963	368	20	stability	stability	NOUN
ejpam-5963	368	21	analysis	analysis	NOUN
ejpam-5963	368	22	.	.	PUNCT
ejpam-5963	369	1	the	the	DET
ejpam-5963	369	2	mentioned	mention	VERB
ejpam-5963	369	3	type	type	NOUN
ejpam-5963	369	4	systems	system	NOUN
ejpam-5963	369	5	have	have	VERB
ejpam-5963	369	6	numerous	numerous	ADJ
ejpam-5963	369	7	applications	application	NOUN
ejpam-5963	369	8	in	in	ADP
ejpam-5963	369	9	variety	variety	NOUN
ejpam-5963	369	10	of	of	ADP
ejpam-5963	369	11	disciplines	discipline	NOUN
ejpam-5963	369	12	of	of	ADP
ejpam-5963	369	13	science	science	NOUN
ejpam-5963	369	14	and	and	CCONJ
ejpam-5963	369	15	technology	technology	NOUN
ejpam-5963	369	16	.	.	PUNCT
ejpam-5963	370	1	also	also	ADV
ejpam-5963	370	2	,	,	PUNCT
ejpam-5963	370	3	in	in	ADP
ejpam-5963	370	4	the	the	DET
ejpam-5963	370	5	future	future	NOUN
ejpam-5963	370	6	,	,	PUNCT
ejpam-5963	370	7	the	the	DET
ejpam-5963	370	8	coupled	couple	VERB
ejpam-5963	370	9	systems	system	NOUN
ejpam-5963	370	10	of	of	ADP
ejpam-5963	370	11	drug	drug	NOUN
ejpam-5963	370	12	therapy	therapy	NOUN
ejpam-5963	370	13	,	,	PUNCT
ejpam-5963	370	14	coupled	couple	VERB
ejpam-5963	370	15	system	system	NOUN
ejpam-5963	370	16	of	of	ADP
ejpam-5963	370	17	mechanical	mechanical	ADJ
ejpam-5963	370	18	oscillators	oscillator	NOUN
ejpam-5963	370	19	and	and	CCONJ
ejpam-5963	370	20	coupled	couple	VERB
ejpam-5963	370	21	system	system	NOUN
ejpam-5963	370	22	of	of	ADP
ejpam-5963	370	23	planetary	planetary	ADJ
ejpam-5963	370	24	system	system	NOUN
ejpam-5963	370	25	can	can	AUX
ejpam-5963	370	26	be	be	AUX
ejpam-5963	370	27	studied	study	VERB
ejpam-5963	370	28	by	by	ADP
ejpam-5963	370	29	following	follow	VERB
ejpam-5963	370	30	our	our	PRON
ejpam-5963	370	31	established	establish	VERB
ejpam-5963	370	32	analysis	analysis	NOUN
ejpam-5963	370	33	.	.	PUNCT
ejpam-5963	371	1	acknowledgements	acknowledgement	NOUN
ejpam-5963	371	2	authors	author	NOUN
ejpam-5963	371	3	are	be	AUX
ejpam-5963	371	4	thankful	thankful	ADJ
ejpam-5963	371	5	to	to	ADP
ejpam-5963	371	6	prince	prince	PROPN
ejpam-5963	371	7	sultan	sultan	PROPN
ejpam-5963	371	8	university	university	PROPN
ejpam-5963	371	9	for	for	ADP
ejpam-5963	371	10	apc	apc	PROPN
ejpam-5963	371	11	and	and	CCONJ
ejpam-5963	371	12	support	support	VERB
ejpam-5963	371	13	through	through	ADP
ejpam-5963	371	14	tas	ta	NOUN
ejpam-5963	371	15	research	research	NOUN
ejpam-5963	371	16	lab	lab	NOUN
ejpam-5963	371	17	.	.	PUNCT
ejpam-5963	372	1	a.	a.	PROPN
ejpam-5963	372	2	ali	ali	PROPN
ejpam-5963	372	3	et	et	PROPN
ejpam-5963	372	4	al	al	PROPN
ejpam-5963	372	5	.	.	PUNCT
ejpam-5963	372	6	/	/	SYM
ejpam-5963	372	7	eur	eur	PROPN
ejpam-5963	372	8	.	.	PUNCT
ejpam-5963	373	1	j.	j.	PROPN
ejpam-5963	373	2	pure	pure	PROPN
ejpam-5963	373	3	appl	appl	PROPN
ejpam-5963	373	4	.	.	PROPN
ejpam-5963	373	5	math	math	PROPN
ejpam-5963	373	6	,	,	PUNCT
ejpam-5963	373	7	18	18	NUM
ejpam-5963	373	8	(	(	PUNCT
ejpam-5963	373	9	2	2	NUM
ejpam-5963	373	10	)	)	PUNCT
ejpam-5963	373	11	(	(	PUNCT
ejpam-5963	373	12	2025	2025	NUM
ejpam-5963	373	13	)	)	PUNCT
ejpam-5963	373	14	,	,	PUNCT
ejpam-5963	373	15	5963	5963	NUM
ejpam-5963	373	16	17	17	NUM
ejpam-5963	373	17	of	of	ADP
ejpam-5963	373	18	19	19	NUM
ejpam-5963	373	19	competing	compete	VERB
ejpam-5963	373	20	interest	interest	NOUN
ejpam-5963	373	21	does	do	AUX
ejpam-5963	373	22	not	not	PART
ejpam-5963	373	23	exist	exist	VERB
ejpam-5963	373	24	.	.	PUNCT
ejpam-5963	374	1	references	reference	NOUN
ejpam-5963	374	2	[	[	X
ejpam-5963	374	3	1	1	NUM
ejpam-5963	374	4	]	]	X
ejpam-5963	374	5	hongguang	hongguang	PROPN
ejpam-5963	374	6	sun	sun	PROPN
ejpam-5963	374	7	,	,	PUNCT
ejpam-5963	374	8	yong	yong	PROPN
ejpam-5963	374	9	zhang	zhang	PROPN
ejpam-5963	374	10	,	,	PUNCT
ejpam-5963	374	11	dumitru	dumitru	PROPN
ejpam-5963	374	12	baleanu	baleanu	PROPN
ejpam-5963	374	13	,	,	PUNCT
ejpam-5963	374	14	wen	wen	PROPN
ejpam-5963	374	15	chen	chen	PROPN
ejpam-5963	374	16	,	,	PUNCT
ejpam-5963	374	17	and	and	CCONJ
ejpam-5963	374	18	yangquan	yangquan	PROPN
ejpam-5963	374	19	chen	chen	PROPN
ejpam-5963	374	20	.	.	PUNCT
ejpam-5963	375	1	a	a	DET
ejpam-5963	375	2	new	new	ADJ
ejpam-5963	375	3	collection	collection	NOUN
ejpam-5963	375	4	of	of	ADP
ejpam-5963	375	5	real	real	ADJ
ejpam-5963	375	6	world	world	NOUN
ejpam-5963	375	7	applications	application	NOUN
ejpam-5963	375	8	of	of	ADP
ejpam-5963	375	9	fractional	fractional	ADJ
ejpam-5963	375	10	calculus	calculus	NOUN
ejpam-5963	375	11	in	in	ADP
ejpam-5963	375	12	science	science	NOUN
ejpam-5963	375	13	and	and	CCONJ
ejpam-5963	375	14	engineering	engineering	NOUN
ejpam-5963	375	15	.	.	PUNCT
ejpam-5963	376	1	communications	communication	NOUN
ejpam-5963	376	2	in	in	ADP
ejpam-5963	376	3	nonlinear	nonlinear	ADJ
ejpam-5963	376	4	science	science	NOUN
ejpam-5963	376	5	and	and	CCONJ
ejpam-5963	376	6	numerical	numerical	PROPN
ejpam-5963	376	7	simulation	simulation	PROPN
ejpam-5963	376	8	,	,	PUNCT
ejpam-5963	376	9	64:213–231	64:213–231	NUM
ejpam-5963	376	10	,	,	PUNCT
ejpam-5963	376	11	2018	2018	NUM
ejpam-5963	376	12	.	.	PUNCT
ejpam-5963	377	1	[	[	X
ejpam-5963	377	2	2	2	NUM
ejpam-5963	377	3	]	]	X
ejpam-5963	377	4	dumitru	dumitru	PROPN
ejpam-5963	377	5	baleanu	baleanu	PROPN
ejpam-5963	377	6	,	,	PUNCT
ejpam-5963	377	7	kai	kai	PROPN
ejpam-5963	377	8	diethelm	diethelm	PROPN
ejpam-5963	377	9	,	,	PUNCT
ejpam-5963	377	10	enrico	enrico	PROPN
ejpam-5963	377	11	scalas	scalas	PROPN
ejpam-5963	377	12	,	,	PUNCT
ejpam-5963	377	13	and	and	CCONJ
ejpam-5963	377	14	juan	juan	PROPN
ejpam-5963	377	15	j	j	PROPN
ejpam-5963	377	16	trujillo	trujillo	PROPN
ejpam-5963	377	17	.	.	PUNCT
ejpam-5963	377	18	fractional	fractional	ADJ
ejpam-5963	377	19	calculus	calculus	NOUN
ejpam-5963	377	20	:	:	PUNCT
ejpam-5963	377	21	models	model	NOUN
ejpam-5963	377	22	and	and	CCONJ
ejpam-5963	377	23	numerical	numerical	ADJ
ejpam-5963	377	24	methods	method	NOUN
ejpam-5963	377	25	,	,	PUNCT
ejpam-5963	377	26	volume	volume	NOUN
ejpam-5963	377	27	3	3	NUM
ejpam-5963	377	28	.	.	PUNCT
ejpam-5963	377	29	world	world	PROPN
ejpam-5963	377	30	scientific	scientific	ADJ
ejpam-5963	377	31	,	,	PUNCT
ejpam-5963	377	32	2012	2012	NUM
ejpam-5963	377	33	.	.	PUNCT
ejpam-5963	378	1	[	[	X
ejpam-5963	378	2	3	3	X
ejpam-5963	378	3	]	]	X
ejpam-5963	378	4	daniel	daniel	PROPN
ejpam-5963	378	5	clemente	clemente	PROPN
ejpam-5963	378	6	-	-	PROPN
ejpam-5963	378	7	lópez	lópez	PROPN
ejpam-5963	378	8	,	,	PUNCT
ejpam-5963	378	9	jesus	jesus	PROPN
ejpam-5963	378	10	mmunoz	mmunoz	PROPN
ejpam-5963	378	11	-	-	PUNCT
ejpam-5963	378	12	pacheco	pacheco	PROPN
ejpam-5963	378	13	,	,	PUNCT
ejpam-5963	378	14	ernesto	ernesto	PROPN
ejpam-5963	378	15	zambrano	zambrano	PROPN
ejpam-5963	378	16	-	-	PUNCT
ejpam-5963	378	17	serrano	serrano	PROPN
ejpam-5963	378	18	,	,	PUNCT
ejpam-5963	378	19	olga	olga	PROPN
ejpam-5963	378	20	g	g	PROPN
ejpam-5963	378	21	félix	félix	ADJ
ejpam-5963	378	22	beltrán	beltrán	NOUN
ejpam-5963	378	23	,	,	PUNCT
ejpam-5963	378	24	and	and	CCONJ
ejpam-5963	378	25	jose	jose	PROPN
ejpam-5963	378	26	de	de	PROPN
ejpam-5963	378	27	jesus	jesus	PROPN
ejpam-5963	378	28	rangel	rangel	PROPN
ejpam-5963	378	29	-	-	PUNCT
ejpam-5963	378	30	magdaleno	magdaleno	NOUN
ejpam-5963	378	31	.	.	PUNCT
ejpam-5963	379	1	a	a	DET
ejpam-5963	379	2	piecewise	piecewise	NOUN
ejpam-5963	379	3	linear	linear	NOUN
ejpam-5963	379	4	approach	approach	NOUN
ejpam-5963	379	5	for	for	ADP
ejpam-5963	379	6	implementing	implement	VERB
ejpam-5963	379	7	fractional	fractional	ADJ
ejpam-5963	379	8	-	-	PUNCT
ejpam-5963	379	9	order	order	NOUN
ejpam-5963	379	10	multi	multi	ADJ
ejpam-5963	379	11	-	-	ADJ
ejpam-5963	379	12	scroll	scroll	ADJ
ejpam-5963	379	13	chaotic	chaotic	ADJ
ejpam-5963	379	14	systems	system	NOUN
ejpam-5963	379	15	on	on	ADP
ejpam-5963	379	16	arms	arm	NOUN
ejpam-5963	379	17	and	and	CCONJ
ejpam-5963	379	18	fpgas	fpgas	NOUN
ejpam-5963	379	19	.	.	PUNCT
ejpam-5963	380	1	fractal	fractal	PROPN
ejpam-5963	380	2	and	and	CCONJ
ejpam-5963	380	3	fractional	fractional	ADJ
ejpam-5963	380	4	,	,	PUNCT
ejpam-5963	380	5	8(7):389	8(7):389	NUM
ejpam-5963	380	6	,	,	PUNCT
ejpam-5963	380	7	2024	2024	NUM
ejpam-5963	380	8	.	.	PUNCT
ejpam-5963	381	1	[	[	X
ejpam-5963	381	2	4	4	X
ejpam-5963	381	3	]	]	PUNCT
ejpam-5963	381	4	jorge	jorge	PROPN
ejpam-5963	381	5	manuel	manuel	PROPN
ejpam-5963	381	6	barrios	barrios	PROPN
ejpam-5963	381	7	-	-	PUNCT
ejpam-5963	381	8	sánchez	sánchez	PROPN
ejpam-5963	381	9	,	,	PUNCT
ejpam-5963	381	10	roberto	roberto	PROPN
ejpam-5963	381	11	baeza	baeza	PROPN
ejpam-5963	381	12	-	-	PUNCT
ejpam-5963	381	13	serrato	serrato	PROPN
ejpam-5963	381	14	,	,	PUNCT
ejpam-5963	381	15	and	and	CCONJ
ejpam-5963	381	16	leonardo	leonardo	PROPN
ejpam-5963	381	17	mart́ınezjiménez	mart́ınezjiménez	PROPN
ejpam-5963	381	18	.	.	PUNCT
ejpam-5963	382	1	fractional	fractional	ADJ
ejpam-5963	382	2	calculus	calculus	NOUN
ejpam-5963	382	3	to	to	PART
ejpam-5963	382	4	analyze	analyze	VERB
ejpam-5963	382	5	efficiency	efficiency	NOUN
ejpam-5963	382	6	behavior	behavior	NOUN
ejpam-5963	382	7	in	in	ADP
ejpam-5963	382	8	a	a	DET
ejpam-5963	382	9	balancing	balancing	NOUN
ejpam-5963	382	10	loop	loop	NOUN
ejpam-5963	382	11	in	in	ADP
ejpam-5963	382	12	a	a	DET
ejpam-5963	382	13	system	system	NOUN
ejpam-5963	382	14	dynamics	dynamic	NOUN
ejpam-5963	382	15	environment	environment	NOUN
ejpam-5963	382	16	.	.	PUNCT
ejpam-5963	383	1	fractal	fractal	PROPN
ejpam-5963	383	2	and	and	CCONJ
ejpam-5963	383	3	fractional	fractional	ADJ
ejpam-5963	383	4	,	,	PUNCT
ejpam-5963	383	5	8(4):212	8(4):212	NUM
ejpam-5963	383	6	,	,	PUNCT
ejpam-5963	383	7	2024	2024	NUM
ejpam-5963	383	8	.	.	PUNCT
ejpam-5963	384	1	[	[	X
ejpam-5963	384	2	5	5	NUM
ejpam-5963	384	3	]	]	PUNCT
ejpam-5963	384	4	wei	wei	PROPN
ejpam-5963	384	5	ding	ding	PROPN
ejpam-5963	384	6	,	,	PUNCT
ejpam-5963	384	7	sansit	sansit	NOUN
ejpam-5963	384	8	patnaik	patnaik	PROPN
ejpam-5963	384	9	,	,	PUNCT
ejpam-5963	384	10	sai	sai	PROPN
ejpam-5963	384	11	sidhardh	sidhardh	PROPN
ejpam-5963	384	12	,	,	PUNCT
ejpam-5963	384	13	and	and	CCONJ
ejpam-5963	384	14	fabio	fabio	PROPN
ejpam-5963	384	15	semperlotti	semperlotti	PROPN
ejpam-5963	384	16	.	.	PUNCT
ejpam-5963	385	1	applications	application	NOUN
ejpam-5963	385	2	of	of	ADP
ejpam-5963	385	3	distributed	distribute	VERB
ejpam-5963	385	4	-	-	PUNCT
ejpam-5963	385	5	order	order	NOUN
ejpam-5963	385	6	fractional	fractional	ADJ
ejpam-5963	385	7	operators	operator	NOUN
ejpam-5963	385	8	:	:	PUNCT
ejpam-5963	385	9	a	a	DET
ejpam-5963	385	10	review	review	NOUN
ejpam-5963	385	11	.	.	PUNCT
ejpam-5963	386	1	entropy	entropy	PROPN
ejpam-5963	386	2	,	,	PUNCT
ejpam-5963	386	3	23(1):110	23(1):110	PROPN
ejpam-5963	386	4	,	,	PUNCT
ejpam-5963	386	5	2021	2021	NUM
ejpam-5963	386	6	.	.	PUNCT
ejpam-5963	387	1	[	[	X
ejpam-5963	387	2	6	6	NUM
ejpam-5963	387	3	]	]	PUNCT
ejpam-5963	387	4	hasib	hasib	PROPN
ejpam-5963	387	5	khan	khan	PROPN
ejpam-5963	387	6	,	,	PUNCT
ejpam-5963	387	7	muhammad	muhammad	PROPN
ejpam-5963	387	8	aslam	aslam	PROPN
ejpam-5963	387	9	,	,	PUNCT
ejpam-5963	387	10	altaf	altaf	PROPN
ejpam-5963	387	11	hussain	hussain	PROPN
ejpam-5963	387	12	rajpar	rajpar	PROPN
ejpam-5963	387	13	,	,	PUNCT
ejpam-5963	387	14	yu	yu	PROPN
ejpam-5963	387	15	-	-	PROPN
ejpam-5963	387	16	ming	ming	PROPN
ejpam-5963	387	17	chu	chu	PROPN
ejpam-5963	387	18	,	,	PUNCT
ejpam-5963	387	19	sina	sina	PROPN
ejpam-5963	387	20	etemad	etemad	PROPN
ejpam-5963	387	21	,	,	PUNCT
ejpam-5963	387	22	shahram	shahram	PROPN
ejpam-5963	387	23	rezapour	rezapour	PROPN
ejpam-5963	387	24	,	,	PUNCT
ejpam-5963	387	25	and	and	CCONJ
ejpam-5963	387	26	hijaz	hijaz	PROPN
ejpam-5963	387	27	ahmad	ahmad	PROPN
ejpam-5963	387	28	.	.	PUNCT
ejpam-5963	388	1	a	a	DET
ejpam-5963	388	2	new	new	ADJ
ejpam-5963	388	3	fractal	fractal	ADJ
ejpam-5963	388	4	-	-	PUNCT
ejpam-5963	388	5	fractional	fractional	ADJ
ejpam-5963	388	6	hybrid	hybrid	ADJ
ejpam-5963	388	7	model	model	NOUN
ejpam-5963	388	8	for	for	ADP
ejpam-5963	388	9	studying	study	VERB
ejpam-5963	388	10	climate	climate	NOUN
ejpam-5963	388	11	change	change	NOUN
ejpam-5963	388	12	on	on	ADP
ejpam-5963	388	13	coastal	coastal	ADJ
ejpam-5963	388	14	ecosystems	ecosystem	NOUN
ejpam-5963	388	15	from	from	ADP
ejpam-5963	388	16	the	the	DET
ejpam-5963	388	17	mathematical	mathematical	ADJ
ejpam-5963	388	18	point	point	NOUN
ejpam-5963	388	19	of	of	ADP
ejpam-5963	388	20	view	view	NOUN
ejpam-5963	388	21	.	.	PUNCT
ejpam-5963	389	1	fractals	fractal	NOUN
ejpam-5963	389	2	,	,	PUNCT
ejpam-5963	389	3	32(02):2440015	32(02):2440015	NUM
ejpam-5963	389	4	,	,	PUNCT
ejpam-5963	389	5	2024	2024	NUM
ejpam-5963	389	6	.	.	PUNCT
ejpam-5963	390	1	[	[	X
ejpam-5963	390	2	7	7	X
ejpam-5963	390	3	]	]	X
ejpam-5963	390	4	abdelhamid	abdelhamid	PROPN
ejpam-5963	390	5	mohammed	mohammed	PROPN
ejpam-5963	390	6	djaouti	djaouti	PROPN
ejpam-5963	390	7	,	,	PUNCT
ejpam-5963	390	8	zareen	zareen	X
ejpam-5963	390	9	a	a	DET
ejpam-5963	390	10	khan	khan	PROPN
ejpam-5963	390	11	,	,	PUNCT
ejpam-5963	390	12	muhammad	muhammad	PROPN
ejpam-5963	390	13	imran	imran	PROPN
ejpam-5963	390	14	liaqat	liaqat	PROPN
ejpam-5963	390	15	,	,	PUNCT
ejpam-5963	390	16	and	and	CCONJ
ejpam-5963	390	17	ashraf	ashraf	PROPN
ejpam-5963	390	18	al	al	PROPN
ejpam-5963	390	19	-	-	PUNCT
ejpam-5963	390	20	quran	quran	PROPN
ejpam-5963	390	21	.	.	PUNCT
ejpam-5963	391	1	a	a	DET
ejpam-5963	391	2	study	study	NOUN
ejpam-5963	391	3	of	of	ADP
ejpam-5963	391	4	some	some	DET
ejpam-5963	391	5	generalized	generalized	ADJ
ejpam-5963	391	6	results	result	NOUN
ejpam-5963	391	7	of	of	ADP
ejpam-5963	391	8	neutral	neutral	ADJ
ejpam-5963	391	9	stochastic	stochastic	ADJ
ejpam-5963	391	10	differential	differential	ADJ
ejpam-5963	391	11	equations	equation	NOUN
ejpam-5963	391	12	in	in	ADP
ejpam-5963	391	13	the	the	DET
ejpam-5963	391	14	framework	framework	NOUN
ejpam-5963	391	15	of	of	ADP
ejpam-5963	391	16	caputo	caputo	PROPN
ejpam-5963	391	17	-	-	PUNCT
ejpam-5963	391	18	katugampola	katugampola	ADJ
ejpam-5963	391	19	fractional	fractional	ADJ
ejpam-5963	391	20	derivatives	derivative	NOUN
ejpam-5963	391	21	.	.	PUNCT
ejpam-5963	392	1	mathematics	mathematic	NOUN
ejpam-5963	392	2	,	,	PUNCT
ejpam-5963	392	3	12(11):1654	12(11):1654	NUM
ejpam-5963	392	4	,	,	PUNCT
ejpam-5963	392	5	2024	2024	NUM
ejpam-5963	392	6	.	.	PUNCT
ejpam-5963	393	1	[	[	X
ejpam-5963	393	2	8	8	NUM
ejpam-5963	393	3	]	]	X
ejpam-5963	393	4	hasib	hasib	PROPN
ejpam-5963	393	5	khan	khan	PROPN
ejpam-5963	393	6	,	,	PUNCT
ejpam-5963	393	7	saim	saim	PROPN
ejpam-5963	393	8	ahmed	ahmed	PROPN
ejpam-5963	393	9	,	,	PUNCT
ejpam-5963	393	10	jehad	jehad	PROPN
ejpam-5963	393	11	alzabut	alzabut	PROPN
ejpam-5963	393	12	,	,	PUNCT
ejpam-5963	393	13	and	and	CCONJ
ejpam-5963	393	14	ahmad	ahmad	PROPN
ejpam-5963	393	15	taher	taher	PROPN
ejpam-5963	393	16	azar	azar	PROPN
ejpam-5963	393	17	.	.	PUNCT
ejpam-5963	394	1	a	a	DET
ejpam-5963	394	2	generalized	generalize	VERB
ejpam-5963	394	3	coupled	couple	VERB
ejpam-5963	394	4	system	system	NOUN
ejpam-5963	394	5	of	of	ADP
ejpam-5963	394	6	fractional	fractional	ADJ
ejpam-5963	394	7	differential	differential	ADJ
ejpam-5963	394	8	equations	equation	NOUN
ejpam-5963	394	9	with	with	ADP
ejpam-5963	394	10	application	application	NOUN
ejpam-5963	394	11	to	to	PART
ejpam-5963	394	12	finite	finite	VERB
ejpam-5963	394	13	time	time	NOUN
ejpam-5963	394	14	sliding	slide	VERB
ejpam-5963	394	15	mode	mode	NOUN
ejpam-5963	394	16	control	control	NOUN
ejpam-5963	394	17	for	for	ADP
ejpam-5963	394	18	leukemia	leukemia	NOUN
ejpam-5963	394	19	therapy	therapy	NOUN
ejpam-5963	394	20	.	.	PUNCT
ejpam-5963	395	1	chaos	chaos	NOUN
ejpam-5963	395	2	,	,	PUNCT
ejpam-5963	395	3	solitons	soliton	NOUN
ejpam-5963	395	4	&	&	CCONJ
ejpam-5963	395	5	fractals	fractal	NOUN
ejpam-5963	395	6	,	,	PUNCT
ejpam-5963	395	7	174:113901	174:113901	NUM
ejpam-5963	395	8	,	,	PUNCT
ejpam-5963	395	9	2023	2023	NUM
ejpam-5963	395	10	.	.	PUNCT
ejpam-5963	396	1	[	[	X
ejpam-5963	396	2	9	9	NUM
ejpam-5963	396	3	]	]	SYM
ejpam-5963	396	4	francisco	francisco	PROPN
ejpam-5963	396	5	mart́ınez	mart́ınez	PROPN
ejpam-5963	396	6	and	and	CCONJ
ejpam-5963	396	7	mohammed	mohammed	PROPN
ejpam-5963	396	8	ka	ka	PROPN
ejpam-5963	396	9	kaabar	kaabar	PROPN
ejpam-5963	396	10	.	.	PUNCT
ejpam-5963	397	1	on	on	ADP
ejpam-5963	397	2	mart́ınez	mart́ınez	PROPN
ejpam-5963	397	3	–	–	PUNCT
ejpam-5963	397	4	kaabar	kaabar	NOUN
ejpam-5963	397	5	fractal	fractal	ADJ
ejpam-5963	397	6	–	–	PUNCT
ejpam-5963	397	7	fractional	fractional	ADJ
ejpam-5963	397	8	volterra	volterra	NOUN
ejpam-5963	397	9	integral	integral	ADJ
ejpam-5963	397	10	equations	equation	NOUN
ejpam-5963	397	11	of	of	ADP
ejpam-5963	397	12	the	the	DET
ejpam-5963	397	13	second	second	ADJ
ejpam-5963	397	14	kind	kind	NOUN
ejpam-5963	397	15	.	.	PUNCT
ejpam-5963	398	1	fractal	fractal	ADJ
ejpam-5963	398	2	and	and	CCONJ
ejpam-5963	398	3	fractional	fractional	ADJ
ejpam-5963	398	4	,	,	PUNCT
ejpam-5963	398	5	8(8):466	8(8):466	NUM
ejpam-5963	398	6	,	,	PUNCT
ejpam-5963	398	7	2024	2024	NUM
ejpam-5963	398	8	.	.	PUNCT
ejpam-5963	399	1	[	[	X
ejpam-5963	399	2	10	10	NUM
ejpam-5963	399	3	]	]	PUNCT
ejpam-5963	399	4	abdon	abdon	PROPN
ejpam-5963	399	5	atangana	atangana	PROPN
ejpam-5963	399	6	.	.	PUNCT
ejpam-5963	400	1	fractal	fractal	ADJ
ejpam-5963	400	2	-	-	PUNCT
ejpam-5963	400	3	fractional	fractional	ADJ
ejpam-5963	400	4	differentiation	differentiation	NOUN
ejpam-5963	400	5	and	and	CCONJ
ejpam-5963	400	6	integration	integration	NOUN
ejpam-5963	400	7	:	:	PUNCT
ejpam-5963	400	8	connecting	connect	VERB
ejpam-5963	400	9	fractal	fractal	ADJ
ejpam-5963	400	10	calculus	calculus	NOUN
ejpam-5963	400	11	and	and	CCONJ
ejpam-5963	400	12	fractional	fractional	ADJ
ejpam-5963	400	13	calculus	calculus	NOUN
ejpam-5963	400	14	to	to	PART
ejpam-5963	400	15	predict	predict	VERB
ejpam-5963	400	16	complex	complex	ADJ
ejpam-5963	400	17	system	system	NOUN
ejpam-5963	400	18	.	.	PUNCT
ejpam-5963	401	1	chaos	chaos	NOUN
ejpam-5963	401	2	,	,	PUNCT
ejpam-5963	401	3	solitons	soliton	NOUN
ejpam-5963	401	4	&	&	CCONJ
ejpam-5963	401	5	fractals	fractal	NOUN
ejpam-5963	401	6	,	,	PUNCT
ejpam-5963	401	7	102:396–406	102:396–406	NUM
ejpam-5963	401	8	,	,	PUNCT
ejpam-5963	401	9	2017	2017	NUM
ejpam-5963	401	10	.	.	PUNCT
ejpam-5963	402	1	[	[	X
ejpam-5963	402	2	11	11	NUM
ejpam-5963	402	3	]	]	PUNCT
ejpam-5963	402	4	markus	markus	PROPN
ejpam-5963	402	5	j	j	PROPN
ejpam-5963	402	6	kloker	kloker	PROPN
ejpam-5963	402	7	.	.	PUNCT
ejpam-5963	403	1	a	a	DET
ejpam-5963	403	2	robust	robust	ADJ
ejpam-5963	403	3	high	high	ADJ
ejpam-5963	403	4	-	-	PUNCT
ejpam-5963	403	5	resolution	resolution	NOUN
ejpam-5963	403	6	split	split	NOUN
ejpam-5963	403	7	-	-	PUNCT
ejpam-5963	403	8	type	type	NOUN
ejpam-5963	403	9	compact	compact	ADJ
ejpam-5963	403	10	fd	fd	NOUN
ejpam-5963	403	11	scheme	scheme	NOUN
ejpam-5963	403	12	for	for	ADP
ejpam-5963	403	13	spatial	spatial	ADJ
ejpam-5963	403	14	direct	direct	ADJ
ejpam-5963	403	15	numerical	numerical	PROPN
ejpam-5963	403	16	simulation	simulation	NOUN
ejpam-5963	403	17	of	of	ADP
ejpam-5963	403	18	boundary	boundary	ADJ
ejpam-5963	403	19	-	-	PUNCT
ejpam-5963	403	20	layer	layer	NOUN
ejpam-5963	403	21	transition	transition	NOUN
ejpam-5963	403	22	.	.	PUNCT
ejpam-5963	404	1	applied	apply	VERB
ejpam-5963	404	2	scientific	scientific	ADJ
ejpam-5963	404	3	research	research	NOUN
ejpam-5963	404	4	,	,	PUNCT
ejpam-5963	404	5	59:353–377	59:353–377	PROPN
ejpam-5963	404	6	,	,	PUNCT
ejpam-5963	404	7	1997	1997	NUM
ejpam-5963	404	8	.	.	PUNCT
ejpam-5963	405	1	[	[	X
ejpam-5963	405	2	12	12	NUM
ejpam-5963	405	3	]	]	X
ejpam-5963	405	4	bruce	bruce	PROPN
ejpam-5963	405	5	j	j	PROPN
ejpam-5963	405	6	west	west	PROPN
ejpam-5963	405	7	.	.	PUNCT
ejpam-5963	406	1	fractal	fractal	ADJ
ejpam-5963	406	2	physiology	physiology	NOUN
ejpam-5963	406	3	and	and	CCONJ
ejpam-5963	406	4	the	the	DET
ejpam-5963	406	5	fractional	fractional	ADJ
ejpam-5963	406	6	calculus	calculus	NOUN
ejpam-5963	406	7	:	:	PUNCT
ejpam-5963	406	8	a	a	DET
ejpam-5963	406	9	perspective	perspective	NOUN
ejpam-5963	406	10	.	.	PUNCT
ejpam-5963	407	1	frontiers	frontier	NOUN
ejpam-5963	407	2	in	in	ADP
ejpam-5963	407	3	physiology	physiology	NOUN
ejpam-5963	407	4	,	,	PUNCT
ejpam-5963	407	5	1:12	1:12	NUM
ejpam-5963	407	6	,	,	PUNCT
ejpam-5963	407	7	2010	2010	NUM
ejpam-5963	407	8	.	.	PUNCT
ejpam-5963	408	1	a.	a.	PROPN
ejpam-5963	408	2	ali	ali	PROPN
ejpam-5963	408	3	et	et	PROPN
ejpam-5963	408	4	al	al	PROPN
ejpam-5963	408	5	.	.	PUNCT
ejpam-5963	408	6	/	/	SYM
ejpam-5963	408	7	eur	eur	PROPN
ejpam-5963	408	8	.	.	PUNCT
ejpam-5963	409	1	j.	j.	PROPN
ejpam-5963	409	2	pure	pure	PROPN
ejpam-5963	409	3	appl	appl	PROPN
ejpam-5963	409	4	.	.	PROPN
ejpam-5963	409	5	math	math	PROPN
ejpam-5963	409	6	,	,	PUNCT
ejpam-5963	409	7	18	18	NUM
ejpam-5963	409	8	(	(	PUNCT
ejpam-5963	409	9	2	2	NUM
ejpam-5963	409	10	)	)	PUNCT
ejpam-5963	409	11	(	(	PUNCT
ejpam-5963	409	12	2025	2025	NUM
ejpam-5963	409	13	)	)	PUNCT
ejpam-5963	409	14	,	,	PUNCT
ejpam-5963	409	15	5963	5963	NUM
ejpam-5963	409	16	18	18	NUM
ejpam-5963	409	17	of	of	ADP
ejpam-5963	409	18	19	19	NUM
ejpam-5963	409	19	[	[	SYM
ejpam-5963	409	20	13	13	NUM
ejpam-5963	409	21	]	]	PUNCT
ejpam-5963	409	22	sonam	sonam	PROPN
ejpam-5963	409	23	khera	khera	PROPN
ejpam-5963	409	24	.	.	PUNCT
ejpam-5963	410	1	analysis	analysis	NOUN
ejpam-5963	410	2	and	and	CCONJ
ejpam-5963	410	3	implementation	implementation	NOUN
ejpam-5963	410	4	of	of	ADP
ejpam-5963	410	5	energy	energy	NOUN
ejpam-5963	410	6	efficient	efficient	ADJ
ejpam-5963	410	7	wireless	wireless	ADJ
ejpam-5963	410	8	sensor	sensor	NOUN
ejpam-5963	410	9	networks	network	NOUN
ejpam-5963	410	10	.	.	PUNCT
ejpam-5963	411	1	phd	phd	NOUN
ejpam-5963	411	2	thesis	thesis	PROPN
ejpam-5963	411	3	,	,	PUNCT
ejpam-5963	411	4	jc	jc	PROPN
ejpam-5963	411	5	bose	bose	PROPN
ejpam-5963	411	6	university	university	PROPN
ejpam-5963	411	7	,	,	PUNCT
ejpam-5963	411	8	2021	2021	NUM
ejpam-5963	411	9	.	.	PUNCT
ejpam-5963	412	1	[	[	X
ejpam-5963	412	2	14	14	NUM
ejpam-5963	412	3	]	]	SYM
ejpam-5963	412	4	yihong	yihong	PROPN
ejpam-5963	412	5	zheng	zheng	PROPN
ejpam-5963	412	6	,	,	PUNCT
ejpam-5963	412	7	zhiqun	zhiqun	PROPN
ejpam-5963	412	8	hu	hu	PROPN
ejpam-5963	412	9	,	,	PUNCT
ejpam-5963	412	10	zhaoming	zhaome	VERB
ejpam-5963	412	11	lu	lu	PROPN
ejpam-5963	412	12	,	,	PUNCT
ejpam-5963	412	13	luhan	luhan	PROPN
ejpam-5963	412	14	wang	wang	PROPN
ejpam-5963	412	15	,	,	PUNCT
ejpam-5963	412	16	and	and	CCONJ
ejpam-5963	412	17	wei	wei	PROPN
ejpam-5963	412	18	zheng	zheng	PROPN
ejpam-5963	412	19	.	.	PUNCT
ejpam-5963	413	1	a	a	DET
ejpam-5963	413	2	bessel	bessel	ADJ
ejpam-5963	413	3	constraint	constraint	NOUN
ejpam-5963	413	4	method	method	NOUN
ejpam-5963	413	5	for	for	ADP
ejpam-5963	413	6	oam	oam	PROPN
ejpam-5963	413	7	waves	wave	NOUN
ejpam-5963	413	8	in	in	ADP
ejpam-5963	413	9	short	short	ADJ
ejpam-5963	413	10	-	-	PUNCT
ejpam-5963	413	11	range	range	NOUN
ejpam-5963	413	12	wireless	wireless	ADJ
ejpam-5963	413	13	communication	communication	NOUN
ejpam-5963	413	14	.	.	PUNCT
ejpam-5963	414	1	in	in	ADP
ejpam-5963	414	2	2024	2024	NUM
ejpam-5963	414	3	ieee	ieee	PROPN
ejpam-5963	414	4	wireless	wireless	NOUN
ejpam-5963	414	5	communications	communication	NOUN
ejpam-5963	414	6	and	and	CCONJ
ejpam-5963	414	7	networking	network	VERB
ejpam-5963	414	8	conference	conference	NOUN
ejpam-5963	414	9	(	(	PUNCT
ejpam-5963	414	10	wcnc	wcnc	ADJ
ejpam-5963	414	11	)	)	PUNCT
ejpam-5963	414	12	,	,	PUNCT
ejpam-5963	414	13	pages	page	NOUN
ejpam-5963	414	14	1–6	1–6	NUM
ejpam-5963	414	15	.	.	PUNCT
ejpam-5963	414	16	ieee	ieee	NOUN
ejpam-5963	414	17	,	,	PUNCT
ejpam-5963	414	18	2024	2024	NUM
ejpam-5963	414	19	.	.	PUNCT
ejpam-5963	415	1	[	[	X
ejpam-5963	415	2	15	15	X
ejpam-5963	415	3	]	]	X
ejpam-5963	415	4	muhammad	muhammad	PROPN
ejpam-5963	415	5	sarwar	sarwar	PROPN
ejpam-5963	415	6	,	,	PUNCT
ejpam-5963	415	7	aiman	aiman	PROPN
ejpam-5963	415	8	mukheimer	mukheimer	PROPN
ejpam-5963	415	9	,	,	PUNCT
ejpam-5963	415	10	syed	syed	ADJ
ejpam-5963	415	11	khayyam	khayyam	PROPN
ejpam-5963	415	12	shah	shah	PROPN
ejpam-5963	415	13	,	,	PUNCT
ejpam-5963	415	14	and	and	CCONJ
ejpam-5963	415	15	arshad	arshad	PROPN
ejpam-5963	415	16	khan	khan	PROPN
ejpam-5963	415	17	.	.	PUNCT
ejpam-5963	416	1	existence	existence	NOUN
ejpam-5963	416	2	of	of	ADP
ejpam-5963	416	3	solutions	solution	NOUN
ejpam-5963	416	4	of	of	ADP
ejpam-5963	416	5	fractal	fractal	ADJ
ejpam-5963	416	6	fractional	fractional	ADJ
ejpam-5963	416	7	partial	partial	ADJ
ejpam-5963	416	8	differential	differential	NOUN
ejpam-5963	416	9	equations	equation	NOUN
ejpam-5963	416	10	through	through	ADP
ejpam-5963	416	11	different	different	ADJ
ejpam-5963	416	12	contractions	contraction	NOUN
ejpam-5963	416	13	.	.	PUNCT
ejpam-5963	417	1	aims	aim	VERB
ejpam-5963	417	2	math	math	NOUN
ejpam-5963	417	3	,	,	PUNCT
ejpam-5963	417	4	9(5):12399–12411	9(5):12399–12411	PROPN
ejpam-5963	417	5	,	,	PUNCT
ejpam-5963	417	6	2024	2024	NUM
ejpam-5963	417	7	.	.	PUNCT
ejpam-5963	418	1	[	[	X
ejpam-5963	418	2	16	16	NUM
ejpam-5963	418	3	]	]	PUNCT
ejpam-5963	418	4	mohammed	mohammed	PROPN
ejpam-5963	418	5	althubyani	althubyani	PROPN
ejpam-5963	418	6	and	and	CCONJ
ejpam-5963	418	7	sayed	say	VERB
ejpam-5963	418	8	saber	saber	PROPN
ejpam-5963	418	9	.	.	PUNCT
ejpam-5963	419	1	hyers	hyer	NOUN
ejpam-5963	419	2	–	–	PUNCT
ejpam-5963	419	3	ulam	ulam	PROPN
ejpam-5963	419	4	stability	stability	NOUN
ejpam-5963	419	5	of	of	ADP
ejpam-5963	419	6	fractal	fractal	ADJ
ejpam-5963	419	7	–	–	PUNCT
ejpam-5963	419	8	fractional	fractional	ADJ
ejpam-5963	419	9	computer	computer	NOUN
ejpam-5963	419	10	virus	virus	NOUN
ejpam-5963	419	11	models	model	NOUN
ejpam-5963	419	12	with	with	ADP
ejpam-5963	419	13	the	the	DET
ejpam-5963	419	14	atangana	atangana	PROPN
ejpam-5963	419	15	–	–	PUNCT
ejpam-5963	419	16	baleanu	baleanu	NOUN
ejpam-5963	419	17	operator	operator	NOUN
ejpam-5963	419	18	.	.	PUNCT
ejpam-5963	420	1	fractal	fractal	PROPN
ejpam-5963	420	2	and	and	CCONJ
ejpam-5963	420	3	fractional	fractional	ADJ
ejpam-5963	420	4	,	,	PUNCT
ejpam-5963	420	5	9(3):158	9(3):158	NUM
ejpam-5963	420	6	,	,	PUNCT
ejpam-5963	420	7	2025	2025	NUM
ejpam-5963	420	8	.	.	PUNCT
ejpam-5963	421	1	[	[	X
ejpam-5963	421	2	17	17	NUM
ejpam-5963	421	3	]	]	X
ejpam-5963	421	4	meriem	meriem	NOUN
ejpam-5963	421	5	mansouria	mansouria	PROPN
ejpam-5963	421	6	belhamiti	belhamiti	PROPN
ejpam-5963	421	7	,	,	PUNCT
ejpam-5963	421	8	zoubir	zoubir	NOUN
ejpam-5963	421	9	dahmani	dahmani	PROPN
ejpam-5963	421	10	,	,	PUNCT
ejpam-5963	421	11	jehad	jehad	PROPN
ejpam-5963	421	12	alzabut	alzabut	PROPN
ejpam-5963	421	13	,	,	PUNCT
ejpam-5963	421	14	dk	dk	PROPN
ejpam-5963	421	15	almutairi	almutairi	NOUN
ejpam-5963	421	16	,	,	PUNCT
ejpam-5963	421	17	and	and	CCONJ
ejpam-5963	421	18	hasib	hasib	PROPN
ejpam-5963	421	19	khan	khan	PROPN
ejpam-5963	421	20	.	.	PUNCT
ejpam-5963	422	1	analyzing	analyze	VERB
ejpam-5963	422	2	chaotic	chaotic	ADJ
ejpam-5963	422	3	systems	system	NOUN
ejpam-5963	422	4	with	with	ADP
ejpam-5963	422	5	multi	multi	ADJ
ejpam-5963	422	6	-	-	ADJ
ejpam-5963	422	7	step	step	ADJ
ejpam-5963	422	8	methods	method	NOUN
ejpam-5963	422	9	:	:	PUNCT
ejpam-5963	422	10	theory	theory	NOUN
ejpam-5963	422	11	and	and	CCONJ
ejpam-5963	422	12	simulations	simulation	NOUN
ejpam-5963	422	13	.	.	PUNCT
ejpam-5963	423	1	alexandria	alexandria	PROPN
ejpam-5963	423	2	engineering	engineering	PROPN
ejpam-5963	423	3	journal	journal	PROPN
ejpam-5963	423	4	,	,	PUNCT
ejpam-5963	423	5	113:516–534	113:516–534	NUM
ejpam-5963	423	6	,	,	PUNCT
ejpam-5963	423	7	2025	2025	NUM
ejpam-5963	423	8	.	.	PUNCT
ejpam-5963	424	1	[	[	X
ejpam-5963	424	2	18	18	NUM
ejpam-5963	424	3	]	]	X
ejpam-5963	424	4	tao	tao	PROPN
ejpam-5963	424	5	yan	yan	PROPN
ejpam-5963	424	6	,	,	PUNCT
ejpam-5963	424	7	muflih	muflih	PROPN
ejpam-5963	424	8	alhazmi	alhazmi	PROPN
ejpam-5963	424	9	,	,	PUNCT
ejpam-5963	424	10	mukhtar	mukhtar	PROPN
ejpam-5963	424	11	y	y	PROPN
ejpam-5963	424	12	youssif	youssif	PROPN
ejpam-5963	424	13	,	,	PUNCT
ejpam-5963	424	14	amna	amna	X
ejpam-5963	424	15	e	e	NOUN
ejpam-5963	424	16	elhag	elhag	NOUN
ejpam-5963	424	17	,	,	PUNCT
ejpam-5963	424	18	abdulrahman	abdulrahman	PROPN
ejpam-5963	424	19	f	f	PROPN
ejpam-5963	424	20	aljohani	aljohani	PROPN
ejpam-5963	424	21	,	,	PUNCT
ejpam-5963	424	22	and	and	CCONJ
ejpam-5963	424	23	sayed	say	VERB
ejpam-5963	424	24	saber	saber	PROPN
ejpam-5963	424	25	.	.	PUNCT
ejpam-5963	425	1	analysis	analysis	NOUN
ejpam-5963	425	2	of	of	ADP
ejpam-5963	425	3	a	a	DET
ejpam-5963	425	4	lorenz	lorenz	PROPN
ejpam-5963	425	5	model	model	NOUN
ejpam-5963	425	6	using	use	VERB
ejpam-5963	425	7	adomian	adomian	NOUN
ejpam-5963	425	8	decomposition	decomposition	NOUN
ejpam-5963	425	9	and	and	CCONJ
ejpam-5963	425	10	fractal	fractal	ADJ
ejpam-5963	425	11	-	-	PUNCT
ejpam-5963	425	12	fractional	fractional	ADJ
ejpam-5963	425	13	operators	operator	NOUN
ejpam-5963	425	14	.	.	PUNCT
ejpam-5963	426	1	thermal	thermal	ADJ
ejpam-5963	426	2	science	science	NOUN
ejpam-5963	426	3	,	,	PUNCT
ejpam-5963	426	4	28(6	28(6	NUM
ejpam-5963	426	5	part	part	NOUN
ejpam-5963	426	6	b):5001–5009	b):5001–5009	ADJ
ejpam-5963	426	7	,	,	PUNCT
ejpam-5963	426	8	2024	2024	NUM
ejpam-5963	426	9	.	.	PUNCT
ejpam-5963	427	1	[	[	X
ejpam-5963	427	2	19	19	NUM
ejpam-5963	427	3	]	]	X
ejpam-5963	427	4	juan	juan	PROPN
ejpam-5963	427	5	carlos	carlos	PROPN
ejpam-5963	427	6	torrico	torrico	PROPN
ejpam-5963	427	7	albino	albino	PROPN
ejpam-5963	427	8	.	.	PUNCT
ejpam-5963	428	1	balancing	balance	VERB
ejpam-5963	428	2	natural	natural	ADJ
ejpam-5963	428	3	and	and	CCONJ
ejpam-5963	428	4	agricultural	agricultural	ADJ
ejpam-5963	428	5	systems	system	NOUN
ejpam-5963	428	6	in	in	ADP
ejpam-5963	428	7	the	the	DET
ejpam-5963	428	8	atlantic	atlantic	PROPN
ejpam-5963	428	9	rainforest	rainforest	NOUN
ejpam-5963	428	10	of	of	ADP
ejpam-5963	428	11	brazil	brazil	PROPN
ejpam-5963	428	12	.	.	PUNCT
ejpam-5963	429	1	phd	phd	NOUN
ejpam-5963	429	2	thesis	thesis	PROPN
ejpam-5963	429	3	,	,	PUNCT
ejpam-5963	429	4	universitäts	universität	NOUN
ejpam-5963	429	5	-	-	PUNCT
ejpam-5963	429	6	und	und	ADJ
ejpam-5963	429	7	landesbibliothek	landesbibliothek	PROPN
ejpam-5963	429	8	bonn	bonn	PROPN
ejpam-5963	429	9	,	,	PUNCT
ejpam-5963	429	10	2006	2006	NUM
ejpam-5963	429	11	.	.	PUNCT
ejpam-5963	430	1	[	[	X
ejpam-5963	430	2	20	20	NUM
ejpam-5963	430	3	]	]	PUNCT
ejpam-5963	430	4	thomas	thomas	PROPN
ejpam-5963	430	5	b	b	PROPN
ejpam-5963	430	6	ward	ward	PROPN
ejpam-5963	430	7	and	and	CCONJ
ejpam-5963	430	8	steven	steven	PROPN
ejpam-5963	430	9	m	m	PROPN
ejpam-5963	430	10	smith	smith	PROPN
ejpam-5963	430	11	.	.	PUNCT
ejpam-5963	431	1	creative	creative	ADJ
ejpam-5963	431	2	cognition	cognition	NOUN
ejpam-5963	431	3	:	:	PUNCT
ejpam-5963	431	4	theory	theory	NOUN
ejpam-5963	431	5	,	,	PUNCT
ejpam-5963	431	6	research	research	NOUN
ejpam-5963	431	7	and	and	CCONJ
ejpam-5963	431	8	applications	application	NOUN
ejpam-5963	431	9	.	.	PUNCT
ejpam-5963	432	1	a	a	DET
ejpam-5963	432	2	bradford	bradford	NOUN
ejpam-5963	432	3	books	book	NOUN
ejpam-5963	432	4	,	,	PUNCT
ejpam-5963	432	5	1992	1992	NUM
ejpam-5963	432	6	.	.	PUNCT
ejpam-5963	433	1	[	[	X
ejpam-5963	433	2	21	21	NUM
ejpam-5963	433	3	]	]	X
ejpam-5963	433	4	fouad	fouad	PROPN
ejpam-5963	433	5	ibrahim	ibrahim	PROPN
ejpam-5963	433	6	abdou	abdou	PROPN
ejpam-5963	433	7	amir	amir	PROPN
ejpam-5963	433	8	,	,	PUNCT
ejpam-5963	433	9	aziz	aziz	PROPN
ejpam-5963	433	10	el	el	PROPN
ejpam-5963	433	11	ghazouani	ghazouani	PROPN
ejpam-5963	433	12	,	,	PUNCT
ejpam-5963	433	13	m’hamed	m’hamed	PROPN
ejpam-5963	433	14	el	el	PROPN
ejpam-5963	433	15	omari	omari	PROPN
ejpam-5963	433	16	,	,	PUNCT
ejpam-5963	433	17	and	and	CCONJ
ejpam-5963	433	18	said	say	VERB
ejpam-5963	433	19	melliani	melliani	ADJ
ejpam-5963	433	20	.	.	PUNCT
ejpam-5963	433	21	fuzzy	fuzzy	ADJ
ejpam-5963	433	22	fractional	fractional	ADJ
ejpam-5963	433	23	differential	differential	NOUN
ejpam-5963	433	24	equation	equation	NOUN
ejpam-5963	433	25	involving	involve	VERB
ejpam-5963	433	26	the	the	DET
ejpam-5963	433	27	fuzzy	fuzzy	ADJ
ejpam-5963	433	28	conformable	conformable	ADJ
ejpam-5963	433	29	derivative	derivative	NOUN
ejpam-5963	433	30	and	and	CCONJ
ejpam-5963	433	31	the	the	DET
ejpam-5963	433	32	αsemigroups	αsemigroup	NOUN
ejpam-5963	433	33	.	.	PUNCT
ejpam-5963	434	1	the	the	DET
ejpam-5963	434	2	scientific	scientific	ADJ
ejpam-5963	434	3	world	world	NOUN
ejpam-5963	434	4	journal	journal	NOUN
ejpam-5963	434	5	,	,	PUNCT
ejpam-5963	434	6	2024(1):9993669	2024(1):9993669	PROPN
ejpam-5963	434	7	,	,	PUNCT
ejpam-5963	434	8	2024	2024	NUM
ejpam-5963	434	9	.	.	PUNCT
ejpam-5963	435	1	[	[	X
ejpam-5963	435	2	22	22	NUM
ejpam-5963	435	3	]	]	PUNCT
ejpam-5963	435	4	benoumran	benoumran	ADJ
ejpam-5963	435	5	telli	telli	NOUN
ejpam-5963	435	6	,	,	PUNCT
ejpam-5963	435	7	mohammed	mohammed	PROPN
ejpam-5963	435	8	said	say	VERB
ejpam-5963	435	9	souid	souid	NOUN
ejpam-5963	435	10	,	,	PUNCT
ejpam-5963	435	11	jehad	jehad	PROPN
ejpam-5963	435	12	alzabut	alzabut	PROPN
ejpam-5963	435	13	,	,	PUNCT
ejpam-5963	435	14	and	and	CCONJ
ejpam-5963	435	15	hasib	hasib	PROPN
ejpam-5963	435	16	khan	khan	PROPN
ejpam-5963	435	17	.	.	PUNCT
ejpam-5963	436	1	existence	existence	NOUN
ejpam-5963	436	2	and	and	CCONJ
ejpam-5963	436	3	uniqueness	uniqueness	ADJ
ejpam-5963	436	4	theorems	theorem	NOUN
ejpam-5963	436	5	for	for	ADP
ejpam-5963	436	6	a	a	DET
ejpam-5963	436	7	variable	variable	ADJ
ejpam-5963	436	8	-	-	PUNCT
ejpam-5963	436	9	order	order	NOUN
ejpam-5963	436	10	fractional	fractional	ADJ
ejpam-5963	436	11	differential	differential	ADJ
ejpam-5963	436	12	equation	equation	NOUN
ejpam-5963	436	13	with	with	ADP
ejpam-5963	436	14	delay	delay	NOUN
ejpam-5963	436	15	.	.	PUNCT
ejpam-5963	437	1	axioms	axiom	NOUN
ejpam-5963	437	2	,	,	PUNCT
ejpam-5963	437	3	12(4):339	12(4):339	NUM
ejpam-5963	437	4	,	,	PUNCT
ejpam-5963	437	5	2023	2023	NUM
ejpam-5963	437	6	.	.	PUNCT
ejpam-5963	438	1	[	[	X
ejpam-5963	438	2	23	23	NUM
ejpam-5963	438	3	]	]	PUNCT
ejpam-5963	438	4	xiaojun	xiaojun	PROPN
ejpam-5963	438	5	lv	lv	PROPN
ejpam-5963	438	6	,	,	PUNCT
ejpam-5963	438	7	kaihong	kaihong	PROPN
ejpam-5963	438	8	zhao	zhao	PROPN
ejpam-5963	438	9	,	,	PUNCT
ejpam-5963	438	10	and	and	CCONJ
ejpam-5963	438	11	haiping	haipe	VERB
ejpam-5963	438	12	xie	xie	PROPN
ejpam-5963	438	13	.	.	PUNCT
ejpam-5963	439	1	stability	stability	PROPN
ejpam-5963	439	2	and	and	CCONJ
ejpam-5963	439	3	numerical	numerical	PROPN
ejpam-5963	439	4	simulation	simulation	NOUN
ejpam-5963	439	5	of	of	ADP
ejpam-5963	439	6	a	a	DET
ejpam-5963	439	7	nonlinear	nonlinear	ADJ
ejpam-5963	439	8	hadamard	hadamard	ADJ
ejpam-5963	439	9	fractional	fractional	ADJ
ejpam-5963	439	10	coupling	coupling	NOUN
ejpam-5963	439	11	laplacian	laplacian	ADJ
ejpam-5963	439	12	system	system	NOUN
ejpam-5963	439	13	with	with	ADP
ejpam-5963	439	14	symmetric	symmetric	ADJ
ejpam-5963	439	15	periodic	periodic	ADJ
ejpam-5963	439	16	boundary	boundary	ADJ
ejpam-5963	439	17	conditions	condition	NOUN
ejpam-5963	439	18	.	.	PUNCT
ejpam-5963	440	1	symmetry	symmetry	NOUN
ejpam-5963	440	2	,	,	PUNCT
ejpam-5963	440	3	16(6):774	16(6):774	NUM
ejpam-5963	440	4	,	,	PUNCT
ejpam-5963	440	5	2024	2024	NUM
ejpam-5963	440	6	.	.	PUNCT
ejpam-5963	441	1	[	[	X
ejpam-5963	441	2	24	24	NUM
ejpam-5963	441	3	]	]	X
ejpam-5963	441	4	shahid	shahid	PROPN
ejpam-5963	441	5	khan	khan	PROPN
ejpam-5963	441	6	,	,	PUNCT
ejpam-5963	441	7	kamal	kamal	PROPN
ejpam-5963	441	8	shah	shah	PROPN
ejpam-5963	441	9	,	,	PUNCT
ejpam-5963	441	10	amar	amar	PROPN
ejpam-5963	441	11	debbouche	debbouche	PROPN
ejpam-5963	441	12	,	,	PUNCT
ejpam-5963	441	13	salman	salman	PROPN
ejpam-5963	441	14	zeb	zeb	PROPN
ejpam-5963	441	15	,	,	PUNCT
ejpam-5963	441	16	and	and	CCONJ
ejpam-5963	441	17	valery	valery	PROPN
ejpam-5963	441	18	antonov	antonov	PROPN
ejpam-5963	441	19	.	.	PUNCT
ejpam-5963	441	20	solvability	solvability	NOUN
ejpam-5963	441	21	and	and	CCONJ
ejpam-5963	441	22	ulam	ulam	NOUN
ejpam-5963	441	23	-	-	PUNCT
ejpam-5963	441	24	hyers	hyer	NOUN
ejpam-5963	441	25	stability	stability	NOUN
ejpam-5963	441	26	analysis	analysis	NOUN
ejpam-5963	441	27	for	for	ADP
ejpam-5963	441	28	nonlinear	nonlinear	ADJ
ejpam-5963	441	29	piecewise	piecewise	NOUN
ejpam-5963	441	30	fractional	fractional	ADJ
ejpam-5963	441	31	cancer	cancer	NOUN
ejpam-5963	441	32	dynamic	dynamic	ADJ
ejpam-5963	441	33	systems	system	NOUN
ejpam-5963	441	34	.	.	PUNCT
ejpam-5963	442	1	physica	physica	PROPN
ejpam-5963	442	2	scripta	scripta	PROPN
ejpam-5963	442	3	,	,	PUNCT
ejpam-5963	442	4	99(2):025225	99(2):025225	PROPN
ejpam-5963	442	5	,	,	PUNCT
ejpam-5963	442	6	2024	2024	NUM
ejpam-5963	442	7	.	.	PUNCT
ejpam-5963	443	1	[	[	X
ejpam-5963	443	2	25	25	NUM
ejpam-5963	443	3	]	]	PUNCT
ejpam-5963	443	4	xiaojie	xiaojie	PROPN
ejpam-5963	443	5	xu	xu	PROPN
ejpam-5963	443	6	,	,	PUNCT
ejpam-5963	443	7	daqing	daqe	VERB
ejpam-5963	443	8	jiang	jiang	PROPN
ejpam-5963	443	9	,	,	PUNCT
ejpam-5963	443	10	and	and	CCONJ
ejpam-5963	443	11	chengjun	chengjun	PROPN
ejpam-5963	443	12	yuan	yuan	PROPN
ejpam-5963	443	13	.	.	PUNCT
ejpam-5963	444	1	multiple	multiple	ADJ
ejpam-5963	444	2	positive	positive	ADJ
ejpam-5963	444	3	solutions	solution	NOUN
ejpam-5963	444	4	for	for	ADP
ejpam-5963	444	5	the	the	DET
ejpam-5963	444	6	boundary	boundary	ADJ
ejpam-5963	444	7	value	value	NOUN
ejpam-5963	444	8	problem	problem	NOUN
ejpam-5963	444	9	of	of	ADP
ejpam-5963	444	10	a	a	DET
ejpam-5963	444	11	nonlinear	nonlinear	ADJ
ejpam-5963	444	12	fractional	fractional	ADJ
ejpam-5963	444	13	differential	differential	NOUN
ejpam-5963	444	14	equation	equation	NOUN
ejpam-5963	444	15	.	.	PUNCT
ejpam-5963	445	1	nonlinear	nonlinear	ADJ
ejpam-5963	445	2	analysis	analysis	NOUN
ejpam-5963	445	3	:	:	PUNCT
ejpam-5963	445	4	theory	theory	NOUN
ejpam-5963	445	5	,	,	PUNCT
ejpam-5963	445	6	methods	method	NOUN
ejpam-5963	445	7	&	&	CCONJ
ejpam-5963	445	8	applications	application	NOUN
ejpam-5963	445	9	,	,	PUNCT
ejpam-5963	445	10	71(10):4676–4688	71(10):4676–4688	NUM
ejpam-5963	445	11	,	,	PUNCT
ejpam-5963	445	12	2009	2009	NUM
ejpam-5963	445	13	.	.	PUNCT
ejpam-5963	446	1	[	[	X
ejpam-5963	446	2	26	26	NUM
ejpam-5963	446	3	]	]	X
ejpam-5963	446	4	kamal	kamal	PROPN
ejpam-5963	446	5	shah	shah	PROPN
ejpam-5963	446	6	,	,	PUNCT
ejpam-5963	446	7	amjad	amjad	PROPN
ejpam-5963	446	8	ali	ali	PROPN
ejpam-5963	446	9	,	,	PUNCT
ejpam-5963	446	10	and	and	CCONJ
ejpam-5963	446	11	rahmat	rahmat	PROPN
ejpam-5963	446	12	ali	ali	PROPN
ejpam-5963	446	13	khan	khan	PROPN
ejpam-5963	446	14	.	.	PUNCT
ejpam-5963	446	15	degree	degree	NOUN
ejpam-5963	446	16	theory	theory	NOUN
ejpam-5963	446	17	and	and	CCONJ
ejpam-5963	446	18	existence	existence	NOUN
ejpam-5963	446	19	of	of	ADP
ejpam-5963	446	20	positive	positive	ADJ
ejpam-5963	446	21	solutions	solution	NOUN
ejpam-5963	446	22	to	to	ADP
ejpam-5963	446	23	coupled	couple	VERB
ejpam-5963	446	24	systems	system	NOUN
ejpam-5963	446	25	of	of	ADP
ejpam-5963	446	26	multi	multi	ADJ
ejpam-5963	446	27	-	-	ADJ
ejpam-5963	446	28	point	point	ADJ
ejpam-5963	446	29	boundary	boundary	ADJ
ejpam-5963	446	30	value	value	NOUN
ejpam-5963	446	31	problems	problem	NOUN
ejpam-5963	446	32	.	.	PUNCT
ejpam-5963	447	1	boundary	boundary	ADJ
ejpam-5963	447	2	value	value	NOUN
ejpam-5963	447	3	problems	problem	NOUN
ejpam-5963	447	4	,	,	PUNCT
ejpam-5963	447	5	2016:1–12	2016:1–12	NUM
ejpam-5963	447	6	,	,	PUNCT
ejpam-5963	447	7	2016	2016	NUM
ejpam-5963	447	8	.	.	PUNCT
ejpam-5963	448	1	[	[	X
ejpam-5963	448	2	27	27	NUM
ejpam-5963	448	3	]	]	X
ejpam-5963	448	4	jinhua	jinhua	PROPN
ejpam-5963	448	5	wang	wang	PROPN
ejpam-5963	448	6	,	,	PUNCT
ejpam-5963	448	7	hongjun	hongjun	PROPN
ejpam-5963	448	8	xiang	xiang	PROPN
ejpam-5963	448	9	,	,	PUNCT
ejpam-5963	448	10	and	and	CCONJ
ejpam-5963	448	11	zhigang	zhigang	PROPN
ejpam-5963	448	12	liu	liu	PROPN
ejpam-5963	448	13	.	.	PUNCT
ejpam-5963	449	1	positive	positive	ADJ
ejpam-5963	449	2	solution	solution	NOUN
ejpam-5963	449	3	to	to	ADP
ejpam-5963	449	4	nonzero	nonzero	PROPN
ejpam-5963	449	5	boundary	boundary	ADJ
ejpam-5963	449	6	values	value	NOUN
ejpam-5963	449	7	problem	problem	NOUN
ejpam-5963	449	8	for	for	ADP
ejpam-5963	449	9	a	a	DET
ejpam-5963	449	10	coupled	couple	VERB
ejpam-5963	449	11	system	system	NOUN
ejpam-5963	449	12	of	of	ADP
ejpam-5963	449	13	nonlinear	nonlinear	ADJ
ejpam-5963	449	14	fractional	fractional	ADJ
ejpam-5963	449	15	differential	differential	ADJ
ejpam-5963	449	16	equations	equation	NOUN
ejpam-5963	449	17	.	.	PUNCT
ejpam-5963	450	1	international	international	ADJ
ejpam-5963	450	2	journal	journal	PROPN
ejpam-5963	450	3	of	of	ADP
ejpam-5963	450	4	differential	differential	ADJ
ejpam-5963	450	5	equations	equation	NOUN
ejpam-5963	450	6	,	,	PUNCT
ejpam-5963	450	7	2010(1):186928	2010(1):186928	NUM
ejpam-5963	450	8	,	,	PUNCT
ejpam-5963	450	9	2010	2010	NUM
ejpam-5963	450	10	.	.	PUNCT
ejpam-5963	451	1	a.	a.	PROPN
ejpam-5963	451	2	ali	ali	PROPN
ejpam-5963	451	3	et	et	PROPN
ejpam-5963	451	4	al	al	PROPN
ejpam-5963	451	5	.	.	PUNCT
ejpam-5963	451	6	/	/	SYM
ejpam-5963	451	7	eur	eur	PROPN
ejpam-5963	451	8	.	.	PUNCT
ejpam-5963	452	1	j.	j.	PROPN
ejpam-5963	452	2	pure	pure	PROPN
ejpam-5963	452	3	appl	appl	PROPN
ejpam-5963	452	4	.	.	PROPN
ejpam-5963	452	5	math	math	PROPN
ejpam-5963	452	6	,	,	PUNCT
ejpam-5963	452	7	18	18	NUM
ejpam-5963	452	8	(	(	PUNCT
ejpam-5963	452	9	2	2	NUM
ejpam-5963	452	10	)	)	PUNCT
ejpam-5963	452	11	(	(	PUNCT
ejpam-5963	452	12	2025	2025	NUM
ejpam-5963	452	13	)	)	PUNCT
ejpam-5963	452	14	,	,	PUNCT
ejpam-5963	452	15	5963	5963	NUM
ejpam-5963	452	16	19	19	NUM
ejpam-5963	452	17	of	of	ADP
ejpam-5963	452	18	19	19	NUM
ejpam-5963	453	1	[	[	SYM
ejpam-5963	453	2	28	28	NUM
ejpam-5963	453	3	]	]	X
ejpam-5963	453	4	wengui	wengui	PROPN
ejpam-5963	453	5	yang	yang	PROPN
ejpam-5963	453	6	.	.	PUNCT
ejpam-5963	454	1	positive	positive	ADJ
ejpam-5963	454	2	solutions	solution	NOUN
ejpam-5963	454	3	for	for	ADP
ejpam-5963	454	4	a	a	DET
ejpam-5963	454	5	coupled	couple	VERB
ejpam-5963	454	6	system	system	NOUN
ejpam-5963	454	7	of	of	ADP
ejpam-5963	454	8	nonlinear	nonlinear	ADJ
ejpam-5963	454	9	fractional	fractional	ADJ
ejpam-5963	454	10	differential	differential	ADJ
ejpam-5963	454	11	equations	equation	NOUN
ejpam-5963	454	12	with	with	ADP
ejpam-5963	454	13	integral	integral	ADJ
ejpam-5963	454	14	boundary	boundary	ADJ
ejpam-5963	454	15	conditions	condition	NOUN
ejpam-5963	454	16	.	.	PUNCT
ejpam-5963	455	1	computers	computer	NOUN
ejpam-5963	455	2	&	&	CCONJ
ejpam-5963	455	3	mathematics	mathematics	PROPN
ejpam-5963	455	4	with	with	ADP
ejpam-5963	455	5	applications	application	NOUN
ejpam-5963	455	6	,	,	PUNCT
ejpam-5963	455	7	63(1):288–297	63(1):288–297	PROPN
ejpam-5963	455	8	,	,	PUNCT
ejpam-5963	455	9	2012	2012	NUM
ejpam-5963	455	10	.	.	PUNCT
ejpam-5963	456	1	[	[	X
ejpam-5963	456	2	29	29	NUM
ejpam-5963	456	3	]	]	X
ejpam-5963	456	4	ravi	ravi	NOUN
ejpam-5963	456	5	p	p	PROPN
ejpam-5963	456	6	agarwal	agarwal	PROPN
ejpam-5963	456	7	,	,	PUNCT
ejpam-5963	456	8	maria	maria	PROPN
ejpam-5963	456	9	meehan	meehan	PROPN
ejpam-5963	456	10	,	,	PUNCT
ejpam-5963	456	11	and	and	CCONJ
ejpam-5963	456	12	donal	donal	PROPN
ejpam-5963	456	13	o’regan	o’regan	PROPN
ejpam-5963	456	14	.	.	PUNCT
ejpam-5963	456	15	fixed	fix	VERB
ejpam-5963	456	16	point	point	NOUN
ejpam-5963	456	17	theory	theory	NOUN
ejpam-5963	456	18	and	and	CCONJ
ejpam-5963	456	19	applications	application	NOUN
ejpam-5963	456	20	,	,	PUNCT
ejpam-5963	456	21	volume	volume	NOUN
ejpam-5963	456	22	141	141	NUM
ejpam-5963	456	23	.	.	PUNCT
ejpam-5963	457	1	cambridge	cambridge	PROPN
ejpam-5963	457	2	university	university	PROPN
ejpam-5963	457	3	press	press	NOUN
ejpam-5963	457	4	,	,	PUNCT
ejpam-5963	457	5	2001	2001	NUM
ejpam-5963	457	6	.	.	PUNCT
ejpam-5963	458	1	[	[	X
ejpam-5963	458	2	30	30	NUM
ejpam-5963	458	3	]	]	X
ejpam-5963	458	4	ta	ta	ADP
ejpam-5963	458	5	burton	burton	PROPN
ejpam-5963	458	6	and	and	CCONJ
ejpam-5963	458	7	tetsuo	tetsuo	PROPN
ejpam-5963	458	8	furumochi	furumochi	PROPN
ejpam-5963	458	9	.	.	PUNCT
ejpam-5963	459	1	krasnoselskii	krasnoselskii	PROPN
ejpam-5963	459	2	’s	’s	PART
ejpam-5963	459	3	fixed	fix	VERB
ejpam-5963	459	4	point	point	NOUN
ejpam-5963	459	5	theorem	theorem	NOUN
ejpam-5963	459	6	and	and	CCONJ
ejpam-5963	459	7	stability	stability	NOUN
ejpam-5963	459	8	.	.	PUNCT
ejpam-5963	460	1	nonlinear	nonlinear	ADJ
ejpam-5963	460	2	analysis	analysis	NOUN
ejpam-5963	460	3	:	:	PUNCT
ejpam-5963	460	4	theory	theory	NOUN
ejpam-5963	460	5	,	,	PUNCT
ejpam-5963	460	6	methods	method	NOUN
ejpam-5963	460	7	&	&	CCONJ
ejpam-5963	460	8	applications	application	NOUN
ejpam-5963	460	9	,	,	PUNCT
ejpam-5963	460	10	49(4):445–454	49(4):445–454	PROPN
ejpam-5963	460	11	,	,	PUNCT
ejpam-5963	460	12	2002	2002	NUM
ejpam-5963	460	13	.	.	PUNCT